1,1,132,0,0.0757274,"\int x^2 (d+e x) \sqrt{d^2-e^2 x^2} \, dx","Int[x^2*(d + e*x)*Sqrt[d^2 - e^2*x^2],x]","\frac{d^3 x \sqrt{d^2-e^2 x^2}}{8 e^2}-\frac{d^2 \left(d^2-e^2 x^2\right)^{3/2}}{3 e^3}-\frac{d x \left(d^2-e^2 x^2\right)^{3/2}}{4 e^2}+\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 e^3}+\frac{d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}","\frac{d^3 x \sqrt{d^2-e^2 x^2}}{8 e^2}-\frac{d^2 \left(d^2-e^2 x^2\right)^{3/2}}{3 e^3}-\frac{d x \left(d^2-e^2 x^2\right)^{3/2}}{4 e^2}+\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 e^3}+\frac{d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}",1,"(d^3*x*Sqrt[d^2 - e^2*x^2])/(8*e^2) - (d^2*(d^2 - e^2*x^2)^(3/2))/(3*e^3) - (d*x*(d^2 - e^2*x^2)^(3/2))/(4*e^2) + (d^2 - e^2*x^2)^(5/2)/(5*e^3) + (d^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^3)","A",10,5,25,0.2000,1,"{797, 641, 195, 217, 203}"
2,1,201,0,0.1493877,"\int x^4 (d+e x) \left(d^2-e^2 x^2\right)^{3/2} \, dx","Int[x^4*(d + e*x)*(d^2 - e^2*x^2)^(3/2),x]","\frac{3 d^7 x \sqrt{d^2-e^2 x^2}}{128 e^4}+\frac{d^5 x \left(d^2-e^2 x^2\right)^{3/2}}{64 e^4}-\frac{d^3 (128 d+315 e x) \left(d^2-e^2 x^2\right)^{5/2}}{5040 e^5}-\frac{4 d^2 x^2 \left(d^2-e^2 x^2\right)^{5/2}}{63 e^3}-\frac{d x^3 \left(d^2-e^2 x^2\right)^{5/2}}{8 e^2}-\frac{x^4 \left(d^2-e^2 x^2\right)^{5/2}}{9 e}+\frac{3 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^5}","\frac{3 d^7 x \sqrt{d^2-e^2 x^2}}{128 e^4}+\frac{d^5 x \left(d^2-e^2 x^2\right)^{3/2}}{64 e^4}-\frac{d^3 (128 d+315 e x) \left(d^2-e^2 x^2\right)^{5/2}}{5040 e^5}-\frac{4 d^2 x^2 \left(d^2-e^2 x^2\right)^{5/2}}{63 e^3}-\frac{d x^3 \left(d^2-e^2 x^2\right)^{5/2}}{8 e^2}-\frac{x^4 \left(d^2-e^2 x^2\right)^{5/2}}{9 e}+\frac{3 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^5}",1,"(3*d^7*x*Sqrt[d^2 - e^2*x^2])/(128*e^4) + (d^5*x*(d^2 - e^2*x^2)^(3/2))/(64*e^4) - (4*d^2*x^2*(d^2 - e^2*x^2)^(5/2))/(63*e^3) - (d*x^3*(d^2 - e^2*x^2)^(5/2))/(8*e^2) - (x^4*(d^2 - e^2*x^2)^(5/2))/(9*e) - (d^3*(128*d + 315*e*x)*(d^2 - e^2*x^2)^(5/2))/(5040*e^5) + (3*d^9*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(128*e^5)","A",8,5,25,0.2000,1,"{833, 780, 195, 217, 203}"
3,1,172,0,0.1008888,"\int x^3 (d+e x) \left(d^2-e^2 x^2\right)^{3/2} \, dx","Int[x^3*(d + e*x)*(d^2 - e^2*x^2)^(3/2),x]","\frac{3 d^6 x \sqrt{d^2-e^2 x^2}}{128 e^3}+\frac{d^4 x \left(d^2-e^2 x^2\right)^{3/2}}{64 e^3}-\frac{d^2 (32 d+35 e x) \left(d^2-e^2 x^2\right)^{5/2}}{560 e^4}-\frac{d x^2 \left(d^2-e^2 x^2\right)^{5/2}}{7 e^2}-\frac{x^3 \left(d^2-e^2 x^2\right)^{5/2}}{8 e}+\frac{3 d^8 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^4}","\frac{3 d^6 x \sqrt{d^2-e^2 x^2}}{128 e^3}+\frac{d^4 x \left(d^2-e^2 x^2\right)^{3/2}}{64 e^3}-\frac{d^2 (32 d+35 e x) \left(d^2-e^2 x^2\right)^{5/2}}{560 e^4}-\frac{d x^2 \left(d^2-e^2 x^2\right)^{5/2}}{7 e^2}-\frac{x^3 \left(d^2-e^2 x^2\right)^{5/2}}{8 e}+\frac{3 d^8 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^4}",1,"(3*d^6*x*Sqrt[d^2 - e^2*x^2])/(128*e^3) + (d^4*x*(d^2 - e^2*x^2)^(3/2))/(64*e^3) - (d*x^2*(d^2 - e^2*x^2)^(5/2))/(7*e^2) - (x^3*(d^2 - e^2*x^2)^(5/2))/(8*e) - (d^2*(32*d + 35*e*x)*(d^2 - e^2*x^2)^(5/2))/(560*e^4) + (3*d^8*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(128*e^4)","A",7,5,25,0.2000,1,"{833, 780, 195, 217, 203}"
4,1,159,0,0.10801,"\int x^2 (d+e x) \left(d^2-e^2 x^2\right)^{3/2} \, dx","Int[x^2*(d + e*x)*(d^2 - e^2*x^2)^(3/2),x]","\frac{d^5 x \sqrt{d^2-e^2 x^2}}{16 e^2}+\frac{d^3 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e^2}-\frac{d^2 \left(d^2-e^2 x^2\right)^{5/2}}{5 e^3}-\frac{d x \left(d^2-e^2 x^2\right)^{5/2}}{6 e^2}+\frac{\left(d^2-e^2 x^2\right)^{7/2}}{7 e^3}+\frac{d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^3}","\frac{d^5 x \sqrt{d^2-e^2 x^2}}{16 e^2}+\frac{d^3 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e^2}-\frac{d^2 \left(d^2-e^2 x^2\right)^{5/2}}{5 e^3}-\frac{d x \left(d^2-e^2 x^2\right)^{5/2}}{6 e^2}+\frac{\left(d^2-e^2 x^2\right)^{7/2}}{7 e^3}+\frac{d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^3}",1,"(d^5*x*Sqrt[d^2 - e^2*x^2])/(16*e^2) + (d^3*x*(d^2 - e^2*x^2)^(3/2))/(24*e^2) - (d^2*(d^2 - e^2*x^2)^(5/2))/(5*e^3) - (d*x*(d^2 - e^2*x^2)^(5/2))/(6*e^2) + (d^2 - e^2*x^2)^(7/2)/(7*e^3) + (d^7*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^3)","A",12,5,25,0.2000,1,"{797, 641, 195, 217, 203}"
5,1,116,0,0.0337452,"\int x (d+e x) \left(d^2-e^2 x^2\right)^{3/2} \, dx","Int[x*(d + e*x)*(d^2 - e^2*x^2)^(3/2),x]","\frac{d^4 x \sqrt{d^2-e^2 x^2}}{16 e}+\frac{d^2 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e}-\frac{(6 d+5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 e^2}+\frac{d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^2}","\frac{d^4 x \sqrt{d^2-e^2 x^2}}{16 e}+\frac{d^2 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e}-\frac{(6 d+5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 e^2}+\frac{d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^2}",1,"(d^4*x*Sqrt[d^2 - e^2*x^2])/(16*e) + (d^2*x*(d^2 - e^2*x^2)^(3/2))/(24*e) - ((6*d + 5*e*x)*(d^2 - e^2*x^2)^(5/2))/(30*e^2) + (d^6*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^2)","A",5,4,23,0.1739,1,"{780, 195, 217, 203}"
6,1,116,0,0.0333767,"\int x (d+e x) \left(d^2-e^2 x^2\right)^{3/2} \, dx","Int[x*(d + e*x)*(d^2 - e^2*x^2)^(3/2),x]","\frac{d^4 x \sqrt{d^2-e^2 x^2}}{16 e}+\frac{d^2 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e}-\frac{(6 d+5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 e^2}+\frac{d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^2}","\frac{d^4 x \sqrt{d^2-e^2 x^2}}{16 e}+\frac{d^2 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e}-\frac{(6 d+5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 e^2}+\frac{d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^2}",1,"(d^4*x*Sqrt[d^2 - e^2*x^2])/(16*e) + (d^2*x*(d^2 - e^2*x^2)^(3/2))/(24*e) - ((6*d + 5*e*x)*(d^2 - e^2*x^2)^(5/2))/(30*e^2) + (d^6*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^2)","A",5,4,23,0.1739,1,"{780, 195, 217, 203}"
7,1,113,0,0.0983893,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{x} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^(3/2))/x,x]","\frac{1}{8} d^2 (8 d+3 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{12} (4 d+3 e x) \left(d^2-e^2 x^2\right)^{3/2}+\frac{3}{8} d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{1}{8} d^2 (8 d+3 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{12} (4 d+3 e x) \left(d^2-e^2 x^2\right)^{3/2}+\frac{3}{8} d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(d^2*(8*d + 3*e*x)*Sqrt[d^2 - e^2*x^2])/8 + ((4*d + 3*e*x)*(d^2 - e^2*x^2)^(3/2))/12 + (3*d^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/8 - d^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",8,7,25,0.2800,1,"{815, 844, 217, 203, 266, 63, 208}"
8,1,117,0,0.0916725,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{x^2} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^(3/2))/x^2,x]","\frac{1}{2} d e (2 d-3 e x) \sqrt{d^2-e^2 x^2}-\frac{(3 d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{3 x}-\frac{3}{2} d^3 e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d^3 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{1}{2} d e (2 d-3 e x) \sqrt{d^2-e^2 x^2}-\frac{(3 d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{3 x}-\frac{3}{2} d^3 e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d^3 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(d*e*(2*d - 3*e*x)*Sqrt[d^2 - e^2*x^2])/2 - ((3*d - e*x)*(d^2 - e^2*x^2)^(3/2))/(3*x) - (3*d^3*e*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/2 - d^3*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",8,8,25,0.3200,1,"{813, 815, 844, 217, 203, 266, 63, 208}"
9,1,121,0,0.0935944,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{x^3} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^(3/2))/x^3,x]","-\frac{3 d e (d+e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{(d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{2 x^2}-\frac{3}{2} d^2 e^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{3}{2} d^2 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{3 d e (d+e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{(d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{2 x^2}-\frac{3}{2} d^2 e^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{3}{2} d^2 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(-3*d*e*(d + e*x)*Sqrt[d^2 - e^2*x^2])/(2*x) - ((d - e*x)*(d^2 - e^2*x^2)^(3/2))/(2*x^2) - (3*d^2*e^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/2 + (3*d^2*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/2","A",8,7,25,0.2800,1,"{813, 844, 217, 203, 266, 63, 208}"
10,1,120,0,0.0921883,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{x^4} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^(3/2))/x^4,x]","\frac{e^2 (2 d-3 e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{(2 d+3 e x) \left(d^2-e^2 x^2\right)^{3/2}}{6 x^3}+d e^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{3}{2} d e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{e^2 (2 d-3 e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{(2 d+3 e x) \left(d^2-e^2 x^2\right)^{3/2}}{6 x^3}+d e^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{3}{2} d e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(e^2*(2*d - 3*e*x)*Sqrt[d^2 - e^2*x^2])/(2*x) - ((2*d + 3*e*x)*(d^2 - e^2*x^2)^(3/2))/(6*x^3) + d*e^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] + (3*d*e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/2","A",8,8,25,0.3200,1,"{811, 813, 844, 217, 203, 266, 63, 208}"
11,1,118,0,0.0922914,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{x^5} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^(3/2))/x^5,x]","\frac{e^2 (3 d+8 e x) \sqrt{d^2-e^2 x^2}}{8 x^2}-\frac{(3 d+4 e x) \left(d^2-e^2 x^2\right)^{3/2}}{12 x^4}+e^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{3}{8} e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{e^2 (3 d+8 e x) \sqrt{d^2-e^2 x^2}}{8 x^2}-\frac{(3 d+4 e x) \left(d^2-e^2 x^2\right)^{3/2}}{12 x^4}+e^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{3}{8} e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(e^2*(3*d + 8*e*x)*Sqrt[d^2 - e^2*x^2])/(8*x^2) - ((3*d + 4*e*x)*(d^2 - e^2*x^2)^(3/2))/(12*x^4) + e^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - (3*e^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/8","A",8,7,25,0.2800,1,"{811, 844, 217, 203, 266, 63, 208}"
12,1,108,0,0.0629703,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{x^6} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^(3/2))/x^6,x]","\frac{3 e^3 \sqrt{d^2-e^2 x^2}}{8 x^2}-\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{4 x^4}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 d x^5}-\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d}","\frac{3 e^3 \sqrt{d^2-e^2 x^2}}{8 x^2}-\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{4 x^4}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 d x^5}-\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d}",1,"(3*e^3*Sqrt[d^2 - e^2*x^2])/(8*x^2) - (e*(d^2 - e^2*x^2)^(3/2))/(4*x^4) - (d^2 - e^2*x^2)^(5/2)/(5*d*x^5) - (3*e^5*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(8*d)","A",6,5,25,0.2000,1,"{807, 266, 47, 63, 208}"
13,1,143,0,0.0948237,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{x^7} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^(3/2))/x^7,x]","\frac{e^4 \sqrt{d^2-e^2 x^2}}{16 d x^2}-\frac{e^2 \left(d^2-e^2 x^2\right)^{3/2}}{24 d x^4}-\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{5 d^2 x^5}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{6 d x^6}-\frac{e^6 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^2}","\frac{e^4 \sqrt{d^2-e^2 x^2}}{16 d x^2}-\frac{e^2 \left(d^2-e^2 x^2\right)^{3/2}}{24 d x^4}-\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{5 d^2 x^5}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{6 d x^6}-\frac{e^6 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^2}",1,"(e^4*Sqrt[d^2 - e^2*x^2])/(16*d*x^2) - (e^2*(d^2 - e^2*x^2)^(3/2))/(24*d*x^4) - (d^2 - e^2*x^2)^(5/2)/(6*d*x^6) - (e*(d^2 - e^2*x^2)^(5/2))/(5*d^2*x^5) - (e^6*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(16*d^2)","A",7,6,25,0.2400,1,"{835, 807, 266, 47, 63, 208}"
14,1,172,0,0.1253976,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{x^8} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^(3/2))/x^8,x]","\frac{e^5 \sqrt{d^2-e^2 x^2}}{16 d^2 x^2}-\frac{e^3 \left(d^2-e^2 x^2\right)^{3/2}}{24 d^2 x^4}-\frac{2 e^2 \left(d^2-e^2 x^2\right)^{5/2}}{35 d^3 x^5}-\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{6 d^2 x^6}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{7 d x^7}-\frac{e^7 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^3}","\frac{e^5 \sqrt{d^2-e^2 x^2}}{16 d^2 x^2}-\frac{e^3 \left(d^2-e^2 x^2\right)^{3/2}}{24 d^2 x^4}-\frac{2 e^2 \left(d^2-e^2 x^2\right)^{5/2}}{35 d^3 x^5}-\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{6 d^2 x^6}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{7 d x^7}-\frac{e^7 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^3}",1,"(e^5*Sqrt[d^2 - e^2*x^2])/(16*d^2*x^2) - (e^3*(d^2 - e^2*x^2)^(3/2))/(24*d^2*x^4) - (d^2 - e^2*x^2)^(5/2)/(7*d*x^7) - (e*(d^2 - e^2*x^2)^(5/2))/(6*d^2*x^6) - (2*e^2*(d^2 - e^2*x^2)^(5/2))/(35*d^3*x^5) - (e^7*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(16*d^3)","A",8,6,25,0.2400,1,"{835, 807, 266, 47, 63, 208}"
15,1,201,0,0.1563952,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{x^9} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^(3/2))/x^9,x]","\frac{3 e^6 \sqrt{d^2-e^2 x^2}}{128 d^3 x^2}-\frac{e^4 \left(d^2-e^2 x^2\right)^{3/2}}{64 d^3 x^4}-\frac{2 e^3 \left(d^2-e^2 x^2\right)^{5/2}}{35 d^4 x^5}-\frac{e^2 \left(d^2-e^2 x^2\right)^{5/2}}{16 d^3 x^6}-\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{7 d^2 x^7}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{8 d x^8}-\frac{3 e^8 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{128 d^4}","\frac{3 e^6 \sqrt{d^2-e^2 x^2}}{128 d^3 x^2}-\frac{e^4 \left(d^2-e^2 x^2\right)^{3/2}}{64 d^3 x^4}-\frac{2 e^3 \left(d^2-e^2 x^2\right)^{5/2}}{35 d^4 x^5}-\frac{e^2 \left(d^2-e^2 x^2\right)^{5/2}}{16 d^3 x^6}-\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{7 d^2 x^7}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{8 d x^8}-\frac{3 e^8 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{128 d^4}",1,"(3*e^6*Sqrt[d^2 - e^2*x^2])/(128*d^3*x^2) - (e^4*(d^2 - e^2*x^2)^(3/2))/(64*d^3*x^4) - (d^2 - e^2*x^2)^(5/2)/(8*d*x^8) - (e*(d^2 - e^2*x^2)^(5/2))/(7*d^2*x^7) - (e^2*(d^2 - e^2*x^2)^(5/2))/(16*d^3*x^6) - (2*e^3*(d^2 - e^2*x^2)^(5/2))/(35*d^4*x^5) - (3*e^8*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(128*d^4)","A",9,6,25,0.2400,1,"{835, 807, 266, 47, 63, 208}"
16,1,103,0,0.0534872,"\int \frac{x^2 (d+e x)}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(x^2*(d + e*x))/Sqrt[d^2 - e^2*x^2],x]","-\frac{d^2 \sqrt{d^2-e^2 x^2}}{e^3}-\frac{d x \sqrt{d^2-e^2 x^2}}{2 e^2}+\frac{\left(d^2-e^2 x^2\right)^{3/2}}{3 e^3}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^3}","-\frac{d^2 \sqrt{d^2-e^2 x^2}}{e^3}-\frac{d x \sqrt{d^2-e^2 x^2}}{2 e^2}+\frac{\left(d^2-e^2 x^2\right)^{3/2}}{3 e^3}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^3}",1,"-((d^2*Sqrt[d^2 - e^2*x^2])/e^3) - (d*x*Sqrt[d^2 - e^2*x^2])/(2*e^2) + (d^2 - e^2*x^2)^(3/2)/(3*e^3) + (d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^3)","A",8,5,25,0.2000,1,"{797, 641, 195, 217, 203}"
17,1,73,0,0.0418788,"\int \frac{x^2 (d+e x)}{\left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[(x^2*(d + e*x))/(d^2 - e^2*x^2)^(3/2),x]","\frac{d (d+e x)}{e^3 \sqrt{d^2-e^2 x^2}}+\frac{\sqrt{d^2-e^2 x^2}}{e^3}-\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}","\frac{d (d+e x)}{e^3 \sqrt{d^2-e^2 x^2}}+\frac{\sqrt{d^2-e^2 x^2}}{e^3}-\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}",1,"(d*(d + e*x))/(e^3*Sqrt[d^2 - e^2*x^2]) + Sqrt[d^2 - e^2*x^2]/e^3 - (d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^3","A",5,5,25,0.2000,1,"{797, 641, 217, 203, 637}"
18,1,58,0,0.0262578,"\int \frac{x^2 (d+e x)}{\left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[(x^2*(d + e*x))/(d^2 - e^2*x^2)^(5/2),x]","\frac{x^2 (d+e x)}{3 d e \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{3 e^3 \sqrt{d^2-e^2 x^2}}","\frac{x^2 (d+e x)}{3 d e \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{3 e^3 \sqrt{d^2-e^2 x^2}}",1,"(x^2*(d + e*x))/(3*d*e*(d^2 - e^2*x^2)^(3/2)) - 2/(3*e^3*Sqrt[d^2 - e^2*x^2])","A",3,3,25,0.1200,1,"{796, 12, 261}"
19,1,161,0,0.1392972,"\int \frac{x^7 (d+e x)}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^7*(d + e*x))/(d^2 - e^2*x^2)^(7/2),x]","\frac{x^6 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^4 (6 d+7 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x^2 (24 d+35 e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{(32 d+35 e x) \sqrt{d^2-e^2 x^2}}{10 e^8}-\frac{7 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^8}","\frac{x^6 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^4 (6 d+7 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x^2 (24 d+35 e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{(32 d+35 e x) \sqrt{d^2-e^2 x^2}}{10 e^8}-\frac{7 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^8}",1,"(x^6*(d + e*x))/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (x^4*(6*d + 7*e*x))/(15*e^4*(d^2 - e^2*x^2)^(3/2)) + (x^2*(24*d + 35*e*x))/(15*e^6*Sqrt[d^2 - e^2*x^2]) + ((32*d + 35*e*x)*Sqrt[d^2 - e^2*x^2])/(10*e^8) - (7*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^8)","A",6,4,25,0.1600,1,"{819, 780, 217, 203}"
20,1,147,0,0.119666,"\int \frac{x^6 (d+e x)}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^6*(d + e*x))/(d^2 - e^2*x^2)^(7/2),x]","\frac{x^5 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^3 (5 d+6 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x (5 d+8 e x)}{5 e^6 \sqrt{d^2-e^2 x^2}}+\frac{16 \sqrt{d^2-e^2 x^2}}{5 e^7}-\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^7}","\frac{x^5 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^3 (5 d+6 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x (5 d+8 e x)}{5 e^6 \sqrt{d^2-e^2 x^2}}+\frac{16 \sqrt{d^2-e^2 x^2}}{5 e^7}-\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^7}",1,"(x^5*(d + e*x))/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (x^3*(5*d + 6*e*x))/(15*e^4*(d^2 - e^2*x^2)^(3/2)) + (x*(5*d + 8*e*x))/(5*e^6*Sqrt[d^2 - e^2*x^2]) + (16*Sqrt[d^2 - e^2*x^2])/(5*e^7) - (d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^7","A",6,4,25,0.1600,1,"{819, 641, 217, 203}"
21,1,122,0,0.080827,"\int \frac{x^5 (d+e x)}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^5*(d + e*x))/(d^2 - e^2*x^2)^(7/2),x]","\frac{x^4 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^2 (4 d+5 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{8 d+15 e x}{15 e^6 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^6}","\frac{x^4 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^2 (4 d+5 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{8 d+15 e x}{15 e^6 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^6}",1,"(x^4*(d + e*x))/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (x^2*(4*d + 5*e*x))/(15*e^4*(d^2 - e^2*x^2)^(3/2)) + (8*d + 15*e*x)/(15*e^6*Sqrt[d^2 - e^2*x^2]) - ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e^6","A",5,4,25,0.1600,1,"{819, 778, 217, 203}"
22,1,84,0,0.0522609,"\int \frac{x^4 (d+e x)}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^4*(d + e*x))/(d^2 - e^2*x^2)^(7/2),x]","\frac{x^4 (d+e x)}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}+\frac{4}{5 e^5 \sqrt{d^2-e^2 x^2}}-\frac{4 d^2}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}","\frac{x^4 (d+e x)}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}+\frac{4}{5 e^5 \sqrt{d^2-e^2 x^2}}-\frac{4 d^2}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}",1,"(x^4*(d + e*x))/(5*d*e*(d^2 - e^2*x^2)^(5/2)) - (4*d^2)/(15*e^5*(d^2 - e^2*x^2)^(3/2)) + 4/(5*e^5*Sqrt[d^2 - e^2*x^2])","A",4,3,25,0.1200,1,"{805, 266, 43}"
23,1,90,0,0.0420948,"\int \frac{x^3 (d+e x)}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^3*(d + e*x))/(d^2 - e^2*x^2)^(7/2),x]","\frac{x^2 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{x}{5 d^2 e^3 \sqrt{d^2-e^2 x^2}}-\frac{2 d+3 e x}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}","\frac{x^2 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{x}{5 d^2 e^3 \sqrt{d^2-e^2 x^2}}-\frac{2 d+3 e x}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}",1,"(x^2*(d + e*x))/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (2*d + 3*e*x)/(15*e^4*(d^2 - e^2*x^2)^(3/2)) + x/(5*d^2*e^3*Sqrt[d^2 - e^2*x^2])","A",3,3,25,0.1200,1,"{819, 778, 191}"
24,1,94,0,0.045912,"\int \frac{x^2 (d+e x)}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^2*(d + e*x))/(d^2 - e^2*x^2)^(7/2),x]","\frac{x^2 (d+e x)}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 x}{15 d^3 e^2 \sqrt{d^2-e^2 x^2}}-\frac{2 (d-e x)}{15 d e^3 \left(d^2-e^2 x^2\right)^{3/2}}","\frac{x^2 (d+e x)}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 x}{15 d^3 e^2 \sqrt{d^2-e^2 x^2}}-\frac{2 (d-e x)}{15 d e^3 \left(d^2-e^2 x^2\right)^{3/2}}",1,"(x^2*(d + e*x))/(5*d*e*(d^2 - e^2*x^2)^(5/2)) - (2*(d - e*x))/(15*d*e^3*(d^2 - e^2*x^2)^(3/2)) - (2*x)/(15*d^3*e^2*Sqrt[d^2 - e^2*x^2])","A",3,3,25,0.1200,1,"{796, 778, 191}"
25,1,83,0,0.022972,"\int \frac{x (d+e x)}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x*(d + e*x))/(d^2 - e^2*x^2)^(7/2),x]","-\frac{2 x}{15 d^4 e \sqrt{d^2-e^2 x^2}}-\frac{x}{15 d^2 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{d+e x}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}","-\frac{2 x}{15 d^4 e \sqrt{d^2-e^2 x^2}}-\frac{x}{15 d^2 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{d+e x}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}",1,"(d + e*x)/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - x/(15*d^2*e*(d^2 - e^2*x^2)^(3/2)) - (2*x)/(15*d^4*e*Sqrt[d^2 - e^2*x^2])","A",3,3,23,0.1304,1,"{778, 192, 191}"
26,1,80,0,0.0209599,"\int \frac{d+e x}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)/(d^2 - e^2*x^2)^(7/2),x]","\frac{8 x}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{4 x}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{d+e x}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}","\frac{8 x}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{4 x}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{d+e x}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}",1,"(d + e*x)/(5*d*e*(d^2 - e^2*x^2)^(5/2)) + (4*x)/(15*d^3*(d^2 - e^2*x^2)^(3/2)) + (8*x)/(15*d^5*Sqrt[d^2 - e^2*x^2])","A",3,3,22,0.1364,1,"{639, 192, 191}"
27,1,117,0,0.1031974,"\int \frac{d+e x}{x \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)/(x*(d^2 - e^2*x^2)^(7/2)),x]","\frac{d+e x}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{15 d+8 e x}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{5 d+4 e x}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}","\frac{d+e x}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{15 d+8 e x}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{5 d+4 e x}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}",1,"(d + e*x)/(5*d^2*(d^2 - e^2*x^2)^(5/2)) + (5*d + 4*e*x)/(15*d^4*(d^2 - e^2*x^2)^(3/2)) + (15*d + 8*e*x)/(15*d^6*Sqrt[d^2 - e^2*x^2]) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^6","A",7,5,25,0.2000,1,"{823, 12, 266, 63, 208}"
28,1,153,0,0.1266766,"\int \frac{d+e x}{x^2 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)/(x^2*(d^2 - e^2*x^2)^(7/2)),x]","\frac{d+e x}{5 d^2 x \left(d^2-e^2 x^2\right)^{5/2}}-\frac{16 \sqrt{d^2-e^2 x^2}}{5 d^7 x}+\frac{8 d+5 e x}{5 d^6 x \sqrt{d^2-e^2 x^2}}+\frac{6 d+5 e x}{15 d^4 x \left(d^2-e^2 x^2\right)^{3/2}}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^7}","\frac{d+e x}{5 d^2 x \left(d^2-e^2 x^2\right)^{5/2}}-\frac{16 \sqrt{d^2-e^2 x^2}}{5 d^7 x}+\frac{8 d+5 e x}{5 d^6 x \sqrt{d^2-e^2 x^2}}+\frac{6 d+5 e x}{15 d^4 x \left(d^2-e^2 x^2\right)^{3/2}}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^7}",1,"(d + e*x)/(5*d^2*x*(d^2 - e^2*x^2)^(5/2)) + (6*d + 5*e*x)/(15*d^4*x*(d^2 - e^2*x^2)^(3/2)) + (8*d + 5*e*x)/(5*d^6*x*Sqrt[d^2 - e^2*x^2]) - (16*Sqrt[d^2 - e^2*x^2])/(5*d^7*x) - (e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^7","A",7,5,25,0.2000,1,"{823, 807, 266, 63, 208}"
29,1,184,0,0.15962,"\int \frac{d+e x}{x^3 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)/(x^3*(d^2 - e^2*x^2)^(7/2)),x]","-\frac{16 e \sqrt{d^2-e^2 x^2}}{5 d^8 x}-\frac{7 \sqrt{d^2-e^2 x^2}}{2 d^7 x^2}+\frac{35 d+24 e x}{15 d^6 x^2 \sqrt{d^2-e^2 x^2}}+\frac{7 d+6 e x}{15 d^4 x^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{d+e x}{5 d^2 x^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{7 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^8}","-\frac{16 e \sqrt{d^2-e^2 x^2}}{5 d^8 x}-\frac{7 \sqrt{d^2-e^2 x^2}}{2 d^7 x^2}+\frac{35 d+24 e x}{15 d^6 x^2 \sqrt{d^2-e^2 x^2}}+\frac{7 d+6 e x}{15 d^4 x^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{d+e x}{5 d^2 x^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{7 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^8}",1,"(d + e*x)/(5*d^2*x^2*(d^2 - e^2*x^2)^(5/2)) + (7*d + 6*e*x)/(15*d^4*x^2*(d^2 - e^2*x^2)^(3/2)) + (35*d + 24*e*x)/(15*d^6*x^2*Sqrt[d^2 - e^2*x^2]) - (7*Sqrt[d^2 - e^2*x^2])/(2*d^7*x^2) - (16*e*Sqrt[d^2 - e^2*x^2])/(5*d^8*x) - (7*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^8)","A",8,6,25,0.2400,1,"{823, 835, 807, 266, 63, 208}"
30,1,121,0,0.0525345,"\int \frac{x^2 (d+e x)}{\left(d^2-e^2 x^2\right)^{9/2}} \, dx","Int[(x^2*(d + e*x))/(d^2 - e^2*x^2)^(9/2),x]","\frac{x^2 (d+e x)}{7 d e \left(d^2-e^2 x^2\right)^{7/2}}-\frac{8 x}{105 d^5 e^2 \sqrt{d^2-e^2 x^2}}-\frac{4 x}{105 d^3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 (d-2 e x)}{35 d e^3 \left(d^2-e^2 x^2\right)^{5/2}}","\frac{x^2 (d+e x)}{7 d e \left(d^2-e^2 x^2\right)^{7/2}}-\frac{8 x}{105 d^5 e^2 \sqrt{d^2-e^2 x^2}}-\frac{4 x}{105 d^3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 (d-2 e x)}{35 d e^3 \left(d^2-e^2 x^2\right)^{5/2}}",1,"(x^2*(d + e*x))/(7*d*e*(d^2 - e^2*x^2)^(7/2)) - (2*(d - 2*e*x))/(35*d*e^3*(d^2 - e^2*x^2)^(5/2)) - (4*x)/(105*d^3*e^2*(d^2 - e^2*x^2)^(3/2)) - (8*x)/(105*d^5*e^2*Sqrt[d^2 - e^2*x^2])","A",4,4,25,0.1600,1,"{796, 778, 192, 191}"
31,1,148,0,0.0617767,"\int \frac{x^2 (d+e x)}{\left(d^2-e^2 x^2\right)^{11/2}} \, dx","Int[(x^2*(d + e*x))/(d^2 - e^2*x^2)^(11/2),x]","\frac{x^2 (d+e x)}{9 d e \left(d^2-e^2 x^2\right)^{9/2}}-\frac{16 x}{315 d^7 e^2 \sqrt{d^2-e^2 x^2}}-\frac{8 x}{315 d^5 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 x}{105 d^3 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 (d-3 e x)}{63 d e^3 \left(d^2-e^2 x^2\right)^{7/2}}","\frac{x^2 (d+e x)}{9 d e \left(d^2-e^2 x^2\right)^{9/2}}-\frac{16 x}{315 d^7 e^2 \sqrt{d^2-e^2 x^2}}-\frac{8 x}{315 d^5 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 x}{105 d^3 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 (d-3 e x)}{63 d e^3 \left(d^2-e^2 x^2\right)^{7/2}}",1,"(x^2*(d + e*x))/(9*d*e*(d^2 - e^2*x^2)^(9/2)) - (2*(d - 3*e*x))/(63*d*e^3*(d^2 - e^2*x^2)^(7/2)) - (2*x)/(105*d^3*e^2*(d^2 - e^2*x^2)^(5/2)) - (8*x)/(315*d^5*e^2*(d^2 - e^2*x^2)^(3/2)) - (16*x)/(315*d^7*e^2*Sqrt[d^2 - e^2*x^2])","A",5,4,25,0.1600,1,"{796, 778, 192, 191}"
32,1,54,0,0.0343437,"\int \frac{x^2 (1-a x)}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(x^2*(1 - a*x))/(1 - a^2*x^2)^(3/2),x]","-\frac{1-a x}{a^3 \sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2}}{a^3}-\frac{\sin ^{-1}(a x)}{a^3}","-\frac{1-a x}{a^3 \sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2}}{a^3}-\frac{\sin ^{-1}(a x)}{a^3}",1,"-((1 - a*x)/(a^3*Sqrt[1 - a^2*x^2])) - Sqrt[1 - a^2*x^2]/a^3 - ArcSin[a*x]/a^3","A",4,4,24,0.1667,1,"{797, 641, 216, 637}"
33,1,173,0,0.2268777,"\int \frac{x^4 (d+e x)^2}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(x^4*(d + e*x)^2)/Sqrt[d^2 - e^2*x^2],x]","-\frac{d^4 (256 d+165 e x) \sqrt{d^2-e^2 x^2}}{240 e^5}-\frac{8 d^3 x^2 \sqrt{d^2-e^2 x^2}}{15 e^3}-\frac{11 d^2 x^3 \sqrt{d^2-e^2 x^2}}{24 e^2}-\frac{2 d x^4 \sqrt{d^2-e^2 x^2}}{5 e}-\frac{1}{6} x^5 \sqrt{d^2-e^2 x^2}+\frac{11 d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^5}","-\frac{d^4 (256 d+165 e x) \sqrt{d^2-e^2 x^2}}{240 e^5}-\frac{8 d^3 x^2 \sqrt{d^2-e^2 x^2}}{15 e^3}-\frac{11 d^2 x^3 \sqrt{d^2-e^2 x^2}}{24 e^2}-\frac{2 d x^4 \sqrt{d^2-e^2 x^2}}{5 e}-\frac{1}{6} x^5 \sqrt{d^2-e^2 x^2}+\frac{11 d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^5}",1,"(-8*d^3*x^2*Sqrt[d^2 - e^2*x^2])/(15*e^3) - (11*d^2*x^3*Sqrt[d^2 - e^2*x^2])/(24*e^2) - (2*d*x^4*Sqrt[d^2 - e^2*x^2])/(5*e) - (x^5*Sqrt[d^2 - e^2*x^2])/6 - (d^4*(256*d + 165*e*x)*Sqrt[d^2 - e^2*x^2])/(240*e^5) + (11*d^6*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^5)","A",7,5,27,0.1852,1,"{1809, 833, 780, 217, 203}"
34,1,144,0,0.1860415,"\int \frac{x^3 (d+e x)^2}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(x^3*(d + e*x)^2)/Sqrt[d^2 - e^2*x^2],x]","-\frac{3 d^3 (8 d+5 e x) \sqrt{d^2-e^2 x^2}}{20 e^4}-\frac{3 d^2 x^2 \sqrt{d^2-e^2 x^2}}{5 e^2}-\frac{d x^3 \sqrt{d^2-e^2 x^2}}{2 e}-\frac{1}{5} x^4 \sqrt{d^2-e^2 x^2}+\frac{3 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{4 e^4}","-\frac{3 d^3 (8 d+5 e x) \sqrt{d^2-e^2 x^2}}{20 e^4}-\frac{3 d^2 x^2 \sqrt{d^2-e^2 x^2}}{5 e^2}-\frac{d x^3 \sqrt{d^2-e^2 x^2}}{2 e}-\frac{1}{5} x^4 \sqrt{d^2-e^2 x^2}+\frac{3 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{4 e^4}",1,"(-3*d^2*x^2*Sqrt[d^2 - e^2*x^2])/(5*e^2) - (d*x^3*Sqrt[d^2 - e^2*x^2])/(2*e) - (x^4*Sqrt[d^2 - e^2*x^2])/5 - (3*d^3*(8*d + 5*e*x)*Sqrt[d^2 - e^2*x^2])/(20*e^4) + (3*d^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(4*e^4)","A",6,5,27,0.1852,1,"{1809, 833, 780, 217, 203}"
35,1,115,0,0.1451278,"\int \frac{x^2 (d+e x)^2}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(x^2*(d + e*x)^2)/Sqrt[d^2 - e^2*x^2],x]","-\frac{d^2 (32 d+21 e x) \sqrt{d^2-e^2 x^2}}{24 e^3}-\frac{2 d x^2 \sqrt{d^2-e^2 x^2}}{3 e}-\frac{1}{4} x^3 \sqrt{d^2-e^2 x^2}+\frac{7 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}","-\frac{d^2 (32 d+21 e x) \sqrt{d^2-e^2 x^2}}{24 e^3}-\frac{2 d x^2 \sqrt{d^2-e^2 x^2}}{3 e}-\frac{1}{4} x^3 \sqrt{d^2-e^2 x^2}+\frac{7 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}",1,"(-2*d*x^2*Sqrt[d^2 - e^2*x^2])/(3*e) - (x^3*Sqrt[d^2 - e^2*x^2])/4 - (d^2*(32*d + 21*e*x)*Sqrt[d^2 - e^2*x^2])/(24*e^3) + (7*d^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^3)","A",5,5,27,0.1852,1,"{1809, 833, 780, 217, 203}"
36,1,83,0,0.084863,"\int \frac{x (d+e x)^2}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(x*(d + e*x)^2)/Sqrt[d^2 - e^2*x^2],x]","-\frac{d (5 d+3 e x) \sqrt{d^2-e^2 x^2}}{3 e^2}-\frac{1}{3} x^2 \sqrt{d^2-e^2 x^2}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^2}","-\frac{d (5 d+3 e x) \sqrt{d^2-e^2 x^2}}{3 e^2}-\frac{1}{3} x^2 \sqrt{d^2-e^2 x^2}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^2}",1,"-(x^2*Sqrt[d^2 - e^2*x^2])/3 - (d*(5*d + 3*e*x)*Sqrt[d^2 - e^2*x^2])/(3*e^2) + (d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^2","A",4,4,25,0.1600,1,"{1809, 780, 217, 203}"
37,1,83,0,0.0277766,"\int \frac{(d+e x)^2}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^2/Sqrt[d^2 - e^2*x^2],x]","-\frac{3 d \sqrt{d^2-e^2 x^2}}{2 e}-\frac{(d+e x) \sqrt{d^2-e^2 x^2}}{2 e}+\frac{3 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}","-\frac{3 d \sqrt{d^2-e^2 x^2}}{2 e}-\frac{(d+e x) \sqrt{d^2-e^2 x^2}}{2 e}+\frac{3 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}",1,"(-3*d*Sqrt[d^2 - e^2*x^2])/(2*e) - ((d + e*x)*Sqrt[d^2 - e^2*x^2])/(2*e) + (3*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e)","A",4,4,24,0.1667,1,"{671, 641, 217, 203}"
38,1,66,0,0.1113858,"\int \frac{(d+e x)^2}{x \sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^2/(x*Sqrt[d^2 - e^2*x^2]),x]","-\sqrt{d^2-e^2 x^2}+2 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\sqrt{d^2-e^2 x^2}+2 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"-Sqrt[d^2 - e^2*x^2] + 2*d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - d*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",7,7,27,0.2593,1,"{1809, 844, 217, 203, 266, 63, 208}"
39,1,68,0,0.115041,"\int \frac{(d+e x)^2}{x^2 \sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^2/(x^2*Sqrt[d^2 - e^2*x^2]),x]","-\frac{\sqrt{d^2-e^2 x^2}}{x}+e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-2 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{\sqrt{d^2-e^2 x^2}}{x}+e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-2 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"-(Sqrt[d^2 - e^2*x^2]/x) + e*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - 2*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",7,7,27,0.2593,1,"{1807, 844, 217, 203, 266, 63, 208}"
40,1,80,0,0.1088828,"\int \frac{(d+e x)^2}{x^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^2/(x^3*Sqrt[d^2 - e^2*x^2]),x]","-\frac{2 e \sqrt{d^2-e^2 x^2}}{d x}-\frac{\sqrt{d^2-e^2 x^2}}{2 x^2}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d}","-\frac{2 e \sqrt{d^2-e^2 x^2}}{d x}-\frac{\sqrt{d^2-e^2 x^2}}{2 x^2}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d}",1,"-Sqrt[d^2 - e^2*x^2]/(2*x^2) - (2*e*Sqrt[d^2 - e^2*x^2])/(d*x) - (3*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d)","A",5,5,27,0.1852,1,"{1807, 807, 266, 63, 208}"
41,1,107,0,0.1370313,"\int \frac{(d+e x)^2}{x^4 \sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^2/(x^4*Sqrt[d^2 - e^2*x^2]),x]","-\frac{5 e^2 \sqrt{d^2-e^2 x^2}}{3 d^2 x}-\frac{e \sqrt{d^2-e^2 x^2}}{d x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 x^3}-\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^2}","-\frac{5 e^2 \sqrt{d^2-e^2 x^2}}{3 d^2 x}-\frac{e \sqrt{d^2-e^2 x^2}}{d x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 x^3}-\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^2}",1,"-Sqrt[d^2 - e^2*x^2]/(3*x^3) - (e*Sqrt[d^2 - e^2*x^2])/(d*x^2) - (5*e^2*Sqrt[d^2 - e^2*x^2])/(3*d^2*x) - (e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^2","A",6,6,27,0.2222,1,"{1807, 835, 807, 266, 63, 208}"
42,1,140,0,0.1715343,"\int \frac{(d+e x)^2}{x^5 \sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^2/(x^5*Sqrt[d^2 - e^2*x^2]),x]","-\frac{4 e^3 \sqrt{d^2-e^2 x^2}}{3 d^3 x}-\frac{7 e^2 \sqrt{d^2-e^2 x^2}}{8 d^2 x^2}-\frac{2 e \sqrt{d^2-e^2 x^2}}{3 d x^3}-\frac{\sqrt{d^2-e^2 x^2}}{4 x^4}-\frac{7 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d^3}","-\frac{4 e^3 \sqrt{d^2-e^2 x^2}}{3 d^3 x}-\frac{7 e^2 \sqrt{d^2-e^2 x^2}}{8 d^2 x^2}-\frac{2 e \sqrt{d^2-e^2 x^2}}{3 d x^3}-\frac{\sqrt{d^2-e^2 x^2}}{4 x^4}-\frac{7 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d^3}",1,"-Sqrt[d^2 - e^2*x^2]/(4*x^4) - (2*e*Sqrt[d^2 - e^2*x^2])/(3*d*x^3) - (7*e^2*Sqrt[d^2 - e^2*x^2])/(8*d^2*x^2) - (4*e^3*Sqrt[d^2 - e^2*x^2])/(3*d^3*x) - (7*e^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(8*d^3)","A",7,6,27,0.2222,1,"{1807, 835, 807, 266, 63, 208}"
43,1,169,0,0.1951762,"\int \frac{(d+e x)^2}{x^6 \sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^2/(x^6*Sqrt[d^2 - e^2*x^2]),x]","-\frac{6 e^4 \sqrt{d^2-e^2 x^2}}{5 d^4 x}-\frac{3 e^3 \sqrt{d^2-e^2 x^2}}{4 d^3 x^2}-\frac{3 e^2 \sqrt{d^2-e^2 x^2}}{5 d^2 x^3}-\frac{e \sqrt{d^2-e^2 x^2}}{2 d x^4}-\frac{\sqrt{d^2-e^2 x^2}}{5 x^5}-\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{4 d^4}","-\frac{6 e^4 \sqrt{d^2-e^2 x^2}}{5 d^4 x}-\frac{3 e^3 \sqrt{d^2-e^2 x^2}}{4 d^3 x^2}-\frac{3 e^2 \sqrt{d^2-e^2 x^2}}{5 d^2 x^3}-\frac{e \sqrt{d^2-e^2 x^2}}{2 d x^4}-\frac{\sqrt{d^2-e^2 x^2}}{5 x^5}-\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{4 d^4}",1,"-Sqrt[d^2 - e^2*x^2]/(5*x^5) - (e*Sqrt[d^2 - e^2*x^2])/(2*d*x^4) - (3*e^2*Sqrt[d^2 - e^2*x^2])/(5*d^2*x^3) - (3*e^3*Sqrt[d^2 - e^2*x^2])/(4*d^3*x^2) - (6*e^4*Sqrt[d^2 - e^2*x^2])/(5*d^4*x) - (3*e^5*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(4*d^4)","A",8,6,27,0.2222,1,"{1807, 835, 807, 266, 63, 208}"
44,1,143,0,0.2711304,"\int \frac{x^5 (d+e x)^2}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^5*(d + e*x)^2)/(d^2 - e^2*x^2)^(7/2),x]","\frac{d^4 (d+e x)^2}{5 e^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{22 d^3 (d+e x)}{15 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 d (30 d+23 e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{\sqrt{d^2-e^2 x^2}}{e^6}-\frac{2 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^6}","\frac{d^4 (d+e x)^2}{5 e^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{22 d^3 (d+e x)}{15 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 d (30 d+23 e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{\sqrt{d^2-e^2 x^2}}{e^6}-\frac{2 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^6}",1,"(d^4*(d + e*x)^2)/(5*e^6*(d^2 - e^2*x^2)^(5/2)) - (22*d^3*(d + e*x))/(15*e^6*(d^2 - e^2*x^2)^(3/2)) + (2*d*(30*d + 23*e*x))/(15*e^6*Sqrt[d^2 - e^2*x^2]) + Sqrt[d^2 - e^2*x^2]/e^6 - (2*d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^6","A",6,5,27,0.1852,1,"{1635, 1814, 641, 217, 203}"
45,1,121,0,0.2076745,"\int \frac{x^4 (d+e x)^2}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^4*(d + e*x)^2)/(d^2 - e^2*x^2)^(7/2),x]","\frac{d^3 (d+e x)^2}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{17 d^2 (d+e x)}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (15 d+13 e x)}{15 e^5 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}","\frac{d^3 (d+e x)^2}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{17 d^2 (d+e x)}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (15 d+13 e x)}{15 e^5 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}",1,"(d^3*(d + e*x)^2)/(5*e^5*(d^2 - e^2*x^2)^(5/2)) - (17*d^2*(d + e*x))/(15*e^5*(d^2 - e^2*x^2)^(3/2)) + (2*(15*d + 13*e*x))/(15*e^5*Sqrt[d^2 - e^2*x^2]) - ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e^5","A",6,5,27,0.1852,1,"{1635, 1814, 12, 217, 203}"
46,1,97,0,0.1726563,"\int \frac{x^3 (d+e x)^2}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^3*(d + e*x)^2)/(d^2 - e^2*x^2)^(7/2),x]","\frac{d^2 (d+e x)^2}{5 e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{4 d (d+e x)}{5 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{5 d+2 e x}{5 d e^4 \sqrt{d^2-e^2 x^2}}","\frac{d^2 (d+e x)^2}{5 e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{4 d (d+e x)}{5 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{5 d+2 e x}{5 d e^4 \sqrt{d^2-e^2 x^2}}",1,"(d^2*(d + e*x)^2)/(5*e^4*(d^2 - e^2*x^2)^(5/2)) - (4*d*(d + e*x))/(5*e^4*(d^2 - e^2*x^2)^(3/2)) + (5*d + 2*e*x)/(5*d*e^4*Sqrt[d^2 - e^2*x^2])","A",3,2,27,0.07407,1,"{1635, 637}"
47,1,87,0,0.1200372,"\int \frac{x^2 (d+e x)^2}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^2*(d + e*x)^2)/(d^2 - e^2*x^2)^(7/2),x]","\frac{d (d+e x)^2}{5 e^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{7 (d+e x)}{15 e^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x}{15 d^2 e^2 \sqrt{d^2-e^2 x^2}}","\frac{d (d+e x)^2}{5 e^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{7 (d+e x)}{15 e^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x}{15 d^2 e^2 \sqrt{d^2-e^2 x^2}}",1,"(d*(d + e*x)^2)/(5*e^3*(d^2 - e^2*x^2)^(5/2)) - (7*(d + e*x))/(15*e^3*(d^2 - e^2*x^2)^(3/2)) + x/(15*d^2*e^2*Sqrt[d^2 - e^2*x^2])","A",3,3,27,0.1111,1,"{1635, 778, 191}"
48,1,89,0,0.033264,"\int \frac{x (d+e x)^2}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x*(d + e*x)^2)/(d^2 - e^2*x^2)^(7/2),x]","\frac{(d+e x)^2}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 (d+e x)}{15 d e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{4 x}{15 d^3 e \sqrt{d^2-e^2 x^2}}","\frac{(d+e x)^2}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 (d+e x)}{15 d e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{4 x}{15 d^3 e \sqrt{d^2-e^2 x^2}}",1,"(d + e*x)^2/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (2*(d + e*x))/(15*d*e^2*(d^2 - e^2*x^2)^(3/2)) - (4*x)/(15*d^3*e*Sqrt[d^2 - e^2*x^2])","A",3,3,25,0.1200,1,"{789, 639, 191}"
49,1,77,0,0.0197757,"\int \frac{(d+e x)^2}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^2/(d^2 - e^2*x^2)^(7/2),x]","\frac{2 x}{5 d^4 \sqrt{d^2-e^2 x^2}}+\frac{x}{5 d^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (d+e x)}{5 e \left(d^2-e^2 x^2\right)^{5/2}}","\frac{2 x}{5 d^4 \sqrt{d^2-e^2 x^2}}+\frac{x}{5 d^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (d+e x)}{5 e \left(d^2-e^2 x^2\right)^{5/2}}",1,"(2*(d + e*x))/(5*e*(d^2 - e^2*x^2)^(5/2)) + x/(5*d^2*(d^2 - e^2*x^2)^(3/2)) + (2*x)/(5*d^4*Sqrt[d^2 - e^2*x^2])","A",3,3,24,0.1250,1,"{653, 192, 191}"
50,1,117,0,0.1587986,"\int \frac{(d+e x)^2}{x \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^2/(x*(d^2 - e^2*x^2)^(7/2)),x]","\frac{2 (d+e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}+\frac{15 d+16 e x}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{5 d+8 e x}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}","\frac{2 (d+e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}+\frac{15 d+16 e x}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{5 d+8 e x}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}",1,"(2*(d + e*x))/(5*d*(d^2 - e^2*x^2)^(5/2)) + (5*d + 8*e*x)/(15*d^3*(d^2 - e^2*x^2)^(3/2)) + (15*d + 16*e*x)/(15*d^5*Sqrt[d^2 - e^2*x^2]) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^5","A",7,6,27,0.2222,1,"{1805, 823, 12, 266, 63, 208}"
51,1,145,0,0.2751179,"\int \frac{(d+e x)^2}{x^2 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^2/(x^2*(d^2 - e^2*x^2)^(7/2)),x]","\frac{2 e (d+e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^6 x}+\frac{e (30 d+41 e x)}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{e (10 d+13 e x)}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}","\frac{2 e (d+e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^6 x}+\frac{e (30 d+41 e x)}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{e (10 d+13 e x)}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}",1,"(2*e*(d + e*x))/(5*d^2*(d^2 - e^2*x^2)^(5/2)) + (e*(10*d + 13*e*x))/(15*d^4*(d^2 - e^2*x^2)^(3/2)) + (e*(30*d + 41*e*x))/(15*d^6*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(d^6*x) - (2*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^6","A",7,5,27,0.1852,1,"{1805, 807, 266, 63, 208}"
52,1,182,0,0.3580161,"\int \frac{(d+e x)^2}{x^3 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^2/(x^3*(d^2 - e^2*x^2)^(7/2)),x]","\frac{2 e^2 (10 d+11 e x)}{5 d^7 \sqrt{d^2-e^2 x^2}}+\frac{e^2 (5 d+6 e x)}{5 d^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 e^2 (d+e x)}{5 d^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 e \sqrt{d^2-e^2 x^2}}{d^7 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^6 x^2}-\frac{9 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^7}","\frac{2 e^2 (10 d+11 e x)}{5 d^7 \sqrt{d^2-e^2 x^2}}+\frac{e^2 (5 d+6 e x)}{5 d^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 e^2 (d+e x)}{5 d^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 e \sqrt{d^2-e^2 x^2}}{d^7 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^6 x^2}-\frac{9 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^7}",1,"(2*e^2*(d + e*x))/(5*d^3*(d^2 - e^2*x^2)^(5/2)) + (e^2*(5*d + 6*e*x))/(5*d^5*(d^2 - e^2*x^2)^(3/2)) + (2*e^2*(10*d + 11*e*x))/(5*d^7*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(2*d^6*x^2) - (2*e*Sqrt[d^2 - e^2*x^2])/(d^7*x) - (9*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^7)","A",8,6,27,0.2222,1,"{1805, 1807, 807, 266, 63, 208}"
53,1,209,0,0.4738859,"\int \frac{(d+e x)^2}{x^4 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^2/(x^4*(d^2 - e^2*x^2)^(7/2)),x]","\frac{2 e^3 (45 d+53 e x)}{15 d^8 \sqrt{d^2-e^2 x^2}}+\frac{e^3 (20 d+23 e x)}{15 d^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 e^3 (d+e x)}{5 d^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{14 e^2 \sqrt{d^2-e^2 x^2}}{3 d^8 x}-\frac{e \sqrt{d^2-e^2 x^2}}{d^7 x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 d^6 x^3}-\frac{7 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^8}","\frac{2 e^3 (45 d+53 e x)}{15 d^8 \sqrt{d^2-e^2 x^2}}+\frac{e^3 (20 d+23 e x)}{15 d^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 e^3 (d+e x)}{5 d^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{14 e^2 \sqrt{d^2-e^2 x^2}}{3 d^8 x}-\frac{e \sqrt{d^2-e^2 x^2}}{d^7 x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 d^6 x^3}-\frac{7 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^8}",1,"(2*e^3*(d + e*x))/(5*d^4*(d^2 - e^2*x^2)^(5/2)) + (e^3*(20*d + 23*e*x))/(15*d^6*(d^2 - e^2*x^2)^(3/2)) + (2*e^3*(45*d + 53*e*x))/(15*d^8*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(3*d^6*x^3) - (e*Sqrt[d^2 - e^2*x^2])/(d^7*x^2) - (14*e^2*Sqrt[d^2 - e^2*x^2])/(3*d^8*x) - (7*e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^8","A",9,6,27,0.2222,1,"{1805, 1807, 807, 266, 63, 208}"
54,1,81,0,0.0932834,"\int \frac{x^3 (1+x)^2}{\sqrt{1-x^2}} \, dx","Int[(x^3*(1 + x)^2)/Sqrt[1 - x^2],x]","-\frac{1}{5} \sqrt{1-x^2} x^4-\frac{1}{2} \sqrt{1-x^2} x^3-\frac{3}{5} \sqrt{1-x^2} x^2-\frac{3}{20} (5 x+8) \sqrt{1-x^2}+\frac{3}{4} \sin ^{-1}(x)","-\frac{1}{5} \sqrt{1-x^2} x^4-\frac{1}{2} \sqrt{1-x^2} x^3-\frac{3}{5} \sqrt{1-x^2} x^2-\frac{3}{20} (5 x+8) \sqrt{1-x^2}+\frac{3}{4} \sin ^{-1}(x)",1,"(-3*x^2*Sqrt[1 - x^2])/5 - (x^3*Sqrt[1 - x^2])/2 - (x^4*Sqrt[1 - x^2])/5 - (3*(8 + 5*x)*Sqrt[1 - x^2])/20 + (3*ArcSin[x])/4","A",5,4,20,0.2000,1,"{1809, 833, 780, 216}"
55,1,63,0,0.080565,"\int \frac{x^2 (1+x)^2}{\sqrt{1-x^2}} \, dx","Int[(x^2*(1 + x)^2)/Sqrt[1 - x^2],x]","-\frac{1}{4} \sqrt{1-x^2} x^3-\frac{2}{3} \sqrt{1-x^2} x^2-\frac{1}{24} (21 x+32) \sqrt{1-x^2}+\frac{7}{8} \sin ^{-1}(x)","-\frac{1}{4} \sqrt{1-x^2} x^3-\frac{2}{3} \sqrt{1-x^2} x^2-\frac{1}{24} (21 x+32) \sqrt{1-x^2}+\frac{7}{8} \sin ^{-1}(x)",1,"(-2*x^2*Sqrt[1 - x^2])/3 - (x^3*Sqrt[1 - x^2])/4 - ((32 + 21*x)*Sqrt[1 - x^2])/24 + (7*ArcSin[x])/8","A",4,4,20,0.2000,1,"{1809, 833, 780, 216}"
56,1,41,0,0.0477031,"\int \frac{x (1+x)^2}{\sqrt{1-x^2}} \, dx","Int[(x*(1 + x)^2)/Sqrt[1 - x^2],x]","-\frac{1}{3} \sqrt{1-x^2} x^2-\frac{1}{3} (3 x+5) \sqrt{1-x^2}+\sin ^{-1}(x)","-\frac{1}{3} \sqrt{1-x^2} x^2-\frac{1}{3} (3 x+5) \sqrt{1-x^2}+\sin ^{-1}(x)",1,"-(x^2*Sqrt[1 - x^2])/3 - ((5 + 3*x)*Sqrt[1 - x^2])/3 + ArcSin[x]","A",3,3,18,0.1667,1,"{1809, 780, 216}"
57,1,40,0,0.0122981,"\int \frac{(1+x)^2}{\sqrt{1-x^2}} \, dx","Int[(1 + x)^2/Sqrt[1 - x^2],x]","-\frac{1}{2} \sqrt{1-x^2} (x+1)-\frac{3 \sqrt{1-x^2}}{2}+\frac{3}{2} \sin ^{-1}(x)","-\frac{1}{2} \sqrt{1-x^2} (x+1)-\frac{3 \sqrt{1-x^2}}{2}+\frac{3}{2} \sin ^{-1}(x)",1,"(-3*Sqrt[1 - x^2])/2 - ((1 + x)*Sqrt[1 - x^2])/2 + (3*ArcSin[x])/2","A",3,3,17,0.1765,1,"{671, 641, 216}"
58,1,32,0,0.0589199,"\int \frac{(1+x)^2}{x \sqrt{1-x^2}} \, dx","Int[(1 + x)^2/(x*Sqrt[1 - x^2]),x]","-\sqrt{1-x^2}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)+2 \sin ^{-1}(x)","-\sqrt{1-x^2}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)+2 \sin ^{-1}(x)",1,"-Sqrt[1 - x^2] + 2*ArcSin[x] - ArcTanh[Sqrt[1 - x^2]]","A",6,6,20,0.3000,1,"{1809, 844, 216, 266, 63, 206}"
59,1,33,0,0.0625413,"\int \frac{(1+x)^2}{x^2 \sqrt{1-x^2}} \, dx","Int[(1 + x)^2/(x^2*Sqrt[1 - x^2]),x]","-\frac{\sqrt{1-x^2}}{x}-2 \tanh ^{-1}\left(\sqrt{1-x^2}\right)+\sin ^{-1}(x)","-\frac{\sqrt{1-x^2}}{x}-2 \tanh ^{-1}\left(\sqrt{1-x^2}\right)+\sin ^{-1}(x)",1,"-(Sqrt[1 - x^2]/x) + ArcSin[x] - 2*ArcTanh[Sqrt[1 - x^2]]","A",6,6,20,0.3000,1,"{1807, 844, 216, 266, 63, 206}"
60,1,51,0,0.0614837,"\int \frac{(1+x)^2}{x^3 \sqrt{1-x^2}} \, dx","Int[(1 + x)^2/(x^3*Sqrt[1 - x^2]),x]","-\frac{2 \sqrt{1-x^2}}{x}-\frac{\sqrt{1-x^2}}{2 x^2}-\frac{3}{2} \tanh ^{-1}\left(\sqrt{1-x^2}\right)","-\frac{2 \sqrt{1-x^2}}{x}-\frac{\sqrt{1-x^2}}{2 x^2}-\frac{3}{2} \tanh ^{-1}\left(\sqrt{1-x^2}\right)",1,"-Sqrt[1 - x^2]/(2*x^2) - (2*Sqrt[1 - x^2])/x - (3*ArcTanh[Sqrt[1 - x^2]])/2","A",5,5,20,0.2500,1,"{1807, 807, 266, 63, 206}"
61,1,67,0,0.0737916,"\int \frac{(1+x)^2}{x^4 \sqrt{1-x^2}} \, dx","Int[(1 + x)^2/(x^4*Sqrt[1 - x^2]),x]","-\frac{5 \sqrt{1-x^2}}{3 x}-\frac{\sqrt{1-x^2}}{x^2}-\frac{\sqrt{1-x^2}}{3 x^3}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)","-\frac{5 \sqrt{1-x^2}}{3 x}-\frac{\sqrt{1-x^2}}{x^2}-\frac{\sqrt{1-x^2}}{3 x^3}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)",1,"-Sqrt[1 - x^2]/(3*x^3) - Sqrt[1 - x^2]/x^2 - (5*Sqrt[1 - x^2])/(3*x) - ArcTanh[Sqrt[1 - x^2]]","A",6,6,20,0.3000,1,"{1807, 835, 807, 266, 63, 206}"
62,1,89,0,0.0895911,"\int \frac{(1+x)^2}{x^5 \sqrt{1-x^2}} \, dx","Int[(1 + x)^2/(x^5*Sqrt[1 - x^2]),x]","-\frac{4 \sqrt{1-x^2}}{3 x}-\frac{7 \sqrt{1-x^2}}{8 x^2}-\frac{2 \sqrt{1-x^2}}{3 x^3}-\frac{\sqrt{1-x^2}}{4 x^4}-\frac{7}{8} \tanh ^{-1}\left(\sqrt{1-x^2}\right)","-\frac{4 \sqrt{1-x^2}}{3 x}-\frac{7 \sqrt{1-x^2}}{8 x^2}-\frac{2 \sqrt{1-x^2}}{3 x^3}-\frac{\sqrt{1-x^2}}{4 x^4}-\frac{7}{8} \tanh ^{-1}\left(\sqrt{1-x^2}\right)",1,"-Sqrt[1 - x^2]/(4*x^4) - (2*Sqrt[1 - x^2])/(3*x^3) - (7*Sqrt[1 - x^2])/(8*x^2) - (4*Sqrt[1 - x^2])/(3*x) - (7*ArcTanh[Sqrt[1 - x^2]])/8","A",7,6,20,0.3000,1,"{1807, 835, 807, 266, 63, 206}"
63,1,107,0,0.1030154,"\int \frac{(1+x)^2}{x^6 \sqrt{1-x^2}} \, dx","Int[(1 + x)^2/(x^6*Sqrt[1 - x^2]),x]","-\frac{6 \sqrt{1-x^2}}{5 x}-\frac{3 \sqrt{1-x^2}}{4 x^2}-\frac{3 \sqrt{1-x^2}}{5 x^3}-\frac{\sqrt{1-x^2}}{2 x^4}-\frac{\sqrt{1-x^2}}{5 x^5}-\frac{3}{4} \tanh ^{-1}\left(\sqrt{1-x^2}\right)","-\frac{6 \sqrt{1-x^2}}{5 x}-\frac{3 \sqrt{1-x^2}}{4 x^2}-\frac{3 \sqrt{1-x^2}}{5 x^3}-\frac{\sqrt{1-x^2}}{2 x^4}-\frac{\sqrt{1-x^2}}{5 x^5}-\frac{3}{4} \tanh ^{-1}\left(\sqrt{1-x^2}\right)",1,"-Sqrt[1 - x^2]/(5*x^5) - Sqrt[1 - x^2]/(2*x^4) - (3*Sqrt[1 - x^2])/(5*x^3) - (3*Sqrt[1 - x^2])/(4*x^2) - (6*Sqrt[1 - x^2])/(5*x) - (3*ArcTanh[Sqrt[1 - x^2]])/4","A",8,6,20,0.3000,1,"{1807, 835, 807, 266, 63, 206}"
64,1,134,0,0.2150961,"\int \frac{(d+e x)^3 \sqrt{d^2-e^2 x^2}}{x^5} \, dx","Int[((d + e*x)^3*Sqrt[d^2 - e^2*x^2])/x^5,x]","-\frac{e^2 (13 d+8 e x) \sqrt{d^2-e^2 x^2}}{8 x^2}-\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{x^3}-\frac{d \left(d^2-e^2 x^2\right)^{3/2}}{4 x^4}+e^4 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)+\frac{13}{8} e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{e^2 (13 d+8 e x) \sqrt{d^2-e^2 x^2}}{8 x^2}-\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{x^3}-\frac{d \left(d^2-e^2 x^2\right)^{3/2}}{4 x^4}+e^4 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)+\frac{13}{8} e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"-(e^2*(13*d + 8*e*x)*Sqrt[d^2 - e^2*x^2])/(8*x^2) - (d*(d^2 - e^2*x^2)^(3/2))/(4*x^4) - (e*(d^2 - e^2*x^2)^(3/2))/x^3 - e^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] + (13*e^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/8","A",9,8,27,0.2963,1,"{1807, 811, 844, 217, 203, 266, 63, 208}"
65,1,310,0,0.4872803,"\int x^5 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[x^5*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2),x]","\frac{35 d^{12} x \sqrt{d^2-e^2 x^2}}{2048 e^5}+\frac{35 d^{10} x \left(d^2-e^2 x^2\right)^{3/2}}{3072 e^5}+\frac{7 d^8 x \left(d^2-e^2 x^2\right)^{5/2}}{768 e^5}-\frac{d^6 (31744 d+63063 e x) \left(d^2-e^2 x^2\right)^{7/2}}{1153152 e^6}-\frac{124 d^5 x^2 \left(d^2-e^2 x^2\right)^{7/2}}{1287 e^4}-\frac{7 d^4 x^3 \left(d^2-e^2 x^2\right)^{7/2}}{48 e^3}-\frac{31 d^3 x^4 \left(d^2-e^2 x^2\right)^{7/2}}{143 e^2}-\frac{7 d^2 x^5 \left(d^2-e^2 x^2\right)^{7/2}}{24 e}-\frac{3}{13} d x^6 \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{14} e x^7 \left(d^2-e^2 x^2\right)^{7/2}+\frac{35 d^{14} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2048 e^6}","\frac{35 d^{12} x \sqrt{d^2-e^2 x^2}}{2048 e^5}+\frac{35 d^{10} x \left(d^2-e^2 x^2\right)^{3/2}}{3072 e^5}+\frac{7 d^8 x \left(d^2-e^2 x^2\right)^{5/2}}{768 e^5}-\frac{d^6 (31744 d+63063 e x) \left(d^2-e^2 x^2\right)^{7/2}}{1153152 e^6}-\frac{124 d^5 x^2 \left(d^2-e^2 x^2\right)^{7/2}}{1287 e^4}-\frac{7 d^4 x^3 \left(d^2-e^2 x^2\right)^{7/2}}{48 e^3}-\frac{31 d^3 x^4 \left(d^2-e^2 x^2\right)^{7/2}}{143 e^2}-\frac{7 d^2 x^5 \left(d^2-e^2 x^2\right)^{7/2}}{24 e}-\frac{3}{13} d x^6 \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{14} e x^7 \left(d^2-e^2 x^2\right)^{7/2}+\frac{35 d^{14} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2048 e^6}",1,"(35*d^12*x*Sqrt[d^2 - e^2*x^2])/(2048*e^5) + (35*d^10*x*(d^2 - e^2*x^2)^(3/2))/(3072*e^5) + (7*d^8*x*(d^2 - e^2*x^2)^(5/2))/(768*e^5) - (124*d^5*x^2*(d^2 - e^2*x^2)^(7/2))/(1287*e^4) - (7*d^4*x^3*(d^2 - e^2*x^2)^(7/2))/(48*e^3) - (31*d^3*x^4*(d^2 - e^2*x^2)^(7/2))/(143*e^2) - (7*d^2*x^5*(d^2 - e^2*x^2)^(7/2))/(24*e) - (3*d*x^6*(d^2 - e^2*x^2)^(7/2))/13 - (e*x^7*(d^2 - e^2*x^2)^(7/2))/14 - (d^6*(31744*d + 63063*e*x)*(d^2 - e^2*x^2)^(7/2))/(1153152*e^6) + (35*d^14*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2048*e^6)","A",12,6,27,0.2222,1,"{1809, 833, 780, 195, 217, 203}"
66,1,281,0,0.405587,"\int x^4 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[x^4*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2),x]","\frac{27 d^{11} x \sqrt{d^2-e^2 x^2}}{1024 e^4}+\frac{9 d^9 x \left(d^2-e^2 x^2\right)^{3/2}}{512 e^4}+\frac{9 d^7 x \left(d^2-e^2 x^2\right)^{5/2}}{640 e^4}-\frac{d^5 (12800 d+27027 e x) \left(d^2-e^2 x^2\right)^{7/2}}{320320 e^5}-\frac{20 d^4 x^2 \left(d^2-e^2 x^2\right)^{7/2}}{143 e^3}-\frac{9 d^3 x^3 \left(d^2-e^2 x^2\right)^{7/2}}{40 e^2}-\frac{45 d^2 x^4 \left(d^2-e^2 x^2\right)^{7/2}}{143 e}-\frac{1}{4} d x^5 \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{13} e x^6 \left(d^2-e^2 x^2\right)^{7/2}+\frac{27 d^{13} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{1024 e^5}","\frac{27 d^{11} x \sqrt{d^2-e^2 x^2}}{1024 e^4}+\frac{9 d^9 x \left(d^2-e^2 x^2\right)^{3/2}}{512 e^4}+\frac{9 d^7 x \left(d^2-e^2 x^2\right)^{5/2}}{640 e^4}-\frac{d^5 (12800 d+27027 e x) \left(d^2-e^2 x^2\right)^{7/2}}{320320 e^5}-\frac{20 d^4 x^2 \left(d^2-e^2 x^2\right)^{7/2}}{143 e^3}-\frac{9 d^3 x^3 \left(d^2-e^2 x^2\right)^{7/2}}{40 e^2}-\frac{45 d^2 x^4 \left(d^2-e^2 x^2\right)^{7/2}}{143 e}-\frac{1}{4} d x^5 \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{13} e x^6 \left(d^2-e^2 x^2\right)^{7/2}+\frac{27 d^{13} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{1024 e^5}",1,"(27*d^11*x*Sqrt[d^2 - e^2*x^2])/(1024*e^4) + (9*d^9*x*(d^2 - e^2*x^2)^(3/2))/(512*e^4) + (9*d^7*x*(d^2 - e^2*x^2)^(5/2))/(640*e^4) - (20*d^4*x^2*(d^2 - e^2*x^2)^(7/2))/(143*e^3) - (9*d^3*x^3*(d^2 - e^2*x^2)^(7/2))/(40*e^2) - (45*d^2*x^4*(d^2 - e^2*x^2)^(7/2))/(143*e) - (d*x^5*(d^2 - e^2*x^2)^(7/2))/4 - (e*x^6*(d^2 - e^2*x^2)^(7/2))/13 - (d^5*(12800*d + 27027*e*x)*(d^2 - e^2*x^2)^(7/2))/(320320*e^5) + (27*d^13*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(1024*e^5)","A",11,6,27,0.2222,1,"{1809, 833, 780, 195, 217, 203}"
67,1,252,0,0.3640372,"\int x^3 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[x^3*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2),x]","\frac{41 d^{10} x \sqrt{d^2-e^2 x^2}}{1024 e^3}+\frac{41 d^8 x \left(d^2-e^2 x^2\right)^{3/2}}{1536 e^3}+\frac{41 d^6 x \left(d^2-e^2 x^2\right)^{5/2}}{1920 e^3}-\frac{d^4 (14720 d+28413 e x) \left(d^2-e^2 x^2\right)^{7/2}}{221760 e^4}-\frac{23 d^3 x^2 \left(d^2-e^2 x^2\right)^{7/2}}{99 e^2}-\frac{41 d^2 x^3 \left(d^2-e^2 x^2\right)^{7/2}}{120 e}-\frac{3}{11} d x^4 \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{12} e x^5 \left(d^2-e^2 x^2\right)^{7/2}+\frac{41 d^{12} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{1024 e^4}","\frac{41 d^{10} x \sqrt{d^2-e^2 x^2}}{1024 e^3}+\frac{41 d^8 x \left(d^2-e^2 x^2\right)^{3/2}}{1536 e^3}+\frac{41 d^6 x \left(d^2-e^2 x^2\right)^{5/2}}{1920 e^3}-\frac{d^4 (14720 d+28413 e x) \left(d^2-e^2 x^2\right)^{7/2}}{221760 e^4}-\frac{23 d^3 x^2 \left(d^2-e^2 x^2\right)^{7/2}}{99 e^2}-\frac{41 d^2 x^3 \left(d^2-e^2 x^2\right)^{7/2}}{120 e}-\frac{3}{11} d x^4 \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{12} e x^5 \left(d^2-e^2 x^2\right)^{7/2}+\frac{41 d^{12} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{1024 e^4}",1,"(41*d^10*x*Sqrt[d^2 - e^2*x^2])/(1024*e^3) + (41*d^8*x*(d^2 - e^2*x^2)^(3/2))/(1536*e^3) + (41*d^6*x*(d^2 - e^2*x^2)^(5/2))/(1920*e^3) - (23*d^3*x^2*(d^2 - e^2*x^2)^(7/2))/(99*e^2) - (41*d^2*x^3*(d^2 - e^2*x^2)^(7/2))/(120*e) - (3*d*x^4*(d^2 - e^2*x^2)^(7/2))/11 - (e*x^5*(d^2 - e^2*x^2)^(7/2))/12 - (d^4*(14720*d + 28413*e*x)*(d^2 - e^2*x^2)^(7/2))/(221760*e^4) + (41*d^12*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(1024*e^4)","A",10,6,27,0.2222,1,"{1809, 833, 780, 195, 217, 203}"
68,1,223,0,0.3056614,"\int x^2 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[x^2*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2),x]","\frac{19 d^9 x \sqrt{d^2-e^2 x^2}}{256 e^2}+\frac{19 d^7 x \left(d^2-e^2 x^2\right)^{3/2}}{384 e^2}+\frac{19 d^5 x \left(d^2-e^2 x^2\right)^{5/2}}{480 e^2}-\frac{d^3 (5920 d+13167 e x) \left(d^2-e^2 x^2\right)^{7/2}}{55440 e^3}-\frac{37 d^2 x^2 \left(d^2-e^2 x^2\right)^{7/2}}{99 e}-\frac{3}{10} d x^3 \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{11} e x^4 \left(d^2-e^2 x^2\right)^{7/2}+\frac{19 d^{11} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{256 e^3}","\frac{19 d^9 x \sqrt{d^2-e^2 x^2}}{256 e^2}+\frac{19 d^7 x \left(d^2-e^2 x^2\right)^{3/2}}{384 e^2}+\frac{19 d^5 x \left(d^2-e^2 x^2\right)^{5/2}}{480 e^2}-\frac{d^3 (5920 d+13167 e x) \left(d^2-e^2 x^2\right)^{7/2}}{55440 e^3}-\frac{37 d^2 x^2 \left(d^2-e^2 x^2\right)^{7/2}}{99 e}-\frac{3}{10} d x^3 \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{11} e x^4 \left(d^2-e^2 x^2\right)^{7/2}+\frac{19 d^{11} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{256 e^3}",1,"(19*d^9*x*Sqrt[d^2 - e^2*x^2])/(256*e^2) + (19*d^7*x*(d^2 - e^2*x^2)^(3/2))/(384*e^2) + (19*d^5*x*(d^2 - e^2*x^2)^(5/2))/(480*e^2) - (37*d^2*x^2*(d^2 - e^2*x^2)^(7/2))/(99*e) - (3*d*x^3*(d^2 - e^2*x^2)^(7/2))/10 - (e*x^4*(d^2 - e^2*x^2)^(7/2))/11 - (d^3*(5920*d + 13167*e*x)*(d^2 - e^2*x^2)^(7/2))/(55440*e^3) + (19*d^11*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(256*e^3)","A",9,6,27,0.2222,1,"{1809, 833, 780, 195, 217, 203}"
69,1,230,0,0.1213672,"\int x (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[x*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2),x]","\frac{33 d^8 x \sqrt{d^2-e^2 x^2}}{256 e}+\frac{11 d^6 x \left(d^2-e^2 x^2\right)^{3/2}}{128 e}+\frac{11 d^4 x \left(d^2-e^2 x^2\right)^{5/2}}{160 e}-\frac{33 d^3 \left(d^2-e^2 x^2\right)^{7/2}}{560 e^2}-\frac{11 d^2 (d+e x) \left(d^2-e^2 x^2\right)^{7/2}}{240 e^2}-\frac{d (d+e x)^2 \left(d^2-e^2 x^2\right)^{7/2}}{30 e^2}-\frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{7/2}}{10 e^2}+\frac{33 d^{10} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{256 e^2}","\frac{33 d^8 x \sqrt{d^2-e^2 x^2}}{256 e}+\frac{11 d^6 x \left(d^2-e^2 x^2\right)^{3/2}}{128 e}+\frac{11 d^4 x \left(d^2-e^2 x^2\right)^{5/2}}{160 e}-\frac{33 d^3 \left(d^2-e^2 x^2\right)^{7/2}}{560 e^2}-\frac{11 d^2 (d+e x) \left(d^2-e^2 x^2\right)^{7/2}}{240 e^2}-\frac{d (d+e x)^2 \left(d^2-e^2 x^2\right)^{7/2}}{30 e^2}-\frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{7/2}}{10 e^2}+\frac{33 d^{10} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{256 e^2}",1,"(33*d^8*x*Sqrt[d^2 - e^2*x^2])/(256*e) + (11*d^6*x*(d^2 - e^2*x^2)^(3/2))/(128*e) + (11*d^4*x*(d^2 - e^2*x^2)^(5/2))/(160*e) - (33*d^3*(d^2 - e^2*x^2)^(7/2))/(560*e^2) - (11*d^2*(d + e*x)*(d^2 - e^2*x^2)^(7/2))/(240*e^2) - (d*(d + e*x)^2*(d^2 - e^2*x^2)^(7/2))/(30*e^2) - ((d + e*x)^3*(d^2 - e^2*x^2)^(7/2))/(10*e^2) + (33*d^10*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(256*e^2)","A",9,6,25,0.2400,1,"{795, 671, 641, 195, 217, 203}"
70,1,188,0,0.082442,"\int (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^3*(d^2 - e^2*x^2)^(5/2),x]","\frac{55}{128} d^7 x \sqrt{d^2-e^2 x^2}+\frac{55}{192} d^5 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{11}{48} d^3 x \left(d^2-e^2 x^2\right)^{5/2}-\frac{11 d^2 \left(d^2-e^2 x^2\right)^{7/2}}{56 e}-\frac{11 d (d+e x) \left(d^2-e^2 x^2\right)^{7/2}}{72 e}-\frac{(d+e x)^2 \left(d^2-e^2 x^2\right)^{7/2}}{9 e}+\frac{55 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e}","\frac{55}{128} d^7 x \sqrt{d^2-e^2 x^2}+\frac{55}{192} d^5 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{11}{48} d^3 x \left(d^2-e^2 x^2\right)^{5/2}-\frac{11 d^2 \left(d^2-e^2 x^2\right)^{7/2}}{56 e}-\frac{11 d (d+e x) \left(d^2-e^2 x^2\right)^{7/2}}{72 e}-\frac{(d+e x)^2 \left(d^2-e^2 x^2\right)^{7/2}}{9 e}+\frac{55 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e}",1,"(55*d^7*x*Sqrt[d^2 - e^2*x^2])/128 + (55*d^5*x*(d^2 - e^2*x^2)^(3/2))/192 + (11*d^3*x*(d^2 - e^2*x^2)^(5/2))/48 - (11*d^2*(d^2 - e^2*x^2)^(7/2))/(56*e) - (11*d*(d + e*x)*(d^2 - e^2*x^2)^(7/2))/(72*e) - ((d + e*x)^2*(d^2 - e^2*x^2)^(7/2))/(9*e) + (55*d^9*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(128*e)","A",8,5,24,0.2083,1,"{671, 641, 195, 217, 203}"
71,1,190,0,0.3070696,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x,x]","\frac{1}{128} d^6 (128 d+125 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{192} d^4 (64 d+125 e x) \left(d^2-e^2 x^2\right)^{3/2}+\frac{1}{240} d^2 (48 d+125 e x) \left(d^2-e^2 x^2\right)^{5/2}-\frac{3}{7} d \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{8} e x \left(d^2-e^2 x^2\right)^{7/2}+\frac{125}{128} d^8 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d^8 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{1}{128} d^6 (128 d+125 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{192} d^4 (64 d+125 e x) \left(d^2-e^2 x^2\right)^{3/2}+\frac{1}{240} d^2 (48 d+125 e x) \left(d^2-e^2 x^2\right)^{5/2}-\frac{3}{7} d \left(d^2-e^2 x^2\right)^{7/2}-\frac{1}{8} e x \left(d^2-e^2 x^2\right)^{7/2}+\frac{125}{128} d^8 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d^8 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(d^6*(128*d + 125*e*x)*Sqrt[d^2 - e^2*x^2])/128 + (d^4*(64*d + 125*e*x)*(d^2 - e^2*x^2)^(3/2))/192 + (d^2*(48*d + 125*e*x)*(d^2 - e^2*x^2)^(5/2))/240 - (3*d*(d^2 - e^2*x^2)^(7/2))/7 - (e*x*(d^2 - e^2*x^2)^(7/2))/8 + (125*d^8*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/128 - d^8*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",11,8,27,0.2963,1,"{1809, 815, 844, 217, 203, 266, 63, 208}"
72,1,193,0,0.3054543,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^2} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^2,x]","\frac{3}{16} d^5 e (16 d-5 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{8} d^3 e (8 d-5 e x) \left(d^2-e^2 x^2\right)^{3/2}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{x}+\frac{1}{10} d e (6 d-5 e x) \left(d^2-e^2 x^2\right)^{5/2}-\frac{1}{7} e \left(d^2-e^2 x^2\right)^{7/2}-\frac{15}{16} d^7 e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-3 d^7 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{3}{16} d^5 e (16 d-5 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{8} d^3 e (8 d-5 e x) \left(d^2-e^2 x^2\right)^{3/2}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{x}+\frac{1}{10} d e (6 d-5 e x) \left(d^2-e^2 x^2\right)^{5/2}-\frac{1}{7} e \left(d^2-e^2 x^2\right)^{7/2}-\frac{15}{16} d^7 e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-3 d^7 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(3*d^5*e*(16*d - 5*e*x)*Sqrt[d^2 - e^2*x^2])/16 + (d^3*e*(8*d - 5*e*x)*(d^2 - e^2*x^2)^(3/2))/8 + (d*e*(6*d - 5*e*x)*(d^2 - e^2*x^2)^(5/2))/10 - (e*(d^2 - e^2*x^2)^(7/2))/7 - (d*(d^2 - e^2*x^2)^(7/2))/x - (15*d^7*e*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/16 - 3*d^7*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",11,9,27,0.3333,1,"{1807, 1809, 815, 844, 217, 203, 266, 63, 208}"
73,1,207,0,0.3129163,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^3} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^3,x]","\frac{1}{16} d^4 e^2 (8 d-85 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{24} d^2 e^2 (4 d-85 e x) \left(d^2-e^2 x^2\right)^{3/2}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{2 x^2}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{x}+\frac{1}{30} e^2 (3 d-85 e x) \left(d^2-e^2 x^2\right)^{5/2}-\frac{85}{16} d^6 e^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{1}{2} d^6 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{1}{16} d^4 e^2 (8 d-85 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{24} d^2 e^2 (4 d-85 e x) \left(d^2-e^2 x^2\right)^{3/2}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{2 x^2}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{x}+\frac{1}{30} e^2 (3 d-85 e x) \left(d^2-e^2 x^2\right)^{5/2}-\frac{85}{16} d^6 e^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{1}{2} d^6 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(d^4*e^2*(8*d - 85*e*x)*Sqrt[d^2 - e^2*x^2])/16 + (d^2*e^2*(4*d - 85*e*x)*(d^2 - e^2*x^2)^(3/2))/24 + (e^2*(3*d - 85*e*x)*(d^2 - e^2*x^2)^(5/2))/30 - (d*(d^2 - e^2*x^2)^(7/2))/(2*x^2) - (3*e*(d^2 - e^2*x^2)^(7/2))/x - (85*d^6*e^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/16 - (d^6*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/2","A",11,8,27,0.2963,1,"{1807, 815, 844, 217, 203, 266, 63, 208}"
74,1,210,0,0.3135645,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^4} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^4,x]","-\frac{1}{8} d^3 e^3 (52 d+25 e x) \sqrt{d^2-e^2 x^2}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{3 x^3}-\frac{1}{12} d e^3 (26 d+25 e x) \left(d^2-e^2 x^2\right)^{3/2}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{2 x^2}-\frac{e^2 (50 d+39 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 x}-\frac{25}{8} d^5 e^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{13}{2} d^5 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{1}{8} d^3 e^3 (52 d+25 e x) \sqrt{d^2-e^2 x^2}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{3 x^3}-\frac{1}{12} d e^3 (26 d+25 e x) \left(d^2-e^2 x^2\right)^{3/2}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{2 x^2}-\frac{e^2 (50 d+39 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 x}-\frac{25}{8} d^5 e^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{13}{2} d^5 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"-(d^3*e^3*(52*d + 25*e*x)*Sqrt[d^2 - e^2*x^2])/8 - (d*e^3*(26*d + 25*e*x)*(d^2 - e^2*x^2)^(3/2))/12 - (e^2*(50*d + 39*e*x)*(d^2 - e^2*x^2)^(5/2))/(30*x) - (d*(d^2 - e^2*x^2)^(7/2))/(3*x^3) - (3*e*(d^2 - e^2*x^2)^(7/2))/(2*x^2) - (25*d^5*e^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/8 + (13*d^5*e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/2","A",11,9,27,0.3333,1,"{1807, 813, 815, 844, 217, 203, 266, 63, 208}"
75,1,209,0,0.319215,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^5} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^5,x]","-\frac{45}{8} d^2 e^4 (d-e x) \sqrt{d^2-e^2 x^2}+\frac{15 d e^3 (2 d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{8 x}-\frac{3 e^2 (3 d+2 e x) \left(d^2-e^2 x^2\right)^{5/2}}{8 x^2}-\frac{e \left(d^2-e^2 x^2\right)^{7/2}}{x^3}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{4 x^4}+\frac{45}{8} d^4 e^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{45}{8} d^4 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{45}{8} d^2 e^4 (d-e x) \sqrt{d^2-e^2 x^2}+\frac{15 d e^3 (2 d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{8 x}-\frac{3 e^2 (3 d+2 e x) \left(d^2-e^2 x^2\right)^{5/2}}{8 x^2}-\frac{e \left(d^2-e^2 x^2\right)^{7/2}}{x^3}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{4 x^4}+\frac{45}{8} d^4 e^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{45}{8} d^4 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(-45*d^2*e^4*(d - e*x)*Sqrt[d^2 - e^2*x^2])/8 + (15*d*e^3*(2*d - e*x)*(d^2 - e^2*x^2)^(3/2))/(8*x) - (3*e^2*(3*d + 2*e*x)*(d^2 - e^2*x^2)^(5/2))/(8*x^2) - (d*(d^2 - e^2*x^2)^(7/2))/(4*x^4) - (e*(d^2 - e^2*x^2)^(7/2))/x^3 + (45*d^4*e^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/8 + (45*d^4*e^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/8","A",11,9,27,0.3333,1,"{1807, 813, 815, 844, 217, 203, 266, 63, 208}"
76,1,216,0,0.3131773,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^6} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^6,x]","\frac{d^2 e^4 (52 d+25 e x) \sqrt{d^2-e^2 x^2}}{8 x}+\frac{d e^3 (25 d-52 e x) \left(d^2-e^2 x^2\right)^{3/2}}{24 x^2}-\frac{e^2 (52 d+25 e x) \left(d^2-e^2 x^2\right)^{5/2}}{60 x^3}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{4 x^4}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{5 x^5}+\frac{13}{2} d^3 e^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{25}{8} d^3 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{d^2 e^4 (52 d+25 e x) \sqrt{d^2-e^2 x^2}}{8 x}+\frac{d e^3 (25 d-52 e x) \left(d^2-e^2 x^2\right)^{3/2}}{24 x^2}-\frac{e^2 (52 d+25 e x) \left(d^2-e^2 x^2\right)^{5/2}}{60 x^3}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{4 x^4}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{5 x^5}+\frac{13}{2} d^3 e^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{25}{8} d^3 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(d^2*e^4*(52*d + 25*e*x)*Sqrt[d^2 - e^2*x^2])/(8*x) + (d*e^3*(25*d - 52*e*x)*(d^2 - e^2*x^2)^(3/2))/(24*x^2) - (e^2*(52*d + 25*e*x)*(d^2 - e^2*x^2)^(5/2))/(60*x^3) - (d*(d^2 - e^2*x^2)^(7/2))/(5*x^5) - (3*e*(d^2 - e^2*x^2)^(7/2))/(4*x^4) + (13*d^3*e^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/2 - (25*d^3*e^5*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/8","A",11,8,27,0.2963,1,"{1807, 813, 844, 217, 203, 266, 63, 208}"
77,1,214,0,0.3117359,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^7} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^7,x]","-\frac{d e^5 (8 d-85 e x) \sqrt{d^2-e^2 x^2}}{16 x}+\frac{d e^3 (8 d+85 e x) \left(d^2-e^2 x^2\right)^{3/2}}{48 x^3}-\frac{e^2 (85 d+12 e x) \left(d^2-e^2 x^2\right)^{5/2}}{120 x^4}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{5 x^5}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{6 x^6}-\frac{1}{2} d^2 e^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{85}{16} d^2 e^6 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{d e^5 (8 d-85 e x) \sqrt{d^2-e^2 x^2}}{16 x}+\frac{d e^3 (8 d+85 e x) \left(d^2-e^2 x^2\right)^{3/2}}{48 x^3}-\frac{e^2 (85 d+12 e x) \left(d^2-e^2 x^2\right)^{5/2}}{120 x^4}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{5 x^5}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{6 x^6}-\frac{1}{2} d^2 e^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{85}{16} d^2 e^6 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"-(d*e^5*(8*d - 85*e*x)*Sqrt[d^2 - e^2*x^2])/(16*x) + (d*e^3*(8*d + 85*e*x)*(d^2 - e^2*x^2)^(3/2))/(48*x^3) - (e^2*(85*d + 12*e*x)*(d^2 - e^2*x^2)^(5/2))/(120*x^4) - (d*(d^2 - e^2*x^2)^(7/2))/(6*x^6) - (3*e*(d^2 - e^2*x^2)^(7/2))/(5*x^5) - (d^2*e^6*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/2 - (85*d^2*e^6*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/16","A",11,9,27,0.3333,1,"{1807, 813, 811, 844, 217, 203, 266, 63, 208}"
78,1,206,0,0.310915,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^8} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^8,x]","-\frac{3 e^6 (16 d-5 e x) \sqrt{d^2-e^2 x^2}}{16 x}+\frac{e^4 (16 d+5 e x) \left(d^2-e^2 x^2\right)^{3/2}}{16 x^3}-\frac{e^2 (24 d+5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{40 x^5}-\frac{e \left(d^2-e^2 x^2\right)^{7/2}}{2 x^6}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{7 x^7}-3 d e^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{15}{16} d e^7 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{3 e^6 (16 d-5 e x) \sqrt{d^2-e^2 x^2}}{16 x}+\frac{e^4 (16 d+5 e x) \left(d^2-e^2 x^2\right)^{3/2}}{16 x^3}-\frac{e^2 (24 d+5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{40 x^5}-\frac{e \left(d^2-e^2 x^2\right)^{7/2}}{2 x^6}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{7 x^7}-3 d e^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{15}{16} d e^7 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(-3*e^6*(16*d - 5*e*x)*Sqrt[d^2 - e^2*x^2])/(16*x) + (e^4*(16*d + 5*e*x)*(d^2 - e^2*x^2)^(3/2))/(16*x^3) - (e^2*(24*d + 5*e*x)*(d^2 - e^2*x^2)^(5/2))/(40*x^5) - (d*(d^2 - e^2*x^2)^(7/2))/(7*x^7) - (e*(d^2 - e^2*x^2)^(7/2))/(2*x^6) - 3*d*e^7*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - (15*d*e^7*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/16","A",11,9,27,0.3333,1,"{1807, 811, 813, 844, 217, 203, 266, 63, 208}"
79,1,204,0,0.3038148,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^9} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^9,x]","-\frac{e^6 (125 d+128 e x) \sqrt{d^2-e^2 x^2}}{128 x^2}+\frac{e^4 (125 d+64 e x) \left(d^2-e^2 x^2\right)^{3/2}}{192 x^4}-\frac{e^2 (125 d+48 e x) \left(d^2-e^2 x^2\right)^{5/2}}{240 x^6}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{7 x^7}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{8 x^8}+e^8 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)+\frac{125}{128} e^8 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{e^6 (125 d+128 e x) \sqrt{d^2-e^2 x^2}}{128 x^2}+\frac{e^4 (125 d+64 e x) \left(d^2-e^2 x^2\right)^{3/2}}{192 x^4}-\frac{e^2 (125 d+48 e x) \left(d^2-e^2 x^2\right)^{5/2}}{240 x^6}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{7 x^7}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{8 x^8}+e^8 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)+\frac{125}{128} e^8 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"-(e^6*(125*d + 128*e*x)*Sqrt[d^2 - e^2*x^2])/(128*x^2) + (e^4*(125*d + 64*e*x)*(d^2 - e^2*x^2)^(3/2))/(192*x^4) - (e^2*(125*d + 48*e*x)*(d^2 - e^2*x^2)^(5/2))/(240*x^6) - (d*(d^2 - e^2*x^2)^(7/2))/(8*x^8) - (3*e*(d^2 - e^2*x^2)^(7/2))/(7*x^7) - e^8*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] + (125*e^8*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/128","A",11,8,27,0.2963,1,"{1807, 811, 844, 217, 203, 266, 63, 208}"
80,1,187,0,0.2603192,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^{10}} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^10,x]","-\frac{55 e^7 \sqrt{d^2-e^2 x^2}}{128 x^2}+\frac{55 e^5 \left(d^2-e^2 x^2\right)^{3/2}}{192 x^4}-\frac{11 e^3 \left(d^2-e^2 x^2\right)^{5/2}}{48 x^6}-\frac{29 e^2 \left(d^2-e^2 x^2\right)^{7/2}}{63 d x^7}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{8 x^8}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{9 x^9}+\frac{55 e^9 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{128 d}","-\frac{55 e^7 \sqrt{d^2-e^2 x^2}}{128 x^2}+\frac{55 e^5 \left(d^2-e^2 x^2\right)^{3/2}}{192 x^4}-\frac{11 e^3 \left(d^2-e^2 x^2\right)^{5/2}}{48 x^6}-\frac{29 e^2 \left(d^2-e^2 x^2\right)^{7/2}}{63 d x^7}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{8 x^8}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{9 x^9}+\frac{55 e^9 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{128 d}",1,"(-55*e^7*Sqrt[d^2 - e^2*x^2])/(128*x^2) + (55*e^5*(d^2 - e^2*x^2)^(3/2))/(192*x^4) - (11*e^3*(d^2 - e^2*x^2)^(5/2))/(48*x^6) - (d*(d^2 - e^2*x^2)^(7/2))/(9*x^9) - (3*e*(d^2 - e^2*x^2)^(7/2))/(8*x^8) - (29*e^2*(d^2 - e^2*x^2)^(7/2))/(63*d*x^7) + (55*e^9*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(128*d)","A",9,6,27,0.2222,1,"{1807, 807, 266, 47, 63, 208}"
81,1,225,0,0.2981685,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^{11}} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^11,x]","-\frac{33 e^8 \sqrt{d^2-e^2 x^2}}{256 d x^2}+\frac{11 e^6 \left(d^2-e^2 x^2\right)^{3/2}}{128 d x^4}-\frac{11 e^4 \left(d^2-e^2 x^2\right)^{5/2}}{160 d x^6}-\frac{5 e^3 \left(d^2-e^2 x^2\right)^{7/2}}{21 d^2 x^7}-\frac{33 e^2 \left(d^2-e^2 x^2\right)^{7/2}}{80 d x^8}-\frac{e \left(d^2-e^2 x^2\right)^{7/2}}{3 x^9}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{10 x^{10}}+\frac{33 e^{10} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{256 d^2}","-\frac{33 e^8 \sqrt{d^2-e^2 x^2}}{256 d x^2}+\frac{11 e^6 \left(d^2-e^2 x^2\right)^{3/2}}{128 d x^4}-\frac{11 e^4 \left(d^2-e^2 x^2\right)^{5/2}}{160 d x^6}-\frac{5 e^3 \left(d^2-e^2 x^2\right)^{7/2}}{21 d^2 x^7}-\frac{33 e^2 \left(d^2-e^2 x^2\right)^{7/2}}{80 d x^8}-\frac{e \left(d^2-e^2 x^2\right)^{7/2}}{3 x^9}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{10 x^{10}}+\frac{33 e^{10} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{256 d^2}",1,"(-33*e^8*Sqrt[d^2 - e^2*x^2])/(256*d*x^2) + (11*e^6*(d^2 - e^2*x^2)^(3/2))/(128*d*x^4) - (11*e^4*(d^2 - e^2*x^2)^(5/2))/(160*d*x^6) - (d*(d^2 - e^2*x^2)^(7/2))/(10*x^10) - (e*(d^2 - e^2*x^2)^(7/2))/(3*x^9) - (33*e^2*(d^2 - e^2*x^2)^(7/2))/(80*d*x^8) - (5*e^3*(d^2 - e^2*x^2)^(7/2))/(21*d^2*x^7) + (33*e^10*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(256*d^2)","A",10,7,27,0.2593,1,"{1807, 835, 807, 266, 47, 63, 208}"
82,1,254,0,0.3290467,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}{x^{12}} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^(5/2))/x^12,x]","-\frac{19 e^9 \sqrt{d^2-e^2 x^2}}{256 d^2 x^2}+\frac{19 e^7 \left(d^2-e^2 x^2\right)^{3/2}}{384 d^2 x^4}-\frac{19 e^5 \left(d^2-e^2 x^2\right)^{5/2}}{480 d^2 x^6}-\frac{74 e^4 \left(d^2-e^2 x^2\right)^{7/2}}{693 d^3 x^7}-\frac{19 e^3 \left(d^2-e^2 x^2\right)^{7/2}}{80 d^2 x^8}-\frac{37 e^2 \left(d^2-e^2 x^2\right)^{7/2}}{99 d x^9}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{10 x^{10}}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{11 x^{11}}+\frac{19 e^{11} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{256 d^3}","-\frac{19 e^9 \sqrt{d^2-e^2 x^2}}{256 d^2 x^2}+\frac{19 e^7 \left(d^2-e^2 x^2\right)^{3/2}}{384 d^2 x^4}-\frac{19 e^5 \left(d^2-e^2 x^2\right)^{5/2}}{480 d^2 x^6}-\frac{74 e^4 \left(d^2-e^2 x^2\right)^{7/2}}{693 d^3 x^7}-\frac{19 e^3 \left(d^2-e^2 x^2\right)^{7/2}}{80 d^2 x^8}-\frac{37 e^2 \left(d^2-e^2 x^2\right)^{7/2}}{99 d x^9}-\frac{3 e \left(d^2-e^2 x^2\right)^{7/2}}{10 x^{10}}-\frac{d \left(d^2-e^2 x^2\right)^{7/2}}{11 x^{11}}+\frac{19 e^{11} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{256 d^3}",1,"(-19*e^9*Sqrt[d^2 - e^2*x^2])/(256*d^2*x^2) + (19*e^7*(d^2 - e^2*x^2)^(3/2))/(384*d^2*x^4) - (19*e^5*(d^2 - e^2*x^2)^(5/2))/(480*d^2*x^6) - (d*(d^2 - e^2*x^2)^(7/2))/(11*x^11) - (3*e*(d^2 - e^2*x^2)^(7/2))/(10*x^10) - (37*e^2*(d^2 - e^2*x^2)^(7/2))/(99*d*x^9) - (19*e^3*(d^2 - e^2*x^2)^(7/2))/(80*d^2*x^8) - (74*e^4*(d^2 - e^2*x^2)^(7/2))/(693*d^3*x^7) + (19*e^11*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(256*d^3)","A",11,7,27,0.2593,1,"{1807, 835, 807, 266, 47, 63, 208}"
83,1,174,0,0.4045624,"\int \frac{x^5 (d+e x)^3}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^5*(d + e*x)^3)/(d^2 - e^2*x^2)^(7/2),x]","\frac{d^4 (d+e x)^3}{5 e^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{23 d^3 (d+e x)^2}{15 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{127 d^2 (d+e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{3 d \sqrt{d^2-e^2 x^2}}{e^6}+\frac{x \sqrt{d^2-e^2 x^2}}{2 e^5}-\frac{13 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^6}","\frac{d^4 (d+e x)^3}{5 e^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{23 d^3 (d+e x)^2}{15 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{127 d^2 (d+e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{3 d \sqrt{d^2-e^2 x^2}}{e^6}+\frac{x \sqrt{d^2-e^2 x^2}}{2 e^5}-\frac{13 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^6}",1,"(d^4*(d + e*x)^3)/(5*e^6*(d^2 - e^2*x^2)^(5/2)) - (23*d^3*(d + e*x)^2)/(15*e^6*(d^2 - e^2*x^2)^(3/2)) + (127*d^2*(d + e*x))/(15*e^6*Sqrt[d^2 - e^2*x^2]) + (3*d*Sqrt[d^2 - e^2*x^2])/e^6 + (x*Sqrt[d^2 - e^2*x^2])/(2*e^5) - (13*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^6)","A",7,5,27,0.1852,1,"{1635, 1815, 641, 217, 203}"
84,1,142,0,0.3248075,"\int \frac{x^4 (d+e x)^3}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^4*(d + e*x)^3)/(d^2 - e^2*x^2)^(7/2),x]","\frac{d^3 (d+e x)^3}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{6 d^2 (d+e x)^2}{5 e^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{24 d (d+e x)}{5 e^5 \sqrt{d^2-e^2 x^2}}+\frac{\sqrt{d^2-e^2 x^2}}{e^5}-\frac{3 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}","\frac{d^3 (d+e x)^3}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{6 d^2 (d+e x)^2}{5 e^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{24 d (d+e x)}{5 e^5 \sqrt{d^2-e^2 x^2}}+\frac{\sqrt{d^2-e^2 x^2}}{e^5}-\frac{3 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}",1,"(d^3*(d + e*x)^3)/(5*e^5*(d^2 - e^2*x^2)^(5/2)) - (6*d^2*(d + e*x)^2)/(5*e^5*(d^2 - e^2*x^2)^(3/2)) + (24*d*(d + e*x))/(5*e^5*Sqrt[d^2 - e^2*x^2]) + Sqrt[d^2 - e^2*x^2]/e^5 - (3*d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^5","A",6,4,27,0.1481,1,"{1635, 641, 217, 203}"
85,1,118,0,0.2159589,"\int \frac{x^3 (d+e x)^3}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^3*(d + e*x)^3)/(d^2 - e^2*x^2)^(7/2),x]","\frac{d^2 (d+e x)^3}{5 e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{13 d (d+e x)^2}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{32 (d+e x)}{15 e^4 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}","\frac{d^2 (d+e x)^3}{5 e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{13 d (d+e x)^2}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{32 (d+e x)}{15 e^4 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}",1,"(d^2*(d + e*x)^3)/(5*e^4*(d^2 - e^2*x^2)^(5/2)) - (13*d*(d + e*x)^2)/(15*e^4*(d^2 - e^2*x^2)^(3/2)) + (32*(d + e*x))/(15*e^4*Sqrt[d^2 - e^2*x^2]) - ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e^4","A",5,4,27,0.1481,1,"{1635, 778, 217, 203}"
86,1,93,0,0.125844,"\int \frac{x^2 (d+e x)^3}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x^2*(d + e*x)^3)/(d^2 - e^2*x^2)^(7/2),x]","\frac{d (d+e x)^3}{5 e^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8 (d+e x)^2}{15 e^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{7 (d+e x)}{15 d e^3 \sqrt{d^2-e^2 x^2}}","\frac{d (d+e x)^3}{5 e^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8 (d+e x)^2}{15 e^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{7 (d+e x)}{15 d e^3 \sqrt{d^2-e^2 x^2}}",1,"(d*(d + e*x)^3)/(5*e^3*(d^2 - e^2*x^2)^(5/2)) - (8*(d + e*x)^2)/(15*e^3*(d^2 - e^2*x^2)^(3/2)) + (7*(d + e*x))/(15*d*e^3*Sqrt[d^2 - e^2*x^2])","A",3,3,27,0.1111,1,"{1635, 789, 637}"
87,1,86,0,0.0355586,"\int \frac{x (d+e x)^3}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(x*(d + e*x)^3)/(d^2 - e^2*x^2)^(7/2),x]","\frac{(d+e x)^3}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{x}{5 d^2 e \sqrt{d^2-e^2 x^2}}","\frac{(d+e x)^3}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 (d+e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{x}{5 d^2 e \sqrt{d^2-e^2 x^2}}",1,"(d + e*x)^3/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (2*(d + e*x))/(5*e^2*(d^2 - e^2*x^2)^(3/2)) - x/(5*d^2*e*Sqrt[d^2 - e^2*x^2])","A",3,3,25,0.1200,1,"{789, 653, 191}"
88,1,103,0,0.0483763,"\int \frac{(d+e x)^3}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^3/(d^2 - e^2*x^2)^(7/2),x]","\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^3 e (d-e x)}+\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^2 e (d-e x)^2}+\frac{\sqrt{d^2-e^2 x^2}}{5 d e (d-e x)^3}","\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^3 e (d-e x)}+\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^2 e (d-e x)^2}+\frac{\sqrt{d^2-e^2 x^2}}{5 d e (d-e x)^3}",1,"Sqrt[d^2 - e^2*x^2]/(5*d*e*(d - e*x)^3) + (2*Sqrt[d^2 - e^2*x^2])/(15*d^2*e*(d - e*x)^2) + (2*Sqrt[d^2 - e^2*x^2])/(15*d^3*e*(d - e*x))","A",4,3,24,0.1250,1,"{655, 659, 651}"
89,1,114,0,0.1589294,"\int \frac{(d+e x)^3}{x \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^3/(x*(d^2 - e^2*x^2)^(7/2)),x]","\frac{4 (d+e x)}{5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{15 d+22 e x}{15 d^4 \sqrt{d^2-e^2 x^2}}+\frac{5 d+11 e x}{15 d^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^4}","\frac{4 (d+e x)}{5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{15 d+22 e x}{15 d^4 \sqrt{d^2-e^2 x^2}}+\frac{5 d+11 e x}{15 d^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^4}",1,"(4*(d + e*x))/(5*(d^2 - e^2*x^2)^(5/2)) + (5*d + 11*e*x)/(15*d^2*(d^2 - e^2*x^2)^(3/2)) + (15*d + 22*e*x)/(15*d^4*Sqrt[d^2 - e^2*x^2]) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^4","A",7,6,27,0.2222,1,"{1805, 823, 12, 266, 63, 208}"
90,1,145,0,0.2873143,"\int \frac{(d+e x)^3}{x^2 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^3/(x^2*(d^2 - e^2*x^2)^(7/2)),x]","\frac{4 e (d+e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^5 x}+\frac{e (15 d+19 e x)}{5 d^5 \sqrt{d^2-e^2 x^2}}+\frac{e (5 d+7 e x)}{5 d^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{3 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}","\frac{4 e (d+e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^5 x}+\frac{e (15 d+19 e x)}{5 d^5 \sqrt{d^2-e^2 x^2}}+\frac{e (5 d+7 e x)}{5 d^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{3 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}",1,"(4*e*(d + e*x))/(5*d*(d^2 - e^2*x^2)^(5/2)) + (e*(5*d + 7*e*x))/(5*d^3*(d^2 - e^2*x^2)^(3/2)) + (e*(15*d + 19*e*x))/(5*d^5*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(d^5*x) - (3*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^5","A",7,5,27,0.1852,1,"{1805, 807, 266, 63, 208}"
91,1,182,0,0.361906,"\int \frac{(d+e x)^3}{x^3 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^3/(x^3*(d^2 - e^2*x^2)^(7/2)),x]","\frac{e^2 (90 d+107 e x)}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{e^2 (25 d+31 e x)}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{4 e^2 (d+e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{3 e \sqrt{d^2-e^2 x^2}}{d^6 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^5 x^2}-\frac{13 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^6}","\frac{e^2 (90 d+107 e x)}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{e^2 (25 d+31 e x)}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{4 e^2 (d+e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{3 e \sqrt{d^2-e^2 x^2}}{d^6 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^5 x^2}-\frac{13 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^6}",1,"(4*e^2*(d + e*x))/(5*d^2*(d^2 - e^2*x^2)^(5/2)) + (e^2*(25*d + 31*e*x))/(15*d^4*(d^2 - e^2*x^2)^(3/2)) + (e^2*(90*d + 107*e*x))/(15*d^6*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(2*d^5*x^2) - (3*e*Sqrt[d^2 - e^2*x^2])/(d^6*x) - (13*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^6)","A",8,6,27,0.2222,1,"{1805, 1807, 807, 266, 63, 208}"
92,1,147,0,0.1416674,"\int \frac{x^4 \sqrt{d^2-e^2 x^2}}{d+e x} \, dx","Int[(x^4*Sqrt[d^2 - e^2*x^2])/(d + e*x),x]","\frac{d^3 (64 d-45 e x) \sqrt{d^2-e^2 x^2}}{120 e^5}+\frac{4 d^2 x^2 \sqrt{d^2-e^2 x^2}}{15 e^3}-\frac{d x^3 \sqrt{d^2-e^2 x^2}}{4 e^2}+\frac{x^4 \sqrt{d^2-e^2 x^2}}{5 e}+\frac{3 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^5}","\frac{d^3 (64 d-45 e x) \sqrt{d^2-e^2 x^2}}{120 e^5}+\frac{4 d^2 x^2 \sqrt{d^2-e^2 x^2}}{15 e^3}-\frac{d x^3 \sqrt{d^2-e^2 x^2}}{4 e^2}+\frac{x^4 \sqrt{d^2-e^2 x^2}}{5 e}+\frac{3 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^5}",1,"(4*d^2*x^2*Sqrt[d^2 - e^2*x^2])/(15*e^3) - (d*x^3*Sqrt[d^2 - e^2*x^2])/(4*e^2) + (x^4*Sqrt[d^2 - e^2*x^2])/(5*e) + (d^3*(64*d - 45*e*x)*Sqrt[d^2 - e^2*x^2])/(120*e^5) + (3*d^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^5)","A",7,5,27,0.1852,1,"{850, 833, 780, 217, 203}"
93,1,118,0,0.0989571,"\int \frac{x^3 \sqrt{d^2-e^2 x^2}}{d+e x} \, dx","Int[(x^3*Sqrt[d^2 - e^2*x^2])/(d + e*x),x]","-\frac{d^2 (16 d-9 e x) \sqrt{d^2-e^2 x^2}}{24 e^4}-\frac{d x^2 \sqrt{d^2-e^2 x^2}}{3 e^2}+\frac{x^3 \sqrt{d^2-e^2 x^2}}{4 e}-\frac{3 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^4}","-\frac{d^2 (16 d-9 e x) \sqrt{d^2-e^2 x^2}}{24 e^4}-\frac{d x^2 \sqrt{d^2-e^2 x^2}}{3 e^2}+\frac{x^3 \sqrt{d^2-e^2 x^2}}{4 e}-\frac{3 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^4}",1,"-(d*x^2*Sqrt[d^2 - e^2*x^2])/(3*e^2) + (x^3*Sqrt[d^2 - e^2*x^2])/(4*e) - (d^2*(16*d - 9*e*x)*Sqrt[d^2 - e^2*x^2])/(24*e^4) - (3*d^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^4)","A",6,5,27,0.1852,1,"{850, 833, 780, 217, 203}"
94,1,86,0,0.1104404,"\int \frac{x^2 \sqrt{d^2-e^2 x^2}}{d+e x} \, dx","Int[(x^2*Sqrt[d^2 - e^2*x^2])/(d + e*x),x]","\frac{d (2 d-e x) \sqrt{d^2-e^2 x^2}}{2 e^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{3 e^3}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^3}","\frac{d (2 d-e x) \sqrt{d^2-e^2 x^2}}{2 e^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{3 e^3}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^3}",1,"(d*(2*d - e*x)*Sqrt[d^2 - e^2*x^2])/(2*e^3) - (d^2 - e^2*x^2)^(3/2)/(3*e^3) + (d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^3)","A",6,6,27,0.2222,1,"{1639, 12, 785, 780, 217, 203}"
95,1,62,0,0.0407475,"\int \frac{x \sqrt{d^2-e^2 x^2}}{d+e x} \, dx","Int[(x*Sqrt[d^2 - e^2*x^2])/(d + e*x),x]","-\frac{(2 d-e x) \sqrt{d^2-e^2 x^2}}{2 e^2}-\frac{d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^2}","-\frac{(2 d-e x) \sqrt{d^2-e^2 x^2}}{2 e^2}-\frac{d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^2}",1,"-((2*d - e*x)*Sqrt[d^2 - e^2*x^2])/(2*e^2) - (d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^2)","A",4,4,25,0.1600,1,"{785, 780, 217, 203}"
96,1,46,0,0.0161483,"\int \frac{\sqrt{d^2-e^2 x^2}}{d+e x} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(d + e*x),x]","\frac{\sqrt{d^2-e^2 x^2}}{e}+\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}","\frac{\sqrt{d^2-e^2 x^2}}{e}+\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}",1,"Sqrt[d^2 - e^2*x^2]/e + (d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e","A",3,3,24,0.1250,1,"{665, 217, 203}"
97,1,46,0,0.059482,"\int \frac{\sqrt{d^2-e^2 x^2}}{x (d+e x)} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(x*(d + e*x)),x]","-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"-ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",7,7,27,0.2593,1,"{850, 844, 217, 203, 266, 63, 208}"
98,1,51,0,0.0573296,"\int \frac{\sqrt{d^2-e^2 x^2}}{x^2 (d+e x)} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(x^2*(d + e*x)),x]","\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d}-\frac{\sqrt{d^2-e^2 x^2}}{d x}","\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d}-\frac{\sqrt{d^2-e^2 x^2}}{d x}",1,"-(Sqrt[d^2 - e^2*x^2]/(d*x)) + (e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d","A",5,5,27,0.1852,1,"{850, 807, 266, 63, 208}"
99,1,82,0,0.0783041,"\int \frac{\sqrt{d^2-e^2 x^2}}{x^3 (d+e x)} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(x^3*(d + e*x)),x]","\frac{e \sqrt{d^2-e^2 x^2}}{d^2 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d x^2}-\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^2}","\frac{e \sqrt{d^2-e^2 x^2}}{d^2 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d x^2}-\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^2}",1,"-Sqrt[d^2 - e^2*x^2]/(2*d*x^2) + (e*Sqrt[d^2 - e^2*x^2])/(d^2*x) - (e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^2)","A",6,6,27,0.2222,1,"{850, 835, 807, 266, 63, 208}"
100,1,114,0,0.1104911,"\int \frac{\sqrt{d^2-e^2 x^2}}{x^4 (d+e x)} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(x^4*(d + e*x)),x]","-\frac{2 e^2 \sqrt{d^2-e^2 x^2}}{3 d^3 x}+\frac{e \sqrt{d^2-e^2 x^2}}{2 d^2 x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 d x^3}+\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^3}","-\frac{2 e^2 \sqrt{d^2-e^2 x^2}}{3 d^3 x}+\frac{e \sqrt{d^2-e^2 x^2}}{2 d^2 x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 d x^3}+\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^3}",1,"-Sqrt[d^2 - e^2*x^2]/(3*d*x^3) + (e*Sqrt[d^2 - e^2*x^2])/(2*d^2*x^2) - (2*e^2*Sqrt[d^2 - e^2*x^2])/(3*d^3*x) + (e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^3)","A",7,6,27,0.2222,1,"{850, 835, 807, 266, 63, 208}"
101,1,143,0,0.1350817,"\int \frac{\sqrt{d^2-e^2 x^2}}{x^5 (d+e x)} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(x^5*(d + e*x)),x]","\frac{2 e^3 \sqrt{d^2-e^2 x^2}}{3 d^4 x}-\frac{3 e^2 \sqrt{d^2-e^2 x^2}}{8 d^3 x^2}+\frac{e \sqrt{d^2-e^2 x^2}}{3 d^2 x^3}-\frac{\sqrt{d^2-e^2 x^2}}{4 d x^4}-\frac{3 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d^4}","\frac{2 e^3 \sqrt{d^2-e^2 x^2}}{3 d^4 x}-\frac{3 e^2 \sqrt{d^2-e^2 x^2}}{8 d^3 x^2}+\frac{e \sqrt{d^2-e^2 x^2}}{3 d^2 x^3}-\frac{\sqrt{d^2-e^2 x^2}}{4 d x^4}-\frac{3 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d^4}",1,"-Sqrt[d^2 - e^2*x^2]/(4*d*x^4) + (e*Sqrt[d^2 - e^2*x^2])/(3*d^2*x^3) - (3*e^2*Sqrt[d^2 - e^2*x^2])/(8*d^3*x^2) + (2*e^3*Sqrt[d^2 - e^2*x^2])/(3*d^4*x) - (3*e^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(8*d^4)","A",8,6,27,0.2222,1,"{850, 835, 807, 266, 63, 208}"
102,1,113,0,0.131154,"\int \frac{x^2 \left(d^2-e^2 x^2\right)^{3/2}}{d+e x} \, dx","Int[(x^2*(d^2 - e^2*x^2)^(3/2))/(d + e*x),x]","\frac{d^3 x \sqrt{d^2-e^2 x^2}}{8 e^2}+\frac{d (4 d-3 e x) \left(d^2-e^2 x^2\right)^{3/2}}{12 e^3}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 e^3}+\frac{d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}","\frac{d^3 x \sqrt{d^2-e^2 x^2}}{8 e^2}+\frac{d (4 d-3 e x) \left(d^2-e^2 x^2\right)^{3/2}}{12 e^3}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 e^3}+\frac{d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}",1,"(d^3*x*Sqrt[d^2 - e^2*x^2])/(8*e^2) + (d*(4*d - 3*e*x)*(d^2 - e^2*x^2)^(3/2))/(12*e^3) - (d^2 - e^2*x^2)^(5/2)/(5*e^3) + (d^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^3)","A",7,7,27,0.2593,1,"{1639, 12, 785, 780, 195, 217, 203}"
103,1,201,0,0.1602575,"\int \frac{x^4 \left(d^2-e^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[(x^4*(d^2 - e^2*x^2)^(5/2))/(d + e*x),x]","\frac{3 d^7 x \sqrt{d^2-e^2 x^2}}{128 e^4}+\frac{d^5 x \left(d^2-e^2 x^2\right)^{3/2}}{64 e^4}+\frac{d^3 (128 d-315 e x) \left(d^2-e^2 x^2\right)^{5/2}}{5040 e^5}+\frac{4 d^2 x^2 \left(d^2-e^2 x^2\right)^{5/2}}{63 e^3}-\frac{d x^3 \left(d^2-e^2 x^2\right)^{5/2}}{8 e^2}+\frac{x^4 \left(d^2-e^2 x^2\right)^{5/2}}{9 e}+\frac{3 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^5}","\frac{3 d^7 x \sqrt{d^2-e^2 x^2}}{128 e^4}+\frac{d^5 x \left(d^2-e^2 x^2\right)^{3/2}}{64 e^4}+\frac{d^3 (128 d-315 e x) \left(d^2-e^2 x^2\right)^{5/2}}{5040 e^5}+\frac{4 d^2 x^2 \left(d^2-e^2 x^2\right)^{5/2}}{63 e^3}-\frac{d x^3 \left(d^2-e^2 x^2\right)^{5/2}}{8 e^2}+\frac{x^4 \left(d^2-e^2 x^2\right)^{5/2}}{9 e}+\frac{3 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^5}",1,"(3*d^7*x*Sqrt[d^2 - e^2*x^2])/(128*e^4) + (d^5*x*(d^2 - e^2*x^2)^(3/2))/(64*e^4) + (4*d^2*x^2*(d^2 - e^2*x^2)^(5/2))/(63*e^3) - (d*x^3*(d^2 - e^2*x^2)^(5/2))/(8*e^2) + (x^4*(d^2 - e^2*x^2)^(5/2))/(9*e) + (d^3*(128*d - 315*e*x)*(d^2 - e^2*x^2)^(5/2))/(5040*e^5) + (3*d^9*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(128*e^5)","A",9,6,27,0.2222,1,"{850, 833, 780, 195, 217, 203}"
104,1,172,0,0.1234883,"\int \frac{x^3 \left(d^2-e^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[(x^3*(d^2 - e^2*x^2)^(5/2))/(d + e*x),x]","-\frac{3 d^6 x \sqrt{d^2-e^2 x^2}}{128 e^3}-\frac{d^4 x \left(d^2-e^2 x^2\right)^{3/2}}{64 e^3}-\frac{d^2 (32 d-35 e x) \left(d^2-e^2 x^2\right)^{5/2}}{560 e^4}-\frac{d x^2 \left(d^2-e^2 x^2\right)^{5/2}}{7 e^2}+\frac{x^3 \left(d^2-e^2 x^2\right)^{5/2}}{8 e}-\frac{3 d^8 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^4}","-\frac{3 d^6 x \sqrt{d^2-e^2 x^2}}{128 e^3}-\frac{d^4 x \left(d^2-e^2 x^2\right)^{3/2}}{64 e^3}-\frac{d^2 (32 d-35 e x) \left(d^2-e^2 x^2\right)^{5/2}}{560 e^4}-\frac{d x^2 \left(d^2-e^2 x^2\right)^{5/2}}{7 e^2}+\frac{x^3 \left(d^2-e^2 x^2\right)^{5/2}}{8 e}-\frac{3 d^8 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^4}",1,"(-3*d^6*x*Sqrt[d^2 - e^2*x^2])/(128*e^3) - (d^4*x*(d^2 - e^2*x^2)^(3/2))/(64*e^3) - (d*x^2*(d^2 - e^2*x^2)^(5/2))/(7*e^2) + (x^3*(d^2 - e^2*x^2)^(5/2))/(8*e) - (d^2*(32*d - 35*e*x)*(d^2 - e^2*x^2)^(5/2))/(560*e^4) - (3*d^8*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(128*e^4)","A",8,6,27,0.2222,1,"{850, 833, 780, 195, 217, 203}"
105,1,140,0,0.1502905,"\int \frac{x^2 \left(d^2-e^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[(x^2*(d^2 - e^2*x^2)^(5/2))/(d + e*x),x]","\frac{d^5 x \sqrt{d^2-e^2 x^2}}{16 e^2}+\frac{d^3 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e^2}+\frac{d (6 d-5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 e^3}-\frac{\left(d^2-e^2 x^2\right)^{7/2}}{7 e^3}+\frac{d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^3}","\frac{d^5 x \sqrt{d^2-e^2 x^2}}{16 e^2}+\frac{d^3 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e^2}+\frac{d (6 d-5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 e^3}-\frac{\left(d^2-e^2 x^2\right)^{7/2}}{7 e^3}+\frac{d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^3}",1,"(d^5*x*Sqrt[d^2 - e^2*x^2])/(16*e^2) + (d^3*x*(d^2 - e^2*x^2)^(3/2))/(24*e^2) + (d*(6*d - 5*e*x)*(d^2 - e^2*x^2)^(5/2))/(30*e^3) - (d^2 - e^2*x^2)^(7/2)/(7*e^3) + (d^7*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^3)","A",8,7,27,0.2593,1,"{1639, 12, 785, 780, 195, 217, 203}"
106,1,116,0,0.0588302,"\int \frac{x \left(d^2-e^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[(x*(d^2 - e^2*x^2)^(5/2))/(d + e*x),x]","-\frac{d^4 x \sqrt{d^2-e^2 x^2}}{16 e}-\frac{d^2 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e}-\frac{(6 d-5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 e^2}-\frac{d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^2}","-\frac{d^4 x \sqrt{d^2-e^2 x^2}}{16 e}-\frac{d^2 x \left(d^2-e^2 x^2\right)^{3/2}}{24 e}-\frac{(6 d-5 e x) \left(d^2-e^2 x^2\right)^{5/2}}{30 e^2}-\frac{d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^2}",1,"-(d^4*x*Sqrt[d^2 - e^2*x^2])/(16*e) - (d^2*x*(d^2 - e^2*x^2)^(3/2))/(24*e) - ((6*d - 5*e*x)*(d^2 - e^2*x^2)^(5/2))/(30*e^2) - (d^6*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^2)","A",6,5,25,0.2000,1,"{785, 780, 195, 217, 203}"
107,1,100,0,0.0305591,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(d + e*x),x]","\frac{3}{8} d^3 x \sqrt{d^2-e^2 x^2}+\frac{1}{4} d x \left(d^2-e^2 x^2\right)^{3/2}+\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 e}+\frac{3 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}","\frac{3}{8} d^3 x \sqrt{d^2-e^2 x^2}+\frac{1}{4} d x \left(d^2-e^2 x^2\right)^{3/2}+\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 e}+\frac{3 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}",1,"(3*d^3*x*Sqrt[d^2 - e^2*x^2])/8 + (d*x*(d^2 - e^2*x^2)^(3/2))/4 + (d^2 - e^2*x^2)^(5/2)/(5*e) + (3*d^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e)","A",5,4,24,0.1667,1,"{665, 195, 217, 203}"
108,1,113,0,0.1160231,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x*(d + e*x)),x]","\frac{1}{8} d^2 (8 d-3 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{12} (4 d-3 e x) \left(d^2-e^2 x^2\right)^{3/2}-\frac{3}{8} d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{1}{8} d^2 (8 d-3 e x) \sqrt{d^2-e^2 x^2}+\frac{1}{12} (4 d-3 e x) \left(d^2-e^2 x^2\right)^{3/2}-\frac{3}{8} d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(d^2*(8*d - 3*e*x)*Sqrt[d^2 - e^2*x^2])/8 + ((4*d - 3*e*x)*(d^2 - e^2*x^2)^(3/2))/12 - (3*d^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/8 - d^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",9,8,27,0.2963,1,"{850, 815, 844, 217, 203, 266, 63, 208}"
109,1,115,0,0.1179308,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^2 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^2*(d + e*x)),x]","-\frac{1}{2} d e (2 d+3 e x) \sqrt{d^2-e^2 x^2}-\frac{(3 d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{3 x}-\frac{3}{2} d^3 e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+d^3 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{1}{2} d e (2 d+3 e x) \sqrt{d^2-e^2 x^2}-\frac{(3 d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{3 x}-\frac{3}{2} d^3 e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+d^3 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"-(d*e*(2*d + 3*e*x)*Sqrt[d^2 - e^2*x^2])/2 - ((3*d + e*x)*(d^2 - e^2*x^2)^(3/2))/(3*x) - (3*d^3*e*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/2 + d^3*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",9,9,27,0.3333,1,"{850, 813, 815, 844, 217, 203, 266, 63, 208}"
110,1,121,0,0.1127217,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^3 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^3*(d + e*x)),x]","\frac{3 d e (d-e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{2 x^2}+\frac{3}{2} d^2 e^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{3}{2} d^2 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{3 d e (d-e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}}{2 x^2}+\frac{3}{2} d^2 e^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+\frac{3}{2} d^2 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(3*d*e*(d - e*x)*Sqrt[d^2 - e^2*x^2])/(2*x) - ((d + e*x)*(d^2 - e^2*x^2)^(3/2))/(2*x^2) + (3*d^2*e^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/2 + (3*d^2*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/2","A",9,8,27,0.2963,1,"{850, 813, 844, 217, 203, 266, 63, 208}"
111,1,120,0,0.114397,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^4 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^4*(d + e*x)),x]","\frac{e^2 (2 d+3 e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{(2 d-3 e x) \left(d^2-e^2 x^2\right)^{3/2}}{6 x^3}+d e^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{3}{2} d e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{e^2 (2 d+3 e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{(2 d-3 e x) \left(d^2-e^2 x^2\right)^{3/2}}{6 x^3}+d e^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{3}{2} d e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(e^2*(2*d + 3*e*x)*Sqrt[d^2 - e^2*x^2])/(2*x) - ((2*d - 3*e*x)*(d^2 - e^2*x^2)^(3/2))/(6*x^3) + d*e^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - (3*d*e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/2","A",9,9,27,0.3333,1,"{850, 811, 813, 844, 217, 203, 266, 63, 208}"
112,1,119,0,0.1146093,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^5 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^5*(d + e*x)),x]","\frac{e^2 (3 d-8 e x) \sqrt{d^2-e^2 x^2}}{8 x^2}-\frac{(3 d-4 e x) \left(d^2-e^2 x^2\right)^{3/2}}{12 x^4}+e^4 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)-\frac{3}{8} e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{e^2 (3 d-8 e x) \sqrt{d^2-e^2 x^2}}{8 x^2}-\frac{(3 d-4 e x) \left(d^2-e^2 x^2\right)^{3/2}}{12 x^4}+e^4 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)-\frac{3}{8} e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(e^2*(3*d - 8*e*x)*Sqrt[d^2 - e^2*x^2])/(8*x^2) - ((3*d - 4*e*x)*(d^2 - e^2*x^2)^(3/2))/(12*x^4) - e^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - (3*e^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/8","A",9,8,27,0.2963,1,"{850, 811, 844, 217, 203, 266, 63, 208}"
113,1,108,0,0.0893033,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^6 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^6*(d + e*x)),x]","-\frac{3 e^3 \sqrt{d^2-e^2 x^2}}{8 x^2}+\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{4 x^4}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 d x^5}+\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d}","-\frac{3 e^3 \sqrt{d^2-e^2 x^2}}{8 x^2}+\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{4 x^4}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{5 d x^5}+\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d}",1,"(-3*e^3*Sqrt[d^2 - e^2*x^2])/(8*x^2) + (e*(d^2 - e^2*x^2)^(3/2))/(4*x^4) - (d^2 - e^2*x^2)^(5/2)/(5*d*x^5) + (3*e^5*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(8*d)","A",7,6,27,0.2222,1,"{850, 807, 266, 47, 63, 208}"
114,1,143,0,0.1201879,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^7 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^7*(d + e*x)),x]","\frac{e^4 \sqrt{d^2-e^2 x^2}}{16 d x^2}-\frac{e^2 \left(d^2-e^2 x^2\right)^{3/2}}{24 d x^4}+\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{5 d^2 x^5}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{6 d x^6}-\frac{e^6 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^2}","\frac{e^4 \sqrt{d^2-e^2 x^2}}{16 d x^2}-\frac{e^2 \left(d^2-e^2 x^2\right)^{3/2}}{24 d x^4}+\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{5 d^2 x^5}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{6 d x^6}-\frac{e^6 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^2}",1,"(e^4*Sqrt[d^2 - e^2*x^2])/(16*d*x^2) - (e^2*(d^2 - e^2*x^2)^(3/2))/(24*d*x^4) - (d^2 - e^2*x^2)^(5/2)/(6*d*x^6) + (e*(d^2 - e^2*x^2)^(5/2))/(5*d^2*x^5) - (e^6*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(16*d^2)","A",8,7,27,0.2593,1,"{850, 835, 807, 266, 47, 63, 208}"
115,1,172,0,0.1539457,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^8 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^8*(d + e*x)),x]","-\frac{e^5 \sqrt{d^2-e^2 x^2}}{16 d^2 x^2}+\frac{e^3 \left(d^2-e^2 x^2\right)^{3/2}}{24 d^2 x^4}-\frac{2 e^2 \left(d^2-e^2 x^2\right)^{5/2}}{35 d^3 x^5}+\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{6 d^2 x^6}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{7 d x^7}+\frac{e^7 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^3}","-\frac{e^5 \sqrt{d^2-e^2 x^2}}{16 d^2 x^2}+\frac{e^3 \left(d^2-e^2 x^2\right)^{3/2}}{24 d^2 x^4}-\frac{2 e^2 \left(d^2-e^2 x^2\right)^{5/2}}{35 d^3 x^5}+\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{6 d^2 x^6}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{7 d x^7}+\frac{e^7 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^3}",1,"-(e^5*Sqrt[d^2 - e^2*x^2])/(16*d^2*x^2) + (e^3*(d^2 - e^2*x^2)^(3/2))/(24*d^2*x^4) - (d^2 - e^2*x^2)^(5/2)/(7*d*x^7) + (e*(d^2 - e^2*x^2)^(5/2))/(6*d^2*x^6) - (2*e^2*(d^2 - e^2*x^2)^(5/2))/(35*d^3*x^5) + (e^7*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(16*d^3)","A",9,7,27,0.2593,1,"{850, 835, 807, 266, 47, 63, 208}"
116,1,201,0,0.1898637,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^9 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^9*(d + e*x)),x]","\frac{3 e^6 \sqrt{d^2-e^2 x^2}}{128 d^3 x^2}-\frac{e^4 \left(d^2-e^2 x^2\right)^{3/2}}{64 d^3 x^4}+\frac{2 e^3 \left(d^2-e^2 x^2\right)^{5/2}}{35 d^4 x^5}-\frac{e^2 \left(d^2-e^2 x^2\right)^{5/2}}{16 d^3 x^6}+\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{7 d^2 x^7}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{8 d x^8}-\frac{3 e^8 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{128 d^4}","\frac{3 e^6 \sqrt{d^2-e^2 x^2}}{128 d^3 x^2}-\frac{e^4 \left(d^2-e^2 x^2\right)^{3/2}}{64 d^3 x^4}+\frac{2 e^3 \left(d^2-e^2 x^2\right)^{5/2}}{35 d^4 x^5}-\frac{e^2 \left(d^2-e^2 x^2\right)^{5/2}}{16 d^3 x^6}+\frac{e \left(d^2-e^2 x^2\right)^{5/2}}{7 d^2 x^7}-\frac{\left(d^2-e^2 x^2\right)^{5/2}}{8 d x^8}-\frac{3 e^8 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{128 d^4}",1,"(3*e^6*Sqrt[d^2 - e^2*x^2])/(128*d^3*x^2) - (e^4*(d^2 - e^2*x^2)^(3/2))/(64*d^3*x^4) - (d^2 - e^2*x^2)^(5/2)/(8*d*x^8) + (e*(d^2 - e^2*x^2)^(5/2))/(7*d^2*x^7) - (e^2*(d^2 - e^2*x^2)^(5/2))/(16*d^3*x^6) + (2*e^3*(d^2 - e^2*x^2)^(5/2))/(35*d^4*x^5) - (3*e^8*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(128*d^4)","A",10,7,27,0.2593,1,"{850, 835, 807, 266, 47, 63, 208}"
117,1,27,0,0.0170649,"\int \frac{x \sqrt{1-x^2}}{1+x} \, dx","Int[(x*Sqrt[1 - x^2])/(1 + x),x]","-\frac{1}{2} \sqrt{1-x^2} (2-x)-\frac{1}{2} \sin ^{-1}(x)","-\frac{1}{2} \sqrt{1-x^2} (2-x)-\frac{1}{2} \sin ^{-1}(x)",1,"-((2 - x)*Sqrt[1 - x^2])/2 - ArcSin[x]/2","A",3,3,18,0.1667,1,"{785, 780, 216}"
118,1,51,0,0.0721489,"\int \frac{\left(1-a^2 x^2\right)^{3/2}}{x^2 (1-a x)} \, dx","Int[(1 - a^2*x^2)^(3/2)/(x^2*(1 - a*x)),x]","-\frac{\sqrt{1-a^2 x^2} (1-a x)}{x}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-a \sin ^{-1}(a x)","-\frac{\sqrt{1-a^2 x^2} (1-a x)}{x}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-a \sin ^{-1}(a x)",1,"-(((1 - a*x)*Sqrt[1 - a^2*x^2])/x) - a*ArcSin[a*x] - a*ArcTanh[Sqrt[1 - a^2*x^2]]","A",7,7,26,0.2692,1,"{850, 813, 844, 216, 266, 63, 208}"
119,1,118,0,0.0961943,"\int \frac{x^4}{(d+e x) \sqrt{d^2-e^2 x^2}} \, dx","Int[x^4/((d + e*x)*Sqrt[d^2 - e^2*x^2]),x]","-\frac{d (16 d-9 e x) \sqrt{d^2-e^2 x^2}}{6 e^5}-\frac{4 x^2 \sqrt{d^2-e^2 x^2}}{3 e^3}+\frac{x^3 (d-e x)}{e^2 \sqrt{d^2-e^2 x^2}}-\frac{3 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^5}","-\frac{d (16 d-9 e x) \sqrt{d^2-e^2 x^2}}{6 e^5}-\frac{4 x^2 \sqrt{d^2-e^2 x^2}}{3 e^3}+\frac{x^3 (d-e x)}{e^2 \sqrt{d^2-e^2 x^2}}-\frac{3 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^5}",1,"(x^3*(d - e*x))/(e^2*Sqrt[d^2 - e^2*x^2]) - (4*x^2*Sqrt[d^2 - e^2*x^2])/(3*e^3) - (d*(16*d - 9*e*x)*Sqrt[d^2 - e^2*x^2])/(6*e^5) - (3*d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^5)","A",6,6,27,0.2222,1,"{850, 819, 833, 780, 217, 203}"
120,1,91,0,0.0635089,"\int \frac{x^3}{(d+e x) \sqrt{d^2-e^2 x^2}} \, dx","Int[x^3/((d + e*x)*Sqrt[d^2 - e^2*x^2]),x]","\frac{(4 d-3 e x) \sqrt{d^2-e^2 x^2}}{2 e^4}+\frac{x^2 (d-e x)}{e^2 \sqrt{d^2-e^2 x^2}}+\frac{3 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^4}","\frac{(4 d-3 e x) \sqrt{d^2-e^2 x^2}}{2 e^4}+\frac{x^2 (d-e x)}{e^2 \sqrt{d^2-e^2 x^2}}+\frac{3 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^4}",1,"(x^2*(d - e*x))/(e^2*Sqrt[d^2 - e^2*x^2]) + ((4*d - 3*e*x)*Sqrt[d^2 - e^2*x^2])/(2*e^4) + (3*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^4)","A",5,5,27,0.1852,1,"{850, 819, 780, 217, 203}"
121,1,77,0,0.0973203,"\int \frac{x^2}{(d+e x) \sqrt{d^2-e^2 x^2}} \, dx","Int[x^2/((d + e*x)*Sqrt[d^2 - e^2*x^2]),x]","-\frac{d \sqrt{d^2-e^2 x^2}}{e^3 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2}}{e^3}-\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}","-\frac{d \sqrt{d^2-e^2 x^2}}{e^3 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2}}{e^3}-\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}",1,"-(Sqrt[d^2 - e^2*x^2]/e^3) - (d*Sqrt[d^2 - e^2*x^2])/(e^3*(d + e*x)) - (d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^3","A",5,5,27,0.1852,1,"{1639, 12, 793, 217, 203}"
122,1,52,0,0.0221245,"\int \frac{x}{(d+e x) \sqrt{d^2-e^2 x^2}} \, dx","Int[x/((d + e*x)*Sqrt[d^2 - e^2*x^2]),x]","\frac{\sqrt{d^2-e^2 x^2}}{e^2 (d+e x)}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^2}","\frac{\sqrt{d^2-e^2 x^2}}{e^2 (d+e x)}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^2}",1,"Sqrt[d^2 - e^2*x^2]/(e^2*(d + e*x)) + ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e^2","A",3,3,25,0.1200,1,"{793, 217, 203}"
123,1,31,0,0.0107353,"\int \frac{1}{(d+e x) \sqrt{d^2-e^2 x^2}} \, dx","Int[1/((d + e*x)*Sqrt[d^2 - e^2*x^2]),x]","-\frac{\sqrt{d^2-e^2 x^2}}{d e (d+e x)}","-\frac{\sqrt{d^2-e^2 x^2}}{d e (d+e x)}",1,"-(Sqrt[d^2 - e^2*x^2]/(d*e*(d + e*x)))","A",1,1,24,0.04167,1,"{651}"
124,1,54,0,0.0443948,"\int \frac{1}{x (d+e x) \sqrt{d^2-e^2 x^2}} \, dx","Int[1/(x*(d + e*x)*Sqrt[d^2 - e^2*x^2]),x]","\frac{\sqrt{d^2-e^2 x^2}}{d^2 (d+e x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^2}","\frac{\sqrt{d^2-e^2 x^2}}{d^2 (d+e x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^2}",1,"Sqrt[d^2 - e^2*x^2]/(d^2*(d + e*x)) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^2","A",5,5,27,0.1852,1,"{857, 12, 266, 63, 208}"
125,1,81,0,0.063554,"\int \frac{1}{x^2 (d+e x) \sqrt{d^2-e^2 x^2}} \, dx","Int[1/(x^2*(d + e*x)*Sqrt[d^2 - e^2*x^2]),x]","-\frac{2 \sqrt{d^2-e^2 x^2}}{d^3 x}+\frac{\sqrt{d^2-e^2 x^2}}{d^2 x (d+e x)}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^3}","-\frac{2 \sqrt{d^2-e^2 x^2}}{d^3 x}+\frac{\sqrt{d^2-e^2 x^2}}{d^2 x (d+e x)}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^3}",1,"(-2*Sqrt[d^2 - e^2*x^2])/(d^3*x) + Sqrt[d^2 - e^2*x^2]/(d^2*x*(d + e*x)) + (e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^3","A",5,5,27,0.1852,1,"{857, 807, 266, 63, 208}"
126,1,113,0,0.0907612,"\int \frac{1}{x^3 (d+e x) \sqrt{d^2-e^2 x^2}} \, dx","Int[1/(x^3*(d + e*x)*Sqrt[d^2 - e^2*x^2]),x]","\frac{2 e \sqrt{d^2-e^2 x^2}}{d^4 x}+\frac{\sqrt{d^2-e^2 x^2}}{d^2 x^2 (d+e x)}-\frac{3 \sqrt{d^2-e^2 x^2}}{2 d^3 x^2}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^4}","\frac{2 e \sqrt{d^2-e^2 x^2}}{d^4 x}+\frac{\sqrt{d^2-e^2 x^2}}{d^2 x^2 (d+e x)}-\frac{3 \sqrt{d^2-e^2 x^2}}{2 d^3 x^2}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^4}",1,"(-3*Sqrt[d^2 - e^2*x^2])/(2*d^3*x^2) + (2*e*Sqrt[d^2 - e^2*x^2])/(d^4*x) + Sqrt[d^2 - e^2*x^2]/(d^2*x^2*(d + e*x)) - (3*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^4)","A",6,6,27,0.2222,1,"{857, 835, 807, 266, 63, 208}"
127,1,128,0,0.105259,"\int \frac{x^5}{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[x^5/((d + e*x)*(d^2 - e^2*x^2)^(3/2)),x]","\frac{x^4 (d-e x)}{3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{x^2 (4 d-5 e x)}{3 e^4 \sqrt{d^2-e^2 x^2}}-\frac{(16 d-15 e x) \sqrt{d^2-e^2 x^2}}{6 e^6}-\frac{5 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^6}","\frac{x^4 (d-e x)}{3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{x^2 (4 d-5 e x)}{3 e^4 \sqrt{d^2-e^2 x^2}}-\frac{(16 d-15 e x) \sqrt{d^2-e^2 x^2}}{6 e^6}-\frac{5 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^6}",1,"(x^4*(d - e*x))/(3*e^2*(d^2 - e^2*x^2)^(3/2)) - (x^2*(4*d - 5*e*x))/(3*e^4*Sqrt[d^2 - e^2*x^2]) - ((16*d - 15*e*x)*Sqrt[d^2 - e^2*x^2])/(6*e^6) - (5*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^6)","A",6,5,27,0.1852,1,"{850, 819, 780, 217, 203}"
128,1,113,0,0.0938843,"\int \frac{x^4}{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[x^4/((d + e*x)*(d^2 - e^2*x^2)^(3/2)),x]","\frac{x^3 (d-e x)}{3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{x (3 d-4 e x)}{3 e^4 \sqrt{d^2-e^2 x^2}}+\frac{8 \sqrt{d^2-e^2 x^2}}{3 e^5}+\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}","\frac{x^3 (d-e x)}{3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{x (3 d-4 e x)}{3 e^4 \sqrt{d^2-e^2 x^2}}+\frac{8 \sqrt{d^2-e^2 x^2}}{3 e^5}+\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}",1,"(x^3*(d - e*x))/(3*e^2*(d^2 - e^2*x^2)^(3/2)) - (x*(3*d - 4*e*x))/(3*e^4*Sqrt[d^2 - e^2*x^2]) + (8*Sqrt[d^2 - e^2*x^2])/(3*e^5) + (d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^5","A",6,5,27,0.1852,1,"{850, 819, 641, 217, 203}"
129,1,89,0,0.0702345,"\int \frac{x^3}{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[x^3/((d + e*x)*(d^2 - e^2*x^2)^(3/2)),x]","\frac{x^2 (d-e x)}{3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 d-3 e x}{3 e^4 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}","\frac{x^2 (d-e x)}{3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 d-3 e x}{3 e^4 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}",1,"(x^2*(d - e*x))/(3*e^2*(d^2 - e^2*x^2)^(3/2)) - (2*d - 3*e*x)/(3*e^4*Sqrt[d^2 - e^2*x^2]) - ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e^4","A",5,5,27,0.1852,1,"{850, 819, 778, 217, 203}"
130,1,60,0,0.0346268,"\int \frac{x^2}{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[x^2/((d + e*x)*(d^2 - e^2*x^2)^(3/2)),x]","\frac{2}{3 e^3 \sqrt{d^2-e^2 x^2}}-\frac{x^2}{3 d e (d+e x) \sqrt{d^2-e^2 x^2}}","\frac{2}{3 e^3 \sqrt{d^2-e^2 x^2}}-\frac{x^2}{3 d e (d+e x) \sqrt{d^2-e^2 x^2}}",1,"2/(3*e^3*Sqrt[d^2 - e^2*x^2]) - x^2/(3*d*e*(d + e*x)*Sqrt[d^2 - e^2*x^2])","A",3,3,27,0.1111,1,"{855, 12, 261}"
131,1,58,0,0.0203455,"\int \frac{x}{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[x/((d + e*x)*(d^2 - e^2*x^2)^(3/2)),x]","\frac{x}{3 d^2 e \sqrt{d^2-e^2 x^2}}+\frac{1}{3 e^2 (d+e x) \sqrt{d^2-e^2 x^2}}","\frac{x}{3 d^2 e \sqrt{d^2-e^2 x^2}}+\frac{1}{3 e^2 (d+e x) \sqrt{d^2-e^2 x^2}}",1,"x/(3*d^2*e*Sqrt[d^2 - e^2*x^2]) + 1/(3*e^2*(d + e*x)*Sqrt[d^2 - e^2*x^2])","A",2,2,25,0.08000,1,"{793, 191}"
132,1,58,0,0.0146012,"\int \frac{1}{(d+e x) \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(d^2 - e^2*x^2)^(3/2)),x]","\frac{2 x}{3 d^3 \sqrt{d^2-e^2 x^2}}-\frac{1}{3 d e (d+e x) \sqrt{d^2-e^2 x^2}}","\frac{2 x}{3 d^3 \sqrt{d^2-e^2 x^2}}-\frac{1}{3 d e (d+e x) \sqrt{d^2-e^2 x^2}}",1,"(2*x)/(3*d^3*Sqrt[d^2 - e^2*x^2]) - 1/(3*d*e*(d + e*x)*Sqrt[d^2 - e^2*x^2])","A",2,2,24,0.08333,1,"{659, 191}"
133,1,88,0,0.0754648,"\int \frac{1}{x (d+e x) \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[1/(x*(d + e*x)*(d^2 - e^2*x^2)^(3/2)),x]","\frac{3 d-2 e x}{3 d^4 \sqrt{d^2-e^2 x^2}}+\frac{1}{3 d^2 (d+e x) \sqrt{d^2-e^2 x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^4}","\frac{3 d-2 e x}{3 d^4 \sqrt{d^2-e^2 x^2}}+\frac{1}{3 d^2 (d+e x) \sqrt{d^2-e^2 x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^4}",1,"(3*d - 2*e*x)/(3*d^4*Sqrt[d^2 - e^2*x^2]) + 1/(3*d^2*(d + e*x)*Sqrt[d^2 - e^2*x^2]) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^4","A",6,6,27,0.2222,1,"{857, 823, 12, 266, 63, 208}"
134,1,120,0,0.102529,"\int \frac{1}{x^2 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[1/(x^2*(d + e*x)*(d^2 - e^2*x^2)^(3/2)),x]","\frac{4 d-3 e x}{3 d^4 x \sqrt{d^2-e^2 x^2}}-\frac{8 \sqrt{d^2-e^2 x^2}}{3 d^5 x}+\frac{1}{3 d^2 x (d+e x) \sqrt{d^2-e^2 x^2}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}","\frac{4 d-3 e x}{3 d^4 x \sqrt{d^2-e^2 x^2}}-\frac{8 \sqrt{d^2-e^2 x^2}}{3 d^5 x}+\frac{1}{3 d^2 x (d+e x) \sqrt{d^2-e^2 x^2}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}",1,"(4*d - 3*e*x)/(3*d^4*x*Sqrt[d^2 - e^2*x^2]) + 1/(3*d^2*x*(d + e*x)*Sqrt[d^2 - e^2*x^2]) - (8*Sqrt[d^2 - e^2*x^2])/(3*d^5*x) + (e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^5","A",6,6,27,0.2222,1,"{857, 823, 807, 266, 63, 208}"
135,1,152,0,0.129039,"\int \frac{1}{x^3 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[1/(x^3*(d + e*x)*(d^2 - e^2*x^2)^(3/2)),x]","\frac{8 e \sqrt{d^2-e^2 x^2}}{3 d^6 x}-\frac{5 \sqrt{d^2-e^2 x^2}}{2 d^5 x^2}+\frac{5 d-4 e x}{3 d^4 x^2 \sqrt{d^2-e^2 x^2}}+\frac{1}{3 d^2 x^2 (d+e x) \sqrt{d^2-e^2 x^2}}-\frac{5 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^6}","\frac{8 e \sqrt{d^2-e^2 x^2}}{3 d^6 x}-\frac{5 \sqrt{d^2-e^2 x^2}}{2 d^5 x^2}+\frac{5 d-4 e x}{3 d^4 x^2 \sqrt{d^2-e^2 x^2}}+\frac{1}{3 d^2 x^2 (d+e x) \sqrt{d^2-e^2 x^2}}-\frac{5 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^6}",1,"(5*d - 4*e*x)/(3*d^4*x^2*Sqrt[d^2 - e^2*x^2]) + 1/(3*d^2*x^2*(d + e*x)*Sqrt[d^2 - e^2*x^2]) - (5*Sqrt[d^2 - e^2*x^2])/(2*d^5*x^2) + (8*e*Sqrt[d^2 - e^2*x^2])/(3*d^6*x) - (5*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^6)","A",7,7,27,0.2593,1,"{857, 823, 835, 807, 266, 63, 208}"
136,1,162,0,0.1604227,"\int \frac{x^7}{(d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[x^7/((d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","\frac{x^6 (d-e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^4 (6 d-7 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x^2 (24 d-35 e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{(32 d-35 e x) \sqrt{d^2-e^2 x^2}}{10 e^8}+\frac{7 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^8}","\frac{x^6 (d-e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^4 (6 d-7 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x^2 (24 d-35 e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{(32 d-35 e x) \sqrt{d^2-e^2 x^2}}{10 e^8}+\frac{7 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^8}",1,"(x^6*(d - e*x))/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (x^4*(6*d - 7*e*x))/(15*e^4*(d^2 - e^2*x^2)^(3/2)) + (x^2*(24*d - 35*e*x))/(15*e^6*Sqrt[d^2 - e^2*x^2]) + ((32*d - 35*e*x)*Sqrt[d^2 - e^2*x^2])/(10*e^8) + (7*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^8)","A",7,5,27,0.1852,1,"{850, 819, 780, 217, 203}"
137,1,148,0,0.1374165,"\int \frac{x^6}{(d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[x^6/((d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","\frac{x^5 (d-e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^3 (5 d-6 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x (5 d-8 e x)}{5 e^6 \sqrt{d^2-e^2 x^2}}-\frac{16 \sqrt{d^2-e^2 x^2}}{5 e^7}-\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^7}","\frac{x^5 (d-e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^3 (5 d-6 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x (5 d-8 e x)}{5 e^6 \sqrt{d^2-e^2 x^2}}-\frac{16 \sqrt{d^2-e^2 x^2}}{5 e^7}-\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^7}",1,"(x^5*(d - e*x))/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (x^3*(5*d - 6*e*x))/(15*e^4*(d^2 - e^2*x^2)^(3/2)) + (x*(5*d - 8*e*x))/(5*e^6*Sqrt[d^2 - e^2*x^2]) - (16*Sqrt[d^2 - e^2*x^2])/(5*e^7) - (d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^7","A",7,5,27,0.1852,1,"{850, 819, 641, 217, 203}"
138,1,122,0,0.1015131,"\int \frac{x^5}{(d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[x^5/((d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","\frac{x^4 (d-e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^2 (4 d-5 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{8 d-15 e x}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^6}","\frac{x^4 (d-e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x^2 (4 d-5 e x)}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{8 d-15 e x}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^6}",1,"(x^4*(d - e*x))/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (x^2*(4*d - 5*e*x))/(15*e^4*(d^2 - e^2*x^2)^(3/2)) + (8*d - 15*e*x)/(15*e^6*Sqrt[d^2 - e^2*x^2]) + ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e^6","A",6,5,27,0.1852,1,"{850, 819, 778, 217, 203}"
139,1,85,0,0.0742674,"\int \frac{x^4}{(d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[x^4/((d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","-\frac{x^4 (d-e x)}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{4}{5 e^5 \sqrt{d^2-e^2 x^2}}+\frac{4 d^2}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}","-\frac{x^4 (d-e x)}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{4}{5 e^5 \sqrt{d^2-e^2 x^2}}+\frac{4 d^2}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}",1,"-(x^4*(d - e*x))/(5*d*e*(d^2 - e^2*x^2)^(5/2)) + (4*d^2)/(15*e^5*(d^2 - e^2*x^2)^(3/2)) - 4/(5*e^5*Sqrt[d^2 - e^2*x^2])","A",5,4,27,0.1481,1,"{850, 805, 266, 43}"
140,1,91,0,0.0694935,"\int \frac{x^3}{(d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[x^3/((d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","\frac{x^2 (d-e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x}{5 d^2 e^3 \sqrt{d^2-e^2 x^2}}-\frac{2 d-3 e x}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}","\frac{x^2 (d-e x)}{5 e^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{x}{5 d^2 e^3 \sqrt{d^2-e^2 x^2}}-\frac{2 d-3 e x}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}",1,"(x^2*(d - e*x))/(5*e^2*(d^2 - e^2*x^2)^(5/2)) - (2*d - 3*e*x)/(15*e^4*(d^2 - e^2*x^2)^(3/2)) - x/(5*d^2*e^3*Sqrt[d^2 - e^2*x^2])","A",4,4,27,0.1481,1,"{850, 819, 778, 191}"
141,1,95,0,0.0533926,"\int \frac{x^2}{(d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[x^2/((d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","-\frac{x^2}{5 d e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 x}{15 d^3 e^2 \sqrt{d^2-e^2 x^2}}+\frac{2 (d+e x)}{15 d e^3 \left(d^2-e^2 x^2\right)^{3/2}}","-\frac{x^2}{5 d e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 x}{15 d^3 e^2 \sqrt{d^2-e^2 x^2}}+\frac{2 (d+e x)}{15 d e^3 \left(d^2-e^2 x^2\right)^{3/2}}",1,"-x^2/(5*d*e*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (2*(d + e*x))/(15*d*e^3*(d^2 - e^2*x^2)^(3/2)) - (2*x)/(15*d^3*e^2*Sqrt[d^2 - e^2*x^2])","A",3,3,27,0.1111,1,"{855, 778, 191}"
142,1,85,0,0.0287794,"\int \frac{x}{(d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[x/((d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","\frac{2 x}{15 d^4 e \sqrt{d^2-e^2 x^2}}+\frac{x}{15 d^2 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{1}{5 e^2 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}","\frac{2 x}{15 d^4 e \sqrt{d^2-e^2 x^2}}+\frac{x}{15 d^2 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{1}{5 e^2 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}",1,"x/(15*d^2*e*(d^2 - e^2*x^2)^(3/2)) + 1/(5*e^2*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (2*x)/(15*d^4*e*Sqrt[d^2 - e^2*x^2])","A",3,3,25,0.1200,1,"{793, 192, 191}"
143,1,82,0,0.0218122,"\int \frac{1}{(d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","\frac{8 x}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{4 x}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{5 d e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}","\frac{8 x}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{4 x}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{5 d e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}",1,"(4*x)/(15*d^3*(d^2 - e^2*x^2)^(3/2)) - 1/(5*d*e*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (8*x)/(15*d^5*Sqrt[d^2 - e^2*x^2])","A",3,3,24,0.1250,1,"{659, 192, 191}"
144,1,119,0,0.1067498,"\int \frac{1}{x (d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[1/(x*(d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","\frac{15 d-8 e x}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{5 d-4 e x}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{1}{5 d^2 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}","\frac{15 d-8 e x}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{5 d-4 e x}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{1}{5 d^2 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}",1,"(5*d - 4*e*x)/(15*d^4*(d^2 - e^2*x^2)^(3/2)) + 1/(5*d^2*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (15*d - 8*e*x)/(15*d^6*Sqrt[d^2 - e^2*x^2]) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^6","A",7,6,27,0.2222,1,"{857, 823, 12, 266, 63, 208}"
145,1,154,0,0.1356119,"\int \frac{1}{x^2 (d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[1/(x^2*(d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","\frac{6 d-5 e x}{15 d^4 x \left(d^2-e^2 x^2\right)^{3/2}}-\frac{16 \sqrt{d^2-e^2 x^2}}{5 d^7 x}+\frac{8 d-5 e x}{5 d^6 x \sqrt{d^2-e^2 x^2}}+\frac{1}{5 d^2 x (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^7}","\frac{6 d-5 e x}{15 d^4 x \left(d^2-e^2 x^2\right)^{3/2}}-\frac{16 \sqrt{d^2-e^2 x^2}}{5 d^7 x}+\frac{8 d-5 e x}{5 d^6 x \sqrt{d^2-e^2 x^2}}+\frac{1}{5 d^2 x (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^7}",1,"(6*d - 5*e*x)/(15*d^4*x*(d^2 - e^2*x^2)^(3/2)) + 1/(5*d^2*x*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (8*d - 5*e*x)/(5*d^6*x*Sqrt[d^2 - e^2*x^2]) - (16*Sqrt[d^2 - e^2*x^2])/(5*d^7*x) + (e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^7","A",7,6,27,0.2222,1,"{857, 823, 807, 266, 63, 208}"
146,1,186,0,0.1682333,"\int \frac{1}{x^3 (d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[1/(x^3*(d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","\frac{16 e \sqrt{d^2-e^2 x^2}}{5 d^8 x}-\frac{7 \sqrt{d^2-e^2 x^2}}{2 d^7 x^2}+\frac{35 d-24 e x}{15 d^6 x^2 \sqrt{d^2-e^2 x^2}}+\frac{7 d-6 e x}{15 d^4 x^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{1}{5 d^2 x^2 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{7 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^8}","\frac{16 e \sqrt{d^2-e^2 x^2}}{5 d^8 x}-\frac{7 \sqrt{d^2-e^2 x^2}}{2 d^7 x^2}+\frac{35 d-24 e x}{15 d^6 x^2 \sqrt{d^2-e^2 x^2}}+\frac{7 d-6 e x}{15 d^4 x^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{1}{5 d^2 x^2 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{7 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^8}",1,"(7*d - 6*e*x)/(15*d^4*x^2*(d^2 - e^2*x^2)^(3/2)) + 1/(5*d^2*x^2*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (35*d - 24*e*x)/(15*d^6*x^2*Sqrt[d^2 - e^2*x^2]) - (7*Sqrt[d^2 - e^2*x^2])/(2*d^7*x^2) + (16*e*Sqrt[d^2 - e^2*x^2])/(5*d^8*x) - (7*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^8)","A",8,7,27,0.2593,1,"{857, 823, 835, 807, 266, 63, 208}"
147,1,215,0,0.2096994,"\int \frac{1}{x^4 (d+e x) \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[1/(x^4*(d + e*x)*(d^2 - e^2*x^2)^(5/2)),x]","-\frac{128 e^2 \sqrt{d^2-e^2 x^2}}{15 d^9 x}+\frac{7 e \sqrt{d^2-e^2 x^2}}{2 d^8 x^2}-\frac{64 \sqrt{d^2-e^2 x^2}}{15 d^7 x^3}+\frac{48 d-35 e x}{15 d^6 x^3 \sqrt{d^2-e^2 x^2}}+\frac{8 d-7 e x}{15 d^4 x^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{1}{5 d^2 x^3 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}+\frac{7 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^9}","-\frac{128 e^2 \sqrt{d^2-e^2 x^2}}{15 d^9 x}+\frac{7 e \sqrt{d^2-e^2 x^2}}{2 d^8 x^2}-\frac{64 \sqrt{d^2-e^2 x^2}}{15 d^7 x^3}+\frac{48 d-35 e x}{15 d^6 x^3 \sqrt{d^2-e^2 x^2}}+\frac{8 d-7 e x}{15 d^4 x^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{1}{5 d^2 x^3 (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}+\frac{7 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^9}",1,"(8*d - 7*e*x)/(15*d^4*x^3*(d^2 - e^2*x^2)^(3/2)) + 1/(5*d^2*x^3*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (48*d - 35*e*x)/(15*d^6*x^3*Sqrt[d^2 - e^2*x^2]) - (64*Sqrt[d^2 - e^2*x^2])/(15*d^7*x^3) + (7*e*Sqrt[d^2 - e^2*x^2])/(2*d^8*x^2) - (128*e^2*Sqrt[d^2 - e^2*x^2])/(15*d^9*x) + (7*e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^9)","A",9,7,27,0.2593,1,"{857, 823, 835, 807, 266, 63, 208}"
148,1,118,0,0.0773119,"\int \frac{x^3}{(d+e x) \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[x^3/((d + e*x)*(d^2 - e^2*x^2)^(7/2)),x]","\frac{x^2 (d-e x)}{7 e^2 \left(d^2-e^2 x^2\right)^{7/2}}-\frac{2 x}{35 d^4 e^3 \sqrt{d^2-e^2 x^2}}-\frac{x}{35 d^2 e^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 d-3 e x}{35 e^4 \left(d^2-e^2 x^2\right)^{5/2}}","\frac{x^2 (d-e x)}{7 e^2 \left(d^2-e^2 x^2\right)^{7/2}}-\frac{2 x}{35 d^4 e^3 \sqrt{d^2-e^2 x^2}}-\frac{x}{35 d^2 e^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 d-3 e x}{35 e^4 \left(d^2-e^2 x^2\right)^{5/2}}",1,"(x^2*(d - e*x))/(7*e^2*(d^2 - e^2*x^2)^(7/2)) - (2*d - 3*e*x)/(35*e^4*(d^2 - e^2*x^2)^(5/2)) - x/(35*d^2*e^3*(d^2 - e^2*x^2)^(3/2)) - (2*x)/(35*d^4*e^3*Sqrt[d^2 - e^2*x^2])","A",5,5,27,0.1852,1,"{850, 819, 778, 192, 191}"
149,1,123,0,0.0575934,"\int \frac{x^2}{(d+e x) \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[x^2/((d + e*x)*(d^2 - e^2*x^2)^(7/2)),x]","-\frac{x^2}{7 d e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8 x}{105 d^5 e^2 \sqrt{d^2-e^2 x^2}}-\frac{4 x}{105 d^3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (d+2 e x)}{35 d e^3 \left(d^2-e^2 x^2\right)^{5/2}}","-\frac{x^2}{7 d e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8 x}{105 d^5 e^2 \sqrt{d^2-e^2 x^2}}-\frac{4 x}{105 d^3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (d+2 e x)}{35 d e^3 \left(d^2-e^2 x^2\right)^{5/2}}",1,"-x^2/(7*d*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (2*(d + 2*e*x))/(35*d*e^3*(d^2 - e^2*x^2)^(5/2)) - (4*x)/(105*d^3*e^2*(d^2 - e^2*x^2)^(3/2)) - (8*x)/(105*d^5*e^2*Sqrt[d^2 - e^2*x^2])","A",4,4,27,0.1481,1,"{855, 778, 192, 191}"
150,1,66,0,0.0538498,"\int \frac{x^3}{(1+a x) \sqrt{1-a^2 x^2}} \, dx","Int[x^3/((1 + a*x)*Sqrt[1 - a^2*x^2]),x]","\frac{x^2 (1-a x)}{a^2 \sqrt{1-a^2 x^2}}+\frac{(4-3 a x) \sqrt{1-a^2 x^2}}{2 a^4}+\frac{3 \sin ^{-1}(a x)}{2 a^4}","\frac{x^2 (1-a x)}{a^2 \sqrt{1-a^2 x^2}}+\frac{(4-3 a x) \sqrt{1-a^2 x^2}}{2 a^4}+\frac{3 \sin ^{-1}(a x)}{2 a^4}",1,"(x^2*(1 - a*x))/(a^2*Sqrt[1 - a^2*x^2]) + ((4 - 3*a*x)*Sqrt[1 - a^2*x^2])/(2*a^4) + (3*ArcSin[a*x])/(2*a^4)","A",4,4,25,0.1600,1,"{850, 819, 780, 216}"
151,1,55,0,0.0863924,"\int \frac{x^2}{(1+a x) \sqrt{1-a^2 x^2}} \, dx","Int[x^2/((1 + a*x)*Sqrt[1 - a^2*x^2]),x]","-\frac{\sqrt{1-a^2 x^2}}{a^3 (a x+1)}-\frac{\sqrt{1-a^2 x^2}}{a^3}-\frac{\sin ^{-1}(a x)}{a^3}","-\frac{\sqrt{1-a^2 x^2}}{a^3 (a x+1)}-\frac{\sqrt{1-a^2 x^2}}{a^3}-\frac{\sin ^{-1}(a x)}{a^3}",1,"-(Sqrt[1 - a^2*x^2]/a^3) - Sqrt[1 - a^2*x^2]/(a^3*(1 + a*x)) - ArcSin[a*x]/a^3","A",4,4,25,0.1600,1,"{1639, 12, 793, 216}"
152,1,34,0,0.0174339,"\int \frac{x}{(1+a x) \sqrt{1-a^2 x^2}} \, dx","Int[x/((1 + a*x)*Sqrt[1 - a^2*x^2]),x]","\frac{\sqrt{1-a^2 x^2}}{a^2 (a x+1)}+\frac{\sin ^{-1}(a x)}{a^2}","\frac{\sqrt{1-a^2 x^2}}{a^2 (a x+1)}+\frac{\sin ^{-1}(a x)}{a^2}",1,"Sqrt[1 - a^2*x^2]/(a^2*(1 + a*x)) + ArcSin[a*x]/a^2","A",2,2,23,0.08696,1,"{793, 216}"
153,1,26,0,0.0095005,"\int \frac{1}{(1+a x) \sqrt{1-a^2 x^2}} \, dx","Int[1/((1 + a*x)*Sqrt[1 - a^2*x^2]),x]","-\frac{\sqrt{1-a^2 x^2}}{a (a x+1)}","-\frac{\sqrt{1-a^2 x^2}}{a (a x+1)}",1,"-(Sqrt[1 - a^2*x^2]/(a*(1 + a*x)))","A",1,1,22,0.04545,1,"{651}"
154,1,41,0,0.0397202,"\int \frac{1}{x (1-a x) \sqrt{1-a^2 x^2}} \, dx","Int[1/(x*(1 - a*x)*Sqrt[1 - a^2*x^2]),x]","\frac{\sqrt{1-a^2 x^2}}{1-a x}-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","\frac{\sqrt{1-a^2 x^2}}{1-a x}-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"Sqrt[1 - a^2*x^2]/(1 - a*x) - ArcTanh[Sqrt[1 - a^2*x^2]]","A",5,5,26,0.1923,1,"{857, 12, 266, 63, 208}"
155,1,64,0,0.0534527,"\int \frac{1}{x^2 (1-a x) \sqrt{1-a^2 x^2}} \, dx","Int[1/(x^2*(1 - a*x)*Sqrt[1 - a^2*x^2]),x]","-\frac{2 \sqrt{1-a^2 x^2}}{x}+\frac{\sqrt{1-a^2 x^2}}{x (1-a x)}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","-\frac{2 \sqrt{1-a^2 x^2}}{x}+\frac{\sqrt{1-a^2 x^2}}{x (1-a x)}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(-2*Sqrt[1 - a^2*x^2])/x + Sqrt[1 - a^2*x^2]/(x*(1 - a*x)) - a*ArcTanh[Sqrt[1 - a^2*x^2]]","A",5,5,26,0.1923,1,"{857, 807, 266, 63, 208}"
156,1,90,0,0.0792337,"\int \frac{1}{x^3 (1-a x) \sqrt{1-a^2 x^2}} \, dx","Int[1/(x^3*(1 - a*x)*Sqrt[1 - a^2*x^2]),x]","-\frac{2 a \sqrt{1-a^2 x^2}}{x}+\frac{\sqrt{1-a^2 x^2}}{x^2 (1-a x)}-\frac{3 \sqrt{1-a^2 x^2}}{2 x^2}-\frac{3}{2} a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","-\frac{2 a \sqrt{1-a^2 x^2}}{x}+\frac{\sqrt{1-a^2 x^2}}{x^2 (1-a x)}-\frac{3 \sqrt{1-a^2 x^2}}{2 x^2}-\frac{3}{2} a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(-3*Sqrt[1 - a^2*x^2])/(2*x^2) - (2*a*Sqrt[1 - a^2*x^2])/x + Sqrt[1 - a^2*x^2]/(x^2*(1 - a*x)) - (3*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",6,6,26,0.2308,1,"{857, 835, 807, 266, 63, 208}"
157,1,229,0,0.3145936,"\int \frac{x^5 \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(x^5*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^2,x]","-\frac{5 d^7 x \sqrt{d^2-e^2 x^2}}{64 e^5}-\frac{d^5 (256 d-315 e x) \left(d^2-e^2 x^2\right)^{3/2}}{2016 e^6}-\frac{4 d^4 x^2 \left(d^2-e^2 x^2\right)^{3/2}}{21 e^4}+\frac{5 d^3 x^3 \left(d^2-e^2 x^2\right)^{3/2}}{24 e^3}-\frac{5 d^2 x^4 \left(d^2-e^2 x^2\right)^{3/2}}{21 e^2}+\frac{d x^5 \left(d^2-e^2 x^2\right)^{3/2}}{4 e}-\frac{1}{9} x^6 \left(d^2-e^2 x^2\right)^{3/2}-\frac{5 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{64 e^6}","-\frac{5 d^7 x \sqrt{d^2-e^2 x^2}}{64 e^5}-\frac{d^5 (256 d-315 e x) \left(d^2-e^2 x^2\right)^{3/2}}{2016 e^6}-\frac{4 d^4 x^2 \left(d^2-e^2 x^2\right)^{3/2}}{21 e^4}+\frac{5 d^3 x^3 \left(d^2-e^2 x^2\right)^{3/2}}{24 e^3}-\frac{5 d^2 x^4 \left(d^2-e^2 x^2\right)^{3/2}}{21 e^2}+\frac{d x^5 \left(d^2-e^2 x^2\right)^{3/2}}{4 e}-\frac{1}{9} x^6 \left(d^2-e^2 x^2\right)^{3/2}-\frac{5 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{64 e^6}",1,"(-5*d^7*x*Sqrt[d^2 - e^2*x^2])/(64*e^5) - (4*d^4*x^2*(d^2 - e^2*x^2)^(3/2))/(21*e^4) + (5*d^3*x^3*(d^2 - e^2*x^2)^(3/2))/(24*e^3) - (5*d^2*x^4*(d^2 - e^2*x^2)^(3/2))/(21*e^2) + (d*x^5*(d^2 - e^2*x^2)^(3/2))/(4*e) - (x^6*(d^2 - e^2*x^2)^(3/2))/9 - (d^5*(256*d - 315*e*x)*(d^2 - e^2*x^2)^(3/2))/(2016*e^6) - (5*d^9*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(64*e^6)","A",10,7,27,0.2593,1,"{852, 1809, 833, 780, 195, 217, 203}"
158,1,200,0,0.2696242,"\int \frac{x^4 \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(x^4*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^2,x]","\frac{13 d^6 x \sqrt{d^2-e^2 x^2}}{128 e^4}+\frac{d^4 (1024 d-1365 e x) \left(d^2-e^2 x^2\right)^{3/2}}{6720 e^5}+\frac{8 d^3 x^2 \left(d^2-e^2 x^2\right)^{3/2}}{35 e^3}-\frac{13 d^2 x^3 \left(d^2-e^2 x^2\right)^{3/2}}{48 e^2}+\frac{2 d x^4 \left(d^2-e^2 x^2\right)^{3/2}}{7 e}-\frac{1}{8} x^5 \left(d^2-e^2 x^2\right)^{3/2}+\frac{13 d^8 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^5}","\frac{13 d^6 x \sqrt{d^2-e^2 x^2}}{128 e^4}+\frac{d^4 (1024 d-1365 e x) \left(d^2-e^2 x^2\right)^{3/2}}{6720 e^5}+\frac{8 d^3 x^2 \left(d^2-e^2 x^2\right)^{3/2}}{35 e^3}-\frac{13 d^2 x^3 \left(d^2-e^2 x^2\right)^{3/2}}{48 e^2}+\frac{2 d x^4 \left(d^2-e^2 x^2\right)^{3/2}}{7 e}-\frac{1}{8} x^5 \left(d^2-e^2 x^2\right)^{3/2}+\frac{13 d^8 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e^5}",1,"(13*d^6*x*Sqrt[d^2 - e^2*x^2])/(128*e^4) + (8*d^3*x^2*(d^2 - e^2*x^2)^(3/2))/(35*e^3) - (13*d^2*x^3*(d^2 - e^2*x^2)^(3/2))/(48*e^2) + (2*d*x^4*(d^2 - e^2*x^2)^(3/2))/(7*e) - (x^5*(d^2 - e^2*x^2)^(3/2))/8 + (d^4*(1024*d - 1365*e*x)*(d^2 - e^2*x^2)^(3/2))/(6720*e^5) + (13*d^8*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(128*e^5)","A",9,7,27,0.2593,1,"{852, 1809, 833, 780, 195, 217, 203}"
159,1,171,0,0.2154673,"\int \frac{x^3 \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(x^3*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^2,x]","-\frac{d^5 x \sqrt{d^2-e^2 x^2}}{8 e^3}-\frac{d^3 (88 d-105 e x) \left(d^2-e^2 x^2\right)^{3/2}}{420 e^4}-\frac{11 d^2 x^2 \left(d^2-e^2 x^2\right)^{3/2}}{35 e^2}+\frac{d x^3 \left(d^2-e^2 x^2\right)^{3/2}}{3 e}-\frac{1}{7} x^4 \left(d^2-e^2 x^2\right)^{3/2}-\frac{d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^4}","-\frac{d^5 x \sqrt{d^2-e^2 x^2}}{8 e^3}-\frac{d^3 (88 d-105 e x) \left(d^2-e^2 x^2\right)^{3/2}}{420 e^4}-\frac{11 d^2 x^2 \left(d^2-e^2 x^2\right)^{3/2}}{35 e^2}+\frac{d x^3 \left(d^2-e^2 x^2\right)^{3/2}}{3 e}-\frac{1}{7} x^4 \left(d^2-e^2 x^2\right)^{3/2}-\frac{d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^4}",1,"-(d^5*x*Sqrt[d^2 - e^2*x^2])/(8*e^3) - (11*d^2*x^2*(d^2 - e^2*x^2)^(3/2))/(35*e^2) + (d*x^3*(d^2 - e^2*x^2)^(3/2))/(3*e) - (x^4*(d^2 - e^2*x^2)^(3/2))/7 - (d^3*(88*d - 105*e*x)*(d^2 - e^2*x^2)^(3/2))/(420*e^4) - (d^7*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^4)","A",8,7,27,0.2593,1,"{852, 1809, 833, 780, 195, 217, 203}"
160,1,142,0,0.1769559,"\int \frac{x^2 \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(x^2*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^2,x]","\frac{3 d^4 x \sqrt{d^2-e^2 x^2}}{16 e^2}+\frac{d^2 (32 d-45 e x) \left(d^2-e^2 x^2\right)^{3/2}}{120 e^3}+\frac{2 d x^2 \left(d^2-e^2 x^2\right)^{3/2}}{5 e}-\frac{1}{6} x^3 \left(d^2-e^2 x^2\right)^{3/2}+\frac{3 d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^3}","\frac{3 d^4 x \sqrt{d^2-e^2 x^2}}{16 e^2}+\frac{d^2 (32 d-45 e x) \left(d^2-e^2 x^2\right)^{3/2}}{120 e^3}+\frac{2 d x^2 \left(d^2-e^2 x^2\right)^{3/2}}{5 e}-\frac{1}{6} x^3 \left(d^2-e^2 x^2\right)^{3/2}+\frac{3 d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^3}",1,"(3*d^4*x*Sqrt[d^2 - e^2*x^2])/(16*e^2) + (2*d*x^2*(d^2 - e^2*x^2)^(3/2))/(5*e) - (x^3*(d^2 - e^2*x^2)^(3/2))/6 + (d^2*(32*d - 45*e*x)*(d^2 - e^2*x^2)^(3/2))/(120*e^3) + (3*d^6*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^3)","A",7,7,27,0.2593,1,"{852, 1809, 833, 780, 195, 217, 203}"
161,1,136,0,0.0566443,"\int \frac{x \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(x*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^2,x]","-\frac{d^3 x \sqrt{d^2-e^2 x^2}}{4 e}-\frac{d x \left(d^2-e^2 x^2\right)^{3/2}}{6 e}-\frac{\left(d^2-e^2 x^2\right)^{7/2}}{3 e^2 (d+e x)^2}-\frac{2 \left(d^2-e^2 x^2\right)^{5/2}}{15 e^2}-\frac{d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{4 e^2}","-\frac{d^3 x \sqrt{d^2-e^2 x^2}}{4 e}-\frac{d x \left(d^2-e^2 x^2\right)^{3/2}}{6 e}-\frac{\left(d^2-e^2 x^2\right)^{7/2}}{3 e^2 (d+e x)^2}-\frac{2 \left(d^2-e^2 x^2\right)^{5/2}}{15 e^2}-\frac{d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{4 e^2}",1,"-(d^3*x*Sqrt[d^2 - e^2*x^2])/(4*e) - (d*x*(d^2 - e^2*x^2)^(3/2))/(6*e) - (2*(d^2 - e^2*x^2)^(5/2))/(15*e^2) - (d^2 - e^2*x^2)^(7/2)/(3*e^2*(d + e*x)^2) - (d^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(4*e^2)","A",6,5,25,0.2000,1,"{793, 665, 195, 217, 203}"
162,1,108,0,0.0418491,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(d + e*x)^2,x]","\frac{5}{8} d^2 x \sqrt{d^2-e^2 x^2}+\frac{5 d \left(d^2-e^2 x^2\right)^{3/2}}{12 e}+\frac{(d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{4 e}+\frac{5 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}","\frac{5}{8} d^2 x \sqrt{d^2-e^2 x^2}+\frac{5 d \left(d^2-e^2 x^2\right)^{3/2}}{12 e}+\frac{(d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{4 e}+\frac{5 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}",1,"(5*d^2*x*Sqrt[d^2 - e^2*x^2])/8 + (5*d*(d^2 - e^2*x^2)^(3/2))/(12*e) + ((d - e*x)*(d^2 - e^2*x^2)^(3/2))/(4*e) + (5*d^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e)","A",6,6,24,0.2500,1,"{655, 671, 641, 195, 217, 203}"
163,1,96,0,0.1615227,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x*(d + e*x)^2),x]","d (d-e x) \sqrt{d^2-e^2 x^2}-\frac{1}{3} \left(d^2-e^2 x^2\right)^{3/2}+d^3 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)-d^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","d (d-e x) \sqrt{d^2-e^2 x^2}-\frac{1}{3} \left(d^2-e^2 x^2\right)^{3/2}+d^3 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)-d^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"d*(d - e*x)*Sqrt[d^2 - e^2*x^2] - (d^2 - e^2*x^2)^(3/2)/3 - d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - d^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",9,9,27,0.3333,1,"{852, 1809, 815, 844, 217, 203, 266, 63, 208}"
164,1,105,0,0.1606896,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^2 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^2*(d + e*x)^2),x]","-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{x}-\frac{1}{2} e (4 d+e x) \sqrt{d^2-e^2 x^2}-\frac{1}{2} d^2 e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+2 d^2 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{x}-\frac{1}{2} e (4 d+e x) \sqrt{d^2-e^2 x^2}-\frac{1}{2} d^2 e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+2 d^2 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"-(e*(4*d + e*x)*Sqrt[d^2 - e^2*x^2])/2 - (d^2 - e^2*x^2)^(3/2)/x - (d^2*e*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/2 + 2*d^2*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",9,9,27,0.3333,1,"{852, 1807, 815, 844, 217, 203, 266, 63, 208}"
165,1,110,0,0.1629171,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^3 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^3*(d + e*x)^2),x]","\frac{e (4 d+e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{2 x^2}+2 d e^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{1}{2} d e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{e (4 d+e x) \sqrt{d^2-e^2 x^2}}{2 x}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{2 x^2}+2 d e^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-\frac{1}{2} d e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(e*(4*d + e*x)*Sqrt[d^2 - e^2*x^2])/(2*x) - (d^2 - e^2*x^2)^(3/2)/(2*x^2) + 2*d*e^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - (d*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/2","A",9,9,27,0.3333,1,"{852, 1807, 813, 844, 217, 203, 266, 63, 208}"
