1,1,131,0,0.0597608,"\int x^3 \sqrt{b x+c x^2} \, dx","Int[x^3*Sqrt[b*x + c*x^2],x]","-\frac{7 b^3 (b+2 c x) \sqrt{b x+c x^2}}{128 c^4}+\frac{7 b^2 \left(b x+c x^2\right)^{3/2}}{48 c^3}+\frac{7 b^5 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{9/2}}-\frac{7 b x \left(b x+c x^2\right)^{3/2}}{40 c^2}+\frac{x^2 \left(b x+c x^2\right)^{3/2}}{5 c}","-\frac{7 b^3 (b+2 c x) \sqrt{b x+c x^2}}{128 c^4}+\frac{7 b^2 \left(b x+c x^2\right)^{3/2}}{48 c^3}+\frac{7 b^5 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{9/2}}-\frac{7 b x \left(b x+c x^2\right)^{3/2}}{40 c^2}+\frac{x^2 \left(b x+c x^2\right)^{3/2}}{5 c}",1,"(-7*b^3*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(128*c^4) + (7*b^2*(b*x + c*x^2)^(3/2))/(48*c^3) - (7*b*x*(b*x + c*x^2)^(3/2))/(40*c^2) + (x^2*(b*x + c*x^2)^(3/2))/(5*c) + (7*b^5*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(9/2))","A",6,5,17,0.2941,1,"{670, 640, 612, 620, 206}"
2,1,105,0,0.0374605,"\int x^2 \sqrt{b x+c x^2} \, dx","Int[x^2*Sqrt[b*x + c*x^2],x]","\frac{5 b^2 (b+2 c x) \sqrt{b x+c x^2}}{64 c^3}-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{7/2}}-\frac{5 b \left(b x+c x^2\right)^{3/2}}{24 c^2}+\frac{x \left(b x+c x^2\right)^{3/2}}{4 c}","\frac{5 b^2 (b+2 c x) \sqrt{b x+c x^2}}{64 c^3}-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{7/2}}-\frac{5 b \left(b x+c x^2\right)^{3/2}}{24 c^2}+\frac{x \left(b x+c x^2\right)^{3/2}}{4 c}",1,"(5*b^2*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(64*c^3) - (5*b*(b*x + c*x^2)^(3/2))/(24*c^2) + (x*(b*x + c*x^2)^(3/2))/(4*c) - (5*b^4*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(7/2))","A",5,5,17,0.2941,1,"{670, 640, 612, 620, 206}"
3,1,81,0,0.0238282,"\int x \sqrt{b x+c x^2} \, dx","Int[x*Sqrt[b*x + c*x^2],x]","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{5/2}}-\frac{b (b+2 c x) \sqrt{b x+c x^2}}{8 c^2}+\frac{\left(b x+c x^2\right)^{3/2}}{3 c}","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{5/2}}-\frac{b (b+2 c x) \sqrt{b x+c x^2}}{8 c^2}+\frac{\left(b x+c x^2\right)^{3/2}}{3 c}",1,"-(b*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(8*c^2) + (b*x + c*x^2)^(3/2)/(3*c) + (b^3*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(5/2))","A",4,4,15,0.2667,1,"{640, 612, 620, 206}"
4,1,60,0,0.0136197,"\int \sqrt{b x+c x^2} \, dx","Int[Sqrt[b*x + c*x^2],x]","\frac{(b+2 c x) \sqrt{b x+c x^2}}{4 c}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{3/2}}","\frac{(b+2 c x) \sqrt{b x+c x^2}}{4 c}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{3/2}}",1,"((b + 2*c*x)*Sqrt[b*x + c*x^2])/(4*c) - (b^2*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(3/2))","A",3,3,13,0.2308,1,"{612, 620, 206}"
5,1,42,0,0.019189,"\int \frac{\sqrt{b x+c x^2}}{x} \, dx","Int[Sqrt[b*x + c*x^2]/x,x]","\sqrt{b x+c x^2}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}","\sqrt{b x+c x^2}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}",1,"Sqrt[b*x + c*x^2] + (b*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/Sqrt[c]","A",3,3,17,0.1765,1,"{664, 620, 206}"
6,1,47,0,0.0177092,"\int \frac{\sqrt{b x+c x^2}}{x^2} \, dx","Int[Sqrt[b*x + c*x^2]/x^2,x]","2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 \sqrt{b x+c x^2}}{x}","2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 \sqrt{b x+c x^2}}{x}",1,"(-2*Sqrt[b*x + c*x^2])/x + 2*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]]","A",3,3,17,0.1765,1,"{662, 620, 206}"
7,1,23,0,0.0064643,"\int \frac{\sqrt{b x+c x^2}}{x^3} \, dx","Int[Sqrt[b*x + c*x^2]/x^3,x]","-\frac{2 \left(b x+c x^2\right)^{3/2}}{3 b x^3}","-\frac{2 \left(b x+c x^2\right)^{3/2}}{3 b x^3}",1,"(-2*(b*x + c*x^2)^(3/2))/(3*b*x^3)","A",1,1,17,0.05882,1,"{650}"
8,1,48,0,0.0165422,"\int \frac{\sqrt{b x+c x^2}}{x^4} \, dx","Int[Sqrt[b*x + c*x^2]/x^4,x]","\frac{4 c \left(b x+c x^2\right)^{3/2}}{15 b^2 x^3}-\frac{2 \left(b x+c x^2\right)^{3/2}}{5 b x^4}","\frac{4 c \left(b x+c x^2\right)^{3/2}}{15 b^2 x^3}-\frac{2 \left(b x+c x^2\right)^{3/2}}{5 b x^4}",1,"(-2*(b*x + c*x^2)^(3/2))/(5*b*x^4) + (4*c*(b*x + c*x^2)^(3/2))/(15*b^2*x^3)","A",2,2,17,0.1176,1,"{658, 650}"
9,1,74,0,0.0282151,"\int \frac{\sqrt{b x+c x^2}}{x^5} \, dx","Int[Sqrt[b*x + c*x^2]/x^5,x]","-\frac{16 c^2 \left(b x+c x^2\right)^{3/2}}{105 b^3 x^3}+\frac{8 c \left(b x+c x^2\right)^{3/2}}{35 b^2 x^4}-\frac{2 \left(b x+c x^2\right)^{3/2}}{7 b x^5}","-\frac{16 c^2 \left(b x+c x^2\right)^{3/2}}{105 b^3 x^3}+\frac{8 c \left(b x+c x^2\right)^{3/2}}{35 b^2 x^4}-\frac{2 \left(b x+c x^2\right)^{3/2}}{7 b x^5}",1,"(-2*(b*x + c*x^2)^(3/2))/(7*b*x^5) + (8*c*(b*x + c*x^2)^(3/2))/(35*b^2*x^4) - (16*c^2*(b*x + c*x^2)^(3/2))/(105*b^3*x^3)","A",3,2,17,0.1176,1,"{658, 650}"
10,1,100,0,0.0407514,"\int \frac{\sqrt{b x+c x^2}}{x^6} \, dx","Int[Sqrt[b*x + c*x^2]/x^6,x]","\frac{32 c^3 \left(b x+c x^2\right)^{3/2}}{315 b^4 x^3}-\frac{16 c^2 \left(b x+c x^2\right)^{3/2}}{105 b^3 x^4}+\frac{4 c \left(b x+c x^2\right)^{3/2}}{21 b^2 x^5}-\frac{2 \left(b x+c x^2\right)^{3/2}}{9 b x^6}","\frac{32 c^3 \left(b x+c x^2\right)^{3/2}}{315 b^4 x^3}-\frac{16 c^2 \left(b x+c x^2\right)^{3/2}}{105 b^3 x^4}+\frac{4 c \left(b x+c x^2\right)^{3/2}}{21 b^2 x^5}-\frac{2 \left(b x+c x^2\right)^{3/2}}{9 b x^6}",1,"(-2*(b*x + c*x^2)^(3/2))/(9*b*x^6) + (4*c*(b*x + c*x^2)^(3/2))/(21*b^2*x^5) - (16*c^2*(b*x + c*x^2)^(3/2))/(105*b^3*x^4) + (32*c^3*(b*x + c*x^2)^(3/2))/(315*b^4*x^3)","A",4,2,17,0.1176,1,"{658, 650}"
11,1,126,0,0.0527275,"\int \frac{\sqrt{b x+c x^2}}{x^7} \, dx","Int[Sqrt[b*x + c*x^2]/x^7,x]","-\frac{256 c^4 \left(b x+c x^2\right)^{3/2}}{3465 b^5 x^3}+\frac{128 c^3 \left(b x+c x^2\right)^{3/2}}{1155 b^4 x^4}-\frac{32 c^2 \left(b x+c x^2\right)^{3/2}}{231 b^3 x^5}+\frac{16 c \left(b x+c x^2\right)^{3/2}}{99 b^2 x^6}-\frac{2 \left(b x+c x^2\right)^{3/2}}{11 b x^7}","-\frac{256 c^4 \left(b x+c x^2\right)^{3/2}}{3465 b^5 x^3}+\frac{128 c^3 \left(b x+c x^2\right)^{3/2}}{1155 b^4 x^4}-\frac{32 c^2 \left(b x+c x^2\right)^{3/2}}{231 b^3 x^5}+\frac{16 c \left(b x+c x^2\right)^{3/2}}{99 b^2 x^6}-\frac{2 \left(b x+c x^2\right)^{3/2}}{11 b x^7}",1,"(-2*(b*x + c*x^2)^(3/2))/(11*b*x^7) + (16*c*(b*x + c*x^2)^(3/2))/(99*b^2*x^6) - (32*c^2*(b*x + c*x^2)^(3/2))/(231*b^3*x^5) + (128*c^3*(b*x + c*x^2)^(3/2))/(1155*b^4*x^4) - (256*c^4*(b*x + c*x^2)^(3/2))/(3465*b^5*x^3)","A",5,2,17,0.1176,1,"{658, 650}"
12,1,134,0,0.0551097,"\int x^2 \left(b x+c x^2\right)^{3/2} \, dx","Int[x^2*(b*x + c*x^2)^(3/2),x]","-\frac{7 b^4 (b+2 c x) \sqrt{b x+c x^2}}{512 c^4}+\frac{7 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2}}{192 c^3}+\frac{7 b^6 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{9/2}}-\frac{7 b \left(b x+c x^2\right)^{5/2}}{60 c^2}+\frac{x \left(b x+c x^2\right)^{5/2}}{6 c}","-\frac{7 b^4 (b+2 c x) \sqrt{b x+c x^2}}{512 c^4}+\frac{7 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2}}{192 c^3}+\frac{7 b^6 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{9/2}}-\frac{7 b \left(b x+c x^2\right)^{5/2}}{60 c^2}+\frac{x \left(b x+c x^2\right)^{5/2}}{6 c}",1,"(-7*b^4*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(512*c^4) + (7*b^2*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(192*c^3) - (7*b*(b*x + c*x^2)^(5/2))/(60*c^2) + (x*(b*x + c*x^2)^(5/2))/(6*c) + (7*b^6*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(512*c^(9/2))","A",6,5,17,0.2941,1,"{670, 640, 612, 620, 206}"
13,1,110,0,0.0350046,"\int x \left(b x+c x^2\right)^{3/2} \, dx","Int[x*(b*x + c*x^2)^(3/2),x]","\frac{3 b^3 (b+2 c x) \sqrt{b x+c x^2}}{128 c^3}-\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{7/2}}-\frac{b (b+2 c x) \left(b x+c x^2\right)^{3/2}}{16 c^2}+\frac{\left(b x+c x^2\right)^{5/2}}{5 c}","\frac{3 b^3 (b+2 c x) \sqrt{b x+c x^2}}{128 c^3}-\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{7/2}}-\frac{b (b+2 c x) \left(b x+c x^2\right)^{3/2}}{16 c^2}+\frac{\left(b x+c x^2\right)^{5/2}}{5 c}",1,"(3*b^3*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(128*c^3) - (b*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(16*c^2) + (b*x + c*x^2)^(5/2)/(5*c) - (3*b^5*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(7/2))","A",5,4,15,0.2667,1,"{640, 612, 620, 206}"
14,1,89,0,0.0232197,"\int \left(b x+c x^2\right)^{3/2} \, dx","Int[(b*x + c*x^2)^(3/2),x]","-\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2}}{64 c^2}+\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{5/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2}}{8 c}","-\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2}}{64 c^2}+\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{5/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2}}{8 c}",1,"(-3*b^2*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(64*c^2) + ((b + 2*c*x)*(b*x + c*x^2)^(3/2))/(8*c) + (3*b^4*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(5/2))","A",4,3,13,0.2308,1,"{612, 620, 206}"
15,1,78,0,0.0265645,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x} \, dx","Int[(b*x + c*x^2)^(3/2)/x,x]","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{3/2}}+\frac{b (b+2 c x) \sqrt{b x+c x^2}}{8 c}+\frac{1}{3} \left(b x+c x^2\right)^{3/2}","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{3/2}}+\frac{b (b+2 c x) \sqrt{b x+c x^2}}{8 c}+\frac{1}{3} \left(b x+c x^2\right)^{3/2}",1,"(b*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(8*c) + (b*x + c*x^2)^(3/2)/3 - (b^3*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(3/2))","A",4,4,17,0.2353,1,"{664, 612, 620, 206}"
16,1,72,0,0.0279387,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^2} \, dx","Int[(b*x + c*x^2)^(3/2)/x^2,x]","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 \sqrt{c}}+\frac{3}{4} b \sqrt{b x+c x^2}+\frac{\left(b x+c x^2\right)^{3/2}}{2 x}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 \sqrt{c}}+\frac{3}{4} b \sqrt{b x+c x^2}+\frac{\left(b x+c x^2\right)^{3/2}}{2 x}",1,"(3*b*Sqrt[b*x + c*x^2])/4 + (b*x + c*x^2)^(3/2)/(2*x) + (3*b^2*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*Sqrt[c])","A",4,3,17,0.1765,1,"{664, 620, 206}"
17,1,64,0,0.027478,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^3} \, dx","Int[(b*x + c*x^2)^(3/2)/x^3,x]","-\frac{2 \left(b x+c x^2\right)^{3/2}}{x^2}+3 c \sqrt{b x+c x^2}+3 b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)","-\frac{2 \left(b x+c x^2\right)^{3/2}}{x^2}+3 c \sqrt{b x+c x^2}+3 b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)",1,"3*c*Sqrt[b*x + c*x^2] - (2*(b*x + c*x^2)^(3/2))/x^2 + 3*b*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]]","A",4,4,17,0.2353,1,"{662, 664, 620, 206}"
18,1,68,0,0.0278444,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^4} \, dx","Int[(b*x + c*x^2)^(3/2)/x^4,x]","2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 c \sqrt{b x+c x^2}}{x}-\frac{2 \left(b x+c x^2\right)^{3/2}}{3 x^3}","2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 c \sqrt{b x+c x^2}}{x}-\frac{2 \left(b x+c x^2\right)^{3/2}}{3 x^3}",1,"(-2*c*Sqrt[b*x + c*x^2])/x - (2*(b*x + c*x^2)^(3/2))/(3*x^3) + 2*c^(3/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]]","A",4,3,17,0.1765,1,"{662, 620, 206}"
19,1,23,0,0.0075107,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^5} \, dx","Int[(b*x + c*x^2)^(3/2)/x^5,x]","-\frac{2 \left(b x+c x^2\right)^{5/2}}{5 b x^5}","-\frac{2 \left(b x+c x^2\right)^{5/2}}{5 b x^5}",1,"(-2*(b*x + c*x^2)^(5/2))/(5*b*x^5)","A",1,1,17,0.05882,1,"{650}"
20,1,48,0,0.0164416,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^6} \, dx","Int[(b*x + c*x^2)^(3/2)/x^6,x]","\frac{4 c \left(b x+c x^2\right)^{5/2}}{35 b^2 x^5}-\frac{2 \left(b x+c x^2\right)^{5/2}}{7 b x^6}","\frac{4 c \left(b x+c x^2\right)^{5/2}}{35 b^2 x^5}-\frac{2 \left(b x+c x^2\right)^{5/2}}{7 b x^6}",1,"(-2*(b*x + c*x^2)^(5/2))/(7*b*x^6) + (4*c*(b*x + c*x^2)^(5/2))/(35*b^2*x^5)","A",2,2,17,0.1176,1,"{658, 650}"
21,1,74,0,0.0270773,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^7} \, dx","Int[(b*x + c*x^2)^(3/2)/x^7,x]","-\frac{16 c^2 \left(b x+c x^2\right)^{5/2}}{315 b^3 x^5}+\frac{8 c \left(b x+c x^2\right)^{5/2}}{63 b^2 x^6}-\frac{2 \left(b x+c x^2\right)^{5/2}}{9 b x^7}","-\frac{16 c^2 \left(b x+c x^2\right)^{5/2}}{315 b^3 x^5}+\frac{8 c \left(b x+c x^2\right)^{5/2}}{63 b^2 x^6}-\frac{2 \left(b x+c x^2\right)^{5/2}}{9 b x^7}",1,"(-2*(b*x + c*x^2)^(5/2))/(9*b*x^7) + (8*c*(b*x + c*x^2)^(5/2))/(63*b^2*x^6) - (16*c^2*(b*x + c*x^2)^(5/2))/(315*b^3*x^5)","A",3,2,17,0.1176,1,"{658, 650}"
22,1,100,0,0.0411665,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^8} \, dx","Int[(b*x + c*x^2)^(3/2)/x^8,x]","\frac{32 c^3 \left(b x+c x^2\right)^{5/2}}{1155 b^4 x^5}-\frac{16 c^2 \left(b x+c x^2\right)^{5/2}}{231 b^3 x^6}+\frac{4 c \left(b x+c x^2\right)^{5/2}}{33 b^2 x^7}-\frac{2 \left(b x+c x^2\right)^{5/2}}{11 b x^8}","\frac{32 c^3 \left(b x+c x^2\right)^{5/2}}{1155 b^4 x^5}-\frac{16 c^2 \left(b x+c x^2\right)^{5/2}}{231 b^3 x^6}+\frac{4 c \left(b x+c x^2\right)^{5/2}}{33 b^2 x^7}-\frac{2 \left(b x+c x^2\right)^{5/2}}{11 b x^8}",1,"(-2*(b*x + c*x^2)^(5/2))/(11*b*x^8) + (4*c*(b*x + c*x^2)^(5/2))/(33*b^2*x^7) - (16*c^2*(b*x + c*x^2)^(5/2))/(231*b^3*x^6) + (32*c^3*(b*x + c*x^2)^(5/2))/(1155*b^4*x^5)","A",4,2,17,0.1176,1,"{658, 650}"
23,1,126,0,0.0574311,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^9} \, dx","Int[(b*x + c*x^2)^(3/2)/x^9,x]","-\frac{256 c^4 \left(b x+c x^2\right)^{5/2}}{15015 b^5 x^5}+\frac{128 c^3 \left(b x+c x^2\right)^{5/2}}{3003 b^4 x^6}-\frac{32 c^2 \left(b x+c x^2\right)^{5/2}}{429 b^3 x^7}+\frac{16 c \left(b x+c x^2\right)^{5/2}}{143 b^2 x^8}-\frac{2 \left(b x+c x^2\right)^{5/2}}{13 b x^9}","-\frac{256 c^4 \left(b x+c x^2\right)^{5/2}}{15015 b^5 x^5}+\frac{128 c^3 \left(b x+c x^2\right)^{5/2}}{3003 b^4 x^6}-\frac{32 c^2 \left(b x+c x^2\right)^{5/2}}{429 b^3 x^7}+\frac{16 c \left(b x+c x^2\right)^{5/2}}{143 b^2 x^8}-\frac{2 \left(b x+c x^2\right)^{5/2}}{13 b x^9}",1,"(-2*(b*x + c*x^2)^(5/2))/(13*b*x^9) + (16*c*(b*x + c*x^2)^(5/2))/(143*b^2*x^8) - (32*c^2*(b*x + c*x^2)^(5/2))/(429*b^3*x^7) + (128*c^3*(b*x + c*x^2)^(5/2))/(3003*b^4*x^6) - (256*c^4*(b*x + c*x^2)^(5/2))/(15015*b^5*x^5)","A",5,2,17,0.1176,1,"{658, 650}"
24,1,163,0,0.0736416,"\int x^2 \left(a x+b x^2\right)^{5/2} \, dx","Int[x^2*(a*x + b*x^2)^(5/2),x]","\frac{45 a^6 (a+2 b x) \sqrt{a x+b x^2}}{16384 b^5}-\frac{15 a^4 (a+2 b x) \left(a x+b x^2\right)^{3/2}}{2048 b^4}+\frac{3 a^2 (a+2 b x) \left(a x+b x^2\right)^{5/2}}{128 b^3}-\frac{45 a^8 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{16384 b^{11/2}}-\frac{9 a \left(a x+b x^2\right)^{7/2}}{112 b^2}+\frac{x \left(a x+b x^2\right)^{7/2}}{8 b}","\frac{45 a^6 (a+2 b x) \sqrt{a x+b x^2}}{16384 b^5}-\frac{15 a^4 (a+2 b x) \left(a x+b x^2\right)^{3/2}}{2048 b^4}+\frac{3 a^2 (a+2 b x) \left(a x+b x^2\right)^{5/2}}{128 b^3}-\frac{45 a^8 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{16384 b^{11/2}}-\frac{9 a \left(a x+b x^2\right)^{7/2}}{112 b^2}+\frac{x \left(a x+b x^2\right)^{7/2}}{8 b}",1,"(45*a^6*(a + 2*b*x)*Sqrt[a*x + b*x^2])/(16384*b^5) - (15*a^4*(a + 2*b*x)*(a*x + b*x^2)^(3/2))/(2048*b^4) + (3*a^2*(a + 2*b*x)*(a*x + b*x^2)^(5/2))/(128*b^3) - (9*a*(a*x + b*x^2)^(7/2))/(112*b^2) + (x*(a*x + b*x^2)^(7/2))/(8*b) - (45*a^8*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/(16384*b^(11/2))","A",7,5,17,0.2941,1,"{670, 640, 612, 620, 206}"
25,1,139,0,0.0504348,"\int x \left(a x+b x^2\right)^{5/2} \, dx","Int[x*(a*x + b*x^2)^(5/2),x]","-\frac{5 a^5 (a+2 b x) \sqrt{a x+b x^2}}{1024 b^4}+\frac{5 a^3 (a+2 b x) \left(a x+b x^2\right)^{3/2}}{384 b^3}+\frac{5 a^7 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{1024 b^{9/2}}-\frac{a (a+2 b x) \left(a x+b x^2\right)^{5/2}}{24 b^2}+\frac{\left(a x+b x^2\right)^{7/2}}{7 b}","-\frac{5 a^5 (a+2 b x) \sqrt{a x+b x^2}}{1024 b^4}+\frac{5 a^3 (a+2 b x) \left(a x+b x^2\right)^{3/2}}{384 b^3}+\frac{5 a^7 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{1024 b^{9/2}}-\frac{a (a+2 b x) \left(a x+b x^2\right)^{5/2}}{24 b^2}+\frac{\left(a x+b x^2\right)^{7/2}}{7 b}",1,"(-5*a^5*(a + 2*b*x)*Sqrt[a*x + b*x^2])/(1024*b^4) + (5*a^3*(a + 2*b*x)*(a*x + b*x^2)^(3/2))/(384*b^3) - (a*(a + 2*b*x)*(a*x + b*x^2)^(5/2))/(24*b^2) + (a*x + b*x^2)^(7/2)/(7*b) + (5*a^7*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/(1024*b^(9/2))","A",6,4,15,0.2667,1,"{640, 612, 620, 206}"
26,1,118,0,0.0359948,"\int \left(a x+b x^2\right)^{5/2} \, dx","Int[(a*x + b*x^2)^(5/2),x]","\frac{5 a^4 (a+2 b x) \sqrt{a x+b x^2}}{512 b^3}-\frac{5 a^2 (a+2 b x) \left(a x+b x^2\right)^{3/2}}{192 b^2}-\frac{5 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{512 b^{7/2}}+\frac{(a+2 b x) \left(a x+b x^2\right)^{5/2}}{12 b}","\frac{5 a^4 (a+2 b x) \sqrt{a x+b x^2}}{512 b^3}-\frac{5 a^2 (a+2 b x) \left(a x+b x^2\right)^{3/2}}{192 b^2}-\frac{5 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{512 b^{7/2}}+\frac{(a+2 b x) \left(a x+b x^2\right)^{5/2}}{12 b}",1,"(5*a^4*(a + 2*b*x)*Sqrt[a*x + b*x^2])/(512*b^3) - (5*a^2*(a + 2*b*x)*(a*x + b*x^2)^(3/2))/(192*b^2) + ((a + 2*b*x)*(a*x + b*x^2)^(5/2))/(12*b) - (5*a^6*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/(512*b^(7/2))","A",5,3,13,0.2308,1,"{612, 620, 206}"
27,1,107,0,0.0389775,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x} \, dx","Int[(a*x + b*x^2)^(5/2)/x,x]","-\frac{3 a^3 (a+2 b x) \sqrt{a x+b x^2}}{128 b^2}+\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{128 b^{5/2}}+\frac{a (a+2 b x) \left(a x+b x^2\right)^{3/2}}{16 b}+\frac{1}{5} \left(a x+b x^2\right)^{5/2}","-\frac{3 a^3 (a+2 b x) \sqrt{a x+b x^2}}{128 b^2}+\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{128 b^{5/2}}+\frac{a (a+2 b x) \left(a x+b x^2\right)^{3/2}}{16 b}+\frac{1}{5} \left(a x+b x^2\right)^{5/2}",1,"(-3*a^3*(a + 2*b*x)*Sqrt[a*x + b*x^2])/(128*b^2) + (a*(a + 2*b*x)*(a*x + b*x^2)^(3/2))/(16*b) + (a*x + b*x^2)^(5/2)/5 + (3*a^5*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/(128*b^(5/2))","A",5,4,17,0.2353,1,"{664, 612, 620, 206}"
28,1,101,0,0.041171,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^2} \, dx","Int[(a*x + b*x^2)^(5/2)/x^2,x]","-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{64 b^{3/2}}+\frac{5 a^2 (a+2 b x) \sqrt{a x+b x^2}}{64 b}+\frac{5}{24} a \left(a x+b x^2\right)^{3/2}+\frac{\left(a x+b x^2\right)^{5/2}}{4 x}","-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{64 b^{3/2}}+\frac{5 a^2 (a+2 b x) \sqrt{a x+b x^2}}{64 b}+\frac{5}{24} a \left(a x+b x^2\right)^{3/2}+\frac{\left(a x+b x^2\right)^{5/2}}{4 x}",1,"(5*a^2*(a + 2*b*x)*Sqrt[a*x + b*x^2])/(64*b) + (5*a*(a*x + b*x^2)^(3/2))/24 + (a*x + b*x^2)^(5/2)/(4*x) - (5*a^4*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/(64*b^(3/2))","A",5,4,17,0.2353,1,"{664, 612, 620, 206}"
29,1,94,0,0.0391494,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^3} \, dx","Int[(a*x + b*x^2)^(5/2)/x^3,x]","\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{8 \sqrt{b}}-\frac{5}{8} a (a+2 b x) \sqrt{a x+b x^2}+\frac{2 \left(a x+b x^2\right)^{5/2}}{x^2}-\frac{5}{3} b \left(a x+b x^2\right)^{3/2}","\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{8 \sqrt{b}}-\frac{5}{8} a (a+2 b x) \sqrt{a x+b x^2}+\frac{2 \left(a x+b x^2\right)^{5/2}}{x^2}-\frac{5}{3} b \left(a x+b x^2\right)^{3/2}",1,"(-5*a*(a + 2*b*x)*Sqrt[a*x + b*x^2])/8 - (5*b*(a*x + b*x^2)^(3/2))/3 + (2*(a*x + b*x^2)^(5/2))/x^2 + (5*a^3*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/(8*Sqrt[b])","A",5,5,17,0.2941,1,"{662, 664, 612, 620, 206}"
30,1,92,0,0.04064,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^4} \, dx","Int[(a*x + b*x^2)^(5/2)/x^4,x]","\frac{15}{4} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)-\frac{2 \left(a x+b x^2\right)^{5/2}}{x^3}+\frac{5 b \left(a x+b x^2\right)^{3/2}}{2 x}+\frac{15}{4} a b \sqrt{a x+b x^2}","\frac{15}{4} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)-\frac{2 \left(a x+b x^2\right)^{5/2}}{x^3}+\frac{5 b \left(a x+b x^2\right)^{3/2}}{2 x}+\frac{15}{4} a b \sqrt{a x+b x^2}",1,"(15*a*b*Sqrt[a*x + b*x^2])/4 + (5*b*(a*x + b*x^2)^(3/2))/(2*x) - (2*(a*x + b*x^2)^(5/2))/x^3 + (15*a^2*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/4","A",5,4,17,0.2353,1,"{662, 664, 620, 206}"
31,1,89,0,0.0405703,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^5} \, dx","Int[(a*x + b*x^2)^(5/2)/x^5,x]","5 b^2 \sqrt{a x+b x^2}+5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)-\frac{2 \left(a x+b x^2\right)^{5/2}}{3 x^4}-\frac{10 b \left(a x+b x^2\right)^{3/2}}{3 x^2}","5 b^2 \sqrt{a x+b x^2}+5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)-\frac{2 \left(a x+b x^2\right)^{5/2}}{3 x^4}-\frac{10 b \left(a x+b x^2\right)^{3/2}}{3 x^2}",1,"5*b^2*Sqrt[a*x + b*x^2] - (10*b*(a*x + b*x^2)^(3/2))/(3*x^2) - (2*(a*x + b*x^2)^(5/2))/(3*x^4) + 5*a*b^(3/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]]","A",5,4,17,0.2353,1,"{662, 664, 620, 206}"
32,1,91,0,0.0406987,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^6} \, dx","Int[(a*x + b*x^2)^(5/2)/x^6,x]","-\frac{2 b^2 \sqrt{a x+b x^2}}{x}+2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)-\frac{2 b \left(a x+b x^2\right)^{3/2}}{3 x^3}-\frac{2 \left(a x+b x^2\right)^{5/2}}{5 x^5}","-\frac{2 b^2 \sqrt{a x+b x^2}}{x}+2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)-\frac{2 b \left(a x+b x^2\right)^{3/2}}{3 x^3}-\frac{2 \left(a x+b x^2\right)^{5/2}}{5 x^5}",1,"(-2*b^2*Sqrt[a*x + b*x^2])/x - (2*b*(a*x + b*x^2)^(3/2))/(3*x^3) - (2*(a*x + b*x^2)^(5/2))/(5*x^5) + 2*b^(5/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]]","A",5,3,17,0.1765,1,"{662, 620, 206}"
33,1,23,0,0.0074363,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^7} \, dx","Int[(a*x + b*x^2)^(5/2)/x^7,x]","-\frac{2 \left(a x+b x^2\right)^{7/2}}{7 a x^7}","-\frac{2 \left(a x+b x^2\right)^{7/2}}{7 a x^7}",1,"(-2*(a*x + b*x^2)^(7/2))/(7*a*x^7)","A",1,1,17,0.05882,1,"{650}"
34,1,48,0,0.0173728,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^8} \, dx","Int[(a*x + b*x^2)^(5/2)/x^8,x]","\frac{4 b \left(a x+b x^2\right)^{7/2}}{63 a^2 x^7}-\frac{2 \left(a x+b x^2\right)^{7/2}}{9 a x^8}","\frac{4 b \left(a x+b x^2\right)^{7/2}}{63 a^2 x^7}-\frac{2 \left(a x+b x^2\right)^{7/2}}{9 a x^8}",1,"(-2*(a*x + b*x^2)^(7/2))/(9*a*x^8) + (4*b*(a*x + b*x^2)^(7/2))/(63*a^2*x^7)","A",2,2,17,0.1176,1,"{658, 650}"
35,1,74,0,0.0281318,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^9} \, dx","Int[(a*x + b*x^2)^(5/2)/x^9,x]","-\frac{16 b^2 \left(a x+b x^2\right)^{7/2}}{693 a^3 x^7}+\frac{8 b \left(a x+b x^2\right)^{7/2}}{99 a^2 x^8}-\frac{2 \left(a x+b x^2\right)^{7/2}}{11 a x^9}","-\frac{16 b^2 \left(a x+b x^2\right)^{7/2}}{693 a^3 x^7}+\frac{8 b \left(a x+b x^2\right)^{7/2}}{99 a^2 x^8}-\frac{2 \left(a x+b x^2\right)^{7/2}}{11 a x^9}",1,"(-2*(a*x + b*x^2)^(7/2))/(11*a*x^9) + (8*b*(a*x + b*x^2)^(7/2))/(99*a^2*x^8) - (16*b^2*(a*x + b*x^2)^(7/2))/(693*a^3*x^7)","A",3,2,17,0.1176,1,"{658, 650}"
36,1,100,0,0.0415272,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^{10}} \, dx","Int[(a*x + b*x^2)^(5/2)/x^10,x]","\frac{32 b^3 \left(a x+b x^2\right)^{7/2}}{3003 a^4 x^7}-\frac{16 b^2 \left(a x+b x^2\right)^{7/2}}{429 a^3 x^8}+\frac{12 b \left(a x+b x^2\right)^{7/2}}{143 a^2 x^9}-\frac{2 \left(a x+b x^2\right)^{7/2}}{13 a x^{10}}","\frac{32 b^3 \left(a x+b x^2\right)^{7/2}}{3003 a^4 x^7}-\frac{16 b^2 \left(a x+b x^2\right)^{7/2}}{429 a^3 x^8}+\frac{12 b \left(a x+b x^2\right)^{7/2}}{143 a^2 x^9}-\frac{2 \left(a x+b x^2\right)^{7/2}}{13 a x^{10}}",1,"(-2*(a*x + b*x^2)^(7/2))/(13*a*x^10) + (12*b*(a*x + b*x^2)^(7/2))/(143*a^2*x^9) - (16*b^2*(a*x + b*x^2)^(7/2))/(429*a^3*x^8) + (32*b^3*(a*x + b*x^2)^(7/2))/(3003*a^4*x^7)","A",4,2,17,0.1176,1,"{658, 650}"
37,1,126,0,0.0568929,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^{11}} \, dx","Int[(a*x + b*x^2)^(5/2)/x^11,x]","-\frac{256 b^4 \left(a x+b x^2\right)^{7/2}}{45045 a^5 x^7}+\frac{128 b^3 \left(a x+b x^2\right)^{7/2}}{6435 a^4 x^8}-\frac{32 b^2 \left(a x+b x^2\right)^{7/2}}{715 a^3 x^9}+\frac{16 b \left(a x+b x^2\right)^{7/2}}{195 a^2 x^{10}}-\frac{2 \left(a x+b x^2\right)^{7/2}}{15 a x^{11}}","-\frac{256 b^4 \left(a x+b x^2\right)^{7/2}}{45045 a^5 x^7}+\frac{128 b^3 \left(a x+b x^2\right)^{7/2}}{6435 a^4 x^8}-\frac{32 b^2 \left(a x+b x^2\right)^{7/2}}{715 a^3 x^9}+\frac{16 b \left(a x+b x^2\right)^{7/2}}{195 a^2 x^{10}}-\frac{2 \left(a x+b x^2\right)^{7/2}}{15 a x^{11}}",1,"(-2*(a*x + b*x^2)^(7/2))/(15*a*x^11) + (16*b*(a*x + b*x^2)^(7/2))/(195*a^2*x^10) - (32*b^2*(a*x + b*x^2)^(7/2))/(715*a^3*x^9) + (128*b^3*(a*x + b*x^2)^(7/2))/(6435*a^4*x^8) - (256*b^4*(a*x + b*x^2)^(7/2))/(45045*a^5*x^7)","A",5,2,17,0.1176,1,"{658, 650}"
38,1,152,0,0.0730637,"\int \frac{\left(a x+b x^2\right)^{5/2}}{x^{12}} \, dx","Int[(a*x + b*x^2)^(5/2)/x^12,x]","\frac{512 b^5 \left(a x+b x^2\right)^{7/2}}{153153 a^6 x^7}-\frac{256 b^4 \left(a x+b x^2\right)^{7/2}}{21879 a^5 x^8}+\frac{64 b^3 \left(a x+b x^2\right)^{7/2}}{2431 a^4 x^9}-\frac{32 b^2 \left(a x+b x^2\right)^{7/2}}{663 a^3 x^{10}}+\frac{4 b \left(a x+b x^2\right)^{7/2}}{51 a^2 x^{11}}-\frac{2 \left(a x+b x^2\right)^{7/2}}{17 a x^{12}}","\frac{512 b^5 \left(a x+b x^2\right)^{7/2}}{153153 a^6 x^7}-\frac{256 b^4 \left(a x+b x^2\right)^{7/2}}{21879 a^5 x^8}+\frac{64 b^3 \left(a x+b x^2\right)^{7/2}}{2431 a^4 x^9}-\frac{32 b^2 \left(a x+b x^2\right)^{7/2}}{663 a^3 x^{10}}+\frac{4 b \left(a x+b x^2\right)^{7/2}}{51 a^2 x^{11}}-\frac{2 \left(a x+b x^2\right)^{7/2}}{17 a x^{12}}",1,"(-2*(a*x + b*x^2)^(7/2))/(17*a*x^12) + (4*b*(a*x + b*x^2)^(7/2))/(51*a^2*x^11) - (32*b^2*(a*x + b*x^2)^(7/2))/(663*a^3*x^10) + (64*b^3*(a*x + b*x^2)^(7/2))/(2431*a^4*x^9) - (256*b^4*(a*x + b*x^2)^(7/2))/(21879*a^5*x^8) + (512*b^5*(a*x + b*x^2)^(7/2))/(153153*a^6*x^7)","A",6,2,17,0.1176,1,"{658, 650}"
39,1,50,0,0.0109595,"\int x \sqrt{2 x-x^2} \, dx","Int[x*Sqrt[2*x - x^2],x]","-\frac{1}{3} \left(2 x-x^2\right)^{3/2}-\frac{1}{2} (1-x) \sqrt{2 x-x^2}-\frac{1}{2} \sin ^{-1}(1-x)","-\frac{1}{3} \left(2 x-x^2\right)^{3/2}-\frac{1}{2} (1-x) \sqrt{2 x-x^2}-\frac{1}{2} \sin ^{-1}(1-x)",1,"-((1 - x)*Sqrt[2*x - x^2])/2 - (2*x - x^2)^(3/2)/3 - ArcSin[1 - x]/2","A",4,4,15,0.2667,1,"{640, 612, 619, 216}"
40,1,52,0,0.0145858,"\int x \sqrt{3 x-4 x^2} \, dx","Int[x*Sqrt[3*x - 4*x^2],x]","-\frac{1}{12} \left(3 x-4 x^2\right)^{3/2}-\frac{3}{128} (3-8 x) \sqrt{3 x-4 x^2}-\frac{27}{512} \sin ^{-1}\left(1-\frac{8 x}{3}\right)","-\frac{1}{12} \left(3 x-4 x^2\right)^{3/2}-\frac{3}{128} (3-8 x) \sqrt{3 x-4 x^2}-\frac{27}{512} \sin ^{-1}\left(1-\frac{8 x}{3}\right)",1,"(-3*(3 - 8*x)*Sqrt[3*x - 4*x^2])/128 - (3*x - 4*x^2)^(3/2)/12 - (27*ArcSin[1 - (8*x)/3])/512","A",4,4,15,0.2667,1,"{640, 612, 619, 216}"
41,1,48,0,0.0099011,"\int x \sqrt{x+x^2} \, dx","Int[x*Sqrt[x + x^2],x]","\frac{1}{3} \left(x^2+x\right)^{3/2}-\frac{1}{8} (2 x+1) \sqrt{x^2+x}+\frac{1}{8} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+x}}\right)","\frac{1}{3} \left(x^2+x\right)^{3/2}-\frac{1}{8} (2 x+1) \sqrt{x^2+x}+\frac{1}{8} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+x}}\right)",1,"-((1 + 2*x)*Sqrt[x + x^2])/8 + (x + x^2)^(3/2)/3 + ArcTanh[x/Sqrt[x + x^2]]/8","A",4,4,11,0.3636,1,"{640, 612, 620, 206}"
42,1,128,0,0.0576066,"\int \frac{x^4}{\sqrt{b x+c x^2}} \, dx","Int[x^4/Sqrt[b*x + c*x^2],x]","-\frac{35 b^3 \sqrt{b x+c x^2}}{64 c^4}+\frac{35 b^2 x \sqrt{b x+c x^2}}{96 c^3}+\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{9/2}}-\frac{7 b x^2 \sqrt{b x+c x^2}}{24 c^2}+\frac{x^3 \sqrt{b x+c x^2}}{4 c}","-\frac{35 b^3 \sqrt{b x+c x^2}}{64 c^4}+\frac{35 b^2 x \sqrt{b x+c x^2}}{96 c^3}+\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{9/2}}-\frac{7 b x^2 \sqrt{b x+c x^2}}{24 c^2}+\frac{x^3 \sqrt{b x+c x^2}}{4 c}",1,"(-35*b^3*Sqrt[b*x + c*x^2])/(64*c^4) + (35*b^2*x*Sqrt[b*x + c*x^2])/(96*c^3) - (7*b*x^2*Sqrt[b*x + c*x^2])/(24*c^2) + (x^3*Sqrt[b*x + c*x^2])/(4*c) + (35*b^4*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(9/2))","A",6,4,17,0.2353,1,"{670, 640, 620, 206}"
43,1,102,0,0.0425747,"\int \frac{x^3}{\sqrt{b x+c x^2}} \, dx","Int[x^3/Sqrt[b*x + c*x^2],x]","\frac{5 b^2 \sqrt{b x+c x^2}}{8 c^3}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{7/2}}-\frac{5 b x \sqrt{b x+c x^2}}{12 c^2}+\frac{x^2 \sqrt{b x+c x^2}}{3 c}","\frac{5 b^2 \sqrt{b x+c x^2}}{8 c^3}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{7/2}}-\frac{5 b x \sqrt{b x+c x^2}}{12 c^2}+\frac{x^2 \sqrt{b x+c x^2}}{3 c}",1,"(5*b^2*Sqrt[b*x + c*x^2])/(8*c^3) - (5*b*x*Sqrt[b*x + c*x^2])/(12*c^2) + (x^2*Sqrt[b*x + c*x^2])/(3*c) - (5*b^3*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(7/2))","A",5,4,17,0.2353,1,"{670, 640, 620, 206}"
44,1,76,0,0.0264775,"\int \frac{x^2}{\sqrt{b x+c x^2}} \, dx","Int[x^2/Sqrt[b*x + c*x^2],x]","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{5/2}}-\frac{3 b \sqrt{b x+c x^2}}{4 c^2}+\frac{x \sqrt{b x+c x^2}}{2 c}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{5/2}}-\frac{3 b \sqrt{b x+c x^2}}{4 c^2}+\frac{x \sqrt{b x+c x^2}}{2 c}",1,"(-3*b*Sqrt[b*x + c*x^2])/(4*c^2) + (x*Sqrt[b*x + c*x^2])/(2*c) + (3*b^2*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(5/2))","A",4,4,17,0.2353,1,"{670, 640, 620, 206}"
45,1,47,0,0.0151187,"\int \frac{x}{\sqrt{b x+c x^2}} \, dx","Int[x/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{b x+c x^2}}{c}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}","\frac{\sqrt{b x+c x^2}}{c}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}",1,"Sqrt[b*x + c*x^2]/c - (b*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(3/2)","A",3,3,15,0.2000,1,"{640, 620, 206}"
46,1,28,0,0.0081746,"\int \frac{1}{\sqrt{b x+c x^2}} \, dx","Int[1/Sqrt[b*x + c*x^2],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}",1,"(2*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/Sqrt[c]","A",2,2,13,0.1538,1,"{620, 206}"
47,1,21,0,0.0073153,"\int \frac{1}{x \sqrt{b x+c x^2}} \, dx","Int[1/(x*Sqrt[b*x + c*x^2]),x]","-\frac{2 \sqrt{b x+c x^2}}{b x}","-\frac{2 \sqrt{b x+c x^2}}{b x}",1,"(-2*Sqrt[b*x + c*x^2])/(b*x)","A",1,1,17,0.05882,1,"{650}"
48,1,48,0,0.0163138,"\int \frac{1}{x^2 \sqrt{b x+c x^2}} \, dx","Int[1/(x^2*Sqrt[b*x + c*x^2]),x]","\frac{4 c \sqrt{b x+c x^2}}{3 b^2 x}-\frac{2 \sqrt{b x+c x^2}}{3 b x^2}","\frac{4 c \sqrt{b x+c x^2}}{3 b^2 x}-\frac{2 \sqrt{b x+c x^2}}{3 b x^2}",1,"(-2*Sqrt[b*x + c*x^2])/(3*b*x^2) + (4*c*Sqrt[b*x + c*x^2])/(3*b^2*x)","A",2,2,17,0.1176,1,"{658, 650}"
49,1,74,0,0.0263216,"\int \frac{1}{x^3 \sqrt{b x+c x^2}} \, dx","Int[1/(x^3*Sqrt[b*x + c*x^2]),x]","-\frac{16 c^2 \sqrt{b x+c x^2}}{15 b^3 x}+\frac{8 c \sqrt{b x+c x^2}}{15 b^2 x^2}-\frac{2 \sqrt{b x+c x^2}}{5 b x^3}","-\frac{16 c^2 \sqrt{b x+c x^2}}{15 b^3 x}+\frac{8 c \sqrt{b x+c x^2}}{15 b^2 x^2}-\frac{2 \sqrt{b x+c x^2}}{5 b x^3}",1,"(-2*Sqrt[b*x + c*x^2])/(5*b*x^3) + (8*c*Sqrt[b*x + c*x^2])/(15*b^2*x^2) - (16*c^2*Sqrt[b*x + c*x^2])/(15*b^3*x)","A",3,2,17,0.1176,1,"{658, 650}"
50,1,100,0,0.0388309,"\int \frac{1}{x^4 \sqrt{b x+c x^2}} \, dx","Int[1/(x^4*Sqrt[b*x + c*x^2]),x]","\frac{32 c^3 \sqrt{b x+c x^2}}{35 b^4 x}-\frac{16 c^2 \sqrt{b x+c x^2}}{35 b^3 x^2}+\frac{12 c \sqrt{b x+c x^2}}{35 b^2 x^3}-\frac{2 \sqrt{b x+c x^2}}{7 b x^4}","\frac{32 c^3 \sqrt{b x+c x^2}}{35 b^4 x}-\frac{16 c^2 \sqrt{b x+c x^2}}{35 b^3 x^2}+\frac{12 c \sqrt{b x+c x^2}}{35 b^2 x^3}-\frac{2 \sqrt{b x+c x^2}}{7 b x^4}",1,"(-2*Sqrt[b*x + c*x^2])/(7*b*x^4) + (12*c*Sqrt[b*x + c*x^2])/(35*b^2*x^3) - (16*c^2*Sqrt[b*x + c*x^2])/(35*b^3*x^2) + (32*c^3*Sqrt[b*x + c*x^2])/(35*b^4*x)","A",4,2,17,0.1176,1,"{658, 650}"
51,1,126,0,0.0547222,"\int \frac{1}{x^5 \sqrt{b x+c x^2}} \, dx","Int[1/(x^5*Sqrt[b*x + c*x^2]),x]","-\frac{256 c^4 \sqrt{b x+c x^2}}{315 b^5 x}+\frac{128 c^3 \sqrt{b x+c x^2}}{315 b^4 x^2}-\frac{32 c^2 \sqrt{b x+c x^2}}{105 b^3 x^3}+\frac{16 c \sqrt{b x+c x^2}}{63 b^2 x^4}-\frac{2 \sqrt{b x+c x^2}}{9 b x^5}","-\frac{256 c^4 \sqrt{b x+c x^2}}{315 b^5 x}+\frac{128 c^3 \sqrt{b x+c x^2}}{315 b^4 x^2}-\frac{32 c^2 \sqrt{b x+c x^2}}{105 b^3 x^3}+\frac{16 c \sqrt{b x+c x^2}}{63 b^2 x^4}-\frac{2 \sqrt{b x+c x^2}}{9 b x^5}",1,"(-2*Sqrt[b*x + c*x^2])/(9*b*x^5) + (16*c*Sqrt[b*x + c*x^2])/(63*b^2*x^4) - (32*c^2*Sqrt[b*x + c*x^2])/(105*b^3*x^3) + (128*c^3*Sqrt[b*x + c*x^2])/(315*b^4*x^2) - (256*c^4*Sqrt[b*x + c*x^2])/(315*b^5*x)","A",5,2,17,0.1176,1,"{658, 650}"
52,1,97,0,0.0398188,"\int \frac{x^4}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x^4/(b*x + c*x^2)^(3/2),x]","\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{7/2}}+\frac{5 x \sqrt{b x+c x^2}}{2 c^2}-\frac{15 b \sqrt{b x+c x^2}}{4 c^3}-\frac{2 x^3}{c \sqrt{b x+c x^2}}","\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{7/2}}+\frac{5 x \sqrt{b x+c x^2}}{2 c^2}-\frac{15 b \sqrt{b x+c x^2}}{4 c^3}-\frac{2 x^3}{c \sqrt{b x+c x^2}}",1,"(-2*x^3)/(c*Sqrt[b*x + c*x^2]) - (15*b*Sqrt[b*x + c*x^2])/(4*c^3) + (5*x*Sqrt[b*x + c*x^2])/(2*c^2) + (15*b^2*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(7/2))","A",5,5,17,0.2941,1,"{668, 670, 640, 620, 206}"
53,1,69,0,0.0266901,"\int \frac{x^3}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x^3/(b*x + c*x^2)^(3/2),x]","\frac{3 \sqrt{b x+c x^2}}{c^2}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}-\frac{2 x^2}{c \sqrt{b x+c x^2}}","\frac{3 \sqrt{b x+c x^2}}{c^2}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}-\frac{2 x^2}{c \sqrt{b x+c x^2}}",1,"(-2*x^2)/(c*Sqrt[b*x + c*x^2]) + (3*Sqrt[b*x + c*x^2])/c^2 - (3*b*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(5/2)","A",4,4,17,0.2353,1,"{668, 640, 620, 206}"
54,1,48,0,0.0175548,"\int \frac{x^2}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x^2/(b*x + c*x^2)^(3/2),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}-\frac{2 x}{c \sqrt{b x+c x^2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}-\frac{2 x}{c \sqrt{b x+c x^2}}",1,"(-2*x)/(c*Sqrt[b*x + c*x^2]) + (2*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(3/2)","A",3,3,17,0.1765,1,"{652, 620, 206}"
55,1,19,0,0.0053672,"\int \frac{x}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x/(b*x + c*x^2)^(3/2),x]","\frac{2 x}{b \sqrt{b x+c x^2}}","\frac{2 x}{b \sqrt{b x+c x^2}}",1,"(2*x)/(b*Sqrt[b*x + c*x^2])","A",1,1,15,0.06667,1,"{636}"
56,1,24,0,0.0033446,"\int \frac{1}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(b*x + c*x^2)^(-3/2),x]","-\frac{2 (b+2 c x)}{b^2 \sqrt{b x+c x^2}}","-\frac{2 (b+2 c x)}{b^2 \sqrt{b x+c x^2}}",1,"(-2*(b + 2*c*x))/(b^2*Sqrt[b*x + c*x^2])","A",1,1,13,0.07692,1,"{613}"
57,1,51,0,0.0129913,"\int \frac{1}{x \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/(x*(b*x + c*x^2)^(3/2)),x]","\frac{8 c (b+2 c x)}{3 b^3 \sqrt{b x+c x^2}}-\frac{2}{3 b x \sqrt{b x+c x^2}}","\frac{8 c (b+2 c x)}{3 b^3 \sqrt{b x+c x^2}}-\frac{2}{3 b x \sqrt{b x+c x^2}}",1,"-2/(3*b*x*Sqrt[b*x + c*x^2]) + (8*c*(b + 2*c*x))/(3*b^3*Sqrt[b*x + c*x^2])","A",2,2,17,0.1176,1,"{658, 613}"
58,1,77,0,0.0244401,"\int \frac{1}{x^2 \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/(x^2*(b*x + c*x^2)^(3/2)),x]","-\frac{16 c^2 (b+2 c x)}{5 b^4 \sqrt{b x+c x^2}}+\frac{4 c}{5 b^2 x \sqrt{b x+c x^2}}-\frac{2}{5 b x^2 \sqrt{b x+c x^2}}","-\frac{16 c^2 (b+2 c x)}{5 b^4 \sqrt{b x+c x^2}}+\frac{4 c}{5 b^2 x \sqrt{b x+c x^2}}-\frac{2}{5 b x^2 \sqrt{b x+c x^2}}",1,"-2/(5*b*x^2*Sqrt[b*x + c*x^2]) + (4*c)/(5*b^2*x*Sqrt[b*x + c*x^2]) - (16*c^2*(b + 2*c*x))/(5*b^4*Sqrt[b*x + c*x^2])","A",3,2,17,0.1176,1,"{658, 613}"
59,1,103,0,0.0394125,"\int \frac{1}{x^3 \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/(x^3*(b*x + c*x^2)^(3/2)),x]","\frac{128 c^3 (b+2 c x)}{35 b^5 \sqrt{b x+c x^2}}-\frac{32 c^2}{35 b^3 x \sqrt{b x+c x^2}}+\frac{16 c}{35 b^2 x^2 \sqrt{b x+c x^2}}-\frac{2}{7 b x^3 \sqrt{b x+c x^2}}","\frac{128 c^3 (b+2 c x)}{35 b^5 \sqrt{b x+c x^2}}-\frac{32 c^2}{35 b^3 x \sqrt{b x+c x^2}}+\frac{16 c}{35 b^2 x^2 \sqrt{b x+c x^2}}-\frac{2}{7 b x^3 \sqrt{b x+c x^2}}",1,"-2/(7*b*x^3*Sqrt[b*x + c*x^2]) + (16*c)/(35*b^2*x^2*Sqrt[b*x + c*x^2]) - (32*c^2)/(35*b^3*x*Sqrt[b*x + c*x^2]) + (128*c^3*(b + 2*c*x))/(35*b^5*Sqrt[b*x + c*x^2])","A",4,2,17,0.1176,1,"{658, 613}"
60,1,122,0,0.0582204,"\int \frac{x^6}{\left(a x+b x^2\right)^{5/2}} \, dx","Int[x^6/(a*x + b*x^2)^(5/2),x]","\frac{35 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{4 b^{9/2}}-\frac{14 x^3}{3 b^2 \sqrt{a x+b x^2}}+\frac{35 x \sqrt{a x+b x^2}}{6 b^3}-\frac{35 a \sqrt{a x+b x^2}}{4 b^4}-\frac{2 x^5}{3 b \left(a x+b x^2\right)^{3/2}}","\frac{35 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{4 b^{9/2}}-\frac{14 x^3}{3 b^2 \sqrt{a x+b x^2}}+\frac{35 x \sqrt{a x+b x^2}}{6 b^3}-\frac{35 a \sqrt{a x+b x^2}}{4 b^4}-\frac{2 x^5}{3 b \left(a x+b x^2\right)^{3/2}}",1,"(-2*x^5)/(3*b*(a*x + b*x^2)^(3/2)) - (14*x^3)/(3*b^2*Sqrt[a*x + b*x^2]) - (35*a*Sqrt[a*x + b*x^2])/(4*b^4) + (35*x*Sqrt[a*x + b*x^2])/(6*b^3) + (35*a^2*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/(4*b^(9/2))","A",6,5,17,0.2941,1,"{668, 670, 640, 620, 206}"
61,1,94,0,0.0414738,"\int \frac{x^5}{\left(a x+b x^2\right)^{5/2}} \, dx","Int[x^5/(a*x + b*x^2)^(5/2),x]","-\frac{10 x^2}{3 b^2 \sqrt{a x+b x^2}}+\frac{5 \sqrt{a x+b x^2}}{b^3}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{b^{7/2}}-\frac{2 x^4}{3 b \left(a x+b x^2\right)^{3/2}}","-\frac{10 x^2}{3 b^2 \sqrt{a x+b x^2}}+\frac{5 \sqrt{a x+b x^2}}{b^3}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{b^{7/2}}-\frac{2 x^4}{3 b \left(a x+b x^2\right)^{3/2}}",1,"(-2*x^4)/(3*b*(a*x + b*x^2)^(3/2)) - (10*x^2)/(3*b^2*Sqrt[a*x + b*x^2]) + (5*Sqrt[a*x + b*x^2])/b^3 - (5*a*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/b^(7/2)","A",5,4,17,0.2353,1,"{668, 640, 620, 206}"
62,1,71,0,0.0300053,"\int \frac{x^4}{\left(a x+b x^2\right)^{5/2}} \, dx","Int[x^4/(a*x + b*x^2)^(5/2),x]","-\frac{2 x}{b^2 \sqrt{a x+b x^2}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{b^{5/2}}-\frac{2 x^3}{3 b \left(a x+b x^2\right)^{3/2}}","-\frac{2 x}{b^2 \sqrt{a x+b x^2}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{b^{5/2}}-\frac{2 x^3}{3 b \left(a x+b x^2\right)^{3/2}}",1,"(-2*x^3)/(3*b*(a*x + b*x^2)^(3/2)) - (2*x)/(b^2*Sqrt[a*x + b*x^2]) + (2*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/b^(5/2)","A",4,4,17,0.2353,1,"{668, 652, 620, 206}"
63,1,23,0,0.0076737,"\int \frac{x^3}{\left(a x+b x^2\right)^{5/2}} \, dx","Int[x^3/(a*x + b*x^2)^(5/2),x]","\frac{2 x^3}{3 a \left(a x+b x^2\right)^{3/2}}","\frac{2 x^3}{3 a \left(a x+b x^2\right)^{3/2}}",1,"(2*x^3)/(3*a*(a*x + b*x^2)^(3/2))","A",1,1,17,0.05882,1,"{650}"
64,1,51,0,0.0134114,"\int \frac{x^2}{\left(a x+b x^2\right)^{5/2}} \, dx","Int[x^2/(a*x + b*x^2)^(5/2),x]","\frac{2 (a+2 b x)}{3 a^2 b \sqrt{a x+b x^2}}-\frac{2 x}{3 b \left(a x+b x^2\right)^{3/2}}","\frac{2 (a+2 b x)}{3 a^2 b \sqrt{a x+b x^2}}-\frac{2 x}{3 b \left(a x+b x^2\right)^{3/2}}",1,"(-2*x)/(3*b*(a*x + b*x^2)^(3/2)) + (2*(a + 2*b*x))/(3*a^2*b*Sqrt[a*x + b*x^2])","A",2,2,17,0.1176,1,"{652, 613}"
65,1,48,0,0.0111226,"\int \frac{x}{\left(a x+b x^2\right)^{5/2}} \, dx","Int[x/(a*x + b*x^2)^(5/2),x]","\frac{2 x}{3 a \left(a x+b x^2\right)^{3/2}}-\frac{8 (a+2 b x)}{3 a^3 \sqrt{a x+b x^2}}","\frac{2 x}{3 a \left(a x+b x^2\right)^{3/2}}-\frac{8 (a+2 b x)}{3 a^3 \sqrt{a x+b x^2}}",1,"(2*x)/(3*a*(a*x + b*x^2)^(3/2)) - (8*(a + 2*b*x))/(3*a^3*Sqrt[a*x + b*x^2])","A",2,2,15,0.1333,1,"{638, 613}"
66,1,54,0,0.0090646,"\int \frac{1}{\left(a x+b x^2\right)^{5/2}} \, dx","Int[(a*x + b*x^2)^(-5/2),x]","\frac{16 b (a+2 b x)}{3 a^4 \sqrt{a x+b x^2}}-\frac{2 (a+2 b x)}{3 a^2 \left(a x+b x^2\right)^{3/2}}","\frac{16 b (a+2 b x)}{3 a^4 \sqrt{a x+b x^2}}-\frac{2 (a+2 b x)}{3 a^2 \left(a x+b x^2\right)^{3/2}}",1,"(-2*(a + 2*b*x))/(3*a^2*(a*x + b*x^2)^(3/2)) + (16*b*(a + 2*b*x))/(3*a^4*Sqrt[a*x + b*x^2])","A",2,2,13,0.1538,1,"{614, 613}"
67,1,80,0,0.0220632,"\int \frac{1}{x \left(a x+b x^2\right)^{5/2}} \, dx","Int[1/(x*(a*x + b*x^2)^(5/2)),x]","-\frac{128 b^2 (a+2 b x)}{15 a^5 \sqrt{a x+b x^2}}+\frac{16 b (a+2 b x)}{15 a^3 \left(a x+b x^2\right)^{3/2}}-\frac{2}{5 a x \left(a x+b x^2\right)^{3/2}}","-\frac{128 b^2 (a+2 b x)}{15 a^5 \sqrt{a x+b x^2}}+\frac{16 b (a+2 b x)}{15 a^3 \left(a x+b x^2\right)^{3/2}}-\frac{2}{5 a x \left(a x+b x^2\right)^{3/2}}",1,"-2/(5*a*x*(a*x + b*x^2)^(3/2)) + (16*b*(a + 2*b*x))/(15*a^3*(a*x + b*x^2)^(3/2)) - (128*b^2*(a + 2*b*x))/(15*a^5*Sqrt[a*x + b*x^2])","A",3,3,17,0.1765,1,"{658, 614, 613}"
68,1,106,0,0.0362233,"\int \frac{1}{x^2 \left(a x+b x^2\right)^{5/2}} \, dx","Int[1/(x^2*(a*x + b*x^2)^(5/2)),x]","\frac{256 b^3 (a+2 b x)}{21 a^6 \sqrt{a x+b x^2}}-\frac{32 b^2 (a+2 b x)}{21 a^4 \left(a x+b x^2\right)^{3/2}}+\frac{4 b}{7 a^2 x \left(a x+b x^2\right)^{3/2}}-\frac{2}{7 a x^2 \left(a x+b x^2\right)^{3/2}}","\frac{256 b^3 (a+2 b x)}{21 a^6 \sqrt{a x+b x^2}}-\frac{32 b^2 (a+2 b x)}{21 a^4 \left(a x+b x^2\right)^{3/2}}+\frac{4 b}{7 a^2 x \left(a x+b x^2\right)^{3/2}}-\frac{2}{7 a x^2 \left(a x+b x^2\right)^{3/2}}",1,"-2/(7*a*x^2*(a*x + b*x^2)^(3/2)) + (4*b)/(7*a^2*x*(a*x + b*x^2)^(3/2)) - (32*b^2*(a + 2*b*x))/(21*a^4*(a*x + b*x^2)^(3/2)) + (256*b^3*(a + 2*b*x))/(21*a^6*Sqrt[a*x + b*x^2])","A",4,3,17,0.1765,1,"{658, 614, 613}"
69,1,26,0,0.010801,"\int \frac{x}{\sqrt{4 x-x^2}} \, dx","Int[x/Sqrt[4*x - x^2],x]","-\sqrt{4 x-x^2}-2 \sin ^{-1}\left(1-\frac{x}{2}\right)","-\sqrt{4 x-x^2}-2 \sin ^{-1}\left(1-\frac{x}{2}\right)",1,"-Sqrt[4*x - x^2] - 2*ArcSin[1 - x/2]","A",3,3,15,0.2000,1,"{640, 619, 216}"
70,1,28,0,0.0074961,"\int \frac{x}{\sqrt{-4 x+x^2}} \, dx","Int[x/Sqrt[-4*x + x^2],x]","\sqrt{x^2-4 x}+4 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-4 x}}\right)","\sqrt{x^2-4 x}+4 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-4 x}}\right)",1,"Sqrt[-4*x + x^2] + 4*ArcTanh[x/Sqrt[-4*x + x^2]]","A",3,3,13,0.2308,1,"{640, 620, 206}"
71,1,46,0,0.0153809,"\int \frac{x^2}{\sqrt{2 x-x^2}} \, dx","Int[x^2/Sqrt[2*x - x^2],x]","-\frac{1}{2} \sqrt{2 x-x^2} x-\frac{3}{2} \sqrt{2 x-x^2}-\frac{3}{2} \sin ^{-1}(1-x)","-\frac{1}{2} \sqrt{2 x-x^2} x-\frac{3}{2} \sqrt{2 x-x^2}-\frac{3}{2} \sin ^{-1}(1-x)",1,"(-3*Sqrt[2*x - x^2])/2 - (x*Sqrt[2*x - x^2])/2 - (3*ArcSin[1 - x])/2","A",4,4,17,0.2353,1,"{670, 640, 619, 216}"
72,1,136,0,0.0551495,"\int x^{7/2} \sqrt{b x+c x^2} \, dx","Int[x^(7/2)*Sqrt[b*x + c*x^2],x]","\frac{256 b^4 \left(b x+c x^2\right)^{3/2}}{3465 c^5 x^{3/2}}-\frac{128 b^3 \left(b x+c x^2\right)^{3/2}}{1155 c^4 \sqrt{x}}+\frac{32 b^2 \sqrt{x} \left(b x+c x^2\right)^{3/2}}{231 c^3}-\frac{16 b x^{3/2} \left(b x+c x^2\right)^{3/2}}{99 c^2}+\frac{2 x^{5/2} \left(b x+c x^2\right)^{3/2}}{11 c}","\frac{256 b^4 \left(b x+c x^2\right)^{3/2}}{3465 c^5 x^{3/2}}-\frac{128 b^3 \left(b x+c x^2\right)^{3/2}}{1155 c^4 \sqrt{x}}+\frac{32 b^2 \sqrt{x} \left(b x+c x^2\right)^{3/2}}{231 c^3}-\frac{16 b x^{3/2} \left(b x+c x^2\right)^{3/2}}{99 c^2}+\frac{2 x^{5/2} \left(b x+c x^2\right)^{3/2}}{11 c}",1,"(256*b^4*(b*x + c*x^2)^(3/2))/(3465*c^5*x^(3/2)) - (128*b^3*(b*x + c*x^2)^(3/2))/(1155*c^4*Sqrt[x]) + (32*b^2*Sqrt[x]*(b*x + c*x^2)^(3/2))/(231*c^3) - (16*b*x^(3/2)*(b*x + c*x^2)^(3/2))/(99*c^2) + (2*x^(5/2)*(b*x + c*x^2)^(3/2))/(11*c)","A",5,2,19,0.1053,1,"{656, 648}"
73,1,108,0,0.0402275,"\int x^{5/2} \sqrt{b x+c x^2} \, dx","Int[x^(5/2)*Sqrt[b*x + c*x^2],x]","-\frac{32 b^3 \left(b x+c x^2\right)^{3/2}}{315 c^4 x^{3/2}}+\frac{16 b^2 \left(b x+c x^2\right)^{3/2}}{105 c^3 \sqrt{x}}-\frac{4 b \sqrt{x} \left(b x+c x^2\right)^{3/2}}{21 c^2}+\frac{2 x^{3/2} \left(b x+c x^2\right)^{3/2}}{9 c}","-\frac{32 b^3 \left(b x+c x^2\right)^{3/2}}{315 c^4 x^{3/2}}+\frac{16 b^2 \left(b x+c x^2\right)^{3/2}}{105 c^3 \sqrt{x}}-\frac{4 b \sqrt{x} \left(b x+c x^2\right)^{3/2}}{21 c^2}+\frac{2 x^{3/2} \left(b x+c x^2\right)^{3/2}}{9 c}",1,"(-32*b^3*(b*x + c*x^2)^(3/2))/(315*c^4*x^(3/2)) + (16*b^2*(b*x + c*x^2)^(3/2))/(105*c^3*Sqrt[x]) - (4*b*Sqrt[x]*(b*x + c*x^2)^(3/2))/(21*c^2) + (2*x^(3/2)*(b*x + c*x^2)^(3/2))/(9*c)","A",4,2,19,0.1053,1,"{656, 648}"
74,1,80,0,0.0267062,"\int x^{3/2} \sqrt{b x+c x^2} \, dx","Int[x^(3/2)*Sqrt[b*x + c*x^2],x]","\frac{16 b^2 \left(b x+c x^2\right)^{3/2}}{105 c^3 x^{3/2}}-\frac{8 b \left(b x+c x^2\right)^{3/2}}{35 c^2 \sqrt{x}}+\frac{2 \sqrt{x} \left(b x+c x^2\right)^{3/2}}{7 c}","\frac{16 b^2 \left(b x+c x^2\right)^{3/2}}{105 c^3 x^{3/2}}-\frac{8 b \left(b x+c x^2\right)^{3/2}}{35 c^2 \sqrt{x}}+\frac{2 \sqrt{x} \left(b x+c x^2\right)^{3/2}}{7 c}",1,"(16*b^2*(b*x + c*x^2)^(3/2))/(105*c^3*x^(3/2)) - (8*b*(b*x + c*x^2)^(3/2))/(35*c^2*Sqrt[x]) + (2*Sqrt[x]*(b*x + c*x^2)^(3/2))/(7*c)","A",3,2,19,0.1053,1,"{656, 648}"
75,1,52,0,0.0152971,"\int \sqrt{x} \sqrt{b x+c x^2} \, dx","Int[Sqrt[x]*Sqrt[b*x + c*x^2],x]","\frac{2 \left(b x+c x^2\right)^{3/2}}{5 c \sqrt{x}}-\frac{4 b \left(b x+c x^2\right)^{3/2}}{15 c^2 x^{3/2}}","\frac{2 \left(b x+c x^2\right)^{3/2}}{5 c \sqrt{x}}-\frac{4 b \left(b x+c x^2\right)^{3/2}}{15 c^2 x^{3/2}}",1,"(-4*b*(b*x + c*x^2)^(3/2))/(15*c^2*x^(3/2)) + (2*(b*x + c*x^2)^(3/2))/(5*c*Sqrt[x])","A",2,2,19,0.1053,1,"{656, 648}"
76,1,25,0,0.0062485,"\int \frac{\sqrt{b x+c x^2}}{\sqrt{x}} \, dx","Int[Sqrt[b*x + c*x^2]/Sqrt[x],x]","\frac{2 \left(b x+c x^2\right)^{3/2}}{3 c x^{3/2}}","\frac{2 \left(b x+c x^2\right)^{3/2}}{3 c x^{3/2}}",1,"(2*(b*x + c*x^2)^(3/2))/(3*c*x^(3/2))","A",1,1,19,0.05263,1,"{648}"
77,1,53,0,0.0205161,"\int \frac{\sqrt{b x+c x^2}}{x^{3/2}} \, dx","Int[Sqrt[b*x + c*x^2]/x^(3/2),x]","\frac{2 \sqrt{b x+c x^2}}{\sqrt{x}}-2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)","\frac{2 \sqrt{b x+c x^2}}{\sqrt{x}}-2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)",1,"(2*Sqrt[b*x + c*x^2])/Sqrt[x] - 2*Sqrt[b]*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])]","A",3,3,19,0.1579,1,"{664, 660, 207}"
78,1,54,0,0.0207981,"\int \frac{\sqrt{b x+c x^2}}{x^{5/2}} \, dx","Int[Sqrt[b*x + c*x^2]/x^(5/2),x]","-\frac{\sqrt{b x+c x^2}}{x^{3/2}}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{\sqrt{b}}","-\frac{\sqrt{b x+c x^2}}{x^{3/2}}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{\sqrt{b}}",1,"-(Sqrt[b*x + c*x^2]/x^(3/2)) - (c*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/Sqrt[b]","A",3,3,19,0.1579,1,"{662, 660, 207}"
79,1,86,0,0.0331965,"\int \frac{\sqrt{b x+c x^2}}{x^{7/2}} \, dx","Int[Sqrt[b*x + c*x^2]/x^(7/2),x]","\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{3/2}}-\frac{c \sqrt{b x+c x^2}}{4 b x^{3/2}}-\frac{\sqrt{b x+c x^2}}{2 x^{5/2}}","\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{3/2}}-\frac{c \sqrt{b x+c x^2}}{4 b x^{3/2}}-\frac{\sqrt{b x+c x^2}}{2 x^{5/2}}",1,"-Sqrt[b*x + c*x^2]/(2*x^(5/2)) - (c*Sqrt[b*x + c*x^2])/(4*b*x^(3/2)) + (c^2*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(4*b^(3/2))","A",4,4,19,0.2105,1,"{662, 672, 660, 207}"
80,1,114,0,0.0516426,"\int \frac{\sqrt{b x+c x^2}}{x^{9/2}} \, dx","Int[Sqrt[b*x + c*x^2]/x^(9/2),x]","\frac{c^2 \sqrt{b x+c x^2}}{8 b^2 x^{3/2}}-\frac{c^3 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{5/2}}-\frac{c \sqrt{b x+c x^2}}{12 b x^{5/2}}-\frac{\sqrt{b x+c x^2}}{3 x^{7/2}}","\frac{c^2 \sqrt{b x+c x^2}}{8 b^2 x^{3/2}}-\frac{c^3 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{5/2}}-\frac{c \sqrt{b x+c x^2}}{12 b x^{5/2}}-\frac{\sqrt{b x+c x^2}}{3 x^{7/2}}",1,"-Sqrt[b*x + c*x^2]/(3*x^(7/2)) - (c*Sqrt[b*x + c*x^2])/(12*b*x^(5/2)) + (c^2*Sqrt[b*x + c*x^2])/(8*b^2*x^(3/2)) - (c^3*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*b^(5/2))","A",5,4,19,0.2105,1,"{662, 672, 660, 207}"
81,1,142,0,0.0648671,"\int \frac{\sqrt{b x+c x^2}}{x^{11/2}} \, dx","Int[Sqrt[b*x + c*x^2]/x^(11/2),x]","-\frac{5 c^3 \sqrt{b x+c x^2}}{64 b^3 x^{3/2}}+\frac{5 c^2 \sqrt{b x+c x^2}}{96 b^2 x^{5/2}}+\frac{5 c^4 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{7/2}}-\frac{c \sqrt{b x+c x^2}}{24 b x^{7/2}}-\frac{\sqrt{b x+c x^2}}{4 x^{9/2}}","-\frac{5 c^3 \sqrt{b x+c x^2}}{64 b^3 x^{3/2}}+\frac{5 c^2 \sqrt{b x+c x^2}}{96 b^2 x^{5/2}}+\frac{5 c^4 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{7/2}}-\frac{c \sqrt{b x+c x^2}}{24 b x^{7/2}}-\frac{\sqrt{b x+c x^2}}{4 x^{9/2}}",1,"-Sqrt[b*x + c*x^2]/(4*x^(9/2)) - (c*Sqrt[b*x + c*x^2])/(24*b*x^(7/2)) + (5*c^2*Sqrt[b*x + c*x^2])/(96*b^2*x^(5/2)) - (5*c^3*Sqrt[b*x + c*x^2])/(64*b^3*x^(3/2)) + (5*c^4*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(64*b^(7/2))","A",6,4,19,0.2105,1,"{662, 672, 660, 207}"
82,1,164,0,0.075216,"\int x^{7/2} \left(b x+c x^2\right)^{3/2} \, dx","Int[x^(7/2)*(b*x + c*x^2)^(3/2),x]","-\frac{512 b^5 \left(b x+c x^2\right)^{5/2}}{45045 c^6 x^{5/2}}+\frac{256 b^4 \left(b x+c x^2\right)^{5/2}}{9009 c^5 x^{3/2}}-\frac{64 b^3 \left(b x+c x^2\right)^{5/2}}{1287 c^4 \sqrt{x}}+\frac{32 b^2 \sqrt{x} \left(b x+c x^2\right)^{5/2}}{429 c^3}-\frac{4 b x^{3/2} \left(b x+c x^2\right)^{5/2}}{39 c^2}+\frac{2 x^{5/2} \left(b x+c x^2\right)^{5/2}}{15 c}","-\frac{512 b^5 \left(b x+c x^2\right)^{5/2}}{45045 c^6 x^{5/2}}+\frac{256 b^4 \left(b x+c x^2\right)^{5/2}}{9009 c^5 x^{3/2}}-\frac{64 b^3 \left(b x+c x^2\right)^{5/2}}{1287 c^4 \sqrt{x}}+\frac{32 b^2 \sqrt{x} \left(b x+c x^2\right)^{5/2}}{429 c^3}-\frac{4 b x^{3/2} \left(b x+c x^2\right)^{5/2}}{39 c^2}+\frac{2 x^{5/2} \left(b x+c x^2\right)^{5/2}}{15 c}",1,"(-512*b^5*(b*x + c*x^2)^(5/2))/(45045*c^6*x^(5/2)) + (256*b^4*(b*x + c*x^2)^(5/2))/(9009*c^5*x^(3/2)) - (64*b^3*(b*x + c*x^2)^(5/2))/(1287*c^4*Sqrt[x]) + (32*b^2*Sqrt[x]*(b*x + c*x^2)^(5/2))/(429*c^3) - (4*b*x^(3/2)*(b*x + c*x^2)^(5/2))/(39*c^2) + (2*x^(5/2)*(b*x + c*x^2)^(5/2))/(15*c)","A",6,2,19,0.1053,1,"{656, 648}"
83,1,136,0,0.0560172,"\int x^{5/2} \left(b x+c x^2\right)^{3/2} \, dx","Int[x^(5/2)*(b*x + c*x^2)^(3/2),x]","\frac{256 b^4 \left(b x+c x^2\right)^{5/2}}{15015 c^5 x^{5/2}}-\frac{128 b^3 \left(b x+c x^2\right)^{5/2}}{3003 c^4 x^{3/2}}+\frac{32 b^2 \left(b x+c x^2\right)^{5/2}}{429 c^3 \sqrt{x}}-\frac{16 b \sqrt{x} \left(b x+c x^2\right)^{5/2}}{143 c^2}+\frac{2 x^{3/2} \left(b x+c x^2\right)^{5/2}}{13 c}","\frac{256 b^4 \left(b x+c x^2\right)^{5/2}}{15015 c^5 x^{5/2}}-\frac{128 b^3 \left(b x+c x^2\right)^{5/2}}{3003 c^4 x^{3/2}}+\frac{32 b^2 \left(b x+c x^2\right)^{5/2}}{429 c^3 \sqrt{x}}-\frac{16 b \sqrt{x} \left(b x+c x^2\right)^{5/2}}{143 c^2}+\frac{2 x^{3/2} \left(b x+c x^2\right)^{5/2}}{13 c}",1,"(256*b^4*(b*x + c*x^2)^(5/2))/(15015*c^5*x^(5/2)) - (128*b^3*(b*x + c*x^2)^(5/2))/(3003*c^4*x^(3/2)) + (32*b^2*(b*x + c*x^2)^(5/2))/(429*c^3*Sqrt[x]) - (16*b*Sqrt[x]*(b*x + c*x^2)^(5/2))/(143*c^2) + (2*x^(3/2)*(b*x + c*x^2)^(5/2))/(13*c)","A",5,2,19,0.1053,1,"{656, 648}"
84,1,108,0,0.0429493,"\int x^{3/2} \left(b x+c x^2\right)^{3/2} \, dx","Int[x^(3/2)*(b*x + c*x^2)^(3/2),x]","-\frac{32 b^3 \left(b x+c x^2\right)^{5/2}}{1155 c^4 x^{5/2}}+\frac{16 b^2 \left(b x+c x^2\right)^{5/2}}{231 c^3 x^{3/2}}-\frac{4 b \left(b x+c x^2\right)^{5/2}}{33 c^2 \sqrt{x}}+\frac{2 \sqrt{x} \left(b x+c x^2\right)^{5/2}}{11 c}","-\frac{32 b^3 \left(b x+c x^2\right)^{5/2}}{1155 c^4 x^{5/2}}+\frac{16 b^2 \left(b x+c x^2\right)^{5/2}}{231 c^3 x^{3/2}}-\frac{4 b \left(b x+c x^2\right)^{5/2}}{33 c^2 \sqrt{x}}+\frac{2 \sqrt{x} \left(b x+c x^2\right)^{5/2}}{11 c}",1,"(-32*b^3*(b*x + c*x^2)^(5/2))/(1155*c^4*x^(5/2)) + (16*b^2*(b*x + c*x^2)^(5/2))/(231*c^3*x^(3/2)) - (4*b*(b*x + c*x^2)^(5/2))/(33*c^2*Sqrt[x]) + (2*Sqrt[x]*(b*x + c*x^2)^(5/2))/(11*c)","A",4,2,19,0.1053,1,"{656, 648}"
85,1,80,0,0.0269342,"\int \sqrt{x} \left(b x+c x^2\right)^{3/2} \, dx","Int[Sqrt[x]*(b*x + c*x^2)^(3/2),x]","\frac{16 b^2 \left(b x+c x^2\right)^{5/2}}{315 c^3 x^{5/2}}-\frac{8 b \left(b x+c x^2\right)^{5/2}}{63 c^2 x^{3/2}}+\frac{2 \left(b x+c x^2\right)^{5/2}}{9 c \sqrt{x}}","\frac{16 b^2 \left(b x+c x^2\right)^{5/2}}{315 c^3 x^{5/2}}-\frac{8 b \left(b x+c x^2\right)^{5/2}}{63 c^2 x^{3/2}}+\frac{2 \left(b x+c x^2\right)^{5/2}}{9 c \sqrt{x}}",1,"(16*b^2*(b*x + c*x^2)^(5/2))/(315*c^3*x^(5/2)) - (8*b*(b*x + c*x^2)^(5/2))/(63*c^2*x^(3/2)) + (2*(b*x + c*x^2)^(5/2))/(9*c*Sqrt[x])","A",3,2,19,0.1053,1,"{656, 648}"
86,1,52,0,0.0163527,"\int \frac{\left(b x+c x^2\right)^{3/2}}{\sqrt{x}} \, dx","Int[(b*x + c*x^2)^(3/2)/Sqrt[x],x]","\frac{2 \left(b x+c x^2\right)^{5/2}}{7 c x^{3/2}}-\frac{4 b \left(b x+c x^2\right)^{5/2}}{35 c^2 x^{5/2}}","\frac{2 \left(b x+c x^2\right)^{5/2}}{7 c x^{3/2}}-\frac{4 b \left(b x+c x^2\right)^{5/2}}{35 c^2 x^{5/2}}",1,"(-4*b*(b*x + c*x^2)^(5/2))/(35*c^2*x^(5/2)) + (2*(b*x + c*x^2)^(5/2))/(7*c*x^(3/2))","A",2,2,19,0.1053,1,"{656, 648}"
87,1,25,0,0.0069109,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^{3/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/x^(3/2),x]","\frac{2 \left(b x+c x^2\right)^{5/2}}{5 c x^{5/2}}","\frac{2 \left(b x+c x^2\right)^{5/2}}{5 c x^{5/2}}",1,"(2*(b*x + c*x^2)^(5/2))/(5*c*x^(5/2))","A",1,1,19,0.05263,1,"{648}"
88,1,76,0,0.0335446,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^{5/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/x^(5/2),x]","-2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 b \sqrt{b x+c x^2}}{\sqrt{x}}+\frac{2 \left(b x+c x^2\right)^{3/2}}{3 x^{3/2}}","-2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 b \sqrt{b x+c x^2}}{\sqrt{x}}+\frac{2 \left(b x+c x^2\right)^{3/2}}{3 x^{3/2}}",1,"(2*b*Sqrt[b*x + c*x^2])/Sqrt[x] + (2*(b*x + c*x^2)^(3/2))/(3*x^(3/2)) - 2*b^(3/2)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])]","A",4,3,19,0.1579,1,"{664, 660, 207}"
89,1,75,0,0.0315328,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^{7/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/x^(7/2),x]","-\frac{\left(b x+c x^2\right)^{3/2}}{x^{5/2}}+\frac{3 c \sqrt{b x+c x^2}}{\sqrt{x}}-3 \sqrt{b} c \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)","-\frac{\left(b x+c x^2\right)^{3/2}}{x^{5/2}}+\frac{3 c \sqrt{b x+c x^2}}{\sqrt{x}}-3 \sqrt{b} c \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)",1,"(3*c*Sqrt[b*x + c*x^2])/Sqrt[x] - (b*x + c*x^2)^(3/2)/x^(5/2) - 3*Sqrt[b]*c*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])]","A",4,4,19,0.2105,1,"{662, 664, 660, 207}"
90,1,83,0,0.0323445,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^{9/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/x^(9/2),x]","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 \sqrt{b}}-\frac{3 c \sqrt{b x+c x^2}}{4 x^{3/2}}-\frac{\left(b x+c x^2\right)^{3/2}}{2 x^{7/2}}","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 \sqrt{b}}-\frac{3 c \sqrt{b x+c x^2}}{4 x^{3/2}}-\frac{\left(b x+c x^2\right)^{3/2}}{2 x^{7/2}}",1,"(-3*c*Sqrt[b*x + c*x^2])/(4*x^(3/2)) - (b*x + c*x^2)^(3/2)/(2*x^(7/2)) - (3*c^2*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(4*Sqrt[b])","A",4,3,19,0.1579,1,"{662, 660, 207}"
91,1,111,0,0.0460828,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^{11/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/x^(11/2),x]","\frac{c^3 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{3/2}}-\frac{c^2 \sqrt{b x+c x^2}}{8 b x^{3/2}}-\frac{c \sqrt{b x+c x^2}}{4 x^{5/2}}-\frac{\left(b x+c x^2\right)^{3/2}}{3 x^{9/2}}","\frac{c^3 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{3/2}}-\frac{c^2 \sqrt{b x+c x^2}}{8 b x^{3/2}}-\frac{c \sqrt{b x+c x^2}}{4 x^{5/2}}-\frac{\left(b x+c x^2\right)^{3/2}}{3 x^{9/2}}",1,"-(c*Sqrt[b*x + c*x^2])/(4*x^(5/2)) - (c^2*Sqrt[b*x + c*x^2])/(8*b*x^(3/2)) - (b*x + c*x^2)^(3/2)/(3*x^(9/2)) + (c^3*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*b^(3/2))","A",5,4,19,0.2105,1,"{662, 672, 660, 207}"
92,1,139,0,0.0646788,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^{13/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/x^(13/2),x]","\frac{3 c^3 \sqrt{b x+c x^2}}{64 b^2 x^{3/2}}-\frac{3 c^4 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{5/2}}-\frac{c^2 \sqrt{b x+c x^2}}{32 b x^{5/2}}-\frac{c \sqrt{b x+c x^2}}{8 x^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2}}{4 x^{11/2}}","\frac{3 c^3 \sqrt{b x+c x^2}}{64 b^2 x^{3/2}}-\frac{3 c^4 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{5/2}}-\frac{c^2 \sqrt{b x+c x^2}}{32 b x^{5/2}}-\frac{c \sqrt{b x+c x^2}}{8 x^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2}}{4 x^{11/2}}",1,"-(c*Sqrt[b*x + c*x^2])/(8*x^(7/2)) - (c^2*Sqrt[b*x + c*x^2])/(32*b*x^(5/2)) + (3*c^3*Sqrt[b*x + c*x^2])/(64*b^2*x^(3/2)) - (b*x + c*x^2)^(3/2)/(4*x^(11/2)) - (3*c^4*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(64*b^(5/2))","A",6,4,19,0.2105,1,"{662, 672, 660, 207}"
93,1,167,0,0.0833269,"\int \frac{\left(b x+c x^2\right)^{3/2}}{x^{15/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/x^(15/2),x]","-\frac{3 c^4 \sqrt{b x+c x^2}}{128 b^3 x^{3/2}}+\frac{c^3 \sqrt{b x+c x^2}}{64 b^2 x^{5/2}}+\frac{3 c^5 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{128 b^{7/2}}-\frac{c^2 \sqrt{b x+c x^2}}{80 b x^{7/2}}-\frac{3 c \sqrt{b x+c x^2}}{40 x^{9/2}}-\frac{\left(b x+c x^2\right)^{3/2}}{5 x^{13/2}}","-\frac{3 c^4 \sqrt{b x+c x^2}}{128 b^3 x^{3/2}}+\frac{c^3 \sqrt{b x+c x^2}}{64 b^2 x^{5/2}}+\frac{3 c^5 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{128 b^{7/2}}-\frac{c^2 \sqrt{b x+c x^2}}{80 b x^{7/2}}-\frac{3 c \sqrt{b x+c x^2}}{40 x^{9/2}}-\frac{\left(b x+c x^2\right)^{3/2}}{5 x^{13/2}}",1,"(-3*c*Sqrt[b*x + c*x^2])/(40*x^(9/2)) - (c^2*Sqrt[b*x + c*x^2])/(80*b*x^(7/2)) + (c^3*Sqrt[b*x + c*x^2])/(64*b^2*x^(5/2)) - (3*c^4*Sqrt[b*x + c*x^2])/(128*b^3*x^(3/2)) - (b*x + c*x^2)^(3/2)/(5*x^(13/2)) + (3*c^5*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(128*b^(7/2))","A",7,4,19,0.2105,1,"{662, 672, 660, 207}"
94,1,108,0,0.040222,"\int \frac{x^{7/2}}{\sqrt{b x+c x^2}} \, dx","Int[x^(7/2)/Sqrt[b*x + c*x^2],x]","-\frac{32 b^3 \sqrt{b x+c x^2}}{35 c^4 \sqrt{x}}+\frac{16 b^2 \sqrt{x} \sqrt{b x+c x^2}}{35 c^3}-\frac{12 b x^{3/2} \sqrt{b x+c x^2}}{35 c^2}+\frac{2 x^{5/2} \sqrt{b x+c x^2}}{7 c}","-\frac{32 b^3 \sqrt{b x+c x^2}}{35 c^4 \sqrt{x}}+\frac{16 b^2 \sqrt{x} \sqrt{b x+c x^2}}{35 c^3}-\frac{12 b x^{3/2} \sqrt{b x+c x^2}}{35 c^2}+\frac{2 x^{5/2} \sqrt{b x+c x^2}}{7 c}",1,"(-32*b^3*Sqrt[b*x + c*x^2])/(35*c^4*Sqrt[x]) + (16*b^2*Sqrt[x]*Sqrt[b*x + c*x^2])/(35*c^3) - (12*b*x^(3/2)*Sqrt[b*x + c*x^2])/(35*c^2) + (2*x^(5/2)*Sqrt[b*x + c*x^2])/(7*c)","A",4,2,19,0.1053,1,"{656, 648}"
95,1,80,0,0.0265036,"\int \frac{x^{5/2}}{\sqrt{b x+c x^2}} \, dx","Int[x^(5/2)/Sqrt[b*x + c*x^2],x]","\frac{16 b^2 \sqrt{b x+c x^2}}{15 c^3 \sqrt{x}}-\frac{8 b \sqrt{x} \sqrt{b x+c x^2}}{15 c^2}+\frac{2 x^{3/2} \sqrt{b x+c x^2}}{5 c}","\frac{16 b^2 \sqrt{b x+c x^2}}{15 c^3 \sqrt{x}}-\frac{8 b \sqrt{x} \sqrt{b x+c x^2}}{15 c^2}+\frac{2 x^{3/2} \sqrt{b x+c x^2}}{5 c}",1,"(16*b^2*Sqrt[b*x + c*x^2])/(15*c^3*Sqrt[x]) - (8*b*Sqrt[x]*Sqrt[b*x + c*x^2])/(15*c^2) + (2*x^(3/2)*Sqrt[b*x + c*x^2])/(5*c)","A",3,2,19,0.1053,1,"{656, 648}"
96,1,52,0,0.0157122,"\int \frac{x^{3/2}}{\sqrt{b x+c x^2}} \, dx","Int[x^(3/2)/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{x} \sqrt{b x+c x^2}}{3 c}-\frac{4 b \sqrt{b x+c x^2}}{3 c^2 \sqrt{x}}","\frac{2 \sqrt{x} \sqrt{b x+c x^2}}{3 c}-\frac{4 b \sqrt{b x+c x^2}}{3 c^2 \sqrt{x}}",1,"(-4*b*Sqrt[b*x + c*x^2])/(3*c^2*Sqrt[x]) + (2*Sqrt[x]*Sqrt[b*x + c*x^2])/(3*c)","A",2,2,19,0.1053,1,"{656, 648}"
97,1,23,0,0.0068375,"\int \frac{\sqrt{x}}{\sqrt{b x+c x^2}} \, dx","Int[Sqrt[x]/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{b x+c x^2}}{c \sqrt{x}}","\frac{2 \sqrt{b x+c x^2}}{c \sqrt{x}}",1,"(2*Sqrt[b*x + c*x^2])/(c*Sqrt[x])","A",1,1,19,0.05263,1,"{648}"
98,1,32,0,0.0124113,"\int \frac{1}{\sqrt{x} \sqrt{b x+c x^2}} \, dx","Int[1/(Sqrt[x]*Sqrt[b*x + c*x^2]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{\sqrt{b}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{\sqrt{b}}",1,"(-2*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/Sqrt[b]","A",2,2,19,0.1053,1,"{660, 207}"
99,1,56,0,0.0220336,"\int \frac{1}{x^{3/2} \sqrt{b x+c x^2}} \, dx","Int[1/(x^(3/2)*Sqrt[b*x + c*x^2]),x]","\frac{c \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{3/2}}-\frac{\sqrt{b x+c x^2}}{b x^{3/2}}","\frac{c \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{3/2}}-\frac{\sqrt{b x+c x^2}}{b x^{3/2}}",1,"-(Sqrt[b*x + c*x^2]/(b*x^(3/2))) + (c*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/b^(3/2)","A",3,3,19,0.1579,1,"{672, 660, 207}"
100,1,89,0,0.0343466,"\int \frac{1}{x^{5/2} \sqrt{b x+c x^2}} \, dx","Int[1/(x^(5/2)*Sqrt[b*x + c*x^2]),x]","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{5/2}}+\frac{3 c \sqrt{b x+c x^2}}{4 b^2 x^{3/2}}-\frac{\sqrt{b x+c x^2}}{2 b x^{5/2}}","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{5/2}}+\frac{3 c \sqrt{b x+c x^2}}{4 b^2 x^{3/2}}-\frac{\sqrt{b x+c x^2}}{2 b x^{5/2}}",1,"-Sqrt[b*x + c*x^2]/(2*b*x^(5/2)) + (3*c*Sqrt[b*x + c*x^2])/(4*b^2*x^(3/2)) - (3*c^2*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(4*b^(5/2))","A",4,3,19,0.1579,1,"{672, 660, 207}"
101,1,117,0,0.0492188,"\int \frac{1}{x^{7/2} \sqrt{b x+c x^2}} \, dx","Int[1/(x^(7/2)*Sqrt[b*x + c*x^2]),x]","-\frac{5 c^2 \sqrt{b x+c x^2}}{8 b^3 x^{3/2}}+\frac{5 c^3 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{7/2}}+\frac{5 c \sqrt{b x+c x^2}}{12 b^2 x^{5/2}}-\frac{\sqrt{b x+c x^2}}{3 b x^{7/2}}","-\frac{5 c^2 \sqrt{b x+c x^2}}{8 b^3 x^{3/2}}+\frac{5 c^3 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{7/2}}+\frac{5 c \sqrt{b x+c x^2}}{12 b^2 x^{5/2}}-\frac{\sqrt{b x+c x^2}}{3 b x^{7/2}}",1,"-Sqrt[b*x + c*x^2]/(3*b*x^(7/2)) + (5*c*Sqrt[b*x + c*x^2])/(12*b^2*x^(5/2)) - (5*c^2*Sqrt[b*x + c*x^2])/(8*b^3*x^(3/2)) + (5*c^3*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*b^(7/2))","A",5,3,19,0.1579,1,"{672, 660, 207}"
102,1,164,0,0.0748355,"\int \frac{x^{13/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x^(13/2)/(b*x + c*x^2)^(3/2),x]","\frac{32 b^2 x^{7/2}}{63 c^3 \sqrt{b x+c x^2}}-\frac{64 b^3 x^{5/2}}{63 c^4 \sqrt{b x+c x^2}}+\frac{256 b^4 x^{3/2}}{63 c^5 \sqrt{b x+c x^2}}+\frac{512 b^5 \sqrt{x}}{63 c^6 \sqrt{b x+c x^2}}-\frac{20 b x^{9/2}}{63 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{11/2}}{9 c \sqrt{b x+c x^2}}","\frac{32 b^2 x^{7/2}}{63 c^3 \sqrt{b x+c x^2}}-\frac{64 b^3 x^{5/2}}{63 c^4 \sqrt{b x+c x^2}}+\frac{256 b^4 x^{3/2}}{63 c^5 \sqrt{b x+c x^2}}+\frac{512 b^5 \sqrt{x}}{63 c^6 \sqrt{b x+c x^2}}-\frac{20 b x^{9/2}}{63 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{11/2}}{9 c \sqrt{b x+c x^2}}",1,"(512*b^5*Sqrt[x])/(63*c^6*Sqrt[b*x + c*x^2]) + (256*b^4*x^(3/2))/(63*c^5*Sqrt[b*x + c*x^2]) - (64*b^3*x^(5/2))/(63*c^4*Sqrt[b*x + c*x^2]) + (32*b^2*x^(7/2))/(63*c^3*Sqrt[b*x + c*x^2]) - (20*b*x^(9/2))/(63*c^2*Sqrt[b*x + c*x^2]) + (2*x^(11/2))/(9*c*Sqrt[b*x + c*x^2])","A",6,2,19,0.1053,1,"{656, 648}"
103,1,136,0,0.0567674,"\int \frac{x^{11/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x^(11/2)/(b*x + c*x^2)^(3/2),x]","\frac{32 b^2 x^{5/2}}{35 c^3 \sqrt{b x+c x^2}}-\frac{128 b^3 x^{3/2}}{35 c^4 \sqrt{b x+c x^2}}-\frac{256 b^4 \sqrt{x}}{35 c^5 \sqrt{b x+c x^2}}-\frac{16 b x^{7/2}}{35 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{9/2}}{7 c \sqrt{b x+c x^2}}","\frac{32 b^2 x^{5/2}}{35 c^3 \sqrt{b x+c x^2}}-\frac{128 b^3 x^{3/2}}{35 c^4 \sqrt{b x+c x^2}}-\frac{256 b^4 \sqrt{x}}{35 c^5 \sqrt{b x+c x^2}}-\frac{16 b x^{7/2}}{35 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{9/2}}{7 c \sqrt{b x+c x^2}}",1,"(-256*b^4*Sqrt[x])/(35*c^5*Sqrt[b*x + c*x^2]) - (128*b^3*x^(3/2))/(35*c^4*Sqrt[b*x + c*x^2]) + (32*b^2*x^(5/2))/(35*c^3*Sqrt[b*x + c*x^2]) - (16*b*x^(7/2))/(35*c^2*Sqrt[b*x + c*x^2]) + (2*x^(9/2))/(7*c*Sqrt[b*x + c*x^2])","A",5,2,19,0.1053,1,"{656, 648}"
104,1,108,0,0.0413416,"\int \frac{x^{9/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x^(9/2)/(b*x + c*x^2)^(3/2),x]","\frac{16 b^2 x^{3/2}}{5 c^3 \sqrt{b x+c x^2}}+\frac{32 b^3 \sqrt{x}}{5 c^4 \sqrt{b x+c x^2}}-\frac{4 b x^{5/2}}{5 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{7/2}}{5 c \sqrt{b x+c x^2}}","\frac{16 b^2 x^{3/2}}{5 c^3 \sqrt{b x+c x^2}}+\frac{32 b^3 \sqrt{x}}{5 c^4 \sqrt{b x+c x^2}}-\frac{4 b x^{5/2}}{5 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{7/2}}{5 c \sqrt{b x+c x^2}}",1,"(32*b^3*Sqrt[x])/(5*c^4*Sqrt[b*x + c*x^2]) + (16*b^2*x^(3/2))/(5*c^3*Sqrt[b*x + c*x^2]) - (4*b*x^(5/2))/(5*c^2*Sqrt[b*x + c*x^2]) + (2*x^(7/2))/(5*c*Sqrt[b*x + c*x^2])","A",4,2,19,0.1053,1,"{656, 648}"
105,1,80,0,0.0275102,"\int \frac{x^{7/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x^(7/2)/(b*x + c*x^2)^(3/2),x]","-\frac{16 b^2 \sqrt{x}}{3 c^3 \sqrt{b x+c x^2}}-\frac{8 b x^{3/2}}{3 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{5/2}}{3 c \sqrt{b x+c x^2}}","-\frac{16 b^2 \sqrt{x}}{3 c^3 \sqrt{b x+c x^2}}-\frac{8 b x^{3/2}}{3 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{5/2}}{3 c \sqrt{b x+c x^2}}",1,"(-16*b^2*Sqrt[x])/(3*c^3*Sqrt[b*x + c*x^2]) - (8*b*x^(3/2))/(3*c^2*Sqrt[b*x + c*x^2]) + (2*x^(5/2))/(3*c*Sqrt[b*x + c*x^2])","A",3,2,19,0.1053,1,"{656, 648}"
106,1,48,0,0.0181612,"\int \frac{x^{5/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x^(5/2)/(b*x + c*x^2)^(3/2),x]","\frac{4 b \sqrt{x}}{c^2 \sqrt{b x+c x^2}}+\frac{2 x^{3/2}}{c \sqrt{b x+c x^2}}","\frac{4 b \sqrt{x}}{c^2 \sqrt{b x+c x^2}}+\frac{2 x^{3/2}}{c \sqrt{b x+c x^2}}",1,"(4*b*Sqrt[x])/(c^2*Sqrt[b*x + c*x^2]) + (2*x^(3/2))/(c*Sqrt[b*x + c*x^2])","A",2,2,19,0.1053,1,"{656, 648}"
107,1,23,0,0.0070982,"\int \frac{x^{3/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[x^(3/2)/(b*x + c*x^2)^(3/2),x]","-\frac{2 \sqrt{x}}{c \sqrt{b x+c x^2}}","-\frac{2 \sqrt{x}}{c \sqrt{b x+c x^2}}",1,"(-2*Sqrt[x])/(c*Sqrt[b*x + c*x^2])","A",1,1,19,0.05263,1,"{648}"
108,1,56,0,0.0216995,"\int \frac{\sqrt{x}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[Sqrt[x]/(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{x}}{b \sqrt{b x+c x^2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{3/2}}","\frac{2 \sqrt{x}}{b \sqrt{b x+c x^2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{3/2}}",1,"(2*Sqrt[x])/(b*Sqrt[b*x + c*x^2]) - (2*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/b^(3/2)","A",3,3,19,0.1579,1,"{666, 660, 207}"
109,1,81,0,0.0334128,"\int \frac{1}{\sqrt{x} \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[x]*(b*x + c*x^2)^(3/2)),x]","-\frac{3 c \sqrt{x}}{b^2 \sqrt{b x+c x^2}}+\frac{3 c \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{5/2}}-\frac{1}{b \sqrt{x} \sqrt{b x+c x^2}}","-\frac{3 c \sqrt{x}}{b^2 \sqrt{b x+c x^2}}+\frac{3 c \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{5/2}}-\frac{1}{b \sqrt{x} \sqrt{b x+c x^2}}",1,"-(1/(b*Sqrt[x]*Sqrt[b*x + c*x^2])) - (3*c*Sqrt[x])/(b^2*Sqrt[b*x + c*x^2]) + (3*c*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/b^(5/2)","A",4,4,19,0.2105,1,"{672, 666, 660, 207}"
110,1,117,0,0.048457,"\int \frac{1}{x^{3/2} \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/(x^(3/2)*(b*x + c*x^2)^(3/2)),x]","\frac{15 c^2 \sqrt{x}}{4 b^3 \sqrt{b x+c x^2}}-\frac{15 c^2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{7/2}}+\frac{5 c}{4 b^2 \sqrt{x} \sqrt{b x+c x^2}}-\frac{1}{2 b x^{3/2} \sqrt{b x+c x^2}}","\frac{15 c^2 \sqrt{x}}{4 b^3 \sqrt{b x+c x^2}}-\frac{15 c^2 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{7/2}}+\frac{5 c}{4 b^2 \sqrt{x} \sqrt{b x+c x^2}}-\frac{1}{2 b x^{3/2} \sqrt{b x+c x^2}}",1,"-1/(2*b*x^(3/2)*Sqrt[b*x + c*x^2]) + (5*c)/(4*b^2*Sqrt[x]*Sqrt[b*x + c*x^2]) + (15*c^2*Sqrt[x])/(4*b^3*Sqrt[b*x + c*x^2]) - (15*c^2*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(4*b^(7/2))","A",5,4,19,0.2105,1,"{672, 666, 660, 207}"
111,1,145,0,0.0660191,"\int \frac{1}{x^{5/2} \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/(x^(5/2)*(b*x + c*x^2)^(3/2)),x]","-\frac{35 c^3 \sqrt{x}}{8 b^4 \sqrt{b x+c x^2}}-\frac{35 c^2}{24 b^3 \sqrt{x} \sqrt{b x+c x^2}}+\frac{35 c^3 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{9/2}}+\frac{7 c}{12 b^2 x^{3/2} \sqrt{b x+c x^2}}-\frac{1}{3 b x^{5/2} \sqrt{b x+c x^2}}","-\frac{35 c^3 \sqrt{x}}{8 b^4 \sqrt{b x+c x^2}}-\frac{35 c^2}{24 b^3 \sqrt{x} \sqrt{b x+c x^2}}+\frac{35 c^3 \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{9/2}}+\frac{7 c}{12 b^2 x^{3/2} \sqrt{b x+c x^2}}-\frac{1}{3 b x^{5/2} \sqrt{b x+c x^2}}",1,"-1/(3*b*x^(5/2)*Sqrt[b*x + c*x^2]) + (7*c)/(12*b^2*x^(3/2)*Sqrt[b*x + c*x^2]) - (35*c^2)/(24*b^3*Sqrt[x]*Sqrt[b*x + c*x^2]) - (35*c^3*Sqrt[x])/(8*b^4*Sqrt[b*x + c*x^2]) + (35*c^3*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*b^(9/2))","A",6,4,19,0.2105,1,"{672, 666, 660, 207}"
112,1,81,0,0.0666968,"\int (d x)^m \left(b x+c x^2\right)^3 \, dx","Int[(d*x)^m*(b*x + c*x^2)^3,x]","\frac{3 b^2 c (d x)^{m+5}}{d^5 (m+5)}+\frac{b^3 (d x)^{m+4}}{d^4 (m+4)}+\frac{3 b c^2 (d x)^{m+6}}{d^6 (m+6)}+\frac{c^3 (d x)^{m+7}}{d^7 (m+7)}","\frac{3 b^2 c (d x)^{m+5}}{d^5 (m+5)}+\frac{b^3 (d x)^{m+4}}{d^4 (m+4)}+\frac{3 b c^2 (d x)^{m+6}}{d^6 (m+6)}+\frac{c^3 (d x)^{m+7}}{d^7 (m+7)}",1,"(b^3*(d*x)^(4 + m))/(d^4*(4 + m)) + (3*b^2*c*(d*x)^(5 + m))/(d^5*(5 + m)) + (3*b*c^2*(d*x)^(6 + m))/(d^6*(6 + m)) + (c^3*(d*x)^(7 + m))/(d^7*(7 + m))","A",3,2,17,0.1176,1,"{647, 43}"
113,1,58,0,0.0408282,"\int (d x)^m \left(b x+c x^2\right)^2 \, dx","Int[(d*x)^m*(b*x + c*x^2)^2,x]","\frac{b^2 (d x)^{m+3}}{d^3 (m+3)}+\frac{2 b c (d x)^{m+4}}{d^4 (m+4)}+\frac{c^2 (d x)^{m+5}}{d^5 (m+5)}","\frac{b^2 (d x)^{m+3}}{d^3 (m+3)}+\frac{2 b c (d x)^{m+4}}{d^4 (m+4)}+\frac{c^2 (d x)^{m+5}}{d^5 (m+5)}",1,"(b^2*(d*x)^(3 + m))/(d^3*(3 + m)) + (2*b*c*(d*x)^(4 + m))/(d^4*(4 + m)) + (c^2*(d*x)^(5 + m))/(d^5*(5 + m))","A",3,2,17,0.1176,1,"{647, 43}"
114,1,35,0,0.0139718,"\int (d x)^m \left(b x+c x^2\right) \, dx","Int[(d*x)^m*(b*x + c*x^2),x]","\frac{b (d x)^{m+2}}{d^2 (m+2)}+\frac{c (d x)^{m+3}}{d^3 (m+3)}","\frac{b (d x)^{m+2}}{d^2 (m+2)}+\frac{c (d x)^{m+3}}{d^3 (m+3)}",1,"(b*(d*x)^(2 + m))/(d^2*(2 + m)) + (c*(d*x)^(3 + m))/(d^3*(3 + m))","A",2,1,15,0.06667,1,"{14}"
115,1,25,0,0.0130205,"\int \frac{(d x)^m}{b x+c x^2} \, dx","Int[(d*x)^m/(b*x + c*x^2),x]","\frac{(d x)^m \, _2F_1\left(1,m;m+1;-\frac{c x}{b}\right)}{b m}","\frac{(d x)^m \, _2F_1\left(1,m;m+1;-\frac{c x}{b}\right)}{b m}",1,"((d*x)^m*Hypergeometric2F1[1, m, 1 + m, -((c*x)/b)])/(b*m)","A",2,2,17,0.1176,1,"{647, 64}"
116,1,33,0,0.0172126,"\int \frac{(d x)^m}{\left(b x+c x^2\right)^2} \, dx","Int[(d*x)^m/(b*x + c*x^2)^2,x]","-\frac{d (d x)^{m-1} \, _2F_1\left(2,m-1;m;-\frac{c x}{b}\right)}{b^2 (1-m)}","-\frac{d (d x)^{m-1} \, _2F_1\left(2,m-1;m;-\frac{c x}{b}\right)}{b^2 (1-m)}",1,"-((d*(d*x)^(-1 + m)*Hypergeometric2F1[2, -1 + m, m, -((c*x)/b)])/(b^2*(1 - m)))","A",2,2,17,0.1176,1,"{647, 64}"
117,1,37,0,0.0189416,"\int \frac{(d x)^m}{\left(b x+c x^2\right)^3} \, dx","Int[(d*x)^m/(b*x + c*x^2)^3,x]","-\frac{d^2 (d x)^{m-2} \, _2F_1\left(3,m-2;m-1;-\frac{c x}{b}\right)}{b^3 (2-m)}","-\frac{d^2 (d x)^{m-2} \, _2F_1\left(3,m-2;m-1;-\frac{c x}{b}\right)}{b^3 (2-m)}",1,"-((d^2*(d*x)^(-2 + m)*Hypergeometric2F1[3, -2 + m, -1 + m, -((c*x)/b)])/(b^3*(2 - m)))","A",2,2,17,0.1176,1,"{647, 64}"
118,1,73,0,0.030488,"\int (d x)^m \left(b x+c x^2\right)^{5/2} \, dx","Int[(d*x)^m*(b*x + c*x^2)^(5/2),x]","\frac{2 b^2 (b+c x) \left(b x+c x^2\right)^{5/2} (d x)^m \left(-\frac{c x}{b}\right)^{-m-\frac{1}{2}} \, _2F_1\left(\frac{7}{2},-m-\frac{5}{2};\frac{9}{2};\frac{c x}{b}+1\right)}{7 c^3 x^2}","\frac{2 b^2 (b+c x) \left(b x+c x^2\right)^{5/2} (d x)^m \left(-\frac{c x}{b}\right)^{-m-\frac{1}{2}} \, _2F_1\left(\frac{7}{2},-m-\frac{5}{2};\frac{9}{2};\frac{c x}{b}+1\right)}{7 c^3 x^2}",1,"(2*b^2*(-((c*x)/b))^(-1/2 - m)*(d*x)^m*(b + c*x)*(b*x + c*x^2)^(5/2)*Hypergeometric2F1[7/2, -5/2 - m, 9/2, 1 + (c*x)/b])/(7*c^3*x^2)","A",3,3,19,0.1579,1,"{674, 67, 65}"
119,1,71,0,0.0294293,"\int (d x)^m \left(b x+c x^2\right)^{3/2} \, dx","Int[(d*x)^m*(b*x + c*x^2)^(3/2),x]","-\frac{2 b (b+c x) \left(b x+c x^2\right)^{3/2} (d x)^m \left(-\frac{c x}{b}\right)^{-m-\frac{1}{2}} \, _2F_1\left(\frac{5}{2},-m-\frac{3}{2};\frac{7}{2};\frac{c x}{b}+1\right)}{5 c^2 x}","-\frac{2 b (b+c x) \left(b x+c x^2\right)^{3/2} (d x)^m \left(-\frac{c x}{b}\right)^{-m-\frac{1}{2}} \, _2F_1\left(\frac{5}{2},-m-\frac{3}{2};\frac{7}{2};\frac{c x}{b}+1\right)}{5 c^2 x}",1,"(-2*b*(-((c*x)/b))^(-1/2 - m)*(d*x)^m*(b + c*x)*(b*x + c*x^2)^(3/2)*Hypergeometric2F1[5/2, -3/2 - m, 7/2, 1 + (c*x)/b])/(5*c^2*x)","A",3,3,19,0.1579,1,"{674, 67, 65}"
120,1,67,0,0.0251237,"\int (d x)^m \sqrt{b x+c x^2} \, dx","Int[(d*x)^m*Sqrt[b*x + c*x^2],x]","\frac{2 (b+c x) \sqrt{b x+c x^2} (d x)^m \left(-\frac{c x}{b}\right)^{-m-\frac{1}{2}} \, _2F_1\left(\frac{3}{2},-m-\frac{1}{2};\frac{5}{2};\frac{c x}{b}+1\right)}{3 c}","\frac{2 (b+c x) \sqrt{b x+c x^2} (d x)^m \left(-\frac{c x}{b}\right)^{-m-\frac{1}{2}} \, _2F_1\left(\frac{3}{2},-m-\frac{1}{2};\frac{5}{2};\frac{c x}{b}+1\right)}{3 c}",1,"(2*(-((c*x)/b))^(-1/2 - m)*(d*x)^m*(b + c*x)*Sqrt[b*x + c*x^2]*Hypergeometric2F1[3/2, -1/2 - m, 5/2, 1 + (c*x)/b])/(3*c)","A",3,3,19,0.1579,1,"{674, 67, 65}"
121,1,65,0,0.0253687,"\int \frac{(d x)^m}{\sqrt{b x+c x^2}} \, dx","Int[(d*x)^m/Sqrt[b*x + c*x^2],x]","\frac{2 (b+c x) (d x)^m \left(-\frac{c x}{b}\right)^{\frac{1}{2}-m} \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{c x}{b}+1\right)}{c \sqrt{b x+c x^2}}","\frac{2 (b+c x) (d x)^m \left(-\frac{c x}{b}\right)^{\frac{1}{2}-m} \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{c x}{b}+1\right)}{c \sqrt{b x+c x^2}}",1,"(2*(-((c*x)/b))^(1/2 - m)*(d*x)^m*(b + c*x)*Hypergeometric2F1[1/2, 1/2 - m, 3/2, 1 + (c*x)/b])/(c*Sqrt[b*x + c*x^2])","A",3,3,19,0.1579,1,"{674, 67, 65}"
122,1,66,0,0.0265839,"\int \frac{(d x)^m}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(d*x)^m/(b*x + c*x^2)^(3/2),x]","\frac{2 x (b+c x) (d x)^m \left(-\frac{c x}{b}\right)^{\frac{1}{2}-m} \, _2F_1\left(-\frac{1}{2},\frac{3}{2}-m;\frac{1}{2};\frac{c x}{b}+1\right)}{b \left(b x+c x^2\right)^{3/2}}","\frac{2 x (b+c x) (d x)^m \left(-\frac{c x}{b}\right)^{\frac{1}{2}-m} \, _2F_1\left(-\frac{1}{2},\frac{3}{2}-m;\frac{1}{2};\frac{c x}{b}+1\right)}{b \left(b x+c x^2\right)^{3/2}}",1,"(2*x*(-((c*x)/b))^(1/2 - m)*(d*x)^m*(b + c*x)*Hypergeometric2F1[-1/2, 3/2 - m, 1/2, 1 + (c*x)/b])/(b*(b*x + c*x^2)^(3/2))","A",3,3,19,0.1579,1,"{674, 67, 65}"
123,1,71,0,0.0281655,"\int \frac{(d x)^m}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(d*x)^m/(b*x + c*x^2)^(5/2),x]","-\frac{2 c x^2 (b+c x) (d x)^m \left(-\frac{c x}{b}\right)^{\frac{1}{2}-m} \, _2F_1\left(-\frac{3}{2},\frac{5}{2}-m;-\frac{1}{2};\frac{c x}{b}+1\right)}{3 b^2 \left(b x+c x^2\right)^{5/2}}","-\frac{2 c x^2 (b+c x) (d x)^m \left(-\frac{c x}{b}\right)^{\frac{1}{2}-m} \, _2F_1\left(-\frac{3}{2},\frac{5}{2}-m;-\frac{1}{2};\frac{c x}{b}+1\right)}{3 b^2 \left(b x+c x^2\right)^{5/2}}",1,"(-2*c*x^2*(-((c*x)/b))^(1/2 - m)*(d*x)^m*(b + c*x)*Hypergeometric2F1[-3/2, 5/2 - m, -1/2, 1 + (c*x)/b])/(3*b^2*(b*x + c*x^2)^(5/2))","A",3,3,19,0.1579,1,"{674, 67, 65}"
124,1,55,0,0.0232367,"\int (d x)^m \left(b x+c x^2\right)^p \, dx","Int[(d*x)^m*(b*x + c*x^2)^p,x]","\frac{x (d x)^m \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,m+p+1;m+p+2;-\frac{c x}{b}\right)}{m+p+1}","\frac{x (d x)^m \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,m+p+1;m+p+2;-\frac{c x}{b}\right)}{m+p+1}",1,"(x*(d*x)^m*(b*x + c*x^2)^p*Hypergeometric2F1[-p, 1 + m + p, 2 + m + p, -((c*x)/b)])/((1 + m + p)*(1 + (c*x)/b)^p)","A",3,3,17,0.1765,1,"{674, 66, 64}"
125,1,49,0,0.0204716,"\int x^3 \left(b x+c x^2\right)^p \, dx","Int[x^3*(b*x + c*x^2)^p,x]","\frac{x^4 \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+4;p+5;-\frac{c x}{b}\right)}{p+4}","\frac{x^4 \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+4;p+5;-\frac{c x}{b}\right)}{p+4}",1,"(x^4*(b*x + c*x^2)^p*Hypergeometric2F1[-p, 4 + p, 5 + p, -((c*x)/b)])/((4 + p)*(1 + (c*x)/b)^p)","A",3,3,15,0.2000,1,"{674, 66, 64}"
126,1,49,0,0.0203876,"\int x^2 \left(b x+c x^2\right)^p \, dx","Int[x^2*(b*x + c*x^2)^p,x]","\frac{x^3 \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+3;p+4;-\frac{c x}{b}\right)}{p+3}","\frac{x^3 \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+3;p+4;-\frac{c x}{b}\right)}{p+3}",1,"(x^3*(b*x + c*x^2)^p*Hypergeometric2F1[-p, 3 + p, 4 + p, -((c*x)/b)])/((3 + p)*(1 + (c*x)/b)^p)","A",3,3,15,0.2000,1,"{674, 66, 64}"
127,1,83,0,0.02233,"\int x \left(b x+c x^2\right)^p \, dx","Int[x*(b*x + c*x^2)^p,x]","\frac{\left(b x+c x^2\right)^{p+1} \left(-\frac{c x}{b}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{b+c x}{b}\right)}{2 c (p+1)}+\frac{\left(b x+c x^2\right)^{p+1}}{2 c (p+1)}","\frac{x^2 \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+2;p+3;-\frac{c x}{b}\right)}{p+2}",1,"(b*x + c*x^2)^(1 + p)/(2*c*(1 + p)) + ((-((c*x)/b))^(-1 - p)*(b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + c*x)/b])/(2*c*(1 + p))","A",2,2,13,0.1538,1,"{640, 624}"
128,1,42,0,0.0188719,"\int \frac{\left(b x+c x^2\right)^p}{x} \, dx","Int[(b*x + c*x^2)^p/x,x]","\frac{\left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p;p+1;-\frac{c x}{b}\right)}{p}","\frac{\left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p;p+1;-\frac{c x}{b}\right)}{p}",1,"((b*x + c*x^2)^p*Hypergeometric2F1[-p, p, 1 + p, -((c*x)/b)])/(p*(1 + (c*x)/b)^p)","A",3,3,15,0.2000,1,"{674, 66, 64}"
129,1,50,0,0.0218345,"\int \frac{\left(b x+c x^2\right)^p}{x^2} \, dx","Int[(b*x + c*x^2)^p/x^2,x]","-\frac{\left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(p-1,-p;p;-\frac{c x}{b}\right)}{(1-p) x}","-\frac{\left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(p-1,-p;p;-\frac{c x}{b}\right)}{(1-p) x}",1,"-(((b*x + c*x^2)^p*Hypergeometric2F1[-1 + p, -p, p, -((c*x)/b)])/((1 - p)*x*(1 + (c*x)/b)^p))","A",3,3,15,0.2000,1,"{674, 66, 64}"
130,1,52,0,0.0223019,"\int \frac{\left(b x+c x^2\right)^p}{x^3} \, dx","Int[(b*x + c*x^2)^p/x^3,x]","-\frac{\left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(p-2,-p;p-1;-\frac{c x}{b}\right)}{(2-p) x^2}","-\frac{\left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(p-2,-p;p-1;-\frac{c x}{b}\right)}{(2-p) x^2}",1,"-(((b*x + c*x^2)^p*Hypergeometric2F1[-2 + p, -p, -1 + p, -((c*x)/b)])/((2 - p)*x^2*(1 + (c*x)/b)^p))","A",3,3,15,0.2000,1,"{674, 66, 64}"
131,1,61,0,0.0246532,"\int (d x)^{5/2} \left(b x+c x^2\right)^p \, dx","Int[(d*x)^(5/2)*(b*x + c*x^2)^p,x]","\frac{2 x (d x)^{5/2} \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+\frac{7}{2};p+\frac{9}{2};-\frac{c x}{b}\right)}{2 p+7}","\frac{2 x (d x)^{5/2} \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+\frac{7}{2};p+\frac{9}{2};-\frac{c x}{b}\right)}{2 p+7}",1,"(2*x*(d*x)^(5/2)*(b*x + c*x^2)^p*Hypergeometric2F1[-p, 7/2 + p, 9/2 + p, -((c*x)/b)])/((7 + 2*p)*(1 + (c*x)/b)^p)","A",3,3,19,0.1579,1,"{674, 66, 64}"
132,1,61,0,0.0243567,"\int (d x)^{3/2} \left(b x+c x^2\right)^p \, dx","Int[(d*x)^(3/2)*(b*x + c*x^2)^p,x]","\frac{2 x (d x)^{3/2} \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+\frac{5}{2};p+\frac{7}{2};-\frac{c x}{b}\right)}{2 p+5}","\frac{2 x (d x)^{3/2} \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+\frac{5}{2};p+\frac{7}{2};-\frac{c x}{b}\right)}{2 p+5}",1,"(2*x*(d*x)^(3/2)*(b*x + c*x^2)^p*Hypergeometric2F1[-p, 5/2 + p, 7/2 + p, -((c*x)/b)])/((5 + 2*p)*(1 + (c*x)/b)^p)","A",3,3,19,0.1579,1,"{674, 66, 64}"
133,1,61,0,0.0236347,"\int \sqrt{d x} \left(b x+c x^2\right)^p \, dx","Int[Sqrt[d*x]*(b*x + c*x^2)^p,x]","\frac{2 x \sqrt{d x} \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+\frac{3}{2};p+\frac{5}{2};-\frac{c x}{b}\right)}{2 p+3}","\frac{2 x \sqrt{d x} \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+\frac{3}{2};p+\frac{5}{2};-\frac{c x}{b}\right)}{2 p+3}",1,"(2*x*Sqrt[d*x]*(b*x + c*x^2)^p*Hypergeometric2F1[-p, 3/2 + p, 5/2 + p, -((c*x)/b)])/((3 + 2*p)*(1 + (c*x)/b)^p)","A",3,3,19,0.1579,1,"{674, 66, 64}"
134,1,61,0,0.0234973,"\int \frac{\left(b x+c x^2\right)^p}{\sqrt{d x}} \, dx","Int[(b*x + c*x^2)^p/Sqrt[d*x],x]","\frac{2 x \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+\frac{1}{2};p+\frac{3}{2};-\frac{c x}{b}\right)}{(2 p+1) \sqrt{d x}}","\frac{2 x \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(-p,p+\frac{1}{2};p+\frac{3}{2};-\frac{c x}{b}\right)}{(2 p+1) \sqrt{d x}}",1,"(2*x*(b*x + c*x^2)^p*Hypergeometric2F1[-p, 1/2 + p, 3/2 + p, -((c*x)/b)])/((1 + 2*p)*Sqrt[d*x]*(1 + (c*x)/b)^p)","A",3,3,19,0.1579,1,"{674, 66, 64}"
135,1,61,0,0.0265773,"\int \frac{\left(b x+c x^2\right)^p}{(d x)^{3/2}} \, dx","Int[(b*x + c*x^2)^p/(d*x)^(3/2),x]","-\frac{2 x \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(p-\frac{1}{2},-p;p+\frac{1}{2};-\frac{c x}{b}\right)}{(1-2 p) (d x)^{3/2}}","-\frac{2 x \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(p-\frac{1}{2},-p;p+\frac{1}{2};-\frac{c x}{b}\right)}{(1-2 p) (d x)^{3/2}}",1,"(-2*x*(b*x + c*x^2)^p*Hypergeometric2F1[-1/2 + p, -p, 1/2 + p, -((c*x)/b)])/((1 - 2*p)*(d*x)^(3/2)*(1 + (c*x)/b)^p)","A",3,3,19,0.1579,1,"{674, 66, 64}"
136,1,61,0,0.0258183,"\int \frac{\left(b x+c x^2\right)^p}{(d x)^{5/2}} \, dx","Int[(b*x + c*x^2)^p/(d*x)^(5/2),x]","-\frac{2 x \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(p-\frac{3}{2},-p;p-\frac{1}{2};-\frac{c x}{b}\right)}{(3-2 p) (d x)^{5/2}}","-\frac{2 x \left(\frac{c x}{b}+1\right)^{-p} \left(b x+c x^2\right)^p \, _2F_1\left(p-\frac{3}{2},-p;p-\frac{1}{2};-\frac{c x}{b}\right)}{(3-2 p) (d x)^{5/2}}",1,"(-2*x*(b*x + c*x^2)^p*Hypergeometric2F1[-3/2 + p, -p, -1/2 + p, -((c*x)/b)])/((3 - 2*p)*(d*x)^(5/2)*(1 + (c*x)/b)^p)","A",3,3,19,0.1579,1,"{674, 66, 64}"
137,1,71,0,0.0256565,"\int x^4 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}+\frac{a x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}","\frac{b x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}+\frac{a x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}",1,"(a*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (b*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
138,1,71,0,0.0235502,"\int x^3 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{a x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}","\frac{b x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{a x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}",1,"(a*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (b*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
139,1,71,0,0.0215479,"\int x^2 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{a x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}","\frac{b x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{a x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}",1,"(a*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (b*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
140,1,61,0,0.0152343,"\int x \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b^2}-\frac{a (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 b^2}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b^2}-\frac{a (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 b^2}",1,"-(a*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^2) + (a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(3*b^2)","A",2,2,22,0.09091,1,"{640, 609}"
141,1,32,0,0.0058244,"\int \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 b}","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 b}",1,"((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b)","A",1,1,20,0.05000,1,"{609}"
142,1,62,0,0.0166675,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{x} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/x,x]","\frac{b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{a \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","\frac{b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{a \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"(b*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (a*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
143,1,65,0,0.018244,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{x^2} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/x^2,x]","\frac{b \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}-\frac{a \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}","\frac{b \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}-\frac{a \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}",1,"-((a*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x))) + (b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
144,1,35,0,0.0130166,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{x^3} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/x^3,x]","-\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 a x^2}","-\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 a x^2}",1,"-((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*a*x^2)","A",2,2,24,0.08333,1,"{646, 37}"
145,1,71,0,0.0186558,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{x^4} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/x^4,x]","-\frac{a \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}","-\frac{a \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}",1,"-(a*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
146,1,71,0,0.0185848,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{x^5} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/x^5,x]","-\frac{a \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}","-\frac{a \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}",1,"-(a*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
147,1,71,0,0.0233714,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{x^6} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/x^6,x]","-\frac{a \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}","-\frac{a \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}",1,"-(a*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
148,1,151,0,0.0457595,"\int x^5 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^5*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^3 x^9 \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{3 a b^2 x^8 \sqrt{a^2+2 a b x+b^2 x^2}}{8 (a+b x)}+\frac{3 a^2 b x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{a^3 x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}","\frac{b^3 x^9 \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{3 a b^2 x^8 \sqrt{a^2+2 a b x+b^2 x^2}}{8 (a+b x)}+\frac{3 a^2 b x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{a^3 x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}",1,"(a^3*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x)) + (3*a^2*b*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (3*a*b^2*x^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*(a + b*x)) + (b^3*x^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
149,1,151,0,0.0415061,"\int x^4 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^4*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^3 x^8 \sqrt{a^2+2 a b x+b^2 x^2}}{8 (a+b x)}+\frac{3 a b^2 x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{a^2 b x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{a^3 x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}","\frac{b^3 x^8 \sqrt{a^2+2 a b x+b^2 x^2}}{8 (a+b x)}+\frac{3 a b^2 x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{a^2 b x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{a^3 x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}",1,"(a^3*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (a^2*b*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (3*a*b^2*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (b^3*x^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
150,1,151,0,0.0413578,"\int x^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^3 x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{a b^2 x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{3 a^2 b x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{a^3 x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}","\frac{b^3 x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{a b^2 x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{3 a^2 b x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{a^3 x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}",1,"(a^3*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (3*a^2*b*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (a*b^2*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (b^3*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
151,1,107,0,0.0310885,"\int x^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^3}-\frac{2 a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{5 b^3}+\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3}{4 b^3}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{6 b^3}-\frac{2 a \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b^3}+\frac{a^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{4 b^3}",1,"(a^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^3) - (2*a*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^3) + ((a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^3)","A",2,1,24,0.04167,1,"{645}"
152,1,61,0,0.014963,"\int x \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b^2}-\frac{a (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{4 b^2}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b^2}-\frac{a (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{4 b^2}",1,"-(a*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b^2) + (a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(5*b^2)","A",2,2,22,0.09091,1,"{640, 609}"
153,1,32,0,0.0048205,"\int \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{4 b}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{4 b}",1,"((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b)","A",1,1,20,0.05000,1,"{609}"
154,1,143,0,0.0341437,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x,x]","\frac{3 a^2 b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{3 a b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{a^3 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","\frac{3 a^2 b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{3 a b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{a^3 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"(3*a^2*b*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (3*a*b^2*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (b^3*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
155,1,142,0,0.0344887,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^2,x]","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{3 a b^2 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{b^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{3 a^2 b \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{3 a b^2 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{b^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{3 a^2 b \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-((a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x))) + (3*a*b^2*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (b^3*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (3*a^2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
156,1,141,0,0.0355548,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^3} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^3,x]","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{3 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^3 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{3 a b^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{3 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^3 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{3 a b^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (b^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (3*a*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
157,1,145,0,0.0344629,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^4} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^4,x]","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{3 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{3 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^3 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{3 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{3 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^3 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
158,1,37,0,0.0136598,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^5} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^5,x]","-\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 a x^4}","-\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 a x^4}",1,"-((a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*a*x^4)","A",2,2,24,0.08333,1,"{646, 37}"
159,1,76,0,0.0234828,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^6} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^6,x]","\frac{b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{20 a^2 x^4}-\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{5 a x^5}","\frac{b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{20 a^2 x^4}-\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{5 a x^5}",1,"-((a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*a*x^5) + (b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(20*a^2*x^4)","A",3,3,24,0.1250,1,"{646, 45, 37}"
160,1,151,0,0.0347421,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^7} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^7,x]","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}-\frac{3 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{3 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}-\frac{3 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{3 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
161,1,151,0,0.0372512,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^8} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^8,x]","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^6 (a+b x)}-\frac{3 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^6 (a+b x)}-\frac{3 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (a^2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^6*(a + b*x)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
162,1,151,0,0.0348462,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^9} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^9,x]","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{8 x^8 (a+b x)}-\frac{3 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^6 (a+b x)}-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}","-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}{8 x^8 (a+b x)}-\frac{3 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^6 (a+b x)}-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (a*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^6*(a + b*x)) - (b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
163,1,231,0,0.061848,"\int x^5 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^5*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{b^5 x^{11} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}+\frac{a b^4 x^{10} \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{10 a^2 b^3 x^9 \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{5 a^3 b^2 x^8 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{5 a^4 b x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{a^5 x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}","\frac{b^5 x^{11} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}+\frac{a b^4 x^{10} \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{10 a^2 b^3 x^9 \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{5 a^3 b^2 x^8 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{5 a^4 b x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{a^5 x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}",1,"(a^5*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x)) + (5*a^4*b*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (5*a^3*b^2*x^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (10*a^2*b^3*x^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (a*b^4*x^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (b^5*x^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
164,1,181,0,0.051446,"\int x^4 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^4*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^5}-\frac{4 a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^5}+\frac{3 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{4 b^5}-\frac{4 a^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^5}+\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^5}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^5}-\frac{4 a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^5}+\frac{3 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{4 b^5}-\frac{4 a^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^5}+\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^5}",1,"(a^4*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^5) - (4*a^3*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^5) + (3*a^2*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^5) - (4*a*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^5) + ((a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*b^5)","A",2,1,24,0.04167,1,"{645}"
165,1,144,0,0.0519569,"\int x^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^4}-\frac{3 a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^4}+\frac{3 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^4}-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^4}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^4}-\frac{3 a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^4}+\frac{3 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^4}-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^4}",1,"-(a^3*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^4) + (3*a^2*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^4) - (3*a*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^4) + ((a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^4)","A",3,2,24,0.08333,1,"{646, 43}"
166,1,107,0,0.0409676,"\int x^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^3}-\frac{2 a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^3}+\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^3}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^3}-\frac{2 a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^3}+\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^3}",1,"(a^2*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^3) - (2*a*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^3) + ((a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^3)","A",3,2,24,0.08333,1,"{646, 43}"
167,1,61,0,0.0145801,"\int x \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b^2}-\frac{a (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{6 b^2}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b^2}-\frac{a (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{6 b^2}",1,"-(a*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b^2) + (a^2 + 2*a*b*x + b^2*x^2)^(7/2)/(7*b^2)","A",2,2,22,0.09091,1,"{640, 609}"
168,1,32,0,0.0053773,"\int \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{6 b}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{6 b}",1,"((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b)","A",1,1,20,0.05000,1,"{609}"
169,1,221,0,0.0493987,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x,x]","\frac{5 a^4 b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a^3 b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{10 a^2 b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{5 a b^4 x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{b^5 x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{a^5 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","\frac{5 a^4 b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a^3 b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{10 a^2 b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{5 a b^4 x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{b^5 x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{a^5 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"(5*a^4*b*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a^3*b^2*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (10*a^2*b^3*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (5*a*b^4*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (b^5*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
170,1,220,0,0.0504543,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^2,x]","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{10 a^3 b^2 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a^2 b^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a b^4 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{b^5 x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{5 a^4 b \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{10 a^3 b^2 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a^2 b^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a b^4 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{b^5 x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{5 a^4 b \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-((a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x))) + (10*a^3*b^2*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a^2*b^3*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a*b^4*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (b^5*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (5*a^4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
171,1,222,0,0.0509013,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^3} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^3,x]","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{10 a^2 b^3 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a b^4 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{b^5 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{10 a^3 b^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{10 a^2 b^3 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a b^4 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{b^5 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{10 a^3 b^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (10*a^2*b^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a*b^4*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (b^5*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
172,1,222,0,0.0532879,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^4} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^4,x]","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{5 a b^4 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{b^5 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{10 a^2 b^3 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{5 a b^4 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{b^5 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{10 a^2 b^3 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (5*a*b^4*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (b^5*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
173,1,219,0,0.0528697,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^5} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^5,x]","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{x^2 (a+b x)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^5 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a b^4 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{x^2 (a+b x)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^5 x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a b^4 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x^2*(a + b*x)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (b^5*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
174,1,223,0,0.0532962,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^6} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^6,x]","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{x^2 (a+b x)}-\frac{5 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^5 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{x^2 (a+b x)}-\frac{5 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^5 \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x^2*(a + b*x)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,24,0.08333,1,"{646, 43}"
175,1,37,0,0.0137379,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^7} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^7,x]","-\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 a x^6}","-\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 a x^6}",1,"-((a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*a*x^6)","A",2,2,24,0.08333,1,"{646, 37}"
176,1,76,0,0.0230251,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^8} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^8,x]","\frac{b (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{42 a^2 x^6}-\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{7 a x^7}","\frac{b (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{42 a^2 x^6}-\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{7 a x^7}",1,"-((a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*a*x^7) + (b*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(42*a^2*x^6)","A",3,3,24,0.1250,1,"{646, 45, 37}"
177,1,116,0,0.0329352,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^9} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^9,x]","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{168 a^3 x^6}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{28 a^2 x^7}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{8 a x^8}","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{168 a^3 x^6}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{28 a^2 x^7}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{8 a x^8}",1,"-((a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*a*x^8) + (b*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(28*a^2*x^7) - (b^2*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(168*a^3*x^6)","A",4,3,24,0.1250,1,"{646, 45, 37}"
178,1,229,0,0.0529566,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{10}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^10,x]","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{8 x^8 (a+b x)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^6 (a+b x)}-\frac{a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{x^5 (a+b x)}-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{8 x^8 (a+b x)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^6 (a+b x)}-\frac{a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{x^5 (a+b x)}-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^6*(a + b*x)) - (a*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x^5*(a + b*x)) - (b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
179,1,231,0,0.0528161,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{11}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^11,x]","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{10 x^{10} (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^8 (a+b x)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{5 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{10 x^{10} (a+b x)}-\frac{5 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^8 (a+b x)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{5 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*x^10*(a + b*x)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^8*(a + b*x)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x)) - (b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
180,1,231,0,0.0560486,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{12}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^12,x]","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{11 x^{11} (a+b x)}-\frac{a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^{10} (a+b x)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^8 (a+b x)}-\frac{5 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}","-\frac{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}{11 x^{11} (a+b x)}-\frac{a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^{10} (a+b x)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^8 (a+b x)}-\frac{5 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*x^11*(a + b*x)) - (a^4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^10*(a + b*x)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^8*(a + b*x)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x))","A",3,2,24,0.08333,1,"{646, 43}"
181,1,182,0,0.0616439,"\int \frac{x^4}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[x^4/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{a^3 x (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x^3 (a+b x)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^4 (a+b x)}{4 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^4 (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a^3 x (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x^3 (a+b x)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^4 (a+b x)}{4 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^4 (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((a^3*x*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + (a^2*x^2*(a + b*x))/(2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a*x^3*(a + b*x))/(3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (x^4*(a + b*x))/(4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (a^4*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
182,1,144,0,0.0466961,"\int \frac{x^3}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[x^3/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{a^2 x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x^2 (a+b x)}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^3 (a+b x)}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^3 (a+b x) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{a^2 x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x^2 (a+b x)}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^3 (a+b x)}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^3 (a+b x) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(a^2*x*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a*x^2*(a + b*x))/(2*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (x^3*(a + b*x))/(3*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a^3*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
183,1,106,0,0.0371791,"\int \frac{x^2}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[x^2/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{a x (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^2 (a+b x)}{2 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 (a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a x (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^2 (a+b x)}{2 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 (a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((a*x*(a + b*x))/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + (x^2*(a + b*x))/(2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (a^2*(a + b*x)*Log[a + b*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
184,1,62,0,0.0172623,"\int \frac{x}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[x/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2}}{b^2}-\frac{a (a+b x) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{\sqrt{a^2+2 a b x+b^2 x^2}}{b^2}-\frac{a (a+b x) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"Sqrt[a^2 + 2*a*b*x + b^2*x^2]/b^2 - (a*(a + b*x)*Log[a + b*x])/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,22,0.1364,1,"{640, 608, 31}"
185,1,35,0,0.0075376,"\int \frac{1}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \log (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) \log (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*Log[a + b*x])/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",2,2,20,0.1000,1,"{608, 31}"
186,1,68,0,0.0215129,"\int \frac{1}{x \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/(x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{\log (x) (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{\log (x) (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*Log[x])/(a*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((a + b*x)*Log[a + b*x])/(a*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,24,0.1667,1,"{646, 36, 29, 31}"
187,1,103,0,0.0350412,"\int \frac{1}{x^2 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/(x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{a+b x}{a x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b \log (x) (a+b x)}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b (a+b x) \log (a+b x)}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a+b x}{a x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b \log (x) (a+b x)}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b (a+b x) \log (a+b x)}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((a + b*x)/(a*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (b*(a + b*x)*Log[x])/(a^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(a + b*x)*Log[a + b*x])/(a^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 44}"
188,1,142,0,0.0447885,"\int \frac{1}{x^3 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/(x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{b (a+b x)}{a^2 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{2 a x^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^2 \log (x) (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b^2 (a+b x) \log (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{b (a+b x)}{a^2 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{2 a x^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^2 \log (x) (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b^2 (a+b x) \log (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(a + b*x)/(2*a*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(a + b*x))/(a^2*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^2*(a + b*x)*Log[x])/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b^2*(a + b*x)*Log[a + b*x])/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 44}"
189,1,181,0,0.0522904,"\int \frac{1}{x^4 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/(x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{b^2 (a+b x)}{a^3 x \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b (a+b x)}{2 a^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{3 a x^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b^3 \log (x) (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^3 (a+b x) \log (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{b^2 (a+b x)}{a^3 x \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b (a+b x)}{2 a^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{3 a x^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b^3 \log (x) (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^3 (a+b x) \log (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(a + b*x)/(3*a*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(a + b*x))/(2*a^2*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b^2*(a + b*x))/(a^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b^3*(a + b*x)*Log[x])/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^3*(a + b*x)*Log[a + b*x])/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 44}"
190,1,172,0,0.0727534,"\int \frac{x^4}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[x^4/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{a^4}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 a^3}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a x (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{6 a^2 (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a^4}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 a^3}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a x (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{6 a^2 (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(4*a^3)/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - a^4/(2*b^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*a*x*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (x^2*(a + b*x))/(2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (6*a^2*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
191,1,133,0,0.0580191,"\int \frac{x^3}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[x^3/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{a^3}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a (a+b x) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{a^3}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a (a+b x) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-3*a^2)/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + a^3/(2*b^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (x*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*a*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
192,1,99,0,0.0447602,"\int \frac{x^2}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[x^2/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{a^2}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a^2}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*a)/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - a^2/(2*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((a + b*x)*Log[a + b*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
193,1,61,0,0.0146494,"\int \frac{x}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[x/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{a}{2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{1}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{a}{2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{1}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(1/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + a/(2*b^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",2,2,22,0.09091,1,"{640, 607}"
194,1,34,0,0.0043055,"\int \frac{1}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(-3/2),x]","-\frac{1}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{1}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-1/(2*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",1,1,20,0.05000,1,"{607}"
195,1,126,0,0.0579414,"\int \frac{1}{x \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/(x*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{1}{2 a (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\log (x) (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{1}{2 a (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\log (x) (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"1/(a^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + 1/(2*a*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((a + b*x)*Log[x])/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((a + b*x)*Log[a + b*x])/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 44}"
196,1,165,0,0.0675738,"\int \frac{1}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{b}{2 a^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 b}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{a^3 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 b \log (x) (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 b (a+b x) \log (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{b}{2 a^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 b}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{a^3 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 b \log (x) (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 b (a+b x) \log (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*b)/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - b/(2*a^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a + b*x)/(a^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*b*(a + b*x)*Log[x])/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b*(a + b*x)*Log[a + b*x])/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 44}"
197,1,209,0,0.0795661,"\int \frac{1}{x^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{b^2}{2 a^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 b^2}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 b (a+b x)}{a^4 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{2 a^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{6 b^2 \log (x) (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{6 b^2 (a+b x) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{b^2}{2 a^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 b^2}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 b (a+b x)}{a^4 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{2 a^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{6 b^2 \log (x) (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{6 b^2 (a+b x) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(3*b^2)/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + b^2/(2*a^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a + b*x)/(2*a^3*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b*(a + b*x))/(a^4*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (6*b^2*(a + b*x)*Log[x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (6*b^2*(a + b*x)*Log[a + b*x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 44}"
198,1,244,0,0.1174507,"\int \frac{x^6}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[x^6/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{a^6}{4 b^7 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^5}{b^7 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{15 a^4}{2 b^7 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{20 a^3}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 a x (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^2 (a+b x)}{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{15 a^2 (a+b x) \log (a+b x)}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a^6}{4 b^7 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^5}{b^7 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{15 a^4}{2 b^7 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{20 a^3}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 a x (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^2 (a+b x)}{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{15 a^2 (a+b x) \log (a+b x)}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(20*a^3)/(b^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - a^6/(4*b^7*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*a^5)/(b^7*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (15*a^4)/(2*b^7*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*a*x*(a + b*x))/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (x^2*(a + b*x))/(2*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (15*a^2*(a + b*x)*Log[a + b*x])/(b^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
199,1,205,0,0.0930691,"\int \frac{x^5}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[x^5/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{a^5}{4 b^6 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 a^4}{3 b^6 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 a^3}{b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{10 a^2}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 a (a+b x) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{a^5}{4 b^6 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 a^4}{3 b^6 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 a^3}{b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{10 a^2}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 a (a+b x) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-10*a^2)/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + a^5/(4*b^6*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*a^4)/(3*b^6*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*a^3)/(b^6*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (x*(a + b*x))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*a*(a + b*x)*Log[a + b*x])/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
200,1,171,0,0.0781741,"\int \frac{x^4}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[x^4/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{a^4}{4 b^5 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 a^3}{3 b^5 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a^2}{b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 a}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a^4}{4 b^5 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 a^3}{3 b^5 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a^2}{b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 a}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(4*a)/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - a^4/(4*b^5*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (4*a^3)/(3*b^5*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*a^2)/(b^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
201,1,37,0,0.0161654,"\int \frac{x^3}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[x^3/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^4}{4 a (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^4}{4 a (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"x^4/(4*a*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",2,2,24,0.08333,1,"{646, 37}"
202,1,107,0,0.0478855,"\int \frac{x^2}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[x^2/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{a^2}{4 b^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a}{3 b^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{1}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a^2}{4 b^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a}{3 b^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{1}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-a^2/(4*b^3*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*a)/(3*b^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(2*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 43}"
203,1,63,0,0.0145728,"\int \frac{x}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[x/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{a}{4 b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{1}{3 b^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","\frac{a}{4 b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{1}{3 b^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-1/(3*b^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) + a/(4*b^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))","A",2,2,22,0.09091,1,"{640, 607}"
204,1,34,0,0.0043447,"\int \frac{1}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(-5/2),x]","-\frac{1}{4 b (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","-\frac{1}{4 b (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-1/(4*b*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))","A",1,1,20,0.05000,1,"{607}"
205,1,194,0,0.0863049,"\int \frac{1}{x \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/(x*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{1}{2 a^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1}{3 a^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1}{4 a (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\log (x) (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{1}{2 a^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1}{3 a^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1}{4 a (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\log (x) (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"1/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + 1/(4*a*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + 1/(3*a^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + 1/(2*a^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((a + b*x)*Log[x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((a + b*x)*Log[a + b*x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 44}"
206,1,235,0,0.1020172,"\int \frac{1}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{3 b}{2 a^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 b}{3 a^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b}{4 a^2 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{4 b}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{a^5 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 b \log (x) (a+b x)}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 b (a+b x) \log (a+b x)}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{3 b}{2 a^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 b}{3 a^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b}{4 a^2 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{4 b}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{a^5 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 b \log (x) (a+b x)}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 b (a+b x) \log (a+b x)}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-4*b)/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - b/(4*a^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*b)/(3*a^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*b)/(2*a^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a + b*x)/(a^5*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*b*(a + b*x)*Log[x])/(a^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*b*(a + b*x)*Log[a + b*x])/(a^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 44}"
207,1,278,0,0.1140665,"\int \frac{1}{x^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{3 b^2}{a^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^2}{a^4 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^2}{4 a^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{10 b^2}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 b (a+b x)}{a^6 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{2 a^5 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{15 b^2 \log (x) (a+b x)}{a^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{15 b^2 (a+b x) \log (a+b x)}{a^7 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{3 b^2}{a^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^2}{a^4 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^2}{4 a^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{10 b^2}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 b (a+b x)}{a^6 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a+b x}{2 a^5 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{15 b^2 \log (x) (a+b x)}{a^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{15 b^2 (a+b x) \log (a+b x)}{a^7 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(10*b^2)/(a^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + b^2/(4*a^3*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + b^2/(a^4*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b^2)/(a^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a + b*x)/(2*a^5*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*b*(a + b*x))/(a^6*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (15*b^2*(a + b*x)*Log[x])/(a^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (15*b^2*(a + b*x)*Log[a + b*x])/(a^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,24,0.08333,1,"{646, 44}"
208,1,42,0,0.0088291,"\int x \left(9+12 x+4 x^2\right)^{5/2} \, dx","Int[x*(9 + 12*x + 4*x^2)^(5/2),x]","\frac{1}{28} \left(4 x^2+12 x+9\right)^{7/2}-\frac{1}{8} (2 x+3) \left(4 x^2+12 x+9\right)^{5/2}","\frac{1}{28} \left(4 x^2+12 x+9\right)^{7/2}-\frac{1}{8} (2 x+3) \left(4 x^2+12 x+9\right)^{5/2}",1,"-((3 + 2*x)*(9 + 12*x + 4*x^2)^(5/2))/8 + (9 + 12*x + 4*x^2)^(7/2)/28","A",2,2,16,0.1250,1,"{640, 609}"
209,1,42,0,0.008506,"\int x \left(9+12 x+4 x^2\right)^{3/2} \, dx","Int[x*(9 + 12*x + 4*x^2)^(3/2),x]","\frac{1}{20} \left(4 x^2+12 x+9\right)^{5/2}-\frac{3}{16} (2 x+3) \left(4 x^2+12 x+9\right)^{3/2}","\frac{1}{20} \left(4 x^2+12 x+9\right)^{5/2}-\frac{3}{16} (2 x+3) \left(4 x^2+12 x+9\right)^{3/2}",1,"(-3*(3 + 2*x)*(9 + 12*x + 4*x^2)^(3/2))/16 + (9 + 12*x + 4*x^2)^(5/2)/20","A",2,2,16,0.1250,1,"{640, 609}"
210,1,42,0,0.0079994,"\int x \sqrt{9+12 x+4 x^2} \, dx","Int[x*Sqrt[9 + 12*x + 4*x^2],x]","\frac{1}{12} \left(4 x^2+12 x+9\right)^{3/2}-\frac{3}{8} (2 x+3) \sqrt{4 x^2+12 x+9}","\frac{1}{12} \left(4 x^2+12 x+9\right)^{3/2}-\frac{3}{8} (2 x+3) \sqrt{4 x^2+12 x+9}",1,"(-3*(3 + 2*x)*Sqrt[9 + 12*x + 4*x^2])/8 + (9 + 12*x + 4*x^2)^(3/2)/12","A",2,2,16,0.1250,1,"{640, 609}"
211,1,48,0,0.0108877,"\int \frac{x}{\sqrt{9+12 x+4 x^2}} \, dx","Int[x/Sqrt[9 + 12*x + 4*x^2],x]","\frac{1}{4} \sqrt{4 x^2+12 x+9}-\frac{3 (2 x+3) \log (2 x+3)}{4 \sqrt{4 x^2+12 x+9}}","\frac{1}{4} \sqrt{4 x^2+12 x+9}-\frac{3 (2 x+3) \log (2 x+3)}{4 \sqrt{4 x^2+12 x+9}}",1,"Sqrt[9 + 12*x + 4*x^2]/4 - (3*(3 + 2*x)*Log[3 + 2*x])/(4*Sqrt[9 + 12*x + 4*x^2])","A",3,3,16,0.1875,1,"{640, 608, 31}"
212,1,44,0,0.0086371,"\int \frac{x}{\left(9+12 x+4 x^2\right)^{3/2}} \, dx","Int[x/(9 + 12*x + 4*x^2)^(3/2),x]","\frac{3}{8 (2 x+3) \sqrt{4 x^2+12 x+9}}-\frac{1}{4 \sqrt{4 x^2+12 x+9}}","\frac{3}{8 (2 x+3) \sqrt{4 x^2+12 x+9}}-\frac{1}{4 \sqrt{4 x^2+12 x+9}}",1,"-1/(4*Sqrt[9 + 12*x + 4*x^2]) + 3/(8*(3 + 2*x)*Sqrt[9 + 12*x + 4*x^2])","A",2,2,16,0.1250,1,"{640, 607}"
213,1,44,0,0.0090006,"\int \frac{x}{\left(9+12 x+4 x^2\right)^{5/2}} \, dx","Int[x/(9 + 12*x + 4*x^2)^(5/2),x]","\frac{3}{16 (2 x+3) \left(4 x^2+12 x+9\right)^{3/2}}-\frac{1}{12 \left(4 x^2+12 x+9\right)^{3/2}}","\frac{3}{16 (2 x+3) \left(4 x^2+12 x+9\right)^{3/2}}-\frac{1}{12 \left(4 x^2+12 x+9\right)^{3/2}}",1,"-1/(12*(9 + 12*x + 4*x^2)^(3/2)) + 3/(16*(3 + 2*x)*(9 + 12*x + 4*x^2)^(3/2))","A",2,2,16,0.1250,1,"{640, 607}"
214,1,44,0,0.0091762,"\int \frac{x}{\left(9+12 x+4 x^2\right)^{7/2}} \, dx","Int[x/(9 + 12*x + 4*x^2)^(7/2),x]","\frac{1}{8 (2 x+3) \left(4 x^2+12 x+9\right)^{5/2}}-\frac{1}{20 \left(4 x^2+12 x+9\right)^{5/2}}","\frac{1}{8 (2 x+3) \left(4 x^2+12 x+9\right)^{5/2}}-\frac{1}{20 \left(4 x^2+12 x+9\right)^{5/2}}",1,"-1/(20*(9 + 12*x + 4*x^2)^(5/2)) + 1/(8*(3 + 2*x)*(9 + 12*x + 4*x^2)^(5/2))","A",2,2,16,0.1250,1,"{640, 607}"
215,1,48,0,0.0113589,"\int \frac{x}{\sqrt{4+12 x+9 x^2}} \, dx","Int[x/Sqrt[4 + 12*x + 9*x^2],x]","\frac{1}{9} \sqrt{9 x^2+12 x+4}-\frac{2 (3 x+2) \log (3 x+2)}{9 \sqrt{9 x^2+12 x+4}}","\frac{1}{9} \sqrt{9 x^2+12 x+4}-\frac{2 (3 x+2) \log (3 x+2)}{9 \sqrt{9 x^2+12 x+4}}",1,"Sqrt[4 + 12*x + 9*x^2]/9 - (2*(2 + 3*x)*Log[2 + 3*x])/(9*Sqrt[4 + 12*x + 9*x^2])","A",3,3,16,0.1875,1,"{640, 608, 31}"
216,1,48,0,0.0109042,"\int \frac{x}{\sqrt{4-12 x+9 x^2}} \, dx","Int[x/Sqrt[4 - 12*x + 9*x^2],x]","\frac{1}{9} \sqrt{9 x^2-12 x+4}-\frac{2 (2-3 x) \log (2-3 x)}{9 \sqrt{9 x^2-12 x+4}}","\frac{1}{9} \sqrt{9 x^2-12 x+4}-\frac{2 (2-3 x) \log (2-3 x)}{9 \sqrt{9 x^2-12 x+4}}",1,"Sqrt[4 - 12*x + 9*x^2]/9 - (2*(2 - 3*x)*Log[2 - 3*x])/(9*Sqrt[4 - 12*x + 9*x^2])","A",3,3,16,0.1875,1,"{640, 608, 31}"
217,1,48,0,0.0105578,"\int \frac{x}{\sqrt{-4+12 x-9 x^2}} \, dx","Int[x/Sqrt[-4 + 12*x - 9*x^2],x]","-\frac{1}{9} \sqrt{-9 x^2+12 x-4}-\frac{2 (2-3 x) \log (2-3 x)}{9 \sqrt{-9 x^2+12 x-4}}","-\frac{1}{9} \sqrt{-9 x^2+12 x-4}-\frac{2 (2-3 x) \log (2-3 x)}{9 \sqrt{-9 x^2+12 x-4}}",1,"-Sqrt[-4 + 12*x - 9*x^2]/9 - (2*(2 - 3*x)*Log[2 - 3*x])/(9*Sqrt[-4 + 12*x - 9*x^2])","A",3,3,16,0.1875,1,"{640, 608, 31}"
218,1,48,0,0.0119671,"\int \frac{x}{\sqrt{-4-12 x-9 x^2}} \, dx","Int[x/Sqrt[-4 - 12*x - 9*x^2],x]","-\frac{1}{9} \sqrt{-9 x^2-12 x-4}-\frac{2 (3 x+2) \log (3 x+2)}{9 \sqrt{-9 x^2-12 x-4}}","-\frac{1}{9} \sqrt{-9 x^2-12 x-4}-\frac{2 (3 x+2) \log (3 x+2)}{9 \sqrt{-9 x^2-12 x-4}}",1,"-Sqrt[-4 - 12*x - 9*x^2]/9 - (2*(2 + 3*x)*Log[2 + 3*x])/(9*Sqrt[-4 - 12*x - 9*x^2])","A",3,3,16,0.1875,1,"{640, 608, 31}"
219,1,12,0,0.0032206,"\int \frac{1+x}{2 x+x^2} \, dx","Int[(1 + x)/(2*x + x^2),x]","\frac{1}{2} \log \left(x^2+2 x\right)","\frac{1}{2} \log \left(x^2+2 x\right)",1,"Log[2*x + x^2]/2","A",1,1,13,0.07692,1,"{628}"
220,1,10,0,0.0039895,"\int \frac{a+2 b x}{a x+b x^2} \, dx","Int[(a + 2*b*x)/(a*x + b*x^2),x]","\log \left(a x+b x^2\right)","\log \left(a x+b x^2\right)",1,"Log[a*x + b*x^2]","A",1,1,18,0.05556,1,"{628}"
221,1,62,0,0.0667449,"\int (d+e x)^4 \left(b x+c x^2\right) \, dx","Int[(d + e*x)^4*(b*x + c*x^2),x]","-\frac{(d+e x)^6 (2 c d-b e)}{6 e^3}+\frac{d (d+e x)^5 (c d-b e)}{5 e^3}+\frac{c (d+e x)^7}{7 e^3}","-\frac{(d+e x)^6 (2 c d-b e)}{6 e^3}+\frac{d (d+e x)^5 (c d-b e)}{5 e^3}+\frac{c (d+e x)^7}{7 e^3}",1,"(d*(c*d - b*e)*(d + e*x)^5)/(5*e^3) - ((2*c*d - b*e)*(d + e*x)^6)/(6*e^3) + (c*(d + e*x)^7)/(7*e^3)","A",2,1,17,0.05882,1,"{698}"
222,1,62,0,0.0488904,"\int (d+e x)^3 \left(b x+c x^2\right) \, dx","Int[(d + e*x)^3*(b*x + c*x^2),x]","-\frac{(d+e x)^5 (2 c d-b e)}{5 e^3}+\frac{d (d+e x)^4 (c d-b e)}{4 e^3}+\frac{c (d+e x)^6}{6 e^3}","-\frac{(d+e x)^5 (2 c d-b e)}{5 e^3}+\frac{d (d+e x)^4 (c d-b e)}{4 e^3}+\frac{c (d+e x)^6}{6 e^3}",1,"(d*(c*d - b*e)*(d + e*x)^4)/(4*e^3) - ((2*c*d - b*e)*(d + e*x)^5)/(5*e^3) + (c*(d + e*x)^6)/(6*e^3)","A",2,1,17,0.05882,1,"{698}"
223,1,55,0,0.0376067,"\int (d+e x)^2 \left(b x+c x^2\right) \, dx","Int[(d + e*x)^2*(b*x + c*x^2),x]","\frac{1}{4} e x^4 (b e+2 c d)+\frac{1}{3} d x^3 (2 b e+c d)+\frac{1}{2} b d^2 x^2+\frac{1}{5} c e^2 x^5","\frac{1}{4} e x^4 (b e+2 c d)+\frac{1}{3} d x^3 (2 b e+c d)+\frac{1}{2} b d^2 x^2+\frac{1}{5} c e^2 x^5",1,"(b*d^2*x^2)/2 + (d*(c*d + 2*b*e)*x^3)/3 + (e*(2*c*d + b*e)*x^4)/4 + (c*e^2*x^5)/5","A",2,1,17,0.05882,1,"{698}"
224,1,33,0,0.0219701,"\int (d+e x) \left(b x+c x^2\right) \, dx","Int[(d + e*x)*(b*x + c*x^2),x]","\frac{1}{3} x^3 (b e+c d)+\frac{1}{2} b d x^2+\frac{1}{4} c e x^4","\frac{1}{3} x^3 (b e+c d)+\frac{1}{2} b d x^2+\frac{1}{4} c e x^4",1,"(b*d*x^2)/2 + ((c*d + b*e)*x^3)/3 + (c*e*x^4)/4","A",2,1,15,0.06667,1,"{631}"
225,1,17,0,0.00323,"\int \left(b x+c x^2\right) \, dx","Int[b*x + c*x^2,x]","\frac{b x^2}{2}+\frac{c x^3}{3}","\frac{b x^2}{2}+\frac{c x^3}{3}",1,"(b*x^2)/2 + (c*x^3)/3","A",1,0,9,0,1,"{}"
226,1,45,0,0.0340222,"\int \frac{b x+c x^2}{d+e x} \, dx","Int[(b*x + c*x^2)/(d + e*x),x]","-\frac{x (c d-b e)}{e^2}+\frac{d (c d-b e) \log (d+e x)}{e^3}+\frac{c x^2}{2 e}","-\frac{x (c d-b e)}{e^2}+\frac{d (c d-b e) \log (d+e x)}{e^3}+\frac{c x^2}{2 e}",1,"-(((c*d - b*e)*x)/e^2) + (c*x^2)/(2*e) + (d*(c*d - b*e)*Log[d + e*x])/e^3","A",2,1,17,0.05882,1,"{698}"
227,1,48,0,0.0367024,"\int \frac{b x+c x^2}{(d+e x)^2} \, dx","Int[(b*x + c*x^2)/(d + e*x)^2,x]","-\frac{d (c d-b e)}{e^3 (d+e x)}-\frac{(2 c d-b e) \log (d+e x)}{e^3}+\frac{c x}{e^2}","-\frac{d (c d-b e)}{e^3 (d+e x)}-\frac{(2 c d-b e) \log (d+e x)}{e^3}+\frac{c x}{e^2}",1,"(c*x)/e^2 - (d*(c*d - b*e))/(e^3*(d + e*x)) - ((2*c*d - b*e)*Log[d + e*x])/e^3","A",2,1,17,0.05882,1,"{698}"
228,1,55,0,0.0373487,"\int \frac{b x+c x^2}{(d+e x)^3} \, dx","Int[(b*x + c*x^2)/(d + e*x)^3,x]","-\frac{d (c d-b e)}{2 e^3 (d+e x)^2}+\frac{2 c d-b e}{e^3 (d+e x)}+\frac{c \log (d+e x)}{e^3}","-\frac{d (c d-b e)}{2 e^3 (d+e x)^2}+\frac{2 c d-b e}{e^3 (d+e x)}+\frac{c \log (d+e x)}{e^3}",1,"-(d*(c*d - b*e))/(2*e^3*(d + e*x)^2) + (2*c*d - b*e)/(e^3*(d + e*x)) + (c*Log[d + e*x])/e^3","A",2,1,17,0.05882,1,"{698}"
229,1,60,0,0.0356667,"\int \frac{b x+c x^2}{(d+e x)^4} \, dx","Int[(b*x + c*x^2)/(d + e*x)^4,x]","\frac{2 c d-b e}{2 e^3 (d+e x)^2}-\frac{d (c d-b e)}{3 e^3 (d+e x)^3}-\frac{c}{e^3 (d+e x)}","\frac{2 c d-b e}{2 e^3 (d+e x)^2}-\frac{d (c d-b e)}{3 e^3 (d+e x)^3}-\frac{c}{e^3 (d+e x)}",1,"-(d*(c*d - b*e))/(3*e^3*(d + e*x)^3) + (2*c*d - b*e)/(2*e^3*(d + e*x)^2) - c/(e^3*(d + e*x))","A",2,1,17,0.05882,1,"{698}"
230,1,62,0,0.0362365,"\int \frac{b x+c x^2}{(d+e x)^5} \, dx","Int[(b*x + c*x^2)/(d + e*x)^5,x]","\frac{2 c d-b e}{3 e^3 (d+e x)^3}-\frac{d (c d-b e)}{4 e^3 (d+e x)^4}-\frac{c}{2 e^3 (d+e x)^2}","\frac{2 c d-b e}{3 e^3 (d+e x)^3}-\frac{d (c d-b e)}{4 e^3 (d+e x)^4}-\frac{c}{2 e^3 (d+e x)^2}",1,"-(d*(c*d - b*e))/(4*e^3*(d + e*x)^4) + (2*c*d - b*e)/(3*e^3*(d + e*x)^3) - c/(2*e^3*(d + e*x)^2)","A",2,1,17,0.05882,1,"{698}"
231,1,137,0,0.1408592,"\int (d+e x)^4 \left(b x+c x^2\right)^2 \, dx","Int[(d + e*x)^4*(b*x + c*x^2)^2,x]","\frac{(d+e x)^7 \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{7 e^5}+\frac{d^2 (d+e x)^5 (c d-b e)^2}{5 e^5}-\frac{c (d+e x)^8 (2 c d-b e)}{4 e^5}-\frac{d (d+e x)^6 (c d-b e) (2 c d-b e)}{3 e^5}+\frac{c^2 (d+e x)^9}{9 e^5}","\frac{(d+e x)^7 \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{7 e^5}+\frac{d^2 (d+e x)^5 (c d-b e)^2}{5 e^5}-\frac{c (d+e x)^8 (2 c d-b e)}{4 e^5}-\frac{d (d+e x)^6 (c d-b e) (2 c d-b e)}{3 e^5}+\frac{c^2 (d+e x)^9}{9 e^5}",1,"(d^2*(c*d - b*e)^2*(d + e*x)^5)/(5*e^5) - (d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^6)/(3*e^5) + ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^7)/(7*e^5) - (c*(2*c*d - b*e)*(d + e*x)^8)/(4*e^5) + (c^2*(d + e*x)^9)/(9*e^5)","A",2,1,19,0.05263,1,"{698}"
232,1,127,0,0.0928371,"\int (d+e x)^3 \left(b x+c x^2\right)^2 \, dx","Int[(d + e*x)^3*(b*x + c*x^2)^2,x]","\frac{1}{6} e x^6 \left(b^2 e^2+6 b c d e+3 c^2 d^2\right)+\frac{1}{5} d x^5 \left(3 b^2 e^2+6 b c d e+c^2 d^2\right)+\frac{1}{3} b^2 d^3 x^3+\frac{1}{4} b d^2 x^4 (3 b e+2 c d)+\frac{1}{7} c e^2 x^7 (2 b e+3 c d)+\frac{1}{8} c^2 e^3 x^8","\frac{1}{6} e x^6 \left(b^2 e^2+6 b c d e+3 c^2 d^2\right)+\frac{1}{5} d x^5 \left(3 b^2 e^2+6 b c d e+c^2 d^2\right)+\frac{1}{3} b^2 d^3 x^3+\frac{1}{4} b d^2 x^4 (3 b e+2 c d)+\frac{1}{7} c e^2 x^7 (2 b e+3 c d)+\frac{1}{8} c^2 e^3 x^8",1,"(b^2*d^3*x^3)/3 + (b*d^2*(2*c*d + 3*b*e)*x^4)/4 + (d*(c^2*d^2 + 6*b*c*d*e + 3*b^2*e^2)*x^5)/5 + (e*(3*c^2*d^2 + 6*b*c*d*e + b^2*e^2)*x^6)/6 + (c*e^2*(3*c*d + 2*b*e)*x^7)/7 + (c^2*e^3*x^8)/8","A",2,1,19,0.05263,1,"{698}"
233,1,87,0,0.0764796,"\int (d+e x)^2 \left(b x+c x^2\right)^2 \, dx","Int[(d + e*x)^2*(b*x + c*x^2)^2,x]","\frac{1}{5} x^5 \left(b^2 e^2+4 b c d e+c^2 d^2\right)+\frac{1}{3} b^2 d^2 x^3+\frac{1}{3} c e x^6 (b e+c d)+\frac{1}{2} b d x^4 (b e+c d)+\frac{1}{7} c^2 e^2 x^7","\frac{1}{5} x^5 \left(b^2 e^2+4 b c d e+c^2 d^2\right)+\frac{1}{3} b^2 d^2 x^3+\frac{1}{3} c e x^6 (b e+c d)+\frac{1}{2} b d x^4 (b e+c d)+\frac{1}{7} c^2 e^2 x^7",1,"(b^2*d^2*x^3)/3 + (b*d*(c*d + b*e)*x^4)/2 + ((c^2*d^2 + 4*b*c*d*e + b^2*e^2)*x^5)/5 + (c*e*(c*d + b*e)*x^6)/3 + (c^2*e^2*x^7)/7","A",2,1,19,0.05263,1,"{698}"
234,1,55,0,0.0400556,"\int (d+e x) \left(b x+c x^2\right)^2 \, dx","Int[(d + e*x)*(b*x + c*x^2)^2,x]","\frac{1}{3} b^2 d x^3+\frac{1}{5} c x^5 (2 b e+c d)+\frac{1}{4} b x^4 (b e+2 c d)+\frac{1}{6} c^2 e x^6","\frac{1}{3} b^2 d x^3+\frac{1}{5} c x^5 (2 b e+c d)+\frac{1}{4} b x^4 (b e+2 c d)+\frac{1}{6} c^2 e x^6",1,"(b^2*d*x^3)/3 + (b*(2*c*d + b*e)*x^4)/4 + (c*(c*d + 2*b*e)*x^5)/5 + (c^2*e*x^6)/6","A",2,1,17,0.05882,1,"{631}"
235,1,30,0,0.0093515,"\int \left(b x+c x^2\right)^2 \, dx","Int[(b*x + c*x^2)^2,x]","\frac{b^2 x^3}{3}+\frac{1}{2} b c x^4+\frac{c^2 x^5}{5}","\frac{b^2 x^3}{3}+\frac{1}{2} b c x^4+\frac{c^2 x^5}{5}",1,"(b^2*x^3)/3 + (b*c*x^4)/2 + (c^2*x^5)/5","A",2,1,11,0.09091,1,"{611}"
236,1,93,0,0.0815552,"\int \frac{\left(b x+c x^2\right)^2}{d+e x} \, dx","Int[(b*x + c*x^2)^2/(d + e*x),x]","\frac{d^2 (c d-b e)^2 \log (d+e x)}{e^5}-\frac{c x^3 (c d-2 b e)}{3 e^2}+\frac{x^2 (c d-b e)^2}{2 e^3}-\frac{d x (c d-b e)^2}{e^4}+\frac{c^2 x^4}{4 e}","\frac{d^2 (c d-b e)^2 \log (d+e x)}{e^5}-\frac{c x^3 (c d-2 b e)}{3 e^2}+\frac{x^2 (c d-b e)^2}{2 e^3}-\frac{d x (c d-b e)^2}{e^4}+\frac{c^2 x^4}{4 e}",1,"-((d*(c*d - b*e)^2*x)/e^4) + ((c*d - b*e)^2*x^2)/(2*e^3) - (c*(c*d - 2*b*e)*x^3)/(3*e^2) + (c^2*x^4)/(4*e) + (d^2*(c*d - b*e)^2*Log[d + e*x])/e^5","A",2,1,19,0.05263,1,"{698}"
237,1,107,0,0.102462,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^2} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^2,x]","-\frac{d^2 (c d-b e)^2}{e^5 (d+e x)}-\frac{c x^2 (c d-b e)}{e^3}+\frac{x (c d-b e) (3 c d-b e)}{e^4}-\frac{2 d (c d-b e) (2 c d-b e) \log (d+e x)}{e^5}+\frac{c^2 x^3}{3 e^2}","-\frac{d^2 (c d-b e)^2}{e^5 (d+e x)}-\frac{c x^2 (c d-b e)}{e^3}+\frac{x (c d-b e) (3 c d-b e)}{e^4}-\frac{2 d (c d-b e) (2 c d-b e) \log (d+e x)}{e^5}+\frac{c^2 x^3}{3 e^2}",1,"((c*d - b*e)*(3*c*d - b*e)*x)/e^4 - (c*(c*d - b*e)*x^2)/e^3 + (c^2*x^3)/(3*e^2) - (d^2*(c*d - b*e)^2)/(e^5*(d + e*x)) - (2*d*(c*d - b*e)*(2*c*d - b*e)*Log[d + e*x])/e^5","A",2,1,19,0.05263,1,"{698}"
238,1,119,0,0.1062064,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^3} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^3,x]","\frac{\left(b^2 e^2-6 b c d e+6 c^2 d^2\right) \log (d+e x)}{e^5}-\frac{d^2 (c d-b e)^2}{2 e^5 (d+e x)^2}+\frac{2 d (2 c d-b e) (c d-b e)}{e^5 (d+e x)}-\frac{c x (3 c d-2 b e)}{e^4}+\frac{c^2 x^2}{2 e^3}","\frac{\left(b^2 e^2-6 b c d e+6 c^2 d^2\right) \log (d+e x)}{e^5}-\frac{d^2 (c d-b e)^2}{2 e^5 (d+e x)^2}+\frac{2 d (2 c d-b e) (c d-b e)}{e^5 (d+e x)}-\frac{c x (3 c d-2 b e)}{e^4}+\frac{c^2 x^2}{2 e^3}",1,"-((c*(3*c*d - 2*b*e)*x)/e^4) + (c^2*x^2)/(2*e^3) - (d^2*(c*d - b*e)^2)/(2*e^5*(d + e*x)^2) + (2*d*(c*d - b*e)*(2*c*d - b*e))/(e^5*(d + e*x)) + ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*Log[d + e*x])/e^5","A",2,1,19,0.05263,1,"{698}"
239,1,120,0,0.0962984,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^4} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^4,x]","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{e^5 (d+e x)}-\frac{d^2 (c d-b e)^2}{3 e^5 (d+e x)^3}+\frac{d (c d-b e) (2 c d-b e)}{e^5 (d+e x)^2}-\frac{2 c (2 c d-b e) \log (d+e x)}{e^5}+\frac{c^2 x}{e^4}","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{e^5 (d+e x)}-\frac{d^2 (c d-b e)^2}{3 e^5 (d+e x)^3}+\frac{d (c d-b e) (2 c d-b e)}{e^5 (d+e x)^2}-\frac{2 c (2 c d-b e) \log (d+e x)}{e^5}+\frac{c^2 x}{e^4}",1,"(c^2*x)/e^4 - (d^2*(c*d - b*e)^2)/(3*e^5*(d + e*x)^3) + (d*(c*d - b*e)*(2*c*d - b*e))/(e^5*(d + e*x)^2) - (6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)/(e^5*(d + e*x)) - (2*c*(2*c*d - b*e)*Log[d + e*x])/e^5","A",2,1,19,0.05263,1,"{698}"
240,1,131,0,0.091824,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^5} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^5,x]","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{2 e^5 (d+e x)^2}-\frac{d^2 (c d-b e)^2}{4 e^5 (d+e x)^4}+\frac{2 c (2 c d-b e)}{e^5 (d+e x)}+\frac{2 d (c d-b e) (2 c d-b e)}{3 e^5 (d+e x)^3}+\frac{c^2 \log (d+e x)}{e^5}","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{2 e^5 (d+e x)^2}-\frac{d^2 (c d-b e)^2}{4 e^5 (d+e x)^4}+\frac{2 c (2 c d-b e)}{e^5 (d+e x)}+\frac{2 d (c d-b e) (2 c d-b e)}{3 e^5 (d+e x)^3}+\frac{c^2 \log (d+e x)}{e^5}",1,"-(d^2*(c*d - b*e)^2)/(4*e^5*(d + e*x)^4) + (2*d*(c*d - b*e)*(2*c*d - b*e))/(3*e^5*(d + e*x)^3) - (6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)/(2*e^5*(d + e*x)^2) + (2*c*(2*c*d - b*e))/(e^5*(d + e*x)) + (c^2*Log[d + e*x])/e^5","A",2,1,19,0.05263,1,"{698}"
241,1,132,0,0.0898765,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^6} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^6,x]","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{3 e^5 (d+e x)^3}-\frac{d^2 (c d-b e)^2}{5 e^5 (d+e x)^5}+\frac{c (2 c d-b e)}{e^5 (d+e x)^2}+\frac{d (c d-b e) (2 c d-b e)}{2 e^5 (d+e x)^4}-\frac{c^2}{e^5 (d+e x)}","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{3 e^5 (d+e x)^3}-\frac{d^2 (c d-b e)^2}{5 e^5 (d+e x)^5}+\frac{c (2 c d-b e)}{e^5 (d+e x)^2}+\frac{d (c d-b e) (2 c d-b e)}{2 e^5 (d+e x)^4}-\frac{c^2}{e^5 (d+e x)}",1,"-(d^2*(c*d - b*e)^2)/(5*e^5*(d + e*x)^5) + (d*(c*d - b*e)*(2*c*d - b*e))/(2*e^5*(d + e*x)^4) - (6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)/(3*e^5*(d + e*x)^3) + (c*(2*c*d - b*e))/(e^5*(d + e*x)^2) - c^2/(e^5*(d + e*x))","A",2,1,19,0.05263,1,"{698}"
242,1,137,0,0.0921652,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^7} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^7,x]","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{4 e^5 (d+e x)^4}-\frac{d^2 (c d-b e)^2}{6 e^5 (d+e x)^6}+\frac{2 c (2 c d-b e)}{3 e^5 (d+e x)^3}+\frac{2 d (c d-b e) (2 c d-b e)}{5 e^5 (d+e x)^5}-\frac{c^2}{2 e^5 (d+e x)^2}","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{4 e^5 (d+e x)^4}-\frac{d^2 (c d-b e)^2}{6 e^5 (d+e x)^6}+\frac{2 c (2 c d-b e)}{3 e^5 (d+e x)^3}+\frac{2 d (c d-b e) (2 c d-b e)}{5 e^5 (d+e x)^5}-\frac{c^2}{2 e^5 (d+e x)^2}",1,"-(d^2*(c*d - b*e)^2)/(6*e^5*(d + e*x)^6) + (2*d*(c*d - b*e)*(2*c*d - b*e))/(5*e^5*(d + e*x)^5) - (6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)/(4*e^5*(d + e*x)^4) + (2*c*(2*c*d - b*e))/(3*e^5*(d + e*x)^3) - c^2/(2*e^5*(d + e*x)^2)","A",2,1,19,0.05263,1,"{698}"
243,1,137,0,0.0880271,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^8} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^8,x]","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{5 e^5 (d+e x)^5}-\frac{d^2 (c d-b e)^2}{7 e^5 (d+e x)^7}+\frac{c (2 c d-b e)}{2 e^5 (d+e x)^4}+\frac{d (c d-b e) (2 c d-b e)}{3 e^5 (d+e x)^6}-\frac{c^2}{3 e^5 (d+e x)^3}","-\frac{b^2 e^2-6 b c d e+6 c^2 d^2}{5 e^5 (d+e x)^5}-\frac{d^2 (c d-b e)^2}{7 e^5 (d+e x)^7}+\frac{c (2 c d-b e)}{2 e^5 (d+e x)^4}+\frac{d (c d-b e) (2 c d-b e)}{3 e^5 (d+e x)^6}-\frac{c^2}{3 e^5 (d+e x)^3}",1,"-(d^2*(c*d - b*e)^2)/(7*e^5*(d + e*x)^7) + (d*(c*d - b*e)*(2*c*d - b*e))/(3*e^5*(d + e*x)^6) - (6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)/(5*e^5*(d + e*x)^5) + (c*(2*c*d - b*e))/(2*e^5*(d + e*x)^4) - c^2/(3*e^5*(d + e*x)^3)","A",2,1,19,0.05263,1,"{698}"
244,1,225,0,0.2154989,"\int (d+e x)^4 \left(b x+c x^2\right)^3 \, dx","Int[(d + e*x)^4*(b*x + c*x^2)^3,x]","\frac{1}{3} c e^2 x^9 \left(b^2 e^2+4 b c d e+2 c^2 d^2\right)+\frac{1}{8} e x^8 \left(12 b^2 c d e^2+b^3 e^3+18 b c^2 d^2 e+4 c^3 d^3\right)+\frac{1}{7} d x^7 \left(18 b^2 c d e^2+4 b^3 e^3+12 b c^2 d^2 e+c^3 d^3\right)+\frac{1}{2} b d^2 x^6 \left(2 b^2 e^2+4 b c d e+c^2 d^2\right)+\frac{1}{5} b^2 d^3 x^5 (4 b e+3 c d)+\frac{1}{4} b^3 d^4 x^4+\frac{1}{10} c^2 e^3 x^{10} (3 b e+4 c d)+\frac{1}{11} c^3 e^4 x^{11}","\frac{1}{3} c e^2 x^9 \left(b^2 e^2+4 b c d e+2 c^2 d^2\right)+\frac{1}{8} e x^8 \left(12 b^2 c d e^2+b^3 e^3+18 b c^2 d^2 e+4 c^3 d^3\right)+\frac{1}{7} d x^7 \left(18 b^2 c d e^2+4 b^3 e^3+12 b c^2 d^2 e+c^3 d^3\right)+\frac{1}{2} b d^2 x^6 \left(2 b^2 e^2+4 b c d e+c^2 d^2\right)+\frac{1}{5} b^2 d^3 x^5 (4 b e+3 c d)+\frac{1}{4} b^3 d^4 x^4+\frac{1}{10} c^2 e^3 x^{10} (3 b e+4 c d)+\frac{1}{11} c^3 e^4 x^{11}",1,"(b^3*d^4*x^4)/4 + (b^2*d^3*(3*c*d + 4*b*e)*x^5)/5 + (b*d^2*(c^2*d^2 + 4*b*c*d*e + 2*b^2*e^2)*x^6)/2 + (d*(c^3*d^3 + 12*b*c^2*d^2*e + 18*b^2*c*d*e^2 + 4*b^3*e^3)*x^7)/7 + (e*(4*c^3*d^3 + 18*b*c^2*d^2*e + 12*b^2*c*d*e^2 + b^3*e^3)*x^8)/8 + (c*e^2*(2*c^2*d^2 + 4*b*c*d*e + b^2*e^2)*x^9)/3 + (c^2*e^3*(4*c*d + 3*b*e)*x^10)/10 + (c^3*e^4*x^11)/11","A",2,1,19,0.05263,1,"{698}"
245,1,162,0,0.1560304,"\int (d+e x)^3 \left(b x+c x^2\right)^3 \, dx","Int[(d + e*x)^3*(b*x + c*x^2)^3,x]","\frac{3}{8} c e x^8 \left(b^2 e^2+3 b c d e+c^2 d^2\right)+\frac{1}{7} x^7 (b e+c d) \left(b^2 e^2+8 b c d e+c^2 d^2\right)+\frac{1}{2} b d x^6 \left(b^2 e^2+3 b c d e+c^2 d^2\right)+\frac{3}{5} b^2 d^2 x^5 (b e+c d)+\frac{1}{4} b^3 d^3 x^4+\frac{1}{3} c^2 e^2 x^9 (b e+c d)+\frac{1}{10} c^3 e^3 x^{10}","\frac{3}{8} c e x^8 \left(b^2 e^2+3 b c d e+c^2 d^2\right)+\frac{1}{7} x^7 (b e+c d) \left(b^2 e^2+8 b c d e+c^2 d^2\right)+\frac{1}{2} b d x^6 \left(b^2 e^2+3 b c d e+c^2 d^2\right)+\frac{3}{5} b^2 d^2 x^5 (b e+c d)+\frac{1}{4} b^3 d^3 x^4+\frac{1}{3} c^2 e^2 x^9 (b e+c d)+\frac{1}{10} c^3 e^3 x^{10}",1,"(b^3*d^3*x^4)/4 + (3*b^2*d^2*(c*d + b*e)*x^5)/5 + (b*d*(c^2*d^2 + 3*b*c*d*e + b^2*e^2)*x^6)/2 + ((c*d + b*e)*(c^2*d^2 + 8*b*c*d*e + b^2*e^2)*x^7)/7 + (3*c*e*(c^2*d^2 + 3*b*c*d*e + b^2*e^2)*x^8)/8 + (c^2*e^2*(c*d + b*e)*x^9)/3 + (c^3*e^3*x^10)/10","A",2,1,19,0.05263,1,"{698}"
246,1,127,0,0.1099107,"\int (d+e x)^2 \left(b x+c x^2\right)^3 \, dx","Int[(d + e*x)^2*(b*x + c*x^2)^3,x]","\frac{1}{7} c x^7 \left(3 b^2 e^2+6 b c d e+c^2 d^2\right)+\frac{1}{6} b x^6 \left(b^2 e^2+6 b c d e+3 c^2 d^2\right)+\frac{1}{5} b^2 d x^5 (2 b e+3 c d)+\frac{1}{4} b^3 d^2 x^4+\frac{1}{8} c^2 e x^8 (3 b e+2 c d)+\frac{1}{9} c^3 e^2 x^9","\frac{1}{7} c x^7 \left(3 b^2 e^2+6 b c d e+c^2 d^2\right)+\frac{1}{6} b x^6 \left(b^2 e^2+6 b c d e+3 c^2 d^2\right)+\frac{1}{5} b^2 d x^5 (2 b e+3 c d)+\frac{1}{4} b^3 d^2 x^4+\frac{1}{8} c^2 e x^8 (3 b e+2 c d)+\frac{1}{9} c^3 e^2 x^9",1,"(b^3*d^2*x^4)/4 + (b^2*d*(3*c*d + 2*b*e)*x^5)/5 + (b*(3*c^2*d^2 + 6*b*c*d*e + b^2*e^2)*x^6)/6 + (c*(c^2*d^2 + 6*b*c*d*e + 3*b^2*e^2)*x^7)/7 + (c^2*e*(2*c*d + 3*b*e)*x^8)/8 + (c^3*e^2*x^9)/9","A",2,1,19,0.05263,1,"{698}"
247,1,75,0,0.062641,"\int (d+e x) \left(b x+c x^2\right)^3 \, dx","Int[(d + e*x)*(b*x + c*x^2)^3,x]","\frac{1}{5} b^2 x^5 (b e+3 c d)+\frac{1}{4} b^3 d x^4+\frac{1}{7} c^2 x^7 (3 b e+c d)+\frac{1}{2} b c x^6 (b e+c d)+\frac{1}{8} c^3 e x^8","\frac{1}{5} b^2 x^5 (b e+3 c d)+\frac{1}{4} b^3 d x^4+\frac{1}{7} c^2 x^7 (3 b e+c d)+\frac{1}{2} b c x^6 (b e+c d)+\frac{1}{8} c^3 e x^8",1,"(b^3*d*x^4)/4 + (b^2*(3*c*d + b*e)*x^5)/5 + (b*c*(c*d + b*e)*x^6)/2 + (c^2*(c*d + 3*b*e)*x^7)/7 + (c^3*e*x^8)/8","A",2,1,17,0.05882,1,"{631}"
248,1,43,0,0.0146033,"\int \left(b x+c x^2\right)^3 \, dx","Int[(b*x + c*x^2)^3,x]","\frac{3}{5} b^2 c x^5+\frac{b^3 x^4}{4}+\frac{1}{2} b c^2 x^6+\frac{c^3 x^7}{7}","\frac{3}{5} b^2 c x^5+\frac{b^3 x^4}{4}+\frac{1}{2} b c^2 x^6+\frac{c^3 x^7}{7}",1,"(b^3*x^4)/4 + (3*b^2*c*x^5)/5 + (b*c^2*x^6)/2 + (c^3*x^7)/7","A",2,1,11,0.09091,1,"{611}"
249,1,151,0,0.151383,"\int \frac{\left(b x+c x^2\right)^3}{d+e x} \, dx","Int[(b*x + c*x^2)^3/(d + e*x),x]","\frac{c x^4 \left(3 b^2 e^2-3 b c d e+c^2 d^2\right)}{4 e^3}-\frac{c^2 x^5 (c d-3 b e)}{5 e^2}-\frac{d^2 x (c d-b e)^3}{e^6}+\frac{d^3 (c d-b e)^3 \log (d+e x)}{e^7}-\frac{x^3 (c d-b e)^3}{3 e^4}+\frac{d x^2 (c d-b e)^3}{2 e^5}+\frac{c^3 x^6}{6 e}","\frac{c x^4 \left(3 b^2 e^2-3 b c d e+c^2 d^2\right)}{4 e^3}-\frac{c^2 x^5 (c d-3 b e)}{5 e^2}-\frac{d^2 x (c d-b e)^3}{e^6}+\frac{d^3 (c d-b e)^3 \log (d+e x)}{e^7}-\frac{x^3 (c d-b e)^3}{3 e^4}+\frac{d x^2 (c d-b e)^3}{2 e^5}+\frac{c^3 x^6}{6 e}",1,"-((d^2*(c*d - b*e)^3*x)/e^6) + (d*(c*d - b*e)^3*x^2)/(2*e^5) - ((c*d - b*e)^3*x^3)/(3*e^4) + (c*(c^2*d^2 - 3*b*c*d*e + 3*b^2*e^2)*x^4)/(4*e^3) - (c^2*(c*d - 3*b*e)*x^5)/(5*e^2) + (c^3*x^6)/(6*e) + (d^3*(c*d - b*e)^3*Log[d + e*x])/e^7","A",2,1,19,0.05263,1,"{698}"
250,1,166,0,0.1862816,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^2} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^2,x]","-\frac{c^2 x^4 (2 c d-3 b e)}{4 e^3}-\frac{d^3 (c d-b e)^3}{e^7 (d+e x)}-\frac{3 d^2 (c d-b e)^2 (2 c d-b e) \log (d+e x)}{e^7}+\frac{c x^3 (c d-b e)^2}{e^4}-\frac{x^2 (c d-b e)^2 (4 c d-b e)}{2 e^5}+\frac{d x (5 c d-2 b e) (c d-b e)^2}{e^6}+\frac{c^3 x^5}{5 e^2}","-\frac{c^2 x^4 (2 c d-3 b e)}{4 e^3}-\frac{d^3 (c d-b e)^3}{e^7 (d+e x)}-\frac{3 d^2 (c d-b e)^2 (2 c d-b e) \log (d+e x)}{e^7}+\frac{c x^3 (c d-b e)^2}{e^4}-\frac{x^2 (c d-b e)^2 (4 c d-b e)}{2 e^5}+\frac{d x (5 c d-2 b e) (c d-b e)^2}{e^6}+\frac{c^3 x^5}{5 e^2}",1,"(d*(5*c*d - 2*b*e)*(c*d - b*e)^2*x)/e^6 - ((c*d - b*e)^2*(4*c*d - b*e)*x^2)/(2*e^5) + (c*(c*d - b*e)^2*x^3)/e^4 - (c^2*(2*c*d - 3*b*e)*x^4)/(4*e^3) + (c^3*x^5)/(5*e^2) - (d^3*(c*d - b*e)^3)/(e^7*(d + e*x)) - (3*d^2*(c*d - b*e)^2*(2*c*d - b*e)*Log[d + e*x])/e^7","A",2,1,19,0.05263,1,"{698}"
251,1,200,0,0.2187298,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^3} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^3,x]","-\frac{x (c d-b e) \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{e^6}+\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) \log (d+e x)}{e^7}-\frac{c^2 x^3 (c d-b e)}{e^4}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{e^7 (d+e x)}-\frac{d^3 (c d-b e)^3}{2 e^7 (d+e x)^2}+\frac{3 c x^2 (c d-b e) (2 c d-b e)}{2 e^5}+\frac{c^3 x^4}{4 e^3}","-\frac{x (c d-b e) \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{e^6}+\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) \log (d+e x)}{e^7}-\frac{c^2 x^3 (c d-b e)}{e^4}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{e^7 (d+e x)}-\frac{d^3 (c d-b e)^3}{2 e^7 (d+e x)^2}+\frac{3 c x^2 (c d-b e) (2 c d-b e)}{2 e^5}+\frac{c^3 x^4}{4 e^3}",1,"-(((c*d - b*e)*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*x)/e^6) + (3*c*(c*d - b*e)*(2*c*d - b*e)*x^2)/(2*e^5) - (c^2*(c*d - b*e)*x^3)/e^4 + (c^3*x^4)/(4*e^3) - (d^3*(c*d - b*e)^3)/(2*e^7*(d + e*x)^2) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(e^7*(d + e*x)) + (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*Log[d + e*x])/e^7","A",2,1,19,0.05263,1,"{698}"
252,1,213,0,0.2149412,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^4} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^4,x]","-\frac{3 d \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) (c d-b e)}{e^7 (d+e x)}+\frac{c x \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{e^6}-\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right) \log (d+e x)}{e^7}-\frac{c^2 x^2 (4 c d-3 b e)}{2 e^5}-\frac{d^3 (c d-b e)^3}{3 e^7 (d+e x)^3}+\frac{3 d^2 (2 c d-b e) (c d-b e)^2}{2 e^7 (d+e x)^2}+\frac{c^3 x^3}{3 e^4}","-\frac{3 d \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) (c d-b e)}{e^7 (d+e x)}+\frac{c x \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{e^6}-\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right) \log (d+e x)}{e^7}-\frac{c^2 x^2 (4 c d-3 b e)}{2 e^5}-\frac{d^3 (c d-b e)^3}{3 e^7 (d+e x)^3}+\frac{3 d^2 (2 c d-b e) (c d-b e)^2}{2 e^7 (d+e x)^2}+\frac{c^3 x^3}{3 e^4}",1,"(c*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2)*x)/e^6 - (c^2*(4*c*d - 3*b*e)*x^2)/(2*e^5) + (c^3*x^3)/(3*e^4) - (d^3*(c*d - b*e)^3)/(3*e^7*(d + e*x)^3) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(2*e^7*(d + e*x)^2) - (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(e^7*(d + e*x)) - ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*Log[d + e*x])/e^7","A",2,1,19,0.05263,1,"{698}"
253,1,213,0,0.1973269,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^5} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^5,x]","\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{e^7 (d+e x)}-\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{2 e^7 (d+e x)^2}+\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) \log (d+e x)}{e^7}-\frac{c^2 x (5 c d-3 b e)}{e^6}+\frac{d^2 (c d-b e)^2 (2 c d-b e)}{e^7 (d+e x)^3}-\frac{d^3 (c d-b e)^3}{4 e^7 (d+e x)^4}+\frac{c^3 x^2}{2 e^5}","\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{e^7 (d+e x)}-\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{2 e^7 (d+e x)^2}+\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) \log (d+e x)}{e^7}-\frac{c^2 x (5 c d-3 b e)}{e^6}+\frac{d^2 (c d-b e)^2 (2 c d-b e)}{e^7 (d+e x)^3}-\frac{d^3 (c d-b e)^3}{4 e^7 (d+e x)^4}+\frac{c^3 x^2}{2 e^5}",1,"-((c^2*(5*c*d - 3*b*e)*x)/e^6) + (c^3*x^2)/(2*e^5) - (d^3*(c*d - b*e)^3)/(4*e^7*(d + e*x)^4) + (d^2*(c*d - b*e)^2*(2*c*d - b*e))/(e^7*(d + e*x)^3) - (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(2*e^7*(d + e*x)^2) + ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2))/(e^7*(d + e*x)) + (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*Log[d + e*x])/e^7","A",2,1,19,0.05263,1,"{698}"
254,1,218,0,0.1835739,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^6} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^6,x]","-\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7 (d+e x)}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{2 e^7 (d+e x)^2}-\frac{d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7 (d+e x)^3}-\frac{3 c^2 (2 c d-b e) \log (d+e x)}{e^7}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{4 e^7 (d+e x)^4}-\frac{d^3 (c d-b e)^3}{5 e^7 (d+e x)^5}+\frac{c^3 x}{e^6}","-\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7 (d+e x)}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{2 e^7 (d+e x)^2}-\frac{d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7 (d+e x)^3}-\frac{3 c^2 (2 c d-b e) \log (d+e x)}{e^7}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{4 e^7 (d+e x)^4}-\frac{d^3 (c d-b e)^3}{5 e^7 (d+e x)^5}+\frac{c^3 x}{e^6}",1,"(c^3*x)/e^6 - (d^3*(c*d - b*e)^3)/(5*e^7*(d + e*x)^5) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(4*e^7*(d + e*x)^4) - (d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(e^7*(d + e*x)^3) + ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2))/(2*e^7*(d + e*x)^2) - (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(e^7*(d + e*x)) - (3*c^2*(2*c*d - b*e)*Log[d + e*x])/e^7","A",2,1,19,0.05263,1,"{698}"
255,1,228,0,0.1745969,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^7} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^7,x]","-\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{2 e^7 (d+e x)^2}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{3 e^7 (d+e x)^3}-\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{4 e^7 (d+e x)^4}+\frac{3 c^2 (2 c d-b e)}{e^7 (d+e x)}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{5 e^7 (d+e x)^5}-\frac{d^3 (c d-b e)^3}{6 e^7 (d+e x)^6}+\frac{c^3 \log (d+e x)}{e^7}","-\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{2 e^7 (d+e x)^2}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{3 e^7 (d+e x)^3}-\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{4 e^7 (d+e x)^4}+\frac{3 c^2 (2 c d-b e)}{e^7 (d+e x)}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{5 e^7 (d+e x)^5}-\frac{d^3 (c d-b e)^3}{6 e^7 (d+e x)^6}+\frac{c^3 \log (d+e x)}{e^7}",1,"-(d^3*(c*d - b*e)^3)/(6*e^7*(d + e*x)^6) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(5*e^7*(d + e*x)^5) - (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(4*e^7*(d + e*x)^4) + ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2))/(3*e^7*(d + e*x)^3) - (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(2*e^7*(d + e*x)^2) + (3*c^2*(2*c*d - b*e))/(e^7*(d + e*x)) + (c^3*Log[d + e*x])/e^7","A",2,1,19,0.05263,1,"{698}"
256,1,230,0,0.1594246,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^8} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^8,x]","-\frac{c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7 (d+e x)^3}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{4 e^7 (d+e x)^4}-\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7 (d+e x)^5}+\frac{3 c^2 (2 c d-b e)}{2 e^7 (d+e x)^2}+\frac{d^2 (c d-b e)^2 (2 c d-b e)}{2 e^7 (d+e x)^6}-\frac{d^3 (c d-b e)^3}{7 e^7 (d+e x)^7}-\frac{c^3}{e^7 (d+e x)}","-\frac{c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7 (d+e x)^3}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{4 e^7 (d+e x)^4}-\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7 (d+e x)^5}+\frac{3 c^2 (2 c d-b e)}{2 e^7 (d+e x)^2}+\frac{d^2 (c d-b e)^2 (2 c d-b e)}{2 e^7 (d+e x)^6}-\frac{d^3 (c d-b e)^3}{7 e^7 (d+e x)^7}-\frac{c^3}{e^7 (d+e x)}",1,"-(d^3*(c*d - b*e)^3)/(7*e^7*(d + e*x)^7) + (d^2*(c*d - b*e)^2*(2*c*d - b*e))/(2*e^7*(d + e*x)^6) - (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(5*e^7*(d + e*x)^5) + ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2))/(4*e^7*(d + e*x)^4) - (c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(e^7*(d + e*x)^3) + (3*c^2*(2*c*d - b*e))/(2*e^7*(d + e*x)^2) - c^3/(e^7*(d + e*x))","A",2,1,19,0.05263,1,"{698}"
257,1,231,0,0.1579364,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^9} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^9,x]","-\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{4 e^7 (d+e x)^4}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{5 e^7 (d+e x)^5}-\frac{d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{2 e^7 (d+e x)^6}+\frac{c^2 (2 c d-b e)}{e^7 (d+e x)^3}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{7 e^7 (d+e x)^7}-\frac{d^3 (c d-b e)^3}{8 e^7 (d+e x)^8}-\frac{c^3}{2 e^7 (d+e x)^2}","-\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{4 e^7 (d+e x)^4}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{5 e^7 (d+e x)^5}-\frac{d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{2 e^7 (d+e x)^6}+\frac{c^2 (2 c d-b e)}{e^7 (d+e x)^3}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{7 e^7 (d+e x)^7}-\frac{d^3 (c d-b e)^3}{8 e^7 (d+e x)^8}-\frac{c^3}{2 e^7 (d+e x)^2}",1,"-(d^3*(c*d - b*e)^3)/(8*e^7*(d + e*x)^8) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(7*e^7*(d + e*x)^7) - (d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(2*e^7*(d + e*x)^6) + ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2))/(5*e^7*(d + e*x)^5) - (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(4*e^7*(d + e*x)^4) + (c^2*(2*c*d - b*e))/(e^7*(d + e*x)^3) - c^3/(2*e^7*(d + e*x)^2)","A",2,1,19,0.05263,1,"{698}"
258,1,234,0,0.1566021,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^{10}} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^10,x]","-\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7 (d+e x)^5}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{6 e^7 (d+e x)^6}-\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{7 e^7 (d+e x)^7}+\frac{3 c^2 (2 c d-b e)}{4 e^7 (d+e x)^4}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{8 e^7 (d+e x)^8}-\frac{d^3 (c d-b e)^3}{9 e^7 (d+e x)^9}-\frac{c^3}{3 e^7 (d+e x)^3}","-\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7 (d+e x)^5}+\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{6 e^7 (d+e x)^6}-\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{7 e^7 (d+e x)^7}+\frac{3 c^2 (2 c d-b e)}{4 e^7 (d+e x)^4}+\frac{3 d^2 (c d-b e)^2 (2 c d-b e)}{8 e^7 (d+e x)^8}-\frac{d^3 (c d-b e)^3}{9 e^7 (d+e x)^9}-\frac{c^3}{3 e^7 (d+e x)^3}",1,"-(d^3*(c*d - b*e)^3)/(9*e^7*(d + e*x)^9) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(8*e^7*(d + e*x)^8) - (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(7*e^7*(d + e*x)^7) + ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2))/(6*e^7*(d + e*x)^6) - (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(5*e^7*(d + e*x)^5) + (3*c^2*(2*c*d - b*e))/(4*e^7*(d + e*x)^4) - c^3/(3*e^7*(d + e*x)^3)","A",2,1,19,0.05263,1,"{698}"
259,1,99,0,0.0908252,"\int \frac{(d+e x)^4}{b x+c x^2} \, dx","Int[(d + e*x)^4/(b*x + c*x^2),x]","\frac{e^2 x \left(b^2 e^2-4 b c d e+6 c^2 d^2\right)}{c^3}+\frac{e^3 x^2 (4 c d-b e)}{2 c^2}-\frac{(c d-b e)^4 \log (b+c x)}{b c^4}+\frac{d^4 \log (x)}{b}+\frac{e^4 x^3}{3 c}","\frac{e^2 x \left(b^2 e^2-4 b c d e+6 c^2 d^2\right)}{c^3}+\frac{e^3 x^2 (4 c d-b e)}{2 c^2}-\frac{(c d-b e)^4 \log (b+c x)}{b c^4}+\frac{d^4 \log (x)}{b}+\frac{e^4 x^3}{3 c}",1,"(e^2*(6*c^2*d^2 - 4*b*c*d*e + b^2*e^2)*x)/c^3 + (e^3*(4*c*d - b*e)*x^2)/(2*c^2) + (e^4*x^3)/(3*c) + (d^4*Log[x])/b - ((c*d - b*e)^4*Log[b + c*x])/(b*c^4)","A",2,1,19,0.05263,1,"{698}"
260,1,64,0,0.0574003,"\int \frac{(d+e x)^3}{b x+c x^2} \, dx","Int[(d + e*x)^3/(b*x + c*x^2),x]","\frac{e^2 x (3 c d-b e)}{c^2}-\frac{(c d-b e)^3 \log (b+c x)}{b c^3}+\frac{d^3 \log (x)}{b}+\frac{e^3 x^2}{2 c}","\frac{e^2 x (3 c d-b e)}{c^2}-\frac{(c d-b e)^3 \log (b+c x)}{b c^3}+\frac{d^3 \log (x)}{b}+\frac{e^3 x^2}{2 c}",1,"(e^2*(3*c*d - b*e)*x)/c^2 + (e^3*x^2)/(2*c) + (d^3*Log[x])/b - ((c*d - b*e)^3*Log[b + c*x])/(b*c^3)","A",2,1,19,0.05263,1,"{698}"
261,1,42,0,0.0335049,"\int \frac{(d+e x)^2}{b x+c x^2} \, dx","Int[(d + e*x)^2/(b*x + c*x^2),x]","-\frac{(c d-b e)^2 \log (b+c x)}{b c^2}+\frac{d^2 \log (x)}{b}+\frac{e^2 x}{c}","-\frac{(c d-b e)^2 \log (b+c x)}{b c^2}+\frac{d^2 \log (x)}{b}+\frac{e^2 x}{c}",1,"(e^2*x)/c + (d^2*Log[x])/b - ((c*d - b*e)^2*Log[b + c*x])/(b*c^2)","A",2,1,19,0.05263,1,"{698}"
262,1,30,0,0.0207153,"\int \frac{d+e x}{b x+c x^2} \, dx","Int[(d + e*x)/(b*x + c*x^2),x]","\frac{d \log (x)}{b}-\frac{(c d-b e) \log (b+c x)}{b c}","\frac{d \log (x)}{b}-\frac{(c d-b e) \log (b+c x)}{b c}",1,"(d*Log[x])/b - ((c*d - b*e)*Log[b + c*x])/(b*c)","A",2,1,17,0.05882,1,"{631}"
263,1,18,0,0.0030771,"\int \frac{1}{b x+c x^2} \, dx","Int[(b*x + c*x^2)^(-1),x]","\frac{\log (x)}{b}-\frac{\log (b+c x)}{b}","\frac{\log (x)}{b}-\frac{\log (b+c x)}{b}",1,"Log[x]/b - Log[b + c*x]/b","A",1,1,11,0.09091,1,"{615}"
264,1,53,0,0.0462377,"\int \frac{1}{(d+e x) \left(b x+c x^2\right)} \, dx","Int[1/((d + e*x)*(b*x + c*x^2)),x]","-\frac{c \log (b+c x)}{b (c d-b e)}+\frac{e \log (d+e x)}{d (c d-b e)}+\frac{\log (x)}{b d}","-\frac{c \log (b+c x)}{b (c d-b e)}+\frac{e \log (d+e x)}{d (c d-b e)}+\frac{\log (x)}{b d}",1,"Log[x]/(b*d) - (c*Log[b + c*x])/(b*(c*d - b*e)) + (e*Log[d + e*x])/(d*(c*d - b*e))","A",2,1,19,0.05263,1,"{698}"
265,1,87,0,0.0776652,"\int \frac{1}{(d+e x)^2 \left(b x+c x^2\right)} \, dx","Int[1/((d + e*x)^2*(b*x + c*x^2)),x]","-\frac{c^2 \log (b+c x)}{b (c d-b e)^2}+\frac{e (2 c d-b e) \log (d+e x)}{d^2 (c d-b e)^2}-\frac{e}{d (d+e x) (c d-b e)}+\frac{\log (x)}{b d^2}","-\frac{c^2 \log (b+c x)}{b (c d-b e)^2}+\frac{e (2 c d-b e) \log (d+e x)}{d^2 (c d-b e)^2}-\frac{e}{d (d+e x) (c d-b e)}+\frac{\log (x)}{b d^2}",1,"-(e/(d*(c*d - b*e)*(d + e*x))) + Log[x]/(b*d^2) - (c^2*Log[b + c*x])/(b*(c*d - b*e)^2) + (e*(2*c*d - b*e)*Log[d + e*x])/(d^2*(c*d - b*e)^2)","A",2,1,19,0.05263,1,"{698}"
266,1,134,0,0.1198241,"\int \frac{1}{(d+e x)^3 \left(b x+c x^2\right)} \, dx","Int[1/((d + e*x)^3*(b*x + c*x^2)),x]","\frac{e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right) \log (d+e x)}{d^3 (c d-b e)^3}-\frac{c^3 \log (b+c x)}{b (c d-b e)^3}-\frac{e (2 c d-b e)}{d^2 (d+e x) (c d-b e)^2}-\frac{e}{2 d (d+e x)^2 (c d-b e)}+\frac{\log (x)}{b d^3}","\frac{e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right) \log (d+e x)}{d^3 (c d-b e)^3}-\frac{c^3 \log (b+c x)}{b (c d-b e)^3}-\frac{e (2 c d-b e)}{d^2 (d+e x) (c d-b e)^2}-\frac{e}{2 d (d+e x)^2 (c d-b e)}+\frac{\log (x)}{b d^3}",1,"-e/(2*d*(c*d - b*e)*(d + e*x)^2) - (e*(2*c*d - b*e))/(d^2*(c*d - b*e)^2*(d + e*x)) + Log[x]/(b*d^3) - (c^3*Log[b + c*x])/(b*(c*d - b*e)^3) + (e*(3*c^2*d^2 - 3*b*c*d*e + b^2*e^2)*Log[d + e*x])/(d^3*(c*d - b*e)^3)","A",2,1,19,0.05263,1,"{698}"
267,1,118,0,0.1377199,"\int \frac{(d+e x)^5}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)^5/(b*x + c*x^2)^2,x]","-\frac{(c d-b e)^5}{b^2 c^4 (b+c x)}+\frac{(c d-b e)^4 (3 b e+2 c d) \log (b+c x)}{b^3 c^4}-\frac{d^4 \log (x) (2 c d-5 b e)}{b^3}-\frac{d^5}{b^2 x}+\frac{e^4 x (5 c d-2 b e)}{c^3}+\frac{e^5 x^2}{2 c^2}","-\frac{(c d-b e)^5}{b^2 c^4 (b+c x)}+\frac{(c d-b e)^4 (3 b e+2 c d) \log (b+c x)}{b^3 c^4}-\frac{d^4 \log (x) (2 c d-5 b e)}{b^3}-\frac{d^5}{b^2 x}+\frac{e^4 x (5 c d-2 b e)}{c^3}+\frac{e^5 x^2}{2 c^2}",1,"-(d^5/(b^2*x)) + (e^4*(5*c*d - 2*b*e)*x)/c^3 + (e^5*x^2)/(2*c^2) - (c*d - b*e)^5/(b^2*c^4*(b + c*x)) - (d^4*(2*c*d - 5*b*e)*Log[x])/b^3 + ((c*d - b*e)^4*(2*c*d + 3*b*e)*Log[b + c*x])/(b^3*c^4)","A",2,1,19,0.05263,1,"{698}"
268,1,94,0,0.1002948,"\int \frac{(d+e x)^4}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)^4/(b*x + c*x^2)^2,x]","-\frac{(c d-b e)^4}{b^2 c^3 (b+c x)}+\frac{2 (c d-b e)^3 (b e+c d) \log (b+c x)}{b^3 c^3}-\frac{2 d^3 \log (x) (c d-2 b e)}{b^3}-\frac{d^4}{b^2 x}+\frac{e^4 x}{c^2}","-\frac{(c d-b e)^4}{b^2 c^3 (b+c x)}+\frac{2 (c d-b e)^3 (b e+c d) \log (b+c x)}{b^3 c^3}-\frac{2 d^3 \log (x) (c d-2 b e)}{b^3}-\frac{d^4}{b^2 x}+\frac{e^4 x}{c^2}",1,"-(d^4/(b^2*x)) + (e^4*x)/c^2 - (c*d - b*e)^4/(b^2*c^3*(b + c*x)) - (2*d^3*(c*d - 2*b*e)*Log[x])/b^3 + (2*(c*d - b*e)^3*(c*d + b*e)*Log[b + c*x])/(b^3*c^3)","A",2,1,19,0.05263,1,"{698}"
269,1,87,0,0.081705,"\int \frac{(d+e x)^3}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)^3/(b*x + c*x^2)^2,x]","-\frac{(c d-b e)^3}{b^2 c^2 (b+c x)}+\frac{(c d-b e)^2 (b e+2 c d) \log (b+c x)}{b^3 c^2}-\frac{d^2 \log (x) (2 c d-3 b e)}{b^3}-\frac{d^3}{b^2 x}","-\frac{(c d-b e)^3}{b^2 c^2 (b+c x)}+\frac{(c d-b e)^2 (b e+2 c d) \log (b+c x)}{b^3 c^2}-\frac{d^2 \log (x) (2 c d-3 b e)}{b^3}-\frac{d^3}{b^2 x}",1,"-(d^3/(b^2*x)) - (c*d - b*e)^3/(b^2*c^2*(b + c*x)) - (d^2*(2*c*d - 3*b*e)*Log[x])/b^3 + ((c*d - b*e)^2*(2*c*d + b*e)*Log[b + c*x])/(b^3*c^2)","A",2,1,19,0.05263,1,"{698}"
270,1,73,0,0.0581193,"\int \frac{(d+e x)^2}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)^2/(b*x + c*x^2)^2,x]","-\frac{(c d-b e)^2}{b^2 c (b+c x)}-\frac{2 d \log (x) (c d-b e)}{b^3}+\frac{2 d (c d-b e) \log (b+c x)}{b^3}-\frac{d^2}{b^2 x}","-\frac{(c d-b e)^2}{b^2 c (b+c x)}-\frac{2 d \log (x) (c d-b e)}{b^3}+\frac{2 d (c d-b e) \log (b+c x)}{b^3}-\frac{d^2}{b^2 x}",1,"-(d^2/(b^2*x)) - (c*d - b*e)^2/(b^2*c*(b + c*x)) - (2*d*(c*d - b*e)*Log[x])/b^3 + (2*d*(c*d - b*e)*Log[b + c*x])/b^3","A",2,1,19,0.05263,1,"{698}"
271,1,65,0,0.0503731,"\int \frac{d+e x}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)/(b*x + c*x^2)^2,x]","-\frac{c d-b e}{b^2 (b+c x)}-\frac{\log (x) (2 c d-b e)}{b^3}+\frac{(2 c d-b e) \log (b+c x)}{b^3}-\frac{d}{b^2 x}","-\frac{c d-b e}{b^2 (b+c x)}-\frac{\log (x) (2 c d-b e)}{b^3}+\frac{(2 c d-b e) \log (b+c x)}{b^3}-\frac{d}{b^2 x}",1,"-(d/(b^2*x)) - (c*d - b*e)/(b^2*(b + c*x)) - ((2*c*d - b*e)*Log[x])/b^3 + ((2*c*d - b*e)*Log[b + c*x])/b^3","A",2,1,17,0.05882,1,"{631}"
272,1,43,0,0.009857,"\int \frac{1}{\left(b x+c x^2\right)^2} \, dx","Int[(b*x + c*x^2)^(-2),x]","-\frac{b+2 c x}{b^2 \left(b x+c x^2\right)}-\frac{2 c \log (x)}{b^3}+\frac{2 c \log (b+c x)}{b^3}","-\frac{b+2 c x}{b^2 \left(b x+c x^2\right)}-\frac{2 c \log (x)}{b^3}+\frac{2 c \log (b+c x)}{b^3}",1,"-((b + 2*c*x)/(b^2*(b*x + c*x^2))) - (2*c*Log[x])/b^3 + (2*c*Log[b + c*x])/b^3","A",2,2,11,0.1818,1,"{614, 615}"
273,1,110,0,0.1180405,"\int \frac{1}{(d+e x) \left(b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)*(b*x + c*x^2)^2),x]","-\frac{c^2}{b^2 (b+c x) (c d-b e)}+\frac{c^2 (2 c d-3 b e) \log (b+c x)}{b^3 (c d-b e)^2}-\frac{\log (x) (b e+2 c d)}{b^3 d^2}-\frac{1}{b^2 d x}+\frac{e^3 \log (d+e x)}{d^2 (c d-b e)^2}","-\frac{c^2}{b^2 (b+c x) (c d-b e)}+\frac{c^2 (2 c d-3 b e) \log (b+c x)}{b^3 (c d-b e)^2}-\frac{\log (x) (b e+2 c d)}{b^3 d^2}-\frac{1}{b^2 d x}+\frac{e^3 \log (d+e x)}{d^2 (c d-b e)^2}",1,"-(1/(b^2*d*x)) - c^2/(b^2*(c*d - b*e)*(b + c*x)) - ((2*c*d + b*e)*Log[x])/(b^3*d^2) + (c^2*(2*c*d - 3*b*e)*Log[b + c*x])/(b^3*(c*d - b*e)^2) + (e^3*Log[d + e*x])/(d^2*(c*d - b*e)^2)","A",2,1,19,0.05263,1,"{698}"
274,1,144,0,0.1672681,"\int \frac{1}{(d+e x)^2 \left(b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)^2*(b*x + c*x^2)^2),x]","-\frac{c^3}{b^2 (b+c x) (c d-b e)^2}+\frac{2 c^3 (c d-2 b e) \log (b+c x)}{b^3 (c d-b e)^3}-\frac{2 \log (x) (b e+c d)}{b^3 d^3}-\frac{1}{b^2 d^2 x}-\frac{e^3}{d^2 (d+e x) (c d-b e)^2}+\frac{2 e^3 (2 c d-b e) \log (d+e x)}{d^3 (c d-b e)^3}","-\frac{c^3}{b^2 (b+c x) (c d-b e)^2}+\frac{2 c^3 (c d-2 b e) \log (b+c x)}{b^3 (c d-b e)^3}-\frac{2 \log (x) (b e+c d)}{b^3 d^3}-\frac{1}{b^2 d^2 x}-\frac{e^3}{d^2 (d+e x) (c d-b e)^2}+\frac{2 e^3 (2 c d-b e) \log (d+e x)}{d^3 (c d-b e)^3}",1,"-(1/(b^2*d^2*x)) - c^3/(b^2*(c*d - b*e)^2*(b + c*x)) - e^3/(d^2*(c*d - b*e)^2*(d + e*x)) - (2*(c*d + b*e)*Log[x])/(b^3*d^3) + (2*c^3*(c*d - 2*b*e)*Log[b + c*x])/(b^3*(c*d - b*e)^3) + (2*e^3*(2*c*d - b*e)*Log[d + e*x])/(d^3*(c*d - b*e)^3)","A",2,1,19,0.05263,1,"{698}"
275,1,203,0,0.2689473,"\int \frac{(d+e x)^7}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^7/(b*x + c*x^2)^3,x]","\frac{3 d^5 \log (x) \left(7 b^2 e^2-7 b c d e+2 c^2 d^2\right)}{b^5}-\frac{3 (c d-b e)^5 \left(2 b^2 e^2+3 b c d e+2 c^2 d^2\right) \log (b+c x)}{b^5 c^5}+\frac{(c d-b e)^6 (4 b e+3 c d)}{b^4 c^5 (b+c x)}+\frac{(c d-b e)^7}{2 b^3 c^5 (b+c x)^2}+\frac{d^6 (3 c d-7 b e)}{b^4 x}-\frac{d^7}{2 b^3 x^2}+\frac{e^6 x (7 c d-3 b e)}{c^4}+\frac{e^7 x^2}{2 c^3}","\frac{3 d^5 \log (x) \left(7 b^2 e^2-7 b c d e+2 c^2 d^2\right)}{b^5}-\frac{3 (c d-b e)^5 \left(2 b^2 e^2+3 b c d e+2 c^2 d^2\right) \log (b+c x)}{b^5 c^5}+\frac{(c d-b e)^6 (4 b e+3 c d)}{b^4 c^5 (b+c x)}+\frac{(c d-b e)^7}{2 b^3 c^5 (b+c x)^2}+\frac{d^6 (3 c d-7 b e)}{b^4 x}-\frac{d^7}{2 b^3 x^2}+\frac{e^6 x (7 c d-3 b e)}{c^4}+\frac{e^7 x^2}{2 c^3}",1,"-d^7/(2*b^3*x^2) + (d^6*(3*c*d - 7*b*e))/(b^4*x) + (e^6*(7*c*d - 3*b*e)*x)/c^4 + (e^7*x^2)/(2*c^3) + (c*d - b*e)^7/(2*b^3*c^5*(b + c*x)^2) + ((c*d - b*e)^6*(3*c*d + 4*b*e))/(b^4*c^5*(b + c*x)) + (3*d^5*(2*c^2*d^2 - 7*b*c*d*e + 7*b^2*e^2)*Log[x])/b^5 - (3*(c*d - b*e)^5*(2*c^2*d^2 + 3*b*c*d*e + 2*b^2*e^2)*Log[b + c*x])/(b^5*c^5)","A",2,1,19,0.05263,1,"{698}"
276,1,179,0,0.2223768,"\int \frac{(d+e x)^6}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^6/(b*x + c*x^2)^3,x]","\frac{3 d^4 \log (x) \left(5 b^2 e^2-6 b c d e+2 c^2 d^2\right)}{b^5}-\frac{3 (c d-b e)^4 \left(b^2 e^2+2 b c d e+2 c^2 d^2\right) \log (b+c x)}{b^5 c^4}+\frac{3 (c d-b e)^5 (b e+c d)}{b^4 c^4 (b+c x)}+\frac{(c d-b e)^6}{2 b^3 c^4 (b+c x)^2}+\frac{3 d^5 (c d-2 b e)}{b^4 x}-\frac{d^6}{2 b^3 x^2}+\frac{e^6 x}{c^3}","\frac{3 d^4 \log (x) \left(5 b^2 e^2-6 b c d e+2 c^2 d^2\right)}{b^5}-\frac{3 (c d-b e)^4 \left(b^2 e^2+2 b c d e+2 c^2 d^2\right) \log (b+c x)}{b^5 c^4}+\frac{3 (c d-b e)^5 (b e+c d)}{b^4 c^4 (b+c x)}+\frac{(c d-b e)^6}{2 b^3 c^4 (b+c x)^2}+\frac{3 d^5 (c d-2 b e)}{b^4 x}-\frac{d^6}{2 b^3 x^2}+\frac{e^6 x}{c^3}",1,"-d^6/(2*b^3*x^2) + (3*d^5*(c*d - 2*b*e))/(b^4*x) + (e^6*x)/c^3 + (c*d - b*e)^6/(2*b^3*c^4*(b + c*x)^2) + (3*(c*d - b*e)^5*(c*d + b*e))/(b^4*c^4*(b + c*x)) + (3*d^4*(2*c^2*d^2 - 6*b*c*d*e + 5*b^2*e^2)*Log[x])/b^5 - (3*(c*d - b*e)^4*(2*c^2*d^2 + 2*b*c*d*e + b^2*e^2)*Log[b + c*x])/(b^5*c^4)","A",2,1,19,0.05263,1,"{698}"
277,1,171,0,0.178273,"\int \frac{(d+e x)^5}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^5/(b*x + c*x^2)^3,x]","\frac{d^3 \log (x) \left(10 b^2 e^2-15 b c d e+6 c^2 d^2\right)}{b^5}-\frac{(c d-b e)^3 \left(b^2 e^2+3 b c d e+6 c^2 d^2\right) \log (b+c x)}{b^5 c^3}+\frac{(c d-b e)^4 (2 b e+3 c d)}{b^4 c^3 (b+c x)}+\frac{(c d-b e)^5}{2 b^3 c^3 (b+c x)^2}+\frac{d^4 (3 c d-5 b e)}{b^4 x}-\frac{d^5}{2 b^3 x^2}","\frac{d^3 \log (x) \left(10 b^2 e^2-15 b c d e+6 c^2 d^2\right)}{b^5}-\frac{(c d-b e)^3 \left(b^2 e^2+3 b c d e+6 c^2 d^2\right) \log (b+c x)}{b^5 c^3}+\frac{(c d-b e)^4 (2 b e+3 c d)}{b^4 c^3 (b+c x)}+\frac{(c d-b e)^5}{2 b^3 c^3 (b+c x)^2}+\frac{d^4 (3 c d-5 b e)}{b^4 x}-\frac{d^5}{2 b^3 x^2}",1,"-d^5/(2*b^3*x^2) + (d^4*(3*c*d - 5*b*e))/(b^4*x) + (c*d - b*e)^5/(2*b^3*c^3*(b + c*x)^2) + ((c*d - b*e)^4*(3*c*d + 2*b*e))/(b^4*c^3*(b + c*x)) + (d^3*(6*c^2*d^2 - 15*b*c*d*e + 10*b^2*e^2)*Log[x])/b^5 - ((c*d - b*e)^3*(6*c^2*d^2 + 3*b*c*d*e + b^2*e^2)*Log[b + c*x])/(b^5*c^3)","A",2,1,19,0.05263,1,"{698}"
278,1,136,0,0.1515471,"\int \frac{(d+e x)^4}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^4/(b*x + c*x^2)^3,x]","\frac{(c d-b e)^3 (b e+3 c d)}{b^4 c^2 (b+c x)}+\frac{(c d-b e)^4}{2 b^3 c^2 (b+c x)^2}+\frac{d^3 (3 c d-4 b e)}{b^4 x}+\frac{6 d^2 \log (x) (c d-b e)^2}{b^5}-\frac{6 d^2 (c d-b e)^2 \log (b+c x)}{b^5}-\frac{d^4}{2 b^3 x^2}","\frac{(c d-b e)^3 (b e+3 c d)}{b^4 c^2 (b+c x)}+\frac{(c d-b e)^4}{2 b^3 c^2 (b+c x)^2}+\frac{d^3 (3 c d-4 b e)}{b^4 x}+\frac{6 d^2 \log (x) (c d-b e)^2}{b^5}-\frac{6 d^2 (c d-b e)^2 \log (b+c x)}{b^5}-\frac{d^4}{2 b^3 x^2}",1,"-d^4/(2*b^3*x^2) + (d^3*(3*c*d - 4*b*e))/(b^4*x) + (c*d - b*e)^4/(2*b^3*c^2*(b + c*x)^2) + ((c*d - b*e)^3*(3*c*d + b*e))/(b^4*c^2*(b + c*x)) + (6*d^2*(c*d - b*e)^2*Log[x])/b^5 - (6*d^2*(c*d - b*e)^2*Log[b + c*x])/b^5","A",2,1,19,0.05263,1,"{698}"
279,1,137,0,0.1471185,"\int \frac{(d+e x)^3}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^3/(b*x + c*x^2)^3,x]","\frac{3 d^2 (c d-b e)}{b^4 x}+\frac{3 d (c d-b e)^2}{b^4 (b+c x)}+\frac{(c d-b e)^3}{2 b^3 c (b+c x)^2}+\frac{3 d \log (x) (c d-b e) (2 c d-b e)}{b^5}-\frac{3 d (c d-b e) (2 c d-b e) \log (b+c x)}{b^5}-\frac{d^3}{2 b^3 x^2}","\frac{3 d^2 (c d-b e)}{b^4 x}+\frac{3 d (c d-b e)^2}{b^4 (b+c x)}+\frac{(c d-b e)^3}{2 b^3 c (b+c x)^2}+\frac{3 d \log (x) (c d-b e) (2 c d-b e)}{b^5}-\frac{3 d (c d-b e) (2 c d-b e) \log (b+c x)}{b^5}-\frac{d^3}{2 b^3 x^2}",1,"-d^3/(2*b^3*x^2) + (3*d^2*(c*d - b*e))/(b^4*x) + (c*d - b*e)^3/(2*b^3*c*(b + c*x)^2) + (3*d*(c*d - b*e)^2)/(b^4*(b + c*x)) + (3*d*(c*d - b*e)*(2*c*d - b*e)*Log[x])/b^5 - (3*d*(c*d - b*e)*(2*c*d - b*e)*Log[b + c*x])/b^5","A",2,1,19,0.05263,1,"{698}"
280,1,144,0,0.1327593,"\int \frac{(d+e x)^2}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^2/(b*x + c*x^2)^3,x]","\frac{\log (x) \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{b^5}-\frac{\left(b^2 e^2-6 b c d e+6 c^2 d^2\right) \log (b+c x)}{b^5}+\frac{d (3 c d-2 b e)}{b^4 x}+\frac{(c d-b e) (3 c d-b e)}{b^4 (b+c x)}+\frac{(c d-b e)^2}{2 b^3 (b+c x)^2}-\frac{d^2}{2 b^3 x^2}","\frac{\log (x) \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{b^5}-\frac{\left(b^2 e^2-6 b c d e+6 c^2 d^2\right) \log (b+c x)}{b^5}+\frac{d (3 c d-2 b e)}{b^4 x}+\frac{(c d-b e) (3 c d-b e)}{b^4 (b+c x)}+\frac{(c d-b e)^2}{2 b^3 (b+c x)^2}-\frac{d^2}{2 b^3 x^2}",1,"-d^2/(2*b^3*x^2) + (d*(3*c*d - 2*b*e))/(b^4*x) + (c*d - b*e)^2/(2*b^3*(b + c*x)^2) + ((c*d - b*e)*(3*c*d - b*e))/(b^4*(b + c*x)) + ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*Log[x])/b^5 - ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*Log[b + c*x])/b^5","A",2,1,19,0.05263,1,"{698}"
281,1,110,0,0.1032719,"\int \frac{d+e x}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)/(b*x + c*x^2)^3,x]","\frac{3 c d-b e}{b^4 x}+\frac{c (3 c d-2 b e)}{b^4 (b+c x)}+\frac{c (c d-b e)}{2 b^3 (b+c x)^2}+\frac{3 c \log (x) (2 c d-b e)}{b^5}-\frac{3 c (2 c d-b e) \log (b+c x)}{b^5}-\frac{d}{2 b^3 x^2}","\frac{3 c d-b e}{b^4 x}+\frac{c (3 c d-2 b e)}{b^4 (b+c x)}+\frac{c (c d-b e)}{2 b^3 (b+c x)^2}+\frac{3 c \log (x) (2 c d-b e)}{b^5}-\frac{3 c (2 c d-b e) \log (b+c x)}{b^5}-\frac{d}{2 b^3 x^2}",1,"-d/(2*b^3*x^2) + (3*c*d - b*e)/(b^4*x) + (c*(c*d - b*e))/(2*b^3*(b + c*x)^2) + (c*(3*c*d - 2*b*e))/(b^4*(b + c*x)) + (3*c*(2*c*d - b*e)*Log[x])/b^5 - (3*c*(2*c*d - b*e)*Log[b + c*x])/b^5","A",2,1,17,0.05882,1,"{631}"
282,1,72,0,0.0192287,"\int \frac{1}{\left(b x+c x^2\right)^3} \, dx","Int[(b*x + c*x^2)^(-3),x]","\frac{6 c^2 \log (x)}{b^5}-\frac{6 c^2 \log (b+c x)}{b^5}+\frac{3 c (b+2 c x)}{b^4 \left(b x+c x^2\right)}-\frac{b+2 c x}{2 b^2 \left(b x+c x^2\right)^2}","\frac{6 c^2 \log (x)}{b^5}-\frac{6 c^2 \log (b+c x)}{b^5}+\frac{3 c (b+2 c x)}{b^4 \left(b x+c x^2\right)}-\frac{b+2 c x}{2 b^2 \left(b x+c x^2\right)^2}",1,"-(b + 2*c*x)/(2*b^2*(b*x + c*x^2)^2) + (3*c*(b + 2*c*x))/(b^4*(b*x + c*x^2)) + (6*c^2*Log[x])/b^5 - (6*c^2*Log[b + c*x])/b^5","A",3,2,11,0.1818,1,"{614, 615}"
283,1,193,0,0.2270958,"\int \frac{1}{(d+e x) \left(b x+c x^2\right)^3} \, dx","Int[1/((d + e*x)*(b*x + c*x^2)^3),x]","\frac{\log (x) \left(b^2 e^2+3 b c d e+6 c^2 d^2\right)}{b^5 d^3}-\frac{c^3 \left(10 b^2 e^2-15 b c d e+6 c^2 d^2\right) \log (b+c x)}{b^5 (c d-b e)^3}+\frac{c^3 (3 c d-4 b e)}{b^4 (b+c x) (c d-b e)^2}+\frac{c^3}{2 b^3 (b+c x)^2 (c d-b e)}+\frac{b e+3 c d}{b^4 d^2 x}-\frac{1}{2 b^3 d x^2}+\frac{e^5 \log (d+e x)}{d^3 (c d-b e)^3}","\frac{\log (x) \left(b^2 e^2+3 b c d e+6 c^2 d^2\right)}{b^5 d^3}-\frac{c^3 \left(10 b^2 e^2-15 b c d e+6 c^2 d^2\right) \log (b+c x)}{b^5 (c d-b e)^3}+\frac{c^3 (3 c d-4 b e)}{b^4 (b+c x) (c d-b e)^2}+\frac{c^3}{2 b^3 (b+c x)^2 (c d-b e)}+\frac{b e+3 c d}{b^4 d^2 x}-\frac{1}{2 b^3 d x^2}+\frac{e^5 \log (d+e x)}{d^3 (c d-b e)^3}",1,"-1/(2*b^3*d*x^2) + (3*c*d + b*e)/(b^4*d^2*x) + c^3/(2*b^3*(c*d - b*e)*(b + c*x)^2) + (c^3*(3*c*d - 4*b*e))/(b^4*(c*d - b*e)^2*(b + c*x)) + ((6*c^2*d^2 + 3*b*c*d*e + b^2*e^2)*Log[x])/(b^5*d^3) - (c^3*(6*c^2*d^2 - 15*b*c*d*e + 10*b^2*e^2)*Log[b + c*x])/(b^5*(c*d - b*e)^3) + (e^5*Log[d + e*x])/(d^3*(c*d - b*e)^3)","A",2,1,19,0.05263,1,"{698}"
284,1,230,0,0.3392302,"\int \frac{1}{(d+e x)^2 \left(b x+c x^2\right)^3} \, dx","Int[1/((d + e*x)^2*(b*x + c*x^2)^3),x]","\frac{3 \log (x) \left(b^2 e^2+2 b c d e+2 c^2 d^2\right)}{b^5 d^4}-\frac{3 c^4 \left(5 b^2 e^2-6 b c d e+2 c^2 d^2\right) \log (b+c x)}{b^5 (c d-b e)^4}+\frac{c^4 (3 c d-5 b e)}{b^4 (b+c x) (c d-b e)^3}+\frac{c^4}{2 b^3 (b+c x)^2 (c d-b e)^2}+\frac{2 b e+3 c d}{b^4 d^3 x}-\frac{1}{2 b^3 d^2 x^2}-\frac{e^5}{d^3 (d+e x) (c d-b e)^3}+\frac{3 e^5 (2 c d-b e) \log (d+e x)}{d^4 (c d-b e)^4}","\frac{3 \log (x) \left(b^2 e^2+2 b c d e+2 c^2 d^2\right)}{b^5 d^4}-\frac{3 c^4 \left(5 b^2 e^2-6 b c d e+2 c^2 d^2\right) \log (b+c x)}{b^5 (c d-b e)^4}+\frac{c^4 (3 c d-5 b e)}{b^4 (b+c x) (c d-b e)^3}+\frac{c^4}{2 b^3 (b+c x)^2 (c d-b e)^2}+\frac{2 b e+3 c d}{b^4 d^3 x}-\frac{1}{2 b^3 d^2 x^2}-\frac{e^5}{d^3 (d+e x) (c d-b e)^3}+\frac{3 e^5 (2 c d-b e) \log (d+e x)}{d^4 (c d-b e)^4}",1,"-1/(2*b^3*d^2*x^2) + (3*c*d + 2*b*e)/(b^4*d^3*x) + c^4/(2*b^3*(c*d - b*e)^2*(b + c*x)^2) + (c^4*(3*c*d - 5*b*e))/(b^4*(c*d - b*e)^3*(b + c*x)) - e^5/(d^3*(c*d - b*e)^3*(d + e*x)) + (3*(2*c^2*d^2 + 2*b*c*d*e + b^2*e^2)*Log[x])/(b^5*d^4) - (3*c^4*(2*c^2*d^2 - 6*b*c*d*e + 5*b^2*e^2)*Log[b + c*x])/(b^5*(c*d - b*e)^4) + (3*e^5*(2*c*d - b*e)*Log[d + e*x])/(d^4*(c*d - b*e)^4)","A",2,1,19,0.05263,1,"{698}"
285,1,210,0,0.269013,"\int (d+e x)^3 \sqrt{b x+c x^2} \, dx","Int[(d + e*x)^3*Sqrt[b*x + c*x^2],x]","\frac{e \left(b x+c x^2\right)^{3/2} \left(35 b^2 e^2+42 c e x (2 c d-b e)-150 b c d e+192 c^2 d^2\right)}{240 c^3}+\frac{(b+2 c x) \sqrt{b x+c x^2} (2 c d-b e) \left(7 b^2 e^2-16 b c d e+16 c^2 d^2\right)}{128 c^4}-\frac{b^2 (2 c d-b e) \left(7 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{9/2}}+\frac{e \left(b x+c x^2\right)^{3/2} (d+e x)^2}{5 c}","\frac{e \left(b x+c x^2\right)^{3/2} \left(35 b^2 e^2+42 c e x (2 c d-b e)-150 b c d e+192 c^2 d^2\right)}{240 c^3}+\frac{(b+2 c x) \sqrt{b x+c x^2} (2 c d-b e) \left(7 b^2 e^2-16 b c d e+16 c^2 d^2\right)}{128 c^4}-\frac{b^2 (2 c d-b e) \left(7 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{9/2}}+\frac{e \left(b x+c x^2\right)^{3/2} (d+e x)^2}{5 c}",1,"((2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + 7*b^2*e^2)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(128*c^4) + (e*(d + e*x)^2*(b*x + c*x^2)^(3/2))/(5*c) + (e*(192*c^2*d^2 - 150*b*c*d*e + 35*b^2*e^2 + 42*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(240*c^3) - (b^2*(2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + 7*b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(9/2))","A",5,5,21,0.2381,1,"{742, 779, 612, 620, 206}"
286,1,162,0,0.1263899,"\int (d+e x)^2 \sqrt{b x+c x^2} \, dx","Int[(d + e*x)^2*Sqrt[b*x + c*x^2],x]","\frac{(b+2 c x) \sqrt{b x+c x^2} \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right)}{64 c^3}-\frac{b^2 \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{7/2}}+\frac{5 e \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{24 c^2}+\frac{e \left(b x+c x^2\right)^{3/2} (d+e x)}{4 c}","\frac{(b+2 c x) \sqrt{b x+c x^2} \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right)}{64 c^3}-\frac{b^2 \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{7/2}}+\frac{5 e \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{24 c^2}+\frac{e \left(b x+c x^2\right)^{3/2} (d+e x)}{4 c}",1,"((16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(64*c^3) + (5*e*(2*c*d - b*e)*(b*x + c*x^2)^(3/2))/(24*c^2) + (e*(d + e*x)*(b*x + c*x^2)^(3/2))/(4*c) - (b^2*(16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(7/2))","A",5,5,21,0.2381,1,"{742, 640, 612, 620, 206}"
287,1,99,0,0.0358537,"\int (d+e x) \sqrt{b x+c x^2} \, dx","Int[(d + e*x)*Sqrt[b*x + c*x^2],x]","-\frac{b^2 (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{5/2}}+\frac{(b+2 c x) \sqrt{b x+c x^2} (2 c d-b e)}{8 c^2}+\frac{e \left(b x+c x^2\right)^{3/2}}{3 c}","-\frac{b^2 (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{5/2}}+\frac{(b+2 c x) \sqrt{b x+c x^2} (2 c d-b e)}{8 c^2}+\frac{e \left(b x+c x^2\right)^{3/2}}{3 c}",1,"((2*c*d - b*e)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(8*c^2) + (e*(b*x + c*x^2)^(3/2))/(3*c) - (b^2*(2*c*d - b*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(5/2))","A",4,4,19,0.2105,1,"{640, 612, 620, 206}"
288,1,60,0,0.0152118,"\int \sqrt{b x+c x^2} \, dx","Int[Sqrt[b*x + c*x^2],x]","\frac{(b+2 c x) \sqrt{b x+c x^2}}{4 c}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{3/2}}","\frac{(b+2 c x) \sqrt{b x+c x^2}}{4 c}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{3/2}}",1,"((b + 2*c*x)*Sqrt[b*x + c*x^2])/(4*c) - (b^2*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(3/2))","A",3,3,13,0.2308,1,"{612, 620, 206}"
289,1,129,0,0.1412615,"\int \frac{\sqrt{b x+c x^2}}{d+e x} \, dx","Int[Sqrt[b*x + c*x^2]/(d + e*x),x]","-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c} e^2}+\frac{\sqrt{d} \sqrt{c d-b e} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^2}+\frac{\sqrt{b x+c x^2}}{e}","-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c} e^2}+\frac{\sqrt{d} \sqrt{c d-b e} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^2}+\frac{\sqrt{b x+c x^2}}{e}",1,"Sqrt[b*x + c*x^2]/e - ((2*c*d - b*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(Sqrt[c]*e^2) + (Sqrt[d]*Sqrt[c*d - b*e]*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/e^2","A",6,5,21,0.2381,1,"{734, 843, 620, 206, 724}"
290,1,140,0,0.1108187,"\int \frac{\sqrt{b x+c x^2}}{(d+e x)^2} \, dx","Int[Sqrt[b*x + c*x^2]/(d + e*x)^2,x]","-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 \sqrt{d} e^2 \sqrt{c d-b e}}-\frac{\sqrt{b x+c x^2}}{e (d+e x)}+\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{e^2}","-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 \sqrt{d} e^2 \sqrt{c d-b e}}-\frac{\sqrt{b x+c x^2}}{e (d+e x)}+\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{e^2}",1,"-(Sqrt[b*x + c*x^2]/(e*(d + e*x))) + (2*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/e^2 - ((2*c*d - b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*Sqrt[d]*e^2*Sqrt[c*d - b*e])","A",6,5,21,0.2381,1,"{732, 843, 620, 206, 724}"
291,1,127,0,0.0876072,"\int \frac{\sqrt{b x+c x^2}}{(d+e x)^3} \, dx","Int[Sqrt[b*x + c*x^2]/(d + e*x)^3,x]","\frac{\sqrt{b x+c x^2} (x (2 c d-b e)+b d)}{4 d (d+e x)^2 (c d-b e)}-\frac{b^2 \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{3/2} (c d-b e)^{3/2}}","\frac{\sqrt{b x+c x^2} (x (2 c d-b e)+b d)}{4 d (d+e x)^2 (c d-b e)}-\frac{b^2 \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{3/2} (c d-b e)^{3/2}}",1,"((b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(4*d*(c*d - b*e)*(d + e*x)^2) - (b^2*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*d^(3/2)*(c*d - b*e)^(3/2))","A",3,3,21,0.1429,1,"{720, 724, 206}"
292,1,183,0,0.1383806,"\int \frac{\sqrt{b x+c x^2}}{(d+e x)^4} \, dx","Int[Sqrt[b*x + c*x^2]/(d + e*x)^4,x]","-\frac{b^2 (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 d^{5/2} (c d-b e)^{5/2}}+\frac{\sqrt{b x+c x^2} (2 c d-b e) (x (2 c d-b e)+b d)}{8 d^2 (d+e x)^2 (c d-b e)^2}-\frac{e \left(b x+c x^2\right)^{3/2}}{3 d (d+e x)^3 (c d-b e)}","-\frac{b^2 (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 d^{5/2} (c d-b e)^{5/2}}+\frac{\sqrt{b x+c x^2} (2 c d-b e) (x (2 c d-b e)+b d)}{8 d^2 (d+e x)^2 (c d-b e)^2}-\frac{e \left(b x+c x^2\right)^{3/2}}{3 d (d+e x)^3 (c d-b e)}",1,"((2*c*d - b*e)*(b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(8*d^2*(c*d - b*e)^2*(d + e*x)^2) - (e*(b*x + c*x^2)^(3/2))/(3*d*(c*d - b*e)*(d + e*x)^3) - (b^2*(2*c*d - b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(16*d^(5/2)*(c*d - b*e)^(5/2))","A",4,4,21,0.1905,1,"{730, 720, 724, 206}"
293,1,258,0,0.3192785,"\int \frac{\sqrt{b x+c x^2}}{(d+e x)^5} \, dx","Int[Sqrt[b*x + c*x^2]/(d + e*x)^5,x]","\frac{\sqrt{b x+c x^2} \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right) (x (2 c d-b e)+b d)}{64 d^3 (d+e x)^2 (c d-b e)^3}-\frac{b^2 \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{128 d^{7/2} (c d-b e)^{7/2}}-\frac{5 e \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{24 d^2 (d+e x)^3 (c d-b e)^2}-\frac{e \left(b x+c x^2\right)^{3/2}}{4 d (d+e x)^4 (c d-b e)}","\frac{\sqrt{b x+c x^2} \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right) (x (2 c d-b e)+b d)}{64 d^3 (d+e x)^2 (c d-b e)^3}-\frac{b^2 \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{128 d^{7/2} (c d-b e)^{7/2}}-\frac{5 e \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{24 d^2 (d+e x)^3 (c d-b e)^2}-\frac{e \left(b x+c x^2\right)^{3/2}}{4 d (d+e x)^4 (c d-b e)}",1,"((16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*(b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(64*d^3*(c*d - b*e)^3*(d + e*x)^2) - (e*(b*x + c*x^2)^(3/2))/(4*d*(c*d - b*e)*(d + e*x)^4) - (5*e*(2*c*d - b*e)*(b*x + c*x^2)^(3/2))/(24*d^2*(c*d - b*e)^2*(d + e*x)^3) - (b^2*(16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(128*d^(7/2)*(c*d - b*e)^(7/2))","A",5,5,21,0.2381,1,"{744, 806, 720, 724, 206}"
294,1,337,0,0.4557597,"\int \frac{\sqrt{b x+c x^2}}{(d+e x)^6} \, dx","Int[Sqrt[b*x + c*x^2]/(d + e*x)^6,x]","-\frac{e \left(b x+c x^2\right)^{3/2} \left(35 b^2 e^2-108 b c d e+108 c^2 d^2\right)}{240 d^3 (d+e x)^3 (c d-b e)^3}+\frac{\sqrt{b x+c x^2} (2 c d-b e) \left(7 b^2 e^2-16 b c d e+16 c^2 d^2\right) (x (2 c d-b e)+b d)}{128 d^4 (d+e x)^2 (c d-b e)^4}-\frac{b^2 (2 c d-b e) \left(7 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{256 d^{9/2} (c d-b e)^{9/2}}-\frac{7 e \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{40 d^2 (d+e x)^4 (c d-b e)^2}-\frac{e \left(b x+c x^2\right)^{3/2}}{5 d (d+e x)^5 (c d-b e)}","-\frac{e \left(b x+c x^2\right)^{3/2} \left(35 b^2 e^2-108 b c d e+108 c^2 d^2\right)}{240 d^3 (d+e x)^3 (c d-b e)^3}+\frac{\sqrt{b x+c x^2} (2 c d-b e) \left(7 b^2 e^2-16 b c d e+16 c^2 d^2\right) (x (2 c d-b e)+b d)}{128 d^4 (d+e x)^2 (c d-b e)^4}-\frac{b^2 (2 c d-b e) \left(7 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{256 d^{9/2} (c d-b e)^{9/2}}-\frac{7 e \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{40 d^2 (d+e x)^4 (c d-b e)^2}-\frac{e \left(b x+c x^2\right)^{3/2}}{5 d (d+e x)^5 (c d-b e)}",1,"((2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + 7*b^2*e^2)*(b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(128*d^4*(c*d - b*e)^4*(d + e*x)^2) - (e*(b*x + c*x^2)^(3/2))/(5*d*(c*d - b*e)*(d + e*x)^5) - (7*e*(2*c*d - b*e)*(b*x + c*x^2)^(3/2))/(40*d^2*(c*d - b*e)^2*(d + e*x)^4) - (e*(108*c^2*d^2 - 108*b*c*d*e + 35*b^2*e^2)*(b*x + c*x^2)^(3/2))/(240*d^3*(c*d - b*e)^3*(d + e*x)^3) - (b^2*(2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + 7*b^2*e^2)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(256*d^(9/2)*(c*d - b*e)^(9/2))","A",6,6,21,0.2857,1,"{744, 834, 806, 720, 724, 206}"
295,1,271,0,0.3496647,"\int (d+e x)^3 \left(b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^3*(b*x + c*x^2)^(3/2),x]","-\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (2 c d-b e) \left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{1024 c^5}+\frac{e \left(b x+c x^2\right)^{5/2} \left(21 b^2 e^2+30 c e x (2 c d-b e)-98 b c d e+128 c^2 d^2\right)}{280 c^3}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (2 c d-b e) \left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{128 c^4}+\frac{3 b^4 (2 c d-b e) \left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{11/2}}+\frac{e \left(b x+c x^2\right)^{5/2} (d+e x)^2}{7 c}","-\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (2 c d-b e) \left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{1024 c^5}+\frac{e \left(b x+c x^2\right)^{5/2} \left(21 b^2 e^2+30 c e x (2 c d-b e)-98 b c d e+128 c^2 d^2\right)}{280 c^3}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (2 c d-b e) \left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{128 c^4}+\frac{3 b^4 (2 c d-b e) \left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{11/2}}+\frac{e \left(b x+c x^2\right)^{5/2} (d+e x)^2}{7 c}",1,"(-3*b^2*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(1024*c^5) + ((2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(128*c^4) + (e*(d + e*x)^2*(b*x + c*x^2)^(5/2))/(7*c) + (e*(128*c^2*d^2 - 98*b*c*d*e + 21*b^2*e^2 + 30*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(5/2))/(280*c^3) + (3*b^4*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(1024*c^(11/2))","A",6,5,21,0.2381,1,"{742, 779, 612, 620, 206}"
296,1,214,0,0.1792989,"\int (d+e x)^2 \left(b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^2*(b*x + c*x^2)^(3/2),x]","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} \left(7 b^2 e^2-24 b c d e+24 c^2 d^2\right)}{512 c^4}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} \left(7 b^2 e^2-24 b c d e+24 c^2 d^2\right)}{192 c^3}+\frac{b^4 \left(7 b^2 e^2-24 b c d e+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{9/2}}+\frac{7 e \left(b x+c x^2\right)^{5/2} (2 c d-b e)}{60 c^2}+\frac{e \left(b x+c x^2\right)^{5/2} (d+e x)}{6 c}","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} \left(7 b^2 e^2-24 b c d e+24 c^2 d^2\right)}{512 c^4}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} \left(7 b^2 e^2-24 b c d e+24 c^2 d^2\right)}{192 c^3}+\frac{b^4 \left(7 b^2 e^2-24 b c d e+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{9/2}}+\frac{7 e \left(b x+c x^2\right)^{5/2} (2 c d-b e)}{60 c^2}+\frac{e \left(b x+c x^2\right)^{5/2} (d+e x)}{6 c}",1,"-(b^2*(24*c^2*d^2 - 24*b*c*d*e + 7*b^2*e^2)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(512*c^4) + ((24*c^2*d^2 - 24*b*c*d*e + 7*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(192*c^3) + (7*e*(2*c*d - b*e)*(b*x + c*x^2)^(5/2))/(60*c^2) + (e*(d + e*x)*(b*x + c*x^2)^(5/2))/(6*c) + (b^4*(24*c^2*d^2 - 24*b*c*d*e + 7*b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(512*c^(9/2))","A",6,5,21,0.2381,1,"{742, 640, 612, 620, 206}"
297,1,137,0,0.0526371,"\int (d+e x) \left(b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)*(b*x + c*x^2)^(3/2),x]","-\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (2 c d-b e)}{128 c^3}+\frac{3 b^4 (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{7/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{16 c^2}+\frac{e \left(b x+c x^2\right)^{5/2}}{5 c}","-\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (2 c d-b e)}{128 c^3}+\frac{3 b^4 (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{7/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{16 c^2}+\frac{e \left(b x+c x^2\right)^{5/2}}{5 c}",1,"(-3*b^2*(2*c*d - b*e)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(128*c^3) + ((2*c*d - b*e)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(16*c^2) + (e*(b*x + c*x^2)^(5/2))/(5*c) + (3*b^4*(2*c*d - b*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(7/2))","A",5,4,19,0.2105,1,"{640, 612, 620, 206}"
298,1,89,0,0.0252396,"\int \left(b x+c x^2\right)^{3/2} \, dx","Int[(b*x + c*x^2)^(3/2),x]","-\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2}}{64 c^2}+\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{5/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2}}{8 c}","-\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2}}{64 c^2}+\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{5/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2}}{8 c}",1,"(-3*b^2*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(64*c^2) + ((b + 2*c*x)*(b*x + c*x^2)^(3/2))/(8*c) + (3*b^4*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(5/2))","A",4,3,13,0.2308,1,"{612, 620, 206}"
299,1,216,0,0.241744,"\int \frac{\left(b x+c x^2\right)^{3/2}}{d+e x} \, dx","Int[(b*x + c*x^2)^(3/2)/(d + e*x),x]","\frac{\sqrt{b x+c x^2} \left(b^2 e^2-2 c e x (2 c d-b e)-10 b c d e+8 c^2 d^2\right)}{8 c e^3}-\frac{(2 c d-b e) \left(-b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{3/2} e^4}+\frac{d^{3/2} (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^4}+\frac{\left(b x+c x^2\right)^{3/2}}{3 e}","\frac{\sqrt{b x+c x^2} \left(b^2 e^2-2 c e x (2 c d-b e)-10 b c d e+8 c^2 d^2\right)}{8 c e^3}-\frac{(2 c d-b e) \left(-b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{3/2} e^4}+\frac{d^{3/2} (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^4}+\frac{\left(b x+c x^2\right)^{3/2}}{3 e}",1,"((8*c^2*d^2 - 10*b*c*d*e + b^2*e^2 - 2*c*e*(2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(8*c*e^3) + (b*x + c*x^2)^(3/2)/(3*e) - ((2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(3/2)*e^4) + (d^(3/2)*(c*d - b*e)^(3/2)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/e^4","A",7,6,21,0.2857,1,"{734, 814, 843, 620, 206, 724}"
300,1,198,0,0.2341349,"\int \frac{\left(b x+c x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[(b*x + c*x^2)^(3/2)/(d + e*x)^2,x]","\frac{3 \left(b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 \sqrt{c} e^4}-\frac{3 \sqrt{b x+c x^2} (-3 b e+4 c d-2 c e x)}{4 e^3}-\frac{3 \sqrt{d} \sqrt{c d-b e} (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 e^4}-\frac{\left(b x+c x^2\right)^{3/2}}{e (d+e x)}","\frac{3 \left(b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 \sqrt{c} e^4}-\frac{3 \sqrt{b x+c x^2} (-3 b e+4 c d-2 c e x)}{4 e^3}-\frac{3 \sqrt{d} \sqrt{c d-b e} (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 e^4}-\frac{\left(b x+c x^2\right)^{3/2}}{e (d+e x)}",1,"(-3*(4*c*d - 3*b*e - 2*c*e*x)*Sqrt[b*x + c*x^2])/(4*e^3) - (b*x + c*x^2)^(3/2)/(e*(d + e*x)) + (3*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*Sqrt[c]*e^4) - (3*Sqrt[d]*Sqrt[c*d - b*e]*(2*c*d - b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*e^4)","A",7,6,21,0.2857,1,"{732, 814, 843, 620, 206, 724}"
301,1,205,0,0.1975789,"\int \frac{\left(b x+c x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[(b*x + c*x^2)^(3/2)/(d + e*x)^3,x]","\frac{3 \left(b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 \sqrt{d} e^4 \sqrt{c d-b e}}+\frac{3 \sqrt{b x+c x^2} (-b e+4 c d+2 c e x)}{4 e^3 (d+e x)}-\frac{3 \sqrt{c} (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{e^4}-\frac{\left(b x+c x^2\right)^{3/2}}{2 e (d+e x)^2}","\frac{3 \left(b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 \sqrt{d} e^4 \sqrt{c d-b e}}+\frac{3 \sqrt{b x+c x^2} (-b e+4 c d+2 c e x)}{4 e^3 (d+e x)}-\frac{3 \sqrt{c} (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{e^4}-\frac{\left(b x+c x^2\right)^{3/2}}{2 e (d+e x)^2}",1,"(3*(4*c*d - b*e + 2*c*e*x)*Sqrt[b*x + c*x^2])/(4*e^3*(d + e*x)) - (b*x + c*x^2)^(3/2)/(2*e*(d + e*x)^2) - (3*Sqrt[c]*(2*c*d - b*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/e^4 + (3*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*Sqrt[d]*e^4*Sqrt[c*d - b*e])","A",7,6,21,0.2857,1,"{732, 812, 843, 620, 206, 724}"