166,1,102,0,0.1625868,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^4 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^4*(d + e*x)^2),x]","\frac{e (d-e x) \sqrt{d^2-e^2 x^2}}{x^2}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{3 x^3}+e^3 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)-e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{e (d-e x) \sqrt{d^2-e^2 x^2}}{x^2}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{3 x^3}+e^3 \left(-\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)\right)-e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(e*(d - e*x)*Sqrt[d^2 - e^2*x^2])/x^2 - (d^2 - e^2*x^2)^(3/2)/(3*x^3) - e^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",9,9,27,0.3333,1,"{852, 1807, 811, 844, 217, 203, 266, 63, 208}"
167,1,108,0,0.1468768,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^5 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^5*(d + e*x)^2),x]","-\frac{5 e^2 \sqrt{d^2-e^2 x^2}}{8 x^2}+\frac{2 e \left(d^2-e^2 x^2\right)^{3/2}}{3 d x^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{4 x^4}+\frac{5 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d}","-\frac{5 e^2 \sqrt{d^2-e^2 x^2}}{8 x^2}+\frac{2 e \left(d^2-e^2 x^2\right)^{3/2}}{3 d x^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{4 x^4}+\frac{5 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d}",1,"(-5*e^2*Sqrt[d^2 - e^2*x^2])/(8*x^2) - (d^2 - e^2*x^2)^(3/2)/(4*x^4) + (2*e*(d^2 - e^2*x^2)^(3/2))/(3*d*x^3) + (5*e^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(8*d)","A",7,7,27,0.2593,1,"{852, 1807, 807, 266, 47, 63, 208}"
168,1,140,0,0.1766866,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^6 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^6*(d + e*x)^2),x]","\frac{e^3 \sqrt{d^2-e^2 x^2}}{4 d x^2}-\frac{7 e^2 \left(d^2-e^2 x^2\right)^{3/2}}{15 d^2 x^3}+\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{2 d x^4}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{5 x^5}-\frac{e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{4 d^2}","\frac{e^3 \sqrt{d^2-e^2 x^2}}{4 d x^2}-\frac{7 e^2 \left(d^2-e^2 x^2\right)^{3/2}}{15 d^2 x^3}+\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{2 d x^4}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{5 x^5}-\frac{e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{4 d^2}",1,"(e^3*Sqrt[d^2 - e^2*x^2])/(4*d*x^2) - (d^2 - e^2*x^2)^(3/2)/(5*x^5) + (e*(d^2 - e^2*x^2)^(3/2))/(2*d*x^4) - (7*e^2*(d^2 - e^2*x^2)^(3/2))/(15*d^2*x^3) - (e^5*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(4*d^2)","A",8,8,27,0.2963,1,"{852, 1807, 835, 807, 266, 47, 63, 208}"
169,1,169,0,0.2077514,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^7 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^7*(d + e*x)^2),x]","-\frac{3 e^4 \sqrt{d^2-e^2 x^2}}{16 d^2 x^2}+\frac{4 e^3 \left(d^2-e^2 x^2\right)^{3/2}}{15 d^3 x^3}-\frac{3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}{8 d^2 x^4}+\frac{2 e \left(d^2-e^2 x^2\right)^{3/2}}{5 d x^5}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{6 x^6}+\frac{3 e^6 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^3}","-\frac{3 e^4 \sqrt{d^2-e^2 x^2}}{16 d^2 x^2}+\frac{4 e^3 \left(d^2-e^2 x^2\right)^{3/2}}{15 d^3 x^3}-\frac{3 e^2 \left(d^2-e^2 x^2\right)^{3/2}}{8 d^2 x^4}+\frac{2 e \left(d^2-e^2 x^2\right)^{3/2}}{5 d x^5}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{6 x^6}+\frac{3 e^6 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{16 d^3}",1,"(-3*e^4*Sqrt[d^2 - e^2*x^2])/(16*d^2*x^2) - (d^2 - e^2*x^2)^(3/2)/(6*x^6) + (2*e*(d^2 - e^2*x^2)^(3/2))/(5*d*x^5) - (3*e^2*(d^2 - e^2*x^2)^(3/2))/(8*d^2*x^4) + (4*e^3*(d^2 - e^2*x^2)^(3/2))/(15*d^3*x^3) + (3*e^6*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(16*d^3)","A",9,8,27,0.2963,1,"{852, 1807, 835, 807, 266, 47, 63, 208}"
170,1,198,0,0.2358182,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^8 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^8*(d + e*x)^2),x]","\frac{e^5 \sqrt{d^2-e^2 x^2}}{8 d^3 x^2}-\frac{22 e^4 \left(d^2-e^2 x^2\right)^{3/2}}{105 d^4 x^3}+\frac{e^3 \left(d^2-e^2 x^2\right)^{3/2}}{4 d^3 x^4}-\frac{11 e^2 \left(d^2-e^2 x^2\right)^{3/2}}{35 d^2 x^5}+\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{3 d x^6}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{7 x^7}-\frac{e^7 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d^4}","\frac{e^5 \sqrt{d^2-e^2 x^2}}{8 d^3 x^2}-\frac{22 e^4 \left(d^2-e^2 x^2\right)^{3/2}}{105 d^4 x^3}+\frac{e^3 \left(d^2-e^2 x^2\right)^{3/2}}{4 d^3 x^4}-\frac{11 e^2 \left(d^2-e^2 x^2\right)^{3/2}}{35 d^2 x^5}+\frac{e \left(d^2-e^2 x^2\right)^{3/2}}{3 d x^6}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{7 x^7}-\frac{e^7 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d^4}",1,"(e^5*Sqrt[d^2 - e^2*x^2])/(8*d^3*x^2) - (d^2 - e^2*x^2)^(3/2)/(7*x^7) + (e*(d^2 - e^2*x^2)^(3/2))/(3*d*x^6) - (11*e^2*(d^2 - e^2*x^2)^(3/2))/(35*d^2*x^5) + (e^3*(d^2 - e^2*x^2)^(3/2))/(4*d^3*x^4) - (22*e^4*(d^2 - e^2*x^2)^(3/2))/(105*d^4*x^3) - (e^7*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(8*d^4)","A",10,8,27,0.2963,1,"{852, 1807, 835, 807, 266, 47, 63, 208}"
171,1,123,0,0.2375058,"\int \frac{x^4}{(d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[x^4/((d + e*x)^2*(d^2 - e^2*x^2)^(3/2)),x]","-\frac{d^3 (d-e x)^2}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{17 d^2 (d-e x)}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 (15 d-13 e x)}{15 e^5 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}","-\frac{d^3 (d-e x)^2}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{17 d^2 (d-e x)}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 (15 d-13 e x)}{15 e^5 \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}",1,"-(d^3*(d - e*x)^2)/(5*e^5*(d^2 - e^2*x^2)^(5/2)) + (17*d^2*(d - e*x))/(15*e^5*(d^2 - e^2*x^2)^(3/2)) - (2*(15*d - 13*e*x))/(15*e^5*Sqrt[d^2 - e^2*x^2]) - ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e^5","A",7,6,27,0.2222,1,"{852, 1635, 1814, 12, 217, 203}"
172,1,99,0,0.2041074,"\int \frac{x^3}{(d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[x^3/((d + e*x)^2*(d^2 - e^2*x^2)^(3/2)),x]","\frac{d^2 (d-e x)^2}{5 e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{4 d (d-e x)}{5 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{5 d-2 e x}{5 d e^4 \sqrt{d^2-e^2 x^2}}","\frac{d^2 (d-e x)^2}{5 e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{4 d (d-e x)}{5 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{5 d-2 e x}{5 d e^4 \sqrt{d^2-e^2 x^2}}",1,"(d^2*(d - e*x)^2)/(5*e^4*(d^2 - e^2*x^2)^(5/2)) - (4*d*(d - e*x))/(5*e^4*(d^2 - e^2*x^2)^(3/2)) + (5*d - 2*e*x)/(5*d*e^4*Sqrt[d^2 - e^2*x^2])","A",4,3,27,0.1111,1,"{852, 1635, 637}"
173,1,89,0,0.1419294,"\int \frac{x^2}{(d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[x^2/((d + e*x)^2*(d^2 - e^2*x^2)^(3/2)),x]","-\frac{d (d-e x)^2}{5 e^3 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{7 (d-e x)}{15 e^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x}{15 d^2 e^2 \sqrt{d^2-e^2 x^2}}","-\frac{d}{5 e^3 (d+e x)^2 \sqrt{d^2-e^2 x^2}}+\frac{7}{15 e^3 (d+e x) \sqrt{d^2-e^2 x^2}}+\frac{x}{15 d^2 e^2 \sqrt{d^2-e^2 x^2}}",1,"-(d*(d - e*x)^2)/(5*e^3*(d^2 - e^2*x^2)^(5/2)) + (7*(d - e*x))/(15*e^3*(d^2 - e^2*x^2)^(3/2)) + x/(15*d^2*e^2*Sqrt[d^2 - e^2*x^2])","A",4,4,27,0.1481,1,"{852, 1635, 778, 191}"
174,1,91,0,0.0364116,"\int \frac{x}{(d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[x/((d + e*x)^2*(d^2 - e^2*x^2)^(3/2)),x]","\frac{4 x}{15 d^3 e \sqrt{d^2-e^2 x^2}}-\frac{2}{15 d e^2 (d+e x) \sqrt{d^2-e^2 x^2}}+\frac{1}{5 e^2 (d+e x)^2 \sqrt{d^2-e^2 x^2}}","\frac{4 x}{15 d^3 e \sqrt{d^2-e^2 x^2}}-\frac{2}{15 d e^2 (d+e x) \sqrt{d^2-e^2 x^2}}+\frac{1}{5 e^2 (d+e x)^2 \sqrt{d^2-e^2 x^2}}",1,"(4*x)/(15*d^3*e*Sqrt[d^2 - e^2*x^2]) + 1/(5*e^2*(d + e*x)^2*Sqrt[d^2 - e^2*x^2]) - 2/(15*d*e^2*(d + e*x)*Sqrt[d^2 - e^2*x^2])","A",3,3,25,0.1200,1,"{793, 659, 191}"
175,1,91,0,0.0311912,"\int \frac{1}{(d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^2*(d^2 - e^2*x^2)^(3/2)),x]","\frac{2 x}{5 d^4 \sqrt{d^2-e^2 x^2}}-\frac{1}{5 d^2 e (d+e x) \sqrt{d^2-e^2 x^2}}-\frac{1}{5 d e (d+e x)^2 \sqrt{d^2-e^2 x^2}}","\frac{2 x}{5 d^4 \sqrt{d^2-e^2 x^2}}-\frac{1}{5 d^2 e (d+e x) \sqrt{d^2-e^2 x^2}}-\frac{1}{5 d e (d+e x)^2 \sqrt{d^2-e^2 x^2}}",1,"(2*x)/(5*d^4*Sqrt[d^2 - e^2*x^2]) - 1/(5*d*e*(d + e*x)^2*Sqrt[d^2 - e^2*x^2]) - 1/(5*d^2*e*(d + e*x)*Sqrt[d^2 - e^2*x^2])","A",3,2,24,0.08333,1,"{659, 191}"
176,1,118,0,0.1776829,"\int \frac{1}{x (d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[1/(x*(d + e*x)^2*(d^2 - e^2*x^2)^(3/2)),x]","\frac{15 d-16 e x}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{5 d-8 e x}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (d-e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}","\frac{15 d-16 e x}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{5 d-8 e x}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (d-e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}",1,"(2*(d - e*x))/(5*d*(d^2 - e^2*x^2)^(5/2)) + (5*d - 8*e*x)/(15*d^3*(d^2 - e^2*x^2)^(3/2)) + (15*d - 16*e*x)/(15*d^5*Sqrt[d^2 - e^2*x^2]) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^5","A",8,7,27,0.2593,1,"{852, 1805, 823, 12, 266, 63, 208}"
177,1,146,0,0.3002158,"\int \frac{1}{x^2 (d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[1/(x^2*(d + e*x)^2*(d^2 - e^2*x^2)^(3/2)),x]","-\frac{e (30 d-41 e x)}{15 d^6 \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^6 x}-\frac{e (10 d-13 e x)}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 e (d-e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{2 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}","-\frac{e (30 d-41 e x)}{15 d^6 \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^6 x}-\frac{e (10 d-13 e x)}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 e (d-e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{2 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}",1,"(-2*e*(d - e*x))/(5*d^2*(d^2 - e^2*x^2)^(5/2)) - (e*(10*d - 13*e*x))/(15*d^4*(d^2 - e^2*x^2)^(3/2)) - (e*(30*d - 41*e*x))/(15*d^6*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(d^6*x) + (2*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^6","A",8,6,27,0.2222,1,"{852, 1805, 807, 266, 63, 208}"
178,1,183,0,0.3746151,"\int \frac{1}{x^3 (d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[1/(x^3*(d + e*x)^2*(d^2 - e^2*x^2)^(3/2)),x]","\frac{2 e^2 (10 d-11 e x)}{5 d^7 \sqrt{d^2-e^2 x^2}}+\frac{e^2 (5 d-6 e x)}{5 d^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 e^2 (d-e x)}{5 d^3 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{2 e \sqrt{d^2-e^2 x^2}}{d^7 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^6 x^2}-\frac{9 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^7}","\frac{2 e^2 (10 d-11 e x)}{5 d^7 \sqrt{d^2-e^2 x^2}}+\frac{e^2 (5 d-6 e x)}{5 d^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 e^2 (d-e x)}{5 d^3 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{2 e \sqrt{d^2-e^2 x^2}}{d^7 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^6 x^2}-\frac{9 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^7}",1,"(2*e^2*(d - e*x))/(5*d^3*(d^2 - e^2*x^2)^(5/2)) + (e^2*(5*d - 6*e*x))/(5*d^5*(d^2 - e^2*x^2)^(3/2)) + (2*e^2*(10*d - 11*e*x))/(5*d^7*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(2*d^6*x^2) + (2*e*Sqrt[d^2 - e^2*x^2])/(d^7*x) - (9*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^7)","A",9,7,27,0.2593,1,"{852, 1805, 1807, 807, 266, 63, 208}"
179,1,177,0,0.4393366,"\int \frac{x^5}{(d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[x^5/((d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","\frac{d^4 (d-e x)^3}{5 e^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{23 d^3 (d-e x)^2}{15 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{127 d^2 (d-e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{3 d \sqrt{d^2-e^2 x^2}}{e^6}-\frac{x \sqrt{d^2-e^2 x^2}}{2 e^5}+\frac{13 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^6}","\frac{d^4 (d-e x)^3}{5 e^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{23 d^3 (d-e x)^2}{15 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{127 d^2 (d-e x)}{15 e^6 \sqrt{d^2-e^2 x^2}}+\frac{3 d \sqrt{d^2-e^2 x^2}}{e^6}-\frac{x \sqrt{d^2-e^2 x^2}}{2 e^5}+\frac{13 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^6}",1,"(d^4*(d - e*x)^3)/(5*e^6*(d^2 - e^2*x^2)^(5/2)) - (23*d^3*(d - e*x)^2)/(15*e^6*(d^2 - e^2*x^2)^(3/2)) + (127*d^2*(d - e*x))/(15*e^6*Sqrt[d^2 - e^2*x^2]) + (3*d*Sqrt[d^2 - e^2*x^2])/e^6 - (x*Sqrt[d^2 - e^2*x^2])/(2*e^5) + (13*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^6)","A",8,6,27,0.2222,1,"{852, 1635, 1815, 641, 217, 203}"
180,1,146,0,0.3650276,"\int \frac{x^4}{(d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[x^4/((d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","-\frac{d^3 (d-e x)^3}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{6 d^2 (d-e x)^2}{5 e^5 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{24 d (d-e x)}{5 e^5 \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{e^5}-\frac{3 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}","-\frac{d^3 (d-e x)^3}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{6 d^2 (d-e x)^2}{5 e^5 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{24 d (d-e x)}{5 e^5 \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{e^5}-\frac{3 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}",1,"-(d^3*(d - e*x)^3)/(5*e^5*(d^2 - e^2*x^2)^(5/2)) + (6*d^2*(d - e*x)^2)/(5*e^5*(d^2 - e^2*x^2)^(3/2)) - (24*d*(d - e*x))/(5*e^5*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/e^5 - (3*d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^5","A",7,5,27,0.1852,1,"{852, 1635, 641, 217, 203}"
181,1,120,0,0.261021,"\int \frac{x^3}{(d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[x^3/((d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","\frac{d^2 (d-e x)^3}{5 e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{13 d (d-e x)^2}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{32 (d-e x)}{15 e^4 \sqrt{d^2-e^2 x^2}}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}","\frac{d^2 (d-e x)^3}{5 e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{13 d (d-e x)^2}{15 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{32 (d-e x)}{15 e^4 \sqrt{d^2-e^2 x^2}}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}",1,"(d^2*(d - e*x)^3)/(5*e^4*(d^2 - e^2*x^2)^(5/2)) - (13*d*(d - e*x)^2)/(15*e^4*(d^2 - e^2*x^2)^(3/2)) + (32*(d - e*x))/(15*e^4*Sqrt[d^2 - e^2*x^2]) + ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e^4","A",6,5,27,0.1852,1,"{852, 1635, 778, 217, 203}"
182,1,95,0,0.128102,"\int \frac{x^2}{(d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[x^2/((d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","-\frac{d \sqrt{d^2-e^2 x^2}}{5 e^3 (d+e x)^3}+\frac{8 \sqrt{d^2-e^2 x^2}}{15 e^3 (d+e x)^2}-\frac{7 \sqrt{d^2-e^2 x^2}}{15 d e^3 (d+e x)}","-\frac{d \sqrt{d^2-e^2 x^2}}{5 e^3 (d+e x)^3}+\frac{8 \sqrt{d^2-e^2 x^2}}{15 e^3 (d+e x)^2}-\frac{7 \sqrt{d^2-e^2 x^2}}{15 d e^3 (d+e x)}",1,"-(d*Sqrt[d^2 - e^2*x^2])/(5*e^3*(d + e*x)^3) + (8*Sqrt[d^2 - e^2*x^2])/(15*e^3*(d + e*x)^2) - (7*Sqrt[d^2 - e^2*x^2])/(15*d*e^3*(d + e*x))","A",4,4,27,0.1481,1,"{1639, 793, 659, 651}"
183,1,97,0,0.0446837,"\int \frac{x}{(d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[x/((d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","-\frac{\sqrt{d^2-e^2 x^2}}{5 d^2 e^2 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2}}{5 d e^2 (d+e x)^2}+\frac{\sqrt{d^2-e^2 x^2}}{5 e^2 (d+e x)^3}","-\frac{\sqrt{d^2-e^2 x^2}}{5 d^2 e^2 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2}}{5 d e^2 (d+e x)^2}+\frac{\sqrt{d^2-e^2 x^2}}{5 e^2 (d+e x)^3}",1,"Sqrt[d^2 - e^2*x^2]/(5*e^2*(d + e*x)^3) - Sqrt[d^2 - e^2*x^2]/(5*d*e^2*(d + e*x)^2) - Sqrt[d^2 - e^2*x^2]/(5*d^2*e^2*(d + e*x))","A",3,3,25,0.1200,1,"{793, 659, 651}"
184,1,100,0,0.0367133,"\int \frac{1}{(d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[1/((d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","-\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^3 e (d+e x)}-\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^2 e (d+e x)^2}-\frac{\sqrt{d^2-e^2 x^2}}{5 d e (d+e x)^3}","-\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^3 e (d+e x)}-\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^2 e (d+e x)^2}-\frac{\sqrt{d^2-e^2 x^2}}{5 d e (d+e x)^3}",1,"-Sqrt[d^2 - e^2*x^2]/(5*d*e*(d + e*x)^3) - (2*Sqrt[d^2 - e^2*x^2])/(15*d^2*e*(d + e*x)^2) - (2*Sqrt[d^2 - e^2*x^2])/(15*d^3*e*(d + e*x))","A",3,2,24,0.08333,1,"{659, 651}"
185,1,115,0,0.1789619,"\int \frac{1}{x (d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[1/(x*(d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","\frac{15 d-22 e x}{15 d^4 \sqrt{d^2-e^2 x^2}}+\frac{5 d-11 e x}{15 d^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{4 (d-e x)}{5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^4}","\frac{15 d-22 e x}{15 d^4 \sqrt{d^2-e^2 x^2}}+\frac{5 d-11 e x}{15 d^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{4 (d-e x)}{5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^4}",1,"(4*(d - e*x))/(5*(d^2 - e^2*x^2)^(5/2)) + (5*d - 11*e*x)/(15*d^2*(d^2 - e^2*x^2)^(3/2)) + (15*d - 22*e*x)/(15*d^4*Sqrt[d^2 - e^2*x^2]) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^4","A",8,7,27,0.2593,1,"{852, 1805, 823, 12, 266, 63, 208}"
186,1,146,0,0.3045728,"\int \frac{1}{x^2 (d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[1/(x^2*(d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","-\frac{e (15 d-19 e x)}{5 d^5 \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^5 x}-\frac{e (5 d-7 e x)}{5 d^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{4 e (d-e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}+\frac{3 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}","-\frac{e (15 d-19 e x)}{5 d^5 \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^5 x}-\frac{e (5 d-7 e x)}{5 d^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{4 e (d-e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}+\frac{3 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^5}",1,"(-4*e*(d - e*x))/(5*d*(d^2 - e^2*x^2)^(5/2)) - (e*(5*d - 7*e*x))/(5*d^3*(d^2 - e^2*x^2)^(3/2)) - (e*(15*d - 19*e*x))/(5*d^5*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(d^5*x) + (3*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^5","A",8,6,27,0.2222,1,"{852, 1805, 807, 266, 63, 208}"
187,1,183,0,0.380112,"\int \frac{1}{x^3 (d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[1/(x^3*(d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","\frac{e^2 (90 d-107 e x)}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{e^2 (25 d-31 e x)}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{4 e^2 (d-e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{3 e \sqrt{d^2-e^2 x^2}}{d^6 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^5 x^2}-\frac{13 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^6}","\frac{e^2 (90 d-107 e x)}{15 d^6 \sqrt{d^2-e^2 x^2}}+\frac{e^2 (25 d-31 e x)}{15 d^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{4 e^2 (d-e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{3 e \sqrt{d^2-e^2 x^2}}{d^6 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^5 x^2}-\frac{13 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^6}",1,"(4*e^2*(d - e*x))/(5*d^2*(d^2 - e^2*x^2)^(5/2)) + (e^2*(25*d - 31*e*x))/(15*d^4*(d^2 - e^2*x^2)^(3/2)) + (e^2*(90*d - 107*e*x))/(15*d^6*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(2*d^5*x^2) + (3*e*Sqrt[d^2 - e^2*x^2])/(d^6*x) - (13*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^6)","A",9,7,27,0.2593,1,"{852, 1805, 1807, 807, 266, 63, 208}"
188,1,204,0,0.5932063,"\int \frac{x^5 \sqrt{d^2-e^2 x^2}}{(d+e x)^4} \, dx","Int[(x^5*Sqrt[d^2 - e^2*x^2])/(d + e*x)^4,x]","\frac{d^4 (d-e x)^4}{5 e^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8 d^3 (d-e x)^3}{5 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{10 d^2 (d-e x)^2}{e^6 \sqrt{d^2-e^2 x^2}}+\frac{x^2 \sqrt{d^2-e^2 x^2}}{3 e^4}-\frac{2 d x \sqrt{d^2-e^2 x^2}}{e^5}+\frac{59 d^2 \sqrt{d^2-e^2 x^2}}{3 e^6}+\frac{18 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^6}","\frac{d^4 (d-e x)^4}{5 e^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8 d^3 (d-e x)^3}{5 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{10 d^2 (d-e x)^2}{e^6 \sqrt{d^2-e^2 x^2}}+\frac{x^2 \sqrt{d^2-e^2 x^2}}{3 e^4}-\frac{2 d x \sqrt{d^2-e^2 x^2}}{e^5}+\frac{59 d^2 \sqrt{d^2-e^2 x^2}}{3 e^6}+\frac{18 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^6}",1,"(d^4*(d - e*x)^4)/(5*e^6*(d^2 - e^2*x^2)^(5/2)) - (8*d^3*(d - e*x)^3)/(5*e^6*(d^2 - e^2*x^2)^(3/2)) + (10*d^2*(d - e*x)^2)/(e^6*Sqrt[d^2 - e^2*x^2]) + (59*d^2*Sqrt[d^2 - e^2*x^2])/(3*e^6) - (2*d*x*Sqrt[d^2 - e^2*x^2])/e^5 + (x^2*Sqrt[d^2 - e^2*x^2])/(3*e^4) + (18*d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^6","A",9,6,27,0.2222,1,"{852, 1635, 1815, 641, 217, 203}"
189,1,160,0,0.4151249,"\int \frac{x^4 \sqrt{d^2-e^2 x^2}}{(d+e x)^4} \, dx","Int[(x^4*Sqrt[d^2 - e^2*x^2])/(d + e*x)^4,x]","-\frac{d^3 (d-e x)^4}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{19 d^2 (d-e x)^3}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{6 d (d-e x)^2}{e^5 \sqrt{d^2-e^2 x^2}}-\frac{(20 d-e x) \sqrt{d^2-e^2 x^2}}{2 e^5}-\frac{19 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^5}","-\frac{d^3 (d-e x)^4}{5 e^5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{19 d^2 (d-e x)^3}{15 e^5 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{6 d (d-e x)^2}{e^5 \sqrt{d^2-e^2 x^2}}-\frac{(20 d-e x) \sqrt{d^2-e^2 x^2}}{2 e^5}-\frac{19 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^5}",1,"-(d^3*(d - e*x)^4)/(5*e^5*(d^2 - e^2*x^2)^(5/2)) + (19*d^2*(d - e*x)^3)/(15*e^5*(d^2 - e^2*x^2)^(3/2)) - (6*d*(d - e*x)^2)/(e^5*Sqrt[d^2 - e^2*x^2]) - ((20*d - e*x)*Sqrt[d^2 - e^2*x^2])/(2*e^5) - (19*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^5)","A",7,5,27,0.1852,1,"{852, 1635, 780, 217, 203}"
190,1,148,0,0.2460611,"\int \frac{x^3 \sqrt{d^2-e^2 x^2}}{(d+e x)^4} \, dx","Int[(x^3*Sqrt[d^2 - e^2*x^2])/(d + e*x)^4,x]","\frac{d^2 \left(d^2-e^2 x^2\right)^{3/2}}{5 e^4 (d+e x)^4}-\frac{14 d \left(d^2-e^2 x^2\right)^{3/2}}{15 e^4 (d+e x)^3}+\frac{8 d \sqrt{d^2-e^2 x^2}}{e^4 (d+e x)}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{e^4 (d+e x)^2}+\frac{4 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}","\frac{d^2 \left(d^2-e^2 x^2\right)^{3/2}}{5 e^4 (d+e x)^4}-\frac{14 d \left(d^2-e^2 x^2\right)^{3/2}}{15 e^4 (d+e x)^3}+\frac{8 d \sqrt{d^2-e^2 x^2}}{e^4 (d+e x)}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{e^4 (d+e x)^2}+\frac{4 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}",1,"(8*d*Sqrt[d^2 - e^2*x^2])/(e^4*(d + e*x)) + (d^2*(d^2 - e^2*x^2)^(3/2))/(5*e^4*(d + e*x)^4) - (14*d*(d^2 - e^2*x^2)^(3/2))/(15*e^4*(d + e*x)^3) - (d^2 - e^2*x^2)^(3/2)/(e^4*(d + e*x)^2) + (4*d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^4","A",9,7,27,0.2593,1,"{1639, 1637, 659, 651, 663, 217, 203}"
191,1,115,0,0.1466867,"\int \frac{x^2 \sqrt{d^2-e^2 x^2}}{(d+e x)^4} \, dx","Int[(x^2*Sqrt[d^2 - e^2*x^2])/(d + e*x)^4,x]","\frac{3 \left(d^2-e^2 x^2\right)^{3/2}}{5 e^3 (d+e x)^3}-\frac{d \left(d^2-e^2 x^2\right)^{3/2}}{5 e^3 (d+e x)^4}-\frac{2 \sqrt{d^2-e^2 x^2}}{e^3 (d+e x)}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}","\frac{3 \left(d^2-e^2 x^2\right)^{3/2}}{5 e^3 (d+e x)^3}-\frac{d \left(d^2-e^2 x^2\right)^{3/2}}{5 e^3 (d+e x)^4}-\frac{2 \sqrt{d^2-e^2 x^2}}{e^3 (d+e x)}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}",1,"(-2*Sqrt[d^2 - e^2*x^2])/(e^3*(d + e*x)) - (d*(d^2 - e^2*x^2)^(3/2))/(5*e^3*(d + e*x)^4) + (3*(d^2 - e^2*x^2)^(3/2))/(5*e^3*(d + e*x)^3) - ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e^3","A",8,6,27,0.2222,1,"{1637, 659, 651, 663, 217, 203}"
192,1,64,0,0.0274207,"\int \frac{x \sqrt{d^2-e^2 x^2}}{(d+e x)^4} \, dx","Int[(x*Sqrt[d^2 - e^2*x^2])/(d + e*x)^4,x]","\frac{\left(d^2-e^2 x^2\right)^{3/2}}{5 e^2 (d+e x)^4}-\frac{4 \left(d^2-e^2 x^2\right)^{3/2}}{15 d e^2 (d+e x)^3}","\frac{\left(d^2-e^2 x^2\right)^{3/2}}{5 e^2 (d+e x)^4}-\frac{4 \left(d^2-e^2 x^2\right)^{3/2}}{15 d e^2 (d+e x)^3}",1,"(d^2 - e^2*x^2)^(3/2)/(5*e^2*(d + e*x)^4) - (4*(d^2 - e^2*x^2)^(3/2))/(15*d*e^2*(d + e*x)^3)","A",2,2,25,0.08000,1,"{793, 651}"
193,1,67,0,0.0236743,"\int \frac{\sqrt{d^2-e^2 x^2}}{(d+e x)^4} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(d + e*x)^4,x]","-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{15 d^2 e (d+e x)^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{5 d e (d+e x)^4}","-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{15 d^2 e (d+e x)^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2}}{5 d e (d+e x)^4}",1,"-(d^2 - e^2*x^2)^(3/2)/(5*d*e*(d + e*x)^4) - (d^2 - e^2*x^2)^(3/2)/(15*d^2*e*(d + e*x)^3)","A",2,2,24,0.08333,1,"{659, 651}"
194,1,110,0,0.2197634,"\int \frac{\sqrt{d^2-e^2 x^2}}{x (d+e x)^4} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(x*(d + e*x)^4),x]","-\frac{4 e x}{5 d \left(d^2-e^2 x^2\right)^{3/2}}+\frac{5 d-8 e x}{5 d^3 \sqrt{d^2-e^2 x^2}}+\frac{8 d (d-e x)}{5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^3}","-\frac{4 e x}{5 d \left(d^2-e^2 x^2\right)^{3/2}}+\frac{5 d-8 e x}{5 d^3 \sqrt{d^2-e^2 x^2}}+\frac{8 d (d-e x)}{5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^3}",1,"(8*d*(d - e*x))/(5*(d^2 - e^2*x^2)^(5/2)) - (4*e*x)/(5*d*(d^2 - e^2*x^2)^(3/2)) + (5*d - 8*e*x)/(5*d^3*Sqrt[d^2 - e^2*x^2]) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^3","A",8,7,27,0.2593,1,"{852, 1805, 823, 12, 266, 63, 208}"
195,1,143,0,0.3058048,"\int \frac{\sqrt{d^2-e^2 x^2}}{x^2 (d+e x)^4} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(x^2*(d + e*x)^4),x]","-\frac{e (60 d-79 e x)}{15 d^4 \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^4 x}-\frac{4 e (5 d-8 e x)}{15 d^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{8 e (d-e x)}{5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{4 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^4}","-\frac{e (60 d-79 e x)}{15 d^4 \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^4 x}-\frac{4 e (5 d-8 e x)}{15 d^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{8 e (d-e x)}{5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{4 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^4}",1,"(-8*e*(d - e*x))/(5*(d^2 - e^2*x^2)^(5/2)) - (4*e*(5*d - 8*e*x))/(15*d^2*(d^2 - e^2*x^2)^(3/2)) - (e*(60*d - 79*e*x))/(15*d^4*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(d^4*x) + (4*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^4","A",8,6,27,0.2222,1,"{852, 1805, 807, 266, 63, 208}"
196,1,183,0,0.3915618,"\int \frac{\sqrt{d^2-e^2 x^2}}{x^3 (d+e x)^4} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(x^3*(d + e*x)^4),x]","\frac{e^2 (135 d-164 e x)}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{4 e^2 (10 d-13 e x)}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{8 e^2 (d-e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}+\frac{4 e \sqrt{d^2-e^2 x^2}}{d^5 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^4 x^2}-\frac{19 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^5}","\frac{e^2 (135 d-164 e x)}{15 d^5 \sqrt{d^2-e^2 x^2}}+\frac{4 e^2 (10 d-13 e x)}{15 d^3 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{8 e^2 (d-e x)}{5 d \left(d^2-e^2 x^2\right)^{5/2}}+\frac{4 e \sqrt{d^2-e^2 x^2}}{d^5 x}-\frac{\sqrt{d^2-e^2 x^2}}{2 d^4 x^2}-\frac{19 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^5}",1,"(8*e^2*(d - e*x))/(5*d*(d^2 - e^2*x^2)^(5/2)) + (4*e^2*(10*d - 13*e*x))/(15*d^3*(d^2 - e^2*x^2)^(3/2)) + (e^2*(135*d - 164*e*x))/(15*d^5*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(2*d^4*x^2) + (4*e*Sqrt[d^2 - e^2*x^2])/(d^5*x) - (19*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^5)","A",9,7,27,0.2593,1,"{852, 1805, 1807, 807, 266, 63, 208}"
197,1,210,0,0.4941225,"\int \frac{\sqrt{d^2-e^2 x^2}}{x^4 (d+e x)^4} \, dx","Int[Sqrt[d^2 - e^2*x^2]/(x^4*(d + e*x)^4),x]","-\frac{e^3 (80 d-93 e x)}{5 d^6 \sqrt{d^2-e^2 x^2}}-\frac{4 e^3 (5 d-6 e x)}{5 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{8 e^3 (d-e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{29 e^2 \sqrt{d^2-e^2 x^2}}{3 d^6 x}+\frac{2 e \sqrt{d^2-e^2 x^2}}{d^5 x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 d^4 x^3}+\frac{18 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}","-\frac{e^3 (80 d-93 e x)}{5 d^6 \sqrt{d^2-e^2 x^2}}-\frac{4 e^3 (5 d-6 e x)}{5 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{8 e^3 (d-e x)}{5 d^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{29 e^2 \sqrt{d^2-e^2 x^2}}{3 d^6 x}+\frac{2 e \sqrt{d^2-e^2 x^2}}{d^5 x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 d^4 x^3}+\frac{18 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^6}",1,"(-8*e^3*(d - e*x))/(5*d^2*(d^2 - e^2*x^2)^(5/2)) - (4*e^3*(5*d - 6*e*x))/(5*d^4*(d^2 - e^2*x^2)^(3/2)) - (e^3*(80*d - 93*e*x))/(5*d^6*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(3*d^4*x^3) + (2*e*Sqrt[d^2 - e^2*x^2])/(d^5*x^2) - (29*e^2*Sqrt[d^2 - e^2*x^2])/(3*d^6*x) + (18*e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^6","A",10,7,27,0.2593,1,"{852, 1805, 1807, 807, 266, 63, 208}"
198,1,252,0,0.6625743,"\int \frac{x^5 \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(x^5*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^4,x]","\frac{515 d^6 \sqrt{d^2-e^2 x^2}}{21 e^6}-\frac{49 d^5 x \sqrt{d^2-e^2 x^2}}{4 e^5}+\frac{121 d^4 x^2 \sqrt{d^2-e^2 x^2}}{21 e^4}+\frac{d^4 (d-e x)^4}{e^6 \sqrt{d^2-e^2 x^2}}-\frac{17 d^3 x^3 \sqrt{d^2-e^2 x^2}}{6 e^3}+\frac{11 d^2 x^4 \sqrt{d^2-e^2 x^2}}{7 e^2}-\frac{2 d x^5 \sqrt{d^2-e^2 x^2}}{3 e}+\frac{1}{7} x^6 \sqrt{d^2-e^2 x^2}+\frac{65 d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{4 e^6}","\frac{515 d^6 \sqrt{d^2-e^2 x^2}}{21 e^6}-\frac{49 d^5 x \sqrt{d^2-e^2 x^2}}{4 e^5}+\frac{121 d^4 x^2 \sqrt{d^2-e^2 x^2}}{21 e^4}+\frac{d^4 (d-e x)^4}{e^6 \sqrt{d^2-e^2 x^2}}-\frac{17 d^3 x^3 \sqrt{d^2-e^2 x^2}}{6 e^3}+\frac{11 d^2 x^4 \sqrt{d^2-e^2 x^2}}{7 e^2}-\frac{2 d x^5 \sqrt{d^2-e^2 x^2}}{3 e}+\frac{1}{7} x^6 \sqrt{d^2-e^2 x^2}+\frac{65 d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{4 e^6}",1,"(d^4*(d - e*x)^4)/(e^6*Sqrt[d^2 - e^2*x^2]) + (515*d^6*Sqrt[d^2 - e^2*x^2])/(21*e^6) - (49*d^5*x*Sqrt[d^2 - e^2*x^2])/(4*e^5) + (121*d^4*x^2*Sqrt[d^2 - e^2*x^2])/(21*e^4) - (17*d^3*x^3*Sqrt[d^2 - e^2*x^2])/(6*e^3) + (11*d^2*x^4*Sqrt[d^2 - e^2*x^2])/(7*e^2) - (2*d*x^5*Sqrt[d^2 - e^2*x^2])/(3*e) + (x^6*Sqrt[d^2 - e^2*x^2])/7 + (65*d^7*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(4*e^6)","A",11,6,27,0.2222,1,"{852, 1635, 1815, 641, 217, 203}"
199,1,224,0,0.5339503,"\int \frac{x^4 \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(x^4*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^4,x]","-\frac{337 d^5 \sqrt{d^2-e^2 x^2}}{15 e^5}+\frac{175 d^4 x \sqrt{d^2-e^2 x^2}}{16 e^4}-\frac{71 d^3 x^2 \sqrt{d^2-e^2 x^2}}{15 e^3}-\frac{d^3 (d-e x)^4}{e^5 \sqrt{d^2-e^2 x^2}}+\frac{47 d^2 x^3 \sqrt{d^2-e^2 x^2}}{24 e^2}-\frac{4 d x^4 \sqrt{d^2-e^2 x^2}}{5 e}+\frac{1}{6} x^5 \sqrt{d^2-e^2 x^2}-\frac{239 d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^5}","-\frac{337 d^5 \sqrt{d^2-e^2 x^2}}{15 e^5}+\frac{175 d^4 x \sqrt{d^2-e^2 x^2}}{16 e^4}-\frac{71 d^3 x^2 \sqrt{d^2-e^2 x^2}}{15 e^3}-\frac{d^3 (d-e x)^4}{e^5 \sqrt{d^2-e^2 x^2}}+\frac{47 d^2 x^3 \sqrt{d^2-e^2 x^2}}{24 e^2}-\frac{4 d x^4 \sqrt{d^2-e^2 x^2}}{5 e}+\frac{1}{6} x^5 \sqrt{d^2-e^2 x^2}-\frac{239 d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e^5}",1,"-((d^3*(d - e*x)^4)/(e^5*Sqrt[d^2 - e^2*x^2])) - (337*d^5*Sqrt[d^2 - e^2*x^2])/(15*e^5) + (175*d^4*x*Sqrt[d^2 - e^2*x^2])/(16*e^4) - (71*d^3*x^2*Sqrt[d^2 - e^2*x^2])/(15*e^3) + (47*d^2*x^3*Sqrt[d^2 - e^2*x^2])/(24*e^2) - (4*d*x^4*Sqrt[d^2 - e^2*x^2])/(5*e) + (x^5*Sqrt[d^2 - e^2*x^2])/6 - (239*d^6*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^5)","A",10,6,27,0.2222,1,"{852, 1635, 1815, 641, 217, 203}"
200,1,192,0,0.4352683,"\int \frac{x^3 \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(x^3*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^4,x]","\frac{101 d^4 \sqrt{d^2-e^2 x^2}}{5 e^4}-\frac{19 d^3 x \sqrt{d^2-e^2 x^2}}{2 e^3}+\frac{18 d^2 x^2 \sqrt{d^2-e^2 x^2}}{5 e^2}+\frac{d^2 (d-e x)^4}{e^4 \sqrt{d^2-e^2 x^2}}-\frac{d x^3 \sqrt{d^2-e^2 x^2}}{e}+\frac{1}{5} x^4 \sqrt{d^2-e^2 x^2}+\frac{27 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^4}","\frac{101 d^4 \sqrt{d^2-e^2 x^2}}{5 e^4}-\frac{19 d^3 x \sqrt{d^2-e^2 x^2}}{2 e^3}+\frac{18 d^2 x^2 \sqrt{d^2-e^2 x^2}}{5 e^2}+\frac{d^2 (d-e x)^4}{e^4 \sqrt{d^2-e^2 x^2}}-\frac{d x^3 \sqrt{d^2-e^2 x^2}}{e}+\frac{1}{5} x^4 \sqrt{d^2-e^2 x^2}+\frac{27 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^4}",1,"(d^2*(d - e*x)^4)/(e^4*Sqrt[d^2 - e^2*x^2]) + (101*d^4*Sqrt[d^2 - e^2*x^2])/(5*e^4) - (19*d^3*x*Sqrt[d^2 - e^2*x^2])/(2*e^3) + (18*d^2*x^2*Sqrt[d^2 - e^2*x^2])/(5*e^2) - (d*x^3*Sqrt[d^2 - e^2*x^2])/e + (x^4*Sqrt[d^2 - e^2*x^2])/5 + (27*d^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^4)","A",9,6,27,0.2222,1,"{852, 1635, 1815, 641, 217, 203}"
201,1,182,0,0.2194325,"\int \frac{x^2 \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(x^2*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^4,x]","-\frac{95 d^3 \sqrt{d^2-e^2 x^2}}{8 e^3}-\frac{95 d^2 (d-e x) \sqrt{d^2-e^2 x^2}}{24 e^3}-\frac{19 d (d-e x)^2 \sqrt{d^2-e^2 x^2}}{12 e^3}-\frac{d (d-e x)^4}{e^3 \sqrt{d^2-e^2 x^2}}-\frac{(d-e x)^3 \sqrt{d^2-e^2 x^2}}{4 e^3}-\frac{95 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}","-\frac{95 d^3 \sqrt{d^2-e^2 x^2}}{8 e^3}-\frac{95 d^2 (d-e x) \sqrt{d^2-e^2 x^2}}{24 e^3}-\frac{19 d (d-e x)^2 \sqrt{d^2-e^2 x^2}}{12 e^3}-\frac{d (d-e x)^4}{e^3 \sqrt{d^2-e^2 x^2}}-\frac{(d-e x)^3 \sqrt{d^2-e^2 x^2}}{4 e^3}-\frac{95 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}",1,"-((d*(d - e*x)^4)/(e^3*Sqrt[d^2 - e^2*x^2])) - (95*d^3*Sqrt[d^2 - e^2*x^2])/(8*e^3) - (95*d^2*(d - e*x)*Sqrt[d^2 - e^2*x^2])/(24*e^3) - (19*d*(d - e*x)^2*Sqrt[d^2 - e^2*x^2])/(12*e^3) - ((d - e*x)^3*Sqrt[d^2 - e^2*x^2])/(4*e^3) - (95*d^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^3)","A",8,7,27,0.2593,1,"{852, 1635, 795, 671, 641, 217, 203}"
202,1,130,0,0.0641239,"\int \frac{x \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(x*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^4,x]","\frac{\left(d^2-e^2 x^2\right)^{7/2}}{e^2 (d+e x)^4}+\frac{8 \left(d^2-e^2 x^2\right)^{5/2}}{e^2 (d+e x)^2}+\frac{20 \left(d^2-e^2 x^2\right)^{3/2}}{3 e^2}+\frac{10 d x \sqrt{d^2-e^2 x^2}}{e}+\frac{10 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^2}","\frac{\left(d^2-e^2 x^2\right)^{7/2}}{e^2 (d+e x)^4}+\frac{8 \left(d^2-e^2 x^2\right)^{5/2}}{e^2 (d+e x)^2}+\frac{20 \left(d^2-e^2 x^2\right)^{3/2}}{3 e^2}+\frac{10 d x \sqrt{d^2-e^2 x^2}}{e}+\frac{10 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^2}",1,"(10*d*x*Sqrt[d^2 - e^2*x^2])/e + (20*(d^2 - e^2*x^2)^(3/2))/(3*e^2) + (8*(d^2 - e^2*x^2)^(5/2))/(e^2*(d + e*x)^2) + (d^2 - e^2*x^2)^(7/2)/(e^2*(d + e*x)^4) + (10*d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^2","A",6,6,25,0.2400,1,"{793, 663, 665, 195, 217, 203}"
203,1,113,0,0.0480503,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(d + e*x)^4,x]","-\frac{2 \left(d^2-e^2 x^2\right)^{5/2}}{e (d+e x)^3}-\frac{5 \left(d^2-e^2 x^2\right)^{3/2}}{2 e (d+e x)}-\frac{15 d \sqrt{d^2-e^2 x^2}}{2 e}-\frac{15 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}","-\frac{2 \left(d^2-e^2 x^2\right)^{5/2}}{e (d+e x)^3}-\frac{5 \left(d^2-e^2 x^2\right)^{3/2}}{2 e (d+e x)}-\frac{15 d \sqrt{d^2-e^2 x^2}}{2 e}-\frac{15 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}",1,"(-15*d*Sqrt[d^2 - e^2*x^2])/(2*e) - (5*(d^2 - e^2*x^2)^(3/2))/(2*e*(d + e*x)) - (2*(d^2 - e^2*x^2)^(5/2))/(e*(d + e*x)^3) - (15*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e)","A",5,4,24,0.1667,1,"{663, 665, 217, 203}"
204,1,89,0,0.2113938,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x*(d + e*x)^4),x]","\frac{8 d (d-e x)}{\sqrt{d^2-e^2 x^2}}+\sqrt{d^2-e^2 x^2}+4 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","\frac{8 d (d-e x)}{\sqrt{d^2-e^2 x^2}}+\sqrt{d^2-e^2 x^2}+4 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)-d \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(8*d*(d - e*x))/Sqrt[d^2 - e^2*x^2] + Sqrt[d^2 - e^2*x^2] + 4*d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] - d*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",9,9,27,0.3333,1,"{852, 1805, 1809, 844, 217, 203, 266, 63, 208}"
205,1,94,0,0.2163307,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^2 (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^2*(d + e*x)^4),x]","-\frac{8 e (d-e x)}{\sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{x}-e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+4 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)","-\frac{8 e (d-e x)}{\sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{x}-e \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)+4 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)",1,"(-8*e*(d - e*x))/Sqrt[d^2 - e^2*x^2] - Sqrt[d^2 - e^2*x^2]/x - e*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]] + 4*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d]","A",9,9,27,0.3333,1,"{852, 1805, 1807, 844, 217, 203, 266, 63, 208}"
206,1,110,0,0.2151461,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^3 (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^3*(d + e*x)^4),x]","\frac{8 e^2 (d-e x)}{d \sqrt{d^2-e^2 x^2}}+\frac{4 e \sqrt{d^2-e^2 x^2}}{d x}-\frac{\sqrt{d^2-e^2 x^2}}{2 x^2}-\frac{15 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d}","\frac{8 e^2 (d-e x)}{d \sqrt{d^2-e^2 x^2}}+\frac{4 e \sqrt{d^2-e^2 x^2}}{d x}-\frac{\sqrt{d^2-e^2 x^2}}{2 x^2}-\frac{15 e^2 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d}",1,"(8*e^2*(d - e*x))/(d*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(2*x^2) + (4*e*Sqrt[d^2 - e^2*x^2])/(d*x) - (15*e^2*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d)","A",7,7,27,0.2593,1,"{852, 1805, 1807, 807, 266, 63, 208}"
207,1,137,0,0.2973468,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^4 (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^4*(d + e*x)^4),x]","-\frac{8 e^3 (d-e x)}{d^2 \sqrt{d^2-e^2 x^2}}-\frac{23 e^2 \sqrt{d^2-e^2 x^2}}{3 d^2 x}+\frac{2 e \sqrt{d^2-e^2 x^2}}{d x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 x^3}+\frac{10 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^2}","-\frac{8 e^3 (d-e x)}{d^2 \sqrt{d^2-e^2 x^2}}-\frac{23 e^2 \sqrt{d^2-e^2 x^2}}{3 d^2 x}+\frac{2 e \sqrt{d^2-e^2 x^2}}{d x^2}-\frac{\sqrt{d^2-e^2 x^2}}{3 x^3}+\frac{10 e^3 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^2}",1,"(-8*e^3*(d - e*x))/(d^2*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(3*x^3) + (2*e*Sqrt[d^2 - e^2*x^2])/(d*x^2) - (23*e^2*Sqrt[d^2 - e^2*x^2])/(3*d^2*x) + (10*e^3*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^2","A",8,7,27,0.2593,1,"{852, 1805, 1807, 807, 266, 63, 208}"
208,1,170,0,0.3944445,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^5 (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^5*(d + e*x)^4),x]","\frac{8 e^4 (d-e x)}{d^3 \sqrt{d^2-e^2 x^2}}+\frac{32 e^3 \sqrt{d^2-e^2 x^2}}{3 d^3 x}-\frac{31 e^2 \sqrt{d^2-e^2 x^2}}{8 d^2 x^2}+\frac{4 e \sqrt{d^2-e^2 x^2}}{3 d x^3}-\frac{\sqrt{d^2-e^2 x^2}}{4 x^4}-\frac{95 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d^3}","\frac{8 e^4 (d-e x)}{d^3 \sqrt{d^2-e^2 x^2}}+\frac{32 e^3 \sqrt{d^2-e^2 x^2}}{3 d^3 x}-\frac{31 e^2 \sqrt{d^2-e^2 x^2}}{8 d^2 x^2}+\frac{4 e \sqrt{d^2-e^2 x^2}}{3 d x^3}-\frac{\sqrt{d^2-e^2 x^2}}{4 x^4}-\frac{95 e^4 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{8 d^3}",1,"(8*e^4*(d - e*x))/(d^3*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(4*x^4) + (4*e*Sqrt[d^2 - e^2*x^2])/(3*d*x^3) - (31*e^2*Sqrt[d^2 - e^2*x^2])/(8*d^2*x^2) + (32*e^3*Sqrt[d^2 - e^2*x^2])/(3*d^3*x) - (95*e^4*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(8*d^3)","A",9,7,27,0.2593,1,"{852, 1805, 1807, 807, 266, 63, 208}"
209,1,196,0,0.5166218,"\int \frac{\left(d^2-e^2 x^2\right)^{5/2}}{x^6 (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^(5/2)/(x^6*(d + e*x)^4),x]","-\frac{8 e^5 (d-e x)}{d^4 \sqrt{d^2-e^2 x^2}}-\frac{66 e^4 \sqrt{d^2-e^2 x^2}}{5 d^4 x}+\frac{11 e^3 \sqrt{d^2-e^2 x^2}}{2 d^3 x^2}-\frac{13 e^2 \sqrt{d^2-e^2 x^2}}{5 d^2 x^3}+\frac{e \sqrt{d^2-e^2 x^2}}{d x^4}-\frac{\sqrt{d^2-e^2 x^2}}{5 x^5}+\frac{27 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^4}","-\frac{8 e^5 (d-e x)}{d^4 \sqrt{d^2-e^2 x^2}}-\frac{66 e^4 \sqrt{d^2-e^2 x^2}}{5 d^4 x}+\frac{11 e^3 \sqrt{d^2-e^2 x^2}}{2 d^3 x^2}-\frac{13 e^2 \sqrt{d^2-e^2 x^2}}{5 d^2 x^3}+\frac{e \sqrt{d^2-e^2 x^2}}{d x^4}-\frac{\sqrt{d^2-e^2 x^2}}{5 x^5}+\frac{27 e^5 \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{2 d^4}",1,"(-8*e^5*(d - e*x))/(d^4*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(5*x^5) + (e*Sqrt[d^2 - e^2*x^2])/(d*x^4) - (13*e^2*Sqrt[d^2 - e^2*x^2])/(5*d^2*x^3) + (11*e^3*Sqrt[d^2 - e^2*x^2])/(2*d^3*x^2) - (66*e^4*Sqrt[d^2 - e^2*x^2])/(5*d^4*x) + (27*e^5*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/(2*d^4)","A",10,7,27,0.2593,1,"{852, 1805, 1807, 807, 266, 63, 208}"
210,1,95,0,0.132497,"\int \frac{x^2 \sqrt{1-a^2 x^2}}{(1-a x)^4} \, dx","Int[(x^2*Sqrt[1 - a^2*x^2])/(1 - a*x)^4,x]","-\frac{3 \left(1-a^2 x^2\right)^{3/2}}{5 a^3 (1-a x)^3}+\frac{\left(1-a^2 x^2\right)^{3/2}}{5 a^3 (1-a x)^4}+\frac{2 \sqrt{1-a^2 x^2}}{a^3 (1-a x)}-\frac{\sin ^{-1}(a x)}{a^3}","-\frac{3 \left(1-a^2 x^2\right)^{3/2}}{5 a^3 (1-a x)^3}+\frac{\left(1-a^2 x^2\right)^{3/2}}{5 a^3 (1-a x)^4}+\frac{2 \sqrt{1-a^2 x^2}}{a^3 (1-a x)}-\frac{\sin ^{-1}(a x)}{a^3}",1,"(2*Sqrt[1 - a^2*x^2])/(a^3*(1 - a*x)) + (1 - a^2*x^2)^(3/2)/(5*a^3*(1 - a*x)^4) - (3*(1 - a^2*x^2)^(3/2))/(5*a^3*(1 - a*x)^3) - ArcSin[a*x]/a^3","A",7,5,26,0.1923,1,"{1637, 659, 651, 663, 216}"
211,1,88,0,0.1233957,"\int \frac{x^2 \sqrt{1-a^2 x^2}}{(1-a x)^5} \, dx","Int[(x^2*Sqrt[1 - a^2*x^2])/(1 - a*x)^5,x]","\frac{23 \left(1-a^2 x^2\right)^{3/2}}{105 a^3 (1-a x)^3}-\frac{12 \left(1-a^2 x^2\right)^{3/2}}{35 a^3 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a^3 (1-a x)^5}","\frac{23 \left(1-a^2 x^2\right)^{3/2}}{105 a^3 (1-a x)^3}-\frac{12 \left(1-a^2 x^2\right)^{3/2}}{35 a^3 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a^3 (1-a x)^5}",1,"(1 - a^2*x^2)^(3/2)/(7*a^3*(1 - a*x)^5) - (12*(1 - a^2*x^2)^(3/2))/(35*a^3*(1 - a*x)^4) + (23*(1 - a^2*x^2)^(3/2))/(105*a^3*(1 - a*x)^3)","A",4,4,26,0.1538,1,"{1639, 793, 659, 651}"
212,1,209,0,0.3146116,"\int \frac{x^3}{(d+e x)^4 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[x^3/((d + e*x)^4*(d^2 - e^2*x^2)^(7/2)),x]","\frac{d^2}{13 e^4 (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{30 d}{143 e^4 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{21}{143 e^4 (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{4}{1001 d e^4 (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{24 x}{5005 d^3 e^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{32 x}{5005 d^5 e^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{64 x}{5005 d^7 e^3 \sqrt{d^2-e^2 x^2}}","\frac{d^2}{13 e^4 (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{30 d}{143 e^4 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{21}{143 e^4 (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{4}{1001 d e^4 (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{24 x}{5005 d^3 e^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{32 x}{5005 d^5 e^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{64 x}{5005 d^7 e^3 \sqrt{d^2-e^2 x^2}}",1,"(-24*x)/(5005*d^3*e^3*(d^2 - e^2*x^2)^(5/2)) + d^2/(13*e^4*(d + e*x)^4*(d^2 - e^2*x^2)^(5/2)) - (30*d)/(143*e^4*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2)) + 21/(143*e^4*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) + 4/(1001*d*e^4*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) - (32*x)/(5005*d^5*e^3*(d^2 - e^2*x^2)^(3/2)) - (64*x)/(5005*d^7*e^3*Sqrt[d^2 - e^2*x^2])","A",9,5,27,0.1852,1,"{1639, 793, 659, 192, 191}"
213,1,209,0,0.2074562,"\int \frac{x^2}{(d+e x)^4 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[x^2/((d + e*x)^4*(d^2 - e^2*x^2)^(7/2)),x]","-\frac{d}{13 e^3 (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{17}{143 e^3 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{7}{1287 d e^3 (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{7}{1287 d^2 e^3 (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}+\frac{14 x}{2145 d^4 e^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{56 x}{6435 d^6 e^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{112 x}{6435 d^8 e^2 \sqrt{d^2-e^2 x^2}}","-\frac{d}{13 e^3 (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{17}{143 e^3 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{7}{1287 d e^3 (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{7}{1287 d^2 e^3 (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}+\frac{14 x}{2145 d^4 e^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{56 x}{6435 d^6 e^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{112 x}{6435 d^8 e^2 \sqrt{d^2-e^2 x^2}}",1,"(14*x)/(2145*d^4*e^2*(d^2 - e^2*x^2)^(5/2)) - d/(13*e^3*(d + e*x)^4*(d^2 - e^2*x^2)^(5/2)) + 17/(143*e^3*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2)) - 7/(1287*d*e^3*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 7/(1287*d^2*e^3*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (56*x)/(6435*d^6*e^2*(d^2 - e^2*x^2)^(3/2)) + (112*x)/(6435*d^8*e^2*Sqrt[d^2 - e^2*x^2])","A",8,5,27,0.1852,1,"{1639, 793, 659, 192, 191}"
214,1,211,0,0.1049493,"\int \frac{x}{(d+e x)^4 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[x/((d + e*x)^4*(d^2 - e^2*x^2)^(7/2)),x]","\frac{512 x}{6435 d^9 e \sqrt{d^2-e^2 x^2}}+\frac{256 x}{6435 d^7 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{64 x}{2145 d^5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{32}{1287 d^3 e^2 (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{32}{1287 d^2 e^2 (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{4}{143 d e^2 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{1}{13 e^2 (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}","\frac{512 x}{6435 d^9 e \sqrt{d^2-e^2 x^2}}+\frac{256 x}{6435 d^7 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{64 x}{2145 d^5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{32}{1287 d^3 e^2 (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{32}{1287 d^2 e^2 (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{4}{143 d e^2 (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{1}{13 e^2 (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}",1,"(64*x)/(2145*d^5*e*(d^2 - e^2*x^2)^(5/2)) + 1/(13*e^2*(d + e*x)^4*(d^2 - e^2*x^2)^(5/2)) - 4/(143*d*e^2*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2)) - 32/(1287*d^2*e^2*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 32/(1287*d^3*e^2*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (256*x)/(6435*d^7*e*(d^2 - e^2*x^2)^(3/2)) + (512*x)/(6435*d^9*e*Sqrt[d^2 - e^2*x^2])","A",7,4,25,0.1600,1,"{793, 659, 192, 191}"
215,1,205,0,0.0906988,"\int \frac{1}{(d+e x)^4 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[1/((d + e*x)^4*(d^2 - e^2*x^2)^(7/2)),x]","\frac{128 x}{715 d^{10} \sqrt{d^2-e^2 x^2}}+\frac{64 x}{715 d^8 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{48 x}{715 d^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8}{143 d^4 e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8}{143 d^3 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{9}{143 d^2 e (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{13 d e (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}","\frac{128 x}{715 d^{10} \sqrt{d^2-e^2 x^2}}+\frac{64 x}{715 d^8 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{48 x}{715 d^6 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8}{143 d^4 e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8}{143 d^3 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{9}{143 d^2 e (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{13 d e (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}",1,"(48*x)/(715*d^6*(d^2 - e^2*x^2)^(5/2)) - 1/(13*d*e*(d + e*x)^4*(d^2 - e^2*x^2)^(5/2)) - 9/(143*d^2*e*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2)) - 8/(143*d^3*e*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 8/(143*d^4*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (64*x)/(715*d^8*(d^2 - e^2*x^2)^(3/2)) + (128*x)/(715*d^10*Sqrt[d^2 - e^2*x^2])","A",7,3,24,0.1250,1,"{659, 192, 191}"
216,1,234,0,0.3845383,"\int \frac{1}{x (d+e x)^4 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[1/(x*(d + e*x)^4*(d^2 - e^2*x^2)^(7/2)),x]","-\frac{4 e x}{13 d \left(d^2-e^2 x^2\right)^{11/2}}+\frac{819 d-1024 e x}{819 d^{11} \sqrt{d^2-e^2 x^2}}+\frac{273 d-512 e x}{819 d^9 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{273 d-640 e x}{1365 d^7 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{117 d-320 e x}{819 d^5 \left(d^2-e^2 x^2\right)^{7/2}}+\frac{13 d-40 e x}{117 d^3 \left(d^2-e^2 x^2\right)^{9/2}}+\frac{8 d (d-e x)}{13 \left(d^2-e^2 x^2\right)^{13/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^{11}}","-\frac{4 e x}{13 d \left(d^2-e^2 x^2\right)^{11/2}}+\frac{819 d-1024 e x}{819 d^{11} \sqrt{d^2-e^2 x^2}}+\frac{273 d-512 e x}{819 d^9 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{273 d-640 e x}{1365 d^7 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{117 d-320 e x}{819 d^5 \left(d^2-e^2 x^2\right)^{7/2}}+\frac{13 d-40 e x}{117 d^3 \left(d^2-e^2 x^2\right)^{9/2}}+\frac{8 d (d-e x)}{13 \left(d^2-e^2 x^2\right)^{13/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^{11}}",1,"(8*d*(d - e*x))/(13*(d^2 - e^2*x^2)^(13/2)) - (4*e*x)/(13*d*(d^2 - e^2*x^2)^(11/2)) + (13*d - 40*e*x)/(117*d^3*(d^2 - e^2*x^2)^(9/2)) + (117*d - 320*e*x)/(819*d^5*(d^2 - e^2*x^2)^(7/2)) + (273*d - 640*e*x)/(1365*d^7*(d^2 - e^2*x^2)^(5/2)) + (273*d - 512*e*x)/(819*d^9*(d^2 - e^2*x^2)^(3/2)) + (819*d - 1024*e*x)/(819*d^11*Sqrt[d^2 - e^2*x^2]) - ArcTanh[Sqrt[d^2 - e^2*x^2]/d]/d^11","A",12,7,27,0.2593,1,"{852, 1805, 823, 12, 266, 63, 208}"
217,1,271,0,0.6798684,"\int \frac{1}{x^2 (d+e x)^4 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[1/(x^2*(d + e*x)^4*(d^2 - e^2*x^2)^(7/2)),x]","-\frac{e (36036 d-52175 e x)}{9009 d^{12} \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^{12} x}-\frac{e (12012 d-21583 e x)}{9009 d^{10} \left(d^2-e^2 x^2\right)^{3/2}}-\frac{e (12012 d-23225 e x)}{15015 d^8 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{e (5148 d-10111 e x)}{9009 d^6 \left(d^2-e^2 x^2\right)^{7/2}}-\frac{e (572 d-1103 e x)}{1287 d^4 \left(d^2-e^2 x^2\right)^{9/2}}-\frac{4 e (13 d-24 e x)}{143 d^2 \left(d^2-e^2 x^2\right)^{11/2}}-\frac{8 e (d-e x)}{13 \left(d^2-e^2 x^2\right)^{13/2}}+\frac{4 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^{12}}","-\frac{e (36036 d-52175 e x)}{9009 d^{12} \sqrt{d^2-e^2 x^2}}-\frac{\sqrt{d^2-e^2 x^2}}{d^{12} x}-\frac{e (12012 d-21583 e x)}{9009 d^{10} \left(d^2-e^2 x^2\right)^{3/2}}-\frac{e (12012 d-23225 e x)}{15015 d^8 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{e (5148 d-10111 e x)}{9009 d^6 \left(d^2-e^2 x^2\right)^{7/2}}-\frac{e (572 d-1103 e x)}{1287 d^4 \left(d^2-e^2 x^2\right)^{9/2}}-\frac{4 e (13 d-24 e x)}{143 d^2 \left(d^2-e^2 x^2\right)^{11/2}}-\frac{8 e (d-e x)}{13 \left(d^2-e^2 x^2\right)^{13/2}}+\frac{4 e \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{d}\right)}{d^{12}}",1,"(-8*e*(d - e*x))/(13*(d^2 - e^2*x^2)^(13/2)) - (4*e*(13*d - 24*e*x))/(143*d^2*(d^2 - e^2*x^2)^(11/2)) - (e*(572*d - 1103*e*x))/(1287*d^4*(d^2 - e^2*x^2)^(9/2)) - (e*(5148*d - 10111*e*x))/(9009*d^6*(d^2 - e^2*x^2)^(7/2)) - (e*(12012*d - 23225*e*x))/(15015*d^8*(d^2 - e^2*x^2)^(5/2)) - (e*(12012*d - 21583*e*x))/(9009*d^10*(d^2 - e^2*x^2)^(3/2)) - (e*(36036*d - 52175*e*x))/(9009*d^12*Sqrt[d^2 - e^2*x^2]) - Sqrt[d^2 - e^2*x^2]/(d^12*x) + (4*e*ArcTanh[Sqrt[d^2 - e^2*x^2]/d])/d^12","A",12,6,27,0.2222,1,"{852, 1805, 807, 266, 63, 208}"
218,1,102,0,0.1116135,"\int \frac{\sqrt{c-a c x} \sqrt{1-a^2 x^2}}{x^2} \, dx","Int[(Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2])/x^2,x]","-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{x (c-a c x)^{3/2}}-\frac{a c \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}+a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)","-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{x (c-a c x)^{3/2}}-\frac{a c \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}+a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)",1,"-((a*c*Sqrt[1 - a^2*x^2])/Sqrt[c - a*c*x]) - (c^2*(1 - a^2*x^2)^(3/2))/(x*(c - a*c*x)^(3/2)) + a*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/Sqrt[c - a*c*x]]","A",4,4,29,0.1379,1,"{879, 865, 875, 208}"
219,1,39,0,0.0399762,"\int \frac{\sqrt{c-a c x}}{x \sqrt{1-a^2 x^2}} \, dx","Int[Sqrt[c - a*c*x]/(x*Sqrt[1 - a^2*x^2]),x]","-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)","-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)",1,"-2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/Sqrt[c - a*c*x]]","A",2,2,29,0.06897,1,"{875, 208}"
220,1,35,0,0.0100174,"\int \frac{\sqrt{1-a x}}{\sqrt{x}} \, dx","Int[Sqrt[1 - a*x]/Sqrt[x],x]","\sqrt{x} \sqrt{1-a x}+\frac{\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}","\sqrt{x} \sqrt{1-a x}+\frac{\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}",1,"Sqrt[x]*Sqrt[1 - a*x] + ArcSin[Sqrt[a]*Sqrt[x]]/Sqrt[a]","A",3,3,16,0.1875,1,"{50, 54, 216}"
221,1,35,0,0.0288091,"\int \frac{\sqrt{1-a^2 x^2}}{\sqrt{x} \sqrt{1+a x}} \, dx","Int[Sqrt[1 - a^2*x^2]/(Sqrt[x]*Sqrt[1 + a*x]),x]","\sqrt{x} \sqrt{1-a x}+\frac{\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}","\sqrt{x} \sqrt{1-a x}+\frac{\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}",1,"Sqrt[x]*Sqrt[1 - a*x] + ArcSin[Sqrt[a]*Sqrt[x]]/Sqrt[a]","A",4,4,29,0.1379,1,"{848, 50, 54, 216}"
222,1,34,0,0.0087351,"\int \frac{\sqrt{1+a x}}{\sqrt{x}} \, dx","Int[Sqrt[1 + a*x]/Sqrt[x],x]","\sqrt{x} \sqrt{a x+1}+\frac{\sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}","\sqrt{x} \sqrt{a x+1}+\frac{\sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}",1,"Sqrt[x]*Sqrt[1 + a*x] + ArcSinh[Sqrt[a]*Sqrt[x]]/Sqrt[a]","A",3,3,15,0.2000,1,"{50, 54, 215}"
223,1,34,0,0.028346,"\int \frac{\sqrt{1-a^2 x^2}}{\sqrt{x} \sqrt{1-a x}} \, dx","Int[Sqrt[1 - a^2*x^2]/(Sqrt[x]*Sqrt[1 - a*x]),x]","\sqrt{x} \sqrt{a x+1}+\frac{\sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}","\sqrt{x} \sqrt{a x+1}+\frac{\sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}",1,"Sqrt[x]*Sqrt[1 + a*x] + ArcSinh[Sqrt[a]*Sqrt[x]]/Sqrt[a]","A",4,4,30,0.1333,1,"{848, 50, 54, 215}"
224,1,63,0,0.0150052,"\int \sqrt{x} \sqrt{1-a x} \, dx","Int[Sqrt[x]*Sqrt[1 - a*x],x]","\frac{\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{4 a^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{1-a x}-\frac{\sqrt{x} \sqrt{1-a x}}{4 a}","\frac{\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{4 a^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{1-a x}-\frac{\sqrt{x} \sqrt{1-a x}}{4 a}",1,"-(Sqrt[x]*Sqrt[1 - a*x])/(4*a) + (x^(3/2)*Sqrt[1 - a*x])/2 + ArcSin[Sqrt[a]*Sqrt[x]]/(4*a^(3/2))","A",4,3,16,0.1875,1,"{50, 54, 216}"
225,1,63,0,0.0329066,"\int \frac{\sqrt{x} \sqrt{1-a^2 x^2}}{\sqrt{1+a x}} \, dx","Int[(Sqrt[x]*Sqrt[1 - a^2*x^2])/Sqrt[1 + a*x],x]","\frac{\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{4 a^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{1-a x}-\frac{\sqrt{x} \sqrt{1-a x}}{4 a}","\frac{\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{4 a^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{1-a x}-\frac{\sqrt{x} \sqrt{1-a x}}{4 a}",1,"-(Sqrt[x]*Sqrt[1 - a*x])/(4*a) + (x^(3/2)*Sqrt[1 - a*x])/2 + ArcSin[Sqrt[a]*Sqrt[x]]/(4*a^(3/2))","A",5,4,29,0.1379,1,"{848, 50, 54, 216}"
226,1,250,0,0.3859156,"\int (g x)^m (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[(g*x)^m*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2),x]","\frac{d^6 e (4 m+29) \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) (m+9) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{e \left(d^2-e^2 x^2\right)^{7/2} (g x)^{m+2}}{g^2 (m+9)}+\frac{d^7 (4 m+11) \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+8) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{3 d \left(d^2-e^2 x^2\right)^{7/2} (g x)^{m+1}}{g (m+8)}","\frac{d^6 e (4 m+29) \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) (m+9) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{e \left(d^2-e^2 x^2\right)^{7/2} (g x)^{m+2}}{g^2 (m+9)}+\frac{d^7 (4 m+11) \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+8) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{3 d \left(d^2-e^2 x^2\right)^{7/2} (g x)^{m+1}}{g (m+8)}",1,"(-3*d*(g*x)^(1 + m)*(d^2 - e^2*x^2)^(7/2))/(g*(8 + m)) - (e*(g*x)^(2 + m)*(d^2 - e^2*x^2)^(7/2))/(g^2*(9 + m)) + (d^7*(11 + 4*m)*(g*x)^(1 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-5/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*(8 + m)*Sqrt[1 - (e^2*x^2)/d^2]) + (d^6*e*(29 + 4*m)*(g*x)^(2 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-5/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(g^2*(2 + m)*(9 + m)*Sqrt[1 - (e^2*x^2)/d^2])","A",7,4,29,0.1379,1,"{1809, 808, 365, 364}"
227,1,206,0,0.2091288,"\int (g x)^m (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[(g*x)^m*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2),x]","\frac{2 d^5 e \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) \sqrt{1-\frac{e^2 x^2}{d^2}}}+\frac{d^6 (2 m+9) \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+8) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{\left(d^2-e^2 x^2\right)^{7/2} (g x)^{m+1}}{g (m+8)}","\frac{2 d^5 e \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) \sqrt{1-\frac{e^2 x^2}{d^2}}}+\frac{d^6 (2 m+9) \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+8) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{\left(d^2-e^2 x^2\right)^{7/2} (g x)^{m+1}}{g (m+8)}",1,"-(((g*x)^(1 + m)*(d^2 - e^2*x^2)^(7/2))/(g*(8 + m))) + (d^6*(9 + 2*m)*(g*x)^(1 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-5/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*(8 + m)*Sqrt[1 - (e^2*x^2)/d^2]) + (2*d^5*e*(g*x)^(2 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-5/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(g^2*(2 + m)*Sqrt[1 - (e^2*x^2)/d^2])","A",6,4,29,0.1379,1,"{1809, 808, 365, 364}"
228,1,162,0,0.0835558,"\int (g x)^m (d+e x) \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[(g*x)^m*(d + e*x)*(d^2 - e^2*x^2)^(5/2),x]","\frac{d^4 e \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) \sqrt{1-\frac{e^2 x^2}{d^2}}}+\frac{d^5 \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) \sqrt{1-\frac{e^2 x^2}{d^2}}}","\frac{d^4 e \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) \sqrt{1-\frac{e^2 x^2}{d^2}}}+\frac{d^5 \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) \sqrt{1-\frac{e^2 x^2}{d^2}}}",1,"(d^5*(g*x)^(1 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-5/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]) + (d^4*e*(g*x)^(2 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-5/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(g^2*(2 + m)*Sqrt[1 - (e^2*x^2)/d^2])","A",5,3,27,0.1111,1,"{808, 365, 364}"
229,1,80,0,0.0248633,"\int (g x)^m \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[(g*x)^m*(d^2 - e^2*x^2)^(5/2),x]","\frac{d^4 \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) \sqrt{1-\frac{e^2 x^2}{d^2}}}","\frac{d^4 \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) \sqrt{1-\frac{e^2 x^2}{d^2}}}",1,"(d^4*(g*x)^(1 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-5/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*Sqrt[1 - (e^2*x^2)/d^2])","A",2,2,22,0.09091,1,"{365, 364}"
230,1,163,0,0.1405003,"\int \frac{(g x)^m \left(d^2-e^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[((g*x)^m*(d^2 - e^2*x^2)^(5/2))/(d + e*x),x]","\frac{d^3 \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{d^2 e \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) \sqrt{1-\frac{e^2 x^2}{d^2}}}","\frac{d^3 \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{d^2 e \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) \sqrt{1-\frac{e^2 x^2}{d^2}}}",1,"(d^3*(g*x)^(1 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-3/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]) - (d^2*e*(g*x)^(2 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-3/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(g^2*(2 + m)*Sqrt[1 - (e^2*x^2)/d^2])","A",8,5,29,0.1724,1,"{892, 82, 126, 365, 364}"
231,1,204,0,0.2154875,"\int \frac{(g x)^m \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[((g*x)^m*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^2,x]","-\frac{2 d e \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) \sqrt{1-\frac{e^2 x^2}{d^2}}}+\frac{d^2 (2 m+5) \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+4) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{\left(d^2-e^2 x^2\right)^{3/2} (g x)^{m+1}}{g (m+4)}","-\frac{2 d e \sqrt{d^2-e^2 x^2} (g x)^{m+2} \, _2F_1\left(-\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) \sqrt{1-\frac{e^2 x^2}{d^2}}}+\frac{d^2 (2 m+5) \sqrt{d^2-e^2 x^2} (g x)^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+4) \sqrt{1-\frac{e^2 x^2}{d^2}}}-\frac{\left(d^2-e^2 x^2\right)^{3/2} (g x)^{m+1}}{g (m+4)}",1,"-(((g*x)^(1 + m)*(d^2 - e^2*x^2)^(3/2))/(g*(4 + m))) + (d^2*(5 + 2*m)*(g*x)^(1 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*(4 + m)*Sqrt[1 - (e^2*x^2)/d^2]) - (2*d*e*(g*x)^(2 + m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[-1/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(g^2*(2 + m)*Sqrt[1 - (e^2*x^2)/d^2])","A",7,5,29,0.1724,1,"{852, 1809, 808, 365, 364}"
232,1,250,0,0.3806611,"\int \frac{(g x)^m \left(d^2-e^2 x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[((g*x)^m*(d^2 - e^2*x^2)^(5/2))/(d + e*x)^3,x]","-\frac{d^2 e (4 m+11) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) (m+3) \sqrt{d^2-e^2 x^2}}+\frac{e \sqrt{d^2-e^2 x^2} (g x)^{m+2}}{g^2 (m+3)}+\frac{d^3 (4 m+5) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+2) \sqrt{d^2-e^2 x^2}}-\frac{3 d \sqrt{d^2-e^2 x^2} (g x)^{m+1}}{g (m+2)}","-\frac{d^2 e (4 m+11) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) (m+3) \sqrt{d^2-e^2 x^2}}+\frac{e \sqrt{d^2-e^2 x^2} (g x)^{m+2}}{g^2 (m+3)}+\frac{d^3 (4 m+5) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+2) \sqrt{d^2-e^2 x^2}}-\frac{3 d \sqrt{d^2-e^2 x^2} (g x)^{m+1}}{g (m+2)}",1,"(-3*d*(g*x)^(1 + m)*Sqrt[d^2 - e^2*x^2])/(g*(2 + m)) + (e*(g*x)^(2 + m)*Sqrt[d^2 - e^2*x^2])/(g^2*(3 + m)) + (d^3*(5 + 4*m)*(g*x)^(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*(2 + m)*Sqrt[d^2 - e^2*x^2]) - (d^2*e*(11 + 4*m)*(g*x)^(2 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(g^2*(2 + m)*(3 + m)*Sqrt[d^2 - e^2*x^2])","A",8,5,29,0.1724,1,"{852, 1809, 808, 365, 364}"
233,1,213,0,0.21292,"\int \frac{(g x)^m (d+e x)^3}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[((g*x)^m*(d + e*x)^3)/(d^2 - e^2*x^2)^(7/2),x]","\frac{e (7-4 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^4 g^2 (m+2) \sqrt{d^2-e^2 x^2}}+\frac{(1-4 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^3 g (m+1) \sqrt{d^2-e^2 x^2}}+\frac{4 (d+e x) (g x)^{m+1}}{5 g \left(d^2-e^2 x^2\right)^{5/2}}","\frac{e (7-4 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^4 g^2 (m+2) \sqrt{d^2-e^2 x^2}}+\frac{(1-4 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^3 g (m+1) \sqrt{d^2-e^2 x^2}}+\frac{4 (d+e x) (g x)^{m+1}}{5 g \left(d^2-e^2 x^2\right)^{5/2}}",1,"(4*(g*x)^(1 + m)*(d + e*x))/(5*g*(d^2 - e^2*x^2)^(5/2)) + ((1 - 4*m)*(g*x)^(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[5/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(5*d^3*g*(1 + m)*Sqrt[d^2 - e^2*x^2]) + (e*(7 - 4*m)*(g*x)^(2 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[5/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(5*d^4*g^2*(2 + m)*Sqrt[d^2 - e^2*x^2])","A",6,4,29,0.1379,1,"{1806, 808, 365, 364}"
234,1,216,0,0.2083583,"\int \frac{(g x)^m (d+e x)^2}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[((g*x)^m*(d + e*x)^2)/(d^2 - e^2*x^2)^(7/2),x]","\frac{2 e (3-m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^5 g^2 (m+2) \sqrt{d^2-e^2 x^2}}+\frac{(3-2 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^4 g (m+1) \sqrt{d^2-e^2 x^2}}+\frac{2 (d+e x) (g x)^{m+1}}{5 d g \left(d^2-e^2 x^2\right)^{5/2}}","\frac{2 e (3-m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^5 g^2 (m+2) \sqrt{d^2-e^2 x^2}}+\frac{(3-2 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^4 g (m+1) \sqrt{d^2-e^2 x^2}}+\frac{2 (d+e x) (g x)^{m+1}}{5 d g \left(d^2-e^2 x^2\right)^{5/2}}",1,"(2*(g*x)^(1 + m)*(d + e*x))/(5*d*g*(d^2 - e^2*x^2)^(5/2)) + ((3 - 2*m)*(g*x)^(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[5/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(5*d^4*g*(1 + m)*Sqrt[d^2 - e^2*x^2]) + (2*e*(3 - m)*(g*x)^(2 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[5/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(5*d^5*g^2*(2 + m)*Sqrt[d^2 - e^2*x^2])","A",6,4,29,0.1379,1,"{1806, 808, 365, 364}"
235,1,162,0,0.0819333,"\int \frac{(g x)^m (d+e x)}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[((g*x)^m*(d + e*x))/(d^2 - e^2*x^2)^(7/2),x]","\frac{e \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{7}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^6 g^2 (m+2) \sqrt{d^2-e^2 x^2}}+\frac{\sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{7}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d^5 g (m+1) \sqrt{d^2-e^2 x^2}}","\frac{e (g x)^{m+2} \, _2F_1\left(1,\frac{m-3}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^2 g^2 (m+2) \left(d^2-e^2 x^2\right)^{5/2}}+\frac{(g x)^{m+1} \, _2F_1\left(1,\frac{m-4}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d g (m+1) \left(d^2-e^2 x^2\right)^{5/2}}",1,"((g*x)^(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[7/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(d^5*g*(1 + m)*Sqrt[d^2 - e^2*x^2]) + (e*(g*x)^(2 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[7/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(d^6*g^2*(2 + m)*Sqrt[d^2 - e^2*x^2])","A",5,3,27,0.1111,1,"{808, 365, 364}"
236,1,80,0,0.0252806,"\int \frac{(g x)^m}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(g*x)^m/(d^2 - e^2*x^2)^(7/2),x]","\frac{\sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{7}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d^6 g (m+1) \sqrt{d^2-e^2 x^2}}","\frac{\sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{7}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d^6 g (m+1) \sqrt{d^2-e^2 x^2}}",1,"((g*x)^(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[7/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(d^6*g*(1 + m)*Sqrt[d^2 - e^2*x^2])","A",2,2,22,0.09091,1,"{365, 364}"
237,1,163,0,0.1456062,"\int \frac{(g x)^m}{(d+e x) \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(g*x)^m/((d + e*x)*(d^2 - e^2*x^2)^(7/2)),x]","\frac{\sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{9}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d^7 g (m+1) \sqrt{d^2-e^2 x^2}}-\frac{e \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{9}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^8 g^2 (m+2) \sqrt{d^2-e^2 x^2}}","\frac{\sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{9}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d^7 g (m+1) \sqrt{d^2-e^2 x^2}}-\frac{e \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{9}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^8 g^2 (m+2) \sqrt{d^2-e^2 x^2}}",1,"((g*x)^(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[9/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(d^7*g*(1 + m)*Sqrt[d^2 - e^2*x^2]) - (e*(g*x)^(2 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[9/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(d^8*g^2*(2 + m)*Sqrt[d^2 - e^2*x^2])","A",8,5,29,0.1724,1,"{892, 82, 126, 365, 364}"
238,1,217,0,0.2311175,"\int \frac{(g x)^m}{(d+e x)^2 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(g*x)^m/((d + e*x)^2*(d^2 - e^2*x^2)^(7/2)),x]","-\frac{2 e (7-m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{9}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{9 d^9 g^2 (m+2) \sqrt{d^2-e^2 x^2}}+\frac{(7-2 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{9}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{9 d^8 g (m+1) \sqrt{d^2-e^2 x^2}}+\frac{2 (d-e x) (g x)^{m+1}}{9 d g \left(d^2-e^2 x^2\right)^{9/2}}","-\frac{2 e (7-m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{9}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{9 d^9 g^2 (m+2) \sqrt{d^2-e^2 x^2}}+\frac{(7-2 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{9}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{9 d^8 g (m+1) \sqrt{d^2-e^2 x^2}}+\frac{2 (d-e x) (g x)^{m+1}}{9 d g \left(d^2-e^2 x^2\right)^{9/2}}",1,"(2*(g*x)^(1 + m)*(d - e*x))/(9*d*g*(d^2 - e^2*x^2)^(9/2)) + ((7 - 2*m)*(g*x)^(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[9/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(9*d^8*g*(1 + m)*Sqrt[d^2 - e^2*x^2]) - (2*e*(7 - m)*(g*x)^(2 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[9/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(9*d^9*g^2*(2 + m)*Sqrt[d^2 - e^2*x^2])","A",7,5,29,0.1724,1,"{852, 1806, 808, 365, 364}"
239,1,214,0,0.2291589,"\int \frac{(g x)^m}{(d+e x)^3 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(g*x)^m/((d + e*x)^3*(d^2 - e^2*x^2)^(7/2)),x]","-\frac{e (25-4 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{11}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{11 d^{10} g^2 (m+2) \sqrt{d^2-e^2 x^2}}+\frac{(7-4 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{11}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{11 d^9 g (m+1) \sqrt{d^2-e^2 x^2}}+\frac{4 (d-e x) (g x)^{m+1}}{11 g \left(d^2-e^2 x^2\right)^{11/2}}","-\frac{e (25-4 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+2} \, _2F_1\left(\frac{11}{2},\frac{m+2}{2};\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{11 d^{10} g^2 (m+2) \sqrt{d^2-e^2 x^2}}+\frac{(7-4 m) \sqrt{1-\frac{e^2 x^2}{d^2}} (g x)^{m+1} \, _2F_1\left(\frac{11}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{11 d^9 g (m+1) \sqrt{d^2-e^2 x^2}}+\frac{4 (d-e x) (g x)^{m+1}}{11 g \left(d^2-e^2 x^2\right)^{11/2}}",1,"(4*(g*x)^(1 + m)*(d - e*x))/(11*g*(d^2 - e^2*x^2)^(11/2)) + ((7 - 4*m)*(g*x)^(1 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[11/2, (1 + m)/2, (3 + m)/2, (e^2*x^2)/d^2])/(11*d^9*g*(1 + m)*Sqrt[d^2 - e^2*x^2]) - (e*(25 - 4*m)*(g*x)^(2 + m)*Sqrt[1 - (e^2*x^2)/d^2]*Hypergeometric2F1[11/2, (2 + m)/2, (4 + m)/2, (e^2*x^2)/d^2])/(11*d^10*g^2*(2 + m)*Sqrt[d^2 - e^2*x^2])","A",7,5,29,0.1724,1,"{852, 1806, 808, 365, 364}"
240,1,148,0,0.0940171,"\int x^5 (d+e x) \left(d^2-e^2 x^2\right)^p \, dx","Int[x^5*(d + e*x)*(d^2 - e^2*x^2)^p,x]","\frac{1}{7} e x^7 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^5 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^6 (p+1)}+\frac{d^3 \left(d^2-e^2 x^2\right)^{p+2}}{e^6 (p+2)}-\frac{d \left(d^2-e^2 x^2\right)^{p+3}}{2 e^6 (p+3)}","\frac{1}{7} e x^7 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^5 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^6 (p+1)}+\frac{d^3 \left(d^2-e^2 x^2\right)^{p+2}}{e^6 (p+2)}-\frac{d \left(d^2-e^2 x^2\right)^{p+3}}{2 e^6 (p+3)}",1,"-(d^5*(d^2 - e^2*x^2)^(1 + p))/(2*e^6*(1 + p)) + (d^3*(d^2 - e^2*x^2)^(2 + p))/(e^6*(2 + p)) - (d*(d^2 - e^2*x^2)^(3 + p))/(2*e^6*(3 + p)) + (e*x^7*(d^2 - e^2*x^2)^p*Hypergeometric2F1[7/2, -p, 9/2, (e^2*x^2)/d^2])/(7*(1 - (e^2*x^2)/d^2)^p)","A",6,5,23,0.2174,1,"{764, 266, 43, 365, 364}"
241,1,147,0,0.0909236,"\int x^4 (d+e x) \left(d^2-e^2 x^2\right)^p \, dx","Int[x^4*(d + e*x)*(d^2 - e^2*x^2)^p,x]","\frac{1}{5} d x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^4 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^5 (p+1)}+\frac{d^2 \left(d^2-e^2 x^2\right)^{p+2}}{e^5 (p+2)}-\frac{\left(d^2-e^2 x^2\right)^{p+3}}{2 e^5 (p+3)}","\frac{1}{5} d x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^4 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^5 (p+1)}+\frac{d^2 \left(d^2-e^2 x^2\right)^{p+2}}{e^5 (p+2)}-\frac{\left(d^2-e^2 x^2\right)^{p+3}}{2 e^5 (p+3)}",1,"-(d^4*(d^2 - e^2*x^2)^(1 + p))/(2*e^5*(1 + p)) + (d^2*(d^2 - e^2*x^2)^(2 + p))/(e^5*(2 + p)) - (d^2 - e^2*x^2)^(3 + p)/(2*e^5*(3 + p)) + (d*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, (e^2*x^2)/d^2])/(5*(1 - (e^2*x^2)/d^2)^p)","A",6,5,23,0.2174,1,"{764, 365, 364, 266, 43}"
242,1,120,0,0.0714619,"\int x^3 (d+e x) \left(d^2-e^2 x^2\right)^p \, dx","Int[x^3*(d + e*x)*(d^2 - e^2*x^2)^p,x]","\frac{1}{5} e x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^3 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 (p+1)}+\frac{d \left(d^2-e^2 x^2\right)^{p+2}}{2 e^4 (p+2)}","\frac{1}{5} e x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^3 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 (p+1)}+\frac{d \left(d^2-e^2 x^2\right)^{p+2}}{2 e^4 (p+2)}",1,"-(d^3*(d^2 - e^2*x^2)^(1 + p))/(2*e^4*(1 + p)) + (d*(d^2 - e^2*x^2)^(2 + p))/(2*e^4*(2 + p)) + (e*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, (e^2*x^2)/d^2])/(5*(1 - (e^2*x^2)/d^2)^p)","A",6,5,23,0.2174,1,"{764, 266, 43, 365, 364}"
243,1,119,0,0.0671999,"\int x^2 (d+e x) \left(d^2-e^2 x^2\right)^p \, dx","Int[x^2*(d + e*x)*(d^2 - e^2*x^2)^p,x]","\frac{1}{3} d x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^2 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+2}}{2 e^3 (p+2)}","\frac{1}{3} d x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^2 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+2}}{2 e^3 (p+2)}",1,"-(d^2*(d^2 - e^2*x^2)^(1 + p))/(2*e^3*(1 + p)) + (d^2 - e^2*x^2)^(2 + p)/(2*e^3*(2 + p)) + (d*x^3*(d^2 - e^2*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, (e^2*x^2)/d^2])/(3*(1 - (e^2*x^2)/d^2)^p)","A",6,5,23,0.2174,1,"{764, 365, 364, 266, 43}"
244,1,89,0,0.0336116,"\int x (d+e x) \left(d^2-e^2 x^2\right)^p \, dx","Int[x*(d + e*x)*(d^2 - e^2*x^2)^p,x]","\frac{1}{3} e x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 e^2 (p+1)}","\frac{1}{3} e x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 e^2 (p+1)}",1,"-(d*(d^2 - e^2*x^2)^(1 + p))/(2*e^2*(1 + p)) + (e*x^3*(d^2 - e^2*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, (e^2*x^2)/d^2])/(3*(1 - (e^2*x^2)/d^2)^p)","A",4,4,21,0.1905,1,"{764, 261, 365, 364}"
245,1,83,0,0.0230472,"\int (d+e x) \left(d^2-e^2 x^2\right)^p \, dx","Int[(d + e*x)*(d^2 - e^2*x^2)^p,x]","d x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e (p+1)}","d x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e (p+1)}",1,"-(d^2 - e^2*x^2)^(1 + p)/(2*e*(1 + p)) + (d*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, (e^2*x^2)/d^2])/(1 - (e^2*x^2)/d^2)^p","A",3,3,20,0.1500,1,"{641, 246, 245}"
246,1,104,0,0.0550911,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^p}{x} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^p)/x,x]","e x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{\left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d (p+1)}","e x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{\left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d (p+1)}",1,"(e*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, (e^2*x^2)/d^2])/(1 - (e^2*x^2)/d^2)^p - ((d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (e^2*x^2)/d^2])/(2*d*(1 + p))","A",5,5,23,0.2174,1,"{764, 266, 65, 246, 245}"
247,1,108,0,0.0573612,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^p}{x^2} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^p)/x^2,x]","-\frac{d \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{x}-\frac{e \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (p+1)}","-\frac{d \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{x}-\frac{e \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (p+1)}",1,"-((d*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, (e^2*x^2)/d^2])/(x*(1 - (e^2*x^2)/d^2)^p)) - (e*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (e^2*x^2)/d^2])/(2*d^2*(1 + p))","A",5,5,23,0.2174,1,"{764, 365, 364, 266, 65}"
248,1,110,0,0.0587357,"\int \frac{(d+e x) \left(d^2-e^2 x^2\right)^p}{x^3} \, dx","Int[((d + e*x)*(d^2 - e^2*x^2)^p)/x^3,x]","-\frac{e \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{x}-\frac{e^2 \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d^3 (p+1)}","-\frac{e \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{x}-\frac{e^2 \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d^3 (p+1)}",1,"-((e*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, (e^2*x^2)/d^2])/(x*(1 - (e^2*x^2)/d^2)^p)) - (e^2*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, 1 - (e^2*x^2)/d^2])/(2*d^3*(1 + p))","A",5,5,23,0.2174,1,"{764, 266, 65, 365, 364}"
249,1,178,0,0.1454667,"\int x^5 (d+e x)^2 \left(d^2-e^2 x^2\right)^p \, dx","Int[x^5*(d + e*x)^2*(d^2 - e^2*x^2)^p,x]","\frac{2}{7} d e x^7 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^6 \left(d^2-e^2 x^2\right)^{p+1}}{e^6 (p+1)}+\frac{5 d^4 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^6 (p+2)}-\frac{2 d^2 \left(d^2-e^2 x^2\right)^{p+3}}{e^6 (p+3)}+\frac{\left(d^2-e^2 x^2\right)^{p+4}}{2 e^6 (p+4)}","\frac{2}{7} d e x^7 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^6 \left(d^2-e^2 x^2\right)^{p+1}}{e^6 (p+1)}+\frac{5 d^4 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^6 (p+2)}-\frac{2 d^2 \left(d^2-e^2 x^2\right)^{p+3}}{e^6 (p+3)}+\frac{\left(d^2-e^2 x^2\right)^{p+4}}{2 e^6 (p+4)}",1,"-((d^6*(d^2 - e^2*x^2)^(1 + p))/(e^6*(1 + p))) + (5*d^4*(d^2 - e^2*x^2)^(2 + p))/(2*e^6*(2 + p)) - (2*d^2*(d^2 - e^2*x^2)^(3 + p))/(e^6*(3 + p)) + (d^2 - e^2*x^2)^(4 + p)/(2*e^6*(4 + p)) + (2*d*e*x^7*(d^2 - e^2*x^2)^p*Hypergeometric2F1[7/2, -p, 9/2, (e^2*x^2)/d^2])/(7*(1 - (e^2*x^2)/d^2)^p)","A",7,6,25,0.2400,1,"{1652, 446, 77, 12, 365, 364}"
250,1,185,0,0.1734063,"\int x^4 (d+e x)^2 \left(d^2-e^2 x^2\right)^p \, dx","Int[x^4*(d + e*x)^2*(d^2 - e^2*x^2)^p,x]","\frac{2 d^2 (p+6) x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 (2 p+7)}-\frac{x^5 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+7}-\frac{d^5 \left(d^2-e^2 x^2\right)^{p+1}}{e^5 (p+1)}+\frac{2 d^3 \left(d^2-e^2 x^2\right)^{p+2}}{e^5 (p+2)}-\frac{d \left(d^2-e^2 x^2\right)^{p+3}}{e^5 (p+3)}","\frac{2 d^2 (p+6) x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 (2 p+7)}-\frac{x^5 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+7}-\frac{d^5 \left(d^2-e^2 x^2\right)^{p+1}}{e^5 (p+1)}+\frac{2 d^3 \left(d^2-e^2 x^2\right)^{p+2}}{e^5 (p+2)}-\frac{d \left(d^2-e^2 x^2\right)^{p+3}}{e^5 (p+3)}",1,"-((d^5*(d^2 - e^2*x^2)^(1 + p))/(e^5*(1 + p))) - (x^5*(d^2 - e^2*x^2)^(1 + p))/(7 + 2*p) + (2*d^3*(d^2 - e^2*x^2)^(2 + p))/(e^5*(2 + p)) - (d*(d^2 - e^2*x^2)^(3 + p))/(e^5*(3 + p)) + (2*d^2*(6 + p)*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, (e^2*x^2)/d^2])/(5*(7 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",8,7,25,0.2800,1,"{1652, 459, 365, 364, 12, 266, 43}"
251,1,149,0,0.1298874,"\int x^3 (d+e x)^2 \left(d^2-e^2 x^2\right)^p \, dx","Int[x^3*(d + e*x)^2*(d^2 - e^2*x^2)^p,x]","\frac{2}{5} d e x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^4 \left(d^2-e^2 x^2\right)^{p+1}}{e^4 (p+1)}+\frac{3 d^2 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^4 (p+2)}-\frac{\left(d^2-e^2 x^2\right)^{p+3}}{2 e^4 (p+3)}","\frac{2}{5} d e x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^4 \left(d^2-e^2 x^2\right)^{p+1}}{e^4 (p+1)}+\frac{3 d^2 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^4 (p+2)}-\frac{\left(d^2-e^2 x^2\right)^{p+3}}{2 e^4 (p+3)}",1,"-((d^4*(d^2 - e^2*x^2)^(1 + p))/(e^4*(1 + p))) + (3*d^2*(d^2 - e^2*x^2)^(2 + p))/(2*e^4*(2 + p)) - (d^2 - e^2*x^2)^(3 + p)/(2*e^4*(3 + p)) + (2*d*e*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, (e^2*x^2)/d^2])/(5*(1 - (e^2*x^2)/d^2)^p)","A",7,6,25,0.2400,1,"{1652, 446, 77, 12, 365, 364}"
252,1,155,0,0.1386828,"\int x^2 (d+e x)^2 \left(d^2-e^2 x^2\right)^p \, dx","Int[x^2*(d + e*x)^2*(d^2 - e^2*x^2)^p,x]","\frac{2 d^2 (p+4) x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 (2 p+5)}-\frac{x^3 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+5}-\frac{d^3 \left(d^2-e^2 x^2\right)^{p+1}}{e^3 (p+1)}+\frac{d \left(d^2-e^2 x^2\right)^{p+2}}{e^3 (p+2)}","\frac{2 d^2 (p+4) x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 (2 p+5)}-\frac{x^3 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+5}-\frac{d^3 \left(d^2-e^2 x^2\right)^{p+1}}{e^3 (p+1)}+\frac{d \left(d^2-e^2 x^2\right)^{p+2}}{e^3 (p+2)}",1,"-((d^3*(d^2 - e^2*x^2)^(1 + p))/(e^3*(1 + p))) - (x^3*(d^2 - e^2*x^2)^(1 + p))/(5 + 2*p) + (d*(d^2 - e^2*x^2)^(2 + p))/(e^3*(2 + p)) + (2*d^2*(4 + p)*x^3*(d^2 - e^2*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, (e^2*x^2)/d^2])/(3*(5 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",8,7,25,0.2800,1,"{1652, 459, 365, 364, 12, 266, 43}"
253,1,118,0,0.0913054,"\int x (d+e x)^2 \left(d^2-e^2 x^2\right)^p \, dx","Int[x*(d + e*x)^2*(d^2 - e^2*x^2)^p,x]","\frac{2}{3} d e x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^2 \left(d^2-e^2 x^2\right)^{p+1}}{e^2 (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+2}}{2 e^2 (p+2)}","\frac{2}{3} d e x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^2 \left(d^2-e^2 x^2\right)^{p+1}}{e^2 (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+2}}{2 e^2 (p+2)}",1,"-((d^2*(d^2 - e^2*x^2)^(1 + p))/(e^2*(1 + p))) + (d^2 - e^2*x^2)^(2 + p)/(2*e^2*(2 + p)) + (2*d*e*x^3*(d^2 - e^2*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, (e^2*x^2)/d^2])/(3*(1 - (e^2*x^2)/d^2)^p)","A",7,6,23,0.2609,1,"{1652, 444, 43, 12, 365, 364}"
254,1,71,0,0.0306384,"\int (d+e x)^2 \left(d^2-e^2 x^2\right)^p \, dx","Int[(d + e*x)^2*(d^2 - e^2*x^2)^p,x]","-\frac{d 2^{p+2} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(-p-2,p+1;p+2;\frac{d-e x}{2 d}\right)}{e (p+1)}","-\frac{d 2^{p+2} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(-p-2,p+1;p+2;\frac{d-e x}{2 d}\right)}{e (p+1)}",1,"-((2^(2 + p)*d*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[-2 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(e*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
255,1,128,0,0.0951983,"\int \frac{(d+e x)^2 \left(d^2-e^2 x^2\right)^p}{x} \, dx","Int[((d + e*x)^2*(d^2 - e^2*x^2)^p)/x,x]","2 d e x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{\left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 (p+1)}","2 d e x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{\left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 (p+1)}",1,"-(d^2 - e^2*x^2)^(1 + p)/(2*(1 + p)) + (2*d*e*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, (e^2*x^2)/d^2])/(1 - (e^2*x^2)/d^2)^p - ((d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (e^2*x^2)/d^2])/(2*(1 + p))","A",7,7,25,0.2800,1,"{1652, 446, 80, 65, 12, 246, 245}"
256,1,128,0,0.1157452,"\int \frac{(d+e x)^2 \left(d^2-e^2 x^2\right)^p}{x^2} \, dx","Int[((d + e*x)^2*(d^2 - e^2*x^2)^p)/x^2,x]","-2 e^2 p x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{e \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{d (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{x}","-2 e^2 p x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{e \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{d (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{x}",1,"-((d^2 - e^2*x^2)^(1 + p)/x) - (2*e^2*p*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, (e^2*x^2)/d^2])/(1 - (e^2*x^2)/d^2)^p - (e*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (e^2*x^2)/d^2])/(d*(1 + p))","A",6,6,25,0.2400,1,"{1807, 764, 266, 65, 246, 245}"
257,1,139,0,0.1246635,"\int \frac{(d+e x)^2 \left(d^2-e^2 x^2\right)^p}{x^3} \, dx","Int[((d + e*x)^2*(d^2 - e^2*x^2)^p)/x^3,x]","-\frac{2 d e \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{x}-\frac{e^2 (1-p) \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 x^2}","-\frac{2 d e \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{x}-\frac{e^2 (1-p) \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 x^2}",1,"-(d^2 - e^2*x^2)^(1 + p)/(2*x^2) - (2*d*e*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, (e^2*x^2)/d^2])/(x*(1 - (e^2*x^2)/d^2)^p) - (e^2*(1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (e^2*x^2)/d^2])/(2*d^2*(1 + p))","A",6,6,25,0.2400,1,"{1807, 764, 365, 364, 266, 65}"
258,1,222,0,0.191047,"\int x^5 (d+e x)^3 \left(d^2-e^2 x^2\right)^p \, dx","Int[x^5*(d + e*x)^3*(d^2 - e^2*x^2)^p,x]","\frac{2 d^2 e (3 p+17) x^7 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};\frac{e^2 x^2}{d^2}\right)}{7 (2 p+9)}-\frac{e x^7 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+9}-\frac{2 d^7 \left(d^2-e^2 x^2\right)^{p+1}}{e^6 (p+1)}+\frac{11 d^5 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^6 (p+2)}-\frac{5 d^3 \left(d^2-e^2 x^2\right)^{p+3}}{e^6 (p+3)}+\frac{3 d \left(d^2-e^2 x^2\right)^{p+4}}{2 e^6 (p+4)}","\frac{2 d^2 e (3 p+17) x^7 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};\frac{e^2 x^2}{d^2}\right)}{7 (2 p+9)}-\frac{e x^7 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+9}-\frac{2 d^7 \left(d^2-e^2 x^2\right)^{p+1}}{e^6 (p+1)}+\frac{11 d^5 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^6 (p+2)}-\frac{5 d^3 \left(d^2-e^2 x^2\right)^{p+3}}{e^6 (p+3)}+\frac{3 d \left(d^2-e^2 x^2\right)^{p+4}}{2 e^6 (p+4)}",1,"(-2*d^7*(d^2 - e^2*x^2)^(1 + p))/(e^6*(1 + p)) - (e*x^7*(d^2 - e^2*x^2)^(1 + p))/(9 + 2*p) + (11*d^5*(d^2 - e^2*x^2)^(2 + p))/(2*e^6*(2 + p)) - (5*d^3*(d^2 - e^2*x^2)^(3 + p))/(e^6*(3 + p)) + (3*d*(d^2 - e^2*x^2)^(4 + p))/(2*e^6*(4 + p)) + (2*d^2*e*(17 + 3*p)*x^7*(d^2 - e^2*x^2)^p*Hypergeometric2F1[7/2, -p, 9/2, (e^2*x^2)/d^2])/(7*(9 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",7,6,25,0.2400,1,"{1652, 446, 77, 459, 365, 364}"
259,1,218,0,0.1771684,"\int x^4 (d+e x)^3 \left(d^2-e^2 x^2\right)^p \, dx","Int[x^4*(d + e*x)^3*(d^2 - e^2*x^2)^p,x]","\frac{2 d^3 (p+11) x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 (2 p+7)}-\frac{3 d x^5 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+7}-\frac{2 d^6 \left(d^2-e^2 x^2\right)^{p+1}}{e^5 (p+1)}+\frac{9 d^4 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^5 (p+2)}-\frac{3 d^2 \left(d^2-e^2 x^2\right)^{p+3}}{e^5 (p+3)}+\frac{\left(d^2-e^2 x^2\right)^{p+4}}{2 e^5 (p+4)}","\frac{2 d^3 (p+11) x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 (2 p+7)}-\frac{3 d x^5 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+7}-\frac{2 d^6 \left(d^2-e^2 x^2\right)^{p+1}}{e^5 (p+1)}+\frac{9 d^4 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^5 (p+2)}-\frac{3 d^2 \left(d^2-e^2 x^2\right)^{p+3}}{e^5 (p+3)}+\frac{\left(d^2-e^2 x^2\right)^{p+4}}{2 e^5 (p+4)}",1,"(-2*d^6*(d^2 - e^2*x^2)^(1 + p))/(e^5*(1 + p)) - (3*d*x^5*(d^2 - e^2*x^2)^(1 + p))/(7 + 2*p) + (9*d^4*(d^2 - e^2*x^2)^(2 + p))/(2*e^5*(2 + p)) - (3*d^2*(d^2 - e^2*x^2)^(3 + p))/(e^5*(3 + p)) + (d^2 - e^2*x^2)^(4 + p)/(2*e^5*(4 + p)) + (2*d^3*(11 + p)*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, (e^2*x^2)/d^2])/(5*(7 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",7,6,25,0.2400,1,"{1652, 459, 365, 364, 446, 77}"
260,1,193,0,0.1824005,"\int x^3 (d+e x)^3 \left(d^2-e^2 x^2\right)^p \, dx","Int[x^3*(d + e*x)^3*(d^2 - e^2*x^2)^p,x]","\frac{2 d^2 e (3 p+13) x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 (2 p+7)}-\frac{e x^5 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+7}-\frac{2 d^5 \left(d^2-e^2 x^2\right)^{p+1}}{e^4 (p+1)}+\frac{7 d^3 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^4 (p+2)}-\frac{3 d \left(d^2-e^2 x^2\right)^{p+3}}{2 e^4 (p+3)}","\frac{2 d^2 e (3 p+13) x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 (2 p+7)}-\frac{e x^5 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+7}-\frac{2 d^5 \left(d^2-e^2 x^2\right)^{p+1}}{e^4 (p+1)}+\frac{7 d^3 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^4 (p+2)}-\frac{3 d \left(d^2-e^2 x^2\right)^{p+3}}{2 e^4 (p+3)}",1,"(-2*d^5*(d^2 - e^2*x^2)^(1 + p))/(e^4*(1 + p)) - (e*x^5*(d^2 - e^2*x^2)^(1 + p))/(7 + 2*p) + (7*d^3*(d^2 - e^2*x^2)^(2 + p))/(2*e^4*(2 + p)) - (3*d*(d^2 - e^2*x^2)^(3 + p))/(2*e^4*(3 + p)) + (2*d^2*e*(13 + 3*p)*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, (e^2*x^2)/d^2])/(5*(7 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",7,6,25,0.2400,1,"{1652, 446, 77, 459, 365, 364}"
261,1,189,0,0.1686453,"\int x^2 (d+e x)^3 \left(d^2-e^2 x^2\right)^p \, dx","Int[x^2*(d + e*x)^3*(d^2 - e^2*x^2)^p,x]","\frac{2 d^3 (p+7) x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 (2 p+5)}-\frac{3 d x^3 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+5}-\frac{2 d^4 \left(d^2-e^2 x^2\right)^{p+1}}{e^3 (p+1)}+\frac{5 d^2 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^3 (p+2)}-\frac{\left(d^2-e^2 x^2\right)^{p+3}}{2 e^3 (p+3)}","\frac{2 d^3 (p+7) x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 (2 p+5)}-\frac{3 d x^3 \left(d^2-e^2 x^2\right)^{p+1}}{2 p+5}-\frac{2 d^4 \left(d^2-e^2 x^2\right)^{p+1}}{e^3 (p+1)}+\frac{5 d^2 \left(d^2-e^2 x^2\right)^{p+2}}{2 e^3 (p+2)}-\frac{\left(d^2-e^2 x^2\right)^{p+3}}{2 e^3 (p+3)}",1,"(-2*d^4*(d^2 - e^2*x^2)^(1 + p))/(e^3*(1 + p)) - (3*d*x^3*(d^2 - e^2*x^2)^(1 + p))/(5 + 2*p) + (5*d^2*(d^2 - e^2*x^2)^(2 + p))/(2*e^3*(2 + p)) - (d^2 - e^2*x^2)^(3 + p)/(2*e^3*(3 + p)) + (2*d^3*(7 + p)*x^3*(d^2 - e^2*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, (e^2*x^2)/d^2])/(3*(5 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",7,6,25,0.2400,1,"{1652, 459, 365, 364, 446, 77}"
262,1,116,0,0.0663772,"\int x (d+e x)^3 \left(d^2-e^2 x^2\right)^p \, dx","Int[x*(d + e*x)^3*(d^2 - e^2*x^2)^p,x]","-\frac{3 d^3 2^{p+3} \left(d^2-e^2 x^2\right)^{p+1} \left(\frac{e x}{d}+1\right)^{-p-1} \, _2F_1\left(-p-3,p+1;p+2;\frac{d-e x}{2 d}\right)}{e^2 (p+1) (2 p+5)}-\frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{p+1}}{e^2 (2 p+5)}","-\frac{3 d^3 2^{p+3} \left(d^2-e^2 x^2\right)^{p+1} \left(\frac{e x}{d}+1\right)^{-p-1} \, _2F_1\left(-p-3,p+1;p+2;\frac{d-e x}{2 d}\right)}{e^2 (p+1) (2 p+5)}-\frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^{p+1}}{e^2 (2 p+5)}",1,"-(((d + e*x)^3*(d^2 - e^2*x^2)^(1 + p))/(e^2*(5 + 2*p))) - (3*2^(3 + p)*d^3*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[-3 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(e^2*(1 + p)*(5 + 2*p))","A",3,3,23,0.1304,1,"{795, 678, 69}"
263,1,73,0,0.0256134,"\int (d+e x)^3 \left(d^2-e^2 x^2\right)^p \, dx","Int[(d + e*x)^3*(d^2 - e^2*x^2)^p,x]","-\frac{d^2 2^{p+3} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(-p-3,p+1;p+2;\frac{d-e x}{2 d}\right)}{e (p+1)}","-\frac{d^2 2^{p+3} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(-p-3,p+1;p+2;\frac{d-e x}{2 d}\right)}{e (p+1)}",1,"-((2^(3 + p)*d^2*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[-3 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(e*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
264,1,171,0,0.1285888,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^p}{x} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^p)/x,x]","\frac{2 d^2 e (3 p+5) x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{2 p+3}-\frac{d \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 (p+1)}-\frac{e x \left(d^2-e^2 x^2\right)^{p+1}}{2 p+3}-\frac{3 d \left(d^2-e^2 x^2\right)^{p+1}}{2 (p+1)}","\frac{2 d^2 e (3 p+5) x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{2 p+3}-\frac{d \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 (p+1)}-\frac{e x \left(d^2-e^2 x^2\right)^{p+1}}{2 p+3}-\frac{3 d \left(d^2-e^2 x^2\right)^{p+1}}{2 (p+1)}",1,"(-3*d*(d^2 - e^2*x^2)^(1 + p))/(2*(1 + p)) - (e*x*(d^2 - e^2*x^2)^(1 + p))/(3 + 2*p) + (2*d^2*e*(5 + 3*p)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, (e^2*x^2)/d^2])/((3 + 2*p)*(1 - (e^2*x^2)/d^2)^p) - (d*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (e^2*x^2)/d^2])/(2*(1 + p))","A",7,7,25,0.2800,1,"{1652, 446, 80, 65, 388, 246, 245}"
265,1,159,0,0.1848132,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^p}{x^2} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^p)/x^2,x]","2 d e^2 (1-p) x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{3 e \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 (p+1)}-\frac{e \left(d^2-e^2 x^2\right)^{p+1}}{2 (p+1)}-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{x}","2 d e^2 (1-p) x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{3 e \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 (p+1)}-\frac{e \left(d^2-e^2 x^2\right)^{p+1}}{2 (p+1)}-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{x}",1,"-(e*(d^2 - e^2*x^2)^(1 + p))/(2*(1 + p)) - (d*(d^2 - e^2*x^2)^(1 + p))/x + (2*d*e^2*(1 - p)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, (e^2*x^2)/d^2])/(1 - (e^2*x^2)/d^2)^p - (3*e*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (e^2*x^2)/d^2])/(2*(1 + p))","A",8,8,25,0.3200,1,"{1807, 1652, 446, 80, 65, 12, 246, 245}"
266,1,166,0,0.2153864,"\int \frac{(d+e x)^3 \left(d^2-e^2 x^2\right)^p}{x^3} \, dx","Int[((d + e*x)^3*(d^2 - e^2*x^2)^p)/x^3,x]","-2 e^3 (3 p+1) x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{e^2 (3-p) \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d (p+1)}-\frac{3 e \left(d^2-e^2 x^2\right)^{p+1}}{x}-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 x^2}","-2 e^3 (3 p+1) x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{e^2 (3-p) \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{e^2 x^2}{d^2}\right)}{2 d (p+1)}-\frac{3 e \left(d^2-e^2 x^2\right)^{p+1}}{x}-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 x^2}",1,"-(d*(d^2 - e^2*x^2)^(1 + p))/(2*x^2) - (3*e*(d^2 - e^2*x^2)^(1 + p))/x - (2*e^3*(1 + 3*p)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, (e^2*x^2)/d^2])/(1 - (e^2*x^2)/d^2)^p - (e^2*(3 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (e^2*x^2)/d^2])/(2*d*(1 + p))","A",7,6,25,0.2400,1,"{1807, 764, 266, 65, 246, 245}"
267,1,148,0,0.1089494,"\int \frac{x^4 \left(d^2-e^2 x^2\right)^p}{d+e x} \, dx","Int[(x^4*(d^2 - e^2*x^2)^p)/(d + e*x),x]","\frac{x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},1-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d}+\frac{d^4 \left(d^2-e^2 x^2\right)^p}{2 e^5 p}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p+1}}{e^5 (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+2}}{2 e^5 (p+2)}","\frac{x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},1-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d}+\frac{d^4 \left(d^2-e^2 x^2\right)^p}{2 e^5 p}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p+1}}{e^5 (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+2}}{2 e^5 (p+2)}",1,"(d^4*(d^2 - e^2*x^2)^p)/(2*e^5*p) - (d^2*(d^2 - e^2*x^2)^(1 + p))/(e^5*(1 + p)) + (d^2 - e^2*x^2)^(2 + p)/(2*e^5*(2 + p)) + (x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, 1 - p, 7/2, (e^2*x^2)/d^2])/(5*d*(1 - (e^2*x^2)/d^2)^p)","A",7,6,25,0.2400,1,"{850, 764, 365, 364, 266, 43}"
268,1,121,0,0.0930484,"\int \frac{x^3 \left(d^2-e^2 x^2\right)^p}{d+e x} \, dx","Int[(x^3*(d^2 - e^2*x^2)^p)/(d + e*x),x]","-\frac{e x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},1-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^2}-\frac{d^3 \left(d^2-e^2 x^2\right)^p}{2 e^4 p}+\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 (p+1)}","-\frac{e x^5 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{5}{2},1-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^2}-\frac{d^3 \left(d^2-e^2 x^2\right)^p}{2 e^4 p}+\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 (p+1)}",1,"-(d^3*(d^2 - e^2*x^2)^p)/(2*e^4*p) + (d*(d^2 - e^2*x^2)^(1 + p))/(2*e^4*(1 + p)) - (e*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, 1 - p, 7/2, (e^2*x^2)/d^2])/(5*d^2*(1 - (e^2*x^2)/d^2)^p)","A",7,6,25,0.2400,1,"{850, 764, 266, 43, 365, 364}"
269,1,119,0,0.0854197,"\int \frac{x^2 \left(d^2-e^2 x^2\right)^p}{d+e x} \, dx","Int[(x^2*(d^2 - e^2*x^2)^p)/(d + e*x),x]","\frac{x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},1-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 d}+\frac{d^2 \left(d^2-e^2 x^2\right)^p}{2 e^3 p}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 (p+1)}","\frac{x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},1-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 d}+\frac{d^2 \left(d^2-e^2 x^2\right)^p}{2 e^3 p}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 (p+1)}",1,"(d^2*(d^2 - e^2*x^2)^p)/(2*e^3*p) - (d^2 - e^2*x^2)^(1 + p)/(2*e^3*(1 + p)) + (x^3*(d^2 - e^2*x^2)^p*Hypergeometric2F1[3/2, 1 - p, 5/2, (e^2*x^2)/d^2])/(3*d*(1 - (e^2*x^2)/d^2)^p)","A",7,6,25,0.2400,1,"{850, 764, 365, 364, 266, 43}"
270,1,90,0,0.0581513,"\int \frac{x \left(d^2-e^2 x^2\right)^p}{d+e x} \, dx","Int[(x*(d^2 - e^2*x^2)^p)/(d + e*x),x]","-\frac{e x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},1-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^2}-\frac{d \left(d^2-e^2 x^2\right)^p}{2 e^2 p}","-\frac{e x^3 \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{3}{2},1-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^2}-\frac{d \left(d^2-e^2 x^2\right)^p}{2 e^2 p}",1,"-(d*(d^2 - e^2*x^2)^p)/(2*e^2*p) - (e*x^3*(d^2 - e^2*x^2)^p*Hypergeometric2F1[3/2, 1 - p, 5/2, (e^2*x^2)/d^2])/(3*d^2*(1 - (e^2*x^2)/d^2)^p)","A",5,5,23,0.2174,1,"{785, 764, 261, 365, 364}"
271,1,73,0,0.0328738,"\int \frac{\left(d^2-e^2 x^2\right)^p}{d+e x} \, dx","Int[(d^2 - e^2*x^2)^p/(d + e*x),x]","-\frac{2^{p-1} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e (p+1)}","-\frac{2^{p-1} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e (p+1)}",1,"-((2^(-1 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^2*e*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
272,1,104,0,0.0679128,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^p/(x*(d + e*x)),x]","-\frac{e x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},1-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^2}-\frac{\left(d^2-e^2 x^2\right)^p \, _2F_1\left(1,p;p+1;1-\frac{e^2 x^2}{d^2}\right)}{2 d p}","-\frac{e x \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},1-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^2}-\frac{\left(d^2-e^2 x^2\right)^p \, _2F_1\left(1,p;p+1;1-\frac{e^2 x^2}{d^2}\right)}{2 d p}",1,"-((e*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 1 - p, 3/2, (e^2*x^2)/d^2])/(d^2*(1 - (e^2*x^2)/d^2)^p)) - ((d^2 - e^2*x^2)^p*Hypergeometric2F1[1, p, 1 + p, 1 - (e^2*x^2)/d^2])/(2*d*p)","A",6,6,25,0.2400,1,"{850, 764, 266, 65, 246, 245}"
273,1,106,0,0.0742381,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^2 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^p/(x^2*(d + e*x)),x]","\frac{e \left(d^2-e^2 x^2\right)^p \, _2F_1\left(1,p;p+1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 p}-\frac{\left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},1-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{d x}","\frac{e \left(d^2-e^2 x^2\right)^p \, _2F_1\left(1,p;p+1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 p}-\frac{\left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},1-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{d x}",1,"-(((d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, 1 - p, 1/2, (e^2*x^2)/d^2])/(d*x*(1 - (e^2*x^2)/d^2)^p)) + (e*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1, p, 1 + p, 1 - (e^2*x^2)/d^2])/(2*d^2*p)","A",6,6,25,0.2400,1,"{850, 764, 365, 364, 266, 65}"
274,1,108,0,0.0798012,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^3 (d+e x)} \, dx","Int[(d^2 - e^2*x^2)^p/(x^3*(d + e*x)),x]","\frac{e \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},1-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{d^2 x}-\frac{e^2 \left(d^2-e^2 x^2\right)^p \, _2F_1\left(2,p;p+1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^3 p}","\frac{e \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2},1-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{d^2 x}-\frac{e^2 \left(d^2-e^2 x^2\right)^p \, _2F_1\left(2,p;p+1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^3 p}",1,"(e*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, 1 - p, 1/2, (e^2*x^2)/d^2])/(d^2*x*(1 - (e^2*x^2)/d^2)^p) - (e^2*(d^2 - e^2*x^2)^p*Hypergeometric2F1[2, p, 1 + p, 1 - (e^2*x^2)/d^2])/(2*d^3*p)","A",6,6,25,0.2400,1,"{850, 764, 266, 65, 365, 364}"
275,1,179,0,0.1886836,"\int \frac{x^5 \left(d^2-e^2 x^2\right)^p}{(d+e x)^2} \, dx","Int[(x^5*(d^2 - e^2*x^2)^p)/(d + e*x)^2,x]","-\frac{2 e x^7 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{7}{2},2-p;\frac{9}{2};\frac{e^2 x^2}{d^2}\right)}{7 d^3}+\frac{d^6 \left(d^2-e^2 x^2\right)^{p-1}}{e^6 (1-p)}+\frac{5 d^4 \left(d^2-e^2 x^2\right)^p}{2 e^6 p}-\frac{2 d^2 \left(d^2-e^2 x^2\right)^{p+1}}{e^6 (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+2}}{2 e^6 (p+2)}","-\frac{2 e x^7 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{7}{2},2-p;\frac{9}{2};\frac{e^2 x^2}{d^2}\right)}{7 d^3}+\frac{d^6 \left(d^2-e^2 x^2\right)^{p-1}}{e^6 (1-p)}+\frac{5 d^4 \left(d^2-e^2 x^2\right)^p}{2 e^6 p}-\frac{2 d^2 \left(d^2-e^2 x^2\right)^{p+1}}{e^6 (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+2}}{2 e^6 (p+2)}",1,"(d^6*(d^2 - e^2*x^2)^(-1 + p))/(e^6*(1 - p)) + (5*d^4*(d^2 - e^2*x^2)^p)/(2*e^6*p) - (2*d^2*(d^2 - e^2*x^2)^(1 + p))/(e^6*(1 + p)) + (d^2 - e^2*x^2)^(2 + p)/(2*e^6*(2 + p)) - (2*e*x^7*(d^2 - e^2*x^2)^p*Hypergeometric2F1[7/2, 2 - p, 9/2, (e^2*x^2)/d^2])/(7*d^3*(1 - (e^2*x^2)/d^2)^p)","A",8,7,25,0.2800,1,"{852, 1652, 446, 77, 12, 365, 364}"
276,1,184,0,0.205062,"\int \frac{x^4 \left(d^2-e^2 x^2\right)^p}{(d+e x)^2} \, dx","Int[(x^4*(d^2 - e^2*x^2)^p)/(d + e*x)^2,x]","\frac{2 (p+4) x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},2-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^2 (2 p+3)}-\frac{x^5 \left(d^2-e^2 x^2\right)^{p-1}}{2 p+3}-\frac{d^5 \left(d^2-e^2 x^2\right)^{p-1}}{e^5 (1-p)}-\frac{2 d^3 \left(d^2-e^2 x^2\right)^p}{e^5 p}+\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{e^5 (p+1)}","\frac{2 (p+4) x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},2-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^2 (2 p+3)}-\frac{x^5 \left(d^2-e^2 x^2\right)^{p-1}}{2 p+3}-\frac{d^5 \left(d^2-e^2 x^2\right)^{p-1}}{e^5 (1-p)}-\frac{2 d^3 \left(d^2-e^2 x^2\right)^p}{e^5 p}+\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{e^5 (p+1)}",1,"-((d^5*(d^2 - e^2*x^2)^(-1 + p))/(e^5*(1 - p))) - (x^5*(d^2 - e^2*x^2)^(-1 + p))/(3 + 2*p) - (2*d^3*(d^2 - e^2*x^2)^p)/(e^5*p) + (d*(d^2 - e^2*x^2)^(1 + p))/(e^5*(1 + p)) + (2*(4 + p)*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, 2 - p, 7/2, (e^2*x^2)/d^2])/(5*d^2*(3 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",9,8,25,0.3200,1,"{852, 1652, 459, 365, 364, 12, 266, 43}"
277,1,150,0,0.1648808,"\int \frac{x^3 \left(d^2-e^2 x^2\right)^p}{(d+e x)^2} \, dx","Int[(x^3*(d^2 - e^2*x^2)^p)/(d + e*x)^2,x]","-\frac{2 e x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},2-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^3}+\frac{d^4 \left(d^2-e^2 x^2\right)^{p-1}}{e^4 (1-p)}+\frac{3 d^2 \left(d^2-e^2 x^2\right)^p}{2 e^4 p}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 (p+1)}","-\frac{2 e x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},2-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^3}+\frac{d^4 \left(d^2-e^2 x^2\right)^{p-1}}{e^4 (1-p)}+\frac{3 d^2 \left(d^2-e^2 x^2\right)^p}{2 e^4 p}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 (p+1)}",1,"(d^4*(d^2 - e^2*x^2)^(-1 + p))/(e^4*(1 - p)) + (3*d^2*(d^2 - e^2*x^2)^p)/(2*e^4*p) - (d^2 - e^2*x^2)^(1 + p)/(2*e^4*(1 + p)) - (2*e*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, 2 - p, 7/2, (e^2*x^2)/d^2])/(5*d^3*(1 - (e^2*x^2)/d^2)^p)","A",8,7,25,0.2800,1,"{852, 1652, 446, 77, 12, 365, 364}"
278,1,156,0,0.1851727,"\int \frac{x^2 \left(d^2-e^2 x^2\right)^p}{(d+e x)^2} \, dx","Int[(x^2*(d^2 - e^2*x^2)^p)/(d + e*x)^2,x]","\frac{2 (p+2) x^3 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{3}{2},2-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^2 (2 p+1)}-\frac{x^3 \left(d^2-e^2 x^2\right)^{p-1}}{2 p+1}-\frac{d^3 \left(d^2-e^2 x^2\right)^{p-1}}{e^3 (1-p)}-\frac{d \left(d^2-e^2 x^2\right)^p}{e^3 p}","\frac{2 (p+2) x^3 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{3}{2},2-p;\frac{5}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^2 (2 p+1)}-\frac{x^3 \left(d^2-e^2 x^2\right)^{p-1}}{2 p+1}-\frac{d^3 \left(d^2-e^2 x^2\right)^{p-1}}{e^3 (1-p)}-\frac{d \left(d^2-e^2 x^2\right)^p}{e^3 p}",1,"-((d^3*(d^2 - e^2*x^2)^(-1 + p))/(e^3*(1 - p))) - (x^3*(d^2 - e^2*x^2)^(-1 + p))/(1 + 2*p) - (d*(d^2 - e^2*x^2)^p)/(e^3*p) + (2*(2 + p)*x^3*(d^2 - e^2*x^2)^p*Hypergeometric2F1[3/2, 2 - p, 5/2, (e^2*x^2)/d^2])/(3*d^2*(1 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",9,8,25,0.3200,1,"{852, 1652, 459, 365, 364, 12, 266, 43}"
279,1,115,0,0.0539433,"\int \frac{x \left(d^2-e^2 x^2\right)^p}{(d+e x)^2} \, dx","Int[(x*(d^2 - e^2*x^2)^p)/(d + e*x)^2,x]","\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^2 (1-p) (d+e x)^2}-\frac{2^{p-1} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e^2 \left(1-p^2\right)}","\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^2 (1-p) (d+e x)^2}-\frac{2^{p-1} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(1-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e^2 \left(1-p^2\right)}",1,"(d^2 - e^2*x^2)^(1 + p)/(2*e^2*(1 - p)*(d + e*x)^2) - (2^(-1 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[1 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^2*e^2*(1 - p^2))","A",3,3,23,0.1304,1,"{793, 678, 69}"
280,1,73,0,0.0347262,"\int \frac{\left(d^2-e^2 x^2\right)^p}{(d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^p/(d + e*x)^2,x]","-\frac{2^{p-2} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(2-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^3 e (p+1)}","-\frac{2^{p-2} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(2-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^3 e (p+1)}",1,"-((2^(-2 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[2 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^3*e*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
281,1,128,0,0.1249083,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^p/(x*(d + e*x)^2),x]","-\frac{2 e x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},2-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^3}-\frac{\left(d^2-e^2 x^2\right)^p \, _2F_1\left(1,p;p+1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 p}+\frac{\left(d^2-e^2 x^2\right)^{p-1}}{1-p}","-\frac{2 e x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},2-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^3}-\frac{\left(d^2-e^2 x^2\right)^p \, _2F_1\left(1,p;p+1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 p}+\frac{\left(d^2-e^2 x^2\right)^{p-1}}{1-p}",1,"(d^2 - e^2*x^2)^(-1 + p)/(1 - p) - (2*e*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 2 - p, 3/2, (e^2*x^2)/d^2])/(d^3*(1 - (e^2*x^2)/d^2)^p) - ((d^2 - e^2*x^2)^p*Hypergeometric2F1[1, p, 1 + p, 1 - (e^2*x^2)/d^2])/(2*d^2*p)","A",8,8,25,0.3200,1,"{852, 1652, 446, 79, 65, 12, 246, 245}"
282,1,137,0,0.1619066,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^2 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^p/(x^2*(d + e*x)^2),x]","-\frac{e \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(1,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{d (1-p)}+\frac{2 e^2 (2-p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},2-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^4}-\frac{\left(d^2-e^2 x^2\right)^{p-1}}{x}","-\frac{e \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(1,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{d (1-p)}+\frac{2 e^2 (2-p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},2-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^4}-\frac{\left(d^2-e^2 x^2\right)^{p-1}}{x}",1,"-((d^2 - e^2*x^2)^(-1 + p)/x) + (2*e^2*(2 - p)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 2 - p, 3/2, (e^2*x^2)/d^2])/(d^4*(1 - (e^2*x^2)/d^2)^p) - (e*(d^2 - e^2*x^2)^(-1 + p)*Hypergeometric2F1[1, -1 + p, p, 1 - (e^2*x^2)/d^2])/(d*(1 - p))","A",7,7,25,0.2800,1,"{852, 1807, 764, 266, 65, 246, 245}"
283,1,143,0,0.1615596,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^3 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^p/(x^3*(d + e*x)^2),x]","\frac{e^2 (3-p) \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(1,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (1-p)}+\frac{2 e \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},2-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{d^3 x}-\frac{\left(d^2-e^2 x^2\right)^{p-1}}{2 x^2}","\frac{e^2 (3-p) \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(1,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (1-p)}+\frac{2 e \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},2-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{d^3 x}-\frac{\left(d^2-e^2 x^2\right)^{p-1}}{2 x^2}",1,"-(d^2 - e^2*x^2)^(-1 + p)/(2*x^2) + (2*e*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, 2 - p, 1/2, (e^2*x^2)/d^2])/(d^3*x*(1 - (e^2*x^2)/d^2)^p) + (e^2*(3 - p)*(d^2 - e^2*x^2)^(-1 + p)*Hypergeometric2F1[1, -1 + p, p, 1 - (e^2*x^2)/d^2])/(2*d^2*(1 - p))","A",7,7,25,0.2800,1,"{852, 1807, 764, 365, 364, 266, 65}"
284,1,145,0,0.1715825,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^4 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^p/(x^4*(d + e*x)^2),x]","-\frac{e^3 \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(2,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{d^3 (1-p)}-\frac{2 e^2 (4-p) \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},2-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^4 x}-\frac{\left(d^2-e^2 x^2\right)^{p-1}}{3 x^3}","-\frac{e^3 \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(2,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{d^3 (1-p)}-\frac{2 e^2 (4-p) \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},2-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^4 x}-\frac{\left(d^2-e^2 x^2\right)^{p-1}}{3 x^3}",1,"-(d^2 - e^2*x^2)^(-1 + p)/(3*x^3) - (2*e^2*(4 - p)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, 2 - p, 1/2, (e^2*x^2)/d^2])/(3*d^4*x*(1 - (e^2*x^2)/d^2)^p) - (e^3*(d^2 - e^2*x^2)^(-1 + p)*Hypergeometric2F1[2, -1 + p, p, 1 - (e^2*x^2)/d^2])/(d^3*(1 - p))","A",7,7,25,0.2800,1,"{852, 1807, 764, 266, 65, 365, 364}"
285,1,145,0,0.1716809,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^5 (d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^p/(x^5*(d + e*x)^2),x]","\frac{e^4 (5-p) \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(2,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{4 d^4 (1-p)}+\frac{2 e \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{3}{2},2-p;-\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^3 x^3}-\frac{\left(d^2-e^2 x^2\right)^{p-1}}{4 x^4}","\frac{e^4 (5-p) \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(2,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{4 d^4 (1-p)}+\frac{2 e \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{3}{2},2-p;-\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^3 x^3}-\frac{\left(d^2-e^2 x^2\right)^{p-1}}{4 x^4}",1,"-(d^2 - e^2*x^2)^(-1 + p)/(4*x^4) + (2*e*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-3/2, 2 - p, -1/2, (e^2*x^2)/d^2])/(3*d^3*x^3*(1 - (e^2*x^2)/d^2)^p) + (e^4*(5 - p)*(d^2 - e^2*x^2)^(-1 + p)*Hypergeometric2F1[2, -1 + p, p, 1 - (e^2*x^2)/d^2])/(4*d^4*(1 - p))","A",7,7,25,0.2800,1,"{852, 1807, 764, 365, 364, 266, 65}"
286,1,220,0,0.2291092,"\int \frac{x^4 \left(d^2-e^2 x^2\right)^p}{(d+e x)^3} \, dx","Int[(x^4*(d^2 - e^2*x^2)^p)/(d + e*x)^3,x]","\frac{2 (p+8) x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},3-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^3 (2 p+1)}-\frac{3 d x^5 \left(d^2-e^2 x^2\right)^{p-2}}{2 p+1}-\frac{2 d^6 \left(d^2-e^2 x^2\right)^{p-2}}{e^5 (2-p)}+\frac{9 d^4 \left(d^2-e^2 x^2\right)^{p-1}}{2 e^5 (1-p)}+\frac{3 d^2 \left(d^2-e^2 x^2\right)^p}{e^5 p}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^5 (p+1)}","\frac{2 (p+8) x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},3-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^3 (2 p+1)}-\frac{3 d x^5 \left(d^2-e^2 x^2\right)^{p-2}}{2 p+1}-\frac{2 d^6 \left(d^2-e^2 x^2\right)^{p-2}}{e^5 (2-p)}+\frac{9 d^4 \left(d^2-e^2 x^2\right)^{p-1}}{2 e^5 (1-p)}+\frac{3 d^2 \left(d^2-e^2 x^2\right)^p}{e^5 p}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^5 (p+1)}",1,"(-2*d^6*(d^2 - e^2*x^2)^(-2 + p))/(e^5*(2 - p)) - (3*d*x^5*(d^2 - e^2*x^2)^(-2 + p))/(1 + 2*p) + (9*d^4*(d^2 - e^2*x^2)^(-1 + p))/(2*e^5*(1 - p)) + (3*d^2*(d^2 - e^2*x^2)^p)/(e^5*p) - (d^2 - e^2*x^2)^(1 + p)/(2*e^5*(1 + p)) + (2*(8 + p)*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, 3 - p, 7/2, (e^2*x^2)/d^2])/(5*d^3*(1 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",8,7,25,0.2800,1,"{852, 1652, 459, 365, 364, 446, 77}"
287,1,194,0,0.2056273,"\int \frac{x^3 \left(d^2-e^2 x^2\right)^p}{(d+e x)^3} \, dx","Int[(x^3*(d^2 - e^2*x^2)^p)/(d + e*x)^3,x]","-\frac{2 e (3 p+4) x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},3-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^4 (2 p+1)}+\frac{e x^5 \left(d^2-e^2 x^2\right)^{p-2}}{2 p+1}+\frac{2 d^5 \left(d^2-e^2 x^2\right)^{p-2}}{e^4 (2-p)}-\frac{7 d^3 \left(d^2-e^2 x^2\right)^{p-1}}{2 e^4 (1-p)}-\frac{3 d \left(d^2-e^2 x^2\right)^p}{2 e^4 p}","-\frac{2 e (3 p+4) x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},3-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^4 (2 p+1)}+\frac{e x^5 \left(d^2-e^2 x^2\right)^{p-2}}{2 p+1}+\frac{2 d^5 \left(d^2-e^2 x^2\right)^{p-2}}{e^4 (2-p)}-\frac{7 d^3 \left(d^2-e^2 x^2\right)^{p-1}}{2 e^4 (1-p)}-\frac{3 d \left(d^2-e^2 x^2\right)^p}{2 e^4 p}",1,"(2*d^5*(d^2 - e^2*x^2)^(-2 + p))/(e^4*(2 - p)) + (e*x^5*(d^2 - e^2*x^2)^(-2 + p))/(1 + 2*p) - (7*d^3*(d^2 - e^2*x^2)^(-1 + p))/(2*e^4*(1 - p)) - (3*d*(d^2 - e^2*x^2)^p)/(2*e^4*p) - (2*e*(4 + 3*p)*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, 3 - p, 7/2, (e^2*x^2)/d^2])/(5*d^4*(1 + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",8,7,25,0.2800,1,"{852, 1652, 446, 77, 459, 365, 364}"
288,1,157,0,0.1830631,"\int \frac{x^2 \left(d^2-e^2 x^2\right)^p}{(d+e x)^3} \, dx","Int[(x^2*(d^2 - e^2*x^2)^p)/(d + e*x)^3,x]","\frac{2^{p-3} (p+4) \left(d^2-e^2 x^2\right)^{p+1} \left(\frac{e x}{d}+1\right)^{-p-1} \, _2F_1\left(2-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e^3 (2-p) p (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 p (d+e x)^2}-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 (2-p) (d+e x)^3}","\frac{2^{p-3} (p+4) \left(d^2-e^2 x^2\right)^{p+1} \left(\frac{e x}{d}+1\right)^{-p-1} \, _2F_1\left(2-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e^3 (2-p) p (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 p (d+e x)^2}-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 (2-p) (d+e x)^3}",1,"-(d*(d^2 - e^2*x^2)^(1 + p))/(2*e^3*(2 - p)*(d + e*x)^3) - (d^2 - e^2*x^2)^(1 + p)/(2*e^3*p*(d + e*x)^2) + (2^(-3 + p)*(4 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[2 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^2*e^3*(2 - p)*p*(1 + p))","A",4,4,25,0.1600,1,"{1639, 793, 678, 69}"
289,1,118,0,0.0533851,"\int \frac{x \left(d^2-e^2 x^2\right)^p}{(d+e x)^3} \, dx","Int[(x*(d^2 - e^2*x^2)^p)/(d + e*x)^3,x]","\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^2 (2-p) (d+e x)^3}-\frac{3\ 2^{p-3} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(2-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^3 e^2 (2-p) (p+1)}","\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^2 (2-p) (d+e x)^3}-\frac{3\ 2^{p-3} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(2-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^3 e^2 (2-p) (p+1)}",1,"(d^2 - e^2*x^2)^(1 + p)/(2*e^2*(2 - p)*(d + e*x)^3) - (3*2^(-3 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[2 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^3*e^2*(2 - p)*(1 + p))","A",3,3,23,0.1304,1,"{793, 678, 69}"
290,1,73,0,0.0289771,"\int \frac{\left(d^2-e^2 x^2\right)^p}{(d+e x)^3} \, dx","Int[(d^2 - e^2*x^2)^p/(d + e*x)^3,x]","-\frac{2^{p-3} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^4 e (p+1)}","-\frac{2^{p-3} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^4 e (p+1)}",1,"-((2^(-3 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[3 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^4*e*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
291,1,175,0,0.1555015,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x (d+e x)^3} \, dx","Int[(d^2 - e^2*x^2)^p/(x*(d + e*x)^3),x]","\frac{\left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(1,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{2 d (1-p)}-\frac{2 e (4-3 p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},3-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^4 (3-2 p)}-\frac{e x \left(d^2-e^2 x^2\right)^{p-2}}{3-2 p}+\frac{2 d \left(d^2-e^2 x^2\right)^{p-2}}{2-p}","\frac{\left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(1,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{2 d (1-p)}-\frac{2 e (4-3 p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},3-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^4 (3-2 p)}-\frac{e x \left(d^2-e^2 x^2\right)^{p-2}}{3-2 p}+\frac{2 d \left(d^2-e^2 x^2\right)^{p-2}}{2-p}",1,"(2*d*(d^2 - e^2*x^2)^(-2 + p))/(2 - p) - (e*x*(d^2 - e^2*x^2)^(-2 + p))/(3 - 2*p) - (2*e*(4 - 3*p)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 3 - p, 3/2, (e^2*x^2)/d^2])/(d^4*(3 - 2*p)*(1 - (e^2*x^2)/d^2)^p) + ((d^2 - e^2*x^2)^(-1 + p)*Hypergeometric2F1[1, -1 + p, p, 1 - (e^2*x^2)/d^2])/(2*d*(1 - p))","A",8,8,25,0.3200,1,"{852, 1652, 446, 79, 65, 388, 246, 245}"
292,1,166,0,0.2257594,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^2 (d+e x)^3} \, dx","Int[(d^2 - e^2*x^2)^p/(x^2*(d + e*x)^3),x]","-\frac{3 e \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(1,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (1-p)}+\frac{2 e^2 (4-p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},3-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^5}-\frac{2 e \left(d^2-e^2 x^2\right)^{p-2}}{2-p}-\frac{d \left(d^2-e^2 x^2\right)^{p-2}}{x}","-\frac{3 e \left(d^2-e^2 x^2\right)^{p-1} \, _2F_1\left(1,p-1;p;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (1-p)}+\frac{2 e^2 (4-p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},3-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^5}-\frac{2 e \left(d^2-e^2 x^2\right)^{p-2}}{2-p}-\frac{d \left(d^2-e^2 x^2\right)^{p-2}}{x}",1,"(-2*e*(d^2 - e^2*x^2)^(-2 + p))/(2 - p) - (d*(d^2 - e^2*x^2)^(-2 + p))/x + (2*e^2*(4 - p)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 3 - p, 3/2, (e^2*x^2)/d^2])/(d^5*(1 - (e^2*x^2)/d^2)^p) - (3*e*(d^2 - e^2*x^2)^(-1 + p)*Hypergeometric2F1[1, -1 + p, p, 1 - (e^2*x^2)/d^2])/(2*d^2*(1 - p))","A",9,9,25,0.3600,1,"{852, 1807, 1652, 446, 79, 65, 12, 246, 245}"
293,1,173,0,0.2657524,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^3 (d+e x)^3} \, dx","Int[(d^2 - e^2*x^2)^p/(x^3*(d + e*x)^3),x]","\frac{e^2 (6-p) \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{2 d (2-p)}-\frac{2 e^3 (8-3 p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},3-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^6}+\frac{3 e \left(d^2-e^2 x^2\right)^{p-2}}{x}-\frac{d \left(d^2-e^2 x^2\right)^{p-2}}{2 x^2}","\frac{e^2 (6-p) \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{2 d (2-p)}-\frac{2 e^3 (8-3 p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},3-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^6}+\frac{3 e \left(d^2-e^2 x^2\right)^{p-2}}{x}-\frac{d \left(d^2-e^2 x^2\right)^{p-2}}{2 x^2}",1,"-(d*(d^2 - e^2*x^2)^(-2 + p))/(2*x^2) + (3*e*(d^2 - e^2*x^2)^(-2 + p))/x - (2*e^3*(8 - 3*p)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 3 - p, 3/2, (e^2*x^2)/d^2])/(d^6*(1 - (e^2*x^2)/d^2)^p) + (e^2*(6 - p)*(d^2 - e^2*x^2)^(-2 + p)*Hypergeometric2F1[1, -2 + p, -1 + p, 1 - (e^2*x^2)/d^2])/(2*d*(2 - p))","A",8,7,25,0.2800,1,"{852, 1807, 764, 266, 65, 246, 245}"
294,1,179,0,0.2747826,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^4 (d+e x)^3} \, dx","Int[(d^2 - e^2*x^2)^p/(x^4*(d + e*x)^3),x]","-\frac{e^3 (10-3 p) \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (2-p)}-\frac{2 e^2 (8-p) \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},3-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^5 x}+\frac{3 e \left(d^2-e^2 x^2\right)^{p-2}}{2 x^2}-\frac{d \left(d^2-e^2 x^2\right)^{p-2}}{3 x^3}","-\frac{e^3 (10-3 p) \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (2-p)}-\frac{2 e^2 (8-p) \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},3-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^5 x}+\frac{3 e \left(d^2-e^2 x^2\right)^{p-2}}{2 x^2}-\frac{d \left(d^2-e^2 x^2\right)^{p-2}}{3 x^3}",1,"-(d*(d^2 - e^2*x^2)^(-2 + p))/(3*x^3) + (3*e*(d^2 - e^2*x^2)^(-2 + p))/(2*x^2) - (2*e^2*(8 - p)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, 3 - p, 1/2, (e^2*x^2)/d^2])/(3*d^5*x*(1 - (e^2*x^2)/d^2)^p) - (e^3*(10 - 3*p)*(d^2 - e^2*x^2)^(-2 + p)*Hypergeometric2F1[1, -2 + p, -1 + p, 1 - (e^2*x^2)/d^2])/(2*d^2*(2 - p))","A",8,7,25,0.2800,1,"{852, 1807, 764, 365, 364, 266, 65}"
295,1,174,0,0.2768598,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^5 (d+e x)^3} \, dx","Int[(d^2 - e^2*x^2)^p/(x^5*(d + e*x)^3),x]","\frac{e^4 (10-p) \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(2,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{4 d^3 (2-p)}+\frac{2 e^3 (4-p) \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},3-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{d^6 x}+\frac{e \left(d^2-e^2 x^2\right)^{p-2}}{x^3}-\frac{d \left(d^2-e^2 x^2\right)^{p-2}}{4 x^4}","\frac{e^4 (10-p) \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(2,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{4 d^3 (2-p)}+\frac{2 e^3 (4-p) \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},3-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{d^6 x}+\frac{e \left(d^2-e^2 x^2\right)^{p-2}}{x^3}-\frac{d \left(d^2-e^2 x^2\right)^{p-2}}{4 x^4}",1,"-(d*(d^2 - e^2*x^2)^(-2 + p))/(4*x^4) + (e*(d^2 - e^2*x^2)^(-2 + p))/x^3 + (2*e^3*(4 - p)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, 3 - p, 1/2, (e^2*x^2)/d^2])/(d^6*x*(1 - (e^2*x^2)/d^2)^p) + (e^4*(10 - p)*(d^2 - e^2*x^2)^(-2 + p)*Hypergeometric2F1[2, -2 + p, -1 + p, 1 - (e^2*x^2)/d^2])/(4*d^3*(2 - p))","A",8,7,25,0.2800,1,"{852, 1807, 764, 266, 65, 365, 364}"
296,1,265,0,0.3055656,"\int \frac{x^4 \left(d^2-e^2 x^2\right)^p}{(d+e x)^4} \, dx","Int[(x^4*(d^2 - e^2*x^2)^p)/(d + e*x)^4,x]","-\frac{4 \left(p^2+15 p+16\right) x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},4-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^4 \left(1-4 p^2\right)}+\frac{d^2 (12 p+13) x^5 \left(d^2-e^2 x^2\right)^{p-3}}{1-4 p^2}-\frac{e^2 x^7 \left(d^2-e^2 x^2\right)^{p-3}}{2 p+1}-\frac{4 d^7 \left(d^2-e^2 x^2\right)^{p-3}}{e^5 (3-p)}+\frac{10 d^5 \left(d^2-e^2 x^2\right)^{p-2}}{e^5 (2-p)}-\frac{8 d^3 \left(d^2-e^2 x^2\right)^{p-1}}{e^5 (1-p)}-\frac{2 d \left(d^2-e^2 x^2\right)^p}{e^5 p}","-\frac{4 \left(p^2+15 p+16\right) x^5 \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{5}{2},4-p;\frac{7}{2};\frac{e^2 x^2}{d^2}\right)}{5 d^4 \left(1-4 p^2\right)}+\frac{d^2 (12 p+13) x^5 \left(d^2-e^2 x^2\right)^{p-3}}{1-4 p^2}-\frac{e^2 x^7 \left(d^2-e^2 x^2\right)^{p-3}}{2 p+1}-\frac{4 d^7 \left(d^2-e^2 x^2\right)^{p-3}}{e^5 (3-p)}+\frac{10 d^5 \left(d^2-e^2 x^2\right)^{p-2}}{e^5 (2-p)}-\frac{8 d^3 \left(d^2-e^2 x^2\right)^{p-1}}{e^5 (1-p)}-\frac{2 d \left(d^2-e^2 x^2\right)^p}{e^5 p}",1,"(-4*d^7*(d^2 - e^2*x^2)^(-3 + p))/(e^5*(3 - p)) + (d^2*(13 + 12*p)*x^5*(d^2 - e^2*x^2)^(-3 + p))/(1 - 4*p^2) - (e^2*x^7*(d^2 - e^2*x^2)^(-3 + p))/(1 + 2*p) + (10*d^5*(d^2 - e^2*x^2)^(-2 + p))/(e^5*(2 - p)) - (8*d^3*(d^2 - e^2*x^2)^(-1 + p))/(e^5*(1 - p)) - (2*d*(d^2 - e^2*x^2)^p)/(e^5*p) - (4*(16 + 15*p + p^2)*x^5*(d^2 - e^2*x^2)^p*Hypergeometric2F1[5/2, 4 - p, 7/2, (e^2*x^2)/d^2])/(5*d^4*(1 - 4*p^2)*(1 - (e^2*x^2)/d^2)^p)","A",9,8,25,0.3200,1,"{852, 1652, 1267, 459, 365, 364, 446, 77}"
297,1,211,0,0.3754522,"\int \frac{x^3 \left(d^2-e^2 x^2\right)^p}{(d+e x)^4} \, dx","Int[(x^3*(d^2 - e^2*x^2)^p)/(d + e*x)^4,x]","\frac{3\ 2^{p-2} (p+2) \left(d^2-e^2 x^2\right)^{p+1} \left(\frac{e x}{d}+1\right)^{-p-1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e^4 (1-2 p) (3-p) p (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 p (d+e x)^2}-\frac{d (2 p+1) \left(d^2-e^2 x^2\right)^{p+1}}{e^4 (1-2 p) p (d+e x)^3}+\frac{d^2 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 (3-p) (d+e x)^4}","\frac{3\ 2^{p-2} (p+2) \left(d^2-e^2 x^2\right)^{p+1} \left(\frac{e x}{d}+1\right)^{-p-1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e^4 (1-2 p) (3-p) p (p+1)}-\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 p (d+e x)^2}-\frac{d (2 p+1) \left(d^2-e^2 x^2\right)^{p+1}}{e^4 (1-2 p) p (d+e x)^3}+\frac{d^2 \left(d^2-e^2 x^2\right)^{p+1}}{2 e^4 (3-p) (d+e x)^4}",1,"(d^2*(d^2 - e^2*x^2)^(1 + p))/(2*e^4*(3 - p)*(d + e*x)^4) - (d*(1 + 2*p)*(d^2 - e^2*x^2)^(1 + p))/(e^4*(1 - 2*p)*p*(d + e*x)^3) - (d^2 - e^2*x^2)^(1 + p)/(2*e^4*p*(d + e*x)^2) + (3*2^(-2 + p)*(2 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[3 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^2*e^4*(1 - 2*p)*(3 - p)*p*(1 + p))","A",5,4,25,0.1600,1,"{1639, 793, 678, 69}"
298,1,163,0,0.1906001,"\int \frac{x^2 \left(d^2-e^2 x^2\right)^p}{(d+e x)^4} \, dx","Int[(x^2*(d^2 - e^2*x^2)^p)/(d + e*x)^4,x]","-\frac{2^{p-3} (p+7) \left(d^2-e^2 x^2\right)^{p+1} \left(\frac{e x}{d}+1\right)^{-p-1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^3 e^3 (1-2 p) (3-p) (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+1}}{e^3 (1-2 p) (d+e x)^3}-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 (3-p) (d+e x)^4}","-\frac{2^{p-3} (p+7) \left(d^2-e^2 x^2\right)^{p+1} \left(\frac{e x}{d}+1\right)^{-p-1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^3 e^3 (1-2 p) (3-p) (p+1)}+\frac{\left(d^2-e^2 x^2\right)^{p+1}}{e^3 (1-2 p) (d+e x)^3}-\frac{d \left(d^2-e^2 x^2\right)^{p+1}}{2 e^3 (3-p) (d+e x)^4}",1,"-(d*(d^2 - e^2*x^2)^(1 + p))/(2*e^3*(3 - p)*(d + e*x)^4) + (d^2 - e^2*x^2)^(1 + p)/(e^3*(1 - 2*p)*(d + e*x)^3) - (2^(-3 + p)*(7 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[3 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^3*e^3*(1 - 2*p)*(3 - p)*(1 + p))","A",4,4,25,0.1600,1,"{1639, 793, 678, 69}"
299,1,118,0,0.0535491,"\int \frac{x \left(d^2-e^2 x^2\right)^p}{(d+e x)^4} \, dx","Int[(x*(d^2 - e^2*x^2)^p)/(d + e*x)^4,x]","\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^2 (3-p) (d+e x)^4}-\frac{2^{p-2} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^4 e^2 (3-p) (p+1)}","\frac{\left(d^2-e^2 x^2\right)^{p+1}}{2 e^2 (3-p) (d+e x)^4}-\frac{2^{p-2} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^4 e^2 (3-p) (p+1)}",1,"(d^2 - e^2*x^2)^(1 + p)/(2*e^2*(3 - p)*(d + e*x)^4) - (2^(-2 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[3 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^4*e^2*(3 - p)*(1 + p))","A",3,3,23,0.1304,1,"{793, 678, 69}"
300,1,73,0,0.0310373,"\int \frac{\left(d^2-e^2 x^2\right)^p}{(d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^p/(d + e*x)^4,x]","-\frac{2^{p-4} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(4-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^5 e (p+1)}","-\frac{2^{p-4} \left(\frac{e x}{d}+1\right)^{-p-1} \left(d^2-e^2 x^2\right)^{p+1} \, _2F_1\left(4-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^5 e (p+1)}",1,"-((2^(-4 + p)*(1 + (e*x)/d)^(-1 - p)*(d^2 - e^2*x^2)^(1 + p)*Hypergeometric2F1[4 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^5*e*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
301,1,204,0,0.2082534,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^p/(x*(d + e*x)^4),x]","\frac{\left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{2 (2-p)}-\frac{8 e (2-p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},4-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^5 (5-2 p)}-\frac{4 d e x \left(d^2-e^2 x^2\right)^{p-3}}{5-2 p}+\frac{4 d^2 \left(d^2-e^2 x^2\right)^{p-3}}{3-p}-\frac{\left(d^2-e^2 x^2\right)^{p-2}}{2 (2-p)}","\frac{\left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{2 (2-p)}-\frac{8 e (2-p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},4-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^5 (5-2 p)}-\frac{4 d e x \left(d^2-e^2 x^2\right)^{p-3}}{5-2 p}+\frac{4 d^2 \left(d^2-e^2 x^2\right)^{p-3}}{3-p}-\frac{\left(d^2-e^2 x^2\right)^{p-2}}{2 (2-p)}",1,"(4*d^2*(d^2 - e^2*x^2)^(-3 + p))/(3 - p) - (4*d*e*x*(d^2 - e^2*x^2)^(-3 + p))/(5 - 2*p) - (d^2 - e^2*x^2)^(-2 + p)/(2*(2 - p)) - (8*e*(2 - p)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 4 - p, 3/2, (e^2*x^2)/d^2])/(d^5*(5 - 2*p)*(1 - (e^2*x^2)/d^2)^p) + ((d^2 - e^2*x^2)^(-2 + p)*Hypergeometric2F1[1, -2 + p, -1 + p, 1 - (e^2*x^2)/d^2])/(2*(2 - p))","A",9,9,25,0.3600,1,"{852, 1652, 1251, 951, 79, 65, 388, 246, 245}"
302,1,207,0,0.2778907,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^2 (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^p/(x^2*(d + e*x)^4),x]","\frac{4 e^2 \left(p^2-9 p+16\right) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},4-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^6 (5-2 p)}-\frac{2 e \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{d (2-p)}+\frac{e^2 x \left(d^2-e^2 x^2\right)^{p-3}}{5-2 p}-\frac{4 d e \left(d^2-e^2 x^2\right)^{p-3}}{3-p}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p-3}}{x}","\frac{4 e^2 \left(p^2-9 p+16\right) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},4-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^6 (5-2 p)}-\frac{2 e \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{d (2-p)}+\frac{e^2 x \left(d^2-e^2 x^2\right)^{p-3}}{5-2 p}-\frac{4 d e \left(d^2-e^2 x^2\right)^{p-3}}{3-p}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p-3}}{x}",1,"(-4*d*e*(d^2 - e^2*x^2)^(-3 + p))/(3 - p) - (d^2*(d^2 - e^2*x^2)^(-3 + p))/x + (e^2*x*(d^2 - e^2*x^2)^(-3 + p))/(5 - 2*p) + (4*e^2*(16 - 9*p + p^2)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 4 - p, 3/2, (e^2*x^2)/d^2])/(d^6*(5 - 2*p)*(1 - (e^2*x^2)/d^2)^p) - (2*e*(d^2 - e^2*x^2)^(-2 + p)*Hypergeometric2F1[1, -2 + p, -1 + p, 1 - (e^2*x^2)/d^2])/(d*(2 - p))","A",9,9,25,0.3600,1,"{852, 1807, 1652, 446, 79, 65, 388, 246, 245}"
303,1,211,0,0.3675072,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^3 (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^p/(x^3*(d + e*x)^4),x]","\frac{e^2 (10-p) \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (2-p)}-\frac{8 e^3 (4-p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},4-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^7}+\frac{e^2 (11-p) \left(d^2-e^2 x^2\right)^{p-3}}{2 (3-p)}+\frac{4 d e \left(d^2-e^2 x^2\right)^{p-3}}{x}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p-3}}{2 x^2}","\frac{e^2 (10-p) \left(d^2-e^2 x^2\right)^{p-2} \, _2F_1\left(1,p-2;p-1;1-\frac{e^2 x^2}{d^2}\right)}{2 d^2 (2-p)}-\frac{8 e^3 (4-p) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},4-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{d^7}+\frac{e^2 (11-p) \left(d^2-e^2 x^2\right)^{p-3}}{2 (3-p)}+\frac{4 d e \left(d^2-e^2 x^2\right)^{p-3}}{x}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p-3}}{2 x^2}",1,"(e^2*(11 - p)*(d^2 - e^2*x^2)^(-3 + p))/(2*(3 - p)) - (d^2*(d^2 - e^2*x^2)^(-3 + p))/(2*x^2) + (4*d*e*(d^2 - e^2*x^2)^(-3 + p))/x - (8*e^3*(4 - p)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 4 - p, 3/2, (e^2*x^2)/d^2])/(d^7*(1 - (e^2*x^2)/d^2)^p) + (e^2*(10 - p)*(d^2 - e^2*x^2)^(-2 + p)*Hypergeometric2F1[1, -2 + p, -1 + p, 1 - (e^2*x^2)/d^2])/(2*d^2*(2 - p))","A",10,9,25,0.3600,1,"{852, 1807, 1652, 446, 79, 65, 12, 246, 245}"
304,1,210,0,0.3909513,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^4 (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^p/(x^4*(d + e*x)^4),x]","\frac{4 e^4 \left(p^2-17 p+48\right) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},4-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^8}-\frac{2 e^3 (5-p) \left(d^2-e^2 x^2\right)^{p-3} \, _2F_1\left(1,p-3;p-2;1-\frac{e^2 x^2}{d^2}\right)}{d (3-p)}-\frac{e^2 (27-2 p) \left(d^2-e^2 x^2\right)^{p-3}}{3 x}+\frac{2 d e \left(d^2-e^2 x^2\right)^{p-3}}{x^2}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p-3}}{3 x^3}","\frac{4 e^4 \left(p^2-17 p+48\right) x \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(\frac{1}{2},4-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^8}-\frac{2 e^3 (5-p) \left(d^2-e^2 x^2\right)^{p-3} \, _2F_1\left(1,p-3;p-2;1-\frac{e^2 x^2}{d^2}\right)}{d (3-p)}-\frac{e^2 (27-2 p) \left(d^2-e^2 x^2\right)^{p-3}}{3 x}+\frac{2 d e \left(d^2-e^2 x^2\right)^{p-3}}{x^2}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p-3}}{3 x^3}",1,"-(d^2*(d^2 - e^2*x^2)^(-3 + p))/(3*x^3) + (2*d*e*(d^2 - e^2*x^2)^(-3 + p))/x^2 - (e^2*(27 - 2*p)*(d^2 - e^2*x^2)^(-3 + p))/(3*x) + (4*e^4*(48 - 17*p + p^2)*x*(d^2 - e^2*x^2)^p*Hypergeometric2F1[1/2, 4 - p, 3/2, (e^2*x^2)/d^2])/(3*d^8*(1 - (e^2*x^2)/d^2)^p) - (2*e^3*(5 - p)*(d^2 - e^2*x^2)^(-3 + p)*Hypergeometric2F1[1, -3 + p, -2 + p, 1 - (e^2*x^2)/d^2])/(d*(3 - p))","A",9,7,25,0.2800,1,"{852, 1807, 764, 266, 65, 246, 245}"
305,1,216,0,0.4146632,"\int \frac{\left(d^2-e^2 x^2\right)^p}{x^5 (d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^p/(x^5*(d + e*x)^4),x]","\frac{e^4 \left(p^2-21 p+70\right) \left(d^2-e^2 x^2\right)^{p-3} \, _2F_1\left(1,p-3;p-2;1-\frac{e^2 x^2}{d^2}\right)}{4 d^2 (3-p)}+\frac{8 e^3 (6-p) \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},4-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^7 x}-\frac{e^2 (17-p) \left(d^2-e^2 x^2\right)^{p-3}}{4 x^2}+\frac{4 d e \left(d^2-e^2 x^2\right)^{p-3}}{3 x^3}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p-3}}{4 x^4}","\frac{e^4 \left(p^2-21 p+70\right) \left(d^2-e^2 x^2\right)^{p-3} \, _2F_1\left(1,p-3;p-2;1-\frac{e^2 x^2}{d^2}\right)}{4 d^2 (3-p)}+\frac{8 e^3 (6-p) \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \left(d^2-e^2 x^2\right)^p \, _2F_1\left(-\frac{1}{2},4-p;\frac{1}{2};\frac{e^2 x^2}{d^2}\right)}{3 d^7 x}-\frac{e^2 (17-p) \left(d^2-e^2 x^2\right)^{p-3}}{4 x^2}+\frac{4 d e \left(d^2-e^2 x^2\right)^{p-3}}{3 x^3}-\frac{d^2 \left(d^2-e^2 x^2\right)^{p-3}}{4 x^4}",1,"-(d^2*(d^2 - e^2*x^2)^(-3 + p))/(4*x^4) + (4*d*e*(d^2 - e^2*x^2)^(-3 + p))/(3*x^3) - (e^2*(17 - p)*(d^2 - e^2*x^2)^(-3 + p))/(4*x^2) + (8*e^3*(6 - p)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[-1/2, 4 - p, 1/2, (e^2*x^2)/d^2])/(3*d^7*x*(1 - (e^2*x^2)/d^2)^p) + (e^4*(70 - 21*p + p^2)*(d^2 - e^2*x^2)^(-3 + p)*Hypergeometric2F1[1, -3 + p, -2 + p, 1 - (e^2*x^2)/d^2])/(4*d^2*(3 - p))","A",9,7,25,0.2800,1,"{852, 1807, 764, 365, 364, 266, 65}"
306,1,264,0,0.3725191,"\int (g x)^m (d+e x)^3 \left(d^2-e^2 x^2\right)^p \, dx","Int[(g*x)^m*(d + e*x)^3*(d^2 - e^2*x^2)^p,x]","\frac{2 d^2 e (2 m+3 p+7) (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) (m+2 p+4)}-\frac{e (g x)^{m+2} \left(d^2-e^2 x^2\right)^{p+1}}{g^2 (m+2 p+4)}+\frac{2 d^3 (2 m+p+3) (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+2 p+3)}-\frac{3 d (g x)^{m+1} \left(d^2-e^2 x^2\right)^{p+1}}{g (m+2 p+3)}","\frac{2 d^2 e (2 m+3 p+7) (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2) (m+2 p+4)}-\frac{e (g x)^{m+2} \left(d^2-e^2 x^2\right)^{p+1}}{g^2 (m+2 p+4)}+\frac{2 d^3 (2 m+p+3) (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+2 p+3)}-\frac{3 d (g x)^{m+1} \left(d^2-e^2 x^2\right)^{p+1}}{g (m+2 p+3)}",1,"(-3*d*(g*x)^(1 + m)*(d^2 - e^2*x^2)^(1 + p))/(g*(3 + m + 2*p)) - (e*(g*x)^(2 + m)*(d^2 - e^2*x^2)^(1 + p))/(g^2*(4 + m + 2*p)) + (2*d^3*(3 + 2*m + p)*(g*x)^(1 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*(3 + m + 2*p)*(1 - (e^2*x^2)/d^2)^p) + (2*d^2*e*(7 + 2*m + 3*p)*(g*x)^(2 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(2 + m)/2, -p, (4 + m)/2, (e^2*x^2)/d^2])/(g^2*(2 + m)*(4 + m + 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",7,4,27,0.1481,1,"{1809, 808, 365, 364}"
307,1,206,0,0.1682217,"\int (g x)^m (d+e x)^2 \left(d^2-e^2 x^2\right)^p \, dx","Int[(g*x)^m*(d + e*x)^2*(d^2 - e^2*x^2)^p,x]","\frac{2 d e (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2)}+\frac{2 d^2 (m+p+2) (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+2 p+3)}-\frac{(g x)^{m+1} \left(d^2-e^2 x^2\right)^{p+1}}{g (m+2 p+3)}","\frac{2 d e (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2)}+\frac{2 d^2 (m+p+2) (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1) (m+2 p+3)}-\frac{(g x)^{m+1} \left(d^2-e^2 x^2\right)^{p+1}}{g (m+2 p+3)}",1,"-(((g*x)^(1 + m)*(d^2 - e^2*x^2)^(1 + p))/(g*(3 + m + 2*p))) + (2*d^2*(2 + m + p)*(g*x)^(1 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*(3 + m + 2*p)*(1 - (e^2*x^2)/d^2)^p) + (2*d*e*(g*x)^(2 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(2 + m)/2, -p, (4 + m)/2, (e^2*x^2)/d^2])/(g^2*(2 + m)*(1 - (e^2*x^2)/d^2)^p)","A",6,4,27,0.1481,1,"{1809, 808, 365, 364}"
308,1,153,0,0.0676501,"\int (g x)^m (d+e x) \left(d^2-e^2 x^2\right)^p \, dx","Int[(g*x)^m*(d + e*x)*(d^2 - e^2*x^2)^p,x]","\frac{e (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2)}+\frac{d (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1)}","\frac{e (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{g^2 (m+2)}+\frac{d (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1)}",1,"(d*(g*x)^(1 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*(1 - (e^2*x^2)/d^2)^p) + (e*(g*x)^(2 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(2 + m)/2, -p, (4 + m)/2, (e^2*x^2)/d^2])/(g^2*(2 + m)*(1 - (e^2*x^2)/d^2)^p)","A",5,3,25,0.1200,1,"{808, 365, 364}"
309,1,75,0,0.0202574,"\int (g x)^m \left(d^2-e^2 x^2\right)^p \, dx","Int[(g*x)^m*(d^2 - e^2*x^2)^p,x]","\frac{(g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1)}","\frac{(g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{g (m+1)}",1,"((g*x)^(1 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, (e^2*x^2)/d^2])/(g*(1 + m)*(1 - (e^2*x^2)/d^2)^p)","A",2,2,20,0.1000,1,"{365, 364}"
310,1,163,0,0.1357514,"\int \frac{(g x)^m \left(d^2-e^2 x^2\right)^p}{d+e x} \, dx","Int[((g*x)^m*(d^2 - e^2*x^2)^p)/(d + e*x),x]","\frac{(g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},1-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d g (m+1)}-\frac{e (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},1-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^2 g^2 (m+2)}","\frac{(g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},1-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d g (m+1)}-\frac{e (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},1-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^2 g^2 (m+2)}",1,"((g*x)^(1 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(1 + m)/2, 1 - p, (3 + m)/2, (e^2*x^2)/d^2])/(d*g*(1 + m)*(1 - (e^2*x^2)/d^2)^p) - (e*(g*x)^(2 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(2 + m)/2, 1 - p, (4 + m)/2, (e^2*x^2)/d^2])/(d^2*g^2*(2 + m)*(1 - (e^2*x^2)/d^2)^p)","A",8,5,27,0.1852,1,"{892, 82, 126, 365, 364}"
311,1,214,0,0.223438,"\int \frac{(g x)^m \left(d^2-e^2 x^2\right)^p}{(d+e x)^2} \, dx","Int[((g*x)^m*(d^2 - e^2*x^2)^p)/(d + e*x)^2,x]","-\frac{2 e (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},2-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^3 g^2 (m+2)}-\frac{2 (m+p) (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},2-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d^2 g (m+1) (-m-2 p+1)}+\frac{(g x)^{m+1} \left(d^2-e^2 x^2\right)^{p-1}}{g (-m-2 p+1)}","-\frac{2 e (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},2-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^3 g^2 (m+2)}-\frac{2 (m+p) (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},2-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d^2 g (m+1) (-m-2 p+1)}+\frac{(g x)^{m+1} \left(d^2-e^2 x^2\right)^{p-1}}{g (-m-2 p+1)}",1,"((g*x)^(1 + m)*(d^2 - e^2*x^2)^(-1 + p))/(g*(1 - m - 2*p)) - (2*(m + p)*(g*x)^(1 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(1 + m)/2, 2 - p, (3 + m)/2, (e^2*x^2)/d^2])/(d^2*g*(1 + m)*(1 - m - 2*p)*(1 - (e^2*x^2)/d^2)^p) - (2*e*(g*x)^(2 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(2 + m)/2, 2 - p, (4 + m)/2, (e^2*x^2)/d^2])/(d^3*g^2*(2 + m)*(1 - (e^2*x^2)/d^2)^p)","A",7,5,27,0.1852,1,"{852, 1809, 808, 365, 364}"
312,1,275,0,0.4415165,"\int \frac{(g x)^m \left(d^2-e^2 x^2\right)^p}{(d+e x)^3} \, dx","Int[((g*x)^m*(d^2 - e^2*x^2)^p)/(d + e*x)^3,x]","-\frac{2 e (-2 m-3 p+2) (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},3-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^4 g^2 (m+2) (-m-2 p+2)}-\frac{e (g x)^{m+2} \left(d^2-e^2 x^2\right)^{p-2}}{g^2 (-m-2 p+2)}-\frac{2 (2 m+p) (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},3-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d^3 g (m+1) (-m-2 p+3)}+\frac{3 d (g x)^{m+1} \left(d^2-e^2 x^2\right)^{p-2}}{g (-m-2 p+3)}","-\frac{2 e (-2 m-3 p+2) (g x)^{m+2} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+2}{2},3-p;\frac{m+4}{2};\frac{e^2 x^2}{d^2}\right)}{d^4 g^2 (m+2) (-m-2 p+2)}-\frac{e (g x)^{m+2} \left(d^2-e^2 x^2\right)^{p-2}}{g^2 (-m-2 p+2)}-\frac{2 (2 m+p) (g x)^{m+1} \left(d^2-e^2 x^2\right)^p \left(1-\frac{e^2 x^2}{d^2}\right)^{-p} \, _2F_1\left(\frac{m+1}{2},3-p;\frac{m+3}{2};\frac{e^2 x^2}{d^2}\right)}{d^3 g (m+1) (-m-2 p+3)}+\frac{3 d (g x)^{m+1} \left(d^2-e^2 x^2\right)^{p-2}}{g (-m-2 p+3)}",1,"(3*d*(g*x)^(1 + m)*(d^2 - e^2*x^2)^(-2 + p))/(g*(3 - m - 2*p)) - (e*(g*x)^(2 + m)*(d^2 - e^2*x^2)^(-2 + p))/(g^2*(2 - m - 2*p)) - (2*(2*m + p)*(g*x)^(1 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(1 + m)/2, 3 - p, (3 + m)/2, (e^2*x^2)/d^2])/(d^3*g*(1 + m)*(3 - m - 2*p)*(1 - (e^2*x^2)/d^2)^p) - (2*e*(2 - 2*m - 3*p)*(g*x)^(2 + m)*(d^2 - e^2*x^2)^p*Hypergeometric2F1[(2 + m)/2, 3 - p, (4 + m)/2, (e^2*x^2)/d^2])/(d^4*g^2*(2 + m)*(2 - m - 2*p)*(1 - (e^2*x^2)/d^2)^p)","A",8,5,27,0.1852,1,"{852, 1809, 808, 365, 364}"
313,1,89,0,0.0555549,"\int \frac{(g x)^m \left(1-a^2 x^2\right)^p}{1+a x} \, dx","Int[((g*x)^m*(1 - a^2*x^2)^p)/(1 + a*x),x]","\frac{(g x)^{m+1} \, _2F_1\left(\frac{m+1}{2},1-p;\frac{m+3}{2};a^2 x^2\right)}{g (m+1)}-\frac{a (g x)^{m+2} \, _2F_1\left(\frac{m+2}{2},1-p;\frac{m+4}{2};a^2 x^2\right)}{g^2 (m+2)}","\frac{(g x)^{m+1} \, _2F_1\left(\frac{m+1}{2},1-p;\frac{m+3}{2};a^2 x^2\right)}{g (m+1)}-\frac{a (g x)^{m+2} \, _2F_1\left(\frac{m+2}{2},1-p;\frac{m+4}{2};a^2 x^2\right)}{g^2 (m+2)}",1,"((g*x)^(1 + m)*Hypergeometric2F1[(1 + m)/2, 1 - p, (3 + m)/2, a^2*x^2])/(g*(1 + m)) - (a*(g*x)^(2 + m)*Hypergeometric2F1[(2 + m)/2, 1 - p, (4 + m)/2, a^2*x^2])/(g^2*(2 + m))","A",6,4,25,0.1600,1,"{890, 82, 125, 364}"
314,1,96,0,0.0829346,"\int (g x)^m (d+e x)^n \left(d^2-e^2 x^2\right)^p \, dx","Int[(g*x)^m*(d + e*x)^n*(d^2 - e^2*x^2)^p,x]","\frac{(g x)^{m+1} (d+e x)^n \left(1-\frac{e x}{d}\right)^{-p} \left(d^2-e^2 x^2\right)^p \left(\frac{e x}{d}+1\right)^{-n-p} F_1\left(m+1;-p,-n-p;m+2;\frac{e x}{d},-\frac{e x}{d}\right)}{g (m+1)}","\frac{(g x)^{m+1} (d+e x)^n \left(1-\frac{e x}{d}\right)^{-p} \left(d^2-e^2 x^2\right)^p \left(\frac{e x}{d}+1\right)^{-n-p} F_1\left(m+1;-p,-n-p;m+2;\frac{e x}{d},-\frac{e x}{d}\right)}{g (m+1)}",1,"((g*x)^(1 + m)*(d + e*x)^n*(1 + (e*x)/d)^(-n - p)*(d^2 - e^2*x^2)^p*AppellF1[1 + m, -p, -n - p, 2 + m, (e*x)/d, -((e*x)/d)])/(g*(1 + m)*(1 - (e*x)/d)^p)","A",4,3,27,0.1111,1,"{892, 135, 133}"
315,1,214,0,0.2465215,"\int \frac{x \sqrt{1+x}}{1+x^2} \, dx","Int[(x*Sqrt[1 + x])/(1 + x^2),x]","2 \sqrt{x+1}+\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \log \left(x-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \log \left(x+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{x+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{\sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt{x+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{\sqrt{2 \left(1+\sqrt{2}\right)}}","2 \sqrt{x+1}+\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \log \left(x-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)-\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \log \left(x+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{x+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{\sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt{x+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{\sqrt{2 \left(1+\sqrt{2}\right)}}",1,"2*Sqrt[1 + x] + ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]]/Sqrt[2*(1 + Sqrt[2])] - ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]]/Sqrt[2*(1 + Sqrt[2])] + (Sqrt[(1 + Sqrt[2])/2]*Log[1 + Sqrt[2] + x - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]])/2 - (Sqrt[(1 + Sqrt[2])/2]*Log[1 + Sqrt[2] + x + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]])/2","A",11,7,16,0.4375,1,"{825, 827, 1169, 634, 618, 204, 628}"
316,1,255,0,0.6292243,"\int \frac{x^4 \sqrt{a+c x^2}}{d+e x} \, dx","Int[(x^4*Sqrt[a + c*x^2])/(d + e*x),x]","-\frac{d \left(-a^2 e^4+4 a c d^2 e^2+8 c^2 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2} e^6}+\frac{\left(a+c x^2\right)^{3/2} \left(47 c d^2-8 a e^2\right)}{60 c^2 e^3}+\frac{d \sqrt{a+c x^2} \left(8 c d^3-e x \left(4 c d^2-a e^2\right)\right)}{8 c e^5}-\frac{d^4 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^6}-\frac{13 d \left(a+c x^2\right)^{3/2} (d+e x)}{20 c e^3}+\frac{\left(a+c x^2\right)^{3/2} (d+e x)^2}{5 c e^3}","-\frac{d \left(-a^2 e^4+4 a c d^2 e^2+8 c^2 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2} e^6}+\frac{\left(a+c x^2\right)^{3/2} \left(47 c d^2-8 a e^2\right)}{60 c^2 e^3}+\frac{d \sqrt{a+c x^2} \left(8 c d^3-e x \left(4 c d^2-a e^2\right)\right)}{8 c e^5}-\frac{d^4 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^6}-\frac{13 d \left(a+c x^2\right)^{3/2} (d+e x)}{20 c e^3}+\frac{\left(a+c x^2\right)^{3/2} (d+e x)^2}{5 c e^3}",1,"(d*(8*c*d^3 - e*(4*c*d^2 - a*e^2)*x)*Sqrt[a + c*x^2])/(8*c*e^5) + ((47*c*d^2 - 8*a*e^2)*(a + c*x^2)^(3/2))/(60*c^2*e^3) - (13*d*(d + e*x)*(a + c*x^2)^(3/2))/(20*c*e^3) + ((d + e*x)^2*(a + c*x^2)^(3/2))/(5*c*e^3) - (d*(8*c^2*d^4 + 4*a*c*d^2*e^2 - a^2*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(3/2)*e^6) - (d^4*Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/e^6","A",9,6,22,0.2727,1,"{1654, 815, 844, 217, 206, 725}"
317,1,211,0,0.3904278,"\int \frac{x^3 \sqrt{a+c x^2}}{d+e x} \, dx","Int[(x^3*Sqrt[a + c*x^2])/(d + e*x),x]","\frac{\left(-a^2 e^4+4 a c d^2 e^2+8 c^2 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2} e^5}-\frac{\sqrt{a+c x^2} \left(8 c d^3-e x \left(4 c d^2-a e^2\right)\right)}{8 c e^4}+\frac{d^3 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^5}-\frac{7 d \left(a+c x^2\right)^{3/2}}{12 c e^2}+\frac{\left(a+c x^2\right)^{3/2} (d+e x)}{4 c e^2}","\frac{\left(-a^2 e^4+4 a c d^2 e^2+8 c^2 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2} e^5}-\frac{\sqrt{a+c x^2} \left(8 c d^3-e x \left(4 c d^2-a e^2\right)\right)}{8 c e^4}+\frac{d^3 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^5}-\frac{7 d \left(a+c x^2\right)^{3/2}}{12 c e^2}+\frac{\left(a+c x^2\right)^{3/2} (d+e x)}{4 c e^2}",1,"-((8*c*d^3 - e*(4*c*d^2 - a*e^2)*x)*Sqrt[a + c*x^2])/(8*c*e^4) - (7*d*(a + c*x^2)^(3/2))/(12*c*e^2) + ((d + e*x)*(a + c*x^2)^(3/2))/(4*c*e^2) + ((8*c^2*d^4 + 4*a*c*d^2*e^2 - a^2*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(3/2)*e^5) + (d^3*Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/e^5","A",8,6,22,0.2727,1,"{1654, 815, 844, 217, 206, 725}"
318,1,153,0,0.2106841,"\int \frac{x^2 \sqrt{a+c x^2}}{d+e x} \, dx","Int[(x^2*Sqrt[a + c*x^2])/(d + e*x),x]","-\frac{d^2 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^4}-\frac{d \left(a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c} e^4}+\frac{d \sqrt{a+c x^2} (2 d-e x)}{2 e^3}+\frac{\left(a+c x^2\right)^{3/2}}{3 c e}","-\frac{d^2 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^4}-\frac{d \left(a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c} e^4}+\frac{d \sqrt{a+c x^2} (2 d-e x)}{2 e^3}+\frac{\left(a+c x^2\right)^{3/2}}{3 c e}",1,"(d*(2*d - e*x)*Sqrt[a + c*x^2])/(2*e^3) + (a + c*x^2)^(3/2)/(3*c*e) - (d*(2*c*d^2 + a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*Sqrt[c]*e^4) - (d^2*Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/e^4","A",8,7,22,0.3182,1,"{1654, 12, 815, 844, 217, 206, 725}"
319,1,127,0,0.1052622,"\int \frac{x \sqrt{a+c x^2}}{d+e x} \, dx","Int[(x*Sqrt[a + c*x^2])/(d + e*x),x]","\frac{\left(a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c} e^3}+\frac{d \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^3}-\frac{\sqrt{a+c x^2} (2 d-e x)}{2 e^2}","\frac{\left(a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c} e^3}+\frac{d \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^3}-\frac{\sqrt{a+c x^2} (2 d-e x)}{2 e^2}",1,"-((2*d - e*x)*Sqrt[a + c*x^2])/(2*e^2) + ((2*c*d^2 + a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*Sqrt[c]*e^3) + (d*Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/e^3","A",6,5,20,0.2500,1,"{815, 844, 217, 206, 725}"
320,1,103,0,0.0709663,"\int \frac{\sqrt{a+c x^2}}{d+e x} \, dx","Int[Sqrt[a + c*x^2]/(d + e*x),x]","-\frac{\sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^2}-\frac{\sqrt{c} d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^2}+\frac{\sqrt{a+c x^2}}{e}","-\frac{\sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^2}-\frac{\sqrt{c} d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^2}+\frac{\sqrt{a+c x^2}}{e}",1,"Sqrt[a + c*x^2]/e - (Sqrt[c]*d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/e^2 - (Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/e^2","A",6,5,19,0.2632,1,"{735, 844, 217, 206, 725}"
321,1,116,0,0.0996047,"\int \frac{\sqrt{a+c x^2}}{x (d+e x)} \, dx","Int[Sqrt[a + c*x^2]/(x*(d + e*x)),x]","\frac{\sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d e}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e}","\frac{\sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d e}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e}",1,"(Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/e + (Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d*e) - (Sqrt[a]*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/d","A",9,8,22,0.3636,1,"{896, 266, 63, 208, 844, 217, 206, 725}"
322,1,105,0,0.1665989,"\int \frac{\sqrt{a+c x^2}}{x^2 (d+e x)} \, dx","Int[Sqrt[a + c*x^2]/(x^2*(d + e*x)),x]","-\frac{\sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2}+\frac{\sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d^2}-\frac{\sqrt{a+c x^2}}{d x}","-\frac{\sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2}+\frac{\sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d^2}-\frac{\sqrt{a+c x^2}}{d x}",1,"-(Sqrt[a + c*x^2]/(d*x)) - (Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/d^2 + (Sqrt[a]*e*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/d^2","A",15,11,22,0.5000,1,"{961, 277, 217, 206, 266, 50, 63, 208, 735, 844, 725}"
323,1,160,0,0.2106595,"\int \frac{\sqrt{a+c x^2}}{x^3 (d+e x)} \, dx","Int[Sqrt[a + c*x^2]/(x^3*(d + e*x)),x]","-\frac{\sqrt{a} e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d^3}+\frac{e \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^3}+\frac{e \sqrt{a+c x^2}}{d^2 x}-\frac{\sqrt{a+c x^2}}{2 d x^2}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a} d}","-\frac{\sqrt{a} e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d^3}+\frac{e \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^3}+\frac{e \sqrt{a+c x^2}}{d^2 x}-\frac{\sqrt{a+c x^2}}{2 d x^2}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a} d}",1,"-Sqrt[a + c*x^2]/(2*d*x^2) + (e*Sqrt[a + c*x^2])/(d^2*x) + (e*Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/d^3 - (c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*Sqrt[a]*d) - (Sqrt[a]*e^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/d^3","A",19,12,22,0.5455,1,"{961, 266, 47, 63, 208, 277, 217, 206, 50, 735, 844, 725}"
324,1,191,0,0.2319329,"\int \frac{\sqrt{a+c x^2}}{x^4 (d+e x)} \, dx","Int[Sqrt[a + c*x^2]/(x^4*(d + e*x)),x]","-\frac{e^2 \sqrt{a+c x^2}}{d^3 x}+\frac{\sqrt{a} e^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d^4}-\frac{e^2 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^4}+\frac{e \sqrt{a+c x^2}}{2 d^2 x^2}+\frac{c e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a} d^2}-\frac{\left(a+c x^2\right)^{3/2}}{3 a d x^3}","-\frac{e^2 \sqrt{a+c x^2}}{d^3 x}+\frac{\sqrt{a} e^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d^4}-\frac{e^2 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^4}+\frac{e \sqrt{a+c x^2}}{2 d^2 x^2}+\frac{c e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a} d^2}-\frac{\left(a+c x^2\right)^{3/2}}{3 a d x^3}",1,"(e*Sqrt[a + c*x^2])/(2*d^2*x^2) - (e^2*Sqrt[a + c*x^2])/(d^3*x) - (a + c*x^2)^(3/2)/(3*a*d*x^3) - (e^2*Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/d^4 + (c*e*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*Sqrt[a]*d^2) + (Sqrt[a]*e^3*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/d^4","A",20,13,22,0.5909,1,"{961, 264, 266, 47, 63, 208, 277, 217, 206, 50, 735, 844, 725}"
325,1,274,0,0.2965599,"\int \frac{\sqrt{a+c x^2}}{x^5 (d+e x)} \, dx","Int[Sqrt[a + c*x^2]/(x^5*(d + e*x)),x]","\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{3/2} d}+\frac{e^3 \sqrt{a+c x^2}}{d^4 x}-\frac{e^2 \sqrt{a+c x^2}}{2 d^3 x^2}-\frac{\sqrt{a} e^4 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d^5}+\frac{e^3 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^5}-\frac{c e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a} d^3}+\frac{e \left(a+c x^2\right)^{3/2}}{3 a d^2 x^3}-\frac{c \sqrt{a+c x^2}}{8 a d x^2}-\frac{\sqrt{a+c x^2}}{4 d x^4}","\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{3/2} d}+\frac{e^3 \sqrt{a+c x^2}}{d^4 x}-\frac{e^2 \sqrt{a+c x^2}}{2 d^3 x^2}-\frac{\sqrt{a} e^4 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{d^5}+\frac{e^3 \sqrt{a e^2+c d^2} \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^5}-\frac{c e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a} d^3}+\frac{e \left(a+c x^2\right)^{3/2}}{3 a d^2 x^3}-\frac{c \sqrt{a+c x^2}}{8 a d x^2}-\frac{\sqrt{a+c x^2}}{4 d x^4}",1,"-Sqrt[a + c*x^2]/(4*d*x^4) - (c*Sqrt[a + c*x^2])/(8*a*d*x^2) - (e^2*Sqrt[a + c*x^2])/(2*d^3*x^2) + (e^3*Sqrt[a + c*x^2])/(d^4*x) + (e*(a + c*x^2)^(3/2))/(3*a*d^2*x^3) + (e^3*Sqrt[c*d^2 + a*e^2]*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/d^5 + (c^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(8*a^(3/2)*d) - (c*e^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*Sqrt[a]*d^3) - (Sqrt[a]*e^4*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/d^5","A",25,14,22,0.6364,1,"{961, 266, 47, 51, 63, 208, 264, 277, 217, 206, 50, 735, 844, 725}"
326,1,195,0,0.4817793,"\int \frac{x^4}{(d+e x) \sqrt{a+c x^2}} \, dx","Int[x^4/((d + e*x)*Sqrt[a + c*x^2]),x]","\frac{\sqrt{a+c x^2} \left(11 c d^2-4 a e^2\right)}{6 c^2 e^3}-\frac{d \left(2 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2} e^4}-\frac{d^4 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^4 \sqrt{a e^2+c d^2}}-\frac{7 d \sqrt{a+c x^2} (d+e x)}{6 c e^3}+\frac{\sqrt{a+c x^2} (d+e x)^2}{3 c e^3}","\frac{\sqrt{a+c x^2} \left(11 c d^2-4 a e^2\right)}{6 c^2 e^3}-\frac{d \left(2 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2} e^4}-\frac{d^4 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^4 \sqrt{a e^2+c d^2}}-\frac{7 d \sqrt{a+c x^2} (d+e x)}{6 c e^3}+\frac{\sqrt{a+c x^2} (d+e x)^2}{3 c e^3}",1,"((11*c*d^2 - 4*a*e^2)*Sqrt[a + c*x^2])/(6*c^2*e^3) - (7*d*(d + e*x)*Sqrt[a + c*x^2])/(6*c*e^3) + ((d + e*x)^2*Sqrt[a + c*x^2])/(3*c*e^3) - (d*(2*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2)*e^4) - (d^4*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e^4*Sqrt[c*d^2 + a*e^2])","A",8,5,22,0.2273,1,"{1654, 844, 217, 206, 725}"
327,1,152,0,0.2735059,"\int \frac{x^3}{(d+e x) \sqrt{a+c x^2}} \, dx","Int[x^3/((d + e*x)*Sqrt[a + c*x^2]),x]","\frac{\left(2 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2} e^3}+\frac{d^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^3 \sqrt{a e^2+c d^2}}-\frac{3 d \sqrt{a+c x^2}}{2 c e^2}+\frac{\sqrt{a+c x^2} (d+e x)}{2 c e^2}","\frac{\left(2 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2} e^3}+\frac{d^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^3 \sqrt{a e^2+c d^2}}-\frac{3 d \sqrt{a+c x^2}}{2 c e^2}+\frac{\sqrt{a+c x^2} (d+e x)}{2 c e^2}",1,"(-3*d*Sqrt[a + c*x^2])/(2*c*e^2) + ((d + e*x)*Sqrt[a + c*x^2])/(2*c*e^2) + ((2*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2)*e^3) + (d^3*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e^3*Sqrt[c*d^2 + a*e^2])","A",7,5,22,0.2273,1,"{1654, 844, 217, 206, 725}"
328,1,109,0,0.1275006,"\int \frac{x^2}{(d+e x) \sqrt{a+c x^2}} \, dx","Int[x^2/((d + e*x)*Sqrt[a + c*x^2]),x]","-\frac{d^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^2 \sqrt{a e^2+c d^2}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} e^2}+\frac{\sqrt{a+c x^2}}{c e}","-\frac{d^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^2 \sqrt{a e^2+c d^2}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} e^2}+\frac{\sqrt{a+c x^2}}{c e}",1,"Sqrt[a + c*x^2]/(c*e) - (d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(Sqrt[c]*e^2) - (d^2*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e^2*Sqrt[c*d^2 + a*e^2])","A",7,6,22,0.2727,1,"{1654, 12, 844, 217, 206, 725}"
329,1,86,0,0.0439798,"\int \frac{x}{(d+e x) \sqrt{a+c x^2}} \, dx","Int[x/((d + e*x)*Sqrt[a + c*x^2]),x]","\frac{d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e \sqrt{a e^2+c d^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} e}","\frac{d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e \sqrt{a e^2+c d^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} e}",1,"ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]]/(Sqrt[c]*e) + (d*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e*Sqrt[c*d^2 + a*e^2])","A",5,4,20,0.2000,1,"{844, 217, 206, 725}"
330,1,54,0,0.0172949,"\int \frac{1}{(d+e x) \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)*Sqrt[a + c*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\sqrt{a e^2+c d^2}}","-\frac{\tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\sqrt{a e^2+c d^2}}",1,"-(ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])]/Sqrt[c*d^2 + a*e^2])","A",2,2,19,0.1053,1,"{725, 206}"
331,1,86,0,0.0830174,"\int \frac{1}{x (d+e x) \sqrt{a+c x^2}} \, dx","Int[1/(x*(d + e*x)*Sqrt[a + c*x^2]),x]","\frac{e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d \sqrt{a e^2+c d^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d}","\frac{e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d \sqrt{a e^2+c d^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(e*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d*Sqrt[c*d^2 + a*e^2]) - ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]/(Sqrt[a]*d)","A",7,6,22,0.2727,1,"{961, 266, 63, 208, 725, 206}"
332,1,111,0,0.0953832,"\int \frac{1}{x^2 (d+e x) \sqrt{a+c x^2}} \, dx","Int[1/(x^2*(d + e*x)*Sqrt[a + c*x^2]),x]","-\frac{e^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2 \sqrt{a e^2+c d^2}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^2}-\frac{\sqrt{a+c x^2}}{a d x}","-\frac{e^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2 \sqrt{a e^2+c d^2}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^2}-\frac{\sqrt{a+c x^2}}{a d x}",1,"-(Sqrt[a + c*x^2]/(a*d*x)) - (e^2*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d^2*Sqrt[c*d^2 + a*e^2]) + (e*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(Sqrt[a]*d^2)","A",8,7,22,0.3182,1,"{961, 264, 266, 63, 208, 725, 206}"
333,1,168,0,0.140467,"\int \frac{1}{x^3 (d+e x) \sqrt{a+c x^2}} \, dx","Int[1/(x^3*(d + e*x)*Sqrt[a + c*x^2]),x]","\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{3/2} d}+\frac{e^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^3 \sqrt{a e^2+c d^2}}-\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^3}+\frac{e \sqrt{a+c x^2}}{a d^2 x}-\frac{\sqrt{a+c x^2}}{2 a d x^2}","\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{3/2} d}+\frac{e^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^3 \sqrt{a e^2+c d^2}}-\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^3}+\frac{e \sqrt{a+c x^2}}{a d^2 x}-\frac{\sqrt{a+c x^2}}{2 a d x^2}",1,"-Sqrt[a + c*x^2]/(2*a*d*x^2) + (e*Sqrt[a + c*x^2])/(a*d^2*x) + (e^3*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d^3*Sqrt[c*d^2 + a*e^2]) + (c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*a^(3/2)*d) - (e^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(Sqrt[a]*d^3)","A",12,8,22,0.3636,1,"{961, 266, 51, 63, 208, 264, 725, 206}"
334,1,146,0,0.3123208,"\int \frac{x^4}{(d+e x) \left(a+c x^2\right)^{3/2}} \, dx","Int[x^4/((d + e*x)*(a + c*x^2)^(3/2)),x]","\frac{a (a e+c d x)}{c^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2} e^2}+\frac{\sqrt{a+c x^2}}{c^2 e}-\frac{d^4 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^2 \left(a e^2+c d^2\right)^{3/2}}","\frac{a (a e+c d x)}{c^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2} e^2}+\frac{\sqrt{a+c x^2}}{c^2 e}-\frac{d^4 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^2 \left(a e^2+c d^2\right)^{3/2}}",1,"(a*(a*e + c*d*x))/(c^2*(c*d^2 + a*e^2)*Sqrt[a + c*x^2]) + Sqrt[a + c*x^2]/(c^2*e) - (d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(c^(3/2)*e^2) - (d^4*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e^2*(c*d^2 + a*e^2)^(3/2))","A",7,6,22,0.2727,1,"{1647, 1654, 844, 217, 206, 725}"
335,1,123,0,0.1648372,"\int \frac{x^3}{(d+e x) \left(a+c x^2\right)^{3/2}} \, dx","Int[x^3/((d + e*x)*(a + c*x^2)^(3/2)),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2} e}+\frac{a (d-e x)}{c \sqrt{a+c x^2} \left(a e^2+c d^2\right)}+\frac{d^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e \left(a e^2+c d^2\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2} e}+\frac{a (d-e x)}{c \sqrt{a+c x^2} \left(a e^2+c d^2\right)}+\frac{d^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e \left(a e^2+c d^2\right)^{3/2}}",1,"(a*(d - e*x))/(c*(c*d^2 + a*e^2)*Sqrt[a + c*x^2]) + ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]]/(c^(3/2)*e) + (d^3*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e*(c*d^2 + a*e^2)^(3/2))","A",6,5,22,0.2273,1,"{1647, 844, 217, 206, 725}"
336,1,95,0,0.1111388,"\int \frac{x^2}{(d+e x) \left(a+c x^2\right)^{3/2}} \, dx","Int[x^2/((d + e*x)*(a + c*x^2)^(3/2)),x]","-\frac{a e+c d x}{c \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{d^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}","-\frac{a e+c d x}{c \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{d^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}",1,"-((a*e + c*d*x)/(c*(c*d^2 + a*e^2)*Sqrt[a + c*x^2])) - (d^2*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(c*d^2 + a*e^2)^(3/2)","A",4,4,22,0.1818,1,"{1647, 12, 725, 206}"
337,1,88,0,0.0519365,"\int \frac{x}{(d+e x) \left(a+c x^2\right)^{3/2}} \, dx","Int[x/((d + e*x)*(a + c*x^2)^(3/2)),x]","\frac{d e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}-\frac{d-e x}{\sqrt{a+c x^2} \left(a e^2+c d^2\right)}","\frac{d e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}-\frac{d-e x}{\sqrt{a+c x^2} \left(a e^2+c d^2\right)}",1,"-((d - e*x)/((c*d^2 + a*e^2)*Sqrt[a + c*x^2])) + (d*e*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(c*d^2 + a*e^2)^(3/2)","A",4,4,20,0.2000,1,"{823, 12, 725, 206}"
338,1,94,0,0.0461382,"\int \frac{1}{(d+e x) \left(a+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(a + c*x^2)^(3/2)),x]","\frac{a e+c d x}{a \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{e^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}","\frac{a e+c d x}{a \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{e^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}",1,"(a*e + c*d*x)/(a*(c*d^2 + a*e^2)*Sqrt[a + c*x^2]) - (e^2*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(c*d^2 + a*e^2)^(3/2)","A",4,4,19,0.2105,1,"{741, 12, 725, 206}"
339,1,147,0,0.1349658,"\int \frac{1}{x (d+e x) \left(a+c x^2\right)^{3/2}} \, dx","Int[1/(x*(d + e*x)*(a + c*x^2)^(3/2)),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2} d}-\frac{e (a e+c d x)}{a d \sqrt{a+c x^2} \left(a e^2+c d^2\right)}+\frac{e^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d \left(a e^2+c d^2\right)^{3/2}}+\frac{1}{a d \sqrt{a+c x^2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2} d}-\frac{e (a e+c d x)}{a d \sqrt{a+c x^2} \left(a e^2+c d^2\right)}+\frac{e^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d \left(a e^2+c d^2\right)^{3/2}}+\frac{1}{a d \sqrt{a+c x^2}}",1,"1/(a*d*Sqrt[a + c*x^2]) - (e*(a*e + c*d*x))/(a*d*(c*d^2 + a*e^2)*Sqrt[a + c*x^2]) + (e^3*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d*(c*d^2 + a*e^2)^(3/2)) - ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]/(a^(3/2)*d)","A",10,9,22,0.4091,1,"{961, 266, 51, 63, 208, 741, 12, 725, 206}"
340,1,194,0,0.1665607,"\int \frac{1}{x^2 (d+e x) \left(a+c x^2\right)^{3/2}} \, dx","Int[1/(x^2*(d + e*x)*(a + c*x^2)^(3/2)),x]","\frac{e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2} d^2}-\frac{2 c x}{a^2 d \sqrt{a+c x^2}}+\frac{e^2 (a e+c d x)}{a d^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{e^4 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2 \left(a e^2+c d^2\right)^{3/2}}-\frac{e}{a d^2 \sqrt{a+c x^2}}-\frac{1}{a d x \sqrt{a+c x^2}}","\frac{e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2} d^2}-\frac{2 c x}{a^2 d \sqrt{a+c x^2}}+\frac{e^2 (a e+c d x)}{a d^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{e^4 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2 \left(a e^2+c d^2\right)^{3/2}}-\frac{e}{a d^2 \sqrt{a+c x^2}}-\frac{1}{a d x \sqrt{a+c x^2}}",1,"-(e/(a*d^2*Sqrt[a + c*x^2])) - 1/(a*d*x*Sqrt[a + c*x^2]) - (2*c*x)/(a^2*d*Sqrt[a + c*x^2]) + (e^2*(a*e + c*d*x))/(a*d^2*(c*d^2 + a*e^2)*Sqrt[a + c*x^2]) - (e^4*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d^2*(c*d^2 + a*e^2)^(3/2)) + (e*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(a^(3/2)*d^2)","A",12,11,22,0.5000,1,"{961, 271, 191, 266, 51, 63, 208, 741, 12, 725, 206}"
341,1,275,0,0.2356884,"\int \frac{1}{x^3 (d+e x) \left(a+c x^2\right)^{3/2}} \, dx","Int[1/(x^3*(d + e*x)*(a + c*x^2)^(3/2)),x]","-\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2} d^3}+\frac{2 c e x}{a^2 d^2 \sqrt{a+c x^2}}-\frac{3 \sqrt{a+c x^2}}{2 a^2 d x^2}+\frac{3 c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{5/2} d}-\frac{e^3 (a e+c d x)}{a d^3 \sqrt{a+c x^2} \left(a e^2+c d^2\right)}+\frac{e^2}{a d^3 \sqrt{a+c x^2}}+\frac{e^5 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^3 \left(a e^2+c d^2\right)^{3/2}}+\frac{e}{a d^2 x \sqrt{a+c x^2}}+\frac{1}{a d x^2 \sqrt{a+c x^2}}","-\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2} d^3}+\frac{2 c e x}{a^2 d^2 \sqrt{a+c x^2}}-\frac{3 c}{2 a^2 d \sqrt{a+c x^2}}+\frac{3 c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{5/2} d}-\frac{e^3 (a e+c d x)}{a d^3 \sqrt{a+c x^2} \left(a e^2+c d^2\right)}+\frac{e^2}{a d^3 \sqrt{a+c x^2}}+\frac{e^5 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^3 \left(a e^2+c d^2\right)^{3/2}}+\frac{e}{a d^2 x \sqrt{a+c x^2}}-\frac{1}{2 a d x^2 \sqrt{a+c x^2}}",1,"e^2/(a*d^3*Sqrt[a + c*x^2]) + 1/(a*d*x^2*Sqrt[a + c*x^2]) + e/(a*d^2*x*Sqrt[a + c*x^2]) + (2*c*e*x)/(a^2*d^2*Sqrt[a + c*x^2]) - (e^3*(a*e + c*d*x))/(a*d^3*(c*d^2 + a*e^2)*Sqrt[a + c*x^2]) - (3*Sqrt[a + c*x^2])/(2*a^2*d*x^2) + (e^5*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d^3*(c*d^2 + a*e^2)^(3/2)) + (3*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*a^(5/2)*d) - (e^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(a^(3/2)*d^3)","A",17,11,22,0.5000,1,"{961, 266, 51, 63, 208, 271, 191, 741, 12, 725, 206}"
342,1,244,0,0.8898322,"\int \frac{x^5}{(d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[x^5/((d + e*x)^2*Sqrt[a + c*x^2]),x]","\frac{\sqrt{a+c x^2} \left(13 c d^2-2 a e^2\right)}{3 c^2 e^4}-\frac{d \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2} e^5}+\frac{d^5 \sqrt{a+c x^2}}{e^4 (d+e x) \left(a e^2+c d^2\right)}-\frac{d^4 \left(5 a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^5 \left(a e^2+c d^2\right)^{3/2}}-\frac{5 d \sqrt{a+c x^2} (d+e x)}{3 c e^4}+\frac{\sqrt{a+c x^2} (d+e x)^2}{3 c e^4}","\frac{\sqrt{a+c x^2} \left(13 c d^2-2 a e^2\right)}{3 c^2 e^4}-\frac{d \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2} e^5}+\frac{d^5 \sqrt{a+c x^2}}{e^4 (d+e x) \left(a e^2+c d^2\right)}-\frac{d^4 \left(5 a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^5 \left(a e^2+c d^2\right)^{3/2}}-\frac{5 d \sqrt{a+c x^2} (d+e x)}{3 c e^4}+\frac{\sqrt{a+c x^2} (d+e x)^2}{3 c e^4}",1,"((13*c*d^2 - 2*a*e^2)*Sqrt[a + c*x^2])/(3*c^2*e^4) + (d^5*Sqrt[a + c*x^2])/(e^4*(c*d^2 + a*e^2)*(d + e*x)) - (5*d*(d + e*x)*Sqrt[a + c*x^2])/(3*c*e^4) + ((d + e*x)^2*Sqrt[a + c*x^2])/(3*c*e^4) - (d*(4*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(c^(3/2)*e^5) - (d^4*(4*c*d^2 + 5*a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e^5*(c*d^2 + a*e^2)^(3/2))","A",9,6,22,0.2727,1,"{1651, 1654, 844, 217, 206, 725}"
343,1,204,0,0.5234237,"\int \frac{x^4}{(d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[x^4/((d + e*x)^2*Sqrt[a + c*x^2]),x]","\frac{\left(6 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2} e^4}-\frac{d^4 \sqrt{a+c x^2}}{e^3 (d+e x) \left(a e^2+c d^2\right)}+\frac{d^3 \left(4 a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^4 \left(a e^2+c d^2\right)^{3/2}}-\frac{5 d \sqrt{a+c x^2}}{2 c e^3}+\frac{\sqrt{a+c x^2} (d+e x)}{2 c e^3}","\frac{\left(6 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2} e^4}-\frac{d^4 \sqrt{a+c x^2}}{e^3 (d+e x) \left(a e^2+c d^2\right)}+\frac{d^3 \left(4 a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^4 \left(a e^2+c d^2\right)^{3/2}}-\frac{5 d \sqrt{a+c x^2}}{2 c e^3}+\frac{\sqrt{a+c x^2} (d+e x)}{2 c e^3}",1,"(-5*d*Sqrt[a + c*x^2])/(2*c*e^3) - (d^4*Sqrt[a + c*x^2])/(e^3*(c*d^2 + a*e^2)*(d + e*x)) + ((d + e*x)*Sqrt[a + c*x^2])/(2*c*e^3) + ((6*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2)*e^4) + (d^3*(3*c*d^2 + 4*a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e^4*(c*d^2 + a*e^2)^(3/2))","A",8,6,22,0.2727,1,"{1651, 1654, 844, 217, 206, 725}"
344,1,160,0,0.3269385,"\int \frac{x^3}{(d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[x^3/((d + e*x)^2*Sqrt[a + c*x^2]),x]","\frac{d^3 \sqrt{a+c x^2}}{e^2 (d+e x) \left(a e^2+c d^2\right)}-\frac{d^2 \left(3 a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^3 \left(a e^2+c d^2\right)^{3/2}}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} e^3}+\frac{\sqrt{a+c x^2}}{c e^2}","\frac{d^3 \sqrt{a+c x^2}}{e^2 (d+e x) \left(a e^2+c d^2\right)}-\frac{d^2 \left(3 a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^3 \left(a e^2+c d^2\right)^{3/2}}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} e^3}+\frac{\sqrt{a+c x^2}}{c e^2}",1,"Sqrt[a + c*x^2]/(c*e^2) + (d^3*Sqrt[a + c*x^2])/(e^2*(c*d^2 + a*e^2)*(d + e*x)) - (2*d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(Sqrt[c]*e^3) - (d^2*(2*c*d^2 + 3*a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e^3*(c*d^2 + a*e^2)^(3/2))","A",7,6,22,0.2727,1,"{1651, 1654, 844, 217, 206, 725}"
345,1,137,0,0.168101,"\int \frac{x^2}{(d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[x^2/((d + e*x)^2*Sqrt[a + c*x^2]),x]","-\frac{d^2 \sqrt{a+c x^2}}{e (d+e x) \left(a e^2+c d^2\right)}+\frac{d \left(2 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^2 \left(a e^2+c d^2\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} e^2}","-\frac{d^2 \sqrt{a+c x^2}}{e (d+e x) \left(a e^2+c d^2\right)}+\frac{d \left(2 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{e^2 \left(a e^2+c d^2\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} e^2}",1,"-((d^2*Sqrt[a + c*x^2])/(e*(c*d^2 + a*e^2)*(d + e*x))) + ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]]/(Sqrt[c]*e^2) + (d*(c*d^2 + 2*a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(e^2*(c*d^2 + a*e^2)^(3/2))","A",6,5,22,0.2273,1,"{1651, 844, 217, 206, 725}"
346,1,90,0,0.0384235,"\int \frac{x}{(d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[x/((d + e*x)^2*Sqrt[a + c*x^2]),x]","\frac{d \sqrt{a+c x^2}}{(d+e x) \left(a e^2+c d^2\right)}-\frac{a e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}","\frac{d \sqrt{a+c x^2}}{(d+e x) \left(a e^2+c d^2\right)}-\frac{a e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}",1,"(d*Sqrt[a + c*x^2])/((c*d^2 + a*e^2)*(d + e*x)) - (a*e*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(c*d^2 + a*e^2)^(3/2)","A",3,3,20,0.1500,1,"{807, 725, 206}"
347,1,91,0,0.0338812,"\int \frac{1}{(d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)^2*Sqrt[a + c*x^2]),x]","-\frac{e \sqrt{a+c x^2}}{(d+e x) \left(a e^2+c d^2\right)}-\frac{c d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}","-\frac{e \sqrt{a+c x^2}}{(d+e x) \left(a e^2+c d^2\right)}-\frac{c d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}",1,"-((e*Sqrt[a + c*x^2])/((c*d^2 + a*e^2)*(d + e*x))) - (c*d*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(c*d^2 + a*e^2)^(3/2)","A",3,3,19,0.1579,1,"{731, 725, 206}"
348,1,179,0,0.1372577,"\int \frac{1}{x (d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[1/(x*(d + e*x)^2*Sqrt[a + c*x^2]),x]","\frac{e^2 \sqrt{a+c x^2}}{d (d+e x) \left(a e^2+c d^2\right)}+\frac{e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2 \sqrt{a e^2+c d^2}}+\frac{c e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^2}","\frac{e^2 \sqrt{a+c x^2}}{d (d+e x) \left(a e^2+c d^2\right)}+\frac{e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2 \sqrt{a e^2+c d^2}}+\frac{c e \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{\left(a e^2+c d^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^2}",1,"(e^2*Sqrt[a + c*x^2])/(d*(c*d^2 + a*e^2)*(d + e*x)) + (c*e*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(c*d^2 + a*e^2)^(3/2) + (e*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d^2*Sqrt[c*d^2 + a*e^2]) - ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]/(Sqrt[a]*d^2)","A",10,7,22,0.3182,1,"{961, 266, 63, 208, 731, 725, 206}"
349,1,212,0,0.1678504,"\int \frac{1}{x^2 (d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[1/(x^2*(d + e*x)^2*Sqrt[a + c*x^2]),x]","-\frac{e^3 \sqrt{a+c x^2}}{d^2 (d+e x) \left(a e^2+c d^2\right)}-\frac{2 e^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^3 \sqrt{a e^2+c d^2}}-\frac{c e^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d \left(a e^2+c d^2\right)^{3/2}}+\frac{2 e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^3}-\frac{\sqrt{a+c x^2}}{a d^2 x}","-\frac{e^3 \sqrt{a+c x^2}}{d^2 (d+e x) \left(a e^2+c d^2\right)}-\frac{2 e^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^3 \sqrt{a e^2+c d^2}}-\frac{c e^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d \left(a e^2+c d^2\right)^{3/2}}+\frac{2 e \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^3}-\frac{\sqrt{a+c x^2}}{a d^2 x}",1,"-(Sqrt[a + c*x^2]/(a*d^2*x)) - (e^3*Sqrt[a + c*x^2])/(d^2*(c*d^2 + a*e^2)*(d + e*x)) - (c*e^2*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d*(c*d^2 + a*e^2)^(3/2)) - (2*e^2*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d^3*Sqrt[c*d^2 + a*e^2]) + (2*e*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(Sqrt[a]*d^3)","A",11,8,22,0.3636,1,"{961, 264, 266, 63, 208, 731, 725, 206}"
350,1,268,0,0.222282,"\int \frac{1}{x^3 (d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[1/(x^3*(d + e*x)^2*Sqrt[a + c*x^2]),x]","\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{3/2} d^2}+\frac{e^4 \sqrt{a+c x^2}}{d^3 (d+e x) \left(a e^2+c d^2\right)}+\frac{3 e^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^4 \sqrt{a e^2+c d^2}}+\frac{c e^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2 \left(a e^2+c d^2\right)^{3/2}}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^4}+\frac{2 e \sqrt{a+c x^2}}{a d^3 x}-\frac{\sqrt{a+c x^2}}{2 a d^2 x^2}","\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{3/2} d^2}+\frac{e^4 \sqrt{a+c x^2}}{d^3 (d+e x) \left(a e^2+c d^2\right)}+\frac{3 e^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^4 \sqrt{a e^2+c d^2}}+\frac{c e^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{d^2 \left(a e^2+c d^2\right)^{3/2}}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a} d^4}+\frac{2 e \sqrt{a+c x^2}}{a d^3 x}-\frac{\sqrt{a+c x^2}}{2 a d^2 x^2}",1,"-Sqrt[a + c*x^2]/(2*a*d^2*x^2) + (2*e*Sqrt[a + c*x^2])/(a*d^3*x) + (e^4*Sqrt[a + c*x^2])/(d^3*(c*d^2 + a*e^2)*(d + e*x)) + (c*e^3*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d^2*(c*d^2 + a*e^2)^(3/2)) + (3*e^3*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(d^4*Sqrt[c*d^2 + a*e^2]) + (c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*a^(3/2)*d^2) - (3*e^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(Sqrt[a]*d^4)","A",15,9,22,0.4091,1,"{961, 266, 51, 63, 208, 264, 731, 725, 206}"
351,1,135,0,0.0815451,"\int x^2 (a+b x)^n \left(c+d x^2\right) \, dx","Int[x^2*(a + b*x)^n*(c + d*x^2),x]","\frac{a^2 \left(a^2 d+b^2 c\right) (a+b x)^{n+1}}{b^5 (n+1)}-\frac{2 a \left(2 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^5 (n+2)}+\frac{\left(6 a^2 d+b^2 c\right) (a+b x)^{n+3}}{b^5 (n+3)}-\frac{4 a d (a+b x)^{n+4}}{b^5 (n+4)}+\frac{d (a+b x)^{n+5}}{b^5 (n+5)}","\frac{a^2 \left(a^2 d+b^2 c\right) (a+b x)^{n+1}}{b^5 (n+1)}-\frac{2 a \left(2 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^5 (n+2)}+\frac{\left(6 a^2 d+b^2 c\right) (a+b x)^{n+3}}{b^5 (n+3)}-\frac{4 a d (a+b x)^{n+4}}{b^5 (n+4)}+\frac{d (a+b x)^{n+5}}{b^5 (n+5)}",1,"(a^2*(b^2*c + a^2*d)*(a + b*x)^(1 + n))/(b^5*(1 + n)) - (2*a*(b^2*c + 2*a^2*d)*(a + b*x)^(2 + n))/(b^5*(2 + n)) + ((b^2*c + 6*a^2*d)*(a + b*x)^(3 + n))/(b^5*(3 + n)) - (4*a*d*(a + b*x)^(4 + n))/(b^5*(4 + n)) + (d*(a + b*x)^(5 + n))/(b^5*(5 + n))","A",2,1,18,0.05556,1,"{948}"
352,1,102,0,0.052293,"\int x (a+b x)^n \left(c+d x^2\right) \, dx","Int[x*(a + b*x)^n*(c + d*x^2),x]","-\frac{a \left(a^2 d+b^2 c\right) (a+b x)^{n+1}}{b^4 (n+1)}+\frac{\left(3 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^4 (n+2)}-\frac{3 a d (a+b x)^{n+3}}{b^4 (n+3)}+\frac{d (a+b x)^{n+4}}{b^4 (n+4)}","-\frac{a \left(a^2 d+b^2 c\right) (a+b x)^{n+1}}{b^4 (n+1)}+\frac{\left(3 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^4 (n+2)}-\frac{3 a d (a+b x)^{n+3}}{b^4 (n+3)}+\frac{d (a+b x)^{n+4}}{b^4 (n+4)}",1,"-((a*(b^2*c + a^2*d)*(a + b*x)^(1 + n))/(b^4*(1 + n))) + ((b^2*c + 3*a^2*d)*(a + b*x)^(2 + n))/(b^4*(2 + n)) - (3*a*d*(a + b*x)^(3 + n))/(b^4*(3 + n)) + (d*(a + b*x)^(4 + n))/(b^4*(4 + n))","A",2,1,16,0.06250,1,"{772}"
353,1,70,0,0.031032,"\int (a+b x)^n \left(c+d x^2\right) \, dx","Int[(a + b*x)^n*(c + d*x^2),x]","\frac{\left(a^2 d+b^2 c\right) (a+b x)^{n+1}}{b^3 (n+1)}-\frac{2 a d (a+b x)^{n+2}}{b^3 (n+2)}+\frac{d (a+b x)^{n+3}}{b^3 (n+3)}","\frac{\left(a^2 d+b^2 c\right) (a+b x)^{n+1}}{b^3 (n+1)}-\frac{2 a d (a+b x)^{n+2}}{b^3 (n+2)}+\frac{d (a+b x)^{n+3}}{b^3 (n+3)}",1,"((b^2*c + a^2*d)*(a + b*x)^(1 + n))/(b^3*(1 + n)) - (2*a*d*(a + b*x)^(2 + n))/(b^3*(2 + n)) + (d*(a + b*x)^(3 + n))/(b^3*(3 + n))","A",2,1,15,0.06667,1,"{697}"
354,1,77,0,0.0508392,"\int \frac{(a+b x)^n \left(c+d x^2\right)}{x} \, dx","Int[((a + b*x)^n*(c + d*x^2))/x,x]","-\frac{a d (a+b x)^{n+1}}{b^2 (n+1)}+\frac{d (a+b x)^{n+2}}{b^2 (n+2)}-\frac{c (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}","-\frac{a d (a+b x)^{n+1}}{b^2 (n+1)}+\frac{d (a+b x)^{n+2}}{b^2 (n+2)}-\frac{c (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"-((a*d*(a + b*x)^(1 + n))/(b^2*(1 + n))) + (d*(a + b*x)^(2 + n))/(b^2*(2 + n)) - (c*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n))","A",3,3,18,0.1667,1,"{952, 80, 65}"
355,1,232,0,0.1390423,"\int x^2 (a+b x)^n \left(c+d x^2\right)^2 \, dx","Int[x^2*(a + b*x)^n*(c + d*x^2)^2,x]","\frac{\left(12 a^2 b^2 c d+15 a^4 d^2+b^4 c^2\right) (a+b x)^{n+3}}{b^7 (n+3)}+\frac{a^2 \left(a^2 d+b^2 c\right)^2 (a+b x)^{n+1}}{b^7 (n+1)}-\frac{2 a \left(a^2 d+b^2 c\right) \left(3 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^7 (n+2)}-\frac{4 a d \left(5 a^2 d+2 b^2 c\right) (a+b x)^{n+4}}{b^7 (n+4)}+\frac{d \left(15 a^2 d+2 b^2 c\right) (a+b x)^{n+5}}{b^7 (n+5)}-\frac{6 a d^2 (a+b x)^{n+6}}{b^7 (n+6)}+\frac{d^2 (a+b x)^{n+7}}{b^7 (n+7)}","\frac{\left(12 a^2 b^2 c d+15 a^4 d^2+b^4 c^2\right) (a+b x)^{n+3}}{b^7 (n+3)}+\frac{a^2 \left(a^2 d+b^2 c\right)^2 (a+b x)^{n+1}}{b^7 (n+1)}-\frac{2 a \left(a^2 d+b^2 c\right) \left(3 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^7 (n+2)}-\frac{4 a d \left(5 a^2 d+2 b^2 c\right) (a+b x)^{n+4}}{b^7 (n+4)}+\frac{d \left(15 a^2 d+2 b^2 c\right) (a+b x)^{n+5}}{b^7 (n+5)}-\frac{6 a d^2 (a+b x)^{n+6}}{b^7 (n+6)}+\frac{d^2 (a+b x)^{n+7}}{b^7 (n+7)}",1,"(a^2*(b^2*c + a^2*d)^2*(a + b*x)^(1 + n))/(b^7*(1 + n)) - (2*a*(b^2*c + a^2*d)*(b^2*c + 3*a^2*d)*(a + b*x)^(2 + n))/(b^7*(2 + n)) + ((b^4*c^2 + 12*a^2*b^2*c*d + 15*a^4*d^2)*(a + b*x)^(3 + n))/(b^7*(3 + n)) - (4*a*d*(2*b^2*c + 5*a^2*d)*(a + b*x)^(4 + n))/(b^7*(4 + n)) + (d*(2*b^2*c + 15*a^2*d)*(a + b*x)^(5 + n))/(b^7*(5 + n)) - (6*a*d^2*(a + b*x)^(6 + n))/(b^7*(6 + n)) + (d^2*(a + b*x)^(7 + n))/(b^7*(7 + n))","A",2,1,20,0.05000,1,"{948}"
356,1,185,0,0.1004924,"\int x (a+b x)^n \left(c+d x^2\right)^2 \, dx","Int[x*(a + b*x)^n*(c + d*x^2)^2,x]","-\frac{a \left(a^2 d+b^2 c\right)^2 (a+b x)^{n+1}}{b^6 (n+1)}+\frac{\left(a^2 d+b^2 c\right) \left(5 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^6 (n+2)}-\frac{2 a d \left(5 a^2 d+3 b^2 c\right) (a+b x)^{n+3}}{b^6 (n+3)}+\frac{2 d \left(5 a^2 d+b^2 c\right) (a+b x)^{n+4}}{b^6 (n+4)}-\frac{5 a d^2 (a+b x)^{n+5}}{b^6 (n+5)}+\frac{d^2 (a+b x)^{n+6}}{b^6 (n+6)}","-\frac{a \left(a^2 d+b^2 c\right)^2 (a+b x)^{n+1}}{b^6 (n+1)}+\frac{\left(a^2 d+b^2 c\right) \left(5 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^6 (n+2)}-\frac{2 a d \left(5 a^2 d+3 b^2 c\right) (a+b x)^{n+3}}{b^6 (n+3)}+\frac{2 d \left(5 a^2 d+b^2 c\right) (a+b x)^{n+4}}{b^6 (n+4)}-\frac{5 a d^2 (a+b x)^{n+5}}{b^6 (n+5)}+\frac{d^2 (a+b x)^{n+6}}{b^6 (n+6)}",1,"-((a*(b^2*c + a^2*d)^2*(a + b*x)^(1 + n))/(b^6*(1 + n))) + ((b^2*c + a^2*d)*(b^2*c + 5*a^2*d)*(a + b*x)^(2 + n))/(b^6*(2 + n)) - (2*a*d*(3*b^2*c + 5*a^2*d)*(a + b*x)^(3 + n))/(b^6*(3 + n)) + (2*d*(b^2*c + 5*a^2*d)*(a + b*x)^(4 + n))/(b^6*(4 + n)) - (5*a*d^2*(a + b*x)^(5 + n))/(b^6*(5 + n)) + (d^2*(a + b*x)^(6 + n))/(b^6*(6 + n))","A",2,1,18,0.05556,1,"{772}"
357,1,140,0,0.0680572,"\int (a+b x)^n \left(c+d x^2\right)^2 \, dx","Int[(a + b*x)^n*(c + d*x^2)^2,x]","\frac{\left(a^2 d+b^2 c\right)^2 (a+b x)^{n+1}}{b^5 (n+1)}-\frac{4 a d \left(a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^5 (n+2)}+\frac{2 d \left(3 a^2 d+b^2 c\right) (a+b x)^{n+3}}{b^5 (n+3)}-\frac{4 a d^2 (a+b x)^{n+4}}{b^5 (n+4)}+\frac{d^2 (a+b x)^{n+5}}{b^5 (n+5)}","\frac{\left(a^2 d+b^2 c\right)^2 (a+b x)^{n+1}}{b^5 (n+1)}-\frac{4 a d \left(a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^5 (n+2)}+\frac{2 d \left(3 a^2 d+b^2 c\right) (a+b x)^{n+3}}{b^5 (n+3)}-\frac{4 a d^2 (a+b x)^{n+4}}{b^5 (n+4)}+\frac{d^2 (a+b x)^{n+5}}{b^5 (n+5)}",1,"((b^2*c + a^2*d)^2*(a + b*x)^(1 + n))/(b^5*(1 + n)) - (4*a*d*(b^2*c + a^2*d)*(a + b*x)^(2 + n))/(b^5*(2 + n)) + (2*d*(b^2*c + 3*a^2*d)*(a + b*x)^(3 + n))/(b^5*(3 + n)) - (4*a*d^2*(a + b*x)^(4 + n))/(b^5*(4 + n)) + (d^2*(a + b*x)^(5 + n))/(b^5*(5 + n))","A",2,1,17,0.05882,1,"{697}"
358,1,148,0,0.2098612,"\int \frac{(a+b x)^n \left(c+d x^2\right)^2}{x} \, dx","Int[((a + b*x)^n*(c + d*x^2)^2)/x,x]","-\frac{a d \left(a^2 d+2 b^2 c\right) (a+b x)^{n+1}}{b^4 (n+1)}+\frac{d \left(3 a^2 d+2 b^2 c\right) (a+b x)^{n+2}}{b^4 (n+2)}-\frac{3 a d^2 (a+b x)^{n+3}}{b^4 (n+3)}+\frac{d^2 (a+b x)^{n+4}}{b^4 (n+4)}-\frac{c^2 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}","-\frac{a d \left(a^2 d+2 b^2 c\right) (a+b x)^{n+1}}{b^4 (n+1)}+\frac{d \left(3 a^2 d+2 b^2 c\right) (a+b x)^{n+2}}{b^4 (n+2)}-\frac{3 a d^2 (a+b x)^{n+3}}{b^4 (n+3)}+\frac{d^2 (a+b x)^{n+4}}{b^4 (n+4)}-\frac{c^2 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"-((a*d*(2*b^2*c + a^2*d)*(a + b*x)^(1 + n))/(b^4*(1 + n))) + (d*(2*b^2*c + 3*a^2*d)*(a + b*x)^(2 + n))/(b^4*(2 + n)) - (3*a*d^2*(a + b*x)^(3 + n))/(b^4*(3 + n)) + (d^2*(a + b*x)^(4 + n))/(b^4*(4 + n)) - (c^2*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n))","A",4,3,20,0.1500,1,"{952, 1620, 65}"
359,1,343,0,0.2105563,"\int x^2 (a+b x)^n \left(c+d x^2\right)^3 \, dx","Int[x^2*(a + b*x)^n*(c + d*x^2)^3,x]","\frac{\left(a^2 d+b^2 c\right) \left(17 a^2 b^2 c d+28 a^4 d^2+b^4 c^2\right) (a+b x)^{n+3}}{b^9 (n+3)}-\frac{4 a d \left(15 a^2 b^2 c d+14 a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+4}}{b^9 (n+4)}+\frac{d \left(45 a^2 b^2 c d+70 a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+5}}{b^9 (n+5)}-\frac{2 a d^2 \left(28 a^2 d+9 b^2 c\right) (a+b x)^{n+6}}{b^9 (n+6)}+\frac{d^2 \left(28 a^2 d+3 b^2 c\right) (a+b x)^{n+7}}{b^9 (n+7)}+\frac{a^2 \left(a^2 d+b^2 c\right)^3 (a+b x)^{n+1}}{b^9 (n+1)}-\frac{2 a \left(a^2 d+b^2 c\right)^2 \left(4 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^9 (n+2)}-\frac{8 a d^3 (a+b x)^{n+8}}{b^9 (n+8)}+\frac{d^3 (a+b x)^{n+9}}{b^9 (n+9)}","\frac{\left(a^2 d+b^2 c\right) \left(17 a^2 b^2 c d+28 a^4 d^2+b^4 c^2\right) (a+b x)^{n+3}}{b^9 (n+3)}-\frac{4 a d \left(15 a^2 b^2 c d+14 a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+4}}{b^9 (n+4)}+\frac{d \left(45 a^2 b^2 c d+70 a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+5}}{b^9 (n+5)}-\frac{2 a d^2 \left(28 a^2 d+9 b^2 c\right) (a+b x)^{n+6}}{b^9 (n+6)}+\frac{d^2 \left(28 a^2 d+3 b^2 c\right) (a+b x)^{n+7}}{b^9 (n+7)}+\frac{a^2 \left(a^2 d+b^2 c\right)^3 (a+b x)^{n+1}}{b^9 (n+1)}-\frac{2 a \left(a^2 d+b^2 c\right)^2 \left(4 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^9 (n+2)}-\frac{8 a d^3 (a+b x)^{n+8}}{b^9 (n+8)}+\frac{d^3 (a+b x)^{n+9}}{b^9 (n+9)}",1,"(a^2*(b^2*c + a^2*d)^3*(a + b*x)^(1 + n))/(b^9*(1 + n)) - (2*a*(b^2*c + a^2*d)^2*(b^2*c + 4*a^2*d)*(a + b*x)^(2 + n))/(b^9*(2 + n)) + ((b^2*c + a^2*d)*(b^4*c^2 + 17*a^2*b^2*c*d + 28*a^4*d^2)*(a + b*x)^(3 + n))/(b^9*(3 + n)) - (4*a*d*(3*b^4*c^2 + 15*a^2*b^2*c*d + 14*a^4*d^2)*(a + b*x)^(4 + n))/(b^9*(4 + n)) + (d*(3*b^4*c^2 + 45*a^2*b^2*c*d + 70*a^4*d^2)*(a + b*x)^(5 + n))/(b^9*(5 + n)) - (2*a*d^2*(9*b^2*c + 28*a^2*d)*(a + b*x)^(6 + n))/(b^9*(6 + n)) + (d^2*(3*b^2*c + 28*a^2*d)*(a + b*x)^(7 + n))/(b^9*(7 + n)) - (8*a*d^3*(a + b*x)^(8 + n))/(b^9*(8 + n)) + (d^3*(a + b*x)^(9 + n))/(b^9*(9 + n))","A",2,1,20,0.05000,1,"{948}"
360,1,282,0,0.1679429,"\int x (a+b x)^n \left(c+d x^2\right)^3 \, dx","Int[x*(a + b*x)^n*(c + d*x^2)^3,x]","\frac{d \left(30 a^2 b^2 c d+35 a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+4}}{b^8 (n+4)}-\frac{5 a d^2 \left(7 a^2 d+3 b^2 c\right) (a+b x)^{n+5}}{b^8 (n+5)}+\frac{3 d^2 \left(7 a^2 d+b^2 c\right) (a+b x)^{n+6}}{b^8 (n+6)}-\frac{a \left(a^2 d+b^2 c\right)^3 (a+b x)^{n+1}}{b^8 (n+1)}+\frac{\left(a^2 d+b^2 c\right)^2 \left(7 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^8 (n+2)}-\frac{3 a d \left(a^2 d+b^2 c\right) \left(7 a^2 d+3 b^2 c\right) (a+b x)^{n+3}}{b^8 (n+3)}-\frac{7 a d^3 (a+b x)^{n+7}}{b^8 (n+7)}+\frac{d^3 (a+b x)^{n+8}}{b^8 (n+8)}","\frac{d \left(30 a^2 b^2 c d+35 a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+4}}{b^8 (n+4)}-\frac{5 a d^2 \left(7 a^2 d+3 b^2 c\right) (a+b x)^{n+5}}{b^8 (n+5)}+\frac{3 d^2 \left(7 a^2 d+b^2 c\right) (a+b x)^{n+6}}{b^8 (n+6)}-\frac{a \left(a^2 d+b^2 c\right)^3 (a+b x)^{n+1}}{b^8 (n+1)}+\frac{\left(a^2 d+b^2 c\right)^2 \left(7 a^2 d+b^2 c\right) (a+b x)^{n+2}}{b^8 (n+2)}-\frac{3 a d \left(a^2 d+b^2 c\right) \left(7 a^2 d+3 b^2 c\right) (a+b x)^{n+3}}{b^8 (n+3)}-\frac{7 a d^3 (a+b x)^{n+7}}{b^8 (n+7)}+\frac{d^3 (a+b x)^{n+8}}{b^8 (n+8)}",1,"-((a*(b^2*c + a^2*d)^3*(a + b*x)^(1 + n))/(b^8*(1 + n))) + ((b^2*c + a^2*d)^2*(b^2*c + 7*a^2*d)*(a + b*x)^(2 + n))/(b^8*(2 + n)) - (3*a*d*(b^2*c + a^2*d)*(3*b^2*c + 7*a^2*d)*(a + b*x)^(3 + n))/(b^8*(3 + n)) + (d*(3*b^4*c^2 + 30*a^2*b^2*c*d + 35*a^4*d^2)*(a + b*x)^(4 + n))/(b^8*(4 + n)) - (5*a*d^2*(3*b^2*c + 7*a^2*d)*(a + b*x)^(5 + n))/(b^8*(5 + n)) + (3*d^2*(b^2*c + 7*a^2*d)*(a + b*x)^(6 + n))/(b^8*(6 + n)) - (7*a*d^3*(a + b*x)^(7 + n))/(b^8*(7 + n)) + (d^3*(a + b*x)^(8 + n))/(b^8*(8 + n))","A",2,1,18,0.05556,1,"{772}"
361,1,223,0,0.1255717,"\int (a+b x)^n \left(c+d x^2\right)^3 \, dx","Int[(a + b*x)^n*(c + d*x^2)^3,x]","-\frac{4 a d^2 \left(5 a^2 d+3 b^2 c\right) (a+b x)^{n+4}}{b^7 (n+4)}+\frac{3 d^2 \left(5 a^2 d+b^2 c\right) (a+b x)^{n+5}}{b^7 (n+5)}+\frac{\left(a^2 d+b^2 c\right)^3 (a+b x)^{n+1}}{b^7 (n+1)}-\frac{6 a d \left(a^2 d+b^2 c\right)^2 (a+b x)^{n+2}}{b^7 (n+2)}+\frac{3 d \left(a^2 d+b^2 c\right) \left(5 a^2 d+b^2 c\right) (a+b x)^{n+3}}{b^7 (n+3)}-\frac{6 a d^3 (a+b x)^{n+6}}{b^7 (n+6)}+\frac{d^3 (a+b x)^{n+7}}{b^7 (n+7)}","-\frac{4 a d^2 \left(5 a^2 d+3 b^2 c\right) (a+b x)^{n+4}}{b^7 (n+4)}+\frac{3 d^2 \left(5 a^2 d+b^2 c\right) (a+b x)^{n+5}}{b^7 (n+5)}+\frac{\left(a^2 d+b^2 c\right)^3 (a+b x)^{n+1}}{b^7 (n+1)}-\frac{6 a d \left(a^2 d+b^2 c\right)^2 (a+b x)^{n+2}}{b^7 (n+2)}+\frac{3 d \left(a^2 d+b^2 c\right) \left(5 a^2 d+b^2 c\right) (a+b x)^{n+3}}{b^7 (n+3)}-\frac{6 a d^3 (a+b x)^{n+6}}{b^7 (n+6)}+\frac{d^3 (a+b x)^{n+7}}{b^7 (n+7)}",1,"((b^2*c + a^2*d)^3*(a + b*x)^(1 + n))/(b^7*(1 + n)) - (6*a*d*(b^2*c + a^2*d)^2*(a + b*x)^(2 + n))/(b^7*(2 + n)) + (3*d*(b^2*c + a^2*d)*(b^2*c + 5*a^2*d)*(a + b*x)^(3 + n))/(b^7*(3 + n)) - (4*a*d^2*(3*b^2*c + 5*a^2*d)*(a + b*x)^(4 + n))/(b^7*(4 + n)) + (3*d^2*(b^2*c + 5*a^2*d)*(a + b*x)^(5 + n))/(b^7*(5 + n)) - (6*a*d^3*(a + b*x)^(6 + n))/(b^7*(6 + n)) + (d^3*(a + b*x)^(7 + n))/(b^7*(7 + n))","A",2,1,17,0.05882,1,"{697}"
362,1,246,0,0.3446164,"\int \frac{(a+b x)^n \left(c+d x^2\right)^3}{x} \, dx","Int[((a + b*x)^n*(c + d*x^2)^3)/x,x]","-\frac{a d \left(3 a^2 b^2 c d+a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+1}}{b^6 (n+1)}+\frac{d \left(9 a^2 b^2 c d+5 a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+2}}{b^6 (n+2)}-\frac{a d^2 \left(10 a^2 d+9 b^2 c\right) (a+b x)^{n+3}}{b^6 (n+3)}+\frac{d^2 \left(10 a^2 d+3 b^2 c\right) (a+b x)^{n+4}}{b^6 (n+4)}-\frac{5 a d^3 (a+b x)^{n+5}}{b^6 (n+5)}+\frac{d^3 (a+b x)^{n+6}}{b^6 (n+6)}-\frac{c^3 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}","-\frac{a d \left(3 a^2 b^2 c d+a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+1}}{b^6 (n+1)}+\frac{d \left(9 a^2 b^2 c d+5 a^4 d^2+3 b^4 c^2\right) (a+b x)^{n+2}}{b^6 (n+2)}-\frac{a d^2 \left(10 a^2 d+9 b^2 c\right) (a+b x)^{n+3}}{b^6 (n+3)}+\frac{d^2 \left(10 a^2 d+3 b^2 c\right) (a+b x)^{n+4}}{b^6 (n+4)}-\frac{5 a d^3 (a+b x)^{n+5}}{b^6 (n+5)}+\frac{d^3 (a+b x)^{n+6}}{b^6 (n+6)}-\frac{c^3 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"-((a*d*(3*b^4*c^2 + 3*a^2*b^2*c*d + a^4*d^2)*(a + b*x)^(1 + n))/(b^6*(1 + n))) + (d*(3*b^4*c^2 + 9*a^2*b^2*c*d + 5*a^4*d^2)*(a + b*x)^(2 + n))/(b^6*(2 + n)) - (a*d^2*(9*b^2*c + 10*a^2*d)*(a + b*x)^(3 + n))/(b^6*(3 + n)) + (d^2*(3*b^2*c + 10*a^2*d)*(a + b*x)^(4 + n))/(b^6*(4 + n)) - (5*a*d^3*(a + b*x)^(5 + n))/(b^6*(5 + n)) + (d^3*(a + b*x)^(6 + n))/(b^6*(6 + n)) - (c^3*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n))","A",4,3,20,0.1500,1,"{952, 1620, 65}"
363,1,250,0,0.4031311,"\int \frac{x^4 (d+e x)^n}{a+c x^2} \, dx","Int[(x^4*(d + e*x)^n)/(a + c*x^2),x]","\frac{\left(c d^2-a e^2\right) (d+e x)^{n+1}}{c^2 e^3 (n+1)}+\frac{(-a)^{3/2} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 c^2 (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{(-a)^{3/2} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 c^2 (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}-\frac{2 d (d+e x)^{n+2}}{c e^3 (n+2)}+\frac{(d+e x)^{n+3}}{c e^3 (n+3)}","\frac{\left(c d^2-a e^2\right) (d+e x)^{n+1}}{c^2 e^3 (n+1)}+\frac{(-a)^{3/2} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 c^2 (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{(-a)^{3/2} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 c^2 (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}-\frac{2 d (d+e x)^{n+2}}{c e^3 (n+2)}+\frac{(d+e x)^{n+3}}{c e^3 (n+3)}",1,"((c*d^2 - a*e^2)*(d + e*x)^(1 + n))/(c^2*e^3*(1 + n)) - (2*d*(d + e*x)^(2 + n))/(c*e^3*(2 + n)) + (d + e*x)^(3 + n)/(c*e^3*(3 + n)) + ((-a)^(3/2)*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*c^2*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + n)) - ((-a)^(3/2)*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*c^2*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + n))","A",6,3,20,0.1500,1,"{1629, 712, 68}"
364,1,209,0,0.2252937,"\int \frac{x^3 (d+e x)^n}{a+c x^2} \, dx","Int[(x^3*(d + e*x)^n)/(a + c*x^2),x]","\frac{a (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 c^{3/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}+\frac{a (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 c^{3/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}-\frac{d (d+e x)^{n+1}}{c e^2 (n+1)}+\frac{(d+e x)^{n+2}}{c e^2 (n+2)}","\frac{a (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 c^{3/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}+\frac{a (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 c^{3/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}-\frac{d (d+e x)^{n+1}}{c e^2 (n+1)}+\frac{(d+e x)^{n+2}}{c e^2 (n+2)}",1,"-((d*(d + e*x)^(1 + n))/(c*e^2*(1 + n))) + (d + e*x)^(2 + n)/(c*e^2*(2 + n)) + (a*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*c^(3/2)*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + n)) + (a*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*c^(3/2)*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + n))","A",6,3,20,0.1500,1,"{1629, 831, 68}"
365,1,194,0,0.2261584,"\int \frac{x^2 (d+e x)^n}{a+c x^2} \, dx","Int[(x^2*(d + e*x)^n)/(a + c*x^2),x]","\frac{\sqrt{-a} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 c (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{\sqrt{-a} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 c (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}+\frac{(d+e x)^{n+1}}{c e (n+1)}","\frac{\sqrt{-a} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 c (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{\sqrt{-a} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 c (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}+\frac{(d+e x)^{n+1}}{c e (n+1)}",1,"(d + e*x)^(1 + n)/(c*e*(1 + n)) + (Sqrt[-a]*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*c*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + n)) - (Sqrt[-a]*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*c*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + n))","A",6,3,20,0.1500,1,"{1629, 712, 68}"
366,1,163,0,0.0942188,"\int \frac{x (d+e x)^n}{a+c x^2} \, dx","Int[(x*(d + e*x)^n)/(a + c*x^2),x]","-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 \sqrt{c} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{c} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}","-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 \sqrt{c} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{c} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}",1,"-((d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*Sqrt[c]*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + n)) - ((d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*Sqrt[c]*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + n))","A",4,2,18,0.1111,1,"{831, 68}"
367,1,167,0,0.0912727,"\int \frac{(d+e x)^n}{a+c x^2} \, dx","Int[(d + e*x)^n/(a + c*x^2),x]","\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 \sqrt{-a} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{-a} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}","\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 \sqrt{-a} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{-a} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}",1,"((d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*Sqrt[-a]*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + n)) - ((d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*Sqrt[-a]*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + n))","A",4,2,17,0.1176,1,"{712, 68}"
368,1,207,0,0.1833174,"\int \frac{(d+e x)^n}{x \left(a+c x^2\right)} \, dx","Int[(d + e*x)^n/(x*(a + c*x^2)),x]","\frac{\sqrt{c} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 a (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}+\frac{\sqrt{c} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 a (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{e x}{d}+1\right)}{a d (n+1)}","\frac{\sqrt{c} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 a (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}+\frac{\sqrt{c} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 a (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{e x}{d}+1\right)}{a d (n+1)}",1,"(Sqrt[c]*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*a*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + n)) + (Sqrt[c]*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*a*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + n)) - ((d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (e*x)/d])/(a*d*(1 + n))","A",7,4,20,0.2000,1,"{961, 65, 831, 68}"
369,1,207,0,0.2206079,"\int \frac{(d+e x)^n}{x^2 \left(a+c x^2\right)} \, dx","Int[(d + e*x)^n/(x^2*(a + c*x^2)),x]","\frac{c (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 (-a)^{3/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{c (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 (-a)^{3/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}+\frac{e (d+e x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{e x}{d}+1\right)}{a d^2 (n+1)}","\frac{c (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 (-a)^{3/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{c (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 (-a)^{3/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}+\frac{e (d+e x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{e x}{d}+1\right)}{a d^2 (n+1)}",1,"(c*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*(-a)^(3/2)*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + n)) - (c*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*(-a)^(3/2)*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + n)) + (e*(d + e*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (e*x)/d])/(a*d^2*(1 + n))","A",7,4,20,0.2000,1,"{961, 65, 712, 68}"
370,1,332,0,0.450803,"\int \frac{x^4 (d+e x)^n}{\left(a+c x^2\right)^2} \, dx","Int[(x^4*(d + e*x)^n)/(a + c*x^2)^2,x]","\frac{(d+e x)^{n+1} \left(3 \sqrt{-a} c d^2+a \sqrt{c} d e n+\sqrt{-a} a e^2 (n+3)\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 c^2 (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}-\frac{(d+e x)^{n+1} \left(3 \sqrt{-a} c d^2-a \sqrt{c} d e n+\sqrt{-a} a e^2 (n+3)\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 c^2 (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{a (d+e x)^{n+1} (a e+c d x)}{2 c^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{n+1}}{c^2 e (n+1)}","\frac{(d+e x)^{n+1} \left(3 \sqrt{-a} c d^2+a \sqrt{c} d e n+\sqrt{-a} a e^2 (n+3)\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 c^2 (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}-\frac{(d+e x)^{n+1} \left(3 \sqrt{-a} c d^2-a \sqrt{c} d e n+\sqrt{-a} a e^2 (n+3)\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 c^2 (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{a (d+e x)^{n+1} (a e+c d x)}{2 c^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{n+1}}{c^2 e (n+1)}",1,"(d + e*x)^(1 + n)/(c^2*e*(1 + n)) + (a*(a*e + c*d*x)*(d + e*x)^(1 + n))/(2*c^2*(c*d^2 + a*e^2)*(a + c*x^2)) + ((3*Sqrt[-a]*c*d^2 + a*Sqrt[c]*d*e*n + Sqrt[-a]*a*e^2*(3 + n))*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(4*c^2*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n)) - ((3*Sqrt[-a]*c*d^2 - a*Sqrt[c]*d*e*n + Sqrt[-a]*a*e^2*(3 + n))*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(4*c^2*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n))","A",5,3,20,0.1500,1,"{1649, 1629, 68}"
371,1,297,0,0.4101048,"\int \frac{x^3 (d+e x)^n}{\left(a+c x^2\right)^2} \, dx","Int[(x^3*(d + e*x)^n)/(a + c*x^2)^2,x]","-\frac{(d+e x)^{n+1} \left(\sqrt{-a} \sqrt{c} d e n+a e^2 (n+2)+2 c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 c^{3/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{n+1} \left(\sqrt{-a} d e n-\frac{a e^2 (n+2)+2 c d^2}{\sqrt{c}}\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 c (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{a (d-e x) (d+e x)^{n+1}}{2 c \left(a+c x^2\right) \left(a e^2+c d^2\right)}","-\frac{(d+e x)^{n+1} \left(\sqrt{-a} \sqrt{c} d e n+a e^2 (n+2)+2 c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 c^{3/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{n+1} \left(\sqrt{-a} d e n-\frac{a e^2 (n+2)+2 c d^2}{\sqrt{c}}\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 c (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{a (d-e x) (d+e x)^{n+1}}{2 c \left(a+c x^2\right) \left(a e^2+c d^2\right)}",1,"(a*(d - e*x)*(d + e*x)^(1 + n))/(2*c*(c*d^2 + a*e^2)*(a + c*x^2)) + ((Sqrt[-a]*d*e*n - (2*c*d^2 + a*e^2*(2 + n))/Sqrt[c])*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(4*c*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n)) - ((2*c*d^2 + Sqrt[-a]*Sqrt[c]*d*e*n + a*e^2*(2 + n))*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(4*c^(3/2)*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n))","A",5,3,20,0.1500,1,"{1649, 831, 68}"
372,1,306,0,0.5301489,"\int \frac{x^2 (d+e x)^n}{\left(a+c x^2\right)^2} \, dx","Int[(x^2*(d + e*x)^n)/(a + c*x^2)^2,x]","\frac{(d+e x)^{n+1} \left(-\sqrt{-a} \sqrt{c} d e n+a e^2 (n+1)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 \sqrt{-a} c (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}-\frac{(d+e x)^{n+1} \left(\sqrt{-a} \sqrt{c} d e n+a e^2 (n+1)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 \sqrt{-a} c (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{(d+e x)^{n+1} (a e+c d x)}{2 c \left(a+c x^2\right) \left(a e^2+c d^2\right)}","\frac{(d+e x)^{n+1} \left(-\sqrt{-a} \sqrt{c} d e n+a e^2 (n+1)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 \sqrt{-a} c (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}-\frac{(d+e x)^{n+1} \left(\sqrt{-a} \sqrt{c} d e n+a e^2 (n+1)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 \sqrt{-a} c (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{(d+e x)^{n+1} (a e+c d x)}{2 c \left(a+c x^2\right) \left(a e^2+c d^2\right)}",1,"-((a*e + c*d*x)*(d + e*x)^(1 + n))/(2*c*(c*d^2 + a*e^2)*(a + c*x^2)) + ((c*d^2 - Sqrt[-a]*Sqrt[c]*d*e*n + a*e^2*(1 + n))*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(4*Sqrt[-a]*c*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n)) - ((c*d^2 + Sqrt[-a]*Sqrt[c]*d*e*n + a*e^2*(1 + n))*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(4*Sqrt[-a]*c*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n))","A",5,3,20,0.1500,1,"{1649, 831, 68}"
373,1,279,0,0.2969658,"\int \frac{x (d+e x)^n}{\left(a+c x^2\right)^2} \, dx","Int[(x*(d + e*x)^n)/(a + c*x^2)^2,x]","\frac{e n \left(\sqrt{-a} e+\sqrt{c} d\right) (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 \sqrt{-a} \sqrt{c} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{e n \left(\sqrt{-a} \sqrt{c} d+a e\right) (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 a \sqrt{c} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{(d-e x) (d+e x)^{n+1}}{2 \left(a+c x^2\right) \left(a e^2+c d^2\right)}","\frac{e n \left(\sqrt{-a} e+\sqrt{c} d\right) (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 \sqrt{-a} \sqrt{c} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{e n \left(\sqrt{-a} \sqrt{c} d+a e\right) (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 a \sqrt{c} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{(d-e x) (d+e x)^{n+1}}{2 \left(a+c x^2\right) \left(a e^2+c d^2\right)}",1,"-((d - e*x)*(d + e*x)^(1 + n))/(2*(c*d^2 + a*e^2)*(a + c*x^2)) + (e*(Sqrt[c]*d + Sqrt[-a]*e)*n*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(4*Sqrt[-a]*Sqrt[c]*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n)) + (e*(Sqrt[-a]*Sqrt[c]*d + a*e)*n*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(4*a*Sqrt[c]*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n))","A",5,3,18,0.1667,1,"{823, 831, 68}"
374,1,304,0,0.4165262,"\int \frac{(d+e x)^n}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^n/(a + c*x^2)^2,x]","-\frac{(d+e x)^{n+1} \left(\sqrt{-a} \sqrt{c} d e n+a e^2 (1-n)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 (-a)^{3/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{n+1} \left(-\sqrt{-a} \sqrt{c} d e n+a e^2 (1-n)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 (-a)^{3/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{n+1} (a e+c d x)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}","-\frac{(d+e x)^{n+1} \left(\sqrt{-a} \sqrt{c} d e n+a e^2 (1-n)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 (-a)^{3/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{n+1} \left(-\sqrt{-a} \sqrt{c} d e n+a e^2 (1-n)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 (-a)^{3/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{n+1} (a e+c d x)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}",1,"((a*e + c*d*x)*(d + e*x)^(1 + n))/(2*a*(c*d^2 + a*e^2)*(a + c*x^2)) - ((c*d^2 + a*e^2*(1 - n) + Sqrt[-a]*Sqrt[c]*d*e*n)*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(4*(-a)^(3/2)*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n)) + ((c*d^2 + a*e^2*(1 - n) - Sqrt[-a]*Sqrt[c]*d*e*n)*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(4*(-a)^(3/2)*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n))","A",5,3,17,0.1765,1,"{741, 831, 68}"
375,1,489,0,0.6048723,"\int \frac{(d+e x)^n}{x \left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^n/(x*(a + c*x^2)^2),x]","-\frac{\sqrt{c} e n \left(\sqrt{-a} \sqrt{c} d+a e\right) (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 a^2 (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{\sqrt{c} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 a^2 (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}+\frac{\sqrt{c} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 a^2 (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{e x}{d}+1\right)}{a^2 d (n+1)}+\frac{\sqrt{c} e n \left(\sqrt{-a} e+\sqrt{c} d\right) (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 (-a)^{3/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{c (d-e x) (d+e x)^{n+1}}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}","-\frac{\sqrt{c} e n \left(\sqrt{-a} \sqrt{c} d+a e\right) (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 a^2 (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{\sqrt{c} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 a^2 (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}+\frac{\sqrt{c} (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 a^2 (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}-\frac{(d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{e x}{d}+1\right)}{a^2 d (n+1)}+\frac{\sqrt{c} e n \left(\sqrt{-a} e+\sqrt{c} d\right) (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 (-a)^{3/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{c (d-e x) (d+e x)^{n+1}}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}",1,"(c*(d - e*x)*(d + e*x)^(1 + n))/(2*a*(c*d^2 + a*e^2)*(a + c*x^2)) + (Sqrt[c]*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*a^2*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + n)) + (Sqrt[c]*e*(Sqrt[c]*d + Sqrt[-a]*e)*n*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(4*(-a)^(3/2)*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n)) + (Sqrt[c]*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*a^2*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + n)) - (Sqrt[c]*e*(Sqrt[-a]*Sqrt[c]*d + a*e)*n*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(4*a^2*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n)) - ((d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (e*x)/d])/(a^2*d*(1 + n))","A",12,5,20,0.2500,1,"{961, 65, 823, 831, 68}"
376,1,513,0,0.6981688,"\int \frac{(d+e x)^n}{x^2 \left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^n/(x^2*(a + c*x^2)^2),x]","-\frac{c (d+e x)^{n+1} (a e+c d x)}{2 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)}+\frac{e (d+e x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{e x}{d}+1\right)}{a^2 d^2 (n+1)}-\frac{c (d+e x)^{n+1} \left(\sqrt{-a} \sqrt{c} d e n+a e^2 (1-n)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 (-a)^{5/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{c (d+e x)^{n+1} \left(-\sqrt{-a} \sqrt{c} d e n+a e^2 (1-n)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 (-a)^{5/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{c (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 (-a)^{5/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}+\frac{c (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 (-a)^{5/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}","-\frac{c (d+e x)^{n+1} (a e+c d x)}{2 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)}+\frac{e (d+e x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{e x}{d}+1\right)}{a^2 d^2 (n+1)}-\frac{c (d+e x)^{n+1} \left(\sqrt{-a} \sqrt{c} d e n+a e^2 (1-n)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 (-a)^{5/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{c (d+e x)^{n+1} \left(-\sqrt{-a} \sqrt{c} d e n+a e^2 (1-n)+c d^2\right) \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 (-a)^{5/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{c (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 (-a)^{5/2} (n+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}+\frac{c (d+e x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 (-a)^{5/2} (n+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}",1,"-(c*(a*e + c*d*x)*(d + e*x)^(1 + n))/(2*a^2*(c*d^2 + a*e^2)*(a + c*x^2)) - (c*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*(-a)^(5/2)*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + n)) - (c*(c*d^2 + a*e^2*(1 - n) + Sqrt[-a]*Sqrt[c]*d*e*n)*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(4*(-a)^(5/2)*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n)) + (c*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*(-a)^(5/2)*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + n)) + (c*(c*d^2 + a*e^2*(1 - n) - Sqrt[-a]*Sqrt[c]*d*e*n)*(d + e*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(4*(-a)^(5/2)*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + n)) + (e*(d + e*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (e*x)/d])/(a^2*d^2*(1 + n))","A",12,6,20,0.3000,1,"{961, 65, 741, 831, 68, 712}"
377,1,377,0,0.7646565,"\int (g x)^m (d+e x)^n \left(a+c x^2\right)^2 \, dx","Int[(g*x)^m*(d + e*x)^n*(a + c*x^2)^2,x]","\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} \left(\frac{a^2}{m+1}+\frac{c d^2 (m+2) \left(2 a e^2 \left(m^2+m (2 n+9)+n^2+9 n+20\right)+c d^2 \left(m^2+7 m+12\right)\right)}{e^4 (m+n+2) (m+n+3) (m+n+4) (m+n+5)}\right) \, _2F_1\left(m+1,-n;m+2;-\frac{e x}{d}\right)}{g}+\frac{c (g x)^{m+2} (d+e x)^{n+1} \left(2 a e^2 \left(m^2+m (2 n+9)+n^2+9 n+20\right)+c d^2 \left(m^2+7 m+12\right)\right)}{e^3 g^2 (m+n+3) (m+n+4) (m+n+5)}-\frac{c d (m+2) (g x)^{m+1} (d+e x)^{n+1} \left(2 a e^2 \left(m^2+m (2 n+9)+n^2+9 n+20\right)+c d^2 \left(m^2+7 m+12\right)\right)}{e^4 g (m+n+2) (m+n+3) (m+n+4) (m+n+5)}-\frac{c^2 d (m+4) (g x)^{m+3} (d+e x)^{n+1}}{e^2 g^3 (m+n+4) (m+n+5)}+\frac{c^2 (g x)^{m+4} (d+e x)^{n+1}}{e g^4 (m+n+5)}","\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} \left(a^2 e^4 (m+n+2) (m+n+3) (m+n+4) (m+n+5)+c d^2 (m+1) (m+2) \left(2 a e^2 \left(m^2+m (2 n+9)+n^2+9 n+20\right)+c d^2 \left(m^2+7 m+12\right)\right)\right) \, _2F_1\left(m+1,-n;m+2;-\frac{e x}{d}\right)}{e^4 g (m+1) (m+n+2) (m+n+3) (m+n+4) (m+n+5)}+\frac{c (g x)^{m+2} (d+e x)^{n+1} \left(2 a e^2 \left(m^2+m (2 n+9)+n^2+9 n+20\right)+c d^2 \left(m^2+7 m+12\right)\right)}{e^3 g^2 (m+n+3) (m+n+4) (m+n+5)}-\frac{c d (m+2) (g x)^{m+1} (d+e x)^{n+1} \left(2 a e^2 \left(m^2+m (2 n+9)+n^2+9 n+20\right)+c d^2 \left(m^2+7 m+12\right)\right)}{e^4 g (m+n+2) (m+n+3) (m+n+4) (m+n+5)}-\frac{c^2 d (m+4) (g x)^{m+3} (d+e x)^{n+1}}{e^2 g^3 (m+n+4) (m+n+5)}+\frac{c^2 (g x)^{m+4} (d+e x)^{n+1}}{e g^4 (m+n+5)}",1,"-((c*d*(2 + m)*(c*d^2*(12 + 7*m + m^2) + 2*a*e^2*(20 + m^2 + 9*n + n^2 + m*(9 + 2*n)))*(g*x)^(1 + m)*(d + e*x)^(1 + n))/(e^4*g*(2 + m + n)*(3 + m + n)*(4 + m + n)*(5 + m + n))) + (c*(c*d^2*(12 + 7*m + m^2) + 2*a*e^2*(20 + m^2 + 9*n + n^2 + m*(9 + 2*n)))*(g*x)^(2 + m)*(d + e*x)^(1 + n))/(e^3*g^2*(3 + m + n)*(4 + m + n)*(5 + m + n)) - (c^2*d*(4 + m)*(g*x)^(3 + m)*(d + e*x)^(1 + n))/(e^2*g^3*(4 + m + n)*(5 + m + n)) + (c^2*(g*x)^(4 + m)*(d + e*x)^(1 + n))/(e*g^4*(5 + m + n)) + ((a^2/(1 + m) + (c*d^2*(2 + m)*(c*d^2*(12 + 7*m + m^2) + 2*a*e^2*(20 + m^2 + 9*n + n^2 + m*(9 + 2*n))))/(e^4*(2 + m + n)*(3 + m + n)*(4 + m + n)*(5 + m + n)))*(g*x)^(1 + m)*(d + e*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((e*x)/d)])/(g*(1 + (e*x)/d)^n)","A",6,5,22,0.2273,1,"{952, 1623, 80, 66, 64}"
378,1,150,0,0.1330658,"\int (g x)^m (d+e x)^n \left(a+c x^2\right) \, dx","Int[(g*x)^m*(d + e*x)^n*(a + c*x^2),x]","\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} \left(\frac{a}{m+1}+\frac{c d^2 (m+2)}{e^2 (m+n+2) (m+n+3)}\right) \, _2F_1\left(m+1,-n;m+2;-\frac{e x}{d}\right)}{g}-\frac{c d (m+2) (g x)^{m+1} (d+e x)^{n+1}}{e^2 g (m+n+2) (m+n+3)}+\frac{c (g x)^{m+2} (d+e x)^{n+1}}{e g^2 (m+n+3)}","\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} \left(a e^2 (m+n+2) (m+n+3)+c d^2 (m+1) (m+2)\right) \, _2F_1\left(m+1,-n;m+2;-\frac{e x}{d}\right)}{e^2 g (m+1) (m+n+2) (m+n+3)}-\frac{c d (m+2) (g x)^{m+1} (d+e x)^{n+1}}{e^2 g (m+n+2) (m+n+3)}+\frac{c (g x)^{m+2} (d+e x)^{n+1}}{e g^2 (m+n+3)}",1,"-((c*d*(2 + m)*(g*x)^(1 + m)*(d + e*x)^(1 + n))/(e^2*g*(2 + m + n)*(3 + m + n))) + (c*(g*x)^(2 + m)*(d + e*x)^(1 + n))/(e*g^2*(3 + m + n)) + ((a/(1 + m) + (c*d^2*(2 + m))/(e^2*(2 + m + n)*(3 + m + n)))*(g*x)^(1 + m)*(d + e*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((e*x)/d)])/(g*(1 + (e*x)/d)^n)","A",4,4,20,0.2000,1,"{952, 80, 66, 64}"
379,1,148,0,0.1768143,"\int \frac{(g x)^m (d+e x)^n}{a+c x^2} \, dx","Int[((g*x)^m*(d + e*x)^n)/(a + c*x^2),x]","\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{e x}{d},-\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{2 a g (m+1)}+\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{e x}{d},\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{2 a g (m+1)}","\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{e x}{d},-\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{2 a g (m+1)}+\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{e x}{d},\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{2 a g (m+1)}",1,"((g*x)^(1 + m)*(d + e*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((e*x)/d), -((Sqrt[c]*x)/Sqrt[-a])])/(2*a*g*(1 + m)*(1 + (e*x)/d)^n) + ((g*x)^(1 + m)*(d + e*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((e*x)/d), (Sqrt[c]*x)/Sqrt[-a]])/(2*a*g*(1 + m)*(1 + (e*x)/d)^n)","A",6,3,22,0.1364,1,"{912, 135, 133}"
380,1,295,0,0.4176432,"\int \frac{(g x)^m (d+e x)^n}{\left(a+c x^2\right)^2} \, dx","Int[((g*x)^m*(d + e*x)^n)/(a + c*x^2)^2,x]","\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{e x}{d},-\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{4 a^2 g (m+1)}+\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{e x}{d},\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{4 a^2 g (m+1)}+\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,2;m+2;-\frac{e x}{d},-\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{4 a^2 g (m+1)}+\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,2;m+2;-\frac{e x}{d},\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{4 a^2 g (m+1)}","\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{e x}{d},-\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{4 a^2 g (m+1)}+\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{e x}{d},\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{4 a^2 g (m+1)}+\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,2;m+2;-\frac{e x}{d},-\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{4 a^2 g (m+1)}+\frac{(g x)^{m+1} (d+e x)^n \left(\frac{e x}{d}+1\right)^{-n} F_1\left(m+1;-n,2;m+2;-\frac{e x}{d},\frac{\sqrt{c} x}{\sqrt{-a}}\right)}{4 a^2 g (m+1)}",1,"((g*x)^(1 + m)*(d + e*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((e*x)/d), -((Sqrt[c]*x)/Sqrt[-a])])/(4*a^2*g*(1 + m)*(1 + (e*x)/d)^n) + ((g*x)^(1 + m)*(d + e*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((e*x)/d), (Sqrt[c]*x)/Sqrt[-a]])/(4*a^2*g*(1 + m)*(1 + (e*x)/d)^n) + ((g*x)^(1 + m)*(d + e*x)^n*AppellF1[1 + m, -n, 2, 2 + m, -((e*x)/d), -((Sqrt[c]*x)/Sqrt[-a])])/(4*a^2*g*(1 + m)*(1 + (e*x)/d)^n) + ((g*x)^(1 + m)*(d + e*x)^n*AppellF1[1 + m, -n, 2, 2 + m, -((e*x)/d), (Sqrt[c]*x)/Sqrt[-a]])/(4*a^2*g*(1 + m)*(1 + (e*x)/d)^n)","A",12,4,22,0.1818,1,"{961, 135, 133, 912}"
381,1,125,0,0.0840607,"\int x^5 (d+e x) \left(a+b x^2\right)^p \, dx","Int[x^5*(d + e*x)*(a + b*x^2)^p,x]","\frac{a^2 d \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}-\frac{a d \left(a+b x^2\right)^{p+2}}{b^3 (p+2)}+\frac{d \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}+\frac{1}{7} e x^7 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};-\frac{b x^2}{a}\right)","\frac{a^2 d \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}-\frac{a d \left(a+b x^2\right)^{p+2}}{b^3 (p+2)}+\frac{d \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}+\frac{1}{7} e x^7 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};-\frac{b x^2}{a}\right)",1,"(a^2*d*(a + b*x^2)^(1 + p))/(2*b^3*(1 + p)) - (a*d*(a + b*x^2)^(2 + p))/(b^3*(2 + p)) + (d*(a + b*x^2)^(3 + p))/(2*b^3*(3 + p)) + (e*x^7*(a + b*x^2)^p*Hypergeometric2F1[7/2, -p, 9/2, -((b*x^2)/a)])/(7*(1 + (b*x^2)/a)^p)","A",6,5,18,0.2778,1,"{764, 266, 43, 365, 364}"
382,1,125,0,0.0848504,"\int x^4 (d+e x) \left(a+b x^2\right)^p \, dx","Int[x^4*(d + e*x)*(a + b*x^2)^p,x]","\frac{a^2 e \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}-\frac{a e \left(a+b x^2\right)^{p+2}}{b^3 (p+2)}+\frac{e \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}+\frac{1}{5} d x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)","\frac{a^2 e \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}-\frac{a e \left(a+b x^2\right)^{p+2}}{b^3 (p+2)}+\frac{e \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}+\frac{1}{5} d x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)",1,"(a^2*e*(a + b*x^2)^(1 + p))/(2*b^3*(1 + p)) - (a*e*(a + b*x^2)^(2 + p))/(b^3*(2 + p)) + (e*(a + b*x^2)^(3 + p))/(2*b^3*(3 + p)) + (d*x^5*(a + b*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, -((b*x^2)/a)])/(5*(1 + (b*x^2)/a)^p)","A",6,5,18,0.2778,1,"{764, 365, 364, 266, 43}"
383,1,100,0,0.064525,"\int x^3 (d+e x) \left(a+b x^2\right)^p \, dx","Int[x^3*(d + e*x)*(a + b*x^2)^p,x]","-\frac{a d \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}+\frac{d \left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}+\frac{1}{5} e x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)","-\frac{a d \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}+\frac{d \left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}+\frac{1}{5} e x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)",1,"-(a*d*(a + b*x^2)^(1 + p))/(2*b^2*(1 + p)) + (d*(a + b*x^2)^(2 + p))/(2*b^2*(2 + p)) + (e*x^5*(a + b*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, -((b*x^2)/a)])/(5*(1 + (b*x^2)/a)^p)","A",6,5,18,0.2778,1,"{764, 266, 43, 365, 364}"
384,1,100,0,0.0590601,"\int x^2 (d+e x) \left(a+b x^2\right)^p \, dx","Int[x^2*(d + e*x)*(a + b*x^2)^p,x]","-\frac{a e \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}+\frac{e \left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}+\frac{1}{3} d x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)","-\frac{a e \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}+\frac{e \left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}+\frac{1}{3} d x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)",1,"-(a*e*(a + b*x^2)^(1 + p))/(2*b^2*(1 + p)) + (e*(a + b*x^2)^(2 + p))/(2*b^2*(2 + p)) + (d*x^3*(a + b*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((b*x^2)/a)])/(3*(1 + (b*x^2)/a)^p)","A",6,5,18,0.2778,1,"{764, 365, 364, 266, 43}"
385,1,75,0,0.0326914,"\int x (d+e x) \left(a+b x^2\right)^p \, dx","Int[x*(d + e*x)*(a + b*x^2)^p,x]","\frac{d \left(a+b x^2\right)^{p+1}}{2 b (p+1)}+\frac{1}{3} e x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)","\frac{d \left(a+b x^2\right)^{p+1}}{2 b (p+1)}+\frac{1}{3} e x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)",1,"(d*(a + b*x^2)^(1 + p))/(2*b*(1 + p)) + (e*x^3*(a + b*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((b*x^2)/a)])/(3*(1 + (b*x^2)/a)^p)","A",4,4,16,0.2500,1,"{764, 261, 365, 364}"
386,1,70,0,0.0197929,"\int (d+e x) \left(a+b x^2\right)^p \, dx","Int[(d + e*x)*(a + b*x^2)^p,x]","d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)+\frac{e \left(a+b x^2\right)^{p+1}}{2 b (p+1)}","d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)+\frac{e \left(a+b x^2\right)^{p+1}}{2 b (p+1)}",1,"(e*(a + b*x^2)^(1 + p))/(2*b*(1 + p)) + (d*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(1 + (b*x^2)/a)^p","A",3,3,15,0.2000,1,"{641, 246, 245}"
387,1,88,0,0.0528735,"\int \frac{(d+e x) \left(a+b x^2\right)^p}{x} \, dx","Int[((d + e*x)*(a + b*x^2)^p)/x,x]","e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)-\frac{d \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}","e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)-\frac{d \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}",1,"(e*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(1 + (b*x^2)/a)^p - (d*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*(1 + p))","A",5,5,18,0.2778,1,"{764, 266, 65, 246, 245}"
388,1,91,0,0.0527079,"\int \frac{(d+e x) \left(a+b x^2\right)^p}{x^2} \, dx","Int[((d + e*x)*(a + b*x^2)^p)/x^2,x]","-\frac{d \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{x}-\frac{e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}","-\frac{d \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{x}-\frac{e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}",1,"-((d*(a + b*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, -((b*x^2)/a)])/(x*(1 + (b*x^2)/a)^p)) - (e*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*(1 + p))","A",5,5,18,0.2778,1,"{764, 365, 364, 266, 65}"
389,1,92,0,0.0529163,"\int \frac{(d+e x) \left(a+b x^2\right)^p}{x^3} \, dx","Int[((d + e*x)*(a + b*x^2)^p)/x^3,x]","\frac{b d \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 (p+1)}-\frac{e \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{x}","\frac{b d \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 (p+1)}-\frac{e \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{x}",1,"-((e*(a + b*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, -((b*x^2)/a)])/(x*(1 + (b*x^2)/a)^p)) + (b*d*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a^2*(1 + p))","A",5,5,18,0.2778,1,"{764, 266, 65, 365, 364}"
390,1,188,0,0.1799713,"\int x^5 (d+e x)^2 \left(a+b x^2\right)^p \, dx","Int[x^5*(d + e*x)^2*(a + b*x^2)^p,x]","\frac{a^2 \left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^4 (p+1)}-\frac{a \left(2 b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^4 (p+2)}+\frac{\left(b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+3}}{2 b^4 (p+3)}+\frac{e^2 \left(a+b x^2\right)^{p+4}}{2 b^4 (p+4)}+\frac{2}{7} d e x^7 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};-\frac{b x^2}{a}\right)","\frac{a^2 \left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^4 (p+1)}-\frac{a \left(2 b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^4 (p+2)}+\frac{\left(b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+3}}{2 b^4 (p+3)}+\frac{e^2 \left(a+b x^2\right)^{p+4}}{2 b^4 (p+4)}+\frac{2}{7} d e x^7 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};-\frac{b x^2}{a}\right)",1,"(a^2*(b*d^2 - a*e^2)*(a + b*x^2)^(1 + p))/(2*b^4*(1 + p)) - (a*(2*b*d^2 - 3*a*e^2)*(a + b*x^2)^(2 + p))/(2*b^4*(2 + p)) + ((b*d^2 - 3*a*e^2)*(a + b*x^2)^(3 + p))/(2*b^4*(3 + p)) + (e^2*(a + b*x^2)^(4 + p))/(2*b^4*(4 + p)) + (2*d*e*x^7*(a + b*x^2)^p*Hypergeometric2F1[7/2, -p, 9/2, -((b*x^2)/a)])/(7*(1 + (b*x^2)/a)^p)","A",7,6,20,0.3000,1,"{1652, 446, 77, 12, 365, 364}"
391,1,169,0,0.1627156,"\int x^4 (d+e x)^2 \left(a+b x^2\right)^p \, dx","Int[x^4*(d + e*x)^2*(a + b*x^2)^p,x]","\frac{a^2 d e \left(a+b x^2\right)^{p+1}}{b^3 (p+1)}-\frac{2 a d e \left(a+b x^2\right)^{p+2}}{b^3 (p+2)}+\frac{d e \left(a+b x^2\right)^{p+3}}{b^3 (p+3)}+\frac{1}{5} x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(d^2-\frac{5 a e^2}{2 b p+7 b}\right) \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)+\frac{e^2 x^5 \left(a+b x^2\right)^{p+1}}{b (2 p+7)}","\frac{a^2 d e \left(a+b x^2\right)^{p+1}}{b^3 (p+1)}-\frac{2 a d e \left(a+b x^2\right)^{p+2}}{b^3 (p+2)}+\frac{d e \left(a+b x^2\right)^{p+3}}{b^3 (p+3)}-\frac{x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(5 a e^2-b d^2 (2 p+7)\right) \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)}{5 b (2 p+7)}+\frac{e^2 x^5 \left(a+b x^2\right)^{p+1}}{b (2 p+7)}",1,"(a^2*d*e*(a + b*x^2)^(1 + p))/(b^3*(1 + p)) + (e^2*x^5*(a + b*x^2)^(1 + p))/(b*(7 + 2*p)) - (2*a*d*e*(a + b*x^2)^(2 + p))/(b^3*(2 + p)) + (d*e*(a + b*x^2)^(3 + p))/(b^3*(3 + p)) + ((d^2 - (5*a*e^2)/(7*b + 2*b*p))*x^5*(a + b*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, -((b*x^2)/a)])/(5*(1 + (b*x^2)/a)^p)","A",8,7,20,0.3500,1,"{1652, 459, 365, 364, 12, 266, 43}"
392,1,149,0,0.1380455,"\int x^3 (d+e x)^2 \left(a+b x^2\right)^p \, dx","Int[x^3*(d + e*x)^2*(a + b*x^2)^p,x]","-\frac{a \left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}+\frac{\left(b d^2-2 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^3 (p+2)}+\frac{e^2 \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}+\frac{2}{5} d e x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)","-\frac{a \left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}+\frac{\left(b d^2-2 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^3 (p+2)}+\frac{e^2 \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}+\frac{2}{5} d e x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)",1,"-(a*(b*d^2 - a*e^2)*(a + b*x^2)^(1 + p))/(2*b^3*(1 + p)) + ((b*d^2 - 2*a*e^2)*(a + b*x^2)^(2 + p))/(2*b^3*(2 + p)) + (e^2*(a + b*x^2)^(3 + p))/(2*b^3*(3 + p)) + (2*d*e*x^5*(a + b*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, -((b*x^2)/a)])/(5*(1 + (b*x^2)/a)^p)","A",7,6,20,0.3000,1,"{1652, 446, 77, 12, 365, 364}"
393,1,144,0,0.1365215,"\int x^2 (d+e x)^2 \left(a+b x^2\right)^p \, dx","Int[x^2*(d + e*x)^2*(a + b*x^2)^p,x]","-\frac{a d e \left(a+b x^2\right)^{p+1}}{b^2 (p+1)}+\frac{d e \left(a+b x^2\right)^{p+2}}{b^2 (p+2)}+\frac{1}{3} x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(d^2-\frac{3 a e^2}{2 b p+5 b}\right) \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)+\frac{e^2 x^3 \left(a+b x^2\right)^{p+1}}{b (2 p+5)}","-\frac{a d e \left(a+b x^2\right)^{p+1}}{b^2 (p+1)}+\frac{d e \left(a+b x^2\right)^{p+2}}{b^2 (p+2)}-\frac{x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a e^2-b d^2 (2 p+5)\right) \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)}{3 b (2 p+5)}+\frac{e^2 x^3 \left(a+b x^2\right)^{p+1}}{b (2 p+5)}",1,"-((a*d*e*(a + b*x^2)^(1 + p))/(b^2*(1 + p))) + (e^2*x^3*(a + b*x^2)^(1 + p))/(b*(5 + 2*p)) + (d*e*(a + b*x^2)^(2 + p))/(b^2*(2 + p)) + ((d^2 - (3*a*e^2)/(5*b + 2*b*p))*x^3*(a + b*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((b*x^2)/a)])/(3*(1 + (b*x^2)/a)^p)","A",8,7,20,0.3500,1,"{1652, 459, 365, 364, 12, 266, 43}"
394,1,113,0,0.0970589,"\int x (d+e x)^2 \left(a+b x^2\right)^p \, dx","Int[x*(d + e*x)^2*(a + b*x^2)^p,x]","\frac{\left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}+\frac{e^2 \left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}+\frac{2}{3} d e x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)","\frac{\left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}+\frac{e^2 \left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}+\frac{2}{3} d e x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)",1,"((b*d^2 - a*e^2)*(a + b*x^2)^(1 + p))/(2*b^2*(1 + p)) + (e^2*(a + b*x^2)^(2 + p))/(2*b^2*(2 + p)) + (2*d*e*x^3*(a + b*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((b*x^2)/a)])/(3*(1 + (b*x^2)/a)^p)","A",7,6,18,0.3333,1,"{1652, 444, 43, 12, 365, 364}"
395,1,125,0,0.0774444,"\int (d+e x)^2 \left(a+b x^2\right)^p \, dx","Int[(d + e*x)^2*(a + b*x^2)^p,x]","x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(d^2-\frac{a e^2}{2 b p+3 b}\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)+\frac{e (d+e x) \left(a+b x^2\right)^{p+1}}{b (2 p+3)}+\frac{d e (p+2) \left(a+b x^2\right)^{p+1}}{b (p+1) (2 p+3)}","-\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2-b d^2 (2 p+3)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{b (2 p+3)}+\frac{e (d+e x) \left(a+b x^2\right)^{p+1}}{b (2 p+3)}+\frac{d e (p+2) \left(a+b x^2\right)^{p+1}}{b (p+1) (2 p+3)}",1,"(d*e*(2 + p)*(a + b*x^2)^(1 + p))/(b*(1 + p)*(3 + 2*p)) + (e*(d + e*x)*(a + b*x^2)^(1 + p))/(b*(3 + 2*p)) + ((d^2 - (a*e^2)/(3*b + 2*b*p))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(1 + (b*x^2)/a)^p","A",4,4,17,0.2353,1,"{743, 641, 246, 245}"
396,1,118,0,0.093041,"\int \frac{(d+e x)^2 \left(a+b x^2\right)^p}{x} \, dx","Int[((d + e*x)^2*(a + b*x^2)^p)/x,x]","-\frac{d^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}+2 d e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)+\frac{e^2 \left(a+b x^2\right)^{p+1}}{2 b (p+1)}","-\frac{d^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}+2 d e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)+\frac{e^2 \left(a+b x^2\right)^{p+1}}{2 b (p+1)}",1,"(e^2*(a + b*x^2)^(1 + p))/(2*b*(1 + p)) + (2*d*e*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(1 + (b*x^2)/a)^p - (d^2*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*(1 + p))","A",7,7,20,0.3500,1,"{1652, 446, 80, 65, 12, 246, 245}"
397,1,127,0,0.1225704,"\int \frac{(d+e x)^2 \left(a+b x^2\right)^p}{x^2} \, dx","Int[((d + e*x)^2*(a + b*x^2)^p)/x^2,x]","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+b d^2 (2 p+1)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{a}-\frac{d^2 \left(a+b x^2\right)^{p+1}}{a x}-\frac{d e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{a (p+1)}","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+b d^2 (2 p+1)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{a}-\frac{d^2 \left(a+b x^2\right)^{p+1}}{a x}-\frac{d e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{a (p+1)}",1,"-((d^2*(a + b*x^2)^(1 + p))/(a*x)) + ((a*e^2 + b*d^2*(1 + 2*p))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(a*(1 + (b*x^2)/a)^p) - (d*e*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(a*(1 + p))","A",6,6,20,0.3000,1,"{1807, 764, 266, 65, 246, 245}"
398,1,127,0,0.1245697,"\int \frac{(d+e x)^2 \left(a+b x^2\right)^p}{x^3} \, dx","Int[((d + e*x)^2*(a + b*x^2)^p)/x^3,x]","-\frac{\left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 p\right) \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 (p+1)}-\frac{d^2 \left(a+b x^2\right)^{p+1}}{2 a x^2}-\frac{2 d e \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{x}","-\frac{\left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 p\right) \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 (p+1)}-\frac{d^2 \left(a+b x^2\right)^{p+1}}{2 a x^2}-\frac{2 d e \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{x}",1,"-(d^2*(a + b*x^2)^(1 + p))/(2*a*x^2) - (2*d*e*(a + b*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, -((b*x^2)/a)])/(x*(1 + (b*x^2)/a)^p) - ((a*e^2 + b*d^2*p)*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a^2*(1 + p))","A",6,6,20,0.3000,1,"{1807, 764, 365, 364, 266, 65}"
399,1,241,0,0.2468021,"\int x^5 (d+e x)^3 \left(a+b x^2\right)^p \, dx","Int[x^5*(d + e*x)^3*(a + b*x^2)^p,x]","\frac{a^2 d \left(b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^4 (p+1)}-\frac{a d \left(2 b d^2-9 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^4 (p+2)}+\frac{d \left(b d^2-9 a e^2\right) \left(a+b x^2\right)^{p+3}}{2 b^4 (p+3)}+\frac{3 d e^2 \left(a+b x^2\right)^{p+4}}{2 b^4 (p+4)}+\frac{1}{7} e x^7 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 d^2-\frac{7 a e^2}{2 b p+9 b}\right) \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};-\frac{b x^2}{a}\right)+\frac{e^3 x^7 \left(a+b x^2\right)^{p+1}}{b (2 p+9)}","\frac{a^2 d \left(b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^4 (p+1)}-\frac{a d \left(2 b d^2-9 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^4 (p+2)}+\frac{d \left(b d^2-9 a e^2\right) \left(a+b x^2\right)^{p+3}}{2 b^4 (p+3)}+\frac{3 d e^2 \left(a+b x^2\right)^{p+4}}{2 b^4 (p+4)}-\frac{e x^7 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(7 a e^2-3 b d^2 (2 p+9)\right) \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};-\frac{b x^2}{a}\right)}{7 b (2 p+9)}+\frac{e^3 x^7 \left(a+b x^2\right)^{p+1}}{b (2 p+9)}",1,"(a^2*d*(b*d^2 - 3*a*e^2)*(a + b*x^2)^(1 + p))/(2*b^4*(1 + p)) + (e^3*x^7*(a + b*x^2)^(1 + p))/(b*(9 + 2*p)) - (a*d*(2*b*d^2 - 9*a*e^2)*(a + b*x^2)^(2 + p))/(2*b^4*(2 + p)) + (d*(b*d^2 - 9*a*e^2)*(a + b*x^2)^(3 + p))/(2*b^4*(3 + p)) + (3*d*e^2*(a + b*x^2)^(4 + p))/(2*b^4*(4 + p)) + (e*(3*d^2 - (7*a*e^2)/(9*b + 2*b*p))*x^7*(a + b*x^2)^p*Hypergeometric2F1[7/2, -p, 9/2, -((b*x^2)/a)])/(7*(1 + (b*x^2)/a)^p)","A",7,6,20,0.3000,1,"{1652, 446, 77, 459, 365, 364}"
400,1,241,0,0.2354651,"\int x^4 (d+e x)^3 \left(a+b x^2\right)^p \, dx","Int[x^4*(d + e*x)^3*(a + b*x^2)^p,x]","\frac{a^2 e \left(3 b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^4 (p+1)}-\frac{3 a e \left(2 b d^2-a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^4 (p+2)}+\frac{3 e \left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+3}}{2 b^4 (p+3)}+\frac{e^3 \left(a+b x^2\right)^{p+4}}{2 b^4 (p+4)}+\frac{1}{5} d x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(d^2-\frac{15 a e^2}{2 b p+7 b}\right) \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)+\frac{3 d e^2 x^5 \left(a+b x^2\right)^{p+1}}{b (2 p+7)}","\frac{a^2 e \left(3 b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^4 (p+1)}-\frac{3 a e \left(2 b d^2-a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^4 (p+2)}+\frac{3 e \left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+3}}{2 b^4 (p+3)}+\frac{e^3 \left(a+b x^2\right)^{p+4}}{2 b^4 (p+4)}-\frac{d x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(15 a e^2-b d^2 (2 p+7)\right) \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)}{5 b (2 p+7)}+\frac{3 d e^2 x^5 \left(a+b x^2\right)^{p+1}}{b (2 p+7)}",1,"(a^2*e*(3*b*d^2 - a*e^2)*(a + b*x^2)^(1 + p))/(2*b^4*(1 + p)) + (3*d*e^2*x^5*(a + b*x^2)^(1 + p))/(b*(7 + 2*p)) - (3*a*e*(2*b*d^2 - a*e^2)*(a + b*x^2)^(2 + p))/(2*b^4*(2 + p)) + (3*e*(b*d^2 - a*e^2)*(a + b*x^2)^(3 + p))/(2*b^4*(3 + p)) + (e^3*(a + b*x^2)^(4 + p))/(2*b^4*(4 + p)) + (d*(d^2 - (15*a*e^2)/(7*b + 2*b*p))*x^5*(a + b*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, -((b*x^2)/a)])/(5*(1 + (b*x^2)/a)^p)","A",7,6,20,0.3000,1,"{1652, 459, 365, 364, 446, 77}"
401,1,201,0,0.2008346,"\int x^3 (d+e x)^3 \left(a+b x^2\right)^p \, dx","Int[x^3*(d + e*x)^3*(a + b*x^2)^p,x]","-\frac{a d \left(b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}+\frac{d \left(b d^2-6 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^3 (p+2)}+\frac{3 d e^2 \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}+\frac{1}{5} e x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 d^2-\frac{5 a e^2}{2 b p+7 b}\right) \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)+\frac{e^3 x^5 \left(a+b x^2\right)^{p+1}}{b (2 p+7)}","-\frac{a d \left(b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}+\frac{d \left(b d^2-6 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^3 (p+2)}+\frac{3 d e^2 \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}-\frac{e x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(5 a e^2-3 b d^2 (2 p+7)\right) \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)}{5 b (2 p+7)}+\frac{e^3 x^5 \left(a+b x^2\right)^{p+1}}{b (2 p+7)}",1,"-(a*d*(b*d^2 - 3*a*e^2)*(a + b*x^2)^(1 + p))/(2*b^3*(1 + p)) + (e^3*x^5*(a + b*x^2)^(1 + p))/(b*(7 + 2*p)) + (d*(b*d^2 - 6*a*e^2)*(a + b*x^2)^(2 + p))/(2*b^3*(2 + p)) + (3*d*e^2*(a + b*x^2)^(3 + p))/(2*b^3*(3 + p)) + (e*(3*d^2 - (5*a*e^2)/(7*b + 2*b*p))*x^5*(a + b*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, -((b*x^2)/a)])/(5*(1 + (b*x^2)/a)^p)","A",7,6,20,0.3000,1,"{1652, 446, 77, 459, 365, 364}"
402,1,202,0,0.2039815,"\int x^2 (d+e x)^3 \left(a+b x^2\right)^p \, dx","Int[x^2*(d + e*x)^3*(a + b*x^2)^p,x]","-\frac{a e \left(3 b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}+\frac{e \left(3 b d^2-2 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^3 (p+2)}+\frac{e^3 \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}+\frac{1}{3} d x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(d^2-\frac{9 a e^2}{2 b p+5 b}\right) \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)+\frac{3 d e^2 x^3 \left(a+b x^2\right)^{p+1}}{b (2 p+5)}","-\frac{a e \left(3 b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}+\frac{e \left(3 b d^2-2 a e^2\right) \left(a+b x^2\right)^{p+2}}{2 b^3 (p+2)}+\frac{e^3 \left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}-\frac{d x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(9 a e^2-b d^2 (2 p+5)\right) \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)}{3 b (2 p+5)}+\frac{3 d e^2 x^3 \left(a+b x^2\right)^{p+1}}{b (2 p+5)}",1,"-(a*e*(3*b*d^2 - a*e^2)*(a + b*x^2)^(1 + p))/(2*b^3*(1 + p)) + (3*d*e^2*x^3*(a + b*x^2)^(1 + p))/(b*(5 + 2*p)) + (e*(3*b*d^2 - 2*a*e^2)*(a + b*x^2)^(2 + p))/(2*b^3*(2 + p)) + (e^3*(a + b*x^2)^(3 + p))/(2*b^3*(3 + p)) + (d*(d^2 - (9*a*e^2)/(5*b + 2*b*p))*x^3*(a + b*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((b*x^2)/a)])/(3*(1 + (b*x^2)/a)^p)","A",7,6,20,0.3000,1,"{1652, 459, 365, 364, 446, 77}"
403,1,159,0,0.1497585,"\int x (d+e x)^3 \left(a+b x^2\right)^p \, dx","Int[x*(d + e*x)^3*(a + b*x^2)^p,x]","\frac{d \left(b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}+\frac{3 d e^2 \left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}+e x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(d^2-\frac{a e^2}{2 b p+5 b}\right) \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)+\frac{e^3 x^3 \left(a+b x^2\right)^{p+1}}{b (2 p+5)}","\frac{d \left(b d^2-3 a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}+\frac{3 d e^2 \left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}-\frac{e x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2-b d^2 (2 p+5)\right) \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)}{b (2 p+5)}+\frac{e^3 x^3 \left(a+b x^2\right)^{p+1}}{b (2 p+5)}",1,"(d*(b*d^2 - 3*a*e^2)*(a + b*x^2)^(1 + p))/(2*b^2*(1 + p)) + (e^3*x^3*(a + b*x^2)^(1 + p))/(b*(5 + 2*p)) + (3*d*e^2*(a + b*x^2)^(2 + p))/(2*b^2*(2 + p)) + (e*(d^2 - (a*e^2)/(5*b + 2*b*p))*x^3*(a + b*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((b*x^2)/a)])/(1 + (b*x^2)/a)^p","A",7,6,18,0.3333,1,"{1652, 444, 43, 459, 365, 364}"
404,1,169,0,0.1494649,"\int (d+e x)^3 \left(a+b x^2\right)^p \, dx","Int[(d + e*x)^3*(a + b*x^2)^p,x]","-\frac{e \left(a+b x^2\right)^{p+1} \left((2 p+3) \left(a e^2-b d^2 (2 p+5)\right)-2 b d e (p+1) (p+3) x\right)}{2 b^2 (p+2) \left(2 p^2+5 p+3\right)}+d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(d^2-\frac{3 a e^2}{2 b p+3 b}\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)+\frac{e (d+e x)^2 \left(a+b x^2\right)^{p+1}}{2 b (p+2)}","-\frac{e \left(a+b x^2\right)^{p+1} \left(a e^2-3 b d^2 (p+2)\right)}{2 b^2 (p+1) (p+2)}-\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a e^2-b d^2 (2 p+3)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{b (2 p+3)}+\frac{3 d e^2 x \left(a+b x^2\right)^{p+1}}{b (2 p+3)}+\frac{e^3 x^2 \left(a+b x^2\right)^{p+1}}{2 b (p+2)}",1,"(e*(d + e*x)^2*(a + b*x^2)^(1 + p))/(2*b*(2 + p)) - (e*((3 + 2*p)*(a*e^2 - b*d^2*(5 + 2*p)) - 2*b*d*e*(1 + p)*(3 + p)*x)*(a + b*x^2)^(1 + p))/(2*b^2*(2 + p)*(3 + 5*p + 2*p^2)) + (d*(d^2 - (3*a*e^2)/(3*b + 2*b*p))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(1 + (b*x^2)/a)^p","A",4,4,17,0.2353,1,"{743, 780, 246, 245}"
405,1,165,0,0.1329438,"\int \frac{(d+e x)^3 \left(a+b x^2\right)^p}{x} \, dx","Int[((d + e*x)^3*(a + b*x^2)^p)/x,x]","e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 d^2-\frac{a e^2}{2 b p+3 b}\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)-\frac{d^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}+\frac{3 d e^2 \left(a+b x^2\right)^{p+1}}{2 b (p+1)}+\frac{e^3 x \left(a+b x^2\right)^{p+1}}{b (2 p+3)}","-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2-3 b d^2 (2 p+3)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{b (2 p+3)}-\frac{d^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}+\frac{3 d e^2 \left(a+b x^2\right)^{p+1}}{2 b (p+1)}+\frac{e^3 x \left(a+b x^2\right)^{p+1}}{b (2 p+3)}",1,"(3*d*e^2*(a + b*x^2)^(1 + p))/(2*b*(1 + p)) + (e^3*x*(a + b*x^2)^(1 + p))/(b*(3 + 2*p)) + (e*(3*d^2 - (a*e^2)/(3*b + 2*b*p))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(1 + (b*x^2)/a)^p - (d^3*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*(1 + p))","A",7,7,20,0.3500,1,"{1652, 446, 80, 65, 388, 246, 245}"
406,1,159,0,0.1892753,"\int \frac{(d+e x)^3 \left(a+b x^2\right)^p}{x^2} \, dx","Int[((d + e*x)^3*(a + b*x^2)^p)/x^2,x]","\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a e^2+b d^2 (2 p+1)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{a}-\frac{3 d^2 e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}-\frac{d^3 \left(a+b x^2\right)^{p+1}}{a x}+\frac{e^3 \left(a+b x^2\right)^{p+1}}{2 b (p+1)}","\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a e^2+b d^2 (2 p+1)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{a}-\frac{3 d^2 e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}-\frac{d^3 \left(a+b x^2\right)^{p+1}}{a x}+\frac{e^3 \left(a+b x^2\right)^{p+1}}{2 b (p+1)}",1,"(e^3*(a + b*x^2)^(1 + p))/(2*b*(1 + p)) - (d^3*(a + b*x^2)^(1 + p))/(a*x) + (d*(3*a*e^2 + b*d^2*(1 + 2*p))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(a*(1 + (b*x^2)/a)^p) - (3*d^2*e*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*(1 + p))","A",8,8,20,0.4000,1,"{1807, 1652, 446, 80, 65, 12, 246, 245}"
407,1,168,0,0.2214997,"\int \frac{(d+e x)^3 \left(a+b x^2\right)^p}{x^3} \, dx","Int[((d + e*x)^3*(a + b*x^2)^p)/x^3,x]","-\frac{d \left(a+b x^2\right)^{p+1} \left(3 a e^2+b d^2 p\right) \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 (p+1)}+\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+3 b d^2 (2 p+1)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{a}-\frac{3 d^2 e \left(a+b x^2\right)^{p+1}}{a x}-\frac{d^3 \left(a+b x^2\right)^{p+1}}{2 a x^2}","-\frac{d \left(a+b x^2\right)^{p+1} \left(3 a e^2+b d^2 p\right) \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 (p+1)}+\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+3 b d^2 (2 p+1)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{a}-\frac{3 d^2 e \left(a+b x^2\right)^{p+1}}{a x}-\frac{d^3 \left(a+b x^2\right)^{p+1}}{2 a x^2}",1,"-(d^3*(a + b*x^2)^(1 + p))/(2*a*x^2) - (3*d^2*e*(a + b*x^2)^(1 + p))/(a*x) + (e*(a*e^2 + 3*b*d^2*(1 + 2*p))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(a*(1 + (b*x^2)/a)^p) - (d*(3*a*e^2 + b*d^2*p)*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a^2*(1 + p))","A",7,6,20,0.3000,1,"{1807, 764, 266, 65, 246, 245}"
408,1,199,0,0.226079,"\int \frac{x^4 \left(a+b x^2\right)^p}{d+e x} \, dx","Int[(x^4*(a + b*x^2)^p)/(d + e*x),x]","\frac{x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{5}{2};-p,1;\frac{7}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{5 d}+\frac{\left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^2 e^3 (p+1)}+\frac{\left(a+b x^2\right)^{p+2}}{2 b^2 e (p+2)}-\frac{d^4 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^3 (p+1) \left(a e^2+b d^2\right)}","\frac{x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{5}{2};-p,1;\frac{7}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{5 d}+\frac{\left(b d^2-a e^2\right) \left(a+b x^2\right)^{p+1}}{2 b^2 e^3 (p+1)}+\frac{\left(a+b x^2\right)^{p+2}}{2 b^2 e (p+2)}-\frac{d^4 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^3 (p+1) \left(a e^2+b d^2\right)}",1,"((b*d^2 - a*e^2)*(a + b*x^2)^(1 + p))/(2*b^2*e^3*(1 + p)) + (a + b*x^2)^(2 + p)/(2*b^2*e*(2 + p)) + (x^5*(a + b*x^2)^p*AppellF1[5/2, -p, 1, 7/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(5*d*(1 + (b*x^2)/a)^p) - (d^4*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*e^3*(b*d^2 + a*e^2)*(1 + p))","A",7,6,20,0.3000,1,"{959, 511, 510, 446, 88, 68}"
409,1,163,0,0.1475753,"\int \frac{x^3 \left(a+b x^2\right)^p}{d+e x} \, dx","Int[(x^3*(a + b*x^2)^p)/(d + e*x),x]","-\frac{e x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{5}{2};-p,1;\frac{7}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{5 d^2}+\frac{d^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^2 (p+1) \left(a e^2+b d^2\right)}-\frac{d \left(a+b x^2\right)^{p+1}}{2 b e^2 (p+1)}","-\frac{e x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{5}{2};-p,1;\frac{7}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{5 d^2}+\frac{d^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^2 (p+1) \left(a e^2+b d^2\right)}-\frac{d \left(a+b x^2\right)^{p+1}}{2 b e^2 (p+1)}",1,"-(d*(a + b*x^2)^(1 + p))/(2*b*e^2*(1 + p)) - (e*x^5*(a + b*x^2)^p*AppellF1[5/2, -p, 1, 7/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(5*d^2*(1 + (b*x^2)/a)^p) + (d^3*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*e^2*(b*d^2 + a*e^2)*(1 + p))","A",6,6,20,0.3000,1,"{959, 446, 80, 68, 511, 510}"
410,1,161,0,0.1481722,"\int \frac{x^2 \left(a+b x^2\right)^p}{d+e x} \, dx","Int[(x^2*(a + b*x^2)^p)/(d + e*x),x]","\frac{x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,1;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d}-\frac{d^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e (p+1) \left(a e^2+b d^2\right)}+\frac{\left(a+b x^2\right)^{p+1}}{2 b e (p+1)}","\frac{x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,1;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d}-\frac{d^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e (p+1) \left(a e^2+b d^2\right)}+\frac{\left(a+b x^2\right)^{p+1}}{2 b e (p+1)}",1,"(a + b*x^2)^(1 + p)/(2*b*e*(1 + p)) + (x^3*(a + b*x^2)^p*AppellF1[3/2, -p, 1, 5/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(3*d*(1 + (b*x^2)/a)^p) - (d^2*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*e*(b*d^2 + a*e^2)*(1 + p))","A",6,6,20,0.3000,1,"{959, 511, 510, 446, 80, 68}"
411,1,173,0,0.1484409,"\int \frac{x \left(a+b x^2\right)^p}{d+e x} \, dx","Int[(x*(a + b*x^2)^p)/(d + e*x),x]","-\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e}+\frac{d \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)}+\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e}","-\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e}+\frac{d \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)}+\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e}",1,"-((x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(e*(1 + (b*x^2)/a)^p)) + (x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(e*(1 + (b*x^2)/a)^p) + (d*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*(b*d^2 + a*e^2)*(1 + p))","A",9,8,18,0.4444,1,"{844, 246, 245, 757, 430, 429, 444, 68}"
412,1,125,0,0.1036113,"\int \frac{\left(a+b x^2\right)^p}{d+e x} \, dx","Int[(a + b*x^2)^p/(d + e*x),x]","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d}-\frac{e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)}","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d}-\frac{e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)}",1,"(x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d*(1 + (b*x^2)/a)^p) - (e*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*(b*d^2 + a*e^2)*(1 + p))","A",6,5,17,0.2941,1,"{757, 430, 429, 444, 68}"
413,1,176,0,0.1485973,"\int \frac{\left(a+b x^2\right)^p}{x (d+e x)} \, dx","Int[(a + b*x^2)^p/(x*(d + e*x)),x]","-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2}+\frac{e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d (p+1) \left(a e^2+b d^2\right)}-\frac{\left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d (p+1)}","-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2}+\frac{e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d (p+1) \left(a e^2+b d^2\right)}-\frac{\left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d (p+1)}",1,"-((e*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^2*(1 + (b*x^2)/a)^p)) + (e^2*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*d*(b*d^2 + a*e^2)*(1 + p)) - ((a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*d*(1 + p))","A",7,7,20,0.3500,1,"{959, 446, 86, 65, 68, 430, 429}"
414,1,178,0,0.1685894,"\int \frac{\left(a+b x^2\right)^p}{x^2 (d+e x)} \, dx","Int[(a + b*x^2)^p/(x^2*(d + e*x)),x]","-\frac{\left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(-\frac{1}{2};-p,1;\frac{1}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d x}-\frac{e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^2 (p+1) \left(a e^2+b d^2\right)}+\frac{e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d^2 (p+1)}","-\frac{\left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(-\frac{1}{2};-p,1;\frac{1}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d x}-\frac{e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^2 (p+1) \left(a e^2+b d^2\right)}+\frac{e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d^2 (p+1)}",1,"-(((a + b*x^2)^p*AppellF1[-1/2, -p, 1, 1/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d*x*(1 + (b*x^2)/a)^p)) - (e^3*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*d^2*(b*d^2 + a*e^2)*(1 + p)) + (e*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*d^2*(1 + p))","A",7,7,20,0.3500,1,"{959, 511, 510, 446, 86, 65, 68}"
415,1,213,0,0.2424372,"\int \frac{\left(a+b x^2\right)^p}{x^3 (d+e x)} \, dx","Int[(a + b*x^2)^p/(x^3*(d + e*x)),x]","-\frac{\left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 p\right) \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 d^3 (p+1)}+\frac{e \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(-\frac{1}{2};-p,1;\frac{1}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2 x}+\frac{e^4 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^3 (p+1) \left(a e^2+b d^2\right)}-\frac{\left(a+b x^2\right)^{p+1}}{2 a d x^2}","-\frac{\left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 p\right) \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 d^3 (p+1)}+\frac{e \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(-\frac{1}{2};-p,1;\frac{1}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2 x}+\frac{e^4 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^3 (p+1) \left(a e^2+b d^2\right)}-\frac{\left(a+b x^2\right)^{p+1}}{2 a d x^2}",1,"-(a + b*x^2)^(1 + p)/(2*a*d*x^2) + (e*(a + b*x^2)^p*AppellF1[-1/2, -p, 1, 1/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^2*x*(1 + (b*x^2)/a)^p) + (e^4*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*d^3*(b*d^2 + a*e^2)*(1 + p)) - ((a*e^2 + b*d^2*p)*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a^2*d^3*(1 + p))","A",8,8,20,0.4000,1,"{959, 446, 103, 156, 65, 68, 511, 510}"
416,1,392,0,0.8880985,"\int \frac{x^4 \left(a+b x^2\right)^p}{(d+e x)^2} \, dx","Int[(x^4*(a + b*x^2)^p)/(d + e*x)^2,x]","-\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a^2 e^4-2 a b d^2 e^2 (3 p+4)-2 b^2 d^4 \left(2 p^2+7 p+6\right)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{b e^4 (2 p+3) \left(a e^2+b d^2\right)}-\frac{2 d^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(2 a e^2+b d^2 (p+2)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^4 \left(a e^2+b d^2\right)}+\frac{d^3 \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+2)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{e^3 (p+1) \left(a e^2+b d^2\right)^2}-\frac{d^4 \left(a+b x^2\right)^{p+1}}{e^3 (d+e x) \left(a e^2+b d^2\right)}-\frac{d (3 p+4) \left(a+b x^2\right)^{p+1}}{b e^3 (p+1) (2 p+3)}+\frac{(d+e x) \left(a+b x^2\right)^{p+1}}{b e^3 (2 p+3)}","-\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a^2 e^4-2 a b d^2 e^2 (3 p+4)-2 b^2 d^4 \left(2 p^2+7 p+6\right)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{b e^4 (2 p+3) \left(a e^2+b d^2\right)}-\frac{2 d^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(2 a e^2+b d^2 (p+2)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^4 \left(a e^2+b d^2\right)}+\frac{d^3 \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+2)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{e^3 (p+1) \left(a e^2+b d^2\right)^2}-\frac{d^4 \left(a+b x^2\right)^{p+1}}{e^3 (d+e x) \left(a e^2+b d^2\right)}-\frac{d (3 p+4) \left(a+b x^2\right)^{p+1}}{b e^3 (p+1) (2 p+3)}+\frac{(d+e x) \left(a+b x^2\right)^{p+1}}{b e^3 (2 p+3)}",1,"-((d*(4 + 3*p)*(a + b*x^2)^(1 + p))/(b*e^3*(1 + p)*(3 + 2*p))) - (d^4*(a + b*x^2)^(1 + p))/(e^3*(b*d^2 + a*e^2)*(d + e*x)) + ((d + e*x)*(a + b*x^2)^(1 + p))/(b*e^3*(3 + 2*p)) - (2*d^2*(2*a*e^2 + b*d^2*(2 + p))*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(e^4*(b*d^2 + a*e^2)*(1 + (b*x^2)/a)^p) - ((a^2*e^4 - 2*a*b*d^2*e^2*(4 + 3*p) - 2*b^2*d^4*(6 + 7*p + 2*p^2))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(b*e^4*(b*d^2 + a*e^2)*(3 + 2*p)*(1 + (b*x^2)/a)^p) + (d^3*(2*a*e^2 + b*d^2*(2 + p))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(e^3*(b*d^2 + a*e^2)^2*(1 + p))","A",12,10,20,0.5000,1,"{1651, 1654, 844, 246, 245, 757, 430, 429, 444, 68}"
417,1,321,0,0.545407,"\int \frac{x^3 \left(a+b x^2\right)^p}{(d+e x)^2} \, dx","Int[(x^3*(a + b*x^2)^p)/(d + e*x)^2,x]","\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a e^2+b d^2 (2 p+3)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^3 \left(a e^2+b d^2\right)}-\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(2 a e^2+b d^2 (2 p+3)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e^3 \left(a e^2+b d^2\right)}-\frac{d^2 \left(a+b x^2\right)^{p+1} \left(3 a e^2+b d^2 (2 p+3)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^2 (p+1) \left(a e^2+b d^2\right)^2}+\frac{d^3 \left(a+b x^2\right)^{p+1}}{e^2 (d+e x) \left(a e^2+b d^2\right)}+\frac{\left(a+b x^2\right)^{p+1}}{2 b e^2 (p+1)}","\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a e^2+b d^2 (2 p+3)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^3 \left(a e^2+b d^2\right)}-\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(2 a e^2+b d^2 (2 p+3)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e^3 \left(a e^2+b d^2\right)}-\frac{d^2 \left(a+b x^2\right)^{p+1} \left(3 a e^2+b d^2 (2 p+3)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^2 (p+1) \left(a e^2+b d^2\right)^2}+\frac{d^3 \left(a+b x^2\right)^{p+1}}{e^2 (d+e x) \left(a e^2+b d^2\right)}+\frac{\left(a+b x^2\right)^{p+1}}{2 b e^2 (p+1)}",1,"(a + b*x^2)^(1 + p)/(2*b*e^2*(1 + p)) + (d^3*(a + b*x^2)^(1 + p))/(e^2*(b*d^2 + a*e^2)*(d + e*x)) + (d*(3*a*e^2 + b*d^2*(3 + 2*p))*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(e^3*(b*d^2 + a*e^2)*(1 + (b*x^2)/a)^p) - (d*(2*a*e^2 + b*d^2*(3 + 2*p))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(e^3*(b*d^2 + a*e^2)*(1 + (b*x^2)/a)^p) - (d^2*(3*a*e^2 + b*d^2*(3 + 2*p))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*e^2*(b*d^2 + a*e^2)^2*(1 + p))","A",11,10,20,0.5000,1,"{1651, 1654, 844, 246, 245, 757, 430, 429, 444, 68}"
418,1,277,0,0.3316841,"\int \frac{x^2 \left(a+b x^2\right)^p}{(d+e x)^2} \, dx","Int[(x^2*(a + b*x^2)^p)/(d + e*x)^2,x]","-\frac{2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+b d^2 (p+1)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^2 \left(a e^2+b d^2\right)}+\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a+\frac{2 b d^2 (p+1)}{e^2}\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{a e^2+b d^2}+\frac{d \left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 (p+1)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{e (p+1) \left(a e^2+b d^2\right)^2}-\frac{d^2 \left(a+b x^2\right)^{p+1}}{e (d+e x) \left(a e^2+b d^2\right)}","-\frac{2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+b d^2 (p+1)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^2 \left(a e^2+b d^2\right)}+\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+2 b d^2 (p+1)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e^2 \left(a e^2+b d^2\right)}+\frac{d \left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 (p+1)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{e (p+1) \left(a e^2+b d^2\right)^2}-\frac{d^2 \left(a+b x^2\right)^{p+1}}{e (d+e x) \left(a e^2+b d^2\right)}",1,"-((d^2*(a + b*x^2)^(1 + p))/(e*(b*d^2 + a*e^2)*(d + e*x))) - (2*(a*e^2 + b*d^2*(1 + p))*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(e^2*(b*d^2 + a*e^2)*(1 + (b*x^2)/a)^p) + ((a + (2*b*d^2*(1 + p))/e^2)*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/((b*d^2 + a*e^2)*(1 + (b*x^2)/a)^p) + (d*(a*e^2 + b*d^2*(1 + p))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(e*(b*d^2 + a*e^2)^2*(1 + p))","A",10,9,20,0.4500,1,"{1651, 844, 246, 245, 757, 430, 429, 444, 68}"
419,1,273,0,0.2306501,"\int \frac{x \left(a+b x^2\right)^p}{(d+e x)^2} \, dx","Int[(x*(a + b*x^2)^p)/(d + e*x)^2,x]","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+b d^2 (2 p+1)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d e \left(a e^2+b d^2\right)}-\frac{b d (2 p+1) x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e \left(a e^2+b d^2\right)}-\frac{\left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 (2 p+1)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^2}+\frac{d \left(a+b x^2\right)^{p+1}}{(d+e x) \left(a e^2+b d^2\right)}","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+b d^2 (2 p+1)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d e \left(a e^2+b d^2\right)}-\frac{b d (2 p+1) x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e \left(a e^2+b d^2\right)}-\frac{\left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 (2 p+1)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^2}+\frac{d \left(a+b x^2\right)^{p+1}}{(d+e x) \left(a e^2+b d^2\right)}",1,"(d*(a + b*x^2)^(1 + p))/((b*d^2 + a*e^2)*(d + e*x)) + ((a*e^2 + b*d^2*(1 + 2*p))*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d*e*(b*d^2 + a*e^2)*(1 + (b*x^2)/a)^p) - (b*d*(1 + 2*p)*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(e*(b*d^2 + a*e^2)*(1 + (b*x^2)/a)^p) - ((a*e^2 + b*d^2*(1 + 2*p))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*(b*d^2 + a*e^2)^2*(1 + p))","A",10,9,18,0.5000,1,"{835, 844, 246, 245, 757, 430, 429, 444, 68}"
420,1,191,0,0.1797924,"\int \frac{\left(a+b x^2\right)^p}{(d+e x)^2} \, dx","Int[(a + b*x^2)^p/(d + e*x)^2,x]","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2}+\frac{e^2 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^4}-\frac{b d e \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{(p+1) \left(a e^2+b d^2\right)^2}","-\frac{2 b p x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{a e^2+b d^2}+\frac{b (2 p+1) x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{a e^2+b d^2}-\frac{b d e \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{(p+1) \left(a e^2+b d^2\right)^2}+\frac{e^2 x \left(a+b x^2\right)^{p+1}}{\left(d^2-e^2 x^2\right) \left(a e^2+b d^2\right)}",1,"(x*(a + b*x^2)^p*AppellF1[1/2, -p, 2, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^2*(1 + (b*x^2)/a)^p) + (e^2*x^3*(a + b*x^2)^p*AppellF1[3/2, -p, 2, 5/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(3*d^4*(1 + (b*x^2)/a)^p) - (b*d*e*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/((b*d^2 + a*e^2)^2*(1 + p))","A",8,7,17,0.4118,0,"{757, 430, 429, 444, 68, 511, 510}"
421,1,368,0,0.4273717,"\int \frac{\left(a+b x^2\right)^p}{x (d+e x)^2} \, dx","Int[(a + b*x^2)^p/(x*(d + e*x)^2),x]","-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3}-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3}-\frac{e^3 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^5}+\frac{e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^2 (p+1) \left(a e^2+b d^2\right)}+\frac{b e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{(p+1) \left(a e^2+b d^2\right)^2}-\frac{\left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d^2 (p+1)}","-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3}-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3}-\frac{e^3 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^5}+\frac{e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^2 (p+1) \left(a e^2+b d^2\right)}+\frac{b e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{(p+1) \left(a e^2+b d^2\right)^2}-\frac{\left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d^2 (p+1)}",1,"-((e*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^3*(1 + (b*x^2)/a)^p)) - (e*x*(a + b*x^2)^p*AppellF1[1/2, -p, 2, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^3*(1 + (b*x^2)/a)^p) - (e^3*x^3*(a + b*x^2)^p*AppellF1[3/2, -p, 2, 5/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(3*d^5*(1 + (b*x^2)/a)^p) + (e^2*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*d^2*(b*d^2 + a*e^2)*(1 + p)) - ((a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*d^2*(1 + p)) + (b*e^2*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/((b*d^2 + a*e^2)^2*(1 + p))","A",18,10,20,0.5000,1,"{961, 266, 65, 757, 430, 429, 444, 68, 511, 510}"
422,1,421,0,0.4464958,"\int \frac{\left(a+b x^2\right)^p}{x^2 (d+e x)^2} \, dx","Int[(a + b*x^2)^p/(x^2*(d + e*x)^2),x]","\frac{2 e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}+\frac{e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}+\frac{e^4 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^6}-\frac{e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{d^3 (p+1) \left(a e^2+b d^2\right)}-\frac{b e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{d (p+1) \left(a e^2+b d^2\right)^2}+\frac{e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{a d^3 (p+1)}-\frac{\left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{d^2 x}","\frac{2 e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}+\frac{e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}+\frac{e^4 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^6}-\frac{e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{d^3 (p+1) \left(a e^2+b d^2\right)}-\frac{b e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{d (p+1) \left(a e^2+b d^2\right)^2}+\frac{e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{a d^3 (p+1)}-\frac{\left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{d^2 x}",1,"(2*e^2*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^4*(1 + (b*x^2)/a)^p) + (e^2*x*(a + b*x^2)^p*AppellF1[1/2, -p, 2, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^4*(1 + (b*x^2)/a)^p) + (e^4*x^3*(a + b*x^2)^p*AppellF1[3/2, -p, 2, 5/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(3*d^6*(1 + (b*x^2)/a)^p) - ((a + b*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, -((b*x^2)/a)])/(d^2*x*(1 + (b*x^2)/a)^p) - (e^3*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(d^3*(b*d^2 + a*e^2)*(1 + p)) + (e*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(a*d^3*(1 + p)) - (b*e^3*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(d*(b*d^2 + a*e^2)^2*(1 + p))","A",20,12,20,0.6000,1,"{961, 365, 364, 266, 65, 757, 430, 429, 444, 68, 511, 510}"
423,1,449,0,0.9384524,"\int \frac{x^4 \left(a+b x^2\right)^p}{(d+e x)^3} \, dx","Int[(x^4*(a + b*x^2)^p)/(d + e*x)^3,x]","\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(6 a^2 e^4+3 a b d^2 e^2 (3 p+4)+b^2 d^4 \left(2 p^2+7 p+6\right)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^4 \left(a e^2+b d^2\right)^2}-\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a^2 e^4+2 a b d^2 e^2 (4 p+5)+b^2 d^4 \left(2 p^2+7 p+6\right)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e^4 \left(a e^2+b d^2\right)^2}-\frac{d^2 \left(a+b x^2\right)^{p+1} \left(6 a^2 e^4+3 a b d^2 e^2 (3 p+4)+b^2 d^4 \left(2 p^2+7 p+6\right)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^3 (p+1) \left(a e^2+b d^2\right)^3}+\frac{d^3 \left(a+b x^2\right)^{p+1} \left(4 a e^2+b d^2 (p+3)\right)}{e^3 (d+e x) \left(a e^2+b d^2\right)^2}-\frac{d^4 \left(a+b x^2\right)^{p+1}}{2 e^3 (d+e x)^2 \left(a e^2+b d^2\right)}+\frac{\left(a+b x^2\right)^{p+1}}{2 b e^3 (p+1)}","\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(6 a^2 e^4+3 a b d^2 e^2 (3 p+4)+b^2 d^4 \left(2 p^2+7 p+6\right)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^4 \left(a e^2+b d^2\right)^2}-\frac{d x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a^2 e^4+2 a b d^2 e^2 (4 p+5)+b^2 d^4 \left(2 p^2+7 p+6\right)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e^4 \left(a e^2+b d^2\right)^2}-\frac{d^2 \left(a+b x^2\right)^{p+1} \left(6 a^2 e^4+3 a b d^2 e^2 (3 p+4)+b^2 d^4 \left(2 p^2+7 p+6\right)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^3 (p+1) \left(a e^2+b d^2\right)^3}+\frac{d^3 \left(a+b x^2\right)^{p+1} \left(4 a e^2+b d^2 (p+3)\right)}{e^3 (d+e x) \left(a e^2+b d^2\right)^2}-\frac{d^4 \left(a+b x^2\right)^{p+1}}{2 e^3 (d+e x)^2 \left(a e^2+b d^2\right)}+\frac{\left(a+b x^2\right)^{p+1}}{2 b e^3 (p+1)}",1,"(a + b*x^2)^(1 + p)/(2*b*e^3*(1 + p)) - (d^4*(a + b*x^2)^(1 + p))/(2*e^3*(b*d^2 + a*e^2)*(d + e*x)^2) + (d^3*(4*a*e^2 + b*d^2*(3 + p))*(a + b*x^2)^(1 + p))/(e^3*(b*d^2 + a*e^2)^2*(d + e*x)) + (d*(6*a^2*e^4 + 3*a*b*d^2*e^2*(4 + 3*p) + b^2*d^4*(6 + 7*p + 2*p^2))*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(e^4*(b*d^2 + a*e^2)^2*(1 + (b*x^2)/a)^p) - (d*(3*a^2*e^4 + 2*a*b*d^2*e^2*(5 + 4*p) + b^2*d^4*(6 + 7*p + 2*p^2))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(e^4*(b*d^2 + a*e^2)^2*(1 + (b*x^2)/a)^p) - (d^2*(6*a^2*e^4 + 3*a*b*d^2*e^2*(4 + 3*p) + b^2*d^4*(6 + 7*p + 2*p^2))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*e^3*(b*d^2 + a*e^2)^3*(1 + p))","A",12,10,20,0.5000,1,"{1651, 1654, 844, 246, 245, 757, 430, 429, 444, 68}"
424,1,416,0,0.5919182,"\int \frac{x^3 \left(a+b x^2\right)^p}{(d+e x)^3} \, dx","Int[(x^3*(a + b*x^2)^p)/(d + e*x)^3,x]","-\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a^2 e^4+a b d^2 e^2 (7 p+6)+b^2 d^4 \left(2 p^2+5 p+3\right)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^3 \left(a e^2+b d^2\right)^2}+\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a^2 e^4+a b d^2 e^2 (6 p+5)+b^2 d^4 \left(2 p^2+5 p+3\right)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e^3 \left(a e^2+b d^2\right)^2}+\frac{d \left(a+b x^2\right)^{p+1} \left(3 a^2 e^4+a b d^2 e^2 (7 p+6)+b^2 d^4 \left(2 p^2+5 p+3\right)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^2 (p+1) \left(a e^2+b d^2\right)^3}-\frac{d^2 \left(a+b x^2\right)^{p+1} \left(3 a e^2+b d^2 (p+2)\right)}{e^2 (d+e x) \left(a e^2+b d^2\right)^2}+\frac{d^3 \left(a+b x^2\right)^{p+1}}{2 e^2 (d+e x)^2 \left(a e^2+b d^2\right)}","-\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a^2 e^4+a b d^2 e^2 (7 p+6)+b^2 d^4 \left(2 p^2+5 p+3\right)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e^3 \left(a e^2+b d^2\right)^2}+\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a^2 e^4+a b d^2 e^2 (6 p+5)+b^2 d^4 \left(2 p^2+5 p+3\right)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e^3 \left(a e^2+b d^2\right)^2}+\frac{d \left(a+b x^2\right)^{p+1} \left(3 a^2 e^4+a b d^2 e^2 (7 p+6)+b^2 d^4 \left(2 p^2+5 p+3\right)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e^2 (p+1) \left(a e^2+b d^2\right)^3}-\frac{d^2 \left(a+b x^2\right)^{p+1} \left(3 a e^2+b d^2 (p+2)\right)}{e^2 (d+e x) \left(a e^2+b d^2\right)^2}+\frac{d^3 \left(a+b x^2\right)^{p+1}}{2 e^2 (d+e x)^2 \left(a e^2+b d^2\right)}",1,"(d^3*(a + b*x^2)^(1 + p))/(2*e^2*(b*d^2 + a*e^2)*(d + e*x)^2) - (d^2*(3*a*e^2 + b*d^2*(2 + p))*(a + b*x^2)^(1 + p))/(e^2*(b*d^2 + a*e^2)^2*(d + e*x)) - ((3*a^2*e^4 + a*b*d^2*e^2*(6 + 7*p) + b^2*d^4*(3 + 5*p + 2*p^2))*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(e^3*(b*d^2 + a*e^2)^2*(1 + (b*x^2)/a)^p) + ((a^2*e^4 + a*b*d^2*e^2*(5 + 6*p) + b^2*d^4*(3 + 5*p + 2*p^2))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(e^3*(b*d^2 + a*e^2)^2*(1 + (b*x^2)/a)^p) + (d*(3*a^2*e^4 + a*b*d^2*e^2*(6 + 7*p) + b^2*d^4*(3 + 5*p + 2*p^2))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*e^2*(b*d^2 + a*e^2)^3*(1 + p))","A",11,9,20,0.4500,1,"{1651, 844, 246, 245, 757, 430, 429, 444, 68}"
425,1,396,0,0.5699181,"\int \frac{x^2 \left(a+b x^2\right)^p}{(d+e x)^3} \, dx","Int[(x^2*(a + b*x^2)^p)/(d + e*x)^3,x]","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a^2 e^4+a b d^2 e^2 (5 p+2)+b^2 d^4 \left(2 p^2+3 p+1\right)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d e^2 \left(a e^2+b d^2\right)^2}-\frac{\left(a+b x^2\right)^{p+1} \left(a^2 e^4+a b d^2 e^2 (5 p+2)+b^2 d^4 \left(2 p^2+3 p+1\right)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e (p+1) \left(a e^2+b d^2\right)^3}-\frac{b d (2 p+1) x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(2 a e^2+b d^2 (p+1)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e^2 \left(a e^2+b d^2\right)^2}+\frac{d \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+1)\right)}{e (d+e x) \left(a e^2+b d^2\right)^2}-\frac{d^2 \left(a+b x^2\right)^{p+1}}{2 e (d+e x)^2 \left(a e^2+b d^2\right)}","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a^2 e^4+a b d^2 e^2 (5 p+2)+b^2 d^4 \left(2 p^2+3 p+1\right)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d e^2 \left(a e^2+b d^2\right)^2}-\frac{\left(a+b x^2\right)^{p+1} \left(a^2 e^4+a b d^2 e^2 (5 p+2)+b^2 d^4 \left(2 p^2+3 p+1\right)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 e (p+1) \left(a e^2+b d^2\right)^3}-\frac{b d (2 p+1) x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(2 a e^2+b d^2 (p+1)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e^2 \left(a e^2+b d^2\right)^2}+\frac{d \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+1)\right)}{e (d+e x) \left(a e^2+b d^2\right)^2}-\frac{d^2 \left(a+b x^2\right)^{p+1}}{2 e (d+e x)^2 \left(a e^2+b d^2\right)}",1,"-(d^2*(a + b*x^2)^(1 + p))/(2*e*(b*d^2 + a*e^2)*(d + e*x)^2) + (d*(2*a*e^2 + b*d^2*(1 + p))*(a + b*x^2)^(1 + p))/(e*(b*d^2 + a*e^2)^2*(d + e*x)) + ((a^2*e^4 + a*b*d^2*e^2*(2 + 5*p) + b^2*d^4*(1 + 3*p + 2*p^2))*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d*e^2*(b*d^2 + a*e^2)^2*(1 + (b*x^2)/a)^p) - (b*d*(1 + 2*p)*(2*a*e^2 + b*d^2*(1 + p))*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(e^2*(b*d^2 + a*e^2)^2*(1 + (b*x^2)/a)^p) - ((a^2*e^4 + a*b*d^2*e^2*(2 + 5*p) + b^2*d^4*(1 + 3*p + 2*p^2))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*e*(b*d^2 + a*e^2)^3*(1 + p))","A",11,10,20,0.5000,1,"{1651, 835, 844, 246, 245, 757, 430, 429, 444, 68}"
426,1,336,0,0.4003595,"\int \frac{x \left(a+b x^2\right)^p}{(d+e x)^3} \, dx","Int[(x*(a + b*x^2)^p)/(d + e*x)^3,x]","-\frac{b p x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a e^2+b d^2 (2 p+1)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e \left(a e^2+b d^2\right)^2}+\frac{b (2 p+1) x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+b d^2 p\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e \left(a e^2+b d^2\right)^2}+\frac{b d p \left(a+b x^2\right)^{p+1} \left(3 a e^2+b d^2 (2 p+1)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^3}-\frac{\left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 p\right)}{(d+e x) \left(a e^2+b d^2\right)^2}+\frac{d \left(a+b x^2\right)^{p+1}}{2 (d+e x)^2 \left(a e^2+b d^2\right)}","-\frac{b p x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(3 a e^2+b d^2 (2 p+1)\right) F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{e \left(a e^2+b d^2\right)^2}+\frac{b (2 p+1) x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a e^2+b d^2 p\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)}{e \left(a e^2+b d^2\right)^2}+\frac{b d p \left(a+b x^2\right)^{p+1} \left(3 a e^2+b d^2 (2 p+1)\right) \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^3}-\frac{\left(a+b x^2\right)^{p+1} \left(a e^2+b d^2 p\right)}{(d+e x) \left(a e^2+b d^2\right)^2}+\frac{d \left(a+b x^2\right)^{p+1}}{2 (d+e x)^2 \left(a e^2+b d^2\right)}",1,"(d*(a + b*x^2)^(1 + p))/(2*(b*d^2 + a*e^2)*(d + e*x)^2) - ((a*e^2 + b*d^2*p)*(a + b*x^2)^(1 + p))/((b*d^2 + a*e^2)^2*(d + e*x)) - (b*p*(3*a*e^2 + b*d^2*(1 + 2*p))*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(e*(b*d^2 + a*e^2)^2*(1 + (b*x^2)/a)^p) + (b*(1 + 2*p)*(a*e^2 + b*d^2*p)*x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(e*(b*d^2 + a*e^2)^2*(1 + (b*x^2)/a)^p) + (b*d*p*(3*a*e^2 + b*d^2*(1 + 2*p))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*(b*d^2 + a*e^2)^3*(1 + p))","A",11,9,18,0.5000,1,"{835, 844, 246, 245, 757, 430, 429, 444, 68}"
427,1,322,0,0.3292856,"\int \frac{\left(a+b x^2\right)^p}{(d+e x)^3} \, dx","Int[(a + b*x^2)^p/(d + e*x)^3,x]","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,3;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3}+\frac{e^2 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,3;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}-\frac{3 b^2 d^2 e \left(a+b x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^3}+\frac{b e \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+1)\right) \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{4 (p+1) \left(a e^2+b d^2\right)^3}-\frac{d^2 e \left(a+b x^2\right)^{p+1}}{4 \left(d^2-e^2 x^2\right)^2 \left(a e^2+b d^2\right)}","\frac{x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,3;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3}+\frac{e^2 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,3;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}-\frac{3 b^2 d^2 e \left(a+b x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^3}+\frac{b e \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+1)\right) \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{4 (p+1) \left(a e^2+b d^2\right)^3}-\frac{d^2 e \left(a+b x^2\right)^{p+1}}{4 \left(d^2-e^2 x^2\right)^2 \left(a e^2+b d^2\right)}",1,"-(d^2*e*(a + b*x^2)^(1 + p))/(4*(b*d^2 + a*e^2)*(d^2 - e^2*x^2)^2) + (x*(a + b*x^2)^p*AppellF1[1/2, -p, 3, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^3*(1 + (b*x^2)/a)^p) + (e^2*x^3*(a + b*x^2)^p*AppellF1[3/2, -p, 3, 5/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^5*(1 + (b*x^2)/a)^p) + (b*e*(2*a*e^2 + b*d^2*(1 + p))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(4*(b*d^2 + a*e^2)^3*(1 + p)) - (3*b^2*d^2*e*(a + b*x^2)^(1 + p)*Hypergeometric2F1[3, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*(b*d^2 + a*e^2)^3*(1 + p))","A",11,9,17,0.5294,1,"{757, 430, 429, 444, 68, 511, 510, 446, 78}"
428,1,700,0,0.8181046,"\int \frac{\left(a+b x^2\right)^p}{x (d+e x)^3} \, dx","Int[(a + b*x^2)^p/(x*(d + e*x)^3),x]","-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,3;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}-\frac{e^3 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^6}-\frac{e^3 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,3;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^6}+\frac{3 b^2 d e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^3}+\frac{e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^3 (p+1) \left(a e^2+b d^2\right)}-\frac{b e^2 \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+1)\right) \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{4 d (p+1) \left(a e^2+b d^2\right)^3}+\frac{b e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{d (p+1) \left(a e^2+b d^2\right)^2}+\frac{d e^2 \left(a+b x^2\right)^{p+1}}{4 \left(d^2-e^2 x^2\right)^2 \left(a e^2+b d^2\right)}-\frac{\left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d^3 (p+1)}","-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}-\frac{e x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,3;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4}-\frac{e^3 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^6}-\frac{e^3 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,3;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^6}+\frac{3 b^2 d e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^3}+\frac{e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^3 (p+1) \left(a e^2+b d^2\right)}-\frac{b e^2 \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+1)\right) \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{4 d (p+1) \left(a e^2+b d^2\right)^3}+\frac{b e^2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{d (p+1) \left(a e^2+b d^2\right)^2}+\frac{d e^2 \left(a+b x^2\right)^{p+1}}{4 \left(d^2-e^2 x^2\right)^2 \left(a e^2+b d^2\right)}-\frac{\left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d^3 (p+1)}",1,"(d*e^2*(a + b*x^2)^(1 + p))/(4*(b*d^2 + a*e^2)*(d^2 - e^2*x^2)^2) - (e*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^4*(1 + (b*x^2)/a)^p) - (e*x*(a + b*x^2)^p*AppellF1[1/2, -p, 2, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^4*(1 + (b*x^2)/a)^p) - (e*x*(a + b*x^2)^p*AppellF1[1/2, -p, 3, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^4*(1 + (b*x^2)/a)^p) - (e^3*x^3*(a + b*x^2)^p*AppellF1[3/2, -p, 2, 5/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(3*d^6*(1 + (b*x^2)/a)^p) - (e^3*x^3*(a + b*x^2)^p*AppellF1[3/2, -p, 3, 5/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^6*(1 + (b*x^2)/a)^p) + (e^2*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*d^3*(b*d^2 + a*e^2)*(1 + p)) - ((a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*d^3*(1 + p)) + (b*e^2*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(d*(b*d^2 + a*e^2)^2*(1 + p)) - (b*e^2*(2*a*e^2 + b*d^2*(1 + p))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(4*d*(b*d^2 + a*e^2)^3*(1 + p)) + (3*b^2*d*e^2*(a + b*x^2)^(1 + p)*Hypergeometric2F1[3, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*(b*d^2 + a*e^2)^3*(1 + p))","A",29,12,20,0.6000,1,"{961, 266, 65, 757, 430, 429, 444, 68, 511, 510, 446, 78}"
429,1,754,0,0.8597682,"\int \frac{\left(a+b x^2\right)^p}{x^2 (d+e x)^3} \, dx","Int[(a + b*x^2)^p/(x^2*(d + e*x)^3),x]","\frac{3 e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}+\frac{2 e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}+\frac{e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,3;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}+\frac{2 e^4 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^7}+\frac{e^4 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,3;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^7}-\frac{3 b^2 e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^3}-\frac{3 e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^4 (p+1) \left(a e^2+b d^2\right)}+\frac{b e^3 \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+1)\right) \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{4 d^2 (p+1) \left(a e^2+b d^2\right)^3}-\frac{2 b e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{d^2 (p+1) \left(a e^2+b d^2\right)^2}-\frac{e^3 \left(a+b x^2\right)^{p+1}}{4 \left(d^2-e^2 x^2\right)^2 \left(a e^2+b d^2\right)}+\frac{3 e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d^4 (p+1)}-\frac{\left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{d^3 x}","\frac{3 e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}+\frac{2 e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}+\frac{e^2 x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,3;\frac{3}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}+\frac{2 e^4 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^7}+\frac{e^4 x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,3;\frac{5}{2};-\frac{b x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^7}-\frac{3 b^2 e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 (p+1) \left(a e^2+b d^2\right)^3}-\frac{3 e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{2 d^4 (p+1) \left(a e^2+b d^2\right)}+\frac{b e^3 \left(a+b x^2\right)^{p+1} \left(2 a e^2+b d^2 (p+1)\right) \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{4 d^2 (p+1) \left(a e^2+b d^2\right)^3}-\frac{2 b e^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(b x^2+a\right)}{b d^2+a e^2}\right)}{d^2 (p+1) \left(a e^2+b d^2\right)^2}-\frac{e^3 \left(a+b x^2\right)^{p+1}}{4 \left(d^2-e^2 x^2\right)^2 \left(a e^2+b d^2\right)}+\frac{3 e \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a d^4 (p+1)}-\frac{\left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{d^3 x}",1,"-(e^3*(a + b*x^2)^(1 + p))/(4*(b*d^2 + a*e^2)*(d^2 - e^2*x^2)^2) + (3*e^2*x*(a + b*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^5*(1 + (b*x^2)/a)^p) + (2*e^2*x*(a + b*x^2)^p*AppellF1[1/2, -p, 2, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^5*(1 + (b*x^2)/a)^p) + (e^2*x*(a + b*x^2)^p*AppellF1[1/2, -p, 3, 3/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^5*(1 + (b*x^2)/a)^p) + (2*e^4*x^3*(a + b*x^2)^p*AppellF1[3/2, -p, 2, 5/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(3*d^7*(1 + (b*x^2)/a)^p) + (e^4*x^3*(a + b*x^2)^p*AppellF1[3/2, -p, 3, 5/2, -((b*x^2)/a), (e^2*x^2)/d^2])/(d^7*(1 + (b*x^2)/a)^p) - ((a + b*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, -((b*x^2)/a)])/(d^3*x*(1 + (b*x^2)/a)^p) - (3*e^3*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*d^4*(b*d^2 + a*e^2)*(1 + p)) + (3*e*(a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*d^4*(1 + p)) - (2*b*e^3*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(d^2*(b*d^2 + a*e^2)^2*(1 + p)) + (b*e^3*(2*a*e^2 + b*d^2*(1 + p))*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(4*d^2*(b*d^2 + a*e^2)^3*(1 + p)) - (3*b^2*e^3*(a + b*x^2)^(1 + p)*Hypergeometric2F1[3, 1 + p, 2 + p, (e^2*(a + b*x^2))/(b*d^2 + a*e^2)])/(2*(b*d^2 + a*e^2)^3*(1 + p))","A",31,14,20,0.7000,1,"{961, 365, 364, 266, 65, 757, 430, 429, 444, 68, 511, 510, 446, 78}"
430,1,254,0,0.4682039,"\int (g x)^m (d+e x)^3 \left(a+c x^2\right)^p \, dx","Int[(g*x)^m*(d + e*x)^3*(a + c*x^2)^p,x]","\frac{e (g x)^{m+2} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(\frac{3 d^2}{m+2}-\frac{a e^2}{c (m+2 p+4)}\right) \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};-\frac{c x^2}{a}\right)}{g^2}+\frac{d (g x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(\frac{d^2}{m+1}-\frac{3 a e^2}{c (m+2 p+3)}\right) \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{g}+\frac{3 d e^2 (g x)^{m+1} \left(a+c x^2\right)^{p+1}}{c g (m+2 p+3)}+\frac{e^3 (g x)^{m+2} \left(a+c x^2\right)^{p+1}}{c g^2 (m+2 p+4)}","-\frac{e (g x)^{m+2} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(a e^2 (m+2)-3 c d^2 (m+2 p+4)\right) \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};-\frac{c x^2}{a}\right)}{c g^2 (m+2) (m+2 p+4)}-\frac{d (g x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(3 a e^2 (m+1)-c d^2 (m+2 p+3)\right) \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{c g (m+1) (m+2 p+3)}+\frac{3 d e^2 (g x)^{m+1} \left(a+c x^2\right)^{p+1}}{c g (m+2 p+3)}+\frac{e^3 (g x)^{m+2} \left(a+c x^2\right)^{p+1}}{c g^2 (m+2 p+4)}",1,"(3*d*e^2*(g*x)^(1 + m)*(a + c*x^2)^(1 + p))/(c*g*(3 + m + 2*p)) + (e^3*(g*x)^(2 + m)*(a + c*x^2)^(1 + p))/(c*g^2*(4 + m + 2*p)) + (d*(d^2/(1 + m) - (3*a*e^2)/(c*(3 + m + 2*p)))*(g*x)^(1 + m)*(a + c*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, -((c*x^2)/a)])/(g*(1 + (c*x^2)/a)^p) + (e*((3*d^2)/(2 + m) - (a*e^2)/(c*(4 + m + 2*p)))*(g*x)^(2 + m)*(a + c*x^2)^p*Hypergeometric2F1[(2 + m)/2, -p, (4 + m)/2, -((c*x^2)/a)])/(g^2*(1 + (c*x^2)/a)^p)","A",7,4,22,0.1818,1,"{1809, 808, 365, 364}"