302,1,332,0,0.4543184,"\int (d+e x)^3 \left(b x+c x^2\right)^{5/2} \, dx","Int[(d + e*x)^3*(b*x + c*x^2)^(5/2),x]","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} (2 c d-b e) \left(11 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{32768 c^6}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (2 c d-b e) \left(11 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{12288 c^5}+\frac{e \left(b x+c x^2\right)^{7/2} \left(99 b^2 e^2+154 c e x (2 c d-b e)-486 b c d e+640 c^2 d^2\right)}{2016 c^3}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} (2 c d-b e) \left(11 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{768 c^4}-\frac{5 b^6 (2 c d-b e) \left(11 b^2 e^2-32 b c d e+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{32768 c^{13/2}}+\frac{e \left(b x+c x^2\right)^{7/2} (d+e x)^2}{9 c}","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} (2 c d-b e) \left(11 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{32768 c^6}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (2 c d-b e) \left(11 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{12288 c^5}+\frac{e \left(b x+c x^2\right)^{7/2} \left(99 b^2 e^2+154 c e x (2 c d-b e)-486 b c d e+640 c^2 d^2\right)}{2016 c^3}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} (2 c d-b e) \left(11 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{768 c^4}-\frac{5 b^6 (2 c d-b e) \left(11 b^2 e^2-32 b c d e+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{32768 c^{13/2}}+\frac{e \left(b x+c x^2\right)^{7/2} (d+e x)^2}{9 c}",1,"(5*b^4*(2*c*d - b*e)*(32*c^2*d^2 - 32*b*c*d*e + 11*b^2*e^2)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(32768*c^6) - (5*b^2*(2*c*d - b*e)*(32*c^2*d^2 - 32*b*c*d*e + 11*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(12288*c^5) + ((2*c*d - b*e)*(32*c^2*d^2 - 32*b*c*d*e + 11*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(768*c^4) + (e*(d + e*x)^2*(b*x + c*x^2)^(7/2))/(9*c) + (e*(640*c^2*d^2 - 486*b*c*d*e + 99*b^2*e^2 + 154*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(7/2))/(2016*c^3) - (5*b^6*(2*c*d - b*e)*(32*c^2*d^2 - 32*b*c*d*e + 11*b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(32768*c^(13/2))","A",7,5,21,0.2381,1,"{742, 779, 612, 620, 206}"
303,1,266,0,0.220245,"\int (d+e x)^2 \left(b x+c x^2\right)^{5/2} \, dx","Int[(d + e*x)^2*(b*x + c*x^2)^(5/2),x]","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} \left(9 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{16384 c^5}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} \left(9 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{6144 c^4}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} \left(9 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{384 c^3}-\frac{5 b^6 \left(9 b^2 e^2-32 b c d e+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{16384 c^{11/2}}+\frac{9 e \left(b x+c x^2\right)^{7/2} (2 c d-b e)}{112 c^2}+\frac{e \left(b x+c x^2\right)^{7/2} (d+e x)}{8 c}","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} \left(9 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{16384 c^5}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} \left(9 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{6144 c^4}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} \left(9 b^2 e^2-32 b c d e+32 c^2 d^2\right)}{384 c^3}-\frac{5 b^6 \left(9 b^2 e^2-32 b c d e+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{16384 c^{11/2}}+\frac{9 e \left(b x+c x^2\right)^{7/2} (2 c d-b e)}{112 c^2}+\frac{e \left(b x+c x^2\right)^{7/2} (d+e x)}{8 c}",1,"(5*b^4*(32*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(16384*c^5) - (5*b^2*(32*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(6144*c^4) + ((32*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(384*c^3) + (9*e*(2*c*d - b*e)*(b*x + c*x^2)^(7/2))/(112*c^2) + (e*(d + e*x)*(b*x + c*x^2)^(7/2))/(8*c) - (5*b^6*(32*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(16384*c^(11/2))","A",7,5,21,0.2381,1,"{742, 640, 612, 620, 206}"
304,1,175,0,0.0737285,"\int (d+e x) \left(b x+c x^2\right)^{5/2} \, dx","Int[(d + e*x)*(b*x + c*x^2)^(5/2),x]","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} (2 c d-b e)}{1024 c^4}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{384 c^3}-\frac{5 b^6 (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{9/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} (2 c d-b e)}{24 c^2}+\frac{e \left(b x+c x^2\right)^{7/2}}{7 c}","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} (2 c d-b e)}{1024 c^4}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (2 c d-b e)}{384 c^3}-\frac{5 b^6 (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{9/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} (2 c d-b e)}{24 c^2}+\frac{e \left(b x+c x^2\right)^{7/2}}{7 c}",1,"(5*b^4*(2*c*d - b*e)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(1024*c^4) - (5*b^2*(2*c*d - b*e)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(384*c^3) + ((2*c*d - b*e)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(24*c^2) + (e*(b*x + c*x^2)^(7/2))/(7*c) - (5*b^6*(2*c*d - b*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(1024*c^(9/2))","A",6,4,19,0.2105,1,"{640, 612, 620, 206}"
305,1,118,0,0.036886,"\int \left(b x+c x^2\right)^{5/2} \, dx","Int[(b*x + c*x^2)^(5/2),x]","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2}}{512 c^3}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2}}{192 c^2}-\frac{5 b^6 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{7/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2}}{12 c}","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2}}{512 c^3}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2}}{192 c^2}-\frac{5 b^6 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{7/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2}}{12 c}",1,"(5*b^4*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(512*c^3) - (5*b^2*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(192*c^2) + ((b + 2*c*x)*(b*x + c*x^2)^(5/2))/(12*c) - (5*b^6*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(512*c^(7/2))","A",5,3,13,0.2308,1,"{612, 620, 206}"
306,1,356,0,0.4344447,"\int \frac{\left(b x+c x^2\right)^{5/2}}{d+e x} \, dx","Int[(b*x + c*x^2)^(5/2)/(d + e*x),x]","\frac{\left(b x+c x^2\right)^{3/2} \left(3 b^2 e^2-6 c e x (2 c d-b e)-22 b c d e+16 c^2 d^2\right)}{48 c e^3}+\frac{\sqrt{b x+c x^2} \left(-2 c e x (2 c d-b e) \left(-3 b^2 e^2-16 b c d e+16 c^2 d^2\right)+176 b^2 c^2 d^2 e^2-10 b^3 c d e^3-3 b^4 e^4-288 b c^3 d^3 e+128 c^4 d^4\right)}{128 c^2 e^5}-\frac{(2 c d-b e) \left(112 b^2 c^2 d^2 e^2+16 b^3 c d e^3+3 b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{5/2} e^6}+\frac{d^{5/2} (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^6}+\frac{\left(b x+c x^2\right)^{5/2}}{5 e}","\frac{\left(b x+c x^2\right)^{3/2} \left(3 b^2 e^2-6 c e x (2 c d-b e)-22 b c d e+16 c^2 d^2\right)}{48 c e^3}+\frac{\sqrt{b x+c x^2} \left(-2 c e x (2 c d-b e) \left(-3 b^2 e^2-16 b c d e+16 c^2 d^2\right)+176 b^2 c^2 d^2 e^2-10 b^3 c d e^3-3 b^4 e^4-288 b c^3 d^3 e+128 c^4 d^4\right)}{128 c^2 e^5}-\frac{(2 c d-b e) \left(112 b^2 c^2 d^2 e^2+16 b^3 c d e^3+3 b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{5/2} e^6}+\frac{d^{5/2} (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^6}+\frac{\left(b x+c x^2\right)^{5/2}}{5 e}",1,"((128*c^4*d^4 - 288*b*c^3*d^3*e + 176*b^2*c^2*d^2*e^2 - 10*b^3*c*d*e^3 - 3*b^4*e^4 - 2*c*e*(2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e - 3*b^2*e^2)*x)*Sqrt[b*x + c*x^2])/(128*c^2*e^5) + ((16*c^2*d^2 - 22*b*c*d*e + 3*b^2*e^2 - 6*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(48*c*e^3) + (b*x + c*x^2)^(5/2)/(5*e) - ((2*c*d - b*e)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 112*b^2*c^2*d^2*e^2 + 16*b^3*c*d*e^3 + 3*b^4*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(5/2)*e^6) + (d^(5/2)*(c*d - b*e)^(5/2)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/e^6","A",8,6,21,0.2857,1,"{734, 814, 843, 620, 206, 724}"
307,1,314,0,0.3934766,"\int \frac{\left(b x+c x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(b*x + c*x^2)^(5/2)/(d + e*x)^2,x]","-\frac{5 \sqrt{b x+c x^2} \left(-2 c e x \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)+48 b^2 c d e^2-b^3 e^3-112 b c^2 d^2 e+64 c^3 d^3\right)}{64 c e^5}+\frac{5 \left(144 b^2 c^2 d^2 e^2-16 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{3/2} e^6}-\frac{5 d^{3/2} (c d-b e)^{3/2} (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 e^6}-\frac{5 \left(b x+c x^2\right)^{3/2} (-7 b e+8 c d-6 c e x)}{24 e^3}-\frac{\left(b x+c x^2\right)^{5/2}}{e (d+e x)}","-\frac{5 \sqrt{b x+c x^2} \left(-2 c e x \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)+48 b^2 c d e^2-b^3 e^3-112 b c^2 d^2 e+64 c^3 d^3\right)}{64 c e^5}+\frac{5 \left(144 b^2 c^2 d^2 e^2-16 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{3/2} e^6}-\frac{5 d^{3/2} (c d-b e)^{3/2} (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 e^6}-\frac{5 \left(b x+c x^2\right)^{3/2} (-7 b e+8 c d-6 c e x)}{24 e^3}-\frac{\left(b x+c x^2\right)^{5/2}}{e (d+e x)}",1,"(-5*(64*c^3*d^3 - 112*b*c^2*d^2*e + 48*b^2*c*d*e^2 - b^3*e^3 - 2*c*e*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*x)*Sqrt[b*x + c*x^2])/(64*c*e^5) - (5*(8*c*d - 7*b*e - 6*c*e*x)*(b*x + c*x^2)^(3/2))/(24*e^3) - (b*x + c*x^2)^(5/2)/(e*(d + e*x)) + (5*(128*c^4*d^4 - 256*b*c^3*d^3*e + 144*b^2*c^2*d^2*e^2 - 16*b^3*c*d*e^3 - b^4*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(3/2)*e^6) - (5*d^(3/2)*(c*d - b*e)^(3/2)*(2*c*d - b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*e^6)","A",8,6,21,0.2857,1,"{732, 814, 843, 620, 206, 724}"
308,1,282,0,0.3257904,"\int \frac{\left(b x+c x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[(b*x + c*x^2)^(5/2)/(d + e*x)^3,x]","\frac{5 \sqrt{b x+c x^2} \left(5 b^2 e^2-4 c e x (2 c d-b e)-20 b c d e+16 c^2 d^2\right)}{8 e^5}-\frac{5 (2 c d-b e) \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 \sqrt{c} e^6}+\frac{5 \left(b x+c x^2\right)^{3/2} (-3 b e+8 c d+2 c e x)}{12 e^3 (d+e x)}+\frac{5 \sqrt{d} (4 c d-3 b e) \sqrt{c d-b e} (4 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 e^6}-\frac{\left(b x+c x^2\right)^{5/2}}{2 e (d+e x)^2}","\frac{5 \sqrt{b x+c x^2} \left(5 b^2 e^2-4 c e x (2 c d-b e)-20 b c d e+16 c^2 d^2\right)}{8 e^5}-\frac{5 (2 c d-b e) \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 \sqrt{c} e^6}+\frac{5 \left(b x+c x^2\right)^{3/2} (-3 b e+8 c d+2 c e x)}{12 e^3 (d+e x)}+\frac{5 \sqrt{d} (4 c d-3 b e) \sqrt{c d-b e} (4 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 e^6}-\frac{\left(b x+c x^2\right)^{5/2}}{2 e (d+e x)^2}",1,"(5*(16*c^2*d^2 - 20*b*c*d*e + 5*b^2*e^2 - 4*c*e*(2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(8*e^5) + (5*(8*c*d - 3*b*e + 2*c*e*x)*(b*x + c*x^2)^(3/2))/(12*e^3*(d + e*x)) - (b*x + c*x^2)^(5/2)/(2*e*(d + e*x)^2) - (5*(2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*Sqrt[c]*e^6) + (5*Sqrt[d]*(4*c*d - 3*b*e)*Sqrt[c*d - b*e]*(4*c*d - b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*e^6)","A",8,7,21,0.3333,1,"{732, 812, 814, 843, 620, 206, 724}"
309,1,26,0,0.0143339,"\int \frac{\sqrt{2 x+x^2}}{1+x} \, dx","Int[Sqrt[2*x + x^2]/(1 + x),x]","\sqrt{x^2+2 x}-\tan ^{-1}\left(\sqrt{x^2+2 x}\right)","\sqrt{x^2+2 x}-\tan ^{-1}\left(\sqrt{x^2+2 x}\right)",1,"Sqrt[2*x + x^2] - ArcTan[Sqrt[2*x + x^2]]","A",3,3,17,0.1765,1,"{685, 688, 203}"
310,1,53,0,0.0241723,"\int \frac{\left(2 x-x^2\right)^{3/2}}{2-2 x} \, dx","Int[(2*x - x^2)^(3/2)/(2 - 2*x),x]","-\frac{1}{6} \left(2 x-x^2\right)^{3/2}-\frac{1}{2} \sqrt{2 x-x^2}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)","-\frac{1}{6} \left(2 x-x^2\right)^{3/2}-\frac{1}{2} \sqrt{2 x-x^2}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)",1,"-Sqrt[2*x - x^2]/2 - (2*x - x^2)^(3/2)/6 + ArcTanh[Sqrt[2*x - x^2]]/2","A",4,3,21,0.1429,1,"{685, 688, 207}"
311,1,36,0,0.0168601,"\int \frac{\sqrt{2 x-x^2}}{2-2 x} \, dx","Int[Sqrt[2*x - x^2]/(2 - 2*x),x]","\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{1}{2} \sqrt{2 x-x^2}","\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{1}{2} \sqrt{2 x-x^2}",1,"-Sqrt[2*x - x^2]/2 + ArcTanh[Sqrt[2*x - x^2]]/2","A",3,3,21,0.1429,1,"{685, 688, 207}"
312,1,18,0,0.009766,"\int \frac{1}{(2-2 x) \sqrt{2 x-x^2}} \, dx","Int[1/((2 - 2*x)*Sqrt[2*x - x^2]),x]","\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)","\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)",1,"ArcTanh[Sqrt[2*x - x^2]]/2","A",2,2,21,0.09524,1,"{688, 207}"
313,1,36,0,0.0169694,"\int \frac{1}{(2-2 x) \left(2 x-x^2\right)^{3/2}} \, dx","Int[1/((2 - 2*x)*(2*x - x^2)^(3/2)),x]","\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{1}{2 \sqrt{2 x-x^2}}","\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{1}{2 \sqrt{2 x-x^2}}",1,"-1/(2*Sqrt[2*x - x^2]) + ArcTanh[Sqrt[2*x - x^2]]/2","A",3,3,21,0.1429,1,"{687, 688, 207}"
314,1,53,0,0.0244244,"\int \frac{1}{(2-2 x) \left(2 x-x^2\right)^{5/2}} \, dx","Int[1/((2 - 2*x)*(2*x - x^2)^(5/2)),x]","-\frac{1}{2 \sqrt{2 x-x^2}}-\frac{1}{6 \left(2 x-x^2\right)^{3/2}}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)","-\frac{1}{2 \sqrt{2 x-x^2}}-\frac{1}{6 \left(2 x-x^2\right)^{3/2}}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)",1,"-1/(6*(2*x - x^2)^(3/2)) - 1/(2*Sqrt[2*x - x^2]) + ArcTanh[Sqrt[2*x - x^2]]/2","A",4,3,21,0.1429,1,"{687, 688, 207}"
315,1,149,0,0.149362,"\int \frac{(d+e x)^3}{\sqrt{b x+c x^2}} \, dx","Int[(d + e*x)^3/Sqrt[b*x + c*x^2],x]","\frac{e \sqrt{b x+c x^2} \left(15 b^2 e^2+10 c e x (2 c d-b e)-54 b c d e+64 c^2 d^2\right)}{24 c^3}+\frac{(2 c d-b e) \left(5 b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{7/2}}+\frac{e \sqrt{b x+c x^2} (d+e x)^2}{3 c}","\frac{e \sqrt{b x+c x^2} \left(15 b^2 e^2+10 c e x (2 c d-b e)-54 b c d e+64 c^2 d^2\right)}{24 c^3}+\frac{(2 c d-b e) \left(5 b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{7/2}}+\frac{e \sqrt{b x+c x^2} (d+e x)^2}{3 c}",1,"(e*(d + e*x)^2*Sqrt[b*x + c*x^2])/(3*c) + (e*(64*c^2*d^2 - 54*b*c*d*e + 15*b^2*e^2 + 10*c*e*(2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(24*c^3) + ((2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 5*b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(7/2))","A",4,4,21,0.1905,1,"{742, 779, 620, 206}"
316,1,110,0,0.0773418,"\int \frac{(d+e x)^2}{\sqrt{b x+c x^2}} \, dx","Int[(d + e*x)^2/Sqrt[b*x + c*x^2],x]","\frac{\left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{5/2}}+\frac{3 e \sqrt{b x+c x^2} (2 c d-b e)}{4 c^2}+\frac{e \sqrt{b x+c x^2} (d+e x)}{2 c}","\frac{\left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{5/2}}+\frac{3 e \sqrt{b x+c x^2} (2 c d-b e)}{4 c^2}+\frac{e \sqrt{b x+c x^2} (d+e x)}{2 c}",1,"(3*e*(2*c*d - b*e)*Sqrt[b*x + c*x^2])/(4*c^2) + (e*(d + e*x)*Sqrt[b*x + c*x^2])/(2*c) + ((8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(5/2))","A",4,4,21,0.1905,1,"{742, 640, 620, 206}"
317,1,55,0,0.0217423,"\int \frac{d+e x}{\sqrt{b x+c x^2}} \, dx","Int[(d + e*x)/Sqrt[b*x + c*x^2],x]","\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}+\frac{e \sqrt{b x+c x^2}}{c}","\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}+\frac{e \sqrt{b x+c x^2}}{c}",1,"(e*Sqrt[b*x + c*x^2])/c + ((2*c*d - b*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(3/2)","A",3,3,19,0.1579,1,"{640, 620, 206}"
318,1,28,0,0.0088108,"\int \frac{1}{\sqrt{b x+c x^2}} \, dx","Int[1/Sqrt[b*x + c*x^2],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}",1,"(2*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/Sqrt[c]","A",2,2,13,0.1538,1,"{620, 206}"
319,1,68,0,0.0305797,"\int \frac{1}{(d+e x) \sqrt{b x+c x^2}} \, dx","Int[1/((d + e*x)*Sqrt[b*x + c*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{\sqrt{d} \sqrt{c d-b e}}","\frac{\tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{\sqrt{d} \sqrt{c d-b e}}",1,"ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])]/(Sqrt[d]*Sqrt[c*d - b*e])","A",2,2,21,0.09524,1,"{724, 206}"
320,1,117,0,0.0746605,"\int \frac{1}{(d+e x)^2 \sqrt{b x+c x^2}} \, dx","Int[1/((d + e*x)^2*Sqrt[b*x + c*x^2]),x]","\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{3/2} (c d-b e)^{3/2}}-\frac{e \sqrt{b x+c x^2}}{d (d+e x) (c d-b e)}","\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{3/2} (c d-b e)^{3/2}}-\frac{e \sqrt{b x+c x^2}}{d (d+e x) (c d-b e)}",1,"-((e*Sqrt[b*x + c*x^2])/(d*(c*d - b*e)*(d + e*x))) + ((2*c*d - b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*d^(3/2)*(c*d - b*e)^(3/2))","A",3,3,21,0.1429,1,"{730, 724, 206}"
321,1,180,0,0.1729794,"\int \frac{1}{(d+e x)^3 \sqrt{b x+c x^2}} \, dx","Int[1/((d + e*x)^3*Sqrt[b*x + c*x^2]),x]","\frac{\left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{5/2} (c d-b e)^{5/2}}-\frac{3 e \sqrt{b x+c x^2} (2 c d-b e)}{4 d^2 (d+e x) (c d-b e)^2}-\frac{e \sqrt{b x+c x^2}}{2 d (d+e x)^2 (c d-b e)}","\frac{\left(3 b^2 e^2-8 b c d e+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{5/2} (c d-b e)^{5/2}}-\frac{3 e \sqrt{b x+c x^2} (2 c d-b e)}{4 d^2 (d+e x) (c d-b e)^2}-\frac{e \sqrt{b x+c x^2}}{2 d (d+e x)^2 (c d-b e)}",1,"-(e*Sqrt[b*x + c*x^2])/(2*d*(c*d - b*e)*(d + e*x)^2) - (3*e*(2*c*d - b*e)*Sqrt[b*x + c*x^2])/(4*d^2*(c*d - b*e)^2*(d + e*x)) + ((8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*d^(5/2)*(c*d - b*e)^(5/2))","A",4,4,21,0.1905,1,"{744, 806, 724, 206}"
322,1,139,0,0.0931574,"\int \frac{(d+e x)^3}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^3/(b*x + c*x^2)^(3/2),x]","\frac{e \sqrt{b x+c x^2} \left(3 b^2 e^2+2 c e x (2 c d-b e)-6 b c d e+8 c^2 d^2\right)}{b^2 c^2}-\frac{2 (d+e x)^2 (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}+\frac{3 e^2 (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}","\frac{e \sqrt{b x+c x^2} \left(3 b^2 e^2+2 c e x (2 c d-b e)-6 b c d e+8 c^2 d^2\right)}{b^2 c^2}-\frac{2 (d+e x)^2 (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}+\frac{3 e^2 (2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}",1,"(-2*(d + e*x)^2*(b*d + (2*c*d - b*e)*x))/(b^2*Sqrt[b*x + c*x^2]) + (e*(8*c^2*d^2 - 6*b*c*d*e + 3*b^2*e^2 + 2*c*e*(2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(b^2*c^2) + (3*e^2*(2*c*d - b*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(5/2)","A",4,4,21,0.1905,1,"{738, 779, 620, 206}"
323,1,101,0,0.061544,"\int \frac{(d+e x)^2}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^2/(b*x + c*x^2)^(3/2),x]","\frac{2 e \sqrt{b x+c x^2} (2 c d-b e)}{b^2 c}-\frac{2 (d+e x) (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}+\frac{2 e^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}","\frac{2 e \sqrt{b x+c x^2} (2 c d-b e)}{b^2 c}-\frac{2 (d+e x) (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}+\frac{2 e^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}",1,"(-2*(d + e*x)*(b*d + (2*c*d - b*e)*x))/(b^2*Sqrt[b*x + c*x^2]) + (2*e*(2*c*d - b*e)*Sqrt[b*x + c*x^2])/(b^2*c) + (2*e^2*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(3/2)","A",4,4,21,0.1905,1,"{738, 640, 620, 206}"
324,1,33,0,0.0103688,"\int \frac{d+e x}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)/(b*x + c*x^2)^(3/2),x]","-\frac{2 (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}","-\frac{2 (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}",1,"(-2*(b*d + (2*c*d - b*e)*x))/(b^2*Sqrt[b*x + c*x^2])","A",1,1,19,0.05263,1,"{636}"
325,1,24,0,0.0036398,"\int \frac{1}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(b*x + c*x^2)^(-3/2),x]","-\frac{2 (b+2 c x)}{b^2 \sqrt{b x+c x^2}}","-\frac{2 (b+2 c x)}{b^2 \sqrt{b x+c x^2}}",1,"(-2*(b + 2*c*x))/(b^2*Sqrt[b*x + c*x^2])","A",1,1,13,0.07692,1,"{613}"
326,1,126,0,0.0962518,"\int \frac{1}{(d+e x) \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(b*x + c*x^2)^(3/2)),x]","\frac{e^2 \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{d^{3/2} (c d-b e)^{3/2}}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (c d-b e)}","\frac{e^2 \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{d^{3/2} (c d-b e)^{3/2}}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (c d-b e)}",1,"(-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*Sqrt[b*x + c*x^2]) + (e^2*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(d^(3/2)*(c*d - b*e)^(3/2))","A",4,4,21,0.1905,1,"{740, 12, 724, 206}"
327,1,207,0,0.2353911,"\int \frac{1}{(d+e x)^2 \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^2*(b*x + c*x^2)^(3/2)),x]","-\frac{e \sqrt{b x+c x^2} \left(3 b^2 e^2-4 b c d e+4 c^2 d^2\right)}{b^2 d^2 (d+e x) (c d-b e)^2}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x) (c d-b e)}+\frac{3 e^2 (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{5/2} (c d-b e)^{5/2}}","-\frac{e \sqrt{b x+c x^2} \left(3 b^2 e^2-4 b c d e+4 c^2 d^2\right)}{b^2 d^2 (d+e x) (c d-b e)^2}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x) (c d-b e)}+\frac{3 e^2 (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{5/2} (c d-b e)^{5/2}}",1,"(-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(d + e*x)*Sqrt[b*x + c*x^2]) - (e*(4*c^2*d^2 - 4*b*c*d*e + 3*b^2*e^2)*Sqrt[b*x + c*x^2])/(b^2*d^2*(c*d - b*e)^2*(d + e*x)) + (3*e^2*(2*c*d - b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*d^(5/2)*(c*d - b*e)^(5/2))","A",4,4,21,0.1905,1,"{740, 806, 724, 206}"
328,1,296,0,0.3435816,"\int \frac{1}{(d+e x)^3 \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^3*(b*x + c*x^2)^(3/2)),x]","-\frac{e \sqrt{b x+c x^2} (2 c d-b e) \left(15 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{4 b^2 d^3 (d+e x) (c d-b e)^3}-\frac{e \sqrt{b x+c x^2} \left(5 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{2 b^2 d^2 (d+e x)^2 (c d-b e)^2}+\frac{3 e^2 \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{7/2} (c d-b e)^{7/2}}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x)^2 (c d-b e)}","-\frac{e \sqrt{b x+c x^2} (2 c d-b e) \left(15 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{4 b^2 d^3 (d+e x) (c d-b e)^3}-\frac{e \sqrt{b x+c x^2} \left(5 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{2 b^2 d^2 (d+e x)^2 (c d-b e)^2}+\frac{3 e^2 \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{7/2} (c d-b e)^{7/2}}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x)^2 (c d-b e)}",1,"(-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(d + e*x)^2*Sqrt[b*x + c*x^2]) - (e*(8*c^2*d^2 - 8*b*c*d*e + 5*b^2*e^2)*Sqrt[b*x + c*x^2])/(2*b^2*d^2*(c*d - b*e)^2*(d + e*x)^2) - (e*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 15*b^2*e^2)*Sqrt[b*x + c*x^2])/(4*b^2*d^3*(c*d - b*e)^3*(d + e*x)) + (3*e^2*(16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*d^(7/2)*(c*d - b*e)^(7/2))","A",5,5,21,0.2381,1,"{740, 834, 806, 724, 206}"
329,1,208,0,0.1980537,"\int \frac{(d+e x)^4}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^4/(b*x + c*x^2)^(5/2),x]","-\frac{2 e \sqrt{b x+c x^2} (2 c d-b e) \left(-3 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{3 b^4 c^2}+\frac{4 (d+e x) \left(x (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)+b c d^2 (4 c d-5 b e)\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{2 (d+e x)^3 (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{2 e^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}","-\frac{2 e \sqrt{b x+c x^2} (2 c d-b e) \left(-3 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{3 b^4 c^2}+\frac{4 (d+e x) \left(x (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)+b c d^2 (4 c d-5 b e)\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{2 (d+e x)^3 (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{2 e^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}",1,"(-2*(d + e*x)^3*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (4*(d + e*x)*(b*c*d^2*(4*c*d - 5*b*e) + (2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*x))/(3*b^4*c*Sqrt[b*x + c*x^2]) - (2*e*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - 3*b^2*e^2)*Sqrt[b*x + c*x^2])/(3*b^4*c^2) + (2*e^4*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(5/2)","A",5,5,21,0.2381,1,"{738, 818, 640, 620, 206}"
330,1,87,0,0.0364209,"\int \frac{(d+e x)^3}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^3/(b*x + c*x^2)^(5/2),x]","\frac{16 d (c d-b e) (x (2 c d-b e)+b d)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (d+e x)^2 (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}","\frac{16 d (c d-b e) (x (2 c d-b e)+b d)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (d+e x)^2 (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^2*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (16*d*(c*d - b*e)*(b*d + (2*c*d - b*e)*x))/(3*b^4*Sqrt[b*x + c*x^2])","A",2,2,21,0.09524,1,"{722, 636}"
331,1,78,0,0.0326602,"\int \frac{(d+e x)^2}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^2/(b*x + c*x^2)^(5/2),x]","\frac{8 (2 c d-b e) (x (2 c d-b e)+b d)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (b+2 c x) (d+e x)^2}{3 b^2 \left(b x+c x^2\right)^{3/2}}","\frac{8 (2 c d-b e) (x (2 c d-b e)+b d)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (b+2 c x) (d+e x)^2}{3 b^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b + 2*c*x)*(d + e*x)^2)/(3*b^2*(b*x + c*x^2)^(3/2)) + (8*(2*c*d - b*e)*(b*d + (2*c*d - b*e)*x))/(3*b^4*Sqrt[b*x + c*x^2])","A",2,2,21,0.09524,1,"{728, 636}"
332,1,71,0,0.0181793,"\int \frac{d+e x}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)/(b*x + c*x^2)^(5/2),x]","\frac{8 (b+2 c x) (2 c d-b e)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}","\frac{8 (b+2 c x) (2 c d-b e)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (8*(2*c*d - b*e)*(b + 2*c*x))/(3*b^4*Sqrt[b*x + c*x^2])","A",2,2,19,0.1053,1,"{638, 613}"
333,1,54,0,0.0101147,"\int \frac{1}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(b*x + c*x^2)^(-5/2),x]","\frac{16 c (b+2 c x)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (b+2 c x)}{3 b^2 \left(b x+c x^2\right)^{3/2}}","\frac{16 c (b+2 c x)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (b+2 c x)}{3 b^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b + 2*c*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (16*c*(b + 2*c*x))/(3*b^4*Sqrt[b*x + c*x^2])","A",2,2,13,0.1538,1,"{614, 613}"
334,1,230,0,0.1794401,"\int \frac{1}{(d+e x) \left(b x+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)*(b*x + c*x^2)^(5/2)),x]","\frac{2 \left(c x (2 c d-b e) \left(-3 b^2 e^2-8 b c d e+8 c^2 d^2\right)+b (c d-b e) \left(-3 b^2 e^2-4 b c d e+8 c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (c d-b e)}+\frac{e^4 \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{d^{5/2} (c d-b e)^{5/2}}","\frac{2 \left(c x (2 c d-b e) \left(-3 b^2 e^2-8 b c d e+8 c^2 d^2\right)+b (c d-b e) \left(-3 b^2 e^2-4 b c d e+8 c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (c d-b e)}+\frac{e^4 \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{d^{5/2} (c d-b e)^{5/2}}",1,"(-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(3*b^2*d*(c*d - b*e)*(b*x + c*x^2)^(3/2)) + (2*(b*(c*d - b*e)*(8*c^2*d^2 - 4*b*c*d*e - 3*b^2*e^2) + c*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - 3*b^2*e^2)*x))/(3*b^4*d^2*(c*d - b*e)^2*Sqrt[b*x + c*x^2]) + (e^4*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(d^(5/2)*(c*d - b*e)^(5/2))","A",5,5,21,0.2381,1,"{740, 822, 12, 724, 206}"
335,1,348,0,0.3487157,"\int \frac{1}{(d+e x)^2 \left(b x+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^2*(b*x + c*x^2)^(5/2)),x]","\frac{e \sqrt{b x+c x^2} \left(12 b^2 c^2 d^2 e^2+20 b^3 c d e^3-15 b^4 e^4-64 b c^3 d^3 e+32 c^4 d^4\right)}{3 b^4 d^3 (d+e x) (c d-b e)^3}+\frac{2 \left(c x (2 c d-b e) \left(-5 b^2 e^2-8 b c d e+8 c^2 d^2\right)+b (c d-b e) \left(-5 b^2 e^2-2 b c d e+8 c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (d+e x) (c d-b e)^2}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (d+e x) (c d-b e)}+\frac{5 e^4 (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{7/2} (c d-b e)^{7/2}}","\frac{e \sqrt{b x+c x^2} \left(12 b^2 c^2 d^2 e^2+20 b^3 c d e^3-15 b^4 e^4-64 b c^3 d^3 e+32 c^4 d^4\right)}{3 b^4 d^3 (d+e x) (c d-b e)^3}+\frac{2 \left(c x (2 c d-b e) \left(-5 b^2 e^2-8 b c d e+8 c^2 d^2\right)+b (c d-b e) \left(-5 b^2 e^2-2 b c d e+8 c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (d+e x) (c d-b e)^2}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (d+e x) (c d-b e)}+\frac{5 e^4 (2 c d-b e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{7/2} (c d-b e)^{7/2}}",1,"(-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(3*b^2*d*(c*d - b*e)*(d + e*x)*(b*x + c*x^2)^(3/2)) + (2*(b*(c*d - b*e)*(8*c^2*d^2 - 2*b*c*d*e - 5*b^2*e^2) + c*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - 5*b^2*e^2)*x))/(3*b^4*d^2*(c*d - b*e)^2*(d + e*x)*Sqrt[b*x + c*x^2]) + (e*(32*c^4*d^4 - 64*b*c^3*d^3*e + 12*b^2*c^2*d^2*e^2 + 20*b^3*c*d*e^3 - 15*b^4*e^4)*Sqrt[b*x + c*x^2])/(3*b^4*d^3*(c*d - b*e)^3*(d + e*x)) + (5*e^4*(2*c*d - b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*d^(7/2)*(c*d - b*e)^(7/2))","A",5,5,21,0.2381,1,"{740, 822, 806, 724, 206}"
336,1,17,0,0.0061051,"\int \frac{1}{(2+x) \sqrt{2 x+x^2}} \, dx","Int[1/((2 + x)*Sqrt[2*x + x^2]),x]","\frac{\sqrt{x^2+2 x}}{x+2}","\frac{\sqrt{x^2+2 x}}{x+2}",1,"Sqrt[2*x + x^2]/(2 + x)","A",1,1,17,0.05882,1,"{650}"
337,1,68,0,0.0292805,"\int (d+e x)^{7/2} \left(b x+c x^2\right) \, dx","Int[(d + e*x)^(7/2)*(b*x + c*x^2),x]","-\frac{2 (d+e x)^{11/2} (2 c d-b e)}{11 e^3}+\frac{2 d (d+e x)^{9/2} (c d-b e)}{9 e^3}+\frac{2 c (d+e x)^{13/2}}{13 e^3}","-\frac{2 (d+e x)^{11/2} (2 c d-b e)}{11 e^3}+\frac{2 d (d+e x)^{9/2} (c d-b e)}{9 e^3}+\frac{2 c (d+e x)^{13/2}}{13 e^3}",1,"(2*d*(c*d - b*e)*(d + e*x)^(9/2))/(9*e^3) - (2*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^3) + (2*c*(d + e*x)^(13/2))/(13*e^3)","A",2,1,19,0.05263,1,"{698}"
338,1,68,0,0.0280261,"\int (d+e x)^{5/2} \left(b x+c x^2\right) \, dx","Int[(d + e*x)^(5/2)*(b*x + c*x^2),x]","-\frac{2 (d+e x)^{9/2} (2 c d-b e)}{9 e^3}+\frac{2 d (d+e x)^{7/2} (c d-b e)}{7 e^3}+\frac{2 c (d+e x)^{11/2}}{11 e^3}","-\frac{2 (d+e x)^{9/2} (2 c d-b e)}{9 e^3}+\frac{2 d (d+e x)^{7/2} (c d-b e)}{7 e^3}+\frac{2 c (d+e x)^{11/2}}{11 e^3}",1,"(2*d*(c*d - b*e)*(d + e*x)^(7/2))/(7*e^3) - (2*(2*c*d - b*e)*(d + e*x)^(9/2))/(9*e^3) + (2*c*(d + e*x)^(11/2))/(11*e^3)","A",2,1,19,0.05263,1,"{698}"
339,1,68,0,0.0283249,"\int (d+e x)^{3/2} \left(b x+c x^2\right) \, dx","Int[(d + e*x)^(3/2)*(b*x + c*x^2),x]","-\frac{2 (d+e x)^{7/2} (2 c d-b e)}{7 e^3}+\frac{2 d (d+e x)^{5/2} (c d-b e)}{5 e^3}+\frac{2 c (d+e x)^{9/2}}{9 e^3}","-\frac{2 (d+e x)^{7/2} (2 c d-b e)}{7 e^3}+\frac{2 d (d+e x)^{5/2} (c d-b e)}{5 e^3}+\frac{2 c (d+e x)^{9/2}}{9 e^3}",1,"(2*d*(c*d - b*e)*(d + e*x)^(5/2))/(5*e^3) - (2*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^3) + (2*c*(d + e*x)^(9/2))/(9*e^3)","A",2,1,19,0.05263,1,"{698}"
340,1,68,0,0.0261583,"\int \sqrt{d+e x} \left(b x+c x^2\right) \, dx","Int[Sqrt[d + e*x]*(b*x + c*x^2),x]","-\frac{2 (d+e x)^{5/2} (2 c d-b e)}{5 e^3}+\frac{2 d (d+e x)^{3/2} (c d-b e)}{3 e^3}+\frac{2 c (d+e x)^{7/2}}{7 e^3}","-\frac{2 (d+e x)^{5/2} (2 c d-b e)}{5 e^3}+\frac{2 d (d+e x)^{3/2} (c d-b e)}{3 e^3}+\frac{2 c (d+e x)^{7/2}}{7 e^3}",1,"(2*d*(c*d - b*e)*(d + e*x)^(3/2))/(3*e^3) - (2*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^3) + (2*c*(d + e*x)^(7/2))/(7*e^3)","A",2,1,19,0.05263,1,"{698}"
341,1,66,0,0.0272946,"\int \frac{b x+c x^2}{\sqrt{d+e x}} \, dx","Int[(b*x + c*x^2)/Sqrt[d + e*x],x]","-\frac{2 (d+e x)^{3/2} (2 c d-b e)}{3 e^3}+\frac{2 d \sqrt{d+e x} (c d-b e)}{e^3}+\frac{2 c (d+e x)^{5/2}}{5 e^3}","-\frac{2 (d+e x)^{3/2} (2 c d-b e)}{3 e^3}+\frac{2 d \sqrt{d+e x} (c d-b e)}{e^3}+\frac{2 c (d+e x)^{5/2}}{5 e^3}",1,"(2*d*(c*d - b*e)*Sqrt[d + e*x])/e^3 - (2*(2*c*d - b*e)*(d + e*x)^(3/2))/(3*e^3) + (2*c*(d + e*x)^(5/2))/(5*e^3)","A",2,1,19,0.05263,1,"{698}"
342,1,64,0,0.0271376,"\int \frac{b x+c x^2}{(d+e x)^{3/2}} \, dx","Int[(b*x + c*x^2)/(d + e*x)^(3/2),x]","-\frac{2 \sqrt{d+e x} (2 c d-b e)}{e^3}-\frac{2 d (c d-b e)}{e^3 \sqrt{d+e x}}+\frac{2 c (d+e x)^{3/2}}{3 e^3}","-\frac{2 \sqrt{d+e x} (2 c d-b e)}{e^3}-\frac{2 d (c d-b e)}{e^3 \sqrt{d+e x}}+\frac{2 c (d+e x)^{3/2}}{3 e^3}",1,"(-2*d*(c*d - b*e))/(e^3*Sqrt[d + e*x]) - (2*(2*c*d - b*e)*Sqrt[d + e*x])/e^3 + (2*c*(d + e*x)^(3/2))/(3*e^3)","A",2,1,19,0.05263,1,"{698}"
343,1,64,0,0.0277594,"\int \frac{b x+c x^2}{(d+e x)^{5/2}} \, dx","Int[(b*x + c*x^2)/(d + e*x)^(5/2),x]","\frac{2 (2 c d-b e)}{e^3 \sqrt{d+e x}}-\frac{2 d (c d-b e)}{3 e^3 (d+e x)^{3/2}}+\frac{2 c \sqrt{d+e x}}{e^3}","\frac{2 (2 c d-b e)}{e^3 \sqrt{d+e x}}-\frac{2 d (c d-b e)}{3 e^3 (d+e x)^{3/2}}+\frac{2 c \sqrt{d+e x}}{e^3}",1,"(-2*d*(c*d - b*e))/(3*e^3*(d + e*x)^(3/2)) + (2*(2*c*d - b*e))/(e^3*Sqrt[d + e*x]) + (2*c*Sqrt[d + e*x])/e^3","A",2,1,19,0.05263,1,"{698}"
344,1,66,0,0.0266006,"\int \frac{b x+c x^2}{(d+e x)^{7/2}} \, dx","Int[(b*x + c*x^2)/(d + e*x)^(7/2),x]","\frac{2 (2 c d-b e)}{3 e^3 (d+e x)^{3/2}}-\frac{2 d (c d-b e)}{5 e^3 (d+e x)^{5/2}}-\frac{2 c}{e^3 \sqrt{d+e x}}","\frac{2 (2 c d-b e)}{3 e^3 (d+e x)^{3/2}}-\frac{2 d (c d-b e)}{5 e^3 (d+e x)^{5/2}}-\frac{2 c}{e^3 \sqrt{d+e x}}",1,"(-2*d*(c*d - b*e))/(5*e^3*(d + e*x)^(5/2)) + (2*(2*c*d - b*e))/(3*e^3*(d + e*x)^(3/2)) - (2*c)/(e^3*Sqrt[d + e*x])","A",2,1,19,0.05263,1,"{698}"
345,1,147,0,0.0722376,"\int (d+e x)^{7/2} \left(b x+c x^2\right)^2 \, dx","Int[(d + e*x)^(7/2)*(b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{13/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{13 e^5}+\frac{2 d^2 (d+e x)^{9/2} (c d-b e)^2}{9 e^5}-\frac{4 c (d+e x)^{15/2} (2 c d-b e)}{15 e^5}-\frac{4 d (d+e x)^{11/2} (c d-b e) (2 c d-b e)}{11 e^5}+\frac{2 c^2 (d+e x)^{17/2}}{17 e^5}","\frac{2 (d+e x)^{13/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{13 e^5}+\frac{2 d^2 (d+e x)^{9/2} (c d-b e)^2}{9 e^5}-\frac{4 c (d+e x)^{15/2} (2 c d-b e)}{15 e^5}-\frac{4 d (d+e x)^{11/2} (c d-b e) (2 c d-b e)}{11 e^5}+\frac{2 c^2 (d+e x)^{17/2}}{17 e^5}",1,"(2*d^2*(c*d - b*e)^2*(d + e*x)^(9/2))/(9*e^5) - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(13/2))/(13*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(15/2))/(15*e^5) + (2*c^2*(d + e*x)^(17/2))/(17*e^5)","A",2,1,21,0.04762,1,"{698}"
346,1,147,0,0.0651057,"\int (d+e x)^{5/2} \left(b x+c x^2\right)^2 \, dx","Int[(d + e*x)^(5/2)*(b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{11/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{11 e^5}+\frac{2 d^2 (d+e x)^{7/2} (c d-b e)^2}{7 e^5}-\frac{4 c (d+e x)^{13/2} (2 c d-b e)}{13 e^5}-\frac{4 d (d+e x)^{9/2} (c d-b e) (2 c d-b e)}{9 e^5}+\frac{2 c^2 (d+e x)^{15/2}}{15 e^5}","\frac{2 (d+e x)^{11/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{11 e^5}+\frac{2 d^2 (d+e x)^{7/2} (c d-b e)^2}{7 e^5}-\frac{4 c (d+e x)^{13/2} (2 c d-b e)}{13 e^5}-\frac{4 d (d+e x)^{9/2} (c d-b e) (2 c d-b e)}{9 e^5}+\frac{2 c^2 (d+e x)^{15/2}}{15 e^5}",1,"(2*d^2*(c*d - b*e)^2*(d + e*x)^(7/2))/(7*e^5) - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(9/2))/(9*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(11/2))/(11*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(13/2))/(13*e^5) + (2*c^2*(d + e*x)^(15/2))/(15*e^5)","A",2,1,21,0.04762,1,"{698}"
347,1,147,0,0.0606813,"\int (d+e x)^{3/2} \left(b x+c x^2\right)^2 \, dx","Int[(d + e*x)^(3/2)*(b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{9/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{9 e^5}+\frac{2 d^2 (d+e x)^{5/2} (c d-b e)^2}{5 e^5}-\frac{4 c (d+e x)^{11/2} (2 c d-b e)}{11 e^5}-\frac{4 d (d+e x)^{7/2} (c d-b e) (2 c d-b e)}{7 e^5}+\frac{2 c^2 (d+e x)^{13/2}}{13 e^5}","\frac{2 (d+e x)^{9/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{9 e^5}+\frac{2 d^2 (d+e x)^{5/2} (c d-b e)^2}{5 e^5}-\frac{4 c (d+e x)^{11/2} (2 c d-b e)}{11 e^5}-\frac{4 d (d+e x)^{7/2} (c d-b e) (2 c d-b e)}{7 e^5}+\frac{2 c^2 (d+e x)^{13/2}}{13 e^5}",1,"(2*d^2*(c*d - b*e)^2*(d + e*x)^(5/2))/(5*e^5) - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(9/2))/(9*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^5) + (2*c^2*(d + e*x)^(13/2))/(13*e^5)","A",2,1,21,0.04762,1,"{698}"
348,1,147,0,0.0586716,"\int \sqrt{d+e x} \left(b x+c x^2\right)^2 \, dx","Int[Sqrt[d + e*x]*(b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{7/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{7 e^5}+\frac{2 d^2 (d+e x)^{3/2} (c d-b e)^2}{3 e^5}-\frac{4 c (d+e x)^{9/2} (2 c d-b e)}{9 e^5}-\frac{4 d (d+e x)^{5/2} (c d-b e) (2 c d-b e)}{5 e^5}+\frac{2 c^2 (d+e x)^{11/2}}{11 e^5}","\frac{2 (d+e x)^{7/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{7 e^5}+\frac{2 d^2 (d+e x)^{3/2} (c d-b e)^2}{3 e^5}-\frac{4 c (d+e x)^{9/2} (2 c d-b e)}{9 e^5}-\frac{4 d (d+e x)^{5/2} (c d-b e) (2 c d-b e)}{5 e^5}+\frac{2 c^2 (d+e x)^{11/2}}{11 e^5}",1,"(2*d^2*(c*d - b*e)^2*(d + e*x)^(3/2))/(3*e^5) - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(7/2))/(7*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(9/2))/(9*e^5) + (2*c^2*(d + e*x)^(11/2))/(11*e^5)","A",2,1,21,0.04762,1,"{698}"
349,1,145,0,0.0589171,"\int \frac{\left(b x+c x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[(b*x + c*x^2)^2/Sqrt[d + e*x],x]","\frac{2 (d+e x)^{5/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{5 e^5}+\frac{2 d^2 \sqrt{d+e x} (c d-b e)^2}{e^5}-\frac{4 c (d+e x)^{7/2} (2 c d-b e)}{7 e^5}-\frac{4 d (d+e x)^{3/2} (c d-b e) (2 c d-b e)}{3 e^5}+\frac{2 c^2 (d+e x)^{9/2}}{9 e^5}","\frac{2 (d+e x)^{5/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{5 e^5}+\frac{2 d^2 \sqrt{d+e x} (c d-b e)^2}{e^5}-\frac{4 c (d+e x)^{7/2} (2 c d-b e)}{7 e^5}-\frac{4 d (d+e x)^{3/2} (c d-b e) (2 c d-b e)}{3 e^5}+\frac{2 c^2 (d+e x)^{9/2}}{9 e^5}",1,"(2*d^2*(c*d - b*e)^2*Sqrt[d + e*x])/e^5 - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(3/2))/(3*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(5/2))/(5*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^5) + (2*c^2*(d + e*x)^(9/2))/(9*e^5)","A",2,1,21,0.04762,1,"{698}"
350,1,143,0,0.0582186,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^(3/2),x]","\frac{2 (d+e x)^{3/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{3 e^5}-\frac{2 d^2 (c d-b e)^2}{e^5 \sqrt{d+e x}}-\frac{4 c (d+e x)^{5/2} (2 c d-b e)}{5 e^5}-\frac{4 d \sqrt{d+e x} (c d-b e) (2 c d-b e)}{e^5}+\frac{2 c^2 (d+e x)^{7/2}}{7 e^5}","\frac{2 (d+e x)^{3/2} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{3 e^5}-\frac{2 d^2 (c d-b e)^2}{e^5 \sqrt{d+e x}}-\frac{4 c (d+e x)^{5/2} (2 c d-b e)}{5 e^5}-\frac{4 d \sqrt{d+e x} (c d-b e) (2 c d-b e)}{e^5}+\frac{2 c^2 (d+e x)^{7/2}}{7 e^5}",1,"(-2*d^2*(c*d - b*e)^2)/(e^5*Sqrt[d + e*x]) - (4*d*(c*d - b*e)*(2*c*d - b*e)*Sqrt[d + e*x])/e^5 + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(3/2))/(3*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^5) + (2*c^2*(d + e*x)^(7/2))/(7*e^5)","A",2,1,21,0.04762,1,"{698}"
351,1,143,0,0.0583636,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{e^5}-\frac{2 d^2 (c d-b e)^2}{3 e^5 (d+e x)^{3/2}}-\frac{4 c (d+e x)^{3/2} (2 c d-b e)}{3 e^5}+\frac{4 d (c d-b e) (2 c d-b e)}{e^5 \sqrt{d+e x}}+\frac{2 c^2 (d+e x)^{5/2}}{5 e^5}","\frac{2 \sqrt{d+e x} \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{e^5}-\frac{2 d^2 (c d-b e)^2}{3 e^5 (d+e x)^{3/2}}-\frac{4 c (d+e x)^{3/2} (2 c d-b e)}{3 e^5}+\frac{4 d (c d-b e) (2 c d-b e)}{e^5 \sqrt{d+e x}}+\frac{2 c^2 (d+e x)^{5/2}}{5 e^5}",1,"(-2*d^2*(c*d - b*e)^2)/(3*e^5*(d + e*x)^(3/2)) + (4*d*(c*d - b*e)*(2*c*d - b*e))/(e^5*Sqrt[d + e*x]) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*Sqrt[d + e*x])/e^5 - (4*c*(2*c*d - b*e)*(d + e*x)^(3/2))/(3*e^5) + (2*c^2*(d + e*x)^(5/2))/(5*e^5)","A",2,1,21,0.04762,1,"{698}"
352,1,143,0,0.0576748,"\int \frac{\left(b x+c x^2\right)^2}{(d+e x)^{7/2}} \, dx","Int[(b*x + c*x^2)^2/(d + e*x)^(7/2),x]","-\frac{2 \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{e^5 \sqrt{d+e x}}-\frac{2 d^2 (c d-b e)^2}{5 e^5 (d+e x)^{5/2}}-\frac{4 c \sqrt{d+e x} (2 c d-b e)}{e^5}+\frac{4 d (c d-b e) (2 c d-b e)}{3 e^5 (d+e x)^{3/2}}+\frac{2 c^2 (d+e x)^{3/2}}{3 e^5}","-\frac{2 \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)}{e^5 \sqrt{d+e x}}-\frac{2 d^2 (c d-b e)^2}{5 e^5 (d+e x)^{5/2}}-\frac{4 c \sqrt{d+e x} (2 c d-b e)}{e^5}+\frac{4 d (c d-b e) (2 c d-b e)}{3 e^5 (d+e x)^{3/2}}+\frac{2 c^2 (d+e x)^{3/2}}{3 e^5}",1,"(-2*d^2*(c*d - b*e)^2)/(5*e^5*(d + e*x)^(5/2)) + (4*d*(c*d - b*e)*(2*c*d - b*e))/(3*e^5*(d + e*x)^(3/2)) - (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2))/(e^5*Sqrt[d + e*x]) - (4*c*(2*c*d - b*e)*Sqrt[d + e*x])/e^5 + (2*c^2*(d + e*x)^(3/2))/(3*e^5)","A",2,1,21,0.04762,1,"{698}"
353,1,248,0,0.139448,"\int (d+e x)^{7/2} \left(b x+c x^2\right)^3 \, dx","Int[(d + e*x)^(7/2)*(b*x + c*x^2)^3,x]","\frac{6 c (d+e x)^{17/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{17 e^7}-\frac{2 (d+e x)^{15/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{15 e^7}+\frac{6 d (d+e x)^{13/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{13 e^7}-\frac{6 c^2 (d+e x)^{19/2} (2 c d-b e)}{19 e^7}-\frac{6 d^2 (d+e x)^{11/2} (c d-b e)^2 (2 c d-b e)}{11 e^7}+\frac{2 d^3 (d+e x)^{9/2} (c d-b e)^3}{9 e^7}+\frac{2 c^3 (d+e x)^{21/2}}{21 e^7}","\frac{6 c (d+e x)^{17/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{17 e^7}-\frac{2 (d+e x)^{15/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{15 e^7}+\frac{6 d (d+e x)^{13/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{13 e^7}-\frac{6 c^2 (d+e x)^{19/2} (2 c d-b e)}{19 e^7}-\frac{6 d^2 (d+e x)^{11/2} (c d-b e)^2 (2 c d-b e)}{11 e^7}+\frac{2 d^3 (d+e x)^{9/2} (c d-b e)^3}{9 e^7}+\frac{2 c^3 (d+e x)^{21/2}}{21 e^7}",1,"(2*d^3*(c*d - b*e)^3*(d + e*x)^(9/2))/(9*e^7) - (6*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^7) + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(13/2))/(13*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(15/2))/(15*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(17/2))/(17*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(19/2))/(19*e^7) + (2*c^3*(d + e*x)^(21/2))/(21*e^7)","A",2,1,21,0.04762,1,"{698}"
354,1,248,0,0.1075451,"\int (d+e x)^{5/2} \left(b x+c x^2\right)^3 \, dx","Int[(d + e*x)^(5/2)*(b*x + c*x^2)^3,x]","\frac{2 c (d+e x)^{15/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{13/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{13 e^7}+\frac{6 d (d+e x)^{11/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{11 e^7}-\frac{6 c^2 (d+e x)^{17/2} (2 c d-b e)}{17 e^7}-\frac{2 d^2 (d+e x)^{9/2} (c d-b e)^2 (2 c d-b e)}{3 e^7}+\frac{2 d^3 (d+e x)^{7/2} (c d-b e)^3}{7 e^7}+\frac{2 c^3 (d+e x)^{19/2}}{19 e^7}","\frac{2 c (d+e x)^{15/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{13/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{13 e^7}+\frac{6 d (d+e x)^{11/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{11 e^7}-\frac{6 c^2 (d+e x)^{17/2} (2 c d-b e)}{17 e^7}-\frac{2 d^2 (d+e x)^{9/2} (c d-b e)^2 (2 c d-b e)}{3 e^7}+\frac{2 d^3 (d+e x)^{7/2} (c d-b e)^3}{7 e^7}+\frac{2 c^3 (d+e x)^{19/2}}{19 e^7}",1,"(2*d^3*(c*d - b*e)^3*(d + e*x)^(7/2))/(7*e^7) - (2*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(9/2))/(3*e^7) + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(11/2))/(11*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(13/2))/(13*e^7) + (2*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(15/2))/(5*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(17/2))/(17*e^7) + (2*c^3*(d + e*x)^(19/2))/(19*e^7)","A",2,1,21,0.04762,1,"{698}"
355,1,248,0,0.105789,"\int (d+e x)^{3/2} \left(b x+c x^2\right)^3 \, dx","Int[(d + e*x)^(3/2)*(b*x + c*x^2)^3,x]","\frac{6 c (d+e x)^{13/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{13 e^7}-\frac{2 (d+e x)^{11/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{11 e^7}+\frac{2 d (d+e x)^{9/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{3 e^7}-\frac{2 c^2 (d+e x)^{15/2} (2 c d-b e)}{5 e^7}-\frac{6 d^2 (d+e x)^{7/2} (c d-b e)^2 (2 c d-b e)}{7 e^7}+\frac{2 d^3 (d+e x)^{5/2} (c d-b e)^3}{5 e^7}+\frac{2 c^3 (d+e x)^{17/2}}{17 e^7}","\frac{6 c (d+e x)^{13/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{13 e^7}-\frac{2 (d+e x)^{11/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{11 e^7}+\frac{2 d (d+e x)^{9/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{3 e^7}-\frac{2 c^2 (d+e x)^{15/2} (2 c d-b e)}{5 e^7}-\frac{6 d^2 (d+e x)^{7/2} (c d-b e)^2 (2 c d-b e)}{7 e^7}+\frac{2 d^3 (d+e x)^{5/2} (c d-b e)^3}{5 e^7}+\frac{2 c^3 (d+e x)^{17/2}}{17 e^7}",1,"(2*d^3*(c*d - b*e)^3*(d + e*x)^(5/2))/(5*e^7) - (6*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^7) + (2*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(9/2))/(3*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(11/2))/(11*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(13/2))/(13*e^7) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(15/2))/(5*e^7) + (2*c^3*(d + e*x)^(17/2))/(17*e^7)","A",2,1,21,0.04762,1,"{698}"
356,1,248,0,0.105513,"\int \sqrt{d+e x} \left(b x+c x^2\right)^3 \, dx","Int[Sqrt[d + e*x]*(b*x + c*x^2)^3,x]","\frac{6 c (d+e x)^{11/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{11 e^7}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{9 e^7}+\frac{6 d (d+e x)^{7/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{7 e^7}-\frac{6 c^2 (d+e x)^{13/2} (2 c d-b e)}{13 e^7}-\frac{6 d^2 (d+e x)^{5/2} (c d-b e)^2 (2 c d-b e)}{5 e^7}+\frac{2 d^3 (d+e x)^{3/2} (c d-b e)^3}{3 e^7}+\frac{2 c^3 (d+e x)^{15/2}}{15 e^7}","\frac{6 c (d+e x)^{11/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{11 e^7}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{9 e^7}+\frac{6 d (d+e x)^{7/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{7 e^7}-\frac{6 c^2 (d+e x)^{13/2} (2 c d-b e)}{13 e^7}-\frac{6 d^2 (d+e x)^{5/2} (c d-b e)^2 (2 c d-b e)}{5 e^7}+\frac{2 d^3 (d+e x)^{3/2} (c d-b e)^3}{3 e^7}+\frac{2 c^3 (d+e x)^{15/2}}{15 e^7}",1,"(2*d^3*(c*d - b*e)^3*(d + e*x)^(3/2))/(3*e^7) - (6*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^7) + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(7/2))/(7*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(9/2))/(9*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(11/2))/(11*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(13/2))/(13*e^7) + (2*c^3*(d + e*x)^(15/2))/(15*e^7)","A",2,1,21,0.04762,1,"{698}"
357,1,244,0,0.1016047,"\int \frac{\left(b x+c x^2\right)^3}{\sqrt{d+e x}} \, dx","Int[(b*x + c*x^2)^3/Sqrt[d + e*x],x]","\frac{2 c (d+e x)^{9/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{3 e^7}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{7 e^7}+\frac{6 d (d+e x)^{5/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7}-\frac{6 c^2 (d+e x)^{11/2} (2 c d-b e)}{11 e^7}-\frac{2 d^2 (d+e x)^{3/2} (c d-b e)^2 (2 c d-b e)}{e^7}+\frac{2 d^3 \sqrt{d+e x} (c d-b e)^3}{e^7}+\frac{2 c^3 (d+e x)^{13/2}}{13 e^7}","\frac{2 c (d+e x)^{9/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{3 e^7}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{7 e^7}+\frac{6 d (d+e x)^{5/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7}-\frac{6 c^2 (d+e x)^{11/2} (2 c d-b e)}{11 e^7}-\frac{2 d^2 (d+e x)^{3/2} (c d-b e)^2 (2 c d-b e)}{e^7}+\frac{2 d^3 \sqrt{d+e x} (c d-b e)^3}{e^7}+\frac{2 c^3 (d+e x)^{13/2}}{13 e^7}",1,"(2*d^3*(c*d - b*e)^3*Sqrt[d + e*x])/e^7 - (2*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(3/2))/e^7 + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(5/2))/(5*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(7/2))/(7*e^7) + (2*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(9/2))/(3*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^7) + (2*c^3*(d + e*x)^(13/2))/(13*e^7)","A",2,1,21,0.04762,1,"{698}"
358,1,242,0,0.1036507,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^{3/2}} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^(3/2),x]","\frac{6 c (d+e x)^{7/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{7 e^7}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{5 e^7}+\frac{2 d (d+e x)^{3/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7}-\frac{2 c^2 (d+e x)^{9/2} (2 c d-b e)}{3 e^7}-\frac{6 d^2 \sqrt{d+e x} (c d-b e)^2 (2 c d-b e)}{e^7}-\frac{2 d^3 (c d-b e)^3}{e^7 \sqrt{d+e x}}+\frac{2 c^3 (d+e x)^{11/2}}{11 e^7}","\frac{6 c (d+e x)^{7/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{7 e^7}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{5 e^7}+\frac{2 d (d+e x)^{3/2} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7}-\frac{2 c^2 (d+e x)^{9/2} (2 c d-b e)}{3 e^7}-\frac{6 d^2 \sqrt{d+e x} (c d-b e)^2 (2 c d-b e)}{e^7}-\frac{2 d^3 (c d-b e)^3}{e^7 \sqrt{d+e x}}+\frac{2 c^3 (d+e x)^{11/2}}{11 e^7}",1,"(-2*d^3*(c*d - b*e)^3)/(e^7*Sqrt[d + e*x]) - (6*d^2*(c*d - b*e)^2*(2*c*d - b*e)*Sqrt[d + e*x])/e^7 + (2*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(3/2))/e^7 - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(5/2))/(5*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(7/2))/(7*e^7) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(9/2))/(3*e^7) + (2*c^3*(d + e*x)^(11/2))/(11*e^7)","A",2,1,21,0.04762,1,"{698}"
359,1,244,0,0.1005828,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^{5/2}} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^(5/2),x]","\frac{6 c (d+e x)^{5/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{3 e^7}+\frac{6 d \sqrt{d+e x} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7}-\frac{6 c^2 (d+e x)^{7/2} (2 c d-b e)}{7 e^7}+\frac{6 d^2 (c d-b e)^2 (2 c d-b e)}{e^7 \sqrt{d+e x}}-\frac{2 d^3 (c d-b e)^3}{3 e^7 (d+e x)^{3/2}}+\frac{2 c^3 (d+e x)^{9/2}}{9 e^7}","\frac{6 c (d+e x)^{5/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{3 e^7}+\frac{6 d \sqrt{d+e x} (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7}-\frac{6 c^2 (d+e x)^{7/2} (2 c d-b e)}{7 e^7}+\frac{6 d^2 (c d-b e)^2 (2 c d-b e)}{e^7 \sqrt{d+e x}}-\frac{2 d^3 (c d-b e)^3}{3 e^7 (d+e x)^{3/2}}+\frac{2 c^3 (d+e x)^{9/2}}{9 e^7}",1,"(-2*d^3*(c*d - b*e)^3)/(3*e^7*(d + e*x)^(3/2)) + (6*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(e^7*Sqrt[d + e*x]) + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*Sqrt[d + e*x])/e^7 - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(3/2))/(3*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(5/2))/(5*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^7) + (2*c^3*(d + e*x)^(9/2))/(9*e^7)","A",2,1,21,0.04762,1,"{698}"
360,1,240,0,0.1063459,"\int \frac{\left(b x+c x^2\right)^3}{(d+e x)^{7/2}} \, dx","Int[(b*x + c*x^2)^3/(d + e*x)^(7/2),x]","\frac{2 c (d+e x)^{3/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{e^7}-\frac{6 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7 \sqrt{d+e x}}-\frac{6 c^2 (d+e x)^{5/2} (2 c d-b e)}{5 e^7}+\frac{2 d^2 (c d-b e)^2 (2 c d-b e)}{e^7 (d+e x)^{3/2}}-\frac{2 d^3 (c d-b e)^3}{5 e^7 (d+e x)^{5/2}}+\frac{2 c^3 (d+e x)^{7/2}}{7 e^7}","\frac{2 c (d+e x)^{3/2} \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)}{e^7}-\frac{6 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)}{e^7 \sqrt{d+e x}}-\frac{6 c^2 (d+e x)^{5/2} (2 c d-b e)}{5 e^7}+\frac{2 d^2 (c d-b e)^2 (2 c d-b e)}{e^7 (d+e x)^{3/2}}-\frac{2 d^3 (c d-b e)^3}{5 e^7 (d+e x)^{5/2}}+\frac{2 c^3 (d+e x)^{7/2}}{7 e^7}",1,"(-2*d^3*(c*d - b*e)^3)/(5*e^7*(d + e*x)^(5/2)) + (2*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(e^7*(d + e*x)^(3/2)) - (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(e^7*Sqrt[d + e*x]) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*Sqrt[d + e*x])/e^7 + (2*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(3/2))/e^7 - (6*c^2*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^7) + (2*c^3*(d + e*x)^(7/2))/(7*e^7)","A",2,1,21,0.04762,1,"{698}"
361,1,157,0,0.3872821,"\int \frac{(d+e x)^{7/2}}{b x+c x^2} \, dx","Int[(d + e*x)^(7/2)/(b*x + c*x^2),x]","\frac{2 e \sqrt{d+e x} \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)}{c^3}+\frac{2 e (d+e x)^{3/2} (2 c d-b e)}{3 c^2}+\frac{2 (c d-b e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{7/2}}-\frac{2 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 e (d+e x)^{5/2}}{5 c}","\frac{2 e \sqrt{d+e x} \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)}{c^3}+\frac{2 e (d+e x)^{3/2} (2 c d-b e)}{3 c^2}+\frac{2 (c d-b e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{7/2}}-\frac{2 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 e (d+e x)^{5/2}}{5 c}",1,"(2*e*(3*c^2*d^2 - 3*b*c*d*e + b^2*e^2)*Sqrt[d + e*x])/c^3 + (2*e*(2*c*d - b*e)*(d + e*x)^(3/2))/(3*c^2) + (2*e*(d + e*x)^(5/2))/(5*c) - (2*d^(7/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b + (2*(c*d - b*e)^(7/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*c^(7/2))","A",7,5,21,0.2381,1,"{703, 824, 826, 1166, 208}"
362,1,118,0,0.2279923,"\int \frac{(d+e x)^{5/2}}{b x+c x^2} \, dx","Int[(d + e*x)^(5/2)/(b*x + c*x^2),x]","\frac{2 e \sqrt{d+e x} (2 c d-b e)}{c^2}+\frac{2 (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{5/2}}-\frac{2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 e (d+e x)^{3/2}}{3 c}","\frac{2 e \sqrt{d+e x} (2 c d-b e)}{c^2}+\frac{2 (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{5/2}}-\frac{2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 e (d+e x)^{3/2}}{3 c}",1,"(2*e*(2*c*d - b*e)*Sqrt[d + e*x])/c^2 + (2*e*(d + e*x)^(3/2))/(3*c) - (2*d^(5/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b + (2*(c*d - b*e)^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*c^(5/2))","A",6,5,21,0.2381,1,"{703, 824, 826, 1166, 208}"
363,1,92,0,0.1955578,"\int \frac{(d+e x)^{3/2}}{b x+c x^2} \, dx","Int[(d + e*x)^(3/2)/(b*x + c*x^2),x]","\frac{2 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{3/2}}-\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 e \sqrt{d+e x}}{c}","\frac{2 (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{3/2}}-\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 e \sqrt{d+e x}}{c}",1,"(2*e*Sqrt[d + e*x])/c - (2*d^(3/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b + (2*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*c^(3/2))","A",5,4,21,0.1905,1,"{703, 826, 1166, 208}"
364,1,77,0,0.0723879,"\int \frac{\sqrt{d+e x}}{b x+c x^2} \, dx","Int[Sqrt[d + e*x]/(b*x + c*x^2),x]","\frac{2 \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b \sqrt{c}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}","\frac{2 \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b \sqrt{c}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}",1,"(-2*Sqrt[d]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b + (2*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*Sqrt[c])","A",4,3,21,0.1429,1,"{699, 1130, 208}"
365,1,77,0,0.0576517,"\int \frac{1}{\sqrt{d+e x} \left(b x+c x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*(b*x + c*x^2)),x]","\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b \sqrt{c d-b e}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b \sqrt{d}}","\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b \sqrt{c d-b e}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b \sqrt{d}}",1,"(-2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b*Sqrt[d]) + (2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*Sqrt[c*d - b*e])","A",4,3,21,0.1429,1,"{707, 1093, 208}"
366,1,102,0,0.3177496,"\int \frac{1}{(d+e x)^{3/2} \left(b x+c x^2\right)} \, dx","Int[1/((d + e*x)^(3/2)*(b*x + c*x^2)),x]","\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{3/2}}-\frac{2 e}{d \sqrt{d+e x} (c d-b e)}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{3/2}}","\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{3/2}}-\frac{2 e}{d \sqrt{d+e x} (c d-b e)}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{3/2}}",1,"(-2*e)/(d*(c*d - b*e)*Sqrt[d + e*x]) - (2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b*d^(3/2)) + (2*c^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*(c*d - b*e)^(3/2))","A",5,4,21,0.1905,1,"{709, 826, 1166, 208}"
367,1,138,0,0.2607934,"\int \frac{1}{(d+e x)^{5/2} \left(b x+c x^2\right)} \, dx","Int[1/((d + e*x)^(5/2)*(b*x + c*x^2)),x]","\frac{2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{5/2}}-\frac{2 e (2 c d-b e)}{d^2 \sqrt{d+e x} (c d-b e)^2}-\frac{2 e}{3 d (d+e x)^{3/2} (c d-b e)}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{5/2}}","\frac{2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{5/2}}-\frac{2 e (2 c d-b e)}{d^2 \sqrt{d+e x} (c d-b e)^2}-\frac{2 e}{3 d (d+e x)^{3/2} (c d-b e)}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{5/2}}",1,"(-2*e)/(3*d*(c*d - b*e)*(d + e*x)^(3/2)) - (2*e*(2*c*d - b*e))/(d^2*(c*d - b*e)^2*Sqrt[d + e*x]) - (2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b*d^(5/2)) + (2*c^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*(c*d - b*e)^(5/2))","A",6,5,21,0.2381,1,"{709, 828, 826, 1166, 208}"
368,1,187,0,0.3767987,"\int \frac{1}{(d+e x)^{7/2} \left(b x+c x^2\right)} \, dx","Int[1/((d + e*x)^(7/2)*(b*x + c*x^2)),x]","-\frac{2 e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)}{d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{7/2}}-\frac{2 e (2 c d-b e)}{3 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 e}{5 d (d+e x)^{5/2} (c d-b e)}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{7/2}}","-\frac{2 e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)}{d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{7/2}}-\frac{2 e (2 c d-b e)}{3 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 e}{5 d (d+e x)^{5/2} (c d-b e)}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{7/2}}",1,"(-2*e)/(5*d*(c*d - b*e)*(d + e*x)^(5/2)) - (2*e*(2*c*d - b*e))/(3*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) - (2*e*(3*c^2*d^2 - 3*b*c*d*e + b^2*e^2))/(d^3*(c*d - b*e)^3*Sqrt[d + e*x]) - (2*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b*d^(7/2)) + (2*c^(7/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*(c*d - b*e)^(7/2))","A",7,5,21,0.2381,1,"{709, 828, 826, 1166, 208}"
369,1,251,0,0.534316,"\int \frac{(d+e x)^{9/2}}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)^(9/2)/(b*x + c*x^2)^2,x]","\frac{e (d+e x)^{3/2} \left(5 b^2 e^2-6 b c d e+6 c^2 d^2\right)}{3 b^2 c^2}+\frac{e \sqrt{d+e x} (2 c d-b e) \left(5 b^2 e^2-b c d e+c^2 d^2\right)}{b^2 c^3}-\frac{(c d-b e)^{7/2} (5 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{7/2}}+\frac{d^{7/2} (4 c d-9 b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3}-\frac{(d+e x)^{7/2} (x (2 c d-b e)+b d)}{b^2 \left(b x+c x^2\right)}+\frac{e (d+e x)^{5/2} (2 c d-b e)}{b^2 c}","\frac{e (d+e x)^{3/2} \left(5 b^2 e^2-6 b c d e+6 c^2 d^2\right)}{3 b^2 c^2}+\frac{e \sqrt{d+e x} (2 c d-b e) \left(5 b^2 e^2-b c d e+c^2 d^2\right)}{b^2 c^3}-\frac{(c d-b e)^{7/2} (5 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{7/2}}+\frac{d^{7/2} (4 c d-9 b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3}-\frac{(d+e x)^{7/2} (x (2 c d-b e)+b d)}{b^2 \left(b x+c x^2\right)}+\frac{e (d+e x)^{5/2} (2 c d-b e)}{b^2 c}",1,"(e*(2*c*d - b*e)*(c^2*d^2 - b*c*d*e + 5*b^2*e^2)*Sqrt[d + e*x])/(b^2*c^3) + (e*(6*c^2*d^2 - 6*b*c*d*e + 5*b^2*e^2)*(d + e*x)^(3/2))/(3*b^2*c^2) + (e*(2*c*d - b*e)*(d + e*x)^(5/2))/(b^2*c) - ((d + e*x)^(7/2)*(b*d + (2*c*d - b*e)*x))/(b^2*(b*x + c*x^2)) + (d^(7/2)*(4*c*d - 9*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b^3 - ((c*d - b*e)^(7/2)*(4*c*d + 5*b*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*c^(7/2))","A",8,5,21,0.2381,1,"{738, 824, 826, 1166, 208}"
370,1,200,0,0.3951529,"\int \frac{(d+e x)^{7/2}}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)^(7/2)/(b*x + c*x^2)^2,x]","\frac{e \sqrt{d+e x} \left(3 b^2 e^2-2 b c d e+2 c^2 d^2\right)}{b^2 c^2}-\frac{(c d-b e)^{5/2} (3 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{5/2}}+\frac{d^{5/2} (4 c d-7 b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3}-\frac{(d+e x)^{5/2} (x (2 c d-b e)+b d)}{b^2 \left(b x+c x^2\right)}+\frac{e (d+e x)^{3/2} (2 c d-b e)}{b^2 c}","\frac{e \sqrt{d+e x} \left(3 b^2 e^2-2 b c d e+2 c^2 d^2\right)}{b^2 c^2}-\frac{(c d-b e)^{5/2} (3 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{5/2}}+\frac{d^{5/2} (4 c d-7 b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3}-\frac{(d+e x)^{5/2} (x (2 c d-b e)+b d)}{b^2 \left(b x+c x^2\right)}+\frac{e (d+e x)^{3/2} (2 c d-b e)}{b^2 c}",1,"(e*(2*c^2*d^2 - 2*b*c*d*e + 3*b^2*e^2)*Sqrt[d + e*x])/(b^2*c^2) + (e*(2*c*d - b*e)*(d + e*x)^(3/2))/(b^2*c) - ((d + e*x)^(5/2)*(b*d + (2*c*d - b*e)*x))/(b^2*(b*x + c*x^2)) + (d^(5/2)*(4*c*d - 7*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b^3 - ((c*d - b*e)^(5/2)*(4*c*d + 3*b*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*c^(5/2))","A",7,5,21,0.2381,1,"{738, 824, 826, 1166, 208}"
371,1,159,0,0.3018999,"\int \frac{(d+e x)^{5/2}}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)^(5/2)/(b*x + c*x^2)^2,x]","-\frac{(c d-b e)^{3/2} (b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{3/2}}+\frac{d^{3/2} (4 c d-5 b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3}-\frac{(d+e x)^{3/2} (x (2 c d-b e)+b d)}{b^2 \left(b x+c x^2\right)}+\frac{e \sqrt{d+e x} (2 c d-b e)}{b^2 c}","-\frac{(c d-b e)^{3/2} (b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{3/2}}+\frac{d^{3/2} (4 c d-5 b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3}-\frac{(d+e x)^{3/2} (x (2 c d-b e)+b d)}{b^2 \left(b x+c x^2\right)}+\frac{e \sqrt{d+e x} (2 c d-b e)}{b^2 c}",1,"(e*(2*c*d - b*e)*Sqrt[d + e*x])/(b^2*c) - ((d + e*x)^(3/2)*(b*d + (2*c*d - b*e)*x))/(b^2*(b*x + c*x^2)) + (d^(3/2)*(4*c*d - 5*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b^3 - ((c*d - b*e)^(3/2)*(4*c*d + b*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*c^(3/2))","A",6,5,21,0.2381,1,"{738, 824, 826, 1166, 208}"
372,1,134,0,0.1833173,"\int \frac{(d+e x)^{3/2}}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)^(3/2)/(b*x + c*x^2)^2,x]","-\frac{\sqrt{d+e x} (x (2 c d-b e)+b d)}{b^2 \left(b x+c x^2\right)}+\frac{\sqrt{d} (4 c d-3 b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3}-\frac{\sqrt{c d-b e} (4 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 \sqrt{c}}","-\frac{\sqrt{d+e x} (x (2 c d-b e)+b d)}{b^2 \left(b x+c x^2\right)}+\frac{\sqrt{d} (4 c d-3 b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3}-\frac{\sqrt{c d-b e} (4 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 \sqrt{c}}",1,"-((Sqrt[d + e*x]*(b*d + (2*c*d - b*e)*x))/(b^2*(b*x + c*x^2))) + (Sqrt[d]*(4*c*d - 3*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b^3 - (Sqrt[c*d - b*e]*(4*c*d - b*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*Sqrt[c])","A",5,4,21,0.1905,1,"{738, 826, 1166, 208}"
373,1,125,0,0.2339635,"\int \frac{\sqrt{d+e x}}{\left(b x+c x^2\right)^2} \, dx","Int[Sqrt[d + e*x]/(b*x + c*x^2)^2,x]","-\frac{(b+2 c x) \sqrt{d+e x}}{b^2 \left(b x+c x^2\right)}+\frac{(4 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 \sqrt{d}}-\frac{\sqrt{c} (4 c d-3 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 \sqrt{c d-b e}}","-\frac{(b+2 c x) \sqrt{d+e x}}{b^2 \left(b x+c x^2\right)}+\frac{(4 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 \sqrt{d}}-\frac{\sqrt{c} (4 c d-3 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 \sqrt{c d-b e}}",1,"-(((b + 2*c*x)*Sqrt[d + e*x])/(b^2*(b*x + c*x^2))) + ((4*c*d - b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*Sqrt[d]) - (Sqrt[c]*(4*c*d - 3*b*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*Sqrt[c*d - b*e])","A",5,4,21,0.1905,1,"{736, 826, 1166, 208}"
374,1,154,0,0.2607339,"\int \frac{1}{\sqrt{d+e x} \left(b x+c x^2\right)^2} \, dx","Int[1/(Sqrt[d + e*x]*(b*x + c*x^2)^2),x]","-\frac{c^{3/2} (4 c d-5 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{3/2}}+\frac{(b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 d^{3/2}}-\frac{\sqrt{d+e x} (c x (2 c d-b e)+b (c d-b e))}{b^2 d \left(b x+c x^2\right) (c d-b e)}","-\frac{c^{3/2} (4 c d-5 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{3/2}}+\frac{(b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 d^{3/2}}-\frac{\sqrt{d+e x} (c x (2 c d-b e)+b (c d-b e))}{b^2 d \left(b x+c x^2\right) (c d-b e)}",1,"-((Sqrt[d + e*x]*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(b*x + c*x^2))) + ((4*c*d + b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*d^(3/2)) - (c^(3/2)*(4*c*d - 5*b*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*(c*d - b*e)^(3/2))","A",5,4,21,0.1905,1,"{740, 826, 1166, 208}"
375,1,206,0,0.3527456,"\int \frac{1}{(d+e x)^{3/2} \left(b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)^(3/2)*(b*x + c*x^2)^2),x]","-\frac{e \left(3 b^2 e^2-2 b c d e+2 c^2 d^2\right)}{b^2 d^2 \sqrt{d+e x} (c d-b e)^2}-\frac{c^{5/2} (4 c d-7 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{5/2}}+\frac{(3 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 d^{5/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{b^2 d \left(b x+c x^2\right) \sqrt{d+e x} (c d-b e)}","-\frac{e \left(3 b^2 e^2-2 b c d e+2 c^2 d^2\right)}{b^2 d^2 \sqrt{d+e x} (c d-b e)^2}-\frac{c^{5/2} (4 c d-7 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{5/2}}+\frac{(3 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 d^{5/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{b^2 d \left(b x+c x^2\right) \sqrt{d+e x} (c d-b e)}",1,"-((e*(2*c^2*d^2 - 2*b*c*d*e + 3*b^2*e^2))/(b^2*d^2*(c*d - b*e)^2*Sqrt[d + e*x])) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(b^2*d*(c*d - b*e)*Sqrt[d + e*x]*(b*x + c*x^2)) + ((4*c*d + 3*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*d^(5/2)) - (c^(5/2)*(4*c*d - 7*b*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*(c*d - b*e)^(5/2))","A",6,5,21,0.2381,1,"{740, 828, 826, 1166, 208}"
376,1,267,0,0.5150506,"\int \frac{1}{(d+e x)^{5/2} \left(b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)^(5/2)*(b*x + c*x^2)^2),x]","-\frac{e (2 c d-b e) \left(5 b^2 e^2-b c d e+c^2 d^2\right)}{b^2 d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{e \left(5 b^2 e^2-6 b c d e+6 c^2 d^2\right)}{3 b^2 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{c^{7/2} (4 c d-9 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{7/2}}+\frac{(5 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 d^{7/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{b^2 d \left(b x+c x^2\right) (d+e x)^{3/2} (c d-b e)}","-\frac{e (2 c d-b e) \left(5 b^2 e^2-b c d e+c^2 d^2\right)}{b^2 d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{e \left(5 b^2 e^2-6 b c d e+6 c^2 d^2\right)}{3 b^2 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{c^{7/2} (4 c d-9 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{7/2}}+\frac{(5 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 d^{7/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{b^2 d \left(b x+c x^2\right) (d+e x)^{3/2} (c d-b e)}",1,"-(e*(6*c^2*d^2 - 6*b*c*d*e + 5*b^2*e^2))/(3*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) - (e*(2*c*d - b*e)*(c^2*d^2 - b*c*d*e + 5*b^2*e^2))/(b^2*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(b^2*d*(c*d - b*e)*(d + e*x)^(3/2)*(b*x + c*x^2)) + ((4*c*d + 5*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*d^(7/2)) - (c^(7/2)*(4*c*d - 9*b*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*(c*d - b*e)^(7/2))","A",7,5,21,0.2381,1,"{740, 828, 826, 1166, 208}"
377,1,349,0,0.7388552,"\int \frac{1}{(d+e x)^{7/2} \left(b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)^(7/2)*(b*x + c*x^2)^2),x]","-\frac{e \left(26 b^2 c^2 d^2 e^2-24 b^3 c d e^3+7 b^4 e^4-4 b c^3 d^3 e+2 c^4 d^4\right)}{b^2 d^4 \sqrt{d+e x} (c d-b e)^4}-\frac{e (2 c d-b e) \left(7 b^2 e^2-3 b c d e+3 c^2 d^2\right)}{3 b^2 d^3 (d+e x)^{3/2} (c d-b e)^3}-\frac{e \left(7 b^2 e^2-10 b c d e+10 c^2 d^2\right)}{5 b^2 d^2 (d+e x)^{5/2} (c d-b e)^2}-\frac{c^{9/2} (4 c d-11 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{9/2}}+\frac{(7 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 d^{9/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{b^2 d \left(b x+c x^2\right) (d+e x)^{5/2} (c d-b e)}","-\frac{e \left(26 b^2 c^2 d^2 e^2-24 b^3 c d e^3+7 b^4 e^4-4 b c^3 d^3 e+2 c^4 d^4\right)}{b^2 d^4 \sqrt{d+e x} (c d-b e)^4}-\frac{e (2 c d-b e) \left(7 b^2 e^2-3 b c d e+3 c^2 d^2\right)}{3 b^2 d^3 (d+e x)^{3/2} (c d-b e)^3}-\frac{e \left(7 b^2 e^2-10 b c d e+10 c^2 d^2\right)}{5 b^2 d^2 (d+e x)^{5/2} (c d-b e)^2}-\frac{c^{9/2} (4 c d-11 b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{9/2}}+\frac{(7 b e+4 c d) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b^3 d^{9/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{b^2 d \left(b x+c x^2\right) (d+e x)^{5/2} (c d-b e)}",1,"-(e*(10*c^2*d^2 - 10*b*c*d*e + 7*b^2*e^2))/(5*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(5/2)) - (e*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 7*b^2*e^2))/(3*b^2*d^3*(c*d - b*e)^3*(d + e*x)^(3/2)) - (e*(2*c^4*d^4 - 4*b*c^3*d^3*e + 26*b^2*c^2*d^2*e^2 - 24*b^3*c*d*e^3 + 7*b^4*e^4))/(b^2*d^4*(c*d - b*e)^4*Sqrt[d + e*x]) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(b^2*d*(c*d - b*e)*(d + e*x)^(5/2)*(b*x + c*x^2)) + ((4*c*d + 7*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*d^(9/2)) - (c^(9/2)*(4*c*d - 11*b*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*(c*d - b*e)^(9/2))","A",8,5,21,0.2381,1,"{740, 828, 826, 1166, 208}"
378,1,300,0,0.5198514,"\int \frac{(d+e x)^{9/2}}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^(9/2)/(b*x + c*x^2)^3,x]","\frac{(d+e x)^{3/2} \left(x (2 c d-b e) \left(-b^2 e^2-12 b c d e+12 c^2 d^2\right)+b c d^2 (12 c d-13 b e)\right)}{4 b^4 c \left(b x+c x^2\right)}-\frac{3 e \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)}{4 b^4 c^2}-\frac{3 d^{5/2} \left(21 b^2 e^2-36 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5}+\frac{3 (c d-b e)^{5/2} \left(b^2 e^2+4 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{5/2}}-\frac{(d+e x)^{7/2} (x (2 c d-b e)+b d)}{2 b^2 \left(b x+c x^2\right)^2}","\frac{(d+e x)^{3/2} \left(x (2 c d-b e) \left(-b^2 e^2-12 b c d e+12 c^2 d^2\right)+b c d^2 (12 c d-13 b e)\right)}{4 b^4 c \left(b x+c x^2\right)}-\frac{3 e \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)}{4 b^4 c^2}-\frac{3 d^{5/2} \left(21 b^2 e^2-36 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5}+\frac{3 (c d-b e)^{5/2} \left(b^2 e^2+4 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{5/2}}-\frac{(d+e x)^{7/2} (x (2 c d-b e)+b d)}{2 b^2 \left(b x+c x^2\right)^2}",1,"(-3*e*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*Sqrt[d + e*x])/(4*b^4*c^2) - ((d + e*x)^(7/2)*(b*d + (2*c*d - b*e)*x))/(2*b^2*(b*x + c*x^2)^2) + ((d + e*x)^(3/2)*(b*c*d^2*(12*c*d - 13*b*e) + (2*c*d - b*e)*(12*c^2*d^2 - 12*b*c*d*e - b^2*e^2)*x))/(4*b^4*c*(b*x + c*x^2)) - (3*d^(5/2)*(16*c^2*d^2 - 36*b*c*d*e + 21*b^2*e^2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5) + (3*(c*d - b*e)^(5/2)*(16*c^2*d^2 + 4*b*c*d*e + b^2*e^2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*c^(5/2))","A",7,6,21,0.2857,1,"{738, 818, 824, 826, 1166, 208}"
379,1,248,0,0.3862615,"\int \frac{(d+e x)^{7/2}}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^(7/2)/(b*x + c*x^2)^3,x]","\frac{\sqrt{d+e x} \left(x (2 c d-b e) \left(b^2 e^2-12 b c d e+12 c^2 d^2\right)+b c d^2 (12 c d-11 b e)\right)}{4 b^4 c \left(b x+c x^2\right)}-\frac{d^{3/2} \left(35 b^2 e^2-84 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5}+\frac{(c d-b e)^{3/2} \left(-b^2 e^2-12 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{3/2}}-\frac{(d+e x)^{5/2} (x (2 c d-b e)+b d)}{2 b^2 \left(b x+c x^2\right)^2}","\frac{\sqrt{d+e x} \left(x (2 c d-b e) \left(b^2 e^2-12 b c d e+12 c^2 d^2\right)+b c d^2 (12 c d-11 b e)\right)}{4 b^4 c \left(b x+c x^2\right)}-\frac{d^{3/2} \left(35 b^2 e^2-84 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5}+\frac{(c d-b e)^{3/2} \left(-b^2 e^2-12 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{3/2}}-\frac{(d+e x)^{5/2} (x (2 c d-b e)+b d)}{2 b^2 \left(b x+c x^2\right)^2}",1,"-((d + e*x)^(5/2)*(b*d + (2*c*d - b*e)*x))/(2*b^2*(b*x + c*x^2)^2) + (Sqrt[d + e*x]*(b*c*d^2*(12*c*d - 11*b*e) + (2*c*d - b*e)*(12*c^2*d^2 - 12*b*c*d*e + b^2*e^2)*x))/(4*b^4*c*(b*x + c*x^2)) - (d^(3/2)*(48*c^2*d^2 - 84*b*c*d*e + 35*b^2*e^2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5) + ((c*d - b*e)^(3/2)*(48*c^2*d^2 - 12*b*c*d*e - b^2*e^2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*c^(3/2))","A",6,5,21,0.2381,1,"{738, 818, 826, 1166, 208}"
380,1,232,0,0.3073287,"\int \frac{(d+e x)^{5/2}}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^(5/2)/(b*x + c*x^2)^3,x]","\frac{3 \sqrt{d+e x} \left(x \left(b^2 e^2-8 b c d e+8 c^2 d^2\right)+b d (4 c d-3 b e)\right)}{4 b^4 \left(b x+c x^2\right)}-\frac{3 \sqrt{d} \left(5 b^2 e^2-20 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5}+\frac{3 \sqrt{c d-b e} \left(b^2 e^2-12 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 \sqrt{c}}-\frac{(d+e x)^{3/2} (x (2 c d-b e)+b d)}{2 b^2 \left(b x+c x^2\right)^2}","\frac{3 \sqrt{d+e x} \left(x \left(b^2 e^2-8 b c d e+8 c^2 d^2\right)+b d (4 c d-3 b e)\right)}{4 b^4 \left(b x+c x^2\right)}-\frac{3 \sqrt{d} \left(5 b^2 e^2-20 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5}+\frac{3 \sqrt{c d-b e} \left(b^2 e^2-12 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 \sqrt{c}}-\frac{(d+e x)^{3/2} (x (2 c d-b e)+b d)}{2 b^2 \left(b x+c x^2\right)^2}",1,"-((d + e*x)^(3/2)*(b*d + (2*c*d - b*e)*x))/(2*b^2*(b*x + c*x^2)^2) + (3*Sqrt[d + e*x]*(b*d*(4*c*d - 3*b*e) + (8*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*x))/(4*b^4*(b*x + c*x^2)) - (3*Sqrt[d]*(16*c^2*d^2 - 20*b*c*d*e + 5*b^2*e^2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5) + (3*Sqrt[c*d - b*e]*(16*c^2*d^2 - 12*b*c*d*e + b^2*e^2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*Sqrt[c])","A",6,5,21,0.2381,1,"{738, 820, 826, 1166, 208}"
381,1,246,0,0.4646369,"\int \frac{(d+e x)^{3/2}}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^(3/2)/(b*x + c*x^2)^3,x]","-\frac{3 \left(b^2 e^2-12 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 \sqrt{d}}+\frac{3 \sqrt{c} \left(5 b^2 e^2-20 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 \sqrt{c d-b e}}-\frac{\sqrt{d+e x} (x (2 c d-b e)+b d)}{2 b^2 \left(b x+c x^2\right)^2}+\frac{\sqrt{d+e x} (12 c x (2 c d-b e) (c d-b e)+b (12 c d-7 b e) (c d-b e))}{4 b^4 \left(b x+c x^2\right) (c d-b e)}","-\frac{3 \left(b^2 e^2-12 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 \sqrt{d}}+\frac{3 \sqrt{c} \left(5 b^2 e^2-20 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 \sqrt{c d-b e}}-\frac{\sqrt{d+e x} (x (2 c d-b e)+b d)}{2 b^2 \left(b x+c x^2\right)^2}+\frac{\sqrt{d+e x} (12 c x (2 c d-b e) (c d-b e)+b (12 c d-7 b e) (c d-b e))}{4 b^4 \left(b x+c x^2\right) (c d-b e)}",1,"-(Sqrt[d + e*x]*(b*d + (2*c*d - b*e)*x))/(2*b^2*(b*x + c*x^2)^2) + (Sqrt[d + e*x]*(b*(12*c*d - 7*b*e)*(c*d - b*e) + 12*c*(c*d - b*e)*(2*c*d - b*e)*x))/(4*b^4*(c*d - b*e)*(b*x + c*x^2)) - (3*(16*c^2*d^2 - 12*b*c*d*e + b^2*e^2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*Sqrt[d]) + (3*Sqrt[c]*(16*c^2*d^2 - 20*b*c*d*e + 5*b^2*e^2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*Sqrt[c*d - b*e])","A",6,5,21,0.2381,1,"{738, 822, 826, 1166, 208}"
382,1,245,0,0.3777422,"\int \frac{\sqrt{d+e x}}{\left(b x+c x^2\right)^3} \, dx","Int[Sqrt[d + e*x]/(b*x + c*x^2)^3,x]","\frac{\sqrt{d+e x} \left(c x \left(b^2 e^2-24 b c d e+24 c^2 d^2\right)+b (c d-b e) (12 c d-b e)\right)}{4 b^4 d \left(b x+c x^2\right) (c d-b e)}+\frac{c^{3/2} \left(35 b^2 e^2-84 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{3/2}}-\frac{\left(-b^2 e^2-12 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 d^{3/2}}-\frac{(b+2 c x) \sqrt{d+e x}}{2 b^2 \left(b x+c x^2\right)^2}","\frac{\sqrt{d+e x} \left(c x \left(b^2 e^2-24 b c d e+24 c^2 d^2\right)+b (c d-b e) (12 c d-b e)\right)}{4 b^4 d \left(b x+c x^2\right) (c d-b e)}+\frac{c^{3/2} \left(35 b^2 e^2-84 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{3/2}}-\frac{\left(-b^2 e^2-12 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 d^{3/2}}-\frac{(b+2 c x) \sqrt{d+e x}}{2 b^2 \left(b x+c x^2\right)^2}",1,"-((b + 2*c*x)*Sqrt[d + e*x])/(2*b^2*(b*x + c*x^2)^2) + (Sqrt[d + e*x]*(b*(c*d - b*e)*(12*c*d - b*e) + c*(24*c^2*d^2 - 24*b*c*d*e + b^2*e^2)*x))/(4*b^4*d*(c*d - b*e)*(b*x + c*x^2)) - ((48*c^2*d^2 - 12*b*c*d*e - b^2*e^2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*d^(3/2)) + (c^(3/2)*(48*c^2*d^2 - 84*b*c*d*e + 35*b^2*e^2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*(c*d - b*e)^(3/2))","A",6,5,21,0.2381,1,"{736, 822, 826, 1166, 208}"
383,1,299,0,0.4295339,"\int \frac{1}{\sqrt{d+e x} \left(b x+c x^2\right)^3} \, dx","Int[1/(Sqrt[d + e*x]*(b*x + c*x^2)^3),x]","\frac{\sqrt{d+e x} \left(3 c x (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)+b (c d-b e) \left(-3 b^2 e^2-7 b c d e+12 c^2 d^2\right)\right)}{4 b^4 d^2 \left(b x+c x^2\right) (c d-b e)^2}+\frac{3 c^{5/2} \left(21 b^2 e^2-36 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{5/2}}-\frac{3 \left(b^2 e^2+4 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 d^{5/2}}-\frac{\sqrt{d+e x} (c x (2 c d-b e)+b (c d-b e))}{2 b^2 d \left(b x+c x^2\right)^2 (c d-b e)}","\frac{\sqrt{d+e x} \left(3 c x (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)+b (c d-b e) \left(-3 b^2 e^2-7 b c d e+12 c^2 d^2\right)\right)}{4 b^4 d^2 \left(b x+c x^2\right) (c d-b e)^2}+\frac{3 c^{5/2} \left(21 b^2 e^2-36 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{5/2}}-\frac{3 \left(b^2 e^2+4 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 d^{5/2}}-\frac{\sqrt{d+e x} (c x (2 c d-b e)+b (c d-b e))}{2 b^2 d \left(b x+c x^2\right)^2 (c d-b e)}",1,"-(Sqrt[d + e*x]*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(2*b^2*d*(c*d - b*e)*(b*x + c*x^2)^2) + (Sqrt[d + e*x]*(b*(c*d - b*e)*(12*c^2*d^2 - 7*b*c*d*e - 3*b^2*e^2) + 3*c*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*x))/(4*b^4*d^2*(c*d - b*e)^2*(b*x + c*x^2)) - (3*(16*c^2*d^2 + 4*b*c*d*e + b^2*e^2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*d^(5/2)) + (3*c^(5/2)*(16*c^2*d^2 - 36*b*c*d*e + 21*b^2*e^2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*(c*d - b*e)^(5/2))","A",6,5,21,0.2381,1,"{740, 822, 826, 1166, 208}"
384,1,370,0,0.6004119,"\int \frac{1}{(d+e x)^{3/2} \left(b x+c x^2\right)^3} \, dx","Int[1/((d + e*x)^(3/2)*(b*x + c*x^2)^3),x]","\frac{c x (2 c d-b e) \left(-5 b^2 e^2-12 b c d e+12 c^2 d^2\right)+b \left(5 b^3 e^3-17 b c^2 d^2 e+12 c^3 d^3\right)}{4 b^4 d^2 \left(b x+c x^2\right) \sqrt{d+e x} (c d-b e)^2}+\frac{3 e \left(-b^2 e^2-b c d e+c^2 d^2\right) \left(5 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{4 b^4 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{3 c^{7/2} \left(33 b^2 e^2-44 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{7/2}}-\frac{3 \left(5 b^2 e^2+12 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 d^{7/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{2 b^2 d \left(b x+c x^2\right)^2 \sqrt{d+e x} (c d-b e)}","\frac{c x (2 c d-b e) \left(-5 b^2 e^2-12 b c d e+12 c^2 d^2\right)+b \left(5 b^3 e^3-17 b c^2 d^2 e+12 c^3 d^3\right)}{4 b^4 d^2 \left(b x+c x^2\right) \sqrt{d+e x} (c d-b e)^2}+\frac{3 e \left(-b^2 e^2-b c d e+c^2 d^2\right) \left(5 b^2 e^2-8 b c d e+8 c^2 d^2\right)}{4 b^4 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{3 c^{7/2} \left(33 b^2 e^2-44 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{7/2}}-\frac{3 \left(5 b^2 e^2+12 b c d e+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 d^{7/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{2 b^2 d \left(b x+c x^2\right)^2 \sqrt{d+e x} (c d-b e)}",1,"(3*e*(c^2*d^2 - b*c*d*e - b^2*e^2)*(8*c^2*d^2 - 8*b*c*d*e + 5*b^2*e^2))/(4*b^4*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(2*b^2*d*(c*d - b*e)*Sqrt[d + e*x]*(b*x + c*x^2)^2) + (b*(12*c^3*d^3 - 17*b*c^2*d^2*e + 5*b^3*e^3) + c*(2*c*d - b*e)*(12*c^2*d^2 - 12*b*c*d*e - 5*b^2*e^2)*x)/(4*b^4*d^2*(c*d - b*e)^2*Sqrt[d + e*x]*(b*x + c*x^2)) - (3*(16*c^2*d^2 + 12*b*c*d*e + 5*b^2*e^2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*d^(7/2)) + (3*c^(7/2)*(16*c^2*d^2 - 44*b*c*d*e + 33*b^2*e^2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*(c*d - b*e)^(7/2))","A",7,6,21,0.2857,1,"{740, 822, 828, 826, 1166, 208}"
385,1,470,0,0.878529,"\int \frac{1}{(d+e x)^{5/2} \left(b x+c x^2\right)^3} \, dx","Int[1/((d + e*x)^(5/2)*(b*x + c*x^2)^3),x]","\frac{c x (2 c d-b e) \left(-7 b^2 e^2-12 b c d e+12 c^2 d^2\right)+b (c d-b e) \left(-7 b^2 e^2-3 b c d e+12 c^2 d^2\right)}{4 b^4 d^2 \left(b x+c x^2\right) (d+e x)^{3/2} (c d-b e)^2}+\frac{e (2 c d-b e) \left(2 b^2 c^2 d^2 e^2+10 b^3 c d e^3-35 b^4 e^4-24 b c^3 d^3 e+12 c^4 d^4\right)}{4 b^4 d^4 \sqrt{d+e x} (c d-b e)^4}+\frac{e \left(27 b^2 c^2 d^2 e^2+45 b^3 c d e^3-35 b^4 e^4-144 b c^3 d^3 e+72 c^4 d^4\right)}{12 b^4 d^3 (d+e x)^{3/2} (c d-b e)^3}+\frac{c^{9/2} \left(143 b^2 e^2-156 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{9/2}}-\frac{\left(35 b^2 e^2+60 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 d^{9/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{2 b^2 d \left(b x+c x^2\right)^2 (d+e x)^{3/2} (c d-b e)}","\frac{c x (2 c d-b e) \left(-7 b^2 e^2-12 b c d e+12 c^2 d^2\right)+b (c d-b e) \left(-7 b^2 e^2-3 b c d e+12 c^2 d^2\right)}{4 b^4 d^2 \left(b x+c x^2\right) (d+e x)^{3/2} (c d-b e)^2}+\frac{e (2 c d-b e) \left(2 b^2 c^2 d^2 e^2+10 b^3 c d e^3-35 b^4 e^4-24 b c^3 d^3 e+12 c^4 d^4\right)}{4 b^4 d^4 \sqrt{d+e x} (c d-b e)^4}+\frac{e \left(27 b^2 c^2 d^2 e^2+45 b^3 c d e^3-35 b^4 e^4-144 b c^3 d^3 e+72 c^4 d^4\right)}{12 b^4 d^3 (d+e x)^{3/2} (c d-b e)^3}+\frac{c^{9/2} \left(143 b^2 e^2-156 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{9/2}}-\frac{\left(35 b^2 e^2+60 b c d e+48 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{4 b^5 d^{9/2}}-\frac{c x (2 c d-b e)+b (c d-b e)}{2 b^2 d \left(b x+c x^2\right)^2 (d+e x)^{3/2} (c d-b e)}",1,"(e*(72*c^4*d^4 - 144*b*c^3*d^3*e + 27*b^2*c^2*d^2*e^2 + 45*b^3*c*d*e^3 - 35*b^4*e^4))/(12*b^4*d^3*(c*d - b*e)^3*(d + e*x)^(3/2)) + (e*(2*c*d - b*e)*(12*c^4*d^4 - 24*b*c^3*d^3*e + 2*b^2*c^2*d^2*e^2 + 10*b^3*c*d*e^3 - 35*b^4*e^4))/(4*b^4*d^4*(c*d - b*e)^4*Sqrt[d + e*x]) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(2*b^2*d*(c*d - b*e)*(d + e*x)^(3/2)*(b*x + c*x^2)^2) + (b*(c*d - b*e)*(12*c^2*d^2 - 3*b*c*d*e - 7*b^2*e^2) + c*(2*c*d - b*e)*(12*c^2*d^2 - 12*b*c*d*e - 7*b^2*e^2)*x)/(4*b^4*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)*(b*x + c*x^2)) - ((48*c^2*d^2 + 60*b*c*d*e + 35*b^2*e^2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*d^(9/2)) + (c^(9/2)*(48*c^2*d^2 - 156*b*c*d*e + 143*b^2*e^2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*(c*d - b*e)^(9/2))","A",8,6,21,0.2857,1,"{740, 822, 828, 826, 1166, 208}"
386,1,362,0,0.3941241,"\int (d+e x)^{3/2} \sqrt{b x+c x^2} \, dx","Int[(d + e*x)^(3/2)*Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-4 b^2 e^2+12 c e x (2 c d-b e)+9 b c d e+3 c^2 d^2\right)}{105 c^2 e}+\frac{4 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{5/2} e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(8 b^2 e^2-3 b c d e+3 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{5/2} e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 e \left(b x+c x^2\right)^{3/2} \sqrt{d+e x}}{7 c}","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-4 b^2 e^2+12 c e x (2 c d-b e)+9 b c d e+3 c^2 d^2\right)}{105 c^2 e}+\frac{4 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{5/2} e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(8 b^2 e^2-3 b c d e+3 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{5/2} e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 e \left(b x+c x^2\right)^{3/2} \sqrt{d+e x}}{7 c}",1,"(2*Sqrt[d + e*x]*(3*c^2*d^2 + 9*b*c*d*e - 4*b^2*e^2 + 12*c*e*(2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(105*c^2*e) + (2*e*Sqrt[d + e*x]*(b*x + c*x^2)^(3/2))/(7*c) - (2*Sqrt[-b]*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 8*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(105*c^(5/2)*e^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (4*Sqrt[-b]*d*(c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(105*c^(5/2)*e^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{742, 814, 843, 715, 112, 110, 117, 116}"
387,1,308,0,0.3412737,"\int \sqrt{d+e x} \sqrt{b x+c x^2} \, dx","Int[Sqrt[d + e*x]*Sqrt[b*x + c*x^2],x]","-\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{3/2} e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{3/2} e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{b x+c x^2} (d+e x)^{3/2}}{5 e}-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} (2 c d-b e)}{15 c e}","-\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{3/2} e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{3/2} e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{b x+c x^2} (d+e x)^{3/2}}{5 e}-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} (2 c d-b e)}{15 c e}",1,"(-2*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(15*c*e) + (2*(d + e*x)^(3/2)*Sqrt[b*x + c*x^2])/(5*e) - (4*Sqrt[-b]*(c^2*d^2 - b*c*d*e + b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*c^(3/2)*e^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*d*(c*d - b*e)*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*c^(3/2)*e^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{734, 832, 843, 715, 112, 110, 117, 116}"
388,1,246,0,0.1897186,"\int \frac{\sqrt{b x+c x^2}}{\sqrt{d+e x}} \, dx","Int[Sqrt[b*x + c*x^2]/Sqrt[d + e*x],x]","\frac{4 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x}}{3 e}","\frac{4 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x}}{3 e}",1,"(2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(3*e) - (2*Sqrt[-b]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*Sqrt[c]*e^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (4*Sqrt[-b]*d*(c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*Sqrt[c]*e^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,23,0.3043,1,"{734, 843, 715, 112, 110, 117, 116}"
389,1,231,0,0.1563095,"\int \frac{\sqrt{b x+c x^2}}{(d+e x)^{3/2}} \, dx","Int[Sqrt[b*x + c*x^2]/(d + e*x)^(3/2),x]","-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{b x+c x^2}}{e \sqrt{d+e x}}","-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{b x+c x^2}}{e \sqrt{d+e x}}",1,"(-2*Sqrt[b*x + c*x^2])/(e*Sqrt[d + e*x]) + (4*Sqrt[-b]*Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(e^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(Sqrt[c]*e^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,23,0.3043,1,"{732, 843, 715, 112, 110, 117, 116}"
390,1,301,0,0.2803289,"\int \frac{\sqrt{b x+c x^2}}{(d+e x)^{5/2}} \, dx","Int[Sqrt[b*x + c*x^2]/(d + e*x)^(5/2),x]","\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}+\frac{2 \sqrt{b x+c x^2} (2 c d-b e)}{3 d e \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{b x+c x^2}}{3 e (d+e x)^{3/2}}","\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 e^2 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}+\frac{2 \sqrt{b x+c x^2} (2 c d-b e)}{3 d e \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{b x+c x^2}}{3 e (d+e x)^{3/2}}",1,"(-2*Sqrt[b*x + c*x^2])/(3*e*(d + e*x)^(3/2)) + (2*(2*c*d - b*e)*Sqrt[b*x + c*x^2])/(3*d*e*(c*d - b*e)*Sqrt[d + e*x]) - (2*Sqrt[-b]*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*d*e^2*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (4*Sqrt[-b]*Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*e^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{732, 834, 843, 715, 112, 110, 117, 116}"
391,1,398,0,0.4911531,"\int \frac{\sqrt{b x+c x^2}}{(d+e x)^{7/2}} \, dx","Int[Sqrt[b*x + c*x^2]/(d + e*x)^(7/2),x]","\frac{4 \sqrt{b x+c x^2} \left(b^2 e^2-b c d e+c^2 d^2\right)}{15 d^2 e \sqrt{d+e x} (c d-b e)^2}-\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^2 e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d e^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}+\frac{2 \sqrt{b x+c x^2} (2 c d-b e)}{15 d e (d+e x)^{3/2} (c d-b e)}-\frac{2 \sqrt{b x+c x^2}}{5 e (d+e x)^{5/2}}","\frac{4 \sqrt{b x+c x^2} \left(b^2 e^2-b c d e+c^2 d^2\right)}{15 d^2 e \sqrt{d+e x} (c d-b e)^2}-\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^2 e^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d e^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}+\frac{2 \sqrt{b x+c x^2} (2 c d-b e)}{15 d e (d+e x)^{3/2} (c d-b e)}-\frac{2 \sqrt{b x+c x^2}}{5 e (d+e x)^{5/2}}",1,"(-2*Sqrt[b*x + c*x^2])/(5*e*(d + e*x)^(5/2)) + (2*(2*c*d - b*e)*Sqrt[b*x + c*x^2])/(15*d*e*(c*d - b*e)*(d + e*x)^(3/2)) + (4*(c^2*d^2 - b*c*d*e + b^2*e^2)*Sqrt[b*x + c*x^2])/(15*d^2*e*(c*d - b*e)^2*Sqrt[d + e*x]) - (4*Sqrt[-b]*Sqrt[c]*(c^2*d^2 - b*c*d*e + b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*d^2*e^2*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*d*e^2*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{732, 834, 843, 715, 112, 110, 117, 116}"
392,1,521,0,0.72893,"\int (d+e x)^{3/2} \left(b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^(3/2)*(b*x + c*x^2)^(3/2),x]","\frac{2 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} \left(-6 b^2 e^2+14 c e x (2 c d-b e)+13 b c d e+c^2 d^2\right)}{231 c^2 e}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 c e x (2 c d-b e) \left(8 b^2 e^2-b c d e+c^2 d^2\right)+6 b^2 c^2 d^2 e^2-19 b^3 c d e^3+8 b^4 e^4-19 b c^3 d^3 e+8 c^4 d^4\right)}{1155 c^3 e^3}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(3 b^2 c^2 d^2 e^2+13 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{1155 c^{7/2} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{16 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (c d-2 b e) (2 c d-b e) (b e+c d) \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{1155 c^{7/2} e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 e \left(b x+c x^2\right)^{5/2} \sqrt{d+e x}}{11 c}","\frac{2 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} \left(-6 b^2 e^2+14 c e x (2 c d-b e)+13 b c d e+c^2 d^2\right)}{231 c^2 e}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 c e x (2 c d-b e) \left(8 b^2 e^2-b c d e+c^2 d^2\right)+6 b^2 c^2 d^2 e^2-19 b^3 c d e^3+8 b^4 e^4-19 b c^3 d^3 e+8 c^4 d^4\right)}{1155 c^3 e^3}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(3 b^2 c^2 d^2 e^2+13 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{1155 c^{7/2} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{16 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (c d-2 b e) (2 c d-b e) (b e+c d) \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{1155 c^{7/2} e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 e \left(b x+c x^2\right)^{5/2} \sqrt{d+e x}}{11 c}",1,"(2*Sqrt[d + e*x]*(8*c^4*d^4 - 19*b*c^3*d^3*e + 6*b^2*c^2*d^2*e^2 - 19*b^3*c*d*e^3 + 8*b^4*e^4 - 3*c*e*(2*c*d - b*e)*(c^2*d^2 - b*c*d*e + 8*b^2*e^2)*x)*Sqrt[b*x + c*x^2])/(1155*c^3*e^3) + (2*Sqrt[d + e*x]*(c^2*d^2 + 13*b*c*d*e - 6*b^2*e^2 + 14*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(231*c^2*e) + (2*e*Sqrt[d + e*x]*(b*x + c*x^2)^(5/2))/(11*c) - (16*Sqrt[-b]*(c*d - 2*b*e)*(2*c*d - b*e)*(c*d + b*e)*(c^2*d^2 - b*c*d*e + b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(1155*c^(7/2)*e^4*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*d*(c*d - b*e)*(16*c^4*d^4 - 32*b*c^3*d^3*e + 3*b^2*c^2*d^2*e^2 + 13*b^3*c*d*e^3 - 8*b^4*e^4)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(1155*c^(7/2)*e^4*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{742, 814, 843, 715, 112, 110, 117, 116}"
393,1,457,0,0.5777509,"\int \sqrt{d+e x} \left(b x+c x^2\right)^{3/2} \, dx","Int[Sqrt[d + e*x]*(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-6 c e x \left(2 b^2 e^2-b c d e+c^2 d^2\right)+3 b^2 c d e^2-4 b^3 e^3-15 b c^2 d^2 e+8 c^3 d^3\right)}{315 c^2 e^3}+\frac{8 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) \left(-b^2 e^2-2 b c d e+2 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{315 c^{5/2} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(9 b^2 c^2 d^2 e^2+7 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{315 c^{5/2} e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} (d+e x)^{3/2}}{9 e}-\frac{2 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (2 c d-b e)}{21 c e}","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-6 c e x \left(2 b^2 e^2-b c d e+c^2 d^2\right)+3 b^2 c d e^2-4 b^3 e^3-15 b c^2 d^2 e+8 c^3 d^3\right)}{315 c^2 e^3}+\frac{8 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) \left(-b^2 e^2-2 b c d e+2 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{315 c^{5/2} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(9 b^2 c^2 d^2 e^2+7 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{315 c^{5/2} e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} (d+e x)^{3/2}}{9 e}-\frac{2 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (2 c d-b e)}{21 c e}",1,"(2*Sqrt[d + e*x]*(8*c^3*d^3 - 15*b*c^2*d^2*e + 3*b^2*c*d*e^2 - 4*b^3*e^3 - 6*c*e*(c^2*d^2 - b*c*d*e + 2*b^2*e^2)*x)*Sqrt[b*x + c*x^2])/(315*c^2*e^3) - (2*(2*c*d - b*e)*Sqrt[d + e*x]*(b*x + c*x^2)^(3/2))/(21*c*e) + (2*(d + e*x)^(3/2)*(b*x + c*x^2)^(3/2))/(9*e) - (2*Sqrt[-b]*(16*c^4*d^4 - 32*b*c^3*d^3*e + 9*b^2*c^2*d^2*e^2 + 7*b^3*c*d*e^3 - 8*b^4*e^4)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(315*c^(5/2)*e^4*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (8*Sqrt[-b]*d*(c*d - b*e)*(2*c*d - b*e)*(2*c^2*d^2 - 2*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(315*c^(5/2)*e^4*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,9,23,0.3913,1,"{734, 832, 814, 843, 715, 112, 110, 117, 116}"
394,1,360,0,0.3526491,"\int \frac{\left(b x+c x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[(b*x + c*x^2)^(3/2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(b^2 e^2-3 c e x (2 c d-b e)-11 b c d e+8 c^2 d^2\right)}{35 c e^3}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 c^{3/2} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 c^{3/2} e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x}}{7 e}","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(b^2 e^2-3 c e x (2 c d-b e)-11 b c d e+8 c^2 d^2\right)}{35 c e^3}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 c^{3/2} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 c^{3/2} e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x}}{7 e}",1,"(2*Sqrt[d + e*x]*(8*c^2*d^2 - 11*b*c*d*e + b^2*e^2 - 3*c*e*(2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(35*c*e^3) + (2*Sqrt[d + e*x]*(b*x + c*x^2)^(3/2))/(7*e) - (4*Sqrt[-b]*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(35*c^(3/2)*e^4*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*d*(c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(35*c^(3/2)*e^4*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{734, 814, 843, 715, 112, 110, 117, 116}"
395,1,309,0,0.338442,"\int \frac{\left(b x+c x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/(d + e*x)^(3/2),x]","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{5 \sqrt{c} e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} (-7 b e+8 c d-6 c e x)}{5 e^3}-\frac{16 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{5 \sqrt{c} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \left(b x+c x^2\right)^{3/2}}{e \sqrt{d+e x}}","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{5 \sqrt{c} e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} (-7 b e+8 c d-6 c e x)}{5 e^3}-\frac{16 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{5 \sqrt{c} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \left(b x+c x^2\right)^{3/2}}{e \sqrt{d+e x}}",1,"(-2*Sqrt[d + e*x]*(8*c*d - 7*b*e - 6*c*e*x)*Sqrt[b*x + c*x^2])/(5*e^3) - (2*(b*x + c*x^2)^(3/2))/(e*Sqrt[d + e*x]) + (2*Sqrt[-b]*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(5*Sqrt[c]*e^4*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (16*Sqrt[-b]*d*(c*d - b*e)*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(5*Sqrt[c]*e^4*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{732, 814, 843, 715, 112, 110, 117, 116}"
396,1,298,0,0.2997294,"\int \frac{\left(b x+c x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/(d + e*x)^(5/2),x]","\frac{2 \sqrt{b x+c x^2} (-3 b e+8 c d+2 c e x)}{3 e^3 \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (4 c d-3 b e) (4 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{16 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \left(b x+c x^2\right)^{3/2}}{3 e (d+e x)^{3/2}}","\frac{2 \sqrt{b x+c x^2} (-3 b e+8 c d+2 c e x)}{3 e^3 \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (4 c d-3 b e) (4 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{16 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \left(b x+c x^2\right)^{3/2}}{3 e (d+e x)^{3/2}}",1,"(2*(8*c*d - 3*b*e + 2*c*e*x)*Sqrt[b*x + c*x^2])/(3*e^3*Sqrt[d + e*x]) - (2*(b*x + c*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) - (16*Sqrt[-b]*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*e^4*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*(4*c*d - 3*b*e)*(4*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*Sqrt[c]*e^4*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{732, 812, 843, 715, 112, 110, 117, 116}"
397,1,354,0,0.3735612,"\int \frac{\left(b x+c x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{b x+c x^2} \left(e x \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)+c d^2 (8 c d-7 b e)\right)}{5 d e^3 (d+e x)^{3/2} (c d-b e)}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{5 d e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{16 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{5 e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \left(b x+c x^2\right)^{3/2}}{5 e (d+e x)^{5/2}}","-\frac{2 \sqrt{b x+c x^2} \left(e x \left(b^2 e^2-10 b c d e+10 c^2 d^2\right)+c d^2 (8 c d-7 b e)\right)}{5 d e^3 (d+e x)^{3/2} (c d-b e)}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{5 d e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{16 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{5 e^4 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \left(b x+c x^2\right)^{3/2}}{5 e (d+e x)^{5/2}}",1,"(-2*(c*d^2*(8*c*d - 7*b*e) + e*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*x)*Sqrt[b*x + c*x^2])/(5*d*e^3*(c*d - b*e)*(d + e*x)^(3/2)) - (2*(b*x + c*x^2)^(3/2))/(5*e*(d + e*x)^(5/2)) + (2*Sqrt[-b]*Sqrt[c]*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(5*d*e^4*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (16*Sqrt[-b]*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(5*e^4*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{732, 810, 843, 715, 112, 110, 117, 116}"
398,1,476,0,0.5880779,"\int \frac{\left(b x+c x^2\right)^{3/2}}{(d+e x)^{9/2}} \, dx","Int[(b*x + c*x^2)^(3/2)/(d + e*x)^(9/2),x]","-\frac{2 \sqrt{b x+c x^2} \left(e x \left(b^2 e^2-14 b c d e+14 c^2 d^2\right)+d \left(-2 b^2 e^2-5 b c d e+8 c^2 d^2\right)\right)}{35 d e^3 (d+e x)^{5/2} (c d-b e)}+\frac{4 \sqrt{b x+c x^2} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)}{35 d^2 e^3 \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 d e^4 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}-\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 d^2 e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 \left(b x+c x^2\right)^{3/2}}{7 e (d+e x)^{7/2}}","-\frac{2 \sqrt{b x+c x^2} \left(e x \left(b^2 e^2-14 b c d e+14 c^2 d^2\right)+d \left(-2 b^2 e^2-5 b c d e+8 c^2 d^2\right)\right)}{35 d e^3 (d+e x)^{5/2} (c d-b e)}+\frac{4 \sqrt{b x+c x^2} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)}{35 d^2 e^3 \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 d e^4 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}-\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 d^2 e^4 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 \left(b x+c x^2\right)^{3/2}}{7 e (d+e x)^{7/2}}",1,"(4*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*Sqrt[b*x + c*x^2])/(35*d^2*e^3*(c*d - b*e)^2*Sqrt[d + e*x]) - (2*(d*(8*c^2*d^2 - 5*b*c*d*e - 2*b^2*e^2) + e*(14*c^2*d^2 - 14*b*c*d*e + b^2*e^2)*x)*Sqrt[b*x + c*x^2])/(35*d*e^3*(c*d - b*e)*(d + e*x)^(5/2)) - (2*(b*x + c*x^2)^(3/2))/(7*e*(d + e*x)^(7/2)) - (4*Sqrt[-b]*Sqrt[c]*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(35*d^2*e^4*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*Sqrt[c]*(16*c^2*d^2 - 16*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(35*d*e^4*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,9,23,0.3913,1,"{732, 810, 834, 843, 715, 112, 110, 117, 116}"
399,1,666,0,0.8325541,"\int \sqrt{d+e x} \left(b x+c x^2\right)^{5/2} \, dx","Int[Sqrt[d + e*x]*(b*x + c*x^2)^(5/2),x]","\frac{10 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} \left(-14 c e x \left(3 b^2 e^2-b c d e+c^2 d^2\right)+9 b^2 c d e^2-18 b^3 e^3-31 b c^2 d^2 e+16 c^3 d^3\right)}{9009 c^2 e^3}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 c e x \left(21 b^2 c^2 d^2 e^2+11 b^3 c d e^3-24 b^4 e^4-64 b c^3 d^3 e+32 c^4 d^4\right)+303 b^2 c^3 d^3 e^2-22 b^3 c^2 d^2 e^3-17 b^4 c d e^4+24 b^5 e^5-368 b c^4 d^4 e+128 c^5 d^5\right)}{9009 c^3 e^5}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) \left(79 b^2 c^2 d^2 e^2+49 b^3 c d e^3+24 b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{9009 c^{7/2} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(343 b^2 c^4 d^4 e^2-46 b^3 c^3 d^3 e^3-21 b^4 c^2 d^2 e^4-20 b^5 c d e^5+24 b^6 e^6-384 b c^5 d^5 e+128 c^6 d^6\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{9009 c^{7/2} e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{5/2} (d+e x)^{3/2}}{13 e}-\frac{10 \left(b x+c x^2\right)^{5/2} \sqrt{d+e x} (2 c d-b e)}{143 c e}","\frac{10 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} \left(-14 c e x \left(3 b^2 e^2-b c d e+c^2 d^2\right)+9 b^2 c d e^2-18 b^3 e^3-31 b c^2 d^2 e+16 c^3 d^3\right)}{9009 c^2 e^3}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 c e x \left(21 b^2 c^2 d^2 e^2+11 b^3 c d e^3-24 b^4 e^4-64 b c^3 d^3 e+32 c^4 d^4\right)+303 b^2 c^3 d^3 e^2-22 b^3 c^2 d^2 e^3-17 b^4 c d e^4+24 b^5 e^5-368 b c^4 d^4 e+128 c^5 d^5\right)}{9009 c^3 e^5}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) \left(79 b^2 c^2 d^2 e^2+49 b^3 c d e^3+24 b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{9009 c^{7/2} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(343 b^2 c^4 d^4 e^2-46 b^3 c^3 d^3 e^3-21 b^4 c^2 d^2 e^4-20 b^5 c d e^5+24 b^6 e^6-384 b c^5 d^5 e+128 c^6 d^6\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{9009 c^{7/2} e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{5/2} (d+e x)^{3/2}}{13 e}-\frac{10 \left(b x+c x^2\right)^{5/2} \sqrt{d+e x} (2 c d-b e)}{143 c e}",1,"(2*Sqrt[d + e*x]*(128*c^5*d^5 - 368*b*c^4*d^4*e + 303*b^2*c^3*d^3*e^2 - 22*b^3*c^2*d^2*e^3 - 17*b^4*c*d*e^4 + 24*b^5*e^5 - 3*c*e*(32*c^4*d^4 - 64*b*c^3*d^3*e + 21*b^2*c^2*d^2*e^2 + 11*b^3*c*d*e^3 - 24*b^4*e^4)*x)*Sqrt[b*x + c*x^2])/(9009*c^3*e^5) + (10*Sqrt[d + e*x]*(16*c^3*d^3 - 31*b*c^2*d^2*e + 9*b^2*c*d*e^2 - 18*b^3*e^3 - 14*c*e*(c^2*d^2 - b*c*d*e + 3*b^2*e^2)*x)*(b*x + c*x^2)^(3/2))/(9009*c^2*e^3) - (10*(2*c*d - b*e)*Sqrt[d + e*x]*(b*x + c*x^2)^(5/2))/(143*c*e) + (2*(d + e*x)^(3/2)*(b*x + c*x^2)^(5/2))/(13*e) - (4*Sqrt[-b]*(128*c^6*d^6 - 384*b*c^5*d^5*e + 343*b^2*c^4*d^4*e^2 - 46*b^3*c^3*d^3*e^3 - 21*b^4*c^2*d^2*e^4 - 20*b^5*c*d*e^5 + 24*b^6*e^6)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(9009*c^(7/2)*e^6*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*d*(c*d - b*e)*(2*c*d - b*e)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 79*b^2*c^2*d^2*e^2 + 49*b^3*c*d*e^3 + 24*b^4*e^4)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(9009*c^(7/2)*e^6*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",11,9,23,0.3913,1,"{734, 832, 814, 843, 715, 112, 110, 117, 116}"
400,1,537,0,0.6037321,"\int \frac{\left(b x+c x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Int[(b*x + c*x^2)^(5/2)/Sqrt[d + e*x],x]","\frac{10 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} \left(3 b^2 e^2-7 c e x (2 c d-b e)-23 b c d e+16 c^2 d^2\right)}{693 c e^3}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-12 c e x (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)+195 b^2 c^2 d^2 e^2-7 b^3 c d e^3-4 b^4 e^4-304 b c^3 d^3 e+128 c^4 d^4\right)}{693 c^2 e^5}+\frac{4 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(123 b^2 c^2 d^2 e^2+5 b^3 c d e^3+2 b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{693 c^{5/2} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(99 b^2 c^2 d^2 e^2+29 b^3 c d e^3+8 b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{693 c^{5/2} e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{5/2} \sqrt{d+e x}}{11 e}","\frac{10 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} \left(3 b^2 e^2-7 c e x (2 c d-b e)-23 b c d e+16 c^2 d^2\right)}{693 c e^3}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-12 c e x (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)+195 b^2 c^2 d^2 e^2-7 b^3 c d e^3-4 b^4 e^4-304 b c^3 d^3 e+128 c^4 d^4\right)}{693 c^2 e^5}+\frac{4 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(123 b^2 c^2 d^2 e^2+5 b^3 c d e^3+2 b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{693 c^{5/2} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(99 b^2 c^2 d^2 e^2+29 b^3 c d e^3+8 b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{693 c^{5/2} e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{5/2} \sqrt{d+e x}}{11 e}",1,"(2*Sqrt[d + e*x]*(128*c^4*d^4 - 304*b*c^3*d^3*e + 195*b^2*c^2*d^2*e^2 - 7*b^3*c*d*e^3 - 4*b^4*e^4 - 12*c*e*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*x)*Sqrt[b*x + c*x^2])/(693*c^2*e^5) + (10*Sqrt[d + e*x]*(16*c^2*d^2 - 23*b*c*d*e + 3*b^2*e^2 - 7*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(693*c*e^3) + (2*Sqrt[d + e*x]*(b*x + c*x^2)^(5/2))/(11*e) - (2*Sqrt[-b]*(2*c*d - b*e)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 99*b^2*c^2*d^2*e^2 + 29*b^3*c*d*e^3 + 8*b^4*e^4)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(693*c^(5/2)*e^6*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (4*Sqrt[-b]*d*(c*d - b*e)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 123*b^2*c^2*d^2*e^2 + 5*b^3*c*d*e^3 + 2*b^4*e^4)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(693*c^(5/2)*e^6*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{734, 814, 843, 715, 112, 110, 117, 116}"
401,1,457,0,0.5884819,"\int \frac{\left(b x+c x^2\right)^{5/2}}{(d+e x)^{3/2}} \, dx","Int[(b*x + c*x^2)^(5/2)/(d + e*x)^(3/2),x]","-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 c e x \left(b^2 e^2-32 b c d e+32 c^2 d^2\right)+111 b^2 c d e^2-b^3 e^3-240 b c^2 d^2 e+128 c^3 d^3\right)}{63 c e^5}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) \left(-b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{63 c^{3/2} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(135 b^2 c^2 d^2 e^2-7 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{63 c^{3/2} e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{10 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (-15 b e+16 c d-14 c e x)}{63 e^3}-\frac{2 \left(b x+c x^2\right)^{5/2}}{e \sqrt{d+e x}}","-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 c e x \left(b^2 e^2-32 b c d e+32 c^2 d^2\right)+111 b^2 c d e^2-b^3 e^3-240 b c^2 d^2 e+128 c^3 d^3\right)}{63 c e^5}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) \left(-b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{63 c^{3/2} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(135 b^2 c^2 d^2 e^2-7 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{63 c^{3/2} e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{10 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (-15 b e+16 c d-14 c e x)}{63 e^3}-\frac{2 \left(b x+c x^2\right)^{5/2}}{e \sqrt{d+e x}}",1,"(-2*Sqrt[d + e*x]*(128*c^3*d^3 - 240*b*c^2*d^2*e + 111*b^2*c*d*e^2 - b^3*e^3 - 3*c*e*(32*c^2*d^2 - 32*b*c*d*e + b^2*e^2)*x)*Sqrt[b*x + c*x^2])/(63*c*e^5) - (10*Sqrt[d + e*x]*(16*c*d - 15*b*e - 14*c*e*x)*(b*x + c*x^2)^(3/2))/(63*e^3) - (2*(b*x + c*x^2)^(5/2))/(e*Sqrt[d + e*x]) + (4*Sqrt[-b]*(128*c^4*d^4 - 256*b*c^3*d^3*e + 135*b^2*c^2*d^2*e^2 - 7*b^3*c*d*e^3 - b^4*e^4)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(63*c^(3/2)*e^6*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*d*(c*d - b*e)*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(63*c^(3/2)*e^6*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{732, 814, 843, 715, 112, 110, 117, 116}"
402,1,401,0,0.476616,"\int \frac{\left(b x+c x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[(b*x + c*x^2)^(5/2)/(d + e*x)^(5/2),x]","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(51 b^2 e^2-48 c e x (2 c d-b e)-176 b c d e+128 c^2 d^2\right)}{21 e^5}+\frac{4 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(27 b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{21 \sqrt{c} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(3 b^2 e^2-128 b c d e+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{21 \sqrt{c} e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{10 \left(b x+c x^2\right)^{3/2} (-7 b e+16 c d+2 c e x)}{21 e^3 \sqrt{d+e x}}-\frac{2 \left(b x+c x^2\right)^{5/2}}{3 e (d+e x)^{3/2}}","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(51 b^2 e^2-48 c e x (2 c d-b e)-176 b c d e+128 c^2 d^2\right)}{21 e^5}+\frac{4 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(27 b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{21 \sqrt{c} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(3 b^2 e^2-128 b c d e+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{21 \sqrt{c} e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{10 \left(b x+c x^2\right)^{3/2} (-7 b e+16 c d+2 c e x)}{21 e^3 \sqrt{d+e x}}-\frac{2 \left(b x+c x^2\right)^{5/2}}{3 e (d+e x)^{3/2}}",1,"(2*Sqrt[d + e*x]*(128*c^2*d^2 - 176*b*c*d*e + 51*b^2*e^2 - 48*c*e*(2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(21*e^5) + (10*(16*c*d - 7*b*e + 2*c*e*x)*(b*x + c*x^2)^(3/2))/(21*e^3*Sqrt[d + e*x]) - (2*(b*x + c*x^2)^(5/2))/(3*e*(d + e*x)^(3/2)) - (2*Sqrt[-b]*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e + 3*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(21*Sqrt[c]*e^6*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (4*Sqrt[-b]*d*(c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e + 27*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(21*Sqrt[c]*e^6*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,9,23,0.3913,1,"{732, 812, 814, 843, 715, 112, 110, 117, 116}"
403,1,392,0,0.4294928,"\int \frac{\left(b x+c x^2\right)^{5/2}}{(d+e x)^{7/2}} \, dx","Int[(b*x + c*x^2)^(5/2)/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{b x+c x^2} \left(15 b^2 e^2+16 c e x (2 c d-b e)-112 b c d e+128 c^2 d^2\right)}{15 e^5 \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) \left(15 b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 \sqrt{c} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(23 b^2 e^2-128 b c d e+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} (-5 b e+16 c d+6 c e x)}{15 e^3 (d+e x)^{3/2}}-\frac{2 \left(b x+c x^2\right)^{5/2}}{5 e (d+e x)^{5/2}}","-\frac{2 \sqrt{b x+c x^2} \left(15 b^2 e^2+16 c e x (2 c d-b e)-112 b c d e+128 c^2 d^2\right)}{15 e^5 \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) \left(15 b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 \sqrt{c} e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(23 b^2 e^2-128 b c d e+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} (-5 b e+16 c d+6 c e x)}{15 e^3 (d+e x)^{3/2}}-\frac{2 \left(b x+c x^2\right)^{5/2}}{5 e (d+e x)^{5/2}}",1,"(-2*(128*c^2*d^2 - 112*b*c*d*e + 15*b^2*e^2 + 16*c*e*(2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(15*e^5*Sqrt[d + e*x]) + (2*(16*c*d - 5*b*e + 6*c*e*x)*(b*x + c*x^2)^(3/2))/(15*e^3*(d + e*x)^(3/2)) - (2*(b*x + c*x^2)^(5/2))/(5*e*(d + e*x)^(5/2)) + (4*Sqrt[-b]*Sqrt[c]*(128*c^2*d^2 - 128*b*c*d*e + 23*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*e^6*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e + 15*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*Sqrt[c]*e^6*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{732, 812, 843, 715, 112, 110, 117, 116}"
404,1,474,0,0.5618031,"\int \frac{\left(b x+c x^2\right)^{5/2}}{(d+e x)^{9/2}} \, dx","Int[(b*x + c*x^2)^(5/2)/(d + e*x)^(9/2),x]","-\frac{2 \left(b x+c x^2\right)^{3/2} \left(e x \left(3 b^2 e^2-22 b c d e+22 c^2 d^2\right)+c d^2 (16 c d-13 b e)\right)}{21 d e^3 (d+e x)^{5/2} (c d-b e)}+\frac{2 c \sqrt{b x+c x^2} \left(e x \left(3 b^2 e^2-32 b c d e+32 c^2 d^2\right)+d \left(51 b^2 e^2-176 b c d e+128 c^2 d^2\right)\right)}{21 d e^5 \sqrt{d+e x} (c d-b e)}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(27 b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{21 e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(3 b^2 e^2-128 b c d e+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{21 d e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{2 \left(b x+c x^2\right)^{5/2}}{7 e (d+e x)^{7/2}}","-\frac{2 \left(b x+c x^2\right)^{3/2} \left(e x \left(3 b^2 e^2-22 b c d e+22 c^2 d^2\right)+c d^2 (16 c d-13 b e)\right)}{21 d e^3 (d+e x)^{5/2} (c d-b e)}+\frac{2 c \sqrt{b x+c x^2} \left(e x \left(3 b^2 e^2-32 b c d e+32 c^2 d^2\right)+d \left(51 b^2 e^2-176 b c d e+128 c^2 d^2\right)\right)}{21 d e^5 \sqrt{d+e x} (c d-b e)}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(27 b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{21 e^6 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(3 b^2 e^2-128 b c d e+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{21 d e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{2 \left(b x+c x^2\right)^{5/2}}{7 e (d+e x)^{7/2}}",1,"(2*c*(d*(128*c^2*d^2 - 176*b*c*d*e + 51*b^2*e^2) + e*(32*c^2*d^2 - 32*b*c*d*e + 3*b^2*e^2)*x)*Sqrt[b*x + c*x^2])/(21*d*e^5*(c*d - b*e)*Sqrt[d + e*x]) - (2*(c*d^2*(16*c*d - 13*b*e) + e*(22*c^2*d^2 - 22*b*c*d*e + 3*b^2*e^2)*x)*(b*x + c*x^2)^(3/2))/(21*d*e^3*(c*d - b*e)*(d + e*x)^(5/2)) - (2*(b*x + c*x^2)^(5/2))/(7*e*(d + e*x)^(7/2)) - (2*Sqrt[-b]*Sqrt[c]*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e + 3*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(21*d*e^6*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (4*Sqrt[-b]*Sqrt[c]*(128*c^2*d^2 - 128*b*c*d*e + 27*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(21*e^6*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,9,23,0.3913,1,"{732, 810, 812, 843, 715, 112, 110, 117, 116}"
405,1,570,0,0.6799174,"\int \frac{\left(b x+c x^2\right)^{5/2}}{(d+e x)^{11/2}} \, dx","Int[(b*x + c*x^2)^(5/2)/(d + e*x)^(11/2),x]","-\frac{2 \left(b x+c x^2\right)^{3/2} \left(e x \left(3 b^2 e^2-26 b c d e+26 c^2 d^2\right)+d \left(-2 b^2 e^2-11 b c d e+16 c^2 d^2\right)\right)}{63 d e^3 (d+e x)^{7/2} (c d-b e)}-\frac{2 \sqrt{b x+c x^2} \left(e x \left(171 b^2 c^2 d^2 e^2-11 b^3 c d e^3-2 b^4 e^4-320 b c^3 d^3 e+160 c^4 d^4\right)+c d^2 \left(111 b^2 c d e^2-b^3 e^3-240 b c^2 d^2 e+128 c^3 d^3\right)\right)}{63 d^2 e^5 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) \left(-b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{63 d e^6 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(135 b^2 c^2 d^2 e^2-7 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{63 d^2 e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 \left(b x+c x^2\right)^{5/2}}{9 e (d+e x)^{9/2}}","-\frac{2 \left(b x+c x^2\right)^{3/2} \left(e x \left(3 b^2 e^2-26 b c d e+26 c^2 d^2\right)+d \left(-2 b^2 e^2-11 b c d e+16 c^2 d^2\right)\right)}{63 d e^3 (d+e x)^{7/2} (c d-b e)}-\frac{2 \sqrt{b x+c x^2} \left(e x \left(171 b^2 c^2 d^2 e^2-11 b^3 c d e^3-2 b^4 e^4-320 b c^3 d^3 e+160 c^4 d^4\right)+c d^2 \left(111 b^2 c d e^2-b^3 e^3-240 b c^2 d^2 e+128 c^3 d^3\right)\right)}{63 d^2 e^5 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) \left(-b^2 e^2-128 b c d e+128 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{63 d e^6 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(135 b^2 c^2 d^2 e^2-7 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{63 d^2 e^6 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 \left(b x+c x^2\right)^{5/2}}{9 e (d+e x)^{9/2}}",1,"(-2*(c*d^2*(128*c^3*d^3 - 240*b*c^2*d^2*e + 111*b^2*c*d*e^2 - b^3*e^3) + e*(160*c^4*d^4 - 320*b*c^3*d^3*e + 171*b^2*c^2*d^2*e^2 - 11*b^3*c*d*e^3 - 2*b^4*e^4)*x)*Sqrt[b*x + c*x^2])/(63*d^2*e^5*(c*d - b*e)^2*(d + e*x)^(3/2)) - (2*(d*(16*c^2*d^2 - 11*b*c*d*e - 2*b^2*e^2) + e*(26*c^2*d^2 - 26*b*c*d*e + 3*b^2*e^2)*x)*(b*x + c*x^2)^(3/2))/(63*d*e^3*(c*d - b*e)*(d + e*x)^(7/2)) - (2*(b*x + c*x^2)^(5/2))/(9*e*(d + e*x)^(9/2)) + (4*Sqrt[-b]*Sqrt[c]*(128*c^4*d^4 - 256*b*c^3*d^3*e + 135*b^2*c^2*d^2*e^2 - 7*b^3*c*d*e^3 - b^4*e^4)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(63*d^2*e^6*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*Sqrt[c]*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(63*d*e^6*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{732, 810, 843, 715, 112, 110, 117, 116}"
406,1,379,0,0.5027281,"\int \frac{(d+e x)^{7/2}}{\sqrt{b x+c x^2}} \, dx","Int[(d + e*x)^(7/2)/Sqrt[b*x + c*x^2],x]","\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(24 b^2 e^2-71 b c d e+71 c^2 d^2\right)}{105 c^3}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(24 b^2 e^2-71 b c d e+71 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{7/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{16 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(6 b^2 e^2-11 b c d e+11 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{7/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{12 e \sqrt{b x+c x^2} (d+e x)^{3/2} (2 c d-b e)}{35 c^2}+\frac{2 e \sqrt{b x+c x^2} (d+e x)^{5/2}}{7 c}","\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(24 b^2 e^2-71 b c d e+71 c^2 d^2\right)}{105 c^3}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(24 b^2 e^2-71 b c d e+71 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{7/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{16 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(6 b^2 e^2-11 b c d e+11 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{7/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{12 e \sqrt{b x+c x^2} (d+e x)^{3/2} (2 c d-b e)}{35 c^2}+\frac{2 e \sqrt{b x+c x^2} (d+e x)^{5/2}}{7 c}",1,"(2*e*(71*c^2*d^2 - 71*b*c*d*e + 24*b^2*e^2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(105*c^3) + (12*e*(2*c*d - b*e)*(d + e*x)^(3/2)*Sqrt[b*x + c*x^2])/(35*c^2) + (2*e*(d + e*x)^(5/2)*Sqrt[b*x + c*x^2])/(7*c) + (16*Sqrt[-b]*(2*c*d - b*e)*(11*c^2*d^2 - 11*b*c*d*e + 6*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(105*c^(7/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*d*(c*d - b*e)*(71*c^2*d^2 - 71*b*c*d*e + 24*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(105*c^(7/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{742, 832, 843, 715, 112, 110, 117, 116}"
407,1,303,0,0.3300661,"\int \frac{(d+e x)^{5/2}}{\sqrt{b x+c x^2}} \, dx","Int[(d + e*x)^(5/2)/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{8 e \sqrt{b x+c x^2} \sqrt{d+e x} (2 c d-b e)}{15 c^2}-\frac{8 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 e \sqrt{b x+c x^2} (d+e x)^{3/2}}{5 c}","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{8 e \sqrt{b x+c x^2} \sqrt{d+e x} (2 c d-b e)}{15 c^2}-\frac{8 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 e \sqrt{b x+c x^2} (d+e x)^{3/2}}{5 c}",1,"(8*e*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(15*c^2) + (2*e*(d + e*x)^(3/2)*Sqrt[b*x + c*x^2])/(5*c) + (2*Sqrt[-b]*(23*c^2*d^2 - 23*b*c*d*e + 8*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*c^(5/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (8*Sqrt[-b]*d*(c*d - b*e)*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*c^(5/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{742, 832, 843, 715, 112, 110, 117, 116}"
408,1,241,0,0.1917161,"\int \frac{(d+e x)^{3/2}}{\sqrt{b x+c x^2}} \, dx","Int[(d + e*x)^(3/2)/Sqrt[b*x + c*x^2],x]","-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x}}{3 c}","-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x}}{3 c}",1,"(2*e*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(3*c) + (4*Sqrt[-b]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*c^(3/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*d*(c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*c^(3/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,23,0.3043,1,"{742, 843, 715, 112, 110, 117, 116}"
409,1,94,0,0.0374351,"\int \frac{\sqrt{d+e x}}{\sqrt{b x+c x^2}} \, dx","Int[Sqrt[d + e*x]/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}",1,"(2*Sqrt[-b]*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(Sqrt[c]*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2])","A",3,3,23,0.1304,1,"{715, 112, 110}"
410,1,94,0,0.0404162,"\int \frac{1}{\sqrt{d+e x} \sqrt{b x+c x^2}} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[b*x + c*x^2]),x]","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}",1,"(2*Sqrt[-b]*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(Sqrt[c]*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",3,3,23,0.1304,1,"{715, 117, 116}"
411,1,146,0,0.0806936,"\int \frac{1}{(d+e x)^{3/2} \sqrt{b x+c x^2}} \, dx","Int[1/((d + e*x)^(3/2)*Sqrt[b*x + c*x^2]),x]","\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{2 e \sqrt{b x+c x^2}}{d \sqrt{d+e x} (c d-b e)}","\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{2 e \sqrt{b x+c x^2}}{d \sqrt{d+e x} (c d-b e)}",1,"(-2*e*Sqrt[b*x + c*x^2])/(d*(c*d - b*e)*Sqrt[d + e*x]) + (2*Sqrt[-b]*Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(d*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2])","A",5,5,23,0.2174,1,"{744, 21, 715, 112, 110}"
412,1,317,0,0.2877646,"\int \frac{1}{(d+e x)^{5/2} \sqrt{b x+c x^2}} \, dx","Int[1/((d + e*x)^(5/2)*Sqrt[b*x + c*x^2]),x]","-\frac{4 e \sqrt{b x+c x^2} (2 c d-b e)}{3 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 e \sqrt{b x+c x^2}}{3 d (d+e x)^{3/2} (c d-b e)}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}","-\frac{4 e \sqrt{b x+c x^2} (2 c d-b e)}{3 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{4 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 e \sqrt{b x+c x^2}}{3 d (d+e x)^{3/2} (c d-b e)}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}",1,"(-2*e*Sqrt[b*x + c*x^2])/(3*d*(c*d - b*e)*(d + e*x)^(3/2)) - (4*e*(2*c*d - b*e)*Sqrt[b*x + c*x^2])/(3*d^2*(c*d - b*e)^2*Sqrt[d + e*x]) + (4*Sqrt[-b]*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*d^2*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*d*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{744, 834, 843, 715, 112, 110, 117, 116}"
413,1,403,0,0.4651878,"\int \frac{1}{(d+e x)^{7/2} \sqrt{b x+c x^2}} \, dx","Int[1/((d + e*x)^(7/2)*Sqrt[b*x + c*x^2]),x]","-\frac{2 e \sqrt{b x+c x^2} \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)}{15 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{8 e \sqrt{b x+c x^2} (2 c d-b e)}{15 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{8 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}-\frac{2 e \sqrt{b x+c x^2}}{5 d (d+e x)^{5/2} (c d-b e)}","-\frac{2 e \sqrt{b x+c x^2} \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)}{15 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{8 e \sqrt{b x+c x^2} (2 c d-b e)}{15 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{8 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}-\frac{2 e \sqrt{b x+c x^2}}{5 d (d+e x)^{5/2} (c d-b e)}",1,"(-2*e*Sqrt[b*x + c*x^2])/(5*d*(c*d - b*e)*(d + e*x)^(5/2)) - (8*e*(2*c*d - b*e)*Sqrt[b*x + c*x^2])/(15*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) - (2*e*(23*c^2*d^2 - 23*b*c*d*e + 8*b^2*e^2)*Sqrt[b*x + c*x^2])/(15*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) + (2*Sqrt[-b]*Sqrt[c]*(23*c^2*d^2 - 23*b*c*d*e + 8*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*d^3*(c*d - b*e)^3*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (8*Sqrt[-b]*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*d^2*(c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{744, 834, 843, 715, 112, 110, 117, 116}"
414,1,395,0,0.5139446,"\int \frac{(d+e x)^{7/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(7/2)/(b*x + c*x^2)^(3/2),x]","\frac{4 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right)}{3 b^2 c^2}-\frac{4 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(8 b^2 e^2-3 b c d e+3 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{5/2} (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}+\frac{2 e \sqrt{b x+c x^2} (d+e x)^{3/2} (2 c d-b e)}{b^2 c}","\frac{4 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right)}{3 b^2 c^2}-\frac{4 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(8 b^2 e^2-3 b c d e+3 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{5/2} (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}+\frac{2 e \sqrt{b x+c x^2} (d+e x)^{3/2} (2 c d-b e)}{b^2 c}",1,"(-2*(d + e*x)^(5/2)*(b*d + (2*c*d - b*e)*x))/(b^2*Sqrt[b*x + c*x^2]) + (4*e*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(3*b^2*c^2) + (2*e*(2*c*d - b*e)*(d + e*x)^(3/2)*Sqrt[b*x + c*x^2])/(b^2*c) + (2*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 8*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(3/2)*c^(5/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (4*d*(c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(3/2)*c^(5/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{738, 832, 843, 715, 112, 110, 117, 116}"
415,1,310,0,0.3390398,"\int \frac{(d+e x)^{5/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(5/2)/(b*x + c*x^2)^(3/2),x]","\frac{4 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{3/2} (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}+\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x} (2 c d-b e)}{b^2 c}-\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}","\frac{4 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{3/2} (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}+\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x} (2 c d-b e)}{b^2 c}-\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}",1,"(-2*(d + e*x)^(3/2)*(b*d + (2*c*d - b*e)*x))/(b^2*Sqrt[b*x + c*x^2]) + (2*e*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(b^2*c) + (4*(c^2*d^2 - b*c*d*e + b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*c^(3/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*d*(c*d - b*e)*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*c^(3/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{738, 832, 843, 715, 112, 110, 117, 116}"
416,1,249,0,0.1906744,"\int \frac{(d+e x)^{3/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/(b*x + c*x^2)^(3/2),x]","-\frac{2 \sqrt{d+e x} (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}-\frac{4 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}","-\frac{2 \sqrt{d+e x} (x (2 c d-b e)+b d)}{b^2 \sqrt{b x+c x^2}}-\frac{4 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}",1,"(-2*Sqrt[d + e*x]*(b*d + (2*c*d - b*e)*x))/(b^2*Sqrt[b*x + c*x^2]) + (2*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*Sqrt[c]*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (4*d*(c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*Sqrt[c]*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,23,0.3043,1,"{738, 843, 715, 112, 110, 117, 116}"
417,1,231,0,0.1540944,"\int \frac{\sqrt{d+e x}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[Sqrt[d + e*x]/(b*x + c*x^2)^(3/2),x]","-\frac{2 (b+2 c x) \sqrt{d+e x}}{b^2 \sqrt{b x+c x^2}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}","-\frac{2 (b+2 c x) \sqrt{d+e x}}{b^2 \sqrt{b x+c x^2}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}",1,"(-2*(b + 2*c*x)*Sqrt[d + e*x])/(b^2*Sqrt[b*x + c*x^2]) + (4*Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*Sqrt[c]*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,23,0.3043,1,"{736, 843, 715, 112, 110, 117, 116}"
418,1,274,0,0.2194326,"\int \frac{1}{\sqrt{d+e x} \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[d + e*x]*(b*x + c*x^2)^(3/2)),x]","-\frac{2 \sqrt{d+e x} (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (c d-b e)}-\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}","-\frac{2 \sqrt{d+e x} (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (c d-b e)}-\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}",1,"(-2*Sqrt[d + e*x]*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*Sqrt[b*x + c*x^2]) + (2*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*d*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (4*Sqrt[c]*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,23,0.3043,1,"{740, 843, 715, 112, 110, 117, 116}"
419,1,370,0,0.3871768,"\int \frac{1}{(d+e x)^{3/2} \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(3/2)*(b*x + c*x^2)^(3/2)),x]","-\frac{4 e \sqrt{b x+c x^2} \left(b^2 e^2-b c d e+c^2 d^2\right)}{b^2 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}","-\frac{4 e \sqrt{b x+c x^2} \left(b^2 e^2-b c d e+c^2 d^2\right)}{b^2 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-b c d e+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}",1,"(-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2]) - (4*e*(c^2*d^2 - b*c*d*e + b^2*e^2)*Sqrt[b*x + c*x^2])/(b^2*d^2*(c*d - b*e)^2*Sqrt[d + e*x]) + (4*Sqrt[c]*(c^2*d^2 - b*c*d*e + b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*d^2*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*d*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{740, 834, 843, 715, 112, 110, 117, 116}"
420,1,478,0,0.5880899,"\int \frac{1}{(d+e x)^{5/2} \left(b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(5/2)*(b*x + c*x^2)^(3/2)),x]","-\frac{4 e \sqrt{b x+c x^2} \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right)}{3 b^2 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 e \sqrt{b x+c x^2} (2 c d-b e) \left(8 b^2 e^2-3 b c d e+3 c^2 d^2\right)}{3 b^2 d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(8 b^2 e^2-3 b c d e+3 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x)^{3/2} (c d-b e)}","-\frac{4 e \sqrt{b x+c x^2} \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right)}{3 b^2 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 e \sqrt{b x+c x^2} (2 c d-b e) \left(8 b^2 e^2-3 b c d e+3 c^2 d^2\right)}{3 b^2 d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(2 b^2 e^2-3 b c d e+3 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(8 b^2 e^2-3 b c d e+3 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x)^{3/2} (c d-b e)}",1,"(-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(d + e*x)^(3/2)*Sqrt[b*x + c*x^2]) - (4*e*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*Sqrt[b*x + c*x^2])/(3*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) - (2*e*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 8*b^2*e^2)*Sqrt[b*x + c*x^2])/(3*b^2*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) + (2*Sqrt[c]*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 8*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(3/2)*d^3*(c*d - b*e)^3*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (4*Sqrt[c]*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(3/2)*d^2*(c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,23,0.3478,1,"{740, 834, 843, 715, 112, 110, 117, 116}"
421,1,470,0,0.5899895,"\int \frac{(d+e x)^{9/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(9/2)/(b*x + c*x^2)^(5/2),x]","\frac{2 (d+e x)^{3/2} \left(x (2 c d-b e) \left(-3 b^2 e^2-8 b c d e+8 c^2 d^2\right)+b c d^2 (8 c d-11 b e)\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{8 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)}{3 b^4 c^2}+\frac{8 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) \left(-b^2 e^2-2 b c d e+2 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(9 b^2 c^2 d^2 e^2+7 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{7/2} (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}","\frac{2 (d+e x)^{3/2} \left(x (2 c d-b e) \left(-3 b^2 e^2-8 b c d e+8 c^2 d^2\right)+b c d^2 (8 c d-11 b e)\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{8 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)}{3 b^4 c^2}+\frac{8 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) \left(-b^2 e^2-2 b c d e+2 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(9 b^2 c^2 d^2 e^2+7 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{7/2} (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(7/2)*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (2*(d + e*x)^(3/2)*(b*c*d^2*(8*c*d - 11*b*e) + (2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - 3*b^2*e^2)*x))/(3*b^4*c*Sqrt[b*x + c*x^2]) - (8*e*(4*c^3*d^3 - 6*b*c^2*d^2*e + b^3*e^3)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(3*b^4*c^2) - (2*(16*c^4*d^4 - 32*b*c^3*d^3*e + 9*b^2*c^2*d^2*e^2 + 7*b^3*c*d*e^3 - 8*b^4*e^4)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*c^(5/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (8*d*(c*d - b*e)*(2*c*d - b*e)*(2*c^2*d^2 - 2*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*c^(5/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,9,23,0.3913,1,"{738, 818, 832, 843, 715, 112, 110, 117, 116}"
422,1,383,0,0.3915543,"\int \frac{(d+e x)^{7/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(7/2)/(b*x + c*x^2)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(x (2 c d-b e) \left(-b^2 e^2-8 b c d e+8 c^2 d^2\right)+b c d^2 (8 c d-9 b e)\right)}{3 b^4 c \sqrt{b x+c x^2}}+\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{5/2} (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}","\frac{2 \sqrt{d+e x} \left(x (2 c d-b e) \left(-b^2 e^2-8 b c d e+8 c^2 d^2\right)+b c d^2 (8 c d-9 b e)\right)}{3 b^4 c \sqrt{b x+c x^2}}+\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{5/2} (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(5/2)*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(b*c*d^2*(8*c*d - 9*b*e) + (2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - b^2*e^2)*x))/(3*b^4*c*Sqrt[b*x + c*x^2]) - (4*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*c^(3/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*d*(c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*c^(3/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{738, 818, 843, 715, 112, 110, 117, 116}"
423,1,343,0,0.3562763,"\int \frac{(d+e x)^{5/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/(b*x + c*x^2)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(x \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)+b d (8 c d-7 b e)\right)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{3/2} (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{16 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \left(x \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)+b d (8 c d-7 b e)\right)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{3/2} (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{16 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}",1,"(-2*(d + e*x)^(3/2)*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(b*d*(8*c*d - 7*b*e) + (16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*x))/(3*b^4*Sqrt[b*x + c*x^2]) - (2*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*Sqrt[c]*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (16*d*(c*d - b*e)*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*Sqrt[c]*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{738, 820, 843, 715, 112, 110, 117, 116}"
424,1,344,0,0.4161953,"\int \frac{(d+e x)^{3/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(3/2)/(b*x + c*x^2)^(5/2),x]","-\frac{2 \sqrt{d+e x} (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{2 \sqrt{d+e x} (8 c x (2 c d-b e) (c d-b e)+b (8 c d-5 b e) (c d-b e))}{3 b^4 \sqrt{b x+c x^2} (c d-b e)}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (4 c d-3 b e) (4 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{16 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}","-\frac{2 \sqrt{d+e x} (x (2 c d-b e)+b d)}{3 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{2 \sqrt{d+e x} (8 c x (2 c d-b e) (c d-b e)+b (8 c d-5 b e) (c d-b e))}{3 b^4 \sqrt{b x+c x^2} (c d-b e)}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (4 c d-3 b e) (4 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{16 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}",1,"(-2*Sqrt[d + e*x]*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(b*(8*c*d - 5*b*e)*(c*d - b*e) + 8*c*(c*d - b*e)*(2*c*d - b*e)*x))/(3*b^4*(c*d - b*e)*Sqrt[b*x + c*x^2]) - (16*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*(4*c*d - 3*b*e)*(4*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*Sqrt[c]*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{738, 822, 843, 715, 112, 110, 117, 116}"
425,1,359,0,0.3982419,"\int \frac{\sqrt{d+e x}}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[Sqrt[d + e*x]/(b*x + c*x^2)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(c x \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)+b (c d-b e) (8 c d-b e)\right)}{3 b^4 d \sqrt{b x+c x^2} (c d-b e)}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{2 (b+2 c x) \sqrt{d+e x}}{3 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{16 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{b x+c x^2} \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \left(c x \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)+b (c d-b e) (8 c d-b e)\right)}{3 b^4 d \sqrt{b x+c x^2} (c d-b e)}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e^2-16 b c d e+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{2 (b+2 c x) \sqrt{d+e x}}{3 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{16 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{b x+c x^2} \sqrt{d+e x}}",1,"(-2*(b + 2*c*x)*Sqrt[d + e*x])/(3*b^2*(b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(b*(c*d - b*e)*(8*c*d - b*e) + c*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*x))/(3*b^4*d*(c*d - b*e)*Sqrt[b*x + c*x^2]) - (2*Sqrt[c]*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (16*Sqrt[c]*(2*c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{736, 822, 843, 715, 112, 110, 117, 116}"
426,1,451,0,0.4328246,"\int \frac{1}{\sqrt{d+e x} \left(b x+c x^2\right)^{5/2}} \, dx","Int[1/(Sqrt[d + e*x]*(b*x + c*x^2)^(5/2)),x]","\frac{2 \sqrt{d+e x} \left(2 c x (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)+b (c d-b e) \left(-2 b^2 e^2-5 b c d e+8 c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}-\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 \sqrt{d+e x} (c x (2 c d-b e)+b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (c d-b e)}","\frac{2 \sqrt{d+e x} \left(2 c x (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right)+b (c d-b e) \left(-2 b^2 e^2-5 b c d e+8 c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}-\frac{4 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 c d-b e) \left(-b^2 e^2-4 b c d e+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 \sqrt{d+e x} (c x (2 c d-b e)+b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (c d-b e)}",1,"(-2*Sqrt[d + e*x]*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(3*b^2*d*(c*d - b*e)*(b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(b*(c*d - b*e)*(8*c^2*d^2 - 5*b*c*d*e - 2*b^2*e^2) + 2*c*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*x))/(3*b^4*d^2*(c*d - b*e)^2*Sqrt[b*x + c*x^2]) - (4*Sqrt[c]*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d^2*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[c]*(16*c^2*d^2 - 16*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,23,0.3478,1,"{740, 822, 843, 715, 112, 110, 117, 116}"
427,1,567,0,0.6451482,"\int \frac{1}{(d+e x)^{3/2} \left(b x+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^(3/2)*(b*x + c*x^2)^(5/2)),x]","\frac{2 e \sqrt{b x+c x^2} \left(9 b^2 c^2 d^2 e^2+7 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right)}{3 b^4 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 \left(4 c x \left(b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)+b (c d-b e) \left(-4 b^2 e^2-3 b c d e+8 c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}+\frac{8 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) \left(-b^2 e^2-2 b c d e+2 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(9 b^2 c^2 d^2 e^2+7 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (c d-b e)}","\frac{2 e \sqrt{b x+c x^2} \left(9 b^2 c^2 d^2 e^2+7 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right)}{3 b^4 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 \left(4 c x \left(b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)+b (c d-b e) \left(-4 b^2 e^2-3 b c d e+8 c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}+\frac{8 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (2 c d-b e) \left(-b^2 e^2-2 b c d e+2 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(9 b^2 c^2 d^2 e^2+7 b^3 c d e^3-8 b^4 e^4-32 b c^3 d^3 e+16 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 (c x (2 c d-b e)+b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (c d-b e)}",1,"(-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(3*b^2*d*(c*d - b*e)*Sqrt[d + e*x]*(b*x + c*x^2)^(3/2)) + (2*(b*(c*d - b*e)*(8*c^2*d^2 - 3*b*c*d*e - 4*b^2*e^2) + 4*c*(4*c^3*d^3 - 6*b*c^2*d^2*e + b^3*e^3)*x))/(3*b^4*d^2*(c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2]) + (2*e*(16*c^4*d^4 - 32*b*c^3*d^3*e + 9*b^2*c^2*d^2*e^2 + 7*b^3*c*d*e^3 - 8*b^4*e^4)*Sqrt[b*x + c*x^2])/(3*b^4*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) - (2*Sqrt[c]*(16*c^4*d^4 - 32*b*c^3*d^3*e + 9*b^2*c^2*d^2*e^2 + 7*b^3*c*d*e^3 - 8*b^4*e^4)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d^3*(c*d - b*e)^3*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (8*Sqrt[c]*(2*c*d - b*e)*(2*c^2*d^2 - 2*b*c*d*e - b^2*e^2)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d^2*(c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,9,23,0.3913,1,"{740, 822, 834, 843, 715, 112, 110, 117, 116}"
428,1,51,0,0.0261794,"\int \frac{\sqrt{d+e x}}{\sqrt{2 x-3 x^2}} \, dx","Int[Sqrt[d + e*x]/Sqrt[2*x - 3*x^2],x]","\frac{2 \sqrt{d+e x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{x}\right)|-\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{\frac{e x}{d}+1}}","\frac{2 \sqrt{d+e x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{x}\right)|-\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{\frac{e x}{d}+1}}",1,"(2*Sqrt[d + e*x]*EllipticE[ArcSin[Sqrt[3/2]*Sqrt[x]], (-2*e)/(3*d)])/(Sqrt[3]*Sqrt[1 + (e*x)/d])","A",4,4,23,0.1739,1,"{714, 12, 112, 110}"
429,1,51,0,0.0253953,"\int \frac{1}{\sqrt{d+e x} \sqrt{2 x-3 x^2}} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[2*x - 3*x^2]),x]","\frac{2 \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{x}\right)|-\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{d+e x}}","\frac{2 \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{x}\right)|-\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{d+e x}}",1,"(2*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[Sqrt[3/2]*Sqrt[x]], (-2*e)/(3*d)])/(Sqrt[3]*Sqrt[d + e*x])","A",4,4,23,0.1739,1,"{714, 12, 117, 115}"
430,1,53,0,0.0259557,"\int \frac{\sqrt{d+e x}}{\sqrt{-2 x-3 x^2}} \, dx","Int[Sqrt[d + e*x]/Sqrt[-2*x - 3*x^2],x]","-\frac{2 \sqrt{d+e x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{-x}\right)|\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{\frac{e x}{d}+1}}","-\frac{2 \sqrt{d+e x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{-x}\right)|\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{\frac{e x}{d}+1}}",1,"(-2*Sqrt[d + e*x]*EllipticE[ArcSin[Sqrt[3/2]*Sqrt[-x]], (2*e)/(3*d)])/(Sqrt[3]*Sqrt[1 + (e*x)/d])","A",4,4,23,0.1739,1,"{714, 12, 112, 110}"
431,1,53,0,0.026315,"\int \frac{1}{\sqrt{d+e x} \sqrt{-2 x-3 x^2}} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[-2*x - 3*x^2]),x]","-\frac{2 \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{-x}\right)|\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{d+e x}}","-\frac{2 \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} \sqrt{-x}\right)|\frac{2 e}{3 d}\right)}{\sqrt{3} \sqrt{d+e x}}",1,"(-2*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[Sqrt[3/2]*Sqrt[-x]], (2*e)/(3*d)])/(Sqrt[3]*Sqrt[d + e*x])","A",4,4,23,0.1739,1,"{714, 12, 117, 115}"
432,1,12,0,0.0040121,"\int \frac{\sqrt{1-x}}{\sqrt{-x} \sqrt{1+x}} \, dx","Int[Sqrt[1 - x]/(Sqrt[-x]*Sqrt[1 + x]),x]","-2 E\left(\left.\sin ^{-1}\left(\sqrt{-x}\right)\right|-1\right)","-2 E\left(\left.\sin ^{-1}\left(\sqrt{-x}\right)\right|-1\right)",1,"-2*EllipticE[ArcSin[Sqrt[-x]], -1]","A",1,1,24,0.04167,1,"{110}"
433,1,12,0,0.0104788,"\int \frac{\sqrt{1-x}}{\sqrt{-x-x^2}} \, dx","Int[Sqrt[1 - x]/Sqrt[-x - x^2],x]","-2 E\left(\left.\sin ^{-1}\left(\sqrt{-x}\right)\right|-1\right)","-2 E\left(\left.\sin ^{-1}\left(\sqrt{-x}\right)\right|-1\right)",1,"-2*EllipticE[ArcSin[Sqrt[-x]], -1]","A",2,2,23,0.08696,1,"{714, 110}"
434,1,95,0,0.0735214,"\int (d+e x)^m \left(c d x+c e x^2\right)^3 \, dx","Int[(d + e*x)^m*(c*d*x + c*e*x^2)^3,x]","-\frac{c^3 d^3 (d+e x)^{m+4}}{e^4 (m+4)}+\frac{3 c^3 d^2 (d+e x)^{m+5}}{e^4 (m+5)}-\frac{3 c^3 d (d+e x)^{m+6}}{e^4 (m+6)}+\frac{c^3 (d+e x)^{m+7}}{e^4 (m+7)}","-\frac{c^3 d^3 (d+e x)^{m+4}}{e^4 (m+4)}+\frac{3 c^3 d^2 (d+e x)^{m+5}}{e^4 (m+5)}-\frac{3 c^3 d (d+e x)^{m+6}}{e^4 (m+6)}+\frac{c^3 (d+e x)^{m+7}}{e^4 (m+7)}",1,"-((c^3*d^3*(d + e*x)^(4 + m))/(e^4*(4 + m))) + (3*c^3*d^2*(d + e*x)^(5 + m))/(e^4*(5 + m)) - (3*c^3*d*(d + e*x)^(6 + m))/(e^4*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^4*(7 + m))","A",4,3,21,0.1429,1,"{626, 12, 43}"
435,1,69,0,0.0435253,"\int (d+e x)^m \left(c d x+c e x^2\right)^2 \, dx","Int[(d + e*x)^m*(c*d*x + c*e*x^2)^2,x]","\frac{c^2 d^2 (d+e x)^{m+3}}{e^3 (m+3)}-\frac{2 c^2 d (d+e x)^{m+4}}{e^3 (m+4)}+\frac{c^2 (d+e x)^{m+5}}{e^3 (m+5)}","\frac{c^2 d^2 (d+e x)^{m+3}}{e^3 (m+3)}-\frac{2 c^2 d (d+e x)^{m+4}}{e^3 (m+4)}+\frac{c^2 (d+e x)^{m+5}}{e^3 (m+5)}",1,"(c^2*d^2*(d + e*x)^(3 + m))/(e^3*(3 + m)) - (2*c^2*d*(d + e*x)^(4 + m))/(e^3*(4 + m)) + (c^2*(d + e*x)^(5 + m))/(e^3*(5 + m))","A",4,3,21,0.1429,1,"{626, 12, 43}"
436,1,41,0,0.0221012,"\int (d+e x)^m \left(c d x+c e x^2\right) \, dx","Int[(d + e*x)^m*(c*d*x + c*e*x^2),x]","\frac{c (d+e x)^{m+3}}{e^2 (m+3)}-\frac{c d (d+e x)^{m+2}}{e^2 (m+2)}","\frac{c (d+e x)^{m+3}}{e^2 (m+3)}-\frac{c d (d+e x)^{m+2}}{e^2 (m+2)}",1,"-((c*d*(d + e*x)^(2 + m))/(e^2*(2 + m))) + (c*(d + e*x)^(3 + m))/(e^2*(3 + m))","A",4,3,19,0.1579,1,"{626, 12, 43}"
437,1,18,0,0.0031172,"\int (d+e x)^m \, dx","Int[(d + e*x)^m,x]","\frac{(d+e x)^{m+1}}{e (m+1)}","\frac{(d+e x)^{m+1}}{e (m+1)}",1,"(d + e*x)^(1 + m)/(e*(1 + m))","A",1,1,7,0.1429,1,"{32}"
438,1,32,0,0.0151232,"\int \frac{(d+e x)^m}{c d x+c e x^2} \, dx","Int[(d + e*x)^m/(c*d*x + c*e*x^2),x]","-\frac{(d+e x)^m \, _2F_1\left(1,m;m+1;\frac{e x}{d}+1\right)}{c d m}","-\frac{(d+e x)^m \, _2F_1\left(1,m;m+1;\frac{e x}{d}+1\right)}{c d m}",1,"-(((d + e*x)^m*Hypergeometric2F1[1, m, 1 + m, 1 + (e*x)/d])/(c*d*m))","A",3,3,21,0.1429,1,"{626, 12, 65}"
439,1,39,0,0.02125,"\int \frac{(d+e x)^m}{\left(c d x+c e x^2\right)^2} \, dx","Int[(d + e*x)^m/(c*d*x + c*e*x^2)^2,x]","-\frac{e (d+e x)^{m-1} \, _2F_1\left(2,m-1;m;\frac{e x}{d}+1\right)}{c^2 d^2 (1-m)}","-\frac{e (d+e x)^{m-1} \, _2F_1\left(2,m-1;m;\frac{e x}{d}+1\right)}{c^2 d^2 (1-m)}",1,"-((e*(d + e*x)^(-1 + m)*Hypergeometric2F1[2, -1 + m, m, 1 + (e*x)/d])/(c^2*d^2*(1 - m)))","A",3,3,21,0.1429,1,"{626, 12, 65}"
440,1,267,0,0.1654428,"\int (d+e x)^m \left(b x+c x^2\right)^3 \, dx","Int[(d + e*x)^m*(b*x + c*x^2)^3,x]","\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) (d+e x)^{m+3}}{e^7 (m+3)}-\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right) (d+e x)^{m+4}}{e^7 (m+4)}+\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) (d+e x)^{m+5}}{e^7 (m+5)}-\frac{3 c^2 (2 c d-b e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{d^3 (c d-b e)^3 (d+e x)^{m+1}}{e^7 (m+1)}-\frac{3 d^2 (c d-b e)^2 (2 c d-b e) (d+e x)^{m+2}}{e^7 (m+2)}+\frac{c^3 (d+e x)^{m+7}}{e^7 (m+7)}","\frac{3 d (c d-b e) \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) (d+e x)^{m+3}}{e^7 (m+3)}-\frac{(2 c d-b e) \left(b^2 e^2-10 b c d e+10 c^2 d^2\right) (d+e x)^{m+4}}{e^7 (m+4)}+\frac{3 c \left(b^2 e^2-5 b c d e+5 c^2 d^2\right) (d+e x)^{m+5}}{e^7 (m+5)}-\frac{3 c^2 (2 c d-b e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{d^3 (c d-b e)^3 (d+e x)^{m+1}}{e^7 (m+1)}-\frac{3 d^2 (c d-b e)^2 (2 c d-b e) (d+e x)^{m+2}}{e^7 (m+2)}+\frac{c^3 (d+e x)^{m+7}}{e^7 (m+7)}",1,"(d^3*(c*d - b*e)^3*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (3*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(3 + m))/(e^7*(3 + m)) - ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (3*c^2*(2*c*d - b*e)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^7*(7 + m))","A",2,1,19,0.05263,1,"{698}"
441,1,159,0,0.0825785,"\int (d+e x)^m \left(b x+c x^2\right)^2 \, dx","Int[(d + e*x)^m*(b*x + c*x^2)^2,x]","\frac{\left(b^2 e^2-6 b c d e+6 c^2 d^2\right) (d+e x)^{m+3}}{e^5 (m+3)}+\frac{d^2 (c d-b e)^2 (d+e x)^{m+1}}{e^5 (m+1)}-\frac{2 d (c d-b e) (2 c d-b e) (d+e x)^{m+2}}{e^5 (m+2)}-\frac{2 c (2 c d-b e) (d+e x)^{m+4}}{e^5 (m+4)}+\frac{c^2 (d+e x)^{m+5}}{e^5 (m+5)}","\frac{\left(b^2 e^2-6 b c d e+6 c^2 d^2\right) (d+e x)^{m+3}}{e^5 (m+3)}+\frac{d^2 (c d-b e)^2 (d+e x)^{m+1}}{e^5 (m+1)}-\frac{2 d (c d-b e) (2 c d-b e) (d+e x)^{m+2}}{e^5 (m+2)}-\frac{2 c (2 c d-b e) (d+e x)^{m+4}}{e^5 (m+4)}+\frac{c^2 (d+e x)^{m+5}}{e^5 (m+5)}",1,"(d^2*(c*d - b*e)^2*(d + e*x)^(1 + m))/(e^5*(1 + m)) - (2*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(2 + m))/(e^5*(2 + m)) + ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(3 + m))/(e^5*(3 + m)) - (2*c*(2*c*d - b*e)*(d + e*x)^(4 + m))/(e^5*(4 + m)) + (c^2*(d + e*x)^(5 + m))/(e^5*(5 + m))","A",2,1,19,0.05263,1,"{698}"
442,1,75,0,0.0356838,"\int (d+e x)^m \left(b x+c x^2\right) \, dx","Int[(d + e*x)^m*(b*x + c*x^2),x]","\frac{d (c d-b e) (d+e x)^{m+1}}{e^3 (m+1)}-\frac{(2 c d-b e) (d+e x)^{m+2}}{e^3 (m+2)}+\frac{c (d+e x)^{m+3}}{e^3 (m+3)}","\frac{d (c d-b e) (d+e x)^{m+1}}{e^3 (m+1)}-\frac{(2 c d-b e) (d+e x)^{m+2}}{e^3 (m+2)}+\frac{c (d+e x)^{m+3}}{e^3 (m+3)}",1,"(d*(c*d - b*e)*(d + e*x)^(1 + m))/(e^3*(1 + m)) - ((2*c*d - b*e)*(d + e*x)^(2 + m))/(e^3*(2 + m)) + (c*(d + e*x)^(3 + m))/(e^3*(3 + m))","A",2,1,17,0.05882,1,"{698}"
443,1,93,0,0.0644153,"\int \frac{(d+e x)^m}{b x+c x^2} \, dx","Int[(d + e*x)^m/(b*x + c*x^2),x]","\frac{c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{c (d+e x)}{c d-b e}\right)}{b (m+1) (c d-b e)}-\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{e x}{d}+1\right)}{b d (m+1)}","\frac{c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{c (d+e x)}{c d-b e}\right)}{b (m+1) (c d-b e)}-\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{e x}{d}+1\right)}{b d (m+1)}",1,"(c*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (c*(d + e*x))/(c*d - b*e)])/(b*(c*d - b*e)*(1 + m)) - ((d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, 1 + (e*x)/d])/(b*d*(1 + m))","A",4,3,19,0.1579,1,"{711, 65, 68}"
444,1,180,0,0.1812703,"\int \frac{(d+e x)^m}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)^m/(b*x + c*x^2)^2,x]","-\frac{c^2 (d+e x)^{m+1} (2 c d-b e (2-m)) \, _2F_1\left(1,m+1;m+2;\frac{c (d+e x)}{c d-b e}\right)}{b^3 (m+1) (c d-b e)^2}+\frac{(d+e x)^{m+1} (2 c d-b e m) \, _2F_1\left(1,m+1;m+2;\frac{e x}{d}+1\right)}{b^3 d^2 (m+1)}-\frac{(d+e x)^{m+1} (c x (2 c d-b e)+b (c d-b e))}{b^2 d \left(b x+c x^2\right) (c d-b e)}","-\frac{c^2 (d+e x)^{m+1} (2 c d-b e (2-m)) \, _2F_1\left(1,m+1;m+2;\frac{c (d+e x)}{c d-b e}\right)}{b^3 (m+1) (c d-b e)^2}+\frac{(d+e x)^{m+1} (2 c d-b e m) \, _2F_1\left(1,m+1;m+2;\frac{e x}{d}+1\right)}{b^3 d^2 (m+1)}-\frac{(d+e x)^{m+1} (c x (2 c d-b e)+b (c d-b e))}{b^2 d \left(b x+c x^2\right) (c d-b e)}",1,"-(((d + e*x)^(1 + m)*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(b*x + c*x^2))) - (c^2*(2*c*d - b*e*(2 - m))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (c*(d + e*x))/(c*d - b*e)])/(b^3*(c*d - b*e)^2*(1 + m)) + ((2*c*d - b*e*m)*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, 1 + (e*x)/d])/(b^3*d^2*(1 + m))","A",5,4,19,0.2105,1,"{740, 830, 65, 68}"
445,1,350,0,0.4278359,"\int \frac{(d+e x)^m}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)^m/(b*x + c*x^2)^3,x]","\frac{c^3 (d+e x)^{m+1} \left(b^2 e^2 \left(m^2-7 m+12\right)-6 b c d e (4-m)+12 c^2 d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{c (d+e x)}{c d-b e}\right)}{2 b^5 (m+1) (c d-b e)^3}-\frac{(d+e x)^{m+1} \left(-b^2 e^2 (1-m) m-6 b c d e m+12 c^2 d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{e x}{d}+1\right)}{2 b^5 d^3 (m+1)}+\frac{(d+e x)^{m+1} \left(c x (2 c d-b e) \left(-b^2 e^2 (1-m)-6 b c d e+6 c^2 d^2\right)+b (c d-b e) \left(-b^2 e^2 (1-m)-b c d e (m+4)+6 c^2 d^2\right)\right)}{2 b^4 d^2 \left(b x+c x^2\right) (c d-b e)^2}-\frac{(d+e x)^{m+1} (c x (2 c d-b e)+b (c d-b e))}{2 b^2 d \left(b x+c x^2\right)^2 (c d-b e)}","\frac{c^3 (d+e x)^{m+1} \left(b^2 e^2 \left(m^2-7 m+12\right)-6 b c d e (4-m)+12 c^2 d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{c (d+e x)}{c d-b e}\right)}{2 b^5 (m+1) (c d-b e)^3}-\frac{(d+e x)^{m+1} \left(-b^2 e^2 (1-m) m-6 b c d e m+12 c^2 d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{e x}{d}+1\right)}{2 b^5 d^3 (m+1)}+\frac{(d+e x)^{m+1} \left(c x (2 c d-b e) \left(-b^2 e^2 (1-m)-6 b c d e+6 c^2 d^2\right)+b (c d-b e) \left(-b^2 e^2 (1-m)-b c d e (m+4)+6 c^2 d^2\right)\right)}{2 b^4 d^2 \left(b x+c x^2\right) (c d-b e)^2}-\frac{(d+e x)^{m+1} (c x (2 c d-b e)+b (c d-b e))}{2 b^2 d \left(b x+c x^2\right)^2 (c d-b e)}",1,"-((d + e*x)^(1 + m)*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(2*b^2*d*(c*d - b*e)*(b*x + c*x^2)^2) + ((d + e*x)^(1 + m)*(b*(c*d - b*e)*(6*c^2*d^2 - b^2*e^2*(1 - m) - b*c*d*e*(4 + m)) + c*(2*c*d - b*e)*(6*c^2*d^2 - 6*b*c*d*e - b^2*e^2*(1 - m))*x))/(2*b^4*d^2*(c*d - b*e)^2*(b*x + c*x^2)) + (c^3*(12*c^2*d^2 - 6*b*c*d*e*(4 - m) + b^2*e^2*(12 - 7*m + m^2))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (c*(d + e*x))/(c*d - b*e)])/(2*b^5*(c*d - b*e)^3*(1 + m)) - ((12*c^2*d^2 - 6*b*c*d*e*m - b^2*e^2*(1 - m)*m)*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, 1 + (e*x)/d])/(2*b^5*d^3*(1 + m))","A",6,5,19,0.2632,1,"{740, 822, 830, 65, 68}"
446,1,105,0,0.0590141,"\int (d+e x)^m \left(b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^m*(b*x + c*x^2)^(3/2),x]","\frac{\left(b x+c x^2\right)^{3/2} (d+e x)^{m+1} F_1\left(m+1;-\frac{3}{2},-\frac{3}{2};m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1) \left(-\frac{e x}{d}\right)^{3/2} \left(1-\frac{c (d+e x)}{c d-b e}\right)^{3/2}}","\frac{\left(b x+c x^2\right)^{3/2} (d+e x)^{m+1} F_1\left(m+1;-\frac{3}{2},-\frac{3}{2};m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1) \left(-\frac{e x}{d}\right)^{3/2} \left(1-\frac{c (d+e x)}{c d-b e}\right)^{3/2}}",1,"((d + e*x)^(1 + m)*(b*x + c*x^2)^(3/2)*AppellF1[1 + m, -3/2, -3/2, 2 + m, (d + e*x)/d, (c*(d + e*x))/(c*d - b*e)])/(e*(1 + m)*(-((e*x)/d))^(3/2)*(1 - (c*(d + e*x))/(c*d - b*e))^(3/2))","A",2,2,21,0.09524,1,"{759, 133}"
447,1,105,0,0.0493167,"\int (d+e x)^m \sqrt{b x+c x^2} \, dx","Int[(d + e*x)^m*Sqrt[b*x + c*x^2],x]","\frac{\sqrt{b x+c x^2} (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1) \sqrt{-\frac{e x}{d}} \sqrt{1-\frac{c (d+e x)}{c d-b e}}}","\frac{\sqrt{b x+c x^2} (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1) \sqrt{-\frac{e x}{d}} \sqrt{1-\frac{c (d+e x)}{c d-b e}}}",1,"((d + e*x)^(1 + m)*Sqrt[b*x + c*x^2]*AppellF1[1 + m, -1/2, -1/2, 2 + m, (d + e*x)/d, (c*(d + e*x))/(c*d - b*e)])/(e*(1 + m)*Sqrt[-((e*x)/d)]*Sqrt[1 - (c*(d + e*x))/(c*d - b*e)])","A",2,2,21,0.09524,1,"{759, 133}"
448,1,105,0,0.0510385,"\int \frac{(d+e x)^m}{\sqrt{b x+c x^2}} \, dx","Int[(d + e*x)^m/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{-\frac{e x}{d}} (d+e x)^{m+1} \sqrt{1-\frac{c (d+e x)}{c d-b e}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1) \sqrt{b x+c x^2}}","\frac{\sqrt{-\frac{e x}{d}} (d+e x)^{m+1} \sqrt{1-\frac{c (d+e x)}{c d-b e}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1) \sqrt{b x+c x^2}}",1,"(Sqrt[-((e*x)/d)]*(d + e*x)^(1 + m)*Sqrt[1 - (c*(d + e*x))/(c*d - b*e)]*AppellF1[1 + m, 1/2, 1/2, 2 + m, (d + e*x)/d, (c*(d + e*x))/(c*d - b*e)])/(e*(1 + m)*Sqrt[b*x + c*x^2])","A",2,2,21,0.09524,1,"{759, 133}"
449,1,105,0,0.0480589,"\int \frac{(d+e x)^m}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^m/(b*x + c*x^2)^(3/2),x]","\frac{\left(-\frac{e x}{d}\right)^{3/2} (d+e x)^{m+1} \left(1-\frac{c (d+e x)}{c d-b e}\right)^{3/2} F_1\left(m+1;\frac{3}{2},\frac{3}{2};m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1) \left(b x+c x^2\right)^{3/2}}","\frac{\left(-\frac{e x}{d}\right)^{3/2} (d+e x)^{m+1} \left(1-\frac{c (d+e x)}{c d-b e}\right)^{3/2} F_1\left(m+1;\frac{3}{2},\frac{3}{2};m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1) \left(b x+c x^2\right)^{3/2}}",1,"((-((e*x)/d))^(3/2)*(d + e*x)^(1 + m)*(1 - (c*(d + e*x))/(c*d - b*e))^(3/2)*AppellF1[1 + m, 3/2, 3/2, 2 + m, (d + e*x)/d, (c*(d + e*x))/(c*d - b*e)])/(e*(1 + m)*(b*x + c*x^2)^(3/2))","A",2,2,21,0.09524,1,"{759, 133}"
450,1,103,0,0.0491622,"\int (d+e x)^m \left(b x+c x^2\right)^p \, dx","Int[(d + e*x)^m*(b*x + c*x^2)^p,x]","\frac{\left(b x+c x^2\right)^p (d+e x)^{m+1} \left(-\frac{e x}{d}\right)^{-p} \left(1-\frac{c (d+e x)}{c d-b e}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1)}","\frac{\left(b x+c x^2\right)^p (d+e x)^{m+1} \left(-\frac{e x}{d}\right)^{-p} \left(1-\frac{c (d+e x)}{c d-b e}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{d+e x}{d},\frac{c (d+e x)}{c d-b e}\right)}{e (m+1)}",1,"((d + e*x)^(1 + m)*(b*x + c*x^2)^p*AppellF1[1 + m, -p, -p, 2 + m, (d + e*x)/d, (c*(d + e*x))/(c*d - b*e)])/(e*(1 + m)*(-((e*x)/d))^p*(1 - (c*(d + e*x))/(c*d - b*e))^p)","A",2,2,19,0.1053,1,"{759, 133}"
451,1,57,0,0.0632473,"\int (d+e x)^4 \left(a+c x^2\right) \, dx","Int[(d + e*x)^4*(a + c*x^2),x]","\frac{(d+e x)^5 \left(a e^2+c d^2\right)}{5 e^3}+\frac{c (d+e x)^7}{7 e^3}-\frac{c d (d+e x)^6}{3 e^3}","\frac{(d+e x)^5 \left(a e^2+c d^2\right)}{5 e^3}+\frac{c (d+e x)^7}{7 e^3}-\frac{c d (d+e x)^6}{3 e^3}",1,"((c*d^2 + a*e^2)*(d + e*x)^5)/(5*e^3) - (c*d*(d + e*x)^6)/(3*e^3) + (c*(d + e*x)^7)/(7*e^3)","A",2,1,15,0.06667,1,"{697}"
452,1,57,0,0.0455637,"\int (d+e x)^3 \left(a+c x^2\right) \, dx","Int[(d + e*x)^3*(a + c*x^2),x]","\frac{(d+e x)^4 \left(a e^2+c d^2\right)}{4 e^3}+\frac{c (d+e x)^6}{6 e^3}-\frac{2 c d (d+e x)^5}{5 e^3}","\frac{(d+e x)^4 \left(a e^2+c d^2\right)}{4 e^3}+\frac{c (d+e x)^6}{6 e^3}-\frac{2 c d (d+e x)^5}{5 e^3}",1,"((c*d^2 + a*e^2)*(d + e*x)^4)/(4*e^3) - (2*c*d*(d + e*x)^5)/(5*e^3) + (c*(d + e*x)^6)/(6*e^3)","A",2,1,15,0.06667,1,"{697}"
453,1,57,0,0.0320099,"\int (d+e x)^2 \left(a+c x^2\right) \, dx","Int[(d + e*x)^2*(a + c*x^2),x]","\frac{(d+e x)^3 \left(a e^2+c d^2\right)}{3 e^3}+\frac{c (d+e x)^5}{5 e^3}-\frac{c d (d+e x)^4}{2 e^3}","\frac{(d+e x)^3 \left(a e^2+c d^2\right)}{3 e^3}+\frac{c (d+e x)^5}{5 e^3}-\frac{c d (d+e x)^4}{2 e^3}",1,"((c*d^2 + a*e^2)*(d + e*x)^3)/(3*e^3) - (c*d*(d + e*x)^4)/(2*e^3) + (c*(d + e*x)^5)/(5*e^3)","A",2,1,15,0.06667,1,"{697}"
454,1,31,0,0.006554,"\int (d+e x) \left(a+c x^2\right) \, dx","Int[(d + e*x)*(a + c*x^2),x]","\frac{e \left(a+c x^2\right)^2}{4 c}+a d x+\frac{1}{3} c d x^3","\frac{e \left(a+c x^2\right)^2}{4 c}+a d x+\frac{1}{3} c d x^3",1,"a*d*x + (c*d*x^3)/3 + (e*(a + c*x^2)^2)/(4*c)","A",2,1,13,0.07692,1,"{641}"
455,1,41,0,0.0300263,"\int \frac{a+c x^2}{d+e x} \, dx","Int[(a + c*x^2)/(d + e*x),x]","\frac{\left(a e^2+c d^2\right) \log (d+e x)}{e^3}-\frac{c d x}{e^2}+\frac{c x^2}{2 e}","\frac{\left(a e^2+c d^2\right) \log (d+e x)}{e^3}-\frac{c d x}{e^2}+\frac{c x^2}{2 e}",1,"-((c*d*x)/e^2) + (c*x^2)/(2*e) + ((c*d^2 + a*e^2)*Log[d + e*x])/e^3","A",2,1,15,0.06667,1,"{697}"
456,1,43,0,0.0282407,"\int \frac{a+c x^2}{(d+e x)^2} \, dx","Int[(a + c*x^2)/(d + e*x)^2,x]","-\frac{a e^2+c d^2}{e^3 (d+e x)}-\frac{2 c d \log (d+e x)}{e^3}+\frac{c x}{e^2}","-\frac{a e^2+c d^2}{e^3 (d+e x)}-\frac{2 c d \log (d+e x)}{e^3}+\frac{c x}{e^2}",1,"(c*x)/e^2 - (c*d^2 + a*e^2)/(e^3*(d + e*x)) - (2*c*d*Log[d + e*x])/e^3","A",2,1,15,0.06667,1,"{697}"
457,1,51,0,0.0324775,"\int \frac{a+c x^2}{(d+e x)^3} \, dx","Int[(a + c*x^2)/(d + e*x)^3,x]","-\frac{a e^2+c d^2}{2 e^3 (d+e x)^2}+\frac{2 c d}{e^3 (d+e x)}+\frac{c \log (d+e x)}{e^3}","-\frac{a e^2+c d^2}{2 e^3 (d+e x)^2}+\frac{2 c d}{e^3 (d+e x)}+\frac{c \log (d+e x)}{e^3}",1,"-(c*d^2 + a*e^2)/(2*e^3*(d + e*x)^2) + (2*c*d)/(e^3*(d + e*x)) + (c*Log[d + e*x])/e^3","A",2,1,15,0.06667,1,"{697}"
458,1,52,0,0.0299414,"\int \frac{a+c x^2}{(d+e x)^4} \, dx","Int[(a + c*x^2)/(d + e*x)^4,x]","-\frac{a e^2+c d^2}{3 e^3 (d+e x)^3}-\frac{c}{e^3 (d+e x)}+\frac{c d}{e^3 (d+e x)^2}","-\frac{a e^2+c d^2}{3 e^3 (d+e x)^3}-\frac{c}{e^3 (d+e x)}+\frac{c d}{e^3 (d+e x)^2}",1,"-(c*d^2 + a*e^2)/(3*e^3*(d + e*x)^3) + (c*d)/(e^3*(d + e*x)^2) - c/(e^3*(d + e*x))","A",2,1,15,0.06667,1,"{697}"
459,1,57,0,0.0302744,"\int \frac{a+c x^2}{(d+e x)^5} \, dx","Int[(a + c*x^2)/(d + e*x)^5,x]","-\frac{a e^2+c d^2}{4 e^3 (d+e x)^4}-\frac{c}{2 e^3 (d+e x)^2}+\frac{2 c d}{3 e^3 (d+e x)^3}","-\frac{a e^2+c d^2}{4 e^3 (d+e x)^4}-\frac{c}{2 e^3 (d+e x)^2}+\frac{2 c d}{3 e^3 (d+e x)^3}",1,"-(c*d^2 + a*e^2)/(4*e^3*(d + e*x)^4) + (2*c*d)/(3*e^3*(d + e*x)^3) - c/(2*e^3*(d + e*x)^2)","A",2,1,15,0.06667,1,"{697}"
460,1,117,0,0.1312771,"\int (d+e x)^4 \left(a+c x^2\right)^2 \, dx","Int[(d + e*x)^4*(a + c*x^2)^2,x]","\frac{2 c (d+e x)^7 \left(a e^2+3 c d^2\right)}{7 e^5}-\frac{2 c d (d+e x)^6 \left(a e^2+c d^2\right)}{3 e^5}+\frac{(d+e x)^5 \left(a e^2+c d^2\right)^2}{5 e^5}+\frac{c^2 (d+e x)^9}{9 e^5}-\frac{c^2 d (d+e x)^8}{2 e^5}","\frac{2 c (d+e x)^7 \left(a e^2+3 c d^2\right)}{7 e^5}-\frac{2 c d (d+e x)^6 \left(a e^2+c d^2\right)}{3 e^5}+\frac{(d+e x)^5 \left(a e^2+c d^2\right)^2}{5 e^5}+\frac{c^2 (d+e x)^9}{9 e^5}-\frac{c^2 d (d+e x)^8}{2 e^5}",1,"((c*d^2 + a*e^2)^2*(d + e*x)^5)/(5*e^5) - (2*c*d*(c*d^2 + a*e^2)*(d + e*x)^6)/(3*e^5) + (2*c*(3*c*d^2 + a*e^2)*(d + e*x)^7)/(7*e^5) - (c^2*d*(d + e*x)^8)/(2*e^5) + (c^2*(d + e*x)^9)/(9*e^5)","A",2,1,17,0.05882,1,"{697}"
461,1,117,0,0.1020174,"\int (d+e x)^3 \left(a+c x^2\right)^2 \, dx","Int[(d + e*x)^3*(a + c*x^2)^2,x]","\frac{c (d+e x)^6 \left(a e^2+3 c d^2\right)}{3 e^5}-\frac{4 c d (d+e x)^5 \left(a e^2+c d^2\right)}{5 e^5}+\frac{(d+e x)^4 \left(a e^2+c d^2\right)^2}{4 e^5}+\frac{c^2 (d+e x)^8}{8 e^5}-\frac{4 c^2 d (d+e x)^7}{7 e^5}","\frac{c (d+e x)^6 \left(a e^2+3 c d^2\right)}{3 e^5}-\frac{4 c d (d+e x)^5 \left(a e^2+c d^2\right)}{5 e^5}+\frac{(d+e x)^4 \left(a e^2+c d^2\right)^2}{4 e^5}+\frac{c^2 (d+e x)^8}{8 e^5}-\frac{4 c^2 d (d+e x)^7}{7 e^5}",1,"((c*d^2 + a*e^2)^2*(d + e*x)^4)/(4*e^5) - (4*c*d*(c*d^2 + a*e^2)*(d + e*x)^5)/(5*e^5) + (c*(3*c*d^2 + a*e^2)*(d + e*x)^6)/(3*e^5) - (4*c^2*d*(d + e*x)^7)/(7*e^5) + (c^2*(d + e*x)^8)/(8*e^5)","A",2,1,17,0.05882,1,"{697}"
462,1,80,0,0.0461326,"\int (d+e x)^2 \left(a+c x^2\right)^2 \, dx","Int[(d + e*x)^2*(a + c*x^2)^2,x]","a^2 d^2 x+\frac{1}{5} c x^5 \left(2 a e^2+c d^2\right)+\frac{1}{3} a x^3 \left(a e^2+2 c d^2\right)+\frac{d e \left(a+c x^2\right)^3}{3 c}+\frac{1}{7} c^2 e^2 x^7","a^2 d^2 x+\frac{1}{5} c x^5 \left(2 a e^2+c d^2\right)+\frac{1}{3} a x^3 \left(a e^2+2 c d^2\right)+\frac{d e \left(a+c x^2\right)^3}{3 c}+\frac{1}{7} c^2 e^2 x^7",1,"a^2*d^2*x + (a*(2*c*d^2 + a*e^2)*x^3)/3 + (c*(c*d^2 + 2*a*e^2)*x^5)/5 + (c^2*e^2*x^7)/7 + (d*e*(a + c*x^2)^3)/(3*c)","A",3,2,17,0.1176,1,"{696, 1810}"
463,1,45,0,0.0152334,"\int (d+e x) \left(a+c x^2\right)^2 \, dx","Int[(d + e*x)*(a + c*x^2)^2,x]","a^2 d x+\frac{2}{3} a c d x^3+\frac{e \left(a+c x^2\right)^3}{6 c}+\frac{1}{5} c^2 d x^5","a^2 d x+\frac{2}{3} a c d x^3+\frac{e \left(a+c x^2\right)^3}{6 c}+\frac{1}{5} c^2 d x^5",1,"a^2*d*x + (2*a*c*d*x^3)/3 + (c^2*d*x^5)/5 + (e*(a + c*x^2)^3)/(6*c)","A",3,2,15,0.1333,1,"{641, 194}"
464,1,94,0,0.0753735,"\int \frac{\left(a+c x^2\right)^2}{d+e x} \, dx","Int[(a + c*x^2)^2/(d + e*x),x]","\frac{c x^2 \left(2 a e^2+c d^2\right)}{2 e^3}-\frac{c d x \left(2 a e^2+c d^2\right)}{e^4}+\frac{\left(a e^2+c d^2\right)^2 \log (d+e x)}{e^5}-\frac{c^2 d x^3}{3 e^2}+\frac{c^2 x^4}{4 e}","\frac{c x^2 \left(2 a e^2+c d^2\right)}{2 e^3}-\frac{c d x \left(2 a e^2+c d^2\right)}{e^4}+\frac{\left(a e^2+c d^2\right)^2 \log (d+e x)}{e^5}-\frac{c^2 d x^3}{3 e^2}+\frac{c^2 x^4}{4 e}",1,"-((c*d*(c*d^2 + 2*a*e^2)*x)/e^4) + (c*(c*d^2 + 2*a*e^2)*x^2)/(2*e^3) - (c^2*d*x^3)/(3*e^2) + (c^2*x^4)/(4*e) + ((c*d^2 + a*e^2)^2*Log[d + e*x])/e^5","A",2,1,17,0.05882,1,"{697}"
465,1,94,0,0.0756636,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^2} \, dx","Int[(a + c*x^2)^2/(d + e*x)^2,x]","\frac{c x \left(2 a e^2+3 c d^2\right)}{e^4}-\frac{\left(a e^2+c d^2\right)^2}{e^5 (d+e x)}-\frac{4 c d \left(a e^2+c d^2\right) \log (d+e x)}{e^5}-\frac{c^2 d x^2}{e^3}+\frac{c^2 x^3}{3 e^2}","\frac{c x \left(2 a e^2+3 c d^2\right)}{e^4}-\frac{\left(a e^2+c d^2\right)^2}{e^5 (d+e x)}-\frac{4 c d \left(a e^2+c d^2\right) \log (d+e x)}{e^5}-\frac{c^2 d x^2}{e^3}+\frac{c^2 x^3}{3 e^2}",1,"(c*(3*c*d^2 + 2*a*e^2)*x)/e^4 - (c^2*d*x^2)/e^3 + (c^2*x^3)/(3*e^2) - (c*d^2 + a*e^2)^2/(e^5*(d + e*x)) - (4*c*d*(c*d^2 + a*e^2)*Log[d + e*x])/e^5","A",2,1,17,0.05882,1,"{697}"
466,1,100,0,0.0810327,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^3} \, dx","Int[(a + c*x^2)^2/(d + e*x)^3,x]","\frac{4 c d \left(a e^2+c d^2\right)}{e^5 (d+e x)}-\frac{\left(a e^2+c d^2\right)^2}{2 e^5 (d+e x)^2}+\frac{2 c \left(a e^2+3 c d^2\right) \log (d+e x)}{e^5}-\frac{3 c^2 d x}{e^4}+\frac{c^2 x^2}{2 e^3}","\frac{4 c d \left(a e^2+c d^2\right)}{e^5 (d+e x)}-\frac{\left(a e^2+c d^2\right)^2}{2 e^5 (d+e x)^2}+\frac{2 c \left(a e^2+3 c d^2\right) \log (d+e x)}{e^5}-\frac{3 c^2 d x}{e^4}+\frac{c^2 x^2}{2 e^3}",1,"(-3*c^2*d*x)/e^4 + (c^2*x^2)/(2*e^3) - (c*d^2 + a*e^2)^2/(2*e^5*(d + e*x)^2) + (4*c*d*(c*d^2 + a*e^2))/(e^5*(d + e*x)) + (2*c*(3*c*d^2 + a*e^2)*Log[d + e*x])/e^5","A",2,1,17,0.05882,1,"{697}"
467,1,101,0,0.0746482,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^4} \, dx","Int[(a + c*x^2)^2/(d + e*x)^4,x]","-\frac{2 c \left(a e^2+3 c d^2\right)}{e^5 (d+e x)}+\frac{2 c d \left(a e^2+c d^2\right)}{e^5 (d+e x)^2}-\frac{\left(a e^2+c d^2\right)^2}{3 e^5 (d+e x)^3}-\frac{4 c^2 d \log (d+e x)}{e^5}+\frac{c^2 x}{e^4}","-\frac{2 c \left(a e^2+3 c d^2\right)}{e^5 (d+e x)}+\frac{2 c d \left(a e^2+c d^2\right)}{e^5 (d+e x)^2}-\frac{\left(a e^2+c d^2\right)^2}{3 e^5 (d+e x)^3}-\frac{4 c^2 d \log (d+e x)}{e^5}+\frac{c^2 x}{e^4}",1,"(c^2*x)/e^4 - (c*d^2 + a*e^2)^2/(3*e^5*(d + e*x)^3) + (2*c*d*(c*d^2 + a*e^2))/(e^5*(d + e*x)^2) - (2*c*(3*c*d^2 + a*e^2))/(e^5*(d + e*x)) - (4*c^2*d*Log[d + e*x])/e^5","A",2,1,17,0.05882,1,"{697}"
468,1,109,0,0.0747606,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^5} \, dx","Int[(a + c*x^2)^2/(d + e*x)^5,x]","-\frac{c \left(a e^2+3 c d^2\right)}{e^5 (d+e x)^2}+\frac{4 c d \left(a e^2+c d^2\right)}{3 e^5 (d+e x)^3}-\frac{\left(a e^2+c d^2\right)^2}{4 e^5 (d+e x)^4}+\frac{4 c^2 d}{e^5 (d+e x)}+\frac{c^2 \log (d+e x)}{e^5}","-\frac{c \left(a e^2+3 c d^2\right)}{e^5 (d+e x)^2}+\frac{4 c d \left(a e^2+c d^2\right)}{3 e^5 (d+e x)^3}-\frac{\left(a e^2+c d^2\right)^2}{4 e^5 (d+e x)^4}+\frac{4 c^2 d}{e^5 (d+e x)}+\frac{c^2 \log (d+e x)}{e^5}",1,"-(c*d^2 + a*e^2)^2/(4*e^5*(d + e*x)^4) + (4*c*d*(c*d^2 + a*e^2))/(3*e^5*(d + e*x)^3) - (c*(3*c*d^2 + a*e^2))/(e^5*(d + e*x)^2) + (4*c^2*d)/(e^5*(d + e*x)) + (c^2*Log[d + e*x])/e^5","A",2,1,17,0.05882,1,"{697}"
469,1,110,0,0.0685907,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^6} \, dx","Int[(a + c*x^2)^2/(d + e*x)^6,x]","-\frac{2 c \left(a e^2+3 c d^2\right)}{3 e^5 (d+e x)^3}+\frac{c d \left(a e^2+c d^2\right)}{e^5 (d+e x)^4}-\frac{\left(a e^2+c d^2\right)^2}{5 e^5 (d+e x)^5}-\frac{c^2}{e^5 (d+e x)}+\frac{2 c^2 d}{e^5 (d+e x)^2}","-\frac{2 c \left(a e^2+3 c d^2\right)}{3 e^5 (d+e x)^3}+\frac{c d \left(a e^2+c d^2\right)}{e^5 (d+e x)^4}-\frac{\left(a e^2+c d^2\right)^2}{5 e^5 (d+e x)^5}-\frac{c^2}{e^5 (d+e x)}+\frac{2 c^2 d}{e^5 (d+e x)^2}",1,"-(c*d^2 + a*e^2)^2/(5*e^5*(d + e*x)^5) + (c*d*(c*d^2 + a*e^2))/(e^5*(d + e*x)^4) - (2*c*(3*c*d^2 + a*e^2))/(3*e^5*(d + e*x)^3) + (2*c^2*d)/(e^5*(d + e*x)^2) - c^2/(e^5*(d + e*x))","A",2,1,17,0.05882,1,"{697}"
470,1,117,0,0.0690073,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^7} \, dx","Int[(a + c*x^2)^2/(d + e*x)^7,x]","-\frac{c \left(a e^2+3 c d^2\right)}{2 e^5 (d+e x)^4}+\frac{4 c d \left(a e^2+c d^2\right)}{5 e^5 (d+e x)^5}-\frac{\left(a e^2+c d^2\right)^2}{6 e^5 (d+e x)^6}-\frac{c^2}{2 e^5 (d+e x)^2}+\frac{4 c^2 d}{3 e^5 (d+e x)^3}","-\frac{c \left(a e^2+3 c d^2\right)}{2 e^5 (d+e x)^4}+\frac{4 c d \left(a e^2+c d^2\right)}{5 e^5 (d+e x)^5}-\frac{\left(a e^2+c d^2\right)^2}{6 e^5 (d+e x)^6}-\frac{c^2}{2 e^5 (d+e x)^2}+\frac{4 c^2 d}{3 e^5 (d+e x)^3}",1,"-(c*d^2 + a*e^2)^2/(6*e^5*(d + e*x)^6) + (4*c*d*(c*d^2 + a*e^2))/(5*e^5*(d + e*x)^5) - (c*(3*c*d^2 + a*e^2))/(2*e^5*(d + e*x)^4) + (4*c^2*d)/(3*e^5*(d + e*x)^3) - c^2/(2*e^5*(d + e*x)^2)","A",2,1,17,0.05882,1,"{697}"
471,1,114,0,0.0695633,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^8} \, dx","Int[(a + c*x^2)^2/(d + e*x)^8,x]","-\frac{2 c \left(a e^2+3 c d^2\right)}{5 e^5 (d+e x)^5}+\frac{2 c d \left(a e^2+c d^2\right)}{3 e^5 (d+e x)^6}-\frac{\left(a e^2+c d^2\right)^2}{7 e^5 (d+e x)^7}-\frac{c^2}{3 e^5 (d+e x)^3}+\frac{c^2 d}{e^5 (d+e x)^4}","-\frac{2 c \left(a e^2+3 c d^2\right)}{5 e^5 (d+e x)^5}+\frac{2 c d \left(a e^2+c d^2\right)}{3 e^5 (d+e x)^6}-\frac{\left(a e^2+c d^2\right)^2}{7 e^5 (d+e x)^7}-\frac{c^2}{3 e^5 (d+e x)^3}+\frac{c^2 d}{e^5 (d+e x)^4}",1,"-(c*d^2 + a*e^2)^2/(7*e^5*(d + e*x)^7) + (2*c*d*(c*d^2 + a*e^2))/(3*e^5*(d + e*x)^6) - (2*c*(3*c*d^2 + a*e^2))/(5*e^5*(d + e*x)^5) + (c^2*d)/(e^5*(d + e*x)^4) - c^2/(3*e^5*(d + e*x)^3)","A",2,1,17,0.05882,1,"{697}"
472,1,190,0,0.3291892,"\int (d+e x)^6 \left(a+c x^2\right)^3 \, dx","Int[(d + e*x)^6*(a + c*x^2)^3,x]","\frac{3 c^2 (d+e x)^{11} \left(a e^2+5 c d^2\right)}{11 e^7}-\frac{2 c^2 d (d+e x)^{10} \left(3 a e^2+5 c d^2\right)}{5 e^7}+\frac{c (d+e x)^9 \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{3 e^7}-\frac{3 c d (d+e x)^8 \left(a e^2+c d^2\right)^2}{4 e^7}+\frac{(d+e x)^7 \left(a e^2+c d^2\right)^3}{7 e^7}+\frac{c^3 (d+e x)^{13}}{13 e^7}-\frac{c^3 d (d+e x)^{12}}{2 e^7}","\frac{3 c^2 (d+e x)^{11} \left(a e^2+5 c d^2\right)}{11 e^7}-\frac{2 c^2 d (d+e x)^{10} \left(3 a e^2+5 c d^2\right)}{5 e^7}+\frac{c (d+e x)^9 \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{3 e^7}-\frac{3 c d (d+e x)^8 \left(a e^2+c d^2\right)^2}{4 e^7}+\frac{(d+e x)^7 \left(a e^2+c d^2\right)^3}{7 e^7}+\frac{c^3 (d+e x)^{13}}{13 e^7}-\frac{c^3 d (d+e x)^{12}}{2 e^7}",1,"((c*d^2 + a*e^2)^3*(d + e*x)^7)/(7*e^7) - (3*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^8)/(4*e^7) + (c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^9)/(3*e^7) - (2*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^10)/(5*e^7) + (3*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^11)/(11*e^7) - (c^3*d*(d + e*x)^12)/(2*e^7) + (c^3*(d + e*x)^13)/(13*e^7)","A",2,1,17,0.05882,1,"{697}"
473,1,190,0,0.2609044,"\int (d+e x)^5 \left(a+c x^2\right)^3 \, dx","Int[(d + e*x)^5*(a + c*x^2)^3,x]","\frac{3 c^2 (d+e x)^{10} \left(a e^2+5 c d^2\right)}{10 e^7}-\frac{4 c^2 d (d+e x)^9 \left(3 a e^2+5 c d^2\right)}{9 e^7}+\frac{3 c (d+e x)^8 \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{8 e^7}-\frac{6 c d (d+e x)^7 \left(a e^2+c d^2\right)^2}{7 e^7}+\frac{(d+e x)^6 \left(a e^2+c d^2\right)^3}{6 e^7}+\frac{c^3 (d+e x)^{12}}{12 e^7}-\frac{6 c^3 d (d+e x)^{11}}{11 e^7}","\frac{3 c^2 (d+e x)^{10} \left(a e^2+5 c d^2\right)}{10 e^7}-\frac{4 c^2 d (d+e x)^9 \left(3 a e^2+5 c d^2\right)}{9 e^7}+\frac{3 c (d+e x)^8 \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{8 e^7}-\frac{6 c d (d+e x)^7 \left(a e^2+c d^2\right)^2}{7 e^7}+\frac{(d+e x)^6 \left(a e^2+c d^2\right)^3}{6 e^7}+\frac{c^3 (d+e x)^{12}}{12 e^7}-\frac{6 c^3 d (d+e x)^{11}}{11 e^7}",1,"((c*d^2 + a*e^2)^3*(d + e*x)^6)/(6*e^7) - (6*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^7)/(7*e^7) + (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^8)/(8*e^7) - (4*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^9)/(9*e^7) + (3*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^10)/(10*e^7) - (6*c^3*d*(d + e*x)^11)/(11*e^7) + (c^3*(d + e*x)^12)/(12*e^7)","A",2,1,17,0.05882,1,"{697}"
474,1,188,0,0.2332642,"\int (d+e x)^4 \left(a+c x^2\right)^3 \, dx","Int[(d + e*x)^4*(a + c*x^2)^3,x]","\frac{c^2 (d+e x)^9 \left(a e^2+5 c d^2\right)}{3 e^7}-\frac{c^2 d (d+e x)^8 \left(3 a e^2+5 c d^2\right)}{2 e^7}+\frac{3 c (d+e x)^7 \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{7 e^7}-\frac{c d (d+e x)^6 \left(a e^2+c d^2\right)^2}{e^7}+\frac{(d+e x)^5 \left(a e^2+c d^2\right)^3}{5 e^7}+\frac{c^3 (d+e x)^{11}}{11 e^7}-\frac{3 c^3 d (d+e x)^{10}}{5 e^7}","\frac{c^2 (d+e x)^9 \left(a e^2+5 c d^2\right)}{3 e^7}-\frac{c^2 d (d+e x)^8 \left(3 a e^2+5 c d^2\right)}{2 e^7}+\frac{3 c (d+e x)^7 \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{7 e^7}-\frac{c d (d+e x)^6 \left(a e^2+c d^2\right)^2}{e^7}+\frac{(d+e x)^5 \left(a e^2+c d^2\right)^3}{5 e^7}+\frac{c^3 (d+e x)^{11}}{11 e^7}-\frac{3 c^3 d (d+e x)^{10}}{5 e^7}",1,"((c*d^2 + a*e^2)^3*(d + e*x)^5)/(5*e^7) - (c*d*(c*d^2 + a*e^2)^2*(d + e*x)^6)/e^7 + (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^7)/(7*e^7) - (c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^8)/(2*e^7) + (c^2*(5*c*d^2 + a*e^2)*(d + e*x)^9)/(3*e^7) - (3*c^3*d*(d + e*x)^10)/(5*e^7) + (c^3*(d + e*x)^11)/(11*e^7)","A",2,1,17,0.05882,1,"{697}"
475,1,161,0,0.1403778,"\int (d+e x)^3 \left(a+c x^2\right)^3 \, dx","Int[(d + e*x)^3*(a + c*x^2)^3,x]","a^2 d x^3 \left(a e^2+c d^2\right)+\frac{1}{2} a^2 c e^3 x^6+a^3 d^3 x+\frac{1}{4} a^3 e^3 x^4+\frac{1}{7} c^2 d x^7 \left(9 a e^2+c d^2\right)+\frac{3}{8} a c^2 e^3 x^8+\frac{3}{5} a c d x^5 \left(3 a e^2+c d^2\right)+\frac{3 d^2 e \left(a+c x^2\right)^4}{8 c}+\frac{1}{3} c^3 d e^2 x^9+\frac{1}{10} c^3 e^3 x^{10}","a^2 d x^3 \left(a e^2+c d^2\right)+\frac{1}{2} a^2 c e^3 x^6+a^3 d^3 x+\frac{1}{4} a^3 e^3 x^4+\frac{1}{7} c^2 d x^7 \left(9 a e^2+c d^2\right)+\frac{3}{8} a c^2 e^3 x^8+\frac{3}{5} a c d x^5 \left(3 a e^2+c d^2\right)+\frac{3 d^2 e \left(a+c x^2\right)^4}{8 c}+\frac{1}{3} c^3 d e^2 x^9+\frac{1}{10} c^3 e^3 x^{10}",1,"a^3*d^3*x + a^2*d*(c*d^2 + a*e^2)*x^3 + (a^3*e^3*x^4)/4 + (3*a*c*d*(c*d^2 + 3*a*e^2)*x^5)/5 + (a^2*c*e^3*x^6)/2 + (c^2*d*(c*d^2 + 9*a*e^2)*x^7)/7 + (3*a*c^2*e^3*x^8)/8 + (c^3*d*e^2*x^9)/3 + (c^3*e^3*x^10)/10 + (3*d^2*e*(a + c*x^2)^4)/(8*c)","A",3,2,17,0.1176,1,"{696, 1810}"
476,1,104,0,0.0630388,"\int (d+e x)^2 \left(a+c x^2\right)^3 \, dx","Int[(d + e*x)^2*(a + c*x^2)^3,x]","\frac{1}{3} a^2 x^3 \left(a e^2+3 c d^2\right)+a^3 d^2 x+\frac{1}{7} c^2 x^7 \left(3 a e^2+c d^2\right)+\frac{3}{5} a c x^5 \left(a e^2+c d^2\right)+\frac{d e \left(a+c x^2\right)^4}{4 c}+\frac{1}{9} c^3 e^2 x^9","\frac{1}{3} a^2 x^3 \left(a e^2+3 c d^2\right)+a^3 d^2 x+\frac{1}{7} c^2 x^7 \left(3 a e^2+c d^2\right)+\frac{3}{5} a c x^5 \left(a e^2+c d^2\right)+\frac{d e \left(a+c x^2\right)^4}{4 c}+\frac{1}{9} c^3 e^2 x^9",1,"a^3*d^2*x + (a^2*(3*c*d^2 + a*e^2)*x^3)/3 + (3*a*c*(c*d^2 + a*e^2)*x^5)/5 + (c^2*(c*d^2 + 3*a*e^2)*x^7)/7 + (c^3*e^2*x^9)/9 + (d*e*(a + c*x^2)^4)/(4*c)","A",3,2,17,0.1176,1,"{696, 1810}"
477,1,56,0,0.021189,"\int (d+e x) \left(a+c x^2\right)^3 \, dx","Int[(d + e*x)*(a + c*x^2)^3,x]","a^2 c d x^3+a^3 d x+\frac{3}{5} a c^2 d x^5+\frac{e \left(a+c x^2\right)^4}{8 c}+\frac{1}{7} c^3 d x^7","a^2 c d x^3+a^3 d x+\frac{3}{5} a c^2 d x^5+\frac{e \left(a+c x^2\right)^4}{8 c}+\frac{1}{7} c^3 d x^7",1,"a^3*d*x + a^2*c*d*x^3 + (3*a*c^2*d*x^5)/5 + (c^3*d*x^7)/7 + (e*(a + c*x^2)^4)/(8*c)","A",3,2,15,0.1333,1,"{641, 194}"
478,1,173,0,0.1445674,"\int \frac{\left(a+c x^2\right)^3}{d+e x} \, dx","Int[(a + c*x^2)^3/(d + e*x),x]","\frac{c x^2 \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right)}{2 e^5}-\frac{c d x \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right)}{e^6}+\frac{c^2 x^4 \left(3 a e^2+c d^2\right)}{4 e^3}-\frac{c^2 d x^3 \left(3 a e^2+c d^2\right)}{3 e^4}+\frac{\left(a e^2+c d^2\right)^3 \log (d+e x)}{e^7}-\frac{c^3 d x^5}{5 e^2}+\frac{c^3 x^6}{6 e}","\frac{c x^2 \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right)}{2 e^5}-\frac{c d x \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right)}{e^6}+\frac{c^2 x^4 \left(3 a e^2+c d^2\right)}{4 e^3}-\frac{c^2 d x^3 \left(3 a e^2+c d^2\right)}{3 e^4}+\frac{\left(a e^2+c d^2\right)^3 \log (d+e x)}{e^7}-\frac{c^3 d x^5}{5 e^2}+\frac{c^3 x^6}{6 e}",1,"-((c*d*(c^2*d^4 + 3*a*c*d^2*e^2 + 3*a^2*e^4)*x)/e^6) + (c*(c^2*d^4 + 3*a*c*d^2*e^2 + 3*a^2*e^4)*x^2)/(2*e^5) - (c^2*d*(c*d^2 + 3*a*e^2)*x^3)/(3*e^4) + (c^2*(c*d^2 + 3*a*e^2)*x^4)/(4*e^3) - (c^3*d*x^5)/(5*e^2) + (c^3*x^6)/(6*e) + ((c*d^2 + a*e^2)^3*Log[d + e*x])/e^7","A",2,1,17,0.05882,1,"{697}"
479,1,158,0,0.1515235,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^2} \, dx","Int[(a + c*x^2)^3/(d + e*x)^2,x]","\frac{c x \left(3 a^2 e^4+9 a c d^2 e^2+5 c^2 d^4\right)}{e^6}+\frac{c^2 x^3 \left(a e^2+c d^2\right)}{e^4}-\frac{c^2 d x^2 \left(3 a e^2+2 c d^2\right)}{e^5}-\frac{\left(a e^2+c d^2\right)^3}{e^7 (d+e x)}-\frac{6 c d \left(a e^2+c d^2\right)^2 \log (d+e x)}{e^7}-\frac{c^3 d x^4}{2 e^3}+\frac{c^3 x^5}{5 e^2}","\frac{c x \left(3 a^2 e^4+9 a c d^2 e^2+5 c^2 d^4\right)}{e^6}+\frac{c^2 x^3 \left(a e^2+c d^2\right)}{e^4}-\frac{c^2 d x^2 \left(3 a e^2+2 c d^2\right)}{e^5}-\frac{\left(a e^2+c d^2\right)^3}{e^7 (d+e x)}-\frac{6 c d \left(a e^2+c d^2\right)^2 \log (d+e x)}{e^7}-\frac{c^3 d x^4}{2 e^3}+\frac{c^3 x^5}{5 e^2}",1,"(c*(5*c^2*d^4 + 9*a*c*d^2*e^2 + 3*a^2*e^4)*x)/e^6 - (c^2*d*(2*c*d^2 + 3*a*e^2)*x^2)/e^5 + (c^2*(c*d^2 + a*e^2)*x^3)/e^4 - (c^3*d*x^4)/(2*e^3) + (c^3*x^5)/(5*e^2) - (c*d^2 + a*e^2)^3/(e^7*(d + e*x)) - (6*c*d*(c*d^2 + a*e^2)^2*Log[d + e*x])/e^7","A",2,1,17,0.05882,1,"{697}"
480,1,163,0,0.1675467,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^3} \, dx","Int[(a + c*x^2)^3/(d + e*x)^3,x]","\frac{3 c^2 x^2 \left(a e^2+2 c d^2\right)}{2 e^5}-\frac{c^2 d x \left(9 a e^2+10 c d^2\right)}{e^6}+\frac{6 c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)}-\frac{\left(a e^2+c d^2\right)^3}{2 e^7 (d+e x)^2}+\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right) \log (d+e x)}{e^7}-\frac{c^3 d x^3}{e^4}+\frac{c^3 x^4}{4 e^3}","\frac{3 c^2 x^2 \left(a e^2+2 c d^2\right)}{2 e^5}-\frac{c^2 d x \left(9 a e^2+10 c d^2\right)}{e^6}+\frac{6 c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)}-\frac{\left(a e^2+c d^2\right)^3}{2 e^7 (d+e x)^2}+\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right) \log (d+e x)}{e^7}-\frac{c^3 d x^3}{e^4}+\frac{c^3 x^4}{4 e^3}",1,"-((c^2*d*(10*c*d^2 + 9*a*e^2)*x)/e^6) + (3*c^2*(2*c*d^2 + a*e^2)*x^2)/(2*e^5) - (c^3*d*x^3)/e^4 + (c^3*x^4)/(4*e^3) - (c*d^2 + a*e^2)^3/(2*e^7*(d + e*x)^2) + (6*c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)) + (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*Log[d + e*x])/e^7","A",2,1,17,0.05882,1,"{697}"
481,1,165,0,0.164905,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^4} \, dx","Int[(a + c*x^2)^3/(d + e*x)^4,x]","\frac{c^2 x \left(3 a e^2+10 c d^2\right)}{e^6}-\frac{4 c^2 d \left(3 a e^2+5 c d^2\right) \log (d+e x)}{e^7}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7 (d+e x)}+\frac{3 c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)^2}-\frac{\left(a e^2+c d^2\right)^3}{3 e^7 (d+e x)^3}-\frac{2 c^3 d x^2}{e^5}+\frac{c^3 x^3}{3 e^4}","\frac{c^2 x \left(3 a e^2+10 c d^2\right)}{e^6}-\frac{4 c^2 d \left(3 a e^2+5 c d^2\right) \log (d+e x)}{e^7}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7 (d+e x)}+\frac{3 c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)^2}-\frac{\left(a e^2+c d^2\right)^3}{3 e^7 (d+e x)^3}-\frac{2 c^3 d x^2}{e^5}+\frac{c^3 x^3}{3 e^4}",1,"(c^2*(10*c*d^2 + 3*a*e^2)*x)/e^6 - (2*c^3*d*x^2)/e^5 + (c^3*x^3)/(3*e^4) - (c*d^2 + a*e^2)^3/(3*e^7*(d + e*x)^3) + (3*c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)^2) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(e^7*(d + e*x)) - (4*c^2*d*(5*c*d^2 + 3*a*e^2)*Log[d + e*x])/e^7","A",2,1,17,0.05882,1,"{697}"
482,1,171,0,0.1571417,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^5} \, dx","Int[(a + c*x^2)^3/(d + e*x)^5,x]","\frac{4 c^2 d \left(3 a e^2+5 c d^2\right)}{e^7 (d+e x)}+\frac{3 c^2 \left(a e^2+5 c d^2\right) \log (d+e x)}{e^7}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{2 e^7 (d+e x)^2}+\frac{2 c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)^3}-\frac{\left(a e^2+c d^2\right)^3}{4 e^7 (d+e x)^4}-\frac{5 c^3 d x}{e^6}+\frac{c^3 x^2}{2 e^5}","\frac{4 c^2 d \left(3 a e^2+5 c d^2\right)}{e^7 (d+e x)}+\frac{3 c^2 \left(a e^2+5 c d^2\right) \log (d+e x)}{e^7}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{2 e^7 (d+e x)^2}+\frac{2 c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)^3}-\frac{\left(a e^2+c d^2\right)^3}{4 e^7 (d+e x)^4}-\frac{5 c^3 d x}{e^6}+\frac{c^3 x^2}{2 e^5}",1,"(-5*c^3*d*x)/e^6 + (c^3*x^2)/(2*e^5) - (c*d^2 + a*e^2)^3/(4*e^7*(d + e*x)^4) + (2*c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)^3) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(2*e^7*(d + e*x)^2) + (4*c^2*d*(5*c*d^2 + 3*a*e^2))/(e^7*(d + e*x)) + (3*c^2*(5*c*d^2 + a*e^2)*Log[d + e*x])/e^7","A",2,1,17,0.05882,1,"{697}"
483,1,172,0,0.1494487,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^6} \, dx","Int[(a + c*x^2)^3/(d + e*x)^6,x]","-\frac{3 c^2 \left(a e^2+5 c d^2\right)}{e^7 (d+e x)}+\frac{2 c^2 d \left(3 a e^2+5 c d^2\right)}{e^7 (d+e x)^2}-\frac{c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7 (d+e x)^3}+\frac{3 c d \left(a e^2+c d^2\right)^2}{2 e^7 (d+e x)^4}-\frac{\left(a e^2+c d^2\right)^3}{5 e^7 (d+e x)^5}-\frac{6 c^3 d \log (d+e x)}{e^7}+\frac{c^3 x}{e^6}","-\frac{3 c^2 \left(a e^2+5 c d^2\right)}{e^7 (d+e x)}+\frac{2 c^2 d \left(3 a e^2+5 c d^2\right)}{e^7 (d+e x)^2}-\frac{c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7 (d+e x)^3}+\frac{3 c d \left(a e^2+c d^2\right)^2}{2 e^7 (d+e x)^4}-\frac{\left(a e^2+c d^2\right)^3}{5 e^7 (d+e x)^5}-\frac{6 c^3 d \log (d+e x)}{e^7}+\frac{c^3 x}{e^6}",1,"(c^3*x)/e^6 - (c*d^2 + a*e^2)^3/(5*e^7*(d + e*x)^5) + (3*c*d*(c*d^2 + a*e^2)^2)/(2*e^7*(d + e*x)^4) - (c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(e^7*(d + e*x)^3) + (2*c^2*d*(5*c*d^2 + 3*a*e^2))/(e^7*(d + e*x)^2) - (3*c^2*(5*c*d^2 + a*e^2))/(e^7*(d + e*x)) - (6*c^3*d*Log[d + e*x])/e^7","A",2,1,17,0.05882,1,"{697}"
484,1,184,0,0.1352926,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^7} \, dx","Int[(a + c*x^2)^3/(d + e*x)^7,x]","-\frac{3 c^2 \left(a e^2+5 c d^2\right)}{2 e^7 (d+e x)^2}+\frac{4 c^2 d \left(3 a e^2+5 c d^2\right)}{3 e^7 (d+e x)^3}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{4 e^7 (d+e x)^4}+\frac{6 c d \left(a e^2+c d^2\right)^2}{5 e^7 (d+e x)^5}-\frac{\left(a e^2+c d^2\right)^3}{6 e^7 (d+e x)^6}+\frac{6 c^3 d}{e^7 (d+e x)}+\frac{c^3 \log (d+e x)}{e^7}","-\frac{3 c^2 \left(a e^2+5 c d^2\right)}{2 e^7 (d+e x)^2}+\frac{4 c^2 d \left(3 a e^2+5 c d^2\right)}{3 e^7 (d+e x)^3}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{4 e^7 (d+e x)^4}+\frac{6 c d \left(a e^2+c d^2\right)^2}{5 e^7 (d+e x)^5}-\frac{\left(a e^2+c d^2\right)^3}{6 e^7 (d+e x)^6}+\frac{6 c^3 d}{e^7 (d+e x)}+\frac{c^3 \log (d+e x)}{e^7}",1,"-(c*d^2 + a*e^2)^3/(6*e^7*(d + e*x)^6) + (6*c*d*(c*d^2 + a*e^2)^2)/(5*e^7*(d + e*x)^5) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(4*e^7*(d + e*x)^4) + (4*c^2*d*(5*c*d^2 + 3*a*e^2))/(3*e^7*(d + e*x)^3) - (3*c^2*(5*c*d^2 + a*e^2))/(2*e^7*(d + e*x)^2) + (6*c^3*d)/(e^7*(d + e*x)) + (c^3*Log[d + e*x])/e^7","A",2,1,17,0.05882,1,"{697}"
485,1,178,0,0.1215614,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^8} \, dx","Int[(a + c*x^2)^3/(d + e*x)^8,x]","-\frac{c^2 \left(a e^2+5 c d^2\right)}{e^7 (d+e x)^3}+\frac{c^2 d \left(3 a e^2+5 c d^2\right)}{e^7 (d+e x)^4}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{5 e^7 (d+e x)^5}+\frac{c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)^6}-\frac{\left(a e^2+c d^2\right)^3}{7 e^7 (d+e x)^7}-\frac{c^3}{e^7 (d+e x)}+\frac{3 c^3 d}{e^7 (d+e x)^2}","-\frac{c^2 \left(a e^2+5 c d^2\right)}{e^7 (d+e x)^3}+\frac{c^2 d \left(3 a e^2+5 c d^2\right)}{e^7 (d+e x)^4}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{5 e^7 (d+e x)^5}+\frac{c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)^6}-\frac{\left(a e^2+c d^2\right)^3}{7 e^7 (d+e x)^7}-\frac{c^3}{e^7 (d+e x)}+\frac{3 c^3 d}{e^7 (d+e x)^2}",1,"-(c*d^2 + a*e^2)^3/(7*e^7*(d + e*x)^7) + (c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)^6) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(5*e^7*(d + e*x)^5) + (c^2*d*(5*c*d^2 + 3*a*e^2))/(e^7*(d + e*x)^4) - (c^2*(5*c*d^2 + a*e^2))/(e^7*(d + e*x)^3) + (3*c^3*d)/(e^7*(d + e*x)^2) - c^3/(e^7*(d + e*x))","A",2,1,17,0.05882,1,"{697}"
486,1,188,0,0.1254104,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^9} \, dx","Int[(a + c*x^2)^3/(d + e*x)^9,x]","-\frac{3 c^2 \left(a e^2+5 c d^2\right)}{4 e^7 (d+e x)^4}+\frac{4 c^2 d \left(3 a e^2+5 c d^2\right)}{5 e^7 (d+e x)^5}-\frac{c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{2 e^7 (d+e x)^6}+\frac{6 c d \left(a e^2+c d^2\right)^2}{7 e^7 (d+e x)^7}-\frac{\left(a e^2+c d^2\right)^3}{8 e^7 (d+e x)^8}-\frac{c^3}{2 e^7 (d+e x)^2}+\frac{2 c^3 d}{e^7 (d+e x)^3}","-\frac{3 c^2 \left(a e^2+5 c d^2\right)}{4 e^7 (d+e x)^4}+\frac{4 c^2 d \left(3 a e^2+5 c d^2\right)}{5 e^7 (d+e x)^5}-\frac{c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{2 e^7 (d+e x)^6}+\frac{6 c d \left(a e^2+c d^2\right)^2}{7 e^7 (d+e x)^7}-\frac{\left(a e^2+c d^2\right)^3}{8 e^7 (d+e x)^8}-\frac{c^3}{2 e^7 (d+e x)^2}+\frac{2 c^3 d}{e^7 (d+e x)^3}",1,"-(c*d^2 + a*e^2)^3/(8*e^7*(d + e*x)^8) + (6*c*d*(c*d^2 + a*e^2)^2)/(7*e^7*(d + e*x)^7) - (c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(2*e^7*(d + e*x)^6) + (4*c^2*d*(5*c*d^2 + 3*a*e^2))/(5*e^7*(d + e*x)^5) - (3*c^2*(5*c*d^2 + a*e^2))/(4*e^7*(d + e*x)^4) + (2*c^3*d)/(e^7*(d + e*x)^3) - c^3/(2*e^7*(d + e*x)^2)","A",2,1,17,0.05882,1,"{697}"
487,1,190,0,0.1207598,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^{10}} \, dx","Int[(a + c*x^2)^3/(d + e*x)^10,x]","-\frac{3 c^2 \left(a e^2+5 c d^2\right)}{5 e^7 (d+e x)^5}+\frac{2 c^2 d \left(3 a e^2+5 c d^2\right)}{3 e^7 (d+e x)^6}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{7 e^7 (d+e x)^7}+\frac{3 c d \left(a e^2+c d^2\right)^2}{4 e^7 (d+e x)^8}-\frac{\left(a e^2+c d^2\right)^3}{9 e^7 (d+e x)^9}-\frac{c^3}{3 e^7 (d+e x)^3}+\frac{3 c^3 d}{2 e^7 (d+e x)^4}","-\frac{3 c^2 \left(a e^2+5 c d^2\right)}{5 e^7 (d+e x)^5}+\frac{2 c^2 d \left(3 a e^2+5 c d^2\right)}{3 e^7 (d+e x)^6}-\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{7 e^7 (d+e x)^7}+\frac{3 c d \left(a e^2+c d^2\right)^2}{4 e^7 (d+e x)^8}-\frac{\left(a e^2+c d^2\right)^3}{9 e^7 (d+e x)^9}-\frac{c^3}{3 e^7 (d+e x)^3}+\frac{3 c^3 d}{2 e^7 (d+e x)^4}",1,"-(c*d^2 + a*e^2)^3/(9*e^7*(d + e*x)^9) + (3*c*d*(c*d^2 + a*e^2)^2)/(4*e^7*(d + e*x)^8) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(7*e^7*(d + e*x)^7) + (2*c^2*d*(5*c*d^2 + 3*a*e^2))/(3*e^7*(d + e*x)^6) - (3*c^2*(5*c*d^2 + a*e^2))/(5*e^7*(d + e*x)^5) + (3*c^3*d)/(2*e^7*(d + e*x)^4) - c^3/(3*e^7*(d + e*x)^3)","A",2,1,17,0.05882,1,"{697}"
488,1,278,0,0.5158549,"\int (d+e x)^7 \left(a+c x^2\right)^4 \, dx","Int[(d + e*x)^7*(a + c*x^2)^4,x]","\frac{c^2 (d+e x)^{12} \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)}{6 e^9}+\frac{2 c^3 (d+e x)^{14} \left(a e^2+7 c d^2\right)}{7 e^9}-\frac{8 c^3 d (d+e x)^{13} \left(3 a e^2+7 c d^2\right)}{13 e^9}-\frac{8 c^2 d (d+e x)^{11} \left(a e^2+c d^2\right) \left(3 a e^2+7 c d^2\right)}{11 e^9}+\frac{2 c (d+e x)^{10} \left(a e^2+c d^2\right)^2 \left(a e^2+7 c d^2\right)}{5 e^9}-\frac{8 c d (d+e x)^9 \left(a e^2+c d^2\right)^3}{9 e^9}+\frac{(d+e x)^8 \left(a e^2+c d^2\right)^4}{8 e^9}+\frac{c^4 (d+e x)^{16}}{16 e^9}-\frac{8 c^4 d (d+e x)^{15}}{15 e^9}","\frac{c^2 (d+e x)^{12} \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)}{6 e^9}+\frac{2 c^3 (d+e x)^{14} \left(a e^2+7 c d^2\right)}{7 e^9}-\frac{8 c^3 d (d+e x)^{13} \left(3 a e^2+7 c d^2\right)}{13 e^9}-\frac{8 c^2 d (d+e x)^{11} \left(a e^2+c d^2\right) \left(3 a e^2+7 c d^2\right)}{11 e^9}+\frac{2 c (d+e x)^{10} \left(a e^2+c d^2\right)^2 \left(a e^2+7 c d^2\right)}{5 e^9}-\frac{8 c d (d+e x)^9 \left(a e^2+c d^2\right)^3}{9 e^9}+\frac{(d+e x)^8 \left(a e^2+c d^2\right)^4}{8 e^9}+\frac{c^4 (d+e x)^{16}}{16 e^9}-\frac{8 c^4 d (d+e x)^{15}}{15 e^9}",1,"((c*d^2 + a*e^2)^4*(d + e*x)^8)/(8*e^9) - (8*c*d*(c*d^2 + a*e^2)^3*(d + e*x)^9)/(9*e^9) + (2*c*(c*d^2 + a*e^2)^2*(7*c*d^2 + a*e^2)*(d + e*x)^10)/(5*e^9) - (8*c^2*d*(c*d^2 + a*e^2)*(7*c*d^2 + 3*a*e^2)*(d + e*x)^11)/(11*e^9) + (c^2*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)*(d + e*x)^12)/(6*e^9) - (8*c^3*d*(7*c*d^2 + 3*a*e^2)*(d + e*x)^13)/(13*e^9) + (2*c^3*(7*c*d^2 + a*e^2)*(d + e*x)^14)/(7*e^9) - (8*c^4*d*(d + e*x)^15)/(15*e^9) + (c^4*(d + e*x)^16)/(16*e^9)","A",2,1,17,0.05882,1,"{697}"
489,1,276,0,0.4583628,"\int (d+e x)^6 \left(a+c x^2\right)^4 \, dx","Int[(d + e*x)^6*(a + c*x^2)^4,x]","\frac{2 c^2 (d+e x)^{11} \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)}{11 e^9}+\frac{4 c^3 (d+e x)^{13} \left(a e^2+7 c d^2\right)}{13 e^9}-\frac{2 c^3 d (d+e x)^{12} \left(3 a e^2+7 c d^2\right)}{3 e^9}-\frac{4 c^2 d (d+e x)^{10} \left(a e^2+c d^2\right) \left(3 a e^2+7 c d^2\right)}{5 e^9}+\frac{4 c (d+e x)^9 \left(a e^2+c d^2\right)^2 \left(a e^2+7 c d^2\right)}{9 e^9}-\frac{c d (d+e x)^8 \left(a e^2+c d^2\right)^3}{e^9}+\frac{(d+e x)^7 \left(a e^2+c d^2\right)^4}{7 e^9}+\frac{c^4 (d+e x)^{15}}{15 e^9}-\frac{4 c^4 d (d+e x)^{14}}{7 e^9}","\frac{2 c^2 (d+e x)^{11} \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)}{11 e^9}+\frac{4 c^3 (d+e x)^{13} \left(a e^2+7 c d^2\right)}{13 e^9}-\frac{2 c^3 d (d+e x)^{12} \left(3 a e^2+7 c d^2\right)}{3 e^9}-\frac{4 c^2 d (d+e x)^{10} \left(a e^2+c d^2\right) \left(3 a e^2+7 c d^2\right)}{5 e^9}+\frac{4 c (d+e x)^9 \left(a e^2+c d^2\right)^2 \left(a e^2+7 c d^2\right)}{9 e^9}-\frac{c d (d+e x)^8 \left(a e^2+c d^2\right)^3}{e^9}+\frac{(d+e x)^7 \left(a e^2+c d^2\right)^4}{7 e^9}+\frac{c^4 (d+e x)^{15}}{15 e^9}-\frac{4 c^4 d (d+e x)^{14}}{7 e^9}",1,"((c*d^2 + a*e^2)^4*(d + e*x)^7)/(7*e^9) - (c*d*(c*d^2 + a*e^2)^3*(d + e*x)^8)/e^9 + (4*c*(c*d^2 + a*e^2)^2*(7*c*d^2 + a*e^2)*(d + e*x)^9)/(9*e^9) - (4*c^2*d*(c*d^2 + a*e^2)*(7*c*d^2 + 3*a*e^2)*(d + e*x)^10)/(5*e^9) + (2*c^2*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)*(d + e*x)^11)/(11*e^9) - (2*c^3*d*(7*c*d^2 + 3*a*e^2)*(d + e*x)^12)/(3*e^9) + (4*c^3*(7*c*d^2 + a*e^2)*(d + e*x)^13)/(13*e^9) - (4*c^4*d*(d + e*x)^14)/(7*e^9) + (c^4*(d + e*x)^15)/(15*e^9)","A",2,1,17,0.05882,1,"{697}"
490,1,278,0,0.4069538,"\int (d+e x)^5 \left(a+c x^2\right)^4 \, dx","Int[(d + e*x)^5*(a + c*x^2)^4,x]","\frac{c^2 (d+e x)^{10} \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)}{5 e^9}+\frac{c^3 (d+e x)^{12} \left(a e^2+7 c d^2\right)}{3 e^9}-\frac{8 c^3 d (d+e x)^{11} \left(3 a e^2+7 c d^2\right)}{11 e^9}-\frac{8 c^2 d (d+e x)^9 \left(a e^2+c d^2\right) \left(3 a e^2+7 c d^2\right)}{9 e^9}+\frac{c (d+e x)^8 \left(a e^2+c d^2\right)^2 \left(a e^2+7 c d^2\right)}{2 e^9}-\frac{8 c d (d+e x)^7 \left(a e^2+c d^2\right)^3}{7 e^9}+\frac{(d+e x)^6 \left(a e^2+c d^2\right)^4}{6 e^9}+\frac{c^4 (d+e x)^{14}}{14 e^9}-\frac{8 c^4 d (d+e x)^{13}}{13 e^9}","\frac{c^2 (d+e x)^{10} \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)}{5 e^9}+\frac{c^3 (d+e x)^{12} \left(a e^2+7 c d^2\right)}{3 e^9}-\frac{8 c^3 d (d+e x)^{11} \left(3 a e^2+7 c d^2\right)}{11 e^9}-\frac{8 c^2 d (d+e x)^9 \left(a e^2+c d^2\right) \left(3 a e^2+7 c d^2\right)}{9 e^9}+\frac{c (d+e x)^8 \left(a e^2+c d^2\right)^2 \left(a e^2+7 c d^2\right)}{2 e^9}-\frac{8 c d (d+e x)^7 \left(a e^2+c d^2\right)^3}{7 e^9}+\frac{(d+e x)^6 \left(a e^2+c d^2\right)^4}{6 e^9}+\frac{c^4 (d+e x)^{14}}{14 e^9}-\frac{8 c^4 d (d+e x)^{13}}{13 e^9}",1,"((c*d^2 + a*e^2)^4*(d + e*x)^6)/(6*e^9) - (8*c*d*(c*d^2 + a*e^2)^3*(d + e*x)^7)/(7*e^9) + (c*(c*d^2 + a*e^2)^2*(7*c*d^2 + a*e^2)*(d + e*x)^8)/(2*e^9) - (8*c^2*d*(c*d^2 + a*e^2)*(7*c*d^2 + 3*a*e^2)*(d + e*x)^9)/(9*e^9) + (c^2*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)*(d + e*x)^10)/(5*e^9) - (8*c^3*d*(7*c*d^2 + 3*a*e^2)*(d + e*x)^11)/(11*e^9) + (c^3*(7*c*d^2 + a*e^2)*(d + e*x)^12)/(3*e^9) - (8*c^4*d*(d + e*x)^13)/(13*e^9) + (c^4*(d + e*x)^14)/(14*e^9)","A",2,1,17,0.05882,1,"{697}"
491,1,270,0,0.2523906,"\int (d+e x)^4 \left(a+c x^2\right)^4 \, dx","Int[(d + e*x)^4*(a + c*x^2)^4,x]","\frac{1}{9} c^2 x^9 \left(6 a^2 e^4+24 a c d^2 e^2+c^2 d^4\right)+\frac{4}{7} a c x^7 \left(a^2 e^4+9 a c d^2 e^2+c^2 d^4\right)+\frac{1}{5} a^2 x^5 \left(a^2 e^4+24 a c d^2 e^2+6 c^2 d^4\right)+3 a^2 c^2 d e^3 x^8+\frac{2}{3} a^3 d^2 x^3 \left(3 a e^2+2 c d^2\right)+\frac{8}{3} a^3 c d e^3 x^6+a^4 d^4 x+a^4 d e^3 x^4+\frac{2}{11} c^3 e^2 x^{11} \left(2 a e^2+3 c d^2\right)+\frac{8}{5} a c^3 d e^3 x^{10}+\frac{2 d^3 e \left(a+c x^2\right)^5}{5 c}+\frac{1}{3} c^4 d e^3 x^{12}+\frac{1}{13} c^4 e^4 x^{13}","\frac{1}{9} c^2 x^9 \left(6 a^2 e^4+24 a c d^2 e^2+c^2 d^4\right)+\frac{4}{7} a c x^7 \left(a^2 e^4+9 a c d^2 e^2+c^2 d^4\right)+\frac{1}{5} a^2 x^5 \left(a^2 e^4+24 a c d^2 e^2+6 c^2 d^4\right)+3 a^2 c^2 d e^3 x^8+\frac{2}{3} a^3 d^2 x^3 \left(3 a e^2+2 c d^2\right)+\frac{8}{3} a^3 c d e^3 x^6+a^4 d^4 x+a^4 d e^3 x^4+\frac{2}{11} c^3 e^2 x^{11} \left(2 a e^2+3 c d^2\right)+\frac{8}{5} a c^3 d e^3 x^{10}+\frac{2 d^3 e \left(a+c x^2\right)^5}{5 c}+\frac{1}{3} c^4 d e^3 x^{12}+\frac{1}{13} c^4 e^4 x^{13}",1,"a^4*d^4*x + (2*a^3*d^2*(2*c*d^2 + 3*a*e^2)*x^3)/3 + a^4*d*e^3*x^4 + (a^2*(6*c^2*d^4 + 24*a*c*d^2*e^2 + a^2*e^4)*x^5)/5 + (8*a^3*c*d*e^3*x^6)/3 + (4*a*c*(c^2*d^4 + 9*a*c*d^2*e^2 + a^2*e^4)*x^7)/7 + 3*a^2*c^2*d*e^3*x^8 + (c^2*(c^2*d^4 + 24*a*c*d^2*e^2 + 6*a^2*e^4)*x^9)/9 + (8*a*c^3*d*e^3*x^10)/5 + (2*c^3*e^2*(3*c*d^2 + 2*a*e^2)*x^11)/11 + (c^4*d*e^3*x^12)/3 + (c^4*e^4*x^13)/13 + (2*d^3*e*(a + c*x^2)^5)/(5*c)","A",3,2,17,0.1176,1,"{696, 1810}"
492,1,209,0,0.1917293,"\int (d+e x)^3 \left(a+c x^2\right)^4 \, dx","Int[(d + e*x)^3*(a + c*x^2)^4,x]","\frac{3}{4} a^2 c^2 e^3 x^8+\frac{6}{5} a^2 c d x^5 \left(2 a e^2+c d^2\right)+\frac{1}{3} a^3 d x^3 \left(3 a e^2+4 c d^2\right)+\frac{2}{3} a^3 c e^3 x^6+a^4 d^3 x+\frac{1}{4} a^4 e^3 x^4+\frac{1}{9} c^3 d x^9 \left(12 a e^2+c d^2\right)+\frac{2}{7} a c^2 d x^7 \left(9 a e^2+2 c d^2\right)+\frac{2}{5} a c^3 e^3 x^{10}+\frac{3 d^2 e \left(a+c x^2\right)^5}{10 c}+\frac{3}{11} c^4 d e^2 x^{11}+\frac{1}{12} c^4 e^3 x^{12}","\frac{3}{4} a^2 c^2 e^3 x^8+\frac{6}{5} a^2 c d x^5 \left(2 a e^2+c d^2\right)+\frac{1}{3} a^3 d x^3 \left(3 a e^2+4 c d^2\right)+\frac{2}{3} a^3 c e^3 x^6+a^4 d^3 x+\frac{1}{4} a^4 e^3 x^4+\frac{1}{9} c^3 d x^9 \left(12 a e^2+c d^2\right)+\frac{2}{7} a c^2 d x^7 \left(9 a e^2+2 c d^2\right)+\frac{2}{5} a c^3 e^3 x^{10}+\frac{3 d^2 e \left(a+c x^2\right)^5}{10 c}+\frac{3}{11} c^4 d e^2 x^{11}+\frac{1}{12} c^4 e^3 x^{12}",1,"a^4*d^3*x + (a^3*d*(4*c*d^2 + 3*a*e^2)*x^3)/3 + (a^4*e^3*x^4)/4 + (6*a^2*c*d*(c*d^2 + 2*a*e^2)*x^5)/5 + (2*a^3*c*e^3*x^6)/3 + (2*a*c^2*d*(2*c*d^2 + 9*a*e^2)*x^7)/7 + (3*a^2*c^2*e^3*x^8)/4 + (c^3*d*(c*d^2 + 12*a*e^2)*x^9)/9 + (2*a*c^3*e^3*x^10)/5 + (3*c^4*d*e^2*x^11)/11 + (c^4*e^3*x^12)/12 + (3*d^2*e*(a + c*x^2)^5)/(10*c)","A",3,2,17,0.1176,1,"{696, 1810}"
493,1,132,0,0.0951265,"\int (d+e x)^2 \left(a+c x^2\right)^4 \, dx","Int[(d + e*x)^2*(a + c*x^2)^4,x]","\frac{2}{5} a^2 c x^5 \left(2 a e^2+3 c d^2\right)+\frac{1}{3} a^3 x^3 \left(a e^2+4 c d^2\right)+a^4 d^2 x+\frac{1}{9} c^3 x^9 \left(4 a e^2+c d^2\right)+\frac{2}{7} a c^2 x^7 \left(3 a e^2+2 c d^2\right)+\frac{d e \left(a+c x^2\right)^5}{5 c}+\frac{1}{11} c^4 e^2 x^{11}","\frac{2}{5} a^2 c x^5 \left(2 a e^2+3 c d^2\right)+\frac{1}{3} a^3 x^3 \left(a e^2+4 c d^2\right)+a^4 d^2 x+\frac{1}{9} c^3 x^9 \left(4 a e^2+c d^2\right)+\frac{2}{7} a c^2 x^7 \left(3 a e^2+2 c d^2\right)+\frac{d e \left(a+c x^2\right)^5}{5 c}+\frac{1}{11} c^4 e^2 x^{11}",1,"a^4*d^2*x + (a^3*(4*c*d^2 + a*e^2)*x^3)/3 + (2*a^2*c*(3*c*d^2 + 2*a*e^2)*x^5)/5 + (2*a*c^2*(2*c*d^2 + 3*a*e^2)*x^7)/7 + (c^3*(c*d^2 + 4*a*e^2)*x^9)/9 + (c^4*e^2*x^11)/11 + (d*e*(a + c*x^2)^5)/(5*c)","A",3,2,17,0.1176,1,"{696, 1810}"
494,1,73,0,0.0288876,"\int (d+e x) \left(a+c x^2\right)^4 \, dx","Int[(d + e*x)*(a + c*x^2)^4,x]","\frac{6}{5} a^2 c^2 d x^5+\frac{4}{3} a^3 c d x^3+a^4 d x+\frac{4}{7} a c^3 d x^7+\frac{e \left(a+c x^2\right)^5}{10 c}+\frac{1}{9} c^4 d x^9","\frac{6}{5} a^2 c^2 d x^5+\frac{4}{3} a^3 c d x^3+a^4 d x+\frac{4}{7} a c^3 d x^7+\frac{e \left(a+c x^2\right)^5}{10 c}+\frac{1}{9} c^4 d x^9",1,"a^4*d*x + (4*a^3*c*d*x^3)/3 + (6*a^2*c^2*d*x^5)/5 + (4*a*c^3*d*x^7)/7 + (c^4*d*x^9)/9 + (e*(a + c*x^2)^5)/(10*c)","A",3,2,15,0.1333,1,"{641, 194}"
495,1,264,0,0.2807777,"\int \frac{\left(a+c x^2\right)^4}{d+e x} \, dx","Int[(a + c*x^2)^4/(d + e*x),x]","\frac{c^2 (d+e x)^4 \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)}{2 e^9}+\frac{2 c^3 (d+e x)^6 \left(a e^2+7 c d^2\right)}{3 e^9}-\frac{8 c^3 d (d+e x)^5 \left(3 a e^2+7 c d^2\right)}{5 e^9}-\frac{8 c^2 d (d+e x)^3 \left(a e^2+c d^2\right) \left(3 a e^2+7 c d^2\right)}{3 e^9}+\frac{2 c (d+e x)^2 \left(a e^2+c d^2\right)^2 \left(a e^2+7 c d^2\right)}{e^9}-\frac{8 c d x \left(a e^2+c d^2\right)^3}{e^8}+\frac{\left(a e^2+c d^2\right)^4 \log (d+e x)}{e^9}+\frac{c^4 (d+e x)^8}{8 e^9}-\frac{8 c^4 d (d+e x)^7}{7 e^9}","\frac{c^2 (d+e x)^4 \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)}{2 e^9}+\frac{2 c^3 (d+e x)^6 \left(a e^2+7 c d^2\right)}{3 e^9}-\frac{8 c^3 d (d+e x)^5 \left(3 a e^2+7 c d^2\right)}{5 e^9}-\frac{8 c^2 d (d+e x)^3 \left(a e^2+c d^2\right) \left(3 a e^2+7 c d^2\right)}{3 e^9}+\frac{2 c (d+e x)^2 \left(a e^2+c d^2\right)^2 \left(a e^2+7 c d^2\right)}{e^9}-\frac{8 c d x \left(a e^2+c d^2\right)^3}{e^8}+\frac{\left(a e^2+c d^2\right)^4 \log (d+e x)}{e^9}+\frac{c^4 (d+e x)^8}{8 e^9}-\frac{8 c^4 d (d+e x)^7}{7 e^9}",1,"(-8*c*d*(c*d^2 + a*e^2)^3*x)/e^8 + (2*c*(c*d^2 + a*e^2)^2*(7*c*d^2 + a*e^2)*(d + e*x)^2)/e^9 - (8*c^2*d*(c*d^2 + a*e^2)*(7*c*d^2 + 3*a*e^2)*(d + e*x)^3)/(3*e^9) + (c^2*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)*(d + e*x)^4)/(2*e^9) - (8*c^3*d*(7*c*d^2 + 3*a*e^2)*(d + e*x)^5)/(5*e^9) + (2*c^3*(7*c*d^2 + a*e^2)*(d + e*x)^6)/(3*e^9) - (8*c^4*d*(d + e*x)^7)/(7*e^9) + (c^4*(d + e*x)^8)/(8*e^9) + ((c*d^2 + a*e^2)^4*Log[d + e*x])/e^9","A",2,1,17,0.05882,1,"{697}"
496,1,255,0,0.2553205,"\int \frac{\left(a+c x^2\right)^4}{(d+e x)^2} \, dx","Int[(a + c*x^2)^4/(d + e*x)^2,x]","\frac{c^2 x^3 \left(6 a^2 e^4+12 a c d^2 e^2+5 c^2 d^4\right)}{3 e^6}-\frac{c^2 d x^2 \left(6 a^2 e^4+8 a c d^2 e^2+3 c^2 d^4\right)}{e^7}+\frac{c x \left(18 a^2 c d^2 e^4+4 a^3 e^6+20 a c^2 d^4 e^2+7 c^3 d^6\right)}{e^8}+\frac{c^3 x^5 \left(4 a e^2+3 c d^2\right)}{5 e^4}-\frac{c^3 d x^4 \left(2 a e^2+c d^2\right)}{e^5}-\frac{\left(a e^2+c d^2\right)^4}{e^9 (d+e x)}-\frac{8 c d \left(a e^2+c d^2\right)^3 \log (d+e x)}{e^9}-\frac{c^4 d x^6}{3 e^3}+\frac{c^4 x^7}{7 e^2}","\frac{c^2 x^3 \left(6 a^2 e^4+12 a c d^2 e^2+5 c^2 d^4\right)}{3 e^6}-\frac{c^2 d x^2 \left(6 a^2 e^4+8 a c d^2 e^2+3 c^2 d^4\right)}{e^7}+\frac{c x \left(18 a^2 c d^2 e^4+4 a^3 e^6+20 a c^2 d^4 e^2+7 c^3 d^6\right)}{e^8}+\frac{c^3 x^5 \left(4 a e^2+3 c d^2\right)}{5 e^4}-\frac{c^3 d x^4 \left(2 a e^2+c d^2\right)}{e^5}-\frac{\left(a e^2+c d^2\right)^4}{e^9 (d+e x)}-\frac{8 c d \left(a e^2+c d^2\right)^3 \log (d+e x)}{e^9}-\frac{c^4 d x^6}{3 e^3}+\frac{c^4 x^7}{7 e^2}",1,"(c*(7*c^3*d^6 + 20*a*c^2*d^4*e^2 + 18*a^2*c*d^2*e^4 + 4*a^3*e^6)*x)/e^8 - (c^2*d*(3*c^2*d^4 + 8*a*c*d^2*e^2 + 6*a^2*e^4)*x^2)/e^7 + (c^2*(5*c^2*d^4 + 12*a*c*d^2*e^2 + 6*a^2*e^4)*x^3)/(3*e^6) - (c^3*d*(c*d^2 + 2*a*e^2)*x^4)/e^5 + (c^3*(3*c*d^2 + 4*a*e^2)*x^5)/(5*e^4) - (c^4*d*x^6)/(3*e^3) + (c^4*x^7)/(7*e^2) - (c*d^2 + a*e^2)^4/(e^9*(d + e*x)) - (8*c*d*(c*d^2 + a*e^2)^3*Log[d + e*x])/e^9","A",2,1,17,0.05882,1,"{697}"
497,1,73,0,0.0306908,"\int (c+d x) \left(a+b x^2\right)^4 \, dx","Int[(c + d*x)*(a + b*x^2)^4,x]","\frac{6}{5} a^2 b^2 c x^5+\frac{4}{3} a^3 b c x^3+a^4 c x+\frac{4}{7} a b^3 c x^7+\frac{d \left(a+b x^2\right)^5}{10 b}+\frac{1}{9} b^4 c x^9","\frac{6}{5} a^2 b^2 c x^5+\frac{4}{3} a^3 b c x^3+a^4 c x+\frac{4}{7} a b^3 c x^7+\frac{d \left(a+b x^2\right)^5}{10 b}+\frac{1}{9} b^4 c x^9",1,"a^4*c*x + (4*a^3*b*c*x^3)/3 + (6*a^2*b^2*c*x^5)/5 + (4*a*b^3*c*x^7)/7 + (b^4*c*x^9)/9 + (d*(a + b*x^2)^5)/(10*b)","A",3,2,15,0.1333,1,"{641, 194}"
498,1,123,0,0.0968408,"\int \frac{(d+e x)^4}{a+c x^2} \, dx","Int[(d + e*x)^4/(a + c*x^2),x]","\frac{\left(a^2 e^4-6 a c d^2 e^2+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} c^{5/2}}+\frac{2 d e \left(c d^2-a e^2\right) \log \left(a+c x^2\right)}{c^2}+\frac{e^2 x \left(6 c d^2-a e^2\right)}{c^2}+\frac{2 d e^3 x^2}{c}+\frac{e^4 x^3}{3 c}","\frac{\left(a^2 e^4-6 a c d^2 e^2+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} c^{5/2}}+\frac{2 d e \left(c d^2-a e^2\right) \log \left(a+c x^2\right)}{c^2}+\frac{e^2 x \left(6 c d^2-a e^2\right)}{c^2}+\frac{2 d e^3 x^2}{c}+\frac{e^4 x^3}{3 c}",1,"(e^2*(6*c*d^2 - a*e^2)*x)/c^2 + (2*d*e^3*x^2)/c + (e^4*x^3)/(3*c) + ((c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(5/2)) + (2*d*e*(c*d^2 - a*e^2)*Log[a + c*x^2])/c^2","A",5,4,17,0.2353,1,"{702, 635, 205, 260}"
499,1,90,0,0.0745295,"\int \frac{(d+e x)^3}{a+c x^2} \, dx","Int[(d + e*x)^3/(a + c*x^2),x]","\frac{e \left(3 c d^2-a e^2\right) \log \left(a+c x^2\right)}{2 c^2}+\frac{d \left(c d^2-3 a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} c^{3/2}}+\frac{3 d e^2 x}{c}+\frac{e^3 x^2}{2 c}","\frac{e \left(3 c d^2-a e^2\right) \log \left(a+c x^2\right)}{2 c^2}+\frac{d \left(c d^2-3 a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} c^{3/2}}+\frac{3 d e^2 x}{c}+\frac{e^3 x^2}{2 c}",1,"(3*d*e^2*x)/c + (e^3*x^2)/(2*c) + (d*(c*d^2 - 3*a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(3/2)) + (e*(3*c*d^2 - a*e^2)*Log[a + c*x^2])/(2*c^2)","A",5,4,17,0.2353,1,"{702, 635, 205, 260}"
500,1,59,0,0.0509034,"\int \frac{(d+e x)^2}{a+c x^2} \, dx","Int[(d + e*x)^2/(a + c*x^2),x]","\frac{\left(c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} c^{3/2}}+\frac{d e \log \left(a+c x^2\right)}{c}+\frac{e^2 x}{c}","\frac{\left(c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} c^{3/2}}+\frac{d e \log \left(a+c x^2\right)}{c}+\frac{e^2 x}{c}",1,"(e^2*x)/c + ((c*d^2 - a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(3/2)) + (d*e*Log[a + c*x^2])/c","A",5,4,17,0.2353,1,"{702, 635, 205, 260}"
501,1,42,0,0.0152003,"\int \frac{d+e x}{a+c x^2} \, dx","Int[(d + e*x)/(a + c*x^2),x]","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}+\frac{e \log \left(a+c x^2\right)}{2 c}","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}+\frac{e \log \left(a+c x^2\right)}{2 c}",1,"(d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[c]) + (e*Log[a + c*x^2])/(2*c)","A",3,3,15,0.2000,1,"{635, 205, 260}"