431,1,194,0,0.1966647,"\int (g x)^m (d+e x)^2 \left(a+c x^2\right)^p \, dx","Int[(g*x)^m*(d + e*x)^2*(a + c*x^2)^p,x]","\frac{(g x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(\frac{d^2}{m+1}-\frac{a e^2}{c (m+2 p+3)}\right) \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{g}+\frac{2 d e (g x)^{m+2} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};-\frac{c x^2}{a}\right)}{g^2 (m+2)}+\frac{e^2 (g x)^{m+1} \left(a+c x^2\right)^{p+1}}{c g (m+2 p+3)}","-\frac{(g x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(a e^2 (m+1)-c d^2 (m+2 p+3)\right) \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{c g (m+1) (m+2 p+3)}+\frac{2 d e (g x)^{m+2} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};-\frac{c x^2}{a}\right)}{g^2 (m+2)}+\frac{e^2 (g x)^{m+1} \left(a+c x^2\right)^{p+1}}{c g (m+2 p+3)}",1,"(e^2*(g*x)^(1 + m)*(a + c*x^2)^(1 + p))/(c*g*(3 + m + 2*p)) + ((d^2/(1 + m) - (a*e^2)/(c*(3 + m + 2*p)))*(g*x)^(1 + m)*(a + c*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, -((c*x^2)/a)])/(g*(1 + (c*x^2)/a)^p) + (2*d*e*(g*x)^(2 + m)*(a + c*x^2)^p*Hypergeometric2F1[(2 + m)/2, -p, (4 + m)/2, -((c*x^2)/a)])/(g^2*(2 + m)*(1 + (c*x^2)/a)^p)","A",6,4,22,0.1818,1,"{1809, 808, 365, 364}"
432,1,135,0,0.0626675,"\int (g x)^m (d+e x) \left(a+c x^2\right)^p \, dx","Int[(g*x)^m*(d + e*x)*(a + c*x^2)^p,x]","\frac{d (g x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{g (m+1)}+\frac{e (g x)^{m+2} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};-\frac{c x^2}{a}\right)}{g^2 (m+2)}","\frac{d (g x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{g (m+1)}+\frac{e (g x)^{m+2} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};-\frac{c x^2}{a}\right)}{g^2 (m+2)}",1,"(d*(g*x)^(1 + m)*(a + c*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, -((c*x^2)/a)])/(g*(1 + m)*(1 + (c*x^2)/a)^p) + (e*(g*x)^(2 + m)*(a + c*x^2)^p*Hypergeometric2F1[(2 + m)/2, -p, (4 + m)/2, -((c*x^2)/a)])/(g^2*(2 + m)*(1 + (c*x^2)/a)^p)","A",5,3,20,0.1500,1,"{808, 365, 364}"
433,1,66,0,0.0187254,"\int (g x)^m \left(a+c x^2\right)^p \, dx","Int[(g*x)^m*(a + c*x^2)^p,x]","\frac{(g x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{g (m+1)}","\frac{(g x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{g (m+1)}",1,"((g*x)^(1 + m)*(a + c*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, -((c*x^2)/a)])/(g*(1 + m)*(1 + (c*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
434,1,157,0,0.143294,"\int \frac{(g x)^m \left(a+c x^2\right)^p}{d+e x} \, dx","Int[((g*x)^m*(a + c*x^2)^p)/(d + e*x),x]","\frac{x (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2};-p,1;\frac{m+3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d (m+1)}-\frac{e x^2 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+2}{2};-p,1;\frac{m+4}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2 (m+2)}","\frac{x (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2};-p,1;\frac{m+3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d (m+1)}-\frac{e x^2 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+2}{2};-p,1;\frac{m+4}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2 (m+2)}",1,"(x*(g*x)^m*(a + c*x^2)^p*AppellF1[(1 + m)/2, -p, 1, (3 + m)/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d*(1 + m)*(1 + (c*x^2)/a)^p) - (e*x^2*(g*x)^m*(a + c*x^2)^p*AppellF1[(2 + m)/2, -p, 1, (4 + m)/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^2*(2 + m)*(1 + (c*x^2)/a)^p)","A",5,3,22,0.1364,1,"{959, 511, 510}"
435,1,238,0,0.2788111,"\int \frac{(g x)^m \left(a+c x^2\right)^p}{(d+e x)^2} \, dx","Int[((g*x)^m*(a + c*x^2)^p)/(d + e*x)^2,x]","\frac{x (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2};-p,2;\frac{m+3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2 (m+1)}-\frac{2 e x^2 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+2}{2};-p,2;\frac{m+4}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3 (m+2)}+\frac{e^2 x^3 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+3}{2};-p,2;\frac{m+5}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4 (m+3)}","\frac{x (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2};-p,2;\frac{m+3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2 (m+1)}-\frac{2 e x^2 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+2}{2};-p,2;\frac{m+4}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3 (m+2)}+\frac{e^2 x^3 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+3}{2};-p,2;\frac{m+5}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4 (m+3)}",1,"(x*(g*x)^m*(a + c*x^2)^p*AppellF1[(1 + m)/2, -p, 2, (3 + m)/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^2*(1 + m)*(1 + (c*x^2)/a)^p) - (2*e*x^2*(g*x)^m*(a + c*x^2)^p*AppellF1[(2 + m)/2, -p, 2, (4 + m)/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^3*(2 + m)*(1 + (c*x^2)/a)^p) + (e^2*x^3*(g*x)^m*(a + c*x^2)^p*AppellF1[(3 + m)/2, -p, 2, (5 + m)/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^4*(3 + m)*(1 + (c*x^2)/a)^p)","A",8,3,22,0.1364,1,"{962, 511, 510}"
436,1,321,0,0.3736227,"\int \frac{(g x)^m \left(a+c x^2\right)^p}{(d+e x)^3} \, dx","Int[((g*x)^m*(a + c*x^2)^p)/(d + e*x)^3,x]","\frac{x (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2};-p,3;\frac{m+3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3 (m+1)}-\frac{3 e x^2 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+2}{2};-p,3;\frac{m+4}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4 (m+2)}+\frac{3 e^2 x^3 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+3}{2};-p,3;\frac{m+5}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5 (m+3)}-\frac{e^3 x^4 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+4}{2};-p,3;\frac{m+6}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^6 (m+4)}","\frac{x (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2};-p,3;\frac{m+3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3 (m+1)}-\frac{3 e x^2 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+2}{2};-p,3;\frac{m+4}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^4 (m+2)}+\frac{3 e^2 x^3 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+3}{2};-p,3;\frac{m+5}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5 (m+3)}-\frac{e^3 x^4 (g x)^m \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{m+4}{2};-p,3;\frac{m+6}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^6 (m+4)}",1,"(x*(g*x)^m*(a + c*x^2)^p*AppellF1[(1 + m)/2, -p, 3, (3 + m)/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^3*(1 + m)*(1 + (c*x^2)/a)^p) - (3*e*x^2*(g*x)^m*(a + c*x^2)^p*AppellF1[(2 + m)/2, -p, 3, (4 + m)/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^4*(2 + m)*(1 + (c*x^2)/a)^p) + (3*e^2*x^3*(g*x)^m*(a + c*x^2)^p*AppellF1[(3 + m)/2, -p, 3, (5 + m)/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^5*(3 + m)*(1 + (c*x^2)/a)^p) - (e^3*x^4*(g*x)^m*(a + c*x^2)^p*AppellF1[(4 + m)/2, -p, 3, (6 + m)/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^6*(4 + m)*(1 + (c*x^2)/a)^p)","A",10,3,22,0.1364,1,"{962, 511, 510}"
437,1,345,0,0.5060876,"\int \frac{x^3 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{d+e x} \, dx","Int[(x^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(d + e*x),x]","-\frac{\left(-2 c d e x \left(-5 a^2 e^4-6 a c d^2 e^2+35 c^2 d^4\right)-17 a^2 c d^2 e^4-15 a^3 e^6-25 a c^2 d^4 e^2+105 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{192 c^3 d^3 e^4}+\frac{\left(c d^2-a e^2\right) \left(9 a^2 c d^2 e^4+5 a^3 e^6+15 a c^2 d^4 e^2+35 c^3 d^6\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 c^{7/2} d^{7/2} e^{9/2}}+\frac{x^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e}+\frac{1}{24} x^2 \left(\frac{a}{c d}-\frac{7 d}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}","-\frac{\left(-2 c d e x \left(-5 a^2 e^4-6 a c d^2 e^2+35 c^2 d^4\right)-17 a^2 c d^2 e^4-15 a^3 e^6-25 a c^2 d^4 e^2+105 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{192 c^3 d^3 e^4}+\frac{\left(c d^2-a e^2\right) \left(9 a^2 c d^2 e^4+5 a^3 e^6+15 a c^2 d^4 e^2+35 c^3 d^6\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 c^{7/2} d^{7/2} e^{9/2}}+\frac{x^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e}+\frac{1}{24} x^2 \left(\frac{a}{c d}-\frac{7 d}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}",1,"((a/(c*d) - (7*d)/e^2)*x^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/24 + (x^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*e) - ((105*c^3*d^6 - 25*a*c^2*d^4*e^2 - 17*a^2*c*d^2*e^4 - 15*a^3*e^6 - 2*c*d*e*(35*c^2*d^4 - 6*a*c*d^2*e^2 - 5*a^2*e^4)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(192*c^3*d^3*e^4) + ((c*d^2 - a*e^2)*(35*c^3*d^6 + 15*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4 + 5*a^3*e^6)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(128*c^(7/2)*d^(7/2)*e^(9/2))","A",6,5,40,0.1250,1,"{849, 832, 779, 621, 206}"
438,1,251,0,0.2599281,"\int \frac{x^2 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{d+e x} \, dx","Int[(x^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(d + e*x),x]","-\frac{\left(c d^2-a e^2\right) \left(a^2 e^4+2 a c d^2 e^2+5 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 c^{5/2} d^{5/2} e^{7/2}}+\frac{\left(\left(5 c d^2-3 a e^2\right) \left(a e^2+3 c d^2\right)-2 c d e x \left(5 c d^2-a e^2\right)\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 c^2 d^2 e^3}+\frac{x^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 e}","-\frac{\left(c d^2-a e^2\right) \left(a^2 e^4+2 a c d^2 e^2+5 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 c^{5/2} d^{5/2} e^{7/2}}+\frac{\left(\left(5 c d^2-3 a e^2\right) \left(a e^2+3 c d^2\right)-2 c d e x \left(5 c d^2-a e^2\right)\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 c^2 d^2 e^3}+\frac{x^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 e}",1,"(x^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*e) + (((5*c*d^2 - 3*a*e^2)*(3*c*d^2 + a*e^2) - 2*c*d*e*(5*c*d^2 - a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(24*c^2*d^2*e^3) - ((c*d^2 - a*e^2)*(5*c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(16*c^(5/2)*d^(5/2)*e^(7/2))","A",5,5,40,0.1250,1,"{851, 832, 779, 621, 206}"
439,1,207,0,0.1915969,"\int \frac{x \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{d+e x} \, dx","Int[(x*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(d + e*x),x]","\frac{\left(c d^2-a e^2\right) \left(a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 c^{3/2} d^{3/2} e^{5/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 c d e (d+e x)}-\frac{1}{4} \left(\frac{a}{c d}+\frac{3 d}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}","\frac{\left(c d^2-a e^2\right) \left(a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 c^{3/2} d^{3/2} e^{5/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 c d e (d+e x)}-\frac{1}{4} \left(\frac{a}{c d}+\frac{3 d}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}",1,"-((a/(c*d) + (3*d)/e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/4 + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(2*c*d*e*(d + e*x)) + ((c*d^2 - a*e^2)*(3*c*d^2 + a*e^2)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*c^(3/2)*d^(3/2)*e^(5/2))","A",4,4,38,0.1053,1,"{794, 664, 621, 206}"
440,1,131,0,0.0703544,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{d+e x} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x),x]","\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e}-\frac{\left(c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 \sqrt{c} \sqrt{d} e^{3/2}}","\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e}-\frac{\left(c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 \sqrt{c} \sqrt{d} e^{3/2}}",1,"Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/e - ((c*d^2 - a*e^2)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2*Sqrt[c]*Sqrt[d]*e^(3/2))","A",3,3,37,0.08108,1,"{664, 621, 206}"
441,1,168,0,0.1668766,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{x (d+e x)} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(x*(d + e*x)),x]","\frac{\sqrt{c} \sqrt{d} \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{\sqrt{e}}-\frac{\sqrt{a} \sqrt{e} \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{\sqrt{d}}","\frac{\sqrt{c} \sqrt{d} \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{\sqrt{e}}-\frac{\sqrt{a} \sqrt{e} \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{\sqrt{d}}",1,"(Sqrt[c]*Sqrt[d]*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/Sqrt[e] - (Sqrt[a]*Sqrt[e]*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/Sqrt[d]","A",6,5,40,0.1250,1,"{849, 843, 621, 206, 724}"
442,1,137,0,0.1421819,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{x^2 (d+e x)} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(x^2*(d + e*x)),x]","-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{d x}-\frac{\left(c d^2-a e^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 \sqrt{a} d^{3/2} \sqrt{e}}","-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{d x}-\frac{\left(c d^2-a e^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 \sqrt{a} d^{3/2} \sqrt{e}}",1,"-(Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d*x)) - ((c*d^2 - a*e^2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2*Sqrt[a]*d^(3/2)*Sqrt[e])","A",4,4,40,0.1000,1,"{849, 806, 724, 206}"
443,1,202,0,0.2758515,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{x^3 (d+e x)} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(x^3*(d + e*x)),x]","\frac{\left(c d^2-a e^2\right) \left(3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 a^{3/2} d^{5/2} e^{3/2}}-\frac{\left(\frac{c}{a e}-\frac{3 e}{d^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 x}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 d x^2}","\frac{\left(c d^2-a e^2\right) \left(3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 a^{3/2} d^{5/2} e^{3/2}}-\frac{\left(\frac{c}{a e}-\frac{3 e}{d^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 x}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 d x^2}",1,"-Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(2*d*x^2) - ((c/(a*e) - (3*e)/d^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*x) + ((c*d^2 - a*e^2)*(c*d^2 + 3*a*e^2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*a^(3/2)*d^(5/2)*e^(3/2))","A",5,5,40,0.1250,1,"{849, 834, 806, 724, 206}"
444,1,286,0,0.4043137,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{x^4 (d+e x)} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(x^4*(d + e*x)),x]","-\frac{\left(c d^2-a e^2\right) \left(5 a^2 e^4+2 a c d^2 e^2+c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 a^{5/2} d^{7/2} e^{5/2}}+\frac{\left(3 c d^2-5 a e^2\right) \left(3 a e^2+c d^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 a^2 d^3 e^2 x}-\frac{\left(\frac{c}{a e}-\frac{5 e}{d^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 x^2}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 d x^3}","-\frac{\left(c d^2-a e^2\right) \left(5 a^2 e^4+2 a c d^2 e^2+c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 a^{5/2} d^{7/2} e^{5/2}}+\frac{\left(3 c d^2-5 a e^2\right) \left(3 a e^2+c d^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 a^2 d^3 e^2 x}-\frac{\left(\frac{c}{a e}-\frac{5 e}{d^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 x^2}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 d x^3}",1,"-Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(3*d*x^3) - ((c/(a*e) - (5*e)/d^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*x^2) + ((3*c*d^2 - 5*a*e^2)*(c*d^2 + 3*a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(24*a^2*d^3*e^2*x) - ((c*d^2 - a*e^2)*(c^2*d^4 + 2*a*c*d^2*e^2 + 5*a^2*e^4)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(16*a^(5/2)*d^(7/2)*e^(5/2))","A",6,5,40,0.1250,1,"{849, 834, 806, 724, 206}"
445,1,389,0,0.5935133,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{x^5 (d+e x)} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(x^5*(d + e*x)),x]","-\frac{\left(25 a^2 c d^2 e^4-105 a^3 e^6+17 a c^2 d^4 e^2+15 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{192 a^3 d^4 e^3 x}+\frac{\left(-35 a^2 e^4+6 a c d^2 e^2+5 c^2 d^4\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{96 a^2 d^3 e^2 x^2}+\frac{\left(c d^2-a e^2\right) \left(15 a^2 c d^2 e^4+35 a^3 e^6+9 a c^2 d^4 e^2+5 c^3 d^6\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 a^{7/2} d^{9/2} e^{7/2}}-\frac{\left(\frac{c}{a e}-\frac{7 e}{d^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 x^3}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 d x^4}","-\frac{\left(25 a^2 c d^2 e^4-105 a^3 e^6+17 a c^2 d^4 e^2+15 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{192 a^3 d^4 e^3 x}+\frac{\left(-35 a^2 e^4+6 a c d^2 e^2+5 c^2 d^4\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{96 a^2 d^3 e^2 x^2}+\frac{\left(c d^2-a e^2\right) \left(15 a^2 c d^2 e^4+35 a^3 e^6+9 a c^2 d^4 e^2+5 c^3 d^6\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 a^{7/2} d^{9/2} e^{7/2}}-\frac{\left(\frac{c}{a e}-\frac{7 e}{d^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 x^3}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 d x^4}",1,"-Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(4*d*x^4) - ((c/(a*e) - (7*e)/d^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(24*x^3) + ((5*c^2*d^4 + 6*a*c*d^2*e^2 - 35*a^2*e^4)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(96*a^2*d^3*e^2*x^2) - ((15*c^3*d^6 + 17*a*c^2*d^4*e^2 + 25*a^2*c*d^2*e^4 - 105*a^3*e^6)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(192*a^3*d^4*e^3*x) + ((c*d^2 - a*e^2)*(5*c^3*d^6 + 9*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 + 35*a^3*e^6)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(128*a^(7/2)*d^(9/2)*e^(7/2))","A",7,5,40,0.1250,1,"{849, 834, 806, 724, 206}"
446,1,449,0,0.5698614,"\int \frac{x^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{d+e x} \, dx","Int[(x^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x),x]","-\frac{\left(-6 c d e x \left(-7 a^2 e^4-6 a c d^2 e^2+21 c^2 d^4\right)-33 a^2 c d^2 e^4-35 a^3 e^6-21 a c^2 d^4 e^2+105 c^3 d^6\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{960 c^3 d^3 e^4}+\frac{\left(-6 a^2 c^2 d^4 e^4-8 a^3 c d^2 e^6-7 a^4 e^8+21 c^4 d^8\right) \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 c^4 d^4 e^5}-\frac{\left(15 a^2 c d^2 e^4+7 a^3 e^6+21 a c^2 d^4 e^2+21 c^3 d^6\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{1024 c^{9/2} d^{9/2} e^{11/2}}+\frac{x^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{6 e}+\frac{1}{20} x^2 \left(\frac{a}{c d}-\frac{3 d}{e^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}","-\frac{\left(-6 c d e x \left(-7 a^2 e^4-6 a c d^2 e^2+21 c^2 d^4\right)-33 a^2 c d^2 e^4-35 a^3 e^6-21 a c^2 d^4 e^2+105 c^3 d^6\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{960 c^3 d^3 e^4}+\frac{\left(-6 a^2 c^2 d^4 e^4-8 a^3 c d^2 e^6-7 a^4 e^8+21 c^4 d^8\right) \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 c^4 d^4 e^5}-\frac{\left(15 a^2 c d^2 e^4+7 a^3 e^6+21 a c^2 d^4 e^2+21 c^3 d^6\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{1024 c^{9/2} d^{9/2} e^{11/2}}+\frac{x^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{6 e}+\frac{1}{20} x^2 \left(\frac{a}{c d}-\frac{3 d}{e^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}",1,"((21*c^4*d^8 - 6*a^2*c^2*d^4*e^4 - 8*a^3*c*d^2*e^6 - 7*a^4*e^8)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(512*c^4*d^4*e^5) + ((a/(c*d) - (3*d)/e^2)*x^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/20 + (x^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(6*e) - ((105*c^3*d^6 - 21*a*c^2*d^4*e^2 - 33*a^2*c*d^2*e^4 - 35*a^3*e^6 - 6*c*d*e*(21*c^2*d^4 - 6*a*c*d^2*e^2 - 7*a^2*e^4)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(960*c^3*d^3*e^4) - ((c*d^2 - a*e^2)^3*(21*c^3*d^6 + 21*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 + 7*a^3*e^6)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(1024*c^(9/2)*d^(9/2)*e^(11/2))","A",7,6,40,0.1500,1,"{849, 832, 779, 612, 621, 206}"
447,1,352,0,0.328369,"\int \frac{x^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{d+e x} \, dx","Int[(x^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x),x]","-\frac{\left(3 a^2 e^4+6 a c d^2 e^2+7 c^2 d^4\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 c^3 d^3 e^4}+\frac{\left(-15 a^2 e^4-6 c d e x \left(7 c d^2-3 a e^2\right)-12 a c d^2 e^2+35 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{240 c^2 d^2 e^3}+\frac{\left(3 a^2 e^4+6 a c d^2 e^2+7 c^2 d^4\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{256 c^{7/2} d^{7/2} e^{9/2}}+\frac{x^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 e}","-\frac{\left(3 a^2 e^4+6 a c d^2 e^2+7 c^2 d^4\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 c^3 d^3 e^4}+\frac{\left(-15 a^2 e^4-6 c d e x \left(7 c d^2-3 a e^2\right)-12 a c d^2 e^2+35 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{240 c^2 d^2 e^3}+\frac{\left(3 a^2 e^4+6 a c d^2 e^2+7 c^2 d^4\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{256 c^{7/2} d^{7/2} e^{9/2}}+\frac{x^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 e}",1,"-((c*d^2 - a*e^2)*(7*c^2*d^4 + 6*a*c*d^2*e^2 + 3*a^2*e^4)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(128*c^3*d^3*e^4) + (x^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(5*e) + ((35*c^2*d^4 - 12*a*c*d^2*e^2 - 15*a^2*e^4 - 6*c*d*e*(7*c*d^2 - 3*a*e^2)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(240*c^2*d^2*e^3) + ((c*d^2 - a*e^2)^3*(7*c^2*d^4 + 6*a*c*d^2*e^2 + 3*a^2*e^4)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(256*c^(7/2)*d^(7/2)*e^(9/2))","A",6,6,40,0.1500,1,"{851, 832, 779, 612, 621, 206}"
448,1,295,0,0.282479,"\int \frac{x \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{d+e x} \, dx","Int[(x*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x),x]","\frac{\left(3 a e^2+5 c d^2\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 c^2 d^2 e^3}-\frac{\left(3 a e^2+5 c d^2\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 c^{5/2} d^{5/2} e^{7/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4 c d e (d+e x)}-\frac{1}{24} \left(\frac{3 a}{c d}+\frac{5 d}{e^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}","\frac{\left(3 a e^2+5 c d^2\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 c^2 d^2 e^3}-\frac{\left(3 a e^2+5 c d^2\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 c^{5/2} d^{5/2} e^{7/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4 c d e (d+e x)}-\frac{1}{24} \left(\frac{3 a}{c d}+\frac{5 d}{e^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}",1,"((c*d^2 - a*e^2)*(5*c*d^2 + 3*a*e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*c^2*d^2*e^3) - (((3*a)/(c*d) + (5*d)/e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/24 + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(4*c*d*e*(d + e*x)) - ((c*d^2 - a*e^2)^3*(5*c*d^2 + 3*a*e^2)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(128*c^(5/2)*d^(5/2)*e^(7/2))","A",5,5,38,0.1316,1,"{794, 664, 612, 621, 206}"
449,1,201,0,0.1174267,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{d+e x} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x),x]","\frac{\left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 c^{3/2} d^{3/2} e^{5/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 e}+\frac{1}{8} \left(\frac{a}{c d}-\frac{d}{e^2}\right) \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}","\frac{\left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 c^{3/2} d^{3/2} e^{5/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 e}+\frac{1}{8} \left(\frac{a}{c d}-\frac{d}{e^2}\right) \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}",1,"((a/(c*d) - d/e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/8 + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(3*e) + ((c*d^2 - a*e^2)^3*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(16*c^(3/2)*d^(3/2)*e^(5/2))","A",4,4,37,0.1081,1,"{664, 612, 621, 206}"
450,1,251,0,0.2763454,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{x (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(x*(d + e*x)),x]","-\frac{\left(-3 a^2 e^4-6 a c d^2 e^2+c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 \sqrt{c} \sqrt{d} e^{3/2}}-a^{3/2} \sqrt{d} e^{3/2} \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)+\frac{\left(5 a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e}","-\frac{\left(-3 a^2 e^4-6 a c d^2 e^2+c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 \sqrt{c} \sqrt{d} e^{3/2}}-a^{3/2} \sqrt{d} e^{3/2} \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)+\frac{\left(5 a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e}",1,"((c*d^2 + 5*a*e^2 + 2*c*d*e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*e) - ((c^2*d^4 - 6*a*c*d^2*e^2 - 3*a^2*e^4)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*Sqrt[c]*Sqrt[d]*e^(3/2)) - a^(3/2)*Sqrt[d]*e^(3/2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])]","A",7,6,40,0.1500,1,"{849, 814, 843, 621, 206, 724}"
451,1,240,0,0.2734742,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{x^2 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(x^2*(d + e*x)),x]","-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (a e-c d x)}{x}+\frac{\sqrt{c} \sqrt{d} \left(3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 \sqrt{e}}-\frac{\sqrt{a} \sqrt{e} \left(a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 \sqrt{d}}","-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (a e-c d x)}{x}+\frac{\sqrt{c} \sqrt{d} \left(3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 \sqrt{e}}-\frac{\sqrt{a} \sqrt{e} \left(a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 \sqrt{d}}",1,"-(((a*e - c*d*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/x) + (Sqrt[c]*Sqrt[d]*(c*d^2 + 3*a*e^2)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2*Sqrt[e]) - (Sqrt[a]*Sqrt[e]*(3*c*d^2 + a*e^2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2*Sqrt[d])","A",7,6,40,0.1500,1,"{849, 812, 843, 621, 206, 724}"
452,1,256,0,0.2827247,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{x^3 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(x^3*(d + e*x)),x]","-\frac{\left(-a^2 e^4+6 a c d^2 e^2+3 c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 \sqrt{a} d^{3/2} \sqrt{e}}+c^{3/2} d^{3/2} \sqrt{e} \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)-\frac{\left(x \left(a e^2+5 c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 d x^2}","-\frac{\left(-a^2 e^4+6 a c d^2 e^2+3 c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 \sqrt{a} d^{3/2} \sqrt{e}}+c^{3/2} d^{3/2} \sqrt{e} \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)-\frac{\left(x \left(a e^2+5 c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 d x^2}",1,"-((2*a*d*e + (5*c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*d*x^2) + c^(3/2)*d^(3/2)*Sqrt[e]*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])] - ((3*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*Sqrt[a]*d^(3/2)*Sqrt[e])","A",7,6,40,0.1500,1,"{849, 810, 843, 621, 206, 724}"
453,1,211,0,0.2364982,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{x^4 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(x^4*(d + e*x)),x]","\frac{\left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 a^{3/2} d^{5/2} e^{3/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 d x^3}-\frac{\left(\frac{c}{a e}-\frac{e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 x^2}","\frac{\left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 a^{3/2} d^{5/2} e^{3/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 d x^3}-\frac{\left(\frac{c}{a e}-\frac{e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 x^2}",1,"-((c/(a*e) - e/d^2)*(2*a*d*e + (c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*x^2) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(3*d*x^3) + ((c*d^2 - a*e^2)^3*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(16*a^(3/2)*d^(5/2)*e^(3/2))","A",5,5,40,0.1250,1,"{849, 806, 720, 724, 206}"
454,1,295,0,0.3859986,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{x^5 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(x^5*(d + e*x)),x]","\frac{\left(5 a e^2+3 c d^2\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 a^2 d^3 e^2 x^2}-\frac{\left(5 a e^2+3 c d^2\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 a^{5/2} d^{7/2} e^{5/2}}-\frac{\left(\frac{3 c}{a e}-\frac{5 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{24 x^3}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 d x^4}","\frac{\left(5 a e^2+3 c d^2\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 a^2 d^3 e^2 x^2}-\frac{\left(5 a e^2+3 c d^2\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 a^{5/2} d^{7/2} e^{5/2}}-\frac{\left(\frac{3 c}{a e}-\frac{5 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{24 x^3}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 d x^4}",1,"((c*d^2 - a*e^2)*(3*c*d^2 + 5*a*e^2)*(2*a*d*e + (c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*a^2*d^3*e^2*x^2) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(4*d*x^4) - (((3*c)/(a*e) - (5*e)/d^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(24*x^3) - ((c*d^2 - a*e^2)^3*(3*c*d^2 + 5*a*e^2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(128*a^(5/2)*d^(7/2)*e^(5/2))","A",6,6,40,0.1500,1,"{849, 834, 806, 720, 724, 206}"
455,1,395,0,0.5139954,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{x^6 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(x^6*(d + e*x)),x]","-\frac{\left(7 a^2 e^4+6 a c d^2 e^2+3 c^2 d^4\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 a^3 d^4 e^3 x^2}+\frac{\left(-35 a^2 e^4+12 a c d^2 e^2+15 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{240 a^2 d^3 e^2 x^3}+\frac{\left(7 a^2 e^4+6 a c d^2 e^2+3 c^2 d^4\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{256 a^{7/2} d^{9/2} e^{7/2}}-\frac{\left(\frac{3 c}{a e}-\frac{7 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{40 x^4}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 d x^5}","-\frac{\left(7 a^2 e^4+6 a c d^2 e^2+3 c^2 d^4\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 a^3 d^4 e^3 x^2}+\frac{\left(-35 a^2 e^4+12 a c d^2 e^2+15 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{240 a^2 d^3 e^2 x^3}+\frac{\left(7 a^2 e^4+6 a c d^2 e^2+3 c^2 d^4\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{256 a^{7/2} d^{9/2} e^{7/2}}-\frac{\left(\frac{3 c}{a e}-\frac{7 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{40 x^4}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 d x^5}",1,"-((c*d^2 - a*e^2)*(3*c^2*d^4 + 6*a*c*d^2*e^2 + 7*a^2*e^4)*(2*a*d*e + (c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(128*a^3*d^4*e^3*x^2) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(5*d*x^5) - (((3*c)/(a*e) - (7*e)/d^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(40*x^4) + ((15*c^2*d^4 + 12*a*c*d^2*e^2 - 35*a^2*e^4)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(240*a^2*d^3*e^2*x^3) + ((c*d^2 - a*e^2)^3*(3*c^2*d^4 + 6*a*c*d^2*e^2 + 7*a^2*e^4)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(256*a^(7/2)*d^(9/2)*e^(7/2))","A",7,6,40,0.1500,1,"{849, 834, 806, 720, 724, 206}"
456,1,498,0,0.7245135,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{x^7 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(x^7*(d + e*x)),x]","-\frac{\left(21 a^2 c d^2 e^4-105 a^3 e^6+33 a c^2 d^4 e^2+35 c^3 d^6\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{960 a^3 d^4 e^3 x^3}+\frac{\left(-21 a^2 e^4+6 a c d^2 e^2+7 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{160 a^2 d^3 e^2 x^4}+\frac{\left(6 a^2 c^2 d^4 e^4-21 a^4 e^8+8 a c^3 d^6 e^2+7 c^4 d^8\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 a^4 d^5 e^4 x^2}-\frac{\left(21 a^2 c d^2 e^4+21 a^3 e^6+15 a c^2 d^4 e^2+7 c^3 d^6\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{1024 a^{9/2} d^{11/2} e^{9/2}}-\frac{\left(\frac{c}{a e}-\frac{3 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{20 x^5}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{6 d x^6}","-\frac{\left(21 a^2 c d^2 e^4-105 a^3 e^6+33 a c^2 d^4 e^2+35 c^3 d^6\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{960 a^3 d^4 e^3 x^3}+\frac{\left(-21 a^2 e^4+6 a c d^2 e^2+7 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{160 a^2 d^3 e^2 x^4}+\frac{\left(6 a^2 c^2 d^4 e^4-21 a^4 e^8+8 a c^3 d^6 e^2+7 c^4 d^8\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 a^4 d^5 e^4 x^2}-\frac{\left(21 a^2 c d^2 e^4+21 a^3 e^6+15 a c^2 d^4 e^2+7 c^3 d^6\right) \left(c d^2-a e^2\right)^3 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{1024 a^{9/2} d^{11/2} e^{9/2}}-\frac{\left(\frac{c}{a e}-\frac{3 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{20 x^5}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{6 d x^6}",1,"((7*c^4*d^8 + 8*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 21*a^4*e^8)*(2*a*d*e + (c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(512*a^4*d^5*e^4*x^2) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(6*d*x^6) - ((c/(a*e) - (3*e)/d^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(20*x^5) + ((7*c^2*d^4 + 6*a*c*d^2*e^2 - 21*a^2*e^4)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(160*a^2*d^3*e^2*x^4) - ((35*c^3*d^6 + 33*a*c^2*d^4*e^2 + 21*a^2*c*d^2*e^4 - 105*a^3*e^6)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(960*a^3*d^4*e^3*x^3) - ((c*d^2 - a*e^2)^3*(7*c^3*d^6 + 15*a*c^2*d^4*e^2 + 21*a^2*c*d^2*e^4 + 21*a^3*e^6)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(1024*a^(9/2)*d^(11/2)*e^(9/2))","A",8,6,40,0.1500,1,"{849, 834, 806, 720, 724, 206}"
457,1,574,0,0.6947621,"\int \frac{x^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{d+e x} \, dx","Int[(x^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x),x]","-\frac{3 \left(35 a^2 c d^2 e^4+15 a^3 e^6+45 a c^2 d^4 e^2+33 c^3 d^6\right) \left(c d^2-a e^2\right)^3 \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{16384 c^5 d^5 e^6}+\frac{\left(35 a^2 c d^2 e^4+15 a^3 e^6+45 a c^2 d^4 e^2+33 c^3 d^6\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2048 c^4 d^4 e^5}-\frac{\left(-10 c d e x \left(-15 a^2 e^4-10 a c d^2 e^2+33 c^2 d^4\right)-95 a^2 c d^2 e^4-105 a^3 e^6-15 a c^2 d^4 e^2+231 c^3 d^6\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4480 c^3 d^3 e^4}+\frac{3 \left(35 a^2 c d^2 e^4+15 a^3 e^6+45 a c^2 d^4 e^2+33 c^3 d^6\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{32768 c^{11/2} d^{11/2} e^{13/2}}+\frac{x^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{8 e}+\frac{1}{112} x^2 \left(\frac{5 a}{c d}-\frac{11 d}{e^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}","-\frac{3 \left(35 a^2 c d^2 e^4+15 a^3 e^6+45 a c^2 d^4 e^2+33 c^3 d^6\right) \left(c d^2-a e^2\right)^3 \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{16384 c^5 d^5 e^6}+\frac{\left(35 a^2 c d^2 e^4+15 a^3 e^6+45 a c^2 d^4 e^2+33 c^3 d^6\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2048 c^4 d^4 e^5}-\frac{\left(-10 c d e x \left(-15 a^2 e^4-10 a c d^2 e^2+33 c^2 d^4\right)-95 a^2 c d^2 e^4-105 a^3 e^6-15 a c^2 d^4 e^2+231 c^3 d^6\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4480 c^3 d^3 e^4}+\frac{3 \left(35 a^2 c d^2 e^4+15 a^3 e^6+45 a c^2 d^4 e^2+33 c^3 d^6\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{32768 c^{11/2} d^{11/2} e^{13/2}}+\frac{x^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{8 e}+\frac{1}{112} x^2 \left(\frac{5 a}{c d}-\frac{11 d}{e^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}",1,"(-3*(c*d^2 - a*e^2)^3*(33*c^3*d^6 + 45*a*c^2*d^4*e^2 + 35*a^2*c*d^2*e^4 + 15*a^3*e^6)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(16384*c^5*d^5*e^6) + ((c*d^2 - a*e^2)*(33*c^3*d^6 + 45*a*c^2*d^4*e^2 + 35*a^2*c*d^2*e^4 + 15*a^3*e^6)*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(2048*c^4*d^4*e^5) + (((5*a)/(c*d) - (11*d)/e^2)*x^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/112 + (x^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(8*e) - ((231*c^3*d^6 - 15*a*c^2*d^4*e^2 - 95*a^2*c*d^2*e^4 - 105*a^3*e^6 - 10*c*d*e*(33*c^2*d^4 - 10*a*c*d^2*e^2 - 15*a^2*e^4)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(4480*c^3*d^3*e^4) + (3*(c*d^2 - a*e^2)^5*(33*c^3*d^6 + 45*a*c^2*d^4*e^2 + 35*a^2*c*d^2*e^4 + 15*a^3*e^6)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(32768*c^(11/2)*d^(11/2)*e^(13/2))","A",8,6,40,0.1500,1,"{849, 832, 779, 612, 621, 206}"
458,1,452,0,0.4101819,"\int \frac{x^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{d+e x} \, dx","Int[(x^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x),x]","\frac{\left(5 a^2 e^4+10 a c d^2 e^2+9 c^2 d^4\right) \left(c d^2-a e^2\right)^3 \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{1024 c^4 d^4 e^5}-\frac{\left(5 a^2 e^4+10 a c d^2 e^2+9 c^2 d^4\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{384 c^3 d^3 e^4}+\frac{\left(-35 a^2 e^4-10 c d e x \left(9 c d^2-5 a e^2\right)-20 a c d^2 e^2+63 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{840 c^2 d^2 e^3}-\frac{\left(5 a^2 e^4+10 a c d^2 e^2+9 c^2 d^4\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2048 c^{9/2} d^{9/2} e^{11/2}}+\frac{x^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 e}","\frac{\left(5 a^2 e^4+10 a c d^2 e^2+9 c^2 d^4\right) \left(c d^2-a e^2\right)^3 \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{1024 c^4 d^4 e^5}-\frac{\left(5 a^2 e^4+10 a c d^2 e^2+9 c^2 d^4\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{384 c^3 d^3 e^4}+\frac{\left(-35 a^2 e^4-10 c d e x \left(9 c d^2-5 a e^2\right)-20 a c d^2 e^2+63 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{840 c^2 d^2 e^3}-\frac{\left(5 a^2 e^4+10 a c d^2 e^2+9 c^2 d^4\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2048 c^{9/2} d^{9/2} e^{11/2}}+\frac{x^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 e}",1,"((c*d^2 - a*e^2)^3*(9*c^2*d^4 + 10*a*c*d^2*e^2 + 5*a^2*e^4)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(1024*c^4*d^4*e^5) - ((c*d^2 - a*e^2)*(9*c^2*d^4 + 10*a*c*d^2*e^2 + 5*a^2*e^4)*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(384*c^3*d^3*e^4) + (x^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(7*e) + ((63*c^2*d^4 - 20*a*c*d^2*e^2 - 35*a^2*e^4 - 10*c*d*e*(9*c*d^2 - 5*a*e^2)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(840*c^2*d^2*e^3) - ((c*d^2 - a*e^2)^5*(9*c^2*d^4 + 10*a*c*d^2*e^2 + 5*a^2*e^4)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2048*c^(9/2)*d^(9/2)*e^(11/2))","A",7,6,40,0.1500,1,"{851, 832, 779, 612, 621, 206}"
459,1,381,0,0.3860239,"\int \frac{x \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{d+e x} \, dx","Int[(x*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x),x]","-\frac{\left(5 a e^2+7 c d^2\right) \left(c d^2-a e^2\right)^3 \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 c^3 d^3 e^4}+\frac{\left(5 a e^2+7 c d^2\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{192 c^2 d^2 e^3}+\frac{\left(5 a e^2+7 c d^2\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{1024 c^{7/2} d^{7/2} e^{9/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{6 c d e (d+e x)}-\frac{1}{60} \left(\frac{5 a}{c d}+\frac{7 d}{e^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}","-\frac{\left(5 a e^2+7 c d^2\right) \left(c d^2-a e^2\right)^3 \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 c^3 d^3 e^4}+\frac{\left(5 a e^2+7 c d^2\right) \left(c d^2-a e^2\right) \left(a e^2+c d^2+2 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{192 c^2 d^2 e^3}+\frac{\left(5 a e^2+7 c d^2\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{1024 c^{7/2} d^{7/2} e^{9/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{6 c d e (d+e x)}-\frac{1}{60} \left(\frac{5 a}{c d}+\frac{7 d}{e^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}",1,"-((c*d^2 - a*e^2)^3*(7*c*d^2 + 5*a*e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(512*c^3*d^3*e^4) + ((c*d^2 - a*e^2)*(7*c*d^2 + 5*a*e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(192*c^2*d^2*e^3) - (((5*a)/(c*d) + (7*d)/e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/60 + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2)/(6*c*d*e*(d + e*x)) + ((c*d^2 - a*e^2)^5*(7*c*d^2 + 5*a*e^2)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(1024*c^(7/2)*d^(7/2)*e^(9/2))","A",6,5,38,0.1316,1,"{794, 664, 612, 621, 206}"
460,1,274,0,0.185465,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{d+e x} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x),x]","\frac{3 \left(c d^2-a e^2\right)^3 \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 c^2 d^2 e^3}-\frac{3 \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{256 c^{5/2} d^{5/2} e^{7/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 e}+\frac{1}{16} \left(\frac{a}{c d}-\frac{d}{e^2}\right) \left(a e^2+c d^2+2 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}","\frac{3 \left(c d^2-a e^2\right)^3 \left(a e^2+c d^2+2 c d e x\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 c^2 d^2 e^3}-\frac{3 \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{256 c^{5/2} d^{5/2} e^{7/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 e}+\frac{1}{16} \left(\frac{a}{c d}-\frac{d}{e^2}\right) \left(a e^2+c d^2+2 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}",1,"(3*(c*d^2 - a*e^2)^3*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(128*c^2*d^2*e^3) + ((a/(c*d) - d/e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/16 + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(5*e) - (3*(c*d^2 - a*e^2)^5*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(256*c^(5/2)*d^(5/2)*e^(7/2))","A",5,4,37,0.1081,1,"{664, 612, 621, 206}"
461,1,394,0,0.449671,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{x (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(x*(d + e*x)),x]","-\frac{\left(-83 a^2 c d^2 e^4-5 a^3 e^6-11 a c^2 d^4 e^2+2 c d e x \left(c d^2-5 a e^2\right) \left(a e^2+3 c d^2\right)+3 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 c d e^2}+\frac{\left(90 a^2 c^2 d^4 e^4+60 a^3 c d^2 e^6-5 a^4 e^8-20 a c^3 d^6 e^2+3 c^4 d^8\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 c^{3/2} d^{3/2} e^{5/2}}-a^{5/2} d^{3/2} e^{5/2} \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)+\frac{\left(11 a e^2+3 c d^2+6 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{24 e}","-\frac{\left(-83 a^2 c d^2 e^4-5 a^3 e^6-11 a c^2 d^4 e^2+2 c d e x \left(c d^2-5 a e^2\right) \left(a e^2+3 c d^2\right)+3 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 c d e^2}+\frac{\left(90 a^2 c^2 d^4 e^4+60 a^3 c d^2 e^6-5 a^4 e^8-20 a c^3 d^6 e^2+3 c^4 d^8\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 c^{3/2} d^{3/2} e^{5/2}}-a^{5/2} d^{3/2} e^{5/2} \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)+\frac{\left(11 a e^2+3 c d^2+6 c d e x\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{24 e}",1,"-((3*c^3*d^6 - 11*a*c^2*d^4*e^2 - 83*a^2*c*d^2*e^4 - 5*a^3*e^6 + 2*c*d*e*(c*d^2 - 5*a*e^2)*(3*c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*c*d*e^2) + ((3*c*d^2 + 11*a*e^2 + 6*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(24*e) + ((3*c^4*d^8 - 20*a*c^3*d^6*e^2 + 90*a^2*c^2*d^4*e^4 + 60*a^3*c*d^2*e^6 - 5*a^4*e^8)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(128*c^(3/2)*d^(3/2)*e^(5/2)) - a^(5/2)*d^(3/2)*e^(5/2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])]","A",8,6,40,0.1500,1,"{849, 814, 843, 621, 206, 724}"
462,1,352,0,0.4321666,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{x^2 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(x^2*(d + e*x)),x]","\frac{\left(19 a^2 e^4+2 c d e x \left(7 a e^2+c d^2\right)+28 a c d^2 e^2+c^2 d^4\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 e}-\frac{\left(-45 a^2 c d^2 e^4-5 a^3 e^6-15 a c^2 d^4 e^2+c^3 d^6\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 \sqrt{c} \sqrt{d} e^{3/2}}-\frac{1}{2} a^{3/2} \sqrt{d} e^{3/2} \left(3 a e^2+5 c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)-\frac{(3 a e-c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 x}","\frac{\left(19 a^2 e^4+2 c d e x \left(7 a e^2+c d^2\right)+28 a c d^2 e^2+c^2 d^4\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 e}-\frac{\left(-45 a^2 c d^2 e^4-5 a^3 e^6-15 a c^2 d^4 e^2+c^3 d^6\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 \sqrt{c} \sqrt{d} e^{3/2}}-\frac{1}{2} a^{3/2} \sqrt{d} e^{3/2} \left(3 a e^2+5 c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)-\frac{(3 a e-c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 x}",1,"((c^2*d^4 + 28*a*c*d^2*e^2 + 19*a^2*e^4 + 2*c*d*e*(c*d^2 + 7*a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*e) - ((3*a*e - c*d*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*x) - ((c^3*d^6 - 15*a*c^2*d^4*e^2 - 45*a^2*c*d^2*e^4 - 5*a^3*e^6)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(16*Sqrt[c]*Sqrt[d]*e^(3/2)) - (a^(3/2)*Sqrt[d]*e^(3/2)*(5*c*d^2 + 3*a*e^2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/2","A",8,7,40,0.1750,1,"{849, 812, 814, 843, 621, 206, 724}"
463,1,339,0,0.3881704,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{x^3 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(x^3*(d + e*x)),x]","\frac{3 \sqrt{c} \sqrt{d} \left(5 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 \sqrt{e}}-\frac{3 \sqrt{a} \sqrt{e} \left(a^2 e^4+10 a c d^2 e^2+5 c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 \sqrt{d}}-\frac{(a e-c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 x^2}-\frac{3 \left(a e \left(a e^2+3 c d^2\right)-c d x \left(3 a e^2+c d^2\right)\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 x}","\frac{3 \sqrt{c} \sqrt{d} \left(5 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 \sqrt{e}}-\frac{3 \sqrt{a} \sqrt{e} \left(a^2 e^4+10 a c d^2 e^2+5 c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 \sqrt{d}}-\frac{(a e-c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 x^2}-\frac{3 \left(a e \left(a e^2+3 c d^2\right)-c d x \left(3 a e^2+c d^2\right)\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 x}",1,"(-3*(a*e*(3*c*d^2 + a*e^2) - c*d*(c*d^2 + 3*a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*x) - ((a*e - c*d*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(2*x^2) + (3*Sqrt[c]*Sqrt[d]*(c^2*d^4 + 10*a*c*d^2*e^2 + 5*a^2*e^4)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*Sqrt[e]) - (3*Sqrt[a]*Sqrt[e]*(5*c^2*d^4 + 10*a*c*d^2*e^2 + a^2*e^4)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*Sqrt[d])","A",8,6,40,0.1500,1,"{849, 812, 843, 621, 206, 724}"
464,1,371,0,0.4702448,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{x^4 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(x^4*(d + e*x)),x]","-\frac{\left(-a^2 e^4-2 c d e x \left(a e^2+7 c d^2\right)+12 a c d^2 e^2+5 c^2 d^4\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 d x}-\frac{\left(15 a^2 c d^2 e^4-a^3 e^6+45 a c^2 d^4 e^2+5 c^3 d^6\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 \sqrt{a} d^{3/2} \sqrt{e}}+\frac{1}{2} c^{3/2} d^{3/2} \sqrt{e} \left(5 a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)-\frac{\left(3 x \left(a e^2+3 c d^2\right)+4 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{12 d x^3}","-\frac{\left(-a^2 e^4-2 c d e x \left(a e^2+7 c d^2\right)+12 a c d^2 e^2+5 c^2 d^4\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 d x}-\frac{\left(15 a^2 c d^2 e^4-a^3 e^6+45 a c^2 d^4 e^2+5 c^3 d^6\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 \sqrt{a} d^{3/2} \sqrt{e}}+\frac{1}{2} c^{3/2} d^{3/2} \sqrt{e} \left(5 a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)-\frac{\left(3 x \left(a e^2+3 c d^2\right)+4 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{12 d x^3}",1,"-((5*c^2*d^4 + 12*a*c*d^2*e^2 - a^2*e^4 - 2*c*d*e*(7*c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*d*x) - ((4*a*d*e + 3*(3*c*d^2 + a*e^2)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(12*d*x^3) + (c^(3/2)*d^(3/2)*Sqrt[e]*(3*c*d^2 + 5*a*e^2)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/2 - ((5*c^3*d^6 + 45*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - a^3*e^6)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(16*Sqrt[a]*d^(3/2)*Sqrt[e])","A",8,7,40,0.1750,1,"{849, 810, 812, 843, 621, 206, 724}"
465,1,404,0,0.4555603,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{x^5 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(x^5*(d + e*x)),x]","-\frac{\left(x \left(11 a^2 c d^2 e^4-3 a^3 e^6+83 a c^2 d^4 e^2+5 c^3 d^6\right)+2 a d e \left(5 c d^2-a e^2\right) \left(3 a e^2+c d^2\right)\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 a d^2 e x^2}+\frac{\left(-90 a^2 c^2 d^4 e^4+20 a^3 c d^2 e^6-3 a^4 e^8-60 a c^3 d^6 e^2+5 c^4 d^8\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 a^{3/2} d^{5/2} e^{3/2}}+c^{5/2} d^{5/2} e^{3/2} \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)-\frac{\left(x \left(3 a e^2+11 c d^2\right)+6 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{24 d x^4}","-\frac{\left(x \left(11 a^2 c d^2 e^4-3 a^3 e^6+83 a c^2 d^4 e^2+5 c^3 d^6\right)+2 a d e \left(5 c d^2-a e^2\right) \left(3 a e^2+c d^2\right)\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 a d^2 e x^2}+\frac{\left(-90 a^2 c^2 d^4 e^4+20 a^3 c d^2 e^6-3 a^4 e^8-60 a c^3 d^6 e^2+5 c^4 d^8\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{128 a^{3/2} d^{5/2} e^{3/2}}+c^{5/2} d^{5/2} e^{3/2} \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)-\frac{\left(x \left(3 a e^2+11 c d^2\right)+6 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{24 d x^4}",1,"-((2*a*d*e*(5*c*d^2 - a*e^2)*(c*d^2 + 3*a*e^2) + (5*c^3*d^6 + 83*a*c^2*d^4*e^2 + 11*a^2*c*d^2*e^4 - 3*a^3*e^6)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*a*d^2*e*x^2) - ((6*a*d*e + (11*c*d^2 + 3*a*e^2)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(24*d*x^4) + c^(5/2)*d^(5/2)*e^(3/2)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])] + ((5*c^4*d^8 - 60*a*c^3*d^6*e^2 - 90*a^2*c^2*d^4*e^4 + 20*a^3*c*d^2*e^6 - 3*a^4*e^8)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(128*a^(3/2)*d^(5/2)*e^(3/2))","A",8,6,40,0.1500,1,"{849, 810, 843, 621, 206, 724}"
466,1,289,0,0.3276557,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{x^6 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(x^6*(d + e*x)),x]","\frac{3 \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 a^2 d^3 e^2 x^2}-\frac{3 \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{256 a^{5/2} d^{7/2} e^{5/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 d x^5}-\frac{\left(\frac{c}{a e}-\frac{e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{16 x^4}","\frac{3 \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 a^2 d^3 e^2 x^2}-\frac{3 \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{256 a^{5/2} d^{7/2} e^{5/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 d x^5}-\frac{\left(\frac{c}{a e}-\frac{e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{16 x^4}",1,"(3*(c*d^2 - a*e^2)^3*(2*a*d*e + (c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(128*a^2*d^3*e^2*x^2) - ((c/(a*e) - e/d^2)*(2*a*d*e + (c*d^2 + a*e^2)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(16*x^4) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(5*d*x^5) - (3*(c*d^2 - a*e^2)^5*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(256*a^(5/2)*d^(7/2)*e^(5/2))","A",6,5,40,0.1250,1,"{849, 806, 720, 724, 206}"
467,1,386,0,0.49468,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{x^7 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(x^7*(d + e*x)),x]","-\frac{\left(7 a e^2+5 c d^2\right) \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 a^3 d^4 e^3 x^2}+\frac{\left(7 a e^2+5 c d^2\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{192 a^2 d^3 e^2 x^4}+\frac{\left(7 a e^2+5 c d^2\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{1024 a^{7/2} d^{9/2} e^{7/2}}-\frac{\left(\frac{5 c}{a e}-\frac{7 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{60 x^5}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{6 d x^6}","-\frac{\left(7 a e^2+5 c d^2\right) \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 a^3 d^4 e^3 x^2}+\frac{\left(7 a e^2+5 c d^2\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{192 a^2 d^3 e^2 x^4}+\frac{\left(7 a e^2+5 c d^2\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{1024 a^{7/2} d^{9/2} e^{7/2}}-\frac{\left(\frac{5 c}{a e}-\frac{7 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{60 x^5}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{6 d x^6}",1,"-((c*d^2 - a*e^2)^3*(5*c*d^2 + 7*a*e^2)*(2*a*d*e + (c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(512*a^3*d^4*e^3*x^2) + ((c*d^2 - a*e^2)*(5*c*d^2 + 7*a*e^2)*(2*a*d*e + (c*d^2 + a*e^2)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(192*a^2*d^3*e^2*x^4) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(6*d*x^6) - (((5*c)/(a*e) - (7*e)/d^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(60*x^5) + ((c*d^2 - a*e^2)^5*(5*c*d^2 + 7*a*e^2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(1024*a^(7/2)*d^(9/2)*e^(7/2))","A",7,6,40,0.1500,1,"{849, 834, 806, 720, 724, 206}"
468,1,500,0,0.6394653,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{x^8 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(x^8*(d + e*x)),x]","\frac{\left(9 a^2 e^4+10 a c d^2 e^2+5 c^2 d^4\right) \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{1024 a^4 d^5 e^4 x^2}-\frac{\left(9 a^2 e^4+10 a c d^2 e^2+5 c^2 d^4\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{384 a^3 d^4 e^3 x^4}+\frac{\left(-63 a^2 e^4+20 a c d^2 e^2+35 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{840 a^2 d^3 e^2 x^5}-\frac{\left(9 a^2 e^4+10 a c d^2 e^2+5 c^2 d^4\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2048 a^{9/2} d^{11/2} e^{9/2}}-\frac{\left(\frac{5 c}{a e}-\frac{9 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{84 x^6}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 d x^7}","\frac{\left(9 a^2 e^4+10 a c d^2 e^2+5 c^2 d^4\right) \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{1024 a^4 d^5 e^4 x^2}-\frac{\left(9 a^2 e^4+10 a c d^2 e^2+5 c^2 d^4\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{384 a^3 d^4 e^3 x^4}+\frac{\left(-63 a^2 e^4+20 a c d^2 e^2+35 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{840 a^2 d^3 e^2 x^5}-\frac{\left(9 a^2 e^4+10 a c d^2 e^2+5 c^2 d^4\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2048 a^{9/2} d^{11/2} e^{9/2}}-\frac{\left(\frac{5 c}{a e}-\frac{9 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{84 x^6}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 d x^7}",1,"((c*d^2 - a*e^2)^3*(5*c^2*d^4 + 10*a*c*d^2*e^2 + 9*a^2*e^4)*(2*a*d*e + (c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(1024*a^4*d^5*e^4*x^2) - ((c*d^2 - a*e^2)*(5*c^2*d^4 + 10*a*c*d^2*e^2 + 9*a^2*e^4)*(2*a*d*e + (c*d^2 + a*e^2)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(384*a^3*d^4*e^3*x^4) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(7*d*x^7) - (((5*c)/(a*e) - (9*e)/d^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(84*x^6) + ((35*c^2*d^4 + 20*a*c*d^2*e^2 - 63*a^2*e^4)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(840*a^2*d^3*e^2*x^5) - ((c*d^2 - a*e^2)^5*(5*c^2*d^4 + 10*a*c*d^2*e^2 + 9*a^2*e^4)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2048*a^(9/2)*d^(11/2)*e^(9/2))","A",8,6,40,0.1500,1,"{849, 834, 806, 720, 724, 206}"
469,1,628,0,0.8852733,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{x^9 (d+e x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(x^9*(d + e*x)),x]","-\frac{3 \left(45 a^2 c d^2 e^4+33 a^3 e^6+35 a c^2 d^4 e^2+15 c^3 d^6\right) \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{16384 a^5 d^6 e^5 x^2}+\frac{\left(45 a^2 c d^2 e^4+33 a^3 e^6+35 a c^2 d^4 e^2+15 c^3 d^6\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2048 a^4 d^5 e^4 x^4}-\frac{\left(15 a^2 c d^2 e^4-231 a^3 e^6+95 a c^2 d^4 e^2+105 c^3 d^6\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4480 a^3 d^4 e^3 x^5}+\frac{\left(-33 a^2 e^4+10 a c d^2 e^2+15 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{448 a^2 d^3 e^2 x^6}+\frac{3 \left(45 a^2 c d^2 e^4+33 a^3 e^6+35 a c^2 d^4 e^2+15 c^3 d^6\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{32768 a^{11/2} d^{13/2} e^{11/2}}-\frac{\left(\frac{5 c}{a e}-\frac{11 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{112 x^7}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{8 d x^8}","-\frac{3 \left(45 a^2 c d^2 e^4+33 a^3 e^6+35 a c^2 d^4 e^2+15 c^3 d^6\right) \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+2 a d e\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{16384 a^5 d^6 e^5 x^2}+\frac{\left(45 a^2 c d^2 e^4+33 a^3 e^6+35 a c^2 d^4 e^2+15 c^3 d^6\right) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+2 a d e\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2048 a^4 d^5 e^4 x^4}-\frac{\left(15 a^2 c d^2 e^4-231 a^3 e^6+95 a c^2 d^4 e^2+105 c^3 d^6\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4480 a^3 d^4 e^3 x^5}+\frac{\left(-33 a^2 e^4+10 a c d^2 e^2+15 c^2 d^4\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{448 a^2 d^3 e^2 x^6}+\frac{3 \left(45 a^2 c d^2 e^4+33 a^3 e^6+35 a c^2 d^4 e^2+15 c^3 d^6\right) \left(c d^2-a e^2\right)^5 \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{32768 a^{11/2} d^{13/2} e^{11/2}}-\frac{\left(\frac{5 c}{a e}-\frac{11 e}{d^2}\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{112 x^7}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{8 d x^8}",1,"(-3*(c*d^2 - a*e^2)^3*(15*c^3*d^6 + 35*a*c^2*d^4*e^2 + 45*a^2*c*d^2*e^4 + 33*a^3*e^6)*(2*a*d*e + (c*d^2 + a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(16384*a^5*d^6*e^5*x^2) + ((c*d^2 - a*e^2)*(15*c^3*d^6 + 35*a*c^2*d^4*e^2 + 45*a^2*c*d^2*e^4 + 33*a^3*e^6)*(2*a*d*e + (c*d^2 + a*e^2)*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(2048*a^4*d^5*e^4*x^4) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(8*d*x^8) - (((5*c)/(a*e) - (11*e)/d^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(112*x^7) + ((15*c^2*d^4 + 10*a*c*d^2*e^2 - 33*a^2*e^4)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(448*a^2*d^3*e^2*x^6) - ((105*c^3*d^6 + 95*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - 231*a^3*e^6)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(4480*a^3*d^4*e^3*x^5) + (3*(c*d^2 - a*e^2)^5*(15*c^3*d^6 + 35*a*c^2*d^4*e^2 + 45*a^2*c*d^2*e^4 + 33*a^3*e^6)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(32768*a^(11/2)*d^(13/2)*e^(11/2))","A",9,6,40,0.1500,1,"{849, 834, 806, 720, 724, 206}"
470,1,298,0,0.3411189,"\int \frac{x^3}{(d+e x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[x^3/((d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{3 \left(a^2 e^4+2 a c d^2 e^2+5 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 c^{5/2} d^{5/2} e^{7/2}}-\frac{\left(\left(5 c d^2-3 a e^2\right) \left(a e^2+3 c d^2\right)-2 c d e x \left(5 c d^2-a e^2\right)\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 c^2 d^2 e^3 \left(c d^2-a e^2\right)}-\frac{2 d x^2 \left(c d x \left(c d^2-a e^2\right)+a e \left(c d^2-a e^2\right)\right)}{e \left(c d^2-a e^2\right)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{3 \left(a^2 e^4+2 a c d^2 e^2+5 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 c^{5/2} d^{5/2} e^{7/2}}-\frac{3 \left(a e^2+3 c d^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 c^2 d^2 e^3}-\frac{2 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^3 (d+e x) \left(c d^2-a e^2\right)}+\frac{(d+e x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 c d e^3}",1,"(-2*d*x^2*(a*e*(c*d^2 - a*e^2) + c*d*(c*d^2 - a*e^2)*x))/(e*(c*d^2 - a*e^2)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (((5*c*d^2 - 3*a*e^2)*(3*c*d^2 + a*e^2) - 2*c*d*e*(5*c*d^2 - a*e^2)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*c^2*d^2*e^3*(c*d^2 - a*e^2)) + (3*(5*c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*c^(5/2)*d^(5/2)*e^(7/2))","A",5,5,40,0.1250,1,"{849, 818, 779, 621, 206}"
471,1,195,0,0.346458,"\int \frac{x^2}{(d+e x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[x^2/((d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","-\frac{\left(a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 c^{3/2} d^{3/2} e^{5/2}}+\frac{2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^2 (d+e x) \left(c d^2-a e^2\right)}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d e^2}","-\frac{\left(a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 c^{3/2} d^{3/2} e^{5/2}}+\frac{2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^2 (d+e x) \left(c d^2-a e^2\right)}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d e^2}",1,"Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(c*d*e^2) + (2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(e^2*(c*d^2 - a*e^2)*(d + e*x)) - ((3*c*d^2 + a*e^2)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2*c^(3/2)*d^(3/2)*e^(5/2))","A",4,4,40,0.1000,1,"{1638, 792, 621, 206}"
472,1,139,0,0.1094964,"\int \frac{x}{(d+e x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[x/((d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{\sqrt{c} \sqrt{d} e^{3/2}}-\frac{2 d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e (d+e x) \left(c d^2-a e^2\right)}","\frac{\tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{\sqrt{c} \sqrt{d} e^{3/2}}-\frac{2 d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e (d+e x) \left(c d^2-a e^2\right)}",1,"(-2*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(e*(c*d^2 - a*e^2)*(d + e*x)) + ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])]/(Sqrt[c]*Sqrt[d]*e^(3/2))","A",3,3,38,0.07895,1,"{792, 621, 206}"
473,1,52,0,0.0235734,"\int \frac{1}{(d+e x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/((d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{(d+e x) \left(c d^2-a e^2\right)}","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{(d+e x) \left(c d^2-a e^2\right)}",1,"(2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/((c*d^2 - a*e^2)*(d + e*x))","A",1,1,37,0.02703,1,"{650}"
474,1,143,0,0.1747218,"\int \frac{1}{x (d+e x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/(x*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","-\frac{2 e (a e+c d x)}{d \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{\tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{\sqrt{a} d^{3/2} \sqrt{e}}","-\frac{2 e (a e+c d x)}{d \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{\tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{\sqrt{a} d^{3/2} \sqrt{e}}",1,"(-2*e*(a*e + c*d*x))/(d*(c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])]/(Sqrt[a]*d^(3/2)*Sqrt[e])","A",5,5,40,0.1250,1,"{851, 822, 12, 724, 206}"
475,1,229,0,0.292443,"\int \frac{1}{x^2 (d+e x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/(x^2*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{\left(3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 a^{3/2} d^{5/2} e^{3/2}}-\frac{\left(c d^2-3 a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{a d^2 e x \left(c d^2-a e^2\right)}-\frac{2 e (a e+c d x)}{d x \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{\left(3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 a^{3/2} d^{5/2} e^{3/2}}-\frac{\left(c d^2-3 a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{a d^2 e x \left(c d^2-a e^2\right)}-\frac{2 e (a e+c d x)}{d x \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*e*(a*e + c*d*x))/(d*(c*d^2 - a*e^2)*x*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - ((c*d^2 - 3*a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(a*d^2*e*(c*d^2 - a*e^2)*x) + ((c*d^2 + 3*a*e^2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2*a^(3/2)*d^(5/2)*e^(3/2))","A",5,5,40,0.1250,1,"{851, 822, 806, 724, 206}"
476,1,329,0,0.5077914,"\int \frac{1}{x^3 (d+e x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/(x^3*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","-\frac{3 \left(5 a^2 e^4+2 a c d^2 e^2+c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 a^{5/2} d^{7/2} e^{5/2}}+\frac{\left(3 c d^2-5 a e^2\right) \left(3 a e^2+c d^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 a^2 d^3 e^2 x \left(c d^2-a e^2\right)}-\frac{\left(c d^2-5 a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 a d^2 e x^2 \left(c d^2-a e^2\right)}-\frac{2 e (a e+c d x)}{d x^2 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","-\frac{3 \left(5 a^2 e^4+2 a c d^2 e^2+c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 a^{5/2} d^{7/2} e^{5/2}}+\frac{\left(3 c d^2-5 a e^2\right) \left(3 a e^2+c d^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 a^2 d^3 e^2 x \left(c d^2-a e^2\right)}-\frac{\left(c d^2-5 a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 a d^2 e x^2 \left(c d^2-a e^2\right)}-\frac{2 e (a e+c d x)}{d x^2 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*e*(a*e + c*d*x))/(d*(c*d^2 - a*e^2)*x^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - ((c*d^2 - 5*a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(2*a*d^2*e*(c*d^2 - a*e^2)*x^2) + ((3*c*d^2 - 5*a*e^2)*(c*d^2 + 3*a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*a^2*d^3*e^2*(c*d^2 - a*e^2)*x) - (3*(c^2*d^4 + 2*a*c*d^2*e^2 + 5*a^2*e^4)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*a^(5/2)*d^(7/2)*e^(5/2))","A",6,6,40,0.1500,1,"{851, 822, 834, 806, 724, 206}"
477,1,515,0,0.6189463,"\int \frac{x^5}{(d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[x^5/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{2 x^2 \left(x \left(c d^2-a e^2\right) \left(-a^2 c d^2 e^4-3 a^3 e^6-11 a c^2 d^4 e^2+7 c^3 d^6\right)+a d e \left(c d^2-a e^2\right) \left(-3 a^2 e^4-12 a c d^2 e^2+7 c^2 d^4\right)\right)}{3 c d e^2 \left(c d^2-a e^2\right)^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{\left(-2 c d e x \left(9 a^2 c d^2 e^4-15 a^3 e^6-61 a c^2 d^4 e^2+35 c^3 d^6\right)+36 a^2 c^2 d^4 e^4+30 a^3 c d^2 e^6-45 a^4 e^8-190 a c^3 d^6 e^2+105 c^4 d^8\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 c^3 d^3 e^4 \left(c d^2-a e^2\right)^3}+\frac{5 \left(3 a^2 e^4+6 a c d^2 e^2+7 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 c^{7/2} d^{7/2} e^{9/2}}-\frac{2 d x^4 \left(c d x \left(c d^2-a e^2\right)+a e \left(c d^2-a e^2\right)\right)}{3 e \left(c d^2-a e^2\right)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","-\frac{2 x^2 \left(x \left(c d^2-a e^2\right) \left(-a^2 c d^2 e^4-3 a^3 e^6-11 a c^2 d^4 e^2+7 c^3 d^6\right)+a d e \left(c d^2-a e^2\right) \left(-3 a^2 e^4-12 a c d^2 e^2+7 c^2 d^4\right)\right)}{3 c d e^2 \left(c d^2-a e^2\right)^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{\left(-2 c d e x \left(9 a^2 c d^2 e^4-15 a^3 e^6-61 a c^2 d^4 e^2+35 c^3 d^6\right)+36 a^2 c^2 d^4 e^4+30 a^3 c d^2 e^6-45 a^4 e^8-190 a c^3 d^6 e^2+105 c^4 d^8\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 c^3 d^3 e^4 \left(c d^2-a e^2\right)^3}+\frac{5 \left(3 a^2 e^4+6 a c d^2 e^2+7 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 c^{7/2} d^{7/2} e^{9/2}}-\frac{2 d x^4 \left(c d x \left(c d^2-a e^2\right)+a e \left(c d^2-a e^2\right)\right)}{3 e \left(c d^2-a e^2\right)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*d*x^4*(a*e*(c*d^2 - a*e^2) + c*d*(c*d^2 - a*e^2)*x))/(3*e*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (2*x^2*(a*d*e*(c*d^2 - a*e^2)*(7*c^2*d^4 - 12*a*c*d^2*e^2 - 3*a^2*e^4) + (c*d^2 - a*e^2)*(7*c^3*d^6 - 11*a*c^2*d^4*e^2 - a^2*c*d^2*e^4 - 3*a^3*e^6)*x))/(3*c*d*e^2*(c*d^2 - a*e^2)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - ((105*c^4*d^8 - 190*a*c^3*d^6*e^2 + 36*a^2*c^2*d^4*e^4 + 30*a^3*c*d^2*e^6 - 45*a^4*e^8 - 2*c*d*e*(35*c^3*d^6 - 61*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4 - 15*a^3*e^6)*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*c^3*d^3*e^4*(c*d^2 - a*e^2)^3) + (5*(7*c^2*d^4 + 6*a*c*d^2*e^2 + 3*a^2*e^4)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*c^(7/2)*d^(7/2)*e^(9/2))","A",6,5,40,0.1250,1,"{849, 818, 779, 621, 206}"
478,1,438,0,0.5414972,"\int \frac{x^4}{(d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[x^4/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{2 x \left(x \left(c d^2-a e^2\right) \left(-a^2 c d^2 e^4-3 a^3 e^6-9 a c^2 d^4 e^2+5 c^3 d^6\right)+a d e \left(c d^2-a e^2\right) \left(-3 a^2 e^4-10 a c d^2 e^2+5 c^2 d^4\right)\right)}{3 c d e^2 \left(c d^2-a e^2\right)^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\left(9 a^2 c d^2 e^4-9 a^3 e^6-31 a c^2 d^4 e^2+15 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^2 d^2 e^3 \left(c d^2-a e^2\right)^3}-\frac{\left(3 a e^2+5 c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 c^{5/2} d^{5/2} e^{7/2}}-\frac{2 d x^3 \left(c d x \left(c d^2-a e^2\right)+a e \left(c d^2-a e^2\right)\right)}{3 e \left(c d^2-a e^2\right)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","-\frac{2 x \left(x \left(c d^2-a e^2\right) \left(-a^2 c d^2 e^4-3 a^3 e^6-9 a c^2 d^4 e^2+5 c^3 d^6\right)+a d e \left(c d^2-a e^2\right) \left(-3 a^2 e^4-10 a c d^2 e^2+5 c^2 d^4\right)\right)}{3 c d e^2 \left(c d^2-a e^2\right)^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\left(9 a^2 c d^2 e^4-9 a^3 e^6-31 a c^2 d^4 e^2+15 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^2 d^2 e^3 \left(c d^2-a e^2\right)^3}-\frac{\left(3 a e^2+5 c d^2\right) \tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 c^{5/2} d^{5/2} e^{7/2}}-\frac{2 d x^3 \left(c d x \left(c d^2-a e^2\right)+a e \left(c d^2-a e^2\right)\right)}{3 e \left(c d^2-a e^2\right)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*d*x^3*(a*e*(c*d^2 - a*e^2) + c*d*(c*d^2 - a*e^2)*x))/(3*e*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (2*x*(a*d*e*(c*d^2 - a*e^2)*(5*c^2*d^4 - 10*a*c*d^2*e^2 - 3*a^2*e^4) + (c*d^2 - a*e^2)*(5*c^3*d^6 - 9*a*c^2*d^4*e^2 - a^2*c*d^2*e^4 - 3*a^3*e^6)*x))/(3*c*d*e^2*(c*d^2 - a*e^2)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + ((15*c^3*d^6 - 31*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4 - 9*a^3*e^6)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c^2*d^2*e^3*(c*d^2 - a*e^2)^3) - ((5*c*d^2 + 3*a*e^2)*ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2*c^(5/2)*d^(5/2)*e^(7/2))","A",6,5,40,0.1250,1,"{849, 818, 640, 621, 206}"
479,1,297,0,0.2925108,"\int \frac{x^3}{(d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[x^3/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{2 \left(x \left(-a^2 c d^2 e^4-3 a^3 e^6-7 a c^2 d^4 e^2+3 c^3 d^6\right)+a d e \left(c d^2-3 a e^2\right) \left(a e^2+3 c d^2\right)\right)}{3 c d e^2 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{c^{3/2} d^{3/2} e^{5/2}}-\frac{2 d x^2 \left(c d x \left(c d^2-a e^2\right)+a e \left(c d^2-a e^2\right)\right)}{3 e \left(c d^2-a e^2\right)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","-\frac{2 \left(x \left(-a^2 c d^2 e^4-3 a^3 e^6-7 a c^2 d^4 e^2+3 c^3 d^6\right)+a d e \left(c d^2-3 a e^2\right) \left(a e^2+3 c d^2\right)\right)}{3 c d e^2 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\tanh ^{-1}\left(\frac{a e^2+c d^2+2 c d e x}{2 \sqrt{c} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{c^{3/2} d^{3/2} e^{5/2}}-\frac{2 d x^2 \left(c d x \left(c d^2-a e^2\right)+a e \left(c d^2-a e^2\right)\right)}{3 e \left(c d^2-a e^2\right)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*d*x^2*(a*e*(c*d^2 - a*e^2) + c*d*(c*d^2 - a*e^2)*x))/(3*e*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (2*(a*d*e*(c*d^2 - 3*a*e^2)*(3*c*d^2 + a*e^2) + (3*c^3*d^6 - 7*a*c^2*d^4*e^2 - a^2*c*d^2*e^4 - 3*a^3*e^6)*x))/(3*c*d*e^2*(c*d^2 - a*e^2)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + ArcTanh[(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*Sqrt[c]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])]/(c^(3/2)*d^(3/2)*e^(5/2))","A",5,5,40,0.1250,1,"{849, 818, 777, 621, 206}"
480,1,126,0,0.107981,"\int \frac{x^2}{(d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[x^2/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","\frac{2 x^2}{3 (d+e x) \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{8 a e \left(x \left(a e^2+c d^2\right)+2 a d e\right)}{3 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{2 x^2}{3 (d+e x) \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{8 a e \left(x \left(a e^2+c d^2\right)+2 a d e\right)}{3 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(2*x^2)/(3*(c*d^2 - a*e^2)*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (8*a*e*(2*a*d*e + (c*d^2 + a*e^2)*x))/(3*(c*d^2 - a*e^2)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",3,3,40,0.07500,1,"{854, 12, 636}"
481,1,138,0,0.0937172,"\int \frac{x}{(d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[x/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","\frac{2 \left(3 a e^2+c d^2\right) \left(a e^2+c d^2+2 c d e x\right)}{3 e \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 d}{3 e (d+e x) \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{2 \left(3 a e^2+c d^2\right) \left(a e^2+c d^2+2 c d e x\right)}{3 e \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 d}{3 e (d+e x) \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*d)/(3*e*(c*d^2 - a*e^2)*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (2*(c*d^2 + 3*a*e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*e*(c*d^2 - a*e^2)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",2,2,38,0.05263,1,"{792, 613}"
482,1,121,0,0.0415744,"\int \frac{1}{(d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","\frac{2}{3 (d+e x) \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{8 c d \left(a e^2+c d^2+2 c d e x\right)}{3 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{2}{3 (d+e x) \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{8 c d \left(a e^2+c d^2+2 c d e x\right)}{3 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"2/(3*(c*d^2 - a*e^2)*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (8*c*d*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*(c*d^2 - a*e^2)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",2,2,37,0.05405,1,"{658, 613}"
483,1,271,0,0.3377033,"\int \frac{1}{x (d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[1/(x*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","\frac{2 \left(7 a^2 c d^2 e^4-3 a^3 e^6+a c^2 d^4 e^2+c d e x \left(3 c d^2-a e^2\right) \left(3 a e^2+c d^2\right)+3 c^3 d^6\right)}{3 a d^2 e \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{\tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{a^{3/2} d^{5/2} e^{3/2}}-\frac{2 e (a e+c d x)}{3 d \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","\frac{2 \left(7 a^2 c d^2 e^4-3 a^3 e^6+a c^2 d^4 e^2+c d e x \left(3 c d^2-a e^2\right) \left(3 a e^2+c d^2\right)+3 c^3 d^6\right)}{3 a d^2 e \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{\tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{a^{3/2} d^{5/2} e^{3/2}}-\frac{2 e (a e+c d x)}{3 d \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*e*(a*e + c*d*x))/(3*d*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (2*(3*c^3*d^6 + a*c^2*d^4*e^2 + 7*a^2*c*d^2*e^4 - 3*a^3*e^6 + c*d*e*(3*c*d^2 - a*e^2)*(c*d^2 + 3*a*e^2)*x))/(3*a*d^2*e*(c*d^2 - a*e^2)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])]/(a^(3/2)*d^(5/2)*e^(3/2))","A",6,5,40,0.1250,1,"{851, 822, 12, 724, 206}"
484,1,394,0,0.5904364,"\int \frac{1}{x^2 (d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[1/(x^2*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{\left(31 a^2 c d^2 e^4-15 a^3 e^6-9 a c^2 d^4 e^2+9 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 a^2 d^3 e^2 x \left(c d^2-a e^2\right)^3}+\frac{2 \left(c d e x \left(-5 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right)+9 a^2 c d^2 e^4-5 a^3 e^6+a c^2 d^4 e^2+3 c^3 d^6\right)}{3 a d^2 e x \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\left(5 a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 a^{5/2} d^{7/2} e^{5/2}}-\frac{2 e (a e+c d x)}{3 d x \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","-\frac{\left(31 a^2 c d^2 e^4-15 a^3 e^6-9 a c^2 d^4 e^2+9 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 a^2 d^3 e^2 x \left(c d^2-a e^2\right)^3}+\frac{2 \left(c d e x \left(-5 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right)+9 a^2 c d^2 e^4-5 a^3 e^6+a c^2 d^4 e^2+3 c^3 d^6\right)}{3 a d^2 e x \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\left(5 a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{2 a^{5/2} d^{7/2} e^{5/2}}-\frac{2 e (a e+c d x)}{3 d x \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*e*(a*e + c*d*x))/(3*d*(c*d^2 - a*e^2)*x*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (2*(3*c^3*d^6 + a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4 - 5*a^3*e^6 + c*d*e*(3*c^2*d^4 + 10*a*c*d^2*e^2 - 5*a^2*e^4)*x))/(3*a*d^2*e*(c*d^2 - a*e^2)^3*x*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - ((9*c^3*d^6 - 9*a*c^2*d^4*e^2 + 31*a^2*c*d^2*e^4 - 15*a^3*e^6)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*a^2*d^3*e^2*(c*d^2 - a*e^2)^3*x) + ((3*c*d^2 + 5*a*e^2)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(2*a^(5/2)*d^(7/2)*e^(5/2))","A",6,5,40,0.1250,1,"{851, 822, 806, 724, 206}"
485,1,522,0,0.8003395,"\int \frac{1}{x^3 (d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[1/(x^3*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{\left(61 a^2 c d^2 e^4-35 a^3 e^6-9 a c^2 d^4 e^2+15 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{6 a^2 d^3 e^2 x^2 \left(c d^2-a e^2\right)^3}+\frac{\left(-36 a^2 c^2 d^4 e^4+190 a^3 c d^2 e^6-105 a^4 e^8-30 a c^3 d^6 e^2+45 c^4 d^8\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 a^3 d^4 e^3 x \left(c d^2-a e^2\right)^3}+\frac{2 \left(c d e x \left(-7 a^2 e^4+12 a c d^2 e^2+3 c^2 d^4\right)+11 a^2 c d^2 e^4-7 a^3 e^6+a c^2 d^4 e^2+3 c^3 d^6\right)}{3 a d^2 e x^2 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{5 \left(7 a^2 e^4+6 a c d^2 e^2+3 c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 a^{7/2} d^{9/2} e^{7/2}}-\frac{2 e (a e+c d x)}{3 d x^2 \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","-\frac{\left(61 a^2 c d^2 e^4-35 a^3 e^6-9 a c^2 d^4 e^2+15 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{6 a^2 d^3 e^2 x^2 \left(c d^2-a e^2\right)^3}+\frac{\left(-36 a^2 c^2 d^4 e^4+190 a^3 c d^2 e^6-105 a^4 e^8-30 a c^3 d^6 e^2+45 c^4 d^8\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 a^3 d^4 e^3 x \left(c d^2-a e^2\right)^3}+\frac{2 \left(c d e x \left(-7 a^2 e^4+12 a c d^2 e^2+3 c^2 d^4\right)+11 a^2 c d^2 e^4-7 a^3 e^6+a c^2 d^4 e^2+3 c^3 d^6\right)}{3 a d^2 e x^2 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{5 \left(7 a^2 e^4+6 a c d^2 e^2+3 c^2 d^4\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{8 a^{7/2} d^{9/2} e^{7/2}}-\frac{2 e (a e+c d x)}{3 d x^2 \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*e*(a*e + c*d*x))/(3*d*(c*d^2 - a*e^2)*x^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (2*(3*c^3*d^6 + a*c^2*d^4*e^2 + 11*a^2*c*d^2*e^4 - 7*a^3*e^6 + c*d*e*(3*c^2*d^4 + 12*a*c*d^2*e^2 - 7*a^2*e^4)*x))/(3*a*d^2*e*(c*d^2 - a*e^2)^3*x^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - ((15*c^3*d^6 - 9*a*c^2*d^4*e^2 + 61*a^2*c*d^2*e^4 - 35*a^3*e^6)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(6*a^2*d^3*e^2*(c*d^2 - a*e^2)^3*x^2) + ((45*c^4*d^8 - 30*a*c^3*d^6*e^2 - 36*a^2*c^2*d^4*e^4 + 190*a^3*c*d^2*e^6 - 105*a^4*e^8)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*a^3*d^4*e^3*(c*d^2 - a*e^2)^3*x) - (5*(3*c^2*d^4 + 6*a*c*d^2*e^2 + 7*a^2*e^4)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(8*a^(7/2)*d^(9/2)*e^(7/2))","A",7,6,40,0.1500,1,"{851, 822, 834, 806, 724, 206}"
486,1,664,0,1.1698808,"\int \frac{1}{x^4 (d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[1/(x^4*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{\left(33 a^2 c d^2 e^4-21 a^3 e^6-3 a c^2 d^4 e^2+7 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 a^2 d^3 e^2 x^3 \left(c d^2-a e^2\right)^3}-\frac{\left(-54 a^2 c^3 d^6 e^4-78 a^3 c^2 d^4 e^6+525 a^4 c d^2 e^8-315 a^5 e^{10}-55 a c^4 d^8 e^2+105 c^5 d^{10}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 a^4 d^5 e^4 x \left(c d^2-a e^2\right)^3}+\frac{\left(-18 a^2 c^2 d^4 e^4+168 a^3 c d^2 e^6-105 a^4 e^8-16 a c^3 d^6 e^2+35 c^4 d^8\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 a^3 d^4 e^3 x^2 \left(c d^2-a e^2\right)^3}+\frac{2 \left(c d e x \left(-9 a^2 e^4+14 a c d^2 e^2+3 c^2 d^4\right)+13 a^2 c d^2 e^4-9 a^3 e^6+a c^2 d^4 e^2+3 c^3 d^6\right)}{3 a d^2 e x^3 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{5 \left(21 a^2 c d^2 e^4+21 a^3 e^6+15 a c^2 d^4 e^2+7 c^3 d^6\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 a^{9/2} d^{11/2} e^{9/2}}-\frac{2 e (a e+c d x)}{3 d x^3 \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","-\frac{\left(33 a^2 c d^2 e^4-21 a^3 e^6-3 a c^2 d^4 e^2+7 c^3 d^6\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 a^2 d^3 e^2 x^3 \left(c d^2-a e^2\right)^3}-\frac{\left(-54 a^2 c^3 d^6 e^4-78 a^3 c^2 d^4 e^6+525 a^4 c d^2 e^8-315 a^5 e^{10}-55 a c^4 d^8 e^2+105 c^5 d^{10}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 a^4 d^5 e^4 x \left(c d^2-a e^2\right)^3}+\frac{\left(-18 a^2 c^2 d^4 e^4+168 a^3 c d^2 e^6-105 a^4 e^8-16 a c^3 d^6 e^2+35 c^4 d^8\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 a^3 d^4 e^3 x^2 \left(c d^2-a e^2\right)^3}+\frac{2 \left(c d e x \left(-9 a^2 e^4+14 a c d^2 e^2+3 c^2 d^4\right)+13 a^2 c d^2 e^4-9 a^3 e^6+a c^2 d^4 e^2+3 c^3 d^6\right)}{3 a d^2 e x^3 \left(c d^2-a e^2\right)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{5 \left(21 a^2 c d^2 e^4+21 a^3 e^6+15 a c^2 d^4 e^2+7 c^3 d^6\right) \tanh ^{-1}\left(\frac{x \left(a e^2+c d^2\right)+2 a d e}{2 \sqrt{a} \sqrt{d} \sqrt{e} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}\right)}{16 a^{9/2} d^{11/2} e^{9/2}}-\frac{2 e (a e+c d x)}{3 d x^3 \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*e*(a*e + c*d*x))/(3*d*(c*d^2 - a*e^2)*x^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (2*(3*c^3*d^6 + a*c^2*d^4*e^2 + 13*a^2*c*d^2*e^4 - 9*a^3*e^6 + c*d*e*(3*c^2*d^4 + 14*a*c*d^2*e^2 - 9*a^2*e^4)*x))/(3*a*d^2*e*(c*d^2 - a*e^2)^3*x^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - ((7*c^3*d^6 - 3*a*c^2*d^4*e^2 + 33*a^2*c*d^2*e^4 - 21*a^3*e^6)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*a^2*d^3*e^2*(c*d^2 - a*e^2)^3*x^3) + ((35*c^4*d^8 - 16*a*c^3*d^6*e^2 - 18*a^2*c^2*d^4*e^4 + 168*a^3*c*d^2*e^6 - 105*a^4*e^8)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*a^3*d^4*e^3*(c*d^2 - a*e^2)^3*x^2) - ((105*c^5*d^10 - 55*a*c^4*d^8*e^2 - 54*a^2*c^3*d^6*e^4 - 78*a^3*c^2*d^4*e^6 + 525*a^4*c*d^2*e^8 - 315*a^5*e^10)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(24*a^4*d^5*e^4*(c*d^2 - a*e^2)^3*x) + (5*(7*c^3*d^6 + 15*a*c^2*d^4*e^2 + 21*a^2*c*d^2*e^4 + 21*a^3*e^6)*ArcTanh[(2*a*d*e + (c*d^2 + a*e^2)*x)/(2*Sqrt[a]*Sqrt[d]*Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])])/(16*a^(9/2)*d^(11/2)*e^(9/2))","A",8,6,40,0.1500,1,"{851, 822, 834, 806, 724, 206}"
487,1,259,0,0.2358263,"\int \frac{x^2}{(d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[x^2/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{8 \left(5 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right) \left(a e^2+c d^2+2 c d e x\right)}{15 e \left(c d^2-a e^2\right)^5 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{8 \left(x \left(a^2 c d^2 e^4-2 a^3 e^6+c^3 d^6\right)+a d e \left(c d^2-a e^2\right) \left(3 a e^2+c d^2\right)\right)}{15 e \left(c d^2-a e^2\right)^4 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}+\frac{2 x^2}{5 (d+e x) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","\frac{8 \left(5 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right) \left(a e^2+c d^2+2 c d e x\right)}{15 e \left(c d^2-a e^2\right)^5 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{8 \left(x \left(a^2 c d^2 e^4-2 a^3 e^6+c^3 d^6\right)+a d e \left(c d^2-a e^2\right) \left(3 a e^2+c d^2\right)\right)}{15 e \left(c d^2-a e^2\right)^4 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}+\frac{2 x^2}{5 (d+e x) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(2*x^2)/(5*(c*d^2 - a*e^2)*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (8*(a*d*e*(c*d^2 - a*e^2)*(c*d^2 + 3*a*e^2) + (c^3*d^6 + a^2*c*d^2*e^4 - 2*a^3*e^6)*x))/(15*e*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (8*(c^2*d^4 + 10*a*c*d^2*e^2 + 5*a^2*e^4)*(c*d^2 + a*e^2 + 2*c*d*e*x))/(15*e*(c*d^2 - a*e^2)^5*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",3,3,40,0.07500,1,"{854, 777, 613}"
488,1,341,0,0.288833,"\int \frac{x^2}{(d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{7/2}} \, dx","Int[x^2/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2)),x]","-\frac{128 c d \left(7 a^2 e^4+14 a c d^2 e^2+3 c^2 d^4\right) \left(a e^2+c d^2+2 c d e x\right)}{105 \left(c d^2-a e^2\right)^7 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{16 \left(7 a^2 e^4+14 a c d^2 e^2+3 c^2 d^4\right) \left(a e^2+c d^2+2 c d e x\right)}{105 e \left(c d^2-a e^2\right)^5 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}-\frac{8 \left(x \left(3 a^2 e^4+a c d^2 e^2+2 c^2 d^4\right)+2 a d e \left(2 a e^2+c d^2\right)\right)}{35 e \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}+\frac{2 x^2}{7 (d+e x) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}","-\frac{128 c d \left(7 a^2 e^4+14 a c d^2 e^2+3 c^2 d^4\right) \left(a e^2+c d^2+2 c d e x\right)}{105 \left(c d^2-a e^2\right)^7 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{16 \left(7 a^2 e^4+14 a c d^2 e^2+3 c^2 d^4\right) \left(a e^2+c d^2+2 c d e x\right)}{105 e \left(c d^2-a e^2\right)^5 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}-\frac{8 \left(x \left(3 a^2 e^4+a c d^2 e^2+2 c^2 d^4\right)+2 a d e \left(2 a e^2+c d^2\right)\right)}{35 e \left(c d^2-a e^2\right)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}+\frac{2 x^2}{7 (d+e x) \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}",1,"(2*x^2)/(7*(c*d^2 - a*e^2)*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)) - (8*(2*a*d*e*(c*d^2 + 2*a*e^2) + (2*c^2*d^4 + a*c*d^2*e^2 + 3*a^2*e^4)*x))/(35*e*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)) + (16*(3*c^2*d^4 + 14*a*c*d^2*e^2 + 7*a^2*e^4)*(c*d^2 + a*e^2 + 2*c*d*e*x))/(105*e*(c*d^2 - a*e^2)^5*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (128*c*d*(3*c^2*d^4 + 14*a*c*d^2*e^2 + 7*a^2*e^4)*(c*d^2 + a*e^2 + 2*c*d*e*x))/(105*(c*d^2 - a*e^2)^7*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",4,4,40,0.1000,1,"{854, 777, 614, 613}"
489,1,170,0,0.0656172,"\int x^3 \sqrt{1+x} \sqrt{1-x+x^2} \, dx","Int[x^3*Sqrt[1 + x]*Sqrt[1 - x + x^2],x]","\frac{2}{11} \sqrt{x+1} \sqrt{x^2-x+1} x^4+\frac{6}{55} \sqrt{x+1} \sqrt{x^2-x+1} x-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","\frac{2}{11} \sqrt{x+1} \sqrt{x^2-x+1} x^4+\frac{6}{55} \sqrt{x+1} \sqrt{x^2-x+1} x-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(6*x*Sqrt[1 + x]*Sqrt[1 - x + x^2])/55 + (2*x^4*Sqrt[1 + x]*Sqrt[1 - x + x^2])/11 - (4*3^(3/4)*Sqrt[2 + Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(55*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",4,4,23,0.1739,1,"{915, 279, 321, 218}"
490,1,23,0,0.0178384,"\int x^2 \sqrt{1+x} \sqrt{1-x+x^2} \, dx","Int[x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2],x]","\frac{2}{9} (x+1)^{3/2} \left(x^2-x+1\right)^{3/2}","\frac{2}{9} (x+1)^{3/2} \left(x^2-x+1\right)^{3/2}",1,"(2*(1 + x)^(3/2)*(1 - x + x^2)^(3/2))/9","A",1,1,23,0.04348,1,"{913}"
491,1,294,0,0.0945421,"\int x \sqrt{1+x} \sqrt{1-x+x^2} \, dx","Int[x*Sqrt[1 + x]*Sqrt[1 - x + x^2],x]","\frac{2}{7} \sqrt{x+1} \sqrt{x^2-x+1} x^2+\frac{6 \sqrt{x+1} \sqrt{x^2-x+1}}{7 \left(x+\sqrt{3}+1\right)}+\frac{2 \sqrt{2} 3^{3/4} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","\frac{2}{7} \sqrt{x+1} \sqrt{x^2-x+1} x^2+\frac{6 \sqrt{x+1} \sqrt{x^2-x+1}}{7 \left(x+\sqrt{3}+1\right)}+\frac{2 \sqrt{2} 3^{3/4} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(2*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2])/7 + (6*Sqrt[1 + x]*Sqrt[1 - x + x^2])/(7*(1 + Sqrt[3] + x)) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(7*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3)) + (2*Sqrt[2]*3^(3/4)*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(7*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",5,5,21,0.2381,1,"{809, 279, 303, 218, 1877}"
492,1,144,0,0.0324381,"\int \sqrt{1+x} \sqrt{1-x+x^2} \, dx","Int[Sqrt[1 + x]*Sqrt[1 - x + x^2],x]","\frac{2}{5} x \sqrt{x^2-x+1} \sqrt{x+1}+\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","\frac{2}{5} x \sqrt{x^2-x+1} \sqrt{x+1}+\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(2*x*Sqrt[1 + x]*Sqrt[1 - x + x^2])/5 + (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(5*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",3,3,20,0.1500,1,"{713, 195, 218}"
493,1,66,0,0.032602,"\int \frac{\sqrt{1+x} \sqrt{1-x+x^2}}{x} \, dx","Int[(Sqrt[1 + x]*Sqrt[1 - x + x^2])/x,x]","\frac{2}{3} \sqrt{x+1} \sqrt{x^2-x+1}-\frac{2 \sqrt{x+1} \sqrt{x^2-x+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x^3+1}}","\frac{2}{3} \sqrt{x+1} \sqrt{x^2-x+1}-\frac{2 \sqrt{x+1} \sqrt{x^2-x+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x^3+1}}",1,"(2*Sqrt[1 + x]*Sqrt[1 - x + x^2])/3 - (2*Sqrt[1 + x]*Sqrt[1 - x + x^2]*ArcTanh[Sqrt[1 + x^3]])/(3*Sqrt[1 + x^3])","A",5,5,23,0.2174,1,"{915, 266, 50, 63, 207}"
494,1,287,0,0.0974466,"\int \frac{\sqrt{1+x} \sqrt{1-x+x^2}}{x^2} \, dx","Int[(Sqrt[1 + x]*Sqrt[1 - x + x^2])/x^2,x]","-\frac{\sqrt{x^2-x+1} \sqrt{x+1}}{x}+\frac{3 \sqrt{x^2-x+1} \sqrt{x+1}}{x+\sqrt{3}+1}+\frac{\sqrt{2} 3^{3/4} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","-\frac{\sqrt{x^2-x+1} \sqrt{x+1}}{x}+\frac{3 \sqrt{x^2-x+1} \sqrt{x+1}}{x+\sqrt{3}+1}+\frac{\sqrt{2} 3^{3/4} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"-((Sqrt[1 + x]*Sqrt[1 - x + x^2])/x) + (3*Sqrt[1 + x]*Sqrt[1 - x + x^2])/(1 + Sqrt[3] + x) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3)) + (Sqrt[2]*3^(3/4)*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",5,5,23,0.2174,1,"{915, 277, 303, 218, 1877}"
495,1,146,0,0.0443619,"\int \frac{\sqrt{1+x} \sqrt{1-x+x^2}}{x^3} \, dx","Int[(Sqrt[1 + x]*Sqrt[1 - x + x^2])/x^3,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{\sqrt{x+1} \sqrt{x^2-x+1}}{2 x^2}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{\sqrt{x+1} \sqrt{x^2-x+1}}{2 x^2}",1,"-(Sqrt[1 + x]*Sqrt[1 - x + x^2])/(2*x^2) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",3,3,23,0.1304,1,"{915, 277, 218}"
496,1,201,0,0.0761565,"\int x^3 (1+x)^{3/2} \left(1-x+x^2\right)^{3/2} \, dx","Int[x^3*(1 + x)^(3/2)*(1 - x + x^2)^(3/2),x]","\frac{2}{17} \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right) x^4+\frac{18}{187} \sqrt{x+1} \sqrt{x^2-x+1} x^4+\frac{54}{935} \sqrt{x+1} \sqrt{x^2-x+1} x-\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{935 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","\frac{2}{17} \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right) x^4+\frac{18}{187} \sqrt{x+1} \sqrt{x^2-x+1} x^4+\frac{54}{935} \sqrt{x+1} \sqrt{x^2-x+1} x-\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{935 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(54*x*Sqrt[1 + x]*Sqrt[1 - x + x^2])/935 + (18*x^4*Sqrt[1 + x]*Sqrt[1 - x + x^2])/187 + (2*x^4*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3))/17 - (36*3^(3/4)*Sqrt[2 + Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(935*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",5,4,23,0.1739,1,"{915, 279, 321, 218}"
497,1,23,0,0.0208217,"\int x^2 (1+x)^{3/2} \left(1-x+x^2\right)^{3/2} \, dx","Int[x^2*(1 + x)^(3/2)*(1 - x + x^2)^(3/2),x]","\frac{2}{15} (x+1)^{5/2} \left(x^2-x+1\right)^{5/2}","\frac{2}{15} (x+1)^{5/2} \left(x^2-x+1\right)^{5/2}",1,"(2*(1 + x)^(5/2)*(1 - x + x^2)^(5/2))/15","A",1,1,23,0.04348,1,"{913}"
498,1,325,0,0.1067913,"\int x (1+x)^{3/2} \left(1-x+x^2\right)^{3/2} \, dx","Int[x*(1 + x)^(3/2)*(1 - x + x^2)^(3/2),x]","\frac{2}{13} \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right) x^2+\frac{18}{91} \sqrt{x+1} \sqrt{x^2-x+1} x^2+\frac{54 \sqrt{x+1} \sqrt{x^2-x+1}}{91 \left(x+\sqrt{3}+1\right)}+\frac{18 \sqrt{2} 3^{3/4} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","\frac{2}{13} \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right) x^2+\frac{18}{91} \sqrt{x+1} \sqrt{x^2-x+1} x^2+\frac{54 \sqrt{x+1} \sqrt{x^2-x+1}}{91 \left(x+\sqrt{3}+1\right)}+\frac{18 \sqrt{2} 3^{3/4} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(18*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2])/91 + (54*Sqrt[1 + x]*Sqrt[1 - x + x^2])/(91*(1 + Sqrt[3] + x)) + (2*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3))/13 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(91*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3)) + (18*Sqrt[2]*3^(3/4)*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(91*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",6,5,21,0.2381,1,"{809, 279, 303, 218, 1877}"
499,1,173,0,0.0457231,"\int (1+x)^{3/2} \left(1-x+x^2\right)^{3/2} \, dx","Int[(1 + x)^(3/2)*(1 - x + x^2)^(3/2),x]","\frac{2}{11} x \sqrt{x^2-x+1} \left(x^3+1\right) \sqrt{x+1}+\frac{18}{55} x \sqrt{x^2-x+1} \sqrt{x+1}+\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","\frac{2}{11} x \sqrt{x^2-x+1} \left(x^3+1\right) \sqrt{x+1}+\frac{18}{55} x \sqrt{x^2-x+1} \sqrt{x+1}+\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(18*x*Sqrt[1 + x]*Sqrt[1 - x + x^2])/55 + (2*x*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3))/11 + (18*3^(3/4)*Sqrt[2 + Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(55*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",4,3,20,0.1500,1,"{713, 195, 218}"
500,1,94,0,0.0406819,"\int \frac{(1+x)^{3/2} \left(1-x+x^2\right)^{3/2}}{x} \, dx","Int[((1 + x)^(3/2)*(1 - x + x^2)^(3/2))/x,x]","\frac{2}{9} \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)+\frac{2}{3} \sqrt{x+1} \sqrt{x^2-x+1}-\frac{2 \sqrt{x+1} \sqrt{x^2-x+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x^3+1}}","\frac{2}{9} \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)+\frac{2}{3} \sqrt{x+1} \sqrt{x^2-x+1}-\frac{2 \sqrt{x+1} \sqrt{x^2-x+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x^3+1}}",1,"(2*Sqrt[1 + x]*Sqrt[1 - x + x^2])/3 + (2*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3))/9 - (2*Sqrt[1 + x]*Sqrt[1 - x + x^2]*ArcTanh[Sqrt[1 + x^3]])/(3*Sqrt[1 + x^3])","A",6,5,23,0.2174,1,"{915, 266, 50, 63, 207}"
501,1,323,0,0.1114327,"\int \frac{(1+x)^{3/2} \left(1-x+x^2\right)^{3/2}}{x^2} \, dx","Int[((1 + x)^(3/2)*(1 - x + x^2)^(3/2))/x^2,x]","\frac{9}{7} \sqrt{x+1} \sqrt{x^2-x+1} x^2+\frac{27 \sqrt{x+1} \sqrt{x^2-x+1}}{7 \left(x+\sqrt{3}+1\right)}-\frac{\sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}{x}+\frac{9 \sqrt{2} 3^{3/4} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{14 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","\frac{9}{7} \sqrt{x+1} \sqrt{x^2-x+1} x^2+\frac{27 \sqrt{x+1} \sqrt{x^2-x+1}}{7 \left(x+\sqrt{3}+1\right)}-\frac{\sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}{x}+\frac{9 \sqrt{2} 3^{3/4} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1)^{3/2} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{14 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(9*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2])/7 + (27*Sqrt[1 + x]*Sqrt[1 - x + x^2])/(7*(1 + Sqrt[3] + x)) - (Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3))/x - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(14*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3)) + (9*Sqrt[2]*3^(3/4)*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(7*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",6,6,23,0.2609,1,"{915, 277, 279, 303, 218, 1877}"
502,1,175,0,0.0584062,"\int \frac{(1+x)^{3/2} \left(1-x+x^2\right)^{3/2}}{x^3} \, dx","Int[((1 + x)^(3/2)*(1 - x + x^2)^(3/2))/x^3,x]","-\frac{\sqrt{x^2-x+1} \left(x^3+1\right) \sqrt{x+1}}{2 x^2}+\frac{9}{10} x \sqrt{x^2-x+1} \sqrt{x+1}+\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{10 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","-\frac{\sqrt{x^2-x+1} \left(x^3+1\right) \sqrt{x+1}}{2 x^2}+\frac{9}{10} x \sqrt{x^2-x+1} \sqrt{x+1}+\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{10 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(9*x*Sqrt[1 + x]*Sqrt[1 - x + x^2])/10 - (Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3))/(2*x^2) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(10*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",4,4,23,0.1739,1,"{915, 277, 195, 218}"
503,1,142,0,0.0472602,"\int \frac{x^3}{\sqrt{1+x} \sqrt{1-x+x^2}} \, dx","Int[x^3/(Sqrt[1 + x]*Sqrt[1 - x + x^2]),x]","\frac{2 x \left(x^3+1\right)}{5 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{4 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{2 x \left(x^3+1\right)}{5 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{4 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(2*x*(1 + x^3))/(5*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (4*Sqrt[2 + Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",3,3,23,0.1304,1,"{915, 321, 218}"
504,1,23,0,0.0187211,"\int \frac{x^2}{\sqrt{1+x} \sqrt{1-x+x^2}} \, dx","Int[x^2/(Sqrt[1 + x]*Sqrt[1 - x + x^2]),x]","\frac{2}{3} \sqrt{x+1} \sqrt{x^2-x+1}","\frac{2}{3} \sqrt{x+1} \sqrt{x^2-x+1}",1,"(2*Sqrt[1 + x]*Sqrt[1 - x + x^2])/3","A",1,1,23,0.04348,1,"{913}"
505,1,253,0,0.0628543,"\int \frac{x}{\sqrt{1+x} \sqrt{1-x+x^2}} \, dx","Int[x/(Sqrt[1 + x]*Sqrt[1 - x + x^2]),x]","\frac{2 \left(x^3+1\right)}{\sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{2 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{2 \left(x^3+1\right)}{\sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{2 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(2*(1 + x^3))/(Sqrt[1 + x]*(1 + Sqrt[3] + x)*Sqrt[1 - x + x^2]) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2]) + (2*Sqrt[2]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",4,4,21,0.1905,1,"{809, 303, 218, 1877}"
506,1,110,0,0.0219877,"\int \frac{1}{\sqrt{1+x} \sqrt{1-x+x^2}} \, dx","Int[1/(Sqrt[1 + x]*Sqrt[1 - x + x^2]),x]","\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(2*Sqrt[2 + Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",2,2,20,0.1000,1,"{713, 218}"
507,1,42,0,0.0263797,"\int \frac{1}{x \sqrt{1+x} \sqrt{1-x+x^2}} \, dx","Int[1/(x*Sqrt[1 + x]*Sqrt[1 - x + x^2]),x]","-\frac{2 \sqrt{x^3+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x+1} \sqrt{x^2-x+1}}","-\frac{2 \sqrt{x^3+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x+1} \sqrt{x^2-x+1}}",1,"(-2*Sqrt[1 + x^3]*ArcTanh[Sqrt[1 + x^3]])/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2])","A",4,4,23,0.1739,1,"{915, 266, 63, 207}"
508,1,282,0,0.0966822,"\int \frac{1}{x^2 \sqrt{1+x} \sqrt{1-x+x^2}} \, dx","Int[1/(x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2]),x]","-\frac{x^3+1}{x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{x^3+1}{\sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{\sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","-\frac{x^3+1}{x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{x^3+1}{\sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{\sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"-((1 + x^3)/(x*Sqrt[1 + x]*Sqrt[1 - x + x^2])) + (1 + x^3)/(Sqrt[1 + x]*(1 + Sqrt[3] + x)*Sqrt[1 - x + x^2]) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2]) + (Sqrt[2]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",5,5,23,0.2174,1,"{915, 325, 303, 218, 1877}"
509,1,144,0,0.0450628,"\int \frac{1}{x^3 \sqrt{1+x} \sqrt{1-x+x^2}} \, dx","Int[1/(x^3*Sqrt[1 + x]*Sqrt[1 - x + x^2]),x]","-\frac{x^3+1}{2 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{\sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","-\frac{x^3+1}{2 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{\sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"-(1 + x^3)/(2*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (Sqrt[2 + Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",3,3,23,0.1304,1,"{915, 325, 218}"
510,1,137,0,0.0483607,"\int \frac{x^3}{(1+x)^{3/2} \left(1-x+x^2\right)^{3/2}} \, dx","Int[x^3/((1 + x)^(3/2)*(1 - x + x^2)^(3/2)),x]","\frac{4 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{2 x}{3 \sqrt{x+1} \sqrt{x^2-x+1}}","\frac{4 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{2 x}{3 \sqrt{x+1} \sqrt{x^2-x+1}}",1,"(-2*x)/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + (4*Sqrt[2 + Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",3,3,23,0.1304,1,"{915, 288, 218}"
511,1,23,0,0.0211387,"\int \frac{x^2}{(1+x)^{3/2} \left(1-x+x^2\right)^{3/2}} \, dx","Int[x^2/((1 + x)^(3/2)*(1 - x + x^2)^(3/2)),x]","-\frac{2}{3 \sqrt{x+1} \sqrt{x^2-x+1}}","-\frac{2}{3 \sqrt{x+1} \sqrt{x^2-x+1}}",1,"-2/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2])","A",1,1,23,0.04348,1,"{913}"
512,1,282,0,0.0839747,"\int \frac{x}{(1+x)^{3/2} \left(1-x+x^2\right)^{3/2}} \, dx","Int[x/((1 + x)^(3/2)*(1 - x + x^2)^(3/2)),x]","\frac{2 x^2}{3 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{2 \left(x^3+1\right)}{3 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}-\frac{2 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}+\frac{\sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{2 x^2}{3 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{2 \left(x^3+1\right)}{3 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}-\frac{2 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}+\frac{\sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(2*x^2)/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (2*(1 + x^3))/(3*Sqrt[1 + x]*(1 + Sqrt[3] + x)*Sqrt[1 - x + x^2]) + (Sqrt[2 - Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2]) - (2*Sqrt[2]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",5,5,21,0.2381,1,"{809, 290, 303, 218, 1877}"
513,1,137,0,0.0330799,"\int \frac{1}{(1+x)^{3/2} \left(1-x+x^2\right)^{3/2}} \, dx","Int[1/((1 + x)^(3/2)*(1 - x + x^2)^(3/2)),x]","\frac{2 x}{3 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{2 x}{3 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(2*x)/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + (2*Sqrt[2 + Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",3,3,20,0.1500,1,"{713, 199, 218}"
514,1,66,0,0.0338986,"\int \frac{1}{x (1+x)^{3/2} \left(1-x+x^2\right)^{3/2}} \, dx","Int[1/(x*(1 + x)^(3/2)*(1 - x + x^2)^(3/2)),x]","\frac{2}{3 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{2 \sqrt{x^3+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x+1} \sqrt{x^2-x+1}}","\frac{2}{3 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{2 \sqrt{x^3+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x+1} \sqrt{x^2-x+1}}",1,"2/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (2*Sqrt[1 + x^3]*ArcTanh[Sqrt[1 + x^3]])/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2])","A",5,5,23,0.2174,1,"{915, 266, 51, 63, 207}"
515,1,316,0,0.1091264,"\int \frac{1}{x^2 (1+x)^{3/2} \left(1-x+x^2\right)^{3/2}} \, dx","Int[1/(x^2*(1 + x)^(3/2)*(1 - x + x^2)^(3/2)),x]","-\frac{5 \left(x^3+1\right)}{3 x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{5 \left(x^3+1\right)}{3 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{2}{3 x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{5 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{5 \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","-\frac{5 \left(x^3+1\right)}{3 x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{5 \left(x^3+1\right)}{3 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{2}{3 x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{5 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{5 \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"2/(3*x*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (5*(1 + x^3))/(3*x*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + (5*(1 + x^3))/(3*Sqrt[1 + x]*(1 + Sqrt[3] + x)*Sqrt[1 - x + x^2]) - (5*Sqrt[2 - Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2]) + (5*Sqrt[2]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",6,6,23,0.2609,1,"{915, 290, 325, 303, 218, 1877}"
516,1,170,0,0.0652856,"\int \frac{1}{x^3 (1+x)^{3/2} \left(1-x+x^2\right)^{3/2}} \, dx","Int[1/(x^3*(1 + x)^(3/2)*(1 - x + x^2)^(3/2)),x]","-\frac{7 \left(x^3+1\right)}{6 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2}{3 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{7 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","-\frac{7 \left(x^3+1\right)}{6 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2}{3 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{7 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"2/(3*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (7*(1 + x^3))/(6*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (7*Sqrt[2 + Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(6*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",4,4,23,0.1739,1,"{915, 290, 325, 218}"
517,1,168,0,0.0573901,"\int \frac{x^3}{(1+x)^{5/2} \left(1-x+x^2\right)^{5/2}} \, dx","Int[x^3/((1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]","\frac{4 x}{27 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{2 x}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}+\frac{4 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{4 x}{27 \sqrt{x+1} \sqrt{x^2-x+1}}-\frac{2 x}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}+\frac{4 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(4*x)/(27*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (2*x)/(9*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3)) + (4*Sqrt[2 + Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",4,4,23,0.1739,1,"{915, 288, 199, 218}"
518,1,23,0,0.0205386,"\int \frac{x^2}{(1+x)^{5/2} \left(1-x+x^2\right)^{5/2}} \, dx","Int[x^2/((1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]","-\frac{2}{9 (x+1)^{3/2} \left(x^2-x+1\right)^{3/2}}","-\frac{2}{9 (x+1)^{3/2} \left(x^2-x+1\right)^{3/2}}",1,"-2/(9*(1 + x)^(3/2)*(1 - x + x^2)^(3/2))","A",1,1,23,0.04348,1,"{913}"
519,1,318,0,0.1047183,"\int \frac{x}{(1+x)^{5/2} \left(1-x+x^2\right)^{5/2}} \, dx","Int[x/((1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]","\frac{10 x^2}{27 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 x^2}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}-\frac{10 \left(x^3+1\right)}{27 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}-\frac{10 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}+\frac{5 \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{10 x^2}{27 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 x^2}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}-\frac{10 \left(x^3+1\right)}{27 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}-\frac{10 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}+\frac{5 \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(10*x^2)/(27*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + (2*x^2)/(9*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3)) - (10*(1 + x^3))/(27*Sqrt[1 + x]*(1 + Sqrt[3] + x)*Sqrt[1 - x + x^2]) + (5*Sqrt[2 - Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2]) - (10*Sqrt[2]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",6,5,21,0.2381,1,"{809, 290, 303, 218, 1877}"
520,1,168,0,0.0438769,"\int \frac{1}{(1+x)^{5/2} \left(1-x+x^2\right)^{5/2}} \, dx","Int[1/((1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]","\frac{14 x}{27 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 x}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}+\frac{14 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{14 x}{27 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 x}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}+\frac{14 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(14*x)/(27*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + (2*x)/(9*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3)) + (14*Sqrt[2 + Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",4,3,20,0.1500,1,"{713, 199, 218}"
521,1,96,0,0.0368954,"\int \frac{1}{x (1+x)^{5/2} \left(1-x+x^2\right)^{5/2}} \, dx","Int[1/(x*(1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]","\frac{2}{3 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}-\frac{2 \sqrt{x^3+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x+1} \sqrt{x^2-x+1}}","\frac{2}{3 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}-\frac{2 \sqrt{x^3+1} \tanh ^{-1}\left(\sqrt{x^3+1}\right)}{3 \sqrt{x+1} \sqrt{x^2-x+1}}",1,"2/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + 2/(9*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3)) - (2*Sqrt[1 + x^3]*ArcTanh[Sqrt[1 + x^3]])/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2])","A",6,5,23,0.2174,1,"{915, 266, 51, 63, 207}"
522,1,349,0,0.139555,"\int \frac{1}{x^2 (1+x)^{5/2} \left(1-x+x^2\right)^{5/2}} \, dx","Int[1/(x^2*(1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]","-\frac{55 \left(x^3+1\right)}{27 x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{55 \left(x^3+1\right)}{27 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{22}{27 x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2}{9 x \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}+\frac{55 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{55 \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{18\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","-\frac{55 \left(x^3+1\right)}{27 x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{55 \left(x^3+1\right)}{27 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{22}{27 x \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2}{9 x \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}+\frac{55 \sqrt{2} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{55 \sqrt{2-\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{18\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"22/(27*x*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + 2/(9*x*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3)) - (55*(1 + x^3))/(27*x*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + (55*(1 + x^3))/(27*Sqrt[1 + x]*(1 + Sqrt[3] + x)*Sqrt[1 - x + x^2]) - (55*Sqrt[2 - Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(18*3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2]) + (55*Sqrt[2]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",7,6,23,0.2609,1,"{915, 290, 325, 303, 218, 1877}"
523,1,203,0,0.0724538,"\int \frac{1}{x^3 (1+x)^{5/2} \left(1-x+x^2\right)^{5/2}} \, dx","Int[1/(x^3*(1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]","-\frac{91 \left(x^3+1\right)}{54 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{26}{27 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2}{9 x^2 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}-\frac{91 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{54 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","-\frac{91 \left(x^3+1\right)}{54 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{26}{27 x^2 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2}{9 x^2 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}-\frac{91 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{54 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"26/(27*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + 2/(9*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3)) - (91*(1 + x^3))/(54*x^2*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (91*Sqrt[2 + Sqrt[3]]*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(54*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",5,4,23,0.1739,1,"{915, 290, 325, 218}"
524,1,97,0,0.0713876,"\int \frac{x}{(-1+x)^3 \left(3+5 x+4 x^2\right)^2} \, dx","Int[x/((-1 + x)^3*(3 + 5*x + 4*x^2)^2),x]","\frac{44 x+39}{276 (1-x)^2 \left(4 x^2+5 x+3\right)}-\frac{11 \log \left(4 x^2+5 x+3\right)}{4608}-\frac{97}{4416 (1-x)}-\frac{21}{736 (1-x)^2}+\frac{11 \log (1-x)}{2304}+\frac{6023 \tan ^{-1}\left(\frac{8 x+5}{\sqrt{23}}\right)}{52992 \sqrt{23}}","\frac{44 x+39}{276 (1-x)^2 \left(4 x^2+5 x+3\right)}-\frac{11 \log \left(4 x^2+5 x+3\right)}{4608}-\frac{97}{4416 (1-x)}-\frac{21}{736 (1-x)^2}+\frac{11 \log (1-x)}{2304}+\frac{6023 \tan ^{-1}\left(\frac{8 x+5}{\sqrt{23}}\right)}{52992 \sqrt{23}}",1,"-21/(736*(1 - x)^2) - 97/(4416*(1 - x)) + (39 + 44*x)/(276*(1 - x)^2*(3 + 5*x + 4*x^2)) + (6023*ArcTan[(5 + 8*x)/Sqrt[23]])/(52992*Sqrt[23]) + (11*Log[1 - x])/2304 - (11*Log[3 + 5*x + 4*x^2])/4608","A",7,6,19,0.3158,1,"{822, 800, 634, 618, 204, 628}"
525,1,490,0,14.846818,"\int \frac{x^4 \sqrt{d+e x}}{a+b x+c x^2} \, dx","Int[(x^4*Sqrt[d + e*x])/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(-\frac{-5 a^2 b c^2 e+2 a^2 c^3 d-4 a b^2 c^2 d+5 a b^3 c e+b^4 c d+b^5 (-e)}{\sqrt{b^2-4 a c}}-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^3 c d+b^4 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{9/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(\frac{-5 a^2 b c^2 e+2 a^2 c^3 d-4 a b^2 c^2 d+5 a b^3 c e+b^4 c d+b^5 (-e)}{\sqrt{b^2-4 a c}}-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^3 c d+b^4 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{9/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 (d+e x)^{3/2} \left(c e (b d-a e)+b^2 e^2+c^2 d^2\right)}{3 c^3 e^3}-\frac{2 b \left(b^2-2 a c\right) \sqrt{d+e x}}{c^4}-\frac{2 (d+e x)^{5/2} (b e+2 c d)}{5 c^2 e^3}+\frac{2 (d+e x)^{7/2}}{7 c e^3}","\frac{\sqrt{2} \left(-\frac{-5 a^2 b c^2 e+2 a^2 c^3 d-4 a b^2 c^2 d+5 a b^3 c e+b^4 c d+b^5 (-e)}{\sqrt{b^2-4 a c}}-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^3 c d+b^4 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{9/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(\frac{-5 a^2 b c^2 e+2 a^2 c^3 d-4 a b^2 c^2 d+5 a b^3 c e+b^4 c d+b^5 (-e)}{\sqrt{b^2-4 a c}}-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^3 c d+b^4 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{9/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 (d+e x)^{3/2} \left(c e (b d-a e)+b^2 e^2+c^2 d^2\right)}{3 c^3 e^3}-\frac{2 b \left(b^2-2 a c\right) \sqrt{d+e x}}{c^4}-\frac{2 (d+e x)^{5/2} (b e+2 c d)}{5 c^2 e^3}+\frac{2 (d+e x)^{7/2}}{7 c e^3}",1,"(-2*b*(b^2 - 2*a*c)*Sqrt[d + e*x])/c^4 + (2*(c^2*d^2 + b^2*e^2 + c*e*(b*d - a*e))*(d + e*x)^(3/2))/(3*c^3*e^3) - (2*(2*c*d + b*e)*(d + e*x)^(5/2))/(5*c^2*e^3) + (2*(d + e*x)^(7/2))/(7*c*e^3) + (Sqrt[2]*(b^3*c*d - 2*a*b*c^2*d - b^4*e + 3*a*b^2*c*e - a^2*c^2*e - (b^4*c*d - 4*a*b^2*c^2*d + 2*a^2*c^3*d - b^5*e + 5*a*b^3*c*e - 5*a^2*b*c^2*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(9/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*(b^3*c*d - 2*a*b*c^2*d - b^4*e + 3*a*b^2*c*e - a^2*c^2*e + (b^4*c*d - 4*a*b^2*c^2*d + 2*a^2*c^3*d - b^5*e + 5*a*b^3*c*e - 5*a^2*b*c^2*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(9/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,4,25,0.1600,1,"{897, 1287, 1166, 208}"
526,1,397,0,7.4658423,"\int \frac{x^3 \sqrt{d+e x}}{a+b x+c x^2} \, dx","Int[(x^3*Sqrt[d + e*x])/(a + b*x + c*x^2),x]","-\frac{\sqrt{2} \left(-\frac{-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)}{\sqrt{b^2-4 a c}}+2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{7/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \left(\frac{-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)}{\sqrt{b^2-4 a c}}+2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{7/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \left(b^2-a c\right) \sqrt{d+e x}}{c^3}-\frac{2 (d+e x)^{3/2} (b e+c d)}{3 c^2 e^2}+\frac{2 (d+e x)^{5/2}}{5 c e^2}","\frac{2 \left(b^2-a c\right) \sqrt{d+e x}}{c^3}+\frac{\left(-\sqrt{b^2-4 a c} \left(b^2-a c\right)-3 a b c+b^3\right) \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{7/2} \sqrt{b^2-4 a c}}-\frac{\left(\sqrt{b^2-4 a c} \left(b^2-a c\right)-3 a b c+b^3\right) \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{7/2} \sqrt{b^2-4 a c}}-\frac{2 (d+e x)^{3/2} (b e+c d)}{3 c^2 e^2}+\frac{2 (d+e x)^{5/2}}{5 c e^2}",1,"(2*(b^2 - a*c)*Sqrt[d + e*x])/c^3 - (2*(c*d + b*e)*(d + e*x)^(3/2))/(3*c^2*e^2) + (2*(d + e*x)^(5/2))/(5*c*e^2) - (Sqrt[2]*(b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e - (b^3*c*d - 3*a*b*c^2*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(7/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*(b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e + (b^3*c*d - 3*a*b*c^2*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(7/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,4,25,0.1600,1,"{897, 1287, 1166, 208}"
527,1,316,0,3.1581663,"\int \frac{x^2 \sqrt{d+e x}}{a+b x+c x^2} \, dx","Int[(x^2*Sqrt[d + e*x])/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 b \sqrt{d+e x}}{c^2}+\frac{2 (d+e x)^{3/2}}{3 c e}","\frac{\sqrt{2} \left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 b \sqrt{d+e x}}{c^2}+\frac{2 (d+e x)^{3/2}}{3 c e}",1,"(-2*b*Sqrt[d + e*x])/c^2 + (2*(d + e*x)^(3/2))/(3*c*e) + (Sqrt[2]*(b*c*d - b^2*e + a*c*e - (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(5/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*(b*c*d - b^2*e + a*c*e + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(5/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,4,25,0.1600,1,"{897, 1287, 1166, 208}"
528,1,287,0,3.1995121,"\int \frac{x \sqrt{d+e x}}{a+b x+c x^2} \, dx","Int[(x*Sqrt[d + e*x])/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(-\sqrt{b^2-4 a c} (c d-b e)+2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \left(\sqrt{b^2-4 a c} (c d-b e)+2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \sqrt{d+e x}}{c}","\frac{\sqrt{2} \left(-\sqrt{b^2-4 a c} (c d-b e)+2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \left(\sqrt{b^2-4 a c} (c d-b e)+2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \sqrt{d+e x}}{c}",1,"(2*Sqrt[d + e*x])/c + (Sqrt[2]*(b*c*d - b^2*e + 2*a*c*e - Sqrt[b^2 - 4*a*c]*(c*d - b*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*(b*c*d - b^2*e + 2*a*c*e + Sqrt[b^2 - 4*a*c]*(c*d - b*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",5,4,23,0.1739,1,"{824, 826, 1166, 208}"
529,1,198,0,0.2714925,"\int \frac{\sqrt{d+e x}}{a+b x+c x^2} \, dx","Int[Sqrt[d + e*x]/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{c} \sqrt{b^2-4 a c}}","\frac{\sqrt{2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{c} \sqrt{b^2-4 a c}}",1,"-((Sqrt[2]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[c]*Sqrt[b^2 - 4*a*c])) + (Sqrt[2]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[c]*Sqrt[b^2 - 4*a*c])","A",4,3,22,0.1364,1,"{699, 1130, 208}"
530,1,275,0,1.1290085,"\int \frac{\sqrt{d+e x}}{x \left(a+b x+c x^2\right)} \, dx","Int[Sqrt[d + e*x]/(x*(a + b*x + c*x^2)),x]","\frac{\sqrt{2} \sqrt{c} \left(d \sqrt{b^2-4 a c}-2 a e+b d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \sqrt{c} \left(-d \sqrt{b^2-4 a c}-2 a e+b d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a}","\frac{\sqrt{2} \sqrt{c} \left(d \sqrt{b^2-4 a c}-2 a e+b d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \sqrt{c} \left(-d \sqrt{b^2-4 a c}-2 a e+b d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a}",1,"(-2*Sqrt[d]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/a + (Sqrt[2]*Sqrt[c]*(b*d + Sqrt[b^2 - 4*a*c]*d - 2*a*e)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(a*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*Sqrt[c]*(b*d - Sqrt[b^2 - 4*a*c]*d - 2*a*e)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(a*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",7,5,25,0.2000,1,"{897, 1287, 206, 1166, 208}"
531,1,356,0,3.6641071,"\int \frac{\sqrt{d+e x}}{x^2 \left(a+b x+c x^2\right)} \, dx","Int[Sqrt[d + e*x]/(x^2*(a + b*x + c*x^2)),x]","-\frac{\sqrt{2} \sqrt{c} \left(\sqrt{b^2-4 a c} (b d-a e)-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \sqrt{c} \left(-\sqrt{b^2-4 a c} (b d-a e)-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 (b d-a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a^2 \sqrt{d}}-\frac{\sqrt{d+e x}}{a x}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a \sqrt{d}}","-\frac{\sqrt{2} \sqrt{c} \left(\sqrt{b^2-4 a c} (b d-a e)-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \sqrt{c} \left(-b \left(d \sqrt{b^2-4 a c}+a e\right)-a \left(2 c d-e \sqrt{b^2-4 a c}\right)+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 (b d-a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a^2 \sqrt{d}}-\frac{\sqrt{d+e x}}{a x}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a \sqrt{d}}",1,"-(Sqrt[d + e*x]/(a*x)) + (e*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(a*Sqrt[d]) + (2*(b*d - a*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(a^2*Sqrt[d]) - (Sqrt[2]*Sqrt[c]*(b^2*d - 2*a*c*d - a*b*e + Sqrt[b^2 - 4*a*c]*(b*d - a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(a^2*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*Sqrt[c]*(b^2*d - 2*a*c*d - a*b*e - Sqrt[b^2 - 4*a*c]*(b*d - a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(a^2*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",9,6,25,0.2400,1,"{897, 1287, 199, 206, 1166, 208}"
532,1,531,0,3.5689978,"\int \frac{\sqrt{d+e x}}{x^3 \left(a+b x+c x^2\right)} \, dx","Int[Sqrt[d + e*x]/(x^3*(a + b*x + c*x^2)),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(-a b e-a c d+b^2 d\right)}{a^3 \sqrt{d}}+\frac{\sqrt{2} \sqrt{c} \left(b^2 \left(d \sqrt{b^2-4 a c}-a e\right)-a b \left(e \sqrt{b^2-4 a c}+3 c d\right)-a c \left(d \sqrt{b^2-4 a c}-2 a e\right)+b^3 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \sqrt{c} \left(-b^2 \left(d \sqrt{b^2-4 a c}+a e\right)-a b \left(3 c d-e \sqrt{b^2-4 a c}\right)+a c \left(d \sqrt{b^2-4 a c}+2 a e\right)+b^3 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{e (b d-a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a^2 d^{3/2}}+\frac{\sqrt{d+e x} (b d-a e)}{a^2 d x}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 a d^{3/2}}-\frac{\sqrt{d+e x}}{2 a x^2}+\frac{3 e \sqrt{d+e x}}{4 a d x}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(-a b e-a c d+b^2 d\right)}{a^3 \sqrt{d}}+\frac{\sqrt{2} \sqrt{c} \left(b^2 \left(d \sqrt{b^2-4 a c}-a e\right)-a b \left(e \sqrt{b^2-4 a c}+3 c d\right)-a c \left(d \sqrt{b^2-4 a c}-2 a e\right)+b^3 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \sqrt{c} \left(-b^2 \left(d \sqrt{b^2-4 a c}+a e\right)-a b \left(3 c d-e \sqrt{b^2-4 a c}\right)+a c \left(d \sqrt{b^2-4 a c}+2 a e\right)+b^3 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{e (b d-a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a^2 d^{3/2}}+\frac{\sqrt{d+e x} (b d-a e)}{a^2 d x}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 a d^{3/2}}-\frac{\sqrt{d+e x}}{2 a x^2}+\frac{3 e \sqrt{d+e x}}{4 a d x}",1,"-Sqrt[d + e*x]/(2*a*x^2) + (3*e*Sqrt[d + e*x])/(4*a*d*x) + ((b*d - a*e)*Sqrt[d + e*x])/(a^2*d*x) - (3*e^2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*a*d^(3/2)) - (e*(b*d - a*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(a^2*d^(3/2)) - (2*(b^2*d - a*c*d - a*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(a^3*Sqrt[d]) + (Sqrt[2]*Sqrt[c]*(b^3*d - a*c*(Sqrt[b^2 - 4*a*c]*d - 2*a*e) + b^2*(Sqrt[b^2 - 4*a*c]*d - a*e) - a*b*(3*c*d + Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(a^3*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*Sqrt[c]*(b^3*d - b^2*(Sqrt[b^2 - 4*a*c]*d + a*e) + a*c*(Sqrt[b^2 - 4*a*c]*d + 2*a*e) - a*b*(3*c*d - Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(a^3*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",12,6,25,0.2400,1,"{897, 1287, 199, 206, 1166, 208}"
533,1,650,0,2.6791786,"\int \frac{x^4 (d+e x)^{3/2}}{a+b x+c x^2} \, dx","Int[(x^4*(d + e*x)^(3/2))/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(\frac{10 a^2 b c^3 d e-2 a^2 c^3 \left(c d^2-a e^2\right)+a b^2 c^2 \left(4 c d^2-9 a e^2\right)-10 a b^3 c^2 d e-b^4 c \left(c d^2-6 a e^2\right)+2 b^5 c d e+b^6 \left(-e^2\right)}{\sqrt{b^2-4 a c}}+\left(a c e+b^2 (-e)+b c d\right) \left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{11/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(\left(a c e+b^2 (-e)+b c d\right) \left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right)-\frac{10 a^2 b c^3 d e-2 a^2 c^3 \left(c d^2-a e^2\right)+a b^2 c^2 \left(4 c d^2-9 a e^2\right)-10 a b^3 c^2 d e-b^4 c \left(c d^2-6 a e^2\right)+2 b^5 c d e+b^6 \left(-e^2\right)}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{11/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{d+e x} \left(-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^3 c d+b^4 (-e)\right)}{c^5}+\frac{2 (d+e x)^{5/2} \left(c e (b d-a e)+b^2 e^2+c^2 d^2\right)}{5 c^3 e^3}-\frac{2 b \left(b^2-2 a c\right) (d+e x)^{3/2}}{3 c^4}-\frac{2 (d+e x)^{7/2} (b e+2 c d)}{7 c^2 e^3}+\frac{2 (d+e x)^{9/2}}{9 c e^3}","\frac{\sqrt{2} \left(\frac{10 a^2 b c^3 d e-2 a^2 c^3 \left(c d^2-a e^2\right)+a b^2 c^2 \left(4 c d^2-9 a e^2\right)-10 a b^3 c^2 d e-b^4 c \left(c d^2-6 a e^2\right)+2 b^5 c d e+b^6 \left(-e^2\right)}{\sqrt{b^2-4 a c}}+\left(a c e+b^2 (-e)+b c d\right) \left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{11/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(\left(a c e+b^2 (-e)+b c d\right) \left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right)-\frac{10 a^2 b c^3 d e-2 a^2 c^3 \left(c d^2-a e^2\right)+a b^2 c^2 \left(4 c d^2-9 a e^2\right)-10 a b^3 c^2 d e-b^4 c \left(c d^2-6 a e^2\right)+2 b^5 c d e+b^6 \left(-e^2\right)}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{11/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{d+e x} \left(-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^3 c d+b^4 (-e)\right)}{c^5}+\frac{2 (d+e x)^{5/2} \left(c e (b d-a e)+b^2 e^2+c^2 d^2\right)}{5 c^3 e^3}-\frac{2 b \left(b^2-2 a c\right) (d+e x)^{3/2}}{3 c^4}-\frac{2 (d+e x)^{7/2} (b e+2 c d)}{7 c^2 e^3}+\frac{2 (d+e x)^{9/2}}{9 c e^3}",1,"(-2*(b^3*c*d - 2*a*b*c^2*d - b^4*e + 3*a*b^2*c*e - a^2*c^2*e)*Sqrt[d + e*x])/c^5 - (2*b*(b^2 - 2*a*c)*(d + e*x)^(3/2))/(3*c^4) + (2*(c^2*d^2 + b^2*e^2 + c*e*(b*d - a*e))*(d + e*x)^(5/2))/(5*c^3*e^3) - (2*(2*c*d + b*e)*(d + e*x)^(7/2))/(7*c^2*e^3) + (2*(d + e*x)^(9/2))/(9*c*e^3) + (Sqrt[2]*((b*c*d - b^2*e + a*c*e)*(b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e) + (2*b^5*c*d*e - 10*a*b^3*c^2*d*e + 10*a^2*b*c^3*d*e - b^6*e^2 + a*b^2*c^2*(4*c*d^2 - 9*a*e^2) - b^4*c*(c*d^2 - 6*a*e^2) - 2*a^2*c^3*(c*d^2 - a*e^2))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(11/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*((b*c*d - b^2*e + a*c*e)*(b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e) - (2*b^5*c*d*e - 10*a*b^3*c^2*d*e + 10*a^2*b*c^3*d*e - b^6*e^2 + a*b^2*c^2*(4*c*d^2 - 9*a*e^2) - b^4*c*(c*d^2 - 6*a*e^2) - 2*a^2*c^3*(c*d^2 - a*e^2))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(11/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,4,25,0.1600,1,"{897, 1287, 1166, 208}"
534,1,581,0,15.2472189,"\int \frac{x^3 (d+e x)^{3/2}}{a+b x+c x^2} \, dx","Int[(x^3*(d + e*x)^(3/2))/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(-\frac{4 a^2 c^3 d e-8 a b^2 c^2 d e-b^3 c \left(c d^2-5 a e^2\right)+a b c^2 \left(3 c d^2-5 a e^2\right)+2 b^4 c d e+b^5 \left(-e^2\right)}{\sqrt{b^2-4 a c}}-b^2 c \left(c d^2-3 a e^2\right)-4 a b c^2 d e+a c^2 \left(c d^2-a e^2\right)+2 b^3 c d e+b^4 \left(-e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{9/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(\frac{4 a^2 c^3 d e-8 a b^2 c^2 d e-b^3 c \left(c d^2-5 a e^2\right)+a b c^2 \left(3 c d^2-5 a e^2\right)+2 b^4 c d e+b^5 \left(-e^2\right)}{\sqrt{b^2-4 a c}}-b^2 c \left(c d^2-3 a e^2\right)-4 a b c^2 d e+a c^2 \left(c d^2-a e^2\right)+2 b^3 c d e+b^4 \left(-e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{9/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \left(b^2-a c\right) (d+e x)^{3/2}}{3 c^3}+\frac{2 \sqrt{d+e x} \left(2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right)}{c^4}-\frac{2 (d+e x)^{5/2} (b e+c d)}{5 c^2 e^2}+\frac{2 (d+e x)^{7/2}}{7 c e^2}","\frac{\sqrt{2} \left(-\frac{4 a^2 c^3 d e-8 a b^2 c^2 d e-b^3 c \left(c d^2-5 a e^2\right)+a b c^2 \left(3 c d^2-5 a e^2\right)+2 b^4 c d e+b^5 \left(-e^2\right)}{\sqrt{b^2-4 a c}}-b^2 c \left(c d^2-3 a e^2\right)-4 a b c^2 d e+a c^2 \left(c d^2-a e^2\right)+2 b^3 c d e+b^4 \left(-e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{9/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(\frac{4 a^2 c^3 d e-8 a b^2 c^2 d e-b^3 c \left(c d^2-5 a e^2\right)+a b c^2 \left(3 c d^2-5 a e^2\right)+2 b^4 c d e+b^5 \left(-e^2\right)}{\sqrt{b^2-4 a c}}-b^2 c \left(c d^2-3 a e^2\right)-4 a b c^2 d e+a c^2 \left(c d^2-a e^2\right)+2 b^3 c d e+b^4 \left(-e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{9/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \left(b^2-a c\right) (d+e x)^{3/2}}{3 c^3}+\frac{2 \sqrt{d+e x} \left(2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right)}{c^4}-\frac{2 (d+e x)^{5/2} (b e+c d)}{5 c^2 e^2}+\frac{2 (d+e x)^{7/2}}{7 c e^2}",1,"(2*(b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e)*Sqrt[d + e*x])/c^4 + (2*(b^2 - a*c)*(d + e*x)^(3/2))/(3*c^3) - (2*(c*d + b*e)*(d + e*x)^(5/2))/(5*c^2*e^2) + (2*(d + e*x)^(7/2))/(7*c*e^2) + (Sqrt[2]*(2*b^3*c*d*e - 4*a*b*c^2*d*e - b^4*e^2 - b^2*c*(c*d^2 - 3*a*e^2) + a*c^2*(c*d^2 - a*e^2) - (2*b^4*c*d*e - 8*a*b^2*c^2*d*e + 4*a^2*c^3*d*e - b^5*e^2 - b^3*c*(c*d^2 - 5*a*e^2) + a*b*c^2*(3*c*d^2 - 5*a*e^2))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(9/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*(2*b^3*c*d*e - 4*a*b*c^2*d*e - b^4*e^2 - b^2*c*(c*d^2 - 3*a*e^2) + a*c^2*(c*d^2 - a*e^2) + (2*b^4*c*d*e - 8*a*b^2*c^2*d*e + 4*a^2*c^3*d*e - b^5*e^2 - b^3*c*(c*d^2 - 5*a*e^2) + a*b*c^2*(3*c*d^2 - 5*a*e^2))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(9/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,4,25,0.1600,1,"{897, 1287, 1166, 208}"
535,1,441,0,2.1504937,"\int \frac{x^2 (d+e x)^{3/2}}{a+b x+c x^2} \, dx","Int[(x^2*(d + e*x)^(3/2))/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(\frac{-b^2 c \left(c d^2-4 a e^2\right)-6 a b c^2 d e+2 a c^2 \left(c d^2-a e^2\right)+2 b^3 c d e+b^4 \left(-e^2\right)}{\sqrt{b^2-4 a c}}+(c d-b e) \left(2 a c e+b^2 (-e)+b c d\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{7/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left((c d-b e) \left(2 a c e+b^2 (-e)+b c d\right)-\frac{-b^2 c \left(c d^2-4 a e^2\right)-6 a b c^2 d e+2 a c^2 \left(c d^2-a e^2\right)+2 b^3 c d e+b^4 \left(-e^2\right)}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{7/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{d+e x} \left(a c e+b^2 (-e)+b c d\right)}{c^3}-\frac{2 b (d+e x)^{3/2}}{3 c^2}+\frac{2 (d+e x)^{5/2}}{5 c e}","\frac{\sqrt{2} \left(\frac{-b^2 c \left(c d^2-4 a e^2\right)-6 a b c^2 d e+2 a c^2 \left(c d^2-a e^2\right)+2 b^3 c d e+b^4 \left(-e^2\right)}{\sqrt{b^2-4 a c}}+(c d-b e) \left(2 a c e+b^2 (-e)+b c d\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{7/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left((c d-b e) \left(2 a c e+b^2 (-e)+b c d\right)-\frac{-b^2 c \left(c d^2-4 a e^2\right)-6 a b c^2 d e+2 a c^2 \left(c d^2-a e^2\right)+2 b^3 c d e+b^4 \left(-e^2\right)}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{7/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{d+e x} \left(a c e+b^2 (-e)+b c d\right)}{c^3}-\frac{2 b (d+e x)^{3/2}}{3 c^2}+\frac{2 (d+e x)^{5/2}}{5 c e}",1,"(-2*(b*c*d - b^2*e + a*c*e)*Sqrt[d + e*x])/c^3 - (2*b*(d + e*x)^(3/2))/(3*c^2) + (2*(d + e*x)^(5/2))/(5*c*e) + (Sqrt[2]*((c*d - b*e)*(b*c*d - b^2*e + 2*a*c*e) + (2*b^3*c*d*e - 6*a*b*c^2*d*e - b^4*e^2 - b^2*c*(c*d^2 - 4*a*e^2) + 2*a*c^2*(c*d^2 - a*e^2))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(7/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*((c*d - b*e)*(b*c*d - b^2*e + 2*a*c*e) - (2*b^3*c*d*e - 6*a*b*c^2*d*e - b^4*e^2 - b^2*c*(c*d^2 - 4*a*e^2) + 2*a*c^2*(c*d^2 - a*e^2))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(7/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,4,25,0.1600,1,"{897, 1287, 1166, 208}"
536,1,453,0,4.5286701,"\int \frac{x (d+e x)^{3/2}}{a+b x+c x^2} \, dx","Int[(x*(d + e*x)^(3/2))/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(b c \left(e \left(2 d \sqrt{b^2-4 a c}-3 a e\right)+c d^2\right)+c \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)\right)-b^2 e \left(e \sqrt{b^2-4 a c}+2 c d\right)+b^3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{5/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \left(b c \left(c d^2-e \left(2 d \sqrt{b^2-4 a c}+3 a e\right)\right)-c \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)\right)-b^2 e \left(2 c d-e \sqrt{b^2-4 a c}\right)+b^3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{5/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \sqrt{d+e x} (c d-b e)}{c^2}+\frac{2 (d+e x)^{3/2}}{3 c}","\frac{\sqrt{2} \left(b c \left(e \left(2 d \sqrt{b^2-4 a c}-3 a e\right)+c d^2\right)+c \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)\right)-b^2 e \left(e \sqrt{b^2-4 a c}+2 c d\right)+b^3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{5/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \left(b c \left(c d^2-e \left(2 d \sqrt{b^2-4 a c}+3 a e\right)\right)-c \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)\right)-b^2 e \left(2 c d-e \sqrt{b^2-4 a c}\right)+b^3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{5/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \sqrt{d+e x} (c d-b e)}{c^2}+\frac{2 (d+e x)^{3/2}}{3 c}",1,"(2*(c*d - b*e)*Sqrt[d + e*x])/c^2 + (2*(d + e*x)^(3/2))/(3*c) + (Sqrt[2]*(b^3*e^2 - b^2*e*(2*c*d + Sqrt[b^2 - 4*a*c]*e) + c*(a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d - 4*a*e)) + b*c*(c*d^2 + e*(2*Sqrt[b^2 - 4*a*c]*d - 3*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(5/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*(b^3*e^2 - b^2*e*(2*c*d - Sqrt[b^2 - 4*a*c]*e) + b*c*(c*d^2 - e*(2*Sqrt[b^2 - 4*a*c]*d + 3*a*e)) - c*(a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(5/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,4,23,0.1739,1,"{824, 826, 1166, 208}"
537,1,322,0,1.2437489,"\int \frac{(d+e x)^{3/2}}{a+b x+c x^2} \, dx","Int[(d + e*x)^(3/2)/(a + b*x + c*x^2),x]","-\frac{\sqrt{2} \left(-2 c e \left(-d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(-2 c e \left(d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 e \sqrt{d+e x}}{c}","-\frac{\sqrt{2} \left(-2 c e \left(-d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(-2 c e \left(d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 e \sqrt{d+e x}}{c}",1,"(2*e*Sqrt[d + e*x])/c - (Sqrt[2]*(2*c^2*d^2 + b*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d - Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*(2*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d + Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",5,4,22,0.1818,1,"{703, 826, 1166, 208}"
538,1,340,0,1.5776771,"\int \frac{(d+e x)^{3/2}}{x \left(a+b x+c x^2\right)} \, dx","Int[(d + e*x)^(3/2)/(x*(a + b*x + c*x^2)),x]","-\frac{\sqrt{2} \left(-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)+a e^2 \sqrt{b^2-4 a c}-b \left(a e^2+c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a \sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \left(-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)+a e^2 \sqrt{b^2-4 a c}+b \left(a e^2+c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a \sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a}","-\frac{\sqrt{2} \left(-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)+a e^2 \sqrt{b^2-4 a c}-b \left(a e^2+c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a \sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \left(-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)+a e^2 \sqrt{b^2-4 a c}+b \left(a e^2+c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a \sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a}",1,"(-2*d^(3/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/a - (Sqrt[2]*(a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d - 4*a*e) - b*(c*d^2 + a*e^2))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(a*Sqrt[c]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*(a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e) + b*(c*d^2 + a*e^2))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(a*Sqrt[c]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",7,5,25,0.2000,1,"{897, 1287, 206, 1166, 208}"
539,1,402,0,3.0745841,"\int \frac{(d+e x)^{3/2}}{x^2 \left(a+b x+c x^2\right)} \, dx","Int[(d + e*x)^(3/2)/(x^2*(a + b*x + c*x^2)),x]","-\frac{\sqrt{2} \sqrt{c} \left(b d \left(d \sqrt{b^2-4 a c}-2 a e\right)-2 a e \left(d \sqrt{b^2-4 a c}-a e\right)-2 a c d^2+b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \sqrt{c} \left(-b d \left(d \sqrt{b^2-4 a c}+2 a e\right)+2 a e \left(d \sqrt{b^2-4 a c}+a e\right)-2 a c d^2+b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \sqrt{d} (b d-2 a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a^2}-\frac{d \sqrt{d+e x}}{a x}+\frac{\sqrt{d} e \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a}","-\frac{\sqrt{2} \sqrt{c} \left(-2 a \left(e \left(d \sqrt{b^2-4 a c}-a e\right)+c d^2\right)+b d \left(d \sqrt{b^2-4 a c}-2 a e\right)+b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \sqrt{c} \left(-2 a \left(c d^2-e \left(d \sqrt{b^2-4 a c}+a e\right)\right)-b d \left(d \sqrt{b^2-4 a c}+2 a e\right)+b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \sqrt{d} (b d-2 a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a^2}-\frac{d \sqrt{d+e x}}{a x}+\frac{\sqrt{d} e \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a}",1,"-((d*Sqrt[d + e*x])/(a*x)) + (Sqrt[d]*e*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/a + (2*Sqrt[d]*(b*d - 2*a*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/a^2 - (Sqrt[2]*Sqrt[c]*(b^2*d^2 - 2*a*c*d^2 + b*d*(Sqrt[b^2 - 4*a*c]*d - 2*a*e) - 2*a*e*(Sqrt[b^2 - 4*a*c]*d - a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(a^2*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*Sqrt[c]*(b^2*d^2 - 2*a*c*d^2 + 2*a*e*(Sqrt[b^2 - 4*a*c]*d + a*e) - b*d*(Sqrt[b^2 - 4*a*c]*d + 2*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(a^2*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",9,6,25,0.2400,1,"{897, 1287, 199, 206, 1166, 208}"
540,1,607,0,3.9306439,"\int \frac{(d+e x)^{3/2}}{x^3 \left(a+b x+c x^2\right)} \, dx","Int[(d + e*x)^(3/2)/(x^3*(a + b*x + c*x^2)),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(-2 a b d e-a \left(c d^2-a e^2\right)+b^2 d^2\right)}{a^3 \sqrt{d}}+\frac{\sqrt{2} \sqrt{c} \left(-a b \left(e \left(2 d \sqrt{b^2-4 a c}-a e\right)+3 c d^2\right)+a \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)\right)+b^2 d \left(d \sqrt{b^2-4 a c}-2 a e\right)+b^3 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \sqrt{c} \left(-a b \left(3 c d^2-e \left(2 d \sqrt{b^2-4 a c}+a e\right)\right)-a \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)\right)-b^2 d \left(d \sqrt{b^2-4 a c}+2 a e\right)+b^3 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d+e x} (b d-2 a e)}{a^2 x}-\frac{e (b d-2 a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a^2 \sqrt{d}}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 a \sqrt{d}}-\frac{d \sqrt{d+e x}}{2 a x^2}+\frac{3 e \sqrt{d+e x}}{4 a x}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(-2 a b d e-a \left(c d^2-a e^2\right)+b^2 d^2\right)}{a^3 \sqrt{d}}+\frac{\sqrt{2} \sqrt{c} \left(-a b \left(e \left(2 d \sqrt{b^2-4 a c}-a e\right)+3 c d^2\right)+a \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)\right)+b^2 d \left(d \sqrt{b^2-4 a c}-2 a e\right)+b^3 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \sqrt{c} \left(-a b \left(3 c d^2-e \left(2 d \sqrt{b^2-4 a c}+a e\right)\right)-a \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)\right)-b^2 d \left(d \sqrt{b^2-4 a c}+2 a e\right)+b^3 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d+e x} (b d-2 a e)}{a^2 x}-\frac{e (b d-2 a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{a^2 \sqrt{d}}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 a \sqrt{d}}-\frac{d \sqrt{d+e x}}{2 a x^2}+\frac{3 e \sqrt{d+e x}}{4 a x}",1,"-(d*Sqrt[d + e*x])/(2*a*x^2) + (3*e*Sqrt[d + e*x])/(4*a*x) + ((b*d - 2*a*e)*Sqrt[d + e*x])/(a^2*x) - (3*e^2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*a*Sqrt[d]) - (e*(b*d - 2*a*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(a^2*Sqrt[d]) - (2*(b^2*d^2 - 2*a*b*d*e - a*(c*d^2 - a*e^2))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(a^3*Sqrt[d]) + (Sqrt[2]*Sqrt[c]*(b^3*d^2 + b^2*d*(Sqrt[b^2 - 4*a*c]*d - 2*a*e) + a*(a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d - 4*a*e)) - a*b*(3*c*d^2 + e*(2*Sqrt[b^2 - 4*a*c]*d - a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(a^3*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*Sqrt[c]*(b^3*d^2 - b^2*d*(Sqrt[b^2 - 4*a*c]*d + 2*a*e) - a*b*(3*c*d^2 - e*(2*Sqrt[b^2 - 4*a*c]*d + a*e)) - a*(a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(a^3*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",12,6,25,0.2400,1,"{897, 1287, 199, 206, 1166, 208}"
541,1,201,0,0.3631505,"\int \frac{x^m (e+f x)^n}{a+b x+c x^2} \, dx","Int[(x^m*(e + f*x)^n)/(a + b*x + c*x^2),x]","\frac{2 c x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{(m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{(m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}","\frac{2 c x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{(m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{(m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}",1,"(2*c*x^(1 + m)*(e + f*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((f*x)/e), (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*(1 + m)*(1 + (f*x)/e)^n) - (2*c*x^(1 + m)*(e + f*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((f*x)/e), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*(1 + m)*(1 + (f*x)/e)^n)","A",6,3,23,0.1304,1,"{911, 135, 133}"