502,1,86,0,0.0380176,"\int \frac{1}{(d+e x) \left(a+c x^2\right)} \, dx","Int[1/((d + e*x)*(a + c*x^2)),x]","-\frac{e \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)}+\frac{e \log (d+e x)}{a e^2+c d^2}+\frac{\sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \left(a e^2+c d^2\right)}","-\frac{e \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)}+\frac{e \log (d+e x)}{a e^2+c d^2}+\frac{\sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \left(a e^2+c d^2\right)}",1,"(Sqrt[c]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*(c*d^2 + a*e^2)) + (e*Log[d + e*x])/(c*d^2 + a*e^2) - (e*Log[a + c*x^2])/(2*(c*d^2 + a*e^2))","A",5,5,17,0.2941,1,"{706, 31, 635, 205, 260}"
503,1,123,0,0.1026225,"\int \frac{1}{(d+e x)^2 \left(a+c x^2\right)} \, dx","Int[1/((d + e*x)^2*(a + c*x^2)),x]","-\frac{c d e \log \left(a+c x^2\right)}{\left(a e^2+c d^2\right)^2}-\frac{e}{(d+e x) \left(a e^2+c d^2\right)}+\frac{2 c d e \log (d+e x)}{\left(a e^2+c d^2\right)^2}+\frac{\sqrt{c} \left(c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \left(a e^2+c d^2\right)^2}","-\frac{c d e \log \left(a+c x^2\right)}{\left(a e^2+c d^2\right)^2}-\frac{e}{(d+e x) \left(a e^2+c d^2\right)}+\frac{2 c d e \log (d+e x)}{\left(a e^2+c d^2\right)^2}+\frac{\sqrt{c} \left(c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \left(a e^2+c d^2\right)^2}",1,"-(e/((c*d^2 + a*e^2)*(d + e*x))) + (Sqrt[c]*(c*d^2 - a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*(c*d^2 + a*e^2)^2) + (2*c*d*e*Log[d + e*x])/(c*d^2 + a*e^2)^2 - (c*d*e*Log[a + c*x^2])/(c*d^2 + a*e^2)^2","A",6,5,17,0.2941,1,"{710, 801, 635, 205, 260}"
504,1,176,0,0.1661544,"\int \frac{1}{(d+e x)^3 \left(a+c x^2\right)} \, dx","Int[1/((d + e*x)^3*(a + c*x^2)),x]","\frac{c^{3/2} d \left(c d^2-3 a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \left(a e^2+c d^2\right)^3}-\frac{c e \left(3 c d^2-a e^2\right) \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)^3}-\frac{2 c d e}{(d+e x) \left(a e^2+c d^2\right)^2}-\frac{e}{2 (d+e x)^2 \left(a e^2+c d^2\right)}+\frac{c e \left(3 c d^2-a e^2\right) \log (d+e x)}{\left(a e^2+c d^2\right)^3}","\frac{c^{3/2} d \left(c d^2-3 a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \left(a e^2+c d^2\right)^3}-\frac{c e \left(3 c d^2-a e^2\right) \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)^3}-\frac{2 c d e}{(d+e x) \left(a e^2+c d^2\right)^2}-\frac{e}{2 (d+e x)^2 \left(a e^2+c d^2\right)}+\frac{c e \left(3 c d^2-a e^2\right) \log (d+e x)}{\left(a e^2+c d^2\right)^3}",1,"-e/(2*(c*d^2 + a*e^2)*(d + e*x)^2) - (2*c*d*e)/((c*d^2 + a*e^2)^2*(d + e*x)) + (c^(3/2)*d*(c*d^2 - 3*a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*(c*d^2 + a*e^2)^3) + (c*e*(3*c*d^2 - a*e^2)*Log[d + e*x])/(c*d^2 + a*e^2)^3 - (c*e*(3*c*d^2 - a*e^2)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^3)","A",6,5,17,0.2941,1,"{710, 801, 635, 205, 260}"
505,1,190,0,0.1769792,"\int \frac{(d+e x)^5}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^5/(a + c*x^2)^2,x]","\frac{d \left(-15 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{5/2}}-\frac{e^3 x^2 \left(2 c d^2-a e^2\right)}{a c^2}+\frac{e^3 \left(5 c d^2-a e^2\right) \log \left(a+c x^2\right)}{c^3}-\frac{3 d e^2 x \left(2 c d^2-5 a e^2\right)}{2 a c^2}-\frac{d e^4 x^3}{2 a c}-\frac{(d+e x)^4 (a e-c d x)}{2 a c \left(a+c x^2\right)}","\frac{d \left(-15 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{5/2}}-\frac{e^3 x^2 \left(2 c d^2-a e^2\right)}{a c^2}+\frac{e^3 \left(5 c d^2-a e^2\right) \log \left(a+c x^2\right)}{c^3}-\frac{3 d e^2 x \left(2 c d^2-5 a e^2\right)}{2 a c^2}-\frac{d e^4 x^3}{2 a c}-\frac{(d+e x)^4 (a e-c d x)}{2 a c \left(a+c x^2\right)}",1,"(-3*d*e^2*(2*c*d^2 - 5*a*e^2)*x)/(2*a*c^2) - (e^3*(2*c*d^2 - a*e^2)*x^2)/(a*c^2) - (d*e^4*x^3)/(2*a*c) - ((a*e - c*d*x)*(d + e*x)^4)/(2*a*c*(a + c*x^2)) + (d*(c^2*d^4 + 10*a*c*d^2*e^2 - 15*a^2*e^4)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(5/2)) + (e^3*(5*c*d^2 - a*e^2)*Log[a + c*x^2])/c^3","A",6,5,17,0.2941,1,"{739, 801, 635, 205, 260}"
506,1,149,0,0.1202469,"\int \frac{(d+e x)^4}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^4/(a + c*x^2)^2,x]","\frac{\left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{5/2}}-\frac{3 e^2 x \left(c d^2-a e^2\right)}{2 a c^2}+\frac{2 d e^3 \log \left(a+c x^2\right)}{c^2}-\frac{d e^3 x^2}{2 a c}-\frac{(d+e x)^3 (a e-c d x)}{2 a c \left(a+c x^2\right)}","\frac{\left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{5/2}}-\frac{3 e^2 x \left(c d^2-a e^2\right)}{2 a c^2}+\frac{2 d e^3 \log \left(a+c x^2\right)}{c^2}-\frac{d e^3 x^2}{2 a c}-\frac{(d+e x)^3 (a e-c d x)}{2 a c \left(a+c x^2\right)}",1,"(-3*e^2*(c*d^2 - a*e^2)*x)/(2*a*c^2) - (d*e^3*x^2)/(2*a*c) - ((a*e - c*d*x)*(d + e*x)^3)/(2*a*c*(a + c*x^2)) + ((c^2*d^4 + 6*a*c*d^2*e^2 - 3*a^2*e^4)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(5/2)) + (2*d*e^3*Log[a + c*x^2])/c^2","A",6,5,17,0.2941,1,"{739, 801, 635, 205, 260}"
507,1,109,0,0.080895,"\int \frac{(d+e x)^3}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^3/(a + c*x^2)^2,x]","\frac{d \left(3 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{3/2}}+\frac{e^3 \log \left(a+c x^2\right)}{2 c^2}-\frac{d e^2 x}{2 a c}-\frac{(d+e x)^2 (a e-c d x)}{2 a c \left(a+c x^2\right)}","\frac{d \left(3 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{3/2}}+\frac{e^3 \log \left(a+c x^2\right)}{2 c^2}-\frac{d e^2 x}{2 a c}-\frac{(d+e x)^2 (a e-c d x)}{2 a c \left(a+c x^2\right)}",1,"-(d*e^2*x)/(2*a*c) - ((a*e - c*d*x)*(d + e*x)^2)/(2*a*c*(a + c*x^2)) + (d*(c*d^2 + 3*a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(3/2)) + (e^3*Log[a + c*x^2])/(2*c^2)","A",5,5,17,0.2941,1,"{739, 774, 635, 205, 260}"
508,1,72,0,0.0210555,"\int \frac{(d+e x)^2}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^2/(a + c*x^2)^2,x]","\frac{\left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{3/2}}-\frac{(d+e x) (a e-c d x)}{2 a c \left(a+c x^2\right)}","\frac{\left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{3/2}}-\frac{(d+e x) (a e-c d x)}{2 a c \left(a+c x^2\right)}",1,"-((a*e - c*d*x)*(d + e*x))/(2*a*c*(a + c*x^2)) + ((c*d^2 + a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(3/2))","A",2,2,17,0.1176,1,"{723, 205}"
509,1,57,0,0.0136079,"\int \frac{d+e x}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)/(a + c*x^2)^2,x]","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}-\frac{a e-c d x}{2 a c \left(a+c x^2\right)}","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}-\frac{a e-c d x}{2 a c \left(a+c x^2\right)}",1,"-(a*e - c*d*x)/(2*a*c*(a + c*x^2)) + (d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[c])","A",2,2,15,0.1333,1,"{639, 205}"
510,1,142,0,0.1259044,"\int \frac{1}{(d+e x) \left(a+c x^2\right)^2} \, dx","Int[1/((d + e*x)*(a + c*x^2)^2),x]","\frac{\sqrt{c} d \left(3 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}-\frac{e^3 \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{e^3 \log (d+e x)}{\left(a e^2+c d^2\right)^2}","\frac{\sqrt{c} d \left(3 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}-\frac{e^3 \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{e^3 \log (d+e x)}{\left(a e^2+c d^2\right)^2}",1,"(a*e + c*d*x)/(2*a*(c*d^2 + a*e^2)*(a + c*x^2)) + (Sqrt[c]*d*(c*d^2 + 3*a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*(c*d^2 + a*e^2)^2) + (e^3*Log[d + e*x])/(c*d^2 + a*e^2)^2 - (e^3*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^2)","A",6,5,17,0.2941,1,"{741, 801, 635, 205, 260}"
511,1,205,0,0.1894607,"\int \frac{1}{(d+e x)^2 \left(a+c x^2\right)^2} \, dx","Int[1/((d + e*x)^2*(a + c*x^2)^2),x]","\frac{\sqrt{c} \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \left(a e^2+c d^2\right)^3}+\frac{a e+c d x}{2 a \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)}-\frac{2 c d e^3 \log \left(a+c x^2\right)}{\left(a e^2+c d^2\right)^3}+\frac{e \left(c d^2-3 a e^2\right)}{2 a (d+e x) \left(a e^2+c d^2\right)^2}+\frac{4 c d e^3 \log (d+e x)}{\left(a e^2+c d^2\right)^3}","\frac{\sqrt{c} \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \left(a e^2+c d^2\right)^3}+\frac{a e+c d x}{2 a \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)}-\frac{2 c d e^3 \log \left(a+c x^2\right)}{\left(a e^2+c d^2\right)^3}+\frac{e \left(c d^2-3 a e^2\right)}{2 a (d+e x) \left(a e^2+c d^2\right)^2}+\frac{4 c d e^3 \log (d+e x)}{\left(a e^2+c d^2\right)^3}",1,"(e*(c*d^2 - 3*a*e^2))/(2*a*(c*d^2 + a*e^2)^2*(d + e*x)) + (a*e + c*d*x)/(2*a*(c*d^2 + a*e^2)*(d + e*x)*(a + c*x^2)) + (Sqrt[c]*(c^2*d^4 + 6*a*c*d^2*e^2 - 3*a^2*e^4)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*(c*d^2 + a*e^2)^3) + (4*c*d*e^3*Log[d + e*x])/(c*d^2 + a*e^2)^3 - (2*c*d*e^3*Log[a + c*x^2])/(c*d^2 + a*e^2)^3","A",6,5,17,0.2941,1,"{741, 801, 635, 205, 260}"
512,1,198,0,0.1854419,"\int \frac{(d+e x)^5}{\left(a+c x^2\right)^3} \, dx","Int[(d + e*x)^5/(a + c*x^2)^3,x]","-\frac{(d+e x)^2 \left(2 a e \left(2 a e^2+c d^2\right)-c d x \left(5 a e^2+3 c d^2\right)\right)}{8 a^2 c^2 \left(a+c x^2\right)}-\frac{d e^2 x \left(7 a e^2+3 c d^2\right)}{8 a^2 c^2}+\frac{d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{5/2}}+\frac{e^5 \log \left(a+c x^2\right)}{2 c^3}-\frac{(d+e x)^4 (a e-c d x)}{4 a c \left(a+c x^2\right)^2}","-\frac{(d+e x)^2 \left(2 a e \left(2 a e^2+c d^2\right)-c d x \left(5 a e^2+3 c d^2\right)\right)}{8 a^2 c^2 \left(a+c x^2\right)}-\frac{d e^2 x \left(7 a e^2+3 c d^2\right)}{8 a^2 c^2}+\frac{d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{5/2}}+\frac{e^5 \log \left(a+c x^2\right)}{2 c^3}-\frac{(d+e x)^4 (a e-c d x)}{4 a c \left(a+c x^2\right)^2}",1,"-(d*e^2*(3*c*d^2 + 7*a*e^2)*x)/(8*a^2*c^2) - ((a*e - c*d*x)*(d + e*x)^4)/(4*a*c*(a + c*x^2)^2) - ((d + e*x)^2*(2*a*e*(c*d^2 + 2*a*e^2) - c*d*(3*c*d^2 + 5*a*e^2)*x))/(8*a^2*c^2*(a + c*x^2)) + (d*(3*c^2*d^4 + 10*a*c*d^2*e^2 + 15*a^2*e^4)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(5/2)) + (e^5*Log[a + c*x^2])/(2*c^3)","A",6,6,17,0.3529,1,"{739, 819, 774, 635, 205, 260}"
513,1,120,0,0.0479793,"\int \frac{(d+e x)^4}{\left(a+c x^2\right)^3} \, dx","Int[(d + e*x)^4/(a + c*x^2)^3,x]","-\frac{3 (d+e x) \left(a e^2+c d^2\right) (a e-c d x)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{3 \left(a e^2+c d^2\right)^2 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{5/2}}-\frac{(d+e x)^3 (a e-c d x)}{4 a c \left(a+c x^2\right)^2}","-\frac{3 (d+e x) \left(a e^2+c d^2\right) (a e-c d x)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{3 \left(a e^2+c d^2\right)^2 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{5/2}}-\frac{(d+e x)^3 (a e-c d x)}{4 a c \left(a+c x^2\right)^2}",1,"-((a*e - c*d*x)*(d + e*x)^3)/(4*a*c*(a + c*x^2)^2) - (3*(c*d^2 + a*e^2)*(a*e - c*d*x)*(d + e*x))/(8*a^2*c^2*(a + c*x^2)) + (3*(c*d^2 + a*e^2)^2*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(5/2))","A",3,2,17,0.1176,1,"{723, 205}"
514,1,98,0,0.0380723,"\int \frac{(d+e x)^3}{\left(a+c x^2\right)^3} \, dx","Int[(d + e*x)^3/(a + c*x^2)^3,x]","\frac{3 d \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{3/2}}-\frac{3 d (d+e x) (a e-c d x)}{8 a^2 c \left(a+c x^2\right)}+\frac{x (d+e x)^3}{4 a \left(a+c x^2\right)^2}","\frac{3 d \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{3/2}}-\frac{3 d (d+e x) (a e-c d x)}{8 a^2 c \left(a+c x^2\right)}+\frac{x (d+e x)^3}{4 a \left(a+c x^2\right)^2}",1,"(x*(d + e*x)^3)/(4*a*(a + c*x^2)^2) - (3*d*(a*e - c*d*x)*(d + e*x))/(8*a^2*c*(a + c*x^2)) + (3*d*(c*d^2 + a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(3/2))","A",3,3,17,0.1765,1,"{729, 723, 205}"
515,1,113,0,0.0493133,"\int \frac{(d+e x)^2}{\left(a+c x^2\right)^3} \, dx","Int[(d + e*x)^2/(a + c*x^2)^3,x]","\frac{\left(a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{3/2}}-\frac{2 a d e-x \left(a e^2+3 c d^2\right)}{8 a^2 c \left(a+c x^2\right)}-\frac{(d+e x) (a e-c d x)}{4 a c \left(a+c x^2\right)^2}","\frac{\left(a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{3/2}}-\frac{2 a d e-x \left(a e^2+3 c d^2\right)}{8 a^2 c \left(a+c x^2\right)}-\frac{(d+e x) (a e-c d x)}{4 a c \left(a+c x^2\right)^2}",1,"-((a*e - c*d*x)*(d + e*x))/(4*a*c*(a + c*x^2)^2) - (2*a*d*e - (3*c*d^2 + a*e^2)*x)/(8*a^2*c*(a + c*x^2)) + ((3*c*d^2 + a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(3/2))","A",3,3,17,0.1765,1,"{739, 639, 205}"
516,1,75,0,0.0197236,"\int \frac{d+e x}{\left(a+c x^2\right)^3} \, dx","Int[(d + e*x)/(a + c*x^2)^3,x]","\frac{3 d x}{8 a^2 \left(a+c x^2\right)}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}-\frac{a e-c d x}{4 a c \left(a+c x^2\right)^2}","\frac{3 d x}{8 a^2 \left(a+c x^2\right)}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}-\frac{a e-c d x}{4 a c \left(a+c x^2\right)^2}",1,"-(a*e - c*d*x)/(4*a*c*(a + c*x^2)^2) + (3*d*x)/(8*a^2*(a + c*x^2)) + (3*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[c])","A",3,3,15,0.2000,1,"{639, 199, 205}"
517,1,212,0,0.2207949,"\int \frac{1}{(d+e x) \left(a+c x^2\right)^3} \, dx","Int[1/((d + e*x)*(a + c*x^2)^3),x]","\frac{\sqrt{c} d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \left(a e^2+c d^2\right)^3}+\frac{4 a^2 e^3+c d x \left(7 a e^2+3 c d^2\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)}-\frac{e^5 \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)^3}+\frac{e^5 \log (d+e x)}{\left(a e^2+c d^2\right)^3}","\frac{\sqrt{c} d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \left(a e^2+c d^2\right)^3}+\frac{4 a^2 e^3+c d x \left(7 a e^2+3 c d^2\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)}-\frac{e^5 \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)^3}+\frac{e^5 \log (d+e x)}{\left(a e^2+c d^2\right)^3}",1,"(a*e + c*d*x)/(4*a*(c*d^2 + a*e^2)*(a + c*x^2)^2) + (4*a^2*e^3 + c*d*(3*c*d^2 + 7*a*e^2)*x)/(8*a^2*(c*d^2 + a*e^2)^2*(a + c*x^2)) + (Sqrt[c]*d*(3*c^2*d^4 + 10*a*c*d^2*e^2 + 15*a^2*e^4)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*(c*d^2 + a*e^2)^3) + (e^5*Log[d + e*x])/(c*d^2 + a*e^2)^3 - (e^5*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^3)","A",7,6,17,0.3529,1,"{741, 823, 801, 635, 205, 260}"
518,1,300,0,0.3568341,"\int \frac{1}{(d+e x)^2 \left(a+c x^2\right)^3} \, dx","Int[1/((d + e*x)^2*(a + c*x^2)^3),x]","\frac{3 \sqrt{c} \left(15 a^2 c d^2 e^4-5 a^3 e^6+5 a c^2 d^4 e^2+c^3 d^6\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \left(a e^2+c d^2\right)^4}-\frac{a e \left(c d^2-5 a e^2\right)-3 c d x \left(3 a e^2+c d^2\right)}{8 a^2 \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)^2}+\frac{3 e \left(c d^2-a e^2\right) \left(5 a e^2+c d^2\right)}{8 a^2 (d+e x) \left(a e^2+c d^2\right)^3}+\frac{a e+c d x}{4 a \left(a+c x^2\right)^2 (d+e x) \left(a e^2+c d^2\right)}-\frac{3 c d e^5 \log \left(a+c x^2\right)}{\left(a e^2+c d^2\right)^4}+\frac{6 c d e^5 \log (d+e x)}{\left(a e^2+c d^2\right)^4}","\frac{3 \sqrt{c} \left(15 a^2 c d^2 e^4-5 a^3 e^6+5 a c^2 d^4 e^2+c^3 d^6\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \left(a e^2+c d^2\right)^4}-\frac{a e \left(c d^2-5 a e^2\right)-3 c d x \left(3 a e^2+c d^2\right)}{8 a^2 \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)^2}+\frac{3 e \left(c d^2-a e^2\right) \left(5 a e^2+c d^2\right)}{8 a^2 (d+e x) \left(a e^2+c d^2\right)^3}+\frac{a e+c d x}{4 a \left(a+c x^2\right)^2 (d+e x) \left(a e^2+c d^2\right)}-\frac{3 c d e^5 \log \left(a+c x^2\right)}{\left(a e^2+c d^2\right)^4}+\frac{6 c d e^5 \log (d+e x)}{\left(a e^2+c d^2\right)^4}",1,"(3*e*(c*d^2 - a*e^2)*(c*d^2 + 5*a*e^2))/(8*a^2*(c*d^2 + a*e^2)^3*(d + e*x)) + (a*e + c*d*x)/(4*a*(c*d^2 + a*e^2)*(d + e*x)*(a + c*x^2)^2) - (a*e*(c*d^2 - 5*a*e^2) - 3*c*d*(c*d^2 + 3*a*e^2)*x)/(8*a^2*(c*d^2 + a*e^2)^2*(d + e*x)*(a + c*x^2)) + (3*Sqrt[c]*(c^3*d^6 + 5*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - 5*a^3*e^6)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*(c*d^2 + a*e^2)^4) + (6*c*d*e^5*Log[d + e*x])/(c*d^2 + a*e^2)^4 - (3*c*d*e^5*Log[a + c*x^2])/(c*d^2 + a*e^2)^4","A",7,6,17,0.3529,1,"{741, 823, 801, 635, 205, 260}"
519,1,155,0,0.0845514,"\int \frac{(d+e x)^4}{\left(a+c x^2\right)^4} \, dx","Int[(d + e*x)^4/(a + c*x^2)^4,x]","-\frac{(d+e x) \left(a e^2+5 c d^2\right) (a e-c d x)}{16 a^3 c^2 \left(a+c x^2\right)}+\frac{\left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} c^{5/2}}-\frac{(d+e x)^3 (a e-5 c d x)}{24 a^2 c \left(a+c x^2\right)^2}+\frac{x (d+e x)^4}{6 a \left(a+c x^2\right)^3}","-\frac{(d+e x) \left(a e^2+5 c d^2\right) (a e-c d x)}{16 a^3 c^2 \left(a+c x^2\right)}+\frac{\left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} c^{5/2}}-\frac{(d+e x)^3 (a e-5 c d x)}{24 a^2 c \left(a+c x^2\right)^2}+\frac{x (d+e x)^4}{6 a \left(a+c x^2\right)^3}",1,"(x*(d + e*x)^4)/(6*a*(a + c*x^2)^3) - ((a*e - 5*c*d*x)*(d + e*x)^3)/(24*a^2*c*(a + c*x^2)^2) - ((5*c*d^2 + a*e^2)*(a*e - c*d*x)*(d + e*x))/(16*a^3*c^2*(a + c*x^2)) + ((c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*c^(5/2))","A",4,4,17,0.2353,1,"{737, 805, 723, 205}"
520,1,156,0,0.1182634,"\int \frac{(d+e x)^3}{\left(a+c x^2\right)^4} \, dx","Int[(d + e*x)^3/(a + c*x^2)^4,x]","-\frac{4 a e \left(a e^2+5 c d^2\right)-c d x \left(15 c d^2-a e^2\right)}{48 a^3 c^2 \left(a+c x^2\right)}+\frac{d \left(3 a e^2+5 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} c^{3/2}}-\frac{(d+e x)^2 (2 a e-5 c d x)}{24 a^2 c \left(a+c x^2\right)^2}+\frac{x (d+e x)^3}{6 a \left(a+c x^2\right)^3}","-\frac{4 a e \left(a e^2+5 c d^2\right)-c d x \left(15 c d^2-a e^2\right)}{48 a^3 c^2 \left(a+c x^2\right)}+\frac{d \left(3 a e^2+5 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} c^{3/2}}-\frac{(d+e x)^2 (2 a e-5 c d x)}{24 a^2 c \left(a+c x^2\right)^2}+\frac{x (d+e x)^3}{6 a \left(a+c x^2\right)^3}",1,"(x*(d + e*x)^3)/(6*a*(a + c*x^2)^3) - ((2*a*e - 5*c*d*x)*(d + e*x)^2)/(24*a^2*c*(a + c*x^2)^2) - (4*a*e*(5*c*d^2 + a*e^2) - c*d*(15*c*d^2 - a*e^2)*x)/(48*a^3*c^2*(a + c*x^2)) + (d*(5*c*d^2 + 3*a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*c^(3/2))","A",4,4,17,0.2353,1,"{737, 821, 778, 205}"
521,1,145,0,0.0640524,"\int \frac{(d+e x)^2}{\left(a+c x^2\right)^4} \, dx","Int[(d + e*x)^2/(a + c*x^2)^4,x]","\frac{\left(a e^2+5 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} c^{3/2}}+\frac{x \left(a e^2+5 c d^2\right)}{16 a^3 c \left(a+c x^2\right)}-\frac{4 a d e-x \left(a e^2+5 c d^2\right)}{24 a^2 c \left(a+c x^2\right)^2}-\frac{(d+e x) (a e-c d x)}{6 a c \left(a+c x^2\right)^3}","\frac{\left(a e^2+5 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} c^{3/2}}+\frac{x \left(a e^2+5 c d^2\right)}{16 a^3 c \left(a+c x^2\right)}-\frac{4 a d e-x \left(a e^2+5 c d^2\right)}{24 a^2 c \left(a+c x^2\right)^2}-\frac{(d+e x) (a e-c d x)}{6 a c \left(a+c x^2\right)^3}",1,"-((a*e - c*d*x)*(d + e*x))/(6*a*c*(a + c*x^2)^3) - (4*a*d*e - (5*c*d^2 + a*e^2)*x)/(24*a^2*c*(a + c*x^2)^2) + ((5*c*d^2 + a*e^2)*x)/(16*a^3*c*(a + c*x^2)) + ((5*c*d^2 + a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*c^(3/2))","A",4,4,17,0.2353,1,"{739, 639, 199, 205}"
522,1,93,0,0.0280046,"\int \frac{d+e x}{\left(a+c x^2\right)^4} \, dx","Int[(d + e*x)/(a + c*x^2)^4,x]","\frac{5 d x}{16 a^3 \left(a+c x^2\right)}+\frac{5 d x}{24 a^2 \left(a+c x^2\right)^2}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} \sqrt{c}}-\frac{a e-c d x}{6 a c \left(a+c x^2\right)^3}","\frac{5 d x}{16 a^3 \left(a+c x^2\right)}+\frac{5 d x}{24 a^2 \left(a+c x^2\right)^2}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} \sqrt{c}}-\frac{a e-c d x}{6 a c \left(a+c x^2\right)^3}",1,"-(a*e - c*d*x)/(6*a*c*(a + c*x^2)^3) + (5*d*x)/(24*a^2*(a + c*x^2)^2) + (5*d*x)/(16*a^3*(a + c*x^2)) + (5*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*Sqrt[c])","A",4,3,15,0.2000,1,"{639, 199, 205}"
523,1,295,0,0.3820499,"\int \frac{1}{(d+e x) \left(a+c x^2\right)^4} \, dx","Int[1/((d + e*x)*(a + c*x^2)^4),x]","\frac{c d x \left(19 a^2 e^4+16 a c d^2 e^2+5 c^2 d^4\right)+8 a^3 e^5}{16 a^3 \left(a+c x^2\right) \left(a e^2+c d^2\right)^3}+\frac{\sqrt{c} d \left(35 a^2 c d^2 e^4+35 a^3 e^6+21 a c^2 d^4 e^2+5 c^3 d^6\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} \left(a e^2+c d^2\right)^4}+\frac{6 a^2 e^3+c d x \left(11 a e^2+5 c d^2\right)}{24 a^2 \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{6 a \left(a+c x^2\right)^3 \left(a e^2+c d^2\right)}-\frac{e^7 \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)^4}+\frac{e^7 \log (d+e x)}{\left(a e^2+c d^2\right)^4}","\frac{c d x \left(19 a^2 e^4+16 a c d^2 e^2+5 c^2 d^4\right)+8 a^3 e^5}{16 a^3 \left(a+c x^2\right) \left(a e^2+c d^2\right)^3}+\frac{\sqrt{c} d \left(35 a^2 c d^2 e^4+35 a^3 e^6+21 a c^2 d^4 e^2+5 c^3 d^6\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} \left(a e^2+c d^2\right)^4}+\frac{6 a^2 e^3+c d x \left(11 a e^2+5 c d^2\right)}{24 a^2 \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{6 a \left(a+c x^2\right)^3 \left(a e^2+c d^2\right)}-\frac{e^7 \log \left(a+c x^2\right)}{2 \left(a e^2+c d^2\right)^4}+\frac{e^7 \log (d+e x)}{\left(a e^2+c d^2\right)^4}",1,"(a*e + c*d*x)/(6*a*(c*d^2 + a*e^2)*(a + c*x^2)^3) + (6*a^2*e^3 + c*d*(5*c*d^2 + 11*a*e^2)*x)/(24*a^2*(c*d^2 + a*e^2)^2*(a + c*x^2)^2) + (8*a^3*e^5 + c*d*(5*c^2*d^4 + 16*a*c*d^2*e^2 + 19*a^2*e^4)*x)/(16*a^3*(c*d^2 + a*e^2)^3*(a + c*x^2)) + (Sqrt[c]*d*(5*c^3*d^6 + 21*a*c^2*d^4*e^2 + 35*a^2*c*d^2*e^4 + 35*a^3*e^6)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*(c*d^2 + a*e^2)^4) + (e^7*Log[d + e*x])/(c*d^2 + a*e^2)^4 - (e^7*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^4)","A",8,6,17,0.3529,1,"{741, 823, 801, 635, 205, 260}"
524,1,430,0,0.5338418,"\int \frac{1}{(d+e x)^2 \left(a+c x^2\right)^4} \, dx","Int[1/((d + e*x)^2*(a + c*x^2)^4),x]","-\frac{a e \left(5 c d^2-7 a e^2\right) \left(5 a e^2+c d^2\right)-3 c d x \left(29 a^2 e^4+18 a c d^2 e^2+5 c^2 d^4\right)}{48 a^3 \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)^3}+\frac{e \left(47 a^2 c d^2 e^4-35 a^3 e^6+23 a c^2 d^4 e^2+5 c^3 d^6\right)}{16 a^3 (d+e x) \left(a e^2+c d^2\right)^4}+\frac{\sqrt{c} \left(70 a^2 c^2 d^4 e^4+140 a^3 c d^2 e^6-35 a^4 e^8+28 a c^3 d^6 e^2+5 c^4 d^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} \left(a e^2+c d^2\right)^5}-\frac{a e \left(c d^2-7 a e^2\right)-c d x \left(13 a e^2+5 c d^2\right)}{24 a^2 \left(a+c x^2\right)^2 (d+e x) \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{6 a \left(a+c x^2\right)^3 (d+e x) \left(a e^2+c d^2\right)}-\frac{4 c d e^7 \log \left(a+c x^2\right)}{\left(a e^2+c d^2\right)^5}+\frac{8 c d e^7 \log (d+e x)}{\left(a e^2+c d^2\right)^5}","-\frac{a e \left(5 c d^2-7 a e^2\right) \left(5 a e^2+c d^2\right)-3 c d x \left(29 a^2 e^4+18 a c d^2 e^2+5 c^2 d^4\right)}{48 a^3 \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)^3}+\frac{e \left(47 a^2 c d^2 e^4-35 a^3 e^6+23 a c^2 d^4 e^2+5 c^3 d^6\right)}{16 a^3 (d+e x) \left(a e^2+c d^2\right)^4}+\frac{\sqrt{c} \left(70 a^2 c^2 d^4 e^4+140 a^3 c d^2 e^6-35 a^4 e^8+28 a c^3 d^6 e^2+5 c^4 d^8\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} \left(a e^2+c d^2\right)^5}-\frac{a e \left(c d^2-7 a e^2\right)-c d x \left(13 a e^2+5 c d^2\right)}{24 a^2 \left(a+c x^2\right)^2 (d+e x) \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{6 a \left(a+c x^2\right)^3 (d+e x) \left(a e^2+c d^2\right)}-\frac{4 c d e^7 \log \left(a+c x^2\right)}{\left(a e^2+c d^2\right)^5}+\frac{8 c d e^7 \log (d+e x)}{\left(a e^2+c d^2\right)^5}",1,"(e*(5*c^3*d^6 + 23*a*c^2*d^4*e^2 + 47*a^2*c*d^2*e^4 - 35*a^3*e^6))/(16*a^3*(c*d^2 + a*e^2)^4*(d + e*x)) + (a*e + c*d*x)/(6*a*(c*d^2 + a*e^2)*(d + e*x)*(a + c*x^2)^3) - (a*e*(c*d^2 - 7*a*e^2) - c*d*(5*c*d^2 + 13*a*e^2)*x)/(24*a^2*(c*d^2 + a*e^2)^2*(d + e*x)*(a + c*x^2)^2) - (a*e*(5*c*d^2 - 7*a*e^2)*(c*d^2 + 5*a*e^2) - 3*c*d*(5*c^2*d^4 + 18*a*c*d^2*e^2 + 29*a^2*e^4)*x)/(48*a^3*(c*d^2 + a*e^2)^3*(d + e*x)*(a + c*x^2)) + (Sqrt[c]*(5*c^4*d^8 + 28*a*c^3*d^6*e^2 + 70*a^2*c^2*d^4*e^4 + 140*a^3*c*d^2*e^6 - 35*a^4*e^8)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*(c*d^2 + a*e^2)^5) + (8*c*d*e^7*Log[d + e*x])/(c*d^2 + a*e^2)^5 - (4*c*d*e^7*Log[a + c*x^2])/(c*d^2 + a*e^2)^5","A",8,6,17,0.3529,1,"{741, 823, 801, 635, 205, 260}"
525,1,207,0,0.208813,"\int (d+e x)^4 \sqrt{a+c x^2} \, dx","Int[(d + e*x)^4*Sqrt[a + c*x^2],x]","\frac{x \sqrt{a+c x^2} \left(a^2 e^4-12 a c d^2 e^2+8 c^2 d^4\right)}{16 c^2}+\frac{a \left(a^2 e^4-12 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)}{16 c^{5/2}}+\frac{e \left(a+c x^2\right)^{3/2} \left(3 e x \left(16 c d^2-5 a e^2\right)+8 d \left(13 c d^2-8 a e^2\right)\right)}{120 c^2}+\frac{e \left(a+c x^2\right)^{3/2} (d+e x)^3}{6 c}+\frac{3 d e \left(a+c x^2\right)^{3/2} (d+e x)^2}{10 c}","\frac{x \sqrt{a+c x^2} \left(a^2 e^4-12 a c d^2 e^2+8 c^2 d^4\right)}{16 c^2}+\frac{a \left(a^2 e^4-12 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)}{16 c^{5/2}}+\frac{e \left(a+c x^2\right)^{3/2} \left(3 e x \left(16 c d^2-5 a e^2\right)+8 d \left(13 c d^2-8 a e^2\right)\right)}{120 c^2}+\frac{e \left(a+c x^2\right)^{3/2} (d+e x)^3}{6 c}+\frac{3 d e \left(a+c x^2\right)^{3/2} (d+e x)^2}{10 c}",1,"((8*c^2*d^4 - 12*a*c*d^2*e^2 + a^2*e^4)*x*Sqrt[a + c*x^2])/(16*c^2) + (3*d*e*(d + e*x)^2*(a + c*x^2)^(3/2))/(10*c) + (e*(d + e*x)^3*(a + c*x^2)^(3/2))/(6*c) + (e*(8*d*(13*c*d^2 - 8*a*e^2) + 3*e*(16*c*d^2 - 5*a*e^2)*x)*(a + c*x^2)^(3/2))/(120*c^2) + (a*(8*c^2*d^4 - 12*a*c*d^2*e^2 + a^2*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(5/2))","A",6,6,19,0.3158,1,"{743, 833, 780, 195, 217, 206}"
526,1,144,0,0.1147138,"\int (d+e x)^3 \sqrt{a+c x^2} \, dx","Int[(d + e*x)^3*Sqrt[a + c*x^2],x]","\frac{e \left(a+c x^2\right)^{3/2} \left(8 \left(6 c d^2-a e^2\right)+21 c d e x\right)}{60 c^2}+\frac{a d \left(4 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}+\frac{d x \sqrt{a+c x^2} \left(4 c d^2-3 a e^2\right)}{8 c}+\frac{e \left(a+c x^2\right)^{3/2} (d+e x)^2}{5 c}","\frac{e \left(a+c x^2\right)^{3/2} \left(8 \left(6 c d^2-a e^2\right)+21 c d e x\right)}{60 c^2}+\frac{a d \left(4 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}+\frac{d x \sqrt{a+c x^2} \left(4 c d^2-3 a e^2\right)}{8 c}+\frac{e \left(a+c x^2\right)^{3/2} (d+e x)^2}{5 c}",1,"(d*(4*c*d^2 - 3*a*e^2)*x*Sqrt[a + c*x^2])/(8*c) + (e*(d + e*x)^2*(a + c*x^2)^(3/2))/(5*c) + (e*(8*(6*c*d^2 - a*e^2) + 21*c*d*e*x)*(a + c*x^2)^(3/2))/(60*c^2) + (a*d*(4*c*d^2 - 3*a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(3/2))","A",5,5,19,0.2632,1,"{743, 780, 195, 217, 206}"
527,1,119,0,0.0537477,"\int (d+e x)^2 \sqrt{a+c x^2} \, dx","Int[(d + e*x)^2*Sqrt[a + c*x^2],x]","\frac{a \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}+\frac{x \sqrt{a+c x^2} \left(4 c d^2-a e^2\right)}{8 c}+\frac{5 d e \left(a+c x^2\right)^{3/2}}{12 c}+\frac{e \left(a+c x^2\right)^{3/2} (d+e x)}{4 c}","\frac{a \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}+\frac{x \sqrt{a+c x^2} \left(4 c d^2-a e^2\right)}{8 c}+\frac{5 d e \left(a+c x^2\right)^{3/2}}{12 c}+\frac{e \left(a+c x^2\right)^{3/2} (d+e x)}{4 c}",1,"((4*c*d^2 - a*e^2)*x*Sqrt[a + c*x^2])/(8*c) + (5*d*e*(a + c*x^2)^(3/2))/(12*c) + (e*(d + e*x)*(a + c*x^2)^(3/2))/(4*c) + (a*(4*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(3/2))","A",5,5,19,0.2632,1,"{743, 641, 195, 217, 206}"
528,1,67,0,0.0178534,"\int (d+e x) \sqrt{a+c x^2} \, dx","Int[(d + e*x)*Sqrt[a + c*x^2],x]","\frac{1}{2} d x \sqrt{a+c x^2}+\frac{a d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c}}+\frac{e \left(a+c x^2\right)^{3/2}}{3 c}","\frac{1}{2} d x \sqrt{a+c x^2}+\frac{a d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c}}+\frac{e \left(a+c x^2\right)^{3/2}}{3 c}",1,"(d*x*Sqrt[a + c*x^2])/2 + (e*(a + c*x^2)^(3/2))/(3*c) + (a*d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*Sqrt[c])","A",4,4,17,0.2353,1,"{641, 195, 217, 206}"
529,1,103,0,0.0814617,"\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}"
530,1,110,0,0.0681209,"\int \frac{\sqrt{a+c x^2}}{(d+e x)^2} \, dx","Int[Sqrt[a + c*x^2]/(d + e*x)^2,x]","\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)}{e^2 \sqrt{a e^2+c d^2}}-\frac{\sqrt{a+c x^2}}{e (d+e x)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^2}","\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)}{e^2 \sqrt{a e^2+c d^2}}-\frac{\sqrt{a+c x^2}}{e (d+e x)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^2}",1,"-(Sqrt[a + c*x^2]/(e*(d + e*x))) + (Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/e^2 + (c*d*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",6,5,19,0.2632,1,"{733, 844, 217, 206, 725}"
531,1,103,0,0.0438794,"\int \frac{\sqrt{a+c x^2}}{(d+e x)^3} \, dx","Int[Sqrt[a + c*x^2]/(d + e*x)^3,x]","-\frac{\sqrt{a+c x^2} (a e-c d x)}{2 (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{a c \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{3/2}}","-\frac{\sqrt{a+c x^2} (a e-c d x)}{2 (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{a c \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{3/2}}",1,"-((a*e - c*d*x)*Sqrt[a + c*x^2])/(2*(c*d^2 + a*e^2)*(d + e*x)^2) - (a*c*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(2*(c*d^2 + a*e^2)^(3/2))","A",3,3,19,0.1579,1,"{721, 725, 206}"
532,1,144,0,0.0863029,"\int \frac{\sqrt{a+c x^2}}{(d+e x)^4} \, dx","Int[Sqrt[a + c*x^2]/(d + e*x)^4,x]","-\frac{a c^2 d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{5/2}}-\frac{c d \sqrt{a+c x^2} (a e-c d x)}{2 (d+e x)^2 \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{3/2}}{3 (d+e x)^3 \left(a e^2+c d^2\right)}","-\frac{a c^2 d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{5/2}}-\frac{c d \sqrt{a+c x^2} (a e-c d x)}{2 (d+e x)^2 \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{3/2}}{3 (d+e x)^3 \left(a e^2+c d^2\right)}",1,"-(c*d*(a*e - c*d*x)*Sqrt[a + c*x^2])/(2*(c*d^2 + a*e^2)^2*(d + e*x)^2) - (e*(a + c*x^2)^(3/2))/(3*(c*d^2 + a*e^2)*(d + e*x)^3) - (a*c^2*d*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(2*(c*d^2 + a*e^2)^(5/2))","A",4,4,19,0.2105,1,"{731, 721, 725, 206}"
533,1,206,0,0.1263005,"\int \frac{\sqrt{a+c x^2}}{(d+e x)^5} \, dx","Int[Sqrt[a + c*x^2]/(d + e*x)^5,x]","-\frac{a c^2 \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 \left(a e^2+c d^2\right)^{7/2}}-\frac{5 c d e \left(a+c x^2\right)^{3/2}}{12 (d+e x)^3 \left(a e^2+c d^2\right)^2}-\frac{c \sqrt{a+c x^2} \left(4 c d^2-a e^2\right) (a e-c d x)}{8 (d+e x)^2 \left(a e^2+c d^2\right)^3}-\frac{e \left(a+c x^2\right)^{3/2}}{4 (d+e x)^4 \left(a e^2+c d^2\right)}","-\frac{a c^2 \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 \left(a e^2+c d^2\right)^{7/2}}-\frac{5 c d e \left(a+c x^2\right)^{3/2}}{12 (d+e x)^3 \left(a e^2+c d^2\right)^2}-\frac{c \sqrt{a+c x^2} \left(4 c d^2-a e^2\right) (a e-c d x)}{8 (d+e x)^2 \left(a e^2+c d^2\right)^3}-\frac{e \left(a+c x^2\right)^{3/2}}{4 (d+e x)^4 \left(a e^2+c d^2\right)}",1,"-(c*(4*c*d^2 - a*e^2)*(a*e - c*d*x)*Sqrt[a + c*x^2])/(8*(c*d^2 + a*e^2)^3*(d + e*x)^2) - (e*(a + c*x^2)^(3/2))/(4*(c*d^2 + a*e^2)*(d + e*x)^4) - (5*c*d*e*(a + c*x^2)^(3/2))/(12*(c*d^2 + a*e^2)^2*(d + e*x)^3) - (a*c^2*(4*c*d^2 - a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(8*(c*d^2 + a*e^2)^(7/2))","A",5,5,19,0.2632,1,"{745, 807, 721, 725, 206}"
534,1,255,0,0.2500846,"\int (d+e x)^4 \left(a+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^4*(a + c*x^2)^(3/2),x]","\frac{x \left(a+c x^2\right)^{3/2} \left(a^2 e^4-16 a c d^2 e^2+16 c^2 d^4\right)}{64 c^2}+\frac{3 a x \sqrt{a+c x^2} \left(a^2 e^4-16 a c d^2 e^2+16 c^2 d^4\right)}{128 c^2}+\frac{3 a^2 \left(a^2 e^4-16 a c d^2 e^2+16 c^2 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{5/2}}+\frac{e \left(a+c x^2\right)^{5/2} \left(5 e x \left(26 c d^2-7 a e^2\right)+4 d \left(67 c d^2-32 a e^2\right)\right)}{560 c^2}+\frac{e \left(a+c x^2\right)^{5/2} (d+e x)^3}{8 c}+\frac{11 d e \left(a+c x^2\right)^{5/2} (d+e x)^2}{56 c}","\frac{x \left(a+c x^2\right)^{3/2} \left(a^2 e^4-16 a c d^2 e^2+16 c^2 d^4\right)}{64 c^2}+\frac{3 a x \sqrt{a+c x^2} \left(a^2 e^4-16 a c d^2 e^2+16 c^2 d^4\right)}{128 c^2}+\frac{3 a^2 \left(a^2 e^4-16 a c d^2 e^2+16 c^2 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{5/2}}+\frac{e \left(a+c x^2\right)^{5/2} \left(5 e x \left(26 c d^2-7 a e^2\right)+4 d \left(67 c d^2-32 a e^2\right)\right)}{560 c^2}+\frac{e \left(a+c x^2\right)^{5/2} (d+e x)^3}{8 c}+\frac{11 d e \left(a+c x^2\right)^{5/2} (d+e x)^2}{56 c}",1,"(3*a*(16*c^2*d^4 - 16*a*c*d^2*e^2 + a^2*e^4)*x*Sqrt[a + c*x^2])/(128*c^2) + ((16*c^2*d^4 - 16*a*c*d^2*e^2 + a^2*e^4)*x*(a + c*x^2)^(3/2))/(64*c^2) + (11*d*e*(d + e*x)^2*(a + c*x^2)^(5/2))/(56*c) + (e*(d + e*x)^3*(a + c*x^2)^(5/2))/(8*c) + (e*(4*d*(67*c*d^2 - 32*a*e^2) + 5*e*(26*c*d^2 - 7*a*e^2)*x)*(a + c*x^2)^(5/2))/(560*c^2) + (3*a^2*(16*c^2*d^4 - 16*a*c*d^2*e^2 + a^2*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(5/2))","A",7,6,19,0.3158,1,"{743, 833, 780, 195, 217, 206}"
535,1,180,0,0.1452632,"\int (d+e x)^3 \left(a+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^3*(a + c*x^2)^(3/2),x]","\frac{3 a^2 d \left(2 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}+\frac{e \left(a+c x^2\right)^{5/2} \left(4 \left(8 c d^2-a e^2\right)+15 c d e x\right)}{70 c^2}+\frac{d x \left(a+c x^2\right)^{3/2} \left(2 c d^2-a e^2\right)}{8 c}+\frac{3 a d x \sqrt{a+c x^2} \left(2 c d^2-a e^2\right)}{16 c}+\frac{e \left(a+c x^2\right)^{5/2} (d+e x)^2}{7 c}","\frac{3 a^2 d \left(2 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}+\frac{e \left(a+c x^2\right)^{5/2} \left(4 \left(8 c d^2-a e^2\right)+15 c d e x\right)}{70 c^2}+\frac{d x \left(a+c x^2\right)^{3/2} \left(2 c d^2-a e^2\right)}{8 c}+\frac{3 a d x \sqrt{a+c x^2} \left(2 c d^2-a e^2\right)}{16 c}+\frac{e \left(a+c x^2\right)^{5/2} (d+e x)^2}{7 c}",1,"(3*a*d*(2*c*d^2 - a*e^2)*x*Sqrt[a + c*x^2])/(16*c) + (d*(2*c*d^2 - a*e^2)*x*(a + c*x^2)^(3/2))/(8*c) + (e*(d + e*x)^2*(a + c*x^2)^(5/2))/(7*c) + (e*(4*(8*c*d^2 - a*e^2) + 15*c*d*e*x)*(a + c*x^2)^(5/2))/(70*c^2) + (3*a^2*d*(2*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(3/2))","A",6,5,19,0.2632,1,"{743, 780, 195, 217, 206}"
536,1,154,0,0.0685449,"\int (d+e x)^2 \left(a+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^2*(a + c*x^2)^(3/2),x]","\frac{a^2 \left(6 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}+\frac{x \left(a+c x^2\right)^{3/2} \left(6 c d^2-a e^2\right)}{24 c}+\frac{a x \sqrt{a+c x^2} \left(6 c d^2-a e^2\right)}{16 c}+\frac{7 d e \left(a+c x^2\right)^{5/2}}{30 c}+\frac{e \left(a+c x^2\right)^{5/2} (d+e x)}{6 c}","\frac{a^2 \left(6 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}+\frac{x \left(a+c x^2\right)^{3/2} \left(6 c d^2-a e^2\right)}{24 c}+\frac{a x \sqrt{a+c x^2} \left(6 c d^2-a e^2\right)}{16 c}+\frac{7 d e \left(a+c x^2\right)^{5/2}}{30 c}+\frac{e \left(a+c x^2\right)^{5/2} (d+e x)}{6 c}",1,"(a*(6*c*d^2 - a*e^2)*x*Sqrt[a + c*x^2])/(16*c) + ((6*c*d^2 - a*e^2)*x*(a + c*x^2)^(3/2))/(24*c) + (7*d*e*(a + c*x^2)^(5/2))/(30*c) + (e*(d + e*x)*(a + c*x^2)^(5/2))/(6*c) + (a^2*(6*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(3/2))","A",6,5,19,0.2632,1,"{743, 641, 195, 217, 206}"
537,1,87,0,0.0253526,"\int (d+e x) \left(a+c x^2\right)^{3/2} \, dx","Int[(d + e*x)*(a + c*x^2)^(3/2),x]","\frac{3 a^2 d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 \sqrt{c}}+\frac{1}{4} d x \left(a+c x^2\right)^{3/2}+\frac{3}{8} a d x \sqrt{a+c x^2}+\frac{e \left(a+c x^2\right)^{5/2}}{5 c}","\frac{3 a^2 d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 \sqrt{c}}+\frac{1}{4} d x \left(a+c x^2\right)^{3/2}+\frac{3}{8} a d x \sqrt{a+c x^2}+\frac{e \left(a+c x^2\right)^{5/2}}{5 c}",1,"(3*a*d*x*Sqrt[a + c*x^2])/8 + (d*x*(a + c*x^2)^(3/2))/4 + (e*(a + c*x^2)^(5/2))/(5*c) + (3*a^2*d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*Sqrt[c])","A",5,4,17,0.2353,1,"{641, 195, 217, 206}"
538,1,159,0,0.1794656,"\int \frac{\left(a+c x^2\right)^{3/2}}{d+e x} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x),x]","\frac{\sqrt{a+c x^2} \left(2 \left(a e^2+c d^2\right)-c d e x\right)}{2 e^3}-\frac{\left(a e^2+c d^2\right)^{3/2} \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{\sqrt{c} d \left(3 a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 e^4}+\frac{\left(a+c x^2\right)^{3/2}}{3 e}","\frac{\sqrt{a+c x^2} \left(2 \left(a e^2+c d^2\right)-c d e x\right)}{2 e^3}-\frac{\left(a e^2+c d^2\right)^{3/2} \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{\sqrt{c} d \left(3 a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 e^4}+\frac{\left(a+c x^2\right)^{3/2}}{3 e}",1,"((2*(c*d^2 + a*e^2) - c*d*e*x)*Sqrt[a + c*x^2])/(2*e^3) + (a + c*x^2)^(3/2)/(3*e) - (Sqrt[c]*d*(2*c*d^2 + 3*a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*e^4) - ((c*d^2 + a*e^2)^(3/2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/e^4","A",7,6,19,0.3158,1,"{735, 815, 844, 217, 206, 725}"
539,1,153,0,0.135716,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^2,x]","\frac{3 \sqrt{c} \left(a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 e^4}+\frac{3 c 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^4}-\frac{3 c \sqrt{a+c x^2} (2 d-e x)}{2 e^3}-\frac{\left(a+c x^2\right)^{3/2}}{e (d+e x)}","\frac{3 \sqrt{c} \left(a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 e^4}+\frac{3 c 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^4}-\frac{3 c \sqrt{a+c x^2} (2 d-e x)}{2 e^3}-\frac{\left(a+c x^2\right)^{3/2}}{e (d+e x)}",1,"(-3*c*(2*d - e*x)*Sqrt[a + c*x^2])/(2*e^3) - (a + c*x^2)^(3/2)/(e*(d + e*x)) + (3*Sqrt[c]*(2*c*d^2 + a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*e^4) + (3*c*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^4","A",7,6,19,0.3158,1,"{733, 815, 844, 217, 206, 725}"
540,1,161,0,0.1237987,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^3,x]","-\frac{3 c^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^4}-\frac{3 c \left(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)}{2 e^4 \sqrt{a e^2+c d^2}}+\frac{3 c \sqrt{a+c x^2} (2 d+e x)}{2 e^3 (d+e x)}-\frac{\left(a+c x^2\right)^{3/2}}{2 e (d+e x)^2}","-\frac{3 c^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^4}-\frac{3 c \left(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)}{2 e^4 \sqrt{a e^2+c d^2}}+\frac{3 c \sqrt{a+c x^2} (2 d+e x)}{2 e^3 (d+e x)}-\frac{\left(a+c x^2\right)^{3/2}}{2 e (d+e x)^2}",1,"(3*c*(2*d + e*x)*Sqrt[a + c*x^2])/(2*e^3*(d + e*x)) - (a + c*x^2)^(3/2)/(2*e*(d + e*x)^2) - (3*c^(3/2)*d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/e^4 - (3*c*(2*c*d^2 + a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(2*e^4*Sqrt[c*d^2 + a*e^2])","A",7,6,19,0.3158,1,"{733, 813, 844, 217, 206, 725}"
541,1,200,0,0.1769348,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^4} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^4,x]","\frac{c^2 d \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)}{2 e^4 \left(a e^2+c d^2\right)^{3/2}}+\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^4}-\frac{c \sqrt{a+c x^2} \left(e x \left(2 a e^2+3 c d^2\right)+d \left(a e^2+2 c d^2\right)\right)}{2 e^3 (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{\left(a+c x^2\right)^{3/2}}{3 e (d+e x)^3}","\frac{c^2 d \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)}{2 e^4 \left(a e^2+c d^2\right)^{3/2}}+\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^4}-\frac{c \sqrt{a+c x^2} \left(e x \left(2 a e^2+3 c d^2\right)+d \left(a e^2+2 c d^2\right)\right)}{2 e^3 (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{\left(a+c x^2\right)^{3/2}}{3 e (d+e x)^3}",1,"-(c*(d*(2*c*d^2 + a*e^2) + e*(3*c*d^2 + 2*a*e^2)*x)*Sqrt[a + c*x^2])/(2*e^3*(c*d^2 + a*e^2)*(d + e*x)^2) - (a + c*x^2)^(3/2)/(3*e*(d + e*x)^3) + (c^(3/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/e^4 + (c^2*d*(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])])/(2*e^4*(c*d^2 + a*e^2)^(3/2))","A",7,6,19,0.3158,1,"{733, 811, 844, 217, 206, 725}"
542,1,153,0,0.0628769,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^5} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^5,x]","-\frac{3 a^2 c^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 \left(a e^2+c d^2\right)^{5/2}}-\frac{3 a c \sqrt{a+c x^2} (a e-c d x)}{8 (d+e x)^2 \left(a e^2+c d^2\right)^2}-\frac{\left(a+c x^2\right)^{3/2} (a e-c d x)}{4 (d+e x)^4 \left(a e^2+c d^2\right)}","-\frac{3 a^2 c^2 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 \left(a e^2+c d^2\right)^{5/2}}-\frac{3 a c \sqrt{a+c x^2} (a e-c d x)}{8 (d+e x)^2 \left(a e^2+c d^2\right)^2}-\frac{\left(a+c x^2\right)^{3/2} (a e-c d x)}{4 (d+e x)^4 \left(a e^2+c d^2\right)}",1,"(-3*a*c*(a*e - c*d*x)*Sqrt[a + c*x^2])/(8*(c*d^2 + a*e^2)^2*(d + e*x)^2) - ((a*e - c*d*x)*(a + c*x^2)^(3/2))/(4*(c*d^2 + a*e^2)*(d + e*x)^4) - (3*a^2*c^2*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(8*(c*d^2 + a*e^2)^(5/2))","A",4,3,19,0.1579,1,"{721, 725, 206}"
543,1,195,0,0.0950982,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^6} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^6,x]","-\frac{3 a^2 c^3 d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 \left(a e^2+c d^2\right)^{7/2}}-\frac{3 a c^2 d \sqrt{a+c x^2} (a e-c d x)}{8 (d+e x)^2 \left(a e^2+c d^2\right)^3}-\frac{c d \left(a+c x^2\right)^{3/2} (a e-c d x)}{4 (d+e x)^4 \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{5/2}}{5 (d+e x)^5 \left(a e^2+c d^2\right)}","-\frac{3 a^2 c^3 d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 \left(a e^2+c d^2\right)^{7/2}}-\frac{3 a c^2 d \sqrt{a+c x^2} (a e-c d x)}{8 (d+e x)^2 \left(a e^2+c d^2\right)^3}-\frac{c d \left(a+c x^2\right)^{3/2} (a e-c d x)}{4 (d+e x)^4 \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{5/2}}{5 (d+e x)^5 \left(a e^2+c d^2\right)}",1,"(-3*a*c^2*d*(a*e - c*d*x)*Sqrt[a + c*x^2])/(8*(c*d^2 + a*e^2)^3*(d + e*x)^2) - (c*d*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(4*(c*d^2 + a*e^2)^2*(d + e*x)^4) - (e*(a + c*x^2)^(5/2))/(5*(c*d^2 + a*e^2)*(d + e*x)^5) - (3*a^2*c^3*d*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(8*(c*d^2 + a*e^2)^(7/2))","A",5,4,19,0.2105,1,"{731, 721, 725, 206}"
544,1,269,0,0.1835948,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^7} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^7,x]","-\frac{a^2 c^3 \left(6 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{16 \left(a e^2+c d^2\right)^{9/2}}-\frac{a c^2 \sqrt{a+c x^2} \left(6 c d^2-a e^2\right) (a e-c d x)}{16 (d+e x)^2 \left(a e^2+c d^2\right)^4}-\frac{7 c d e \left(a+c x^2\right)^{5/2}}{30 (d+e x)^5 \left(a e^2+c d^2\right)^2}-\frac{c \left(a+c x^2\right)^{3/2} \left(6 c d^2-a e^2\right) (a e-c d x)}{24 (d+e x)^4 \left(a e^2+c d^2\right)^3}-\frac{e \left(a+c x^2\right)^{5/2}}{6 (d+e x)^6 \left(a e^2+c d^2\right)}","-\frac{a^2 c^3 \left(6 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{16 \left(a e^2+c d^2\right)^{9/2}}-\frac{a c^2 \sqrt{a+c x^2} \left(6 c d^2-a e^2\right) (a e-c d x)}{16 (d+e x)^2 \left(a e^2+c d^2\right)^4}-\frac{7 c d e \left(a+c x^2\right)^{5/2}}{30 (d+e x)^5 \left(a e^2+c d^2\right)^2}-\frac{c \left(a+c x^2\right)^{3/2} \left(6 c d^2-a e^2\right) (a e-c d x)}{24 (d+e x)^4 \left(a e^2+c d^2\right)^3}-\frac{e \left(a+c x^2\right)^{5/2}}{6 (d+e x)^6 \left(a e^2+c d^2\right)}",1,"-(a*c^2*(6*c*d^2 - a*e^2)*(a*e - c*d*x)*Sqrt[a + c*x^2])/(16*(c*d^2 + a*e^2)^4*(d + e*x)^2) - (c*(6*c*d^2 - a*e^2)*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(24*(c*d^2 + a*e^2)^3*(d + e*x)^4) - (e*(a + c*x^2)^(5/2))/(6*(c*d^2 + a*e^2)*(d + e*x)^6) - (7*c*d*e*(a + c*x^2)^(5/2))/(30*(c*d^2 + a*e^2)^2*(d + e*x)^5) - (a^2*c^3*(6*c*d^2 - a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(16*(c*d^2 + a*e^2)^(9/2))","A",6,5,19,0.2632,1,"{745, 807, 721, 725, 206}"
545,1,307,0,0.2933232,"\int (d+e x)^4 \left(a+c x^2\right)^{5/2} \, dx","Int[(d + e*x)^4*(a + c*x^2)^(5/2),x]","\frac{x \left(a+c x^2\right)^{5/2} \left(3 a^2 e^4-60 a c d^2 e^2+80 c^2 d^4\right)}{480 c^2}+\frac{a x \left(a+c x^2\right)^{3/2} \left(3 a^2 e^4-60 a c d^2 e^2+80 c^2 d^4\right)}{384 c^2}+\frac{a^2 x \sqrt{a+c x^2} \left(3 a^2 e^4-60 a c d^2 e^2+80 c^2 d^4\right)}{256 c^2}+\frac{a^3 \left(3 a^2 e^4-60 a c d^2 e^2+80 c^2 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{256 c^{5/2}}+\frac{e \left(a+c x^2\right)^{7/2} \left(7 e x \left(116 c d^2-27 a e^2\right)+16 d \left(103 c d^2-40 a e^2\right)\right)}{5040 c^2}+\frac{e \left(a+c x^2\right)^{7/2} (d+e x)^3}{10 c}+\frac{13 d e \left(a+c x^2\right)^{7/2} (d+e x)^2}{90 c}","\frac{x \left(a+c x^2\right)^{5/2} \left(3 a^2 e^4-60 a c d^2 e^2+80 c^2 d^4\right)}{480 c^2}+\frac{a x \left(a+c x^2\right)^{3/2} \left(3 a^2 e^4-60 a c d^2 e^2+80 c^2 d^4\right)}{384 c^2}+\frac{a^2 x \sqrt{a+c x^2} \left(3 a^2 e^4-60 a c d^2 e^2+80 c^2 d^4\right)}{256 c^2}+\frac{a^3 \left(3 a^2 e^4-60 a c d^2 e^2+80 c^2 d^4\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{256 c^{5/2}}+\frac{e \left(a+c x^2\right)^{7/2} \left(7 e x \left(116 c d^2-27 a e^2\right)+16 d \left(103 c d^2-40 a e^2\right)\right)}{5040 c^2}+\frac{e \left(a+c x^2\right)^{7/2} (d+e x)^3}{10 c}+\frac{13 d e \left(a+c x^2\right)^{7/2} (d+e x)^2}{90 c}",1,"(a^2*(80*c^2*d^4 - 60*a*c*d^2*e^2 + 3*a^2*e^4)*x*Sqrt[a + c*x^2])/(256*c^2) + (a*(80*c^2*d^4 - 60*a*c*d^2*e^2 + 3*a^2*e^4)*x*(a + c*x^2)^(3/2))/(384*c^2) + ((80*c^2*d^4 - 60*a*c*d^2*e^2 + 3*a^2*e^4)*x*(a + c*x^2)^(5/2))/(480*c^2) + (13*d*e*(d + e*x)^2*(a + c*x^2)^(7/2))/(90*c) + (e*(d + e*x)^3*(a + c*x^2)^(7/2))/(10*c) + (e*(16*d*(103*c*d^2 - 40*a*e^2) + 7*e*(116*c*d^2 - 27*a*e^2)*x)*(a + c*x^2)^(7/2))/(5040*c^2) + (a^3*(80*c^2*d^4 - 60*a*c*d^2*e^2 + 3*a^2*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(256*c^(5/2))","A",8,6,19,0.3158,1,"{743, 833, 780, 195, 217, 206}"
546,1,216,0,0.1638362,"\int (d+e x)^3 \left(a+c x^2\right)^{5/2} \, dx","Int[(d + e*x)^3*(a + c*x^2)^(5/2),x]","\frac{5 a^3 d \left(8 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}+\frac{5 a^2 d x \sqrt{a+c x^2} \left(8 c d^2-3 a e^2\right)}{128 c}+\frac{e \left(a+c x^2\right)^{7/2} \left(16 \left(10 c d^2-a e^2\right)+77 c d e x\right)}{504 c^2}+\frac{d x \left(a+c x^2\right)^{5/2} \left(8 c d^2-3 a e^2\right)}{48 c}+\frac{5 a d x \left(a+c x^2\right)^{3/2} \left(8 c d^2-3 a e^2\right)}{192 c}+\frac{e \left(a+c x^2\right)^{7/2} (d+e x)^2}{9 c}","\frac{5 a^3 d \left(8 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}+\frac{5 a^2 d x \sqrt{a+c x^2} \left(8 c d^2-3 a e^2\right)}{128 c}+\frac{e \left(a+c x^2\right)^{7/2} \left(16 \left(10 c d^2-a e^2\right)+77 c d e x\right)}{504 c^2}+\frac{d x \left(a+c x^2\right)^{5/2} \left(8 c d^2-3 a e^2\right)}{48 c}+\frac{5 a d x \left(a+c x^2\right)^{3/2} \left(8 c d^2-3 a e^2\right)}{192 c}+\frac{e \left(a+c x^2\right)^{7/2} (d+e x)^2}{9 c}",1,"(5*a^2*d*(8*c*d^2 - 3*a*e^2)*x*Sqrt[a + c*x^2])/(128*c) + (5*a*d*(8*c*d^2 - 3*a*e^2)*x*(a + c*x^2)^(3/2))/(192*c) + (d*(8*c*d^2 - 3*a*e^2)*x*(a + c*x^2)^(5/2))/(48*c) + (e*(d + e*x)^2*(a + c*x^2)^(7/2))/(9*c) + (e*(16*(10*c*d^2 - a*e^2) + 77*c*d*e*x)*(a + c*x^2)^(7/2))/(504*c^2) + (5*a^3*d*(8*c*d^2 - 3*a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(3/2))","A",7,5,19,0.2632,1,"{743, 780, 195, 217, 206}"
547,1,189,0,0.087727,"\int (d+e x)^2 \left(a+c x^2\right)^{5/2} \, dx","Int[(d + e*x)^2*(a + c*x^2)^(5/2),x]","\frac{5 a^3 \left(8 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}+\frac{5 a^2 x \sqrt{a+c x^2} \left(8 c d^2-a e^2\right)}{128 c}+\frac{x \left(a+c x^2\right)^{5/2} \left(8 c d^2-a e^2\right)}{48 c}+\frac{5 a x \left(a+c x^2\right)^{3/2} \left(8 c d^2-a e^2\right)}{192 c}+\frac{9 d e \left(a+c x^2\right)^{7/2}}{56 c}+\frac{e \left(a+c x^2\right)^{7/2} (d+e x)}{8 c}","\frac{5 a^3 \left(8 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}+\frac{5 a^2 x \sqrt{a+c x^2} \left(8 c d^2-a e^2\right)}{128 c}+\frac{x \left(a+c x^2\right)^{5/2} \left(8 c d^2-a e^2\right)}{48 c}+\frac{5 a x \left(a+c x^2\right)^{3/2} \left(8 c d^2-a e^2\right)}{192 c}+\frac{9 d e \left(a+c x^2\right)^{7/2}}{56 c}+\frac{e \left(a+c x^2\right)^{7/2} (d+e x)}{8 c}",1,"(5*a^2*(8*c*d^2 - a*e^2)*x*Sqrt[a + c*x^2])/(128*c) + (5*a*(8*c*d^2 - a*e^2)*x*(a + c*x^2)^(3/2))/(192*c) + ((8*c*d^2 - a*e^2)*x*(a + c*x^2)^(5/2))/(48*c) + (9*d*e*(a + c*x^2)^(7/2))/(56*c) + (e*(d + e*x)*(a + c*x^2)^(7/2))/(8*c) + (5*a^3*(8*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(3/2))","A",7,5,19,0.2632,1,"{743, 641, 195, 217, 206}"
548,1,107,0,0.0337156,"\int (d+e x) \left(a+c x^2\right)^{5/2} \, dx","Int[(d + e*x)*(a + c*x^2)^(5/2),x]","\frac{5}{16} a^2 d x \sqrt{a+c x^2}+\frac{5 a^3 d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{1}{6} d x \left(a+c x^2\right)^{5/2}+\frac{5}{24} a d x \left(a+c x^2\right)^{3/2}+\frac{e \left(a+c x^2\right)^{7/2}}{7 c}","\frac{5}{16} a^2 d x \sqrt{a+c x^2}+\frac{5 a^3 d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{1}{6} d x \left(a+c x^2\right)^{5/2}+\frac{5}{24} a d x \left(a+c x^2\right)^{3/2}+\frac{e \left(a+c x^2\right)^{7/2}}{7 c}",1,"(5*a^2*d*x*Sqrt[a + c*x^2])/16 + (5*a*d*x*(a + c*x^2)^(3/2))/24 + (d*x*(a + c*x^2)^(5/2))/6 + (e*(a + c*x^2)^(7/2))/(7*c) + (5*a^3*d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*Sqrt[c])","A",6,4,17,0.2353,1,"{641, 195, 217, 206}"
549,1,226,0,0.2593475,"\int \frac{\left(a+c x^2\right)^{5/2}}{d+e x} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x),x]","-\frac{\sqrt{c} d \left(15 a^2 e^4+20 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 e^6}+\frac{\left(a+c x^2\right)^{3/2} \left(4 \left(a e^2+c d^2\right)-3 c d e x\right)}{12 e^3}+\frac{\sqrt{a+c x^2} \left(8 \left(a e^2+c d^2\right)^2-c d e x \left(7 a e^2+4 c d^2\right)\right)}{8 e^5}-\frac{\left(a e^2+c d^2\right)^{5/2} \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{\left(a+c x^2\right)^{5/2}}{5 e}","-\frac{\sqrt{c} d \left(15 a^2 e^4+20 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 e^6}+\frac{\left(a+c x^2\right)^{3/2} \left(4 \left(a e^2+c d^2\right)-3 c d e x\right)}{12 e^3}+\frac{\sqrt{a+c x^2} \left(8 \left(a e^2+c d^2\right)^2-c d e x \left(7 a e^2+4 c d^2\right)\right)}{8 e^5}-\frac{\left(a e^2+c d^2\right)^{5/2} \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{\left(a+c x^2\right)^{5/2}}{5 e}",1,"((8*(c*d^2 + a*e^2)^2 - c*d*e*(4*c*d^2 + 7*a*e^2)*x)*Sqrt[a + c*x^2])/(8*e^5) + ((4*(c*d^2 + a*e^2) - 3*c*d*e*x)*(a + c*x^2)^(3/2))/(12*e^3) + (a + c*x^2)^(5/2)/(5*e) - (Sqrt[c]*d*(8*c^2*d^4 + 20*a*c*d^2*e^2 + 15*a^2*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*e^6) - ((c*d^2 + a*e^2)^(5/2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/e^6","A",8,6,19,0.3158,1,"{735, 815, 844, 217, 206, 725}"
550,1,219,0,0.2439013,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^2,x]","\frac{5 \sqrt{c} \left(3 a^2 e^4+12 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 e^6}-\frac{5 c \sqrt{a+c x^2} \left(8 d \left(a e^2+c d^2\right)-e x \left(3 a e^2+4 c d^2\right)\right)}{8 e^5}+\frac{5 c d \left(a e^2+c d^2\right)^{3/2} \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{5 c \left(a+c x^2\right)^{3/2} (4 d-3 e x)}{12 e^3}-\frac{\left(a+c x^2\right)^{5/2}}{e (d+e x)}","\frac{5 \sqrt{c} \left(3 a^2 e^4+12 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 e^6}-\frac{5 c \sqrt{a+c x^2} \left(8 d \left(a e^2+c d^2\right)-e x \left(3 a e^2+4 c d^2\right)\right)}{8 e^5}+\frac{5 c d \left(a e^2+c d^2\right)^{3/2} \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{5 c \left(a+c x^2\right)^{3/2} (4 d-3 e x)}{12 e^3}-\frac{\left(a+c x^2\right)^{5/2}}{e (d+e x)}",1,"(-5*c*(8*d*(c*d^2 + a*e^2) - e*(4*c*d^2 + 3*a*e^2)*x)*Sqrt[a + c*x^2])/(8*e^5) - (5*c*(4*d - 3*e*x)*(a + c*x^2)^(3/2))/(12*e^3) - (a + c*x^2)^(5/2)/(e*(d + e*x)) + (5*Sqrt[c]*(8*c^2*d^4 + 12*a*c*d^2*e^2 + 3*a^2*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*e^6) + (5*c*d*(c*d^2 + a*e^2)^(3/2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/e^6","A",8,6,19,0.3158,1,"{733, 815, 844, 217, 206, 725}"
551,1,213,0,0.2386048,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^3,x]","-\frac{5 c^{3/2} d \left(3 a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 e^6}+\frac{5 c \sqrt{a+c x^2} \left(a e^2+4 c d^2-2 c d e x\right)}{2 e^5}-\frac{5 c \sqrt{a e^2+c d^2} \left(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)}{2 e^6}+\frac{5 c \left(a+c x^2\right)^{3/2} (4 d+e x)}{6 e^3 (d+e x)}-\frac{\left(a+c x^2\right)^{5/2}}{2 e (d+e x)^2}","-\frac{5 c^{3/2} d \left(3 a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 e^6}+\frac{5 c \sqrt{a+c x^2} \left(a e^2+4 c d^2-2 c d e x\right)}{2 e^5}-\frac{5 c \sqrt{a e^2+c d^2} \left(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)}{2 e^6}+\frac{5 c \left(a+c x^2\right)^{3/2} (4 d+e x)}{6 e^3 (d+e x)}-\frac{\left(a+c x^2\right)^{5/2}}{2 e (d+e x)^2}",1,"(5*c*(4*c*d^2 + a*e^2 - 2*c*d*e*x)*Sqrt[a + c*x^2])/(2*e^5) + (5*c*(4*d + e*x)*(a + c*x^2)^(3/2))/(6*e^3*(d + e*x)) - (a + c*x^2)^(5/2)/(2*e*(d + e*x)^2) - (5*c^(3/2)*d*(4*c*d^2 + 3*a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*e^6) - (5*c*Sqrt[c*d^2 + a*e^2]*(4*c*d^2 + a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(2*e^6)","A",8,7,19,0.3684,1,"{733, 813, 815, 844, 217, 206, 725}"
552,1,222,0,0.2179839,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^4,x]","\frac{5 c^{3/2} \left(a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 e^6}+\frac{5 c^2 d \left(3 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)}{2 e^6 \sqrt{a e^2+c d^2}}-\frac{5 c \sqrt{a+c x^2} \left(a e^2+4 c d^2+2 c d e x\right)}{2 e^5 (d+e x)}+\frac{5 c \left(a+c x^2\right)^{3/2} (2 d+e x)}{6 e^3 (d+e x)^2}-\frac{\left(a+c x^2\right)^{5/2}}{3 e (d+e x)^3}","\frac{5 c^{3/2} \left(a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 e^6}+\frac{5 c^2 d \left(3 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)}{2 e^6 \sqrt{a e^2+c d^2}}-\frac{5 c \sqrt{a+c x^2} \left(a e^2+4 c d^2+2 c d e x\right)}{2 e^5 (d+e x)}+\frac{5 c \left(a+c x^2\right)^{3/2} (2 d+e x)}{6 e^3 (d+e x)^2}-\frac{\left(a+c x^2\right)^{5/2}}{3 e (d+e x)^3}",1,"(-5*c*(4*c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[a + c*x^2])/(2*e^5*(d + e*x)) + (5*c*(2*d + e*x)*(a + c*x^2)^(3/2))/(6*e^3*(d + e*x)^2) - (a + c*x^2)^(5/2)/(3*e*(d + e*x)^3) + (5*c^(3/2)*(4*c*d^2 + a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*e^6) + (5*c^2*d*(4*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])])/(2*e^6*Sqrt[c*d^2 + a*e^2])","A",8,6,19,0.3158,1,"{733, 813, 844, 217, 206, 725}"
553,1,287,0,0.3025732,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^5} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^5,x]","-\frac{5 c^2 \left(3 a^2 e^4+12 a c d^2 e^2+8 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 e^6 \left(a e^2+c d^2\right)^{3/2}}+\frac{5 c^2 \sqrt{a+c x^2} \left(e x \left(3 a e^2+4 c d^2\right)+8 d \left(a e^2+c d^2\right)\right)}{8 e^5 (d+e x) \left(a e^2+c d^2\right)}-\frac{5 c^{5/2} d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^6}-\frac{5 c \left(a+c x^2\right)^{3/2} \left(3 e x \left(a e^2+2 c d^2\right)+d \left(a e^2+4 c d^2\right)\right)}{24 e^3 (d+e x)^3 \left(a e^2+c d^2\right)}-\frac{\left(a+c x^2\right)^{5/2}}{4 e (d+e x)^4}","-\frac{5 c^2 \left(3 a^2 e^4+12 a c d^2 e^2+8 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 e^6 \left(a e^2+c d^2\right)^{3/2}}+\frac{5 c^2 \sqrt{a+c x^2} \left(e x \left(3 a e^2+4 c d^2\right)+8 d \left(a e^2+c d^2\right)\right)}{8 e^5 (d+e x) \left(a e^2+c d^2\right)}-\frac{5 c^{5/2} d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^6}-\frac{5 c \left(a+c x^2\right)^{3/2} \left(3 e x \left(a e^2+2 c d^2\right)+d \left(a e^2+4 c d^2\right)\right)}{24 e^3 (d+e x)^3 \left(a e^2+c d^2\right)}-\frac{\left(a+c x^2\right)^{5/2}}{4 e (d+e x)^4}",1,"(5*c^2*(8*d*(c*d^2 + a*e^2) + e*(4*c*d^2 + 3*a*e^2)*x)*Sqrt[a + c*x^2])/(8*e^5*(c*d^2 + a*e^2)*(d + e*x)) - (5*c*(d*(4*c*d^2 + a*e^2) + 3*e*(2*c*d^2 + a*e^2)*x)*(a + c*x^2)^(3/2))/(24*e^3*(c*d^2 + a*e^2)*(d + e*x)^3) - (a + c*x^2)^(5/2)/(4*e*(d + e*x)^4) - (5*c^(5/2)*d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/e^6 - (5*c^2*(8*c^2*d^4 + 12*a*c*d^2*e^2 + 3*a^2*e^4)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(8*e^6*(c*d^2 + a*e^2)^(3/2))","A",8,7,19,0.3684,1,"{733, 811, 813, 844, 217, 206, 725}"
554,1,314,0,0.3432718,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^6} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^6,x]","-\frac{c^2 \sqrt{a+c x^2} \left(e x \left(8 a^2 e^4+23 a c d^2 e^2+12 c^2 d^4\right)+d \left(a^2 e^4+12 a c d^2 e^2+8 c^2 d^4\right)\right)}{8 e^5 (d+e x)^2 \left(a e^2+c d^2\right)^2}+\frac{c^3 d \left(15 a^2 e^4+20 a c d^2 e^2+8 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 e^6 \left(a e^2+c d^2\right)^{5/2}}+\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^6}-\frac{c \left(a+c x^2\right)^{3/2} \left(e x \left(4 a e^2+7 c d^2\right)+d \left(a e^2+4 c d^2\right)\right)}{12 e^3 (d+e x)^4 \left(a e^2+c d^2\right)}-\frac{\left(a+c x^2\right)^{5/2}}{5 e (d+e x)^5}","-\frac{c^2 \sqrt{a+c x^2} \left(e x \left(8 a^2 e^4+23 a c d^2 e^2+12 c^2 d^4\right)+d \left(a^2 e^4+12 a c d^2 e^2+8 c^2 d^4\right)\right)}{8 e^5 (d+e x)^2 \left(a e^2+c d^2\right)^2}+\frac{c^3 d \left(15 a^2 e^4+20 a c d^2 e^2+8 c^2 d^4\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{8 e^6 \left(a e^2+c d^2\right)^{5/2}}+\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{e^6}-\frac{c \left(a+c x^2\right)^{3/2} \left(e x \left(4 a e^2+7 c d^2\right)+d \left(a e^2+4 c d^2\right)\right)}{12 e^3 (d+e x)^4 \left(a e^2+c d^2\right)}-\frac{\left(a+c x^2\right)^{5/2}}{5 e (d+e x)^5}",1,"-(c^2*(d*(8*c^2*d^4 + 12*a*c*d^2*e^2 + a^2*e^4) + e*(12*c^2*d^4 + 23*a*c*d^2*e^2 + 8*a^2*e^4)*x)*Sqrt[a + c*x^2])/(8*e^5*(c*d^2 + a*e^2)^2*(d + e*x)^2) - (c*(d*(4*c*d^2 + a*e^2) + e*(7*c*d^2 + 4*a*e^2)*x)*(a + c*x^2)^(3/2))/(12*e^3*(c*d^2 + a*e^2)*(d + e*x)^4) - (a + c*x^2)^(5/2)/(5*e*(d + e*x)^5) + (c^(5/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/e^6 + (c^3*d*(8*c^2*d^4 + 20*a*c*d^2*e^2 + 15*a^2*e^4)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(8*e^6*(c*d^2 + a*e^2)^(5/2))","A",8,6,19,0.3158,1,"{733, 811, 844, 217, 206, 725}"
555,1,203,0,0.1054143,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^7} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^7,x]","-\frac{5 a^2 c^2 \sqrt{a+c x^2} (a e-c d x)}{16 (d+e x)^2 \left(a e^2+c d^2\right)^3}-\frac{5 a^3 c^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{16 \left(a e^2+c d^2\right)^{7/2}}-\frac{5 a c \left(a+c x^2\right)^{3/2} (a e-c d x)}{24 (d+e x)^4 \left(a e^2+c d^2\right)^2}-\frac{\left(a+c x^2\right)^{5/2} (a e-c d x)}{6 (d+e x)^6 \left(a e^2+c d^2\right)}","-\frac{5 a^2 c^2 \sqrt{a+c x^2} (a e-c d x)}{16 (d+e x)^2 \left(a e^2+c d^2\right)^3}-\frac{5 a^3 c^3 \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{16 \left(a e^2+c d^2\right)^{7/2}}-\frac{5 a c \left(a+c x^2\right)^{3/2} (a e-c d x)}{24 (d+e x)^4 \left(a e^2+c d^2\right)^2}-\frac{\left(a+c x^2\right)^{5/2} (a e-c d x)}{6 (d+e x)^6 \left(a e^2+c d^2\right)}",1,"(-5*a^2*c^2*(a*e - c*d*x)*Sqrt[a + c*x^2])/(16*(c*d^2 + a*e^2)^3*(d + e*x)^2) - (5*a*c*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(24*(c*d^2 + a*e^2)^2*(d + e*x)^4) - ((a*e - c*d*x)*(a + c*x^2)^(5/2))/(6*(c*d^2 + a*e^2)*(d + e*x)^6) - (5*a^3*c^3*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(16*(c*d^2 + a*e^2)^(7/2))","A",5,3,19,0.1579,1,"{721, 725, 206}"
556,1,246,0,0.124018,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^8} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^8,x]","-\frac{5 a^2 c^3 d \sqrt{a+c x^2} (a e-c d x)}{16 (d+e x)^2 \left(a e^2+c d^2\right)^4}-\frac{5 a^3 c^4 d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{16 \left(a e^2+c d^2\right)^{9/2}}-\frac{5 a c^2 d \left(a+c x^2\right)^{3/2} (a e-c d x)}{24 (d+e x)^4 \left(a e^2+c d^2\right)^3}-\frac{c d \left(a+c x^2\right)^{5/2} (a e-c d x)}{6 (d+e x)^6 \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{7/2}}{7 (d+e x)^7 \left(a e^2+c d^2\right)}","-\frac{5 a^2 c^3 d \sqrt{a+c x^2} (a e-c d x)}{16 (d+e x)^2 \left(a e^2+c d^2\right)^4}-\frac{5 a^3 c^4 d \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{16 \left(a e^2+c d^2\right)^{9/2}}-\frac{5 a c^2 d \left(a+c x^2\right)^{3/2} (a e-c d x)}{24 (d+e x)^4 \left(a e^2+c d^2\right)^3}-\frac{c d \left(a+c x^2\right)^{5/2} (a e-c d x)}{6 (d+e x)^6 \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{7/2}}{7 (d+e x)^7 \left(a e^2+c d^2\right)}",1,"(-5*a^2*c^3*d*(a*e - c*d*x)*Sqrt[a + c*x^2])/(16*(c*d^2 + a*e^2)^4*(d + e*x)^2) - (5*a*c^2*d*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(24*(c*d^2 + a*e^2)^3*(d + e*x)^4) - (c*d*(a*e - c*d*x)*(a + c*x^2)^(5/2))/(6*(c*d^2 + a*e^2)^2*(d + e*x)^6) - (e*(a + c*x^2)^(7/2))/(7*(c*d^2 + a*e^2)*(d + e*x)^7) - (5*a^3*c^4*d*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(16*(c*d^2 + a*e^2)^(9/2))","A",6,4,19,0.2105,1,"{731, 721, 725, 206}"
557,1,332,0,0.2577732,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^9} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^9,x]","-\frac{5 a^2 c^3 \sqrt{a+c x^2} \left(8 c d^2-a e^2\right) (a e-c d x)}{128 (d+e x)^2 \left(a e^2+c d^2\right)^5}-\frac{5 a^3 c^4 \left(8 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{128 \left(a e^2+c d^2\right)^{11/2}}-\frac{5 a c^2 \left(a+c x^2\right)^{3/2} \left(8 c d^2-a e^2\right) (a e-c d x)}{192 (d+e x)^4 \left(a e^2+c d^2\right)^4}-\frac{9 c d e \left(a+c x^2\right)^{7/2}}{56 (d+e x)^7 \left(a e^2+c d^2\right)^2}-\frac{c \left(a+c x^2\right)^{5/2} \left(8 c d^2-a e^2\right) (a e-c d x)}{48 (d+e x)^6 \left(a e^2+c d^2\right)^3}-\frac{e \left(a+c x^2\right)^{7/2}}{8 (d+e x)^8 \left(a e^2+c d^2\right)}","-\frac{5 a^2 c^3 \sqrt{a+c x^2} \left(8 c d^2-a e^2\right) (a e-c d x)}{128 (d+e x)^2 \left(a e^2+c d^2\right)^5}-\frac{5 a^3 c^4 \left(8 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{128 \left(a e^2+c d^2\right)^{11/2}}-\frac{5 a c^2 \left(a+c x^2\right)^{3/2} \left(8 c d^2-a e^2\right) (a e-c d x)}{192 (d+e x)^4 \left(a e^2+c d^2\right)^4}-\frac{9 c d e \left(a+c x^2\right)^{7/2}}{56 (d+e x)^7 \left(a e^2+c d^2\right)^2}-\frac{c \left(a+c x^2\right)^{5/2} \left(8 c d^2-a e^2\right) (a e-c d x)}{48 (d+e x)^6 \left(a e^2+c d^2\right)^3}-\frac{e \left(a+c x^2\right)^{7/2}}{8 (d+e x)^8 \left(a e^2+c d^2\right)}",1,"(-5*a^2*c^3*(8*c*d^2 - a*e^2)*(a*e - c*d*x)*Sqrt[a + c*x^2])/(128*(c*d^2 + a*e^2)^5*(d + e*x)^2) - (5*a*c^2*(8*c*d^2 - a*e^2)*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(192*(c*d^2 + a*e^2)^4*(d + e*x)^4) - (c*(8*c*d^2 - a*e^2)*(a*e - c*d*x)*(a + c*x^2)^(5/2))/(48*(c*d^2 + a*e^2)^3*(d + e*x)^6) - (e*(a + c*x^2)^(7/2))/(8*(c*d^2 + a*e^2)*(d + e*x)^8) - (9*c*d*e*(a + c*x^2)^(7/2))/(56*(c*d^2 + a*e^2)^2*(d + e*x)^7) - (5*a^3*c^4*(8*c*d^2 - a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(128*(c*d^2 + a*e^2)^(11/2))","A",7,5,19,0.2632,1,"{745, 807, 721, 725, 206}"
558,1,56,0,0.0327453,"\int \frac{\sqrt{2+x^2}}{1+4 x} \, dx","Int[Sqrt[2 + x^2]/(1 + 4*x),x]","\frac{\sqrt{x^2+2}}{4}-\frac{1}{16} \sqrt{33} \tanh ^{-1}\left(\frac{8-x}{\sqrt{33} \sqrt{x^2+2}}\right)-\frac{1}{16} \sinh ^{-1}\left(\frac{x}{\sqrt{2}}\right)","\frac{\sqrt{x^2+2}}{4}-\frac{1}{16} \sqrt{33} \tanh ^{-1}\left(\frac{8-x}{\sqrt{33} \sqrt{x^2+2}}\right)-\frac{1}{16} \sinh ^{-1}\left(\frac{x}{\sqrt{2}}\right)",1,"Sqrt[2 + x^2]/4 - ArcSinh[x/Sqrt[2]]/16 - (Sqrt[33]*ArcTanh[(8 - x)/(Sqrt[33]*Sqrt[2 + x^2])])/16","A",5,5,17,0.2941,1,"{735, 844, 215, 725, 206}"
559,1,67,0,0.0439505,"\int \frac{\sqrt{2+4 x^2}}{5+4 x} \, dx","Int[Sqrt[2 + 4*x^2]/(5 + 4*x),x]","\frac{\sqrt{2 x^2+1}}{2 \sqrt{2}}-\frac{1}{8} \sqrt{33} \tanh ^{-1}\left(\frac{\sqrt{\frac{2}{33}} (2-5 x)}{\sqrt{2 x^2+1}}\right)-\frac{5}{8} \sinh ^{-1}\left(\sqrt{2} x\right)","\frac{\sqrt{2 x^2+1}}{2 \sqrt{2}}-\frac{1}{8} \sqrt{33} \tanh ^{-1}\left(\frac{\sqrt{\frac{2}{33}} (2-5 x)}{\sqrt{2 x^2+1}}\right)-\frac{5}{8} \sinh ^{-1}\left(\sqrt{2} x\right)",1,"Sqrt[1 + 2*x^2]/(2*Sqrt[2]) - (5*ArcSinh[Sqrt[2]*x])/8 - (Sqrt[33]*ArcTanh[(Sqrt[2/33]*(2 - 5*x))/Sqrt[1 + 2*x^2]])/8","A",5,5,19,0.2632,1,"{735, 844, 215, 725, 206}"
560,1,55,0,0.0152842,"\int (2+3 x) \sqrt{-5+7 x^2} \, dx","Int[(2 + 3*x)*Sqrt[-5 + 7*x^2],x]","\frac{1}{7} \left(7 x^2-5\right)^{3/2}+x \sqrt{7 x^2-5}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{7} x}{\sqrt{7 x^2-5}}\right)}{\sqrt{7}}","\frac{1}{7} \left(7 x^2-5\right)^{3/2}+x \sqrt{7 x^2-5}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{7} x}{\sqrt{7 x^2-5}}\right)}{\sqrt{7}}",1,"x*Sqrt[-5 + 7*x^2] + (-5 + 7*x^2)^(3/2)/7 - (5*ArcTanh[(Sqrt[7]*x)/Sqrt[-5 + 7*x^2]])/Sqrt[7]","A",4,4,17,0.2353,1,"{641, 195, 217, 206}"
561,1,161,0,0.1614336,"\int \frac{(d+e x)^4}{\sqrt{a+c x^2}} \, dx","Int[(d + e*x)^4/Sqrt[a + c*x^2],x]","\frac{\left(3 a^2 e^4-24 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^{5/2}}+\frac{e \sqrt{a+c x^2} \left(e x \left(26 c d^2-9 a e^2\right)+4 d \left(19 c d^2-16 a e^2\right)\right)}{24 c^2}+\frac{e \sqrt{a+c x^2} (d+e x)^3}{4 c}+\frac{7 d e \sqrt{a+c x^2} (d+e x)^2}{12 c}","\frac{\left(3 a^2 e^4-24 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^{5/2}}+\frac{e \sqrt{a+c x^2} \left(e x \left(26 c d^2-9 a e^2\right)+4 d \left(19 c d^2-16 a e^2\right)\right)}{24 c^2}+\frac{e \sqrt{a+c x^2} (d+e x)^3}{4 c}+\frac{7 d e \sqrt{a+c x^2} (d+e x)^2}{12 c}",1,"(7*d*e*(d + e*x)^2*Sqrt[a + c*x^2])/(12*c) + (e*(d + e*x)^3*Sqrt[a + c*x^2])/(4*c) + (e*(4*d*(19*c*d^2 - 16*a*e^2) + e*(26*c*d^2 - 9*a*e^2)*x)*Sqrt[a + c*x^2])/(24*c^2) + ((8*c^2*d^4 - 24*a*c*d^2*e^2 + 3*a^2*e^4)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(5/2))","A",5,5,19,0.2632,1,"{743, 833, 780, 217, 206}"
562,1,110,0,0.0753626,"\int \frac{(d+e x)^3}{\sqrt{a+c x^2}} \, dx","Int[(d + e*x)^3/Sqrt[a + c*x^2],x]","\frac{e \sqrt{a+c x^2} \left(4 \left(4 c d^2-a e^2\right)+5 c d e x\right)}{6 c^2}+\frac{d \left(2 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2}}+\frac{e \sqrt{a+c x^2} (d+e x)^2}{3 c}","\frac{e \sqrt{a+c x^2} \left(4 \left(4 c d^2-a e^2\right)+5 c d e x\right)}{6 c^2}+\frac{d \left(2 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2}}+\frac{e \sqrt{a+c x^2} (d+e x)^2}{3 c}",1,"(e*(d + e*x)^2*Sqrt[a + c*x^2])/(3*c) + (e*(4*(4*c*d^2 - a*e^2) + 5*c*d*e*x)*Sqrt[a + c*x^2])/(6*c^2) + (d*(2*c*d^2 - 3*a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2))","A",4,4,19,0.2105,1,"{743, 780, 217, 206}"
563,1,86,0,0.0402104,"\int \frac{(d+e x)^2}{\sqrt{a+c x^2}} \, dx","Int[(d + e*x)^2/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}}+\frac{3 d e \sqrt{a+c x^2}}{2 c}+\frac{e \sqrt{a+c x^2} (d+e x)}{2 c}","\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}}+\frac{3 d e \sqrt{a+c x^2}}{2 c}+\frac{e \sqrt{a+c x^2} (d+e x)}{2 c}",1,"(3*d*e*Sqrt[a + c*x^2])/(2*c) + (e*(d + e*x)*Sqrt[a + c*x^2])/(2*c) + ((2*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2))","A",4,4,19,0.2105,1,"{743, 641, 217, 206}"
564,1,43,0,0.0129593,"\int \frac{d+e x}{\sqrt{a+c x^2}} \, dx","Int[(d + e*x)/Sqrt[a + c*x^2],x]","\frac{d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c}}+\frac{e \sqrt{a+c x^2}}{c}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c}}+\frac{e \sqrt{a+c x^2}}{c}",1,"(e*Sqrt[a + c*x^2])/c + (d*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/Sqrt[c]","A",3,3,17,0.1765,1,"{641, 217, 206}"
565,1,54,0,0.0166401,"\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}"
566,1,91,0,0.0339196,"\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}"
567,1,145,0,0.0707614,"\int \frac{1}{(d+e x)^3 \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)^3*Sqrt[a + c*x^2]),x]","-\frac{3 c d e \sqrt{a+c x^2}}{2 (d+e x) \left(a e^2+c d^2\right)^2}-\frac{e \sqrt{a+c x^2}}{2 (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{c \left(2 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{5/2}}","-\frac{3 c d e \sqrt{a+c x^2}}{2 (d+e x) \left(a e^2+c d^2\right)^2}-\frac{e \sqrt{a+c x^2}}{2 (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{c \left(2 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{5/2}}",1,"-(e*Sqrt[a + c*x^2])/(2*(c*d^2 + a*e^2)*(d + e*x)^2) - (3*c*d*e*Sqrt[a + c*x^2])/(2*(c*d^2 + a*e^2)^2*(d + e*x)) - (c*(2*c*d^2 - a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(2*(c*d^2 + a*e^2)^(5/2))","A",4,4,19,0.2105,1,"{745, 807, 725, 206}"
568,1,198,0,0.1638198,"\int \frac{1}{(d+e x)^4 \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)^4*Sqrt[a + c*x^2]),x]","-\frac{c^2 d \left(2 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{7/2}}-\frac{c e \sqrt{a+c x^2} \left(11 c d^2-4 a e^2\right)}{6 (d+e x) \left(a e^2+c d^2\right)^3}-\frac{5 c d e \sqrt{a+c x^2}}{6 (d+e x)^2 \left(a e^2+c d^2\right)^2}-\frac{e \sqrt{a+c x^2}}{3 (d+e x)^3 \left(a e^2+c d^2\right)}","-\frac{c^2 d \left(2 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{7/2}}-\frac{c e \sqrt{a+c x^2} \left(11 c d^2-4 a e^2\right)}{6 (d+e x) \left(a e^2+c d^2\right)^3}-\frac{5 c d e \sqrt{a+c x^2}}{6 (d+e x)^2 \left(a e^2+c d^2\right)^2}-\frac{e \sqrt{a+c x^2}}{3 (d+e x)^3 \left(a e^2+c d^2\right)}",1,"-(e*Sqrt[a + c*x^2])/(3*(c*d^2 + a*e^2)*(d + e*x)^3) - (5*c*d*e*Sqrt[a + c*x^2])/(6*(c*d^2 + a*e^2)^2*(d + e*x)^2) - (c*e*(11*c*d^2 - 4*a*e^2)*Sqrt[a + c*x^2])/(6*(c*d^2 + a*e^2)^3*(d + e*x)) - (c^2*d*(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])])/(2*(c*d^2 + a*e^2)^(7/2))","A",5,5,19,0.2632,1,"{745, 835, 807, 725, 206}"
569,1,162,0,0.1475536,"\int \frac{(d+e x)^4}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^4/(a + c*x^2)^(3/2),x]","-\frac{e \sqrt{a+c x^2} \left(e x \left(2 c d^2-3 a e^2\right)+4 d \left(c d^2-4 a e^2\right)\right)}{2 a c^2}+\frac{3 e^2 \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{5/2}}-\frac{(d+e x)^3 (a e-c d x)}{a c \sqrt{a+c x^2}}-\frac{d e \sqrt{a+c x^2} (d+e x)^2}{a c}","-\frac{e \sqrt{a+c x^2} \left(e x \left(2 c d^2-3 a e^2\right)+4 d \left(c d^2-4 a e^2\right)\right)}{2 a c^2}+\frac{3 e^2 \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{5/2}}-\frac{(d+e x)^3 (a e-c d x)}{a c \sqrt{a+c x^2}}-\frac{d e \sqrt{a+c x^2} (d+e x)^2}{a c}",1,"-(((a*e - c*d*x)*(d + e*x)^3)/(a*c*Sqrt[a + c*x^2])) - (d*e*(d + e*x)^2*Sqrt[a + c*x^2])/(a*c) - (e*(4*d*(c*d^2 - 4*a*e^2) + e*(2*c*d^2 - 3*a*e^2)*x)*Sqrt[a + c*x^2])/(2*a*c^2) + (3*e^2*(4*c*d^2 - a*e^2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(5/2))","A",5,5,19,0.2632,1,"{739, 833, 780, 217, 206}"
570,1,106,0,0.0574783,"\int \frac{(d+e x)^3}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^3/(a + c*x^2)^(3/2),x]","-\frac{e \sqrt{a+c x^2} \left(2 \left(c d^2-a e^2\right)+c d e x\right)}{a c^2}+\frac{3 d e^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}-\frac{(d+e x)^2 (a e-c d x)}{a c \sqrt{a+c x^2}}","-\frac{e \sqrt{a+c x^2} \left(2 \left(c d^2-a e^2\right)+c d e x\right)}{a c^2}+\frac{3 d e^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}-\frac{(d+e x)^2 (a e-c d x)}{a c \sqrt{a+c x^2}}",1,"-(((a*e - c*d*x)*(d + e*x)^2)/(a*c*Sqrt[a + c*x^2])) - (e*(2*(c*d^2 - a*e^2) + c*d*e*x)*Sqrt[a + c*x^2])/(a*c^2) + (3*d*e^2*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(3/2)","A",4,4,19,0.2105,1,"{739, 780, 217, 206}"
571,1,83,0,0.0345132,"\int \frac{(d+e x)^2}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^2/(a + c*x^2)^(3/2),x]","\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}-\frac{d e \sqrt{a+c x^2}}{a c}-\frac{(d+e x) (a e-c d x)}{a c \sqrt{a+c x^2}}","\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}-\frac{d e \sqrt{a+c x^2}}{a c}-\frac{(d+e x) (a e-c d x)}{a c \sqrt{a+c x^2}}",1,"-(((a*e - c*d*x)*(d + e*x))/(a*c*Sqrt[a + c*x^2])) - (d*e*Sqrt[a + c*x^2])/(a*c) + (e^2*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(3/2)","A",4,4,19,0.2105,1,"{739, 641, 217, 206}"
572,1,28,0,0.0070311,"\int \frac{d+e x}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)/(a + c*x^2)^(3/2),x]","-\frac{a e-c d x}{a c \sqrt{a+c x^2}}","-\frac{a e-c d x}{a c \sqrt{a+c x^2}}",1,"-((a*e - c*d*x)/(a*c*Sqrt[a + c*x^2]))","A",1,1,17,0.05882,1,"{637}"
573,1,94,0,0.0584725,"\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}"
574,1,151,0,0.0844861,"\int \frac{1}{(d+e x)^2 \left(a+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^2*(a + c*x^2)^(3/2)),x]","\frac{e \sqrt{a+c x^2} \left(c d^2-2 a e^2\right)}{a (d+e x) \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} (d+e x) \left(a e^2+c d^2\right)}-\frac{3 c d 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)^{5/2}}","\frac{e \sqrt{a+c x^2} \left(c d^2-2 a e^2\right)}{a (d+e x) \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} (d+e x) \left(a e^2+c d^2\right)}-\frac{3 c d 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)^{5/2}}",1,"(a*e + c*d*x)/(a*(c*d^2 + a*e^2)*(d + e*x)*Sqrt[a + c*x^2]) + (e*(c*d^2 - 2*a*e^2)*Sqrt[a + c*x^2])/(a*(c*d^2 + a*e^2)^2*(d + e*x)) - (3*c*d*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)^(5/2)","A",4,4,19,0.2105,1,"{741, 807, 725, 206}"
575,1,223,0,0.1984638,"\int \frac{1}{(d+e x)^3 \left(a+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^3*(a + c*x^2)^(3/2)),x]","\frac{c d e \sqrt{a+c x^2} \left(2 c d^2-13 a e^2\right)}{2 a (d+e x) \left(a e^2+c d^2\right)^3}+\frac{e \sqrt{a+c x^2} \left(2 c d^2-3 a e^2\right)}{2 a (d+e x)^2 \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{3 c e^2 \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{7/2}}","\frac{c d e \sqrt{a+c x^2} \left(2 c d^2-13 a e^2\right)}{2 a (d+e x) \left(a e^2+c d^2\right)^3}+\frac{e \sqrt{a+c x^2} \left(2 c d^2-3 a e^2\right)}{2 a (d+e x)^2 \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{3 c e^2 \left(4 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{7/2}}",1,"(a*e + c*d*x)/(a*(c*d^2 + a*e^2)*(d + e*x)^2*Sqrt[a + c*x^2]) + (e*(2*c*d^2 - 3*a*e^2)*Sqrt[a + c*x^2])/(2*a*(c*d^2 + a*e^2)^2*(d + e*x)^2) + (c*d*e*(2*c*d^2 - 13*a*e^2)*Sqrt[a + c*x^2])/(2*a*(c*d^2 + a*e^2)^3*(d + e*x)) - (3*c*e^2*(4*c*d^2 - a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(2*(c*d^2 + a*e^2)^(7/2))","A",5,5,19,0.2632,1,"{741, 835, 807, 725, 206}"
576,1,293,0,0.3738607,"\int \frac{1}{(d+e x)^4 \left(a+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^4*(a + c*x^2)^(3/2)),x]","\frac{c e \sqrt{a+c x^2} \left(16 a^2 e^4-83 a c d^2 e^2+6 c^2 d^4\right)}{6 a (d+e x) \left(a e^2+c d^2\right)^4}-\frac{5 c^2 d e^2 \left(4 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{9/2}}+\frac{c d e \sqrt{a+c x^2} \left(6 c d^2-29 a e^2\right)}{6 a (d+e x)^2 \left(a e^2+c d^2\right)^3}+\frac{e \sqrt{a+c x^2} \left(3 c d^2-4 a e^2\right)}{3 a (d+e x)^3 \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} (d+e x)^3 \left(a e^2+c d^2\right)}","\frac{c e \sqrt{a+c x^2} \left(16 a^2 e^4-83 a c d^2 e^2+6 c^2 d^4\right)}{6 a (d+e x) \left(a e^2+c d^2\right)^4}-\frac{5 c^2 d e^2 \left(4 c d^2-3 a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{9/2}}+\frac{c d e \sqrt{a+c x^2} \left(6 c d^2-29 a e^2\right)}{6 a (d+e x)^2 \left(a e^2+c d^2\right)^3}+\frac{e \sqrt{a+c x^2} \left(3 c d^2-4 a e^2\right)}{3 a (d+e x)^3 \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} (d+e x)^3 \left(a e^2+c d^2\right)}",1,"(a*e + c*d*x)/(a*(c*d^2 + a*e^2)*(d + e*x)^3*Sqrt[a + c*x^2]) + (e*(3*c*d^2 - 4*a*e^2)*Sqrt[a + c*x^2])/(3*a*(c*d^2 + a*e^2)^2*(d + e*x)^3) + (c*d*e*(6*c*d^2 - 29*a*e^2)*Sqrt[a + c*x^2])/(6*a*(c*d^2 + a*e^2)^3*(d + e*x)^2) + (c*e*(6*c^2*d^4 - 83*a*c*d^2*e^2 + 16*a^2*e^4)*Sqrt[a + c*x^2])/(6*a*(c*d^2 + a*e^2)^4*(d + e*x)) - (5*c^2*d*e^2*(4*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])])/(2*(c*d^2 + a*e^2)^(9/2))","A",6,5,19,0.2632,1,"{741, 835, 807, 725, 206}"
577,1,191,0,0.1632137,"\int \frac{(d+e x)^5}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^5/(a + c*x^2)^(5/2),x]","-\frac{e \sqrt{a+c x^2} \left(4 \left(-2 a^2 e^4+4 a c d^2 e^2+c^2 d^4\right)+c d e x \left(7 a e^2+2 c d^2\right)\right)}{3 a^2 c^3}-\frac{2 (d+e x)^2 \left(2 a^2 e^3-c d x \left(3 a e^2+c d^2\right)\right)}{3 a^2 c^2 \sqrt{a+c x^2}}+\frac{5 d e^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{5/2}}-\frac{(d+e x)^4 (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}","-\frac{e \sqrt{a+c x^2} \left(4 \left(-2 a^2 e^4+4 a c d^2 e^2+c^2 d^4\right)+c d e x \left(7 a e^2+2 c d^2\right)\right)}{3 a^2 c^3}-\frac{2 (d+e x)^2 \left(2 a^2 e^3-c d x \left(3 a e^2+c d^2\right)\right)}{3 a^2 c^2 \sqrt{a+c x^2}}+\frac{5 d e^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{5/2}}-\frac{(d+e x)^4 (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-((a*e - c*d*x)*(d + e*x)^4)/(3*a*c*(a + c*x^2)^(3/2)) - (2*(d + e*x)^2*(2*a^2*e^3 - c*d*(c*d^2 + 3*a*e^2)*x))/(3*a^2*c^2*Sqrt[a + c*x^2]) - (e*(4*(c^2*d^4 + 4*a*c*d^2*e^2 - 2*a^2*e^4) + c*d*e*(2*c*d^2 + 7*a*e^2)*x)*Sqrt[a + c*x^2])/(3*a^2*c^3) + (5*d*e^4*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(5/2)","A",5,5,19,0.2632,1,"{739, 819, 780, 217, 206}"
578,1,161,0,0.1181666,"\int \frac{(d+e x)^4}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^4/(a + c*x^2)^(5/2),x]","-\frac{d e \sqrt{a+c x^2} \left(5 a e^2+2 c d^2\right)}{3 a^2 c^2}-\frac{(d+e x) \left(a e \left(3 a e^2+c d^2\right)-2 c d x \left(2 a e^2+c d^2\right)\right)}{3 a^2 c^2 \sqrt{a+c x^2}}+\frac{e^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{5/2}}-\frac{(d+e x)^3 (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}","-\frac{d e \sqrt{a+c x^2} \left(5 a e^2+2 c d^2\right)}{3 a^2 c^2}-\frac{(d+e x) \left(a e \left(3 a e^2+c d^2\right)-2 c d x \left(2 a e^2+c d^2\right)\right)}{3 a^2 c^2 \sqrt{a+c x^2}}+\frac{e^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{5/2}}-\frac{(d+e x)^3 (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-((a*e - c*d*x)*(d + e*x)^3)/(3*a*c*(a + c*x^2)^(3/2)) - ((d + e*x)*(a*e*(c*d^2 + 3*a*e^2) - 2*c*d*(c*d^2 + 2*a*e^2)*x))/(3*a^2*c^2*Sqrt[a + c*x^2]) - (d*e*(2*c*d^2 + 5*a*e^2)*Sqrt[a + c*x^2])/(3*a^2*c^2) + (e^4*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(5/2)","A",5,5,19,0.2632,1,"{739, 819, 641, 217, 206}"
579,1,79,0,0.0267251,"\int \frac{(d+e x)^3}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^3/(a + c*x^2)^(5/2),x]","-\frac{2 \left(a e^2+c d^2\right) (a e-c d x)}{3 a^2 c^2 \sqrt{a+c x^2}}-\frac{(d+e x)^2 (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}","-\frac{2 \left(a e^2+c d^2\right) (a e-c d x)}{3 a^2 c^2 \sqrt{a+c x^2}}-\frac{(d+e x)^2 (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-((a*e - c*d*x)*(d + e*x)^2)/(3*a*c*(a + c*x^2)^(3/2)) - (2*(c*d^2 + a*e^2)*(a*e - c*d*x))/(3*a^2*c^2*Sqrt[a + c*x^2])","A",2,2,19,0.1053,1,"{723, 637}"
580,1,58,0,0.0202496,"\int \frac{(d+e x)^2}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^2/(a + c*x^2)^(5/2),x]","\frac{x (d+e x)^2}{3 a \left(a+c x^2\right)^{3/2}}-\frac{2 d (a e-c d x)}{3 a^2 c \sqrt{a+c x^2}}","\frac{x (d+e x)^2}{3 a \left(a+c x^2\right)^{3/2}}-\frac{2 d (a e-c d x)}{3 a^2 c \sqrt{a+c x^2}}",1,"(x*(d + e*x)^2)/(3*a*(a + c*x^2)^(3/2)) - (2*d*(a*e - c*d*x))/(3*a^2*c*Sqrt[a + c*x^2])","A",2,2,19,0.1053,1,"{729, 637}"
581,1,51,0,0.0114975,"\int \frac{d+e x}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)/(a + c*x^2)^(5/2),x]","\frac{2 d x}{3 a^2 \sqrt{a+c x^2}}-\frac{a e-c d x}{3 a c \left(a+c x^2\right)^{3/2}}","\frac{2 d x}{3 a^2 \sqrt{a+c x^2}}-\frac{a e-c d x}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-(a*e - c*d*x)/(3*a*c*(a + c*x^2)^(3/2)) + (2*d*x)/(3*a^2*Sqrt[a + c*x^2])","A",2,2,17,0.1176,1,"{639, 191}"
582,1,154,0,0.1263134,"\int \frac{1}{(d+e x) \left(a+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)*(a + c*x^2)^(5/2)),x]","\frac{3 a^2 e^3+c d x \left(5 a e^2+2 c d^2\right)}{3 a^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{3 a \left(a+c x^2\right)^{3/2} \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)}{\left(a e^2+c d^2\right)^{5/2}}","\frac{3 a^2 e^3+c d x \left(5 a e^2+2 c d^2\right)}{3 a^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{3 a \left(a+c x^2\right)^{3/2} \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)}{\left(a e^2+c d^2\right)^{5/2}}",1,"(a*e + c*d*x)/(3*a*(c*d^2 + a*e^2)*(a + c*x^2)^(3/2)) + (3*a^2*e^3 + c*d*(2*c*d^2 + 5*a*e^2)*x)/(3*a^2*(c*d^2 + a*e^2)^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])])/(c*d^2 + a*e^2)^(5/2)","A",5,5,19,0.2632,1,"{741, 823, 12, 725, 206}"
583,1,244,0,0.2332538,"\int \frac{1}{(d+e x)^2 \left(a+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^2*(a + c*x^2)^(5/2)),x]","\frac{e \sqrt{a+c x^2} \left(-8 a^2 e^4+9 a c d^2 e^2+2 c^2 d^4\right)}{3 a^2 (d+e x) \left(a e^2+c d^2\right)^3}-\frac{a e \left(c d^2-4 a e^2\right)-c d x \left(7 a e^2+2 c d^2\right)}{3 a^2 \sqrt{a+c x^2} (d+e x) \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{3 a \left(a+c x^2\right)^{3/2} (d+e x) \left(a e^2+c d^2\right)}-\frac{5 c d e^4 \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)^{7/2}}","\frac{e \sqrt{a+c x^2} \left(-8 a^2 e^4+9 a c d^2 e^2+2 c^2 d^4\right)}{3 a^2 (d+e x) \left(a e^2+c d^2\right)^3}-\frac{a e \left(c d^2-4 a e^2\right)-c d x \left(7 a e^2+2 c d^2\right)}{3 a^2 \sqrt{a+c x^2} (d+e x) \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{3 a \left(a+c x^2\right)^{3/2} (d+e x) \left(a e^2+c d^2\right)}-\frac{5 c d e^4 \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)^{7/2}}",1,"(a*e + c*d*x)/(3*a*(c*d^2 + a*e^2)*(d + e*x)*(a + c*x^2)^(3/2)) - (a*e*(c*d^2 - 4*a*e^2) - c*d*(2*c*d^2 + 7*a*e^2)*x)/(3*a^2*(c*d^2 + a*e^2)^2*(d + e*x)*Sqrt[a + c*x^2]) + (e*(2*c^2*d^4 + 9*a*c*d^2*e^2 - 8*a^2*e^4)*Sqrt[a + c*x^2])/(3*a^2*(c*d^2 + a*e^2)^3*(d + e*x)) - (5*c*d*e^4*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(c*d^2 + a*e^2)^(7/2)","A",5,5,19,0.2632,1,"{741, 823, 807, 725, 206}"
584,1,327,0,0.3717942,"\int \frac{1}{(d+e x)^3 \left(a+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^3*(a + c*x^2)^(5/2)),x]","\frac{c d e \sqrt{a+c x^2} \left(-81 a^2 e^4+28 a c d^2 e^2+4 c^2 d^4\right)}{6 a^2 (d+e x) \left(a e^2+c d^2\right)^4}+\frac{e \sqrt{a+c x^2} \left(-15 a^2 e^4+24 a c d^2 e^2+4 c^2 d^4\right)}{6 a^2 (d+e x)^2 \left(a e^2+c d^2\right)^3}-\frac{a e \left(2 c d^2-5 a e^2\right)-c d x \left(9 a e^2+2 c d^2\right)}{3 a^2 \sqrt{a+c x^2} (d+e x)^2 \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{3 a \left(a+c x^2\right)^{3/2} (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{5 c e^4 \left(6 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{9/2}}","\frac{c d e \sqrt{a+c x^2} \left(-81 a^2 e^4+28 a c d^2 e^2+4 c^2 d^4\right)}{6 a^2 (d+e x) \left(a e^2+c d^2\right)^4}+\frac{e \sqrt{a+c x^2} \left(-15 a^2 e^4+24 a c d^2 e^2+4 c^2 d^4\right)}{6 a^2 (d+e x)^2 \left(a e^2+c d^2\right)^3}-\frac{a e \left(2 c d^2-5 a e^2\right)-c d x \left(9 a e^2+2 c d^2\right)}{3 a^2 \sqrt{a+c x^2} (d+e x)^2 \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{3 a \left(a+c x^2\right)^{3/2} (d+e x)^2 \left(a e^2+c d^2\right)}-\frac{5 c e^4 \left(6 c d^2-a e^2\right) \tanh ^{-1}\left(\frac{a e-c d x}{\sqrt{a+c x^2} \sqrt{a e^2+c d^2}}\right)}{2 \left(a e^2+c d^2\right)^{9/2}}",1,"(a*e + c*d*x)/(3*a*(c*d^2 + a*e^2)*(d + e*x)^2*(a + c*x^2)^(3/2)) - (a*e*(2*c*d^2 - 5*a*e^2) - c*d*(2*c*d^2 + 9*a*e^2)*x)/(3*a^2*(c*d^2 + a*e^2)^2*(d + e*x)^2*Sqrt[a + c*x^2]) + (e*(4*c^2*d^4 + 24*a*c*d^2*e^2 - 15*a^2*e^4)*Sqrt[a + c*x^2])/(6*a^2*(c*d^2 + a*e^2)^3*(d + e*x)^2) + (c*d*e*(4*c^2*d^4 + 28*a*c*d^2*e^2 - 81*a^2*e^4)*Sqrt[a + c*x^2])/(6*a^2*(c*d^2 + a*e^2)^4*(d + e*x)) - (5*c*e^4*(6*c*d^2 - a*e^2)*ArcTanh[(a*e - c*d*x)/(Sqrt[c*d^2 + a*e^2]*Sqrt[a + c*x^2])])/(2*(c*d^2 + a*e^2)^(9/2))","A",6,6,19,0.3158,1,"{741, 823, 835, 807, 725, 206}"
585,1,18,0,0.0049978,"\int \frac{3+x}{\sqrt{1-x^2}} \, dx","Int[(3 + x)/Sqrt[1 - x^2],x]","3 \sin ^{-1}(x)-\sqrt{1-x^2}","3 \sin ^{-1}(x)-\sqrt{1-x^2}",1,"-Sqrt[1 - x^2] + 3*ArcSin[x]","A",2,2,15,0.1333,1,"{641, 216}"
586,1,20,0,0.0048059,"\int \frac{1+x}{\sqrt{4-x^2}} \, dx","Int[(1 + x)/Sqrt[4 - x^2],x]","\sin ^{-1}\left(\frac{x}{2}\right)-\sqrt{4-x^2}","\sin ^{-1}\left(\frac{x}{2}\right)-\sqrt{4-x^2}",1,"-Sqrt[4 - x^2] + ArcSin[x/2]","A",2,2,15,0.1333,1,"{641, 216}"
587,1,18,0,0.0044369,"\int \frac{2+x}{\sqrt{9+x^2}} \, dx","Int[(2 + x)/Sqrt[9 + x^2],x]","\sqrt{x^2+9}+2 \sinh ^{-1}\left(\frac{x}{3}\right)","\sqrt{x^2+9}+2 \sinh ^{-1}\left(\frac{x}{3}\right)",1,"Sqrt[9 + x^2] + 2*ArcSinh[x/3]","A",2,2,13,0.1538,1,"{641, 215}"
588,1,54,0,0.023162,"\int \frac{(a+b x)^2}{\sqrt{1-x^2}} \, dx","Int[(a + b*x)^2/Sqrt[1 - x^2],x]","\frac{1}{2} \left(2 a^2+b^2\right) \sin ^{-1}(x)-\frac{3}{2} a b \sqrt{1-x^2}-\frac{1}{2} b \sqrt{1-x^2} (a+b x)","\frac{1}{2} \left(2 a^2+b^2\right) \sin ^{-1}(x)-\frac{3}{2} a b \sqrt{1-x^2}-\frac{1}{2} b \sqrt{1-x^2} (a+b x)",1,"(-3*a*b*Sqrt[1 - x^2])/2 - (b*(a + b*x)*Sqrt[1 - x^2])/2 + ((2*a^2 + b^2)*ArcSin[x])/2","A",3,3,19,0.1579,1,"{743, 641, 216}"
589,1,52,0,0.0203178,"\int \frac{(a+b x)^2}{\sqrt{1+x^2}} \, dx","Int[(a + b*x)^2/Sqrt[1 + x^2],x]","\frac{1}{2} \left(2 a^2-b^2\right) \sinh ^{-1}(x)+\frac{3}{2} a b \sqrt{x^2+1}+\frac{1}{2} b \sqrt{x^2+1} (a+b x)","\frac{1}{2} \left(2 a^2-b^2\right) \sinh ^{-1}(x)+\frac{3}{2} a b \sqrt{x^2+1}+\frac{1}{2} b \sqrt{x^2+1} (a+b x)",1,"(3*a*b*Sqrt[1 + x^2])/2 + (b*(a + b*x)*Sqrt[1 + x^2])/2 + ((2*a^2 - b^2)*ArcSinh[x])/2","A",3,3,17,0.1765,1,"{743, 641, 215}"
590,1,18,0,0.0040183,"\int \frac{2+3 x}{\left(4+x^2\right)^{3/2}} \, dx","Int[(2 + 3*x)/(4 + x^2)^(3/2),x]","-\frac{6-x}{2 \sqrt{x^2+4}}","-\frac{6-x}{2 \sqrt{x^2+4}}",1,"-(6 - x)/(2*Sqrt[4 + x^2])","A",1,1,15,0.06667,1,"{637}"
591,1,63,0,0.0238877,"\int (d+e x)^{5/2} \left(a+c x^2\right) \, dx","Int[(d + e*x)^(5/2)*(a + c*x^2),x]","\frac{2 (d+e x)^{7/2} \left(a e^2+c d^2\right)}{7 e^3}+\frac{2 c (d+e x)^{11/2}}{11 e^3}-\frac{4 c d (d+e x)^{9/2}}{9 e^3}","\frac{2 (d+e x)^{7/2} \left(a e^2+c d^2\right)}{7 e^3}+\frac{2 c (d+e x)^{11/2}}{11 e^3}-\frac{4 c d (d+e x)^{9/2}}{9 e^3}",1,"(2*(c*d^2 + a*e^2)*(d + e*x)^(7/2))/(7*e^3) - (4*c*d*(d + e*x)^(9/2))/(9*e^3) + (2*c*(d + e*x)^(11/2))/(11*e^3)","A",2,1,17,0.05882,1,"{697}"
592,1,63,0,0.0210846,"\int (d+e x)^{3/2} \left(a+c x^2\right) \, dx","Int[(d + e*x)^(3/2)*(a + c*x^2),x]","\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right)}{5 e^3}+\frac{2 c (d+e x)^{9/2}}{9 e^3}-\frac{4 c d (d+e x)^{7/2}}{7 e^3}","\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right)}{5 e^3}+\frac{2 c (d+e x)^{9/2}}{9 e^3}-\frac{4 c d (d+e x)^{7/2}}{7 e^3}",1,"(2*(c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^3) - (4*c*d*(d + e*x)^(7/2))/(7*e^3) + (2*c*(d + e*x)^(9/2))/(9*e^3)","A",2,1,17,0.05882,1,"{697}"
593,1,63,0,0.0207032,"\int \sqrt{d+e x} \left(a+c x^2\right) \, dx","Int[Sqrt[d + e*x]*(a + c*x^2),x]","\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)}{3 e^3}+\frac{2 c (d+e x)^{7/2}}{7 e^3}-\frac{4 c d (d+e x)^{5/2}}{5 e^3}","\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)}{3 e^3}+\frac{2 c (d+e x)^{7/2}}{7 e^3}-\frac{4 c d (d+e x)^{5/2}}{5 e^3}",1,"(2*(c*d^2 + a*e^2)*(d + e*x)^(3/2))/(3*e^3) - (4*c*d*(d + e*x)^(5/2))/(5*e^3) + (2*c*(d + e*x)^(7/2))/(7*e^3)","A",2,1,17,0.05882,1,"{697}"
594,1,61,0,0.0208208,"\int \frac{a+c x^2}{\sqrt{d+e x}} \, dx","Int[(a + c*x^2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)}{e^3}+\frac{2 c (d+e x)^{5/2}}{5 e^3}-\frac{4 c d (d+e x)^{3/2}}{3 e^3}","\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)}{e^3}+\frac{2 c (d+e x)^{5/2}}{5 e^3}-\frac{4 c d (d+e x)^{3/2}}{3 e^3}",1,"(2*(c*d^2 + a*e^2)*Sqrt[d + e*x])/e^3 - (4*c*d*(d + e*x)^(3/2))/(3*e^3) + (2*c*(d + e*x)^(5/2))/(5*e^3)","A",2,1,17,0.05882,1,"{697}"
595,1,59,0,0.0208537,"\int \frac{a+c x^2}{(d+e x)^{3/2}} \, dx","Int[(a + c*x^2)/(d + e*x)^(3/2),x]","-\frac{2 \left(a e^2+c d^2\right)}{e^3 \sqrt{d+e x}}+\frac{2 c (d+e x)^{3/2}}{3 e^3}-\frac{4 c d \sqrt{d+e x}}{e^3}","-\frac{2 \left(a e^2+c d^2\right)}{e^3 \sqrt{d+e x}}+\frac{2 c (d+e x)^{3/2}}{3 e^3}-\frac{4 c d \sqrt{d+e x}}{e^3}",1,"(-2*(c*d^2 + a*e^2))/(e^3*Sqrt[d + e*x]) - (4*c*d*Sqrt[d + e*x])/e^3 + (2*c*(d + e*x)^(3/2))/(3*e^3)","A",2,1,17,0.05882,1,"{697}"
596,1,59,0,0.0222372,"\int \frac{a+c x^2}{(d+e x)^{5/2}} \, dx","Int[(a + c*x^2)/(d + e*x)^(5/2),x]","-\frac{2 \left(a e^2+c d^2\right)}{3 e^3 (d+e x)^{3/2}}+\frac{2 c \sqrt{d+e x}}{e^3}+\frac{4 c d}{e^3 \sqrt{d+e x}}","-\frac{2 \left(a e^2+c d^2\right)}{3 e^3 (d+e x)^{3/2}}+\frac{2 c \sqrt{d+e x}}{e^3}+\frac{4 c d}{e^3 \sqrt{d+e x}}",1,"(-2*(c*d^2 + a*e^2))/(3*e^3*(d + e*x)^(3/2)) + (4*c*d)/(e^3*Sqrt[d + e*x]) + (2*c*Sqrt[d + e*x])/e^3","A",2,1,17,0.05882,1,"{697}"
597,1,61,0,0.0225897,"\int \frac{a+c x^2}{(d+e x)^{7/2}} \, dx","Int[(a + c*x^2)/(d + e*x)^(7/2),x]","-\frac{2 \left(a e^2+c d^2\right)}{5 e^3 (d+e x)^{5/2}}-\frac{2 c}{e^3 \sqrt{d+e x}}+\frac{4 c d}{3 e^3 (d+e x)^{3/2}}","-\frac{2 \left(a e^2+c d^2\right)}{5 e^3 (d+e x)^{5/2}}-\frac{2 c}{e^3 \sqrt{d+e x}}+\frac{4 c d}{3 e^3 (d+e x)^{3/2}}",1,"(-2*(c*d^2 + a*e^2))/(5*e^3*(d + e*x)^(5/2)) + (4*c*d)/(3*e^3*(d + e*x)^(3/2)) - (2*c)/(e^3*Sqrt[d + e*x])","A",2,1,17,0.05882,1,"{697}"
598,1,127,0,0.0568408,"\int (d+e x)^{5/2} \left(a+c x^2\right)^2 \, dx","Int[(d + e*x)^(5/2)*(a + c*x^2)^2,x]","\frac{4 c (d+e x)^{11/2} \left(a e^2+3 c d^2\right)}{11 e^5}-\frac{8 c d (d+e x)^{9/2} \left(a e^2+c d^2\right)}{9 e^5}+\frac{2 (d+e x)^{7/2} \left(a e^2+c d^2\right)^2}{7 e^5}+\frac{2 c^2 (d+e x)^{15/2}}{15 e^5}-\frac{8 c^2 d (d+e x)^{13/2}}{13 e^5}","\frac{4 c (d+e x)^{11/2} \left(a e^2+3 c d^2\right)}{11 e^5}-\frac{8 c d (d+e x)^{9/2} \left(a e^2+c d^2\right)}{9 e^5}+\frac{2 (d+e x)^{7/2} \left(a e^2+c d^2\right)^2}{7 e^5}+\frac{2 c^2 (d+e x)^{15/2}}{15 e^5}-\frac{8 c^2 d (d+e x)^{13/2}}{13 e^5}",1,"(2*(c*d^2 + a*e^2)^2*(d + e*x)^(7/2))/(7*e^5) - (8*c*d*(c*d^2 + a*e^2)*(d + e*x)^(9/2))/(9*e^5) + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(11/2))/(11*e^5) - (8*c^2*d*(d + e*x)^(13/2))/(13*e^5) + (2*c^2*(d + e*x)^(15/2))/(15*e^5)","A",2,1,19,0.05263,1,"{697}"
599,1,127,0,0.0476634,"\int (d+e x)^{3/2} \left(a+c x^2\right)^2 \, dx","Int[(d + e*x)^(3/2)*(a + c*x^2)^2,x]","\frac{4 c (d+e x)^{9/2} \left(a e^2+3 c d^2\right)}{9 e^5}-\frac{8 c d (d+e x)^{7/2} \left(a e^2+c d^2\right)}{7 e^5}+\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right)^2}{5 e^5}+\frac{2 c^2 (d+e x)^{13/2}}{13 e^5}-\frac{8 c^2 d (d+e x)^{11/2}}{11 e^5}","\frac{4 c (d+e x)^{9/2} \left(a e^2+3 c d^2\right)}{9 e^5}-\frac{8 c d (d+e x)^{7/2} \left(a e^2+c d^2\right)}{7 e^5}+\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right)^2}{5 e^5}+\frac{2 c^2 (d+e x)^{13/2}}{13 e^5}-\frac{8 c^2 d (d+e x)^{11/2}}{11 e^5}",1,"(2*(c*d^2 + a*e^2)^2*(d + e*x)^(5/2))/(5*e^5) - (8*c*d*(c*d^2 + a*e^2)*(d + e*x)^(7/2))/(7*e^5) + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(9/2))/(9*e^5) - (8*c^2*d*(d + e*x)^(11/2))/(11*e^5) + (2*c^2*(d + e*x)^(13/2))/(13*e^5)","A",2,1,19,0.05263,1,"{697}"
600,1,127,0,0.0460433,"\int \sqrt{d+e x} \left(a+c x^2\right)^2 \, dx","Int[Sqrt[d + e*x]*(a + c*x^2)^2,x]","\frac{4 c (d+e x)^{7/2} \left(a e^2+3 c d^2\right)}{7 e^5}-\frac{8 c d (d+e x)^{5/2} \left(a e^2+c d^2\right)}{5 e^5}+\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}{3 e^5}+\frac{2 c^2 (d+e x)^{11/2}}{11 e^5}-\frac{8 c^2 d (d+e x)^{9/2}}{9 e^5}","\frac{4 c (d+e x)^{7/2} \left(a e^2+3 c d^2\right)}{7 e^5}-\frac{8 c d (d+e x)^{5/2} \left(a e^2+c d^2\right)}{5 e^5}+\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}{3 e^5}+\frac{2 c^2 (d+e x)^{11/2}}{11 e^5}-\frac{8 c^2 d (d+e x)^{9/2}}{9 e^5}",1,"(2*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2))/(3*e^5) - (8*c*d*(c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^5) + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(7/2))/(7*e^5) - (8*c^2*d*(d + e*x)^(9/2))/(9*e^5) + (2*c^2*(d + e*x)^(11/2))/(11*e^5)","A",2,1,19,0.05263,1,"{697}"
601,1,125,0,0.0453817,"\int \frac{\left(a+c x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[(a + c*x^2)^2/Sqrt[d + e*x],x]","\frac{4 c (d+e x)^{5/2} \left(a e^2+3 c d^2\right)}{5 e^5}-\frac{8 c d (d+e x)^{3/2} \left(a e^2+c d^2\right)}{3 e^5}+\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^2}{e^5}+\frac{2 c^2 (d+e x)^{9/2}}{9 e^5}-\frac{8 c^2 d (d+e x)^{7/2}}{7 e^5}","\frac{4 c (d+e x)^{5/2} \left(a e^2+3 c d^2\right)}{5 e^5}-\frac{8 c d (d+e x)^{3/2} \left(a e^2+c d^2\right)}{3 e^5}+\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^2}{e^5}+\frac{2 c^2 (d+e x)^{9/2}}{9 e^5}-\frac{8 c^2 d (d+e x)^{7/2}}{7 e^5}",1,"(2*(c*d^2 + a*e^2)^2*Sqrt[d + e*x])/e^5 - (8*c*d*(c*d^2 + a*e^2)*(d + e*x)^(3/2))/(3*e^5) + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^5) - (8*c^2*d*(d + e*x)^(7/2))/(7*e^5) + (2*c^2*(d + e*x)^(9/2))/(9*e^5)","A",2,1,19,0.05263,1,"{697}"
602,1,123,0,0.0472858,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[(a + c*x^2)^2/(d + e*x)^(3/2),x]","\frac{4 c (d+e x)^{3/2} \left(a e^2+3 c d^2\right)}{3 e^5}-\frac{8 c d \sqrt{d+e x} \left(a e^2+c d^2\right)}{e^5}-\frac{2 \left(a e^2+c d^2\right)^2}{e^5 \sqrt{d+e x}}+\frac{2 c^2 (d+e x)^{7/2}}{7 e^5}-\frac{8 c^2 d (d+e x)^{5/2}}{5 e^5}","\frac{4 c (d+e x)^{3/2} \left(a e^2+3 c d^2\right)}{3 e^5}-\frac{8 c d \sqrt{d+e x} \left(a e^2+c d^2\right)}{e^5}-\frac{2 \left(a e^2+c d^2\right)^2}{e^5 \sqrt{d+e x}}+\frac{2 c^2 (d+e x)^{7/2}}{7 e^5}-\frac{8 c^2 d (d+e x)^{5/2}}{5 e^5}",1,"(-2*(c*d^2 + a*e^2)^2)/(e^5*Sqrt[d + e*x]) - (8*c*d*(c*d^2 + a*e^2)*Sqrt[d + e*x])/e^5 + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(3/2))/(3*e^5) - (8*c^2*d*(d + e*x)^(5/2))/(5*e^5) + (2*c^2*(d + e*x)^(7/2))/(7*e^5)","A",2,1,19,0.05263,1,"{697}"
603,1,123,0,0.0472387,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[(a + c*x^2)^2/(d + e*x)^(5/2),x]","\frac{4 c \sqrt{d+e x} \left(a e^2+3 c d^2\right)}{e^5}+\frac{8 c d \left(a e^2+c d^2\right)}{e^5 \sqrt{d+e x}}-\frac{2 \left(a e^2+c d^2\right)^2}{3 e^5 (d+e x)^{3/2}}+\frac{2 c^2 (d+e x)^{5/2}}{5 e^5}-\frac{8 c^2 d (d+e x)^{3/2}}{3 e^5}","\frac{4 c \sqrt{d+e x} \left(a e^2+3 c d^2\right)}{e^5}+\frac{8 c d \left(a e^2+c d^2\right)}{e^5 \sqrt{d+e x}}-\frac{2 \left(a e^2+c d^2\right)^2}{3 e^5 (d+e x)^{3/2}}+\frac{2 c^2 (d+e x)^{5/2}}{5 e^5}-\frac{8 c^2 d (d+e x)^{3/2}}{3 e^5}",1,"(-2*(c*d^2 + a*e^2)^2)/(3*e^5*(d + e*x)^(3/2)) + (8*c*d*(c*d^2 + a*e^2))/(e^5*Sqrt[d + e*x]) + (4*c*(3*c*d^2 + a*e^2)*Sqrt[d + e*x])/e^5 - (8*c^2*d*(d + e*x)^(3/2))/(3*e^5) + (2*c^2*(d + e*x)^(5/2))/(5*e^5)","A",2,1,19,0.05263,1,"{697}"
604,1,123,0,0.046406,"\int \frac{\left(a+c x^2\right)^2}{(d+e x)^{7/2}} \, dx","Int[(a + c*x^2)^2/(d + e*x)^(7/2),x]","-\frac{4 c \left(a e^2+3 c d^2\right)}{e^5 \sqrt{d+e x}}+\frac{8 c d \left(a e^2+c d^2\right)}{3 e^5 (d+e x)^{3/2}}-\frac{2 \left(a e^2+c d^2\right)^2}{5 e^5 (d+e x)^{5/2}}+\frac{2 c^2 (d+e x)^{3/2}}{3 e^5}-\frac{8 c^2 d \sqrt{d+e x}}{e^5}","-\frac{4 c \left(a e^2+3 c d^2\right)}{e^5 \sqrt{d+e x}}+\frac{8 c d \left(a e^2+c d^2\right)}{3 e^5 (d+e x)^{3/2}}-\frac{2 \left(a e^2+c d^2\right)^2}{5 e^5 (d+e x)^{5/2}}+\frac{2 c^2 (d+e x)^{3/2}}{3 e^5}-\frac{8 c^2 d \sqrt{d+e x}}{e^5}",1,"(-2*(c*d^2 + a*e^2)^2)/(5*e^5*(d + e*x)^(5/2)) + (8*c*d*(c*d^2 + a*e^2))/(3*e^5*(d + e*x)^(3/2)) - (4*c*(3*c*d^2 + a*e^2))/(e^5*Sqrt[d + e*x]) - (8*c^2*d*Sqrt[d + e*x])/e^5 + (2*c^2*(d + e*x)^(3/2))/(3*e^5)","A",2,1,19,0.05263,1,"{697}"
605,1,204,0,0.1029969,"\int (d+e x)^{5/2} \left(a+c x^2\right)^3 \, dx","Int[(d + e*x)^(5/2)*(a + c*x^2)^3,x]","\frac{2 c^2 (d+e x)^{15/2} \left(a e^2+5 c d^2\right)}{5 e^7}-\frac{8 c^2 d (d+e x)^{13/2} \left(3 a e^2+5 c d^2\right)}{13 e^7}+\frac{6 c (d+e x)^{11/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{11 e^7}-\frac{4 c d (d+e x)^{9/2} \left(a e^2+c d^2\right)^2}{3 e^7}+\frac{2 (d+e x)^{7/2} \left(a e^2+c d^2\right)^3}{7 e^7}+\frac{2 c^3 (d+e x)^{19/2}}{19 e^7}-\frac{12 c^3 d (d+e x)^{17/2}}{17 e^7}","\frac{2 c^2 (d+e x)^{15/2} \left(a e^2+5 c d^2\right)}{5 e^7}-\frac{8 c^2 d (d+e x)^{13/2} \left(3 a e^2+5 c d^2\right)}{13 e^7}+\frac{6 c (d+e x)^{11/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{11 e^7}-\frac{4 c d (d+e x)^{9/2} \left(a e^2+c d^2\right)^2}{3 e^7}+\frac{2 (d+e x)^{7/2} \left(a e^2+c d^2\right)^3}{7 e^7}+\frac{2 c^3 (d+e x)^{19/2}}{19 e^7}-\frac{12 c^3 d (d+e x)^{17/2}}{17 e^7}",1,"(2*(c*d^2 + a*e^2)^3*(d + e*x)^(7/2))/(7*e^7) - (4*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^(9/2))/(3*e^7) + (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(11/2))/(11*e^7) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(13/2))/(13*e^7) + (2*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(15/2))/(5*e^7) - (12*c^3*d*(d + e*x)^(17/2))/(17*e^7) + (2*c^3*(d + e*x)^(19/2))/(19*e^7)","A",2,1,19,0.05263,1,"{697}"
606,1,204,0,0.0850612,"\int (d+e x)^{3/2} \left(a+c x^2\right)^3 \, dx","Int[(d + e*x)^(3/2)*(a + c*x^2)^3,x]","\frac{6 c^2 (d+e x)^{13/2} \left(a e^2+5 c d^2\right)}{13 e^7}-\frac{8 c^2 d (d+e x)^{11/2} \left(3 a e^2+5 c d^2\right)}{11 e^7}+\frac{2 c (d+e x)^{9/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{3 e^7}-\frac{12 c d (d+e x)^{7/2} \left(a e^2+c d^2\right)^2}{7 e^7}+\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right)^3}{5 e^7}+\frac{2 c^3 (d+e x)^{17/2}}{17 e^7}-\frac{4 c^3 d (d+e x)^{15/2}}{5 e^7}","\frac{6 c^2 (d+e x)^{13/2} \left(a e^2+5 c d^2\right)}{13 e^7}-\frac{8 c^2 d (d+e x)^{11/2} \left(3 a e^2+5 c d^2\right)}{11 e^7}+\frac{2 c (d+e x)^{9/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{3 e^7}-\frac{12 c d (d+e x)^{7/2} \left(a e^2+c d^2\right)^2}{7 e^7}+\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right)^3}{5 e^7}+\frac{2 c^3 (d+e x)^{17/2}}{17 e^7}-\frac{4 c^3 d (d+e x)^{15/2}}{5 e^7}",1,"(2*(c*d^2 + a*e^2)^3*(d + e*x)^(5/2))/(5*e^7) - (12*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^(7/2))/(7*e^7) + (2*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(9/2))/(3*e^7) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(11/2))/(11*e^7) + (6*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(13/2))/(13*e^7) - (4*c^3*d*(d + e*x)^(15/2))/(5*e^7) + (2*c^3*(d + e*x)^(17/2))/(17*e^7)","A",2,1,19,0.05263,1,"{697}"
607,1,204,0,0.0826531,"\int \sqrt{d+e x} \left(a+c x^2\right)^3 \, dx","Int[Sqrt[d + e*x]*(a + c*x^2)^3,x]","\frac{6 c^2 (d+e x)^{11/2} \left(a e^2+5 c d^2\right)}{11 e^7}-\frac{8 c^2 d (d+e x)^{9/2} \left(3 a e^2+5 c d^2\right)}{9 e^7}+\frac{6 c (d+e x)^{7/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{7 e^7}-\frac{12 c d (d+e x)^{5/2} \left(a e^2+c d^2\right)^2}{5 e^7}+\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)^3}{3 e^7}+\frac{2 c^3 (d+e x)^{15/2}}{15 e^7}-\frac{12 c^3 d (d+e x)^{13/2}}{13 e^7}","\frac{6 c^2 (d+e x)^{11/2} \left(a e^2+5 c d^2\right)}{11 e^7}-\frac{8 c^2 d (d+e x)^{9/2} \left(3 a e^2+5 c d^2\right)}{9 e^7}+\frac{6 c (d+e x)^{7/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{7 e^7}-\frac{12 c d (d+e x)^{5/2} \left(a e^2+c d^2\right)^2}{5 e^7}+\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)^3}{3 e^7}+\frac{2 c^3 (d+e x)^{15/2}}{15 e^7}-\frac{12 c^3 d (d+e x)^{13/2}}{13 e^7}",1,"(2*(c*d^2 + a*e^2)^3*(d + e*x)^(3/2))/(3*e^7) - (12*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^(5/2))/(5*e^7) + (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(7/2))/(7*e^7) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(9/2))/(9*e^7) + (6*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(11/2))/(11*e^7) - (12*c^3*d*(d + e*x)^(13/2))/(13*e^7) + (2*c^3*(d + e*x)^(15/2))/(15*e^7)","A",2,1,19,0.05263,1,"{697}"
608,1,200,0,0.0822133,"\int \frac{\left(a+c x^2\right)^3}{\sqrt{d+e x}} \, dx","Int[(a + c*x^2)^3/Sqrt[d + e*x],x]","\frac{2 c^2 (d+e x)^{9/2} \left(a e^2+5 c d^2\right)}{3 e^7}-\frac{8 c^2 d (d+e x)^{7/2} \left(3 a e^2+5 c d^2\right)}{7 e^7}+\frac{6 c (d+e x)^{5/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{5 e^7}-\frac{4 c d (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}{e^7}+\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^3}{e^7}+\frac{2 c^3 (d+e x)^{13/2}}{13 e^7}-\frac{12 c^3 d (d+e x)^{11/2}}{11 e^7}","\frac{2 c^2 (d+e x)^{9/2} \left(a e^2+5 c d^2\right)}{3 e^7}-\frac{8 c^2 d (d+e x)^{7/2} \left(3 a e^2+5 c d^2\right)}{7 e^7}+\frac{6 c (d+e x)^{5/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{5 e^7}-\frac{4 c d (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}{e^7}+\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^3}{e^7}+\frac{2 c^3 (d+e x)^{13/2}}{13 e^7}-\frac{12 c^3 d (d+e x)^{11/2}}{11 e^7}",1,"(2*(c*d^2 + a*e^2)^3*Sqrt[d + e*x])/e^7 - (4*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2))/e^7 + (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^7) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(7/2))/(7*e^7) + (2*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(9/2))/(3*e^7) - (12*c^3*d*(d + e*x)^(11/2))/(11*e^7) + (2*c^3*(d + e*x)^(13/2))/(13*e^7)","A",2,1,19,0.05263,1,"{697}"
609,1,198,0,0.0834626,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^{3/2}} \, dx","Int[(a + c*x^2)^3/(d + e*x)^(3/2),x]","\frac{6 c^2 (d+e x)^{7/2} \left(a e^2+5 c d^2\right)}{7 e^7}-\frac{8 c^2 d (d+e x)^{5/2} \left(3 a e^2+5 c d^2\right)}{5 e^7}+\frac{2 c (d+e x)^{3/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7}-\frac{12 c d \sqrt{d+e x} \left(a e^2+c d^2\right)^2}{e^7}-\frac{2 \left(a e^2+c d^2\right)^3}{e^7 \sqrt{d+e x}}+\frac{2 c^3 (d+e x)^{11/2}}{11 e^7}-\frac{4 c^3 d (d+e x)^{9/2}}{3 e^7}","\frac{6 c^2 (d+e x)^{7/2} \left(a e^2+5 c d^2\right)}{7 e^7}-\frac{8 c^2 d (d+e x)^{5/2} \left(3 a e^2+5 c d^2\right)}{5 e^7}+\frac{2 c (d+e x)^{3/2} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7}-\frac{12 c d \sqrt{d+e x} \left(a e^2+c d^2\right)^2}{e^7}-\frac{2 \left(a e^2+c d^2\right)^3}{e^7 \sqrt{d+e x}}+\frac{2 c^3 (d+e x)^{11/2}}{11 e^7}-\frac{4 c^3 d (d+e x)^{9/2}}{3 e^7}",1,"(-2*(c*d^2 + a*e^2)^3)/(e^7*Sqrt[d + e*x]) - (12*c*d*(c*d^2 + a*e^2)^2*Sqrt[d + e*x])/e^7 + (2*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(3/2))/e^7 - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(5/2))/(5*e^7) + (6*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(7/2))/(7*e^7) - (4*c^3*d*(d + e*x)^(9/2))/(3*e^7) + (2*c^3*(d + e*x)^(11/2))/(11*e^7)","A",2,1,19,0.05263,1,"{697}"
610,1,200,0,0.082786,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^{5/2}} \, dx","Int[(a + c*x^2)^3/(d + e*x)^(5/2),x]","\frac{6 c^2 (d+e x)^{5/2} \left(a e^2+5 c d^2\right)}{5 e^7}-\frac{8 c^2 d (d+e x)^{3/2} \left(3 a e^2+5 c d^2\right)}{3 e^7}+\frac{6 c \sqrt{d+e x} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7}+\frac{12 c d \left(a e^2+c d^2\right)^2}{e^7 \sqrt{d+e x}}-\frac{2 \left(a e^2+c d^2\right)^3}{3 e^7 (d+e x)^{3/2}}+\frac{2 c^3 (d+e x)^{9/2}}{9 e^7}-\frac{12 c^3 d (d+e x)^{7/2}}{7 e^7}","\frac{6 c^2 (d+e x)^{5/2} \left(a e^2+5 c d^2\right)}{5 e^7}-\frac{8 c^2 d (d+e x)^{3/2} \left(3 a e^2+5 c d^2\right)}{3 e^7}+\frac{6 c \sqrt{d+e x} \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7}+\frac{12 c d \left(a e^2+c d^2\right)^2}{e^7 \sqrt{d+e x}}-\frac{2 \left(a e^2+c d^2\right)^3}{3 e^7 (d+e x)^{3/2}}+\frac{2 c^3 (d+e x)^{9/2}}{9 e^7}-\frac{12 c^3 d (d+e x)^{7/2}}{7 e^7}",1,"(-2*(c*d^2 + a*e^2)^3)/(3*e^7*(d + e*x)^(3/2)) + (12*c*d*(c*d^2 + a*e^2)^2)/(e^7*Sqrt[d + e*x]) + (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*Sqrt[d + e*x])/e^7 - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(3/2))/(3*e^7) + (6*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^7) - (12*c^3*d*(d + e*x)^(7/2))/(7*e^7) + (2*c^3*(d + e*x)^(9/2))/(9*e^7)","A",2,1,19,0.05263,1,"{697}"
611,1,196,0,0.0807837,"\int \frac{\left(a+c x^2\right)^3}{(d+e x)^{7/2}} \, dx","Int[(a + c*x^2)^3/(d + e*x)^(7/2),x]","\frac{2 c^2 (d+e x)^{3/2} \left(a e^2+5 c d^2\right)}{e^7}-\frac{8 c^2 d \sqrt{d+e x} \left(3 a e^2+5 c d^2\right)}{e^7}-\frac{6 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7 \sqrt{d+e x}}+\frac{4 c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)^{3/2}}-\frac{2 \left(a e^2+c d^2\right)^3}{5 e^7 (d+e x)^{5/2}}+\frac{2 c^3 (d+e x)^{7/2}}{7 e^7}-\frac{12 c^3 d (d+e x)^{5/2}}{5 e^7}","\frac{2 c^2 (d+e x)^{3/2} \left(a e^2+5 c d^2\right)}{e^7}-\frac{8 c^2 d \sqrt{d+e x} \left(3 a e^2+5 c d^2\right)}{e^7}-\frac{6 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right)}{e^7 \sqrt{d+e x}}+\frac{4 c d \left(a e^2+c d^2\right)^2}{e^7 (d+e x)^{3/2}}-\frac{2 \left(a e^2+c d^2\right)^3}{5 e^7 (d+e x)^{5/2}}+\frac{2 c^3 (d+e x)^{7/2}}{7 e^7}-\frac{12 c^3 d (d+e x)^{5/2}}{5 e^7}",1,"(-2*(c*d^2 + a*e^2)^3)/(5*e^7*(d + e*x)^(5/2)) + (4*c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)^(3/2)) - (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(e^7*Sqrt[d + e*x]) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*Sqrt[d + e*x])/e^7 + (2*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(3/2))/e^7 - (12*c^3*d*(d + e*x)^(5/2))/(5*e^7) + (2*c^3*(d + e*x)^(7/2))/(7*e^7)","A",2,1,19,0.05263,1,"{697}"
612,1,167,0,0.3978271,"\int \frac{(d+e x)^{5/2}}{a-c x^2} \, dx","Int[(d + e*x)^(5/2)/(a - c*x^2),x]","-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{7/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{7/4}}-\frac{2 e (d+e x)^{3/2}}{3 c}-\frac{4 d e \sqrt{d+e x}}{c}","-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{7/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{7/4}}-\frac{2 e (d+e x)^{3/2}}{3 c}-\frac{4 d e \sqrt{d+e x}}{c}",1,"(-4*d*e*Sqrt[d + e*x])/c - (2*e*(d + e*x)^(3/2))/(3*c) - ((Sqrt[c]*d - Sqrt[a]*e)^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*c^(7/4)) + ((Sqrt[c]*d + Sqrt[a]*e)^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*c^(7/4))","A",6,5,20,0.2500,1,"{704, 825, 827, 1166, 208}"
613,1,149,0,0.2818624,"\int \frac{(d+e x)^{3/2}}{a-c x^2} \, dx","Int[(d + e*x)^(3/2)/(a - c*x^2),x]","-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{5/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{5/4}}-\frac{2 e \sqrt{d+e x}}{c}","-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{5/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{5/4}}-\frac{2 e \sqrt{d+e x}}{c}",1,"(-2*e*Sqrt[d + e*x])/c - ((Sqrt[c]*d - Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*c^(5/4)) + ((Sqrt[c]*d + Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*c^(5/4))","A",5,4,20,0.2000,1,"{704, 827, 1166, 208}"
614,1,134,0,0.1086121,"\int \frac{\sqrt{d+e x}}{a-c x^2} \, dx","Int[Sqrt[d + e*x]/(a - c*x^2),x]","\frac{\sqrt{\sqrt{a} e+\sqrt{c} d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{3/4}}-\frac{\sqrt{\sqrt{c} d-\sqrt{a} e} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{3/4}}","\frac{\sqrt{\sqrt{a} e+\sqrt{c} d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{3/4}}-\frac{\sqrt{\sqrt{c} d-\sqrt{a} e} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{3/4}}",1,"-((Sqrt[Sqrt[c]*d - Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*c^(3/4))) + (Sqrt[Sqrt[c]*d + Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*c^(3/4))","A",4,3,20,0.1500,1,"{700, 1130, 208}"
615,1,134,0,0.1139456,"\int \frac{1}{\sqrt{d+e x} \left(a-c x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*(a - c*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \sqrt[4]{c} \sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \sqrt[4]{c} \sqrt{\sqrt{c} d-\sqrt{a} e}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \sqrt[4]{c} \sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \sqrt[4]{c} \sqrt{\sqrt{c} d-\sqrt{a} e}}",1,"-(ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]]/(Sqrt[a]*c^(1/4)*Sqrt[Sqrt[c]*d - Sqrt[a]*e])) + ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]]/(Sqrt[a]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[a]*e])","A",4,3,20,0.1500,1,"{708, 1093, 208}"
616,1,160,0,0.2080489,"\int \frac{1}{(d+e x)^{3/2} \left(a-c x^2\right)} \, dx","Int[1/((d + e*x)^(3/2)*(a - c*x^2)),x]","\frac{2 e}{\sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{\sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}","\frac{2 e}{\sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{\sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}",1,"(2*e)/((c*d^2 - a*e^2)*Sqrt[d + e*x]) - (c^(1/4)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)) + (c^(1/4)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*(Sqrt[c]*d + Sqrt[a]*e)^(3/2))","A",5,4,20,0.2000,1,"{710, 827, 1166, 208}"
617,1,190,0,0.3798851,"\int \frac{1}{(d+e x)^{5/2} \left(a-c x^2\right)} \, dx","Int[1/((d + e*x)^(5/2)*(a - c*x^2)),x]","-\frac{c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}+\frac{4 c d e}{\sqrt{d+e x} \left(c d^2-a e^2\right)^2}+\frac{2 e}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)}","-\frac{c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}+\frac{4 c d e}{\sqrt{d+e x} \left(c d^2-a e^2\right)^2}+\frac{2 e}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)}",1,"(2*e)/(3*(c*d^2 - a*e^2)*(d + e*x)^(3/2)) + (4*c*d*e)/((c*d^2 - a*e^2)^2*Sqrt[d + e*x]) - (c^(3/4)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*(Sqrt[c]*d - Sqrt[a]*e)^(5/2)) + (c^(3/4)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*(Sqrt[c]*d + Sqrt[a]*e)^(5/2))","A",6,5,20,0.2500,1,"{710, 829, 827, 1166, 208}"
618,1,781,0,3.0434513,"\int \frac{(d+e x)^{5/2}}{a+c x^2} \, dx","Int[(d + e*x)^(5/2)/(a + c*x^2),x]","\frac{e \left(\left(3 c d^2-a e^2\right) \sqrt{a e^2+c d^2}+2 a \sqrt{c} d e^2+2 c^{3/2} d^3\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{7/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \left(\left(3 c d^2-a e^2\right) \sqrt{a e^2+c d^2}+2 a \sqrt{c} d e^2+2 c^{3/2} d^3\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{7/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \left(-\left(3 c d^2-a e^2\right) \sqrt{a e^2+c d^2}+2 a \sqrt{c} d e^2+2 c^{3/2} d^3\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{7/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{e \left(-\left(3 c d^2-a e^2\right) \sqrt{a e^2+c d^2}+2 a \sqrt{c} d e^2+2 c^{3/2} d^3\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{7/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{2 e (d+e x)^{3/2}}{3 c}+\frac{4 d e \sqrt{d+e x}}{c}","\frac{e \left(\left(3 c d^2-a e^2\right) \sqrt{a e^2+c d^2}+2 a \sqrt{c} d e^2+2 c^{3/2} d^3\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{7/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \left(\left(3 c d^2-a e^2\right) \sqrt{a e^2+c d^2}+2 a \sqrt{c} d e^2+2 c^{3/2} d^3\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{7/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \left(-\left(3 c d^2-a e^2\right) \sqrt{a e^2+c d^2}+2 a \sqrt{c} d e^2+2 c^{3/2} d^3\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{7/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{e \left(-\left(3 c d^2-a e^2\right) \sqrt{a e^2+c d^2}+2 a \sqrt{c} d e^2+2 c^{3/2} d^3\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{7/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{2 e (d+e x)^{3/2}}{3 c}+\frac{4 d e \sqrt{d+e x}}{c}",1,"(4*d*e*Sqrt[d + e*x])/c + (2*e*(d + e*x)^(3/2))/(3*c) - (e*(2*c^(3/2)*d^3 + 2*a*Sqrt[c]*d*e^2 - (3*c*d^2 - a*e^2)*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) + (e*(2*c^(3/2)*d^3 + 2*a*Sqrt[c]*d*e^2 - (3*c*d^2 - a*e^2)*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) + (e*(2*c^(3/2)*d^3 + 2*a*Sqrt[c]*d*e^2 + (3*c*d^2 - a*e^2)*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) - (e*(2*c^(3/2)*d^3 + 2*a*Sqrt[c]*d*e^2 + (3*c*d^2 - a*e^2)*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",12,8,19,0.4211,1,"{704, 825, 827, 1169, 634, 618, 206, 628}"
619,1,689,0,1.4765974,"\int \frac{(d+e x)^{3/2}}{a+c x^2} \, dx","Int[(d + e*x)^(3/2)/(a + c*x^2),x]","\frac{e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{2 e \sqrt{d+e x}}{c}","\frac{e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{2 e \sqrt{d+e x}}{c}",1,"(2*e*Sqrt[d + e*x])/c - (e*(c*d^2 + a*e^2 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) + (e*(c*d^2 + a*e^2 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) + (e*(c*d^2 + a*e^2 + 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) - (e*(c*d^2 + a*e^2 + 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",11,7,19,0.3684,1,"{704, 827, 1169, 634, 618, 206, 628}"
620,1,478,0,0.4048631,"\int \frac{\sqrt{d+e x}}{a+c x^2} \, dx","Int[Sqrt[d + e*x]/(a + c*x^2),x]","\frac{e \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{3/4} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{3/4} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{3/4} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{3/4} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}","\frac{e \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{3/4} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}-\frac{e \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} c^{3/4} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{3/4} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} c^{3/4} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}",1,"(e*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*c^(3/4)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*c^(3/4)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) + (e*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*c^(3/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) - (e*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*c^(3/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",10,6,19,0.3158,1,"{700, 1129, 634, 618, 206, 628}"
621,1,538,0,0.4468334,"\int \frac{1}{\sqrt{d+e x} \left(a+c x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*(a + c*x^2)),x]","-\frac{e \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}","-\frac{e \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}",1,"(e*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*c^(1/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*c^(1/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*c^(1/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (e*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*c^(1/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",10,6,19,0.3158,1,"{708, 1094, 634, 618, 206, 628}"
622,1,663,0,0.9686505,"\int \frac{1}{(d+e x)^{3/2} \left(a+c x^2\right)} \, dx","Int[1/((d + e*x)^(3/2)*(a + c*x^2)),x]","-\frac{2 e}{\sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{c} e \left(\sqrt{a e^2+c d^2}+2 \sqrt{c} d\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{\sqrt[4]{c} e \left(\sqrt{a e^2+c d^2}+2 \sqrt{c} d\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{\sqrt[4]{c} e \left(2 \sqrt{c} d-\sqrt{a e^2+c d^2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{\sqrt[4]{c} e \left(2 \sqrt{c} d-\sqrt{a e^2+c d^2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}","-\frac{2 e}{\sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{c} e \left(\sqrt{a e^2+c d^2}+2 \sqrt{c} d\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{\sqrt[4]{c} e \left(\sqrt{a e^2+c d^2}+2 \sqrt{c} d\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{\sqrt[4]{c} e \left(2 \sqrt{c} d-\sqrt{a e^2+c d^2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{\sqrt[4]{c} e \left(2 \sqrt{c} d-\sqrt{a e^2+c d^2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}",1,"(-2*e)/((c*d^2 + a*e^2)*Sqrt[d + e*x]) + (c^(1/4)*e*(2*Sqrt[c]*d - Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (c^(1/4)*e*(2*Sqrt[c]*d - Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (c^(1/4)*e*(2*Sqrt[c]*d + Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (c^(1/4)*e*(2*Sqrt[c]*d + Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",11,7,19,0.3684,1,"{710, 827, 1169, 634, 618, 206, 628}"
623,1,736,0,1.7318068,"\int \frac{1}{(d+e x)^{5/2} \left(a+c x^2\right)} \, dx","Int[1/((d + e*x)^(5/2)*(a + c*x^2)),x]","-\frac{c^{3/4} e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}-a e^2+3 c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \left(a e^2+c d^2\right)^{5/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{c^{3/4} e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}-a e^2+3 c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \left(a e^2+c d^2\right)^{5/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{c^{3/4} e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}-a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \left(a e^2+c d^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{c^{3/4} e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}-a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \left(a e^2+c d^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{4 c d e}{\sqrt{d+e x} \left(a e^2+c d^2\right)^2}-\frac{2 e}{3 (d+e x)^{3/2} \left(a e^2+c d^2\right)}","-\frac{c^{3/4} e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}-a e^2+3 c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \left(a e^2+c d^2\right)^{5/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{c^{3/4} e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}-a e^2+3 c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{2 \sqrt{2} \left(a e^2+c d^2\right)^{5/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{c^{3/4} e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}-a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \left(a e^2+c d^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{c^{3/4} e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}-a e^2+3 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{\sqrt{2} \left(a e^2+c d^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{4 c d e}{\sqrt{d+e x} \left(a e^2+c d^2\right)^2}-\frac{2 e}{3 (d+e x)^{3/2} \left(a e^2+c d^2\right)}",1,"(-2*e)/(3*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) - (4*c*d*e)/((c*d^2 + a*e^2)^2*Sqrt[d + e*x]) + (c^(3/4)*e*(3*c*d^2 - a*e^2 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (c^(3/4)*e*(3*c*d^2 - a*e^2 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(Sqrt[2]*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (c^(3/4)*e*(3*c*d^2 - a*e^2 + 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (c^(3/4)*e*(3*c*d^2 - a*e^2 + 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[2]*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",12,8,19,0.4211,1,"{710, 829, 827, 1169, 634, 618, 206, 628}"
624,1,263,0,0.5341547,"\int \frac{(d+e x)^{7/2}}{\left(a-c x^2\right)^2} \, dx","Int[(d + e*x)^(7/2)/(a - c*x^2)^2,x]","-\frac{\left(5 \sqrt{a} e+2 \sqrt{c} d\right) \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{9/4}}+\frac{\left(2 \sqrt{c} d-5 \sqrt{a} e\right) \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{9/4}}+\frac{e \sqrt{d+e x} \left(5 a e^2+c d^2\right)}{2 a c^2}+\frac{(d+e x)^{5/2} (a e+c d x)}{2 a c \left(a-c x^2\right)}+\frac{d e (d+e x)^{3/2}}{2 a c}","-\frac{\left(5 \sqrt{a} e+2 \sqrt{c} d\right) \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{9/4}}+\frac{\left(2 \sqrt{c} d-5 \sqrt{a} e\right) \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{9/4}}+\frac{e \sqrt{d+e x} \left(5 a e^2+c d^2\right)}{2 a c^2}+\frac{(d+e x)^{5/2} (a e+c d x)}{2 a c \left(a-c x^2\right)}+\frac{d e (d+e x)^{3/2}}{2 a c}",1,"(e*(c*d^2 + 5*a*e^2)*Sqrt[d + e*x])/(2*a*c^2) + (d*e*(d + e*x)^(3/2))/(2*a*c) + ((a*e + c*d*x)*(d + e*x)^(5/2))/(2*a*c*(a - c*x^2)) - ((Sqrt[c]*d - Sqrt[a]*e)^(5/2)*(2*Sqrt[c]*d + 5*Sqrt[a]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*c^(9/4)) + ((2*Sqrt[c]*d - 5*Sqrt[a]*e)*(Sqrt[c]*d + Sqrt[a]*e)^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(9/4))","A",7,5,20,0.2500,1,"{739, 825, 827, 1166, 208}"
625,1,231,0,0.3747717,"\int \frac{(d+e x)^{5/2}}{\left(a-c x^2\right)^2} \, dx","Int[(d + e*x)^(5/2)/(a - c*x^2)^2,x]","-\frac{\left(3 \sqrt{a} e+2 \sqrt{c} d\right) \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{7/4}}+\frac{\left(2 \sqrt{c} d-3 \sqrt{a} e\right) \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{7/4}}+\frac{(d+e x)^{3/2} (a e+c d x)}{2 a c \left(a-c x^2\right)}+\frac{d e \sqrt{d+e x}}{2 a c}","-\frac{\left(3 \sqrt{a} e+2 \sqrt{c} d\right) \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{7/4}}+\frac{\left(2 \sqrt{c} d-3 \sqrt{a} e\right) \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{7/4}}+\frac{(d+e x)^{3/2} (a e+c d x)}{2 a c \left(a-c x^2\right)}+\frac{d e \sqrt{d+e x}}{2 a c}",1,"(d*e*Sqrt[d + e*x])/(2*a*c) + ((a*e + c*d*x)*(d + e*x)^(3/2))/(2*a*c*(a - c*x^2)) - ((Sqrt[c]*d - Sqrt[a]*e)^(3/2)*(2*Sqrt[c]*d + 3*Sqrt[a]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*c^(7/4)) + ((2*Sqrt[c]*d - 3*Sqrt[a]*e)*(Sqrt[c]*d + Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(7/4))","A",6,5,20,0.2500,1,"{739, 825, 827, 1166, 208}"
626,1,209,0,0.269905,"\int \frac{(d+e x)^{3/2}}{\left(a-c x^2\right)^2} \, dx","Int[(d + e*x)^(3/2)/(a - c*x^2)^2,x]","-\frac{\sqrt{\sqrt{c} d-\sqrt{a} e} \left(\sqrt{a} e+2 \sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{5/4}}+\frac{\left(2 \sqrt{c} d-\sqrt{a} e\right) \sqrt{\sqrt{a} e+\sqrt{c} d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{5/4}}+\frac{\sqrt{d+e x} (a e+c d x)}{2 a c \left(a-c x^2\right)}","-\frac{\sqrt{\sqrt{c} d-\sqrt{a} e} \left(\sqrt{a} e+2 \sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{5/4}}+\frac{\left(2 \sqrt{c} d-\sqrt{a} e\right) \sqrt{\sqrt{a} e+\sqrt{c} d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{5/4}}+\frac{\sqrt{d+e x} (a e+c d x)}{2 a c \left(a-c x^2\right)}",1,"((a*e + c*d*x)*Sqrt[d + e*x])/(2*a*c*(a - c*x^2)) - (Sqrt[Sqrt[c]*d - Sqrt[a]*e]*(2*Sqrt[c]*d + Sqrt[a]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*c^(5/4)) + ((2*Sqrt[c]*d - Sqrt[a]*e)*Sqrt[Sqrt[c]*d + Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(5/4))","A",5,4,20,0.2000,1,"{739, 827, 1166, 208}"
627,1,194,0,0.1862648,"\int \frac{\sqrt{d+e x}}{\left(a-c x^2\right)^2} \, dx","Int[Sqrt[d + e*x]/(a - c*x^2)^2,x]","-\frac{\left(\frac{2 \sqrt{c} d}{\sqrt{a}}-e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a c^{3/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}+\frac{\left(\frac{2 \sqrt{c} d}{\sqrt{a}}+e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a c^{3/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}+\frac{x \sqrt{d+e x}}{2 a \left(a-c x^2\right)}","-\frac{\left(\frac{2 \sqrt{c} d}{\sqrt{a}}-e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a c^{3/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}+\frac{\left(\frac{2 \sqrt{c} d}{\sqrt{a}}+e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a c^{3/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}+\frac{x \sqrt{d+e x}}{2 a \left(a-c x^2\right)}",1,"(x*Sqrt[d + e*x])/(2*a*(a - c*x^2)) - (((2*Sqrt[c]*d)/Sqrt[a] - e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a*c^(3/4)*Sqrt[Sqrt[c]*d - Sqrt[a]*e]) + (((2*Sqrt[c]*d)/Sqrt[a] + e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a*c^(3/4)*Sqrt[Sqrt[c]*d + Sqrt[a]*e])","A",5,4,20,0.2000,1,"{737, 827, 1166, 208}"
628,1,222,0,0.3385579,"\int \frac{1}{\sqrt{d+e x} \left(a-c x^2\right)^2} \, dx","Int[1/(Sqrt[d + e*x]*(a - c*x^2)^2),x]","-\frac{\left(2 \sqrt{c} d-3 \sqrt{a} e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} \sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\left(3 \sqrt{a} e+2 \sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} \sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}-\frac{\sqrt{d+e x} (a e-c d x)}{2 a \left(a-c x^2\right) \left(c d^2-a e^2\right)}","-\frac{\left(2 \sqrt{c} d-3 \sqrt{a} e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} \sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\left(3 \sqrt{a} e+2 \sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} \sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}-\frac{\sqrt{d+e x} (a e-c d x)}{2 a \left(a-c x^2\right) \left(c d^2-a e^2\right)}",1,"-((a*e - c*d*x)*Sqrt[d + e*x])/(2*a*(c*d^2 - a*e^2)*(a - c*x^2)) - ((2*Sqrt[c]*d - 3*Sqrt[a]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*c^(1/4)*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)) + ((2*Sqrt[c]*d + 3*Sqrt[a]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(1/4)*(Sqrt[c]*d + Sqrt[a]*e)^(3/2))","A",5,4,20,0.2000,1,"{741, 827, 1166, 208}"
629,1,265,0,0.4794245,"\int \frac{1}{(d+e x)^{3/2} \left(a-c x^2\right)^2} \, dx","Int[1/((d + e*x)^(3/2)*(a - c*x^2)^2),x]","-\frac{\sqrt[4]{c} \left(2 \sqrt{c} d-5 \sqrt{a} e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{\sqrt[4]{c} \left(5 \sqrt{a} e+2 \sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}-\frac{a e-c d x}{2 a \left(a-c x^2\right) \sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{e \left(5 a e^2+c d^2\right)}{2 a \sqrt{d+e x} \left(c d^2-a e^2\right)^2}","-\frac{\sqrt[4]{c} \left(2 \sqrt{c} d-5 \sqrt{a} e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{\sqrt[4]{c} \left(5 \sqrt{a} e+2 \sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}-\frac{a e-c d x}{2 a \left(a-c x^2\right) \sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{e \left(5 a e^2+c d^2\right)}{2 a \sqrt{d+e x} \left(c d^2-a e^2\right)^2}",1,"-(e*(c*d^2 + 5*a*e^2))/(2*a*(c*d^2 - a*e^2)^2*Sqrt[d + e*x]) - (a*e - c*d*x)/(2*a*(c*d^2 - a*e^2)*Sqrt[d + e*x]*(a - c*x^2)) - (c^(1/4)*(2*Sqrt[c]*d - 5*Sqrt[a]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*(Sqrt[c]*d - Sqrt[a]*e)^(5/2)) + (c^(1/4)*(2*Sqrt[c]*d + 5*Sqrt[a]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*(Sqrt[c]*d + Sqrt[a]*e)^(5/2))","A",6,5,20,0.2500,1,"{741, 829, 827, 1166, 208}"
630,1,311,0,0.7225763,"\int \frac{1}{(d+e x)^{5/2} \left(a-c x^2\right)^2} \, dx","Int[1/((d + e*x)^(5/2)*(a - c*x^2)^2),x]","-\frac{c^{3/4} \left(2 \sqrt{c} d-7 \sqrt{a} e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} \left(\sqrt{c} d-\sqrt{a} e\right)^{7/2}}+\frac{c^{3/4} \left(7 \sqrt{a} e+2 \sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} \left(\sqrt{a} e+\sqrt{c} d\right)^{7/2}}-\frac{a e-c d x}{2 a \left(a-c x^2\right) (d+e x)^{3/2} \left(c d^2-a e^2\right)}-\frac{e \left(7 a e^2+3 c d^2\right)}{6 a (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}-\frac{c d e \left(19 a e^2+c d^2\right)}{2 a \sqrt{d+e x} \left(c d^2-a e^2\right)^3}","-\frac{c^{3/4} \left(2 \sqrt{c} d-7 \sqrt{a} e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} \left(\sqrt{c} d-\sqrt{a} e\right)^{7/2}}+\frac{c^{3/4} \left(7 \sqrt{a} e+2 \sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} \left(\sqrt{a} e+\sqrt{c} d\right)^{7/2}}-\frac{a e-c d x}{2 a \left(a-c x^2\right) (d+e x)^{3/2} \left(c d^2-a e^2\right)}-\frac{e \left(7 a e^2+3 c d^2\right)}{6 a (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}-\frac{c d e \left(19 a e^2+c d^2\right)}{2 a \sqrt{d+e x} \left(c d^2-a e^2\right)^3}",1,"-(e*(3*c*d^2 + 7*a*e^2))/(6*a*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) - (c*d*e*(c*d^2 + 19*a*e^2))/(2*a*(c*d^2 - a*e^2)^3*Sqrt[d + e*x]) - (a*e - c*d*x)/(2*a*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*(a - c*x^2)) - (c^(3/4)*(2*Sqrt[c]*d - 7*Sqrt[a]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*(Sqrt[c]*d - Sqrt[a]*e)^(7/2)) + (c^(3/4)*(2*Sqrt[c]*d + 7*Sqrt[a]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*(Sqrt[c]*d + Sqrt[a]*e)^(7/2))","A",7,5,20,0.2500,1,"{741, 829, 827, 1166, 208}"
631,1,887,0,6.4485766,"\int \frac{(d+e x)^{7/2}}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^(7/2)/(a + c*x^2)^2,x]","-\frac{(a e-c d x) (d+e x)^{5/2}}{2 a c \left(c x^2+a\right)}-\frac{d e (d+e x)^{3/2}}{2 a c}-\frac{e \left(c d^2-5 a e^2\right) \sqrt{d+e x}}{2 a c^2}+\frac{e \left(c^2 d^4-4 a c e^2 d^2+\sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+13 a e^2\right) d-5 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(c^2 d^4-4 a c e^2 d^2+\sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+13 a e^2\right) d-5 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(c^2 d^4-4 a c e^2 d^2-\sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+13 a e^2\right) d-5 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{e \left(c^2 d^4-4 a c e^2 d^2-\sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+13 a e^2\right) d-5 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}","-\frac{(a e-c d x) (d+e x)^{5/2}}{2 a c \left(c x^2+a\right)}-\frac{d e (d+e x)^{3/2}}{2 a c}-\frac{e \left(c d^2-5 a e^2\right) \sqrt{d+e x}}{2 a c^2}+\frac{e \left(c^2 d^4-4 a c e^2 d^2+\sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+13 a e^2\right) d-5 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(c^2 d^4-4 a c e^2 d^2+\sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+13 a e^2\right) d-5 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(c^2 d^4-4 a c e^2 d^2-\sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+13 a e^2\right) d-5 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{e \left(c^2 d^4-4 a c e^2 d^2-\sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+13 a e^2\right) d-5 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}",1,"-(e*(c*d^2 - 5*a*e^2)*Sqrt[d + e*x])/(2*a*c^2) - (d*e*(d + e*x)^(3/2))/(2*a*c) - ((a*e - c*d*x)*(d + e*x)^(5/2))/(2*a*c*(a + c*x^2)) + (e*(c^2*d^4 - 4*a*c*d^2*e^2 - 5*a^2*e^4 + Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(c*d^2 + 13*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(9/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(c^2*d^4 - 4*a*c*d^2*e^2 - 5*a^2*e^4 + Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(c*d^2 + 13*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(9/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(c^2*d^4 - 4*a*c*d^2*e^2 - 5*a^2*e^4 - Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(c*d^2 + 13*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(9/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (e*(c^2*d^4 - 4*a*c*d^2*e^2 - 5*a^2*e^4 - Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(c*d^2 + 13*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(9/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",13,8,19,0.4211,1,"{739, 825, 827, 1169, 634, 618, 206, 628}"
632,1,811,0,2.8393872,"\int \frac{(d+e x)^{5/2}}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^(5/2)/(a + c*x^2)^2,x]","-\frac{(a e-c d x) (d+e x)^{3/2}}{2 a c \left(c x^2+a\right)}-\frac{d e \sqrt{d+e x}}{2 a c}+\frac{e \left(c^{3/2} d^3+a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(c d^2+3 a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(c^{3/2} d^3+a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(c d^2+3 a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(c^{3/2} d^3+a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(c d^2+3 a e^2\right)\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{e \left(c^{3/2} d^3+a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(c d^2+3 a e^2\right)\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}","-\frac{(a e-c d x) (d+e x)^{3/2}}{2 a c \left(c x^2+a\right)}-\frac{d e \sqrt{d+e x}}{2 a c}+\frac{e \left(c^{3/2} d^3+a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(c d^2+3 a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(c^{3/2} d^3+a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(c d^2+3 a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(c^{3/2} d^3+a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(c d^2+3 a e^2\right)\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{e \left(c^{3/2} d^3+a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(c d^2+3 a e^2\right)\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}",1,"-(d*e*Sqrt[d + e*x])/(2*a*c) - ((a*e - c*d*x)*(d + e*x)^(3/2))/(2*a*c*(a + c*x^2)) + (e*(c^(3/2)*d^3 + a*Sqrt[c]*d*e^2 + Sqrt[c*d^2 + a*e^2]*(c*d^2 + 3*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(c^(3/2)*d^3 + a*Sqrt[c]*d*e^2 + Sqrt[c*d^2 + a*e^2]*(c*d^2 + 3*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(c^(3/2)*d^3 + a*Sqrt[c]*d*e^2 - Sqrt[c*d^2 + a*e^2]*(c*d^2 + 3*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (e*(c^(3/2)*d^3 + a*Sqrt[c]*d*e^2 - Sqrt[c*d^2 + a*e^2]*(c*d^2 + 3*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",12,8,19,0.4211,1,"{739, 825, 827, 1169, 634, 618, 206, 628}"
633,1,726,0,1.2979938,"\int \frac{(d+e x)^{3/2}}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^(3/2)/(a + c*x^2)^2,x]","-\frac{e \left(-\sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(-\sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(\sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \left(\sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{\sqrt{d+e x} (a e-c d x)}{2 a c \left(a+c x^2\right)}","-\frac{e \left(-\sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(-\sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(\sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \left(\sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{\sqrt{d+e x} (a e-c d x)}{2 a c \left(a+c x^2\right)}",1,"-((a*e - c*d*x)*Sqrt[d + e*x])/(2*a*c*(a + c*x^2)) + (e*(c*d^2 + a*e^2 + Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(c*d^2 + a*e^2 + Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(c*d^2 + a*e^2 - Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (e*(c*d^2 + a*e^2 - Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",11,7,19,0.3684,1,"{739, 827, 1169, 634, 618, 206, 628}"
634,1,675,0,1.0175507,"\int \frac{\sqrt{d+e x}}{\left(a+c x^2\right)^2} \, dx","Int[Sqrt[d + e*x]/(a + c*x^2)^2,x]","\frac{e \left(\sqrt{a e^2+c d^2}+\sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a c^{3/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \left(\sqrt{a e^2+c d^2}+\sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a c^{3/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \left(d-\frac{\sqrt{a e^2+c d^2}}{\sqrt{c}}\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(d-\frac{\sqrt{a e^2+c d^2}}{\sqrt{c}}\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{x \sqrt{d+e x}}{2 a \left(a+c x^2\right)}","\frac{e \left(\sqrt{a e^2+c d^2}+\sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a c^{3/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \left(\sqrt{a e^2+c d^2}+\sqrt{c} d\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a c^{3/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \left(d-\frac{\sqrt{a e^2+c d^2}}{\sqrt{c}}\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(d-\frac{\sqrt{a e^2+c d^2}}{\sqrt{c}}\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a \sqrt[4]{c} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{x \sqrt{d+e x}}{2 a \left(a+c x^2\right)}",1,"(x*Sqrt[d + e*x])/(2*a*(a + c*x^2)) + (e*(Sqrt[c]*d + Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(3/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(Sqrt[c]*d + Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(3/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(d - Sqrt[c*d^2 + a*e^2]/Sqrt[c])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(1/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (e*(d - Sqrt[c*d^2 + a*e^2]/Sqrt[c])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(1/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",11,7,19,0.3684,1,"{737, 827, 1169, 634, 618, 206, 628}"
635,1,739,0,1.4983488,"\int \frac{1}{\sqrt{d+e x} \left(a+c x^2\right)^2} \, dx","Int[1/(Sqrt[d + e*x]*(a + c*x^2)^2),x]","\frac{\sqrt{d+e x} (a e+c d x)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}-\frac{e \left(-\sqrt{c} d \sqrt{a e^2+c d^2}+3 a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a \sqrt[4]{c} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(-\sqrt{c} d \sqrt{a e^2+c d^2}+3 a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a \sqrt[4]{c} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(\sqrt{c} d \sqrt{a e^2+c d^2}+3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a \sqrt[4]{c} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \left(\sqrt{c} d \sqrt{a e^2+c d^2}+3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a \sqrt[4]{c} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}","\frac{\sqrt{d+e x} (a e+c d x)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}-\frac{e \left(-\sqrt{c} d \sqrt{a e^2+c d^2}+3 a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a \sqrt[4]{c} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(-\sqrt{c} d \sqrt{a e^2+c d^2}+3 a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{8 \sqrt{2} a \sqrt[4]{c} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{e \left(\sqrt{c} d \sqrt{a e^2+c d^2}+3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a \sqrt[4]{c} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{e \left(\sqrt{c} d \sqrt{a e^2+c d^2}+3 a e^2+c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{4 \sqrt{2} a \sqrt[4]{c} \left(a e^2+c d^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}",1,"((a*e + c*d*x)*Sqrt[d + e*x])/(2*a*(c*d^2 + a*e^2)*(a + c*x^2)) + (e*(c*d^2 + 3*a*e^2 + Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(1/4)*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(c*d^2 + 3*a*e^2 + Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*c^(1/4)*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(c*d^2 + 3*a*e^2 - Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(1/4)*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (e*(c*d^2 + 3*a*e^2 - Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*c^(1/4)*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",11,7,19,0.3684,1,"{741, 827, 1169, 634, 618, 206, 628}"
636,1,845,0,3.3435086,"\int \frac{1}{(d+e x)^{3/2} \left(a+c x^2\right)^2} \, dx","Int[1/((d + e*x)^(3/2)*(a + c*x^2)^2),x]","\frac{e \left(c d^2-5 a e^2\right)}{2 a \left(c d^2+a e^2\right)^2 \sqrt{d+e x}}+\frac{\sqrt[4]{c} e \left(c^{3/2} d^3+13 a \sqrt{c} e^2 d+\left(c d^2-5 a e^2\right) \sqrt{c d^2+a e^2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{\sqrt[4]{c} e \left(c^{3/2} d^3+13 a \sqrt{c} e^2 d+\left(c d^2-5 a e^2\right) \sqrt{c d^2+a e^2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{\sqrt[4]{c} e \left(c^{3/2} d^3+13 a \sqrt{c} e^2 d-\left(c d^2-5 a e^2\right) \sqrt{c d^2+a e^2}\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{\sqrt[4]{c} e \left(c^{3/2} d^3+13 a \sqrt{c} e^2 d-\left(c d^2-5 a e^2\right) \sqrt{c d^2+a e^2}\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{a e+c d x}{2 a \left(c d^2+a e^2\right) \sqrt{d+e x} \left(c x^2+a\right)}","\frac{e \left(c d^2-5 a e^2\right)}{2 a \left(c d^2+a e^2\right)^2 \sqrt{d+e x}}+\frac{\sqrt[4]{c} e \left(c^{3/2} d^3+13 a \sqrt{c} e^2 d+\left(c d^2-5 a e^2\right) \sqrt{c d^2+a e^2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{\sqrt[4]{c} e \left(c^{3/2} d^3+13 a \sqrt{c} e^2 d+\left(c d^2-5 a e^2\right) \sqrt{c d^2+a e^2}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{\sqrt[4]{c} e \left(c^{3/2} d^3+13 a \sqrt{c} e^2 d-\left(c d^2-5 a e^2\right) \sqrt{c d^2+a e^2}\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{\sqrt[4]{c} e \left(c^{3/2} d^3+13 a \sqrt{c} e^2 d-\left(c d^2-5 a e^2\right) \sqrt{c d^2+a e^2}\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{a e+c d x}{2 a \left(c d^2+a e^2\right) \sqrt{d+e x} \left(c x^2+a\right)}",1,"(e*(c*d^2 - 5*a*e^2))/(2*a*(c*d^2 + a*e^2)^2*Sqrt[d + e*x]) + (a*e + c*d*x)/(2*a*(c*d^2 + a*e^2)*Sqrt[d + e*x]*(a + c*x^2)) + (c^(1/4)*e*(c^(3/2)*d^3 + 13*a*Sqrt[c]*d*e^2 + (c*d^2 - 5*a*e^2)*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (c^(1/4)*e*(c^(3/2)*d^3 + 13*a*Sqrt[c]*d*e^2 + (c*d^2 - 5*a*e^2)*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (c^(1/4)*e*(c^(3/2)*d^3 + 13*a*Sqrt[c]*d*e^2 - (c*d^2 - 5*a*e^2)*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (c^(1/4)*e*(c^(3/2)*d^3 + 13*a*Sqrt[c]*d*e^2 - (c*d^2 - 5*a*e^2)*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",12,8,19,0.4211,1,"{741, 829, 827, 1169, 634, 618, 206, 628}"
637,1,930,0,6.488626,"\int \frac{1}{(d+e x)^{5/2} \left(a+c x^2\right)^2} \, dx","Int[1/((d + e*x)^(5/2)*(a + c*x^2)^2),x]","\frac{c d e \left(c d^2-19 a e^2\right)}{2 a \left(c d^2+a e^2\right)^3 \sqrt{d+e x}}+\frac{c^{3/4} e \left(c^2 d^4+34 a c e^2 d^2+\sqrt{c} \left(c d^2-19 a e^2\right) \sqrt{c d^2+a e^2} d-7 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a \left(c d^2+a e^2\right)^{7/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{c^{3/4} e \left(c^2 d^4+34 a c e^2 d^2+\sqrt{c} \left(c d^2-19 a e^2\right) \sqrt{c d^2+a e^2} d-7 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a \left(c d^2+a e^2\right)^{7/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{c^{3/4} e \left(c^2 d^4+34 a c e^2 d^2-\sqrt{c} \left(c d^2-19 a e^2\right) \sqrt{c d^2+a e^2} d-7 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a \left(c d^2+a e^2\right)^{7/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{c^{3/4} e \left(c^2 d^4+34 a c e^2 d^2-\sqrt{c} \left(c d^2-19 a e^2\right) \sqrt{c d^2+a e^2} d-7 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a \left(c d^2+a e^2\right)^{7/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{a e+c d x}{2 a \left(c d^2+a e^2\right) (d+e x)^{3/2} \left(c x^2+a\right)}+\frac{e \left(3 c d^2-7 a e^2\right)}{6 a \left(c d^2+a e^2\right)^2 (d+e x)^{3/2}}","\frac{c d e \left(c d^2-19 a e^2\right)}{2 a \left(c d^2+a e^2\right)^3 \sqrt{d+e x}}+\frac{c^{3/4} e \left(c^2 d^4+34 a c e^2 d^2+\sqrt{c} \left(c d^2-19 a e^2\right) \sqrt{c d^2+a e^2} d-7 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a \left(c d^2+a e^2\right)^{7/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{c^{3/4} e \left(c^2 d^4+34 a c e^2 d^2+\sqrt{c} \left(c d^2-19 a e^2\right) \sqrt{c d^2+a e^2} d-7 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{4 \sqrt{2} a \left(c d^2+a e^2\right)^{7/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{c^{3/4} e \left(c^2 d^4+34 a c e^2 d^2-\sqrt{c} \left(c d^2-19 a e^2\right) \sqrt{c d^2+a e^2} d-7 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a \left(c d^2+a e^2\right)^{7/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{c^{3/4} e \left(c^2 d^4+34 a c e^2 d^2-\sqrt{c} \left(c d^2-19 a e^2\right) \sqrt{c d^2+a e^2} d-7 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{8 \sqrt{2} a \left(c d^2+a e^2\right)^{7/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{a e+c d x}{2 a \left(c d^2+a e^2\right) (d+e x)^{3/2} \left(c x^2+a\right)}+\frac{e \left(3 c d^2-7 a e^2\right)}{6 a \left(c d^2+a e^2\right)^2 (d+e x)^{3/2}}",1,"(e*(3*c*d^2 - 7*a*e^2))/(6*a*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2)) + (c*d*e*(c*d^2 - 19*a*e^2))/(2*a*(c*d^2 + a*e^2)^3*Sqrt[d + e*x]) + (a*e + c*d*x)/(2*a*(c*d^2 + a*e^2)*(d + e*x)^(3/2)*(a + c*x^2)) + (c^(3/4)*e*(c^2*d^4 + 34*a*c*d^2*e^2 - 7*a^2*e^4 + Sqrt[c]*d*(c*d^2 - 19*a*e^2)*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*(c*d^2 + a*e^2)^(7/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (c^(3/4)*e*(c^2*d^4 + 34*a*c*d^2*e^2 - 7*a^2*e^4 + Sqrt[c]*d*(c*d^2 - 19*a*e^2)*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(4*Sqrt[2]*a*(c*d^2 + a*e^2)^(7/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (c^(3/4)*e*(c^2*d^4 + 34*a*c*d^2*e^2 - 7*a^2*e^4 - Sqrt[c]*d*(c*d^2 - 19*a*e^2)*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*(c*d^2 + a*e^2)^(7/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (c^(3/4)*e*(c^2*d^4 + 34*a*c*d^2*e^2 - 7*a^2*e^4 - Sqrt[c]*d*(c*d^2 - 19*a*e^2)*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(8*Sqrt[2]*a*(c*d^2 + a*e^2)^(7/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",13,8,19,0.4211,1,"{741, 829, 827, 1169, 634, 618, 206, 628}"
638,1,294,0,0.5247513,"\int \frac{(d+e x)^{7/2}}{\left(a-c x^2\right)^3} \, dx","Int[(d + e*x)^(7/2)/(a - c*x^2)^3,x]","\frac{\sqrt{d+e x} \left(2 c d x \left(3 c d^2-2 a e^2\right)+a e \left(7 c d^2-5 a e^2\right)\right)}{16 a^2 c^2 \left(a-c x^2\right)}-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \left(18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{9/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \left(-18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{9/4}}+\frac{(d+e x)^{5/2} (a e+c d x)}{4 a c \left(a-c x^2\right)^2}","\frac{\sqrt{d+e x} \left(2 c d x \left(3 c d^2-2 a e^2\right)+a e \left(7 c d^2-5 a e^2\right)\right)}{16 a^2 c^2 \left(a-c x^2\right)}-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \left(18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{9/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \left(-18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{9/4}}+\frac{(d+e x)^{5/2} (a e+c d x)}{4 a c \left(a-c x^2\right)^2}",1,"((a*e + c*d*x)*(d + e*x)^(5/2))/(4*a*c*(a - c*x^2)^2) + (Sqrt[d + e*x]*(a*e*(7*c*d^2 - 5*a*e^2) + 2*c*d*(3*c*d^2 - 2*a*e^2)*x))/(16*a^2*c^2*(a - c*x^2)) - ((Sqrt[c]*d - Sqrt[a]*e)^(3/2)*(12*c*d^2 + 18*Sqrt[a]*Sqrt[c]*d*e + 5*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(9/4)) + ((Sqrt[c]*d + Sqrt[a]*e)^(3/2)*(12*c*d^2 - 18*Sqrt[a]*Sqrt[c]*d*e + 5*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(9/4))","A",6,5,20,0.2500,1,"{739, 819, 827, 1166, 208}"
639,1,279,0,0.4585887,"\int \frac{(d+e x)^{5/2}}{\left(a-c x^2\right)^3} \, dx","Int[(d + e*x)^(5/2)/(a - c*x^2)^3,x]","-\frac{3 \sqrt{\sqrt{c} d-\sqrt{a} e} \left(2 \sqrt{a} \sqrt{c} d e-a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{7/4}}+\frac{3 \sqrt{\sqrt{a} e+\sqrt{c} d} \left(-2 \sqrt{a} \sqrt{c} d e-a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{7/4}}+\frac{3 \sqrt{d+e x} \left(x \left(2 c d^2-a e^2\right)+a d e\right)}{16 a^2 c \left(a-c x^2\right)}+\frac{(d+e x)^{3/2} (a e+c d x)}{4 a c \left(a-c x^2\right)^2}","-\frac{3 \sqrt{\sqrt{c} d-\sqrt{a} e} \left(2 \sqrt{a} \sqrt{c} d e-a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{7/4}}+\frac{3 \sqrt{\sqrt{a} e+\sqrt{c} d} \left(-2 \sqrt{a} \sqrt{c} d e-a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{7/4}}+\frac{3 \sqrt{d+e x} \left(x \left(2 c d^2-a e^2\right)+a d e\right)}{16 a^2 c \left(a-c x^2\right)}+\frac{(d+e x)^{3/2} (a e+c d x)}{4 a c \left(a-c x^2\right)^2}",1,"((a*e + c*d*x)*(d + e*x)^(3/2))/(4*a*c*(a - c*x^2)^2) + (3*Sqrt[d + e*x]*(a*d*e + (2*c*d^2 - a*e^2)*x))/(16*a^2*c*(a - c*x^2)) - (3*Sqrt[Sqrt[c]*d - Sqrt[a]*e]*(4*c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(7/4)) + (3*Sqrt[Sqrt[c]*d + Sqrt[a]*e]*(4*c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(7/4))","A",6,5,20,0.2500,1,"{739, 821, 827, 1166, 208}"
640,1,268,0,0.5055573,"\int \frac{(d+e x)^{3/2}}{\left(a-c x^2\right)^3} \, dx","Int[(d + e*x)^(3/2)/(a - c*x^2)^3,x]","-\frac{3 \left(-2 \sqrt{a} \sqrt{c} d e-a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{5/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}+\frac{3 \left(2 \sqrt{a} \sqrt{c} d e-a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{5/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{\sqrt{d+e x} (a e-6 c d x)}{16 a^2 c \left(a-c x^2\right)}+\frac{\sqrt{d+e x} (a e+c d x)}{4 a c \left(a-c x^2\right)^2}","-\frac{3 \left(-2 \sqrt{a} \sqrt{c} d e-a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{5/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}+\frac{3 \left(2 \sqrt{a} \sqrt{c} d e-a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{5/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{\sqrt{d+e x} (a e-6 c d x)}{16 a^2 c \left(a-c x^2\right)}+\frac{\sqrt{d+e x} (a e+c d x)}{4 a c \left(a-c x^2\right)^2}",1,"((a*e + c*d*x)*Sqrt[d + e*x])/(4*a*c*(a - c*x^2)^2) - ((a*e - 6*c*d*x)*Sqrt[d + e*x])/(16*a^2*c*(a - c*x^2)) - (3*(4*c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(5/4)*Sqrt[Sqrt[c]*d - Sqrt[a]*e]) + (3*(4*c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(5/4)*Sqrt[Sqrt[c]*d + Sqrt[a]*e])","A",6,5,20,0.2500,1,"{739, 823, 827, 1166, 208}"
641,1,281,0,0.4901519,"\int \frac{\sqrt{d+e x}}{\left(a-c x^2\right)^3} \, dx","Int[Sqrt[d + e*x]/(a - c*x^2)^3,x]","-\frac{\left(-18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{3/4} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\left(18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{3/4} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}-\frac{\sqrt{d+e x} \left(a d e-x \left(6 c d^2-5 a e^2\right)\right)}{16 a^2 \left(a-c x^2\right) \left(c d^2-a e^2\right)}+\frac{x \sqrt{d+e x}}{4 a \left(a-c x^2\right)^2}","-\frac{\left(-18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{3/4} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\left(18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{3/4} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}-\frac{\sqrt{d+e x} \left(a d e-x \left(6 c d^2-5 a e^2\right)\right)}{16 a^2 \left(a-c x^2\right) \left(c d^2-a e^2\right)}+\frac{x \sqrt{d+e x}}{4 a \left(a-c x^2\right)^2}",1,"(x*Sqrt[d + e*x])/(4*a*(a - c*x^2)^2) - (Sqrt[d + e*x]*(a*d*e - (6*c*d^2 - 5*a*e^2)*x))/(16*a^2*(c*d^2 - a*e^2)*(a - c*x^2)) - ((12*c*d^2 - 18*Sqrt[a]*Sqrt[c]*d*e + 5*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(3/4)*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)) + ((12*c*d^2 + 18*Sqrt[a]*Sqrt[c]*d*e + 5*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(3/4)*(Sqrt[c]*d + Sqrt[a]*e)^(3/2))","A",6,5,20,0.2500,1,"{737, 823, 827, 1166, 208}"
642,1,315,0,0.6340205,"\int \frac{1}{\sqrt{d+e x} \left(a-c x^2\right)^3} \, dx","Int[1/(Sqrt[d + e*x]*(a - c*x^2)^3),x]","-\frac{\sqrt{d+e x} \left(a e \left(c d^2-7 a e^2\right)-6 c d x \left(c d^2-2 a e^2\right)\right)}{16 a^2 \left(a-c x^2\right) \left(c d^2-a e^2\right)^2}-\frac{3 \left(-10 \sqrt{a} \sqrt{c} d e+7 a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} \sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{3 \left(10 \sqrt{a} \sqrt{c} d e+7 a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} \sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}-\frac{\sqrt{d+e x} (a e-c d x)}{4 a \left(a-c x^2\right)^2 \left(c d^2-a e^2\right)}","-\frac{\sqrt{d+e x} \left(a e \left(c d^2-7 a e^2\right)-6 c d x \left(c d^2-2 a e^2\right)\right)}{16 a^2 \left(a-c x^2\right) \left(c d^2-a e^2\right)^2}-\frac{3 \left(-10 \sqrt{a} \sqrt{c} d e+7 a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} \sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{3 \left(10 \sqrt{a} \sqrt{c} d e+7 a e^2+4 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} \sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}-\frac{\sqrt{d+e x} (a e-c d x)}{4 a \left(a-c x^2\right)^2 \left(c d^2-a e^2\right)}",1,"-((a*e - c*d*x)*Sqrt[d + e*x])/(4*a*(c*d^2 - a*e^2)*(a - c*x^2)^2) - (Sqrt[d + e*x]*(a*e*(c*d^2 - 7*a*e^2) - 6*c*d*(c*d^2 - 2*a*e^2)*x))/(16*a^2*(c*d^2 - a*e^2)^2*(a - c*x^2)) - (3*(4*c*d^2 - 10*Sqrt[a]*Sqrt[c]*d*e + 7*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(1/4)*(Sqrt[c]*d - Sqrt[a]*e)^(5/2)) + (3*(4*c*d^2 + 10*Sqrt[a]*Sqrt[c]*d*e + 7*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(1/4)*(Sqrt[c]*d + Sqrt[a]*e)^(5/2))","A",6,5,20,0.2500,1,"{741, 823, 827, 1166, 208}"
643,1,905,0,5.6354181,"\int \frac{(d+e x)^{7/2}}{\left(a+c x^2\right)^3} \, dx","Int[(d + e*x)^(7/2)/(a + c*x^2)^3,x]","-\frac{(a e-c d x) (d+e x)^{5/2}}{4 a c \left(c x^2+a\right)^2}-\frac{\left(a e \left(7 c d^2+5 a e^2\right)-2 c d \left(3 c d^2+2 a e^2\right) x\right) \sqrt{d+e x}}{16 a^2 c^2 \left(c x^2+a\right)}+\frac{e \left(6 c^2 d^4+11 a c e^2 d^2+\sqrt{c} \sqrt{c d^2+a e^2} \left(6 c d^2+8 a e^2\right) d+5 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(6 c^2 d^4+11 a c e^2 d^2+\sqrt{c} \sqrt{c d^2+a e^2} \left(6 c d^2+8 a e^2\right) d+5 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(6 c^2 d^4+11 a c e^2 d^2-2 \sqrt{c} \sqrt{c d^2+a e^2} \left(3 c d^2+4 a e^2\right) d+5 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{e \left(6 c^2 d^4+11 a c e^2 d^2-2 \sqrt{c} \sqrt{c d^2+a e^2} \left(3 c d^2+4 a e^2\right) d+5 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}","-\frac{(a e-c d x) (d+e x)^{5/2}}{4 a c \left(c x^2+a\right)^2}-\frac{\left(a e \left(7 c d^2+5 a e^2\right)-2 c d \left(3 c d^2+2 a e^2\right) x\right) \sqrt{d+e x}}{16 a^2 c^2 \left(c x^2+a\right)}+\frac{e \left(6 c^2 d^4+11 a c e^2 d^2+\sqrt{c} \sqrt{c d^2+a e^2} \left(6 c d^2+8 a e^2\right) d+5 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(6 c^2 d^4+11 a c e^2 d^2+\sqrt{c} \sqrt{c d^2+a e^2} \left(6 c d^2+8 a e^2\right) d+5 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(6 c^2 d^4+11 a c e^2 d^2-2 \sqrt{c} \sqrt{c d^2+a e^2} \left(3 c d^2+4 a e^2\right) d+5 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{e \left(6 c^2 d^4+11 a c e^2 d^2-2 \sqrt{c} \sqrt{c d^2+a e^2} \left(3 c d^2+4 a e^2\right) d+5 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{9/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}",1,"-((a*e - c*d*x)*(d + e*x)^(5/2))/(4*a*c*(a + c*x^2)^2) - (Sqrt[d + e*x]*(a*e*(7*c*d^2 + 5*a*e^2) - 2*c*d*(3*c*d^2 + 2*a*e^2)*x))/(16*a^2*c^2*(a + c*x^2)) + (e*(6*c^2*d^4 + 11*a*c*d^2*e^2 + 5*a^2*e^4 + Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(6*c*d^2 + 8*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(9/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(6*c^2*d^4 + 11*a*c*d^2*e^2 + 5*a^2*e^4 + Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(6*c*d^2 + 8*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(9/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(6*c^2*d^4 + 11*a*c*d^2*e^2 + 5*a^2*e^4 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(3*c*d^2 + 4*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(9/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (e*(6*c^2*d^4 + 11*a*c*d^2*e^2 + 5*a^2*e^4 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(3*c*d^2 + 4*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(9/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",12,8,19,0.4211,1,"{739, 819, 827, 1169, 634, 618, 206, 628}"
644,1,846,0,3.3958289,"\int \frac{(d+e x)^{5/2}}{\left(a+c x^2\right)^3} \, dx","Int[(d + e*x)^(5/2)/(a + c*x^2)^3,x]","-\frac{(a e-c d x) (d+e x)^{3/2}}{4 a c \left(c x^2+a\right)^2}-\frac{3 \left(a d e-\left(2 c d^2+a e^2\right) x\right) \sqrt{d+e x}}{16 a^2 c \left(c x^2+a\right)}+\frac{3 e \left(2 c^{3/2} d^3+2 a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(2 c d^2+a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{3 e \left(2 c^{3/2} d^3+2 a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(2 c d^2+a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{3 e \left(2 c^{3/2} d^3+2 a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(2 c d^2+a e^2\right)\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{3 e \left(2 c^{3/2} d^3+2 a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(2 c d^2+a e^2\right)\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}","-\frac{(a e-c d x) (d+e x)^{3/2}}{4 a c \left(c x^2+a\right)^2}-\frac{3 \left(a d e-\left(2 c d^2+a e^2\right) x\right) \sqrt{d+e x}}{16 a^2 c \left(c x^2+a\right)}+\frac{3 e \left(2 c^{3/2} d^3+2 a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(2 c d^2+a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{3 e \left(2 c^{3/2} d^3+2 a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(2 c d^2+a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{3 e \left(2 c^{3/2} d^3+2 a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(2 c d^2+a e^2\right)\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{3 e \left(2 c^{3/2} d^3+2 a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(2 c d^2+a e^2\right)\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{7/4} \sqrt{c d^2+a e^2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}",1,"-((a*e - c*d*x)*(d + e*x)^(3/2))/(4*a*c*(a + c*x^2)^2) - (3*Sqrt[d + e*x]*(a*d*e - (2*c*d^2 + a*e^2)*x))/(16*a^2*c*(a + c*x^2)) + (3*e*(2*c^(3/2)*d^3 + 2*a*Sqrt[c]*d*e^2 + Sqrt[c*d^2 + a*e^2]*(2*c*d^2 + a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (3*e*(2*c^(3/2)*d^3 + 2*a*Sqrt[c]*d*e^2 + Sqrt[c*d^2 + a*e^2]*(2*c*d^2 + a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (3*e*(2*c^(3/2)*d^3 + 2*a*Sqrt[c]*d*e^2 - Sqrt[c*d^2 + a*e^2]*(2*c*d^2 + a*e^2))*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (3*e*(2*c^(3/2)*d^3 + 2*a*Sqrt[c]*d*e^2 - Sqrt[c*d^2 + a*e^2]*(2*c*d^2 + a*e^2))*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(7/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",12,8,19,0.4211,1,"{739, 821, 827, 1169, 634, 618, 206, 628}"
645,1,769,0,1.9355466,"\int \frac{(d+e x)^{3/2}}{\left(a+c x^2\right)^3} \, dx","Int[(d + e*x)^(3/2)/(a + c*x^2)^3,x]","-\frac{3 e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+2 c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{64 \sqrt{2} a^2 c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{3 e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+2 c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{64 \sqrt{2} a^2 c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{3 e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{32 \sqrt{2} a^2 c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{3 e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{32 \sqrt{2} a^2 c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{\sqrt{d+e x} (a e+6 c d x)}{16 a^2 c \left(a+c x^2\right)}-\frac{\sqrt{d+e x} (a e-c d x)}{4 a c \left(a+c x^2\right)^2}","-\frac{3 e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+2 c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{64 \sqrt{2} a^2 c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{3 e \left(-2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+2 c d^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt{d+e x} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{a e^2+c d^2}+\sqrt{c} (d+e x)\right)}{64 \sqrt{2} a^2 c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}}+\frac{3 e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{32 \sqrt{2} a^2 c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}-\frac{3 e \left(2 \sqrt{c} d \sqrt{a e^2+c d^2}+a e^2+2 c d^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a e^2+c d^2}+\sqrt{c} d}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}\right)}{32 \sqrt{2} a^2 c^{5/4} \sqrt{a e^2+c d^2} \sqrt{\sqrt{c} d-\sqrt{a e^2+c d^2}}}+\frac{\sqrt{d+e x} (a e+6 c d x)}{16 a^2 c \left(a+c x^2\right)}-\frac{\sqrt{d+e x} (a e-c d x)}{4 a c \left(a+c x^2\right)^2}",1,"-((a*e - c*d*x)*Sqrt[d + e*x])/(4*a*c*(a + c*x^2)^2) + ((a*e + 6*c*d*x)*Sqrt[d + e*x])/(16*a^2*c*(a + c*x^2)) + (3*e*(2*c*d^2 + a*e^2 + 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (3*e*(2*c*d^2 + a*e^2 + 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (3*e*(2*c*d^2 + a*e^2 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (3*e*(2*c*d^2 + a*e^2 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2])*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(5/4)*Sqrt[c*d^2 + a*e^2]*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",12,8,19,0.4211,1,"{739, 823, 827, 1169, 634, 618, 206, 628}"
646,1,849,0,2.8834824,"\int \frac{\sqrt{d+e x}}{\left(a+c x^2\right)^3} \, dx","Int[Sqrt[d + e*x]/(a + c*x^2)^3,x]","\frac{\sqrt{d+e x} x}{4 a \left(c x^2+a\right)^2}+\frac{e \left(6 c^{3/2} d^3+8 a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(6 c d^2+5 a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{3/4} \left(c d^2+a e^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(6 c^{3/2} d^3+8 a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(6 c d^2+5 a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{3/4} \left(c d^2+a e^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(6 c^{3/2} d^3+8 a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(6 c d^2+5 a e^2\right)\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{3/4} \left(c d^2+a e^2\right)^{3/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{e \left(6 c^{3/2} d^3+8 a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(6 c d^2+5 a e^2\right)\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{3/4} \left(c d^2+a e^2\right)^{3/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{\sqrt{d+e x} \left(a d e+\left(6 c d^2+5 a e^2\right) x\right)}{16 a^2 \left(c d^2+a e^2\right) \left(c x^2+a\right)}","\frac{\sqrt{d+e x} x}{4 a \left(c x^2+a\right)^2}+\frac{e \left(6 c^{3/2} d^3+8 a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(6 c d^2+5 a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{3/4} \left(c d^2+a e^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(6 c^{3/2} d^3+8 a \sqrt{c} e^2 d+\sqrt{c d^2+a e^2} \left(6 c d^2+5 a e^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 c^{3/4} \left(c d^2+a e^2\right)^{3/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{e \left(6 c^{3/2} d^3+8 a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(6 c d^2+5 a e^2\right)\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{3/4} \left(c d^2+a e^2\right)^{3/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{e \left(6 c^{3/2} d^3+8 a \sqrt{c} e^2 d-\sqrt{c d^2+a e^2} \left(6 c d^2+5 a e^2\right)\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 c^{3/4} \left(c d^2+a e^2\right)^{3/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{\sqrt{d+e x} \left(a d e+\left(6 c d^2+5 a e^2\right) x\right)}{16 a^2 \left(c d^2+a e^2\right) \left(c x^2+a\right)}",1,"(x*Sqrt[d + e*x])/(4*a*(a + c*x^2)^2) + (Sqrt[d + e*x]*(a*d*e + (6*c*d^2 + 5*a*e^2)*x))/(16*a^2*(c*d^2 + a*e^2)*(a + c*x^2)) + (e*(6*c^(3/2)*d^3 + 8*a*Sqrt[c]*d*e^2 + Sqrt[c*d^2 + a*e^2]*(6*c*d^2 + 5*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(3/4)*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(6*c^(3/2)*d^3 + 8*a*Sqrt[c]*d*e^2 + Sqrt[c*d^2 + a*e^2]*(6*c*d^2 + 5*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(3/4)*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (e*(6*c^(3/2)*d^3 + 8*a*Sqrt[c]*d*e^2 - Sqrt[c*d^2 + a*e^2]*(6*c*d^2 + 5*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(3/4)*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (e*(6*c^(3/2)*d^3 + 8*a*Sqrt[c]*d*e^2 - Sqrt[c*d^2 + a*e^2]*(6*c*d^2 + 5*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(3/4)*(c*d^2 + a*e^2)^(3/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",12,8,19,0.4211,1,"{737, 823, 827, 1169, 634, 618, 206, 628}"
647,1,920,0,5.8512972,"\int \frac{1}{\sqrt{d+e x} \left(a+c x^2\right)^3} \, dx","Int[1/(Sqrt[d + e*x]*(a + c*x^2)^3),x]","\frac{\sqrt{d+e x} (a e+c d x)}{4 a \left(c d^2+a e^2\right) \left(c x^2+a\right)^2}+\frac{3 e \left(2 c^2 d^4+5 a c e^2 d^2+2 \sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+2 a e^2\right) d+7 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 \sqrt[4]{c} \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{3 e \left(2 c^2 d^4+5 a c e^2 d^2+2 \sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+2 a e^2\right) d+7 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 \sqrt[4]{c} \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{3 e \left(2 c^2 d^4+5 a c e^2 d^2-2 \sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+2 a e^2\right) d+7 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 \sqrt[4]{c} \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{3 e \left(2 c^2 d^4+5 a c e^2 d^2-2 \sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+2 a e^2\right) d+7 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 \sqrt[4]{c} \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{\sqrt{d+e x} \left(a e \left(c d^2+7 a e^2\right)+6 c d \left(c d^2+2 a e^2\right) x\right)}{16 a^2 \left(c d^2+a e^2\right)^2 \left(c x^2+a\right)}","\frac{\sqrt{d+e x} (a e+c d x)}{4 a \left(c d^2+a e^2\right) \left(c x^2+a\right)^2}+\frac{3 e \left(2 c^2 d^4+5 a c e^2 d^2+2 \sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+2 a e^2\right) d+7 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}-\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 \sqrt[4]{c} \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{3 e \left(2 c^2 d^4+5 a c e^2 d^2+2 \sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+2 a e^2\right) d+7 a^2 e^4\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}+\sqrt{2} \sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}\right)}{32 \sqrt{2} a^2 \sqrt[4]{c} \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d-\sqrt{c d^2+a e^2}}}-\frac{3 e \left(2 c^2 d^4+5 a c e^2 d^2-2 \sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+2 a e^2\right) d+7 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)-\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 \sqrt[4]{c} \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{3 e \left(2 c^2 d^4+5 a c e^2 d^2-2 \sqrt{c} \sqrt{c d^2+a e^2} \left(c d^2+2 a e^2\right) d+7 a^2 e^4\right) \log \left(\sqrt{c} (d+e x)+\sqrt{2} \sqrt[4]{c} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}} \sqrt{d+e x}+\sqrt{c d^2+a e^2}\right)}{64 \sqrt{2} a^2 \sqrt[4]{c} \left(c d^2+a e^2\right)^{5/2} \sqrt{\sqrt{c} d+\sqrt{c d^2+a e^2}}}+\frac{\sqrt{d+e x} \left(a e \left(c d^2+7 a e^2\right)+6 c d \left(c d^2+2 a e^2\right) x\right)}{16 a^2 \left(c d^2+a e^2\right)^2 \left(c x^2+a\right)}",1,"((a*e + c*d*x)*Sqrt[d + e*x])/(4*a*(c*d^2 + a*e^2)*(a + c*x^2)^2) + (Sqrt[d + e*x]*(a*e*(c*d^2 + 7*a*e^2) + 6*c*d*(c*d^2 + 2*a*e^2)*x))/(16*a^2*(c*d^2 + a*e^2)^2*(a + c*x^2)) + (3*e*(2*c^2*d^4 + 5*a*c*d^2*e^2 + 7*a^2*e^4 + 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(c*d^2 + 2*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] - Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(1/4)*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (3*e*(2*c^2*d^4 + 5*a*c*d^2*e^2 + 7*a^2*e^4 + 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(c*d^2 + 2*a*e^2))*ArcTanh[(Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]] + Sqrt[2]*c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]])/(32*Sqrt[2]*a^2*c^(1/4)*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d - Sqrt[c*d^2 + a*e^2]]) - (3*e*(2*c^2*d^4 + 5*a*c*d^2*e^2 + 7*a^2*e^4 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(c*d^2 + 2*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] - Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(1/4)*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]) + (3*e*(2*c^2*d^4 + 5*a*c*d^2*e^2 + 7*a^2*e^4 - 2*Sqrt[c]*d*Sqrt[c*d^2 + a*e^2]*(c*d^2 + 2*a*e^2))*Log[Sqrt[c*d^2 + a*e^2] + Sqrt[2]*c^(1/4)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(64*Sqrt[2]*a^2*c^(1/4)*(c*d^2 + a*e^2)^(5/2)*Sqrt[Sqrt[c]*d + Sqrt[c*d^2 + a*e^2]])","A",12,8,19,0.4211,1,"{741, 823, 827, 1169, 634, 618, 206, 628}"
648,1,214,0,0.230092,"\int \frac{\sqrt{2+3 x}}{1+x^2} \, dx","Int[Sqrt[2 + 3*x]/(1 + x^2),x]","\frac{3 \log \left(3 x-\sqrt{2 \left(2+\sqrt{13}\right)} \sqrt{3 x+2}+\sqrt{13}+2\right)}{2 \sqrt{2 \left(2+\sqrt{13}\right)}}-\frac{3 \log \left(3 x+\sqrt{2 \left(2+\sqrt{13}\right)} \sqrt{3 x+2}+\sqrt{13}+2\right)}{2 \sqrt{2 \left(2+\sqrt{13}\right)}}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2 \left(2+\sqrt{13}\right)}-2 \sqrt{3 x+2}}{\sqrt{2 \left(\sqrt{13}-2\right)}}\right)}{\sqrt{2 \left(\sqrt{13}-2\right)}}+\frac{3 \tan ^{-1}\left(\frac{2 \sqrt{3 x+2}+\sqrt{2 \left(2+\sqrt{13}\right)}}{\sqrt{2 \left(\sqrt{13}-2\right)}}\right)}{\sqrt{2 \left(\sqrt{13}-2\right)}}","\frac{3 \log \left(3 x-\sqrt{2 \left(2+\sqrt{13}\right)} \sqrt{3 x+2}+\sqrt{13}+2\right)}{2 \sqrt{2 \left(2+\sqrt{13}\right)}}-\frac{3 \log \left(3 x+\sqrt{2 \left(2+\sqrt{13}\right)} \sqrt{3 x+2}+\sqrt{13}+2\right)}{2 \sqrt{2 \left(2+\sqrt{13}\right)}}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2 \left(2+\sqrt{13}\right)}-2 \sqrt{3 x+2}}{\sqrt{2 \left(\sqrt{13}-2\right)}}\right)}{\sqrt{2 \left(\sqrt{13}-2\right)}}+\frac{3 \tan ^{-1}\left(\frac{2 \sqrt{3 x+2}+\sqrt{2 \left(2+\sqrt{13}\right)}}{\sqrt{2 \left(\sqrt{13}-2\right)}}\right)}{\sqrt{2 \left(\sqrt{13}-2\right)}}",1,"(-3*ArcTan[(Sqrt[2*(2 + Sqrt[13])] - 2*Sqrt[2 + 3*x])/Sqrt[2*(-2 + Sqrt[13])]])/Sqrt[2*(-2 + Sqrt[13])] + (3*ArcTan[(Sqrt[2*(2 + Sqrt[13])] + 2*Sqrt[2 + 3*x])/Sqrt[2*(-2 + Sqrt[13])]])/Sqrt[2*(-2 + Sqrt[13])] + (3*Log[2 + Sqrt[13] + 3*x - Sqrt[2*(2 + Sqrt[13])]*Sqrt[2 + 3*x]])/(2*Sqrt[2*(2 + Sqrt[13])]) - (3*Log[2 + Sqrt[13] + 3*x + Sqrt[2*(2 + Sqrt[13])]*Sqrt[2 + 3*x]])/(2*Sqrt[2*(2 + Sqrt[13])])","A",10,7,17,0.4118,1,"{700, 1127, 1161, 618, 204, 1164, 628}"
649,1,316,0,0.3466848,"\int \frac{\sqrt{c+d x}}{1+x^2} \, dx","Int[Sqrt[c + d*x]/(1 + x^2),x]","\frac{d \log \left(-\sqrt{2} \sqrt{\sqrt{c^2+d^2}+c} \sqrt{c+d x}+\sqrt{c^2+d^2}+c+d x\right)}{2 \sqrt{2} \sqrt{\sqrt{c^2+d^2}+c}}-\frac{d \log \left(\sqrt{2} \sqrt{\sqrt{c^2+d^2}+c} \sqrt{c+d x}+\sqrt{c^2+d^2}+c+d x\right)}{2 \sqrt{2} \sqrt{\sqrt{c^2+d^2}+c}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c^2+d^2}+c}-\sqrt{2} \sqrt{c+d x}}{\sqrt{c-\sqrt{c^2+d^2}}}\right)}{\sqrt{2} \sqrt{c-\sqrt{c^2+d^2}}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c^2+d^2}+c}+\sqrt{2} \sqrt{c+d x}}{\sqrt{c-\sqrt{c^2+d^2}}}\right)}{\sqrt{2} \sqrt{c-\sqrt{c^2+d^2}}}","\frac{d \log \left(-\sqrt{2} \sqrt{\sqrt{c^2+d^2}+c} \sqrt{c+d x}+\sqrt{c^2+d^2}+c+d x\right)}{2 \sqrt{2} \sqrt{\sqrt{c^2+d^2}+c}}-\frac{d \log \left(\sqrt{2} \sqrt{\sqrt{c^2+d^2}+c} \sqrt{c+d x}+\sqrt{c^2+d^2}+c+d x\right)}{2 \sqrt{2} \sqrt{\sqrt{c^2+d^2}+c}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c^2+d^2}+c}-\sqrt{2} \sqrt{c+d x}}{\sqrt{c-\sqrt{c^2+d^2}}}\right)}{\sqrt{2} \sqrt{c-\sqrt{c^2+d^2}}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{\sqrt{c^2+d^2}+c}+\sqrt{2} \sqrt{c+d x}}{\sqrt{c-\sqrt{c^2+d^2}}}\right)}{\sqrt{2} \sqrt{c-\sqrt{c^2+d^2}}}",1,"(d*ArcTanh[(Sqrt[c + Sqrt[c^2 + d^2]] - Sqrt[2]*Sqrt[c + d*x])/Sqrt[c - Sqrt[c^2 + d^2]]])/(Sqrt[2]*Sqrt[c - Sqrt[c^2 + d^2]]) - (d*ArcTanh[(Sqrt[c + Sqrt[c^2 + d^2]] + Sqrt[2]*Sqrt[c + d*x])/Sqrt[c - Sqrt[c^2 + d^2]]])/(Sqrt[2]*Sqrt[c - Sqrt[c^2 + d^2]]) + (d*Log[c + Sqrt[c^2 + d^2] + d*x - Sqrt[2]*Sqrt[c + Sqrt[c^2 + d^2]]*Sqrt[c + d*x]])/(2*Sqrt[2]*Sqrt[c + Sqrt[c^2 + d^2]]) - (d*Log[c + Sqrt[c^2 + d^2] + d*x + Sqrt[2]*Sqrt[c + Sqrt[c^2 + d^2]]*Sqrt[c + d*x]])/(2*Sqrt[2]*Sqrt[c + Sqrt[c^2 + d^2]])","A",10,6,17,0.3529,1,"{700, 1129, 634, 618, 206, 628}"
650,1,35,0,0.0203036,"\int \frac{\sqrt{2+3 x}}{1-x^2} \, dx","Int[Sqrt[2 + 3*x]/(1 - x^2),x]","\sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{3 x+2}}{\sqrt{5}}\right)-\tan ^{-1}\left(\sqrt{3 x+2}\right)","\sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{3 x+2}}{\sqrt{5}}\right)-\tan ^{-1}\left(\sqrt{3 x+2}\right)",1,"-ArcTan[Sqrt[2 + 3*x]] + Sqrt[5]*ArcTanh[Sqrt[2 + 3*x]/Sqrt[5]]","A",4,4,19,0.2105,1,"{700, 1130, 206, 204}"
651,1,58,0,0.0580653,"\int \frac{\sqrt{c+d x}}{1-x^2} \, dx","Int[Sqrt[c + d*x]/(1 - x^2),x]","\sqrt{c+d} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c+d}}\right)-\sqrt{c-d} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c-d}}\right)","\sqrt{c+d} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c+d}}\right)-\sqrt{c-d} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c-d}}\right)",1,"-(Sqrt[c - d]*ArcTanh[Sqrt[c + d*x]/Sqrt[c - d]]) + Sqrt[c + d]*ArcTanh[Sqrt[c + d*x]/Sqrt[c + d]]","A",4,3,19,0.1579,1,"{700, 1130, 206}"
652,1,427,0,0.5308455,"\int \frac{\sqrt{2+3 x}}{a+b x^2} \, dx","Int[Sqrt[2 + 3*x]/(a + b*x^2),x]","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt{3 x+2} \sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}+\sqrt{9 a+4 b}+\sqrt{b} (3 x+2)\right)}{2 \sqrt{2} b^{3/4} \sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt{3 x+2} \sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}+\sqrt{9 a+4 b}+\sqrt{b} (3 x+2)\right)}{2 \sqrt{2} b^{3/4} \sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}-\sqrt{2} \sqrt[4]{b} \sqrt{3 x+2}}{\sqrt{2 \sqrt{b}-\sqrt{9 a+4 b}}}\right)}{\sqrt{2} b^{3/4} \sqrt{2 \sqrt{b}-\sqrt{9 a+4 b}}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}+\sqrt{2} \sqrt[4]{b} \sqrt{3 x+2}}{\sqrt{2 \sqrt{b}-\sqrt{9 a+4 b}}}\right)}{\sqrt{2} b^{3/4} \sqrt{2 \sqrt{b}-\sqrt{9 a+4 b}}}","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt{3 x+2} \sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}+\sqrt{9 a+4 b}+\sqrt{b} (3 x+2)\right)}{2 \sqrt{2} b^{3/4} \sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt{3 x+2} \sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}+\sqrt{9 a+4 b}+\sqrt{b} (3 x+2)\right)}{2 \sqrt{2} b^{3/4} \sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}-\sqrt{2} \sqrt[4]{b} \sqrt{3 x+2}}{\sqrt{2 \sqrt{b}-\sqrt{9 a+4 b}}}\right)}{\sqrt{2} b^{3/4} \sqrt{2 \sqrt{b}-\sqrt{9 a+4 b}}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{9 a+4 b}+2 \sqrt{b}}+\sqrt{2} \sqrt[4]{b} \sqrt{3 x+2}}{\sqrt{2 \sqrt{b}-\sqrt{9 a+4 b}}}\right)}{\sqrt{2} b^{3/4} \sqrt{2 \sqrt{b}-\sqrt{9 a+4 b}}}",1,"(3*ArcTanh[(Sqrt[2*Sqrt[b] + Sqrt[9*a + 4*b]] - Sqrt[2]*b^(1/4)*Sqrt[2 + 3*x])/Sqrt[2*Sqrt[b] - Sqrt[9*a + 4*b]]])/(Sqrt[2]*b^(3/4)*Sqrt[2*Sqrt[b] - Sqrt[9*a + 4*b]]) - (3*ArcTanh[(Sqrt[2*Sqrt[b] + Sqrt[9*a + 4*b]] + Sqrt[2]*b^(1/4)*Sqrt[2 + 3*x])/Sqrt[2*Sqrt[b] - Sqrt[9*a + 4*b]]])/(Sqrt[2]*b^(3/4)*Sqrt[2*Sqrt[b] - Sqrt[9*a + 4*b]]) + (3*Log[Sqrt[9*a + 4*b] - Sqrt[2]*b^(1/4)*Sqrt[2*Sqrt[b] + Sqrt[9*a + 4*b]]*Sqrt[2 + 3*x] + Sqrt[b]*(2 + 3*x)])/(2*Sqrt[2]*b^(3/4)*Sqrt[2*Sqrt[b] + Sqrt[9*a + 4*b]]) - (3*Log[Sqrt[9*a + 4*b] + Sqrt[2]*b^(1/4)*Sqrt[2*Sqrt[b] + Sqrt[9*a + 4*b]]*Sqrt[2 + 3*x] + Sqrt[b]*(2 + 3*x)])/(2*Sqrt[2]*b^(3/4)*Sqrt[2*Sqrt[b] + Sqrt[9*a + 4*b]])","A",10,6,19,0.3158,1,"{700, 1129, 634, 618, 206, 628}"
653,1,132,0,0.1321671,"\int \frac{\sqrt{2+3 x}}{a-b x^2} \, dx","Int[Sqrt[2 + 3*x]/(a - b*x^2),x]","\frac{\sqrt{3 \sqrt{a}+2 \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{3 x+2}}{\sqrt{3 \sqrt{a}+2 \sqrt{b}}}\right)}{\sqrt{a} b^{3/4}}-\frac{\sqrt{3 \sqrt{a}-2 \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{3 x+2}}{\sqrt{3 \sqrt{a}-2 \sqrt{b}}}\right)}{\sqrt{a} b^{3/4}}","\frac{\sqrt{3 \sqrt{a}+2 \sqrt{b}} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{3 x+2}}{\sqrt{3 \sqrt{a}+2 \sqrt{b}}}\right)}{\sqrt{a} b^{3/4}}-\frac{\sqrt{3 \sqrt{a}-2 \sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{3 x+2}}{\sqrt{3 \sqrt{a}-2 \sqrt{b}}}\right)}{\sqrt{a} b^{3/4}}",1,"-((Sqrt[3*Sqrt[a] - 2*Sqrt[b]]*ArcTan[(b^(1/4)*Sqrt[2 + 3*x])/Sqrt[3*Sqrt[a] - 2*Sqrt[b]]])/(Sqrt[a]*b^(3/4))) + (Sqrt[3*Sqrt[a] + 2*Sqrt[b]]*ArcTanh[(b^(1/4)*Sqrt[2 + 3*x])/Sqrt[3*Sqrt[a] + 2*Sqrt[b]]])/(Sqrt[a]*b^(3/4))","A",4,4,20,0.2000,1,"{700, 1130, 208, 205}"
654,1,205,0,0.2230125,"\int \frac{\sqrt{1+x}}{1+x^2} \, dx","Int[Sqrt[1 + x]/(1 + x^2),x]","\frac{\log \left(x-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{\log \left(x+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)}}-\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{x+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{x+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)","\frac{\log \left(x-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{\log \left(x+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)}}-\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{x+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{x+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)",1,"-(Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]]) + Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]] + Log[1 + Sqrt[2] + x - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]]/(2*Sqrt[2*(1 + Sqrt[2])]) - Log[1 + Sqrt[2] + x + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]]/(2*Sqrt[2*(1 + Sqrt[2])])","A",10,7,15,0.4667,1,"{700, 1127, 1161, 618, 204, 1164, 628}"
655,1,198,0,0.1320412,"\int \frac{1}{\sqrt{1+x} \left(1+x^2\right)} \, dx","Int[1/(Sqrt[1 + x]*(1 + x^2)),x]","-\frac{\log \left(x-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}}}+\frac{\log \left(x+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}}}-\frac{1}{2} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{x+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\frac{1}{2} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{x+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)","-\frac{\log \left(x-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}}}+\frac{\log \left(x+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}}}-\frac{1}{2} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{x+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\frac{1}{2} \sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{x+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)",1,"-(Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]])/2 + (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]])/2 - Log[1 + Sqrt[2] + x - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]]/(4*Sqrt[1 + Sqrt[2]]) + Log[1 + Sqrt[2] + x + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]]/(4*Sqrt[1 + Sqrt[2]])","A",10,6,15,0.4000,1,"{708, 1094, 634, 618, 204, 628}"
656,1,272,0,0.3640432,"\int \frac{\sqrt{-1+x}}{\left(1+x^2\right)^3} \, dx","Int[Sqrt[-1 + x]/(1 + x^2)^3,x]","-\frac{\sqrt{x-1} (1-11 x)}{32 \left(x^2+1\right)}+\frac{\sqrt{x-1} x}{4 \left(x^2+1\right)^2}-\frac{1}{128} \sqrt{\frac{1}{2} \left(527+373 \sqrt{2}\right)} \log \left(-x-\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{x-1}-\sqrt{2}+1\right)+\frac{1}{128} \sqrt{\frac{1}{2} \left(527+373 \sqrt{2}\right)} \log \left(-x+\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{x-1}-\sqrt{2}+1\right)-\frac{1}{64} \sqrt{\frac{1}{2} \left(373 \sqrt{2}-527\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)}-2 \sqrt{x-1}}{\sqrt{2 \left(1+\sqrt{2}\right)}}\right)+\frac{1}{64} \sqrt{\frac{1}{2} \left(373 \sqrt{2}-527\right)} \tan ^{-1}\left(\frac{2 \sqrt{x-1}+\sqrt{2 \left(\sqrt{2}-1\right)}}{\sqrt{2 \left(1+\sqrt{2}\right)}}\right)","-\frac{\sqrt{x-1} (1-11 x)}{32 \left(x^2+1\right)}+\frac{\sqrt{x-1} x}{4 \left(x^2+1\right)^2}-\frac{1}{128} \sqrt{\frac{1}{2} \left(527+373 \sqrt{2}\right)} \log \left(-x-\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{x-1}-\sqrt{2}+1\right)+\frac{1}{128} \sqrt{\frac{1}{2} \left(527+373 \sqrt{2}\right)} \log \left(-x+\sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{x-1}-\sqrt{2}+1\right)-\frac{1}{64} \sqrt{\frac{1}{2} \left(373 \sqrt{2}-527\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)}-2 \sqrt{x-1}}{\sqrt{2 \left(1+\sqrt{2}\right)}}\right)+\frac{1}{64} \sqrt{\frac{1}{2} \left(373 \sqrt{2}-527\right)} \tan ^{-1}\left(\frac{2 \sqrt{x-1}+\sqrt{2 \left(\sqrt{2}-1\right)}}{\sqrt{2 \left(1+\sqrt{2}\right)}}\right)",1,"(Sqrt[-1 + x]*x)/(4*(1 + x^2)^2) - ((1 - 11*x)*Sqrt[-1 + x])/(32*(1 + x^2)) - (Sqrt[(-527 + 373*Sqrt[2])/2]*ArcTan[(Sqrt[2*(-1 + Sqrt[2])] - 2*Sqrt[-1 + x])/Sqrt[2*(1 + Sqrt[2])]])/64 + (Sqrt[(-527 + 373*Sqrt[2])/2]*ArcTan[(Sqrt[2*(-1 + Sqrt[2])] + 2*Sqrt[-1 + x])/Sqrt[2*(1 + Sqrt[2])]])/64 - (Sqrt[(527 + 373*Sqrt[2])/2]*Log[1 - Sqrt[2] - Sqrt[2*(-1 + Sqrt[2])]*Sqrt[-1 + x] - x])/128 + (Sqrt[(527 + 373*Sqrt[2])/2]*Log[1 - Sqrt[2] + Sqrt[2*(-1 + Sqrt[2])]*Sqrt[-1 + x] - x])/128","A",12,8,15,0.5333,1,"{737, 823, 827, 1169, 634, 618, 204, 628}"
657,1,398,0,0.4412832,"\int (d+e x)^{3/2} \sqrt{a+c x^2} \, dx","Int[(d + e*x)^(3/2)*Sqrt[a + c*x^2],x]","-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(3 c d^2-5 a e^2\right) \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 c^{3/2} e^2 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{a+c x^2} \sqrt{d+e x} \left(-5 a e^2+3 c d^2+24 c d e x\right)}{105 c e}+\frac{4 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 c d^2-29 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 \sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 e \left(a+c x^2\right)^{3/2} \sqrt{d+e x}}{7 c}","-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(3 c d^2-5 a e^2\right) \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 c^{3/2} e^2 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{a+c x^2} \sqrt{d+e x} \left(-5 a e^2+3 c d^2+24 c d e x\right)}{105 c e}+\frac{4 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 c d^2-29 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 \sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 e \left(a+c x^2\right)^{3/2} \sqrt{d+e x}}{7 c}",1,"(2*Sqrt[d + e*x]*(3*c*d^2 - 5*a*e^2 + 24*c*d*e*x)*Sqrt[a + c*x^2])/(105*c*e) + (2*e*Sqrt[d + e*x]*(a + c*x^2)^(3/2))/(7*c) + (4*Sqrt[-a]*d*(3*c*d^2 - 29*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(105*Sqrt[c]*e^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*(3*c*d^2 - 5*a*e^2)*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(105*c^(3/2)*e^2*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{743, 815, 844, 719, 424, 419}"
658,1,362,0,0.2986112,"\int \sqrt{d+e x} \sqrt{a+c x^2} \, dx","Int[Sqrt[d + e*x]*Sqrt[a + c*x^2],x]","-\frac{4 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \sqrt{a+c x^2} (d+e x)^{3/2}}{5 e}-\frac{4 d \sqrt{a+c x^2} \sqrt{d+e x}}{15 e}","-\frac{4 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \sqrt{a+c x^2} (d+e x)^{3/2}}{5 e}-\frac{4 d \sqrt{a+c x^2} \sqrt{d+e x}}{15 e}",1,"(-4*d*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(15*e) + (2*(d + e*x)^(3/2)*Sqrt[a + c*x^2])/(5*e) + (4*Sqrt[-a]*(c*d^2 - 3*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*Sqrt[c]*e^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*d*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*Sqrt[c]*e^2*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{735, 833, 844, 719, 424, 419}"
659,1,322,0,0.2035772,"\int \frac{\sqrt{a+c x^2}}{\sqrt{d+e x}} \, dx","Int[Sqrt[a + c*x^2]/Sqrt[d + e*x],x]","-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \sqrt{a+c x^2} \sqrt{d+e x}}{3 e}","-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{c} e^2 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{4 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \sqrt{a+c x^2} \sqrt{d+e x}}{3 e}",1,"(2*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(3*e) + (4*Sqrt[-a]*Sqrt[c]*d*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*e^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*Sqrt[c]*e^2*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,21,0.2381,1,"{735, 844, 719, 424, 419}"
660,1,305,0,0.1830421,"\int \frac{\sqrt{a+c x^2}}{(d+e x)^{3/2}} \, dx","Int[Sqrt[a + c*x^2]/(d + e*x)^(3/2),x]","\frac{4 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{e^2 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 \sqrt{a+c x^2}}{e \sqrt{d+e x}}","\frac{4 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{e^2 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{e^2 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 \sqrt{a+c x^2}}{e \sqrt{d+e x}}",1,"(-2*Sqrt[a + c*x^2])/(e*Sqrt[d + e*x]) - (4*Sqrt[-a]*Sqrt[c]*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(e^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (4*Sqrt[-a]*Sqrt[c]*d*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(e^2*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,21,0.2381,1,"{733, 844, 719, 424, 419}"
661,1,366,0,0.2729542,"\int \frac{\sqrt{a+c x^2}}{(d+e x)^{5/2}} \, dx","Int[Sqrt[a + c*x^2]/(d + e*x)^(5/2),x]","\frac{4 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 c d \sqrt{a+c x^2}}{3 e \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^2 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{a+c x^2}}{3 e (d+e x)^{3/2}}","\frac{4 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 c d \sqrt{a+c x^2}}{3 e \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^2 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{a+c x^2}}{3 e (d+e x)^{3/2}}",1,"(-2*Sqrt[a + c*x^2])/(3*e*(d + e*x)^(3/2)) + (4*c*d*Sqrt[a + c*x^2])/(3*e*(c*d^2 + a*e^2)*Sqrt[d + e*x]) + (4*Sqrt[-a]*c^(3/2)*d*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*e^2*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*Sqrt[c]*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*e^2*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{733, 835, 844, 719, 424, 419}"
662,1,444,0,0.3818399,"\int \frac{\sqrt{a+c x^2}}{(d+e x)^{7/2}} \, dx","Int[Sqrt[a + c*x^2]/(d + e*x)^(7/2),x]","-\frac{4 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^2 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{4 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 c \sqrt{a+c x^2} \left(c d^2-3 a e^2\right)}{15 e \sqrt{d+e x} \left(a e^2+c d^2\right)^2}+\frac{4 c d \sqrt{a+c x^2}}{15 e (d+e x)^{3/2} \left(a e^2+c d^2\right)}-\frac{2 \sqrt{a+c x^2}}{5 e (d+e x)^{5/2}}","-\frac{4 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^2 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{4 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 c \sqrt{a+c x^2} \left(c d^2-3 a e^2\right)}{15 e \sqrt{d+e x} \left(a e^2+c d^2\right)^2}+\frac{4 c d \sqrt{a+c x^2}}{15 e (d+e x)^{3/2} \left(a e^2+c d^2\right)}-\frac{2 \sqrt{a+c x^2}}{5 e (d+e x)^{5/2}}",1,"(-2*Sqrt[a + c*x^2])/(5*e*(d + e*x)^(5/2)) + (4*c*d*Sqrt[a + c*x^2])/(15*e*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) + (4*c*(c*d^2 - 3*a*e^2)*Sqrt[a + c*x^2])/(15*e*(c*d^2 + a*e^2)^2*Sqrt[d + e*x]) + (4*Sqrt[-a]*c^(3/2)*(c*d^2 - 3*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*e^2*(c*d^2 + a*e^2)^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*c^(3/2)*d*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*e^2*(c*d^2 + a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{733, 835, 844, 719, 424, 419}"
663,1,497,0,0.5593444,"\int (d+e x)^{3/2} \left(a+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^(3/2)*(a + c*x^2)^(3/2),x]","\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(-15 a^2 e^4-3 c d e x \left(c d^2-31 a e^2\right)+21 a c d^2 e^2+4 c^2 d^4\right)}{1155 c e^3}-\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(-15 a^2 e^4+21 a c d^2 e^2+4 c^2 d^4\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{1155 c^{3/2} e^4 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \left(a+c x^2\right)^{3/2} \sqrt{d+e x} \left(-3 a e^2+c d^2+28 c d e x\right)}{231 c e}+\frac{32 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) \left(9 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{1155 \sqrt{c} e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 e \left(a+c x^2\right)^{5/2} \sqrt{d+e x}}{11 c}","\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(-15 a^2 e^4-3 c d e x \left(c d^2-31 a e^2\right)+21 a c d^2 e^2+4 c^2 d^4\right)}{1155 c e^3}-\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(-15 a^2 e^4+21 a c d^2 e^2+4 c^2 d^4\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{1155 c^{3/2} e^4 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \left(a+c x^2\right)^{3/2} \sqrt{d+e x} \left(-3 a e^2+c d^2+28 c d e x\right)}{231 c e}+\frac{32 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) \left(9 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{1155 \sqrt{c} e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 e \left(a+c x^2\right)^{5/2} \sqrt{d+e x}}{11 c}",1,"(4*Sqrt[d + e*x]*(4*c^2*d^4 + 21*a*c*d^2*e^2 - 15*a^2*e^4 - 3*c*d*e*(c*d^2 - 31*a*e^2)*x)*Sqrt[a + c*x^2])/(1155*c*e^3) + (2*Sqrt[d + e*x]*(c*d^2 - 3*a*e^2 + 28*c*d*e*x)*(a + c*x^2)^(3/2))/(231*c*e) + (2*e*Sqrt[d + e*x]*(a + c*x^2)^(5/2))/(11*c) + (32*Sqrt[-a]*d*(c*d^2 - 3*a*e^2)*(c*d^2 + 9*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(1155*Sqrt[c]*e^4*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (8*Sqrt[-a]*(c*d^2 + a*e^2)*(4*c^2*d^4 + 21*a*c*d^2*e^2 - 15*a^2*e^4)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(1155*c^(3/2)*e^4*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{743, 815, 844, 719, 424, 419}"
664,1,448,0,0.4671106,"\int \sqrt{d+e x} \left(a+c x^2\right)^{3/2} \, dx","Int[Sqrt[d + e*x]*(a + c*x^2)^(3/2),x]","\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-21 a^2 e^4+15 a c d^2 e^2+4 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{315 \sqrt{c} e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(4 d \left(3 a e^2+c d^2\right)-3 e x \left(c d^2-7 a e^2\right)\right)}{315 e^3}-\frac{32 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(3 a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{315 \sqrt{c} e^4 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \left(a+c x^2\right)^{3/2} (d+e x)^{3/2}}{9 e}-\frac{4 d \left(a+c x^2\right)^{3/2} \sqrt{d+e x}}{21 e}","\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-21 a^2 e^4+15 a c d^2 e^2+4 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{315 \sqrt{c} e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(4 d \left(3 a e^2+c d^2\right)-3 e x \left(c d^2-7 a e^2\right)\right)}{315 e^3}-\frac{32 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(3 a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{315 \sqrt{c} e^4 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \left(a+c x^2\right)^{3/2} (d+e x)^{3/2}}{9 e}-\frac{4 d \left(a+c x^2\right)^{3/2} \sqrt{d+e x}}{21 e}",1,"(4*Sqrt[d + e*x]*(4*d*(c*d^2 + 3*a*e^2) - 3*e*(c*d^2 - 7*a*e^2)*x)*Sqrt[a + c*x^2])/(315*e^3) - (4*d*Sqrt[d + e*x]*(a + c*x^2)^(3/2))/(21*e) + (2*(d + e*x)^(3/2)*(a + c*x^2)^(3/2))/(9*e) + (8*Sqrt[-a]*(4*c^2*d^4 + 15*a*c*d^2*e^2 - 21*a^2*e^4)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(315*Sqrt[c]*e^4*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (32*Sqrt[-a]*d*(c*d^2 + a*e^2)*(c*d^2 + 3*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(315*Sqrt[c]*e^4*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,7,21,0.3333,1,"{735, 833, 815, 844, 719, 424, 419}"
665,1,393,0,0.357265,"\int \frac{\left(a+c x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[(a + c*x^2)^(3/2)/Sqrt[d + e*x],x]","\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(5 a e^2+4 c d^2-3 c d e x\right)}{35 e^3}-\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(5 a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 \sqrt{c} e^4 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{32 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(2 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \left(a+c x^2\right)^{3/2} \sqrt{d+e x}}{7 e}","\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(5 a e^2+4 c d^2-3 c d e x\right)}{35 e^3}-\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(5 a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 \sqrt{c} e^4 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{32 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(2 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \left(a+c x^2\right)^{3/2} \sqrt{d+e x}}{7 e}",1,"(4*Sqrt[d + e*x]*(4*c*d^2 + 5*a*e^2 - 3*c*d*e*x)*Sqrt[a + c*x^2])/(35*e^3) + (2*Sqrt[d + e*x]*(a + c*x^2)^(3/2))/(7*e) + (32*Sqrt[-a]*Sqrt[c]*d*(c*d^2 + 2*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(35*e^4*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (8*Sqrt[-a]*(c*d^2 + a*e^2)*(4*c*d^2 + 5*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(35*Sqrt[c]*e^4*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{735, 815, 844, 719, 424, 419}"
666,1,369,0,0.3068889,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^(3/2),x]","\frac{32 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{5 e^4 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a e^2+4 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{5 e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{4 c \sqrt{a+c x^2} (4 d-3 e x) \sqrt{d+e x}}{5 e^3}-\frac{2 \left(a+c x^2\right)^{3/2}}{e \sqrt{d+e x}}","\frac{32 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{5 e^4 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a e^2+4 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{5 e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{4 c \sqrt{a+c x^2} (4 d-3 e x) \sqrt{d+e x}}{5 e^3}-\frac{2 \left(a+c x^2\right)^{3/2}}{e \sqrt{d+e x}}",1,"(-4*c*(4*d - 3*e*x)*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(5*e^3) - (2*(a + c*x^2)^(3/2))/(e*Sqrt[d + e*x]) - (8*Sqrt[-a]*Sqrt[c]*(4*c*d^2 + 3*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(5*e^4*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (32*Sqrt[-a]*Sqrt[c]*d*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(5*e^4*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{733, 815, 844, 719, 424, 419}"
667,1,358,0,0.2554923,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^(5/2),x]","\frac{32 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^4 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{4 c \sqrt{a+c x^2} (4 d+e x)}{3 e^3 \sqrt{d+e x}}-\frac{2 \left(a+c x^2\right)^{3/2}}{3 e (d+e x)^{3/2}}","\frac{32 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^4 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^4 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{4 c \sqrt{a+c x^2} (4 d+e x)}{3 e^3 \sqrt{d+e x}}-\frac{2 \left(a+c x^2\right)^{3/2}}{3 e (d+e x)^{3/2}}",1,"(4*c*(4*d + e*x)*Sqrt[a + c*x^2])/(3*e^3*Sqrt[d + e*x]) - (2*(a + c*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) + (32*Sqrt[-a]*c^(3/2)*d*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*e^4*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (8*Sqrt[-a]*Sqrt[c]*(4*c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*e^4*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{733, 813, 844, 719, 424, 419}"
668,1,410,0,0.3140884,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^(7/2),x]","-\frac{8 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a e^2+4 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{5 e^4 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{32 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{5 e^4 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{4 c \sqrt{a+c x^2} \left(e x \left(3 a e^2+5 c d^2\right)+2 d \left(a e^2+2 c d^2\right)\right)}{5 e^3 (d+e x)^{3/2} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{3/2}}{5 e (d+e x)^{5/2}}","-\frac{8 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a e^2+4 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{5 e^4 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{32 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{5 e^4 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{4 c \sqrt{a+c x^2} \left(e x \left(3 a e^2+5 c d^2\right)+2 d \left(a e^2+2 c d^2\right)\right)}{5 e^3 (d+e x)^{3/2} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{3/2}}{5 e (d+e x)^{5/2}}",1,"(-4*c*(2*d*(2*c*d^2 + a*e^2) + e*(5*c*d^2 + 3*a*e^2)*x)*Sqrt[a + c*x^2])/(5*e^3*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) - (2*(a + c*x^2)^(3/2))/(5*e*(d + e*x)^(5/2)) - (8*Sqrt[-a]*c^(3/2)*(4*c*d^2 + 3*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(5*e^4*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (32*Sqrt[-a]*c^(3/2)*d*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(5*e^4*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{733, 811, 844, 719, 424, 419}"
669,1,491,0,0.4757943,"\int \frac{\left(a+c x^2\right)^{3/2}}{(d+e x)^{9/2}} \, dx","Int[(a + c*x^2)^(3/2)/(d + e*x)^(9/2),x]","\frac{32 c^2 d \sqrt{a+c x^2} \left(2 a e^2+c d^2\right)}{35 e^3 \sqrt{d+e x} \left(a e^2+c d^2\right)^2}-\frac{8 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \left(5 a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 e^4 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{32 \sqrt{-a} c^{5/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(2 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 e^4 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{4 c \sqrt{a+c x^2} \left(e x \left(5 a e^2+7 c d^2\right)+2 d \left(a e^2+2 c d^2\right)\right)}{35 e^3 (d+e x)^{5/2} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{3/2}}{7 e (d+e x)^{7/2}}","\frac{32 c^2 d \sqrt{a+c x^2} \left(2 a e^2+c d^2\right)}{35 e^3 \sqrt{d+e x} \left(a e^2+c d^2\right)^2}-\frac{8 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \left(5 a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 e^4 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{32 \sqrt{-a} c^{5/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(2 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 e^4 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{4 c \sqrt{a+c x^2} \left(e x \left(5 a e^2+7 c d^2\right)+2 d \left(a e^2+2 c d^2\right)\right)}{35 e^3 (d+e x)^{5/2} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{3/2}}{7 e (d+e x)^{7/2}}",1,"(32*c^2*d*(c*d^2 + 2*a*e^2)*Sqrt[a + c*x^2])/(35*e^3*(c*d^2 + a*e^2)^2*Sqrt[d + e*x]) - (4*c*(2*d*(2*c*d^2 + a*e^2) + e*(7*c*d^2 + 5*a*e^2)*x)*Sqrt[a + c*x^2])/(35*e^3*(c*d^2 + a*e^2)*(d + e*x)^(5/2)) - (2*(a + c*x^2)^(3/2))/(7*e*(d + e*x)^(7/2)) + (32*Sqrt[-a]*c^(5/2)*d*(c*d^2 + 2*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(35*e^4*(c*d^2 + a*e^2)^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (8*Sqrt[-a]*c^(3/2)*(4*c*d^2 + 5*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(35*e^4*(c*d^2 + a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,7,21,0.3333,1,"{733, 811, 835, 844, 719, 424, 419}"
670,1,566,0,0.6655355,"\int \sqrt{d+e x} \left(a+c x^2\right)^{5/2} \, dx","Int[Sqrt[d + e*x]*(a + c*x^2)^(5/2),x]","\frac{8 \sqrt{a+c x^2} \sqrt{d+e x} \left(d \left(177 a^2 e^4+113 a c d^2 e^2+32 c^2 d^4\right)-3 e x \left(-77 a^2 e^4+27 a c d^2 e^2+8 c^2 d^4\right)\right)}{9009 e^5}-\frac{16 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(177 a^2 e^4+113 a c d^2 e^2+32 c^2 d^4\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{9009 \sqrt{c} e^6 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{16 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(258 a^2 c d^2 e^4-231 a^3 e^6+137 a c^2 d^4 e^2+32 c^3 d^6\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{9009 \sqrt{c} e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{20 \left(a+c x^2\right)^{3/2} \sqrt{d+e x} \left(4 d \left(5 a e^2+2 c d^2\right)-7 e x \left(c d^2-11 a e^2\right)\right)}{9009 e^3}+\frac{2 \left(a+c x^2\right)^{5/2} (d+e x)^{3/2}}{13 e}-\frac{20 d \left(a+c x^2\right)^{5/2} \sqrt{d+e x}}{143 e}","\frac{8 \sqrt{a+c x^2} \sqrt{d+e x} \left(d \left(177 a^2 e^4+113 a c d^2 e^2+32 c^2 d^4\right)-3 e x \left(-77 a^2 e^4+27 a c d^2 e^2+8 c^2 d^4\right)\right)}{9009 e^5}-\frac{16 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(177 a^2 e^4+113 a c d^2 e^2+32 c^2 d^4\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{9009 \sqrt{c} e^6 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{16 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(258 a^2 c d^2 e^4-231 a^3 e^6+137 a c^2 d^4 e^2+32 c^3 d^6\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{9009 \sqrt{c} e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{20 \left(a+c x^2\right)^{3/2} \sqrt{d+e x} \left(4 d \left(5 a e^2+2 c d^2\right)-7 e x \left(c d^2-11 a e^2\right)\right)}{9009 e^3}+\frac{2 \left(a+c x^2\right)^{5/2} (d+e x)^{3/2}}{13 e}-\frac{20 d \left(a+c x^2\right)^{5/2} \sqrt{d+e x}}{143 e}",1,"(8*Sqrt[d + e*x]*(d*(32*c^2*d^4 + 113*a*c*d^2*e^2 + 177*a^2*e^4) - 3*e*(8*c^2*d^4 + 27*a*c*d^2*e^2 - 77*a^2*e^4)*x)*Sqrt[a + c*x^2])/(9009*e^5) + (20*Sqrt[d + e*x]*(4*d*(2*c*d^2 + 5*a*e^2) - 7*e*(c*d^2 - 11*a*e^2)*x)*(a + c*x^2)^(3/2))/(9009*e^3) - (20*d*Sqrt[d + e*x]*(a + c*x^2)^(5/2))/(143*e) + (2*(d + e*x)^(3/2)*(a + c*x^2)^(5/2))/(13*e) + (16*Sqrt[-a]*(32*c^3*d^6 + 137*a*c^2*d^4*e^2 + 258*a^2*c*d^2*e^4 - 231*a^3*e^6)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(9009*Sqrt[c]*e^6*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (16*Sqrt[-a]*d*(c*d^2 + a*e^2)*(32*c^2*d^4 + 113*a*c*d^2*e^2 + 177*a^2*e^4)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(9009*Sqrt[c]*e^6*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",9,7,21,0.3333,1,"{735, 833, 815, 844, 719, 424, 419}"
671,1,494,0,0.4819061,"\int \frac{\left(a+c x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Int[(a + c*x^2)^(5/2)/Sqrt[d + e*x],x]","\frac{8 \sqrt{a+c x^2} \sqrt{d+e x} \left(45 a^2 e^4-24 c d e x \left(2 a e^2+c d^2\right)+69 a c d^2 e^2+32 c^2 d^4\right)}{693 e^5}-\frac{16 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(45 a^2 e^4+69 a c d^2 e^2+32 c^2 d^4\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{693 \sqrt{c} e^6 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{16 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(93 a^2 e^4+93 a c d^2 e^2+32 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{693 e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{20 \left(a+c x^2\right)^{3/2} \sqrt{d+e x} \left(9 a e^2+8 c d^2-7 c d e x\right)}{693 e^3}+\frac{2 \left(a+c x^2\right)^{5/2} \sqrt{d+e x}}{11 e}","\frac{8 \sqrt{a+c x^2} \sqrt{d+e x} \left(45 a^2 e^4-24 c d e x \left(2 a e^2+c d^2\right)+69 a c d^2 e^2+32 c^2 d^4\right)}{693 e^5}-\frac{16 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(45 a^2 e^4+69 a c d^2 e^2+32 c^2 d^4\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{693 \sqrt{c} e^6 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{16 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(93 a^2 e^4+93 a c d^2 e^2+32 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{693 e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{20 \left(a+c x^2\right)^{3/2} \sqrt{d+e x} \left(9 a e^2+8 c d^2-7 c d e x\right)}{693 e^3}+\frac{2 \left(a+c x^2\right)^{5/2} \sqrt{d+e x}}{11 e}",1,"(8*Sqrt[d + e*x]*(32*c^2*d^4 + 69*a*c*d^2*e^2 + 45*a^2*e^4 - 24*c*d*e*(c*d^2 + 2*a*e^2)*x)*Sqrt[a + c*x^2])/(693*e^5) + (20*Sqrt[d + e*x]*(8*c*d^2 + 9*a*e^2 - 7*c*d*e*x)*(a + c*x^2)^(3/2))/(693*e^3) + (2*Sqrt[d + e*x]*(a + c*x^2)^(5/2))/(11*e) + (16*Sqrt[-a]*Sqrt[c]*d*(32*c^2*d^4 + 93*a*c*d^2*e^2 + 93*a^2*e^4)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(693*e^6*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (16*Sqrt[-a]*(c*d^2 + a*e^2)*(32*c^2*d^4 + 69*a*c*d^2*e^2 + 45*a^2*e^4)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(693*Sqrt[c]*e^6*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{735, 815, 844, 719, 424, 419}"
672,1,457,0,0.4554614,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^{3/2}} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^(3/2),x]","-\frac{16 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(21 a^2 e^4+57 a c d^2 e^2+32 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{63 e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{8 c \sqrt{a+c x^2} \sqrt{d+e x} \left(d \left(33 a e^2+32 c d^2\right)-3 e x \left(7 a e^2+8 c d^2\right)\right)}{63 e^5}+\frac{16 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(33 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{63 e^6 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{20 c \left(a+c x^2\right)^{3/2} (8 d-7 e x) \sqrt{d+e x}}{63 e^3}-\frac{2 \left(a+c x^2\right)^{5/2}}{e \sqrt{d+e x}}","-\frac{16 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(21 a^2 e^4+57 a c d^2 e^2+32 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{63 e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{8 c \sqrt{a+c x^2} \sqrt{d+e x} \left(d \left(33 a e^2+32 c d^2\right)-3 e x \left(7 a e^2+8 c d^2\right)\right)}{63 e^5}+\frac{16 \sqrt{-a} \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(33 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{63 e^6 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{20 c \left(a+c x^2\right)^{3/2} (8 d-7 e x) \sqrt{d+e x}}{63 e^3}-\frac{2 \left(a+c x^2\right)^{5/2}}{e \sqrt{d+e x}}",1,"(-8*c*Sqrt[d + e*x]*(d*(32*c*d^2 + 33*a*e^2) - 3*e*(8*c*d^2 + 7*a*e^2)*x)*Sqrt[a + c*x^2])/(63*e^5) - (20*c*(8*d - 7*e*x)*Sqrt[d + e*x]*(a + c*x^2)^(3/2))/(63*e^3) - (2*(a + c*x^2)^(5/2))/(e*Sqrt[d + e*x]) - (16*Sqrt[-a]*Sqrt[c]*(32*c^2*d^4 + 57*a*c*d^2*e^2 + 21*a^2*e^4)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(63*e^6*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (16*Sqrt[-a]*Sqrt[c]*d*(c*d^2 + a*e^2)*(32*c*d^2 + 33*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(63*e^6*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{733, 815, 844, 719, 424, 419}"