542,1,290,0,0.7695341,"\int \frac{x^3 (e+f x)^n}{a+b x+c x^2} \, dx","Int[(x^3*(e + f*x)^n)/(a + b*x + c*x^2),x]","\frac{\left(\frac{b \left(b^2-3 a c\right)}{c \sqrt{b^2-4 a c}}+a-\frac{b^2}{c}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{c (n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{\left(-\frac{b \left(b^2-3 a c\right)}{c \sqrt{b^2-4 a c}}+a-\frac{b^2}{c}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{c (n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{(b f+c e) (e+f x)^{n+1}}{c^2 f^2 (n+1)}+\frac{(e+f x)^{n+2}}{c f^2 (n+2)}","\frac{\left(\frac{b \left(b^2-3 a c\right)}{c \sqrt{b^2-4 a c}}+a-\frac{b^2}{c}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{c (n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{\left(-\frac{b \left(b^2-3 a c\right)}{c \sqrt{b^2-4 a c}}+a-\frac{b^2}{c}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{c (n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{(b f+c e) (e+f x)^{n+1}}{c^2 f^2 (n+1)}+\frac{(e+f x)^{n+2}}{c f^2 (n+2)}",1,"-(((c*e + b*f)*(e + f*x)^(1 + n))/(c^2*f^2*(1 + n))) + (e + f*x)^(2 + n)/(c*f^2*(2 + n)) + ((a - b^2/c + (b*(b^2 - 3*a*c))/(c*Sqrt[b^2 - 4*a*c]))*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)])/(c*(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)*(1 + n)) + ((a - b^2/c - (b*(b^2 - 3*a*c))/(c*Sqrt[b^2 - 4*a*c]))*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)])/(c*(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)*(1 + n))","A",4,2,23,0.08696,1,"{1628, 68}"
543,1,237,0,0.3820537,"\int \frac{x^2 (e+f x)^n}{a+b x+c x^2} \, dx","Int[(x^2*(e + f*x)^n)/(a + b*x + c*x^2),x]","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{c (n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{c (n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}+\frac{(e+f x)^{n+1}}{c f (n+1)}","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{c (n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{c (n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}+\frac{(e+f x)^{n+1}}{c f (n+1)}",1,"(e + f*x)^(1 + n)/(c*f*(1 + n)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)])/(c*(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)*(1 + n)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)])/(c*(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)*(1 + n))","A",4,2,23,0.08696,1,"{1628, 68}"
544,1,198,0,0.189035,"\int \frac{x (e+f x)^n}{a+b x+c x^2} \, dx","Int[(x*(e + f*x)^n)/(a + b*x + c*x^2),x]","-\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{(n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{(n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}","-\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{(n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{(n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}",1,"-(((1 - b/Sqrt[b^2 - 4*a*c])*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)])/((2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)*(1 + n))) - ((1 + b/Sqrt[b^2 - 4*a*c])*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)])/((2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)*(1 + n))","A",4,2,21,0.09524,1,"{830, 68}"
545,1,191,0,0.2595666,"\int \frac{(e+f x)^n}{a+b x+c x^2} \, dx","Int[(e + f*x)^n/(a + b*x + c*x^2),x]","\frac{2 c (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{(n+1) \sqrt{b^2-4 a c} \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{2 c (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{(n+1) \sqrt{b^2-4 a c} \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}","\frac{2 c (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{(n+1) \sqrt{b^2-4 a c} \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{2 c (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{(n+1) \sqrt{b^2-4 a c} \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}",1,"(-2*c*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)])/(Sqrt[b^2 - 4*a*c]*(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)*(1 + n)) + (2*c*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)])/(Sqrt[b^2 - 4*a*c]*(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)*(1 + n))","A",4,2,20,0.1000,1,"{711, 68}"
546,1,242,0,0.385396,"\int \frac{(e+f x)^n}{x \left(a+b x+c x^2\right)} \, dx","Int[(e + f*x)^n/(x*(a + b*x + c*x^2)),x]","\frac{c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{a (n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{a (n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)}{a e (n+1)}","\frac{c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{a (n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{a (n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)}{a e (n+1)}",1,"(c*(1 + b/Sqrt[b^2 - 4*a*c])*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)])/(a*(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)*(1 + n)) + (c*(1 - b/Sqrt[b^2 - 4*a*c])*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)])/(a*(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)*(1 + n)) - ((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (f*x)/e])/(a*e*(1 + n))","A",7,4,23,0.1739,1,"{960, 65, 830, 68}"
547,1,296,0,0.4772449,"\int \frac{(e+f x)^n}{x^2 \left(a+b x+c x^2\right)} \, dx","Int[(e + f*x)^n/(x^2*(a + b*x + c*x^2)),x]","-\frac{c \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{a^2 (n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{c \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{a^2 (n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}+\frac{b (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)}{a^2 e (n+1)}+\frac{f (e+f x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{f x}{e}+1\right)}{a e^2 (n+1)}","-\frac{c \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b-\sqrt{b^2-4 a c}\right) f}\right)}{a^2 (n+1) \left(2 c e-f \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{c \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{2 c (e+f x)}{2 c e-\left(b+\sqrt{b^2-4 a c}\right) f}\right)}{a^2 (n+1) \left(2 c e-f \left(\sqrt{b^2-4 a c}+b\right)\right)}+\frac{b (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)}{a^2 e (n+1)}+\frac{f (e+f x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{f x}{e}+1\right)}{a e^2 (n+1)}",1,"-((c*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)])/(a^2*(2*c*e - (b - Sqrt[b^2 - 4*a*c])*f)*(1 + n))) - (c*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (2*c*(e + f*x))/(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)])/(a^2*(2*c*e - (b + Sqrt[b^2 - 4*a*c])*f)*(1 + n)) + (b*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (f*x)/e])/(a^2*e*(1 + n)) + (f*(e + f*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (f*x)/e])/(a*e^2*(1 + n))","A",8,4,23,0.1739,1,"{960, 65, 830, 68}"
548,1,141,0,0.1828089,"\int \frac{(d+e x)^4 (f+g x)^2}{d^2-e^2 x^2} \, dx","Int[((d + e*x)^4*(f + g*x)^2)/(d^2 - e^2*x^2),x]","-\frac{d x^2 \left(4 d^2 g^2+7 d e f g+2 e^2 f^2\right)}{e}-\frac{d^2 x \left(8 d^2 g^2+16 d e f g+7 e^2 f^2\right)}{e^2}-\frac{8 d^3 (d g+e f)^2 \log (d-e x)}{e^3}-\frac{1}{2} e g x^4 (2 d g+e f)-\frac{1}{3} x^3 (d g+e f) (7 d g+e f)-\frac{1}{5} e^2 g^2 x^5","-\frac{d x^2 \left(4 d^2 g^2+7 d e f g+2 e^2 f^2\right)}{e}-\frac{d^2 x \left(8 d^2 g^2+16 d e f g+7 e^2 f^2\right)}{e^2}-\frac{8 d^3 (d g+e f)^2 \log (d-e x)}{e^3}-\frac{1}{2} e g x^4 (2 d g+e f)-\frac{1}{3} x^3 (d g+e f) (7 d g+e f)-\frac{1}{5} e^2 g^2 x^5",1,"-((d^2*(7*e^2*f^2 + 16*d*e*f*g + 8*d^2*g^2)*x)/e^2) - (d*(2*e^2*f^2 + 7*d*e*f*g + 4*d^2*g^2)*x^2)/e - ((e*f + d*g)*(e*f + 7*d*g)*x^3)/3 - (e*g*(e*f + 2*d*g)*x^4)/2 - (e^2*g^2*x^5)/5 - (8*d^3*(e*f + d*g)^2*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 88}"
549,1,109,0,0.1358037,"\int \frac{(d+e x)^3 (f+g x)^2}{d^2-e^2 x^2} \, dx","Int[((d + e*x)^3*(f + g*x)^2)/(d^2 - e^2*x^2),x]","-\frac{x^2 \left(4 d^2 g^2+6 d e f g+e^2 f^2\right)}{2 e}-\frac{4 d^2 (d g+e f)^2 \log (d-e x)}{e^3}-\frac{d x (2 d g+e f) (2 d g+3 e f)}{e^2}-\frac{1}{3} g x^3 (3 d g+2 e f)-\frac{1}{4} e g^2 x^4","-\frac{x^2 \left(4 d^2 g^2+6 d e f g+e^2 f^2\right)}{2 e}-\frac{4 d^2 (d g+e f)^2 \log (d-e x)}{e^3}-\frac{d x (2 d g+e f) (2 d g+3 e f)}{e^2}-\frac{1}{3} g x^3 (3 d g+2 e f)-\frac{1}{4} e g^2 x^4",1,"-((d*(e*f + 2*d*g)*(3*e*f + 2*d*g)*x)/e^2) - ((e^2*f^2 + 6*d*e*f*g + 4*d^2*g^2)*x^2)/(2*e) - (g*(2*e*f + 3*d*g)*x^3)/3 - (e*g^2*x^4)/4 - (4*d^2*(e*f + d*g)^2*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 88}"
550,1,65,0,0.0600605,"\int \frac{(d+e x)^2 (f+g x)^2}{d^2-e^2 x^2} \, dx","Int[((d + e*x)^2*(f + g*x)^2)/(d^2 - e^2*x^2),x]","-\frac{2 d g x (d g+e f)}{e^2}-\frac{2 d (d g+e f)^2 \log (d-e x)}{e^3}-\frac{d (f+g x)^2}{e}-\frac{(f+g x)^3}{3 g}","-\frac{2 d g x (d g+e f)}{e^2}-\frac{2 d (d g+e f)^2 \log (d-e x)}{e^3}-\frac{d (f+g x)^2}{e}-\frac{(f+g x)^3}{3 g}",1,"(-2*d*g*(e*f + d*g)*x)/e^2 - (d*(f + g*x)^2)/e - (f + g*x)^3/(3*g) - (2*d*(e*f + d*g)^2*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 77}"
551,1,50,0,0.0340709,"\int \frac{(d+e x) (f+g x)^2}{d^2-e^2 x^2} \, dx","Int[((d + e*x)*(f + g*x)^2)/(d^2 - e^2*x^2),x]","-\frac{g x (d g+e f)}{e^2}-\frac{(d g+e f)^2 \log (d-e x)}{e^3}-\frac{(f+g x)^2}{2 e}","-\frac{g x (d g+e f)}{e^2}-\frac{(d g+e f)^2 \log (d-e x)}{e^3}-\frac{(f+g x)^2}{2 e}",1,"-((g*(e*f + d*g)*x)/e^2) - (f + g*x)^2/(2*e) - ((e*f + d*g)^2*Log[d - e*x])/e^3","A",3,2,27,0.07407,1,"{799, 43}"
552,1,62,0,0.0800188,"\int \frac{(f+g x)^2}{d^2-e^2 x^2} \, dx","Int[(f + g*x)^2/(d^2 - e^2*x^2),x]","-\frac{(d g+e f)^2 \log (d-e x)}{2 d e^3}+\frac{(e f-d g)^2 \log (d+e x)}{2 d e^3}-\frac{g^2 x}{e^2}","-\frac{(d g+e f)^2 \log (d-e x)}{2 d e^3}+\frac{(e f-d g)^2 \log (d+e x)}{2 d e^3}-\frac{g^2 x}{e^2}",1,"-((g^2*x)/e^2) - ((e*f + d*g)^2*Log[d - e*x])/(2*d*e^3) + ((e*f - d*g)^2*Log[d + e*x])/(2*d*e^3)","A",5,3,22,0.1364,1,"{702, 633, 31}"
553,1,86,0,0.0855682,"\int \frac{(f+g x)^2}{(d+e x) \left(d^2-e^2 x^2\right)} \, dx","Int[(f + g*x)^2/((d + e*x)*(d^2 - e^2*x^2)),x]","\frac{(3 d g+e f) (e f-d g) \log (d+e x)}{4 d^2 e^3}-\frac{(d g+e f)^2 \log (d-e x)}{4 d^2 e^3}-\frac{(e f-d g)^2}{2 d e^3 (d+e x)}","\frac{(3 d g+e f) (e f-d g) \log (d+e x)}{4 d^2 e^3}-\frac{(d g+e f)^2 \log (d-e x)}{4 d^2 e^3}-\frac{(e f-d g)^2}{2 d e^3 (d+e x)}",1,"-(e*f - d*g)^2/(2*d*e^3*(d + e*x)) - ((e*f + d*g)^2*Log[d - e*x])/(4*d^2*e^3) + ((e*f - d*g)*(e*f + 3*d*g)*Log[d + e*x])/(4*d^2*e^3)","A",3,2,29,0.06897,1,"{848, 88}"
554,1,87,0,0.0966412,"\int \frac{(f+g x)^2}{(d+e x)^2 \left(d^2-e^2 x^2\right)} \, dx","Int[(f + g*x)^2/((d + e*x)^2*(d^2 - e^2*x^2)),x]","-\frac{(3 d g+e f) (e f-d g)}{4 d^2 e^3 (d+e x)}+\frac{(d g+e f)^2 \tanh ^{-1}\left(\frac{e x}{d}\right)}{4 d^3 e^3}-\frac{(e f-d g)^2}{4 d e^3 (d+e x)^2}","-\frac{(3 d g+e f) (e f-d g)}{4 d^2 e^3 (d+e x)}+\frac{(d g+e f)^2 \tanh ^{-1}\left(\frac{e x}{d}\right)}{4 d^3 e^3}-\frac{(e f-d g)^2}{4 d e^3 (d+e x)^2}",1,"-(e*f - d*g)^2/(4*d*e^3*(d + e*x)^2) - ((e*f - d*g)*(e*f + 3*d*g))/(4*d^2*e^3*(d + e*x)) + ((e*f + d*g)^2*ArcTanh[(e*x)/d])/(4*d^3*e^3)","A",4,3,29,0.1034,1,"{848, 88, 208}"
555,1,113,0,0.1159188,"\int \frac{(f+g x)^2}{(d+e x)^3 \left(d^2-e^2 x^2\right)} \, dx","Int[(f + g*x)^2/((d + e*x)^3*(d^2 - e^2*x^2)),x]","-\frac{(3 d g+e f) (e f-d g)}{8 d^2 e^3 (d+e x)^2}-\frac{(d g+e f)^2}{8 d^3 e^3 (d+e x)}+\frac{(d g+e f)^2 \tanh ^{-1}\left(\frac{e x}{d}\right)}{8 d^4 e^3}-\frac{(e f-d g)^2}{6 d e^3 (d+e x)^3}","-\frac{(3 d g+e f) (e f-d g)}{8 d^2 e^3 (d+e x)^2}-\frac{(d g+e f)^2}{8 d^3 e^3 (d+e x)}+\frac{(d g+e f)^2 \tanh ^{-1}\left(\frac{e x}{d}\right)}{8 d^4 e^3}-\frac{(e f-d g)^2}{6 d e^3 (d+e x)^3}",1,"-(e*f - d*g)^2/(6*d*e^3*(d + e*x)^3) - ((e*f - d*g)*(e*f + 3*d*g))/(8*d^2*e^3*(d + e*x)^2) - (e*f + d*g)^2/(8*d^3*e^3*(d + e*x)) + ((e*f + d*g)^2*ArcTanh[(e*x)/d])/(8*d^4*e^3)","A",4,3,29,0.1034,1,"{848, 88, 208}"
556,1,139,0,0.1330731,"\int \frac{(f+g x)^2}{(d+e x)^4 \left(d^2-e^2 x^2\right)} \, dx","Int[(f + g*x)^2/((d + e*x)^4*(d^2 - e^2*x^2)),x]","-\frac{(3 d g+e f) (e f-d g)}{12 d^2 e^3 (d+e x)^3}-\frac{(d g+e f)^2}{16 d^4 e^3 (d+e x)}-\frac{(d g+e f)^2}{16 d^3 e^3 (d+e x)^2}+\frac{(d g+e f)^2 \tanh ^{-1}\left(\frac{e x}{d}\right)}{16 d^5 e^3}-\frac{(e f-d g)^2}{8 d e^3 (d+e x)^4}","-\frac{(3 d g+e f) (e f-d g)}{12 d^2 e^3 (d+e x)^3}-\frac{(d g+e f)^2}{16 d^4 e^3 (d+e x)}-\frac{(d g+e f)^2}{16 d^3 e^3 (d+e x)^2}+\frac{(d g+e f)^2 \tanh ^{-1}\left(\frac{e x}{d}\right)}{16 d^5 e^3}-\frac{(e f-d g)^2}{8 d e^3 (d+e x)^4}",1,"-(e*f - d*g)^2/(8*d*e^3*(d + e*x)^4) - ((e*f - d*g)*(e*f + 3*d*g))/(12*d^2*e^3*(d + e*x)^3) - (e*f + d*g)^2/(16*d^3*e^3*(d + e*x)^2) - (e*f + d*g)^2/(16*d^4*e^3*(d + e*x)) + ((e*f + d*g)^2*ArcTanh[(e*x)/d])/(16*d^5*e^3)","A",4,3,29,0.1034,1,"{848, 88, 208}"
557,1,218,0,0.2837195,"\int \frac{(d+e x)^7 (f+g x)^2}{\left(d^2-e^2 x^2\right)^2} \, dx","Int[((d + e*x)^7*(f + g*x)^2)/(d^2 - e^2*x^2)^2,x]","\frac{1}{4} e x^4 \left(23 d^2 g^2+14 d e f g+e^2 f^2\right)+\frac{1}{3} d x^3 \left(49 d^2 g^2+46 d e f g+7 e^2 f^2\right)+\frac{d^2 x^2 \left(80 d^2 g^2+98 d e f g+23 e^2 f^2\right)}{2 e}+\frac{d^3 x \left(112 d^2 g^2+160 d e f g+49 e^2 f^2\right)}{e^2}+\frac{32 d^5 (d g+e f)^2}{e^3 (d-e x)}+\frac{16 d^4 (d g+e f) (9 d g+5 e f) \log (d-e x)}{e^3}+\frac{1}{5} e^2 g x^5 (7 d g+2 e f)+\frac{1}{6} e^3 g^2 x^6","\frac{1}{4} e x^4 \left(23 d^2 g^2+14 d e f g+e^2 f^2\right)+\frac{1}{3} d x^3 \left(49 d^2 g^2+46 d e f g+7 e^2 f^2\right)+\frac{d^2 x^2 \left(80 d^2 g^2+98 d e f g+23 e^2 f^2\right)}{2 e}+\frac{d^3 x \left(112 d^2 g^2+160 d e f g+49 e^2 f^2\right)}{e^2}+\frac{32 d^5 (d g+e f)^2}{e^3 (d-e x)}+\frac{16 d^4 (d g+e f) (9 d g+5 e f) \log (d-e x)}{e^3}+\frac{1}{5} e^2 g x^5 (7 d g+2 e f)+\frac{1}{6} e^3 g^2 x^6",1,"(d^3*(49*e^2*f^2 + 160*d*e*f*g + 112*d^2*g^2)*x)/e^2 + (d^2*(23*e^2*f^2 + 98*d*e*f*g + 80*d^2*g^2)*x^2)/(2*e) + (d*(7*e^2*f^2 + 46*d*e*f*g + 49*d^2*g^2)*x^3)/3 + (e*(e^2*f^2 + 14*d*e*f*g + 23*d^2*g^2)*x^4)/4 + (e^2*g*(2*e*f + 7*d*g)*x^5)/5 + (e^3*g^2*x^6)/6 + (32*d^5*(e*f + d*g)^2)/(e^3*(d - e*x)) + (16*d^4*(e*f + d*g)*(5*e*f + 9*d*g)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 88}"
558,1,177,0,0.2321963,"\int \frac{(d+e x)^6 (f+g x)^2}{\left(d^2-e^2 x^2\right)^2} \, dx","Int[((d + e*x)^6*(f + g*x)^2)/(d^2 - e^2*x^2)^2,x]","\frac{1}{3} x^3 \left(17 d^2 g^2+12 d e f g+e^2 f^2\right)+\frac{d x^2 \left(16 d^2 g^2+17 d e f g+3 e^2 f^2\right)}{e}+\frac{d^2 x \left(48 d^2 g^2+64 d e f g+17 e^2 f^2\right)}{e^2}+\frac{16 d^4 (d g+e f)^2}{e^3 (d-e x)}+\frac{32 d^3 (d g+e f) (2 d g+e f) \log (d-e x)}{e^3}+\frac{1}{2} e g x^4 (3 d g+e f)+\frac{1}{5} e^2 g^2 x^5","\frac{1}{3} x^3 \left(17 d^2 g^2+12 d e f g+e^2 f^2\right)+\frac{d x^2 \left(16 d^2 g^2+17 d e f g+3 e^2 f^2\right)}{e}+\frac{d^2 x \left(48 d^2 g^2+64 d e f g+17 e^2 f^2\right)}{e^2}+\frac{16 d^4 (d g+e f)^2}{e^3 (d-e x)}+\frac{32 d^3 (d g+e f) (2 d g+e f) \log (d-e x)}{e^3}+\frac{1}{2} e g x^4 (3 d g+e f)+\frac{1}{5} e^2 g^2 x^5",1,"(d^2*(17*e^2*f^2 + 64*d*e*f*g + 48*d^2*g^2)*x)/e^2 + (d*(3*e^2*f^2 + 17*d*e*f*g + 16*d^2*g^2)*x^2)/e + ((e^2*f^2 + 12*d*e*f*g + 17*d^2*g^2)*x^3)/3 + (e*g*(e*f + 3*d*g)*x^4)/2 + (e^2*g^2*x^5)/5 + (16*d^4*(e*f + d*g)^2)/(e^3*(d - e*x)) + (32*d^3*(e*f + d*g)*(e*f + 2*d*g)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 88}"
559,1,146,0,0.181323,"\int \frac{(d+e x)^5 (f+g x)^2}{\left(d^2-e^2 x^2\right)^2} \, dx","Int[((d + e*x)^5*(f + g*x)^2)/(d^2 - e^2*x^2)^2,x]","\frac{x^2 \left(12 d^2 g^2+10 d e f g+e^2 f^2\right)}{2 e}+\frac{d x \left(20 d^2 g^2+24 d e f g+5 e^2 f^2\right)}{e^2}+\frac{8 d^3 (d g+e f)^2}{e^3 (d-e x)}+\frac{4 d^2 (d g+e f) (7 d g+3 e f) \log (d-e x)}{e^3}+\frac{1}{3} g x^3 (5 d g+2 e f)+\frac{1}{4} e g^2 x^4","\frac{x^2 \left(12 d^2 g^2+10 d e f g+e^2 f^2\right)}{2 e}+\frac{d x \left(20 d^2 g^2+24 d e f g+5 e^2 f^2\right)}{e^2}+\frac{8 d^3 (d g+e f)^2}{e^3 (d-e x)}+\frac{4 d^2 (d g+e f) (7 d g+3 e f) \log (d-e x)}{e^3}+\frac{1}{3} g x^3 (5 d g+2 e f)+\frac{1}{4} e g^2 x^4",1,"(d*(5*e^2*f^2 + 24*d*e*f*g + 20*d^2*g^2)*x)/e^2 + ((e^2*f^2 + 10*d*e*f*g + 12*d^2*g^2)*x^2)/(2*e) + (g*(2*e*f + 5*d*g)*x^3)/3 + (e*g^2*x^4)/4 + (8*d^3*(e*f + d*g)^2)/(e^3*(d - e*x)) + (4*d^2*(e*f + d*g)*(3*e*f + 7*d*g)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 88}"
560,1,107,0,0.1360724,"\int \frac{(d+e x)^4 (f+g x)^2}{\left(d^2-e^2 x^2\right)^2} \, dx","Int[((d + e*x)^4*(f + g*x)^2)/(d^2 - e^2*x^2)^2,x]","\frac{x \left(8 d^2 g^2+8 d e f g+e^2 f^2\right)}{e^2}+\frac{4 d^2 (d g+e f)^2}{e^3 (d-e x)}+\frac{4 d (d g+e f) (3 d g+e f) \log (d-e x)}{e^3}+\frac{g x^2 (2 d g+e f)}{e}+\frac{g^2 x^3}{3}","\frac{x \left(8 d^2 g^2+8 d e f g+e^2 f^2\right)}{e^2}+\frac{4 d^2 (d g+e f)^2}{e^3 (d-e x)}+\frac{4 d (d g+e f) (3 d g+e f) \log (d-e x)}{e^3}+\frac{g x^2 (2 d g+e f)}{e}+\frac{g^2 x^3}{3}",1,"((e^2*f^2 + 8*d*e*f*g + 8*d^2*g^2)*x)/e^2 + (g*(e*f + 2*d*g)*x^2)/e + (g^2*x^3)/3 + (4*d^2*(e*f + d*g)^2)/(e^3*(d - e*x)) + (4*d*(e*f + d*g)*(e*f + 3*d*g)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 88}"
561,1,78,0,0.0961631,"\int \frac{(d+e x)^3 (f+g x)^2}{\left(d^2-e^2 x^2\right)^2} \, dx","Int[((d + e*x)^3*(f + g*x)^2)/(d^2 - e^2*x^2)^2,x]","\frac{2 d (d g+e f)^2}{e^3 (d-e x)}+\frac{g x (3 d g+2 e f)}{e^2}+\frac{(5 d g+e f) (d g+e f) \log (d-e x)}{e^3}+\frac{g^2 x^2}{2 e}","\frac{2 d (d g+e f)^2}{e^3 (d-e x)}+\frac{g x (3 d g+2 e f)}{e^2}+\frac{(5 d g+e f) (d g+e f) \log (d-e x)}{e^3}+\frac{g^2 x^2}{2 e}",1,"(g*(2*e*f + 3*d*g)*x)/e^2 + (g^2*x^2)/(2*e) + (2*d*(e*f + d*g)^2)/(e^3*(d - e*x)) + ((e*f + d*g)*(e*f + 5*d*g)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 77}"
562,1,50,0,0.0570058,"\int \frac{(d+e x)^2 (f+g x)^2}{\left(d^2-e^2 x^2\right)^2} \, dx","Int[((d + e*x)^2*(f + g*x)^2)/(d^2 - e^2*x^2)^2,x]","\frac{(d g+e f)^2}{e^3 (d-e x)}+\frac{2 g (d g+e f) \log (d-e x)}{e^3}+\frac{g^2 x}{e^2}","\frac{(d g+e f)^2}{e^3 (d-e x)}+\frac{2 g (d g+e f) \log (d-e x)}{e^3}+\frac{g^2 x}{e^2}",1,"(g^2*x)/e^2 + (e*f + d*g)^2/(e^3*(d - e*x)) + (2*g*(e*f + d*g)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 43}"
563,1,86,0,0.0815934,"\int \frac{(d+e x) (f+g x)^2}{\left(d^2-e^2 x^2\right)^2} \, dx","Int[((d + e*x)*(f + g*x)^2)/(d^2 - e^2*x^2)^2,x]","\frac{(e f-d g)^2 \log (d+e x)}{4 d^2 e^3}-\frac{(e f-3 d g) (d g+e f) \log (d-e x)}{4 d^2 e^3}+\frac{(d g+e f)^2}{2 d e^3 (d-e x)}","\frac{(e f-d g)^2 \log (d+e x)}{4 d^2 e^3}-\frac{(e f-3 d g) (d g+e f) \log (d-e x)}{4 d^2 e^3}+\frac{(d g+e f)^2}{2 d e^3 (d-e x)}",1,"(e*f + d*g)^2/(2*d*e^3*(d - e*x)) - ((e*f - 3*d*g)*(e*f + d*g)*Log[d - e*x])/(4*d^2*e^3) + ((e*f - d*g)^2*Log[d + e*x])/(4*d^2*e^3)","A",3,2,27,0.07407,1,"{799, 88}"
564,1,74,0,0.0291274,"\int \frac{(f+g x)^2}{\left(d^2-e^2 x^2\right)^2} \, dx","Int[(f + g*x)^2/(d^2 - e^2*x^2)^2,x]","\frac{(f+g x) \left(d^2 g+e^2 f x\right)}{2 d^2 e^2 \left(d^2-e^2 x^2\right)}+\frac{(e f-d g) (d g+e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{2 d^3 e^3}","\frac{(f+g x) \left(d^2 g+e^2 f x\right)}{2 d^2 e^2 \left(d^2-e^2 x^2\right)}+\frac{(e f-d g) (d g+e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{2 d^3 e^3}",1,"((d^2*g + e^2*f*x)*(f + g*x))/(2*d^2*e^2*(d^2 - e^2*x^2)) + ((e*f - d*g)*(e*f + d*g)*ArcTanh[(e*x)/d])/(2*d^3*e^3)","A",2,2,22,0.09091,1,"{723, 208}"
565,1,121,0,0.1358014,"\int \frac{(f+g x)^2}{(d+e x) \left(d^2-e^2 x^2\right)^2} \, dx","Int[(f + g*x)^2/((d + e*x)*(d^2 - e^2*x^2)^2),x]","-\frac{e^2 f^2-d^2 g^2}{4 d^3 e^3 (d+e x)}-\frac{(e f-d g)^2}{8 d^2 e^3 (d+e x)^2}+\frac{(d g+e f)^2}{8 d^3 e^3 (d-e x)}+\frac{(3 e f-d g) (d g+e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{8 d^4 e^3}","-\frac{e^2 f^2-d^2 g^2}{4 d^3 e^3 (d+e x)}-\frac{(e f-d g)^2}{8 d^2 e^3 (d+e x)^2}+\frac{(d g+e f)^2}{8 d^3 e^3 (d-e x)}+\frac{(3 e f-d g) (d g+e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{8 d^4 e^3}",1,"(e*f + d*g)^2/(8*d^3*e^3*(d - e*x)) - (e*f - d*g)^2/(8*d^2*e^3*(d + e*x)^2) - (e^2*f^2 - d^2*g^2)/(4*d^3*e^3*(d + e*x)) + ((3*e*f - d*g)*(e*f + d*g)*ArcTanh[(e*x)/d])/(8*d^4*e^3)","A",4,3,29,0.1034,1,"{848, 88, 208}"
566,1,146,0,0.1552934,"\int \frac{(f+g x)^2}{(d+e x)^2 \left(d^2-e^2 x^2\right)^2} \, dx","Int[(f + g*x)^2/((d + e*x)^2*(d^2 - e^2*x^2)^2),x]","-\frac{e^2 f^2-d^2 g^2}{8 d^3 e^3 (d+e x)^2}-\frac{(e f-d g)^2}{12 d^2 e^3 (d+e x)^3}+\frac{(d g+e f)^2}{16 d^4 e^3 (d-e x)}-\frac{(3 e f-d g) (d g+e f)}{16 d^4 e^3 (d+e x)}+\frac{f (d g+e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{4 d^5 e^2}","-\frac{e^2 f^2-d^2 g^2}{8 d^3 e^3 (d+e x)^2}-\frac{(e f-d g)^2}{12 d^2 e^3 (d+e x)^3}+\frac{(d g+e f)^2}{16 d^4 e^3 (d-e x)}-\frac{(3 e f-d g) (d g+e f)}{16 d^4 e^3 (d+e x)}+\frac{f (d g+e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{4 d^5 e^2}",1,"(e*f + d*g)^2/(16*d^4*e^3*(d - e*x)) - (e*f - d*g)^2/(12*d^2*e^3*(d + e*x)^3) - (e^2*f^2 - d^2*g^2)/(8*d^3*e^3*(d + e*x)^2) - ((3*e*f - d*g)*(e*f + d*g))/(16*d^4*e^3*(d + e*x)) + (f*(e*f + d*g)*ArcTanh[(e*x)/d])/(4*d^5*e^2)","A",4,3,29,0.1034,1,"{848, 88, 208}"
567,1,178,0,0.1995614,"\int \frac{(f+g x)^2}{(d+e x)^3 \left(d^2-e^2 x^2\right)^2} \, dx","Int[(f + g*x)^2/((d + e*x)^3*(d^2 - e^2*x^2)^2),x]","-\frac{e^2 f^2-d^2 g^2}{12 d^3 e^3 (d+e x)^3}-\frac{(e f-d g)^2}{16 d^2 e^3 (d+e x)^4}+\frac{(d g+e f)^2}{32 d^5 e^3 (d-e x)}-\frac{f (d g+e f)}{8 d^5 e^2 (d+e x)}-\frac{(3 e f-d g) (d g+e f)}{32 d^4 e^3 (d+e x)^2}+\frac{(d g+e f) (d g+5 e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{32 d^6 e^3}","-\frac{e^2 f^2-d^2 g^2}{12 d^3 e^3 (d+e x)^3}-\frac{(e f-d g)^2}{16 d^2 e^3 (d+e x)^4}+\frac{(d g+e f)^2}{32 d^5 e^3 (d-e x)}-\frac{f (d g+e f)}{8 d^5 e^2 (d+e x)}-\frac{(3 e f-d g) (d g+e f)}{32 d^4 e^3 (d+e x)^2}+\frac{(d g+e f) (d g+5 e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{32 d^6 e^3}",1,"(e*f + d*g)^2/(32*d^5*e^3*(d - e*x)) - (e*f - d*g)^2/(16*d^2*e^3*(d + e*x)^4) - (e^2*f^2 - d^2*g^2)/(12*d^3*e^3*(d + e*x)^3) - ((3*e*f - d*g)*(e*f + d*g))/(32*d^4*e^3*(d + e*x)^2) - (f*(e*f + d*g))/(8*d^5*e^2*(d + e*x)) + ((e*f + d*g)*(5*e*f + d*g)*ArcTanh[(e*x)/d])/(32*d^6*e^3)","A",4,3,29,0.1034,1,"{848, 88, 208}"
568,1,210,0,0.2419342,"\int \frac{(f+g x)^2}{(d+e x)^4 \left(d^2-e^2 x^2\right)^2} \, dx","Int[(f + g*x)^2/((d + e*x)^4*(d^2 - e^2*x^2)^2),x]","-\frac{e^2 f^2-d^2 g^2}{16 d^3 e^3 (d+e x)^4}-\frac{(e f-d g)^2}{20 d^2 e^3 (d+e x)^5}+\frac{(d g+e f)^2}{64 d^6 e^3 (d-e x)}-\frac{(d g+e f) (d g+5 e f)}{64 d^6 e^3 (d+e x)}-\frac{f (d g+e f)}{16 d^5 e^2 (d+e x)^2}-\frac{(3 e f-d g) (d g+e f)}{48 d^4 e^3 (d+e x)^3}+\frac{(d g+e f) (d g+3 e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{32 d^7 e^3}","-\frac{e^2 f^2-d^2 g^2}{16 d^3 e^3 (d+e x)^4}-\frac{(e f-d g)^2}{20 d^2 e^3 (d+e x)^5}+\frac{(d g+e f)^2}{64 d^6 e^3 (d-e x)}-\frac{(d g+e f) (d g+5 e f)}{64 d^6 e^3 (d+e x)}-\frac{f (d g+e f)}{16 d^5 e^2 (d+e x)^2}-\frac{(3 e f-d g) (d g+e f)}{48 d^4 e^3 (d+e x)^3}+\frac{(d g+e f) (d g+3 e f) \tanh ^{-1}\left(\frac{e x}{d}\right)}{32 d^7 e^3}",1,"(e*f + d*g)^2/(64*d^6*e^3*(d - e*x)) - (e*f - d*g)^2/(20*d^2*e^3*(d + e*x)^5) - (e^2*f^2 - d^2*g^2)/(16*d^3*e^3*(d + e*x)^4) - ((3*e*f - d*g)*(e*f + d*g))/(48*d^4*e^3*(d + e*x)^3) - (f*(e*f + d*g))/(16*d^5*e^2*(d + e*x)^2) - ((e*f + d*g)*(5*e*f + d*g))/(64*d^6*e^3*(d + e*x)) + ((e*f + d*g)*(3*e*f + d*g)*ArcTanh[(e*x)/d])/(32*d^7*e^3)","A",4,3,29,0.1034,1,"{848, 88, 208}"
569,1,179,0,0.2411373,"\int \frac{(d+e x)^7 (f+g x)^2}{\left(d^2-e^2 x^2\right)^3} \, dx","Int[((d + e*x)^7*(f + g*x)^2)/(d^2 - e^2*x^2)^3,x]","-\frac{d x \left(56 d^2 g^2+48 d e f g+7 e^2 f^2\right)}{e^2}-\frac{8 d^2 \left(13 d^2 g^2+14 d e f g+3 e^2 f^2\right) \log (d-e x)}{e^3}+\frac{8 d^4 (d g+e f)^2}{e^3 (d-e x)^2}-\frac{32 d^3 (d g+e f) (2 d g+e f)}{e^3 (d-e x)}-\frac{1}{3} g x^3 (7 d g+2 e f)-\frac{x^2 (2 d g+e f) (12 d g+e f)}{2 e}-\frac{1}{4} e g^2 x^4","-\frac{d x \left(56 d^2 g^2+48 d e f g+7 e^2 f^2\right)}{e^2}-\frac{8 d^2 \left(13 d^2 g^2+14 d e f g+3 e^2 f^2\right) \log (d-e x)}{e^3}+\frac{8 d^4 (d g+e f)^2}{e^3 (d-e x)^2}-\frac{32 d^3 (d g+e f) (2 d g+e f)}{e^3 (d-e x)}-\frac{1}{3} g x^3 (7 d g+2 e f)-\frac{x^2 (2 d g+e f) (12 d g+e f)}{2 e}-\frac{1}{4} e g^2 x^4",1,"-((d*(7*e^2*f^2 + 48*d*e*f*g + 56*d^2*g^2)*x)/e^2) - ((e*f + 2*d*g)*(e*f + 12*d*g)*x^2)/(2*e) - (g*(2*e*f + 7*d*g)*x^3)/3 - (e*g^2*x^4)/4 + (8*d^4*(e*f + d*g)^2)/(e^3*(d - e*x)^2) - (32*d^3*(e*f + d*g)*(e*f + 2*d*g))/(e^3*(d - e*x)) - (8*d^2*(3*e^2*f^2 + 14*d*e*f*g + 13*d^2*g^2)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 88}"
570,1,149,0,0.1972552,"\int \frac{(d+e x)^6 (f+g x)^2}{\left(d^2-e^2 x^2\right)^3} \, dx","Int[((d + e*x)^6*(f + g*x)^2)/(d^2 - e^2*x^2)^3,x]","-\frac{x \left(18 d^2 g^2+12 d e f g+e^2 f^2\right)}{e^2}-\frac{2 d \left(19 d^2 g^2+18 d e f g+3 e^2 f^2\right) \log (d-e x)}{e^3}+\frac{4 d^3 (d g+e f)^2}{e^3 (d-e x)^2}-\frac{4 d^2 (d g+e f) (7 d g+3 e f)}{e^3 (d-e x)}-\frac{g x^2 (3 d g+e f)}{e}-\frac{g^2 x^3}{3}","-\frac{x \left(18 d^2 g^2+12 d e f g+e^2 f^2\right)}{e^2}-\frac{2 d \left(19 d^2 g^2+18 d e f g+3 e^2 f^2\right) \log (d-e x)}{e^3}+\frac{4 d^3 (d g+e f)^2}{e^3 (d-e x)^2}-\frac{4 d^2 (d g+e f) (7 d g+3 e f)}{e^3 (d-e x)}-\frac{g x^2 (3 d g+e f)}{e}-\frac{g^2 x^3}{3}",1,"-(((e^2*f^2 + 12*d*e*f*g + 18*d^2*g^2)*x)/e^2) - (g*(e*f + 3*d*g)*x^2)/e - (g^2*x^3)/3 + (4*d^3*(e*f + d*g)^2)/(e^3*(d - e*x)^2) - (4*d^2*(e*f + d*g)*(3*e*f + 7*d*g))/(e^3*(d - e*x)) - (2*d*(3*e^2*f^2 + 18*d*e*f*g + 19*d^2*g^2)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 88}"
571,1,118,0,0.1430057,"\int \frac{(d+e x)^5 (f+g x)^2}{\left(d^2-e^2 x^2\right)^3} \, dx","Int[((d + e*x)^5*(f + g*x)^2)/(d^2 - e^2*x^2)^3,x]","-\frac{\left(13 d^2 g^2+10 d e f g+e^2 f^2\right) \log (d-e x)}{e^3}+\frac{2 d^2 (d g+e f)^2}{e^3 (d-e x)^2}-\frac{4 d (3 d g+e f) (d g+e f)}{e^3 (d-e x)}-\frac{g x (5 d g+2 e f)}{e^2}-\frac{g^2 x^2}{2 e}","-\frac{\left(13 d^2 g^2+10 d e f g+e^2 f^2\right) \log (d-e x)}{e^3}+\frac{2 d^2 (d g+e f)^2}{e^3 (d-e x)^2}-\frac{4 d (3 d g+e f) (d g+e f)}{e^3 (d-e x)}-\frac{g x (5 d g+2 e f)}{e^2}-\frac{g^2 x^2}{2 e}",1,"-((g*(2*e*f + 5*d*g)*x)/e^2) - (g^2*x^2)/(2*e) + (2*d^2*(e*f + d*g)^2)/(e^3*(d - e*x)^2) - (4*d*(e*f + d*g)*(e*f + 3*d*g))/(e^3*(d - e*x)) - ((e^2*f^2 + 10*d*e*f*g + 13*d^2*g^2)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 88}"
572,1,81,0,0.1008749,"\int \frac{(d+e x)^4 (f+g x)^2}{\left(d^2-e^2 x^2\right)^3} \, dx","Int[((d + e*x)^4*(f + g*x)^2)/(d^2 - e^2*x^2)^3,x]","-\frac{(d g+e f) (5 d g+e f)}{e^3 (d-e x)}+\frac{d (d g+e f)^2}{e^3 (d-e x)^2}-\frac{2 g (2 d g+e f) \log (d-e x)}{e^3}-\frac{g^2 x}{e^2}","-\frac{(d g+e f) (5 d g+e f)}{e^3 (d-e x)}+\frac{d (d g+e f)^2}{e^3 (d-e x)^2}-\frac{2 g (2 d g+e f) \log (d-e x)}{e^3}-\frac{g^2 x}{e^2}",1,"-((g^2*x)/e^2) + (d*(e*f + d*g)^2)/(e^3*(d - e*x)^2) - ((e*f + d*g)*(e*f + 5*d*g))/(e^3*(d - e*x)) - (2*g*(e*f + 2*d*g)*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 77}"
573,1,61,0,0.0597248,"\int \frac{(d+e x)^3 (f+g x)^2}{\left(d^2-e^2 x^2\right)^3} \, dx","Int[((d + e*x)^3*(f + g*x)^2)/(d^2 - e^2*x^2)^3,x]","-\frac{2 g (d g+e f)}{e^3 (d-e x)}+\frac{(d g+e f)^2}{2 e^3 (d-e x)^2}-\frac{g^2 \log (d-e x)}{e^3}","-\frac{2 g (d g+e f)}{e^3 (d-e x)}+\frac{(d g+e f)^2}{2 e^3 (d-e x)^2}-\frac{g^2 \log (d-e x)}{e^3}",1,"(e*f + d*g)^2/(2*e^3*(d - e*x)^2) - (2*g*(e*f + d*g))/(e^3*(d - e*x)) - (g^2*Log[d - e*x])/e^3","A",3,2,29,0.06897,1,"{848, 43}"
574,1,88,0,0.0985019,"\int \frac{(d+e x)^2 (f+g x)^2}{\left(d^2-e^2 x^2\right)^3} \, dx","Int[((d + e*x)^2*(f + g*x)^2)/(d^2 - e^2*x^2)^3,x]","\frac{(e f-3 d g) (d g+e f)}{4 d^2 e^3 (d-e x)}+\frac{(e f-d g)^2 \tanh ^{-1}\left(\frac{e x}{d}\right)}{4 d^3 e^3}+\frac{(d g+e f)^2}{4 d e^3 (d-e x)^2}","\frac{(e f-3 d g) (d g+e f)}{4 d^2 e^3 (d-e x)}+\frac{(e f-d g)^2 \tanh ^{-1}\left(\frac{e x}{d}\right)}{4 d^3 e^3}+\frac{(d g+e f)^2}{4 d e^3 (d-e x)^2}",1,"(e*f + d*g)^2/(4*d*e^3*(d - e*x)^2) + ((e*f - 3*d*g)*(e*f + d*g))/(4*d^2*e^3*(d - e*x)) + ((e*f - d*g)^2*ArcTanh[(e*x)/d])/(4*d^3*e^3)","A",4,3,29,0.1034,1,"{848, 88, 208}"
575,1,122,0,0.1153903,"\int \frac{(d+e x) (f+g x)^2}{\left(d^2-e^2 x^2\right)^3} \, dx","Int[((d + e*x)*(f + g*x)^2)/(d^2 - e^2*x^2)^3,x]","\frac{e^2 f^2-d^2 g^2}{4 d^3 e^3 (d-e x)}-\frac{(e f-d g)^2}{8 d^3 e^3 (d+e x)}+\frac{(d g+e f)^2}{8 d^2 e^3 (d-e x)^2}+\frac{(d g+3 e f) (e f-d g) \tanh ^{-1}\left(\frac{e x}{d}\right)}{8 d^4 e^3}","\frac{e^2 f^2-d^2 g^2}{4 d^3 e^3 (d-e x)}-\frac{(e f-d g)^2}{8 d^3 e^3 (d+e x)}+\frac{(d g+e f)^2}{8 d^2 e^3 (d-e x)^2}+\frac{(d g+3 e f) (e f-d g) \tanh ^{-1}\left(\frac{e x}{d}\right)}{8 d^4 e^3}",1,"(e*f + d*g)^2/(8*d^2*e^3*(d - e*x)^2) + (e^2*f^2 - d^2*g^2)/(4*d^3*e^3*(d - e*x)) - (e*f - d*g)^2/(8*d^3*e^3*(d + e*x)) + ((e*f - d*g)*(3*e*f + d*g)*ArcTanh[(e*x)/d])/(8*d^4*e^3)","A",4,3,27,0.1111,1,"{799, 88, 208}"
576,1,127,0,0.0614481,"\int \frac{(f+g x)^2}{\left(d^2-e^2 x^2\right)^3} \, dx","Int[(f + g*x)^2/(d^2 - e^2*x^2)^3,x]","\frac{x \left(3 e^2 f^2-d^2 g^2\right)+2 d^2 f g}{8 d^4 e^2 \left(d^2-e^2 x^2\right)}+\frac{\left(3 e^2 f^2-d^2 g^2\right) \tanh ^{-1}\left(\frac{e x}{d}\right)}{8 d^5 e^3}+\frac{(f+g x) \left(d^2 g+e^2 f x\right)}{4 d^2 e^2 \left(d^2-e^2 x^2\right)^2}","\frac{x \left(3 e^2 f^2-d^2 g^2\right)+2 d^2 f g}{8 d^4 e^2 \left(d^2-e^2 x^2\right)}+\frac{\left(3 e^2 f^2-d^2 g^2\right) \tanh ^{-1}\left(\frac{e x}{d}\right)}{8 d^5 e^3}+\frac{(f+g x) \left(d^2 g+e^2 f x\right)}{4 d^2 e^2 \left(d^2-e^2 x^2\right)^2}",1,"((d^2*g + e^2*f*x)*(f + g*x))/(4*d^2*e^2*(d^2 - e^2*x^2)^2) + (2*d^2*f*g + (3*e^2*f^2 - d^2*g^2)*x)/(8*d^4*e^2*(d^2 - e^2*x^2)) + ((3*e^2*f^2 - d^2*g^2)*ArcTanh[(e*x)/d])/(8*d^5*e^3)","A",3,3,22,0.1364,1,"{739, 639, 208}"
577,1,188,0,0.2096894,"\int \frac{(f+g x)^2}{(d+e x) \left(d^2-e^2 x^2\right)^3} \, dx","Int[(f + g*x)^2/((d + e*x)*(d^2 - e^2*x^2)^3),x]","-\frac{3 e^2 f^2-d^2 g^2}{16 d^5 e^3 (d+e x)}+\frac{\left(-d^2 g^2+2 d e f g+5 e^2 f^2\right) \tanh ^{-1}\left(\frac{e x}{d}\right)}{16 d^6 e^3}-\frac{(e f-d g)^2}{24 d^3 e^3 (d+e x)^3}-\frac{(d g+3 e f) (e f-d g)}{32 d^4 e^3 (d+e x)^2}+\frac{f (d g+e f)}{8 d^5 e^2 (d-e x)}+\frac{(d g+e f)^2}{32 d^4 e^3 (d-e x)^2}","-\frac{3 e^2 f^2-d^2 g^2}{16 d^5 e^3 (d+e x)}+\frac{\left(-d^2 g^2+2 d e f g+5 e^2 f^2\right) \tanh ^{-1}\left(\frac{e x}{d}\right)}{16 d^6 e^3}-\frac{(e f-d g)^2}{24 d^3 e^3 (d+e x)^3}-\frac{(d g+3 e f) (e f-d g)}{32 d^4 e^3 (d+e x)^2}+\frac{f (d g+e f)}{8 d^5 e^2 (d-e x)}+\frac{(d g+e f)^2}{32 d^4 e^3 (d-e x)^2}",1,"(e*f + d*g)^2/(32*d^4*e^3*(d - e*x)^2) + (f*(e*f + d*g))/(8*d^5*e^2*(d - e*x)) - (e*f - d*g)^2/(24*d^3*e^3*(d + e*x)^3) - ((e*f - d*g)*(3*e*f + d*g))/(32*d^4*e^3*(d + e*x)^2) - (3*e^2*f^2 - d^2*g^2)/(16*d^5*e^3*(d + e*x)) + ((5*e^2*f^2 + 2*d*e*f*g - d^2*g^2)*ArcTanh[(e*x)/d])/(16*d^6*e^3)","A",4,3,29,0.1034,1,"{848, 88, 208}"
578,1,235,0,0.273199,"\int \frac{(f+g x)^2}{(d+e x)^2 \left(d^2-e^2 x^2\right)^3} \, dx","Int[(f + g*x)^2/((d + e*x)^2*(d^2 - e^2*x^2)^3),x]","-\frac{-d^2 g^2+2 d e f g+5 e^2 f^2}{32 d^6 e^3 (d+e x)}-\frac{3 e^2 f^2-d^2 g^2}{32 d^5 e^3 (d+e x)^2}+\frac{\left(-d^2 g^2+10 d e f g+15 e^2 f^2\right) \tanh ^{-1}\left(\frac{e x}{d}\right)}{64 d^7 e^3}-\frac{(e f-d g)^2}{32 d^3 e^3 (d+e x)^4}-\frac{(d g+3 e f) (e f-d g)}{48 d^4 e^3 (d+e x)^3}+\frac{(d g+e f) (d g+5 e f)}{64 d^6 e^3 (d-e x)}+\frac{(d g+e f)^2}{64 d^5 e^3 (d-e x)^2}","-\frac{-d^2 g^2+2 d e f g+5 e^2 f^2}{32 d^6 e^3 (d+e x)}-\frac{3 e^2 f^2-d^2 g^2}{32 d^5 e^3 (d+e x)^2}+\frac{\left(-d^2 g^2+10 d e f g+15 e^2 f^2\right) \tanh ^{-1}\left(\frac{e x}{d}\right)}{64 d^7 e^3}-\frac{(e f-d g)^2}{32 d^3 e^3 (d+e x)^4}-\frac{(d g+3 e f) (e f-d g)}{48 d^4 e^3 (d+e x)^3}+\frac{(d g+e f) (d g+5 e f)}{64 d^6 e^3 (d-e x)}+\frac{(d g+e f)^2}{64 d^5 e^3 (d-e x)^2}",1,"(e*f + d*g)^2/(64*d^5*e^3*(d - e*x)^2) + ((e*f + d*g)*(5*e*f + d*g))/(64*d^6*e^3*(d - e*x)) - (e*f - d*g)^2/(32*d^3*e^3*(d + e*x)^4) - ((e*f - d*g)*(3*e*f + d*g))/(48*d^4*e^3*(d + e*x)^3) - (3*e^2*f^2 - d^2*g^2)/(32*d^5*e^3*(d + e*x)^2) - (5*e^2*f^2 + 2*d*e*f*g - d^2*g^2)/(32*d^6*e^3*(d + e*x)) + ((15*e^2*f^2 + 10*d*e*f*g - d^2*g^2)*ArcTanh[(e*x)/d])/(64*d^7*e^3)","A",4,3,29,0.1034,1,"{848, 88, 208}"
579,1,269,0,0.9745981,"\int \frac{(d+e x)^3 (f+g x)^5}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[((d + e*x)^3*(f + g*x)^5)/(d^2 - e^2*x^2)^(7/2),x]","\frac{(d+e x) (d g+e f)^3 \left(127 d^2 g^2-21 d e f g+2 e^2 f^2\right)}{15 d^3 e^6 \sqrt{d^2-e^2 x^2}}-\frac{g^3 \left(13 d^2 g^2+30 d e f g+20 e^2 f^2\right) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^6}+\frac{g^4 \sqrt{d^2-e^2 x^2} (3 d g+5 e f)}{e^6}+\frac{(d+e x)^2 (2 e f-23 d g) (d g+e f)^4}{15 d^2 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{(d+e x)^3 (d g+e f)^5}{5 d e^6 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{g^5 x \sqrt{d^2-e^2 x^2}}{2 e^5}","\frac{(d+e x) (d g+e f)^3 \left(127 d^2 g^2-21 d e f g+2 e^2 f^2\right)}{15 d^3 e^6 \sqrt{d^2-e^2 x^2}}-\frac{g^3 \left(13 d^2 g^2+30 d e f g+20 e^2 f^2\right) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^6}+\frac{g^4 \sqrt{d^2-e^2 x^2} (3 d g+5 e f)}{e^6}+\frac{(d+e x)^2 (2 e f-23 d g) (d g+e f)^4}{15 d^2 e^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{(d+e x)^3 (d g+e f)^5}{5 d e^6 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{g^5 x \sqrt{d^2-e^2 x^2}}{2 e^5}",1,"((e*f + d*g)^5*(d + e*x)^3)/(5*d*e^6*(d^2 - e^2*x^2)^(5/2)) + ((2*e*f - 23*d*g)*(e*f + d*g)^4*(d + e*x)^2)/(15*d^2*e^6*(d^2 - e^2*x^2)^(3/2)) + ((e*f + d*g)^3*(2*e^2*f^2 - 21*d*e*f*g + 127*d^2*g^2)*(d + e*x))/(15*d^3*e^6*Sqrt[d^2 - e^2*x^2]) + (g^4*(5*e*f + 3*d*g)*Sqrt[d^2 - e^2*x^2])/e^6 + (g^5*x*Sqrt[d^2 - e^2*x^2])/(2*e^5) - (g^3*(20*e^2*f^2 + 30*d*e*f*g + 13*d^2*g^2)*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^6)","A",7,5,31,0.1613,1,"{1635, 1815, 641, 217, 203}"
580,1,215,0,0.6661902,"\int \frac{(d+e x)^3 (f+g x)^4}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[((d + e*x)^3*(f + g*x)^4)/(d^2 - e^2*x^2)^(7/2),x]","\frac{2 (d+e x) (d g+e f)^2 \left(36 d^2 g^2-8 d e f g+e^2 f^2\right)}{15 d^3 e^5 \sqrt{d^2-e^2 x^2}}-\frac{g^3 (3 d g+4 e f) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}+\frac{2 (d+e x)^2 (e f-9 d g) (d g+e f)^3}{15 d^2 e^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{(d+e x)^3 (d g+e f)^4}{5 d e^5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{g^4 \sqrt{d^2-e^2 x^2}}{e^5}","\frac{2 (d+e x) (d g+e f)^2 \left(36 d^2 g^2-8 d e f g+e^2 f^2\right)}{15 d^3 e^5 \sqrt{d^2-e^2 x^2}}-\frac{g^3 (3 d g+4 e f) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^5}+\frac{2 (d+e x)^2 (e f-9 d g) (d g+e f)^3}{15 d^2 e^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{(d+e x)^3 (d g+e f)^4}{5 d e^5 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{g^4 \sqrt{d^2-e^2 x^2}}{e^5}",1,"((e*f + d*g)^4*(d + e*x)^3)/(5*d*e^5*(d^2 - e^2*x^2)^(5/2)) + (2*(e*f - 9*d*g)*(e*f + d*g)^3*(d + e*x)^2)/(15*d^2*e^5*(d^2 - e^2*x^2)^(3/2)) + (2*(e*f + d*g)^2*(e^2*f^2 - 8*d*e*f*g + 36*d^2*g^2)*(d + e*x))/(15*d^3*e^5*Sqrt[d^2 - e^2*x^2]) + (g^4*Sqrt[d^2 - e^2*x^2])/e^5 - (g^3*(4*e*f + 3*d*g)*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^5","A",6,4,31,0.1290,1,"{1635, 641, 217, 203}"
581,1,183,0,0.4034897,"\int \frac{(d+e x)^3 (f+g x)^3}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[((d + e*x)^3*(f + g*x)^3)/(d^2 - e^2*x^2)^(7/2),x]","\frac{(d+e x) (d g+e f) \left(32 d^2 g^2-11 d e f g+2 e^2 f^2\right)}{15 d^3 e^4 \sqrt{d^2-e^2 x^2}}+\frac{(d+e x)^2 (2 e f-13 d g) (d g+e f)^2}{15 d^2 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{(d+e x)^3 (d g+e f)^3}{5 d e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{g^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}","\frac{(d+e x) (d g+e f) \left(32 d^2 g^2-11 d e f g+2 e^2 f^2\right)}{15 d^3 e^4 \sqrt{d^2-e^2 x^2}}+\frac{(d+e x)^2 (2 e f-13 d g) (d g+e f)^2}{15 d^2 e^4 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{(d+e x)^3 (d g+e f)^3}{5 d e^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{g^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^4}",1,"((e*f + d*g)^3*(d + e*x)^3)/(5*d*e^4*(d^2 - e^2*x^2)^(5/2)) + ((2*e*f - 13*d*g)*(e*f + d*g)^2*(d + e*x)^2)/(15*d^2*e^4*(d^2 - e^2*x^2)^(3/2)) + ((e*f + d*g)*(2*e^2*f^2 - 11*d*e*f*g + 32*d^2*g^2)*(d + e*x))/(15*d^3*e^4*Sqrt[d^2 - e^2*x^2]) - (g^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^4","A",5,4,31,0.1290,1,"{1635, 778, 217, 203}"
582,1,145,0,0.2239164,"\int \frac{(d+e x)^3 (f+g x)^2}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[((d + e*x)^3*(f + g*x)^2)/(d^2 - e^2*x^2)^(7/2),x]","\frac{(d+e x) \left(7 d^2 g^2-6 d e f g+2 e^2 f^2\right)}{15 d^3 e^3 \sqrt{d^2-e^2 x^2}}+\frac{(d+e x)^3 (d g+e f)^2}{5 d e^3 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{2 (d+e x)^2 (e f-4 d g) (d g+e f)}{15 d^2 e^3 \left(d^2-e^2 x^2\right)^{3/2}}","\frac{(d+e x) \left(7 d^2 g^2-6 d e f g+2 e^2 f^2\right)}{15 d^3 e^3 \sqrt{d^2-e^2 x^2}}+\frac{(d+e x)^3 (d g+e f)^2}{5 d e^3 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{2 (d+e x)^2 (e f-4 d g) (d g+e f)}{15 d^2 e^3 \left(d^2-e^2 x^2\right)^{3/2}}",1,"((e*f + d*g)^2*(d + e*x)^3)/(5*d*e^3*(d^2 - e^2*x^2)^(5/2)) + (2*(e*f - 4*d*g)*(e*f + d*g)*(d + e*x)^2)/(15*d^2*e^3*(d^2 - e^2*x^2)^(3/2)) + ((2*e^2*f^2 - 6*d*e*f*g + 7*d^2*g^2)*(d + e*x))/(15*d^3*e^3*Sqrt[d^2 - e^2*x^2])","A",3,3,31,0.09677,1,"{1635, 789, 637}"
583,1,117,0,0.0593807,"\int \frac{(d+e x)^3 (f+g x)}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[((d + e*x)^3*(f + g*x))/(d^2 - e^2*x^2)^(7/2),x]","\frac{(d+e x)^3 (d g+e f)}{5 d e^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{2 (d+e x) (2 e f-3 d g)}{15 d e^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x (2 e f-3 d g)}{15 d^3 e \sqrt{d^2-e^2 x^2}}","\frac{(d+e x)^3 (d g+e f)}{5 d e^2 \left(d^2-e^2 x^2\right)^{5/2}}+\frac{2 (d+e x) (2 e f-3 d g)}{15 d e^2 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{x (2 e f-3 d g)}{15 d^3 e \sqrt{d^2-e^2 x^2}}",1,"((e*f + d*g)*(d + e*x)^3)/(5*d*e^2*(d^2 - e^2*x^2)^(5/2)) + (2*(2*e*f - 3*d*g)*(d + e*x))/(15*d*e^2*(d^2 - e^2*x^2)^(3/2)) + ((2*e*f - 3*d*g)*x)/(15*d^3*e*Sqrt[d^2 - e^2*x^2])","A",3,3,29,0.1034,1,"{789, 653, 191}"
584,1,103,0,0.0493467,"\int \frac{(d+e x)^3}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^3/(d^2 - e^2*x^2)^(7/2),x]","\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^3 e (d-e x)}+\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^2 e (d-e x)^2}+\frac{\sqrt{d^2-e^2 x^2}}{5 d e (d-e x)^3}","\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^3 e (d-e x)}+\frac{2 \sqrt{d^2-e^2 x^2}}{15 d^2 e (d-e x)^2}+\frac{\sqrt{d^2-e^2 x^2}}{5 d e (d-e x)^3}",1,"Sqrt[d^2 - e^2*x^2]/(5*d*e*(d - e*x)^3) + (2*Sqrt[d^2 - e^2*x^2])/(15*d^2*e*(d - e*x)^2) + (2*Sqrt[d^2 - e^2*x^2])/(15*d^3*e*(d - e*x))","A",4,3,24,0.1250,1,"{655, 659, 651}"
585,1,242,0,0.6175264,"\int \frac{(d+e x)^3}{(f+g x) \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^3/((f + g*x)*(d^2 - e^2*x^2)^(7/2)),x]","\frac{e x \left(22 d^2 g^2+9 d e f g+2 e^2 f^2\right)+15 d^3 g^2}{15 d^3 \sqrt{d^2-e^2 x^2} (d g+e f)^3}+\frac{g^3 \tan ^{-1}\left(\frac{d^2 g+e^2 f x}{\sqrt{d^2-e^2 x^2} \sqrt{e^2 f^2-d^2 g^2}}\right)}{(d g+e f)^3 \sqrt{e^2 f^2-d^2 g^2}}-\frac{5 d (e f-d g)-e x (11 d g+e f)}{15 d \left(d^2-e^2 x^2\right)^{3/2} (d g+e f)^2}+\frac{4 d (d+e x)}{5 \left(d^2-e^2 x^2\right)^{5/2} (d g+e f)}","\frac{e x \left(22 d^2 g^2+9 d e f g+2 e^2 f^2\right)+15 d^3 g^2}{15 d^3 \sqrt{d^2-e^2 x^2} (d g+e f)^3}+\frac{g^3 \tan ^{-1}\left(\frac{d^2 g+e^2 f x}{\sqrt{d^2-e^2 x^2} \sqrt{e^2 f^2-d^2 g^2}}\right)}{(d g+e f)^3 \sqrt{e^2 f^2-d^2 g^2}}-\frac{5 d (e f-d g)-e x (11 d g+e f)}{15 d \left(d^2-e^2 x^2\right)^{3/2} (d g+e f)^2}+\frac{4 d (d+e x)}{5 \left(d^2-e^2 x^2\right)^{5/2} (d g+e f)}",1,"(4*d*(d + e*x))/(5*(e*f + d*g)*(d^2 - e^2*x^2)^(5/2)) - (5*d*(e*f - d*g) - e*(e*f + 11*d*g)*x)/(15*d*(e*f + d*g)^2*(d^2 - e^2*x^2)^(3/2)) + (15*d^3*g^2 + e*(2*e^2*f^2 + 9*d*e*f*g + 22*d^2*g^2)*x)/(15*d^3*(e*f + d*g)^3*Sqrt[d^2 - e^2*x^2]) + (g^3*ArcTan[(d^2*g + e^2*f*x)/(Sqrt[e^2*f^2 - d^2*g^2]*Sqrt[d^2 - e^2*x^2])])/((e*f + d*g)^3*Sqrt[e^2*f^2 - d^2*g^2])","A",6,5,31,0.1613,1,"{1647, 823, 12, 725, 204}"
586,1,311,0,1.2644766,"\int \frac{(d+e x)^3}{(f+g x)^2 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^3/((f + g*x)^2*(d^2 - e^2*x^2)^(7/2)),x]","\frac{e \left(e x \left(57 d^2 g^2+14 d e f g+2 e^2 f^2\right)+45 d^3 g^2\right)}{15 d^3 \sqrt{d^2-e^2 x^2} (d g+e f)^4}+\frac{e g^3 (4 e f-3 d g) \tan ^{-1}\left(\frac{d^2 g+e^2 f x}{\sqrt{d^2-e^2 x^2} \sqrt{e^2 f^2-d^2 g^2}}\right)}{(e f-d g) (d g+e f)^4 \sqrt{e^2 f^2-d^2 g^2}}+\frac{g^4 \sqrt{d^2-e^2 x^2}}{(f+g x) (e f-d g) (d g+e f)^4}-\frac{e (5 d (e f-3 d g)-e x (21 d g+e f))}{15 d \left(d^2-e^2 x^2\right)^{3/2} (d g+e f)^3}+\frac{4 d e (d+e x)}{5 \left(d^2-e^2 x^2\right)^{5/2} (d g+e f)^2}","\frac{e \left(e x \left(57 d^2 g^2+14 d e f g+2 e^2 f^2\right)+45 d^3 g^2\right)}{15 d^3 \sqrt{d^2-e^2 x^2} (d g+e f)^4}+\frac{e g^3 (4 e f-3 d g) \tan ^{-1}\left(\frac{d^2 g+e^2 f x}{\sqrt{d^2-e^2 x^2} \sqrt{e^2 f^2-d^2 g^2}}\right)}{(e f-d g) (d g+e f)^4 \sqrt{e^2 f^2-d^2 g^2}}+\frac{g^4 \sqrt{d^2-e^2 x^2}}{(f+g x) (e f-d g) (d g+e f)^4}-\frac{e (5 d (e f-3 d g)-e x (21 d g+e f))}{15 d \left(d^2-e^2 x^2\right)^{3/2} (d g+e f)^3}+\frac{4 d e (d+e x)}{5 \left(d^2-e^2 x^2\right)^{5/2} (d g+e f)^2}",1,"(4*d*e*(d + e*x))/(5*(e*f + d*g)^2*(d^2 - e^2*x^2)^(5/2)) - (e*(5*d*(e*f - 3*d*g) - e*(e*f + 21*d*g)*x))/(15*d*(e*f + d*g)^3*(d^2 - e^2*x^2)^(3/2)) + (e*(45*d^3*g^2 + e*(2*e^2*f^2 + 14*d*e*f*g + 57*d^2*g^2)*x))/(15*d^3*(e*f + d*g)^4*Sqrt[d^2 - e^2*x^2]) + (g^4*Sqrt[d^2 - e^2*x^2])/((e*f - d*g)*(e*f + d*g)^4*(f + g*x)) + (e*g^3*(4*e*f - 3*d*g)*ArcTan[(d^2*g + e^2*f*x)/(Sqrt[e^2*f^2 - d^2*g^2]*Sqrt[d^2 - e^2*x^2])])/((e*f - d*g)*(e*f + d*g)^4*Sqrt[e^2*f^2 - d^2*g^2])","A",6,4,31,0.1290,1,"{1647, 807, 725, 204}"
587,1,398,0,2.5684229,"\int \frac{(d+e x)^3}{(f+g x)^3 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^3/((f + g*x)^3*(d^2 - e^2*x^2)^(7/2)),x]","\frac{e^2 \left(e x \left(107 d^2 g^2+19 d e f g+2 e^2 f^2\right)+90 d^3 g^2\right)}{15 d^3 \sqrt{d^2-e^2 x^2} (d g+e f)^5}+\frac{e^2 g^3 \left(13 d^2 g^2-30 d e f g+20 e^2 f^2\right) \tan ^{-1}\left(\frac{d^2 g+e^2 f x}{\sqrt{d^2-e^2 x^2} \sqrt{e^2 f^2-d^2 g^2}}\right)}{2 (e f-d g)^2 (d g+e f)^5 \sqrt{e^2 f^2-d^2 g^2}}+\frac{3 e g^4 \sqrt{d^2-e^2 x^2} (3 e f-2 d g)}{2 (f+g x) (e f-d g)^2 (d g+e f)^5}+\frac{g^4 \sqrt{d^2-e^2 x^2}}{2 (f+g x)^2 (e f-d g) (d g+e f)^4}-\frac{e^2 (5 d (e f-5 d g)-e x (31 d g+e f))}{15 d \left(d^2-e^2 x^2\right)^{3/2} (d g+e f)^4}+\frac{4 d e^2 (d+e x)}{5 \left(d^2-e^2 x^2\right)^{5/2} (d g+e f)^3}","\frac{e^2 \left(e x \left(107 d^2 g^2+19 d e f g+2 e^2 f^2\right)+90 d^3 g^2\right)}{15 d^3 \sqrt{d^2-e^2 x^2} (d g+e f)^5}+\frac{e^2 g^3 \left(13 d^2 g^2-30 d e f g+20 e^2 f^2\right) \tan ^{-1}\left(\frac{d^2 g+e^2 f x}{\sqrt{d^2-e^2 x^2} \sqrt{e^2 f^2-d^2 g^2}}\right)}{2 (e f-d g)^2 (d g+e f)^5 \sqrt{e^2 f^2-d^2 g^2}}+\frac{3 e g^4 \sqrt{d^2-e^2 x^2} (3 e f-2 d g)}{2 (f+g x) (e f-d g)^2 (d g+e f)^5}+\frac{g^4 \sqrt{d^2-e^2 x^2}}{2 (f+g x)^2 (e f-d g) (d g+e f)^4}-\frac{e^2 (5 d (e f-5 d g)-e x (31 d g+e f))}{15 d \left(d^2-e^2 x^2\right)^{3/2} (d g+e f)^4}+\frac{4 d e^2 (d+e x)}{5 \left(d^2-e^2 x^2\right)^{5/2} (d g+e f)^3}",1,"(4*d*e^2*(d + e*x))/(5*(e*f + d*g)^3*(d^2 - e^2*x^2)^(5/2)) - (e^2*(5*d*(e*f - 5*d*g) - e*(e*f + 31*d*g)*x))/(15*d*(e*f + d*g)^4*(d^2 - e^2*x^2)^(3/2)) + (e^2*(90*d^3*g^2 + e*(2*e^2*f^2 + 19*d*e*f*g + 107*d^2*g^2)*x))/(15*d^3*(e*f + d*g)^5*Sqrt[d^2 - e^2*x^2]) + (g^4*Sqrt[d^2 - e^2*x^2])/(2*(e*f - d*g)*(e*f + d*g)^4*(f + g*x)^2) + (3*e*g^4*(3*e*f - 2*d*g)*Sqrt[d^2 - e^2*x^2])/(2*(e*f - d*g)^2*(e*f + d*g)^5*(f + g*x)) + (e^2*g^3*(20*e^2*f^2 - 30*d*e*f*g + 13*d^2*g^2)*ArcTan[(d^2*g + e^2*f*x)/(Sqrt[e^2*f^2 - d^2*g^2]*Sqrt[d^2 - e^2*x^2])])/(2*(e*f - d*g)^2*(e*f + d*g)^5*Sqrt[e^2*f^2 - d^2*g^2])","A",7,5,31,0.1613,1,"{1647, 1651, 807, 725, 204}"
588,1,112,0,0.215486,"\int \frac{a+c x^2}{(d+e x)^{3/2} (f+g x)} \, dx","Int[(a + c*x^2)/((d + e*x)^(3/2)*(f + g*x)),x]","-\frac{2 \left(a e^2+c d^2\right)}{e^2 \sqrt{d+e x} (e f-d g)}-\frac{2 \left(a g^2+c f^2\right) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e f-d g}}\right)}{g^{3/2} (e f-d g)^{3/2}}+\frac{2 c \sqrt{d+e x}}{e^2 g}","-\frac{2 \left(a e^2+c d^2\right)}{e^2 \sqrt{d+e x} (e f-d g)}-\frac{2 \left(a g^2+c f^2\right) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e f-d g}}\right)}{g^{3/2} (e f-d g)^{3/2}}+\frac{2 c \sqrt{d+e x}}{e^2 g}",1,"(-2*(c*d^2 + a*e^2))/(e^2*(e*f - d*g)*Sqrt[d + e*x]) + (2*c*Sqrt[d + e*x])/(e^2*g) - (2*(c*f^2 + a*g^2)*ArcTan[(Sqrt[g]*Sqrt[d + e*x])/Sqrt[e*f - d*g]])/(g^(3/2)*(e*f - d*g)^(3/2))","A",4,3,24,0.1250,1,"{898, 1261, 205}"
589,1,240,0,0.3449772,"\int \frac{(d+e x)^3 \left(a+c x^2\right)}{\sqrt{f+g x}} \, dx","Int[((d + e*x)^3*(a + c*x^2))/Sqrt[f + g*x],x]","\frac{2 e (f+g x)^{7/2} \left(a e^2 g^2+c \left(3 d^2 g^2-12 d e f g+10 e^2 f^2\right)\right)}{7 g^6}-\frac{2 (f+g x)^{5/2} (e f-d g) \left(3 a e^2 g^2+c \left(d^2 g^2-8 d e f g+10 e^2 f^2\right)\right)}{5 g^6}-\frac{2 \sqrt{f+g x} \left(a g^2+c f^2\right) (e f-d g)^3}{g^6}+\frac{2 (f+g x)^{3/2} (e f-d g)^2 \left(3 a e g^2+c f (5 e f-2 d g)\right)}{3 g^6}-\frac{2 c e^2 (f+g x)^{9/2} (5 e f-3 d g)}{9 g^6}+\frac{2 c e^3 (f+g x)^{11/2}}{11 g^6}","\frac{2 e (f+g x)^{7/2} \left(a e^2 g^2+c \left(3 d^2 g^2-12 d e f g+10 e^2 f^2\right)\right)}{7 g^6}-\frac{2 (f+g x)^{5/2} (e f-d g) \left(3 a e^2 g^2+c \left(d^2 g^2-8 d e f g+10 e^2 f^2\right)\right)}{5 g^6}-\frac{2 \sqrt{f+g x} \left(a g^2+c f^2\right) (e f-d g)^3}{g^6}+\frac{2 (f+g x)^{3/2} (e f-d g)^2 \left(3 a e g^2+c f (5 e f-2 d g)\right)}{3 g^6}-\frac{2 c e^2 (f+g x)^{9/2} (5 e f-3 d g)}{9 g^6}+\frac{2 c e^3 (f+g x)^{11/2}}{11 g^6}",1,"(-2*(e*f - d*g)^3*(c*f^2 + a*g^2)*Sqrt[f + g*x])/g^6 + (2*(e*f - d*g)^2*(3*a*e*g^2 + c*f*(5*e*f - 2*d*g))*(f + g*x)^(3/2))/(3*g^6) - (2*(e*f - d*g)*(3*a*e^2*g^2 + c*(10*e^2*f^2 - 8*d*e*f*g + d^2*g^2))*(f + g*x)^(5/2))/(5*g^6) + (2*e*(a*e^2*g^2 + c*(10*e^2*f^2 - 12*d*e*f*g + 3*d^2*g^2))*(f + g*x)^(7/2))/(7*g^6) - (2*c*e^2*(5*e*f - 3*d*g)*(f + g*x)^(9/2))/(9*g^6) + (2*c*e^3*(f + g*x)^(11/2))/(11*g^6)","A",3,2,24,0.08333,1,"{898, 1153}"
590,1,175,0,0.2370118,"\int \frac{(d+e x)^2 \left(a+c x^2\right)}{\sqrt{f+g x}} \, dx","Int[((d + e*x)^2*(a + c*x^2))/Sqrt[f + g*x],x]","\frac{2 (f+g x)^{5/2} \left(a e^2 g^2+c \left(d^2 g^2-6 d e f g+6 e^2 f^2\right)\right)}{5 g^5}+\frac{2 \sqrt{f+g x} \left(a g^2+c f^2\right) (e f-d g)^2}{g^5}-\frac{4 (f+g x)^{3/2} (e f-d g) \left(a e g^2+c f (2 e f-d g)\right)}{3 g^5}-\frac{4 c e (f+g x)^{7/2} (2 e f-d g)}{7 g^5}+\frac{2 c e^2 (f+g x)^{9/2}}{9 g^5}","\frac{2 (f+g x)^{5/2} \left(a e^2 g^2+c \left(d^2 g^2-6 d e f g+6 e^2 f^2\right)\right)}{5 g^5}+\frac{2 \sqrt{f+g x} \left(a g^2+c f^2\right) (e f-d g)^2}{g^5}-\frac{4 (f+g x)^{3/2} (e f-d g) \left(a e g^2+c f (2 e f-d g)\right)}{3 g^5}-\frac{4 c e (f+g x)^{7/2} (2 e f-d g)}{7 g^5}+\frac{2 c e^2 (f+g x)^{9/2}}{9 g^5}",1,"(2*(e*f - d*g)^2*(c*f^2 + a*g^2)*Sqrt[f + g*x])/g^5 - (4*(e*f - d*g)*(a*e*g^2 + c*f*(2*e*f - d*g))*(f + g*x)^(3/2))/(3*g^5) + (2*(a*e^2*g^2 + c*(6*e^2*f^2 - 6*d*e*f*g + d^2*g^2))*(f + g*x)^(5/2))/(5*g^5) - (4*c*e*(2*e*f - d*g)*(f + g*x)^(7/2))/(7*g^5) + (2*c*e^2*(f + g*x)^(9/2))/(9*g^5)","A",3,2,24,0.08333,1,"{898, 1153}"
591,1,113,0,0.0742448,"\int \frac{(d+e x) \left(a+c x^2\right)}{\sqrt{f+g x}} \, dx","Int[((d + e*x)*(a + c*x^2))/Sqrt[f + g*x],x]","-\frac{2 \sqrt{f+g x} \left(a g^2+c f^2\right) (e f-d g)}{g^4}+\frac{2 (f+g x)^{3/2} \left(a e g^2+c f (3 e f-2 d g)\right)}{3 g^4}-\frac{2 c (f+g x)^{5/2} (3 e f-d g)}{5 g^4}+\frac{2 c e (f+g x)^{7/2}}{7 g^4}","-\frac{2 \sqrt{f+g x} \left(a g^2+c f^2\right) (e f-d g)}{g^4}+\frac{2 (f+g x)^{3/2} \left(a e g^2+c f (3 e f-2 d g)\right)}{3 g^4}-\frac{2 c (f+g x)^{5/2} (3 e f-d g)}{5 g^4}+\frac{2 c e (f+g x)^{7/2}}{7 g^4}",1,"(-2*(e*f - d*g)*(c*f^2 + a*g^2)*Sqrt[f + g*x])/g^4 + (2*(a*e*g^2 + c*f*(3*e*f - 2*d*g))*(f + g*x)^(3/2))/(3*g^4) - (2*c*(3*e*f - d*g)*(f + g*x)^(5/2))/(5*g^4) + (2*c*e*(f + g*x)^(7/2))/(7*g^4)","A",2,1,22,0.04545,1,"{772}"
592,1,61,0,0.0262261,"\int \frac{a+c x^2}{\sqrt{f+g x}} \, dx","Int[(a + c*x^2)/Sqrt[f + g*x],x]","\frac{2 \sqrt{f+g x} \left(a g^2+c f^2\right)}{g^3}+\frac{2 c (f+g x)^{5/2}}{5 g^3}-\frac{4 c f (f+g x)^{3/2}}{3 g^3}","\frac{2 \sqrt{f+g x} \left(a g^2+c f^2\right)}{g^3}+\frac{2 c (f+g x)^{5/2}}{5 g^3}-\frac{4 c f (f+g x)^{3/2}}{3 g^3}",1,"(2*(c*f^2 + a*g^2)*Sqrt[f + g*x])/g^3 - (4*c*f*(f + g*x)^(3/2))/(3*g^3) + (2*c*(f + g*x)^(5/2))/(5*g^3)","A",2,1,17,0.05882,1,"{697}"
593,1,104,0,0.1237587,"\int \frac{a+c x^2}{(d+e x) \sqrt{f+g x}} \, dx","Int[(a + c*x^2)/((d + e*x)*Sqrt[f + g*x]),x]","-\frac{2 \left(a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{5/2} \sqrt{e f-d g}}-\frac{2 c \sqrt{f+g x} (d g+e f)}{e^2 g^2}+\frac{2 c (f+g x)^{3/2}}{3 e g^2}","-\frac{2 \left(a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{5/2} \sqrt{e f-d g}}-\frac{2 c \sqrt{f+g x} (d g+e f)}{e^2 g^2}+\frac{2 c (f+g x)^{3/2}}{3 e g^2}",1,"(-2*c*(e*f + d*g)*Sqrt[f + g*x])/(e^2*g^2) + (2*c*(f + g*x)^(3/2))/(3*e*g^2) - (2*(c*d^2 + a*e^2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(e^(5/2)*Sqrt[e*f - d*g])","A",4,3,24,0.1250,1,"{898, 1153, 208}"
594,1,122,0,0.2034159,"\int \frac{a+c x^2}{(d+e x)^2 \sqrt{f+g x}} \, dx","Int[(a + c*x^2)/((d + e*x)^2*Sqrt[f + g*x]),x]","-\frac{\sqrt{f+g x} \left(a+\frac{c d^2}{e^2}\right)}{(d+e x) (e f-d g)}+\frac{\left(a e^2 g+c d (4 e f-3 d g)\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{5/2} (e f-d g)^{3/2}}+\frac{2 c \sqrt{f+g x}}{e^2 g}","-\frac{\sqrt{f+g x} \left(a+\frac{c d^2}{e^2}\right)}{(d+e x) (e f-d g)}+\frac{\left(a e^2 g+c d (4 e f-3 d g)\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{5/2} (e f-d g)^{3/2}}+\frac{2 c \sqrt{f+g x}}{e^2 g}",1,"(2*c*Sqrt[f + g*x])/(e^2*g) - ((a + (c*d^2)/e^2)*Sqrt[f + g*x])/((e*f - d*g)*(d + e*x)) + ((a*e^2*g + c*d*(4*e*f - 3*d*g))*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(e^(5/2)*(e*f - d*g)^(3/2))","A",4,4,24,0.1667,1,"{898, 1157, 388, 208}"
595,1,178,0,0.3030497,"\int \frac{a+c x^2}{(d+e x)^3 \sqrt{f+g x}} \, dx","Int[(a + c*x^2)/((d + e*x)^3*Sqrt[f + g*x]),x]","-\frac{\left(3 a e^2 g^2+c \left(3 d^2 g^2-8 d e f g+8 e^2 f^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{4 e^{5/2} (e f-d g)^{5/2}}-\frac{\sqrt{f+g x} \left(a+\frac{c d^2}{e^2}\right)}{2 (d+e x)^2 (e f-d g)}+\frac{\sqrt{f+g x} \left(3 a e^2 g+c d (8 e f-5 d g)\right)}{4 e^2 (d+e x) (e f-d g)^2}","-\frac{\left(3 a e^2 g^2+c \left(3 d^2 g^2-8 d e f g+8 e^2 f^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{4 e^{5/2} (e f-d g)^{5/2}}-\frac{\sqrt{f+g x} \left(a+\frac{c d^2}{e^2}\right)}{2 (d+e x)^2 (e f-d g)}+\frac{\sqrt{f+g x} \left(3 a e^2 g+c d (8 e f-5 d g)\right)}{4 e^2 (d+e x) (e f-d g)^2}",1,"-((a + (c*d^2)/e^2)*Sqrt[f + g*x])/(2*(e*f - d*g)*(d + e*x)^2) + ((3*a*e^2*g + c*d*(8*e*f - 5*d*g))*Sqrt[f + g*x])/(4*e^2*(e*f - d*g)^2*(d + e*x)) - ((3*a*e^2*g^2 + c*(8*e^2*f^2 - 8*d*e*f*g + 3*d^2*g^2))*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(4*e^(5/2)*(e*f - d*g)^(5/2))","A",4,4,24,0.1667,1,"{898, 1157, 385, 208}"
596,1,238,0,0.2682986,"\int \frac{(d+e x)^3 \left(a+c x^2\right)}{(f+g x)^{3/2}} \, dx","Int[((d + e*x)^3*(a + c*x^2))/(f + g*x)^(3/2),x]","\frac{2 e (f+g x)^{5/2} \left(a e^2 g^2+c \left(3 d^2 g^2-12 d e f g+10 e^2 f^2\right)\right)}{5 g^6}-\frac{2 (f+g x)^{3/2} (e f-d g) \left(3 a e^2 g^2+c \left(d^2 g^2-8 d e f g+10 e^2 f^2\right)\right)}{3 g^6}+\frac{2 \left(a g^2+c f^2\right) (e f-d g)^3}{g^6 \sqrt{f+g x}}+\frac{2 \sqrt{f+g x} (e f-d g)^2 \left(3 a e g^2+c f (5 e f-2 d g)\right)}{g^6}-\frac{2 c e^2 (f+g x)^{7/2} (5 e f-3 d g)}{7 g^6}+\frac{2 c e^3 (f+g x)^{9/2}}{9 g^6}","\frac{2 e (f+g x)^{5/2} \left(a e^2 g^2+c \left(3 d^2 g^2-12 d e f g+10 e^2 f^2\right)\right)}{5 g^6}-\frac{2 (f+g x)^{3/2} (e f-d g) \left(3 a e^2 g^2+c \left(d^2 g^2-8 d e f g+10 e^2 f^2\right)\right)}{3 g^6}+\frac{2 \left(a g^2+c f^2\right) (e f-d g)^3}{g^6 \sqrt{f+g x}}+\frac{2 \sqrt{f+g x} (e f-d g)^2 \left(3 a e g^2+c f (5 e f-2 d g)\right)}{g^6}-\frac{2 c e^2 (f+g x)^{7/2} (5 e f-3 d g)}{7 g^6}+\frac{2 c e^3 (f+g x)^{9/2}}{9 g^6}",1,"(2*(e*f - d*g)^3*(c*f^2 + a*g^2))/(g^6*Sqrt[f + g*x]) + (2*(e*f - d*g)^2*(3*a*e*g^2 + c*f*(5*e*f - 2*d*g))*Sqrt[f + g*x])/g^6 - (2*(e*f - d*g)*(3*a*e^2*g^2 + c*(10*e^2*f^2 - 8*d*e*f*g + d^2*g^2))*(f + g*x)^(3/2))/(3*g^6) + (2*e*(a*e^2*g^2 + c*(10*e^2*f^2 - 12*d*e*f*g + 3*d^2*g^2))*(f + g*x)^(5/2))/(5*g^6) - (2*c*e^2*(5*e*f - 3*d*g)*(f + g*x)^(7/2))/(7*g^6) + (2*c*e^3*(f + g*x)^(9/2))/(9*g^6)","A",3,2,24,0.08333,1,"{898, 1261}"
597,1,173,0,0.2035248,"\int \frac{(d+e x)^2 \left(a+c x^2\right)}{(f+g x)^{3/2}} \, dx","Int[((d + e*x)^2*(a + c*x^2))/(f + g*x)^(3/2),x]","\frac{2 (f+g x)^{3/2} \left(a e^2 g^2+c \left(d^2 g^2-6 d e f g+6 e^2 f^2\right)\right)}{3 g^5}-\frac{2 \left(a g^2+c f^2\right) (e f-d g)^2}{g^5 \sqrt{f+g x}}-\frac{4 \sqrt{f+g x} (e f-d g) \left(a e g^2+c f (2 e f-d g)\right)}{g^5}-\frac{4 c e (f+g x)^{5/2} (2 e f-d g)}{5 g^5}+\frac{2 c e^2 (f+g x)^{7/2}}{7 g^5}","\frac{2 (f+g x)^{3/2} \left(a e^2 g^2+c \left(d^2 g^2-6 d e f g+6 e^2 f^2\right)\right)}{3 g^5}-\frac{2 \left(a g^2+c f^2\right) (e f-d g)^2}{g^5 \sqrt{f+g x}}-\frac{4 \sqrt{f+g x} (e f-d g) \left(a e g^2+c f (2 e f-d g)\right)}{g^5}-\frac{4 c e (f+g x)^{5/2} (2 e f-d g)}{5 g^5}+\frac{2 c e^2 (f+g x)^{7/2}}{7 g^5}",1,"(-2*(e*f - d*g)^2*(c*f^2 + a*g^2))/(g^5*Sqrt[f + g*x]) - (4*(e*f - d*g)*(a*e*g^2 + c*f*(2*e*f - d*g))*Sqrt[f + g*x])/g^5 + (2*(a*e^2*g^2 + c*(6*e^2*f^2 - 6*d*e*f*g + d^2*g^2))*(f + g*x)^(3/2))/(3*g^5) - (4*c*e*(2*e*f - d*g)*(f + g*x)^(5/2))/(5*g^5) + (2*c*e^2*(f + g*x)^(7/2))/(7*g^5)","A",3,2,24,0.08333,1,"{898, 1261}"
598,1,111,0,0.0661105,"\int \frac{(d+e x) \left(a+c x^2\right)}{(f+g x)^{3/2}} \, dx","Int[((d + e*x)*(a + c*x^2))/(f + g*x)^(3/2),x]","\frac{2 \left(a g^2+c f^2\right) (e f-d g)}{g^4 \sqrt{f+g x}}+\frac{2 \sqrt{f+g x} \left(a e g^2+c f (3 e f-2 d g)\right)}{g^4}-\frac{2 c (f+g x)^{3/2} (3 e f-d g)}{3 g^4}+\frac{2 c e (f+g x)^{5/2}}{5 g^4}","\frac{2 \left(a g^2+c f^2\right) (e f-d g)}{g^4 \sqrt{f+g x}}+\frac{2 \sqrt{f+g x} \left(a e g^2+c f (3 e f-2 d g)\right)}{g^4}-\frac{2 c (f+g x)^{3/2} (3 e f-d g)}{3 g^4}+\frac{2 c e (f+g x)^{5/2}}{5 g^4}",1,"(2*(e*f - d*g)*(c*f^2 + a*g^2))/(g^4*Sqrt[f + g*x]) + (2*(a*e*g^2 + c*f*(3*e*f - 2*d*g))*Sqrt[f + g*x])/g^4 - (2*c*(3*e*f - d*g)*(f + g*x)^(3/2))/(3*g^4) + (2*c*e*(f + g*x)^(5/2))/(5*g^4)","A",2,1,22,0.04545,1,"{772}"
599,1,59,0,0.0257772,"\int \frac{a+c x^2}{(f+g x)^{3/2}} \, dx","Int[(a + c*x^2)/(f + g*x)^(3/2),x]","-\frac{2 \left(a g^2+c f^2\right)}{g^3 \sqrt{f+g x}}+\frac{2 c (f+g x)^{3/2}}{3 g^3}-\frac{4 c f \sqrt{f+g x}}{g^3}","-\frac{2 \left(a g^2+c f^2\right)}{g^3 \sqrt{f+g x}}+\frac{2 c (f+g x)^{3/2}}{3 g^3}-\frac{4 c f \sqrt{f+g x}}{g^3}",1,"(-2*(c*f^2 + a*g^2))/(g^3*Sqrt[f + g*x]) - (4*c*f*Sqrt[f + g*x])/g^3 + (2*c*(f + g*x)^(3/2))/(3*g^3)","A",2,1,17,0.05882,1,"{697}"
600,1,112,0,0.1736823,"\int \frac{a+c x^2}{(d+e x) (f+g x)^{3/2}} \, dx","Int[(a + c*x^2)/((d + e*x)*(f + g*x)^(3/2)),x]","-\frac{2 \left(a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2} (e f-d g)^{3/2}}+\frac{2 \left(a g^2+c f^2\right)}{g^2 \sqrt{f+g x} (e f-d g)}+\frac{2 c \sqrt{f+g x}}{e g^2}","-\frac{2 \left(a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2} (e f-d g)^{3/2}}+\frac{2 \left(a g^2+c f^2\right)}{g^2 \sqrt{f+g x} (e f-d g)}+\frac{2 c \sqrt{f+g x}}{e g^2}",1,"(2*(c*f^2 + a*g^2))/(g^2*(e*f - d*g)*Sqrt[f + g*x]) + (2*c*Sqrt[f + g*x])/(e*g^2) - (2*(c*d^2 + a*e^2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(e^(3/2)*(e*f - d*g)^(3/2))","A",4,3,24,0.1250,1,"{898, 1261, 208}"
601,1,144,0,0.2712307,"\int \frac{a+c x^2}{(d+e x)^2 (f+g x)^{3/2}} \, dx","Int[(a + c*x^2)/((d + e*x)^2*(f + g*x)^(3/2)),x]","-\frac{\sqrt{f+g x} \left(a e^2+c d^2\right)}{e (d+e x) (e f-d g)^2}+\frac{\left(3 a e^2 g+c d (4 e f-d g)\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2} (e f-d g)^{5/2}}-\frac{2 \left(a g^2+c f^2\right)}{g \sqrt{f+g x} (e f-d g)^2}","-\frac{\sqrt{f+g x} \left(a e^2+c d^2\right)}{e (d+e x) (e f-d g)^2}+\frac{\left(3 a e^2 g+c d (4 e f-d g)\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2} (e f-d g)^{5/2}}-\frac{2 \left(a g^2+c f^2\right)}{g \sqrt{f+g x} (e f-d g)^2}",1,"(-2*(c*f^2 + a*g^2))/(g*(e*f - d*g)^2*Sqrt[f + g*x]) - ((c*d^2 + a*e^2)*Sqrt[f + g*x])/(e*(e*f - d*g)^2*(d + e*x)) + ((3*a*e^2*g + c*d*(4*e*f - d*g))*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(e^(3/2)*(e*f - d*g)^(5/2))","A",4,4,24,0.1667,1,"{898, 1259, 453, 208}"
602,1,214,0,0.5045427,"\int \frac{a+c x^2}{(d+e x)^3 (f+g x)^{3/2}} \, dx","Int[(a + c*x^2)/((d + e*x)^3*(f + g*x)^(3/2)),x]","-\frac{\left(15 a e^2 g^2+c \left(-d^2 g^2+8 d e f g+8 e^2 f^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{4 e^{3/2} (e f-d g)^{7/2}}-\frac{\sqrt{f+g x} \left(a e^2+c d^2\right)}{2 e (d+e x)^2 (e f-d g)^2}+\frac{\sqrt{f+g x} \left(7 a e^2 g+c d (8 e f-d g)\right)}{4 e (d+e x) (e f-d g)^3}+\frac{2 \left(a g^2+c f^2\right)}{\sqrt{f+g x} (e f-d g)^3}","-\frac{\left(15 a e^2 g^2+c \left(-d^2 g^2+8 d e f g+8 e^2 f^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{4 e^{3/2} (e f-d g)^{7/2}}-\frac{\sqrt{f+g x} \left(a e^2+c d^2\right)}{2 e (d+e x)^2 (e f-d g)^2}+\frac{\sqrt{f+g x} \left(7 a e^2 g+c d (8 e f-d g)\right)}{4 e (d+e x) (e f-d g)^3}+\frac{2 \left(a g^2+c f^2\right)}{\sqrt{f+g x} (e f-d g)^3}",1,"(2*(c*f^2 + a*g^2))/((e*f - d*g)^3*Sqrt[f + g*x]) - ((c*d^2 + a*e^2)*Sqrt[f + g*x])/(2*e*(e*f - d*g)^2*(d + e*x)^2) + ((7*a*e^2*g + c*d*(8*e*f - d*g))*Sqrt[f + g*x])/(4*e*(e*f - d*g)^3*(d + e*x)) - ((15*a*e^2*g^2 + c*(8*e^2*f^2 + 8*d*e*f*g - d^2*g^2))*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(4*e^(3/2)*(e*f - d*g)^(7/2))","A",5,5,24,0.2083,1,"{898, 1259, 456, 453, 208}"
603,1,147,0,0.1410734,"\int \frac{a+c x^2}{\sqrt{d+e x} \sqrt{f+g x}} \, dx","Int[(a + c*x^2)/(Sqrt[d + e*x]*Sqrt[f + g*x]),x]","\frac{\left(8 a e^2 g^2+c \left(3 d^2 g^2+2 d e f g+3 e^2 f^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{4 e^{5/2} g^{5/2}}-\frac{c \sqrt{d+e x} \sqrt{f+g x} (5 d g+3 e f)}{4 e^2 g^2}+\frac{c (d+e x)^{3/2} \sqrt{f+g x}}{2 e^2 g}","\frac{\left(8 a e^2 g^2+c \left(3 d^2 g^2+2 d e f g+3 e^2 f^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{4 e^{5/2} g^{5/2}}-\frac{c \sqrt{d+e x} \sqrt{f+g x} (5 d g+3 e f)}{4 e^2 g^2}+\frac{c (d+e x)^{3/2} \sqrt{f+g x}}{2 e^2 g}",1,"-(c*(3*e*f + 5*d*g)*Sqrt[d + e*x]*Sqrt[f + g*x])/(4*e^2*g^2) + (c*(d + e*x)^(3/2)*Sqrt[f + g*x])/(2*e^2*g) + ((8*a*e^2*g^2 + c*(3*e^2*f^2 + 2*d*e*f*g + 3*d^2*g^2))*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(4*e^(5/2)*g^(5/2))","A",5,5,26,0.1923,1,"{952, 80, 63, 217, 206}"
604,1,16,0,0.0091387,"\int \frac{-1+2 x^2}{\sqrt{-1+x} \sqrt{1+x}} \, dx","Int[(-1 + 2*x^2)/(Sqrt[-1 + x]*Sqrt[1 + x]),x]","\sqrt{x-1} x \sqrt{x+1}","\sqrt{x-1} x \sqrt{x+1}",1,"Sqrt[-1 + x]*x*Sqrt[1 + x]","A",1,1,22,0.04545,1,"{384}"
605,1,411,0,2.5113945,"\int \frac{(d+e x)^{3/2} \sqrt{f+g x}}{a+c x^2} \, dx","Int[((d + e*x)^(3/2)*Sqrt[f + g*x])/(a + c*x^2),x]","\frac{\left(\frac{a \left(a e^2 g-c d (d g+2 e f)\right)}{\sqrt{c}}-\sqrt{-a} \left(c d^2 f-a e (2 d g+e f)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{a c \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g}}+\frac{\left(\sqrt{-a} \left(c d^2 f-a e (2 d g+e f)\right)+\frac{a \left(a e^2 g-c d (d g+2 e f)\right)}{\sqrt{c}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{a c \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f}}+\frac{e \sqrt{d+e x} \sqrt{f+g x}}{c}+\frac{\sqrt{e} (3 d g+e f) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{c \sqrt{g}}","\frac{\left(\frac{a \left(a e^2 g-c d (d g+2 e f)\right)}{\sqrt{c}}-\sqrt{-a} \left(c d^2 f-a e (2 d g+e f)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{a c \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g}}+\frac{\left(\sqrt{-a} \left(c d^2 f-a e (2 d g+e f)\right)+\frac{a \left(a e^2 g-c d (d g+2 e f)\right)}{\sqrt{c}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{a c \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f}}+\frac{e \sqrt{d+e x} \sqrt{f+g x}}{c}+\frac{\sqrt{e} (3 d g+e f) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{c \sqrt{g}}",1,"(e*Sqrt[d + e*x]*Sqrt[f + g*x])/c + (Sqrt[e]*(e*f + 3*d*g)*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(c*Sqrt[g]) + (((a*(a*e^2*g - c*d*(2*e*f + d*g)))/Sqrt[c] - Sqrt[-a]*(c*d^2*f - a*e*(e*f + 2*d*g)))*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(a*c*Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]) + (((a*(a*e^2*g - c*d*(2*e*f + d*g)))/Sqrt[c] + Sqrt[-a]*(c*d^2*f - a*e*(e*f + 2*d*g)))*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(a*c*Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[Sqrt[c]*f + Sqrt[-a]*g])","A",11,8,28,0.2857,1,"{904, 80, 63, 217, 206, 6725, 93, 208}"
606,1,342,0,2.0857377,"\int \frac{\sqrt{d+e x} \sqrt{f+g x}}{a+c x^2} \, dx","Int[(Sqrt[d + e*x]*Sqrt[f + g*x])/(a + c*x^2),x]","\frac{\left(-\sqrt{-a} \sqrt{c} (d g+e f)-a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} c \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\left(\sqrt{-a} \sqrt{c} (d g+e f)-a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} c \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f}}+\frac{2 \sqrt{e} \sqrt{g} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{c}","\frac{\left(-\sqrt{-a} \sqrt{c} (d g+e f)-a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} c \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\left(\sqrt{-a} \sqrt{c} (d g+e f)-a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} c \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f}}+\frac{2 \sqrt{e} \sqrt{g} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{c}",1,"(2*Sqrt[e]*Sqrt[g]*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/c + ((c*d*f - a*e*g - Sqrt[-a]*Sqrt[c]*(e*f + d*g))*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*c*Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]) - ((c*d*f - a*e*g + Sqrt[-a]*Sqrt[c]*(e*f + d*g))*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*c*Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[Sqrt[c]*f + Sqrt[-a]*g])","A",10,7,28,0.2500,1,"{906, 63, 217, 206, 6725, 93, 208}"
607,1,240,0,0.3406629,"\int \frac{\sqrt{f+g x}}{\sqrt{d+e x} \left(a+c x^2\right)} \, dx","Int[Sqrt[f + g*x]/(Sqrt[d + e*x]*(a + c*x^2)),x]","\frac{\sqrt{\sqrt{c} f-\sqrt{-a} g} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{c} d-\sqrt{-a} e}}-\frac{\sqrt{\sqrt{-a} g+\sqrt{c} f} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{-a} e+\sqrt{c} d}}","\frac{\sqrt{\sqrt{c} f-\sqrt{-a} g} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{c} d-\sqrt{-a} e}}-\frac{\sqrt{\sqrt{-a} g+\sqrt{c} f} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{-a} e+\sqrt{c} d}}",1,"(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[c]*Sqrt[Sqrt[c]*d - Sqrt[-a]*e]) - (Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[c]*Sqrt[Sqrt[c]*d + Sqrt[-a]*e])","A",6,3,28,0.1071,1,"{910, 93, 208}"
608,1,351,0,2.153353,"\int \frac{\sqrt{f+g x}}{(d+e x)^{3/2} \left(a+c x^2\right)} \, dx","Int[Sqrt[f + g*x]/((d + e*x)^(3/2)*(a + c*x^2)),x]","-\frac{2 e \sqrt{f+g x}}{\sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{\left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{\sqrt{c} d-\sqrt{-a} e} \left(a e^2+c d^2\right) \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{\sqrt{-a} e+\sqrt{c} d} \left(a e^2+c d^2\right) \sqrt{\sqrt{-a} g+\sqrt{c} f}}","-\frac{2 e \sqrt{f+g x}}{\sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{\left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{\sqrt{c} d-\sqrt{-a} e} \left(a e^2+c d^2\right) \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{\sqrt{-a} e+\sqrt{c} d} \left(a e^2+c d^2\right) \sqrt{\sqrt{-a} g+\sqrt{c} f}}",1,"(-2*e*Sqrt[f + g*x])/((c*d^2 + a*e^2)*Sqrt[d + e*x]) + ((c*d*f + a*e*g + Sqrt[-a]*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*(c*d^2 + a*e^2)*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]) - ((c*d*f + a*e*g - Sqrt[-a]*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*(c*d^2 + a*e^2)*Sqrt[Sqrt[c]*f + Sqrt[-a]*g])","A",8,5,28,0.1786,1,"{908, 37, 6725, 93, 208}"
609,1,613,0,3.1601964,"\int \frac{\sqrt{f+g x}}{(d+e x)^{5/2} \left(a+c x^2\right)} \, dx","Int[Sqrt[f + g*x]/((d + e*x)^(5/2)*(a + c*x^2)),x]","\frac{e \sqrt{f+g x} \left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right)}{\sqrt{-a} \sqrt{d+e x} \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right) (e f-d g)}-\frac{e \sqrt{f+g x} \left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right)}{\sqrt{-a} \sqrt{d+e x} \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right) (e f-d g)}+\frac{4 e g \sqrt{f+g x}}{3 \sqrt{d+e x} \left(a e^2+c d^2\right) (e f-d g)}-\frac{2 e \sqrt{f+g x}}{3 (d+e x)^{3/2} \left(a e^2+c d^2\right)}+\frac{\sqrt{c} \left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \left(\sqrt{c} d-\sqrt{-a} e\right)^{3/2} \left(a e^2+c d^2\right) \sqrt{\sqrt{c} f-\sqrt{-a} g}}+\frac{\sqrt{c} \left(a \sqrt{c} (e f-d g)+\sqrt{-a} c d f+\sqrt{-a} a e g\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{a \left(\sqrt{-a} e+\sqrt{c} d\right)^{3/2} \left(a e^2+c d^2\right) \sqrt{\sqrt{-a} g+\sqrt{c} f}}","\frac{e \sqrt{f+g x} \left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right)}{\sqrt{-a} \sqrt{d+e x} \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right) (e f-d g)}-\frac{e \sqrt{f+g x} \left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right)}{\sqrt{-a} \sqrt{d+e x} \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right) (e f-d g)}+\frac{4 e g \sqrt{f+g x}}{3 \sqrt{d+e x} \left(a e^2+c d^2\right) (e f-d g)}-\frac{2 e \sqrt{f+g x}}{3 (d+e x)^{3/2} \left(a e^2+c d^2\right)}+\frac{\sqrt{c} \left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \left(\sqrt{c} d-\sqrt{-a} e\right)^{3/2} \left(a e^2+c d^2\right) \sqrt{\sqrt{c} f-\sqrt{-a} g}}+\frac{\sqrt{c} \left(a \sqrt{c} (e f-d g)+\sqrt{-a} c d f+\sqrt{-a} a e g\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{a \left(\sqrt{-a} e+\sqrt{c} d\right)^{3/2} \left(a e^2+c d^2\right) \sqrt{\sqrt{-a} g+\sqrt{c} f}}",1,"(-2*e*Sqrt[f + g*x])/(3*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) + (4*e*g*Sqrt[f + g*x])/(3*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[d + e*x]) + (e*(c*d*f + a*e*g - Sqrt[-a]*Sqrt[c]*(e*f - d*g))*Sqrt[f + g*x])/(Sqrt[-a]*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[d + e*x]) - (e*(c*d*f + a*e*g + Sqrt[-a]*Sqrt[c]*(e*f - d*g))*Sqrt[f + g*x])/(Sqrt[-a]*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[d + e*x]) + (Sqrt[c]*(c*d*f + a*e*g + Sqrt[-a]*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*(Sqrt[c]*d - Sqrt[-a]*e)^(3/2)*(c*d^2 + a*e^2)*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]) + (Sqrt[c]*(Sqrt[-a]*c*d*f + Sqrt[-a]*a*e*g + a*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(a*(Sqrt[c]*d + Sqrt[-a]*e)^(3/2)*(c*d^2 + a*e^2)*Sqrt[Sqrt[c]*f + Sqrt[-a]*g])","A",11,7,28,0.2500,1,"{908, 45, 37, 6725, 96, 93, 208}"
610,1,337,0,2.4627943,"\int \frac{(d+e x)^{3/2}}{\sqrt{f+g x} \left(a+c x^2\right)} \, dx","Int[(d + e*x)^(3/2)/(Sqrt[f + g*x]*(a + c*x^2)),x]","\frac{\left(-2 \sqrt{-a} \sqrt{c} d e-a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} c \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\left(2 \sqrt{-a} \sqrt{c} d e-a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} c \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f}}+\frac{2 e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{c \sqrt{g}}","\frac{\left(-2 \sqrt{-a} \sqrt{c} d e-a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} c \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\left(2 \sqrt{-a} \sqrt{c} d e-a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} c \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f}}+\frac{2 e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{c \sqrt{g}}",1,"(2*e^(3/2)*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(c*Sqrt[g]) + ((c*d^2 - 2*Sqrt[-a]*Sqrt[c]*d*e - a*e^2)*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*c*Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]) - ((c*d^2 + 2*Sqrt[-a]*Sqrt[c]*d*e - a*e^2)*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*c*Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[Sqrt[c]*f + Sqrt[-a]*g])","A",11,7,28,0.2500,1,"{910, 63, 217, 206, 6725, 93, 208}"
611,1,240,0,0.3338445,"\int \frac{\sqrt{d+e x}}{\sqrt{f+g x} \left(a+c x^2\right)} \, dx","Int[Sqrt[d + e*x]/(Sqrt[f + g*x]*(a + c*x^2)),x]","\frac{\sqrt{\sqrt{c} d-\sqrt{-a} e} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\sqrt{\sqrt{-a} e+\sqrt{c} d} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{-a} g+\sqrt{c} f}}","\frac{\sqrt{\sqrt{c} d-\sqrt{-a} e} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\sqrt{\sqrt{-a} e+\sqrt{c} d} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{-a} g+\sqrt{c} f}}",1,"(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[c]*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]) - (Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[c]*Sqrt[Sqrt[c]*f + Sqrt[-a]*g])","A",6,3,28,0.1071,1,"{910, 93, 208}"
612,1,230,0,0.2039937,"\int \frac{1}{\sqrt{d+e x} \sqrt{f+g x} \left(a+c x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[f + g*x]*(a + c*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f}}",1,"ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])]/(Sqrt[-a]*Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]) - ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])]/(Sqrt[-a]*Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[Sqrt[c]*f + Sqrt[-a]*g])","A",6,3,28,0.1071,1,"{912, 93, 208}"
613,1,354,0,0.6135986,"\int \frac{1}{(d+e x)^{3/2} \sqrt{f+g x} \left(a+c x^2\right)} \, dx","Int[1/((d + e*x)^(3/2)*Sqrt[f + g*x]*(a + c*x^2)),x]","-\frac{e \sqrt{f+g x}}{\sqrt{-a} \sqrt{d+e x} \left(\sqrt{c} d-\sqrt{-a} e\right) (e f-d g)}+\frac{e \sqrt{f+g x}}{\sqrt{-a} \sqrt{d+e x} \left(\sqrt{-a} e+\sqrt{c} d\right) (e f-d g)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \left(\sqrt{c} d-\sqrt{-a} e\right)^{3/2} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \left(\sqrt{-a} e+\sqrt{c} d\right)^{3/2} \sqrt{\sqrt{-a} g+\sqrt{c} f}}","-\frac{e \sqrt{f+g x}}{\sqrt{-a} \sqrt{d+e x} \left(\sqrt{c} d-\sqrt{-a} e\right) (e f-d g)}+\frac{e \sqrt{f+g x}}{\sqrt{-a} \sqrt{d+e x} \left(\sqrt{-a} e+\sqrt{c} d\right) (e f-d g)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \left(\sqrt{c} d-\sqrt{-a} e\right)^{3/2} \sqrt{\sqrt{c} f-\sqrt{-a} g}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \left(\sqrt{-a} e+\sqrt{c} d\right)^{3/2} \sqrt{\sqrt{-a} g+\sqrt{c} f}}",1,"-((e*Sqrt[f + g*x])/(Sqrt[-a]*(Sqrt[c]*d - Sqrt[-a]*e)*(e*f - d*g)*Sqrt[d + e*x])) + (e*Sqrt[f + g*x])/(Sqrt[-a]*(Sqrt[c]*d + Sqrt[-a]*e)*(e*f - d*g)*Sqrt[d + e*x]) + (Sqrt[c]*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*(Sqrt[c]*d - Sqrt[-a]*e)^(3/2)*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]) - (Sqrt[c]*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*(Sqrt[c]*d + Sqrt[-a]*e)^(3/2)*Sqrt[Sqrt[c]*f + Sqrt[-a]*g])","A",8,4,28,0.1429,1,"{912, 96, 93, 208}"
614,1,625,0,2.5305064,"\int \frac{(d+e x)^{3/2}}{(f+g x)^{3/2} \left(a+c x^2\right)} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)^(3/2)*(a + c*x^2)),x]","\frac{2 \sqrt{d+e x} (e f-d g)}{\sqrt{f+g x} \left(a g^2+c f^2\right)}-\frac{2 \sqrt{e} (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{\sqrt{g} \left(a g^2+c f^2\right)}-\frac{\sqrt{e} \left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{g} \left(a g^2+c f^2\right)}+\frac{\sqrt{e} \left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{g} \left(a g^2+c f^2\right)}+\frac{\sqrt{\sqrt{c} d-\sqrt{-a} e} \left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{c} f-\sqrt{-a} g} \left(a g^2+c f^2\right)}-\frac{\sqrt{\sqrt{-a} e+\sqrt{c} d} \left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{-a} g+\sqrt{c} f} \left(a g^2+c f^2\right)}","\frac{2 \sqrt{d+e x} (e f-d g)}{\sqrt{f+g x} \left(a g^2+c f^2\right)}-\frac{2 \sqrt{e} (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{\sqrt{g} \left(a g^2+c f^2\right)}-\frac{\sqrt{e} \left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{g} \left(a g^2+c f^2\right)}+\frac{\sqrt{e} \left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{g} \left(a g^2+c f^2\right)}+\frac{\sqrt{\sqrt{c} d-\sqrt{-a} e} \left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{c} f-\sqrt{-a} g} \left(a g^2+c f^2\right)}-\frac{\sqrt{\sqrt{-a} e+\sqrt{c} d} \left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{c} \sqrt{\sqrt{-a} g+\sqrt{c} f} \left(a g^2+c f^2\right)}",1,"(2*(e*f - d*g)*Sqrt[d + e*x])/((c*f^2 + a*g^2)*Sqrt[f + g*x]) - (2*Sqrt[e]*(e*f - d*g)*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(Sqrt[g]*(c*f^2 + a*g^2)) - (Sqrt[e]*(c*d*f + a*e*g - Sqrt[-a]*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[c]*Sqrt[g]*(c*f^2 + a*g^2)) + (Sqrt[e]*(c*d*f + a*e*g + Sqrt[-a]*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[c]*Sqrt[g]*(c*f^2 + a*g^2)) + (Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*(c*d*f + a*e*g - Sqrt[-a]*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[c]*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*(c*f^2 + a*g^2)) - (Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*(c*d*f + a*e*g + Sqrt[-a]*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[c]*Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*(c*f^2 + a*g^2))","A",19,9,28,0.3214,1,"{908, 47, 63, 217, 206, 6725, 105, 93, 208}"
615,1,351,0,1.8061495,"\int \frac{\sqrt{d+e x}}{(f+g x)^{3/2} \left(a+c x^2\right)} \, dx","Int[Sqrt[d + e*x]/((f + g*x)^(3/2)*(a + c*x^2)),x]","-\frac{2 g \sqrt{d+e x}}{\sqrt{f+g x} \left(a g^2+c f^2\right)}+\frac{\left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g} \left(a g^2+c f^2\right)}-\frac{\left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f} \left(a g^2+c f^2\right)}","-\frac{2 g \sqrt{d+e x}}{\sqrt{f+g x} \left(a g^2+c f^2\right)}+\frac{\left(-\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{\sqrt{c} d-\sqrt{-a} e} \sqrt{\sqrt{c} f-\sqrt{-a} g} \left(a g^2+c f^2\right)}-\frac{\left(\sqrt{-a} \sqrt{c} (e f-d g)+a e g+c d f\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{\sqrt{-a} e+\sqrt{c} d} \sqrt{\sqrt{-a} g+\sqrt{c} f} \left(a g^2+c f^2\right)}",1,"(-2*g*Sqrt[d + e*x])/((c*f^2 + a*g^2)*Sqrt[f + g*x]) + ((c*d*f + a*e*g - Sqrt[-a]*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*(c*f^2 + a*g^2)) - ((c*d*f + a*e*g + Sqrt[-a]*Sqrt[c]*(e*f - d*g))*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*(c*f^2 + a*g^2))","A",8,5,28,0.1786,1,"{908, 37, 6725, 93, 208}"
616,1,354,0,0.7626311,"\int \frac{1}{\sqrt{d+e x} (f+g x)^{3/2} \left(a+c x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*(f + g*x)^(3/2)*(a + c*x^2)),x]","\frac{g \sqrt{d+e x}}{\sqrt{-a} \sqrt{f+g x} \left(\sqrt{c} f-\sqrt{-a} g\right) (e f-d g)}-\frac{g \sqrt{d+e x}}{\sqrt{-a} \sqrt{f+g x} \left(\sqrt{-a} g+\sqrt{c} f\right) (e f-d g)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{\sqrt{c} d-\sqrt{-a} e} \left(\sqrt{c} f-\sqrt{-a} g\right)^{3/2}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{\sqrt{-a} e+\sqrt{c} d} \left(\sqrt{-a} g+\sqrt{c} f\right)^{3/2}}","\frac{g \sqrt{d+e x}}{\sqrt{-a} \sqrt{f+g x} \left(\sqrt{c} f-\sqrt{-a} g\right) (e f-d g)}-\frac{g \sqrt{d+e x}}{\sqrt{-a} \sqrt{f+g x} \left(\sqrt{-a} g+\sqrt{c} f\right) (e f-d g)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \sqrt{\sqrt{c} d-\sqrt{-a} e} \left(\sqrt{c} f-\sqrt{-a} g\right)^{3/2}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \sqrt{\sqrt{-a} e+\sqrt{c} d} \left(\sqrt{-a} g+\sqrt{c} f\right)^{3/2}}",1,"(g*Sqrt[d + e*x])/(Sqrt[-a]*(Sqrt[c]*f - Sqrt[-a]*g)*(e*f - d*g)*Sqrt[f + g*x]) - (g*Sqrt[d + e*x])/(Sqrt[-a]*(Sqrt[c]*f + Sqrt[-a]*g)*(e*f - d*g)*Sqrt[f + g*x]) + (Sqrt[c]*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*(Sqrt[c]*f - Sqrt[-a]*g)^(3/2)) - (Sqrt[c]*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*(Sqrt[c]*f + Sqrt[-a]*g)^(3/2))","A",8,4,28,0.1429,1,"{912, 96, 93, 208}"
617,1,543,0,1.3236212,"\int \frac{1}{(d+e x)^{3/2} (f+g x)^{3/2} \left(a+c x^2\right)} \, dx","Int[1/((d + e*x)^(3/2)*(f + g*x)^(3/2)*(a + c*x^2)),x]","-\frac{e}{\sqrt{-a} \sqrt{d+e x} \sqrt{f+g x} \left(\sqrt{c} d-\sqrt{-a} e\right) (e f-d g)}+\frac{e}{\sqrt{-a} \sqrt{d+e x} \sqrt{f+g x} \left(\sqrt{-a} e+\sqrt{c} d\right) (e f-d g)}+\frac{g \sqrt{d+e x} \left(2 a e g-\sqrt{-a} \sqrt{c} (d g+e f)\right)}{a \sqrt{f+g x} \left(\sqrt{-a} e+\sqrt{c} d\right) \left(\sqrt{-a} g+\sqrt{c} f\right) (e f-d g)^2}+\frac{g \sqrt{d+e x} \left(\sqrt{-a} \sqrt{c} (d g+e f)+2 a e g\right)}{a \sqrt{f+g x} \left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{c} f-\sqrt{-a} g\right) (e f-d g)^2}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \left(\sqrt{c} d-\sqrt{-a} e\right)^{3/2} \left(\sqrt{c} f-\sqrt{-a} g\right)^{3/2}}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \left(\sqrt{-a} e+\sqrt{c} d\right)^{3/2} \left(\sqrt{-a} g+\sqrt{c} f\right)^{3/2}}","-\frac{e}{\sqrt{-a} \sqrt{d+e x} \sqrt{f+g x} \left(\sqrt{c} d-\sqrt{-a} e\right) (e f-d g)}+\frac{e}{\sqrt{-a} \sqrt{d+e x} \sqrt{f+g x} \left(\sqrt{-a} e+\sqrt{c} d\right) (e f-d g)}+\frac{g \sqrt{d+e x} \left(2 \sqrt{-a} e g-\sqrt{c} (d g+e f)\right)}{\sqrt{-a} \sqrt{f+g x} \left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{c} f-\sqrt{-a} g\right) (e f-d g)^2}+\frac{g \sqrt{d+e x} \left(2 \sqrt{-a} e g+\sqrt{c} (d g+e f)\right)}{\sqrt{-a} \sqrt{f+g x} \left(\sqrt{-a} e+\sqrt{c} d\right) \left(\sqrt{-a} g+\sqrt{c} f\right) (e f-d g)^2}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{c} f-\sqrt{-a} g}}{\sqrt{f+g x} \sqrt{\sqrt{c} d-\sqrt{-a} e}}\right)}{\sqrt{-a} \left(\sqrt{c} d-\sqrt{-a} e\right)^{3/2} \left(\sqrt{c} f-\sqrt{-a} g\right)^{3/2}}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{\sqrt{-a} g+\sqrt{c} f}}{\sqrt{f+g x} \sqrt{\sqrt{-a} e+\sqrt{c} d}}\right)}{\sqrt{-a} \left(\sqrt{-a} e+\sqrt{c} d\right)^{3/2} \left(\sqrt{-a} g+\sqrt{c} f\right)^{3/2}}",1,"-(e/(Sqrt[-a]*(Sqrt[c]*d - Sqrt[-a]*e)*(e*f - d*g)*Sqrt[d + e*x]*Sqrt[f + g*x])) + e/(Sqrt[-a]*(Sqrt[c]*d + Sqrt[-a]*e)*(e*f - d*g)*Sqrt[d + e*x]*Sqrt[f + g*x]) + (g*(2*a*e*g - Sqrt[-a]*Sqrt[c]*(e*f + d*g))*Sqrt[d + e*x])/(a*(Sqrt[c]*d + Sqrt[-a]*e)*(Sqrt[c]*f + Sqrt[-a]*g)*(e*f - d*g)^2*Sqrt[f + g*x]) + (g*(2*a*e*g + Sqrt[-a]*Sqrt[c]*(e*f + d*g))*Sqrt[d + e*x])/(a*(Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[c]*f - Sqrt[-a]*g)*(e*f - d*g)^2*Sqrt[f + g*x]) + (c*ArcTanh[(Sqrt[Sqrt[c]*f - Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d - Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*(Sqrt[c]*d - Sqrt[-a]*e)^(3/2)*(Sqrt[c]*f - Sqrt[-a]*g)^(3/2)) - (c*ArcTanh[(Sqrt[Sqrt[c]*f + Sqrt[-a]*g]*Sqrt[d + e*x])/(Sqrt[Sqrt[c]*d + Sqrt[-a]*e]*Sqrt[f + g*x])])/(Sqrt[-a]*(Sqrt[c]*d + Sqrt[-a]*e)^(3/2)*(Sqrt[c]*f + Sqrt[-a]*g)^(3/2))","A",12,6,28,0.2143,1,"{912, 104, 152, 12, 93, 208}"
618,1,65,0,0.048894,"\int \frac{\sqrt{x}}{\sqrt{1+x} \left(1+x^2\right)} \, dx","Int[Sqrt[x]/(Sqrt[1 + x]*(1 + x^2)),x]","-\frac{1}{2} (1-i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{1-i} \sqrt{x}}{\sqrt{x+1}}\right)-\frac{1}{2} (1+i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{1+i} \sqrt{x}}{\sqrt{x+1}}\right)","-\frac{1}{2} (1-i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{1-i} \sqrt{x}}{\sqrt{x+1}}\right)-\frac{1}{2} (1+i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{1+i} \sqrt{x}}{\sqrt{x+1}}\right)",1,"-((1 - I)^(3/2)*ArcTanh[(Sqrt[1 - I]*Sqrt[x])/Sqrt[1 + x]])/2 - ((1 + I)^(3/2)*ArcTanh[(Sqrt[1 + I]*Sqrt[x])/Sqrt[1 + x]])/2","A",6,3,20,0.1500,1,"{910, 93, 208}"
619,1,80,0,0.1432464,"\int \frac{(f+g x)^2 \sqrt{1-x^2}}{(1-x)^4} \, dx","Int[((f + g*x)^2*Sqrt[1 - x^2])/(1 - x)^4,x]","\frac{(x+1)^4 (f+g)^2}{5 \left(1-x^2\right)^{5/2}}+\frac{(x+1)^3 (f-9 g) (f+g)}{15 \left(1-x^2\right)^{3/2}}+\frac{2 g^2 (x+1)}{\sqrt{1-x^2}}-g^2 \sin ^{-1}(x)","\frac{(x+1)^4 (f+g)^2}{5 \left(1-x^2\right)^{5/2}}+\frac{(x+1)^3 (f-9 g) (f+g)}{15 \left(1-x^2\right)^{3/2}}+\frac{2 g^2 (x+1)}{\sqrt{1-x^2}}-g^2 \sin ^{-1}(x)",1,"((f + g)^2*(1 + x)^4)/(5*(1 - x^2)^(5/2)) + ((f - 9*g)*(f + g)*(1 + x)^3)/(15*(1 - x^2)^(3/2)) + (2*g^2*(1 + x))/Sqrt[1 - x^2] - g^2*ArcSin[x]","A",5,5,26,0.1923,1,"{853, 1635, 789, 653, 216}"
620,1,107,0,0.2407692,"\int \frac{\left(1-a^2 x^2\right)^{3/2}}{(1-a x)^2 (c+d x)} \, dx","Int[(1 - a^2*x^2)^(3/2)/((1 - a*x)^2*(c + d*x)),x]","\frac{(a c-d)^2 \tan ^{-1}\left(\frac{a^2 c x+d}{\sqrt{1-a^2 x^2} \sqrt{a^2 c^2-d^2}}\right)}{d^2 \sqrt{a^2 c^2-d^2}}-\frac{\sqrt{1-a^2 x^2}}{d}-\frac{(a c-2 d) \sin ^{-1}(a x)}{d^2}","\frac{(a c-d)^2 \tan ^{-1}\left(\frac{a^2 c x+d}{\sqrt{1-a^2 x^2} \sqrt{a^2 c^2-d^2}}\right)}{d^2 \sqrt{a^2 c^2-d^2}}-\frac{\sqrt{1-a^2 x^2}}{d}-\frac{(a c-2 d) \sin ^{-1}(a x)}{d^2}",1,"-(Sqrt[1 - a^2*x^2]/d) - ((a*c - 2*d)*ArcSin[a*x])/d^2 + ((a*c - d)^2*ArcTan[(d + a^2*c*x)/(Sqrt[a^2*c^2 - d^2]*Sqrt[1 - a^2*x^2])])/(d^2*Sqrt[a^2*c^2 - d^2])","A",6,6,30,0.2000,1,"{853, 1654, 844, 216, 725, 204}"
621,1,107,0,0.1794279,"\int \frac{(1+a x)^2}{(c+d x) \sqrt{1-a^2 x^2}} \, dx","Int[(1 + a*x)^2/((c + d*x)*Sqrt[1 - a^2*x^2]),x]","\frac{(a c-d)^2 \tan ^{-1}\left(\frac{a^2 c x+d}{\sqrt{1-a^2 x^2} \sqrt{a^2 c^2-d^2}}\right)}{d^2 \sqrt{a^2 c^2-d^2}}-\frac{\sqrt{1-a^2 x^2}}{d}-\frac{(a c-2 d) \sin ^{-1}(a x)}{d^2}","\frac{(a c-d)^2 \tan ^{-1}\left(\frac{a^2 c x+d}{\sqrt{1-a^2 x^2} \sqrt{a^2 c^2-d^2}}\right)}{d^2 \sqrt{a^2 c^2-d^2}}-\frac{\sqrt{1-a^2 x^2}}{d}-\frac{(a c-2 d) \sin ^{-1}(a x)}{d^2}",1,"-(Sqrt[1 - a^2*x^2]/d) - ((a*c - 2*d)*ArcSin[a*x])/d^2 + ((a*c - d)^2*ArcTan[(d + a^2*c*x)/(Sqrt[a^2*c^2 - d^2]*Sqrt[1 - a^2*x^2])])/(d^2*Sqrt[a^2*c^2 - d^2])","A",5,5,29,0.1724,1,"{1654, 844, 216, 725, 204}"
622,1,851,0,2.696794,"\int (d+e x)^3 \sqrt{f+g x} \sqrt{a+c x^2} \, dx","Int[(d + e*x)^3*Sqrt[f + g*x]*Sqrt[a + c*x^2],x]","\frac{2 \sqrt{f+g x} \sqrt{c x^2+a} (d+e x)^4}{11 e}+\frac{4 \sqrt{-a} \left(3 a^2 e^2 (26 e f+231 d g) g^4-9 a c \left(6 e^3 f^3-33 d e^2 g f^2+88 d^2 e g^2 f+77 d^3 g^3\right) g^2-c^2 f^2 \left(64 e^3 f^3-264 d e^2 g f^2+396 d^2 e g^2 f-231 d^3 g^3\right)\right) \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3465 c^{3/2} g^5 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}-\frac{4 \sqrt{-a} \left(c f^2+a g^2\right) \left(75 a^2 e^3 g^4-3 a c e \left(2 e^2 f^2-33 d e g f+165 d^2 g^2\right) g^2-c^2 f \left(64 e^3 f^3-264 d e^2 g f^2+396 d^2 e g^2 f-231 d^3 g^3\right)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3465 c^{5/2} g^5 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{2 e^2 (e f-3 d g) (f+g x)^{7/2} \sqrt{c x^2+a}}{99 g^4}+\frac{2 e \left(18 a e^2 g^2-c \left(29 e^2 f^2-96 d e g f+81 d^2 g^2\right)\right) (f+g x)^{5/2} \sqrt{c x^2+a}}{693 c g^4}-\frac{2 \left(2 a e^2 g^2 (74 e f-231 d g)-c \left(233 e^3 f^3-843 d e^2 g f^2+1107 d^2 e g^2 f-567 d^3 g^3\right)\right) (f+g x)^{3/2} \sqrt{c x^2+a}}{3465 c g^4}-\frac{2 \left(150 a^2 e^4 g^4-6 a c e^2 \left(2 e^2 f^2-33 d e g f+165 d^2 g^2\right) g^2+c^2 \left(187 e^4 f^4-732 d e^3 g f^3+1098 d^2 e^2 g^2 f^2-798 d^3 e g^3 f+315 d^4 g^4\right)\right) \sqrt{f+g x} \sqrt{c x^2+a}}{3465 c^2 e g^4}","\frac{2 \sqrt{f+g x} \sqrt{c x^2+a} (d+e x)^4}{11 e}+\frac{4 \sqrt{-a} \left(3 a^2 e^2 (26 e f+231 d g) g^4-9 a c \left(6 e^3 f^3-33 d e^2 g f^2+88 d^2 e g^2 f+77 d^3 g^3\right) g^2-c^2 f^2 \left(64 e^3 f^3-264 d e^2 g f^2+396 d^2 e g^2 f-231 d^3 g^3\right)\right) \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3465 c^{3/2} g^5 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}-\frac{4 \sqrt{-a} \left(c f^2+a g^2\right) \left(75 a^2 e^3 g^4-3 a c e \left(2 e^2 f^2-33 d e g f+165 d^2 g^2\right) g^2-c^2 f \left(64 e^3 f^3-264 d e^2 g f^2+396 d^2 e g^2 f-231 d^3 g^3\right)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3465 c^{5/2} g^5 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{2 e^2 (e f-3 d g) (f+g x)^{7/2} \sqrt{c x^2+a}}{99 g^4}+\frac{2 e \left(18 a e^2 g^2-c \left(29 e^2 f^2-96 d e g f+81 d^2 g^2\right)\right) (f+g x)^{5/2} \sqrt{c x^2+a}}{693 c g^4}-\frac{2 \left(2 a e^2 g^2 (74 e f-231 d g)-c \left(233 e^3 f^3-843 d e^2 g f^2+1107 d^2 e g^2 f-567 d^3 g^3\right)\right) (f+g x)^{3/2} \sqrt{c x^2+a}}{3465 c g^4}-\frac{2 \left(150 a^2 e^4 g^4-6 a c e^2 \left(2 e^2 f^2-33 d e g f+165 d^2 g^2\right) g^2+c^2 \left(187 e^4 f^4-732 d e^3 g f^3+1098 d^2 e^2 g^2 f^2-798 d^3 e g^3 f+315 d^4 g^4\right)\right) \sqrt{f+g x} \sqrt{c x^2+a}}{3465 c^2 e g^4}",1,"(-2*(150*a^2*e^4*g^4 - 6*a*c*e^2*g^2*(2*e^2*f^2 - 33*d*e*f*g + 165*d^2*g^2) + c^2*(187*e^4*f^4 - 732*d*e^3*f^3*g + 1098*d^2*e^2*f^2*g^2 - 798*d^3*e*f*g^3 + 315*d^4*g^4))*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(3465*c^2*e*g^4) + (2*(d + e*x)^4*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(11*e) - (2*(2*a*e^2*g^2*(74*e*f - 231*d*g) - c*(233*e^3*f^3 - 843*d*e^2*f^2*g + 1107*d^2*e*f*g^2 - 567*d^3*g^3))*(f + g*x)^(3/2)*Sqrt[a + c*x^2])/(3465*c*g^4) + (2*e*(18*a*e^2*g^2 - c*(29*e^2*f^2 - 96*d*e*f*g + 81*d^2*g^2))*(f + g*x)^(5/2)*Sqrt[a + c*x^2])/(693*c*g^4) + (2*e^2*(e*f - 3*d*g)*(f + g*x)^(7/2)*Sqrt[a + c*x^2])/(99*g^4) + (4*Sqrt[-a]*(3*a^2*e^2*g^4*(26*e*f + 231*d*g) - c^2*f^2*(64*e^3*f^3 - 264*d*e^2*f^2*g + 396*d^2*e*f*g^2 - 231*d^3*g^3) - 9*a*c*g^2*(6*e^3*f^3 - 33*d*e^2*f^2*g + 88*d^2*e*f*g^2 + 77*d^3*g^3))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3465*c^(3/2)*g^5*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*(c*f^2 + a*g^2)*(75*a^2*e^3*g^4 - 3*a*c*e*g^2*(2*e^2*f^2 - 33*d*e*f*g + 165*d^2*g^2) - c^2*f*(64*e^3*f^3 - 264*d*e^2*f^2*g + 396*d^2*e*f*g^2 - 231*d^3*g^3))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3465*c^(5/2)*g^5*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",10,6,28,0.2143,1,"{919, 1654, 844, 719, 424, 419}"
623,1,635,0,1.6222837,"\int (d+e x)^2 \sqrt{f+g x} \sqrt{a+c x^2} \, dx","Int[(d + e*x)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2],x]","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(21 a^2 e^2 g^4+3 a c g^2 \left(-21 d^2 g^2-16 d e f g+3 e^2 f^2\right)+c^2 f^2 \left(21 d^2 g^2-24 d e f g+8 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{315 c^{3/2} g^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(3 a e g^2 (e f-10 d g)+c f \left(21 d^2 g^2-24 d e f g+8 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{315 c^{3/2} g^4 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{a+c x^2} (f+g x)^{3/2} \left(7 a e^2 g^2-c \left(21 d^2 g^2-24 d e f g+8 e^2 f^2\right)\right)}{315 c g^3}-\frac{2 \sqrt{a+c x^2} \sqrt{f+g x} \left(6 a e^2 g^2 (e f-10 d g)-c \left(63 d^2 e f g^2-35 d^3 g^3-57 d e^2 f^2 g+19 e^3 f^3\right)\right)}{315 c e g^3}+\frac{2 e \sqrt{a+c x^2} (f+g x)^{5/2} (e f-3 d g)}{63 g^3}+\frac{2 \sqrt{a+c x^2} (d+e x)^3 \sqrt{f+g x}}{9 e}","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(21 a^2 e^2 g^4+3 a c g^2 \left(-21 d^2 g^2-16 d e f g+3 e^2 f^2\right)+c^2 f^2 \left(21 d^2 g^2-24 d e f g+8 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{315 c^{3/2} g^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(3 a e g^2 (e f-10 d g)+c f \left(21 d^2 g^2-24 d e f g+8 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{315 c^{3/2} g^4 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{a+c x^2} (f+g x)^{3/2} \left(7 a e^2 g^2-c \left(21 d^2 g^2-24 d e f g+8 e^2 f^2\right)\right)}{315 c g^3}-\frac{2 \sqrt{a+c x^2} \sqrt{f+g x} \left(6 a e^2 g^2 (e f-10 d g)-c \left(63 d^2 e f g^2-35 d^3 g^3-57 d e^2 f^2 g+19 e^3 f^3\right)\right)}{315 c e g^3}+\frac{2 e \sqrt{a+c x^2} (f+g x)^{5/2} (e f-3 d g)}{63 g^3}+\frac{2 \sqrt{a+c x^2} (d+e x)^3 \sqrt{f+g x}}{9 e}",1,"(-2*(6*a*e^2*g^2*(e*f - 10*d*g) - c*(19*e^3*f^3 - 57*d*e^2*f^2*g + 63*d^2*e*f*g^2 - 35*d^3*g^3))*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(315*c*e*g^3) + (2*(d + e*x)^3*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(9*e) + (4*(7*a*e^2*g^2 - c*(8*e^2*f^2 - 24*d*e*f*g + 21*d^2*g^2))*(f + g*x)^(3/2)*Sqrt[a + c*x^2])/(315*c*g^3) + (2*e*(e*f - 3*d*g)*(f + g*x)^(5/2)*Sqrt[a + c*x^2])/(63*g^3) + (4*Sqrt[-a]*(21*a^2*e^2*g^4 + 3*a*c*g^2*(3*e^2*f^2 - 16*d*e*f*g - 21*d^2*g^2) + c^2*f^2*(8*e^2*f^2 - 24*d*e*f*g + 21*d^2*g^2))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(315*c^(3/2)*g^4*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*(c*f^2 + a*g^2)*(3*a*e*g^2*(e*f - 10*d*g) + c*f*(8*e^2*f^2 - 24*d*e*f*g + 21*d^2*g^2))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(315*c^(3/2)*g^4*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",9,6,28,0.2143,1,"{919, 1654, 844, 719, 424, 419}"
624,1,434,0,0.4882743,"\int (d+e x) \sqrt{f+g x} \sqrt{a+c x^2} \, dx","Int[(d + e*x)*Sqrt[f + g*x]*Sqrt[a + c*x^2],x]","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(5 a e g^2+c f (4 e f-7 d g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 c^{3/2} g^3 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(a g^2 (21 d g+8 e f)+c f^2 (4 e f-7 d g)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 \sqrt{c} g^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{2 \sqrt{a+c x^2} \sqrt{f+g x} \left(5 a e g^2-3 c g x (7 d g+e f)+c f (4 e f-7 d g)\right)}{105 c g^2}+\frac{2 e \left(a+c x^2\right)^{3/2} \sqrt{f+g x}}{7 c}","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(5 a e g^2+c f (4 e f-7 d g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 c^{3/2} g^3 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(a g^2 (21 d g+8 e f)+c f^2 (4 e f-7 d g)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 \sqrt{c} g^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{2 \sqrt{a+c x^2} \sqrt{f+g x} \left(5 a e g^2-3 c g x (7 d g+e f)+c f (4 e f-7 d g)\right)}{105 c g^2}+\frac{2 e \left(a+c x^2\right)^{3/2} \sqrt{f+g x}}{7 c}",1,"(-2*Sqrt[f + g*x]*(5*a*e*g^2 + c*f*(4*e*f - 7*d*g) - 3*c*g*(e*f + 7*d*g)*x)*Sqrt[a + c*x^2])/(105*c*g^2) + (2*e*Sqrt[f + g*x]*(a + c*x^2)^(3/2))/(7*c) - (4*Sqrt[-a]*(c*f^2*(4*e*f - 7*d*g) + a*g^2*(8*e*f + 21*d*g))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(105*Sqrt[c]*g^3*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (4*Sqrt[-a]*(c*f^2 + a*g^2)*(5*a*e*g^2 + c*f*(4*e*f - 7*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(105*c^(3/2)*g^3*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",7,6,26,0.2308,1,"{833, 815, 844, 719, 424, 419}"
625,1,362,0,0.3173747,"\int \sqrt{f+g x} \sqrt{a+c x^2} \, dx","Int[Sqrt[f + g*x]*Sqrt[a + c*x^2],x]","-\frac{4 \sqrt{-a} f \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 \sqrt{c} g^2 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(c f^2-3 a g^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 \sqrt{c} g^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 \sqrt{a+c x^2} (f+g x)^{3/2}}{5 g}-\frac{4 f \sqrt{a+c x^2} \sqrt{f+g x}}{15 g}","-\frac{4 \sqrt{-a} f \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 \sqrt{c} g^2 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(c f^2-3 a g^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 \sqrt{c} g^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 \sqrt{a+c x^2} (f+g x)^{3/2}}{5 g}-\frac{4 f \sqrt{a+c x^2} \sqrt{f+g x}}{15 g}",1,"(-4*f*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(15*g) + (2*(f + g*x)^(3/2)*Sqrt[a + c*x^2])/(5*g) + (4*Sqrt[-a]*(c*f^2 - 3*a*g^2)*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(15*Sqrt[c]*g^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*f*(c*f^2 + a*g^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(15*Sqrt[c]*g^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{735, 833, 844, 719, 424, 419}"
626,1,683,0,2.1221058,"\int \frac{\sqrt{f+g x} \sqrt{a+c x^2}}{d+e x} \, dx","Int[(Sqrt[f + g*x]*Sqrt[a + c*x^2])/(d + e*x),x]","-\frac{2 \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^3 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}+\frac{2 \sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} (e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 e^2 g \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(2 a e^2 g-3 c d (e f-d g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} (e f-3 d g) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 e^2 g \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 \sqrt{a+c x^2} \sqrt{f+g x}}{3 e}","-\frac{2 \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^3 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}+\frac{2 \sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} (e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 e^2 g \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(2 a e^2 g-3 c d (e f-d g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} (e f-3 d g) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 e^2 g \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 \sqrt{a+c x^2} \sqrt{f+g x}}{3 e}",1,"(2*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(3*e) - (2*Sqrt[-a]*Sqrt[c]*(e*f - 3*d*g)*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*e^2*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*Sqrt[c]*f*(e*f - 3*d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*e^2*g*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (2*Sqrt[-a]*(2*a*e^2*g - 3*c*d*(e*f - d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*Sqrt[c]*e^3*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (2*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e^3*((Sqrt[c]*d)/Sqrt[-a] + e)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",14,10,28,0.3571,1,"{919, 6742, 719, 419, 844, 424, 933, 168, 538, 537}"
627,1,650,0,1.6614058,"\int \frac{\sqrt{f+g x} \sqrt{a+c x^2}}{(d+e x)^2} \, dx","Int[(Sqrt[f + g*x]*Sqrt[a + c*x^2])/(d + e*x)^2,x]","-\frac{\sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} (2 e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^3 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g-c d (2 e f-3 d g)\right) \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^3 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}-\frac{\sqrt{a+c x^2} \sqrt{f+g x}}{e (d+e x)}+\frac{3 \sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{3 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}","-\frac{\sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} (2 e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^3 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g-c d (2 e f-3 d g)\right) \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^3 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}-\frac{\sqrt{a+c x^2} \sqrt{f+g x}}{e (d+e x)}+\frac{3 \sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{3 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}",1,"-((Sqrt[f + g*x]*Sqrt[a + c*x^2])/(e*(d + e*x))) - (3*Sqrt[-a]*Sqrt[c]*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(e^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (3*Sqrt[-a]*Sqrt[c]*f*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(e^2*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (Sqrt[-a]*Sqrt[c]*(2*e*f - 3*d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(e^3*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - ((a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e^3*((Sqrt[c]*d)/Sqrt[-a] + e)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",14,10,28,0.3571,1,"{917, 6742, 719, 419, 844, 424, 933, 168, 538, 537}"
628,1,1205,0,4.1989209,"\int \frac{\sqrt{f+g x} \sqrt{a+c x^2}}{(d+e x)^3} \, dx","Int[(Sqrt[f + g*x]*Sqrt[a + c*x^2])/(d + e*x)^3,x]","\frac{\sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right) \left(a e^2 g-c d (2 e f-3 d g)\right)^2}{4 e^3 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{-a} \sqrt{c} \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(a e^2 g-c d (2 e f-3 d g)\right)}{4 e^2 \left(c d^2+a e^2\right) (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} f \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(a e^2 g-c d (2 e f-3 d g)\right)}{4 e^2 \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{-a} \sqrt{c} d g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(a e^2 g-c d (2 e f-3 d g)\right)}{4 e^3 \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+a} \left(a e^2 g-c d (2 e f-3 d g)\right)}{4 e \left(c d^2+a e^2\right) (e f-d g) (d+e x)}-\frac{3 \sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{2 e^3 \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{c (e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^3 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+a}}{2 e (d+e x)^2}","\frac{\sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right) \left(a e^2 g-c d (2 e f-3 d g)\right)^2}{4 e^3 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{-a} \sqrt{c} \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(a e^2 g-c d (2 e f-3 d g)\right)}{4 e^2 \left(c d^2+a e^2\right) (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} f \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(a e^2 g-c d (2 e f-3 d g)\right)}{4 e^2 \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{-a} \sqrt{c} d g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(a e^2 g-c d (2 e f-3 d g)\right)}{4 e^3 \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+a} \left(a e^2 g-c d (2 e f-3 d g)\right)}{4 e \left(c d^2+a e^2\right) (e f-d g) (d+e x)}-\frac{3 \sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{2 e^3 \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{c (e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^3 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+a}}{2 e (d+e x)^2}",1,"-(Sqrt[f + g*x]*Sqrt[a + c*x^2])/(2*e*(d + e*x)^2) - ((a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(4*e*(c*d^2 + a*e^2)*(e*f - d*g)*(d + e*x)) - (Sqrt[-a]*Sqrt[c]*(a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*e^2*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (3*Sqrt[-a]*Sqrt[c]*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(2*e^3*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + (Sqrt[-a]*Sqrt[c]*f*(a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*e^2*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (Sqrt[-a]*Sqrt[c]*d*g*(a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*e^3*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (c*(e*f - 3*d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e^3*((Sqrt[c]*d)/Sqrt[-a] + e)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + ((a*e^2*g - c*d*(2*e*f - 3*d*g))^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(4*e^3*((Sqrt[c]*d)/Sqrt[-a] + e)*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",23,11,28,0.3929,1,"{917, 6742, 719, 419, 940, 844, 424, 933, 168, 538, 537}"
629,1,666,0,1.5714123,"\int \frac{(d+e x)^3 \sqrt{a+c x^2}}{\sqrt{f+g x}} \, dx","Int[((d + e*x)^3*Sqrt[a + c*x^2])/Sqrt[f + g*x],x]","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(21 a^2 e^3 g^4-3 a c e g^2 \left(63 d^2 g^2-39 d e f g+10 e^2 f^2\right)-c^2 f \left(252 d^2 e f g^2-105 d^3 g^3-216 d e^2 f^2 g+64 e^3 f^3\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{315 c^{3/2} g^5 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(9 a e^2 g^2 (2 e f-5 d g)-c \left(252 d^2 e f g^2-105 d^3 g^3-216 d e^2 f^2 g+64 e^3 f^3\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{315 c^{3/2} g^5 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 e \sqrt{a+c x^2} (f+g x)^{3/2} \left(7 a e^2 g^2+c \left(42 d^2 g^2-111 d e f g+64 e^2 f^2\right)\right)}{315 c g^4}-\frac{4 \sqrt{a+c x^2} \sqrt{f+g x} \left(9 a e^2 g^2 (2 e f-5 d g)+c \left(168 d^2 e f g^2-35 d^3 g^3-204 d e^2 f^2 g+76 e^3 f^3\right)\right)}{315 c g^4}-\frac{4 e^2 \sqrt{a+c x^2} (f+g x)^{5/2} (4 e f-3 d g)}{63 g^4}+\frac{2 \sqrt{a+c x^2} (d+e x)^3 \sqrt{f+g x}}{9 g}","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(21 a^2 e^3 g^4-3 a c e g^2 \left(63 d^2 g^2-39 d e f g+10 e^2 f^2\right)-c^2 f \left(252 d^2 e f g^2-105 d^3 g^3-216 d e^2 f^2 g+64 e^3 f^3\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{315 c^{3/2} g^5 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(9 a e^2 g^2 (2 e f-5 d g)-c \left(252 d^2 e f g^2-105 d^3 g^3-216 d e^2 f^2 g+64 e^3 f^3\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{315 c^{3/2} g^5 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 e \sqrt{a+c x^2} (f+g x)^{3/2} \left(7 a e^2 g^2+c \left(42 d^2 g^2-111 d e f g+64 e^2 f^2\right)\right)}{315 c g^4}-\frac{4 \sqrt{a+c x^2} \sqrt{f+g x} \left(9 a e^2 g^2 (2 e f-5 d g)+c \left(168 d^2 e f g^2-35 d^3 g^3-204 d e^2 f^2 g+76 e^3 f^3\right)\right)}{315 c g^4}-\frac{4 e^2 \sqrt{a+c x^2} (f+g x)^{5/2} (4 e f-3 d g)}{63 g^4}+\frac{2 \sqrt{a+c x^2} (d+e x)^3 \sqrt{f+g x}}{9 g}",1,"(-4*(9*a*e^2*g^2*(2*e*f - 5*d*g) + c*(76*e^3*f^3 - 204*d*e^2*f^2*g + 168*d^2*e*f*g^2 - 35*d^3*g^3))*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(315*c*g^4) + (2*(d + e*x)^3*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(9*g) + (4*e*(7*a*e^2*g^2 + c*(64*e^2*f^2 - 111*d*e*f*g + 42*d^2*g^2))*(f + g*x)^(3/2)*Sqrt[a + c*x^2])/(315*c*g^4) - (4*e^2*(4*e*f - 3*d*g)*(f + g*x)^(5/2)*Sqrt[a + c*x^2])/(63*g^4) + (4*Sqrt[-a]*(21*a^2*e^3*g^4 - 3*a*c*e*g^2*(10*e^2*f^2 - 39*d*e*f*g + 63*d^2*g^2) - c^2*f*(64*e^3*f^3 - 216*d*e^2*f^2*g + 252*d^2*e*f*g^2 - 105*d^3*g^3))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(315*c^(3/2)*g^5*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*(c*f^2 + a*g^2)*(9*a*e^2*g^2*(2*e*f - 5*d*g) - c*(64*e^3*f^3 - 216*d*e^2*f^2*g + 252*d^2*e*f*g^2 - 105*d^3*g^3))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(315*c^(3/2)*g^5*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",9,6,28,0.2143,1,"{921, 1654, 844, 719, 424, 419}"
630,1,503,0,0.977467,"\int \frac{(d+e x)^2 \sqrt{a+c x^2}}{\sqrt{f+g x}} \, dx","Int[((d + e*x)^2*Sqrt[a + c*x^2])/Sqrt[f + g*x],x]","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(5 a e^2 g^2-c \left(35 d^2 g^2-56 d e f g+24 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 c^{3/2} g^4 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{a+c x^2} \sqrt{f+g x} \left(e^2 \left(\frac{5 a}{c}+\frac{21 f^2}{g^2}\right)+10 d^2-\frac{34 d e f}{g}\right)}{105 g}+\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(a e g^2 (13 e f-42 d g)+c f \left(35 d^2 g^2-56 d e f g+24 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 \sqrt{c} g^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{4 e \sqrt{a+c x^2} (f+g x)^{3/2} (3 e f-2 d g)}{35 g^3}+\frac{2 \sqrt{a+c x^2} (d+e x)^2 \sqrt{f+g x}}{7 g}","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(5 a e^2 g^2-c \left(35 d^2 g^2-56 d e f g+24 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 c^{3/2} g^4 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{a+c x^2} \sqrt{f+g x} \left(5 a e^2 g^2+c \left(10 d^2 g^2-34 d e f g+21 e^2 f^2\right)\right)}{105 c g^3}+\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(a e g^2 (13 e f-42 d g)+c f \left(35 d^2 g^2-56 d e f g+24 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 \sqrt{c} g^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{4 e \sqrt{a+c x^2} (f+g x)^{3/2} (3 e f-2 d g)}{35 g^3}+\frac{2 \sqrt{a+c x^2} (d+e x)^2 \sqrt{f+g x}}{7 g}",1,"(4*(10*d^2 + e^2*((5*a)/c + (21*f^2)/g^2) - (34*d*e*f)/g)*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(105*g) + (2*(d + e*x)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(7*g) - (4*e*(3*e*f - 2*d*g)*(f + g*x)^(3/2)*Sqrt[a + c*x^2])/(35*g^3) + (4*Sqrt[-a]*(a*e*g^2*(13*e*f - 42*d*g) + c*f*(24*e^2*f^2 - 56*d*e*f*g + 35*d^2*g^2))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(105*Sqrt[c]*g^4*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (4*Sqrt[-a]*(c*f^2 + a*g^2)*(5*a*e^2*g^2 - c*(24*e^2*f^2 - 56*d*e*f*g + 35*d^2*g^2))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(105*c^(3/2)*g^4*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",8,6,28,0.2143,1,"{921, 1654, 844, 719, 424, 419}"
631,1,364,0,0.3771446,"\int \frac{(d+e x) \sqrt{a+c x^2}}{\sqrt{f+g x}} \, dx","Int[((d + e*x)*Sqrt[a + c*x^2])/Sqrt[f + g*x],x]","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) (4 e f-5 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 \sqrt{c} g^3 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{a+c x^2} \sqrt{f+g x} (-5 d g+4 e f-3 e g x)}{15 g^2}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(3 a e g^2+c f (4 e f-5 d g)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 \sqrt{c} g^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) (4 e f-5 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 \sqrt{c} g^3 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{a+c x^2} \sqrt{f+g x} (-5 d g+4 e f-3 e g x)}{15 g^2}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(3 a e g^2+c f (4 e f-5 d g)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 \sqrt{c} g^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}",1,"(-2*Sqrt[f + g*x]*(4*e*f - 5*d*g - 3*e*g*x)*Sqrt[a + c*x^2])/(15*g^2) - (4*Sqrt[-a]*(3*a*e*g^2 + c*f*(4*e*f - 5*d*g))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(15*Sqrt[c]*g^3*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (4*Sqrt[-a]*(4*e*f - 5*d*g)*(c*f^2 + a*g^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(15*Sqrt[c]*g^3*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{815, 844, 719, 424, 419}"
632,1,322,0,0.2044859,"\int \frac{\sqrt{a+c x^2}}{\sqrt{f+g x}} \, dx","Int[Sqrt[a + c*x^2]/Sqrt[f + g*x],x]","-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 \sqrt{c} g^2 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 g^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 \sqrt{a+c x^2} \sqrt{f+g x}}{3 g}","-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 \sqrt{c} g^2 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 g^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 \sqrt{a+c x^2} \sqrt{f+g x}}{3 g}",1,"(2*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(3*g) + (4*Sqrt[-a]*Sqrt[c]*f*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*g^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*(c*f^2 + a*g^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*Sqrt[c]*g^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",6,5,21,0.2381,1,"{735, 844, 719, 424, 419}"
633,1,473,0,0.6393872,"\int \frac{\sqrt{a+c x^2}}{(d+e x) \sqrt{f+g x}} \, dx","Int[Sqrt[a + c*x^2]/((d + e*x)*Sqrt[f + g*x]),x]","-\frac{2 \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}+\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} (d g+e f) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^2 g \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e g \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}","-\frac{2 \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}+\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} (d g+e f) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^2 g \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e g \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}",1,"(-2*Sqrt[-a]*Sqrt[c]*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(e*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*Sqrt[c]*(e*f + d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(e^2*g*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (2*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e^2*((Sqrt[c]*d)/Sqrt[-a] + e)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",10,9,28,0.3214,1,"{923, 933, 168, 538, 537, 844, 719, 424, 419}"
634,1,694,0,1.7224436,"\int \frac{\sqrt{a+c x^2}}{(d+e x)^2 \sqrt{f+g x}} \, dx","Int[Sqrt[a + c*x^2]/((d + e*x)^2*Sqrt[f + g*x]),x]","-\frac{\sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} (2 e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x} (e f-d g)}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g+c d (2 e f-d g)\right) \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) (e f-d g)}-\frac{\sqrt{a+c x^2} \sqrt{f+g x}}{(d+e x) (e f-d g)}+\frac{\sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e \sqrt{a+c x^2} \sqrt{f+g x} (e f-d g)}-\frac{\sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e \sqrt{a+c x^2} (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}","-\frac{\sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} (2 e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x} (e f-d g)}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g+c d (2 e f-d g)\right) \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) (e f-d g)}-\frac{\sqrt{a+c x^2} \sqrt{f+g x}}{(d+e x) (e f-d g)}+\frac{\sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e \sqrt{a+c x^2} \sqrt{f+g x} (e f-d g)}-\frac{\sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e \sqrt{a+c x^2} (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}",1,"-((Sqrt[f + g*x]*Sqrt[a + c*x^2])/((e*f - d*g)*(d + e*x))) - (Sqrt[-a]*Sqrt[c]*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(e*(e*f - d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (Sqrt[-a]*Sqrt[c]*f*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(e*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (Sqrt[-a]*Sqrt[c]*(2*e*f - d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(e^2*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + ((a*e^2*g + c*d*(2*e*f - d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e^2*((Sqrt[c]*d)/Sqrt[-a] + e)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",14,10,28,0.3571,1,"{925, 6742, 719, 419, 844, 424, 933, 168, 538, 537}"
635,1,1241,0,4.236632,"\int \frac{\sqrt{a+c x^2}}{(d+e x)^3 \sqrt{f+g x}} \, dx","Int[Sqrt[a + c*x^2]/((d + e*x)^3*Sqrt[f + g*x]),x]","\frac{\sqrt{-a} \sqrt{c} \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(3 a g e^2+c d (2 e f+d g)\right)}{4 e \left(c d^2+a e^2\right) (e f-d g)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}-\frac{\sqrt{-a} \sqrt{c} f \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(3 a g e^2+c d (2 e f+d g)\right)}{4 e \left(c d^2+a e^2\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} d g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(3 a g e^2+c d (2 e f+d g)\right)}{4 e^2 \left(c d^2+a e^2\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right) \left(3 a g e^2+c d (2 e f+d g)\right)}{4 e^2 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{\sqrt{f+g x} \sqrt{c x^2+a} \left(3 a g e^2+c d (2 e f+d g)\right)}{4 \left(c d^2+a e^2\right) (e f-d g)^2 (d+e x)}+\frac{\sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{2 e^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{c (e f+d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^2 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+a}}{2 (e f-d g) (d+e x)^2}","\frac{\sqrt{-a} \sqrt{c} \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(3 a g e^2+c d (2 e f+d g)\right)}{4 e \left(c d^2+a e^2\right) (e f-d g)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}-\frac{\sqrt{-a} \sqrt{c} f \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(3 a g e^2+c d (2 e f+d g)\right)}{4 e \left(c d^2+a e^2\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} d g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) \left(3 a g e^2+c d (2 e f+d g)\right)}{4 e^2 \left(c d^2+a e^2\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right) \left(3 a g e^2+c d (2 e f+d g)\right)}{4 e^2 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{\sqrt{f+g x} \sqrt{c x^2+a} \left(3 a g e^2+c d (2 e f+d g)\right)}{4 \left(c d^2+a e^2\right) (e f-d g)^2 (d+e x)}+\frac{\sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{2 e^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{c (e f+d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^2 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+a}}{2 (e f-d g) (d+e x)^2}",1,"-(Sqrt[f + g*x]*Sqrt[a + c*x^2])/(2*(e*f - d*g)*(d + e*x)^2) + ((3*a*e^2*g + c*d*(2*e*f + d*g))*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(4*(c*d^2 + a*e^2)*(e*f - d*g)^2*(d + e*x)) + (Sqrt[-a]*Sqrt[c]*(3*a*e^2*g + c*d*(2*e*f + d*g))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*e*(c*d^2 + a*e^2)*(e*f - d*g)^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (Sqrt[-a]*Sqrt[c]*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(2*e^2*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (Sqrt[-a]*Sqrt[c]*f*(3*a*e^2*g + c*d*(2*e*f + d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*e*(c*d^2 + a*e^2)*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + (Sqrt[-a]*Sqrt[c]*d*g*(3*a*e^2*g + c*d*(2*e*f + d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*e^2*(c*d^2 + a*e^2)*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (c*(e*f + d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e^2*((Sqrt[c]*d)/Sqrt[-a] + e)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - ((a*e^2*g - c*d*(2*e*f - 3*d*g))*(3*a*e^2*g + c*d*(2*e*f + d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(4*e^2*((Sqrt[c]*d)/Sqrt[-a] + e)*(c*d^2 + a*e^2)*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",23,11,28,0.3929,1,"{925, 6742, 719, 419, 940, 844, 424, 933, 168, 538, 537}"
636,1,527,0,1.1224087,"\int \frac{(d+e x)^3 \sqrt{f+g x}}{\sqrt{a+c x^2}} \, dx","Int[((d + e*x)^3*Sqrt[f + g*x])/Sqrt[a + c*x^2],x]","-\frac{2 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(25 a e^2 g^2-c \left(105 d^2 g^2-42 d e f g+8 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 c^{5/2} g^3 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(a e^2 g^2 (189 d g+19 e f)-c \left(105 d^2 e f g^2+105 d^3 g^3-42 d e^2 f^2 g+8 e^3 f^3\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 c^{3/2} g^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 e \sqrt{a+c x^2} \sqrt{f+g x} \left(-e^2 \left(\frac{25 a}{c}+\frac{7 f^2}{g^2}\right)+90 d^2-\frac{12 d e f}{g}\right)}{105 c}+\frac{2 e^2 \sqrt{a+c x^2} (f+g x)^{3/2} (11 d g+e f)}{35 c g^2}+\frac{2 e \sqrt{a+c x^2} (d+e x)^2 \sqrt{f+g x}}{7 c}","-\frac{2 e \sqrt{a+c x^2} \sqrt{f+g x} \left(25 a e^2 g^2+c \left(-90 d^2 g^2+12 d e f g+7 e^2 f^2\right)\right)}{105 c^2 g^2}-\frac{2 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(25 a e^2 g^2-c \left(105 d^2 g^2-42 d e f g+8 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 c^{5/2} g^3 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(a e^2 g^2 (189 d g+19 e f)-c \left(105 d^2 e f g^2+105 d^3 g^3-42 d e^2 f^2 g+8 e^3 f^3\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{105 c^{3/2} g^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 e^2 \sqrt{a+c x^2} (f+g x)^{3/2} (11 d g+e f)}{35 c g^2}+\frac{2 e \sqrt{a+c x^2} (d+e x)^2 \sqrt{f+g x}}{7 c}",1,"(2*e*(90*d^2 - e^2*((25*a)/c + (7*f^2)/g^2) - (12*d*e*f)/g)*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(105*c) + (2*e*(d + e*x)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(7*c) + (2*e^2*(e*f + 11*d*g)*(f + g*x)^(3/2)*Sqrt[a + c*x^2])/(35*c*g^2) + (2*Sqrt[-a]*(a*e^2*g^2*(19*e*f + 189*d*g) - c*(8*e^3*f^3 - 42*d*e^2*f^2*g + 105*d^2*e*f*g^2 + 105*d^3*g^3))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(105*c^(3/2)*g^3*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (2*Sqrt[-a]*e*(c*f^2 + a*g^2)*(25*a*e^2*g^2 - c*(8*e^2*f^2 - 42*d*e*f*g + 105*d^2*g^2))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(105*c^(5/2)*g^3*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",8,6,28,0.2143,1,"{942, 1654, 844, 719, 424, 419}"
637,1,410,0,0.5640195,"\int \frac{(d+e x)^2 \sqrt{f+g x}}{\sqrt{a+c x^2}} \, dx","Int[((d + e*x)^2*Sqrt[f + g*x])/Sqrt[a + c*x^2],x]","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(9 a e^2 g^2+c \left(-15 d^2 g^2-10 d e f g+2 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 c^{3/2} g^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{4 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) (e f-5 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 c^{3/2} g^2 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{2 e \sqrt{a+c x^2} \sqrt{f+g x} (7 d g+e f)}{15 c g}+\frac{2 e \sqrt{a+c x^2} (d+e x) \sqrt{f+g x}}{5 c}","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(9 a e^2 g^2+c \left(-15 d^2 g^2-10 d e f g+2 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 c^{3/2} g^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{4 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) (e f-5 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 c^{3/2} g^2 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{2 e \sqrt{a+c x^2} \sqrt{f+g x} (7 d g+e f)}{15 c g}+\frac{2 e \sqrt{a+c x^2} (d+e x) \sqrt{f+g x}}{5 c}",1,"(2*e*(e*f + 7*d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(15*c*g) + (2*e*(d + e*x)*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(5*c) + (2*Sqrt[-a]*(9*a*e^2*g^2 + c*(2*e^2*f^2 - 10*d*e*f*g - 15*d^2*g^2))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(15*c^(3/2)*g^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*e*(e*f - 5*d*g)*(c*f^2 + a*g^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(15*c^(3/2)*g^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",7,6,28,0.2143,1,"{942, 1654, 844, 719, 424, 419}"
638,1,331,0,0.2641307,"\int \frac{(d+e x) \sqrt{f+g x}}{\sqrt{a+c x^2}} \, dx","Int[((d + e*x)*Sqrt[f + g*x])/Sqrt[a + c*x^2],x]","\frac{2 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 c^{3/2} g \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} (3 d g+e f) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 \sqrt{c} g \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 e \sqrt{a+c x^2} \sqrt{f+g x}}{3 c}","\frac{2 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \left(a g^2+c f^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 c^{3/2} g \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} (3 d g+e f) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 \sqrt{c} g \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 e \sqrt{a+c x^2} \sqrt{f+g x}}{3 c}",1,"(2*e*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(3*c) - (2*Sqrt[-a]*(e*f + 3*d*g)*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*Sqrt[c]*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*e*(c*f^2 + a*g^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*c^(3/2)*g*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{833, 844, 719, 424, 419}"
639,1,136,0,0.0573208,"\int \frac{\sqrt{f+g x}}{\sqrt{a+c x^2}} \, dx","Int[Sqrt[f + g*x]/Sqrt[a + c*x^2],x]","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}",1,"(-2*Sqrt[-a]*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(Sqrt[c]*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2])","A",2,2,21,0.09524,1,"{719, 424}"
640,1,319,0,0.4879248,"\int \frac{\sqrt{f+g x}}{(d+e x) \sqrt{a+c x^2}} \, dx","Int[Sqrt[f + g*x]/((d + e*x)*Sqrt[a + c*x^2]),x]","-\frac{2 \sqrt{\frac{c x^2}{a}+1} (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}-\frac{2 \sqrt{-a} g \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{f+g x}}","-\frac{2 \sqrt{\frac{c x^2}{a}+1} (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}-\frac{2 \sqrt{-a} g \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{f+g x}}",1,"(-2*Sqrt[-a]*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(Sqrt[c]*e*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (2*(e*f - d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e*((Sqrt[c]*d)/Sqrt[-a] + e)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",7,7,28,0.2500,1,"{944, 719, 419, 933, 168, 538, 537}"
641,1,698,0,1.9326945,"\int \frac{\sqrt{f+g x}}{(d+e x)^2 \sqrt{a+c x^2}} \, dx","Int[Sqrt[f + g*x]/((d + e*x)^2*Sqrt[a + c*x^2]),x]","-\frac{e \sqrt{a+c x^2} \sqrt{f+g x}}{(d+e x) \left(a e^2+c d^2\right)}+\frac{\sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(a e^2+c d^2\right)}-\frac{\sqrt{-a} \sqrt{c} d g \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e \sqrt{a+c x^2} \sqrt{f+g x} \left(a e^2+c d^2\right)}-\frac{\sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g+c d (2 e f-d g)\right) \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(a e^2+c d^2\right)}","-\frac{e \sqrt{a+c x^2} \sqrt{f+g x}}{(d+e x) \left(a e^2+c d^2\right)}+\frac{\sqrt{-a} \sqrt{c} f \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(a e^2+c d^2\right)}-\frac{\sqrt{-a} \sqrt{c} d g \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{e \sqrt{a+c x^2} \sqrt{f+g x} \left(a e^2+c d^2\right)}-\frac{\sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g+c d (2 e f-d g)\right) \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(a e^2+c d^2\right)}",1,"-((e*Sqrt[f + g*x]*Sqrt[a + c*x^2])/((c*d^2 + a*e^2)*(d + e*x))) - (Sqrt[-a]*Sqrt[c]*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/((c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (Sqrt[-a]*Sqrt[c]*f*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/((c*d^2 + a*e^2)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (Sqrt[-a]*Sqrt[c]*d*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(e*(c*d^2 + a*e^2)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - ((a*e^2*g + c*d*(2*e*f - d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e*((Sqrt[c]*d)/Sqrt[-a] + e)*(c*d^2 + a*e^2)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",14,10,28,0.3571,1,"{946, 6742, 719, 419, 844, 424, 933, 168, 538, 537}"
642,1,1246,0,4.4022781,"\int \frac{\sqrt{f+g x}}{(d+e x)^3 \sqrt{a+c x^2}} \, dx","Int[Sqrt[f + g*x]/((d + e*x)^3*Sqrt[a + c*x^2]),x]","-\frac{\left(a g e^2+c d (6 e f-5 d g)\right) \sqrt{f+g x} \sqrt{c x^2+a} e}{4 \left(c d^2+a e^2\right)^2 (e f-d g) (d+e x)}-\frac{\sqrt{f+g x} \sqrt{c x^2+a} e}{2 \left(c d^2+a e^2\right) (d+e x)^2}-\frac{\sqrt{-a} \sqrt{c} \left(a g e^2+c d (6 e f-5 d g)\right) \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{4 \left(c d^2+a e^2\right)^2 (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} f \left(a g e^2+c d (6 e f-5 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{4 \left(c d^2+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{2 \left(c d^2+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+a} e}-\frac{\sqrt{-a} \sqrt{c} d g \left(a g e^2+c d (6 e f-5 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{4 \left(c d^2+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a} e}+\frac{c (e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+a} e}+\frac{\left(a g e^2+c d (6 e f-5 d g)\right) \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{4 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a} e}","-\frac{\left(a g e^2+c d (6 e f-5 d g)\right) \sqrt{f+g x} \sqrt{c x^2+a} e}{4 \left(c d^2+a e^2\right)^2 (e f-d g) (d+e x)}-\frac{\sqrt{f+g x} \sqrt{c x^2+a} e}{2 \left(c d^2+a e^2\right) (d+e x)^2}-\frac{\sqrt{-a} \sqrt{c} \left(a g e^2+c d (6 e f-5 d g)\right) \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{4 \left(c d^2+a e^2\right)^2 (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} f \left(a g e^2+c d (6 e f-5 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{4 \left(c d^2+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{2 \left(c d^2+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+a} e}-\frac{\sqrt{-a} \sqrt{c} d g \left(a g e^2+c d (6 e f-5 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{4 \left(c d^2+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a} e}+\frac{c (e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+a} e}+\frac{\left(a g e^2+c d (6 e f-5 d g)\right) \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{4 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a} e}",1,"-(e*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(2*(c*d^2 + a*e^2)*(d + e*x)^2) - (e*(a*e^2*g + c*d*(6*e*f - 5*d*g))*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(4*(c*d^2 + a*e^2)^2*(e*f - d*g)*(d + e*x)) - (Sqrt[-a]*Sqrt[c]*(a*e^2*g + c*d*(6*e*f - 5*d*g))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*(c*d^2 + a*e^2)^2*(e*f - d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (Sqrt[-a]*Sqrt[c]*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(2*e*(c*d^2 + a*e^2)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + (Sqrt[-a]*Sqrt[c]*f*(a*e^2*g + c*d*(6*e*f - 5*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*(c*d^2 + a*e^2)^2*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (Sqrt[-a]*Sqrt[c]*d*g*(a*e^2*g + c*d*(6*e*f - 5*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*e*(c*d^2 + a*e^2)^2*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + (c*(e*f - 3*d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e*((Sqrt[c]*d)/Sqrt[-a] + e)*(c*d^2 + a*e^2)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + ((a*e^2*g + c*d*(6*e*f - 5*d*g))*(a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(4*e*((Sqrt[c]*d)/Sqrt[-a] + e)*(c*d^2 + a*e^2)^2*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",23,11,28,0.3929,1,"{946, 6742, 719, 419, 940, 844, 424, 933, 168, 538, 537}"
643,1,808,0,0.9461931,"\int \frac{(f+g x)^{5/2}}{(d+e x) \sqrt{a+c x^2}} \, dx","Int[(f + g*x)^(5/2)/((d + e*x)*Sqrt[a + c*x^2]),x]","-\frac{2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right) (e f-d g)^3}{e^3 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{2 \sqrt{-a} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) (e f-d g)^2}{\sqrt{c} e^3 \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{2 \sqrt{-a} g \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) (e f-d g)}{\sqrt{c} e^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}-\frac{8 \sqrt{-a} f g \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 \sqrt{c} e \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}+\frac{2 \sqrt{-a} g \left(c f^2+a g^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 c^{3/2} e \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{2 g^2 \sqrt{f+g x} \sqrt{c x^2+a}}{3 c e}","\frac{2 \sqrt{-a} g \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g^2+c \left(-3 d^2 g^2+6 d e f g-2 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{a \sqrt{c} x}{(-a)^{3/2}}+1}}{\sqrt{2}}\right)|\frac{2 a g}{a g-\sqrt{-a} \sqrt{c} f}\right)}{3 c^{3/2} e^3 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} g \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} (7 e f-3 d g) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{a \sqrt{c} x}{(-a)^{3/2}}+1}}{\sqrt{2}}\right)|\frac{2 a g}{a g-\sqrt{-a} \sqrt{c} f}\right)}{3 \sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{2 (e f-d g)^2 \sqrt{\frac{g \left(\sqrt{-a}-\sqrt{c} x\right)}{\sqrt{-a} g+\sqrt{c} f}} \sqrt{-\frac{g \left(\sqrt{-a}+\sqrt{c} x\right)}{\sqrt{c} f-\sqrt{-a} g}} \Pi \left(\frac{e \left(f+\frac{\sqrt{-a} g}{\sqrt{c}}\right)}{e f-d g};\sin ^{-1}\left(\sqrt{\frac{c}{c f+\sqrt{-a} \sqrt{c} g}} \sqrt{f+g x}\right)|\frac{\sqrt{c} f+\sqrt{-a} g}{\sqrt{c} f-\sqrt{-a} g}\right)}{e^3 \sqrt{a+c x^2} \sqrt{\frac{c}{\sqrt{-a} \sqrt{c} g+c f}}}+\frac{2 g^2 \sqrt{a+c x^2} \sqrt{f+g x}}{3 c e}",1,"(2*g^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(3*c*e) - (8*Sqrt[-a]*f*g*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*Sqrt[c]*e*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (2*Sqrt[-a]*g*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(Sqrt[c]*e^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (2*Sqrt[-a]*g*(e*f - d*g)^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(Sqrt[c]*e^3*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*g*(c*f^2 + a*g^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*c^(3/2)*e*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (2*(e*f - d*g)^3*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e^3*((Sqrt[c]*d)/Sqrt[-a] + e)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",16,10,28,0.3571,1,"{958, 719, 419, 933, 168, 538, 537, 424, 743, 844}"
644,1,469,0,0.6373113,"\int \frac{(f+g x)^{3/2}}{(d+e x) \sqrt{a+c x^2}} \, dx","Int[(f + g*x)^(3/2)/((d + e*x)*Sqrt[a + c*x^2]),x]","-\frac{2 \sqrt{-a} g \sqrt{\frac{c x^2}{a}+1} (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{\frac{c x^2}{a}+1} (e f-d g)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}-\frac{2 \sqrt{-a} g \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}","-\frac{2 \sqrt{-a} g \sqrt{\frac{c x^2}{a}+1} (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{\frac{c x^2}{a}+1} (e f-d g)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{e^2 \sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}-\frac{2 \sqrt{-a} g \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}",1,"(-2*Sqrt[-a]*g*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(Sqrt[c]*e*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (2*Sqrt[-a]*g*(e*f - d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(Sqrt[c]*e^2*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (2*(e*f - d*g)^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(e^2*((Sqrt[c]*d)/Sqrt[-a] + e)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",10,8,28,0.2857,1,"{958, 719, 419, 933, 168, 538, 537, 424}"
645,1,457,0,0.6131269,"\int \frac{(d+e x)^3}{\sqrt{f+g x} \sqrt{a+c x^2}} \, dx","Int[(d + e*x)^3/(Sqrt[f + g*x]*Sqrt[a + c*x^2]),x]","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g^2 (7 e f-15 d g)-c \left(45 d^2 e f g^2-15 d^3 g^3-30 d e^2 f^2 g+8 e^3 f^3\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 c^{3/2} g^3 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{2 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(9 a e^2 g^2-c \left(45 d^2 g^2-30 d e f g+8 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 c^{3/2} g^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{8 e^2 \sqrt{a+c x^2} \sqrt{f+g x} (e f-3 d g)}{15 c g^2}+\frac{2 e^2 \sqrt{a+c x^2} (d+e x) \sqrt{f+g x}}{5 c g}","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g^2 (7 e f-15 d g)-c \left(45 d^2 e f g^2-15 d^3 g^3-30 d e^2 f^2 g+8 e^3 f^3\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 c^{3/2} g^3 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{2 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} \left(9 a e^2 g^2-c \left(45 d^2 g^2-30 d e f g+8 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{15 c^{3/2} g^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{8 e^2 \sqrt{a+c x^2} \sqrt{f+g x} (e f-3 d g)}{15 c g^2}+\frac{2 e^2 \sqrt{a+c x^2} (d+e x) \sqrt{f+g x}}{5 c g}",1,"(-8*e^2*(e*f - 3*d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(15*c*g^2) + (2*e^2*(d + e*x)*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(5*c*g) + (2*Sqrt[-a]*e*(9*a*e^2*g^2 - c*(8*e^2*f^2 - 30*d*e*f*g + 45*d^2*g^2))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(15*c^(3/2)*g^3*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (2*Sqrt[-a]*(a*e^2*g^2*(7*e*f - 15*d*g) - c*(8*e^3*f^3 - 30*d*e^2*f^2*g + 45*d^2*e*f*g^2 - 15*d^3*g^3))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(15*c^(3/2)*g^3*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",7,6,28,0.2143,1,"{931, 1654, 844, 719, 424, 419}"
646,1,356,0,0.4048719,"\int \frac{(d+e x)^2}{\sqrt{f+g x} \sqrt{a+c x^2}} \, dx","Int[(d + e*x)^2/(Sqrt[f + g*x]*Sqrt[a + c*x^2]),x]","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(g^2 \left(3 c d^2-a e^2\right)+2 c e f (e f-3 d g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 c^{3/2} g^2 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} (e f-3 d g) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 \sqrt{c} g^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 e^2 \sqrt{a+c x^2} \sqrt{f+g x}}{3 c g}","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(g^2 \left(3 c d^2-a e^2\right)+2 c e f (e f-3 d g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 c^{3/2} g^2 \sqrt{a+c x^2} \sqrt{f+g x}}+\frac{4 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} (e f-3 d g) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 \sqrt{c} g^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{2 e^2 \sqrt{a+c x^2} \sqrt{f+g x}}{3 c g}",1,"(2*e^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(3*c*g) + (4*Sqrt[-a]*e*(e*f - 3*d*g)*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*Sqrt[c]*g^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (2*Sqrt[-a]*((3*c*d^2 - a*e^2)*g^2 + 2*c*e*f*(e*f - 3*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*c^(3/2)*g^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",7,6,28,0.2143,1,"{931, 24, 844, 719, 424, 419}"
647,1,288,0,0.1633416,"\int \frac{d+e x}{\sqrt{f+g x} \sqrt{a+c x^2}} \, dx","Int[(d + e*x)/(Sqrt[f + g*x]*Sqrt[a + c*x^2]),x]","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} g \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} g \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} g \sqrt{a+c x^2} \sqrt{f+g x}}-\frac{2 \sqrt{-a} e \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} g \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}",1,"(-2*Sqrt[-a]*e*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(Sqrt[c]*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*(e*f - d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(Sqrt[c]*g*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",5,4,26,0.1538,1,"{844, 719, 424, 419}"
648,1,136,0,0.0592399,"\int \frac{1}{\sqrt{f+g x} \sqrt{a+c x^2}} \, dx","Int[1/(Sqrt[f + g*x]*Sqrt[a + c*x^2]),x]","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} \sqrt{a+c x^2} \sqrt{f+g x}}","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{c} \sqrt{a+c x^2} \sqrt{f+g x}}",1,"(-2*Sqrt[-a]*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(Sqrt[c]*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",2,2,21,0.09524,1,"{719, 419}"
649,1,167,0,0.3361809,"\int \frac{1}{(d+e x) \sqrt{f+g x} \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)*Sqrt[f + g*x]*Sqrt[a + c*x^2]),x]","-\frac{2 \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}","-\frac{2 \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right)}",1,"(-2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(((Sqrt[c]*d)/Sqrt[-a] + e)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",4,4,28,0.1429,1,"{933, 168, 538, 537}"
650,1,746,0,2.1089793,"\int \frac{1}{(d+e x)^2 \sqrt{f+g x} \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2]),x]","-\frac{e^2 \sqrt{a+c x^2} \sqrt{f+g x}}{(d+e x) \left(a e^2+c d^2\right) (e f-d g)}+\frac{\sqrt{-a} \sqrt{c} e f \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(a e^2+c d^2\right) (e f-d g)}-\frac{\sqrt{-a} \sqrt{c} d g \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(a e^2+c d^2\right) (e f-d g)}-\frac{\sqrt{-a} \sqrt{c} e \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \left(a e^2+c d^2\right) (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g-c d (2 e f-3 d g)\right) \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(a e^2+c d^2\right) (e f-d g)}","-\frac{e^2 \sqrt{a+c x^2} \sqrt{f+g x}}{(d+e x) \left(a e^2+c d^2\right) (e f-d g)}+\frac{\sqrt{-a} \sqrt{c} e f \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(a e^2+c d^2\right) (e f-d g)}-\frac{\sqrt{-a} \sqrt{c} d g \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(a e^2+c d^2\right) (e f-d g)}-\frac{\sqrt{-a} \sqrt{c} e \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \left(a e^2+c d^2\right) (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \left(a e^2 g-c d (2 e f-3 d g)\right) \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(a e^2+c d^2\right) (e f-d g)}",1,"-((e^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])/((c*d^2 + a*e^2)*(e*f - d*g)*(d + e*x))) - (Sqrt[-a]*Sqrt[c]*e*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/((c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (Sqrt[-a]*Sqrt[c]*e*f*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/((c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (Sqrt[-a]*Sqrt[c]*d*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/((c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + ((a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(((Sqrt[c]*d)/Sqrt[-a] + e)*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",14,10,28,0.3571,1,"{940, 6742, 719, 419, 844, 424, 933, 168, 538, 537}"
651,1,1257,0,4.3331884,"\int \frac{1}{(d+e x)^3 \sqrt{f+g x} \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)^3*Sqrt[f + g*x]*Sqrt[a + c*x^2]),x]","\frac{3 \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{f+g x} \sqrt{c x^2+a} e^2}{4 \left(c d^2+a e^2\right)^2 (e f-d g)^2 (d+e x)}-\frac{\sqrt{f+g x} \sqrt{c x^2+a} e^2}{2 \left(c d^2+a e^2\right) (e f-d g) (d+e x)^2}+\frac{3 \sqrt{-a} \sqrt{c} \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) e}{4 \left(c d^2+a e^2\right)^2 (e f-d g)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}-\frac{3 \sqrt{-a} \sqrt{c} f \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) e}{4 \left(c d^2+a e^2\right)^2 (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{3 \sqrt{-a} \sqrt{c} d g \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{4 \left(c d^2+a e^2\right)^2 (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{2 \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{3 \left(a e^2 g-c d (2 e f-3 d g)\right)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{4 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right)^2 (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{c (e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}","\frac{3 \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{f+g x} \sqrt{c x^2+a} e^2}{4 \left(c d^2+a e^2\right)^2 (e f-d g)^2 (d+e x)}-\frac{\sqrt{f+g x} \sqrt{c x^2+a} e^2}{2 \left(c d^2+a e^2\right) (e f-d g) (d+e x)^2}+\frac{3 \sqrt{-a} \sqrt{c} \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) e}{4 \left(c d^2+a e^2\right)^2 (e f-d g)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}-\frac{3 \sqrt{-a} \sqrt{c} f \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) e}{4 \left(c d^2+a e^2\right)^2 (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{3 \sqrt{-a} \sqrt{c} d g \left(a e^2 g-c d (2 e f-3 d g)\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{4 \left(c d^2+a e^2\right)^2 (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{\sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{2 \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}-\frac{3 \left(a e^2 g-c d (2 e f-3 d g)\right)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{4 \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right)^2 (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{c (e f-3 d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) \left(c d^2+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+a}}",1,"-(e^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(2*(c*d^2 + a*e^2)*(e*f - d*g)*(d + e*x)^2) + (3*e^2*(a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[f + g*x]*Sqrt[a + c*x^2])/(4*(c*d^2 + a*e^2)^2*(e*f - d*g)^2*(d + e*x)) + (3*Sqrt[-a]*Sqrt[c]*e*(a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*(c*d^2 + a*e^2)^2*(e*f - d*g)^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (Sqrt[-a]*Sqrt[c]*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(2*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (3*Sqrt[-a]*Sqrt[c]*e*f*(a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*(c*d^2 + a*e^2)^2*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + (3*Sqrt[-a]*Sqrt[c]*d*g*(a*e^2*g - c*d*(2*e*f - 3*d*g))*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(4*(c*d^2 + a*e^2)^2*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2]) + (c*(e*f - 3*d*g)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(((Sqrt[c]*d)/Sqrt[-a] + e)*(c*d^2 + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (3*(a*e^2*g - c*d*(2*e*f - 3*d*g))^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(4*((Sqrt[c]*d)/Sqrt[-a] + e)*(c*d^2 + a*e^2)^2*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",23,10,28,0.3571,1,"{940, 6742, 719, 419, 844, 424, 933, 168, 538, 537}"
652,1,387,0,0.5744651,"\int \frac{1}{(d+e x) (f+g x)^{3/2} \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)*(f + g*x)^(3/2)*Sqrt[a + c*x^2]),x]","\frac{2 g^2 \sqrt{a+c x^2}}{\sqrt{f+g x} \left(a g^2+c f^2\right) (e f-d g)}+\frac{2 \sqrt{-a} \sqrt{c} g \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \left(a g^2+c f^2\right) (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{2 e \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) (e f-d g)}","\frac{2 g^2 \sqrt{a+c x^2}}{\sqrt{f+g x} \left(a g^2+c f^2\right) (e f-d g)}+\frac{2 \sqrt{-a} \sqrt{c} g \sqrt{\frac{c x^2}{a}+1} \sqrt{f+g x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{\sqrt{a+c x^2} \left(a g^2+c f^2\right) (e f-d g) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}}}-\frac{2 e \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{-a} g+\sqrt{c} f}} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right)}{\sqrt{a+c x^2} \sqrt{f+g x} \left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) (e f-d g)}",1,"(2*g^2*Sqrt[a + c*x^2])/((e*f - d*g)*(c*f^2 + a*g^2)*Sqrt[f + g*x]) + (2*Sqrt[-a]*Sqrt[c]*g*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/((e*f - d*g)*(c*f^2 + a*g^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (2*e*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(((Sqrt[c]*d)/Sqrt[-a] + e)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",10,9,28,0.3214,1,"{958, 745, 21, 719, 424, 933, 168, 538, 537}"
653,1,818,0,0.9963859,"\int \frac{1}{(d+e x) (f+g x)^{5/2} \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)*(f + g*x)^(5/2)*Sqrt[a + c*x^2]),x]","-\frac{2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right) e^2}{\left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{2 \sqrt{-a} \sqrt{c} g \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) e}{(e f-d g)^2 \left(c f^2+a g^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}+\frac{2 g^2 \sqrt{c x^2+a} e}{(e f-d g)^2 \left(c f^2+a g^2\right) \sqrt{f+g x}}+\frac{8 \sqrt{-a} c^{3/2} f g \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 (e f-d g) \left(c f^2+a g^2\right)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}-\frac{2 \sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 (e f-d g) \left(c f^2+a g^2\right) \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{8 c f g^2 \sqrt{c x^2+a}}{3 (e f-d g) \left(c f^2+a g^2\right)^2 \sqrt{f+g x}}+\frac{2 g^2 \sqrt{c x^2+a}}{3 (e f-d g) \left(c f^2+a g^2\right) (f+g x)^{3/2}}","-\frac{2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} \Pi \left(\frac{2 e}{\frac{\sqrt{c} d}{\sqrt{-a}}+e};\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{-a} g}{\sqrt{c} f+\sqrt{-a} g}\right) e^2}{\left(\frac{\sqrt{c} d}{\sqrt{-a}}+e\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{2 \sqrt{-a} \sqrt{c} g \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right) e}{(e f-d g)^2 \left(c f^2+a g^2\right) \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}+\frac{2 g^2 \sqrt{c x^2+a} e}{(e f-d g)^2 \left(c f^2+a g^2\right) \sqrt{f+g x}}+\frac{8 \sqrt{-a} c^{3/2} f g \sqrt{f+g x} \sqrt{\frac{c x^2}{a}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 (e f-d g) \left(c f^2+a g^2\right)^2 \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{c x^2+a}}-\frac{2 \sqrt{-a} \sqrt{c} g \sqrt{\frac{\sqrt{c} (f+g x)}{\sqrt{c} f+\sqrt{-a} g}} \sqrt{\frac{c x^2}{a}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a g}{\sqrt{-a} \sqrt{c} f-a g}\right)}{3 (e f-d g) \left(c f^2+a g^2\right) \sqrt{f+g x} \sqrt{c x^2+a}}+\frac{8 c f g^2 \sqrt{c x^2+a}}{3 (e f-d g) \left(c f^2+a g^2\right)^2 \sqrt{f+g x}}+\frac{2 g^2 \sqrt{c x^2+a}}{3 (e f-d g) \left(c f^2+a g^2\right) (f+g x)^{3/2}}",1,"(2*g^2*Sqrt[a + c*x^2])/(3*(e*f - d*g)*(c*f^2 + a*g^2)*(f + g*x)^(3/2)) + (8*c*f*g^2*Sqrt[a + c*x^2])/(3*(e*f - d*g)*(c*f^2 + a*g^2)^2*Sqrt[f + g*x]) + (2*e*g^2*Sqrt[a + c*x^2])/((e*f - d*g)^2*(c*f^2 + a*g^2)*Sqrt[f + g*x]) + (8*Sqrt[-a]*c^(3/2)*f*g*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*(e*f - d*g)*(c*f^2 + a*g^2)^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*Sqrt[c]*e*g*Sqrt[f + g*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/((e*f - d*g)^2*(c*f^2 + a*g^2)*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[a + c*x^2]) - (2*Sqrt[-a]*Sqrt[c]*g*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*g)/(Sqrt[-a]*Sqrt[c]*f - a*g)])/(3*(e*f - d*g)*(c*f^2 + a*g^2)*Sqrt[f + g*x]*Sqrt[a + c*x^2]) - (2*e^2*Sqrt[(Sqrt[c]*(f + g*x))/(Sqrt[c]*f + Sqrt[-a]*g)]*Sqrt[1 + (c*x^2)/a]*EllipticPi[(2*e)/((Sqrt[c]*d)/Sqrt[-a] + e), ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (2*Sqrt[-a]*g)/(Sqrt[c]*f + Sqrt[-a]*g)])/(((Sqrt[c]*d)/Sqrt[-a] + e)*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + c*x^2])","A",17,12,28,0.4286,1,"{958, 745, 835, 844, 719, 424, 419, 21, 933, 168, 538, 537}"
654,1,110,0,0.3042732,"\int \frac{1}{(d+e x) \sqrt{f+g x} \sqrt{1+c x^2}} \, dx","Int[1/((d + e*x)*Sqrt[f + g*x]*Sqrt[1 + c*x^2]),x]","-\frac{2 \sqrt{\frac{\sqrt{-c} (f+g x)}{\sqrt{-c} f+g}} \Pi \left(\frac{2 e}{\sqrt{-c} d+e};\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c} x}}{\sqrt{2}}\right)|\frac{2 g}{\sqrt{-c} f+g}\right)}{\left(\sqrt{-c} d+e\right) \sqrt{f+g x}}","-\frac{2 \sqrt{\frac{\sqrt{-c} (f+g x)}{\sqrt{-c} f+g}} \Pi \left(\frac{2 e}{\sqrt{-c} d+e};\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c} x}}{\sqrt{2}}\right)|\frac{2 g}{\sqrt{-c} f+g}\right)}{\left(\sqrt{-c} d+e\right) \sqrt{f+g x}}",1,"(-2*Sqrt[(Sqrt[-c]*(f + g*x))/(Sqrt[-c]*f + g)]*EllipticPi[(2*e)/(Sqrt[-c]*d + e), ArcSin[Sqrt[1 - Sqrt[-c]*x]/Sqrt[2]], (2*g)/(Sqrt[-c]*f + g)])/((Sqrt[-c]*d + e)*Sqrt[f + g*x])","A",4,4,28,0.1429,1,"{932, 168, 538, 537}"
655,1,454,0,0.6288508,"\int \frac{1}{\sqrt{d+e x} \sqrt{f+g x} \sqrt{a+c x^2}} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[f + g*x]*Sqrt[a + c*x^2]),x]","-\frac{(d+e x) \sqrt[4]{a g^2+c f^2} \sqrt{\frac{\left(a+c x^2\right) (e f-d g)^2}{(d+e x)^2 \left(a g^2+c f^2\right)}} \left(\frac{(f+g x) \sqrt{a e^2+c d^2}}{(d+e x) \sqrt{a g^2+c f^2}}+1\right) \sqrt{\frac{\frac{(f+g x)^2 \left(a e^2+c d^2\right)}{(d+e x)^2 \left(a g^2+c f^2\right)}-\frac{2 (f+g x) (a e g+c d f)}{(d+e x) \left(a g^2+c f^2\right)}+1}{\left(\frac{(f+g x) \sqrt{a e^2+c d^2}}{(d+e x) \sqrt{a g^2+c f^2}}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c d^2+a e^2} \sqrt{f+g x}}{\sqrt[4]{c f^2+a g^2} \sqrt{d+e x}}\right)|\frac{1}{2} \left(\frac{c d f+a e g}{\sqrt{c d^2+a e^2} \sqrt{c f^2+a g^2}}+1\right)\right)}{\sqrt{a+c x^2} \sqrt[4]{a e^2+c d^2} (e f-d g) \sqrt{\frac{(f+g x)^2 \left(a e^2+c d^2\right)}{(d+e x)^2 \left(a g^2+c f^2\right)}-\frac{2 (f+g x) (a e g+c d f)}{(d+e x) \left(a g^2+c f^2\right)}+1}}","-\frac{(d+e x) \sqrt[4]{a g^2+c f^2} \sqrt{\frac{\left(a+c x^2\right) (e f-d g)^2}{(d+e x)^2 \left(a g^2+c f^2\right)}} \left(\frac{(f+g x) \sqrt{a e^2+c d^2}}{(d+e x) \sqrt{a g^2+c f^2}}+1\right) \sqrt{\frac{\frac{(f+g x)^2 \left(a e^2+c d^2\right)}{(d+e x)^2 \left(a g^2+c f^2\right)}-\frac{2 (f+g x) (a e g+c d f)}{(d+e x) \left(a g^2+c f^2\right)}+1}{\left(\frac{(f+g x) \sqrt{a e^2+c d^2}}{(d+e x) \sqrt{a g^2+c f^2}}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c d^2+a e^2} \sqrt{f+g x}}{\sqrt[4]{c f^2+a g^2} \sqrt{d+e x}}\right)|\frac{1}{2} \left(\frac{c d f+a e g}{\sqrt{c d^2+a e^2} \sqrt{c f^2+a g^2}}+1\right)\right)}{\sqrt{a+c x^2} \sqrt[4]{a e^2+c d^2} (e f-d g) \sqrt{\frac{(f+g x)^2 \left(a e^2+c d^2\right)}{(d+e x)^2 \left(a g^2+c f^2\right)}-\frac{2 (f+g x) (a e g+c d f)}{(d+e x) \left(a g^2+c f^2\right)}+1}}",1,"-(((c*f^2 + a*g^2)^(1/4)*(d + e*x)*Sqrt[((e*f - d*g)^2*(a + c*x^2))/((c*f^2 + a*g^2)*(d + e*x)^2)]*(1 + (Sqrt[c*d^2 + a*e^2]*(f + g*x))/(Sqrt[c*f^2 + a*g^2]*(d + e*x)))*Sqrt[(1 - (2*(c*d*f + a*e*g)*(f + g*x))/((c*f^2 + a*g^2)*(d + e*x)) + ((c*d^2 + a*e^2)*(f + g*x)^2)/((c*f^2 + a*g^2)*(d + e*x)^2))/(1 + (Sqrt[c*d^2 + a*e^2]*(f + g*x))/(Sqrt[c*f^2 + a*g^2]*(d + e*x)))^2]*EllipticF[2*ArcTan[((c*d^2 + a*e^2)^(1/4)*Sqrt[f + g*x])/((c*f^2 + a*g^2)^(1/4)*Sqrt[d + e*x])], (1 + (c*d*f + a*e*g)/(Sqrt[c*d^2 + a*e^2]*Sqrt[c*f^2 + a*g^2]))/2])/((c*d^2 + a*e^2)^(1/4)*(e*f - d*g)*Sqrt[a + c*x^2]*Sqrt[1 - (2*(c*d*f + a*e*g)*(f + g*x))/((c*f^2 + a*g^2)*(d + e*x)) + ((c*d^2 + a*e^2)*(f + g*x)^2)/((c*f^2 + a*g^2)*(d + e*x)^2)]))","A",2,2,30,0.06667,1,"{936, 1103}"
656,1,52,0,0.0463509,"\int \frac{1}{\sqrt{-1+x} \sqrt{1+x} \sqrt{-1+2 x^2}} \, dx","Int[1/(Sqrt[-1 + x]*Sqrt[1 + x]*Sqrt[-1 + 2*x^2]),x]","\frac{\sqrt{1-2 x^2} \sqrt{1-x^2} F\left(\left.\sin ^{-1}(x)\right|2\right)}{\sqrt{x-1} \sqrt{x+1} \sqrt{2 x^2-1}}","\frac{\sqrt{1-2 x^2} \sqrt{1-x^2} F\left(\left.\sin ^{-1}(x)\right|2\right)}{\sqrt{x-1} \sqrt{x+1} \sqrt{2 x^2-1}}",1,"(Sqrt[1 - 2*x^2]*Sqrt[1 - x^2]*EllipticF[ArcSin[x], 2])/(Sqrt[-1 + x]*Sqrt[1 + x]*Sqrt[-1 + 2*x^2])","A",4,3,26,0.1154,1,"{519, 421, 419}"
657,1,269,0,0.4232843,"\int \frac{\sqrt{d+e x} (f+g x)^3}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(Sqrt[d + e*x]*(f + g*x)^3)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{12 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{35 c^2 d^2 \sqrt{d+e x}}+\frac{16 g \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{35 c^3 d^3 e}-\frac{16 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2 \left(2 a e^2 g-c d (3 e f-d g)\right)}{35 c^4 d^4 e \sqrt{d+e x}}+\frac{2 (f+g x)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 c d \sqrt{d+e x}}","\frac{12 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{35 c^2 d^2 \sqrt{d+e x}}+\frac{16 g \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{35 c^3 d^3 e}-\frac{16 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2 \left(2 a e^2 g-c d (3 e f-d g)\right)}{35 c^4 d^4 e \sqrt{d+e x}}+\frac{2 (f+g x)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 c d \sqrt{d+e x}}",1,"(-16*(c*d*f - a*e*g)^2*(2*a*e^2*g - c*d*(3*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*c^4*d^4*e*Sqrt[d + e*x]) + (16*g*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*c^3*d^3*e) + (12*(c*d*f - a*e*g)*(f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*c^2*d^2*Sqrt[d + e*x]) + (2*(f + g*x)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(7*c*d*Sqrt[d + e*x])","A",4,3,46,0.06522,1,"{870, 794, 648}"
658,1,200,0,0.2329586,"\int \frac{\sqrt{d+e x} (f+g x)^2}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(Sqrt[d + e*x]*(f + g*x)^2)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{8 g \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{15 c^2 d^2 e}-\frac{8 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(2 a e^2 g-c d (3 e f-d g)\right)}{15 c^3 d^3 e \sqrt{d+e x}}+\frac{2 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 c d \sqrt{d+e x}}","\frac{8 g \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{15 c^2 d^2 e}-\frac{8 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(2 a e^2 g-c d (3 e f-d g)\right)}{15 c^3 d^3 e \sqrt{d+e x}}+\frac{2 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 c d \sqrt{d+e x}}",1,"(-8*(c*d*f - a*e*g)*(2*a*e^2*g - c*d*(3*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(15*c^3*d^3*e*Sqrt[d + e*x]) + (8*g*(c*d*f - a*e*g)*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(15*c^2*d^2*e) + (2*(f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*c*d*Sqrt[d + e*x])","A",3,3,46,0.06522,1,"{870, 794, 648}"
659,1,125,0,0.0917179,"\int \frac{\sqrt{d+e x} (f+g x)}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(Sqrt[d + e*x]*(f + g*x))/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{2 g \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c d e}-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (3 e f-d g)\right)}{3 c^2 d^2 e \sqrt{d+e x}}","\frac{2 g \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c d e}-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (3 e f-d g)\right)}{3 c^2 d^2 e \sqrt{d+e x}}",1,"(-2*(2*a*e^2*g - c*d*(3*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c^2*d^2*e*Sqrt[d + e*x]) + (2*g*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c*d*e)","A",2,2,44,0.04545,1,"{794, 648}"
660,1,46,0,0.0206646,"\int \frac{\sqrt{d+e x}}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d \sqrt{d+e x}}","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d \sqrt{d+e x}}",1,"(2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(c*d*Sqrt[d + e*x])","A",1,1,39,0.02564,1,"{648}"
661,1,80,0,0.1314195,"\int \frac{\sqrt{d+e x}}{(f+g x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/((f + g*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{\sqrt{g} \sqrt{c d f-a e g}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{\sqrt{g} \sqrt{c d f-a e g}}",1,"(2*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(Sqrt[g]*Sqrt[c*d*f - a*e*g])","A",2,2,46,0.04348,1,"{874, 205}"
662,1,140,0,0.1913196,"\int \frac{\sqrt{d+e x}}{(f+g x)^2 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/((f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} (f+g x) (c d f-a e g)}+\frac{c d \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{\sqrt{g} (c d f-a e g)^{3/2}}","\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} (f+g x) (c d f-a e g)}+\frac{c d \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{\sqrt{g} (c d f-a e g)^{3/2}}",1,"Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/((c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)) + (c*d*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(Sqrt[g]*(c*d*f - a*e*g)^(3/2))","A",3,3,46,0.06522,1,"{872, 874, 205}"
663,1,213,0,0.3135839,"\int \frac{\sqrt{d+e x}}{(f+g x)^3 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/((f + g*x)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{3 c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 \sqrt{g} (c d f-a e g)^{5/2}}+\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 \sqrt{d+e x} (f+g x) (c d f-a e g)^2}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}","\frac{3 c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 \sqrt{g} (c d f-a e g)^{5/2}}+\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 \sqrt{d+e x} (f+g x) (c d f-a e g)^2}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}",1,"Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(2*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^2) + (3*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)) + (3*c^2*d^2*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(4*Sqrt[g]*(c*d*f - a*e*g)^(5/2))","A",4,3,46,0.06522,1,"{872, 874, 205}"
664,1,280,0,0.4239731,"\int \frac{\sqrt{d+e x}}{(f+g x)^4 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/((f + g*x)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{5 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 \sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{5 c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 \sqrt{g} (c d f-a e g)^{7/2}}+\frac{5 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}","\frac{5 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 \sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{5 c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 \sqrt{g} (c d f-a e g)^{7/2}}+\frac{5 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}",1,"Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(3*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^3) + (5*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^2) + (5*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)) + (5*c^3*d^3*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(8*Sqrt[g]*(c*d*f - a*e*g)^(7/2))","A",5,3,46,0.06522,1,"{872, 874, 205}"
665,1,257,0,0.330761,"\int \frac{(d+e x)^{3/2} (f+g x)^3}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x)^3)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{16 g^2 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{5 c^3 d^3 e}+\frac{12 g (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 c^2 d^2 \sqrt{d+e x}}-\frac{16 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(2 a e^2 g-c d (3 e f-d g)\right)}{5 c^4 d^4 e \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} (f+g x)^3}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{16 g^2 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{5 c^3 d^3 e}+\frac{12 g (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 c^2 d^2 \sqrt{d+e x}}-\frac{16 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(2 a e^2 g-c d (3 e f-d g)\right)}{5 c^4 d^4 e \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} (f+g x)^3}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*Sqrt[d + e*x]*(f + g*x)^3)/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (16*g*(c*d*f - a*e*g)*(2*a*e^2*g - c*d*(3*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*c^4*d^4*e*Sqrt[d + e*x]) + (16*g^2*(c*d*f - a*e*g)*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*c^3*d^3*e) + (12*g*(f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*c^2*d^2*Sqrt[d + e*x])","A",4,4,46,0.08696,1,"{866, 870, 794, 648}"
666,1,181,0,0.18466,"\int \frac{(d+e x)^{3/2} (f+g x)^2}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x)^2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","-\frac{8 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (3 e f-d g)\right)}{3 c^3 d^3 e \sqrt{d+e x}}+\frac{8 g^2 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^2 d^2 e}-\frac{2 \sqrt{d+e x} (f+g x)^2}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","-\frac{8 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (3 e f-d g)\right)}{3 c^3 d^3 e \sqrt{d+e x}}+\frac{8 g^2 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^2 d^2 e}-\frac{2 \sqrt{d+e x} (f+g x)^2}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*Sqrt[d + e*x]*(f + g*x)^2)/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (8*g*(2*a*e^2*g - c*d*(3*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c^3*d^3*e*Sqrt[d + e*x]) + (8*g^2*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c^2*d^2*e)","A",3,3,46,0.06522,1,"{866, 794, 648}"
667,1,150,0,0.1436139,"\int \frac{(d+e x)^{3/2} (f+g x)}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x))/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (d g+e f)\right)}{c^2 d^2 \sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{2 (d+e x)^{3/2} (c d f-a e g)}{c d \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (d g+e f)\right)}{c^2 d^2 \sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{2 (d+e x)^{3/2} (c d f-a e g)}{c d \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*(c*d*f - a*e*g)*(d + e*x)^(3/2))/(c*d*(c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (2*(2*a*e^2*g - c*d*(e*f + d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(c^2*d^2*(c*d^2 - a*e^2)*Sqrt[d + e*x])","A",2,2,44,0.04545,1,"{788, 648}"
668,1,46,0,0.0216481,"\int \frac{(d+e x)^{3/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","-\frac{2 \sqrt{d+e x}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","-\frac{2 \sqrt{d+e x}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*Sqrt[d + e*x])/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",1,1,39,0.02564,1,"{648}"
669,1,133,0,0.1762756,"\int \frac{(d+e x)^{3/2}}{(f+g x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{2 \sqrt{d+e x}}{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}-\frac{2 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{(c d f-a e g)^{3/2}}","-\frac{2 \sqrt{d+e x}}{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}-\frac{2 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{(c d f-a e g)^{3/2}}",1,"(-2*Sqrt[d + e*x])/((c*d*f - a*e*g)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (2*Sqrt[g]*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(c*d*f - a*e*g)^(3/2)","A",3,3,46,0.06522,1,"{868, 874, 205}"
670,1,202,0,0.2566495,"\int \frac{(d+e x)^{3/2}}{(f+g x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{3 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} (f+g x) (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{(f+g x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}-\frac{3 c d \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{(c d f-a e g)^{5/2}}","-\frac{3 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} (f+g x) (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{(f+g x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}-\frac{3 c d \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{(c d f-a e g)^{5/2}}",1,"(-2*Sqrt[d + e*x])/((c*d*f - a*e*g)*(f + g*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (3*g*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/((c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)) - (3*c*d*Sqrt[g]*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(c*d*f - a*e*g)^(5/2)","A",4,4,46,0.08696,1,"{868, 872, 874, 205}"
671,1,274,0,0.3523334,"\int \frac{(d+e x)^{3/2}}{(f+g x)^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{15 c^2 d^2 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 (c d f-a e g)^{7/2}}-\frac{15 c d g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 \sqrt{d+e x} (f+g x) (c d f-a e g)^3}-\frac{5 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{(f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}","-\frac{15 c^2 d^2 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 (c d f-a e g)^{7/2}}-\frac{15 c d g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 \sqrt{d+e x} (f+g x) (c d f-a e g)^3}-\frac{5 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{(f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}",1,"(-2*Sqrt[d + e*x])/((c*d*f - a*e*g)*(f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (5*g*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(2*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^2) - (15*c*d*g*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)) - (15*c^2*d^2*Sqrt[g]*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(4*(c*d*f - a*e*g)^(7/2))","A",5,4,46,0.08696,1,"{868, 872, 874, 205}"
672,1,239,0,0.2796484,"\int \frac{(d+e x)^{5/2} (f+g x)^3}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(5/2)*(f + g*x)^3)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","-\frac{16 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (3 e f-d g)\right)}{3 c^4 d^4 e \sqrt{d+e x}}-\frac{4 g \sqrt{d+e x} (f+g x)^2}{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{16 g^3 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^3 d^3 e}-\frac{2 (d+e x)^{3/2} (f+g x)^3}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","-\frac{16 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (3 e f-d g)\right)}{3 c^4 d^4 e \sqrt{d+e x}}-\frac{4 g \sqrt{d+e x} (f+g x)^2}{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{16 g^3 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^3 d^3 e}-\frac{2 (d+e x)^{3/2} (f+g x)^3}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(3/2)*(f + g*x)^3)/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (4*g*Sqrt[d + e*x]*(f + g*x)^2)/(c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (16*g^2*(2*a*e^2*g - c*d*(3*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c^4*d^4*e*Sqrt[d + e*x]) + (16*g^3*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c^3*d^3*e)","A",4,3,46,0.06522,1,"{866, 794, 648}"
673,1,211,0,0.2195144,"\int \frac{(d+e x)^{5/2} (f+g x)^2}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(5/2)*(f + g*x)^2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","-\frac{8 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (d g+e f)\right)}{3 c^3 d^3 \sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{8 g (d+e x)^{3/2} (c d f-a e g)}{3 c^2 d^2 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 (d+e x)^{3/2} (f+g x)^2}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","-\frac{8 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(2 a e^2 g-c d (d g+e f)\right)}{3 c^3 d^3 \sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{8 g (d+e x)^{3/2} (c d f-a e g)}{3 c^2 d^2 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 (d+e x)^{3/2} (f+g x)^2}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(3/2)*(f + g*x)^2)/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (8*g*(c*d*f - a*e*g)*(d + e*x)^(3/2))/(3*c^2*d^2*(c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (8*g*(2*a*e^2*g - c*d*(e*f + d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c^3*d^3*(c*d^2 - a*e^2)*Sqrt[d + e*x])","A",3,3,46,0.06522,1,"{866, 788, 648}"
674,1,154,0,0.1337253,"\int \frac{(d+e x)^{5/2} (f+g x)}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(5/2)*(f + g*x))/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(2 a e^2 g+c d (e f-3 d g)\right)}{3 c^2 d^2 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 (d+e x)^{5/2} (c d f-a e g)}{3 c d \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","\frac{2 \sqrt{d+e x} \left(2 a e^2 g+c d (e f-3 d g)\right)}{3 c^2 d^2 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 (d+e x)^{5/2} (c d f-a e g)}{3 c d \left(c d^2-a e^2\right) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*(c*d*f - a*e*g)*(d + e*x)^(5/2))/(3*c*d*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (2*(2*a*e^2*g + c*d*(e*f - 3*d*g))*Sqrt[d + e*x])/(3*c^2*d^2*(c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",2,2,44,0.04545,1,"{788, 648}"
675,1,48,0,0.0215449,"\int \frac{(d+e x)^{5/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","-\frac{2 (d+e x)^{3/2}}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","-\frac{2 (d+e x)^{3/2}}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(3/2))/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))","A",1,1,39,0.02564,1,"{648}"
676,1,188,0,0.269652,"\int \frac{(d+e x)^{5/2}}{(f+g x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/((f + g*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{2 g^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{(c d f-a e g)^{5/2}}+\frac{2 g \sqrt{d+e x}}{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}","\frac{2 g^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{(c d f-a e g)^{5/2}}+\frac{2 g \sqrt{d+e x}}{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}",1,"(-2*(d + e*x)^(3/2))/(3*(c*d*f - a*e*g)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (2*g*Sqrt[d + e*x])/((c*d*f - a*e*g)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (2*g^(3/2)*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(c*d*f - a*e*g)^(5/2)","A",4,3,46,0.06522,1,"{868, 874, 205}"
677,1,268,0,0.3401958,"\int \frac{(d+e x)^{5/2}}{(f+g x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/((f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{5 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{5 c d g^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{(c d f-a e g)^{7/2}}+\frac{10 g \sqrt{d+e x}}{3 (f+g x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 (f+g x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}","\frac{5 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{5 c d g^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{(c d f-a e g)^{7/2}}+\frac{10 g \sqrt{d+e x}}{3 (f+g x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 (f+g x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}",1,"(-2*(d + e*x)^(3/2))/(3*(c*d*f - a*e*g)*(f + g*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (10*g*Sqrt[d + e*x])/(3*(c*d*f - a*e*g)^2*(f + g*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (5*g^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/((c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)) + (5*c*d*g^(3/2)*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(c*d*f - a*e*g)^(7/2)","A",5,4,46,0.08696,1,"{868, 872, 874, 205}"
678,1,342,0,0.5381707,"\int \frac{(d+e x)^{5/2}}{(f+g x)^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/((f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{35 c^2 d^2 g^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 (c d f-a e g)^{9/2}}+\frac{35 c d g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 \sqrt{d+e x} (f+g x) (c d f-a e g)^4}+\frac{35 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{6 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^3}+\frac{14 g \sqrt{d+e x}}{3 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}","\frac{35 c^2 d^2 g^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 (c d f-a e g)^{9/2}}+\frac{35 c d g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 \sqrt{d+e x} (f+g x) (c d f-a e g)^4}+\frac{35 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{6 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^3}+\frac{14 g \sqrt{d+e x}}{3 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}",1,"(-2*(d + e*x)^(3/2))/(3*(c*d*f - a*e*g)*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (14*g*Sqrt[d + e*x])/(3*(c*d*f - a*e*g)^2*(f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (35*g^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(6*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)^2) + (35*c*d*g^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*(c*d*f - a*e*g)^4*Sqrt[d + e*x]*(f + g*x)) + (35*c^2*d^2*g^(3/2)*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(4*(c*d*f - a*e*g)^(9/2))","A",6,4,46,0.08696,1,"{868, 872, 874, 205}"
679,1,336,0,0.6072507,"\int \frac{(f+g x)^4 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/Sqrt[d + e*x],x]","\frac{16 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{99 c^2 d^2 (d+e x)^{3/2}}+\frac{32 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^2}{231 c^3 d^3 (d+e x)^{3/2}}+\frac{128 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^3}{1155 c^4 d^4 e \sqrt{d+e x}}-\frac{128 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^3 \left(2 a e^2 g-c d (5 e f-3 d g)\right)}{3465 c^5 d^5 e (d+e x)^{3/2}}+\frac{2 (f+g x)^4 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{11 c d (d+e x)^{3/2}}","\frac{16 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{99 c^2 d^2 (d+e x)^{3/2}}+\frac{32 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^2}{231 c^3 d^3 (d+e x)^{3/2}}+\frac{128 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^3}{1155 c^4 d^4 e \sqrt{d+e x}}-\frac{128 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^3 \left(2 a e^2 g-c d (5 e f-3 d g)\right)}{3465 c^5 d^5 e (d+e x)^{3/2}}+\frac{2 (f+g x)^4 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{11 c d (d+e x)^{3/2}}",1,"(-128*(c*d*f - a*e*g)^3*(2*a*e^2*g - c*d*(5*e*f - 3*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3465*c^5*d^5*e*(d + e*x)^(3/2)) + (128*g*(c*d*f - a*e*g)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(1155*c^4*d^4*e*Sqrt[d + e*x]) + (32*(c*d*f - a*e*g)^2*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(231*c^3*d^3*(d + e*x)^(3/2)) + (16*(c*d*f - a*e*g)*(f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(99*c^2*d^2*(d + e*x)^(3/2)) + (2*(f + g*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(11*c*d*(d + e*x)^(3/2))","A",5,3,46,0.06522,1,"{870, 794, 648}"
680,1,269,0,0.3899999,"\int \frac{(f+g x)^3 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/Sqrt[d + e*x],x]","\frac{4 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{21 c^2 d^2 (d+e x)^{3/2}}+\frac{16 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^2}{105 c^3 d^3 e \sqrt{d+e x}}-\frac{16 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^2 \left(2 a e^2 g-c d (5 e f-3 d g)\right)}{315 c^4 d^4 e (d+e x)^{3/2}}+\frac{2 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{9 c d (d+e x)^{3/2}}","\frac{4 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{21 c^2 d^2 (d+e x)^{3/2}}+\frac{16 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^2}{105 c^3 d^3 e \sqrt{d+e x}}-\frac{16 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)^2 \left(2 a e^2 g-c d (5 e f-3 d g)\right)}{315 c^4 d^4 e (d+e x)^{3/2}}+\frac{2 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{9 c d (d+e x)^{3/2}}",1,"(-16*(c*d*f - a*e*g)^2*(2*a*e^2*g - c*d*(5*e*f - 3*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(315*c^4*d^4*e*(d + e*x)^(3/2)) + (16*g*(c*d*f - a*e*g)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*c^3*d^3*e*Sqrt[d + e*x]) + (4*(c*d*f - a*e*g)*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(21*c^2*d^2*(d + e*x)^(3/2)) + (2*(f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(9*c*d*(d + e*x)^(3/2))","A",4,3,46,0.06522,1,"{870, 794, 648}"
681,1,200,0,0.2283831,"\int \frac{(f+g x)^2 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/Sqrt[d + e*x],x]","\frac{8 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{35 c^2 d^2 e \sqrt{d+e x}}-\frac{8 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g) \left(2 a e^2 g-c d (5 e f-3 d g)\right)}{105 c^3 d^3 e (d+e x)^{3/2}}+\frac{2 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{7 c d (d+e x)^{3/2}}","\frac{8 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{35 c^2 d^2 e \sqrt{d+e x}}-\frac{8 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g) \left(2 a e^2 g-c d (5 e f-3 d g)\right)}{105 c^3 d^3 e (d+e x)^{3/2}}+\frac{2 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{7 c d (d+e x)^{3/2}}",1,"(-8*(c*d*f - a*e*g)*(2*a*e^2*g - c*d*(5*e*f - 3*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*c^3*d^3*e*(d + e*x)^(3/2)) + (8*g*(c*d*f - a*e*g)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(35*c^2*d^2*e*Sqrt[d + e*x]) + (2*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(7*c*d*(d + e*x)^(3/2))","A",3,3,46,0.06522,1,"{870, 794, 648}"
682,1,125,0,0.0951645,"\int \frac{(f+g x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/Sqrt[d + e*x],x]","\frac{2 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 c d e \sqrt{d+e x}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} \left(2 a e^2 g-c d (5 e f-3 d g)\right)}{15 c^2 d^2 e (d+e x)^{3/2}}","\frac{2 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 c d e \sqrt{d+e x}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} \left(2 a e^2 g-c d (5 e f-3 d g)\right)}{15 c^2 d^2 e (d+e x)^{3/2}}",1,"(-2*(2*a*e^2*g - c*d*(5*e*f - 3*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(15*c^2*d^2*e*(d + e*x)^(3/2)) + (2*g*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(5*c*d*e*Sqrt[d + e*x])","A",2,2,44,0.04545,1,"{794, 648}"
683,1,48,0,0.0206349,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/Sqrt[d + e*x],x]","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 c d (d+e x)^{3/2}}","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 c d (d+e x)^{3/2}}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*c*d*(d + e*x)^(3/2))","A",1,1,39,0.02564,1,"{648}"
684,1,124,0,0.1863607,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)),x]","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x}}-\frac{2 \sqrt{c d f-a e g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{3/2}}","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x}}-\frac{2 \sqrt{c d f-a e g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{3/2}}",1,"(2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g*Sqrt[d + e*x]) - (2*Sqrt[c*d*f - a*e*g]*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/g^(3/2)","A",3,3,46,0.06522,1,"{864, 874, 205}"
685,1,132,0,0.1609694,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)^2} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)^2),x]","\frac{c d \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{3/2} \sqrt{c d f-a e g}}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x} (f+g x)}","\frac{c d \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{3/2} \sqrt{c d f-a e g}}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x} (f+g x)}",1,"-(Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(g*Sqrt[d + e*x]*(f + g*x))) + (c*d*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(g^(3/2)*Sqrt[c*d*f - a*e*g])","A",3,3,46,0.06522,1,"{862, 874, 205}"
686,1,207,0,0.2733236,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)^3} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)^3),x]","\frac{c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 g^{3/2} (c d f-a e g)^{3/2}}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g \sqrt{d+e x} (f+g x) (c d f-a e g)}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 g \sqrt{d+e x} (f+g x)^2}","\frac{c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 g^{3/2} (c d f-a e g)^{3/2}}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g \sqrt{d+e x} (f+g x) (c d f-a e g)}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 g \sqrt{d+e x} (f+g x)^2}",1,"-Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(2*g*Sqrt[d + e*x]*(f + g*x)^2) + (c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*g*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)) + (c^2*d^2*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(4*g^(3/2)*(c*d*f - a*e*g)^(3/2))","A",4,4,46,0.08696,1,"{862, 872, 874, 205}"
687,1,277,0,0.3496679,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)^4} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)^4),x]","\frac{c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 g^{3/2} (c d f-a e g)^{5/2}}+\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 g \sqrt{d+e x} (f+g x) (c d f-a e g)^2}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 g \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 g \sqrt{d+e x} (f+g x)^3}","\frac{c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 g^{3/2} (c d f-a e g)^{5/2}}+\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 g \sqrt{d+e x} (f+g x) (c d f-a e g)^2}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 g \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 g \sqrt{d+e x} (f+g x)^3}",1,"-Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(3*g*Sqrt[d + e*x]*(f + g*x)^3) + (c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*g*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^2) + (c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*g*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)) + (c^3*d^3*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(8*g^(3/2)*(c*d*f - a*e*g)^(5/2))","A",5,4,46,0.08696,1,"{862, 872, 874, 205}"
688,1,347,0,0.4544393,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)^5} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)^5),x]","\frac{5 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{64 g^{3/2} (c d f-a e g)^{7/2}}+\frac{5 c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g \sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{5 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{96 g \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 g \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g \sqrt{d+e x} (f+g x)^4}","\frac{5 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{64 g^{3/2} (c d f-a e g)^{7/2}}+\frac{5 c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g \sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{5 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{96 g \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{24 g \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g \sqrt{d+e x} (f+g x)^4}",1,"-Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(4*g*Sqrt[d + e*x]*(f + g*x)^4) + (c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(24*g*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^3) + (5*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(96*g*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^2) + (5*c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*g*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)) + (5*c^4*d^4*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(64*g^(3/2)*(c*d*f - a*e*g)^(7/2))","A",6,4,46,0.08696,1,"{862, 872, 874, 205}"
689,1,336,0,0.6065421,"\int \frac{(f+g x)^4 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((f + g*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{16 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)}{143 c^2 d^2 (d+e x)^{5/2}}+\frac{32 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^2}{429 c^3 d^3 (d+e x)^{5/2}}+\frac{128 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^3}{3003 c^4 d^4 e (d+e x)^{3/2}}-\frac{128 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^3 \left(2 a e^2 g-c d (7 e f-5 d g)\right)}{15015 c^5 d^5 e (d+e x)^{5/2}}+\frac{2 (f+g x)^4 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{13 c d (d+e x)^{5/2}}","\frac{16 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)}{143 c^2 d^2 (d+e x)^{5/2}}+\frac{32 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^2}{429 c^3 d^3 (d+e x)^{5/2}}+\frac{128 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^3}{3003 c^4 d^4 e (d+e x)^{3/2}}-\frac{128 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^3 \left(2 a e^2 g-c d (7 e f-5 d g)\right)}{15015 c^5 d^5 e (d+e x)^{5/2}}+\frac{2 (f+g x)^4 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{13 c d (d+e x)^{5/2}}",1,"(-128*(c*d*f - a*e*g)^3*(2*a*e^2*g - c*d*(7*e*f - 5*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(15015*c^5*d^5*e*(d + e*x)^(5/2)) + (128*g*(c*d*f - a*e*g)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(3003*c^4*d^4*e*(d + e*x)^(3/2)) + (32*(c*d*f - a*e*g)^2*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(429*c^3*d^3*(d + e*x)^(5/2)) + (16*(c*d*f - a*e*g)*(f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(143*c^2*d^2*(d + e*x)^(5/2)) + (2*(f + g*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(13*c*d*(d + e*x)^(5/2))","A",5,3,46,0.06522,1,"{870, 794, 648}"
690,1,269,0,0.4072571,"\int \frac{(f+g x)^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{4 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)}{33 c^2 d^2 (d+e x)^{5/2}}+\frac{16 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^2}{231 c^3 d^3 e (d+e x)^{3/2}}-\frac{16 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^2 \left(2 a e^2 g-c d (7 e f-5 d g)\right)}{1155 c^4 d^4 e (d+e x)^{5/2}}+\frac{2 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{11 c d (d+e x)^{5/2}}","\frac{4 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)}{33 c^2 d^2 (d+e x)^{5/2}}+\frac{16 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^2}{231 c^3 d^3 e (d+e x)^{3/2}}-\frac{16 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)^2 \left(2 a e^2 g-c d (7 e f-5 d g)\right)}{1155 c^4 d^4 e (d+e x)^{5/2}}+\frac{2 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{11 c d (d+e x)^{5/2}}",1,"(-16*(c*d*f - a*e*g)^2*(2*a*e^2*g - c*d*(7*e*f - 5*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(1155*c^4*d^4*e*(d + e*x)^(5/2)) + (16*g*(c*d*f - a*e*g)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(231*c^3*d^3*e*(d + e*x)^(3/2)) + (4*(c*d*f - a*e*g)*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(33*c^2*d^2*(d + e*x)^(5/2)) + (2*(f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(11*c*d*(d + e*x)^(5/2))","A",4,3,46,0.06522,1,"{870, 794, 648}"
691,1,200,0,0.2325277,"\int \frac{(f+g x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{8 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)}{63 c^2 d^2 e (d+e x)^{3/2}}-\frac{8 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g) \left(2 a e^2 g-c d (7 e f-5 d g)\right)}{315 c^3 d^3 e (d+e x)^{5/2}}+\frac{2 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{9 c d (d+e x)^{5/2}}","\frac{8 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)}{63 c^2 d^2 e (d+e x)^{3/2}}-\frac{8 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g) \left(2 a e^2 g-c d (7 e f-5 d g)\right)}{315 c^3 d^3 e (d+e x)^{5/2}}+\frac{2 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{9 c d (d+e x)^{5/2}}",1,"(-8*(c*d*f - a*e*g)*(2*a*e^2*g - c*d*(7*e*f - 5*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(315*c^3*d^3*e*(d + e*x)^(5/2)) + (8*g*(c*d*f - a*e*g)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(63*c^2*d^2*e*(d + e*x)^(3/2)) + (2*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(9*c*d*(d + e*x)^(5/2))","A",3,3,46,0.06522,1,"{870, 794, 648}"
692,1,125,0,0.1006064,"\int \frac{(f+g x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((f + g*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{2 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 c d e (d+e x)^{3/2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} \left(2 a e^2 g-c d (7 e f-5 d g)\right)}{35 c^2 d^2 e (d+e x)^{5/2}}","\frac{2 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 c d e (d+e x)^{3/2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} \left(2 a e^2 g-c d (7 e f-5 d g)\right)}{35 c^2 d^2 e (d+e x)^{5/2}}",1,"(-2*(2*a*e^2*g - c*d*(7*e*f - 5*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(35*c^2*d^2*e*(d + e*x)^(5/2)) + (2*g*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(7*c*d*e*(d + e*x)^(3/2))","A",2,2,44,0.04545,1,"{794, 648}"
693,1,48,0,0.0232197,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(3/2),x]","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 c d (d+e x)^{5/2}}","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 c d (d+e x)^{5/2}}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*c*d*(d + e*x)^(5/2))","A",1,1,39,0.02564,1,"{648}"
694,1,179,0,0.3044459,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)),x]","-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{g^2 \sqrt{d+e x}}+\frac{2 (c d f-a e g)^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{5/2}}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g (d+e x)^{3/2}}","-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{g^2 \sqrt{d+e x}}+\frac{2 (c d f-a e g)^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{5/2}}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g (d+e x)^{3/2}}",1,"(-2*(c*d*f - a*e*g)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g^2*Sqrt[d + e*x]) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*g*(d + e*x)^(3/2)) + (2*(c*d*f - a*e*g)^(3/2)*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/g^(5/2)","A",4,3,46,0.06522,1,"{864, 874, 205}"
695,1,178,0,0.2508132,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^2),x]","-\frac{3 c d \sqrt{c d f-a e g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{5/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{g (d+e x)^{3/2} (f+g x)}+\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^2 \sqrt{d+e x}}","-\frac{3 c d \sqrt{c d f-a e g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{5/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{g (d+e x)^{3/2} (f+g x)}+\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^2 \sqrt{d+e x}}",1,"(3*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g^2*Sqrt[d + e*x]) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(g*(d + e*x)^(3/2)*(f + g*x)) - (3*c*d*Sqrt[c*d*f - a*e*g]*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/g^(5/2)","A",4,4,46,0.08696,1,"{862, 864, 874, 205}"
696,1,195,0,0.2560161,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^3} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^3),x]","\frac{3 c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 g^{5/2} \sqrt{c d f-a e g}}-\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g^2 \sqrt{d+e x} (f+g x)}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 g (d+e x)^{3/2} (f+g x)^2}","\frac{3 c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 g^{5/2} \sqrt{c d f-a e g}}-\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g^2 \sqrt{d+e x} (f+g x)}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 g (d+e x)^{3/2} (f+g x)^2}",1,"(-3*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*g^2*Sqrt[d + e*x]*(f + g*x)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(2*g*(d + e*x)^(3/2)*(f + g*x)^2) + (3*c^2*d^2*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(4*g^(5/2)*Sqrt[c*d*f - a*e*g])","A",4,3,46,0.06522,1,"{862, 874, 205}"
697,1,265,0,0.3494877,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^4} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^4),x]","\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 g^2 \sqrt{d+e x} (f+g x) (c d f-a e g)}+\frac{c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 g^{5/2} (c d f-a e g)^{3/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g^2 \sqrt{d+e x} (f+g x)^2}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g (d+e x)^{3/2} (f+g x)^3}","\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 g^2 \sqrt{d+e x} (f+g x) (c d f-a e g)}+\frac{c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 g^{5/2} (c d f-a e g)^{3/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g^2 \sqrt{d+e x} (f+g x)^2}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g (d+e x)^{3/2} (f+g x)^3}",1,"-(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*g^2*Sqrt[d + e*x]*(f + g*x)^2) + (c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*g^2*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(3*g*(d + e*x)^(3/2)*(f + g*x)^3) + (c^3*d^3*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(8*g^(5/2)*(c*d*f - a*e*g)^(3/2))","A",5,4,46,0.08696,1,"{862, 872, 874, 205}"
698,1,335,0,0.4523128,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^5} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^5),x]","\frac{3 c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g^2 \sqrt{d+e x} (f+g x) (c d f-a e g)^2}+\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{32 g^2 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}+\frac{3 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{64 g^{5/2} (c d f-a e g)^{5/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 g^2 \sqrt{d+e x} (f+g x)^3}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 g (d+e x)^{3/2} (f+g x)^4}","\frac{3 c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g^2 \sqrt{d+e x} (f+g x) (c d f-a e g)^2}+\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{32 g^2 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}+\frac{3 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{64 g^{5/2} (c d f-a e g)^{5/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 g^2 \sqrt{d+e x} (f+g x)^3}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 g (d+e x)^{3/2} (f+g x)^4}",1,"-(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*g^2*Sqrt[d + e*x]*(f + g*x)^3) + (c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(32*g^2*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^2) + (3*c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*g^2*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(4*g*(d + e*x)^(3/2)*(f + g*x)^4) + (3*c^4*d^4*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(64*g^(5/2)*(c*d*f - a*e*g)^(5/2))","A",6,4,46,0.08696,1,"{862, 872, 874, 205}"
699,1,405,0,0.5630565,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^6} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^6),x]","\frac{3 c^4 d^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 g^2 \sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g^2 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}+\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{80 g^2 \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}+\frac{3 c^5 d^5 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{128 g^{5/2} (c d f-a e g)^{7/2}}-\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{40 g^2 \sqrt{d+e x} (f+g x)^4}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 g (d+e x)^{3/2} (f+g x)^5}","\frac{3 c^4 d^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 g^2 \sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g^2 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}+\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{80 g^2 \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}+\frac{3 c^5 d^5 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{128 g^{5/2} (c d f-a e g)^{7/2}}-\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{40 g^2 \sqrt{d+e x} (f+g x)^4}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 g (d+e x)^{3/2} (f+g x)^5}",1,"(-3*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(40*g^2*Sqrt[d + e*x]*(f + g*x)^4) + (c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(80*g^2*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^3) + (c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*g^2*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^2) + (3*c^4*d^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(128*g^2*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(5*g*(d + e*x)^(3/2)*(f + g*x)^5) + (3*c^5*d^5*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(128*g^(5/2)*(c*d*f - a*e*g)^(7/2))","A",7,4,46,0.08696,1,"{862, 872, 874, 205}"
700,1,336,0,0.6180585,"\int \frac{(f+g x)^4 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[((f + g*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x)^(5/2),x]","\frac{16 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)}{195 c^2 d^2 (d+e x)^{7/2}}+\frac{32 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^2}{715 c^3 d^3 (d+e x)^{7/2}}+\frac{128 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^3}{6435 c^4 d^4 e (d+e x)^{5/2}}-\frac{128 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^3 \left(2 a e^2 g-c d (9 e f-7 d g)\right)}{45045 c^5 d^5 e (d+e x)^{7/2}}+\frac{2 (f+g x)^4 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{15 c d (d+e x)^{7/2}}","\frac{16 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)}{195 c^2 d^2 (d+e x)^{7/2}}+\frac{32 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^2}{715 c^3 d^3 (d+e x)^{7/2}}+\frac{128 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^3}{6435 c^4 d^4 e (d+e x)^{5/2}}-\frac{128 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^3 \left(2 a e^2 g-c d (9 e f-7 d g)\right)}{45045 c^5 d^5 e (d+e x)^{7/2}}+\frac{2 (f+g x)^4 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{15 c d (d+e x)^{7/2}}",1,"(-128*(c*d*f - a*e*g)^3*(2*a*e^2*g - c*d*(9*e*f - 7*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(45045*c^5*d^5*e*(d + e*x)^(7/2)) + (128*g*(c*d*f - a*e*g)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(6435*c^4*d^4*e*(d + e*x)^(5/2)) + (32*(c*d*f - a*e*g)^2*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(715*c^3*d^3*(d + e*x)^(7/2)) + (16*(c*d*f - a*e*g)*(f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(195*c^2*d^2*(d + e*x)^(7/2)) + (2*(f + g*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(15*c*d*(d + e*x)^(7/2))","A",5,3,46,0.06522,1,"{870, 794, 648}"
701,1,269,0,0.3966516,"\int \frac{(f+g x)^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[((f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x)^(5/2),x]","\frac{12 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)}{143 c^2 d^2 (d+e x)^{7/2}}+\frac{16 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^2}{429 c^3 d^3 e (d+e x)^{5/2}}-\frac{16 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^2 \left(2 a e^2 g-c d (9 e f-7 d g)\right)}{3003 c^4 d^4 e (d+e x)^{7/2}}+\frac{2 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{13 c d (d+e x)^{7/2}}","\frac{12 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)}{143 c^2 d^2 (d+e x)^{7/2}}+\frac{16 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^2}{429 c^3 d^3 e (d+e x)^{5/2}}-\frac{16 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)^2 \left(2 a e^2 g-c d (9 e f-7 d g)\right)}{3003 c^4 d^4 e (d+e x)^{7/2}}+\frac{2 (f+g x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{13 c d (d+e x)^{7/2}}",1,"(-16*(c*d*f - a*e*g)^2*(2*a*e^2*g - c*d*(9*e*f - 7*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(3003*c^4*d^4*e*(d + e*x)^(7/2)) + (16*g*(c*d*f - a*e*g)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(429*c^3*d^3*e*(d + e*x)^(5/2)) + (12*(c*d*f - a*e*g)*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(143*c^2*d^2*(d + e*x)^(7/2)) + (2*(f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(13*c*d*(d + e*x)^(7/2))","A",4,3,46,0.06522,1,"{870, 794, 648}"
702,1,200,0,0.2349378,"\int \frac{(f+g x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[((f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x)^(5/2),x]","\frac{8 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)}{99 c^2 d^2 e (d+e x)^{5/2}}-\frac{8 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g) \left(2 a e^2 g-c d (9 e f-7 d g)\right)}{693 c^3 d^3 e (d+e x)^{7/2}}+\frac{2 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{11 c d (d+e x)^{7/2}}","\frac{8 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g)}{99 c^2 d^2 e (d+e x)^{5/2}}-\frac{8 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} (c d f-a e g) \left(2 a e^2 g-c d (9 e f-7 d g)\right)}{693 c^3 d^3 e (d+e x)^{7/2}}+\frac{2 (f+g x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{11 c d (d+e x)^{7/2}}",1,"(-8*(c*d*f - a*e*g)*(2*a*e^2*g - c*d*(9*e*f - 7*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(693*c^3*d^3*e*(d + e*x)^(7/2)) + (8*g*(c*d*f - a*e*g)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(99*c^2*d^2*e*(d + e*x)^(5/2)) + (2*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(11*c*d*(d + e*x)^(7/2))","A",3,3,46,0.06522,1,"{870, 794, 648}"
703,1,125,0,0.1001515,"\int \frac{(f+g x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[((f + g*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x)^(5/2),x]","\frac{2 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{9 c d e (d+e x)^{5/2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} \left(2 a e^2 g-c d (9 e f-7 d g)\right)}{63 c^2 d^2 e (d+e x)^{7/2}}","\frac{2 g \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{9 c d e (d+e x)^{5/2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2} \left(2 a e^2 g-c d (9 e f-7 d g)\right)}{63 c^2 d^2 e (d+e x)^{7/2}}",1,"(-2*(2*a*e^2*g - c*d*(9*e*f - 7*d*g))*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(63*c^2*d^2*e*(d + e*x)^(7/2)) + (2*g*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(9*c*d*e*(d + e*x)^(5/2))","A",2,2,44,0.04545,1,"{794, 648}"
704,1,48,0,0.0212911,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(5/2),x]","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{7 c d (d+e x)^{7/2}}","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{7 c d (d+e x)^{7/2}}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(7*c*d*(d + e*x)^(7/2))","A",1,1,39,0.02564,1,"{648}"
705,1,236,0,0.4668663,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)),x]","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{g^3 \sqrt{d+e x}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{3 g^2 (d+e x)^{3/2}}-\frac{2 (c d f-a e g)^{5/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{7/2}}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 g (d+e x)^{5/2}}","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{g^3 \sqrt{d+e x}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{3 g^2 (d+e x)^{3/2}}-\frac{2 (c d f-a e g)^{5/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{7/2}}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 g (d+e x)^{5/2}}",1,"(2*(c*d*f - a*e*g)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g^3*Sqrt[d + e*x]) - (2*(c*d*f - a*e*g)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*g^2*(d + e*x)^(3/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*g*(d + e*x)^(5/2)) - (2*(c*d*f - a*e*g)^(5/2)*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/g^(7/2)","A",5,3,46,0.06522,1,"{864, 874, 205}"
706,1,235,0,0.377965,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^2),x]","-\frac{5 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{g^3 \sqrt{d+e x}}+\frac{5 c d (c d f-a e g)^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{7/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{g (d+e x)^{5/2} (f+g x)}+\frac{5 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g^2 (d+e x)^{3/2}}","-\frac{5 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{g^3 \sqrt{d+e x}}+\frac{5 c d (c d f-a e g)^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{7/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{g (d+e x)^{5/2} (f+g x)}+\frac{5 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g^2 (d+e x)^{3/2}}",1,"(-5*c*d*(c*d*f - a*e*g)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g^3*Sqrt[d + e*x]) + (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*g^2*(d + e*x)^(3/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(g*(d + e*x)^(5/2)*(f + g*x)) + (5*c*d*(c*d*f - a*e*g)^(3/2)*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/g^(7/2)","A",5,4,46,0.08696,1,"{862, 864, 874, 205}"
707,1,246,0,0.3418619,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^3} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^3),x]","-\frac{15 c^2 d^2 \sqrt{c d f-a e g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 g^{7/2}}+\frac{15 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g^3 \sqrt{d+e x}}-\frac{5 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 g^2 (d+e x)^{3/2} (f+g x)}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{2 g (d+e x)^{5/2} (f+g x)^2}","-\frac{15 c^2 d^2 \sqrt{c d f-a e g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 g^{7/2}}+\frac{15 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g^3 \sqrt{d+e x}}-\frac{5 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 g^2 (d+e x)^{3/2} (f+g x)}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{2 g (d+e x)^{5/2} (f+g x)^2}",1,"(15*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*g^3*Sqrt[d + e*x]) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(4*g^2*(d + e*x)^(3/2)*(f + g*x)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(2*g*(d + e*x)^(5/2)*(f + g*x)^2) - (15*c^2*d^2*Sqrt[c*d*f - a*e*g]*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(4*g^(7/2))","A",5,4,46,0.08696,1,"{862, 864, 874, 205}"
708,1,253,0,0.3362867,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^4} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^4),x]","-\frac{5 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 g^3 \sqrt{d+e x} (f+g x)}+\frac{5 c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 g^{7/2} \sqrt{c d f-a e g}}-\frac{5 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{12 g^2 (d+e x)^{3/2} (f+g x)^2}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{3 g (d+e x)^{5/2} (f+g x)^3}","-\frac{5 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 g^3 \sqrt{d+e x} (f+g x)}+\frac{5 c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 g^{7/2} \sqrt{c d f-a e g}}-\frac{5 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{12 g^2 (d+e x)^{3/2} (f+g x)^2}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{3 g (d+e x)^{5/2} (f+g x)^3}",1,"(-5*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*g^3*Sqrt[d + e*x]*(f + g*x)) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(12*g^2*(d + e*x)^(3/2)*(f + g*x)^2) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(3*g*(d + e*x)^(5/2)*(f + g*x)^3) + (5*c^3*d^3*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(8*g^(7/2)*Sqrt[c*d*f - a*e*g])","A",5,3,46,0.06522,1,"{862, 874, 205}"
709,1,323,0,0.4733581,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^5} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^5),x]","\frac{5 c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g^3 \sqrt{d+e x} (f+g x) (c d f-a e g)}-\frac{5 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{32 g^3 \sqrt{d+e x} (f+g x)^2}+\frac{5 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{64 g^{7/2} (c d f-a e g)^{3/2}}-\frac{5 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{24 g^2 (d+e x)^{3/2} (f+g x)^3}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4 g (d+e x)^{5/2} (f+g x)^4}","\frac{5 c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g^3 \sqrt{d+e x} (f+g x) (c d f-a e g)}-\frac{5 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{32 g^3 \sqrt{d+e x} (f+g x)^2}+\frac{5 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{64 g^{7/2} (c d f-a e g)^{3/2}}-\frac{5 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{24 g^2 (d+e x)^{3/2} (f+g x)^3}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4 g (d+e x)^{5/2} (f+g x)^4}",1,"(-5*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(32*g^3*Sqrt[d + e*x]*(f + g*x)^2) + (5*c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*g^3*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(24*g^2*(d + e*x)^(3/2)*(f + g*x)^3) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(4*g*(d + e*x)^(5/2)*(f + g*x)^4) + (5*c^4*d^4*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(64*g^(7/2)*(c*d*f - a*e*g)^(3/2))","A",6,4,46,0.08696,1,"{862, 872, 874, 205}"
710,1,393,0,0.5716597,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^6} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^6),x]","\frac{3 c^4 d^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 g^3 \sqrt{d+e x} (f+g x) (c d f-a e g)^2}+\frac{c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g^3 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}-\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{16 g^3 \sqrt{d+e x} (f+g x)^3}+\frac{3 c^5 d^5 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{128 g^{7/2} (c d f-a e g)^{5/2}}-\frac{c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{8 g^2 (d+e x)^{3/2} (f+g x)^4}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 g (d+e x)^{5/2} (f+g x)^5}","\frac{3 c^4 d^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{128 g^3 \sqrt{d+e x} (f+g x) (c d f-a e g)^2}+\frac{c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{64 g^3 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}-\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{16 g^3 \sqrt{d+e x} (f+g x)^3}+\frac{3 c^5 d^5 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{128 g^{7/2} (c d f-a e g)^{5/2}}-\frac{c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{8 g^2 (d+e x)^{3/2} (f+g x)^4}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 g (d+e x)^{5/2} (f+g x)^5}",1,"-(c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(16*g^3*Sqrt[d + e*x]*(f + g*x)^3) + (c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*g^3*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^2) + (3*c^4*d^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(128*g^3*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)) - (c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(8*g^2*(d + e*x)^(3/2)*(f + g*x)^4) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(5*g*(d + e*x)^(5/2)*(f + g*x)^5) + (3*c^5*d^5*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(128*g^(7/2)*(c*d*f - a*e*g)^(5/2))","A",7,4,46,0.08696,1,"{862, 872, 874, 205}"
711,1,463,0,0.7164605,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^7} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^7),x]","\frac{5 c^5 d^5 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 g^3 \sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{5 c^4 d^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{768 g^3 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}+\frac{c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{192 g^3 \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}-\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{32 g^3 \sqrt{d+e x} (f+g x)^4}+\frac{5 c^6 d^6 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{512 g^{7/2} (c d f-a e g)^{7/2}}-\frac{c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{12 g^2 (d+e x)^{3/2} (f+g x)^5}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{6 g (d+e x)^{5/2} (f+g x)^6}","\frac{5 c^5 d^5 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{512 g^3 \sqrt{d+e x} (f+g x) (c d f-a e g)^3}+\frac{5 c^4 d^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{768 g^3 \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}+\frac{c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{192 g^3 \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}-\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{32 g^3 \sqrt{d+e x} (f+g x)^4}+\frac{5 c^6 d^6 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{512 g^{7/2} (c d f-a e g)^{7/2}}-\frac{c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{12 g^2 (d+e x)^{3/2} (f+g x)^5}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{6 g (d+e x)^{5/2} (f+g x)^6}",1,"-(c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(32*g^3*Sqrt[d + e*x]*(f + g*x)^4) + (c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(192*g^3*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^3) + (5*c^4*d^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(768*g^3*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^2) + (5*c^5*d^5*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(512*g^3*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)) - (c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(12*g^2*(d + e*x)^(3/2)*(f + g*x)^5) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(6*g*(d + e*x)^(5/2)*(f + g*x)^6) + (5*c^6*d^6*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(512*g^(7/2)*(c*d*f - a*e*g)^(7/2))","A",8,4,46,0.08696,1,"{862, 872, 874, 205}"
712,1,313,0,0.5624784,"\int \frac{\sqrt{d+e x} (f+g x)^{5/2}}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(Sqrt[d + e*x]*(f + g*x)^(5/2))/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{5 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{8 c^3 d^3 \sqrt{d+e x}}+\frac{5 (f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{12 c^2 d^2 \sqrt{d+e x}}+\frac{5 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^3 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{8 c^{7/2} d^{7/2} \sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c d \sqrt{d+e x}}","\frac{5 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{8 c^3 d^3 \sqrt{d+e x}}+\frac{5 (f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{12 c^2 d^2 \sqrt{d+e x}}+\frac{5 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^3 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{8 c^{7/2} d^{7/2} \sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c d \sqrt{d+e x}}",1,"(5*(c*d*f - a*e*g)^2*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*c^3*d^3*Sqrt[d + e*x]) + (5*(c*d*f - a*e*g)*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*c^2*d^2*Sqrt[d + e*x]) + ((f + g*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c*d*Sqrt[d + e*x]) + (5*(c*d*f - a*e*g)^3*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(8*c^(7/2)*d^(7/2)*Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",7,5,48,0.1042,1,"{870, 891, 63, 217, 206}"
713,1,244,0,0.3661157,"\int \frac{\sqrt{d+e x} (f+g x)^{3/2}}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(Sqrt[d + e*x]*(f + g*x)^(3/2))/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 c^2 d^2 \sqrt{d+e x}}+\frac{3 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 c^{5/2} d^{5/2} \sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 c d \sqrt{d+e x}}","\frac{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 c^2 d^2 \sqrt{d+e x}}+\frac{3 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 c^{5/2} d^{5/2} \sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 c d \sqrt{d+e x}}",1,"(3*(c*d*f - a*e*g)*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*c^2*d^2*Sqrt[d + e*x]) + ((f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(2*c*d*Sqrt[d + e*x]) + (3*(c*d*f - a*e*g)^2*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(4*c^(5/2)*d^(5/2)*Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",6,5,48,0.1042,1,"{870, 891, 63, 217, 206}"
714,1,169,0,0.2224801,"\int \frac{\sqrt{d+e x} \sqrt{f+g x}}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(Sqrt[d + e*x]*Sqrt[f + g*x])/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{3/2} d^{3/2} \sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d \sqrt{d+e x}}","\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{3/2} d^{3/2} \sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d \sqrt{d+e x}}",1,"(Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(c*d*Sqrt[d + e*x]) + ((c*d*f - a*e*g)*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(c^(3/2)*d^(3/2)*Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",5,5,48,0.1042,1,"{870, 891, 63, 217, 206}"
715,1,105,0,0.118487,"\int \frac{\sqrt{d+e x}}{\sqrt{f+g x} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/(Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{2 \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{\sqrt{c} \sqrt{d} \sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{2 \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{\sqrt{c} \sqrt{d} \sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(2*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(Sqrt[c]*Sqrt[d]*Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",4,4,48,0.08333,1,"{891, 63, 217, 206}"
716,1,61,0,0.0652654,"\int \frac{\sqrt{d+e x}}{(f+g x)^{3/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/((f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)}","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)}",1,"(2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/((c*d*f - a*e*g)*Sqrt[d + e*x]*Sqrt[f + g*x])","A",1,1,48,0.02083,1,"{860}"
717,1,129,0,0.1433161,"\int \frac{\sqrt{d+e x}}{(f+g x)^{5/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/((f + g*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{4 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)}","\frac{4 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)}",1,"(2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^(3/2)) + (4*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*Sqrt[f + g*x])","A",2,2,48,0.04167,1,"{872, 860}"
718,1,198,0,0.2187385,"\int \frac{\sqrt{d+e x}}{(f+g x)^{7/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/((f + g*x)^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{16 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{15 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^3}+\frac{8 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{15 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 \sqrt{d+e x} (f+g x)^{5/2} (c d f-a e g)}","\frac{16 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{15 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^3}+\frac{8 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{15 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 \sqrt{d+e x} (f+g x)^{5/2} (c d f-a e g)}",1,"(2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^(5/2)) + (8*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(15*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^(3/2)) + (16*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(15*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*Sqrt[f + g*x])","A",3,2,48,0.04167,1,"{872, 860}"
719,1,267,0,0.3130174,"\int \frac{\sqrt{d+e x}}{(f+g x)^{9/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[Sqrt[d + e*x]/((f + g*x)^(9/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{32 c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{35 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^4}+\frac{16 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{35 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^3}+\frac{12 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{35 \sqrt{d+e x} (f+g x)^{5/2} (c d f-a e g)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 \sqrt{d+e x} (f+g x)^{7/2} (c d f-a e g)}","\frac{32 c^3 d^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{35 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^4}+\frac{16 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{35 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^3}+\frac{12 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{35 \sqrt{d+e x} (f+g x)^{5/2} (c d f-a e g)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 \sqrt{d+e x} (f+g x)^{7/2} (c d f-a e g)}",1,"(2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(7*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^(7/2)) + (12*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^(5/2)) + (16*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)^(3/2)) + (32*c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*(c*d*f - a*e*g)^4*Sqrt[d + e*x]*Sqrt[f + g*x])","A",4,2,48,0.04167,1,"{872, 860}"
720,1,301,0,0.4689042,"\int \frac{(d+e x)^{3/2} (f+g x)^{5/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x)^(5/2))/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{5 g (f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 c^2 d^2 \sqrt{d+e x}}+\frac{15 g \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 c^3 d^3 \sqrt{d+e x}}+\frac{15 \sqrt{g} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 c^{7/2} d^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \sqrt{d+e x} (f+g x)^{5/2}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{5 g (f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 c^2 d^2 \sqrt{d+e x}}+\frac{15 g \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 c^3 d^3 \sqrt{d+e x}}+\frac{15 \sqrt{g} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 c^{7/2} d^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \sqrt{d+e x} (f+g x)^{5/2}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*Sqrt[d + e*x]*(f + g*x)^(5/2))/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (15*g*(c*d*f - a*e*g)*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*c^3*d^3*Sqrt[d + e*x]) + (5*g*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(2*c^2*d^2*Sqrt[d + e*x]) + (15*Sqrt[g]*(c*d*f - a*e*g)^2*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(4*c^(7/2)*d^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",7,6,48,0.1250,1,"{866, 870, 891, 63, 217, 206}"
721,1,227,0,0.3142173,"\int \frac{(d+e x)^{3/2} (f+g x)^{3/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x)^(3/2))/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{3 g \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c^2 d^2 \sqrt{d+e x}}+\frac{3 \sqrt{g} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{5/2} d^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \sqrt{d+e x} (f+g x)^{3/2}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{3 g \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c^2 d^2 \sqrt{d+e x}}+\frac{3 \sqrt{g} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{5/2} d^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \sqrt{d+e x} (f+g x)^{3/2}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*Sqrt[d + e*x]*(f + g*x)^(3/2))/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (3*g*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(c^2*d^2*Sqrt[d + e*x]) + (3*Sqrt[g]*(c*d*f - a*e*g)*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(c^(5/2)*d^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",6,6,48,0.1250,1,"{866, 870, 891, 63, 217, 206}"
722,1,161,0,0.1960423,"\int \frac{(d+e x)^{3/2} \sqrt{f+g x}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(3/2)*Sqrt[f + g*x])/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{2 \sqrt{g} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{3/2} d^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \sqrt{d+e x} \sqrt{f+g x}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{2 \sqrt{g} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{3/2} d^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \sqrt{d+e x} \sqrt{f+g x}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*Sqrt[d + e*x]*Sqrt[f + g*x])/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (2*Sqrt[g]*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(c^(3/2)*d^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",5,5,48,0.1042,1,"{866, 891, 63, 217, 206}"
723,1,61,0,0.0692246,"\int \frac{(d+e x)^{3/2}}{\sqrt{f+g x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/(Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{2 \sqrt{d+e x} \sqrt{f+g x}}{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}","-\frac{2 \sqrt{d+e x} \sqrt{f+g x}}{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}",1,"(-2*Sqrt[d + e*x]*Sqrt[f + g*x])/((c*d*f - a*e*g)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",1,1,48,0.02083,1,"{860}"
724,1,124,0,0.1541246,"\int \frac{(d+e x)^{3/2}}{(f+g x)^{3/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{4 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}","-\frac{4 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}",1,"(-2*Sqrt[d + e*x])/((c*d*f - a*e*g)*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (4*g*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/((c*d*f - a*e*g)^2*Sqrt[d + e*x]*Sqrt[f + g*x])","A",2,2,48,0.04167,1,"{868, 860}"
725,1,192,0,0.2474165,"\int \frac{(d+e x)^{3/2}}{(f+g x)^{5/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{16 c d g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^3}-\frac{8 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}","-\frac{16 c d g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^3}-\frac{8 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}",1,"(-2*Sqrt[d + e*x])/((c*d*f - a*e*g)*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (8*g*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^(3/2)) - (16*c*d*g*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*Sqrt[f + g*x])","A",3,3,48,0.06250,1,"{868, 872, 860}"
726,1,262,0,0.3293663,"\int \frac{(d+e x)^{3/2}}{(f+g x)^{7/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{32 c^2 d^2 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^4}-\frac{16 c d g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^3}-\frac{12 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 \sqrt{d+e x} (f+g x)^{5/2} (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}","-\frac{32 c^2 d^2 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^4}-\frac{16 c d g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^3}-\frac{12 g \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 \sqrt{d+e x} (f+g x)^{5/2} (c d f-a e g)^2}-\frac{2 \sqrt{d+e x}}{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}",1,"(-2*Sqrt[d + e*x])/((c*d*f - a*e*g)*(f + g*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (12*g*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^(5/2)) - (16*c*d*g*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)^(3/2)) - (32*c^2*d^2*g*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*(c*d*f - a*e*g)^4*Sqrt[d + e*x]*Sqrt[f + g*x])","A",4,3,48,0.06250,1,"{868, 872, 860}"
727,1,289,0,0.4317636,"\int \frac{(d+e x)^{5/2} (f+g x)^{5/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(5/2)*(f + g*x)^(5/2))/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{5 g^2 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c^3 d^3 \sqrt{d+e x}}+\frac{5 g^{3/2} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{7/2} d^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{10 g \sqrt{d+e x} (f+g x)^{3/2}}{3 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 (d+e x)^{3/2} (f+g x)^{5/2}}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","\frac{5 g^2 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c^3 d^3 \sqrt{d+e x}}+\frac{5 g^{3/2} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{7/2} d^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{10 g \sqrt{d+e x} (f+g x)^{3/2}}{3 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 (d+e x)^{3/2} (f+g x)^{5/2}}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(3/2)*(f + g*x)^(5/2))/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (10*g*Sqrt[d + e*x]*(f + g*x)^(3/2))/(3*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (5*g^2*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(c^3*d^3*Sqrt[d + e*x]) + (5*g^(3/2)*(c*d*f - a*e*g)*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(c^(7/2)*d^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",7,6,48,0.1250,1,"{866, 870, 891, 63, 217, 206}"
728,1,219,0,0.2887455,"\int \frac{(d+e x)^{5/2} (f+g x)^{3/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(5/2)*(f + g*x)^(3/2))/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{2 g^{3/2} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{5/2} d^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 g \sqrt{d+e x} \sqrt{f+g x}}{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 (d+e x)^{3/2} (f+g x)^{3/2}}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","\frac{2 g^{3/2} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{c^{5/2} d^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 g \sqrt{d+e x} \sqrt{f+g x}}{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 (d+e x)^{3/2} (f+g x)^{3/2}}{3 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(3/2)*(f + g*x)^(3/2))/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (2*g*Sqrt[d + e*x]*Sqrt[f + g*x])/(c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (2*g^(3/2)*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(c^(5/2)*d^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",6,5,48,0.1042,1,"{866, 891, 63, 217, 206}"
729,1,63,0,0.0663038,"\int \frac{(d+e x)^{5/2} \sqrt{f+g x}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(5/2)*Sqrt[f + g*x])/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","-\frac{2 (d+e x)^{3/2} (f+g x)^{3/2}}{3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}","-\frac{2 (d+e x)^{3/2} (f+g x)^{3/2}}{3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}",1,"(-2*(d + e*x)^(3/2)*(f + g*x)^(3/2))/(3*(c*d*f - a*e*g)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))","A",1,1,48,0.02083,1,"{860}"
730,1,128,0,0.1411206,"\int \frac{(d+e x)^{5/2}}{\sqrt{f+g x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/(Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{4 g \sqrt{d+e x} \sqrt{f+g x}}{3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2} \sqrt{f+g x}}{3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}","\frac{4 g \sqrt{d+e x} \sqrt{f+g x}}{3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2} \sqrt{f+g x}}{3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}",1,"(-2*(d + e*x)^(3/2)*Sqrt[f + g*x])/(3*(c*d*f - a*e*g)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (4*g*Sqrt[d + e*x]*Sqrt[f + g*x])/(3*(c*d*f - a*e*g)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",2,2,48,0.04167,1,"{868, 860}"
731,1,194,0,0.2196041,"\int \frac{(d+e x)^{5/2}}{(f+g x)^{3/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/((f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{16 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^3}+\frac{8 g \sqrt{d+e x}}{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 \sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}","\frac{16 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^3}+\frac{8 g \sqrt{d+e x}}{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 \sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}",1,"(-2*(d + e*x)^(3/2))/(3*(c*d*f - a*e*g)*Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (8*g*Sqrt[d + e*x])/(3*(c*d*f - a*e*g)^2*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (16*g^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*Sqrt[f + g*x])","A",3,2,48,0.04167,1,"{868, 860}"
732,1,260,0,0.3128678,"\int \frac{(d+e x)^{5/2}}{(f+g x)^{5/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/((f + g*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{32 c d g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^4}+\frac{16 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^3}+\frac{4 g \sqrt{d+e x}}{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 (f+g x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}","\frac{32 c d g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} \sqrt{f+g x} (c d f-a e g)^4}+\frac{16 g^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 \sqrt{d+e x} (f+g x)^{3/2} (c d f-a e g)^3}+\frac{4 g \sqrt{d+e x}}{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}-\frac{2 (d+e x)^{3/2}}{3 (f+g x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}",1,"(-2*(d + e*x)^(3/2))/(3*(c*d*f - a*e*g)*(f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (4*g*Sqrt[d + e*x])/((c*d*f - a*e*g)^2*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (16*g^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)^(3/2)) + (32*c*d*g^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*(c*d*f - a*e*g)^4*Sqrt[d + e*x]*Sqrt[f + g*x])","A",4,3,48,0.06250,1,"{868, 872, 860}"
733,1,385,0,0.7180575,"\int \frac{(f+g x)^{5/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/Sqrt[d + e*x],x]","-\frac{5 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^4 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{64 c^{7/2} d^{7/2} g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{5 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3}{64 c^3 d^3 g \sqrt{d+e x}}-\frac{5 (f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{96 c^2 d^2 g \sqrt{d+e x}}+\frac{(f+g x)^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g \sqrt{d+e x}}+\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(\frac{a e}{c d}-\frac{f}{g}\right)}{24 \sqrt{d+e x}}","-\frac{5 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^4 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{64 c^{7/2} d^{7/2} g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{5 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3}{64 c^3 d^3 g \sqrt{d+e x}}-\frac{5 (f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{96 c^2 d^2 g \sqrt{d+e x}}+\frac{(f+g x)^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 g \sqrt{d+e x}}+\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(\frac{a e}{c d}-\frac{f}{g}\right)}{24 \sqrt{d+e x}}",1,"(-5*(c*d*f - a*e*g)^3*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*c^3*d^3*g*Sqrt[d + e*x]) - (5*(c*d*f - a*e*g)^2*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(96*c^2*d^2*g*Sqrt[d + e*x]) + (((a*e)/(c*d) - f/g)*(f + g*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(24*Sqrt[d + e*x]) + ((f + g*x)^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*g*Sqrt[d + e*x]) - (5*(c*d*f - a*e*g)^4*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(64*c^(7/2)*d^(7/2)*g^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",8,6,48,0.1250,1,"{864, 870, 891, 63, 217, 206}"
734,1,313,0,0.5178202,"\int \frac{(f+g x)^{3/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/Sqrt[d + e*x],x]","-\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^3 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{8 c^{5/2} d^{5/2} g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{8 c^2 d^2 g \sqrt{d+e x}}+\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 g \sqrt{d+e x}}+\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(\frac{a e}{c d}-\frac{f}{g}\right)}{12 \sqrt{d+e x}}","-\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^3 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{8 c^{5/2} d^{5/2} g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{8 c^2 d^2 g \sqrt{d+e x}}+\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 g \sqrt{d+e x}}+\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(\frac{a e}{c d}-\frac{f}{g}\right)}{12 \sqrt{d+e x}}",1,"-((c*d*f - a*e*g)^2*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*c^2*d^2*g*Sqrt[d + e*x]) + (((a*e)/(c*d) - f/g)*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*Sqrt[d + e*x]) + ((f + g*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*g*Sqrt[d + e*x]) - ((c*d*f - a*e*g)^3*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(8*c^(5/2)*d^(5/2)*g^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",7,6,48,0.1250,1,"{864, 870, 891, 63, 217, 206}"
735,1,241,0,0.3524127,"\int \frac{\sqrt{f+g x} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x}} \, dx","Int[(Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/Sqrt[d + e*x],x]","-\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 c^{3/2} d^{3/2} g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 g \sqrt{d+e x}}+\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(\frac{a e}{c d}-\frac{f}{g}\right)}{4 \sqrt{d+e x}}","-\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 c^{3/2} d^{3/2} g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 g \sqrt{d+e x}}+\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(\frac{a e}{c d}-\frac{f}{g}\right)}{4 \sqrt{d+e x}}",1,"(((a*e)/(c*d) - f/g)*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*Sqrt[d + e*x]) + ((f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(2*g*Sqrt[d + e*x]) - ((c*d*f - a*e*g)^2*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(4*c^(3/2)*d^(3/2)*g^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",6,6,48,0.1250,1,"{864, 870, 891, 63, 217, 206}"
736,1,167,0,0.2094375,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} \sqrt{f+g x}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*Sqrt[f + g*x]),x]","\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x}}-\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{\sqrt{c} \sqrt{d} g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x}}-\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{\sqrt{c} \sqrt{d} g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g*Sqrt[d + e*x]) - ((c*d*f - a*e*g)*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(Sqrt[c]*Sqrt[d]*g^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",5,5,48,0.1042,1,"{864, 891, 63, 217, 206}"
737,1,158,0,0.1881974,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)^{3/2}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)^(3/2)),x]","\frac{2 \sqrt{c} \sqrt{d} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x} \sqrt{f+g x}}","\frac{2 \sqrt{c} \sqrt{d} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x} \sqrt{f+g x}}",1,"(-2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g*Sqrt[d + e*x]*Sqrt[f + g*x]) + (2*Sqrt[c]*Sqrt[d]*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(g^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",5,5,48,0.1042,1,"{862, 891, 63, 217, 206}"
738,1,63,0,0.064531,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)^{5/2}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)^(5/2)),x]","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 (d+e x)^{3/2} (f+g x)^{3/2} (c d f-a e g)}","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 (d+e x)^{3/2} (f+g x)^{3/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*(c*d*f - a*e*g)*(d + e*x)^(3/2)*(f + g*x)^(3/2))","A",1,1,48,0.02083,1,"{860}"
739,1,129,0,0.138755,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)^{7/2}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)^(7/2)),x]","\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{15 (d+e x)^{3/2} (f+g x)^{3/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 (d+e x)^{3/2} (f+g x)^{5/2} (c d f-a e g)}","\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{15 (d+e x)^{3/2} (f+g x)^{3/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 (d+e x)^{3/2} (f+g x)^{5/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(5*(c*d*f - a*e*g)*(d + e*x)^(3/2)*(f + g*x)^(5/2)) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(15*(c*d*f - a*e*g)^2*(d + e*x)^(3/2)*(f + g*x)^(3/2))","A",2,2,48,0.04167,1,"{872, 860}"
740,1,198,0,0.219924,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)^{9/2}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)^(9/2)),x]","\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{105 (d+e x)^{3/2} (f+g x)^{3/2} (c d f-a e g)^3}+\frac{8 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{35 (d+e x)^{3/2} (f+g x)^{5/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{7 (d+e x)^{3/2} (f+g x)^{7/2} (c d f-a e g)}","\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{105 (d+e x)^{3/2} (f+g x)^{3/2} (c d f-a e g)^3}+\frac{8 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{35 (d+e x)^{3/2} (f+g x)^{5/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{7 (d+e x)^{3/2} (f+g x)^{7/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(7*(c*d*f - a*e*g)*(d + e*x)^(3/2)*(f + g*x)^(7/2)) + (8*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(35*(c*d*f - a*e*g)^2*(d + e*x)^(3/2)*(f + g*x)^(5/2)) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*(c*d*f - a*e*g)^3*(d + e*x)^(3/2)*(f + g*x)^(3/2))","A",3,2,48,0.04167,1,"{872, 860}"
741,1,267,0,0.3080327,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x} (f+g x)^{11/2}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(Sqrt[d + e*x]*(f + g*x)^(11/2)),x]","\frac{32 c^3 d^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{315 (d+e x)^{3/2} (f+g x)^{3/2} (c d f-a e g)^4}+\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{105 (d+e x)^{3/2} (f+g x)^{5/2} (c d f-a e g)^3}+\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{21 (d+e x)^{3/2} (f+g x)^{7/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{9 (d+e x)^{3/2} (f+g x)^{9/2} (c d f-a e g)}","\frac{32 c^3 d^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{315 (d+e x)^{3/2} (f+g x)^{3/2} (c d f-a e g)^4}+\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{105 (d+e x)^{3/2} (f+g x)^{5/2} (c d f-a e g)^3}+\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{21 (d+e x)^{3/2} (f+g x)^{7/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{9 (d+e x)^{3/2} (f+g x)^{9/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(9*(c*d*f - a*e*g)*(d + e*x)^(3/2)*(f + g*x)^(9/2)) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(21*(c*d*f - a*e*g)^2*(d + e*x)^(3/2)*(f + g*x)^(7/2)) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*(c*d*f - a*e*g)^3*(d + e*x)^(3/2)*(f + g*x)^(5/2)) + (32*c^3*d^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(315*(c*d*f - a*e*g)^4*(d + e*x)^(3/2)*(f + g*x)^(3/2))","A",4,2,48,0.04167,1,"{872, 860}"
742,1,382,0,0.7113589,"\int \frac{(f+g x)^{3/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3}{64 c^2 d^2 g^2 \sqrt{d+e x}}+\frac{3 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^4 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{64 c^{5/2} d^{5/2} g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{32 c d g^2 \sqrt{d+e x}}-\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{8 g^2 \sqrt{d+e x}}+\frac{(f+g x)^{5/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 g (d+e x)^{3/2}}","\frac{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3}{64 c^2 d^2 g^2 \sqrt{d+e x}}+\frac{3 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^4 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{64 c^{5/2} d^{5/2} g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{32 c d g^2 \sqrt{d+e x}}-\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{8 g^2 \sqrt{d+e x}}+\frac{(f+g x)^{5/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 g (d+e x)^{3/2}}",1,"(3*(c*d*f - a*e*g)^3*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*c^2*d^2*g^2*Sqrt[d + e*x]) + ((c*d*f - a*e*g)^2*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(32*c*d*g^2*Sqrt[d + e*x]) - ((c*d*f - a*e*g)*(f + g*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*g^2*Sqrt[d + e*x]) + ((f + g*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(4*g*(d + e*x)^(3/2)) + (3*(c*d*f - a*e*g)^4*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(64*c^(5/2)*d^(5/2)*g^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",8,6,48,0.1250,1,"{864, 870, 891, 63, 217, 206}"
743,1,310,0,0.5334528,"\int \frac{\sqrt{f+g x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[(Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^3 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{8 c^{3/2} d^{3/2} g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{8 c d g^2 \sqrt{d+e x}}-\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 g^2 \sqrt{d+e x}}+\frac{(f+g x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g (d+e x)^{3/2}}","\frac{\sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^3 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{8 c^{3/2} d^{3/2} g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{8 c d g^2 \sqrt{d+e x}}-\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 g^2 \sqrt{d+e x}}+\frac{(f+g x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g (d+e x)^{3/2}}",1,"((c*d*f - a*e*g)^2*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*c*d*g^2*Sqrt[d + e*x]) - ((c*d*f - a*e*g)*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*g^2*Sqrt[d + e*x]) + ((f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*g*(d + e*x)^(3/2)) + ((c*d*f - a*e*g)^3*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(8*c^(3/2)*d^(3/2)*g^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",7,6,48,0.1250,1,"{864, 870, 891, 63, 217, 206}"
744,1,238,0,0.3450872,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} \sqrt{f+g x}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*Sqrt[f + g*x]),x]","-\frac{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 g^2 \sqrt{d+e x}}+\frac{3 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 \sqrt{c} \sqrt{d} g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 g (d+e x)^{3/2}}","-\frac{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 g^2 \sqrt{d+e x}}+\frac{3 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 \sqrt{c} \sqrt{d} g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 g (d+e x)^{3/2}}",1,"(-3*(c*d*f - a*e*g)*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*g^2*Sqrt[d + e*x]) + (Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(2*g*(d + e*x)^(3/2)) + (3*(c*d*f - a*e*g)^2*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(4*Sqrt[c]*Sqrt[d]*g^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",6,5,48,0.1042,1,"{864, 891, 63, 217, 206}"
745,1,222,0,0.3031244,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^{3/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^(3/2)),x]","\frac{3 c d \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^2 \sqrt{d+e x}}-\frac{3 \sqrt{c} \sqrt{d} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{g (d+e x)^{3/2} \sqrt{f+g x}}","\frac{3 c d \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^2 \sqrt{d+e x}}-\frac{3 \sqrt{c} \sqrt{d} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{g (d+e x)^{3/2} \sqrt{f+g x}}",1,"(3*c*d*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g^2*Sqrt[d + e*x]) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(g*(d + e*x)^(3/2)*Sqrt[f + g*x]) - (3*Sqrt[c]*Sqrt[d]*(c*d*f - a*e*g)*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(g^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",6,6,48,0.1250,1,"{862, 864, 891, 63, 217, 206}"
746,1,214,0,0.2777685,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^{5/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^(5/2)),x]","\frac{2 c^{3/2} d^{3/2} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^2 \sqrt{d+e x} \sqrt{f+g x}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g (d+e x)^{3/2} (f+g x)^{3/2}}","\frac{2 c^{3/2} d^{3/2} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^2 \sqrt{d+e x} \sqrt{f+g x}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g (d+e x)^{3/2} (f+g x)^{3/2}}",1,"(-2*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g^2*Sqrt[d + e*x]*Sqrt[f + g*x]) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*g*(d + e*x)^(3/2)*(f + g*x)^(3/2)) + (2*c^(3/2)*d^(3/2)*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(g^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",6,5,48,0.1042,1,"{862, 891, 63, 217, 206}"
747,1,63,0,0.0702738,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^{7/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^(7/2)),x]","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 (d+e x)^{5/2} (f+g x)^{5/2} (c d f-a e g)}","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 (d+e x)^{5/2} (f+g x)^{5/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*(c*d*f - a*e*g)*(d + e*x)^(5/2)*(f + g*x)^(5/2))","A",1,1,48,0.02083,1,"{860}"
748,1,129,0,0.1478634,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^{9/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^(9/2)),x]","\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{35 (d+e x)^{5/2} (f+g x)^{5/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 (d+e x)^{5/2} (f+g x)^{7/2} (c d f-a e g)}","\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{35 (d+e x)^{5/2} (f+g x)^{5/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 (d+e x)^{5/2} (f+g x)^{7/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(7*(c*d*f - a*e*g)*(d + e*x)^(5/2)*(f + g*x)^(7/2)) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(35*(c*d*f - a*e*g)^2*(d + e*x)^(5/2)*(f + g*x)^(5/2))","A",2,2,48,0.04167,1,"{872, 860}"
749,1,198,0,0.2279191,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^{11/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^(11/2)),x]","\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{315 (d+e x)^{5/2} (f+g x)^{5/2} (c d f-a e g)^3}+\frac{8 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{63 (d+e x)^{5/2} (f+g x)^{7/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{9 (d+e x)^{5/2} (f+g x)^{9/2} (c d f-a e g)}","\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{315 (d+e x)^{5/2} (f+g x)^{5/2} (c d f-a e g)^3}+\frac{8 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{63 (d+e x)^{5/2} (f+g x)^{7/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{9 (d+e x)^{5/2} (f+g x)^{9/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(9*(c*d*f - a*e*g)*(d + e*x)^(5/2)*(f + g*x)^(9/2)) + (8*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(63*(c*d*f - a*e*g)^2*(d + e*x)^(5/2)*(f + g*x)^(7/2)) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(315*(c*d*f - a*e*g)^3*(d + e*x)^(5/2)*(f + g*x)^(5/2))","A",3,2,48,0.04167,1,"{872, 860}"
750,1,267,0,0.3239447,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2} (f+g x)^{13/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/((d + e*x)^(3/2)*(f + g*x)^(13/2)),x]","\frac{32 c^3 d^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{1155 (d+e x)^{5/2} (f+g x)^{5/2} (c d f-a e g)^4}+\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{231 (d+e x)^{5/2} (f+g x)^{7/2} (c d f-a e g)^3}+\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{33 (d+e x)^{5/2} (f+g x)^{9/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{11 (d+e x)^{5/2} (f+g x)^{11/2} (c d f-a e g)}","\frac{32 c^3 d^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{1155 (d+e x)^{5/2} (f+g x)^{5/2} (c d f-a e g)^4}+\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{231 (d+e x)^{5/2} (f+g x)^{7/2} (c d f-a e g)^3}+\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{33 (d+e x)^{5/2} (f+g x)^{9/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{11 (d+e x)^{5/2} (f+g x)^{11/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(11*(c*d*f - a*e*g)*(d + e*x)^(5/2)*(f + g*x)^(11/2)) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(33*(c*d*f - a*e*g)^2*(d + e*x)^(5/2)*(f + g*x)^(9/2)) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(231*(c*d*f - a*e*g)^3*(d + e*x)^(5/2)*(f + g*x)^(7/2)) + (32*c^3*d^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(1155*(c*d*f - a*e*g)^4*(d + e*x)^(5/2)*(f + g*x)^(5/2))","A",4,2,48,0.04167,1,"{872, 860}"
751,1,448,0,0.888996,"\int \frac{(f+g x)^{3/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[((f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x)^(5/2),x]","-\frac{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^4}{128 c^2 d^2 g^3 \sqrt{d+e x}}-\frac{3 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^5 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{128 c^{5/2} d^{5/2} g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3}{64 c d g^3 \sqrt{d+e x}}+\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{16 g^3 \sqrt{d+e x}}-\frac{(f+g x)^{5/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{8 g^2 (d+e x)^{3/2}}+\frac{(f+g x)^{5/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 g (d+e x)^{5/2}}","-\frac{3 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^4}{128 c^2 d^2 g^3 \sqrt{d+e x}}-\frac{3 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^5 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{128 c^{5/2} d^{5/2} g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{(f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3}{64 c d g^3 \sqrt{d+e x}}+\frac{(f+g x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{16 g^3 \sqrt{d+e x}}-\frac{(f+g x)^{5/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{8 g^2 (d+e x)^{3/2}}+\frac{(f+g x)^{5/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 g (d+e x)^{5/2}}",1,"(-3*(c*d*f - a*e*g)^4*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(128*c^2*d^2*g^3*Sqrt[d + e*x]) - ((c*d*f - a*e*g)^3*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*c*d*g^3*Sqrt[d + e*x]) + ((c*d*f - a*e*g)^2*(f + g*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(16*g^3*Sqrt[d + e*x]) - ((c*d*f - a*e*g)*(f + g*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(8*g^2*(d + e*x)^(3/2)) + ((f + g*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*g*(d + e*x)^(5/2)) - (3*(c*d*f - a*e*g)^5*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(128*c^(5/2)*d^(5/2)*g^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",9,6,48,0.1250,1,"{864, 870, 891, 63, 217, 206}"
752,1,376,0,0.6780943,"\int \frac{\sqrt{f+g x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[(Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x)^(5/2),x]","-\frac{5 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^4 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{64 c^{3/2} d^{3/2} g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{5 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3}{64 c d g^3 \sqrt{d+e x}}+\frac{5 (f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{32 g^3 \sqrt{d+e x}}-\frac{5 (f+g x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{24 g^2 (d+e x)^{3/2}}+\frac{(f+g x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4 g (d+e x)^{5/2}}","-\frac{5 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^4 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{64 c^{3/2} d^{3/2} g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{5 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3}{64 c d g^3 \sqrt{d+e x}}+\frac{5 (f+g x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{32 g^3 \sqrt{d+e x}}-\frac{5 (f+g x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{24 g^2 (d+e x)^{3/2}}+\frac{(f+g x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4 g (d+e x)^{5/2}}",1,"(-5*(c*d*f - a*e*g)^3*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*c*d*g^3*Sqrt[d + e*x]) + (5*(c*d*f - a*e*g)^2*(f + g*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(32*g^3*Sqrt[d + e*x]) - (5*(c*d*f - a*e*g)*(f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(24*g^2*(d + e*x)^(3/2)) + ((f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(4*g*(d + e*x)^(5/2)) - (5*(c*d*f - a*e*g)^4*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(64*c^(3/2)*d^(3/2)*g^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",8,6,48,0.1250,1,"{864, 870, 891, 63, 217, 206}"
753,1,304,0,0.4870251,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} \sqrt{f+g x}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*Sqrt[f + g*x]),x]","\frac{5 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{8 g^3 \sqrt{d+e x}}-\frac{5 \sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{12 g^2 (d+e x)^{3/2}}-\frac{5 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^3 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{8 \sqrt{c} \sqrt{d} g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{3 g (d+e x)^{5/2}}","\frac{5 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2}{8 g^3 \sqrt{d+e x}}-\frac{5 \sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}{12 g^2 (d+e x)^{3/2}}-\frac{5 \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^3 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{8 \sqrt{c} \sqrt{d} g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{\sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{3 g (d+e x)^{5/2}}",1,"(5*(c*d*f - a*e*g)^2*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*g^3*Sqrt[d + e*x]) - (5*(c*d*f - a*e*g)*Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(12*g^2*(d + e*x)^(3/2)) + (Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(3*g*(d + e*x)^(5/2)) - (5*(c*d*f - a*e*g)^3*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(8*Sqrt[c]*Sqrt[d]*g^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",7,5,48,0.1042,1,"{864, 891, 63, 217, 206}"
754,1,294,0,0.4283585,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^{3/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^(3/2)),x]","\frac{5 c d \sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 g^2 (d+e x)^{3/2}}-\frac{15 c d \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 g^3 \sqrt{d+e x}}+\frac{15 \sqrt{c} \sqrt{d} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{g (d+e x)^{5/2} \sqrt{f+g x}}","\frac{5 c d \sqrt{f+g x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 g^2 (d+e x)^{3/2}}-\frac{15 c d \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}{4 g^3 \sqrt{d+e x}}+\frac{15 \sqrt{c} \sqrt{d} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{4 g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{g (d+e x)^{5/2} \sqrt{f+g x}}",1,"(-15*c*d*(c*d*f - a*e*g)*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*g^3*Sqrt[d + e*x]) + (5*c*d*Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(2*g^2*(d + e*x)^(3/2)) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(g*(d + e*x)^(5/2)*Sqrt[f + g*x]) + (15*Sqrt[c]*Sqrt[d]*(c*d*f - a*e*g)^2*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(4*g^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",7,6,48,0.1250,1,"{862, 864, 891, 63, 217, 206}"
755,1,284,0,0.4036845,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^{5/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^(5/2)),x]","\frac{5 c^2 d^2 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^3 \sqrt{d+e x}}-\frac{5 c^{3/2} d^{3/2} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{10 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g^2 (d+e x)^{3/2} \sqrt{f+g x}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{3 g (d+e x)^{5/2} (f+g x)^{3/2}}","\frac{5 c^2 d^2 \sqrt{f+g x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^3 \sqrt{d+e x}}-\frac{5 c^{3/2} d^{3/2} \sqrt{d+e x} \sqrt{a e+c d x} (c d f-a e g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{10 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g^2 (d+e x)^{3/2} \sqrt{f+g x}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{3 g (d+e x)^{5/2} (f+g x)^{3/2}}",1,"(5*c^2*d^2*Sqrt[f + g*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g^3*Sqrt[d + e*x]) - (10*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*g^2*(d + e*x)^(3/2)*Sqrt[f + g*x]) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(3*g*(d + e*x)^(5/2)*(f + g*x)^(3/2)) - (5*c^(3/2)*d^(3/2)*(c*d*f - a*e*g)*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(g^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",7,6,48,0.1250,1,"{862, 864, 891, 63, 217, 206}"
756,1,274,0,0.3660097,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^{7/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^(7/2)),x]","-\frac{2 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^3 \sqrt{d+e x} \sqrt{f+g x}}+\frac{2 c^{5/2} d^{5/2} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g^2 (d+e x)^{3/2} (f+g x)^{3/2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 g (d+e x)^{5/2} (f+g x)^{5/2}}","-\frac{2 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g^3 \sqrt{d+e x} \sqrt{f+g x}}+\frac{2 c^{5/2} d^{5/2} \sqrt{d+e x} \sqrt{a e+c d x} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{a e+c d x}}{\sqrt{c} \sqrt{d} \sqrt{f+g x}}\right)}{g^{7/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{2 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{3 g^2 (d+e x)^{3/2} (f+g x)^{3/2}}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 g (d+e x)^{5/2} (f+g x)^{5/2}}",1,"(-2*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g^3*Sqrt[d + e*x]*Sqrt[f + g*x]) - (2*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*g^2*(d + e*x)^(3/2)*(f + g*x)^(3/2)) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*g*(d + e*x)^(5/2)*(f + g*x)^(5/2)) + (2*c^(5/2)*d^(5/2)*Sqrt[a*e + c*d*x]*Sqrt[d + e*x]*ArcTanh[(Sqrt[g]*Sqrt[a*e + c*d*x])/(Sqrt[c]*Sqrt[d]*Sqrt[f + g*x])])/(g^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",7,5,48,0.1042,1,"{862, 891, 63, 217, 206}"
757,1,63,0,0.0689705,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^{9/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^(9/2)),x]","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{7 (d+e x)^{7/2} (f+g x)^{7/2} (c d f-a e g)}","\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{7 (d+e x)^{7/2} (f+g x)^{7/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(7*(c*d*f - a*e*g)*(d + e*x)^(7/2)*(f + g*x)^(7/2))","A",1,1,48,0.02083,1,"{860}"
758,1,129,0,0.1488758,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^{11/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^(11/2)),x]","\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{63 (d+e x)^{7/2} (f+g x)^{7/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{9 (d+e x)^{7/2} (f+g x)^{9/2} (c d f-a e g)}","\frac{4 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{63 (d+e x)^{7/2} (f+g x)^{7/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{9 (d+e x)^{7/2} (f+g x)^{9/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(9*(c*d*f - a*e*g)*(d + e*x)^(7/2)*(f + g*x)^(9/2)) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(63*(c*d*f - a*e*g)^2*(d + e*x)^(7/2)*(f + g*x)^(7/2))","A",2,2,48,0.04167,1,"{872, 860}"
759,1,198,0,0.2296371,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^{13/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^(13/2)),x]","\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{693 (d+e x)^{7/2} (f+g x)^{7/2} (c d f-a e g)^3}+\frac{8 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{99 (d+e x)^{7/2} (f+g x)^{9/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{11 (d+e x)^{7/2} (f+g x)^{11/2} (c d f-a e g)}","\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{693 (d+e x)^{7/2} (f+g x)^{7/2} (c d f-a e g)^3}+\frac{8 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{99 (d+e x)^{7/2} (f+g x)^{9/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{11 (d+e x)^{7/2} (f+g x)^{11/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(11*(c*d*f - a*e*g)*(d + e*x)^(7/2)*(f + g*x)^(11/2)) + (8*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(99*(c*d*f - a*e*g)^2*(d + e*x)^(7/2)*(f + g*x)^(9/2)) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(693*(c*d*f - a*e*g)^3*(d + e*x)^(7/2)*(f + g*x)^(7/2))","A",3,2,48,0.04167,1,"{872, 860}"
760,1,267,0,0.3236457,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2} (f+g x)^{15/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/((d + e*x)^(5/2)*(f + g*x)^(15/2)),x]","\frac{32 c^3 d^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{3003 (d+e x)^{7/2} (f+g x)^{7/2} (c d f-a e g)^4}+\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{429 (d+e x)^{7/2} (f+g x)^{9/2} (c d f-a e g)^3}+\frac{12 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{143 (d+e x)^{7/2} (f+g x)^{11/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{13 (d+e x)^{7/2} (f+g x)^{13/2} (c d f-a e g)}","\frac{32 c^3 d^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{3003 (d+e x)^{7/2} (f+g x)^{7/2} (c d f-a e g)^4}+\frac{16 c^2 d^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{429 (d+e x)^{7/2} (f+g x)^{9/2} (c d f-a e g)^3}+\frac{12 c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{143 (d+e x)^{7/2} (f+g x)^{11/2} (c d f-a e g)^2}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{13 (d+e x)^{7/2} (f+g x)^{13/2} (c d f-a e g)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(13*(c*d*f - a*e*g)*(d + e*x)^(7/2)*(f + g*x)^(13/2)) + (12*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(143*(c*d*f - a*e*g)^2*(d + e*x)^(7/2)*(f + g*x)^(11/2)) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(429*(c*d*f - a*e*g)^3*(d + e*x)^(7/2)*(f + g*x)^(9/2)) + (32*c^3*d^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(3003*(c*d*f - a*e*g)^4*(d + e*x)^(7/2)*(f + g*x)^(7/2))","A",4,2,48,0.04167,1,"{872, 860}"
761,1,122,0,0.1192119,"\int \frac{(d+e x)^{5/2} (f+g x)^n}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(5/2)*(f + g*x)^n)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","-\frac{2 \sqrt{d+e x} (f+g x)^n \left(\frac{c d (f+g x)}{c d f-a e g}\right)^{-n} \, _2F_1\left(-\frac{3}{2},-n;-\frac{1}{2};-\frac{g (a e+c d x)}{c d f-a e g}\right)}{3 c d (a e+c d x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","-\frac{(d+e x)^{5/2} (f+g x)^{n+1} (a e+c d x) \, _2F_1\left(1,n-\frac{1}{2};n+2;\frac{c d (f+g x)}{c d f-a e g}\right)}{(n+1) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} (c d f-a e g)}",1,"(-2*Sqrt[d + e*x]*(f + g*x)^n*Hypergeometric2F1[-3/2, -n, -1/2, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/(3*c*d*(a*e + c*d*x)*((c*d*(f + g*x))/(c*d*f - a*e*g))^n*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",3,3,46,0.06522,1,"{891, 70, 69}"
762,1,110,0,0.1101145,"\int \frac{(d+e x)^{3/2} (f+g x)^n}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x)^n)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","-\frac{2 \sqrt{d+e x} (f+g x)^n \left(\frac{c d (f+g x)}{c d f-a e g}\right)^{-n} \, _2F_1\left(-\frac{1}{2},-n;\frac{1}{2};-\frac{g (a e+c d x)}{c d f-a e g}\right)}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","-\frac{(d+e x)^{3/2} (f+g x)^{n+1} (a e+c d x) \, _2F_1\left(1,n+\frac{1}{2};n+2;\frac{c d (f+g x)}{c d f-a e g}\right)}{(n+1) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} (c d f-a e g)}",1,"(-2*Sqrt[d + e*x]*(f + g*x)^n*Hypergeometric2F1[-1/2, -n, 1/2, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/(c*d*((c*d*(f + g*x))/(c*d*f - a*e*g))^n*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",3,3,46,0.06522,1,"{891, 70, 69}"
763,1,118,0,0.1063652,"\int \frac{\sqrt{d+e x} (f+g x)^n}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(Sqrt[d + e*x]*(f + g*x)^n)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{2 \sqrt{d+e x} (f+g x)^n (a e+c d x) \left(\frac{c d (f+g x)}{c d f-a e g}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};-\frac{g (a e+c d x)}{c d f-a e g}\right)}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","-\frac{\sqrt{d+e x} (f+g x)^{n+1} (a e+c d x) \, _2F_1\left(1,n+\frac{3}{2};n+2;\frac{c d (f+g x)}{c d f-a e g}\right)}{(n+1) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}",1,"(2*(a*e + c*d*x)*Sqrt[d + e*x]*(f + g*x)^n*Hypergeometric2F1[1/2, -n, 3/2, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/(c*d*((c*d*(f + g*x))/(c*d*f - a*e*g))^n*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",3,3,46,0.06522,1,"{891, 70, 69}"
764,1,120,0,0.1020018,"\int \frac{(f+g x)^n \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)^n*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/Sqrt[d + e*x],x]","\frac{2 (f+g x)^n (a e+c d x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(\frac{c d (f+g x)}{c d f-a e g}\right)^{-n} \, _2F_1\left(\frac{3}{2},-n;\frac{5}{2};-\frac{g (a e+c d x)}{c d f-a e g}\right)}{3 c d \sqrt{d+e x}}","-\frac{(f+g x)^{n+1} (a e+c d x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \, _2F_1\left(1,n+\frac{5}{2};n+2;\frac{c d (f+g x)}{c d f-a e g}\right)}{(n+1) \sqrt{d+e x} (c d f-a e g)}",1,"(2*(a*e + c*d*x)*(f + g*x)^n*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]*Hypergeometric2F1[3/2, -n, 5/2, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/(3*c*d*Sqrt[d + e*x]*((c*d*(f + g*x))/(c*d*f - a*e*g))^n)","A",3,3,46,0.06522,1,"{891, 70, 69}"
765,1,122,0,0.109082,"\int \frac{(f+g x)^n \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((f + g*x)^n*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{2 (f+g x)^n (a e+c d x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(\frac{c d (f+g x)}{c d f-a e g}\right)^{-n} \, _2F_1\left(\frac{5}{2},-n;\frac{7}{2};-\frac{g (a e+c d x)}{c d f-a e g}\right)}{5 c d \sqrt{d+e x}}","-\frac{(f+g x)^{n+1} (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2} \, _2F_1\left(1,n+\frac{7}{2};n+2;\frac{c d (f+g x)}{c d f-a e g}\right)}{(n+1) (d+e x)^{3/2} (c d f-a e g)}",1,"(2*(a*e + c*d*x)^2*(f + g*x)^n*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]*Hypergeometric2F1[5/2, -n, 7/2, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/(5*c*d*Sqrt[d + e*x]*((c*d*(f + g*x))/(c*d*f - a*e*g))^n)","A",3,3,46,0.06522,1,"{891, 70, 69}"
766,1,122,0,0.1117147,"\int \frac{(f+g x)^n \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[((f + g*x)^n*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(d + e*x)^(5/2),x]","\frac{2 (f+g x)^n (a e+c d x)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(\frac{c d (f+g x)}{c d f-a e g}\right)^{-n} \, _2F_1\left(\frac{7}{2},-n;\frac{9}{2};-\frac{g (a e+c d x)}{c d f-a e g}\right)}{7 c d \sqrt{d+e x}}","-\frac{(f+g x)^{n+1} (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2} \, _2F_1\left(1,n+\frac{9}{2};n+2;\frac{c d (f+g x)}{c d f-a e g}\right)}{(n+1) (d+e x)^{5/2} (c d f-a e g)}",1,"(2*(a*e + c*d*x)^3*(f + g*x)^n*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]*Hypergeometric2F1[7/2, -n, 9/2, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/(7*c*d*Sqrt[d + e*x]*((c*d*(f + g*x))/(c*d*f - a*e*g))^n)","A",3,3,46,0.06522,1,"{891, 70, 69}"
767,1,107,0,0.0854224,"\int (d+e x)^m (f+g x)^n \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m} \, dx","Int[((d + e*x)^m*(f + g*x)^n)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m,x]","\frac{(d+e x)^m (f+g x)^{n+1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(m,n+1;n+2;\frac{c d (f+g x)}{c d f-a e g}\right)}{g (n+1)}","-\frac{(d+e x)^m (f+g x)^{n+1} (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \, _2F_1\left(1,-m+n+2;n+2;\frac{c d (f+g x)}{c d f-a e g}\right)}{(n+1) (c d f-a e g)}",1,"((-((g*(a*e + c*d*x))/(c*d*f - a*e*g)))^m*(d + e*x)^m*(f + g*x)^(1 + n)*Hypergeometric2F1[m, 1 + n, 2 + n, (c*d*(f + g*x))/(c*d*f - a*e*g)])/(g*(1 + n)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m)","A",3,3,44,0.06818,1,"{891, 70, 69}"
768,1,343,0,0.4491585,"\int (d+e x)^m (f+g x)^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m} \, dx","Int[((d + e*x)^m*(f + g*x)^3)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m,x]","-\frac{6 (d+e x)^{m-1} (c d f-a e g)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m} \left(a e^2 g+c d (d g (1-m)-e f (2-m))\right)}{c^4 d^4 e (1-m) (2-m) (3-m) (4-m)}+\frac{6 g (d+e x)^m (c d f-a e g)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c^3 d^3 e (2-m) (3-m) (4-m)}+\frac{3 (f+g x)^2 (d+e x)^{m-1} (c d f-a e g) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c^2 d^2 (3-m) (4-m)}+\frac{(f+g x)^3 (d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c d (4-m)}","-\frac{6 (d+e x)^{m-1} (c d f-a e g)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m} \left(a e^2 g+c d (d g (1-m)-e f (2-m))\right)}{c^4 d^4 e (1-m) (2-m) (3-m) (4-m)}+\frac{6 g (d+e x)^m (c d f-a e g)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c^3 d^3 e (2-m) (3-m) (4-m)}+\frac{3 (f+g x)^2 (d+e x)^{m-1} (c d f-a e g) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c^2 d^2 (3-m) (4-m)}+\frac{(f+g x)^3 (d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c d (4-m)}",1,"(-6*(c*d*f - a*e*g)^2*(a*e^2*g + c*d*(d*g*(1 - m) - e*f*(2 - m)))*(d + e*x)^(-1 + m)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c^4*d^4*e*(1 - m)*(2 - m)*(3 - m)*(4 - m)) + (6*g*(c*d*f - a*e*g)^2*(d + e*x)^m*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c^3*d^3*e*(2 - m)*(3 - m)*(4 - m)) + (3*(c*d*f - a*e*g)*(d + e*x)^(-1 + m)*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c^2*d^2*(3 - m)*(4 - m)) + ((d + e*x)^(-1 + m)*(f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c*d*(4 - m))","A",4,3,44,0.06818,1,"{870, 794, 648}"
769,1,246,0,0.2045937,"\int (d+e x)^m (f+g x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m} \, dx","Int[((d + e*x)^m*(f + g*x)^2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m,x]","-\frac{2 (d+e x)^{m-1} (c d f-a e g) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m} \left(a e^2 g+c d (d g (1-m)-e f (2-m))\right)}{c^3 d^3 e (1-m) (2-m) (3-m)}+\frac{2 g (d+e x)^m (c d f-a e g) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c^2 d^2 e (2-m) (3-m)}+\frac{(f+g x)^2 (d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c d (3-m)}","-\frac{2 (d+e x)^{m-1} (c d f-a e g) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m} \left(a e^2 g+c d (d g (1-m)-e f (2-m))\right)}{c^3 d^3 e (1-m) (2-m) (3-m)}+\frac{2 g (d+e x)^m (c d f-a e g) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c^2 d^2 e (2-m) (3-m)}+\frac{(f+g x)^2 (d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c d (3-m)}",1,"(-2*(c*d*f - a*e*g)*(a*e^2*g + c*d*(d*g*(1 - m) - e*f*(2 - m)))*(d + e*x)^(-1 + m)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c^3*d^3*e*(1 - m)*(2 - m)*(3 - m)) + (2*g*(c*d*f - a*e*g)*(d + e*x)^m*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c^2*d^2*e*(2 - m)*(3 - m)) + ((d + e*x)^(-1 + m)*(f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c*d*(3 - m))","A",3,3,44,0.06818,1,"{870, 794, 648}"
770,1,150,0,0.0816185,"\int (d+e x)^m (f+g x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m} \, dx","Int[((d + e*x)^m*(f + g*x))/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m,x]","\frac{g (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c d e (2-m)}-\frac{(d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m} \left(a e^2 g+c d (d g (1-m)-e f (2-m))\right)}{c^2 d^2 e (1-m) (2-m)}","\frac{g (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c d e (2-m)}-\frac{(d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m} \left(a e^2 g+c d (d g (1-m)-e f (2-m))\right)}{c^2 d^2 e (1-m) (2-m)}",1,"-(((a*e^2*g + c*d*(d*g*(1 - m) - e*f*(2 - m)))*(d + e*x)^(-1 + m)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c^2*d^2*e*(1 - m)*(2 - m))) + (g*(d + e*x)^m*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c*d*e*(2 - m))","A",2,2,42,0.04762,1,"{794, 648}"
771,1,54,0,0.0149937,"\int (d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m} \, dx","Int[(d + e*x)^m/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m,x]","\frac{(d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c d (1-m)}","\frac{(d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m}}{c d (1-m)}",1,"((d + e*x)^(-1 + m)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c*d*(1 - m))","A",1,1,37,0.02703,1,"{648}"
772,1,99,0,0.0612081,"\int \frac{(d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m}}{f+g x} \, dx","Int[(d + e*x)^m/((f + g*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m),x]","\frac{(d+e x)^m (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \, _2F_1\left(1,1-m;2-m;-\frac{g (a e+c d x)}{c d f-a e g}\right)}{(1-m) (c d f-a e g)}","\frac{(d+e x)^m (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \, _2F_1\left(1,1-m;2-m;-\frac{g (a e+c d x)}{c d f-a e g}\right)}{(1-m) (c d f-a e g)}",1,"((a*e + c*d*x)*(d + e*x)^m*Hypergeometric2F1[1, 1 - m, 2 - m, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/((c*d*f - a*e*g)*(1 - m)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m)","A",2,2,44,0.04545,1,"{891, 68}"
773,1,101,0,0.0601161,"\int \frac{(d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m}}{(f+g x)^2} \, dx","Int[(d + e*x)^m/((f + g*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m),x]","\frac{c d (d+e x)^m (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \, _2F_1\left(2,1-m;2-m;-\frac{g (a e+c d x)}{c d f-a e g}\right)}{(1-m) (c d f-a e g)^2}","\frac{c d (d+e x)^m (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \, _2F_1\left(2,1-m;2-m;-\frac{g (a e+c d x)}{c d f-a e g}\right)}{(1-m) (c d f-a e g)^2}",1,"(c*d*(a*e + c*d*x)*(d + e*x)^m*Hypergeometric2F1[2, 1 - m, 2 - m, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/((c*d*f - a*e*g)^2*(1 - m)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m)","A",2,2,44,0.04545,1,"{891, 68}"
774,1,105,0,0.0747857,"\int \frac{(d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m}}{(f+g x)^3} \, dx","Int[(d + e*x)^m/((f + g*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m),x]","\frac{c^2 d^2 (d+e x)^m (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \, _2F_1\left(3,1-m;2-m;-\frac{g (a e+c d x)}{c d f-a e g}\right)}{(1-m) (c d f-a e g)^3}","\frac{c^2 d^2 (d+e x)^m (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \, _2F_1\left(3,1-m;2-m;-\frac{g (a e+c d x)}{c d f-a e g}\right)}{(1-m) (c d f-a e g)^3}",1,"(c^2*d^2*(a*e + c*d*x)*(d + e*x)^m*Hypergeometric2F1[3, 1 - m, 2 - m, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/((c*d*f - a*e*g)^3*(1 - m)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m)","A",2,2,44,0.04545,1,"{891, 68}"
775,1,105,0,0.080604,"\int (d+e x)^m (f+g x)^{3/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m} \, dx","Int[((d + e*x)^m*(f + g*x)^(3/2))/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m,x]","\frac{2 (f+g x)^{5/2} (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(\frac{5}{2},m;\frac{7}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{5 g}","\frac{2 (f+g x)^{5/2} (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(\frac{5}{2},m;\frac{7}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{5 g}",1,"(2*(-((g*(a*e + c*d*x))/(c*d*f - a*e*g)))^m*(d + e*x)^m*(f + g*x)^(5/2)*Hypergeometric2F1[5/2, m, 7/2, (c*d*(f + g*x))/(c*d*f - a*e*g)])/(5*g*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m)","A",3,3,46,0.06522,1,"{891, 70, 69}"
776,1,105,0,0.0761664,"\int (d+e x)^m \sqrt{f+g x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m} \, dx","Int[((d + e*x)^m*Sqrt[f + g*x])/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m,x]","\frac{2 (f+g x)^{3/2} (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(\frac{3}{2},m;\frac{5}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{3 g}","\frac{2 (f+g x)^{3/2} (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(\frac{3}{2},m;\frac{5}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{3 g}",1,"(2*(-((g*(a*e + c*d*x))/(c*d*f - a*e*g)))^m*(d + e*x)^m*(f + g*x)^(3/2)*Hypergeometric2F1[3/2, m, 5/2, (c*d*(f + g*x))/(c*d*f - a*e*g)])/(3*g*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m)","A",3,3,46,0.06522,1,"{891, 70, 69}"
777,1,103,0,0.0751331,"\int \frac{(d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m}}{\sqrt{f+g x}} \, dx","Int[(d + e*x)^m/(Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m),x]","\frac{2 \sqrt{f+g x} (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(\frac{1}{2},m;\frac{3}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{g}","\frac{2 \sqrt{f+g x} (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(\frac{1}{2},m;\frac{3}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{g}",1,"(2*(-((g*(a*e + c*d*x))/(c*d*f - a*e*g)))^m*(d + e*x)^m*Sqrt[f + g*x]*Hypergeometric2F1[1/2, m, 3/2, (c*d*(f + g*x))/(c*d*f - a*e*g)])/(g*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m)","A",3,3,46,0.06522,1,"{891, 70, 69}"
778,1,103,0,0.0754757,"\int \frac{(d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m}}{(f+g x)^{3/2}} \, dx","Int[(d + e*x)^m/((f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m),x]","-\frac{2 (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(-\frac{1}{2},m;\frac{1}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{g \sqrt{f+g x}}","-\frac{2 (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(-\frac{1}{2},m;\frac{1}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{g \sqrt{f+g x}}",1,"(-2*(-((g*(a*e + c*d*x))/(c*d*f - a*e*g)))^m*(d + e*x)^m*Hypergeometric2F1[-1/2, m, 1/2, (c*d*(f + g*x))/(c*d*f - a*e*g)])/(g*Sqrt[f + g*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m)","A",3,3,46,0.06522,1,"{891, 70, 69}"
779,1,105,0,0.0755164,"\int \frac{(d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m}}{(f+g x)^{5/2}} \, dx","Int[(d + e*x)^m/((f + g*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m),x]","-\frac{2 (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(-\frac{3}{2},m;-\frac{1}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{3 g (f+g x)^{3/2}}","-\frac{2 (d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \left(-\frac{g (a e+c d x)}{c d f-a e g}\right)^m \, _2F_1\left(-\frac{3}{2},m;-\frac{1}{2};\frac{c d (f+g x)}{c d f-a e g}\right)}{3 g (f+g x)^{3/2}}",1,"(-2*(-((g*(a*e + c*d*x))/(c*d*f - a*e*g)))^m*(d + e*x)^m*Hypergeometric2F1[-3/2, m, -1/2, (c*d*(f + g*x))/(c*d*f - a*e*g)])/(3*g*(f + g*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m)","A",3,3,46,0.06522,1,"{891, 70, 69}"
780,1,65,0,0.0442912,"\int (a e+c d x)^n (d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m} \, dx","Int[((a*e + c*d*x)^n*(d + e*x)^m)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m,x]","\frac{(d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m} (a e+c d x)^n}{c d (-m+n+1)}","\frac{(d+e x)^{m-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{1-m} (a e+c d x)^n}{c d (-m+n+1)}",1,"((a*e + c*d*x)^n*(d + e*x)^(-1 + m)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 - m))/(c*d*(1 - m + n))","A",1,1,47,0.02128,1,"{858}"
781,1,78,0,0.1500913,"\int (d+e x)^m \left(c d^2 e g-e \left(c d^2+a e^2\right) g-c d e^2 g x\right)^{-1+m} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{-m} \, dx","Int[((d + e*x)^m*(c*d^2*e*g - e*(c*d^2 + a*e^2)*g - c*d*e^2*g*x)^(-1 + m))/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m,x]","-\frac{(d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \log (a e+c d x) \left(-a e^3 g-c d e^2 g x\right)^m}{c d e^2 g}","-\frac{(d+e x)^m \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{-m} \log (a e+c d x) \left(-a e^3 g-c d e^2 g x\right)^m}{c d e^2 g}",1,"-(((d + e*x)^m*(-(a*e^3*g) - c*d*e^2*g*x)^m*Log[a*e + c*d*x])/(c*d*e^2*g*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^m))","A",3,3,73,0.04110,1,"{891, 23, 31}"
782,1,222,0,0.2784044,"\int \frac{(d+e x)^{3/2} (f+g x)^n}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x)^n)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{2 e (f+g x)^{n+1} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d g (2 n+3) \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} (f+g x)^n (a e+c d x) \left(2 a e^2 g (n+1)+c d (e f-d g (2 n+3))\right) \left(\frac{c d (f+g x)}{c d f-a e g}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};-\frac{g (a e+c d x)}{c d f-a e g}\right)}{c^2 d^2 g (2 n+3) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{\sqrt{d+e x} (f+g x)^{n+1} (a e+c d x) \left(2 a e^2 g (n+1)+c d (e f-d g (2 n+3))\right) \, _2F_1\left(1,n+\frac{3}{2};n+2;\frac{c d (f+g x)}{c d f-a e g}\right)}{c d g (n+1) (2 n+3) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)}+\frac{2 e (f+g x)^{n+1} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d g (2 n+3) \sqrt{d+e x}}",1,"(2*e*(f + g*x)^(1 + n)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(c*d*g*(3 + 2*n)*Sqrt[d + e*x]) - (2*(2*a*e^2*g*(1 + n) + c*d*(e*f - d*g*(3 + 2*n)))*(a*e + c*d*x)*Sqrt[d + e*x]*(f + g*x)^n*Hypergeometric2F1[1/2, -n, 3/2, -((g*(a*e + c*d*x))/(c*d*f - a*e*g))])/(c^2*d^2*g*(3 + 2*n)*((c*d*(f + g*x))/(c*d*f - a*e*g))^n*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",4,4,46,0.08696,1,"{880, 891, 70, 69}"
783,1,501,0,0.8935907,"\int \frac{(d+e x)^{3/2} (f+g x)^4}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x)^4)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","-\frac{2 (f+g x)^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(10 a e^2 g+c d (e f-11 d g)\right)}{99 c^2 d^2 g \sqrt{d+e x}}-\frac{16 (f+g x)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(10 a e^2 g+c d (e f-11 d g)\right)}{693 c^3 d^3 g \sqrt{d+e x}}-\frac{32 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2 \left(10 a e^2 g+c d (e f-11 d g)\right)}{1155 c^4 d^4 g \sqrt{d+e x}}-\frac{128 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3 \left(10 a e^2 g+c d (e f-11 d g)\right)}{3465 c^5 d^5 e}+\frac{128 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3 \left(10 a e^2 g+c d (e f-11 d g)\right) \left(2 a e^2 g-c d (3 e f-d g)\right)}{3465 c^6 d^6 e g \sqrt{d+e x}}+\frac{2 e (f+g x)^5 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{11 c d g \sqrt{d+e x}}","-\frac{2 (f+g x)^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(10 a e^2 g+c d (e f-11 d g)\right)}{99 c^2 d^2 g \sqrt{d+e x}}-\frac{16 (f+g x)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(10 a e^2 g+c d (e f-11 d g)\right)}{693 c^3 d^3 g \sqrt{d+e x}}-\frac{32 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2 \left(10 a e^2 g+c d (e f-11 d g)\right)}{1155 c^4 d^4 g \sqrt{d+e x}}-\frac{128 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3 \left(10 a e^2 g+c d (e f-11 d g)\right)}{3465 c^5 d^5 e}+\frac{128 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^3 \left(10 a e^2 g+c d (e f-11 d g)\right) \left(2 a e^2 g-c d (3 e f-d g)\right)}{3465 c^6 d^6 e g \sqrt{d+e x}}+\frac{2 e (f+g x)^5 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{11 c d g \sqrt{d+e x}}",1,"(128*(c*d*f - a*e*g)^3*(10*a*e^2*g + c*d*(e*f - 11*d*g))*(2*a*e^2*g - c*d*(3*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3465*c^6*d^6*e*g*Sqrt[d + e*x]) - (128*(c*d*f - a*e*g)^3*(10*a*e^2*g + c*d*(e*f - 11*d*g))*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3465*c^5*d^5*e) - (32*(c*d*f - a*e*g)^2*(10*a*e^2*g + c*d*(e*f - 11*d*g))*(f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(1155*c^4*d^4*g*Sqrt[d + e*x]) - (16*(c*d*f - a*e*g)*(10*a*e^2*g + c*d*(e*f - 11*d*g))*(f + g*x)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(693*c^3*d^3*g*Sqrt[d + e*x]) - (2*(10*a*e^2*g + c*d*(e*f - 11*d*g))*(f + g*x)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(99*c^2*d^2*g*Sqrt[d + e*x]) + (2*e*(f + g*x)^5*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(11*c*d*g*Sqrt[d + e*x])","A",6,4,46,0.08696,1,"{880, 870, 794, 648}"
784,1,412,0,0.6270979,"\int \frac{(d+e x)^{3/2} (f+g x)^3}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x)^3)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","-\frac{2 (f+g x)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(8 a e^2 g+c d (e f-9 d g)\right)}{63 c^2 d^2 g \sqrt{d+e x}}-\frac{4 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(8 a e^2 g+c d (e f-9 d g)\right)}{105 c^3 d^3 g \sqrt{d+e x}}-\frac{16 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2 \left(8 a e^2 g+c d (e f-9 d g)\right)}{315 c^4 d^4 e}+\frac{16 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2 \left(8 a e^2 g+c d (e f-9 d g)\right) \left(2 a e^2 g-c d (3 e f-d g)\right)}{315 c^5 d^5 e g \sqrt{d+e x}}+\frac{2 e (f+g x)^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{9 c d g \sqrt{d+e x}}","-\frac{2 (f+g x)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(8 a e^2 g+c d (e f-9 d g)\right)}{63 c^2 d^2 g \sqrt{d+e x}}-\frac{4 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(8 a e^2 g+c d (e f-9 d g)\right)}{105 c^3 d^3 g \sqrt{d+e x}}-\frac{16 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2 \left(8 a e^2 g+c d (e f-9 d g)\right)}{315 c^4 d^4 e}+\frac{16 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g)^2 \left(8 a e^2 g+c d (e f-9 d g)\right) \left(2 a e^2 g-c d (3 e f-d g)\right)}{315 c^5 d^5 e g \sqrt{d+e x}}+\frac{2 e (f+g x)^4 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{9 c d g \sqrt{d+e x}}",1,"(16*(c*d*f - a*e*g)^2*(8*a*e^2*g + c*d*(e*f - 9*d*g))*(2*a*e^2*g - c*d*(3*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(315*c^5*d^5*e*g*Sqrt[d + e*x]) - (16*(c*d*f - a*e*g)^2*(8*a*e^2*g + c*d*(e*f - 9*d*g))*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(315*c^4*d^4*e) - (4*(c*d*f - a*e*g)*(8*a*e^2*g + c*d*(e*f - 9*d*g))*(f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(105*c^3*d^3*g*Sqrt[d + e*x]) - (2*(8*a*e^2*g + c*d*(e*f - 9*d*g))*(f + g*x)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(63*c^2*d^2*g*Sqrt[d + e*x]) + (2*e*(f + g*x)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(9*c*d*g*Sqrt[d + e*x])","A",5,4,46,0.08696,1,"{880, 870, 794, 648}"
785,1,321,0,0.4198449,"\int \frac{(d+e x)^{3/2} (f+g x)^2}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x)^2)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","-\frac{2 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(6 a e^2 g+c d (e f-7 d g)\right)}{35 c^2 d^2 g \sqrt{d+e x}}-\frac{8 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(6 a e^2 g+c d (e f-7 d g)\right)}{105 c^3 d^3 e}+\frac{8 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(6 a e^2 g+c d (e f-7 d g)\right) \left(2 a e^2 g-c d (3 e f-d g)\right)}{105 c^4 d^4 e g \sqrt{d+e x}}+\frac{2 e (f+g x)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 c d g \sqrt{d+e x}}","-\frac{2 (f+g x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(6 a e^2 g+c d (e f-7 d g)\right)}{35 c^2 d^2 g \sqrt{d+e x}}-\frac{8 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(6 a e^2 g+c d (e f-7 d g)\right)}{105 c^3 d^3 e}+\frac{8 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} (c d f-a e g) \left(6 a e^2 g+c d (e f-7 d g)\right) \left(2 a e^2 g-c d (3 e f-d g)\right)}{105 c^4 d^4 e g \sqrt{d+e x}}+\frac{2 e (f+g x)^3 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 c d g \sqrt{d+e x}}",1,"(8*(c*d*f - a*e*g)*(6*a*e^2*g + c*d*(e*f - 7*d*g))*(2*a*e^2*g - c*d*(3*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(105*c^4*d^4*e*g*Sqrt[d + e*x]) - (8*(c*d*f - a*e*g)*(6*a*e^2*g + c*d*(e*f - 7*d*g))*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(105*c^3*d^3*e) - (2*(6*a*e^2*g + c*d*(e*f - 7*d*g))*(f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*c^2*d^2*g*Sqrt[d + e*x]) + (2*e*(f + g*x)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(7*c*d*g*Sqrt[d + e*x])","A",4,4,46,0.08696,1,"{880, 870, 794, 648}"