673,1,430,0,0.4379408,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^(5/2),x]","\frac{16 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(29 a e^2+32 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{21 e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{8 c \sqrt{a+c x^2} \sqrt{d+e x} \left(5 a e^2+32 c d^2-24 c d e x\right)}{21 e^5}-\frac{16 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(5 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{21 e^6 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{20 c \left(a+c x^2\right)^{3/2} (8 d+e x)}{21 e^3 \sqrt{d+e x}}-\frac{2 \left(a+c x^2\right)^{5/2}}{3 e (d+e x)^{3/2}}","\frac{16 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(29 a e^2+32 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{21 e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{8 c \sqrt{a+c x^2} \sqrt{d+e x} \left(5 a e^2+32 c d^2-24 c d e x\right)}{21 e^5}-\frac{16 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(5 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{21 e^6 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{20 c \left(a+c x^2\right)^{3/2} (8 d+e x)}{21 e^3 \sqrt{d+e x}}-\frac{2 \left(a+c x^2\right)^{5/2}}{3 e (d+e x)^{3/2}}",1,"(8*c*Sqrt[d + e*x]*(32*c*d^2 + 5*a*e^2 - 24*c*d*e*x)*Sqrt[a + c*x^2])/(21*e^5) + (20*c*(8*d + e*x)*(a + c*x^2)^(3/2))/(21*e^3*Sqrt[d + e*x]) - (2*(a + c*x^2)^(5/2))/(3*e*(d + e*x)^(3/2)) + (16*Sqrt[-a]*c^(3/2)*d*(32*c*d^2 + 29*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(21*e^6*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (16*Sqrt[-a]*Sqrt[c]*(c*d^2 + a*e^2)*(32*c*d^2 + 5*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(21*e^6*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,7,21,0.3333,1,"{733, 813, 815, 844, 719, 424, 419}"
674,1,420,0,0.3624217,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^{7/2}} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^(7/2),x]","\frac{16 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \left(17 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^6 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{16 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(9 a e^2+32 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{8 c \sqrt{a+c x^2} \left(9 a e^2+32 c d^2+8 c d e x\right)}{15 e^5 \sqrt{d+e x}}+\frac{4 c \left(a+c x^2\right)^{3/2} (8 d+3 e x)}{15 e^3 (d+e x)^{3/2}}-\frac{2 \left(a+c x^2\right)^{5/2}}{5 e (d+e x)^{5/2}}","\frac{16 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \left(17 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^6 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{16 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(9 a e^2+32 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^6 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{8 c \sqrt{a+c x^2} \left(9 a e^2+32 c d^2+8 c d e x\right)}{15 e^5 \sqrt{d+e x}}+\frac{4 c \left(a+c x^2\right)^{3/2} (8 d+3 e x)}{15 e^3 (d+e x)^{3/2}}-\frac{2 \left(a+c x^2\right)^{5/2}}{5 e (d+e x)^{5/2}}",1,"(-8*c*(32*c*d^2 + 9*a*e^2 + 8*c*d*e*x)*Sqrt[a + c*x^2])/(15*e^5*Sqrt[d + e*x]) + (4*c*(8*d + 3*e*x)*(a + c*x^2)^(3/2))/(15*e^3*(d + e*x)^(3/2)) - (2*(a + c*x^2)^(5/2))/(5*e*(d + e*x)^(5/2)) - (16*Sqrt[-a]*c^(3/2)*(32*c*d^2 + 9*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*e^6*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (16*Sqrt[-a]*c^(3/2)*d*(32*c*d^2 + 17*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*e^6*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{733, 813, 844, 719, 424, 419}"
675,1,498,0,0.4545969,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^{9/2}} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^(9/2),x]","\frac{8 c^2 \sqrt{a+c x^2} \left(e x \left(5 a e^2+8 c d^2\right)+d \left(29 a e^2+32 c d^2\right)\right)}{21 e^5 \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{16 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \left(5 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{21 e^6 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{16 \sqrt{-a} c^{5/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(29 a e^2+32 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{21 e^6 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{4 c \left(a+c x^2\right)^{3/2} \left(e x \left(5 a e^2+11 c d^2\right)+2 d \left(a e^2+4 c d^2\right)\right)}{21 e^3 (d+e x)^{5/2} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{5/2}}{7 e (d+e x)^{7/2}}","\frac{8 c^2 \sqrt{a+c x^2} \left(e x \left(5 a e^2+8 c d^2\right)+d \left(29 a e^2+32 c d^2\right)\right)}{21 e^5 \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{16 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \left(5 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{21 e^6 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{16 \sqrt{-a} c^{5/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(29 a e^2+32 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{21 e^6 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{4 c \left(a+c x^2\right)^{3/2} \left(e x \left(5 a e^2+11 c d^2\right)+2 d \left(a e^2+4 c d^2\right)\right)}{21 e^3 (d+e x)^{5/2} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{5/2}}{7 e (d+e x)^{7/2}}",1,"(8*c^2*(d*(32*c*d^2 + 29*a*e^2) + e*(8*c*d^2 + 5*a*e^2)*x)*Sqrt[a + c*x^2])/(21*e^5*(c*d^2 + a*e^2)*Sqrt[d + e*x]) - (4*c*(2*d*(4*c*d^2 + a*e^2) + e*(11*c*d^2 + 5*a*e^2)*x)*(a + c*x^2)^(3/2))/(21*e^3*(c*d^2 + a*e^2)*(d + e*x)^(5/2)) - (2*(a + c*x^2)^(5/2))/(7*e*(d + e*x)^(7/2)) + (16*Sqrt[-a]*c^(5/2)*d*(32*c*d^2 + 29*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(21*e^6*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (16*Sqrt[-a]*c^(3/2)*(32*c*d^2 + 5*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(21*e^6*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,7,21,0.3333,1,"{733, 811, 813, 844, 719, 424, 419}"
676,1,553,0,0.4921123,"\int \frac{\left(a+c x^2\right)^{5/2}}{(d+e x)^{11/2}} \, dx","Int[(a + c*x^2)^(5/2)/(d + e*x)^(11/2),x]","-\frac{8 c^2 \sqrt{a+c x^2} \left(e x \left(21 a^2 e^4+69 a c d^2 e^2+40 c^2 d^4\right)+d \left(9 a^2 e^4+49 a c d^2 e^2+32 c^2 d^4\right)\right)}{63 e^5 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}-\frac{16 \sqrt{-a} c^{5/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(21 a^2 e^4+57 a c d^2 e^2+32 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{63 e^6 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{16 \sqrt{-a} c^{5/2} d \sqrt{\frac{c x^2}{a}+1} \left(33 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{63 e^6 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{4 c \left(a+c x^2\right)^{3/2} \left(e x \left(7 a e^2+13 c d^2\right)+2 d \left(a e^2+4 c d^2\right)\right)}{63 e^3 (d+e x)^{7/2} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{5/2}}{9 e (d+e x)^{9/2}}","-\frac{8 c^2 \sqrt{a+c x^2} \left(e x \left(21 a^2 e^4+69 a c d^2 e^2+40 c^2 d^4\right)+d \left(9 a^2 e^4+49 a c d^2 e^2+32 c^2 d^4\right)\right)}{63 e^5 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}-\frac{16 \sqrt{-a} c^{5/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(21 a^2 e^4+57 a c d^2 e^2+32 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{63 e^6 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{16 \sqrt{-a} c^{5/2} d \sqrt{\frac{c x^2}{a}+1} \left(33 a e^2+32 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{63 e^6 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{4 c \left(a+c x^2\right)^{3/2} \left(e x \left(7 a e^2+13 c d^2\right)+2 d \left(a e^2+4 c d^2\right)\right)}{63 e^3 (d+e x)^{7/2} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{5/2}}{9 e (d+e x)^{9/2}}",1,"(-8*c^2*(d*(32*c^2*d^4 + 49*a*c*d^2*e^2 + 9*a^2*e^4) + e*(40*c^2*d^4 + 69*a*c*d^2*e^2 + 21*a^2*e^4)*x)*Sqrt[a + c*x^2])/(63*e^5*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2)) - (4*c*(2*d*(4*c*d^2 + a*e^2) + e*(13*c*d^2 + 7*a*e^2)*x)*(a + c*x^2)^(3/2))/(63*e^3*(c*d^2 + a*e^2)*(d + e*x)^(7/2)) - (2*(a + c*x^2)^(5/2))/(9*e*(d + e*x)^(9/2)) - (16*Sqrt[-a]*c^(5/2)*(32*c^2*d^4 + 57*a*c*d^2*e^2 + 21*a^2*e^4)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(63*e^6*(c*d^2 + a*e^2)^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (16*Sqrt[-a]*c^(5/2)*d*(32*c*d^2 + 33*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(63*e^6*(c*d^2 + a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{733, 811, 844, 719, 424, 419}"
677,1,413,0,0.4347134,"\int \frac{(d+e x)^{7/2}}{\sqrt{a+c x^2}} \, dx","Int[(d + e*x)^(7/2)/Sqrt[a + c*x^2],x]","\frac{2 e \sqrt{a+c x^2} \sqrt{d+e x} \left(71 c d^2-25 a e^2\right)}{105 c^2}+\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(71 c d^2-25 a e^2\right) \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 c^{5/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{32 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(11 c d^2-13 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 e \sqrt{a+c x^2} (d+e x)^{5/2}}{7 c}+\frac{24 d e \sqrt{a+c x^2} (d+e x)^{3/2}}{35 c}","\frac{2 e \sqrt{a+c x^2} \sqrt{d+e x} \left(71 c d^2-25 a e^2\right)}{105 c^2}+\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(71 c d^2-25 a e^2\right) \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 c^{5/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{32 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(11 c d^2-13 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 e \sqrt{a+c x^2} (d+e x)^{5/2}}{7 c}+\frac{24 d e \sqrt{a+c x^2} (d+e x)^{3/2}}{35 c}",1,"(2*e*(71*c*d^2 - 25*a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(105*c^2) + (24*d*e*(d + e*x)^(3/2)*Sqrt[a + c*x^2])/(35*c) + (2*e*(d + e*x)^(5/2)*Sqrt[a + c*x^2])/(7*c) - (32*Sqrt[-a]*d*(11*c*d^2 - 13*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(105*c^(3/2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*(71*c*d^2 - 25*a*e^2)*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(105*c^(5/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{743, 833, 844, 719, 424, 419}"
678,1,359,0,0.3249796,"\int \frac{(d+e x)^{5/2}}{\sqrt{a+c x^2}} \, dx","Int[(d + e*x)^(5/2)/Sqrt[a + c*x^2],x]","\frac{16 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(23 c d^2-9 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 e \sqrt{a+c x^2} (d+e x)^{3/2}}{5 c}+\frac{16 d e \sqrt{a+c x^2} \sqrt{d+e x}}{15 c}","\frac{16 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(23 c d^2-9 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 e \sqrt{a+c x^2} (d+e x)^{3/2}}{5 c}+\frac{16 d e \sqrt{a+c x^2} \sqrt{d+e x}}{15 c}",1,"(16*d*e*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(15*c) + (2*e*(d + e*x)^(3/2)*Sqrt[a + c*x^2])/(5*c) - (2*Sqrt[-a]*(23*c*d^2 - 9*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*c^(3/2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (16*Sqrt[-a]*d*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*c^(3/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{743, 833, 844, 719, 424, 419}"
679,1,317,0,0.212071,"\int \frac{(d+e x)^{3/2}}{\sqrt{a+c x^2}} \, dx","Int[(d + e*x)^(3/2)/Sqrt[a + c*x^2],x]","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 e \sqrt{a+c x^2} \sqrt{d+e x}}{3 c}-\frac{8 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 e \sqrt{a+c x^2} \sqrt{d+e x}}{3 c}-\frac{8 \sqrt{-a} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"(2*e*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(3*c) - (8*Sqrt[-a]*d*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*Sqrt[c]*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*c^(3/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,21,0.2381,1,"{743, 844, 719, 424, 419}"
680,1,136,0,0.0531155,"\int \frac{\sqrt{d+e x}}{\sqrt{a+c x^2}} \, dx","Int[Sqrt[d + e*x]/Sqrt[a + c*x^2],x]","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"(-2*Sqrt[-a]*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[c]*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2])","A",2,2,21,0.09524,1,"{719, 424}"
681,1,136,0,0.0565435,"\int \frac{1}{\sqrt{d+e x} \sqrt{a+c x^2}} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[a + c*x^2]),x]","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}",1,"(-2*Sqrt[-a]*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[c]*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",2,2,21,0.09524,1,"{719, 419}"
682,1,186,0,0.090379,"\int \frac{1}{(d+e x)^{3/2} \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)^(3/2)*Sqrt[a + c*x^2]),x]","-\frac{2 e \sqrt{a+c x^2}}{\sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","-\frac{2 e \sqrt{a+c x^2}}{\sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"(-2*e*Sqrt[a + c*x^2])/((c*d^2 + a*e^2)*Sqrt[d + e*x]) - (2*Sqrt[-a]*Sqrt[c]*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/((c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2])","A",4,4,21,0.1905,1,"{745, 21, 719, 424}"
683,1,382,0,0.2655216,"\int \frac{1}{(d+e x)^{5/2} \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)^(5/2)*Sqrt[a + c*x^2]),x]","-\frac{8 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{8 c d e \sqrt{a+c x^2}}{3 \sqrt{d+e x} \left(a e^2+c d^2\right)^2}-\frac{2 e \sqrt{a+c x^2}}{3 (d+e x)^{3/2} \left(a e^2+c d^2\right)}+\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}","-\frac{8 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{8 c d e \sqrt{a+c x^2}}{3 \sqrt{d+e x} \left(a e^2+c d^2\right)^2}-\frac{2 e \sqrt{a+c x^2}}{3 (d+e x)^{3/2} \left(a e^2+c d^2\right)}+\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}",1,"(-2*e*Sqrt[a + c*x^2])/(3*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) - (8*c*d*e*Sqrt[a + c*x^2])/(3*(c*d^2 + a*e^2)^2*Sqrt[d + e*x]) - (8*Sqrt[-a]*c^(3/2)*d*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*(c*d^2 + a*e^2)^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*Sqrt[c]*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*(c*d^2 + a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{745, 835, 844, 719, 424, 419}"
684,1,447,0,0.4082622,"\int \frac{1}{(d+e x)^{7/2} \sqrt{a+c x^2}} \, dx","Int[1/((d + e*x)^(7/2)*Sqrt[a + c*x^2]),x]","\frac{16 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)^2}-\frac{2 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(23 c d^2-9 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^3 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 c e \sqrt{a+c x^2} \left(23 c d^2-9 a e^2\right)}{15 \sqrt{d+e x} \left(a e^2+c d^2\right)^3}-\frac{16 c d e \sqrt{a+c x^2}}{15 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}-\frac{2 e \sqrt{a+c x^2}}{5 (d+e x)^{5/2} \left(a e^2+c d^2\right)}","\frac{16 \sqrt{-a} c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)^2}-\frac{2 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(23 c d^2-9 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^3 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 c e \sqrt{a+c x^2} \left(23 c d^2-9 a e^2\right)}{15 \sqrt{d+e x} \left(a e^2+c d^2\right)^3}-\frac{16 c d e \sqrt{a+c x^2}}{15 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}-\frac{2 e \sqrt{a+c x^2}}{5 (d+e x)^{5/2} \left(a e^2+c d^2\right)}",1,"(-2*e*Sqrt[a + c*x^2])/(5*(c*d^2 + a*e^2)*(d + e*x)^(5/2)) - (16*c*d*e*Sqrt[a + c*x^2])/(15*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2)) - (2*c*e*(23*c*d^2 - 9*a*e^2)*Sqrt[a + c*x^2])/(15*(c*d^2 + a*e^2)^3*Sqrt[d + e*x]) - (2*Sqrt[-a]*c^(3/2)*(23*c*d^2 - 9*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*(c*d^2 + a*e^2)^3*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (16*Sqrt[-a]*c^(3/2)*d*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*(c*d^2 + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{745, 835, 844, 719, 424, 419}"
685,1,426,0,0.4693314,"\int \frac{(d+e x)^{7/2}}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(7/2)/(a + c*x^2)^(3/2),x]","-\frac{e \sqrt{a+c x^2} \sqrt{d+e x} \left(3 c d^2-5 a e^2\right)}{3 a c^2}+\frac{\sqrt{\frac{c x^2}{a}+1} \left(3 c d^2-5 a e^2\right) \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{-a} c^{5/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 c d^2-29 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{(d+e x)^{5/2} (a e-c d x)}{a c \sqrt{a+c x^2}}-\frac{d e \sqrt{a+c x^2} (d+e x)^{3/2}}{a c}","-\frac{e \sqrt{a+c x^2} \sqrt{d+e x} \left(3 c d^2-5 a e^2\right)}{3 a c^2}+\frac{\sqrt{\frac{c x^2}{a}+1} \left(3 c d^2-5 a e^2\right) \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{-a} c^{5/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 c d^2-29 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{(d+e x)^{5/2} (a e-c d x)}{a c \sqrt{a+c x^2}}-\frac{d e \sqrt{a+c x^2} (d+e x)^{3/2}}{a c}",1,"-(((a*e - c*d*x)*(d + e*x)^(5/2))/(a*c*Sqrt[a + c*x^2])) - (e*(3*c*d^2 - 5*a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(3*a*c^2) - (d*e*(d + e*x)^(3/2)*Sqrt[a + c*x^2])/(a*c) - (d*(3*c*d^2 - 29*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*Sqrt[-a]*c^(3/2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + ((3*c*d^2 - 5*a*e^2)*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*Sqrt[-a]*c^(5/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{739, 833, 844, 719, 424, 419}"
686,1,363,0,0.314003,"\int \frac{(d+e x)^{5/2}}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(5/2)/(a + c*x^2)^(3/2),x]","\frac{d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{(d+e x)^{3/2} (a e-c d x)}{a c \sqrt{a+c x^2}}-\frac{d e \sqrt{a+c x^2} \sqrt{d+e x}}{a c}","\frac{d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{(d+e x)^{3/2} (a e-c d x)}{a c \sqrt{a+c x^2}}-\frac{d e \sqrt{a+c x^2} \sqrt{d+e x}}{a c}",1,"-(((a*e - c*d*x)*(d + e*x)^(3/2))/(a*c*Sqrt[a + c*x^2])) - (d*e*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(a*c) - ((c*d^2 - 3*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*c^(3/2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (d*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*c^(3/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{739, 833, 844, 719, 424, 419}"
687,1,321,0,0.2127912,"\int \frac{(d+e x)^{3/2}}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/(a + c*x^2)^(3/2),x]","\frac{\sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{d+e x} (a e-c d x)}{a c \sqrt{a+c x^2}}-\frac{d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","\frac{\sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{d+e x} (a e-c d x)}{a c \sqrt{a+c x^2}}-\frac{d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"-(((a*e - c*d*x)*Sqrt[d + e*x])/(a*c*Sqrt[a + c*x^2])) - (d*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*Sqrt[c]*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + ((c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*c^(3/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,21,0.2381,1,"{739, 844, 719, 424, 419}"
688,1,298,0,0.2093213,"\int \frac{\sqrt{d+e x}}{\left(a+c x^2\right)^{3/2}} \, dx","Int[Sqrt[d + e*x]/(a + c*x^2)^(3/2),x]","\frac{x \sqrt{d+e x}}{a \sqrt{a+c x^2}}+\frac{d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","\frac{x \sqrt{d+e x}}{a \sqrt{a+c x^2}}+\frac{d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"(x*Sqrt[d + e*x])/(a*Sqrt[a + c*x^2]) - (Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*Sqrt[c]*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (d*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*Sqrt[c]*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{737, 12, 844, 719, 424, 419}"
689,1,331,0,0.2197496,"\int \frac{1}{\sqrt{d+e x} \left(a+c x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[d + e*x]*(a + c*x^2)^(3/2)),x]","\frac{\sqrt{d+e x} (a e+c d x)}{a \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{\sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}","\frac{\sqrt{d+e x} (a e+c d x)}{a \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{\sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}",1,"((a*e + c*d*x)*Sqrt[d + e*x])/(a*(c*d^2 + a*e^2)*Sqrt[a + c*x^2]) - (Sqrt[c]*d*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*Sqrt[c]*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,21,0.2381,1,"{741, 844, 719, 424, 419}"
690,1,406,0,0.3037459,"\int \frac{1}{(d+e x)^{3/2} \left(a+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(3/2)*(a + c*x^2)^(3/2)),x]","\frac{e \sqrt{a+c x^2} \left(c d^2-3 a e^2\right)}{a \sqrt{d+e x} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{\sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{\sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","\frac{e \sqrt{a+c x^2} \left(c d^2-3 a e^2\right)}{a \sqrt{d+e x} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{\sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{\sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(c d^2-3 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"(a*e + c*d*x)/(a*(c*d^2 + a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2]) + (e*(c*d^2 - 3*a*e^2)*Sqrt[a + c*x^2])/(a*(c*d^2 + a*e^2)^2*Sqrt[d + e*x]) - (Sqrt[c]*(c*d^2 - 3*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*(c*d^2 + a*e^2)^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (Sqrt[c]*d*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*(c*d^2 + a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{741, 835, 844, 719, 424, 419}"
691,1,485,0,0.4945631,"\int \frac{1}{(d+e x)^{5/2} \left(a+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(5/2)*(a + c*x^2)^(3/2)),x]","-\frac{c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 c d^2-29 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{-a} \sqrt{a+c x^2} \left(a e^2+c d^2\right)^3 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{c d e \sqrt{a+c x^2} \left(3 c d^2-29 a e^2\right)}{3 a \sqrt{d+e x} \left(a e^2+c d^2\right)^3}+\frac{e \sqrt{a+c x^2} \left(3 c d^2-5 a e^2\right)}{3 a (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} (d+e x)^{3/2} \left(a e^2+c d^2\right)}+\frac{\sqrt{c} \sqrt{\frac{c x^2}{a}+1} \left(3 c d^2-5 a e^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{-a} \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)^2}","-\frac{c^{3/2} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 c d^2-29 a e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{-a} \sqrt{a+c x^2} \left(a e^2+c d^2\right)^3 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{c d e \sqrt{a+c x^2} \left(3 c d^2-29 a e^2\right)}{3 a \sqrt{d+e x} \left(a e^2+c d^2\right)^3}+\frac{e \sqrt{a+c x^2} \left(3 c d^2-5 a e^2\right)}{3 a (d+e x)^{3/2} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{a \sqrt{a+c x^2} (d+e x)^{3/2} \left(a e^2+c d^2\right)}+\frac{\sqrt{c} \sqrt{\frac{c x^2}{a}+1} \left(3 c d^2-5 a e^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{-a} \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)^2}",1,"(a*e + c*d*x)/(a*(c*d^2 + a*e^2)*(d + e*x)^(3/2)*Sqrt[a + c*x^2]) + (e*(3*c*d^2 - 5*a*e^2)*Sqrt[a + c*x^2])/(3*a*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2)) + (c*d*e*(3*c*d^2 - 29*a*e^2)*Sqrt[a + c*x^2])/(3*a*(c*d^2 + a*e^2)^3*Sqrt[d + e*x]) - (c^(3/2)*d*(3*c*d^2 - 29*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*Sqrt[-a]*(c*d^2 + a*e^2)^3*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (Sqrt[c]*(3*c*d^2 - 5*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*Sqrt[-a]*(c*d^2 + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,6,21,0.2857,1,"{741, 835, 844, 719, 424, 419}"
692,1,475,0,0.5049205,"\int \frac{(d+e x)^{9/2}}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(9/2)/(a + c*x^2)^(5/2),x]","-\frac{(d+e x)^{3/2} \left(a e \left(7 a e^2+c d^2\right)-2 c d x \left(5 a e^2+2 c d^2\right)\right)}{6 a^2 c^2 \sqrt{a+c x^2}}-\frac{2 d e \sqrt{a+c x^2} \sqrt{d+e x} \left(3 a e^2+c d^2\right)}{3 a^2 c^2}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-21 a^2 e^4+15 a c d^2 e^2+4 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} c^{5/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(3 a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} c^{5/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{(d+e x)^{7/2} (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}","-\frac{(d+e x)^{3/2} \left(a e \left(7 a e^2+c d^2\right)-2 c d x \left(5 a e^2+2 c d^2\right)\right)}{6 a^2 c^2 \sqrt{a+c x^2}}-\frac{2 d e \sqrt{a+c x^2} \sqrt{d+e x} \left(3 a e^2+c d^2\right)}{3 a^2 c^2}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-21 a^2 e^4+15 a c d^2 e^2+4 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} c^{5/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(3 a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} c^{5/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{(d+e x)^{7/2} (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-((a*e - c*d*x)*(d + e*x)^(7/2))/(3*a*c*(a + c*x^2)^(3/2)) - ((d + e*x)^(3/2)*(a*e*(c*d^2 + 7*a*e^2) - 2*c*d*(2*c*d^2 + 5*a*e^2)*x))/(6*a^2*c^2*Sqrt[a + c*x^2]) - (2*d*e*(c*d^2 + 3*a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(3*a^2*c^2) + ((4*c^2*d^4 + 15*a*c*d^2*e^2 - 21*a^2*e^4)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(6*(-a)^(3/2)*c^(5/2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (2*d*(c*d^2 + a*e^2)*(c*d^2 + 3*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*(-a)^(3/2)*c^(5/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,7,21,0.3333,1,"{739, 819, 833, 844, 719, 424, 419}"
693,1,418,0,0.3798809,"\int \frac{(d+e x)^{7/2}}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(7/2)/(a + c*x^2)^(5/2),x]","-\frac{\sqrt{d+e x} \left(a e \left(5 a e^2+3 c d^2\right)-2 c d x \left(3 a e^2+2 c d^2\right)\right)}{6 a^2 c^2 \sqrt{a+c x^2}}-\frac{\sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(5 a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} c^{5/2} \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(2 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{(d+e x)^{5/2} (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}","-\frac{\sqrt{d+e x} \left(a e \left(5 a e^2+3 c d^2\right)-2 c d x \left(3 a e^2+2 c d^2\right)\right)}{6 a^2 c^2 \sqrt{a+c x^2}}-\frac{\sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \left(5 a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} c^{5/2} \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(2 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{(d+e x)^{5/2} (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-((a*e - c*d*x)*(d + e*x)^(5/2))/(3*a*c*(a + c*x^2)^(3/2)) - (Sqrt[d + e*x]*(a*e*(3*c*d^2 + 5*a*e^2) - 2*c*d*(2*c*d^2 + 3*a*e^2)*x))/(6*a^2*c^2*Sqrt[a + c*x^2]) + (2*d*(c*d^2 + 2*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*(-a)^(3/2)*c^(3/2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - ((c*d^2 + a*e^2)*(4*c*d^2 + 5*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(6*(-a)^(3/2)*c^(5/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{739, 819, 844, 719, 424, 419}"
694,1,392,0,0.32543,"\int \frac{(d+e x)^{5/2}}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/(a + c*x^2)^(5/2),x]","-\frac{\sqrt{d+e x} \left(a d e-x \left(3 a e^2+4 c d^2\right)\right)}{6 a^2 c \sqrt{a+c x^2}}-\frac{2 d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a e^2+4 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{(d+e x)^{3/2} (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}","-\frac{\sqrt{d+e x} \left(a d e-x \left(3 a e^2+4 c d^2\right)\right)}{6 a^2 c \sqrt{a+c x^2}}-\frac{2 d \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a e^2+4 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{(d+e x)^{3/2} (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-((a*e - c*d*x)*(d + e*x)^(3/2))/(3*a*c*(a + c*x^2)^(3/2)) - (Sqrt[d + e*x]*(a*d*e - (4*c*d^2 + 3*a*e^2)*x))/(6*a^2*c*Sqrt[a + c*x^2]) + ((4*c*d^2 + 3*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(6*(-a)^(3/2)*c^(3/2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (2*d*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*(-a)^(3/2)*c^(3/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{739, 821, 844, 719, 424, 419}"
695,1,368,0,0.351321,"\int \frac{(d+e x)^{3/2}}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(3/2)/(a + c*x^2)^(5/2),x]","\frac{\sqrt{d+e x} (a e+4 c d x)}{6 a^2 c \sqrt{a+c x^2}}-\frac{\sqrt{\frac{c x^2}{a}+1} \left(a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{d+e x} (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}+\frac{2 d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","\frac{\sqrt{d+e x} (a e+4 c d x)}{6 a^2 c \sqrt{a+c x^2}}-\frac{\sqrt{\frac{c x^2}{a}+1} \left(a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{d+e x} (a e-c d x)}{3 a c \left(a+c x^2\right)^{3/2}}+\frac{2 d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"-((a*e - c*d*x)*Sqrt[d + e*x])/(3*a*c*(a + c*x^2)^(3/2)) + ((a*e + 4*c*d*x)*Sqrt[d + e*x])/(6*a^2*c*Sqrt[a + c*x^2]) + (2*d*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*(-a)^(3/2)*Sqrt[c]*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - ((4*c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(6*(-a)^(3/2)*c^(3/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{739, 823, 844, 719, 424, 419}"
696,1,392,0,0.3220092,"\int \frac{\sqrt{d+e x}}{\left(a+c x^2\right)^{5/2}} \, dx","Int[Sqrt[d + e*x]/(a + c*x^2)^(5/2),x]","\frac{\sqrt{d+e x} \left(x \left(3 a e^2+4 c d^2\right)+a d e\right)}{6 a^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a e^2+4 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} \sqrt{c} \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{x \sqrt{d+e x}}{3 a \left(a+c x^2\right)^{3/2}}-\frac{2 d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}","\frac{\sqrt{d+e x} \left(x \left(3 a e^2+4 c d^2\right)+a d e\right)}{6 a^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)}+\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a e^2+4 c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} \sqrt{c} \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{x \sqrt{d+e x}}{3 a \left(a+c x^2\right)^{3/2}}-\frac{2 d \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}",1,"(x*Sqrt[d + e*x])/(3*a*(a + c*x^2)^(3/2)) + (Sqrt[d + e*x]*(a*d*e + (4*c*d^2 + 3*a*e^2)*x))/(6*a^2*(c*d^2 + a*e^2)*Sqrt[a + c*x^2]) + ((4*c*d^2 + 3*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(6*(-a)^(3/2)*Sqrt[c]*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (2*d*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*(-a)^(3/2)*Sqrt[c]*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{737, 823, 844, 719, 424, 419}"
697,1,450,0,0.3848169,"\int \frac{1}{\sqrt{d+e x} \left(a+c x^2\right)^{5/2}} \, dx","Int[1/(Sqrt[d + e*x]*(a + c*x^2)^(5/2)),x]","\frac{\sqrt{d+e x} \left(4 c d x \left(2 a e^2+c d^2\right)+a e \left(5 a e^2+c d^2\right)\right)}{6 a^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2}+\frac{\sqrt{d+e x} (a e+c d x)}{3 a \left(a+c x^2\right)^{3/2} \left(a e^2+c d^2\right)}-\frac{\sqrt{\frac{c x^2}{a}+1} \left(5 a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{2 \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(2 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","\frac{\sqrt{d+e x} \left(4 c d x \left(2 a e^2+c d^2\right)+a e \left(5 a e^2+c d^2\right)\right)}{6 a^2 \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2}+\frac{\sqrt{d+e x} (a e+c d x)}{3 a \left(a+c x^2\right)^{3/2} \left(a e^2+c d^2\right)}-\frac{\sqrt{\frac{c x^2}{a}+1} \left(5 a e^2+4 c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{2 \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(2 a e^2+c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} \sqrt{a+c x^2} \left(a e^2+c d^2\right)^2 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"((a*e + c*d*x)*Sqrt[d + e*x])/(3*a*(c*d^2 + a*e^2)*(a + c*x^2)^(3/2)) + (Sqrt[d + e*x]*(a*e*(c*d^2 + 5*a*e^2) + 4*c*d*(c*d^2 + 2*a*e^2)*x))/(6*a^2*(c*d^2 + a*e^2)^2*Sqrt[a + c*x^2]) + (2*Sqrt[c]*d*(c*d^2 + 2*a*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*(-a)^(3/2)*(c*d^2 + a*e^2)^2*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - ((4*c*d^2 + 5*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(6*(-a)^(3/2)*Sqrt[c]*(c*d^2 + a*e^2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,21,0.2857,1,"{741, 823, 844, 719, 424, 419}"
698,1,532,0,0.5309864,"\int \frac{1}{(d+e x)^{3/2} \left(a+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^(3/2)*(a + c*x^2)^(5/2)),x]","\frac{e \sqrt{a+c x^2} \left(-21 a^2 e^4+15 a c d^2 e^2+4 c^2 d^4\right)}{6 a^2 \sqrt{d+e x} \left(a e^2+c d^2\right)^3}+\frac{\sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-21 a^2 e^4+15 a c d^2 e^2+4 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} \sqrt{a+c x^2} \left(a e^2+c d^2\right)^3 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{a e \left(c d^2-7 a e^2\right)-4 c d x \left(3 a e^2+c d^2\right)}{6 a^2 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{3 a \left(a+c x^2\right)^{3/2} \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{2 \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \left(3 a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)^2}","\frac{e \sqrt{a+c x^2} \left(-21 a^2 e^4+15 a c d^2 e^2+4 c^2 d^4\right)}{6 a^2 \sqrt{d+e x} \left(a e^2+c d^2\right)^3}+\frac{\sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-21 a^2 e^4+15 a c d^2 e^2+4 c^2 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{6 (-a)^{3/2} \sqrt{a+c x^2} \left(a e^2+c d^2\right)^3 \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{a e \left(c d^2-7 a e^2\right)-4 c d x \left(3 a e^2+c d^2\right)}{6 a^2 \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x}{3 a \left(a+c x^2\right)^{3/2} \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{2 \sqrt{c} d \sqrt{\frac{c x^2}{a}+1} \left(3 a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 (-a)^{3/2} \sqrt{a+c x^2} \sqrt{d+e x} \left(a e^2+c d^2\right)^2}",1,"(a*e + c*d*x)/(3*a*(c*d^2 + a*e^2)*Sqrt[d + e*x]*(a + c*x^2)^(3/2)) - (a*e*(c*d^2 - 7*a*e^2) - 4*c*d*(c*d^2 + 3*a*e^2)*x)/(6*a^2*(c*d^2 + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + c*x^2]) + (e*(4*c^2*d^4 + 15*a*c*d^2*e^2 - 21*a^2*e^4)*Sqrt[a + c*x^2])/(6*a^2*(c*d^2 + a*e^2)^3*Sqrt[d + e*x]) + (Sqrt[c]*(4*c^2*d^4 + 15*a*c*d^2*e^2 - 21*a^2*e^4)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(6*(-a)^(3/2)*(c*d^2 + a*e^2)^3*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (2*Sqrt[c]*d*(c*d^2 + 3*a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*(-a)^(3/2)*(c*d^2 + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",8,7,21,0.3333,1,"{741, 823, 835, 844, 719, 424, 419}"
699,1,151,0,0.0391441,"\int \frac{1}{(d+e x) \sqrt[3]{d^2+3 e^2 x^2}} \, dx","Int[1/((d + e*x)*(d^2 + 3*e^2*x^2)^(1/3)),x]","\frac{\log \left(-3 \sqrt[3]{2} \sqrt[3]{d} e^2 \sqrt[3]{d^2+3 e^2 x^2}+3 d e^2-3 e^3 x\right)}{2\ 2^{2/3} d^{2/3} e}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (d-e x)}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{d^2+3 e^2 x^2}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} d^{2/3} e}-\frac{\log (d+e x)}{2\ 2^{2/3} d^{2/3} e}","\frac{\log \left(-3 \sqrt[3]{2} \sqrt[3]{d} e^2 \sqrt[3]{d^2+3 e^2 x^2}+3 d e^2-3 e^3 x\right)}{2\ 2^{2/3} d^{2/3} e}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (d-e x)}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{d^2+3 e^2 x^2}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} d^{2/3} e}-\frac{\log (d+e x)}{2\ 2^{2/3} d^{2/3} e}",1,"-(ArcTan[1/Sqrt[3] + (2^(2/3)*(d - e*x))/(Sqrt[3]*d^(1/3)*(d^2 + 3*e^2*x^2)^(1/3))]/(2^(2/3)*Sqrt[3]*d^(2/3)*e)) - Log[d + e*x]/(2*2^(2/3)*d^(2/3)*e) + Log[3*d*e^2 - 3*e^3*x - 3*2^(1/3)*d^(1/3)*e^2*(d^2 + 3*e^2*x^2)^(1/3)]/(2*2^(2/3)*d^(2/3)*e)","A",1,1,24,0.04167,1,"{751}"
700,1,558,0,0.4101497,"\int \frac{(2+3 x)^3}{\sqrt[3]{4+27 x^2}} \, dx","Int[(2 + 3*x)^3/(4 + 27*x^2)^(1/3),x]","\frac{1}{30} \left(27 x^2+4\right)^{2/3} (3 x+2)^2+\frac{4}{35} (4 x+7) \left(27 x^2+4\right)^{2/3}-\frac{96 x}{7 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)}-\frac{32\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{63 \sqrt[4]{3} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}}}+\frac{16 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{21\ 3^{3/4} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}}}","\frac{1}{30} \left(27 x^2+4\right)^{2/3} (3 x+2)^2+\frac{4}{35} (4 x+7) \left(27 x^2+4\right)^{2/3}-\frac{96 x}{7 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)}-\frac{32\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{63 \sqrt[4]{3} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}}}+\frac{16 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{21\ 3^{3/4} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}}}",1,"((2 + 3*x)^2*(4 + 27*x^2)^(2/3))/30 + (4*(7 + 4*x)*(4 + 27*x^2)^(2/3))/35 - (96*x)/(7*(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))) + (16*2^(1/3)*Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(21*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)]) - (32*2^(5/6)*(2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(63*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)])","A",6,6,19,0.3158,1,"{743, 780, 235, 304, 219, 1879}"
701,1,551,0,0.3129082,"\int \frac{(2+3 x)^2}{\sqrt[3]{4+27 x^2}} \, dx","Int[(2 + 3*x)^2/(4 + 27*x^2)^(1/3),x]","-\frac{72 x}{7 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)}+\frac{1}{21} (3 x+2) \left(27 x^2+4\right)^{2/3}+\frac{5}{21} \left(27 x^2+4\right)^{2/3}-\frac{8\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{21 \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}+\frac{4 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{7\ 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}","-\frac{72 x}{7 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)}+\frac{1}{21} (3 x+2) \left(27 x^2+4\right)^{2/3}+\frac{5}{21} \left(27 x^2+4\right)^{2/3}-\frac{8\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{21 \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}+\frac{4 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{7\ 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}",1,"(5*(4 + 27*x^2)^(2/3))/21 + ((2 + 3*x)*(4 + 27*x^2)^(2/3))/21 - (72*x)/(7*(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))) + (4*2^(1/3)*Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(7*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)]) - (8*2^(5/6)*(2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(21*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)])","A",6,6,19,0.3158,1,"{743, 641, 235, 304, 219, 1879}"
702,1,529,0,0.2658394,"\int \frac{2+3 x}{\sqrt[3]{4+27 x^2}} \, dx","Int[(2 + 3*x)/(4 + 27*x^2)^(1/3),x]","-\frac{6 x}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}+\frac{1}{12} \left(27 x^2+4\right)^{2/3}-\frac{2\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}+\frac{\sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}","-\frac{6 x}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}+\frac{1}{12} \left(27 x^2+4\right)^{2/3}-\frac{2\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}+\frac{\sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}",1,"(4 + 27*x^2)^(2/3)/12 - (6*x)/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3)) + (2^(1/3)*Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(3*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)]) - (2*2^(5/6)*(2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)])","A",5,5,17,0.2941,1,"{641, 235, 304, 219, 1879}"
703,1,97,0,0.0143885,"\int \frac{1}{(2+3 x) \sqrt[3]{4+27 x^2}} \, dx","Int[1/((2 + 3*x)*(4 + 27*x^2)^(1/3)),x]","\frac{\log \left(-27\ 2^{2/3} \sqrt[3]{27 x^2+4}-81 x+54\right)}{12 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} (2-3 x)}{\sqrt{3} \sqrt[3]{27 x^2+4}}+\frac{1}{\sqrt{3}}\right)}{6 \sqrt[3]{2} \sqrt{3}}-\frac{\log (3 x+2)}{12 \sqrt[3]{2}}","\frac{\log \left(-27\ 2^{2/3} \sqrt[3]{27 x^2+4}-81 x+54\right)}{12 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} (2-3 x)}{\sqrt{3} \sqrt[3]{27 x^2+4}}+\frac{1}{\sqrt{3}}\right)}{6 \sqrt[3]{2} \sqrt{3}}-\frac{\log (3 x+2)}{12 \sqrt[3]{2}}",1,"-ArcTan[1/Sqrt[3] + (2^(1/3)*(2 - 3*x))/(Sqrt[3]*(4 + 27*x^2)^(1/3))]/(6*2^(1/3)*Sqrt[3]) - Log[2 + 3*x]/(12*2^(1/3)) + Log[54 - 81*x - 27*2^(2/3)*(4 + 27*x^2)^(1/3)]/(12*2^(1/3))","A",1,1,19,0.05263,1,"{751}"
704,1,634,0,0.3643882,"\int \frac{1}{(2+3 x)^2 \sqrt[3]{4+27 x^2}} \, dx","Int[1/((2 + 3*x)^2*(4 + 27*x^2)^(1/3)),x]","-\frac{3 x}{16 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)}-\frac{\left(27 x^2+4\right)^{2/3}}{48 (3 x+2)}+\frac{\log \left(-27\ 2^{2/3} \sqrt[3]{27 x^2+4}-81 x+54\right)}{48 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} (2-3 x)}{\sqrt{3} \sqrt[3]{27 x^2+4}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt[3]{2} \sqrt{3}}-\frac{\left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{72 \sqrt[6]{2} \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}+\frac{\sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{48\ 2^{2/3} 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}-\frac{\log (3 x+2)}{48 \sqrt[3]{2}}","-\frac{3 x}{16 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)}-\frac{\left(27 x^2+4\right)^{2/3}}{48 (3 x+2)}+\frac{\log \left(-27\ 2^{2/3} \sqrt[3]{27 x^2+4}-81 x+54\right)}{48 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} (2-3 x)}{\sqrt{3} \sqrt[3]{27 x^2+4}}+\frac{1}{\sqrt{3}}\right)}{24 \sqrt[3]{2} \sqrt{3}}-\frac{\left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{72 \sqrt[6]{2} \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}+\frac{\sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{48\ 2^{2/3} 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}-\frac{\log (3 x+2)}{48 \sqrt[3]{2}}",1,"-(4 + 27*x^2)^(2/3)/(48*(2 + 3*x)) - (3*x)/(16*(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))) - ArcTan[1/Sqrt[3] + (2^(1/3)*(2 - 3*x))/(Sqrt[3]*(4 + 27*x^2)^(1/3))]/(24*2^(1/3)*Sqrt[3]) + (Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(48*2^(2/3)*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)]) - ((2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(72*2^(1/6)*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)]) - Log[2 + 3*x]/(48*2^(1/3)) + Log[54 - 81*x - 27*2^(2/3)*(4 + 27*x^2)^(1/3)]/(48*2^(1/3))","A",7,7,19,0.3684,1,"{745, 844, 235, 304, 219, 1879, 751}"
705,1,656,0,0.4119073,"\int \frac{1}{(2+3 x)^3 \sqrt[3]{4+27 x^2}} \, dx","Int[1/((2 + 3*x)^3*(4 + 27*x^2)^(1/3)),x]","-\frac{3 x}{32 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)}-\frac{\left(27 x^2+4\right)^{2/3}}{96 (3 x+2)}-\frac{\left(27 x^2+4\right)^{2/3}}{96 (3 x+2)^2}+\frac{\log \left(-27\ 2^{2/3} \sqrt[3]{27 x^2+4}-81 x+54\right)}{192 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} (2-3 x)}{\sqrt{3} \sqrt[3]{27 x^2+4}}+\frac{1}{\sqrt{3}}\right)}{96 \sqrt[3]{2} \sqrt{3}}-\frac{\left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{144 \sqrt[6]{2} \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}+\frac{\sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{96\ 2^{2/3} 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}-\frac{\log (3 x+2)}{192 \sqrt[3]{2}}","-\frac{3 x}{32 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)}-\frac{\left(27 x^2+4\right)^{2/3}}{96 (3 x+2)}-\frac{\left(27 x^2+4\right)^{2/3}}{96 (3 x+2)^2}+\frac{\log \left(-27\ 2^{2/3} \sqrt[3]{27 x^2+4}-81 x+54\right)}{192 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2} (2-3 x)}{\sqrt{3} \sqrt[3]{27 x^2+4}}+\frac{1}{\sqrt{3}}\right)}{96 \sqrt[3]{2} \sqrt{3}}-\frac{\left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{144 \sqrt[6]{2} \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}+\frac{\sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{27 x^2+4}\right) \sqrt{\frac{\left(27 x^2+4\right)^{2/3}+2^{2/3} \sqrt[3]{27 x^2+4}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}}\right)|-7+4 \sqrt{3}\right)}{96\ 2^{2/3} 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{27 x^2+4}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{27 x^2+4}\right)^2}} x}-\frac{\log (3 x+2)}{192 \sqrt[3]{2}}",1,"-(4 + 27*x^2)^(2/3)/(96*(2 + 3*x)^2) - (4 + 27*x^2)^(2/3)/(96*(2 + 3*x)) - (3*x)/(32*(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))) - ArcTan[1/Sqrt[3] + (2^(1/3)*(2 - 3*x))/(Sqrt[3]*(4 + 27*x^2)^(1/3))]/(96*2^(1/3)*Sqrt[3]) + (Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(96*2^(2/3)*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)]) - ((2^(2/3) - (4 + 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(144*2^(1/6)*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 + 27*x^2)^(1/3))^2)]) - Log[2 + 3*x]/(192*2^(1/3)) + Log[54 - 81*x - 27*2^(2/3)*(4 + 27*x^2)^(1/3)]/(192*2^(1/3))","A",8,8,19,0.4211,1,"{745, 835, 844, 235, 304, 219, 1879, 751}"
706,1,564,0,0.3628085,"\int \frac{(2+3 i x)^3}{\sqrt[3]{4-27 x^2}} \, dx","Int[(2 + (3*I)*x)^3/(4 - 27*x^2)^(1/3),x]","-\frac{1}{30} i \left(4-27 x^2\right)^{2/3} (2+3 i x)^2-\frac{4}{35} (-4 x+7 i) \left(4-27 x^2\right)^{2/3}-\frac{96 x}{7 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)}+\frac{32\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{63 \sqrt[4]{3} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}}}-\frac{16 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{21\ 3^{3/4} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}}}","-\frac{1}{30} i \left(4-27 x^2\right)^{2/3} (2+3 i x)^2-\frac{4}{35} (-4 x+7 i) \left(4-27 x^2\right)^{2/3}-\frac{96 x}{7 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)}+\frac{32\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{63 \sqrt[4]{3} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}}}-\frac{16 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{21\ 3^{3/4} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}}}",1,"(-4*(7*I - 4*x)*(4 - 27*x^2)^(2/3))/35 - (I/30)*(2 + (3*I)*x)^2*(4 - 27*x^2)^(2/3) - (96*x)/(7*(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))) - (16*2^(1/3)*Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(21*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)]) + (32*2^(5/6)*(2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(63*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)])","A",6,6,21,0.2857,1,"{743, 780, 235, 304, 219, 1879}"
707,1,557,0,0.3152232,"\int \frac{(2+3 i x)^2}{\sqrt[3]{4-27 x^2}} \, dx","Int[(2 + (3*I)*x)^2/(4 - 27*x^2)^(1/3),x]","-\frac{1}{21} i \left(4-27 x^2\right)^{2/3} (2+3 i x)-\frac{5}{21} i \left(4-27 x^2\right)^{2/3}-\frac{72 x}{7 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)}+\frac{8\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{21 \sqrt[4]{3} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}}}-\frac{4 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{7\ 3^{3/4} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}}}","-\frac{1}{21} i \left(4-27 x^2\right)^{2/3} (2+3 i x)-\frac{5}{21} i \left(4-27 x^2\right)^{2/3}-\frac{72 x}{7 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)}+\frac{8\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{21 \sqrt[4]{3} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}}}-\frac{4 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{7\ 3^{3/4} x \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}}}",1,"((-5*I)/21)*(4 - 27*x^2)^(2/3) - (I/21)*(2 + (3*I)*x)*(4 - 27*x^2)^(2/3) - (72*x)/(7*(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))) - (4*2^(1/3)*Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(7*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)]) + (8*2^(5/6)*(2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(21*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)])","A",6,6,21,0.2857,1,"{743, 641, 235, 304, 219, 1879}"
708,1,531,0,0.2614193,"\int \frac{2+3 i x}{\sqrt[3]{4-27 x^2}} \, dx","Int[(2 + (3*I)*x)/(4 - 27*x^2)^(1/3),x]","-\frac{6 x}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}-\frac{1}{12} i \left(4-27 x^2\right)^{2/3}+\frac{2\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}-\frac{\sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}","-\frac{6 x}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}-\frac{1}{12} i \left(4-27 x^2\right)^{2/3}+\frac{2\ 2^{5/6} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}-\frac{\sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}",1,"(-I/12)*(4 - 27*x^2)^(2/3) - (6*x)/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3)) - (2^(1/3)*Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(3*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)]) + (2*2^(5/6)*(2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)])","A",5,5,19,0.2632,1,"{641, 235, 304, 219, 1879}"
709,1,109,0,0.0162252,"\int \frac{1}{(2+3 i x) \sqrt[3]{4-27 x^2}} \, dx","Int[1/((2 + (3*I)*x)*(4 - 27*x^2)^(1/3)),x]","-\frac{i \log \left(27\ 2^{2/3} \sqrt[3]{4-27 x^2}+81 i x-54\right)}{12 \sqrt[3]{2}}+\frac{i \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{\sqrt[3]{2} (2-3 i x)}{\sqrt{3} \sqrt[3]{4-27 x^2}}\right)}{6 \sqrt[3]{2} \sqrt{3}}+\frac{i \log (2+3 i x)}{12 \sqrt[3]{2}}","-\frac{i \log \left(27\ 2^{2/3} \sqrt[3]{4-27 x^2}+81 i x-54\right)}{12 \sqrt[3]{2}}+\frac{i \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{\sqrt[3]{2} (2-3 i x)}{\sqrt{3} \sqrt[3]{4-27 x^2}}\right)}{6 \sqrt[3]{2} \sqrt{3}}+\frac{i \log (2+3 i x)}{12 \sqrt[3]{2}}",1,"((I/6)*ArcTan[1/Sqrt[3] + (2^(1/3)*(2 - (3*I)*x))/(Sqrt[3]*(4 - 27*x^2)^(1/3))])/(2^(1/3)*Sqrt[3]) + ((I/12)*Log[2 + (3*I)*x])/2^(1/3) - ((I/12)*Log[-54 + (81*I)*x + 27*2^(2/3)*(4 - 27*x^2)^(1/3)])/2^(1/3)","A",1,1,21,0.04762,1,"{751}"
710,1,650,0,0.3500235,"\int \frac{1}{(2+3 i x)^2 \sqrt[3]{4-27 x^2}} \, dx","Int[1/((2 + (3*I)*x)^2*(4 - 27*x^2)^(1/3)),x]","-\frac{3 x}{16 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)}+\frac{i \left(4-27 x^2\right)^{2/3}}{48 (2+3 i x)}-\frac{i \log \left(27\ 2^{2/3} \sqrt[3]{4-27 x^2}+81 i x-54\right)}{48 \sqrt[3]{2}}+\frac{i \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{\sqrt[3]{2} (2-3 i x)}{\sqrt{3} \sqrt[3]{4-27 x^2}}\right)}{24 \sqrt[3]{2} \sqrt{3}}+\frac{\left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{72 \sqrt[6]{2} \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}-\frac{\sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{48\ 2^{2/3} 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}+\frac{i \log (2+3 i x)}{48 \sqrt[3]{2}}","-\frac{3 x}{16 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)}+\frac{i \left(4-27 x^2\right)^{2/3}}{48 (2+3 i x)}-\frac{i \log \left(27\ 2^{2/3} \sqrt[3]{4-27 x^2}+81 i x-54\right)}{48 \sqrt[3]{2}}+\frac{i \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{\sqrt[3]{2} (2-3 i x)}{\sqrt{3} \sqrt[3]{4-27 x^2}}\right)}{24 \sqrt[3]{2} \sqrt{3}}+\frac{\left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{72 \sqrt[6]{2} \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}-\frac{\sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{48\ 2^{2/3} 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}+\frac{i \log (2+3 i x)}{48 \sqrt[3]{2}}",1,"((I/48)*(4 - 27*x^2)^(2/3))/(2 + (3*I)*x) - (3*x)/(16*(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))) + ((I/24)*ArcTan[1/Sqrt[3] + (2^(1/3)*(2 - (3*I)*x))/(Sqrt[3]*(4 - 27*x^2)^(1/3))])/(2^(1/3)*Sqrt[3]) - (Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(48*2^(2/3)*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)]) + ((2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(72*2^(1/6)*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)]) + ((I/48)*Log[2 + (3*I)*x])/2^(1/3) - ((I/48)*Log[-54 + (81*I)*x + 27*2^(2/3)*(4 - 27*x^2)^(1/3)])/2^(1/3)","A",7,7,21,0.3333,1,"{745, 844, 235, 304, 219, 1879, 751}"
711,1,676,0,0.4125137,"\int \frac{1}{(2+3 i x)^3 \sqrt[3]{4-27 x^2}} \, dx","Int[1/((2 + (3*I)*x)^3*(4 - 27*x^2)^(1/3)),x]","-\frac{3 x}{32 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)}+\frac{i \left(4-27 x^2\right)^{2/3}}{96 (2+3 i x)}+\frac{i \left(4-27 x^2\right)^{2/3}}{96 (2+3 i x)^2}-\frac{i \log \left(27\ 2^{2/3} \sqrt[3]{4-27 x^2}+81 i x-54\right)}{192 \sqrt[3]{2}}+\frac{i \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{\sqrt[3]{2} (2-3 i x)}{\sqrt{3} \sqrt[3]{4-27 x^2}}\right)}{96 \sqrt[3]{2} \sqrt{3}}+\frac{\left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{144 \sqrt[6]{2} \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}-\frac{\sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{96\ 2^{2/3} 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}+\frac{i \log (2+3 i x)}{192 \sqrt[3]{2}}","-\frac{3 x}{32 \left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)}+\frac{i \left(4-27 x^2\right)^{2/3}}{96 (2+3 i x)}+\frac{i \left(4-27 x^2\right)^{2/3}}{96 (2+3 i x)^2}-\frac{i \log \left(27\ 2^{2/3} \sqrt[3]{4-27 x^2}+81 i x-54\right)}{192 \sqrt[3]{2}}+\frac{i \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{\sqrt[3]{2} (2-3 i x)}{\sqrt{3} \sqrt[3]{4-27 x^2}}\right)}{96 \sqrt[3]{2} \sqrt{3}}+\frac{\left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{144 \sqrt[6]{2} \sqrt[4]{3} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}-\frac{\sqrt{2+\sqrt{3}} \left(2^{2/3}-\sqrt[3]{4-27 x^2}\right) \sqrt{\frac{\left(4-27 x^2\right)^{2/3}+2^{2/3} \sqrt[3]{4-27 x^2}+2 \sqrt[3]{2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{2^{2/3} \left(1+\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}{2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}}\right)|-7+4 \sqrt{3}\right)}{96\ 2^{2/3} 3^{3/4} \sqrt{-\frac{2^{2/3}-\sqrt[3]{4-27 x^2}}{\left(2^{2/3} \left(1-\sqrt{3}\right)-\sqrt[3]{4-27 x^2}\right)^2}} x}+\frac{i \log (2+3 i x)}{192 \sqrt[3]{2}}",1,"((I/96)*(4 - 27*x^2)^(2/3))/(2 + (3*I)*x)^2 + ((I/96)*(4 - 27*x^2)^(2/3))/(2 + (3*I)*x) - (3*x)/(32*(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))) + ((I/96)*ArcTan[1/Sqrt[3] + (2^(1/3)*(2 - (3*I)*x))/(Sqrt[3]*(4 - 27*x^2)^(1/3))])/(2^(1/3)*Sqrt[3]) - (Sqrt[2 + Sqrt[3]]*(2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticE[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(96*2^(2/3)*3^(3/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)]) + ((2^(2/3) - (4 - 27*x^2)^(1/3))*Sqrt[(2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2]*EllipticF[ArcSin[(2^(2/3)*(1 + Sqrt[3]) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(144*2^(1/6)*3^(1/4)*x*Sqrt[-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - Sqrt[3]) - (4 - 27*x^2)^(1/3))^2)]) + ((I/192)*Log[2 + (3*I)*x])/2^(1/3) - ((I/192)*Log[-54 + (81*I)*x + 27*2^(2/3)*(4 - 27*x^2)^(1/3)])/2^(1/3)","A",8,8,21,0.3810,1,"{745, 835, 844, 235, 304, 219, 1879, 751}"
712,1,104,0,0.0129699,"\int \frac{1}{\left(\sqrt{3}+x\right) \sqrt[3]{1+x^2}} \, dx","Int[1/((Sqrt[3] + x)*(1 + x^2)^(1/3)),x]","\frac{\log \left(-\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^2+1}-x+\sqrt{3}\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \left(\sqrt{3}-x\right)}{3 \sqrt[3]{x^2+1}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log \left(x+\sqrt{3}\right)}{2\ 2^{2/3}}","\frac{\log \left(-\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^2+1}-x+\sqrt{3}\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \left(\sqrt{3}-x\right)}{3 \sqrt[3]{x^2+1}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log \left(x+\sqrt{3}\right)}{2\ 2^{2/3}}",1,"-(ArcTan[1/Sqrt[3] + (2^(2/3)*(Sqrt[3] - x))/(3*(1 + x^2)^(1/3))]/(2^(2/3)*Sqrt[3])) - Log[Sqrt[3] + x]/(2*2^(2/3)) + Log[Sqrt[3] - x - 2^(1/3)*Sqrt[3]*(1 + x^2)^(1/3)]/(2*2^(2/3))","A",1,1,19,0.05263,1,"{751}"
713,1,101,0,0.0144118,"\int \frac{1}{\left(\sqrt{3}-x\right) \sqrt[3]{1+x^2}} \, dx","Int[1/((Sqrt[3] - x)*(1 + x^2)^(1/3)),x]","-\frac{\log \left(-\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^2+1}+x+\sqrt{3}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \left(x+\sqrt{3}\right)}{3 \sqrt[3]{x^2+1}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\log \left(\sqrt{3}-x\right)}{2\ 2^{2/3}}","-\frac{\log \left(-\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^2+1}+x+\sqrt{3}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \left(x+\sqrt{3}\right)}{3 \sqrt[3]{x^2+1}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\log \left(\sqrt{3}-x\right)}{2\ 2^{2/3}}",1,"ArcTan[1/Sqrt[3] + (2^(2/3)*(Sqrt[3] + x))/(3*(1 + x^2)^(1/3))]/(2^(2/3)*Sqrt[3]) + Log[Sqrt[3] - x]/(2*2^(2/3)) - Log[Sqrt[3] + x - 2^(1/3)*Sqrt[3]*(1 + x^2)^(1/3)]/(2*2^(2/3))","A",1,1,21,0.04762,1,"{751}"
714,1,78,0,0.0155426,"\int \frac{1}{(3-x) \sqrt[3]{1-x^2}} \, dx","Int[1/((3 - x)*(1 - x^2)^(1/3)),x]","-\frac{1}{4} \log (3-x)+\frac{3}{8} \log \left(-\frac{1}{2} (x+1)^{2/3}-\sqrt[3]{1-x}\right)-\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{(x+1)^{2/3}}{\sqrt{3} \sqrt[3]{1-x}}\right)","-\frac{1}{4} \log (3-x)+\frac{3}{8} \log \left(-\frac{1}{2} (x+1)^{2/3}-\sqrt[3]{1-x}\right)-\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{(x+1)^{2/3}}{\sqrt{3} \sqrt[3]{1-x}}\right)",1,"-(Sqrt[3]*ArcTan[1/Sqrt[3] - (1 + x)^(2/3)/(Sqrt[3]*(1 - x)^(1/3))])/4 - Log[3 - x]/4 + (3*Log[-(1 - x)^(1/3) - (1 + x)^(2/3)/2])/8","A",2,2,19,0.1053,1,"{753, 123}"
715,1,76,0,0.0144284,"\int \frac{1}{(3+x) \sqrt[3]{1-x^2}} \, dx","Int[1/((3 + x)*(1 - x^2)^(1/3)),x]","\frac{1}{4} \log (x+3)-\frac{3}{8} \log \left(-\frac{1}{2} (1-x)^{2/3}-\sqrt[3]{x+1}\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{(1-x)^{2/3}}{\sqrt{3} \sqrt[3]{x+1}}\right)","\frac{1}{4} \log (x+3)-\frac{3}{8} \log \left(-\frac{1}{2} (1-x)^{2/3}-\sqrt[3]{x+1}\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{(1-x)^{2/3}}{\sqrt{3} \sqrt[3]{x+1}}\right)",1,"(Sqrt[3]*ArcTan[1/Sqrt[3] - (1 - x)^(2/3)/(Sqrt[3]*(1 + x)^(1/3))])/4 + Log[3 + x]/4 - (3*Log[-(1 - x)^(2/3)/2 - (1 + x)^(1/3)])/8","A",2,2,17,0.1176,1,"{753, 123}"
716,1,206,0,0.0651082,"\int \frac{1}{(d+e x) \sqrt[3]{d^2-9 e^2 x^2}} \, dx","Int[1/((d + e*x)*(d^2 - 9*e^2*x^2)^(1/3)),x]","\frac{\sqrt[3]{1-\frac{9 e^2 x^2}{d^2}} \log (d+e x)}{4 e \sqrt[3]{d^2-9 e^2 x^2}}-\frac{3 \sqrt[3]{1-\frac{9 e^2 x^2}{d^2}} \log \left(-\frac{1}{2} \left(1-\frac{3 e x}{d}\right)^{2/3}-\sqrt[3]{\frac{3 e x}{d}+1}\right)}{8 e \sqrt[3]{d^2-9 e^2 x^2}}+\frac{\sqrt{3} \sqrt[3]{1-\frac{9 e^2 x^2}{d^2}} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\left(1-\frac{3 e x}{d}\right)^{2/3}}{\sqrt{3} \sqrt[3]{\frac{3 e x}{d}+1}}\right)}{4 e \sqrt[3]{d^2-9 e^2 x^2}}","\frac{\sqrt[3]{1-\frac{9 e^2 x^2}{d^2}} \log (d+e x)}{4 e \sqrt[3]{d^2-9 e^2 x^2}}-\frac{3 \sqrt[3]{1-\frac{9 e^2 x^2}{d^2}} \log \left(-\frac{1}{2} \left(1-\frac{3 e x}{d}\right)^{2/3}-\sqrt[3]{\frac{3 e x}{d}+1}\right)}{8 e \sqrt[3]{d^2-9 e^2 x^2}}+\frac{\sqrt{3} \sqrt[3]{1-\frac{9 e^2 x^2}{d^2}} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\left(1-\frac{3 e x}{d}\right)^{2/3}}{\sqrt{3} \sqrt[3]{\frac{3 e x}{d}+1}}\right)}{4 e \sqrt[3]{d^2-9 e^2 x^2}}",1,"(Sqrt[3]*(1 - (9*e^2*x^2)/d^2)^(1/3)*ArcTan[1/Sqrt[3] - (1 - (3*e*x)/d)^(2/3)/(Sqrt[3]*(1 + (3*e*x)/d)^(1/3))])/(4*e*(d^2 - 9*e^2*x^2)^(1/3)) + ((1 - (9*e^2*x^2)/d^2)^(1/3)*Log[d + e*x])/(4*e*(d^2 - 9*e^2*x^2)^(1/3)) - (3*(1 - (9*e^2*x^2)/d^2)^(1/3)*Log[-(1 - (3*e*x)/d)^(2/3)/2 - (1 + (3*e*x)/d)^(1/3)])/(8*e*(d^2 - 9*e^2*x^2)^(1/3))","A",3,3,24,0.1250,1,"{754, 753, 123}"
717,1,278,0,0.2826892,"\int \frac{1}{(a+b x) \sqrt[4]{c+d x^2}} \, dx","Int[1/((a + b*x)*(c + d*x^2)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{c+d x^2}}{\sqrt[4]{a^2 d+b^2 c}}\right)}{\sqrt{b} \sqrt[4]{a^2 d+b^2 c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{c+d x^2}}{\sqrt[4]{a^2 d+b^2 c}}\right)}{\sqrt{b} \sqrt[4]{a^2 d+b^2 c}}-\frac{a \sqrt[4]{c} \sqrt{-\frac{d x^2}{c}} \Pi \left(-\frac{b \sqrt{c}}{\sqrt{d a^2+b^2 c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d x^2+c}}{\sqrt[4]{c}}\right)\right|-1\right)}{b x \sqrt{a^2 d+b^2 c}}+\frac{a \sqrt[4]{c} \sqrt{-\frac{d x^2}{c}} \Pi \left(\frac{b \sqrt{c}}{\sqrt{d a^2+b^2 c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d x^2+c}}{\sqrt[4]{c}}\right)\right|-1\right)}{b x \sqrt{a^2 d+b^2 c}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{c+d x^2}}{\sqrt[4]{a^2 d+b^2 c}}\right)}{\sqrt{b} \sqrt[4]{a^2 d+b^2 c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{c+d x^2}}{\sqrt[4]{a^2 d+b^2 c}}\right)}{\sqrt{b} \sqrt[4]{a^2 d+b^2 c}}-\frac{a \sqrt[4]{c} \sqrt{-\frac{d x^2}{c}} \Pi \left(-\frac{b \sqrt{c}}{\sqrt{d a^2+b^2 c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d x^2+c}}{\sqrt[4]{c}}\right)\right|-1\right)}{b x \sqrt{a^2 d+b^2 c}}+\frac{a \sqrt[4]{c} \sqrt{-\frac{d x^2}{c}} \Pi \left(\frac{b \sqrt{c}}{\sqrt{d a^2+b^2 c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d x^2+c}}{\sqrt[4]{c}}\right)\right|-1\right)}{b x \sqrt{a^2 d+b^2 c}}",1,"ArcTan[(Sqrt[b]*(c + d*x^2)^(1/4))/(b^2*c + a^2*d)^(1/4)]/(Sqrt[b]*(b^2*c + a^2*d)^(1/4)) - ArcTanh[(Sqrt[b]*(c + d*x^2)^(1/4))/(b^2*c + a^2*d)^(1/4)]/(Sqrt[b]*(b^2*c + a^2*d)^(1/4)) - (a*c^(1/4)*Sqrt[-((d*x^2)/c)]*EllipticPi[-((b*Sqrt[c])/Sqrt[b^2*c + a^2*d]), ArcSin[(c + d*x^2)^(1/4)/c^(1/4)], -1])/(b*Sqrt[b^2*c + a^2*d]*x) + (a*c^(1/4)*Sqrt[-((d*x^2)/c)]*EllipticPi[(b*Sqrt[c])/Sqrt[b^2*c + a^2*d], ArcSin[(c + d*x^2)^(1/4)/c^(1/4)], -1])/(b*Sqrt[b^2*c + a^2*d]*x)","A",10,9,19,0.4737,1,"{746, 399, 490, 1218, 444, 63, 298, 205, 208}"
718,1,268,0,0.2695147,"\int \frac{1}{(a+b x) \left(c+d x^2\right)^{3/4}} \, dx","Int[1/((a + b*x)*(c + d*x^2)^(3/4)),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{c+d x^2}}{\sqrt[4]{a^2 d+b^2 c}}\right)}{\left(a^2 d+b^2 c\right)^{3/4}}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{c+d x^2}}{\sqrt[4]{a^2 d+b^2 c}}\right)}{\left(a^2 d+b^2 c\right)^{3/4}}+\frac{a \sqrt[4]{c} \sqrt{-\frac{d x^2}{c}} \Pi \left(-\frac{b \sqrt{c}}{\sqrt{d a^2+b^2 c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d x^2+c}}{\sqrt[4]{c}}\right)\right|-1\right)}{x \left(a^2 d+b^2 c\right)}+\frac{a \sqrt[4]{c} \sqrt{-\frac{d x^2}{c}} \Pi \left(\frac{b \sqrt{c}}{\sqrt{d a^2+b^2 c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d x^2+c}}{\sqrt[4]{c}}\right)\right|-1\right)}{x \left(a^2 d+b^2 c\right)}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{c+d x^2}}{\sqrt[4]{a^2 d+b^2 c}}\right)}{\left(a^2 d+b^2 c\right)^{3/4}}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{c+d x^2}}{\sqrt[4]{a^2 d+b^2 c}}\right)}{\left(a^2 d+b^2 c\right)^{3/4}}+\frac{a \sqrt[4]{c} \sqrt{-\frac{d x^2}{c}} \Pi \left(-\frac{b \sqrt{c}}{\sqrt{d a^2+b^2 c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d x^2+c}}{\sqrt[4]{c}}\right)\right|-1\right)}{x \left(a^2 d+b^2 c\right)}+\frac{a \sqrt[4]{c} \sqrt{-\frac{d x^2}{c}} \Pi \left(\frac{b \sqrt{c}}{\sqrt{d a^2+b^2 c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d x^2+c}}{\sqrt[4]{c}}\right)\right|-1\right)}{x \left(a^2 d+b^2 c\right)}",1,"-((Sqrt[b]*ArcTan[(Sqrt[b]*(c + d*x^2)^(1/4))/(b^2*c + a^2*d)^(1/4)])/(b^2*c + a^2*d)^(3/4)) - (Sqrt[b]*ArcTanh[(Sqrt[b]*(c + d*x^2)^(1/4))/(b^2*c + a^2*d)^(1/4)])/(b^2*c + a^2*d)^(3/4) + (a*c^(1/4)*Sqrt[-((d*x^2)/c)]*EllipticPi[-((b*Sqrt[c])/Sqrt[b^2*c + a^2*d]), ArcSin[(c + d*x^2)^(1/4)/c^(1/4)], -1])/((b^2*c + a^2*d)*x) + (a*c^(1/4)*Sqrt[-((d*x^2)/c)]*EllipticPi[(b*Sqrt[c])/Sqrt[b^2*c + a^2*d], ArcSin[(c + d*x^2)^(1/4)/c^(1/4)], -1])/((b^2*c + a^2*d)*x)","A",11,10,19,0.5263,1,"{747, 401, 108, 409, 1218, 444, 63, 212, 208, 205}"
719,1,200,0,0.0944947,"\int \frac{1}{(d+e x)^{3/2} \sqrt[4]{a+c x^2}} \, dx","Int[1/((d + e*x)^(3/2)*(a + c*x^2)^(1/4)),x]","-\frac{2 \left(\sqrt{-a}-\sqrt{c} x\right) \sqrt[4]{-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{\sqrt[4]{a+c x^2} \sqrt{d+e x} \left(\sqrt{-a} e+\sqrt{c} d\right)}","-\frac{2 \left(\sqrt{-a}-\sqrt{c} x\right) \sqrt[4]{-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{\sqrt[4]{a+c x^2} \sqrt{d+e x} \left(\sqrt{-a} e+\sqrt{c} d\right)}",1,"(-2*(Sqrt[-a] - Sqrt[c]*x)*(-(((Sqrt[c]*d + Sqrt[-a]*e)*(Sqrt[-a] + Sqrt[c]*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))))^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, (2*Sqrt[-a]*Sqrt[c]*(d + e*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))])/((Sqrt[c]*d + Sqrt[-a]*e)*Sqrt[d + e*x]*(a + c*x^2)^(1/4))","A",1,1,21,0.04762,1,"{727}"
720,1,203,0,0.3676754,"\int \frac{1}{(1+x) \sqrt[6]{1+x^2}} \, dx","Int[1/((1 + x)*(1 + x^2)^(1/6)),x]","x F_1\left(\frac{1}{2};1,\frac{1}{6};\frac{3}{2};x^2,-x^2\right)+\frac{\log \left(\sqrt[3]{x^2+1}-\sqrt[6]{2} \sqrt[6]{x^2+1}+\sqrt[3]{2}\right)}{4 \sqrt[6]{2}}-\frac{\log \left(\sqrt[3]{x^2+1}+\sqrt[6]{2} \sqrt[6]{x^2+1}+\sqrt[3]{2}\right)}{4 \sqrt[6]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-2^{5/6} \sqrt[6]{x^2+1}}{\sqrt{3}}\right)}{2 \sqrt[6]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{5/6} \sqrt[6]{x^2+1}+1}{\sqrt{3}}\right)}{2 \sqrt[6]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{x^2+1}}{\sqrt[6]{2}}\right)}{\sqrt[6]{2}}","x F_1\left(\frac{1}{2};1,\frac{1}{6};\frac{3}{2};x^2,-x^2\right)+\frac{\log \left(\sqrt[3]{x^2+1}-\sqrt[6]{2} \sqrt[6]{x^2+1}+\sqrt[3]{2}\right)}{4 \sqrt[6]{2}}-\frac{\log \left(\sqrt[3]{x^2+1}+\sqrt[6]{2} \sqrt[6]{x^2+1}+\sqrt[3]{2}\right)}{4 \sqrt[6]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-2^{5/6} \sqrt[6]{x^2+1}}{\sqrt{3}}\right)}{2 \sqrt[6]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{5/6} \sqrt[6]{x^2+1}+1}{\sqrt{3}}\right)}{2 \sqrt[6]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{x^2+1}}{\sqrt[6]{2}}\right)}{\sqrt[6]{2}}",1,"x*AppellF1[1/2, 1, 1/6, 3/2, x^2, -x^2] - (Sqrt[3]*ArcTan[(1 - 2^(5/6)*(1 + x^2)^(1/6))/Sqrt[3]])/(2*2^(1/6)) + (Sqrt[3]*ArcTan[(1 + 2^(5/6)*(1 + x^2)^(1/6))/Sqrt[3]])/(2*2^(1/6)) - ArcTanh[(1 + x^2)^(1/6)/2^(1/6)]/2^(1/6) + Log[2^(1/3) - 2^(1/6)*(1 + x^2)^(1/6) + (1 + x^2)^(1/3)]/(4*2^(1/6)) - Log[2^(1/3) + 2^(1/6)*(1 + x^2)^(1/6) + (1 + x^2)^(1/3)]/(4*2^(1/6))","A",15,10,15,0.6667,1,"{757, 429, 444, 63, 296, 634, 618, 204, 628, 206}"
721,1,223,0,0.1331015,"\int (d+e x)^m \left(a+c x^2\right)^3 \, dx","Int[(d + e*x)^m*(a + c*x^2)^3,x]","-\frac{4 c^2 d \left(3 a e^2+5 c d^2\right) (d+e x)^{m+4}}{e^7 (m+4)}+\frac{3 c^2 \left(a e^2+5 c d^2\right) (d+e x)^{m+5}}{e^7 (m+5)}+\frac{\left(a e^2+c d^2\right)^3 (d+e x)^{m+1}}{e^7 (m+1)}-\frac{6 c d \left(a e^2+c d^2\right)^2 (d+e x)^{m+2}}{e^7 (m+2)}+\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right) (d+e x)^{m+3}}{e^7 (m+3)}-\frac{6 c^3 d (d+e x)^{m+6}}{e^7 (m+6)}+\frac{c^3 (d+e x)^{m+7}}{e^7 (m+7)}","-\frac{4 c^2 d \left(3 a e^2+5 c d^2\right) (d+e x)^{m+4}}{e^7 (m+4)}+\frac{3 c^2 \left(a e^2+5 c d^2\right) (d+e x)^{m+5}}{e^7 (m+5)}+\frac{\left(a e^2+c d^2\right)^3 (d+e x)^{m+1}}{e^7 (m+1)}-\frac{6 c d \left(a e^2+c d^2\right)^2 (d+e x)^{m+2}}{e^7 (m+2)}+\frac{3 c \left(a e^2+c d^2\right) \left(a e^2+5 c d^2\right) (d+e x)^{m+3}}{e^7 (m+3)}-\frac{6 c^3 d (d+e x)^{m+6}}{e^7 (m+6)}+\frac{c^3 (d+e x)^{m+7}}{e^7 (m+7)}",1,"((c*d^2 + a*e^2)^3*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (6*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(3 + m))/(e^7*(3 + m)) - (4*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (3*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (6*c^3*d*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^7*(7 + m))","A",2,1,17,0.05882,1,"{697}"
722,1,140,0,0.0687169,"\int (d+e x)^m \left(a+c x^2\right)^2 \, dx","Int[(d + e*x)^m*(a + c*x^2)^2,x]","\frac{\left(a e^2+c d^2\right)^2 (d+e x)^{m+1}}{e^5 (m+1)}-\frac{4 c d \left(a e^2+c d^2\right) (d+e x)^{m+2}}{e^5 (m+2)}+\frac{2 c \left(a e^2+3 c d^2\right) (d+e x)^{m+3}}{e^5 (m+3)}-\frac{4 c^2 d (d+e x)^{m+4}}{e^5 (m+4)}+\frac{c^2 (d+e x)^{m+5}}{e^5 (m+5)}","\frac{\left(a e^2+c d^2\right)^2 (d+e x)^{m+1}}{e^5 (m+1)}-\frac{4 c d \left(a e^2+c d^2\right) (d+e x)^{m+2}}{e^5 (m+2)}+\frac{2 c \left(a e^2+3 c d^2\right) (d+e x)^{m+3}}{e^5 (m+3)}-\frac{4 c^2 d (d+e x)^{m+4}}{e^5 (m+4)}+\frac{c^2 (d+e x)^{m+5}}{e^5 (m+5)}",1,"((c*d^2 + a*e^2)^2*(d + e*x)^(1 + m))/(e^5*(1 + m)) - (4*c*d*(c*d^2 + a*e^2)*(d + e*x)^(2 + m))/(e^5*(2 + m)) + (2*c*(3*c*d^2 + a*e^2)*(d + e*x)^(3 + m))/(e^5*(3 + m)) - (4*c^2*d*(d + e*x)^(4 + m))/(e^5*(4 + m)) + (c^2*(d + e*x)^(5 + m))/(e^5*(5 + m))","A",2,1,17,0.05882,1,"{697}"
723,1,70,0,0.0295774,"\int (d+e x)^m \left(a+c x^2\right) \, dx","Int[(d + e*x)^m*(a + c*x^2),x]","\frac{\left(a e^2+c d^2\right) (d+e x)^{m+1}}{e^3 (m+1)}-\frac{2 c d (d+e x)^{m+2}}{e^3 (m+2)}+\frac{c (d+e x)^{m+3}}{e^3 (m+3)}","\frac{\left(a e^2+c d^2\right) (d+e x)^{m+1}}{e^3 (m+1)}-\frac{2 c d (d+e x)^{m+2}}{e^3 (m+2)}+\frac{c (d+e x)^{m+3}}{e^3 (m+3)}",1,"((c*d^2 + a*e^2)*(d + e*x)^(1 + m))/(e^3*(1 + m)) - (2*c*d*(d + e*x)^(2 + m))/(e^3*(2 + m)) + (c*(d + e*x)^(3 + m))/(e^3*(3 + m))","A",2,1,15,0.06667,1,"{697}"
724,1,167,0,0.2082839,"\int \frac{(d+e x)^m}{a+c x^2} \, dx","Int[(d + e*x)^m/(a + c*x^2),x]","\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 \sqrt{-a} (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{-a} (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}","\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 \sqrt{-a} (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{-a} (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}",1,"((d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*Sqrt[-a]*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + m)) - ((d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*Sqrt[-a]*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + m))","A",4,2,17,0.1176,1,"{712, 68}"
725,1,304,0,0.3806765,"\int \frac{(d+e x)^m}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)^m/(a + c*x^2)^2,x]","-\frac{(d+e x)^{m+1} \left(\sqrt{-a} \sqrt{c} d e m+a e^2 (1-m)+c d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 (-a)^{3/2} (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{m+1} \left(-\sqrt{-a} \sqrt{c} d e m+a e^2 (1-m)+c d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 (-a)^{3/2} (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{m+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)^{m+1} \left(\sqrt{-a} \sqrt{c} d e m+a e^2 (1-m)+c d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 (-a)^{3/2} (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{m+1} \left(-\sqrt{-a} \sqrt{c} d e m+a e^2 (1-m)+c d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 (-a)^{3/2} (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{m+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 + m))/(2*a*(c*d^2 + a*e^2)*(a + c*x^2)) - ((c*d^2 + a*e^2*(1 - m) + Sqrt[-a]*Sqrt[c]*d*e*m)*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (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 + m)) + ((c*d^2 + a*e^2*(1 - m) - Sqrt[-a]*Sqrt[c]*d*e*m)*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (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 + m))","A",5,3,17,0.1765,1,"{741, 831, 68}"
726,1,472,0,0.8120504,"\int \frac{(d+e x)^m}{\left(a+c x^2\right)^3} \, dx","Int[(d + e*x)^m/(a + c*x^2)^3,x]","\frac{(d+e x)^{m+1} \left(a \sqrt{c} d e m \left(a e^2 (5-2 m)+3 c d^2\right)-\sqrt{-a} \left(a^2 e^4 \left(m^2-4 m+3\right)+a c d^2 e^2 \left(-m^2-2 m+6\right)+3 c^2 d^4\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{16 a^3 (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)^2}+\frac{(d+e x)^{m+1} \left(\sqrt{-a} \left(a^2 e^4 \left(m^2-4 m+3\right)+a c d^2 e^2 \left(-m^2-2 m+6\right)+3 c^2 d^4\right)+a \sqrt{c} d e m \left(a e^2 (5-2 m)+3 c d^2\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{16 a^3 (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)^2}+\frac{(d+e x)^{m+1} \left(c d x \left(a e^2 (5-2 m)+3 c d^2\right)+a e \left(a e^2 (3-m)+c d^2 (m+1)\right)\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}+\frac{(d+e x)^{m+1} (a e+c d x)}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)}","\frac{(d+e x)^{m+1} \left(a \sqrt{c} d e m \left(a e^2 (5-2 m)+3 c d^2\right)-\sqrt{-a} \left(a^2 e^4 \left(m^2-4 m+3\right)+a c d^2 e^2 \left(-m^2-2 m+6\right)+3 c^2 d^4\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{16 a^3 (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)^2}+\frac{(d+e x)^{m+1} \left(\sqrt{-a} \left(a^2 e^4 \left(m^2-4 m+3\right)+a c d^2 e^2 \left(-m^2-2 m+6\right)+3 c^2 d^4\right)+a \sqrt{c} d e m \left(a e^2 (5-2 m)+3 c d^2\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{16 a^3 (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)^2}+\frac{(d+e x)^{m+1} \left(c d x \left(a e^2 (5-2 m)+3 c d^2\right)+a e \left(a e^2 (3-m)+c d^2 (m+1)\right)\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}+\frac{(d+e x)^{m+1} (a e+c d x)}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)}",1,"((a*e + c*d*x)*(d + e*x)^(1 + m))/(4*a*(c*d^2 + a*e^2)*(a + c*x^2)^2) + ((d + e*x)^(1 + m)*(a*e*(a*e^2*(3 - m) + c*d^2*(1 + m)) + c*d*(3*c*d^2 + a*e^2*(5 - 2*m))*x))/(8*a^2*(c*d^2 + a*e^2)^2*(a + c*x^2)) + ((a*Sqrt[c]*d*e*(3*c*d^2 + a*e^2*(5 - 2*m))*m - Sqrt[-a]*(3*c^2*d^4 + a*c*d^2*e^2*(6 - 2*m - m^2) + a^2*e^4*(3 - 4*m + m^2)))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(16*a^3*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)^2*(1 + m)) + ((a*Sqrt[c]*d*e*(3*c*d^2 + a*e^2*(5 - 2*m))*m + Sqrt[-a]*(3*c^2*d^4 + a*c*d^2*e^2*(6 - 2*m - m^2) + a^2*e^4*(3 - 4*m + m^2)))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(16*a^3*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)^2*(1 + m))","A",6,4,17,0.2353,1,"{741, 823, 831, 68}"
727,1,154,0,0.1352349,"\int (d+e x)^m \left(a+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^m*(a + c*x^2)^(3/2),x]","\frac{\left(a+c x^2\right)^{3/2} (d+e x)^{m+1} F_1\left(m+1;-\frac{3}{2},-\frac{3}{2};m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1) \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{3/2} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{3/2}}","\frac{\left(a+c x^2\right)^{3/2} (d+e x)^{m+1} F_1\left(m+1;-\frac{3}{2},-\frac{3}{2};m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1) \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{3/2} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{3/2}}",1,"((d + e*x)^(1 + m)*(a + c*x^2)^(3/2)*AppellF1[1 + m, -3/2, -3/2, 2 + m, (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]), (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c])])/(e*(1 + m)*(1 - (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]))^(3/2)*(1 - (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c]))^(3/2))","A",2,2,19,0.1053,1,"{760, 133}"
728,1,154,0,0.0659291,"\int (d+e x)^m \sqrt{a+c x^2} \, dx","Int[(d + e*x)^m*Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1) \sqrt{1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}} \sqrt{1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}}}","\frac{\sqrt{a+c x^2} (d+e x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1) \sqrt{1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}} \sqrt{1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}}}",1,"((d + e*x)^(1 + m)*Sqrt[a + c*x^2]*AppellF1[1 + m, -1/2, -1/2, 2 + m, (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]), (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c])])/(e*(1 + m)*Sqrt[1 - (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c])]*Sqrt[1 - (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c])])","A",2,2,19,0.1053,1,"{760, 133}"
729,1,154,0,0.0615328,"\int \frac{(d+e x)^m}{\sqrt{a+c x^2}} \, dx","Int[(d + e*x)^m/Sqrt[a + c*x^2],x]","\frac{(d+e x)^{m+1} \sqrt{1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}} \sqrt{1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1) \sqrt{a+c x^2}}","\frac{(d+e x)^{m+1} \sqrt{1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}} \sqrt{1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1) \sqrt{a+c x^2}}",1,"((d + e*x)^(1 + m)*Sqrt[1 - (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c])]*Sqrt[1 - (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c])]*AppellF1[1 + m, 1/2, 1/2, 2 + m, (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]), (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c])])/(e*(1 + m)*Sqrt[a + c*x^2])","A",2,2,19,0.1053,1,"{760, 133}"
730,1,154,0,0.0625726,"\int \frac{(d+e x)^m}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^m/(a + c*x^2)^(3/2),x]","\frac{(d+e x)^{m+1} \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{3/2} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{3/2} F_1\left(m+1;\frac{3}{2},\frac{3}{2};m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1) \left(a+c x^2\right)^{3/2}}","\frac{(d+e x)^{m+1} \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{3/2} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{3/2} F_1\left(m+1;\frac{3}{2},\frac{3}{2};m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1) \left(a+c x^2\right)^{3/2}}",1,"((d + e*x)^(1 + m)*(1 - (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]))^(3/2)*(1 - (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c]))^(3/2)*AppellF1[1 + m, 3/2, 3/2, 2 + m, (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]), (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c])])/(e*(1 + m)*(a + c*x^2)^(3/2))","A",2,2,19,0.1053,1,"{760, 133}"
731,1,152,0,0.064112,"\int (d+e x)^m \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^m*(a + c*x^2)^p,x]","\frac{\left(a+c x^2\right)^p (d+e x)^{m+1} \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{-p} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1)}","\frac{\left(a+c x^2\right)^p (d+e x)^{m+1} \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{-p} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (m+1)}",1,"((d + e*x)^(1 + m)*(a + c*x^2)^p*AppellF1[1 + m, -p, -p, 2 + m, (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]), (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c])])/(e*(1 + m)*(1 - (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]))^p*(1 - (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c]))^p)","A",2,2,17,0.1176,1,"{760, 133}"
732,1,169,0,0.1519589,"\int (d+e x)^3 \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^3*(a + c*x^2)^p,x]","-\frac{e \left(a+c x^2\right)^{p+1} \left((2 p+3) \left(a e^2-c d^2 (2 p+5)\right)-2 c d e (p+1) (p+3) x\right)}{2 c^2 (p+2) \left(2 p^2+5 p+3\right)}+d x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d^2-\frac{3 a e^2}{2 c p+3 c}\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)+\frac{e (d+e x)^2 \left(a+c x^2\right)^{p+1}}{2 c (p+2)}","-\frac{e \left(a+c x^2\right)^{p+1} \left((2 p+3) \left(a e^2-c d^2 (2 p+5)\right)-2 c d e (p+1) (p+3) x\right)}{2 c^2 (p+2) \left(2 p^2+5 p+3\right)}-\frac{d x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(3 a e^2-c d^2 (2 p+3)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)}{c (2 p+3)}+\frac{e (d+e x)^2 \left(a+c x^2\right)^{p+1}}{2 c (p+2)}",1,"(e*(d + e*x)^2*(a + c*x^2)^(1 + p))/(2*c*(2 + p)) - (e*((3 + 2*p)*(a*e^2 - c*d^2*(5 + 2*p)) - 2*c*d*e*(1 + p)*(3 + p)*x)*(a + c*x^2)^(1 + p))/(2*c^2*(2 + p)*(3 + 5*p + 2*p^2)) + (d*(d^2 - (3*a*e^2)/(3*c + 2*c*p))*x*(a + c*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((c*x^2)/a)])/(1 + (c*x^2)/a)^p","A",4,4,17,0.2353,1,"{743, 780, 246, 245}"
733,1,125,0,0.0730234,"\int (d+e x)^2 \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^2*(a + c*x^2)^p,x]","x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d^2-\frac{a e^2}{2 c p+3 c}\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)+\frac{e (d+e x) \left(a+c x^2\right)^{p+1}}{c (2 p+3)}+\frac{d e (p+2) \left(a+c x^2\right)^{p+1}}{c (p+1) (2 p+3)}","-\frac{x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(a e^2-c d^2 (2 p+3)\right) \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)}{c (2 p+3)}+\frac{e (d+e x) \left(a+c x^2\right)^{p+1}}{c (2 p+3)}+\frac{d e (p+2) \left(a+c x^2\right)^{p+1}}{c (p+1) (2 p+3)}",1,"(d*e*(2 + p)*(a + c*x^2)^(1 + p))/(c*(1 + p)*(3 + 2*p)) + (e*(d + e*x)*(a + c*x^2)^(1 + p))/(c*(3 + 2*p)) + ((d^2 - (a*e^2)/(3*c + 2*c*p))*x*(a + c*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((c*x^2)/a)])/(1 + (c*x^2)/a)^p","A",4,4,17,0.2353,1,"{743, 641, 246, 245}"
734,1,70,0,0.0203105,"\int (d+e x) \left(a+c x^2\right)^p \, dx","Int[(d + e*x)*(a + c*x^2)^p,x]","d x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)+\frac{e \left(a+c x^2\right)^{p+1}}{2 c (p+1)}","\frac{d x \left(a+c x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{3}{2};\frac{3}{2};-\frac{c x^2}{a}\right)}{a}+\frac{e \left(a+c x^2\right)^{p+1}}{2 c (p+1)}",1,"(e*(a + c*x^2)^(1 + p))/(2*c*(1 + p)) + (d*x*(a + c*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((c*x^2)/a)])/(1 + (c*x^2)/a)^p","A",3,3,15,0.2000,1,"{641, 246, 245}"
735,1,44,0,0.0091919,"\int \left(a+c x^2\right)^p \, dx","Int[(a + c*x^2)^p,x]","x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)","\frac{x \left(a+c x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{3}{2};\frac{3}{2};-\frac{c x^2}{a}\right)}{a}",1,"(x*(a + c*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((c*x^2)/a)])/(1 + (c*x^2)/a)^p","A",2,2,9,0.2222,1,"{246, 245}"
736,1,125,0,0.1181905,"\int \frac{\left(a+c x^2\right)^p}{d+e x} \, dx","Int[(a + c*x^2)^p/(d + e*x),x]","\frac{x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d}-\frac{e \left(a+c x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(c x^2+a\right)}{c d^2+a e^2}\right)}{2 (p+1) \left(a e^2+c d^2\right)}","\frac{x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,1;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d}-\frac{e \left(a+c x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{e^2 \left(c x^2+a\right)}{c d^2+a e^2}\right)}{2 (p+1) \left(a e^2+c d^2\right)}",1,"(x*(a + c*x^2)^p*AppellF1[1/2, -p, 1, 3/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d*(1 + (c*x^2)/a)^p) - (e*(a + c*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (e^2*(a + c*x^2))/(c*d^2 + a*e^2)])/(2*(c*d^2 + a*e^2)*(1 + p))","A",6,5,17,0.2941,1,"{757, 430, 429, 444, 68}"
737,1,191,0,0.1789328,"\int \frac{\left(a+c x^2\right)^p}{(d+e x)^2} \, dx","Int[(a + c*x^2)^p/(d + e*x)^2,x]","\frac{x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2}+\frac{e^2 x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^4}-\frac{c d e \left(a+c x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(c x^2+a\right)}{c d^2+a e^2}\right)}{(p+1) \left(a e^2+c d^2\right)^2}","\frac{x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,2;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^2}+\frac{e^2 x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,2;\frac{5}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{3 d^4}-\frac{c d e \left(a+c x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(c x^2+a\right)}{c d^2+a e^2}\right)}{(p+1) \left(a e^2+c d^2\right)^2}",1,"(x*(a + c*x^2)^p*AppellF1[1/2, -p, 2, 3/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^2*(1 + (c*x^2)/a)^p) + (e^2*x^3*(a + c*x^2)^p*AppellF1[3/2, -p, 2, 5/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(3*d^4*(1 + (c*x^2)/a)^p) - (c*d*e*(a + c*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + c*x^2))/(c*d^2 + a*e^2)])/((c*d^2 + a*e^2)^2*(1 + p))","A",8,7,17,0.4118,1,"{757, 430, 429, 444, 68, 511, 510}"
738,1,322,0,0.3158158,"\int \frac{\left(a+c x^2\right)^p}{(d+e x)^3} \, dx","Int[(a + c*x^2)^p/(d + e*x)^3,x]","\frac{x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,3;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3}+\frac{e^2 x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,3;\frac{5}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}-\frac{3 c^2 d^2 e \left(a+c x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{e^2 \left(c x^2+a\right)}{c d^2+a e^2}\right)}{2 (p+1) \left(a e^2+c d^2\right)^3}+\frac{c e \left(a+c x^2\right)^{p+1} \left(2 a e^2+c d^2 (p+1)\right) \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(c x^2+a\right)}{c d^2+a e^2}\right)}{4 (p+1) \left(a e^2+c d^2\right)^3}-\frac{d^2 e \left(a+c x^2\right)^{p+1}}{4 \left(d^2-e^2 x^2\right)^2 \left(a e^2+c d^2\right)}","\frac{x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-p,3;\frac{3}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^3}+\frac{e^2 x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} F_1\left(\frac{3}{2};-p,3;\frac{5}{2};-\frac{c x^2}{a},\frac{e^2 x^2}{d^2}\right)}{d^5}-\frac{3 c^2 d^2 e \left(a+c x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{e^2 \left(c x^2+a\right)}{c d^2+a e^2}\right)}{2 (p+1) \left(a e^2+c d^2\right)^3}+\frac{c e \left(a+c x^2\right)^{p+1} \left(2 a e^2+c d^2 (p+1)\right) \, _2F_1\left(2,p+1;p+2;\frac{e^2 \left(c x^2+a\right)}{c d^2+a e^2}\right)}{4 (p+1) \left(a e^2+c d^2\right)^3}-\frac{d^2 e \left(a+c x^2\right)^{p+1}}{4 \left(d^2-e^2 x^2\right)^2 \left(a e^2+c d^2\right)}",1,"-(d^2*e*(a + c*x^2)^(1 + p))/(4*(c*d^2 + a*e^2)*(d^2 - e^2*x^2)^2) + (x*(a + c*x^2)^p*AppellF1[1/2, -p, 3, 3/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^3*(1 + (c*x^2)/a)^p) + (e^2*x^3*(a + c*x^2)^p*AppellF1[3/2, -p, 3, 5/2, -((c*x^2)/a), (e^2*x^2)/d^2])/(d^5*(1 + (c*x^2)/a)^p) + (c*e*(2*a*e^2 + c*d^2*(1 + p))*(a + c*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, (e^2*(a + c*x^2))/(c*d^2 + a*e^2)])/(4*(c*d^2 + a*e^2)^3*(1 + p)) - (3*c^2*d^2*e*(a + c*x^2)^(1 + p)*Hypergeometric2F1[3, 1 + p, 2 + p, (e^2*(a + c*x^2))/(c*d^2 + a*e^2)])/(2*(c*d^2 + a*e^2)^3*(1 + p))","A",11,9,17,0.5294,1,"{757, 430, 429, 444, 68, 511, 510, 446, 78}"
739,1,160,0,0.0852414,"\int (d+e x)^{-2 p} \left(a+c x^2\right)^p \, dx","Int[(a + c*x^2)^p/(d + e*x)^(2*p),x]","\frac{\left(a+c x^2\right)^p (d+e x)^{1-2 p} \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{-p} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{-p} F_1\left(1-2 p;-p,-p;2-2 p;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (1-2 p)}","\frac{\left(a+c x^2\right)^p (d+e x)^{1-2 p} \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{-p} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{-p} F_1\left(1-2 p;-p,-p;2-2 p;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{e (1-2 p)}",1,"((d + e*x)^(1 - 2*p)*(a + c*x^2)^p*AppellF1[1 - 2*p, -p, -p, 2 - 2*p, (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]), (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c])])/(e*(1 - 2*p)*(1 - (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]))^p*(1 - (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c]))^p)","A",2,2,19,0.1053,1,"{760, 133}"
740,1,155,0,0.0650256,"\int (d+e x)^{-1-2 p} \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p,x]","-\frac{\left(a+c x^2\right)^p (d+e x)^{-2 p} \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{-p} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{-p} F_1\left(-2 p;-p,-p;1-2 p;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{2 e p}","-\frac{\left(a+c x^2\right)^p (d+e x)^{-2 p} \left(1-\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}}\right)^{-p} \left(1-\frac{d+e x}{\frac{\sqrt{-a} e}{\sqrt{c}}+d}\right)^{-p} F_1\left(-2 p;-p,-p;1-2 p;\frac{d+e x}{d-\frac{\sqrt{-a} e}{\sqrt{c}}},\frac{d+e x}{d+\frac{\sqrt{-a} e}{\sqrt{c}}}\right)}{2 e p}",1,"-((a + c*x^2)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]), (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c])])/(2*e*p*(d + e*x)^(2*p)*(1 - (d + e*x)/(d - (Sqrt[-a]*e)/Sqrt[c]))^p*(1 - (d + e*x)/(d + (Sqrt[-a]*e)/Sqrt[c]))^p)","A",2,2,21,0.09524,1,"{760, 133}"
741,1,209,0,0.0839888,"\int (d+e x)^{-2-2 p} \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^(-2 - 2*p)*(a + c*x^2)^p,x]","-\frac{\left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}","-\frac{\left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}",1,"-(((Sqrt[-a] - Sqrt[c]*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (2*Sqrt[-a]*Sqrt[c]*(d + e*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))])/((Sqrt[c]*d + Sqrt[-a]*e)*(1 + 2*p)*(-(((Sqrt[c]*d + Sqrt[-a]*e)*(Sqrt[-a] + Sqrt[c]*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))))^p))","A",1,1,21,0.04762,1,"{727}"
742,1,270,0,0.0857186,"\int (d+e x)^{-3-2 p} \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^(-3 - 2*p)*(a + c*x^2)^p,x]","-\frac{c d \left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)}}{2 (p+1) \left(a e^2+c d^2\right)}","-\frac{c d \left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)}}{2 (p+1) \left(a e^2+c d^2\right)}",1,"-(e*(a + c*x^2)^(1 + p))/(2*(c*d^2 + a*e^2)*(1 + p)*(d + e*x)^(2*(1 + p))) - (c*d*(Sqrt[-a] - Sqrt[c]*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (2*Sqrt[-a]*Sqrt[c]*(d + e*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))])/((Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + 2*p)*(-(((Sqrt[c]*d + Sqrt[-a]*e)*(Sqrt[-a] + Sqrt[c]*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))))^p)","A",2,2,21,0.09524,1,"{731, 727}"
743,1,347,0,0.1825881,"\int (d+e x)^{-4-2 p} \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^(-4 - 2*p)*(a + c*x^2)^p,x]","\frac{c \left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(a e^2-c d^2 (2 p+3)\right) \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) (2 p+3) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 p-3}}{(2 p+3) \left(a e^2+c d^2\right)}-\frac{c d e (p+2) \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)}}{(p+1) (2 p+3) \left(a e^2+c d^2\right)^2}","\frac{c \left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(a e^2-c d^2 (2 p+3)\right) \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) (2 p+3) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 p-3}}{(2 p+3) \left(a e^2+c d^2\right)}-\frac{c d e (p+2) \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)}}{(p+1) (2 p+3) \left(a e^2+c d^2\right)^2}",1,"-((e*(d + e*x)^(-3 - 2*p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)*(3 + 2*p))) - (c*d*e*(2 + p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)^2*(1 + p)*(3 + 2*p)*(d + e*x)^(2*(1 + p))) + (c*(a*e^2 - c*d^2*(3 + 2*p))*(Sqrt[-a] - Sqrt[c]*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (2*Sqrt[-a]*Sqrt[c]*(d + e*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))])/((Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)^2*(1 + 2*p)*(3 + 2*p)*(-(((Sqrt[c]*d + Sqrt[-a]*e)*(Sqrt[-a] + Sqrt[c]*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))))^p)","A",3,3,21,0.1429,1,"{745, 807, 727}"
744,1,436,0,0.4543561,"\int (d+e x)^{-5-2 p} \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^(-5 - 2*p)*(a + c*x^2)^p,x]","\frac{c^2 d \left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(3 a e^2-c d^2 (2 p+3)\right) \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) (2 p+3) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)^3}+\frac{c e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)} \left(a e^2 (2 p+3)-c d^2 \left(2 p^2+8 p+9\right)\right)}{2 (p+1) (p+2) (2 p+3) \left(a e^2+c d^2\right)^3}-\frac{c d e (p+3) \left(a+c x^2\right)^{p+1} (d+e x)^{-2 p-3}}{(p+2) (2 p+3) \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+2)}}{2 (p+2) \left(a e^2+c d^2\right)}","\frac{c^2 d \left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(3 a e^2-c d^2 (2 p+3)\right) \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) (2 p+3) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)^3}+\frac{c e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)} \left(a e^2 (2 p+3)-c d^2 \left(2 p^2+8 p+9\right)\right)}{2 (p+1) (p+2) (2 p+3) \left(a e^2+c d^2\right)^3}-\frac{c d e (p+3) \left(a+c x^2\right)^{p+1} (d+e x)^{-2 p-3}}{(p+2) (2 p+3) \left(a e^2+c d^2\right)^2}-\frac{e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+2)}}{2 (p+2) \left(a e^2+c d^2\right)}",1,"-((c*d*e*(3 + p)*(d + e*x)^(-3 - 2*p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)^2*(2 + p)*(3 + 2*p))) + (c*e*(a*e^2*(3 + 2*p) - c*d^2*(9 + 8*p + 2*p^2))*(a + c*x^2)^(1 + p))/(2*(c*d^2 + a*e^2)^3*(1 + p)*(2 + p)*(3 + 2*p)*(d + e*x)^(2*(1 + p))) - (e*(a + c*x^2)^(1 + p))/(2*(c*d^2 + a*e^2)*(2 + p)*(d + e*x)^(2*(2 + p))) + (c^2*d*(3*a*e^2 - c*d^2*(3 + 2*p))*(Sqrt[-a] - Sqrt[c]*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (2*Sqrt[-a]*Sqrt[c]*(d + e*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))])/((Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)^3*(1 + 2*p)*(3 + 2*p)*(-(((Sqrt[c]*d + Sqrt[-a]*e)*(Sqrt[-a] + Sqrt[c]*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))))^p)","A",4,4,21,0.1905,1,"{745, 837, 807, 727}"
745,1,559,0,0.731034,"\int (d+e x)^{-6-2 p} \left(a+c x^2\right)^p \, dx","Int[(d + e*x)^(-6 - 2*p)*(a + c*x^2)^p,x]","-\frac{c^2 \left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(3 a^2 e^4-6 a c d^2 e^2 (2 p+5)+c^2 d^4 \left(4 p^2+16 p+15\right)\right) \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) (2 p+3) (2 p+5) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)^4}+\frac{c^2 d e (p+3) \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)} \left(a e^2 (5 p+8)-c d^2 \left(2 p^2+7 p+8\right)\right)}{(p+1) (p+2) (2 p+3) (2 p+5) \left(a e^2+c d^2\right)^4}+\frac{c e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 p-3} \left(3 a e^2 (p+2)-c d^2 \left(2 p^2+11 p+18\right)\right)}{(p+2) (2 p+3) (2 p+5) \left(a e^2+c d^2\right)^3}-\frac{e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 p-5}}{(2 p+5) \left(a e^2+c d^2\right)}-\frac{c d e (p+4) \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+2)}}{(p+2) (2 p+5) \left(a e^2+c d^2\right)^2}","-\frac{c^2 \left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (d+e x)^{-2 p-1} \left(3 a^2 e^4-6 a c d^2 e^2 (2 p+5)+c^2 d^4 \left(4 p^2+16 p+15\right)\right) \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} e+\sqrt{c} d\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} d-\sqrt{-a} e\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (d+e x)}{\left(\sqrt{c} d-\sqrt{-a} e\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{(2 p+1) (2 p+3) (2 p+5) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)^4}+\frac{c^2 d e (p+3) \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)} \left(a e^2 (5 p+8)-c d^2 \left(2 p^2+7 p+8\right)\right)}{(p+1) (p+2) (2 p+3) (2 p+5) \left(a e^2+c d^2\right)^4}+\frac{c e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 p-3} \left(3 a e^2 (p+2)-c d^2 \left(2 p^2+11 p+18\right)\right)}{(p+2) (2 p+3) (2 p+5) \left(a e^2+c d^2\right)^3}-\frac{e \left(a+c x^2\right)^{p+1} (d+e x)^{-2 p-5}}{(2 p+5) \left(a e^2+c d^2\right)}-\frac{c d e (p+4) \left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+2)}}{(p+2) (2 p+5) \left(a e^2+c d^2\right)^2}",1,"-((e*(d + e*x)^(-5 - 2*p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)*(5 + 2*p))) + (c*e*(3*a*e^2*(2 + p) - c*d^2*(18 + 11*p + 2*p^2))*(d + e*x)^(-3 - 2*p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)^3*(2 + p)*(3 + 2*p)*(5 + 2*p)) + (c^2*d*e*(3 + p)*(a*e^2*(8 + 5*p) - c*d^2*(8 + 7*p + 2*p^2))*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)^4*(1 + p)*(2 + p)*(3 + 2*p)*(5 + 2*p)*(d + e*x)^(2*(1 + p))) - (c*d*e*(4 + p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)^2*(2 + p)*(5 + 2*p)*(d + e*x)^(2*(2 + p))) - (c^2*(3*a^2*e^4 - 6*a*c*d^2*e^2*(5 + 2*p) + c^2*d^4*(15 + 16*p + 4*p^2))*(Sqrt[-a] - Sqrt[c]*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (2*Sqrt[-a]*Sqrt[c]*(d + e*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))])/((Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)^4*(1 + 2*p)*(3 + 2*p)*(5 + 2*p)*(-(((Sqrt[c]*d + Sqrt[-a]*e)*(Sqrt[-a] + Sqrt[c]*x))/((Sqrt[c]*d - Sqrt[-a]*e)*(Sqrt[-a] - Sqrt[c]*x))))^p)","A",5,4,21,0.1905,1,"{745, 837, 807, 727}"
746,1,43,0,0.0209597,"\int \frac{(3-4 x)^n}{\sqrt{1-x^2}} \, dx","Int[(3 - 4*x)^n/Sqrt[1 - x^2],x]","\sqrt{2} 7^n \sqrt{x+1} F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{4 (x+1)}{7},\frac{x+1}{2}\right)","\sqrt{2} 7^n \sqrt{x+1} F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{4 (x+1)}{7},\frac{x+1}{2}\right)",1,"Sqrt[2]*7^n*Sqrt[1 + x]*AppellF1[1/2, -n, 1/2, 3/2, (4*(1 + x))/7, (1 + x)/2]","A",2,2,19,0.1053,1,"{756, 138}"
747,1,83,0,0.0319296,"\int \frac{(a+b x)^6}{a^2-b^2 x^2} \, dx","Int[(a + b*x)^6/(a^2 - b^2*x^2),x]","-\frac{4 a^3 (a+b x)^2}{b}-\frac{4 a^2 (a+b x)^3}{3 b}-\frac{32 a^5 \log (a-b x)}{b}-16 a^4 x-\frac{a (a+b x)^4}{2 b}-\frac{(a+b x)^5}{5 b}","-\frac{4 a^3 (a+b x)^2}{b}-\frac{4 a^2 (a+b x)^3}{3 b}-\frac{32 a^5 \log (a-b x)}{b}-16 a^4 x-\frac{a (a+b x)^4}{2 b}-\frac{(a+b x)^5}{5 b}",1,"-16*a^4*x - (4*a^3*(a + b*x)^2)/b - (4*a^2*(a + b*x)^3)/(3*b) - (a*(a + b*x)^4)/(2*b) - (a + b*x)^5/(5*b) - (32*a^5*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
748,1,66,0,0.0253941,"\int \frac{(a+b x)^5}{a^2-b^2 x^2} \, dx","Int[(a + b*x)^5/(a^2 - b^2*x^2),x]","-\frac{2 a^2 (a+b x)^2}{b}-\frac{16 a^4 \log (a-b x)}{b}-8 a^3 x-\frac{2 a (a+b x)^3}{3 b}-\frac{(a+b x)^4}{4 b}","-\frac{2 a^2 (a+b x)^2}{b}-\frac{16 a^4 \log (a-b x)}{b}-8 a^3 x-\frac{2 a (a+b x)^3}{3 b}-\frac{(a+b x)^4}{4 b}",1,"-8*a^3*x - (2*a^2*(a + b*x)^2)/b - (2*a*(a + b*x)^3)/(3*b) - (a + b*x)^4/(4*b) - (16*a^4*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
749,1,49,0,0.0205057,"\int \frac{(a+b x)^4}{a^2-b^2 x^2} \, dx","Int[(a + b*x)^4/(a^2 - b^2*x^2),x]","-\frac{8 a^3 \log (a-b x)}{b}-4 a^2 x-\frac{a (a+b x)^2}{b}-\frac{(a+b x)^3}{3 b}","-\frac{8 a^3 \log (a-b x)}{b}-4 a^2 x-\frac{a (a+b x)^2}{b}-\frac{(a+b x)^3}{3 b}",1,"-4*a^2*x - (a*(a + b*x)^2)/b - (a + b*x)^3/(3*b) - (8*a^3*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
750,1,28,0,0.0146225,"\int \frac{(a+b x)^3}{a^2-b^2 x^2} \, dx","Int[(a + b*x)^3/(a^2 - b^2*x^2),x]","-\frac{4 a^2 \log (a-b x)}{b}-3 a x-\frac{b x^2}{2}","-\frac{4 a^2 \log (a-b x)}{b}-3 a x-\frac{b x^2}{2}",1,"-3*a*x - (b*x^2)/2 - (4*a^2*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
751,1,17,0,0.0142805,"\int \frac{(a+b x)^2}{a^2-b^2 x^2} \, dx","Int[(a + b*x)^2/(a^2 - b^2*x^2),x]","-\frac{2 a \log (a-b x)}{b}-x","-\frac{2 a \log (a-b x)}{b}-x",1,"-x - (2*a*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
752,1,12,0,0.0044518,"\int \frac{a+b x}{a^2-b^2 x^2} \, dx","Int[(a + b*x)/(a^2 - b^2*x^2),x]","-\frac{\log (a-b x)}{b}","-\frac{\log (a-b x)}{b}",1,"-(Log[a - b*x]/b)","A",2,2,20,0.1000,1,"{627, 31}"
753,1,35,0,0.0308144,"\int \frac{1}{(a+b x) \left(a^2-b^2 x^2\right)} \, dx","Int[1/((a + b*x)*(a^2 - b^2*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^2 b}-\frac{1}{2 a b (a+b x)}","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^2 b}-\frac{1}{2 a b (a+b x)}",1,"-1/(2*a*b*(a + b*x)) + ArcTanh[(b*x)/a]/(2*a^2*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
754,1,52,0,0.0373936,"\int \frac{1}{(a+b x)^2 \left(a^2-b^2 x^2\right)} \, dx","Int[1/((a + b*x)^2*(a^2 - b^2*x^2)),x]","-\frac{1}{4 a^2 b (a+b x)}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^3 b}-\frac{1}{4 a b (a+b x)^2}","-\frac{1}{4 a^2 b (a+b x)}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^3 b}-\frac{1}{4 a b (a+b x)^2}",1,"-1/(4*a*b*(a + b*x)^2) - 1/(4*a^2*b*(a + b*x)) + ArcTanh[(b*x)/a]/(4*a^3*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
755,1,69,0,0.0457732,"\int \frac{1}{(a+b x)^3 \left(a^2-b^2 x^2\right)} \, dx","Int[1/((a + b*x)^3*(a^2 - b^2*x^2)),x]","-\frac{1}{8 a^3 b (a+b x)}-\frac{1}{8 a^2 b (a+b x)^2}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{8 a^4 b}-\frac{1}{6 a b (a+b x)^3}","-\frac{1}{8 a^3 b (a+b x)}-\frac{1}{8 a^2 b (a+b x)^2}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{8 a^4 b}-\frac{1}{6 a b (a+b x)^3}",1,"-1/(6*a*b*(a + b*x)^3) - 1/(8*a^2*b*(a + b*x)^2) - 1/(8*a^3*b*(a + b*x)) + ArcTanh[(b*x)/a]/(8*a^4*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
756,1,86,0,0.0530616,"\int \frac{1}{(a+b x)^4 \left(a^2-b^2 x^2\right)} \, dx","Int[1/((a + b*x)^4*(a^2 - b^2*x^2)),x]","-\frac{1}{16 a^4 b (a+b x)}-\frac{1}{16 a^3 b (a+b x)^2}-\frac{1}{12 a^2 b (a+b x)^3}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{16 a^5 b}-\frac{1}{8 a b (a+b x)^4}","-\frac{1}{16 a^4 b (a+b x)}-\frac{1}{16 a^3 b (a+b x)^2}-\frac{1}{12 a^2 b (a+b x)^3}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{16 a^5 b}-\frac{1}{8 a b (a+b x)^4}",1,"-1/(8*a*b*(a + b*x)^4) - 1/(12*a^2*b*(a + b*x)^3) - 1/(16*a^3*b*(a + b*x)^2) - 1/(16*a^4*b*(a + b*x)) + ArcTanh[(b*x)/a]/(16*a^5*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
757,1,70,0,0.0509393,"\int \frac{(a+b x)^7}{\left(a^2-b^2 x^2\right)^2} \, dx","Int[(a + b*x)^7/(a^2 - b^2*x^2)^2,x]","\frac{23}{2} a^2 b x^2+\frac{32 a^5}{b (a-b x)}+\frac{80 a^4 \log (a-b x)}{b}+49 a^3 x+\frac{7}{3} a b^2 x^3+\frac{b^3 x^4}{4}","\frac{23}{2} a^2 b x^2+\frac{32 a^5}{b (a-b x)}+\frac{80 a^4 \log (a-b x)}{b}+49 a^3 x+\frac{7}{3} a b^2 x^3+\frac{b^3 x^4}{4}",1,"49*a^3*x + (23*a^2*b*x^2)/2 + (7*a*b^2*x^3)/3 + (b^3*x^4)/4 + (32*a^5)/(b*(a - b*x)) + (80*a^4*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
758,1,55,0,0.0410961,"\int \frac{(a+b x)^6}{\left(a^2-b^2 x^2\right)^2} \, dx","Int[(a + b*x)^6/(a^2 - b^2*x^2)^2,x]","\frac{16 a^4}{b (a-b x)}+\frac{32 a^3 \log (a-b x)}{b}+17 a^2 x+3 a b x^2+\frac{b^2 x^3}{3}","\frac{16 a^4}{b (a-b x)}+\frac{32 a^3 \log (a-b x)}{b}+17 a^2 x+3 a b x^2+\frac{b^2 x^3}{3}",1,"17*a^2*x + 3*a*b*x^2 + (b^2*x^3)/3 + (16*a^4)/(b*(a - b*x)) + (32*a^3*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
759,1,44,0,0.0309178,"\int \frac{(a+b x)^5}{\left(a^2-b^2 x^2\right)^2} \, dx","Int[(a + b*x)^5/(a^2 - b^2*x^2)^2,x]","\frac{8 a^3}{b (a-b x)}+\frac{12 a^2 \log (a-b x)}{b}+5 a x+\frac{b x^2}{2}","\frac{8 a^3}{b (a-b x)}+\frac{12 a^2 \log (a-b x)}{b}+5 a x+\frac{b x^2}{2}",1,"5*a*x + (b*x^2)/2 + (8*a^3)/(b*(a - b*x)) + (12*a^2*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
760,1,31,0,0.0214676,"\int \frac{(a+b x)^4}{\left(a^2-b^2 x^2\right)^2} \, dx","Int[(a + b*x)^4/(a^2 - b^2*x^2)^2,x]","\frac{4 a^2}{b (a-b x)}+\frac{4 a \log (a-b x)}{b}+x","\frac{4 a^2}{b (a-b x)}+\frac{4 a \log (a-b x)}{b}+x",1,"x + (4*a^2)/(b*(a - b*x)) + (4*a*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
761,1,26,0,0.017393,"\int \frac{(a+b x)^3}{\left(a^2-b^2 x^2\right)^2} \, dx","Int[(a + b*x)^3/(a^2 - b^2*x^2)^2,x]","\frac{2 a}{b (a-b x)}+\frac{\log (a-b x)}{b}","\frac{2 a}{b (a-b x)}+\frac{\log (a-b x)}{b}",1,"(2*a)/(b*(a - b*x)) + Log[a - b*x]/b","A",3,2,22,0.09091,1,"{627, 43}"
762,1,12,0,0.0061974,"\int \frac{(a+b x)^2}{\left(a^2-b^2 x^2\right)^2} \, dx","Int[(a + b*x)^2/(a^2 - b^2*x^2)^2,x]","\frac{1}{b (a-b x)}","\frac{1}{b (a-b x)}",1,"1/(b*(a - b*x))","A",2,2,22,0.09091,1,"{627, 32}"
763,1,36,0,0.0261313,"\int \frac{a+b x}{\left(a^2-b^2 x^2\right)^2} \, dx","Int[(a + b*x)/(a^2 - b^2*x^2)^2,x]","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^2 b}+\frac{1}{2 a b (a-b x)}","\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{2 a^2 b}+\frac{1}{2 a b (a-b x)}",1,"1/(2*a*b*(a - b*x)) + ArcTanh[(b*x)/a]/(2*a^2*b)","A",4,3,20,0.1500,1,"{627, 44, 208}"
764,1,70,0,0.0460265,"\int \frac{1}{(a+b x) \left(a^2-b^2 x^2\right)^2} \, dx","Int[1/((a + b*x)*(a^2 - b^2*x^2)^2),x]","\frac{1}{8 a^3 b (a-b x)}-\frac{1}{4 a^3 b (a+b x)}-\frac{1}{8 a^2 b (a+b x)^2}+\frac{3 \tanh ^{-1}\left(\frac{b x}{a}\right)}{8 a^4 b}","\frac{1}{8 a^3 b (a-b x)}-\frac{1}{4 a^3 b (a+b x)}-\frac{1}{8 a^2 b (a+b x)^2}+\frac{3 \tanh ^{-1}\left(\frac{b x}{a}\right)}{8 a^4 b}",1,"1/(8*a^3*b*(a - b*x)) - 1/(8*a^2*b*(a + b*x)^2) - 1/(4*a^3*b*(a + b*x)) + (3*ArcTanh[(b*x)/a])/(8*a^4*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
765,1,87,0,0.0527658,"\int \frac{1}{(a+b x)^2 \left(a^2-b^2 x^2\right)^2} \, dx","Int[1/((a + b*x)^2*(a^2 - b^2*x^2)^2),x]","\frac{1}{16 a^4 b (a-b x)}-\frac{3}{16 a^4 b (a+b x)}-\frac{1}{8 a^3 b (a+b x)^2}-\frac{1}{12 a^2 b (a+b x)^3}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^5 b}","\frac{1}{16 a^4 b (a-b x)}-\frac{3}{16 a^4 b (a+b x)}-\frac{1}{8 a^3 b (a+b x)^2}-\frac{1}{12 a^2 b (a+b x)^3}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^5 b}",1,"1/(16*a^4*b*(a - b*x)) - 1/(12*a^2*b*(a + b*x)^3) - 1/(8*a^3*b*(a + b*x)^2) - 3/(16*a^4*b*(a + b*x)) + ArcTanh[(b*x)/a]/(4*a^5*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
766,1,104,0,0.0658568,"\int \frac{1}{(a+b x)^3 \left(a^2-b^2 x^2\right)^2} \, dx","Int[1/((a + b*x)^3*(a^2 - b^2*x^2)^2),x]","\frac{1}{32 a^5 b (a-b x)}-\frac{1}{8 a^5 b (a+b x)}-\frac{3}{32 a^4 b (a+b x)^2}-\frac{1}{12 a^3 b (a+b x)^3}-\frac{1}{16 a^2 b (a+b x)^4}+\frac{5 \tanh ^{-1}\left(\frac{b x}{a}\right)}{32 a^6 b}","\frac{1}{32 a^5 b (a-b x)}-\frac{1}{8 a^5 b (a+b x)}-\frac{3}{32 a^4 b (a+b x)^2}-\frac{1}{12 a^3 b (a+b x)^3}-\frac{1}{16 a^2 b (a+b x)^4}+\frac{5 \tanh ^{-1}\left(\frac{b x}{a}\right)}{32 a^6 b}",1,"1/(32*a^5*b*(a - b*x)) - 1/(16*a^2*b*(a + b*x)^4) - 1/(12*a^3*b*(a + b*x)^3) - 3/(32*a^4*b*(a + b*x)^2) - 1/(8*a^5*b*(a + b*x)) + (5*ArcTanh[(b*x)/a])/(32*a^6*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
767,1,71,0,0.0514683,"\int \frac{(a+b x)^8}{\left(a^2-b^2 x^2\right)^3} \, dx","Int[(a + b*x)^8/(a^2 - b^2*x^2)^3,x]","\frac{16 a^5}{b (a-b x)^2}-\frac{80 a^4}{b (a-b x)}-\frac{80 a^3 \log (a-b x)}{b}-31 a^2 x-4 a b x^2-\frac{b^2 x^3}{3}","\frac{16 a^5}{b (a-b x)^2}-\frac{80 a^4}{b (a-b x)}-\frac{80 a^3 \log (a-b x)}{b}-31 a^2 x-4 a b x^2-\frac{b^2 x^3}{3}",1,"-31*a^2*x - 4*a*b*x^2 - (b^2*x^3)/3 + (16*a^5)/(b*(a - b*x)^2) - (80*a^4)/(b*(a - b*x)) - (80*a^3*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
768,1,60,0,0.0406074,"\int \frac{(a+b x)^7}{\left(a^2-b^2 x^2\right)^3} \, dx","Int[(a + b*x)^7/(a^2 - b^2*x^2)^3,x]","\frac{8 a^4}{b (a-b x)^2}-\frac{32 a^3}{b (a-b x)}-\frac{24 a^2 \log (a-b x)}{b}-7 a x-\frac{b x^2}{2}","\frac{8 a^4}{b (a-b x)^2}-\frac{32 a^3}{b (a-b x)}-\frac{24 a^2 \log (a-b x)}{b}-7 a x-\frac{b x^2}{2}",1,"-7*a*x - (b*x^2)/2 + (8*a^4)/(b*(a - b*x)^2) - (32*a^3)/(b*(a - b*x)) - (24*a^2*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
769,1,49,0,0.0295678,"\int \frac{(a+b x)^6}{\left(a^2-b^2 x^2\right)^3} \, dx","Int[(a + b*x)^6/(a^2 - b^2*x^2)^3,x]","\frac{4 a^3}{b (a-b x)^2}-\frac{12 a^2}{b (a-b x)}-\frac{6 a \log (a-b x)}{b}-x","\frac{4 a^3}{b (a-b x)^2}-\frac{12 a^2}{b (a-b x)}-\frac{6 a \log (a-b x)}{b}-x",1,"-x + (4*a^3)/(b*(a - b*x)^2) - (12*a^2)/(b*(a - b*x)) - (6*a*Log[a - b*x])/b","A",3,2,22,0.09091,1,"{627, 43}"
770,1,43,0,0.0246914,"\int \frac{(a+b x)^5}{\left(a^2-b^2 x^2\right)^3} \, dx","Int[(a + b*x)^5/(a^2 - b^2*x^2)^3,x]","\frac{2 a^2}{b (a-b x)^2}-\frac{4 a}{b (a-b x)}-\frac{\log (a-b x)}{b}","\frac{2 a^2}{b (a-b x)^2}-\frac{4 a}{b (a-b x)}-\frac{\log (a-b x)}{b}",1,"(2*a^2)/(b*(a - b*x)^2) - (4*a)/(b*(a - b*x)) - Log[a - b*x]/b","A",3,2,22,0.09091,1,"{627, 43}"
771,1,10,0,0.0070928,"\int \frac{(a+b x)^4}{\left(a^2-b^2 x^2\right)^3} \, dx","Int[(a + b*x)^4/(a^2 - b^2*x^2)^3,x]","\frac{x}{(a-b x)^2}","\frac{x}{(a-b x)^2}",1,"x/(a - b*x)^2","A",2,2,22,0.09091,1,"{627, 34}"
772,1,15,0,0.0066662,"\int \frac{(a+b x)^3}{\left(a^2-b^2 x^2\right)^3} \, dx","Int[(a + b*x)^3/(a^2 - b^2*x^2)^3,x]","\frac{1}{2 b (a-b x)^2}","\frac{1}{2 b (a-b x)^2}",1,"1/(2*b*(a - b*x)^2)","A",2,2,22,0.09091,1,"{627, 32}"
773,1,54,0,0.0348784,"\int \frac{(a+b x)^2}{\left(a^2-b^2 x^2\right)^3} \, dx","Int[(a + b*x)^2/(a^2 - b^2*x^2)^3,x]","\frac{1}{4 a^2 b (a-b x)}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^3 b}+\frac{1}{4 a b (a-b x)^2}","\frac{1}{4 a^2 b (a-b x)}+\frac{\tanh ^{-1}\left(\frac{b x}{a}\right)}{4 a^3 b}+\frac{1}{4 a b (a-b x)^2}",1,"1/(4*a*b*(a - b*x)^2) + 1/(4*a^2*b*(a - b*x)) + ArcTanh[(b*x)/a]/(4*a^3*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
774,1,71,0,0.0418414,"\int \frac{a+b x}{\left(a^2-b^2 x^2\right)^3} \, dx","Int[(a + b*x)/(a^2 - b^2*x^2)^3,x]","\frac{1}{4 a^3 b (a-b x)}-\frac{1}{8 a^3 b (a+b x)}+\frac{1}{8 a^2 b (a-b x)^2}+\frac{3 \tanh ^{-1}\left(\frac{b x}{a}\right)}{8 a^4 b}","\frac{1}{4 a^3 b (a-b x)}-\frac{1}{8 a^3 b (a+b x)}+\frac{1}{8 a^2 b (a-b x)^2}+\frac{3 \tanh ^{-1}\left(\frac{b x}{a}\right)}{8 a^4 b}",1,"1/(8*a^2*b*(a - b*x)^2) + 1/(4*a^3*b*(a - b*x)) - 1/(8*a^3*b*(a + b*x)) + (3*ArcTanh[(b*x)/a])/(8*a^4*b)","A",4,3,20,0.1500,1,"{627, 44, 208}"
775,1,105,0,0.0655311,"\int \frac{1}{(a+b x) \left(a^2-b^2 x^2\right)^3} \, dx","Int[1/((a + b*x)*(a^2 - b^2*x^2)^3),x]","\frac{1}{8 a^5 b (a-b x)}-\frac{3}{16 a^5 b (a+b x)}+\frac{1}{32 a^4 b (a-b x)^2}-\frac{3}{32 a^4 b (a+b x)^2}-\frac{1}{24 a^3 b (a+b x)^3}+\frac{5 \tanh ^{-1}\left(\frac{b x}{a}\right)}{16 a^6 b}","\frac{1}{8 a^5 b (a-b x)}-\frac{3}{16 a^5 b (a+b x)}+\frac{1}{32 a^4 b (a-b x)^2}-\frac{3}{32 a^4 b (a+b x)^2}-\frac{1}{24 a^3 b (a+b x)^3}+\frac{5 \tanh ^{-1}\left(\frac{b x}{a}\right)}{16 a^6 b}",1,"1/(32*a^4*b*(a - b*x)^2) + 1/(8*a^5*b*(a - b*x)) - 1/(24*a^3*b*(a + b*x)^3) - 3/(32*a^4*b*(a + b*x)^2) - 3/(16*a^5*b*(a + b*x)) + (5*ArcTanh[(b*x)/a])/(16*a^6*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
776,1,122,0,0.0788462,"\int \frac{1}{(a+b x)^2 \left(a^2-b^2 x^2\right)^3} \, dx","Int[1/((a + b*x)^2*(a^2 - b^2*x^2)^3),x]","\frac{5}{64 a^6 b (a-b x)}-\frac{5}{32 a^6 b (a+b x)}+\frac{1}{64 a^5 b (a-b x)^2}-\frac{3}{32 a^5 b (a+b x)^2}-\frac{1}{16 a^4 b (a+b x)^3}-\frac{1}{32 a^3 b (a+b x)^4}+\frac{15 \tanh ^{-1}\left(\frac{b x}{a}\right)}{64 a^7 b}","\frac{5}{64 a^6 b (a-b x)}-\frac{5}{32 a^6 b (a+b x)}+\frac{1}{64 a^5 b (a-b x)^2}-\frac{3}{32 a^5 b (a+b x)^2}-\frac{1}{16 a^4 b (a+b x)^3}-\frac{1}{32 a^3 b (a+b x)^4}+\frac{15 \tanh ^{-1}\left(\frac{b x}{a}\right)}{64 a^7 b}",1,"1/(64*a^5*b*(a - b*x)^2) + 5/(64*a^6*b*(a - b*x)) - 1/(32*a^3*b*(a + b*x)^4) - 1/(16*a^4*b*(a + b*x)^3) - 3/(32*a^5*b*(a + b*x)^2) - 5/(32*a^6*b*(a + b*x)) + (15*ArcTanh[(b*x)/a])/(64*a^7*b)","A",4,3,22,0.1364,1,"{627, 44, 208}"
777,1,173,0,0.0757016,"\int (a+b x)^4 \sqrt{a^2-b^2 x^2} \, dx","Int[(a + b*x)^4*Sqrt[a^2 - b^2*x^2],x]","\frac{21}{16} a^4 x \sqrt{a^2-b^2 x^2}-\frac{7 a^3 \left(a^2-b^2 x^2\right)^{3/2}}{8 b}-\frac{21 a^2 (a+b x) \left(a^2-b^2 x^2\right)^{3/2}}{40 b}-\frac{3 a (a+b x)^2 \left(a^2-b^2 x^2\right)^{3/2}}{10 b}-\frac{(a+b x)^3 \left(a^2-b^2 x^2\right)^{3/2}}{6 b}+\frac{21 a^6 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{16 b}","\frac{21}{16} a^4 x \sqrt{a^2-b^2 x^2}-\frac{7 a^3 \left(a^2-b^2 x^2\right)^{3/2}}{8 b}-\frac{21 a^2 (a+b x) \left(a^2-b^2 x^2\right)^{3/2}}{40 b}-\frac{3 a (a+b x)^2 \left(a^2-b^2 x^2\right)^{3/2}}{10 b}-\frac{(a+b x)^3 \left(a^2-b^2 x^2\right)^{3/2}}{6 b}+\frac{21 a^6 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{16 b}",1,"(21*a^4*x*Sqrt[a^2 - b^2*x^2])/16 - (7*a^3*(a^2 - b^2*x^2)^(3/2))/(8*b) - (21*a^2*(a + b*x)*(a^2 - b^2*x^2)^(3/2))/(40*b) - (3*a*(a + b*x)^2*(a^2 - b^2*x^2)^(3/2))/(10*b) - ((a + b*x)^3*(a^2 - b^2*x^2)^(3/2))/(6*b) + (21*a^6*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/(16*b)","A",7,5,24,0.2083,1,"{671, 641, 195, 217, 203}"
778,1,140,0,0.0501128,"\int (a+b x)^3 \sqrt{a^2-b^2 x^2} \, dx","Int[(a + b*x)^3*Sqrt[a^2 - b^2*x^2],x]","\frac{7}{8} a^3 x \sqrt{a^2-b^2 x^2}-\frac{7 a^2 \left(a^2-b^2 x^2\right)^{3/2}}{12 b}-\frac{7 a (a+b x) \left(a^2-b^2 x^2\right)^{3/2}}{20 b}-\frac{(a+b x)^2 \left(a^2-b^2 x^2\right)^{3/2}}{5 b}+\frac{7 a^5 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{8 b}","\frac{7}{8} a^3 x \sqrt{a^2-b^2 x^2}-\frac{7 a^2 \left(a^2-b^2 x^2\right)^{3/2}}{12 b}-\frac{7 a (a+b x) \left(a^2-b^2 x^2\right)^{3/2}}{20 b}-\frac{(a+b x)^2 \left(a^2-b^2 x^2\right)^{3/2}}{5 b}+\frac{7 a^5 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{8 b}",1,"(7*a^3*x*Sqrt[a^2 - b^2*x^2])/8 - (7*a^2*(a^2 - b^2*x^2)^(3/2))/(12*b) - (7*a*(a + b*x)*(a^2 - b^2*x^2)^(3/2))/(20*b) - ((a + b*x)^2*(a^2 - b^2*x^2)^(3/2))/(5*b) + (7*a^5*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/(8*b)","A",6,5,24,0.2083,1,"{671, 641, 195, 217, 203}"
779,1,107,0,0.0339475,"\int (a+b x)^2 \sqrt{a^2-b^2 x^2} \, dx","Int[(a + b*x)^2*Sqrt[a^2 - b^2*x^2],x]","\frac{5}{8} a^2 x \sqrt{a^2-b^2 x^2}-\frac{5 a \left(a^2-b^2 x^2\right)^{3/2}}{12 b}-\frac{(a+b x) \left(a^2-b^2 x^2\right)^{3/2}}{4 b}+\frac{5 a^4 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{8 b}","\frac{5}{8} a^2 x \sqrt{a^2-b^2 x^2}-\frac{5 a \left(a^2-b^2 x^2\right)^{3/2}}{12 b}-\frac{(a+b x) \left(a^2-b^2 x^2\right)^{3/2}}{4 b}+\frac{5 a^4 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{8 b}",1,"(5*a^2*x*Sqrt[a^2 - b^2*x^2])/8 - (5*a*(a^2 - b^2*x^2)^(3/2))/(12*b) - ((a + b*x)*(a^2 - b^2*x^2)^(3/2))/(4*b) + (5*a^4*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/(8*b)","A",5,5,24,0.2083,1,"{671, 641, 195, 217, 203}"
780,1,76,0,0.0201091,"\int (a+b x) \sqrt{a^2-b^2 x^2} \, dx","Int[(a + b*x)*Sqrt[a^2 - b^2*x^2],x]","\frac{1}{2} a x \sqrt{a^2-b^2 x^2}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{3 b}+\frac{a^3 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{2 b}","\frac{1}{2} a x \sqrt{a^2-b^2 x^2}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{3 b}+\frac{a^3 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{2 b}",1,"(a*x*Sqrt[a^2 - b^2*x^2])/2 - (a^2 - b^2*x^2)^(3/2)/(3*b) + (a^3*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/(2*b)","A",4,4,22,0.1818,1,"{641, 195, 217, 203}"
781,1,46,0,0.0161951,"\int \frac{\sqrt{a^2-b^2 x^2}}{a+b x} \, dx","Int[Sqrt[a^2 - b^2*x^2]/(a + b*x),x]","\frac{\sqrt{a^2-b^2 x^2}}{b}+\frac{a \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}","\frac{\sqrt{a^2-b^2 x^2}}{b}+\frac{a \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}",1,"Sqrt[a^2 - b^2*x^2]/b + (a*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/b","A",3,3,24,0.1250,1,"{665, 217, 203}"
782,1,54,0,0.0140286,"\int \frac{\sqrt{a^2-b^2 x^2}}{(a+b x)^2} \, dx","Int[Sqrt[a^2 - b^2*x^2]/(a + b*x)^2,x]","-\frac{2 \sqrt{a^2-b^2 x^2}}{b (a+b x)}-\frac{\tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}","-\frac{2 \sqrt{a^2-b^2 x^2}}{b (a+b x)}-\frac{\tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}",1,"(-2*Sqrt[a^2 - b^2*x^2])/(b*(a + b*x)) - ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]]/b","A",3,3,24,0.1250,1,"{663, 217, 203}"
783,1,33,0,0.0094301,"\int \frac{\sqrt{a^2-b^2 x^2}}{(a+b x)^3} \, dx","Int[Sqrt[a^2 - b^2*x^2]/(a + b*x)^3,x]","-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{3 a b (a+b x)^3}","-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{3 a b (a+b x)^3}",1,"-(a^2 - b^2*x^2)^(3/2)/(3*a*b*(a + b*x)^3)","A",1,1,24,0.04167,1,"{651}"
784,1,67,0,0.0208856,"\int \frac{\sqrt{a^2-b^2 x^2}}{(a+b x)^4} \, dx","Int[Sqrt[a^2 - b^2*x^2]/(a + b*x)^4,x]","-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{15 a^2 b (a+b x)^3}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{5 a b (a+b x)^4}","-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{15 a^2 b (a+b x)^3}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{5 a b (a+b x)^4}",1,"-(a^2 - b^2*x^2)^(3/2)/(5*a*b*(a + b*x)^4) - (a^2 - b^2*x^2)^(3/2)/(15*a^2*b*(a + b*x)^3)","A",2,2,24,0.08333,1,"{659, 651}"
785,1,100,0,0.0357099,"\int \frac{\sqrt{a^2-b^2 x^2}}{(a+b x)^5} \, dx","Int[Sqrt[a^2 - b^2*x^2]/(a + b*x)^5,x]","-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{105 a^3 b (a+b x)^3}-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{35 a^2 b (a+b x)^4}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{7 a b (a+b x)^5}","-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{105 a^3 b (a+b x)^3}-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{35 a^2 b (a+b x)^4}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{7 a b (a+b x)^5}",1,"-(a^2 - b^2*x^2)^(3/2)/(7*a*b*(a + b*x)^5) - (2*(a^2 - b^2*x^2)^(3/2))/(35*a^2*b*(a + b*x)^4) - (2*(a^2 - b^2*x^2)^(3/2))/(105*a^3*b*(a + b*x)^3)","A",3,2,24,0.08333,1,"{659, 651}"
786,1,133,0,0.0533064,"\int \frac{\sqrt{a^2-b^2 x^2}}{(a+b x)^6} \, dx","Int[Sqrt[a^2 - b^2*x^2]/(a + b*x)^6,x]","-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{315 a^4 b (a+b x)^3}-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{105 a^3 b (a+b x)^4}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{21 a^2 b (a+b x)^5}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{9 a b (a+b x)^6}","-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{315 a^4 b (a+b x)^3}-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{105 a^3 b (a+b x)^4}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{21 a^2 b (a+b x)^5}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{9 a b (a+b x)^6}",1,"-(a^2 - b^2*x^2)^(3/2)/(9*a*b*(a + b*x)^6) - (a^2 - b^2*x^2)^(3/2)/(21*a^2*b*(a + b*x)^5) - (2*(a^2 - b^2*x^2)^(3/2))/(105*a^3*b*(a + b*x)^4) - (2*(a^2 - b^2*x^2)^(3/2))/(315*a^4*b*(a + b*x)^3)","A",4,2,24,0.08333,1,"{659, 651}"
787,1,166,0,0.0708873,"\int \frac{\sqrt{a^2-b^2 x^2}}{(a+b x)^7} \, dx","Int[Sqrt[a^2 - b^2*x^2]/(a + b*x)^7,x]","-\frac{8 \left(a^2-b^2 x^2\right)^{3/2}}{3465 a^5 b (a+b x)^3}-\frac{8 \left(a^2-b^2 x^2\right)^{3/2}}{1155 a^4 b (a+b x)^4}-\frac{4 \left(a^2-b^2 x^2\right)^{3/2}}{231 a^3 b (a+b x)^5}-\frac{4 \left(a^2-b^2 x^2\right)^{3/2}}{99 a^2 b (a+b x)^6}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{11 a b (a+b x)^7}","-\frac{8 \left(a^2-b^2 x^2\right)^{3/2}}{3465 a^5 b (a+b x)^3}-\frac{8 \left(a^2-b^2 x^2\right)^{3/2}}{1155 a^4 b (a+b x)^4}-\frac{4 \left(a^2-b^2 x^2\right)^{3/2}}{231 a^3 b (a+b x)^5}-\frac{4 \left(a^2-b^2 x^2\right)^{3/2}}{99 a^2 b (a+b x)^6}-\frac{\left(a^2-b^2 x^2\right)^{3/2}}{11 a b (a+b x)^7}",1,"-(a^2 - b^2*x^2)^(3/2)/(11*a*b*(a + b*x)^7) - (4*(a^2 - b^2*x^2)^(3/2))/(99*a^2*b*(a + b*x)^6) - (4*(a^2 - b^2*x^2)^(3/2))/(231*a^3*b*(a + b*x)^5) - (8*(a^2 - b^2*x^2)^(3/2))/(1155*a^4*b*(a + b*x)^4) - (8*(a^2 - b^2*x^2)^(3/2))/(3465*a^5*b*(a + b*x)^3)","A",5,2,24,0.08333,1,"{659, 651}"
788,1,164,0,0.0629918,"\int (a+b x)^3 \left(a^2-b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)^3*(a^2 - b^2*x^2)^(3/2),x]","\frac{9}{16} a^5 x \sqrt{a^2-b^2 x^2}+\frac{3}{8} a^3 x \left(a^2-b^2 x^2\right)^{3/2}-\frac{3 a^2 \left(a^2-b^2 x^2\right)^{5/2}}{10 b}-\frac{3 a (a+b x) \left(a^2-b^2 x^2\right)^{5/2}}{14 b}-\frac{(a+b x)^2 \left(a^2-b^2 x^2\right)^{5/2}}{7 b}+\frac{9 a^7 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{16 b}","\frac{9}{16} a^5 x \sqrt{a^2-b^2 x^2}+\frac{3}{8} a^3 x \left(a^2-b^2 x^2\right)^{3/2}-\frac{3 a^2 \left(a^2-b^2 x^2\right)^{5/2}}{10 b}-\frac{3 a (a+b x) \left(a^2-b^2 x^2\right)^{5/2}}{14 b}-\frac{(a+b x)^2 \left(a^2-b^2 x^2\right)^{5/2}}{7 b}+\frac{9 a^7 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{16 b}",1,"(9*a^5*x*Sqrt[a^2 - b^2*x^2])/16 + (3*a^3*x*(a^2 - b^2*x^2)^(3/2))/8 - (3*a^2*(a^2 - b^2*x^2)^(5/2))/(10*b) - (3*a*(a + b*x)*(a^2 - b^2*x^2)^(5/2))/(14*b) - ((a + b*x)^2*(a^2 - b^2*x^2)^(5/2))/(7*b) + (9*a^7*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/(16*b)","A",7,5,24,0.2083,1,"{671, 641, 195, 217, 203}"
789,1,131,0,0.0437812,"\int (a+b x)^2 \left(a^2-b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)^2*(a^2 - b^2*x^2)^(3/2),x]","\frac{7}{16} a^4 x \sqrt{a^2-b^2 x^2}+\frac{7}{24} a^2 x \left(a^2-b^2 x^2\right)^{3/2}-\frac{7 a \left(a^2-b^2 x^2\right)^{5/2}}{30 b}-\frac{(a+b x) \left(a^2-b^2 x^2\right)^{5/2}}{6 b}+\frac{7 a^6 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{16 b}","\frac{7}{16} a^4 x \sqrt{a^2-b^2 x^2}+\frac{7}{24} a^2 x \left(a^2-b^2 x^2\right)^{3/2}-\frac{7 a \left(a^2-b^2 x^2\right)^{5/2}}{30 b}-\frac{(a+b x) \left(a^2-b^2 x^2\right)^{5/2}}{6 b}+\frac{7 a^6 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{16 b}",1,"(7*a^4*x*Sqrt[a^2 - b^2*x^2])/16 + (7*a^2*x*(a^2 - b^2*x^2)^(3/2))/24 - (7*a*(a^2 - b^2*x^2)^(5/2))/(30*b) - ((a + b*x)*(a^2 - b^2*x^2)^(5/2))/(6*b) + (7*a^6*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/(16*b)","A",6,5,24,0.2083,1,"{671, 641, 195, 217, 203}"
790,1,100,0,0.0262414,"\int (a+b x) \left(a^2-b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(a^2 - b^2*x^2)^(3/2),x]","\frac{3}{8} a^3 x \sqrt{a^2-b^2 x^2}+\frac{1}{4} a x \left(a^2-b^2 x^2\right)^{3/2}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{5 b}+\frac{3 a^5 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{8 b}","\frac{3}{8} a^3 x \sqrt{a^2-b^2 x^2}+\frac{1}{4} a x \left(a^2-b^2 x^2\right)^{3/2}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{5 b}+\frac{3 a^5 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{8 b}",1,"(3*a^3*x*Sqrt[a^2 - b^2*x^2])/8 + (a*x*(a^2 - b^2*x^2)^(3/2))/4 - (a^2 - b^2*x^2)^(5/2)/(5*b) + (3*a^5*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/(8*b)","A",5,4,22,0.1818,1,"{641, 195, 217, 203}"
791,1,76,0,0.0221436,"\int \frac{\left(a^2-b^2 x^2\right)^{3/2}}{a+b x} \, dx","Int[(a^2 - b^2*x^2)^(3/2)/(a + b*x),x]","\frac{1}{2} a x \sqrt{a^2-b^2 x^2}+\frac{\left(a^2-b^2 x^2\right)^{3/2}}{3 b}+\frac{a^3 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{2 b}","\frac{1}{2} a x \sqrt{a^2-b^2 x^2}+\frac{\left(a^2-b^2 x^2\right)^{3/2}}{3 b}+\frac{a^3 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{2 b}",1,"(a*x*Sqrt[a^2 - b^2*x^2])/2 + (a^2 - b^2*x^2)^(3/2)/(3*b) + (a^3*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/(2*b)","A",4,4,24,0.1667,1,"{665, 195, 217, 203}"
792,1,85,0,0.0293329,"\int \frac{\left(a^2-b^2 x^2\right)^{3/2}}{(a+b x)^2} \, dx","Int[(a^2 - b^2*x^2)^(3/2)/(a + b*x)^2,x]","\frac{3 a \sqrt{a^2-b^2 x^2}}{2 b}+\frac{\left(a^2-b^2 x^2\right)^{3/2}}{2 b (a+b x)}+\frac{3 a^2 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{2 b}","\frac{3 a \sqrt{a^2-b^2 x^2}}{2 b}+\frac{\left(a^2-b^2 x^2\right)^{3/2}}{2 b (a+b x)}+\frac{3 a^2 \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{2 b}",1,"(3*a*Sqrt[a^2 - b^2*x^2])/(2*b) + (a^2 - b^2*x^2)^(3/2)/(2*b*(a + b*x)) + (3*a^2*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/(2*b)","A",4,3,24,0.1250,1,"{665, 217, 203}"
793,1,76,0,0.0277218,"\int \frac{\left(a^2-b^2 x^2\right)^{3/2}}{(a+b x)^3} \, dx","Int[(a^2 - b^2*x^2)^(3/2)/(a + b*x)^3,x]","-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{b (a+b x)^2}-\frac{3 \sqrt{a^2-b^2 x^2}}{b}-\frac{3 a \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}","-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{b (a+b x)^2}-\frac{3 \sqrt{a^2-b^2 x^2}}{b}-\frac{3 a \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}",1,"(-3*Sqrt[a^2 - b^2*x^2])/b - (2*(a^2 - b^2*x^2)^(3/2))/(b*(a + b*x)^2) - (3*a*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/b","A",4,4,24,0.1667,1,"{663, 665, 217, 203}"
794,1,83,0,0.0229014,"\int \frac{\left(a^2-b^2 x^2\right)^{3/2}}{(a+b x)^4} \, dx","Int[(a^2 - b^2*x^2)^(3/2)/(a + b*x)^4,x]","-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{3 b (a+b x)^3}+\frac{2 \sqrt{a^2-b^2 x^2}}{b (a+b x)}+\frac{\tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}","-\frac{2 \left(a^2-b^2 x^2\right)^{3/2}}{3 b (a+b x)^3}+\frac{2 \sqrt{a^2-b^2 x^2}}{b (a+b x)}+\frac{\tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}",1,"(2*Sqrt[a^2 - b^2*x^2])/(b*(a + b*x)) - (2*(a^2 - b^2*x^2)^(3/2))/(3*b*(a + b*x)^3) + ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]]/b","A",4,3,24,0.1250,1,"{663, 217, 203}"
795,1,33,0,0.0090839,"\int \frac{\left(a^2-b^2 x^2\right)^{3/2}}{(a+b x)^5} \, dx","Int[(a^2 - b^2*x^2)^(3/2)/(a + b*x)^5,x]","-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{5 a b (a+b x)^5}","-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{5 a b (a+b x)^5}",1,"-(a^2 - b^2*x^2)^(5/2)/(5*a*b*(a + b*x)^5)","A",1,1,24,0.04167,1,"{651}"
796,1,67,0,0.0211747,"\int \frac{\left(a^2-b^2 x^2\right)^{3/2}}{(a+b x)^6} \, dx","Int[(a^2 - b^2*x^2)^(3/2)/(a + b*x)^6,x]","-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{35 a^2 b (a+b x)^5}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{7 a b (a+b x)^6}","-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{35 a^2 b (a+b x)^5}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{7 a b (a+b x)^6}",1,"-(a^2 - b^2*x^2)^(5/2)/(7*a*b*(a + b*x)^6) - (a^2 - b^2*x^2)^(5/2)/(35*a^2*b*(a + b*x)^5)","A",2,2,24,0.08333,1,"{659, 651}"
797,1,100,0,0.0367267,"\int \frac{\left(a^2-b^2 x^2\right)^{3/2}}{(a+b x)^7} \, dx","Int[(a^2 - b^2*x^2)^(3/2)/(a + b*x)^7,x]","-\frac{2 \left(a^2-b^2 x^2\right)^{5/2}}{315 a^3 b (a+b x)^5}-\frac{2 \left(a^2-b^2 x^2\right)^{5/2}}{63 a^2 b (a+b x)^6}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{9 a b (a+b x)^7}","-\frac{2 \left(a^2-b^2 x^2\right)^{5/2}}{315 a^3 b (a+b x)^5}-\frac{2 \left(a^2-b^2 x^2\right)^{5/2}}{63 a^2 b (a+b x)^6}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{9 a b (a+b x)^7}",1,"-(a^2 - b^2*x^2)^(5/2)/(9*a*b*(a + b*x)^7) - (2*(a^2 - b^2*x^2)^(5/2))/(63*a^2*b*(a + b*x)^6) - (2*(a^2 - b^2*x^2)^(5/2))/(315*a^3*b*(a + b*x)^5)","A",3,2,24,0.08333,1,"{659, 651}"
798,1,133,0,0.0554768,"\int \frac{\left(a^2-b^2 x^2\right)^{3/2}}{(a+b x)^8} \, dx","Int[(a^2 - b^2*x^2)^(3/2)/(a + b*x)^8,x]","-\frac{2 \left(a^2-b^2 x^2\right)^{5/2}}{1155 a^4 b (a+b x)^5}-\frac{2 \left(a^2-b^2 x^2\right)^{5/2}}{231 a^3 b (a+b x)^6}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{33 a^2 b (a+b x)^7}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{11 a b (a+b x)^8}","-\frac{2 \left(a^2-b^2 x^2\right)^{5/2}}{1155 a^4 b (a+b x)^5}-\frac{2 \left(a^2-b^2 x^2\right)^{5/2}}{231 a^3 b (a+b x)^6}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{33 a^2 b (a+b x)^7}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{11 a b (a+b x)^8}",1,"-(a^2 - b^2*x^2)^(5/2)/(11*a*b*(a + b*x)^8) - (a^2 - b^2*x^2)^(5/2)/(33*a^2*b*(a + b*x)^7) - (2*(a^2 - b^2*x^2)^(5/2))/(231*a^3*b*(a + b*x)^6) - (2*(a^2 - b^2*x^2)^(5/2))/(1155*a^4*b*(a + b*x)^5)","A",4,2,24,0.08333,1,"{659, 651}"
799,1,166,0,0.0750511,"\int \frac{\left(a^2-b^2 x^2\right)^{3/2}}{(a+b x)^9} \, dx","Int[(a^2 - b^2*x^2)^(3/2)/(a + b*x)^9,x]","-\frac{8 \left(a^2-b^2 x^2\right)^{5/2}}{15015 a^5 b (a+b x)^5}-\frac{8 \left(a^2-b^2 x^2\right)^{5/2}}{3003 a^4 b (a+b x)^6}-\frac{4 \left(a^2-b^2 x^2\right)^{5/2}}{429 a^3 b (a+b x)^7}-\frac{4 \left(a^2-b^2 x^2\right)^{5/2}}{143 a^2 b (a+b x)^8}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{13 a b (a+b x)^9}","-\frac{8 \left(a^2-b^2 x^2\right)^{5/2}}{15015 a^5 b (a+b x)^5}-\frac{8 \left(a^2-b^2 x^2\right)^{5/2}}{3003 a^4 b (a+b x)^6}-\frac{4 \left(a^2-b^2 x^2\right)^{5/2}}{429 a^3 b (a+b x)^7}-\frac{4 \left(a^2-b^2 x^2\right)^{5/2}}{143 a^2 b (a+b x)^8}-\frac{\left(a^2-b^2 x^2\right)^{5/2}}{13 a b (a+b x)^9}",1,"-(a^2 - b^2*x^2)^(5/2)/(13*a*b*(a + b*x)^9) - (4*(a^2 - b^2*x^2)^(5/2))/(143*a^2*b*(a + b*x)^8) - (4*(a^2 - b^2*x^2)^(5/2))/(429*a^3*b*(a + b*x)^7) - (8*(a^2 - b^2*x^2)^(5/2))/(3003*a^4*b*(a + b*x)^6) - (8*(a^2 - b^2*x^2)^(5/2))/(15015*a^5*b*(a + b*x)^5)","A",5,2,24,0.08333,1,"{659, 651}"
800,1,212,0,0.0900898,"\int (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{91}{256} d^9 x \sqrt{d^2-e^2 x^2}+\frac{91}{384} d^7 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{91}{480} d^5 x \left(d^2-e^2 x^2\right)^{5/2}+\frac{13}{80} d^3 x \left(d^2-e^2 x^2\right)^{7/2}-\frac{13 d^2 \left(d^2-e^2 x^2\right)^{9/2}}{90 e}-\frac{13 d (d+e x) \left(d^2-e^2 x^2\right)^{9/2}}{110 e}-\frac{(d+e x)^2 \left(d^2-e^2 x^2\right)^{9/2}}{11 e}+\frac{91 d^{11} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{256 e}","\frac{91}{256} d^9 x \sqrt{d^2-e^2 x^2}+\frac{91}{384} d^7 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{91}{480} d^5 x \left(d^2-e^2 x^2\right)^{5/2}+\frac{13}{80} d^3 x \left(d^2-e^2 x^2\right)^{7/2}-\frac{13 d^2 \left(d^2-e^2 x^2\right)^{9/2}}{90 e}-\frac{13 d (d+e x) \left(d^2-e^2 x^2\right)^{9/2}}{110 e}-\frac{(d+e x)^2 \left(d^2-e^2 x^2\right)^{9/2}}{11 e}+\frac{91 d^{11} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{256 e}",1,"(91*d^9*x*Sqrt[d^2 - e^2*x^2])/256 + (91*d^7*x*(d^2 - e^2*x^2)^(3/2))/384 + (91*d^5*x*(d^2 - e^2*x^2)^(5/2))/480 + (13*d^3*x*(d^2 - e^2*x^2)^(7/2))/80 - (13*d^2*(d^2 - e^2*x^2)^(9/2))/(90*e) - (13*d*(d + e*x)*(d^2 - e^2*x^2)^(9/2))/(110*e) - ((d + e*x)^2*(d^2 - e^2*x^2)^(9/2))/(11*e) + (91*d^11*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(256*e)","A",9,5,24,0.2083,1,"{671, 641, 195, 217, 203}"
801,1,179,0,0.0669763,"\int (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{77}{256} d^8 x \sqrt{d^2-e^2 x^2}+\frac{77}{384} d^6 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{77}{480} d^4 x \left(d^2-e^2 x^2\right)^{5/2}+\frac{11}{80} d^2 x \left(d^2-e^2 x^2\right)^{7/2}-\frac{11 d \left(d^2-e^2 x^2\right)^{9/2}}{90 e}-\frac{(d+e x) \left(d^2-e^2 x^2\right)^{9/2}}{10 e}+\frac{77 d^{10} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{256 e}","\frac{77}{256} d^8 x \sqrt{d^2-e^2 x^2}+\frac{77}{384} d^6 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{77}{480} d^4 x \left(d^2-e^2 x^2\right)^{5/2}+\frac{11}{80} d^2 x \left(d^2-e^2 x^2\right)^{7/2}-\frac{11 d \left(d^2-e^2 x^2\right)^{9/2}}{90 e}-\frac{(d+e x) \left(d^2-e^2 x^2\right)^{9/2}}{10 e}+\frac{77 d^{10} \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{256 e}",1,"(77*d^8*x*Sqrt[d^2 - e^2*x^2])/256 + (77*d^6*x*(d^2 - e^2*x^2)^(3/2))/384 + (77*d^4*x*(d^2 - e^2*x^2)^(5/2))/480 + (11*d^2*x*(d^2 - e^2*x^2)^(7/2))/80 - (11*d*(d^2 - e^2*x^2)^(9/2))/(90*e) - ((d + e*x)*(d^2 - e^2*x^2)^(9/2))/(10*e) + (77*d^10*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(256*e)","A",8,5,24,0.2083,1,"{671, 641, 195, 217, 203}"
802,1,148,0,0.0466568,"\int (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{35}{128} d^7 x \sqrt{d^2-e^2 x^2}+\frac{35}{192} d^5 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{7}{48} d^3 x \left(d^2-e^2 x^2\right)^{5/2}+\frac{1}{8} d x \left(d^2-e^2 x^2\right)^{7/2}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{9 e}+\frac{35 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e}","\frac{35}{128} d^7 x \sqrt{d^2-e^2 x^2}+\frac{35}{192} d^5 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{7}{48} d^3 x \left(d^2-e^2 x^2\right)^{5/2}+\frac{1}{8} d x \left(d^2-e^2 x^2\right)^{7/2}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{9 e}+\frac{35 d^9 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{128 e}",1,"(35*d^7*x*Sqrt[d^2 - e^2*x^2])/128 + (35*d^5*x*(d^2 - e^2*x^2)^(3/2))/192 + (7*d^3*x*(d^2 - e^2*x^2)^(5/2))/48 + (d*x*(d^2 - e^2*x^2)^(7/2))/8 - (d^2 - e^2*x^2)^(9/2)/(9*e) + (35*d^9*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(128*e)","A",7,4,22,0.1818,1,"{641, 195, 217, 203}"
803,1,124,0,0.0385643,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{d+e x} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x),x]","\frac{5}{16} d^5 x \sqrt{d^2-e^2 x^2}+\frac{5}{24} d^3 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{1}{6} d x \left(d^2-e^2 x^2\right)^{5/2}+\frac{\left(d^2-e^2 x^2\right)^{7/2}}{7 e}+\frac{5 d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e}","\frac{5}{16} d^5 x \sqrt{d^2-e^2 x^2}+\frac{5}{24} d^3 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{1}{6} d x \left(d^2-e^2 x^2\right)^{5/2}+\frac{\left(d^2-e^2 x^2\right)^{7/2}}{7 e}+\frac{5 d^7 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e}",1,"(5*d^5*x*Sqrt[d^2 - e^2*x^2])/16 + (5*d^3*x*(d^2 - e^2*x^2)^(3/2))/24 + (d*x*(d^2 - e^2*x^2)^(5/2))/6 + (d^2 - e^2*x^2)^(7/2)/(7*e) + (5*d^7*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e)","A",6,4,24,0.1667,1,"{665, 195, 217, 203}"
804,1,132,0,0.0508933,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^2} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^2,x]","\frac{7}{16} d^4 x \sqrt{d^2-e^2 x^2}+\frac{7}{24} d^2 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{7 d \left(d^2-e^2 x^2\right)^{5/2}}{30 e}+\frac{(d-e x) \left(d^2-e^2 x^2\right)^{5/2}}{6 e}+\frac{7 d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e}","\frac{7}{16} d^4 x \sqrt{d^2-e^2 x^2}+\frac{7}{24} d^2 x \left(d^2-e^2 x^2\right)^{3/2}+\frac{7 d \left(d^2-e^2 x^2\right)^{5/2}}{30 e}+\frac{(d-e x) \left(d^2-e^2 x^2\right)^{5/2}}{6 e}+\frac{7 d^6 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{16 e}",1,"(7*d^4*x*Sqrt[d^2 - e^2*x^2])/16 + (7*d^2*x*(d^2 - e^2*x^2)^(3/2))/24 + (7*d*(d^2 - e^2*x^2)^(5/2))/(30*e) + ((d - e*x)*(d^2 - e^2*x^2)^(5/2))/(6*e) + (7*d^6*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e)","A",7,6,24,0.2500,1,"{655, 671, 641, 195, 217, 203}"
805,1,142,0,0.0594916,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^3} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^3,x]","\frac{7}{8} d^3 x \sqrt{d^2-e^2 x^2}+\frac{7 d^2 \left(d^2-e^2 x^2\right)^{3/2}}{12 e}+\frac{7 d (d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{20 e}+\frac{(d-e x)^2 \left(d^2-e^2 x^2\right)^{3/2}}{5 e}+\frac{7 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}","\frac{7}{8} d^3 x \sqrt{d^2-e^2 x^2}+\frac{7 d^2 \left(d^2-e^2 x^2\right)^{3/2}}{12 e}+\frac{7 d (d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{20 e}+\frac{(d-e x)^2 \left(d^2-e^2 x^2\right)^{3/2}}{5 e}+\frac{7 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}",1,"(7*d^3*x*Sqrt[d^2 - e^2*x^2])/8 + (7*d^2*(d^2 - e^2*x^2)^(3/2))/(12*e) + (7*d*(d - e*x)*(d^2 - e^2*x^2)^(3/2))/(20*e) + ((d - e*x)^2*(d^2 - e^2*x^2)^(3/2))/(5*e) + (7*d^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e)","A",7,6,24,0.2500,1,"{655, 671, 641, 195, 217, 203}"
806,1,136,0,0.0566787,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^4} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^4,x]","\frac{35}{8} d^2 x \sqrt{d^2-e^2 x^2}+\frac{35 d \left(d^2-e^2 x^2\right)^{3/2}}{12 e}+\frac{2 \left(d^2-e^2 x^2\right)^{7/2}}{e (d+e x)^3}+\frac{7 (d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{4 e}+\frac{35 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}","\frac{35}{8} d^2 x \sqrt{d^2-e^2 x^2}+\frac{35 d \left(d^2-e^2 x^2\right)^{3/2}}{12 e}+\frac{2 \left(d^2-e^2 x^2\right)^{7/2}}{e (d+e x)^3}+\frac{7 (d-e x) \left(d^2-e^2 x^2\right)^{3/2}}{4 e}+\frac{35 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}",1,"(35*d^2*x*Sqrt[d^2 - e^2*x^2])/8 + (35*d*(d^2 - e^2*x^2)^(3/2))/(12*e) + (7*(d - e*x)*(d^2 - e^2*x^2)^(3/2))/(4*e) + (2*(d^2 - e^2*x^2)^(7/2))/(e*(d + e*x)^3) + (35*d^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e)","A",7,7,24,0.2917,1,"{663, 655, 671, 641, 195, 217, 203}"
807,1,132,0,0.0508519,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^5} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^5,x]","-\frac{2 \left(d^2-e^2 x^2\right)^{7/2}}{e (d+e x)^4}-\frac{14 \left(d^2-e^2 x^2\right)^{5/2}}{e (d+e x)^2}-\frac{35 \left(d^2-e^2 x^2\right)^{3/2}}{3 e}-\frac{35}{2} d x \sqrt{d^2-e^2 x^2}-\frac{35 d^3 \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)^{7/2}}{e (d+e x)^4}-\frac{14 \left(d^2-e^2 x^2\right)^{5/2}}{e (d+e x)^2}-\frac{35 \left(d^2-e^2 x^2\right)^{3/2}}{3 e}-\frac{35}{2} d x \sqrt{d^2-e^2 x^2}-\frac{35 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}",1,"(-35*d*x*Sqrt[d^2 - e^2*x^2])/2 - (35*(d^2 - e^2*x^2)^(3/2))/(3*e) - (14*(d^2 - e^2*x^2)^(5/2))/(e*(d + e*x)^2) - (2*(d^2 - e^2*x^2)^(7/2))/(e*(d + e*x)^4) - (35*d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e)","A",6,5,24,0.2083,1,"{663, 665, 195, 217, 203}"
808,1,145,0,0.0587709,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^6} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^6,x]","-\frac{2 \left(d^2-e^2 x^2\right)^{7/2}}{3 e (d+e x)^5}+\frac{14 \left(d^2-e^2 x^2\right)^{5/2}}{3 e (d+e x)^3}+\frac{35 \left(d^2-e^2 x^2\right)^{3/2}}{6 e (d+e x)}+\frac{35 d \sqrt{d^2-e^2 x^2}}{2 e}+\frac{35 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)^{7/2}}{3 e (d+e x)^5}+\frac{14 \left(d^2-e^2 x^2\right)^{5/2}}{3 e (d+e x)^3}+\frac{35 \left(d^2-e^2 x^2\right)^{3/2}}{6 e (d+e x)}+\frac{35 d \sqrt{d^2-e^2 x^2}}{2 e}+\frac{35 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}",1,"(35*d*Sqrt[d^2 - e^2*x^2])/(2*e) + (35*(d^2 - e^2*x^2)^(3/2))/(6*e*(d + e*x)) + (14*(d^2 - e^2*x^2)^(5/2))/(3*e*(d + e*x)^3) - (2*(d^2 - e^2*x^2)^(7/2))/(3*e*(d + e*x)^5) + (35*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e)","A",6,4,24,0.1667,1,"{663, 665, 217, 203}"
809,1,138,0,0.0588687,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^7} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^7,x]","-\frac{2 \left(d^2-e^2 x^2\right)^{7/2}}{5 e (d+e x)^6}+\frac{14 \left(d^2-e^2 x^2\right)^{5/2}}{15 e (d+e x)^4}-\frac{14 \left(d^2-e^2 x^2\right)^{3/2}}{3 e (d+e x)^2}-\frac{7 \sqrt{d^2-e^2 x^2}}{e}-\frac{7 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}","-\frac{2 \left(d^2-e^2 x^2\right)^{7/2}}{5 e (d+e x)^6}+\frac{14 \left(d^2-e^2 x^2\right)^{5/2}}{15 e (d+e x)^4}-\frac{14 \left(d^2-e^2 x^2\right)^{3/2}}{3 e (d+e x)^2}-\frac{7 \sqrt{d^2-e^2 x^2}}{e}-\frac{7 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}",1,"(-7*Sqrt[d^2 - e^2*x^2])/e - (14*(d^2 - e^2*x^2)^(3/2))/(3*e*(d + e*x)^2) + (14*(d^2 - e^2*x^2)^(5/2))/(15*e*(d + e*x)^4) - (2*(d^2 - e^2*x^2)^(7/2))/(5*e*(d + e*x)^6) - (7*d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e","A",6,4,24,0.1667,1,"{663, 665, 217, 203}"
810,1,143,0,0.041401,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^8} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^8,x]","-\frac{2 \left(d^2-e^2 x^2\right)^{7/2}}{7 e (d+e x)^7}+\frac{2 \left(d^2-e^2 x^2\right)^{5/2}}{5 e (d+e x)^5}-\frac{2 \left(d^2-e^2 x^2\right)^{3/2}}{3 e (d+e x)^3}+\frac{2 \sqrt{d^2-e^2 x^2}}{e (d+e x)}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}","-\frac{2 \left(d^2-e^2 x^2\right)^{7/2}}{7 e (d+e x)^7}+\frac{2 \left(d^2-e^2 x^2\right)^{5/2}}{5 e (d+e x)^5}-\frac{2 \left(d^2-e^2 x^2\right)^{3/2}}{3 e (d+e x)^3}+\frac{2 \sqrt{d^2-e^2 x^2}}{e (d+e x)}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}",1,"(2*Sqrt[d^2 - e^2*x^2])/(e*(d + e*x)) - (2*(d^2 - e^2*x^2)^(3/2))/(3*e*(d + e*x)^3) + (2*(d^2 - e^2*x^2)^(5/2))/(5*e*(d + e*x)^5) - (2*(d^2 - e^2*x^2)^(7/2))/(7*e*(d + e*x)^7) + ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e","A",6,3,24,0.1250,1,"{663, 217, 203}"
811,1,33,0,0.0090743,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^9} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^9,x]","-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{9 d e (d+e x)^9}","-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{9 d e (d+e x)^9}",1,"-(d^2 - e^2*x^2)^(9/2)/(9*d*e*(d + e*x)^9)","A",1,1,24,0.04167,1,"{651}"
812,1,67,0,0.021408,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^{10}} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^10,x]","-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{99 d^2 e (d+e x)^9}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{11 d e (d+e x)^{10}}","-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{99 d^2 e (d+e x)^9}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{11 d e (d+e x)^{10}}",1,"-(d^2 - e^2*x^2)^(9/2)/(11*d*e*(d + e*x)^10) - (d^2 - e^2*x^2)^(9/2)/(99*d^2*e*(d + e*x)^9)","A",2,2,24,0.08333,1,"{659, 651}"
813,1,100,0,0.0359951,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^{11}} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^11,x]","-\frac{2 \left(d^2-e^2 x^2\right)^{9/2}}{1287 d^3 e (d+e x)^9}-\frac{2 \left(d^2-e^2 x^2\right)^{9/2}}{143 d^2 e (d+e x)^{10}}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{13 d e (d+e x)^{11}}","-\frac{2 \left(d^2-e^2 x^2\right)^{9/2}}{1287 d^3 e (d+e x)^9}-\frac{2 \left(d^2-e^2 x^2\right)^{9/2}}{143 d^2 e (d+e x)^{10}}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{13 d e (d+e x)^{11}}",1,"-(d^2 - e^2*x^2)^(9/2)/(13*d*e*(d + e*x)^11) - (2*(d^2 - e^2*x^2)^(9/2))/(143*d^2*e*(d + e*x)^10) - (2*(d^2 - e^2*x^2)^(9/2))/(1287*d^3*e*(d + e*x)^9)","A",3,2,24,0.08333,1,"{659, 651}"
814,1,133,0,0.0559151,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^{12}} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^12,x]","-\frac{2 \left(d^2-e^2 x^2\right)^{9/2}}{6435 d^4 e (d+e x)^9}-\frac{2 \left(d^2-e^2 x^2\right)^{9/2}}{715 d^3 e (d+e x)^{10}}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{65 d^2 e (d+e x)^{11}}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{15 d e (d+e x)^{12}}","-\frac{2 \left(d^2-e^2 x^2\right)^{9/2}}{6435 d^4 e (d+e x)^9}-\frac{2 \left(d^2-e^2 x^2\right)^{9/2}}{715 d^3 e (d+e x)^{10}}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{65 d^2 e (d+e x)^{11}}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{15 d e (d+e x)^{12}}",1,"-(d^2 - e^2*x^2)^(9/2)/(15*d*e*(d + e*x)^12) - (d^2 - e^2*x^2)^(9/2)/(65*d^2*e*(d + e*x)^11) - (2*(d^2 - e^2*x^2)^(9/2))/(715*d^3*e*(d + e*x)^10) - (2*(d^2 - e^2*x^2)^(9/2))/(6435*d^4*e*(d + e*x)^9)","A",4,2,24,0.08333,1,"{659, 651}"
815,1,166,0,0.0758125,"\int \frac{\left(d^2-e^2 x^2\right)^{7/2}}{(d+e x)^{13}} \, dx","Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^13,x]","-\frac{8 \left(d^2-e^2 x^2\right)^{9/2}}{109395 d^5 e (d+e x)^9}-\frac{8 \left(d^2-e^2 x^2\right)^{9/2}}{12155 d^4 e (d+e x)^{10}}-\frac{4 \left(d^2-e^2 x^2\right)^{9/2}}{1105 d^3 e (d+e x)^{11}}-\frac{4 \left(d^2-e^2 x^2\right)^{9/2}}{255 d^2 e (d+e x)^{12}}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{17 d e (d+e x)^{13}}","-\frac{8 \left(d^2-e^2 x^2\right)^{9/2}}{109395 d^5 e (d+e x)^9}-\frac{8 \left(d^2-e^2 x^2\right)^{9/2}}{12155 d^4 e (d+e x)^{10}}-\frac{4 \left(d^2-e^2 x^2\right)^{9/2}}{1105 d^3 e (d+e x)^{11}}-\frac{4 \left(d^2-e^2 x^2\right)^{9/2}}{255 d^2 e (d+e x)^{12}}-\frac{\left(d^2-e^2 x^2\right)^{9/2}}{17 d e (d+e x)^{13}}",1,"-(d^2 - e^2*x^2)^(9/2)/(17*d*e*(d + e*x)^13) - (4*(d^2 - e^2*x^2)^(9/2))/(255*d^2*e*(d + e*x)^12) - (4*(d^2 - e^2*x^2)^(9/2))/(1105*d^3*e*(d + e*x)^11) - (8*(d^2 - e^2*x^2)^(9/2))/(12155*d^4*e*(d + e*x)^10) - (8*(d^2 - e^2*x^2)^(9/2))/(109395*d^5*e*(d + e*x)^9)","A",5,2,24,0.08333,1,"{659, 651}"
816,1,47,0,0.015241,"\int \frac{\sqrt{a^2-b^2 x^2}}{a-b x} \, dx","Int[Sqrt[a^2 - b^2*x^2]/(a - b*x),x]","\frac{a \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}-\frac{\sqrt{a^2-b^2 x^2}}{b}","\frac{a \tan ^{-1}\left(\frac{b x}{\sqrt{a^2-b^2 x^2}}\right)}{b}-\frac{\sqrt{a^2-b^2 x^2}}{b}",1,"-(Sqrt[a^2 - b^2*x^2]/b) + (a*ArcTan[(b*x)/Sqrt[a^2 - b^2*x^2]])/b","A",3,3,25,0.1200,1,"{665, 217, 203}"
817,1,130,0,0.0531535,"\int (a+b x)^2 \sqrt{-\frac{a^2 c}{b^2}+c x^2} \, dx","Int[(a + b*x)^2*Sqrt[-((a^2*c)/b^2) + c*x^2],x]","\frac{5}{8} a^2 x \sqrt{c x^2-\frac{a^2 c}{b^2}}+\frac{5 a b \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{12 c}+\frac{b (a+b x) \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{4 c}-\frac{5 a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{c x^2-\frac{a^2 c}{b^2}}}\right)}{8 b^2}","\frac{5}{8} a^2 x \sqrt{c x^2-\frac{a^2 c}{b^2}}+\frac{5 a b \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{12 c}+\frac{b (a+b x) \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{4 c}-\frac{5 a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{c x^2-\frac{a^2 c}{b^2}}}\right)}{8 b^2}",1,"(5*a^2*x*Sqrt[-((a^2*c)/b^2) + c*x^2])/8 + (5*a*b*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(12*c) + (b*(a + b*x)*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(4*c) - (5*a^4*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[-((a^2*c)/b^2) + c*x^2]])/(8*b^2)","A",5,5,27,0.1852,1,"{671, 641, 195, 217, 206}"
818,1,167,0,0.0783444,"\int (a+b x)^3 \sqrt{-\frac{a^2 c}{b^2}+c x^2} \, dx","Int[(a + b*x)^3*Sqrt[-((a^2*c)/b^2) + c*x^2],x]","\frac{7}{8} a^3 x \sqrt{c x^2-\frac{a^2 c}{b^2}}+\frac{7 a^2 b \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{12 c}+\frac{7 a b (a+b x) \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{20 c}+\frac{b (a+b x)^2 \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{5 c}-\frac{7 a^5 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{c x^2-\frac{a^2 c}{b^2}}}\right)}{8 b^2}","\frac{7}{8} a^3 x \sqrt{c x^2-\frac{a^2 c}{b^2}}+\frac{7 a^2 b \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{12 c}+\frac{7 a b (a+b x) \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{20 c}+\frac{b (a+b x)^2 \left(c x^2-\frac{a^2 c}{b^2}\right)^{3/2}}{5 c}-\frac{7 a^5 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{c x^2-\frac{a^2 c}{b^2}}}\right)}{8 b^2}",1,"(7*a^3*x*Sqrt[-((a^2*c)/b^2) + c*x^2])/8 + (7*a^2*b*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(12*c) + (7*a*b*(a + b*x)*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(20*c) + (b*(a + b*x)^2*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(5*c) - (7*a^5*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[-((a^2*c)/b^2) + c*x^2]])/(8*b^2)","A",6,5,27,0.1852,1,"{671, 641, 195, 217, 206}"
819,1,44,0,0.0069667,"\int (1+x) \sqrt{-1+x^2} \, dx","Int[(1 + x)*Sqrt[-1 + x^2],x]","\frac{1}{3} \left(x^2-1\right)^{3/2}+\frac{1}{2} x \sqrt{x^2-1}-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)","\frac{1}{3} \left(x^2-1\right)^{3/2}+\frac{1}{2} x \sqrt{x^2-1}-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)",1,"(x*Sqrt[-1 + x^2])/2 + (-1 + x^2)^(3/2)/3 - ArcTanh[x/Sqrt[-1 + x^2]]/2","A",4,4,13,0.3077,1,"{641, 195, 217, 206}"
820,1,38,0,0.0062876,"\int (1+x) \sqrt{1-x^2} \, dx","Int[(1 + x)*Sqrt[1 - x^2],x]","-\frac{1}{3} \left(1-x^2\right)^{3/2}+\frac{1}{2} x \sqrt{1-x^2}+\frac{1}{2} \sin ^{-1}(x)","-\frac{1}{3} \left(1-x^2\right)^{3/2}+\frac{1}{2} x \sqrt{1-x^2}+\frac{1}{2} \sin ^{-1}(x)",1,"(x*Sqrt[1 - x^2])/2 - (1 - x^2)^(3/2)/3 + ArcSin[x]/2","A",3,3,15,0.2000,1,"{641, 195, 216}"
821,1,14,0,0.0058539,"\int \frac{\sqrt{1-x^2}}{1+x} \, dx","Int[Sqrt[1 - x^2]/(1 + x),x]","\sqrt{1-x^2}+\sin ^{-1}(x)","\sqrt{1-x^2}+\sin ^{-1}(x)",1,"Sqrt[1 - x^2] + ArcSin[x]","A",2,2,17,0.1176,1,"{665, 216}"
822,1,38,0,0.0061408,"\int (1-x) \sqrt{1-x^2} \, dx","Int[(1 - x)*Sqrt[1 - x^2],x]","\frac{1}{3} \left(1-x^2\right)^{3/2}+\frac{1}{2} x \sqrt{1-x^2}+\frac{1}{2} \sin ^{-1}(x)","\frac{1}{3} \left(1-x^2\right)^{3/2}+\frac{1}{2} x \sqrt{1-x^2}+\frac{1}{2} \sin ^{-1}(x)",1,"(x*Sqrt[1 - x^2])/2 + (1 - x^2)^(3/2)/3 + ArcSin[x]/2","A",3,3,17,0.1765,1,"{641, 195, 216}"
823,1,16,0,0.0064882,"\int \frac{\sqrt{1-x^2}}{1-x} \, dx","Int[Sqrt[1 - x^2]/(1 - x),x]","\sin ^{-1}(x)-\sqrt{1-x^2}","\sin ^{-1}(x)-\sqrt{1-x^2}",1,"-Sqrt[1 - x^2] + ArcSin[x]","A",2,2,19,0.1053,1,"{665, 216}"
824,1,25,0,0.0068515,"\int \frac{\sqrt{1-x^2}}{(1-x)^2} \, dx","Int[Sqrt[1 - x^2]/(1 - x)^2,x]","\frac{2 \sqrt{1-x^2}}{1-x}-\sin ^{-1}(x)","\frac{2 \sqrt{1-x^2}}{1-x}-\sin ^{-1}(x)",1,"(2*Sqrt[1 - x^2])/(1 - x) - ArcSin[x]","A",2,2,19,0.1053,1,"{663, 216}"
825,1,22,0,0.0057352,"\int \frac{\sqrt{1-x^2}}{(1-x)^3} \, dx","Int[Sqrt[1 - x^2]/(1 - x)^3,x]","\frac{\left(1-x^2\right)^{3/2}}{3 (1-x)^3}","\frac{\left(1-x^2\right)^{3/2}}{3 (1-x)^3}",1,"(1 - x^2)^(3/2)/(3*(1 - x)^3)","A",1,1,19,0.05263,1,"{651}"
826,1,182,0,0.078631,"\int \frac{(d+e x)^5}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^5/Sqrt[d^2 - e^2*x^2],x]","-\frac{63 d^4 \sqrt{d^2-e^2 x^2}}{8 e}-\frac{21 d^3 (d+e x) \sqrt{d^2-e^2 x^2}}{8 e}-\frac{21 d^2 (d+e x)^2 \sqrt{d^2-e^2 x^2}}{20 e}-\frac{9 d (d+e x)^3 \sqrt{d^2-e^2 x^2}}{20 e}-\frac{(d+e x)^4 \sqrt{d^2-e^2 x^2}}{5 e}+\frac{63 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}","-\frac{63 d^4 \sqrt{d^2-e^2 x^2}}{8 e}-\frac{21 d^3 (d+e x) \sqrt{d^2-e^2 x^2}}{8 e}-\frac{21 d^2 (d+e x)^2 \sqrt{d^2-e^2 x^2}}{20 e}-\frac{9 d (d+e x)^3 \sqrt{d^2-e^2 x^2}}{20 e}-\frac{(d+e x)^4 \sqrt{d^2-e^2 x^2}}{5 e}+\frac{63 d^5 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}",1,"(-63*d^4*Sqrt[d^2 - e^2*x^2])/(8*e) - (21*d^3*(d + e*x)*Sqrt[d^2 - e^2*x^2])/(8*e) - (21*d^2*(d + e*x)^2*Sqrt[d^2 - e^2*x^2])/(20*e) - (9*d*(d + e*x)^3*Sqrt[d^2 - e^2*x^2])/(20*e) - ((d + e*x)^4*Sqrt[d^2 - e^2*x^2])/(5*e) + (63*d^5*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e)","A",7,4,24,0.1667,1,"{671, 641, 217, 203}"
827,1,149,0,0.0618129,"\int \frac{(d+e x)^4}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^4/Sqrt[d^2 - e^2*x^2],x]","-\frac{35 d^3 \sqrt{d^2-e^2 x^2}}{8 e}-\frac{35 d^2 (d+e x) \sqrt{d^2-e^2 x^2}}{24 e}-\frac{7 d (d+e x)^2 \sqrt{d^2-e^2 x^2}}{12 e}-\frac{(d+e x)^3 \sqrt{d^2-e^2 x^2}}{4 e}+\frac{35 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}","-\frac{35 d^3 \sqrt{d^2-e^2 x^2}}{8 e}-\frac{35 d^2 (d+e x) \sqrt{d^2-e^2 x^2}}{24 e}-\frac{7 d (d+e x)^2 \sqrt{d^2-e^2 x^2}}{12 e}-\frac{(d+e x)^3 \sqrt{d^2-e^2 x^2}}{4 e}+\frac{35 d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e}",1,"(-35*d^3*Sqrt[d^2 - e^2*x^2])/(8*e) - (35*d^2*(d + e*x)*Sqrt[d^2 - e^2*x^2])/(24*e) - (7*d*(d + e*x)^2*Sqrt[d^2 - e^2*x^2])/(12*e) - ((d + e*x)^3*Sqrt[d^2 - e^2*x^2])/(4*e) + (35*d^4*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e)","A",6,4,24,0.1667,1,"{671, 641, 217, 203}"
828,1,116,0,0.0427732,"\int \frac{(d+e x)^3}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^3/Sqrt[d^2 - e^2*x^2],x]","-\frac{5 d^2 \sqrt{d^2-e^2 x^2}}{2 e}-\frac{5 d (d+e x) \sqrt{d^2-e^2 x^2}}{6 e}-\frac{(d+e x)^2 \sqrt{d^2-e^2 x^2}}{3 e}+\frac{5 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}","-\frac{5 d^2 \sqrt{d^2-e^2 x^2}}{2 e}-\frac{5 d (d+e x) \sqrt{d^2-e^2 x^2}}{6 e}-\frac{(d+e x)^2 \sqrt{d^2-e^2 x^2}}{3 e}+\frac{5 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}",1,"(-5*d^2*Sqrt[d^2 - e^2*x^2])/(2*e) - (5*d*(d + e*x)*Sqrt[d^2 - e^2*x^2])/(6*e) - ((d + e*x)^2*Sqrt[d^2 - e^2*x^2])/(3*e) + (5*d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e)","A",5,4,24,0.1667,1,"{671, 641, 217, 203}"
829,1,83,0,0.0267756,"\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{2 d \sqrt{d^2-e^2 x^2}}{e}-\frac{1}{2} x \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}",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}"
830,1,47,0,0.0123493,"\int \frac{d+e x}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)/Sqrt[d^2 - e^2*x^2],x]","\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}-\frac{\sqrt{d^2-e^2 x^2}}{e}",1,"-(Sqrt[d^2 - e^2*x^2]/e) + (d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e","A",3,3,22,0.1364,1,"{641, 217, 203}"
831,1,31,0,0.0094422,"\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}"
832,1,67,0,0.02218,"\int \frac{1}{(d+e x)^2 \sqrt{d^2-e^2 x^2}} \, dx","Int[1/((d + e*x)^2*Sqrt[d^2 - e^2*x^2]),x]","-\frac{\sqrt{d^2-e^2 x^2}}{3 d^2 e (d+e x)}-\frac{\sqrt{d^2-e^2 x^2}}{3 d e (d+e x)^2}","-\frac{\sqrt{d^2-e^2 x^2}}{3 d^2 e (d+e x)}-\frac{\sqrt{d^2-e^2 x^2}}{3 d e (d+e x)^2}",1,"-Sqrt[d^2 - e^2*x^2]/(3*d*e*(d + e*x)^2) - Sqrt[d^2 - e^2*x^2]/(3*d^2*e*(d + e*x))","A",2,2,24,0.08333,1,"{659, 651}"
833,1,100,0,0.0376555,"\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}"
834,1,133,0,0.0552447,"\int \frac{1}{(d+e x)^4 \sqrt{d^2-e^2 x^2}} \, dx","Int[1/((d + e*x)^4*Sqrt[d^2 - e^2*x^2]),x]","-\frac{2 \sqrt{d^2-e^2 x^2}}{35 d^4 e (d+e x)}-\frac{2 \sqrt{d^2-e^2 x^2}}{35 d^3 e (d+e x)^2}-\frac{3 \sqrt{d^2-e^2 x^2}}{35 d^2 e (d+e x)^3}-\frac{\sqrt{d^2-e^2 x^2}}{7 d e (d+e x)^4}","-\frac{2 \sqrt{d^2-e^2 x^2}}{35 d^4 e (d+e x)}-\frac{2 \sqrt{d^2-e^2 x^2}}{35 d^3 e (d+e x)^2}-\frac{3 \sqrt{d^2-e^2 x^2}}{35 d^2 e (d+e x)^3}-\frac{\sqrt{d^2-e^2 x^2}}{7 d e (d+e x)^4}",1,"-Sqrt[d^2 - e^2*x^2]/(7*d*e*(d + e*x)^4) - (3*Sqrt[d^2 - e^2*x^2])/(35*d^2*e*(d + e*x)^3) - (2*Sqrt[d^2 - e^2*x^2])/(35*d^3*e*(d + e*x)^2) - (2*Sqrt[d^2 - e^2*x^2])/(35*d^4*e*(d + e*x))","A",4,2,24,0.08333,1,"{659, 651}"
835,1,166,0,0.0721729,"\int \frac{1}{(d+e x)^5 \sqrt{d^2-e^2 x^2}} \, dx","Int[1/((d + e*x)^5*Sqrt[d^2 - e^2*x^2]),x]","-\frac{8 \sqrt{d^2-e^2 x^2}}{315 d^5 e (d+e x)}-\frac{8 \sqrt{d^2-e^2 x^2}}{315 d^4 e (d+e x)^2}-\frac{4 \sqrt{d^2-e^2 x^2}}{105 d^3 e (d+e x)^3}-\frac{4 \sqrt{d^2-e^2 x^2}}{63 d^2 e (d+e x)^4}-\frac{\sqrt{d^2-e^2 x^2}}{9 d e (d+e x)^5}","-\frac{8 \sqrt{d^2-e^2 x^2}}{315 d^5 e (d+e x)}-\frac{8 \sqrt{d^2-e^2 x^2}}{315 d^4 e (d+e x)^2}-\frac{4 \sqrt{d^2-e^2 x^2}}{105 d^3 e (d+e x)^3}-\frac{4 \sqrt{d^2-e^2 x^2}}{63 d^2 e (d+e x)^4}-\frac{\sqrt{d^2-e^2 x^2}}{9 d e (d+e x)^5}",1,"-Sqrt[d^2 - e^2*x^2]/(9*d*e*(d + e*x)^5) - (4*Sqrt[d^2 - e^2*x^2])/(63*d^2*e*(d + e*x)^4) - (4*Sqrt[d^2 - e^2*x^2])/(105*d^3*e*(d + e*x)^3) - (8*Sqrt[d^2 - e^2*x^2])/(315*d^4*e*(d + e*x)^2) - (8*Sqrt[d^2 - e^2*x^2])/(315*d^5*e*(d + e*x))","A",5,2,24,0.08333,1,"{659, 651}"
836,1,143,0,0.0584483,"\int \frac{(d+e x)^6}{\left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^6/(d^2 - e^2*x^2)^(5/2),x]","\frac{2 (d+e x)^5}{3 e \left(d^2-e^2 x^2\right)^{3/2}}-\frac{14 (d+e x)^3}{3 e \sqrt{d^2-e^2 x^2}}-\frac{35 \sqrt{d^2-e^2 x^2} (d+e x)}{6 e}-\frac{35 d \sqrt{d^2-e^2 x^2}}{2 e}+\frac{35 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}","\frac{2 (d+e x)^5}{3 e \left(d^2-e^2 x^2\right)^{3/2}}-\frac{14 (d+e x)^3}{3 e \sqrt{d^2-e^2 x^2}}-\frac{35 \sqrt{d^2-e^2 x^2} (d+e x)}{6 e}-\frac{35 d \sqrt{d^2-e^2 x^2}}{2 e}+\frac{35 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}",1,"(2*(d + e*x)^5)/(3*e*(d^2 - e^2*x^2)^(3/2)) - (14*(d + e*x)^3)/(3*e*Sqrt[d^2 - e^2*x^2]) - (35*d*Sqrt[d^2 - e^2*x^2])/(2*e) - (35*(d + e*x)*Sqrt[d^2 - e^2*x^2])/(6*e) + (35*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e)","A",6,5,24,0.2083,1,"{669, 671, 641, 217, 203}"
837,1,108,0,0.0398871,"\int \frac{(d+e x)^5}{\left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^5/(d^2 - e^2*x^2)^(5/2),x]","\frac{2 (d+e x)^4}{3 e \left(d^2-e^2 x^2\right)^{3/2}}-\frac{10 (d+e x)^2}{3 e \sqrt{d^2-e^2 x^2}}-\frac{5 \sqrt{d^2-e^2 x^2}}{e}+\frac{5 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}","\frac{2 (d+e x)^4}{3 e \left(d^2-e^2 x^2\right)^{3/2}}-\frac{10 (d+e x)^2}{3 e \sqrt{d^2-e^2 x^2}}-\frac{5 \sqrt{d^2-e^2 x^2}}{e}+\frac{5 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}",1,"(2*(d + e*x)^4)/(3*e*(d^2 - e^2*x^2)^(3/2)) - (10*(d + e*x)^2)/(3*e*Sqrt[d^2 - e^2*x^2]) - (5*Sqrt[d^2 - e^2*x^2])/e + (5*d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e","A",5,4,24,0.1667,1,"{669, 641, 217, 203}"
838,1,81,0,0.0231172,"\int \frac{(d+e x)^4}{\left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^4/(d^2 - e^2*x^2)^(5/2),x]","\frac{2 (d+e x)^3}{3 e \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 (d+e x)}{e \sqrt{d^2-e^2 x^2}}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}","\frac{2 (d+e x)^3}{3 e \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2 (d+e x)}{e \sqrt{d^2-e^2 x^2}}+\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}",1,"(2*(d + e*x)^3)/(3*e*(d^2 - e^2*x^2)^(3/2)) - (2*(d + e*x))/(e*Sqrt[d^2 - e^2*x^2]) + ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e","A",4,4,24,0.1667,1,"{669, 653, 217, 203}"
839,1,33,0,0.0099128,"\int \frac{(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{(d+e x)^3}{3 d e \left(d^2-e^2 x^2\right)^{3/2}}","\frac{(d+e x)^3}{3 d e \left(d^2-e^2 x^2\right)^{3/2}}",1,"(d + e*x)^3/(3*d*e*(d^2 - e^2*x^2)^(3/2))","A",1,1,24,0.04167,1,"{651}"
840,1,53,0,0.0133077,"\int \frac{(d+e x)^2}{\left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^2/(d^2 - e^2*x^2)^(5/2),x]","\frac{x}{3 d^2 \sqrt{d^2-e^2 x^2}}+\frac{2 (d+e x)}{3 e \left(d^2-e^2 x^2\right)^{3/2}}","\frac{x}{3 d^2 \sqrt{d^2-e^2 x^2}}+\frac{2 (d+e x)}{3 e \left(d^2-e^2 x^2\right)^{3/2}}",1,"(2*(d + e*x))/(3*e*(d^2 - e^2*x^2)^(3/2)) + x/(3*d^2*Sqrt[d^2 - e^2*x^2])","A",2,2,24,0.08333,1,"{653, 191}"
841,1,56,0,0.0123644,"\int \frac{d+e x}{\left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)/(d^2 - e^2*x^2)^(5/2),x]","\frac{2 x}{3 d^3 \sqrt{d^2-e^2 x^2}}+\frac{d+e x}{3 d e \left(d^2-e^2 x^2\right)^{3/2}}","\frac{2 x}{3 d^3 \sqrt{d^2-e^2 x^2}}+\frac{d+e x}{3 d e \left(d^2-e^2 x^2\right)^{3/2}}",1,"(d + e*x)/(3*d*e*(d^2 - e^2*x^2)^(3/2)) + (2*x)/(3*d^3*Sqrt[d^2 - e^2*x^2])","A",2,2,22,0.09091,1,"{639, 191}"
842,1,82,0,0.0206295,"\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}"
843,1,115,0,0.0353934,"\int \frac{1}{(d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^2*(d^2 - e^2*x^2)^(5/2)),x]","\frac{8 x}{21 d^6 \sqrt{d^2-e^2 x^2}}+\frac{4 x}{21 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{7 d^2 e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{7 d e (d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}}","\frac{8 x}{21 d^6 \sqrt{d^2-e^2 x^2}}+\frac{4 x}{21 d^4 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{7 d^2 e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{7 d e (d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}}",1,"(4*x)/(21*d^4*(d^2 - e^2*x^2)^(3/2)) - 1/(7*d*e*(d + e*x)^2*(d^2 - e^2*x^2)^(3/2)) - 1/(7*d^2*e*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (8*x)/(21*d^6*Sqrt[d^2 - e^2*x^2])","A",4,3,24,0.1250,1,"{659, 192, 191}"
844,1,148,0,0.053541,"\int \frac{1}{(d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^3*(d^2 - e^2*x^2)^(5/2)),x]","\frac{16 x}{63 d^7 \sqrt{d^2-e^2 x^2}}+\frac{8 x}{63 d^5 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{21 d^3 e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{21 d^2 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{9 d e (d+e x)^3 \left(d^2-e^2 x^2\right)^{3/2}}","\frac{16 x}{63 d^7 \sqrt{d^2-e^2 x^2}}+\frac{8 x}{63 d^5 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{21 d^3 e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{21 d^2 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{9 d e (d+e x)^3 \left(d^2-e^2 x^2\right)^{3/2}}",1,"(8*x)/(63*d^5*(d^2 - e^2*x^2)^(3/2)) - 1/(9*d*e*(d + e*x)^3*(d^2 - e^2*x^2)^(3/2)) - 2/(21*d^2*e*(d + e*x)^2*(d^2 - e^2*x^2)^(3/2)) - 2/(21*d^3*e*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (16*x)/(63*d^7*Sqrt[d^2 - e^2*x^2])","A",5,3,24,0.1250,1,"{659, 192, 191}"
845,1,181,0,0.0747313,"\int \frac{1}{(d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^4*(d^2 - e^2*x^2)^(5/2)),x]","\frac{16 x}{99 d^8 \sqrt{d^2-e^2 x^2}}+\frac{8 x}{99 d^6 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{33 d^4 e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{33 d^3 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{7}{99 d^2 e (d+e x)^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{11 d e (d+e x)^4 \left(d^2-e^2 x^2\right)^{3/2}}","\frac{16 x}{99 d^8 \sqrt{d^2-e^2 x^2}}+\frac{8 x}{99 d^6 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{33 d^4 e (d+e x) \left(d^2-e^2 x^2\right)^{3/2}}-\frac{2}{33 d^3 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{7}{99 d^2 e (d+e x)^3 \left(d^2-e^2 x^2\right)^{3/2}}-\frac{1}{11 d e (d+e x)^4 \left(d^2-e^2 x^2\right)^{3/2}}",1,"(8*x)/(99*d^6*(d^2 - e^2*x^2)^(3/2)) - 1/(11*d*e*(d + e*x)^4*(d^2 - e^2*x^2)^(3/2)) - 7/(99*d^2*e*(d + e*x)^3*(d^2 - e^2*x^2)^(3/2)) - 2/(33*d^3*e*(d + e*x)^2*(d^2 - e^2*x^2)^(3/2)) - 2/(33*d^4*e*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (16*x)/(99*d^8*Sqrt[d^2 - e^2*x^2])","A",6,3,24,0.1250,1,"{659, 192, 191}"
846,1,206,0,0.1014816,"\int \frac{(d+e x)^9}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^9/(d^2 - e^2*x^2)^(7/2),x]","\frac{2 (d+e x)^8}{5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{22 (d+e x)^6}{15 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{66 (d+e x)^4}{5 e \sqrt{d^2-e^2 x^2}}+\frac{77 \sqrt{d^2-e^2 x^2} (d+e x)^2}{5 e}+\frac{77 d \sqrt{d^2-e^2 x^2} (d+e x)}{2 e}+\frac{231 d^2 \sqrt{d^2-e^2 x^2}}{2 e}-\frac{231 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}","\frac{2 (d+e x)^8}{5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{22 (d+e x)^6}{15 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{66 (d+e x)^4}{5 e \sqrt{d^2-e^2 x^2}}+\frac{77 \sqrt{d^2-e^2 x^2} (d+e x)^2}{5 e}+\frac{77 d \sqrt{d^2-e^2 x^2} (d+e x)}{2 e}+\frac{231 d^2 \sqrt{d^2-e^2 x^2}}{2 e}-\frac{231 d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}",1,"(2*(d + e*x)^8)/(5*e*(d^2 - e^2*x^2)^(5/2)) - (22*(d + e*x)^6)/(15*e*(d^2 - e^2*x^2)^(3/2)) + (66*(d + e*x)^4)/(5*e*Sqrt[d^2 - e^2*x^2]) + (231*d^2*Sqrt[d^2 - e^2*x^2])/(2*e) + (77*d*(d + e*x)*Sqrt[d^2 - e^2*x^2])/(2*e) + (77*(d + e*x)^2*Sqrt[d^2 - e^2*x^2])/(5*e) - (231*d^3*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e)","A",8,5,24,0.2083,1,"{669, 671, 641, 217, 203}"
847,1,173,0,0.0768588,"\int \frac{(d+e x)^8}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^8/(d^2 - e^2*x^2)^(7/2),x]","\frac{2 (d+e x)^7}{5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{6 (d+e x)^5}{5 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{42 (d+e x)^3}{5 e \sqrt{d^2-e^2 x^2}}+\frac{21 \sqrt{d^2-e^2 x^2} (d+e x)}{2 e}+\frac{63 d \sqrt{d^2-e^2 x^2}}{2 e}-\frac{63 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}","\frac{2 (d+e x)^7}{5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{6 (d+e x)^5}{5 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{42 (d+e x)^3}{5 e \sqrt{d^2-e^2 x^2}}+\frac{21 \sqrt{d^2-e^2 x^2} (d+e x)}{2 e}+\frac{63 d \sqrt{d^2-e^2 x^2}}{2 e}-\frac{63 d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e}",1,"(2*(d + e*x)^7)/(5*e*(d^2 - e^2*x^2)^(5/2)) - (6*(d + e*x)^5)/(5*e*(d^2 - e^2*x^2)^(3/2)) + (42*(d + e*x)^3)/(5*e*Sqrt[d^2 - e^2*x^2]) + (63*d*Sqrt[d^2 - e^2*x^2])/(2*e) + (21*(d + e*x)*Sqrt[d^2 - e^2*x^2])/(2*e) - (63*d^2*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e)","A",7,5,24,0.2083,1,"{669, 671, 641, 217, 203}"
848,1,138,0,0.0572427,"\int \frac{(d+e x)^7}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^7/(d^2 - e^2*x^2)^(7/2),x]","\frac{2 (d+e x)^6}{5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{14 (d+e x)^4}{15 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{14 (d+e x)^2}{3 e \sqrt{d^2-e^2 x^2}}+\frac{7 \sqrt{d^2-e^2 x^2}}{e}-\frac{7 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}","\frac{2 (d+e x)^6}{5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{14 (d+e x)^4}{15 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{14 (d+e x)^2}{3 e \sqrt{d^2-e^2 x^2}}+\frac{7 \sqrt{d^2-e^2 x^2}}{e}-\frac{7 d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}",1,"(2*(d + e*x)^6)/(5*e*(d^2 - e^2*x^2)^(5/2)) - (14*(d + e*x)^4)/(15*e*(d^2 - e^2*x^2)^(3/2)) + (14*(d + e*x)^2)/(3*e*Sqrt[d^2 - e^2*x^2]) + (7*Sqrt[d^2 - e^2*x^2])/e - (7*d*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e","A",6,4,24,0.1667,1,"{669, 641, 217, 203}"
849,1,112,0,0.0331972,"\int \frac{(d+e x)^6}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^6/(d^2 - e^2*x^2)^(7/2),x]","\frac{2 (d+e x)^5}{5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 (d+e x)^3}{3 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (d+e x)}{e \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}","\frac{2 (d+e x)^5}{5 e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2 (d+e x)^3}{3 e \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 (d+e x)}{e \sqrt{d^2-e^2 x^2}}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e}",1,"(2*(d + e*x)^5)/(5*e*(d^2 - e^2*x^2)^(5/2)) - (2*(d + e*x)^3)/(3*e*(d^2 - e^2*x^2)^(3/2)) + (2*(d + e*x))/(e*Sqrt[d^2 - e^2*x^2]) - ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]]/e","A",5,4,24,0.1667,1,"{669, 653, 217, 203}"
850,1,33,0,0.0094206,"\int \frac{(d+e x)^5}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^5/(d^2 - e^2*x^2)^(7/2),x]","\frac{(d+e x)^5}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}","\frac{(d+e x)^5}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}",1,"(d + e*x)^5/(5*d*e*(d^2 - e^2*x^2)^(5/2))","A",1,1,24,0.04167,1,"{651}"
851,1,67,0,0.0227085,"\int \frac{(d+e x)^4}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^4/(d^2 - e^2*x^2)^(7/2),x]","\frac{(d+e x)^4}{3 d e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{(d+e x)^5}{15 d^2 e \left(d^2-e^2 x^2\right)^{5/2}}","\frac{(d+e x)^4}{3 d e \left(d^2-e^2 x^2\right)^{5/2}}-\frac{(d+e x)^5}{15 d^2 e \left(d^2-e^2 x^2\right)^{5/2}}",1,"(d + e*x)^4/(3*d*e*(d^2 - e^2*x^2)^(5/2)) - (d + e*x)^5/(15*d^2*e*(d^2 - e^2*x^2)^(5/2))","A",2,2,24,0.08333,1,"{659, 651}"
852,1,103,0,0.0436404,"\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}"
853,1,77,0,0.018428,"\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}"
854,1,80,0,0.0193956,"\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}"
855,1,106,0,0.0277526,"\int \frac{1}{(d+e x) \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[1/((d + e*x)*(d^2 - e^2*x^2)^(7/2)),x]","\frac{16 x}{35 d^7 \sqrt{d^2-e^2 x^2}}+\frac{8 x}{35 d^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{6 x}{35 d^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{7 d e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}","\frac{16 x}{35 d^7 \sqrt{d^2-e^2 x^2}}+\frac{8 x}{35 d^5 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{6 x}{35 d^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{7 d e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}",1,"(6*x)/(35*d^3*(d^2 - e^2*x^2)^(5/2)) - 1/(7*d*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (8*x)/(35*d^5*(d^2 - e^2*x^2)^(3/2)) + (16*x)/(35*d^7*Sqrt[d^2 - e^2*x^2])","A",4,3,24,0.1250,1,"{659, 192, 191}"
856,1,139,0,0.0466924,"\int \frac{1}{(d+e x)^2 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[1/((d + e*x)^2*(d^2 - e^2*x^2)^(7/2)),x]","\frac{16 x}{45 d^8 \sqrt{d^2-e^2 x^2}}+\frac{8 x}{45 d^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 x}{15 d^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{9 d^2 e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{9 d e (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}","\frac{16 x}{45 d^8 \sqrt{d^2-e^2 x^2}}+\frac{8 x}{45 d^6 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{2 x}{15 d^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{9 d^2 e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{9 d e (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}",1,"(2*x)/(15*d^4*(d^2 - e^2*x^2)^(5/2)) - 1/(9*d*e*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 1/(9*d^2*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (8*x)/(45*d^6*(d^2 - e^2*x^2)^(3/2)) + (16*x)/(45*d^8*Sqrt[d^2 - e^2*x^2])","A",5,3,24,0.1250,1,"{659, 192, 191}"
857,1,172,0,0.0639118,"\int \frac{1}{(d+e x)^3 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[1/((d + e*x)^3*(d^2 - e^2*x^2)^(7/2)),x]","\frac{128 x}{495 d^9 \sqrt{d^2-e^2 x^2}}+\frac{64 x}{495 d^7 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{16 x}{165 d^5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8}{99 d^3 e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8}{99 d^2 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{11 d e (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}","\frac{128 x}{495 d^9 \sqrt{d^2-e^2 x^2}}+\frac{64 x}{495 d^7 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{16 x}{165 d^5 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8}{99 d^3 e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{8}{99 d^2 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{11 d e (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}",1,"(16*x)/(165*d^5*(d^2 - e^2*x^2)^(5/2)) - 1/(11*d*e*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2)) - 8/(99*d^2*e*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 8/(99*d^3*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (64*x)/(495*d^7*(d^2 - e^2*x^2)^(3/2)) + (128*x)/(495*d^9*Sqrt[d^2 - e^2*x^2])","A",6,3,24,0.1250,1,"{659, 192, 191}"
858,1,205,0,0.0889444,"\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}"
859,1,238,0,0.1129642,"\int \frac{1}{(d+e x)^5 \left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[1/((d + e*x)^5*(d^2 - e^2*x^2)^(7/2)),x]","\frac{256 x}{2145 d^{11} \sqrt{d^2-e^2 x^2}}+\frac{128 x}{2145 d^9 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{32 x}{715 d^7 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{16}{429 d^5 e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{16}{429 d^4 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{6}{143 d^3 e (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2}{39 d^2 e (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{15 d e (d+e x)^5 \left(d^2-e^2 x^2\right)^{5/2}}","\frac{256 x}{2145 d^{11} \sqrt{d^2-e^2 x^2}}+\frac{128 x}{2145 d^9 \left(d^2-e^2 x^2\right)^{3/2}}+\frac{32 x}{715 d^7 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{16}{429 d^5 e (d+e x) \left(d^2-e^2 x^2\right)^{5/2}}-\frac{16}{429 d^4 e (d+e x)^2 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{6}{143 d^3 e (d+e x)^3 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{2}{39 d^2 e (d+e x)^4 \left(d^2-e^2 x^2\right)^{5/2}}-\frac{1}{15 d e (d+e x)^5 \left(d^2-e^2 x^2\right)^{5/2}}",1,"(32*x)/(715*d^7*(d^2 - e^2*x^2)^(5/2)) - 1/(15*d*e*(d + e*x)^5*(d^2 - e^2*x^2)^(5/2)) - 2/(39*d^2*e*(d + e*x)^4*(d^2 - e^2*x^2)^(5/2)) - 6/(143*d^3*e*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2)) - 16/(429*d^4*e*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 16/(429*d^5*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (128*x)/(2145*d^9*(d^2 - e^2*x^2)^(3/2)) + (256*x)/(2145*d^11*Sqrt[d^2 - e^2*x^2])","A",8,3,24,0.1250,1,"{659, 192, 191}"
860,1,16,0,0.0043927,"\int \frac{1+x}{\sqrt{1-x^2}} \, dx","Int[(1 + x)/Sqrt[1 - x^2],x]","\sin ^{-1}(x)-\sqrt{1-x^2}","\sin ^{-1}(x)-\sqrt{1-x^2}",1,"-Sqrt[1 - x^2] + ArcSin[x]","A",2,2,15,0.1333,1,"{641, 216}"
861,1,14,0,0.0042074,"\int \frac{1-x}{\sqrt{1-x^2}} \, dx","Int[(1 - x)/Sqrt[1 - x^2],x]","\sqrt{1-x^2}+\sin ^{-1}(x)","\sqrt{1-x^2}+\sin ^{-1}(x)",1,"Sqrt[1 - x^2] + ArcSin[x]","A",2,2,17,0.1176,1,"{641, 216}"
862,1,160,0,0.0729391,"\int (d+e x)^{5/2} \sqrt{c d^2-c e^2 x^2} \, dx","Int[(d + e*x)^(5/2)*Sqrt[c*d^2 - c*e^2*x^2],x]","-\frac{256 d^3 \left(c d^2-c e^2 x^2\right)^{3/2}}{315 c e (d+e x)^{3/2}}-\frac{64 d^2 \left(c d^2-c e^2 x^2\right)^{3/2}}{105 c e \sqrt{d+e x}}-\frac{8 d \sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{3/2}}{21 c e}-\frac{2 (d+e x)^{3/2} \left(c d^2-c e^2 x^2\right)^{3/2}}{9 c e}","-\frac{256 d^3 \left(c d^2-c e^2 x^2\right)^{3/2}}{315 c e (d+e x)^{3/2}}-\frac{64 d^2 \left(c d^2-c e^2 x^2\right)^{3/2}}{105 c e \sqrt{d+e x}}-\frac{8 d \sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{3/2}}{21 c e}-\frac{2 (d+e x)^{3/2} \left(c d^2-c e^2 x^2\right)^{3/2}}{9 c e}",1,"(-256*d^3*(c*d^2 - c*e^2*x^2)^(3/2))/(315*c*e*(d + e*x)^(3/2)) - (64*d^2*(c*d^2 - c*e^2*x^2)^(3/2))/(105*c*e*Sqrt[d + e*x]) - (8*d*Sqrt[d + e*x]*(c*d^2 - c*e^2*x^2)^(3/2))/(21*c*e) - (2*(d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(3/2))/(9*c*e)","A",4,2,29,0.06897,1,"{657, 649}"
863,1,119,0,0.0476059,"\int (d+e x)^{3/2} \sqrt{c d^2-c e^2 x^2} \, dx","Int[(d + e*x)^(3/2)*Sqrt[c*d^2 - c*e^2*x^2],x]","-\frac{64 d^2 \left(c d^2-c e^2 x^2\right)^{3/2}}{105 c e (d+e x)^{3/2}}-\frac{16 d \left(c d^2-c e^2 x^2\right)^{3/2}}{35 c e \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{3/2}}{7 c e}","-\frac{64 d^2 \left(c d^2-c e^2 x^2\right)^{3/2}}{105 c e (d+e x)^{3/2}}-\frac{16 d \left(c d^2-c e^2 x^2\right)^{3/2}}{35 c e \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{3/2}}{7 c e}",1,"(-64*d^2*(c*d^2 - c*e^2*x^2)^(3/2))/(105*c*e*(d + e*x)^(3/2)) - (16*d*(c*d^2 - c*e^2*x^2)^(3/2))/(35*c*e*Sqrt[d + e*x]) - (2*Sqrt[d + e*x]*(c*d^2 - c*e^2*x^2)^(3/2))/(7*c*e)","A",3,2,29,0.06897,1,"{657, 649}"
864,1,78,0,0.0279207,"\int \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2} \, dx","Int[Sqrt[d + e*x]*Sqrt[c*d^2 - c*e^2*x^2],x]","-\frac{2 \left(c d^2-c e^2 x^2\right)^{3/2}}{5 c e \sqrt{d+e x}}-\frac{8 d \left(c d^2-c e^2 x^2\right)^{3/2}}{15 c e (d+e x)^{3/2}}","-\frac{2 \left(c d^2-c e^2 x^2\right)^{3/2}}{5 c e \sqrt{d+e x}}-\frac{8 d \left(c d^2-c e^2 x^2\right)^{3/2}}{15 c e (d+e x)^{3/2}}",1,"(-8*d*(c*d^2 - c*e^2*x^2)^(3/2))/(15*c*e*(d + e*x)^(3/2)) - (2*(c*d^2 - c*e^2*x^2)^(3/2))/(5*c*e*Sqrt[d + e*x])","A",2,2,29,0.06897,1,"{657, 649}"
865,1,38,0,0.012885,"\int \frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{d+e x}} \, dx","Int[Sqrt[c*d^2 - c*e^2*x^2]/Sqrt[d + e*x],x]","-\frac{2 \left(c d^2-c e^2 x^2\right)^{3/2}}{3 c e (d+e x)^{3/2}}","-\frac{2 \left(c d^2-c e^2 x^2\right)^{3/2}}{3 c e (d+e x)^{3/2}}",1,"(-2*(c*d^2 - c*e^2*x^2)^(3/2))/(3*c*e*(d + e*x)^(3/2))","A",1,1,29,0.03448,1,"{649}"
866,1,99,0,0.0553575,"\int \frac{\sqrt{c d^2-c e^2 x^2}}{(d+e x)^{3/2}} \, dx","Int[Sqrt[c*d^2 - c*e^2*x^2]/(d + e*x)^(3/2),x]","\frac{2 \sqrt{c d^2-c e^2 x^2}}{e \sqrt{d+e x}}-\frac{2 \sqrt{2} \sqrt{c} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{e}","\frac{2 \sqrt{c d^2-c e^2 x^2}}{e \sqrt{d+e x}}-\frac{2 \sqrt{2} \sqrt{c} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{e}",1,"(2*Sqrt[c*d^2 - c*e^2*x^2])/(e*Sqrt[d + e*x]) - (2*Sqrt[2]*Sqrt[c]*Sqrt[d]*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/e","A",3,3,29,0.1034,1,"{665, 661, 208}"
867,1,98,0,0.0482074,"\int \frac{\sqrt{c d^2-c e^2 x^2}}{(d+e x)^{5/2}} \, dx","Int[Sqrt[c*d^2 - c*e^2*x^2]/(d + e*x)^(5/2),x]","\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{\sqrt{2} \sqrt{d} e}-\frac{\sqrt{c d^2-c e^2 x^2}}{e (d+e x)^{3/2}}","\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{\sqrt{2} \sqrt{d} e}-\frac{\sqrt{c d^2-c e^2 x^2}}{e (d+e x)^{3/2}}",1,"-(Sqrt[c*d^2 - c*e^2*x^2]/(e*(d + e*x)^(3/2))) + (Sqrt[c]*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/(Sqrt[2]*Sqrt[d]*e)","A",3,3,29,0.1034,1,"{663, 661, 208}"
868,1,141,0,0.0776742,"\int \frac{\sqrt{c d^2-c e^2 x^2}}{(d+e x)^{7/2}} \, dx","Int[Sqrt[c*d^2 - c*e^2*x^2]/(d + e*x)^(7/2),x]","\frac{\sqrt{c d^2-c e^2 x^2}}{8 d e (d+e x)^{3/2}}-\frac{\sqrt{c d^2-c e^2 x^2}}{2 e (d+e x)^{5/2}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{8 \sqrt{2} d^{3/2} e}","\frac{\sqrt{c d^2-c e^2 x^2}}{8 d e (d+e x)^{3/2}}-\frac{\sqrt{c d^2-c e^2 x^2}}{2 e (d+e x)^{5/2}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{8 \sqrt{2} d^{3/2} e}",1,"-Sqrt[c*d^2 - c*e^2*x^2]/(2*e*(d + e*x)^(5/2)) + Sqrt[c*d^2 - c*e^2*x^2]/(8*d*e*(d + e*x)^(3/2)) + (Sqrt[c]*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/(8*Sqrt[2]*d^(3/2)*e)","A",4,4,29,0.1379,1,"{663, 673, 661, 208}"
869,1,201,0,0.0996525,"\int (d+e x)^{5/2} \left(c d^2-c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^(5/2)*(c*d^2 - c*e^2*x^2)^(3/2),x]","-\frac{4096 d^4 \left(c d^2-c e^2 x^2\right)^{5/2}}{15015 c e (d+e x)^{5/2}}-\frac{1024 d^3 \left(c d^2-c e^2 x^2\right)^{5/2}}{3003 c e (d+e x)^{3/2}}-\frac{128 d^2 \left(c d^2-c e^2 x^2\right)^{5/2}}{429 c e \sqrt{d+e x}}-\frac{32 d \sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{5/2}}{143 c e}-\frac{2 (d+e x)^{3/2} \left(c d^2-c e^2 x^2\right)^{5/2}}{13 c e}","-\frac{4096 d^4 \left(c d^2-c e^2 x^2\right)^{5/2}}{15015 c e (d+e x)^{5/2}}-\frac{1024 d^3 \left(c d^2-c e^2 x^2\right)^{5/2}}{3003 c e (d+e x)^{3/2}}-\frac{128 d^2 \left(c d^2-c e^2 x^2\right)^{5/2}}{429 c e \sqrt{d+e x}}-\frac{32 d \sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{5/2}}{143 c e}-\frac{2 (d+e x)^{3/2} \left(c d^2-c e^2 x^2\right)^{5/2}}{13 c e}",1,"(-4096*d^4*(c*d^2 - c*e^2*x^2)^(5/2))/(15015*c*e*(d + e*x)^(5/2)) - (1024*d^3*(c*d^2 - c*e^2*x^2)^(5/2))/(3003*c*e*(d + e*x)^(3/2)) - (128*d^2*(c*d^2 - c*e^2*x^2)^(5/2))/(429*c*e*Sqrt[d + e*x]) - (32*d*Sqrt[d + e*x]*(c*d^2 - c*e^2*x^2)^(5/2))/(143*c*e) - (2*(d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(5/2))/(13*c*e)","A",5,2,29,0.06897,1,"{657, 649}"
870,1,160,0,0.0700215,"\int (d+e x)^{3/2} \left(c d^2-c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(3/2),x]","-\frac{256 d^3 \left(c d^2-c e^2 x^2\right)^{5/2}}{1155 c e (d+e x)^{5/2}}-\frac{64 d^2 \left(c d^2-c e^2 x^2\right)^{5/2}}{231 c e (d+e x)^{3/2}}-\frac{8 d \left(c d^2-c e^2 x^2\right)^{5/2}}{33 c e \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{5/2}}{11 c e}","-\frac{256 d^3 \left(c d^2-c e^2 x^2\right)^{5/2}}{1155 c e (d+e x)^{5/2}}-\frac{64 d^2 \left(c d^2-c e^2 x^2\right)^{5/2}}{231 c e (d+e x)^{3/2}}-\frac{8 d \left(c d^2-c e^2 x^2\right)^{5/2}}{33 c e \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{5/2}}{11 c e}",1,"(-256*d^3*(c*d^2 - c*e^2*x^2)^(5/2))/(1155*c*e*(d + e*x)^(5/2)) - (64*d^2*(c*d^2 - c*e^2*x^2)^(5/2))/(231*c*e*(d + e*x)^(3/2)) - (8*d*(c*d^2 - c*e^2*x^2)^(5/2))/(33*c*e*Sqrt[d + e*x]) - (2*Sqrt[d + e*x]*(c*d^2 - c*e^2*x^2)^(5/2))/(11*c*e)","A",4,2,29,0.06897,1,"{657, 649}"
871,1,119,0,0.0498016,"\int \sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{3/2} \, dx","Int[Sqrt[d + e*x]*(c*d^2 - c*e^2*x^2)^(3/2),x]","-\frac{2 \left(c d^2-c e^2 x^2\right)^{5/2}}{9 c e \sqrt{d+e x}}-\frac{16 d \left(c d^2-c e^2 x^2\right)^{5/2}}{63 c e (d+e x)^{3/2}}-\frac{64 d^2 \left(c d^2-c e^2 x^2\right)^{5/2}}{315 c e (d+e x)^{5/2}}","-\frac{2 \left(c d^2-c e^2 x^2\right)^{5/2}}{9 c e \sqrt{d+e x}}-\frac{16 d \left(c d^2-c e^2 x^2\right)^{5/2}}{63 c e (d+e x)^{3/2}}-\frac{64 d^2 \left(c d^2-c e^2 x^2\right)^{5/2}}{315 c e (d+e x)^{5/2}}",1,"(-64*d^2*(c*d^2 - c*e^2*x^2)^(5/2))/(315*c*e*(d + e*x)^(5/2)) - (16*d*(c*d^2 - c*e^2*x^2)^(5/2))/(63*c*e*(d + e*x)^(3/2)) - (2*(c*d^2 - c*e^2*x^2)^(5/2))/(9*c*e*Sqrt[d + e*x])","A",3,2,29,0.06897,1,"{657, 649}"
872,1,78,0,0.0306673,"\int \frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[(c*d^2 - c*e^2*x^2)^(3/2)/Sqrt[d + e*x],x]","-\frac{2 \left(c d^2-c e^2 x^2\right)^{5/2}}{7 c e (d+e x)^{3/2}}-\frac{8 d \left(c d^2-c e^2 x^2\right)^{5/2}}{35 c e (d+e x)^{5/2}}","-\frac{2 \left(c d^2-c e^2 x^2\right)^{5/2}}{7 c e (d+e x)^{3/2}}-\frac{8 d \left(c d^2-c e^2 x^2\right)^{5/2}}{35 c e (d+e x)^{5/2}}",1,"(-8*d*(c*d^2 - c*e^2*x^2)^(5/2))/(35*c*e*(d + e*x)^(5/2)) - (2*(c*d^2 - c*e^2*x^2)^(5/2))/(7*c*e*(d + e*x)^(3/2))","A",2,2,29,0.06897,1,"{657, 649}"
873,1,38,0,0.0134863,"\int \frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[(c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(3/2),x]","-\frac{2 \left(c d^2-c e^2 x^2\right)^{5/2}}{5 c e (d+e x)^{5/2}}","-\frac{2 \left(c d^2-c e^2 x^2\right)^{5/2}}{5 c e (d+e x)^{5/2}}",1,"(-2*(c*d^2 - c*e^2*x^2)^(5/2))/(5*c*e*(d + e*x)^(5/2))","A",1,1,29,0.03448,1,"{649}"
874,1,136,0,0.0719828,"\int \frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[(c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(5/2),x]","-\frac{4 \sqrt{2} c^{3/2} d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{e}+\frac{4 c d \sqrt{c d^2-c e^2 x^2}}{e \sqrt{d+e x}}+\frac{2 \left(c d^2-c e^2 x^2\right)^{3/2}}{3 e (d+e x)^{3/2}}","-\frac{4 \sqrt{2} c^{3/2} d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{e}+\frac{4 c d \sqrt{c d^2-c e^2 x^2}}{e \sqrt{d+e x}}+\frac{2 \left(c d^2-c e^2 x^2\right)^{3/2}}{3 e (d+e x)^{3/2}}",1,"(4*c*d*Sqrt[c*d^2 - c*e^2*x^2])/(e*Sqrt[d + e*x]) + (2*(c*d^2 - c*e^2*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) - (4*Sqrt[2]*c^(3/2)*d^(3/2)*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/e","A",4,3,29,0.1034,1,"{665, 661, 208}"
875,1,133,0,0.0789978,"\int \frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[(c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(7/2),x]","\frac{3 \sqrt{2} c^{3/2} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{e}-\frac{3 c \sqrt{c d^2-c e^2 x^2}}{e \sqrt{d+e x}}-\frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{e (d+e x)^{5/2}}","\frac{3 \sqrt{2} c^{3/2} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{e}-\frac{3 c \sqrt{c d^2-c e^2 x^2}}{e \sqrt{d+e x}}-\frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{e (d+e x)^{5/2}}",1,"(-3*c*Sqrt[c*d^2 - c*e^2*x^2])/(e*Sqrt[d + e*x]) - (c*d^2 - c*e^2*x^2)^(3/2)/(e*(d + e*x)^(5/2)) + (3*Sqrt[2]*c^(3/2)*Sqrt[d]*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/e","A",4,4,29,0.1379,1,"{663, 665, 661, 208}"
876,1,139,0,0.0706147,"\int \frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{(d+e x)^{9/2}} \, dx","Int[(c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(9/2),x]","-\frac{3 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{4 \sqrt{2} \sqrt{d} e}+\frac{3 c \sqrt{c d^2-c e^2 x^2}}{4 e (d+e x)^{3/2}}-\frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{2 e (d+e x)^{7/2}}","-\frac{3 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{4 \sqrt{2} \sqrt{d} e}+\frac{3 c \sqrt{c d^2-c e^2 x^2}}{4 e (d+e x)^{3/2}}-\frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{2 e (d+e x)^{7/2}}",1,"(3*c*Sqrt[c*d^2 - c*e^2*x^2])/(4*e*(d + e*x)^(3/2)) - (c*d^2 - c*e^2*x^2)^(3/2)/(2*e*(d + e*x)^(7/2)) - (3*c^(3/2)*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/(4*Sqrt[2]*Sqrt[d]*e)","A",4,3,29,0.1034,1,"{663, 661, 208}"
877,1,178,0,0.0967206,"\int \frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{(d+e x)^{11/2}} \, dx","Int[(c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(11/2),x]","-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{16 \sqrt{2} d^{3/2} e}-\frac{c \sqrt{c d^2-c e^2 x^2}}{16 d e (d+e x)^{3/2}}+\frac{c \sqrt{c d^2-c e^2 x^2}}{4 e (d+e x)^{5/2}}-\frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{3 e (d+e x)^{9/2}}","-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{16 \sqrt{2} d^{3/2} e}-\frac{c \sqrt{c d^2-c e^2 x^2}}{16 d e (d+e x)^{3/2}}+\frac{c \sqrt{c d^2-c e^2 x^2}}{4 e (d+e x)^{5/2}}-\frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{3 e (d+e x)^{9/2}}",1,"(c*Sqrt[c*d^2 - c*e^2*x^2])/(4*e*(d + e*x)^(5/2)) - (c*Sqrt[c*d^2 - c*e^2*x^2])/(16*d*e*(d + e*x)^(3/2)) - (c*d^2 - c*e^2*x^2)^(3/2)/(3*e*(d + e*x)^(9/2)) - (c^(3/2)*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/(16*Sqrt[2]*d^(3/2)*e)","A",5,4,29,0.1379,1,"{663, 673, 661, 208}"
878,1,217,0,0.1343713,"\int \frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{(d+e x)^{13/2}} \, dx","Int[(c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(13/2),x]","-\frac{3 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{256 \sqrt{2} d^{5/2} e}-\frac{3 c \sqrt{c d^2-c e^2 x^2}}{256 d^2 e (d+e x)^{3/2}}-\frac{c \sqrt{c d^2-c e^2 x^2}}{64 d e (d+e x)^{5/2}}+\frac{c \sqrt{c d^2-c e^2 x^2}}{8 e (d+e x)^{7/2}}-\frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{4 e (d+e x)^{11/2}}","-\frac{3 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{256 \sqrt{2} d^{5/2} e}-\frac{3 c \sqrt{c d^2-c e^2 x^2}}{256 d^2 e (d+e x)^{3/2}}-\frac{c \sqrt{c d^2-c e^2 x^2}}{64 d e (d+e x)^{5/2}}+\frac{c \sqrt{c d^2-c e^2 x^2}}{8 e (d+e x)^{7/2}}-\frac{\left(c d^2-c e^2 x^2\right)^{3/2}}{4 e (d+e x)^{11/2}}",1,"(c*Sqrt[c*d^2 - c*e^2*x^2])/(8*e*(d + e*x)^(7/2)) - (c*Sqrt[c*d^2 - c*e^2*x^2])/(64*d*e*(d + e*x)^(5/2)) - (3*c*Sqrt[c*d^2 - c*e^2*x^2])/(256*d^2*e*(d + e*x)^(3/2)) - (c*d^2 - c*e^2*x^2)^(3/2)/(4*e*(d + e*x)^(11/2)) - (3*c^(3/2)*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/(256*Sqrt[2]*d^(5/2)*e)","A",6,4,29,0.1379,1,"{663, 673, 661, 208}"
879,1,160,0,0.0800169,"\int \frac{(d+e x)^{7/2}}{\sqrt{c d^2-c e^2 x^2}} \, dx","Int[(d + e*x)^(7/2)/Sqrt[c*d^2 - c*e^2*x^2],x]","-\frac{256 d^3 \sqrt{c d^2-c e^2 x^2}}{35 c e \sqrt{d+e x}}-\frac{64 d^2 \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}{35 c e}-\frac{24 d (d+e x)^{3/2} \sqrt{c d^2-c e^2 x^2}}{35 c e}-\frac{2 (d+e x)^{5/2} \sqrt{c d^2-c e^2 x^2}}{7 c e}","-\frac{256 d^3 \sqrt{c d^2-c e^2 x^2}}{35 c e \sqrt{d+e x}}-\frac{64 d^2 \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}{35 c e}-\frac{24 d (d+e x)^{3/2} \sqrt{c d^2-c e^2 x^2}}{35 c e}-\frac{2 (d+e x)^{5/2} \sqrt{c d^2-c e^2 x^2}}{7 c e}",1,"(-256*d^3*Sqrt[c*d^2 - c*e^2*x^2])/(35*c*e*Sqrt[d + e*x]) - (64*d^2*Sqrt[d + e*x]*Sqrt[c*d^2 - c*e^2*x^2])/(35*c*e) - (24*d*(d + e*x)^(3/2)*Sqrt[c*d^2 - c*e^2*x^2])/(35*c*e) - (2*(d + e*x)^(5/2)*Sqrt[c*d^2 - c*e^2*x^2])/(7*c*e)","A",4,2,29,0.06897,1,"{657, 649}"
880,1,119,0,0.0490256,"\int \frac{(d+e x)^{5/2}}{\sqrt{c d^2-c e^2 x^2}} \, dx","Int[(d + e*x)^(5/2)/Sqrt[c*d^2 - c*e^2*x^2],x]","-\frac{64 d^2 \sqrt{c d^2-c e^2 x^2}}{15 c e \sqrt{d+e x}}-\frac{16 d \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}{15 c e}-\frac{2 (d+e x)^{3/2} \sqrt{c d^2-c e^2 x^2}}{5 c e}","-\frac{64 d^2 \sqrt{c d^2-c e^2 x^2}}{15 c e \sqrt{d+e x}}-\frac{16 d \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}{15 c e}-\frac{2 (d+e x)^{3/2} \sqrt{c d^2-c e^2 x^2}}{5 c e}",1,"(-64*d^2*Sqrt[c*d^2 - c*e^2*x^2])/(15*c*e*Sqrt[d + e*x]) - (16*d*Sqrt[d + e*x]*Sqrt[c*d^2 - c*e^2*x^2])/(15*c*e) - (2*(d + e*x)^(3/2)*Sqrt[c*d^2 - c*e^2*x^2])/(5*c*e)","A",3,2,29,0.06897,1,"{657, 649}"
881,1,78,0,0.0301264,"\int \frac{(d+e x)^{3/2}}{\sqrt{c d^2-c e^2 x^2}} \, dx","Int[(d + e*x)^(3/2)/Sqrt[c*d^2 - c*e^2*x^2],x]","-\frac{8 d \sqrt{c d^2-c e^2 x^2}}{3 c e \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}{3 c e}","-\frac{8 d \sqrt{c d^2-c e^2 x^2}}{3 c e \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}{3 c e}",1,"(-8*d*Sqrt[c*d^2 - c*e^2*x^2])/(3*c*e*Sqrt[d + e*x]) - (2*Sqrt[d + e*x]*Sqrt[c*d^2 - c*e^2*x^2])/(3*c*e)","A",2,2,29,0.06897,1,"{657, 649}"
882,1,36,0,0.0127333,"\int \frac{\sqrt{d+e x}}{\sqrt{c d^2-c e^2 x^2}} \, dx","Int[Sqrt[d + e*x]/Sqrt[c*d^2 - c*e^2*x^2],x]","-\frac{2 \sqrt{c d^2-c e^2 x^2}}{c e \sqrt{d+e x}}","-\frac{2 \sqrt{c d^2-c e^2 x^2}}{c e \sqrt{d+e x}}",1,"(-2*Sqrt[c*d^2 - c*e^2*x^2])/(c*e*Sqrt[d + e*x])","A",1,1,29,0.03448,1,"{649}"
883,1,65,0,0.0287519,"\int \frac{1}{\sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[c*d^2 - c*e^2*x^2]),x]","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{\sqrt{c} \sqrt{d} e}","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{\sqrt{c} \sqrt{d} e}",1,"-((Sqrt[2]*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/(Sqrt[c]*Sqrt[d]*e))","A",2,2,29,0.06897,1,"{661, 208}"
884,1,109,0,0.0510786,"\int \frac{1}{(d+e x)^{3/2} \sqrt{c d^2-c e^2 x^2}} \, dx","Int[1/((d + e*x)^(3/2)*Sqrt[c*d^2 - c*e^2*x^2]),x]","-\frac{\sqrt{c d^2-c e^2 x^2}}{2 c d e (d+e x)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{2 \sqrt{2} \sqrt{c} d^{3/2} e}","-\frac{\sqrt{c d^2-c e^2 x^2}}{2 c d e (d+e x)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{2 \sqrt{2} \sqrt{c} d^{3/2} e}",1,"-Sqrt[c*d^2 - c*e^2*x^2]/(2*c*d*e*(d + e*x)^(3/2)) - ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])]/(2*Sqrt[2]*Sqrt[c]*d^(3/2)*e)","A",3,3,29,0.1034,1,"{673, 661, 208}"
885,1,150,0,0.0720232,"\int \frac{1}{(d+e x)^{5/2} \sqrt{c d^2-c e^2 x^2}} \, dx","Int[1/((d + e*x)^(5/2)*Sqrt[c*d^2 - c*e^2*x^2]),x]","-\frac{3 \sqrt{c d^2-c e^2 x^2}}{16 c d^2 e (d+e x)^{3/2}}-\frac{\sqrt{c d^2-c e^2 x^2}}{4 c d e (d+e x)^{5/2}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{16 \sqrt{2} \sqrt{c} d^{5/2} e}","-\frac{3 \sqrt{c d^2-c e^2 x^2}}{16 c d^2 e (d+e x)^{3/2}}-\frac{\sqrt{c d^2-c e^2 x^2}}{4 c d e (d+e x)^{5/2}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{16 \sqrt{2} \sqrt{c} d^{5/2} e}",1,"-Sqrt[c*d^2 - c*e^2*x^2]/(4*c*d*e*(d + e*x)^(5/2)) - (3*Sqrt[c*d^2 - c*e^2*x^2])/(16*c*d^2*e*(d + e*x)^(3/2)) - (3*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/(16*Sqrt[2]*Sqrt[c]*d^(5/2)*e)","A",4,3,29,0.1034,1,"{673, 661, 208}"
886,1,160,0,0.0726321,"\int \frac{(d+e x)^{9/2}}{\left(c d^2-c e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(9/2)/(c*d^2 - c*e^2*x^2)^(3/2),x]","-\frac{2 (d+e x)^{7/2}}{5 c e \sqrt{c d^2-c e^2 x^2}}-\frac{8 d (d+e x)^{5/2}}{5 c e \sqrt{c d^2-c e^2 x^2}}-\frac{64 d^2 (d+e x)^{3/2}}{5 c e \sqrt{c d^2-c e^2 x^2}}+\frac{256 d^3 \sqrt{d+e x}}{5 c e \sqrt{c d^2-c e^2 x^2}}","-\frac{2 (d+e x)^{7/2}}{5 c e \sqrt{c d^2-c e^2 x^2}}-\frac{8 d (d+e x)^{5/2}}{5 c e \sqrt{c d^2-c e^2 x^2}}-\frac{64 d^2 (d+e x)^{3/2}}{5 c e \sqrt{c d^2-c e^2 x^2}}+\frac{256 d^3 \sqrt{d+e x}}{5 c e \sqrt{c d^2-c e^2 x^2}}",1,"(256*d^3*Sqrt[d + e*x])/(5*c*e*Sqrt[c*d^2 - c*e^2*x^2]) - (64*d^2*(d + e*x)^(3/2))/(5*c*e*Sqrt[c*d^2 - c*e^2*x^2]) - (8*d*(d + e*x)^(5/2))/(5*c*e*Sqrt[c*d^2 - c*e^2*x^2]) - (2*(d + e*x)^(7/2))/(5*c*e*Sqrt[c*d^2 - c*e^2*x^2])","A",4,2,29,0.06897,1,"{657, 649}"
887,1,119,0,0.0486483,"\int \frac{(d+e x)^{7/2}}{\left(c d^2-c e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(7/2)/(c*d^2 - c*e^2*x^2)^(3/2),x]","-\frac{2 (d+e x)^{5/2}}{3 c e \sqrt{c d^2-c e^2 x^2}}-\frac{16 d (d+e x)^{3/2}}{3 c e \sqrt{c d^2-c e^2 x^2}}+\frac{64 d^2 \sqrt{d+e x}}{3 c e \sqrt{c d^2-c e^2 x^2}}","-\frac{2 (d+e x)^{5/2}}{3 c e \sqrt{c d^2-c e^2 x^2}}-\frac{16 d (d+e x)^{3/2}}{3 c e \sqrt{c d^2-c e^2 x^2}}+\frac{64 d^2 \sqrt{d+e x}}{3 c e \sqrt{c d^2-c e^2 x^2}}",1,"(64*d^2*Sqrt[d + e*x])/(3*c*e*Sqrt[c*d^2 - c*e^2*x^2]) - (16*d*(d + e*x)^(3/2))/(3*c*e*Sqrt[c*d^2 - c*e^2*x^2]) - (2*(d + e*x)^(5/2))/(3*c*e*Sqrt[c*d^2 - c*e^2*x^2])","A",3,2,29,0.06897,1,"{657, 649}"
888,1,74,0,0.0288803,"\int \frac{(d+e x)^{5/2}}{\left(c d^2-c e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(5/2)/(c*d^2 - c*e^2*x^2)^(3/2),x]","\frac{8 d \sqrt{d+e x}}{c e \sqrt{c d^2-c e^2 x^2}}-\frac{2 (d+e x)^{3/2}}{c e \sqrt{c d^2-c e^2 x^2}}","\frac{8 d \sqrt{d+e x}}{c e \sqrt{c d^2-c e^2 x^2}}-\frac{2 (d+e x)^{3/2}}{c e \sqrt{c d^2-c e^2 x^2}}",1,"(8*d*Sqrt[d + e*x])/(c*e*Sqrt[c*d^2 - c*e^2*x^2]) - (2*(d + e*x)^(3/2))/(c*e*Sqrt[c*d^2 - c*e^2*x^2])","A",2,2,29,0.06897,1,"{657, 649}"
889,1,36,0,0.0130347,"\int \frac{(d+e x)^{3/2}}{\left(c d^2-c e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/(c*d^2 - c*e^2*x^2)^(3/2),x]","\frac{2 \sqrt{d+e x}}{c e \sqrt{c d^2-c e^2 x^2}}","\frac{2 \sqrt{d+e x}}{c e \sqrt{c d^2-c e^2 x^2}}",1,"(2*Sqrt[d + e*x])/(c*e*Sqrt[c*d^2 - c*e^2*x^2])","A",1,1,29,0.03448,1,"{649}"
890,1,104,0,0.0506586,"\int \frac{\sqrt{d+e x}}{\left(c d^2-c e^2 x^2\right)^{3/2}} \, dx","Int[Sqrt[d + e*x]/(c*d^2 - c*e^2*x^2)^(3/2),x]","\frac{\sqrt{d+e x}}{c d e \sqrt{c d^2-c e^2 x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{\sqrt{2} c^{3/2} d^{3/2} e}","\frac{\sqrt{d+e x}}{c d e \sqrt{c d^2-c e^2 x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{\sqrt{2} c^{3/2} d^{3/2} e}",1,"Sqrt[d + e*x]/(c*d*e*Sqrt[c*d^2 - c*e^2*x^2]) - ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])]/(Sqrt[2]*c^(3/2)*d^(3/2)*e)","A",3,3,29,0.1034,1,"{667, 661, 208}"
891,1,150,0,0.0727255,"\int \frac{1}{\sqrt{d+e x} \left(c d^2-c e^2 x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[d + e*x]*(c*d^2 - c*e^2*x^2)^(3/2)),x]","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{4 \sqrt{2} c^{3/2} d^{5/2} e}+\frac{3 \sqrt{d+e x}}{4 c d^2 e \sqrt{c d^2-c e^2 x^2}}-\frac{1}{2 c d e \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{4 \sqrt{2} c^{3/2} d^{5/2} e}+\frac{3 \sqrt{d+e x}}{4 c d^2 e \sqrt{c d^2-c e^2 x^2}}-\frac{1}{2 c d e \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}",1,"-1/(2*c*d*e*Sqrt[d + e*x]*Sqrt[c*d^2 - c*e^2*x^2]) + (3*Sqrt[d + e*x])/(4*c*d^2*e*Sqrt[c*d^2 - c*e^2*x^2]) - (3*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/(4*Sqrt[2]*c^(3/2)*d^(5/2)*e)","A",4,4,29,0.1379,1,"{673, 667, 661, 208}"
892,1,191,0,0.1065119,"\int \frac{1}{(d+e x)^{3/2} \left(c d^2-c e^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(3/2)),x]","-\frac{15 \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{32 \sqrt{2} c^{3/2} d^{7/2} e}+\frac{15 \sqrt{d+e x}}{32 c d^3 e \sqrt{c d^2-c e^2 x^2}}-\frac{5}{16 c d^2 e \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}-\frac{1}{4 c d e (d+e x)^{3/2} \sqrt{c d^2-c e^2 x^2}}","-\frac{15 \tanh ^{-1}\left(\frac{\sqrt{c d^2-c e^2 x^2}}{\sqrt{2} \sqrt{c} \sqrt{d} \sqrt{d+e x}}\right)}{32 \sqrt{2} c^{3/2} d^{7/2} e}+\frac{15 \sqrt{d+e x}}{32 c d^3 e \sqrt{c d^2-c e^2 x^2}}-\frac{5}{16 c d^2 e \sqrt{d+e x} \sqrt{c d^2-c e^2 x^2}}-\frac{1}{4 c d e (d+e x)^{3/2} \sqrt{c d^2-c e^2 x^2}}",1,"-1/(4*c*d*e*(d + e*x)^(3/2)*Sqrt[c*d^2 - c*e^2*x^2]) - 5/(16*c*d^2*e*Sqrt[d + e*x]*Sqrt[c*d^2 - c*e^2*x^2]) + (15*Sqrt[d + e*x])/(32*c*d^3*e*Sqrt[c*d^2 - c*e^2*x^2]) - (15*ArcTanh[Sqrt[c*d^2 - c*e^2*x^2]/(Sqrt[2]*Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])])/(32*Sqrt[2]*c^(3/2)*d^(7/2)*e)","A",5,4,29,0.1379,1,"{673, 667, 661, 208}"
893,1,31,0,0.0103923,"\int \frac{1}{\sqrt{-1+x} \sqrt{1-x^2}} \, dx","Int[1/(Sqrt[-1 + x]*Sqrt[1 - x^2]),x]","\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{1-x^2}}{\sqrt{2} \sqrt{x-1}}\right)","\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{1-x^2}}{\sqrt{2} \sqrt{x-1}}\right)",1,"Sqrt[2]*ArcTan[Sqrt[1 - x^2]/(Sqrt[2]*Sqrt[-1 + x])]","A",2,2,19,0.1053,1,"{661, 203}"
894,1,87,0,0.0267335,"\int (2+e x)^{5/2} \sqrt{12-3 e^2 x^2} \, dx","Int[(2 + e*x)^(5/2)*Sqrt[12 - 3*e^2*x^2],x]","\frac{2 (2-e x)^{9/2}}{3 \sqrt{3} e}-\frac{24 \sqrt{3} (2-e x)^{7/2}}{7 e}+\frac{96 \sqrt{3} (2-e x)^{5/2}}{5 e}-\frac{128 (2-e x)^{3/2}}{\sqrt{3} e}","\frac{2 (2-e x)^{9/2}}{3 \sqrt{3} e}-\frac{24 \sqrt{3} (2-e x)^{7/2}}{7 e}+\frac{96 \sqrt{3} (2-e x)^{5/2}}{5 e}-\frac{128 (2-e x)^{3/2}}{\sqrt{3} e}",1,"(-128*(2 - e*x)^(3/2))/(Sqrt[3]*e) + (96*Sqrt[3]*(2 - e*x)^(5/2))/(5*e) - (24*Sqrt[3]*(2 - e*x)^(7/2))/(7*e) + (2*(2 - e*x)^(9/2))/(3*Sqrt[3]*e)","A",3,2,24,0.08333,1,"{627, 43}"
895,1,65,0,0.0202403,"\int (2+e x)^{3/2} \sqrt{12-3 e^2 x^2} \, dx","Int[(2 + e*x)^(3/2)*Sqrt[12 - 3*e^2*x^2],x]","-\frac{2 \sqrt{3} (2-e x)^{7/2}}{7 e}+\frac{16 \sqrt{3} (2-e x)^{5/2}}{5 e}-\frac{32 (2-e x)^{3/2}}{\sqrt{3} e}","-\frac{2 \sqrt{3} (2-e x)^{7/2}}{7 e}+\frac{16 \sqrt{3} (2-e x)^{5/2}}{5 e}-\frac{32 (2-e x)^{3/2}}{\sqrt{3} e}",1,"(-32*(2 - e*x)^(3/2))/(Sqrt[3]*e) + (16*Sqrt[3]*(2 - e*x)^(5/2))/(5*e) - (2*Sqrt[3]*(2 - e*x)^(7/2))/(7*e)","A",3,2,24,0.08333,1,"{627, 43}"
896,1,43,0,0.0153062,"\int \sqrt{2+e x} \sqrt{12-3 e^2 x^2} \, dx","Int[Sqrt[2 + e*x]*Sqrt[12 - 3*e^2*x^2],x]","\frac{2 \sqrt{3} (2-e x)^{5/2}}{5 e}-\frac{8 (2-e x)^{3/2}}{\sqrt{3} e}","\frac{2 \sqrt{3} (2-e x)^{5/2}}{5 e}-\frac{8 (2-e x)^{3/2}}{\sqrt{3} e}",1,"(-8*(2 - e*x)^(3/2))/(Sqrt[3]*e) + (2*Sqrt[3]*(2 - e*x)^(5/2))/(5*e)","A",3,2,24,0.08333,1,"{627, 43}"
897,1,20,0,0.0090526,"\int \frac{\sqrt{12-3 e^2 x^2}}{\sqrt{2+e x}} \, dx","Int[Sqrt[12 - 3*e^2*x^2]/Sqrt[2 + e*x],x]","-\frac{2 (2-e x)^{3/2}}{\sqrt{3} e}","-\frac{2 (2-e x)^{3/2}}{\sqrt{3} e}",1,"(-2*(2 - e*x)^(3/2))/(Sqrt[3]*e)","A",2,2,24,0.08333,1,"{627, 32}"
898,1,46,0,0.0202946,"\int \frac{\sqrt{12-3 e^2 x^2}}{(2+e x)^{3/2}} \, dx","Int[Sqrt[12 - 3*e^2*x^2]/(2 + e*x)^(3/2),x]","\frac{2 \sqrt{3} \sqrt{2-e x}}{e}-\frac{4 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{e}","\frac{2 \sqrt{3} \sqrt{2-e x}}{e}-\frac{4 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{e}",1,"(2*Sqrt[3]*Sqrt[2 - e*x])/e - (4*Sqrt[3]*ArcTanh[Sqrt[2 - e*x]/2])/e","A",4,4,24,0.1667,1,"{627, 50, 63, 206}"
899,1,55,0,0.020318,"\int \frac{\sqrt{12-3 e^2 x^2}}{(2+e x)^{5/2}} \, dx","Int[Sqrt[12 - 3*e^2*x^2]/(2 + e*x)^(5/2),x]","\frac{\sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{2 e}-\frac{\sqrt{3} \sqrt{2-e x}}{e (e x+2)}","\frac{\sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{2 e}-\frac{\sqrt{3} \sqrt{2-e x}}{e (e x+2)}",1,"-((Sqrt[3]*Sqrt[2 - e*x])/(e*(2 + e*x))) + (Sqrt[3]*ArcTanh[Sqrt[2 - e*x]/2])/(2*e)","A",4,4,24,0.1667,1,"{627, 47, 63, 206}"
900,1,86,0,0.0290316,"\int \frac{\sqrt{12-3 e^2 x^2}}{(2+e x)^{7/2}} \, dx","Int[Sqrt[12 - 3*e^2*x^2]/(2 + e*x)^(7/2),x]","\frac{\sqrt{3} \sqrt{2-e x}}{16 e (e x+2)}-\frac{\sqrt{3} \sqrt{2-e x}}{2 e (e x+2)^2}+\frac{\sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{32 e}","\frac{\sqrt{3} \sqrt{2-e x}}{16 e (e x+2)}-\frac{\sqrt{3} \sqrt{2-e x}}{2 e (e x+2)^2}+\frac{\sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{32 e}",1,"-(Sqrt[3]*Sqrt[2 - e*x])/(2*e*(2 + e*x)^2) + (Sqrt[3]*Sqrt[2 - e*x])/(16*e*(2 + e*x)) + (Sqrt[3]*ArcTanh[Sqrt[2 - e*x]/2])/(32*e)","A",5,5,24,0.2083,1,"{627, 47, 51, 63, 206}"
901,1,109,0,0.0274405,"\int (2+e x)^{5/2} \left(12-3 e^2 x^2\right)^{3/2} \, dx","Int[(2 + e*x)^(5/2)*(12 - 3*e^2*x^2)^(3/2),x]","-\frac{6 \sqrt{3} (2-e x)^{13/2}}{13 e}+\frac{96 \sqrt{3} (2-e x)^{11/2}}{11 e}-\frac{64 \sqrt{3} (2-e x)^{9/2}}{e}+\frac{1536 \sqrt{3} (2-e x)^{7/2}}{7 e}-\frac{1536 \sqrt{3} (2-e x)^{5/2}}{5 e}","-\frac{6 \sqrt{3} (2-e x)^{13/2}}{13 e}+\frac{96 \sqrt{3} (2-e x)^{11/2}}{11 e}-\frac{64 \sqrt{3} (2-e x)^{9/2}}{e}+\frac{1536 \sqrt{3} (2-e x)^{7/2}}{7 e}-\frac{1536 \sqrt{3} (2-e x)^{5/2}}{5 e}",1,"(-1536*Sqrt[3]*(2 - e*x)^(5/2))/(5*e) + (1536*Sqrt[3]*(2 - e*x)^(7/2))/(7*e) - (64*Sqrt[3]*(2 - e*x)^(9/2))/e + (96*Sqrt[3]*(2 - e*x)^(11/2))/(11*e) - (6*Sqrt[3]*(2 - e*x)^(13/2))/(13*e)","A",3,2,24,0.08333,1,"{627, 43}"
902,1,87,0,0.0239898,"\int (2+e x)^{3/2} \left(12-3 e^2 x^2\right)^{3/2} \, dx","Int[(2 + e*x)^(3/2)*(12 - 3*e^2*x^2)^(3/2),x]","\frac{6 \sqrt{3} (2-e x)^{11/2}}{11 e}-\frac{8 \sqrt{3} (2-e x)^{9/2}}{e}+\frac{288 \sqrt{3} (2-e x)^{7/2}}{7 e}-\frac{384 \sqrt{3} (2-e x)^{5/2}}{5 e}","\frac{6 \sqrt{3} (2-e x)^{11/2}}{11 e}-\frac{8 \sqrt{3} (2-e x)^{9/2}}{e}+\frac{288 \sqrt{3} (2-e x)^{7/2}}{7 e}-\frac{384 \sqrt{3} (2-e x)^{5/2}}{5 e}",1,"(-384*Sqrt[3]*(2 - e*x)^(5/2))/(5*e) + (288*Sqrt[3]*(2 - e*x)^(7/2))/(7*e) - (8*Sqrt[3]*(2 - e*x)^(9/2))/e + (6*Sqrt[3]*(2 - e*x)^(11/2))/(11*e)","A",3,2,24,0.08333,1,"{627, 43}"
903,1,65,0,0.0196335,"\int \sqrt{2+e x} \left(12-3 e^2 x^2\right)^{3/2} \, dx","Int[Sqrt[2 + e*x]*(12 - 3*e^2*x^2)^(3/2),x]","-\frac{2 (2-e x)^{9/2}}{\sqrt{3} e}+\frac{48 \sqrt{3} (2-e x)^{7/2}}{7 e}-\frac{96 \sqrt{3} (2-e x)^{5/2}}{5 e}","-\frac{2 (2-e x)^{9/2}}{\sqrt{3} e}+\frac{48 \sqrt{3} (2-e x)^{7/2}}{7 e}-\frac{96 \sqrt{3} (2-e x)^{5/2}}{5 e}",1,"(-96*Sqrt[3]*(2 - e*x)^(5/2))/(5*e) + (48*Sqrt[3]*(2 - e*x)^(7/2))/(7*e) - (2*(2 - e*x)^(9/2))/(Sqrt[3]*e)","A",3,2,24,0.08333,1,"{627, 43}"
904,1,45,0,0.0156231,"\int \frac{\left(12-3 e^2 x^2\right)^{3/2}}{\sqrt{2+e x}} \, dx","Int[(12 - 3*e^2*x^2)^(3/2)/Sqrt[2 + e*x],x]","\frac{6 \sqrt{3} (2-e x)^{7/2}}{7 e}-\frac{24 \sqrt{3} (2-e x)^{5/2}}{5 e}","\frac{6 \sqrt{3} (2-e x)^{7/2}}{7 e}-\frac{24 \sqrt{3} (2-e x)^{5/2}}{5 e}",1,"(-24*Sqrt[3]*(2 - e*x)^(5/2))/(5*e) + (6*Sqrt[3]*(2 - e*x)^(7/2))/(7*e)","A",3,2,24,0.08333,1,"{627, 43}"
905,1,22,0,0.0094595,"\int \frac{\left(12-3 e^2 x^2\right)^{3/2}}{(2+e x)^{3/2}} \, dx","Int[(12 - 3*e^2*x^2)^(3/2)/(2 + e*x)^(3/2),x]","-\frac{6 \sqrt{3} (2-e x)^{5/2}}{5 e}","-\frac{6 \sqrt{3} (2-e x)^{5/2}}{5 e}",1,"(-6*Sqrt[3]*(2 - e*x)^(5/2))/(5*e)","A",2,2,24,0.08333,1,"{627, 32}"
906,1,66,0,0.028687,"\int \frac{\left(12-3 e^2 x^2\right)^{3/2}}{(2+e x)^{5/2}} \, dx","Int[(12 - 3*e^2*x^2)^(3/2)/(2 + e*x)^(5/2),x]","\frac{2 \sqrt{3} (2-e x)^{3/2}}{e}+\frac{24 \sqrt{3} \sqrt{2-e x}}{e}-\frac{48 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{e}","\frac{2 \sqrt{3} (2-e x)^{3/2}}{e}+\frac{24 \sqrt{3} \sqrt{2-e x}}{e}-\frac{48 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{e}",1,"(24*Sqrt[3]*Sqrt[2 - e*x])/e + (2*Sqrt[3]*(2 - e*x)^(3/2))/e - (48*Sqrt[3]*ArcTanh[Sqrt[2 - e*x]/2])/e","A",5,4,24,0.1667,1,"{627, 50, 63, 206}"
907,1,73,0,0.0276186,"\int \frac{\left(12-3 e^2 x^2\right)^{3/2}}{(2+e x)^{7/2}} \, dx","Int[(12 - 3*e^2*x^2)^(3/2)/(2 + e*x)^(7/2),x]","-\frac{3 \sqrt{3} (2-e x)^{3/2}}{e (e x+2)}-\frac{9 \sqrt{3} \sqrt{2-e x}}{e}+\frac{18 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{e}","-\frac{3 \sqrt{3} (2-e x)^{3/2}}{e (e x+2)}-\frac{9 \sqrt{3} \sqrt{2-e x}}{e}+\frac{18 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{e}",1,"(-9*Sqrt[3]*Sqrt[2 - e*x])/e - (3*Sqrt[3]*(2 - e*x)^(3/2))/(e*(2 + e*x)) + (18*Sqrt[3]*ArcTanh[Sqrt[2 - e*x]/2])/e","A",5,5,24,0.2083,1,"{627, 47, 50, 63, 206}"
908,1,86,0,0.0290324,"\int \frac{\left(12-3 e^2 x^2\right)^{3/2}}{(2+e x)^{9/2}} \, dx","Int[(12 - 3*e^2*x^2)^(3/2)/(2 + e*x)^(9/2),x]","-\frac{3 \sqrt{3} (2-e x)^{3/2}}{2 e (e x+2)^2}+\frac{9 \sqrt{3} \sqrt{2-e x}}{4 e (e x+2)}-\frac{9 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{8 e}","-\frac{3 \sqrt{3} (2-e x)^{3/2}}{2 e (e x+2)^2}+\frac{9 \sqrt{3} \sqrt{2-e x}}{4 e (e x+2)}-\frac{9 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{8 e}",1,"(-3*Sqrt[3]*(2 - e*x)^(3/2))/(2*e*(2 + e*x)^2) + (9*Sqrt[3]*Sqrt[2 - e*x])/(4*e*(2 + e*x)) - (9*Sqrt[3]*ArcTanh[Sqrt[2 - e*x]/2])/(8*e)","A",5,4,24,0.1667,1,"{627, 47, 63, 206}"
909,1,113,0,0.0389677,"\int \frac{\left(12-3 e^2 x^2\right)^{3/2}}{(2+e x)^{11/2}} \, dx","Int[(12 - 3*e^2*x^2)^(3/2)/(2 + e*x)^(11/2),x]","-\frac{\sqrt{3} (2-e x)^{3/2}}{e (e x+2)^3}-\frac{3 \sqrt{3} \sqrt{2-e x}}{32 e (e x+2)}+\frac{3 \sqrt{3} \sqrt{2-e x}}{4 e (e x+2)^2}-\frac{3 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{64 e}","-\frac{\sqrt{3} (2-e x)^{3/2}}{e (e x+2)^3}-\frac{3 \sqrt{3} \sqrt{2-e x}}{32 e (e x+2)}+\frac{3 \sqrt{3} \sqrt{2-e x}}{4 e (e x+2)^2}-\frac{3 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{64 e}",1,"-((Sqrt[3]*(2 - e*x)^(3/2))/(e*(2 + e*x)^3)) + (3*Sqrt[3]*Sqrt[2 - e*x])/(4*e*(2 + e*x)^2) - (3*Sqrt[3]*Sqrt[2 - e*x])/(32*e*(2 + e*x)) - (3*Sqrt[3]*ArcTanh[Sqrt[2 - e*x]/2])/(64*e)","A",6,5,24,0.2083,1,"{627, 47, 51, 63, 206}"
910,1,144,0,0.0516731,"\int \frac{\left(12-3 e^2 x^2\right)^{3/2}}{(2+e x)^{13/2}} \, dx","Int[(12 - 3*e^2*x^2)^(3/2)/(2 + e*x)^(13/2),x]","-\frac{3 \sqrt{3} (2-e x)^{3/2}}{4 e (e x+2)^4}-\frac{9 \sqrt{3} \sqrt{2-e x}}{1024 e (e x+2)}-\frac{3 \sqrt{3} \sqrt{2-e x}}{128 e (e x+2)^2}+\frac{3 \sqrt{3} \sqrt{2-e x}}{8 e (e x+2)^3}-\frac{9 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{2048 e}","-\frac{3 \sqrt{3} (2-e x)^{3/2}}{4 e (e x+2)^4}-\frac{9 \sqrt{3} \sqrt{2-e x}}{1024 e (e x+2)}-\frac{3 \sqrt{3} \sqrt{2-e x}}{128 e (e x+2)^2}+\frac{3 \sqrt{3} \sqrt{2-e x}}{8 e (e x+2)^3}-\frac{9 \sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{2048 e}",1,"(-3*Sqrt[3]*(2 - e*x)^(3/2))/(4*e*(2 + e*x)^4) + (3*Sqrt[3]*Sqrt[2 - e*x])/(8*e*(2 + e*x)^3) - (3*Sqrt[3]*Sqrt[2 - e*x])/(128*e*(2 + e*x)^2) - (9*Sqrt[3]*Sqrt[2 - e*x])/(1024*e*(2 + e*x)) - (9*Sqrt[3]*ArcTanh[Sqrt[2 - e*x]/2])/(2048*e)","A",7,5,24,0.2083,1,"{627, 47, 51, 63, 206}"
911,1,85,0,0.0233863,"\int \frac{(2+e x)^{7/2}}{\sqrt{12-3 e^2 x^2}} \, dx","Int[(2 + e*x)^(7/2)/Sqrt[12 - 3*e^2*x^2],x]","\frac{2 (2-e x)^{7/2}}{7 \sqrt{3} e}-\frac{8 \sqrt{3} (2-e x)^{5/2}}{5 e}+\frac{32 (2-e x)^{3/2}}{\sqrt{3} e}-\frac{128 \sqrt{2-e x}}{\sqrt{3} e}","\frac{2 (2-e x)^{7/2}}{7 \sqrt{3} e}-\frac{8 \sqrt{3} (2-e x)^{5/2}}{5 e}+\frac{32 (2-e x)^{3/2}}{\sqrt{3} e}-\frac{128 \sqrt{2-e x}}{\sqrt{3} e}",1,"(-128*Sqrt[2 - e*x])/(Sqrt[3]*e) + (32*(2 - e*x)^(3/2))/(Sqrt[3]*e) - (8*Sqrt[3]*(2 - e*x)^(5/2))/(5*e) + (2*(2 - e*x)^(7/2))/(7*Sqrt[3]*e)","A",3,2,24,0.08333,1,"{627, 43}"
912,1,65,0,0.0199924,"\int \frac{(2+e x)^{5/2}}{\sqrt{12-3 e^2 x^2}} \, dx","Int[(2 + e*x)^(5/2)/Sqrt[12 - 3*e^2*x^2],x]","-\frac{2 (2-e x)^{5/2}}{5 \sqrt{3} e}+\frac{16 (2-e x)^{3/2}}{3 \sqrt{3} e}-\frac{32 \sqrt{2-e x}}{\sqrt{3} e}","-\frac{2 (2-e x)^{5/2}}{5 \sqrt{3} e}+\frac{16 (2-e x)^{3/2}}{3 \sqrt{3} e}-\frac{32 \sqrt{2-e x}}{\sqrt{3} e}",1,"(-32*Sqrt[2 - e*x])/(Sqrt[3]*e) + (16*(2 - e*x)^(3/2))/(3*Sqrt[3]*e) - (2*(2 - e*x)^(5/2))/(5*Sqrt[3]*e)","A",3,2,24,0.08333,1,"{627, 43}"