786,1,209,0,0.1975911,"\int \frac{(d+e x)^{3/2} (f+g x)}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x))/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","-\frac{2 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(4 a e^2 g-c d (5 e f-d g)\right)}{15 c^2 d^2 e}-\frac{4 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(4 a e^2 g-c d (5 e f-d g)\right)}{15 c^3 d^3 e \sqrt{d+e x}}+\frac{2 g (d+e x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 c d e}","-\frac{2 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(4 a e^2 g-c d (5 e f-d g)\right)}{15 c^2 d^2 e}-\frac{4 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(4 a e^2 g-c d (5 e f-d g)\right)}{15 c^3 d^3 e \sqrt{d+e x}}+\frac{2 g (d+e x)^{3/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 c d e}",1,"(-4*(c*d^2 - a*e^2)*(4*a*e^2*g - c*d*(5*e*f - d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(15*c^3*d^3*e*Sqrt[d + e*x]) - (2*(4*a*e^2*g - c*d*(5*e*f - d*g))*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(15*c^2*d^2*e) + (2*g*(d + e*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*c*d*e)","A",3,3,44,0.06818,1,"{794, 656, 648}"
787,1,109,0,0.0594681,"\int \frac{(d+e x)^{3/2}}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)^(3/2)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{4 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^2 d^2 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c d}","\frac{4 \left(c d^2-a e^2\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^2 d^2 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c d}",1,"(4*(c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c^2*d^2*Sqrt[d + e*x]) + (2*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c*d)","A",2,2,39,0.05128,1,"{656, 648}"
788,1,139,0,0.1919499,"\int \frac{(d+e x)^{3/2}}{(f+g x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","\frac{2 e \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d g \sqrt{d+e x}}-\frac{2 (e f-d g) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{3/2} \sqrt{c d f-a e g}}","\frac{2 e \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d g \sqrt{d+e x}}-\frac{2 (e f-d g) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{3/2} \sqrt{c d f-a e g}}",1,"(2*e*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(c*d*g*Sqrt[d + e*x]) - (2*(e*f - d*g)*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(g^(3/2)*Sqrt[c*d*f - a*e*g])","A",3,3,46,0.06522,1,"{880, 874, 205}"
789,1,170,0,0.2336274,"\int \frac{(d+e x)^{3/2}}{(f+g x)^2 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","-\frac{\left(2 a e^2 g-c d (d g+e f)\right) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{3/2} (c d f-a e g)^{3/2}}-\frac{(e f-d g) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x} (f+g x) (c d f-a e g)}","-\frac{\left(2 a e^2 g-c d (d g+e f)\right) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{g^{3/2} (c d f-a e g)^{3/2}}-\frac{(e f-d g) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{g \sqrt{d+e x} (f+g x) (c d f-a e g)}",1,"-(((e*f - d*g)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(g*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x))) - ((2*a*e^2*g - c*d*(e*f + d*g))*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(g^(3/2)*(c*d*f - a*e*g)^(3/2))","A",3,3,46,0.06522,1,"{878, 874, 205}"
790,1,261,0,0.355034,"\int \frac{(d+e x)^{3/2}}{(f+g x)^3 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","-\frac{c d \left(4 a e^2 g-c d (3 d g+e f)\right) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 g^{3/2} (c d f-a e g)^{5/2}}-\frac{(e f-d g) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 g \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(4 a e^2 g-c d (3 d g+e f)\right)}{4 g \sqrt{d+e x} (f+g x) (c d f-a e g)^2}","-\frac{c d \left(4 a e^2 g-c d (3 d g+e f)\right) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{4 g^{3/2} (c d f-a e g)^{5/2}}-\frac{(e f-d g) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 g \sqrt{d+e x} (f+g x)^2 (c d f-a e g)}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(4 a e^2 g-c d (3 d g+e f)\right)}{4 g \sqrt{d+e x} (f+g x) (c d f-a e g)^2}",1,"-((e*f - d*g)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(2*g*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^2) - ((4*a*e^2*g - c*d*(e*f + 3*d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*g*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)) - (c*d*(4*a*e^2*g - c*d*(e*f + 3*d*g))*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(4*g^(3/2)*(c*d*f - a*e*g)^(5/2))","A",4,4,46,0.08696,1,"{878, 872, 874, 205}"
791,1,351,0,0.557881,"\int \frac{(d+e x)^{3/2}}{(f+g x)^4 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)^(3/2)/((f + g*x)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]),x]","-\frac{c^2 d^2 \left(6 a e^2 g-c d (5 d g+e f)\right) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 g^{3/2} (c d f-a e g)^{7/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(6 a e^2 g-c d (5 d g+e f)\right)}{8 g \sqrt{d+e x} (f+g x) (c d f-a e g)^3}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(6 a e^2 g-c d (5 d g+e f)\right)}{12 g \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}-\frac{(e f-d g) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 g \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}","-\frac{c^2 d^2 \left(6 a e^2 g-c d (5 d g+e f)\right) \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x} \sqrt{c d f-a e g}}\right)}{8 g^{3/2} (c d f-a e g)^{7/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(6 a e^2 g-c d (5 d g+e f)\right)}{8 g \sqrt{d+e x} (f+g x) (c d f-a e g)^3}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \left(6 a e^2 g-c d (5 d g+e f)\right)}{12 g \sqrt{d+e x} (f+g x)^2 (c d f-a e g)^2}-\frac{(e f-d g) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 g \sqrt{d+e x} (f+g x)^3 (c d f-a e g)}",1,"-((e*f - d*g)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*g*(c*d*f - a*e*g)*Sqrt[d + e*x]*(f + g*x)^3) - ((6*a*e^2*g - c*d*(e*f + 5*d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*g*(c*d*f - a*e*g)^2*Sqrt[d + e*x]*(f + g*x)^2) - (c*d*(6*a*e^2*g - c*d*(e*f + 5*d*g))*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*g*(c*d*f - a*e*g)^3*Sqrt[d + e*x]*(f + g*x)) - (c^2*d^2*(6*a*e^2*g - c*d*(e*f + 5*d*g))*ArcTan[(Sqrt[g]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d*f - a*e*g]*Sqrt[d + e*x])])/(8*g^(3/2)*(c*d*f - a*e*g)^(7/2))","A",5,4,46,0.08696,1,"{878, 872, 874, 205}"
792,1,324,0,0.9335108,"\int \frac{\left(a+b x+c x^2\right)^3}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)^3/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{x \sqrt{1-d^2 x^2} \left(24 a^2 c d^4+24 a b^2 d^4+18 a c^2 d^2+18 b^2 c d^2+5 c^3\right)}{16 d^6}-\frac{b \sqrt{1-d^2 x^2} \left(45 a^2 d^4+60 a c d^2+10 b^2 d^2+24 c^2\right)}{15 d^6}+\frac{\sin ^{-1}(d x) \left(24 a^2 c d^4+16 a^3 d^6+24 a b^2 d^4+18 a c^2 d^2+18 b^2 c d^2+5 c^3\right)}{16 d^7}-\frac{c x^3 \sqrt{1-d^2 x^2} \left(18 a c d^2+18 b^2 d^2+5 c^2\right)}{24 d^4}-\frac{b x^2 \sqrt{1-d^2 x^2} \left(30 a c d^2+5 b^2 d^2+12 c^2\right)}{15 d^4}-\frac{3 b c^2 x^4 \sqrt{1-d^2 x^2}}{5 d^2}-\frac{c^3 x^5 \sqrt{1-d^2 x^2}}{6 d^2}","-\frac{x \sqrt{1-d^2 x^2} \left(24 a^2 c d^4+24 a b^2 d^4+18 a c^2 d^2+18 b^2 c d^2+5 c^3\right)}{16 d^6}-\frac{b \sqrt{1-d^2 x^2} \left(45 a^2 d^4+60 a c d^2+10 b^2 d^2+24 c^2\right)}{15 d^6}+\frac{\sin ^{-1}(d x) \left(24 a^2 c d^4+16 a^3 d^6+24 a b^2 d^4+18 a c^2 d^2+18 b^2 c d^2+5 c^3\right)}{16 d^7}-\frac{c x^3 \sqrt{1-d^2 x^2} \left(18 a c d^2+18 b^2 d^2+5 c^2\right)}{24 d^4}-\frac{b x^2 \sqrt{1-d^2 x^2} \left(30 a c d^2+5 b^2 d^2+12 c^2\right)}{15 d^4}-\frac{3 b c^2 x^4 \sqrt{1-d^2 x^2}}{5 d^2}-\frac{c^3 x^5 \sqrt{1-d^2 x^2}}{6 d^2}",1,"-(b*(24*c^2 + 10*b^2*d^2 + 60*a*c*d^2 + 45*a^2*d^4)*Sqrt[1 - d^2*x^2])/(15*d^6) - ((5*c^3 + 18*b^2*c*d^2 + 18*a*c^2*d^2 + 24*a*b^2*d^4 + 24*a^2*c*d^4)*x*Sqrt[1 - d^2*x^2])/(16*d^6) - (b*(12*c^2 + 5*b^2*d^2 + 30*a*c*d^2)*x^2*Sqrt[1 - d^2*x^2])/(15*d^4) - (c*(5*c^2 + 18*b^2*d^2 + 18*a*c*d^2)*x^3*Sqrt[1 - d^2*x^2])/(24*d^4) - (3*b*c^2*x^4*Sqrt[1 - d^2*x^2])/(5*d^2) - (c^3*x^5*Sqrt[1 - d^2*x^2])/(6*d^2) + ((5*c^3 + 18*b^2*c*d^2 + 18*a*c^2*d^2 + 24*a*b^2*d^4 + 24*a^2*c*d^4 + 16*a^3*d^6)*ArcSin[d*x])/(16*d^7)","A",8,4,32,0.1250,1,"{899, 1815, 641, 216}"
793,1,166,0,0.31886,"\int \frac{\left(a+b x+c x^2\right)^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)^2/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\frac{\sin ^{-1}(d x) \left(8 a^2 d^4+8 a c d^2+4 b^2 d^2+3 c^2\right)}{8 d^5}-\frac{x \sqrt{1-d^2 x^2} \left(c \left(8 a+\frac{3 c}{d^2}\right)+4 b^2\right)}{8 d^2}-\frac{2 b \sqrt{1-d^2 x^2} \left(3 a d^2+2 c\right)}{3 d^4}-\frac{2 b c x^2 \sqrt{1-d^2 x^2}}{3 d^2}-\frac{c^2 x^3 \sqrt{1-d^2 x^2}}{4 d^2}","\frac{\sin ^{-1}(d x) \left(8 a^2 d^4+8 a c d^2+4 b^2 d^2+3 c^2\right)}{8 d^5}-\frac{x \sqrt{1-d^2 x^2} \left(c \left(8 a+\frac{3 c}{d^2}\right)+4 b^2\right)}{8 d^2}-\frac{2 b \sqrt{1-d^2 x^2} \left(3 a d^2+2 c\right)}{3 d^4}-\frac{2 b c x^2 \sqrt{1-d^2 x^2}}{3 d^2}-\frac{c^2 x^3 \sqrt{1-d^2 x^2}}{4 d^2}",1,"(-2*b*(2*c + 3*a*d^2)*Sqrt[1 - d^2*x^2])/(3*d^4) - ((4*b^2 + c*(8*a + (3*c)/d^2))*x*Sqrt[1 - d^2*x^2])/(8*d^2) - (2*b*c*x^2*Sqrt[1 - d^2*x^2])/(3*d^2) - (c^2*x^3*Sqrt[1 - d^2*x^2])/(4*d^2) + ((3*c^2 + 4*b^2*d^2 + 8*a*c*d^2 + 8*a^2*d^4)*ArcSin[d*x])/(8*d^5)","A",6,4,32,0.1250,1,"{899, 1815, 641, 216}"
794,1,63,0,0.0627523,"\int \frac{a+b x+c x^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\frac{\left(2 a d^2+c\right) \sin ^{-1}(d x)}{2 d^3}-\frac{b \sqrt{1-d^2 x^2}}{d^2}-\frac{c x \sqrt{1-d^2 x^2}}{2 d^2}","\frac{\left(2 a d^2+c\right) \sin ^{-1}(d x)}{2 d^3}-\frac{b \sqrt{1-d^2 x^2}}{d^2}-\frac{c x \sqrt{1-d^2 x^2}}{2 d^2}",1,"-((b*Sqrt[1 - d^2*x^2])/d^2) - (c*x*Sqrt[1 - d^2*x^2])/(2*d^2) + ((c + 2*a*d^2)*ArcSin[d*x])/(2*d^3)","A",4,4,30,0.1333,1,"{899, 1815, 641, 216}"
795,1,282,0,0.5223696,"\int \frac{1}{\sqrt{1-d x} \sqrt{1+d x} \left(a+b x+c x^2\right)} \, dx","Int[1/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(a + b*x + c*x^2)),x]","\frac{\sqrt{2} c \tanh ^{-1}\left(\frac{d^2 x \left(\sqrt{b^2-4 a c}+b\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2}}-\frac{\sqrt{2} c \tanh ^{-1}\left(\frac{d^2 x \left(b-\sqrt{b^2-4 a c}\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2}}","\frac{\sqrt{2} c \tanh ^{-1}\left(\frac{d^2 x \left(\sqrt{b^2-4 a c}+b\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2}}-\frac{\sqrt{2} c \tanh ^{-1}\left(\frac{d^2 x \left(b-\sqrt{b^2-4 a c}\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2}}",1,"-((Sqrt[2]*c*ArcTanh[(2*c + (b - Sqrt[b^2 - 4*a*c])*d^2*x)/(Sqrt[2]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*d^2]*Sqrt[1 - d^2*x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*d^2])) + (Sqrt[2]*c*ArcTanh[(2*c + (b + Sqrt[b^2 - 4*a*c])*d^2*x)/(Sqrt[2]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*d^2]*Sqrt[1 - d^2*x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*d^2])","A",6,4,32,0.1250,1,"{899, 985, 725, 206}"
796,1,571,0,5.2347467,"\int \frac{1}{\sqrt{1-d x} \sqrt{1+d x} \left(a+b x+c x^2\right)^2} \, dx","Int[1/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(a + b*x + c*x^2)^2),x]","-\frac{c \left(-c d^2 \left(-8 a^2 d^2-b \sqrt{b^2-4 a c}+5 b^2\right)-a b d^4 \left(\sqrt{b^2-4 a c}+b\right)+12 a c^2 d^2+4 c^3\right) \tanh ^{-1}\left(\frac{d^2 x \left(b-\sqrt{b^2-4 a c}\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}+\frac{c \left(-4 c d^2 \left(b^2-2 a^2 d^2\right)-b d^2 \left(\sqrt{b^2-4 a c}+b\right) \left(c-a d^2\right)-2 a b^2 d^4+12 a c^2 d^2+4 c^3\right) \tanh ^{-1}\left(\frac{d^2 x \left(\sqrt{b^2-4 a c}+b\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}-\frac{\sqrt{1-d^2 x^2} \left(b \left(b^2 d^2-c \left(3 a d^2+c\right)\right)-c x \left(2 a c d^2-b^2 d^2+2 c^2\right)\right)}{\left(b^2-4 a c\right) \left(b^2 d^2-\left(a d^2+c\right)^2\right) \left(a+b x+c x^2\right)}","-\frac{c \left(-c d^2 \left(-8 a^2 d^2-b \sqrt{b^2-4 a c}+5 b^2\right)-a b d^4 \left(\sqrt{b^2-4 a c}+b\right)+12 a c^2 d^2+4 c^3\right) \tanh ^{-1}\left(\frac{d^2 x \left(b-\sqrt{b^2-4 a c}\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}+\frac{c \left(-4 c d^2 \left(b^2-2 a^2 d^2\right)-b d^2 \left(\sqrt{b^2-4 a c}+b\right) \left(c-a d^2\right)-2 a b^2 d^4+12 a c^2 d^2+4 c^3\right) \tanh ^{-1}\left(\frac{d^2 x \left(\sqrt{b^2-4 a c}+b\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}-\frac{\sqrt{1-d^2 x^2} \left(b \left(b^2 d^2-c \left(3 a d^2+c\right)\right)-c x \left(2 a c d^2-b^2 d^2+2 c^2\right)\right)}{\left(b^2-4 a c\right) \left(b^2 d^2-\left(a d^2+c\right)^2\right) \left(a+b x+c x^2\right)}",1,"-(((b*(b^2*d^2 - c*(c + 3*a*d^2)) - c*(2*c^2 - b^2*d^2 + 2*a*c*d^2)*x)*Sqrt[1 - d^2*x^2])/((b^2 - 4*a*c)*(b^2*d^2 - (c + a*d^2)^2)*(a + b*x + c*x^2))) - (c*(4*c^3 + 12*a*c^2*d^2 - a*b*(b + Sqrt[b^2 - 4*a*c])*d^4 - c*d^2*(5*b^2 - b*Sqrt[b^2 - 4*a*c] - 8*a^2*d^2))*ArcTanh[(2*c + (b - Sqrt[b^2 - 4*a*c])*d^2*x)/(Sqrt[2]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*d^2]*Sqrt[1 - d^2*x^2])])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*d^2]*(b^2*d^2 - (c + a*d^2)^2)) + (c*(4*c^3 + 12*a*c^2*d^2 - 2*a*b^2*d^4 - b*(b + Sqrt[b^2 - 4*a*c])*d^2*(c - a*d^2) - 4*c*d^2*(b^2 - 2*a^2*d^2))*ArcTanh[(2*c + (b + Sqrt[b^2 - 4*a*c])*d^2*x)/(Sqrt[2]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*d^2]*Sqrt[1 - d^2*x^2])])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*d^2]*(b^2*d^2 - (c + a*d^2)^2))","A",7,5,32,0.1562,1,"{899, 975, 1034, 725, 206}"
797,1,276,0,0.5978372,"\int \frac{\left(a+b x+c x^2\right)^3}{(1-d x)^{3/2} (1+d x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^3/((1 - d*x)^(3/2)*(1 + d*x)^(3/2)),x]","\frac{x \left(a d^2+c\right) \left(a^2 d^4+2 a c d^2+3 b^2 d^2+c^2\right)+b d^4 \left(3 a^2+\frac{6 a c}{d^2}+\frac{b^2}{d^2}+\frac{3 c^2}{d^4}\right)}{d^6 \sqrt{1-d^2 x^2}}-\frac{3 \sin ^{-1}(d x) \left(8 a^2 c d^4+8 a b^2 d^4+12 a c^2 d^2+12 b^2 c d^2+5 c^3\right)}{8 d^7}+\frac{c x \sqrt{1-d^2 x^2} \left(12 a c d^2+12 b^2 d^2+7 c^2\right)}{8 d^6}+\frac{b \sqrt{1-d^2 x^2} \left(6 a c d^2+b^2 d^2+5 c^2\right)}{d^6}+\frac{b c^2 x^2 \sqrt{1-d^2 x^2}}{d^4}+\frac{c^3 x^3 \sqrt{1-d^2 x^2}}{4 d^4}","\frac{x \left(a d^2+c\right) \left(a^2 d^4+2 a c d^2+3 b^2 d^2+c^2\right)+b d^4 \left(3 a^2+\frac{6 a c}{d^2}+\frac{b^2}{d^2}+\frac{3 c^2}{d^4}\right)}{d^6 \sqrt{1-d^2 x^2}}-\frac{3 \sin ^{-1}(d x) \left(8 a^2 c d^4+8 a b^2 d^4+12 a c^2 d^2+12 b^2 c d^2+5 c^3\right)}{8 d^7}+\frac{c x \sqrt{1-d^2 x^2} \left(12 a c d^2+12 b^2 d^2+7 c^2\right)}{8 d^6}+\frac{b \sqrt{1-d^2 x^2} \left(6 a c d^2+b^2 d^2+5 c^2\right)}{d^6}+\frac{b c^2 x^2 \sqrt{1-d^2 x^2}}{d^4}+\frac{c^3 x^3 \sqrt{1-d^2 x^2}}{4 d^4}",1,"(b*(3*a^2 + (3*c^2)/d^4 + b^2/d^2 + (6*a*c)/d^2)*d^4 + (c + a*d^2)*(c^2 + 3*b^2*d^2 + 2*a*c*d^2 + a^2*d^4)*x)/(d^6*Sqrt[1 - d^2*x^2]) + (b*(5*c^2 + b^2*d^2 + 6*a*c*d^2)*Sqrt[1 - d^2*x^2])/d^6 + (c*(7*c^2 + 12*b^2*d^2 + 12*a*c*d^2)*x*Sqrt[1 - d^2*x^2])/(8*d^6) + (b*c^2*x^2*Sqrt[1 - d^2*x^2])/d^4 + (c^3*x^3*Sqrt[1 - d^2*x^2])/(4*d^4) - (3*(5*c^3 + 12*b^2*c*d^2 + 12*a*c^2*d^2 + 8*a*b^2*d^4 + 8*a^2*c*d^4)*ArcSin[d*x])/(8*d^7)","A",7,5,32,0.1562,1,"{899, 1814, 1815, 641, 216}"
798,1,135,0,0.1945777,"\int \frac{\left(a+b x+c x^2\right)^2}{(1-d x)^{3/2} (1+d x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^2/((1 - d*x)^(3/2)*(1 + d*x)^(3/2)),x]","\frac{x \left(a^2 d^4+2 a c d^2+b^2 d^2+c^2\right)+2 b d^2 \left(a+\frac{c}{d^2}\right)}{d^4 \sqrt{1-d^2 x^2}}-\frac{\sin ^{-1}(d x) \left(c \left(4 a+\frac{3 c}{d^2}\right)+2 b^2\right)}{2 d^3}+\frac{2 b c \sqrt{1-d^2 x^2}}{d^4}+\frac{c^2 x \sqrt{1-d^2 x^2}}{2 d^4}","\frac{x \left(a^2 d^4+2 a c d^2+b^2 d^2+c^2\right)+2 b d^2 \left(a+\frac{c}{d^2}\right)}{d^4 \sqrt{1-d^2 x^2}}-\frac{\sin ^{-1}(d x) \left(c \left(4 a+\frac{3 c}{d^2}\right)+2 b^2\right)}{2 d^3}+\frac{2 b c \sqrt{1-d^2 x^2}}{d^4}+\frac{c^2 x \sqrt{1-d^2 x^2}}{2 d^4}",1,"(2*b*(a + c/d^2)*d^2 + (c^2 + b^2*d^2 + 2*a*c*d^2 + a^2*d^4)*x)/(d^4*Sqrt[1 - d^2*x^2]) + (2*b*c*Sqrt[1 - d^2*x^2])/d^4 + (c^2*x*Sqrt[1 - d^2*x^2])/(2*d^4) - ((2*b^2 + c*(4*a + (3*c)/d^2))*ArcSin[d*x])/(2*d^3)","A",5,5,32,0.1562,1,"{899, 1814, 1815, 641, 216}"
799,1,40,0,0.0511869,"\int \frac{a+b x+c x^2}{(1-d x)^{3/2} (1+d x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)/((1 - d*x)^(3/2)*(1 + d*x)^(3/2)),x]","\frac{x \left(a d^2+c\right)+b}{d^2 \sqrt{1-d^2 x^2}}-\frac{c \sin ^{-1}(d x)}{d^3}","\frac{x \left(a d^2+c\right)+b}{d^2 \sqrt{1-d^2 x^2}}-\frac{c \sin ^{-1}(d x)}{d^3}",1,"(b + (c + a*d^2)*x)/(d^2*Sqrt[1 - d^2*x^2]) - (c*ArcSin[d*x])/d^3","A",4,4,30,0.1333,1,"{899, 1814, 12, 216}"
800,1,443,0,1.4426719,"\int \frac{1}{(1-d x)^{3/2} (1+d x)^{3/2} \left(a+b x+c x^2\right)} \, dx","Int[1/((1 - d*x)^(3/2)*(1 + d*x)^(3/2)*(a + b*x + c*x^2)),x]","\frac{c \left(-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2\right) \tanh ^{-1}\left(\frac{d^2 x \left(b-\sqrt{b^2-4 a c}\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}-\frac{c \left(-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2\right) \tanh ^{-1}\left(\frac{d^2 x \left(\sqrt{b^2-4 a c}+b\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}+\frac{d^2 \left(b-x \left(a d^2+c\right)\right)}{\sqrt{1-d^2 x^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}","\frac{c \left(-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2\right) \tanh ^{-1}\left(\frac{d^2 x \left(b-\sqrt{b^2-4 a c}\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}-\frac{c \left(-b d^2 \left(b-\sqrt{b^2-4 a c}\right)+2 a c d^2+2 c^2\right) \tanh ^{-1}\left(\frac{d^2 x \left(\sqrt{b^2-4 a c}+b\right)+2 c}{\sqrt{2} \sqrt{1-d^2 x^2} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{-b d^2 \left(\sqrt{b^2-4 a c}+b\right)+2 a c d^2+2 c^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}+\frac{d^2 \left(b-x \left(a d^2+c\right)\right)}{\sqrt{1-d^2 x^2} \left(b^2 d^2-\left(a d^2+c\right)^2\right)}",1,"(d^2*(b - (c + a*d^2)*x))/((b^2*d^2 - (c + a*d^2)^2)*Sqrt[1 - d^2*x^2]) + (c*(2*c^2 + 2*a*c*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*d^2)*ArcTanh[(2*c + (b - Sqrt[b^2 - 4*a*c])*d^2*x)/(Sqrt[2]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*d^2]*Sqrt[1 - d^2*x^2])])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*d^2]*(b^2*d^2 - (c + a*d^2)^2)) - (c*(2*c^2 + 2*a*c*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*d^2)*ArcTanh[(2*c + (b + Sqrt[b^2 - 4*a*c])*d^2*x)/(Sqrt[2]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*d^2]*Sqrt[1 - d^2*x^2])])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*d^2]*(b^2*d^2 - (c + a*d^2)^2))","A",7,5,32,0.1562,1,"{899, 976, 1034, 725, 206}"
801,1,938,0,11.8441171,"\int \frac{1}{(1-d x)^{3/2} (1+d x)^{3/2} \left(a+b x+c x^2\right)^2} \, dx","Int[1/((1 - d*x)^(3/2)*(1 + d*x)^(3/2)*(a + b*x + c*x^2)^2),x]","-\frac{\left(b \left(3 a b^2 d^4-11 a^2 c d^4-10 a c^2 d^2+2 b^2 c d^2+c^3\right)-\left(2 c^4-d^2 \left(b^2+6 a^2 d^2\right) c^2-\left(4 a^3 d^6+6 a b^2 d^4\right) c+b^2 d^4 \left(2 b^2+a^2 d^2\right)\right) x\right) d^2}{\left(b^2-4 a c\right) \left(a d^2-b d+c\right)^2 \left(a d^2+b d+c\right)^2 \sqrt{1-d^2 x^2}}+\frac{c \left(3 a b^3 \left(b+\sqrt{b^2-4 a c}\right) d^6-2 a c^2 \left(7 b^2+5 \sqrt{b^2-4 a c} b-8 a^2 d^2\right) d^4+b c \left(2 b^3+2 \sqrt{b^2-4 a c} b^2-17 a^2 d^2 b-11 a^2 \sqrt{b^2-4 a c} d^2\right) d^4+24 a c^4 d^2-c^3 \left(9 b^2-\sqrt{b^2-4 a c} b-36 a^2 d^2\right) d^2+4 c^5\right) \tanh ^{-1}\left(\frac{\left(b-\sqrt{b^2-4 a c}\right) x d^2+2 c}{\sqrt{2} \sqrt{2 c^2+2 a d^2 c-b \left(b-\sqrt{b^2-4 a c}\right) d^2} \sqrt{1-d^2 x^2}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c^2+2 a d^2 c-b \left(b-\sqrt{b^2-4 a c}\right) d^2} \left(a^2 d^4-b^2 d^2+2 a c d^2+c^2\right)^2}-\frac{b \left(b^2 d^2-c \left(3 a d^2+c\right)\right)-c \left(2 c^2+2 a d^2 c-b^2 d^2\right) x}{\left(b^2-4 a c\right) \left(b^2 d^2-\left(a d^2+c\right)^2\right) \left(c x^2+b x+a\right) \sqrt{1-d^2 x^2}}-\frac{c \left(6 a b^4 d^8+4 b^2 c \left(b^2-7 a^2 d^2\right) d^6+24 a c^4 d^4-b \left(b+\sqrt{b^2-4 a c}\right) \left(3 a b^2 d^4-11 a^2 c d^4-10 a c^2 d^2+2 b^2 c d^2+c^3\right) d^4+4 c^5 d^2-4 c^3 \left(2 b^2 d^4-9 a^2 d^6\right)-8 c^2 \left(3 a b^2 d^6-2 a^3 d^8\right)\right) \tanh ^{-1}\left(\frac{\left(b+\sqrt{b^2-4 a c}\right) x d^2+2 c}{\sqrt{2} \sqrt{2 c^2+2 a d^2 c-b \left(b+\sqrt{b^2-4 a c}\right) d^2} \sqrt{1-d^2 x^2}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c^2+2 a d^2 c-b \left(b+\sqrt{b^2-4 a c}\right) d^2} \left(a^2 d^4-b^2 d^2+2 a c d^2+c^2\right)^2 d^2}","-\frac{\left(b \left(3 a b^2 d^4-11 a^2 c d^4-10 a c^2 d^2+2 b^2 c d^2+c^3\right)-\left(2 c^4-d^2 \left(b^2+6 a^2 d^2\right) c^2-\left(4 a^3 d^6+6 a b^2 d^4\right) c+b^2 d^4 \left(2 b^2+a^2 d^2\right)\right) x\right) d^2}{\left(b^2-4 a c\right) \left(a d^2-b d+c\right)^2 \left(a d^2+b d+c\right)^2 \sqrt{1-d^2 x^2}}+\frac{c \left(3 a b^3 \left(b+\sqrt{b^2-4 a c}\right) d^6-2 a c^2 \left(7 b^2+5 \sqrt{b^2-4 a c} b-8 a^2 d^2\right) d^4+b c \left(2 b^3+2 \sqrt{b^2-4 a c} b^2-17 a^2 d^2 b-11 a^2 \sqrt{b^2-4 a c} d^2\right) d^4+24 a c^4 d^2-c^3 \left(9 b^2-\sqrt{b^2-4 a c} b-36 a^2 d^2\right) d^2+4 c^5\right) \tanh ^{-1}\left(\frac{\left(b-\sqrt{b^2-4 a c}\right) x d^2+2 c}{\sqrt{2} \sqrt{2 c^2+2 a d^2 c-b \left(b-\sqrt{b^2-4 a c}\right) d^2} \sqrt{1-d^2 x^2}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c^2+2 a d^2 c-b \left(b-\sqrt{b^2-4 a c}\right) d^2} \left(a^2 d^4-b^2 d^2+2 a c d^2+c^2\right)^2}-\frac{b \left(b^2 d^2-c \left(3 a d^2+c\right)\right)-c \left(2 c^2+2 a d^2 c-b^2 d^2\right) x}{\left(b^2-4 a c\right) \left(b^2 d^2-\left(a d^2+c\right)^2\right) \left(c x^2+b x+a\right) \sqrt{1-d^2 x^2}}+\frac{c \left(b \left(b+\sqrt{b^2-4 a c}\right) d^4 \left(3 a b^2 d^4-11 a^2 c d^4-10 a c^2 d^2+2 b^2 c d^2+c^3\right)-2 \left(3 a b^4 d^8+2 b^2 c \left(b^2-7 a^2 d^2\right) d^6+12 a c^4 d^4+2 c^5 d^2-c^3 \left(4 b^2 d^4-18 a^2 d^6\right)-4 c^2 \left(3 a b^2 d^6-2 a^3 d^8\right)\right)\right) \tanh ^{-1}\left(\frac{\left(b+\sqrt{b^2-4 a c}\right) x d^2+2 c}{\sqrt{2} \sqrt{2 c^2+2 a d^2 c-b \left(b+\sqrt{b^2-4 a c}\right) d^2} \sqrt{1-d^2 x^2}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c^2+2 a d^2 c-b \left(b+\sqrt{b^2-4 a c}\right) d^2} \left(a^2 d^4-b^2 d^2+2 a c d^2+c^2\right)^2 d^2}",1,"-((d^2*(b*(c^3 + 2*b^2*c*d^2 - 10*a*c^2*d^2 + 3*a*b^2*d^4 - 11*a^2*c*d^4) - (2*c^4 + b^2*d^4*(2*b^2 + a^2*d^2) - c^2*d^2*(b^2 + 6*a^2*d^2) - c*(6*a*b^2*d^4 + 4*a^3*d^6))*x))/((b^2 - 4*a*c)*(c - b*d + a*d^2)^2*(c + b*d + a*d^2)^2*Sqrt[1 - d^2*x^2])) - (b*(b^2*d^2 - c*(c + 3*a*d^2)) - c*(2*c^2 - b^2*d^2 + 2*a*c*d^2)*x)/((b^2 - 4*a*c)*(b^2*d^2 - (c + a*d^2)^2)*(a + b*x + c*x^2)*Sqrt[1 - d^2*x^2]) + (c*(4*c^5 + 24*a*c^4*d^2 + 3*a*b^3*(b + Sqrt[b^2 - 4*a*c])*d^6 - c^3*d^2*(9*b^2 - b*Sqrt[b^2 - 4*a*c] - 36*a^2*d^2) - 2*a*c^2*d^4*(7*b^2 + 5*b*Sqrt[b^2 - 4*a*c] - 8*a^2*d^2) + b*c*d^4*(2*b^3 + 2*b^2*Sqrt[b^2 - 4*a*c] - 17*a^2*b*d^2 - 11*a^2*Sqrt[b^2 - 4*a*c]*d^2))*ArcTanh[(2*c + (b - Sqrt[b^2 - 4*a*c])*d^2*x)/(Sqrt[2]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*d^2]*Sqrt[1 - d^2*x^2])])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*d^2]*(c^2 - b^2*d^2 + 2*a*c*d^2 + a^2*d^4)^2) - (c*(4*c^5*d^2 + 24*a*c^4*d^4 + 6*a*b^4*d^8 + 4*b^2*c*d^6*(b^2 - 7*a^2*d^2) - b*(b + Sqrt[b^2 - 4*a*c])*d^4*(c^3 + 2*b^2*c*d^2 - 10*a*c^2*d^2 + 3*a*b^2*d^4 - 11*a^2*c*d^4) - 4*c^3*(2*b^2*d^4 - 9*a^2*d^6) - 8*c^2*(3*a*b^2*d^6 - 2*a^3*d^8))*ArcTanh[(2*c + (b + Sqrt[b^2 - 4*a*c])*d^2*x)/(Sqrt[2]*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*d^2]*Sqrt[1 - d^2*x^2])])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*d^2*Sqrt[2*c^2 + 2*a*c*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*d^2]*(c^2 - b^2*d^2 + 2*a*c*d^2 + a^2*d^4)^2)","A",8,6,32,0.1875,1,"{899, 975, 1062, 1034, 725, 206}"
802,1,54,0,0.0448021,"\int (1-e x)^m (1+e x)^m \left(a+c x^2\right)^p \, dx","Int[(1 - e*x)^m*(1 + e*x)^m*(a + c*x^2)^p,x]","x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,-m;\frac{3}{2};-\frac{c x^2}{a},e^2 x^2\right)","x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,-m;\frac{3}{2};-\frac{c x^2}{a},e^2 x^2\right)",1,"(x*(a + c*x^2)^p*AppellF1[1/2, -p, -m, 3/2, -((c*x^2)/a), e^2*x^2])/(1 + (c*x^2)/a)^p","A",3,3,25,0.1200,1,"{517, 430, 429}"
803,1,89,0,0.077514,"\int (d-e x)^m (d+e x)^m \left(a+c x^2\right)^p \, dx","Int[(d - e*x)^m*(d + e*x)^m*(a + c*x^2)^p,x]","x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} (d-e x)^m (d+e x)^m \left(1-\frac{e^2 x^2}{d^2}\right)^{-m} F_1\left(\frac{1}{2};-p,-m;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)","x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} (d-e x)^m (d+e x)^m \left(1-\frac{e^2 x^2}{d^2}\right)^{-m} F_1\left(\frac{1}{2};-p,-m;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)",1,"(x*(d - e*x)^m*(d + e*x)^m*(a + c*x^2)^p*AppellF1[1/2, -p, -m, 3/2, -((c*x^2)/a), (e^2*x^2)/d^2])/((1 + (c*x^2)/a)^p*(1 - (e^2*x^2)/d^2)^m)","A",4,3,25,0.1200,1,"{519, 430, 429}"
804,1,92,0,0.0841984,"\int (d+e x)^m (d f-e f x)^m \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^m*(d*f - e*f*x)^m*(a + c*x^2)^p,x]","x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} (d+e x)^m \left(1-\frac{e^2 x^2}{d^2}\right)^{-m} (d f-e f x)^m F_1\left(\frac{1}{2};-p,-m;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)","x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} (d+e x)^m \left(1-\frac{e^2 x^2}{d^2}\right)^{-m} (d f-e f x)^m F_1\left(\frac{1}{2};-p,-m;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)",1,"(x*(d + e*x)^m*(d*f - e*f*x)^m*(a + c*x^2)^p*AppellF1[1/2, -p, -m, 3/2, -((c*x^2)/a), (e^2*x^2)/d^2])/((1 + (c*x^2)/a)^p*(1 - (e^2*x^2)/d^2)^m)","A",4,3,28,0.1071,1,"{519, 430, 429}"
805,1,275,0,0.2632943,"\int (d+e x)^3 (f+g x)^n \left(a+2 c d x+c e x^2\right) \, dx","Int[(d + e*x)^3*(f + g*x)^n*(a + 2*c*d*x + c*e*x^2),x]","\frac{(e f-d g)^2 (f+g x)^{n+2} \left(3 a e g^2+c \left(2 d^2 g^2-10 d e f g+5 e^2 f^2\right)\right)}{g^6 (n+2)}-\frac{e (e f-d g) (f+g x)^{n+3} \left(3 a e g^2+c \left(7 d^2 g^2-20 d e f g+10 e^2 f^2\right)\right)}{g^6 (n+3)}+\frac{e^2 (f+g x)^{n+4} \left(a e g^2+c \left(9 d^2 g^2-20 d e f g+10 e^2 f^2\right)\right)}{g^6 (n+4)}-\frac{(e f-d g)^3 (f+g x)^{n+1} \left(a g^2+c f (e f-2 d g)\right)}{g^6 (n+1)}-\frac{5 c e^3 (e f-d g) (f+g x)^{n+5}}{g^6 (n+5)}+\frac{c e^4 (f+g x)^{n+6}}{g^6 (n+6)}","\frac{(e f-d g)^2 (f+g x)^{n+2} \left(3 a e g^2+c \left(2 d^2 g^2-10 d e f g+5 e^2 f^2\right)\right)}{g^6 (n+2)}-\frac{e (e f-d g) (f+g x)^{n+3} \left(3 a e g^2+c \left(7 d^2 g^2-20 d e f g+10 e^2 f^2\right)\right)}{g^6 (n+3)}+\frac{e^2 (f+g x)^{n+4} \left(a e g^2+c \left(9 d^2 g^2-20 d e f g+10 e^2 f^2\right)\right)}{g^6 (n+4)}-\frac{(e f-d g)^3 (f+g x)^{n+1} \left(a g^2+c f (e f-2 d g)\right)}{g^6 (n+1)}-\frac{5 c e^3 (e f-d g) (f+g x)^{n+5}}{g^6 (n+5)}+\frac{c e^4 (f+g x)^{n+6}}{g^6 (n+6)}",1,"-(((e*f - d*g)^3*(a*g^2 + c*f*(e*f - 2*d*g))*(f + g*x)^(1 + n))/(g^6*(1 + n))) + ((e*f - d*g)^2*(3*a*e*g^2 + c*(5*e^2*f^2 - 10*d*e*f*g + 2*d^2*g^2))*(f + g*x)^(2 + n))/(g^6*(2 + n)) - (e*(e*f - d*g)*(3*a*e*g^2 + c*(10*e^2*f^2 - 20*d*e*f*g + 7*d^2*g^2))*(f + g*x)^(3 + n))/(g^6*(3 + n)) + (e^2*(a*e*g^2 + c*(10*e^2*f^2 - 20*d*e*f*g + 9*d^2*g^2))*(f + g*x)^(4 + n))/(g^6*(4 + n)) - (5*c*e^3*(e*f - d*g)*(f + g*x)^(5 + n))/(g^6*(5 + n)) + (c*e^4*(f + g*x)^(6 + n))/(g^6*(6 + n))","A",2,1,28,0.03571,1,"{947}"
806,1,208,0,0.1876818,"\int (d+e x)^2 (f+g x)^n \left(a+2 c d x+c e x^2\right) \, dx","Int[(d + e*x)^2*(f + g*x)^n*(a + 2*c*d*x + c*e*x^2),x]","-\frac{2 (e f-d g) (f+g x)^{n+2} \left(a e g^2+c \left(d^2 g^2-4 d e f g+2 e^2 f^2\right)\right)}{g^5 (n+2)}+\frac{e (f+g x)^{n+3} \left(a e g^2+c \left(5 d^2 g^2-12 d e f g+6 e^2 f^2\right)\right)}{g^5 (n+3)}+\frac{(e f-d g)^2 (f+g x)^{n+1} \left(a g^2+c f (e f-2 d g)\right)}{g^5 (n+1)}-\frac{4 c e^2 (e f-d g) (f+g x)^{n+4}}{g^5 (n+4)}+\frac{c e^3 (f+g x)^{n+5}}{g^5 (n+5)}","-\frac{2 (e f-d g) (f+g x)^{n+2} \left(a e g^2+c \left(d^2 g^2-4 d e f g+2 e^2 f^2\right)\right)}{g^5 (n+2)}+\frac{e (f+g x)^{n+3} \left(a e g^2+c \left(5 d^2 g^2-12 d e f g+6 e^2 f^2\right)\right)}{g^5 (n+3)}+\frac{(e f-d g)^2 (f+g x)^{n+1} \left(a g^2+c f (e f-2 d g)\right)}{g^5 (n+1)}-\frac{4 c e^2 (e f-d g) (f+g x)^{n+4}}{g^5 (n+4)}+\frac{c e^3 (f+g x)^{n+5}}{g^5 (n+5)}",1,"((e*f - d*g)^2*(a*g^2 + c*f*(e*f - 2*d*g))*(f + g*x)^(1 + n))/(g^5*(1 + n)) - (2*(e*f - d*g)*(a*e*g^2 + c*(2*e^2*f^2 - 4*d*e*f*g + d^2*g^2))*(f + g*x)^(2 + n))/(g^5*(2 + n)) + (e*(a*e*g^2 + c*(6*e^2*f^2 - 12*d*e*f*g + 5*d^2*g^2))*(f + g*x)^(3 + n))/(g^5*(3 + n)) - (4*c*e^2*(e*f - d*g)*(f + g*x)^(4 + n))/(g^5*(4 + n)) + (c*e^3*(f + g*x)^(5 + n))/(g^5*(5 + n))","A",2,1,28,0.03571,1,"{947}"
807,1,146,0,0.1121705,"\int (d+e x) (f+g x)^n \left(a+2 c d x+c e x^2\right) \, dx","Int[(d + e*x)*(f + g*x)^n*(a + 2*c*d*x + c*e*x^2),x]","\frac{(f+g x)^{n+2} \left(a e g^2+c \left(2 d^2 g^2-6 d e f g+3 e^2 f^2\right)\right)}{g^4 (n+2)}-\frac{(e f-d g) (f+g x)^{n+1} \left(a g^2+c f (e f-2 d g)\right)}{g^4 (n+1)}-\frac{3 c e (e f-d g) (f+g x)^{n+3}}{g^4 (n+3)}+\frac{c e^2 (f+g x)^{n+4}}{g^4 (n+4)}","\frac{(f+g x)^{n+2} \left(a e g^2+c \left(2 d^2 g^2-6 d e f g+3 e^2 f^2\right)\right)}{g^4 (n+2)}-\frac{(e f-d g) (f+g x)^{n+1} \left(a g^2+c f (e f-2 d g)\right)}{g^4 (n+1)}-\frac{3 c e (e f-d g) (f+g x)^{n+3}}{g^4 (n+3)}+\frac{c e^2 (f+g x)^{n+4}}{g^4 (n+4)}",1,"-(((e*f - d*g)*(a*g^2 + c*f*(e*f - 2*d*g))*(f + g*x)^(1 + n))/(g^4*(1 + n))) + ((a*e*g^2 + c*(3*e^2*f^2 - 6*d*e*f*g + 2*d^2*g^2))*(f + g*x)^(2 + n))/(g^4*(2 + n)) - (3*c*e*(e*f - d*g)*(f + g*x)^(3 + n))/(g^4*(3 + n)) + (c*e^2*(f + g*x)^(4 + n))/(g^4*(4 + n))","A",2,1,26,0.03846,1,"{771}"
808,1,84,0,0.0634219,"\int (f+g x)^n \left(a+2 c d x+c e x^2\right) \, dx","Int[(f + g*x)^n*(a + 2*c*d*x + c*e*x^2),x]","\frac{(f+g x)^{n+1} \left(a g^2+c f (e f-2 d g)\right)}{g^3 (n+1)}-\frac{2 c (e f-d g) (f+g x)^{n+2}}{g^3 (n+2)}+\frac{c e (f+g x)^{n+3}}{g^3 (n+3)}","\frac{(f+g x)^{n+1} \left(a g^2+c f (e f-2 d g)\right)}{g^3 (n+1)}-\frac{2 c (e f-d g) (f+g x)^{n+2}}{g^3 (n+2)}+\frac{c e (f+g x)^{n+3}}{g^3 (n+3)}",1,"((a*g^2 + c*f*(e*f - 2*d*g))*(f + g*x)^(1 + n))/(g^3*(1 + n)) - (2*c*(e*f - d*g)*(f + g*x)^(2 + n))/(g^3*(2 + n)) + (c*e*(f + g*x)^(3 + n))/(g^3*(3 + n))","A",2,1,21,0.04762,1,"{698}"
809,1,114,0,0.1528701,"\int \frac{(f+g x)^n \left(a+2 c d x+c e x^2\right)}{d+e x} \, dx","Int[((f + g*x)^n*(a + 2*c*d*x + c*e*x^2))/(d + e*x),x]","\frac{\left(c d^2-a e\right) (f+g x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{e (f+g x)}{e f-d g}\right)}{e (n+1) (e f-d g)}-\frac{c (e f-d g) (f+g x)^{n+1}}{e g^2 (n+1)}+\frac{c (f+g x)^{n+2}}{g^2 (n+2)}","\frac{\left(c d^2-a e\right) (f+g x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{e (f+g x)}{e f-d g}\right)}{e (n+1) (e f-d g)}-\frac{c (e f-d g) (f+g x)^{n+1}}{e g^2 (n+1)}+\frac{c (f+g x)^{n+2}}{g^2 (n+2)}",1,"-((c*(e*f - d*g)*(f + g*x)^(1 + n))/(e*g^2*(1 + n))) + (c*(f + g*x)^(2 + n))/(g^2*(2 + n)) + ((c*d^2 - a*e)*(f + g*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (e*(f + g*x))/(e*f - d*g)])/(e*(e*f - d*g)*(1 + n))","A",3,3,28,0.1071,1,"{951, 80, 68}"
810,1,88,0,0.0830026,"\int \frac{(f+g x)^n \left(a+2 c d x+c e x^2\right)}{(d+e x)^2} \, dx","Int[((f + g*x)^n*(a + 2*c*d*x + c*e*x^2))/(d + e*x)^2,x]","\frac{c (f+g x)^{n+1}}{e g (n+1)}-\frac{g \left(c d^2-a e\right) (f+g x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{e (f+g x)}{e f-d g}\right)}{e (n+1) (e f-d g)^2}","\frac{c (f+g x)^{n+1}}{e g (n+1)}-\frac{g \left(c d^2-a e\right) (f+g x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{e (f+g x)}{e f-d g}\right)}{e (n+1) (e f-d g)^2}",1,"(c*(f + g*x)^(1 + n))/(e*g*(1 + n)) - ((c*d^2 - a*e)*g*(f + g*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, (e*(f + g*x))/(e*f - d*g)])/(e*(e*f - d*g)^2*(1 + n))","A",3,2,28,0.07143,1,"{947, 68}"
811,1,193,0,0.2240525,"\int \frac{(f+g x)^n \left(a+2 c d x+c e x^2\right)}{(d+e x)^3} \, dx","Int[((f + g*x)^n*(a + 2*c*d*x + c*e*x^2))/(d + e*x)^3,x]","\frac{(f+g x)^{n+1} \left(a e g^2 (1-n) n-c \left(d^2 g^2 \left(-n^2+n+2\right)-4 d e f g+2 e^2 f^2\right)\right) \, _2F_1\left(1,n+1;n+2;\frac{e (f+g x)}{e f-d g}\right)}{2 e (n+1) (e f-d g)^3}-\frac{g (1-n) \left(c d^2-a e\right) (f+g x)^{n+1}}{2 e (d+e x) (e f-d g)^2}-\frac{\left(a-\frac{c d^2}{e}\right) (f+g x)^{n+1}}{2 (d+e x)^2 (e f-d g)}","\frac{(f+g x)^{n+1} \left(a e g^2 (1-n) n-c \left(d^2 g^2 \left(-n^2+n+2\right)-4 d e f g+2 e^2 f^2\right)\right) \, _2F_1\left(1,n+1;n+2;\frac{e (f+g x)}{e f-d g}\right)}{2 e (n+1) (e f-d g)^3}-\frac{g (1-n) \left(c d^2-a e\right) (f+g x)^{n+1}}{2 e (d+e x) (e f-d g)^2}-\frac{\left(a-\frac{c d^2}{e}\right) (f+g x)^{n+1}}{2 (d+e x)^2 (e f-d g)}",1,"-((a - (c*d^2)/e)*(f + g*x)^(1 + n))/(2*(e*f - d*g)*(d + e*x)^2) - ((c*d^2 - a*e)*g*(1 - n)*(f + g*x)^(1 + n))/(2*e*(e*f - d*g)^2*(d + e*x)) + ((a*e*g^2*(1 - n)*n - c*(2*e^2*f^2 - 4*d*e*f*g + d^2*g^2*(2 + n - n^2)))*(f + g*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (e*(f + g*x))/(e*f - d*g)])/(2*e*(e*f - d*g)^3*(1 + n))","A",3,3,28,0.1071,1,"{949, 78, 68}"
812,1,197,0,0.2334551,"\int \frac{(f+g x)^n \left(a+2 c d x+c e x^2\right)}{(d+e x)^4} \, dx","Int[((f + g*x)^n*(a + 2*c*d*x + c*e*x^2))/(d + e*x)^4,x]","\frac{g (f+g x)^{n+1} \left(a e g^2 \left(n^2-3 n+2\right)+c \left(d^2 g^2 \left(-n^2+3 n+4\right)-12 d e f g+6 e^2 f^2\right)\right) \, _2F_1\left(2,n+1;n+2;\frac{e (f+g x)}{e f-d g}\right)}{6 e (n+1) (e f-d g)^4}-\frac{g (2-n) \left(c d^2-a e\right) (f+g x)^{n+1}}{6 e (d+e x)^2 (e f-d g)^2}-\frac{\left(a-\frac{c d^2}{e}\right) (f+g x)^{n+1}}{3 (d+e x)^3 (e f-d g)}","\frac{g (f+g x)^{n+1} \left(a e g^2 \left(n^2-3 n+2\right)+c \left(d^2 g^2 \left(-n^2+3 n+4\right)-12 d e f g+6 e^2 f^2\right)\right) \, _2F_1\left(2,n+1;n+2;\frac{e (f+g x)}{e f-d g}\right)}{6 e (n+1) (e f-d g)^4}-\frac{g (2-n) \left(c d^2-a e\right) (f+g x)^{n+1}}{6 e (d+e x)^2 (e f-d g)^2}-\frac{\left(a-\frac{c d^2}{e}\right) (f+g x)^{n+1}}{3 (d+e x)^3 (e f-d g)}",1,"-((a - (c*d^2)/e)*(f + g*x)^(1 + n))/(3*(e*f - d*g)*(d + e*x)^3) - ((c*d^2 - a*e)*g*(2 - n)*(f + g*x)^(1 + n))/(6*e*(e*f - d*g)^2*(d + e*x)^2) + (g*(a*e*g^2*(2 - 3*n + n^2) + c*(6*e^2*f^2 - 12*d*e*f*g + d^2*g^2*(4 + 3*n - n^2)))*(f + g*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, (e*(f + g*x))/(e*f - d*g)])/(6*e*(e*f - d*g)^4*(1 + n))","A",3,3,28,0.1071,1,"{949, 78, 68}"
813,1,227,0,0.2615324,"\int (d+e x)^m (f+g x)^n \left(a+2 c d x+c e x^2\right) \, dx","Int[(d + e*x)^m*(f + g*x)^n*(a + 2*c*d*x + c*e*x^2),x]","\frac{(d+e x)^{m+1} (f+g x)^n \left(\frac{e (f+g x)}{e f-d g}\right)^{-n} \left(a e g (m+n+3)+\frac{c (m+2) (e f-d g) (d g (n+1)+e f (m+1))}{g (m+n+2)}-c d (d g (n+1)+e f (m+2))\right) \, _2F_1\left(m+1,-n;m+2;-\frac{g (d+e x)}{e f-d g}\right)}{e^2 g (m+1) (m+n+3)}-\frac{c (m+2) (e f-d g) (d+e x)^{m+1} (f+g x)^{n+1}}{e g^2 (m+n+2) (m+n+3)}+\frac{c (d+e x)^{m+2} (f+g x)^{n+1}}{e g (m+n+3)}","\frac{(d+e x)^{m+1} (f+g x)^n \left(\frac{e (f+g x)}{e f-d g}\right)^{-n} (g (m+n+2) (a e g (m+n+3)-c d (d g (n+1)+e f (m+2)))+c (m+2) (e f-d g) (d g (n+1)+e f (m+1))) \, _2F_1\left(m+1,-n;m+2;-\frac{g (d+e x)}{e f-d g}\right)}{e^2 g^2 (m+1) (m+n+2) (m+n+3)}-\frac{c (m+2) (e f-d g) (d+e x)^{m+1} (f+g x)^{n+1}}{e g^2 (m+n+2) (m+n+3)}+\frac{c (d+e x)^{m+2} (f+g x)^{n+1}}{e g (m+n+3)}",1,"-((c*(e*f - d*g)*(2 + m)*(d + e*x)^(1 + m)*(f + g*x)^(1 + n))/(e*g^2*(2 + m + n)*(3 + m + n))) + (c*(d + e*x)^(2 + m)*(f + g*x)^(1 + n))/(e*g*(3 + m + n)) + ((a*e*g*(3 + m + n) + (c*(e*f - d*g)*(2 + m)*(e*f*(1 + m) + d*g*(1 + n)))/(g*(2 + m + n)) - c*d*(e*f*(2 + m) + d*g*(1 + n)))*(d + e*x)^(1 + m)*(f + g*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((g*(d + e*x))/(e*f - d*g))])/(e^2*g*(1 + m)*(3 + m + n)*((e*(f + g*x))/(e*f - d*g))^n)","A",4,4,28,0.1429,1,"{951, 80, 70, 69}"
814,1,83,0,0.1000249,"\int \frac{a+b x+c x^2}{(d+e x) (f+g x)} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)*(f + g*x)),x]","\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^2 (e f-d g)}-\frac{\log (f+g x) \left(a g^2-b f g+c f^2\right)}{g^2 (e f-d g)}+\frac{c x}{e g}","\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^2 (e f-d g)}-\frac{\log (f+g x) \left(a g^2-b f g+c f^2\right)}{g^2 (e f-d g)}+\frac{c x}{e g}",1,"(c*x)/(e*g) + ((c*d^2 - b*d*e + a*e^2)*Log[d + e*x])/(e^2*(e*f - d*g)) - ((c*f^2 - b*f*g + a*g^2)*Log[f + g*x])/(g^2*(e*f - d*g))","A",2,1,25,0.04000,1,"{893}"
815,1,184,0,0.3121819,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x) (f+g x)} \, dx","Int[(a + b*x + c*x^2)^2/((d + e*x)*(f + g*x)),x]","\frac{x \left(-2 c e g (-a e g+b d g+b e f)+b^2 e^2 g^2+c^2 \left(d^2 g^2+d e f g+e^2 f^2\right)\right)}{e^3 g^3}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^4 (e f-d g)}-\frac{\log (f+g x) \left(a g^2-b f g+c f^2\right)^2}{g^4 (e f-d g)}-\frac{c x^2 (-2 b e g+c d g+c e f)}{2 e^2 g^2}+\frac{c^2 x^3}{3 e g}","\frac{x \left(-2 c e g (-a e g+b d g+b e f)+b^2 e^2 g^2+c^2 \left(d^2 g^2+d e f g+e^2 f^2\right)\right)}{e^3 g^3}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^4 (e f-d g)}-\frac{\log (f+g x) \left(a g^2-b f g+c f^2\right)^2}{g^4 (e f-d g)}-\frac{c x^2 (-2 b e g+c d g+c e f)}{2 e^2 g^2}+\frac{c^2 x^3}{3 e g}",1,"((b^2*e^2*g^2 - 2*c*e*g*(b*e*f + b*d*g - a*e*g) + c^2*(e^2*f^2 + d*e*f*g + d^2*g^2))*x)/(e^3*g^3) - (c*(c*e*f + c*d*g - 2*b*e*g)*x^2)/(2*e^2*g^2) + (c^2*x^3)/(3*e*g) + ((c*d^2 - b*d*e + a*e^2)^2*Log[d + e*x])/(e^4*(e*f - d*g)) - ((c*f^2 - b*f*g + a*g^2)^2*Log[f + g*x])/(g^4*(e*f - d*g))","A",2,1,27,0.03704,1,"{893}"
816,1,531,0,0.9882911,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x) (f+g x)} \, dx","Int[(a + b*x + c*x^2)^3/((d + e*x)*(f + g*x)),x]","-\frac{x \left(-3 c e^2 g^2 \left(a^2 e^2 g^2-2 a b e g (d g+e f)+b^2 \left(d^2 g^2+d e f g+e^2 f^2\right)\right)+b^2 e^3 g^3 (-3 a e g+b d g+b e f)-3 c^2 e g \left(a e g \left(d^2 g^2+d e f g+e^2 f^2\right)-b \left(d^2 e f g^2+d^3 g^3+d e^2 f^2 g+e^3 f^3\right)\right)+c^3 \left(-\left(d^2 e^2 f^2 g^2+d^3 e f g^3+d^4 g^4+d e^3 f^3 g+e^4 f^4\right)\right)\right)}{e^5 g^5}+\frac{c x^3 \left(-3 c e g (-a e g+b d g+b e f)+3 b^2 e^2 g^2+c^2 \left(d^2 g^2+d e f g+e^2 f^2\right)\right)}{3 e^3 g^3}+\frac{x^2 \left(-3 c^2 e g \left(a e g (d g+e f)-b \left(d^2 g^2+d e f g+e^2 f^2\right)\right)-3 b c e^2 g^2 (-2 a e g+b d g+b e f)+b^3 e^3 g^3+c^3 \left(-\left(d^2 e f g^2+d^3 g^3+d e^2 f^2 g+e^3 f^3\right)\right)\right)}{2 e^4 g^4}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^6 (e f-d g)}-\frac{\log (f+g x) \left(a g^2-b f g+c f^2\right)^3}{g^6 (e f-d g)}-\frac{c^2 x^4 (-3 b e g+c d g+c e f)}{4 e^2 g^2}+\frac{c^3 x^5}{5 e g}","-\frac{x \left(-3 c e^2 g^2 \left(a^2 e^2 g^2-2 a b e g (d g+e f)+b^2 \left(d^2 g^2+d e f g+e^2 f^2\right)\right)+b^2 e^3 g^3 (-3 a e g+b d g+b e f)-3 c^2 e g \left(a e g \left(d^2 g^2+d e f g+e^2 f^2\right)-b \left(d^2 e f g^2+d^3 g^3+d e^2 f^2 g+e^3 f^3\right)\right)+c^3 \left(-\left(d^2 e^2 f^2 g^2+d^3 e f g^3+d^4 g^4+d e^3 f^3 g+e^4 f^4\right)\right)\right)}{e^5 g^5}+\frac{c x^3 \left(-3 c e g (-a e g+b d g+b e f)+3 b^2 e^2 g^2+c^2 \left(d^2 g^2+d e f g+e^2 f^2\right)\right)}{3 e^3 g^3}+\frac{x^2 \left(-3 c^2 e g \left(a e g (d g+e f)-b \left(d^2 g^2+d e f g+e^2 f^2\right)\right)-3 b c e^2 g^2 (-2 a e g+b d g+b e f)+b^3 e^3 g^3+c^3 \left(-\left(d^2 e f g^2+d^3 g^3+d e^2 f^2 g+e^3 f^3\right)\right)\right)}{2 e^4 g^4}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^6 (e f-d g)}-\frac{\log (f+g x) \left(a g^2-b f g+c f^2\right)^3}{g^6 (e f-d g)}-\frac{c^2 x^4 (-3 b e g+c d g+c e f)}{4 e^2 g^2}+\frac{c^3 x^5}{5 e g}",1,"-(((b^2*e^3*g^3*(b*e*f + b*d*g - 3*a*e*g) - c^3*(e^4*f^4 + d*e^3*f^3*g + d^2*e^2*f^2*g^2 + d^3*e*f*g^3 + d^4*g^4) - 3*c*e^2*g^2*(a^2*e^2*g^2 - 2*a*b*e*g*(e*f + d*g) + b^2*(e^2*f^2 + d*e*f*g + d^2*g^2)) - 3*c^2*e*g*(a*e*g*(e^2*f^2 + d*e*f*g + d^2*g^2) - b*(e^3*f^3 + d*e^2*f^2*g + d^2*e*f*g^2 + d^3*g^3)))*x)/(e^5*g^5)) + ((b^3*e^3*g^3 - 3*b*c*e^2*g^2*(b*e*f + b*d*g - 2*a*e*g) - c^3*(e^3*f^3 + d*e^2*f^2*g + d^2*e*f*g^2 + d^3*g^3) - 3*c^2*e*g*(a*e*g*(e*f + d*g) - b*(e^2*f^2 + d*e*f*g + d^2*g^2)))*x^2)/(2*e^4*g^4) + (c*(3*b^2*e^2*g^2 - 3*c*e*g*(b*e*f + b*d*g - a*e*g) + c^2*(e^2*f^2 + d*e*f*g + d^2*g^2))*x^3)/(3*e^3*g^3) - (c^2*(c*e*f + c*d*g - 3*b*e*g)*x^4)/(4*e^2*g^2) + (c^3*x^5)/(5*e*g) + ((c*d^2 - b*d*e + a*e^2)^3*Log[d + e*x])/(e^6*(e*f - d*g)) - ((c*f^2 - b*f*g + a*g^2)^3*Log[f + g*x])/(g^6*(e*f - d*g))","A",2,1,27,0.03704,1,"{893}"
817,1,246,0,0.4678493,"\int \frac{1}{(d+e x) (f+g x) \left(a+b x+c x^2\right)} \, dx","Int[1/((d + e*x)*(f + g*x)*(a + b*x + c*x^2)),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right) \left(c f^2-g (b f-a g)\right)}-\frac{\log \left(a+b x+c x^2\right) (-b e g+c d g+c e f)}{2 \left(a e^2-b d e+c d^2\right) \left(c f^2-g (b f-a g)\right)}+\frac{e^2 \log (d+e x)}{(e f-d g) \left(a e^2-b d e+c d^2\right)}-\frac{g^2 \log (f+g x)}{(e f-d g) \left(a g^2-b f g+c f^2\right)}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right) \left(c f^2-g (b f-a g)\right)}-\frac{\log \left(a+b x+c x^2\right) (-b e g+c d g+c e f)}{2 \left(a e^2-b d e+c d^2\right) \left(c f^2-g (b f-a g)\right)}+\frac{e^2 \log (d+e x)}{(e f-d g) \left(a e^2-b d e+c d^2\right)}-\frac{g^2 \log (f+g x)}{(e f-d g) \left(a g^2-b f g+c f^2\right)}",1,"-(((2*c^2*d*f + b^2*e*g - c*(b*e*f + b*d*g + 2*a*e*g))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(c*f^2 - g*(b*f - a*g)))) + (e^2*Log[d + e*x])/((c*d^2 - b*d*e + a*e^2)*(e*f - d*g)) - (g^2*Log[f + g*x])/((e*f - d*g)*(c*f^2 - b*f*g + a*g^2)) - ((c*e*f + c*d*g - b*e*g)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)*(c*f^2 - g*(b*f - a*g)))","A",6,5,27,0.1852,1,"{893, 634, 618, 206, 628}"
818,1,644,0,2.0523217,"\int \frac{1}{(d+e x) (f+g x) \left(a+b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)*(f + g*x)*(a + b*x + c*x^2)^2),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 c e g \left(a^2 e^2 g^2+a b e g (d g+e f)-b^2 (d g+e f)^2\right)+b^2 e^2 g^2 (-2 a e g+b d g+b e f)-c^2 \left(4 a d e^2 f g^2-b \left(5 d^2 e f g^2+d^3 g^3+5 d e^2 f^2 g+e^3 f^3\right)\right)-2 c^3 d f \left(d^2 g^2+d e f g+e^2 f^2\right)\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2 \left(c f^2-g (b f-a g)\right)^2}-\frac{c x \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)+b c (c d f-3 a e g)+2 a c^2 (d g+e f)-b^2 c (d g+e f)+b^3 e g}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right) \left(c f^2-g (b f-a g)\right)}+\frac{2 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right) \left(c f^2-g (b f-a g)\right)}-\frac{\log \left(a+b x+c x^2\right) (-b e g+c d g+c e f) \left(e g (2 a e g-b (d g+e f))+c \left(d^2 g^2+e^2 f^2\right)\right)}{2 \left(a e^2-b d e+c d^2\right)^2 \left(c f^2-g (b f-a g)\right)^2}+\frac{e^4 \log (d+e x)}{(e f-d g) \left(a e^2-b d e+c d^2\right)^2}-\frac{g^4 \log (f+g x)}{(e f-d g) \left(a g^2-b f g+c f^2\right)^2}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 c e g \left(a^2 e^2 g^2+a b e g (d g+e f)-b^2 (d g+e f)^2\right)+b^2 e^2 g^2 (-2 a e g+b d g+b e f)-c^2 \left(4 a d e^2 f g^2-b \left(5 d^2 e f g^2+d^3 g^3+5 d e^2 f^2 g+e^3 f^3\right)\right)-2 c^3 d f \left(d^2 g^2+d e f g+e^2 f^2\right)\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2 \left(c f^2-g (b f-a g)\right)^2}-\frac{c x \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)+b c (c d f-3 a e g)+2 a c^2 (d g+e f)-b^2 c (d g+e f)+b^3 e g}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right) \left(c f^2-g (b f-a g)\right)}+\frac{2 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right) \left(c f^2-g (b f-a g)\right)}-\frac{\log \left(a+b x+c x^2\right) (-b e g+c d g+c e f) \left(e g (2 a e g-b (d g+e f))+c \left(d^2 g^2+e^2 f^2\right)\right)}{2 \left(a e^2-b d e+c d^2\right)^2 \left(c f^2-g (b f-a g)\right)^2}+\frac{e^4 \log (d+e x)}{(e f-d g) \left(a e^2-b d e+c d^2\right)^2}-\frac{g^4 \log (f+g x)}{(e f-d g) \left(a g^2-b f g+c f^2\right)^2}",1,"-((b^3*e*g - b^2*c*(e*f + d*g) + 2*a*c^2*(e*f + d*g) + b*c*(c*d*f - 3*a*e*g) + c*(2*c^2*d*f + b^2*e*g - c*(b*e*f + b*d*g + 2*a*e*g))*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(c*f^2 - g*(b*f - a*g))*(a + b*x + c*x^2))) + (2*c*(2*c^2*d*f + b^2*e*g - c*(b*e*f + b*d*g + 2*a*e*g))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)*(c*f^2 - g*(b*f - a*g))) + ((b^2*e^2*g^2*(b*e*f + b*d*g - 2*a*e*g) - 2*c^3*d*f*(e^2*f^2 + d*e*f*g + d^2*g^2) + 2*c*e*g*(a^2*e^2*g^2 + a*b*e*g*(e*f + d*g) - b^2*(e*f + d*g)^2) - c^2*(4*a*d*e^2*f*g^2 - b*(e^3*f^3 + 5*d*e^2*f^2*g + 5*d^2*e*f*g^2 + d^3*g^3)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2*(c*f^2 - g*(b*f - a*g))^2) + (e^4*Log[d + e*x])/((c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)) - (g^4*Log[f + g*x])/((e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^2) - ((c*e*f + c*d*g - b*e*g)*(c*(e^2*f^2 + d^2*g^2) + e*g*(2*a*e*g - b*(e*f + d*g)))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^2*(c*f^2 - g*(b*f - a*g))^2)","A",9,6,27,0.2222,1,"{893, 638, 618, 206, 634, 628}"
819,1,287,0,0.4950037,"\int \frac{(d+e x)^3 \left(a+b x+c x^2\right)}{\sqrt{f+g x}} \, dx","Int[((d + e*x)^3*(a + b*x + c*x^2))/Sqrt[f + g*x],x]","-\frac{2 e (f+g x)^{7/2} \left(e g (-a e g-3 b d g+4 b e f)-c \left(3 d^2 g^2-12 d e f g+10 e^2 f^2\right)\right)}{7 g^6}+\frac{2 (f+g x)^{5/2} (e f-d g) \left(3 e g (-a e g-b d g+2 b e f)-c \left(d^2 g^2-8 d e f g+10 e^2 f^2\right)\right)}{5 g^6}-\frac{2 \sqrt{f+g x} (e f-d g)^3 \left(a g^2-b f g+c f^2\right)}{g^6}+\frac{2 (f+g x)^{3/2} (e f-d g)^2 (c f (5 e f-2 d g)-g (-3 a e g-b d g+4 b e f))}{3 g^6}-\frac{2 e^2 (f+g x)^{9/2} (-b e g-3 c d g+5 c e f)}{9 g^6}+\frac{2 c e^3 (f+g x)^{11/2}}{11 g^6}","-\frac{2 e (f+g x)^{7/2} \left(e g (-a e g-3 b d g+4 b e f)-c \left(3 d^2 g^2-12 d e f g+10 e^2 f^2\right)\right)}{7 g^6}+\frac{2 (f+g x)^{5/2} (e f-d g) \left(3 e g (-a e g-b d g+2 b e f)-c \left(d^2 g^2-8 d e f g+10 e^2 f^2\right)\right)}{5 g^6}-\frac{2 \sqrt{f+g x} (e f-d g)^3 \left(a g^2-b f g+c f^2\right)}{g^6}+\frac{2 (f+g x)^{3/2} (e f-d g)^2 (c f (5 e f-2 d g)-g (-3 a e g-b d g+4 b e f))}{3 g^6}-\frac{2 e^2 (f+g x)^{9/2} (-b e g-3 c d g+5 c e f)}{9 g^6}+\frac{2 c e^3 (f+g x)^{11/2}}{11 g^6}",1,"(-2*(e*f - d*g)^3*(c*f^2 - b*f*g + a*g^2)*Sqrt[f + g*x])/g^6 + (2*(e*f - d*g)^2*(c*f*(5*e*f - 2*d*g) - g*(4*b*e*f - b*d*g - 3*a*e*g))*(f + g*x)^(3/2))/(3*g^6) + (2*(e*f - d*g)*(3*e*g*(2*b*e*f - b*d*g - a*e*g) - c*(10*e^2*f^2 - 8*d*e*f*g + d^2*g^2))*(f + g*x)^(5/2))/(5*g^6) - (2*e*(e*g*(4*b*e*f - 3*b*d*g - a*e*g) - c*(10*e^2*f^2 - 12*d*e*f*g + 3*d^2*g^2))*(f + g*x)^(7/2))/(7*g^6) - (2*e^2*(5*c*e*f - 3*c*d*g - b*e*g)*(f + g*x)^(9/2))/(9*g^6) + (2*c*e^3*(f + g*x)^(11/2))/(11*g^6)","A",3,2,27,0.07407,1,"{897, 1153}"
820,1,212,0,0.3394922,"\int \frac{(d+e x)^2 \left(a+b x+c x^2\right)}{\sqrt{f+g x}} \, dx","Int[((d + e*x)^2*(a + b*x + c*x^2))/Sqrt[f + g*x],x]","-\frac{2 (f+g x)^{5/2} \left(e g (-a e g-2 b d g+3 b e f)-c \left(d^2 g^2-6 d e f g+6 e^2 f^2\right)\right)}{5 g^5}+\frac{2 \sqrt{f+g x} (e f-d g)^2 \left(a g^2-b f g+c f^2\right)}{g^5}-\frac{2 (f+g x)^{3/2} (e f-d g) (2 c f (2 e f-d g)-g (-2 a e g-b d g+3 b e f))}{3 g^5}-\frac{2 e (f+g x)^{7/2} (-b e g-2 c d g+4 c e f)}{7 g^5}+\frac{2 c e^2 (f+g x)^{9/2}}{9 g^5}","-\frac{2 (f+g x)^{5/2} \left(e g (-a e g-2 b d g+3 b e f)-c \left(d^2 g^2-6 d e f g+6 e^2 f^2\right)\right)}{5 g^5}+\frac{2 \sqrt{f+g x} (e f-d g)^2 \left(a g^2-b f g+c f^2\right)}{g^5}-\frac{2 (f+g x)^{3/2} (e f-d g) (2 c f (2 e f-d g)-g (-2 a e g-b d g+3 b e f))}{3 g^5}-\frac{2 e (f+g x)^{7/2} (-b e g-2 c d g+4 c e f)}{7 g^5}+\frac{2 c e^2 (f+g x)^{9/2}}{9 g^5}",1,"(2*(e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)*Sqrt[f + g*x])/g^5 - (2*(e*f - d*g)*(2*c*f*(2*e*f - d*g) - g*(3*b*e*f - b*d*g - 2*a*e*g))*(f + g*x)^(3/2))/(3*g^5) - (2*(e*g*(3*b*e*f - 2*b*d*g - a*e*g) - c*(6*e^2*f^2 - 6*d*e*f*g + d^2*g^2))*(f + g*x)^(5/2))/(5*g^5) - (2*e*(4*c*e*f - 2*c*d*g - b*e*g)*(f + g*x)^(7/2))/(7*g^5) + (2*c*e^2*(f + g*x)^(9/2))/(9*g^5)","A",3,2,27,0.07407,1,"{897, 1153}"
821,1,137,0,0.109117,"\int \frac{(d+e x) \left(a+b x+c x^2\right)}{\sqrt{f+g x}} \, dx","Int[((d + e*x)*(a + b*x + c*x^2))/Sqrt[f + g*x],x]","-\frac{2 \sqrt{f+g x} (e f-d g) \left(a g^2-b f g+c f^2\right)}{g^4}+\frac{2 (f+g x)^{3/2} (c f (3 e f-2 d g)-g (-a e g-b d g+2 b e f))}{3 g^4}-\frac{2 (f+g x)^{5/2} (-b e g-c d g+3 c e f)}{5 g^4}+\frac{2 c e (f+g x)^{7/2}}{7 g^4}","-\frac{2 \sqrt{f+g x} (e f-d g) \left(a g^2-b f g+c f^2\right)}{g^4}+\frac{2 (f+g x)^{3/2} (c f (3 e f-2 d g)-g (-a e g-b d g+2 b e f))}{3 g^4}-\frac{2 (f+g x)^{5/2} (-b e g-c d g+3 c e f)}{5 g^4}+\frac{2 c e (f+g x)^{7/2}}{7 g^4}",1,"(-2*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*Sqrt[f + g*x])/g^4 + (2*(c*f*(3*e*f - 2*d*g) - g*(2*b*e*f - b*d*g - a*e*g))*(f + g*x)^(3/2))/(3*g^4) - (2*(3*c*e*f - c*d*g - b*e*g)*(f + g*x)^(5/2))/(5*g^4) + (2*c*e*(f + g*x)^(7/2))/(7*g^4)","A",2,1,25,0.04000,1,"{771}"
822,1,73,0,0.042033,"\int \frac{a+b x+c x^2}{\sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/Sqrt[f + g*x],x]","\frac{2 \sqrt{f+g x} \left(a g^2-b f g+c f^2\right)}{g^3}-\frac{2 (f+g x)^{3/2} (2 c f-b g)}{3 g^3}+\frac{2 c (f+g x)^{5/2}}{5 g^3}","\frac{2 \sqrt{f+g x} \left(a g^2-b f g+c f^2\right)}{g^3}-\frac{2 (f+g x)^{3/2} (2 c f-b g)}{3 g^3}+\frac{2 c (f+g x)^{5/2}}{5 g^3}",1,"(2*(c*f^2 - b*f*g + a*g^2)*Sqrt[f + g*x])/g^3 - (2*(2*c*f - b*g)*(f + g*x)^(3/2))/(3*g^3) + (2*c*(f + g*x)^(5/2))/(5*g^3)","A",2,1,20,0.05000,1,"{698}"
823,1,116,0,0.1683509,"\int \frac{a+b x+c x^2}{(d+e x) \sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)*Sqrt[f + g*x]),x]","-\frac{2 \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{5/2} \sqrt{e f-d g}}+\frac{2 \sqrt{f+g x} (b e g-c (d g+e f))}{e^2 g^2}+\frac{2 c (f+g x)^{3/2}}{3 e g^2}","-\frac{2 \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{5/2} \sqrt{e f-d g}}+\frac{2 \sqrt{f+g x} (b e g-c (d g+e f))}{e^2 g^2}+\frac{2 c (f+g x)^{3/2}}{3 e g^2}",1,"(2*(b*e*g - c*(e*f + d*g))*Sqrt[f + g*x])/(e^2*g^2) + (2*c*(f + g*x)^(3/2))/(3*e*g^2) - (2*(c*d^2 - b*d*e + a*e^2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(e^(5/2)*Sqrt[e*f - d*g])","A",4,3,27,0.1111,1,"{897, 1153, 208}"
824,1,140,0,0.2900206,"\int \frac{a+b x+c x^2}{(d+e x)^2 \sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)^2*Sqrt[f + g*x]),x]","-\frac{\sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{(d+e x) (e f-d g)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) (c d (4 e f-3 d g)-e (-a e g-b d g+2 b e f))}{e^{5/2} (e f-d g)^{3/2}}+\frac{2 c \sqrt{f+g x}}{e^2 g}","-\frac{\sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{(d+e x) (e f-d g)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) (c d (4 e f-3 d g)-e (-a e g-b d g+2 b e f))}{e^{5/2} (e f-d g)^{3/2}}+\frac{2 c \sqrt{f+g x}}{e^2 g}",1,"(2*c*Sqrt[f + g*x])/(e^2*g) - ((a + (d*(c*d - b*e))/e^2)*Sqrt[f + g*x])/((e*f - d*g)*(d + e*x)) + ((c*d*(4*e*f - 3*d*g) - e*(2*b*e*f - b*d*g - a*e*g))*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(e^(5/2)*(e*f - d*g)^(3/2))","A",4,4,27,0.1481,1,"{897, 1157, 388, 208}"
825,1,206,0,0.3860824,"\int \frac{a+b x+c x^2}{(d+e x)^3 \sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)^3*Sqrt[f + g*x]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(e g (-3 a e g-b d g+4 b e f)-c \left(3 d^2 g^2-8 d e f g+8 e^2 f^2\right)\right)}{4 e^{5/2} (e f-d g)^{5/2}}-\frac{\sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{2 (d+e x)^2 (e f-d g)}+\frac{\sqrt{f+g x} (c d (8 e f-5 d g)-e (-3 a e g-b d g+4 b e f))}{4 e^2 (d+e x) (e f-d g)^2}","\frac{\tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(e g (-3 a e g-b d g+4 b e f)-c \left(3 d^2 g^2-8 d e f g+8 e^2 f^2\right)\right)}{4 e^{5/2} (e f-d g)^{5/2}}-\frac{\sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{2 (d+e x)^2 (e f-d g)}+\frac{\sqrt{f+g x} (c d (8 e f-5 d g)-e (-3 a e g-b d g+4 b e f))}{4 e^2 (d+e x) (e f-d g)^2}",1,"-((a + (d*(c*d - b*e))/e^2)*Sqrt[f + g*x])/(2*(e*f - d*g)*(d + e*x)^2) + ((c*d*(8*e*f - 5*d*g) - e*(4*b*e*f - b*d*g - 3*a*e*g))*Sqrt[f + g*x])/(4*e^2*(e*f - d*g)^2*(d + e*x)) + ((e*g*(4*b*e*f - b*d*g - 3*a*e*g) - c*(8*e^2*f^2 - 8*d*e*f*g + 3*d^2*g^2))*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(4*e^(5/2)*(e*f - d*g)^(5/2))","A",4,4,27,0.1481,1,"{897, 1157, 385, 208}"
826,1,285,0,0.4053129,"\int \frac{(d+e x)^3 \left(a+b x+c x^2\right)}{(f+g x)^{3/2}} \, dx","Int[((d + e*x)^3*(a + b*x + c*x^2))/(f + g*x)^(3/2),x]","-\frac{2 e (f+g x)^{5/2} \left(e g (-a e g-3 b d g+4 b e f)-c \left(3 d^2 g^2-12 d e f g+10 e^2 f^2\right)\right)}{5 g^6}+\frac{2 (f+g x)^{3/2} (e f-d g) \left(3 e g (-a e g-b d g+2 b e f)-c \left(d^2 g^2-8 d e f g+10 e^2 f^2\right)\right)}{3 g^6}+\frac{2 (e f-d g)^3 \left(a g^2-b f g+c f^2\right)}{g^6 \sqrt{f+g x}}+\frac{2 \sqrt{f+g x} (e f-d g)^2 (c f (5 e f-2 d g)-g (-3 a e g-b d g+4 b e f))}{g^6}-\frac{2 e^2 (f+g x)^{7/2} (-b e g-3 c d g+5 c e f)}{7 g^6}+\frac{2 c e^3 (f+g x)^{9/2}}{9 g^6}","-\frac{2 e (f+g x)^{5/2} \left(e g (-a e g-3 b d g+4 b e f)-c \left(3 d^2 g^2-12 d e f g+10 e^2 f^2\right)\right)}{5 g^6}+\frac{2 (f+g x)^{3/2} (e f-d g) \left(3 e g (-a e g-b d g+2 b e f)-c \left(d^2 g^2-8 d e f g+10 e^2 f^2\right)\right)}{3 g^6}+\frac{2 (e f-d g)^3 \left(a g^2-b f g+c f^2\right)}{g^6 \sqrt{f+g x}}+\frac{2 \sqrt{f+g x} (e f-d g)^2 (c f (5 e f-2 d g)-g (-3 a e g-b d g+4 b e f))}{g^6}-\frac{2 e^2 (f+g x)^{7/2} (-b e g-3 c d g+5 c e f)}{7 g^6}+\frac{2 c e^3 (f+g x)^{9/2}}{9 g^6}",1,"(2*(e*f - d*g)^3*(c*f^2 - b*f*g + a*g^2))/(g^6*Sqrt[f + g*x]) + (2*(e*f - d*g)^2*(c*f*(5*e*f - 2*d*g) - g*(4*b*e*f - b*d*g - 3*a*e*g))*Sqrt[f + g*x])/g^6 + (2*(e*f - d*g)*(3*e*g*(2*b*e*f - b*d*g - a*e*g) - c*(10*e^2*f^2 - 8*d*e*f*g + d^2*g^2))*(f + g*x)^(3/2))/(3*g^6) - (2*e*(e*g*(4*b*e*f - 3*b*d*g - a*e*g) - c*(10*e^2*f^2 - 12*d*e*f*g + 3*d^2*g^2))*(f + g*x)^(5/2))/(5*g^6) - (2*e^2*(5*c*e*f - 3*c*d*g - b*e*g)*(f + g*x)^(7/2))/(7*g^6) + (2*c*e^3*(f + g*x)^(9/2))/(9*g^6)","A",3,2,27,0.07407,1,"{897, 1261}"
827,1,210,0,0.2887642,"\int \frac{(d+e x)^2 \left(a+b x+c x^2\right)}{(f+g x)^{3/2}} \, dx","Int[((d + e*x)^2*(a + b*x + c*x^2))/(f + g*x)^(3/2),x]","-\frac{2 (f+g x)^{3/2} \left(e g (-a e g-2 b d g+3 b e f)-c \left(d^2 g^2-6 d e f g+6 e^2 f^2\right)\right)}{3 g^5}-\frac{2 (e f-d g)^2 \left(a g^2-b f g+c f^2\right)}{g^5 \sqrt{f+g x}}-\frac{2 \sqrt{f+g x} (e f-d g) (2 c f (2 e f-d g)-g (-2 a e g-b d g+3 b e f))}{g^5}-\frac{2 e (f+g x)^{5/2} (-b e g-2 c d g+4 c e f)}{5 g^5}+\frac{2 c e^2 (f+g x)^{7/2}}{7 g^5}","-\frac{2 (f+g x)^{3/2} \left(e g (-a e g-2 b d g+3 b e f)-c \left(d^2 g^2-6 d e f g+6 e^2 f^2\right)\right)}{3 g^5}-\frac{2 (e f-d g)^2 \left(a g^2-b f g+c f^2\right)}{g^5 \sqrt{f+g x}}-\frac{2 \sqrt{f+g x} (e f-d g) (2 c f (2 e f-d g)-g (-2 a e g-b d g+3 b e f))}{g^5}-\frac{2 e (f+g x)^{5/2} (-b e g-2 c d g+4 c e f)}{5 g^5}+\frac{2 c e^2 (f+g x)^{7/2}}{7 g^5}",1,"(-2*(e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2))/(g^5*Sqrt[f + g*x]) - (2*(e*f - d*g)*(2*c*f*(2*e*f - d*g) - g*(3*b*e*f - b*d*g - 2*a*e*g))*Sqrt[f + g*x])/g^5 - (2*(e*g*(3*b*e*f - 2*b*d*g - a*e*g) - c*(6*e^2*f^2 - 6*d*e*f*g + d^2*g^2))*(f + g*x)^(3/2))/(3*g^5) - (2*e*(4*c*e*f - 2*c*d*g - b*e*g)*(f + g*x)^(5/2))/(5*g^5) + (2*c*e^2*(f + g*x)^(7/2))/(7*g^5)","A",3,2,27,0.07407,1,"{897, 1261}"
828,1,135,0,0.098059,"\int \frac{(d+e x) \left(a+b x+c x^2\right)}{(f+g x)^{3/2}} \, dx","Int[((d + e*x)*(a + b*x + c*x^2))/(f + g*x)^(3/2),x]","\frac{2 (e f-d g) \left(a g^2-b f g+c f^2\right)}{g^4 \sqrt{f+g x}}+\frac{2 \sqrt{f+g x} (c f (3 e f-2 d g)-g (-a e g-b d g+2 b e f))}{g^4}-\frac{2 (f+g x)^{3/2} (-b e g-c d g+3 c e f)}{3 g^4}+\frac{2 c e (f+g x)^{5/2}}{5 g^4}","\frac{2 (e f-d g) \left(a g^2-b f g+c f^2\right)}{g^4 \sqrt{f+g x}}+\frac{2 \sqrt{f+g x} (c f (3 e f-2 d g)-g (-a e g-b d g+2 b e f))}{g^4}-\frac{2 (f+g x)^{3/2} (-b e g-c d g+3 c e f)}{3 g^4}+\frac{2 c e (f+g x)^{5/2}}{5 g^4}",1,"(2*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2))/(g^4*Sqrt[f + g*x]) + (2*(c*f*(3*e*f - 2*d*g) - g*(2*b*e*f - b*d*g - a*e*g))*Sqrt[f + g*x])/g^4 - (2*(3*c*e*f - c*d*g - b*e*g)*(f + g*x)^(3/2))/(3*g^4) + (2*c*e*(f + g*x)^(5/2))/(5*g^4)","A",2,1,25,0.04000,1,"{771}"
829,1,71,0,0.0422612,"\int \frac{a+b x+c x^2}{(f+g x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)/(f + g*x)^(3/2),x]","-\frac{2 \left(a g^2-b f g+c f^2\right)}{g^3 \sqrt{f+g x}}-\frac{2 \sqrt{f+g x} (2 c f-b g)}{g^3}+\frac{2 c (f+g x)^{3/2}}{3 g^3}","-\frac{2 \left(a g^2-b f g+c f^2\right)}{g^3 \sqrt{f+g x}}-\frac{2 \sqrt{f+g x} (2 c f-b g)}{g^3}+\frac{2 c (f+g x)^{3/2}}{3 g^3}",1,"(-2*(c*f^2 - b*f*g + a*g^2))/(g^3*Sqrt[f + g*x]) - (2*(2*c*f - b*g)*Sqrt[f + g*x])/g^3 + (2*c*(f + g*x)^(3/2))/(3*g^3)","A",2,1,20,0.05000,1,"{698}"
830,1,122,0,0.2210453,"\int \frac{a+b x+c x^2}{(d+e x) (f+g x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)*(f + g*x)^(3/2)),x]","-\frac{2 \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2} (e f-d g)^{3/2}}+\frac{2 \left(a g^2-b f g+c f^2\right)}{g^2 \sqrt{f+g x} (e f-d g)}+\frac{2 c \sqrt{f+g x}}{e g^2}","-\frac{2 \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right)}{e^{3/2} (e f-d g)^{3/2}}+\frac{2 \left(a g^2-b f g+c f^2\right)}{g^2 \sqrt{f+g x} (e f-d g)}+\frac{2 c \sqrt{f+g x}}{e g^2}",1,"(2*(c*f^2 - b*f*g + a*g^2))/(g^2*(e*f - d*g)*Sqrt[f + g*x]) + (2*c*Sqrt[f + g*x])/(e*g^2) - (2*(c*d^2 - b*d*e + a*e^2)*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(e^(3/2)*(e*f - d*g)^(3/2))","A",4,3,27,0.1111,1,"{897, 1261, 208}"
831,1,165,0,0.3667585,"\int \frac{a+b x+c x^2}{(d+e x)^2 (f+g x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)^2*(f + g*x)^(3/2)),x]","-\frac{\sqrt{f+g x} \left(a e^2-b d e+c d^2\right)}{e (d+e x) (e f-d g)^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) (c d (4 e f-d g)-e (-3 a e g+b d g+2 b e f))}{e^{3/2} (e f-d g)^{5/2}}-\frac{2 \left(a g^2-b f g+c f^2\right)}{g \sqrt{f+g x} (e f-d g)^2}","-\frac{\sqrt{f+g x} \left(a e^2-b d e+c d^2\right)}{e (d+e x) (e f-d g)^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) (c d (4 e f-d g)-e (-3 a e g+b d g+2 b e f))}{e^{3/2} (e f-d g)^{5/2}}-\frac{2 \left(a g^2-b f g+c f^2\right)}{g \sqrt{f+g x} (e f-d g)^2}",1,"(-2*(c*f^2 - b*f*g + a*g^2))/(g*(e*f - d*g)^2*Sqrt[f + g*x]) - ((c*d^2 - b*d*e + a*e^2)*Sqrt[f + g*x])/(e*(e*f - d*g)^2*(d + e*x)) + ((c*d*(4*e*f - d*g) - e*(2*b*e*f + b*d*g - 3*a*e*g))*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(e^(3/2)*(e*f - d*g)^(5/2))","A",4,4,27,0.1481,1,"{897, 1259, 453, 208}"
832,1,248,0,0.628685,"\int \frac{a+b x+c x^2}{(d+e x)^3 (f+g x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)^3*(f + g*x)^(3/2)),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(3 e g (5 a e g-b (d g+4 e f))+c \left(-d^2 g^2+8 d e f g+8 e^2 f^2\right)\right)}{4 e^{3/2} (e f-d g)^{7/2}}-\frac{\sqrt{f+g x} \left(a e^2-b d e+c d^2\right)}{2 e (d+e x)^2 (e f-d g)^2}+\frac{2 \left(a g^2-b f g+c f^2\right)}{\sqrt{f+g x} (e f-d g)^3}+\frac{\sqrt{f+g x} (c d (8 e f-d g)-e (-7 a e g+3 b d g+4 b e f))}{4 e (d+e x) (e f-d g)^3}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{f+g x}}{\sqrt{e f-d g}}\right) \left(3 e g (5 a e g-b (d g+4 e f))+c \left(-d^2 g^2+8 d e f g+8 e^2 f^2\right)\right)}{4 e^{3/2} (e f-d g)^{7/2}}-\frac{\sqrt{f+g x} \left(a e^2-b d e+c d^2\right)}{2 e (d+e x)^2 (e f-d g)^2}+\frac{2 \left(a g^2-b f g+c f^2\right)}{\sqrt{f+g x} (e f-d g)^3}+\frac{\sqrt{f+g x} (c d (8 e f-d g)-e (-7 a e g+3 b d g+4 b e f))}{4 e (d+e x) (e f-d g)^3}",1,"(2*(c*f^2 - b*f*g + a*g^2))/((e*f - d*g)^3*Sqrt[f + g*x]) - ((c*d^2 - b*d*e + a*e^2)*Sqrt[f + g*x])/(2*e*(e*f - d*g)^2*(d + e*x)^2) + ((c*d*(8*e*f - d*g) - e*(4*b*e*f + 3*b*d*g - 7*a*e*g))*Sqrt[f + g*x])/(4*e*(e*f - d*g)^3*(d + e*x)) - ((c*(8*e^2*f^2 + 8*d*e*f*g - d^2*g^2) + 3*e*g*(5*a*e*g - b*(4*e*f + d*g)))*ArcTanh[(Sqrt[e]*Sqrt[f + g*x])/Sqrt[e*f - d*g]])/(4*e^(3/2)*(e*f - d*g)^(7/2))","A",5,5,27,0.1852,1,"{897, 1259, 456, 453, 208}"
833,1,191,0,0.1405563,"\int \frac{\sqrt{-1+x} \sqrt{1+x}}{1+x-x^2} \, dx","Int[(Sqrt[-1 + x]*Sqrt[1 + x])/(1 + x - x^2),x]","\frac{\sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \sqrt{x-1} \sqrt{x+1} \tan ^{-1}\left(\frac{2-\left(1-\sqrt{5}\right) x}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)}{\sqrt{x^2-1}}-\frac{\sqrt{x-1} \sqrt{x+1} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)}{\sqrt{x^2-1}}-\frac{\sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \sqrt{x-1} \sqrt{x+1} \tanh ^{-1}\left(\frac{2-\left(1+\sqrt{5}\right) x}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)}{\sqrt{x^2-1}}","\sqrt{\frac{2}{5} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{\sqrt{5}-2} \sqrt{x-1}}\right)-\cosh ^{-1}(x)+\sqrt{\frac{2}{5} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2+\sqrt{5}} \sqrt{x-1}}\right)",1,"(Sqrt[(-1 + Sqrt[5])/10]*Sqrt[-1 + x]*Sqrt[1 + x]*ArcTan[(2 - (1 - Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])])/Sqrt[-1 + x^2] - (Sqrt[-1 + x]*Sqrt[1 + x]*ArcTanh[x/Sqrt[-1 + x^2]])/Sqrt[-1 + x^2] - (Sqrt[(1 + Sqrt[5])/10]*Sqrt[-1 + x]*Sqrt[1 + x]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])])/Sqrt[-1 + x^2]","B",9,7,25,0.2800,1,"{901, 991, 217, 206, 1034, 725, 204}"
834,1,164,0,0.179186,"\int \frac{a+b x+c x^2}{\sqrt{d+e x} \sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/(Sqrt[d + e*x]*Sqrt[f + g*x]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right) \left(4 e g (2 a e g-b (d g+e f))+c \left(3 d^2 g^2+2 d e f g+3 e^2 f^2\right)\right)}{4 e^{5/2} g^{5/2}}-\frac{\sqrt{d+e x} \sqrt{f+g x} (-4 b e g+5 c d g+3 c e f)}{4 e^2 g^2}+\frac{c (d+e x)^{3/2} \sqrt{f+g x}}{2 e^2 g}","\frac{\tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right) \left(4 e g (2 a e g-b (d g+e f))+c \left(3 d^2 g^2+2 d e f g+3 e^2 f^2\right)\right)}{4 e^{5/2} g^{5/2}}-\frac{\sqrt{d+e x} \sqrt{f+g x} (-4 b e g+5 c d g+3 c e f)}{4 e^2 g^2}+\frac{c (d+e x)^{3/2} \sqrt{f+g x}}{2 e^2 g}",1,"-((3*c*e*f + 5*c*d*g - 4*b*e*g)*Sqrt[d + e*x]*Sqrt[f + g*x])/(4*e^2*g^2) + (c*(d + e*x)^(3/2)*Sqrt[f + g*x])/(2*e^2*g) + ((c*(3*e^2*f^2 + 2*d*e*f*g + 3*d^2*g^2) + 4*e*g*(2*a*e*g - b*(e*f + d*g)))*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(4*e^(5/2)*g^(5/2))","A",5,5,29,0.1724,1,"{951, 80, 63, 217, 206}"
835,1,333,0,0.3534877,"\int \frac{(d+e x)^{3/2} \left(a+b x+c x^2\right)}{\sqrt{f+g x}} \, dx","Int[((d + e*x)^(3/2)*(a + b*x + c*x^2))/Sqrt[f + g*x],x]","\frac{(d+e x)^{3/2} \sqrt{f+g x} \left(8 e g (6 a e g-b (d g+5 e f))+c \left(3 d^2 g^2+10 d e f g+35 e^2 f^2\right)\right)}{96 e^2 g^3}-\frac{\sqrt{d+e x} \sqrt{f+g x} (e f-d g) \left(8 e g (6 a e g-b (d g+5 e f))+c \left(3 d^2 g^2+10 d e f g+35 e^2 f^2\right)\right)}{64 e^2 g^4}+\frac{(e f-d g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right) \left(8 e g (6 a e g-b (d g+5 e f))+c \left(3 d^2 g^2+10 d e f g+35 e^2 f^2\right)\right)}{64 e^{5/2} g^{9/2}}-\frac{(d+e x)^{5/2} \sqrt{f+g x} (-8 b e g+9 c d g+7 c e f)}{24 e^2 g^2}+\frac{c (d+e x)^{7/2} \sqrt{f+g x}}{4 e^2 g}","\frac{(d+e x)^{3/2} \sqrt{f+g x} \left(8 e g (6 a e g-b (d g+5 e f))+c \left(3 d^2 g^2+10 d e f g+35 e^2 f^2\right)\right)}{96 e^2 g^3}-\frac{\sqrt{d+e x} \sqrt{f+g x} (e f-d g) \left(8 e g (6 a e g-b (d g+5 e f))+c \left(3 d^2 g^2+10 d e f g+35 e^2 f^2\right)\right)}{64 e^2 g^4}+\frac{(e f-d g)^2 \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right) \left(8 e g (6 a e g-b (d g+5 e f))+c \left(3 d^2 g^2+10 d e f g+35 e^2 f^2\right)\right)}{64 e^{5/2} g^{9/2}}-\frac{(d+e x)^{5/2} \sqrt{f+g x} (-8 b e g+9 c d g+7 c e f)}{24 e^2 g^2}+\frac{c (d+e x)^{7/2} \sqrt{f+g x}}{4 e^2 g}",1,"-((e*f - d*g)*(c*(35*e^2*f^2 + 10*d*e*f*g + 3*d^2*g^2) + 8*e*g*(6*a*e*g - b*(5*e*f + d*g)))*Sqrt[d + e*x]*Sqrt[f + g*x])/(64*e^2*g^4) + ((c*(35*e^2*f^2 + 10*d*e*f*g + 3*d^2*g^2) + 8*e*g*(6*a*e*g - b*(5*e*f + d*g)))*(d + e*x)^(3/2)*Sqrt[f + g*x])/(96*e^2*g^3) - ((7*c*e*f + 9*c*d*g - 8*b*e*g)*(d + e*x)^(5/2)*Sqrt[f + g*x])/(24*e^2*g^2) + (c*(d + e*x)^(7/2)*Sqrt[f + g*x])/(4*e^2*g) + ((e*f - d*g)^2*(c*(35*e^2*f^2 + 10*d*e*f*g + 3*d^2*g^2) + 8*e*g*(6*a*e*g - b*(5*e*f + d*g)))*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(64*e^(5/2)*g^(9/2))","A",7,6,29,0.2069,1,"{951, 80, 50, 63, 217, 206}"
836,1,246,0,0.2555053,"\int \frac{\sqrt{d+e x} \left(a+b x+c x^2\right)}{\sqrt{f+g x}} \, dx","Int[(Sqrt[d + e*x]*(a + b*x + c*x^2))/Sqrt[f + g*x],x]","\frac{\sqrt{d+e x} \sqrt{f+g x} \left(2 e g (4 a e g-b (d g+3 e f))+c \left(d^2 g^2+2 d e f g+5 e^2 f^2\right)\right)}{8 e^2 g^3}-\frac{(e f-d g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right) \left(2 e g (4 a e g-b (d g+3 e f))+c \left(d^2 g^2+2 d e f g+5 e^2 f^2\right)\right)}{8 e^{5/2} g^{7/2}}-\frac{(d+e x)^{3/2} \sqrt{f+g x} (-6 b e g+7 c d g+5 c e f)}{12 e^2 g^2}+\frac{c (d+e x)^{5/2} \sqrt{f+g x}}{3 e^2 g}","\frac{\sqrt{d+e x} \sqrt{f+g x} \left(2 e g (4 a e g-b (d g+3 e f))+c \left(d^2 g^2+2 d e f g+5 e^2 f^2\right)\right)}{8 e^2 g^3}-\frac{(e f-d g) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right) \left(2 e g (4 a e g-b (d g+3 e f))+c \left(d^2 g^2+2 d e f g+5 e^2 f^2\right)\right)}{8 e^{5/2} g^{7/2}}-\frac{(d+e x)^{3/2} \sqrt{f+g x} (-6 b e g+7 c d g+5 c e f)}{12 e^2 g^2}+\frac{c (d+e x)^{5/2} \sqrt{f+g x}}{3 e^2 g}",1,"((c*(5*e^2*f^2 + 2*d*e*f*g + d^2*g^2) + 2*e*g*(4*a*e*g - b*(3*e*f + d*g)))*Sqrt[d + e*x]*Sqrt[f + g*x])/(8*e^2*g^3) - ((5*c*e*f + 7*c*d*g - 6*b*e*g)*(d + e*x)^(3/2)*Sqrt[f + g*x])/(12*e^2*g^2) + (c*(d + e*x)^(5/2)*Sqrt[f + g*x])/(3*e^2*g) - ((e*f - d*g)*(c*(5*e^2*f^2 + 2*d*e*f*g + d^2*g^2) + 2*e*g*(4*a*e*g - b*(3*e*f + d*g)))*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(8*e^(5/2)*g^(7/2))","A",6,6,29,0.2069,1,"{951, 80, 50, 63, 217, 206}"
837,1,164,0,0.1427975,"\int \frac{a+b x+c x^2}{\sqrt{d+e x} \sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/(Sqrt[d + e*x]*Sqrt[f + g*x]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right) \left(4 e g (2 a e g-b (d g+e f))+c \left(3 d^2 g^2+2 d e f g+3 e^2 f^2\right)\right)}{4 e^{5/2} g^{5/2}}-\frac{\sqrt{d+e x} \sqrt{f+g x} (-4 b e g+5 c d g+3 c e f)}{4 e^2 g^2}+\frac{c (d+e x)^{3/2} \sqrt{f+g x}}{2 e^2 g}","\frac{\tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right) \left(4 e g (2 a e g-b (d g+e f))+c \left(3 d^2 g^2+2 d e f g+3 e^2 f^2\right)\right)}{4 e^{5/2} g^{5/2}}-\frac{\sqrt{d+e x} \sqrt{f+g x} (-4 b e g+5 c d g+3 c e f)}{4 e^2 g^2}+\frac{c (d+e x)^{3/2} \sqrt{f+g x}}{2 e^2 g}",1,"-((3*c*e*f + 5*c*d*g - 4*b*e*g)*Sqrt[d + e*x]*Sqrt[f + g*x])/(4*e^2*g^2) + (c*(d + e*x)^(3/2)*Sqrt[f + g*x])/(2*e^2*g) + ((c*(3*e^2*f^2 + 2*d*e*f*g + 3*d^2*g^2) + 4*e*g*(2*a*e*g - b*(e*f + d*g)))*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(4*e^(5/2)*g^(5/2))","A",5,5,29,0.1724,1,"{951, 80, 63, 217, 206}"
838,1,129,0,0.1348986,"\int \frac{a+b x+c x^2}{(d+e x)^{3/2} \sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)^(3/2)*Sqrt[f + g*x]),x]","-\frac{2 \sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{\sqrt{d+e x} (e f-d g)}-\frac{(-2 b e g+3 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{e^{5/2} g^{3/2}}+\frac{c \sqrt{d+e x} \sqrt{f+g x}}{e^2 g}","-\frac{2 \sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{\sqrt{d+e x} (e f-d g)}-\frac{(-2 b e g+3 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{e^{5/2} g^{3/2}}+\frac{c \sqrt{d+e x} \sqrt{f+g x}}{e^2 g}",1,"(-2*(a + (d*(c*d - b*e))/e^2)*Sqrt[f + g*x])/((e*f - d*g)*Sqrt[d + e*x]) + (c*Sqrt[d + e*x]*Sqrt[f + g*x])/(e^2*g) - ((c*e*f + 3*c*d*g - 2*b*e*g)*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(e^(5/2)*g^(3/2))","A",5,5,29,0.1724,1,"{949, 80, 63, 217, 206}"
839,1,160,0,0.1804853,"\int \frac{a+b x+c x^2}{(d+e x)^{5/2} \sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)^(5/2)*Sqrt[f + g*x]),x]","\frac{2 \sqrt{f+g x} \left(c \left(6 d e f-4 d^2 g\right)-e (-2 a e g-b d g+3 b e f)\right)}{3 e^2 \sqrt{d+e x} (e f-d g)^2}-\frac{2 \sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{3 (d+e x)^{3/2} (e f-d g)}+\frac{2 c \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{e^{5/2} \sqrt{g}}","\frac{2 \sqrt{f+g x} \left(c \left(6 d e f-4 d^2 g\right)-e (-2 a e g-b d g+3 b e f)\right)}{3 e^2 \sqrt{d+e x} (e f-d g)^2}-\frac{2 \sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{3 (d+e x)^{3/2} (e f-d g)}+\frac{2 c \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{e^{5/2} \sqrt{g}}",1,"(-2*(a + (d*(c*d - b*e))/e^2)*Sqrt[f + g*x])/(3*(e*f - d*g)*(d + e*x)^(3/2)) + (2*(c*(6*d*e*f - 4*d^2*g) - e*(3*b*e*f - b*d*g - 2*a*e*g))*Sqrt[f + g*x])/(3*e^2*(e*f - d*g)^2*Sqrt[d + e*x]) + (2*c*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(e^(5/2)*Sqrt[g])","A",5,5,29,0.1724,1,"{949, 78, 63, 217, 206}"
840,1,198,0,0.2120914,"\int \frac{a+b x+c x^2}{(d+e x)^{7/2} \sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)^(7/2)*Sqrt[f + g*x]),x]","\frac{2 \sqrt{f+g x} \left(2 e g (-4 a e g-b d g+5 b e f)-c \left(3 d^2 g^2-10 d e f g+15 e^2 f^2\right)\right)}{15 e^2 \sqrt{d+e x} (e f-d g)^3}-\frac{2 \sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{5 (d+e x)^{5/2} (e f-d g)}+\frac{2 \sqrt{f+g x} (2 c d (5 e f-3 d g)-e (-4 a e g-b d g+5 b e f))}{15 e^2 (d+e x)^{3/2} (e f-d g)^2}","\frac{2 \sqrt{f+g x} \left(2 e g (-4 a e g-b d g+5 b e f)-c \left(3 d^2 g^2-10 d e f g+15 e^2 f^2\right)\right)}{15 e^2 \sqrt{d+e x} (e f-d g)^3}-\frac{2 \sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{5 (d+e x)^{5/2} (e f-d g)}+\frac{2 \sqrt{f+g x} (2 c d (5 e f-3 d g)-e (-4 a e g-b d g+5 b e f))}{15 e^2 (d+e x)^{3/2} (e f-d g)^2}",1,"(-2*(a + (d*(c*d - b*e))/e^2)*Sqrt[f + g*x])/(5*(e*f - d*g)*(d + e*x)^(5/2)) + (2*(2*c*d*(5*e*f - 3*d*g) - e*(5*b*e*f - b*d*g - 4*a*e*g))*Sqrt[f + g*x])/(15*e^2*(e*f - d*g)^2*(d + e*x)^(3/2)) + (2*(2*e*g*(5*b*e*f - b*d*g - 4*a*e*g) - c*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2))*Sqrt[f + g*x])/(15*e^2*(e*f - d*g)^3*Sqrt[d + e*x])","A",3,3,29,0.1034,1,"{949, 78, 37}"
841,1,281,0,0.2910328,"\int \frac{a+b x+c x^2}{(d+e x)^{9/2} \sqrt{f+g x}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)^(9/2)*Sqrt[f + g*x]),x]","-\frac{4 g \sqrt{f+g x} \left(4 e g (-6 a e g-b d g+7 b e f)-c \left(3 d^2 g^2-14 d e f g+35 e^2 f^2\right)\right)}{105 e^2 \sqrt{d+e x} (e f-d g)^4}+\frac{2 \sqrt{f+g x} \left(4 e g (-6 a e g-b d g+7 b e f)-c \left(3 d^2 g^2-14 d e f g+35 e^2 f^2\right)\right)}{105 e^2 (d+e x)^{3/2} (e f-d g)^3}-\frac{2 \sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{7 (d+e x)^{7/2} (e f-d g)}+\frac{2 \sqrt{f+g x} (2 c d (7 e f-4 d g)-e (-6 a e g-b d g+7 b e f))}{35 e^2 (d+e x)^{5/2} (e f-d g)^2}","-\frac{4 g \sqrt{f+g x} \left(4 e g (-6 a e g-b d g+7 b e f)-c \left(3 d^2 g^2-14 d e f g+35 e^2 f^2\right)\right)}{105 e^2 \sqrt{d+e x} (e f-d g)^4}+\frac{2 \sqrt{f+g x} \left(4 e g (-6 a e g-b d g+7 b e f)-c \left(3 d^2 g^2-14 d e f g+35 e^2 f^2\right)\right)}{105 e^2 (d+e x)^{3/2} (e f-d g)^3}-\frac{2 \sqrt{f+g x} \left(a+\frac{d (c d-b e)}{e^2}\right)}{7 (d+e x)^{7/2} (e f-d g)}+\frac{2 \sqrt{f+g x} (2 c d (7 e f-4 d g)-e (-6 a e g-b d g+7 b e f))}{35 e^2 (d+e x)^{5/2} (e f-d g)^2}",1,"(-2*(a + (d*(c*d - b*e))/e^2)*Sqrt[f + g*x])/(7*(e*f - d*g)*(d + e*x)^(7/2)) + (2*(2*c*d*(7*e*f - 4*d*g) - e*(7*b*e*f - b*d*g - 6*a*e*g))*Sqrt[f + g*x])/(35*e^2*(e*f - d*g)^2*(d + e*x)^(5/2)) + (2*(4*e*g*(7*b*e*f - b*d*g - 6*a*e*g) - c*(35*e^2*f^2 - 14*d*e*f*g + 3*d^2*g^2))*Sqrt[f + g*x])/(105*e^2*(e*f - d*g)^3*(d + e*x)^(3/2)) - (4*g*(4*e*g*(7*b*e*f - b*d*g - 6*a*e*g) - c*(35*e^2*f^2 - 14*d*e*f*g + 3*d^2*g^2))*Sqrt[f + g*x])/(105*e^2*(e*f - d*g)^4*Sqrt[d + e*x])","A",4,4,29,0.1379,1,"{949, 78, 45, 37}"
842,1,249,0,0.2804443,"\int \frac{\sqrt{d+e x} \left(a+b x+c x^2\right)}{(e+f x)^{3/2}} \, dx","Int[(Sqrt[d + e*x]*(a + b*x + c*x^2))/(e + f*x)^(3/2),x]","\frac{\sqrt{d+e x} \sqrt{e+f x} \left(4 e f \left(-2 a e f-b d f+3 b e^2\right)-c \left(-d^2 f^2-6 d e^2 f+15 e^4\right)\right)}{4 e f^3 \left(e^2-d f\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{d+e x}}{\sqrt{e} \sqrt{e+f x}}\right) \left(4 e f \left(-2 a e f-b d f+3 b e^2\right)-c \left(-d^2 f^2-6 d e^2 f+15 e^4\right)\right)}{4 e^{3/2} f^{7/2}}+\frac{2 (d+e x)^{3/2} \left(a+\frac{e (c e-b f)}{f^2}\right)}{\left(e^2-d f\right) \sqrt{e+f x}}+\frac{c (d+e x)^{3/2} \sqrt{e+f x}}{2 e f^2}","\frac{\sqrt{d+e x} \sqrt{e+f x} \left(4 e f \left(-2 a e f-b d f+3 b e^2\right)-c \left(-d^2 f^2-6 d e^2 f+15 e^4\right)\right)}{4 e f^3 \left(e^2-d f\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{d+e x}}{\sqrt{e} \sqrt{e+f x}}\right) \left(4 e f \left(-2 a e f-b d f+3 b e^2\right)-c \left(-d^2 f^2-6 d e^2 f+15 e^4\right)\right)}{4 e^{3/2} f^{7/2}}+\frac{2 (d+e x)^{3/2} \left(a+\frac{e (c e-b f)}{f^2}\right)}{\left(e^2-d f\right) \sqrt{e+f x}}+\frac{c (d+e x)^{3/2} \sqrt{e+f x}}{2 e f^2}",1,"(2*(a + (e*(c*e - b*f))/f^2)*(d + e*x)^(3/2))/((e^2 - d*f)*Sqrt[e + f*x]) + ((4*e*f*(3*b*e^2 - b*d*f - 2*a*e*f) - c*(15*e^4 - 6*d*e^2*f - d^2*f^2))*Sqrt[d + e*x]*Sqrt[e + f*x])/(4*e*f^3*(e^2 - d*f)) + (c*(d + e*x)^(3/2)*Sqrt[e + f*x])/(2*e*f^2) - ((4*e*f*(3*b*e^2 - b*d*f - 2*a*e*f) - c*(15*e^4 - 6*d*e^2*f - d^2*f^2))*ArcTanh[(Sqrt[f]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[e + f*x])])/(4*e^(3/2)*f^(7/2))","A",6,6,29,0.2069,1,"{949, 80, 50, 63, 217, 206}"
843,1,240,0,0.2250808,"\int \frac{(d+e x)^{3/2} \left(15 d^2+20 d e x+8 e^2 x^2\right)}{\sqrt{a+b x}} \, dx","Int[((d + e*x)^(3/2)*(15*d^2 + 20*d*e*x + 8*e^2*x^2))/Sqrt[a + b*x],x]","\frac{\sqrt{a+b x} (d+e x)^{3/2} \left(35 a^2 e^2-90 a b d e+73 b^2 d^2\right)}{12 b^3}+\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e) \left(35 a^2 e^2-90 a b d e+73 b^2 d^2\right)}{8 b^4}+\frac{(b d-a e)^2 \left(35 a^2 e^2-90 a b d e+73 b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{8 b^{9/2} \sqrt{e}}+\frac{2 e (a+b x)^{3/2} (d+e x)^{5/2}}{b^2}+\frac{\sqrt{a+b x} (d+e x)^{5/2} (17 b d-13 a e)}{3 b^2}","\frac{\sqrt{a+b x} (d+e x)^{3/2} \left(35 a^2 e^2-90 a b d e+73 b^2 d^2\right)}{12 b^3}+\frac{\sqrt{a+b x} \sqrt{d+e x} (b d-a e) \left(35 a^2 e^2-90 a b d e+73 b^2 d^2\right)}{8 b^4}+\frac{(b d-a e)^2 \left(35 a^2 e^2-90 a b d e+73 b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{8 b^{9/2} \sqrt{e}}+\frac{2 e (a+b x)^{3/2} (d+e x)^{5/2}}{b^2}+\frac{\sqrt{a+b x} (d+e x)^{5/2} (17 b d-13 a e)}{3 b^2}",1,"((b*d - a*e)*(73*b^2*d^2 - 90*a*b*d*e + 35*a^2*e^2)*Sqrt[a + b*x]*Sqrt[d + e*x])/(8*b^4) + ((73*b^2*d^2 - 90*a*b*d*e + 35*a^2*e^2)*Sqrt[a + b*x]*(d + e*x)^(3/2))/(12*b^3) + ((17*b*d - 13*a*e)*Sqrt[a + b*x]*(d + e*x)^(5/2))/(3*b^2) + (2*e*(a + b*x)^(3/2)*(d + e*x)^(5/2))/b^2 + ((b*d - a*e)^2*(73*b^2*d^2 - 90*a*b*d*e + 35*a^2*e^2)*ArcTanh[(Sqrt[e]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[d + e*x])])/(8*b^(9/2)*Sqrt[e])","A",7,6,38,0.1579,1,"{951, 80, 50, 63, 217, 206}"
844,1,176,0,0.1713265,"\int \frac{\sqrt{d+e x} \left(15 d^2+20 d e x+8 e^2 x^2\right)}{\sqrt{a+b x}} \, dx","Int[(Sqrt[d + e*x]*(15*d^2 + 20*d*e*x + 8*e^2*x^2))/Sqrt[a + b*x],x]","\frac{\sqrt{a+b x} \sqrt{d+e x} \left(5 a^2 e^2-13 a b d e+11 b^2 d^2\right)}{b^3}+\frac{(b d-a e) \left(5 a^2 e^2-13 a b d e+11 b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{7/2} \sqrt{e}}+\frac{8 e (a+b x)^{3/2} (d+e x)^{3/2}}{3 b^2}+\frac{2 \sqrt{a+b x} (d+e x)^{3/2} (4 b d-3 a e)}{b^2}","\frac{\sqrt{a+b x} \sqrt{d+e x} \left(5 a^2 e^2-13 a b d e+11 b^2 d^2\right)}{b^3}+\frac{(b d-a e) \left(5 a^2 e^2-13 a b d e+11 b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{7/2} \sqrt{e}}+\frac{8 e (a+b x)^{3/2} (d+e x)^{3/2}}{3 b^2}+\frac{2 \sqrt{a+b x} (d+e x)^{3/2} (4 b d-3 a e)}{b^2}",1,"((11*b^2*d^2 - 13*a*b*d*e + 5*a^2*e^2)*Sqrt[a + b*x]*Sqrt[d + e*x])/b^3 + (2*(4*b*d - 3*a*e)*Sqrt[a + b*x]*(d + e*x)^(3/2))/b^2 + (8*e*(a + b*x)^(3/2)*(d + e*x)^(3/2))/(3*b^2) + ((b*d - a*e)*(11*b^2*d^2 - 13*a*b*d*e + 5*a^2*e^2)*ArcTanh[(Sqrt[e]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[d + e*x])])/(b^(7/2)*Sqrt[e])","A",6,6,38,0.1579,1,"{951, 80, 50, 63, 217, 206}"
845,1,122,0,0.1235171,"\int \frac{15 d^2+20 d e x+8 e^2 x^2}{\sqrt{a+b x} \sqrt{d+e x}} \, dx","Int[(15*d^2 + 20*d*e*x + 8*e^2*x^2)/(Sqrt[a + b*x]*Sqrt[d + e*x]),x]","\frac{2 \left(3 a^2 e^2-8 a b d e+8 b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{5/2} \sqrt{e}}+\frac{4 e (a+b x)^{3/2} \sqrt{d+e x}}{b^2}+\frac{2 \sqrt{a+b x} \sqrt{d+e x} (7 b d-5 a e)}{b^2}","\frac{2 \left(3 a^2 e^2-8 a b d e+8 b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{5/2} \sqrt{e}}+\frac{4 e (a+b x)^{3/2} \sqrt{d+e x}}{b^2}+\frac{2 \sqrt{a+b x} \sqrt{d+e x} (7 b d-5 a e)}{b^2}",1,"(2*(7*b*d - 5*a*e)*Sqrt[a + b*x]*Sqrt[d + e*x])/b^2 + (4*e*(a + b*x)^(3/2)*Sqrt[d + e*x])/b^2 + (2*(8*b^2*d^2 - 8*a*b*d*e + 3*a^2*e^2)*ArcTanh[(Sqrt[e]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[d + e*x])])/(b^(5/2)*Sqrt[e])","A",5,5,38,0.1316,1,"{951, 80, 63, 217, 206}"
846,1,108,0,0.119984,"\int \frac{15 d^2+20 d e x+8 e^2 x^2}{\sqrt{a+b x} (d+e x)^{3/2}} \, dx","Int[(15*d^2 + 20*d*e*x + 8*e^2*x^2)/(Sqrt[a + b*x]*(d + e*x)^(3/2)),x]","\frac{8 (2 b d-a e) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{3/2} \sqrt{e}}+\frac{6 d^2 \sqrt{a+b x}}{\sqrt{d+e x} (b d-a e)}+\frac{8 \sqrt{a+b x} \sqrt{d+e x}}{b}","\frac{8 (2 b d-a e) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{b^{3/2} \sqrt{e}}+\frac{6 d^2 \sqrt{a+b x}}{\sqrt{d+e x} (b d-a e)}+\frac{8 \sqrt{a+b x} \sqrt{d+e x}}{b}",1,"(6*d^2*Sqrt[a + b*x])/((b*d - a*e)*Sqrt[d + e*x]) + (8*Sqrt[a + b*x]*Sqrt[d + e*x])/b + (8*(2*b*d - a*e)*ArcTanh[(Sqrt[e]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[d + e*x])])/(b^(3/2)*Sqrt[e])","A",5,5,38,0.1316,1,"{949, 80, 63, 217, 206}"
847,1,116,0,0.1213506,"\int \frac{15 d^2+20 d e x+8 e^2 x^2}{\sqrt{a+b x} (d+e x)^{5/2}} \, dx","Int[(15*d^2 + 20*d*e*x + 8*e^2*x^2)/(Sqrt[a + b*x]*(d + e*x)^(5/2)),x]","\frac{2 d^2 \sqrt{a+b x}}{(d+e x)^{3/2} (b d-a e)}+\frac{4 d \sqrt{a+b x} (3 b d-2 a e)}{\sqrt{d+e x} (b d-a e)^2}+\frac{16 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{\sqrt{b} \sqrt{e}}","\frac{2 d^2 \sqrt{a+b x}}{(d+e x)^{3/2} (b d-a e)}+\frac{4 d \sqrt{a+b x} (3 b d-2 a e)}{\sqrt{d+e x} (b d-a e)^2}+\frac{16 \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{a+b x}}{\sqrt{b} \sqrt{d+e x}}\right)}{\sqrt{b} \sqrt{e}}",1,"(2*d^2*Sqrt[a + b*x])/((b*d - a*e)*(d + e*x)^(3/2)) + (4*d*(3*b*d - 2*a*e)*Sqrt[a + b*x])/((b*d - a*e)^2*Sqrt[d + e*x]) + (16*ArcTanh[(Sqrt[e]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[d + e*x])])/(Sqrt[b]*Sqrt[e])","A",5,5,38,0.1316,1,"{949, 78, 63, 217, 206}"
848,1,133,0,0.1295995,"\int \frac{15 d^2+20 d e x+8 e^2 x^2}{\sqrt{a+b x} (d+e x)^{7/2}} \, dx","Int[(15*d^2 + 20*d*e*x + 8*e^2*x^2)/(Sqrt[a + b*x]*(d + e*x)^(7/2)),x]","\frac{16 \sqrt{a+b x} \left(15 a^2 e^2-35 a b d e+23 b^2 d^2\right)}{15 \sqrt{d+e x} (b d-a e)^3}+\frac{6 d^2 \sqrt{a+b x}}{5 (d+e x)^{5/2} (b d-a e)}+\frac{8 d \sqrt{a+b x} (8 b d-5 a e)}{15 (d+e x)^{3/2} (b d-a e)^2}","\frac{16 \sqrt{a+b x} \left(15 a^2 e^2-35 a b d e+23 b^2 d^2\right)}{15 \sqrt{d+e x} (b d-a e)^3}+\frac{6 d^2 \sqrt{a+b x}}{5 (d+e x)^{5/2} (b d-a e)}+\frac{8 d \sqrt{a+b x} (8 b d-5 a e)}{15 (d+e x)^{3/2} (b d-a e)^2}",1,"(6*d^2*Sqrt[a + b*x])/(5*(b*d - a*e)*(d + e*x)^(5/2)) + (8*d*(8*b*d - 5*a*e)*Sqrt[a + b*x])/(15*(b*d - a*e)^2*(d + e*x)^(3/2)) + (16*(23*b^2*d^2 - 35*a*b*d*e + 15*a^2*e^2)*Sqrt[a + b*x])/(15*(b*d - a*e)^3*Sqrt[d + e*x])","A",3,3,38,0.07895,1,"{949, 78, 37}"
849,1,189,0,0.1922201,"\int \frac{15 d^2+20 d e x+8 e^2 x^2}{\sqrt{a+b x} (d+e x)^{9/2}} \, dx","Int[(15*d^2 + 20*d*e*x + 8*e^2*x^2)/(Sqrt[a + b*x]*(d + e*x)^(9/2)),x]","\frac{32 b \sqrt{a+b x} \left(35 a^2 e^2-84 a b d e+58 b^2 d^2\right)}{105 \sqrt{d+e x} (b d-a e)^4}+\frac{16 \sqrt{a+b x} \left(35 a^2 e^2-84 a b d e+58 b^2 d^2\right)}{105 (d+e x)^{3/2} (b d-a e)^3}+\frac{6 d^2 \sqrt{a+b x}}{7 (d+e x)^{7/2} (b d-a e)}+\frac{4 d \sqrt{a+b x} (23 b d-14 a e)}{35 (d+e x)^{5/2} (b d-a e)^2}","\frac{32 b \sqrt{a+b x} \left(35 a^2 e^2-84 a b d e+58 b^2 d^2\right)}{105 \sqrt{d+e x} (b d-a e)^4}+\frac{16 \sqrt{a+b x} \left(35 a^2 e^2-84 a b d e+58 b^2 d^2\right)}{105 (d+e x)^{3/2} (b d-a e)^3}+\frac{6 d^2 \sqrt{a+b x}}{7 (d+e x)^{7/2} (b d-a e)}+\frac{4 d \sqrt{a+b x} (23 b d-14 a e)}{35 (d+e x)^{5/2} (b d-a e)^2}",1,"(6*d^2*Sqrt[a + b*x])/(7*(b*d - a*e)*(d + e*x)^(7/2)) + (4*d*(23*b*d - 14*a*e)*Sqrt[a + b*x])/(35*(b*d - a*e)^2*(d + e*x)^(5/2)) + (16*(58*b^2*d^2 - 84*a*b*d*e + 35*a^2*e^2)*Sqrt[a + b*x])/(105*(b*d - a*e)^3*(d + e*x)^(3/2)) + (32*b*(58*b^2*d^2 - 84*a*b*d*e + 35*a^2*e^2)*Sqrt[a + b*x])/(105*(b*d - a*e)^4*Sqrt[d + e*x])","A",4,4,38,0.1053,1,"{949, 78, 45, 37}"
850,1,417,0,3.1405163,"\int \frac{(d+e x)^{3/2}}{\sqrt{f+g x} \left(a+b x+c x^2\right)} \, dx","Int[(d + e*x)^(3/2)/(Sqrt[f + g*x]*(a + b*x + c*x^2)),x]","-\frac{2 \left(\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{\sqrt{b^2-4 a c}}+e (2 c d-b e)\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{2 \left(e (2 c d-b e)-\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{c \sqrt{g}}","-\frac{2 \left(\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{\sqrt{b^2-4 a c}}+e (2 c d-b e)\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{2 \left(e (2 c d-b e)-\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{g} \sqrt{d+e x}}{\sqrt{e} \sqrt{f+g x}}\right)}{c \sqrt{g}}",1,"(2*e^(3/2)*ArcTanh[(Sqrt[g]*Sqrt[d + e*x])/(Sqrt[e]*Sqrt[f + g*x])])/(c*Sqrt[g]) - (2*(e*(2*c*d - b*e) + (2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[d + e*x])/(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[f + g*x])])/(c*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]) - (2*(e*(2*c*d - b*e) - (2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g]*Sqrt[d + e*x])/(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*Sqrt[f + g*x])])/(c*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g])","A",11,7,31,0.2258,1,"{909, 63, 217, 206, 6728, 93, 208}"
851,1,285,0,0.5257695,"\int \frac{\sqrt{d+e x}}{\sqrt{f+g x} \left(a+b x+c x^2\right)} \, dx","Int[Sqrt[d + e*x]/(Sqrt[f + g*x]*(a + b*x + c*x^2)),x]","\frac{2 \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}","\frac{2 \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}",1,"(-2*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*ArcTanh[(Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[d + e*x])/(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[f + g*x])])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]) + (2*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*ArcTanh[(Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g]*Sqrt[d + e*x])/(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*Sqrt[f + g*x])])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g])","A",6,3,31,0.09677,1,"{909, 93, 208}"
852,1,287,0,0.4145192,"\int \frac{1}{\sqrt{d+e x} \sqrt{f+g x} \left(a+b x+c x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[f + g*x]*(a + b*x + c*x^2)),x]","\frac{4 c \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{4 c \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}","\frac{4 c \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{4 c \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}",1,"(-4*c*ArcTanh[(Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[d + e*x])/(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[f + g*x])])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]) + (4*c*ArcTanh[(Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g]*Sqrt[d + e*x])/(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*Sqrt[f + g*x])])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g])","A",6,3,31,0.09677,1,"{911, 93, 208}"
853,1,429,0,1.3561443,"\int \frac{1}{(d+e x)^{3/2} \sqrt{f+g x} \left(a+b x+c x^2\right)} \, dx","Int[1/((d + e*x)^(3/2)*Sqrt[f + g*x]*(a + b*x + c*x^2)),x]","-\frac{8 c^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)^{3/2} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{8 c^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)^{3/2} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{4 c e \sqrt{f+g x}}{\sqrt{b^2-4 a c} \sqrt{d+e x} (e f-d g) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{4 c e \sqrt{f+g x}}{\sqrt{b^2-4 a c} \sqrt{d+e x} (e f-d g) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}","-\frac{8 c^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)^{3/2} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{8 c^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{f+g x} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)^{3/2} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{4 c e \sqrt{f+g x}}{\sqrt{b^2-4 a c} \sqrt{d+e x} (e f-d g) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{4 c e \sqrt{f+g x}}{\sqrt{b^2-4 a c} \sqrt{d+e x} (e f-d g) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}",1,"(4*c*e*Sqrt[f + g*x])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(e*f - d*g)*Sqrt[d + e*x]) - (4*c*e*Sqrt[f + g*x])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(e*f - d*g)*Sqrt[d + e*x]) - (8*c^2*ArcTanh[(Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[d + e*x])/(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*Sqrt[f + g*x])])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)^(3/2)*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]) + (8*c^2*ArcTanh[(Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g]*Sqrt[d + e*x])/(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*Sqrt[f + g*x])])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)^(3/2)*Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g])","A",8,4,31,0.1290,1,"{911, 96, 93, 208}"
854,1,532,0,1.704094,"\int \frac{(f+g x)^3 \sqrt{a+b x+c x^2}}{d+e x} \, dx","Int[((f + g*x)^3*Sqrt[a + b*x + c*x^2])/(d + e*x),x]","\frac{\sqrt{a+b x+c x^2} \left(2 c e g x \left(-4 c e g (a e g-2 b d g+6 b e f)+5 b^2 e^2 g^2+16 c^2 \left(d^2 g^2-3 d e f g+3 e^2 f^2\right)\right)-4 b c e^2 g^2 (a e g-2 b d g+6 b e f)+5 b^3 e^3 g^3+16 b c^2 e g \left(d^2 g^2-3 d e f g+3 e^2 f^2\right)+64 c^3 (e f-d g)^3\right)}{64 c^3 e^4}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 c e (2 c d-b e) \left(-4 c d g^2 (a e g-2 b d g+6 b e f)+5 b^2 d e g^3+16 c^2 e^2 f^3\right)-2 g \left(-2 c e (b d-a e)-\frac{b^2 e^2}{2}+4 c^2 d^2\right) \left(-4 c e g (a e g-2 b d g+6 b e f)+5 b^2 e^2 g^2+16 c^2 \left(d^2 g^2-3 d e f g+3 e^2 f^2\right)\right)\right)}{128 c^{7/2} e^5}+\frac{g^2 \left(a+b x+c x^2\right)^{3/2} (-5 b e g-14 c d g+24 c e f)}{24 c^2 e^2}+\frac{(e f-d g)^3 \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^5}+\frac{g^3 (d+e x) \left(a+b x+c x^2\right)^{3/2}}{4 c e^2}","\frac{\sqrt{a+b x+c x^2} \left(2 c e g x \left(-4 c e g (a e g-2 b d g+6 b e f)+5 b^2 e^2 g^2+16 c^2 \left(d^2 g^2-3 d e f g+3 e^2 f^2\right)\right)-4 b c e^2 g^2 (a e g-2 b d g+6 b e f)+5 b^3 e^3 g^3+16 b c^2 e g \left(d^2 g^2-3 d e f g+3 e^2 f^2\right)+64 c^3 (e f-d g)^3\right)}{64 c^3 e^4}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 c e (2 c d-b e) \left(-4 c d g^2 (a e g-2 b d g+6 b e f)+5 b^2 d e g^3+16 c^2 e^2 f^3\right)-2 g \left(-2 c e (b d-a e)-\frac{b^2 e^2}{2}+4 c^2 d^2\right) \left(-4 c e g (a e g-2 b d g+6 b e f)+5 b^2 e^2 g^2+16 c^2 \left(d^2 g^2-3 d e f g+3 e^2 f^2\right)\right)\right)}{128 c^{7/2} e^5}+\frac{g^2 \left(a+b x+c x^2\right)^{3/2} (-5 b e g-14 c d g+24 c e f)}{24 c^2 e^2}+\frac{(e f-d g)^3 \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^5}+\frac{g^3 (d+e x) \left(a+b x+c x^2\right)^{3/2}}{4 c e^2}",1,"((5*b^3*e^3*g^3 + 64*c^3*(e*f - d*g)^3 - 4*b*c*e^2*g^2*(6*b*e*f - 2*b*d*g + a*e*g) + 16*b*c^2*e*g*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2) + 2*c*e*g*(5*b^2*e^2*g^2 - 4*c*e*g*(6*b*e*f - 2*b*d*g + a*e*g) + 16*c^2*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2))*x)*Sqrt[a + b*x + c*x^2])/(64*c^3*e^4) + (g^2*(24*c*e*f - 14*c*d*g - 5*b*e*g)*(a + b*x + c*x^2)^(3/2))/(24*c^2*e^2) + (g^3*(d + e*x)*(a + b*x + c*x^2)^(3/2))/(4*c*e^2) - ((4*c*e*(2*c*d - b*e)*(16*c^2*e^2*f^3 + 5*b^2*d*e*g^3 - 4*c*d*g^2*(6*b*e*f - 2*b*d*g + a*e*g)) - 2*(4*c^2*d^2 - (b^2*e^2)/2 - 2*c*e*(b*d - a*e))*g*(5*b^2*e^2*g^2 - 4*c*e*g*(6*b*e*f - 2*b*d*g + a*e*g) + 16*c^2*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(7/2)*e^5) + (Sqrt[c*d^2 - b*d*e + a*e^2]*(e*f - d*g)^3*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^5","A",8,6,29,0.2069,1,"{1653, 814, 843, 621, 206, 724}"
855,1,325,0,0.7077231,"\int \frac{(f+g x)^2 \sqrt{a+b x+c x^2}}{d+e x} \, dx","Int[((f + g*x)^2*Sqrt[a + b*x + c*x^2])/(d + e*x),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(g \left(-4 c e (b d-a e)-b^2 e^2+8 c^2 d^2\right) (-b e g-2 c d g+4 c e f)-4 c e (2 c d-b e) \left(2 c e f^2-b d g^2\right)\right)}{16 c^{5/2} e^4}-\frac{\sqrt{a+b x+c x^2} \left(b^2 e^2 g^2-2 c e g x (-b e g-2 c d g+4 c e f)-2 b c e g (2 e f-d g)-8 c^2 (e f-d g)^2\right)}{8 c^2 e^3}+\frac{(e f-d g)^2 \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^4}+\frac{g^2 \left(a+b x+c x^2\right)^{3/2}}{3 c e}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(g \left(-4 c e (b d-a e)-b^2 e^2+8 c^2 d^2\right) (-b e g-2 c d g+4 c e f)-4 c e (2 c d-b e) \left(2 c e f^2-b d g^2\right)\right)}{16 c^{5/2} e^4}-\frac{\sqrt{a+b x+c x^2} \left(b^2 e^2 g^2-2 c e g x (-b e g-2 c d g+4 c e f)-2 b c e g (2 e f-d g)-8 c^2 (e f-d g)^2\right)}{8 c^2 e^3}+\frac{(e f-d g)^2 \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^4}+\frac{g^2 \left(a+b x+c x^2\right)^{3/2}}{3 c e}",1,"-((b^2*e^2*g^2 - 8*c^2*(e*f - d*g)^2 - 2*b*c*e*g*(2*e*f - d*g) - 2*c*e*g*(4*c*e*f - 2*c*d*g - b*e*g)*x)*Sqrt[a + b*x + c*x^2])/(8*c^2*e^3) + (g^2*(a + b*x + c*x^2)^(3/2))/(3*c*e) + (((8*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - a*e))*g*(4*c*e*f - 2*c*d*g - b*e*g) - 4*c*e*(2*c*d - b*e)*(2*c*e*f^2 - b*d*g^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(5/2)*e^4) + (Sqrt[c*d^2 - b*d*e + a*e^2]*(e*f - d*g)^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^4","A",7,6,29,0.2069,1,"{1653, 814, 843, 621, 206, 724}"
856,1,219,0,0.3243124,"\int \frac{(f+g x) \sqrt{a+b x+c x^2}}{d+e x} \, dx","Int[((f + g*x)*Sqrt[a + b*x + c*x^2])/(d + e*x),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c e (a e g-b d g+b e f)+b^2 e^2 g+8 c^2 d (e f-d g)\right)}{8 c^{3/2} e^3}+\frac{(e f-d g) \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^3}+\frac{\sqrt{a+b x+c x^2} (b e g-4 c d g+4 c e f+2 c e g x)}{4 c e^2}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c e (a e g-b d g+b e f)+b^2 e^2 g+8 c^2 d (e f-d g)\right)}{8 c^{3/2} e^3}+\frac{(e f-d g) \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^3}+\frac{\sqrt{a+b x+c x^2} (b e g-4 c d g+4 c e f+2 c e g x)}{4 c e^2}",1,"((4*c*e*f - 4*c*d*g + b*e*g + 2*c*e*g*x)*Sqrt[a + b*x + c*x^2])/(4*c*e^2) - ((b^2*e^2*g + 8*c^2*d*(e*f - d*g) - 4*c*e*(b*e*f - b*d*g + a*e*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(3/2)*e^3) + (Sqrt[c*d^2 - b*d*e + a*e^2]*(e*f - d*g)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^3","A",6,5,27,0.1852,1,"{814, 843, 621, 206, 724}"
857,1,152,0,0.1510496,"\int \frac{\sqrt{a+b x+c x^2}}{d+e x} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x),x]","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^2}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} e^2}+\frac{\sqrt{a+b x+c x^2}}{e}","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^2}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} e^2}+\frac{\sqrt{a+b x+c x^2}}{e}",1,"Sqrt[a + b*x + c*x^2]/e - ((2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*e^2) + (Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^2","A",6,5,22,0.2273,1,"{734, 843, 621, 206, 724}"
858,1,228,0,0.3305106,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x) (f+g x)} \, dx","Int[Sqrt[a + b*x + c*x^2]/((d + e*x)*(f + g*x)),x]","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e (e f-d g)}-\frac{\sqrt{a g^2-b f g+c f^2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g (e f-d g)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e g}","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e (e f-d g)}-\frac{\sqrt{a g^2-b f g+c f^2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g (e f-d g)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e g}",1,"(Sqrt[c]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(e*g) + (Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e*(e*f - d*g)) - (Sqrt[c*f^2 - b*f*g + a*g^2]*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(g*(e*f - d*g))","A",8,5,29,0.1724,1,"{895, 724, 206, 843, 621}"
859,1,490,0,0.6950245,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x) (f+g x)^2} \, dx","Int[Sqrt[a + b*x + c*x^2]/((d + e*x)*(f + g*x)^2),x]","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^2}-\frac{e \sqrt{a g^2-b f g+c f^2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g (e f-d g)^2}+\frac{(2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 g (e f-d g) \sqrt{a g^2-b f g+c f^2}}+\frac{\sqrt{a+b x+c x^2}}{(f+g x) (e f-d g)}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{g (e f-d g)}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} (e f-d g)^2}+\frac{e (2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} g (e f-d g)^2}","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^2}-\frac{e \sqrt{a g^2-b f g+c f^2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g (e f-d g)^2}+\frac{(2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 g (e f-d g) \sqrt{a g^2-b f g+c f^2}}+\frac{\sqrt{a+b x+c x^2}}{(f+g x) (e f-d g)}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{g (e f-d g)}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} (e f-d g)^2}+\frac{e (2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} g (e f-d g)^2}",1,"Sqrt[a + b*x + c*x^2]/((e*f - d*g)*(f + g*x)) - ((2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*(e*f - d*g)^2) + (e*(2*c*f - b*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*g*(e*f - d*g)^2) - (Sqrt[c]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(g*(e*f - d*g)) + (Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e*f - d*g)^2 + ((2*c*f - b*g)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(2*g*(e*f - d*g)*Sqrt[c*f^2 - b*f*g + a*g^2]) - (e*Sqrt[c*f^2 - b*f*g + a*g^2]*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(g*(e*f - d*g)^2)","A",20,7,29,0.2414,1,"{960, 734, 843, 621, 206, 724, 732}"
860,1,673,0,0.8618063,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x) (f+g x)^3} \, dx","Int[Sqrt[a + b*x + c*x^2]/((d + e*x)*(f + g*x)^3),x]","\frac{g \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{8 (e f-d g) \left(a g^2-b f g+c f^2\right)^{3/2}}+\frac{e \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^3}-\frac{e^2 \sqrt{a g^2-b f g+c f^2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g (e f-d g)^3}+\frac{e^2 (2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} g (e f-d g)^3}-\frac{g \sqrt{a+b x+c x^2} (-2 a g+x (2 c f-b g)+b f)}{4 (f+g x)^2 (e f-d g) \left(a g^2-b f g+c f^2\right)}+\frac{e (2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 g (e f-d g)^2 \sqrt{a g^2-b f g+c f^2}}+\frac{e \sqrt{a+b x+c x^2}}{(f+g x) (e f-d g)^2}-\frac{\sqrt{c} e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{g (e f-d g)^2}-\frac{e (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} (e f-d g)^3}","\frac{g \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{8 (e f-d g) \left(a g^2-b f g+c f^2\right)^{3/2}}+\frac{e \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^3}-\frac{e^2 \sqrt{a g^2-b f g+c f^2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g (e f-d g)^3}+\frac{e^2 (2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} g (e f-d g)^3}-\frac{g \sqrt{a+b x+c x^2} (-2 a g+x (2 c f-b g)+b f)}{4 (f+g x)^2 (e f-d g) \left(a g^2-b f g+c f^2\right)}+\frac{e (2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 g (e f-d g)^2 \sqrt{a g^2-b f g+c f^2}}+\frac{e \sqrt{a+b x+c x^2}}{(f+g x) (e f-d g)^2}-\frac{\sqrt{c} e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{g (e f-d g)^2}-\frac{e (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} (e f-d g)^3}",1,"(e*Sqrt[a + b*x + c*x^2])/((e*f - d*g)^2*(f + g*x)) - (g*(b*f - 2*a*g + (2*c*f - b*g)*x)*Sqrt[a + b*x + c*x^2])/(4*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*(f + g*x)^2) - (e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*(e*f - d*g)^3) + (e^2*(2*c*f - b*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*g*(e*f - d*g)^3) - (Sqrt[c]*e*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(g*(e*f - d*g)^2) + (e*Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e*f - d*g)^3 + ((b^2 - 4*a*c)*g*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(8*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^(3/2)) + (e*(2*c*f - b*g)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(2*g*(e*f - d*g)^2*Sqrt[c*f^2 - b*f*g + a*g^2]) - (e^2*Sqrt[c*f^2 - b*f*g + a*g^2]*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(g*(e*f - d*g)^3)","A",23,8,29,0.2759,1,"{960, 734, 843, 621, 206, 724, 720, 732}"
861,1,933,0,1.2248226,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x) (f+g x)^4} \, dx","Int[Sqrt[a + b*x + c*x^2]/((d + e*x)*(f + g*x)^4),x]","\frac{(2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^3}{2 \sqrt{c} g (e f-d g)^4}-\frac{\sqrt{c f^2-b g f+a g^2} \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e^3}{g (e f-d g)^4}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^2}{g (e f-d g)^3}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^2}{2 \sqrt{c} (e f-d g)^4}+\frac{\sqrt{c d^2-b e d+a e^2} \tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right) e^2}{(e f-d g)^4}+\frac{(2 c f-b g) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e^2}{2 g (e f-d g)^3 \sqrt{c f^2-b g f+a g^2}}+\frac{\sqrt{c x^2+b x+a} e^2}{(e f-d g)^3 (f+g x)}+\frac{\left(b^2-4 a c\right) g \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e}{8 (e f-d g)^2 \left(c f^2-b g f+a g^2\right)^{3/2}}-\frac{g (b f-2 a g+(2 c f-b g) x) \sqrt{c x^2+b x+a} e}{4 (e f-d g)^2 \left(c f^2-b g f+a g^2\right) (f+g x)^2}+\frac{g^2 \left(c x^2+b x+a\right)^{3/2}}{3 (e f-d g) \left(c f^2-b g f+a g^2\right) (f+g x)^3}+\frac{\left(b^2-4 a c\right) g (2 c f-b g) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right)}{16 (e f-d g) \left(c f^2-b g f+a g^2\right)^{5/2}}-\frac{g (2 c f-b g) (b f-2 a g+(2 c f-b g) x) \sqrt{c x^2+b x+a}}{8 (e f-d g) \left(c f^2-b g f+a g^2\right)^2 (f+g x)^2}","\frac{(2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^3}{2 \sqrt{c} g (e f-d g)^4}-\frac{\sqrt{c f^2-b g f+a g^2} \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e^3}{g (e f-d g)^4}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^2}{g (e f-d g)^3}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^2}{2 \sqrt{c} (e f-d g)^4}+\frac{\sqrt{c d^2-b e d+a e^2} \tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right) e^2}{(e f-d g)^4}+\frac{(2 c f-b g) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e^2}{2 g (e f-d g)^3 \sqrt{c f^2-b g f+a g^2}}+\frac{\sqrt{c x^2+b x+a} e^2}{(e f-d g)^3 (f+g x)}+\frac{\left(b^2-4 a c\right) g \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e}{8 (e f-d g)^2 \left(c f^2-b g f+a g^2\right)^{3/2}}-\frac{g (b f-2 a g+(2 c f-b g) x) \sqrt{c x^2+b x+a} e}{4 (e f-d g)^2 \left(c f^2-b g f+a g^2\right) (f+g x)^2}+\frac{g^2 \left(c x^2+b x+a\right)^{3/2}}{3 (e f-d g) \left(c f^2-b g f+a g^2\right) (f+g x)^3}+\frac{\left(b^2-4 a c\right) g (2 c f-b g) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right)}{16 (e f-d g) \left(c f^2-b g f+a g^2\right)^{5/2}}-\frac{g (2 c f-b g) (b f-2 a g+(2 c f-b g) x) \sqrt{c x^2+b x+a}}{8 (e f-d g) \left(c f^2-b g f+a g^2\right)^2 (f+g x)^2}",1,"(e^2*Sqrt[a + b*x + c*x^2])/((e*f - d*g)^3*(f + g*x)) - (g*(2*c*f - b*g)*(b*f - 2*a*g + (2*c*f - b*g)*x)*Sqrt[a + b*x + c*x^2])/(8*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^2*(f + g*x)^2) - (e*g*(b*f - 2*a*g + (2*c*f - b*g)*x)*Sqrt[a + b*x + c*x^2])/(4*(e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)*(f + g*x)^2) + (g^2*(a + b*x + c*x^2)^(3/2))/(3*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*(f + g*x)^3) - (e^2*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*(e*f - d*g)^4) + (e^3*(2*c*f - b*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*g*(e*f - d*g)^4) - (Sqrt[c]*e^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(g*(e*f - d*g)^3) + (e^2*Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e*f - d*g)^4 + ((b^2 - 4*a*c)*g*(2*c*f - b*g)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(16*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^(5/2)) + ((b^2 - 4*a*c)*e*g*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(8*(e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)^(3/2)) + (e^2*(2*c*f - b*g)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(2*g*(e*f - d*g)^3*Sqrt[c*f^2 - b*f*g + a*g^2]) - (e^3*Sqrt[c*f^2 - b*f*g + a*g^2]*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(g*(e*f - d*g)^4)","A",27,9,29,0.3103,1,"{960, 734, 843, 621, 206, 724, 730, 720, 732}"
862,1,1098,0,3.8637373,"\int \frac{(f+g x)^3 \left(a+b x+c x^2\right)^{3/2}}{d+e x} \, dx","Int[((f + g*x)^3*(a + b*x + c*x^2)^(3/2))/(d + e*x),x]","\frac{(d+e x) \left(c x^2+b x+a\right)^{5/2} g^3}{6 c e^2}+\frac{(36 c e f-22 c d g-7 b e g) \left(c x^2+b x+a\right)^{5/2} g^2}{60 c^2 e^2}+\frac{\left(7 b^3 e^3 g^3-4 b c e^2 (9 b e f-3 b d g+a e g) g^2+24 b c^2 e \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) g+2 c e \left(24 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) c^2-4 e g (9 b e f-3 b d g+a e g) c+7 b^2 e^2 g^2\right) x g+64 c^3 (e f-d g)^3\right) \left(c x^2+b x+a\right)^{3/2}}{192 c^3 e^4}+\frac{\left(4 c e (2 c d-b e) \left(8 c e (b d-2 a e) \left(24 c^2 e^2 f^3+7 b^2 d e g^3-4 c d g^2 (9 b e f-3 b d g+a e g)\right)-d \left(-3 e b^2+8 c d b-4 a c e\right) g \left(24 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) c^2-4 e g (9 b e f-3 b d g+a e g) c+7 b^2 e^2 g^2\right)\right)-2 \left(4 c^2 d^2-\frac{b^2 e^2}{2}-2 c e (b d-a e)\right) \left(8 c e (2 c d-b e) \left(24 c^2 e^2 f^3+7 b^2 d e g^3-4 c d g^2 (9 b e f-3 b d g+a e g)\right)-2 \left(8 c^2 d^2-4 b c e d-\frac{3 b^2 e^2}{2}+6 a c e^2\right) g \left(24 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) c^2-4 e g (9 b e f-3 b d g+a e g) c+7 b^2 e^2 g^2\right)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{3072 c^{9/2} e^7}+\frac{\left(c d^2-b e d+a e^2\right)^{3/2} (e f-d g)^3 \tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right)}{e^7}-\frac{\left(3 \left(-512 d^2 (e f-d g)^3 c^5+128 e (5 b d-4 a e) (e f-d g)^3 c^4-32 b e^2 \left(2 b (e f-d g)^3+3 a e g \left(3 e^2 f^2-3 d e g f+d^2 g^2\right)\right) c^3+8 b e^3 g \left(3 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) b^2+6 a e g (3 e f-d g) b+2 a^2 e^2 g^2\right) c^2-4 b^3 e^4 g^2 (9 b e f-3 b d g+8 a e g) c+7 b^5 e^5 g^3\right)+2 c e \left(8 c e (2 c d-b e) \left(24 c^2 e^2 f^3+7 b^2 d e g^3-4 c d g^2 (9 b e f-3 b d g+a e g)\right)-2 \left(8 c^2 d^2-4 b c e d-\frac{3 b^2 e^2}{2}+6 a c e^2\right) g \left(24 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) c^2-4 e g (9 b e f-3 b d g+a e g) c+7 b^2 e^2 g^2\right)\right) x\right) \sqrt{c x^2+b x+a}}{1536 c^4 e^6}","\frac{(d+e x) \left(c x^2+b x+a\right)^{5/2} g^3}{6 c e^2}+\frac{(36 c e f-22 c d g-7 b e g) \left(c x^2+b x+a\right)^{5/2} g^2}{60 c^2 e^2}+\frac{\left(7 b^3 e^3 g^3-4 b c e^2 (9 b e f-3 b d g+a e g) g^2+24 b c^2 e \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) g+2 c e \left(24 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) c^2-4 e g (9 b e f-3 b d g+a e g) c+7 b^2 e^2 g^2\right) x g+64 c^3 (e f-d g)^3\right) \left(c x^2+b x+a\right)^{3/2}}{192 c^3 e^4}+\frac{\left(4 c e (2 c d-b e) \left(8 c e (b d-2 a e) \left(24 c^2 e^2 f^3+7 b^2 d e g^3-4 c d g^2 (9 b e f-3 b d g+a e g)\right)-d \left(-3 e b^2+8 c d b-4 a c e\right) g \left(24 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) c^2-4 e g (9 b e f-3 b d g+a e g) c+7 b^2 e^2 g^2\right)\right)-2 \left(4 c^2 d^2-\frac{b^2 e^2}{2}-2 c e (b d-a e)\right) \left(8 c e (2 c d-b e) \left(24 c^2 e^2 f^3+7 b^2 d e g^3-4 c d g^2 (9 b e f-3 b d g+a e g)\right)-2 \left(8 c^2 d^2-4 b c e d-\frac{3 b^2 e^2}{2}+6 a c e^2\right) g \left(24 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) c^2-4 e g (9 b e f-3 b d g+a e g) c+7 b^2 e^2 g^2\right)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{3072 c^{9/2} e^7}+\frac{\left(c d^2-b e d+a e^2\right)^{3/2} (e f-d g)^3 \tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right)}{e^7}-\frac{\left(3 \left(-512 d^2 (e f-d g)^3 c^5+128 e (5 b d-4 a e) (e f-d g)^3 c^4-32 b e^2 \left(2 b (e f-d g)^3+3 a e g \left(3 e^2 f^2-3 d e g f+d^2 g^2\right)\right) c^3+8 b e^3 g \left(3 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) b^2+6 a e g (3 e f-d g) b+2 a^2 e^2 g^2\right) c^2-4 b^3 e^4 g^2 (9 b e f-3 b d g+8 a e g) c+7 b^5 e^5 g^3\right)+2 c e \left(8 c e (2 c d-b e) \left(24 c^2 e^2 f^3+7 b^2 d e g^3-4 c d g^2 (9 b e f-3 b d g+a e g)\right)-2 \left(8 c^2 d^2-4 b c e d-\frac{3 b^2 e^2}{2}+6 a c e^2\right) g \left(24 \left(3 e^2 f^2-3 d e g f+d^2 g^2\right) c^2-4 e g (9 b e f-3 b d g+a e g) c+7 b^2 e^2 g^2\right)\right) x\right) \sqrt{c x^2+b x+a}}{1536 c^4 e^6}",1,"-((3*(7*b^5*e^5*g^3 - 512*c^5*d^2*(e*f - d*g)^3 + 128*c^4*e*(5*b*d - 4*a*e)*(e*f - d*g)^3 - 4*b^3*c*e^4*g^2*(9*b*e*f - 3*b*d*g + 8*a*e*g) + 8*b*c^2*e^3*g*(2*a^2*e^2*g^2 + 6*a*b*e*g*(3*e*f - d*g) + 3*b^2*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2)) - 32*b*c^3*e^2*(2*b*(e*f - d*g)^3 + 3*a*e*g*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2))) + 2*c*e*(8*c*e*(2*c*d - b*e)*(24*c^2*e^2*f^3 + 7*b^2*d*e*g^3 - 4*c*d*g^2*(9*b*e*f - 3*b*d*g + a*e*g)) - 2*(8*c^2*d^2 - 4*b*c*d*e - (3*b^2*e^2)/2 + 6*a*c*e^2)*g*(7*b^2*e^2*g^2 - 4*c*e*g*(9*b*e*f - 3*b*d*g + a*e*g) + 24*c^2*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2)))*x)*Sqrt[a + b*x + c*x^2])/(1536*c^4*e^6) + ((7*b^3*e^3*g^3 + 64*c^3*(e*f - d*g)^3 - 4*b*c*e^2*g^2*(9*b*e*f - 3*b*d*g + a*e*g) + 24*b*c^2*e*g*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2) + 2*c*e*g*(7*b^2*e^2*g^2 - 4*c*e*g*(9*b*e*f - 3*b*d*g + a*e*g) + 24*c^2*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2))*x)*(a + b*x + c*x^2)^(3/2))/(192*c^3*e^4) + (g^2*(36*c*e*f - 22*c*d*g - 7*b*e*g)*(a + b*x + c*x^2)^(5/2))/(60*c^2*e^2) + (g^3*(d + e*x)*(a + b*x + c*x^2)^(5/2))/(6*c*e^2) + ((4*c*e*(2*c*d - b*e)*(8*c*e*(b*d - 2*a*e)*(24*c^2*e^2*f^3 + 7*b^2*d*e*g^3 - 4*c*d*g^2*(9*b*e*f - 3*b*d*g + a*e*g)) - d*(8*b*c*d - 3*b^2*e - 4*a*c*e)*g*(7*b^2*e^2*g^2 - 4*c*e*g*(9*b*e*f - 3*b*d*g + a*e*g) + 24*c^2*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2))) - 2*(4*c^2*d^2 - (b^2*e^2)/2 - 2*c*e*(b*d - a*e))*(8*c*e*(2*c*d - b*e)*(24*c^2*e^2*f^3 + 7*b^2*d*e*g^3 - 4*c*d*g^2*(9*b*e*f - 3*b*d*g + a*e*g)) - 2*(8*c^2*d^2 - 4*b*c*d*e - (3*b^2*e^2)/2 + 6*a*c*e^2)*g*(7*b^2*e^2*g^2 - 4*c*e*g*(9*b*e*f - 3*b*d*g + a*e*g) + 24*c^2*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2))))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(3072*c^(9/2)*e^7) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*(e*f - d*g)^3*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^7","A",9,6,29,0.2069,1,"{1653, 814, 843, 621, 206, 724}"
863,1,662,0,1.5540798,"\int \frac{(f+g x)^2 \left(a+b x+c x^2\right)^{3/2}}{d+e x} \, dx","Int[((f + g*x)^2*(a + b*x + c*x^2)^(3/2))/(d + e*x),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(16 b c^2 e^3 \left(3 a^2 e^2 g^2+3 a b e g (2 e f-d g)+b^2 (e f-d g)^2\right)+96 c^3 e^2 \left(-a^2 e^2 g (2 e f-d g)-2 a b e (e f-d g)^2+b^2 d (e f-d g)^2\right)-6 b^3 c e^4 g (4 a e g-b d g+2 b e f)-384 c^4 d e (b d-a e) (e f-d g)^2+3 b^5 e^5 g^2+256 c^5 d^3 (e f-d g)^2\right)}{256 c^{7/2} e^6}+\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(g \left(-4 c e (2 b d-3 a e)-3 b^2 e^2+16 c^2 d^2\right) (-b e g-2 c d g+4 c e f)-8 c e (2 c d-b e) \left(2 c e f^2-b d g^2\right)\right)-6 b^2 c e^3 g (2 a e g-b d g+2 b e f)+8 b c^2 e^2 \left(3 a e g (2 e f-d g)+2 b (e f-d g)^2\right)-32 c^3 e (5 b d-4 a e) (e f-d g)^2+3 b^4 e^4 g^2+128 c^4 d^2 (e f-d g)^2\right)}{128 c^3 e^5}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(3 b^2 e^2 g^2-6 c e g x (-b e g-2 c d g+4 c e f)-6 b c e g (2 e f-d g)-16 c^2 (e f-d g)^2\right)}{48 c^2 e^3}+\frac{(e f-d g)^2 \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^6}+\frac{g^2 \left(a+b x+c x^2\right)^{5/2}}{5 c e}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(16 b c^2 e^3 \left(3 a^2 e^2 g^2+3 a b e g (2 e f-d g)+b^2 (e f-d g)^2\right)+96 c^3 e^2 \left(-a^2 e^2 g (2 e f-d g)-2 a b e (e f-d g)^2+b^2 d (e f-d g)^2\right)-6 b^3 c e^4 g (4 a e g-b d g+2 b e f)-384 c^4 d e (b d-a e) (e f-d g)^2+3 b^5 e^5 g^2+256 c^5 d^3 (e f-d g)^2\right)}{256 c^{7/2} e^6}+\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(g \left(-4 c e (2 b d-3 a e)-3 b^2 e^2+16 c^2 d^2\right) (-b e g-2 c d g+4 c e f)-8 c e (2 c d-b e) \left(2 c e f^2-b d g^2\right)\right)-6 b^2 c e^3 g (2 a e g-b d g+2 b e f)+8 b c^2 e^2 \left(3 a e g (2 e f-d g)+2 b (e f-d g)^2\right)-32 c^3 e (5 b d-4 a e) (e f-d g)^2+3 b^4 e^4 g^2+128 c^4 d^2 (e f-d g)^2\right)}{128 c^3 e^5}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(3 b^2 e^2 g^2-6 c e g x (-b e g-2 c d g+4 c e f)-6 b c e g (2 e f-d g)-16 c^2 (e f-d g)^2\right)}{48 c^2 e^3}+\frac{(e f-d g)^2 \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^6}+\frac{g^2 \left(a+b x+c x^2\right)^{5/2}}{5 c e}",1,"((3*b^4*e^4*g^2 + 128*c^4*d^2*(e*f - d*g)^2 - 32*c^3*e*(5*b*d - 4*a*e)*(e*f - d*g)^2 - 6*b^2*c*e^3*g*(2*b*e*f - b*d*g + 2*a*e*g) + 8*b*c^2*e^2*(2*b*(e*f - d*g)^2 + 3*a*e*g*(2*e*f - d*g)) + 2*c*e*((16*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*g*(4*c*e*f - 2*c*d*g - b*e*g) - 8*c*e*(2*c*d - b*e)*(2*c*e*f^2 - b*d*g^2))*x)*Sqrt[a + b*x + c*x^2])/(128*c^3*e^5) - ((3*b^2*e^2*g^2 - 16*c^2*(e*f - d*g)^2 - 6*b*c*e*g*(2*e*f - d*g) - 6*c*e*g*(4*c*e*f - 2*c*d*g - b*e*g)*x)*(a + b*x + c*x^2)^(3/2))/(48*c^2*e^3) + (g^2*(a + b*x + c*x^2)^(5/2))/(5*c*e) - ((3*b^5*e^5*g^2 + 256*c^5*d^3*(e*f - d*g)^2 - 384*c^4*d*e*(b*d - a*e)*(e*f - d*g)^2 - 6*b^3*c*e^4*g*(2*b*e*f - b*d*g + 4*a*e*g) + 16*b*c^2*e^3*(3*a^2*e^2*g^2 + b^2*(e*f - d*g)^2 + 3*a*b*e*g*(2*e*f - d*g)) + 96*c^3*e^2*(b^2*d*(e*f - d*g)^2 - 2*a*b*e*(e*f - d*g)^2 - a^2*e^2*g*(2*e*f - d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(7/2)*e^6) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*(e*f - d*g)^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^6","A",8,6,29,0.2069,1,"{1653, 814, 843, 621, 206, 724}"
864,1,441,0,0.8532143,"\int \frac{(f+g x) \left(a+b x+c x^2\right)^{3/2}}{d+e x} \, dx","Int[((f + g*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 c^2 e^2 \left(a^2 e^2 g+2 a b e (e f-d g)+b^2 (-d) (e f-d g)\right)-8 b^2 c e^3 (3 a e g-b d g+b e f)+192 c^3 d e (b d-a e) (e f-d g)+3 b^4 e^4 g-128 c^4 d^3 (e f-d g)\right)}{128 c^{5/2} e^5}-\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (3 a e g-2 b d g+2 b e f)+3 b^2 e^2 g+16 c^2 d (e f-d g)\right)+16 c^2 e (5 b d-4 a e) (e f-d g)-4 b c e^2 (3 a e g-2 b d g+2 b e f)+3 b^3 e^3 g-64 c^3 d^2 (e f-d g)\right)}{64 c^2 e^4}+\frac{(e f-d g) \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^5}+\frac{\left(a+b x+c x^2\right)^{3/2} (3 b e g-8 c d g+8 c e f+6 c e g x)}{24 c e^2}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 c^2 e^2 \left(a^2 e^2 g+2 a b e (e f-d g)+b^2 (-d) (e f-d g)\right)-8 b^2 c e^3 (3 a e g-b d g+b e f)+192 c^3 d e (b d-a e) (e f-d g)+3 b^4 e^4 g-128 c^4 d^3 (e f-d g)\right)}{128 c^{5/2} e^5}-\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (3 a e g-2 b d g+2 b e f)+3 b^2 e^2 g+16 c^2 d (e f-d g)\right)+16 c^2 e (5 b d-4 a e) (e f-d g)-4 b c e^2 (3 a e g-2 b d g+2 b e f)+3 b^3 e^3 g-64 c^3 d^2 (e f-d g)\right)}{64 c^2 e^4}+\frac{(e f-d g) \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^5}+\frac{\left(a+b x+c x^2\right)^{3/2} (3 b e g-8 c d g+8 c e f+6 c e g x)}{24 c e^2}",1,"-((3*b^3*e^3*g - 64*c^3*d^2*(e*f - d*g) + 16*c^2*e*(5*b*d - 4*a*e)*(e*f - d*g) - 4*b*c*e^2*(2*b*e*f - 2*b*d*g + 3*a*e*g) + 2*c*e*(3*b^2*e^2*g + 16*c^2*d*(e*f - d*g) - 4*c*e*(2*b*e*f - 2*b*d*g + 3*a*e*g))*x)*Sqrt[a + b*x + c*x^2])/(64*c^2*e^4) + ((8*c*e*f - 8*c*d*g + 3*b*e*g + 6*c*e*g*x)*(a + b*x + c*x^2)^(3/2))/(24*c*e^2) + ((3*b^4*e^4*g - 128*c^4*d^3*(e*f - d*g) + 192*c^3*d*e*(b*d - a*e)*(e*f - d*g) - 8*b^2*c*e^3*(b*e*f - b*d*g + 3*a*e*g) + 48*c^2*e^2*(a^2*e^2*g - b^2*d*(e*f - d*g) + 2*a*b*e*(e*f - d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(5/2)*e^5) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*(e*f - d*g)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^5","A",7,5,27,0.1852,1,"{814, 843, 621, 206, 724}"
865,1,252,0,0.3456111,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{d+e x} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x),x]","\frac{\sqrt{a+b x+c x^2} \left(-2 c e (5 b d-4 a e)+b^2 e^2-2 c e x (2 c d-b e)+8 c^2 d^2\right)}{8 c e^3}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2} e^4}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^4}+\frac{\left(a+b x+c x^2\right)^{3/2}}{3 e}","\frac{\sqrt{a+b x+c x^2} \left(-2 c e (5 b d-4 a e)+b^2 e^2-2 c e x (2 c d-b e)+8 c^2 d^2\right)}{8 c e^3}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2} e^4}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^4}+\frac{\left(a+b x+c x^2\right)^{3/2}}{3 e}",1,"((8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*c*e^3) + (a + b*x + c*x^2)^(3/2)/(3*e) - ((2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2)*e^4) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^4","A",7,6,22,0.2727,1,"{734, 814, 843, 621, 206, 724}"
866,1,491,0,0.8414362,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x) (f+g x)} \, dx","Int[(a + b*x + c*x^2)^(3/2)/((d + e*x)*(f + g*x)),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c g \left(3 b e f^2-a g (3 e f-d g)\right)+b g^2 (-4 a e g+b d g+3 b e f)+8 c^2 e f^3\right)}{8 \sqrt{c} e g^3 (e f-d g)}+\frac{\sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}{e^2 (e f-d g)}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^3 (e f-d g)}-\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} e^3 (e f-d g)}-\frac{\sqrt{a+b x+c x^2} \left(-g (-4 a e g-b d g+5 b e f)-2 c g x (e f-d g)+4 c e f^2\right)}{4 e g^2 (e f-d g)}-\frac{\left(a g^2-b f g+c f^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g^3 (e f-d g)}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c g \left(3 b e f^2-a g (3 e f-d g)\right)+b g^2 (-4 a e g+b d g+3 b e f)+8 c^2 e f^3\right)}{8 \sqrt{c} e g^3 (e f-d g)}+\frac{\sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}{e^2 (e f-d g)}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^3 (e f-d g)}-\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c} e^3 (e f-d g)}-\frac{\sqrt{a+b x+c x^2} \left(-g (-4 a e g-b d g+5 b e f)-2 c g x (e f-d g)+4 c e f^2\right)}{4 e g^2 (e f-d g)}-\frac{\left(a g^2-b f g+c f^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g^3 (e f-d g)}",1,"((c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2])/(e^2*(e*f - d*g)) - ((4*c*e*f^2 - g*(5*b*e*f - b*d*g - 4*a*e*g) - 2*c*g*(e*f - d*g)*x)*Sqrt[a + b*x + c*x^2])/(4*e*g^2*(e*f - d*g)) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*e^3*(e*f - d*g)) + ((8*c^2*e*f^3 + b*g^2*(3*b*e*f + b*d*g - 4*a*e*g) - 4*c*g*(3*b*e*f^2 - a*g*(3*e*f - d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[c]*e*g^3*(e*f - d*g)) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e^3*(e*f - d*g)) - ((c*f^2 - b*f*g + a*g^2)^(3/2)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(g^3*(e*f - d*g))","A",13,7,29,0.2414,1,"{895, 734, 843, 621, 206, 724, 814}"
867,1,787,0,1.3760968,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x) (f+g x)^2} \, dx","Int[(a + b*x + c*x^2)^(3/2)/((d + e*x)*(f + g*x)^2),x]","\frac{\sqrt{a+b x+c x^2} \left(-2 c e (5 b d-4 a e)+b^2 e^2-2 c e x (2 c d-b e)+8 c^2 d^2\right)}{8 c e (e f-d g)^2}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2} e^2 (e f-d g)^2}-\frac{e \sqrt{a+b x+c x^2} \left(-2 c g (5 b f-4 a g)+b^2 g^2-2 c g x (2 c f-b g)+8 c^2 f^2\right)}{8 c g^2 (e f-d g)^2}+\frac{e (2 c f-b g) \left(-4 c g (2 b f-3 a g)-b^2 g^2+8 c^2 f^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2} g^3 (e f-d g)^2}-\frac{3 \left(-4 c g (2 b f-a g)+b^2 g^2+8 c^2 f^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{c} g^3 (e f-d g)}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^2 (e f-d g)^2}-\frac{e \left(a g^2-b f g+c f^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g^3 (e f-d g)^2}+\frac{3 (2 c f-b g) \sqrt{a g^2-b f g+c f^2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 g^3 (e f-d g)}+\frac{3 \sqrt{a+b x+c x^2} (-3 b g+4 c f-2 c g x)}{4 g^2 (e f-d g)}+\frac{\left(a+b x+c x^2\right)^{3/2}}{(f+g x) (e f-d g)}","\frac{\sqrt{a+b x+c x^2} \left(-2 c e (5 b d-4 a e)+b^2 e^2-2 c e x (2 c d-b e)+8 c^2 d^2\right)}{8 c e (e f-d g)^2}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2} e^2 (e f-d g)^2}-\frac{e \sqrt{a+b x+c x^2} \left(-2 c g (5 b f-4 a g)+b^2 g^2-2 c g x (2 c f-b g)+8 c^2 f^2\right)}{8 c g^2 (e f-d g)^2}+\frac{e (2 c f-b g) \left(-4 c g (2 b f-3 a g)-b^2 g^2+8 c^2 f^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2} g^3 (e f-d g)^2}-\frac{3 \left(-4 c g (2 b f-a g)+b^2 g^2+8 c^2 f^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{c} g^3 (e f-d g)}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^2 (e f-d g)^2}-\frac{e \left(a g^2-b f g+c f^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{g^3 (e f-d g)^2}+\frac{3 (2 c f-b g) \sqrt{a g^2-b f g+c f^2} \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 g^3 (e f-d g)}+\frac{3 \sqrt{a+b x+c x^2} (-3 b g+4 c f-2 c g x)}{4 g^2 (e f-d g)}+\frac{\left(a+b x+c x^2\right)^{3/2}}{(f+g x) (e f-d g)}",1,"((8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*c*e*(e*f - d*g)^2) + (3*(4*c*f - 3*b*g - 2*c*g*x)*Sqrt[a + b*x + c*x^2])/(4*g^2*(e*f - d*g)) - (e*(8*c^2*f^2 + b^2*g^2 - 2*c*g*(5*b*f - 4*a*g) - 2*c*g*(2*c*f - b*g)*x)*Sqrt[a + b*x + c*x^2])/(8*c*g^2*(e*f - d*g)^2) + (a + b*x + c*x^2)^(3/2)/((e*f - d*g)*(f + g*x)) - ((2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2)*e^2*(e*f - d*g)^2) + (e*(2*c*f - b*g)*(8*c^2*f^2 - b^2*g^2 - 4*c*g*(2*b*f - 3*a*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2)*g^3*(e*f - d*g)^2) - (3*(8*c^2*f^2 + b^2*g^2 - 4*c*g*(2*b*f - a*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[c]*g^3*(e*f - d*g)) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e^2*(e*f - d*g)^2) + (3*(2*c*f - b*g)*Sqrt[c*f^2 - b*f*g + a*g^2]*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(2*g^3*(e*f - d*g)) - (e*(c*f^2 - b*f*g + a*g^2)^(3/2)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(g^3*(e*f - d*g)^2)","A",23,8,29,0.2759,1,"{960, 734, 814, 843, 621, 206, 724, 732}"
868,1,1066,0,1.7059002,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x) (f+g x)^3} \, dx","Int[(a + b*x + c*x^2)^(3/2)/((d + e*x)*(f + g*x)^3),x]","\frac{(2 c f-b g) \left(8 c^2 f^2-b^2 g^2-4 c g (2 b f-3 a g)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^2}{16 c^{3/2} g^3 (e f-d g)^3}-\frac{\left(c f^2-b g f+a g^2\right)^{3/2} \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e^2}{g^3 (e f-d g)^3}-\frac{\left(8 c^2 f^2+b^2 g^2-2 c g (5 b f-4 a g)-2 c g (2 c f-b g) x\right) \sqrt{c x^2+b x+a} e^2}{8 c g^2 (e f-d g)^3}+\frac{\left(c x^2+b x+a\right)^{3/2} e}{(e f-d g)^2 (f+g x)}-\frac{3 \left(8 c^2 f^2+b^2 g^2-4 c g (2 b f-a g)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e}{8 \sqrt{c} g^3 (e f-d g)^2}+\frac{3 (2 c f-b g) \sqrt{c f^2-b g f+a g^2} \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e}{2 g^3 (e f-d g)^2}+\frac{3 (4 c f-3 b g-2 c g x) \sqrt{c x^2+b x+a} e}{4 g^2 (e f-d g)^2}+\frac{\left(c x^2+b x+a\right)^{3/2}}{2 (e f-d g) (f+g x)^2}+\frac{3 \sqrt{c} (2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{2 g^3 (e f-d g)}-\frac{3 \left(8 c^2 f^2+b^2 g^2-4 c g (2 b f-a g)\right) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right)}{8 g^3 (e f-d g) \sqrt{c f^2-b g f+a g^2}}+\frac{\left(8 c^2 d^2+b^2 e^2-2 c e (5 b d-4 a e)-2 c e (2 c d-b e) x\right) \sqrt{c x^2+b x+a}}{8 c (e f-d g)^3}-\frac{3 (4 c f-b g+2 c g x) \sqrt{c x^2+b x+a}}{4 g^2 (e f-d g) (f+g x)}-\frac{(2 c d-b e) \left(8 c^2 d^2-b^2 e^2-4 c e (2 b d-3 a e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{16 c^{3/2} (e f-d g)^3 e}+\frac{\left(c d^2-b e d+a e^2\right)^{3/2} \tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right)}{(e f-d g)^3 e}","\frac{(2 c f-b g) \left(8 c^2 f^2-b^2 g^2-4 c g (2 b f-3 a g)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^2}{16 c^{3/2} g^3 (e f-d g)^3}-\frac{\left(c f^2-b g f+a g^2\right)^{3/2} \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e^2}{g^3 (e f-d g)^3}-\frac{\left(8 c^2 f^2+b^2 g^2-2 c g (5 b f-4 a g)-2 c g (2 c f-b g) x\right) \sqrt{c x^2+b x+a} e^2}{8 c g^2 (e f-d g)^3}+\frac{\left(c x^2+b x+a\right)^{3/2} e}{(e f-d g)^2 (f+g x)}-\frac{3 \left(8 c^2 f^2+b^2 g^2-4 c g (2 b f-a g)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e}{8 \sqrt{c} g^3 (e f-d g)^2}+\frac{3 (2 c f-b g) \sqrt{c f^2-b g f+a g^2} \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e}{2 g^3 (e f-d g)^2}+\frac{3 (4 c f-3 b g-2 c g x) \sqrt{c x^2+b x+a} e}{4 g^2 (e f-d g)^2}+\frac{\left(c x^2+b x+a\right)^{3/2}}{2 (e f-d g) (f+g x)^2}+\frac{3 \sqrt{c} (2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{2 g^3 (e f-d g)}-\frac{3 \left(8 c^2 f^2+b^2 g^2-4 c g (2 b f-a g)\right) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right)}{8 g^3 (e f-d g) \sqrt{c f^2-b g f+a g^2}}+\frac{\left(8 c^2 d^2+b^2 e^2-2 c e (5 b d-4 a e)-2 c e (2 c d-b e) x\right) \sqrt{c x^2+b x+a}}{8 c (e f-d g)^3}-\frac{3 (4 c f-b g+2 c g x) \sqrt{c x^2+b x+a}}{4 g^2 (e f-d g) (f+g x)}-\frac{(2 c d-b e) \left(8 c^2 d^2-b^2 e^2-4 c e (2 b d-3 a e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{16 c^{3/2} (e f-d g)^3 e}+\frac{\left(c d^2-b e d+a e^2\right)^{3/2} \tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right)}{(e f-d g)^3 e}",1,"((8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*c*(e*f - d*g)^3) + (3*e*(4*c*f - 3*b*g - 2*c*g*x)*Sqrt[a + b*x + c*x^2])/(4*g^2*(e*f - d*g)^2) - (3*(4*c*f - b*g + 2*c*g*x)*Sqrt[a + b*x + c*x^2])/(4*g^2*(e*f - d*g)*(f + g*x)) - (e^2*(8*c^2*f^2 + b^2*g^2 - 2*c*g*(5*b*f - 4*a*g) - 2*c*g*(2*c*f - b*g)*x)*Sqrt[a + b*x + c*x^2])/(8*c*g^2*(e*f - d*g)^3) + (a + b*x + c*x^2)^(3/2)/(2*(e*f - d*g)*(f + g*x)^2) + (e*(a + b*x + c*x^2)^(3/2))/((e*f - d*g)^2*(f + g*x)) - ((2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2)*e*(e*f - d*g)^3) + (3*Sqrt[c]*(2*c*f - b*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*g^3*(e*f - d*g)) + (e^2*(2*c*f - b*g)*(8*c^2*f^2 - b^2*g^2 - 4*c*g*(2*b*f - 3*a*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2)*g^3*(e*f - d*g)^3) - (3*e*(8*c^2*f^2 + b^2*g^2 - 4*c*g*(2*b*f - a*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[c]*g^3*(e*f - d*g)^2) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e*(e*f - d*g)^3) + (3*e*(2*c*f - b*g)*Sqrt[c*f^2 - b*f*g + a*g^2]*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(2*g^3*(e*f - d*g)^2) - (e^2*(c*f^2 - b*f*g + a*g^2)^(3/2)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(g^3*(e*f - d*g)^3) - (3*(8*c^2*f^2 + b^2*g^2 - 4*c*g*(2*b*f - a*g))*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(8*g^3*(e*f - d*g)*Sqrt[c*f^2 - b*f*g + a*g^2])","A",30,9,29,0.3103,1,"{960, 734, 814, 843, 621, 206, 724, 732, 812}"
869,1,886,0,1.8002759,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x) (f+g x)} \, dx","Int[(a + b*x + c*x^2)^(5/2)/((d + e*x)*(f + g*x)),x]","\frac{\tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right) \left(c d^2-b e d+a e^2\right)^{5/2}}{e^5 (e f-d g)}+\frac{\left(c x^2+b x+a\right)^{3/2} \left(c d^2-b e d+a e^2\right)}{3 e^2 (e f-d g)}-\frac{(2 c d-b e) \left(8 c^2 d^2-b^2 e^2-4 c e (2 b d-3 a e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) \left(c d^2-b e d+a e^2\right)}{16 c^{3/2} e^5 (e f-d g)}+\frac{\left(8 c^2 d^2+b^2 e^2-2 c e (5 b d-4 a e)-2 c e (2 c d-b e) x\right) \sqrt{c x^2+b x+a} \left(c d^2-b e d+a e^2\right)}{8 c e^4 (e f-d g)}-\frac{\left(8 c e f^2-g (11 b e f-3 b d g-8 a e g)-6 c g (e f-d g) x\right) \left(c x^2+b x+a\right)^{3/2}}{24 e g^2 (e f-d g)}+\frac{\left(128 c^4 e f^5-320 c^3 e g (b f-a g) f^3-b^3 g^4 (5 b e f+3 b d g-8 a e g)+48 c^2 g^2 \left(5 b^2 e f^3-10 a b e g f^2+a^2 g^2 (5 e f-d g)\right)-8 b c g^3 \left(5 b^2 e f^2+12 a^2 e g^2-3 a b g (5 e f+d g)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{128 c^{3/2} e g^5 (e f-d g)}-\frac{\left(c f^2-b g f+a g^2\right)^{5/2} \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right)}{g^5 (e f-d g)}-\frac{\left(64 c^3 e f^4-16 c^2 e g (9 b f-8 a g) f^2-b^2 g^3 (5 b e f+3 b d g-8 a e g)+4 c g^2 \left(22 b^2 e f^2+16 a^2 e g^2-3 a b g (13 e f-d g)\right)-2 c g \left(16 c^2 e f^3+b g^2 (5 b e f+3 b d g-8 a e g)-4 c g \left(6 b e f^2-a g (7 e f-3 d g)\right)\right) x\right) \sqrt{c x^2+b x+a}}{64 c e g^4 (e f-d g)}","\frac{\tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right) \left(c d^2-b e d+a e^2\right)^{5/2}}{e^5 (e f-d g)}+\frac{\left(c x^2+b x+a\right)^{3/2} \left(c d^2-b e d+a e^2\right)}{3 e^2 (e f-d g)}-\frac{(2 c d-b e) \left(8 c^2 d^2-b^2 e^2-4 c e (2 b d-3 a e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) \left(c d^2-b e d+a e^2\right)}{16 c^{3/2} e^5 (e f-d g)}+\frac{\left(8 c^2 d^2+b^2 e^2-2 c e (5 b d-4 a e)-2 c e (2 c d-b e) x\right) \sqrt{c x^2+b x+a} \left(c d^2-b e d+a e^2\right)}{8 c e^4 (e f-d g)}-\frac{\left(8 c e f^2-g (11 b e f-3 b d g-8 a e g)-6 c g (e f-d g) x\right) \left(c x^2+b x+a\right)^{3/2}}{24 e g^2 (e f-d g)}+\frac{\left(128 c^4 e f^5-320 c^3 e g (b f-a g) f^3-b^3 g^4 (5 b e f+3 b d g-8 a e g)+48 c^2 g^2 \left(5 b^2 e f^3-10 a b e g f^2+a^2 g^2 (5 e f-d g)\right)-8 b c g^3 \left(5 b^2 e f^2+12 a^2 e g^2-3 a b g (5 e f+d g)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{128 c^{3/2} e g^5 (e f-d g)}-\frac{\left(c f^2-b g f+a g^2\right)^{5/2} \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right)}{g^5 (e f-d g)}-\frac{\left(64 c^3 e f^4-16 c^2 e g (9 b f-8 a g) f^2-b^2 g^3 (5 b e f+3 b d g-8 a e g)+4 c g^2 \left(22 b^2 e f^2+16 a^2 e g^2-3 a b g (13 e f-d g)\right)-2 c g \left(16 c^2 e f^3+b g^2 (5 b e f+3 b d g-8 a e g)-4 c g \left(6 b e f^2-a g (7 e f-3 d g)\right)\right) x\right) \sqrt{c x^2+b x+a}}{64 c e g^4 (e f-d g)}",1,"((c*d^2 - b*d*e + a*e^2)*(8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*c*e^4*(e*f - d*g)) - ((64*c^3*e*f^4 - 16*c^2*e*f^2*g*(9*b*f - 8*a*g) - b^2*g^3*(5*b*e*f + 3*b*d*g - 8*a*e*g) + 4*c*g^2*(22*b^2*e*f^2 + 16*a^2*e*g^2 - 3*a*b*g*(13*e*f - d*g)) - 2*c*g*(16*c^2*e*f^3 + b*g^2*(5*b*e*f + 3*b*d*g - 8*a*e*g) - 4*c*g*(6*b*e*f^2 - a*g*(7*e*f - 3*d*g)))*x)*Sqrt[a + b*x + c*x^2])/(64*c*e*g^4*(e*f - d*g)) + ((c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(3/2))/(3*e^2*(e*f - d*g)) - ((8*c*e*f^2 - g*(11*b*e*f - 3*b*d*g - 8*a*e*g) - 6*c*g*(e*f - d*g)*x)*(a + b*x + c*x^2)^(3/2))/(24*e*g^2*(e*f - d*g)) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2)*e^5*(e*f - d*g)) + ((128*c^4*e*f^5 - 320*c^3*e*f^3*g*(b*f - a*g) - b^3*g^4*(5*b*e*f + 3*b*d*g - 8*a*e*g) + 48*c^2*g^2*(5*b^2*e*f^3 - 10*a*b*e*f^2*g + a^2*g^2*(5*e*f - d*g)) - 8*b*c*g^3*(5*b^2*e*f^2 + 12*a^2*e*g^2 - 3*a*b*g*(5*e*f + d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(3/2)*e*g^5*(e*f - d*g)) + ((c*d^2 - b*d*e + a*e^2)^(5/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e^5*(e*f - d*g)) - ((c*f^2 - b*f*g + a*g^2)^(5/2)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(g^5*(e*f - d*g))","A",15,7,29,0.2414,1,"{895, 734, 814, 843, 621, 206, 724}"
870,1,431,0,1.3703397,"\int \frac{(f+g x)^4}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[(f + g*x)^4/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{g^2 \sqrt{a+b x+c x^2} \left(-4 c e g (4 a e g-7 b d g+18 b e f)+15 b^2 e^2 g^2+4 c^2 \left(11 d^2 g^2-36 d e f g+36 e^2 f^2\right)\right)}{24 c^3 e^3}-\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(8 c^2 e g \left(a e g (4 e f-d g)+b \left(d^2 g^2-4 d e f g+6 e^2 f^2\right)\right)-6 b c e^2 g^2 (2 a e g-b d g+4 b e f)+5 b^3 e^3 g^3-16 c^3 \left(4 d^2 e f g^2-d^3 g^3-6 d e^2 f^2 g+4 e^3 f^3\right)\right)}{16 c^{7/2} e^4}+\frac{g^3 (d+e x) \sqrt{a+b x+c x^2} (-5 b e g-14 c d g+24 c e f)}{12 c^2 e^3}+\frac{(e f-d g)^4 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^4 \sqrt{a e^2-b d e+c d^2}}+\frac{g^4 (d+e x)^2 \sqrt{a+b x+c x^2}}{3 c e^3}","\frac{g^2 \sqrt{a+b x+c x^2} \left(-4 c e g (4 a e g-7 b d g+18 b e f)+15 b^2 e^2 g^2+4 c^2 \left(11 d^2 g^2-36 d e f g+36 e^2 f^2\right)\right)}{24 c^3 e^3}-\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(8 c^2 e g \left(a e g (4 e f-d g)+b \left(d^2 g^2-4 d e f g+6 e^2 f^2\right)\right)-6 b c e^2 g^2 (2 a e g-b d g+4 b e f)+5 b^3 e^3 g^3-16 c^3 \left(4 d^2 e f g^2-d^3 g^3-6 d e^2 f^2 g+4 e^3 f^3\right)\right)}{16 c^{7/2} e^4}+\frac{g^3 (d+e x) \sqrt{a+b x+c x^2} (-5 b e g-14 c d g+24 c e f)}{12 c^2 e^3}+\frac{(e f-d g)^4 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^4 \sqrt{a e^2-b d e+c d^2}}+\frac{g^4 (d+e x)^2 \sqrt{a+b x+c x^2}}{3 c e^3}",1,"(g^2*(15*b^2*e^2*g^2 - 4*c*e*g*(18*b*e*f - 7*b*d*g + 4*a*e*g) + 4*c^2*(36*e^2*f^2 - 36*d*e*f*g + 11*d^2*g^2))*Sqrt[a + b*x + c*x^2])/(24*c^3*e^3) + (g^3*(24*c*e*f - 14*c*d*g - 5*b*e*g)*(d + e*x)*Sqrt[a + b*x + c*x^2])/(12*c^2*e^3) + (g^4*(d + e*x)^2*Sqrt[a + b*x + c*x^2])/(3*c*e^3) - (g*(5*b^3*e^3*g^3 - 6*b*c*e^2*g^2*(4*b*e*f - b*d*g + 2*a*e*g) - 16*c^3*(4*e^3*f^3 - 6*d*e^2*f^2*g + 4*d^2*e*f*g^2 - d^3*g^3) + 8*c^2*e*g*(a*e*g*(4*e*f - d*g) + b*(6*e^2*f^2 - 4*d*e*f*g + d^2*g^2)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(7/2)*e^4) + ((e*f - d*g)^4*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e^4*Sqrt[c*d^2 - b*d*e + a*e^2])","A",8,5,29,0.1724,1,"{1653, 843, 621, 206, 724}"
871,1,270,0,0.7081676,"\int \frac{(f+g x)^3}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[(f + g*x)^3/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c e g (a e g-b d g+3 b e f)+3 b^2 e^2 g^2+8 c^2 \left(d^2 g^2-3 d e f g+3 e^2 f^2\right)\right)}{8 c^{5/2} e^3}+\frac{3 g^2 \sqrt{a+b x+c x^2} (-b e g-2 c d g+4 c e f)}{4 c^2 e^2}+\frac{(e f-d g)^3 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^3 \sqrt{a e^2-b d e+c d^2}}+\frac{g^3 (d+e x) \sqrt{a+b x+c x^2}}{2 c e^2}","\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c e g (a e g-b d g+3 b e f)+3 b^2 e^2 g^2+8 c^2 \left(d^2 g^2-3 d e f g+3 e^2 f^2\right)\right)}{8 c^{5/2} e^3}+\frac{3 g^2 \sqrt{a+b x+c x^2} (-b e g-2 c d g+4 c e f)}{4 c^2 e^2}+\frac{(e f-d g)^3 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^3 \sqrt{a e^2-b d e+c d^2}}+\frac{g^3 (d+e x) \sqrt{a+b x+c x^2}}{2 c e^2}",1,"(3*g^2*(4*c*e*f - 2*c*d*g - b*e*g)*Sqrt[a + b*x + c*x^2])/(4*c^2*e^2) + (g^3*(d + e*x)*Sqrt[a + b*x + c*x^2])/(2*c*e^2) + (g*(3*b^2*e^2*g^2 - 4*c*e*g*(3*b*e*f - b*d*g + a*e*g) + 8*c^2*(3*e^2*f^2 - 3*d*e*f*g + d^2*g^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(5/2)*e^3) + ((e*f - d*g)^3*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e^3*Sqrt[c*d^2 - b*d*e + a*e^2])","A",7,5,29,0.1724,1,"{1653, 843, 621, 206, 724}"
872,1,176,0,0.3049162,"\int \frac{(f+g x)^2}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[(f + g*x)^2/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (-b e g-2 c d g+4 c e f)}{2 c^{3/2} e^2}+\frac{(e f-d g)^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^2 \sqrt{a e^2-b d e+c d^2}}+\frac{g^2 \sqrt{a+b x+c x^2}}{c e}","\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (-b e g-2 c d g+4 c e f)}{2 c^{3/2} e^2}+\frac{(e f-d g)^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^2 \sqrt{a e^2-b d e+c d^2}}+\frac{g^2 \sqrt{a+b x+c x^2}}{c e}",1,"(g^2*Sqrt[a + b*x + c*x^2])/(c*e) + (g*(4*c*e*f - 2*c*d*g - b*e*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(3/2)*e^2) + ((e*f - d*g)^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e^2*Sqrt[c*d^2 - b*d*e + a*e^2])","A",6,5,29,0.1724,1,"{1653, 843, 621, 206, 724}"
873,1,131,0,0.0932019,"\int \frac{f+g x}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[(f + g*x)/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{(e f-d g) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e \sqrt{a e^2-b d e+c d^2}}+\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c} e}","\frac{(e f-d g) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e \sqrt{a e^2-b d e+c d^2}}+\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c} e}",1,"(g*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c]*e) + ((e*f - d*g)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e*Sqrt[c*d^2 - b*d*e + a*e^2])","A",5,4,27,0.1481,1,"{843, 621, 206, 724}"
874,1,79,0,0.0378462,"\int \frac{1}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\sqrt{a e^2-b d e+c d^2}}","\frac{\tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\sqrt{a e^2-b d e+c d^2}}",1,"ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])]/Sqrt[c*d^2 - b*d*e + a*e^2]","A",2,2,22,0.09091,1,"{724, 206}"
875,1,182,0,0.218878,"\int \frac{1}{(d+e x) (f+g x) \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)*(f + g*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{e \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g) \sqrt{a e^2-b d e+c d^2}}-\frac{g \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g) \sqrt{a g^2-b f g+c f^2}}","\frac{e \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g) \sqrt{a e^2-b d e+c d^2}}-\frac{g \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g) \sqrt{a g^2-b f g+c f^2}}",1,"(e*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c*d^2 - b*d*e + a*e^2]*(e*f - d*g)) - (g*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/((e*f - d*g)*Sqrt[c*f^2 - b*f*g + a*g^2])","A",6,3,29,0.1034,1,"{960, 724, 206}"
876,1,340,0,0.3935708,"\int \frac{1}{(d+e x) (f+g x)^2 \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)*(f + g*x)^2*Sqrt[a + b*x + c*x^2]),x]","\frac{e^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^2 \sqrt{a e^2-b d e+c d^2}}+\frac{g^2 \sqrt{a+b x+c x^2}}{(f+g x) (e f-d g) \left(a g^2-b f g+c f^2\right)}-\frac{e g \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g)^2 \sqrt{a g^2-b f g+c f^2}}-\frac{g (2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 (e f-d g) \left(a g^2-b f g+c f^2\right)^{3/2}}","\frac{e^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^2 \sqrt{a e^2-b d e+c d^2}}+\frac{g^2 \sqrt{a+b x+c x^2}}{(f+g x) (e f-d g) \left(a g^2-b f g+c f^2\right)}-\frac{e g \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g)^2 \sqrt{a g^2-b f g+c f^2}}-\frac{g (2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 (e f-d g) \left(a g^2-b f g+c f^2\right)^{3/2}}",1,"(g^2*Sqrt[a + b*x + c*x^2])/((e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*(f + g*x)) + (e^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c*d^2 - b*d*e + a*e^2]*(e*f - d*g)^2) - (g*(2*c*f - b*g)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(2*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^(3/2)) - (e*g*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/((e*f - d*g)^2*Sqrt[c*f^2 - b*f*g + a*g^2])","A",9,4,29,0.1379,1,"{960, 724, 206, 730}"
877,1,587,0,0.8101419,"\int \frac{1}{(d+e x) (f+g x)^3 \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)*(f + g*x)^3*Sqrt[a + b*x + c*x^2]),x]","-\frac{g \left(-4 c g (a g+2 b f)+3 b^2 g^2+8 c^2 f^2\right) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{8 (e f-d g) \left(a g^2-b f g+c f^2\right)^{5/2}}+\frac{e^3 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^3 \sqrt{a e^2-b d e+c d^2}}-\frac{e^2 g \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g)^3 \sqrt{a g^2-b f g+c f^2}}+\frac{e g^2 \sqrt{a+b x+c x^2}}{(f+g x) (e f-d g)^2 \left(a g^2-b f g+c f^2\right)}+\frac{3 g^2 \sqrt{a+b x+c x^2} (2 c f-b g)}{4 (f+g x) (e f-d g) \left(a g^2-b f g+c f^2\right)^2}+\frac{g^2 \sqrt{a+b x+c x^2}}{2 (f+g x)^2 (e f-d g) \left(a g^2-b f g+c f^2\right)}-\frac{e g (2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 (e f-d g)^2 \left(a g^2-b f g+c f^2\right)^{3/2}}","-\frac{g \left(-4 c g (a g+2 b f)+3 b^2 g^2+8 c^2 f^2\right) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{8 (e f-d g) \left(a g^2-b f g+c f^2\right)^{5/2}}+\frac{e^3 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^3 \sqrt{a e^2-b d e+c d^2}}-\frac{e^2 g \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g)^3 \sqrt{a g^2-b f g+c f^2}}+\frac{e g^2 \sqrt{a+b x+c x^2}}{(f+g x) (e f-d g)^2 \left(a g^2-b f g+c f^2\right)}+\frac{3 g^2 \sqrt{a+b x+c x^2} (2 c f-b g)}{4 (f+g x) (e f-d g) \left(a g^2-b f g+c f^2\right)^2}+\frac{g^2 \sqrt{a+b x+c x^2}}{2 (f+g x)^2 (e f-d g) \left(a g^2-b f g+c f^2\right)}-\frac{e g (2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 (e f-d g)^2 \left(a g^2-b f g+c f^2\right)^{3/2}}",1,"(g^2*Sqrt[a + b*x + c*x^2])/(2*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*(f + g*x)^2) + (3*g^2*(2*c*f - b*g)*Sqrt[a + b*x + c*x^2])/(4*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^2*(f + g*x)) + (e*g^2*Sqrt[a + b*x + c*x^2])/((e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)*(f + g*x)) + (e^3*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c*d^2 - b*d*e + a*e^2]*(e*f - d*g)^3) - (e*g*(2*c*f - b*g)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(2*(e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)^(3/2)) - (e^2*g*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/((e*f - d*g)^3*Sqrt[c*f^2 - b*f*g + a*g^2]) - (g*(8*c^2*f^2 + 3*b^2*g^2 - 4*c*g*(2*b*f + a*g))*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(8*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^(5/2))","A",13,6,29,0.2069,1,"{960, 724, 206, 744, 806, 730}"
878,1,496,0,1.1994316,"\int \frac{(f+g x)^4}{(d+e x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(f + g*x)^4/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{2 \left(x \left(2 c^2 g^2 \left(a^2 (-g) (4 e f-d g)-3 a b f (e f-2 d g)+3 b^2 d f^2\right)-b c g^3 \left(-3 a^2 e g-4 a b (e f-d g)+4 b^2 d f\right)+b^3 g^4 (b d-a e)+c^3 f^2 (4 a g (2 e f-3 d g)-b f (4 d g+e f))+2 c^4 d f^4\right)-b^2 \left(a^2 e g^4+4 a c d f g^3+c^2 e f^4\right)+b c \left(a^2 g^3 (4 e f-3 d g)+2 a c f^2 g (3 d g+2 e f)+c^2 d f^4\right)+2 a c \left(a^2 e g^4-2 a c f g^2 (3 e f-2 d g)+c^2 f^3 (e f-4 d g)\right)+a b^3 d g^4\right)}{c^2 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{g^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (-3 b e g-2 c d g+8 c e f)}{2 c^{5/2} e^2}+\frac{g^4 \sqrt{a+b x+c x^2}}{c^2 e}+\frac{(e f-d g)^4 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^2 \left(a e^2-b d e+c d^2\right)^{3/2}}","-\frac{2 \left(x \left(2 c^2 g^2 \left(a^2 (-g) (4 e f-d g)-3 a b f (e f-2 d g)+3 b^2 d f^2\right)-b c g^3 \left(-3 a^2 e g-4 a b (e f-d g)+4 b^2 d f\right)+b^3 g^4 (b d-a e)+c^3 f^2 (4 a g (2 e f-3 d g)-b f (4 d g+e f))+2 c^4 d f^4\right)-b^2 \left(a^2 e g^4+4 a c d f g^3+c^2 e f^4\right)+b c \left(a^2 g^3 (4 e f-3 d g)+2 a c f^2 g (3 d g+2 e f)+c^2 d f^4\right)+2 a c \left(a^2 e g^4-2 a c f g^2 (3 e f-2 d g)+c^2 f^3 (e f-4 d g)\right)+a b^3 d g^4\right)}{c^2 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{g^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (-3 b e g-2 c d g+8 c e f)}{2 c^{5/2} e^2}+\frac{g^4 \sqrt{a+b x+c x^2}}{c^2 e}+\frac{(e f-d g)^4 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^2 \left(a e^2-b d e+c d^2\right)^{3/2}}",1,"(-2*(a*b^3*d*g^4 - b^2*(c^2*e*f^4 + 4*a*c*d*f*g^3 + a^2*e*g^4) + 2*a*c*(a^2*e*g^4 + c^2*f^3*(e*f - 4*d*g) - 2*a*c*f*g^2*(3*e*f - 2*d*g)) + b*c*(c^2*d*f^4 + a^2*g^3*(4*e*f - 3*d*g) + 2*a*c*f^2*g*(2*e*f + 3*d*g)) + (2*c^4*d*f^4 + b^3*(b*d - a*e)*g^4 - b*c*g^3*(4*b^2*d*f - 3*a^2*e*g - 4*a*b*(e*f - d*g)) + 2*c^2*g^2*(3*b^2*d*f^2 - 3*a*b*f*(e*f - 2*d*g) - a^2*g*(4*e*f - d*g)) + c^3*f^2*(4*a*g*(2*e*f - 3*d*g) - b*f*(e*f + 4*d*g)))*x))/(c^2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) + (g^4*Sqrt[a + b*x + c*x^2])/(c^2*e) + (g^3*(8*c*e*f - 2*c*d*g - 3*b*e*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(5/2)*e^2) + ((e*f - d*g)^4*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e^2*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",7,6,29,0.2069,1,"{1646, 1653, 843, 621, 206, 724}"
879,1,357,0,0.5280499,"\int \frac{(f+g x)^3}{(d+e x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(f + g*x)^3/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \left(-x \left(c g^2 \left(-2 a^2 e g+3 a b d g-3 a b e f+3 b^2 d f\right)-b^2 g^3 (b d-a e)+c^2 f (6 a g (e f-d g)-b f (3 d g+e f))+2 c^3 d f^3\right)-b \left(a^2 e g^3+3 a c f g (d g+e f)+c^2 d f^3\right)+b^2 \left(a d g^3+c e f^3\right)-2 a c \left(c f^2 (e f-3 d g)-a g^2 (3 e f-d g)\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{g^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2} e}+\frac{(e f-d g)^3 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e \left(a e^2-b d e+c d^2\right)^{3/2}}","\frac{2 \left(-x \left(c g^2 \left(-2 a^2 e g+3 a b d g-3 a b e f+3 b^2 d f\right)-b^2 g^3 (b d-a e)+c^2 f (6 a g (e f-d g)-b f (3 d g+e f))+2 c^3 d f^3\right)-b \left(a^2 e g^3+3 a c f g (d g+e f)+c^2 d f^3\right)+b^2 \left(a d g^3+c e f^3\right)-2 a c \left(c f^2 (e f-3 d g)-a g^2 (3 e f-d g)\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{g^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2} e}+\frac{(e f-d g)^3 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e \left(a e^2-b d e+c d^2\right)^{3/2}}",1,"(2*(b^2*(c*e*f^3 + a*d*g^3) - 2*a*c*(c*f^2*(e*f - 3*d*g) - a*g^2*(3*e*f - d*g)) - b*(c^2*d*f^3 + a^2*e*g^3 + 3*a*c*f*g*(e*f + d*g)) - (2*c^3*d*f^3 - b^2*(b*d - a*e)*g^3 + c*g^2*(3*b^2*d*f - 3*a*b*e*f + 3*a*b*d*g - 2*a^2*e*g) + c^2*f*(6*a*g*(e*f - d*g) - b*f*(e*f + 3*d*g)))*x))/(c*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) + (g^3*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(c^(3/2)*e) + ((e*f - d*g)^3*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",6,5,29,0.1724,1,"{1646, 843, 621, 206, 724}"