913,1,43,0,0.0167946,"\int \frac{(2+e x)^{3/2}}{\sqrt{12-3 e^2 x^2}} \, dx","Int[(2 + e*x)^(3/2)/Sqrt[12 - 3*e^2*x^2],x]","\frac{2 (2-e x)^{3/2}}{3 \sqrt{3} e}-\frac{8 \sqrt{2-e x}}{\sqrt{3} e}","\frac{2 (2-e x)^{3/2}}{3 \sqrt{3} e}-\frac{8 \sqrt{2-e x}}{\sqrt{3} e}",1,"(-8*Sqrt[2 - e*x])/(Sqrt[3]*e) + (2*(2 - e*x)^(3/2))/(3*Sqrt[3]*e)","A",3,2,24,0.08333,1,"{627, 43}"
914,1,20,0,0.0085675,"\int \frac{\sqrt{2+e x}}{\sqrt{12-3 e^2 x^2}} \, dx","Int[Sqrt[2 + e*x]/Sqrt[12 - 3*e^2*x^2],x]","-\frac{2 \sqrt{2-e x}}{\sqrt{3} e}","-\frac{2 \sqrt{2-e x}}{\sqrt{3} e}",1,"(-2*Sqrt[2 - e*x])/(Sqrt[3]*e)","A",2,2,24,0.08333,1,"{627, 32}"
915,1,25,0,0.0153917,"\int \frac{1}{\sqrt{2+e x} \sqrt{12-3 e^2 x^2}} \, dx","Int[1/(Sqrt[2 + e*x]*Sqrt[12 - 3*e^2*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{\sqrt{3} e}","-\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{\sqrt{3} e}",1,"-(ArcTanh[Sqrt[2 - e*x]/2]/(Sqrt[3]*e))","A",3,3,24,0.1250,1,"{627, 63, 206}"
916,1,57,0,0.0207186,"\int \frac{1}{(2+e x)^{3/2} \sqrt{12-3 e^2 x^2}} \, dx","Int[1/((2 + e*x)^(3/2)*Sqrt[12 - 3*e^2*x^2]),x]","-\frac{\sqrt{2-e x}}{4 \sqrt{3} e (e x+2)}-\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{8 \sqrt{3} e}","-\frac{\sqrt{2-e x}}{4 \sqrt{3} e (e x+2)}-\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{8 \sqrt{3} e}",1,"-Sqrt[2 - e*x]/(4*Sqrt[3]*e*(2 + e*x)) - ArcTanh[Sqrt[2 - e*x]/2]/(8*Sqrt[3]*e)","A",4,4,24,0.1667,1,"{627, 51, 63, 206}"
917,1,86,0,0.0278343,"\int \frac{1}{(2+e x)^{5/2} \sqrt{12-3 e^2 x^2}} \, dx","Int[1/((2 + e*x)^(5/2)*Sqrt[12 - 3*e^2*x^2]),x]","-\frac{\sqrt{3} \sqrt{2-e x}}{64 e (e x+2)}-\frac{\sqrt{2-e x}}{8 \sqrt{3} e (e x+2)^2}-\frac{\sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{128 e}","-\frac{\sqrt{3} \sqrt{2-e x}}{64 e (e x+2)}-\frac{\sqrt{2-e x}}{8 \sqrt{3} e (e x+2)^2}-\frac{\sqrt{3} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{128 e}",1,"-Sqrt[2 - e*x]/(8*Sqrt[3]*e*(2 + e*x)^2) - (Sqrt[3]*Sqrt[2 - e*x])/(64*e*(2 + e*x)) - (Sqrt[3]*ArcTanh[Sqrt[2 - e*x]/2])/(128*e)","A",5,4,24,0.1667,1,"{627, 51, 63, 206}"
918,1,111,0,0.0285124,"\int \frac{(2+e x)^{11/2}}{\left(12-3 e^2 x^2\right)^{3/2}} \, dx","Int[(2 + e*x)^(11/2)/(12 - 3*e^2*x^2)^(3/2),x]","-\frac{2 (2-e x)^{7/2}}{21 \sqrt{3} e}+\frac{32 (2-e x)^{5/2}}{15 \sqrt{3} e}-\frac{64 (2-e x)^{3/2}}{3 \sqrt{3} e}+\frac{512 \sqrt{2-e x}}{3 \sqrt{3} e}+\frac{512}{3 \sqrt{3} e \sqrt{2-e x}}","-\frac{2 (2-e x)^{7/2}}{21 \sqrt{3} e}+\frac{32 (2-e x)^{5/2}}{15 \sqrt{3} e}-\frac{64 (2-e x)^{3/2}}{3 \sqrt{3} e}+\frac{512 \sqrt{2-e x}}{3 \sqrt{3} e}+\frac{512}{3 \sqrt{3} e \sqrt{2-e x}}",1,"512/(3*Sqrt[3]*e*Sqrt[2 - e*x]) + (512*Sqrt[2 - e*x])/(3*Sqrt[3]*e) - (64*(2 - e*x)^(3/2))/(3*Sqrt[3]*e) + (32*(2 - e*x)^(5/2))/(15*Sqrt[3]*e) - (2*(2 - e*x)^(7/2))/(21*Sqrt[3]*e)","A",3,2,24,0.08333,1,"{627, 43}"
919,1,87,0,0.0245445,"\int \frac{(2+e x)^{9/2}}{\left(12-3 e^2 x^2\right)^{3/2}} \, dx","Int[(2 + e*x)^(9/2)/(12 - 3*e^2*x^2)^(3/2),x]","\frac{2 (2-e x)^{5/2}}{15 \sqrt{3} e}-\frac{8 (2-e x)^{3/2}}{3 \sqrt{3} e}+\frac{32 \sqrt{2-e x}}{\sqrt{3} e}+\frac{128}{3 \sqrt{3} e \sqrt{2-e x}}","\frac{2 (2-e x)^{5/2}}{15 \sqrt{3} e}-\frac{8 (2-e x)^{3/2}}{3 \sqrt{3} e}+\frac{32 \sqrt{2-e x}}{\sqrt{3} e}+\frac{128}{3 \sqrt{3} e \sqrt{2-e x}}",1,"128/(3*Sqrt[3]*e*Sqrt[2 - e*x]) + (32*Sqrt[2 - e*x])/(Sqrt[3]*e) - (8*(2 - e*x)^(3/2))/(3*Sqrt[3]*e) + (2*(2 - e*x)^(5/2))/(15*Sqrt[3]*e)","A",3,2,24,0.08333,1,"{627, 43}"
920,1,67,0,0.021156,"\int \frac{(2+e x)^{7/2}}{\left(12-3 e^2 x^2\right)^{3/2}} \, dx","Int[(2 + e*x)^(7/2)/(12 - 3*e^2*x^2)^(3/2),x]","-\frac{2 (2-e x)^{3/2}}{9 \sqrt{3} e}+\frac{16 \sqrt{2-e x}}{3 \sqrt{3} e}+\frac{32}{3 \sqrt{3} e \sqrt{2-e x}}","-\frac{2 (2-e x)^{3/2}}{9 \sqrt{3} e}+\frac{16 \sqrt{2-e x}}{3 \sqrt{3} e}+\frac{32}{3 \sqrt{3} e \sqrt{2-e x}}",1,"32/(3*Sqrt[3]*e*Sqrt[2 - e*x]) + (16*Sqrt[2 - e*x])/(3*Sqrt[3]*e) - (2*(2 - e*x)^(3/2))/(9*Sqrt[3]*e)","A",3,2,24,0.08333,1,"{627, 43}"
921,1,45,0,0.0171074,"\int \frac{(2+e x)^{5/2}}{\left(12-3 e^2 x^2\right)^{3/2}} \, dx","Int[(2 + e*x)^(5/2)/(12 - 3*e^2*x^2)^(3/2),x]","\frac{2 \sqrt{2-e x}}{3 \sqrt{3} e}+\frac{8}{3 \sqrt{3} e \sqrt{2-e x}}","\frac{2 \sqrt{2-e x}}{3 \sqrt{3} e}+\frac{8}{3 \sqrt{3} e \sqrt{2-e x}}",1,"8/(3*Sqrt[3]*e*Sqrt[2 - e*x]) + (2*Sqrt[2 - e*x])/(3*Sqrt[3]*e)","A",3,2,24,0.08333,1,"{627, 43}"
922,1,22,0,0.0096814,"\int \frac{(2+e x)^{3/2}}{\left(12-3 e^2 x^2\right)^{3/2}} \, dx","Int[(2 + e*x)^(3/2)/(12 - 3*e^2*x^2)^(3/2),x]","\frac{2}{3 \sqrt{3} e \sqrt{2-e x}}","\frac{2}{3 \sqrt{3} e \sqrt{2-e x}}",1,"2/(3*Sqrt[3]*e*Sqrt[2 - e*x])","A",2,2,24,0.08333,1,"{627, 32}"
923,1,50,0,0.0209086,"\int \frac{\sqrt{2+e x}}{\left(12-3 e^2 x^2\right)^{3/2}} \, dx","Int[Sqrt[2 + e*x]/(12 - 3*e^2*x^2)^(3/2),x]","\frac{1}{6 \sqrt{3} e \sqrt{2-e x}}-\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{12 \sqrt{3} e}","\frac{1}{6 \sqrt{3} e \sqrt{2-e x}}-\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{12 \sqrt{3} e}",1,"1/(6*Sqrt[3]*e*Sqrt[2 - e*x]) - ArcTanh[Sqrt[2 - e*x]/2]/(12*Sqrt[3]*e)","A",4,4,24,0.1667,1,"{627, 51, 63, 206}"
924,1,86,0,0.0303714,"\int \frac{1}{\sqrt{2+e x} \left(12-3 e^2 x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[2 + e*x]*(12 - 3*e^2*x^2)^(3/2)),x]","-\frac{\sqrt{2-e x}}{16 \sqrt{3} e (e x+2)}+\frac{1}{6 \sqrt{3} e \sqrt{2-e x} (e x+2)}-\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{32 \sqrt{3} e}","\frac{1}{16 \sqrt{3} e \sqrt{2-e x}}-\frac{1}{12 \sqrt{3} e \sqrt{2-e x} (e x+2)}-\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{32 \sqrt{3} e}",1,"1/(6*Sqrt[3]*e*Sqrt[2 - e*x]*(2 + e*x)) - Sqrt[2 - e*x]/(16*Sqrt[3]*e*(2 + e*x)) - ArcTanh[Sqrt[2 - e*x]/2]/(32*Sqrt[3]*e)","A",5,4,24,0.1667,1,"{627, 51, 63, 206}"
925,1,115,0,0.0414894,"\int \frac{1}{(2+e x)^{3/2} \left(12-3 e^2 x^2\right)^{3/2}} \, dx","Int[1/((2 + e*x)^(3/2)*(12 - 3*e^2*x^2)^(3/2)),x]","-\frac{5 \sqrt{2-e x}}{256 \sqrt{3} e (e x+2)}-\frac{5 \sqrt{2-e x}}{96 \sqrt{3} e (e x+2)^2}+\frac{1}{6 \sqrt{3} e \sqrt{2-e x} (e x+2)^2}-\frac{5 \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{512 \sqrt{3} e}","\frac{5}{256 \sqrt{3} e \sqrt{2-e x}}-\frac{5}{192 \sqrt{3} e \sqrt{2-e x} (e x+2)}-\frac{1}{24 \sqrt{3} e \sqrt{2-e x} (e x+2)^2}-\frac{5 \tanh ^{-1}\left(\frac{1}{2} \sqrt{2-e x}\right)}{512 \sqrt{3} e}",1,"1/(6*Sqrt[3]*e*Sqrt[2 - e*x]*(2 + e*x)^2) - (5*Sqrt[2 - e*x])/(96*Sqrt[3]*e*(2 + e*x)^2) - (5*Sqrt[2 - e*x])/(256*Sqrt[3]*e*(2 + e*x)) - (5*ArcTanh[Sqrt[2 - e*x]/2])/(512*Sqrt[3]*e)","A",6,4,24,0.1667,1,"{627, 51, 63, 206}"
926,1,23,0,0.0061987,"\int \frac{1}{\sqrt{1-x} (1+x)} \, dx","Int[1/(Sqrt[1 - x]*(1 + x)),x]","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)",1,"-(Sqrt[2]*ArcTanh[Sqrt[1 - x]/Sqrt[2]])","A",2,2,15,0.1333,1,"{63, 206}"
927,1,23,0,0.0103184,"\int \frac{1}{\sqrt{1+x} \sqrt{1-x^2}} \, dx","Int[1/(Sqrt[1 + x]*Sqrt[1 - x^2]),x]","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)",1,"-(Sqrt[2]*ArcTanh[Sqrt[1 - x]/Sqrt[2]])","A",3,3,19,0.1579,1,"{627, 63, 206}"
928,1,27,0,0.0081858,"\int \frac{1}{\sqrt{1-a x} (1+a x)} \, dx","Int[1/(Sqrt[1 - a*x]*(1 + a*x)),x]","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{a}","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{a}",1,"-((Sqrt[2]*ArcTanh[Sqrt[1 - a*x]/Sqrt[2]])/a)","A",2,2,18,0.1111,1,"{63, 206}"
929,1,27,0,0.0140314,"\int \frac{1}{\sqrt{1+a x} \sqrt{1-a^2 x^2}} \, dx","Int[1/(Sqrt[1 + a*x]*Sqrt[1 - a^2*x^2]),x]","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{a}","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{a}",1,"-((Sqrt[2]*ArcTanh[Sqrt[1 - a*x]/Sqrt[2]])/a)","A",3,3,24,0.1250,1,"{627, 63, 206}"
930,1,309,0,0.3350618,"\int \sqrt{2+e x} \sqrt[4]{12-3 e^2 x^2} \, dx","Int[Sqrt[2 + e*x]*(12 - 3*e^2*x^2)^(1/4),x]","-\frac{\sqrt[4]{3} (e x+2)^{3/4} (2-e x)^{5/4}}{2 e}+\frac{3 \sqrt[4]{3} (e x+2)^{3/4} \sqrt[4]{2-e x}}{2 e}+\frac{3 \sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} e}-\frac{3 \sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} e}+\frac{3 \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt{2} e}-\frac{3 \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt{2} e}","-\frac{\sqrt[4]{3} (e x+2)^{3/4} (2-e x)^{5/4}}{2 e}+\frac{3 \sqrt[4]{3} (e x+2)^{3/4} \sqrt[4]{2-e x}}{2 e}+\frac{3 \sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} e}-\frac{3 \sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} e}+\frac{3 \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt{2} e}-\frac{3 \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt{2} e}",1,"(3*3^(1/4)*(2 - e*x)^(1/4)*(2 + e*x)^(3/4))/(2*e) - (3^(1/4)*(2 - e*x)^(5/4)*(2 + e*x)^(3/4))/(2*e) + (3*3^(1/4)*ArcTan[1 - (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(Sqrt[2]*e) - (3*3^(1/4)*ArcTan[1 + (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(Sqrt[2]*e) + (3*3^(1/4)*Log[(Sqrt[6 - 3*e*x] - Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(2*Sqrt[2]*e) - (3*3^(1/4)*Log[(Sqrt[6 - 3*e*x] + Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(2*Sqrt[2]*e)","A",14,10,24,0.4167,1,"{675, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
931,1,269,0,0.2613398,"\int \frac{\sqrt[4]{12-3 e^2 x^2}}{\sqrt{2+e x}} \, dx","Int[(12 - 3*e^2*x^2)^(1/4)/Sqrt[2 + e*x],x]","\frac{\sqrt[4]{3} \sqrt[4]{2-e x} (e x+2)^{3/4}}{e}+\frac{\sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} e}-\frac{\sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} e}+\frac{\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{e}-\frac{\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{e}","\frac{\sqrt[4]{3} \sqrt[4]{2-e x} (e x+2)^{3/4}}{e}+\frac{\sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} e}-\frac{\sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} e}+\frac{\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{e}-\frac{\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{e}",1,"(3^(1/4)*(2 - e*x)^(1/4)*(2 + e*x)^(3/4))/e + (Sqrt[2]*3^(1/4)*ArcTan[1 - (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/e - (Sqrt[2]*3^(1/4)*ArcTan[1 + (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/e + (3^(1/4)*Log[(Sqrt[6 - 3*e*x] - Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(Sqrt[2]*e) - (3^(1/4)*Log[(Sqrt[6 - 3*e*x] + Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(Sqrt[2]*e)","A",13,10,24,0.4167,1,"{675, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
932,1,270,0,0.2625225,"\int \frac{\sqrt[4]{12-3 e^2 x^2}}{(2+e x)^{3/2}} \, dx","Int[(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(3/2),x]","-\frac{4 \sqrt[4]{3} \sqrt[4]{2-e x}}{e \sqrt[4]{e x+2}}-\frac{\sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} e}+\frac{\sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} e}-\frac{\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{e}+\frac{\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{e}","-\frac{4 \sqrt[4]{3} \sqrt[4]{2-e x}}{e \sqrt[4]{e x+2}}-\frac{\sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} e}+\frac{\sqrt[4]{3} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} e}-\frac{\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{e}+\frac{\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{e}",1,"(-4*3^(1/4)*(2 - e*x)^(1/4))/(e*(2 + e*x)^(1/4)) - (Sqrt[2]*3^(1/4)*ArcTan[1 - (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/e + (Sqrt[2]*3^(1/4)*ArcTan[1 + (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/e - (3^(1/4)*Log[(Sqrt[6 - 3*e*x] - Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(Sqrt[2]*e) + (3^(1/4)*Log[(Sqrt[6 - 3*e*x] + Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(Sqrt[2]*e)","A",13,10,24,0.4167,1,"{675, 47, 63, 240, 211, 1165, 628, 1162, 617, 204}"
933,1,35,0,0.0100162,"\int \frac{\sqrt[4]{12-3 e^2 x^2}}{(2+e x)^{5/2}} \, dx","Int[(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(5/2),x]","-\frac{\sqrt[4]{3} \left(4-e^2 x^2\right)^{5/4}}{5 e (e x+2)^{5/2}}","-\frac{\sqrt[4]{3} \left(4-e^2 x^2\right)^{5/4}}{5 e (e x+2)^{5/2}}",1,"-(3^(1/4)*(4 - e^2*x^2)^(5/4))/(5*e*(2 + e*x)^(5/2))","A",1,1,24,0.04167,1,"{651}"
934,1,71,0,0.0260016,"\int \frac{\sqrt[4]{12-3 e^2 x^2}}{(2+e x)^{7/2}} \, dx","Int[(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(7/2),x]","-\frac{\left(4-e^2 x^2\right)^{5/4}}{15\ 3^{3/4} e (e x+2)^{5/2}}-\frac{\left(4-e^2 x^2\right)^{5/4}}{3\ 3^{3/4} e (e x+2)^{7/2}}","-\frac{\left(4-e^2 x^2\right)^{5/4}}{15\ 3^{3/4} e (e x+2)^{5/2}}-\frac{\left(4-e^2 x^2\right)^{5/4}}{3\ 3^{3/4} e (e x+2)^{7/2}}",1,"-(4 - e^2*x^2)^(5/4)/(3*3^(3/4)*e*(2 + e*x)^(7/2)) - (4 - e^2*x^2)^(5/4)/(15*3^(3/4)*e*(2 + e*x)^(5/2))","A",2,2,24,0.08333,1,"{659, 651}"
935,1,106,0,0.040833,"\int \frac{\sqrt[4]{12-3 e^2 x^2}}{(2+e x)^{9/2}} \, dx","Int[(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(9/2),x]","-\frac{2 \left(4-e^2 x^2\right)^{5/4}}{195\ 3^{3/4} e (e x+2)^{5/2}}-\frac{2 \left(4-e^2 x^2\right)^{5/4}}{39\ 3^{3/4} e (e x+2)^{7/2}}-\frac{\sqrt[4]{3} \left(4-e^2 x^2\right)^{5/4}}{13 e (e x+2)^{9/2}}","-\frac{2 \left(4-e^2 x^2\right)^{5/4}}{195\ 3^{3/4} e (e x+2)^{5/2}}-\frac{2 \left(4-e^2 x^2\right)^{5/4}}{39\ 3^{3/4} e (e x+2)^{7/2}}-\frac{\sqrt[4]{3} \left(4-e^2 x^2\right)^{5/4}}{13 e (e x+2)^{9/2}}",1,"-(3^(1/4)*(4 - e^2*x^2)^(5/4))/(13*e*(2 + e*x)^(9/2)) - (2*(4 - e^2*x^2)^(5/4))/(39*3^(3/4)*e*(2 + e*x)^(7/2)) - (2*(4 - e^2*x^2)^(5/4))/(195*3^(3/4)*e*(2 + e*x)^(5/2))","A",3,2,24,0.08333,1,"{659, 651}"
936,1,141,0,0.0577388,"\int \frac{\sqrt[4]{12-3 e^2 x^2}}{(2+e x)^{11/2}} \, dx","Int[(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(11/2),x]","-\frac{2 \left(4-e^2 x^2\right)^{5/4}}{1105\ 3^{3/4} e (e x+2)^{5/2}}-\frac{2 \left(4-e^2 x^2\right)^{5/4}}{221\ 3^{3/4} e (e x+2)^{7/2}}-\frac{3 \sqrt[4]{3} \left(4-e^2 x^2\right)^{5/4}}{221 e (e x+2)^{9/2}}-\frac{\sqrt[4]{3} \left(4-e^2 x^2\right)^{5/4}}{17 e (e x+2)^{11/2}}","-\frac{2 \left(4-e^2 x^2\right)^{5/4}}{1105\ 3^{3/4} e (e x+2)^{5/2}}-\frac{2 \left(4-e^2 x^2\right)^{5/4}}{221\ 3^{3/4} e (e x+2)^{7/2}}-\frac{3 \sqrt[4]{3} \left(4-e^2 x^2\right)^{5/4}}{221 e (e x+2)^{9/2}}-\frac{\sqrt[4]{3} \left(4-e^2 x^2\right)^{5/4}}{17 e (e x+2)^{11/2}}",1,"-(3^(1/4)*(4 - e^2*x^2)^(5/4))/(17*e*(2 + e*x)^(11/2)) - (3*3^(1/4)*(4 - e^2*x^2)^(5/4))/(221*e*(2 + e*x)^(9/2)) - (2*(4 - e^2*x^2)^(5/4))/(221*3^(3/4)*e*(2 + e*x)^(7/2)) - (2*(4 - e^2*x^2)^(5/4))/(1105*3^(3/4)*e*(2 + e*x)^(5/2))","A",4,2,24,0.08333,1,"{659, 651}"
937,1,340,0,0.2980827,"\int \frac{(2+e x)^{5/2}}{\sqrt[4]{12-3 e^2 x^2}} \, dx","Int[(2 + e*x)^(5/2)/(12 - 3*e^2*x^2)^(1/4),x]","-\frac{(2-e x)^{3/4} (e x+2)^{9/4}}{3 \sqrt[4]{3} e}-\frac{3^{3/4} (2-e x)^{3/4} (e x+2)^{5/4}}{2 e}-\frac{5\ 3^{3/4} (2-e x)^{3/4} \sqrt[4]{e x+2}}{2 e}-\frac{5\ 3^{3/4} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} e}+\frac{5\ 3^{3/4} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} e}+\frac{5\ 3^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt{2} e}-\frac{5\ 3^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt{2} e}","-\frac{(2-e x)^{3/4} (e x+2)^{9/4}}{3 \sqrt[4]{3} e}-\frac{3^{3/4} (2-e x)^{3/4} (e x+2)^{5/4}}{2 e}-\frac{5\ 3^{3/4} (2-e x)^{3/4} \sqrt[4]{e x+2}}{2 e}-\frac{5\ 3^{3/4} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} e}+\frac{5\ 3^{3/4} \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} e}+\frac{5\ 3^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt{2} e}-\frac{5\ 3^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt{2} e}",1,"(-5*3^(3/4)*(2 - e*x)^(3/4)*(2 + e*x)^(1/4))/(2*e) - (3^(3/4)*(2 - e*x)^(3/4)*(2 + e*x)^(5/4))/(2*e) - ((2 - e*x)^(3/4)*(2 + e*x)^(9/4))/(3*3^(1/4)*e) + (5*3^(3/4)*ArcTan[1 - (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(Sqrt[2]*e) - (5*3^(3/4)*ArcTan[1 + (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(Sqrt[2]*e) - (5*3^(3/4)*Log[(Sqrt[6 - 3*e*x] - Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(2*Sqrt[2]*e) + (5*3^(3/4)*Log[(Sqrt[6 - 3*e*x] + Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(2*Sqrt[2]*e)","A",15,10,24,0.4167,1,"{675, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
938,1,309,0,0.2694181,"\int \frac{(2+e x)^{3/2}}{\sqrt[4]{12-3 e^2 x^2}} \, dx","Int[(2 + e*x)^(3/2)/(12 - 3*e^2*x^2)^(1/4),x]","-\frac{(2-e x)^{3/4} (e x+2)^{5/4}}{2 \sqrt[4]{3} e}-\frac{5 (2-e x)^{3/4} \sqrt[4]{e x+2}}{2 \sqrt[4]{3} e}-\frac{5 \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} \sqrt[4]{3} e}+\frac{5 \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} \sqrt[4]{3} e}+\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt{2} \sqrt[4]{3} e}","-\frac{(2-e x)^{3/4} (e x+2)^{5/4}}{2 \sqrt[4]{3} e}-\frac{5 (2-e x)^{3/4} \sqrt[4]{e x+2}}{2 \sqrt[4]{3} e}-\frac{5 \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} \sqrt[4]{3} e}+\frac{5 \log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{2 \sqrt{2} \sqrt[4]{3} e}+\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt{2} \sqrt[4]{3} e}",1,"(-5*(2 - e*x)^(3/4)*(2 + e*x)^(1/4))/(2*3^(1/4)*e) - ((2 - e*x)^(3/4)*(2 + e*x)^(5/4))/(2*3^(1/4)*e) + (5*ArcTan[1 - (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(Sqrt[2]*3^(1/4)*e) - (5*ArcTan[1 + (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(Sqrt[2]*3^(1/4)*e) - (5*Log[(Sqrt[6 - 3*e*x] - Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(2*Sqrt[2]*3^(1/4)*e) + (5*Log[(Sqrt[6 - 3*e*x] + Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]])/(2*Sqrt[2]*3^(1/4)*e)","A",14,10,24,0.4167,1,"{675, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
939,1,270,0,0.23944,"\int \frac{\sqrt{2+e x}}{\sqrt[4]{12-3 e^2 x^2}} \, dx","Int[Sqrt[2 + e*x]/(12 - 3*e^2*x^2)^(1/4),x]","-\frac{(2-e x)^{3/4} \sqrt[4]{e x+2}}{\sqrt[4]{3} e}-\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt[4]{3} e}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt[4]{3} e}","-\frac{(2-e x)^{3/4} \sqrt[4]{e x+2}}{\sqrt[4]{3} e}-\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt[4]{3} e}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt[4]{3} e}",1,"-(((2 - e*x)^(3/4)*(2 + e*x)^(1/4))/(3^(1/4)*e)) + (Sqrt[2]*ArcTan[1 - (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(3^(1/4)*e) - (Sqrt[2]*ArcTan[1 + (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(3^(1/4)*e) - Log[(Sqrt[6 - 3*e*x] - Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]]/(Sqrt[2]*3^(1/4)*e) + Log[(Sqrt[6 - 3*e*x] + Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]]/(Sqrt[2]*3^(1/4)*e)","A",13,10,24,0.4167,1,"{675, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
940,1,241,0,0.2448007,"\int \frac{1}{\sqrt{2+e x} \sqrt[4]{12-3 e^2 x^2}} \, dx","Int[1/(Sqrt[2 + e*x]*(12 - 3*e^2*x^2)^(1/4)),x]","-\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt[4]{3} e}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt[4]{3} e}","-\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}-\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\log \left(\frac{\sqrt{6-3 e x}+\sqrt{3} \sqrt{e x+2}+\sqrt{6} \sqrt[4]{2-e x} \sqrt[4]{e x+2}}{\sqrt{e x+2}}\right)}{\sqrt{2} \sqrt[4]{3} e}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}\right)}{\sqrt[4]{3} e}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{2-e x}}{\sqrt[4]{e x+2}}+1\right)}{\sqrt[4]{3} e}",1,"(Sqrt[2]*ArcTan[1 - (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(3^(1/4)*e) - (Sqrt[2]*ArcTan[1 + (Sqrt[2]*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)])/(3^(1/4)*e) - Log[(Sqrt[6 - 3*e*x] - Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]]/(Sqrt[2]*3^(1/4)*e) + Log[(Sqrt[6 - 3*e*x] + Sqrt[6]*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + Sqrt[3]*Sqrt[2 + e*x])/Sqrt[2 + e*x]]/(Sqrt[2]*3^(1/4)*e)","A",12,9,24,0.3750,1,"{675, 63, 331, 297, 1162, 617, 204, 1165, 628}"
941,1,35,0,0.0141082,"\int \frac{1}{(2+e x)^{3/2} \sqrt[4]{12-3 e^2 x^2}} \, dx","Int[1/((2 + e*x)^(3/2)*(12 - 3*e^2*x^2)^(1/4)),x]","-\frac{\left(4-e^2 x^2\right)^{3/4}}{3 \sqrt[4]{3} e (e x+2)^{3/2}}","-\frac{\left(4-e^2 x^2\right)^{3/4}}{3 \sqrt[4]{3} e (e x+2)^{3/2}}",1,"-(4 - e^2*x^2)^(3/4)/(3*3^(1/4)*e*(2 + e*x)^(3/2))","A",1,1,24,0.04167,1,"{651}"
942,1,71,0,0.0264299,"\int \frac{1}{(2+e x)^{5/2} \sqrt[4]{12-3 e^2 x^2}} \, dx","Int[1/((2 + e*x)^(5/2)*(12 - 3*e^2*x^2)^(1/4)),x]","-\frac{\left(4-e^2 x^2\right)^{3/4}}{21 \sqrt[4]{3} e (e x+2)^{3/2}}-\frac{\left(4-e^2 x^2\right)^{3/4}}{7 \sqrt[4]{3} e (e x+2)^{5/2}}","-\frac{\left(4-e^2 x^2\right)^{3/4}}{21 \sqrt[4]{3} e (e x+2)^{3/2}}-\frac{\left(4-e^2 x^2\right)^{3/4}}{7 \sqrt[4]{3} e (e x+2)^{5/2}}",1,"-(4 - e^2*x^2)^(3/4)/(7*3^(1/4)*e*(2 + e*x)^(5/2)) - (4 - e^2*x^2)^(3/4)/(21*3^(1/4)*e*(2 + e*x)^(3/2))","A",2,2,24,0.08333,1,"{659, 651}"
943,1,106,0,0.0510352,"\int \frac{1}{(2+e x)^{7/2} \sqrt[4]{12-3 e^2 x^2}} \, dx","Int[1/((2 + e*x)^(7/2)*(12 - 3*e^2*x^2)^(1/4)),x]","-\frac{2 \left(4-e^2 x^2\right)^{3/4}}{231 \sqrt[4]{3} e (e x+2)^{3/2}}-\frac{2 \left(4-e^2 x^2\right)^{3/4}}{77 \sqrt[4]{3} e (e x+2)^{5/2}}-\frac{\left(4-e^2 x^2\right)^{3/4}}{11 \sqrt[4]{3} e (e x+2)^{7/2}}","-\frac{2 \left(4-e^2 x^2\right)^{3/4}}{231 \sqrt[4]{3} e (e x+2)^{3/2}}-\frac{2 \left(4-e^2 x^2\right)^{3/4}}{77 \sqrt[4]{3} e (e x+2)^{5/2}}-\frac{\left(4-e^2 x^2\right)^{3/4}}{11 \sqrt[4]{3} e (e x+2)^{7/2}}",1,"-(4 - e^2*x^2)^(3/4)/(11*3^(1/4)*e*(2 + e*x)^(7/2)) - (2*(4 - e^2*x^2)^(3/4))/(77*3^(1/4)*e*(2 + e*x)^(5/2)) - (2*(4 - e^2*x^2)^(3/4))/(231*3^(1/4)*e*(2 + e*x)^(3/2))","A",3,2,24,0.08333,1,"{659, 651}"
944,1,141,0,0.0729962,"\int \frac{1}{(2+e x)^{9/2} \sqrt[4]{12-3 e^2 x^2}} \, dx","Int[1/((2 + e*x)^(9/2)*(12 - 3*e^2*x^2)^(1/4)),x]","-\frac{2 \left(4-e^2 x^2\right)^{3/4}}{1155 \sqrt[4]{3} e (e x+2)^{3/2}}-\frac{2 \left(4-e^2 x^2\right)^{3/4}}{385 \sqrt[4]{3} e (e x+2)^{5/2}}-\frac{\left(4-e^2 x^2\right)^{3/4}}{55 \sqrt[4]{3} e (e x+2)^{7/2}}-\frac{\left(4-e^2 x^2\right)^{3/4}}{15 \sqrt[4]{3} e (e x+2)^{9/2}}","-\frac{2 \left(4-e^2 x^2\right)^{3/4}}{1155 \sqrt[4]{3} e (e x+2)^{3/2}}-\frac{2 \left(4-e^2 x^2\right)^{3/4}}{385 \sqrt[4]{3} e (e x+2)^{5/2}}-\frac{\left(4-e^2 x^2\right)^{3/4}}{55 \sqrt[4]{3} e (e x+2)^{7/2}}-\frac{\left(4-e^2 x^2\right)^{3/4}}{15 \sqrt[4]{3} e (e x+2)^{9/2}}",1,"-(4 - e^2*x^2)^(3/4)/(15*3^(1/4)*e*(2 + e*x)^(9/2)) - (4 - e^2*x^2)^(3/4)/(55*3^(1/4)*e*(2 + e*x)^(7/2)) - (2*(4 - e^2*x^2)^(3/4))/(385*3^(1/4)*e*(2 + e*x)^(5/2)) - (2*(4 - e^2*x^2)^(3/4))/(1155*3^(1/4)*e*(2 + e*x)^(3/2))","A",4,2,24,0.08333,1,"{659, 651}"
945,1,84,0,0.0418968,"\int (a+b x)^m \left(a^2-b^2 x^2\right)^3 \, dx","Int[(a + b*x)^m*(a^2 - b^2*x^2)^3,x]","\frac{8 a^3 (a+b x)^{m+4}}{b (m+4)}-\frac{12 a^2 (a+b x)^{m+5}}{b (m+5)}+\frac{6 a (a+b x)^{m+6}}{b (m+6)}-\frac{(a+b x)^{m+7}}{b (m+7)}","\frac{8 a^3 (a+b x)^{m+4}}{b (m+4)}-\frac{12 a^2 (a+b x)^{m+5}}{b (m+5)}+\frac{6 a (a+b x)^{m+6}}{b (m+6)}-\frac{(a+b x)^{m+7}}{b (m+7)}",1,"(8*a^3*(a + b*x)^(4 + m))/(b*(4 + m)) - (12*a^2*(a + b*x)^(5 + m))/(b*(5 + m)) + (6*a*(a + b*x)^(6 + m))/(b*(6 + m)) - (a + b*x)^(7 + m)/(b*(7 + m))","A",3,2,22,0.09091,1,"{627, 43}"
946,1,61,0,0.0279287,"\int (a+b x)^m \left(a^2-b^2 x^2\right)^2 \, dx","Int[(a + b*x)^m*(a^2 - b^2*x^2)^2,x]","\frac{4 a^2 (a+b x)^{m+3}}{b (m+3)}-\frac{4 a (a+b x)^{m+4}}{b (m+4)}+\frac{(a+b x)^{m+5}}{b (m+5)}","\frac{4 a^2 (a+b x)^{m+3}}{b (m+3)}-\frac{4 a (a+b x)^{m+4}}{b (m+4)}+\frac{(a+b x)^{m+5}}{b (m+5)}",1,"(4*a^2*(a + b*x)^(3 + m))/(b*(3 + m)) - (4*a*(a + b*x)^(4 + m))/(b*(4 + m)) + (a + b*x)^(5 + m)/(b*(5 + m))","A",3,2,22,0.09091,1,"{627, 43}"
947,1,40,0,0.0165849,"\int (a+b x)^m \left(a^2-b^2 x^2\right) \, dx","Int[(a + b*x)^m*(a^2 - b^2*x^2),x]","\frac{2 a (a+b x)^{m+2}}{b (m+2)}-\frac{(a+b x)^{m+3}}{b (m+3)}","\frac{2 a (a+b x)^{m+2}}{b (m+2)}-\frac{(a+b x)^{m+3}}{b (m+3)}",1,"(2*a*(a + b*x)^(2 + m))/(b*(2 + m)) - (a + b*x)^(3 + m)/(b*(3 + m))","A",3,2,20,0.1000,1,"{627, 43}"
948,1,38,0,0.0133872,"\int \frac{(a+b x)^m}{a^2-b^2 x^2} \, dx","Int[(a + b*x)^m/(a^2 - b^2*x^2),x]","\frac{(a+b x)^m \, _2F_1\left(1,m;m+1;\frac{a+b x}{2 a}\right)}{2 a b m}","\frac{(a+b x)^m \, _2F_1\left(1,m;m+1;\frac{a+b x}{2 a}\right)}{2 a b m}",1,"((a + b*x)^m*Hypergeometric2F1[1, m, 1 + m, (a + b*x)/(2*a)])/(2*a*b*m)","A",2,2,22,0.09091,1,"{627, 68}"
949,1,44,0,0.0154593,"\int \frac{(a+b x)^m}{\left(a^2-b^2 x^2\right)^2} \, dx","Int[(a + b*x)^m/(a^2 - b^2*x^2)^2,x]","-\frac{(a+b x)^{m-1} \, _2F_1\left(2,m-1;m;\frac{a+b x}{2 a}\right)}{4 a^2 b (1-m)}","-\frac{(a+b x)^{m-1} \, _2F_1\left(2,m-1;m;\frac{a+b x}{2 a}\right)}{4 a^2 b (1-m)}",1,"-((a + b*x)^(-1 + m)*Hypergeometric2F1[2, -1 + m, m, (a + b*x)/(2*a)])/(4*a^2*b*(1 - m))","A",2,2,22,0.09091,1,"{627, 68}"
950,1,46,0,0.0151704,"\int \frac{(a+b x)^m}{\left(a^2-b^2 x^2\right)^3} \, dx","Int[(a + b*x)^m/(a^2 - b^2*x^2)^3,x]","-\frac{(a+b x)^{m-2} \, _2F_1\left(3,m-2;m-1;\frac{a+b x}{2 a}\right)}{8 a^3 b (2-m)}","-\frac{(a+b x)^{m-2} \, _2F_1\left(3,m-2;m-1;\frac{a+b x}{2 a}\right)}{8 a^3 b (2-m)}",1,"-((a + b*x)^(-2 + m)*Hypergeometric2F1[3, -2 + m, -1 + m, (a + b*x)/(2*a)])/(8*a^3*b*(2 - m))","A",2,2,22,0.09091,1,"{627, 68}"
951,1,83,0,0.0490376,"\int (d+e x)^m \left(d^2-e^2 x^2\right)^{7/2} \, dx","Int[(d + e*x)^m*(d^2 - e^2*x^2)^(7/2),x]","-\frac{2^{m+\frac{9}{2}} \left(d^2-e^2 x^2\right)^{9/2} (d+e x)^m \left(\frac{e x}{d}+1\right)^{-m-\frac{9}{2}} \, _2F_1\left(\frac{9}{2},-m-\frac{7}{2};\frac{11}{2};\frac{d-e x}{2 d}\right)}{9 d e}","\frac{\left(d^2-e^2 x^2\right)^{9/2} (d+e x)^m \, _2F_1\left(1,m+9;m+\frac{11}{2};\frac{d+e x}{2 d}\right)}{d e (2 m+9)}",1,"-(2^(9/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-9/2 - m)*(d^2 - e^2*x^2)^(9/2)*Hypergeometric2F1[9/2, -7/2 - m, 11/2, (d - e*x)/(2*d)])/(9*d*e)","A",3,3,24,0.1250,1,"{680, 678, 69}"
952,1,83,0,0.0475875,"\int (d+e x)^m \left(d^2-e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^m*(d^2 - e^2*x^2)^(5/2),x]","-\frac{2^{m+\frac{7}{2}} \left(d^2-e^2 x^2\right)^{7/2} (d+e x)^m \left(\frac{e x}{d}+1\right)^{-m-\frac{7}{2}} \, _2F_1\left(\frac{7}{2},-m-\frac{5}{2};\frac{9}{2};\frac{d-e x}{2 d}\right)}{7 d e}","-\frac{2^{m+\frac{7}{2}} \left(d^2-e^2 x^2\right)^{7/2} (d+e x)^m \left(\frac{e x}{d}+1\right)^{-m-\frac{7}{2}} \, _2F_1\left(\frac{7}{2},-m-\frac{5}{2};\frac{9}{2};\frac{d-e x}{2 d}\right)}{7 d e}",1,"-(2^(7/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-7/2 - m)*(d^2 - e^2*x^2)^(7/2)*Hypergeometric2F1[7/2, -5/2 - m, 9/2, (d - e*x)/(2*d)])/(7*d*e)","A",3,3,24,0.1250,1,"{680, 678, 69}"
953,1,83,0,0.0473627,"\int (d+e x)^m \left(d^2-e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^m*(d^2 - e^2*x^2)^(3/2),x]","-\frac{2^{m+\frac{5}{2}} \left(d^2-e^2 x^2\right)^{5/2} (d+e x)^m \left(\frac{e x}{d}+1\right)^{-m-\frac{5}{2}} \, _2F_1\left(\frac{5}{2},-m-\frac{3}{2};\frac{7}{2};\frac{d-e x}{2 d}\right)}{5 d e}","\frac{\left(d^2-e^2 x^2\right)^{5/2} (d+e x)^m \, _2F_1\left(1,m+5;m+\frac{7}{2};\frac{d+e x}{2 d}\right)}{d e (2 m+5)}",1,"-(2^(5/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-5/2 - m)*(d^2 - e^2*x^2)^(5/2)*Hypergeometric2F1[5/2, -3/2 - m, 7/2, (d - e*x)/(2*d)])/(5*d*e)","A",3,3,24,0.1250,1,"{680, 678, 69}"
954,1,83,0,0.0469089,"\int (d+e x)^m \sqrt{d^2-e^2 x^2} \, dx","Int[(d + e*x)^m*Sqrt[d^2 - e^2*x^2],x]","-\frac{2^{m+\frac{3}{2}} \left(d^2-e^2 x^2\right)^{3/2} (d+e x)^m \left(\frac{e x}{d}+1\right)^{-m-\frac{3}{2}} \, _2F_1\left(\frac{3}{2},-m-\frac{1}{2};\frac{5}{2};\frac{d-e x}{2 d}\right)}{3 d e}","\frac{(d-e x) \sqrt{d^2-e^2 x^2} (d+e x)^{m+1} \, _2F_1\left(1,m+3;m+\frac{5}{2};\frac{d+e x}{2 d}\right)}{d e (2 m+3)}",1,"-(2^(3/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-3/2 - m)*(d^2 - e^2*x^2)^(3/2)*Hypergeometric2F1[3/2, -1/2 - m, 5/2, (d - e*x)/(2*d)])/(3*d*e)","A",3,3,24,0.1250,1,"{680, 678, 69}"
955,1,81,0,0.0451431,"\int \frac{(d+e x)^m}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(d + e*x)^m/Sqrt[d^2 - e^2*x^2],x]","-\frac{2^{m+\frac{1}{2}} \sqrt{d^2-e^2 x^2} (d+e x)^m \left(\frac{e x}{d}+1\right)^{-m-\frac{1}{2}} \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{d-e x}{2 d}\right)}{d e}","\frac{(d-e x) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+\frac{3}{2};\frac{d+e x}{2 d}\right)}{d e (2 m+1) \sqrt{d^2-e^2 x^2}}",1,"-((2^(1/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-1/2 - m)*Sqrt[d^2 - e^2*x^2]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (d - e*x)/(2*d)])/(d*e))","A",3,3,24,0.1250,1,"{680, 678, 69}"
956,1,80,0,0.0539989,"\int \frac{(d+e x)^m}{\left(d^2-e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^m/(d^2 - e^2*x^2)^(3/2),x]","\frac{2^{m-\frac{1}{2}} (d+e x)^m \left(\frac{e x}{d}+1\right)^{\frac{1}{2}-m} \, _2F_1\left(-\frac{1}{2},\frac{3}{2}-m;\frac{1}{2};\frac{d-e x}{2 d}\right)}{d e \sqrt{d^2-e^2 x^2}}","\frac{2^{m-\frac{1}{2}} (d+e x)^m \left(\frac{e x}{d}+1\right)^{\frac{1}{2}-m} \, _2F_1\left(-\frac{1}{2},\frac{3}{2}-m;\frac{1}{2};\frac{d-e x}{2 d}\right)}{d e \sqrt{d^2-e^2 x^2}}",1,"(2^(-1/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(1/2 - m)*Hypergeometric2F1[-1/2, 3/2 - m, 1/2, (d - e*x)/(2*d)])/(d*e*Sqrt[d^2 - e^2*x^2])","A",3,3,24,0.1250,1,"{680, 678, 69}"
957,1,83,0,0.052316,"\int \frac{(d+e x)^m}{\left(d^2-e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^m/(d^2 - e^2*x^2)^(5/2),x]","\frac{2^{m-\frac{3}{2}} (d+e x)^m \left(\frac{e x}{d}+1\right)^{\frac{3}{2}-m} \, _2F_1\left(-\frac{3}{2},\frac{5}{2}-m;-\frac{1}{2};\frac{d-e x}{2 d}\right)}{3 d e \left(d^2-e^2 x^2\right)^{3/2}}","-\frac{(d+e x)^m \, _2F_1\left(1,m-3;m-\frac{1}{2};\frac{d+e x}{2 d}\right)}{d e (3-2 m) \left(d^2-e^2 x^2\right)^{3/2}}",1,"(2^(-3/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(3/2 - m)*Hypergeometric2F1[-3/2, 5/2 - m, -1/2, (d - e*x)/(2*d)])/(3*d*e*(d^2 - e^2*x^2)^(3/2))","A",3,3,24,0.1250,1,"{680, 678, 69}"
958,1,83,0,0.0566717,"\int \frac{(d+e x)^m}{\left(d^2-e^2 x^2\right)^{7/2}} \, dx","Int[(d + e*x)^m/(d^2 - e^2*x^2)^(7/2),x]","\frac{2^{m-\frac{5}{2}} (d+e x)^m \left(\frac{e x}{d}+1\right)^{\frac{5}{2}-m} \, _2F_1\left(-\frac{5}{2},\frac{7}{2}-m;-\frac{3}{2};\frac{d-e x}{2 d}\right)}{5 d e \left(d^2-e^2 x^2\right)^{5/2}}","-\frac{(d-e x) (d+e x)^{m+1} \, _2F_1\left(1,m-5;m-\frac{3}{2};\frac{d+e x}{2 d}\right)}{d e (5-2 m) \left(d^2-e^2 x^2\right)^{7/2}}",1,"(2^(-5/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(5/2 - m)*Hypergeometric2F1[-5/2, 7/2 - m, -3/2, (d - e*x)/(2*d)])/(5*d*e*(d^2 - e^2*x^2)^(5/2))","A",3,3,24,0.1250,1,"{680, 678, 69}"
959,1,85,0,0.055875,"\int (a+b x)^m \left(a^2-b^2 x^2\right)^p \, dx","Int[(a + b*x)^m*(a^2 - b^2*x^2)^p,x]","-\frac{2^{m+p} (a+b x)^m \left(a^2-b^2 x^2\right)^{p+1} \left(\frac{b x}{a}+1\right)^{-m-p-1} \, _2F_1\left(-m-p,p+1;p+2;\frac{a-b x}{2 a}\right)}{a b (p+1)}","\frac{(a+b x)^m \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(1,m+2 p+2;m+p+2;\frac{a+b x}{2 a}\right)}{2 a b (m+p+1)}",1,"-((2^(m + p)*(a + b*x)^m*(1 + (b*x)/a)^(-1 - m - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[-m - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(a*b*(1 + p)))","A",3,3,22,0.1364,1,"{680, 678, 69}"
960,1,57,0,0.0386394,"\int (d+e x)^3 \left(1-\frac{e^2 x^2}{d^2}\right)^p \, dx","Int[(d + e*x)^3*(1 - (e^2*x^2)/d^2)^p,x]","-\frac{d^4 2^{p+3} \left(\frac{d-e x}{d}\right)^{p+1} \, _2F_1\left(-p-3,p+1;p+2;\frac{d-e x}{2 d}\right)}{e (p+1)}","-\frac{d^4 2^{p+3} \left(\frac{d-e x}{d}\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^4*((d - e*x)/d)^(1 + p)*Hypergeometric2F1[-3 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(e*(1 + p)))","A",2,2,23,0.08696,1,"{676, 69}"
961,1,57,0,0.0345681,"\int (d+e x)^2 \left(1-\frac{e^2 x^2}{d^2}\right)^p \, dx","Int[(d + e*x)^2*(1 - (e^2*x^2)/d^2)^p,x]","-\frac{d^3 2^{p+2} \left(\frac{d-e x}{d}\right)^{p+1} \, _2F_1\left(-p-2,p+1;p+2;\frac{d-e x}{2 d}\right)}{e (p+1)}","-\frac{d^3 2^{p+2} \left(\frac{d-e x}{d}\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^3*((d - e*x)/d)^(1 + p)*Hypergeometric2F1[-2 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(e*(1 + p)))","A",2,2,23,0.08696,1,"{676, 69}"
962,1,56,0,0.0156348,"\int (d+e x) \left(1-\frac{e^2 x^2}{d^2}\right)^p \, dx","Int[(d + e*x)*(1 - (e^2*x^2)/d^2)^p,x]","d x \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)-\frac{d^2 \left(1-\frac{e^2 x^2}{d^2}\right)^{p+1}}{2 e (p+1)}","-\frac{d^2 2^{p+1} \left(\frac{d-e x}{d}\right)^{p+1} \, _2F_1\left(-p-1,p+1;p+2;\frac{d-e x}{2 d}\right)}{e (p+1)}",1,"-(d^2*(1 - (e^2*x^2)/d^2)^(1 + p))/(2*e*(1 + p)) + d*x*Hypergeometric2F1[1/2, -p, 3/2, (e^2*x^2)/d^2]","A",2,2,21,0.09524,1,"{641, 245}"
963,1,22,0,0.0049424,"\int \left(1-\frac{e^2 x^2}{d^2}\right)^p \, dx","Int[(1 - (e^2*x^2)/d^2)^p,x]","x \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)","x \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{e^2 x^2}{d^2}\right)",1,"x*Hypergeometric2F1[1/2, -p, 3/2, (e^2*x^2)/d^2]","A",1,1,15,0.06667,1,"{245}"
964,1,54,0,0.03575,"\int \frac{\left(1-\frac{e^2 x^2}{d^2}\right)^p}{d+e x} \, dx","Int[(1 - (e^2*x^2)/d^2)^p/(d + e*x),x]","-\frac{2^{p-1} \left(\frac{d-e x}{d}\right)^{p+1} \, _2F_1\left(1-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{e (p+1)}","\frac{2^p \left(\frac{d+e x}{d}\right)^p \, _2F_1\left(-p,p;p+1;\frac{d+e x}{2 d}\right)}{e p}",1,"-((2^(-1 + p)*((d - e*x)/d)^(1 + p)*Hypergeometric2F1[1 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(e*(1 + p)))","A",2,2,23,0.08696,1,"{676, 69}"
965,1,57,0,0.0396949,"\int \frac{\left(1-\frac{e^2 x^2}{d^2}\right)^p}{(d+e x)^2} \, dx","Int[(1 - (e^2*x^2)/d^2)^p/(d + e*x)^2,x]","-\frac{2^{p-2} \left(\frac{d-e x}{d}\right)^{p+1} \, _2F_1\left(2-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d e (p+1)}","-\frac{2^{p-2} \left(\frac{d-e x}{d}\right)^{p+1} \, _2F_1\left(2-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d e (p+1)}",1,"-((2^(-2 + p)*((d - e*x)/d)^(1 + p)*Hypergeometric2F1[2 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d*e*(1 + p)))","A",2,2,23,0.08696,1,"{676, 69}"
966,1,57,0,0.0365362,"\int \frac{\left(1-\frac{e^2 x^2}{d^2}\right)^p}{(d+e x)^3} \, dx","Int[(1 - (e^2*x^2)/d^2)^p/(d + e*x)^3,x]","-\frac{2^{p-3} \left(\frac{d-e x}{d}\right)^{p+1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e (p+1)}","-\frac{2^{p-3} \left(\frac{d-e x}{d}\right)^{p+1} \, _2F_1\left(3-p,p+1;p+2;\frac{d-e x}{2 d}\right)}{d^2 e (p+1)}",1,"-((2^(-3 + p)*((d - e*x)/d)^(1 + p)*Hypergeometric2F1[3 - p, 1 + p, 2 + p, (d - e*x)/(2*d)])/(d^2*e*(1 + p)))","A",2,2,23,0.08696,1,"{676, 69}"
967,1,73,0,0.0305929,"\int (a+b x)^3 \left(a^2-b^2 x^2\right)^p \, dx","Int[(a + b*x)^3*(a^2 - b^2*x^2)^p,x]","-\frac{a^2 2^{p+3} \left(\frac{b x}{a}+1\right)^{-p-1} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(-p-3,p+1;p+2;\frac{a-b x}{2 a}\right)}{b (p+1)}","\frac{(a+b x)^3 \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(1,2 p+5;p+5;\frac{a+b x}{2 a}\right)}{2 a b (p+4)}",1,"-((2^(3 + p)*a^2*(1 + (b*x)/a)^(-1 - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[-3 - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(b*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
968,1,71,0,0.0289164,"\int (a+b x)^2 \left(a^2-b^2 x^2\right)^p \, dx","Int[(a + b*x)^2*(a^2 - b^2*x^2)^p,x]","-\frac{a 2^{p+2} \left(\frac{b x}{a}+1\right)^{-p-1} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(-p-2,p+1;p+2;\frac{a-b x}{2 a}\right)}{b (p+1)}","\frac{(a+b x)^2 \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(1,2 (p+2);p+4;\frac{a+b x}{2 a}\right)}{2 a b (p+3)}",1,"-((2^(2 + p)*a*(1 + (b*x)/a)^(-1 - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[-2 - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(b*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
969,1,83,0,0.022037,"\int (a+b x) \left(a^2-b^2 x^2\right)^p \, dx","Int[(a + b*x)*(a^2 - b^2*x^2)^p,x]","a x \left(a^2-b^2 x^2\right)^p \left(1-\frac{b^2 x^2}{a^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{b^2 x^2}{a^2}\right)-\frac{\left(a^2-b^2 x^2\right)^{p+1}}{2 b (p+1)}","a x \left(a^2-b^2 x^2\right)^p \left(1-\frac{b^2 x^2}{a^2}\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};\frac{b^2 x^2}{a^2}\right)-\frac{\left(a^2-b^2 x^2\right)^{p+1}}{2 b (p+1)}",1,"-(a^2 - b^2*x^2)^(1 + p)/(2*b*(1 + p)) + (a*x*(a^2 - b^2*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, (b^2*x^2)/a^2])/(1 - (b^2*x^2)/a^2)^p","A",3,3,20,0.1500,1,"{641, 246, 245}"
970,1,73,0,0.0299029,"\int \frac{\left(a^2-b^2 x^2\right)^p}{a+b x} \, dx","Int[(a^2 - b^2*x^2)^p/(a + b*x),x]","-\frac{2^{p-1} \left(\frac{b x}{a}+1\right)^{-p-1} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(1-p,p+1;p+2;\frac{a-b x}{2 a}\right)}{a^2 b (p+1)}","\frac{(a-b x) \left(a^2-b^2 x^2\right)^p \, _2F_1\left(1,2 p+1;p+1;\frac{a+b x}{2 a}\right)}{2 a b p}",1,"-((2^(-1 + p)*(1 + (b*x)/a)^(-1 - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[1 - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(a^2*b*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
971,1,73,0,0.0309562,"\int \frac{\left(a^2-b^2 x^2\right)^p}{(a+b x)^2} \, dx","Int[(a^2 - b^2*x^2)^p/(a + b*x)^2,x]","-\frac{2^{p-2} \left(\frac{b x}{a}+1\right)^{-p-1} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(2-p,p+1;p+2;\frac{a-b x}{2 a}\right)}{a^3 b (p+1)}","-\frac{\left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(1,2 p;p;\frac{a+b x}{2 a}\right)}{2 a b (1-p) (a+b x)^2}",1,"-((2^(-2 + p)*(1 + (b*x)/a)^(-1 - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[2 - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(a^3*b*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
972,1,73,0,0.0305619,"\int \frac{\left(a^2-b^2 x^2\right)^p}{(a+b x)^3} \, dx","Int[(a^2 - b^2*x^2)^p/(a + b*x)^3,x]","-\frac{2^{p-3} \left(\frac{b x}{a}+1\right)^{-p-1} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(3-p,p+1;p+2;\frac{a-b x}{2 a}\right)}{a^4 b (p+1)}","-\frac{\left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(1,2 p-1;p-1;\frac{a+b x}{2 a}\right)}{2 a b (2-p) (a+b x)^3}",1,"-((2^(-3 + p)*(1 + (b*x)/a)^(-1 - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[3 - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(a^4*b*(1 + p)))","A",2,2,22,0.09091,1,"{678, 69}"
973,1,85,0,0.0638669,"\int (a+b x)^{3/2} \left(a^2-b^2 x^2\right)^p \, dx","Int[(a + b*x)^(3/2)*(a^2 - b^2*x^2)^p,x]","-\frac{2^{p+\frac{3}{2}} \sqrt{a+b x} \left(\frac{b x}{a}+1\right)^{-p-\frac{3}{2}} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(-p-\frac{3}{2},p+1;p+2;\frac{a-b x}{2 a}\right)}{b (p+1)}","-\frac{2^{p+\frac{3}{2}} \sqrt{a+b x} \left(\frac{b x}{a}+1\right)^{-p-\frac{3}{2}} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(-p-\frac{3}{2},p+1;p+2;\frac{a-b x}{2 a}\right)}{b (p+1)}",1,"-((2^(3/2 + p)*Sqrt[a + b*x]*(1 + (b*x)/a)^(-3/2 - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[-3/2 - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(b*(1 + p)))","A",3,3,24,0.1250,1,"{680, 678, 69}"
974,1,88,0,0.0587131,"\int \sqrt{a+b x} \left(a^2-b^2 x^2\right)^p \, dx","Int[Sqrt[a + b*x]*(a^2 - b^2*x^2)^p,x]","-\frac{2^{p+\frac{1}{2}} \sqrt{a+b x} \left(\frac{b x}{a}+1\right)^{-p-\frac{3}{2}} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(-p-\frac{1}{2},p+1;p+2;\frac{a-b x}{2 a}\right)}{a b (p+1)}","-\frac{2^{p+\frac{1}{2}} \sqrt{a+b x} \left(\frac{b x}{a}+1\right)^{-p-\frac{3}{2}} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(-p-\frac{1}{2},p+1;p+2;\frac{a-b x}{2 a}\right)}{a b (p+1)}",1,"-((2^(1/2 + p)*Sqrt[a + b*x]*(1 + (b*x)/a)^(-3/2 - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[-1/2 - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(a*b*(1 + p)))","A",3,3,24,0.1250,1,"{680, 678, 69}"
975,1,88,0,0.0666792,"\int \frac{\left(a^2-b^2 x^2\right)^p}{\sqrt{a+b x}} \, dx","Int[(a^2 - b^2*x^2)^p/Sqrt[a + b*x],x]","-\frac{2^{p-\frac{1}{2}} \left(\frac{b x}{a}+1\right)^{-p-\frac{1}{2}} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(\frac{1}{2}-p,p+1;p+2;\frac{a-b x}{2 a}\right)}{a b (p+1) \sqrt{a+b x}}","-\frac{2^{p-\frac{1}{2}} \left(\frac{b x}{a}+1\right)^{-p-\frac{1}{2}} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(\frac{1}{2}-p,p+1;p+2;\frac{a-b x}{2 a}\right)}{a b (p+1) \sqrt{a+b x}}",1,"-((2^(-1/2 + p)*(1 + (b*x)/a)^(-1/2 - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[1/2 - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(a*b*(1 + p)*Sqrt[a + b*x]))","A",3,3,24,0.1250,1,"{680, 678, 69}"
976,1,88,0,0.0717756,"\int \frac{\left(a^2-b^2 x^2\right)^p}{(a+b x)^{3/2}} \, dx","Int[(a^2 - b^2*x^2)^p/(a + b*x)^(3/2),x]","-\frac{2^{p-\frac{3}{2}} \left(\frac{b x}{a}+1\right)^{-p-\frac{1}{2}} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(\frac{3}{2}-p,p+1;p+2;\frac{a-b x}{2 a}\right)}{a^2 b (p+1) \sqrt{a+b x}}","-\frac{2^{p-\frac{3}{2}} \left(\frac{b x}{a}+1\right)^{-p-\frac{1}{2}} \left(a^2-b^2 x^2\right)^{p+1} \, _2F_1\left(\frac{3}{2}-p,p+1;p+2;\frac{a-b x}{2 a}\right)}{a^2 b (p+1) \sqrt{a+b x}}",1,"-((2^(-3/2 + p)*(1 + (b*x)/a)^(-1/2 - p)*(a^2 - b^2*x^2)^(1 + p)*Hypergeometric2F1[3/2 - p, 1 + p, 2 + p, (a - b*x)/(2*a)])/(a^2*b*(1 + p)*Sqrt[a + b*x]))","A",3,3,24,0.1250,1,"{680, 678, 69}"
977,1,28,0,0.0413844,"\int \left(-a \left(a^2-b^2 x^2\right)^p+(a+b x) \left(a^2-b^2 x^2\right)^p\right) \, dx","Int[-(a*(a^2 - b^2*x^2)^p) + (a + b*x)*(a^2 - b^2*x^2)^p,x]","-\frac{\left(a^2-b^2 x^2\right)^{p+1}}{2 b (p+1)}","-\frac{\left(a^2-b^2 x^2\right)^{p+1}}{2 b (p+1)}",1,"-(a^2 - b^2*x^2)^(1 + p)/(2*b*(1 + p))","A",6,3,38,0.07895,1,"{246, 245, 641}"
978,1,15,0,0.0044967,"\int (d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right) \, dx","Int[(d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]","\frac{c (d+e x)^5}{5 e}","\frac{c (d+e x)^5}{5 e}",1,"(c*(d + e*x)^5)/(5*e)","A",3,3,28,0.1071,1,"{27, 12, 32}"
979,1,15,0,0.0040956,"\int (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right) \, dx","Int[(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]","\frac{c (d+e x)^4}{4 e}","\frac{c (d+e x)^4}{4 e}",1,"(c*(d + e*x)^4)/(4*e)","A",3,3,26,0.1154,1,"{27, 12, 32}"
980,1,25,0,0.0058733,"\int \left(c d^2+2 c d e x+c e^2 x^2\right) \, dx","Int[c*d^2 + 2*c*d*e*x + c*e^2*x^2,x]","c d^2 x+c d e x^2+\frac{1}{3} c e^2 x^3","c d^2 x+c d e x^2+\frac{1}{3} c e^2 x^3",1,"c*d^2*x + c*d*e*x^2 + (c*e^2*x^3)/3","A",1,0,20,0,1,"{}"
981,1,14,0,0.0083603,"\int \frac{c d^2+2 c d e x+c e^2 x^2}{d+e x} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)/(d + e*x),x]","c d x+\frac{1}{2} c e x^2","c d x+\frac{1}{2} c e x^2",1,"c*d*x + (c*e*x^2)/2","A",2,1,28,0.03571,1,"{24}"
982,1,3,0,0.0037241,"\int \frac{c d^2+2 c d e x+c e^2 x^2}{(d+e x)^2} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)/(d + e*x)^2,x]","c x","c x",1,"c*x","A",3,3,28,0.1071,1,"{24, 21, 8}"
983,1,11,0,0.0061493,"\int \frac{c d^2+2 c d e x+c e^2 x^2}{(d+e x)^3} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)/(d + e*x)^3,x]","\frac{c \log (d+e x)}{e}","\frac{c \log (d+e x)}{e}",1,"(c*Log[d + e*x])/e","A",3,3,28,0.1071,1,"{24, 21, 31}"
984,1,13,0,0.0064377,"\int \frac{c d^2+2 c d e x+c e^2 x^2}{(d+e x)^4} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)/(d + e*x)^4,x]","-\frac{c}{e (d+e x)}","-\frac{c}{e (d+e x)}",1,"-(c/(e*(d + e*x)))","A",3,3,28,0.1071,1,"{24, 21, 32}"
985,1,15,0,0.0063687,"\int \frac{c d^2+2 c d e x+c e^2 x^2}{(d+e x)^5} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)/(d + e*x)^5,x]","-\frac{c}{2 e (d+e x)^2}","-\frac{c}{2 e (d+e x)^2}",1,"-c/(2*e*(d + e*x)^2)","A",3,3,28,0.1071,1,"{24, 21, 32}"
986,1,15,0,0.0063929,"\int \frac{c d^2+2 c d e x+c e^2 x^2}{(d+e x)^6} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)/(d + e*x)^6,x]","-\frac{c}{3 e (d+e x)^3}","-\frac{c}{3 e (d+e x)^3}",1,"-c/(3*e*(d + e*x)^3)","A",3,3,28,0.1071,1,"{24, 21, 32}"
987,1,17,0,0.0048802,"\int (d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right)^2 \, dx","Int[(d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","\frac{c^2 (d+e x)^7}{7 e}","\frac{c^2 (d+e x)^7}{7 e}",1,"(c^2*(d + e*x)^7)/(7*e)","A",3,3,30,0.1000,1,"{27, 12, 32}"
988,1,17,0,0.0043832,"\int (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^2 \, dx","Int[(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","\frac{c^2 (d+e x)^6}{6 e}","\frac{c^2 (d+e x)^6}{6 e}",1,"(c^2*(d + e*x)^6)/(6*e)","A",3,3,28,0.1071,1,"{27, 12, 32}"
989,1,17,0,0.003937,"\int \left(c d^2+2 c d e x+c e^2 x^2\right)^2 \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","\frac{c^2 (d+e x)^5}{5 e}","\frac{c^2 (d+e x)^5}{5 e}",1,"(c^2*(d + e*x)^5)/(5*e)","A",3,3,22,0.1364,1,"{27, 12, 32}"
990,1,17,0,0.0047706,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^2}{d+e x} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x),x]","\frac{c^2 (d+e x)^4}{4 e}","\frac{c^2 (d+e x)^4}{4 e}",1,"(c^2*(d + e*x)^4)/(4*e)","A",3,3,30,0.1000,1,"{27, 12, 32}"
991,1,17,0,0.0051889,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^2}{(d+e x)^2} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^2,x]","\frac{c^2 (d+e x)^3}{3 e}","\frac{c^2 (d+e x)^3}{3 e}",1,"(c^2*(d + e*x)^3)/(3*e)","A",3,3,30,0.1000,1,"{27, 12, 32}"
992,1,17,0,0.0035307,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^2}{(d+e x)^3} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^3,x]","\frac{c^2 (d+e x)^2}{2 e}","\frac{c^2 (d+e x)^2}{2 e}",1,"(c^2*(d + e*x)^2)/(2*e)","A",2,2,30,0.06667,1,"{27, 9}"
993,1,5,0,0.0022651,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^2}{(d+e x)^4} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^4,x]","c^2 x","c^2 x",1,"c^2*x","A",2,2,30,0.06667,1,"{27, 8}"
994,1,13,0,0.0044983,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^2}{(d+e x)^5} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^5,x]","\frac{c^2 \log (d+e x)}{e}","\frac{c^2 \log (d+e x)}{e}",1,"(c^2*Log[d + e*x])/e","A",3,3,30,0.1000,1,"{27, 12, 31}"
995,1,15,0,0.0046743,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^2}{(d+e x)^6} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^6,x]","-\frac{c^2}{e (d+e x)}","-\frac{c^2}{e (d+e x)}",1,"-(c^2/(e*(d + e*x)))","A",3,3,30,0.1000,1,"{27, 12, 32}"
996,1,17,0,0.0051904,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^2}{(d+e x)^7} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^7,x]","-\frac{c^2}{2 e (d+e x)^2}","-\frac{c^2}{2 e (d+e x)^2}",1,"-c^2/(2*e*(d + e*x)^2)","A",3,3,30,0.1000,1,"{27, 12, 32}"
997,1,17,0,0.0047521,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^2}{(d+e x)^8} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2/(d + e*x)^8,x]","-\frac{c^2}{3 e (d+e x)^3}","-\frac{c^2}{3 e (d+e x)^3}",1,"-c^2/(3*e*(d + e*x)^3)","A",3,3,30,0.1000,1,"{27, 12, 32}"
998,1,17,0,0.0047771,"\int \frac{(d+e x)^5}{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)^5/(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]","\frac{(d+e x)^4}{4 c e}","\frac{(d+e x)^4}{4 c e}",1,"(d + e*x)^4/(4*c*e)","A",3,3,30,0.1000,1,"{27, 12, 32}"
999,1,17,0,0.0047593,"\int \frac{(d+e x)^4}{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)^4/(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]","\frac{(d+e x)^3}{3 c e}","\frac{(d+e x)^3}{3 c e}",1,"(d + e*x)^3/(3*c*e)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1000,1,17,0,0.0034212,"\int \frac{(d+e x)^3}{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)^3/(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]","\frac{(d+e x)^2}{2 c e}","\frac{(d+e x)^2}{2 c e}",1,"(d + e*x)^2/(2*c*e)","A",2,2,30,0.06667,1,"{27, 9}"
1001,1,5,0,0.0023776,"\int \frac{(d+e x)^2}{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)^2/(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]","\frac{x}{c}","\frac{x}{c}",1,"x/c","A",2,2,30,0.06667,1,"{27, 8}"
1002,1,13,0,0.0040553,"\int \frac{d+e x}{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)/(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]","\frac{\log (d+e x)}{c e}","\frac{\log (d+e x)}{c e}",1,"Log[d + e*x]/(c*e)","A",3,3,28,0.1071,1,"{27, 12, 31}"
1003,1,15,0,0.0040105,"\int \frac{1}{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(-1),x]","-\frac{1}{c e (d+e x)}","-\frac{1}{c e (d+e x)}",1,"-(1/(c*e*(d + e*x)))","A",3,3,22,0.1364,1,"{27, 12, 32}"
1004,1,17,0,0.0047097,"\int \frac{1}{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)} \, dx","Int[1/((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)),x]","-\frac{1}{2 c e (d+e x)^2}","-\frac{1}{2 c e (d+e x)^2}",1,"-1/(2*c*e*(d + e*x)^2)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1005,1,17,0,0.0046357,"\int \frac{1}{(d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right)} \, dx","Int[1/((d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)),x]","-\frac{1}{3 c e (d+e x)^3}","-\frac{1}{3 c e (d+e x)^3}",1,"-1/(3*c*e*(d + e*x)^3)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1006,1,17,0,0.004754,"\int \frac{1}{(d+e x)^3 \left(c d^2+2 c d e x+c e^2 x^2\right)} \, dx","Int[1/((d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)),x]","-\frac{1}{4 c e (d+e x)^4}","-\frac{1}{4 c e (d+e x)^4}",1,"-1/(4*c*e*(d + e*x)^4)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1007,1,17,0,0.0049706,"\int \frac{(d+e x)^7}{\left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[(d + e*x)^7/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","\frac{(d+e x)^4}{4 c^2 e}","\frac{(d+e x)^4}{4 c^2 e}",1,"(d + e*x)^4/(4*c^2*e)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1008,1,17,0,0.0048266,"\int \frac{(d+e x)^6}{\left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[(d + e*x)^6/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","\frac{(d+e x)^3}{3 c^2 e}","\frac{(d+e x)^3}{3 c^2 e}",1,"(d + e*x)^3/(3*c^2*e)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1009,1,17,0,0.0035537,"\int \frac{(d+e x)^5}{\left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[(d + e*x)^5/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","\frac{(d+e x)^2}{2 c^2 e}","\frac{(d+e x)^2}{2 c^2 e}",1,"(d + e*x)^2/(2*c^2*e)","A",2,2,30,0.06667,1,"{27, 9}"
1010,1,5,0,0.0027614,"\int \frac{(d+e x)^4}{\left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[(d + e*x)^4/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","\frac{x}{c^2}","\frac{x}{c^2}",1,"x/c^2","A",2,2,30,0.06667,1,"{27, 8}"
1011,1,13,0,0.0046287,"\int \frac{(d+e x)^3}{\left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[(d + e*x)^3/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","\frac{\log (d+e x)}{c^2 e}","\frac{\log (d+e x)}{c^2 e}",1,"Log[d + e*x]/(c^2*e)","A",3,3,30,0.1000,1,"{27, 12, 31}"
1012,1,15,0,0.0048716,"\int \frac{(d+e x)^2}{\left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[(d + e*x)^2/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","-\frac{1}{c^2 e (d+e x)}","-\frac{1}{c^2 e (d+e x)}",1,"-(1/(c^2*e*(d + e*x)))","A",3,3,30,0.1000,1,"{27, 12, 32}"
1013,1,17,0,0.0043401,"\int \frac{d+e x}{\left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[(d + e*x)/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","-\frac{1}{2 c^2 e (d+e x)^2}","-\frac{1}{2 c^2 e (d+e x)^2}",1,"-1/(2*c^2*e*(d + e*x)^2)","A",3,3,28,0.1071,1,"{27, 12, 32}"
1014,1,17,0,0.004028,"\int \frac{1}{\left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(-2),x]","-\frac{1}{3 c^2 e (d+e x)^3}","-\frac{1}{3 c^2 e (d+e x)^3}",1,"-1/(3*c^2*e*(d + e*x)^3)","A",3,3,22,0.1364,1,"{27, 12, 32}"
1015,1,17,0,0.0047134,"\int \frac{1}{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[1/((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2),x]","-\frac{1}{4 c^2 e (d+e x)^4}","-\frac{1}{4 c^2 e (d+e x)^4}",1,"-1/(4*c^2*e*(d + e*x)^4)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1016,1,17,0,0.0047017,"\int \frac{1}{(d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[1/((d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2),x]","-\frac{1}{5 c^2 e (d+e x)^5}","-\frac{1}{5 c^2 e (d+e x)^5}",1,"-1/(5*c^2*e*(d + e*x)^5)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1017,1,17,0,0.0050063,"\int \frac{(d+e x)^9}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)^9/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","\frac{(d+e x)^4}{4 c^3 e}","\frac{(d+e x)^4}{4 c^3 e}",1,"(d + e*x)^4/(4*c^3*e)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1018,1,17,0,0.0048614,"\int \frac{(d+e x)^8}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)^8/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","\frac{(d+e x)^3}{3 c^3 e}","\frac{(d+e x)^3}{3 c^3 e}",1,"(d + e*x)^3/(3*c^3*e)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1019,1,17,0,0.0035288,"\int \frac{(d+e x)^7}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)^7/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","\frac{(d+e x)^2}{2 c^3 e}","\frac{(d+e x)^2}{2 c^3 e}",1,"(d + e*x)^2/(2*c^3*e)","A",2,2,30,0.06667,1,"{27, 9}"
1020,1,5,0,0.002476,"\int \frac{(d+e x)^6}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)^6/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","\frac{x}{c^3}","\frac{x}{c^3}",1,"x/c^3","A",2,2,30,0.06667,1,"{27, 8}"
1021,1,13,0,0.0046667,"\int \frac{(d+e x)^5}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)^5/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","\frac{\log (d+e x)}{c^3 e}","\frac{\log (d+e x)}{c^3 e}",1,"Log[d + e*x]/(c^3*e)","A",3,3,30,0.1000,1,"{27, 12, 31}"
1022,1,15,0,0.0048168,"\int \frac{(d+e x)^4}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)^4/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","-\frac{1}{c^3 e (d+e x)}","-\frac{1}{c^3 e (d+e x)}",1,"-(1/(c^3*e*(d + e*x)))","A",3,3,30,0.1000,1,"{27, 12, 32}"
1023,1,17,0,0.004698,"\int \frac{(d+e x)^3}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)^3/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","-\frac{1}{2 c^3 e (d+e x)^2}","-\frac{1}{2 c^3 e (d+e x)^2}",1,"-1/(2*c^3*e*(d + e*x)^2)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1024,1,17,0,0.0055453,"\int \frac{(d+e x)^2}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)^2/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","-\frac{1}{3 c^3 e (d+e x)^3}","-\frac{1}{3 c^3 e (d+e x)^3}",1,"-1/(3*c^3*e*(d + e*x)^3)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1025,1,17,0,0.0044241,"\int \frac{d+e x}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","-\frac{1}{4 c^3 e (d+e x)^4}","-\frac{1}{4 c^3 e (d+e x)^4}",1,"-1/(4*c^3*e*(d + e*x)^4)","A",3,3,28,0.1071,1,"{27, 12, 32}"
1026,1,17,0,0.0040724,"\int \frac{1}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(-3),x]","-\frac{1}{5 c^3 e (d+e x)^5}","-\frac{1}{5 c^3 e (d+e x)^5}",1,"-1/(5*c^3*e*(d + e*x)^5)","A",3,3,22,0.1364,1,"{27, 12, 32}"
1027,1,17,0,0.0046868,"\int \frac{1}{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[1/((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3),x]","-\frac{1}{6 c^3 e (d+e x)^6}","-\frac{1}{6 c^3 e (d+e x)^6}",1,"-1/(6*c^3*e*(d + e*x)^6)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1028,1,17,0,0.0047815,"\int \frac{1}{(d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[1/((d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3),x]","-\frac{1}{7 c^3 e (d+e x)^7}","-\frac{1}{7 c^3 e (d+e x)^7}",1,"-1/(7*c^3*e*(d + e*x)^7)","A",3,3,30,0.1000,1,"{27, 12, 32}"
1029,1,34,0,0.0235951,"\int (d+e x)^3 \sqrt{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)^3*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{5 c^2 e}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{5 c^2 e}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(5*c^2*e)","A",2,2,32,0.06250,1,"{643, 629}"
1030,1,39,0,0.0215713,"\int (d+e x)^2 \sqrt{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)^2*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{4 c e}","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{4 c e}",1,"((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))/(4*c*e)","A",2,2,32,0.06250,1,"{642, 609}"
1031,1,34,0,0.0087348,"\int (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{3 c e}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{3 c e}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(3*c*e)","A",1,1,30,0.03333,1,"{629}"
1032,1,36,0,0.0061876,"\int \sqrt{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{(d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 e}","\frac{(d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 e}",1,"((d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])/(2*e)","A",1,1,24,0.04167,1,"{609}"
1033,1,28,0,0.0237031,"\int \frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{d+e x} \, dx","Int[Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/(d + e*x),x]","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{e}","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{e}",1,"Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/e","A",2,2,32,0.06250,1,"{643, 629}"
1034,1,40,0,0.0253335,"\int \frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{(d+e x)^2} \, dx","Int[Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/(d + e*x)^2,x]","\frac{c (d+e x) \log (d+e x)}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","\frac{c (d+e x) \log (d+e x)}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"(c*(d + e*x)*Log[d + e*x])/(e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",3,3,32,0.09375,1,"{642, 608, 31}"
1035,1,30,0,0.0233458,"\int \frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{(d+e x)^3} \, dx","Int[Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/(d + e*x)^3,x]","-\frac{c}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{c}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-(c/(e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]))","A",2,2,32,0.06250,1,"{643, 629}"
1036,1,39,0,0.0193965,"\int \frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{(d+e x)^4} \, dx","Int[Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/(d + e*x)^4,x]","-\frac{c}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{c}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-c/(2*e*(d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",2,2,32,0.06250,1,"{642, 607}"
1037,1,34,0,0.0229168,"\int \frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{(d+e x)^5} \, dx","Int[Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/(d + e*x)^5,x]","-\frac{c^2}{3 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{c^2}{3 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-c^2/(3*e*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))","A",2,2,32,0.06250,1,"{643, 629}"
1038,1,41,0,0.0192795,"\int \frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{(d+e x)^6} \, dx","Int[Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/(d + e*x)^6,x]","-\frac{c^2}{4 e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{c^2}{4 e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-c^2/(4*e*(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))","A",2,2,32,0.06250,1,"{642, 607}"
1039,1,34,0,0.0244234,"\int (d+e x)^3 \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{7/2}}{7 c^2 e}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{7/2}}{7 c^2 e}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(7/2)/(7*c^2*e)","A",2,2,32,0.06250,1,"{643, 629}"
1040,1,39,0,0.0210601,"\int (d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{6 c e}","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{6 c e}",1,"((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2))/(6*c*e)","A",2,2,32,0.06250,1,"{642, 609}"
1041,1,34,0,0.0089651,"\int (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{5 c e}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{5 c e}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(5*c*e)","A",1,1,30,0.03333,1,"{629}"
1042,1,36,0,0.0060748,"\int \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{4 e}","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{4 e}",1,"((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))/(4*e)","A",1,1,24,0.04167,1,"{609}"
1043,1,31,0,0.0232013,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{d+e x} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(d + e*x),x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{3 e}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{3 e}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(3*e)","A",2,2,32,0.06250,1,"{643, 629}"
1044,1,37,0,0.0209133,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(d + e*x)^2,x]","\frac{c (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 e}","\frac{c (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 e}",1,"(c*(d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])/(2*e)","A",2,2,32,0.06250,1,"{642, 609}"
1045,1,29,0,0.0224896,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(d + e*x)^3,x]","\frac{c \sqrt{c d^2+2 c d e x+c e^2 x^2}}{e}","\frac{c \sqrt{c d^2+2 c d e x+c e^2 x^2}}{e}",1,"(c*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])/e","A",2,2,32,0.06250,1,"{643, 629}"
1046,1,42,0,0.0246343,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{(d+e x)^4} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(d + e*x)^4,x]","\frac{c^2 (d+e x) \log (d+e x)}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","\frac{c^2 (d+e x) \log (d+e x)}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"(c^2*(d + e*x)*Log[d + e*x])/(e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",3,3,32,0.09375,1,"{642, 608, 31}"
1047,1,32,0,0.0233844,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{(d+e x)^5} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(d + e*x)^5,x]","-\frac{c^2}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{c^2}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-(c^2/(e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]))","A",2,2,32,0.06250,1,"{643, 629}"
1048,1,41,0,0.0197819,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{(d+e x)^6} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(d + e*x)^6,x]","-\frac{c^2}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{c^2}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-c^2/(2*e*(d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",2,2,32,0.06250,1,"{642, 607}"
1049,1,34,0,0.0236374,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{(d+e x)^7} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(d + e*x)^7,x]","-\frac{c^3}{3 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{c^3}{3 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-c^3/(3*e*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))","A",2,2,32,0.06250,1,"{643, 629}"
1050,1,34,0,0.0238558,"\int (d+e x)^3 \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{9/2}}{9 c^2 e}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{9/2}}{9 c^2 e}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(9/2)/(9*c^2*e)","A",2,2,32,0.06250,1,"{643, 629}"
1051,1,39,0,0.0207566,"\int (d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{7/2}}{8 c e}","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{7/2}}{8 c e}",1,"((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(7/2))/(8*c*e)","A",2,2,32,0.06250,1,"{642, 609}"
1052,1,34,0,0.0090822,"\int (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{7/2}}{7 c e}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{7/2}}{7 c e}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(7/2)/(7*c*e)","A",1,1,30,0.03333,1,"{629}"
1053,1,36,0,0.0067982,"\int \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{6 e}","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{6 e}",1,"((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2))/(6*e)","A",1,1,24,0.04167,1,"{609}"
1054,1,31,0,0.0237312,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x),x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{5 e}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{5 e}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(5*e)","A",2,2,32,0.06250,1,"{643, 629}"
1055,1,37,0,0.0209725,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^2,x]","\frac{c (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{4 e}","\frac{c (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{4 e}",1,"(c*(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))/(4*e)","A",2,2,32,0.06250,1,"{642, 609}"
1056,1,32,0,0.0227479,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^3,x]","\frac{c \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{3 e}","\frac{c \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{3 e}",1,"(c*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))/(3*e)","A",2,2,32,0.06250,1,"{643, 629}"
1057,1,39,0,0.0208637,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^4,x]","\frac{c^2 (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 e}","\frac{c^2 (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 e}",1,"(c^2*(d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])/(2*e)","A",2,2,32,0.06250,1,"{642, 609}"
1058,1,31,0,0.0227217,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{(d+e x)^5} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^5,x]","\frac{c^2 \sqrt{c d^2+2 c d e x+c e^2 x^2}}{e}","\frac{c^2 \sqrt{c d^2+2 c d e x+c e^2 x^2}}{e}",1,"(c^2*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])/e","A",2,2,32,0.06250,1,"{643, 629}"
1059,1,42,0,0.0249265,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{(d+e x)^6} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^6,x]","\frac{c^3 (d+e x) \log (d+e x)}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","\frac{c^3 (d+e x) \log (d+e x)}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"(c^3*(d + e*x)*Log[d + e*x])/(e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",3,3,32,0.09375,1,"{642, 608, 31}"
1060,1,32,0,0.0238005,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{(d+e x)^7} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^7,x]","-\frac{c^3}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{c^3}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-(c^3/(e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]))","A",2,2,32,0.06250,1,"{643, 629}"
1061,1,41,0,0.0215237,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}{(d+e x)^8} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^8,x]","-\frac{c^3}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{c^3}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-c^3/(2*e*(d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",2,2,32,0.06250,1,"{642, 607}"
1062,1,39,0,0.0215258,"\int \frac{(d+e x)^4}{\sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[(d + e*x)^4/Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{4 c^2 e}","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{4 c^2 e}",1,"((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))/(4*c^2*e)","A",2,2,32,0.06250,1,"{642, 609}"
1063,1,34,0,0.0232877,"\int \frac{(d+e x)^3}{\sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[(d + e*x)^3/Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{3 c^2 e}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}{3 c^2 e}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)/(3*c^2*e)","A",2,2,32,0.06250,1,"{643, 629}"
1064,1,39,0,0.0215158,"\int \frac{(d+e x)^2}{\sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[(d + e*x)^2/Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{(d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 c e}","\frac{(d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 c e}",1,"((d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])/(2*c*e)","A",2,2,32,0.06250,1,"{642, 609}"
1065,1,31,0,0.0087882,"\int \frac{d+e x}{\sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[(d + e*x)/Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{c e}","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{c e}",1,"Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/(c*e)","A",1,1,30,0.03333,1,"{629}"
1066,1,39,0,0.0093111,"\int \frac{1}{\sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[1/Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{(d+e x) \log (d+e x)}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","\frac{(d+e x) \log (d+e x)}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"((d + e*x)*Log[d + e*x])/(e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",2,2,24,0.08333,1,"{608, 31}"
1067,1,29,0,0.0244909,"\int \frac{1}{(d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[1/((d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]),x]","-\frac{1}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{1}{e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-(1/(e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]))","A",2,2,32,0.06250,1,"{643, 629}"
1068,1,38,0,0.0193157,"\int \frac{1}{(d+e x)^2 \sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[1/((d + e*x)^2*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]),x]","-\frac{1}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{1}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-1/(2*e*(d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",2,2,32,0.06250,1,"{642, 607}"
1069,1,32,0,0.0235819,"\int \frac{1}{(d+e x)^3 \sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[1/((d + e*x)^3*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]),x]","-\frac{c}{3 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{c}{3 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-c/(3*e*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))","A",2,2,32,0.06250,1,"{643, 629}"
1070,1,39,0,0.0193221,"\int \frac{1}{(d+e x)^4 \sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[1/((d + e*x)^4*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]),x]","-\frac{c}{4 e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{c}{4 e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-c/(4*e*(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))","A",2,2,32,0.06250,1,"{642, 607}"
1071,1,39,0,0.0223517,"\int \frac{(d+e x)^4}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^4/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","\frac{(d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 c^2 e}","\frac{(d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 c^2 e}",1,"((d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])/(2*c^2*e)","A",2,2,32,0.06250,1,"{642, 609}"
1072,1,31,0,0.0238644,"\int \frac{(d+e x)^3}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^3/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{c^2 e}","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{c^2 e}",1,"Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/(c^2*e)","A",2,2,32,0.06250,1,"{643, 629}"
1073,1,42,0,0.0252252,"\int \frac{(d+e x)^2}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^2/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","\frac{(d+e x) \log (d+e x)}{c e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","\frac{(d+e x) \log (d+e x)}{c e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"((d + e*x)*Log[d + e*x])/(c*e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",3,3,32,0.09375,1,"{642, 608, 31}"
1074,1,32,0,0.0092454,"\int \frac{d+e x}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","-\frac{1}{c e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{1}{c e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-(1/(c*e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]))","A",1,1,30,0.03333,1,"{629}"
1075,1,41,0,0.0051423,"\int \frac{1}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(-3/2),x]","-\frac{1}{2 c e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{1}{2 c e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-1/(2*c*e*(d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",1,1,24,0.04167,1,"{607}"
1076,1,31,0,0.0251365,"\int \frac{1}{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)),x]","-\frac{1}{3 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{1}{3 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-1/(3*e*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))","A",2,2,32,0.06250,1,"{643, 629}"
1077,1,38,0,0.0202065,"\int \frac{1}{(d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)),x]","-\frac{1}{4 e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{1}{4 e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-1/(4*e*(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))","A",2,2,32,0.06250,1,"{642, 607}"
1078,1,32,0,0.023793,"\int \frac{1}{(d+e x)^3 \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)),x]","-\frac{c}{5 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}","-\frac{c}{5 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}",1,"-c/(5*e*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2))","A",2,2,32,0.06250,1,"{643, 629}"
1079,1,39,0,0.0225454,"\int \frac{(d+e x)^6}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^6/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","\frac{(d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 c^3 e}","\frac{(d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}{2 c^3 e}",1,"((d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])/(2*c^3*e)","A",2,2,32,0.06250,1,"{642, 609}"
1080,1,31,0,0.0237814,"\int \frac{(d+e x)^5}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^5/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{c^3 e}","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2}}{c^3 e}",1,"Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]/(c^3*e)","A",2,2,32,0.06250,1,"{643, 629}"
1081,1,42,0,0.0258827,"\int \frac{(d+e x)^4}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^4/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","\frac{(d+e x) \log (d+e x)}{c^2 e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","\frac{(d+e x) \log (d+e x)}{c^2 e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"((d + e*x)*Log[d + e*x])/(c^2*e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",3,3,32,0.09375,1,"{642, 608, 31}"
1082,1,32,0,0.0246531,"\int \frac{(d+e x)^3}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^3/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","-\frac{1}{c^2 e \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{1}{c^2 e \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-(1/(c^2*e*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2]))","A",2,2,32,0.06250,1,"{643, 629}"
1083,1,41,0,0.0215117,"\int \frac{(d+e x)^2}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^2/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","-\frac{1}{2 c^2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}","-\frac{1}{2 c^2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"-1/(2*c^2*e*(d + e*x)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",2,2,32,0.06250,1,"{642, 607}"
1084,1,34,0,0.0093726,"\int \frac{d+e x}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2),x]","-\frac{1}{3 c e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{1}{3 c e \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-1/(3*c*e*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))","A",1,1,30,0.03333,1,"{629}"
1085,1,41,0,0.0050822,"\int \frac{1}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(-5/2),x]","-\frac{1}{4 c e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{1}{4 c e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-1/(4*c*e*(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))","A",1,1,24,0.04167,1,"{607}"
1086,1,31,0,0.0242698,"\int \frac{1}{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)),x]","-\frac{1}{5 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}","-\frac{1}{5 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}",1,"-1/(5*e*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2))","A",2,2,32,0.06250,1,"{643, 629}"
1087,1,38,0,0.0206601,"\int \frac{1}{(d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)),x]","-\frac{1}{6 e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}","-\frac{1}{6 e (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}}",1,"-1/(6*e*(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2))","A",2,2,32,0.06250,1,"{642, 607}"
1088,1,32,0,0.0231345,"\int \frac{1}{(d+e x)^3 \left(c d^2+2 c d e x+c e^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)),x]","-\frac{c}{7 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{7/2}}","-\frac{c}{7 e \left(c d^2+2 c d e x+c e^2 x^2\right)^{7/2}}",1,"-c/(7*e*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(7/2))","A",2,2,32,0.06250,1,"{643, 629}"
1089,1,21,0,0.0093606,"\int (d+e x)^m \left(c d^2+2 c d e x+c e^2 x^2\right)^2 \, dx","Int[(d + e*x)^m*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","\frac{c^2 (d+e x)^{m+5}}{e (m+5)}","\frac{c^2 (d+e x)^{m+5}}{e (m+5)}",1,"(c^2*(d + e*x)^(5 + m))/(e*(5 + m))","A",3,3,30,0.1000,1,"{27, 12, 32}"
1090,1,19,0,0.0077997,"\int (d+e x)^m \left(c d^2+2 c d e x+c e^2 x^2\right) \, dx","Int[(d + e*x)^m*(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]","\frac{c (d+e x)^{m+3}}{e (m+3)}","\frac{c (d+e x)^{m+3}}{e (m+3)}",1,"(c*(d + e*x)^(3 + m))/(e*(3 + m))","A",3,3,28,0.1071,1,"{27, 12, 32}"
1091,1,24,0,0.0115782,"\int \frac{(d+e x)^m}{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)^m/(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]","-\frac{(d+e x)^{m-1}}{c e (1-m)}","-\frac{(d+e x)^{m-1}}{c e (1-m)}",1,"-((d + e*x)^(-1 + m)/(c*e*(1 - m)))","A",3,3,30,0.1000,1,"{27, 12, 32}"
1092,1,24,0,0.0101768,"\int \frac{(d+e x)^m}{\left(c d^2+2 c d e x+c e^2 x^2\right)^2} \, dx","Int[(d + e*x)^m/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2,x]","-\frac{(d+e x)^{m-3}}{c^2 e (3-m)}","-\frac{(d+e x)^{m-3}}{c^2 e (3-m)}",1,"-((d + e*x)^(-3 + m)/(c^2*e*(3 - m)))","A",3,3,30,0.1000,1,"{27, 12, 32}"
1093,1,24,0,0.0102396,"\int \frac{(d+e x)^m}{\left(c d^2+2 c d e x+c e^2 x^2\right)^3} \, dx","Int[(d + e*x)^m/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]","-\frac{(d+e x)^{m-5}}{c^3 e (5-m)}","-\frac{(d+e x)^{m-5}}{c^3 e (5-m)}",1,"-((d + e*x)^(-5 + m)/(c^3*e*(5 - m)))","A",3,3,30,0.1000,1,"{27, 12, 32}"
1094,1,42,0,0.0189694,"\int (d+e x)^m \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^m*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2} (d+e x)^{m+1}}{e (m+4)}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2} (d+e x)^{m+1}}{e (m+4)}",1,"((d + e*x)^(1 + m)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))/(e*(4 + m))","A",2,2,32,0.06250,1,"{644, 32}"
1095,1,42,0,0.0181988,"\int (d+e x)^m \sqrt{c d^2+2 c d e x+c e^2 x^2} \, dx","Int[(d + e*x)^m*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2} (d+e x)^{m+1}}{e (m+2)}","\frac{\sqrt{c d^2+2 c d e x+c e^2 x^2} (d+e x)^{m+1}}{e (m+2)}",1,"((d + e*x)^(1 + m)*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])/(e*(2 + m))","A",2,2,32,0.06250,1,"{644, 32}"
1096,1,40,0,0.018051,"\int \frac{(d+e x)^m}{\sqrt{c d^2+2 c d e x+c e^2 x^2}} \, dx","Int[(d + e*x)^m/Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2],x]","\frac{(d+e x)^{m+1}}{e m \sqrt{c d^2+2 c d e x+c e^2 x^2}}","\frac{(d+e x)^{m+1}}{e m \sqrt{c d^2+2 c d e x+c e^2 x^2}}",1,"(d + e*x)^(1 + m)/(e*m*Sqrt[c*d^2 + 2*c*d*e*x + c*e^2*x^2])","A",2,2,32,0.06250,1,"{644, 32}"
1097,1,45,0,0.0202965,"\int \frac{(d+e x)^m}{\left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^m/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2),x]","-\frac{(d+e x)^{m+1}}{e (2-m) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}","-\frac{(d+e x)^{m+1}}{e (2-m) \left(c d^2+2 c d e x+c e^2 x^2\right)^{3/2}}",1,"-((d + e*x)^(1 + m)/(e*(2 - m)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2)))","A",2,2,32,0.06250,1,"{644, 32}"
1098,1,43,0,0.0177609,"\int (d+e x)^m \left(c d^2+2 c d e x+c e^2 x^2\right)^p \, dx","Int[(d + e*x)^m*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p,x]","\frac{(d+e x)^{m+1} \left(c d^2+2 c d e x+c e^2 x^2\right)^p}{e (m+2 p+1)}","\frac{(d+e x)^{m+1} \left(c d^2+2 c d e x+c e^2 x^2\right)^p}{e (m+2 p+1)}",1,"((d + e*x)^(1 + m)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p)/(e*(1 + m + 2*p))","A",2,2,30,0.06667,1,"{644, 32}"
1099,1,44,0,0.0173963,"\int (d+e x)^p \left(c d^2+2 c d e x+c e^2 x^2\right)^{-p} \, dx","Int[(d + e*x)^p/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p,x]","\frac{(d+e x)^{p+1} \left(c d^2+2 c d e x+c e^2 x^2\right)^{-p}}{e (1-p)}","\frac{(d+e x)^{p+1} \left(c d^2+2 c d e x+c e^2 x^2\right)^{-p}}{e (1-p)}",1,"(d + e*x)^(1 + p)/(e*(1 - p)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p)","A",2,2,32,0.06250,1,"{644, 32}"
1100,1,39,0,0.0256012,"\int (d+e x)^3 \left(c d^2+2 c d e x+c e^2 x^2\right)^p \, dx","Int[(d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p,x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{p+2}}{2 c^2 e (p+2)}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{p+2}}{2 c^2 e (p+2)}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(2 + p)/(2*c^2*e*(2 + p))","A",2,2,30,0.06667,1,"{643, 629}"
1101,1,43,0,0.0259138,"\int (d+e x)^2 \left(c d^2+2 c d e x+c e^2 x^2\right)^p \, dx","Int[(d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p,x]","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{p+1}}{c e (2 p+3)}","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{p+1}}{c e (2 p+3)}",1,"((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(1 + p))/(c*e*(3 + 2*p))","A",2,2,30,0.06667,1,"{642, 609}"
1102,1,39,0,0.0103326,"\int (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^p \, dx","Int[(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p,x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{p+1}}{2 c e (p+1)}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^{p+1}}{2 c e (p+1)}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(1 + p)/(2*c*e*(1 + p))","A",1,1,28,0.03571,1,"{629}"
1103,1,38,0,0.0097498,"\int \left(c d^2+2 c d e x+c e^2 x^2\right)^p \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p,x]","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^p}{e (2 p+1)}","\frac{(d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^p}{e (2 p+1)}",1,"((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p)/(e*(1 + 2*p))","A",1,1,22,0.04545,1,"{609}"
1104,1,32,0,0.0212296,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^p}{d+e x} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p/(d + e*x),x]","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^p}{2 e p}","\frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^p}{2 e p}",1,"(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p/(2*e*p)","A",2,2,30,0.06667,1,"{643, 629}"
1105,1,42,0,0.0256373,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^p}{(d+e x)^2} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p/(d + e*x)^2,x]","-\frac{c (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{p-1}}{e (1-2 p)}","-\frac{c (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{p-1}}{e (1-2 p)}",1,"-((c*(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(-1 + p))/(e*(1 - 2*p)))","A",2,2,30,0.06667,1,"{642, 609}"
1106,1,39,0,0.0256884,"\int \frac{\left(c d^2+2 c d e x+c e^2 x^2\right)^p}{(d+e x)^3} \, dx","Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p/(d + e*x)^3,x]","-\frac{c \left(c d^2+2 c d e x+c e^2 x^2\right)^{p-1}}{2 e (1-p)}","-\frac{c \left(c d^2+2 c d e x+c e^2 x^2\right)^{p-1}}{2 e (1-p)}",1,"-(c*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(-1 + p))/(2*e*(1 - p))","A",2,2,30,0.06667,1,"{643, 629}"
1107,1,41,0,0.0147421,"\int (d+e x)^{-1-2 p} \left(c d^2+2 c d e x+c e^2 x^2\right)^p \, dx","Int[(d + e*x)^(-1 - 2*p)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p,x]","\frac{(d+e x)^{-2 p} \log (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^p}{e}","\frac{(d+e x)^{-2 p} \log (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^p}{e}",1,"((c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p*Log[d + e*x])/(e*(d + e*x)^(2*p))","A",2,2,34,0.05882,1,"{644, 31}"
1108,1,43,0,0.0146628,"\int (d+e x)^{-1+2 p} \left(c d^2+2 c d e x+c e^2 x^2\right)^{-p} \, dx","Int[(d + e*x)^(-1 + 2*p)/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p,x]","\frac{(d+e x)^{2 p} \log (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{-p}}{e}","\frac{(d+e x)^{2 p} \log (d+e x) \left(c d^2+2 c d e x+c e^2 x^2\right)^{-p}}{e}",1,"((d + e*x)^(2*p)*Log[d + e*x])/(e*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p)","A",2,2,36,0.05556,1,"{644, 31}"
1109,1,45,0,0.0751143,"\int (b d+2 c d x)^4 \left(a+b x+c x^2\right) \, dx","Int[(b*d + 2*c*d*x)^4*(a + b*x + c*x^2),x]","\frac{d^4 (b+2 c x)^7}{56 c^2}-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^5}{40 c^2}","\frac{d^4 (b+2 c x)^7}{56 c^2}-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^5}{40 c^2}",1,"-((b^2 - 4*a*c)*d^4*(b + 2*c*x)^5)/(40*c^2) + (d^4*(b + 2*c*x)^7)/(56*c^2)","A",2,1,22,0.04545,1,"{683}"
1110,1,45,0,0.0535636,"\int (b d+2 c d x)^3 \left(a+b x+c x^2\right) \, dx","Int[(b*d + 2*c*d*x)^3*(a + b*x + c*x^2),x]","\frac{d^3 (b+2 c x)^6}{48 c^2}-\frac{d^3 \left(b^2-4 a c\right) (b+2 c x)^4}{32 c^2}","\frac{d^3 (b+2 c x)^6}{48 c^2}-\frac{d^3 \left(b^2-4 a c\right) (b+2 c x)^4}{32 c^2}",1,"-((b^2 - 4*a*c)*d^3*(b + 2*c*x)^4)/(32*c^2) + (d^3*(b + 2*c*x)^6)/(48*c^2)","A",2,1,22,0.04545,1,"{683}"
1111,1,45,0,0.0397384,"\int (b d+2 c d x)^2 \left(a+b x+c x^2\right) \, dx","Int[(b*d + 2*c*d*x)^2*(a + b*x + c*x^2),x]","\frac{d^2 (b+2 c x)^5}{40 c^2}-\frac{d^2 \left(b^2-4 a c\right) (b+2 c x)^3}{24 c^2}","\frac{d^2 (b+2 c x)^5}{40 c^2}-\frac{d^2 \left(b^2-4 a c\right) (b+2 c x)^3}{24 c^2}",1,"-((b^2 - 4*a*c)*d^2*(b + 2*c*x)^3)/(24*c^2) + (d^2*(b + 2*c*x)^5)/(40*c^2)","A",2,1,22,0.04545,1,"{683}"
1112,1,17,0,0.004063,"\int (b d+2 c d x) \left(a+b x+c x^2\right) \, dx","Int[(b*d + 2*c*d*x)*(a + b*x + c*x^2),x]","\frac{1}{2} d \left(a+b x+c x^2\right)^2","\frac{1}{2} d \left(a+b x+c x^2\right)^2",1,"(d*(a + b*x + c*x^2)^2)/2","A",1,1,20,0.05000,1,"{629}"
1113,1,48,0,0.0350725,"\int \frac{a+b x+c x^2}{b d+2 c d x} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x),x]","-\frac{\left(b^2-4 a c\right) \log (b+2 c x)}{8 c^2 d}+\frac{b x}{4 c d}+\frac{x^2}{4 d}","-\frac{\left(b^2-4 a c\right) \log (b+2 c x)}{8 c^2 d}+\frac{b x}{4 c d}+\frac{x^2}{4 d}",1,"(b*x)/(4*c*d) + x^2/(4*d) - ((b^2 - 4*a*c)*Log[b + 2*c*x])/(8*c^2*d)","A",2,1,22,0.04545,1,"{683}"
1114,1,38,0,0.0276715,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^2} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^2,x]","\frac{b^2-4 a c}{8 c^2 d^2 (b+2 c x)}+\frac{x}{4 c d^2}","\frac{b^2-4 a c}{8 c^2 d^2 (b+2 c x)}+\frac{x}{4 c d^2}",1,"x/(4*c*d^2) + (b^2 - 4*a*c)/(8*c^2*d^2*(b + 2*c*x))","A",2,1,22,0.04545,1,"{683}"
1115,1,44,0,0.0326059,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^3} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^3,x]","\frac{b^2-4 a c}{16 c^2 d^3 (b+2 c x)^2}+\frac{\log (b+2 c x)}{8 c^2 d^3}","\frac{b^2-4 a c}{16 c^2 d^3 (b+2 c x)^2}+\frac{\log (b+2 c x)}{8 c^2 d^3}",1,"(b^2 - 4*a*c)/(16*c^2*d^3*(b + 2*c*x)^2) + Log[b + 2*c*x]/(8*c^2*d^3)","A",2,1,22,0.04545,1,"{683}"
1116,1,45,0,0.0317319,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^4} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^4,x]","\frac{b^2-4 a c}{24 c^2 d^4 (b+2 c x)^3}-\frac{1}{8 c^2 d^4 (b+2 c x)}","\frac{b^2-4 a c}{24 c^2 d^4 (b+2 c x)^3}-\frac{1}{8 c^2 d^4 (b+2 c x)}",1,"(b^2 - 4*a*c)/(24*c^2*d^4*(b + 2*c*x)^3) - 1/(8*c^2*d^4*(b + 2*c*x))","A",2,1,22,0.04545,1,"{683}"
1117,1,37,0,0.010164,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^5} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^5,x]","\frac{\left(a+b x+c x^2\right)^2}{2 d^5 \left(b^2-4 a c\right) (b+2 c x)^4}","\frac{\left(a+b x+c x^2\right)^2}{2 d^5 \left(b^2-4 a c\right) (b+2 c x)^4}",1,"(a + b*x + c*x^2)^2/(2*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^4)","A",1,1,22,0.04545,1,"{682}"
1118,1,45,0,0.0328772,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^6} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^6,x]","\frac{b^2-4 a c}{40 c^2 d^6 (b+2 c x)^5}-\frac{1}{24 c^2 d^6 (b+2 c x)^3}","\frac{b^2-4 a c}{40 c^2 d^6 (b+2 c x)^5}-\frac{1}{24 c^2 d^6 (b+2 c x)^3}",1,"(b^2 - 4*a*c)/(40*c^2*d^6*(b + 2*c*x)^5) - 1/(24*c^2*d^6*(b + 2*c*x)^3)","A",2,1,22,0.04545,1,"{683}"
1119,1,45,0,0.0325614,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^7} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^7,x]","\frac{b^2-4 a c}{48 c^2 d^7 (b+2 c x)^6}-\frac{1}{32 c^2 d^7 (b+2 c x)^4}","\frac{b^2-4 a c}{48 c^2 d^7 (b+2 c x)^6}-\frac{1}{32 c^2 d^7 (b+2 c x)^4}",1,"(b^2 - 4*a*c)/(48*c^2*d^7*(b + 2*c*x)^6) - 1/(32*c^2*d^7*(b + 2*c*x)^4)","A",2,1,22,0.04545,1,"{683}"
1120,1,45,0,0.0322843,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^8} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^8,x]","\frac{b^2-4 a c}{56 c^2 d^8 (b+2 c x)^7}-\frac{1}{40 c^2 d^8 (b+2 c x)^5}","\frac{b^2-4 a c}{56 c^2 d^8 (b+2 c x)^7}-\frac{1}{40 c^2 d^8 (b+2 c x)^5}",1,"(b^2 - 4*a*c)/(56*c^2*d^8*(b + 2*c*x)^7) - 1/(40*c^2*d^8*(b + 2*c*x)^5)","A",2,1,22,0.04545,1,"{683}"
1121,1,73,0,0.1696354,"\int (b d+2 c d x)^5 \left(a+b x+c x^2\right)^2 \, dx","Int[(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^2,x]","-\frac{d^5 \left(b^2-4 a c\right) (b+2 c x)^8}{128 c^3}+\frac{d^5 \left(b^2-4 a c\right)^2 (b+2 c x)^6}{192 c^3}+\frac{d^5 (b+2 c x)^{10}}{320 c^3}","-\frac{d^5 \left(b^2-4 a c\right) (b+2 c x)^8}{128 c^3}+\frac{d^5 \left(b^2-4 a c\right)^2 (b+2 c x)^6}{192 c^3}+\frac{d^5 (b+2 c x)^{10}}{320 c^3}",1,"((b^2 - 4*a*c)^2*d^5*(b + 2*c*x)^6)/(192*c^3) - ((b^2 - 4*a*c)*d^5*(b + 2*c*x)^8)/(128*c^3) + (d^5*(b + 2*c*x)^10)/(320*c^3)","A",2,1,24,0.04167,1,"{683}"
1122,1,73,0,0.1242371,"\int (b d+2 c d x)^4 \left(a+b x+c x^2\right)^2 \, dx","Int[(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^2,x]","-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^7}{112 c^3}+\frac{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^5}{160 c^3}+\frac{d^4 (b+2 c x)^9}{288 c^3}","-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^7}{112 c^3}+\frac{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^5}{160 c^3}+\frac{d^4 (b+2 c x)^9}{288 c^3}",1,"((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^5)/(160*c^3) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^7)/(112*c^3) + (d^4*(b + 2*c*x)^9)/(288*c^3)","A",2,1,24,0.04167,1,"{683}"
1123,1,55,0,0.0244556,"\int (b d+2 c d x)^3 \left(a+b x+c x^2\right)^2 \, dx","Int[(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^2,x]","\frac{1}{12} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3+\frac{1}{4} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^3","\frac{1}{12} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3+\frac{1}{4} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^3",1,"((b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^3)/12 + (d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^3)/4","A",2,2,24,0.08333,1,"{692, 629}"
1124,1,73,0,0.0843479,"\int (b d+2 c d x)^2 \left(a+b x+c x^2\right)^2 \, dx","Int[(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^2,x]","-\frac{d^2 \left(b^2-4 a c\right) (b+2 c x)^5}{80 c^3}+\frac{d^2 \left(b^2-4 a c\right)^2 (b+2 c x)^3}{96 c^3}+\frac{d^2 (b+2 c x)^7}{224 c^3}","-\frac{d^2 \left(b^2-4 a c\right) (b+2 c x)^5}{80 c^3}+\frac{d^2 \left(b^2-4 a c\right)^2 (b+2 c x)^3}{96 c^3}+\frac{d^2 (b+2 c x)^7}{224 c^3}",1,"((b^2 - 4*a*c)^2*d^2*(b + 2*c*x)^3)/(96*c^3) - ((b^2 - 4*a*c)*d^2*(b + 2*c*x)^5)/(80*c^3) + (d^2*(b + 2*c*x)^7)/(224*c^3)","A",2,1,24,0.04167,1,"{683}"
1125,1,17,0,0.0055592,"\int (b d+2 c d x) \left(a+b x+c x^2\right)^2 \, dx","Int[(b*d + 2*c*d*x)*(a + b*x + c*x^2)^2,x]","\frac{1}{3} d \left(a+b x+c x^2\right)^3","\frac{1}{3} d \left(a+b x+c x^2\right)^3",1,"(d*(a + b*x + c*x^2)^3)/3","A",1,1,22,0.04545,1,"{629}"
1126,1,72,0,0.0722829,"\int \frac{\left(a+b x+c x^2\right)^2}{b d+2 c d x} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x),x]","-\frac{\left(b^2-4 a c\right) (b+2 c x)^2}{32 c^3 d}+\frac{\left(b^2-4 a c\right)^2 \log (b+2 c x)}{32 c^3 d}+\frac{(b+2 c x)^4}{128 c^3 d}","-\frac{\left(b^2-4 a c\right) (b+2 c x)^2}{32 c^3 d}+\frac{\left(b^2-4 a c\right)^2 \log (b+2 c x)}{32 c^3 d}+\frac{(b+2 c x)^4}{128 c^3 d}",1,"-((b^2 - 4*a*c)*(b + 2*c*x)^2)/(32*c^3*d) + (b + 2*c*x)^4/(128*c^3*d) + ((b^2 - 4*a*c)^2*Log[b + 2*c*x])/(32*c^3*d)","A",2,1,24,0.04167,1,"{683}"
1127,1,72,0,0.0598793,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^2} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^2,x]","-\frac{x \left(b^2-8 a c\right)}{16 c^2 d^2}-\frac{\left(b^2-4 a c\right)^2}{32 c^3 d^2 (b+2 c x)}+\frac{b x^2}{8 c d^2}+\frac{x^3}{12 d^2}","-\frac{x \left(b^2-8 a c\right)}{16 c^2 d^2}-\frac{\left(b^2-4 a c\right)^2}{32 c^3 d^2 (b+2 c x)}+\frac{b x^2}{8 c d^2}+\frac{x^3}{12 d^2}",1,"-((b^2 - 8*a*c)*x)/(16*c^2*d^2) + (b*x^2)/(8*c*d^2) + x^3/(12*d^2) - (b^2 - 4*a*c)^2/(32*c^3*d^2*(b + 2*c*x))","A",2,1,24,0.04167,1,"{683}"
1128,1,79,0,0.0635056,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^3} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^3,x]","-\frac{\left(b^2-4 a c\right)^2}{64 c^3 d^3 (b+2 c x)^2}-\frac{\left(b^2-4 a c\right) \log (b+2 c x)}{16 c^3 d^3}+\frac{b x}{16 c^2 d^3}+\frac{x^2}{16 c d^3}","-\frac{\left(b^2-4 a c\right)^2}{64 c^3 d^3 (b+2 c x)^2}-\frac{\left(b^2-4 a c\right) \log (b+2 c x)}{16 c^3 d^3}+\frac{b x}{16 c^2 d^3}+\frac{x^2}{16 c d^3}",1,"(b*x)/(16*c^2*d^3) + x^2/(16*c*d^3) - (b^2 - 4*a*c)^2/(64*c^3*d^3*(b + 2*c*x)^2) - ((b^2 - 4*a*c)*Log[b + 2*c*x])/(16*c^3*d^3)","A",2,1,24,0.04167,1,"{683}"
1129,1,66,0,0.0541672,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^4} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^4,x]","-\frac{\left(b^2-4 a c\right)^2}{96 c^3 d^4 (b+2 c x)^3}+\frac{b^2-4 a c}{16 c^3 d^4 (b+2 c x)}+\frac{x}{16 c^2 d^4}","-\frac{\left(b^2-4 a c\right)^2}{96 c^3 d^4 (b+2 c x)^3}+\frac{b^2-4 a c}{16 c^3 d^4 (b+2 c x)}+\frac{x}{16 c^2 d^4}",1,"x/(16*c^2*d^4) - (b^2 - 4*a*c)^2/(96*c^3*d^4*(b + 2*c*x)^3) + (b^2 - 4*a*c)/(16*c^3*d^4*(b + 2*c*x))","A",2,1,24,0.04167,1,"{683}"
1130,1,72,0,0.0576435,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^5} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^5,x]","-\frac{\left(b^2-4 a c\right)^2}{128 c^3 d^5 (b+2 c x)^4}+\frac{b^2-4 a c}{32 c^3 d^5 (b+2 c x)^2}+\frac{\log (b+2 c x)}{32 c^3 d^5}","-\frac{\left(b^2-4 a c\right)^2}{128 c^3 d^5 (b+2 c x)^4}+\frac{b^2-4 a c}{32 c^3 d^5 (b+2 c x)^2}+\frac{\log (b+2 c x)}{32 c^3 d^5}",1,"-(b^2 - 4*a*c)^2/(128*c^3*d^5*(b + 2*c*x)^4) + (b^2 - 4*a*c)/(32*c^3*d^5*(b + 2*c*x)^2) + Log[b + 2*c*x]/(32*c^3*d^5)","A",2,1,24,0.04167,1,"{683}"
1131,1,73,0,0.0569732,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^6} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^6,x]","-\frac{\left(b^2-4 a c\right)^2}{160 c^3 d^6 (b+2 c x)^5}+\frac{b^2-4 a c}{48 c^3 d^6 (b+2 c x)^3}-\frac{1}{32 c^3 d^6 (b+2 c x)}","-\frac{\left(b^2-4 a c\right)^2}{160 c^3 d^6 (b+2 c x)^5}+\frac{b^2-4 a c}{48 c^3 d^6 (b+2 c x)^3}-\frac{1}{32 c^3 d^6 (b+2 c x)}",1,"-(b^2 - 4*a*c)^2/(160*c^3*d^6*(b + 2*c*x)^5) + (b^2 - 4*a*c)/(48*c^3*d^6*(b + 2*c*x)^3) - 1/(32*c^3*d^6*(b + 2*c*x))","A",2,1,24,0.04167,1,"{683}"
1132,1,37,0,0.0143671,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^7} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^7,x]","\frac{\left(a+b x+c x^2\right)^3}{3 d^7 \left(b^2-4 a c\right) (b+2 c x)^6}","\frac{\left(a+b x+c x^2\right)^3}{3 d^7 \left(b^2-4 a c\right) (b+2 c x)^6}",1,"(a + b*x + c*x^2)^3/(3*(b^2 - 4*a*c)*d^7*(b + 2*c*x)^6)","A",1,1,24,0.04167,1,"{682}"
1133,1,73,0,0.0566795,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^8} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^8,x]","-\frac{\left(b^2-4 a c\right)^2}{224 c^3 d^8 (b+2 c x)^7}+\frac{b^2-4 a c}{80 c^3 d^8 (b+2 c x)^5}-\frac{1}{96 c^3 d^8 (b+2 c x)^3}","-\frac{\left(b^2-4 a c\right)^2}{224 c^3 d^8 (b+2 c x)^7}+\frac{b^2-4 a c}{80 c^3 d^8 (b+2 c x)^5}-\frac{1}{96 c^3 d^8 (b+2 c x)^3}",1,"-(b^2 - 4*a*c)^2/(224*c^3*d^8*(b + 2*c*x)^7) + (b^2 - 4*a*c)/(80*c^3*d^8*(b + 2*c*x)^5) - 1/(96*c^3*d^8*(b + 2*c*x)^3)","A",2,1,24,0.04167,1,"{683}"
1134,1,73,0,0.0548289,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^9} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^9,x]","-\frac{\left(b^2-4 a c\right)^2}{256 c^3 d^9 (b+2 c x)^8}+\frac{b^2-4 a c}{96 c^3 d^9 (b+2 c x)^6}-\frac{1}{128 c^3 d^9 (b+2 c x)^4}","-\frac{\left(b^2-4 a c\right)^2}{256 c^3 d^9 (b+2 c x)^8}+\frac{b^2-4 a c}{96 c^3 d^9 (b+2 c x)^6}-\frac{1}{128 c^3 d^9 (b+2 c x)^4}",1,"-(b^2 - 4*a*c)^2/(256*c^3*d^9*(b + 2*c*x)^8) + (b^2 - 4*a*c)/(96*c^3*d^9*(b + 2*c*x)^6) - 1/(128*c^3*d^9*(b + 2*c*x)^4)","A",2,1,24,0.04167,1,"{683}"
1135,1,73,0,0.0575813,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^{10}} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^10,x]","-\frac{\left(b^2-4 a c\right)^2}{288 c^3 d^{10} (b+2 c x)^9}+\frac{b^2-4 a c}{112 c^3 d^{10} (b+2 c x)^7}-\frac{1}{160 c^3 d^{10} (b+2 c x)^5}","-\frac{\left(b^2-4 a c\right)^2}{288 c^3 d^{10} (b+2 c x)^9}+\frac{b^2-4 a c}{112 c^3 d^{10} (b+2 c x)^7}-\frac{1}{160 c^3 d^{10} (b+2 c x)^5}",1,"-(b^2 - 4*a*c)^2/(288*c^3*d^10*(b + 2*c*x)^9) + (b^2 - 4*a*c)/(112*c^3*d^10*(b + 2*c*x)^7) - 1/(160*c^3*d^10*(b + 2*c*x)^5)","A",2,1,24,0.04167,1,"{683}"
1136,1,73,0,0.0542056,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^{11}} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^11,x]","-\frac{\left(b^2-4 a c\right)^2}{320 c^3 d^{11} (b+2 c x)^{10}}+\frac{b^2-4 a c}{128 c^3 d^{11} (b+2 c x)^8}-\frac{1}{192 c^3 d^{11} (b+2 c x)^6}","-\frac{\left(b^2-4 a c\right)^2}{320 c^3 d^{11} (b+2 c x)^{10}}+\frac{b^2-4 a c}{128 c^3 d^{11} (b+2 c x)^8}-\frac{1}{192 c^3 d^{11} (b+2 c x)^6}",1,"-(b^2 - 4*a*c)^2/(320*c^3*d^11*(b + 2*c*x)^10) + (b^2 - 4*a*c)/(128*c^3*d^11*(b + 2*c*x)^8) - 1/(192*c^3*d^11*(b + 2*c*x)^6)","A",2,1,24,0.04167,1,"{683}"
1137,1,101,0,0.2448759,"\int (b d+2 c d x)^5 \left(a+b x+c x^2\right)^3 \, dx","Int[(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^3,x]","-\frac{3 d^5 \left(b^2-4 a c\right) (b+2 c x)^{10}}{1280 c^4}+\frac{3 d^5 \left(b^2-4 a c\right)^2 (b+2 c x)^8}{1024 c^4}-\frac{d^5 \left(b^2-4 a c\right)^3 (b+2 c x)^6}{768 c^4}+\frac{d^5 (b+2 c x)^{12}}{1536 c^4}","-\frac{3 d^5 \left(b^2-4 a c\right) (b+2 c x)^{10}}{1280 c^4}+\frac{3 d^5 \left(b^2-4 a c\right)^2 (b+2 c x)^8}{1024 c^4}-\frac{d^5 \left(b^2-4 a c\right)^3 (b+2 c x)^6}{768 c^4}+\frac{d^5 (b+2 c x)^{12}}{1536 c^4}",1,"-((b^2 - 4*a*c)^3*d^5*(b + 2*c*x)^6)/(768*c^4) + (3*(b^2 - 4*a*c)^2*d^5*(b + 2*c*x)^8)/(1024*c^4) - (3*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^10)/(1280*c^4) + (d^5*(b + 2*c*x)^12)/(1536*c^4)","A",2,1,24,0.04167,1,"{683}"
1138,1,101,0,0.1916343,"\int (b d+2 c d x)^4 \left(a+b x+c x^2\right)^3 \, dx","Int[(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^3,x]","-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^9}{384 c^4}+\frac{3 d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^7}{896 c^4}-\frac{d^4 \left(b^2-4 a c\right)^3 (b+2 c x)^5}{640 c^4}+\frac{d^4 (b+2 c x)^{11}}{1408 c^4}","-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^9}{384 c^4}+\frac{3 d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^7}{896 c^4}-\frac{d^4 \left(b^2-4 a c\right)^3 (b+2 c x)^5}{640 c^4}+\frac{d^4 (b+2 c x)^{11}}{1408 c^4}",1,"-((b^2 - 4*a*c)^3*d^4*(b + 2*c*x)^5)/(640*c^4) + (3*(b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^7)/(896*c^4) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^9)/(384*c^4) + (d^4*(b + 2*c*x)^11)/(1408*c^4)","A",2,1,24,0.04167,1,"{683}"
1139,1,55,0,0.0250731,"\int (b d+2 c d x)^3 \left(a+b x+c x^2\right)^3 \, dx","Int[(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^3,x]","\frac{1}{20} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4+\frac{1}{5} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^4","\frac{1}{20} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4+\frac{1}{5} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^4",1,"((b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^4)/20 + (d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^4)/5","A",2,2,24,0.08333,1,"{692, 629}"
1140,1,101,0,0.1289695,"\int (b d+2 c d x)^2 \left(a+b x+c x^2\right)^3 \, dx","Int[(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^3,x]","-\frac{3 d^2 \left(b^2-4 a c\right) (b+2 c x)^7}{896 c^4}+\frac{3 d^2 \left(b^2-4 a c\right)^2 (b+2 c x)^5}{640 c^4}-\frac{d^2 \left(b^2-4 a c\right)^3 (b+2 c x)^3}{384 c^4}+\frac{d^2 (b+2 c x)^9}{1152 c^4}","-\frac{3 d^2 \left(b^2-4 a c\right) (b+2 c x)^7}{896 c^4}+\frac{3 d^2 \left(b^2-4 a c\right)^2 (b+2 c x)^5}{640 c^4}-\frac{d^2 \left(b^2-4 a c\right)^3 (b+2 c x)^3}{384 c^4}+\frac{d^2 (b+2 c x)^9}{1152 c^4}",1,"-((b^2 - 4*a*c)^3*d^2*(b + 2*c*x)^3)/(384*c^4) + (3*(b^2 - 4*a*c)^2*d^2*(b + 2*c*x)^5)/(640*c^4) - (3*(b^2 - 4*a*c)*d^2*(b + 2*c*x)^7)/(896*c^4) + (d^2*(b + 2*c*x)^9)/(1152*c^4)","A",2,1,24,0.04167,1,"{683}"
1141,1,17,0,0.0054493,"\int (b d+2 c d x) \left(a+b x+c x^2\right)^3 \, dx","Int[(b*d + 2*c*d*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{4} d \left(a+b x+c x^2\right)^4","\frac{1}{4} d \left(a+b x+c x^2\right)^4",1,"(d*(a + b*x + c*x^2)^4)/4","A",1,1,22,0.04545,1,"{629}"
1142,1,100,0,0.1177781,"\int \frac{\left(a+b x+c x^2\right)^3}{b d+2 c d x} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x),x]","-\frac{3 \left(b^2-4 a c\right) (b+2 c x)^4}{512 c^4 d}+\frac{3 \left(b^2-4 a c\right)^2 (b+2 c x)^2}{256 c^4 d}-\frac{\left(b^2-4 a c\right)^3 \log (b+2 c x)}{128 c^4 d}+\frac{(b+2 c x)^6}{768 c^4 d}","-\frac{3 \left(b^2-4 a c\right) (b+2 c x)^4}{512 c^4 d}+\frac{3 \left(b^2-4 a c\right)^2 (b+2 c x)^2}{256 c^4 d}-\frac{\left(b^2-4 a c\right)^3 \log (b+2 c x)}{128 c^4 d}+\frac{(b+2 c x)^6}{768 c^4 d}",1,"(3*(b^2 - 4*a*c)^2*(b + 2*c*x)^2)/(256*c^4*d) - (3*(b^2 - 4*a*c)*(b + 2*c*x)^4)/(512*c^4*d) + (b + 2*c*x)^6/(768*c^4*d) - ((b^2 - 4*a*c)^3*Log[b + 2*c*x])/(128*c^4*d)","A",2,1,24,0.04167,1,"{683}"
1143,1,94,0,0.0945815,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^2} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^2,x]","-\frac{\left(b^2-4 a c\right) (b+2 c x)^3}{128 c^4 d^2}+\frac{3 x \left(b^2-4 a c\right)^2}{64 c^3 d^2}+\frac{\left(b^2-4 a c\right)^3}{128 c^4 d^2 (b+2 c x)}+\frac{(b+2 c x)^5}{640 c^4 d^2}","-\frac{\left(b^2-4 a c\right) (b+2 c x)^3}{128 c^4 d^2}+\frac{3 x \left(b^2-4 a c\right)^2}{64 c^3 d^2}+\frac{\left(b^2-4 a c\right)^3}{128 c^4 d^2 (b+2 c x)}+\frac{(b+2 c x)^5}{640 c^4 d^2}",1,"(3*(b^2 - 4*a*c)^2*x)/(64*c^3*d^2) + (b^2 - 4*a*c)^3/(128*c^4*d^2*(b + 2*c*x)) - ((b^2 - 4*a*c)*(b + 2*c*x)^3)/(128*c^4*d^2) + (b + 2*c*x)^5/(640*c^4*d^2)","A",2,1,24,0.04167,1,"{683}"
1144,1,100,0,0.0982906,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^3} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^3,x]","-\frac{3 \left(b^2-4 a c\right) (b+2 c x)^2}{256 c^4 d^3}+\frac{\left(b^2-4 a c\right)^3}{256 c^4 d^3 (b+2 c x)^2}+\frac{3 \left(b^2-4 a c\right)^2 \log (b+2 c x)}{128 c^4 d^3}+\frac{(b+2 c x)^4}{512 c^4 d^3}","-\frac{3 \left(b^2-4 a c\right) (b+2 c x)^2}{256 c^4 d^3}+\frac{\left(b^2-4 a c\right)^3}{256 c^4 d^3 (b+2 c x)^2}+\frac{3 \left(b^2-4 a c\right)^2 \log (b+2 c x)}{128 c^4 d^3}+\frac{(b+2 c x)^4}{512 c^4 d^3}",1,"(b^2 - 4*a*c)^3/(256*c^4*d^3*(b + 2*c*x)^2) - (3*(b^2 - 4*a*c)*(b + 2*c*x)^2)/(256*c^4*d^3) + (b + 2*c*x)^4/(512*c^4*d^3) + (3*(b^2 - 4*a*c)^2*Log[b + 2*c*x])/(128*c^4*d^3)","A",2,1,24,0.04167,1,"{683}"
1145,1,103,0,0.0941266,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^4} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^4,x]","\frac{\left(b^2-4 a c\right)^3}{384 c^4 d^4 (b+2 c x)^3}-\frac{3 \left(b^2-4 a c\right)^2}{128 c^4 d^4 (b+2 c x)}-\frac{x \left(b^2-6 a c\right)}{32 c^3 d^4}+\frac{b x^2}{32 c^2 d^4}+\frac{x^3}{48 c d^4}","\frac{\left(b^2-4 a c\right)^3}{384 c^4 d^4 (b+2 c x)^3}-\frac{3 \left(b^2-4 a c\right)^2}{128 c^4 d^4 (b+2 c x)}-\frac{x \left(b^2-6 a c\right)}{32 c^3 d^4}+\frac{b x^2}{32 c^2 d^4}+\frac{x^3}{48 c d^4}",1,"-((b^2 - 6*a*c)*x)/(32*c^3*d^4) + (b*x^2)/(32*c^2*d^4) + x^3/(48*c*d^4) + (b^2 - 4*a*c)^3/(384*c^4*d^4*(b + 2*c*x)^3) - (3*(b^2 - 4*a*c)^2)/(128*c^4*d^4*(b + 2*c*x))","A",2,1,24,0.04167,1,"{683}"
1146,1,107,0,0.0982241,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^5} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^5,x]","\frac{\left(b^2-4 a c\right)^3}{512 c^4 d^5 (b+2 c x)^4}-\frac{3 \left(b^2-4 a c\right)^2}{256 c^4 d^5 (b+2 c x)^2}-\frac{3 \left(b^2-4 a c\right) \log (b+2 c x)}{128 c^4 d^5}+\frac{b x}{64 c^3 d^5}+\frac{x^2}{64 c^2 d^5}","\frac{\left(b^2-4 a c\right)^3}{512 c^4 d^5 (b+2 c x)^4}-\frac{3 \left(b^2-4 a c\right)^2}{256 c^4 d^5 (b+2 c x)^2}-\frac{3 \left(b^2-4 a c\right) \log (b+2 c x)}{128 c^4 d^5}+\frac{b x}{64 c^3 d^5}+\frac{x^2}{64 c^2 d^5}",1,"(b*x)/(64*c^3*d^5) + x^2/(64*c^2*d^5) + (b^2 - 4*a*c)^3/(512*c^4*d^5*(b + 2*c*x)^4) - (3*(b^2 - 4*a*c)^2)/(256*c^4*d^5*(b + 2*c*x)^2) - (3*(b^2 - 4*a*c)*Log[b + 2*c*x])/(128*c^4*d^5)","A",2,1,24,0.04167,1,"{683}"
1147,1,94,0,0.0854048,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^6} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^6,x]","\frac{\left(b^2-4 a c\right)^3}{640 c^4 d^6 (b+2 c x)^5}-\frac{\left(b^2-4 a c\right)^2}{128 c^4 d^6 (b+2 c x)^3}+\frac{3 \left(b^2-4 a c\right)}{128 c^4 d^6 (b+2 c x)}+\frac{x}{64 c^3 d^6}","\frac{\left(b^2-4 a c\right)^3}{640 c^4 d^6 (b+2 c x)^5}-\frac{\left(b^2-4 a c\right)^2}{128 c^4 d^6 (b+2 c x)^3}+\frac{3 \left(b^2-4 a c\right)}{128 c^4 d^6 (b+2 c x)}+\frac{x}{64 c^3 d^6}",1,"x/(64*c^3*d^6) + (b^2 - 4*a*c)^3/(640*c^4*d^6*(b + 2*c*x)^5) - (b^2 - 4*a*c)^2/(128*c^4*d^6*(b + 2*c*x)^3) + (3*(b^2 - 4*a*c))/(128*c^4*d^6*(b + 2*c*x))","A",2,1,24,0.04167,1,"{683}"
1148,1,100,0,0.0828874,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^7} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^7,x]","\frac{\left(b^2-4 a c\right)^3}{768 c^4 d^7 (b+2 c x)^6}-\frac{3 \left(b^2-4 a c\right)^2}{512 c^4 d^7 (b+2 c x)^4}+\frac{3 \left(b^2-4 a c\right)}{256 c^4 d^7 (b+2 c x)^2}+\frac{\log (b+2 c x)}{128 c^4 d^7}","\frac{\left(b^2-4 a c\right)^3}{768 c^4 d^7 (b+2 c x)^6}-\frac{3 \left(b^2-4 a c\right)^2}{512 c^4 d^7 (b+2 c x)^4}+\frac{3 \left(b^2-4 a c\right)}{256 c^4 d^7 (b+2 c x)^2}+\frac{\log (b+2 c x)}{128 c^4 d^7}",1,"(b^2 - 4*a*c)^3/(768*c^4*d^7*(b + 2*c*x)^6) - (3*(b^2 - 4*a*c)^2)/(512*c^4*d^7*(b + 2*c*x)^4) + (3*(b^2 - 4*a*c))/(256*c^4*d^7*(b + 2*c*x)^2) + Log[b + 2*c*x]/(128*c^4*d^7)","A",2,1,24,0.04167,1,"{683}"
1149,1,101,0,0.080555,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^8} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^8,x]","\frac{\left(b^2-4 a c\right)^3}{896 c^4 d^8 (b+2 c x)^7}-\frac{3 \left(b^2-4 a c\right)^2}{640 c^4 d^8 (b+2 c x)^5}+\frac{b^2-4 a c}{128 c^4 d^8 (b+2 c x)^3}-\frac{1}{128 c^4 d^8 (b+2 c x)}","\frac{\left(b^2-4 a c\right)^3}{896 c^4 d^8 (b+2 c x)^7}-\frac{3 \left(b^2-4 a c\right)^2}{640 c^4 d^8 (b+2 c x)^5}+\frac{b^2-4 a c}{128 c^4 d^8 (b+2 c x)^3}-\frac{1}{128 c^4 d^8 (b+2 c x)}",1,"(b^2 - 4*a*c)^3/(896*c^4*d^8*(b + 2*c*x)^7) - (3*(b^2 - 4*a*c)^2)/(640*c^4*d^8*(b + 2*c*x)^5) + (b^2 - 4*a*c)/(128*c^4*d^8*(b + 2*c*x)^3) - 1/(128*c^4*d^8*(b + 2*c*x))","A",2,1,24,0.04167,1,"{683}"
1150,1,37,0,0.0133028,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^9} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^9,x]","\frac{\left(a+b x+c x^2\right)^4}{4 d^9 \left(b^2-4 a c\right) (b+2 c x)^8}","\frac{\left(a+b x+c x^2\right)^4}{4 d^9 \left(b^2-4 a c\right) (b+2 c x)^8}",1,"(a + b*x + c*x^2)^4/(4*(b^2 - 4*a*c)*d^9*(b + 2*c*x)^8)","A",1,1,24,0.04167,1,"{682}"
1151,1,101,0,0.0816032,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^{10}} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^10,x]","\frac{\left(b^2-4 a c\right)^3}{1152 c^4 d^{10} (b+2 c x)^9}-\frac{3 \left(b^2-4 a c\right)^2}{896 c^4 d^{10} (b+2 c x)^7}+\frac{3 \left(b^2-4 a c\right)}{640 c^4 d^{10} (b+2 c x)^5}-\frac{1}{384 c^4 d^{10} (b+2 c x)^3}","\frac{\left(b^2-4 a c\right)^3}{1152 c^4 d^{10} (b+2 c x)^9}-\frac{3 \left(b^2-4 a c\right)^2}{896 c^4 d^{10} (b+2 c x)^7}+\frac{3 \left(b^2-4 a c\right)}{640 c^4 d^{10} (b+2 c x)^5}-\frac{1}{384 c^4 d^{10} (b+2 c x)^3}",1,"(b^2 - 4*a*c)^3/(1152*c^4*d^10*(b + 2*c*x)^9) - (3*(b^2 - 4*a*c)^2)/(896*c^4*d^10*(b + 2*c*x)^7) + (3*(b^2 - 4*a*c))/(640*c^4*d^10*(b + 2*c*x)^5) - 1/(384*c^4*d^10*(b + 2*c*x)^3)","A",2,1,24,0.04167,1,"{683}"
1152,1,101,0,0.0814115,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^{11}} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^11,x]","\frac{\left(b^2-4 a c\right)^3}{1280 c^4 d^{11} (b+2 c x)^{10}}-\frac{3 \left(b^2-4 a c\right)^2}{1024 c^4 d^{11} (b+2 c x)^8}+\frac{b^2-4 a c}{256 c^4 d^{11} (b+2 c x)^6}-\frac{1}{512 c^4 d^{11} (b+2 c x)^4}","\frac{\left(b^2-4 a c\right)^3}{1280 c^4 d^{11} (b+2 c x)^{10}}-\frac{3 \left(b^2-4 a c\right)^2}{1024 c^4 d^{11} (b+2 c x)^8}+\frac{b^2-4 a c}{256 c^4 d^{11} (b+2 c x)^6}-\frac{1}{512 c^4 d^{11} (b+2 c x)^4}",1,"(b^2 - 4*a*c)^3/(1280*c^4*d^11*(b + 2*c*x)^10) - (3*(b^2 - 4*a*c)^2)/(1024*c^4*d^11*(b + 2*c*x)^8) + (b^2 - 4*a*c)/(256*c^4*d^11*(b + 2*c*x)^6) - 1/(512*c^4*d^11*(b + 2*c*x)^4)","A",2,1,24,0.04167,1,"{683}"
1153,1,101,0,0.0846991,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^{12}} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^12,x]","\frac{\left(b^2-4 a c\right)^3}{1408 c^4 d^{12} (b+2 c x)^{11}}-\frac{\left(b^2-4 a c\right)^2}{384 c^4 d^{12} (b+2 c x)^9}+\frac{3 \left(b^2-4 a c\right)}{896 c^4 d^{12} (b+2 c x)^7}-\frac{1}{640 c^4 d^{12} (b+2 c x)^5}","\frac{\left(b^2-4 a c\right)^3}{1408 c^4 d^{12} (b+2 c x)^{11}}-\frac{\left(b^2-4 a c\right)^2}{384 c^4 d^{12} (b+2 c x)^9}+\frac{3 \left(b^2-4 a c\right)}{896 c^4 d^{12} (b+2 c x)^7}-\frac{1}{640 c^4 d^{12} (b+2 c x)^5}",1,"(b^2 - 4*a*c)^3/(1408*c^4*d^12*(b + 2*c*x)^11) - (b^2 - 4*a*c)^2/(384*c^4*d^12*(b + 2*c*x)^9) + (3*(b^2 - 4*a*c))/(896*c^4*d^12*(b + 2*c*x)^7) - 1/(640*c^4*d^12*(b + 2*c*x)^5)","A",2,1,24,0.04167,1,"{683}"
1154,1,122,0,0.1504045,"\int \frac{(b d+2 c d x)^8}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^8/(a + b*x + c*x^2),x]","\frac{2}{5} d^8 \left(b^2-4 a c\right) (b+2 c x)^5+\frac{2}{3} d^8 \left(b^2-4 a c\right)^2 (b+2 c x)^3+2 d^8 \left(b^2-4 a c\right)^3 (b+2 c x)-2 d^8 \left(b^2-4 a c\right)^{7/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+\frac{2}{7} d^8 (b+2 c x)^7","\frac{2}{5} d^8 \left(b^2-4 a c\right) (b+2 c x)^5+\frac{2}{3} d^8 \left(b^2-4 a c\right)^2 (b+2 c x)^3+2 d^8 \left(b^2-4 a c\right)^3 (b+2 c x)-2 d^8 \left(b^2-4 a c\right)^{7/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+\frac{2}{7} d^8 (b+2 c x)^7",1,"2*(b^2 - 4*a*c)^3*d^8*(b + 2*c*x) + (2*(b^2 - 4*a*c)^2*d^8*(b + 2*c*x)^3)/3 + (2*(b^2 - 4*a*c)*d^8*(b + 2*c*x)^5)/5 + (2*d^8*(b + 2*c*x)^7)/7 - 2*(b^2 - 4*a*c)^(7/2)*d^8*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",6,3,24,0.1250,1,"{692, 618, 206}"
1155,1,86,0,0.0701957,"\int \frac{(b d+2 c d x)^7}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^7/(a + b*x + c*x^2),x]","d^7 \left(b^2-4 a c\right)^3 \log \left(a+b x+c x^2\right)+\frac{1}{2} d^7 \left(b^2-4 a c\right) (b+2 c x)^4+d^7 \left(b^2-4 a c\right)^2 (b+2 c x)^2+\frac{1}{3} d^7 (b+2 c x)^6","d^7 \left(b^2-4 a c\right)^3 \log \left(a+b x+c x^2\right)+\frac{1}{2} d^7 \left(b^2-4 a c\right) (b+2 c x)^4+d^7 \left(b^2-4 a c\right)^2 (b+2 c x)^2+\frac{1}{3} d^7 (b+2 c x)^6",1,"(b^2 - 4*a*c)^2*d^7*(b + 2*c*x)^2 + ((b^2 - 4*a*c)*d^7*(b + 2*c*x)^4)/2 + (d^7*(b + 2*c*x)^6)/3 + (b^2 - 4*a*c)^3*d^7*Log[a + b*x + c*x^2]","A",4,2,24,0.08333,1,"{692, 628}"
1156,1,97,0,0.0804153,"\int \frac{(b d+2 c d x)^6}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^6/(a + b*x + c*x^2),x]","\frac{2}{3} d^6 \left(b^2-4 a c\right) (b+2 c x)^3+2 d^6 \left(b^2-4 a c\right)^2 (b+2 c x)-2 d^6 \left(b^2-4 a c\right)^{5/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+\frac{2}{5} d^6 (b+2 c x)^5","\frac{2}{3} d^6 \left(b^2-4 a c\right) (b+2 c x)^3+2 d^6 \left(b^2-4 a c\right)^2 (b+2 c x)-2 d^6 \left(b^2-4 a c\right)^{5/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+\frac{2}{5} d^6 (b+2 c x)^5",1,"2*(b^2 - 4*a*c)^2*d^6*(b + 2*c*x) + (2*(b^2 - 4*a*c)*d^6*(b + 2*c*x)^3)/3 + (2*d^6*(b + 2*c*x)^5)/5 - 2*(b^2 - 4*a*c)^(5/2)*d^6*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",5,3,24,0.1250,1,"{692, 618, 206}"
1157,1,61,0,0.0426205,"\int \frac{(b d+2 c d x)^5}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^5/(a + b*x + c*x^2),x]","d^5 \left(b^2-4 a c\right)^2 \log \left(a+b x+c x^2\right)+d^5 \left(b^2-4 a c\right) (b+2 c x)^2+\frac{1}{2} d^5 (b+2 c x)^4","d^5 \left(b^2-4 a c\right)^2 \log \left(a+b x+c x^2\right)+d^5 \left(b^2-4 a c\right) (b+2 c x)^2+\frac{1}{2} d^5 (b+2 c x)^4",1,"(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2 + (d^5*(b + 2*c*x)^4)/2 + (b^2 - 4*a*c)^2*d^5*Log[a + b*x + c*x^2]","A",3,2,24,0.08333,1,"{692, 628}"
1158,1,72,0,0.070038,"\int \frac{(b d+2 c d x)^4}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^4/(a + b*x + c*x^2),x]","2 d^4 \left(b^2-4 a c\right) (b+2 c x)-2 d^4 \left(b^2-4 a c\right)^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+\frac{2}{3} d^4 (b+2 c x)^3","2 d^4 \left(b^2-4 a c\right) (b+2 c x)-2 d^4 \left(b^2-4 a c\right)^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)+\frac{2}{3} d^4 (b+2 c x)^3",1,"2*(b^2 - 4*a*c)*d^4*(b + 2*c*x) + (2*d^4*(b + 2*c*x)^3)/3 - 2*(b^2 - 4*a*c)^(3/2)*d^4*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",4,3,24,0.1250,1,"{692, 618, 206}"
1159,1,36,0,0.0228052,"\int \frac{(b d+2 c d x)^3}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^3/(a + b*x + c*x^2),x]","d^3 \left(b^2-4 a c\right) \log \left(a+b x+c x^2\right)+d^3 (b+2 c x)^2","d^3 \left(b^2-4 a c\right) \log \left(a+b x+c x^2\right)+d^3 (b+2 c x)^2",1,"d^3*(b + 2*c*x)^2 + (b^2 - 4*a*c)*d^3*Log[a + b*x + c*x^2]","A",2,2,24,0.08333,1,"{692, 628}"
1160,1,49,0,0.0308715,"\int \frac{(b d+2 c d x)^2}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^2/(a + b*x + c*x^2),x]","2 d^2 (b+2 c x)-2 d^2 \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)","2 d^2 (b+2 c x)-2 d^2 \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)",1,"2*d^2*(b + 2*c*x) - 2*Sqrt[b^2 - 4*a*c]*d^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",3,3,24,0.1250,1,"{692, 618, 206}"
1161,1,13,0,0.0048115,"\int \frac{b d+2 c d x}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)/(a + b*x + c*x^2),x]","d \log \left(a+b x+c x^2\right)","d \log \left(a+b x+c x^2\right)",1,"d*Log[a + b*x + c*x^2]","A",1,1,22,0.04545,1,"{628}"
1162,1,48,0,0.0233232,"\int \frac{1}{(b d+2 c d x) \left(a+b x+c x^2\right)} \, dx","Int[1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)),x]","\frac{\log \left(a+b x+c x^2\right)}{d \left(b^2-4 a c\right)}-\frac{2 \log (b+2 c x)}{d \left(b^2-4 a c\right)}","\frac{\log \left(a+b x+c x^2\right)}{d \left(b^2-4 a c\right)}-\frac{2 \log (b+2 c x)}{d \left(b^2-4 a c\right)}",1,"(-2*Log[b + 2*c*x])/((b^2 - 4*a*c)*d) + Log[a + b*x + c*x^2]/((b^2 - 4*a*c)*d)","A",3,3,24,0.1250,1,"{681, 31, 628}"
1163,1,61,0,0.040675,"\int \frac{1}{(b d+2 c d x)^2 \left(a+b x+c x^2\right)} \, dx","Int[1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)),x]","\frac{2}{d^2 \left(b^2-4 a c\right) (b+2 c x)}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^2 \left(b^2-4 a c\right)^{3/2}}","\frac{2}{d^2 \left(b^2-4 a c\right) (b+2 c x)}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^2 \left(b^2-4 a c\right)^{3/2}}",1,"2/((b^2 - 4*a*c)*d^2*(b + 2*c*x)) - (2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*d^2)","A",3,3,24,0.1250,1,"{693, 618, 206}"
1164,1,70,0,0.0403733,"\int \frac{1}{(b d+2 c d x)^3 \left(a+b x+c x^2\right)} \, dx","Int[1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)),x]","\frac{\log \left(a+b x+c x^2\right)}{d^3 \left(b^2-4 a c\right)^2}+\frac{1}{d^3 \left(b^2-4 a c\right) (b+2 c x)^2}-\frac{2 \log (b+2 c x)}{d^3 \left(b^2-4 a c\right)^2}","\frac{\log \left(a+b x+c x^2\right)}{d^3 \left(b^2-4 a c\right)^2}+\frac{1}{d^3 \left(b^2-4 a c\right) (b+2 c x)^2}-\frac{2 \log (b+2 c x)}{d^3 \left(b^2-4 a c\right)^2}",1,"1/((b^2 - 4*a*c)*d^3*(b + 2*c*x)^2) - (2*Log[b + 2*c*x])/((b^2 - 4*a*c)^2*d^3) + Log[a + b*x + c*x^2]/((b^2 - 4*a*c)^2*d^3)","A",4,4,24,0.1667,1,"{693, 681, 31, 628}"
1165,1,86,0,0.0670583,"\int \frac{1}{(b d+2 c d x)^4 \left(a+b x+c x^2\right)} \, dx","Int[1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)),x]","\frac{2}{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)}+\frac{2}{3 d^4 \left(b^2-4 a c\right) (b+2 c x)^3}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^4 \left(b^2-4 a c\right)^{5/2}}","\frac{2}{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)}+\frac{2}{3 d^4 \left(b^2-4 a c\right) (b+2 c x)^3}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^4 \left(b^2-4 a c\right)^{5/2}}",1,"2/(3*(b^2 - 4*a*c)*d^4*(b + 2*c*x)^3) + 2/((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)) - (2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*d^4)","A",4,3,24,0.1250,1,"{693, 618, 206}"
1166,1,126,0,0.1047323,"\int \frac{(b d+2 c d x)^8}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^8/(a + b*x + c*x^2)^2,x]","\frac{28}{3} c d^8 \left(b^2-4 a c\right) (b+2 c x)^3+28 c d^8 \left(b^2-4 a c\right)^2 (b+2 c x)-28 c d^8 \left(b^2-4 a c\right)^{5/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{d^8 (b+2 c x)^7}{a+b x+c x^2}+\frac{28}{5} c d^8 (b+2 c x)^5","\frac{28}{3} c d^8 \left(b^2-4 a c\right) (b+2 c x)^3+28 c d^8 \left(b^2-4 a c\right)^2 (b+2 c x)-28 c d^8 \left(b^2-4 a c\right)^{5/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{d^8 (b+2 c x)^7}{a+b x+c x^2}+\frac{28}{5} c d^8 (b+2 c x)^5",1,"28*c*(b^2 - 4*a*c)^2*d^8*(b + 2*c*x) + (28*c*(b^2 - 4*a*c)*d^8*(b + 2*c*x)^3)/3 + (28*c*d^8*(b + 2*c*x)^5)/5 - (d^8*(b + 2*c*x)^7)/(a + b*x + c*x^2) - 28*c*(b^2 - 4*a*c)^(5/2)*d^8*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",6,4,24,0.1667,1,"{686, 692, 618, 206}"
1167,1,89,0,0.06212,"\int \frac{(b d+2 c d x)^7}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^7/(a + b*x + c*x^2)^2,x]","12 c d^7 \left(b^2-4 a c\right)^2 \log \left(a+b x+c x^2\right)+12 c d^7 \left(b^2-4 a c\right) (b+2 c x)^2-\frac{d^7 (b+2 c x)^6}{a+b x+c x^2}+6 c d^7 (b+2 c x)^4","12 c d^7 \left(b^2-4 a c\right)^2 \log \left(a+b x+c x^2\right)+12 c d^7 \left(b^2-4 a c\right) (b+2 c x)^2-\frac{d^7 (b+2 c x)^6}{a+b x+c x^2}+6 c d^7 (b+2 c x)^4",1,"12*c*(b^2 - 4*a*c)*d^7*(b + 2*c*x)^2 + 6*c*d^7*(b + 2*c*x)^4 - (d^7*(b + 2*c*x)^6)/(a + b*x + c*x^2) + 12*c*(b^2 - 4*a*c)^2*d^7*Log[a + b*x + c*x^2]","A",4,3,24,0.1250,1,"{686, 692, 628}"
1168,1,100,0,0.0742676,"\int \frac{(b d+2 c d x)^6}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^2,x]","20 c d^6 \left(b^2-4 a c\right) (b+2 c x)-20 c d^6 \left(b^2-4 a c\right)^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{d^6 (b+2 c x)^5}{a+b x+c x^2}+\frac{20}{3} c d^6 (b+2 c x)^3","20 c d^6 \left(b^2-4 a c\right) (b+2 c x)-20 c d^6 \left(b^2-4 a c\right)^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{d^6 (b+2 c x)^5}{a+b x+c x^2}+\frac{20}{3} c d^6 (b+2 c x)^3",1,"20*c*(b^2 - 4*a*c)*d^6*(b + 2*c*x) + (20*c*d^6*(b + 2*c*x)^3)/3 - (d^6*(b + 2*c*x)^5)/(a + b*x + c*x^2) - 20*c*(b^2 - 4*a*c)^(3/2)*d^6*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",5,4,24,0.1667,1,"{686, 692, 618, 206}"
1169,1,65,0,0.039496,"\int \frac{(b d+2 c d x)^5}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^5/(a + b*x + c*x^2)^2,x]","8 c d^5 \left(b^2-4 a c\right) \log \left(a+b x+c x^2\right)-\frac{d^5 (b+2 c x)^4}{a+b x+c x^2}+8 c d^5 (b+2 c x)^2","8 c d^5 \left(b^2-4 a c\right) \log \left(a+b x+c x^2\right)-\frac{d^5 (b+2 c x)^4}{a+b x+c x^2}+8 c d^5 (b+2 c x)^2",1,"8*c*d^5*(b + 2*c*x)^2 - (d^5*(b + 2*c*x)^4)/(a + b*x + c*x^2) + 8*c*(b^2 - 4*a*c)*d^5*Log[a + b*x + c*x^2]","A",3,3,24,0.1250,1,"{686, 692, 628}"
1170,1,76,0,0.0507377,"\int \frac{(b d+2 c d x)^4}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^2,x]","-12 c d^4 \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{d^4 (b+2 c x)^3}{a+b x+c x^2}+12 c d^4 (b+2 c x)","-12 c d^4 \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{d^4 (b+2 c x)^3}{a+b x+c x^2}+12 c d^4 (b+2 c x)",1,"12*c*d^4*(b + 2*c*x) - (d^4*(b + 2*c*x)^3)/(a + b*x + c*x^2) - 12*c*Sqrt[b^2 - 4*a*c]*d^4*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",4,4,24,0.1667,1,"{686, 692, 618, 206}"
1171,1,43,0,0.0202037,"\int \frac{(b d+2 c d x)^3}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^2,x]","4 c d^3 \log \left(a+b x+c x^2\right)-\frac{d^3 (b+2 c x)^2}{a+b x+c x^2}","4 c d^3 \log \left(a+b x+c x^2\right)-\frac{d^3 (b+2 c x)^2}{a+b x+c x^2}",1,"-((d^3*(b + 2*c*x)^2)/(a + b*x + c*x^2)) + 4*c*d^3*Log[a + b*x + c*x^2]","A",2,2,24,0.08333,1,"{686, 628}"
1172,1,62,0,0.0359027,"\int \frac{(b d+2 c d x)^2}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^2,x]","-\frac{4 c d^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}-\frac{d^2 (b+2 c x)}{a+b x+c x^2}","-\frac{4 c d^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}-\frac{d^2 (b+2 c x)}{a+b x+c x^2}",1,"-((d^2*(b + 2*c*x))/(a + b*x + c*x^2)) - (4*c*d^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",3,3,24,0.1250,1,"{686, 618, 206}"
1173,1,15,0,0.0051263,"\int \frac{b d+2 c d x}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)/(a + b*x + c*x^2)^2,x]","-\frac{d}{a+b x+c x^2}","-\frac{d}{a+b x+c x^2}",1,"-(d/(a + b*x + c*x^2))","A",1,1,22,0.04545,1,"{629}"
1174,1,78,0,0.0382858,"\int \frac{1}{(b d+2 c d x) \left(a+b x+c x^2\right)^2} \, dx","Int[1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^2),x]","-\frac{1}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{4 c \log \left(a+b x+c x^2\right)}{d \left(b^2-4 a c\right)^2}+\frac{8 c \log (b+2 c x)}{d \left(b^2-4 a c\right)^2}","-\frac{1}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{4 c \log \left(a+b x+c x^2\right)}{d \left(b^2-4 a c\right)^2}+\frac{8 c \log (b+2 c x)}{d \left(b^2-4 a c\right)^2}",1,"-(1/((b^2 - 4*a*c)*d*(a + b*x + c*x^2))) + (8*c*Log[b + 2*c*x])/((b^2 - 4*a*c)^2*d) - (4*c*Log[a + b*x + c*x^2])/((b^2 - 4*a*c)^2*d)","A",4,4,24,0.1667,1,"{687, 681, 31, 628}"
1175,1,98,0,0.0575797,"\int \frac{1}{(b d+2 c d x)^2 \left(a+b x+c x^2\right)^2} \, dx","Int[1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^2),x]","-\frac{1}{d^2 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)}-\frac{12 c}{d^2 \left(b^2-4 a c\right)^2 (b+2 c x)}+\frac{12 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^2 \left(b^2-4 a c\right)^{5/2}}","-\frac{1}{d^2 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)}-\frac{12 c}{d^2 \left(b^2-4 a c\right)^2 (b+2 c x)}+\frac{12 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^2 \left(b^2-4 a c\right)^{5/2}}",1,"(-12*c)/((b^2 - 4*a*c)^2*d^2*(b + 2*c*x)) - 1/((b^2 - 4*a*c)*d^2*(b + 2*c*x)*(a + b*x + c*x^2)) + (12*c*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*d^2)","A",4,4,24,0.1667,1,"{687, 693, 618, 206}"
1176,1,110,0,0.0621794,"\int \frac{1}{(b d+2 c d x)^3 \left(a+b x+c x^2\right)^2} \, dx","Int[1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^2),x]","-\frac{1}{d^3 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)}-\frac{8 c \log \left(a+b x+c x^2\right)}{d^3 \left(b^2-4 a c\right)^3}-\frac{8 c}{d^3 \left(b^2-4 a c\right)^2 (b+2 c x)^2}+\frac{16 c \log (b+2 c x)}{d^3 \left(b^2-4 a c\right)^3}","-\frac{1}{d^3 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)}-\frac{8 c \log \left(a+b x+c x^2\right)}{d^3 \left(b^2-4 a c\right)^3}-\frac{8 c}{d^3 \left(b^2-4 a c\right)^2 (b+2 c x)^2}+\frac{16 c \log (b+2 c x)}{d^3 \left(b^2-4 a c\right)^3}",1,"(-8*c)/((b^2 - 4*a*c)^2*d^3*(b + 2*c*x)^2) - 1/((b^2 - 4*a*c)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)) + (16*c*Log[b + 2*c*x])/((b^2 - 4*a*c)^3*d^3) - (8*c*Log[a + b*x + c*x^2])/((b^2 - 4*a*c)^3*d^3)","A",5,5,24,0.2083,1,"{687, 693, 681, 31, 628}"
1177,1,160,0,0.1371599,"\int \frac{(b d+2 c d x)^{10}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^10/(a + b*x + c*x^2)^3,x]","84 c^2 d^{10} \left(b^2-4 a c\right) (b+2 c x)^3+252 c^2 d^{10} \left(b^2-4 a c\right)^2 (b+2 c x)-252 c^2 d^{10} \left(b^2-4 a c\right)^{5/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{9 c d^{10} (b+2 c x)^7}{a+b x+c x^2}-\frac{d^{10} (b+2 c x)^9}{2 \left(a+b x+c x^2\right)^2}+\frac{252}{5} c^2 d^{10} (b+2 c x)^5","84 c^2 d^{10} \left(b^2-4 a c\right) (b+2 c x)^3+252 c^2 d^{10} \left(b^2-4 a c\right)^2 (b+2 c x)-252 c^2 d^{10} \left(b^2-4 a c\right)^{5/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{9 c d^{10} (b+2 c x)^7}{a+b x+c x^2}-\frac{d^{10} (b+2 c x)^9}{2 \left(a+b x+c x^2\right)^2}+\frac{252}{5} c^2 d^{10} (b+2 c x)^5",1,"252*c^2*(b^2 - 4*a*c)^2*d^10*(b + 2*c*x) + 84*c^2*(b^2 - 4*a*c)*d^10*(b + 2*c*x)^3 + (252*c^2*d^10*(b + 2*c*x)^5)/5 - (d^10*(b + 2*c*x)^9)/(2*(a + b*x + c*x^2)^2) - (9*c*d^10*(b + 2*c*x)^7)/(a + b*x + c*x^2) - 252*c^2*(b^2 - 4*a*c)^(5/2)*d^10*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",7,4,24,0.1667,1,"{686, 692, 618, 206}"
1178,1,123,0,0.0848583,"\int \frac{(b d+2 c d x)^9}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^9/(a + b*x + c*x^2)^3,x]","96 c^2 d^9 \left(b^2-4 a c\right)^2 \log \left(a+b x+c x^2\right)+96 c^2 d^9 \left(b^2-4 a c\right) (b+2 c x)^2-\frac{8 c d^9 (b+2 c x)^6}{a+b x+c x^2}-\frac{d^9 (b+2 c x)^8}{2 \left(a+b x+c x^2\right)^2}+48 c^2 d^9 (b+2 c x)^4","96 c^2 d^9 \left(b^2-4 a c\right)^2 \log \left(a+b x+c x^2\right)+96 c^2 d^9 \left(b^2-4 a c\right) (b+2 c x)^2-\frac{8 c d^9 (b+2 c x)^6}{a+b x+c x^2}-\frac{d^9 (b+2 c x)^8}{2 \left(a+b x+c x^2\right)^2}+48 c^2 d^9 (b+2 c x)^4",1,"96*c^2*(b^2 - 4*a*c)*d^9*(b + 2*c*x)^2 + 48*c^2*d^9*(b + 2*c*x)^4 - (d^9*(b + 2*c*x)^8)/(2*(a + b*x + c*x^2)^2) - (8*c*d^9*(b + 2*c*x)^6)/(a + b*x + c*x^2) + 96*c^2*(b^2 - 4*a*c)^2*d^9*Log[a + b*x + c*x^2]","A",5,3,24,0.1250,1,"{686, 692, 628}"
1179,1,134,0,0.1010948,"\int \frac{(b d+2 c d x)^8}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^8/(a + b*x + c*x^2)^3,x]","140 c^2 d^8 \left(b^2-4 a c\right) (b+2 c x)-140 c^2 d^8 \left(b^2-4 a c\right)^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{7 c d^8 (b+2 c x)^5}{a+b x+c x^2}-\frac{d^8 (b+2 c x)^7}{2 \left(a+b x+c x^2\right)^2}+\frac{140}{3} c^2 d^8 (b+2 c x)^3","140 c^2 d^8 \left(b^2-4 a c\right) (b+2 c x)-140 c^2 d^8 \left(b^2-4 a c\right)^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{7 c d^8 (b+2 c x)^5}{a+b x+c x^2}-\frac{d^8 (b+2 c x)^7}{2 \left(a+b x+c x^2\right)^2}+\frac{140}{3} c^2 d^8 (b+2 c x)^3",1,"140*c^2*(b^2 - 4*a*c)*d^8*(b + 2*c*x) + (140*c^2*d^8*(b + 2*c*x)^3)/3 - (d^8*(b + 2*c*x)^7)/(2*(a + b*x + c*x^2)^2) - (7*c*d^8*(b + 2*c*x)^5)/(a + b*x + c*x^2) - 140*c^2*(b^2 - 4*a*c)^(3/2)*d^8*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",6,4,24,0.1667,1,"{686, 692, 618, 206}"
1180,1,97,0,0.0604783,"\int \frac{(b d+2 c d x)^7}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^7/(a + b*x + c*x^2)^3,x]","48 c^2 d^7 \left(b^2-4 a c\right) \log \left(a+b x+c x^2\right)-\frac{6 c d^7 (b+2 c x)^4}{a+b x+c x^2}-\frac{d^7 (b+2 c x)^6}{2 \left(a+b x+c x^2\right)^2}+48 c^2 d^7 (b+2 c x)^2","48 c^2 d^7 \left(b^2-4 a c\right) \log \left(a+b x+c x^2\right)-\frac{6 c d^7 (b+2 c x)^4}{a+b x+c x^2}-\frac{d^7 (b+2 c x)^6}{2 \left(a+b x+c x^2\right)^2}+48 c^2 d^7 (b+2 c x)^2",1,"48*c^2*d^7*(b + 2*c*x)^2 - (d^7*(b + 2*c*x)^6)/(2*(a + b*x + c*x^2)^2) - (6*c*d^7*(b + 2*c*x)^4)/(a + b*x + c*x^2) + 48*c^2*(b^2 - 4*a*c)*d^7*Log[a + b*x + c*x^2]","A",4,3,24,0.1250,1,"{686, 692, 628}"
1181,1,108,0,0.0726404,"\int \frac{(b d+2 c d x)^6}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^3,x]","-60 c^2 d^6 \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{5 c d^6 (b+2 c x)^3}{a+b x+c x^2}-\frac{d^6 (b+2 c x)^5}{2 \left(a+b x+c x^2\right)^2}+60 c^2 d^6 (b+2 c x)","-60 c^2 d^6 \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)-\frac{5 c d^6 (b+2 c x)^3}{a+b x+c x^2}-\frac{d^6 (b+2 c x)^5}{2 \left(a+b x+c x^2\right)^2}+60 c^2 d^6 (b+2 c x)",1,"60*c^2*d^6*(b + 2*c*x) - (d^6*(b + 2*c*x)^5)/(2*(a + b*x + c*x^2)^2) - (5*c*d^6*(b + 2*c*x)^3)/(a + b*x + c*x^2) - 60*c^2*Sqrt[b^2 - 4*a*c]*d^6*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]]","A",5,4,24,0.1667,1,"{686, 692, 618, 206}"
1182,1,73,0,0.0379107,"\int \frac{(b d+2 c d x)^5}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^5/(a + b*x + c*x^2)^3,x]","16 c^2 d^5 \log \left(a+b x+c x^2\right)-\frac{4 c d^5 (b+2 c x)^2}{a+b x+c x^2}-\frac{d^5 (b+2 c x)^4}{2 \left(a+b x+c x^2\right)^2}","16 c^2 d^5 \log \left(a+b x+c x^2\right)-\frac{4 c d^5 (b+2 c x)^2}{a+b x+c x^2}-\frac{d^5 (b+2 c x)^4}{2 \left(a+b x+c x^2\right)^2}",1,"-(d^5*(b + 2*c*x)^4)/(2*(a + b*x + c*x^2)^2) - (4*c*d^5*(b + 2*c*x)^2)/(a + b*x + c*x^2) + 16*c^2*d^5*Log[a + b*x + c*x^2]","A",3,2,24,0.08333,1,"{686, 628}"
1183,1,92,0,0.0566576,"\int \frac{(b d+2 c d x)^4}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^3,x]","-\frac{12 c^2 d^4 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}-\frac{3 c d^4 (b+2 c x)}{a+b x+c x^2}-\frac{d^4 (b+2 c x)^3}{2 \left(a+b x+c x^2\right)^2}","-\frac{12 c^2 d^4 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}-\frac{3 c d^4 (b+2 c x)}{a+b x+c x^2}-\frac{d^4 (b+2 c x)^3}{2 \left(a+b x+c x^2\right)^2}",1,"-(d^4*(b + 2*c*x)^3)/(2*(a + b*x + c*x^2)^2) - (3*c*d^4*(b + 2*c*x))/(a + b*x + c*x^2) - (12*c^2*d^4*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",4,3,24,0.1250,1,"{686, 618, 206}"
1184,1,37,0,0.0145966,"\int \frac{(b d+2 c d x)^3}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^3,x]","-\frac{d^3 (b+2 c x)^4}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{d^3 (b+2 c x)^4}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-(d^3*(b + 2*c*x)^4)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)","A",1,1,24,0.04167,1,"{682}"
1185,1,100,0,0.0528953,"\int \frac{(b d+2 c d x)^2}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^3,x]","\frac{4 c^2 d^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{c d^2 (b+2 c x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{d^2 (b+2 c x)}{2 \left(a+b x+c x^2\right)^2}","\frac{4 c^2 d^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{c d^2 (b+2 c x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{d^2 (b+2 c x)}{2 \left(a+b x+c x^2\right)^2}",1,"-(d^2*(b + 2*c*x))/(2*(a + b*x + c*x^2)^2) - (c*d^2*(b + 2*c*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (4*c^2*d^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,24,0.1667,1,"{686, 614, 618, 206}"
1186,1,17,0,0.0048227,"\int \frac{b d+2 c d x}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)/(a + b*x + c*x^2)^3,x]","-\frac{d}{2 \left(a+b x+c x^2\right)^2}","-\frac{d}{2 \left(a+b x+c x^2\right)^2}",1,"-d/(2*(a + b*x + c*x^2)^2)","A",1,1,22,0.04545,1,"{629}"
1187,1,112,0,0.0596157,"\int \frac{1}{(b d+2 c d x) \left(a+b x+c x^2\right)^3} \, dx","Int[1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^3),x]","\frac{16 c^2 \log \left(a+b x+c x^2\right)}{d \left(b^2-4 a c\right)^3}-\frac{32 c^2 \log (b+2 c x)}{d \left(b^2-4 a c\right)^3}+\frac{4 c}{d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{1}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{16 c^2 \log \left(a+b x+c x^2\right)}{d \left(b^2-4 a c\right)^3}-\frac{32 c^2 \log (b+2 c x)}{d \left(b^2-4 a c\right)^3}+\frac{4 c}{d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{1}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-1/(2*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^2) + (4*c)/((b^2 - 4*a*c)^2*d*(a + b*x + c*x^2)) - (32*c^2*Log[b + 2*c*x])/((b^2 - 4*a*c)^3*d) + (16*c^2*Log[a + b*x + c*x^2])/((b^2 - 4*a*c)^3*d)","A",5,4,24,0.1667,1,"{687, 681, 31, 628}"
1188,1,140,0,0.0993551,"\int \frac{1}{(b d+2 c d x)^2 \left(a+b x+c x^2\right)^3} \, dx","Int[1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^3),x]","\frac{60 c^2}{d^2 \left(b^2-4 a c\right)^3 (b+2 c x)}-\frac{60 c^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^2 \left(b^2-4 a c\right)^{7/2}}+\frac{5 c}{d^2 \left(b^2-4 a c\right)^2 (b+2 c x) \left(a+b x+c x^2\right)}-\frac{1}{2 d^2 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^2}","\frac{60 c^2}{d^2 \left(b^2-4 a c\right)^3 (b+2 c x)}-\frac{60 c^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^2 \left(b^2-4 a c\right)^{7/2}}+\frac{5 c}{d^2 \left(b^2-4 a c\right)^2 (b+2 c x) \left(a+b x+c x^2\right)}-\frac{1}{2 d^2 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^2}",1,"(60*c^2)/((b^2 - 4*a*c)^3*d^2*(b + 2*c*x)) - 1/(2*(b^2 - 4*a*c)*d^2*(b + 2*c*x)*(a + b*x + c*x^2)^2) + (5*c)/((b^2 - 4*a*c)^2*d^2*(b + 2*c*x)*(a + b*x + c*x^2)) - (60*c^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(7/2)*d^2)","A",5,4,24,0.1667,1,"{687, 693, 618, 206}"
1189,1,154,0,0.0881354,"\int \frac{1}{(b d+2 c d x)^3 \left(a+b x+c x^2\right)^3} \, dx","Int[1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^3),x]","\frac{48 c^2 \log \left(a+b x+c x^2\right)}{d^3 \left(b^2-4 a c\right)^4}+\frac{48 c^2}{d^3 \left(b^2-4 a c\right)^3 (b+2 c x)^2}-\frac{96 c^2 \log (b+2 c x)}{d^3 \left(b^2-4 a c\right)^4}+\frac{6 c}{d^3 \left(b^2-4 a c\right)^2 (b+2 c x)^2 \left(a+b x+c x^2\right)}-\frac{1}{2 d^3 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^2}","\frac{48 c^2 \log \left(a+b x+c x^2\right)}{d^3 \left(b^2-4 a c\right)^4}+\frac{48 c^2}{d^3 \left(b^2-4 a c\right)^3 (b+2 c x)^2}-\frac{96 c^2 \log (b+2 c x)}{d^3 \left(b^2-4 a c\right)^4}+\frac{6 c}{d^3 \left(b^2-4 a c\right)^2 (b+2 c x)^2 \left(a+b x+c x^2\right)}-\frac{1}{2 d^3 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^2}",1,"(48*c^2)/((b^2 - 4*a*c)^3*d^3*(b + 2*c*x)^2) - 1/(2*(b^2 - 4*a*c)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^2) + (6*c)/((b^2 - 4*a*c)^2*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)) - (96*c^2*Log[b + 2*c*x])/((b^2 - 4*a*c)^4*d^3) + (48*c^2*Log[a + b*x + c*x^2])/((b^2 - 4*a*c)^4*d^3)","A",6,5,24,0.2083,1,"{687, 693, 681, 31, 628}"
1190,1,168,0,0.1461131,"\int \frac{1}{(b d+2 c d x)^4 \left(a+b x+c x^2\right)^3} \, dx","Int[1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^3),x]","\frac{140 c^2}{d^4 \left(b^2-4 a c\right)^4 (b+2 c x)}+\frac{140 c^2}{3 d^4 \left(b^2-4 a c\right)^3 (b+2 c x)^3}-\frac{140 c^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^4 \left(b^2-4 a c\right)^{9/2}}+\frac{7 c}{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^3 \left(a+b x+c x^2\right)}-\frac{1}{2 d^4 \left(b^2-4 a c\right) (b+2 c x)^3 \left(a+b x+c x^2\right)^2}","\frac{140 c^2}{d^4 \left(b^2-4 a c\right)^4 (b+2 c x)}+\frac{140 c^2}{3 d^4 \left(b^2-4 a c\right)^3 (b+2 c x)^3}-\frac{140 c^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{d^4 \left(b^2-4 a c\right)^{9/2}}+\frac{7 c}{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^3 \left(a+b x+c x^2\right)}-\frac{1}{2 d^4 \left(b^2-4 a c\right) (b+2 c x)^3 \left(a+b x+c x^2\right)^2}",1,"(140*c^2)/(3*(b^2 - 4*a*c)^3*d^4*(b + 2*c*x)^3) + (140*c^2)/((b^2 - 4*a*c)^4*d^4*(b + 2*c*x)) - 1/(2*(b^2 - 4*a*c)*d^4*(b + 2*c*x)^3*(a + b*x + c*x^2)^2) + (7*c)/((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^3*(a + b*x + c*x^2)) - (140*c^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(9/2)*d^4)","A",6,4,24,0.1667,1,"{687, 693, 618, 206}"
1191,1,165,0,0.0976735,"\int (b d+2 c d x)^4 \sqrt{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^4*Sqrt[a + b*x + c*x^2],x]","-\frac{d^4 \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{3/2}}-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^3 \sqrt{a+b x+c x^2}}{48 c}-\frac{d^4 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}{32 c}+\frac{d^4 (b+2 c x)^5 \sqrt{a+b x+c x^2}}{12 c}","-\frac{d^4 \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{3/2}}-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^3 \sqrt{a+b x+c x^2}}{48 c}-\frac{d^4 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}{32 c}+\frac{d^4 (b+2 c x)^5 \sqrt{a+b x+c x^2}}{12 c}",1,"-((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(32*c) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^3*Sqrt[a + b*x + c*x^2])/(48*c) + (d^4*(b + 2*c*x)^5*Sqrt[a + b*x + c*x^2])/(12*c) - ((b^2 - 4*a*c)^3*d^4*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(64*c^(3/2))","A",5,4,26,0.1538,1,"{685, 692, 621, 206}"
1192,1,59,0,0.0262283,"\int (b d+2 c d x)^3 \sqrt{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^3*Sqrt[a + b*x + c*x^2],x]","\frac{4}{15} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}+\frac{2}{5} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^{3/2}","\frac{4}{15} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}+\frac{2}{5} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^{3/2}",1,"(4*(b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^(3/2))/15 + (2*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(3/2))/5","A",2,2,26,0.07692,1,"{692, 629}"
1193,1,123,0,0.0559653,"\int (b d+2 c d x)^2 \sqrt{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^2*Sqrt[a + b*x + c*x^2],x]","-\frac{d^2 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32 c^{3/2}}-\frac{d^2 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}{16 c}+\frac{d^2 (b+2 c x)^3 \sqrt{a+b x+c x^2}}{8 c}","-\frac{d^2 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32 c^{3/2}}-\frac{d^2 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}{16 c}+\frac{d^2 (b+2 c x)^3 \sqrt{a+b x+c x^2}}{8 c}",1,"-((b^2 - 4*a*c)*d^2*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(16*c) + (d^2*(b + 2*c*x)^3*Sqrt[a + b*x + c*x^2])/(8*c) - ((b^2 - 4*a*c)^2*d^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32*c^(3/2))","A",4,4,26,0.1538,1,"{685, 692, 621, 206}"
1194,1,19,0,0.0063804,"\int (b d+2 c d x) \sqrt{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)*Sqrt[a + b*x + c*x^2],x]","\frac{2}{3} d \left(a+b x+c x^2\right)^{3/2}","\frac{2}{3} d \left(a+b x+c x^2\right)^{3/2}",1,"(2*d*(a + b*x + c*x^2)^(3/2))/3","A",1,1,24,0.04167,1,"{629}"
1195,1,83,0,0.063362,"\int \frac{\sqrt{a+b x+c x^2}}{b d+2 c d x} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x),x]","\frac{\sqrt{a+b x+c x^2}}{2 c d}-\frac{\sqrt{b^2-4 a c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{4 c^{3/2} d}","\frac{\sqrt{a+b x+c x^2}}{2 c d}-\frac{\sqrt{b^2-4 a c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{4 c^{3/2} d}",1,"Sqrt[a + b*x + c*x^2]/(2*c*d) - (Sqrt[b^2 - 4*a*c]*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(4*c^(3/2)*d)","A",3,3,26,0.1154,1,"{685, 688, 205}"
1196,1,75,0,0.0287825,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^2} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^2,x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 c^{3/2} d^2}-\frac{\sqrt{a+b x+c x^2}}{2 c d^2 (b+2 c x)}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 c^{3/2} d^2}-\frac{\sqrt{a+b x+c x^2}}{2 c d^2 (b+2 c x)}",1,"-Sqrt[a + b*x + c*x^2]/(2*c*d^2*(b + 2*c*x)) + ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]/(4*c^(3/2)*d^2)","A",3,3,26,0.1154,1,"{684, 621, 206}"
1197,1,91,0,0.051964,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^3} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^3,x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{8 c^{3/2} d^3 \sqrt{b^2-4 a c}}-\frac{\sqrt{a+b x+c x^2}}{4 c d^3 (b+2 c x)^2}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{8 c^{3/2} d^3 \sqrt{b^2-4 a c}}-\frac{\sqrt{a+b x+c x^2}}{4 c d^3 (b+2 c x)^2}",1,"-Sqrt[a + b*x + c*x^2]/(4*c*d^3*(b + 2*c*x)^2) + ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]]/(8*c^(3/2)*Sqrt[b^2 - 4*a*c]*d^3)","A",3,3,26,0.1154,1,"{684, 688, 205}"
1198,1,39,0,0.0140489,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^4} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^4,x]","\frac{2 \left(a+b x+c x^2\right)^{3/2}}{3 d^4 \left(b^2-4 a c\right) (b+2 c x)^3}","\frac{2 \left(a+b x+c x^2\right)^{3/2}}{3 d^4 \left(b^2-4 a c\right) (b+2 c x)^3}",1,"(2*(a + b*x + c*x^2)^(3/2))/(3*(b^2 - 4*a*c)*d^4*(b + 2*c*x)^3)","A",1,1,26,0.03846,1,"{682}"
1199,1,133,0,0.0892683,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^5} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^5,x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{32 c^{3/2} d^5 \left(b^2-4 a c\right)^{3/2}}+\frac{\sqrt{a+b x+c x^2}}{16 c d^5 \left(b^2-4 a c\right) (b+2 c x)^2}-\frac{\sqrt{a+b x+c x^2}}{8 c d^5 (b+2 c x)^4}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{32 c^{3/2} d^5 \left(b^2-4 a c\right)^{3/2}}+\frac{\sqrt{a+b x+c x^2}}{16 c d^5 \left(b^2-4 a c\right) (b+2 c x)^2}-\frac{\sqrt{a+b x+c x^2}}{8 c d^5 (b+2 c x)^4}",1,"-Sqrt[a + b*x + c*x^2]/(8*c*d^5*(b + 2*c*x)^4) + Sqrt[a + b*x + c*x^2]/(16*c*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2) + ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]]/(32*c^(3/2)*(b^2 - 4*a*c)^(3/2)*d^5)","A",4,4,26,0.1538,1,"{684, 693, 688, 205}"
1200,1,79,0,0.0348507,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^6} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^6,x]","\frac{4 \left(a+b x+c x^2\right)^{3/2}}{15 d^6 \left(b^2-4 a c\right)^2 (b+2 c x)^3}+\frac{2 \left(a+b x+c x^2\right)^{3/2}}{5 d^6 \left(b^2-4 a c\right) (b+2 c x)^5}","\frac{4 \left(a+b x+c x^2\right)^{3/2}}{15 d^6 \left(b^2-4 a c\right)^2 (b+2 c x)^3}+\frac{2 \left(a+b x+c x^2\right)^{3/2}}{5 d^6 \left(b^2-4 a c\right) (b+2 c x)^5}",1,"(2*(a + b*x + c*x^2)^(3/2))/(5*(b^2 - 4*a*c)*d^6*(b + 2*c*x)^5) + (4*(a + b*x + c*x^2)^(3/2))/(15*(b^2 - 4*a*c)^2*d^6*(b + 2*c*x)^3)","A",2,2,26,0.07692,1,"{693, 682}"
1201,1,175,0,0.125092,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^7} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^7,x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{64 c^{3/2} d^7 \left(b^2-4 a c\right)^{5/2}}+\frac{\sqrt{a+b x+c x^2}}{32 c d^7 \left(b^2-4 a c\right)^2 (b+2 c x)^2}+\frac{\sqrt{a+b x+c x^2}}{48 c d^7 \left(b^2-4 a c\right) (b+2 c x)^4}-\frac{\sqrt{a+b x+c x^2}}{12 c d^7 (b+2 c x)^6}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{64 c^{3/2} d^7 \left(b^2-4 a c\right)^{5/2}}+\frac{\sqrt{a+b x+c x^2}}{32 c d^7 \left(b^2-4 a c\right)^2 (b+2 c x)^2}+\frac{\sqrt{a+b x+c x^2}}{48 c d^7 \left(b^2-4 a c\right) (b+2 c x)^4}-\frac{\sqrt{a+b x+c x^2}}{12 c d^7 (b+2 c x)^6}",1,"-Sqrt[a + b*x + c*x^2]/(12*c*d^7*(b + 2*c*x)^6) + Sqrt[a + b*x + c*x^2]/(48*c*(b^2 - 4*a*c)*d^7*(b + 2*c*x)^4) + Sqrt[a + b*x + c*x^2]/(32*c*(b^2 - 4*a*c)^2*d^7*(b + 2*c*x)^2) + ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]]/(64*c^(3/2)*(b^2 - 4*a*c)^(5/2)*d^7)","A",5,4,26,0.1538,1,"{684, 693, 688, 205}"
1202,1,98,0,0.0512991,"\int (b d+2 c d x)^5 \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^(3/2),x]","\frac{16}{315} d^5 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{5/2}+\frac{8}{63} d^5 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^{5/2}+\frac{2}{9} d^5 (b+2 c x)^4 \left(a+b x+c x^2\right)^{5/2}","\frac{16}{315} d^5 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{5/2}+\frac{8}{63} d^5 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^{5/2}+\frac{2}{9} d^5 (b+2 c x)^4 \left(a+b x+c x^2\right)^{5/2}",1,"(16*(b^2 - 4*a*c)^2*d^5*(a + b*x + c*x^2)^(5/2))/315 + (8*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2*(a + b*x + c*x^2)^(5/2))/63 + (2*d^5*(b + 2*c*x)^4*(a + b*x + c*x^2)^(5/2))/9","A",3,2,26,0.07692,1,"{692, 629}"
1203,1,207,0,0.1286421,"\int (b d+2 c d x)^4 \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(3/2),x]","-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^5 \sqrt{a+b x+c x^2}}{128 c^2}+\frac{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^3 \sqrt{a+b x+c x^2}}{512 c^2}+\frac{3 d^4 \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2}}{1024 c^2}+\frac{3 d^4 \left(b^2-4 a c\right)^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{5/2}}+\frac{d^4 (b+2 c x)^5 \left(a+b x+c x^2\right)^{3/2}}{16 c}","-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^5 \sqrt{a+b x+c x^2}}{128 c^2}+\frac{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^3 \sqrt{a+b x+c x^2}}{512 c^2}+\frac{3 d^4 \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2}}{1024 c^2}+\frac{3 d^4 \left(b^2-4 a c\right)^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{5/2}}+\frac{d^4 (b+2 c x)^5 \left(a+b x+c x^2\right)^{3/2}}{16 c}",1,"(3*(b^2 - 4*a*c)^3*d^4*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^2) + ((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^3*Sqrt[a + b*x + c*x^2])/(512*c^2) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^5*Sqrt[a + b*x + c*x^2])/(128*c^2) + (d^4*(b + 2*c*x)^5*(a + b*x + c*x^2)^(3/2))/(16*c) + (3*(b^2 - 4*a*c)^4*d^4*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(5/2))","A",6,4,26,0.1538,1,"{685, 692, 621, 206}"
1204,1,59,0,0.0269461,"\int (b d+2 c d x)^3 \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(3/2),x]","\frac{4}{35} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}+\frac{2}{7} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^{5/2}","\frac{4}{35} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}+\frac{2}{7} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^{5/2}",1,"(4*(b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^(5/2))/35 + (2*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(5/2))/7","A",2,2,26,0.07692,1,"{692, 629}"
1205,1,165,0,0.0887438,"\int (b d+2 c d x)^2 \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(3/2),x]","\frac{d^2 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}{128 c^2}-\frac{d^2 \left(b^2-4 a c\right) (b+2 c x)^3 \sqrt{a+b x+c x^2}}{64 c^2}+\frac{d^2 \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{5/2}}+\frac{d^2 (b+2 c x)^3 \left(a+b x+c x^2\right)^{3/2}}{12 c}","\frac{d^2 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}{128 c^2}-\frac{d^2 \left(b^2-4 a c\right) (b+2 c x)^3 \sqrt{a+b x+c x^2}}{64 c^2}+\frac{d^2 \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{5/2}}+\frac{d^2 (b+2 c x)^3 \left(a+b x+c x^2\right)^{3/2}}{12 c}",1,"((b^2 - 4*a*c)^2*d^2*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(128*c^2) - ((b^2 - 4*a*c)*d^2*(b + 2*c*x)^3*Sqrt[a + b*x + c*x^2])/(64*c^2) + (d^2*(b + 2*c*x)^3*(a + b*x + c*x^2)^(3/2))/(12*c) + ((b^2 - 4*a*c)^3*d^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(5/2))","A",5,4,26,0.1538,1,"{685, 692, 621, 206}"
1206,1,19,0,0.0066193,"\int (b d+2 c d x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b*d + 2*c*d*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{2}{5} d \left(a+b x+c x^2\right)^{5/2}","\frac{2}{5} d \left(a+b x+c x^2\right)^{5/2}",1,"(2*d*(a + b*x + c*x^2)^(5/2))/5","A",1,1,24,0.04167,1,"{629}"
1207,1,115,0,0.0827866,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{b d+2 c d x} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x),x]","-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}{8 c^2 d}+\frac{\left(b^2-4 a c\right)^{3/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{16 c^{5/2} d}+\frac{\left(a+b x+c x^2\right)^{3/2}}{6 c d}","-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}{8 c^2 d}+\frac{\left(b^2-4 a c\right)^{3/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{16 c^{5/2} d}+\frac{\left(a+b x+c x^2\right)^{3/2}}{6 c d}",1,"-((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2])/(8*c^2*d) + (a + b*x + c*x^2)^(3/2)/(6*c*d) + ((b^2 - 4*a*c)^(3/2)*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(16*c^(5/2)*d)","A",4,3,26,0.1154,1,"{685, 688, 205}"
1208,1,113,0,0.0457616,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^2} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^2,x]","-\frac{3 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32 c^{5/2} d^2}+\frac{3 (b+2 c x) \sqrt{a+b x+c x^2}}{16 c^2 d^2}-\frac{\left(a+b x+c x^2\right)^{3/2}}{2 c d^2 (b+2 c x)}","-\frac{3 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32 c^{5/2} d^2}+\frac{3 (b+2 c x) \sqrt{a+b x+c x^2}}{16 c^2 d^2}-\frac{\left(a+b x+c x^2\right)^{3/2}}{2 c d^2 (b+2 c x)}",1,"(3*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(16*c^2*d^2) - (a + b*x + c*x^2)^(3/2)/(2*c*d^2*(b + 2*c*x)) - (3*(b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32*c^(5/2)*d^2)","A",4,4,26,0.1538,1,"{684, 612, 621, 206}"
1209,1,115,0,0.0711629,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^3} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^3,x]","-\frac{3 \sqrt{b^2-4 a c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{32 c^{5/2} d^3}+\frac{3 \sqrt{a+b x+c x^2}}{16 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{3/2}}{4 c d^3 (b+2 c x)^2}","-\frac{3 \sqrt{b^2-4 a c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{32 c^{5/2} d^3}+\frac{3 \sqrt{a+b x+c x^2}}{16 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{3/2}}{4 c d^3 (b+2 c x)^2}",1,"(3*Sqrt[a + b*x + c*x^2])/(16*c^2*d^3) - (a + b*x + c*x^2)^(3/2)/(4*c*d^3*(b + 2*c*x)^2) - (3*Sqrt[b^2 - 4*a*c]*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(32*c^(5/2)*d^3)","A",4,4,26,0.1538,1,"{684, 685, 688, 205}"
1210,1,107,0,0.0501314,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^4} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^4,x]","-\frac{\sqrt{a+b x+c x^2}}{8 c^2 d^4 (b+2 c x)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{5/2} d^4}-\frac{\left(a+b x+c x^2\right)^{3/2}}{6 c d^4 (b+2 c x)^3}","-\frac{\sqrt{a+b x+c x^2}}{8 c^2 d^4 (b+2 c x)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{5/2} d^4}-\frac{\left(a+b x+c x^2\right)^{3/2}}{6 c d^4 (b+2 c x)^3}",1,"-Sqrt[a + b*x + c*x^2]/(8*c^2*d^4*(b + 2*c*x)) - (a + b*x + c*x^2)^(3/2)/(6*c*d^4*(b + 2*c*x)^3) + ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]/(16*c^(5/2)*d^4)","A",4,3,26,0.1154,1,"{684, 621, 206}"
1211,1,123,0,0.0731791,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^5} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^5,x]","\frac{3 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{128 c^{5/2} d^5 \sqrt{b^2-4 a c}}-\frac{3 \sqrt{a+b x+c x^2}}{64 c^2 d^5 (b+2 c x)^2}-\frac{\left(a+b x+c x^2\right)^{3/2}}{8 c d^5 (b+2 c x)^4}","\frac{3 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{128 c^{5/2} d^5 \sqrt{b^2-4 a c}}-\frac{3 \sqrt{a+b x+c x^2}}{64 c^2 d^5 (b+2 c x)^2}-\frac{\left(a+b x+c x^2\right)^{3/2}}{8 c d^5 (b+2 c x)^4}",1,"(-3*Sqrt[a + b*x + c*x^2])/(64*c^2*d^5*(b + 2*c*x)^2) - (a + b*x + c*x^2)^(3/2)/(8*c*d^5*(b + 2*c*x)^4) + (3*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(128*c^(5/2)*Sqrt[b^2 - 4*a*c]*d^5)","A",4,3,26,0.1154,1,"{684, 688, 205}"
1212,1,39,0,0.0164574,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^6} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^6,x]","\frac{2 \left(a+b x+c x^2\right)^{5/2}}{5 d^6 \left(b^2-4 a c\right) (b+2 c x)^5}","\frac{2 \left(a+b x+c x^2\right)^{5/2}}{5 d^6 \left(b^2-4 a c\right) (b+2 c x)^5}",1,"(2*(a + b*x + c*x^2)^(5/2))/(5*(b^2 - 4*a*c)*d^6*(b + 2*c*x)^5)","A",1,1,26,0.03846,1,"{682}"
1213,1,165,0,0.1139577,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^7} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^7,x]","\frac{\sqrt{a+b x+c x^2}}{128 c^2 d^7 \left(b^2-4 a c\right) (b+2 c x)^2}+\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{256 c^{5/2} d^7 \left(b^2-4 a c\right)^{3/2}}-\frac{\sqrt{a+b x+c x^2}}{64 c^2 d^7 (b+2 c x)^4}-\frac{\left(a+b x+c x^2\right)^{3/2}}{12 c d^7 (b+2 c x)^6}","\frac{\sqrt{a+b x+c x^2}}{128 c^2 d^7 \left(b^2-4 a c\right) (b+2 c x)^2}+\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{256 c^{5/2} d^7 \left(b^2-4 a c\right)^{3/2}}-\frac{\sqrt{a+b x+c x^2}}{64 c^2 d^7 (b+2 c x)^4}-\frac{\left(a+b x+c x^2\right)^{3/2}}{12 c d^7 (b+2 c x)^6}",1,"-Sqrt[a + b*x + c*x^2]/(64*c^2*d^7*(b + 2*c*x)^4) + Sqrt[a + b*x + c*x^2]/(128*c^2*(b^2 - 4*a*c)*d^7*(b + 2*c*x)^2) - (a + b*x + c*x^2)^(3/2)/(12*c*d^7*(b + 2*c*x)^6) + ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]]/(256*c^(5/2)*(b^2 - 4*a*c)^(3/2)*d^7)","A",5,4,26,0.1538,1,"{684, 693, 688, 205}"
1214,1,79,0,0.0348012,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^8} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^8,x]","\frac{4 \left(a+b x+c x^2\right)^{5/2}}{35 d^8 \left(b^2-4 a c\right)^2 (b+2 c x)^5}+\frac{2 \left(a+b x+c x^2\right)^{5/2}}{7 d^8 \left(b^2-4 a c\right) (b+2 c x)^7}","\frac{4 \left(a+b x+c x^2\right)^{5/2}}{35 d^8 \left(b^2-4 a c\right)^2 (b+2 c x)^5}+\frac{2 \left(a+b x+c x^2\right)^{5/2}}{7 d^8 \left(b^2-4 a c\right) (b+2 c x)^7}",1,"(2*(a + b*x + c*x^2)^(5/2))/(7*(b^2 - 4*a*c)*d^8*(b + 2*c*x)^7) + (4*(a + b*x + c*x^2)^(5/2))/(35*(b^2 - 4*a*c)^2*d^8*(b + 2*c*x)^5)","A",2,2,26,0.07692,1,"{693, 682}"
1215,1,207,0,0.1463019,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^9} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^9,x]","\frac{3 \sqrt{a+b x+c x^2}}{1024 c^2 d^9 \left(b^2-4 a c\right)^2 (b+2 c x)^2}+\frac{\sqrt{a+b x+c x^2}}{512 c^2 d^9 \left(b^2-4 a c\right) (b+2 c x)^4}+\frac{3 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{2048 c^{5/2} d^9 \left(b^2-4 a c\right)^{5/2}}-\frac{\sqrt{a+b x+c x^2}}{128 c^2 d^9 (b+2 c x)^6}-\frac{\left(a+b x+c x^2\right)^{3/2}}{16 c d^9 (b+2 c x)^8}","\frac{3 \sqrt{a+b x+c x^2}}{1024 c^2 d^9 \left(b^2-4 a c\right)^2 (b+2 c x)^2}+\frac{\sqrt{a+b x+c x^2}}{512 c^2 d^9 \left(b^2-4 a c\right) (b+2 c x)^4}+\frac{3 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{2048 c^{5/2} d^9 \left(b^2-4 a c\right)^{5/2}}-\frac{\sqrt{a+b x+c x^2}}{128 c^2 d^9 (b+2 c x)^6}-\frac{\left(a+b x+c x^2\right)^{3/2}}{16 c d^9 (b+2 c x)^8}",1,"-Sqrt[a + b*x + c*x^2]/(128*c^2*d^9*(b + 2*c*x)^6) + Sqrt[a + b*x + c*x^2]/(512*c^2*(b^2 - 4*a*c)*d^9*(b + 2*c*x)^4) + (3*Sqrt[a + b*x + c*x^2])/(1024*c^2*(b^2 - 4*a*c)^2*d^9*(b + 2*c*x)^2) - (a + b*x + c*x^2)^(3/2)/(16*c*d^9*(b + 2*c*x)^8) + (3*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(2048*c^(5/2)*(b^2 - 4*a*c)^(5/2)*d^9)","A",6,4,26,0.1538,1,"{684, 693, 688, 205}"
1216,1,118,0,0.0572946,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^{10}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^10,x]","\frac{16 \left(a+b x+c x^2\right)^{5/2}}{315 d^{10} \left(b^2-4 a c\right)^3 (b+2 c x)^5}+\frac{8 \left(a+b x+c x^2\right)^{5/2}}{63 d^{10} \left(b^2-4 a c\right)^2 (b+2 c x)^7}+\frac{2 \left(a+b x+c x^2\right)^{5/2}}{9 d^{10} \left(b^2-4 a c\right) (b+2 c x)^9}","\frac{16 \left(a+b x+c x^2\right)^{5/2}}{315 d^{10} \left(b^2-4 a c\right)^3 (b+2 c x)^5}+\frac{8 \left(a+b x+c x^2\right)^{5/2}}{63 d^{10} \left(b^2-4 a c\right)^2 (b+2 c x)^7}+\frac{2 \left(a+b x+c x^2\right)^{5/2}}{9 d^{10} \left(b^2-4 a c\right) (b+2 c x)^9}",1,"(2*(a + b*x + c*x^2)^(5/2))/(9*(b^2 - 4*a*c)*d^10*(b + 2*c*x)^9) + (8*(a + b*x + c*x^2)^(5/2))/(63*(b^2 - 4*a*c)^2*d^10*(b + 2*c*x)^7) + (16*(a + b*x + c*x^2)^(5/2))/(315*(b^2 - 4*a*c)^3*d^10*(b + 2*c*x)^5)","A",3,2,26,0.07692,1,"{693, 682}"
1217,1,98,0,0.0508876,"\int (b d+2 c d x)^5 \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^(5/2),x]","\frac{16}{693} d^5 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{7/2}+\frac{8}{99} d^5 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^{7/2}+\frac{2}{11} d^5 (b+2 c x)^4 \left(a+b x+c x^2\right)^{7/2}","\frac{16}{693} d^5 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{7/2}+\frac{8}{99} d^5 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^{7/2}+\frac{2}{11} d^5 (b+2 c x)^4 \left(a+b x+c x^2\right)^{7/2}",1,"(16*(b^2 - 4*a*c)^2*d^5*(a + b*x + c*x^2)^(7/2))/693 + (8*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2*(a + b*x + c*x^2)^(7/2))/99 + (2*d^5*(b + 2*c*x)^4*(a + b*x + c*x^2)^(7/2))/11","A",3,2,26,0.07692,1,"{692, 629}"
1218,1,249,0,0.1707786,"\int (b d+2 c d x)^4 \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(5/2),x]","-\frac{3 d^4 \left(b^2-4 a c\right)^4 (b+2 c x) \sqrt{a+b x+c x^2}}{8192 c^3}-\frac{d^4 \left(b^2-4 a c\right)^3 (b+2 c x)^3 \sqrt{a+b x+c x^2}}{4096 c^3}+\frac{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^5 \sqrt{a+b x+c x^2}}{1024 c^3}-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^5 \left(a+b x+c x^2\right)^{3/2}}{128 c^2}-\frac{3 d^4 \left(b^2-4 a c\right)^5 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16384 c^{7/2}}+\frac{d^4 (b+2 c x)^5 \left(a+b x+c x^2\right)^{5/2}}{20 c}","-\frac{3 d^4 \left(b^2-4 a c\right)^4 (b+2 c x) \sqrt{a+b x+c x^2}}{8192 c^3}-\frac{d^4 \left(b^2-4 a c\right)^3 (b+2 c x)^3 \sqrt{a+b x+c x^2}}{4096 c^3}+\frac{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^5 \sqrt{a+b x+c x^2}}{1024 c^3}-\frac{d^4 \left(b^2-4 a c\right) (b+2 c x)^5 \left(a+b x+c x^2\right)^{3/2}}{128 c^2}-\frac{3 d^4 \left(b^2-4 a c\right)^5 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16384 c^{7/2}}+\frac{d^4 (b+2 c x)^5 \left(a+b x+c x^2\right)^{5/2}}{20 c}",1,"(-3*(b^2 - 4*a*c)^4*d^4*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(8192*c^3) - ((b^2 - 4*a*c)^3*d^4*(b + 2*c*x)^3*Sqrt[a + b*x + c*x^2])/(4096*c^3) + ((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^5*Sqrt[a + b*x + c*x^2])/(1024*c^3) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^5*(a + b*x + c*x^2)^(3/2))/(128*c^2) + (d^4*(b + 2*c*x)^5*(a + b*x + c*x^2)^(5/2))/(20*c) - (3*(b^2 - 4*a*c)^5*d^4*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16384*c^(7/2))","A",7,4,26,0.1538,1,"{685, 692, 621, 206}"
1219,1,59,0,0.0264323,"\int (b d+2 c d x)^3 \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(5/2),x]","\frac{4}{63} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{7/2}+\frac{2}{9} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^{7/2}","\frac{4}{63} d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{7/2}+\frac{2}{9} d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^{7/2}",1,"(4*(b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^(7/2))/63 + (2*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(7/2))/9","A",2,2,26,0.07692,1,"{692, 629}"
1220,1,207,0,0.1242751,"\int (b d+2 c d x)^2 \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(5/2),x]","-\frac{5 d^2 \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2}}{4096 c^3}+\frac{5 d^2 \left(b^2-4 a c\right)^2 (b+2 c x)^3 \sqrt{a+b x+c x^2}}{2048 c^3}-\frac{5 d^2 \left(b^2-4 a c\right) (b+2 c x)^3 \left(a+b x+c x^2\right)^{3/2}}{384 c^2}-\frac{5 d^2 \left(b^2-4 a c\right)^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8192 c^{7/2}}+\frac{d^2 (b+2 c x)^3 \left(a+b x+c x^2\right)^{5/2}}{16 c}","-\frac{5 d^2 \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2}}{4096 c^3}+\frac{5 d^2 \left(b^2-4 a c\right)^2 (b+2 c x)^3 \sqrt{a+b x+c x^2}}{2048 c^3}-\frac{5 d^2 \left(b^2-4 a c\right) (b+2 c x)^3 \left(a+b x+c x^2\right)^{3/2}}{384 c^2}-\frac{5 d^2 \left(b^2-4 a c\right)^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8192 c^{7/2}}+\frac{d^2 (b+2 c x)^3 \left(a+b x+c x^2\right)^{5/2}}{16 c}",1,"(-5*(b^2 - 4*a*c)^3*d^2*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(4096*c^3) + (5*(b^2 - 4*a*c)^2*d^2*(b + 2*c*x)^3*Sqrt[a + b*x + c*x^2])/(2048*c^3) - (5*(b^2 - 4*a*c)*d^2*(b + 2*c*x)^3*(a + b*x + c*x^2)^(3/2))/(384*c^2) + (d^2*(b + 2*c*x)^3*(a + b*x + c*x^2)^(5/2))/(16*c) - (5*(b^2 - 4*a*c)^4*d^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8192*c^(7/2))","A",6,4,26,0.1538,1,"{685, 692, 621, 206}"
1221,1,19,0,0.0066538,"\int (b d+2 c d x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b*d + 2*c*d*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{2}{7} d \left(a+b x+c x^2\right)^{7/2}","\frac{2}{7} d \left(a+b x+c x^2\right)^{7/2}",1,"(2*d*(a + b*x + c*x^2)^(7/2))/7","A",1,1,24,0.04167,1,"{629}"
1222,1,149,0,0.1206697,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{b d+2 c d x} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x),x]","\frac{\left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}{32 c^3 d}-\frac{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}{24 c^2 d}-\frac{\left(b^2-4 a c\right)^{5/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{64 c^{7/2} d}+\frac{\left(a+b x+c x^2\right)^{5/2}}{10 c d}","\frac{\left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}{32 c^3 d}-\frac{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}{24 c^2 d}-\frac{\left(b^2-4 a c\right)^{5/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{64 c^{7/2} d}+\frac{\left(a+b x+c x^2\right)^{5/2}}{10 c d}",1,"((b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])/(32*c^3*d) - ((b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))/(24*c^2*d) + (a + b*x + c*x^2)^(5/2)/(10*c*d) - ((b^2 - 4*a*c)^(5/2)*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(64*c^(7/2)*d)","A",5,3,26,0.1154,1,"{685, 688, 205}"
1223,1,153,0,0.064322,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^2} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^2,x]","-\frac{15 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}{256 c^3 d^2}+\frac{15 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{7/2} d^2}+\frac{5 (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{32 c^2 d^2}-\frac{\left(a+b x+c x^2\right)^{5/2}}{2 c d^2 (b+2 c x)}","-\frac{15 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}{256 c^3 d^2}+\frac{15 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{7/2} d^2}+\frac{5 (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{32 c^2 d^2}-\frac{\left(a+b x+c x^2\right)^{5/2}}{2 c d^2 (b+2 c x)}",1,"(-15*(b^2 - 4*a*c)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(256*c^3*d^2) + (5*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(32*c^2*d^2) - (a + b*x + c*x^2)^(5/2)/(2*c*d^2*(b + 2*c*x)) + (15*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(512*c^(7/2)*d^2)","A",5,4,26,0.1538,1,"{684, 612, 621, 206}"
1224,1,147,0,0.111583,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^3} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^3,x]","-\frac{5 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}{64 c^3 d^3}+\frac{5 \left(b^2-4 a c\right)^{3/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{128 c^{7/2} d^3}+\frac{5 \left(a+b x+c x^2\right)^{3/2}}{48 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{5/2}}{4 c d^3 (b+2 c x)^2}","-\frac{5 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}{64 c^3 d^3}+\frac{5 \left(b^2-4 a c\right)^{3/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{128 c^{7/2} d^3}+\frac{5 \left(a+b x+c x^2\right)^{3/2}}{48 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{5/2}}{4 c d^3 (b+2 c x)^2}",1,"(-5*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2])/(64*c^3*d^3) + (5*(a + b*x + c*x^2)^(3/2))/(48*c^2*d^3) - (a + b*x + c*x^2)^(5/2)/(4*c*d^3*(b + 2*c*x)^2) + (5*(b^2 - 4*a*c)^(3/2)*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(128*c^(7/2)*d^3)","A",5,4,26,0.1538,1,"{684, 685, 688, 205}"
1225,1,145,0,0.0695159,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^4} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^4,x]","-\frac{5 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2} d^4}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{24 c^2 d^4 (b+2 c x)}+\frac{5 (b+2 c x) \sqrt{a+b x+c x^2}}{64 c^3 d^4}-\frac{\left(a+b x+c x^2\right)^{5/2}}{6 c d^4 (b+2 c x)^3}","-\frac{5 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2} d^4}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{24 c^2 d^4 (b+2 c x)}+\frac{5 (b+2 c x) \sqrt{a+b x+c x^2}}{64 c^3 d^4}-\frac{\left(a+b x+c x^2\right)^{5/2}}{6 c d^4 (b+2 c x)^3}",1,"(5*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(64*c^3*d^4) - (5*(a + b*x + c*x^2)^(3/2))/(24*c^2*d^4*(b + 2*c*x)) - (a + b*x + c*x^2)^(5/2)/(6*c*d^4*(b + 2*c*x)^3) - (5*(b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(7/2)*d^4)","A",5,4,26,0.1538,1,"{684, 612, 621, 206}"
1226,1,147,0,0.1019163,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^5} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^5,x]","-\frac{15 \sqrt{b^2-4 a c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{512 c^{7/2} d^5}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{64 c^2 d^5 (b+2 c x)^2}+\frac{15 \sqrt{a+b x+c x^2}}{256 c^3 d^5}-\frac{\left(a+b x+c x^2\right)^{5/2}}{8 c d^5 (b+2 c x)^4}","-\frac{15 \sqrt{b^2-4 a c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{512 c^{7/2} d^5}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{64 c^2 d^5 (b+2 c x)^2}+\frac{15 \sqrt{a+b x+c x^2}}{256 c^3 d^5}-\frac{\left(a+b x+c x^2\right)^{5/2}}{8 c d^5 (b+2 c x)^4}",1,"(15*Sqrt[a + b*x + c*x^2])/(256*c^3*d^5) - (5*(a + b*x + c*x^2)^(3/2))/(64*c^2*d^5*(b + 2*c*x)^2) - (a + b*x + c*x^2)^(5/2)/(8*c*d^5*(b + 2*c*x)^4) - (15*Sqrt[b^2 - 4*a*c]*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(512*c^(7/2)*d^5)","A",5,4,26,0.1538,1,"{684, 685, 688, 205}"
1227,1,139,0,0.0745528,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^6} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^6,x]","-\frac{\left(a+b x+c x^2\right)^{3/2}}{24 c^2 d^6 (b+2 c x)^3}-\frac{\sqrt{a+b x+c x^2}}{32 c^3 d^6 (b+2 c x)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{7/2} d^6}-\frac{\left(a+b x+c x^2\right)^{5/2}}{10 c d^6 (b+2 c x)^5}","-\frac{\left(a+b x+c x^2\right)^{3/2}}{24 c^2 d^6 (b+2 c x)^3}-\frac{\sqrt{a+b x+c x^2}}{32 c^3 d^6 (b+2 c x)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{7/2} d^6}-\frac{\left(a+b x+c x^2\right)^{5/2}}{10 c d^6 (b+2 c x)^5}",1,"-Sqrt[a + b*x + c*x^2]/(32*c^3*d^6*(b + 2*c*x)) - (a + b*x + c*x^2)^(3/2)/(24*c^2*d^6*(b + 2*c*x)^3) - (a + b*x + c*x^2)^(5/2)/(10*c*d^6*(b + 2*c*x)^5) + ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]/(64*c^(7/2)*d^6)","A",5,3,26,0.1154,1,"{684, 621, 206}"
1228,1,155,0,0.0988183,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^7} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^7,x]","\frac{5 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{1024 c^{7/2} d^7 \sqrt{b^2-4 a c}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{192 c^2 d^7 (b+2 c x)^4}-\frac{5 \sqrt{a+b x+c x^2}}{512 c^3 d^7 (b+2 c x)^2}-\frac{\left(a+b x+c x^2\right)^{5/2}}{12 c d^7 (b+2 c x)^6}","\frac{5 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{1024 c^{7/2} d^7 \sqrt{b^2-4 a c}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{192 c^2 d^7 (b+2 c x)^4}-\frac{5 \sqrt{a+b x+c x^2}}{512 c^3 d^7 (b+2 c x)^2}-\frac{\left(a+b x+c x^2\right)^{5/2}}{12 c d^7 (b+2 c x)^6}",1,"(-5*Sqrt[a + b*x + c*x^2])/(512*c^3*d^7*(b + 2*c*x)^2) - (5*(a + b*x + c*x^2)^(3/2))/(192*c^2*d^7*(b + 2*c*x)^4) - (a + b*x + c*x^2)^(5/2)/(12*c*d^7*(b + 2*c*x)^6) + (5*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(1024*c^(7/2)*Sqrt[b^2 - 4*a*c]*d^7)","A",5,3,26,0.1154,1,"{684, 688, 205}"
1229,1,39,0,0.0157464,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^8} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^8,x]","\frac{2 \left(a+b x+c x^2\right)^{7/2}}{7 d^8 \left(b^2-4 a c\right) (b+2 c x)^7}","\frac{2 \left(a+b x+c x^2\right)^{7/2}}{7 d^8 \left(b^2-4 a c\right) (b+2 c x)^7}",1,"(2*(a + b*x + c*x^2)^(7/2))/(7*(b^2 - 4*a*c)*d^8*(b + 2*c*x)^7)","A",1,1,26,0.03846,1,"{682}"
1230,1,197,0,0.149922,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^9} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^9,x]","\frac{5 \sqrt{a+b x+c x^2}}{4096 c^3 d^9 \left(b^2-4 a c\right) (b+2 c x)^2}+\frac{5 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{8192 c^{7/2} d^9 \left(b^2-4 a c\right)^{3/2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{384 c^2 d^9 (b+2 c x)^6}-\frac{5 \sqrt{a+b x+c x^2}}{2048 c^3 d^9 (b+2 c x)^4}-\frac{\left(a+b x+c x^2\right)^{5/2}}{16 c d^9 (b+2 c x)^8}","\frac{5 \sqrt{a+b x+c x^2}}{4096 c^3 d^9 \left(b^2-4 a c\right) (b+2 c x)^2}+\frac{5 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{8192 c^{7/2} d^9 \left(b^2-4 a c\right)^{3/2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{384 c^2 d^9 (b+2 c x)^6}-\frac{5 \sqrt{a+b x+c x^2}}{2048 c^3 d^9 (b+2 c x)^4}-\frac{\left(a+b x+c x^2\right)^{5/2}}{16 c d^9 (b+2 c x)^8}",1,"(-5*Sqrt[a + b*x + c*x^2])/(2048*c^3*d^9*(b + 2*c*x)^4) + (5*Sqrt[a + b*x + c*x^2])/(4096*c^3*(b^2 - 4*a*c)*d^9*(b + 2*c*x)^2) - (5*(a + b*x + c*x^2)^(3/2))/(384*c^2*d^9*(b + 2*c*x)^6) - (a + b*x + c*x^2)^(5/2)/(16*c*d^9*(b + 2*c*x)^8) + (5*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(8192*c^(7/2)*(b^2 - 4*a*c)^(3/2)*d^9)","A",6,4,26,0.1538,1,"{684, 693, 688, 205}"
1231,1,79,0,0.0336197,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{10}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^10,x]","\frac{4 \left(a+b x+c x^2\right)^{7/2}}{63 d^{10} \left(b^2-4 a c\right)^2 (b+2 c x)^7}+\frac{2 \left(a+b x+c x^2\right)^{7/2}}{9 d^{10} \left(b^2-4 a c\right) (b+2 c x)^9}","\frac{4 \left(a+b x+c x^2\right)^{7/2}}{63 d^{10} \left(b^2-4 a c\right)^2 (b+2 c x)^7}+\frac{2 \left(a+b x+c x^2\right)^{7/2}}{9 d^{10} \left(b^2-4 a c\right) (b+2 c x)^9}",1,"(2*(a + b*x + c*x^2)^(7/2))/(9*(b^2 - 4*a*c)*d^10*(b + 2*c*x)^9) + (4*(a + b*x + c*x^2)^(7/2))/(63*(b^2 - 4*a*c)^2*d^10*(b + 2*c*x)^7)","A",2,2,26,0.07692,1,"{693, 682}"
1232,1,239,0,0.1849086,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{11}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^11,x]","\frac{3 \sqrt{a+b x+c x^2}}{8192 c^3 d^{11} \left(b^2-4 a c\right)^2 (b+2 c x)^2}+\frac{\sqrt{a+b x+c x^2}}{4096 c^3 d^{11} \left(b^2-4 a c\right) (b+2 c x)^4}+\frac{3 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{16384 c^{7/2} d^{11} \left(b^2-4 a c\right)^{5/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{128 c^2 d^{11} (b+2 c x)^8}-\frac{\sqrt{a+b x+c x^2}}{1024 c^3 d^{11} (b+2 c x)^6}-\frac{\left(a+b x+c x^2\right)^{5/2}}{20 c d^{11} (b+2 c x)^{10}}","\frac{3 \sqrt{a+b x+c x^2}}{8192 c^3 d^{11} \left(b^2-4 a c\right)^2 (b+2 c x)^2}+\frac{\sqrt{a+b x+c x^2}}{4096 c^3 d^{11} \left(b^2-4 a c\right) (b+2 c x)^4}+\frac{3 \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{16384 c^{7/2} d^{11} \left(b^2-4 a c\right)^{5/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{128 c^2 d^{11} (b+2 c x)^8}-\frac{\sqrt{a+b x+c x^2}}{1024 c^3 d^{11} (b+2 c x)^6}-\frac{\left(a+b x+c x^2\right)^{5/2}}{20 c d^{11} (b+2 c x)^{10}}",1,"-Sqrt[a + b*x + c*x^2]/(1024*c^3*d^11*(b + 2*c*x)^6) + Sqrt[a + b*x + c*x^2]/(4096*c^3*(b^2 - 4*a*c)*d^11*(b + 2*c*x)^4) + (3*Sqrt[a + b*x + c*x^2])/(8192*c^3*(b^2 - 4*a*c)^2*d^11*(b + 2*c*x)^2) - (a + b*x + c*x^2)^(3/2)/(128*c^2*d^11*(b + 2*c*x)^8) - (a + b*x + c*x^2)^(5/2)/(20*c*d^11*(b + 2*c*x)^10) + (3*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(16384*c^(7/2)*(b^2 - 4*a*c)^(5/2)*d^11)","A",7,4,26,0.1538,1,"{684, 693, 688, 205}"
1233,1,118,0,0.056215,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{12}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^12,x]","\frac{16 \left(a+b x+c x^2\right)^{7/2}}{693 d^{12} \left(b^2-4 a c\right)^3 (b+2 c x)^7}+\frac{8 \left(a+b x+c x^2\right)^{7/2}}{99 d^{12} \left(b^2-4 a c\right)^2 (b+2 c x)^9}+\frac{2 \left(a+b x+c x^2\right)^{7/2}}{11 d^{12} \left(b^2-4 a c\right) (b+2 c x)^{11}}","\frac{16 \left(a+b x+c x^2\right)^{7/2}}{693 d^{12} \left(b^2-4 a c\right)^3 (b+2 c x)^7}+\frac{8 \left(a+b x+c x^2\right)^{7/2}}{99 d^{12} \left(b^2-4 a c\right)^2 (b+2 c x)^9}+\frac{2 \left(a+b x+c x^2\right)^{7/2}}{11 d^{12} \left(b^2-4 a c\right) (b+2 c x)^{11}}",1,"(2*(a + b*x + c*x^2)^(7/2))/(11*(b^2 - 4*a*c)*d^12*(b + 2*c*x)^11) + (8*(a + b*x + c*x^2)^(7/2))/(99*(b^2 - 4*a*c)^2*d^12*(b + 2*c*x)^9) + (16*(a + b*x + c*x^2)^(7/2))/(693*(b^2 - 4*a*c)^3*d^12*(b + 2*c*x)^7)","A",3,2,26,0.07692,1,"{693, 682}"
1234,1,117,0,0.0547876,"\int \frac{(b d+2 c d x)^4}{\sqrt{a+b x+c x^2}} \, dx","Int[(b*d + 2*c*d*x)^4/Sqrt[a + b*x + c*x^2],x]","\frac{3}{4} d^4 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}+\frac{3 d^4 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{c}}+\frac{1}{2} d^4 (b+2 c x)^3 \sqrt{a+b x+c x^2}","\frac{3}{4} d^4 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}+\frac{3 d^4 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{c}}+\frac{1}{2} d^4 (b+2 c x)^3 \sqrt{a+b x+c x^2}",1,"(3*(b^2 - 4*a*c)*d^4*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/4 + (d^4*(b + 2*c*x)^3*Sqrt[a + b*x + c*x^2])/2 + (3*(b^2 - 4*a*c)^2*d^4*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[c])","A",4,3,26,0.1154,1,"{692, 621, 206}"
1235,1,59,0,0.0259978,"\int \frac{(b d+2 c d x)^3}{\sqrt{a+b x+c x^2}} \, dx","Int[(b*d + 2*c*d*x)^3/Sqrt[a + b*x + c*x^2],x]","\frac{4}{3} d^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}+\frac{2}{3} d^3 (b+2 c x)^2 \sqrt{a+b x+c x^2}","\frac{4}{3} d^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}+\frac{2}{3} d^3 (b+2 c x)^2 \sqrt{a+b x+c x^2}",1,"(4*(b^2 - 4*a*c)*d^3*Sqrt[a + b*x + c*x^2])/3 + (2*d^3*(b + 2*c*x)^2*Sqrt[a + b*x + c*x^2])/3","A",2,2,26,0.07692,1,"{692, 629}"
1236,1,75,0,0.0297058,"\int \frac{(b d+2 c d x)^2}{\sqrt{a+b x+c x^2}} \, dx","Int[(b*d + 2*c*d*x)^2/Sqrt[a + b*x + c*x^2],x]","\frac{d^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c}}+d^2 (b+2 c x) \sqrt{a+b x+c x^2}","\frac{d^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c}}+d^2 (b+2 c x) \sqrt{a+b x+c x^2}",1,"d^2*(b + 2*c*x)*Sqrt[a + b*x + c*x^2] + ((b^2 - 4*a*c)*d^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c])","A",3,3,26,0.1154,1,"{692, 621, 206}"
1237,1,17,0,0.0060926,"\int \frac{b d+2 c d x}{\sqrt{a+b x+c x^2}} \, dx","Int[(b*d + 2*c*d*x)/Sqrt[a + b*x + c*x^2],x]","2 d \sqrt{a+b x+c x^2}","2 d \sqrt{a+b x+c x^2}",1,"2*d*Sqrt[a + b*x + c*x^2]","A",1,1,24,0.04167,1,"{629}"
1238,1,55,0,0.0333378,"\int \frac{1}{(b d+2 c d x) \sqrt{a+b x+c x^2}} \, dx","Int[1/((b*d + 2*c*d*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{\sqrt{c} d \sqrt{b^2-4 a c}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{\sqrt{c} d \sqrt{b^2-4 a c}}",1,"ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]]/(Sqrt[c]*Sqrt[b^2 - 4*a*c]*d)","A",2,2,26,0.07692,1,"{688, 205}"
1239,1,37,0,0.0151481,"\int \frac{1}{(b d+2 c d x)^2 \sqrt{a+b x+c x^2}} \, dx","Int[1/((b*d + 2*c*d*x)^2*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{a+b x+c x^2}}{d^2 \left(b^2-4 a c\right) (b+2 c x)}","\frac{2 \sqrt{a+b x+c x^2}}{d^2 \left(b^2-4 a c\right) (b+2 c x)}",1,"(2*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)*d^2*(b + 2*c*x))","A",1,1,26,0.03846,1,"{682}"
1240,1,95,0,0.055632,"\int \frac{1}{(b d+2 c d x)^3 \sqrt{a+b x+c x^2}} \, dx","Int[1/((b*d + 2*c*d*x)^3*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+b x+c x^2}}{d^3 \left(b^2-4 a c\right) (b+2 c x)^2}+\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{2 \sqrt{c} d^3 \left(b^2-4 a c\right)^{3/2}}","\frac{\sqrt{a+b x+c x^2}}{d^3 \left(b^2-4 a c\right) (b+2 c x)^2}+\frac{\tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{2 \sqrt{c} d^3 \left(b^2-4 a c\right)^{3/2}}",1,"Sqrt[a + b*x + c*x^2]/((b^2 - 4*a*c)*d^3*(b + 2*c*x)^2) + ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]]/(2*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*d^3)","A",3,3,26,0.1154,1,"{693, 688, 205}"
1241,1,79,0,0.0319232,"\int \frac{1}{(b d+2 c d x)^4 \sqrt{a+b x+c x^2}} \, dx","Int[1/((b*d + 2*c*d*x)^4*Sqrt[a + b*x + c*x^2]),x]","\frac{4 \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^2 (b+2 c x)}+\frac{2 \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right) (b+2 c x)^3}","\frac{4 \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^2 (b+2 c x)}+\frac{2 \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right) (b+2 c x)^3}",1,"(2*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)*d^4*(b + 2*c*x)^3) + (4*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^2*d^4*(b + 2*c*x))","A",2,2,26,0.07692,1,"{693, 682}"
1242,1,102,0,0.0533681,"\int \frac{(b d+2 c d x)^4}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(3/2),x]","6 \sqrt{c} d^4 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)+12 c d^4 (b+2 c x) \sqrt{a+b x+c x^2}-\frac{2 d^4 (b+2 c x)^3}{\sqrt{a+b x+c x^2}}","6 \sqrt{c} d^4 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)+12 c d^4 (b+2 c x) \sqrt{a+b x+c x^2}-\frac{2 d^4 (b+2 c x)^3}{\sqrt{a+b x+c x^2}}",1,"(-2*d^4*(b + 2*c*x)^3)/Sqrt[a + b*x + c*x^2] + 12*c*d^4*(b + 2*c*x)*Sqrt[a + b*x + c*x^2] + 6*Sqrt[c]*(b^2 - 4*a*c)*d^4*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]","A",4,4,26,0.1538,1,"{686, 692, 621, 206}"
1243,1,48,0,0.0229013,"\int \frac{(b d+2 c d x)^3}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^(3/2),x]","16 c d^3 \sqrt{a+b x+c x^2}-\frac{2 d^3 (b+2 c x)^2}{\sqrt{a+b x+c x^2}}","16 c d^3 \sqrt{a+b x+c x^2}-\frac{2 d^3 (b+2 c x)^2}{\sqrt{a+b x+c x^2}}",1,"(-2*d^3*(b + 2*c*x)^2)/Sqrt[a + b*x + c*x^2] + 16*c*d^3*Sqrt[a + b*x + c*x^2]","A",2,2,26,0.07692,1,"{686, 629}"
1244,1,66,0,0.0269304,"\int \frac{(b d+2 c d x)^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^(3/2),x]","4 \sqrt{c} d^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)-\frac{2 d^2 (b+2 c x)}{\sqrt{a+b x+c x^2}}","4 \sqrt{c} d^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)-\frac{2 d^2 (b+2 c x)}{\sqrt{a+b x+c x^2}}",1,"(-2*d^2*(b + 2*c*x))/Sqrt[a + b*x + c*x^2] + 4*Sqrt[c]*d^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]","A",3,3,26,0.1154,1,"{686, 621, 206}"
1245,1,17,0,0.0061819,"\int \frac{b d+2 c d x}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 d}{\sqrt{a+b x+c x^2}}","-\frac{2 d}{\sqrt{a+b x+c x^2}}",1,"(-2*d)/Sqrt[a + b*x + c*x^2]","A",1,1,24,0.04167,1,"{629}"
1246,1,86,0,0.0582978,"\int \frac{1}{(b d+2 c d x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{2}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{4 \sqrt{c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{d \left(b^2-4 a c\right)^{3/2}}","-\frac{2}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{4 \sqrt{c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{d \left(b^2-4 a c\right)^{3/2}}",1,"-2/((b^2 - 4*a*c)*d*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[c]*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*d)","A",3,3,26,0.1154,1,"{687, 688, 205}"
1247,1,76,0,0.0340286,"\int \frac{1}{(b d+2 c d x)^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(3/2)),x]","-\frac{16 c \sqrt{a+b x+c x^2}}{d^2 \left(b^2-4 a c\right)^2 (b+2 c x)}-\frac{2}{d^2 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}","-\frac{16 c \sqrt{a+b x+c x^2}}{d^2 \left(b^2-4 a c\right)^2 (b+2 c x)}-\frac{2}{d^2 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}",1,"-2/((b^2 - 4*a*c)*d^2*(b + 2*c*x)*Sqrt[a + b*x + c*x^2]) - (16*c*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)^2*d^2*(b + 2*c*x))","A",2,2,26,0.07692,1,"{687, 682}"
1248,1,132,0,0.0845561,"\int \frac{1}{(b d+2 c d x)^3 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(3/2)),x]","-\frac{12 c \sqrt{a+b x+c x^2}}{d^3 \left(b^2-4 a c\right)^2 (b+2 c x)^2}-\frac{2}{d^3 \left(b^2-4 a c\right) (b+2 c x)^2 \sqrt{a+b x+c x^2}}-\frac{6 \sqrt{c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{d^3 \left(b^2-4 a c\right)^{5/2}}","-\frac{12 c \sqrt{a+b x+c x^2}}{d^3 \left(b^2-4 a c\right)^2 (b+2 c x)^2}-\frac{2}{d^3 \left(b^2-4 a c\right) (b+2 c x)^2 \sqrt{a+b x+c x^2}}-\frac{6 \sqrt{c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{d^3 \left(b^2-4 a c\right)^{5/2}}",1,"-2/((b^2 - 4*a*c)*d^3*(b + 2*c*x)^2*Sqrt[a + b*x + c*x^2]) - (12*c*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)^2*d^3*(b + 2*c*x)^2) - (6*Sqrt[c]*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*d^3)","A",4,4,26,0.1538,1,"{687, 693, 688, 205}"
1249,1,118,0,0.0552308,"\int \frac{1}{(b d+2 c d x)^4 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(3/2)),x]","-\frac{64 c \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^3 (b+2 c x)}-\frac{32 c \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^3}-\frac{2}{d^4 \left(b^2-4 a c\right) (b+2 c x)^3 \sqrt{a+b x+c x^2}}","-\frac{64 c \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^3 (b+2 c x)}-\frac{32 c \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^3}-\frac{2}{d^4 \left(b^2-4 a c\right) (b+2 c x)^3 \sqrt{a+b x+c x^2}}",1,"-2/((b^2 - 4*a*c)*d^4*(b + 2*c*x)^3*Sqrt[a + b*x + c*x^2]) - (32*c*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^3) - (64*c*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^3*d^4*(b + 2*c*x))","A",3,3,26,0.1154,1,"{687, 693, 682}"
1250,1,136,0,0.0771676,"\int \frac{(b d+2 c d x)^6}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^(5/2),x]","40 c^{3/2} d^6 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)+80 c^2 d^6 (b+2 c x) \sqrt{a+b x+c x^2}-\frac{40 c d^6 (b+2 c x)^3}{3 \sqrt{a+b x+c x^2}}-\frac{2 d^6 (b+2 c x)^5}{3 \left(a+b x+c x^2\right)^{3/2}}","40 c^{3/2} d^6 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)+80 c^2 d^6 (b+2 c x) \sqrt{a+b x+c x^2}-\frac{40 c d^6 (b+2 c x)^3}{3 \sqrt{a+b x+c x^2}}-\frac{2 d^6 (b+2 c x)^5}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d^6*(b + 2*c*x)^5)/(3*(a + b*x + c*x^2)^(3/2)) - (40*c*d^6*(b + 2*c*x)^3)/(3*Sqrt[a + b*x + c*x^2]) + 80*c^2*d^6*(b + 2*c*x)*Sqrt[a + b*x + c*x^2] + 40*c^(3/2)*(b^2 - 4*a*c)*d^6*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]","A",5,4,26,0.1538,1,"{686, 692, 621, 206}"
1251,1,84,0,0.0439912,"\int \frac{(b d+2 c d x)^5}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^5/(a + b*x + c*x^2)^(5/2),x]","\frac{256}{3} c^2 d^5 \sqrt{a+b x+c x^2}-\frac{32 c d^5 (b+2 c x)^2}{3 \sqrt{a+b x+c x^2}}-\frac{2 d^5 (b+2 c x)^4}{3 \left(a+b x+c x^2\right)^{3/2}}","\frac{256}{3} c^2 d^5 \sqrt{a+b x+c x^2}-\frac{32 c d^5 (b+2 c x)^2}{3 \sqrt{a+b x+c x^2}}-\frac{2 d^5 (b+2 c x)^4}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d^5*(b + 2*c*x)^4)/(3*(a + b*x + c*x^2)^(3/2)) - (32*c*d^5*(b + 2*c*x)^2)/(3*Sqrt[a + b*x + c*x^2]) + (256*c^2*d^5*Sqrt[a + b*x + c*x^2])/3","A",3,2,26,0.07692,1,"{686, 629}"
1252,1,96,0,0.0499499,"\int \frac{(b d+2 c d x)^4}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(5/2),x]","16 c^{3/2} d^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)-\frac{8 c d^4 (b+2 c x)}{\sqrt{a+b x+c x^2}}-\frac{2 d^4 (b+2 c x)^3}{3 \left(a+b x+c x^2\right)^{3/2}}","16 c^{3/2} d^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)-\frac{8 c d^4 (b+2 c x)}{\sqrt{a+b x+c x^2}}-\frac{2 d^4 (b+2 c x)^3}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d^4*(b + 2*c*x)^3)/(3*(a + b*x + c*x^2)^(3/2)) - (8*c*d^4*(b + 2*c*x))/Sqrt[a + b*x + c*x^2] + 16*c^(3/2)*d^4*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]","A",4,3,26,0.1154,1,"{686, 621, 206}"
1253,1,52,0,0.0233337,"\int \frac{(b d+2 c d x)^3}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^(5/2),x]","-\frac{16 c d^3}{3 \sqrt{a+b x+c x^2}}-\frac{2 d^3 (b+2 c x)^2}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{16 c d^3}{3 \sqrt{a+b x+c x^2}}-\frac{2 d^3 (b+2 c x)^2}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d^3*(b + 2*c*x)^2)/(3*(a + b*x + c*x^2)^(3/2)) - (16*c*d^3)/(3*Sqrt[a + b*x + c*x^2])","A",2,2,26,0.07692,1,"{686, 629}"
1254,1,39,0,0.0142451,"\int \frac{(b d+2 c d x)^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 d^2 (b+2 c x)^3}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","-\frac{2 d^2 (b+2 c x)^3}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d^2*(b + 2*c*x)^3)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))","A",1,1,26,0.03846,1,"{682}"
1255,1,19,0,0.0062324,"\int \frac{b d+2 c d x}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 d}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{2 d}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d)/(3*(a + b*x + c*x^2)^(3/2))","A",1,1,24,0.04167,1,"{629}"
1256,1,118,0,0.0767907,"\int \frac{1}{(b d+2 c d x) \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(5/2)),x]","\frac{16 c^{3/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{d \left(b^2-4 a c\right)^{5/2}}+\frac{8 c}{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{16 c^{3/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{d \left(b^2-4 a c\right)^{5/2}}+\frac{8 c}{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"-2/(3*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^(3/2)) + (8*c)/((b^2 - 4*a*c)^2*d*Sqrt[a + b*x + c*x^2]) + (16*c^(3/2)*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*d)","A",4,3,26,0.1154,1,"{687, 688, 205}"
1257,1,122,0,0.0557404,"\int \frac{1}{(b d+2 c d x)^2 \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(5/2)),x]","\frac{256 c^2 \sqrt{a+b x+c x^2}}{3 d^2 \left(b^2-4 a c\right)^3 (b+2 c x)}+\frac{32 c}{3 d^2 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}-\frac{2}{3 d^2 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}","\frac{256 c^2 \sqrt{a+b x+c x^2}}{3 d^2 \left(b^2-4 a c\right)^3 (b+2 c x)}+\frac{32 c}{3 d^2 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}-\frac{2}{3 d^2 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}",1,"-2/(3*(b^2 - 4*a*c)*d^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2)) + (32*c)/(3*(b^2 - 4*a*c)^2*d^2*(b + 2*c*x)*Sqrt[a + b*x + c*x^2]) + (256*c^2*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^3*d^2*(b + 2*c*x))","A",3,2,26,0.07692,1,"{687, 682}"
1258,1,176,0,0.1057921,"\int \frac{1}{(b d+2 c d x)^3 \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(5/2)),x]","\frac{80 c^2 \sqrt{a+b x+c x^2}}{d^3 \left(b^2-4 a c\right)^3 (b+2 c x)^2}+\frac{40 c^{3/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{d^3 \left(b^2-4 a c\right)^{7/2}}+\frac{40 c}{3 d^3 \left(b^2-4 a c\right)^2 (b+2 c x)^2 \sqrt{a+b x+c x^2}}-\frac{2}{3 d^3 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^{3/2}}","\frac{80 c^2 \sqrt{a+b x+c x^2}}{d^3 \left(b^2-4 a c\right)^3 (b+2 c x)^2}+\frac{40 c^{3/2} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{d^3 \left(b^2-4 a c\right)^{7/2}}+\frac{40 c}{3 d^3 \left(b^2-4 a c\right)^2 (b+2 c x)^2 \sqrt{a+b x+c x^2}}-\frac{2}{3 d^3 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^{3/2}}",1,"-2/(3*(b^2 - 4*a*c)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(3/2)) + (40*c)/(3*(b^2 - 4*a*c)^2*d^3*(b + 2*c*x)^2*Sqrt[a + b*x + c*x^2]) + (80*c^2*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)^3*d^3*(b + 2*c*x)^2) + (40*c^(3/2)*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(7/2)*d^3)","A",5,4,26,0.1538,1,"{687, 693, 688, 205}"
1259,1,162,0,0.0794517,"\int \frac{1}{(b d+2 c d x)^4 \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(5/2)),x]","\frac{512 c^2 \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^4 (b+2 c x)}+\frac{256 c^2 \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^3 (b+2 c x)^3}+\frac{16 c}{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^3 \sqrt{a+b x+c x^2}}-\frac{2}{3 d^4 \left(b^2-4 a c\right) (b+2 c x)^3 \left(a+b x+c x^2\right)^{3/2}}","\frac{512 c^2 \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^4 (b+2 c x)}+\frac{256 c^2 \sqrt{a+b x+c x^2}}{3 d^4 \left(b^2-4 a c\right)^3 (b+2 c x)^3}+\frac{16 c}{d^4 \left(b^2-4 a c\right)^2 (b+2 c x)^3 \sqrt{a+b x+c x^2}}-\frac{2}{3 d^4 \left(b^2-4 a c\right) (b+2 c x)^3 \left(a+b x+c x^2\right)^{3/2}}",1,"-2/(3*(b^2 - 4*a*c)*d^4*(b + 2*c*x)^3*(a + b*x + c*x^2)^(3/2)) + (16*c)/((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^3*Sqrt[a + b*x + c*x^2]) + (256*c^2*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^3*d^4*(b + 2*c*x)^3) + (512*c^2*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^4*d^4*(b + 2*c*x))","A",4,3,26,0.1154,1,"{687, 693, 682}"
1260,1,27,0,0.0206604,"\int \frac{1}{(a+b x) \sqrt{1+a^2+2 a b x+b^2 x^2}} \, dx","Int[1/((a + b*x)*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{\tanh ^{-1}\left(\sqrt{a^2+2 a b x+b^2 x^2+1}\right)}{b}","-\frac{\tanh ^{-1}\left(\sqrt{a^2+2 a b x+b^2 x^2+1}\right)}{b}",1,"-(ArcTanh[Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]]/b)","A",2,2,29,0.06897,1,"{688, 208}"
1261,1,55,0,0.0238854,"\int (b d+2 c d x)^{5/2} \left(a+b x+c x^2\right) \, dx","Int[(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2),x]","\frac{(b d+2 c d x)^{11/2}}{44 c^2 d^3}-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}{28 c^2 d}","\frac{(b d+2 c d x)^{11/2}}{44 c^2 d^3}-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}{28 c^2 d}",1,"-((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2))/(28*c^2*d) + (b*d + 2*c*d*x)^(11/2)/(44*c^2*d^3)","A",2,1,24,0.04167,1,"{683}"
1262,1,55,0,0.0227016,"\int (b d+2 c d x)^{3/2} \left(a+b x+c x^2\right) \, dx","Int[(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2),x]","\frac{(b d+2 c d x)^{9/2}}{36 c^2 d^3}-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}{20 c^2 d}","\frac{(b d+2 c d x)^{9/2}}{36 c^2 d^3}-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}{20 c^2 d}",1,"-((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2))/(20*c^2*d) + (b*d + 2*c*d*x)^(9/2)/(36*c^2*d^3)","A",2,1,24,0.04167,1,"{683}"
1263,1,55,0,0.0221096,"\int \sqrt{b d+2 c d x} \left(a+b x+c x^2\right) \, dx","Int[Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2),x]","\frac{(b d+2 c d x)^{7/2}}{28 c^2 d^3}-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}{12 c^2 d}","\frac{(b d+2 c d x)^{7/2}}{28 c^2 d^3}-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}{12 c^2 d}",1,"-((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2))/(12*c^2*d) + (b*d + 2*c*d*x)^(7/2)/(28*c^2*d^3)","A",2,1,24,0.04167,1,"{683}"
1264,1,55,0,0.0219751,"\int \frac{a+b x+c x^2}{\sqrt{b d+2 c d x}} \, dx","Int[(a + b*x + c*x^2)/Sqrt[b*d + 2*c*d*x],x]","\frac{(b d+2 c d x)^{5/2}}{20 c^2 d^3}-\frac{\left(b^2-4 a c\right) \sqrt{b d+2 c d x}}{4 c^2 d}","\frac{(b d+2 c d x)^{5/2}}{20 c^2 d^3}-\frac{\left(b^2-4 a c\right) \sqrt{b d+2 c d x}}{4 c^2 d}",1,"-((b^2 - 4*a*c)*Sqrt[b*d + 2*c*d*x])/(4*c^2*d) + (b*d + 2*c*d*x)^(5/2)/(20*c^2*d^3)","A",2,1,24,0.04167,1,"{683}"
1265,1,55,0,0.0233488,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^(3/2),x]","\frac{b^2-4 a c}{4 c^2 d \sqrt{b d+2 c d x}}+\frac{(b d+2 c d x)^{3/2}}{12 c^2 d^3}","\frac{b^2-4 a c}{4 c^2 d \sqrt{b d+2 c d x}}+\frac{(b d+2 c d x)^{3/2}}{12 c^2 d^3}",1,"(b^2 - 4*a*c)/(4*c^2*d*Sqrt[b*d + 2*c*d*x]) + (b*d + 2*c*d*x)^(3/2)/(12*c^2*d^3)","A",2,1,24,0.04167,1,"{683}"
1266,1,55,0,0.0216346,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^(5/2),x]","\frac{b^2-4 a c}{12 c^2 d (b d+2 c d x)^{3/2}}+\frac{\sqrt{b d+2 c d x}}{4 c^2 d^3}","\frac{b^2-4 a c}{12 c^2 d (b d+2 c d x)^{3/2}}+\frac{\sqrt{b d+2 c d x}}{4 c^2 d^3}",1,"(b^2 - 4*a*c)/(12*c^2*d*(b*d + 2*c*d*x)^(3/2)) + Sqrt[b*d + 2*c*d*x]/(4*c^2*d^3)","A",2,1,24,0.04167,1,"{683}"
1267,1,55,0,0.0223381,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^(7/2),x]","\frac{b^2-4 a c}{20 c^2 d (b d+2 c d x)^{5/2}}-\frac{1}{4 c^2 d^3 \sqrt{b d+2 c d x}}","\frac{b^2-4 a c}{20 c^2 d (b d+2 c d x)^{5/2}}-\frac{1}{4 c^2 d^3 \sqrt{b d+2 c d x}}",1,"(b^2 - 4*a*c)/(20*c^2*d*(b*d + 2*c*d*x)^(5/2)) - 1/(4*c^2*d^3*Sqrt[b*d + 2*c*d*x])","A",2,1,24,0.04167,1,"{683}"
1268,1,55,0,0.023352,"\int \frac{a+b x+c x^2}{(b d+2 c d x)^{9/2}} \, dx","Int[(a + b*x + c*x^2)/(b*d + 2*c*d*x)^(9/2),x]","\frac{b^2-4 a c}{28 c^2 d (b d+2 c d x)^{7/2}}-\frac{1}{12 c^2 d^3 (b d+2 c d x)^{3/2}}","\frac{b^2-4 a c}{28 c^2 d (b d+2 c d x)^{7/2}}-\frac{1}{12 c^2 d^3 (b d+2 c d x)^{3/2}}",1,"(b^2 - 4*a*c)/(28*c^2*d*(b*d + 2*c*d*x)^(7/2)) - 1/(12*c^2*d^3*(b*d + 2*c*d*x)^(3/2))","A",2,1,24,0.04167,1,"{683}"
1269,1,88,0,0.0549081,"\int (b d+2 c d x)^{3/2} \left(a+b x+c x^2\right)^2 \, dx","Int[(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^2,x]","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{9/2}}{72 c^3 d^3}+\frac{\left(b^2-4 a c\right)^2 (b d+2 c d x)^{5/2}}{80 c^3 d}+\frac{(b d+2 c d x)^{13/2}}{208 c^3 d^5}","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{9/2}}{72 c^3 d^3}+\frac{\left(b^2-4 a c\right)^2 (b d+2 c d x)^{5/2}}{80 c^3 d}+\frac{(b d+2 c d x)^{13/2}}{208 c^3 d^5}",1,"((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(5/2))/(80*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(9/2))/(72*c^3*d^3) + (b*d + 2*c*d*x)^(13/2)/(208*c^3*d^5)","A",2,1,26,0.03846,1,"{683}"
1270,1,88,0,0.039476,"\int \sqrt{b d+2 c d x} \left(a+b x+c x^2\right)^2 \, dx","Int[Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^2,x]","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}{56 c^3 d^3}+\frac{\left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}{48 c^3 d}+\frac{(b d+2 c d x)^{11/2}}{176 c^3 d^5}","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}{56 c^3 d^3}+\frac{\left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}{48 c^3 d}+\frac{(b d+2 c d x)^{11/2}}{176 c^3 d^5}",1,"((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(3/2))/(48*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2))/(56*c^3*d^3) + (b*d + 2*c*d*x)^(11/2)/(176*c^3*d^5)","A",2,1,26,0.03846,1,"{683}"
1271,1,88,0,0.0381218,"\int \frac{\left(a+b x+c x^2\right)^2}{\sqrt{b d+2 c d x}} \, dx","Int[(a + b*x + c*x^2)^2/Sqrt[b*d + 2*c*d*x],x]","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}{40 c^3 d^3}+\frac{\left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}{16 c^3 d}+\frac{(b d+2 c d x)^{9/2}}{144 c^3 d^5}","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}{40 c^3 d^3}+\frac{\left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}{16 c^3 d}+\frac{(b d+2 c d x)^{9/2}}{144 c^3 d^5}",1,"((b^2 - 4*a*c)^2*Sqrt[b*d + 2*c*d*x])/(16*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2))/(40*c^3*d^3) + (b*d + 2*c*d*x)^(9/2)/(144*c^3*d^5)","A",2,1,26,0.03846,1,"{683}"
1272,1,88,0,0.0382175,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(3/2),x]","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}{24 c^3 d^3}-\frac{\left(b^2-4 a c\right)^2}{16 c^3 d \sqrt{b d+2 c d x}}+\frac{(b d+2 c d x)^{7/2}}{112 c^3 d^5}","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}{24 c^3 d^3}-\frac{\left(b^2-4 a c\right)^2}{16 c^3 d \sqrt{b d+2 c d x}}+\frac{(b d+2 c d x)^{7/2}}{112 c^3 d^5}",1,"-(b^2 - 4*a*c)^2/(16*c^3*d*Sqrt[b*d + 2*c*d*x]) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2))/(24*c^3*d^3) + (b*d + 2*c*d*x)^(7/2)/(112*c^3*d^5)","A",2,1,26,0.03846,1,"{683}"
1273,1,88,0,0.0403534,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(5/2),x]","-\frac{\left(b^2-4 a c\right) \sqrt{b d+2 c d x}}{8 c^3 d^3}-\frac{\left(b^2-4 a c\right)^2}{48 c^3 d (b d+2 c d x)^{3/2}}+\frac{(b d+2 c d x)^{5/2}}{80 c^3 d^5}","-\frac{\left(b^2-4 a c\right) \sqrt{b d+2 c d x}}{8 c^3 d^3}-\frac{\left(b^2-4 a c\right)^2}{48 c^3 d (b d+2 c d x)^{3/2}}+\frac{(b d+2 c d x)^{5/2}}{80 c^3 d^5}",1,"-(b^2 - 4*a*c)^2/(48*c^3*d*(b*d + 2*c*d*x)^(3/2)) - ((b^2 - 4*a*c)*Sqrt[b*d + 2*c*d*x])/(8*c^3*d^3) + (b*d + 2*c*d*x)^(5/2)/(80*c^3*d^5)","A",2,1,26,0.03846,1,"{683}"
1274,1,88,0,0.0383003,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(7/2),x]","\frac{b^2-4 a c}{8 c^3 d^3 \sqrt{b d+2 c d x}}-\frac{\left(b^2-4 a c\right)^2}{80 c^3 d (b d+2 c d x)^{5/2}}+\frac{(b d+2 c d x)^{3/2}}{48 c^3 d^5}","\frac{b^2-4 a c}{8 c^3 d^3 \sqrt{b d+2 c d x}}-\frac{\left(b^2-4 a c\right)^2}{80 c^3 d (b d+2 c d x)^{5/2}}+\frac{(b d+2 c d x)^{3/2}}{48 c^3 d^5}",1,"-(b^2 - 4*a*c)^2/(80*c^3*d*(b*d + 2*c*d*x)^(5/2)) + (b^2 - 4*a*c)/(8*c^3*d^3*Sqrt[b*d + 2*c*d*x]) + (b*d + 2*c*d*x)^(3/2)/(48*c^3*d^5)","A",2,1,26,0.03846,1,"{683}"
1275,1,88,0,0.0374583,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^{9/2}} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(9/2),x]","\frac{b^2-4 a c}{24 c^3 d^3 (b d+2 c d x)^{3/2}}-\frac{\left(b^2-4 a c\right)^2}{112 c^3 d (b d+2 c d x)^{7/2}}+\frac{\sqrt{b d+2 c d x}}{16 c^3 d^5}","\frac{b^2-4 a c}{24 c^3 d^3 (b d+2 c d x)^{3/2}}-\frac{\left(b^2-4 a c\right)^2}{112 c^3 d (b d+2 c d x)^{7/2}}+\frac{\sqrt{b d+2 c d x}}{16 c^3 d^5}",1,"-(b^2 - 4*a*c)^2/(112*c^3*d*(b*d + 2*c*d*x)^(7/2)) + (b^2 - 4*a*c)/(24*c^3*d^3*(b*d + 2*c*d*x)^(3/2)) + Sqrt[b*d + 2*c*d*x]/(16*c^3*d^5)","A",2,1,26,0.03846,1,"{683}"
1276,1,88,0,0.0372918,"\int \frac{\left(a+b x+c x^2\right)^2}{(b d+2 c d x)^{11/2}} \, dx","Int[(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(11/2),x]","\frac{b^2-4 a c}{40 c^3 d^3 (b d+2 c d x)^{5/2}}-\frac{\left(b^2-4 a c\right)^2}{144 c^3 d (b d+2 c d x)^{9/2}}-\frac{1}{16 c^3 d^5 \sqrt{b d+2 c d x}}","\frac{b^2-4 a c}{40 c^3 d^3 (b d+2 c d x)^{5/2}}-\frac{\left(b^2-4 a c\right)^2}{144 c^3 d (b d+2 c d x)^{9/2}}-\frac{1}{16 c^3 d^5 \sqrt{b d+2 c d x}}",1,"-(b^2 - 4*a*c)^2/(144*c^3*d*(b*d + 2*c*d*x)^(9/2)) + (b^2 - 4*a*c)/(40*c^3*d^3*(b*d + 2*c*d*x)^(5/2)) - 1/(16*c^3*d^5*Sqrt[b*d + 2*c*d*x])","A",2,1,26,0.03846,1,"{683}"
1277,1,121,0,0.0512324,"\int \sqrt{b d+2 c d x} \left(a+b x+c x^2\right)^3 \, dx","Int[Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^3,x]","-\frac{3 \left(b^2-4 a c\right) (b d+2 c d x)^{11/2}}{704 c^4 d^5}+\frac{3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{7/2}}{448 c^4 d^3}-\frac{\left(b^2-4 a c\right)^3 (b d+2 c d x)^{3/2}}{192 c^4 d}+\frac{(b d+2 c d x)^{15/2}}{960 c^4 d^7}","-\frac{3 \left(b^2-4 a c\right) (b d+2 c d x)^{11/2}}{704 c^4 d^5}+\frac{3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{7/2}}{448 c^4 d^3}-\frac{\left(b^2-4 a c\right)^3 (b d+2 c d x)^{3/2}}{192 c^4 d}+\frac{(b d+2 c d x)^{15/2}}{960 c^4 d^7}",1,"-((b^2 - 4*a*c)^3*(b*d + 2*c*d*x)^(3/2))/(192*c^4*d) + (3*(b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(7/2))/(448*c^4*d^3) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(11/2))/(704*c^4*d^5) + (b*d + 2*c*d*x)^(15/2)/(960*c^4*d^7)","A",2,1,26,0.03846,1,"{683}"
1278,1,121,0,0.0499577,"\int \frac{\left(a+b x+c x^2\right)^3}{\sqrt{b d+2 c d x}} \, dx","Int[(a + b*x + c*x^2)^3/Sqrt[b*d + 2*c*d*x],x]","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{9/2}}{192 c^4 d^5}+\frac{3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{5/2}}{320 c^4 d^3}-\frac{\left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}{64 c^4 d}+\frac{(b d+2 c d x)^{13/2}}{832 c^4 d^7}","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{9/2}}{192 c^4 d^5}+\frac{3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{5/2}}{320 c^4 d^3}-\frac{\left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}{64 c^4 d}+\frac{(b d+2 c d x)^{13/2}}{832 c^4 d^7}",1,"-((b^2 - 4*a*c)^3*Sqrt[b*d + 2*c*d*x])/(64*c^4*d) + (3*(b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(5/2))/(320*c^4*d^3) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(9/2))/(192*c^4*d^5) + (b*d + 2*c*d*x)^(13/2)/(832*c^4*d^7)","A",2,1,26,0.03846,1,"{683}"
1279,1,121,0,0.049329,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(3/2),x]","-\frac{3 \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}{448 c^4 d^5}+\frac{\left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}{64 c^4 d^3}+\frac{\left(b^2-4 a c\right)^3}{64 c^4 d \sqrt{b d+2 c d x}}+\frac{(b d+2 c d x)^{11/2}}{704 c^4 d^7}","-\frac{3 \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}{448 c^4 d^5}+\frac{\left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}{64 c^4 d^3}+\frac{\left(b^2-4 a c\right)^3}{64 c^4 d \sqrt{b d+2 c d x}}+\frac{(b d+2 c d x)^{11/2}}{704 c^4 d^7}",1,"(b^2 - 4*a*c)^3/(64*c^4*d*Sqrt[b*d + 2*c*d*x]) + ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(3/2))/(64*c^4*d^3) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2))/(448*c^4*d^5) + (b*d + 2*c*d*x)^(11/2)/(704*c^4*d^7)","A",2,1,26,0.03846,1,"{683}"
1280,1,121,0,0.049903,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(5/2),x]","-\frac{3 \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}{320 c^4 d^5}+\frac{3 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}{64 c^4 d^3}+\frac{\left(b^2-4 a c\right)^3}{192 c^4 d (b d+2 c d x)^{3/2}}+\frac{(b d+2 c d x)^{9/2}}{576 c^4 d^7}","-\frac{3 \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}{320 c^4 d^5}+\frac{3 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}{64 c^4 d^3}+\frac{\left(b^2-4 a c\right)^3}{192 c^4 d (b d+2 c d x)^{3/2}}+\frac{(b d+2 c d x)^{9/2}}{576 c^4 d^7}",1,"(b^2 - 4*a*c)^3/(192*c^4*d*(b*d + 2*c*d*x)^(3/2)) + (3*(b^2 - 4*a*c)^2*Sqrt[b*d + 2*c*d*x])/(64*c^4*d^3) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2))/(320*c^4*d^5) + (b*d + 2*c*d*x)^(9/2)/(576*c^4*d^7)","A",2,1,26,0.03846,1,"{683}"
1281,1,121,0,0.048796,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(7/2),x]","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}{64 c^4 d^5}-\frac{3 \left(b^2-4 a c\right)^2}{64 c^4 d^3 \sqrt{b d+2 c d x}}+\frac{\left(b^2-4 a c\right)^3}{320 c^4 d (b d+2 c d x)^{5/2}}+\frac{(b d+2 c d x)^{7/2}}{448 c^4 d^7}","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}{64 c^4 d^5}-\frac{3 \left(b^2-4 a c\right)^2}{64 c^4 d^3 \sqrt{b d+2 c d x}}+\frac{\left(b^2-4 a c\right)^3}{320 c^4 d (b d+2 c d x)^{5/2}}+\frac{(b d+2 c d x)^{7/2}}{448 c^4 d^7}",1,"(b^2 - 4*a*c)^3/(320*c^4*d*(b*d + 2*c*d*x)^(5/2)) - (3*(b^2 - 4*a*c)^2)/(64*c^4*d^3*Sqrt[b*d + 2*c*d*x]) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2))/(64*c^4*d^5) + (b*d + 2*c*d*x)^(7/2)/(448*c^4*d^7)","A",2,1,26,0.03846,1,"{683}"
1282,1,121,0,0.0504371,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^{9/2}} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(9/2),x]","-\frac{\left(b^2-4 a c\right)^2}{64 c^4 d^3 (b d+2 c d x)^{3/2}}-\frac{3 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}{64 c^4 d^5}+\frac{\left(b^2-4 a c\right)^3}{448 c^4 d (b d+2 c d x)^{7/2}}+\frac{(b d+2 c d x)^{5/2}}{320 c^4 d^7}","-\frac{\left(b^2-4 a c\right)^2}{64 c^4 d^3 (b d+2 c d x)^{3/2}}-\frac{3 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}{64 c^4 d^5}+\frac{\left(b^2-4 a c\right)^3}{448 c^4 d (b d+2 c d x)^{7/2}}+\frac{(b d+2 c d x)^{5/2}}{320 c^4 d^7}",1,"(b^2 - 4*a*c)^3/(448*c^4*d*(b*d + 2*c*d*x)^(7/2)) - (b^2 - 4*a*c)^2/(64*c^4*d^3*(b*d + 2*c*d*x)^(3/2)) - (3*(b^2 - 4*a*c)*Sqrt[b*d + 2*c*d*x])/(64*c^4*d^5) + (b*d + 2*c*d*x)^(5/2)/(320*c^4*d^7)","A",2,1,26,0.03846,1,"{683}"
1283,1,121,0,0.0500006,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^{11/2}} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(11/2),x]","-\frac{3 \left(b^2-4 a c\right)^2}{320 c^4 d^3 (b d+2 c d x)^{5/2}}+\frac{3 \left(b^2-4 a c\right)}{64 c^4 d^5 \sqrt{b d+2 c d x}}+\frac{\left(b^2-4 a c\right)^3}{576 c^4 d (b d+2 c d x)^{9/2}}+\frac{(b d+2 c d x)^{3/2}}{192 c^4 d^7}","-\frac{3 \left(b^2-4 a c\right)^2}{320 c^4 d^3 (b d+2 c d x)^{5/2}}+\frac{3 \left(b^2-4 a c\right)}{64 c^4 d^5 \sqrt{b d+2 c d x}}+\frac{\left(b^2-4 a c\right)^3}{576 c^4 d (b d+2 c d x)^{9/2}}+\frac{(b d+2 c d x)^{3/2}}{192 c^4 d^7}",1,"(b^2 - 4*a*c)^3/(576*c^4*d*(b*d + 2*c*d*x)^(9/2)) - (3*(b^2 - 4*a*c)^2)/(320*c^4*d^3*(b*d + 2*c*d*x)^(5/2)) + (3*(b^2 - 4*a*c))/(64*c^4*d^5*Sqrt[b*d + 2*c*d*x]) + (b*d + 2*c*d*x)^(3/2)/(192*c^4*d^7)","A",2,1,26,0.03846,1,"{683}"