880,1,240,0,0.3053134,"\int \frac{(f+g x)^2}{(d+e x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(f + g*x)^2/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \left(-x \left(c (2 a g (2 e f-d g)-b f (2 d g+e f))+b g^2 (b d-a e)+2 c^2 d f^2\right)-b \left(a g (d g+2 e f)+c d f^2\right)+2 a \left(a e g^2-c f (e f-2 d g)\right)+b^2 e f^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{(e f-d g)^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}","\frac{2 \left(-x \left(c (2 a g (2 e f-d g)-b f (2 d g+e f))+b g^2 (b d-a e)+2 c^2 d f^2\right)-b \left(a g (d g+2 e f)+c d f^2\right)+2 a \left(a e g^2-c f (e f-2 d g)\right)+b^2 e f^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{(e f-d g)^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}",1,"(2*(b^2*e*f^2 + 2*a*(a*e*g^2 - c*f*(e*f - 2*d*g)) - b*(c*d*f^2 + a*g*(2*e*f + d*g)) - (2*c^2*d*f^2 + b*(b*d - a*e)*g^2 + c*(2*a*g*(2*e*f - d*g) - b*f*(e*f + 2*d*g)))*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) + ((e*f - d*g)^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(c*d^2 - b*d*e + a*e^2)^(3/2)","A",4,4,29,0.1379,1,"{1646, 12, 724, 206}"
881,1,187,0,0.1349676,"\int \frac{f+g x}{(d+e x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(f + g*x)/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x]","\frac{e (e f-d g) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{2 \left(c x (2 a e g-b (d g+e f)+2 c d f)+a b e g-2 a c d g+2 a c e f+b^2 (-e) f+b c d f\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}","\frac{e (e f-d g) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{2 \left(c x (2 a e g-b (d g+e f)+2 c d f)+a b e g-2 a c d g+2 a c e f+b^2 (-e) f+b c d f\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}",1,"(-2*(b*c*d*f - b^2*e*f + 2*a*c*e*f - 2*a*c*d*g + a*b*e*g + c*(2*c*d*f + 2*a*e*g - b*(e*f + d*g))*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) + (e*(e*f - d*g)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(c*d^2 - b*d*e + a*e^2)^(3/2)","A",4,4,27,0.1481,1,"{822, 12, 724, 206}"
882,1,155,0,0.1011101,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x]","\frac{e^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}","\frac{e^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}",1,"(-2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) + (e^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(c*d^2 - b*d*e + a*e^2)^(3/2)","A",4,4,22,0.1818,1,"{740, 12, 724, 206}"
883,1,352,0,0.4433552,"\int \frac{1}{(d+e x) (f+g x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(f + g*x)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{2 e \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (e f-d g) \left(a e^2-b d e+c d^2\right)}+\frac{2 g \left(2 a c g+b^2 (-g)+c x (2 c f-b g)+b c f\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (e f-d g) \left(a g^2-b f g+c f^2\right)}+\frac{e^3 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g) \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{g^3 \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g) \left(a g^2-b f g+c f^2\right)^{3/2}}","-\frac{2 e \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (e f-d g) \left(a e^2-b d e+c d^2\right)}+\frac{2 g \left(2 a c g+b^2 (-g)+c x (2 c f-b g)+b c f\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (e f-d g) \left(a g^2-b f g+c f^2\right)}+\frac{e^3 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g) \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{g^3 \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g) \left(a g^2-b f g+c f^2\right)^{3/2}}",1,"(-2*e*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[a + b*x + c*x^2]) + (2*g*(b*c*f - b^2*g + 2*a*c*g + c*(2*c*f - b*g)*x))/((b^2 - 4*a*c)*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*Sqrt[a + b*x + c*x^2]) + (e^3*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/((c*d^2 - b*d*e + a*e^2)^(3/2)*(e*f - d*g)) - (g^3*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/((e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^(3/2))","A",10,5,29,0.1724,1,"{960, 740, 12, 724, 206}"
884,1,642,0,0.9106845,"\int \frac{1}{(d+e x) (f+g x)^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(f + g*x)^2*(a + b*x + c*x^2)^(3/2)),x]","\frac{g^2 \sqrt{a+b x+c x^2} \left(-4 c g (2 a g+b f)+3 b^2 g^2+4 c^2 f^2\right)}{\left(b^2-4 a c\right) (f+g x) (e f-d g) \left(a g^2-b f g+c f^2\right)^2}-\frac{2 e^2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (e f-d g)^2 \left(a e^2-b d e+c d^2\right)}+\frac{2 e g \left(2 a c g+b^2 (-g)+c x (2 c f-b g)+b c f\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (e f-d g)^2 \left(a g^2-b f g+c f^2\right)}+\frac{2 g \left(2 a c g+b^2 (-g)+c x (2 c f-b g)+b c f\right)}{\left(b^2-4 a c\right) (f+g x) \sqrt{a+b x+c x^2} (e f-d g) \left(a g^2-b f g+c f^2\right)}+\frac{e^4 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^2 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{e g^3 \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g)^2 \left(a g^2-b f g+c f^2\right)^{3/2}}-\frac{3 g^3 (2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 (e f-d g) \left(a g^2-b f g+c f^2\right)^{5/2}}","\frac{g^2 \sqrt{a+b x+c x^2} \left(-4 c g (2 a g+b f)+3 b^2 g^2+4 c^2 f^2\right)}{\left(b^2-4 a c\right) (f+g x) (e f-d g) \left(a g^2-b f g+c f^2\right)^2}-\frac{2 e^2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (e f-d g)^2 \left(a e^2-b d e+c d^2\right)}+\frac{2 e g \left(2 a c g+b^2 (-g)+c x (2 c f-b g)+b c f\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (e f-d g)^2 \left(a g^2-b f g+c f^2\right)}+\frac{2 g \left(2 a c g+b^2 (-g)+c x (2 c f-b g)+b c f\right)}{\left(b^2-4 a c\right) (f+g x) \sqrt{a+b x+c x^2} (e f-d g) \left(a g^2-b f g+c f^2\right)}+\frac{e^4 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{(e f-d g)^2 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{e g^3 \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{(e f-d g)^2 \left(a g^2-b f g+c f^2\right)^{3/2}}-\frac{3 g^3 (2 c f-b g) \tanh ^{-1}\left(\frac{-2 a g+x (2 c f-b g)+b f}{2 \sqrt{a+b x+c x^2} \sqrt{a g^2-b f g+c f^2}}\right)}{2 (e f-d g) \left(a g^2-b f g+c f^2\right)^{5/2}}",1,"(-2*e^2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^2*Sqrt[a + b*x + c*x^2]) + (2*e*g*(b*c*f - b^2*g + 2*a*c*g + c*(2*c*f - b*g)*x))/((b^2 - 4*a*c)*(e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)*Sqrt[a + b*x + c*x^2]) + (2*g*(b*c*f - b^2*g + 2*a*c*g + c*(2*c*f - b*g)*x))/((b^2 - 4*a*c)*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*(f + g*x)*Sqrt[a + b*x + c*x^2]) + (g^2*(4*c^2*f^2 + 3*b^2*g^2 - 4*c*g*(b*f + 2*a*g))*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^2*(f + g*x)) + (e^4*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/((c*d^2 - b*d*e + a*e^2)^(3/2)*(e*f - d*g)^2) - (3*g^3*(2*c*f - b*g)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(2*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^(5/2)) - (e*g^3*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/((e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)^(3/2))","A",14,6,29,0.2069,1,"{960, 740, 12, 724, 206, 806}"
885,1,1064,0,1.8979521,"\int \frac{1}{(d+e x) (f+g x)^3 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(f + g*x)^3*(a + b*x + c*x^2)^(3/2)),x]","\frac{\tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right) e^5}{\left(c d^2-b e d+a e^2\right)^{3/2} (e f-d g)^3}-\frac{2 \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right) e^3}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (e f-d g)^3 \sqrt{c x^2+b x+a}}-\frac{g^3 \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e^2}{(e f-d g)^3 \left(c f^2-b g f+a g^2\right)^{3/2}}+\frac{2 g \left(-g b^2+c f b+2 a c g+c (2 c f-b g) x\right) e^2}{\left(b^2-4 a c\right) (e f-d g)^3 \left(c f^2-b g f+a g^2\right) \sqrt{c x^2+b x+a}}-\frac{3 g^3 (2 c f-b g) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e}{2 (e f-d g)^2 \left(c f^2-b g f+a g^2\right)^{5/2}}+\frac{g^2 \left(4 c^2 f^2+3 b^2 g^2-4 c g (b f+2 a g)\right) \sqrt{c x^2+b x+a} e}{\left(b^2-4 a c\right) (e f-d g)^2 \left(c f^2-b g f+a g^2\right)^2 (f+g x)}+\frac{2 g \left(-g b^2+c f b+2 a c g+c (2 c f-b g) x\right) e}{\left(b^2-4 a c\right) (e f-d g)^2 \left(c f^2-b g f+a g^2\right) (f+g x) \sqrt{c x^2+b x+a}}-\frac{3 g^3 \left(16 c^2 f^2+5 b^2 g^2-4 c g (4 b f+a g)\right) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right)}{8 (e f-d g) \left(c f^2-b g f+a g^2\right)^{7/2}}+\frac{g^2 (2 c f-b g) \left(8 c^2 f^2+15 b^2 g^2-4 c g (2 b f+13 a g)\right) \sqrt{c x^2+b x+a}}{4 \left(b^2-4 a c\right) (e f-d g) \left(c f^2-b g f+a g^2\right)^3 (f+g x)}+\frac{g^2 \left(8 c^2 f^2+5 b^2 g^2-4 c g (2 b f+3 a g)\right) \sqrt{c x^2+b x+a}}{2 \left(b^2-4 a c\right) (e f-d g) \left(c f^2-b g f+a g^2\right)^2 (f+g x)^2}+\frac{2 g \left(-g b^2+c f b+2 a c g+c (2 c f-b g) x\right)}{\left(b^2-4 a c\right) (e f-d g) \left(c f^2-b g f+a g^2\right) (f+g x)^2 \sqrt{c x^2+b x+a}}","\frac{\tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right) e^5}{\left(c d^2-b e d+a e^2\right)^{3/2} (e f-d g)^3}-\frac{2 \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right) e^3}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (e f-d g)^3 \sqrt{c x^2+b x+a}}-\frac{g^3 \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e^2}{(e f-d g)^3 \left(c f^2-b g f+a g^2\right)^{3/2}}+\frac{2 g \left(-g b^2+c f b+2 a c g+c (2 c f-b g) x\right) e^2}{\left(b^2-4 a c\right) (e f-d g)^3 \left(c f^2-b g f+a g^2\right) \sqrt{c x^2+b x+a}}-\frac{3 g^3 (2 c f-b g) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right) e}{2 (e f-d g)^2 \left(c f^2-b g f+a g^2\right)^{5/2}}+\frac{g^2 \left(4 c^2 f^2+3 b^2 g^2-4 c g (b f+2 a g)\right) \sqrt{c x^2+b x+a} e}{\left(b^2-4 a c\right) (e f-d g)^2 \left(c f^2-b g f+a g^2\right)^2 (f+g x)}+\frac{2 g \left(-g b^2+c f b+2 a c g+c (2 c f-b g) x\right) e}{\left(b^2-4 a c\right) (e f-d g)^2 \left(c f^2-b g f+a g^2\right) (f+g x) \sqrt{c x^2+b x+a}}-\frac{3 g^3 \left(16 c^2 f^2+5 b^2 g^2-4 c g (4 b f+a g)\right) \tanh ^{-1}\left(\frac{b f-2 a g+(2 c f-b g) x}{2 \sqrt{c f^2-b g f+a g^2} \sqrt{c x^2+b x+a}}\right)}{8 (e f-d g) \left(c f^2-b g f+a g^2\right)^{7/2}}+\frac{g^2 (2 c f-b g) \left(8 c^2 f^2+15 b^2 g^2-4 c g (2 b f+13 a g)\right) \sqrt{c x^2+b x+a}}{4 \left(b^2-4 a c\right) (e f-d g) \left(c f^2-b g f+a g^2\right)^3 (f+g x)}+\frac{g^2 \left(8 c^2 f^2+5 b^2 g^2-4 c g (2 b f+3 a g)\right) \sqrt{c x^2+b x+a}}{2 \left(b^2-4 a c\right) (e f-d g) \left(c f^2-b g f+a g^2\right)^2 (f+g x)^2}+\frac{2 g \left(-g b^2+c f b+2 a c g+c (2 c f-b g) x\right)}{\left(b^2-4 a c\right) (e f-d g) \left(c f^2-b g f+a g^2\right) (f+g x)^2 \sqrt{c x^2+b x+a}}",1,"(-2*e^3*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^3*Sqrt[a + b*x + c*x^2]) + (2*e^2*g*(b*c*f - b^2*g + 2*a*c*g + c*(2*c*f - b*g)*x))/((b^2 - 4*a*c)*(e*f - d*g)^3*(c*f^2 - b*f*g + a*g^2)*Sqrt[a + b*x + c*x^2]) + (2*g*(b*c*f - b^2*g + 2*a*c*g + c*(2*c*f - b*g)*x))/((b^2 - 4*a*c)*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*(f + g*x)^2*Sqrt[a + b*x + c*x^2]) + (2*e*g*(b*c*f - b^2*g + 2*a*c*g + c*(2*c*f - b*g)*x))/((b^2 - 4*a*c)*(e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)*(f + g*x)*Sqrt[a + b*x + c*x^2]) + (g^2*(8*c^2*f^2 + 5*b^2*g^2 - 4*c*g*(2*b*f + 3*a*g))*Sqrt[a + b*x + c*x^2])/(2*(b^2 - 4*a*c)*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^2*(f + g*x)^2) + (e*g^2*(4*c^2*f^2 + 3*b^2*g^2 - 4*c*g*(b*f + 2*a*g))*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)*(e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)^2*(f + g*x)) + (g^2*(2*c*f - b*g)*(8*c^2*f^2 + 15*b^2*g^2 - 4*c*g*(2*b*f + 13*a*g))*Sqrt[a + b*x + c*x^2])/(4*(b^2 - 4*a*c)*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^3*(f + g*x)) + (e^5*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/((c*d^2 - b*d*e + a*e^2)^(3/2)*(e*f - d*g)^3) - (3*e*g^3*(2*c*f - b*g)*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(2*(e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)^(5/2)) - (e^2*g^3*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/((e*f - d*g)^3*(c*f^2 - b*f*g + a*g^2)^(3/2)) - (3*g^3*(16*c^2*f^2 + 5*b^2*g^2 - 4*c*g*(4*b*f + a*g))*ArcTanh[(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*Sqrt[c*f^2 - b*f*g + a*g^2]*Sqrt[a + b*x + c*x^2])])/(8*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^(7/2))","A",19,7,29,0.2414,1,"{960, 740, 12, 724, 206, 834, 806}"
886,1,1551,0,8.0932414,"\int (d+e x)^3 \sqrt{f+g x} \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{f+g x} \sqrt{c x^2+b x+a} (d+e x)^4}{11 e}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(2 f^2 \left(64 e^3 f^3-264 d e^2 g f^2+396 d^2 e g^2 f-231 d^3 g^3\right) c^5-g \left(b f \left(56 e^3 f^3-264 d e^2 g f^2+495 d^2 e g^2 f-462 d^3 g^3\right)-18 a g \left(6 e^3 f^3-33 d e^2 g f^2+88 d^2 e g^2 f+77 d^3 g^3\right)\right) c^4-g^2 \left(\left(37 e^3 f^3-198 d e^2 g f^2+495 d^2 e g^2 f+462 d^3 g^3\right) b^2-9 a e g \left(15 e^2 f^2-110 d e g f-319 d^2 g^2\right) b+6 a^2 e^2 g^2 (26 e f+231 d g)\right) c^3+b e g^3 \left(-\left(37 e^2 f^2-264 d e g f-792 d^2 g^2\right) b^2+6 a e g (43 e f+396 d g) b+771 a^2 e^2 g^2\right) c^2-8 b^3 e^2 g^4 (7 b e f+66 b d g+87 a e g) c+128 b^5 e^3 g^5\right) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3465 c^5 g^5 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c f^2-b g f+a g^2\right) \left(-2 f \left(64 e^3 f^3-264 d e^2 g f^2+396 d^2 e g^2 f-231 d^3 g^3\right) c^4-g \left(6 a e g \left(2 e^2 f^2-33 d e g f+165 d^2 g^2\right)+b \left(8 e^3 f^3-99 d^2 e g^2 f+231 d^3 g^3\right)\right) c^3+3 e g^2 \left(3 \left(e^2 f^2-11 d e g f+44 d^2 g^2\right) b^2-a e g (29 e f-297 d g) b+50 a^2 e^2 g^2\right) c^2+4 b^2 e^2 g^3 (7 b e f-66 b d g-69 a e g) c+64 b^4 e^3 g^4\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3465 c^5 g^5 \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{2 e^2 (c e f-3 c d g+b e g) (f+g x)^{7/2} \sqrt{c x^2+b x+a}}{99 c g^4}-\frac{2 e \left(\left(29 e^2 f^2-96 d e g f+81 d^2 g^2\right) c^2+e g (19 b e f-33 b d g-18 a e g) c+8 b^2 e^2 g^2\right) (f+g x)^{5/2} \sqrt{c x^2+b x+a}}{693 c^2 g^4}+\frac{2 \left(\left(233 e^3 f^3-843 d e^2 g f^2+1107 d^2 e g^2 f-567 d^3 g^3\right) c^3-e g \left(2 a e g (74 e f-231 d g)-3 b \left(24 e^2 f^2-88 d e g f+99 d^2 g^2\right)\right) c^2+b e^2 g^2 (67 b e f-198 b d g-157 a e g) c+48 b^3 e^3 g^3\right) (f+g x)^{3/2} \sqrt{c x^2+b x+a}}{3465 c^3 g^4}-\frac{2 \left(\left(187 e^4 f^4-732 d e^3 g f^3+1098 d^2 e^2 g^2 f^2-798 d^3 e g^3 f+315 d^4 g^4\right) c^4-e g \left(6 a e g \left(2 e^2 f^2-33 d e g f+165 d^2 g^2\right)+b \left(8 e^3 f^3-99 d^2 e g^2 f+231 d^3 g^3\right)\right) c^3+3 e^2 g^2 \left(3 \left(e^2 f^2-11 d e g f+44 d^2 g^2\right) b^2-a e g (29 e f-297 d g) b+50 a^2 e^2 g^2\right) c^2+4 b^2 e^3 g^3 (7 b e f-66 b d g-69 a e g) c+64 b^4 e^4 g^4\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}{3465 c^4 e g^4}","\frac{2 \sqrt{f+g x} \sqrt{c x^2+b x+a} (d+e x)^4}{11 e}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(2 f^2 \left(64 e^3 f^3-264 d e^2 g f^2+396 d^2 e g^2 f-231 d^3 g^3\right) c^5-g \left(b f \left(56 e^3 f^3-264 d e^2 g f^2+495 d^2 e g^2 f-462 d^3 g^3\right)-18 a g \left(6 e^3 f^3-33 d e^2 g f^2+88 d^2 e g^2 f+77 d^3 g^3\right)\right) c^4-g^2 \left(\left(37 e^3 f^3-198 d e^2 g f^2+495 d^2 e g^2 f+462 d^3 g^3\right) b^2-9 a e g \left(15 e^2 f^2-110 d e g f-319 d^2 g^2\right) b+6 a^2 e^2 g^2 (26 e f+231 d g)\right) c^3+b e g^3 \left(-\left(37 e^2 f^2-264 d e g f-792 d^2 g^2\right) b^2+6 a e g (43 e f+396 d g) b+771 a^2 e^2 g^2\right) c^2-8 b^3 e^2 g^4 (7 b e f+66 b d g+87 a e g) c+128 b^5 e^3 g^5\right) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3465 c^5 g^5 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c f^2-b g f+a g^2\right) \left(-2 f \left(64 e^3 f^3-264 d e^2 g f^2+396 d^2 e g^2 f-231 d^3 g^3\right) c^4-g \left(6 a e g \left(2 e^2 f^2-33 d e g f+165 d^2 g^2\right)+b \left(8 e^3 f^3-99 d^2 e g^2 f+231 d^3 g^3\right)\right) c^3+3 e g^2 \left(3 \left(e^2 f^2-11 d e g f+44 d^2 g^2\right) b^2-a e g (29 e f-297 d g) b+50 a^2 e^2 g^2\right) c^2+4 b^2 e^2 g^3 (7 b e f-66 b d g-69 a e g) c+64 b^4 e^3 g^4\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3465 c^5 g^5 \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{2 e^2 (c e f-3 c d g+b e g) (f+g x)^{7/2} \sqrt{c x^2+b x+a}}{99 c g^4}-\frac{2 e \left(\left(29 e^2 f^2-96 d e g f+81 d^2 g^2\right) c^2+e g (19 b e f-33 b d g-18 a e g) c+8 b^2 e^2 g^2\right) (f+g x)^{5/2} \sqrt{c x^2+b x+a}}{693 c^2 g^4}+\frac{2 \left(\left(233 e^3 f^3-843 d e^2 g f^2+1107 d^2 e g^2 f-567 d^3 g^3\right) c^3-e g \left(2 a e g (74 e f-231 d g)-3 b \left(24 e^2 f^2-88 d e g f+99 d^2 g^2\right)\right) c^2+b e^2 g^2 (67 b e f-198 b d g-157 a e g) c+48 b^3 e^3 g^3\right) (f+g x)^{3/2} \sqrt{c x^2+b x+a}}{3465 c^3 g^4}-\frac{2 \left(\left(187 e^4 f^4-732 d e^3 g f^3+1098 d^2 e^2 g^2 f^2-798 d^3 e g^3 f+315 d^4 g^4\right) c^4-e g \left(6 a e g \left(2 e^2 f^2-33 d e g f+165 d^2 g^2\right)+b \left(8 e^3 f^3-99 d^2 e g^2 f+231 d^3 g^3\right)\right) c^3+3 e^2 g^2 \left(3 \left(e^2 f^2-11 d e g f+44 d^2 g^2\right) b^2-a e g (29 e f-297 d g) b+50 a^2 e^2 g^2\right) c^2+4 b^2 e^3 g^3 (7 b e f-66 b d g-69 a e g) c+64 b^4 e^4 g^4\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}{3465 c^4 e g^4}",1,"(-2*(64*b^4*e^4*g^4 + 4*b^2*c*e^3*g^3*(7*b*e*f - 66*b*d*g - 69*a*e*g) + c^4*(187*e^4*f^4 - 732*d*e^3*f^3*g + 1098*d^2*e^2*f^2*g^2 - 798*d^3*e*f*g^3 + 315*d^4*g^4) + 3*c^2*e^2*g^2*(50*a^2*e^2*g^2 - a*b*e*g*(29*e*f - 297*d*g) + 3*b^2*(e^2*f^2 - 11*d*e*f*g + 44*d^2*g^2)) - c^3*e*g*(6*a*e*g*(2*e^2*f^2 - 33*d*e*f*g + 165*d^2*g^2) + b*(8*e^3*f^3 - 99*d^2*e*f*g^2 + 231*d^3*g^3)))*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(3465*c^4*e*g^4) + (2*(d + e*x)^4*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(11*e) + (2*(48*b^3*e^3*g^3 + b*c*e^2*g^2*(67*b*e*f - 198*b*d*g - 157*a*e*g) + c^3*(233*e^3*f^3 - 843*d*e^2*f^2*g + 1107*d^2*e*f*g^2 - 567*d^3*g^3) - c^2*e*g*(2*a*e*g*(74*e*f - 231*d*g) - 3*b*(24*e^2*f^2 - 88*d*e*f*g + 99*d^2*g^2)))*(f + g*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(3465*c^3*g^4) - (2*e*(8*b^2*e^2*g^2 + c*e*g*(19*b*e*f - 33*b*d*g - 18*a*e*g) + c^2*(29*e^2*f^2 - 96*d*e*f*g + 81*d^2*g^2))*(f + g*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(693*c^2*g^4) + (2*e^2*(c*e*f - 3*c*d*g + b*e*g)*(f + g*x)^(7/2)*Sqrt[a + b*x + c*x^2])/(99*c*g^4) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(128*b^5*e^3*g^5 - 8*b^3*c*e^2*g^4*(7*b*e*f + 66*b*d*g + 87*a*e*g) + 2*c^5*f^2*(64*e^3*f^3 - 264*d*e^2*f^2*g + 396*d^2*e*f*g^2 - 231*d^3*g^3) + b*c^2*e*g^3*(771*a^2*e^2*g^2 + 6*a*b*e*g*(43*e*f + 396*d*g) - b^2*(37*e^2*f^2 - 264*d*e*f*g - 792*d^2*g^2)) - c^4*g*(b*f*(56*e^3*f^3 - 264*d*e^2*f^2*g + 495*d^2*e*f*g^2 - 462*d^3*g^3) - 18*a*g*(6*e^3*f^3 - 33*d*e^2*f^2*g + 88*d^2*e*f*g^2 + 77*d^3*g^3)) - c^3*g^2*(6*a^2*e^2*g^2*(26*e*f + 231*d*g) - 9*a*b*e*g*(15*e^2*f^2 - 110*d*e*f*g - 319*d^2*g^2) + b^2*(37*e^3*f^3 - 198*d*e^2*f^2*g + 495*d^2*e*f*g^2 + 462*d^3*g^3)))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3465*c^5*g^5*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*f^2 - b*f*g + a*g^2)*(64*b^4*e^3*g^4 + 4*b^2*c*e^2*g^3*(7*b*e*f - 66*b*d*g - 69*a*e*g) - 2*c^4*f*(64*e^3*f^3 - 264*d*e^2*f^2*g + 396*d^2*e*f*g^2 - 231*d^3*g^3) + 3*c^2*e*g^2*(50*a^2*e^2*g^2 - a*b*e*g*(29*e*f - 297*d*g) + 3*b^2*(e^2*f^2 - 11*d*e*f*g + 44*d^2*g^2)) - c^3*g*(6*a*e*g*(2*e^2*f^2 - 33*d*e*f*g + 165*d^2*g^2) + b*(8*e^3*f^3 - 99*d^2*e*f*g^2 + 231*d^3*g^3)))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3465*c^5*g^5*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",10,6,31,0.1935,1,"{918, 1653, 843, 718, 424, 419}"
887,1,1015,0,3.7753285,"\int (d+e x)^2 \sqrt{f+g x} \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{f+g x} \sqrt{c x^2+b x+a} (d+e x)^3}{9 e}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(f^2 \left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right) c^4+g \left(3 a g \left(3 e^2 f^2-16 d e g f-21 d^2 g^2\right)-b f \left(4 e^2 f^2-15 d e g f+21 d^2 g^2\right)\right) c^3+3 g^2 \left(-\left(e^2 f^2-5 d e g f-7 d^2 g^2\right) b^2+a e g (5 e f+29 d g) b+7 a^2 e^2 g^2\right) c^2-4 b^2 e g^3 (b e f+6 b d g+9 a e g) c+8 b^4 e^2 g^4\right) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{315 c^4 g^4 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c f^2-b g f+a g^2\right) \left(-2 f \left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right) c^3-3 g^2 (2 a e (e f-10 d g)+b d (2 e f-7 d g)) c^2+3 b e g^2 (b e f-8 b d g-9 a e g) c+8 b^3 e^2 g^3\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{315 c^4 g^4 \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{2 e (c e f-3 c d g+b e g) (f+g x)^{5/2} \sqrt{c x^2+b x+a}}{63 c g^3}-\frac{4 \left(\left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right) c^2+e g (4 b e f-9 b d g-7 a e g) c+3 b^2 e^2 g^2\right) (f+g x)^{3/2} \sqrt{c x^2+b x+a}}{315 c^2 g^3}+\frac{2 \left(\left(19 e^3 f^3-57 d e^2 g f^2+63 d^2 e g^2 f-35 d^3 g^3\right) c^3-3 e g^2 (2 a e (e f-10 d g)+b d (2 e f-7 d g)) c^2+3 b e^2 g^2 (b e f-8 b d g-9 a e g) c+8 b^3 e^3 g^3\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}{315 c^3 e g^3}","\frac{2 \sqrt{f+g x} \sqrt{c x^2+b x+a} (d+e x)^3}{9 e}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(f^2 \left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right) c^4+g \left(3 a g \left(3 e^2 f^2-16 d e g f-21 d^2 g^2\right)-b f \left(4 e^2 f^2-15 d e g f+21 d^2 g^2\right)\right) c^3+3 g^2 \left(-\left(e^2 f^2-5 d e g f-7 d^2 g^2\right) b^2+a e g (5 e f+29 d g) b+7 a^2 e^2 g^2\right) c^2-4 b^2 e g^3 (b e f+6 b d g+9 a e g) c+8 b^4 e^2 g^4\right) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{315 c^4 g^4 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c f^2-b g f+a g^2\right) \left(-2 f \left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right) c^3-3 g^2 (2 a e (e f-10 d g)+b d (2 e f-7 d g)) c^2+3 b e g^2 (b e f-8 b d g-9 a e g) c+8 b^3 e^2 g^3\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{315 c^4 g^4 \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{2 e (c e f-3 c d g+b e g) (f+g x)^{5/2} \sqrt{c x^2+b x+a}}{63 c g^3}-\frac{4 \left(\left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right) c^2+e g (4 b e f-9 b d g-7 a e g) c+3 b^2 e^2 g^2\right) (f+g x)^{3/2} \sqrt{c x^2+b x+a}}{315 c^2 g^3}+\frac{2 \left(\left(19 e^3 f^3-57 d e^2 g f^2+63 d^2 e g^2 f-35 d^3 g^3\right) c^3-3 e g^2 (2 a e (e f-10 d g)+b d (2 e f-7 d g)) c^2+3 b e^2 g^2 (b e f-8 b d g-9 a e g) c+8 b^3 e^3 g^3\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}{315 c^3 e g^3}",1,"(2*(8*b^3*e^3*g^3 + 3*b*c*e^2*g^2*(b*e*f - 8*b*d*g - 9*a*e*g) + c^3*(19*e^3*f^3 - 57*d*e^2*f^2*g + 63*d^2*e*f*g^2 - 35*d^3*g^3) - 3*c^2*e*g^2*(2*a*e*(e*f - 10*d*g) + b*d*(2*e*f - 7*d*g)))*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(315*c^3*e*g^3) + (2*(d + e*x)^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(9*e) - (4*(3*b^2*e^2*g^2 + c*e*g*(4*b*e*f - 9*b*d*g - 7*a*e*g) + c^2*(8*e^2*f^2 - 24*d*e*f*g + 21*d^2*g^2))*(f + g*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(315*c^2*g^3) + (2*e*(c*e*f - 3*c*d*g + b*e*g)*(f + g*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(63*c*g^3) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(8*b^4*e^2*g^4 - 4*b^2*c*e*g^3*(b*e*f + 6*b*d*g + 9*a*e*g) + c^4*f^2*(8*e^2*f^2 - 24*d*e*f*g + 21*d^2*g^2) + 3*c^2*g^2*(7*a^2*e^2*g^2 + a*b*e*g*(5*e*f + 29*d*g) - b^2*(e^2*f^2 - 5*d*e*f*g - 7*d^2*g^2)) + c^3*g*(3*a*g*(3*e^2*f^2 - 16*d*e*f*g - 21*d^2*g^2) - b*f*(4*e^2*f^2 - 15*d*e*f*g + 21*d^2*g^2)))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(315*c^4*g^4*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*f^2 - b*f*g + a*g^2)*(8*b^3*e^2*g^3 + 3*b*c*e*g^2*(b*e*f - 8*b*d*g - 9*a*e*g) - 2*c^3*f*(8*e^2*f^2 - 24*d*e*f*g + 21*d^2*g^2) - 3*c^2*g^2*(2*a*e*(e*f - 10*d*g) + b*d*(2*e*f - 7*d*g)))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(315*c^4*g^4*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",9,6,31,0.1935,1,"{918, 1653, 843, 718, 424, 419}"
888,1,652,0,1.1123346,"\int (d+e x) \sqrt{f+g x} \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(c g (-10 a e g-7 b d g+b e f)+4 b^2 e g^2-2 c^2 f (4 e f-7 d g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^3 g^3 \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(\left(-3 c g (b f-2 a g)-2 b^2 g^2+8 c^2 f^2\right) (-4 b e g+7 c d g+c e f)-5 c g (2 c f-b g) (7 c d f-e (a g+3 b f))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^3 g^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{f+g x} \sqrt{a+b x+c x^2} \left(-c g (-5 a e g+7 b d g+2 b e f)+4 b^2 e g^2-3 c g x (-4 b e g+7 c d g+c e f)+c^2 f (4 e f-7 d g)\right)}{105 c^2 g^2}+\frac{2 e \sqrt{f+g x} \left(a+b x+c x^2\right)^{3/2}}{7 c}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(c g (-10 a e g-7 b d g+b e f)+4 b^2 e g^2-2 c^2 f (4 e f-7 d g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^3 g^3 \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(\left(-3 c g (b f-2 a g)-2 b^2 g^2+8 c^2 f^2\right) (-4 b e g+7 c d g+c e f)-5 c g (2 c f-b g) (7 c d f-e (a g+3 b f))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^3 g^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{f+g x} \sqrt{a+b x+c x^2} \left(-c g (-5 a e g+7 b d g+2 b e f)+4 b^2 e g^2-3 c g x (-4 b e g+7 c d g+c e f)+c^2 f (4 e f-7 d g)\right)}{105 c^2 g^2}+\frac{2 e \sqrt{f+g x} \left(a+b x+c x^2\right)^{3/2}}{7 c}",1,"(-2*Sqrt[f + g*x]*(4*b^2*e*g^2 + c^2*f*(4*e*f - 7*d*g) - c*g*(2*b*e*f + 7*b*d*g - 5*a*e*g) - 3*c*g*(c*e*f + 7*c*d*g - 4*b*e*g)*x)*Sqrt[a + b*x + c*x^2])/(105*c^2*g^2) + (2*e*Sqrt[f + g*x]*(a + b*x + c*x^2)^(3/2))/(7*c) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*((c*e*f + 7*c*d*g - 4*b*e*g)*(8*c^2*f^2 - 2*b^2*g^2 - 3*c*g*(b*f - 2*a*g)) - 5*c*g*(2*c*f - b*g)*(7*c*d*f - e*(3*b*f + a*g)))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(105*c^3*g^3*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*f^2 - b*f*g + a*g^2)*(4*b^2*e*g^2 - 2*c^2*f*(4*e*f - 7*d*g) + c*g*(b*e*f - 7*b*d*g - 10*a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(105*c^3*g^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",7,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
889,1,513,0,0.5355239,"\int \sqrt{f+g x} \sqrt{a+b x+c x^2} \, dx","Int[Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c f-b g) \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^2 g^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c g (3 a g+b f)+b^2 g^2+c^2 f^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^2 g^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 (f+g x)^{3/2} \sqrt{a+b x+c x^2}}{5 g}-\frac{2 \sqrt{f+g x} \sqrt{a+b x+c x^2} (2 c f-b g)}{15 c g}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c f-b g) \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^2 g^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c g (3 a g+b f)+b^2 g^2+c^2 f^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^2 g^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 (f+g x)^{3/2} \sqrt{a+b x+c x^2}}{5 g}-\frac{2 \sqrt{f+g x} \sqrt{a+b x+c x^2} (2 c f-b g)}{15 c g}",1,"(-2*(2*c*f - b*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(15*c*g) + (2*(f + g*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(5*g) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c^2*f^2 + b^2*g^2 - c*g*(b*f + 3*a*g))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(15*c^2*g^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*f - b*g)*(c*f^2 - b*f*g + a*g^2)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(15*c^2*g^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{734, 832, 843, 718, 424, 419}"
890,1,969,0,4.0987462,"\int \frac{\sqrt{f+g x} \sqrt{a+b x+c x^2}}{d+e x} \, dx","Int[(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(d + e*x),x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} (c e f-3 c d g+b e g) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c e^2 g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} f (c e f-3 c d g+b e g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c e^2 g \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} (3 c d (e f-d g)-e (2 b e f-3 b d g+2 a e g)) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c e^3 \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \left(c d^2-b e d+a e^2\right) \sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e^3 \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{f+g x} \sqrt{c x^2+b x+a}}{3 e}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{\frac{c (a+x (b+c x))}{4 a c-b^2}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(e g (2 a e g-3 b d g+b e f)+c \left(3 d^2 g^2-e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{b^2-4 a c} g}{\left(b+\sqrt{b^2-4 a c}\right) g-2 c f}\right)}{3 c e^3 g \sqrt{f+g x} \sqrt{a+x (b+c x)}}-\frac{\sqrt{2} \left(a e^2-b d e+c d^2\right) \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e^3 \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (b e g-3 c d g+c e f) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c e^2 g \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}{3 e}",1,"(2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(3*e) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*e*f - 3*c*d*g + b*e*g)*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c*e^2*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*f*(c*e*f - 3*c*d*g + b*e*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c*e^2*g*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(3*c*d*(e*f - d*g) - e*(2*b*e*f - 3*b*d*g + 2*a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c*e^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[c]*e^3*Sqrt[a + b*x + c*x^2])","A",15,10,31,0.3226,1,"{918, 6742, 718, 419, 843, 424, 934, 169, 538, 537}"
891,1,934,0,3.3164123,"\int \frac{\sqrt{f+g x} \sqrt{a+b x+c x^2}}{(d+e x)^2} \, dx","Int[(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(d + e*x)^2,x]","\frac{3 \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} e^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{3 \sqrt{2} \sqrt{b^2-4 a c} f \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{e^2 \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} (2 c e f-3 c d g+2 b e g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c e^3 \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} e^3 (e f-d g) \sqrt{c x^2+b x+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a}}{e (d+e x)}","\frac{\sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} (c d (2 e f-3 d g)-e (a e g-2 b d g+b e f)) \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} e^3 \sqrt{a+b x+c x^2} (e f-d g)}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{\frac{c (a+x (b+c x))}{4 a c-b^2}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} (2 b e g-c (3 d g+e f)) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{b^2-4 a c} g}{\left(b+\sqrt{b^2-4 a c}\right) g-2 c f}\right)}{c e^3 \sqrt{f+g x} \sqrt{a+x (b+c x)}}+\frac{3 \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{\sqrt{f+g x} \sqrt{a+b x+c x^2}}{e (d+e x)}",1,"-((Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(e*(d + e*x))) + (3*Sqrt[b^2 - 4*a*c]*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(Sqrt[2]*e^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (3*Sqrt[2]*Sqrt[b^2 - 4*a*c]*f*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(e^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*e*f - 3*c*d*g + 2*b*e*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*e^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[2]*Sqrt[c]*e^3*(e*f - d*g)*Sqrt[a + b*x + c*x^2])","A",15,10,31,0.3226,1,"{916, 6742, 718, 419, 843, 424, 934, 169, 538, 537}"
892,1,1705,0,8.0908307,"\int \frac{\sqrt{f+g x} \sqrt{a+b x+c x^2}}{(d+e x)^3} \, dx","Int[(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(d + e*x)^3,x]","\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right) (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g))^2}{4 \sqrt{2} \sqrt{c} e^3 \left(c d^2-b e d+a e^2\right) (e f-d g)^2 \sqrt{c x^2+b x+a}}-\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g))}{4 \sqrt{2} e^2 \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{\sqrt{b^2-4 a c} f \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g))}{2 \sqrt{2} e^2 \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{b^2-4 a c} d g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g))}{2 \sqrt{2} e^3 \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g))}{4 e \left(c d^2-b e d+a e^2\right) (e f-d g) (d+e x)}+\frac{3 \sqrt{b^2-4 a c} g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} e^3 \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c e f-3 c d g+b e g) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} e^3 (e f-d g) \sqrt{c x^2+b x+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a}}{2 e (d+e x)^2}","-\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g))}{4 \sqrt{2} e^2 \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g))}{4 e \left(c d^2-b e d+a e^2\right) (e f-d g) (d+e x)}-\frac{\sqrt{b^2-4 a c} (e (b e f+4 b d g-5 a e g)-c d (2 e f+3 d g)) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{\frac{c (a+x (b+c x))}{4 a c-b^2}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{b^2-4 a c} g}{\left(b+\sqrt{b^2-4 a c}\right) g-2 c f}\right)}{2 \sqrt{2} e^3 \left(c d^2+e (a e-b d)\right) \sqrt{f+g x} \sqrt{a+x (b+c x)}}+\frac{\sqrt{2 c f-b g+\sqrt{b^2-4 a c} g} \left(b^2 f^2 e^4+a^2 g^2 e^4-2 a c \left(2 e^2 f^2-6 d e g f+3 d^2 g^2\right) e^2-2 b g \left(a f e^3+c d^2 (3 e f-2 d g)\right) e+c^2 d^3 g (4 e f-3 d g)\right) \sqrt{\frac{g \left(-b-2 c x+\sqrt{b^2-4 a c}\right)}{2 c f+\left(\sqrt{b^2-4 a c}-b\right) g}} \sqrt{\frac{g \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{\left(b+\sqrt{b^2-4 a c}\right) g-2 c f}} \Pi \left(\frac{2 c e f-b e g+\sqrt{b^2-4 a c} e g}{2 c e f-2 c d g};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-b g+\sqrt{b^2-4 a c} g}}\right)|\frac{2 c f+\left(\sqrt{b^2-4 a c}-b\right) g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{4 \sqrt{2} \sqrt{c} e^3 \left(c d^2+e (a e-b d)\right) (e f-d g)^2 \sqrt{a+x (b+c x)}}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a}}{2 e (d+e x)^2}",1,"-(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(2*e*(d + e*x)^2) + ((c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(4*e*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*(d + e*x)) - (Sqrt[b^2 - 4*a*c]*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(4*Sqrt[2]*e^2*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (3*Sqrt[b^2 - 4*a*c]*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(Sqrt[2]*e^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[b^2 - 4*a*c]*f*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(2*Sqrt[2]*e^2*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[b^2 - 4*a*c]*d*g*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(2*Sqrt[2]*e^3*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*e*f - 3*c*d*g + b*e*g)*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[2]*Sqrt[c]*e^3*(e*f - d*g)*Sqrt[a + b*x + c*x^2]) + (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))^2*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(4*Sqrt[2]*Sqrt[c]*e^3*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^2*Sqrt[a + b*x + c*x^2])","A",25,11,31,0.3548,1,"{916, 6742, 718, 419, 939, 843, 424, 934, 169, 538, 537}"
893,1,1098,0,5.7639558,"\int \frac{(d+e x)^3 \sqrt{a+b x+c x^2}}{\sqrt{f+g x}} \, dx","Int[((d + e*x)^3*Sqrt[a + b*x + c*x^2])/Sqrt[f + g*x],x]","\frac{2 \sqrt{f+g x} \sqrt{c x^2+b x+a} (d+e x)^3}{9 g}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(-2 f \left(64 e^3 f^3-216 d e^2 g f^2+252 d^2 e g^2 f-105 d^3 g^3\right) c^4-g \left(6 a e g \left(10 e^2 f^2-39 d e g f+63 d^2 g^2\right)-b \left(40 e^3 f^3-144 d e^2 g f^2+189 d^2 e g^2 f-105 d^3 g^3\right)\right) c^3+3 e g^2 \left(\left(7 e^2 f^2-27 d e g f+42 d^2 g^2\right) b^2-a e g (19 e f-87 d g) b+14 a^2 e^2 g^2\right) c^2+8 b^2 e^2 g^3 (2 b e f-9 b d g-9 a e g) c+16 b^4 e^3 g^4\right) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{315 c^4 g^5 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c f^2-b g f+a g^2\right) \left(2 \left(64 e^3 f^3-216 d e^2 g f^2+252 d^2 e g^2 f-105 d^3 g^3\right) c^3-3 e g \left(6 a e g (2 e f-5 d g)-b \left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right)\right) c^2+3 b e^2 g^2 (5 b e f-12 b d g-9 a e g) c+8 b^3 e^3 g^3\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{315 c^4 g^5 \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{2 e^2 (8 c e f-6 c d g-b e g) (f+g x)^{5/2} \sqrt{c x^2+b x+a}}{63 c g^4}-\frac{2 e \left(-2 \left(64 e^2 f^2-111 d e g f+42 d^2 g^2\right) c^2+e g (17 b e f-27 b d g-14 a e g) c+6 b^2 e^2 g^2\right) (f+g x)^{3/2} \sqrt{c x^2+b x+a}}{315 c^2 g^4}+\frac{2 \left(-\left(152 e^3 f^3-408 d e^2 g f^2+336 d^2 e g^2 f-70 d^3 g^3\right) c^3-3 e g \left(6 a e g (2 e f-5 d g)-b \left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right)\right) c^2+3 b e^2 g^2 (5 b e f-12 b d g-9 a e g) c+8 b^3 e^3 g^3\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}{315 c^3 g^4}","\frac{2 \sqrt{f+g x} \sqrt{c x^2+b x+a} (d+e x)^3}{9 g}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(-2 f \left(64 e^3 f^3-216 d e^2 g f^2+252 d^2 e g^2 f-105 d^3 g^3\right) c^4-g \left(6 a e g \left(10 e^2 f^2-39 d e g f+63 d^2 g^2\right)-b \left(40 e^3 f^3-144 d e^2 g f^2+189 d^2 e g^2 f-105 d^3 g^3\right)\right) c^3+3 e g^2 \left(\left(7 e^2 f^2-27 d e g f+42 d^2 g^2\right) b^2-a e g (19 e f-87 d g) b+14 a^2 e^2 g^2\right) c^2+8 b^2 e^2 g^3 (2 b e f-9 b d g-9 a e g) c+16 b^4 e^3 g^4\right) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{315 c^4 g^5 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c f^2-b g f+a g^2\right) \left(2 \left(64 e^3 f^3-216 d e^2 g f^2+252 d^2 e g^2 f-105 d^3 g^3\right) c^3-3 e g \left(6 a e g (2 e f-5 d g)-b \left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right)\right) c^2+3 b e^2 g^2 (5 b e f-12 b d g-9 a e g) c+8 b^3 e^3 g^3\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{315 c^4 g^5 \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{2 e^2 (8 c e f-6 c d g-b e g) (f+g x)^{5/2} \sqrt{c x^2+b x+a}}{63 c g^4}-\frac{2 e \left(-2 \left(64 e^2 f^2-111 d e g f+42 d^2 g^2\right) c^2+e g (17 b e f-27 b d g-14 a e g) c+6 b^2 e^2 g^2\right) (f+g x)^{3/2} \sqrt{c x^2+b x+a}}{315 c^2 g^4}+\frac{2 \left(-\left(152 e^3 f^3-408 d e^2 g f^2+336 d^2 e g^2 f-70 d^3 g^3\right) c^3-3 e g \left(6 a e g (2 e f-5 d g)-b \left(8 e^2 f^2-24 d e g f+21 d^2 g^2\right)\right) c^2+3 b e^2 g^2 (5 b e f-12 b d g-9 a e g) c+8 b^3 e^3 g^3\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}{315 c^3 g^4}",1,"(2*(8*b^3*e^3*g^3 + 3*b*c*e^2*g^2*(5*b*e*f - 12*b*d*g - 9*a*e*g) - c^3*(152*e^3*f^3 - 408*d*e^2*f^2*g + 336*d^2*e*f*g^2 - 70*d^3*g^3) - 3*c^2*e*g*(6*a*e*g*(2*e*f - 5*d*g) - b*(8*e^2*f^2 - 24*d*e*f*g + 21*d^2*g^2)))*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(315*c^3*g^4) + (2*(d + e*x)^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(9*g) - (2*e*(6*b^2*e^2*g^2 + c*e*g*(17*b*e*f - 27*b*d*g - 14*a*e*g) - 2*c^2*(64*e^2*f^2 - 111*d*e*f*g + 42*d^2*g^2))*(f + g*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(315*c^2*g^4) - (2*e^2*(8*c*e*f - 6*c*d*g - b*e*g)*(f + g*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(63*c*g^4) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*b^4*e^3*g^4 + 8*b^2*c*e^2*g^3*(2*b*e*f - 9*b*d*g - 9*a*e*g) - 2*c^4*f*(64*e^3*f^3 - 216*d*e^2*f^2*g + 252*d^2*e*f*g^2 - 105*d^3*g^3) + 3*c^2*e*g^2*(14*a^2*e^2*g^2 - a*b*e*g*(19*e*f - 87*d*g) + b^2*(7*e^2*f^2 - 27*d*e*f*g + 42*d^2*g^2)) - c^3*g*(6*a*e*g*(10*e^2*f^2 - 39*d*e*f*g + 63*d^2*g^2) - b*(40*e^3*f^3 - 144*d*e^2*f^2*g + 189*d^2*e*f*g^2 - 105*d^3*g^3)))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(315*c^4*g^5*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*f^2 - b*f*g + a*g^2)*(8*b^3*e^3*g^3 + 3*b*c*e^2*g^2*(5*b*e*f - 12*b*d*g - 9*a*e*g) + 2*c^3*(64*e^3*f^3 - 216*d*e^2*f^2*g + 252*d^2*e*f*g^2 - 105*d^3*g^3) - 3*c^2*e*g*(6*a*e*g*(2*e*f - 5*d*g) - b*(8*e^2*f^2 - 24*d*e*f*g + 21*d^2*g^2)))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(315*c^4*g^5*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",9,6,31,0.1935,1,"{920, 1653, 843, 718, 424, 419}"
894,1,755,0,1.930676,"\int \frac{(d+e x)^2 \sqrt{a+b x+c x^2}}{\sqrt{f+g x}} \, dx","Int[((d + e*x)^2*Sqrt[a + b*x + c*x^2])/Sqrt[f + g*x],x]","-\frac{4 \sqrt{f+g x} \sqrt{a+b x+c x^2} \left(c e g (-5 a e g-7 b d g+4 b e f)+2 b^2 e^2 g^2+c^2 \left(-\left(10 d^2 g^2-34 d e f g+21 e^2 f^2\right)\right)\right)}{105 c^2 g^3}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(c e g (-5 a e g-7 b d g+4 b e f)+2 b^2 e^2 g^2+c^2 \left(35 d^2 g^2-56 d e f g+24 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^3 g^4 \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c^2 g \left(2 a e g (13 e f-42 d g)-b \left(35 d^2 g^2-42 d e f g+16 e^2 f^2\right)\right)+b c e g^2 (-29 a e g-28 b d g+9 b e f)+8 b^3 e^2 g^3-2 c^3 f \left(35 d^2 g^2-56 d e f g+24 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^3 g^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 e (f+g x)^{3/2} \sqrt{a+b x+c x^2} (-b e g-4 c d g+6 c e f)}{35 c g^3}+\frac{2 (d+e x)^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}{7 g}","-\frac{4 \sqrt{f+g x} \sqrt{a+b x+c x^2} \left(c e g (-5 a e g-7 b d g+4 b e f)+2 b^2 e^2 g^2+c^2 \left(-\left(10 d^2 g^2-34 d e f g+21 e^2 f^2\right)\right)\right)}{105 c^2 g^3}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(c e g (-5 a e g-7 b d g+4 b e f)+2 b^2 e^2 g^2+c^2 \left(35 d^2 g^2-56 d e f g+24 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^3 g^4 \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c^2 g \left(2 a e g (13 e f-42 d g)-b \left(35 d^2 g^2-42 d e f g+16 e^2 f^2\right)\right)+b c e g^2 (-29 a e g-28 b d g+9 b e f)+8 b^3 e^2 g^3-2 c^3 f \left(35 d^2 g^2-56 d e f g+24 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^3 g^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 e (f+g x)^{3/2} \sqrt{a+b x+c x^2} (-b e g-4 c d g+6 c e f)}{35 c g^3}+\frac{2 (d+e x)^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}{7 g}",1,"(-4*(2*b^2*e^2*g^2 + c*e*g*(4*b*e*f - 7*b*d*g - 5*a*e*g) - c^2*(21*e^2*f^2 - 34*d*e*f*g + 10*d^2*g^2))*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(105*c^2*g^3) + (2*(d + e*x)^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(7*g) - (2*e*(6*c*e*f - 4*c*d*g - b*e*g)*(f + g*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(35*c*g^3) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(8*b^3*e^2*g^3 + b*c*e*g^2*(9*b*e*f - 28*b*d*g - 29*a*e*g) - 2*c^3*f*(24*e^2*f^2 - 56*d*e*f*g + 35*d^2*g^2) - c^2*g*(2*a*e*g*(13*e*f - 42*d*g) - b*(16*e^2*f^2 - 42*d*e*f*g + 35*d^2*g^2)))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(105*c^3*g^4*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*f^2 - b*f*g + a*g^2)*(2*b^2*e^2*g^2 + c*e*g*(4*b*e*f - 7*b*d*g - 5*a*e*g) + c^2*(24*e^2*f^2 - 56*d*e*f*g + 35*d^2*g^2))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(105*c^3*g^4*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",8,6,31,0.1935,1,"{920, 1653, 843, 718, 424, 419}"
895,1,519,0,0.5350077,"\int \frac{(d+e x) \sqrt{a+b x+c x^2}}{\sqrt{f+g x}} \, dx","Int[((d + e*x)*Sqrt[a + b*x + c*x^2])/Sqrt[f + g*x],x]","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} (b e g-10 c d g+8 c e f) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^2 g^3 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c g (-6 a e g-5 b d g+3 b e f)+2 b^2 e g^2-2 c^2 f (4 e f-5 d g)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^2 g^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{f+g x} \sqrt{a+b x+c x^2} (-b e g-5 c d g+4 c e f-3 c e g x)}{15 c g^2}","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} (b e g-10 c d g+8 c e f) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^2 g^3 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c g (-6 a e g-5 b d g+3 b e f)+2 b^2 e g^2-2 c^2 f (4 e f-5 d g)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^2 g^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{f+g x} \sqrt{a+b x+c x^2} (-b e g-5 c d g+4 c e f-3 c e g x)}{15 c g^2}",1,"(-2*Sqrt[f + g*x]*(4*c*e*f - 5*c*d*g - b*e*g - 3*c*e*g*x)*Sqrt[a + b*x + c*x^2])/(15*c*g^2) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*b^2*e*g^2 - 2*c^2*f*(4*e*f - 5*d*g) + c*g*(3*b*e*f - 5*b*d*g - 6*a*e*g))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(15*c^2*g^3*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(8*c*e*f - 10*c*d*g + b*e*g)*(c*f^2 - b*f*g + a*g^2)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(15*c^2*g^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",6,5,29,0.1724,1,"{814, 843, 718, 424, 419}"
896,1,444,0,0.321993,"\int \frac{\sqrt{a+b x+c x^2}}{\sqrt{f+g x}} \, dx","Int[Sqrt[a + b*x + c*x^2]/Sqrt[f + g*x],x]","\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c g^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c f-b g) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c g^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}{3 g}","\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c g^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c f-b g) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c g^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}{3 g}",1,"(2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(3*g) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*f - b*g)*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c*g^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*f^2 - b*f*g + a*g^2)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c*g^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",6,5,24,0.2083,1,"{734, 843, 718, 424, 419}"
897,1,700,0,1.9528386,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x) \sqrt{f+g x}} \, dx","Int[Sqrt[a + b*x + c*x^2]/((d + e*x)*Sqrt[f + g*x]),x]","-\frac{\sqrt{2} \left(a e^2-b d e+c d^2\right) \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e^2 \sqrt{a+b x+c x^2} (e f-d g)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} (-b e g+c d g+c e f) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c e^2 g \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{e g \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}","-\frac{\sqrt{2} \left(a e^2-b d e+c d^2\right) \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e^2 \sqrt{a+b x+c x^2} (e f-d g)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} (-b e g+c d g+c e f) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c e^2 g \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{e g \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(e*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*e*f + c*d*g - b*e*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*e^2*g*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[c]*e^2*(e*f - d*g)*Sqrt[a + b*x + c*x^2])","A",11,9,31,0.2903,1,"{922, 934, 169, 538, 537, 843, 718, 424, 419}"
898,1,957,0,3.2300395,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^2 \sqrt{f+g x}} \, dx","Int[Sqrt[a + b*x + c*x^2]/((d + e*x)^2*Sqrt[f + g*x]),x]","\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} e (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} (2 e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{e^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} f \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{e (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} \left(e^2 (b f-a g)-c d (2 e f-d g)\right) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} e^2 (e f-d g)^2 \sqrt{c x^2+b x+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a}}{(e f-d g) (d+e x)}","-\frac{\sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(e^2 (b f-a g)-c d (2 e f-d g)\right) \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} e^2 \sqrt{a+b x+c x^2} (e f-d g)^2}+\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} e \sqrt{a+b x+c x^2} (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{\frac{c (a+x (b+c x))}{4 a c-b^2}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{b^2-4 a c} g}{\left(b+\sqrt{b^2-4 a c}\right) g-2 c f}\right)}{e^2 \sqrt{f+g x} \sqrt{a+x (b+c x)}}-\frac{\sqrt{f+g x} \sqrt{a+b x+c x^2}}{(d+e x) (e f-d g)}",1,"-((Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/((e*f - d*g)*(d + e*x))) + (Sqrt[b^2 - 4*a*c]*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(Sqrt[2]*e*(e*f - d*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*f*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(e*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*e*f - d*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(e^2*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(e^2*(b*f - a*g) - c*d*(2*e*f - d*g))*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[2]*Sqrt[c]*e^2*(e*f - d*g)^2*Sqrt[a + b*x + c*x^2])","A",15,10,31,0.3226,1,"{924, 6742, 718, 419, 843, 424, 934, 169, 538, 537}"
899,1,1747,0,8.1844371,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^3 \sqrt{f+g x}} \, dx","Int[Sqrt[a + b*x + c*x^2]/((d + e*x)^3*Sqrt[f + g*x]),x]","-\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) (c d (2 e f+d g)-e (b e f+2 b d g-3 a e g))}{4 \sqrt{2} e \left(c d^2-b e d+a e^2\right) (e f-d g)^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{\sqrt{b^2-4 a c} f \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) (c d (2 e f+d g)-e (b e f+2 b d g-3 a e g))}{2 \sqrt{2} e \left(c d^2-b e d+a e^2\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{b^2-4 a c} d g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) (c d (2 e f+d g)-e (b e f+2 b d g-3 a e g))}{2 \sqrt{2} e^2 \left(c d^2-b e d+a e^2\right) (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right) (c d (2 e f+d g)-e (b e f+2 b d g-3 a e g))}{4 \sqrt{2} \sqrt{c} e^2 \left(c d^2-b e d+a e^2\right) (e f-d g)^3 \sqrt{c x^2+b x+a}}+\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} (c d (2 e f+d g)-e (b e f+2 b d g-3 a e g))}{4 \left(c d^2-b e d+a e^2\right) (e f-d g)^2 (d+e x)}-\frac{\sqrt{b^2-4 a c} g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} e^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c e f+c d g-b e g) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} e^2 (e f-d g)^2 \sqrt{c x^2+b x+a}}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a}}{2 (e f-d g) (d+e x)^2}","-\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) (c d (2 e f+d g)-e (b e f+2 b d g-3 a e g))}{4 \sqrt{2} e \left(c d^2-b e d+a e^2\right) (e f-d g)^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} (c d (2 e f+d g)-e (b e f+2 b d g-3 a e g))}{4 \left(c d^2-b e d+a e^2\right) (e f-d g)^2 (d+e x)}-\frac{\sqrt{b^2-4 a c} \left((b f-a g) e^2+c d (d g-2 e f)\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{\frac{c (a+x (b+c x))}{4 a c-b^2}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{b^2-4 a c} g}{\left(b+\sqrt{b^2-4 a c}\right) g-2 c f}\right)}{2 \sqrt{2} e^2 \left(c d^2+e (a e-b d)\right) (e f-d g) \sqrt{f+g x} \sqrt{a+x (b+c x)}}-\frac{\sqrt{2 c f-b g+\sqrt{b^2-4 a c} g} \left(3 a^2 g^2 e^4+b^2 f (4 d g-e f) e^3+2 a c \left(2 e^2 f^2-2 d e g f+3 d^2 g^2\right) e^2-2 b g \left(3 c f d^2+a e (e f+2 d g)\right) e^2+c^2 d^3 g (4 e f-d g)\right) \sqrt{\frac{g \left(-b-2 c x+\sqrt{b^2-4 a c}\right)}{2 c f+\left(\sqrt{b^2-4 a c}-b\right) g}} \sqrt{\frac{g \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{\left(b+\sqrt{b^2-4 a c}\right) g-2 c f}} \Pi \left(\frac{2 c e f-b e g+\sqrt{b^2-4 a c} e g}{2 c e f-2 c d g};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-b g+\sqrt{b^2-4 a c} g}}\right)|\frac{2 c f+\left(\sqrt{b^2-4 a c}-b\right) g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{4 \sqrt{2} \sqrt{c} e^2 \left(c d^2+e (a e-b d)\right) (e f-d g)^3 \sqrt{a+x (b+c x)}}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a}}{2 (e f-d g) (d+e x)^2}",1,"-(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(2*(e*f - d*g)*(d + e*x)^2) + ((c*d*(2*e*f + d*g) - e*(b*e*f + 2*b*d*g - 3*a*e*g))*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(4*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^2*(d + e*x)) - (Sqrt[b^2 - 4*a*c]*(c*d*(2*e*f + d*g) - e*(b*e*f + 2*b*d*g - 3*a*e*g))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(4*Sqrt[2]*e*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (Sqrt[b^2 - 4*a*c]*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(Sqrt[2]*e^2*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[b^2 - 4*a*c]*f*(c*d*(2*e*f + d*g) - e*(b*e*f + 2*b*d*g - 3*a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(2*Sqrt[2]*e*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[b^2 - 4*a*c]*d*g*(c*d*(2*e*f + d*g) - e*(b*e*f + 2*b*d*g - 3*a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(2*Sqrt[2]*e^2*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*e*f + c*d*g - b*e*g)*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[2]*Sqrt[c]*e^2*(e*f - d*g)^2*Sqrt[a + b*x + c*x^2]) + (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*d*(2*e*f + d*g) - e*(b*e*f + 2*b*d*g - 3*a*e*g))*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(4*Sqrt[2]*Sqrt[c]*e^2*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^3*Sqrt[a + b*x + c*x^2])","A",25,11,31,0.3548,1,"{924, 6742, 718, 419, 939, 843, 424, 934, 169, 538, 537}"
900,1,774,0,2.10553,"\int \frac{(d+e x)^3 \sqrt{f+g x}}{\sqrt{a+b x+c x^2}} \, dx","Int[((d + e*x)^3*Sqrt[f + g*x])/Sqrt[a + b*x + c*x^2],x]","\frac{2 e \sqrt{f+g x} \sqrt{a+b x+c x^2} \left(c e g (-25 a e g-84 b d g+13 b e f)+24 b^2 e^2 g^2+c^2 \left(-\left(-90 d^2 g^2+12 d e f g+7 e^2 f^2\right)\right)\right)}{105 c^3 g^2}-\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(c e g (-25 a e g-84 b d g+13 b e f)+24 b^2 e^2 g^2+c^2 \left(105 d^2 g^2-42 d e f g+8 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^4 g^3 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c^2 e g \left(a e g (189 d g+19 e f)-b \left(-210 d^2 g^2-63 d e f g+9 e^2 f^2\right)\right)-8 b c e^2 g^2 (13 a e g+21 b d g+2 b e f)+48 b^3 e^3 g^3+c^3 \left(-\left(105 d^2 e f g^2+105 d^3 g^3-42 d e^2 f^2 g+8 e^3 f^3\right)\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^4 g^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e^2 (f+g x)^{3/2} \sqrt{a+b x+c x^2} (-6 b e g+11 c d g+c e f)}{35 c^2 g^2}+\frac{2 e (d+e x)^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}{7 c}","\frac{2 e \sqrt{f+g x} \sqrt{a+b x+c x^2} \left(c e g (-25 a e g-84 b d g+13 b e f)+24 b^2 e^2 g^2+c^2 \left(-\left(-90 d^2 g^2+12 d e f g+7 e^2 f^2\right)\right)\right)}{105 c^3 g^2}-\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(c e g (-25 a e g-84 b d g+13 b e f)+24 b^2 e^2 g^2+c^2 \left(105 d^2 g^2-42 d e f g+8 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^4 g^3 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c^2 e g \left(a e g (189 d g+19 e f)-b \left(-210 d^2 g^2-63 d e f g+9 e^2 f^2\right)\right)-8 b c e^2 g^2 (13 a e g+21 b d g+2 b e f)+48 b^3 e^3 g^3+c^3 \left(-\left(105 d^2 e f g^2+105 d^3 g^3-42 d e^2 f^2 g+8 e^3 f^3\right)\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{105 c^4 g^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e^2 (f+g x)^{3/2} \sqrt{a+b x+c x^2} (-6 b e g+11 c d g+c e f)}{35 c^2 g^2}+\frac{2 e (d+e x)^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}{7 c}",1,"(2*e*(24*b^2*e^2*g^2 + c*e*g*(13*b*e*f - 84*b*d*g - 25*a*e*g) - c^2*(7*e^2*f^2 + 12*d*e*f*g - 90*d^2*g^2))*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(105*c^3*g^2) + (2*e*(d + e*x)^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(7*c) + (2*e^2*(c*e*f + 11*c*d*g - 6*b*e*g)*(f + g*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(35*c^2*g^2) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(48*b^3*e^3*g^3 - 8*b*c*e^2*g^2*(2*b*e*f + 21*b*d*g + 13*a*e*g) - c^3*(8*e^3*f^3 - 42*d*e^2*f^2*g + 105*d^2*e*f*g^2 + 105*d^3*g^3) + c^2*e*g*(a*e*g*(19*e*f + 189*d*g) - b*(9*e^2*f^2 - 63*d*e*f*g - 210*d^2*g^2)))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(105*c^4*g^3*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(c*f^2 - b*f*g + a*g^2)*(24*b^2*e^2*g^2 + c*e*g*(13*b*e*f - 84*b*d*g - 25*a*e*g) + c^2*(8*e^2*f^2 - 42*d*e*f*g + 105*d^2*g^2))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(105*c^4*g^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",8,6,31,0.1935,1,"{941, 1653, 843, 718, 424, 419}"
901,1,567,0,0.9305404,"\int \frac{(d+e x)^2 \sqrt{f+g x}}{\sqrt{a+b x+c x^2}} \, dx","Int[((d + e*x)^2*Sqrt[f + g*x])/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e g (9 a e g+20 b d g+3 b e f)+8 b^2 e^2 g^2+c^2 \left(-\left(-15 d^2 g^2-10 d e f g+2 e^2 f^2\right)\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^3 g^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} (2 b e g-5 c d g+c e f) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^3 g^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{2 e \sqrt{f+g x} \sqrt{a+b x+c x^2} (-4 b e g+7 c d g+c e f)}{15 c^2 g}+\frac{2 e (d+e x) \sqrt{f+g x} \sqrt{a+b x+c x^2}}{5 c}","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e g (9 a e g+20 b d g+3 b e f)+8 b^2 e^2 g^2+c^2 \left(-\left(-15 d^2 g^2-10 d e f g+2 e^2 f^2\right)\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^3 g^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} (2 b e g-5 c d g+c e f) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^3 g^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{2 e \sqrt{f+g x} \sqrt{a+b x+c x^2} (-4 b e g+7 c d g+c e f)}{15 c^2 g}+\frac{2 e (d+e x) \sqrt{f+g x} \sqrt{a+b x+c x^2}}{5 c}",1,"(2*e*(c*e*f + 7*c*d*g - 4*b*e*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(15*c^2*g) + (2*e*(d + e*x)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(5*c) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(8*b^2*e^2*g^2 - c*e*g*(3*b*e*f + 20*b*d*g + 9*a*e*g) - c^2*(2*e^2*f^2 - 10*d*e*f*g - 15*d^2*g^2))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(15*c^3*g^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(c*e*f - 5*c*d*g + 2*b*e*g)*(c*f^2 - b*f*g + a*g^2)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(15*c^3*g^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",7,6,31,0.1935,1,"{941, 1653, 843, 718, 424, 419}"
902,1,452,0,0.4367862,"\int \frac{(d+e x) \sqrt{f+g x}}{\sqrt{a+b x+c x^2}} \, dx","Int[((d + e*x)*Sqrt[f + g*x])/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (-2 b e g+3 c d g+c e f) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c^2 g \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c^2 g \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{2 e \sqrt{f+g x} \sqrt{a+b x+c x^2}}{3 c}","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (-2 b e g+3 c d g+c e f) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c^2 g \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c^2 g \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{2 e \sqrt{f+g x} \sqrt{a+b x+c x^2}}{3 c}",1,"(2*e*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(3*c) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*e*f + 3*c*d*g - 2*b*e*g)*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c^2*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(c*f^2 - b*f*g + a*g^2)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c^2*g*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",6,5,29,0.1724,1,"{832, 843, 718, 424, 419}"
903,1,188,0,0.064988,"\int \frac{\sqrt{f+g x}}{\sqrt{a+b x+c x^2}} \, dx","Int[Sqrt[f + g*x]/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2])","A",2,2,24,0.08333,1,"{718, 424}"
904,1,467,0,1.6024577,"\int \frac{\sqrt{f+g x}}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[Sqrt[f + g*x]/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{2} g \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c e \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e \sqrt{a+b x+c x^2}}","\frac{2 \sqrt{2} g \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c e \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e \sqrt{a+b x+c x^2}}",1,"(2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*e*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[c]*e*Sqrt[a + b*x + c*x^2])","A",8,7,31,0.2258,1,"{943, 718, 419, 934, 169, 538, 537}"
905,1,994,0,3.7006397,"\int \frac{\sqrt{f+g x}}{(d+e x)^2 \sqrt{a+b x+c x^2}} \, dx","Int[Sqrt[f + g*x]/((d + e*x)^2*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} e}{\left(c d^2-b e d+a e^2\right) (d+e x)}+\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} \left(c d^2-b e d+a e^2\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} f \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\left(c d^2-b e d+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} d g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\left(c d^2-b e d+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+b x+a} e}+\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} \left(e^2 (b f-a g)-c d (2 e f-d g)\right) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{c x^2+b x+a} e}","-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} e}{\left(c d^2-b e d+a e^2\right) (d+e x)}+\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} \left(c d^2-b e d+a e^2\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} f \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\left(c d^2-b e d+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} d g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\left(c d^2-b e d+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+b x+a} e}+\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} \left(e^2 (b f-a g)-c d (2 e f-d g)\right) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{c x^2+b x+a} e}",1,"-((e*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)*(d + e*x))) + (Sqrt[b^2 - 4*a*c]*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*f*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/((c*d^2 - b*d*e + a*e^2)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*d*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(e*(c*d^2 - b*d*e + a*e^2)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(e^2*(b*f - a*g) - c*d*(2*e*f - d*g))*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[2]*Sqrt[c]*e*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[a + b*x + c*x^2])","A",15,10,31,0.3226,1,"{945, 6742, 718, 419, 843, 424, 934, 169, 538, 537}"
906,1,1786,0,8.3957815,"\int \frac{\sqrt{f+g x}}{(d+e x)^3 \sqrt{a+b x+c x^2}} \, dx","Int[Sqrt[f + g*x]/((d + e*x)^3*Sqrt[a + b*x + c*x^2]),x]","-\frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \sqrt{f+g x} \sqrt{c x^2+b x+a} e}{4 \left(c d^2-b e d+a e^2\right)^2 (e f-d g) (d+e x)}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} e}{2 \left(c d^2-b e d+a e^2\right) (d+e x)^2}+\frac{\sqrt{b^2-4 a c} (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{4 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{\sqrt{b^2-4 a c} f (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{2 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{b^2-4 a c} g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} \left(c d^2-b e d+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+b x+a} e}+\frac{\sqrt{b^2-4 a c} d g (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{2 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a} e}+\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c e f-3 c d g+b e g) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{c x^2+b x+a} e}-\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{4 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^2 (e f-d g)^2 \sqrt{c x^2+b x+a} e}","-\frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \sqrt{f+g x} \sqrt{c x^2+b x+a} e}{4 \left(c d^2-b e d+a e^2\right)^2 (e f-d g) (d+e x)}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} e}{2 \left(c d^2-b e d+a e^2\right) (d+e x)^2}+\frac{\sqrt{b^2-4 a c} (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{4 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{\sqrt{b^2-4 a c} f (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{2 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{b^2-4 a c} g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} \left(c d^2-b e d+a e^2\right) \sqrt{f+g x} \sqrt{c x^2+b x+a} e}+\frac{\sqrt{b^2-4 a c} d g (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{2 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a} e}+\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c e f-3 c d g+b e g) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{c x^2+b x+a} e}-\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{4 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^2 (e f-d g)^2 \sqrt{c x^2+b x+a} e}",1,"-(e*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (e*(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*g))*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(4*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)*(d + e*x)) + (Sqrt[b^2 - 4*a*c]*(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*g))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(4*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (Sqrt[b^2 - 4*a*c]*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(Sqrt[2]*e*(c*d^2 - b*d*e + a*e^2)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[b^2 - 4*a*c]*f*(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(2*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[b^2 - 4*a*c]*d*g*(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(2*Sqrt[2]*e*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*e*f - 3*c*d*g + b*e*g)*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[2]*Sqrt[c]*e*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[a + b*x + c*x^2]) - (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*g))*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(4*Sqrt[2]*Sqrt[c]*e*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)^2*Sqrt[a + b*x + c*x^2])","A",25,11,31,0.3548,1,"{945, 6742, 718, 419, 939, 843, 424, 934, 169, 538, 537}"
907,1,675,0,1.6546516,"\int \frac{(f+g x)^{3/2}}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[(f + g*x)^(3/2)/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{2} g \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c e^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} (e f-d g) \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e^2 \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} g \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c e \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}","\frac{2 \sqrt{2} g \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c e^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} (e f-d g) \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e^2 \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} g \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c e \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*e*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*(e*f - d*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*e^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(e*f - d*g)*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[c]*e^2*Sqrt[a + b*x + c*x^2])","A",11,8,31,0.2581,1,"{957, 718, 419, 934, 169, 538, 537, 424}"
908,1,1138,0,2.1381901,"\int \frac{(f+g x)^{5/2}}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[(f + g*x)^(5/2)/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{f+g x} \sqrt{c x^2+b x+a} g^2}{3 c e}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} (2 c f-b g) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) g}{3 c^2 e \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} (e f-d g) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) g}{c e^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} (e f-d g)^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) g}{c e^3 \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c f^2-b g f+a g^2\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) g}{3 c^2 e \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (e f-d g)^2 \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e^3 \sqrt{c x^2+b x+a}}","\frac{2 \sqrt{f+g x} \sqrt{c x^2+b x+a} g^2}{3 c e}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} (2 c f-b g) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) g}{3 c^2 e \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} (e f-d g) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) g}{c e^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} (e f-d g)^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) g}{c e^3 \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c f^2-b g f+a g^2\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) g}{3 c^2 e \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (e f-d g)^2 \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} e^3 \sqrt{c x^2+b x+a}}",1,"(2*g^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(3*c*e) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*(2*c*f - b*g)*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c^2*e*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*e^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*(e*f - d*g)^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*e^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*(c*f^2 - b*f*g + a*g^2)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c^2*e*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(e*f - d*g)^2*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[c]*e^3*Sqrt[a + b*x + c*x^2])","A",17,10,31,0.3226,1,"{957, 718, 419, 934, 169, 538, 537, 424, 742, 843}"
909,1,631,0,1.0902124,"\int \frac{(d+e x)^3}{\sqrt{f+g x} \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^3/(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]),x]","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(-c e^2 g (a g (7 e f-15 d g)-3 b f (e f-5 d g))+4 b e^3 g^2 (b f-a g)+c^2 \left(45 d^2 e f g^2-15 d^3 g^3-30 d e^2 f^2 g+8 e^3 f^3\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^3 g^3 \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} e \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c e g (-9 a e g-30 b d g+7 b e f)+8 b^2 e^2 g^2+c^2 \left(45 d^2 g^2-30 d e f g+8 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^3 g^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{8 e^2 \sqrt{f+g x} \sqrt{a+b x+c x^2} (b e g-3 c d g+c e f)}{15 c^2 g^2}+\frac{2 e^2 (d+e x) \sqrt{f+g x} \sqrt{a+b x+c x^2}}{5 c g}","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(-c e^2 g (a g (7 e f-15 d g)-3 b f (e f-5 d g))+4 b e^3 g^2 (b f-a g)+c^2 \left(45 d^2 e f g^2-15 d^3 g^3-30 d e^2 f^2 g+8 e^3 f^3\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^3 g^3 \sqrt{f+g x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} e \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c e g (-9 a e g-30 b d g+7 b e f)+8 b^2 e^2 g^2+c^2 \left(45 d^2 g^2-30 d e f g+8 e^2 f^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{15 c^3 g^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{8 e^2 \sqrt{f+g x} \sqrt{a+b x+c x^2} (b e g-3 c d g+c e f)}{15 c^2 g^2}+\frac{2 e^2 (d+e x) \sqrt{f+g x} \sqrt{a+b x+c x^2}}{5 c g}",1,"(-8*e^2*(c*e*f - 3*c*d*g + b*e*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(15*c^2*g^2) + (2*e^2*(d + e*x)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(5*c*g) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(8*b^2*e^2*g^2 + c*e*g*(7*b*e*f - 30*b*d*g - 9*a*e*g) + c^2*(8*e^2*f^2 - 30*d*e*f*g + 45*d^2*g^2))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(15*c^3*g^3*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(4*b*e^3*g^2*(b*f - a*g) + c^2*(8*e^3*f^3 - 30*d*e^2*f^2*g + 45*d^2*e*f*g^2 - 15*d^3*g^3) - c*e^2*g*(a*g*(7*e*f - 15*d*g) - 3*b*f*(e*f - 5*d*g)))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(15*c^3*g^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",7,6,31,0.1935,1,"{930, 1653, 843, 718, 424, 419}"
910,1,479,0,0.5533473,"\int \frac{(d+e x)^2}{\sqrt{f+g x} \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^2/(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(e^2 g (b f-a g)+c \left(3 d^2 g^2-6 d e f g+2 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c^2 g^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (b e g-3 c d g+c e f) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c^2 g^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}{3 c g}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \left(e^2 g (b f-a g)+c \left(3 d^2 g^2-6 d e f g+2 e^2 f^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c^2 g^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (b e g-3 c d g+c e f) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 c^2 g^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}}{3 c g}",1,"(2*e^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(3*c*g) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(c*e*f - 3*c*d*g + b*e*g)*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c^2*g^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(e^2*g*(b*f - a*g) + c*(2*e^2*f^2 - 6*d*e*f*g + 3*d^2*g^2))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*c^2*g^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",7,6,31,0.1935,1,"{930, 24, 843, 718, 424, 419}"
911,1,393,0,0.2095917,"\int \frac{d+e x}{\sqrt{f+g x} \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)/(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{2} e \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c g \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c g \sqrt{f+g x} \sqrt{a+b x+c x^2}}","\frac{\sqrt{2} e \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c g \sqrt{a+b x+c x^2} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c g \sqrt{f+g x} \sqrt{a+b x+c x^2}}",1,"(Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(e*f - d*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*g*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",5,4,29,0.1379,1,"{843, 718, 424, 419}"
912,1,189,0,0.0722348,"\int \frac{1}{\sqrt{f+g x} \sqrt{a+b x+c x^2}} \, dx","Int[1/(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c \sqrt{f+g x} \sqrt{a+b x+c x^2}}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{c \sqrt{f+g x} \sqrt{a+b x+c x^2}}",1,"(2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(c*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])","A",2,2,24,0.08333,1,"{718, 419}"
913,1,280,0,1.2469847,"\int \frac{1}{(d+e x) \sqrt{f+g x} \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{2} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} \sqrt{a+b x+c x^2} (e f-d g)}","-\frac{\sqrt{2} \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} \sqrt{a+b x+c x^2} (e f-d g)}",1,"-((Sqrt[2]*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[c]*(e*f - d*g)*Sqrt[a + b*x + c*x^2]))","A",5,4,31,0.1290,1,"{934, 169, 538, 537}"
914,1,1037,0,3.5270875,"\int \frac{1}{(d+e x)^2 \sqrt{f+g x} \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} e^2}{\left(c d^2-b e d+a e^2\right) (e f-d g) (d+e x)}+\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) e}{\sqrt{2} \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} f \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) e}{\left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} d g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right) (e f-d g)^2 \sqrt{c x^2+b x+a}}","-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} e^2}{\left(c d^2-b e d+a e^2\right) (e f-d g) (d+e x)}+\frac{\sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) e}{\sqrt{2} \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} f \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) e}{\left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} d g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right) (e f-d g)^2 \sqrt{c x^2+b x+a}}",1,"-((e^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*(d + e*x))) + (Sqrt[b^2 - 4*a*c]*e*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*f*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/((c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*d*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/((c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[2]*Sqrt[c]*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^2*Sqrt[a + b*x + c*x^2])","A",15,10,31,0.3226,1,"{939, 6742, 718, 419, 843, 424, 934, 169, 538, 537}"
915,1,1762,0,8.0118148,"\int \frac{1}{(d+e x)^3 \sqrt{f+g x} \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^3*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]),x]","-\frac{3 (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{f+g x} \sqrt{c x^2+b x+a} e^2}{4 \left(c d^2-b e d+a e^2\right)^2 (e f-d g)^2 (d+e x)}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} e^2}{2 \left(c d^2-b e d+a e^2\right) (e f-d g) (d+e x)^2}+\frac{3 \sqrt{b^2-4 a c} (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) e}{4 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g)^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}-\frac{3 \sqrt{b^2-4 a c} f (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) e}{2 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{3 \sqrt{b^2-4 a c} d g (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{2 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g)^2 \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{\sqrt{b^2-4 a c} g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{2} \left(c d^2-b e d+a e^2\right) (e f-d g) \sqrt{f+g x} \sqrt{c x^2+b x+a}}-\frac{3 \sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g))^2 \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{4 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^2 (e f-d g)^3 \sqrt{c x^2+b x+a}}+\frac{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} (c e f-3 c d g+b e g) \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right) (e f-d g)^2 \sqrt{c x^2+b x+a}}","-\frac{3 (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{f+g x} \sqrt{c x^2+b x+a} e^2}{4 \left(c d^2-b e d+a e^2\right)^2 (e f-d g)^2 (d+e x)}-\frac{\sqrt{f+g x} \sqrt{c x^2+b x+a} e^2}{2 \left(c d^2-b e d+a e^2\right) (e f-d g) (d+e x)^2}+\frac{3 \sqrt{b^2-4 a c} (c d (2 e f-3 d g)-e (b e f-2 b d g+a e g)) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) e}{4 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (e f-d g)^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{\sqrt{b^2-4 a c} (c d (7 d g-6 e f)+e (3 b e f-4 b d g+a e g)) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{\frac{c (a+x (b+c x))}{4 a c-b^2}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|\frac{2 \sqrt{b^2-4 a c} g}{\left(b+\sqrt{b^2-4 a c}\right) g-2 c f}\right)}{2 \sqrt{2} \left(c d^2+e (a e-b d)\right)^2 (e f-d g) \sqrt{f+g x} \sqrt{a+x (b+c x)}}+\frac{\sqrt{2 c f-b g+\sqrt{b^2-4 a c} g} \left(c^2 \left(8 e^2 f^2-20 d e g f+15 d^2 g^2\right) d^2+2 c e \left(b d \left(-4 e^2 f^2+11 d e g f-10 d^2 g^2\right)+a e \left(-2 e^2 f^2+2 d e g f+3 d^2 g^2\right)\right)+e^2 \left(\left(3 e^2 f^2-8 d e g f+8 d^2 g^2\right) b^2+2 a e g (e f-4 d g) b+3 a^2 e^2 g^2\right)\right) \sqrt{\frac{g \left(-b-2 c x+\sqrt{b^2-4 a c}\right)}{2 c f+\left(\sqrt{b^2-4 a c}-b\right) g}} \sqrt{\frac{g \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{\left(b+\sqrt{b^2-4 a c}\right) g-2 c f}} \Pi \left(\frac{2 c e f-b e g+\sqrt{b^2-4 a c} e g}{2 c e f-2 c d g};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-b g+\sqrt{b^2-4 a c} g}}\right)|\frac{2 c f+\left(\sqrt{b^2-4 a c}-b\right) g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{4 \sqrt{2} \sqrt{c} \left(c d^2+e (a e-b d)\right)^2 (d g-e f)^3 \sqrt{a+x (b+c x)}}",1,"-(e^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*(d + e*x)^2) - (3*e^2*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2])/(4*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)^2*(d + e*x)) + (3*Sqrt[b^2 - 4*a*c]*e*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(4*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (Sqrt[b^2 - 4*a*c]*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (3*Sqrt[b^2 - 4*a*c]*e*f*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(2*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (3*Sqrt[b^2 - 4*a*c]*d*g*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(2*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)^2*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) + (Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*e*f - 3*c*d*g + b*e*g)*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[2]*Sqrt[c]*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^2*Sqrt[a + b*x + c*x^2]) - (3*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))^2*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(4*Sqrt[2]*Sqrt[c]*(c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)^3*Sqrt[a + b*x + c*x^2])","A",25,10,31,0.3226,1,"{939, 6742, 718, 419, 843, 424, 934, 169, 538, 537}"
916,1,553,0,1.612995,"\int \frac{1}{(d+e x) (f+g x)^{3/2} \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)*(f + g*x)^(3/2)*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{2} g \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{a+b x+c x^2} (e f-d g) \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{\sqrt{2} e \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} \sqrt{a+b x+c x^2} (e f-d g)^2}+\frac{2 g^2 \sqrt{a+b x+c x^2}}{\sqrt{f+g x} (e f-d g) \left(a g^2-b f g+c f^2\right)}","-\frac{\sqrt{2} g \sqrt{b^2-4 a c} \sqrt{f+g x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{\sqrt{a+b x+c x^2} (e f-d g) \left(a g^2-b f g+c f^2\right) \sqrt{\frac{c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{\sqrt{2} e \sqrt{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right)}{\sqrt{c} \sqrt{a+b x+c x^2} (e f-d g)^2}+\frac{2 g^2 \sqrt{a+b x+c x^2}}{\sqrt{f+g x} (e f-d g) \left(a g^2-b f g+c f^2\right)}",1,"(2*g^2*Sqrt[a + b*x + c*x^2])/((e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*Sqrt[f + g*x]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/((e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*e*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[c]*(e*f - d*g)^2*Sqrt[a + b*x + c*x^2])","A",11,9,31,0.2903,1,"{957, 744, 21, 718, 424, 934, 169, 538, 537}"
917,1,1125,0,2.3104813,"\int \frac{1}{(d+e x) (f+g x)^{5/2} \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)*(f + g*x)^(5/2)*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{2} \sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right) e^2}{\sqrt{c} (e f-d g)^3 \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} g \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) e}{(e f-d g)^2 \left(c f^2-b g f+a g^2\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{2 g^2 \sqrt{c x^2+b x+a} e}{(e f-d g)^2 \left(c f^2-b g f+a g^2\right) \sqrt{f+g x}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} g (2 c f-b g) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 (e f-d g) \left(c f^2-b g f+a g^2\right)^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 (e f-d g) \left(c f^2-b g f+a g^2\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{4 g^2 (2 c f-b g) \sqrt{c x^2+b x+a}}{3 (e f-d g) \left(c f^2-b g f+a g^2\right)^2 \sqrt{f+g x}}+\frac{2 g^2 \sqrt{c x^2+b x+a}}{3 (e f-d g) \left(c f^2-b g f+a g^2\right) (f+g x)^{3/2}}","-\frac{\sqrt{2} \sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}} \sqrt{1-\frac{2 c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \Pi \left(\frac{e \left(2 c f-b g+\sqrt{b^2-4 a c} g\right)}{2 c (e f-d g)};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{f+g x}}{\sqrt{2 c f-\left(b-\sqrt{b^2-4 a c}\right) g}}\right)|\frac{b-\sqrt{b^2-4 a c}-\frac{2 c f}{g}}{b+\sqrt{b^2-4 a c}-\frac{2 c f}{g}}\right) e^2}{\sqrt{c} (e f-d g)^3 \sqrt{c x^2+b x+a}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} g \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right) e}{(e f-d g)^2 \left(c f^2-b g f+a g^2\right) \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{2 g^2 \sqrt{c x^2+b x+a} e}{(e f-d g)^2 \left(c f^2-b g f+a g^2\right) \sqrt{f+g x}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} g (2 c f-b g) \sqrt{f+g x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 (e f-d g) \left(c f^2-b g f+a g^2\right)^2 \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} g \sqrt{\frac{c (f+g x)}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} g}{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g}\right)}{3 (e f-d g) \left(c f^2-b g f+a g^2\right) \sqrt{f+g x} \sqrt{c x^2+b x+a}}+\frac{4 g^2 (2 c f-b g) \sqrt{c x^2+b x+a}}{3 (e f-d g) \left(c f^2-b g f+a g^2\right)^2 \sqrt{f+g x}}+\frac{2 g^2 \sqrt{c x^2+b x+a}}{3 (e f-d g) \left(c f^2-b g f+a g^2\right) (f+g x)^{3/2}}",1,"(2*g^2*Sqrt[a + b*x + c*x^2])/(3*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*(f + g*x)^(3/2)) + (4*g^2*(2*c*f - b*g)*Sqrt[a + b*x + c*x^2])/(3*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^2*Sqrt[f + g*x]) + (2*e*g^2*Sqrt[a + b*x + c*x^2])/((e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)*Sqrt[f + g*x]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*(2*c*f - b*g)*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^2*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*g*Sqrt[f + g*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/((e*f - d*g)^2*(c*f^2 - b*f*g + a*g^2)*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*g*Sqrt[(c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*g)/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)])/(3*(e*f - d*g)*(c*f^2 - b*f*g + a*g^2)*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*e^2*Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b - Sqrt[b^2 - 4*a*c])*g)]*Sqrt[1 - (2*c*(f + g*x))/(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)]*EllipticPi[(e*(2*c*f - b*g + Sqrt[b^2 - 4*a*c]*g))/(2*c*(e*f - d*g)), ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[f + g*x])/Sqrt[2*c*f - (b - Sqrt[b^2 - 4*a*c])*g]], (b - Sqrt[b^2 - 4*a*c] - (2*c*f)/g)/(b + Sqrt[b^2 - 4*a*c] - (2*c*f)/g)])/(Sqrt[c]*(e*f - d*g)^3*Sqrt[a + b*x + c*x^2])","A",18,12,31,0.3871,1,"{957, 744, 834, 843, 718, 424, 419, 21, 934, 169, 538, 537}"
918,1,475,0,0.4193293,"\int \frac{\sqrt{d+e x}}{\sqrt{f+g x} \sqrt{a+b x+c x^2}} \, dx","Int[Sqrt[d + e*x]/(Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{2} (d+e x) \sqrt{-\sqrt{b^2-4 a c}+b+2 c x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)} \sqrt{\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) (e f-d g)}{(d+e x) \left(2 c f-g \left(\sqrt{b^2-4 a c}+b\right)\right)}} \sqrt{\frac{\left(x \left(\sqrt{b^2-4 a c}+b\right)+2 a\right) (e f-d g)}{(d+e x) \left(f \sqrt{b^2-4 a c}-2 a g+b f\right)}} \Pi \left(\frac{e \left(2 c f-\left(b+\sqrt{b^2-4 a c}\right) g\right)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) g};\sin ^{-1}\left(\frac{\sqrt{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e} \sqrt{f+g x}}{\sqrt{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g} \sqrt{d+e x}}\right)|\frac{\left(b d+\sqrt{b^2-4 a c} d-2 a e\right) \left(2 c f-\left(b+\sqrt{b^2-4 a c}\right) g\right)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b f+\sqrt{b^2-4 a c} f-2 a g\right)}\right)}{g \sqrt{\frac{2 a c}{\sqrt{b^2-4 a c}+b}+c x} \sqrt{a+b x+c x^2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}","\frac{\sqrt{2} (d+e x) \sqrt{-\sqrt{b^2-4 a c}+b+2 c x} \sqrt{2 c f-g \left(\sqrt{b^2-4 a c}+b\right)} \sqrt{\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) (e f-d g)}{(d+e x) \left(2 c f-g \left(\sqrt{b^2-4 a c}+b\right)\right)}} \sqrt{\frac{\left(x \left(\sqrt{b^2-4 a c}+b\right)+2 a\right) (e f-d g)}{(d+e x) \left(f \sqrt{b^2-4 a c}-2 a g+b f\right)}} \Pi \left(\frac{e \left(2 c f-\left(b+\sqrt{b^2-4 a c}\right) g\right)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) g};\sin ^{-1}\left(\frac{\sqrt{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e} \sqrt{f+g x}}{\sqrt{2 c f-\left(b+\sqrt{b^2-4 a c}\right) g} \sqrt{d+e x}}\right)|\frac{\left(b d+\sqrt{b^2-4 a c} d-2 a e\right) \left(2 c f-\left(b+\sqrt{b^2-4 a c}\right) g\right)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b f+\sqrt{b^2-4 a c} f-2 a g\right)}\right)}{g \sqrt{\frac{2 a c}{\sqrt{b^2-4 a c}+b}+c x} \sqrt{a+b x+c x^2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}",1,"(Sqrt[2]*Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g]*Sqrt[b - Sqrt[b^2 - 4*a*c] + 2*c*x]*Sqrt[((e*f - d*g)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*f - (b + Sqrt[b^2 - 4*a*c])*g)*(d + e*x))]*Sqrt[((e*f - d*g)*(2*a + (b + Sqrt[b^2 - 4*a*c])*x))/((b*f + Sqrt[b^2 - 4*a*c]*f - 2*a*g)*(d + e*x))]*(d + e*x)*EllipticPi[(e*(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*g), ArcSin[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*Sqrt[f + g*x])/(Sqrt[2*c*f - (b + Sqrt[b^2 - 4*a*c])*g]*Sqrt[d + e*x])], ((b*d + Sqrt[b^2 - 4*a*c]*d - 2*a*e)*(2*c*f - (b + Sqrt[b^2 - 4*a*c])*g))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b*f + Sqrt[b^2 - 4*a*c]*f - 2*a*g))])/(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*g*Sqrt[(2*a*c)/(b + Sqrt[b^2 - 4*a*c]) + c*x]*Sqrt[a + b*x + c*x^2])","A",1,1,33,0.03030,1,"{926}"
919,1,588,0,1.1669214,"\int \frac{1}{\sqrt{d+e x} \sqrt{f+g x} \sqrt{a+b x+c x^2}} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[f + g*x]*Sqrt[a + b*x + c*x^2]),x]","-\frac{(d+e x) \sqrt[4]{c f^2-g (b f-a g)} \sqrt{\frac{\left(a+b x+c x^2\right) (e f-d g)^2}{(d+e x)^2 \left(a g^2-b f g+c f^2\right)}} \left(\frac{(f+g x) \sqrt{a e^2-b d e+c d^2}}{(d+e x) \sqrt{c f^2-g (b f-a g)}}+1\right) \sqrt{\frac{\frac{(f+g x)^2 \left(a e^2-b d e+c d^2\right)}{(d+e x)^2 \left(c f^2-g (b f-a g)\right)}-\frac{(f+g x) (2 a e g-b (d g+e f)+2 c d f)}{(d+e x) \left(a g^2-b f g+c f^2\right)}+1}{\left(\frac{(f+g x) \sqrt{a e^2-b d e+c d^2}}{(d+e x) \sqrt{c f^2-g (b f-a g)}}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c d^2-b e d+a e^2} \sqrt{f+g x}}{\sqrt[4]{c f^2-b g f+a g^2} \sqrt{d+e x}}\right)|\frac{1}{4} \left(\frac{2 c d f+2 a e g-b (e f+d g)}{\sqrt{c d^2-e (b d-a e)} \sqrt{c f^2-g (b f-a g)}}+2\right)\right)}{\sqrt{a+b x+c x^2} (e f-d g) \sqrt[4]{a e^2-b d e+c d^2} \sqrt{\frac{(f+g x)^2 \left(a e^2-b d e+c d^2\right)}{(d+e x)^2 \left(c f^2-g (b f-a g)\right)}-\frac{(f+g x) (2 a e g-b (d g+e f)+2 c d f)}{(d+e x) \left(a g^2-b f g+c f^2\right)}+1}}","-\frac{(d+e x) \sqrt[4]{c f^2-g (b f-a g)} \sqrt{\frac{\left(a+b x+c x^2\right) (e f-d g)^2}{(d+e x)^2 \left(a g^2-b f g+c f^2\right)}} \left(\frac{(f+g x) \sqrt{a e^2-b d e+c d^2}}{(d+e x) \sqrt{c f^2-g (b f-a g)}}+1\right) \sqrt{\frac{\frac{(f+g x)^2 \left(a e^2-b d e+c d^2\right)}{(d+e x)^2 \left(c f^2-g (b f-a g)\right)}-\frac{(f+g x) (2 a e g-b (d g+e f)+2 c d f)}{(d+e x) \left(a g^2-b f g+c f^2\right)}+1}{\left(\frac{(f+g x) \sqrt{a e^2-b d e+c d^2}}{(d+e x) \sqrt{c f^2-g (b f-a g)}}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c d^2-b e d+a e^2} \sqrt{f+g x}}{\sqrt[4]{c f^2-b g f+a g^2} \sqrt{d+e x}}\right)|\frac{1}{4} \left(\frac{2 c d f+2 a e g-b (e f+d g)}{\sqrt{c d^2-e (b d-a e)} \sqrt{c f^2-g (b f-a g)}}+2\right)\right)}{\sqrt{a+b x+c x^2} (e f-d g) \sqrt[4]{a e^2-b d e+c d^2} \sqrt{\frac{(f+g x)^2 \left(a e^2-b d e+c d^2\right)}{(d+e x)^2 \left(c f^2-g (b f-a g)\right)}-\frac{(f+g x) (2 a e g-b (d g+e f)+2 c d f)}{(d+e x) \left(a g^2-b f g+c f^2\right)}+1}}",1,"-(((c*f^2 - g*(b*f - a*g))^(1/4)*(d + e*x)*Sqrt[((e*f - d*g)^2*(a + b*x + c*x^2))/((c*f^2 - b*f*g + a*g^2)*(d + e*x)^2)]*(1 + (Sqrt[c*d^2 - b*d*e + a*e^2]*(f + g*x))/(Sqrt[c*f^2 - g*(b*f - a*g)]*(d + e*x)))*Sqrt[(1 - ((2*c*d*f + 2*a*e*g - b*(e*f + d*g))*(f + g*x))/((c*f^2 - b*f*g + a*g^2)*(d + e*x)) + ((c*d^2 - b*d*e + a*e^2)*(f + g*x)^2)/((c*f^2 - g*(b*f - a*g))*(d + e*x)^2))/(1 + (Sqrt[c*d^2 - b*d*e + a*e^2]*(f + g*x))/(Sqrt[c*f^2 - g*(b*f - a*g)]*(d + e*x)))^2]*EllipticF[2*ArcTan[((c*d^2 - b*d*e + a*e^2)^(1/4)*Sqrt[f + g*x])/((c*f^2 - b*f*g + a*g^2)^(1/4)*Sqrt[d + e*x])], (2 + (2*c*d*f + 2*a*e*g - b*(e*f + d*g))/(Sqrt[c*d^2 - e*(b*d - a*e)]*Sqrt[c*f^2 - g*(b*f - a*g)]))/4])/((c*d^2 - b*d*e + a*e^2)^(1/4)*(e*f - d*g)*Sqrt[a + b*x + c*x^2]*Sqrt[1 - ((2*c*d*f + 2*a*e*g - b*(e*f + d*g))*(f + g*x))/((c*f^2 - b*f*g + a*g^2)*(d + e*x)) + ((c*d^2 - b*d*e + a*e^2)*(f + g*x)^2)/((c*f^2 - g*(b*f - a*g))*(d + e*x)^2)]))","A",2,2,33,0.06061,1,"{935, 1103}"
920,1,220,0,0.215489,"\int (d+e x)^m (f+g x)^2 \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^m*(f + g*x)^2*(a + b*x + c*x^2),x]","\frac{(d+e x)^{m+3} \left(e g (a e g-3 b d g+2 b e f)+c \left(6 d^2 g^2-6 d e f g+e^2 f^2\right)\right)}{e^5 (m+3)}+\frac{(e f-d g)^2 (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^5 (m+1)}-\frac{(e f-d g) (d+e x)^{m+2} (2 c d (e f-2 d g)-e (2 a e g-3 b d g+b e f))}{e^5 (m+2)}+\frac{g (d+e x)^{m+4} (b e g-4 c d g+2 c e f)}{e^5 (m+4)}+\frac{c g^2 (d+e x)^{m+5}}{e^5 (m+5)}","\frac{(d+e x)^{m+3} \left(e g (a e g-3 b d g+2 b e f)+c \left(6 d^2 g^2-6 d e f g+e^2 f^2\right)\right)}{e^5 (m+3)}+\frac{(e f-d g)^2 (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^5 (m+1)}-\frac{(e f-d g) (d+e x)^{m+2} (2 c d (e f-2 d g)-e (2 a e g-3 b d g+b e f))}{e^5 (m+2)}+\frac{g (d+e x)^{m+4} (b e g-4 c d g+2 c e f)}{e^5 (m+4)}+\frac{c g^2 (d+e x)^{m+5}}{e^5 (m+5)}",1,"((c*d^2 - b*d*e + a*e^2)*(e*f - d*g)^2*(d + e*x)^(1 + m))/(e^5*(1 + m)) - ((e*f - d*g)*(2*c*d*(e*f - 2*d*g) - e*(b*e*f - 3*b*d*g + 2*a*e*g))*(d + e*x)^(2 + m))/(e^5*(2 + m)) + ((e*g*(2*b*e*f - 3*b*d*g + a*e*g) + c*(e^2*f^2 - 6*d*e*f*g + 6*d^2*g^2))*(d + e*x)^(3 + m))/(e^5*(3 + m)) + (g*(2*c*e*f - 4*c*d*g + b*e*g)*(d + e*x)^(4 + m))/(e^5*(4 + m)) + (c*g^2*(d + e*x)^(5 + m))/(e^5*(5 + m))","A",2,1,25,0.04000,1,"{947}"
921,1,144,0,0.1132688,"\int (d+e x)^m (f+g x) \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^m*(f + g*x)*(a + b*x + c*x^2),x]","\frac{(e f-d g) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^4 (m+1)}-\frac{(d+e x)^{m+2} (c d (2 e f-3 d g)-e (a e g-2 b d g+b e f))}{e^4 (m+2)}+\frac{(d+e x)^{m+3} (b e g-3 c d g+c e f)}{e^4 (m+3)}+\frac{c g (d+e x)^{m+4}}{e^4 (m+4)}","\frac{(e f-d g) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^4 (m+1)}-\frac{(d+e x)^{m+2} (c d (2 e f-3 d g)-e (a e g-2 b d g+b e f))}{e^4 (m+2)}+\frac{(d+e x)^{m+3} (b e g-3 c d g+c e f)}{e^4 (m+3)}+\frac{c g (d+e x)^{m+4}}{e^4 (m+4)}",1,"((c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*(d + e*x)^(1 + m))/(e^4*(1 + m)) - ((c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*(d + e*x)^(2 + m))/(e^4*(2 + m)) + ((c*e*f - 3*c*d*g + b*e*g)*(d + e*x)^(3 + m))/(e^4*(3 + m)) + (c*g*(d + e*x)^(4 + m))/(e^4*(4 + m))","A",2,1,23,0.04348,1,"{771}"
922,1,129,0,0.1594529,"\int \frac{(d+e x)^m \left(a+b x+c x^2\right)}{f+g x} \, dx","Int[((d + e*x)^m*(a + b*x + c*x^2))/(f + g*x),x]","\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right) \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right)}{g^2 (m+1) (e f-d g)}-\frac{(d+e x)^{m+1} (-b e g+c d g+c e f)}{e^2 g^2 (m+1)}+\frac{c (d+e x)^{m+2}}{e^2 g (m+2)}","\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right) \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right)}{g^2 (m+1) (e f-d g)}-\frac{(d+e x)^{m+1} (-b e g+c d g+c e f)}{e^2 g^2 (m+1)}+\frac{c (d+e x)^{m+2}}{e^2 g (m+2)}",1,"-(((c*e*f + c*d*g - b*e*g)*(d + e*x)^(1 + m))/(e^2*g^2*(1 + m))) + (c*(d + e*x)^(2 + m))/(e^2*g*(2 + m)) + ((c*f^2 - b*f*g + a*g^2)*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((g*(d + e*x))/(e*f - d*g))])/(g^2*(e*f - d*g)*(1 + m))","A",3,3,25,0.1200,1,"{951, 80, 68}"
923,1,157,0,0.2040889,"\int \frac{(d+e x)^m \left(a+b x+c x^2\right)}{(f+g x)^2} \, dx","Int[((d + e*x)^m*(a + b*x + c*x^2))/(f + g*x)^2,x]","-\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right) (g (a e g m+b d g-b e f (m+1))-c f (2 d g-e f (m+2)))}{g^2 (m+1) (e f-d g)^2}+\frac{(d+e x)^{m+1} \left(a+\frac{f (c f-b g)}{g^2}\right)}{(f+g x) (e f-d g)}+\frac{c (d+e x)^{m+1}}{e g^2 (m+1)}","\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right) (c f (2 d g-e f (m+2))-g (a e g m+b (d g-e f (m+1))))}{g^2 (m+1) (e f-d g)^2}+\frac{(d+e x)^{m+1} \left(a+\frac{f (c f-b g)}{g^2}\right)}{(f+g x) (e f-d g)}+\frac{c (d+e x)^{m+1}}{e g^2 (m+1)}",1,"(c*(d + e*x)^(1 + m))/(e*g^2*(1 + m)) + ((a + (f*(c*f - b*g))/g^2)*(d + e*x)^(1 + m))/((e*f - d*g)*(f + g*x)) - ((g*(b*d*g + a*e*g*m - b*e*f*(1 + m)) - c*f*(2*d*g - e*f*(2 + m)))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((g*(d + e*x))/(e*f - d*g))])/(g^2*(e*f - d*g)^2*(1 + m))","A",3,3,25,0.1200,1,"{949, 80, 68}"
924,1,243,0,0.3174715,"\int \frac{(d+e x)^m \left(a+b x+c x^2\right)}{(f+g x)^3} \, dx","Int[((d + e*x)^m*(a + b*x + c*x^2))/(f + g*x)^3,x]","\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right) \left(e g m (-a e g (1-m)+2 b d g-b e f (m+1))+c \left(2 d^2 g^2-4 d e f g (m+1)+e^2 f^2 \left(m^2+3 m+2\right)\right)\right)}{2 g^2 (m+1) (e f-d g)^3}-\frac{(d+e x)^{m+1} (g (-a e g (1-m)+2 b d g-b e f (m+1))-c f (4 d g-e f (m+3)))}{2 g^2 (f+g x) (e f-d g)^2}+\frac{(d+e x)^{m+1} \left(a+\frac{f (c f-b g)}{g^2}\right)}{2 (f+g x)^2 (e f-d g)}","\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right) \left(c \left(2 d^2 g^2-4 d e f g (m+1)+e^2 f^2 \left(m^2+3 m+2\right)\right)-e g m (a e g (1-m)-b (2 d g-e f (m+1)))\right)}{2 g^2 (m+1) (e f-d g)^3}+\frac{(d+e x)^{m+1} (g (a e g (1-m)-b (2 d g-e f (m+1)))+c f (4 d g-e f (m+3)))}{2 g^2 (f+g x) (e f-d g)^2}+\frac{(d+e x)^{m+1} \left(a+\frac{f (c f-b g)}{g^2}\right)}{2 (f+g x)^2 (e f-d g)}",1,"((a + (f*(c*f - b*g))/g^2)*(d + e*x)^(1 + m))/(2*(e*f - d*g)*(f + g*x)^2) - ((g*(2*b*d*g - a*e*g*(1 - m) - b*e*f*(1 + m)) - c*f*(4*d*g - e*f*(3 + m)))*(d + e*x)^(1 + m))/(2*g^2*(e*f - d*g)^2*(f + g*x)) + ((e*g*m*(2*b*d*g - a*e*g*(1 - m) - b*e*f*(1 + m)) + c*(2*d^2*g^2 - 4*d*e*f*g*(1 + m) + e^2*f^2*(2 + 3*m + m^2)))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((g*(d + e*x))/(e*f - d*g))])/(2*g^2*(e*f - d*g)^3*(1 + m))","A",3,3,25,0.1200,1,"{949, 78, 68}"
925,1,525,0,0.6149803,"\int (d+e x)^m (f+g x)^2 \left(a+b x+c x^2\right)^2 \, dx","Int[(d + e*x)^m*(f + g*x)^2*(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^{m+3} \left(e^2 \left(a^2 e^2 g^2+2 a b e g (2 e f-3 d g)+b^2 \left(6 d^2 g^2-6 d e f g+e^2 f^2\right)\right)+2 c e \left(a e \left(6 d^2 g^2-6 d e f g+e^2 f^2\right)-b d \left(10 d^2 g^2-12 d e f g+3 e^2 f^2\right)\right)+c^2 d^2 \left(15 d^2 g^2-20 d e f g+6 e^2 f^2\right)\right)}{e^7 (m+3)}+\frac{(d+e x)^{m+5} \left(2 c e g (a e g-5 b d g+2 b e f)+b^2 e^2 g^2+c^2 \left(15 d^2 g^2-10 d e f g+e^2 f^2\right)\right)}{e^7 (m+5)}+\frac{2 (d+e x)^{m+4} \left(c e \left(2 a e g (e f-2 d g)+b \left(10 d^2 g^2-8 d e f g+e^2 f^2\right)\right)+b e^2 g (a e g-2 b d g+b e f)-2 c^2 d \left(5 d^2 g^2-5 d e f g+e^2 f^2\right)\right)}{e^7 (m+4)}+\frac{(e f-d g)^2 (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^7 (m+1)}-\frac{2 (e f-d g) (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right) (c d (2 e f-3 d g)-e (a e g-2 b d g+b e f))}{e^7 (m+2)}+\frac{2 c g (d+e x)^{m+6} (b e g-3 c d g+c e f)}{e^7 (m+6)}+\frac{c^2 g^2 (d+e x)^{m+7}}{e^7 (m+7)}","\frac{(d+e x)^{m+3} \left(e^2 \left(a^2 e^2 g^2+2 a b e g (2 e f-3 d g)+b^2 \left(6 d^2 g^2-6 d e f g+e^2 f^2\right)\right)+2 c e \left(a e \left(6 d^2 g^2-6 d e f g+e^2 f^2\right)-b d \left(10 d^2 g^2-12 d e f g+3 e^2 f^2\right)\right)+c^2 d^2 \left(15 d^2 g^2-20 d e f g+6 e^2 f^2\right)\right)}{e^7 (m+3)}+\frac{(d+e x)^{m+5} \left(2 c e g (a e g-5 b d g+2 b e f)+b^2 e^2 g^2+c^2 \left(15 d^2 g^2-10 d e f g+e^2 f^2\right)\right)}{e^7 (m+5)}+\frac{2 (d+e x)^{m+4} \left(c e \left(2 a e g (e f-2 d g)+b \left(10 d^2 g^2-8 d e f g+e^2 f^2\right)\right)+b e^2 g (a e g-2 b d g+b e f)-2 c^2 d \left(5 d^2 g^2-5 d e f g+e^2 f^2\right)\right)}{e^7 (m+4)}+\frac{(e f-d g)^2 (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^7 (m+1)}-\frac{2 (e f-d g) (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right) (c d (2 e f-3 d g)-e (a e g-2 b d g+b e f))}{e^7 (m+2)}+\frac{2 c g (d+e x)^{m+6} (b e g-3 c d g+c e f)}{e^7 (m+6)}+\frac{c^2 g^2 (d+e x)^{m+7}}{e^7 (m+7)}",1,"((c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)^2*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (2*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*(c*d*(2*e*f - 3*d*g) - e*(b*e*f - 2*b*d*g + a*e*g))*(d + e*x)^(2 + m))/(e^7*(2 + m)) + ((c^2*d^2*(6*e^2*f^2 - 20*d*e*f*g + 15*d^2*g^2) + e^2*(a^2*e^2*g^2 + 2*a*b*e*g*(2*e*f - 3*d*g) + b^2*(e^2*f^2 - 6*d*e*f*g + 6*d^2*g^2)) + 2*c*e*(a*e*(e^2*f^2 - 6*d*e*f*g + 6*d^2*g^2) - b*d*(3*e^2*f^2 - 12*d*e*f*g + 10*d^2*g^2)))*(d + e*x)^(3 + m))/(e^7*(3 + m)) + (2*(b*e^2*g*(b*e*f - 2*b*d*g + a*e*g) - 2*c^2*d*(e^2*f^2 - 5*d*e*f*g + 5*d^2*g^2) + c*e*(2*a*e*g*(e*f - 2*d*g) + b*(e^2*f^2 - 8*d*e*f*g + 10*d^2*g^2)))*(d + e*x)^(4 + m))/(e^7*(4 + m)) + ((b^2*e^2*g^2 + 2*c*e*g*(2*b*e*f - 5*b*d*g + a*e*g) + c^2*(e^2*f^2 - 10*d*e*f*g + 15*d^2*g^2))*(d + e*x)^(5 + m))/(e^7*(5 + m)) + (2*c*g*(c*e*f - 3*c*d*g + b*e*g)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (c^2*g^2*(d + e*x)^(7 + m))/(e^7*(7 + m))","A",2,1,27,0.03704,1,"{947}"
926,1,311,0,0.3921873,"\int (d+e x)^m (f+g x) \left(a+b x+c x^2\right)^2 \, dx","Int[(d + e*x)^m*(f + g*x)*(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^{m+4} \left(2 c e (a e g-4 b d g+b e f)+b^2 e^2 g-2 c^2 d (2 e f-5 d g)\right)}{e^6 (m+4)}+\frac{(d+e x)^{m+3} \left(2 c e (a e (e f-3 d g)-3 b d (e f-2 d g))+b e^2 (2 a e g-3 b d g+b e f)+2 c^2 d^2 (3 e f-5 d g)\right)}{e^6 (m+3)}+\frac{(e f-d g) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^6 (m+1)}-\frac{(d+e x)^{m+2} \left(a e^2-b d e+c d^2\right) (c d (4 e f-5 d g)-e (a e g-3 b d g+2 b e f))}{e^6 (m+2)}+\frac{c (d+e x)^{m+5} (2 b e g-5 c d g+c e f)}{e^6 (m+5)}+\frac{c^2 g (d+e x)^{m+6}}{e^6 (m+6)}","\frac{(d+e x)^{m+4} \left(2 c e (a e g-4 b d g+b e f)+b^2 e^2 g-2 c^2 d (2 e f-5 d g)\right)}{e^6 (m+4)}+\frac{(d+e x)^{m+3} \left(2 c e (a e (e f-3 d g)-3 b d (e f-2 d g))+b e^2 (2 a e g-3 b d g+b e f)+2 c^2 d^2 (3 e f-5 d g)\right)}{e^6 (m+3)}+\frac{(e f-d g) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^6 (m+1)}-\frac{(d+e x)^{m+2} \left(a e^2-b d e+c d^2\right) (c d (4 e f-5 d g)-e (a e g-3 b d g+2 b e f))}{e^6 (m+2)}+\frac{c (d+e x)^{m+5} (2 b e g-5 c d g+c e f)}{e^6 (m+5)}+\frac{c^2 g (d+e x)^{m+6}}{e^6 (m+6)}",1,"((c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)*(d + e*x)^(1 + m))/(e^6*(1 + m)) - ((c*d^2 - b*d*e + a*e^2)*(c*d*(4*e*f - 5*d*g) - e*(2*b*e*f - 3*b*d*g + a*e*g))*(d + e*x)^(2 + m))/(e^6*(2 + m)) + ((2*c^2*d^2*(3*e*f - 5*d*g) + b*e^2*(b*e*f - 3*b*d*g + 2*a*e*g) + 2*c*e*(a*e*(e*f - 3*d*g) - 3*b*d*(e*f - 2*d*g)))*(d + e*x)^(3 + m))/(e^6*(3 + m)) + ((b^2*e^2*g - 2*c^2*d*(2*e*f - 5*d*g) + 2*c*e*(b*e*f - 4*b*d*g + a*e*g))*(d + e*x)^(4 + m))/(e^6*(4 + m)) + (c*(c*e*f - 5*c*d*g + 2*b*e*g)*(d + e*x)^(5 + m))/(e^6*(5 + m)) + (c^2*g*(d + e*x)^(6 + m))/(e^6*(6 + m))","A",2,1,25,0.04000,1,"{771}"
927,1,287,0,0.8651865,"\int \frac{(d+e x)^m \left(a+b x+c x^2\right)^2}{f+g x} \, dx","Int[((d + e*x)^m*(a + b*x + c*x^2)^2)/(f + g*x),x]","\frac{(d+e x)^{m+2} \left(2 c e g (a e g-b (2 d g+e f))+b^2 e^2 g^2+c^2 \left(3 d^2 g^2+2 d e f g+e^2 f^2\right)\right)}{e^4 g^3 (m+2)}+\frac{(d+e x)^{m+1} (b e g-c (d g+e f)) \left(e g (2 a e g-b (d g+e f))+c \left(d^2 g^2+e^2 f^2\right)\right)}{e^4 g^4 (m+1)}+\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right)^2 \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right)}{g^4 (m+1) (e f-d g)}-\frac{c (d+e x)^{m+3} (-2 b e g+3 c d g+c e f)}{e^4 g^2 (m+3)}+\frac{c^2 (d+e x)^{m+4}}{e^4 g (m+4)}","\frac{(d+e x)^{m+2} \left(2 c e g (a e g-b (2 d g+e f))+b^2 e^2 g^2+c^2 \left(3 d^2 g^2+2 d e f g+e^2 f^2\right)\right)}{e^4 g^3 (m+2)}+\frac{(d+e x)^{m+1} (b e g-c (d g+e f)) \left(e g (2 a e g-b (d g+e f))+c \left(d^2 g^2+e^2 f^2\right)\right)}{e^4 g^4 (m+1)}+\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right)^2 \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right)}{g^4 (m+1) (e f-d g)}-\frac{c (d+e x)^{m+3} (-2 b e g+3 c d g+c e f)}{e^4 g^2 (m+3)}+\frac{c^2 (d+e x)^{m+4}}{e^4 g (m+4)}",1,"((b*e*g - c*(e*f + d*g))*(c*(e^2*f^2 + d^2*g^2) + e*g*(2*a*e*g - b*(e*f + d*g)))*(d + e*x)^(1 + m))/(e^4*g^4*(1 + m)) + ((b^2*e^2*g^2 + c^2*(e^2*f^2 + 2*d*e*f*g + 3*d^2*g^2) + 2*c*e*g*(a*e*g - b*(e*f + 2*d*g)))*(d + e*x)^(2 + m))/(e^4*g^3*(2 + m)) - (c*(c*e*f + 3*c*d*g - 2*b*e*g)*(d + e*x)^(3 + m))/(e^4*g^2*(3 + m)) + (c^2*(d + e*x)^(4 + m))/(e^4*g*(4 + m)) + ((c*f^2 - b*f*g + a*g^2)^2*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((g*(d + e*x))/(e*f - d*g))])/(g^4*(e*f - d*g)*(1 + m))","A",4,3,27,0.1111,1,"{951, 1620, 68}"
928,1,298,0,1.1408835,"\int \frac{(d+e x)^m \left(a+b x+c x^2\right)^2}{(f+g x)^2} \, dx","Int[((d + e*x)^m*(a + b*x + c*x^2)^2)/(f + g*x)^2,x]","\frac{(d+e x)^{m+1} \left(2 c e g (a e g-b (d g+2 e f))+b^2 e^2 g^2+c^2 \left(d^2 g^2+2 d e f g+3 e^2 f^2\right)\right)}{e^3 g^4 (m+1)}-\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right) \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right) (g (a e g m+2 b d g-b e f (m+2))-c f (4 d g-e f (m+4)))}{g^4 (m+1) (e f-d g)^2}+\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right)^2}{g^4 (f+g x) (e f-d g)}-\frac{2 c (d+e x)^{m+2} (-b e g+c d g+c e f)}{e^3 g^3 (m+2)}+\frac{c^2 (d+e x)^{m+3}}{e^3 g^2 (m+3)}","\frac{(d+e x)^{m+1} \left(2 c e g (a e g-b (d g+2 e f))+b^2 e^2 g^2+c^2 \left(d^2 g^2+2 d e f g+3 e^2 f^2\right)\right)}{e^3 g^4 (m+1)}+\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right) \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right) (c f (4 d g-e f (m+4))-g (a e g m+b (2 d g-e f (m+2))))}{g^4 (m+1) (e f-d g)^2}+\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right)^2}{g^4 (f+g x) (e f-d g)}-\frac{2 c (d+e x)^{m+2} (-b e g+c d g+c e f)}{e^3 g^3 (m+2)}+\frac{c^2 (d+e x)^{m+3}}{e^3 g^2 (m+3)}",1,"((b^2*e^2*g^2 + c^2*(3*e^2*f^2 + 2*d*e*f*g + d^2*g^2) + 2*c*e*g*(a*e*g - b*(2*e*f + d*g)))*(d + e*x)^(1 + m))/(e^3*g^4*(1 + m)) - (2*c*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(2 + m))/(e^3*g^3*(2 + m)) + (c^2*(d + e*x)^(3 + m))/(e^3*g^2*(3 + m)) + ((c*f^2 - b*f*g + a*g^2)^2*(d + e*x)^(1 + m))/(g^4*(e*f - d*g)*(f + g*x)) - ((c*f^2 - b*f*g + a*g^2)*(g*(2*b*d*g + a*e*g*m - b*e*f*(2 + m)) - c*f*(4*d*g - e*f*(4 + m)))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((g*(d + e*x))/(e*f - d*g))])/(g^4*(e*f - d*g)^2*(1 + m))","A",4,3,27,0.1111,1,"{949, 1620, 68}"
929,1,461,0,1.4870859,"\int \frac{(d+e x)^m \left(a+b x+c x^2\right)^2}{(f+g x)^3} \, dx","Int[((d + e*x)^m*(a + b*x + c*x^2)^2)/(f + g*x)^3,x]","\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right) \left(-g^2 \left(a^2 e^2 g^2 (1-m) m-2 a b e g m (2 d g-e f (m+1))+b^2 \left(-\left(2 d^2 g^2-4 d e f g (m+1)+e^2 f^2 \left(m^2+3 m+2\right)\right)\right)\right)+2 c g \left(a g \left(2 d^2 g^2-4 d e f g (m+1)+e^2 f^2 \left(m^2+3 m+2\right)\right)-b f \left(6 d^2 g^2-6 d e f g (m+2)+e^2 f^2 \left(m^2+5 m+6\right)\right)\right)+c^2 f^2 \left(12 d^2 g^2-8 d e f g (m+3)+e^2 f^2 \left(m^2+7 m+12\right)\right)\right)}{2 g^4 (m+1) (e f-d g)^3}-\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right) (g (-a e g (1-m)+4 b d g-b e f (m+3))-c f (8 d g-e f (m+7)))}{2 g^4 (f+g x) (e f-d g)^2}+\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right)^2}{2 g^4 (f+g x)^2 (e f-d g)}-\frac{c (d+e x)^{m+1} (-2 b e g+c d g+3 c e f)}{e^2 g^4 (m+1)}+\frac{c^2 (d+e x)^{m+2}}{e^2 g^3 (m+2)}","\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{g (d+e x)}{e f-d g}\right) \left(-g^2 \left(a^2 e^2 g^2 (1-m) m-2 a b e g m (2 d g-e f (m+1))+b^2 \left(-\left(2 d^2 g^2-4 d e f g (m+1)+e^2 f^2 \left(m^2+3 m+2\right)\right)\right)\right)+2 c g \left(a g \left(2 d^2 g^2-4 d e f g (m+1)+e^2 f^2 \left(m^2+3 m+2\right)\right)-b f \left(6 d^2 g^2-6 d e f g (m+2)+e^2 f^2 \left(m^2+5 m+6\right)\right)\right)+c^2 f^2 \left(12 d^2 g^2-8 d e f g (m+3)+e^2 f^2 \left(m^2+7 m+12\right)\right)\right)}{2 g^4 (m+1) (e f-d g)^3}+\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right) (g (a e g (1-m)-b (4 d g-e f (m+3)))+c f (8 d g-e f (m+7)))}{2 g^4 (f+g x) (e f-d g)^2}+\frac{(d+e x)^{m+1} \left(a g^2-b f g+c f^2\right)^2}{2 g^4 (f+g x)^2 (e f-d g)}-\frac{c (d+e x)^{m+1} (-2 b e g+c d g+3 c e f)}{e^2 g^4 (m+1)}+\frac{c^2 (d+e x)^{m+2}}{e^2 g^3 (m+2)}",1,"-((c*(3*c*e*f + c*d*g - 2*b*e*g)*(d + e*x)^(1 + m))/(e^2*g^4*(1 + m))) + (c^2*(d + e*x)^(2 + m))/(e^2*g^3*(2 + m)) + ((c*f^2 - b*f*g + a*g^2)^2*(d + e*x)^(1 + m))/(2*g^4*(e*f - d*g)*(f + g*x)^2) - ((c*f^2 - b*f*g + a*g^2)*(g*(4*b*d*g - a*e*g*(1 - m) - b*e*f*(3 + m)) - c*f*(8*d*g - e*f*(7 + m)))*(d + e*x)^(1 + m))/(2*g^4*(e*f - d*g)^2*(f + g*x)) + ((c^2*f^2*(12*d^2*g^2 - 8*d*e*f*g*(3 + m) + e^2*f^2*(12 + 7*m + m^2)) - g^2*(a^2*e^2*g^2*(1 - m)*m - 2*a*b*e*g*m*(2*d*g - e*f*(1 + m)) - b^2*(2*d^2*g^2 - 4*d*e*f*g*(1 + m) + e^2*f^2*(2 + 3*m + m^2))) + 2*c*g*(a*g*(2*d^2*g^2 - 4*d*e*f*g*(1 + m) + e^2*f^2*(2 + 3*m + m^2)) - b*f*(6*d^2*g^2 - 6*d*e*f*g*(2 + m) + e^2*f^2*(6 + 5*m + m^2))))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((g*(d + e*x))/(e*f - d*g))])/(2*g^4*(e*f - d*g)^3*(1 + m))","A",5,5,27,0.1852,1,"{949, 1621, 951, 80, 68}"
930,1,183,0,0.2331098,"\int \frac{(2+3 x)^4 (1+4 x)^m}{1-5 x+3 x^2} \, dx","Int[((2 + 3*x)^4*(1 + 4*x)^m)/(1 - 5*x + 3*x^2),x]","-\frac{3 \left(5499-1631 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{26 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 \left(5499+1631 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{26 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{3687 (4 x+1)^{m+1}}{64 (m+1)}+\frac{207 (4 x+1)^{m+2}}{32 (m+2)}+\frac{27 (4 x+1)^{m+3}}{64 (m+3)}","-\frac{3 \left(5499-1631 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{26 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 \left(5499+1631 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{26 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{3687 (4 x+1)^{m+1}}{64 (m+1)}+\frac{207 (4 x+1)^{m+2}}{32 (m+2)}+\frac{27 (4 x+1)^{m+3}}{64 (m+3)}",1,"(3687*(1 + 4*x)^(1 + m))/(64*(1 + m)) + (207*(1 + 4*x)^(2 + m))/(32*(2 + m)) + (27*(1 + 4*x)^(3 + m))/(64*(3 + m)) - (3*(5499 - 1631*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(26*(13 - 2*Sqrt[13])*(1 + m)) - (3*(5499 + 1631*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(26*(13 + 2*Sqrt[13])*(1 + m))","A",4,2,27,0.07407,1,"{1628, 68}"
931,1,165,0,0.1523477,"\int \frac{(2+3 x)^3 (1+4 x)^m}{1-5 x+3 x^2} \, dx","Int[((2 + 3*x)^3*(1 + 4*x)^m)/(1 - 5*x + 3*x^2),x]","-\frac{3 \left(416-135 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{13 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 \left(416+135 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{13 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{123 (4 x+1)^{m+1}}{16 (m+1)}+\frac{9 (4 x+1)^{m+2}}{16 (m+2)}","-\frac{3 \left(416-135 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{13 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 \left(416+135 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{13 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{123 (4 x+1)^{m+1}}{16 (m+1)}+\frac{9 (4 x+1)^{m+2}}{16 (m+2)}",1,"(123*(1 + 4*x)^(1 + m))/(16*(1 + m)) + (9*(1 + 4*x)^(2 + m))/(16*(2 + m)) - (3*(416 - 135*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(13*(13 - 2*Sqrt[13])*(1 + m)) - (3*(416 + 135*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(13*(13 + 2*Sqrt[13])*(1 + m))","A",4,2,27,0.07407,1,"{1628, 68}"
932,1,147,0,0.1521458,"\int \frac{(2+3 x)^2 (1+4 x)^m}{1-5 x+3 x^2} \, dx","Int[((2 + 3*x)^2*(1 + 4*x)^m)/(1 - 5*x + 3*x^2),x]","-\frac{3 \left(117-47 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{26 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 \left(117+47 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{26 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{3 (4 x+1)^{m+1}}{4 (m+1)}","-\frac{3 \left(117-47 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{26 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 \left(117+47 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{26 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{3 (4 x+1)^{m+1}}{4 (m+1)}",1,"(3*(1 + 4*x)^(1 + m))/(4*(1 + m)) - (3*(117 - 47*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(26*(13 - 2*Sqrt[13])*(1 + m)) - (3*(117 + 47*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(26*(13 + 2*Sqrt[13])*(1 + m))","A",4,2,27,0.07407,1,"{1628, 68}"
933,1,129,0,0.1085368,"\int \frac{(2+3 x) (1+4 x)^m}{1-5 x+3 x^2} \, dx","Int[((2 + 3*x)*(1 + 4*x)^m)/(1 - 5*x + 3*x^2),x]","-\frac{3 \left(13-9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{26 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 \left(13+9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{26 \left(13+2 \sqrt{13}\right) (m+1)}","-\frac{3 \left(13-9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{26 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 \left(13+9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{26 \left(13+2 \sqrt{13}\right) (m+1)}",1,"(-3*(13 - 9*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(26*(13 - 2*Sqrt[13])*(1 + m)) - (3*(13 + 9*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(26*(13 + 2*Sqrt[13])*(1 + m))","A",4,2,25,0.08000,1,"{830, 68}"
934,1,117,0,0.1136812,"\int \frac{(1+4 x)^m}{1-5 x+3 x^2} \, dx","Int[(1 + 4*x)^m/(1 - 5*x + 3*x^2),x]","\frac{3 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{\sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{\sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}","\frac{3 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{\sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}-\frac{3 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{\sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}",1,"(3*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(Sqrt[13]*(13 - 2*Sqrt[13])*(1 + m)) - (3*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(Sqrt[13]*(13 + 2*Sqrt[13])*(1 + m))","A",4,2,20,0.1000,1,"{711, 68}"
935,1,164,0,0.2005818,"\int \frac{(1+4 x)^m}{(2+3 x) \left(1-5 x+3 x^2\right)} \, dx","Int[(1 + 4*x)^m/((2 + 3*x)*(1 - 5*x + 3*x^2)),x]","\frac{3 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{85 (m+1)}+\frac{3 \left(13+9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{442 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{3 \left(13-9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{442 \left(13+2 \sqrt{13}\right) (m+1)}","\frac{3 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{85 (m+1)}+\frac{3 \left(13+9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{442 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{3 \left(13-9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{442 \left(13+2 \sqrt{13}\right) (m+1)}",1,"(3*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-3*(1 + 4*x))/5])/(85*(1 + m)) + (3*(13 + 9*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(442*(13 - 2*Sqrt[13])*(1 + m)) + (3*(13 - 9*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(442*(13 + 2*Sqrt[13])*(1 + m))","A",7,3,27,0.1111,1,"{960, 68, 830}"
936,1,199,0,0.2211828,"\int \frac{(1+4 x)^m}{(2+3 x)^2 \left(1-5 x+3 x^2\right)} \, dx","Int[(1 + 4*x)^m/((2 + 3*x)^2*(1 - 5*x + 3*x^2)),x]","\frac{27 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{1445 (m+1)}+\frac{3 \left(117+47 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{7514 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{3 \left(117-47 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{7514 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{12 (4 x+1)^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{425 (m+1)}","\frac{27 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{1445 (m+1)}+\frac{3 \left(117+47 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{7514 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{3 \left(117-47 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{7514 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{12 (4 x+1)^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{425 (m+1)}",1,"(27*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-3*(1 + 4*x))/5])/(1445*(1 + m)) + (3*(117 + 47*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(7514*(13 - 2*Sqrt[13])*(1 + m)) + (3*(117 - 47*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(7514*(13 + 2*Sqrt[13])*(1 + m)) + (12*(1 + 4*x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, (-3*(1 + 4*x))/5])/(425*(1 + m))","A",8,3,27,0.1111,1,"{960, 68, 830}"
937,1,202,0,0.2948856,"\int \frac{(2+3 x)^4 (1+4 x)^m}{\left(1-5 x+3 x^2\right)^2} \, dx","Int[((2 + 3*x)^4*(1 + 4*x)^m)/(1 - 5*x + 3*x^2)^2,x]","-\frac{\left(13689-\sqrt{13} \left(-1570 \sqrt{13} m+4474 m+297\right)\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{169 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{\left(\sqrt{13} \left(1570 \sqrt{13} m+4474 m+297\right)+13689\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{169 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(844-2355 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}+\frac{9 (4 x+1)^{m+1}}{4 (m+1)}","-\frac{\left(13689-\sqrt{13} \left(-1570 \sqrt{13} m+4474 m+297\right)\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{169 \left(13-2 \sqrt{13}\right) (m+1)}-\frac{\left(\sqrt{13} \left(1570 \sqrt{13} m+4474 m+297\right)+13689\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{169 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(844-2355 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}+\frac{9 (4 x+1)^{m+1}}{4 (m+1)}",1,"(9*(1 + 4*x)^(1 + m))/(4*(1 + m)) + ((844 - 2355*x)*(1 + 4*x)^(1 + m))/(39*(1 - 5*x + 3*x^2)) - ((13689 - Sqrt[13]*(297 + 4474*m - 1570*Sqrt[13]*m))*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(169*(13 - 2*Sqrt[13])*(1 + m)) - ((13689 + Sqrt[13]*(297 + 4474*m + 1570*Sqrt[13]*m))*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(169*(13 + 2*Sqrt[13])*(1 + m))","A",5,3,27,0.1111,1,"{1648, 1628, 68}"
938,1,181,0,0.280688,"\int \frac{(2+3 x)^3 (1+4 x)^m}{\left(1-5 x+3 x^2\right)^2} \, dx","Int[((2 + 3*x)^3*(1 + 4*x)^m)/(1 - 5*x + 3*x^2)^2,x]","-\frac{\left(\sqrt{13} \left(568 \sqrt{13} m-1168 m+1701\right)+1521\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{338 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{\left(\sqrt{13} (1701-1168 m)-13 (568 m+117)\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{338 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(209-426 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}","-\frac{\left(\sqrt{13} \left(568 \sqrt{13} m-1168 m+1701\right)+1521\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{338 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{\left(\sqrt{13} (1701-1168 m)-13 (568 m+117)\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{338 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(209-426 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}",1,"((209 - 426*x)*(1 + 4*x)^(1 + m))/(39*(1 - 5*x + 3*x^2)) - ((1521 + Sqrt[13]*(1701 - 1168*m + 568*Sqrt[13]*m))*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(338*(13 - 2*Sqrt[13])*(1 + m)) + ((Sqrt[13]*(1701 - 1168*m) - 13*(117 + 568*m))*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(338*(13 + 2*Sqrt[13])*(1 + m))","A",5,3,27,0.1111,1,"{1648, 830, 68}"
939,1,179,0,0.2487984,"\int \frac{(2+3 x)^2 (1+4 x)^m}{\left(1-5 x+3 x^2\right)^2} \, dx","Int[((2 + 3*x)^2*(1 + 4*x)^m)/(1 - 5*x + 3*x^2)^2,x]","-\frac{2 \left(153-\left(23-29 \sqrt{13}\right) m\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{2 \left(153-\left(23+29 \sqrt{13}\right) m\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(61-87 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}","-\frac{2 \left(153-\left(23-29 \sqrt{13}\right) m\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{2 \left(153-\left(23+29 \sqrt{13}\right) m\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(61-87 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}",1,"((61 - 87*x)*(1 + 4*x)^(1 + m))/(39*(1 - 5*x + 3*x^2)) - (2*(153 - (23 - 29*Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(13*Sqrt[13]*(13 - 2*Sqrt[13])*(1 + m)) + (2*(153 - (23 + 29*Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(13*Sqrt[13]*(13 + 2*Sqrt[13])*(1 + m))","A",5,3,27,0.1111,1,"{1648, 830, 68}"
940,1,179,0,0.2120969,"\int \frac{(2+3 x) (1+4 x)^m}{\left(1-5 x+3 x^2\right)^2} \, dx","Int[((2 + 3*x)*(1 + 4*x)^m)/(1 - 5*x + 3*x^2)^2,x]","-\frac{\left(2 \left(5+7 \sqrt{13}\right) m+81\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{\left(2 \left(5-7 \sqrt{13}\right) m+81\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(20-21 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}","-\frac{\left(2 \left(5+7 \sqrt{13}\right) m+81\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{\left(2 \left(5-7 \sqrt{13}\right) m+81\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(20-21 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}",1,"((20 - 21*x)*(1 + 4*x)^(1 + m))/(39*(1 - 5*x + 3*x^2)) - ((81 + 2*(5 + 7*Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(13*Sqrt[13]*(13 - 2*Sqrt[13])*(1 + m)) + ((81 + 2*(5 - 7*Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(13*Sqrt[13]*(13 + 2*Sqrt[13])*(1 + m))","A",5,3,25,0.1200,1,"{822, 830, 68}"
941,1,177,0,0.1992954,"\int \frac{(1+4 x)^m}{\left(1-5 x+3 x^2\right)^2} \, dx","Int[(1 + 4*x)^m/(1 - 5*x + 3*x^2)^2,x]","-\frac{2 \left(2 \left(2+\sqrt{13}\right) m+9\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{2 \left(2 \left(2-\sqrt{13}\right) m+9\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(7-6 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}","-\frac{2 \left(2 \left(2+\sqrt{13}\right) m+9\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{2 \left(2 \left(2-\sqrt{13}\right) m+9\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{13 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(7-6 x) (4 x+1)^{m+1}}{39 \left(3 x^2-5 x+1\right)}",1,"((7 - 6*x)*(1 + 4*x)^(1 + m))/(39*(1 - 5*x + 3*x^2)) - (2*(9 + 2*(2 + Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(13*Sqrt[13]*(13 - 2*Sqrt[13])*(1 + m)) + (2*(9 + 2*(2 - Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(13*Sqrt[13]*(13 + 2*Sqrt[13])*(1 + m))","A",5,3,20,0.1500,1,"{740, 830, 68}"
942,1,340,0,0.5044699,"\int \frac{(1+4 x)^m}{(2+3 x) \left(1-5 x+3 x^2\right)^2} \, dx","Int[(1 + 4*x)^m/((2 + 3*x)*(1 - 5*x + 3*x^2)^2),x]","\frac{9 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{1445 (m+1)}-\frac{\left(\left(62+22 \sqrt{13}\right) m+81\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{221 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{9 \left(13+9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{7514 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{\left(\left(62-22 \sqrt{13}\right) m+81\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{221 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{9 \left(13-9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{7514 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(43-33 x) (4 x+1)^{m+1}}{663 \left(3 x^2-5 x+1\right)}","\frac{9 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{1445 (m+1)}-\frac{\left(\left(62+22 \sqrt{13}\right) m+81\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{221 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{9 \left(13+9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{7514 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{\left(\left(62-22 \sqrt{13}\right) m+81\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{221 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{9 \left(13-9 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{7514 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{(43-33 x) (4 x+1)^{m+1}}{663 \left(3 x^2-5 x+1\right)}",1,"((43 - 33*x)*(1 + 4*x)^(1 + m))/(663*(1 - 5*x + 3*x^2)) + (9*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-3*(1 + 4*x))/5])/(1445*(1 + m)) + (9*(13 + 9*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(7514*(13 - 2*Sqrt[13])*(1 + m)) - ((81 + (62 + 22*Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(221*Sqrt[13]*(13 - 2*Sqrt[13])*(1 + m)) + (9*(13 - 9*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(7514*(13 + 2*Sqrt[13])*(1 + m)) + ((81 + (62 - 22*Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(221*Sqrt[13]*(13 + 2*Sqrt[13])*(1 + m))","A",12,4,27,0.1481,1,"{960, 68, 822, 830}"
943,1,376,0,0.4932323,"\int \frac{(1+4 x)^m}{(2+3 x)^2 \left(1-5 x+3 x^2\right)^2} \, dx","Int[(1 + 4*x)^m/((2 + 3*x)^2*(1 - 5*x + 3*x^2)^2),x]","\frac{162 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{24565 (m+1)}-\frac{\left(2 \left(211+65 \sqrt{13}\right) m+423\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{3757 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{9 \left(117+64 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{63869 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{\left(\left(422-130 \sqrt{13}\right) m+423\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{3757 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{9 \left(117-64 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{63869 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{36 (4 x+1)^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{7225 (m+1)}+\frac{(268-195 x) (4 x+1)^{m+1}}{11271 \left(3 x^2-5 x+1\right)}","\frac{162 (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{24565 (m+1)}-\frac{\left(2 \left(211+65 \sqrt{13}\right) m+423\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{3757 \sqrt{13} \left(13-2 \sqrt{13}\right) (m+1)}+\frac{9 \left(117+64 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13-2 \sqrt{13}}\right)}{63869 \left(13-2 \sqrt{13}\right) (m+1)}+\frac{\left(\left(422-130 \sqrt{13}\right) m+423\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{3757 \sqrt{13} \left(13+2 \sqrt{13}\right) (m+1)}+\frac{9 \left(117-64 \sqrt{13}\right) (4 x+1)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{3 (4 x+1)}{13+2 \sqrt{13}}\right)}{63869 \left(13+2 \sqrt{13}\right) (m+1)}+\frac{36 (4 x+1)^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{3}{5} (4 x+1)\right)}{7225 (m+1)}+\frac{(268-195 x) (4 x+1)^{m+1}}{11271 \left(3 x^2-5 x+1\right)}",1,"((268 - 195*x)*(1 + 4*x)^(1 + m))/(11271*(1 - 5*x + 3*x^2)) + (162*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-3*(1 + 4*x))/5])/(24565*(1 + m)) + (9*(117 + 64*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(63869*(13 - 2*Sqrt[13])*(1 + m)) - ((423 + 2*(211 + 65*Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 - 2*Sqrt[13])])/(3757*Sqrt[13]*(13 - 2*Sqrt[13])*(1 + m)) + (9*(117 - 64*Sqrt[13])*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(63869*(13 + 2*Sqrt[13])*(1 + m)) + ((423 + (422 - 130*Sqrt[13])*m)*(1 + 4*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (3*(1 + 4*x))/(13 + 2*Sqrt[13])])/(3757*Sqrt[13]*(13 + 2*Sqrt[13])*(1 + m)) + (36*(1 + 4*x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, (-3*(1 + 4*x))/5])/(7225*(1 + m))","A",13,4,27,0.1481,1,"{960, 68, 822, 830}"
944,1,230,0,0.348564,"\int \frac{(d+e x)^m \left(a+b x+c x^2\right)}{(e+f x)^{3/2}} \, dx","Int[((d + e*x)^m*(a + b*x + c*x^2))/(e + f*x)^(3/2),x]","-\frac{2 \sqrt{e+f x} (d+e x)^m \left(-\frac{f (d+e x)}{e^2-d f}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{e (e+f x)}{e^2-d f}\right) \left(f \left(a e f (2 m+1)+b d f-2 b e^2 (m+1)\right)-\frac{c \left(d^2 f^2+4 d e^2 f (m+1)-4 e^4 \left(m^2+3 m+2\right)\right)}{e (2 m+3)}\right)}{f^3 \left(e^2-d f\right)}+\frac{2 (d+e x)^{m+1} \left(a+\frac{e (c e-b f)}{f^2}\right)}{\left(e^2-d f\right) \sqrt{e+f x}}+\frac{2 c \sqrt{e+f x} (d+e x)^{m+1}}{e f^2 (2 m+3)}","\frac{2 \sqrt{e+f x} (d+e x)^m \left(-\frac{f (d+e x)}{e^2-d f}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{e (e+f x)}{e^2-d f}\right) \left(c \left(d^2 f^2+4 d e^2 f (m+1)-4 e^4 \left(m^2+3 m+2\right)\right)-e f (2 m+3) \left(a e f (2 m+1)+b \left(d f-2 e^2 (m+1)\right)\right)\right)}{e f^3 (2 m+3) \left(e^2-d f\right)}+\frac{2 (d+e x)^{m+1} \left(a+\frac{e (c e-b f)}{f^2}\right)}{\left(e^2-d f\right) \sqrt{e+f x}}+\frac{2 c \sqrt{e+f x} (d+e x)^{m+1}}{e f^2 (2 m+3)}",1,"(2*(a + (e*(c*e - b*f))/f^2)*(d + e*x)^(1 + m))/((e^2 - d*f)*Sqrt[e + f*x]) + (2*c*(d + e*x)^(1 + m)*Sqrt[e + f*x])/(e*f^2*(3 + 2*m)) - (2*(f*(b*d*f - 2*b*e^2*(1 + m) + a*e*f*(1 + 2*m)) - (c*(d^2*f^2 + 4*d*e^2*f*(1 + m) - 4*e^4*(2 + 3*m + m^2)))/(e*(3 + 2*m)))*(d + e*x)^m*Sqrt[e + f*x]*Hypergeometric2F1[1/2, -m, 3/2, (e*(e + f*x))/(e^2 - d*f)])/(f^3*(e^2 - d*f)*(-((f*(d + e*x))/(e^2 - d*f)))^m)","A",4,4,27,0.1481,1,"{949, 80, 70, 69}"
945,1,506,0,0.8417203,"\int (d+e x)^m (f+g x)^2 \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)^m*(f + g*x)^2*Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) \left(g^2 (b d-a e)+\frac{c \left(3 d^2 g^2-2 d e f g (m+4)+e^2 f^2 (m+4)\right)}{e (m+1)}\right)}{c e^2 (m+4) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{g \sqrt{a+b x+c x^2} (d+e x)^{m+2} (b e g (2 m+5)+6 c d g-4 c e f (m+4)) F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 c e^3 (m+2) (m+4) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{g^2 \left(a+b x+c x^2\right)^{3/2} (d+e x)^{m+1}}{c e (m+4)}","\frac{\sqrt{a+b x+c x^2} (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) \left(e g^2 (m+1) (b d-a e)+c \left(3 d^2 g^2-2 d e f g (m+4)+e^2 f^2 (m+4)\right)\right)}{c e^3 (m+1) (m+4) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{g \sqrt{a+b x+c x^2} (d+e x)^{m+2} (b e g (2 m+5)+2 c (3 d g-2 e f (m+4))) F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 c e^3 (m+2) (m+4) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{g^2 \left(a+b x+c x^2\right)^{3/2} (d+e x)^{m+1}}{c e (m+4)}",1,"(g^2*(d + e*x)^(1 + m)*(a + b*x + c*x^2)^(3/2))/(c*e*(4 + m)) + (((b*d - a*e)*g^2 + (c*(3*d^2*g^2 + e^2*f^2*(4 + m) - 2*d*e*f*g*(4 + m)))/(e*(1 + m)))*(d + e*x)^(1 + m)*Sqrt[a + b*x + c*x^2]*AppellF1[1 + m, -1/2, -1/2, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e^2*(4 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]) - (g*(6*c*d*g - 4*c*e*f*(4 + m) + b*e*g*(5 + 2*m))*(d + e*x)^(2 + m)*Sqrt[a + b*x + c*x^2]*AppellF1[2 + m, -1/2, -1/2, 3 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(2*c*e^3*(2 + m)*(4 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])","A",6,4,29,0.1379,1,"{1653, 843, 759, 133}"
946,1,388,0,0.3599706,"\int (d+e x)^m (f+g x) \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)^m*(f + g*x)*Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} (e f-d g) (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+1) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{g \sqrt{a+b x+c x^2} (d+e x)^{m+2} F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+2) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","\frac{\sqrt{a+b x+c x^2} (e f-d g) (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+1) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{g \sqrt{a+b x+c x^2} (d+e x)^{m+2} F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+2) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"((e*f - d*g)*(d + e*x)^(1 + m)*Sqrt[a + b*x + c*x^2]*AppellF1[1 + m, -1/2, -1/2, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e^2*(1 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]) + (g*(d + e*x)^(2 + m)*Sqrt[a + b*x + c*x^2]*AppellF1[2 + m, -1/2, -1/2, 3 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e^2*(2 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])","A",5,3,27,0.1111,1,"{843, 759, 133}"
947,1,189,0,0.1244774,"\int (d+e x)^m \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)^m*Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e (m+1) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","\frac{\sqrt{a+b x+c x^2} (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e (m+1) \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"((d + e*x)^(1 + m)*Sqrt[a + b*x + c*x^2]*AppellF1[1 + m, -1/2, -1/2, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e*(1 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])","A",2,2,22,0.09091,1,"{759, 133}"
948,0,0,0,0.0344326,"\int \frac{(d+e x)^m \sqrt{a+b x+c x^2}}{f+g x} \, dx","Int[((d + e*x)^m*Sqrt[a + b*x + c*x^2])/(f + g*x),x]","\int \frac{(d+e x)^m \sqrt{a+b x+c x^2}}{f+g x} \, dx","\text{Int}\left(\frac{\sqrt{a+b x+c x^2} (d+e x)^m}{f+g x},x\right)",0,"Defer[Int][((d + e*x)^m*Sqrt[a + b*x + c*x^2])/(f + g*x), x]","A",0,0,0,0,-1,"{}"
949,1,500,0,0.6809998,"\int \frac{(d+e x)^m (f+g x)^2}{\sqrt{a+b x+c x^2}} \, dx","Int[((d + e*x)^m*(f + g*x)^2)/Sqrt[a + b*x + c*x^2],x]","\frac{(d+e x)^{m+1} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) \left(g^2 (b d-a e)+\frac{c \left(d^2 g^2-2 d e f g (m+2)+e^2 f^2 (m+2)\right)}{e (m+1)}\right)}{c e^2 (m+2) \sqrt{a+b x+c x^2}}-\frac{g (d+e x)^{m+2} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (b e g (2 m+3)+2 c d g-4 c e f (m+2)) F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 c e^3 (m+2)^2 \sqrt{a+b x+c x^2}}+\frac{g^2 \sqrt{a+b x+c x^2} (d+e x)^{m+1}}{c e (m+2)}","\frac{(d+e x)^{m+1} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) \left(e g^2 (m+1) (b d-a e)+c \left(d^2 g^2-2 d e f g (m+2)+e^2 f^2 (m+2)\right)\right)}{c e^3 (m+1) (m+2) \sqrt{a+b x+c x^2}}-\frac{g (d+e x)^{m+2} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (b e g (2 m+3)+c (2 d g-4 e f (m+2))) F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 c e^3 (m+2)^2 \sqrt{a+b x+c x^2}}+\frac{g^2 \sqrt{a+b x+c x^2} (d+e x)^{m+1}}{c e (m+2)}",1,"(g^2*(d + e*x)^(1 + m)*Sqrt[a + b*x + c*x^2])/(c*e*(2 + m)) + (((b*d - a*e)*g^2 + (c*(d^2*g^2 + e^2*f^2*(2 + m) - 2*d*e*f*g*(2 + m)))/(e*(1 + m)))*(d + e*x)^(1 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*AppellF1[1 + m, 1/2, 1/2, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e^2*(2 + m)*Sqrt[a + b*x + c*x^2]) - (g*(2*c*d*g - 4*c*e*f*(2 + m) + b*e*g*(3 + 2*m))*(d + e*x)^(2 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*AppellF1[2 + m, 1/2, 1/2, 3 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(2*c*e^3*(2 + m)^2*Sqrt[a + b*x + c*x^2])","A",6,4,29,0.1379,1,"{1653, 843, 759, 133}"
950,1,388,0,0.3465349,"\int \frac{(d+e x)^m (f+g x)}{\sqrt{a+b x+c x^2}} \, dx","Int[((d + e*x)^m*(f + g*x))/Sqrt[a + b*x + c*x^2],x]","\frac{(e f-d g) (d+e x)^{m+1} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+1) \sqrt{a+b x+c x^2}}+\frac{g (d+e x)^{m+2} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+2) \sqrt{a+b x+c x^2}}","\frac{(e f-d g) (d+e x)^{m+1} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+1) \sqrt{a+b x+c x^2}}+\frac{g (d+e x)^{m+2} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+2) \sqrt{a+b x+c x^2}}",1,"((e*f - d*g)*(d + e*x)^(1 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*AppellF1[1 + m, 1/2, 1/2, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e^2*(1 + m)*Sqrt[a + b*x + c*x^2]) + (g*(d + e*x)^(2 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*AppellF1[2 + m, 1/2, 1/2, 3 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e^2*(2 + m)*Sqrt[a + b*x + c*x^2])","A",5,3,27,0.1111,1,"{843, 759, 133}"
951,1,189,0,0.1260139,"\int \frac{(d+e x)^m}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^m/Sqrt[a + b*x + c*x^2],x]","\frac{(d+e x)^{m+1} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e (m+1) \sqrt{a+b x+c x^2}}","\frac{(d+e x)^{m+1} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e (m+1) \sqrt{a+b x+c x^2}}",1,"((d + e*x)^(1 + m)*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)]*Sqrt[1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*AppellF1[1 + m, 1/2, 1/2, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e*(1 + m)*Sqrt[a + b*x + c*x^2])","A",2,2,22,0.09091,1,"{759, 133}"
952,0,0,0,0.0355541,"\int \frac{(d+e x)^m}{(f+g x) \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^m/((f + g*x)*Sqrt[a + b*x + c*x^2]),x]","\int \frac{(d+e x)^m}{(f+g x) \sqrt{a+b x+c x^2}} \, dx","\text{Int}\left(\frac{(d+e x)^m}{(f+g x) \sqrt{a+b x+c x^2}},x\right)",0,"Defer[Int][(d + e*x)^m/((f + g*x)*Sqrt[a + b*x + c*x^2]), x]","A",0,0,0,0,-1,"{}"
953,1,263,0,0.3508574,"\int (d+e x)^m (f+g x)^n \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^m*(f + g*x)^n*(a + b*x + c*x^2),x]","\frac{(d+e x)^{m+1} (f+g x)^n \left(\frac{e (f+g x)}{e f-d g}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{g (d+e x)}{e f-d g}\right) \left(g (m+n+2) \left(a e^2 g (m+n+3)-c d (d g (n+1)+e f (m+2))\right)+(d g (n+1)+e f (m+1)) (-b e g (m+n+3)+c d g (m+2 n+4)+c e f (m+2))\right)}{e^3 g^2 (m+1) (m+n+2) (m+n+3)}-\frac{(d+e x)^{m+1} (f+g x)^{n+1} (-b e g (m+n+3)+c d g (m+2 n+4)+c e f (m+2))}{e^2 g^2 (m+n+2) (m+n+3)}+\frac{c (d+e x)^{m+2} (f+g x)^{n+1}}{e^2 g (m+n+3)}","\frac{(d+e x)^{m+1} (f+g x)^n \left(\frac{e (f+g x)}{e f-d g}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{g (d+e x)}{e f-d g}\right) \left(g (m+n+2) \left(a e^2 g (m+n+3)-c d (d g (n+1)+e f (m+2))\right)-(d g (n+1)+e f (m+1)) (b e g (m+n+3)-c (d g (m+2 n+4)+e f (m+2)))\right)}{e^3 g^2 (m+1) (m+n+2) (m+n+3)}+\frac{(d+e x)^{m+1} (f+g x)^{n+1} (b e g (m+n+3)-c (d g (m+2 n+4)+e f (m+2)))}{e^2 g^2 (m+n+2) (m+n+3)}+\frac{c (d+e x)^{m+2} (f+g x)^{n+1}}{e^2 g (m+n+3)}",1,"-(((c*e*f*(2 + m) - b*e*g*(3 + m + n) + c*d*g*(4 + m + 2*n))*(d + e*x)^(1 + m)*(f + g*x)^(1 + n))/(e^2*g^2*(2 + m + n)*(3 + m + n))) + (c*(d + e*x)^(2 + m)*(f + g*x)^(1 + n))/(e^2*g*(3 + m + n)) + (((e*f*(1 + m) + d*g*(1 + n))*(c*e*f*(2 + m) - b*e*g*(3 + m + n) + c*d*g*(4 + m + 2*n)) + g*(2 + m + n)*(a*e^2*g*(3 + m + n) - c*d*(e*f*(2 + m) + d*g*(1 + n))))*(d + e*x)^(1 + m)*(f + g*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((g*(d + e*x))/(e*f - d*g))])/(e^3*g^2*(1 + m)*(2 + m + n)*(3 + m + n)*((e*(f + g*x))/(e*f - d*g))^n)","A",4,4,25,0.1600,1,"{951, 80, 70, 69}"
954,1,523,0,0.7017532,"\int (d+e x)^m (f+g x)^2 \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^m*(f + g*x)^2*(a + b*x + c*x^2)^p,x]","\frac{(d+e x)^{m+1} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) \left(g^2 (b d-a e)+\frac{c \left(2 d^2 g^2 (p+1)-2 d e f g (m+2 p+3)+e^2 f^2 (m+2 p+3)\right)}{e (m+1)}\right)}{c e^2 (m+2 p+3)}-\frac{g (d+e x)^{m+2} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} (b e g (m+p+2)+2 c d g (p+1)-2 c e f (m+2 p+3)) F_1\left(m+2;-p,-p;m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e^3 (m+2) (m+2 p+3)}+\frac{g^2 (d+e x)^{m+1} \left(a+b x+c x^2\right)^{p+1}}{c e (m+2 p+3)}","\frac{(d+e x)^{m+1} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) \left(e g^2 (m+1) (b d-a e)+c \left(2 d^2 g^2 (p+1)-2 d e f g (m+2 p+3)+e^2 f^2 (m+2 p+3)\right)\right)}{c e^3 (m+1) (m+2 p+3)}-\frac{g (d+e x)^{m+2} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} (b e g (m+p+2)+2 c (d g (p+1)-e f (m+2 p+3))) F_1\left(m+2;-p,-p;m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e^3 (m+2) (m+2 p+3)}+\frac{g^2 (d+e x)^{m+1} \left(a+b x+c x^2\right)^{p+1}}{c e (m+2 p+3)}",1,"(g^2*(d + e*x)^(1 + m)*(a + b*x + c*x^2)^(1 + p))/(c*e*(3 + m + 2*p)) + (((b*d - a*e)*g^2 + (c*(2*d^2*g^2*(1 + p) + e^2*f^2*(3 + m + 2*p) - 2*d*e*f*g*(3 + m + 2*p)))/(e*(1 + m)))*(d + e*x)^(1 + m)*(a + b*x + c*x^2)^p*AppellF1[1 + m, -p, -p, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e^2*(3 + m + 2*p)*(1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))^p*(1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))^p) - (g*(2*c*d*g*(1 + p) + b*e*g*(2 + m + p) - 2*c*e*f*(3 + m + 2*p))*(d + e*x)^(2 + m)*(a + b*x + c*x^2)^p*AppellF1[2 + m, -p, -p, 3 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e^3*(2 + m)*(3 + m + 2*p)*(1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))^p*(1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))^p)","A",6,4,27,0.1481,1,"{1653, 843, 759, 133}"
955,1,384,0,0.3374781,"\int (d+e x)^m (f+g x) \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^m*(f + g*x)*(a + b*x + c*x^2)^p,x]","\frac{(e f-d g) (d+e x)^{m+1} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+1)}+\frac{g (d+e x)^{m+2} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+2;-p,-p;m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+2)}","\frac{(e f-d g) (d+e x)^{m+1} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+1)}+\frac{g (d+e x)^{m+2} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+2;-p,-p;m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 (m+2)}",1,"((e*f - d*g)*(d + e*x)^(1 + m)*(a + b*x + c*x^2)^p*AppellF1[1 + m, -p, -p, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e^2*(1 + m)*(1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))^p*(1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))^p) + (g*(d + e*x)^(2 + m)*(a + b*x + c*x^2)^p*AppellF1[2 + m, -p, -p, 3 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e^2*(2 + m)*(1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))^p*(1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))^p)","A",5,3,25,0.1200,1,"{843, 759, 133}"
956,1,187,0,0.1272718,"\int (d+e x)^m \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^m*(a + b*x + c*x^2)^p,x]","\frac{(d+e x)^{m+1} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e (m+1)}","\frac{(d+e x)^{m+1} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e},\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e (m+1)}",1,"((d + e*x)^(1 + m)*(a + b*x + c*x^2)^p*AppellF1[1 + m, -p, -p, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e), (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e*(1 + m)*(1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))^p*(1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))^p)","A",2,2,20,0.1000,1,"{759, 133}"
957,0,0,0,0.0269876,"\int \frac{(d+e x)^m \left(a+b x+c x^2\right)^p}{f+g x} \, dx","Int[((d + e*x)^m*(a + b*x + c*x^2)^p)/(f + g*x),x]","\int \frac{(d+e x)^m \left(a+b x+c x^2\right)^p}{f+g x} \, dx","\text{Int}\left(\frac{(d+e x)^m \left(a+b x+c x^2\right)^p}{f+g x},x\right)",0,"Defer[Int][((d + e*x)^m*(a + b*x + c*x^2)^p)/(f + g*x), x]","A",0,0,0,0,-1,"{}"
958,1,89,0,0.2269792,"\int \frac{1}{\sqrt{1-\frac{1}{c^2 x^2}} x^2 \sqrt{d+e x}} \, dx","Int[1/(Sqrt[1 - 1/(c^2*x^2)]*x^2*Sqrt[d + e*x]),x]","-\frac{2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}","-\frac{2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}",1,"(-2*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",5,5,27,0.1852,1,"{1574, 933, 168, 538, 537}"