1284,1,121,0,0.0533011,"\int \frac{\left(a+b x+c x^2\right)^3}{(b d+2 c d x)^{13/2}} \, dx","Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(13/2),x]","-\frac{3 \left(b^2-4 a c\right)^2}{448 c^4 d^3 (b d+2 c d x)^{7/2}}+\frac{b^2-4 a c}{64 c^4 d^5 (b d+2 c d x)^{3/2}}+\frac{\left(b^2-4 a c\right)^3}{704 c^4 d (b d+2 c d x)^{11/2}}+\frac{\sqrt{b d+2 c d x}}{64 c^4 d^7}","-\frac{3 \left(b^2-4 a c\right)^2}{448 c^4 d^3 (b d+2 c d x)^{7/2}}+\frac{b^2-4 a c}{64 c^4 d^5 (b d+2 c d x)^{3/2}}+\frac{\left(b^2-4 a c\right)^3}{704 c^4 d (b d+2 c d x)^{11/2}}+\frac{\sqrt{b d+2 c d x}}{64 c^4 d^7}",1,"(b^2 - 4*a*c)^3/(704*c^4*d*(b*d + 2*c*d*x)^(11/2)) - (3*(b^2 - 4*a*c)^2)/(448*c^4*d^3*(b*d + 2*c*d*x)^(7/2)) + (b^2 - 4*a*c)/(64*c^4*d^5*(b*d + 2*c*d*x)^(3/2)) + Sqrt[b*d + 2*c*d*x]/(64*c^4*d^7)","A",2,1,26,0.03846,1,"{683}"
1285,1,175,0,0.2146033,"\int \frac{(b d+2 c d x)^{11/2}}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2),x]","4 d^5 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}+\frac{4}{5} d^3 \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}-2 d^{11/2} \left(b^2-4 a c\right)^{9/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{11/2} \left(b^2-4 a c\right)^{9/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+\frac{4}{9} d (b d+2 c d x)^{9/2}","4 d^5 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}+\frac{4}{5} d^3 \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}-2 d^{11/2} \left(b^2-4 a c\right)^{9/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{11/2} \left(b^2-4 a c\right)^{9/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+\frac{4}{9} d (b d+2 c d x)^{9/2}",1,"4*(b^2 - 4*a*c)^2*d^5*Sqrt[b*d + 2*c*d*x] + (4*(b^2 - 4*a*c)*d^3*(b*d + 2*c*d*x)^(5/2))/5 + (4*d*(b*d + 2*c*d*x)^(9/2))/9 - 2*(b^2 - 4*a*c)^(9/4)*d^(11/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 2*(b^2 - 4*a*c)^(9/4)*d^(11/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",8,6,26,0.2308,1,"{692, 694, 329, 212, 206, 203}"
1286,1,147,0,0.1381457,"\int \frac{(b d+2 c d x)^{9/2}}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2),x]","\frac{4}{3} d^3 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}+2 d^{9/2} \left(b^2-4 a c\right)^{7/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{9/2} \left(b^2-4 a c\right)^{7/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+\frac{4}{7} d (b d+2 c d x)^{7/2}","\frac{4}{3} d^3 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}+2 d^{9/2} \left(b^2-4 a c\right)^{7/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{9/2} \left(b^2-4 a c\right)^{7/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+\frac{4}{7} d (b d+2 c d x)^{7/2}",1,"(4*(b^2 - 4*a*c)*d^3*(b*d + 2*c*d*x)^(3/2))/3 + (4*d*(b*d + 2*c*d*x)^(7/2))/7 + 2*(b^2 - 4*a*c)^(7/4)*d^(9/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 2*(b^2 - 4*a*c)^(7/4)*d^(9/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",7,6,26,0.2308,1,"{692, 694, 329, 298, 203, 206}"
1287,1,145,0,0.1205896,"\int \frac{(b d+2 c d x)^{7/2}}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2),x]","4 d^3 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}-2 d^{7/2} \left(b^2-4 a c\right)^{5/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{7/2} \left(b^2-4 a c\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+\frac{4}{5} d (b d+2 c d x)^{5/2}","4 d^3 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}-2 d^{7/2} \left(b^2-4 a c\right)^{5/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{7/2} \left(b^2-4 a c\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+\frac{4}{5} d (b d+2 c d x)^{5/2}",1,"4*(b^2 - 4*a*c)*d^3*Sqrt[b*d + 2*c*d*x] + (4*d*(b*d + 2*c*d*x)^(5/2))/5 - 2*(b^2 - 4*a*c)^(5/4)*d^(7/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 2*(b^2 - 4*a*c)^(5/4)*d^(7/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",7,6,26,0.2308,1,"{692, 694, 329, 212, 206, 203}"
1288,1,119,0,0.0956372,"\int \frac{(b d+2 c d x)^{5/2}}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2),x]","2 d^{5/2} \left(b^2-4 a c\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{5/2} \left(b^2-4 a c\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+\frac{4}{3} d (b d+2 c d x)^{3/2}","2 d^{5/2} \left(b^2-4 a c\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{5/2} \left(b^2-4 a c\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+\frac{4}{3} d (b d+2 c d x)^{3/2}",1,"(4*d*(b*d + 2*c*d*x)^(3/2))/3 + 2*(b^2 - 4*a*c)^(3/4)*d^(5/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 2*(b^2 - 4*a*c)^(3/4)*d^(5/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",6,6,26,0.2308,1,"{692, 694, 329, 298, 203, 206}"
1289,1,117,0,0.0963116,"\int \frac{(b d+2 c d x)^{3/2}}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2),x]","-2 d^{3/2} \sqrt[4]{b^2-4 a c} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{3/2} \sqrt[4]{b^2-4 a c} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+4 d \sqrt{b d+2 c d x}","-2 d^{3/2} \sqrt[4]{b^2-4 a c} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-2 d^{3/2} \sqrt[4]{b^2-4 a c} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)+4 d \sqrt{b d+2 c d x}",1,"4*d*Sqrt[b*d + 2*c*d*x] - 2*(b^2 - 4*a*c)^(1/4)*d^(3/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 2*(b^2 - 4*a*c)^(1/4)*d^(3/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",6,6,26,0.2308,1,"{692, 694, 329, 212, 206, 203}"
1290,1,101,0,0.0722369,"\int \frac{\sqrt{b d+2 c d x}}{a+b x+c x^2} \, dx","Int[Sqrt[b*d + 2*c*d*x]/(a + b*x + c*x^2),x]","\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}","\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}",1,"(2*Sqrt[d]*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(1/4) - (2*Sqrt[d]*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(1/4)","A",5,5,26,0.1923,1,"{694, 329, 298, 203, 206}"
1291,1,101,0,0.0774185,"\int \frac{1}{\sqrt{b d+2 c d x} \left(a+b x+c x^2\right)} \, dx","Int[1/(Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{3/4}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{3/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{3/4}}",1,"(-2*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(3/4)*Sqrt[d]) - (2*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(3/4)*Sqrt[d])","A",5,5,26,0.1923,1,"{694, 329, 212, 206, 203}"
1292,1,129,0,0.1084929,"\int \frac{1}{(b d+2 c d x)^{3/2} \left(a+b x+c x^2\right)} \, dx","Int[1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{5/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{5/4}}+\frac{4}{d \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{5/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{5/4}}+\frac{4}{d \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}",1,"4/((b^2 - 4*a*c)*d*Sqrt[b*d + 2*c*d*x]) + (2*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(5/4)*d^(3/2)) - (2*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(5/4)*d^(3/2))","A",6,6,26,0.2308,1,"{693, 694, 329, 298, 203, 206}"
1293,1,131,0,0.1072075,"\int \frac{1}{(b d+2 c d x)^{5/2} \left(a+b x+c x^2\right)} \, dx","Int[1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{7/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{7/4}}+\frac{4}{3 d \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{7/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{7/4}}+\frac{4}{3 d \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}",1,"4/(3*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)) - (2*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(7/4)*d^(5/2)) - (2*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(7/4)*d^(5/2))","A",6,6,26,0.2308,1,"{693, 694, 329, 212, 206, 203}"
1294,1,159,0,0.1315019,"\int \frac{1}{(b d+2 c d x)^{7/2} \left(a+b x+c x^2\right)} \, dx","Int[1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)),x]","\frac{4}{d^3 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{9/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{9/4}}+\frac{4}{5 d \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}","\frac{4}{d^3 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{9/4}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{9/4}}+\frac{4}{5 d \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}",1,"4/(5*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)) + 4/((b^2 - 4*a*c)^2*d^3*Sqrt[b*d + 2*c*d*x]) + (2*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(9/4)*d^(7/2)) - (2*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(9/4)*d^(7/2))","A",7,6,26,0.2308,1,"{693, 694, 329, 298, 203, 206}"
1295,1,210,0,0.1799783,"\int \frac{(b d+2 c d x)^{15/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^2,x]","52 c d^7 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}+\frac{52}{5} c d^5 \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}-26 c d^{15/2} \left(b^2-4 a c\right)^{9/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-26 c d^{15/2} \left(b^2-4 a c\right)^{9/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{13/2}}{a+b x+c x^2}+\frac{52}{9} c d^3 (b d+2 c d x)^{9/2}","52 c d^7 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}+\frac{52}{5} c d^5 \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}-26 c d^{15/2} \left(b^2-4 a c\right)^{9/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-26 c d^{15/2} \left(b^2-4 a c\right)^{9/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{13/2}}{a+b x+c x^2}+\frac{52}{9} c d^3 (b d+2 c d x)^{9/2}",1,"52*c*(b^2 - 4*a*c)^2*d^7*Sqrt[b*d + 2*c*d*x] + (52*c*(b^2 - 4*a*c)*d^5*(b*d + 2*c*d*x)^(5/2))/5 + (52*c*d^3*(b*d + 2*c*d*x)^(9/2))/9 - (d*(b*d + 2*c*d*x)^(13/2))/(a + b*x + c*x^2) - 26*c*(b^2 - 4*a*c)^(9/4)*d^(15/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 26*c*(b^2 - 4*a*c)^(9/4)*d^(15/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",9,7,26,0.2692,1,"{686, 692, 694, 329, 212, 206, 203}"
1296,1,181,0,0.1596128,"\int \frac{(b d+2 c d x)^{13/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^2,x]","\frac{44}{3} c d^5 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}+22 c d^{13/2} \left(b^2-4 a c\right)^{7/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-22 c d^{13/2} \left(b^2-4 a c\right)^{7/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{11/2}}{a+b x+c x^2}+\frac{44}{7} c d^3 (b d+2 c d x)^{7/2}","\frac{44}{3} c d^5 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}+22 c d^{13/2} \left(b^2-4 a c\right)^{7/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-22 c d^{13/2} \left(b^2-4 a c\right)^{7/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{11/2}}{a+b x+c x^2}+\frac{44}{7} c d^3 (b d+2 c d x)^{7/2}",1,"(44*c*(b^2 - 4*a*c)*d^5*(b*d + 2*c*d*x)^(3/2))/3 + (44*c*d^3*(b*d + 2*c*d*x)^(7/2))/7 - (d*(b*d + 2*c*d*x)^(11/2))/(a + b*x + c*x^2) + 22*c*(b^2 - 4*a*c)^(7/4)*d^(13/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 22*c*(b^2 - 4*a*c)^(7/4)*d^(13/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",8,7,26,0.2692,1,"{686, 692, 694, 329, 298, 203, 206}"
1297,1,179,0,0.1504748,"\int \frac{(b d+2 c d x)^{11/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^2,x]","36 c d^5 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}-18 c d^{11/2} \left(b^2-4 a c\right)^{5/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-18 c d^{11/2} \left(b^2-4 a c\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{9/2}}{a+b x+c x^2}+\frac{36}{5} c d^3 (b d+2 c d x)^{5/2}","36 c d^5 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}-18 c d^{11/2} \left(b^2-4 a c\right)^{5/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-18 c d^{11/2} \left(b^2-4 a c\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{9/2}}{a+b x+c x^2}+\frac{36}{5} c d^3 (b d+2 c d x)^{5/2}",1,"36*c*(b^2 - 4*a*c)*d^5*Sqrt[b*d + 2*c*d*x] + (36*c*d^3*(b*d + 2*c*d*x)^(5/2))/5 - (d*(b*d + 2*c*d*x)^(9/2))/(a + b*x + c*x^2) - 18*c*(b^2 - 4*a*c)^(5/4)*d^(11/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 18*c*(b^2 - 4*a*c)^(5/4)*d^(11/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",8,7,26,0.2692,1,"{686, 692, 694, 329, 212, 206, 203}"
1298,1,152,0,0.1208096,"\int \frac{(b d+2 c d x)^{9/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^2,x]","14 c d^{9/2} \left(b^2-4 a c\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-14 c d^{9/2} \left(b^2-4 a c\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{7/2}}{a+b x+c x^2}+\frac{28}{3} c d^3 (b d+2 c d x)^{3/2}","14 c d^{9/2} \left(b^2-4 a c\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-14 c d^{9/2} \left(b^2-4 a c\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{7/2}}{a+b x+c x^2}+\frac{28}{3} c d^3 (b d+2 c d x)^{3/2}",1,"(28*c*d^3*(b*d + 2*c*d*x)^(3/2))/3 - (d*(b*d + 2*c*d*x)^(7/2))/(a + b*x + c*x^2) + 14*c*(b^2 - 4*a*c)^(3/4)*d^(9/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 14*c*(b^2 - 4*a*c)^(3/4)*d^(9/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",7,7,26,0.2692,1,"{686, 692, 694, 329, 298, 203, 206}"
1299,1,150,0,0.1196508,"\int \frac{(b d+2 c d x)^{7/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^2,x]","-10 c d^{7/2} \sqrt[4]{b^2-4 a c} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-10 c d^{7/2} \sqrt[4]{b^2-4 a c} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{5/2}}{a+b x+c x^2}+20 c d^3 \sqrt{b d+2 c d x}","-10 c d^{7/2} \sqrt[4]{b^2-4 a c} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-10 c d^{7/2} \sqrt[4]{b^2-4 a c} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{d (b d+2 c d x)^{5/2}}{a+b x+c x^2}+20 c d^3 \sqrt{b d+2 c d x}",1,"20*c*d^3*Sqrt[b*d + 2*c*d*x] - (d*(b*d + 2*c*d*x)^(5/2))/(a + b*x + c*x^2) - 10*c*(b^2 - 4*a*c)^(1/4)*d^(7/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 10*c*(b^2 - 4*a*c)^(1/4)*d^(7/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",7,7,26,0.2692,1,"{686, 692, 694, 329, 212, 206, 203}"
1300,1,131,0,0.0988734,"\int \frac{(b d+2 c d x)^{5/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^2,x]","\frac{6 c d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{6 c d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{d (b d+2 c d x)^{3/2}}{a+b x+c x^2}","\frac{6 c d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{6 c d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{d (b d+2 c d x)^{3/2}}{a+b x+c x^2}",1,"-((d*(b*d + 2*c*d*x)^(3/2))/(a + b*x + c*x^2)) + (6*c*d^(5/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(1/4) - (6*c*d^(5/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(1/4)","A",6,6,26,0.2308,1,"{686, 694, 329, 298, 203, 206}"
1301,1,131,0,0.0993918,"\int \frac{(b d+2 c d x)^{3/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^2,x]","-\frac{2 c d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/4}}-\frac{2 c d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/4}}-\frac{d \sqrt{b d+2 c d x}}{a+b x+c x^2}","-\frac{2 c d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/4}}-\frac{2 c d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/4}}-\frac{d \sqrt{b d+2 c d x}}{a+b x+c x^2}",1,"-((d*Sqrt[b*d + 2*c*d*x])/(a + b*x + c*x^2)) - (2*c*d^(3/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(3/4) - (2*c*d^(3/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(3/4)","A",6,6,26,0.2308,1,"{686, 694, 329, 212, 206, 203}"
1302,1,143,0,0.097171,"\int \frac{\sqrt{b d+2 c d x}}{\left(a+b x+c x^2\right)^2} \, dx","Int[Sqrt[b*d + 2*c*d*x]/(a + b*x + c*x^2)^2,x]","-\frac{(b d+2 c d x)^{3/2}}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{2 c \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/4}}+\frac{2 c \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/4}}","-\frac{(b d+2 c d x)^{3/2}}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{2 c \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/4}}+\frac{2 c \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/4}}",1,"-((b*d + 2*c*d*x)^(3/2)/((b^2 - 4*a*c)*d*(a + b*x + c*x^2))) - (2*c*Sqrt[d]*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(5/4) + (2*c*Sqrt[d]*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(5/4)","A",6,6,26,0.2308,1,"{687, 694, 329, 298, 203, 206}"
1303,1,143,0,0.1024494,"\int \frac{1}{\sqrt{b d+2 c d x} \left(a+b x+c x^2\right)^2} \, dx","Int[1/(Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^2),x]","-\frac{\sqrt{b d+2 c d x}}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{6 c \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{7/4}}+\frac{6 c \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{7/4}}","-\frac{\sqrt{b d+2 c d x}}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{6 c \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{7/4}}+\frac{6 c \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{7/4}}",1,"-(Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)*d*(a + b*x + c*x^2))) + (6*c*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(7/4)*Sqrt[d]) + (6*c*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(7/4)*Sqrt[d])","A",6,6,26,0.2308,1,"{687, 694, 329, 212, 206, 203}"
1304,1,172,0,0.1231087,"\int \frac{1}{(b d+2 c d x)^{3/2} \left(a+b x+c x^2\right)^2} \, dx","Int[1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^2),x]","-\frac{10 c \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{9/4}}+\frac{10 c \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{9/4}}-\frac{1}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right) \sqrt{b d+2 c d x}}-\frac{20 c}{d \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}","-\frac{10 c \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{9/4}}+\frac{10 c \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{9/4}}-\frac{1}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right) \sqrt{b d+2 c d x}}-\frac{20 c}{d \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}",1,"(-20*c)/((b^2 - 4*a*c)^2*d*Sqrt[b*d + 2*c*d*x]) - 1/((b^2 - 4*a*c)*d*Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)) - (10*c*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(9/4)*d^(3/2)) + (10*c*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(9/4)*d^(3/2))","A",7,7,26,0.2692,1,"{687, 693, 694, 329, 298, 203, 206}"
1305,1,174,0,0.1419515,"\int \frac{1}{(b d+2 c d x)^{5/2} \left(a+b x+c x^2\right)^2} \, dx","Int[1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^2),x]","\frac{14 c \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{11/4}}+\frac{14 c \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{11/4}}-\frac{1}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right) (b d+2 c d x)^{3/2}}-\frac{28 c}{3 d \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}","\frac{14 c \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{11/4}}+\frac{14 c \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{11/4}}-\frac{1}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right) (b d+2 c d x)^{3/2}}-\frac{28 c}{3 d \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}",1,"(-28*c)/(3*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2)) - 1/((b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)) + (14*c*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(11/4)*d^(5/2)) + (14*c*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(11/4)*d^(5/2))","A",7,7,26,0.2692,1,"{687, 693, 694, 329, 212, 206, 203}"
1306,1,203,0,0.1718607,"\int \frac{1}{(b d+2 c d x)^{7/2} \left(a+b x+c x^2\right)^2} \, dx","Int[1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^2),x]","-\frac{36 c}{d^3 \left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}-\frac{18 c \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{13/4}}+\frac{18 c \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{13/4}}-\frac{1}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right) (b d+2 c d x)^{5/2}}-\frac{36 c}{5 d \left(b^2-4 a c\right)^2 (b d+2 c d x)^{5/2}}","-\frac{36 c}{d^3 \left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}-\frac{18 c \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{13/4}}+\frac{18 c \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{13/4}}-\frac{1}{d \left(b^2-4 a c\right) \left(a+b x+c x^2\right) (b d+2 c d x)^{5/2}}-\frac{36 c}{5 d \left(b^2-4 a c\right)^2 (b d+2 c d x)^{5/2}}",1,"(-36*c)/(5*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(5/2)) - (36*c)/((b^2 - 4*a*c)^3*d^3*Sqrt[b*d + 2*c*d*x]) - 1/((b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)) - (18*c*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(13/4)*d^(7/2)) + (18*c*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(13/4)*d^(7/2))","A",8,7,26,0.2692,1,"{687, 693, 694, 329, 298, 203, 206}"
1307,1,222,0,0.1913604,"\int \frac{(b d+2 c d x)^{17/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^(17/2)/(a + b*x + c*x^2)^3,x]","110 c^2 d^7 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}+165 c^2 d^{17/2} \left(b^2-4 a c\right)^{7/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-165 c^2 d^{17/2} \left(b^2-4 a c\right)^{7/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{15 c d^3 (b d+2 c d x)^{11/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{15/2}}{2 \left(a+b x+c x^2\right)^2}+\frac{330}{7} c^2 d^5 (b d+2 c d x)^{7/2}","110 c^2 d^7 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}+165 c^2 d^{17/2} \left(b^2-4 a c\right)^{7/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-165 c^2 d^{17/2} \left(b^2-4 a c\right)^{7/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{15 c d^3 (b d+2 c d x)^{11/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{15/2}}{2 \left(a+b x+c x^2\right)^2}+\frac{330}{7} c^2 d^5 (b d+2 c d x)^{7/2}",1,"110*c^2*(b^2 - 4*a*c)*d^7*(b*d + 2*c*d*x)^(3/2) + (330*c^2*d^5*(b*d + 2*c*d*x)^(7/2))/7 - (d*(b*d + 2*c*d*x)^(15/2))/(2*(a + b*x + c*x^2)^2) - (15*c*d^3*(b*d + 2*c*d*x)^(11/2))/(2*(a + b*x + c*x^2)) + 165*c^2*(b^2 - 4*a*c)^(7/4)*d^(17/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 165*c^2*(b^2 - 4*a*c)^(7/4)*d^(17/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",9,7,26,0.2692,1,"{686, 692, 694, 329, 298, 203, 206}"
1308,1,222,0,0.1819196,"\int \frac{(b d+2 c d x)^{15/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^3,x]","234 c^2 d^7 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}-117 c^2 d^{15/2} \left(b^2-4 a c\right)^{5/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-117 c^2 d^{15/2} \left(b^2-4 a c\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{13 c d^3 (b d+2 c d x)^{9/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{13/2}}{2 \left(a+b x+c x^2\right)^2}+\frac{234}{5} c^2 d^5 (b d+2 c d x)^{5/2}","234 c^2 d^7 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}-117 c^2 d^{15/2} \left(b^2-4 a c\right)^{5/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-117 c^2 d^{15/2} \left(b^2-4 a c\right)^{5/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{13 c d^3 (b d+2 c d x)^{9/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{13/2}}{2 \left(a+b x+c x^2\right)^2}+\frac{234}{5} c^2 d^5 (b d+2 c d x)^{5/2}",1,"234*c^2*(b^2 - 4*a*c)*d^7*Sqrt[b*d + 2*c*d*x] + (234*c^2*d^5*(b*d + 2*c*d*x)^(5/2))/5 - (d*(b*d + 2*c*d*x)^(13/2))/(2*(a + b*x + c*x^2)^2) - (13*c*d^3*(b*d + 2*c*d*x)^(9/2))/(2*(a + b*x + c*x^2)) - 117*c^2*(b^2 - 4*a*c)^(5/4)*d^(15/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 117*c^2*(b^2 - 4*a*c)^(5/4)*d^(15/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",9,7,26,0.2692,1,"{686, 692, 694, 329, 212, 206, 203}"
1309,1,193,0,0.1480142,"\int \frac{(b d+2 c d x)^{13/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^3,x]","77 c^2 d^{13/2} \left(b^2-4 a c\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-77 c^2 d^{13/2} \left(b^2-4 a c\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{11 c d^3 (b d+2 c d x)^{7/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{11/2}}{2 \left(a+b x+c x^2\right)^2}+\frac{154}{3} c^2 d^5 (b d+2 c d x)^{3/2}","77 c^2 d^{13/2} \left(b^2-4 a c\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-77 c^2 d^{13/2} \left(b^2-4 a c\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{11 c d^3 (b d+2 c d x)^{7/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{11/2}}{2 \left(a+b x+c x^2\right)^2}+\frac{154}{3} c^2 d^5 (b d+2 c d x)^{3/2}",1,"(154*c^2*d^5*(b*d + 2*c*d*x)^(3/2))/3 - (d*(b*d + 2*c*d*x)^(11/2))/(2*(a + b*x + c*x^2)^2) - (11*c*d^3*(b*d + 2*c*d*x)^(7/2))/(2*(a + b*x + c*x^2)) + 77*c^2*(b^2 - 4*a*c)^(3/4)*d^(13/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 77*c^2*(b^2 - 4*a*c)^(3/4)*d^(13/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",8,7,26,0.2692,1,"{686, 692, 694, 329, 298, 203, 206}"
1310,1,191,0,0.1477676,"\int \frac{(b d+2 c d x)^{11/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^3,x]","-45 c^2 d^{11/2} \sqrt[4]{b^2-4 a c} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-45 c^2 d^{11/2} \sqrt[4]{b^2-4 a c} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{9 c d^3 (b d+2 c d x)^{5/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{9/2}}{2 \left(a+b x+c x^2\right)^2}+90 c^2 d^5 \sqrt{b d+2 c d x}","-45 c^2 d^{11/2} \sqrt[4]{b^2-4 a c} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-45 c^2 d^{11/2} \sqrt[4]{b^2-4 a c} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)-\frac{9 c d^3 (b d+2 c d x)^{5/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{9/2}}{2 \left(a+b x+c x^2\right)^2}+90 c^2 d^5 \sqrt{b d+2 c d x}",1,"90*c^2*d^5*Sqrt[b*d + 2*c*d*x] - (d*(b*d + 2*c*d*x)^(9/2))/(2*(a + b*x + c*x^2)^2) - (9*c*d^3*(b*d + 2*c*d*x)^(5/2))/(2*(a + b*x + c*x^2)) - 45*c^2*(b^2 - 4*a*c)^(1/4)*d^(11/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])] - 45*c^2*(b^2 - 4*a*c)^(1/4)*d^(11/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])]","A",8,7,26,0.2692,1,"{686, 692, 694, 329, 212, 206, 203}"
1311,1,170,0,0.1233748,"\int \frac{(b d+2 c d x)^{9/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^3,x]","\frac{21 c^2 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{21 c^2 d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{7 c d^3 (b d+2 c d x)^{3/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{7/2}}{2 \left(a+b x+c x^2\right)^2}","\frac{21 c^2 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{21 c^2 d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt[4]{b^2-4 a c}}-\frac{7 c d^3 (b d+2 c d x)^{3/2}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{7/2}}{2 \left(a+b x+c x^2\right)^2}",1,"-(d*(b*d + 2*c*d*x)^(7/2))/(2*(a + b*x + c*x^2)^2) - (7*c*d^3*(b*d + 2*c*d*x)^(3/2))/(2*(a + b*x + c*x^2)) + (21*c^2*d^(9/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(1/4) - (21*c^2*d^(9/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(1/4)","A",7,6,26,0.2308,1,"{686, 694, 329, 298, 203, 206}"
1312,1,170,0,0.1244669,"\int \frac{(b d+2 c d x)^{7/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^3,x]","-\frac{5 c^2 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/4}}-\frac{5 c^2 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/4}}-\frac{5 c d^3 \sqrt{b d+2 c d x}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{5/2}}{2 \left(a+b x+c x^2\right)^2}","-\frac{5 c^2 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/4}}-\frac{5 c^2 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/4}}-\frac{5 c d^3 \sqrt{b d+2 c d x}}{2 \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{5/2}}{2 \left(a+b x+c x^2\right)^2}",1,"-(d*(b*d + 2*c*d*x)^(5/2))/(2*(a + b*x + c*x^2)^2) - (5*c*d^3*Sqrt[b*d + 2*c*d*x])/(2*(a + b*x + c*x^2)) - (5*c^2*d^(7/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(3/4) - (5*c^2*d^(7/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(3/4)","A",7,6,26,0.2308,1,"{686, 694, 329, 212, 206, 203}"
1313,1,178,0,0.1281106,"\int \frac{(b d+2 c d x)^{5/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^3,x]","-\frac{3 c^2 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/4}}+\frac{3 c^2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/4}}-\frac{3 c d (b d+2 c d x)^{3/2}}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{3/2}}{2 \left(a+b x+c x^2\right)^2}","-\frac{3 c^2 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/4}}+\frac{3 c^2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/4}}-\frac{3 c d (b d+2 c d x)^{3/2}}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{d (b d+2 c d x)^{3/2}}{2 \left(a+b x+c x^2\right)^2}",1,"-(d*(b*d + 2*c*d*x)^(3/2))/(2*(a + b*x + c*x^2)^2) - (3*c*d*(b*d + 2*c*d*x)^(3/2))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)) - (3*c^2*d^(5/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(5/4) + (3*c^2*d^(5/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(5/4)","A",7,7,26,0.2692,1,"{686, 687, 694, 329, 298, 203, 206}"
1314,1,178,0,0.1288633,"\int \frac{(b d+2 c d x)^{3/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^3,x]","\frac{3 c^2 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/4}}+\frac{3 c^2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/4}}-\frac{c d \sqrt{b d+2 c d x}}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{d \sqrt{b d+2 c d x}}{2 \left(a+b x+c x^2\right)^2}","\frac{3 c^2 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/4}}+\frac{3 c^2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/4}}-\frac{c d \sqrt{b d+2 c d x}}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{d \sqrt{b d+2 c d x}}{2 \left(a+b x+c x^2\right)^2}",1,"-(d*Sqrt[b*d + 2*c*d*x])/(2*(a + b*x + c*x^2)^2) - (c*d*Sqrt[b*d + 2*c*d*x])/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (3*c^2*d^(3/2)*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(7/4) + (3*c^2*d^(3/2)*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(7/4)","A",7,7,26,0.2692,1,"{686, 687, 694, 329, 212, 206, 203}"
1315,1,192,0,0.1296883,"\int \frac{\sqrt{b d+2 c d x}}{\left(a+b x+c x^2\right)^3} \, dx","Int[Sqrt[b*d + 2*c*d*x]/(a + b*x + c*x^2)^3,x]","\frac{5 c^2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/4}}-\frac{5 c^2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/4}}+\frac{5 c (b d+2 c d x)^{3/2}}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{(b d+2 c d x)^{3/2}}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{5 c^2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/4}}-\frac{5 c^2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/4}}+\frac{5 c (b d+2 c d x)^{3/2}}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{(b d+2 c d x)^{3/2}}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-(b*d + 2*c*d*x)^(3/2)/(2*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^2) + (5*c*(b*d + 2*c*d*x)^(3/2))/(2*(b^2 - 4*a*c)^2*d*(a + b*x + c*x^2)) + (5*c^2*Sqrt[d]*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(9/4) - (5*c^2*Sqrt[d]*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/(b^2 - 4*a*c)^(9/4)","A",7,6,26,0.2308,1,"{687, 694, 329, 298, 203, 206}"
1316,1,192,0,0.1350952,"\int \frac{1}{\sqrt{b d+2 c d x} \left(a+b x+c x^2\right)^3} \, dx","Int[1/(Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^3),x]","-\frac{21 c^2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{11/4}}-\frac{21 c^2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{11/4}}+\frac{7 c \sqrt{b d+2 c d x}}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{\sqrt{b d+2 c d x}}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{21 c^2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{11/4}}-\frac{21 c^2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{\sqrt{d} \left(b^2-4 a c\right)^{11/4}}+\frac{7 c \sqrt{b d+2 c d x}}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{\sqrt{b d+2 c d x}}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-Sqrt[b*d + 2*c*d*x]/(2*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^2) + (7*c*Sqrt[b*d + 2*c*d*x])/(2*(b^2 - 4*a*c)^2*d*(a + b*x + c*x^2)) - (21*c^2*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(11/4)*Sqrt[d]) - (21*c^2*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(11/4)*Sqrt[d])","A",7,6,26,0.2308,1,"{687, 694, 329, 212, 206, 203}"
1317,1,223,0,0.1682617,"\int \frac{1}{(b d+2 c d x)^{3/2} \left(a+b x+c x^2\right)^3} \, dx","Int[1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^3),x]","\frac{45 c^2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{13/4}}-\frac{45 c^2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{13/4}}+\frac{90 c^2}{d \left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}+\frac{9 c}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) \sqrt{b d+2 c d x}}-\frac{1}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \sqrt{b d+2 c d x}}","\frac{45 c^2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{13/4}}-\frac{45 c^2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{3/2} \left(b^2-4 a c\right)^{13/4}}+\frac{90 c^2}{d \left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}+\frac{9 c}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) \sqrt{b d+2 c d x}}-\frac{1}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \sqrt{b d+2 c d x}}",1,"(90*c^2)/((b^2 - 4*a*c)^3*d*Sqrt[b*d + 2*c*d*x]) - 1/(2*(b^2 - 4*a*c)*d*Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^2) + (9*c)/(2*(b^2 - 4*a*c)^2*d*Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)) + (45*c^2*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(13/4)*d^(3/2)) - (45*c^2*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(13/4)*d^(3/2))","A",8,7,26,0.2692,1,"{687, 693, 694, 329, 298, 203, 206}"
1318,1,225,0,0.1911976,"\int \frac{1}{(b d+2 c d x)^{5/2} \left(a+b x+c x^2\right)^3} \, dx","Int[1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^3),x]","-\frac{77 c^2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{15/4}}-\frac{77 c^2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{15/4}}+\frac{154 c^2}{3 d \left(b^2-4 a c\right)^3 (b d+2 c d x)^{3/2}}+\frac{11 c}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) (b d+2 c d x)^{3/2}}-\frac{1}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 (b d+2 c d x)^{3/2}}","-\frac{77 c^2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{15/4}}-\frac{77 c^2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{5/2} \left(b^2-4 a c\right)^{15/4}}+\frac{154 c^2}{3 d \left(b^2-4 a c\right)^3 (b d+2 c d x)^{3/2}}+\frac{11 c}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) (b d+2 c d x)^{3/2}}-\frac{1}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 (b d+2 c d x)^{3/2}}",1,"(154*c^2)/(3*(b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(3/2)) - 1/(2*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^2) + (11*c)/(2*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)) - (77*c^2*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(15/4)*d^(5/2)) - (77*c^2*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(15/4)*d^(5/2))","A",8,7,26,0.2692,1,"{687, 693, 694, 329, 212, 206, 203}"
1319,1,256,0,0.2278091,"\int \frac{1}{(b d+2 c d x)^{7/2} \left(a+b x+c x^2\right)^3} \, dx","Int[1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^3),x]","\frac{234 c^2}{d^3 \left(b^2-4 a c\right)^4 \sqrt{b d+2 c d x}}+\frac{117 c^2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{17/4}}-\frac{117 c^2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{17/4}}+\frac{234 c^2}{5 d \left(b^2-4 a c\right)^3 (b d+2 c d x)^{5/2}}+\frac{13 c}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) (b d+2 c d x)^{5/2}}-\frac{1}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 (b d+2 c d x)^{5/2}}","\frac{234 c^2}{d^3 \left(b^2-4 a c\right)^4 \sqrt{b d+2 c d x}}+\frac{117 c^2 \tan ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{17/4}}-\frac{117 c^2 \tanh ^{-1}\left(\frac{\sqrt{d (b+2 c x)}}{\sqrt{d} \sqrt[4]{b^2-4 a c}}\right)}{d^{7/2} \left(b^2-4 a c\right)^{17/4}}+\frac{234 c^2}{5 d \left(b^2-4 a c\right)^3 (b d+2 c d x)^{5/2}}+\frac{13 c}{2 d \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) (b d+2 c d x)^{5/2}}-\frac{1}{2 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 (b d+2 c d x)^{5/2}}",1,"(234*c^2)/(5*(b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(5/2)) + (234*c^2)/((b^2 - 4*a*c)^4*d^3*Sqrt[b*d + 2*c*d*x]) - 1/(2*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^2) + (13*c)/(2*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)) + (117*c^2*ArcTan[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(17/4)*d^(7/2)) - (117*c^2*ArcTanh[Sqrt[d*(b + 2*c*x)]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])])/((b^2 - 4*a*c)^(17/4)*d^(7/2))","A",9,7,26,0.2692,1,"{687, 693, 694, 329, 298, 203, 206}"
1320,1,183,0,0.1713402,"\int \frac{(1+2 x)^{7/2}}{1+x+x^2} \, dx","Int[(1 + 2*x)^(7/2)/(1 + x + x^2),x]","\frac{4}{5} (2 x+1)^{5/2}-12 \sqrt{2 x+1}-\frac{3 \sqrt[4]{3} \log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}+\frac{3 \sqrt[4]{3} \log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}-3 \sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)+3 \sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)","\frac{4}{5} (2 x+1)^{5/2}-12 \sqrt{2 x+1}-\frac{3 \sqrt[4]{3} \log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}+\frac{3 \sqrt[4]{3} \log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}-3 \sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)+3 \sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)",1,"-12*Sqrt[1 + 2*x] + (4*(1 + 2*x)^(5/2))/5 - 3*Sqrt[2]*3^(1/4)*ArcTan[1 - (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)] + 3*Sqrt[2]*3^(1/4)*ArcTan[1 + (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)] - (3*3^(1/4)*Log[1 + Sqrt[3] + 2*x - Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]])/Sqrt[2] + (3*3^(1/4)*Log[1 + Sqrt[3] + 2*x + Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]])/Sqrt[2]","A",13,9,18,0.5000,1,"{692, 694, 329, 211, 1165, 628, 1162, 617, 204}"
1321,1,170,0,0.1369143,"\int \frac{(1+2 x)^{5/2}}{1+x+x^2} \, dx","Int[(1 + 2*x)^(5/2)/(1 + x + x^2),x]","\frac{4}{3} (2 x+1)^{3/2}-\frac{3^{3/4} \log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}+\frac{3^{3/4} \log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}+\sqrt{2} 3^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)-\sqrt{2} 3^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)","\frac{4}{3} (2 x+1)^{3/2}-\frac{3^{3/4} \log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}+\frac{3^{3/4} \log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}+\sqrt{2} 3^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)-\sqrt{2} 3^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)",1,"(4*(1 + 2*x)^(3/2))/3 + Sqrt[2]*3^(3/4)*ArcTan[1 - (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)] - Sqrt[2]*3^(3/4)*ArcTan[1 + (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)] - (3^(3/4)*Log[1 + Sqrt[3] + 2*x - Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]])/Sqrt[2] + (3^(3/4)*Log[1 + Sqrt[3] + 2*x + Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]])/Sqrt[2]","A",12,9,18,0.5000,1,"{692, 694, 329, 297, 1162, 617, 204, 1165, 628}"
1322,1,168,0,0.1351548,"\int \frac{(1+2 x)^{3/2}}{1+x+x^2} \, dx","Int[(1 + 2*x)^(3/2)/(1 + x + x^2),x]","4 \sqrt{2 x+1}+\frac{\sqrt[4]{3} \log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}-\frac{\sqrt[4]{3} \log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}+\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)-\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)","4 \sqrt{2 x+1}+\frac{\sqrt[4]{3} \log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}-\frac{\sqrt[4]{3} \log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2}}+\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)-\sqrt{2} \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)",1,"4*Sqrt[1 + 2*x] + Sqrt[2]*3^(1/4)*ArcTan[1 - (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)] - Sqrt[2]*3^(1/4)*ArcTan[1 + (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)] + (3^(1/4)*Log[1 + Sqrt[3] + 2*x - Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]])/Sqrt[2] - (3^(1/4)*Log[1 + Sqrt[3] + 2*x + Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]])/Sqrt[2]","A",12,9,18,0.5000,1,"{692, 694, 329, 211, 1165, 628, 1162, 617, 204}"
1323,1,157,0,0.1205142,"\int \frac{\sqrt{1+2 x}}{1+x+x^2} \, dx","Int[Sqrt[1 + 2*x]/(1 + x + x^2),x]","\frac{\log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2} \sqrt[4]{3}}-\frac{\log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2} \sqrt[4]{3}}-\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)}{\sqrt[4]{3}}+\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)}{\sqrt[4]{3}}","\frac{\log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2} \sqrt[4]{3}}-\frac{\log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2} \sqrt[4]{3}}-\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)}{\sqrt[4]{3}}+\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)}{\sqrt[4]{3}}",1,"-((Sqrt[2]*ArcTan[1 - (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)])/3^(1/4)) + (Sqrt[2]*ArcTan[1 + (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)])/3^(1/4) + Log[1 + Sqrt[3] + 2*x - Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]]/(Sqrt[2]*3^(1/4)) - Log[1 + Sqrt[3] + 2*x + Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]]/(Sqrt[2]*3^(1/4))","A",11,8,18,0.4444,1,"{694, 329, 297, 1162, 617, 204, 1165, 628}"
1324,1,157,0,0.119428,"\int \frac{1}{\sqrt{1+2 x} \left(1+x+x^2\right)} \, dx","Int[1/(Sqrt[1 + 2*x]*(1 + x + x^2)),x]","-\frac{\log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2} 3^{3/4}}+\frac{\log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2} 3^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)}{3^{3/4}}+\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)}{3^{3/4}}","-\frac{\log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2} 3^{3/4}}+\frac{\log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{\sqrt{2} 3^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)}{3^{3/4}}+\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)}{3^{3/4}}",1,"-((Sqrt[2]*ArcTan[1 - (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)])/3^(3/4)) + (Sqrt[2]*ArcTan[1 + (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)])/3^(3/4) - Log[1 + Sqrt[3] + 2*x - Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]]/(Sqrt[2]*3^(3/4)) + Log[1 + Sqrt[3] + 2*x + Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]]/(Sqrt[2]*3^(3/4))","A",11,8,18,0.4444,1,"{694, 329, 211, 1165, 628, 1162, 617, 204}"
1325,1,180,0,0.1392299,"\int \frac{1}{(1+2 x)^{3/2} \left(1+x+x^2\right)} \, dx","Int[1/((1 + 2*x)^(3/2)*(1 + x + x^2)),x]","-\frac{4}{3 \sqrt{2 x+1}}-\frac{\log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{3 \sqrt{2} \sqrt[4]{3}}+\frac{\log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{3 \sqrt{2} \sqrt[4]{3}}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)}{3 \sqrt[4]{3}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)}{3 \sqrt[4]{3}}","-\frac{4}{3 \sqrt{2 x+1}}-\frac{\log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{3 \sqrt{2} \sqrt[4]{3}}+\frac{\log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{3 \sqrt{2} \sqrt[4]{3}}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)}{3 \sqrt[4]{3}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)}{3 \sqrt[4]{3}}",1,"-4/(3*Sqrt[1 + 2*x]) + (Sqrt[2]*ArcTan[1 - (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)])/(3*3^(1/4)) - (Sqrt[2]*ArcTan[1 + (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)])/(3*3^(1/4)) - Log[1 + Sqrt[3] + 2*x - Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]]/(3*Sqrt[2]*3^(1/4)) + Log[1 + Sqrt[3] + 2*x + Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]]/(3*Sqrt[2]*3^(1/4))","A",12,9,18,0.5000,1,"{693, 694, 329, 297, 1162, 617, 204, 1165, 628}"
1326,1,180,0,0.1327901,"\int \frac{1}{(1+2 x)^{5/2} \left(1+x+x^2\right)} \, dx","Int[1/((1 + 2*x)^(5/2)*(1 + x + x^2)),x]","-\frac{4}{9 (2 x+1)^{3/2}}+\frac{\log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{3 \sqrt{2} 3^{3/4}}-\frac{\log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{3 \sqrt{2} 3^{3/4}}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)}{3\ 3^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)}{3\ 3^{3/4}}","-\frac{4}{9 (2 x+1)^{3/2}}+\frac{\log \left(2 x-\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{3 \sqrt{2} 3^{3/4}}-\frac{\log \left(2 x+\sqrt{2} \sqrt[4]{3} \sqrt{2 x+1}+\sqrt{3}+1\right)}{3 \sqrt{2} 3^{3/4}}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}\right)}{3\ 3^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{2 x+1}}{\sqrt[4]{3}}+1\right)}{3\ 3^{3/4}}",1,"-4/(9*(1 + 2*x)^(3/2)) + (Sqrt[2]*ArcTan[1 - (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)])/(3*3^(3/4)) - (Sqrt[2]*ArcTan[1 + (Sqrt[2]*Sqrt[1 + 2*x])/3^(1/4)])/(3*3^(3/4)) + Log[1 + Sqrt[3] + 2*x - Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]]/(3*Sqrt[2]*3^(3/4)) - Log[1 + Sqrt[3] + 2*x + Sqrt[2]*3^(1/4)*Sqrt[1 + 2*x]]/(3*Sqrt[2]*3^(3/4))","A",12,9,18,0.5000,1,"{693, 694, 329, 211, 1165, 628, 1162, 617, 204}"
1327,1,227,0,0.2072172,"\int (b d+2 c d x)^{7/2} \sqrt{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^(7/2)*Sqrt[a + b*x + c*x^2],x]","-\frac{5 d^{7/2} \left(b^2-4 a c\right)^{13/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{231 c^2 \sqrt{a+b x+c x^2}}-\frac{10 d^3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{231 c}-\frac{2 d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{77 c}+\frac{\sqrt{a+b x+c x^2} (b d+2 c d x)^{9/2}}{11 c d}","-\frac{5 d^{7/2} \left(b^2-4 a c\right)^{13/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{231 c^2 \sqrt{a+b x+c x^2}}-\frac{10 d^3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{231 c}-\frac{2 d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{77 c}+\frac{\sqrt{a+b x+c x^2} (b d+2 c d x)^{9/2}}{11 c d}",1,"(-10*(b^2 - 4*a*c)^2*d^3*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(231*c) - (2*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(77*c) + ((b*d + 2*c*d*x)^(9/2)*Sqrt[a + b*x + c*x^2])/(11*c*d) - (5*(b^2 - 4*a*c)^(13/4)*d^(7/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(231*c^2*Sqrt[a + b*x + c*x^2])","A",6,5,28,0.1786,1,"{685, 692, 691, 689, 221}"
1328,1,180,0,0.1488448,"\int (b d+2 c d x)^{3/2} \sqrt{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2],x]","-\frac{d^{3/2} \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{21 c^2 \sqrt{a+b x+c x^2}}-\frac{2 d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{21 c}+\frac{\sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{7 c d}","-\frac{d^{3/2} \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{21 c^2 \sqrt{a+b x+c x^2}}-\frac{2 d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{21 c}+\frac{\sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{7 c d}",1,"(-2*(b^2 - 4*a*c)*d*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(21*c) + ((b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(7*c*d) - ((b^2 - 4*a*c)^(9/4)*d^(3/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(21*c^2*Sqrt[a + b*x + c*x^2])","A",5,5,28,0.1786,1,"{685, 692, 691, 689, 221}"
1329,1,137,0,0.1200078,"\int \frac{\sqrt{a+b x+c x^2}}{\sqrt{b d+2 c d x}} \, dx","Int[Sqrt[a + b*x + c*x^2]/Sqrt[b*d + 2*c*d*x],x]","\frac{\sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{3 c d}-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 c^2 \sqrt{d} \sqrt{a+b x+c x^2}}","\frac{\sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{3 c d}-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 c^2 \sqrt{d} \sqrt{a+b x+c x^2}}",1,"(Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(3*c*d) - ((b^2 - 4*a*c)^(5/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(3*c^2*Sqrt[d]*Sqrt[a + b*x + c*x^2])","A",4,4,28,0.1429,1,"{685, 691, 689, 221}"
1330,1,137,0,0.1170374,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^{5/2}} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^(5/2),x]","\frac{\sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 c^2 d^{5/2} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{3 c d (b d+2 c d x)^{3/2}}","\frac{\sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 c^2 d^{5/2} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{3 c d (b d+2 c d x)^{3/2}}",1,"-Sqrt[a + b*x + c*x^2]/(3*c*d*(b*d + 2*c*d*x)^(3/2)) + ((b^2 - 4*a*c)^(1/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(3*c^2*d^(5/2)*Sqrt[a + b*x + c*x^2])","A",4,4,28,0.1429,1,"{684, 691, 689, 221}"
1331,1,184,0,0.1554419,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^{9/2}} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^(9/2),x]","\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{21 c^2 d^{9/2} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{a+b x+c x^2}}{21 c d^3 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}-\frac{\sqrt{a+b x+c x^2}}{7 c d (b d+2 c d x)^{7/2}}","\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{21 c^2 d^{9/2} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{a+b x+c x^2}}{21 c d^3 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}-\frac{\sqrt{a+b x+c x^2}}{7 c d (b d+2 c d x)^{7/2}}",1,"-Sqrt[a + b*x + c*x^2]/(7*c*d*(b*d + 2*c*d*x)^(7/2)) + (2*Sqrt[a + b*x + c*x^2])/(21*c*(b^2 - 4*a*c)*d^3*(b*d + 2*c*d*x)^(3/2)) + (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(21*c^2*(b^2 - 4*a*c)^(3/4)*d^(9/2)*Sqrt[a + b*x + c*x^2])","A",5,5,28,0.1786,1,"{684, 693, 691, 689, 221}"
1332,1,231,0,0.1869014,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^{13/2}} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^(13/2),x]","\frac{5 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{231 c^2 d^{13/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}+\frac{10 \sqrt{a+b x+c x^2}}{231 c d^5 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}+\frac{2 \sqrt{a+b x+c x^2}}{77 c d^3 \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}-\frac{\sqrt{a+b x+c x^2}}{11 c d (b d+2 c d x)^{11/2}}","\frac{5 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{231 c^2 d^{13/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}+\frac{10 \sqrt{a+b x+c x^2}}{231 c d^5 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}+\frac{2 \sqrt{a+b x+c x^2}}{77 c d^3 \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}-\frac{\sqrt{a+b x+c x^2}}{11 c d (b d+2 c d x)^{11/2}}",1,"-Sqrt[a + b*x + c*x^2]/(11*c*d*(b*d + 2*c*d*x)^(11/2)) + (2*Sqrt[a + b*x + c*x^2])/(77*c*(b^2 - 4*a*c)*d^3*(b*d + 2*c*d*x)^(7/2)) + (10*Sqrt[a + b*x + c*x^2])/(231*c*(b^2 - 4*a*c)^2*d^5*(b*d + 2*c*d*x)^(3/2)) + (5*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(231*c^2*(b^2 - 4*a*c)^(7/4)*d^(13/2)*Sqrt[a + b*x + c*x^2])","A",6,5,28,0.1786,1,"{684, 693, 691, 689, 221}"
1333,1,279,0,0.2675961,"\int (b d+2 c d x)^{5/2} \sqrt{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2],x]","\frac{d^{5/2} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{15 c^2 \sqrt{a+b x+c x^2}}-\frac{d^{5/2} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{15 c^2 \sqrt{a+b x+c x^2}}-\frac{2 d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{45 c}+\frac{\sqrt{a+b x+c x^2} (b d+2 c d x)^{7/2}}{9 c d}","\frac{d^{5/2} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{15 c^2 \sqrt{a+b x+c x^2}}-\frac{d^{5/2} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{15 c^2 \sqrt{a+b x+c x^2}}-\frac{2 d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{45 c}+\frac{\sqrt{a+b x+c x^2} (b d+2 c d x)^{7/2}}{9 c d}",1,"(-2*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(45*c) + ((b*d + 2*c*d*x)^(7/2)*Sqrt[a + b*x + c*x^2])/(9*c*d) - ((b^2 - 4*a*c)^(11/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(15*c^2*Sqrt[a + b*x + c*x^2]) + ((b^2 - 4*a*c)^(11/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(15*c^2*Sqrt[a + b*x + c*x^2])","A",8,8,28,0.2857,1,"{685, 692, 691, 690, 307, 221, 1199, 424}"
1334,1,236,0,0.2152066,"\int \sqrt{b d+2 c d x} \sqrt{a+b x+c x^2} \, dx","Int[Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{d} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c^2 \sqrt{a+b x+c x^2}}-\frac{\sqrt{d} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c^2 \sqrt{a+b x+c x^2}}+\frac{\sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{5 c d}","\frac{\sqrt{d} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c^2 \sqrt{a+b x+c x^2}}-\frac{\sqrt{d} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c^2 \sqrt{a+b x+c x^2}}+\frac{\sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{5 c d}",1,"((b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(5*c*d) - ((b^2 - 4*a*c)^(7/4)*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*c^2*Sqrt[a + b*x + c*x^2]) + ((b^2 - 4*a*c)^(7/4)*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*c^2*Sqrt[a + b*x + c*x^2])","A",7,7,28,0.2500,1,"{685, 691, 690, 307, 221, 1199, 424}"
1335,1,229,0,0.2128115,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^{3/2}} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^(3/2),x]","-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c^2 d^{3/2} \sqrt{a+b x+c x^2}}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c^2 d^{3/2} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{c d \sqrt{b d+2 c d x}}","-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c^2 d^{3/2} \sqrt{a+b x+c x^2}}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c^2 d^{3/2} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{c d \sqrt{b d+2 c d x}}",1,"-(Sqrt[a + b*x + c*x^2]/(c*d*Sqrt[b*d + 2*c*d*x])) + ((b^2 - 4*a*c)^(3/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(c^2*d^(3/2)*Sqrt[a + b*x + c*x^2]) - ((b^2 - 4*a*c)^(3/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(c^2*d^(3/2)*Sqrt[a + b*x + c*x^2])","A",7,7,28,0.2500,1,"{684, 691, 690, 307, 221, 1199, 424}"
1336,1,283,0,0.2518506,"\int \frac{\sqrt{a+b x+c x^2}}{(b d+2 c d x)^{7/2}} \, dx","Int[Sqrt[a + b*x + c*x^2]/(b*d + 2*c*d*x)^(7/2),x]","\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c^2 d^{7/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c^2 d^{7/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{a+b x+c x^2}}{5 c d^3 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}-\frac{\sqrt{a+b x+c x^2}}{5 c d (b d+2 c d x)^{5/2}}","\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c^2 d^{7/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c^2 d^{7/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{a+b x+c x^2}}{5 c d^3 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}-\frac{\sqrt{a+b x+c x^2}}{5 c d (b d+2 c d x)^{5/2}}",1,"-Sqrt[a + b*x + c*x^2]/(5*c*d*(b*d + 2*c*d*x)^(5/2)) + (2*Sqrt[a + b*x + c*x^2])/(5*c*(b^2 - 4*a*c)*d^3*Sqrt[b*d + 2*c*d*x]) - (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*c^2*(b^2 - 4*a*c)^(1/4)*d^(7/2)*Sqrt[a + b*x + c*x^2]) + (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*c^2*(b^2 - 4*a*c)^(1/4)*d^(7/2)*Sqrt[a + b*x + c*x^2])","A",8,8,28,0.2857,1,"{684, 693, 691, 690, 307, 221, 1199, 424}"
1337,1,274,0,0.2238848,"\int (b d+2 c d x)^{7/2} \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2),x]","\frac{d^3 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{231 c^2}+\frac{d^{7/2} \left(b^2-4 a c\right)^{17/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{462 c^3 \sqrt{a+b x+c x^2}}-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{9/2}}{110 c^2 d}+\frac{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{385 c^2}+\frac{\left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{9/2}}{15 c d}","\frac{d^3 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{231 c^2}+\frac{d^{7/2} \left(b^2-4 a c\right)^{17/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{462 c^3 \sqrt{a+b x+c x^2}}-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{9/2}}{110 c^2 d}+\frac{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{385 c^2}+\frac{\left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{9/2}}{15 c d}",1,"((b^2 - 4*a*c)^3*d^3*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(231*c^2) + ((b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(385*c^2) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(9/2)*Sqrt[a + b*x + c*x^2])/(110*c^2*d) + ((b*d + 2*c*d*x)^(9/2)*(a + b*x + c*x^2)^(3/2))/(15*c*d) + ((b^2 - 4*a*c)^(17/4)*d^(7/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(462*c^3*Sqrt[a + b*x + c*x^2])","A",7,5,28,0.1786,1,"{685, 692, 691, 689, 221}"
1338,1,227,0,0.1831124,"\int (b d+2 c d x)^{3/2} \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2),x]","\frac{d^{3/2} \left(b^2-4 a c\right)^{13/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{154 c^3 \sqrt{a+b x+c x^2}}+\frac{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{77 c^2}-\frac{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{154 c^2 d}+\frac{\left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{5/2}}{11 c d}","\frac{d^{3/2} \left(b^2-4 a c\right)^{13/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{154 c^3 \sqrt{a+b x+c x^2}}+\frac{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{77 c^2}-\frac{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{154 c^2 d}+\frac{\left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{5/2}}{11 c d}",1,"((b^2 - 4*a*c)^2*d*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(77*c^2) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(154*c^2*d) + ((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2))/(11*c*d) + ((b^2 - 4*a*c)^(13/4)*d^(3/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(154*c^3*Sqrt[a + b*x + c*x^2])","A",6,5,28,0.1786,1,"{685, 692, 691, 689, 221}"
1339,1,182,0,0.1499491,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{\sqrt{b d+2 c d x}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/Sqrt[b*d + 2*c*d*x],x]","-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{14 c^2 d}+\frac{\left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{14 c^3 \sqrt{d} \sqrt{a+b x+c x^2}}+\frac{\left(a+b x+c x^2\right)^{3/2} \sqrt{b d+2 c d x}}{7 c d}","-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{14 c^2 d}+\frac{\left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{14 c^3 \sqrt{d} \sqrt{a+b x+c x^2}}+\frac{\left(a+b x+c x^2\right)^{3/2} \sqrt{b d+2 c d x}}{7 c d}",1,"-((b^2 - 4*a*c)*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(14*c^2*d) + (Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^(3/2))/(7*c*d) + ((b^2 - 4*a*c)^(9/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(14*c^3*Sqrt[d]*Sqrt[a + b*x + c*x^2])","A",5,4,28,0.1429,1,"{685, 691, 689, 221}"
1340,1,174,0,0.1435026,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(5/2),x]","-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{6 c^3 d^{5/2} \sqrt{a+b x+c x^2}}+\frac{\sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{6 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{3/2}}{3 c d (b d+2 c d x)^{3/2}}","-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{6 c^3 d^{5/2} \sqrt{a+b x+c x^2}}+\frac{\sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{6 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{3/2}}{3 c d (b d+2 c d x)^{3/2}}",1,"(Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(6*c^2*d^3) - (a + b*x + c*x^2)^(3/2)/(3*c*d*(b*d + 2*c*d*x)^(3/2)) - ((b^2 - 4*a*c)^(5/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(6*c^3*d^(5/2)*Sqrt[a + b*x + c*x^2])","A",5,5,28,0.1786,1,"{684, 685, 691, 689, 221}"
1341,1,174,0,0.1424404,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^{9/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(9/2),x]","\frac{\sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{14 c^3 d^{9/2} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{14 c^2 d^3 (b d+2 c d x)^{3/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{7 c d (b d+2 c d x)^{7/2}}","\frac{\sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{14 c^3 d^{9/2} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{14 c^2 d^3 (b d+2 c d x)^{3/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{7 c d (b d+2 c d x)^{7/2}}",1,"-Sqrt[a + b*x + c*x^2]/(14*c^2*d^3*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(3/2)/(7*c*d*(b*d + 2*c*d*x)^(7/2)) + ((b^2 - 4*a*c)^(1/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(14*c^3*d^(9/2)*Sqrt[a + b*x + c*x^2])","A",5,4,28,0.1429,1,"{684, 691, 689, 221}"
1342,1,221,0,0.1800901,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^{13/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(13/2),x]","\frac{\sqrt{a+b x+c x^2}}{77 c^2 d^5 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{154 c^3 d^{13/2} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}-\frac{3 \sqrt{a+b x+c x^2}}{154 c^2 d^3 (b d+2 c d x)^{7/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{11 c d (b d+2 c d x)^{11/2}}","\frac{\sqrt{a+b x+c x^2}}{77 c^2 d^5 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{154 c^3 d^{13/2} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}-\frac{3 \sqrt{a+b x+c x^2}}{154 c^2 d^3 (b d+2 c d x)^{7/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{11 c d (b d+2 c d x)^{11/2}}",1,"(-3*Sqrt[a + b*x + c*x^2])/(154*c^2*d^3*(b*d + 2*c*d*x)^(7/2)) + Sqrt[a + b*x + c*x^2]/(77*c^2*(b^2 - 4*a*c)*d^5*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(3/2)/(11*c*d*(b*d + 2*c*d*x)^(11/2)) + (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(154*c^3*(b^2 - 4*a*c)^(3/4)*d^(13/2)*Sqrt[a + b*x + c*x^2])","A",6,5,28,0.1786,1,"{684, 693, 691, 689, 221}"
1343,1,268,0,0.2185668,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^{17/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(17/2),x]","\frac{\sqrt{a+b x+c x^2}}{231 c^2 d^7 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}+\frac{\sqrt{a+b x+c x^2}}{385 c^2 d^5 \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{462 c^3 d^{17/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{110 c^2 d^3 (b d+2 c d x)^{11/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{15 c d (b d+2 c d x)^{15/2}}","\frac{\sqrt{a+b x+c x^2}}{231 c^2 d^7 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}+\frac{\sqrt{a+b x+c x^2}}{385 c^2 d^5 \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{462 c^3 d^{17/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{110 c^2 d^3 (b d+2 c d x)^{11/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{15 c d (b d+2 c d x)^{15/2}}",1,"-Sqrt[a + b*x + c*x^2]/(110*c^2*d^3*(b*d + 2*c*d*x)^(11/2)) + Sqrt[a + b*x + c*x^2]/(385*c^2*(b^2 - 4*a*c)*d^5*(b*d + 2*c*d*x)^(7/2)) + Sqrt[a + b*x + c*x^2]/(231*c^2*(b^2 - 4*a*c)^2*d^7*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(3/2)/(15*c*d*(b*d + 2*c*d*x)^(15/2)) + (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(462*c^3*(b^2 - 4*a*c)^(7/4)*d^(17/2)*Sqrt[a + b*x + c*x^2])","A",7,5,28,0.1786,1,"{684, 693, 691, 689, 221}"
1344,1,326,0,0.2961198,"\int (b d+2 c d x)^{5/2} \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2),x]","-\frac{d^{5/2} \left(b^2-4 a c\right)^{15/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{130 c^3 \sqrt{a+b x+c x^2}}+\frac{d^{5/2} \left(b^2-4 a c\right)^{15/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{130 c^3 \sqrt{a+b x+c x^2}}+\frac{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{195 c^2}-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{7/2}}{78 c^2 d}+\frac{\left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{7/2}}{13 c d}","-\frac{d^{5/2} \left(b^2-4 a c\right)^{15/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{130 c^3 \sqrt{a+b x+c x^2}}+\frac{d^{5/2} \left(b^2-4 a c\right)^{15/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{130 c^3 \sqrt{a+b x+c x^2}}+\frac{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{195 c^2}-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{7/2}}{78 c^2 d}+\frac{\left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{7/2}}{13 c d}",1,"((b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(195*c^2) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2)*Sqrt[a + b*x + c*x^2])/(78*c^2*d) + ((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2))/(13*c*d) + ((b^2 - 4*a*c)^(15/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(130*c^3*Sqrt[a + b*x + c*x^2]) - ((b^2 - 4*a*c)^(15/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(130*c^3*Sqrt[a + b*x + c*x^2])","A",9,8,28,0.2857,1,"{685, 692, 691, 690, 307, 221, 1199, 424}"
1345,1,281,0,0.2487775,"\int \sqrt{b d+2 c d x} \left(a+b x+c x^2\right)^{3/2} \, dx","Int[Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^(3/2),x]","-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{30 c^2 d}-\frac{\sqrt{d} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{30 c^3 \sqrt{a+b x+c x^2}}+\frac{\sqrt{d} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{30 c^3 \sqrt{a+b x+c x^2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{3/2}}{9 c d}","-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{30 c^2 d}-\frac{\sqrt{d} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{30 c^3 \sqrt{a+b x+c x^2}}+\frac{\sqrt{d} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{30 c^3 \sqrt{a+b x+c x^2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{3/2}}{9 c d}",1,"-((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(30*c^2*d) + ((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(9*c*d) + ((b^2 - 4*a*c)^(11/4)*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(30*c^3*Sqrt[a + b*x + c*x^2]) - ((b^2 - 4*a*c)^(11/4)*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(30*c^3*Sqrt[a + b*x + c*x^2])","A",8,7,28,0.2500,1,"{685, 691, 690, 307, 221, 1199, 424}"
1346,1,271,0,0.2483651,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(3/2),x]","\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{10 c^3 d^{3/2} \sqrt{a+b x+c x^2}}-\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{10 c^3 d^{3/2} \sqrt{a+b x+c x^2}}+\frac{3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{10 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{3/2}}{c d \sqrt{b d+2 c d x}}","\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{10 c^3 d^{3/2} \sqrt{a+b x+c x^2}}-\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{10 c^3 d^{3/2} \sqrt{a+b x+c x^2}}+\frac{3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{10 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{3/2}}{c d \sqrt{b d+2 c d x}}",1,"(3*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(10*c^2*d^3) - (a + b*x + c*x^2)^(3/2)/(c*d*Sqrt[b*d + 2*c*d*x]) - (3*(b^2 - 4*a*c)^(7/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(10*c^3*d^(3/2)*Sqrt[a + b*x + c*x^2]) + (3*(b^2 - 4*a*c)^(7/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(10*c^3*d^(3/2)*Sqrt[a + b*x + c*x^2])","A",8,8,28,0.2857,1,"{684, 685, 691, 690, 307, 221, 1199, 424}"
1347,1,273,0,0.2437226,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(7/2),x]","-\frac{3 \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{10 c^3 d^{7/2} \sqrt{a+b x+c x^2}}+\frac{3 \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{10 c^3 d^{7/2} \sqrt{a+b x+c x^2}}-\frac{3 \sqrt{a+b x+c x^2}}{10 c^2 d^3 \sqrt{b d+2 c d x}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{5 c d (b d+2 c d x)^{5/2}}","-\frac{3 \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{10 c^3 d^{7/2} \sqrt{a+b x+c x^2}}+\frac{3 \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{10 c^3 d^{7/2} \sqrt{a+b x+c x^2}}-\frac{3 \sqrt{a+b x+c x^2}}{10 c^2 d^3 \sqrt{b d+2 c d x}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{5 c d (b d+2 c d x)^{5/2}}",1,"(-3*Sqrt[a + b*x + c*x^2])/(10*c^2*d^3*Sqrt[b*d + 2*c*d*x]) - (a + b*x + c*x^2)^(3/2)/(5*c*d*(b*d + 2*c*d*x)^(5/2)) + (3*(b^2 - 4*a*c)^(3/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(10*c^3*d^(7/2)*Sqrt[a + b*x + c*x^2]) - (3*(b^2 - 4*a*c)^(3/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(10*c^3*d^(7/2)*Sqrt[a + b*x + c*x^2])","A",8,7,28,0.2500,1,"{684, 691, 690, 307, 221, 1199, 424}"
1348,1,320,0,0.2912623,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(b d+2 c d x)^{11/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(11/2),x]","\frac{\sqrt{a+b x+c x^2}}{15 c^2 d^5 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{30 c^3 d^{11/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{30 c^3 d^{11/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{30 c^2 d^3 (b d+2 c d x)^{5/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{9 c d (b d+2 c d x)^{9/2}}","\frac{\sqrt{a+b x+c x^2}}{15 c^2 d^5 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{30 c^3 d^{11/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{30 c^3 d^{11/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{\sqrt{a+b x+c x^2}}{30 c^2 d^3 (b d+2 c d x)^{5/2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{9 c d (b d+2 c d x)^{9/2}}",1,"-Sqrt[a + b*x + c*x^2]/(30*c^2*d^3*(b*d + 2*c*d*x)^(5/2)) + Sqrt[a + b*x + c*x^2]/(15*c^2*(b^2 - 4*a*c)*d^5*Sqrt[b*d + 2*c*d*x]) - (a + b*x + c*x^2)^(3/2)/(9*c*d*(b*d + 2*c*d*x)^(9/2)) - (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(30*c^3*(b^2 - 4*a*c)^(1/4)*d^(11/2)*Sqrt[a + b*x + c*x^2]) + (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(30*c^3*(b^2 - 4*a*c)^(1/4)*d^(11/2)*Sqrt[a + b*x + c*x^2])","A",9,8,28,0.2857,1,"{684, 693, 691, 690, 307, 221, 1199, 424}"
1349,1,321,0,0.2955173,"\int (b d+2 c d x)^{7/2} \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(5/2),x]","-\frac{5 d^3 \left(b^2-4 a c\right)^4 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{8778 c^3}-\frac{5 d^{7/2} \left(b^2-4 a c\right)^{21/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{17556 c^4 \sqrt{a+b x+c x^2}}-\frac{d \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{2926 c^3}+\frac{\left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{9/2}}{836 c^3 d}-\frac{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{9/2}}{114 c^2 d}+\frac{\left(a+b x+c x^2\right)^{5/2} (b d+2 c d x)^{9/2}}{19 c d}","-\frac{5 d^3 \left(b^2-4 a c\right)^4 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{8778 c^3}-\frac{5 d^{7/2} \left(b^2-4 a c\right)^{21/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{17556 c^4 \sqrt{a+b x+c x^2}}-\frac{d \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{2926 c^3}+\frac{\left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{9/2}}{836 c^3 d}-\frac{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{9/2}}{114 c^2 d}+\frac{\left(a+b x+c x^2\right)^{5/2} (b d+2 c d x)^{9/2}}{19 c d}",1,"(-5*(b^2 - 4*a*c)^4*d^3*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(8778*c^3) - ((b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(2926*c^3) + ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(9/2)*Sqrt[a + b*x + c*x^2])/(836*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(9/2)*(a + b*x + c*x^2)^(3/2))/(114*c^2*d) + ((b*d + 2*c*d*x)^(9/2)*(a + b*x + c*x^2)^(5/2))/(19*c*d) - (5*(b^2 - 4*a*c)^(21/4)*d^(7/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(17556*c^4*Sqrt[a + b*x + c*x^2])","A",8,5,28,0.1786,1,"{685, 692, 691, 689, 221}"
1350,1,274,0,0.2211896,"\int (b d+2 c d x)^{3/2} \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2),x]","-\frac{d^{3/2} \left(b^2-4 a c\right)^{17/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{924 c^4 \sqrt{a+b x+c x^2}}-\frac{d \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{462 c^3}+\frac{\left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{308 c^3 d}-\frac{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{5/2}}{66 c^2 d}+\frac{\left(a+b x+c x^2\right)^{5/2} (b d+2 c d x)^{5/2}}{15 c d}","-\frac{d^{3/2} \left(b^2-4 a c\right)^{17/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{924 c^4 \sqrt{a+b x+c x^2}}-\frac{d \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{462 c^3}+\frac{\left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}{308 c^3 d}-\frac{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{5/2}}{66 c^2 d}+\frac{\left(a+b x+c x^2\right)^{5/2} (b d+2 c d x)^{5/2}}{15 c d}",1,"-((b^2 - 4*a*c)^3*d*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(462*c^3) + ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(308*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2))/(66*c^2*d) + ((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2))/(15*c*d) - ((b^2 - 4*a*c)^(17/4)*d^(3/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(924*c^4*Sqrt[a + b*x + c*x^2])","A",7,5,28,0.1786,1,"{685, 692, 691, 689, 221}"
1351,1,229,0,0.1870225,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{\sqrt{b d+2 c d x}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/Sqrt[b*d + 2*c*d*x],x]","\frac{5 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{308 c^3 d}-\frac{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \sqrt{b d+2 c d x}}{154 c^2 d}-\frac{5 \left(b^2-4 a c\right)^{13/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{308 c^4 \sqrt{d} \sqrt{a+b x+c x^2}}+\frac{\left(a+b x+c x^2\right)^{5/2} \sqrt{b d+2 c d x}}{11 c d}","\frac{5 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{308 c^3 d}-\frac{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \sqrt{b d+2 c d x}}{154 c^2 d}-\frac{5 \left(b^2-4 a c\right)^{13/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{308 c^4 \sqrt{d} \sqrt{a+b x+c x^2}}+\frac{\left(a+b x+c x^2\right)^{5/2} \sqrt{b d+2 c d x}}{11 c d}",1,"(5*(b^2 - 4*a*c)^2*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(308*c^3*d) - (5*(b^2 - 4*a*c)*Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^(3/2))/(154*c^2*d) + (Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^(5/2))/(11*c*d) - (5*(b^2 - 4*a*c)^(13/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(308*c^4*Sqrt[d]*Sqrt[a + b*x + c*x^2])","A",6,4,28,0.1429,1,"{685, 691, 689, 221}"
1352,1,219,0,0.1833861,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(5/2),x]","-\frac{5 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{84 c^3 d^3}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{84 c^4 d^{5/2} \sqrt{a+b x+c x^2}}+\frac{5 \left(a+b x+c x^2\right)^{3/2} \sqrt{b d+2 c d x}}{42 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{5/2}}{3 c d (b d+2 c d x)^{3/2}}","-\frac{5 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{84 c^3 d^3}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{84 c^4 d^{5/2} \sqrt{a+b x+c x^2}}+\frac{5 \left(a+b x+c x^2\right)^{3/2} \sqrt{b d+2 c d x}}{42 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{5/2}}{3 c d (b d+2 c d x)^{3/2}}",1,"(-5*(b^2 - 4*a*c)*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(84*c^3*d^3) + (5*Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^(3/2))/(42*c^2*d^3) - (a + b*x + c*x^2)^(5/2)/(3*c*d*(b*d + 2*c*d*x)^(3/2)) + (5*(b^2 - 4*a*c)^(9/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(84*c^4*d^(5/2)*Sqrt[a + b*x + c*x^2])","A",6,5,28,0.1786,1,"{684, 685, 691, 689, 221}"
1353,1,211,0,0.1794247,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{9/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(9/2),x]","-\frac{5 \left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{84 c^4 d^{9/2} \sqrt{a+b x+c x^2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{42 c^2 d^3 (b d+2 c d x)^{3/2}}+\frac{5 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{84 c^3 d^5}-\frac{\left(a+b x+c x^2\right)^{5/2}}{7 c d (b d+2 c d x)^{7/2}}","-\frac{5 \left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{84 c^4 d^{9/2} \sqrt{a+b x+c x^2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{42 c^2 d^3 (b d+2 c d x)^{3/2}}+\frac{5 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}{84 c^3 d^5}-\frac{\left(a+b x+c x^2\right)^{5/2}}{7 c d (b d+2 c d x)^{7/2}}",1,"(5*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/(84*c^3*d^5) - (5*(a + b*x + c*x^2)^(3/2))/(42*c^2*d^3*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(5/2)/(7*c*d*(b*d + 2*c*d*x)^(7/2)) - (5*(b^2 - 4*a*c)^(5/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(84*c^4*d^(9/2)*Sqrt[a + b*x + c*x^2])","A",6,5,28,0.1786,1,"{684, 685, 691, 689, 221}"
1354,1,211,0,0.1789514,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{13/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(13/2),x]","\frac{5 \sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{308 c^4 d^{13/2} \sqrt{a+b x+c x^2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{154 c^2 d^3 (b d+2 c d x)^{7/2}}-\frac{5 \sqrt{a+b x+c x^2}}{308 c^3 d^5 (b d+2 c d x)^{3/2}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{11 c d (b d+2 c d x)^{11/2}}","\frac{5 \sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{308 c^4 d^{13/2} \sqrt{a+b x+c x^2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{154 c^2 d^3 (b d+2 c d x)^{7/2}}-\frac{5 \sqrt{a+b x+c x^2}}{308 c^3 d^5 (b d+2 c d x)^{3/2}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{11 c d (b d+2 c d x)^{11/2}}",1,"(-5*Sqrt[a + b*x + c*x^2])/(308*c^3*d^5*(b*d + 2*c*d*x)^(3/2)) - (5*(a + b*x + c*x^2)^(3/2))/(154*c^2*d^3*(b*d + 2*c*d*x)^(7/2)) - (a + b*x + c*x^2)^(5/2)/(11*c*d*(b*d + 2*c*d*x)^(11/2)) + (5*(b^2 - 4*a*c)^(1/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(308*c^4*d^(13/2)*Sqrt[a + b*x + c*x^2])","A",6,4,28,0.1429,1,"{684, 691, 689, 221}"
1355,1,258,0,0.2138094,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{17/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(17/2),x]","\frac{\sqrt{a+b x+c x^2}}{462 c^3 d^7 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{924 c^4 d^{17/2} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{66 c^2 d^3 (b d+2 c d x)^{11/2}}-\frac{\sqrt{a+b x+c x^2}}{308 c^3 d^5 (b d+2 c d x)^{7/2}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{15 c d (b d+2 c d x)^{15/2}}","\frac{\sqrt{a+b x+c x^2}}{462 c^3 d^7 \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{924 c^4 d^{17/2} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{66 c^2 d^3 (b d+2 c d x)^{11/2}}-\frac{\sqrt{a+b x+c x^2}}{308 c^3 d^5 (b d+2 c d x)^{7/2}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{15 c d (b d+2 c d x)^{15/2}}",1,"-Sqrt[a + b*x + c*x^2]/(308*c^3*d^5*(b*d + 2*c*d*x)^(7/2)) + Sqrt[a + b*x + c*x^2]/(462*c^3*(b^2 - 4*a*c)*d^7*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(3/2)/(66*c^2*d^3*(b*d + 2*c*d*x)^(11/2)) - (a + b*x + c*x^2)^(5/2)/(15*c*d*(b*d + 2*c*d*x)^(15/2)) + (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(924*c^4*(b^2 - 4*a*c)^(3/4)*d^(17/2)*Sqrt[a + b*x + c*x^2])","A",7,5,28,0.1786,1,"{684, 693, 691, 689, 221}"
1356,1,305,0,0.262961,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{21/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(21/2),x]","\frac{5 \sqrt{a+b x+c x^2}}{8778 c^3 d^9 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}+\frac{\sqrt{a+b x+c x^2}}{2926 c^3 d^7 \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}+\frac{5 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{17556 c^4 d^{21/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{114 c^2 d^3 (b d+2 c d x)^{15/2}}-\frac{\sqrt{a+b x+c x^2}}{836 c^3 d^5 (b d+2 c d x)^{11/2}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{19 c d (b d+2 c d x)^{19/2}}","\frac{5 \sqrt{a+b x+c x^2}}{8778 c^3 d^9 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}+\frac{\sqrt{a+b x+c x^2}}{2926 c^3 d^7 \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}+\frac{5 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{17556 c^4 d^{21/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{114 c^2 d^3 (b d+2 c d x)^{15/2}}-\frac{\sqrt{a+b x+c x^2}}{836 c^3 d^5 (b d+2 c d x)^{11/2}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{19 c d (b d+2 c d x)^{19/2}}",1,"-Sqrt[a + b*x + c*x^2]/(836*c^3*d^5*(b*d + 2*c*d*x)^(11/2)) + Sqrt[a + b*x + c*x^2]/(2926*c^3*(b^2 - 4*a*c)*d^7*(b*d + 2*c*d*x)^(7/2)) + (5*Sqrt[a + b*x + c*x^2])/(8778*c^3*(b^2 - 4*a*c)^2*d^9*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(3/2)/(114*c^2*d^3*(b*d + 2*c*d*x)^(15/2)) - (a + b*x + c*x^2)^(5/2)/(19*c*d*(b*d + 2*c*d*x)^(19/2)) + (5*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(17556*c^4*(b^2 - 4*a*c)^(7/4)*d^(21/2)*Sqrt[a + b*x + c*x^2])","A",8,5,28,0.1786,1,"{684, 693, 691, 689, 221}"
1357,1,373,0,0.3729432,"\int (b d+2 c d x)^{5/2} \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2),x]","\frac{d^{5/2} \left(b^2-4 a c\right)^{19/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{884 c^4 \sqrt{a+b x+c x^2}}-\frac{d^{5/2} \left(b^2-4 a c\right)^{19/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{884 c^4 \sqrt{a+b x+c x^2}}-\frac{d \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{1326 c^3}+\frac{5 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{7/2}}{2652 c^3 d}-\frac{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{7/2}}{442 c^2 d}+\frac{\left(a+b x+c x^2\right)^{5/2} (b d+2 c d x)^{7/2}}{17 c d}","\frac{d^{5/2} \left(b^2-4 a c\right)^{19/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{884 c^4 \sqrt{a+b x+c x^2}}-\frac{d^{5/2} \left(b^2-4 a c\right)^{19/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{884 c^4 \sqrt{a+b x+c x^2}}-\frac{d \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{1326 c^3}+\frac{5 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{7/2}}{2652 c^3 d}-\frac{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{7/2}}{442 c^2 d}+\frac{\left(a+b x+c x^2\right)^{5/2} (b d+2 c d x)^{7/2}}{17 c d}",1,"-((b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(1326*c^3) + (5*(b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(7/2)*Sqrt[a + b*x + c*x^2])/(2652*c^3*d) - (5*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2))/(442*c^2*d) + ((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(5/2))/(17*c*d) - ((b^2 - 4*a*c)^(19/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(884*c^4*Sqrt[a + b*x + c*x^2]) + ((b^2 - 4*a*c)^(19/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(884*c^4*Sqrt[a + b*x + c*x^2])","A",10,8,28,0.2857,1,"{685, 692, 691, 690, 307, 221, 1199, 424}"
1358,1,328,0,0.2987749,"\int \sqrt{b d+2 c d x} \left(a+b x+c x^2\right)^{5/2} \, dx","Int[Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^(5/2),x]","\frac{\left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{156 c^3 d}-\frac{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{3/2}}{234 c^2 d}+\frac{\sqrt{d} \left(b^2-4 a c\right)^{15/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{156 c^4 \sqrt{a+b x+c x^2}}-\frac{\sqrt{d} \left(b^2-4 a c\right)^{15/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{156 c^4 \sqrt{a+b x+c x^2}}+\frac{\left(a+b x+c x^2\right)^{5/2} (b d+2 c d x)^{3/2}}{13 c d}","\frac{\left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{156 c^3 d}-\frac{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{3/2}}{234 c^2 d}+\frac{\sqrt{d} \left(b^2-4 a c\right)^{15/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{156 c^4 \sqrt{a+b x+c x^2}}-\frac{\sqrt{d} \left(b^2-4 a c\right)^{15/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{156 c^4 \sqrt{a+b x+c x^2}}+\frac{\left(a+b x+c x^2\right)^{5/2} (b d+2 c d x)^{3/2}}{13 c d}",1,"((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(156*c^3*d) - (5*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(234*c^2*d) + ((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2))/(13*c*d) - ((b^2 - 4*a*c)^(15/4)*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(156*c^4*Sqrt[a + b*x + c*x^2]) + ((b^2 - 4*a*c)^(15/4)*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(156*c^4*Sqrt[a + b*x + c*x^2])","A",9,7,28,0.2500,1,"{685, 691, 690, 307, 221, 1199, 424}"
1359,1,316,0,0.2920518,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(3/2),x]","-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{12 c^3 d^3}-\frac{\left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{12 c^4 d^{3/2} \sqrt{a+b x+c x^2}}+\frac{\left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{12 c^4 d^{3/2} \sqrt{a+b x+c x^2}}+\frac{5 \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{3/2}}{18 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{5/2}}{c d \sqrt{b d+2 c d x}}","-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{12 c^3 d^3}-\frac{\left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{12 c^4 d^{3/2} \sqrt{a+b x+c x^2}}+\frac{\left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{12 c^4 d^{3/2} \sqrt{a+b x+c x^2}}+\frac{5 \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{3/2}}{18 c^2 d^3}-\frac{\left(a+b x+c x^2\right)^{5/2}}{c d \sqrt{b d+2 c d x}}",1,"-((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(12*c^3*d^3) + (5*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(18*c^2*d^3) - (a + b*x + c*x^2)^(5/2)/(c*d*Sqrt[b*d + 2*c*d*x]) + ((b^2 - 4*a*c)^(11/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(12*c^4*d^(3/2)*Sqrt[a + b*x + c*x^2]) - ((b^2 - 4*a*c)^(11/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(12*c^4*d^(3/2)*Sqrt[a + b*x + c*x^2])","A",9,8,28,0.2857,1,"{684, 685, 691, 690, 307, 221, 1199, 424}"
1360,1,310,0,0.2856413,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(7/2),x]","\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{20 c^4 d^{7/2} \sqrt{a+b x+c x^2}}-\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{20 c^4 d^{7/2} \sqrt{a+b x+c x^2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{2 c^2 d^3 \sqrt{b d+2 c d x}}+\frac{3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{20 c^3 d^5}-\frac{\left(a+b x+c x^2\right)^{5/2}}{5 c d (b d+2 c d x)^{5/2}}","\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{20 c^4 d^{7/2} \sqrt{a+b x+c x^2}}-\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{20 c^4 d^{7/2} \sqrt{a+b x+c x^2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{2 c^2 d^3 \sqrt{b d+2 c d x}}+\frac{3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}{20 c^3 d^5}-\frac{\left(a+b x+c x^2\right)^{5/2}}{5 c d (b d+2 c d x)^{5/2}}",1,"(3*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(20*c^3*d^5) - (a + b*x + c*x^2)^(3/2)/(2*c^2*d^3*Sqrt[b*d + 2*c*d*x]) - (a + b*x + c*x^2)^(5/2)/(5*c*d*(b*d + 2*c*d*x)^(5/2)) - (3*(b^2 - 4*a*c)^(7/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(20*c^4*d^(7/2)*Sqrt[a + b*x + c*x^2]) + (3*(b^2 - 4*a*c)^(7/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(20*c^4*d^(7/2)*Sqrt[a + b*x + c*x^2])","A",9,8,28,0.2857,1,"{684, 685, 691, 690, 307, 221, 1199, 424}"
1361,1,310,0,0.2872384,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{11/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(11/2),x]","-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{12 c^4 d^{11/2} \sqrt{a+b x+c x^2}}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{12 c^4 d^{11/2} \sqrt{a+b x+c x^2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{18 c^2 d^3 (b d+2 c d x)^{5/2}}-\frac{\sqrt{a+b x+c x^2}}{12 c^3 d^5 \sqrt{b d+2 c d x}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{9 c d (b d+2 c d x)^{9/2}}","-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{12 c^4 d^{11/2} \sqrt{a+b x+c x^2}}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{12 c^4 d^{11/2} \sqrt{a+b x+c x^2}}-\frac{\left(a+b x+c x^2\right)^{3/2}}{18 c^2 d^3 (b d+2 c d x)^{5/2}}-\frac{\sqrt{a+b x+c x^2}}{12 c^3 d^5 \sqrt{b d+2 c d x}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{9 c d (b d+2 c d x)^{9/2}}",1,"-Sqrt[a + b*x + c*x^2]/(12*c^3*d^5*Sqrt[b*d + 2*c*d*x]) - (a + b*x + c*x^2)^(3/2)/(18*c^2*d^3*(b*d + 2*c*d*x)^(5/2)) - (a + b*x + c*x^2)^(5/2)/(9*c*d*(b*d + 2*c*d*x)^(9/2)) + ((b^2 - 4*a*c)^(3/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(12*c^4*d^(11/2)*Sqrt[a + b*x + c*x^2]) - ((b^2 - 4*a*c)^(3/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(12*c^4*d^(11/2)*Sqrt[a + b*x + c*x^2])","A",9,7,28,0.2500,1,"{684, 691, 690, 307, 221, 1199, 424}"
1362,1,357,0,0.3370424,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(b d+2 c d x)^{15/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(15/2),x]","\frac{\sqrt{a+b x+c x^2}}{78 c^3 d^7 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{156 c^4 d^{15/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{156 c^4 d^{15/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{234 c^2 d^3 (b d+2 c d x)^{9/2}}-\frac{\sqrt{a+b x+c x^2}}{156 c^3 d^5 (b d+2 c d x)^{5/2}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{13 c d (b d+2 c d x)^{13/2}}","\frac{\sqrt{a+b x+c x^2}}{78 c^3 d^7 \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}+\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{156 c^4 d^{15/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{\sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{156 c^4 d^{15/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2}}{234 c^2 d^3 (b d+2 c d x)^{9/2}}-\frac{\sqrt{a+b x+c x^2}}{156 c^3 d^5 (b d+2 c d x)^{5/2}}-\frac{\left(a+b x+c x^2\right)^{5/2}}{13 c d (b d+2 c d x)^{13/2}}",1,"-Sqrt[a + b*x + c*x^2]/(156*c^3*d^5*(b*d + 2*c*d*x)^(5/2)) + Sqrt[a + b*x + c*x^2]/(78*c^3*(b^2 - 4*a*c)*d^7*Sqrt[b*d + 2*c*d*x]) - (5*(a + b*x + c*x^2)^(3/2))/(234*c^2*d^3*(b*d + 2*c*d*x)^(9/2)) - (a + b*x + c*x^2)^(5/2)/(13*c*d*(b*d + 2*c*d*x)^(13/2)) - (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(156*c^4*(b^2 - 4*a*c)^(1/4)*d^(15/2)*Sqrt[a + b*x + c*x^2]) + (Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(156*c^4*(b^2 - 4*a*c)^(1/4)*d^(15/2)*Sqrt[a + b*x + c*x^2])","A",10,8,28,0.2857,1,"{684, 693, 691, 690, 307, 221, 1199, 424}"
1363,1,174,0,0.1441817,"\int \frac{(b d+2 c d x)^{7/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[(b*d + 2*c*d*x)^(7/2)/Sqrt[a + b*x + c*x^2],x]","\frac{20}{21} d^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}+\frac{10 d^{7/2} \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{21 c \sqrt{a+b x+c x^2}}+\frac{4}{7} d \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}","\frac{20}{21} d^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}+\frac{10 d^{7/2} \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{21 c \sqrt{a+b x+c x^2}}+\frac{4}{7} d \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}",1,"(20*(b^2 - 4*a*c)*d^3*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/21 + (4*d*(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2])/7 + (10*(b^2 - 4*a*c)^(9/4)*d^(7/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(21*c*Sqrt[a + b*x + c*x^2])","A",5,4,28,0.1429,1,"{692, 691, 689, 221}"
1364,1,132,0,0.1163924,"\int \frac{(b d+2 c d x)^{3/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[(b*d + 2*c*d*x)^(3/2)/Sqrt[a + b*x + c*x^2],x]","\frac{2 d^{3/2} \left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 c \sqrt{a+b x+c x^2}}+\frac{4}{3} d \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}","\frac{2 d^{3/2} \left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 c \sqrt{a+b x+c x^2}}+\frac{4}{3} d \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}",1,"(4*d*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/3 + (2*(b^2 - 4*a*c)^(5/4)*d^(3/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(3*c*Sqrt[a + b*x + c*x^2])","A",4,4,28,0.1429,1,"{692, 691, 689, 221}"
1365,1,97,0,0.0918113,"\int \frac{1}{\sqrt{b d+2 c d x} \sqrt{a+b x+c x^2}} \, dx","Int[1/(Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c \sqrt{d} \sqrt{a+b x+c x^2}}","\frac{2 \sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c \sqrt{d} \sqrt{a+b x+c x^2}}",1,"(2*(b^2 - 4*a*c)^(1/4)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(c*Sqrt[d]*Sqrt[a + b*x + c*x^2])","A",3,3,28,0.1071,1,"{691, 689, 221}"
1366,1,144,0,0.1168167,"\int \frac{1}{(b d+2 c d x)^{5/2} \sqrt{a+b x+c x^2}} \, dx","Int[1/((b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 c d^{5/2} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{a+b x+c x^2}}{3 d \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}","\frac{2 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 c d^{5/2} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{a+b x+c x^2}}{3 d \left(b^2-4 a c\right) (b d+2 c d x)^{3/2}}",1,"(4*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)) + (2*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(3*c*(b^2 - 4*a*c)^(3/4)*d^(5/2)*Sqrt[a + b*x + c*x^2])","A",4,4,28,0.1429,1,"{693, 691, 689, 221}"
1367,1,188,0,0.146826,"\int \frac{1}{(b d+2 c d x)^{9/2} \sqrt{a+b x+c x^2}} \, dx","Int[1/((b*d + 2*c*d*x)^(9/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{20 \sqrt{a+b x+c x^2}}{21 d^3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}+\frac{10 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{21 c d^{9/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{a+b x+c x^2}}{7 d \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}","\frac{20 \sqrt{a+b x+c x^2}}{21 d^3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}+\frac{10 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{21 c d^{9/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{a+b x+c x^2}}{7 d \left(b^2-4 a c\right) (b d+2 c d x)^{7/2}}",1,"(4*Sqrt[a + b*x + c*x^2])/(7*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(7/2)) + (20*Sqrt[a + b*x + c*x^2])/(21*(b^2 - 4*a*c)^2*d^3*(b*d + 2*c*d*x)^(3/2)) + (10*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(21*c*(b^2 - 4*a*c)^(7/4)*d^(9/2)*Sqrt[a + b*x + c*x^2])","A",5,4,28,0.1429,1,"{693, 691, 689, 221}"
1368,1,273,0,0.2519197,"\int \frac{(b d+2 c d x)^{9/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[(b*d + 2*c*d*x)^(9/2)/Sqrt[a + b*x + c*x^2],x]","\frac{28}{45} d^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}-\frac{14 d^{9/2} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{15 c \sqrt{a+b x+c x^2}}+\frac{14 d^{9/2} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{15 c \sqrt{a+b x+c x^2}}+\frac{4}{9} d \sqrt{a+b x+c x^2} (b d+2 c d x)^{7/2}","\frac{28}{45} d^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}-\frac{14 d^{9/2} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{15 c \sqrt{a+b x+c x^2}}+\frac{14 d^{9/2} \left(b^2-4 a c\right)^{11/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{15 c \sqrt{a+b x+c x^2}}+\frac{4}{9} d \sqrt{a+b x+c x^2} (b d+2 c d x)^{7/2}",1,"(28*(b^2 - 4*a*c)*d^3*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/45 + (4*d*(b*d + 2*c*d*x)^(7/2)*Sqrt[a + b*x + c*x^2])/9 + (14*(b^2 - 4*a*c)^(11/4)*d^(9/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(15*c*Sqrt[a + b*x + c*x^2]) - (14*(b^2 - 4*a*c)^(11/4)*d^(9/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(15*c*Sqrt[a + b*x + c*x^2])","A",8,7,28,0.2500,1,"{692, 691, 690, 307, 221, 1199, 424}"
1369,1,231,0,0.2153933,"\int \frac{(b d+2 c d x)^{5/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[(b*d + 2*c*d*x)^(5/2)/Sqrt[a + b*x + c*x^2],x]","-\frac{6 d^{5/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c \sqrt{a+b x+c x^2}}+\frac{6 d^{5/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c \sqrt{a+b x+c x^2}}+\frac{4}{5} d \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}","-\frac{6 d^{5/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c \sqrt{a+b x+c x^2}}+\frac{6 d^{5/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c \sqrt{a+b x+c x^2}}+\frac{4}{5} d \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}",1,"(4*d*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/5 + (6*(b^2 - 4*a*c)^(7/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*c*Sqrt[a + b*x + c*x^2]) - (6*(b^2 - 4*a*c)^(7/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*c*Sqrt[a + b*x + c*x^2])","A",7,7,28,0.2500,1,"{692, 691, 690, 307, 221, 1199, 424}"
1370,1,195,0,0.1791065,"\int \frac{\sqrt{b d+2 c d x}}{\sqrt{a+b x+c x^2}} \, dx","Int[Sqrt[b*d + 2*c*d*x]/Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{d} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c \sqrt{a+b x+c x^2}}","\frac{2 \sqrt{d} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c \sqrt{a+b x+c x^2}}",1,"(2*(b^2 - 4*a*c)^(3/4)*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(c*Sqrt[a + b*x + c*x^2]) - (2*(b^2 - 4*a*c)^(3/4)*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(c*Sqrt[a + b*x + c*x^2])","A",6,6,28,0.2143,1,"{691, 690, 307, 221, 1199, 424}"
1371,1,237,0,0.2090003,"\int \frac{1}{(b d+2 c d x)^{3/2} \sqrt{a+b x+c x^2}} \, dx","Int[1/((b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c d^{3/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c d^{3/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{a+b x+c x^2}}{d \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}","\frac{2 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c d^{3/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{c d^{3/2} \sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{a+b x+c x^2}}{d \left(b^2-4 a c\right) \sqrt{b d+2 c d x}}",1,"(4*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)*d*Sqrt[b*d + 2*c*d*x]) - (2*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(c*(b^2 - 4*a*c)^(1/4)*d^(3/2)*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(c*(b^2 - 4*a*c)^(1/4)*d^(3/2)*Sqrt[a + b*x + c*x^2])","A",7,7,28,0.2500,1,"{693, 691, 690, 307, 221, 1199, 424}"
1372,1,287,0,0.2482305,"\int \frac{1}{(b d+2 c d x)^{7/2} \sqrt{a+b x+c x^2}} \, dx","Int[1/((b*d + 2*c*d*x)^(7/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{12 \sqrt{a+b x+c x^2}}{5 d^3 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}+\frac{6 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c d^{7/2} \left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}-\frac{6 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c d^{7/2} \left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{a+b x+c x^2}}{5 d \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}","\frac{12 \sqrt{a+b x+c x^2}}{5 d^3 \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}+\frac{6 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c d^{7/2} \left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}-\frac{6 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 c d^{7/2} \left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{a+b x+c x^2}}{5 d \left(b^2-4 a c\right) (b d+2 c d x)^{5/2}}",1,"(4*Sqrt[a + b*x + c*x^2])/(5*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)) + (12*Sqrt[a + b*x + c*x^2])/(5*(b^2 - 4*a*c)^2*d^3*Sqrt[b*d + 2*c*d*x]) - (6*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*c*(b^2 - 4*a*c)^(5/4)*d^(7/2)*Sqrt[a + b*x + c*x^2]) + (6*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*c*(b^2 - 4*a*c)^(5/4)*d^(7/2)*Sqrt[a + b*x + c*x^2])","A",8,7,28,0.2500,1,"{693, 691, 690, 307, 221, 1199, 424}"
1373,1,79,0,0.0391474,"\int \frac{(3-2 x)^{3/2}}{\sqrt{1-3 x+x^2}} \, dx","Int[(3 - 2*x)^(3/2)/Sqrt[1 - 3*x + x^2],x]","-\frac{4}{3} \sqrt{3-2 x} \sqrt{x^2-3 x+1}-\frac{2\ 5^{3/4} \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{3 \sqrt{x^2-3 x+1}}","-\frac{4}{3} \sqrt{3-2 x} \sqrt{x^2-3 x+1}-\frac{2\ 5^{3/4} \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{3 \sqrt{x^2-3 x+1}}",1,"(-4*Sqrt[3 - 2*x]*Sqrt[1 - 3*x + x^2])/3 - (2*5^(3/4)*Sqrt[-1 + 3*x - x^2]*EllipticF[ArcSin[Sqrt[3 - 2*x]/5^(1/4)], -1])/(3*Sqrt[1 - 3*x + x^2])","A",4,4,22,0.1818,1,"{692, 691, 689, 221}"
1374,1,51,0,0.0240225,"\int \frac{1}{\sqrt{3-2 x} \sqrt{1-3 x+x^2}} \, dx","Int[1/(Sqrt[3 - 2*x]*Sqrt[1 - 3*x + x^2]),x]","-\frac{2 \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt[4]{5} \sqrt{x^2-3 x+1}}","-\frac{2 \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt[4]{5} \sqrt{x^2-3 x+1}}",1,"(-2*Sqrt[-1 + 3*x - x^2]*EllipticF[ArcSin[Sqrt[3 - 2*x]/5^(1/4)], -1])/(5^(1/4)*Sqrt[1 - 3*x + x^2])","A",3,3,22,0.1364,1,"{691, 689, 221}"
1375,1,79,0,0.0344653,"\int \frac{1}{(3-2 x)^{5/2} \sqrt{1-3 x+x^2}} \, dx","Int[1/((3 - 2*x)^(5/2)*Sqrt[1 - 3*x + x^2]),x]","-\frac{4 \sqrt{x^2-3 x+1}}{15 (3-2 x)^{3/2}}-\frac{2 \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{15 \sqrt[4]{5} \sqrt{x^2-3 x+1}}","-\frac{4 \sqrt{x^2-3 x+1}}{15 (3-2 x)^{3/2}}-\frac{2 \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{15 \sqrt[4]{5} \sqrt{x^2-3 x+1}}",1,"(-4*Sqrt[1 - 3*x + x^2])/(15*(3 - 2*x)^(3/2)) - (2*Sqrt[-1 + 3*x - x^2]*EllipticF[ArcSin[Sqrt[3 - 2*x]/5^(1/4)], -1])/(15*5^(1/4)*Sqrt[1 - 3*x + x^2])","A",4,4,22,0.1818,1,"{693, 691, 689, 221}"
1376,1,128,0,0.0711873,"\int \frac{(3-2 x)^{5/2}}{\sqrt{1-3 x+x^2}} \, dx","Int[(3 - 2*x)^(5/2)/Sqrt[1 - 3*x + x^2],x]","-\frac{4}{5} \sqrt{x^2-3 x+1} (3-2 x)^{3/2}+\frac{6 \sqrt[4]{5} \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt{x^2-3 x+1}}-\frac{6 \sqrt[4]{5} \sqrt{-x^2+3 x-1} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt{x^2-3 x+1}}","-\frac{4}{5} \sqrt{x^2-3 x+1} (3-2 x)^{3/2}+\frac{6 \sqrt[4]{5} \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt{x^2-3 x+1}}-\frac{6 \sqrt[4]{5} \sqrt{-x^2+3 x-1} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt{x^2-3 x+1}}",1,"(-4*(3 - 2*x)^(3/2)*Sqrt[1 - 3*x + x^2])/5 - (6*5^(1/4)*Sqrt[-1 + 3*x - x^2]*EllipticE[ArcSin[Sqrt[3 - 2*x]/5^(1/4)], -1])/Sqrt[1 - 3*x + x^2] + (6*5^(1/4)*Sqrt[-1 + 3*x - x^2]*EllipticF[ArcSin[Sqrt[3 - 2*x]/5^(1/4)], -1])/Sqrt[1 - 3*x + x^2]","A",8,8,22,0.3636,1,"{692, 691, 690, 307, 221, 1181, 21, 424}"
1377,1,103,0,0.0523656,"\int \frac{\sqrt{3-2 x}}{\sqrt{1-3 x+x^2}} \, dx","Int[Sqrt[3 - 2*x]/Sqrt[1 - 3*x + x^2],x]","\frac{2 \sqrt[4]{5} \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt{x^2-3 x+1}}-\frac{2 \sqrt[4]{5} \sqrt{-x^2+3 x-1} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt{x^2-3 x+1}}","\frac{2 \sqrt[4]{5} \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt{x^2-3 x+1}}-\frac{2 \sqrt[4]{5} \sqrt{-x^2+3 x-1} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{\sqrt{x^2-3 x+1}}",1,"(-2*5^(1/4)*Sqrt[-1 + 3*x - x^2]*EllipticE[ArcSin[Sqrt[3 - 2*x]/5^(1/4)], -1])/Sqrt[1 - 3*x + x^2] + (2*5^(1/4)*Sqrt[-1 + 3*x - x^2]*EllipticF[ArcSin[Sqrt[3 - 2*x]/5^(1/4)], -1])/Sqrt[1 - 3*x + x^2]","A",7,7,22,0.3182,1,"{691, 690, 307, 221, 1181, 21, 424}"
1378,1,128,0,0.0681879,"\int \frac{1}{(3-2 x)^{3/2} \sqrt{1-3 x+x^2}} \, dx","Int[1/((3 - 2*x)^(3/2)*Sqrt[1 - 3*x + x^2]),x]","-\frac{4 \sqrt{x^2-3 x+1}}{5 \sqrt{3-2 x}}-\frac{2 \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{5^{3/4} \sqrt{x^2-3 x+1}}+\frac{2 \sqrt{-x^2+3 x-1} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{5^{3/4} \sqrt{x^2-3 x+1}}","-\frac{4 \sqrt{x^2-3 x+1}}{5 \sqrt{3-2 x}}-\frac{2 \sqrt{-x^2+3 x-1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{5^{3/4} \sqrt{x^2-3 x+1}}+\frac{2 \sqrt{-x^2+3 x-1} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-2 x}}{\sqrt[4]{5}}\right)\right|-1\right)}{5^{3/4} \sqrt{x^2-3 x+1}}",1,"(-4*Sqrt[1 - 3*x + x^2])/(5*Sqrt[3 - 2*x]) + (2*Sqrt[-1 + 3*x - x^2]*EllipticE[ArcSin[Sqrt[3 - 2*x]/5^(1/4)], -1])/(5^(3/4)*Sqrt[1 - 3*x + x^2]) - (2*Sqrt[-1 + 3*x - x^2]*EllipticF[ArcSin[Sqrt[3 - 2*x]/5^(1/4)], -1])/(5^(3/4)*Sqrt[1 - 3*x + x^2])","A",8,8,22,0.3636,1,"{693, 691, 690, 307, 221, 1181, 21, 424}"
1379,1,205,0,0.1759727,"\int \frac{(b d+2 c d x)^{11/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^(3/2),x]","\frac{120}{7} c d^5 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}+\frac{60 d^{11/2} \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{7 \sqrt{a+b x+c x^2}}+\frac{72}{7} c d^3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}-\frac{2 d (b d+2 c d x)^{9/2}}{\sqrt{a+b x+c x^2}}","\frac{120}{7} c d^5 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}+\frac{60 d^{11/2} \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{7 \sqrt{a+b x+c x^2}}+\frac{72}{7} c d^3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}-\frac{2 d (b d+2 c d x)^{9/2}}{\sqrt{a+b x+c x^2}}",1,"(-2*d*(b*d + 2*c*d*x)^(9/2))/Sqrt[a + b*x + c*x^2] + (120*c*(b^2 - 4*a*c)*d^5*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/7 + (72*c*d^3*(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2])/7 + (60*(b^2 - 4*a*c)^(9/4)*d^(11/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(7*Sqrt[a + b*x + c*x^2])","A",6,5,28,0.1786,1,"{686, 692, 691, 689, 221}"
1380,1,162,0,0.1422986,"\int \frac{(b d+2 c d x)^{7/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(3/2),x]","\frac{20 d^{7/2} \left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 \sqrt{a+b x+c x^2}}+\frac{40}{3} c d^3 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}-\frac{2 d (b d+2 c d x)^{5/2}}{\sqrt{a+b x+c x^2}}","\frac{20 d^{7/2} \left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 \sqrt{a+b x+c x^2}}+\frac{40}{3} c d^3 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}-\frac{2 d (b d+2 c d x)^{5/2}}{\sqrt{a+b x+c x^2}}",1,"(-2*d*(b*d + 2*c*d*x)^(5/2))/Sqrt[a + b*x + c*x^2] + (40*c*d^3*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/3 + (20*(b^2 - 4*a*c)^(5/4)*d^(7/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(3*Sqrt[a + b*x + c*x^2])","A",5,5,28,0.1786,1,"{686, 692, 691, 689, 221}"
1381,1,125,0,0.1132329,"\int \frac{(b d+2 c d x)^{3/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(3/2),x]","\frac{4 d^{3/2} \sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}-\frac{2 d \sqrt{b d+2 c d x}}{\sqrt{a+b x+c x^2}}","\frac{4 d^{3/2} \sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}-\frac{2 d \sqrt{b d+2 c d x}}{\sqrt{a+b x+c x^2}}",1,"(-2*d*Sqrt[b*d + 2*c*d*x])/Sqrt[a + b*x + c*x^2] + (4*(b^2 - 4*a*c)^(1/4)*d^(3/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/Sqrt[a + b*x + c*x^2]","A",4,4,28,0.1429,1,"{686, 691, 689, 221}"
1382,1,137,0,0.1126906,"\int \frac{1}{\sqrt{b d+2 c d x} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^(3/2)),x]","-\frac{2 \sqrt{b d+2 c d x}}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{4 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{d} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}","-\frac{2 \sqrt{b d+2 c d x}}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{4 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{d} \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}",1,"(-2*Sqrt[b*d + 2*c*d*x])/((b^2 - 4*a*c)*d*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(3/4)*Sqrt[d]*Sqrt[a + b*x + c*x^2])","A",4,4,28,0.1429,1,"{687, 691, 689, 221}"
1383,1,184,0,0.1438522,"\int \frac{1}{(b d+2 c d x)^{5/2} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{20 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 d^{5/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}-\frac{40 c \sqrt{a+b x+c x^2}}{3 d \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}-\frac{2}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}","-\frac{20 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 d^{5/2} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}-\frac{40 c \sqrt{a+b x+c x^2}}{3 d \left(b^2-4 a c\right)^2 (b d+2 c d x)^{3/2}}-\frac{2}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}",1,"-2/((b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2]) - (40*c*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2)) - (20*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(3*(b^2 - 4*a*c)^(7/4)*d^(5/2)*Sqrt[a + b*x + c*x^2])","A",5,5,28,0.1786,1,"{687, 693, 691, 689, 221}"
1384,1,258,0,0.2460769,"\int \frac{(b d+2 c d x)^{9/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(3/2),x]","-\frac{84 d^{9/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 \sqrt{a+b x+c x^2}}+\frac{84 d^{9/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 \sqrt{a+b x+c x^2}}+\frac{56}{5} c d^3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}-\frac{2 d (b d+2 c d x)^{7/2}}{\sqrt{a+b x+c x^2}}","-\frac{84 d^{9/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 \sqrt{a+b x+c x^2}}+\frac{84 d^{9/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 \sqrt{a+b x+c x^2}}+\frac{56}{5} c d^3 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}-\frac{2 d (b d+2 c d x)^{7/2}}{\sqrt{a+b x+c x^2}}",1,"(-2*d*(b*d + 2*c*d*x)^(7/2))/Sqrt[a + b*x + c*x^2] + (56*c*d^3*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/5 + (84*(b^2 - 4*a*c)^(7/4)*d^(9/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*Sqrt[a + b*x + c*x^2]) - (84*(b^2 - 4*a*c)^(7/4)*d^(9/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*Sqrt[a + b*x + c*x^2])","A",8,8,28,0.2857,1,"{686, 692, 691, 690, 307, 221, 1199, 424}"
1385,1,219,0,0.204948,"\int \frac{(b d+2 c d x)^{5/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(3/2),x]","-\frac{12 d^{5/2} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}+\frac{12 d^{5/2} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{3/2}}{\sqrt{a+b x+c x^2}}","-\frac{12 d^{5/2} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}+\frac{12 d^{5/2} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{3/2}}{\sqrt{a+b x+c x^2}}",1,"(-2*d*(b*d + 2*c*d*x)^(3/2))/Sqrt[a + b*x + c*x^2] + (12*(b^2 - 4*a*c)^(3/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/Sqrt[a + b*x + c*x^2] - (12*(b^2 - 4*a*c)^(3/4)*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/Sqrt[a + b*x + c*x^2]","A",7,7,28,0.2500,1,"{686, 691, 690, 307, 221, 1199, 424}"
1386,1,231,0,0.2061032,"\int \frac{\sqrt{b d+2 c d x}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[Sqrt[b*d + 2*c*d*x]/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 (b d+2 c d x)^{3/2}}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{4 \sqrt{d} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{d} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}","-\frac{2 (b d+2 c d x)^{3/2}}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{4 \sqrt{d} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt{d} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}",1,"(-2*(b*d + 2*c*d*x)^(3/2))/((b^2 - 4*a*c)*d*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(1/4)*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(1/4)*Sqrt[a + b*x + c*x^2])","A",7,7,28,0.2500,1,"{687, 691, 690, 307, 221, 1199, 424}"
1387,1,274,0,0.2449044,"\int \frac{1}{(b d+2 c d x)^{3/2} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{12 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{3/2} \left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}+\frac{12 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{3/2} \left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}-\frac{24 c \sqrt{a+b x+c x^2}}{d \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}-\frac{2}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}","-\frac{12 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{3/2} \left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}+\frac{12 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{3/2} \left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}-\frac{24 c \sqrt{a+b x+c x^2}}{d \left(b^2-4 a c\right)^2 \sqrt{b d+2 c d x}}-\frac{2}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}",1,"-2/((b^2 - 4*a*c)*d*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2]) - (24*c*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)^2*d*Sqrt[b*d + 2*c*d*x]) + (12*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(5/4)*d^(3/2)*Sqrt[a + b*x + c*x^2]) - (12*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(5/4)*d^(3/2)*Sqrt[a + b*x + c*x^2])","A",8,8,28,0.2857,1,"{687, 693, 691, 690, 307, 221, 1199, 424}"
1388,1,325,0,0.2938542,"\int \frac{1}{(b d+2 c d x)^{7/2} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{168 c \sqrt{a+b x+c x^2}}{5 d^3 \left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}-\frac{84 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 d^{7/2} \left(b^2-4 a c\right)^{9/4} \sqrt{a+b x+c x^2}}+\frac{84 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 d^{7/2} \left(b^2-4 a c\right)^{9/4} \sqrt{a+b x+c x^2}}-\frac{56 c \sqrt{a+b x+c x^2}}{5 d \left(b^2-4 a c\right)^2 (b d+2 c d x)^{5/2}}-\frac{2}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}","-\frac{168 c \sqrt{a+b x+c x^2}}{5 d^3 \left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}-\frac{84 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 d^{7/2} \left(b^2-4 a c\right)^{9/4} \sqrt{a+b x+c x^2}}+\frac{84 \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 d^{7/2} \left(b^2-4 a c\right)^{9/4} \sqrt{a+b x+c x^2}}-\frac{56 c \sqrt{a+b x+c x^2}}{5 d \left(b^2-4 a c\right)^2 (b d+2 c d x)^{5/2}}-\frac{2}{d \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}}",1,"-2/((b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2]) - (56*c*Sqrt[a + b*x + c*x^2])/(5*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(5/2)) - (168*c*Sqrt[a + b*x + c*x^2])/(5*(b^2 - 4*a*c)^3*d^3*Sqrt[b*d + 2*c*d*x]) + (84*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*(b^2 - 4*a*c)^(9/4)*d^(7/2)*Sqrt[a + b*x + c*x^2]) - (84*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*(b^2 - 4*a*c)^(9/4)*d^(7/2)*Sqrt[a + b*x + c*x^2])","A",9,8,28,0.2857,1,"{687, 693, 691, 690, 307, 221, 1199, 424}"
1389,1,247,0,0.2026167,"\int \frac{(b d+2 c d x)^{15/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^(5/2),x]","\frac{1040}{7} c^2 d^7 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}+\frac{520 c d^{15/2} \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{7 \sqrt{a+b x+c x^2}}+\frac{624}{7} c^2 d^5 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}-\frac{52 c d^3 (b d+2 c d x)^{9/2}}{3 \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{13/2}}{3 \left(a+b x+c x^2\right)^{3/2}}","\frac{1040}{7} c^2 d^7 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}+\frac{520 c d^{15/2} \left(b^2-4 a c\right)^{9/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{7 \sqrt{a+b x+c x^2}}+\frac{624}{7} c^2 d^5 \sqrt{a+b x+c x^2} (b d+2 c d x)^{5/2}-\frac{52 c d^3 (b d+2 c d x)^{9/2}}{3 \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{13/2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d*(b*d + 2*c*d*x)^(13/2))/(3*(a + b*x + c*x^2)^(3/2)) - (52*c*d^3*(b*d + 2*c*d*x)^(9/2))/(3*Sqrt[a + b*x + c*x^2]) + (1040*c^2*(b^2 - 4*a*c)*d^7*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2])/7 + (624*c^2*d^5*(b*d + 2*c*d*x)^(5/2)*Sqrt[a + b*x + c*x^2])/7 + (520*c*(b^2 - 4*a*c)^(9/4)*d^(15/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(7*Sqrt[a + b*x + c*x^2])","A",7,5,28,0.1786,1,"{686, 692, 691, 689, 221}"
1390,1,196,0,0.166264,"\int \frac{(b d+2 c d x)^{11/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^(5/2),x]","\frac{40 c d^{11/2} \left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}+80 c^2 d^5 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}-\frac{12 c d^3 (b d+2 c d x)^{5/2}}{\sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{9/2}}{3 \left(a+b x+c x^2\right)^{3/2}}","\frac{40 c d^{11/2} \left(b^2-4 a c\right)^{5/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}+80 c^2 d^5 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}-\frac{12 c d^3 (b d+2 c d x)^{5/2}}{\sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{9/2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d*(b*d + 2*c*d*x)^(9/2))/(3*(a + b*x + c*x^2)^(3/2)) - (12*c*d^3*(b*d + 2*c*d*x)^(5/2))/Sqrt[a + b*x + c*x^2] + 80*c^2*d^5*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2] + (40*c*(b^2 - 4*a*c)^(5/4)*d^(11/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/Sqrt[a + b*x + c*x^2]","A",6,5,28,0.1786,1,"{686, 692, 691, 689, 221}"
1391,1,165,0,0.1362091,"\int \frac{(b d+2 c d x)^{7/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(5/2),x]","\frac{40 c d^{7/2} \sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 \sqrt{a+b x+c x^2}}-\frac{20 c d^3 \sqrt{b d+2 c d x}}{3 \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{5/2}}{3 \left(a+b x+c x^2\right)^{3/2}}","\frac{40 c d^{7/2} \sqrt[4]{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 \sqrt{a+b x+c x^2}}-\frac{20 c d^3 \sqrt{b d+2 c d x}}{3 \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{5/2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d*(b*d + 2*c*d*x)^(5/2))/(3*(a + b*x + c*x^2)^(3/2)) - (20*c*d^3*Sqrt[b*d + 2*c*d*x])/(3*Sqrt[a + b*x + c*x^2]) + (40*c*(b^2 - 4*a*c)^(1/4)*d^(7/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(3*Sqrt[a + b*x + c*x^2])","A",5,4,28,0.1429,1,"{686, 691, 689, 221}"
1392,1,173,0,0.1383126,"\int \frac{(b d+2 c d x)^{3/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(5/2),x]","-\frac{8 c d^{3/2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}-\frac{4 c d \sqrt{b d+2 c d x}}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 d \sqrt{b d+2 c d x}}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{8 c d^{3/2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 \left(b^2-4 a c\right)^{3/4} \sqrt{a+b x+c x^2}}-\frac{4 c d \sqrt{b d+2 c d x}}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 d \sqrt{b d+2 c d x}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d*Sqrt[b*d + 2*c*d*x])/(3*(a + b*x + c*x^2)^(3/2)) - (4*c*d*Sqrt[b*d + 2*c*d*x])/(3*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) - (8*c*d^(3/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(3*(b^2 - 4*a*c)^(3/4)*Sqrt[a + b*x + c*x^2])","A",5,5,28,0.1786,1,"{686, 687, 691, 689, 221}"
1393,1,187,0,0.1400252,"\int \frac{1}{\sqrt{b d+2 c d x} \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/(Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^(5/2)),x]","\frac{20 c \sqrt{b d+2 c d x}}{3 d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{b d+2 c d x}}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{40 c \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 \sqrt{d} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}","\frac{20 c \sqrt{b d+2 c d x}}{3 d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{b d+2 c d x}}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{40 c \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{3 \sqrt{d} \left(b^2-4 a c\right)^{7/4} \sqrt{a+b x+c x^2}}",1,"(-2*Sqrt[b*d + 2*c*d*x])/(3*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^(3/2)) + (20*c*Sqrt[b*d + 2*c*d*x])/(3*(b^2 - 4*a*c)^2*d*Sqrt[a + b*x + c*x^2]) + (40*c*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(3*(b^2 - 4*a*c)^(7/4)*Sqrt[d]*Sqrt[a + b*x + c*x^2])","A",5,4,28,0.1429,1,"{687, 691, 689, 221}"
1394,1,228,0,0.1766116,"\int \frac{1}{(b d+2 c d x)^{5/2} \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2)),x]","\frac{80 c^2 \sqrt{a+b x+c x^2}}{d \left(b^2-4 a c\right)^3 (b d+2 c d x)^{3/2}}+\frac{40 c \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{5/2} \left(b^2-4 a c\right)^{11/4} \sqrt{a+b x+c x^2}}+\frac{12 c}{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}-\frac{2}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{3/2}}","\frac{80 c^2 \sqrt{a+b x+c x^2}}{d \left(b^2-4 a c\right)^3 (b d+2 c d x)^{3/2}}+\frac{40 c \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{5/2} \left(b^2-4 a c\right)^{11/4} \sqrt{a+b x+c x^2}}+\frac{12 c}{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}}-\frac{2}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} (b d+2 c d x)^{3/2}}",1,"-2/(3*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2)) + (12*c)/((b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2]) + (80*c^2*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(3/2)) + (40*c*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(11/4)*d^(5/2)*Sqrt[a + b*x + c*x^2])","A",6,5,28,0.1786,1,"{687, 693, 691, 689, 221}"
1395,1,299,0,0.2860271,"\int \frac{(b d+2 c d x)^{13/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^(5/2),x]","-\frac{616 c d^{13/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 \sqrt{a+b x+c x^2}}+\frac{616 c d^{13/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 \sqrt{a+b x+c x^2}}+\frac{1232}{15} c^2 d^5 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}-\frac{44 c d^3 (b d+2 c d x)^{7/2}}{3 \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{11/2}}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{616 c d^{13/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 \sqrt{a+b x+c x^2}}+\frac{616 c d^{13/2} \left(b^2-4 a c\right)^{7/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{5 \sqrt{a+b x+c x^2}}+\frac{1232}{15} c^2 d^5 \sqrt{a+b x+c x^2} (b d+2 c d x)^{3/2}-\frac{44 c d^3 (b d+2 c d x)^{7/2}}{3 \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{11/2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d*(b*d + 2*c*d*x)^(11/2))/(3*(a + b*x + c*x^2)^(3/2)) - (44*c*d^3*(b*d + 2*c*d*x)^(7/2))/(3*Sqrt[a + b*x + c*x^2]) + (1232*c^2*d^5*(b*d + 2*c*d*x)^(3/2)*Sqrt[a + b*x + c*x^2])/15 + (616*c*(b^2 - 4*a*c)^(7/4)*d^(13/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*Sqrt[a + b*x + c*x^2]) - (616*c*(b^2 - 4*a*c)^(7/4)*d^(13/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/(5*Sqrt[a + b*x + c*x^2])","A",9,8,28,0.2857,1,"{686, 692, 691, 690, 307, 221, 1199, 424}"
1396,1,258,0,0.237905,"\int \frac{(b d+2 c d x)^{9/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(5/2),x]","-\frac{56 c d^{9/2} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}+\frac{56 c d^{9/2} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}-\frac{28 c d^3 (b d+2 c d x)^{3/2}}{3 \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{7/2}}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{56 c d^{9/2} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}+\frac{56 c d^{9/2} \left(b^2-4 a c\right)^{3/4} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt{a+b x+c x^2}}-\frac{28 c d^3 (b d+2 c d x)^{3/2}}{3 \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{7/2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d*(b*d + 2*c*d*x)^(7/2))/(3*(a + b*x + c*x^2)^(3/2)) - (28*c*d^3*(b*d + 2*c*d*x)^(3/2))/(3*Sqrt[a + b*x + c*x^2]) + (56*c*(b^2 - 4*a*c)^(3/4)*d^(9/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/Sqrt[a + b*x + c*x^2] - (56*c*(b^2 - 4*a*c)^(3/4)*d^(9/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/Sqrt[a + b*x + c*x^2]","A",8,7,28,0.2500,1,"{686, 691, 690, 307, 221, 1199, 424}"
1397,1,264,0,0.237248,"\int \frac{(b d+2 c d x)^{5/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(5/2),x]","-\frac{8 c d^{5/2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}+\frac{8 c d^{5/2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{4 c d (b d+2 c d x)^{3/2}}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{3/2}}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{8 c d^{5/2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}+\frac{8 c d^{5/2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\sqrt[4]{b^2-4 a c} \sqrt{a+b x+c x^2}}-\frac{4 c d (b d+2 c d x)^{3/2}}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 d (b d+2 c d x)^{3/2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*d*(b*d + 2*c*d*x)^(3/2))/(3*(a + b*x + c*x^2)^(3/2)) - (4*c*d*(b*d + 2*c*d*x)^(3/2))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (8*c*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(1/4)*Sqrt[a + b*x + c*x^2]) - (8*c*d^(5/2)*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(1/4)*Sqrt[a + b*x + c*x^2])","A",8,8,28,0.2857,1,"{686, 687, 691, 690, 307, 221, 1199, 424}"
1398,1,278,0,0.2472878,"\int \frac{\sqrt{b d+2 c d x}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[Sqrt[b*d + 2*c*d*x]/(a + b*x + c*x^2)^(5/2),x]","\frac{4 c (b d+2 c d x)^{3/2}}{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (b d+2 c d x)^{3/2}}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{8 c \sqrt{d} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}-\frac{8 c \sqrt{d} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}","\frac{4 c (b d+2 c d x)^{3/2}}{d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (b d+2 c d x)^{3/2}}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{8 c \sqrt{d} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}-\frac{8 c \sqrt{d} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{\left(b^2-4 a c\right)^{5/4} \sqrt{a+b x+c x^2}}",1,"(-2*(b*d + 2*c*d*x)^(3/2))/(3*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^(3/2)) + (4*c*(b*d + 2*c*d*x)^(3/2))/((b^2 - 4*a*c)^2*d*Sqrt[a + b*x + c*x^2]) - (8*c*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(5/4)*Sqrt[a + b*x + c*x^2]) + (8*c*Sqrt[d]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(5/4)*Sqrt[a + b*x + c*x^2])","A",8,7,28,0.2500,1,"{687, 691, 690, 307, 221, 1199, 424}"
1399,1,325,0,0.2839731,"\int \frac{1}{(b d+2 c d x)^{3/2} \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2)),x]","\frac{112 c^2 \sqrt{a+b x+c x^2}}{d \left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}+\frac{56 c \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{3/2} \left(b^2-4 a c\right)^{9/4} \sqrt{a+b x+c x^2}}-\frac{56 c \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{3/2} \left(b^2-4 a c\right)^{9/4} \sqrt{a+b x+c x^2}}+\frac{28 c}{3 d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}-\frac{2}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \sqrt{b d+2 c d x}}","\frac{112 c^2 \sqrt{a+b x+c x^2}}{d \left(b^2-4 a c\right)^3 \sqrt{b d+2 c d x}}+\frac{56 c \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{3/2} \left(b^2-4 a c\right)^{9/4} \sqrt{a+b x+c x^2}}-\frac{56 c \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{b d+2 c x d}}{\sqrt[4]{b^2-4 a c} \sqrt{d}}\right)\right|-1\right)}{d^{3/2} \left(b^2-4 a c\right)^{9/4} \sqrt{a+b x+c x^2}}+\frac{28 c}{3 d \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \sqrt{b d+2 c d x}}-\frac{2}{3 d \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \sqrt{b d+2 c d x}}",1,"-2/(3*(b^2 - 4*a*c)*d*Sqrt[b*d + 2*c*d*x]*(a + b*x + c*x^2)^(3/2)) + (28*c)/(3*(b^2 - 4*a*c)^2*d*Sqrt[b*d + 2*c*d*x]*Sqrt[a + b*x + c*x^2]) + (112*c^2*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)^3*d*Sqrt[b*d + 2*c*d*x]) - (56*c*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(9/4)*d^(3/2)*Sqrt[a + b*x + c*x^2]) + (56*c*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[b*d + 2*c*d*x]/((b^2 - 4*a*c)^(1/4)*Sqrt[d])], -1])/((b^2 - 4*a*c)^(9/4)*d^(3/2)*Sqrt[a + b*x + c*x^2])","A",9,8,28,0.2857,1,"{687, 693, 691, 690, 307, 221, 1199, 424}"
1400,1,170,0,0.145616,"\int \frac{(c e+d e x)^{11/2}}{\sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[(c*e + d*e*x)^(11/2)/Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2],x]","-\frac{30 e^5 \sqrt{-c^2-2 c d x-d^2 x^2+1} \sqrt{c e+d e x}}{77 d}-\frac{18 e^3 \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{5/2}}{77 d}-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{9/2}}{11 d}+\frac{30 e^{11/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{77 d}","-\frac{30 e^5 \sqrt{-c^2-2 c d x-d^2 x^2+1} \sqrt{c e+d e x}}{77 d}-\frac{18 e^3 \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{5/2}}{77 d}-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{9/2}}{11 d}+\frac{30 e^{11/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{77 d}",1,"(-30*e^5*Sqrt[c*e + d*e*x]*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(77*d) - (18*e^3*(c*e + d*e*x)^(5/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(77*d) - (2*e*(c*e + d*e*x)^(9/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(11*d) + (30*e^(11/2)*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(77*d)","A",5,3,37,0.08108,1,"{692, 689, 221}"
1401,1,124,0,0.0952692,"\int \frac{(c e+d e x)^{7/2}}{\sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[(c*e + d*e*x)^(7/2)/Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2],x]","-\frac{10 e^3 \sqrt{-c^2-2 c d x-d^2 x^2+1} \sqrt{c e+d e x}}{21 d}-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{5/2}}{7 d}+\frac{10 e^{7/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{21 d}","-\frac{10 e^3 \sqrt{-c^2-2 c d x-d^2 x^2+1} \sqrt{c e+d e x}}{21 d}-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{5/2}}{7 d}+\frac{10 e^{7/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{21 d}",1,"(-10*e^3*Sqrt[c*e + d*e*x]*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(21*d) - (2*e*(c*e + d*e*x)^(5/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(7*d) + (10*e^(7/2)*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(21*d)","A",4,3,37,0.08108,1,"{692, 689, 221}"
1402,1,78,0,0.0587986,"\int \frac{(c e+d e x)^{3/2}}{\sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[(c*e + d*e*x)^(3/2)/Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2],x]","\frac{2 e^{3/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{3 d}-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} \sqrt{c e+d e x}}{3 d}","\frac{2 e^{3/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{3 d}-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} \sqrt{c e+d e x}}{3 d}",1,"(-2*e*Sqrt[c*e + d*e*x]*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(3*d) + (2*e^(3/2)*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(3*d)","A",3,3,37,0.08108,1,"{692, 689, 221}"
1403,1,31,0,0.0291083,"\int \frac{1}{\sqrt{c e+d e x} \sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[1/(Sqrt[c*e + d*e*x]*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2]),x]","\frac{2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d \sqrt{e}}","\frac{2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d \sqrt{e}}",1,"(2*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(d*Sqrt[e])","A",2,2,37,0.05405,1,"{689, 221}"
1404,1,80,0,0.0579532,"\int \frac{1}{(c e+d e x)^{5/2} \sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[1/((c*e + d*e*x)^(5/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2]),x]","\frac{2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{3 d e^{5/2}}-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{3 d e (c e+d e x)^{3/2}}","\frac{2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{3 d e^{5/2}}-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{3 d e (c e+d e x)^{3/2}}",1,"(-2*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(3*d*e*(c*e + d*e*x)^(3/2)) + (2*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(3*d*e^(5/2))","A",3,3,37,0.08108,1,"{693, 689, 221}"
1405,1,126,0,0.0858568,"\int \frac{1}{(c e+d e x)^{9/2} \sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[1/((c*e + d*e*x)^(9/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2]),x]","-\frac{10 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{21 d e^3 (c e+d e x)^{3/2}}-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{7 d e (c e+d e x)^{7/2}}+\frac{10 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{21 d e^{9/2}}","-\frac{10 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{21 d e^3 (c e+d e x)^{3/2}}-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{7 d e (c e+d e x)^{7/2}}+\frac{10 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{21 d e^{9/2}}",1,"(-2*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(7*d*e*(c*e + d*e*x)^(7/2)) - (10*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(21*d*e^3*(c*e + d*e*x)^(3/2)) + (10*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(21*d*e^(9/2))","A",4,3,37,0.08108,1,"{693, 689, 221}"
1406,1,172,0,0.1183871,"\int \frac{1}{(c e+d e x)^{13/2} \sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[1/((c*e + d*e*x)^(13/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2]),x]","-\frac{30 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{77 d e^5 (c e+d e x)^{3/2}}-\frac{18 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{77 d e^3 (c e+d e x)^{7/2}}-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{11 d e (c e+d e x)^{11/2}}+\frac{30 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{77 d e^{13/2}}","-\frac{30 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{77 d e^5 (c e+d e x)^{3/2}}-\frac{18 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{77 d e^3 (c e+d e x)^{7/2}}-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{11 d e (c e+d e x)^{11/2}}+\frac{30 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{77 d e^{13/2}}",1,"(-2*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(11*d*e*(c*e + d*e*x)^(11/2)) - (18*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(77*d*e^3*(c*e + d*e*x)^(7/2)) - (30*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(77*d*e^5*(c*e + d*e*x)^(3/2)) + (30*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(77*d*e^(13/2))","A",5,3,37,0.08108,1,"{693, 689, 221}"
1407,1,157,0,0.1344372,"\int \frac{(c e+d e x)^{9/2}}{\sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[(c*e + d*e*x)^(9/2)/Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2],x]","-\frac{14 e^3 \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{3/2}}{45 d}-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{7/2}}{9 d}-\frac{14 e^{9/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{15 d}+\frac{14 e^{9/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{15 d}","-\frac{14 e^3 \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{3/2}}{45 d}-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{7/2}}{9 d}-\frac{14 e^{9/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{15 d}+\frac{14 e^{9/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{15 d}",1,"(-14*e^3*(c*e + d*e*x)^(3/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(45*d) - (2*e*(c*e + d*e*x)^(7/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(9*d) + (14*e^(9/2)*EllipticE[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(15*d) - (14*e^(9/2)*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(15*d)","A",7,6,37,0.1622,1,"{692, 690, 307, 221, 1199, 424}"
1408,1,111,0,0.090528,"\int \frac{(c e+d e x)^{5/2}}{\sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[(c*e + d*e*x)^(5/2)/Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2],x]","-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{3/2}}{5 d}-\frac{6 e^{5/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{5 d}+\frac{6 e^{5/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{5 d}","-\frac{2 e \sqrt{-c^2-2 c d x-d^2 x^2+1} (c e+d e x)^{3/2}}{5 d}-\frac{6 e^{5/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{5 d}+\frac{6 e^{5/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{5 d}",1,"(-2*e*(c*e + d*e*x)^(3/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(5*d) + (6*e^(5/2)*EllipticE[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(5*d) - (6*e^(5/2)*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(5*d)","A",6,6,37,0.1622,1,"{692, 690, 307, 221, 1199, 424}"
1409,1,63,0,0.0553057,"\int \frac{\sqrt{c e+d e x}}{\sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[Sqrt[c*e + d*e*x]/Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2],x]","\frac{2 \sqrt{e} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d}-\frac{2 \sqrt{e} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d}","\frac{2 \sqrt{e} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d}-\frac{2 \sqrt{e} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d}",1,"(2*Sqrt[e]*EllipticE[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/d - (2*Sqrt[e]*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/d","A",5,5,37,0.1351,1,"{690, 307, 221, 1199, 424}"
1410,1,107,0,0.0851578,"\int \frac{1}{(c e+d e x)^{3/2} \sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[1/((c*e + d*e*x)^(3/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2]),x]","-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{d e \sqrt{c e+d e x}}+\frac{2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d e^{3/2}}-\frac{2 E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d e^{3/2}}","-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{d e \sqrt{c e+d e x}}+\frac{2 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d e^{3/2}}-\frac{2 E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{d e^{3/2}}",1,"(-2*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(d*e*Sqrt[c*e + d*e*x]) - (2*EllipticE[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(d*e^(3/2)) + (2*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(d*e^(3/2))","A",6,6,37,0.1622,1,"{693, 690, 307, 221, 1199, 424}"
1411,1,159,0,0.1180386,"\int \frac{1}{(c e+d e x)^{7/2} \sqrt{1-c^2-2 c d x-d^2 x^2}} \, dx","Int[1/((c*e + d*e*x)^(7/2)*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2]),x]","-\frac{6 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{5 d e^3 \sqrt{c e+d e x}}-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{5 d e (c e+d e x)^{5/2}}+\frac{6 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{5 d e^{7/2}}-\frac{6 E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{5 d e^{7/2}}","-\frac{6 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{5 d e^3 \sqrt{c e+d e x}}-\frac{2 \sqrt{-c^2-2 c d x-d^2 x^2+1}}{5 d e (c e+d e x)^{5/2}}+\frac{6 F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{5 d e^{7/2}}-\frac{6 E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c e+d x e}}{\sqrt{e}}\right)\right|-1\right)}{5 d e^{7/2}}",1,"(-2*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(5*d*e*(c*e + d*e*x)^(5/2)) - (6*Sqrt[1 - c^2 - 2*c*d*x - d^2*x^2])/(5*d*e^3*Sqrt[c*e + d*e*x]) - (6*EllipticE[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(5*d*e^(7/2)) + (6*EllipticF[ArcSin[Sqrt[c*e + d*e*x]/Sqrt[e]], -1])/(5*d*e^(7/2))","A",7,6,37,0.1622,1,"{693, 690, 307, 221, 1199, 424}"
1412,1,468,0,1.2821416,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{11/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(11/3),x]","-\frac{3 \sqrt[3]{a+b x+c x^2} (d (b+2 c x))^{4/3}}{16 c^2 d^5 \left(b^2-4 a c\right)}-\frac{9 \left(a+b x+c x^2\right)^{7/3}}{4 d^3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{2/3}}+\frac{9 \left(a+b x+c x^2\right)^{4/3} (d (b+2 c x))^{4/3}}{16 c d^5 \left(b^2-4 a c\right)^2}+\frac{3 \left(a+b x+c x^2\right)^{7/3}}{4 d \left(b^2-4 a c\right) (b d+2 c d x)^{8/3}}-\frac{\log \left(-\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}-2 \sqrt[3]{c} d^{2/3} \sqrt[3]{a+b x+c x^2}}{\sqrt[3]{a+b x+c x^2}}\right)}{16\ 2^{2/3} c^{7/3} d^{11/3}}+\frac{\log \left(\frac{2 \sqrt[3]{2} c^{2/3} d^{4/3} \left(a+b x+c x^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} d^{2/3} \sqrt[3]{a+b x+c x^2} (d (b+2 c x))^{2/3}+(d (b+2 c x))^{4/3}}{\left(a+b x+c x^2\right)^{2/3}}\right)}{32\ 2^{2/3} c^{7/3} d^{11/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}+\sqrt[3]{c} d^{2/3}}{\sqrt{3} \sqrt[3]{c} d^{2/3}}\right)}{16\ 2^{2/3} c^{7/3} d^{11/3}}","-\frac{3 \sqrt[3]{a+b x+c x^2} (d (b+2 c x))^{4/3}}{16 c^2 d^5 \left(b^2-4 a c\right)}-\frac{9 \left(a+b x+c x^2\right)^{7/3}}{4 d^3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{2/3}}+\frac{9 \left(a+b x+c x^2\right)^{4/3} (d (b+2 c x))^{4/3}}{16 c d^5 \left(b^2-4 a c\right)^2}+\frac{3 \left(a+b x+c x^2\right)^{7/3}}{4 d \left(b^2-4 a c\right) (b d+2 c d x)^{8/3}}-\frac{3 \log \left((d (b+2 c x))^{2/3}-2^{2/3} \sqrt[3]{c} d^{2/3} \sqrt[3]{a+b x+c x^2}\right)}{32\ 2^{2/3} c^{7/3} d^{11/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{c} d^{2/3} \sqrt[3]{a+b x+c x^2}}+1}{\sqrt{3}}\right)}{16\ 2^{2/3} c^{7/3} d^{11/3}}",1,"(-3*(d*(b + 2*c*x))^(4/3)*(a + b*x + c*x^2)^(1/3))/(16*c^2*(b^2 - 4*a*c)*d^5) + (9*(d*(b + 2*c*x))^(4/3)*(a + b*x + c*x^2)^(4/3))/(16*c*(b^2 - 4*a*c)^2*d^5) + (3*(a + b*x + c*x^2)^(7/3))/(4*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(8/3)) - (9*(a + b*x + c*x^2)^(7/3))/(4*(b^2 - 4*a*c)^2*d^3*(b*d + 2*c*d*x)^(2/3)) - (Sqrt[3]*ArcTan[(c^(1/3)*d^(2/3) + (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(Sqrt[3]*c^(1/3)*d^(2/3))])/(16*2^(2/3)*c^(7/3)*d^(11/3)) - Log[-((2^(1/3)*(d*(b + 2*c*x))^(2/3) - 2*c^(1/3)*d^(2/3)*(a + b*x + c*x^2)^(1/3))/(a + b*x + c*x^2)^(1/3))]/(16*2^(2/3)*c^(7/3)*d^(11/3)) + Log[((d*(b + 2*c*x))^(4/3) + 2^(2/3)*c^(1/3)*d^(2/3)*(d*(b + 2*c*x))^(2/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*d^(4/3)*(a + b*x + c*x^2)^(2/3))/(a + b*x + c*x^2)^(2/3)]/(32*2^(2/3)*c^(7/3)*d^(11/3))","A",14,12,28,0.4286,1,"{693, 694, 279, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
1413,1,44,0,0.0177368,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{17/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(17/3),x]","\frac{3 \left(a+b x+c x^2\right)^{7/3}}{7 d \left(b^2-4 a c\right) (b d+2 c d x)^{14/3}}","\frac{3 \left(a+b x+c x^2\right)^{7/3}}{7 d \left(b^2-4 a c\right) (b d+2 c d x)^{14/3}}",1,"(3*(a + b*x + c*x^2)^(7/3))/(7*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(14/3))","A",1,1,28,0.03571,1,"{682}"
1414,1,89,0,0.0395993,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{23/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(23/3),x]","\frac{9 \left(a+b x+c x^2\right)^{7/3}}{70 d^3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{14/3}}+\frac{3 \left(a+b x+c x^2\right)^{7/3}}{10 d \left(b^2-4 a c\right) (b d+2 c d x)^{20/3}}","\frac{9 \left(a+b x+c x^2\right)^{7/3}}{70 d^3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{14/3}}+\frac{3 \left(a+b x+c x^2\right)^{7/3}}{10 d \left(b^2-4 a c\right) (b d+2 c d x)^{20/3}}",1,"(3*(a + b*x + c*x^2)^(7/3))/(10*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(20/3)) + (9*(a + b*x + c*x^2)^(7/3))/(70*(b^2 - 4*a*c)^2*d^3*(b*d + 2*c*d*x)^(14/3))","A",2,2,28,0.07143,1,"{693, 682}"
1415,1,133,0,0.0658108,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{29/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(29/3),x]","\frac{27 \left(a+b x+c x^2\right)^{7/3}}{455 d^5 \left(b^2-4 a c\right)^3 (b d+2 c d x)^{14/3}}+\frac{9 \left(a+b x+c x^2\right)^{7/3}}{65 d^3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{20/3}}+\frac{3 \left(a+b x+c x^2\right)^{7/3}}{13 d \left(b^2-4 a c\right) (b d+2 c d x)^{26/3}}","\frac{27 \left(a+b x+c x^2\right)^{7/3}}{455 d^5 \left(b^2-4 a c\right)^3 (b d+2 c d x)^{14/3}}+\frac{9 \left(a+b x+c x^2\right)^{7/3}}{65 d^3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{20/3}}+\frac{3 \left(a+b x+c x^2\right)^{7/3}}{13 d \left(b^2-4 a c\right) (b d+2 c d x)^{26/3}}",1,"(3*(a + b*x + c*x^2)^(7/3))/(13*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(26/3)) + (9*(a + b*x + c*x^2)^(7/3))/(65*(b^2 - 4*a*c)^2*d^3*(b*d + 2*c*d*x)^(20/3)) + (27*(a + b*x + c*x^2)^(7/3))/(455*(b^2 - 4*a*c)^3*d^5*(b*d + 2*c*d*x)^(14/3))","A",3,2,28,0.07143,1,"{693, 682}"
1416,1,597,0,2.5202375,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{2/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(2/3),x]","\frac{\left(b^2-4 a c\right) \left(-4 a c+b^2-(b+2 c x)^2\right) \sqrt[3]{d (b+2 c x)} \left(2 \sqrt[3]{c} d^{2/3}-\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right) \sqrt{\frac{\frac{2^{2/3} \sqrt[3]{c} d^{2/3} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}+\frac{(d (b+2 c x))^{4/3}}{\left(a+b x+c x^2\right)^{2/3}}+2 \sqrt[3]{2} c^{2/3} d^{4/3}}{\left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1-\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{72 \sqrt[4]{3} c^{10/3} d^{5/3} \left(a+b x+c x^2\right)^{2/3} \sqrt{-\frac{(d (b+2 c x))^{2/3} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{(d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)}{\sqrt[3]{a+b x+c x^2} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}}}-\frac{\left(b^2-4 a c\right) \sqrt[3]{a+b x+c x^2} \sqrt[3]{d (b+2 c x)}}{9 c^2 d}+\frac{\left(a+b x+c x^2\right)^{4/3} \sqrt[3]{d (b+2 c x)}}{6 c d}","\frac{\left(b^2-4 a c\right) \left(-4 a c+b^2-(b+2 c x)^2\right) \sqrt[3]{d (b+2 c x)} \left(2 \sqrt[3]{c} d^{2/3}-\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right) \sqrt{\frac{\frac{2^{2/3} \sqrt[3]{c} d^{2/3} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}+\frac{(d (b+2 c x))^{4/3}}{\left(a+b x+c x^2\right)^{2/3}}+2 \sqrt[3]{2} c^{2/3} d^{4/3}}{\left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1-\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{72 \sqrt[4]{3} c^{10/3} d^{5/3} \left(a+b x+c x^2\right)^{2/3} \sqrt{-\frac{(d (b+2 c x))^{2/3} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{(d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)}{\sqrt[3]{a+b x+c x^2} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}}}-\frac{\left(b^2-4 a c\right) \sqrt[3]{a+b x+c x^2} \sqrt[3]{d (b+2 c x)}}{9 c^2 d}+\frac{\left(a+b x+c x^2\right)^{4/3} \sqrt[3]{d (b+2 c x)}}{6 c d}",1,"-((b^2 - 4*a*c)*(d*(b + 2*c*x))^(1/3)*(a + b*x + c*x^2)^(1/3))/(9*c^2*d) + ((d*(b + 2*c*x))^(1/3)*(a + b*x + c*x^2)^(4/3))/(6*c*d) + ((b^2 - 4*a*c)*(d*(b + 2*c*x))^(1/3)*(b^2 - 4*a*c - (b + 2*c*x)^2)*(2*c^(1/3)*d^(2/3) - (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))*Sqrt[(2*2^(1/3)*c^(2/3)*d^(4/3) + (d*(b + 2*c*x))^(4/3)/(a + b*x + c*x^2)^(2/3) + (2^(2/3)*c^(1/3)*d^(2/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcCos[(2^(2/3)*c^(1/3)*d^(2/3) - ((1 - Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))], (2 + Sqrt[3])/4])/(72*3^(1/4)*c^(10/3)*d^(5/3)*(a + b*x + c*x^2)^(2/3)*Sqrt[-(((d*(b + 2*c*x))^(2/3)*(2^(2/3)*c^(1/3)*d^(2/3) - (d*(b + 2*c*x))^(2/3)/(a + b*x + c*x^2)^(1/3)))/((a + b*x + c*x^2)^(1/3)*(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2))])","A",6,5,28,0.1786,1,"{694, 279, 329, 241, 225}"
1417,1,581,0,1.949992,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{8/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(8/3),x]","-\frac{\left(-4 a c+b^2-(b+2 c x)^2\right) \sqrt[3]{d (b+2 c x)} \left(2 \sqrt[3]{c} d^{2/3}-\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right) \sqrt{\frac{\frac{2^{2/3} \sqrt[3]{c} d^{2/3} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}+\frac{(d (b+2 c x))^{4/3}}{\left(a+b x+c x^2\right)^{2/3}}+2 \sqrt[3]{2} c^{2/3} d^{4/3}}{\left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1-\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 \sqrt[4]{3} c^{10/3} d^{11/3} \left(a+b x+c x^2\right)^{2/3} \sqrt{-\frac{(d (b+2 c x))^{2/3} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{(d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)}{\sqrt[3]{a+b x+c x^2} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}}}+\frac{\sqrt[3]{a+b x+c x^2} \sqrt[3]{d (b+2 c x)}}{5 c^2 d^3}-\frac{3 \left(a+b x+c x^2\right)^{4/3}}{10 c d (d (b+2 c x))^{5/3}}","-\frac{\left(-4 a c+b^2-(b+2 c x)^2\right) \sqrt[3]{d (b+2 c x)} \left(2 \sqrt[3]{c} d^{2/3}-\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right) \sqrt{\frac{\frac{2^{2/3} \sqrt[3]{c} d^{2/3} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}+\frac{(d (b+2 c x))^{4/3}}{\left(a+b x+c x^2\right)^{2/3}}+2 \sqrt[3]{2} c^{2/3} d^{4/3}}{\left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1-\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 \sqrt[4]{3} c^{10/3} d^{11/3} \left(a+b x+c x^2\right)^{2/3} \sqrt{-\frac{(d (b+2 c x))^{2/3} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{(d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)}{\sqrt[3]{a+b x+c x^2} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}}}+\frac{\sqrt[3]{a+b x+c x^2} \sqrt[3]{d (b+2 c x)}}{5 c^2 d^3}-\frac{3 \left(a+b x+c x^2\right)^{4/3}}{10 c d (d (b+2 c x))^{5/3}}",1,"((d*(b + 2*c*x))^(1/3)*(a + b*x + c*x^2)^(1/3))/(5*c^2*d^3) - (3*(a + b*x + c*x^2)^(4/3))/(10*c*d*(d*(b + 2*c*x))^(5/3)) - ((d*(b + 2*c*x))^(1/3)*(b^2 - 4*a*c - (b + 2*c*x)^2)*(2*c^(1/3)*d^(2/3) - (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))*Sqrt[(2*2^(1/3)*c^(2/3)*d^(4/3) + (d*(b + 2*c*x))^(4/3)/(a + b*x + c*x^2)^(2/3) + (2^(2/3)*c^(1/3)*d^(2/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcCos[(2^(2/3)*c^(1/3)*d^(2/3) - ((1 - Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))], (2 + Sqrt[3])/4])/(40*3^(1/4)*c^(10/3)*d^(11/3)*(a + b*x + c*x^2)^(2/3)*Sqrt[-(((d*(b + 2*c*x))^(2/3)*(2^(2/3)*c^(1/3)*d^(2/3) - (d*(b + 2*c*x))^(2/3)/(a + b*x + c*x^2)^(1/3)))/((a + b*x + c*x^2)^(1/3)*(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2))])","A",6,6,28,0.2143,1,"{694, 277, 279, 329, 241, 225}"
1418,1,591,0,2.0047151,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{14/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(14/3),x]","\frac{3^{3/4} \left(-4 a c+b^2-(b+2 c x)^2\right) \sqrt[3]{d (b+2 c x)} \left(2 \sqrt[3]{c} d^{2/3}-\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right) \sqrt{\frac{\frac{2^{2/3} \sqrt[3]{c} d^{2/3} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}+\frac{(d (b+2 c x))^{4/3}}{\left(a+b x+c x^2\right)^{2/3}}+2 \sqrt[3]{2} c^{2/3} d^{4/3}}{\left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1-\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{440 c^{10/3} d^{17/3} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{2/3} \sqrt{-\frac{(d (b+2 c x))^{2/3} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{(d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)}{\sqrt[3]{a+b x+c x^2} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}}}-\frac{3 \sqrt[3]{a+b x+c x^2}}{55 c^2 d^3 (d (b+2 c x))^{5/3}}-\frac{3 \left(a+b x+c x^2\right)^{4/3}}{22 c d (d (b+2 c x))^{11/3}}","\frac{3^{3/4} \left(-4 a c+b^2-(b+2 c x)^2\right) \sqrt[3]{d (b+2 c x)} \left(2 \sqrt[3]{c} d^{2/3}-\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right) \sqrt{\frac{\frac{2^{2/3} \sqrt[3]{c} d^{2/3} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}+\frac{(d (b+2 c x))^{4/3}}{\left(a+b x+c x^2\right)^{2/3}}+2 \sqrt[3]{2} c^{2/3} d^{4/3}}{\left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1-\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{440 c^{10/3} d^{17/3} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{2/3} \sqrt{-\frac{(d (b+2 c x))^{2/3} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{(d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)}{\sqrt[3]{a+b x+c x^2} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}}}-\frac{3 \sqrt[3]{a+b x+c x^2}}{55 c^2 d^3 (d (b+2 c x))^{5/3}}-\frac{3 \left(a+b x+c x^2\right)^{4/3}}{22 c d (d (b+2 c x))^{11/3}}",1,"(-3*(a + b*x + c*x^2)^(1/3))/(55*c^2*d^3*(d*(b + 2*c*x))^(5/3)) - (3*(a + b*x + c*x^2)^(4/3))/(22*c*d*(d*(b + 2*c*x))^(11/3)) + (3^(3/4)*(d*(b + 2*c*x))^(1/3)*(b^2 - 4*a*c - (b + 2*c*x)^2)*(2*c^(1/3)*d^(2/3) - (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))*Sqrt[(2*2^(1/3)*c^(2/3)*d^(4/3) + (d*(b + 2*c*x))^(4/3)/(a + b*x + c*x^2)^(2/3) + (2^(2/3)*c^(1/3)*d^(2/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcCos[(2^(2/3)*c^(1/3)*d^(2/3) - ((1 - Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))], (2 + Sqrt[3])/4])/(440*c^(10/3)*(b^2 - 4*a*c)*d^(17/3)*(a + b*x + c*x^2)^(2/3)*Sqrt[-(((d*(b + 2*c*x))^(2/3)*(2^(2/3)*c^(1/3)*d^(2/3) - (d*(b + 2*c*x))^(2/3)/(a + b*x + c*x^2)^(1/3)))/((a + b*x + c*x^2)^(1/3)*(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2))])","A",6,5,28,0.1786,1,"{694, 277, 329, 241, 225}"
1419,1,637,0,2.1398973,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{20/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(20/3),x]","\frac{6 \sqrt[3]{a+b x+c x^2}}{935 c^2 d^5 \left(b^2-4 a c\right) (d (b+2 c x))^{5/3}}+\frac{3\ 3^{3/4} \left(-4 a c+b^2-(b+2 c x)^2\right) \sqrt[3]{d (b+2 c x)} \left(2 \sqrt[3]{c} d^{2/3}-\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right) \sqrt{\frac{\frac{2^{2/3} \sqrt[3]{c} d^{2/3} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}+\frac{(d (b+2 c x))^{4/3}}{\left(a+b x+c x^2\right)^{2/3}}+2 \sqrt[3]{2} c^{2/3} d^{4/3}}{\left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1-\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{7480 c^{10/3} d^{23/3} \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{2/3} \sqrt{-\frac{(d (b+2 c x))^{2/3} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{(d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)}{\sqrt[3]{a+b x+c x^2} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}}}-\frac{3 \sqrt[3]{a+b x+c x^2}}{187 c^2 d^3 (d (b+2 c x))^{11/3}}-\frac{3 \left(a+b x+c x^2\right)^{4/3}}{34 c d (d (b+2 c x))^{17/3}}","\frac{6 \sqrt[3]{a+b x+c x^2}}{935 c^2 d^5 \left(b^2-4 a c\right) (d (b+2 c x))^{5/3}}+\frac{3\ 3^{3/4} \left(-4 a c+b^2-(b+2 c x)^2\right) \sqrt[3]{d (b+2 c x)} \left(2 \sqrt[3]{c} d^{2/3}-\frac{\sqrt[3]{2} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right) \sqrt{\frac{\frac{2^{2/3} \sqrt[3]{c} d^{2/3} (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}+\frac{(d (b+2 c x))^{4/3}}{\left(a+b x+c x^2\right)^{2/3}}+2 \sqrt[3]{2} c^{2/3} d^{4/3}}{\left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1-\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}{2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{c x^2+b x+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{7480 c^{10/3} d^{23/3} \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{2/3} \sqrt{-\frac{(d (b+2 c x))^{2/3} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{(d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)}{\sqrt[3]{a+b x+c x^2} \left(2^{2/3} \sqrt[3]{c} d^{2/3}-\frac{\left(1+\sqrt{3}\right) (d (b+2 c x))^{2/3}}{\sqrt[3]{a+b x+c x^2}}\right)^2}}}-\frac{3 \sqrt[3]{a+b x+c x^2}}{187 c^2 d^3 (d (b+2 c x))^{11/3}}-\frac{3 \left(a+b x+c x^2\right)^{4/3}}{34 c d (d (b+2 c x))^{17/3}}",1,"(-3*(a + b*x + c*x^2)^(1/3))/(187*c^2*d^3*(d*(b + 2*c*x))^(11/3)) + (6*(a + b*x + c*x^2)^(1/3))/(935*c^2*(b^2 - 4*a*c)*d^5*(d*(b + 2*c*x))^(5/3)) - (3*(a + b*x + c*x^2)^(4/3))/(34*c*d*(d*(b + 2*c*x))^(17/3)) + (3*3^(3/4)*(d*(b + 2*c*x))^(1/3)*(b^2 - 4*a*c - (b + 2*c*x)^2)*(2*c^(1/3)*d^(2/3) - (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))*Sqrt[(2*2^(1/3)*c^(2/3)*d^(4/3) + (d*(b + 2*c*x))^(4/3)/(a + b*x + c*x^2)^(2/3) + (2^(2/3)*c^(1/3)*d^(2/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcCos[(2^(2/3)*c^(1/3)*d^(2/3) - ((1 - Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))], (2 + Sqrt[3])/4])/(7480*c^(10/3)*(b^2 - 4*a*c)^2*d^(23/3)*(a + b*x + c*x^2)^(2/3)*Sqrt[-(((d*(b + 2*c*x))^(2/3)*(2^(2/3)*c^(1/3)*d^(2/3) - (d*(b + 2*c*x))^(2/3)/(a + b*x + c*x^2)^(1/3)))/((a + b*x + c*x^2)^(1/3)*(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + Sqrt[3])*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2))])","A",7,6,28,0.2143,1,"{694, 277, 325, 329, 241, 225}"
1420,1,99,0,0.1242469,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{4/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(4/3),x]","\frac{3 \left(b^2-4 a c\right) \sqrt[3]{a+b x+c x^2} \, _2F_1\left(-\frac{4}{3},-\frac{1}{6};\frac{5}{6};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{8 c^2 d \sqrt[3]{1-\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[3]{d (b+2 c x)}}","\frac{3 \left(b^2-4 a c\right) \sqrt[3]{a+b x+c x^2} \, _2F_1\left(-\frac{4}{3},-\frac{1}{6};\frac{5}{6};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{8 c^2 d \sqrt[3]{1-\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[3]{d (b+2 c x)}}",1,"(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/3)*Hypergeometric2F1[-4/3, -1/6, 5/6, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(8*c^2*d*(d*(b + 2*c*x))^(1/3)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/3))","A",3,3,28,0.1071,1,"{694, 365, 364}"
1421,1,99,0,0.1127507,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{10/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(10/3),x]","\frac{3 \left(b^2-4 a c\right) \sqrt[3]{a+b x+c x^2} \, _2F_1\left(-\frac{4}{3},-\frac{7}{6};-\frac{1}{6};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{56 c^2 d \sqrt[3]{1-\frac{(b+2 c x)^2}{b^2-4 a c}} (d (b+2 c x))^{7/3}}","\frac{3 \left(b^2-4 a c\right) \sqrt[3]{a+b x+c x^2} \, _2F_1\left(-\frac{4}{3},-\frac{7}{6};-\frac{1}{6};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{56 c^2 d \sqrt[3]{1-\frac{(b+2 c x)^2}{b^2-4 a c}} (d (b+2 c x))^{7/3}}",1,"(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/3)*Hypergeometric2F1[-4/3, -7/6, -1/6, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(56*c^2*d*(d*(b + 2*c*x))^(7/3)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/3))","A",3,3,28,0.1071,1,"{694, 365, 364}"
1422,1,99,0,0.1163805,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(b d+2 c d x)^{16/3}} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(16/3),x]","\frac{3 \left(b^2-4 a c\right) \sqrt[3]{a+b x+c x^2} \, _2F_1\left(-\frac{13}{6},-\frac{4}{3};-\frac{7}{6};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{104 c^2 d \sqrt[3]{1-\frac{(b+2 c x)^2}{b^2-4 a c}} (d (b+2 c x))^{13/3}}","\frac{3 \left(b^2-4 a c\right) \sqrt[3]{a+b x+c x^2} \, _2F_1\left(-\frac{13}{6},-\frac{4}{3};-\frac{7}{6};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{104 c^2 d \sqrt[3]{1-\frac{(b+2 c x)^2}{b^2-4 a c}} (d (b+2 c x))^{13/3}}",1,"(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/3)*Hypergeometric2F1[-13/6, -4/3, -7/6, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(104*c^2*d*(d*(b + 2*c*x))^(13/3)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/3))","A",3,3,28,0.1071,1,"{694, 365, 364}"
1423,1,141,0,0.0786644,"\int (b d+2 c d x)^m \left(a+b x+c x^2\right)^3 \, dx","Int[(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^3,x]","\frac{3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{m+3}}{128 c^4 d^3 (m+3)}-\frac{3 \left(b^2-4 a c\right) (b d+2 c d x)^{m+5}}{128 c^4 d^5 (m+5)}-\frac{\left(b^2-4 a c\right)^3 (b d+2 c d x)^{m+1}}{128 c^4 d (m+1)}+\frac{(b d+2 c d x)^{m+7}}{128 c^4 d^7 (m+7)}","\frac{3 \left(b^2-4 a c\right)^2 (b d+2 c d x)^{m+3}}{128 c^4 d^3 (m+3)}-\frac{3 \left(b^2-4 a c\right) (b d+2 c d x)^{m+5}}{128 c^4 d^5 (m+5)}-\frac{\left(b^2-4 a c\right)^3 (b d+2 c d x)^{m+1}}{128 c^4 d (m+1)}+\frac{(b d+2 c d x)^{m+7}}{128 c^4 d^7 (m+7)}",1,"-((b^2 - 4*a*c)^3*(b*d + 2*c*d*x)^(1 + m))/(128*c^4*d*(1 + m)) + (3*(b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(3 + m))/(128*c^4*d^3*(3 + m)) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5 + m))/(128*c^4*d^5*(5 + m)) + (b*d + 2*c*d*x)^(7 + m)/(128*c^4*d^7*(7 + m))","A",2,1,24,0.04167,1,"{683}"
1424,1,103,0,0.0505594,"\int (b d+2 c d x)^m \left(a+b x+c x^2\right)^2 \, dx","Int[(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^2,x]","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{m+3}}{16 c^3 d^3 (m+3)}+\frac{\left(b^2-4 a c\right)^2 (b d+2 c d x)^{m+1}}{32 c^3 d (m+1)}+\frac{(b d+2 c d x)^{m+5}}{32 c^3 d^5 (m+5)}","-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{m+3}}{16 c^3 d^3 (m+3)}+\frac{\left(b^2-4 a c\right)^2 (b d+2 c d x)^{m+1}}{32 c^3 d (m+1)}+\frac{(b d+2 c d x)^{m+5}}{32 c^3 d^5 (m+5)}",1,"((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(1 + m))/(32*c^3*d*(1 + m)) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3 + m))/(16*c^3*d^3*(3 + m)) + (b*d + 2*c*d*x)^(5 + m)/(32*c^3*d^5*(5 + m))","A",2,1,24,0.04167,1,"{683}"
1425,1,65,0,0.0284689,"\int (b d+2 c d x)^m \left(a+b x+c x^2\right) \, dx","Int[(b*d + 2*c*d*x)^m*(a + b*x + c*x^2),x]","\frac{(b d+2 c d x)^{m+3}}{8 c^2 d^3 (m+3)}-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{m+1}}{8 c^2 d (m+1)}","\frac{(b d+2 c d x)^{m+3}}{8 c^2 d^3 (m+3)}-\frac{\left(b^2-4 a c\right) (b d+2 c d x)^{m+1}}{8 c^2 d (m+1)}",1,"-((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(1 + m))/(8*c^2*d*(1 + m)) + (b*d + 2*c*d*x)^(3 + m)/(8*c^2*d^3*(3 + m))","A",2,1,22,0.04545,1,"{683}"
1426,1,67,0,0.0437272,"\int \frac{(b d+2 c d x)^m}{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^m/(a + b*x + c*x^2),x]","-\frac{2 (d (b+2 c x))^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)}","-\frac{2 (d (b+2 c x))^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)}",1,"(-2*(d*(b + 2*c*x))^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/((b^2 - 4*a*c)*d*(1 + m))","A",2,2,24,0.08333,1,"{694, 364}"
1427,1,68,0,0.0466202,"\int \frac{(b d+2 c d x)^m}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^2,x]","\frac{8 c (d (b+2 c x))^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)^2}","\frac{8 c (d (b+2 c x))^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)^2}",1,"(8*c*(d*(b + 2*c*x))^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/((b^2 - 4*a*c)^2*d*(1 + m))","A",2,2,24,0.08333,1,"{694, 364}"
1428,1,70,0,0.0516068,"\int \frac{(b d+2 c d x)^m}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^3,x]","-\frac{32 c^2 (d (b+2 c x))^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)^3}","-\frac{32 c^2 (d (b+2 c x))^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)^3}",1,"(-32*c^2*(d*(b + 2*c*x))^(1 + m)*Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/((b^2 - 4*a*c)^3*d*(1 + m))","A",2,2,24,0.08333,1,"{694, 364}"
1429,1,114,0,0.119357,"\int (b d+2 c d x)^m \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(5/2),x]","\frac{\left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} (d (b+2 c x))^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{32 c^3 d (m+1) \sqrt{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}","-\frac{2 \left(a+b x+c x^2\right)^{7/2} (b d+2 c d x)^{m+1} \, _2F_1\left(1,\frac{m+8}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)}",1,"((b^2 - 4*a*c)^2*(d*(b + 2*c*x))^(1 + m)*Sqrt[a + b*x + c*x^2]*Hypergeometric2F1[-5/2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(32*c^3*d*(1 + m)*Sqrt[1 - (b + 2*c*x)^2/(b^2 - 4*a*c)])","A",3,3,26,0.1154,1,"{694, 365, 364}"
1430,1,112,0,0.1196402,"\int (b d+2 c d x)^m \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(3/2),x]","-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (d (b+2 c x))^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{8 c^2 d (m+1) \sqrt{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}","-\frac{\left(4 a-\frac{b^2}{c}+\frac{(b+2 c x)^2}{c}\right)^{5/2} (b d+2 c d x)^{m+1} \, _2F_1\left(1,\frac{m+6}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{16 d (m+1) \left(b^2-4 a c\right)}",1,"-((b^2 - 4*a*c)*(d*(b + 2*c*x))^(1 + m)*Sqrt[a + b*x + c*x^2]*Hypergeometric2F1[-3/2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(8*c^2*d*(1 + m)*Sqrt[1 - (b + 2*c*x)^2/(b^2 - 4*a*c)])","A",3,3,26,0.1154,1,"{694, 365, 364}"
1431,1,104,0,0.1083484,"\int (b d+2 c d x)^m \sqrt{a+b x+c x^2} \, dx","Int[(b*d + 2*c*d*x)^m*Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} (d (b+2 c x))^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{2 c d (m+1) \sqrt{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}","-\frac{\left(4 a-\frac{b^2}{c}+\frac{(b+2 c x)^2}{c}\right)^{3/2} (b d+2 c d x)^{m+1} \, _2F_1\left(1,\frac{m+4}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{4 d (m+1) \left(b^2-4 a c\right)}",1,"((d*(b + 2*c*x))^(1 + m)*Sqrt[a + b*x + c*x^2]*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(2*c*d*(1 + m)*Sqrt[1 - (b + 2*c*x)^2/(b^2 - 4*a*c)])","A",3,3,26,0.1154,1,"{694, 365, 364}"
1432,1,104,0,0.1068374,"\int \frac{(b d+2 c d x)^m}{\sqrt{a+b x+c x^2}} \, dx","Int[(b*d + 2*c*d*x)^m/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{1-\frac{(b+2 c x)^2}{b^2-4 a c}} (d (b+2 c x))^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{2 c d (m+1) \sqrt{a+b x+c x^2}}","-\frac{\sqrt{4 a-\frac{b^2}{c}+\frac{(b+2 c x)^2}{c}} (b d+2 c d x)^{m+1} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)}",1,"((d*(b + 2*c*x))^(1 + m)*Sqrt[1 - (b + 2*c*x)^2/(b^2 - 4*a*c)]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(2*c*d*(1 + m)*Sqrt[a + b*x + c*x^2])","A",3,3,26,0.1154,1,"{694, 365, 364}"
1433,1,109,0,0.1143323,"\int \frac{(b d+2 c d x)^m}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 \sqrt{1-\frac{(b+2 c x)^2}{b^2-4 a c}} (d (b+2 c x))^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{4 (b d+2 c d x)^{m+1} \, _2F_1\left(1,\frac{m}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right) \sqrt{4 a-\frac{b^2}{c}+\frac{(b+2 c x)^2}{c}}}",1,"(-2*(d*(b + 2*c*x))^(1 + m)*Sqrt[1 - (b + 2*c*x)^2/(b^2 - 4*a*c)]*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/((b^2 - 4*a*c)*d*(1 + m)*Sqrt[a + b*x + c*x^2])","A",3,3,26,0.1154,1,"{694, 365, 364}"
1434,1,110,0,0.1169537,"\int \frac{(b d+2 c d x)^m}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(5/2),x]","\frac{8 c \sqrt{1-\frac{(b+2 c x)^2}{b^2-4 a c}} (d (b+2 c x))^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}","-\frac{16 (b d+2 c d x)^{m+1} \, _2F_1\left(1,\frac{m-2}{2};\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right) \left(4 a-\frac{b^2}{c}+\frac{(b+2 c x)^2}{c}\right)^{3/2}}",1,"(8*c*(d*(b + 2*c*x))^(1 + m)*Sqrt[1 - (b + 2*c*x)^2/(b^2 - 4*a*c)]*Hypergeometric2F1[5/2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/((b^2 - 4*a*c)^2*d*(1 + m)*Sqrt[a + b*x + c*x^2])","A",3,3,26,0.1154,1,"{694, 365, 364}"
1435,1,102,0,0.074085,"\int (b d+2 c d x)^m \left(a+b x+c x^2\right)^p \, dx","Int[(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^p,x]","\frac{\left(a+b x+c x^2\right)^p \left(1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)^{-p} (d (b+2 c x))^{m+1} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{2 c d (m+1)}","-\frac{2 \left(\frac{1}{4} \left(4 a-\frac{b^2}{c}\right)+\frac{(b+2 c x)^2}{4 c}\right)^{p+1} (b d+2 c d x)^{m+1} \, _2F_1\left(1,\frac{1}{2} (m+2 p+3);\frac{m+3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (m+1) \left(b^2-4 a c\right)}",1,"((d*(b + 2*c*x))^(1 + m)*(a + b*x + c*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(2*c*d*(1 + m)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p)","A",3,3,24,0.1250,1,"{694, 365, 364}"
1436,1,121,0,0.0730149,"\int (b d+2 c d x)^5 \left(a+b x+c x^2\right)^p \, dx","Int[(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^p,x]","\frac{2 d^5 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^{p+1}}{(p+2) (p+3)}+\frac{2 d^5 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{p+1}}{(p+1) (p+2) (p+3)}+\frac{d^5 (b+2 c x)^4 \left(a+b x+c x^2\right)^{p+1}}{p+3}","\frac{2 d^5 \left(b^2-4 a c\right) (b+2 c x)^2 \left(a+b x+c x^2\right)^{p+1}}{(p+2) (p+3)}+\frac{2 d^5 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{p+1}}{(p+1) (p+2) (p+3)}+\frac{d^5 (b+2 c x)^4 \left(a+b x+c x^2\right)^{p+1}}{p+3}",1,"(2*(b^2 - 4*a*c)^2*d^5*(a + b*x + c*x^2)^(1 + p))/((1 + p)*(2 + p)*(3 + p)) + (2*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2*(a + b*x + c*x^2)^(1 + p))/((2 + p)*(3 + p)) + (d^5*(b + 2*c*x)^4*(a + b*x + c*x^2)^(1 + p))/(3 + p)","A",3,2,24,0.08333,1,"{692, 629}"
1437,1,85,0,0.0695637,"\int (b d+2 c d x)^4 \left(a+b x+c x^2\right)^p \, dx","Int[(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^p,x]","\frac{d^4 (b+2 c x)^5 \left(a+b x+c x^2\right)^p \left(1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{10 c}","-\frac{2 d^4 (b+2 c x)^5 \left(\frac{1}{4} \left(4 a-\frac{b^2}{c}\right)+\frac{(b+2 c x)^2}{4 c}\right)^{p+1} \, _2F_1\left(1,p+\frac{7}{2};\frac{7}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{5 \left(b^2-4 a c\right)}",1,"(d^4*(b + 2*c*x)^5*(a + b*x + c*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(10*c*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p)","A",3,3,24,0.1250,1,"{694, 365, 364}"
1438,1,68,0,0.0266789,"\int (b d+2 c d x)^3 \left(a+b x+c x^2\right)^p \, dx","Int[(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^p,x]","\frac{d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{p+1}}{(p+1) (p+2)}+\frac{d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^{p+1}}{p+2}","\frac{d^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{p+1}}{(p+1) (p+2)}+\frac{d^3 (b+2 c x)^2 \left(a+b x+c x^2\right)^{p+1}}{p+2}",1,"((b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^(1 + p))/((1 + p)*(2 + p)) + (d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(1 + p))/(2 + p)","A",2,2,24,0.08333,1,"{692, 629}"
1439,1,85,0,0.0691887,"\int (b d+2 c d x)^2 \left(a+b x+c x^2\right)^p \, dx","Int[(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^p,x]","\frac{d^2 (b+2 c x)^3 \left(a+b x+c x^2\right)^p \left(1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{6 c}","-\frac{2 d^2 (b+2 c x)^3 \left(\frac{1}{4} \left(4 a-\frac{b^2}{c}\right)+\frac{(b+2 c x)^2}{4 c}\right)^{p+1} \, _2F_1\left(1,p+\frac{5}{2};\frac{5}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{3 \left(b^2-4 a c\right)}",1,"(d^2*(b + 2*c*x)^3*(a + b*x + c*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(6*c*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p)","A",3,3,24,0.1250,1,"{694, 365, 364}"
1440,1,21,0,0.0055643,"\int (b d+2 c d x) \left(a+b x+c x^2\right)^p \, dx","Int[(b*d + 2*c*d*x)*(a + b*x + c*x^2)^p,x]","\frac{d \left(a+b x+c x^2\right)^{p+1}}{p+1}","\frac{d \left(a+b x+c x^2\right)^{p+1}}{p+1}",1,"(d*(a + b*x + c*x^2)^(1 + p))/(1 + p)","A",1,1,22,0.04545,1,"{629}"
1441,1,63,0,0.1023143,"\int \frac{\left(a+b x+c x^2\right)^p}{b d+2 c d x} \, dx","Int[(a + b*x + c*x^2)^p/(b*d + 2*c*d*x),x]","\frac{\left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (p+1) \left(b^2-4 a c\right)}","\frac{\left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d (p+1) \left(b^2-4 a c\right)}",1,"((a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (b + 2*c*x)^2/(b^2 - 4*a*c)])/((b^2 - 4*a*c)*d*(1 + p))","A",3,3,24,0.1250,1,"{694, 266, 65}"
1442,1,85,0,0.0671433,"\int \frac{\left(a+b x+c x^2\right)^p}{(b d+2 c d x)^2} \, dx","Int[(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^2,x]","-\frac{\left(a+b x+c x^2\right)^p \left(1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{2 c d^2 (b+2 c x)}","\frac{2 \left(\frac{1}{4} \left(4 a-\frac{b^2}{c}\right)+\frac{(b+2 c x)^2}{4 c}\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{2};\frac{1}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d^2 \left(b^2-4 a c\right) (b+2 c x)}",1,"-((a + b*x + c*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(2*c*d^2*(b + 2*c*x)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p)","A",3,3,24,0.1250,1,"{694, 365, 364}"
1443,1,63,0,0.1016221,"\int \frac{\left(a+b x+c x^2\right)^p}{(b d+2 c d x)^3} \, dx","Int[(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^3,x]","\frac{\left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d^3 (p+1) \left(b^2-4 a c\right)^2}","\frac{\left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d^3 (p+1) \left(b^2-4 a c\right)^2}",1,"((a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, 1 - (b + 2*c*x)^2/(b^2 - 4*a*c)])/((b^2 - 4*a*c)^2*d^3*(1 + p))","A",3,3,24,0.1250,1,"{694, 266, 65}"
1444,1,85,0,0.0682533,"\int \frac{\left(a+b x+c x^2\right)^p}{(b d+2 c d x)^4} \, dx","Int[(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^4,x]","-\frac{\left(a+b x+c x^2\right)^p \left(1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)^{-p} \, _2F_1\left(-\frac{3}{2},-p;-\frac{1}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{6 c d^4 (b+2 c x)^3}","\frac{2 \left(\frac{1}{4} \left(4 a-\frac{b^2}{c}\right)+\frac{(b+2 c x)^2}{4 c}\right)^{p+1} \, _2F_1\left(1,p-\frac{1}{2};-\frac{1}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{3 d^4 \left(b^2-4 a c\right) (b+2 c x)^3}",1,"-((a + b*x + c*x^2)^p*Hypergeometric2F1[-3/2, -p, -1/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(6*c*d^4*(b + 2*c*x)^3*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p)","A",3,3,24,0.1250,1,"{694, 365, 364}"
1445,1,63,0,0.1054989,"\int \frac{\left(a+b x+c x^2\right)^p}{(b d+2 c d x)^5} \, dx","Int[(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^5,x]","\frac{\left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d^5 (p+1) \left(b^2-4 a c\right)^3}","\frac{\left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(3,p+1;p+2;1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{d^5 (p+1) \left(b^2-4 a c\right)^3}",1,"((a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[3, 1 + p, 2 + p, 1 - (b + 2*c*x)^2/(b^2 - 4*a*c)])/((b^2 - 4*a*c)^3*d^5*(1 + p))","A",3,3,24,0.1250,1,"{694, 266, 65}"
1446,1,85,0,0.0679028,"\int \frac{\left(a+b x+c x^2\right)^p}{(b d+2 c d x)^6} \, dx","Int[(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^6,x]","-\frac{\left(a+b x+c x^2\right)^p \left(1-\frac{(b+2 c x)^2}{b^2-4 a c}\right)^{-p} \, _2F_1\left(-\frac{5}{2},-p;-\frac{3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{10 c d^6 (b+2 c x)^5}","\frac{2 \left(\frac{1}{4} \left(4 a-\frac{b^2}{c}\right)+\frac{(b+2 c x)^2}{4 c}\right)^{p+1} \, _2F_1\left(1,p-\frac{3}{2};-\frac{3}{2};\frac{(b+2 c x)^2}{b^2-4 a c}\right)}{5 d^6 \left(b^2-4 a c\right) (b+2 c x)^5}",1,"-((a + b*x + c*x^2)^p*Hypergeometric2F1[-5/2, -p, -3/2, (b + 2*c*x)^2/(b^2 - 4*a*c)])/(10*c*d^6*(b + 2*c*x)^5*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p)","A",3,3,24,0.1250,1,"{694, 365, 364}"
1447,1,16,0,0.0039318,"\int \frac{1+x}{\left(-3+2 x+x^2\right)^{2/3}} \, dx","Int[(1 + x)/(-3 + 2*x + x^2)^(2/3),x]","\frac{3}{2} \sqrt[3]{x^2+2 x-3}","\frac{3}{2} \sqrt[3]{x^2+2 x-3}",1,"(3*(-3 + 2*x + x^2)^(1/3))/2","A",1,1,16,0.06250,1,"{629}"
1448,1,19,0,0.0064562,"\int \frac{b+c x}{\left(a+2 b x+c x^2\right)^{3/7}} \, dx","Int[(b + c*x)/(a + 2*b*x + c*x^2)^(3/7),x]","\frac{7}{8} \left(a+2 b x+c x^2\right)^{4/7}","\frac{7}{8} \left(a+2 b x+c x^2\right)^{4/7}",1,"(7*(a + 2*b*x + c*x^2)^(4/7))/8","A",1,1,21,0.04762,1,"{629}"
1449,1,26,0,0.0108419,"\int (1+x)^m \left(1+2 x+x^2\right)^n \, dx","Int[(1 + x)^m*(1 + 2*x + x^2)^n,x]","\frac{(x+1)^{m+1} \left(x^2+2 x+1\right)^n}{m+2 n+1}","\frac{(x+1)^{m+1} \left(x^2+2 x+1\right)^n}{m+2 n+1}",1,"((1 + x)^(1 + m)*(1 + 2*x + x^2)^n)/(1 + m + 2*n)","A",2,2,16,0.1250,1,"{644, 32}"
1450,1,50,0,0.0205833,"\int \left(\frac{b e}{2 c}+e x\right)^m \left(\frac{b^2}{4 c}+b x+c x^2\right)^n \, dx","Int[((b*e)/(2*c) + e*x)^m*(b^2/(4*c) + b*x + c*x^2)^n,x]","\frac{\left(\frac{b^2}{4 c}+b x+c x^2\right)^n \left(\frac{b e}{2 c}+e x\right)^{m+1}}{e (m+2 n+1)}","\frac{\left(\frac{b^2}{4 c}+b x+c x^2\right)^n \left(\frac{b e}{2 c}+e x\right)^{m+1}}{e (m+2 n+1)}",1,"(((b*e)/(2*c) + e*x)^(1 + m)*(b^2/(4*c) + b*x + c*x^2)^n)/(e*(1 + m + 2*n))","A",2,2,37,0.05405,1,"{644, 32}"
1451,1,65,0,0.0977775,"\int (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{b (d+e x)^6 (b d-a e)}{3 e^3}+\frac{(d+e x)^5 (b d-a e)^2}{5 e^3}+\frac{b^2 (d+e x)^7}{7 e^3}","-\frac{b (d+e x)^6 (b d-a e)}{3 e^3}+\frac{(d+e x)^5 (b d-a e)^2}{5 e^3}+\frac{b^2 (d+e x)^7}{7 e^3}",1,"((b*d - a*e)^2*(d + e*x)^5)/(5*e^3) - (b*(b*d - a*e)*(d + e*x)^6)/(3*e^3) + (b^2*(d + e*x)^7)/(7*e^3)","A",3,2,24,0.08333,1,"{27, 43}"
1452,1,65,0,0.0679921,"\int (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{2 b (d+e x)^5 (b d-a e)}{5 e^3}+\frac{(d+e x)^4 (b d-a e)^2}{4 e^3}+\frac{b^2 (d+e x)^6}{6 e^3}","-\frac{2 b (d+e x)^5 (b d-a e)}{5 e^3}+\frac{(d+e x)^4 (b d-a e)^2}{4 e^3}+\frac{b^2 (d+e x)^6}{6 e^3}",1,"((b*d - a*e)^2*(d + e*x)^4)/(4*e^3) - (2*b*(b*d - a*e)*(d + e*x)^5)/(5*e^3) + (b^2*(d + e*x)^6)/(6*e^3)","A",3,2,24,0.08333,1,"{27, 43}"
1453,1,65,0,0.07521,"\int (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e (a+b x)^4 (b d-a e)}{2 b^3}+\frac{(a+b x)^3 (b d-a e)^2}{3 b^3}+\frac{e^2 (a+b x)^5}{5 b^3}","\frac{e (a+b x)^4 (b d-a e)}{2 b^3}+\frac{(a+b x)^3 (b d-a e)^2}{3 b^3}+\frac{e^2 (a+b x)^5}{5 b^3}",1,"((b*d - a*e)^2*(a + b*x)^3)/(3*b^3) + (e*(b*d - a*e)*(a + b*x)^4)/(2*b^3) + (e^2*(a + b*x)^5)/(5*b^3)","A",3,2,24,0.08333,1,"{27, 43}"
1454,1,38,0,0.0297702,"\int (d+e x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(a+b x)^3 (b d-a e)}{3 b^2}+\frac{e (a+b x)^4}{4 b^2}","\frac{(a+b x)^3 (b d-a e)}{3 b^2}+\frac{e (a+b x)^4}{4 b^2}",1,"((b*d - a*e)*(a + b*x)^3)/(3*b^2) + (e*(a + b*x)^4)/(4*b^2)","A",3,2,22,0.09091,1,"{27, 43}"
1455,1,22,0,0.004962,"\int \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[a^2 + 2*a*b*x + b^2*x^2,x]","a^2 x+a b x^2+\frac{b^2 x^3}{3}","a^2 x+a b x^2+\frac{b^2 x^3}{3}",1,"a^2*x + a*b*x^2 + (b^2*x^3)/3","A",1,0,16,0,1,"{}"
1456,1,50,0,0.021483,"\int \frac{a^2+2 a b x+b^2 x^2}{d+e x} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x),x]","-\frac{b x (b d-a e)}{e^2}+\frac{(b d-a e)^2 \log (d+e x)}{e^3}+\frac{(a+b x)^2}{2 e}","-\frac{b x (b d-a e)}{e^2}+\frac{(b d-a e)^2 \log (d+e x)}{e^3}+\frac{(a+b x)^2}{2 e}",1,"-((b*(b*d - a*e)*x)/e^2) + (a + b*x)^2/(2*e) + ((b*d - a*e)^2*Log[d + e*x])/e^3","A",3,2,24,0.08333,1,"{27, 43}"
1457,1,51,0,0.0477378,"\int \frac{a^2+2 a b x+b^2 x^2}{(d+e x)^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x)^2,x]","-\frac{(b d-a e)^2}{e^3 (d+e x)}-\frac{2 b (b d-a e) \log (d+e x)}{e^3}+\frac{b^2 x}{e^2}","-\frac{(b d-a e)^2}{e^3 (d+e x)}-\frac{2 b (b d-a e) \log (d+e x)}{e^3}+\frac{b^2 x}{e^2}",1,"(b^2*x)/e^2 - (b*d - a*e)^2/(e^3*(d + e*x)) - (2*b*(b*d - a*e)*Log[d + e*x])/e^3","A",3,2,24,0.08333,1,"{27, 43}"
1458,1,59,0,0.0379732,"\int \frac{a^2+2 a b x+b^2 x^2}{(d+e x)^3} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x)^3,x]","\frac{2 b (b d-a e)}{e^3 (d+e x)}-\frac{(b d-a e)^2}{2 e^3 (d+e x)^2}+\frac{b^2 \log (d+e x)}{e^3}","\frac{2 b (b d-a e)}{e^3 (d+e x)}-\frac{(b d-a e)^2}{2 e^3 (d+e x)^2}+\frac{b^2 \log (d+e x)}{e^3}",1,"-(b*d - a*e)^2/(2*e^3*(d + e*x)^2) + (2*b*(b*d - a*e))/(e^3*(d + e*x)) + (b^2*Log[d + e*x])/e^3","A",3,2,24,0.08333,1,"{27, 43}"
1459,1,28,0,0.0054238,"\int \frac{a^2+2 a b x+b^2 x^2}{(d+e x)^4} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x)^4,x]","\frac{(a+b x)^3}{3 (d+e x)^3 (b d-a e)}","\frac{(a+b x)^3}{3 (d+e x)^3 (b d-a e)}",1,"(a + b*x)^3/(3*(b*d - a*e)*(d + e*x)^3)","A",2,2,24,0.08333,1,"{27, 37}"
1460,1,65,0,0.0371152,"\int \frac{a^2+2 a b x+b^2 x^2}{(d+e x)^5} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x)^5,x]","\frac{2 b (b d-a e)}{3 e^3 (d+e x)^3}-\frac{(b d-a e)^2}{4 e^3 (d+e x)^4}-\frac{b^2}{2 e^3 (d+e x)^2}","\frac{2 b (b d-a e)}{3 e^3 (d+e x)^3}-\frac{(b d-a e)^2}{4 e^3 (d+e x)^4}-\frac{b^2}{2 e^3 (d+e x)^2}",1,"-(b*d - a*e)^2/(4*e^3*(d + e*x)^4) + (2*b*(b*d - a*e))/(3*e^3*(d + e*x)^3) - b^2/(2*e^3*(d + e*x)^2)","A",3,2,24,0.08333,1,"{27, 43}"
1461,1,65,0,0.0364159,"\int \frac{a^2+2 a b x+b^2 x^2}{(d+e x)^6} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x)^6,x]","\frac{b (b d-a e)}{2 e^3 (d+e x)^4}-\frac{(b d-a e)^2}{5 e^3 (d+e x)^5}-\frac{b^2}{3 e^3 (d+e x)^3}","\frac{b (b d-a e)}{2 e^3 (d+e x)^4}-\frac{(b d-a e)^2}{5 e^3 (d+e x)^5}-\frac{b^2}{3 e^3 (d+e x)^3}",1,"-(b*d - a*e)^2/(5*e^3*(d + e*x)^5) + (b*(b*d - a*e))/(2*e^3*(d + e*x)^4) - b^2/(3*e^3*(d + e*x)^3)","A",3,2,24,0.08333,1,"{27, 43}"
1462,1,65,0,0.0365427,"\int \frac{a^2+2 a b x+b^2 x^2}{(d+e x)^7} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x)^7,x]","\frac{2 b (b d-a e)}{5 e^3 (d+e x)^5}-\frac{(b d-a e)^2}{6 e^3 (d+e x)^6}-\frac{b^2}{4 e^3 (d+e x)^4}","\frac{2 b (b d-a e)}{5 e^3 (d+e x)^5}-\frac{(b d-a e)^2}{6 e^3 (d+e x)^6}-\frac{b^2}{4 e^3 (d+e x)^4}",1,"-(b*d - a*e)^2/(6*e^3*(d + e*x)^6) + (2*b*(b*d - a*e))/(5*e^3*(d + e*x)^5) - b^2/(4*e^3*(d + e*x)^4)","A",3,2,24,0.08333,1,"{27, 43}"
1463,1,119,0,0.2668674,"\int (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{2 b^3 (d+e x)^{10} (b d-a e)}{5 e^5}+\frac{2 b^2 (d+e x)^9 (b d-a e)^2}{3 e^5}-\frac{b (d+e x)^8 (b d-a e)^3}{2 e^5}+\frac{(d+e x)^7 (b d-a e)^4}{7 e^5}+\frac{b^4 (d+e x)^{11}}{11 e^5}","-\frac{2 b^3 (d+e x)^{10} (b d-a e)}{5 e^5}+\frac{2 b^2 (d+e x)^9 (b d-a e)^2}{3 e^5}-\frac{b (d+e x)^8 (b d-a e)^3}{2 e^5}+\frac{(d+e x)^7 (b d-a e)^4}{7 e^5}+\frac{b^4 (d+e x)^{11}}{11 e^5}",1,"((b*d - a*e)^4*(d + e*x)^7)/(7*e^5) - (b*(b*d - a*e)^3*(d + e*x)^8)/(2*e^5) + (2*b^2*(b*d - a*e)^2*(d + e*x)^9)/(3*e^5) - (2*b^3*(b*d - a*e)*(d + e*x)^10)/(5*e^5) + (b^4*(d + e*x)^11)/(11*e^5)","A",3,2,26,0.07692,1,"{27, 43}"
1464,1,119,0,0.2081236,"\int (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{4 b^3 (d+e x)^9 (b d-a e)}{9 e^5}+\frac{3 b^2 (d+e x)^8 (b d-a e)^2}{4 e^5}-\frac{4 b (d+e x)^7 (b d-a e)^3}{7 e^5}+\frac{(d+e x)^6 (b d-a e)^4}{6 e^5}+\frac{b^4 (d+e x)^{10}}{10 e^5}","-\frac{4 b^3 (d+e x)^9 (b d-a e)}{9 e^5}+\frac{3 b^2 (d+e x)^8 (b d-a e)^2}{4 e^5}-\frac{4 b (d+e x)^7 (b d-a e)^3}{7 e^5}+\frac{(d+e x)^6 (b d-a e)^4}{6 e^5}+\frac{b^4 (d+e x)^{10}}{10 e^5}",1,"((b*d - a*e)^4*(d + e*x)^6)/(6*e^5) - (4*b*(b*d - a*e)^3*(d + e*x)^7)/(7*e^5) + (3*b^2*(b*d - a*e)^2*(d + e*x)^8)/(4*e^5) - (4*b^3*(b*d - a*e)*(d + e*x)^9)/(9*e^5) + (b^4*(d + e*x)^10)/(10*e^5)","A",3,2,26,0.07692,1,"{27, 43}"
1465,1,119,0,0.1649311,"\int (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^3 (a+b x)^8 (b d-a e)}{2 b^5}+\frac{6 e^2 (a+b x)^7 (b d-a e)^2}{7 b^5}+\frac{2 e (a+b x)^6 (b d-a e)^3}{3 b^5}+\frac{(a+b x)^5 (b d-a e)^4}{5 b^5}+\frac{e^4 (a+b x)^9}{9 b^5}","\frac{e^3 (a+b x)^8 (b d-a e)}{2 b^5}+\frac{6 e^2 (a+b x)^7 (b d-a e)^2}{7 b^5}+\frac{2 e (a+b x)^6 (b d-a e)^3}{3 b^5}+\frac{(a+b x)^5 (b d-a e)^4}{5 b^5}+\frac{e^4 (a+b x)^9}{9 b^5}",1,"((b*d - a*e)^4*(a + b*x)^5)/(5*b^5) + (2*e*(b*d - a*e)^3*(a + b*x)^6)/(3*b^5) + (6*e^2*(b*d - a*e)^2*(a + b*x)^7)/(7*b^5) + (e^3*(b*d - a*e)*(a + b*x)^8)/(2*b^5) + (e^4*(a + b*x)^9)/(9*b^5)","A",3,2,26,0.07692,1,"{27, 43}"
1466,1,92,0,0.1300129,"\int (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{3 e^2 (a+b x)^7 (b d-a e)}{7 b^4}+\frac{e (a+b x)^6 (b d-a e)^2}{2 b^4}+\frac{(a+b x)^5 (b d-a e)^3}{5 b^4}+\frac{e^3 (a+b x)^8}{8 b^4}","\frac{3 e^2 (a+b x)^7 (b d-a e)}{7 b^4}+\frac{e (a+b x)^6 (b d-a e)^2}{2 b^4}+\frac{(a+b x)^5 (b d-a e)^3}{5 b^4}+\frac{e^3 (a+b x)^8}{8 b^4}",1,"((b*d - a*e)^3*(a + b*x)^5)/(5*b^4) + (e*(b*d - a*e)^2*(a + b*x)^6)/(2*b^4) + (3*e^2*(b*d - a*e)*(a + b*x)^7)/(7*b^4) + (e^3*(a + b*x)^8)/(8*b^4)","A",3,2,26,0.07692,1,"{27, 43}"
1467,1,65,0,0.086089,"\int (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e (a+b x)^6 (b d-a e)}{3 b^3}+\frac{(a+b x)^5 (b d-a e)^2}{5 b^3}+\frac{e^2 (a+b x)^7}{7 b^3}","\frac{e (a+b x)^6 (b d-a e)}{3 b^3}+\frac{(a+b x)^5 (b d-a e)^2}{5 b^3}+\frac{e^2 (a+b x)^7}{7 b^3}",1,"((b*d - a*e)^2*(a + b*x)^5)/(5*b^3) + (e*(b*d - a*e)*(a + b*x)^6)/(3*b^3) + (e^2*(a + b*x)^7)/(7*b^3)","A",3,2,26,0.07692,1,"{27, 43}"
1468,1,38,0,0.0158858,"\int (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(a+b x)^5 (b d-a e)}{5 b^2}+\frac{e (a+b x)^6}{6 b^2}","\frac{(a+b x)^5 (b d-a e)}{5 b^2}+\frac{e (a+b x)^6}{6 b^2}",1,"((b*d - a*e)*(a + b*x)^5)/(5*b^2) + (e*(a + b*x)^6)/(6*b^2)","A",3,2,24,0.08333,1,"{27, 43}"
1469,1,14,0,0.0023447,"\int \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(a+b x)^5}{5 b}","\frac{(a+b x)^5}{5 b}",1,"(a + b*x)^5/(5*b)","A",2,2,18,0.1111,1,"{27, 32}"
1470,1,98,0,0.0423296,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{d+e x} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x),x]","-\frac{b x (b d-a e)^3}{e^4}+\frac{(a+b x)^2 (b d-a e)^2}{2 e^3}-\frac{(a+b x)^3 (b d-a e)}{3 e^2}+\frac{(b d-a e)^4 \log (d+e x)}{e^5}+\frac{(a+b x)^4}{4 e}","-\frac{b x (b d-a e)^3}{e^4}+\frac{(a+b x)^2 (b d-a e)^2}{2 e^3}-\frac{(a+b x)^3 (b d-a e)}{3 e^2}+\frac{(b d-a e)^4 \log (d+e x)}{e^5}+\frac{(a+b x)^4}{4 e}",1,"-((b*(b*d - a*e)^3*x)/e^4) + ((b*d - a*e)^2*(a + b*x)^2)/(2*e^3) - ((b*d - a*e)*(a + b*x)^3)/(3*e^2) + (a + b*x)^4/(4*e) + ((b*d - a*e)^4*Log[d + e*x])/e^5","A",3,2,26,0.07692,1,"{27, 43}"
1471,1,104,0,0.1000237,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^2,x]","-\frac{2 b^3 (d+e x)^2 (b d-a e)}{e^5}+\frac{6 b^2 x (b d-a e)^2}{e^4}-\frac{(b d-a e)^4}{e^5 (d+e x)}-\frac{4 b (b d-a e)^3 \log (d+e x)}{e^5}+\frac{b^4 (d+e x)^3}{3 e^5}","-\frac{2 b^3 (d+e x)^2 (b d-a e)}{e^5}+\frac{6 b^2 x (b d-a e)^2}{e^4}-\frac{(b d-a e)^4}{e^5 (d+e x)}-\frac{4 b (b d-a e)^3 \log (d+e x)}{e^5}+\frac{b^4 (d+e x)^3}{3 e^5}",1,"(6*b^2*(b*d - a*e)^2*x)/e^4 - (b*d - a*e)^4/(e^5*(d + e*x)) - (2*b^3*(b*d - a*e)*(d + e*x)^2)/e^5 + (b^4*(d + e*x)^3)/(3*e^5) - (4*b*(b*d - a*e)^3*Log[d + e*x])/e^5","A",3,2,26,0.07692,1,"{27, 43}"
1472,1,103,0,0.0852951,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^3} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^3,x]","-\frac{b^3 x (3 b d-4 a e)}{e^4}+\frac{6 b^2 (b d-a e)^2 \log (d+e x)}{e^5}+\frac{4 b (b d-a e)^3}{e^5 (d+e x)}-\frac{(b d-a e)^4}{2 e^5 (d+e x)^2}+\frac{b^4 x^2}{2 e^3}","-\frac{b^3 x (3 b d-4 a e)}{e^4}+\frac{6 b^2 (b d-a e)^2 \log (d+e x)}{e^5}+\frac{4 b (b d-a e)^3}{e^5 (d+e x)}-\frac{(b d-a e)^4}{2 e^5 (d+e x)^2}+\frac{b^4 x^2}{2 e^3}",1,"-((b^3*(3*b*d - 4*a*e)*x)/e^4) + (b^4*x^2)/(2*e^3) - (b*d - a*e)^4/(2*e^5*(d + e*x)^2) + (4*b*(b*d - a*e)^3)/(e^5*(d + e*x)) + (6*b^2*(b*d - a*e)^2*Log[d + e*x])/e^5","A",3,2,26,0.07692,1,"{27, 43}"
1473,1,103,0,0.0798661,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^4} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^4,x]","-\frac{6 b^2 (b d-a e)^2}{e^5 (d+e x)}-\frac{4 b^3 (b d-a e) \log (d+e x)}{e^5}+\frac{2 b (b d-a e)^3}{e^5 (d+e x)^2}-\frac{(b d-a e)^4}{3 e^5 (d+e x)^3}+\frac{b^4 x}{e^4}","-\frac{6 b^2 (b d-a e)^2}{e^5 (d+e x)}-\frac{4 b^3 (b d-a e) \log (d+e x)}{e^5}+\frac{2 b (b d-a e)^3}{e^5 (d+e x)^2}-\frac{(b d-a e)^4}{3 e^5 (d+e x)^3}+\frac{b^4 x}{e^4}",1,"(b^4*x)/e^4 - (b*d - a*e)^4/(3*e^5*(d + e*x)^3) + (2*b*(b*d - a*e)^3)/(e^5*(d + e*x)^2) - (6*b^2*(b*d - a*e)^2)/(e^5*(d + e*x)) - (4*b^3*(b*d - a*e)*Log[d + e*x])/e^5","A",3,2,26,0.07692,1,"{27, 43}"
1474,1,111,0,0.0765808,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^5} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^5,x]","\frac{4 b^3 (b d-a e)}{e^5 (d+e x)}-\frac{3 b^2 (b d-a e)^2}{e^5 (d+e x)^2}+\frac{4 b (b d-a e)^3}{3 e^5 (d+e x)^3}-\frac{(b d-a e)^4}{4 e^5 (d+e x)^4}+\frac{b^4 \log (d+e x)}{e^5}","\frac{4 b^3 (b d-a e)}{e^5 (d+e x)}-\frac{3 b^2 (b d-a e)^2}{e^5 (d+e x)^2}+\frac{4 b (b d-a e)^3}{3 e^5 (d+e x)^3}-\frac{(b d-a e)^4}{4 e^5 (d+e x)^4}+\frac{b^4 \log (d+e x)}{e^5}",1,"-(b*d - a*e)^4/(4*e^5*(d + e*x)^4) + (4*b*(b*d - a*e)^3)/(3*e^5*(d + e*x)^3) - (3*b^2*(b*d - a*e)^2)/(e^5*(d + e*x)^2) + (4*b^3*(b*d - a*e))/(e^5*(d + e*x)) + (b^4*Log[d + e*x])/e^5","A",3,2,26,0.07692,1,"{27, 43}"
1475,1,28,0,0.004715,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^6} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^6,x]","\frac{(a+b x)^5}{5 (d+e x)^5 (b d-a e)}","\frac{(a+b x)^5}{5 (d+e x)^5 (b d-a e)}",1,"(a + b*x)^5/(5*(b*d - a*e)*(d + e*x)^5)","A",2,2,26,0.07692,1,"{27, 37}"
1476,1,58,0,0.0142256,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^7} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^7,x]","\frac{b (a+b x)^5}{30 (d+e x)^5 (b d-a e)^2}+\frac{(a+b x)^5}{6 (d+e x)^6 (b d-a e)}","\frac{b (a+b x)^5}{30 (d+e x)^5 (b d-a e)^2}+\frac{(a+b x)^5}{6 (d+e x)^6 (b d-a e)}",1,"(a + b*x)^5/(6*(b*d - a*e)*(d + e*x)^6) + (b*(a + b*x)^5)/(30*(b*d - a*e)^2*(d + e*x)^5)","A",3,3,26,0.1154,1,"{27, 45, 37}"
1477,1,89,0,0.0214929,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^8} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^8,x]","\frac{b^2 (a+b x)^5}{105 (d+e x)^5 (b d-a e)^3}+\frac{b (a+b x)^5}{21 (d+e x)^6 (b d-a e)^2}+\frac{(a+b x)^5}{7 (d+e x)^7 (b d-a e)}","\frac{b^2 (a+b x)^5}{105 (d+e x)^5 (b d-a e)^3}+\frac{b (a+b x)^5}{21 (d+e x)^6 (b d-a e)^2}+\frac{(a+b x)^5}{7 (d+e x)^7 (b d-a e)}",1,"(a + b*x)^5/(7*(b*d - a*e)*(d + e*x)^7) + (b*(a + b*x)^5)/(21*(b*d - a*e)^2*(d + e*x)^6) + (b^2*(a + b*x)^5)/(105*(b*d - a*e)^3*(d + e*x)^5)","A",4,3,26,0.1154,1,"{27, 45, 37}"
1478,1,117,0,0.0713198,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^9} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^9,x]","\frac{4 b^3 (b d-a e)}{5 e^5 (d+e x)^5}-\frac{b^2 (b d-a e)^2}{e^5 (d+e x)^6}+\frac{4 b (b d-a e)^3}{7 e^5 (d+e x)^7}-\frac{(b d-a e)^4}{8 e^5 (d+e x)^8}-\frac{b^4}{4 e^5 (d+e x)^4}","\frac{4 b^3 (b d-a e)}{5 e^5 (d+e x)^5}-\frac{b^2 (b d-a e)^2}{e^5 (d+e x)^6}+\frac{4 b (b d-a e)^3}{7 e^5 (d+e x)^7}-\frac{(b d-a e)^4}{8 e^5 (d+e x)^8}-\frac{b^4}{4 e^5 (d+e x)^4}",1,"-(b*d - a*e)^4/(8*e^5*(d + e*x)^8) + (4*b*(b*d - a*e)^3)/(7*e^5*(d + e*x)^7) - (b^2*(b*d - a*e)^2)/(e^5*(d + e*x)^6) + (4*b^3*(b*d - a*e))/(5*e^5*(d + e*x)^5) - b^4/(4*e^5*(d + e*x)^4)","A",3,2,26,0.07692,1,"{27, 43}"
1479,1,119,0,0.06821,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{10}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^10,x]","\frac{2 b^3 (b d-a e)}{3 e^5 (d+e x)^6}-\frac{6 b^2 (b d-a e)^2}{7 e^5 (d+e x)^7}+\frac{b (b d-a e)^3}{2 e^5 (d+e x)^8}-\frac{(b d-a e)^4}{9 e^5 (d+e x)^9}-\frac{b^4}{5 e^5 (d+e x)^5}","\frac{2 b^3 (b d-a e)}{3 e^5 (d+e x)^6}-\frac{6 b^2 (b d-a e)^2}{7 e^5 (d+e x)^7}+\frac{b (b d-a e)^3}{2 e^5 (d+e x)^8}-\frac{(b d-a e)^4}{9 e^5 (d+e x)^9}-\frac{b^4}{5 e^5 (d+e x)^5}",1,"-(b*d - a*e)^4/(9*e^5*(d + e*x)^9) + (b*(b*d - a*e)^3)/(2*e^5*(d + e*x)^8) - (6*b^2*(b*d - a*e)^2)/(7*e^5*(d + e*x)^7) + (2*b^3*(b*d - a*e))/(3*e^5*(d + e*x)^6) - b^4/(5*e^5*(d + e*x)^5)","A",3,2,26,0.07692,1,"{27, 43}"
1480,1,119,0,0.0682365,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{11}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^11,x]","\frac{4 b^3 (b d-a e)}{7 e^5 (d+e x)^7}-\frac{3 b^2 (b d-a e)^2}{4 e^5 (d+e x)^8}+\frac{4 b (b d-a e)^3}{9 e^5 (d+e x)^9}-\frac{(b d-a e)^4}{10 e^5 (d+e x)^{10}}-\frac{b^4}{6 e^5 (d+e x)^6}","\frac{4 b^3 (b d-a e)}{7 e^5 (d+e x)^7}-\frac{3 b^2 (b d-a e)^2}{4 e^5 (d+e x)^8}+\frac{4 b (b d-a e)^3}{9 e^5 (d+e x)^9}-\frac{(b d-a e)^4}{10 e^5 (d+e x)^{10}}-\frac{b^4}{6 e^5 (d+e x)^6}",1,"-(b*d - a*e)^4/(10*e^5*(d + e*x)^10) + (4*b*(b*d - a*e)^3)/(9*e^5*(d + e*x)^9) - (3*b^2*(b*d - a*e)^2)/(4*e^5*(d + e*x)^8) + (4*b^3*(b*d - a*e))/(7*e^5*(d + e*x)^7) - b^4/(6*e^5*(d + e*x)^6)","A",3,2,26,0.07692,1,"{27, 43}"
1481,1,173,0,0.516546,"\int (d+e x)^8 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^8*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{3 b^5 (d+e x)^{14} (b d-a e)}{7 e^7}+\frac{15 b^4 (d+e x)^{13} (b d-a e)^2}{13 e^7}-\frac{5 b^3 (d+e x)^{12} (b d-a e)^3}{3 e^7}+\frac{15 b^2 (d+e x)^{11} (b d-a e)^4}{11 e^7}-\frac{3 b (d+e x)^{10} (b d-a e)^5}{5 e^7}+\frac{(d+e x)^9 (b d-a e)^6}{9 e^7}+\frac{b^6 (d+e x)^{15}}{15 e^7}","-\frac{3 b^5 (d+e x)^{14} (b d-a e)}{7 e^7}+\frac{15 b^4 (d+e x)^{13} (b d-a e)^2}{13 e^7}-\frac{5 b^3 (d+e x)^{12} (b d-a e)^3}{3 e^7}+\frac{15 b^2 (d+e x)^{11} (b d-a e)^4}{11 e^7}-\frac{3 b (d+e x)^{10} (b d-a e)^5}{5 e^7}+\frac{(d+e x)^9 (b d-a e)^6}{9 e^7}+\frac{b^6 (d+e x)^{15}}{15 e^7}",1,"((b*d - a*e)^6*(d + e*x)^9)/(9*e^7) - (3*b*(b*d - a*e)^5*(d + e*x)^10)/(5*e^7) + (15*b^2*(b*d - a*e)^4*(d + e*x)^11)/(11*e^7) - (5*b^3*(b*d - a*e)^3*(d + e*x)^12)/(3*e^7) + (15*b^4*(b*d - a*e)^2*(d + e*x)^13)/(13*e^7) - (3*b^5*(b*d - a*e)*(d + e*x)^14)/(7*e^7) + (b^6*(d + e*x)^15)/(15*e^7)","A",3,2,26,0.07692,1,"{27, 43}"
1482,1,173,0,0.4325708,"\int (d+e x)^7 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{6 b^5 (d+e x)^{13} (b d-a e)}{13 e^7}+\frac{5 b^4 (d+e x)^{12} (b d-a e)^2}{4 e^7}-\frac{20 b^3 (d+e x)^{11} (b d-a e)^3}{11 e^7}+\frac{3 b^2 (d+e x)^{10} (b d-a e)^4}{2 e^7}-\frac{2 b (d+e x)^9 (b d-a e)^5}{3 e^7}+\frac{(d+e x)^8 (b d-a e)^6}{8 e^7}+\frac{b^6 (d+e x)^{14}}{14 e^7}","-\frac{6 b^5 (d+e x)^{13} (b d-a e)}{13 e^7}+\frac{5 b^4 (d+e x)^{12} (b d-a e)^2}{4 e^7}-\frac{20 b^3 (d+e x)^{11} (b d-a e)^3}{11 e^7}+\frac{3 b^2 (d+e x)^{10} (b d-a e)^4}{2 e^7}-\frac{2 b (d+e x)^9 (b d-a e)^5}{3 e^7}+\frac{(d+e x)^8 (b d-a e)^6}{8 e^7}+\frac{b^6 (d+e x)^{14}}{14 e^7}",1,"((b*d - a*e)^6*(d + e*x)^8)/(8*e^7) - (2*b*(b*d - a*e)^5*(d + e*x)^9)/(3*e^7) + (3*b^2*(b*d - a*e)^4*(d + e*x)^10)/(2*e^7) - (20*b^3*(b*d - a*e)^3*(d + e*x)^11)/(11*e^7) + (5*b^4*(b*d - a*e)^2*(d + e*x)^12)/(4*e^7) - (6*b^5*(b*d - a*e)*(d + e*x)^13)/(13*e^7) + (b^6*(d + e*x)^14)/(14*e^7)","A",3,2,26,0.07692,1,"{27, 43}"
1483,1,171,0,0.3581831,"\int (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{e^5 (a+b x)^{12} (b d-a e)}{2 b^7}+\frac{15 e^4 (a+b x)^{11} (b d-a e)^2}{11 b^7}+\frac{2 e^3 (a+b x)^{10} (b d-a e)^3}{b^7}+\frac{5 e^2 (a+b x)^9 (b d-a e)^4}{3 b^7}+\frac{3 e (a+b x)^8 (b d-a e)^5}{4 b^7}+\frac{(a+b x)^7 (b d-a e)^6}{7 b^7}+\frac{e^6 (a+b x)^{13}}{13 b^7}","\frac{e^5 (a+b x)^{12} (b d-a e)}{2 b^7}+\frac{15 e^4 (a+b x)^{11} (b d-a e)^2}{11 b^7}+\frac{2 e^3 (a+b x)^{10} (b d-a e)^3}{b^7}+\frac{5 e^2 (a+b x)^9 (b d-a e)^4}{3 b^7}+\frac{3 e (a+b x)^8 (b d-a e)^5}{4 b^7}+\frac{(a+b x)^7 (b d-a e)^6}{7 b^7}+\frac{e^6 (a+b x)^{13}}{13 b^7}",1,"((b*d - a*e)^6*(a + b*x)^7)/(7*b^7) + (3*e*(b*d - a*e)^5*(a + b*x)^8)/(4*b^7) + (5*e^2*(b*d - a*e)^4*(a + b*x)^9)/(3*b^7) + (2*e^3*(b*d - a*e)^3*(a + b*x)^10)/b^7 + (15*e^4*(b*d - a*e)^2*(a + b*x)^11)/(11*b^7) + (e^5*(b*d - a*e)*(a + b*x)^12)/(2*b^7) + (e^6*(a + b*x)^13)/(13*b^7)","A",3,2,26,0.07692,1,"{27, 43}"
1484,1,143,0,0.3056587,"\int (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{5 e^4 (a+b x)^{11} (b d-a e)}{11 b^6}+\frac{e^3 (a+b x)^{10} (b d-a e)^2}{b^6}+\frac{10 e^2 (a+b x)^9 (b d-a e)^3}{9 b^6}+\frac{5 e (a+b x)^8 (b d-a e)^4}{8 b^6}+\frac{(a+b x)^7 (b d-a e)^5}{7 b^6}+\frac{e^5 (a+b x)^{12}}{12 b^6}","\frac{5 e^4 (a+b x)^{11} (b d-a e)}{11 b^6}+\frac{e^3 (a+b x)^{10} (b d-a e)^2}{b^6}+\frac{10 e^2 (a+b x)^9 (b d-a e)^3}{9 b^6}+\frac{5 e (a+b x)^8 (b d-a e)^4}{8 b^6}+\frac{(a+b x)^7 (b d-a e)^5}{7 b^6}+\frac{e^5 (a+b x)^{12}}{12 b^6}",1,"((b*d - a*e)^5*(a + b*x)^7)/(7*b^6) + (5*e*(b*d - a*e)^4*(a + b*x)^8)/(8*b^6) + (10*e^2*(b*d - a*e)^3*(a + b*x)^9)/(9*b^6) + (e^3*(b*d - a*e)^2*(a + b*x)^10)/b^6 + (5*e^4*(b*d - a*e)*(a + b*x)^11)/(11*b^6) + (e^5*(a + b*x)^12)/(12*b^6)","A",3,2,26,0.07692,1,"{27, 43}"
1485,1,119,0,0.251798,"\int (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 e^3 (a+b x)^{10} (b d-a e)}{5 b^5}+\frac{2 e^2 (a+b x)^9 (b d-a e)^2}{3 b^5}+\frac{e (a+b x)^8 (b d-a e)^3}{2 b^5}+\frac{(a+b x)^7 (b d-a e)^4}{7 b^5}+\frac{e^4 (a+b x)^{11}}{11 b^5}","\frac{2 e^3 (a+b x)^{10} (b d-a e)}{5 b^5}+\frac{2 e^2 (a+b x)^9 (b d-a e)^2}{3 b^5}+\frac{e (a+b x)^8 (b d-a e)^3}{2 b^5}+\frac{(a+b x)^7 (b d-a e)^4}{7 b^5}+\frac{e^4 (a+b x)^{11}}{11 b^5}",1,"((b*d - a*e)^4*(a + b*x)^7)/(7*b^5) + (e*(b*d - a*e)^3*(a + b*x)^8)/(2*b^5) + (2*e^2*(b*d - a*e)^2*(a + b*x)^9)/(3*b^5) + (2*e^3*(b*d - a*e)*(a + b*x)^10)/(5*b^5) + (e^4*(a + b*x)^11)/(11*b^5)","A",3,2,26,0.07692,1,"{27, 43}"
1486,1,92,0,0.1915232,"\int (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{e^2 (a+b x)^9 (b d-a e)}{3 b^4}+\frac{3 e (a+b x)^8 (b d-a e)^2}{8 b^4}+\frac{(a+b x)^7 (b d-a e)^3}{7 b^4}+\frac{e^3 (a+b x)^{10}}{10 b^4}","\frac{e^2 (a+b x)^9 (b d-a e)}{3 b^4}+\frac{3 e (a+b x)^8 (b d-a e)^2}{8 b^4}+\frac{(a+b x)^7 (b d-a e)^3}{7 b^4}+\frac{e^3 (a+b x)^{10}}{10 b^4}",1,"((b*d - a*e)^3*(a + b*x)^7)/(7*b^4) + (3*e*(b*d - a*e)^2*(a + b*x)^8)/(8*b^4) + (e^2*(b*d - a*e)*(a + b*x)^9)/(3*b^4) + (e^3*(a + b*x)^10)/(10*b^4)","A",3,2,26,0.07692,1,"{27, 43}"
1487,1,65,0,0.1357566,"\int (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{e (a+b x)^8 (b d-a e)}{4 b^3}+\frac{(a+b x)^7 (b d-a e)^2}{7 b^3}+\frac{e^2 (a+b x)^9}{9 b^3}","\frac{e (a+b x)^8 (b d-a e)}{4 b^3}+\frac{(a+b x)^7 (b d-a e)^2}{7 b^3}+\frac{e^2 (a+b x)^9}{9 b^3}",1,"((b*d - a*e)^2*(a + b*x)^7)/(7*b^3) + (e*(b*d - a*e)*(a + b*x)^8)/(4*b^3) + (e^2*(a + b*x)^9)/(9*b^3)","A",3,2,26,0.07692,1,"{27, 43}"
1488,1,38,0,0.0163301,"\int (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(a+b x)^7 (b d-a e)}{7 b^2}+\frac{e (a+b x)^8}{8 b^2}","\frac{(a+b x)^7 (b d-a e)}{7 b^2}+\frac{e (a+b x)^8}{8 b^2}",1,"((b*d - a*e)*(a + b*x)^7)/(7*b^2) + (e*(a + b*x)^8)/(8*b^2)","A",3,2,24,0.08333,1,"{27, 43}"
1489,1,14,0,0.0021366,"\int \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(a+b x)^7}{7 b}","\frac{(a+b x)^7}{7 b}",1,"(a + b*x)^7/(7*b)","A",2,2,18,0.1111,1,"{27, 32}"
1490,1,146,0,0.0642648,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{d+e x} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x),x]","-\frac{b x (b d-a e)^5}{e^6}+\frac{(a+b x)^2 (b d-a e)^4}{2 e^5}-\frac{(a+b x)^3 (b d-a e)^3}{3 e^4}+\frac{(a+b x)^4 (b d-a e)^2}{4 e^3}-\frac{(a+b x)^5 (b d-a e)}{5 e^2}+\frac{(b d-a e)^6 \log (d+e x)}{e^7}+\frac{(a+b x)^6}{6 e}","-\frac{b x (b d-a e)^5}{e^6}+\frac{(a+b x)^2 (b d-a e)^4}{2 e^5}-\frac{(a+b x)^3 (b d-a e)^3}{3 e^4}+\frac{(a+b x)^4 (b d-a e)^2}{4 e^3}-\frac{(a+b x)^5 (b d-a e)}{5 e^2}+\frac{(b d-a e)^6 \log (d+e x)}{e^7}+\frac{(a+b x)^6}{6 e}",1,"-((b*(b*d - a*e)^5*x)/e^6) + ((b*d - a*e)^4*(a + b*x)^2)/(2*e^5) - ((b*d - a*e)^3*(a + b*x)^3)/(3*e^4) + ((b*d - a*e)^2*(a + b*x)^4)/(4*e^3) - ((b*d - a*e)*(a + b*x)^5)/(5*e^2) + (a + b*x)^6/(6*e) + ((b*d - a*e)^6*Log[d + e*x])/e^7","A",3,2,26,0.07692,1,"{27, 43}"
1491,1,156,0,0.2125519,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^2,x]","-\frac{3 b^5 (d+e x)^4 (b d-a e)}{2 e^7}+\frac{5 b^4 (d+e x)^3 (b d-a e)^2}{e^7}-\frac{10 b^3 (d+e x)^2 (b d-a e)^3}{e^7}+\frac{15 b^2 x (b d-a e)^4}{e^6}-\frac{(b d-a e)^6}{e^7 (d+e x)}-\frac{6 b (b d-a e)^5 \log (d+e x)}{e^7}+\frac{b^6 (d+e x)^5}{5 e^7}","-\frac{3 b^5 (d+e x)^4 (b d-a e)}{2 e^7}+\frac{5 b^4 (d+e x)^3 (b d-a e)^2}{e^7}-\frac{10 b^3 (d+e x)^2 (b d-a e)^3}{e^7}+\frac{15 b^2 x (b d-a e)^4}{e^6}-\frac{(b d-a e)^6}{e^7 (d+e x)}-\frac{6 b (b d-a e)^5 \log (d+e x)}{e^7}+\frac{b^6 (d+e x)^5}{5 e^7}",1,"(15*b^2*(b*d - a*e)^4*x)/e^6 - (b*d - a*e)^6/(e^7*(d + e*x)) - (10*b^3*(b*d - a*e)^3*(d + e*x)^2)/e^7 + (5*b^4*(b*d - a*e)^2*(d + e*x)^3)/e^7 - (3*b^5*(b*d - a*e)*(d + e*x)^4)/(2*e^7) + (b^6*(d + e*x)^5)/(5*e^7) - (6*b*(b*d - a*e)^5*Log[d + e*x])/e^7","A",3,2,26,0.07692,1,"{27, 43}"
1492,1,158,0,0.1792079,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^3} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^3,x]","-\frac{2 b^5 (d+e x)^3 (b d-a e)}{e^7}+\frac{15 b^4 (d+e x)^2 (b d-a e)^2}{2 e^7}-\frac{20 b^3 x (b d-a e)^3}{e^6}+\frac{15 b^2 (b d-a e)^4 \log (d+e x)}{e^7}+\frac{6 b (b d-a e)^5}{e^7 (d+e x)}-\frac{(b d-a e)^6}{2 e^7 (d+e x)^2}+\frac{b^6 (d+e x)^4}{4 e^7}","-\frac{2 b^5 (d+e x)^3 (b d-a e)}{e^7}+\frac{15 b^4 (d+e x)^2 (b d-a e)^2}{2 e^7}-\frac{20 b^3 x (b d-a e)^3}{e^6}+\frac{15 b^2 (b d-a e)^4 \log (d+e x)}{e^7}+\frac{6 b (b d-a e)^5}{e^7 (d+e x)}-\frac{(b d-a e)^6}{2 e^7 (d+e x)^2}+\frac{b^6 (d+e x)^4}{4 e^7}",1,"(-20*b^3*(b*d - a*e)^3*x)/e^6 - (b*d - a*e)^6/(2*e^7*(d + e*x)^2) + (6*b*(b*d - a*e)^5)/(e^7*(d + e*x)) + (15*b^4*(b*d - a*e)^2*(d + e*x)^2)/(2*e^7) - (2*b^5*(b*d - a*e)*(d + e*x)^3)/e^7 + (b^6*(d + e*x)^4)/(4*e^7) + (15*b^2*(b*d - a*e)^4*Log[d + e*x])/e^7","A",3,2,26,0.07692,1,"{27, 43}"
1493,1,156,0,0.1605764,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^4} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^4,x]","-\frac{3 b^5 (d+e x)^2 (b d-a e)}{e^7}+\frac{15 b^4 x (b d-a e)^2}{e^6}-\frac{15 b^2 (b d-a e)^4}{e^7 (d+e x)}-\frac{20 b^3 (b d-a e)^3 \log (d+e x)}{e^7}+\frac{3 b (b d-a e)^5}{e^7 (d+e x)^2}-\frac{(b d-a e)^6}{3 e^7 (d+e x)^3}+\frac{b^6 (d+e x)^3}{3 e^7}","-\frac{3 b^5 (d+e x)^2 (b d-a e)}{e^7}+\frac{15 b^4 x (b d-a e)^2}{e^6}-\frac{15 b^2 (b d-a e)^4}{e^7 (d+e x)}-\frac{20 b^3 (b d-a e)^3 \log (d+e x)}{e^7}+\frac{3 b (b d-a e)^5}{e^7 (d+e x)^2}-\frac{(b d-a e)^6}{3 e^7 (d+e x)^3}+\frac{b^6 (d+e x)^3}{3 e^7}",1,"(15*b^4*(b*d - a*e)^2*x)/e^6 - (b*d - a*e)^6/(3*e^7*(d + e*x)^3) + (3*b*(b*d - a*e)^5)/(e^7*(d + e*x)^2) - (15*b^2*(b*d - a*e)^4)/(e^7*(d + e*x)) - (3*b^5*(b*d - a*e)*(d + e*x)^2)/e^7 + (b^6*(d + e*x)^3)/(3*e^7) - (20*b^3*(b*d - a*e)^3*Log[d + e*x])/e^7","A",3,2,26,0.07692,1,"{27, 43}"
1494,1,155,0,0.1464426,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^5} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^5,x]","-\frac{b^5 x (5 b d-6 a e)}{e^6}+\frac{20 b^3 (b d-a e)^3}{e^7 (d+e x)}-\frac{15 b^2 (b d-a e)^4}{2 e^7 (d+e x)^2}+\frac{15 b^4 (b d-a e)^2 \log (d+e x)}{e^7}+\frac{2 b (b d-a e)^5}{e^7 (d+e x)^3}-\frac{(b d-a e)^6}{4 e^7 (d+e x)^4}+\frac{b^6 x^2}{2 e^5}","-\frac{b^5 x (5 b d-6 a e)}{e^6}+\frac{20 b^3 (b d-a e)^3}{e^7 (d+e x)}-\frac{15 b^2 (b d-a e)^4}{2 e^7 (d+e x)^2}+\frac{15 b^4 (b d-a e)^2 \log (d+e x)}{e^7}+\frac{2 b (b d-a e)^5}{e^7 (d+e x)^3}-\frac{(b d-a e)^6}{4 e^7 (d+e x)^4}+\frac{b^6 x^2}{2 e^5}",1,"-((b^5*(5*b*d - 6*a*e)*x)/e^6) + (b^6*x^2)/(2*e^5) - (b*d - a*e)^6/(4*e^7*(d + e*x)^4) + (2*b*(b*d - a*e)^5)/(e^7*(d + e*x)^3) - (15*b^2*(b*d - a*e)^4)/(2*e^7*(d + e*x)^2) + (20*b^3*(b*d - a*e)^3)/(e^7*(d + e*x)) + (15*b^4*(b*d - a*e)^2*Log[d + e*x])/e^7","A",3,2,26,0.07692,1,"{27, 43}"
1495,1,155,0,0.1400433,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^6} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^6,x]","-\frac{15 b^4 (b d-a e)^2}{e^7 (d+e x)}+\frac{10 b^3 (b d-a e)^3}{e^7 (d+e x)^2}-\frac{5 b^2 (b d-a e)^4}{e^7 (d+e x)^3}-\frac{6 b^5 (b d-a e) \log (d+e x)}{e^7}+\frac{3 b (b d-a e)^5}{2 e^7 (d+e x)^4}-\frac{(b d-a e)^6}{5 e^7 (d+e x)^5}+\frac{b^6 x}{e^6}","-\frac{15 b^4 (b d-a e)^2}{e^7 (d+e x)}+\frac{10 b^3 (b d-a e)^3}{e^7 (d+e x)^2}-\frac{5 b^2 (b d-a e)^4}{e^7 (d+e x)^3}-\frac{6 b^5 (b d-a e) \log (d+e x)}{e^7}+\frac{3 b (b d-a e)^5}{2 e^7 (d+e x)^4}-\frac{(b d-a e)^6}{5 e^7 (d+e x)^5}+\frac{b^6 x}{e^6}",1,"(b^6*x)/e^6 - (b*d - a*e)^6/(5*e^7*(d + e*x)^5) + (3*b*(b*d - a*e)^5)/(2*e^7*(d + e*x)^4) - (5*b^2*(b*d - a*e)^4)/(e^7*(d + e*x)^3) + (10*b^3*(b*d - a*e)^3)/(e^7*(d + e*x)^2) - (15*b^4*(b*d - a*e)^2)/(e^7*(d + e*x)) - (6*b^5*(b*d - a*e)*Log[d + e*x])/e^7","A",3,2,26,0.07692,1,"{27, 43}"
1496,1,167,0,0.1315258,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^7} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^7,x]","\frac{6 b^5 (b d-a e)}{e^7 (d+e x)}-\frac{15 b^4 (b d-a e)^2}{2 e^7 (d+e x)^2}+\frac{20 b^3 (b d-a e)^3}{3 e^7 (d+e x)^3}-\frac{15 b^2 (b d-a e)^4}{4 e^7 (d+e x)^4}+\frac{6 b (b d-a e)^5}{5 e^7 (d+e x)^5}-\frac{(b d-a e)^6}{6 e^7 (d+e x)^6}+\frac{b^6 \log (d+e x)}{e^7}","\frac{6 b^5 (b d-a e)}{e^7 (d+e x)}-\frac{15 b^4 (b d-a e)^2}{2 e^7 (d+e x)^2}+\frac{20 b^3 (b d-a e)^3}{3 e^7 (d+e x)^3}-\frac{15 b^2 (b d-a e)^4}{4 e^7 (d+e x)^4}+\frac{6 b (b d-a e)^5}{5 e^7 (d+e x)^5}-\frac{(b d-a e)^6}{6 e^7 (d+e x)^6}+\frac{b^6 \log (d+e x)}{e^7}",1,"-(b*d - a*e)^6/(6*e^7*(d + e*x)^6) + (6*b*(b*d - a*e)^5)/(5*e^7*(d + e*x)^5) - (15*b^2*(b*d - a*e)^4)/(4*e^7*(d + e*x)^4) + (20*b^3*(b*d - a*e)^3)/(3*e^7*(d + e*x)^3) - (15*b^4*(b*d - a*e)^2)/(2*e^7*(d + e*x)^2) + (6*b^5*(b*d - a*e))/(e^7*(d + e*x)) + (b^6*Log[d + e*x])/e^7","A",3,2,26,0.07692,1,"{27, 43}"
1497,1,28,0,0.0046189,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^8} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^8,x]","\frac{(a+b x)^7}{7 (d+e x)^7 (b d-a e)}","\frac{(a+b x)^7}{7 (d+e x)^7 (b d-a e)}",1,"(a + b*x)^7/(7*(b*d - a*e)*(d + e*x)^7)","A",2,2,26,0.07692,1,"{27, 37}"
1498,1,58,0,0.011517,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^9} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^9,x]","\frac{b (a+b x)^7}{56 (d+e x)^7 (b d-a e)^2}+\frac{(a+b x)^7}{8 (d+e x)^8 (b d-a e)}","\frac{b (a+b x)^7}{56 (d+e x)^7 (b d-a e)^2}+\frac{(a+b x)^7}{8 (d+e x)^8 (b d-a e)}",1,"(a + b*x)^7/(8*(b*d - a*e)*(d + e*x)^8) + (b*(a + b*x)^7)/(56*(b*d - a*e)^2*(d + e*x)^7)","A",3,3,26,0.1154,1,"{27, 45, 37}"
1499,1,89,0,0.0205223,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{10}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^10,x]","\frac{b^2 (a+b x)^7}{252 (d+e x)^7 (b d-a e)^3}+\frac{b (a+b x)^7}{36 (d+e x)^8 (b d-a e)^2}+\frac{(a+b x)^7}{9 (d+e x)^9 (b d-a e)}","\frac{b^2 (a+b x)^7}{252 (d+e x)^7 (b d-a e)^3}+\frac{b (a+b x)^7}{36 (d+e x)^8 (b d-a e)^2}+\frac{(a+b x)^7}{9 (d+e x)^9 (b d-a e)}",1,"(a + b*x)^7/(9*(b*d - a*e)*(d + e*x)^9) + (b*(a + b*x)^7)/(36*(b*d - a*e)^2*(d + e*x)^8) + (b^2*(a + b*x)^7)/(252*(b*d - a*e)^3*(d + e*x)^7)","A",4,3,26,0.1154,1,"{27, 45, 37}"
1500,1,120,0,0.0350822,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{11}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^11,x]","\frac{b^3 (a+b x)^7}{840 (d+e x)^7 (b d-a e)^4}+\frac{b^2 (a+b x)^7}{120 (d+e x)^8 (b d-a e)^3}+\frac{b (a+b x)^7}{30 (d+e x)^9 (b d-a e)^2}+\frac{(a+b x)^7}{10 (d+e x)^{10} (b d-a e)}","\frac{b^3 (a+b x)^7}{840 (d+e x)^7 (b d-a e)^4}+\frac{b^2 (a+b x)^7}{120 (d+e x)^8 (b d-a e)^3}+\frac{b (a+b x)^7}{30 (d+e x)^9 (b d-a e)^2}+\frac{(a+b x)^7}{10 (d+e x)^{10} (b d-a e)}",1,"(a + b*x)^7/(10*(b*d - a*e)*(d + e*x)^10) + (b*(a + b*x)^7)/(30*(b*d - a*e)^2*(d + e*x)^9) + (b^2*(a + b*x)^7)/(120*(b*d - a*e)^3*(d + e*x)^8) + (b^3*(a + b*x)^7)/(840*(b*d - a*e)^4*(d + e*x)^7)","A",5,3,26,0.1154,1,"{27, 45, 37}"
1501,1,170,0,0.1286608,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{12}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^12,x]","\frac{b^5 (b d-a e)}{e^7 (d+e x)^6}-\frac{15 b^4 (b d-a e)^2}{7 e^7 (d+e x)^7}+\frac{5 b^3 (b d-a e)^3}{2 e^7 (d+e x)^8}-\frac{5 b^2 (b d-a e)^4}{3 e^7 (d+e x)^9}+\frac{3 b (b d-a e)^5}{5 e^7 (d+e x)^{10}}-\frac{(b d-a e)^6}{11 e^7 (d+e x)^{11}}-\frac{b^6}{5 e^7 (d+e x)^5}","\frac{b^5 (b d-a e)}{e^7 (d+e x)^6}-\frac{15 b^4 (b d-a e)^2}{7 e^7 (d+e x)^7}+\frac{5 b^3 (b d-a e)^3}{2 e^7 (d+e x)^8}-\frac{5 b^2 (b d-a e)^4}{3 e^7 (d+e x)^9}+\frac{3 b (b d-a e)^5}{5 e^7 (d+e x)^{10}}-\frac{(b d-a e)^6}{11 e^7 (d+e x)^{11}}-\frac{b^6}{5 e^7 (d+e x)^5}",1,"-(b*d - a*e)^6/(11*e^7*(d + e*x)^11) + (3*b*(b*d - a*e)^5)/(5*e^7*(d + e*x)^10) - (5*b^2*(b*d - a*e)^4)/(3*e^7*(d + e*x)^9) + (5*b^3*(b*d - a*e)^3)/(2*e^7*(d + e*x)^8) - (15*b^4*(b*d - a*e)^2)/(7*e^7*(d + e*x)^7) + (b^5*(b*d - a*e))/(e^7*(d + e*x)^6) - b^6/(5*e^7*(d + e*x)^5)","A",3,2,26,0.07692,1,"{27, 43}"
1502,1,173,0,0.1183246,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{13}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^13,x]","\frac{6 b^5 (b d-a e)}{7 e^7 (d+e x)^7}-\frac{15 b^4 (b d-a e)^2}{8 e^7 (d+e x)^8}+\frac{20 b^3 (b d-a e)^3}{9 e^7 (d+e x)^9}-\frac{3 b^2 (b d-a e)^4}{2 e^7 (d+e x)^{10}}+\frac{6 b (b d-a e)^5}{11 e^7 (d+e x)^{11}}-\frac{(b d-a e)^6}{12 e^7 (d+e x)^{12}}-\frac{b^6}{6 e^7 (d+e x)^6}","\frac{6 b^5 (b d-a e)}{7 e^7 (d+e x)^7}-\frac{15 b^4 (b d-a e)^2}{8 e^7 (d+e x)^8}+\frac{20 b^3 (b d-a e)^3}{9 e^7 (d+e x)^9}-\frac{3 b^2 (b d-a e)^4}{2 e^7 (d+e x)^{10}}+\frac{6 b (b d-a e)^5}{11 e^7 (d+e x)^{11}}-\frac{(b d-a e)^6}{12 e^7 (d+e x)^{12}}-\frac{b^6}{6 e^7 (d+e x)^6}",1,"-(b*d - a*e)^6/(12*e^7*(d + e*x)^12) + (6*b*(b*d - a*e)^5)/(11*e^7*(d + e*x)^11) - (3*b^2*(b*d - a*e)^4)/(2*e^7*(d + e*x)^10) + (20*b^3*(b*d - a*e)^3)/(9*e^7*(d + e*x)^9) - (15*b^4*(b*d - a*e)^2)/(8*e^7*(d + e*x)^8) + (6*b^5*(b*d - a*e))/(7*e^7*(d + e*x)^7) - b^6/(6*e^7*(d + e*x)^6)","A",3,2,26,0.07692,1,"{27, 43}"
1503,1,171,0,0.1307403,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{14}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^14,x]","\frac{3 b^5 (b d-a e)}{4 e^7 (d+e x)^8}-\frac{5 b^4 (b d-a e)^2}{3 e^7 (d+e x)^9}+\frac{2 b^3 (b d-a e)^3}{e^7 (d+e x)^{10}}-\frac{15 b^2 (b d-a e)^4}{11 e^7 (d+e x)^{11}}+\frac{b (b d-a e)^5}{2 e^7 (d+e x)^{12}}-\frac{(b d-a e)^6}{13 e^7 (d+e x)^{13}}-\frac{b^6}{7 e^7 (d+e x)^7}","\frac{3 b^5 (b d-a e)}{4 e^7 (d+e x)^8}-\frac{5 b^4 (b d-a e)^2}{3 e^7 (d+e x)^9}+\frac{2 b^3 (b d-a e)^3}{e^7 (d+e x)^{10}}-\frac{15 b^2 (b d-a e)^4}{11 e^7 (d+e x)^{11}}+\frac{b (b d-a e)^5}{2 e^7 (d+e x)^{12}}-\frac{(b d-a e)^6}{13 e^7 (d+e x)^{13}}-\frac{b^6}{7 e^7 (d+e x)^7}",1,"-(b*d - a*e)^6/(13*e^7*(d + e*x)^13) + (b*(b*d - a*e)^5)/(2*e^7*(d + e*x)^12) - (15*b^2*(b*d - a*e)^4)/(11*e^7*(d + e*x)^11) + (2*b^3*(b*d - a*e)^3)/(e^7*(d + e*x)^10) - (5*b^4*(b*d - a*e)^2)/(3*e^7*(d + e*x)^9) + (3*b^5*(b*d - a*e))/(4*e^7*(d + e*x)^8) - b^6/(7*e^7*(d + e*x)^7)","A",3,2,26,0.07692,1,"{27, 43}"
1504,1,173,0,0.1151816,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{15}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^15,x]","\frac{2 b^5 (b d-a e)}{3 e^7 (d+e x)^9}-\frac{3 b^4 (b d-a e)^2}{2 e^7 (d+e x)^{10}}+\frac{20 b^3 (b d-a e)^3}{11 e^7 (d+e x)^{11}}-\frac{5 b^2 (b d-a e)^4}{4 e^7 (d+e x)^{12}}+\frac{6 b (b d-a e)^5}{13 e^7 (d+e x)^{13}}-\frac{(b d-a e)^6}{14 e^7 (d+e x)^{14}}-\frac{b^6}{8 e^7 (d+e x)^8}","\frac{2 b^5 (b d-a e)}{3 e^7 (d+e x)^9}-\frac{3 b^4 (b d-a e)^2}{2 e^7 (d+e x)^{10}}+\frac{20 b^3 (b d-a e)^3}{11 e^7 (d+e x)^{11}}-\frac{5 b^2 (b d-a e)^4}{4 e^7 (d+e x)^{12}}+\frac{6 b (b d-a e)^5}{13 e^7 (d+e x)^{13}}-\frac{(b d-a e)^6}{14 e^7 (d+e x)^{14}}-\frac{b^6}{8 e^7 (d+e x)^8}",1,"-(b*d - a*e)^6/(14*e^7*(d + e*x)^14) + (6*b*(b*d - a*e)^5)/(13*e^7*(d + e*x)^13) - (5*b^2*(b*d - a*e)^4)/(4*e^7*(d + e*x)^12) + (20*b^3*(b*d - a*e)^3)/(11*e^7*(d + e*x)^11) - (3*b^4*(b*d - a*e)^2)/(2*e^7*(d + e*x)^10) + (2*b^5*(b*d - a*e))/(3*e^7*(d + e*x)^9) - b^6/(8*e^7*(d + e*x)^8)","A",3,2,26,0.07692,1,"{27, 43}"
1505,1,131,0,0.1463667,"\int \frac{(d+e x)^5}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^5/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{5 e^4 (a+b x)^3 (b d-a e)}{3 b^6}+\frac{5 e^3 (a+b x)^2 (b d-a e)^2}{b^6}+\frac{10 e^2 x (b d-a e)^3}{b^5}-\frac{(b d-a e)^5}{b^6 (a+b x)}+\frac{5 e (b d-a e)^4 \log (a+b x)}{b^6}+\frac{e^5 (a+b x)^4}{4 b^6}","\frac{5 e^4 (a+b x)^3 (b d-a e)}{3 b^6}+\frac{5 e^3 (a+b x)^2 (b d-a e)^2}{b^6}+\frac{10 e^2 x (b d-a e)^3}{b^5}-\frac{(b d-a e)^5}{b^6 (a+b x)}+\frac{5 e (b d-a e)^4 \log (a+b x)}{b^6}+\frac{e^5 (a+b x)^4}{4 b^6}",1,"(10*e^2*(b*d - a*e)^3*x)/b^5 - (b*d - a*e)^5/(b^6*(a + b*x)) + (5*e^3*(b*d - a*e)^2*(a + b*x)^2)/b^6 + (5*e^4*(b*d - a*e)*(a + b*x)^3)/(3*b^6) + (e^5*(a + b*x)^4)/(4*b^6) + (5*e*(b*d - a*e)^4*Log[a + b*x])/b^6","A",3,2,26,0.07692,1,"{27, 43}"
1506,1,104,0,0.1021779,"\int \frac{(d+e x)^4}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^4/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 e^3 (a+b x)^2 (b d-a e)}{b^5}+\frac{6 e^2 x (b d-a e)^2}{b^4}-\frac{(b d-a e)^4}{b^5 (a+b x)}+\frac{4 e (b d-a e)^3 \log (a+b x)}{b^5}+\frac{e^4 (a+b x)^3}{3 b^5}","\frac{2 e^3 (a+b x)^2 (b d-a e)}{b^5}+\frac{6 e^2 x (b d-a e)^2}{b^4}-\frac{(b d-a e)^4}{b^5 (a+b x)}+\frac{4 e (b d-a e)^3 \log (a+b x)}{b^5}+\frac{e^4 (a+b x)^3}{3 b^5}",1,"(6*e^2*(b*d - a*e)^2*x)/b^4 - (b*d - a*e)^4/(b^5*(a + b*x)) + (2*e^3*(b*d - a*e)*(a + b*x)^2)/b^5 + (e^4*(a + b*x)^3)/(3*b^5) + (4*e*(b*d - a*e)^3*Log[a + b*x])/b^5","A",3,2,26,0.07692,1,"{27, 43}"
1507,1,75,0,0.0641327,"\int \frac{(d+e x)^3}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^3/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e^2 x (3 b d-2 a e)}{b^3}-\frac{(b d-a e)^3}{b^4 (a+b x)}+\frac{3 e (b d-a e)^2 \log (a+b x)}{b^4}+\frac{e^3 x^2}{2 b^2}","\frac{e^2 x (3 b d-2 a e)}{b^3}-\frac{(b d-a e)^3}{b^4 (a+b x)}+\frac{3 e (b d-a e)^2 \log (a+b x)}{b^4}+\frac{e^3 x^2}{2 b^2}",1,"(e^2*(3*b*d - 2*a*e)*x)/b^3 + (e^3*x^2)/(2*b^2) - (b*d - a*e)^3/(b^4*(a + b*x)) + (3*e*(b*d - a*e)^2*Log[a + b*x])/b^4","A",3,2,26,0.07692,1,"{27, 43}"
1508,1,51,0,0.0393365,"\int \frac{(d+e x)^2}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^2/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{(b d-a e)^2}{b^3 (a+b x)}+\frac{2 e (b d-a e) \log (a+b x)}{b^3}+\frac{e^2 x}{b^2}","-\frac{(b d-a e)^2}{b^3 (a+b x)}+\frac{2 e (b d-a e) \log (a+b x)}{b^3}+\frac{e^2 x}{b^2}",1,"(e^2*x)/b^2 - (b*d - a*e)^2/(b^3*(a + b*x)) + (2*e*(b*d - a*e)*Log[a + b*x])/b^3","A",3,2,26,0.07692,1,"{27, 43}"
1509,1,32,0,0.0216175,"\int \frac{d+e x}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e \log (a+b x)}{b^2}-\frac{b d-a e}{b^2 (a+b x)}","\frac{e \log (a+b x)}{b^2}-\frac{b d-a e}{b^2 (a+b x)}",1,"-((b*d - a*e)/(b^2*(a + b*x))) + (e*Log[a + b*x])/b^2","A",3,2,24,0.08333,1,"{27, 43}"
1510,1,12,0,0.0022466,"\int \frac{1}{a^2+2 a b x+b^2 x^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(-1),x]","-\frac{1}{b (a+b x)}","-\frac{1}{b (a+b x)}",1,"-(1/(b*(a + b*x)))","A",2,2,18,0.1111,1,"{27, 32}"
1511,1,57,0,0.0351234,"\int \frac{1}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[1/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{1}{(a+b x) (b d-a e)}-\frac{e \log (a+b x)}{(b d-a e)^2}+\frac{e \log (d+e x)}{(b d-a e)^2}","-\frac{1}{(a+b x) (b d-a e)}-\frac{e \log (a+b x)}{(b d-a e)^2}+\frac{e \log (d+e x)}{(b d-a e)^2}",1,"-(1/((b*d - a*e)*(a + b*x))) - (e*Log[a + b*x])/(b*d - a*e)^2 + (e*Log[d + e*x])/(b*d - a*e)^2","A",3,2,26,0.07692,1,"{27, 44}"
1512,1,81,0,0.0533884,"\int \frac{1}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[1/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{b}{(a+b x) (b d-a e)^2}-\frac{e}{(d+e x) (b d-a e)^2}-\frac{2 b e \log (a+b x)}{(b d-a e)^3}+\frac{2 b e \log (d+e x)}{(b d-a e)^3}","-\frac{b}{(a+b x) (b d-a e)^2}-\frac{e}{(d+e x) (b d-a e)^2}-\frac{2 b e \log (a+b x)}{(b d-a e)^3}+\frac{2 b e \log (d+e x)}{(b d-a e)^3}",1,"-(b/((b*d - a*e)^2*(a + b*x))) - e/((b*d - a*e)^2*(d + e*x)) - (2*b*e*Log[a + b*x])/(b*d - a*e)^3 + (2*b*e*Log[d + e*x])/(b*d - a*e)^3","A",3,2,26,0.07692,1,"{27, 44}"
1513,1,110,0,0.0786082,"\int \frac{1}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[1/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{b^2}{(a+b x) (b d-a e)^3}-\frac{3 b^2 e \log (a+b x)}{(b d-a e)^4}+\frac{3 b^2 e \log (d+e x)}{(b d-a e)^4}-\frac{2 b e}{(d+e x) (b d-a e)^3}-\frac{e}{2 (d+e x)^2 (b d-a e)^2}","-\frac{b^2}{(a+b x) (b d-a e)^3}-\frac{3 b^2 e \log (a+b x)}{(b d-a e)^4}+\frac{3 b^2 e \log (d+e x)}{(b d-a e)^4}-\frac{2 b e}{(d+e x) (b d-a e)^3}-\frac{e}{2 (d+e x)^2 (b d-a e)^2}",1,"-(b^2/((b*d - a*e)^3*(a + b*x))) - e/(2*(b*d - a*e)^2*(d + e*x)^2) - (2*b*e)/((b*d - a*e)^3*(d + e*x)) - (3*b^2*e*Log[a + b*x])/(b*d - a*e)^4 + (3*b^2*e*Log[d + e*x])/(b*d - a*e)^4","A",3,2,26,0.07692,1,"{27, 44}"
1514,1,133,0,0.1076458,"\int \frac{1}{(d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[1/((d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{b^3}{(a+b x) (b d-a e)^4}-\frac{3 b^2 e}{(d+e x) (b d-a e)^4}-\frac{4 b^3 e \log (a+b x)}{(b d-a e)^5}+\frac{4 b^3 e \log (d+e x)}{(b d-a e)^5}-\frac{b e}{(d+e x)^2 (b d-a e)^3}-\frac{e}{3 (d+e x)^3 (b d-a e)^2}","-\frac{b^3}{(a+b x) (b d-a e)^4}-\frac{3 b^2 e}{(d+e x) (b d-a e)^4}-\frac{4 b^3 e \log (a+b x)}{(b d-a e)^5}+\frac{4 b^3 e \log (d+e x)}{(b d-a e)^5}-\frac{b e}{(d+e x)^2 (b d-a e)^3}-\frac{e}{3 (d+e x)^3 (b d-a e)^2}",1,"-(b^3/((b*d - a*e)^4*(a + b*x))) - e/(3*(b*d - a*e)^2*(d + e*x)^3) - (b*e)/((b*d - a*e)^3*(d + e*x)^2) - (3*b^2*e)/((b*d - a*e)^4*(d + e*x)) - (4*b^3*e*Log[a + b*x])/(b*d - a*e)^5 + (4*b^3*e*Log[d + e*x])/(b*d - a*e)^5","A",3,2,26,0.07692,1,"{27, 44}"
1515,1,156,0,0.1799175,"\int \frac{(d+e x)^6}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^6/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{3 e^5 (a+b x)^2 (b d-a e)}{b^7}+\frac{15 e^4 x (b d-a e)^2}{b^6}-\frac{15 e^2 (b d-a e)^4}{b^7 (a+b x)}+\frac{20 e^3 (b d-a e)^3 \log (a+b x)}{b^7}-\frac{3 e (b d-a e)^5}{b^7 (a+b x)^2}-\frac{(b d-a e)^6}{3 b^7 (a+b x)^3}+\frac{e^6 (a+b x)^3}{3 b^7}","\frac{3 e^5 (a+b x)^2 (b d-a e)}{b^7}+\frac{15 e^4 x (b d-a e)^2}{b^6}-\frac{15 e^2 (b d-a e)^4}{b^7 (a+b x)}+\frac{20 e^3 (b d-a e)^3 \log (a+b x)}{b^7}-\frac{3 e (b d-a e)^5}{b^7 (a+b x)^2}-\frac{(b d-a e)^6}{3 b^7 (a+b x)^3}+\frac{e^6 (a+b x)^3}{3 b^7}",1,"(15*e^4*(b*d - a*e)^2*x)/b^6 - (b*d - a*e)^6/(3*b^7*(a + b*x)^3) - (3*e*(b*d - a*e)^5)/(b^7*(a + b*x)^2) - (15*e^2*(b*d - a*e)^4)/(b^7*(a + b*x)) + (3*e^5*(b*d - a*e)*(a + b*x)^2)/b^7 + (e^6*(a + b*x)^3)/(3*b^7) + (20*e^3*(b*d - a*e)^3*Log[a + b*x])/b^7","A",3,2,26,0.07692,1,"{27, 43}"
1516,1,129,0,0.1246578,"\int \frac{(d+e x)^5}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^5/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^4 x (5 b d-4 a e)}{b^5}-\frac{10 e^2 (b d-a e)^3}{b^6 (a+b x)}+\frac{10 e^3 (b d-a e)^2 \log (a+b x)}{b^6}-\frac{5 e (b d-a e)^4}{2 b^6 (a+b x)^2}-\frac{(b d-a e)^5}{3 b^6 (a+b x)^3}+\frac{e^5 x^2}{2 b^4}","\frac{e^4 x (5 b d-4 a e)}{b^5}-\frac{10 e^2 (b d-a e)^3}{b^6 (a+b x)}+\frac{10 e^3 (b d-a e)^2 \log (a+b x)}{b^6}-\frac{5 e (b d-a e)^4}{2 b^6 (a+b x)^2}-\frac{(b d-a e)^5}{3 b^6 (a+b x)^3}+\frac{e^5 x^2}{2 b^4}",1,"(e^4*(5*b*d - 4*a*e)*x)/b^5 + (e^5*x^2)/(2*b^4) - (b*d - a*e)^5/(3*b^6*(a + b*x)^3) - (5*e*(b*d - a*e)^4)/(2*b^6*(a + b*x)^2) - (10*e^2*(b*d - a*e)^3)/(b^6*(a + b*x)) + (10*e^3*(b*d - a*e)^2*Log[a + b*x])/b^6","A",3,2,26,0.07692,1,"{27, 43}"
1517,1,103,0,0.0884639,"\int \frac{(d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^4/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{6 e^2 (b d-a e)^2}{b^5 (a+b x)}+\frac{4 e^3 (b d-a e) \log (a+b x)}{b^5}-\frac{2 e (b d-a e)^3}{b^5 (a+b x)^2}-\frac{(b d-a e)^4}{3 b^5 (a+b x)^3}+\frac{e^4 x}{b^4}","-\frac{6 e^2 (b d-a e)^2}{b^5 (a+b x)}+\frac{4 e^3 (b d-a e) \log (a+b x)}{b^5}-\frac{2 e (b d-a e)^3}{b^5 (a+b x)^2}-\frac{(b d-a e)^4}{3 b^5 (a+b x)^3}+\frac{e^4 x}{b^4}",1,"(e^4*x)/b^4 - (b*d - a*e)^4/(3*b^5*(a + b*x)^3) - (2*e*(b*d - a*e)^3)/(b^5*(a + b*x)^2) - (6*e^2*(b*d - a*e)^2)/(b^5*(a + b*x)) + (4*e^3*(b*d - a*e)*Log[a + b*x])/b^5","A",3,2,26,0.07692,1,"{27, 43}"
1518,1,86,0,0.0595502,"\int \frac{(d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^3/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{3 e^2 (b d-a e)}{b^4 (a+b x)}-\frac{3 e (b d-a e)^2}{2 b^4 (a+b x)^2}-\frac{(b d-a e)^3}{3 b^4 (a+b x)^3}+\frac{e^3 \log (a+b x)}{b^4}","-\frac{3 e^2 (b d-a e)}{b^4 (a+b x)}-\frac{3 e (b d-a e)^2}{2 b^4 (a+b x)^2}-\frac{(b d-a e)^3}{3 b^4 (a+b x)^3}+\frac{e^3 \log (a+b x)}{b^4}",1,"-(b*d - a*e)^3/(3*b^4*(a + b*x)^3) - (3*e*(b*d - a*e)^2)/(2*b^4*(a + b*x)^2) - (3*e^2*(b*d - a*e))/(b^4*(a + b*x)) + (e^3*Log[a + b*x])/b^4","A",3,2,26,0.07692,1,"{27, 43}"
1519,1,28,0,0.0046141,"\int \frac{(d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^2/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{(d+e x)^3}{3 (a+b x)^3 (b d-a e)}","-\frac{(d+e x)^3}{3 (a+b x)^3 (b d-a e)}",1,"-(d + e*x)^3/(3*(b*d - a*e)*(a + b*x)^3)","A",2,2,26,0.07692,1,"{27, 37}"
1520,1,38,0,0.0219057,"\int \frac{d+e x}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{b d-a e}{3 b^2 (a+b x)^3}-\frac{e}{2 b^2 (a+b x)^2}","-\frac{b d-a e}{3 b^2 (a+b x)^3}-\frac{e}{2 b^2 (a+b x)^2}",1,"-(b*d - a*e)/(3*b^2*(a + b*x)^3) - e/(2*b^2*(a + b*x)^2)","A",3,2,24,0.08333,1,"{27, 43}"
1521,1,14,0,0.0023577,"\int \frac{1}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(-2),x]","-\frac{1}{3 b (a+b x)^3}","-\frac{1}{3 b (a+b x)^3}",1,"-1/(3*b*(a + b*x)^3)","A",2,2,18,0.1111,1,"{27, 32}"
1522,1,107,0,0.0680284,"\int \frac{1}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[1/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{e^2}{(a+b x) (b d-a e)^3}-\frac{e^3 \log (a+b x)}{(b d-a e)^4}+\frac{e^3 \log (d+e x)}{(b d-a e)^4}+\frac{e}{2 (a+b x)^2 (b d-a e)^2}-\frac{1}{3 (a+b x)^3 (b d-a e)}","-\frac{e^2}{(a+b x) (b d-a e)^3}-\frac{e^3 \log (a+b x)}{(b d-a e)^4}+\frac{e^3 \log (d+e x)}{(b d-a e)^4}+\frac{e}{2 (a+b x)^2 (b d-a e)^2}-\frac{1}{3 (a+b x)^3 (b d-a e)}",1,"-1/(3*(b*d - a*e)*(a + b*x)^3) + e/(2*(b*d - a*e)^2*(a + b*x)^2) - e^2/((b*d - a*e)^3*(a + b*x)) - (e^3*Log[a + b*x])/(b*d - a*e)^4 + (e^3*Log[d + e*x])/(b*d - a*e)^4","A",3,2,26,0.07692,1,"{27, 44}"
1523,1,132,0,0.1011664,"\int \frac{1}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[1/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{e^3}{(d+e x) (b d-a e)^4}-\frac{3 b e^2}{(a+b x) (b d-a e)^4}-\frac{4 b e^3 \log (a+b x)}{(b d-a e)^5}+\frac{4 b e^3 \log (d+e x)}{(b d-a e)^5}+\frac{b e}{(a+b x)^2 (b d-a e)^3}-\frac{b}{3 (a+b x)^3 (b d-a e)^2}","-\frac{e^3}{(d+e x) (b d-a e)^4}-\frac{3 b e^2}{(a+b x) (b d-a e)^4}-\frac{4 b e^3 \log (a+b x)}{(b d-a e)^5}+\frac{4 b e^3 \log (d+e x)}{(b d-a e)^5}+\frac{b e}{(a+b x)^2 (b d-a e)^3}-\frac{b}{3 (a+b x)^3 (b d-a e)^2}",1,"-b/(3*(b*d - a*e)^2*(a + b*x)^3) + (b*e)/((b*d - a*e)^3*(a + b*x)^2) - (3*b*e^2)/((b*d - a*e)^4*(a + b*x)) - e^3/((b*d - a*e)^4*(d + e*x)) - (4*b*e^3*Log[a + b*x])/(b*d - a*e)^5 + (4*b*e^3*Log[d + e*x])/(b*d - a*e)^5","A",3,2,26,0.07692,1,"{27, 44}"
1524,1,170,0,0.1482811,"\int \frac{1}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[1/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{6 b^2 e^2}{(a+b x) (b d-a e)^5}-\frac{10 b^2 e^3 \log (a+b x)}{(b d-a e)^6}+\frac{10 b^2 e^3 \log (d+e x)}{(b d-a e)^6}+\frac{3 b^2 e}{2 (a+b x)^2 (b d-a e)^4}-\frac{b^2}{3 (a+b x)^3 (b d-a e)^3}-\frac{4 b e^3}{(d+e x) (b d-a e)^5}-\frac{e^3}{2 (d+e x)^2 (b d-a e)^4}","-\frac{6 b^2 e^2}{(a+b x) (b d-a e)^5}-\frac{10 b^2 e^3 \log (a+b x)}{(b d-a e)^6}+\frac{10 b^2 e^3 \log (d+e x)}{(b d-a e)^6}+\frac{3 b^2 e}{2 (a+b x)^2 (b d-a e)^4}-\frac{b^2}{3 (a+b x)^3 (b d-a e)^3}-\frac{4 b e^3}{(d+e x) (b d-a e)^5}-\frac{e^3}{2 (d+e x)^2 (b d-a e)^4}",1,"-b^2/(3*(b*d - a*e)^3*(a + b*x)^3) + (3*b^2*e)/(2*(b*d - a*e)^4*(a + b*x)^2) - (6*b^2*e^2)/((b*d - a*e)^5*(a + b*x)) - e^3/(2*(b*d - a*e)^4*(d + e*x)^2) - (4*b*e^3)/((b*d - a*e)^5*(d + e*x)) - (10*b^2*e^3*Log[a + b*x])/(b*d - a*e)^6 + (10*b^2*e^3*Log[d + e*x])/(b*d - a*e)^6","A",3,2,26,0.07692,1,"{27, 44}"
1525,1,208,0,0.3114926,"\int \frac{(d+e x)^8}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^8/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{4 e^7 (a+b x)^2 (b d-a e)}{b^9}+\frac{28 e^6 x (b d-a e)^2}{b^8}-\frac{70 e^4 (b d-a e)^4}{b^9 (a+b x)}-\frac{28 e^3 (b d-a e)^5}{b^9 (a+b x)^2}-\frac{28 e^2 (b d-a e)^6}{3 b^9 (a+b x)^3}+\frac{56 e^5 (b d-a e)^3 \log (a+b x)}{b^9}-\frac{2 e (b d-a e)^7}{b^9 (a+b x)^4}-\frac{(b d-a e)^8}{5 b^9 (a+b x)^5}+\frac{e^8 (a+b x)^3}{3 b^9}","\frac{4 e^7 (a+b x)^2 (b d-a e)}{b^9}+\frac{28 e^6 x (b d-a e)^2}{b^8}-\frac{70 e^4 (b d-a e)^4}{b^9 (a+b x)}-\frac{28 e^3 (b d-a e)^5}{b^9 (a+b x)^2}-\frac{28 e^2 (b d-a e)^6}{3 b^9 (a+b x)^3}+\frac{56 e^5 (b d-a e)^3 \log (a+b x)}{b^9}-\frac{2 e (b d-a e)^7}{b^9 (a+b x)^4}-\frac{(b d-a e)^8}{5 b^9 (a+b x)^5}+\frac{e^8 (a+b x)^3}{3 b^9}",1,"(28*e^6*(b*d - a*e)^2*x)/b^8 - (b*d - a*e)^8/(5*b^9*(a + b*x)^5) - (2*e*(b*d - a*e)^7)/(b^9*(a + b*x)^4) - (28*e^2*(b*d - a*e)^6)/(3*b^9*(a + b*x)^3) - (28*e^3*(b*d - a*e)^5)/(b^9*(a + b*x)^2) - (70*e^4*(b*d - a*e)^4)/(b^9*(a + b*x)) + (4*e^7*(b*d - a*e)*(a + b*x)^2)/b^9 + (e^8*(a + b*x)^3)/(3*b^9) + (56*e^5*(b*d - a*e)^3*Log[a + b*x])/b^9","A",3,2,26,0.07692,1,"{27, 43}"
1526,1,181,0,0.2347662,"\int \frac{(d+e x)^7}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^7/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{e^6 x (7 b d-6 a e)}{b^7}-\frac{35 e^4 (b d-a e)^3}{b^8 (a+b x)}-\frac{35 e^3 (b d-a e)^4}{2 b^8 (a+b x)^2}-\frac{7 e^2 (b d-a e)^5}{b^8 (a+b x)^3}+\frac{21 e^5 (b d-a e)^2 \log (a+b x)}{b^8}-\frac{7 e (b d-a e)^6}{4 b^8 (a+b x)^4}-\frac{(b d-a e)^7}{5 b^8 (a+b x)^5}+\frac{e^7 x^2}{2 b^6}","\frac{e^6 x (7 b d-6 a e)}{b^7}-\frac{35 e^4 (b d-a e)^3}{b^8 (a+b x)}-\frac{35 e^3 (b d-a e)^4}{2 b^8 (a+b x)^2}-\frac{7 e^2 (b d-a e)^5}{b^8 (a+b x)^3}+\frac{21 e^5 (b d-a e)^2 \log (a+b x)}{b^8}-\frac{7 e (b d-a e)^6}{4 b^8 (a+b x)^4}-\frac{(b d-a e)^7}{5 b^8 (a+b x)^5}+\frac{e^7 x^2}{2 b^6}",1,"(e^6*(7*b*d - 6*a*e)*x)/b^7 + (e^7*x^2)/(2*b^6) - (b*d - a*e)^7/(5*b^8*(a + b*x)^5) - (7*e*(b*d - a*e)^6)/(4*b^8*(a + b*x)^4) - (7*e^2*(b*d - a*e)^5)/(b^8*(a + b*x)^3) - (35*e^3*(b*d - a*e)^4)/(2*b^8*(a + b*x)^2) - (35*e^4*(b*d - a*e)^3)/(b^8*(a + b*x)) + (21*e^5*(b*d - a*e)^2*Log[a + b*x])/b^8","A",3,2,26,0.07692,1,"{27, 43}"
1527,1,155,0,0.1691306,"\int \frac{(d+e x)^6}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^6/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{15 e^4 (b d-a e)^2}{b^7 (a+b x)}-\frac{10 e^3 (b d-a e)^3}{b^7 (a+b x)^2}-\frac{5 e^2 (b d-a e)^4}{b^7 (a+b x)^3}+\frac{6 e^5 (b d-a e) \log (a+b x)}{b^7}-\frac{3 e (b d-a e)^5}{2 b^7 (a+b x)^4}-\frac{(b d-a e)^6}{5 b^7 (a+b x)^5}+\frac{e^6 x}{b^6}","-\frac{15 e^4 (b d-a e)^2}{b^7 (a+b x)}-\frac{10 e^3 (b d-a e)^3}{b^7 (a+b x)^2}-\frac{5 e^2 (b d-a e)^4}{b^7 (a+b x)^3}+\frac{6 e^5 (b d-a e) \log (a+b x)}{b^7}-\frac{3 e (b d-a e)^5}{2 b^7 (a+b x)^4}-\frac{(b d-a e)^6}{5 b^7 (a+b x)^5}+\frac{e^6 x}{b^6}",1,"(e^6*x)/b^6 - (b*d - a*e)^6/(5*b^7*(a + b*x)^5) - (3*e*(b*d - a*e)^5)/(2*b^7*(a + b*x)^4) - (5*e^2*(b*d - a*e)^4)/(b^7*(a + b*x)^3) - (10*e^3*(b*d - a*e)^3)/(b^7*(a + b*x)^2) - (15*e^4*(b*d - a*e)^2)/(b^7*(a + b*x)) + (6*e^5*(b*d - a*e)*Log[a + b*x])/b^7","A",3,2,26,0.07692,1,"{27, 43}"
1528,1,138,0,0.1165991,"\int \frac{(d+e x)^5}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^5/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{5 e^4 (b d-a e)}{b^6 (a+b x)}-\frac{5 e^3 (b d-a e)^2}{b^6 (a+b x)^2}-\frac{10 e^2 (b d-a e)^3}{3 b^6 (a+b x)^3}-\frac{5 e (b d-a e)^4}{4 b^6 (a+b x)^4}-\frac{(b d-a e)^5}{5 b^6 (a+b x)^5}+\frac{e^5 \log (a+b x)}{b^6}","-\frac{5 e^4 (b d-a e)}{b^6 (a+b x)}-\frac{5 e^3 (b d-a e)^2}{b^6 (a+b x)^2}-\frac{10 e^2 (b d-a e)^3}{3 b^6 (a+b x)^3}-\frac{5 e (b d-a e)^4}{4 b^6 (a+b x)^4}-\frac{(b d-a e)^5}{5 b^6 (a+b x)^5}+\frac{e^5 \log (a+b x)}{b^6}",1,"-(b*d - a*e)^5/(5*b^6*(a + b*x)^5) - (5*e*(b*d - a*e)^4)/(4*b^6*(a + b*x)^4) - (10*e^2*(b*d - a*e)^3)/(3*b^6*(a + b*x)^3) - (5*e^3*(b*d - a*e)^2)/(b^6*(a + b*x)^2) - (5*e^4*(b*d - a*e))/(b^6*(a + b*x)) + (e^5*Log[a + b*x])/b^6","A",3,2,26,0.07692,1,"{27, 43}"
1529,1,28,0,0.0047047,"\int \frac{(d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^4/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{(d+e x)^5}{5 (a+b x)^5 (b d-a e)}","-\frac{(d+e x)^5}{5 (a+b x)^5 (b d-a e)}",1,"-(d + e*x)^5/(5*(b*d - a*e)*(a + b*x)^5)","A",2,2,26,0.07692,1,"{27, 37}"
1530,1,58,0,0.0110566,"\int \frac{(d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^3/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{e (d+e x)^4}{20 (a+b x)^4 (b d-a e)^2}-\frac{(d+e x)^4}{5 (a+b x)^5 (b d-a e)}","\frac{e (d+e x)^4}{20 (a+b x)^4 (b d-a e)^2}-\frac{(d+e x)^4}{5 (a+b x)^5 (b d-a e)}",1,"-(d + e*x)^4/(5*(b*d - a*e)*(a + b*x)^5) + (e*(d + e*x)^4)/(20*(b*d - a*e)^2*(a + b*x)^4)","A",3,3,26,0.1154,1,"{27, 45, 37}"
1531,1,65,0,0.0401324,"\int \frac{(d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^2/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{e (b d-a e)}{2 b^3 (a+b x)^4}-\frac{(b d-a e)^2}{5 b^3 (a+b x)^5}-\frac{e^2}{3 b^3 (a+b x)^3}","-\frac{e (b d-a e)}{2 b^3 (a+b x)^4}-\frac{(b d-a e)^2}{5 b^3 (a+b x)^5}-\frac{e^2}{3 b^3 (a+b x)^3}",1,"-(b*d - a*e)^2/(5*b^3*(a + b*x)^5) - (e*(b*d - a*e))/(2*b^3*(a + b*x)^4) - e^2/(3*b^3*(a + b*x)^3)","A",3,2,26,0.07692,1,"{27, 43}"
1532,1,38,0,0.024086,"\int \frac{d+e x}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{b d-a e}{5 b^2 (a+b x)^5}-\frac{e}{4 b^2 (a+b x)^4}","-\frac{b d-a e}{5 b^2 (a+b x)^5}-\frac{e}{4 b^2 (a+b x)^4}",1,"-(b*d - a*e)/(5*b^2*(a + b*x)^5) - e/(4*b^2*(a + b*x)^4)","A",3,2,24,0.08333,1,"{27, 43}"
1533,1,14,0,0.0022241,"\int \frac{1}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(-3),x]","-\frac{1}{5 b (a+b x)^5}","-\frac{1}{5 b (a+b x)^5}",1,"-1/(5*b*(a + b*x)^5)","A",2,2,18,0.1111,1,"{27, 32}"
1534,1,155,0,0.1138133,"\int \frac{1}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[1/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{e^4}{(a+b x) (b d-a e)^5}+\frac{e^3}{2 (a+b x)^2 (b d-a e)^4}-\frac{e^2}{3 (a+b x)^3 (b d-a e)^3}-\frac{e^5 \log (a+b x)}{(b d-a e)^6}+\frac{e^5 \log (d+e x)}{(b d-a e)^6}+\frac{e}{4 (a+b x)^4 (b d-a e)^2}-\frac{1}{5 (a+b x)^5 (b d-a e)}","-\frac{e^4}{(a+b x) (b d-a e)^5}+\frac{e^3}{2 (a+b x)^2 (b d-a e)^4}-\frac{e^2}{3 (a+b x)^3 (b d-a e)^3}-\frac{e^5 \log (a+b x)}{(b d-a e)^6}+\frac{e^5 \log (d+e x)}{(b d-a e)^6}+\frac{e}{4 (a+b x)^4 (b d-a e)^2}-\frac{1}{5 (a+b x)^5 (b d-a e)}",1,"-1/(5*(b*d - a*e)*(a + b*x)^5) + e/(4*(b*d - a*e)^2*(a + b*x)^4) - e^2/(3*(b*d - a*e)^3*(a + b*x)^3) + e^3/(2*(b*d - a*e)^4*(a + b*x)^2) - e^4/((b*d - a*e)^5*(a + b*x)) - (e^5*Log[a + b*x])/(b*d - a*e)^6 + (e^5*Log[d + e*x])/(b*d - a*e)^6","A",3,2,26,0.07692,1,"{27, 44}"
1535,1,181,0,0.1839393,"\int \frac{1}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[1/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{e^5}{(d+e x) (b d-a e)^6}-\frac{5 b e^4}{(a+b x) (b d-a e)^6}+\frac{2 b e^3}{(a+b x)^2 (b d-a e)^5}-\frac{b e^2}{(a+b x)^3 (b d-a e)^4}-\frac{6 b e^5 \log (a+b x)}{(b d-a e)^7}+\frac{6 b e^5 \log (d+e x)}{(b d-a e)^7}+\frac{b e}{2 (a+b x)^4 (b d-a e)^3}-\frac{b}{5 (a+b x)^5 (b d-a e)^2}","-\frac{e^5}{(d+e x) (b d-a e)^6}-\frac{5 b e^4}{(a+b x) (b d-a e)^6}+\frac{2 b e^3}{(a+b x)^2 (b d-a e)^5}-\frac{b e^2}{(a+b x)^3 (b d-a e)^4}-\frac{6 b e^5 \log (a+b x)}{(b d-a e)^7}+\frac{6 b e^5 \log (d+e x)}{(b d-a e)^7}+\frac{b e}{2 (a+b x)^4 (b d-a e)^3}-\frac{b}{5 (a+b x)^5 (b d-a e)^2}",1,"-b/(5*(b*d - a*e)^2*(a + b*x)^5) + (b*e)/(2*(b*d - a*e)^3*(a + b*x)^4) - (b*e^2)/((b*d - a*e)^4*(a + b*x)^3) + (2*b*e^3)/((b*d - a*e)^5*(a + b*x)^2) - (5*b*e^4)/((b*d - a*e)^6*(a + b*x)) - e^5/((b*d - a*e)^6*(d + e*x)) - (6*b*e^5*Log[a + b*x])/(b*d - a*e)^7 + (6*b*e^5*Log[d + e*x])/(b*d - a*e)^7","A",3,2,26,0.07692,1,"{27, 44}"
1536,1,220,0,0.2517975,"\int \frac{1}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[1/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{15 b^2 e^4}{(a+b x) (b d-a e)^7}+\frac{5 b^2 e^3}{(a+b x)^2 (b d-a e)^6}-\frac{2 b^2 e^2}{(a+b x)^3 (b d-a e)^5}-\frac{21 b^2 e^5 \log (a+b x)}{(b d-a e)^8}+\frac{21 b^2 e^5 \log (d+e x)}{(b d-a e)^8}+\frac{3 b^2 e}{4 (a+b x)^4 (b d-a e)^4}-\frac{b^2}{5 (a+b x)^5 (b d-a e)^3}-\frac{6 b e^5}{(d+e x) (b d-a e)^7}-\frac{e^5}{2 (d+e x)^2 (b d-a e)^6}","-\frac{15 b^2 e^4}{(a+b x) (b d-a e)^7}+\frac{5 b^2 e^3}{(a+b x)^2 (b d-a e)^6}-\frac{2 b^2 e^2}{(a+b x)^3 (b d-a e)^5}-\frac{21 b^2 e^5 \log (a+b x)}{(b d-a e)^8}+\frac{21 b^2 e^5 \log (d+e x)}{(b d-a e)^8}+\frac{3 b^2 e}{4 (a+b x)^4 (b d-a e)^4}-\frac{b^2}{5 (a+b x)^5 (b d-a e)^3}-\frac{6 b e^5}{(d+e x) (b d-a e)^7}-\frac{e^5}{2 (d+e x)^2 (b d-a e)^6}",1,"-b^2/(5*(b*d - a*e)^3*(a + b*x)^5) + (3*b^2*e)/(4*(b*d - a*e)^4*(a + b*x)^4) - (2*b^2*e^2)/((b*d - a*e)^5*(a + b*x)^3) + (5*b^2*e^3)/((b*d - a*e)^6*(a + b*x)^2) - (15*b^2*e^4)/((b*d - a*e)^7*(a + b*x)) - e^5/(2*(b*d - a*e)^6*(d + e*x)^2) - (6*b*e^5)/((b*d - a*e)^7*(d + e*x)) - (21*b^2*e^5*Log[a + b*x])/(b*d - a*e)^8 + (21*b^2*e^5*Log[d + e*x])/(b*d - a*e)^8","A",3,2,26,0.07692,1,"{27, 44}"
1537,1,31,0,0.0115803,"\int (d+e x) \left(9+12 x+4 x^2\right)^3 \, dx","Int[(d + e*x)*(9 + 12*x + 4*x^2)^3,x]","\frac{1}{28} (2 x+3)^7 (2 d-3 e)+\frac{1}{32} e (2 x+3)^8","\frac{1}{28} (2 x+3)^7 (2 d-3 e)+\frac{1}{32} e (2 x+3)^8",1,"((2*d - 3*e)*(3 + 2*x)^7)/28 + (e*(3 + 2*x)^8)/32","A",3,2,18,0.1111,1,"{27, 43}"
1538,1,31,0,0.0108392,"\int (d+e x) \left(9+12 x+4 x^2\right)^2 \, dx","Int[(d + e*x)*(9 + 12*x + 4*x^2)^2,x]","\frac{1}{20} (2 x+3)^5 (2 d-3 e)+\frac{1}{24} e (2 x+3)^6","\frac{1}{20} (2 x+3)^5 (2 d-3 e)+\frac{1}{24} e (2 x+3)^6",1,"((2*d - 3*e)*(3 + 2*x)^5)/20 + (e*(3 + 2*x)^6)/24","A",3,2,18,0.1111,1,"{27, 43}"
1539,1,31,0,0.0206185,"\int (d+e x) \left(9+12 x+4 x^2\right) \, dx","Int[(d + e*x)*(9 + 12*x + 4*x^2),x]","\frac{1}{12} (2 x+3)^3 (2 d-3 e)+\frac{1}{16} e (2 x+3)^4","\frac{1}{12} (2 x+3)^3 (2 d-3 e)+\frac{1}{16} e (2 x+3)^4",1,"((2*d - 3*e)*(3 + 2*x)^3)/12 + (e*(3 + 2*x)^4)/16","A",3,2,16,0.1250,1,"{27, 43}"
1540,1,30,0,0.0168794,"\int \frac{d+e x}{9+12 x+4 x^2} \, dx","Int[(d + e*x)/(9 + 12*x + 4*x^2),x]","\frac{1}{4} e \log (2 x+3)-\frac{2 d-3 e}{4 (2 x+3)}","\frac{1}{4} e \log (2 x+3)-\frac{2 d-3 e}{4 (2 x+3)}",1,"-(2*d - 3*e)/(4*(3 + 2*x)) + (e*Log[3 + 2*x])/4","A",3,2,18,0.1111,1,"{27, 43}"
1541,1,31,0,0.0162679,"\int \frac{d+e x}{\left(9+12 x+4 x^2\right)^2} \, dx","Int[(d + e*x)/(9 + 12*x + 4*x^2)^2,x]","-\frac{2 d-3 e}{12 (2 x+3)^3}-\frac{e}{8 (2 x+3)^2}","-\frac{2 d-3 e}{12 (2 x+3)^3}-\frac{e}{8 (2 x+3)^2}",1,"-(2*d - 3*e)/(12*(3 + 2*x)^3) - e/(8*(3 + 2*x)^2)","A",3,2,18,0.1111,1,"{27, 43}"
1542,1,31,0,0.0165174,"\int \frac{d+e x}{\left(9+12 x+4 x^2\right)^3} \, dx","Int[(d + e*x)/(9 + 12*x + 4*x^2)^3,x]","-\frac{2 d-3 e}{20 (2 x+3)^5}-\frac{e}{16 (2 x+3)^4}","-\frac{2 d-3 e}{20 (2 x+3)^5}-\frac{e}{16 (2 x+3)^4}",1,"-(2*d - 3*e)/(20*(3 + 2*x)^5) - e/(16*(3 + 2*x)^4)","A",3,2,18,0.1111,1,"{27, 43}"
1543,1,92,0,0.0400595,"\int (d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6}{6 e^2 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)}{5 e^2 (a+b x)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6}{6 e^2 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)}{5 e^2 (a+b x)}",1,"-((b*d - a*e)*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^2*(a + b*x)) + (b*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^2*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1544,1,92,0,0.0358736,"\int (d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5}{5 e^2 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (b d-a e)}{4 e^2 (a+b x)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5}{5 e^2 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (b d-a e)}{4 e^2 (a+b x)}",1,"-((b*d - a*e)*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^2*(a + b*x)) + (b*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^2*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1545,1,92,0,0.0489773,"\int (d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}{4 e^2 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}{3 e^2 (a+b x)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}{4 e^2 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}{3 e^2 (a+b x)}",1,"-((b*d - a*e)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^2*(a + b*x)) + (b*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^2*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1546,1,69,0,0.0208345,"\int (d+e x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 b^2}+\frac{e \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b^2}","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 b^2}+\frac{e \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b^2}",1,"((b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^2) + (e*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(3*b^2)","A",2,2,26,0.07692,1,"{640, 609}"
1547,1,32,0,0.005164,"\int \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 b}","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 b}",1,"((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b)","A",1,1,20,0.05000,1,"{609}"
1548,1,80,0,0.0373813,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{d+e x} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/(d + e*x),x]","\frac{b x \sqrt{a^2+2 a b x+b^2 x^2}}{e (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^2 (a+b x)}","\frac{b x \sqrt{a^2+2 a b x+b^2 x^2}}{e (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^2 (a+b x)}",1,"(b*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e*(a + b*x)) - ((b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^2*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1549,1,85,0,0.0405717,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^2} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/(d + e*x)^2,x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^2 (a+b x) (d+e x)}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^2 (a+b x)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^2 (a+b x) (d+e x)}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^2 (a+b x)}",1,"((b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(a + b*x)*(d + e*x)) + (b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^2*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1550,1,46,0,0.0198825,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^3} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/(d + e*x)^3,x]","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 (d+e x)^2 (b d-a e)}","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 (d+e x)^2 (b d-a e)}",1,"((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(b*d - a*e)*(d + e*x)^2)","A",2,2,28,0.07143,1,"{646, 37}"
1551,1,92,0,0.0420961,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^4} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/(d + e*x)^4,x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^2 (a+b x) (d+e x)^3}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^2 (a+b x) (d+e x)^2}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^2 (a+b x) (d+e x)^3}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^2 (a+b x) (d+e x)^2}",1,"((b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^2*(a + b*x)*(d + e*x)^3) - (b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^2*(a + b*x)*(d + e*x)^2)","A",3,2,28,0.07143,1,"{646, 43}"
1552,1,92,0,0.0413642,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^5} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/(d + e*x)^5,x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{4 e^2 (a+b x) (d+e x)^4}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^2 (a+b x) (d+e x)^3}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{4 e^2 (a+b x) (d+e x)^4}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^2 (a+b x) (d+e x)^3}",1,"((b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^2*(a + b*x)*(d + e*x)^4) - (b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^2*(a + b*x)*(d + e*x)^3)","A",3,2,28,0.07143,1,"{646, 43}"
1553,1,92,0,0.042384,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^6} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/(d + e*x)^6,x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^2 (a+b x) (d+e x)^5}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^2 (a+b x) (d+e x)^4}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^2 (a+b x) (d+e x)^5}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^2 (a+b x) (d+e x)^4}",1,"((b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^2*(a + b*x)*(d + e*x)^5) - (b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^2*(a + b*x)*(d + e*x)^4)","A",3,2,28,0.07143,1,"{646, 43}"
1554,1,200,0,0.1977074,"\int (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9}{9 e^4 (a+b x)}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)}{8 e^4 (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^2}{7 e^4 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^3}{6 e^4 (a+b x)}","\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9}{9 e^4 (a+b x)}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)}{8 e^4 (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^2}{7 e^4 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^3}{6 e^4 (a+b x)}",1,"-((b*d - a*e)^3*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^4*(a + b*x)) + (3*b*(b*d - a*e)^2*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x)) - (3*b^2*(b*d - a*e)*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^4*(a + b*x)) + (b^3*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^4*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1555,1,200,0,0.1599733,"\int (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8}{8 e^4 (a+b x)}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)}{7 e^4 (a+b x)}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^2}{2 e^4 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)^3}{5 e^4 (a+b x)}","\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8}{8 e^4 (a+b x)}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)}{7 e^4 (a+b x)}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^2}{2 e^4 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)^3}{5 e^4 (a+b x)}",1,"-((b*d - a*e)^3*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)) + (b*(b*d - a*e)^2*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^4*(a + b*x)) - (3*b^2*(b*d - a*e)*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x)) + (b^3*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^4*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1556,1,172,0,0.1317523,"\int (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)}{2 b^4}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^2}{5 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (b d-a e)^3}{4 b^4}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^4}","\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)}{2 b^4}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^2}{5 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (b d-a e)^3}{4 b^4}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^4}",1,"((b*d - a*e)^3*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^4) + (3*e*(b*d - a*e)^2*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^4) + (e^2*(b*d - a*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^4) + (e^3*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^4)","A",3,2,28,0.07143,1,"{646, 43}"
1557,1,125,0,0.0499471,"\int (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)}{5 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (b d-a e)^2}{4 b^3}+\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^3}","\frac{2 e \left(a^2+2 a b x+b^2 x^2\right)^{5/2} (b d-a e)}{5 b^3}+\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (b d-a e)^2}{4 b^3}+\frac{e^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{6 b^3}",1,"((b*d - a*e)^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^3) + (2*e*(b*d - a*e)*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^3) + (e^2*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^3)","A",2,1,28,0.03571,1,"{645}"
1558,1,69,0,0.0211858,"\int (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (b d-a e)}{4 b^2}+\frac{e \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b^2}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (b d-a e)}{4 b^2}+\frac{e \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b^2}",1,"((b*d - a*e)*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b^2) + (e*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(5*b^2)","A",2,2,26,0.07692,1,"{640, 609}"
1559,1,32,0,0.0049789,"\int \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{4 b}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{4 b}",1,"((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b)","A",1,1,20,0.05000,1,"{609}"
1560,1,166,0,0.0678044,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{d+e x} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x),x]","\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^3 (a+b x)}-\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 e^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x)}{e^4 (a+b x)}+\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e}","\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^3 (a+b x)}-\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 e^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x)}{e^4 (a+b x)}+\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e}",1,"(b*(b*d - a*e)^2*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)) - ((b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^2) + ((a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e) - ((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^4*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1561,1,183,0,0.0922766,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^2,x]","-\frac{b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (2 b d-3 a e)}{e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^4 (a+b x) (d+e x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^4 (a+b x)}+\frac{b^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^2 (a+b x)}","-\frac{b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (2 b d-3 a e)}{e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^4 (a+b x) (d+e x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^4 (a+b x)}+\frac{b^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^2 (a+b x)}",1,"-((b^2*(2*b*d - 3*a*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x))) + (b^3*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^2*(a + b*x)) + ((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)*(d + e*x)) + (3*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^4*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1562,1,186,0,0.0856378,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^3,x]","-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^4 (a+b x) (d+e x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{2 e^4 (a+b x) (d+e x)^2}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^4 (a+b x)}+\frac{b^3 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^3 (a+b x)}","-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^4 (a+b x) (d+e x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{2 e^4 (a+b x) (d+e x)^2}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^4 (a+b x)}+\frac{b^3 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^3 (a+b x)}",1,"(b^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)) + ((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^4*(a + b*x)*(d + e*x)^2) - (3*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)*(d + e*x)) - (3*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^4*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1563,1,194,0,0.0883131,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^4} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^4,x]","\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^4 (a+b x) (d+e x)}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^4 (a+b x) (d+e x)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^4 (a+b x) (d+e x)^3}+\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^4 (a+b x)}","\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^4 (a+b x) (d+e x)}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^4 (a+b x) (d+e x)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^4 (a+b x) (d+e x)^3}+\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^4 (a+b x)}",1,"((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4*(a + b*x)*(d + e*x)^3) - (3*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^4*(a + b*x)*(d + e*x)^2) + (3*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)*(d + e*x)) + (b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^4*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1564,1,48,0,0.0190633,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^5} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^5,x]","\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (d+e x)^4 (b d-a e)}","\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (d+e x)^4 (b d-a e)}",1,"((a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(b*d - a*e)*(d + e*x)^4)","A",2,2,28,0.07143,1,"{646, 37}"
1565,1,98,0,0.0382047,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^6} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^6,x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3}{20 (d+e x)^4 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3}{5 (d+e x)^5 (b d-a e)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3}{20 (d+e x)^4 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3}{5 (d+e x)^5 (b d-a e)}",1,"((a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(b*d - a*e)*(d + e*x)^5) + (b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(20*(b*d - a*e)^2*(d + e*x)^4)","A",3,3,28,0.1071,1,"{646, 45, 37}"
1566,1,200,0,0.0861064,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^7} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^7,x]","-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^4 (a+b x) (d+e x)^3}+\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{4 e^4 (a+b x) (d+e x)^4}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{5 e^4 (a+b x) (d+e x)^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{6 e^4 (a+b x) (d+e x)^6}","\frac{b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{60 (d+e x)^4 (b d-a e)^3}+\frac{b (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{15 (d+e x)^5 (b d-a e)^2}+\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{6 (d+e x)^6 (b d-a e)}",1,"((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^4*(a + b*x)*(d + e*x)^6) - (3*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)*(d + e*x)^5) + (3*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^4*(a + b*x)*(d + e*x)^4) - (b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4*(a + b*x)*(d + e*x)^3)","A",3,2,28,0.07143,1,"{646, 43}"
1567,1,200,0,0.0885224,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^8} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^8,x]","-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^4 (a+b x) (d+e x)^4}+\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^4 (a+b x) (d+e x)^5}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^4 (a+b x) (d+e x)^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^4 (a+b x) (d+e x)^7}","-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^4 (a+b x) (d+e x)^4}+\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^4 (a+b x) (d+e x)^5}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^4 (a+b x) (d+e x)^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^4 (a+b x) (d+e x)^7}",1,"((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x)*(d + e*x)^7) - (b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^4*(a + b*x)*(d + e*x)^6) + (3*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)*(d + e*x)^5) - (b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^4*(a + b*x)*(d + e*x)^4)","A",3,2,28,0.07143,1,"{646, 43}"
1568,1,200,0,0.0868989,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^9} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^9,x]","-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^4 (a+b x) (d+e x)^5}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 e^4 (a+b x) (d+e x)^6}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^4 (a+b x) (d+e x)^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{8 e^4 (a+b x) (d+e x)^8}","-\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^4 (a+b x) (d+e x)^5}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 e^4 (a+b x) (d+e x)^6}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^4 (a+b x) (d+e x)^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{8 e^4 (a+b x) (d+e x)^8}",1,"((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^4*(a + b*x)*(d + e*x)^8) - (3*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x)*(d + e*x)^7) + (b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^4*(a + b*x)*(d + e*x)^6) - (b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)*(d + e*x)^5)","A",3,2,28,0.07143,1,"{646, 43}"
1569,1,266,0,0.3027778,"\int (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e)}{2 b^6}+\frac{10 e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^2}{9 b^6}+\frac{5 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^3}{4 b^6}+\frac{5 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^4}{7 b^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^5}{6 b^6}+\frac{e^5 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10}}{11 b^6}","\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e)}{2 b^6}+\frac{10 e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^2}{9 b^6}+\frac{5 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^3}{4 b^6}+\frac{5 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^4}{7 b^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^5}{6 b^6}+\frac{e^5 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10}}{11 b^6}",1,"((b*d - a*e)^5*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^6) + (5*e*(b*d - a*e)^4*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^6) + (5*e^2*(b*d - a*e)^3*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^6) + (10*e^3*(b*d - a*e)^2*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^6) + (e^4*(b*d - a*e)*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^6) + (e^5*(a + b*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*b^6)","A",3,2,28,0.07143,1,"{646, 43}"
1570,1,219,0,0.0896996,"\int (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{4 e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)}{9 b^5}+\frac{3 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^2}{4 b^5}+\frac{4 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^3}{7 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^4}{6 b^5}+\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^5}","\frac{4 e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)}{9 b^5}+\frac{3 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^2}{4 b^5}+\frac{4 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^3}{7 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^4}{6 b^5}+\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^5}",1,"((b*d - a*e)^4*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^5) + (4*e*(b*d - a*e)^3*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^5) + (3*e^2*(b*d - a*e)^2*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^5) + (4*e^3*(b*d - a*e)*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^5) + (e^4*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*b^5)","A",2,1,28,0.03571,1,"{645}"
1571,1,172,0,0.1801726,"\int (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{3 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)}{8 b^4}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^2}{7 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^3}{6 b^4}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^4}","\frac{3 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)}{8 b^4}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^2}{7 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^3}{6 b^4}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^4}",1,"((b*d - a*e)^3*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^4) + (3*e*(b*d - a*e)^2*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^4) + (3*e^2*(b*d - a*e)*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^4) + (e^3*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^4)","A",3,2,28,0.07143,1,"{646, 43}"
1572,1,125,0,0.1399138,"\int (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)}{7 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^2}{6 b^3}+\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^3}","\frac{2 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)}{7 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^2}{6 b^3}+\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^3}",1,"((b*d - a*e)^2*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^3) + (2*e*(b*d - a*e)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^3) + (e^2*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^3)","A",3,2,28,0.07143,1,"{646, 43}"
1573,1,69,0,0.0235983,"\int (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} (b d-a e)}{6 b^2}+\frac{e \left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b^2}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} (b d-a e)}{6 b^2}+\frac{e \left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b^2}",1,"((b*d - a*e)*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b^2) + (e*(a^2 + 2*a*b*x + b^2*x^2)^(7/2))/(7*b^2)","A",2,2,26,0.07692,1,"{640, 609}"
1574,1,32,0,0.0055318,"\int \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{6 b}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{6 b}",1,"((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b)","A",1,1,20,0.05000,1,"{609}"
1575,1,254,0,0.1254858,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x),x]","\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^5 (a+b x)}-\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{2 e^4}+\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^3}-\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{4 e^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 \log (d+e x)}{e^6 (a+b x)}+\frac{(a+b x)^4 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e}","\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^5 (a+b x)}-\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{2 e^4}+\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^3}-\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{4 e^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 \log (d+e x)}{e^6 (a+b x)}+\frac{(a+b x)^4 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e}",1,"(b*(b*d - a*e)^4*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) - ((b*d - a*e)^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^4) + ((b*d - a*e)^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3) - ((b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^2) + ((a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e) - ((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^6*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1576,1,292,0,0.2105836,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^2,x]","\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}{4 e^6 (a+b x)}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}{3 e^6 (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}{e^6 (a+b x)}-\frac{10 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^6 (a+b x) (d+e x)}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 \log (d+e x)}{e^6 (a+b x)}","\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}{4 e^6 (a+b x)}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}{3 e^6 (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}{e^6 (a+b x)}-\frac{10 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^6 (a+b x) (d+e x)}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 \log (d+e x)}{e^6 (a+b x)}",1,"(-10*b^2*(b*d - a*e)^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) + ((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)) + (5*b^3*(b*d - a*e)^2*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - (5*b^4*(b*d - a*e)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)) + (b^5*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^6*(a + b*x)) + (5*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^6*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1577,1,295,0,0.1896055,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^3,x]","\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^6 (a+b x)}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}{2 e^6 (a+b x)}+\frac{10 b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x)}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^6 (a+b x) (d+e x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{2 e^6 (a+b x) (d+e x)^2}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x)}{e^6 (a+b x)}","\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^6 (a+b x)}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}{2 e^6 (a+b x)}+\frac{10 b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x)}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^6 (a+b x) (d+e x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{2 e^6 (a+b x) (d+e x)^2}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x)}{e^6 (a+b x)}",1,"(10*b^3*(b*d - a*e)^2*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) + ((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^6*(a + b*x)*(d + e*x)^2) - (5*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)) - (5*b^4*(b*d - a*e)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^6*(a + b*x)) + (b^5*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)) - (10*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^6*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1578,1,292,0,0.1574453,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^4,x]","-\frac{b^4 x \sqrt{a^2+2 a b x+b^2 x^2} (4 b d-5 a e)}{e^5 (a+b x)}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x) (d+e x)}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^6 (a+b x) (d+e x)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{3 e^6 (a+b x) (d+e x)^3}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^6 (a+b x)}+\frac{b^5 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^4 (a+b x)}","-\frac{b^4 x \sqrt{a^2+2 a b x+b^2 x^2} (4 b d-5 a e)}{e^5 (a+b x)}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x) (d+e x)}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^6 (a+b x) (d+e x)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{3 e^6 (a+b x) (d+e x)^3}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^6 (a+b x)}+\frac{b^5 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^4 (a+b x)}",1,"-((b^4*(4*b*d - 5*a*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x))) + (b^5*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^4*(a + b*x)) + ((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)*(d + e*x)^3) - (5*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^6*(a + b*x)*(d + e*x)^2) + (10*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)) + (10*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^6*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1579,1,292,0,0.1483871,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^5} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^5,x]","-\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x) (d+e x)}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x) (d+e x)^2}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^6 (a+b x) (d+e x)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{4 e^6 (a+b x) (d+e x)^4}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^6 (a+b x)}+\frac{b^5 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^5 (a+b x)}","-\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x) (d+e x)}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x) (d+e x)^2}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^6 (a+b x) (d+e x)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{4 e^6 (a+b x) (d+e x)^4}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^6 (a+b x)}+\frac{b^5 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^5 (a+b x)}",1,"(b^5*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) + ((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^6*(a + b*x)*(d + e*x)^4) - (5*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)*(d + e*x)^3) + (5*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)^2) - (10*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)) - (5*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^6*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1580,1,300,0,0.1438038,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^6} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^6,x]","\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^6 (a+b x) (d+e x)}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x) (d+e x)^2}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^6 (a+b x) (d+e x)^3}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^6 (a+b x) (d+e x)^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^6 (a+b x) (d+e x)^5}+\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^6 (a+b x)}","\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^6 (a+b x) (d+e x)}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x) (d+e x)^2}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^6 (a+b x) (d+e x)^3}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^6 (a+b x) (d+e x)^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^6 (a+b x) (d+e x)^5}+\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^6 (a+b x)}",1,"((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^6*(a + b*x)*(d + e*x)^5) - (5*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^6*(a + b*x)*(d + e*x)^4) + (10*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)*(d + e*x)^3) - (5*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)^2) + (5*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)) + (b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^6*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1581,1,48,0,0.0194524,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^7} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^7,x]","\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (d+e x)^6 (b d-a e)}","\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (d+e x)^6 (b d-a e)}",1,"((a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(b*d - a*e)*(d + e*x)^6)","A",2,2,28,0.07143,1,"{646, 37}"
1582,1,98,0,0.0360393,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^8} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^8,x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{42 (d+e x)^6 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{7 (d+e x)^7 (b d-a e)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{42 (d+e x)^6 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{7 (d+e x)^7 (b d-a e)}",1,"((a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(b*d - a*e)*(d + e*x)^7) + (b*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(42*(b*d - a*e)^2*(d + e*x)^6)","A",3,3,28,0.1071,1,"{646, 45, 37}"
1583,1,149,0,0.0510391,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^9} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^9,x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{168 (d+e x)^6 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{28 (d+e x)^7 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{8 (d+e x)^8 (b d-a e)}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{168 (d+e x)^6 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{28 (d+e x)^7 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{8 (d+e x)^8 (b d-a e)}",1,"((a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*(b*d - a*e)*(d + e*x)^8) + (b*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(28*(b*d - a*e)^2*(d + e*x)^7) + (b^2*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(168*(b*d - a*e)^3*(d + e*x)^6)","A",4,3,28,0.1071,1,"{646, 45, 37}"
1584,1,200,0,0.0678561,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{10}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^10,x]","\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{504 (d+e x)^6 (b d-a e)^4}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{84 (d+e x)^7 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{24 (d+e x)^8 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{9 (d+e x)^9 (b d-a e)}","\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{504 (d+e x)^6 (b d-a e)^4}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{84 (d+e x)^7 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{24 (d+e x)^8 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{9 (d+e x)^9 (b d-a e)}",1,"((a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(b*d - a*e)*(d + e*x)^9) + (b*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(24*(b*d - a*e)^2*(d + e*x)^8) + (b^2*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(84*(b*d - a*e)^3*(d + e*x)^7) + (b^3*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(504*(b*d - a*e)^4*(d + e*x)^6)","A",5,3,28,0.1071,1,"{646, 45, 37}"
1585,1,308,0,0.1400805,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{11}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^11,x]","-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^6 (a+b x) (d+e x)^5}+\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{6 e^6 (a+b x) (d+e x)^6}-\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^6 (a+b x) (d+e x)^7}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{4 e^6 (a+b x) (d+e x)^8}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{9 e^6 (a+b x) (d+e x)^9}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{10 e^6 (a+b x) (d+e x)^{10}}","-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^6 (a+b x) (d+e x)^5}+\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{6 e^6 (a+b x) (d+e x)^6}-\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^6 (a+b x) (d+e x)^7}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{4 e^6 (a+b x) (d+e x)^8}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{9 e^6 (a+b x) (d+e x)^9}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{10 e^6 (a+b x) (d+e x)^{10}}",1,"((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^6*(a + b*x)*(d + e*x)^10) - (5*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x)*(d + e*x)^9) + (5*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^6*(a + b*x)*(d + e*x)^8) - (10*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)*(d + e*x)^7) + (5*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^6*(a + b*x)*(d + e*x)^6) - (b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^6*(a + b*x)*(d + e*x)^5)","A",3,2,28,0.07143,1,"{646, 43}"
1586,1,308,0,0.1380081,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{12}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^12,x]","-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^6 (a+b x) (d+e x)^6}+\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{7 e^6 (a+b x) (d+e x)^7}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^6 (a+b x) (d+e x)^8}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^6 (a+b x) (d+e x)^9}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^6 (a+b x) (d+e x)^{10}}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{11 e^6 (a+b x) (d+e x)^{11}}","-\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^6 (a+b x) (d+e x)^6}+\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{7 e^6 (a+b x) (d+e x)^7}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^6 (a+b x) (d+e x)^8}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^6 (a+b x) (d+e x)^9}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^6 (a+b x) (d+e x)^{10}}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{11 e^6 (a+b x) (d+e x)^{11}}",1,"((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^6*(a + b*x)*(d + e*x)^11) - (b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^6*(a + b*x)*(d + e*x)^10) + (10*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x)*(d + e*x)^9) - (5*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^6*(a + b*x)*(d + e*x)^8) + (5*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)*(d + e*x)^7) - (b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^6*(a + b*x)*(d + e*x)^6)","A",3,2,28,0.07143,1,"{646, 43}"
1587,1,222,0,0.0803956,"\int \frac{(d+e x)^4}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(d + e*x)^4/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{e x (a+b x) (b d-a e)^3}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^2 (b d-a e)^2}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^3 (b d-a e)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^4}{4 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (b d-a e)^4 \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e x (a+b x) (b d-a e)^3}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^2 (b d-a e)^2}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^3 (b d-a e)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^4}{4 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (b d-a e)^4 \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(e*(b*d - a*e)^3*x*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((b*d - a*e)^2*(a + b*x)*(d + e*x)^2)/(2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((b*d - a*e)*(a + b*x)*(d + e*x)^3)/(3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((a + b*x)*(d + e*x)^4)/(4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((b*d - a*e)^4*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1588,1,173,0,0.0619336,"\int \frac{(d+e x)^3}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(d + e*x)^3/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{e x (a+b x) (b d-a e)^2}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^2 (b d-a e)}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^3}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (b d-a e)^3 \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e x (a+b x) (b d-a e)^2}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^2 (b d-a e)}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^3}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (b d-a e)^3 \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(e*(b*d - a*e)^2*x*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((b*d - a*e)*(a + b*x)*(d + e*x)^2)/(2*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((a + b*x)*(d + e*x)^3)/(3*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((b*d - a*e)^3*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1589,1,124,0,0.0458448,"\int \frac{(d+e x)^2}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(d + e*x)^2/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{e x (a+b x) (b d-a e)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^2}{2 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (b d-a e)^2 \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e x (a+b x) (b d-a e)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^2}{2 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (b d-a e)^2 \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(e*(b*d - a*e)*x*(a + b*x))/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((a + b*x)*(d + e*x)^2)/(2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((b*d - a*e)^2*(a + b*x)*Log[a + b*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1590,1,69,0,0.0233859,"\int \frac{d+e x}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(d + e*x)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (b d-a e) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2}}{b^2}","\frac{(a+b x) (b d-a e) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2}}{b^2}",1,"(e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/b^2 + ((b*d - a*e)*(a + b*x)*Log[a + b*x])/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,26,0.1154,1,"{640, 608, 31}"
1591,1,35,0,0.0081635,"\int \frac{1}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \log (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) \log (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*Log[a + b*x])/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",2,2,20,0.1000,1,"{608, 31}"
1592,1,86,0,0.0307776,"\int \frac{1}{(d+e x) \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/((d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","\frac{(a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"((a + b*x)*Log[a + b*x])/((b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((a + b*x)*Log[d + e*x])/((b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,28,0.1071,1,"{646, 36, 31}"
1593,1,131,0,0.0620819,"\int \frac{1}{(d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/((d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{a+b x}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)}+\frac{b (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{b (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}","\frac{a+b x}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)}+\frac{b (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{b (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}",1,"(a + b*x)/((b*d - a*e)*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(a + b*x)*Log[a + b*x])/((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*(a + b*x)*Log[d + e*x])/((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 44}"
1594,1,182,0,0.0813618,"\int \frac{1}{(d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/((d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{b (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^2}+\frac{a+b x}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}+\frac{b^2 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b^2 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}","\frac{b (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^2}+\frac{a+b x}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}+\frac{b^2 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b^2 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}",1,"(a + b*x)/(2*(b*d - a*e)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(a + b*x))/((b*d - a*e)^2*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^2*(a + b*x)*Log[a + b*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b^2*(a + b*x)*Log[d + e*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 44}"
1595,1,231,0,0.1022613,"\int \frac{1}{(d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/((d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{b^2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}+\frac{b (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}+\frac{a+b x}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}+\frac{b^3 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b^3 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}","\frac{b^2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}+\frac{b (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}+\frac{a+b x}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}+\frac{b^3 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b^3 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}",1,"(a + b*x)/(3*(b*d - a*e)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(a + b*x))/(2*(b*d - a*e)^2*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^2*(a + b*x))/((b*d - a*e)^3*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^3*(a + b*x)*Log[a + b*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b^3*(a + b*x)*Log[d + e*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 44}"
1596,1,210,0,0.1347298,"\int \frac{(d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^4/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e^3 x (a+b x) (4 b d-3 a e)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{6 e^2 (a+b x) (b d-a e)^2 \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{4 e (b d-a e)^3}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^4}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^4 x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e^3 x (a+b x) (4 b d-3 a e)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{6 e^2 (a+b x) (b d-a e)^2 \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{4 e (b d-a e)^3}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^4}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^4 x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-4*e*(b*d - a*e)^3)/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*d - a*e)^4/(2*b^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*(4*b*d - 3*a*e)*x*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^4*x^2*(a + b*x))/(2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (6*e^2*(b*d - a*e)^2*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1597,1,161,0,0.0940398,"\int \frac{(d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^3/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{3 e^2 (a+b x) (b d-a e) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 e (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^3}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^3 x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{3 e^2 (a+b x) (b d-a e) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 e (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^3}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^3 x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-3*e*(b*d - a*e)^2)/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*d - a*e)^3/(2*b^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*x*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*e^2*(b*d - a*e)*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1598,1,117,0,0.0688655,"\int \frac{(d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^2/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{2 e (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^2}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^2 (a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{2 e (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^2}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^2 (a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*e*(b*d - a*e))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*d - a*e)^2/(2*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^2*(a + b*x)*Log[a + b*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1599,1,69,0,0.0218046,"\int \frac{d+e x}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{b d-a e}{2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{b d-a e}{2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(e/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (b*d - a*e)/(2*b^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",2,2,26,0.07692,1,"{640, 607}"
1600,1,34,0,0.0047325,"\int \frac{1}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(-3/2),x]","-\frac{1}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{1}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-1/(2*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",1,1,20,0.05000,1,"{607}"
1601,1,165,0,0.0969946,"\int \frac{1}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{e^2 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{e^2 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{e}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{1}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","\frac{e^2 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{e^2 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{e}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{1}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"e/((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(2*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^2*(a + b*x)*Log[a + b*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^2*(a + b*x)*Log[d + e*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 44}"
1602,1,217,0,0.126441,"\int \frac{1}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{e^2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}+\frac{3 b e^2 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{3 b e^2 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{2 b e}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}","\frac{e^2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}+\frac{3 b e^2 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{3 b e^2 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{2 b e}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}",1,"(2*b*e)/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - b/(2*(b*d - a*e)^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^2*(a + b*x))/((b*d - a*e)^3*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b*e^2*(a + b*x)*Log[a + b*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*b*e^2*(a + b*x)*Log[d + e*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 44}"
1603,1,276,0,0.1517046,"\int \frac{1}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{3 b e^2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^4}+\frac{e^2 (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^3}+\frac{6 b^2 e^2 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{6 b^2 e^2 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{b^2}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{3 b^2 e}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}","\frac{3 b e^2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^4}+\frac{e^2 (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^3}+\frac{6 b^2 e^2 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{6 b^2 e^2 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{b^2}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{3 b^2 e}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}",1,"(3*b^2*e)/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - b^2/(2*(b*d - a*e)^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^2*(a + b*x))/(2*(b*d - a*e)^3*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b*e^2*(a + b*x))/((b*d - a*e)^4*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (6*b^2*e^2*(a + b*x)*Log[a + b*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (6*b^2*e^2*(a + b*x)*Log[d + e*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 44}"
1604,1,302,0,0.2388038,"\int \frac{(d+e x)^6}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^6/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^5 x (a+b x) (6 b d-5 a e)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{20 e^3 (b d-a e)^3}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{15 e^2 (b d-a e)^4}{2 b^7 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{15 e^4 (a+b x) (b d-a e)^2 \log (a+b x)}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 e (b d-a e)^5}{b^7 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^6}{4 b^7 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^6 x^2 (a+b x)}{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e^5 x (a+b x) (6 b d-5 a e)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{20 e^3 (b d-a e)^3}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{15 e^2 (b d-a e)^4}{2 b^7 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{15 e^4 (a+b x) (b d-a e)^2 \log (a+b x)}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 e (b d-a e)^5}{b^7 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^6}{4 b^7 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^6 x^2 (a+b x)}{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-20*e^3*(b*d - a*e)^3)/(b^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*d - a*e)^6/(4*b^7*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*e*(b*d - a*e)^5)/(b^7*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (15*e^2*(b*d - a*e)^4)/(2*b^7*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^5*(6*b*d - 5*a*e)*x*(a + b*x))/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^6*x^2*(a + b*x))/(2*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (15*e^4*(b*d - a*e)^2*(a + b*x)*Log[a + b*x])/(b^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1605,1,253,0,0.1750314,"\int \frac{(d+e x)^5}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^5/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{10 e^3 (b d-a e)^2}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e^2 (b d-a e)^3}{b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e^4 (a+b x) (b d-a e) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (b d-a e)^4}{3 b^6 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^5}{4 b^6 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^5 x (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{10 e^3 (b d-a e)^2}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e^2 (b d-a e)^3}{b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e^4 (a+b x) (b d-a e) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (b d-a e)^4}{3 b^6 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^5}{4 b^6 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^5 x (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-10*e^3*(b*d - a*e)^2)/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*d - a*e)^5/(4*b^6*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(b*d - a*e)^4)/(3*b^6*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e^2*(b*d - a*e)^3)/(b^6*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^5*x*(a + b*x))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e^4*(b*d - a*e)*(a + b*x)*Log[a + b*x])/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1606,1,209,0,0.1268869,"\int \frac{(d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^4/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{4 e^3 (b d-a e)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 e^2 (b d-a e)^2}{b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{4 e (b d-a e)^3}{3 b^5 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^4}{4 b^5 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^4 (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{4 e^3 (b d-a e)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 e^2 (b d-a e)^2}{b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{4 e (b d-a e)^3}{3 b^5 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^4}{4 b^5 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^4 (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-4*e^3*(b*d - a*e))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*d - a*e)^4/(4*b^5*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (4*e*(b*d - a*e)^3)/(3*b^5*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*e^2*(b*d - a*e)^2)/(b^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^4*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1607,1,48,0,0.0220864,"\int \frac{(d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^3/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{(d+e x)^4}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{(d+e x)^4}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"-(d + e*x)^4/(4*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",2,2,28,0.07143,1,"{646, 37}"
1608,1,125,0,0.0697736,"\int \frac{(d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^2/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{2 e (b d-a e)}{3 b^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^2}{4 b^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e^2}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{2 e (b d-a e)}{3 b^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^2}{4 b^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e^2}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(b*d - a*e)^2/(4*b^3*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*e*(b*d - a*e))/(3*b^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - e^2/(2*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 43}"
1609,1,71,0,0.0214001,"\int \frac{d+e x}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{b d-a e}{4 b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{e}{3 b^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","-\frac{b d-a e}{4 b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{e}{3 b^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-e/(3*b^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - (b*d - a*e)/(4*b^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))","A",2,2,26,0.07692,1,"{640, 607}"
1610,1,34,0,0.0045317,"\int \frac{1}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(-5/2),x]","-\frac{1}{4 b (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","-\frac{1}{4 b (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-1/(4*b*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))","A",1,1,20,0.05000,1,"{607}"
1611,1,253,0,0.1572731,"\int \frac{1}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{e^3}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{e^2}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{e^4 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{e^4 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{e}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{1}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","\frac{e^3}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{e^2}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{e^4 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{e^4 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{e}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{1}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"e^3/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(4*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + e/(3*(b*d - a*e)^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - e^2/(2*(b*d - a*e)^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^4*(a + b*x)*Log[a + b*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^4*(a + b*x)*Log[d + e*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 44}"
1612,1,307,0,0.2101043,"\int \frac{1}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{e^4 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^5}+\frac{4 b e^3}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{3 b e^2}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{5 b e^4 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}-\frac{5 b e^4 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{2 b e}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}","\frac{e^4 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^5}+\frac{4 b e^3}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{3 b e^2}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{5 b e^4 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}-\frac{5 b e^4 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{2 b e}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}",1,"(4*b*e^3)/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - b/(4*(b*d - a*e)^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*b*e)/(3*(b*d - a*e)^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*b*e^2)/(2*(b*d - a*e)^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^4*(a + b*x))/((b*d - a*e)^5*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*b*e^4*(a + b*x)*Log[a + b*x])/((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*b*e^4*(a + b*x)*Log[d + e*x])/((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 44}"
1613,1,365,0,0.2633099,"\int \frac{1}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{5 b e^4 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^6}+\frac{e^4 (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^5}+\frac{10 b^2 e^3}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}-\frac{3 b^2 e^2}{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{15 b^2 e^4 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^7}-\frac{15 b^2 e^4 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^7}+\frac{b^2 e}{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b^2}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}","\frac{5 b e^4 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^6}+\frac{e^4 (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^5}+\frac{10 b^2 e^3}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}-\frac{3 b^2 e^2}{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{15 b^2 e^4 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^7}-\frac{15 b^2 e^4 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^7}+\frac{b^2 e}{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b^2}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}",1,"(10*b^2*e^3)/((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - b^2/(4*(b*d - a*e)^3*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^2*e)/((b*d - a*e)^4*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*b^2*e^2)/((b*d - a*e)^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^4*(a + b*x))/(2*(b*d - a*e)^5*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*b*e^4*(a + b*x))/((b*d - a*e)^6*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (15*b^2*e^4*(a + b*x)*Log[a + b*x])/((b*d - a*e)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (15*b^2*e^4*(a + b*x)*Log[d + e*x])/((b*d - a*e)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,28,0.07143,1,"{646, 44}"
1614,1,50,0,0.0127645,"\int (d+e x) \left(9+12 x+4 x^2\right)^{5/2} \, dx","Int[(d + e*x)*(9 + 12*x + 4*x^2)^(5/2),x]","\frac{1}{24} (2 x+3) \left(4 x^2+12 x+9\right)^{5/2} (2 d-3 e)+\frac{1}{28} e \left(4 x^2+12 x+9\right)^{7/2}","\frac{1}{24} (2 x+3) \left(4 x^2+12 x+9\right)^{5/2} (2 d-3 e)+\frac{1}{28} e \left(4 x^2+12 x+9\right)^{7/2}",1,"((2*d - 3*e)*(3 + 2*x)*(9 + 12*x + 4*x^2)^(5/2))/24 + (e*(9 + 12*x + 4*x^2)^(7/2))/28","A",2,2,20,0.1000,1,"{640, 609}"
1615,1,50,0,0.0121757,"\int (d+e x) \left(9+12 x+4 x^2\right)^{3/2} \, dx","Int[(d + e*x)*(9 + 12*x + 4*x^2)^(3/2),x]","\frac{1}{16} (2 x+3) \left(4 x^2+12 x+9\right)^{3/2} (2 d-3 e)+\frac{1}{20} e \left(4 x^2+12 x+9\right)^{5/2}","\frac{1}{16} (2 x+3) \left(4 x^2+12 x+9\right)^{3/2} (2 d-3 e)+\frac{1}{20} e \left(4 x^2+12 x+9\right)^{5/2}",1,"((2*d - 3*e)*(3 + 2*x)*(9 + 12*x + 4*x^2)^(3/2))/16 + (e*(9 + 12*x + 4*x^2)^(5/2))/20","A",2,2,20,0.1000,1,"{640, 609}"
1616,1,50,0,0.0120345,"\int (d+e x) \sqrt{9+12 x+4 x^2} \, dx","Int[(d + e*x)*Sqrt[9 + 12*x + 4*x^2],x]","\frac{1}{8} (2 x+3) \sqrt{4 x^2+12 x+9} (2 d-3 e)+\frac{1}{12} e \left(4 x^2+12 x+9\right)^{3/2}","\frac{1}{8} (2 x+3) \sqrt{4 x^2+12 x+9} (2 d-3 e)+\frac{1}{12} e \left(4 x^2+12 x+9\right)^{3/2}",1,"((2*d - 3*e)*(3 + 2*x)*Sqrt[9 + 12*x + 4*x^2])/8 + (e*(9 + 12*x + 4*x^2)^(3/2))/12","A",2,2,20,0.1000,1,"{640, 609}"
1617,1,56,0,0.0156218,"\int \frac{d+e x}{\sqrt{9+12 x+4 x^2}} \, dx","Int[(d + e*x)/Sqrt[9 + 12*x + 4*x^2],x]","\frac{(2 x+3) (2 d-3 e) \log (2 x+3)}{4 \sqrt{4 x^2+12 x+9}}+\frac{1}{4} e \sqrt{4 x^2+12 x+9}","\frac{(2 x+3) (2 d-3 e) \log (2 x+3)}{4 \sqrt{4 x^2+12 x+9}}+\frac{1}{4} e \sqrt{4 x^2+12 x+9}",1,"(e*Sqrt[9 + 12*x + 4*x^2])/4 + ((2*d - 3*e)*(3 + 2*x)*Log[3 + 2*x])/(4*Sqrt[9 + 12*x + 4*x^2])","A",3,3,20,0.1500,1,"{640, 608, 31}"
1618,1,52,0,0.0135592,"\int \frac{d+e x}{\left(9+12 x+4 x^2\right)^{3/2}} \, dx","Int[(d + e*x)/(9 + 12*x + 4*x^2)^(3/2),x]","-\frac{2 d-3 e}{8 (2 x+3) \sqrt{4 x^2+12 x+9}}-\frac{e}{4 \sqrt{4 x^2+12 x+9}}","-\frac{2 d-3 e}{8 (2 x+3) \sqrt{4 x^2+12 x+9}}-\frac{e}{4 \sqrt{4 x^2+12 x+9}}",1,"-e/(4*Sqrt[9 + 12*x + 4*x^2]) - (2*d - 3*e)/(8*(3 + 2*x)*Sqrt[9 + 12*x + 4*x^2])","A",2,2,20,0.1000,1,"{640, 607}"
1619,1,52,0,0.0126159,"\int \frac{d+e x}{\left(9+12 x+4 x^2\right)^{5/2}} \, dx","Int[(d + e*x)/(9 + 12*x + 4*x^2)^(5/2),x]","-\frac{2 d-3 e}{16 (2 x+3) \left(4 x^2+12 x+9\right)^{3/2}}-\frac{e}{12 \left(4 x^2+12 x+9\right)^{3/2}}","-\frac{2 d-3 e}{16 (2 x+3) \left(4 x^2+12 x+9\right)^{3/2}}-\frac{e}{12 \left(4 x^2+12 x+9\right)^{3/2}}",1,"-e/(12*(9 + 12*x + 4*x^2)^(3/2)) - (2*d - 3*e)/(16*(3 + 2*x)*(9 + 12*x + 4*x^2)^(3/2))","A",2,2,20,0.1000,1,"{640, 607}"
1620,1,52,0,0.0141922,"\int \frac{d+e x}{\left(9+12 x+4 x^2\right)^{7/2}} \, dx","Int[(d + e*x)/(9 + 12*x + 4*x^2)^(7/2),x]","-\frac{2 d-3 e}{24 (2 x+3) \left(4 x^2+12 x+9\right)^{5/2}}-\frac{e}{20 \left(4 x^2+12 x+9\right)^{5/2}}","-\frac{2 d-3 e}{24 (2 x+3) \left(4 x^2+12 x+9\right)^{5/2}}-\frac{e}{20 \left(4 x^2+12 x+9\right)^{5/2}}",1,"-e/(20*(9 + 12*x + 4*x^2)^(5/2)) - (2*d - 3*e)/(24*(3 + 2*x)*(9 + 12*x + 4*x^2)^(5/2))","A",2,2,20,0.1000,1,"{640, 607}"
1621,1,71,0,0.0283148,"\int (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{4 b (d+e x)^{11/2} (b d-a e)}{11 e^3}+\frac{2 (d+e x)^{9/2} (b d-a e)^2}{9 e^3}+\frac{2 b^2 (d+e x)^{13/2}}{13 e^3}","-\frac{4 b (d+e x)^{11/2} (b d-a e)}{11 e^3}+\frac{2 (d+e x)^{9/2} (b d-a e)^2}{9 e^3}+\frac{2 b^2 (d+e x)^{13/2}}{13 e^3}",1,"(2*(b*d - a*e)^2*(d + e*x)^(9/2))/(9*e^3) - (4*b*(b*d - a*e)*(d + e*x)^(11/2))/(11*e^3) + (2*b^2*(d + e*x)^(13/2))/(13*e^3)","A",3,2,26,0.07692,1,"{27, 43}"
1622,1,71,0,0.0233756,"\int (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{4 b (d+e x)^{9/2} (b d-a e)}{9 e^3}+\frac{2 (d+e x)^{7/2} (b d-a e)^2}{7 e^3}+\frac{2 b^2 (d+e x)^{11/2}}{11 e^3}","-\frac{4 b (d+e x)^{9/2} (b d-a e)}{9 e^3}+\frac{2 (d+e x)^{7/2} (b d-a e)^2}{7 e^3}+\frac{2 b^2 (d+e x)^{11/2}}{11 e^3}",1,"(2*(b*d - a*e)^2*(d + e*x)^(7/2))/(7*e^3) - (4*b*(b*d - a*e)*(d + e*x)^(9/2))/(9*e^3) + (2*b^2*(d + e*x)^(11/2))/(11*e^3)","A",3,2,26,0.07692,1,"{27, 43}"
1623,1,71,0,0.0228057,"\int (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{4 b (d+e x)^{7/2} (b d-a e)}{7 e^3}+\frac{2 (d+e x)^{5/2} (b d-a e)^2}{5 e^3}+\frac{2 b^2 (d+e x)^{9/2}}{9 e^3}","-\frac{4 b (d+e x)^{7/2} (b d-a e)}{7 e^3}+\frac{2 (d+e x)^{5/2} (b d-a e)^2}{5 e^3}+\frac{2 b^2 (d+e x)^{9/2}}{9 e^3}",1,"(2*(b*d - a*e)^2*(d + e*x)^(5/2))/(5*e^3) - (4*b*(b*d - a*e)*(d + e*x)^(7/2))/(7*e^3) + (2*b^2*(d + e*x)^(9/2))/(9*e^3)","A",3,2,26,0.07692,1,"{27, 43}"
1624,1,71,0,0.0225009,"\int \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{4 b (d+e x)^{5/2} (b d-a e)}{5 e^3}+\frac{2 (d+e x)^{3/2} (b d-a e)^2}{3 e^3}+\frac{2 b^2 (d+e x)^{7/2}}{7 e^3}","-\frac{4 b (d+e x)^{5/2} (b d-a e)}{5 e^3}+\frac{2 (d+e x)^{3/2} (b d-a e)^2}{3 e^3}+\frac{2 b^2 (d+e x)^{7/2}}{7 e^3}",1,"(2*(b*d - a*e)^2*(d + e*x)^(3/2))/(3*e^3) - (4*b*(b*d - a*e)*(d + e*x)^(5/2))/(5*e^3) + (2*b^2*(d + e*x)^(7/2))/(7*e^3)","A",3,2,26,0.07692,1,"{27, 43}"
1625,1,69,0,0.022423,"\int \frac{a^2+2 a b x+b^2 x^2}{\sqrt{d+e x}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/Sqrt[d + e*x],x]","-\frac{4 b (d+e x)^{3/2} (b d-a e)}{3 e^3}+\frac{2 \sqrt{d+e x} (b d-a e)^2}{e^3}+\frac{2 b^2 (d+e x)^{5/2}}{5 e^3}","-\frac{4 b (d+e x)^{3/2} (b d-a e)}{3 e^3}+\frac{2 \sqrt{d+e x} (b d-a e)^2}{e^3}+\frac{2 b^2 (d+e x)^{5/2}}{5 e^3}",1,"(2*(b*d - a*e)^2*Sqrt[d + e*x])/e^3 - (4*b*(b*d - a*e)*(d + e*x)^(3/2))/(3*e^3) + (2*b^2*(d + e*x)^(5/2))/(5*e^3)","A",3,2,26,0.07692,1,"{27, 43}"
1626,1,67,0,0.0221356,"\int \frac{a^2+2 a b x+b^2 x^2}{(d+e x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x)^(3/2),x]","-\frac{4 b \sqrt{d+e x} (b d-a e)}{e^3}-\frac{2 (b d-a e)^2}{e^3 \sqrt{d+e x}}+\frac{2 b^2 (d+e x)^{3/2}}{3 e^3}","-\frac{4 b \sqrt{d+e x} (b d-a e)}{e^3}-\frac{2 (b d-a e)^2}{e^3 \sqrt{d+e x}}+\frac{2 b^2 (d+e x)^{3/2}}{3 e^3}",1,"(-2*(b*d - a*e)^2)/(e^3*Sqrt[d + e*x]) - (4*b*(b*d - a*e)*Sqrt[d + e*x])/e^3 + (2*b^2*(d + e*x)^(3/2))/(3*e^3)","A",3,2,26,0.07692,1,"{27, 43}"
1627,1,67,0,0.0222164,"\int \frac{a^2+2 a b x+b^2 x^2}{(d+e x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x)^(5/2),x]","\frac{4 b (b d-a e)}{e^3 \sqrt{d+e x}}-\frac{2 (b d-a e)^2}{3 e^3 (d+e x)^{3/2}}+\frac{2 b^2 \sqrt{d+e x}}{e^3}","\frac{4 b (b d-a e)}{e^3 \sqrt{d+e x}}-\frac{2 (b d-a e)^2}{3 e^3 (d+e x)^{3/2}}+\frac{2 b^2 \sqrt{d+e x}}{e^3}",1,"(-2*(b*d - a*e)^2)/(3*e^3*(d + e*x)^(3/2)) + (4*b*(b*d - a*e))/(e^3*Sqrt[d + e*x]) + (2*b^2*Sqrt[d + e*x])/e^3","A",3,2,26,0.07692,1,"{27, 43}"
1628,1,69,0,0.0260152,"\int \frac{a^2+2 a b x+b^2 x^2}{(d+e x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)/(d + e*x)^(7/2),x]","\frac{4 b (b d-a e)}{3 e^3 (d+e x)^{3/2}}-\frac{2 (b d-a e)^2}{5 e^3 (d+e x)^{5/2}}-\frac{2 b^2}{e^3 \sqrt{d+e x}}","\frac{4 b (b d-a e)}{3 e^3 (d+e x)^{3/2}}-\frac{2 (b d-a e)^2}{5 e^3 (d+e x)^{5/2}}-\frac{2 b^2}{e^3 \sqrt{d+e x}}",1,"(-2*(b*d - a*e)^2)/(5*e^3*(d + e*x)^(5/2)) + (4*b*(b*d - a*e))/(3*e^3*(d + e*x)^(3/2)) - (2*b^2)/(e^3*Sqrt[d + e*x])","A",3,2,26,0.07692,1,"{27, 43}"
1629,1,129,0,0.0707597,"\int (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{8 b^3 (d+e x)^{15/2} (b d-a e)}{15 e^5}+\frac{12 b^2 (d+e x)^{13/2} (b d-a e)^2}{13 e^5}-\frac{8 b (d+e x)^{11/2} (b d-a e)^3}{11 e^5}+\frac{2 (d+e x)^{9/2} (b d-a e)^4}{9 e^5}+\frac{2 b^4 (d+e x)^{17/2}}{17 e^5}","-\frac{8 b^3 (d+e x)^{15/2} (b d-a e)}{15 e^5}+\frac{12 b^2 (d+e x)^{13/2} (b d-a e)^2}{13 e^5}-\frac{8 b (d+e x)^{11/2} (b d-a e)^3}{11 e^5}+\frac{2 (d+e x)^{9/2} (b d-a e)^4}{9 e^5}+\frac{2 b^4 (d+e x)^{17/2}}{17 e^5}",1,"(2*(b*d - a*e)^4*(d + e*x)^(9/2))/(9*e^5) - (8*b*(b*d - a*e)^3*(d + e*x)^(11/2))/(11*e^5) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(13/2))/(13*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(15/2))/(15*e^5) + (2*b^4*(d + e*x)^(17/2))/(17*e^5)","A",3,2,28,0.07143,1,"{27, 43}"
1630,1,129,0,0.041644,"\int (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{8 b^3 (d+e x)^{13/2} (b d-a e)}{13 e^5}+\frac{12 b^2 (d+e x)^{11/2} (b d-a e)^2}{11 e^5}-\frac{8 b (d+e x)^{9/2} (b d-a e)^3}{9 e^5}+\frac{2 (d+e x)^{7/2} (b d-a e)^4}{7 e^5}+\frac{2 b^4 (d+e x)^{15/2}}{15 e^5}","-\frac{8 b^3 (d+e x)^{13/2} (b d-a e)}{13 e^5}+\frac{12 b^2 (d+e x)^{11/2} (b d-a e)^2}{11 e^5}-\frac{8 b (d+e x)^{9/2} (b d-a e)^3}{9 e^5}+\frac{2 (d+e x)^{7/2} (b d-a e)^4}{7 e^5}+\frac{2 b^4 (d+e x)^{15/2}}{15 e^5}",1,"(2*(b*d - a*e)^4*(d + e*x)^(7/2))/(7*e^5) - (8*b*(b*d - a*e)^3*(d + e*x)^(9/2))/(9*e^5) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(11/2))/(11*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(13/2))/(13*e^5) + (2*b^4*(d + e*x)^(15/2))/(15*e^5)","A",3,2,28,0.07143,1,"{27, 43}"
1631,1,129,0,0.0428612,"\int (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{8 b^3 (d+e x)^{11/2} (b d-a e)}{11 e^5}+\frac{4 b^2 (d+e x)^{9/2} (b d-a e)^2}{3 e^5}-\frac{8 b (d+e x)^{7/2} (b d-a e)^3}{7 e^5}+\frac{2 (d+e x)^{5/2} (b d-a e)^4}{5 e^5}+\frac{2 b^4 (d+e x)^{13/2}}{13 e^5}","-\frac{8 b^3 (d+e x)^{11/2} (b d-a e)}{11 e^5}+\frac{4 b^2 (d+e x)^{9/2} (b d-a e)^2}{3 e^5}-\frac{8 b (d+e x)^{7/2} (b d-a e)^3}{7 e^5}+\frac{2 (d+e x)^{5/2} (b d-a e)^4}{5 e^5}+\frac{2 b^4 (d+e x)^{13/2}}{13 e^5}",1,"(2*(b*d - a*e)^4*(d + e*x)^(5/2))/(5*e^5) - (8*b*(b*d - a*e)^3*(d + e*x)^(7/2))/(7*e^5) + (4*b^2*(b*d - a*e)^2*(d + e*x)^(9/2))/(3*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(11/2))/(11*e^5) + (2*b^4*(d + e*x)^(13/2))/(13*e^5)","A",3,2,28,0.07143,1,"{27, 43}"
1632,1,129,0,0.0540715,"\int \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{8 b^3 (d+e x)^{9/2} (b d-a e)}{9 e^5}+\frac{12 b^2 (d+e x)^{7/2} (b d-a e)^2}{7 e^5}-\frac{8 b (d+e x)^{5/2} (b d-a e)^3}{5 e^5}+\frac{2 (d+e x)^{3/2} (b d-a e)^4}{3 e^5}+\frac{2 b^4 (d+e x)^{11/2}}{11 e^5}","-\frac{8 b^3 (d+e x)^{9/2} (b d-a e)}{9 e^5}+\frac{12 b^2 (d+e x)^{7/2} (b d-a e)^2}{7 e^5}-\frac{8 b (d+e x)^{5/2} (b d-a e)^3}{5 e^5}+\frac{2 (d+e x)^{3/2} (b d-a e)^4}{3 e^5}+\frac{2 b^4 (d+e x)^{11/2}}{11 e^5}",1,"(2*(b*d - a*e)^4*(d + e*x)^(3/2))/(3*e^5) - (8*b*(b*d - a*e)^3*(d + e*x)^(5/2))/(5*e^5) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(7/2))/(7*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(9/2))/(9*e^5) + (2*b^4*(d + e*x)^(11/2))/(11*e^5)","A",3,2,28,0.07143,1,"{27, 43}"
1633,1,127,0,0.0414936,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/Sqrt[d + e*x],x]","-\frac{8 b^3 (d+e x)^{7/2} (b d-a e)}{7 e^5}+\frac{12 b^2 (d+e x)^{5/2} (b d-a e)^2}{5 e^5}-\frac{8 b (d+e x)^{3/2} (b d-a e)^3}{3 e^5}+\frac{2 \sqrt{d+e x} (b d-a e)^4}{e^5}+\frac{2 b^4 (d+e x)^{9/2}}{9 e^5}","-\frac{8 b^3 (d+e x)^{7/2} (b d-a e)}{7 e^5}+\frac{12 b^2 (d+e x)^{5/2} (b d-a e)^2}{5 e^5}-\frac{8 b (d+e x)^{3/2} (b d-a e)^3}{3 e^5}+\frac{2 \sqrt{d+e x} (b d-a e)^4}{e^5}+\frac{2 b^4 (d+e x)^{9/2}}{9 e^5}",1,"(2*(b*d - a*e)^4*Sqrt[d + e*x])/e^5 - (8*b*(b*d - a*e)^3*(d + e*x)^(3/2))/(3*e^5) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(5/2))/(5*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(7/2))/(7*e^5) + (2*b^4*(d + e*x)^(9/2))/(9*e^5)","A",3,2,28,0.07143,1,"{27, 43}"
1634,1,123,0,0.0406202,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^(3/2),x]","-\frac{8 b^3 (d+e x)^{5/2} (b d-a e)}{5 e^5}+\frac{4 b^2 (d+e x)^{3/2} (b d-a e)^2}{e^5}-\frac{8 b \sqrt{d+e x} (b d-a e)^3}{e^5}-\frac{2 (b d-a e)^4}{e^5 \sqrt{d+e x}}+\frac{2 b^4 (d+e x)^{7/2}}{7 e^5}","-\frac{8 b^3 (d+e x)^{5/2} (b d-a e)}{5 e^5}+\frac{4 b^2 (d+e x)^{3/2} (b d-a e)^2}{e^5}-\frac{8 b \sqrt{d+e x} (b d-a e)^3}{e^5}-\frac{2 (b d-a e)^4}{e^5 \sqrt{d+e x}}+\frac{2 b^4 (d+e x)^{7/2}}{7 e^5}",1,"(-2*(b*d - a*e)^4)/(e^5*Sqrt[d + e*x]) - (8*b*(b*d - a*e)^3*Sqrt[d + e*x])/e^5 + (4*b^2*(b*d - a*e)^2*(d + e*x)^(3/2))/e^5 - (8*b^3*(b*d - a*e)*(d + e*x)^(5/2))/(5*e^5) + (2*b^4*(d + e*x)^(7/2))/(7*e^5)","A",3,2,28,0.07143,1,"{27, 43}"
1635,1,125,0,0.0415078,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^(5/2),x]","-\frac{8 b^3 (d+e x)^{3/2} (b d-a e)}{3 e^5}+\frac{12 b^2 \sqrt{d+e x} (b d-a e)^2}{e^5}+\frac{8 b (b d-a e)^3}{e^5 \sqrt{d+e x}}-\frac{2 (b d-a e)^4}{3 e^5 (d+e x)^{3/2}}+\frac{2 b^4 (d+e x)^{5/2}}{5 e^5}","-\frac{8 b^3 (d+e x)^{3/2} (b d-a e)}{3 e^5}+\frac{12 b^2 \sqrt{d+e x} (b d-a e)^2}{e^5}+\frac{8 b (b d-a e)^3}{e^5 \sqrt{d+e x}}-\frac{2 (b d-a e)^4}{3 e^5 (d+e x)^{3/2}}+\frac{2 b^4 (d+e x)^{5/2}}{5 e^5}",1,"(-2*(b*d - a*e)^4)/(3*e^5*(d + e*x)^(3/2)) + (8*b*(b*d - a*e)^3)/(e^5*Sqrt[d + e*x]) + (12*b^2*(b*d - a*e)^2*Sqrt[d + e*x])/e^5 - (8*b^3*(b*d - a*e)*(d + e*x)^(3/2))/(3*e^5) + (2*b^4*(d + e*x)^(5/2))/(5*e^5)","A",3,2,28,0.07143,1,"{27, 43}"
1636,1,125,0,0.0430044,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^(7/2),x]","-\frac{8 b^3 \sqrt{d+e x} (b d-a e)}{e^5}-\frac{12 b^2 (b d-a e)^2}{e^5 \sqrt{d+e x}}+\frac{8 b (b d-a e)^3}{3 e^5 (d+e x)^{3/2}}-\frac{2 (b d-a e)^4}{5 e^5 (d+e x)^{5/2}}+\frac{2 b^4 (d+e x)^{3/2}}{3 e^5}","-\frac{8 b^3 \sqrt{d+e x} (b d-a e)}{e^5}-\frac{12 b^2 (b d-a e)^2}{e^5 \sqrt{d+e x}}+\frac{8 b (b d-a e)^3}{3 e^5 (d+e x)^{3/2}}-\frac{2 (b d-a e)^4}{5 e^5 (d+e x)^{5/2}}+\frac{2 b^4 (d+e x)^{3/2}}{3 e^5}",1,"(-2*(b*d - a*e)^4)/(5*e^5*(d + e*x)^(5/2)) + (8*b*(b*d - a*e)^3)/(3*e^5*(d + e*x)^(3/2)) - (12*b^2*(b*d - a*e)^2)/(e^5*Sqrt[d + e*x]) - (8*b^3*(b*d - a*e)*Sqrt[d + e*x])/e^5 + (2*b^4*(d + e*x)^(3/2))/(3*e^5)","A",3,2,28,0.07143,1,"{27, 43}"
1637,1,187,0,0.082821,"\int (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{12 b^5 (d+e x)^{19/2} (b d-a e)}{19 e^7}+\frac{30 b^4 (d+e x)^{17/2} (b d-a e)^2}{17 e^7}-\frac{8 b^3 (d+e x)^{15/2} (b d-a e)^3}{3 e^7}+\frac{30 b^2 (d+e x)^{13/2} (b d-a e)^4}{13 e^7}-\frac{12 b (d+e x)^{11/2} (b d-a e)^5}{11 e^7}+\frac{2 (d+e x)^{9/2} (b d-a e)^6}{9 e^7}+\frac{2 b^6 (d+e x)^{21/2}}{21 e^7}","-\frac{12 b^5 (d+e x)^{19/2} (b d-a e)}{19 e^7}+\frac{30 b^4 (d+e x)^{17/2} (b d-a e)^2}{17 e^7}-\frac{8 b^3 (d+e x)^{15/2} (b d-a e)^3}{3 e^7}+\frac{30 b^2 (d+e x)^{13/2} (b d-a e)^4}{13 e^7}-\frac{12 b (d+e x)^{11/2} (b d-a e)^5}{11 e^7}+\frac{2 (d+e x)^{9/2} (b d-a e)^6}{9 e^7}+\frac{2 b^6 (d+e x)^{21/2}}{21 e^7}",1,"(2*(b*d - a*e)^6*(d + e*x)^(9/2))/(9*e^7) - (12*b*(b*d - a*e)^5*(d + e*x)^(11/2))/(11*e^7) + (30*b^2*(b*d - a*e)^4*(d + e*x)^(13/2))/(13*e^7) - (8*b^3*(b*d - a*e)^3*(d + e*x)^(15/2))/(3*e^7) + (30*b^4*(b*d - a*e)^2*(d + e*x)^(17/2))/(17*e^7) - (12*b^5*(b*d - a*e)*(d + e*x)^(19/2))/(19*e^7) + (2*b^6*(d + e*x)^(21/2))/(21*e^7)","A",3,2,28,0.07143,1,"{27, 43}"
1638,1,185,0,0.0608597,"\int (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{12 b^5 (d+e x)^{17/2} (b d-a e)}{17 e^7}+\frac{2 b^4 (d+e x)^{15/2} (b d-a e)^2}{e^7}-\frac{40 b^3 (d+e x)^{13/2} (b d-a e)^3}{13 e^7}+\frac{30 b^2 (d+e x)^{11/2} (b d-a e)^4}{11 e^7}-\frac{4 b (d+e x)^{9/2} (b d-a e)^5}{3 e^7}+\frac{2 (d+e x)^{7/2} (b d-a e)^6}{7 e^7}+\frac{2 b^6 (d+e x)^{19/2}}{19 e^7}","-\frac{12 b^5 (d+e x)^{17/2} (b d-a e)}{17 e^7}+\frac{2 b^4 (d+e x)^{15/2} (b d-a e)^2}{e^7}-\frac{40 b^3 (d+e x)^{13/2} (b d-a e)^3}{13 e^7}+\frac{30 b^2 (d+e x)^{11/2} (b d-a e)^4}{11 e^7}-\frac{4 b (d+e x)^{9/2} (b d-a e)^5}{3 e^7}+\frac{2 (d+e x)^{7/2} (b d-a e)^6}{7 e^7}+\frac{2 b^6 (d+e x)^{19/2}}{19 e^7}",1,"(2*(b*d - a*e)^6*(d + e*x)^(7/2))/(7*e^7) - (4*b*(b*d - a*e)^5*(d + e*x)^(9/2))/(3*e^7) + (30*b^2*(b*d - a*e)^4*(d + e*x)^(11/2))/(11*e^7) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(13/2))/(13*e^7) + (2*b^4*(b*d - a*e)^2*(d + e*x)^(15/2))/e^7 - (12*b^5*(b*d - a*e)*(d + e*x)^(17/2))/(17*e^7) + (2*b^6*(d + e*x)^(19/2))/(19*e^7)","A",3,2,28,0.07143,1,"{27, 43}"
1639,1,187,0,0.0609793,"\int (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{4 b^5 (d+e x)^{15/2} (b d-a e)}{5 e^7}+\frac{30 b^4 (d+e x)^{13/2} (b d-a e)^2}{13 e^7}-\frac{40 b^3 (d+e x)^{11/2} (b d-a e)^3}{11 e^7}+\frac{10 b^2 (d+e x)^{9/2} (b d-a e)^4}{3 e^7}-\frac{12 b (d+e x)^{7/2} (b d-a e)^5}{7 e^7}+\frac{2 (d+e x)^{5/2} (b d-a e)^6}{5 e^7}+\frac{2 b^6 (d+e x)^{17/2}}{17 e^7}","-\frac{4 b^5 (d+e x)^{15/2} (b d-a e)}{5 e^7}+\frac{30 b^4 (d+e x)^{13/2} (b d-a e)^2}{13 e^7}-\frac{40 b^3 (d+e x)^{11/2} (b d-a e)^3}{11 e^7}+\frac{10 b^2 (d+e x)^{9/2} (b d-a e)^4}{3 e^7}-\frac{12 b (d+e x)^{7/2} (b d-a e)^5}{7 e^7}+\frac{2 (d+e x)^{5/2} (b d-a e)^6}{5 e^7}+\frac{2 b^6 (d+e x)^{17/2}}{17 e^7}",1,"(2*(b*d - a*e)^6*(d + e*x)^(5/2))/(5*e^7) - (12*b*(b*d - a*e)^5*(d + e*x)^(7/2))/(7*e^7) + (10*b^2*(b*d - a*e)^4*(d + e*x)^(9/2))/(3*e^7) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(11/2))/(11*e^7) + (30*b^4*(b*d - a*e)^2*(d + e*x)^(13/2))/(13*e^7) - (4*b^5*(b*d - a*e)*(d + e*x)^(15/2))/(5*e^7) + (2*b^6*(d + e*x)^(17/2))/(17*e^7)","A",3,2,28,0.07143,1,"{27, 43}"
1640,1,187,0,0.0589647,"\int \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{12 b^5 (d+e x)^{13/2} (b d-a e)}{13 e^7}+\frac{30 b^4 (d+e x)^{11/2} (b d-a e)^2}{11 e^7}-\frac{40 b^3 (d+e x)^{9/2} (b d-a e)^3}{9 e^7}+\frac{30 b^2 (d+e x)^{7/2} (b d-a e)^4}{7 e^7}-\frac{12 b (d+e x)^{5/2} (b d-a e)^5}{5 e^7}+\frac{2 (d+e x)^{3/2} (b d-a e)^6}{3 e^7}+\frac{2 b^6 (d+e x)^{15/2}}{15 e^7}","-\frac{12 b^5 (d+e x)^{13/2} (b d-a e)}{13 e^7}+\frac{30 b^4 (d+e x)^{11/2} (b d-a e)^2}{11 e^7}-\frac{40 b^3 (d+e x)^{9/2} (b d-a e)^3}{9 e^7}+\frac{30 b^2 (d+e x)^{7/2} (b d-a e)^4}{7 e^7}-\frac{12 b (d+e x)^{5/2} (b d-a e)^5}{5 e^7}+\frac{2 (d+e x)^{3/2} (b d-a e)^6}{3 e^7}+\frac{2 b^6 (d+e x)^{15/2}}{15 e^7}",1,"(2*(b*d - a*e)^6*(d + e*x)^(3/2))/(3*e^7) - (12*b*(b*d - a*e)^5*(d + e*x)^(5/2))/(5*e^7) + (30*b^2*(b*d - a*e)^4*(d + e*x)^(7/2))/(7*e^7) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(9/2))/(9*e^7) + (30*b^4*(b*d - a*e)^2*(d + e*x)^(11/2))/(11*e^7) - (12*b^5*(b*d - a*e)*(d + e*x)^(13/2))/(13*e^7) + (2*b^6*(d + e*x)^(15/2))/(15*e^7)","A",3,2,28,0.07143,1,"{27, 43}"
1641,1,181,0,0.0602919,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{\sqrt{d+e x}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/Sqrt[d + e*x],x]","-\frac{12 b^5 (d+e x)^{11/2} (b d-a e)}{11 e^7}+\frac{10 b^4 (d+e x)^{9/2} (b d-a e)^2}{3 e^7}-\frac{40 b^3 (d+e x)^{7/2} (b d-a e)^3}{7 e^7}+\frac{6 b^2 (d+e x)^{5/2} (b d-a e)^4}{e^7}-\frac{4 b (d+e x)^{3/2} (b d-a e)^5}{e^7}+\frac{2 \sqrt{d+e x} (b d-a e)^6}{e^7}+\frac{2 b^6 (d+e x)^{13/2}}{13 e^7}","-\frac{12 b^5 (d+e x)^{11/2} (b d-a e)}{11 e^7}+\frac{10 b^4 (d+e x)^{9/2} (b d-a e)^2}{3 e^7}-\frac{40 b^3 (d+e x)^{7/2} (b d-a e)^3}{7 e^7}+\frac{6 b^2 (d+e x)^{5/2} (b d-a e)^4}{e^7}-\frac{4 b (d+e x)^{3/2} (b d-a e)^5}{e^7}+\frac{2 \sqrt{d+e x} (b d-a e)^6}{e^7}+\frac{2 b^6 (d+e x)^{13/2}}{13 e^7}",1,"(2*(b*d - a*e)^6*Sqrt[d + e*x])/e^7 - (4*b*(b*d - a*e)^5*(d + e*x)^(3/2))/e^7 + (6*b^2*(b*d - a*e)^4*(d + e*x)^(5/2))/e^7 - (40*b^3*(b*d - a*e)^3*(d + e*x)^(7/2))/(7*e^7) + (10*b^4*(b*d - a*e)^2*(d + e*x)^(9/2))/(3*e^7) - (12*b^5*(b*d - a*e)*(d + e*x)^(11/2))/(11*e^7) + (2*b^6*(d + e*x)^(13/2))/(13*e^7)","A",3,2,28,0.07143,1,"{27, 43}"
1642,1,179,0,0.0590916,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^(3/2),x]","-\frac{4 b^5 (d+e x)^{9/2} (b d-a e)}{3 e^7}+\frac{30 b^4 (d+e x)^{7/2} (b d-a e)^2}{7 e^7}-\frac{8 b^3 (d+e x)^{5/2} (b d-a e)^3}{e^7}+\frac{10 b^2 (d+e x)^{3/2} (b d-a e)^4}{e^7}-\frac{12 b \sqrt{d+e x} (b d-a e)^5}{e^7}-\frac{2 (b d-a e)^6}{e^7 \sqrt{d+e x}}+\frac{2 b^6 (d+e x)^{11/2}}{11 e^7}","-\frac{4 b^5 (d+e x)^{9/2} (b d-a e)}{3 e^7}+\frac{30 b^4 (d+e x)^{7/2} (b d-a e)^2}{7 e^7}-\frac{8 b^3 (d+e x)^{5/2} (b d-a e)^3}{e^7}+\frac{10 b^2 (d+e x)^{3/2} (b d-a e)^4}{e^7}-\frac{12 b \sqrt{d+e x} (b d-a e)^5}{e^7}-\frac{2 (b d-a e)^6}{e^7 \sqrt{d+e x}}+\frac{2 b^6 (d+e x)^{11/2}}{11 e^7}",1,"(-2*(b*d - a*e)^6)/(e^7*Sqrt[d + e*x]) - (12*b*(b*d - a*e)^5*Sqrt[d + e*x])/e^7 + (10*b^2*(b*d - a*e)^4*(d + e*x)^(3/2))/e^7 - (8*b^3*(b*d - a*e)^3*(d + e*x)^(5/2))/e^7 + (30*b^4*(b*d - a*e)^2*(d + e*x)^(7/2))/(7*e^7) - (4*b^5*(b*d - a*e)*(d + e*x)^(9/2))/(3*e^7) + (2*b^6*(d + e*x)^(11/2))/(11*e^7)","A",3,2,28,0.07143,1,"{27, 43}"
1643,1,181,0,0.0592892,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^(5/2),x]","-\frac{12 b^5 (d+e x)^{7/2} (b d-a e)}{7 e^7}+\frac{6 b^4 (d+e x)^{5/2} (b d-a e)^2}{e^7}-\frac{40 b^3 (d+e x)^{3/2} (b d-a e)^3}{3 e^7}+\frac{30 b^2 \sqrt{d+e x} (b d-a e)^4}{e^7}+\frac{12 b (b d-a e)^5}{e^7 \sqrt{d+e x}}-\frac{2 (b d-a e)^6}{3 e^7 (d+e x)^{3/2}}+\frac{2 b^6 (d+e x)^{9/2}}{9 e^7}","-\frac{12 b^5 (d+e x)^{7/2} (b d-a e)}{7 e^7}+\frac{6 b^4 (d+e x)^{5/2} (b d-a e)^2}{e^7}-\frac{40 b^3 (d+e x)^{3/2} (b d-a e)^3}{3 e^7}+\frac{30 b^2 \sqrt{d+e x} (b d-a e)^4}{e^7}+\frac{12 b (b d-a e)^5}{e^7 \sqrt{d+e x}}-\frac{2 (b d-a e)^6}{3 e^7 (d+e x)^{3/2}}+\frac{2 b^6 (d+e x)^{9/2}}{9 e^7}",1,"(-2*(b*d - a*e)^6)/(3*e^7*(d + e*x)^(3/2)) + (12*b*(b*d - a*e)^5)/(e^7*Sqrt[d + e*x]) + (30*b^2*(b*d - a*e)^4*Sqrt[d + e*x])/e^7 - (40*b^3*(b*d - a*e)^3*(d + e*x)^(3/2))/(3*e^7) + (6*b^4*(b*d - a*e)^2*(d + e*x)^(5/2))/e^7 - (12*b^5*(b*d - a*e)*(d + e*x)^(7/2))/(7*e^7) + (2*b^6*(d + e*x)^(9/2))/(9*e^7)","A",3,2,28,0.07143,1,"{27, 43}"
1644,1,179,0,0.0591365,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^(7/2),x]","-\frac{12 b^5 (d+e x)^{5/2} (b d-a e)}{5 e^7}+\frac{10 b^4 (d+e x)^{3/2} (b d-a e)^2}{e^7}-\frac{40 b^3 \sqrt{d+e x} (b d-a e)^3}{e^7}-\frac{30 b^2 (b d-a e)^4}{e^7 \sqrt{d+e x}}+\frac{4 b (b d-a e)^5}{e^7 (d+e x)^{3/2}}-\frac{2 (b d-a e)^6}{5 e^7 (d+e x)^{5/2}}+\frac{2 b^6 (d+e x)^{7/2}}{7 e^7}","-\frac{12 b^5 (d+e x)^{5/2} (b d-a e)}{5 e^7}+\frac{10 b^4 (d+e x)^{3/2} (b d-a e)^2}{e^7}-\frac{40 b^3 \sqrt{d+e x} (b d-a e)^3}{e^7}-\frac{30 b^2 (b d-a e)^4}{e^7 \sqrt{d+e x}}+\frac{4 b (b d-a e)^5}{e^7 (d+e x)^{3/2}}-\frac{2 (b d-a e)^6}{5 e^7 (d+e x)^{5/2}}+\frac{2 b^6 (d+e x)^{7/2}}{7 e^7}",1,"(-2*(b*d - a*e)^6)/(5*e^7*(d + e*x)^(5/2)) + (4*b*(b*d - a*e)^5)/(e^7*(d + e*x)^(3/2)) - (30*b^2*(b*d - a*e)^4)/(e^7*Sqrt[d + e*x]) - (40*b^3*(b*d - a*e)^3*Sqrt[d + e*x])/e^7 + (10*b^4*(b*d - a*e)^2*(d + e*x)^(3/2))/e^7 - (12*b^5*(b*d - a*e)*(d + e*x)^(5/2))/(5*e^7) + (2*b^6*(d + e*x)^(7/2))/(7*e^7)","A",3,2,28,0.07143,1,"{27, 43}"
1645,1,162,0,0.1827517,"\int \frac{(d+e x)^{9/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^(9/2)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{9 e (d+e x)^{5/2} (b d-a e)}{5 b^3}+\frac{3 e (d+e x)^{3/2} (b d-a e)^2}{b^4}+\frac{9 e \sqrt{d+e x} (b d-a e)^3}{b^5}-\frac{9 e (b d-a e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{11/2}}-\frac{(d+e x)^{9/2}}{b (a+b x)}+\frac{9 e (d+e x)^{7/2}}{7 b^2}","\frac{9 e (d+e x)^{5/2} (b d-a e)}{5 b^3}+\frac{3 e (d+e x)^{3/2} (b d-a e)^2}{b^4}+\frac{9 e \sqrt{d+e x} (b d-a e)^3}{b^5}-\frac{9 e (b d-a e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{11/2}}-\frac{(d+e x)^{9/2}}{b (a+b x)}+\frac{9 e (d+e x)^{7/2}}{7 b^2}",1,"(9*e*(b*d - a*e)^3*Sqrt[d + e*x])/b^5 + (3*e*(b*d - a*e)^2*(d + e*x)^(3/2))/b^4 + (9*e*(b*d - a*e)*(d + e*x)^(5/2))/(5*b^3) + (9*e*(d + e*x)^(7/2))/(7*b^2) - (d + e*x)^(9/2)/(b*(a + b*x)) - (9*e*(b*d - a*e)^(7/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(11/2)","A",8,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1646,1,137,0,0.0757445,"\int \frac{(d+e x)^{7/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^(7/2)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{7 e (d+e x)^{3/2} (b d-a e)}{3 b^3}+\frac{7 e \sqrt{d+e x} (b d-a e)^2}{b^4}-\frac{7 e (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2}}-\frac{(d+e x)^{7/2}}{b (a+b x)}+\frac{7 e (d+e x)^{5/2}}{5 b^2}","\frac{7 e (d+e x)^{3/2} (b d-a e)}{3 b^3}+\frac{7 e \sqrt{d+e x} (b d-a e)^2}{b^4}-\frac{7 e (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2}}-\frac{(d+e x)^{7/2}}{b (a+b x)}+\frac{7 e (d+e x)^{5/2}}{5 b^2}",1,"(7*e*(b*d - a*e)^2*Sqrt[d + e*x])/b^4 + (7*e*(b*d - a*e)*(d + e*x)^(3/2))/(3*b^3) + (7*e*(d + e*x)^(5/2))/(5*b^2) - (d + e*x)^(7/2)/(b*(a + b*x)) - (7*e*(b*d - a*e)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(9/2)","A",7,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1647,1,110,0,0.0575072,"\int \frac{(d+e x)^{5/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^(5/2)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{5 e \sqrt{d+e x} (b d-a e)}{b^3}-\frac{5 e (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2}}-\frac{(d+e x)^{5/2}}{b (a+b x)}+\frac{5 e (d+e x)^{3/2}}{3 b^2}","\frac{5 e \sqrt{d+e x} (b d-a e)}{b^3}-\frac{5 e (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2}}-\frac{(d+e x)^{5/2}}{b (a+b x)}+\frac{5 e (d+e x)^{3/2}}{3 b^2}",1,"(5*e*(b*d - a*e)*Sqrt[d + e*x])/b^3 + (5*e*(d + e*x)^(3/2))/(3*b^2) - (d + e*x)^(5/2)/(b*(a + b*x)) - (5*e*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(7/2)","A",6,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1648,1,85,0,0.0400498,"\int \frac{(d+e x)^{3/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^(3/2)/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{3 e \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2}}-\frac{(d+e x)^{3/2}}{b (a+b x)}+\frac{3 e \sqrt{d+e x}}{b^2}","-\frac{3 e \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2}}-\frac{(d+e x)^{3/2}}{b (a+b x)}+\frac{3 e \sqrt{d+e x}}{b^2}",1,"(3*e*Sqrt[d + e*x])/b^2 - (d + e*x)^(3/2)/(b*(a + b*x)) - (3*e*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(5/2)","A",5,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1649,1,70,0,0.0314011,"\int \frac{\sqrt{d+e x}}{a^2+2 a b x+b^2 x^2} \, dx","Int[Sqrt[d + e*x]/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} \sqrt{b d-a e}}-\frac{\sqrt{d+e x}}{b (a+b x)}","-\frac{e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} \sqrt{b d-a e}}-\frac{\sqrt{d+e x}}{b (a+b x)}",1,"-(Sqrt[d + e*x]/(b*(a + b*x))) - (e*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(3/2)*Sqrt[b*d - a*e])","A",4,4,28,0.1429,1,"{27, 47, 63, 208}"
1650,1,76,0,0.0444152,"\int \frac{1}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} (b d-a e)^{3/2}}-\frac{\sqrt{d+e x}}{(a+b x) (b d-a e)}","\frac{e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} (b d-a e)^{3/2}}-\frac{\sqrt{d+e x}}{(a+b x) (b d-a e)}",1,"-(Sqrt[d + e*x]/((b*d - a*e)*(a + b*x))) + (e*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(Sqrt[b]*(b*d - a*e)^(3/2))","A",4,4,28,0.1429,1,"{27, 51, 63, 208}"
1651,1,99,0,0.0539409,"\int \frac{1}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[1/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{3 e}{\sqrt{d+e x} (b d-a e)^2}-\frac{1}{(a+b x) \sqrt{d+e x} (b d-a e)}+\frac{3 \sqrt{b} e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{5/2}}","-\frac{3 e}{\sqrt{d+e x} (b d-a e)^2}-\frac{1}{(a+b x) \sqrt{d+e x} (b d-a e)}+\frac{3 \sqrt{b} e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{5/2}}",1,"(-3*e)/((b*d - a*e)^2*Sqrt[d + e*x]) - 1/((b*d - a*e)*(a + b*x)*Sqrt[d + e*x]) + (3*Sqrt[b]*e*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b*d - a*e)^(5/2)","A",5,4,28,0.1429,1,"{27, 51, 63, 208}"
1652,1,124,0,0.0641323,"\int \frac{1}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[1/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{5 b^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{7/2}}-\frac{5 b e}{\sqrt{d+e x} (b d-a e)^3}-\frac{1}{(a+b x) (d+e x)^{3/2} (b d-a e)}-\frac{5 e}{3 (d+e x)^{3/2} (b d-a e)^2}","\frac{5 b^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{7/2}}-\frac{5 b e}{\sqrt{d+e x} (b d-a e)^3}-\frac{1}{(a+b x) (d+e x)^{3/2} (b d-a e)}-\frac{5 e}{3 (d+e x)^{3/2} (b d-a e)^2}",1,"(-5*e)/(3*(b*d - a*e)^2*(d + e*x)^(3/2)) - 1/((b*d - a*e)*(a + b*x)*(d + e*x)^(3/2)) - (5*b*e)/((b*d - a*e)^3*Sqrt[d + e*x]) + (5*b^(3/2)*e*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b*d - a*e)^(7/2)","A",6,4,28,0.1429,1,"{27, 51, 63, 208}"
1653,1,151,0,0.0996385,"\int \frac{1}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[1/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{7 b^2 e}{\sqrt{d+e x} (b d-a e)^4}+\frac{7 b^{5/2} e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{9/2}}-\frac{7 b e}{3 (d+e x)^{3/2} (b d-a e)^3}-\frac{1}{(a+b x) (d+e x)^{5/2} (b d-a e)}-\frac{7 e}{5 (d+e x)^{5/2} (b d-a e)^2}","-\frac{7 b^2 e}{\sqrt{d+e x} (b d-a e)^4}+\frac{7 b^{5/2} e \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{9/2}}-\frac{7 b e}{3 (d+e x)^{3/2} (b d-a e)^3}-\frac{1}{(a+b x) (d+e x)^{5/2} (b d-a e)}-\frac{7 e}{5 (d+e x)^{5/2} (b d-a e)^2}",1,"(-7*e)/(5*(b*d - a*e)^2*(d + e*x)^(5/2)) - 1/((b*d - a*e)*(a + b*x)*(d + e*x)^(5/2)) - (7*b*e)/(3*(b*d - a*e)^3*(d + e*x)^(3/2)) - (7*b^2*e)/((b*d - a*e)^4*Sqrt[d + e*x]) + (7*b^(5/2)*e*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b*d - a*e)^(9/2)","A",7,4,28,0.1429,1,"{27, 51, 63, 208}"
1654,1,201,0,0.1307381,"\int \frac{(d+e x)^{11/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^(11/2)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{33 e^2 (d+e x)^{7/2}}{8 b^3 (a+b x)}+\frac{77 e^3 (d+e x)^{3/2} (b d-a e)}{8 b^5}+\frac{231 e^3 \sqrt{d+e x} (b d-a e)^2}{8 b^6}-\frac{231 e^3 (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{13/2}}-\frac{11 e (d+e x)^{9/2}}{12 b^2 (a+b x)^2}-\frac{(d+e x)^{11/2}}{3 b (a+b x)^3}+\frac{231 e^3 (d+e x)^{5/2}}{40 b^4}","-\frac{33 e^2 (d+e x)^{7/2}}{8 b^3 (a+b x)}+\frac{77 e^3 (d+e x)^{3/2} (b d-a e)}{8 b^5}+\frac{231 e^3 \sqrt{d+e x} (b d-a e)^2}{8 b^6}-\frac{231 e^3 (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{13/2}}-\frac{11 e (d+e x)^{9/2}}{12 b^2 (a+b x)^2}-\frac{(d+e x)^{11/2}}{3 b (a+b x)^3}+\frac{231 e^3 (d+e x)^{5/2}}{40 b^4}",1,"(231*e^3*(b*d - a*e)^2*Sqrt[d + e*x])/(8*b^6) + (77*e^3*(b*d - a*e)*(d + e*x)^(3/2))/(8*b^5) + (231*e^3*(d + e*x)^(5/2))/(40*b^4) - (33*e^2*(d + e*x)^(7/2))/(8*b^3*(a + b*x)) - (11*e*(d + e*x)^(9/2))/(12*b^2*(a + b*x)^2) - (d + e*x)^(11/2)/(3*b*(a + b*x)^3) - (231*e^3*(b*d - a*e)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(13/2))","A",9,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1655,1,172,0,0.0973135,"\int \frac{(d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^(9/2)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{21 e^2 (d+e x)^{5/2}}{8 b^3 (a+b x)}+\frac{105 e^3 \sqrt{d+e x} (b d-a e)}{8 b^5}-\frac{105 e^3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{11/2}}-\frac{3 e (d+e x)^{7/2}}{4 b^2 (a+b x)^2}-\frac{(d+e x)^{9/2}}{3 b (a+b x)^3}+\frac{35 e^3 (d+e x)^{3/2}}{8 b^4}","-\frac{21 e^2 (d+e x)^{5/2}}{8 b^3 (a+b x)}+\frac{105 e^3 \sqrt{d+e x} (b d-a e)}{8 b^5}-\frac{105 e^3 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{11/2}}-\frac{3 e (d+e x)^{7/2}}{4 b^2 (a+b x)^2}-\frac{(d+e x)^{9/2}}{3 b (a+b x)^3}+\frac{35 e^3 (d+e x)^{3/2}}{8 b^4}",1,"(105*e^3*(b*d - a*e)*Sqrt[d + e*x])/(8*b^5) + (35*e^3*(d + e*x)^(3/2))/(8*b^4) - (21*e^2*(d + e*x)^(5/2))/(8*b^3*(a + b*x)) - (3*e*(d + e*x)^(7/2))/(4*b^2*(a + b*x)^2) - (d + e*x)^(9/2)/(3*b*(a + b*x)^3) - (105*e^3*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(11/2))","A",8,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1656,1,145,0,0.0692103,"\int \frac{(d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^(7/2)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{35 e^2 (d+e x)^{3/2}}{24 b^3 (a+b x)}-\frac{35 e^3 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{9/2}}-\frac{7 e (d+e x)^{5/2}}{12 b^2 (a+b x)^2}-\frac{(d+e x)^{7/2}}{3 b (a+b x)^3}+\frac{35 e^3 \sqrt{d+e x}}{8 b^4}","-\frac{35 e^2 (d+e x)^{3/2}}{24 b^3 (a+b x)}-\frac{35 e^3 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{9/2}}-\frac{7 e (d+e x)^{5/2}}{12 b^2 (a+b x)^2}-\frac{(d+e x)^{7/2}}{3 b (a+b x)^3}+\frac{35 e^3 \sqrt{d+e x}}{8 b^4}",1,"(35*e^3*Sqrt[d + e*x])/(8*b^4) - (35*e^2*(d + e*x)^(3/2))/(24*b^3*(a + b*x)) - (7*e*(d + e*x)^(5/2))/(12*b^2*(a + b*x)^2) - (d + e*x)^(7/2)/(3*b*(a + b*x)^3) - (35*e^3*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(9/2))","A",7,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1657,1,126,0,0.0593683,"\int \frac{(d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^(5/2)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{5 e^2 \sqrt{d+e x}}{8 b^3 (a+b x)}-\frac{5 e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{7/2} \sqrt{b d-a e}}-\frac{5 e (d+e x)^{3/2}}{12 b^2 (a+b x)^2}-\frac{(d+e x)^{5/2}}{3 b (a+b x)^3}","-\frac{5 e^2 \sqrt{d+e x}}{8 b^3 (a+b x)}-\frac{5 e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{7/2} \sqrt{b d-a e}}-\frac{5 e (d+e x)^{3/2}}{12 b^2 (a+b x)^2}-\frac{(d+e x)^{5/2}}{3 b (a+b x)^3}",1,"(-5*e^2*Sqrt[d + e*x])/(8*b^3*(a + b*x)) - (5*e*(d + e*x)^(3/2))/(12*b^2*(a + b*x)^2) - (d + e*x)^(5/2)/(3*b*(a + b*x)^3) - (5*e^3*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(7/2)*Sqrt[b*d - a*e])","A",6,4,28,0.1429,1,"{27, 47, 63, 208}"
1658,1,136,0,0.0719368,"\int \frac{(d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^(3/2)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{e^2 \sqrt{d+e x}}{8 b^2 (a+b x) (b d-a e)}+\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{5/2} (b d-a e)^{3/2}}-\frac{e \sqrt{d+e x}}{4 b^2 (a+b x)^2}-\frac{(d+e x)^{3/2}}{3 b (a+b x)^3}","-\frac{e^2 \sqrt{d+e x}}{8 b^2 (a+b x) (b d-a e)}+\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{5/2} (b d-a e)^{3/2}}-\frac{e \sqrt{d+e x}}{4 b^2 (a+b x)^2}-\frac{(d+e x)^{3/2}}{3 b (a+b x)^3}",1,"-(e*Sqrt[d + e*x])/(4*b^2*(a + b*x)^2) - (e^2*Sqrt[d + e*x])/(8*b^2*(b*d - a*e)*(a + b*x)) - (d + e*x)^(3/2)/(3*b*(a + b*x)^3) + (e^3*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(5/2)*(b*d - a*e)^(3/2))","A",6,5,28,0.1786,1,"{27, 47, 51, 63, 208}"
1659,1,146,0,0.0687249,"\int \frac{\sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[Sqrt[d + e*x]/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{3/2} (b d-a e)^{5/2}}+\frac{e^2 \sqrt{d+e x}}{8 b (a+b x) (b d-a e)^2}-\frac{e \sqrt{d+e x}}{12 b (a+b x)^2 (b d-a e)}-\frac{\sqrt{d+e x}}{3 b (a+b x)^3}","-\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{3/2} (b d-a e)^{5/2}}+\frac{e^2 \sqrt{d+e x}}{8 b (a+b x) (b d-a e)^2}-\frac{e \sqrt{d+e x}}{12 b (a+b x)^2 (b d-a e)}-\frac{\sqrt{d+e x}}{3 b (a+b x)^3}",1,"-Sqrt[d + e*x]/(3*b*(a + b*x)^3) - (e*Sqrt[d + e*x])/(12*b*(b*d - a*e)*(a + b*x)^2) + (e^2*Sqrt[d + e*x])/(8*b*(b*d - a*e)^2*(a + b*x)) - (e^3*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(3/2)*(b*d - a*e)^(5/2))","A",6,5,28,0.1786,1,"{27, 47, 51, 63, 208}"
1660,1,147,0,0.0718597,"\int \frac{1}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[1/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{5 e^2 \sqrt{d+e x}}{8 (a+b x) (b d-a e)^3}+\frac{5 e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{b} (b d-a e)^{7/2}}+\frac{5 e \sqrt{d+e x}}{12 (a+b x)^2 (b d-a e)^2}-\frac{\sqrt{d+e x}}{3 (a+b x)^3 (b d-a e)}","-\frac{5 e^2 \sqrt{d+e x}}{8 (a+b x) (b d-a e)^3}+\frac{5 e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{b} (b d-a e)^{7/2}}+\frac{5 e \sqrt{d+e x}}{12 (a+b x)^2 (b d-a e)^2}-\frac{\sqrt{d+e x}}{3 (a+b x)^3 (b d-a e)}",1,"-Sqrt[d + e*x]/(3*(b*d - a*e)*(a + b*x)^3) + (5*e*Sqrt[d + e*x])/(12*(b*d - a*e)^2*(a + b*x)^2) - (5*e^2*Sqrt[d + e*x])/(8*(b*d - a*e)^3*(a + b*x)) + (5*e^3*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*Sqrt[b]*(b*d - a*e)^(7/2))","A",6,4,28,0.1429,1,"{27, 51, 63, 208}"
1661,1,173,0,0.0835521,"\int \frac{1}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[1/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{35 e^3}{8 \sqrt{d+e x} (b d-a e)^4}-\frac{35 e^2}{24 (a+b x) \sqrt{d+e x} (b d-a e)^3}+\frac{35 \sqrt{b} e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{9/2}}+\frac{7 e}{12 (a+b x)^2 \sqrt{d+e x} (b d-a e)^2}-\frac{1}{3 (a+b x)^3 \sqrt{d+e x} (b d-a e)}","-\frac{35 e^3}{8 \sqrt{d+e x} (b d-a e)^4}-\frac{35 e^2}{24 (a+b x) \sqrt{d+e x} (b d-a e)^3}+\frac{35 \sqrt{b} e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{9/2}}+\frac{7 e}{12 (a+b x)^2 \sqrt{d+e x} (b d-a e)^2}-\frac{1}{3 (a+b x)^3 \sqrt{d+e x} (b d-a e)}",1,"(-35*e^3)/(8*(b*d - a*e)^4*Sqrt[d + e*x]) - 1/(3*(b*d - a*e)*(a + b*x)^3*Sqrt[d + e*x]) + (7*e)/(12*(b*d - a*e)^2*(a + b*x)^2*Sqrt[d + e*x]) - (35*e^2)/(24*(b*d - a*e)^3*(a + b*x)*Sqrt[d + e*x]) + (35*Sqrt[b]*e^3*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*(b*d - a*e)^(9/2))","A",7,4,28,0.1429,1,"{27, 51, 63, 208}"
1662,1,200,0,0.1402789,"\int \frac{1}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[1/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{105 b^{3/2} e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{11/2}}-\frac{105 b e^3}{8 \sqrt{d+e x} (b d-a e)^5}-\frac{35 e^3}{8 (d+e x)^{3/2} (b d-a e)^4}-\frac{21 e^2}{8 (a+b x) (d+e x)^{3/2} (b d-a e)^3}+\frac{3 e}{4 (a+b x)^2 (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{3 (a+b x)^3 (d+e x)^{3/2} (b d-a e)}","\frac{105 b^{3/2} e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{11/2}}-\frac{105 b e^3}{8 \sqrt{d+e x} (b d-a e)^5}-\frac{35 e^3}{8 (d+e x)^{3/2} (b d-a e)^4}-\frac{21 e^2}{8 (a+b x) (d+e x)^{3/2} (b d-a e)^3}+\frac{3 e}{4 (a+b x)^2 (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{3 (a+b x)^3 (d+e x)^{3/2} (b d-a e)}",1,"(-35*e^3)/(8*(b*d - a*e)^4*(d + e*x)^(3/2)) - 1/(3*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(3/2)) + (3*e)/(4*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(3/2)) - (21*e^2)/(8*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(3/2)) - (105*b*e^3)/(8*(b*d - a*e)^5*Sqrt[d + e*x]) + (105*b^(3/2)*e^3*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*(b*d - a*e)^(11/2))","A",8,4,28,0.1429,1,"{27, 51, 63, 208}"
1663,1,229,0,0.1845728,"\int \frac{1}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[1/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{231 b^2 e^3}{8 \sqrt{d+e x} (b d-a e)^6}+\frac{231 b^{5/2} e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{13/2}}-\frac{77 b e^3}{8 (d+e x)^{3/2} (b d-a e)^5}-\frac{231 e^3}{40 (d+e x)^{5/2} (b d-a e)^4}-\frac{33 e^2}{8 (a+b x) (d+e x)^{5/2} (b d-a e)^3}+\frac{11 e}{12 (a+b x)^2 (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{3 (a+b x)^3 (d+e x)^{5/2} (b d-a e)}","-\frac{231 b^2 e^3}{8 \sqrt{d+e x} (b d-a e)^6}+\frac{231 b^{5/2} e^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{13/2}}-\frac{77 b e^3}{8 (d+e x)^{3/2} (b d-a e)^5}-\frac{231 e^3}{40 (d+e x)^{5/2} (b d-a e)^4}-\frac{33 e^2}{8 (a+b x) (d+e x)^{5/2} (b d-a e)^3}+\frac{11 e}{12 (a+b x)^2 (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{3 (a+b x)^3 (d+e x)^{5/2} (b d-a e)}",1,"(-231*e^3)/(40*(b*d - a*e)^4*(d + e*x)^(5/2)) - 1/(3*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(5/2)) + (11*e)/(12*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(5/2)) - (33*e^2)/(8*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(5/2)) - (77*b*e^3)/(8*(b*d - a*e)^5*(d + e*x)^(3/2)) - (231*b^2*e^3)/(8*(b*d - a*e)^6*Sqrt[d + e*x]) + (231*b^(5/2)*e^3*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*(b*d - a*e)^(13/2))","A",9,4,28,0.1429,1,"{27, 51, 63, 208}"
1664,1,253,0,0.1832648,"\int \frac{(d+e x)^{15/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^(15/2)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{13 e^2 (d+e x)^{11/2}}{16 b^3 (a+b x)^3}-\frac{143 e^3 (d+e x)^{9/2}}{64 b^4 (a+b x)^2}-\frac{1287 e^4 (d+e x)^{7/2}}{128 b^5 (a+b x)}+\frac{3003 e^5 (d+e x)^{3/2} (b d-a e)}{128 b^7}+\frac{9009 e^5 \sqrt{d+e x} (b d-a e)^2}{128 b^8}-\frac{9009 e^5 (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{17/2}}-\frac{3 e (d+e x)^{13/2}}{8 b^2 (a+b x)^4}-\frac{(d+e x)^{15/2}}{5 b (a+b x)^5}+\frac{9009 e^5 (d+e x)^{5/2}}{640 b^6}","-\frac{13 e^2 (d+e x)^{11/2}}{16 b^3 (a+b x)^3}-\frac{143 e^3 (d+e x)^{9/2}}{64 b^4 (a+b x)^2}-\frac{1287 e^4 (d+e x)^{7/2}}{128 b^5 (a+b x)}+\frac{3003 e^5 (d+e x)^{3/2} (b d-a e)}{128 b^7}+\frac{9009 e^5 \sqrt{d+e x} (b d-a e)^2}{128 b^8}-\frac{9009 e^5 (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{17/2}}-\frac{3 e (d+e x)^{13/2}}{8 b^2 (a+b x)^4}-\frac{(d+e x)^{15/2}}{5 b (a+b x)^5}+\frac{9009 e^5 (d+e x)^{5/2}}{640 b^6}",1,"(9009*e^5*(b*d - a*e)^2*Sqrt[d + e*x])/(128*b^8) + (3003*e^5*(b*d - a*e)*(d + e*x)^(3/2))/(128*b^7) + (9009*e^5*(d + e*x)^(5/2))/(640*b^6) - (1287*e^4*(d + e*x)^(7/2))/(128*b^5*(a + b*x)) - (143*e^3*(d + e*x)^(9/2))/(64*b^4*(a + b*x)^2) - (13*e^2*(d + e*x)^(11/2))/(16*b^3*(a + b*x)^3) - (3*e*(d + e*x)^(13/2))/(8*b^2*(a + b*x)^4) - (d + e*x)^(15/2)/(5*b*(a + b*x)^5) - (9009*e^5*(b*d - a*e)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(17/2))","A",11,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1665,1,224,0,0.1392221,"\int \frac{(d+e x)^{13/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^(13/2)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{143 e^2 (d+e x)^{9/2}}{240 b^3 (a+b x)^3}-\frac{429 e^3 (d+e x)^{7/2}}{320 b^4 (a+b x)^2}-\frac{3003 e^4 (d+e x)^{5/2}}{640 b^5 (a+b x)}+\frac{3003 e^5 \sqrt{d+e x} (b d-a e)}{128 b^7}-\frac{3003 e^5 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{15/2}}-\frac{13 e (d+e x)^{11/2}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{13/2}}{5 b (a+b x)^5}+\frac{1001 e^5 (d+e x)^{3/2}}{128 b^6}","-\frac{143 e^2 (d+e x)^{9/2}}{240 b^3 (a+b x)^3}-\frac{429 e^3 (d+e x)^{7/2}}{320 b^4 (a+b x)^2}-\frac{3003 e^4 (d+e x)^{5/2}}{640 b^5 (a+b x)}+\frac{3003 e^5 \sqrt{d+e x} (b d-a e)}{128 b^7}-\frac{3003 e^5 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{15/2}}-\frac{13 e (d+e x)^{11/2}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{13/2}}{5 b (a+b x)^5}+\frac{1001 e^5 (d+e x)^{3/2}}{128 b^6}",1,"(3003*e^5*(b*d - a*e)*Sqrt[d + e*x])/(128*b^7) + (1001*e^5*(d + e*x)^(3/2))/(128*b^6) - (3003*e^4*(d + e*x)^(5/2))/(640*b^5*(a + b*x)) - (429*e^3*(d + e*x)^(7/2))/(320*b^4*(a + b*x)^2) - (143*e^2*(d + e*x)^(9/2))/(240*b^3*(a + b*x)^3) - (13*e*(d + e*x)^(11/2))/(40*b^2*(a + b*x)^4) - (d + e*x)^(13/2)/(5*b*(a + b*x)^5) - (3003*e^5*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(15/2))","A",10,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1666,1,197,0,0.1028901,"\int \frac{(d+e x)^{11/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^(11/2)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{33 e^2 (d+e x)^{7/2}}{80 b^3 (a+b x)^3}-\frac{231 e^3 (d+e x)^{5/2}}{320 b^4 (a+b x)^2}-\frac{231 e^4 (d+e x)^{3/2}}{128 b^5 (a+b x)}-\frac{693 e^5 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{13/2}}-\frac{11 e (d+e x)^{9/2}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{11/2}}{5 b (a+b x)^5}+\frac{693 e^5 \sqrt{d+e x}}{128 b^6}","-\frac{33 e^2 (d+e x)^{7/2}}{80 b^3 (a+b x)^3}-\frac{231 e^3 (d+e x)^{5/2}}{320 b^4 (a+b x)^2}-\frac{231 e^4 (d+e x)^{3/2}}{128 b^5 (a+b x)}-\frac{693 e^5 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{13/2}}-\frac{11 e (d+e x)^{9/2}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{11/2}}{5 b (a+b x)^5}+\frac{693 e^5 \sqrt{d+e x}}{128 b^6}",1,"(693*e^5*Sqrt[d + e*x])/(128*b^6) - (231*e^4*(d + e*x)^(3/2))/(128*b^5*(a + b*x)) - (231*e^3*(d + e*x)^(5/2))/(320*b^4*(a + b*x)^2) - (33*e^2*(d + e*x)^(7/2))/(80*b^3*(a + b*x)^3) - (11*e*(d + e*x)^(9/2))/(40*b^2*(a + b*x)^4) - (d + e*x)^(11/2)/(5*b*(a + b*x)^5) - (693*e^5*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(13/2))","A",9,5,28,0.1786,1,"{27, 47, 50, 63, 208}"
1667,1,178,0,0.0901336,"\int \frac{(d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^(9/2)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{63 e^4 \sqrt{d+e x}}{128 b^5 (a+b x)}-\frac{21 e^3 (d+e x)^{3/2}}{64 b^4 (a+b x)^2}-\frac{21 e^2 (d+e x)^{5/2}}{80 b^3 (a+b x)^3}-\frac{63 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{11/2} \sqrt{b d-a e}}-\frac{9 e (d+e x)^{7/2}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{9/2}}{5 b (a+b x)^5}","-\frac{63 e^4 \sqrt{d+e x}}{128 b^5 (a+b x)}-\frac{21 e^3 (d+e x)^{3/2}}{64 b^4 (a+b x)^2}-\frac{21 e^2 (d+e x)^{5/2}}{80 b^3 (a+b x)^3}-\frac{63 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{11/2} \sqrt{b d-a e}}-\frac{9 e (d+e x)^{7/2}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{9/2}}{5 b (a+b x)^5}",1,"(-63*e^4*Sqrt[d + e*x])/(128*b^5*(a + b*x)) - (21*e^3*(d + e*x)^(3/2))/(64*b^4*(a + b*x)^2) - (21*e^2*(d + e*x)^(5/2))/(80*b^3*(a + b*x)^3) - (9*e*(d + e*x)^(7/2))/(40*b^2*(a + b*x)^4) - (d + e*x)^(9/2)/(5*b*(a + b*x)^5) - (63*e^5*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(11/2)*Sqrt[b*d - a*e])","A",8,4,28,0.1429,1,"{27, 47, 63, 208}"
1668,1,188,0,0.1061396,"\int \frac{(d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^(7/2)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{7 e^4 \sqrt{d+e x}}{128 b^4 (a+b x) (b d-a e)}-\frac{7 e^3 \sqrt{d+e x}}{64 b^4 (a+b x)^2}-\frac{7 e^2 (d+e x)^{3/2}}{48 b^3 (a+b x)^3}+\frac{7 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{9/2} (b d-a e)^{3/2}}-\frac{7 e (d+e x)^{5/2}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{7/2}}{5 b (a+b x)^5}","-\frac{7 e^4 \sqrt{d+e x}}{128 b^4 (a+b x) (b d-a e)}-\frac{7 e^3 \sqrt{d+e x}}{64 b^4 (a+b x)^2}-\frac{7 e^2 (d+e x)^{3/2}}{48 b^3 (a+b x)^3}+\frac{7 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{9/2} (b d-a e)^{3/2}}-\frac{7 e (d+e x)^{5/2}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{7/2}}{5 b (a+b x)^5}",1,"(-7*e^3*Sqrt[d + e*x])/(64*b^4*(a + b*x)^2) - (7*e^4*Sqrt[d + e*x])/(128*b^4*(b*d - a*e)*(a + b*x)) - (7*e^2*(d + e*x)^(3/2))/(48*b^3*(a + b*x)^3) - (7*e*(d + e*x)^(5/2))/(40*b^2*(a + b*x)^4) - (d + e*x)^(7/2)/(5*b*(a + b*x)^5) + (7*e^5*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(9/2)*(b*d - a*e)^(3/2))","A",8,5,28,0.1786,1,"{27, 47, 51, 63, 208}"
1669,1,198,0,0.1025119,"\int \frac{(d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^(5/2)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{3 e^4 \sqrt{d+e x}}{128 b^3 (a+b x) (b d-a e)^2}-\frac{e^3 \sqrt{d+e x}}{64 b^3 (a+b x)^2 (b d-a e)}-\frac{e^2 \sqrt{d+e x}}{16 b^3 (a+b x)^3}-\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{7/2} (b d-a e)^{5/2}}-\frac{e (d+e x)^{3/2}}{8 b^2 (a+b x)^4}-\frac{(d+e x)^{5/2}}{5 b (a+b x)^5}","\frac{3 e^4 \sqrt{d+e x}}{128 b^3 (a+b x) (b d-a e)^2}-\frac{e^3 \sqrt{d+e x}}{64 b^3 (a+b x)^2 (b d-a e)}-\frac{e^2 \sqrt{d+e x}}{16 b^3 (a+b x)^3}-\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{7/2} (b d-a e)^{5/2}}-\frac{e (d+e x)^{3/2}}{8 b^2 (a+b x)^4}-\frac{(d+e x)^{5/2}}{5 b (a+b x)^5}",1,"-(e^2*Sqrt[d + e*x])/(16*b^3*(a + b*x)^3) - (e^3*Sqrt[d + e*x])/(64*b^3*(b*d - a*e)*(a + b*x)^2) + (3*e^4*Sqrt[d + e*x])/(128*b^3*(b*d - a*e)^2*(a + b*x)) - (e*(d + e*x)^(3/2))/(8*b^2*(a + b*x)^4) - (d + e*x)^(5/2)/(5*b*(a + b*x)^5) - (3*e^5*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(7/2)*(b*d - a*e)^(5/2))","A",8,5,28,0.1786,1,"{27, 47, 51, 63, 208}"
1670,1,208,0,0.1232464,"\int \frac{(d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^(3/2)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{3 e^4 \sqrt{d+e x}}{128 b^2 (a+b x) (b d-a e)^3}+\frac{e^3 \sqrt{d+e x}}{64 b^2 (a+b x)^2 (b d-a e)^2}-\frac{e^2 \sqrt{d+e x}}{80 b^2 (a+b x)^3 (b d-a e)}+\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{5/2} (b d-a e)^{7/2}}-\frac{3 e \sqrt{d+e x}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{3/2}}{5 b (a+b x)^5}","-\frac{3 e^4 \sqrt{d+e x}}{128 b^2 (a+b x) (b d-a e)^3}+\frac{e^3 \sqrt{d+e x}}{64 b^2 (a+b x)^2 (b d-a e)^2}-\frac{e^2 \sqrt{d+e x}}{80 b^2 (a+b x)^3 (b d-a e)}+\frac{3 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{5/2} (b d-a e)^{7/2}}-\frac{3 e \sqrt{d+e x}}{40 b^2 (a+b x)^4}-\frac{(d+e x)^{3/2}}{5 b (a+b x)^5}",1,"(-3*e*Sqrt[d + e*x])/(40*b^2*(a + b*x)^4) - (e^2*Sqrt[d + e*x])/(80*b^2*(b*d - a*e)*(a + b*x)^3) + (e^3*Sqrt[d + e*x])/(64*b^2*(b*d - a*e)^2*(a + b*x)^2) - (3*e^4*Sqrt[d + e*x])/(128*b^2*(b*d - a*e)^3*(a + b*x)) - (d + e*x)^(3/2)/(5*b*(a + b*x)^5) + (3*e^5*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(5/2)*(b*d - a*e)^(7/2))","A",8,5,28,0.1786,1,"{27, 47, 51, 63, 208}"
1671,1,218,0,0.1504613,"\int \frac{\sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[Sqrt[d + e*x]/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{7 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{3/2} (b d-a e)^{9/2}}+\frac{7 e^4 \sqrt{d+e x}}{128 b (a+b x) (b d-a e)^4}-\frac{7 e^3 \sqrt{d+e x}}{192 b (a+b x)^2 (b d-a e)^3}+\frac{7 e^2 \sqrt{d+e x}}{240 b (a+b x)^3 (b d-a e)^2}-\frac{e \sqrt{d+e x}}{40 b (a+b x)^4 (b d-a e)}-\frac{\sqrt{d+e x}}{5 b (a+b x)^5}","-\frac{7 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{3/2} (b d-a e)^{9/2}}+\frac{7 e^4 \sqrt{d+e x}}{128 b (a+b x) (b d-a e)^4}-\frac{7 e^3 \sqrt{d+e x}}{192 b (a+b x)^2 (b d-a e)^3}+\frac{7 e^2 \sqrt{d+e x}}{240 b (a+b x)^3 (b d-a e)^2}-\frac{e \sqrt{d+e x}}{40 b (a+b x)^4 (b d-a e)}-\frac{\sqrt{d+e x}}{5 b (a+b x)^5}",1,"-Sqrt[d + e*x]/(5*b*(a + b*x)^5) - (e*Sqrt[d + e*x])/(40*b*(b*d - a*e)*(a + b*x)^4) + (7*e^2*Sqrt[d + e*x])/(240*b*(b*d - a*e)^2*(a + b*x)^3) - (7*e^3*Sqrt[d + e*x])/(192*b*(b*d - a*e)^3*(a + b*x)^2) + (7*e^4*Sqrt[d + e*x])/(128*b*(b*d - a*e)^4*(a + b*x)) - (7*e^5*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(3/2)*(b*d - a*e)^(9/2))","A",8,5,28,0.1786,1,"{27, 47, 51, 63, 208}"
1672,1,213,0,0.116132,"\int \frac{1}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[1/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{63 e^4 \sqrt{d+e x}}{128 (a+b x) (b d-a e)^5}+\frac{21 e^3 \sqrt{d+e x}}{64 (a+b x)^2 (b d-a e)^4}-\frac{21 e^2 \sqrt{d+e x}}{80 (a+b x)^3 (b d-a e)^3}+\frac{63 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 \sqrt{b} (b d-a e)^{11/2}}+\frac{9 e \sqrt{d+e x}}{40 (a+b x)^4 (b d-a e)^2}-\frac{\sqrt{d+e x}}{5 (a+b x)^5 (b d-a e)}","-\frac{63 e^4 \sqrt{d+e x}}{128 (a+b x) (b d-a e)^5}+\frac{21 e^3 \sqrt{d+e x}}{64 (a+b x)^2 (b d-a e)^4}-\frac{21 e^2 \sqrt{d+e x}}{80 (a+b x)^3 (b d-a e)^3}+\frac{63 e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 \sqrt{b} (b d-a e)^{11/2}}+\frac{9 e \sqrt{d+e x}}{40 (a+b x)^4 (b d-a e)^2}-\frac{\sqrt{d+e x}}{5 (a+b x)^5 (b d-a e)}",1,"-Sqrt[d + e*x]/(5*(b*d - a*e)*(a + b*x)^5) + (9*e*Sqrt[d + e*x])/(40*(b*d - a*e)^2*(a + b*x)^4) - (21*e^2*Sqrt[d + e*x])/(80*(b*d - a*e)^3*(a + b*x)^3) + (21*e^3*Sqrt[d + e*x])/(64*(b*d - a*e)^4*(a + b*x)^2) - (63*e^4*Sqrt[d + e*x])/(128*(b*d - a*e)^5*(a + b*x)) + (63*e^5*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*Sqrt[b]*(b*d - a*e)^(11/2))","A",8,4,28,0.1429,1,"{27, 51, 63, 208}"
1673,1,239,0,0.1629404,"\int \frac{1}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[1/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{693 e^5}{128 \sqrt{d+e x} (b d-a e)^6}-\frac{231 e^4}{128 (a+b x) \sqrt{d+e x} (b d-a e)^5}+\frac{231 e^3}{320 (a+b x)^2 \sqrt{d+e x} (b d-a e)^4}-\frac{33 e^2}{80 (a+b x)^3 \sqrt{d+e x} (b d-a e)^3}+\frac{693 \sqrt{b} e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{13/2}}+\frac{11 e}{40 (a+b x)^4 \sqrt{d+e x} (b d-a e)^2}-\frac{1}{5 (a+b x)^5 \sqrt{d+e x} (b d-a e)}","-\frac{693 e^5}{128 \sqrt{d+e x} (b d-a e)^6}-\frac{231 e^4}{128 (a+b x) \sqrt{d+e x} (b d-a e)^5}+\frac{231 e^3}{320 (a+b x)^2 \sqrt{d+e x} (b d-a e)^4}-\frac{33 e^2}{80 (a+b x)^3 \sqrt{d+e x} (b d-a e)^3}+\frac{693 \sqrt{b} e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{13/2}}+\frac{11 e}{40 (a+b x)^4 \sqrt{d+e x} (b d-a e)^2}-\frac{1}{5 (a+b x)^5 \sqrt{d+e x} (b d-a e)}",1,"(-693*e^5)/(128*(b*d - a*e)^6*Sqrt[d + e*x]) - 1/(5*(b*d - a*e)*(a + b*x)^5*Sqrt[d + e*x]) + (11*e)/(40*(b*d - a*e)^2*(a + b*x)^4*Sqrt[d + e*x]) - (33*e^2)/(80*(b*d - a*e)^3*(a + b*x)^3*Sqrt[d + e*x]) + (231*e^3)/(320*(b*d - a*e)^4*(a + b*x)^2*Sqrt[d + e*x]) - (231*e^4)/(128*(b*d - a*e)^5*(a + b*x)*Sqrt[d + e*x]) + (693*Sqrt[b]*e^5*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*(b*d - a*e)^(13/2))","A",9,4,28,0.1429,1,"{27, 51, 63, 208}"
1674,1,266,0,0.2433146,"\int \frac{1}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[1/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{3003 b^{3/2} e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{15/2}}-\frac{3003 b e^5}{128 \sqrt{d+e x} (b d-a e)^7}-\frac{1001 e^5}{128 (d+e x)^{3/2} (b d-a e)^6}-\frac{3003 e^4}{640 (a+b x) (d+e x)^{3/2} (b d-a e)^5}+\frac{429 e^3}{320 (a+b x)^2 (d+e x)^{3/2} (b d-a e)^4}-\frac{143 e^2}{240 (a+b x)^3 (d+e x)^{3/2} (b d-a e)^3}+\frac{13 e}{40 (a+b x)^4 (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{5 (a+b x)^5 (d+e x)^{3/2} (b d-a e)}","\frac{3003 b^{3/2} e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{15/2}}-\frac{3003 b e^5}{128 \sqrt{d+e x} (b d-a e)^7}-\frac{1001 e^5}{128 (d+e x)^{3/2} (b d-a e)^6}-\frac{3003 e^4}{640 (a+b x) (d+e x)^{3/2} (b d-a e)^5}+\frac{429 e^3}{320 (a+b x)^2 (d+e x)^{3/2} (b d-a e)^4}-\frac{143 e^2}{240 (a+b x)^3 (d+e x)^{3/2} (b d-a e)^3}+\frac{13 e}{40 (a+b x)^4 (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{5 (a+b x)^5 (d+e x)^{3/2} (b d-a e)}",1,"(-1001*e^5)/(128*(b*d - a*e)^6*(d + e*x)^(3/2)) - 1/(5*(b*d - a*e)*(a + b*x)^5*(d + e*x)^(3/2)) + (13*e)/(40*(b*d - a*e)^2*(a + b*x)^4*(d + e*x)^(3/2)) - (143*e^2)/(240*(b*d - a*e)^3*(a + b*x)^3*(d + e*x)^(3/2)) + (429*e^3)/(320*(b*d - a*e)^4*(a + b*x)^2*(d + e*x)^(3/2)) - (3003*e^4)/(640*(b*d - a*e)^5*(a + b*x)*(d + e*x)^(3/2)) - (3003*b*e^5)/(128*(b*d - a*e)^7*Sqrt[d + e*x]) + (3003*b^(3/2)*e^5*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*(b*d - a*e)^(15/2))","A",10,4,28,0.1429,1,"{27, 51, 63, 208}"
1675,1,295,0,0.2700572,"\int \frac{1}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[1/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{9009 b^2 e^5}{128 \sqrt{d+e x} (b d-a e)^8}+\frac{9009 b^{5/2} e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{17/2}}-\frac{3003 b e^5}{128 (d+e x)^{3/2} (b d-a e)^7}-\frac{9009 e^5}{640 (d+e x)^{5/2} (b d-a e)^6}-\frac{1287 e^4}{128 (a+b x) (d+e x)^{5/2} (b d-a e)^5}+\frac{143 e^3}{64 (a+b x)^2 (d+e x)^{5/2} (b d-a e)^4}-\frac{13 e^2}{16 (a+b x)^3 (d+e x)^{5/2} (b d-a e)^3}+\frac{3 e}{8 (a+b x)^4 (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{5 (a+b x)^5 (d+e x)^{5/2} (b d-a e)}","-\frac{9009 b^2 e^5}{128 \sqrt{d+e x} (b d-a e)^8}+\frac{9009 b^{5/2} e^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{17/2}}-\frac{3003 b e^5}{128 (d+e x)^{3/2} (b d-a e)^7}-\frac{9009 e^5}{640 (d+e x)^{5/2} (b d-a e)^6}-\frac{1287 e^4}{128 (a+b x) (d+e x)^{5/2} (b d-a e)^5}+\frac{143 e^3}{64 (a+b x)^2 (d+e x)^{5/2} (b d-a e)^4}-\frac{13 e^2}{16 (a+b x)^3 (d+e x)^{5/2} (b d-a e)^3}+\frac{3 e}{8 (a+b x)^4 (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{5 (a+b x)^5 (d+e x)^{5/2} (b d-a e)}",1,"(-9009*e^5)/(640*(b*d - a*e)^6*(d + e*x)^(5/2)) - 1/(5*(b*d - a*e)*(a + b*x)^5*(d + e*x)^(5/2)) + (3*e)/(8*(b*d - a*e)^2*(a + b*x)^4*(d + e*x)^(5/2)) - (13*e^2)/(16*(b*d - a*e)^3*(a + b*x)^3*(d + e*x)^(5/2)) + (143*e^3)/(64*(b*d - a*e)^4*(a + b*x)^2*(d + e*x)^(5/2)) - (1287*e^4)/(128*(b*d - a*e)^5*(a + b*x)*(d + e*x)^(5/2)) - (3003*b*e^5)/(128*(b*d - a*e)^7*(d + e*x)^(3/2)) - (9009*b^2*e^5)/(128*(b*d - a*e)^8*Sqrt[d + e*x]) + (9009*b^(5/2)*e^5*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*(b*d - a*e)^(17/2))","A",11,4,28,0.1429,1,"{27, 51, 63, 208}"
1676,1,96,0,0.039625,"\int (d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^2 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^2 (a+b x)}","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^2 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^2 (a+b x)}",1,"(-2*(b*d - a*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^2*(a + b*x)) + (2*b*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^2*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1677,1,96,0,0.0380268,"\int (d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^2 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^2 (a+b x)}","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^2 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^2 (a+b x)}",1,"(-2*(b*d - a*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^2*(a + b*x)) + (2*b*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^2*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1678,1,96,0,0.0374104,"\int \sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^2 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{3 e^2 (a+b x)}","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^2 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{3 e^2 (a+b x)}",1,"(-2*(b*d - a*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^2*(a + b*x)) + (2*b*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^2*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1679,1,94,0,0.0359643,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{d+e x}} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/Sqrt[d + e*x],x]","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^2 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^2 (a+b x)}","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^2 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^2 (a+b x)}",1,"(-2*(b*d - a*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(a + b*x)) + (2*b*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^2*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1680,1,92,0,0.0357957,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{3/2}} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/(d + e*x)^(3/2),x]","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^2 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^2 (a+b x) \sqrt{d+e x}}","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^2 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^2 (a+b x) \sqrt{d+e x}}",1,"(2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(a + b*x)*Sqrt[d + e*x]) + (2*b*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1681,1,94,0,0.0365931,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{5/2}} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/(d + e*x)^(5/2),x]","\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^2 (a+b x) (d+e x)^{3/2}}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2}}{e^2 (a+b x) \sqrt{d+e x}}","\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^2 (a+b x) (d+e x)^{3/2}}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2}}{e^2 (a+b x) \sqrt{d+e x}}",1,"(2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^2*(a + b*x)*(d + e*x)^(3/2)) - (2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(a + b*x)*Sqrt[d + e*x])","A",3,2,30,0.06667,1,"{646, 43}"
1682,1,96,0,0.0352242,"\int \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{7/2}} \, dx","Int[Sqrt[a^2 + 2*a*b*x + b^2*x^2]/(d + e*x)^(7/2),x]","\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^2 (a+b x) (d+e x)^{5/2}}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^2 (a+b x) (d+e x)^{3/2}}","\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^2 (a+b x) (d+e x)^{5/2}}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^2 (a+b x) (d+e x)^{3/2}}",1,"(2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^2*(a + b*x)*(d + e*x)^(5/2)) - (2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^2*(a + b*x)*(d + e*x)^(3/2))","A",3,2,30,0.06667,1,"{646, 43}"
1683,1,208,0,0.07289,"\int (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^4 (a+b x)}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^4 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{3 e^4 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3}{7 e^4 (a+b x)}","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^4 (a+b x)}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^4 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{3 e^4 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3}{7 e^4 (a+b x)}",1,"(-2*(b*d - a*e)^3*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x)) + (2*b*(b*d - a*e)^2*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4*(a + b*x)) - (6*b^2*(b*d - a*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^4*(a + b*x)) + (2*b^3*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^4*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1684,1,208,0,0.0651006,"\int (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^4 (a+b x)}-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{3 e^4 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^4 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}{5 e^4 (a+b x)}","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^4 (a+b x)}-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{3 e^4 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^4 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}{5 e^4 (a+b x)}",1,"(-2*(b*d - a*e)^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)) + (6*b*(b*d - a*e)^2*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x)) - (2*b^2*(b*d - a*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4*(a + b*x)) + (2*b^3*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^4*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1685,1,208,0,0.0664567,"\int \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^4 (a+b x)}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^4 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{5 e^4 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}{3 e^4 (a+b x)}","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^4 (a+b x)}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^4 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{5 e^4 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}{3 e^4 (a+b x)}",1,"(-2*(b*d - a*e)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4*(a + b*x)) + (6*b*(b*d - a*e)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)) - (6*b^2*(b*d - a*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x)) + (2*b^3*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^4*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1686,1,204,0,0.0635751,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/Sqrt[d + e*x],x]","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^4 (a+b x)}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^4 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{e^4 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}{e^4 (a+b x)}","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^4 (a+b x)}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^4 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{e^4 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}{e^4 (a+b x)}",1,"(-2*(b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)) + (2*b*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)) - (6*b^2*(b*d - a*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)) + (2*b^3*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1687,1,202,0,0.0645532,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^(3/2),x]","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^4 (a+b x)}-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{e^4 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^4 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^4 (a+b x) \sqrt{d+e x}}","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^4 (a+b x)}-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{e^4 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^4 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^4 (a+b x) \sqrt{d+e x}}",1,"(2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)*Sqrt[d + e*x]) + (6*b*(b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)) - (2*b^2*(b*d - a*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)) + (2*b^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1688,1,204,0,0.0677803,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^(5/2),x]","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^4 (a+b x)}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^4 (a+b x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^4 (a+b x) \sqrt{d+e x}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^4 (a+b x) (d+e x)^{3/2}}","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^4 (a+b x)}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^4 (a+b x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^4 (a+b x) \sqrt{d+e x}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^4 (a+b x) (d+e x)^{3/2}}",1,"(2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4*(a + b*x)*(d + e*x)^(3/2)) - (6*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)*Sqrt[d + e*x]) - (6*b^2*(b*d - a*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)) + (2*b^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1689,1,202,0,0.066247,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^(7/2),x]","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^4 (a+b x)}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^4 (a+b x) \sqrt{d+e x}}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^4 (a+b x) (d+e x)^{3/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{5 e^4 (a+b x) (d+e x)^{5/2}}","\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^4 (a+b x)}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^4 (a+b x) \sqrt{d+e x}}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^4 (a+b x) (d+e x)^{3/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{5 e^4 (a+b x) (d+e x)^{5/2}}",1,"(2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)*(d + e*x)^(5/2)) - (2*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)*(d + e*x)^(3/2)) + (6*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)*Sqrt[d + e*x]) + (2*b^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1690,1,204,0,0.0634645,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{9/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^(9/2),x]","-\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{e^4 (a+b x) \sqrt{d+e x}}+\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^4 (a+b x) (d+e x)^{3/2}}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{5 e^4 (a+b x) (d+e x)^{5/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^4 (a+b x) (d+e x)^{7/2}}","-\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{e^4 (a+b x) \sqrt{d+e x}}+\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^4 (a+b x) (d+e x)^{3/2}}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{5 e^4 (a+b x) (d+e x)^{5/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^4 (a+b x) (d+e x)^{7/2}}",1,"(2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x)*(d + e*x)^(7/2)) - (6*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)*(d + e*x)^(5/2)) + (2*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)*(d + e*x)^(3/2)) - (2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)*Sqrt[d + e*x])","A",3,2,30,0.06667,1,"{646, 43}"
1691,1,208,0,0.0659555,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{11/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^(11/2),x]","-\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^4 (a+b x) (d+e x)^{3/2}}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^4 (a+b x) (d+e x)^{5/2}}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^4 (a+b x) (d+e x)^{7/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^4 (a+b x) (d+e x)^{9/2}}","-\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^4 (a+b x) (d+e x)^{3/2}}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^4 (a+b x) (d+e x)^{5/2}}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^4 (a+b x) (d+e x)^{7/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^4 (a+b x) (d+e x)^{9/2}}",1,"(2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^4*(a + b*x)*(d + e*x)^(9/2)) - (6*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^4*(a + b*x)*(d + e*x)^(7/2)) + (6*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^4*(a + b*x)*(d + e*x)^(5/2)) - (2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4*(a + b*x)*(d + e*x)^(3/2))","A",3,2,30,0.06667,1,"{646, 43}"
1692,1,320,0,0.1161437,"\int (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2}}{17 e^6 (a+b x)}-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e)}{3 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^2}{13 e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^3}{11 e^6 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^4}{9 e^6 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^5}{7 e^6 (a+b x)}","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2}}{17 e^6 (a+b x)}-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e)}{3 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^2}{13 e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^3}{11 e^6 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^4}{9 e^6 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^5}{7 e^6 (a+b x)}",1,"(-2*(b*d - a*e)^5*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)) + (10*b*(b*d - a*e)^4*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x)) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^6*(a + b*x)) - (2*b^4*(b*d - a*e)*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*e^6*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1693,1,320,0,0.0960453,"\int (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)}{13 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2}{11 e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3}{9 e^6 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^4}{7 e^6 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5}{5 e^6 (a+b x)}","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)}{13 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2}{11 e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3}{9 e^6 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^4}{7 e^6 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5}{5 e^6 (a+b x)}",1,"(-2*(b*d - a*e)^5*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^6*(a + b*x)) + (10*b*(b*d - a*e)^4*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^6*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1694,1,318,0,0.0943637,"\int \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{9 e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3}{7 e^6 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}{e^6 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}{3 e^6 (a+b x)}","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{9 e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3}{7 e^6 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}{e^6 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}{3 e^6 (a+b x)}",1,"(-2*(b*d - a*e)^5*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)) + (2*b*(b*d - a*e)^4*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^6*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1695,1,316,0,0.0966293,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/Sqrt[d + e*x],x]","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{9 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^6 (a+b x)}-\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}{e^6 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}{3 e^6 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}{e^6 (a+b x)}","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{9 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^6 (a+b x)}-\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}{e^6 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}{3 e^6 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}{e^6 (a+b x)}",1,"(-2*(b*d - a*e)^5*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) + (10*b*(b*d - a*e)^4*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)) - (4*b^2*(b*d - a*e)^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^6*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1696,1,314,0,0.0950377,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(3/2),x]","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^6 (a+b x)}+\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}{3 e^6 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}{e^6 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^6 (a+b x) \sqrt{d+e x}}","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^6 (a+b x)}+\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}{3 e^6 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}{e^6 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^6 (a+b x) \sqrt{d+e x}}",1,"(2*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*Sqrt[d + e*x]) + (10*b*(b*d - a*e)^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)) + (4*b^3*(b*d - a*e)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1697,1,314,0,0.0969155,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(5/2),x]","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^6 (a+b x)}-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{3 e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}{e^6 (a+b x)}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^6 (a+b x) \sqrt{d+e x}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{3 e^6 (a+b x) (d+e x)^{3/2}}","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^6 (a+b x)}-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{3 e^6 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}{e^6 (a+b x)}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^6 (a+b x) \sqrt{d+e x}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{3 e^6 (a+b x) (d+e x)^{3/2}}",1,"(2*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) - (10*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*Sqrt[d + e*x]) - (20*b^2*(b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)) - (2*b^4*(b*d - a*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) + (2*b^5*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1698,1,316,0,0.0972174,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(7/2),x]","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{3 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^6 (a+b x)}+\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x) \sqrt{d+e x}}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^6 (a+b x) (d+e x)^{3/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^6 (a+b x) (d+e x)^{5/2}}","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{3 e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^6 (a+b x)}+\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x) \sqrt{d+e x}}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^6 (a+b x) (d+e x)^{3/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^6 (a+b x) (d+e x)^{5/2}}",1,"(2*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^6*(a + b*x)*(d + e*x)^(5/2)) - (10*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) + (20*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*Sqrt[d + e*x]) + (20*b^3*(b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^6*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1699,1,314,0,0.0942204,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{9/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(9/2),x]","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^6 (a+b x)}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x) \sqrt{d+e x}}+\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^6 (a+b x) (d+e x)^{3/2}}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^6 (a+b x) (d+e x)^{5/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{7 e^6 (a+b x) (d+e x)^{7/2}}","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^6 (a+b x)}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^6 (a+b x)}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x) \sqrt{d+e x}}+\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^6 (a+b x) (d+e x)^{3/2}}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^6 (a+b x) (d+e x)^{5/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{7 e^6 (a+b x) (d+e x)^{7/2}}",1,"(2*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)*(d + e*x)^(7/2)) - (2*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)^(5/2)) + (20*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) - (20*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*Sqrt[d + e*x]) - (10*b^4*(b*d - a*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) + (2*b^5*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1700,1,314,0,0.0963662,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{11/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(11/2),x]","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^6 (a+b x)}+\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^6 (a+b x) \sqrt{d+e x}}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^6 (a+b x) (d+e x)^{3/2}}+\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x) (d+e x)^{5/2}}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{7 e^6 (a+b x) (d+e x)^{7/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{9 e^6 (a+b x) (d+e x)^{9/2}}","\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^6 (a+b x)}+\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^6 (a+b x) \sqrt{d+e x}}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^6 (a+b x) (d+e x)^{3/2}}+\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x) (d+e x)^{5/2}}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{7 e^6 (a+b x) (d+e x)^{7/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{9 e^6 (a+b x) (d+e x)^{9/2}}",1,"(2*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x)*(d + e*x)^(9/2)) - (10*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)*(d + e*x)^(7/2)) + (4*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)^(5/2)) - (20*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) + (10*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*Sqrt[d + e*x]) + (2*b^5*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x))","A",3,2,30,0.06667,1,"{646, 43}"
1701,1,316,0,0.0957733,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{13/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(13/2),x]","-\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{e^6 (a+b x) \sqrt{d+e x}}+\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^6 (a+b x) (d+e x)^{3/2}}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x) (d+e x)^{5/2}}+\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^6 (a+b x) (d+e x)^{7/2}}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{9 e^6 (a+b x) (d+e x)^{9/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{11 e^6 (a+b x) (d+e x)^{11/2}}","-\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{e^6 (a+b x) \sqrt{d+e x}}+\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^6 (a+b x) (d+e x)^{3/2}}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x) (d+e x)^{5/2}}+\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^6 (a+b x) (d+e x)^{7/2}}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{9 e^6 (a+b x) (d+e x)^{9/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{11 e^6 (a+b x) (d+e x)^{11/2}}",1,"(2*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^6*(a + b*x)*(d + e*x)^(11/2)) - (10*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x)*(d + e*x)^(9/2)) + (20*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)*(d + e*x)^(7/2)) - (4*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)^(5/2)) + (10*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) - (2*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*Sqrt[d + e*x])","A",3,2,30,0.06667,1,"{646, 43}"
1702,1,318,0,0.09774,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{15/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(15/2),x]","-\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^6 (a+b x) (d+e x)^{3/2}}+\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^6 (a+b x) (d+e x)^{5/2}}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^6 (a+b x) (d+e x)^{7/2}}+\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^6 (a+b x) (d+e x)^{9/2}}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^6 (a+b x) (d+e x)^{11/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{13 e^6 (a+b x) (d+e x)^{13/2}}","-\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^6 (a+b x) (d+e x)^{3/2}}+\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^6 (a+b x) (d+e x)^{5/2}}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^6 (a+b x) (d+e x)^{7/2}}+\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^6 (a+b x) (d+e x)^{9/2}}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^6 (a+b x) (d+e x)^{11/2}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{13 e^6 (a+b x) (d+e x)^{13/2}}",1,"(2*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^6*(a + b*x)*(d + e*x)^(13/2)) - (10*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^6*(a + b*x)*(d + e*x)^(11/2)) + (20*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^6*(a + b*x)*(d + e*x)^(9/2)) - (20*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^6*(a + b*x)*(d + e*x)^(7/2)) + (2*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)*(d + e*x)^(5/2)) - (2*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^6*(a + b*x)*(d + e*x)^(3/2))","A",3,2,30,0.06667,1,"{646, 43}"
1703,1,263,0,0.1693102,"\int \frac{(d+e x)^{7/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(d + e*x)^(7/2)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \sqrt{d+e x} (b d-a e)^3}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{3/2} (b d-a e)^2}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{5/2} (b d-a e)}{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{7/2}}{7 b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (b d-a e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) \sqrt{d+e x} (b d-a e)^3}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{3/2} (b d-a e)^2}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{5/2} (b d-a e)}{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{7/2}}{7 b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (b d-a e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(b*d - a*e)^3*(a + b*x)*Sqrt[d + e*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(b*d - a*e)^2*(a + b*x)*(d + e*x)^(3/2))/(3*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(b*d - a*e)*(a + b*x)*(d + e*x)^(5/2))/(5*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(a + b*x)*(d + e*x)^(7/2))/(7*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*(b*d - a*e)^(7/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,4,30,0.1333,1,"{646, 50, 63, 208}"
1704,1,212,0,0.1092139,"\int \frac{(d+e x)^{5/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(d + e*x)^(5/2)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \sqrt{d+e x} (b d-a e)^2}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{3/2} (b d-a e)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{5/2}}{5 b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) \sqrt{d+e x} (b d-a e)^2}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{3/2} (b d-a e)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{5/2}}{5 b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2))/(3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(a + b*x)*(d + e*x)^(5/2))/(5*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*(b*d - a*e)^(5/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,4,30,0.1333,1,"{646, 50, 63, 208}"
1705,1,161,0,0.0780594,"\int \frac{(d+e x)^{3/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(d + e*x)^(3/2)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \sqrt{d+e x} (b d-a e)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{3/2}}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) \sqrt{d+e x} (b d-a e)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{3/2}}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(b*d - a*e)*(a + b*x)*Sqrt[d + e*x])/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(a + b*x)*(d + e*x)^(3/2))/(3*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*(b*d - a*e)^(3/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,4,30,0.1333,1,"{646, 50, 63, 208}"
1706,1,112,0,0.0532999,"\int \frac{\sqrt{d+e x}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[Sqrt[d + e*x]/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \sqrt{d+e x}}{b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) \sqrt{d+e x}}{b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(a + b*x)*Sqrt[d + e*x])/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*Sqrt[b*d - a*e]*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,30,0.1333,1,"{646, 50, 63, 208}"
1707,1,72,0,0.0393768,"\int \frac{1}{\sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}","-\frac{2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}",1,"(-2*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(Sqrt[b]*Sqrt[b*d - a*e]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,30,0.1000,1,"{646, 63, 208}"
1708,1,119,0,0.0666665,"\int \frac{1}{(d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/((d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}-\frac{2 \sqrt{b} (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}","\frac{2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}-\frac{2 \sqrt{b} (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}",1,"(2*(a + b*x))/((b*d - a*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*Sqrt[b]*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/((b*d - a*e)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,30,0.1333,1,"{646, 51, 63, 208}"
1709,1,168,0,0.0708907,"\int \frac{1}{(d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/((d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 b (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}+\frac{2 (a+b x)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}-\frac{2 b^{3/2} (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}","\frac{2 b (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}+\frac{2 (a+b x)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}-\frac{2 b^{3/2} (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}",1,"(2*(a + b*x))/(3*(b*d - a*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*b*(a + b*x))/((b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*b^(3/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/((b*d - a*e)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,4,30,0.1333,1,"{646, 51, 63, 208}"
1710,1,219,0,0.0914409,"\int \frac{1}{(d+e x)^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/((d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 b^2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}+\frac{2 b (a+b x)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}+\frac{2 (a+b x)}{5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}-\frac{2 b^{5/2} (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}","\frac{2 b^2 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}+\frac{2 b (a+b x)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}+\frac{2 (a+b x)}{5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}-\frac{2 b^{5/2} (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}",1,"(2*(a + b*x))/(5*(b*d - a*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*b*(a + b*x))/(3*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*b^2*(a + b*x))/((b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*b^(5/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/((b*d - a*e)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,4,30,0.1333,1,"{646, 51, 63, 208}"
1711,1,308,0,0.1743069,"\int \frac{(d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(9/2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{63 e^2 (a+b x) (d+e x)^{5/2}}{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{21 e^2 (a+b x) (d+e x)^{3/2} (b d-a e)}{4 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{63 e^2 (a+b x) \sqrt{d+e x} (b d-a e)^2}{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{63 e^2 (a+b x) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{9/2}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{9 e (d+e x)^{7/2}}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{63 e^2 (a+b x) (d+e x)^{5/2}}{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{21 e^2 (a+b x) (d+e x)^{3/2} (b d-a e)}{4 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{63 e^2 (a+b x) \sqrt{d+e x} (b d-a e)^2}{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{63 e^2 (a+b x) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{9/2}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{9 e (d+e x)^{7/2}}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(63*e^2*(b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x])/(4*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (21*e^2*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2))/(4*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (63*e^2*(a + b*x)*(d + e*x)^(5/2))/(20*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (9*e*(d + e*x)^(7/2))/(4*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(9/2)/(2*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (63*e^2*(b*d - a*e)^(5/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,5,30,0.1667,1,"{646, 47, 50, 63, 208}"
1712,1,254,0,0.1287549,"\int \frac{(d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(7/2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{35 e^2 (a+b x) (d+e x)^{3/2}}{12 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 e^2 (a+b x) \sqrt{d+e x} (b d-a e)}{4 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 e^2 (a+b x) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{7/2}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 e (d+e x)^{5/2}}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{35 e^2 (a+b x) (d+e x)^{3/2}}{12 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 e^2 (a+b x) \sqrt{d+e x} (b d-a e)}{4 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 e^2 (a+b x) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{7/2}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 e (d+e x)^{5/2}}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(35*e^2*(b*d - a*e)*(a + b*x)*Sqrt[d + e*x])/(4*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (35*e^2*(a + b*x)*(d + e*x)^(3/2))/(12*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*e*(d + e*x)^(5/2))/(4*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(7/2)/(2*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^2*(b*d - a*e)^(3/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,30,0.1667,1,"{646, 47, 50, 63, 208}"
1713,1,202,0,0.094029,"\int \frac{(d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(5/2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{15 e^2 (a+b x) \sqrt{d+e x}}{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{15 e^2 (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{5/2}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (d+e x)^{3/2}}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{15 e^2 (a+b x) \sqrt{d+e x}}{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{15 e^2 (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{5/2}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (d+e x)^{3/2}}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(15*e^2*(a + b*x)*Sqrt[d + e*x])/(4*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(d + e*x)^(3/2))/(4*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(5/2)/(2*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (15*e^2*Sqrt[b*d - a*e]*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,30,0.1667,1,"{646, 47, 50, 63, 208}"
1714,1,158,0,0.075453,"\int \frac{(d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{3 e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}-\frac{3 e \sqrt{d+e x}}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{3/2}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{3 e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}-\frac{3 e \sqrt{d+e x}}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{3/2}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-3*e*Sqrt[d + e*x])/(4*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(3/2)/(2*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*e^2*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(5/2)*Sqrt[b*d - a*e]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,4,30,0.1333,1,"{646, 47, 63, 208}"
1715,1,168,0,0.0875864,"\int \frac{\sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[Sqrt[d + e*x]/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{e \sqrt{d+e x}}{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{e \sqrt{d+e x}}{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(e*Sqrt[d + e*x])/(4*b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - Sqrt[d + e*x]/(2*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^2*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(3/2)*(b*d - a*e)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,30,0.1667,1,"{646, 47, 51, 63, 208}"
1716,1,172,0,0.0871563,"\int \frac{1}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{3 e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}+\frac{3 e \sqrt{d+e x}}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{\sqrt{d+e x}}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{3 e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}+\frac{3 e \sqrt{d+e x}}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{\sqrt{d+e x}}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(3*e*Sqrt[d + e*x])/(4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - Sqrt[d + e*x]/(2*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*e^2*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*Sqrt[b]*(b*d - a*e)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,4,30,0.1333,1,"{646, 51, 63, 208}"
1717,1,223,0,0.106826,"\int \frac{1}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{15 e^2 (a+b x)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}-\frac{15 \sqrt{b} e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}+\frac{5 e}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{1}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}","\frac{15 e^2 (a+b x)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}-\frac{15 \sqrt{b} e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}+\frac{5 e}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{1}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}",1,"(5*e)/(4*(b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(2*(b*d - a*e)*(a + b*x)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (15*e^2*(a + b*x))/(4*(b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (15*Sqrt[b]*e^2*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*(b*d - a*e)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,4,30,0.1333,1,"{646, 51, 63, 208}"
1718,1,275,0,0.1246409,"\int \frac{1}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{35 b e^2 (a+b x)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}+\frac{35 e^2 (a+b x)}{12 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}-\frac{35 b^{3/2} e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}+\frac{7 e}{4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}","\frac{35 b e^2 (a+b x)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}+\frac{35 e^2 (a+b x)}{12 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}-\frac{35 b^{3/2} e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}+\frac{7 e}{4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}",1,"(7*e)/(4*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(2*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (35*e^2*(a + b*x))/(12*(b*d - a*e)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (35*b*e^2*(a + b*x))/(4*(b*d - a*e)^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*b^(3/2)*e^2*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*(b*d - a*e)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,4,30,0.1333,1,"{646, 51, 63, 208}"
1719,1,329,0,0.1606394,"\int \frac{1}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{63 b^2 e^2 (a+b x)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}+\frac{21 b e^2 (a+b x)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}+\frac{63 e^2 (a+b x)}{20 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}-\frac{63 b^{5/2} e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}-\frac{1}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}+\frac{9 e}{4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}","\frac{63 b^2 e^2 (a+b x)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}+\frac{21 b e^2 (a+b x)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}+\frac{63 e^2 (a+b x)}{20 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}-\frac{63 b^{5/2} e^2 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}-\frac{1}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}+\frac{9 e}{4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}",1,"(9*e)/(4*(b*d - a*e)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(2*(b*d - a*e)*(a + b*x)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (63*e^2*(a + b*x))/(20*(b*d - a*e)^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (21*b*e^2*(a + b*x))/(4*(b*d - a*e)^4*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (63*b^2*e^2*(a + b*x))/(4*(b*d - a*e)^5*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (63*b^(5/2)*e^2*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*(b*d - a*e)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,4,30,0.1333,1,"{646, 51, 63, 208}"
1720,1,400,0,0.2378238,"\int \frac{(d+e x)^{13/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(13/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{143 e^2 (d+e x)^{9/2}}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{429 e^3 (d+e x)^{7/2}}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3003 e^4 (a+b x) (d+e x)^{5/2}}{320 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1001 e^4 (a+b x) (d+e x)^{3/2} (b d-a e)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3003 e^4 (a+b x) \sqrt{d+e x} (b d-a e)^2}{64 b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3003 e^4 (a+b x) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{13/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{13 e (d+e x)^{11/2}}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{143 e^2 (d+e x)^{9/2}}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{429 e^3 (d+e x)^{7/2}}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3003 e^4 (a+b x) (d+e x)^{5/2}}{320 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1001 e^4 (a+b x) (d+e x)^{3/2} (b d-a e)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3003 e^4 (a+b x) \sqrt{d+e x} (b d-a e)^2}{64 b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3003 e^4 (a+b x) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{13/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{13 e (d+e x)^{11/2}}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(3003*e^4*(b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x])/(64*b^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (1001*e^4*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2))/(64*b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3003*e^4*(a + b*x)*(d + e*x)^(5/2))/(320*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (429*e^3*(d + e*x)^(7/2))/(64*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (143*e^2*(d + e*x)^(9/2))/(96*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (13*e*(d + e*x)^(11/2))/(24*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(13/2)/(4*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3003*e^4*(b*d - a*e)^(5/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",10,5,30,0.1667,1,"{646, 47, 50, 63, 208}"
1721,1,346,0,0.1883138,"\int \frac{(d+e x)^{11/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(11/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{33 e^2 (d+e x)^{7/2}}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 e^3 (d+e x)^{5/2}}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{385 e^4 (a+b x) (d+e x)^{3/2}}{64 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1155 e^4 (a+b x) \sqrt{d+e x} (b d-a e)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{1155 e^4 (a+b x) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{11/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{11 e (d+e x)^{9/2}}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{33 e^2 (d+e x)^{7/2}}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 e^3 (d+e x)^{5/2}}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{385 e^4 (a+b x) (d+e x)^{3/2}}{64 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{1155 e^4 (a+b x) \sqrt{d+e x} (b d-a e)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{1155 e^4 (a+b x) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{11/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{11 e (d+e x)^{9/2}}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(1155*e^4*(b*d - a*e)*(a + b*x)*Sqrt[d + e*x])/(64*b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (385*e^4*(a + b*x)*(d + e*x)^(3/2))/(64*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*e^3*(d + e*x)^(5/2))/(64*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (33*e^2*(d + e*x)^(7/2))/(32*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (11*e*(d + e*x)^(9/2))/(24*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(11/2)/(4*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (1155*e^4*(b*d - a*e)^(3/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",9,5,30,0.1667,1,"{646, 47, 50, 63, 208}"
1722,1,294,0,0.1413297,"\int \frac{(d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(9/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{21 e^2 (d+e x)^{5/2}}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{105 e^3 (d+e x)^{3/2}}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{315 e^4 (a+b x) \sqrt{d+e x}}{64 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{315 e^4 (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{9/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 e (d+e x)^{7/2}}{8 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{21 e^2 (d+e x)^{5/2}}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{105 e^3 (d+e x)^{3/2}}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{315 e^4 (a+b x) \sqrt{d+e x}}{64 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{315 e^4 (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{9/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 e (d+e x)^{7/2}}{8 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(315*e^4*(a + b*x)*Sqrt[d + e*x])/(64*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (105*e^3*(d + e*x)^(3/2))/(64*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (21*e^2*(d + e*x)^(5/2))/(32*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*e*(d + e*x)^(7/2))/(8*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(9/2)/(4*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (315*e^4*Sqrt[b*d - a*e]*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,5,30,0.1667,1,"{646, 47, 50, 63, 208}"
1723,1,250,0,0.1179201,"\int \frac{(d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(7/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{35 e^3 \sqrt{d+e x}}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 e^2 (d+e x)^{3/2}}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}-\frac{7 e (d+e x)^{5/2}}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{7/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{35 e^3 \sqrt{d+e x}}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 e^2 (d+e x)^{3/2}}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}-\frac{7 e (d+e x)^{5/2}}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{7/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-35*e^3*Sqrt[d + e*x])/(64*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^2*(d + e*x)^(3/2))/(96*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*e*(d + e*x)^(5/2))/(24*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(7/2)/(4*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^4*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(9/2)*Sqrt[b*d - a*e]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,4,30,0.1333,1,"{646, 47, 63, 208}"
1724,1,260,0,0.139203,"\int \frac{(d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{5 e^3 \sqrt{d+e x}}{64 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{5 e^2 \sqrt{d+e x}}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{5 e (d+e x)^{3/2}}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{5/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{5 e^3 \sqrt{d+e x}}{64 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{5 e^2 \sqrt{d+e x}}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{5 e (d+e x)^{3/2}}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{5/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-5*e^3*Sqrt[d + e*x])/(64*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e^2*Sqrt[d + e*x])/(32*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(d + e*x)^(3/2))/(24*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(5/2)/(4*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e^4*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(7/2)*(b*d - a*e)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,30,0.1667,1,"{646, 47, 51, 63, 208}"
1725,1,270,0,0.1393022,"\int \frac{(d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(3/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{3 e^3 \sqrt{d+e x}}{64 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{e^2 \sqrt{d+e x}}{32 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{3 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x}}{8 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{3/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{3 e^3 \sqrt{d+e x}}{64 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{e^2 \sqrt{d+e x}}{32 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{3 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x}}{8 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{3/2}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(3*e^3*Sqrt[d + e*x])/(64*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*Sqrt[d + e*x])/(8*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^2*Sqrt[d + e*x])/(32*b^2*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(3/2)/(4*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*e^4*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(5/2)*(b*d - a*e)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,30,0.1667,1,"{646, 47, 51, 63, 208}"
1726,1,280,0,0.1512758,"\int \frac{\sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[Sqrt[d + e*x]/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{5 e^3 \sqrt{d+e x}}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{5 e^2 \sqrt{d+e x}}{96 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}+\frac{5 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}-\frac{e \sqrt{d+e x}}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{5 e^3 \sqrt{d+e x}}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{5 e^2 \sqrt{d+e x}}{96 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}+\frac{5 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}-\frac{e \sqrt{d+e x}}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x}}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-5*e^3*Sqrt[d + e*x])/(64*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - Sqrt[d + e*x]/(4*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*Sqrt[d + e*x])/(24*b*(b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e^2*Sqrt[d + e*x])/(96*b*(b*d - a*e)^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e^4*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(3/2)*(b*d - a*e)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,30,0.1667,1,"{646, 47, 51, 63, 208}"
1727,1,278,0,0.1428368,"\int \frac{1}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{35 e^3 \sqrt{d+e x}}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{35 e^2 \sqrt{d+e x}}{96 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{35 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}+\frac{7 e \sqrt{d+e x}}{24 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{\sqrt{d+e x}}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","\frac{35 e^3 \sqrt{d+e x}}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{35 e^2 \sqrt{d+e x}}{96 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{35 e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}+\frac{7 e \sqrt{d+e x}}{24 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{\sqrt{d+e x}}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(35*e^3*Sqrt[d + e*x])/(64*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - Sqrt[d + e*x]/(4*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*e*Sqrt[d + e*x])/(24*(b*d - a*e)^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^2*Sqrt[d + e*x])/(96*(b*d - a*e)^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^4*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*Sqrt[b]*(b*d - a*e)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,4,30,0.1333,1,"{646, 51, 63, 208}"
1728,1,329,0,0.1818073,"\int \frac{1}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{315 e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}+\frac{105 e^3}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}-\frac{21 e^2}{32 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}-\frac{315 \sqrt{b} e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}+\frac{3 e}{8 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{1}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}","\frac{315 e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}+\frac{105 e^3}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}-\frac{21 e^2}{32 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}-\frac{315 \sqrt{b} e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}+\frac{3 e}{8 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{1}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}",1,"(105*e^3)/(64*(b*d - a*e)^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(4*(b*d - a*e)*(a + b*x)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*e)/(8*(b*d - a*e)^2*(a + b*x)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (21*e^2)/(32*(b*d - a*e)^3*(a + b*x)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (315*e^4*(a + b*x))/(64*(b*d - a*e)^5*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (315*Sqrt[b]*e^4*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*(b*d - a*e)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,4,30,0.1333,1,"{646, 51, 63, 208}"
1729,1,381,0,0.2373961,"\int \frac{1}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{1155 b e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^6}+\frac{385 e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}+\frac{231 e^3}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}-\frac{33 e^2}{32 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}-\frac{1155 b^{3/2} e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{13/2}}+\frac{11 e}{24 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}","\frac{1155 b e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^6}+\frac{385 e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}+\frac{231 e^3}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}-\frac{33 e^2}{32 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}-\frac{1155 b^{3/2} e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{13/2}}+\frac{11 e}{24 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}",1,"(231*e^3)/(64*(b*d - a*e)^4*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(4*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (11*e)/(24*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (33*e^2)/(32*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (385*e^4*(a + b*x))/(64*(b*d - a*e)^5*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (1155*b*e^4*(a + b*x))/(64*(b*d - a*e)^6*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (1155*b^(3/2)*e^4*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*(b*d - a*e)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",9,4,30,0.1333,1,"{646, 51, 63, 208}"
1730,1,435,0,0.255969,"\int \frac{1}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{3003 b^2 e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^7}+\frac{1001 b e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^6}+\frac{3003 e^4 (a+b x)}{320 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5}+\frac{429 e^3}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}-\frac{143 e^2}{96 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}-\frac{3003 b^{5/2} e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{15/2}}+\frac{13 e}{24 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}","\frac{3003 b^2 e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^7}+\frac{1001 b e^4 (a+b x)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^6}+\frac{3003 e^4 (a+b x)}{320 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5}+\frac{429 e^3}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}-\frac{143 e^2}{96 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}-\frac{3003 b^{5/2} e^4 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{15/2}}+\frac{13 e}{24 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}",1,"(429*e^3)/(64*(b*d - a*e)^4*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(4*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (13*e)/(24*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (143*e^2)/(96*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3003*e^4*(a + b*x))/(320*(b*d - a*e)^5*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (1001*b*e^4*(a + b*x))/(64*(b*d - a*e)^6*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3003*b^2*e^4*(a + b*x))/(64*(b*d - a*e)^7*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3003*b^(5/2)*e^4*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*(b*d - a*e)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",10,4,30,0.1333,1,"{646, 51, 63, 208}"
1731,1,206,0,0.1099744,"\int (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{15 b^2 (b d-a e)^4 (d+e x)^{m+3}}{e^7 (m+3)}-\frac{20 b^3 (b d-a e)^3 (d+e x)^{m+4}}{e^7 (m+4)}+\frac{15 b^4 (b d-a e)^2 (d+e x)^{m+5}}{e^7 (m+5)}-\frac{6 b^5 (b d-a e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{(b d-a e)^6 (d+e x)^{m+1}}{e^7 (m+1)}-\frac{6 b (b d-a e)^5 (d+e x)^{m+2}}{e^7 (m+2)}+\frac{b^6 (d+e x)^{m+7}}{e^7 (m+7)}","\frac{15 b^2 (b d-a e)^4 (d+e x)^{m+3}}{e^7 (m+3)}-\frac{20 b^3 (b d-a e)^3 (d+e x)^{m+4}}{e^7 (m+4)}+\frac{15 b^4 (b d-a e)^2 (d+e x)^{m+5}}{e^7 (m+5)}-\frac{6 b^5 (b d-a e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{(b d-a e)^6 (d+e x)^{m+1}}{e^7 (m+1)}-\frac{6 b (b d-a e)^5 (d+e x)^{m+2}}{e^7 (m+2)}+\frac{b^6 (d+e x)^{m+7}}{e^7 (m+7)}",1,"((b*d - a*e)^6*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (6*b*(b*d - a*e)^5*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (15*b^2*(b*d - a*e)^4*(d + e*x)^(3 + m))/(e^7*(3 + m)) - (20*b^3*(b*d - a*e)^3*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (15*b^4*(b*d - a*e)^2*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (6*b^5*(b*d - a*e)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (b^6*(d + e*x)^(7 + m))/(e^7*(7 + m))","A",3,2,26,0.07692,1,"{27, 43}"
1732,1,142,0,0.0673952,"\int (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{6 b^2 (b d-a e)^2 (d+e x)^{m+3}}{e^5 (m+3)}-\frac{4 b^3 (b d-a e) (d+e x)^{m+4}}{e^5 (m+4)}+\frac{(b d-a e)^4 (d+e x)^{m+1}}{e^5 (m+1)}-\frac{4 b (b d-a e)^3 (d+e x)^{m+2}}{e^5 (m+2)}+\frac{b^4 (d+e x)^{m+5}}{e^5 (m+5)}","\frac{6 b^2 (b d-a e)^2 (d+e x)^{m+3}}{e^5 (m+3)}-\frac{4 b^3 (b d-a e) (d+e x)^{m+4}}{e^5 (m+4)}+\frac{(b d-a e)^4 (d+e x)^{m+1}}{e^5 (m+1)}-\frac{4 b (b d-a e)^3 (d+e x)^{m+2}}{e^5 (m+2)}+\frac{b^4 (d+e x)^{m+5}}{e^5 (m+5)}",1,"((b*d - a*e)^4*(d + e*x)^(1 + m))/(e^5*(1 + m)) - (4*b*(b*d - a*e)^3*(d + e*x)^(2 + m))/(e^5*(2 + m)) + (6*b^2*(b*d - a*e)^2*(d + e*x)^(3 + m))/(e^5*(3 + m)) - (4*b^3*(b*d - a*e)*(d + e*x)^(4 + m))/(e^5*(4 + m)) + (b^4*(d + e*x)^(5 + m))/(e^5*(5 + m))","A",3,2,26,0.07692,1,"{27, 43}"
1733,1,78,0,0.0331921,"\int (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(b d-a e)^2 (d+e x)^{m+1}}{e^3 (m+1)}-\frac{2 b (b d-a e) (d+e x)^{m+2}}{e^3 (m+2)}+\frac{b^2 (d+e x)^{m+3}}{e^3 (m+3)}","\frac{(b d-a e)^2 (d+e x)^{m+1}}{e^3 (m+1)}-\frac{2 b (b d-a e) (d+e x)^{m+2}}{e^3 (m+2)}+\frac{b^2 (d+e x)^{m+3}}{e^3 (m+3)}",1,"((b*d - a*e)^2*(d + e*x)^(1 + m))/(e^3*(1 + m)) - (2*b*(b*d - a*e)*(d + e*x)^(2 + m))/(e^3*(2 + m)) + (b^2*(d + e*x)^(3 + m))/(e^3*(3 + m))","A",3,2,24,0.08333,1,"{27, 43}"
1734,1,51,0,0.0176339,"\int \frac{(d+e x)^m}{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e (d+e x)^{m+1} \, _2F_1\left(2,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)^2}","\frac{e (d+e x)^{m+1} \, _2F_1\left(2,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)^2}",1,"(e*(d + e*x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^2*(1 + m))","A",2,2,26,0.07692,1,"{27, 68}"
1735,1,53,0,0.0152125,"\int \frac{(d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^3 (d+e x)^{m+1} \, _2F_1\left(4,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)^4}","\frac{e^3 (d+e x)^{m+1} \, _2F_1\left(4,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)^4}",1,"(e^3*(d + e*x)^(1 + m)*Hypergeometric2F1[4, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^4*(1 + m))","A",2,2,26,0.07692,1,"{27, 68}"
1736,1,53,0,0.0168016,"\int \frac{(d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{e^5 (d+e x)^{m+1} \, _2F_1\left(6,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)^6}","\frac{e^5 (d+e x)^{m+1} \, _2F_1\left(6,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)^6}",1,"(e^5*(d + e*x)^(1 + m)*Hypergeometric2F1[6, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^6*(1 + m))","A",2,2,26,0.07692,1,"{27, 68}"
1737,1,337,0,0.1418639,"\int (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (d+e x)^{m+1}}{e^6 (m+1) (a+b x)}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (d+e x)^{m+2}}{e^6 (m+2) (a+b x)}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+3}}{e^6 (m+3) (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+4}}{e^6 (m+4) (a+b x)}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+5}}{e^6 (m+5) (a+b x)}+\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+6}}{e^6 (m+6) (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (d+e x)^{m+1}}{e^6 (m+1) (a+b x)}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (d+e x)^{m+2}}{e^6 (m+2) (a+b x)}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+3}}{e^6 (m+3) (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+4}}{e^6 (m+4) (a+b x)}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+5}}{e^6 (m+5) (a+b x)}+\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+6}}{e^6 (m+6) (a+b x)}",1,"-(((b*d - a*e)^5*(d + e*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(1 + m)*(a + b*x))) + (5*b*(b*d - a*e)^4*(d + e*x)^(2 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(2 + m)*(a + b*x)) - (10*b^2*(b*d - a*e)^3*(d + e*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(3 + m)*(a + b*x)) + (10*b^3*(b*d - a*e)^2*(d + e*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(4 + m)*(a + b*x)) - (5*b^4*(b*d - a*e)*(d + e*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(5 + m)*(a + b*x)) + (b^5*(d + e*x)^(6 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(6 + m)*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1738,1,219,0,0.0876123,"\int (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+1}}{e^4 (m+1) (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+2}}{e^4 (m+2) (a+b x)}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+3}}{e^4 (m+3) (a+b x)}+\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+4}}{e^4 (m+4) (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+1}}{e^4 (m+1) (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+2}}{e^4 (m+2) (a+b x)}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+3}}{e^4 (m+3) (a+b x)}+\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+4}}{e^4 (m+4) (a+b x)}",1,"-(((b*d - a*e)^3*(d + e*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(1 + m)*(a + b*x))) + (3*b*(b*d - a*e)^2*(d + e*x)^(2 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(2 + m)*(a + b*x)) - (3*b^2*(b*d - a*e)*(d + e*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(3 + m)*(a + b*x)) + (b^3*(d + e*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(4 + m)*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1739,1,101,0,0.0446243,"\int (d+e x)^m \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(d + e*x)^m*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+2}}{e^2 (m+2) (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+1}}{e^2 (m+1) (a+b x)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+2}}{e^2 (m+2) (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+1}}{e^2 (m+1) (a+b x)}",1,"-(((b*d - a*e)*(d + e*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(1 + m)*(a + b*x))) + (b*(d + e*x)^(2 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(2 + m)*(a + b*x))","A",3,2,28,0.07143,1,"{646, 43}"
1740,1,76,0,0.0374753,"\int \frac{(d+e x)^m}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(d + e*x)^m/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{(a+b x) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{(a+b x) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"-(((a + b*x)*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)*(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]))","A",2,2,28,0.07143,1,"{646, 68}"
1741,1,79,0,0.0467206,"\int \frac{(d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{e^2 (a+b x) (d+e x)^{m+1} \, _2F_1\left(3,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}","-\frac{e^2 (a+b x) (d+e x)^{m+1} \, _2F_1\left(3,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}",1,"-((e^2*(a + b*x)*(d + e*x)^(1 + m)*Hypergeometric2F1[3, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^3*(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]))","A",2,2,28,0.07143,1,"{646, 68}"
1742,1,79,0,0.0501979,"\int \frac{(d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{e^4 (a+b x) (d+e x)^{m+1} \, _2F_1\left(5,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}","-\frac{e^4 (a+b x) (d+e x)^{m+1} \, _2F_1\left(5,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}",1,"-((e^4*(a + b*x)*(d + e*x)^(1 + m)*Hypergeometric2F1[5, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^5*(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]))","A",2,2,28,0.07143,1,"{646, 68}"
1743,1,85,0,0.0543152,"\int (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{m+1} \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(m+1,-2 p;m+2;\frac{b (d+e x)}{b d-a e}\right)}{e (m+1)}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{m+1} \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(m+1,-2 p;m+2;\frac{b (d+e x)}{b d-a e}\right)}{e (m+1)}",1,"((d + e*x)^(1 + m)*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[1 + m, -2*p, 2 + m, (b*(d + e*x))/(b*d - a*e)])/(e*(1 + m)*(-((e*(a + b*x))/(b*d - a*e)))^(2*p))","A",3,3,26,0.1154,1,"{646, 70, 69}"
1744,1,181,0,0.0923914,"\int (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{3 e^2 (a+b x)^3 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{b^4 (2 p+3)}+\frac{3 e (a+b x)^2 (b d-a e)^2 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^4 (p+1)}+\frac{(a+b x) (b d-a e)^3 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^4 (2 p+1)}+\frac{e^3 (a+b x)^4 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^4 (p+2)}","\frac{3 e^2 (a+b x)^3 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{b^4 (2 p+3)}+\frac{3 e (a+b x)^2 (b d-a e)^2 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^4 (p+1)}+\frac{(a+b x) (b d-a e)^3 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^4 (2 p+1)}+\frac{e^3 (a+b x)^4 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^4 (p+2)}",1,"((b*d - a*e)^3*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^4*(1 + 2*p)) + (3*e*(b*d - a*e)^2*(a + b*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*b^4*(1 + p)) + (3*e^2*(b*d - a*e)*(a + b*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^4*(3 + 2*p)) + (e^3*(a + b*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*b^4*(2 + p))","A",3,2,26,0.07692,1,"{646, 43}"
1745,1,127,0,0.0611493,"\int (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{e (a+b x)^2 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{b^3 (p+1)}+\frac{(a+b x) (b d-a e)^2 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^3 (2 p+1)}+\frac{e^2 (a+b x)^3 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^3 (2 p+3)}","\frac{e (a+b x)^2 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{b^3 (p+1)}+\frac{(a+b x) (b d-a e)^2 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^3 (2 p+1)}+\frac{e^2 (a+b x)^3 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^3 (2 p+3)}",1,"((b*d - a*e)^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^3*(1 + 2*p)) + (e*(b*d - a*e)*(a + b*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^3*(1 + p)) + (e^2*(a + b*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^3*(3 + 2*p))","A",3,2,26,0.07692,1,"{646, 43}"
1746,1,76,0,0.0238942,"\int (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{(a+b x) (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{b^2 (2 p+1)}+\frac{e \left(a^2+2 a b x+b^2 x^2\right)^{p+1}}{2 b^2 (p+1)}","\frac{(a+b x) (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{b^2 (2 p+1)}+\frac{e \left(a^2+2 a b x+b^2 x^2\right)^{p+1}}{2 b^2 (p+1)}",1,"((b*d - a*e)*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^2*(1 + 2*p)) + (e*(a^2 + 2*a*b*x + b^2*x^2)^(1 + p))/(2*b^2*(1 + p))","A",2,2,24,0.08333,1,"{640, 609}"
1747,1,34,0,0.0056333,"\int \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p}{b (2 p+1)}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p}{b (2 p+1)}",1,"((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b*(1 + 2*p))","A",1,1,18,0.05556,1,"{609}"
1748,1,71,0,0.0323544,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^p}{d+e x} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^p/(d + e*x),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p \, _2F_1\left(1,2 p+1;2 (p+1);-\frac{e (a+b x)}{b d-a e}\right)}{(2 p+1) (b d-a e)}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p \, _2F_1\left(1,2 p+1;2 (p+1);-\frac{e (a+b x)}{b d-a e}\right)}{(2 p+1) (b d-a e)}",1,"((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[1, 1 + 2*p, 2*(1 + p), -((e*(a + b*x))/(b*d - a*e))])/((b*d - a*e)*(1 + 2*p))","A",2,2,26,0.07692,1,"{646, 68}"
1749,1,72,0,0.0304151,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^p}{(d+e x)^2} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^p/(d + e*x)^2,x]","\frac{b (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);-\frac{e (a+b x)}{b d-a e}\right)}{(2 p+1) (b d-a e)^2}","\frac{b (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);-\frac{e (a+b x)}{b d-a e}\right)}{(2 p+1) (b d-a e)^2}",1,"(b*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[2, 1 + 2*p, 2*(1 + p), -((e*(a + b*x))/(b*d - a*e))])/((b*d - a*e)^2*(1 + 2*p))","A",2,2,26,0.07692,1,"{646, 68}"
1750,1,74,0,0.0296786,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^p}{(d+e x)^3} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^p/(d + e*x)^3,x]","\frac{b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p \, _2F_1\left(3,2 p+1;2 (p+1);-\frac{e (a+b x)}{b d-a e}\right)}{(2 p+1) (b d-a e)^3}","\frac{b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p \, _2F_1\left(3,2 p+1;2 (p+1);-\frac{e (a+b x)}{b d-a e}\right)}{(2 p+1) (b d-a e)^3}",1,"(b^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[3, 1 + 2*p, 2*(1 + p), -((e*(a + b*x))/(b*d - a*e))])/((b*d - a*e)^3*(1 + 2*p))","A",2,2,26,0.07692,1,"{646, 68}"
1751,1,83,0,0.0409771,"\int (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{2 (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(\frac{5}{2},-2 p;\frac{7}{2};\frac{b (d+e x)}{b d-a e}\right)}{5 e}","\frac{2 (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(\frac{5}{2},-2 p;\frac{7}{2};\frac{b (d+e x)}{b d-a e}\right)}{5 e}",1,"(2*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[5/2, -2*p, 7/2, (b*(d + e*x))/(b*d - a*e)])/(5*e*(-((e*(a + b*x))/(b*d - a*e)))^(2*p))","A",3,3,28,0.1071,1,"{646, 70, 69}"
1752,1,83,0,0.038224,"\int \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{2 (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(\frac{3}{2},-2 p;\frac{5}{2};\frac{b (d+e x)}{b d-a e}\right)}{3 e}","\frac{2 (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(\frac{3}{2},-2 p;\frac{5}{2};\frac{b (d+e x)}{b d-a e}\right)}{3 e}",1,"(2*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[3/2, -2*p, 5/2, (b*(d + e*x))/(b*d - a*e)])/(3*e*(-((e*(a + b*x))/(b*d - a*e)))^(2*p))","A",3,3,28,0.1071,1,"{646, 70, 69}"
1753,1,81,0,0.0379554,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^p}{\sqrt{d+e x}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^p/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(\frac{1}{2},-2 p;\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{e}","\frac{2 \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(\frac{1}{2},-2 p;\frac{3}{2};\frac{b (d+e x)}{b d-a e}\right)}{e}",1,"(2*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[1/2, -2*p, 3/2, (b*(d + e*x))/(b*d - a*e)])/(e*(-((e*(a + b*x))/(b*d - a*e)))^(2*p))","A",3,3,28,0.1071,1,"{646, 70, 69}"
1754,1,81,0,0.0390484,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^p}{(d+e x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^p/(d + e*x)^(3/2),x]","-\frac{2 \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(-\frac{1}{2},-2 p;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{e \sqrt{d+e x}}","-\frac{2 \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(-\frac{1}{2},-2 p;\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{e \sqrt{d+e x}}",1,"(-2*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[-1/2, -2*p, 1/2, (b*(d + e*x))/(b*d - a*e)])/(e*(-((e*(a + b*x))/(b*d - a*e)))^(2*p)*Sqrt[d + e*x])","A",3,3,28,0.1071,1,"{646, 70, 69}"
1755,1,83,0,0.0400015,"\int \frac{\left(a^2+2 a b x+b^2 x^2\right)^p}{(d+e x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x + b^2*x^2)^p/(d + e*x)^(5/2),x]","-\frac{2 \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(-\frac{3}{2},-2 p;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{3 e (d+e x)^{3/2}}","-\frac{2 \left(a^2+2 a b x+b^2 x^2\right)^p \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(-\frac{3}{2},-2 p;-\frac{1}{2};\frac{b (d+e x)}{b d-a e}\right)}{3 e (d+e x)^{3/2}}",1,"(-2*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[-3/2, -2*p, -1/2, (b*(d + e*x))/(b*d - a*e)])/(3*e*(-((e*(a + b*x))/(b*d - a*e)))^(2*p)*(d + e*x)^(3/2))","A",3,3,28,0.1071,1,"{646, 70, 69}"
1756,1,97,0,0.0632328,"\int (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{5+p} \, dx","Int[(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(5 + p),x]","\frac{(b d-a e)^{10} \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{m+1} \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(m+1,-2 (p+5);m+2;\frac{b (d+e x)}{b d-a e}\right)}{e^{11} (m+1)}","\frac{(b d-a e)^{10} \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{m+1} \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} \, _2F_1\left(m+1,-2 (p+5);m+2;\frac{b (d+e x)}{b d-a e}\right)}{e^{11} (m+1)}",1,"((b*d - a*e)^10*(d + e*x)^(1 + m)*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[1 + m, -2*(5 + p), 2 + m, (b*(d + e*x))/(b*d - a*e)])/(e^11*(1 + m)*(-((e*(a + b*x))/(b*d - a*e)))^(2*p))","A",3,3,28,0.1071,1,"{646, 70, 69}"
1757,1,115,0,0.0482377,"\int (d+e x)^{-3-2 p} \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(d + e*x)^(-3 - 2*p)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{b (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{-2 p-1}}{2 (p+1) (2 p+1) (b d-a e)^2}+\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{-2 (p+1)}}{2 (p+1) (b d-a e)}","\frac{b (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{-2 p-1}}{2 (p+1) (2 p+1) (b d-a e)^2}+\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{-2 (p+1)}}{2 (p+1) (b d-a e)}",1,"(b*(a + b*x)*(d + e*x)^(-1 - 2*p)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*(b*d - a*e)^2*(1 + p)*(1 + 2*p)) + ((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*(b*d - a*e)*(1 + p)*(d + e*x)^(2*(1 + p)))","A",3,3,30,0.1000,1,"{646, 45, 37}"
1758,1,60,0,0.0149501,"\int (d+e x) \left(9+12 x+4 x^2\right)^p \, dx","Int[(d + e*x)*(9 + 12*x + 4*x^2)^p,x]","\frac{(2 x+3) (2 d-3 e) \left(4 x^2+12 x+9\right)^p}{4 (2 p+1)}+\frac{e \left(4 x^2+12 x+9\right)^{p+1}}{8 (p+1)}","\frac{(2 x+3) (2 d-3 e) \left(4 x^2+12 x+9\right)^p}{4 (2 p+1)}+\frac{e \left(4 x^2+12 x+9\right)^{p+1}}{8 (p+1)}",1,"((2*d - 3*e)*(3 + 2*x)*(9 + 12*x + 4*x^2)^p)/(4*(1 + 2*p)) + (e*(9 + 12*x + 4*x^2)^(1 + p))/(8*(1 + p))","A",2,2,18,0.1111,1,"{640, 609}"
1759,1,38,0,0.0178423,"\int (a+b x)^3 \left(a c+(b c+a d) x+b d x^2\right) \, dx","Int[(a + b*x)^3*(a*c + (b*c + a*d)*x + b*d*x^2),x]","\frac{(a+b x)^5 (b c-a d)}{5 b^2}+\frac{d (a+b x)^6}{6 b^2}","\frac{(a+b x)^5 (b c-a d)}{5 b^2}+\frac{d (a+b x)^6}{6 b^2}",1,"((b*c - a*d)*(a + b*x)^5)/(5*b^2) + (d*(a + b*x)^6)/(6*b^2)","A",3,2,27,0.07407,1,"{626, 43}"
1760,1,38,0,0.0156864,"\int (a+b x)^2 \left(a c+(b c+a d) x+b d x^2\right) \, dx","Int[(a + b*x)^2*(a*c + (b*c + a*d)*x + b*d*x^2),x]","\frac{(a+b x)^4 (b c-a d)}{4 b^2}+\frac{d (a+b x)^5}{5 b^2}","\frac{(a+b x)^4 (b c-a d)}{4 b^2}+\frac{d (a+b x)^5}{5 b^2}",1,"((b*c - a*d)*(a + b*x)^4)/(4*b^2) + (d*(a + b*x)^5)/(5*b^2)","A",3,2,27,0.07407,1,"{626, 43}"
1761,1,38,0,0.0284002,"\int (a+b x) \left(a c+(b c+a d) x+b d x^2\right) \, dx","Int[(a + b*x)*(a*c + (b*c + a*d)*x + b*d*x^2),x]","\frac{(a+b x)^3 (b c-a d)}{3 b^2}+\frac{d (a+b x)^4}{4 b^2}","\frac{(a+b x)^3 (b c-a d)}{3 b^2}+\frac{d (a+b x)^4}{4 b^2}",1,"((b*c - a*d)*(a + b*x)^3)/(3*b^2) + (d*(a + b*x)^4)/(4*b^2)","A",3,2,25,0.08000,1,"{626, 43}"
1762,1,28,0,0.0077028,"\int \left(a c+(b c+a d) x+b d x^2\right) \, dx","Int[a*c + (b*c + a*d)*x + b*d*x^2,x]","\frac{1}{2} x^2 (a d+b c)+a c x+\frac{1}{3} b d x^3","\frac{1}{2} x^2 (a d+b c)+a c x+\frac{1}{3} b d x^3",1,"a*c*x + ((b*c + a*d)*x^2)/2 + (b*d*x^3)/3","A",1,0,19,0,1,"{}"
1763,1,12,0,0.0065882,"\int \frac{a c+(b c+a d) x+b d x^2}{a+b x} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)/(a + b*x),x]","c x+\frac{d x^2}{2}","c x+\frac{d x^2}{2}",1,"c*x + (d*x^2)/2","A",2,1,27,0.03704,1,"{24}"
1764,1,25,0,0.0207689,"\int \frac{a c+(b c+a d) x+b d x^2}{(a+b x)^2} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)/(a + b*x)^2,x]","\frac{(b c-a d) \log (a+b x)}{b^2}+\frac{d x}{b}","\frac{(b c-a d) \log (a+b x)}{b^2}+\frac{d x}{b}",1,"(d*x)/b + ((b*c - a*d)*Log[a + b*x])/b^2","A",3,2,27,0.07407,1,"{24, 43}"
1765,1,32,0,0.024534,"\int \frac{a c+(b c+a d) x+b d x^2}{(a+b x)^3} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)/(a + b*x)^3,x]","\frac{d \log (a+b x)}{b^2}-\frac{b c-a d}{b^2 (a+b x)}","\frac{d \log (a+b x)}{b^2}-\frac{b c-a d}{b^2 (a+b x)}",1,"-((b*c - a*d)/(b^2*(a + b*x))) + (d*Log[a + b*x])/b^2","A",3,2,27,0.07407,1,"{24, 43}"
1766,1,28,0,0.0109377,"\int \frac{a c+(b c+a d) x+b d x^2}{(a+b x)^4} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)/(a + b*x)^4,x]","-\frac{(c+d x)^2}{2 (a+b x)^2 (b c-a d)}","-\frac{(c+d x)^2}{2 (a+b x)^2 (b c-a d)}",1,"-(c + d*x)^2/(2*(b*c - a*d)*(a + b*x)^2)","A",2,2,27,0.07407,1,"{24, 37}"
1767,1,38,0,0.0242644,"\int \frac{a c+(b c+a d) x+b d x^2}{(a+b x)^5} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)/(a + b*x)^5,x]","-\frac{b c-a d}{3 b^2 (a+b x)^3}-\frac{d}{2 b^2 (a+b x)^2}","-\frac{b c-a d}{3 b^2 (a+b x)^3}-\frac{d}{2 b^2 (a+b x)^2}",1,"-(b*c - a*d)/(3*b^2*(a + b*x)^3) - d/(2*b^2*(a + b*x)^2)","A",3,2,27,0.07407,1,"{24, 43}"
1768,1,38,0,0.0260423,"\int \frac{a c+(b c+a d) x+b d x^2}{(a+b x)^6} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)/(a + b*x)^6,x]","-\frac{b c-a d}{4 b^2 (a+b x)^4}-\frac{d}{3 b^2 (a+b x)^3}","-\frac{b c-a d}{4 b^2 (a+b x)^4}-\frac{d}{3 b^2 (a+b x)^3}",1,"-(b*c - a*d)/(4*b^2*(a + b*x)^4) - d/(3*b^2*(a + b*x)^3)","A",3,2,27,0.07407,1,"{24, 43}"
1769,1,65,0,0.1299752,"\int (a+b x)^3 \left(a c+(b c+a d) x+b d x^2\right)^2 \, dx","Int[(a + b*x)^3*(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","\frac{2 d (a+b x)^7 (b c-a d)}{7 b^3}+\frac{(a+b x)^6 (b c-a d)^2}{6 b^3}+\frac{d^2 (a+b x)^8}{8 b^3}","\frac{2 d (a+b x)^7 (b c-a d)}{7 b^3}+\frac{(a+b x)^6 (b c-a d)^2}{6 b^3}+\frac{d^2 (a+b x)^8}{8 b^3}",1,"((b*c - a*d)^2*(a + b*x)^6)/(6*b^3) + (2*d*(b*c - a*d)*(a + b*x)^7)/(7*b^3) + (d^2*(a + b*x)^8)/(8*b^3)","A",3,2,29,0.06897,1,"{626, 43}"
1770,1,65,0,0.0897019,"\int (a+b x)^2 \left(a c+(b c+a d) x+b d x^2\right)^2 \, dx","Int[(a + b*x)^2*(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","\frac{d (a+b x)^6 (b c-a d)}{3 b^3}+\frac{(a+b x)^5 (b c-a d)^2}{5 b^3}+\frac{d^2 (a+b x)^7}{7 b^3}","\frac{d (a+b x)^6 (b c-a d)}{3 b^3}+\frac{(a+b x)^5 (b c-a d)^2}{5 b^3}+\frac{d^2 (a+b x)^7}{7 b^3}",1,"((b*c - a*d)^2*(a + b*x)^5)/(5*b^3) + (d*(b*c - a*d)*(a + b*x)^6)/(3*b^3) + (d^2*(a + b*x)^7)/(7*b^3)","A",3,2,29,0.06897,1,"{626, 43}"
1771,1,65,0,0.0657123,"\int (a+b x) \left(a c+(b c+a d) x+b d x^2\right)^2 \, dx","Int[(a + b*x)*(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","\frac{2 d (a+b x)^5 (b c-a d)}{5 b^3}+\frac{(a+b x)^4 (b c-a d)^2}{4 b^3}+\frac{d^2 (a+b x)^6}{6 b^3}","\frac{2 d (a+b x)^5 (b c-a d)}{5 b^3}+\frac{(a+b x)^4 (b c-a d)^2}{4 b^3}+\frac{d^2 (a+b x)^6}{6 b^3}",1,"((b*c - a*d)^2*(a + b*x)^4)/(4*b^3) + (2*d*(b*c - a*d)*(a + b*x)^5)/(5*b^3) + (d^2*(a + b*x)^6)/(6*b^3)","A",3,2,27,0.07407,1,"{626, 43}"
1772,1,65,0,0.0692441,"\int \left(a c+(b c+a d) x+b d x^2\right)^2 \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","-\frac{b (c+d x)^4 (b c-a d)}{2 d^3}+\frac{(c+d x)^3 (b c-a d)^2}{3 d^3}+\frac{b^2 (c+d x)^5}{5 d^3}","-\frac{b (c+d x)^4 (b c-a d)}{2 d^3}+\frac{(c+d x)^3 (b c-a d)^2}{3 d^3}+\frac{b^2 (c+d x)^5}{5 d^3}",1,"((b*c - a*d)^2*(c + d*x)^3)/(3*d^3) - (b*(b*c - a*d)*(c + d*x)^4)/(2*d^3) + (b^2*(c + d*x)^5)/(5*d^3)","A",3,2,21,0.09524,1,"{610, 43}"
1773,1,38,0,0.034688,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{a+b x} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x),x]","\frac{b (c+d x)^4}{4 d^2}-\frac{(c+d x)^3 (b c-a d)}{3 d^2}","\frac{b (c+d x)^4}{4 d^2}-\frac{(c+d x)^3 (b c-a d)}{3 d^2}",1,"-((b*c - a*d)*(c + d*x)^3)/(3*d^2) + (b*(c + d*x)^4)/(4*d^2)","A",3,2,29,0.06897,1,"{626, 43}"
1774,1,14,0,0.0099224,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{(a+b x)^2} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x)^2,x]","\frac{(c+d x)^3}{3 d}","\frac{(c+d x)^3}{3 d}",1,"(c + d*x)^3/(3*d)","A",2,2,29,0.06897,1,"{626, 32}"
1775,1,49,0,0.0281078,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{(a+b x)^3} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x)^3,x]","\frac{d x (b c-a d)}{b^2}+\frac{(b c-a d)^2 \log (a+b x)}{b^3}+\frac{(c+d x)^2}{2 b}","\frac{d x (b c-a d)}{b^2}+\frac{(b c-a d)^2 \log (a+b x)}{b^3}+\frac{(c+d x)^2}{2 b}",1,"(d*(b*c - a*d)*x)/b^2 + (c + d*x)^2/(2*b) + ((b*c - a*d)^2*Log[a + b*x])/b^3","A",3,2,29,0.06897,1,"{626, 43}"
1776,1,51,0,0.0442666,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{(a+b x)^4} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x)^4,x]","-\frac{(b c-a d)^2}{b^3 (a+b x)}+\frac{2 d (b c-a d) \log (a+b x)}{b^3}+\frac{d^2 x}{b^2}","-\frac{(b c-a d)^2}{b^3 (a+b x)}+\frac{2 d (b c-a d) \log (a+b x)}{b^3}+\frac{d^2 x}{b^2}",1,"(d^2*x)/b^2 - (b*c - a*d)^2/(b^3*(a + b*x)) + (2*d*(b*c - a*d)*Log[a + b*x])/b^3","A",3,2,29,0.06897,1,"{626, 43}"
1777,1,59,0,0.0431223,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{(a+b x)^5} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x)^5,x]","-\frac{2 d (b c-a d)}{b^3 (a+b x)}-\frac{(b c-a d)^2}{2 b^3 (a+b x)^2}+\frac{d^2 \log (a+b x)}{b^3}","-\frac{2 d (b c-a d)}{b^3 (a+b x)}-\frac{(b c-a d)^2}{2 b^3 (a+b x)^2}+\frac{d^2 \log (a+b x)}{b^3}",1,"-(b*c - a*d)^2/(2*b^3*(a + b*x)^2) - (2*d*(b*c - a*d))/(b^3*(a + b*x)) + (d^2*Log[a + b*x])/b^3","A",3,2,29,0.06897,1,"{626, 43}"
1778,1,28,0,0.0112407,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{(a+b x)^6} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x)^6,x]","-\frac{(c+d x)^3}{3 (a+b x)^3 (b c-a d)}","-\frac{(c+d x)^3}{3 (a+b x)^3 (b c-a d)}",1,"-(c + d*x)^3/(3*(b*c - a*d)*(a + b*x)^3)","A",2,2,29,0.06897,1,"{626, 37}"
1779,1,65,0,0.0435792,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{(a+b x)^7} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x)^7,x]","-\frac{2 d (b c-a d)}{3 b^3 (a+b x)^3}-\frac{(b c-a d)^2}{4 b^3 (a+b x)^4}-\frac{d^2}{2 b^3 (a+b x)^2}","-\frac{2 d (b c-a d)}{3 b^3 (a+b x)^3}-\frac{(b c-a d)^2}{4 b^3 (a+b x)^4}-\frac{d^2}{2 b^3 (a+b x)^2}",1,"-(b*c - a*d)^2/(4*b^3*(a + b*x)^4) - (2*d*(b*c - a*d))/(3*b^3*(a + b*x)^3) - d^2/(2*b^3*(a + b*x)^2)","A",3,2,29,0.06897,1,"{626, 43}"
1780,1,65,0,0.0435076,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{(a+b x)^8} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x)^8,x]","-\frac{d (b c-a d)}{2 b^3 (a+b x)^4}-\frac{(b c-a d)^2}{5 b^3 (a+b x)^5}-\frac{d^2}{3 b^3 (a+b x)^3}","-\frac{d (b c-a d)}{2 b^3 (a+b x)^4}-\frac{(b c-a d)^2}{5 b^3 (a+b x)^5}-\frac{d^2}{3 b^3 (a+b x)^3}",1,"-(b*c - a*d)^2/(5*b^3*(a + b*x)^5) - (d*(b*c - a*d))/(2*b^3*(a + b*x)^4) - d^2/(3*b^3*(a + b*x)^3)","A",3,2,29,0.06897,1,"{626, 43}"
1781,1,65,0,0.0411441,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{(a+b x)^9} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x)^9,x]","-\frac{2 d (b c-a d)}{5 b^3 (a+b x)^5}-\frac{(b c-a d)^2}{6 b^3 (a+b x)^6}-\frac{d^2}{4 b^3 (a+b x)^4}","-\frac{2 d (b c-a d)}{5 b^3 (a+b x)^5}-\frac{(b c-a d)^2}{6 b^3 (a+b x)^6}-\frac{d^2}{4 b^3 (a+b x)^4}",1,"-(b*c - a*d)^2/(6*b^3*(a + b*x)^6) - (2*d*(b*c - a*d))/(5*b^3*(a + b*x)^5) - d^2/(4*b^3*(a + b*x)^4)","A",3,2,29,0.06897,1,"{626, 43}"
1782,1,65,0,0.0413255,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^2}{(a+b x)^{10}} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^2/(a + b*x)^10,x]","-\frac{d (b c-a d)}{3 b^3 (a+b x)^6}-\frac{(b c-a d)^2}{7 b^3 (a+b x)^7}-\frac{d^2}{5 b^3 (a+b x)^5}","-\frac{d (b c-a d)}{3 b^3 (a+b x)^6}-\frac{(b c-a d)^2}{7 b^3 (a+b x)^7}-\frac{d^2}{5 b^3 (a+b x)^5}",1,"-(b*c - a*d)^2/(7*b^3*(a + b*x)^7) - (d*(b*c - a*d))/(3*b^3*(a + b*x)^6) - d^2/(5*b^3*(a + b*x)^5)","A",3,2,29,0.06897,1,"{626, 43}"
1783,1,92,0,0.2196939,"\int (a+b x)^3 \left(a c+(b c+a d) x+b d x^2\right)^3 \, dx","Int[(a + b*x)^3*(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","\frac{d^2 (a+b x)^9 (b c-a d)}{3 b^4}+\frac{3 d (a+b x)^8 (b c-a d)^2}{8 b^4}+\frac{(a+b x)^7 (b c-a d)^3}{7 b^4}+\frac{d^3 (a+b x)^{10}}{10 b^4}","\frac{d^2 (a+b x)^9 (b c-a d)}{3 b^4}+\frac{3 d (a+b x)^8 (b c-a d)^2}{8 b^4}+\frac{(a+b x)^7 (b c-a d)^3}{7 b^4}+\frac{d^3 (a+b x)^{10}}{10 b^4}",1,"((b*c - a*d)^3*(a + b*x)^7)/(7*b^4) + (3*d*(b*c - a*d)^2*(a + b*x)^8)/(8*b^4) + (d^2*(b*c - a*d)*(a + b*x)^9)/(3*b^4) + (d^3*(a + b*x)^10)/(10*b^4)","A",3,2,29,0.06897,1,"{626, 43}"
1784,1,92,0,0.1572599,"\int (a+b x)^2 \left(a c+(b c+a d) x+b d x^2\right)^3 \, dx","Int[(a + b*x)^2*(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","\frac{3 d^2 (a+b x)^8 (b c-a d)}{8 b^4}+\frac{3 d (a+b x)^7 (b c-a d)^2}{7 b^4}+\frac{(a+b x)^6 (b c-a d)^3}{6 b^4}+\frac{d^3 (a+b x)^9}{9 b^4}","\frac{3 d^2 (a+b x)^8 (b c-a d)}{8 b^4}+\frac{3 d (a+b x)^7 (b c-a d)^2}{7 b^4}+\frac{(a+b x)^6 (b c-a d)^3}{6 b^4}+\frac{d^3 (a+b x)^9}{9 b^4}",1,"((b*c - a*d)^3*(a + b*x)^6)/(6*b^4) + (3*d*(b*c - a*d)^2*(a + b*x)^7)/(7*b^4) + (3*d^2*(b*c - a*d)*(a + b*x)^8)/(8*b^4) + (d^3*(a + b*x)^9)/(9*b^4)","A",3,2,29,0.06897,1,"{626, 43}"
1785,1,92,0,0.1205382,"\int (a+b x) \left(a c+(b c+a d) x+b d x^2\right)^3 \, dx","Int[(a + b*x)*(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","\frac{3 d^2 (a+b x)^7 (b c-a d)}{7 b^4}+\frac{d (a+b x)^6 (b c-a d)^2}{2 b^4}+\frac{(a+b x)^5 (b c-a d)^3}{5 b^4}+\frac{d^3 (a+b x)^8}{8 b^4}","\frac{3 d^2 (a+b x)^7 (b c-a d)}{7 b^4}+\frac{d (a+b x)^6 (b c-a d)^2}{2 b^4}+\frac{(a+b x)^5 (b c-a d)^3}{5 b^4}+\frac{d^3 (a+b x)^8}{8 b^4}",1,"((b*c - a*d)^3*(a + b*x)^5)/(5*b^4) + (d*(b*c - a*d)^2*(a + b*x)^6)/(2*b^4) + (3*d^2*(b*c - a*d)*(a + b*x)^7)/(7*b^4) + (d^3*(a + b*x)^8)/(8*b^4)","A",3,2,27,0.07407,1,"{626, 43}"
1786,1,92,0,0.1171047,"\int \left(a c+(b c+a d) x+b d x^2\right)^3 \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","-\frac{b^2 (c+d x)^6 (b c-a d)}{2 d^4}+\frac{3 b (c+d x)^5 (b c-a d)^2}{5 d^4}-\frac{(c+d x)^4 (b c-a d)^3}{4 d^4}+\frac{b^3 (c+d x)^7}{7 d^4}","-\frac{b^2 (c+d x)^6 (b c-a d)}{2 d^4}+\frac{3 b (c+d x)^5 (b c-a d)^2}{5 d^4}-\frac{(c+d x)^4 (b c-a d)^3}{4 d^4}+\frac{b^3 (c+d x)^7}{7 d^4}",1,"-((b*c - a*d)^3*(c + d*x)^4)/(4*d^4) + (3*b*(b*c - a*d)^2*(c + d*x)^5)/(5*d^4) - (b^2*(b*c - a*d)*(c + d*x)^6)/(2*d^4) + (b^3*(c + d*x)^7)/(7*d^4)","A",3,2,21,0.09524,1,"{610, 43}"
1787,1,65,0,0.0718319,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{a+b x} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x),x]","-\frac{2 b (c+d x)^5 (b c-a d)}{5 d^3}+\frac{(c+d x)^4 (b c-a d)^2}{4 d^3}+\frac{b^2 (c+d x)^6}{6 d^3}","-\frac{2 b (c+d x)^5 (b c-a d)}{5 d^3}+\frac{(c+d x)^4 (b c-a d)^2}{4 d^3}+\frac{b^2 (c+d x)^6}{6 d^3}",1,"((b*c - a*d)^2*(c + d*x)^4)/(4*d^3) - (2*b*(b*c - a*d)*(c + d*x)^5)/(5*d^3) + (b^2*(c + d*x)^6)/(6*d^3)","A",3,2,29,0.06897,1,"{626, 43}"
1788,1,38,0,0.0228092,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^2} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^2,x]","\frac{b (c+d x)^5}{5 d^2}-\frac{(c+d x)^4 (b c-a d)}{4 d^2}","\frac{b (c+d x)^5}{5 d^2}-\frac{(c+d x)^4 (b c-a d)}{4 d^2}",1,"-((b*c - a*d)*(c + d*x)^4)/(4*d^2) + (b*(c + d*x)^5)/(5*d^2)","A",3,2,29,0.06897,1,"{626, 43}"
1789,1,14,0,0.0099483,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^3} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^3,x]","\frac{(c+d x)^4}{4 d}","\frac{(c+d x)^4}{4 d}",1,"(c + d*x)^4/(4*d)","A",2,2,29,0.06897,1,"{626, 32}"
1790,1,73,0,0.0371784,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^4} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^4,x]","\frac{d x (b c-a d)^2}{b^3}+\frac{(c+d x)^2 (b c-a d)}{2 b^2}+\frac{(b c-a d)^3 \log (a+b x)}{b^4}+\frac{(c+d x)^3}{3 b}","\frac{d x (b c-a d)^2}{b^3}+\frac{(c+d x)^2 (b c-a d)}{2 b^2}+\frac{(b c-a d)^3 \log (a+b x)}{b^4}+\frac{(c+d x)^3}{3 b}",1,"(d*(b*c - a*d)^2*x)/b^3 + ((b*c - a*d)*(c + d*x)^2)/(2*b^2) + (c + d*x)^3/(3*b) + ((b*c - a*d)^3*Log[a + b*x])/b^4","A",3,2,29,0.06897,1,"{626, 43}"
1791,1,75,0,0.0670233,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^5} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^5,x]","\frac{d^2 x (3 b c-2 a d)}{b^3}-\frac{(b c-a d)^3}{b^4 (a+b x)}+\frac{3 d (b c-a d)^2 \log (a+b x)}{b^4}+\frac{d^3 x^2}{2 b^2}","\frac{d^2 x (3 b c-2 a d)}{b^3}-\frac{(b c-a d)^3}{b^4 (a+b x)}+\frac{3 d (b c-a d)^2 \log (a+b x)}{b^4}+\frac{d^3 x^2}{2 b^2}",1,"(d^2*(3*b*c - 2*a*d)*x)/b^3 + (d^3*x^2)/(2*b^2) - (b*c - a*d)^3/(b^4*(a + b*x)) + (3*d*(b*c - a*d)^2*Log[a + b*x])/b^4","A",3,2,29,0.06897,1,"{626, 43}"
1792,1,78,0,0.0606103,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^6} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^6,x]","\frac{3 d^2 (b c-a d) \log (a+b x)}{b^4}-\frac{3 d (b c-a d)^2}{b^4 (a+b x)}-\frac{(b c-a d)^3}{2 b^4 (a+b x)^2}+\frac{d^3 x}{b^3}","\frac{3 d^2 (b c-a d) \log (a+b x)}{b^4}-\frac{3 d (b c-a d)^2}{b^4 (a+b x)}-\frac{(b c-a d)^3}{2 b^4 (a+b x)^2}+\frac{d^3 x}{b^3}",1,"(d^3*x)/b^3 - (b*c - a*d)^3/(2*b^4*(a + b*x)^2) - (3*d*(b*c - a*d)^2)/(b^4*(a + b*x)) + (3*d^2*(b*c - a*d)*Log[a + b*x])/b^4","A",3,2,29,0.06897,1,"{626, 43}"
1793,1,86,0,0.0600761,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^7} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^7,x]","-\frac{3 d^2 (b c-a d)}{b^4 (a+b x)}-\frac{3 d (b c-a d)^2}{2 b^4 (a+b x)^2}-\frac{(b c-a d)^3}{3 b^4 (a+b x)^3}+\frac{d^3 \log (a+b x)}{b^4}","-\frac{3 d^2 (b c-a d)}{b^4 (a+b x)}-\frac{3 d (b c-a d)^2}{2 b^4 (a+b x)^2}-\frac{(b c-a d)^3}{3 b^4 (a+b x)^3}+\frac{d^3 \log (a+b x)}{b^4}",1,"-(b*c - a*d)^3/(3*b^4*(a + b*x)^3) - (3*d*(b*c - a*d)^2)/(2*b^4*(a + b*x)^2) - (3*d^2*(b*c - a*d))/(b^4*(a + b*x)) + (d^3*Log[a + b*x])/b^4","A",3,2,29,0.06897,1,"{626, 43}"
1794,1,28,0,0.0116204,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^8} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^8,x]","-\frac{(c+d x)^4}{4 (a+b x)^4 (b c-a d)}","-\frac{(c+d x)^4}{4 (a+b x)^4 (b c-a d)}",1,"-(c + d*x)^4/(4*(b*c - a*d)*(a + b*x)^4)","A",2,2,29,0.06897,1,"{626, 37}"
1795,1,58,0,0.0189528,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^9} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^9,x]","\frac{d (c+d x)^4}{20 (a+b x)^4 (b c-a d)^2}-\frac{(c+d x)^4}{5 (a+b x)^5 (b c-a d)}","\frac{d (c+d x)^4}{20 (a+b x)^4 (b c-a d)^2}-\frac{(c+d x)^4}{5 (a+b x)^5 (b c-a d)}",1,"-(c + d*x)^4/(5*(b*c - a*d)*(a + b*x)^5) + (d*(c + d*x)^4)/(20*(b*c - a*d)^2*(a + b*x)^4)","A",3,3,29,0.1034,1,"{626, 45, 37}"
1796,1,92,0,0.0611387,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^{10}} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^10,x]","-\frac{3 d^2 (b c-a d)}{4 b^4 (a+b x)^4}-\frac{3 d (b c-a d)^2}{5 b^4 (a+b x)^5}-\frac{(b c-a d)^3}{6 b^4 (a+b x)^6}-\frac{d^3}{3 b^4 (a+b x)^3}","-\frac{3 d^2 (b c-a d)}{4 b^4 (a+b x)^4}-\frac{3 d (b c-a d)^2}{5 b^4 (a+b x)^5}-\frac{(b c-a d)^3}{6 b^4 (a+b x)^6}-\frac{d^3}{3 b^4 (a+b x)^3}",1,"-(b*c - a*d)^3/(6*b^4*(a + b*x)^6) - (3*d*(b*c - a*d)^2)/(5*b^4*(a + b*x)^5) - (3*d^2*(b*c - a*d))/(4*b^4*(a + b*x)^4) - d^3/(3*b^4*(a + b*x)^3)","A",3,2,29,0.06897,1,"{626, 43}"
1797,1,92,0,0.0576906,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^{11}} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^11,x]","-\frac{3 d^2 (b c-a d)}{5 b^4 (a+b x)^5}-\frac{d (b c-a d)^2}{2 b^4 (a+b x)^6}-\frac{(b c-a d)^3}{7 b^4 (a+b x)^7}-\frac{d^3}{4 b^4 (a+b x)^4}","-\frac{3 d^2 (b c-a d)}{5 b^4 (a+b x)^5}-\frac{d (b c-a d)^2}{2 b^4 (a+b x)^6}-\frac{(b c-a d)^3}{7 b^4 (a+b x)^7}-\frac{d^3}{4 b^4 (a+b x)^4}",1,"-(b*c - a*d)^3/(7*b^4*(a + b*x)^7) - (d*(b*c - a*d)^2)/(2*b^4*(a + b*x)^6) - (3*d^2*(b*c - a*d))/(5*b^4*(a + b*x)^5) - d^3/(4*b^4*(a + b*x)^4)","A",3,2,29,0.06897,1,"{626, 43}"
1798,1,92,0,0.0551401,"\int \frac{\left(a c+(b c+a d) x+b d x^2\right)^3}{(a+b x)^{12}} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^12,x]","-\frac{d^2 (b c-a d)}{2 b^4 (a+b x)^6}-\frac{3 d (b c-a d)^2}{7 b^4 (a+b x)^7}-\frac{(b c-a d)^3}{8 b^4 (a+b x)^8}-\frac{d^3}{5 b^4 (a+b x)^5}","-\frac{d^2 (b c-a d)}{2 b^4 (a+b x)^6}-\frac{3 d (b c-a d)^2}{7 b^4 (a+b x)^7}-\frac{(b c-a d)^3}{8 b^4 (a+b x)^8}-\frac{d^3}{5 b^4 (a+b x)^5}",1,"-(b*c - a*d)^3/(8*b^4*(a + b*x)^8) - (3*d*(b*c - a*d)^2)/(7*b^4*(a + b*x)^7) - (d^2*(b*c - a*d))/(2*b^4*(a + b*x)^6) - d^3/(5*b^4*(a + b*x)^5)","A",3,2,29,0.06897,1,"{626, 43}"
1799,1,122,0,0.0626873,"\int \frac{(a+b x)^6}{a c+(b c+a d) x+b d x^2} \, dx","Int[(a + b*x)^6/(a*c + (b*c + a*d)*x + b*d*x^2),x]","\frac{b x (b c-a d)^4}{d^5}-\frac{(a+b x)^2 (b c-a d)^3}{2 d^4}+\frac{(a+b x)^3 (b c-a d)^2}{3 d^3}-\frac{(a+b x)^4 (b c-a d)}{4 d^2}-\frac{(b c-a d)^5 \log (c+d x)}{d^6}+\frac{(a+b x)^5}{5 d}","\frac{b x (b c-a d)^4}{d^5}-\frac{(a+b x)^2 (b c-a d)^3}{2 d^4}+\frac{(a+b x)^3 (b c-a d)^2}{3 d^3}-\frac{(a+b x)^4 (b c-a d)}{4 d^2}-\frac{(b c-a d)^5 \log (c+d x)}{d^6}+\frac{(a+b x)^5}{5 d}",1,"(b*(b*c - a*d)^4*x)/d^5 - ((b*c - a*d)^3*(a + b*x)^2)/(2*d^4) + ((b*c - a*d)^2*(a + b*x)^3)/(3*d^3) - ((b*c - a*d)*(a + b*x)^4)/(4*d^2) + (a + b*x)^5/(5*d) - ((b*c - a*d)^5*Log[c + d*x])/d^6","A",3,2,29,0.06897,1,"{626, 43}"
1800,1,98,0,0.046089,"\int \frac{(a+b x)^5}{a c+(b c+a d) x+b d x^2} \, dx","Int[(a + b*x)^5/(a*c + (b*c + a*d)*x + b*d*x^2),x]","-\frac{b x (b c-a d)^3}{d^4}+\frac{(a+b x)^2 (b c-a d)^2}{2 d^3}-\frac{(a+b x)^3 (b c-a d)}{3 d^2}+\frac{(b c-a d)^4 \log (c+d x)}{d^5}+\frac{(a+b x)^4}{4 d}","-\frac{b x (b c-a d)^3}{d^4}+\frac{(a+b x)^2 (b c-a d)^2}{2 d^3}-\frac{(a+b x)^3 (b c-a d)}{3 d^2}+\frac{(b c-a d)^4 \log (c+d x)}{d^5}+\frac{(a+b x)^4}{4 d}",1,"-((b*(b*c - a*d)^3*x)/d^4) + ((b*c - a*d)^2*(a + b*x)^2)/(2*d^3) - ((b*c - a*d)*(a + b*x)^3)/(3*d^2) + (a + b*x)^4/(4*d) + ((b*c - a*d)^4*Log[c + d*x])/d^5","A",3,2,29,0.06897,1,"{626, 43}"
1801,1,74,0,0.0361576,"\int \frac{(a+b x)^4}{a c+(b c+a d) x+b d x^2} \, dx","Int[(a + b*x)^4/(a*c + (b*c + a*d)*x + b*d*x^2),x]","\frac{b x (b c-a d)^2}{d^3}-\frac{(a+b x)^2 (b c-a d)}{2 d^2}-\frac{(b c-a d)^3 \log (c+d x)}{d^4}+\frac{(a+b x)^3}{3 d}","\frac{b x (b c-a d)^2}{d^3}-\frac{(a+b x)^2 (b c-a d)}{2 d^2}-\frac{(b c-a d)^3 \log (c+d x)}{d^4}+\frac{(a+b x)^3}{3 d}",1,"(b*(b*c - a*d)^2*x)/d^3 - ((b*c - a*d)*(a + b*x)^2)/(2*d^2) + (a + b*x)^3/(3*d) - ((b*c - a*d)^3*Log[c + d*x])/d^4","A",3,2,29,0.06897,1,"{626, 43}"
1802,1,50,0,0.0254921,"\int \frac{(a+b x)^3}{a c+(b c+a d) x+b d x^2} \, dx","Int[(a + b*x)^3/(a*c + (b*c + a*d)*x + b*d*x^2),x]","-\frac{b x (b c-a d)}{d^2}+\frac{(b c-a d)^2 \log (c+d x)}{d^3}+\frac{(a+b x)^2}{2 d}","-\frac{b x (b c-a d)}{d^2}+\frac{(b c-a d)^2 \log (c+d x)}{d^3}+\frac{(a+b x)^2}{2 d}",1,"-((b*(b*c - a*d)*x)/d^2) + (a + b*x)^2/(2*d) + ((b*c - a*d)^2*Log[c + d*x])/d^3","A",3,2,29,0.06897,1,"{626, 43}"
1803,1,26,0,0.0220228,"\int \frac{(a+b x)^2}{a c+(b c+a d) x+b d x^2} \, dx","Int[(a + b*x)^2/(a*c + (b*c + a*d)*x + b*d*x^2),x]","\frac{b x}{d}-\frac{(b c-a d) \log (c+d x)}{d^2}","\frac{b x}{d}-\frac{(b c-a d) \log (c+d x)}{d^2}",1,"(b*x)/d - ((b*c - a*d)*Log[c + d*x])/d^2","A",3,2,29,0.06897,1,"{626, 43}"
1804,1,10,0,0.0050334,"\int \frac{a+b x}{a c+(b c+a d) x+b d x^2} \, dx","Int[(a + b*x)/(a*c + (b*c + a*d)*x + b*d*x^2),x]","\frac{\log (c+d x)}{d}","\frac{\log (c+d x)}{d}",1,"Log[c + d*x]/d","A",2,2,27,0.07407,1,"{626, 31}"
1805,1,36,0,0.0122863,"\int \frac{1}{a c+(b c+a d) x+b d x^2} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^(-1),x]","\frac{\log (a+b x)}{b c-a d}-\frac{\log (c+d x)}{b c-a d}","\frac{\log (a+b x)}{b c-a d}-\frac{\log (c+d x)}{b c-a d}",1,"Log[a + b*x]/(b*c - a*d) - Log[c + d*x]/(b*c - a*d)","A",3,2,21,0.09524,1,"{616, 31}"
1806,1,57,0,0.0355253,"\int \frac{1}{(a+b x) \left(a c+(b c+a d) x+b d x^2\right)} \, dx","Int[1/((a + b*x)*(a*c + (b*c + a*d)*x + b*d*x^2)),x]","-\frac{1}{(a+b x) (b c-a d)}-\frac{d \log (a+b x)}{(b c-a d)^2}+\frac{d \log (c+d x)}{(b c-a d)^2}","-\frac{1}{(a+b x) (b c-a d)}-\frac{d \log (a+b x)}{(b c-a d)^2}+\frac{d \log (c+d x)}{(b c-a d)^2}",1,"-(1/((b*c - a*d)*(a + b*x))) - (d*Log[a + b*x])/(b*c - a*d)^2 + (d*Log[c + d*x])/(b*c - a*d)^2","A",3,2,29,0.06897,1,"{626, 44}"
1807,1,82,0,0.0563078,"\int \frac{1}{(a+b x)^2 \left(a c+(b c+a d) x+b d x^2\right)} \, dx","Int[1/((a + b*x)^2*(a*c + (b*c + a*d)*x + b*d*x^2)),x]","\frac{d^2 \log (a+b x)}{(b c-a d)^3}-\frac{d^2 \log (c+d x)}{(b c-a d)^3}+\frac{d}{(a+b x) (b c-a d)^2}-\frac{1}{2 (a+b x)^2 (b c-a d)}","\frac{d^2 \log (a+b x)}{(b c-a d)^3}-\frac{d^2 \log (c+d x)}{(b c-a d)^3}+\frac{d}{(a+b x) (b c-a d)^2}-\frac{1}{2 (a+b x)^2 (b c-a d)}",1,"-1/(2*(b*c - a*d)*(a + b*x)^2) + d/((b*c - a*d)^2*(a + b*x)) + (d^2*Log[a + b*x])/(b*c - a*d)^3 - (d^2*Log[c + d*x])/(b*c - a*d)^3","A",3,2,29,0.06897,1,"{626, 44}"
1808,1,107,0,0.0712196,"\int \frac{1}{(a+b x)^3 \left(a c+(b c+a d) x+b d x^2\right)} \, dx","Int[1/((a + b*x)^3*(a*c + (b*c + a*d)*x + b*d*x^2)),x]","-\frac{d^2}{(a+b x) (b c-a d)^3}-\frac{d^3 \log (a+b x)}{(b c-a d)^4}+\frac{d^3 \log (c+d x)}{(b c-a d)^4}+\frac{d}{2 (a+b x)^2 (b c-a d)^2}-\frac{1}{3 (a+b x)^3 (b c-a d)}","-\frac{d^2}{(a+b x) (b c-a d)^3}-\frac{d^3 \log (a+b x)}{(b c-a d)^4}+\frac{d^3 \log (c+d x)}{(b c-a d)^4}+\frac{d}{2 (a+b x)^2 (b c-a d)^2}-\frac{1}{3 (a+b x)^3 (b c-a d)}",1,"-1/(3*(b*c - a*d)*(a + b*x)^3) + d/(2*(b*c - a*d)^2*(a + b*x)^2) - d^2/((b*c - a*d)^3*(a + b*x)) - (d^3*Log[a + b*x])/(b*c - a*d)^4 + (d^3*Log[c + d*x])/(b*c - a*d)^4","A",3,2,29,0.06897,1,"{626, 44}"
1809,1,130,0,0.0922863,"\int \frac{1}{(a+b x)^4 \left(a c+(b c+a d) x+b d x^2\right)} \, dx","Int[1/((a + b*x)^4*(a*c + (b*c + a*d)*x + b*d*x^2)),x]","\frac{d^3}{(a+b x) (b c-a d)^4}-\frac{d^2}{2 (a+b x)^2 (b c-a d)^3}+\frac{d^4 \log (a+b x)}{(b c-a d)^5}-\frac{d^4 \log (c+d x)}{(b c-a d)^5}+\frac{d}{3 (a+b x)^3 (b c-a d)^2}-\frac{1}{4 (a+b x)^4 (b c-a d)}","\frac{d^3}{(a+b x) (b c-a d)^4}-\frac{d^2}{2 (a+b x)^2 (b c-a d)^3}+\frac{d^4 \log (a+b x)}{(b c-a d)^5}-\frac{d^4 \log (c+d x)}{(b c-a d)^5}+\frac{d}{3 (a+b x)^3 (b c-a d)^2}-\frac{1}{4 (a+b x)^4 (b c-a d)}",1,"-1/(4*(b*c - a*d)*(a + b*x)^4) + d/(3*(b*c - a*d)^2*(a + b*x)^3) - d^2/(2*(b*c - a*d)^3*(a + b*x)^2) + d^3/((b*c - a*d)^4*(a + b*x)) + (d^4*Log[a + b*x])/(b*c - a*d)^5 - (d^4*Log[c + d*x])/(b*c - a*d)^5","A",3,2,29,0.06897,1,"{626, 44}"
1810,1,104,0,0.1047872,"\int \frac{(a+b x)^6}{\left(a c+(b c+a d) x+b d x^2\right)^2} \, dx","Int[(a + b*x)^6/(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","-\frac{2 b^3 (c+d x)^2 (b c-a d)}{d^5}+\frac{6 b^2 x (b c-a d)^2}{d^4}-\frac{(b c-a d)^4}{d^5 (c+d x)}-\frac{4 b (b c-a d)^3 \log (c+d x)}{d^5}+\frac{b^4 (c+d x)^3}{3 d^5}","-\frac{2 b^3 (c+d x)^2 (b c-a d)}{d^5}+\frac{6 b^2 x (b c-a d)^2}{d^4}-\frac{(b c-a d)^4}{d^5 (c+d x)}-\frac{4 b (b c-a d)^3 \log (c+d x)}{d^5}+\frac{b^4 (c+d x)^3}{3 d^5}",1,"(6*b^2*(b*c - a*d)^2*x)/d^4 - (b*c - a*d)^4/(d^5*(c + d*x)) - (2*b^3*(b*c - a*d)*(c + d*x)^2)/d^5 + (b^4*(c + d*x)^3)/(3*d^5) - (4*b*(b*c - a*d)^3*Log[c + d*x])/d^5","A",3,2,29,0.06897,1,"{626, 43}"
1811,1,75,0,0.0664855,"\int \frac{(a+b x)^5}{\left(a c+(b c+a d) x+b d x^2\right)^2} \, dx","Int[(a + b*x)^5/(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","-\frac{b^2 x (2 b c-3 a d)}{d^3}+\frac{(b c-a d)^3}{d^4 (c+d x)}+\frac{3 b (b c-a d)^2 \log (c+d x)}{d^4}+\frac{b^3 x^2}{2 d^2}","-\frac{b^2 x (2 b c-3 a d)}{d^3}+\frac{(b c-a d)^3}{d^4 (c+d x)}+\frac{3 b (b c-a d)^2 \log (c+d x)}{d^4}+\frac{b^3 x^2}{2 d^2}",1,"-((b^2*(2*b*c - 3*a*d)*x)/d^3) + (b^3*x^2)/(2*d^2) + (b*c - a*d)^3/(d^4*(c + d*x)) + (3*b*(b*c - a*d)^2*Log[c + d*x])/d^4","A",3,2,29,0.06897,1,"{626, 43}"
1812,1,51,0,0.0434578,"\int \frac{(a+b x)^4}{\left(a c+(b c+a d) x+b d x^2\right)^2} \, dx","Int[(a + b*x)^4/(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","-\frac{(b c-a d)^2}{d^3 (c+d x)}-\frac{2 b (b c-a d) \log (c+d x)}{d^3}+\frac{b^2 x}{d^2}","-\frac{(b c-a d)^2}{d^3 (c+d x)}-\frac{2 b (b c-a d) \log (c+d x)}{d^3}+\frac{b^2 x}{d^2}",1,"(b^2*x)/d^2 - (b*c - a*d)^2/(d^3*(c + d*x)) - (2*b*(b*c - a*d)*Log[c + d*x])/d^3","A",3,2,29,0.06897,1,"{626, 43}"
1813,1,31,0,0.0254543,"\int \frac{(a+b x)^3}{\left(a c+(b c+a d) x+b d x^2\right)^2} \, dx","Int[(a + b*x)^3/(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","\frac{b c-a d}{d^2 (c+d x)}+\frac{b \log (c+d x)}{d^2}","\frac{b c-a d}{d^2 (c+d x)}+\frac{b \log (c+d x)}{d^2}",1,"(b*c - a*d)/(d^2*(c + d*x)) + (b*Log[c + d*x])/d^2","A",3,2,29,0.06897,1,"{626, 43}"
1814,1,12,0,0.0081565,"\int \frac{(a+b x)^2}{\left(a c+(b c+a d) x+b d x^2\right)^2} \, dx","Int[(a + b*x)^2/(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","-\frac{1}{d (c+d x)}","-\frac{1}{d (c+d x)}",1,"-(1/(d*(c + d*x)))","A",2,2,29,0.06897,1,"{626, 32}"
1815,1,56,0,0.0316406,"\int \frac{a+b x}{\left(a c+(b c+a d) x+b d x^2\right)^2} \, dx","Int[(a + b*x)/(a*c + (b*c + a*d)*x + b*d*x^2)^2,x]","\frac{1}{(c+d x) (b c-a d)}+\frac{b \log (a+b x)}{(b c-a d)^2}-\frac{b \log (c+d x)}{(b c-a d)^2}","\frac{1}{(c+d x) (b c-a d)}+\frac{b \log (a+b x)}{(b c-a d)^2}-\frac{b \log (c+d x)}{(b c-a d)^2}",1,"1/((b*c - a*d)*(c + d*x)) + (b*Log[a + b*x])/(b*c - a*d)^2 - (b*Log[c + d*x])/(b*c - a*d)^2","A",3,2,27,0.07407,1,"{626, 44}"
1816,1,86,0,0.0261368,"\int \frac{1}{\left(a c+(b c+a d) x+b d x^2\right)^2} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^(-2),x]","-\frac{a d+b c+2 b d x}{(b c-a d)^2 \left(x (a d+b c)+a c+b d x^2\right)}-\frac{2 b d \log (a+b x)}{(b c-a d)^3}+\frac{2 b d \log (c+d x)}{(b c-a d)^3}","-\frac{a d+b c+2 b d x}{(b c-a d)^2 \left(x (a d+b c)+a c+b d x^2\right)}-\frac{2 b d \log (a+b x)}{(b c-a d)^3}+\frac{2 b d \log (c+d x)}{(b c-a d)^3}",1,"-((b*c + a*d + 2*b*d*x)/((b*c - a*d)^2*(a*c + (b*c + a*d)*x + b*d*x^2))) - (2*b*d*Log[a + b*x])/(b*c - a*d)^3 + (2*b*d*Log[c + d*x])/(b*c - a*d)^3","A",4,3,21,0.1429,1,"{614, 616, 31}"
1817,1,109,0,0.0778673,"\int \frac{1}{(a+b x) \left(a c+(b c+a d) x+b d x^2\right)^2} \, dx","Int[1/((a + b*x)*(a*c + (b*c + a*d)*x + b*d*x^2)^2),x]","\frac{d^2}{(c+d x) (b c-a d)^3}+\frac{3 b d^2 \log (a+b x)}{(b c-a d)^4}-\frac{3 b d^2 \log (c+d x)}{(b c-a d)^4}+\frac{2 b d}{(a+b x) (b c-a d)^3}-\frac{b}{2 (a+b x)^2 (b c-a d)^2}","\frac{d^2}{(c+d x) (b c-a d)^3}+\frac{3 b d^2 \log (a+b x)}{(b c-a d)^4}-\frac{3 b d^2 \log (c+d x)}{(b c-a d)^4}+\frac{2 b d}{(a+b x) (b c-a d)^3}-\frac{b}{2 (a+b x)^2 (b c-a d)^2}",1,"-b/(2*(b*c - a*d)^2*(a + b*x)^2) + (2*b*d)/((b*c - a*d)^3*(a + b*x)) + d^2/((b*c - a*d)^3*(c + d*x)) + (3*b*d^2*Log[a + b*x])/(b*c - a*d)^4 - (3*b*d^2*Log[c + d*x])/(b*c - a*d)^4","A",3,2,29,0.06897,1,"{626, 44}"
1818,1,133,0,0.1358288,"\int \frac{(a+b x)^8}{\left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[(a + b*x)^8/(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","-\frac{5 b^4 (c+d x)^2 (b c-a d)}{2 d^6}+\frac{10 b^3 x (b c-a d)^2}{d^5}-\frac{10 b^2 (b c-a d)^3 \log (c+d x)}{d^6}-\frac{5 b (b c-a d)^4}{d^6 (c+d x)}+\frac{(b c-a d)^5}{2 d^6 (c+d x)^2}+\frac{b^5 (c+d x)^3}{3 d^6}","-\frac{5 b^4 (c+d x)^2 (b c-a d)}{2 d^6}+\frac{10 b^3 x (b c-a d)^2}{d^5}-\frac{10 b^2 (b c-a d)^3 \log (c+d x)}{d^6}-\frac{5 b (b c-a d)^4}{d^6 (c+d x)}+\frac{(b c-a d)^5}{2 d^6 (c+d x)^2}+\frac{b^5 (c+d x)^3}{3 d^6}",1,"(10*b^3*(b*c - a*d)^2*x)/d^5 + (b*c - a*d)^5/(2*d^6*(c + d*x)^2) - (5*b*(b*c - a*d)^4)/(d^6*(c + d*x)) - (5*b^4*(b*c - a*d)*(c + d*x)^2)/(2*d^6) + (b^5*(c + d*x)^3)/(3*d^6) - (10*b^2*(b*c - a*d)^3*Log[c + d*x])/d^6","A",3,2,29,0.06897,1,"{626, 43}"
1819,1,103,0,0.0881793,"\int \frac{(a+b x)^7}{\left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[(a + b*x)^7/(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","-\frac{b^3 x (3 b c-4 a d)}{d^4}+\frac{6 b^2 (b c-a d)^2 \log (c+d x)}{d^5}+\frac{4 b (b c-a d)^3}{d^5 (c+d x)}-\frac{(b c-a d)^4}{2 d^5 (c+d x)^2}+\frac{b^4 x^2}{2 d^3}","-\frac{b^3 x (3 b c-4 a d)}{d^4}+\frac{6 b^2 (b c-a d)^2 \log (c+d x)}{d^5}+\frac{4 b (b c-a d)^3}{d^5 (c+d x)}-\frac{(b c-a d)^4}{2 d^5 (c+d x)^2}+\frac{b^4 x^2}{2 d^3}",1,"-((b^3*(3*b*c - 4*a*d)*x)/d^4) + (b^4*x^2)/(2*d^3) - (b*c - a*d)^4/(2*d^5*(c + d*x)^2) + (4*b*(b*c - a*d)^3)/(d^5*(c + d*x)) + (6*b^2*(b*c - a*d)^2*Log[c + d*x])/d^5","A",3,2,29,0.06897,1,"{626, 43}"
1820,1,78,0,0.0613338,"\int \frac{(a+b x)^6}{\left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[(a + b*x)^6/(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","-\frac{3 b^2 (b c-a d) \log (c+d x)}{d^4}-\frac{3 b (b c-a d)^2}{d^4 (c+d x)}+\frac{(b c-a d)^3}{2 d^4 (c+d x)^2}+\frac{b^3 x}{d^3}","-\frac{3 b^2 (b c-a d) \log (c+d x)}{d^4}-\frac{3 b (b c-a d)^2}{d^4 (c+d x)}+\frac{(b c-a d)^3}{2 d^4 (c+d x)^2}+\frac{b^3 x}{d^3}",1,"(b^3*x)/d^3 + (b*c - a*d)^3/(2*d^4*(c + d*x)^2) - (3*b*(b*c - a*d)^2)/(d^4*(c + d*x)) - (3*b^2*(b*c - a*d)*Log[c + d*x])/d^4","A",3,2,29,0.06897,1,"{626, 43}"
1821,1,59,0,0.0432568,"\int \frac{(a+b x)^5}{\left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[(a + b*x)^5/(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","\frac{2 b (b c-a d)}{d^3 (c+d x)}-\frac{(b c-a d)^2}{2 d^3 (c+d x)^2}+\frac{b^2 \log (c+d x)}{d^3}","\frac{2 b (b c-a d)}{d^3 (c+d x)}-\frac{(b c-a d)^2}{2 d^3 (c+d x)^2}+\frac{b^2 \log (c+d x)}{d^3}",1,"-(b*c - a*d)^2/(2*d^3*(c + d*x)^2) + (2*b*(b*c - a*d))/(d^3*(c + d*x)) + (b^2*Log[c + d*x])/d^3","A",3,2,29,0.06897,1,"{626, 43}"
1822,1,28,0,0.0093834,"\int \frac{(a+b x)^4}{\left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[(a + b*x)^4/(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","\frac{(a+b x)^2}{2 (c+d x)^2 (b c-a d)}","\frac{(a+b x)^2}{2 (c+d x)^2 (b c-a d)}",1,"(a + b*x)^2/(2*(b*c - a*d)*(c + d*x)^2)","A",2,2,29,0.06897,1,"{626, 37}"
1823,1,14,0,0.0081064,"\int \frac{(a+b x)^3}{\left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[(a + b*x)^3/(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","-\frac{1}{2 d (c+d x)^2}","-\frac{1}{2 d (c+d x)^2}",1,"-1/(2*d*(c + d*x)^2)","A",2,2,29,0.06897,1,"{626, 32}"
1824,1,82,0,0.0507484,"\int \frac{(a+b x)^2}{\left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[(a + b*x)^2/(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","\frac{b^2 \log (a+b x)}{(b c-a d)^3}-\frac{b^2 \log (c+d x)}{(b c-a d)^3}+\frac{b}{(c+d x) (b c-a d)^2}+\frac{1}{2 (c+d x)^2 (b c-a d)}","\frac{b^2 \log (a+b x)}{(b c-a d)^3}-\frac{b^2 \log (c+d x)}{(b c-a d)^3}+\frac{b}{(c+d x) (b c-a d)^2}+\frac{1}{2 (c+d x)^2 (b c-a d)}",1,"1/(2*(b*c - a*d)*(c + d*x)^2) + b/((b*c - a*d)^2*(c + d*x)) + (b^2*Log[a + b*x])/(b*c - a*d)^3 - (b^2*Log[c + d*x])/(b*c - a*d)^3","A",3,2,29,0.06897,1,"{626, 44}"
1825,1,110,0,0.0764191,"\int \frac{a+b x}{\left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[(a + b*x)/(a*c + (b*c + a*d)*x + b*d*x^2)^3,x]","-\frac{b^2}{(a+b x) (b c-a d)^3}-\frac{3 b^2 d \log (a+b x)}{(b c-a d)^4}+\frac{3 b^2 d \log (c+d x)}{(b c-a d)^4}-\frac{2 b d}{(c+d x) (b c-a d)^3}-\frac{d}{2 (c+d x)^2 (b c-a d)^2}","-\frac{b^2}{(a+b x) (b c-a d)^3}-\frac{3 b^2 d \log (a+b x)}{(b c-a d)^4}+\frac{3 b^2 d \log (c+d x)}{(b c-a d)^4}-\frac{2 b d}{(c+d x) (b c-a d)^3}-\frac{d}{2 (c+d x)^2 (b c-a d)^2}",1,"-(b^2/((b*c - a*d)^3*(a + b*x))) - d/(2*(b*c - a*d)^2*(c + d*x)^2) - (2*b*d)/((b*c - a*d)^3*(c + d*x)) - (3*b^2*d*Log[a + b*x])/(b*c - a*d)^4 + (3*b^2*d*Log[c + d*x])/(b*c - a*d)^4","A",3,2,27,0.07407,1,"{626, 44}"
1826,1,143,0,0.0486094,"\int \frac{1}{\left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[(a*c + (b*c + a*d)*x + b*d*x^2)^(-3),x]","\frac{6 b^2 d^2 \log (a+b x)}{(b c-a d)^5}-\frac{6 b^2 d^2 \log (c+d x)}{(b c-a d)^5}+\frac{3 b d (a d+b c+2 b d x)}{(b c-a d)^4 \left(x (a d+b c)+a c+b d x^2\right)}-\frac{a d+b c+2 b d x}{2 (b c-a d)^2 \left(x (a d+b c)+a c+b d x^2\right)^2}","\frac{6 b^2 d^2 \log (a+b x)}{(b c-a d)^5}-\frac{6 b^2 d^2 \log (c+d x)}{(b c-a d)^5}+\frac{3 b d (a d+b c+2 b d x)}{(b c-a d)^4 \left(x (a d+b c)+a c+b d x^2\right)}-\frac{a d+b c+2 b d x}{2 (b c-a d)^2 \left(x (a d+b c)+a c+b d x^2\right)^2}",1,"-(b*c + a*d + 2*b*d*x)/(2*(b*c - a*d)^2*(a*c + (b*c + a*d)*x + b*d*x^2)^2) + (3*b*d*(b*c + a*d + 2*b*d*x))/((b*c - a*d)^4*(a*c + (b*c + a*d)*x + b*d*x^2)) + (6*b^2*d^2*Log[a + b*x])/(b*c - a*d)^5 - (6*b^2*d^2*Log[c + d*x])/(b*c - a*d)^5","A",5,3,21,0.1429,1,"{614, 616, 31}"
1827,1,170,0,0.1599184,"\int \frac{1}{(a+b x) \left(a c+(b c+a d) x+b d x^2\right)^3} \, dx","Int[1/((a + b*x)*(a*c + (b*c + a*d)*x + b*d*x^2)^3),x]","-\frac{6 b^2 d^2}{(a+b x) (b c-a d)^5}-\frac{10 b^2 d^3 \log (a+b x)}{(b c-a d)^6}+\frac{10 b^2 d^3 \log (c+d x)}{(b c-a d)^6}+\frac{3 b^2 d}{2 (a+b x)^2 (b c-a d)^4}-\frac{b^2}{3 (a+b x)^3 (b c-a d)^3}-\frac{4 b d^3}{(c+d x) (b c-a d)^5}-\frac{d^3}{2 (c+d x)^2 (b c-a d)^4}","-\frac{6 b^2 d^2}{(a+b x) (b c-a d)^5}-\frac{10 b^2 d^3 \log (a+b x)}{(b c-a d)^6}+\frac{10 b^2 d^3 \log (c+d x)}{(b c-a d)^6}+\frac{3 b^2 d}{2 (a+b x)^2 (b c-a d)^4}-\frac{b^2}{3 (a+b x)^3 (b c-a d)^3}-\frac{4 b d^3}{(c+d x) (b c-a d)^5}-\frac{d^3}{2 (c+d x)^2 (b c-a d)^4}",1,"-b^2/(3*(b*c - a*d)^3*(a + b*x)^3) + (3*b^2*d)/(2*(b*c - a*d)^4*(a + b*x)^2) - (6*b^2*d^2)/((b*c - a*d)^5*(a + b*x)) - d^3/(2*(b*c - a*d)^4*(c + d*x)^2) - (4*b*d^3)/((b*c - a*d)^5*(c + d*x)) - (10*b^2*d^3*Log[a + b*x])/(b*c - a*d)^6 + (10*b^2*d^3*Log[c + d*x])/(b*c - a*d)^6","A",3,2,29,0.06897,1,"{626, 44}"
1828,1,39,0,0.0226517,"\int (d+e x)^4 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right) \, dx","Int[(d + e*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{1}{6} (d+e x)^6 \left(a-\frac{c d^2}{e^2}\right)+\frac{c d (d+e x)^7}{7 e^2}","\frac{1}{6} (d+e x)^6 \left(a-\frac{c d^2}{e^2}\right)+\frac{c d (d+e x)^7}{7 e^2}",1,"((a - (c*d^2)/e^2)*(d + e*x)^6)/6 + (c*d*(d + e*x)^7)/(7*e^2)","A",3,2,33,0.06061,1,"{626, 43}"
1829,1,39,0,0.0180514,"\int (d+e x)^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right) \, dx","Int[(d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{1}{5} (d+e x)^5 \left(a-\frac{c d^2}{e^2}\right)+\frac{c d (d+e x)^6}{6 e^2}","\frac{1}{5} (d+e x)^5 \left(a-\frac{c d^2}{e^2}\right)+\frac{c d (d+e x)^6}{6 e^2}",1,"((a - (c*d^2)/e^2)*(d + e*x)^5)/5 + (c*d*(d + e*x)^6)/(6*e^2)","A",3,2,33,0.06061,1,"{626, 43}"
1830,1,39,0,0.0171029,"\int (d+e x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right) \, dx","Int[(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{1}{4} (d+e x)^4 \left(a-\frac{c d^2}{e^2}\right)+\frac{c d (d+e x)^5}{5 e^2}","\frac{1}{4} (d+e x)^4 \left(a-\frac{c d^2}{e^2}\right)+\frac{c d (d+e x)^5}{5 e^2}",1,"((a - (c*d^2)/e^2)*(d + e*x)^4)/4 + (c*d*(d + e*x)^5)/(5*e^2)","A",3,2,33,0.06061,1,"{626, 43}"
1831,1,39,0,0.033846,"\int (d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right) \, dx","Int[(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{1}{3} (d+e x)^3 \left(a-\frac{c d^2}{e^2}\right)+\frac{c d (d+e x)^4}{4 e^2}","\frac{1}{3} (d+e x)^3 \left(a-\frac{c d^2}{e^2}\right)+\frac{c d (d+e x)^4}{4 e^2}",1,"((a - (c*d^2)/e^2)*(d + e*x)^3)/3 + (c*d*(d + e*x)^4)/(4*e^2)","A",3,2,31,0.06452,1,"{626, 43}"
1832,1,34,0,0.0089247,"\int \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right) \, dx","Int[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2,x]","\frac{1}{2} x^2 \left(a e^2+c d^2\right)+a d e x+\frac{1}{3} c d e x^3","\frac{1}{2} x^2 \left(a e^2+c d^2\right)+a d e x+\frac{1}{3} c d e x^3",1,"a*d*e*x + ((c*d^2 + a*e^2)*x^2)/2 + (c*d*e*x^3)/3","A",1,0,25,0,1,"{}"
1833,1,14,0,0.0079364,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{d+e x} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x),x]","a e x+\frac{1}{2} c d x^2","a e x+\frac{1}{2} c d x^2",1,"a*e*x + (c*d*x^2)/2","A",2,1,33,0.03030,1,"{24}"
1834,1,26,0,0.0281776,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^2,x]","\left(a-\frac{c d^2}{e^2}\right) \log (d+e x)+\frac{c d x}{e}","\left(a-\frac{c d^2}{e^2}\right) \log (d+e x)+\frac{c d x}{e}",1,"(c*d*x)/e + (a - (c*d^2)/e^2)*Log[d + e*x]","A",3,2,33,0.06061,1,"{24, 43}"
1835,1,33,0,0.0282534,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^3} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^3,x]","\frac{c d \log (d+e x)}{e^2}-\frac{a-\frac{c d^2}{e^2}}{d+e x}","\frac{c d \log (d+e x)}{e^2}-\frac{a-\frac{c d^2}{e^2}}{d+e x}",1,"-((a - (c*d^2)/e^2)/(d + e*x)) + (c*d*Log[d + e*x])/e^2","A",3,2,33,0.06061,1,"{24, 43}"
1836,1,35,0,0.0137279,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^4} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^4,x]","\frac{(a e+c d x)^2}{2 (d+e x)^2 \left(c d^2-a e^2\right)}","\frac{(a e+c d x)^2}{2 (d+e x)^2 \left(c d^2-a e^2\right)}",1,"(a*e + c*d*x)^2/(2*(c*d^2 - a*e^2)*(d + e*x)^2)","A",2,2,33,0.06061,1,"{24, 37}"
1837,1,39,0,0.0276398,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^5} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^5,x]","-\frac{a-\frac{c d^2}{e^2}}{3 (d+e x)^3}-\frac{c d}{2 e^2 (d+e x)^2}","-\frac{a-\frac{c d^2}{e^2}}{3 (d+e x)^3}-\frac{c d}{2 e^2 (d+e x)^2}",1,"-(a - (c*d^2)/e^2)/(3*(d + e*x)^3) - (c*d)/(2*e^2*(d + e*x)^2)","A",3,2,33,0.06061,1,"{24, 43}"
1838,1,39,0,0.0278199,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^6} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^6,x]","-\frac{a-\frac{c d^2}{e^2}}{4 (d+e x)^4}-\frac{c d}{3 e^2 (d+e x)^3}","-\frac{a-\frac{c d^2}{e^2}}{4 (d+e x)^4}-\frac{c d}{3 e^2 (d+e x)^3}",1,"-(a - (c*d^2)/e^2)/(4*(d + e*x)^4) - (c*d)/(3*e^2*(d + e*x)^3)","A",3,2,33,0.06061,1,"{24, 43}"
1839,1,77,0,0.1318667,"\int (d+e x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2 \, dx","Int[(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{c d (d+e x)^6 \left(c d^2-a e^2\right)}{3 e^3}+\frac{(d+e x)^5 \left(c d^2-a e^2\right)^2}{5 e^3}+\frac{c^2 d^2 (d+e x)^7}{7 e^3}","-\frac{c d (d+e x)^6 \left(c d^2-a e^2\right)}{3 e^3}+\frac{(d+e x)^5 \left(c d^2-a e^2\right)^2}{5 e^3}+\frac{c^2 d^2 (d+e x)^7}{7 e^3}",1,"((c*d^2 - a*e^2)^2*(d + e*x)^5)/(5*e^3) - (c*d*(c*d^2 - a*e^2)*(d + e*x)^6)/(3*e^3) + (c^2*d^2*(d + e*x)^7)/(7*e^3)","A",3,2,35,0.05714,1,"{626, 43}"
1840,1,77,0,0.0792925,"\int (d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2 \, dx","Int[(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{2 c d (d+e x)^5 \left(c d^2-a e^2\right)}{5 e^3}+\frac{(d+e x)^4 \left(c d^2-a e^2\right)^2}{4 e^3}+\frac{c^2 d^2 (d+e x)^6}{6 e^3}","-\frac{2 c d (d+e x)^5 \left(c d^2-a e^2\right)}{5 e^3}+\frac{(d+e x)^4 \left(c d^2-a e^2\right)^2}{4 e^3}+\frac{c^2 d^2 (d+e x)^6}{6 e^3}",1,"((c*d^2 - a*e^2)^2*(d + e*x)^4)/(4*e^3) - (2*c*d*(c*d^2 - a*e^2)*(d + e*x)^5)/(5*e^3) + (c^2*d^2*(d + e*x)^6)/(6*e^3)","A",3,2,33,0.06061,1,"{626, 43}"
1841,1,77,0,0.0882099,"\int \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2 \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{c d (d+e x)^4 \left(c d^2-a e^2\right)}{2 e^3}+\frac{(d+e x)^3 \left(c d^2-a e^2\right)^2}{3 e^3}+\frac{c^2 d^2 (d+e x)^5}{5 e^3}","-\frac{c d (d+e x)^4 \left(c d^2-a e^2\right)}{2 e^3}+\frac{(d+e x)^3 \left(c d^2-a e^2\right)^2}{3 e^3}+\frac{c^2 d^2 (d+e x)^5}{5 e^3}",1,"((c*d^2 - a*e^2)^2*(d + e*x)^3)/(3*e^3) - (c*d*(c*d^2 - a*e^2)*(d + e*x)^4)/(2*e^3) + (c^2*d^2*(d + e*x)^5)/(5*e^3)","A",3,2,27,0.07407,1,"{610, 43}"
1842,1,54,0,0.0490563,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{d+e x} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x),x]","\frac{\left(c d^2-a e^2\right) (a e+c d x)^3}{3 c^2 d^2}+\frac{e (a e+c d x)^4}{4 c^2 d^2}","\frac{\left(c d^2-a e^2\right) (a e+c d x)^3}{3 c^2 d^2}+\frac{e (a e+c d x)^4}{4 c^2 d^2}",1,"((c*d^2 - a*e^2)*(a*e + c*d*x)^3)/(3*c^2*d^2) + (e*(a*e + c*d*x)^4)/(4*c^2*d^2)","A",3,2,35,0.05714,1,"{626, 43}"
1843,1,20,0,0.012909,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^2,x]","\frac{(a e+c d x)^3}{3 c d}","\frac{(a e+c d x)^3}{3 c d}",1,"(a*e + c*d*x)^3/(3*c*d)","A",2,2,35,0.05714,1,"{626, 32}"
1844,1,62,0,0.0391704,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^3} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^3,x]","-\frac{c d x \left(c d^2-a e^2\right)}{e^2}+\frac{\left(c d^2-a e^2\right)^2 \log (d+e x)}{e^3}+\frac{(a e+c d x)^2}{2 e}","-\frac{c d x \left(c d^2-a e^2\right)}{e^2}+\frac{\left(c d^2-a e^2\right)^2 \log (d+e x)}{e^3}+\frac{(a e+c d x)^2}{2 e}",1,"-((c*d*(c*d^2 - a*e^2)*x)/e^2) + (a*e + c*d*x)^2/(2*e) + ((c*d^2 - a*e^2)^2*Log[d + e*x])/e^3","A",3,2,35,0.05714,1,"{626, 43}"
1845,1,63,0,0.0520952,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^4} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^4,x]","-\frac{\left(c d^2-a e^2\right)^2}{e^3 (d+e x)}-\frac{2 c d \left(c d^2-a e^2\right) \log (d+e x)}{e^3}+\frac{c^2 d^2 x}{e^2}","-\frac{\left(c d^2-a e^2\right)^2}{e^3 (d+e x)}-\frac{2 c d \left(c d^2-a e^2\right) \log (d+e x)}{e^3}+\frac{c^2 d^2 x}{e^2}",1,"(c^2*d^2*x)/e^2 - (c*d^2 - a*e^2)^2/(e^3*(d + e*x)) - (2*c*d*(c*d^2 - a*e^2)*Log[d + e*x])/e^3","A",3,2,35,0.05714,1,"{626, 43}"
1846,1,71,0,0.0519226,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^5} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^5,x]","\frac{2 c d \left(c d^2-a e^2\right)}{e^3 (d+e x)}-\frac{\left(c d^2-a e^2\right)^2}{2 e^3 (d+e x)^2}+\frac{c^2 d^2 \log (d+e x)}{e^3}","\frac{2 c d \left(c d^2-a e^2\right)}{e^3 (d+e x)}-\frac{\left(c d^2-a e^2\right)^2}{2 e^3 (d+e x)^2}+\frac{c^2 d^2 \log (d+e x)}{e^3}",1,"-(c*d^2 - a*e^2)^2/(2*e^3*(d + e*x)^2) + (2*c*d*(c*d^2 - a*e^2))/(e^3*(d + e*x)) + (c^2*d^2*Log[d + e*x])/e^3","A",3,2,35,0.05714,1,"{626, 43}"
1847,1,35,0,0.0141029,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^6} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^6,x]","\frac{(a e+c d x)^3}{3 (d+e x)^3 \left(c d^2-a e^2\right)}","\frac{(a e+c d x)^3}{3 (d+e x)^3 \left(c d^2-a e^2\right)}",1,"(a*e + c*d*x)^3/(3*(c*d^2 - a*e^2)*(d + e*x)^3)","A",2,2,35,0.05714,1,"{626, 37}"
1848,1,77,0,0.0498161,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^7} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^7,x]","\frac{2 c d \left(c d^2-a e^2\right)}{3 e^3 (d+e x)^3}-\frac{\left(c d^2-a e^2\right)^2}{4 e^3 (d+e x)^4}-\frac{c^2 d^2}{2 e^3 (d+e x)^2}","\frac{2 c d \left(c d^2-a e^2\right)}{3 e^3 (d+e x)^3}-\frac{\left(c d^2-a e^2\right)^2}{4 e^3 (d+e x)^4}-\frac{c^2 d^2}{2 e^3 (d+e x)^2}",1,"-(c*d^2 - a*e^2)^2/(4*e^3*(d + e*x)^4) + (2*c*d*(c*d^2 - a*e^2))/(3*e^3*(d + e*x)^3) - (c^2*d^2)/(2*e^3*(d + e*x)^2)","A",3,2,35,0.05714,1,"{626, 43}"
1849,1,77,0,0.04866,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^8} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^8,x]","\frac{c d \left(c d^2-a e^2\right)}{2 e^3 (d+e x)^4}-\frac{\left(c d^2-a e^2\right)^2}{5 e^3 (d+e x)^5}-\frac{c^2 d^2}{3 e^3 (d+e x)^3}","\frac{c d \left(c d^2-a e^2\right)}{2 e^3 (d+e x)^4}-\frac{\left(c d^2-a e^2\right)^2}{5 e^3 (d+e x)^5}-\frac{c^2 d^2}{3 e^3 (d+e x)^3}",1,"-(c*d^2 - a*e^2)^2/(5*e^3*(d + e*x)^5) + (c*d*(c*d^2 - a*e^2))/(2*e^3*(d + e*x)^4) - (c^2*d^2)/(3*e^3*(d + e*x)^3)","A",3,2,35,0.05714,1,"{626, 43}"
1850,1,77,0,0.0491455,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^9} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^9,x]","\frac{2 c d \left(c d^2-a e^2\right)}{5 e^3 (d+e x)^5}-\frac{\left(c d^2-a e^2\right)^2}{6 e^3 (d+e x)^6}-\frac{c^2 d^2}{4 e^3 (d+e x)^4}","\frac{2 c d \left(c d^2-a e^2\right)}{5 e^3 (d+e x)^5}-\frac{\left(c d^2-a e^2\right)^2}{6 e^3 (d+e x)^6}-\frac{c^2 d^2}{4 e^3 (d+e x)^4}",1,"-(c*d^2 - a*e^2)^2/(6*e^3*(d + e*x)^6) + (2*c*d*(c*d^2 - a*e^2))/(5*e^3*(d + e*x)^5) - (c^2*d^2)/(4*e^3*(d + e*x)^4)","A",3,2,35,0.05714,1,"{626, 43}"
1851,1,111,0,0.2332565,"\int (d+e x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3 \, dx","Int[(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{3 c^2 d^2 (d+e x)^8 \left(c d^2-a e^2\right)}{8 e^4}+\frac{3 c d (d+e x)^7 \left(c d^2-a e^2\right)^2}{7 e^4}-\frac{(d+e x)^6 \left(c d^2-a e^2\right)^3}{6 e^4}+\frac{c^3 d^3 (d+e x)^9}{9 e^4}","-\frac{3 c^2 d^2 (d+e x)^8 \left(c d^2-a e^2\right)}{8 e^4}+\frac{3 c d (d+e x)^7 \left(c d^2-a e^2\right)^2}{7 e^4}-\frac{(d+e x)^6 \left(c d^2-a e^2\right)^3}{6 e^4}+\frac{c^3 d^3 (d+e x)^9}{9 e^4}",1,"-((c*d^2 - a*e^2)^3*(d + e*x)^6)/(6*e^4) + (3*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^7)/(7*e^4) - (3*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^8)/(8*e^4) + (c^3*d^3*(d + e*x)^9)/(9*e^4)","A",3,2,35,0.05714,1,"{626, 43}"
1852,1,111,0,0.1603259,"\int (d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3 \, dx","Int[(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{3 c^2 d^2 (d+e x)^7 \left(c d^2-a e^2\right)}{7 e^4}+\frac{c d (d+e x)^6 \left(c d^2-a e^2\right)^2}{2 e^4}-\frac{(d+e x)^5 \left(c d^2-a e^2\right)^3}{5 e^4}+\frac{c^3 d^3 (d+e x)^8}{8 e^4}","-\frac{3 c^2 d^2 (d+e x)^7 \left(c d^2-a e^2\right)}{7 e^4}+\frac{c d (d+e x)^6 \left(c d^2-a e^2\right)^2}{2 e^4}-\frac{(d+e x)^5 \left(c d^2-a e^2\right)^3}{5 e^4}+\frac{c^3 d^3 (d+e x)^8}{8 e^4}",1,"-((c*d^2 - a*e^2)^3*(d + e*x)^5)/(5*e^4) + (c*d*(c*d^2 - a*e^2)^2*(d + e*x)^6)/(2*e^4) - (3*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^7)/(7*e^4) + (c^3*d^3*(d + e*x)^8)/(8*e^4)","A",3,2,33,0.06061,1,"{626, 43}"
1853,1,111,0,0.1486125,"\int \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3 \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{c^2 d^2 (d+e x)^6 \left(c d^2-a e^2\right)}{2 e^4}+\frac{3 c d (d+e x)^5 \left(c d^2-a e^2\right)^2}{5 e^4}-\frac{(d+e x)^4 \left(c d^2-a e^2\right)^3}{4 e^4}+\frac{c^3 d^3 (d+e x)^7}{7 e^4}","-\frac{c^2 d^2 (d+e x)^6 \left(c d^2-a e^2\right)}{2 e^4}+\frac{3 c d (d+e x)^5 \left(c d^2-a e^2\right)^2}{5 e^4}-\frac{(d+e x)^4 \left(c d^2-a e^2\right)^3}{4 e^4}+\frac{c^3 d^3 (d+e x)^7}{7 e^4}",1,"-((c*d^2 - a*e^2)^3*(d + e*x)^4)/(4*e^4) + (3*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^5)/(5*e^4) - (c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^6)/(2*e^4) + (c^3*d^3*(d + e*x)^7)/(7*e^4)","A",3,2,27,0.07407,1,"{610, 43}"
1854,1,91,0,0.0992741,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{d+e x} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x),x]","\frac{e^2 (a e+c d x)^6}{6 c^3 d^3}+\frac{2 e \left(c d^2-a e^2\right) (a e+c d x)^5}{5 c^3 d^3}+\frac{\left(c d^2-a e^2\right)^2 (a e+c d x)^4}{4 c^3 d^3}","\frac{e^2 (a e+c d x)^6}{6 c^3 d^3}+\frac{2 e \left(c d^2-a e^2\right) (a e+c d x)^5}{5 c^3 d^3}+\frac{\left(c d^2-a e^2\right)^2 (a e+c d x)^4}{4 c^3 d^3}",1,"((c*d^2 - a*e^2)^2*(a*e + c*d*x)^4)/(4*c^3*d^3) + (2*e*(c*d^2 - a*e^2)*(a*e + c*d*x)^5)/(5*c^3*d^3) + (e^2*(a*e + c*d*x)^6)/(6*c^3*d^3)","A",3,2,35,0.05714,1,"{626, 43}"
1855,1,54,0,0.0312005,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^2,x]","\frac{\left(c d^2-a e^2\right) (a e+c d x)^4}{4 c^2 d^2}+\frac{e (a e+c d x)^5}{5 c^2 d^2}","\frac{\left(c d^2-a e^2\right) (a e+c d x)^4}{4 c^2 d^2}+\frac{e (a e+c d x)^5}{5 c^2 d^2}",1,"((c*d^2 - a*e^2)*(a*e + c*d*x)^4)/(4*c^2*d^2) + (e*(a*e + c*d*x)^5)/(5*c^2*d^2)","A",3,2,35,0.05714,1,"{626, 43}"
1856,1,20,0,0.0133856,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^3} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^3,x]","\frac{(a e+c d x)^4}{4 c d}","\frac{(a e+c d x)^4}{4 c d}",1,"(a*e + c*d*x)^4/(4*c*d)","A",2,2,35,0.05714,1,"{626, 32}"
1857,1,89,0,0.0486573,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^4} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^4,x]","\frac{c d x \left(c d^2-a e^2\right)^2}{e^3}+\frac{1}{2} \left(a-\frac{c d^2}{e^2}\right) (a e+c d x)^2-\frac{\left(c d^2-a e^2\right)^3 \log (d+e x)}{e^4}+\frac{(a e+c d x)^3}{3 e}","\frac{c d x \left(c d^2-a e^2\right)^2}{e^3}+\frac{1}{2} \left(a-\frac{c d^2}{e^2}\right) (a e+c d x)^2-\frac{\left(c d^2-a e^2\right)^3 \log (d+e x)}{e^4}+\frac{(a e+c d x)^3}{3 e}",1,"(c*d*(c*d^2 - a*e^2)^2*x)/e^3 + ((a - (c*d^2)/e^2)*(a*e + c*d*x)^2)/2 + (a*e + c*d*x)^3/(3*e) - ((c*d^2 - a*e^2)^3*Log[d + e*x])/e^4","A",3,2,35,0.05714,1,"{626, 43}"
1858,1,94,0,0.0814272,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^5} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^5,x]","-\frac{c^2 d^2 x \left(2 c d^2-3 a e^2\right)}{e^3}+\frac{\left(c d^2-a e^2\right)^3}{e^4 (d+e x)}+\frac{3 c d \left(c d^2-a e^2\right)^2 \log (d+e x)}{e^4}+\frac{c^3 d^3 x^2}{2 e^2}","-\frac{c^2 d^2 x \left(2 c d^2-3 a e^2\right)}{e^3}+\frac{\left(c d^2-a e^2\right)^3}{e^4 (d+e x)}+\frac{3 c d \left(c d^2-a e^2\right)^2 \log (d+e x)}{e^4}+\frac{c^3 d^3 x^2}{2 e^2}",1,"-((c^2*d^2*(2*c*d^2 - 3*a*e^2)*x)/e^3) + (c^3*d^3*x^2)/(2*e^2) + (c*d^2 - a*e^2)^3/(e^4*(d + e*x)) + (3*c*d*(c*d^2 - a*e^2)^2*Log[d + e*x])/e^4","A",3,2,35,0.05714,1,"{626, 43}"
1859,1,97,0,0.0737391,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^6} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^6,x]","-\frac{3 c^2 d^2 \left(c d^2-a e^2\right) \log (d+e x)}{e^4}-\frac{3 c d \left(c d^2-a e^2\right)^2}{e^4 (d+e x)}+\frac{\left(c d^2-a e^2\right)^3}{2 e^4 (d+e x)^2}+\frac{c^3 d^3 x}{e^3}","-\frac{3 c^2 d^2 \left(c d^2-a e^2\right) \log (d+e x)}{e^4}-\frac{3 c d \left(c d^2-a e^2\right)^2}{e^4 (d+e x)}+\frac{\left(c d^2-a e^2\right)^3}{2 e^4 (d+e x)^2}+\frac{c^3 d^3 x}{e^3}",1,"(c^3*d^3*x)/e^3 + (c*d^2 - a*e^2)^3/(2*e^4*(d + e*x)^2) - (3*c*d*(c*d^2 - a*e^2)^2)/(e^4*(d + e*x)) - (3*c^2*d^2*(c*d^2 - a*e^2)*Log[d + e*x])/e^4","A",3,2,35,0.05714,1,"{626, 43}"
1860,1,105,0,0.0750259,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^7} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^7,x]","\frac{3 c^2 d^2 \left(c d^2-a e^2\right)}{e^4 (d+e x)}-\frac{3 c d \left(c d^2-a e^2\right)^2}{2 e^4 (d+e x)^2}+\frac{\left(c d^2-a e^2\right)^3}{3 e^4 (d+e x)^3}+\frac{c^3 d^3 \log (d+e x)}{e^4}","\frac{3 c^2 d^2 \left(c d^2-a e^2\right)}{e^4 (d+e x)}-\frac{3 c d \left(c d^2-a e^2\right)^2}{2 e^4 (d+e x)^2}+\frac{\left(c d^2-a e^2\right)^3}{3 e^4 (d+e x)^3}+\frac{c^3 d^3 \log (d+e x)}{e^4}",1,"(c*d^2 - a*e^2)^3/(3*e^4*(d + e*x)^3) - (3*c*d*(c*d^2 - a*e^2)^2)/(2*e^4*(d + e*x)^2) + (3*c^2*d^2*(c*d^2 - a*e^2))/(e^4*(d + e*x)) + (c^3*d^3*Log[d + e*x])/e^4","A",3,2,35,0.05714,1,"{626, 43}"
1861,1,35,0,0.0152227,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^8} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^8,x]","\frac{(a e+c d x)^4}{4 (d+e x)^4 \left(c d^2-a e^2\right)}","\frac{(a e+c d x)^4}{4 (d+e x)^4 \left(c d^2-a e^2\right)}",1,"(a*e + c*d*x)^4/(4*(c*d^2 - a*e^2)*(d + e*x)^4)","A",2,2,35,0.05714,1,"{626, 37}"
1862,1,73,0,0.0262825,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^9} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^9,x]","\frac{c d (a e+c d x)^4}{20 (d+e x)^4 \left(c d^2-a e^2\right)^2}+\frac{(a e+c d x)^4}{5 (d+e x)^5 \left(c d^2-a e^2\right)}","\frac{c d (a e+c d x)^4}{20 (d+e x)^4 \left(c d^2-a e^2\right)^2}+\frac{(a e+c d x)^4}{5 (d+e x)^5 \left(c d^2-a e^2\right)}",1,"(a*e + c*d*x)^4/(5*(c*d^2 - a*e^2)*(d + e*x)^5) + (c*d*(a*e + c*d*x)^4)/(20*(c*d^2 - a*e^2)^2*(d + e*x)^4)","A",3,3,35,0.08571,1,"{626, 45, 37}"
1863,1,111,0,0.071321,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^{10}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^10,x]","\frac{3 c^2 d^2 \left(c d^2-a e^2\right)}{4 e^4 (d+e x)^4}-\frac{3 c d \left(c d^2-a e^2\right)^2}{5 e^4 (d+e x)^5}+\frac{\left(c d^2-a e^2\right)^3}{6 e^4 (d+e x)^6}-\frac{c^3 d^3}{3 e^4 (d+e x)^3}","\frac{3 c^2 d^2 \left(c d^2-a e^2\right)}{4 e^4 (d+e x)^4}-\frac{3 c d \left(c d^2-a e^2\right)^2}{5 e^4 (d+e x)^5}+\frac{\left(c d^2-a e^2\right)^3}{6 e^4 (d+e x)^6}-\frac{c^3 d^3}{3 e^4 (d+e x)^3}",1,"(c*d^2 - a*e^2)^3/(6*e^4*(d + e*x)^6) - (3*c*d*(c*d^2 - a*e^2)^2)/(5*e^4*(d + e*x)^5) + (3*c^2*d^2*(c*d^2 - a*e^2))/(4*e^4*(d + e*x)^4) - (c^3*d^3)/(3*e^4*(d + e*x)^3)","A",3,2,35,0.05714,1,"{626, 43}"
1864,1,111,0,0.0682159,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^{11}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^11,x]","\frac{3 c^2 d^2 \left(c d^2-a e^2\right)}{5 e^4 (d+e x)^5}-\frac{c d \left(c d^2-a e^2\right)^2}{2 e^4 (d+e x)^6}+\frac{\left(c d^2-a e^2\right)^3}{7 e^4 (d+e x)^7}-\frac{c^3 d^3}{4 e^4 (d+e x)^4}","\frac{3 c^2 d^2 \left(c d^2-a e^2\right)}{5 e^4 (d+e x)^5}-\frac{c d \left(c d^2-a e^2\right)^2}{2 e^4 (d+e x)^6}+\frac{\left(c d^2-a e^2\right)^3}{7 e^4 (d+e x)^7}-\frac{c^3 d^3}{4 e^4 (d+e x)^4}",1,"(c*d^2 - a*e^2)^3/(7*e^4*(d + e*x)^7) - (c*d*(c*d^2 - a*e^2)^2)/(2*e^4*(d + e*x)^6) + (3*c^2*d^2*(c*d^2 - a*e^2))/(5*e^4*(d + e*x)^5) - (c^3*d^3)/(4*e^4*(d + e*x)^4)","A",3,2,35,0.05714,1,"{626, 43}"
1865,1,131,0,0.0674149,"\int \frac{(d+e x)^5}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{e x \left(c d^2-a e^2\right)^3}{c^4 d^4}+\frac{(d+e x)^2 \left(c d^2-a e^2\right)^2}{2 c^3 d^3}+\frac{(d+e x)^3 \left(c d^2-a e^2\right)}{3 c^2 d^2}+\frac{\left(c d^2-a e^2\right)^4 \log (a e+c d x)}{c^5 d^5}+\frac{(d+e x)^4}{4 c d}","\frac{e x \left(c d^2-a e^2\right)^3}{c^4 d^4}+\frac{(d+e x)^2 \left(c d^2-a e^2\right)^2}{2 c^3 d^3}+\frac{(d+e x)^3 \left(c d^2-a e^2\right)}{3 c^2 d^2}+\frac{\left(c d^2-a e^2\right)^4 \log (a e+c d x)}{c^5 d^5}+\frac{(d+e x)^4}{4 c d}",1,"(e*(c*d^2 - a*e^2)^3*x)/(c^4*d^4) + ((c*d^2 - a*e^2)^2*(d + e*x)^2)/(2*c^3*d^3) + ((c*d^2 - a*e^2)*(d + e*x)^3)/(3*c^2*d^2) + (d + e*x)^4/(4*c*d) + ((c*d^2 - a*e^2)^4*Log[a*e + c*d*x])/(c^5*d^5)","A",3,2,35,0.05714,1,"{626, 43}"
1866,1,100,0,0.0452864,"\int \frac{(d+e x)^4}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{e x \left(c d^2-a e^2\right)^2}{c^3 d^3}+\frac{(d+e x)^2 \left(c d^2-a e^2\right)}{2 c^2 d^2}+\frac{\left(c d^2-a e^2\right)^3 \log (a e+c d x)}{c^4 d^4}+\frac{(d+e x)^3}{3 c d}","\frac{e x \left(c d^2-a e^2\right)^2}{c^3 d^3}+\frac{(d+e x)^2 \left(c d^2-a e^2\right)}{2 c^2 d^2}+\frac{\left(c d^2-a e^2\right)^3 \log (a e+c d x)}{c^4 d^4}+\frac{(d+e x)^3}{3 c d}",1,"(e*(c*d^2 - a*e^2)^2*x)/(c^3*d^3) + ((c*d^2 - a*e^2)*(d + e*x)^2)/(2*c^2*d^2) + (d + e*x)^3/(3*c*d) + ((c*d^2 - a*e^2)^3*Log[a*e + c*d*x])/(c^4*d^4)","A",3,2,35,0.05714,1,"{626, 43}"
1867,1,69,0,0.0331473,"\int \frac{(d+e x)^3}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{e x \left(c d^2-a e^2\right)}{c^2 d^2}+\frac{\left(c d^2-a e^2\right)^2 \log (a e+c d x)}{c^3 d^3}+\frac{(d+e x)^2}{2 c d}","\frac{e x \left(c d^2-a e^2\right)}{c^2 d^2}+\frac{\left(c d^2-a e^2\right)^2 \log (a e+c d x)}{c^3 d^3}+\frac{(d+e x)^2}{2 c d}",1,"(e*(c*d^2 - a*e^2)*x)/(c^2*d^2) + (d + e*x)^2/(2*c*d) + ((c*d^2 - a*e^2)^2*Log[a*e + c*d*x])/(c^3*d^3)","A",3,2,35,0.05714,1,"{626, 43}"
1868,1,38,0,0.0323342,"\int \frac{(d+e x)^2}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{\left(c d^2-a e^2\right) \log (a e+c d x)}{c^2 d^2}+\frac{e x}{c d}","\frac{\left(c d^2-a e^2\right) \log (a e+c d x)}{c^2 d^2}+\frac{e x}{c d}",1,"(e*x)/(c*d) + ((c*d^2 - a*e^2)*Log[a*e + c*d*x])/(c^2*d^2)","A",3,2,35,0.05714,1,"{626, 43}"
1869,1,16,0,0.0061629,"\int \frac{d+e x}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{\log (a e+c d x)}{c d}","\frac{\log (a e+c d x)}{c d}",1,"Log[a*e + c*d*x]/(c*d)","A",2,2,33,0.06061,1,"{626, 31}"
1870,1,47,0,0.0154168,"\int \frac{1}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(-1),x]","\frac{\log (a e+c d x)}{c d^2-a e^2}-\frac{\log (d+e x)}{c d^2-a e^2}","\frac{\log (a e+c d x)}{c d^2-a e^2}-\frac{\log (d+e x)}{c d^2-a e^2}",1,"Log[a*e + c*d*x]/(c*d^2 - a*e^2) - Log[d + e*x]/(c*d^2 - a*e^2)","A",3,2,27,0.07407,1,"{616, 31}"
1871,1,73,0,0.0505175,"\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)} \, dx","Int[1/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)),x]","\frac{1}{(d+e x) \left(c d^2-a e^2\right)}+\frac{c d \log (a e+c d x)}{\left(c d^2-a e^2\right)^2}-\frac{c d \log (d+e x)}{\left(c d^2-a e^2\right)^2}","\frac{1}{(d+e x) \left(c d^2-a e^2\right)}+\frac{c d \log (a e+c d x)}{\left(c d^2-a e^2\right)^2}-\frac{c d \log (d+e x)}{\left(c d^2-a e^2\right)^2}",1,"1/((c*d^2 - a*e^2)*(d + e*x)) + (c*d*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^2 - (c*d*Log[d + e*x])/(c*d^2 - a*e^2)^2","A",3,2,35,0.05714,1,"{626, 44}"
1872,1,108,0,0.0720214,"\int \frac{1}{(d+e x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)} \, dx","Int[1/((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)),x]","\frac{c^2 d^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^3}-\frac{c^2 d^2 \log (d+e x)}{\left(c d^2-a e^2\right)^3}+\frac{c d}{(d+e x) \left(c d^2-a e^2\right)^2}+\frac{1}{2 (d+e x)^2 \left(c d^2-a e^2\right)}","\frac{c^2 d^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^3}-\frac{c^2 d^2 \log (d+e x)}{\left(c d^2-a e^2\right)^3}+\frac{c d}{(d+e x) \left(c d^2-a e^2\right)^2}+\frac{1}{2 (d+e x)^2 \left(c d^2-a e^2\right)}",1,"1/(2*(c*d^2 - a*e^2)*(d + e*x)^2) + (c*d)/((c*d^2 - a*e^2)^2*(d + e*x)) + (c^2*d^2*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^3 - (c^2*d^2*Log[d + e*x])/(c*d^2 - a*e^2)^3","A",3,2,35,0.05714,1,"{626, 44}"
1873,1,139,0,0.0989909,"\int \frac{1}{(d+e x)^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)} \, dx","Int[1/((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)),x]","\frac{c^2 d^2}{(d+e x) \left(c d^2-a e^2\right)^3}+\frac{c^3 d^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^4}-\frac{c^3 d^3 \log (d+e x)}{\left(c d^2-a e^2\right)^4}+\frac{c d}{2 (d+e x)^2 \left(c d^2-a e^2\right)^2}+\frac{1}{3 (d+e x)^3 \left(c d^2-a e^2\right)}","\frac{c^2 d^2}{(d+e x) \left(c d^2-a e^2\right)^3}+\frac{c^3 d^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^4}-\frac{c^3 d^3 \log (d+e x)}{\left(c d^2-a e^2\right)^4}+\frac{c d}{2 (d+e x)^2 \left(c d^2-a e^2\right)^2}+\frac{1}{3 (d+e x)^3 \left(c d^2-a e^2\right)}",1,"1/(3*(c*d^2 - a*e^2)*(d + e*x)^3) + (c*d)/(2*(c*d^2 - a*e^2)^2*(d + e*x)^2) + (c^2*d^2)/((c*d^2 - a*e^2)^3*(d + e*x)) + (c^3*d^3*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^4 - (c^3*d^3*Log[d + e*x])/(c*d^2 - a*e^2)^4","A",3,2,35,0.05714,1,"{626, 44}"
1874,1,219,0,0.2752304,"\int \frac{(d+e x)^8}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^8/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{e^6 (a e+c d x)^5}{5 c^7 d^7}+\frac{3 e^5 \left(c d^2-a e^2\right) (a e+c d x)^4}{2 c^7 d^7}+\frac{5 e^4 \left(c d^2-a e^2\right)^2 (a e+c d x)^3}{c^7 d^7}+\frac{10 e^3 \left(c d^2-a e^2\right)^3 (a e+c d x)^2}{c^7 d^7}+\frac{15 e^2 x \left(c d^2-a e^2\right)^4}{c^6 d^6}-\frac{\left(c d^2-a e^2\right)^6}{c^7 d^7 (a e+c d x)}+\frac{6 e \left(c d^2-a e^2\right)^5 \log (a e+c d x)}{c^7 d^7}","\frac{e^6 (a e+c d x)^5}{5 c^7 d^7}+\frac{3 e^5 \left(c d^2-a e^2\right) (a e+c d x)^4}{2 c^7 d^7}+\frac{5 e^4 \left(c d^2-a e^2\right)^2 (a e+c d x)^3}{c^7 d^7}+\frac{10 e^3 \left(c d^2-a e^2\right)^3 (a e+c d x)^2}{c^7 d^7}+\frac{15 e^2 x \left(c d^2-a e^2\right)^4}{c^6 d^6}-\frac{\left(c d^2-a e^2\right)^6}{c^7 d^7 (a e+c d x)}+\frac{6 e \left(c d^2-a e^2\right)^5 \log (a e+c d x)}{c^7 d^7}",1,"(15*e^2*(c*d^2 - a*e^2)^4*x)/(c^6*d^6) - (c*d^2 - a*e^2)^6/(c^7*d^7*(a*e + c*d*x)) + (10*e^3*(c*d^2 - a*e^2)^3*(a*e + c*d*x)^2)/(c^7*d^7) + (5*e^4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^3)/(c^7*d^7) + (3*e^5*(c*d^2 - a*e^2)*(a*e + c*d*x)^4)/(2*c^7*d^7) + (e^6*(a*e + c*d*x)^5)/(5*c^7*d^7) + (6*e*(c*d^2 - a*e^2)^5*Log[a*e + c*d*x])/(c^7*d^7)","A",3,2,35,0.05714,1,"{626, 43}"
1875,1,184,0,0.1972957,"\int \frac{(d+e x)^7}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^7/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{e^5 (a e+c d x)^4}{4 c^6 d^6}+\frac{5 e^4 \left(c d^2-a e^2\right) (a e+c d x)^3}{3 c^6 d^6}+\frac{5 e^3 \left(c d^2-a e^2\right)^2 (a e+c d x)^2}{c^6 d^6}+\frac{10 e^2 x \left(c d^2-a e^2\right)^3}{c^5 d^5}-\frac{\left(c d^2-a e^2\right)^5}{c^6 d^6 (a e+c d x)}+\frac{5 e \left(c d^2-a e^2\right)^4 \log (a e+c d x)}{c^6 d^6}","\frac{e^5 (a e+c d x)^4}{4 c^6 d^6}+\frac{5 e^4 \left(c d^2-a e^2\right) (a e+c d x)^3}{3 c^6 d^6}+\frac{5 e^3 \left(c d^2-a e^2\right)^2 (a e+c d x)^2}{c^6 d^6}+\frac{10 e^2 x \left(c d^2-a e^2\right)^3}{c^5 d^5}-\frac{\left(c d^2-a e^2\right)^5}{c^6 d^6 (a e+c d x)}+\frac{5 e \left(c d^2-a e^2\right)^4 \log (a e+c d x)}{c^6 d^6}",1,"(10*e^2*(c*d^2 - a*e^2)^3*x)/(c^5*d^5) - (c*d^2 - a*e^2)^5/(c^6*d^6*(a*e + c*d*x)) + (5*e^3*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^2)/(c^6*d^6) + (5*e^4*(c*d^2 - a*e^2)*(a*e + c*d*x)^3)/(3*c^6*d^6) + (e^5*(a*e + c*d*x)^4)/(4*c^6*d^6) + (5*e*(c*d^2 - a*e^2)^4*Log[a*e + c*d*x])/(c^6*d^6)","A",3,2,35,0.05714,1,"{626, 43}"
1876,1,145,0,0.1518507,"\int \frac{(d+e x)^6}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^6/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{e^2 x \left(3 a^2 e^4-8 a c d^2 e^2+6 c^2 d^4\right)}{c^4 d^4}+\frac{e^3 x^2 \left(2 c d^2-a e^2\right)}{c^3 d^3}-\frac{\left(c d^2-a e^2\right)^4}{c^5 d^5 (a e+c d x)}+\frac{4 e \left(c d^2-a e^2\right)^3 \log (a e+c d x)}{c^5 d^5}+\frac{e^4 x^3}{3 c^2 d^2}","\frac{e^2 x \left(3 a^2 e^4-8 a c d^2 e^2+6 c^2 d^4\right)}{c^4 d^4}+\frac{e^3 x^2 \left(2 c d^2-a e^2\right)}{c^3 d^3}-\frac{\left(c d^2-a e^2\right)^4}{c^5 d^5 (a e+c d x)}+\frac{4 e \left(c d^2-a e^2\right)^3 \log (a e+c d x)}{c^5 d^5}+\frac{e^4 x^3}{3 c^2 d^2}",1,"(e^2*(6*c^2*d^4 - 8*a*c*d^2*e^2 + 3*a^2*e^4)*x)/(c^4*d^4) + (e^3*(2*c*d^2 - a*e^2)*x^2)/(c^3*d^3) + (e^4*x^3)/(3*c^2*d^2) - (c*d^2 - a*e^2)^4/(c^5*d^5*(a*e + c*d*x)) + (4*e*(c*d^2 - a*e^2)^3*Log[a*e + c*d*x])/(c^5*d^5)","A",3,2,35,0.05714,1,"{626, 43}"
1877,1,105,0,0.0928664,"\int \frac{(d+e x)^5}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{e^2 x \left(3 c d^2-2 a e^2\right)}{c^3 d^3}-\frac{\left(c d^2-a e^2\right)^3}{c^4 d^4 (a e+c d x)}+\frac{3 e \left(c d^2-a e^2\right)^2 \log (a e+c d x)}{c^4 d^4}+\frac{e^3 x^2}{2 c^2 d^2}","\frac{e^2 x \left(3 c d^2-2 a e^2\right)}{c^3 d^3}-\frac{\left(c d^2-a e^2\right)^3}{c^4 d^4 (a e+c d x)}+\frac{3 e \left(c d^2-a e^2\right)^2 \log (a e+c d x)}{c^4 d^4}+\frac{e^3 x^2}{2 c^2 d^2}",1,"(e^2*(3*c*d^2 - 2*a*e^2)*x)/(c^3*d^3) + (e^3*x^2)/(2*c^2*d^2) - (c*d^2 - a*e^2)^3/(c^4*d^4*(a*e + c*d*x)) + (3*e*(c*d^2 - a*e^2)^2*Log[a*e + c*d*x])/(c^4*d^4)","A",3,2,35,0.05714,1,"{626, 43}"
1878,1,74,0,0.0591841,"\int \frac{(d+e x)^4}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{\left(c d^2-a e^2\right)^2}{c^3 d^3 (a e+c d x)}+\frac{2 e \left(c d^2-a e^2\right) \log (a e+c d x)}{c^3 d^3}+\frac{e^2 x}{c^2 d^2}","-\frac{\left(c d^2-a e^2\right)^2}{c^3 d^3 (a e+c d x)}+\frac{2 e \left(c d^2-a e^2\right) \log (a e+c d x)}{c^3 d^3}+\frac{e^2 x}{c^2 d^2}",1,"(e^2*x)/(c^2*d^2) - (c*d^2 - a*e^2)^2/(c^3*d^3*(a*e + c*d*x)) + (2*e*(c*d^2 - a*e^2)*Log[a*e + c*d*x])/(c^3*d^3)","A",3,2,35,0.05714,1,"{626, 43}"
1879,1,48,0,0.0363662,"\int \frac{(d+e x)^3}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{e \log (a e+c d x)}{c^2 d^2}-\frac{c d^2-a e^2}{c^2 d^2 (a e+c d x)}","\frac{e \log (a e+c d x)}{c^2 d^2}-\frac{c d^2-a e^2}{c^2 d^2 (a e+c d x)}",1,"-((c*d^2 - a*e^2)/(c^2*d^2*(a*e + c*d*x))) + (e*Log[a*e + c*d*x])/(c^2*d^2)","A",3,2,35,0.05714,1,"{626, 43}"
1880,1,18,0,0.0098234,"\int \frac{(d+e x)^2}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{1}{c d (a e+c d x)}","-\frac{1}{c d (a e+c d x)}",1,"-(1/(c*d*(a*e + c*d*x)))","A",2,2,35,0.05714,1,"{626, 32}"
1881,1,75,0,0.0446562,"\int \frac{d+e x}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{1}{\left(c d^2-a e^2\right) (a e+c d x)}-\frac{e \log (a e+c d x)}{\left(c d^2-a e^2\right)^2}+\frac{e \log (d+e x)}{\left(c d^2-a e^2\right)^2}","-\frac{1}{\left(c d^2-a e^2\right) (a e+c d x)}-\frac{e \log (a e+c d x)}{\left(c d^2-a e^2\right)^2}+\frac{e \log (d+e x)}{\left(c d^2-a e^2\right)^2}",1,"-(1/((c*d^2 - a*e^2)*(a*e + c*d*x))) - (e*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^2 + (e*Log[d + e*x])/(c*d^2 - a*e^2)^2","A",3,2,33,0.06061,1,"{626, 44}"
1882,1,114,0,0.0331131,"\int \frac{1}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(-2),x]","-\frac{a e^2+c d^2+2 c d e x}{\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)}-\frac{2 c d e \log (a e+c d x)}{\left(c d^2-a e^2\right)^3}+\frac{2 c d e \log (d+e x)}{\left(c d^2-a e^2\right)^3}","-\frac{a e^2+c d^2+2 c d e x}{\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)}-\frac{2 c d e \log (a e+c d x)}{\left(c d^2-a e^2\right)^3}+\frac{2 c d e \log (d+e x)}{\left(c d^2-a e^2\right)^3}",1,"-((c*d^2 + a*e^2 + 2*c*d*e*x)/((c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))) - (2*c*d*e*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^3 + (2*c*d*e*Log[d + e*x])/(c*d^2 - a*e^2)^3","A",4,3,27,0.1111,1,"{614, 616, 31}"
1883,1,146,0,0.1096906,"\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)^2} \, dx","Int[1/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2),x]","-\frac{c^2 d^2}{\left(c d^2-a e^2\right)^3 (a e+c d x)}-\frac{3 c^2 d^2 e \log (a e+c d x)}{\left(c d^2-a e^2\right)^4}+\frac{3 c^2 d^2 e \log (d+e x)}{\left(c d^2-a e^2\right)^4}-\frac{2 c d e}{(d+e x) \left(c d^2-a e^2\right)^3}-\frac{e}{2 (d+e x)^2 \left(c d^2-a e^2\right)^2}","-\frac{c^2 d^2}{\left(c d^2-a e^2\right)^3 (a e+c d x)}-\frac{3 c^2 d^2 e \log (a e+c d x)}{\left(c d^2-a e^2\right)^4}+\frac{3 c^2 d^2 e \log (d+e x)}{\left(c d^2-a e^2\right)^4}-\frac{2 c d e}{(d+e x) \left(c d^2-a e^2\right)^3}-\frac{e}{2 (d+e x)^2 \left(c d^2-a e^2\right)^2}",1,"-((c^2*d^2)/((c*d^2 - a*e^2)^3*(a*e + c*d*x))) - e/(2*(c*d^2 - a*e^2)^2*(d + e*x)^2) - (2*c*d*e)/((c*d^2 - a*e^2)^3*(d + e*x)) - (3*c^2*d^2*e*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^4 + (3*c^2*d^2*e*Log[d + e*x])/(c*d^2 - a*e^2)^4","A",3,2,35,0.05714,1,"{626, 44}"
1884,1,176,0,0.1534756,"\int \frac{1}{(d+e x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[1/((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2),x]","-\frac{c^3 d^3}{\left(c d^2-a e^2\right)^4 (a e+c d x)}-\frac{3 c^2 d^2 e}{(d+e x) \left(c d^2-a e^2\right)^4}-\frac{4 c^3 d^3 e \log (a e+c d x)}{\left(c d^2-a e^2\right)^5}+\frac{4 c^3 d^3 e \log (d+e x)}{\left(c d^2-a e^2\right)^5}-\frac{c d e}{(d+e x)^2 \left(c d^2-a e^2\right)^3}-\frac{e}{3 (d+e x)^3 \left(c d^2-a e^2\right)^2}","-\frac{c^3 d^3}{\left(c d^2-a e^2\right)^4 (a e+c d x)}-\frac{3 c^2 d^2 e}{(d+e x) \left(c d^2-a e^2\right)^4}-\frac{4 c^3 d^3 e \log (a e+c d x)}{\left(c d^2-a e^2\right)^5}+\frac{4 c^3 d^3 e \log (d+e x)}{\left(c d^2-a e^2\right)^5}-\frac{c d e}{(d+e x)^2 \left(c d^2-a e^2\right)^3}-\frac{e}{3 (d+e x)^3 \left(c d^2-a e^2\right)^2}",1,"-((c^3*d^3)/((c*d^2 - a*e^2)^4*(a*e + c*d*x))) - e/(3*(c*d^2 - a*e^2)^2*(d + e*x)^3) - (c*d*e)/((c*d^2 - a*e^2)^3*(d + e*x)^2) - (3*c^2*d^2*e)/((c*d^2 - a*e^2)^4*(d + e*x)) - (4*c^3*d^3*e*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^5 + (4*c^3*d^3*e*Log[d + e*x])/(c*d^2 - a*e^2)^5","A",3,2,35,0.05714,1,"{626, 44}"
1885,1,221,0,0.2614049,"\int \frac{(d+e x)^9}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^9/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{e^6 (a e+c d x)^4}{4 c^7 d^7}+\frac{2 e^5 \left(c d^2-a e^2\right) (a e+c d x)^3}{c^7 d^7}+\frac{15 e^4 \left(c d^2-a e^2\right)^2 (a e+c d x)^2}{2 c^7 d^7}+\frac{20 e^3 x \left(c d^2-a e^2\right)^3}{c^6 d^6}-\frac{6 e \left(c d^2-a e^2\right)^5}{c^7 d^7 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^6}{2 c^7 d^7 (a e+c d x)^2}+\frac{15 e^2 \left(c d^2-a e^2\right)^4 \log (a e+c d x)}{c^7 d^7}","\frac{e^6 (a e+c d x)^4}{4 c^7 d^7}+\frac{2 e^5 \left(c d^2-a e^2\right) (a e+c d x)^3}{c^7 d^7}+\frac{15 e^4 \left(c d^2-a e^2\right)^2 (a e+c d x)^2}{2 c^7 d^7}+\frac{20 e^3 x \left(c d^2-a e^2\right)^3}{c^6 d^6}-\frac{6 e \left(c d^2-a e^2\right)^5}{c^7 d^7 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^6}{2 c^7 d^7 (a e+c d x)^2}+\frac{15 e^2 \left(c d^2-a e^2\right)^4 \log (a e+c d x)}{c^7 d^7}",1,"(20*e^3*(c*d^2 - a*e^2)^3*x)/(c^6*d^6) - (c*d^2 - a*e^2)^6/(2*c^7*d^7*(a*e + c*d*x)^2) - (6*e*(c*d^2 - a*e^2)^5)/(c^7*d^7*(a*e + c*d*x)) + (15*e^4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^2)/(2*c^7*d^7) + (2*e^5*(c*d^2 - a*e^2)*(a*e + c*d*x)^3)/(c^7*d^7) + (e^6*(a*e + c*d*x)^4)/(4*c^7*d^7) + (15*e^2*(c*d^2 - a*e^2)^4*Log[a*e + c*d*x])/(c^7*d^7)","A",3,2,35,0.05714,1,"{626, 43}"
1886,1,185,0,0.1840278,"\int \frac{(d+e x)^8}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^8/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{e^3 x \left(6 a^2 e^4-15 a c d^2 e^2+10 c^2 d^4\right)}{c^5 d^5}+\frac{e^4 x^2 \left(5 c d^2-3 a e^2\right)}{2 c^4 d^4}-\frac{5 e \left(c d^2-a e^2\right)^4}{c^6 d^6 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^5}{2 c^6 d^6 (a e+c d x)^2}+\frac{10 e^2 \left(c d^2-a e^2\right)^3 \log (a e+c d x)}{c^6 d^6}+\frac{e^5 x^3}{3 c^3 d^3}","\frac{e^3 x \left(6 a^2 e^4-15 a c d^2 e^2+10 c^2 d^4\right)}{c^5 d^5}+\frac{e^4 x^2 \left(5 c d^2-3 a e^2\right)}{2 c^4 d^4}-\frac{5 e \left(c d^2-a e^2\right)^4}{c^6 d^6 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^5}{2 c^6 d^6 (a e+c d x)^2}+\frac{10 e^2 \left(c d^2-a e^2\right)^3 \log (a e+c d x)}{c^6 d^6}+\frac{e^5 x^3}{3 c^3 d^3}",1,"(e^3*(10*c^2*d^4 - 15*a*c*d^2*e^2 + 6*a^2*e^4)*x)/(c^5*d^5) + (e^4*(5*c*d^2 - 3*a*e^2)*x^2)/(2*c^4*d^4) + (e^5*x^3)/(3*c^3*d^3) - (c*d^2 - a*e^2)^5/(2*c^6*d^6*(a*e + c*d*x)^2) - (5*e*(c*d^2 - a*e^2)^4)/(c^6*d^6*(a*e + c*d*x)) + (10*e^2*(c*d^2 - a*e^2)^3*Log[a*e + c*d*x])/(c^6*d^6)","A",3,2,35,0.05714,1,"{626, 43}"
1887,1,142,0,0.1353447,"\int \frac{(d+e x)^7}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^7/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{e^3 x \left(4 c d^2-3 a e^2\right)}{c^4 d^4}-\frac{4 e \left(c d^2-a e^2\right)^3}{c^5 d^5 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^4}{2 c^5 d^5 (a e+c d x)^2}+\frac{6 e^2 \left(c d^2-a e^2\right)^2 \log (a e+c d x)}{c^5 d^5}+\frac{e^4 x^2}{2 c^3 d^3}","\frac{e^3 x \left(4 c d^2-3 a e^2\right)}{c^4 d^4}-\frac{4 e \left(c d^2-a e^2\right)^3}{c^5 d^5 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^4}{2 c^5 d^5 (a e+c d x)^2}+\frac{6 e^2 \left(c d^2-a e^2\right)^2 \log (a e+c d x)}{c^5 d^5}+\frac{e^4 x^2}{2 c^3 d^3}",1,"(e^3*(4*c*d^2 - 3*a*e^2)*x)/(c^4*d^4) + (e^4*x^2)/(2*c^3*d^3) - (c*d^2 - a*e^2)^4/(2*c^5*d^5*(a*e + c*d*x)^2) - (4*e*(c*d^2 - a*e^2)^3)/(c^5*d^5*(a*e + c*d*x)) + (6*e^2*(c*d^2 - a*e^2)^2*Log[a*e + c*d*x])/(c^5*d^5)","A",3,2,35,0.05714,1,"{626, 43}"
1888,1,111,0,0.0920715,"\int \frac{(d+e x)^6}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^6/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{3 e \left(c d^2-a e^2\right)^2}{c^4 d^4 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^3}{2 c^4 d^4 (a e+c d x)^2}+\frac{3 e^2 \left(c d^2-a e^2\right) \log (a e+c d x)}{c^4 d^4}+\frac{e^3 x}{c^3 d^3}","-\frac{3 e \left(c d^2-a e^2\right)^2}{c^4 d^4 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^3}{2 c^4 d^4 (a e+c d x)^2}+\frac{3 e^2 \left(c d^2-a e^2\right) \log (a e+c d x)}{c^4 d^4}+\frac{e^3 x}{c^3 d^3}",1,"(e^3*x)/(c^3*d^3) - (c*d^2 - a*e^2)^3/(2*c^4*d^4*(a*e + c*d*x)^2) - (3*e*(c*d^2 - a*e^2)^2)/(c^4*d^4*(a*e + c*d*x)) + (3*e^2*(c*d^2 - a*e^2)*Log[a*e + c*d*x])/(c^4*d^4)","A",3,2,35,0.05714,1,"{626, 43}"
1889,1,85,0,0.0614312,"\int \frac{(d+e x)^5}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{2 e \left(c d^2-a e^2\right)}{c^3 d^3 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^2}{2 c^3 d^3 (a e+c d x)^2}+\frac{e^2 \log (a e+c d x)}{c^3 d^3}","-\frac{2 e \left(c d^2-a e^2\right)}{c^3 d^3 (a e+c d x)}-\frac{\left(c d^2-a e^2\right)^2}{2 c^3 d^3 (a e+c d x)^2}+\frac{e^2 \log (a e+c d x)}{c^3 d^3}",1,"-(c*d^2 - a*e^2)^2/(2*c^3*d^3*(a*e + c*d*x)^2) - (2*e*(c*d^2 - a*e^2))/(c^3*d^3*(a*e + c*d*x)) + (e^2*Log[a*e + c*d*x])/(c^3*d^3)","A",3,2,35,0.05714,1,"{626, 43}"
1890,1,35,0,0.0131445,"\int \frac{(d+e x)^4}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{(d+e x)^2}{2 \left(c d^2-a e^2\right) (a e+c d x)^2}","-\frac{(d+e x)^2}{2 \left(c d^2-a e^2\right) (a e+c d x)^2}",1,"-(d + e*x)^2/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2)","A",2,2,35,0.05714,1,"{626, 37}"
1891,1,20,0,0.0102619,"\int \frac{(d+e x)^3}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{1}{2 c d (a e+c d x)^2}","-\frac{1}{2 c d (a e+c d x)^2}",1,"-1/(2*c*d*(a*e + c*d*x)^2)","A",2,2,35,0.05714,1,"{626, 32}"
1892,1,107,0,0.0710984,"\int \frac{(d+e x)^2}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{e}{\left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{1}{2 \left(c d^2-a e^2\right) (a e+c d x)^2}+\frac{e^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^3}-\frac{e^2 \log (d+e x)}{\left(c d^2-a e^2\right)^3}","\frac{e}{\left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{1}{2 \left(c d^2-a e^2\right) (a e+c d x)^2}+\frac{e^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^3}-\frac{e^2 \log (d+e x)}{\left(c d^2-a e^2\right)^3}",1,"-1/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2) + e/((c*d^2 - a*e^2)^2*(a*e + c*d*x)) + (e^2*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^3 - (e^2*Log[d + e*x])/(c*d^2 - a*e^2)^3","A",3,2,35,0.05714,1,"{626, 44}"
1893,1,142,0,0.1128444,"\int \frac{d+e x}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{e^2}{(d+e x) \left(c d^2-a e^2\right)^3}+\frac{2 c d e}{\left(c d^2-a e^2\right)^3 (a e+c d x)}-\frac{c d}{2 \left(c d^2-a e^2\right)^2 (a e+c d x)^2}+\frac{3 c d e^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^4}-\frac{3 c d e^2 \log (d+e x)}{\left(c d^2-a e^2\right)^4}","\frac{e^2}{(d+e x) \left(c d^2-a e^2\right)^3}+\frac{2 c d e}{\left(c d^2-a e^2\right)^3 (a e+c d x)}-\frac{c d}{2 \left(c d^2-a e^2\right)^2 (a e+c d x)^2}+\frac{3 c d e^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^4}-\frac{3 c d e^2 \log (d+e x)}{\left(c d^2-a e^2\right)^4}",1,"-(c*d)/(2*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^2) + (2*c*d*e)/((c*d^2 - a*e^2)^3*(a*e + c*d*x)) + e^2/((c*d^2 - a*e^2)^3*(d + e*x)) + (3*c*d*e^2*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^4 - (3*c*d*e^2*Log[d + e*x])/(c*d^2 - a*e^2)^4","A",3,2,33,0.06061,1,"{626, 44}"
1894,1,191,0,0.0648698,"\int \frac{1}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(-3),x]","\frac{6 c^2 d^2 e^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^5}-\frac{6 c^2 d^2 e^2 \log (d+e x)}{\left(c d^2-a e^2\right)^5}+\frac{3 c d e \left(a e^2+c d^2+2 c d e x\right)}{\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)}-\frac{a e^2+c d^2+2 c d e x}{2 \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)^2}","\frac{6 c^2 d^2 e^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^5}-\frac{6 c^2 d^2 e^2 \log (d+e x)}{\left(c d^2-a e^2\right)^5}+\frac{3 c d e \left(a e^2+c d^2+2 c d e x\right)}{\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)}-\frac{a e^2+c d^2+2 c d e x}{2 \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)^2}",1,"-(c*d^2 + a*e^2 + 2*c*d*e*x)/(2*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2) + (3*c*d*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/((c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (6*c^2*d^2*e^2*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^5 - (6*c^2*d^2*e^2*Log[d + e*x])/(c*d^2 - a*e^2)^5","A",5,3,27,0.1111,1,"{614, 616, 31}"
1895,1,223,0,0.2238588,"\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} \, dx","Int[1/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3),x]","\frac{4 c^3 d^3 e}{\left(c d^2-a e^2\right)^5 (a e+c d x)}-\frac{c^3 d^3}{2 \left(c d^2-a e^2\right)^4 (a e+c d x)^2}+\frac{6 c^2 d^2 e^2}{(d+e x) \left(c d^2-a e^2\right)^5}+\frac{10 c^3 d^3 e^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^6}-\frac{10 c^3 d^3 e^2 \log (d+e x)}{\left(c d^2-a e^2\right)^6}+\frac{3 c d e^2}{2 (d+e x)^2 \left(c d^2-a e^2\right)^4}+\frac{e^2}{3 (d+e x)^3 \left(c d^2-a e^2\right)^3}","\frac{4 c^3 d^3 e}{\left(c d^2-a e^2\right)^5 (a e+c d x)}-\frac{c^3 d^3}{2 \left(c d^2-a e^2\right)^4 (a e+c d x)^2}+\frac{6 c^2 d^2 e^2}{(d+e x) \left(c d^2-a e^2\right)^5}+\frac{10 c^3 d^3 e^2 \log (a e+c d x)}{\left(c d^2-a e^2\right)^6}-\frac{10 c^3 d^3 e^2 \log (d+e x)}{\left(c d^2-a e^2\right)^6}+\frac{3 c d e^2}{2 (d+e x)^2 \left(c d^2-a e^2\right)^4}+\frac{e^2}{3 (d+e x)^3 \left(c d^2-a e^2\right)^3}",1,"-(c^3*d^3)/(2*(c*d^2 - a*e^2)^4*(a*e + c*d*x)^2) + (4*c^3*d^3*e)/((c*d^2 - a*e^2)^5*(a*e + c*d*x)) + e^2/(3*(c*d^2 - a*e^2)^3*(d + e*x)^3) + (3*c*d*e^2)/(2*(c*d^2 - a*e^2)^4*(d + e*x)^2) + (6*c^2*d^2*e^2)/((c*d^2 - a*e^2)^5*(d + e*x)) + (10*c^3*d^3*e^2*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^6 - (10*c^3*d^3*e^2*Log[d + e*x])/(c*d^2 - a*e^2)^6","A",3,2,35,0.05714,1,"{626, 44}"
1896,1,217,0,0.2712066,"\int \frac{(d+e x)^{10}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)^10/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","\frac{e^4 x \left(10 a^2 e^4-24 a c d^2 e^2+15 c^2 d^4\right)}{c^6 d^6}+\frac{e^5 x^2 \left(3 c d^2-2 a e^2\right)}{c^5 d^5}-\frac{15 e^2 \left(c d^2-a e^2\right)^4}{c^7 d^7 (a e+c d x)}-\frac{3 e \left(c d^2-a e^2\right)^5}{c^7 d^7 (a e+c d x)^2}-\frac{\left(c d^2-a e^2\right)^6}{3 c^7 d^7 (a e+c d x)^3}+\frac{20 e^3 \left(c d^2-a e^2\right)^3 \log (a e+c d x)}{c^7 d^7}+\frac{e^6 x^3}{3 c^4 d^4}","\frac{e^4 x \left(10 a^2 e^4-24 a c d^2 e^2+15 c^2 d^4\right)}{c^6 d^6}+\frac{e^5 x^2 \left(3 c d^2-2 a e^2\right)}{c^5 d^5}-\frac{15 e^2 \left(c d^2-a e^2\right)^4}{c^7 d^7 (a e+c d x)}-\frac{3 e \left(c d^2-a e^2\right)^5}{c^7 d^7 (a e+c d x)^2}-\frac{\left(c d^2-a e^2\right)^6}{3 c^7 d^7 (a e+c d x)^3}+\frac{20 e^3 \left(c d^2-a e^2\right)^3 \log (a e+c d x)}{c^7 d^7}+\frac{e^6 x^3}{3 c^4 d^4}",1,"(e^4*(15*c^2*d^4 - 24*a*c*d^2*e^2 + 10*a^2*e^4)*x)/(c^6*d^6) + (e^5*(3*c*d^2 - 2*a*e^2)*x^2)/(c^5*d^5) + (e^6*x^3)/(3*c^4*d^4) - (c*d^2 - a*e^2)^6/(3*c^7*d^7*(a*e + c*d*x)^3) - (3*e*(c*d^2 - a*e^2)^5)/(c^7*d^7*(a*e + c*d*x)^2) - (15*e^2*(c*d^2 - a*e^2)^4)/(c^7*d^7*(a*e + c*d*x)) + (20*e^3*(c*d^2 - a*e^2)^3*Log[a*e + c*d*x])/(c^7*d^7)","A",3,2,35,0.05714,1,"{626, 43}"
1897,1,179,0,0.1735335,"\int \frac{(d+e x)^9}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)^9/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","\frac{e^4 x \left(5 c d^2-4 a e^2\right)}{c^5 d^5}-\frac{10 e^2 \left(c d^2-a e^2\right)^3}{c^6 d^6 (a e+c d x)}-\frac{5 e \left(c d^2-a e^2\right)^4}{2 c^6 d^6 (a e+c d x)^2}-\frac{\left(c d^2-a e^2\right)^5}{3 c^6 d^6 (a e+c d x)^3}+\frac{10 e^3 \left(c d^2-a e^2\right)^2 \log (a e+c d x)}{c^6 d^6}+\frac{e^5 x^2}{2 c^4 d^4}","\frac{e^4 x \left(5 c d^2-4 a e^2\right)}{c^5 d^5}-\frac{10 e^2 \left(c d^2-a e^2\right)^3}{c^6 d^6 (a e+c d x)}-\frac{5 e \left(c d^2-a e^2\right)^4}{2 c^6 d^6 (a e+c d x)^2}-\frac{\left(c d^2-a e^2\right)^5}{3 c^6 d^6 (a e+c d x)^3}+\frac{10 e^3 \left(c d^2-a e^2\right)^2 \log (a e+c d x)}{c^6 d^6}+\frac{e^5 x^2}{2 c^4 d^4}",1,"(e^4*(5*c*d^2 - 4*a*e^2)*x)/(c^5*d^5) + (e^5*x^2)/(2*c^4*d^4) - (c*d^2 - a*e^2)^5/(3*c^6*d^6*(a*e + c*d*x)^3) - (5*e*(c*d^2 - a*e^2)^4)/(2*c^6*d^6*(a*e + c*d*x)^2) - (10*e^2*(c*d^2 - a*e^2)^3)/(c^6*d^6*(a*e + c*d*x)) + (10*e^3*(c*d^2 - a*e^2)^2*Log[a*e + c*d*x])/(c^6*d^6)","A",3,2,35,0.05714,1,"{626, 43}"
1898,1,146,0,0.1334139,"\int \frac{(d+e x)^8}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)^8/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","-\frac{6 e^2 \left(c d^2-a e^2\right)^2}{c^5 d^5 (a e+c d x)}-\frac{2 e \left(c d^2-a e^2\right)^3}{c^5 d^5 (a e+c d x)^2}-\frac{\left(c d^2-a e^2\right)^4}{3 c^5 d^5 (a e+c d x)^3}+\frac{4 e^3 \left(c d^2-a e^2\right) \log (a e+c d x)}{c^5 d^5}+\frac{e^4 x}{c^4 d^4}","-\frac{6 e^2 \left(c d^2-a e^2\right)^2}{c^5 d^5 (a e+c d x)}-\frac{2 e \left(c d^2-a e^2\right)^3}{c^5 d^5 (a e+c d x)^2}-\frac{\left(c d^2-a e^2\right)^4}{3 c^5 d^5 (a e+c d x)^3}+\frac{4 e^3 \left(c d^2-a e^2\right) \log (a e+c d x)}{c^5 d^5}+\frac{e^4 x}{c^4 d^4}",1,"(e^4*x)/(c^4*d^4) - (c*d^2 - a*e^2)^4/(3*c^5*d^5*(a*e + c*d*x)^3) - (2*e*(c*d^2 - a*e^2)^3)/(c^5*d^5*(a*e + c*d*x)^2) - (6*e^2*(c*d^2 - a*e^2)^2)/(c^5*d^5*(a*e + c*d*x)) + (4*e^3*(c*d^2 - a*e^2)*Log[a*e + c*d*x])/(c^5*d^5)","A",3,2,35,0.05714,1,"{626, 43}"
1899,1,122,0,0.0882848,"\int \frac{(d+e x)^7}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)^7/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","-\frac{3 e^2 \left(c d^2-a e^2\right)}{c^4 d^4 (a e+c d x)}-\frac{3 e \left(c d^2-a e^2\right)^2}{2 c^4 d^4 (a e+c d x)^2}-\frac{\left(c d^2-a e^2\right)^3}{3 c^4 d^4 (a e+c d x)^3}+\frac{e^3 \log (a e+c d x)}{c^4 d^4}","-\frac{3 e^2 \left(c d^2-a e^2\right)}{c^4 d^4 (a e+c d x)}-\frac{3 e \left(c d^2-a e^2\right)^2}{2 c^4 d^4 (a e+c d x)^2}-\frac{\left(c d^2-a e^2\right)^3}{3 c^4 d^4 (a e+c d x)^3}+\frac{e^3 \log (a e+c d x)}{c^4 d^4}",1,"-(c*d^2 - a*e^2)^3/(3*c^4*d^4*(a*e + c*d*x)^3) - (3*e*(c*d^2 - a*e^2)^2)/(2*c^4*d^4*(a*e + c*d*x)^2) - (3*e^2*(c*d^2 - a*e^2))/(c^4*d^4*(a*e + c*d*x)) + (e^3*Log[a*e + c*d*x])/(c^4*d^4)","A",3,2,35,0.05714,1,"{626, 43}"
1900,1,35,0,0.0125113,"\int \frac{(d+e x)^6}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)^6/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","-\frac{(d+e x)^3}{3 \left(c d^2-a e^2\right) (a e+c d x)^3}","-\frac{(d+e x)^3}{3 \left(c d^2-a e^2\right) (a e+c d x)^3}",1,"-(d + e*x)^3/(3*(c*d^2 - a*e^2)*(a*e + c*d*x)^3)","A",2,2,35,0.05714,1,"{626, 37}"
1901,1,54,0,0.0390207,"\int \frac{(d+e x)^5}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","-\frac{c d^2-a e^2}{3 c^2 d^2 (a e+c d x)^3}-\frac{e}{2 c^2 d^2 (a e+c d x)^2}","-\frac{c d^2-a e^2}{3 c^2 d^2 (a e+c d x)^3}-\frac{e}{2 c^2 d^2 (a e+c d x)^2}",1,"-(c*d^2 - a*e^2)/(3*c^2*d^2*(a*e + c*d*x)^3) - e/(2*c^2*d^2*(a*e + c*d*x)^2)","A",3,2,35,0.05714,1,"{626, 43}"
1902,1,20,0,0.0106371,"\int \frac{(d+e x)^4}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","-\frac{1}{3 c d (a e+c d x)^3}","-\frac{1}{3 c d (a e+c d x)^3}",1,"-1/(3*c*d*(a*e + c*d*x)^3)","A",2,2,35,0.05714,1,"{626, 32}"
1903,1,139,0,0.0984611,"\int \frac{(d+e x)^3}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","-\frac{e^2}{\left(c d^2-a e^2\right)^3 (a e+c d x)}+\frac{e}{2 \left(c d^2-a e^2\right)^2 (a e+c d x)^2}-\frac{1}{3 \left(c d^2-a e^2\right) (a e+c d x)^3}-\frac{e^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^4}+\frac{e^3 \log (d+e x)}{\left(c d^2-a e^2\right)^4}","-\frac{e^2}{\left(c d^2-a e^2\right)^3 (a e+c d x)}+\frac{e}{2 \left(c d^2-a e^2\right)^2 (a e+c d x)^2}-\frac{1}{3 \left(c d^2-a e^2\right) (a e+c d x)^3}-\frac{e^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^4}+\frac{e^3 \log (d+e x)}{\left(c d^2-a e^2\right)^4}",1,"-1/(3*(c*d^2 - a*e^2)*(a*e + c*d*x)^3) + e/(2*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^2) - e^2/((c*d^2 - a*e^2)^3*(a*e + c*d*x)) - (e^3*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^4 + (e^3*Log[d + e*x])/(c*d^2 - a*e^2)^4","A",3,2,35,0.05714,1,"{626, 44}"
1904,1,173,0,0.1525265,"\int \frac{(d+e x)^2}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","-\frac{e^3}{(d+e x) \left(c d^2-a e^2\right)^4}-\frac{3 c d e^2}{\left(c d^2-a e^2\right)^4 (a e+c d x)}+\frac{c d e}{\left(c d^2-a e^2\right)^3 (a e+c d x)^2}-\frac{c d}{3 \left(c d^2-a e^2\right)^2 (a e+c d x)^3}-\frac{4 c d e^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^5}+\frac{4 c d e^3 \log (d+e x)}{\left(c d^2-a e^2\right)^5}","-\frac{e^3}{(d+e x) \left(c d^2-a e^2\right)^4}-\frac{3 c d e^2}{\left(c d^2-a e^2\right)^4 (a e+c d x)}+\frac{c d e}{\left(c d^2-a e^2\right)^3 (a e+c d x)^2}-\frac{c d}{3 \left(c d^2-a e^2\right)^2 (a e+c d x)^3}-\frac{4 c d e^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^5}+\frac{4 c d e^3 \log (d+e x)}{\left(c d^2-a e^2\right)^5}",1,"-(c*d)/(3*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^3) + (c*d*e)/((c*d^2 - a*e^2)^3*(a*e + c*d*x)^2) - (3*c*d*e^2)/((c*d^2 - a*e^2)^4*(a*e + c*d*x)) - e^3/((c*d^2 - a*e^2)^4*(d + e*x)) - (4*c*d*e^3*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^5 + (4*c*d*e^3*Log[d + e*x])/(c*d^2 - a*e^2)^5","A",3,2,35,0.05714,1,"{626, 44}"
1905,1,226,0,0.2077642,"\int \frac{d+e x}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(d + e*x)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","-\frac{6 c^2 d^2 e^2}{\left(c d^2-a e^2\right)^5 (a e+c d x)}+\frac{3 c^2 d^2 e}{2 \left(c d^2-a e^2\right)^4 (a e+c d x)^2}-\frac{c^2 d^2}{3 \left(c d^2-a e^2\right)^3 (a e+c d x)^3}-\frac{10 c^2 d^2 e^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^6}+\frac{10 c^2 d^2 e^3 \log (d+e x)}{\left(c d^2-a e^2\right)^6}-\frac{4 c d e^3}{(d+e x) \left(c d^2-a e^2\right)^5}-\frac{e^3}{2 (d+e x)^2 \left(c d^2-a e^2\right)^4}","-\frac{6 c^2 d^2 e^2}{\left(c d^2-a e^2\right)^5 (a e+c d x)}+\frac{3 c^2 d^2 e}{2 \left(c d^2-a e^2\right)^4 (a e+c d x)^2}-\frac{c^2 d^2}{3 \left(c d^2-a e^2\right)^3 (a e+c d x)^3}-\frac{10 c^2 d^2 e^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^6}+\frac{10 c^2 d^2 e^3 \log (d+e x)}{\left(c d^2-a e^2\right)^6}-\frac{4 c d e^3}{(d+e x) \left(c d^2-a e^2\right)^5}-\frac{e^3}{2 (d+e x)^2 \left(c d^2-a e^2\right)^4}",1,"-(c^2*d^2)/(3*(c*d^2 - a*e^2)^3*(a*e + c*d*x)^3) + (3*c^2*d^2*e)/(2*(c*d^2 - a*e^2)^4*(a*e + c*d*x)^2) - (6*c^2*d^2*e^2)/((c*d^2 - a*e^2)^5*(a*e + c*d*x)) - e^3/(2*(c*d^2 - a*e^2)^4*(d + e*x)^2) - (4*c*d*e^3)/((c*d^2 - a*e^2)^5*(d + e*x)) - (10*c^2*d^2*e^3*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^6 + (10*c^2*d^2*e^3*Log[d + e*x])/(c*d^2 - a*e^2)^6","A",3,2,33,0.06061,1,"{626, 44}"
1906,1,262,0,0.1035067,"\int \frac{1}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^4} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(-4),x]","-\frac{10 c^2 d^2 e^2 \left(a e^2+c d^2+2 c d e x\right)}{\left(c d^2-a e^2\right)^6 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)}-\frac{20 c^3 d^3 e^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^7}+\frac{20 c^3 d^3 e^3 \log (d+e x)}{\left(c d^2-a e^2\right)^7}+\frac{5 c d e \left(a e^2+c d^2+2 c d e x\right)}{3 \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)^2}-\frac{a e^2+c d^2+2 c d e x}{3 \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}","-\frac{10 c^2 d^2 e^2 \left(a e^2+c d^2+2 c d e x\right)}{\left(c d^2-a e^2\right)^6 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)}-\frac{20 c^3 d^3 e^3 \log (a e+c d x)}{\left(c d^2-a e^2\right)^7}+\frac{20 c^3 d^3 e^3 \log (d+e x)}{\left(c d^2-a e^2\right)^7}+\frac{5 c d e \left(a e^2+c d^2+2 c d e x\right)}{3 \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)^2}-\frac{a e^2+c d^2+2 c d e x}{3 \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}",1,"-(c*d^2 + a*e^2 + 2*c*d*e*x)/(3*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3) + (5*c*d*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2) - (10*c^2*d^2*e^2*(c*d^2 + a*e^2 + 2*c*d*e*x))/((c*d^2 - a*e^2)^6*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (20*c^3*d^3*e^3*Log[a*e + c*d*x])/(c*d^2 - a*e^2)^7 + (20*c^3*d^3*e^3*Log[d + e*x])/(c*d^2 - a*e^2)^7","A",6,3,27,0.1111,1,"{614, 616, 31}"
1907,1,388,0,0.4411126,"\int (d+e 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)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{21 \left(c d^2-a e^2\right)^4 \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^5 d^5 e}+\frac{7 \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)^{3/2}}{64 c^4 d^4}+\frac{21 (d+e x) \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}}{160 c^3 d^3}+\frac{3 (d+e 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}}{20 c^2 d^2}-\frac{21 \left(c d^2-a e^2\right)^6 \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^{11/2} d^{11/2} e^{3/2}}+\frac{(d+e x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{6 c d}","\frac{21 \left(c d^2-a e^2\right)^4 \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^5 d^5 e}+\frac{7 \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)^{3/2}}{64 c^4 d^4}+\frac{21 (d+e x) \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}}{160 c^3 d^3}+\frac{3 (d+e 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}}{20 c^2 d^2}-\frac{21 \left(c d^2-a e^2\right)^6 \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^{11/2} d^{11/2} e^{3/2}}+\frac{(d+e x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{6 c d}",1,"(21*(c*d^2 - a*e^2)^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])/(512*c^5*d^5*e) + (7*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(64*c^4*d^4) + (21*(c*d^2 - a*e^2)^2*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(160*c^3*d^3) + (3*(c*d^2 - a*e^2)*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(20*c^2*d^2) + ((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(6*c*d) - (21*(c*d^2 - a*e^2)^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^(11/2)*d^(11/2)*e^(3/2))","A",7,5,37,0.1351,1,"{670, 640, 612, 621, 206}"
1908,1,328,0,0.2756293,"\int (d+e 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*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{7 \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^4 d^4 e}+\frac{7 \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}}{48 c^3 d^3}+\frac{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)^{3/2}}{40 c^2 d^2}-\frac{7 \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^{9/2} d^{9/2} e^{3/2}}+\frac{(d+e x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 c d}","\frac{7 \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^4 d^4 e}+\frac{7 \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}}{48 c^3 d^3}+\frac{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)^{3/2}}{40 c^2 d^2}-\frac{7 \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^{9/2} d^{9/2} e^{3/2}}+\frac{(d+e x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{5 c d}",1,"(7*(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^4*d^4*e) + (7*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(48*c^3*d^3) + (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)^(3/2))/(40*c^2*d^2) + ((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(5*c*d) - (7*(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^(9/2)*d^(9/2)*e^(3/2))","A",6,5,37,0.1351,1,"{670, 640, 612, 621, 206}"
1909,1,268,0,0.1886902,"\int (d+e 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)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{5 \left(c d^2-a e^2\right)^2 \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^3 d^3 e}+\frac{5 \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}}{24 c^2 d^2}-\frac{5 \left(c d^2-a e^2\right)^4 \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^{3/2}}+\frac{(d+e x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 c d}","\frac{5 \left(c d^2-a e^2\right)^2 \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^3 d^3 e}+\frac{5 \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}}{24 c^2 d^2}-\frac{5 \left(c d^2-a e^2\right)^4 \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^{3/2}}+\frac{(d+e x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 c d}",1,"(5*(c*d^2 - a*e^2)^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^3*d^3*e) + (5*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(24*c^2*d^2) + ((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(4*c*d) - (5*(c*d^2 - a*e^2)^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])])/(128*c^(7/2)*d^(7/2)*e^(3/2))","A",5,5,37,0.1351,1,"{670, 640, 612, 621, 206}"
1910,1,210,0,0.1041325,"\int (d+e x) \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{\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}}{8 c^2 d^2 e}-\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^{5/2} 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 c d}","\frac{\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}}{8 c^2 d^2 e}-\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^{5/2} 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 c d}",1,"((c*d^2 - 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])/(8*c^2*d^2*e) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(3*c*d) - ((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^(5/2)*d^(5/2)*e^(3/2))","A",4,4,35,0.1143,1,"{640, 612, 621, 206}"
1911,1,159,0,0.0502793,"\int \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{\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}}{4 c d e}-\frac{\left(c d^2-a e^2\right)^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)}{8 c^{3/2} d^{3/2} e^{3/2}}","\frac{\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}}{4 c d e}-\frac{\left(c d^2-a e^2\right)^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)}{8 c^{3/2} d^{3/2} e^{3/2}}",1,"((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])/(4*c*d*e) - ((c*d^2 - a*e^2)^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^(3/2))","A",3,3,29,0.1034,1,"{612, 621, 206}"
1912,1,131,0,0.0672677,"\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}"
1913,1,124,0,0.054264,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{(d+e x)^2} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^2,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)}{e^{3/2}}-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e (d+e 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)}{e^{3/2}}-\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e (d+e x)}",1,"(-2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(e*(d + e*x)) + (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])])/e^(3/2)","A",3,3,37,0.08108,1,"{662, 621, 206}"
1914,1,54,0,0.020352,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{(d+e x)^3} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^3,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 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*(c*d^2 - a*e^2)*(d + e*x)^3)","A",1,1,37,0.02703,1,"{650}"
1915,1,111,0,0.0469014,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{(d+e x)^4} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^4,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 \left(c d^2-a e^2\right)^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)^4 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)^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)^4 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(5*(c*d^2 - a*e^2)*(d + e*x)^4) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(15*(c*d^2 - a*e^2)^2*(d + e*x)^3)","A",2,2,37,0.05405,1,"{658, 650}"
1916,1,171,0,0.080947,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{(d+e x)^5} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^5,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 \left(c d^2-a e^2\right)^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)^4 \left(c d^2-a e^2\right)^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)^5 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)^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)^4 \left(c d^2-a e^2\right)^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)^5 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(7*(c*d^2 - a*e^2)*(d + e*x)^5) + (8*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(35*(c*d^2 - a*e^2)^2*(d + e*x)^4) + (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^2 - a*e^2)^3*(d + e*x)^3)","A",3,2,37,0.05405,1,"{658, 650}"
1917,1,231,0,0.1151045,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{(d+e x)^6} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^6,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 \left(c d^2-a e^2\right)^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)^4 \left(c d^2-a e^2\right)^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)^5 \left(c d^2-a e^2\right)^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)^6 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)^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)^4 \left(c d^2-a e^2\right)^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)^5 \left(c d^2-a e^2\right)^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)^6 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(9*(c*d^2 - a*e^2)*(d + e*x)^6) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(21*(c*d^2 - a*e^2)^2*(d + e*x)^5) + (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^2 - a*e^2)^3*(d + e*x)^4) + (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^2 - a*e^2)^4*(d + e*x)^3)","A",4,2,37,0.05405,1,"{658, 650}"
1918,1,461,0,0.5488072,"\int (d+e x)^4 \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)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","-\frac{99 \left(c d^2-a e^2\right)^6 \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^6 d^6 e^2}+\frac{33 \left(c d^2-a e^2\right)^4 \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^5 d^5 e}+\frac{33 \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}}{640 c^4 d^4}+\frac{33 (d+e x) \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)^{5/2}}{448 c^3 d^3}+\frac{11 (d+e 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)^{5/2}}{112 c^2 d^2}+\frac{99 \left(c d^2-a e^2\right)^8 \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^{13/2} d^{13/2} e^{5/2}}+\frac{(d+e x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{8 c d}","-\frac{99 \left(c d^2-a e^2\right)^6 \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^6 d^6 e^2}+\frac{33 \left(c d^2-a e^2\right)^4 \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^5 d^5 e}+\frac{33 \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}}{640 c^4 d^4}+\frac{33 (d+e x) \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)^{5/2}}{448 c^3 d^3}+\frac{11 (d+e 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)^{5/2}}{112 c^2 d^2}+\frac{99 \left(c d^2-a e^2\right)^8 \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^{13/2} d^{13/2} e^{5/2}}+\frac{(d+e x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{8 c d}",1,"(-99*(c*d^2 - a*e^2)^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^6*d^6*e^2) + (33*(c*d^2 - a*e^2)^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))/(2048*c^5*d^5*e) + (33*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(640*c^4*d^4) + (33*(c*d^2 - a*e^2)^2*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(448*c^3*d^3) + (11*(c*d^2 - a*e^2)*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(112*c^2*d^2) + ((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(8*c*d) + (99*(c*d^2 - a*e^2)^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])])/(32768*c^(13/2)*d^(13/2)*e^(5/2))","A",8,5,37,0.1351,1,"{670, 640, 612, 621, 206}"
1919,1,401,0,0.3725872,"\int (d+e 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*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","-\frac{9 \left(c d^2-a e^2\right)^5 \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^5 d^5 e^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) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{128 c^4 d^4 e}+\frac{3 \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)^{5/2}}{40 c^3 d^3}+\frac{3 (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}}{28 c^2 d^2}+\frac{9 \left(c d^2-a e^2\right)^7 \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^{11/2} d^{11/2} e^{5/2}}+\frac{(d+e x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 c d}","-\frac{9 \left(c d^2-a e^2\right)^5 \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^5 d^5 e^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) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{128 c^4 d^4 e}+\frac{3 \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)^{5/2}}{40 c^3 d^3}+\frac{3 (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}}{28 c^2 d^2}+\frac{9 \left(c d^2-a e^2\right)^7 \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^{11/2} d^{11/2} e^{5/2}}+\frac{(d+e x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{7 c d}",1,"(-9*(c*d^2 - a*e^2)^5*(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^5*d^5*e^2) + (3*(c*d^2 - a*e^2)^3*(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))/(128*c^4*d^4*e) + (3*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(40*c^3*d^3) + (3*(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))/(28*c^2*d^2) + ((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(7*c*d) + (9*(c*d^2 - a*e^2)^7*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^(11/2)*d^(11/2)*e^(5/2))","A",7,5,37,0.1351,1,"{670, 640, 612, 621, 206}"
1920,1,341,0,0.2638485,"\int (d+e 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)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","-\frac{7 \left(c d^2-a e^2\right)^4 \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^2}+\frac{7 \left(c d^2-a e^2\right)^2 \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^3 d^3 e}+\frac{7 \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}}{60 c^2 d^2}+\frac{7 \left(c d^2-a e^2\right)^6 \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^{5/2}}+\frac{(d+e x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{6 c d}","-\frac{7 \left(c d^2-a e^2\right)^4 \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^2}+\frac{7 \left(c d^2-a e^2\right)^2 \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^3 d^3 e}+\frac{7 \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}}{60 c^2 d^2}+\frac{7 \left(c d^2-a e^2\right)^6 \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^{5/2}}+\frac{(d+e x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{6 c d}",1,"(-7*(c*d^2 - a*e^2)^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])/(512*c^4*d^4*e^2) + (7*(c*d^2 - a*e^2)^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^3*d^3*e) + (7*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(60*c^2*d^2) + ((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(6*c*d) + (7*(c*d^2 - a*e^2)^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^(5/2))","A",6,5,37,0.1351,1,"{670, 640, 612, 621, 206}"
1921,1,283,0,0.1616922,"\int (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[(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),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^3 d^3 e^2}+\frac{\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}}{16 c^2 d^2 e}+\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^{7/2} 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 c d}","-\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^3 d^3 e^2}+\frac{\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}}{16 c^2 d^2 e}+\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^{7/2} 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 c d}",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^3*d^3*e^2) + ((c*d^2 - 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))/(16*c^2*d^2*e) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(5*c*d) + (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^(7/2)*d^(7/2)*e^(5/2))","A",5,4,35,0.1143,1,"{640, 612, 621, 206}"
1922,1,232,0,0.0885656,"\int \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","-\frac{3 \left(c d^2-a e^2\right)^2 \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^2}+\frac{3 \left(c d^2-a e^2\right)^4 \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^{5/2}}+\frac{\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}}{8 c d e}","-\frac{3 \left(c d^2-a e^2\right)^2 \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^2}+\frac{3 \left(c d^2-a e^2\right)^4 \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^{5/2}}+\frac{\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}}{8 c d e}",1,"(-3*(c*d^2 - a*e^2)^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^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))/(8*c*d*e) + (3*(c*d^2 - a*e^2)^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])])/(128*c^(5/2)*d^(5/2)*e^(5/2))","A",4,3,29,0.1034,1,"{612, 621, 206}"
1923,1,201,0,0.1109949,"\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}"
1924,1,187,0,0.1262635,"\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)^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^2,x]","\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 e (d+e x)}+\frac{3}{4} \left(a-\frac{c d^2}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}+\frac{3 \left(c d^2-a e^2\right)^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)}{8 \sqrt{c} \sqrt{d} 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 e (d+e x)}+\frac{3}{4} \left(a-\frac{c d^2}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}+\frac{3 \left(c d^2-a e^2\right)^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)}{8 \sqrt{c} \sqrt{d} e^{5/2}}",1,"(3*(a - (c*d^2)/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*e*(d + e*x)) + (3*(c*d^2 - a*e^2)^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*Sqrt[c]*Sqrt[d]*e^(5/2))","A",4,3,37,0.08108,1,"{664, 621, 206}"
1925,1,175,0,0.1040341,"\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} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^3,x]","-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{e (d+e x)^2}+\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^2}-\frac{3 \sqrt{c} \sqrt{d} \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 e^{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}}{e (d+e x)^2}+\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^2}-\frac{3 \sqrt{c} \sqrt{d} \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 e^{5/2}}",1,"(3*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/e^2 - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(e*(d + e*x)^2) - (3*Sqrt[c]*Sqrt[d]*(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*e^(5/2))","A",4,4,37,0.1081,1,"{662, 664, 621, 206}"
1926,1,169,0,0.0915419,"\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)^4} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^4,x]","\frac{c^{3/2} d^{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)}{e^{5/2}}-\frac{2 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^2 (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}}{3 e (d+e x)^3}","\frac{c^{3/2} d^{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)}{e^{5/2}}-\frac{2 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^2 (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}}{3 e (d+e x)^3}",1,"(-2*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(e^2*(d + e*x)) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e*(d + e*x)^3) + (c^(3/2)*d^(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])])/e^(5/2)","A",4,3,37,0.08108,1,"{662, 621, 206}"
1927,1,54,0,0.0205957,"\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)^5} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^5,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 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*(c*d^2 - a*e^2)*(d + e*x)^5)","A",1,1,37,0.02703,1,"{650}"
1928,1,111,0,0.0479102,"\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)^6} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^6,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 \left(c d^2-a e^2\right)^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)^6 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)^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)^6 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(7*(c*d^2 - a*e^2)*(d + e*x)^6) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(35*(c*d^2 - a*e^2)^2*(d + e*x)^5)","A",2,2,37,0.05405,1,"{658, 650}"
1929,1,171,0,0.0780033,"\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)^7} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^7,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 \left(c d^2-a e^2\right)^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)^6 \left(c d^2-a e^2\right)^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)^7 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)^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)^6 \left(c d^2-a e^2\right)^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)^7 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(9*(c*d^2 - a*e^2)*(d + e*x)^7) + (8*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(63*(c*d^2 - a*e^2)^2*(d + e*x)^6) + (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^2 - a*e^2)^3*(d + e*x)^5)","A",3,2,37,0.05405,1,"{658, 650}"
1930,1,231,0,0.1157172,"\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)^8} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^8,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 \left(c d^2-a e^2\right)^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)^6 \left(c d^2-a e^2\right)^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)^7 \left(c d^2-a e^2\right)^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)^8 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)^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)^6 \left(c d^2-a e^2\right)^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)^7 \left(c d^2-a e^2\right)^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)^8 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(11*(c*d^2 - a*e^2)*(d + e*x)^8) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(33*(c*d^2 - a*e^2)^2*(d + e*x)^7) + (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^2 - a*e^2)^3*(d + e*x)^6) + (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^2 - a*e^2)^4*(d + e*x)^5)","A",4,2,37,0.05405,1,"{658, 650}"
1931,1,534,0,0.6763724,"\int (d+e x)^4 \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)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{143 \left(c d^2-a e^2\right)^8 \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}}{131072 c^7 d^7 e^3}-\frac{143 \left(c d^2-a e^2\right)^6 \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}}{49152 c^6 d^6 e^2}+\frac{143 \left(c d^2-a e^2\right)^4 \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)^{5/2}}{15360 c^5 d^5 e}+\frac{143 \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)^{7/2}}{4480 c^4 d^4}+\frac{143 (d+e x) \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)^{7/2}}{2880 c^3 d^3}+\frac{13 (d+e 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)^{7/2}}{180 c^2 d^2}-\frac{143 \left(c d^2-a e^2\right)^{10} \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)}{262144 c^{15/2} d^{15/2} e^{7/2}}+\frac{(d+e x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{10 c d}","\frac{143 \left(c d^2-a e^2\right)^8 \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}}{131072 c^7 d^7 e^3}-\frac{143 \left(c d^2-a e^2\right)^6 \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}}{49152 c^6 d^6 e^2}+\frac{143 \left(c d^2-a e^2\right)^4 \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)^{5/2}}{15360 c^5 d^5 e}+\frac{143 \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)^{7/2}}{4480 c^4 d^4}+\frac{143 (d+e x) \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)^{7/2}}{2880 c^3 d^3}+\frac{13 (d+e 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)^{7/2}}{180 c^2 d^2}-\frac{143 \left(c d^2-a e^2\right)^{10} \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)}{262144 c^{15/2} d^{15/2} e^{7/2}}+\frac{(d+e x)^3 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{10 c d}",1,"(143*(c*d^2 - a*e^2)^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])/(131072*c^7*d^7*e^3) - (143*(c*d^2 - a*e^2)^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))/(49152*c^6*d^6*e^2) + (143*(c*d^2 - a*e^2)^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)^(5/2))/(15360*c^5*d^5*e) + (143*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(4480*c^4*d^4) + (143*(c*d^2 - a*e^2)^2*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(2880*c^3*d^3) + (13*(c*d^2 - a*e^2)*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(180*c^2*d^2) + ((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(10*c*d) - (143*(c*d^2 - a*e^2)^10*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])])/(262144*c^(15/2)*d^(15/2)*e^(7/2))","A",9,5,37,0.1351,1,"{670, 640, 612, 621, 206}"
1932,1,474,0,0.4927171,"\int (d+e 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)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{55 \left(c d^2-a e^2\right)^7 \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}}{32768 c^6 d^6 e^3}-\frac{55 \left(c d^2-a e^2\right)^5 \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}}{12288 c^5 d^5 e^2}+\frac{11 \left(c d^2-a e^2\right)^3 \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)^{5/2}}{768 c^4 d^4 e}+\frac{11 \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)^{7/2}}{224 c^3 d^3}+\frac{11 (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)^{7/2}}{144 c^2 d^2}-\frac{55 \left(c d^2-a e^2\right)^9 \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)}{65536 c^{13/2} d^{13/2} e^{7/2}}+\frac{(d+e x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{9 c d}","\frac{55 \left(c d^2-a e^2\right)^7 \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}}{32768 c^6 d^6 e^3}-\frac{55 \left(c d^2-a e^2\right)^5 \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}}{12288 c^5 d^5 e^2}+\frac{11 \left(c d^2-a e^2\right)^3 \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)^{5/2}}{768 c^4 d^4 e}+\frac{11 \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)^{7/2}}{224 c^3 d^3}+\frac{11 (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)^{7/2}}{144 c^2 d^2}-\frac{55 \left(c d^2-a e^2\right)^9 \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)}{65536 c^{13/2} d^{13/2} e^{7/2}}+\frac{(d+e x)^2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{9 c d}",1,"(55*(c*d^2 - a*e^2)^7*(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])/(32768*c^6*d^6*e^3) - (55*(c*d^2 - a*e^2)^5*(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))/(12288*c^5*d^5*e^2) + (11*(c*d^2 - a*e^2)^3*(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)^(5/2))/(768*c^4*d^4*e) + (11*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(224*c^3*d^3) + (11*(c*d^2 - a*e^2)*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(144*c^2*d^2) + ((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(9*c*d) - (55*(c*d^2 - a*e^2)^9*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])])/(65536*c^(13/2)*d^(13/2)*e^(7/2))","A",8,5,37,0.1351,1,"{670, 640, 612, 621, 206}"
1933,1,414,0,0.3543396,"\int (d+e 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)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{45 \left(c d^2-a e^2\right)^6 \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^3}-\frac{15 \left(c d^2-a e^2\right)^4 \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^2}+\frac{3 \left(c d^2-a e^2\right)^2 \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)^{5/2}}{128 c^3 d^3 e}+\frac{9 \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)^{7/2}}{112 c^2 d^2}-\frac{45 \left(c d^2-a e^2\right)^8 \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^{7/2}}+\frac{(d+e x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{8 c d}","\frac{45 \left(c d^2-a e^2\right)^6 \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^3}-\frac{15 \left(c d^2-a e^2\right)^4 \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^2}+\frac{3 \left(c d^2-a e^2\right)^2 \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)^{5/2}}{128 c^3 d^3 e}+\frac{9 \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)^{7/2}}{112 c^2 d^2}-\frac{45 \left(c d^2-a e^2\right)^8 \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^{7/2}}+\frac{(d+e x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{8 c d}",1,"(45*(c*d^2 - a*e^2)^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^3) - (15*(c*d^2 - a*e^2)^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))/(2048*c^4*d^4*e^2) + (3*(c*d^2 - a*e^2)^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)^(5/2))/(128*c^3*d^3*e) + (9*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(112*c^2*d^2) + ((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(8*c*d) - (45*(c*d^2 - a*e^2)^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])])/(32768*c^(11/2)*d^(11/2)*e^(7/2))","A",7,5,37,0.1351,1,"{670, 640, 612, 621, 206}"
1934,1,356,0,0.2385342,"\int (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[(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{5 \left(c d^2-a e^2\right)^5 \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^3}-\frac{5 \left(c d^2-a e^2\right)^3 \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^2}+\frac{\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)^{5/2}}{24 c^2 d^2 e}-\frac{5 \left(c d^2-a e^2\right)^7 \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^{7/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{7 c d}","\frac{5 \left(c d^2-a e^2\right)^5 \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^3}-\frac{5 \left(c d^2-a e^2\right)^3 \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^2}+\frac{\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)^{5/2}}{24 c^2 d^2 e}-\frac{5 \left(c d^2-a e^2\right)^7 \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^{7/2}}+\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{7 c d}",1,"(5*(c*d^2 - a*e^2)^5*(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^3) - (5*(c*d^2 - a*e^2)^3*(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^2) + ((c*d^2 - 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)^(5/2))/(24*c^2*d^2*e) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2)/(7*c*d) - (5*(c*d^2 - a*e^2)^7*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^(7/2))","A",6,4,35,0.1143,1,"{640, 612, 621, 206}"
1935,1,305,0,0.1475492,"\int \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{5 \left(c d^2-a e^2\right)^4 \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^3}-\frac{5 \left(c d^2-a e^2\right)^2 \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^2}-\frac{5 \left(c d^2-a e^2\right)^6 \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^{7/2}}+\frac{\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)^{5/2}}{12 c d e}","\frac{5 \left(c d^2-a e^2\right)^4 \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^3}-\frac{5 \left(c d^2-a e^2\right)^2 \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^2}-\frac{5 \left(c d^2-a e^2\right)^6 \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^{7/2}}+\frac{\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)^{5/2}}{12 c d e}",1,"(5*(c*d^2 - a*e^2)^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])/(512*c^3*d^3*e^3) - (5*(c*d^2 - a*e^2)^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^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)^(5/2))/(12*c*d*e) - (5*(c*d^2 - a*e^2)^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^(7/2)*d^(7/2)*e^(7/2))","A",5,3,29,0.1034,1,"{612, 621, 206}"
1936,1,274,0,0.1785941,"\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}"
1937,1,261,0,0.2204564,"\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)^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^2,x]","-\frac{5 \left(c d^2-a e^2\right)^4 \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^{7/2}}+\frac{5 \left(c d^2-a e^2\right)^2 \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 d e^3}+\frac{5}{24} \left(a-\frac{c d^2}{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{(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}}{4 e}","-\frac{5 \left(c d^2-a e^2\right)^4 \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^{7/2}}+\frac{5 \left(c d^2-a e^2\right)^2 \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 d e^3}+\frac{5}{24} \left(a-\frac{c d^2}{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{(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}}{4 e}",1,"(5*(c*d^2 - a*e^2)^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*d*e^3) + (5*(a - (c*d^2)/e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/24 + ((a*e + c*d*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(4*e) - (5*(c*d^2 - a*e^2)^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])])/(128*c^(3/2)*d^(3/2)*e^(7/2))","A",6,6,37,0.1622,1,"{654, 670, 640, 612, 621, 206}"
1938,1,244,0,0.2023802,"\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)^3} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^3,x]","\frac{5 \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}}{8 e^3}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{e (d+e x)^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}}{3 e^2}-\frac{5 \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 \sqrt{c} \sqrt{d} e^{7/2}}","\frac{5 \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}}{8 e^3}+\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{e (d+e x)^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}}{3 e^2}-\frac{5 \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 \sqrt{c} \sqrt{d} e^{7/2}}",1,"(5*(c*d^2 - 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])/(8*e^3) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e^2) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(e*(d + e*x)^2) - (5*(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*Sqrt[c]*Sqrt[d]*e^(7/2))","A",5,5,37,0.1351,1,"{662, 664, 612, 621, 206}"
1939,1,235,0,0.2116238,"\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)^4} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^4,x]","-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{e (d+e x)^3}+\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}}{2 e^2 (d+e x)}+\frac{15 c d \left(a-\frac{c d^2}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e}+\frac{15 \sqrt{c} \sqrt{d} \left(c d^2-a e^2\right)^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)}{8 e^{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}}{e (d+e x)^3}+\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}}{2 e^2 (d+e x)}+\frac{15 c d \left(a-\frac{c d^2}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e}+\frac{15 \sqrt{c} \sqrt{d} \left(c d^2-a e^2\right)^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)}{8 e^{7/2}}",1,"(15*c*d*(a - (c*d^2)/e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*e) + (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(2*e^2*(d + e*x)) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(e*(d + e*x)^3) + (15*Sqrt[c]*Sqrt[d]*(c*d^2 - a*e^2)^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*e^(7/2))","A",5,4,37,0.1081,1,"{662, 664, 621, 206}"
1940,1,226,0,0.1477493,"\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} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^5,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}}{e^3}-\frac{5 c^{3/2} d^{3/2} \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 e^{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}}{3 e (d+e x)^4}-\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 e^2 (d+e x)^2}","\frac{5 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^3}-\frac{5 c^{3/2} d^{3/2} \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 e^{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}}{3 e (d+e x)^4}-\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 e^2 (d+e x)^2}",1,"(5*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/e^3 - (10*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e^2*(d + e*x)^2) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(3*e*(d + e*x)^4) - (5*c^(3/2)*d^(3/2)*(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*e^(7/2))","A",5,4,37,0.1081,1,"{662, 664, 621, 206}"
1941,1,218,0,0.1325491,"\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)^6} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^6,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}}{e^3 (d+e x)}+\frac{c^{5/2} d^{5/2} \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)}{e^{7/2}}-\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 e^2 (d+e x)^3}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 e (d+e x)^5}","-\frac{2 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^3 (d+e x)}+\frac{c^{5/2} d^{5/2} \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)}{e^{7/2}}-\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 e^2 (d+e x)^3}-\frac{2 \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 e (d+e x)^5}",1,"(-2*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(e^3*(d + e*x)) - (2*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e^2*(d + e*x)^3) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*e*(d + e*x)^5) + (c^(5/2)*d^(5/2)*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])])/e^(7/2)","A",5,3,37,0.08108,1,"{662, 621, 206}"
1942,1,54,0,0.020905,"\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)^7} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^7,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 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(7*(c*d^2 - a*e^2)*(d + e*x)^7)","A",1,1,37,0.02703,1,"{650}"
1943,1,111,0,0.0488611,"\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)^8} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^8,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 \left(c d^2-a e^2\right)^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)^8 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)^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)^8 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(9*(c*d^2 - a*e^2)*(d + e*x)^8) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(63*(c*d^2 - a*e^2)^2*(d + e*x)^7)","A",2,2,37,0.05405,1,"{658, 650}"
1944,1,171,0,0.0804385,"\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)^9} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^9,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 \left(c d^2-a e^2\right)^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)^8 \left(c d^2-a e^2\right)^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)^9 \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)^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)^8 \left(c d^2-a e^2\right)^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)^9 \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(11*(c*d^2 - a*e^2)*(d + e*x)^9) + (8*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(99*(c*d^2 - a*e^2)^2*(d + e*x)^8) + (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^2 - a*e^2)^3*(d + e*x)^7)","A",3,2,37,0.05405,1,"{658, 650}"
1945,1,231,0,0.1205498,"\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)^{10}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^10,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 \left(c d^2-a e^2\right)^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)^8 \left(c d^2-a e^2\right)^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)^9 \left(c d^2-a e^2\right)^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)^{10} \left(c d^2-a e^2\right)}","\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 \left(c d^2-a e^2\right)^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)^8 \left(c d^2-a e^2\right)^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)^9 \left(c d^2-a e^2\right)^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)^{10} \left(c d^2-a e^2\right)}",1,"(2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(13*(c*d^2 - a*e^2)*(d + e*x)^10) + (12*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(143*(c*d^2 - a*e^2)^2*(d + e*x)^9) + (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^2 - a*e^2)^3*(d + e*x)^8) + (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^2 - a*e^2)^4*(d + e*x)^7)","A",4,2,37,0.05405,1,"{658, 650}"
1946,1,255,0,0.1965328,"\int \frac{(d+e 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/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{5 \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}}{8 c^3 d^3}+\frac{5 (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}}{12 c^2 d^2}+\frac{5 \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^{7/2} d^{7/2} \sqrt{e}}+\frac{(d+e x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c d}","\frac{5 \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}}{8 c^3 d^3}+\frac{5 (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}}{12 c^2 d^2}+\frac{5 \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^{7/2} d^{7/2} \sqrt{e}}+\frac{(d+e x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c d}",1,"(5*(c*d^2 - a*e^2)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*c^3*d^3) + (5*(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])/(12*c^2*d^2) + ((d + e*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c*d) + (5*(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^(7/2)*d^(7/2)*Sqrt[e])","A",5,4,37,0.1081,1,"{670, 640, 621, 206}"
1947,1,195,0,0.1153179,"\int \frac{(d+e 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)^2/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{3 \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}}{4 c^2 d^2}+\frac{3 \left(c d^2-a e^2\right)^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)}{8 c^{5/2} d^{5/2} \sqrt{e}}+\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}","\frac{3 \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}}{4 c^2 d^2}+\frac{3 \left(c d^2-a e^2\right)^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)}{8 c^{5/2} d^{5/2} \sqrt{e}}+\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}",1,"(3*(c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*c^2*d^2) + ((d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(2*c*d) + (3*(c*d^2 - a*e^2)^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^(5/2)*d^(5/2)*Sqrt[e])","A",4,4,37,0.1081,1,"{670, 640, 621, 206}"
1948,1,134,0,0.055865,"\int \frac{d+e x}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\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 c^{3/2} d^{3/2} \sqrt{e}}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d}","\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 c^{3/2} d^{3/2} \sqrt{e}}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c d}",1,"Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(c*d) + ((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)*Sqrt[e])","A",3,3,35,0.08571,1,"{640, 621, 206}"
1949,1,82,0,0.0250971,"\int \frac{1}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/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} \sqrt{e}}","\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} \sqrt{e}}",1,"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]*Sqrt[e])","A",2,2,29,0.06897,1,"{621, 206}"
1950,1,52,0,0.0198817,"\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}"
1951,1,111,0,0.0470202,"\int \frac{1}{(d+e x)^2 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/((d + e*x)^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 (d+e x) \left(c d^2-a e^2\right)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 (d+e x)^2 \left(c d^2-a e^2\right)}","\frac{4 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 (d+e x) \left(c d^2-a e^2\right)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 (d+e x)^2 \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])/(3*(c*d^2 - a*e^2)*(d + e*x)^2) + (4*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*(c*d^2 - a*e^2)^2*(d + e*x))","A",2,2,37,0.05405,1,"{658, 650}"
1952,1,171,0,0.078461,"\int \frac{1}{(d+e x)^3 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/((d + e*x)^3*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 (d+e x) \left(c d^2-a e^2\right)^3}+\frac{8 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{15 (d+e x)^2 \left(c d^2-a e^2\right)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 (d+e x)^3 \left(c d^2-a e^2\right)}","\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 (d+e x) \left(c d^2-a e^2\right)^3}+\frac{8 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{15 (d+e x)^2 \left(c d^2-a e^2\right)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{5 (d+e x)^3 \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])/(5*(c*d^2 - a*e^2)*(d + e*x)^3) + (8*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(15*(c*d^2 - a*e^2)^2*(d + e*x)^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^2 - a*e^2)^3*(d + e*x))","A",3,2,37,0.05405,1,"{658, 650}"
1953,1,231,0,0.1153567,"\int \frac{1}{(d+e x)^4 \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/((d + e*x)^4*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 (d+e x) \left(c d^2-a e^2\right)^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 (d+e x)^2 \left(c d^2-a e^2\right)^3}+\frac{12 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{35 (d+e x)^3 \left(c d^2-a e^2\right)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 (d+e x)^4 \left(c d^2-a e^2\right)}","\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 (d+e x) \left(c d^2-a e^2\right)^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 (d+e x)^2 \left(c d^2-a e^2\right)^3}+\frac{12 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{35 (d+e x)^3 \left(c d^2-a e^2\right)^2}+\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 (d+e x)^4 \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])/(7*(c*d^2 - a*e^2)*(d + e*x)^4) + (12*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*(c*d^2 - a*e^2)^2*(d + e*x)^3) + (16*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*(c*d^2 - a*e^2)^3*(d + e*x)^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^2 - a*e^2)^4*(d + e*x))","A",4,2,37,0.05405,1,"{658, 650}"
1954,1,302,0,0.2436899,"\int \frac{(d+e x)^5}{\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)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{7 e (d+e x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^2 d^2}+\frac{35 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}}{12 c^3 d^3}+\frac{35 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}}{8 c^4 d^4}+\frac{35 \sqrt{e} \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^{9/2} d^{9/2}}-\frac{2 (d+e x)^4}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{7 e (d+e x)^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 c^2 d^2}+\frac{35 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}}{12 c^3 d^3}+\frac{35 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}}{8 c^4 d^4}+\frac{35 \sqrt{e} \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^{9/2} d^{9/2}}-\frac{2 (d+e x)^4}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*(d + e*x)^4)/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (35*e*(c*d^2 - a*e^2)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*c^4*d^4) + (35*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])/(12*c^3*d^3) + (7*e*(d + e*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(3*c^2*d^2) + (35*Sqrt[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^(9/2)*d^(9/2))","A",6,5,37,0.1351,1,"{668, 670, 640, 621, 206}"
1955,1,241,0,0.1619155,"\int \frac{(d+e x)^4}{\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)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{5 e (d+e x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 c^2 d^2}+\frac{15 e \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}}{4 c^3 d^3}+\frac{15 \sqrt{e} \left(c d^2-a e^2\right)^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)}{8 c^{7/2} d^{7/2}}-\frac{2 (d+e x)^3}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{5 e (d+e x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 c^2 d^2}+\frac{15 e \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}}{4 c^3 d^3}+\frac{15 \sqrt{e} \left(c d^2-a e^2\right)^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)}{8 c^{7/2} d^{7/2}}-\frac{2 (d+e x)^3}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*(d + e*x)^3)/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (15*e*(c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*c^3*d^3) + (5*e*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(2*c^2*d^2) + (15*Sqrt[e]*(c*d^2 - a*e^2)^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^(7/2)*d^(7/2))","A",5,5,37,0.1351,1,"{668, 670, 640, 621, 206}"
1956,1,180,0,0.0991254,"\int \frac{(d+e 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/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{3 e \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c^2 d^2}+\frac{3 \sqrt{e} \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 c^{5/2} d^{5/2}}-\frac{2 (d+e x)^2}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{3 e \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c^2 d^2}+\frac{3 \sqrt{e} \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 c^{5/2} d^{5/2}}-\frac{2 (d+e x)^2}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-2*(d + e*x)^2)/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (3*e*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(c^2*d^2) + (3*Sqrt[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*c^(5/2)*d^(5/2))","A",4,4,37,0.1081,1,"{668, 640, 621, 206}"
1957,1,125,0,0.0582064,"\int \frac{(d+e 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)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{\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)}{c^{3/2} d^{3/2}}-\frac{2 (d+e x)}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{\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)}{c^{3/2} d^{3/2}}-\frac{2 (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*(d + e*x))/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^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])])/(c^(3/2)*d^(3/2))","A",3,3,37,0.08108,1,"{652, 621, 206}"
1958,1,50,0,0.0249906,"\int \frac{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[(d + e*x)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","-\frac{2 (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 (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 + e*x))/((c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",1,1,35,0.02857,1,"{636}"
1959,1,62,0,0.0089736,"\int \frac{1}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(-3/2),x]","-\frac{2 \left(a e^2+c d^2+2 c d e x\right)}{\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{2 \left(a e^2+c d^2+2 c d e x\right)}{\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}}",1,"(-2*(c*d^2 + a*e^2 + 2*c*d*e*x))/((c*d^2 - a*e^2)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",1,1,29,0.03448,1,"{613}"
1960,1,121,0,0.0386184,"\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}"
1961,1,181,0,0.0713613,"\int \frac{1}{(d+e 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[1/((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{16 c^2 d^2 \left(a e^2+c d^2+2 c d e x\right)}{5 \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{4 c d}{5 (d+e x) \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{2}{5 (d+e 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{16 c^2 d^2 \left(a e^2+c d^2+2 c d e x\right)}{5 \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{4 c d}{5 (d+e x) \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{2}{5 (d+e 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/(5*(c*d^2 - a*e^2)*(d + e*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (4*c*d)/(5*(c*d^2 - a*e^2)^2*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (16*c^2*d^2*(c*d^2 + a*e^2 + 2*c*d*e*x))/(5*(c*d^2 - a*e^2)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",3,2,37,0.05405,1,"{658, 613}"
1962,1,241,0,0.1113018,"\int \frac{1}{(d+e 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[1/((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{128 c^3 d^3 \left(a e^2+c d^2+2 c d e x\right)}{35 \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{32 c^2 d^2}{35 (d+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{16 c d}{35 (d+e x)^2 \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{2}{7 (d+e x)^3 \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{128 c^3 d^3 \left(a e^2+c d^2+2 c d e x\right)}{35 \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{32 c^2 d^2}{35 (d+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{16 c d}{35 (d+e x)^2 \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{2}{7 (d+e x)^3 \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/(7*(c*d^2 - a*e^2)*(d + e*x)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (16*c*d)/(35*(c*d^2 - a*e^2)^2*(d + e*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (32*c^2*d^2)/(35*(c*d^2 - a*e^2)^3*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (128*c^3*d^3*(c*d^2 + a*e^2 + 2*c*d*e*x))/(35*(c*d^2 - a*e^2)^5*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",4,2,37,0.05405,1,"{658, 613}"
1963,1,301,0,0.1586446,"\int \frac{1}{(d+e x)^4 \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)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{256 c^4 d^4 \left(a e^2+c d^2+2 c d e x\right)}{63 \left(c d^2-a e^2\right)^6 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{64 c^3 d^3}{63 (d+e x) \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{32 c^2 d^2}{63 (d+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{20 c d}{63 (d+e x)^3 \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{2}{9 (d+e x)^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}}","-\frac{256 c^4 d^4 \left(a e^2+c d^2+2 c d e x\right)}{63 \left(c d^2-a e^2\right)^6 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{64 c^3 d^3}{63 (d+e x) \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{32 c^2 d^2}{63 (d+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{20 c d}{63 (d+e x)^3 \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{2}{9 (d+e x)^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}}",1,"2/(9*(c*d^2 - a*e^2)*(d + e*x)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (20*c*d)/(63*(c*d^2 - a*e^2)^2*(d + e*x)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (32*c^2*d^2)/(63*(c*d^2 - a*e^2)^3*(d + e*x)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (64*c^3*d^3)/(63*(c*d^2 - a*e^2)^4*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (256*c^4*d^4*(c*d^2 + a*e^2 + 2*c*d*e*x))/(63*(c*d^2 - a*e^2)^6*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",5,2,37,0.05405,1,"{658, 613}"
1964,1,294,0,0.2117505,"\int \frac{(d+e x)^6}{\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)^6/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","-\frac{14 e (d+e x)^3}{3 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{35 e^2 (d+e x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{6 c^3 d^3}+\frac{35 e^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}}{4 c^4 d^4}+\frac{35 e^{3/2} \left(c d^2-a e^2\right)^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)}{8 c^{9/2} d^{9/2}}-\frac{2 (d+e x)^5}{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{14 e (d+e x)^3}{3 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{35 e^2 (d+e x) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{6 c^3 d^3}+\frac{35 e^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}}{4 c^4 d^4}+\frac{35 e^{3/2} \left(c d^2-a e^2\right)^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)}{8 c^{9/2} d^{9/2}}-\frac{2 (d+e x)^5}{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)^5)/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (14*e*(d + e*x)^3)/(3*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (35*e^2*(c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*c^4*d^4) + (35*e^2*(d + e*x)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(6*c^3*d^3) + (35*e^(3/2)*(c*d^2 - a*e^2)^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^(9/2)*d^(9/2))","A",6,5,37,0.1351,1,"{668, 670, 640, 621, 206}"
1965,1,231,0,0.1398674,"\int \frac{(d+e x)^5}{\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/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","-\frac{10 e (d+e x)^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{5 e^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c^3 d^3}+\frac{5 e^{3/2} \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 c^{7/2} d^{7/2}}-\frac{2 (d+e x)^4}{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{10 e (d+e x)^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{5 e^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{c^3 d^3}+\frac{5 e^{3/2} \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 c^{7/2} d^{7/2}}-\frac{2 (d+e x)^4}{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)^4)/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (10*e*(d + e*x)^2)/(3*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (5*e^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(c^3*d^3) + (5*e^(3/2)*(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^(7/2)*d^(7/2))","A",5,4,37,0.1081,1,"{668, 640, 621, 206}"
1966,1,172,0,0.0887596,"\int \frac{(d+e x)^4}{\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)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","-\frac{2 e (d+e x)}{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{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)}{c^{5/2} d^{5/2}}-\frac{2 (d+e 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{2 e (d+e x)}{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}+\frac{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)}{c^{5/2} d^{5/2}}-\frac{2 (d+e 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)/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (2*e*(d + e*x))/(c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^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])])/(c^(5/2)*d^(5/2))","A",4,4,37,0.1081,1,"{668, 652, 621, 206}"
1967,1,54,0,0.0213717,"\int \frac{(d+e 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)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","-\frac{2 (d+e x)^3}{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{2 (d+e x)^3}{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*(d + e*x)^3)/(3*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))","A",1,1,37,0.02703,1,"{650}"
1968,1,116,0,0.0432223,"\int \frac{(d+e 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)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{2 e \left(a e^2+c d^2+2 c d e x\right)}{3 c d \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{2 (d+e x)}{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 e \left(a e^2+c d^2+2 c d e x\right)}{3 c d \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{2 (d+e x)}{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*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (2*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*c*d*(c*d^2 - a*e^2)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",2,2,37,0.05405,1,"{652, 613}"
1969,1,118,0,0.0498806,"\int \frac{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[(d + e*x)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{8 e \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 (d+e 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{8 e \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 (d+e 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*(d + e*x))/(3*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (8*e*(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",2,2,35,0.05714,1,"{638, 613}"
1970,1,132,0,0.024465,"\int \frac{1}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(-5/2),x]","\frac{16 c d e \left(a e^2+c d^2+2 c d e x\right)}{3 \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{2 \left(a e^2+c d^2+2 c d e x\right)}{3 \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{16 c d e \left(a e^2+c d^2+2 c d e x\right)}{3 \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{2 \left(a e^2+c d^2+2 c d e x\right)}{3 \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*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (16*c*d*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*(c*d^2 - a*e^2)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",2,2,29,0.06897,1,"{614, 613}"
1971,1,192,0,0.0624783,"\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)^{5/2}} \, dx","Int[1/((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{128 c^2 d^2 e \left(a e^2+c d^2+2 c d e x\right)}{15 \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{16 c d \left(a e^2+c d^2+2 c d e x\right)}{15 \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)^{3/2}}+\frac{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{128 c^2 d^2 e \left(a e^2+c d^2+2 c d e x\right)}{15 \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{16 c d \left(a e^2+c d^2+2 c d e x\right)}{15 \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)^{3/2}}+\frac{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/(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)) - (16*c*d*(c*d^2 + a*e^2 + 2*c*d*e*x))/(15*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (128*c^2*d^2*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(15*(c*d^2 - a*e^2)^5*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",3,3,37,0.08108,1,"{658, 614, 613}"
1972,1,252,0,0.1017492,"\int \frac{1}{(d+e 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[1/((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{256 c^3 d^3 e \left(a e^2+c d^2+2 c d e x\right)}{21 \left(c d^2-a e^2\right)^6 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{32 c^2 d^2 \left(a e^2+c d^2+2 c d e x\right)}{21 \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{4 c d}{7 (d+e x) \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}{7 (d+e 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{256 c^3 d^3 e \left(a e^2+c d^2+2 c d e x\right)}{21 \left(c d^2-a e^2\right)^6 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{32 c^2 d^2 \left(a e^2+c d^2+2 c d e x\right)}{21 \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{4 c d}{7 (d+e x) \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}{7 (d+e 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/(7*(c*d^2 - a*e^2)*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (4*c*d)/(7*(c*d^2 - a*e^2)^2*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (32*c^2*d^2*(c*d^2 + a*e^2 + 2*c*d*e*x))/(21*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (256*c^3*d^3*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(21*(c*d^2 - a*e^2)^6*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",4,3,37,0.08108,1,"{658, 614, 613}"
1973,1,312,0,0.1517074,"\int \frac{1}{(d+e 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[1/((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{1024 c^4 d^4 e \left(a e^2+c d^2+2 c d e x\right)}{63 \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{128 c^3 d^3 \left(a e^2+c d^2+2 c d e x\right)}{63 \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{16 c^2 d^2}{21 (d+e x) \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)^{3/2}}+\frac{8 c d}{21 (d+e x)^2 \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}{9 (d+e 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{1024 c^4 d^4 e \left(a e^2+c d^2+2 c d e x\right)}{63 \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{128 c^3 d^3 \left(a e^2+c d^2+2 c d e x\right)}{63 \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{16 c^2 d^2}{21 (d+e x) \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)^{3/2}}+\frac{8 c d}{21 (d+e x)^2 \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}{9 (d+e 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/(9*(c*d^2 - a*e^2)*(d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (8*c*d)/(21*(c*d^2 - a*e^2)^2*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (16*c^2*d^2)/(21*(c*d^2 - a*e^2)^3*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (128*c^3*d^3*(c*d^2 + a*e^2 + 2*c*d*e*x))/(63*(c*d^2 - a*e^2)^5*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (1024*c^4*d^4*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(63*(c*d^2 - a*e^2)^7*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",5,3,37,0.08108,1,"{658, 614, 613}"
1974,1,1485,0,2.236187,"\int \frac{d+e x}{\sqrt[3]{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/3),x]","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{4/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)} \left(c d^2-a e^2\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} ((a e+c d x) (d+e x))^{2/3}}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}{\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}\right)|-7-4 \sqrt{3}\right) \left(c d^2-a e^2\right)^{5/3}}{4 \sqrt[3]{2} c^{5/3} d^{5/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{2/3} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}+\frac{3^{3/4} \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{4/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)} \left(c d^2-a e^2\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} ((a e+c d x) (d+e x))^{2/3}}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}{\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}\right)|-7-4 \sqrt{3}\right) \left(c d^2-a e^2\right)^{5/3}}{2^{5/6} c^{5/3} d^{5/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{2/3} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}+\frac{3 \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2} \left(c d^2-a e^2\right)}{2 \sqrt[3]{2} c^{5/3} d^{5/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}+\frac{3 \left(c d e x^2+\left(c d^2+a e^2\right) x+a d e\right)^{2/3}}{4 c d}","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{4/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)} \left(c d^2-a e^2\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} ((a e+c d x) (d+e x))^{2/3}}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}{\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}\right)|-7-4 \sqrt{3}\right) \left(c d^2-a e^2\right)^{5/3}}{4 \sqrt[3]{2} c^{5/3} d^{5/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{2/3} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}+\frac{3^{3/4} \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{4/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)} \left(c d^2-a e^2\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} ((a e+c d x) (d+e x))^{2/3}}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}{\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}\right)|-7-4 \sqrt{3}\right) \left(c d^2-a e^2\right)^{5/3}}{2^{5/6} c^{5/3} d^{5/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{2/3} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}+\frac{3 \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2} \left(c d^2-a e^2\right)}{2 \sqrt[3]{2} c^{5/3} d^{5/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}+\frac{3 \left(c d e x^2+\left(c d^2+a e^2\right) x+a d e\right)^{2/3}}{4 c d}",1,"(3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(2/3))/(4*c*d) + (3*(c*d^2 - a*e^2)*Sqrt[(c*d^2 + a*e^2 + 2*c*d*e*x)^2]*Sqrt[(a*e^2 + c*d*(d + 2*e*x))^2])/(2*2^(1/3)*c^(5/3)*d^(5/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(c*d^2 - a*e^2)^(5/3)*Sqrt[(c*d^2 + a*e^2 + 2*c*d*e*x)^2]*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))*Sqrt[((c*d^2 - a*e^2)^(4/3) - 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*(c*d^2 - a*e^2)^(2/3)*((a*e + c*d*x)*(d + e*x))^(1/3) + 2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*((a*e + c*d*x)*(d + e*x))^(2/3))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))], -7 - 4*Sqrt[3]])/(4*2^(1/3)*c^(5/3)*d^(5/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[((c*d^2 - a*e^2)^(2/3)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3)))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2]*Sqrt[(a*e^2 + c*d*(d + 2*e*x))^2]) + (3^(3/4)*(c*d^2 - a*e^2)^(5/3)*Sqrt[(c*d^2 + a*e^2 + 2*c*d*e*x)^2]*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))*Sqrt[((c*d^2 - a*e^2)^(4/3) - 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*(c*d^2 - a*e^2)^(2/3)*((a*e + c*d*x)*(d + e*x))^(1/3) + 2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*((a*e + c*d*x)*(d + e*x))^(2/3))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))], -7 - 4*Sqrt[3]])/(2^(5/6)*c^(5/3)*d^(5/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[((c*d^2 - a*e^2)^(2/3)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3)))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2]*Sqrt[(a*e^2 + c*d*(d + 2*e*x))^2])","A",5,5,35,0.1429,1,"{640, 623, 303, 218, 1877}"
1975,1,1432,0,1.3091016,"\int \frac{1}{\sqrt[3]{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(-1/3),x]","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(c d^2-a e^2\right)^{2/3} \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{4/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)} \left(c d^2-a e^2\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} ((a e+c d x) (d+e x))^{2/3}}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}{\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{2/3} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}+\frac{\sqrt[6]{2} 3^{3/4} \left(c d^2-a e^2\right)^{2/3} \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{4/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)} \left(c d^2-a e^2\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} ((a e+c d x) (d+e x))^{2/3}}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}{\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}\right)|-7-4 \sqrt{3}\right)}{c^{2/3} d^{2/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{2/3} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}+\frac{3 \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}{\sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(c d^2-a e^2\right)^{2/3} \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{4/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)} \left(c d^2-a e^2\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} ((a e+c d x) (d+e x))^{2/3}}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}{\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{2/3} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}+\frac{\sqrt[6]{2} 3^{3/4} \left(c d^2-a e^2\right)^{2/3} \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{4/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)} \left(c d^2-a e^2\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} ((a e+c d x) (d+e x))^{2/3}}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}{\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}}\right)|-7-4 \sqrt{3}\right)}{c^{2/3} d^{2/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \sqrt{\frac{\left(c d^2-a e^2\right)^{2/3} \left(\left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}{\left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)^2}} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}+\frac{3 \sqrt{\left(c d^2+2 c e x d+a e^2\right)^2} \sqrt{\left(a e^2+c d (d+2 e x)\right)^2}}{\sqrt[3]{2} c^{2/3} d^{2/3} e^{2/3} \left(c d^2+2 c e x d+a e^2\right) \left(\left(1+\sqrt{3}\right) \left(c d^2-a e^2\right)^{2/3}+2^{2/3} \sqrt[3]{c} \sqrt[3]{d} \sqrt[3]{e} \sqrt[3]{(a e+c d x) (d+e x)}\right)}",1,"(3*Sqrt[(c*d^2 + a*e^2 + 2*c*d*e*x)^2]*Sqrt[(a*e^2 + c*d*(d + 2*e*x))^2])/(2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(c*d^2 - a*e^2)^(2/3)*Sqrt[(c*d^2 + a*e^2 + 2*c*d*e*x)^2]*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))*Sqrt[((c*d^2 - a*e^2)^(4/3) - 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*(c*d^2 - a*e^2)^(2/3)*((a*e + c*d*x)*(d + e*x))^(1/3) + 2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*((a*e + c*d*x)*(d + e*x))^(2/3))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))], -7 - 4*Sqrt[3]])/(2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[((c*d^2 - a*e^2)^(2/3)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3)))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2]*Sqrt[(a*e^2 + c*d*(d + 2*e*x))^2]) + (2^(1/6)*3^(3/4)*(c*d^2 - a*e^2)^(2/3)*Sqrt[(c*d^2 + a*e^2 + 2*c*d*e*x)^2]*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))*Sqrt[((c*d^2 - a*e^2)^(4/3) - 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*(c*d^2 - a*e^2)^(2/3)*((a*e + c*d*x)*(d + e*x))^(1/3) + 2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*((a*e + c*d*x)*(d + e*x))^(2/3))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))], -7 - 4*Sqrt[3]])/(c^(2/3)*d^(2/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*Sqrt[((c*d^2 - a*e^2)^(2/3)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3)))/((1 + Sqrt[3])*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2]*Sqrt[(a*e^2 + c*d*(d + 2*e*x))^2])","A",4,4,29,0.1379,1,"{623, 303, 218, 1877}"
1976,1,43,0,0.0199979,"\int (d+e x)^{3/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right) \, dx","Int[(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{2}{7} (d+e x)^{7/2} \left(a-\frac{c d^2}{e^2}\right)+\frac{2 c d (d+e x)^{9/2}}{9 e^2}","\frac{2}{7} (d+e x)^{7/2} \left(a-\frac{c d^2}{e^2}\right)+\frac{2 c d (d+e x)^{9/2}}{9 e^2}",1,"(2*(a - (c*d^2)/e^2)*(d + e*x)^(7/2))/7 + (2*c*d*(d + e*x)^(9/2))/(9*e^2)","A",3,2,35,0.05714,1,"{626, 43}"
1977,1,43,0,0.0193963,"\int \sqrt{d+e x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right) \, dx","Int[Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{2}{5} (d+e x)^{5/2} \left(a-\frac{c d^2}{e^2}\right)+\frac{2 c d (d+e x)^{7/2}}{7 e^2}","\frac{2}{5} (d+e x)^{5/2} \left(a-\frac{c d^2}{e^2}\right)+\frac{2 c d (d+e x)^{7/2}}{7 e^2}",1,"(2*(a - (c*d^2)/e^2)*(d + e*x)^(5/2))/5 + (2*c*d*(d + e*x)^(7/2))/(7*e^2)","A",3,2,35,0.05714,1,"{626, 43}"
1978,1,43,0,0.0191914,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{\sqrt{d+e x}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/Sqrt[d + e*x],x]","\frac{2}{3} (d+e x)^{3/2} \left(a-\frac{c d^2}{e^2}\right)+\frac{2 c d (d+e x)^{5/2}}{5 e^2}","\frac{2}{3} (d+e x)^{3/2} \left(a-\frac{c d^2}{e^2}\right)+\frac{2 c d (d+e x)^{5/2}}{5 e^2}",1,"(2*(a - (c*d^2)/e^2)*(d + e*x)^(3/2))/3 + (2*c*d*(d + e*x)^(5/2))/(5*e^2)","A",3,2,35,0.05714,1,"{626, 43}"
1979,1,41,0,0.024613,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^{3/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^(3/2),x]","2 \sqrt{d+e x} \left(a-\frac{c d^2}{e^2}\right)+\frac{2 c d (d+e x)^{3/2}}{3 e^2}","2 \sqrt{d+e x} \left(a-\frac{c d^2}{e^2}\right)+\frac{2 c d (d+e x)^{3/2}}{3 e^2}",1,"2*(a - (c*d^2)/e^2)*Sqrt[d + e*x] + (2*c*d*(d + e*x)^(3/2))/(3*e^2)","A",3,2,35,0.05714,1,"{24, 43}"
1980,1,39,0,0.0231704,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^{5/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^(5/2),x]","\frac{2 c d \sqrt{d+e x}}{e^2}-\frac{2 \left(a-\frac{c d^2}{e^2}\right)}{\sqrt{d+e x}}","\frac{2 c d \sqrt{d+e x}}{e^2}-\frac{2 \left(a-\frac{c d^2}{e^2}\right)}{\sqrt{d+e x}}",1,"(-2*(a - (c*d^2)/e^2))/Sqrt[d + e*x] + (2*c*d*Sqrt[d + e*x])/e^2","A",3,2,35,0.05714,1,"{24, 43}"
1981,1,41,0,0.0221359,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^{7/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^(7/2),x]","-\frac{2 \left(a-\frac{c d^2}{e^2}\right)}{3 (d+e x)^{3/2}}-\frac{2 c d}{e^2 \sqrt{d+e x}}","-\frac{2 \left(a-\frac{c d^2}{e^2}\right)}{3 (d+e x)^{3/2}}-\frac{2 c d}{e^2 \sqrt{d+e x}}",1,"(-2*(a - (c*d^2)/e^2))/(3*(d + e*x)^(3/2)) - (2*c*d)/(e^2*Sqrt[d + e*x])","A",3,2,35,0.05714,1,"{24, 43}"
1982,1,43,0,0.0233258,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^{9/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^(9/2),x]","-\frac{2 \left(a-\frac{c d^2}{e^2}\right)}{5 (d+e x)^{5/2}}-\frac{2 c d}{3 e^2 (d+e x)^{3/2}}","-\frac{2 \left(a-\frac{c d^2}{e^2}\right)}{5 (d+e x)^{5/2}}-\frac{2 c d}{3 e^2 (d+e x)^{3/2}}",1,"(-2*(a - (c*d^2)/e^2))/(5*(d + e*x)^(5/2)) - (2*c*d)/(3*e^2*(d + e*x)^(3/2))","A",3,2,35,0.05714,1,"{24, 43}"
1983,1,43,0,0.0217398,"\int \frac{a d e+\left(c d^2+a e^2\right) x+c d e x^2}{(d+e x)^{11/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(d + e*x)^(11/2),x]","-\frac{2 \left(a-\frac{c d^2}{e^2}\right)}{7 (d+e x)^{7/2}}-\frac{2 c d}{5 e^2 (d+e x)^{5/2}}","-\frac{2 \left(a-\frac{c d^2}{e^2}\right)}{7 (d+e x)^{7/2}}-\frac{2 c d}{5 e^2 (d+e x)^{5/2}}",1,"(-2*(a - (c*d^2)/e^2))/(7*(d + e*x)^(7/2)) - (2*c*d)/(5*e^2*(d + e*x)^(5/2))","A",3,2,35,0.05714,1,"{24, 43}"
1984,1,83,0,0.0577019,"\int \sqrt{d+e x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2 \, dx","Int[Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{4 c d (d+e x)^{9/2} \left(c d^2-a e^2\right)}{9 e^3}+\frac{2 (d+e x)^{7/2} \left(c d^2-a e^2\right)^2}{7 e^3}+\frac{2 c^2 d^2 (d+e x)^{11/2}}{11 e^3}","-\frac{4 c d (d+e x)^{9/2} \left(c d^2-a e^2\right)}{9 e^3}+\frac{2 (d+e x)^{7/2} \left(c d^2-a e^2\right)^2}{7 e^3}+\frac{2 c^2 d^2 (d+e x)^{11/2}}{11 e^3}",1,"(2*(c*d^2 - a*e^2)^2*(d + e*x)^(7/2))/(7*e^3) - (4*c*d*(c*d^2 - a*e^2)*(d + e*x)^(9/2))/(9*e^3) + (2*c^2*d^2*(d + e*x)^(11/2))/(11*e^3)","A",3,2,37,0.05405,1,"{626, 43}"
1985,1,83,0,0.0389183,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/Sqrt[d + e*x],x]","-\frac{4 c d (d+e x)^{7/2} \left(c d^2-a e^2\right)}{7 e^3}+\frac{2 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}{5 e^3}+\frac{2 c^2 d^2 (d+e x)^{9/2}}{9 e^3}","-\frac{4 c d (d+e x)^{7/2} \left(c d^2-a e^2\right)}{7 e^3}+\frac{2 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}{5 e^3}+\frac{2 c^2 d^2 (d+e x)^{9/2}}{9 e^3}",1,"(2*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2))/(5*e^3) - (4*c*d*(c*d^2 - a*e^2)*(d + e*x)^(7/2))/(7*e^3) + (2*c^2*d^2*(d + e*x)^(9/2))/(9*e^3)","A",3,2,37,0.05405,1,"{626, 43}"
1986,1,83,0,0.0391043,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^(3/2),x]","-\frac{4 c d (d+e x)^{5/2} \left(c d^2-a e^2\right)}{5 e^3}+\frac{2 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}{3 e^3}+\frac{2 c^2 d^2 (d+e x)^{7/2}}{7 e^3}","-\frac{4 c d (d+e x)^{5/2} \left(c d^2-a e^2\right)}{5 e^3}+\frac{2 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}{3 e^3}+\frac{2 c^2 d^2 (d+e x)^{7/2}}{7 e^3}",1,"(2*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2))/(3*e^3) - (4*c*d*(c*d^2 - a*e^2)*(d + e*x)^(5/2))/(5*e^3) + (2*c^2*d^2*(d + e*x)^(7/2))/(7*e^3)","A",3,2,37,0.05405,1,"{626, 43}"
1987,1,81,0,0.0392762,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^(5/2),x]","-\frac{4 c d (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 e^3}+\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{e^3}+\frac{2 c^2 d^2 (d+e x)^{5/2}}{5 e^3}","-\frac{4 c d (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 e^3}+\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{e^3}+\frac{2 c^2 d^2 (d+e x)^{5/2}}{5 e^3}",1,"(2*(c*d^2 - a*e^2)^2*Sqrt[d + e*x])/e^3 - (4*c*d*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(3*e^3) + (2*c^2*d^2*(d + e*x)^(5/2))/(5*e^3)","A",3,2,37,0.05405,1,"{626, 43}"
1988,1,79,0,0.0410338,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^{7/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^(7/2),x]","-\frac{4 c d \sqrt{d+e x} \left(c d^2-a e^2\right)}{e^3}-\frac{2 \left(c d^2-a e^2\right)^2}{e^3 \sqrt{d+e x}}+\frac{2 c^2 d^2 (d+e x)^{3/2}}{3 e^3}","-\frac{4 c d \sqrt{d+e x} \left(c d^2-a e^2\right)}{e^3}-\frac{2 \left(c d^2-a e^2\right)^2}{e^3 \sqrt{d+e x}}+\frac{2 c^2 d^2 (d+e x)^{3/2}}{3 e^3}",1,"(-2*(c*d^2 - a*e^2)^2)/(e^3*Sqrt[d + e*x]) - (4*c*d*(c*d^2 - a*e^2)*Sqrt[d + e*x])/e^3 + (2*c^2*d^2*(d + e*x)^(3/2))/(3*e^3)","A",3,2,37,0.05405,1,"{626, 43}"
1989,1,79,0,0.0394922,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^{9/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^(9/2),x]","\frac{4 c d \left(c d^2-a e^2\right)}{e^3 \sqrt{d+e x}}-\frac{2 \left(c d^2-a e^2\right)^2}{3 e^3 (d+e x)^{3/2}}+\frac{2 c^2 d^2 \sqrt{d+e x}}{e^3}","\frac{4 c d \left(c d^2-a e^2\right)}{e^3 \sqrt{d+e x}}-\frac{2 \left(c d^2-a e^2\right)^2}{3 e^3 (d+e x)^{3/2}}+\frac{2 c^2 d^2 \sqrt{d+e x}}{e^3}",1,"(-2*(c*d^2 - a*e^2)^2)/(3*e^3*(d + e*x)^(3/2)) + (4*c*d*(c*d^2 - a*e^2))/(e^3*Sqrt[d + e*x]) + (2*c^2*d^2*Sqrt[d + e*x])/e^3","A",3,2,37,0.05405,1,"{626, 43}"
1990,1,81,0,0.0395864,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^{11/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^(11/2),x]","\frac{4 c d \left(c d^2-a e^2\right)}{3 e^3 (d+e x)^{3/2}}-\frac{2 \left(c d^2-a e^2\right)^2}{5 e^3 (d+e x)^{5/2}}-\frac{2 c^2 d^2}{e^3 \sqrt{d+e x}}","\frac{4 c d \left(c d^2-a e^2\right)}{3 e^3 (d+e x)^{3/2}}-\frac{2 \left(c d^2-a e^2\right)^2}{5 e^3 (d+e x)^{5/2}}-\frac{2 c^2 d^2}{e^3 \sqrt{d+e x}}",1,"(-2*(c*d^2 - a*e^2)^2)/(5*e^3*(d + e*x)^(5/2)) + (4*c*d*(c*d^2 - a*e^2))/(3*e^3*(d + e*x)^(3/2)) - (2*c^2*d^2)/(e^3*Sqrt[d + e*x])","A",3,2,37,0.05405,1,"{626, 43}"
1991,1,83,0,0.0388828,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2}{(d+e x)^{13/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^(13/2),x]","\frac{4 c d \left(c d^2-a e^2\right)}{5 e^3 (d+e x)^{5/2}}-\frac{2 \left(c d^2-a e^2\right)^2}{7 e^3 (d+e x)^{7/2}}-\frac{2 c^2 d^2}{3 e^3 (d+e x)^{3/2}}","\frac{4 c d \left(c d^2-a e^2\right)}{5 e^3 (d+e x)^{5/2}}-\frac{2 \left(c d^2-a e^2\right)^2}{7 e^3 (d+e x)^{7/2}}-\frac{2 c^2 d^2}{3 e^3 (d+e x)^{3/2}}",1,"(-2*(c*d^2 - a*e^2)^2)/(7*e^3*(d + e*x)^(7/2)) + (4*c*d*(c*d^2 - a*e^2))/(5*e^3*(d + e*x)^(5/2)) - (2*c^2*d^2)/(3*e^3*(d + e*x)^(3/2))","A",3,2,37,0.05405,1,"{626, 43}"
1992,1,119,0,0.0816524,"\int \sqrt{d+e x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3 \, dx","Int[Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{6 c^2 d^2 (d+e x)^{13/2} \left(c d^2-a e^2\right)}{13 e^4}+\frac{6 c d (d+e x)^{11/2} \left(c d^2-a e^2\right)^2}{11 e^4}-\frac{2 (d+e x)^{9/2} \left(c d^2-a e^2\right)^3}{9 e^4}+\frac{2 c^3 d^3 (d+e x)^{15/2}}{15 e^4}","-\frac{6 c^2 d^2 (d+e x)^{13/2} \left(c d^2-a e^2\right)}{13 e^4}+\frac{6 c d (d+e x)^{11/2} \left(c d^2-a e^2\right)^2}{11 e^4}-\frac{2 (d+e x)^{9/2} \left(c d^2-a e^2\right)^3}{9 e^4}+\frac{2 c^3 d^3 (d+e x)^{15/2}}{15 e^4}",1,"(-2*(c*d^2 - a*e^2)^3*(d + e*x)^(9/2))/(9*e^4) + (6*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^(11/2))/(11*e^4) - (6*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^(13/2))/(13*e^4) + (2*c^3*d^3*(d + e*x)^(15/2))/(15*e^4)","A",3,2,37,0.05405,1,"{626, 43}"
1993,1,119,0,0.0569964,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{\sqrt{d+e x}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/Sqrt[d + e*x],x]","-\frac{6 c^2 d^2 (d+e x)^{11/2} \left(c d^2-a e^2\right)}{11 e^4}+\frac{2 c d (d+e x)^{9/2} \left(c d^2-a e^2\right)^2}{3 e^4}-\frac{2 (d+e x)^{7/2} \left(c d^2-a e^2\right)^3}{7 e^4}+\frac{2 c^3 d^3 (d+e x)^{13/2}}{13 e^4}","-\frac{6 c^2 d^2 (d+e x)^{11/2} \left(c d^2-a e^2\right)}{11 e^4}+\frac{2 c d (d+e x)^{9/2} \left(c d^2-a e^2\right)^2}{3 e^4}-\frac{2 (d+e x)^{7/2} \left(c d^2-a e^2\right)^3}{7 e^4}+\frac{2 c^3 d^3 (d+e x)^{13/2}}{13 e^4}",1,"(-2*(c*d^2 - a*e^2)^3*(d + e*x)^(7/2))/(7*e^4) + (2*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^(9/2))/(3*e^4) - (6*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^(11/2))/(11*e^4) + (2*c^3*d^3*(d + e*x)^(13/2))/(13*e^4)","A",3,2,37,0.05405,1,"{626, 43}"
1994,1,119,0,0.0576717,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^{3/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^(3/2),x]","-\frac{2 c^2 d^2 (d+e x)^{9/2} \left(c d^2-a e^2\right)}{3 e^4}+\frac{6 c d (d+e x)^{7/2} \left(c d^2-a e^2\right)^2}{7 e^4}-\frac{2 (d+e x)^{5/2} \left(c d^2-a e^2\right)^3}{5 e^4}+\frac{2 c^3 d^3 (d+e x)^{11/2}}{11 e^4}","-\frac{2 c^2 d^2 (d+e x)^{9/2} \left(c d^2-a e^2\right)}{3 e^4}+\frac{6 c d (d+e x)^{7/2} \left(c d^2-a e^2\right)^2}{7 e^4}-\frac{2 (d+e x)^{5/2} \left(c d^2-a e^2\right)^3}{5 e^4}+\frac{2 c^3 d^3 (d+e x)^{11/2}}{11 e^4}",1,"(-2*(c*d^2 - a*e^2)^3*(d + e*x)^(5/2))/(5*e^4) + (6*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^(7/2))/(7*e^4) - (2*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^(9/2))/(3*e^4) + (2*c^3*d^3*(d + e*x)^(11/2))/(11*e^4)","A",3,2,37,0.05405,1,"{626, 43}"
1995,1,119,0,0.051909,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^{5/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^(5/2),x]","-\frac{6 c^2 d^2 (d+e x)^{7/2} \left(c d^2-a e^2\right)}{7 e^4}+\frac{6 c d (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}{5 e^4}-\frac{2 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}{3 e^4}+\frac{2 c^3 d^3 (d+e x)^{9/2}}{9 e^4}","-\frac{6 c^2 d^2 (d+e x)^{7/2} \left(c d^2-a e^2\right)}{7 e^4}+\frac{6 c d (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}{5 e^4}-\frac{2 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}{3 e^4}+\frac{2 c^3 d^3 (d+e x)^{9/2}}{9 e^4}",1,"(-2*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2))/(3*e^4) + (6*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2))/(5*e^4) - (6*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^(7/2))/(7*e^4) + (2*c^3*d^3*(d + e*x)^(9/2))/(9*e^4)","A",3,2,37,0.05405,1,"{626, 43}"
1996,1,115,0,0.0545124,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^{7/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^(7/2),x]","-\frac{6 c^2 d^2 (d+e x)^{5/2} \left(c d^2-a e^2\right)}{5 e^4}+\frac{2 c d (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}{e^4}-\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)^3}{e^4}+\frac{2 c^3 d^3 (d+e x)^{7/2}}{7 e^4}","-\frac{6 c^2 d^2 (d+e x)^{5/2} \left(c d^2-a e^2\right)}{5 e^4}+\frac{2 c d (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}{e^4}-\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)^3}{e^4}+\frac{2 c^3 d^3 (d+e x)^{7/2}}{7 e^4}",1,"(-2*(c*d^2 - a*e^2)^3*Sqrt[d + e*x])/e^4 + (2*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2))/e^4 - (6*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^(5/2))/(5*e^4) + (2*c^3*d^3*(d + e*x)^(7/2))/(7*e^4)","A",3,2,37,0.05405,1,"{626, 43}"
1997,1,113,0,0.0515285,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^{9/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^(9/2),x]","-\frac{2 c^2 d^2 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{e^4}+\frac{6 c d \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{e^4}+\frac{2 \left(c d^2-a e^2\right)^3}{e^4 \sqrt{d+e x}}+\frac{2 c^3 d^3 (d+e x)^{5/2}}{5 e^4}","-\frac{2 c^2 d^2 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{e^4}+\frac{6 c d \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{e^4}+\frac{2 \left(c d^2-a e^2\right)^3}{e^4 \sqrt{d+e x}}+\frac{2 c^3 d^3 (d+e x)^{5/2}}{5 e^4}",1,"(2*(c*d^2 - a*e^2)^3)/(e^4*Sqrt[d + e*x]) + (6*c*d*(c*d^2 - a*e^2)^2*Sqrt[d + e*x])/e^4 - (2*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/e^4 + (2*c^3*d^3*(d + e*x)^(5/2))/(5*e^4)","A",3,2,37,0.05405,1,"{626, 43}"
1998,1,115,0,0.0520726,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^{11/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^(11/2),x]","-\frac{6 c^2 d^2 \sqrt{d+e x} \left(c d^2-a e^2\right)}{e^4}-\frac{6 c d \left(c d^2-a e^2\right)^2}{e^4 \sqrt{d+e x}}+\frac{2 \left(c d^2-a e^2\right)^3}{3 e^4 (d+e x)^{3/2}}+\frac{2 c^3 d^3 (d+e x)^{3/2}}{3 e^4}","-\frac{6 c^2 d^2 \sqrt{d+e x} \left(c d^2-a e^2\right)}{e^4}-\frac{6 c d \left(c d^2-a e^2\right)^2}{e^4 \sqrt{d+e x}}+\frac{2 \left(c d^2-a e^2\right)^3}{3 e^4 (d+e x)^{3/2}}+\frac{2 c^3 d^3 (d+e x)^{3/2}}{3 e^4}",1,"(2*(c*d^2 - a*e^2)^3)/(3*e^4*(d + e*x)^(3/2)) - (6*c*d*(c*d^2 - a*e^2)^2)/(e^4*Sqrt[d + e*x]) - (6*c^2*d^2*(c*d^2 - a*e^2)*Sqrt[d + e*x])/e^4 + (2*c^3*d^3*(d + e*x)^(3/2))/(3*e^4)","A",3,2,37,0.05405,1,"{626, 43}"
1999,1,113,0,0.0530466,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3}{(d+e x)^{13/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^(13/2),x]","\frac{6 c^2 d^2 \left(c d^2-a e^2\right)}{e^4 \sqrt{d+e x}}-\frac{2 c d \left(c d^2-a e^2\right)^2}{e^4 (d+e x)^{3/2}}+\frac{2 \left(c d^2-a e^2\right)^3}{5 e^4 (d+e x)^{5/2}}+\frac{2 c^3 d^3 \sqrt{d+e x}}{e^4}","\frac{6 c^2 d^2 \left(c d^2-a e^2\right)}{e^4 \sqrt{d+e x}}-\frac{2 c d \left(c d^2-a e^2\right)^2}{e^4 (d+e x)^{3/2}}+\frac{2 \left(c d^2-a e^2\right)^3}{5 e^4 (d+e x)^{5/2}}+\frac{2 c^3 d^3 \sqrt{d+e x}}{e^4}",1,"(2*(c*d^2 - a*e^2)^3)/(5*e^4*(d + e*x)^(5/2)) - (2*c*d*(c*d^2 - a*e^2)^2)/(e^4*(d + e*x)^(3/2)) + (6*c^2*d^2*(c*d^2 - a*e^2))/(e^4*Sqrt[d + e*x]) + (2*c^3*d^3*Sqrt[d + e*x])/e^4","A",3,2,37,0.05405,1,"{626, 43}"
2000,1,180,0,0.2374407,"\int \frac{(d+e x)^{9/2}}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^(9/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)^3}{c^4 d^4}+\frac{2 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}{3 c^3 d^3}+\frac{2 (d+e x)^{5/2} \left(c d^2-a e^2\right)}{5 c^2 d^2}-\frac{2 \left(c d^2-a e^2\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{9/2} d^{9/2}}+\frac{2 (d+e x)^{7/2}}{7 c d}","\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)^3}{c^4 d^4}+\frac{2 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}{3 c^3 d^3}+\frac{2 (d+e x)^{5/2} \left(c d^2-a e^2\right)}{5 c^2 d^2}-\frac{2 \left(c d^2-a e^2\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{9/2} d^{9/2}}+\frac{2 (d+e x)^{7/2}}{7 c d}",1,"(2*(c*d^2 - a*e^2)^3*Sqrt[d + e*x])/(c^4*d^4) + (2*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2))/(3*c^3*d^3) + (2*(c*d^2 - a*e^2)*(d + e*x)^(5/2))/(5*c^2*d^2) + (2*(d + e*x)^(7/2))/(7*c*d) - (2*(c*d^2 - a*e^2)^(7/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(9/2)*d^(9/2))","A",7,4,37,0.1081,1,"{626, 50, 63, 208}"
2001,1,147,0,0.0917097,"\int \frac{(d+e x)^{7/2}}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{c^3 d^3}+\frac{2 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 c^2 d^2}-\frac{2 \left(c d^2-a e^2\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{7/2} d^{7/2}}+\frac{2 (d+e x)^{5/2}}{5 c d}","\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{c^3 d^3}+\frac{2 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 c^2 d^2}-\frac{2 \left(c d^2-a e^2\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{7/2} d^{7/2}}+\frac{2 (d+e x)^{5/2}}{5 c d}",1,"(2*(c*d^2 - a*e^2)^2*Sqrt[d + e*x])/(c^3*d^3) + (2*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(3*c^2*d^2) + (2*(d + e*x)^(5/2))/(5*c*d) - (2*(c*d^2 - a*e^2)^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(7/2)*d^(7/2))","A",6,4,37,0.1081,1,"{626, 50, 63, 208}"
2002,1,114,0,0.0712063,"\int \frac{(d+e x)^{5/2}}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)}{c^2 d^2}-\frac{2 \left(c d^2-a e^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{5/2} d^{5/2}}+\frac{2 (d+e x)^{3/2}}{3 c d}","\frac{2 \sqrt{d+e x} \left(c d^2-a e^2\right)}{c^2 d^2}-\frac{2 \left(c d^2-a e^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{5/2} d^{5/2}}+\frac{2 (d+e x)^{3/2}}{3 c d}",1,"(2*(c*d^2 - a*e^2)*Sqrt[d + e*x])/(c^2*d^2) + (2*(d + e*x)^(3/2))/(3*c*d) - (2*(c*d^2 - a*e^2)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(5/2)*d^(5/2))","A",5,4,37,0.1081,1,"{626, 50, 63, 208}"
2003,1,83,0,0.0546732,"\int \frac{(d+e x)^{3/2}}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{2 \sqrt{d+e x}}{c d}-\frac{2 \sqrt{c d^2-a e^2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{3/2} d^{3/2}}","\frac{2 \sqrt{d+e x}}{c d}-\frac{2 \sqrt{c d^2-a e^2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{3/2} d^{3/2}}",1,"(2*Sqrt[d + e*x])/(c*d) - (2*Sqrt[c*d^2 - a*e^2]*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(3/2)*d^(3/2))","A",4,4,37,0.1081,1,"{626, 50, 63, 208}"
2004,1,65,0,0.0445752,"\int \frac{\sqrt{d+e x}}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[Sqrt[d + e*x]/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\sqrt{c} \sqrt{d} \sqrt{c d^2-a e^2}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\sqrt{c} \sqrt{d} \sqrt{c d^2-a e^2}}",1,"(-2*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(Sqrt[c]*Sqrt[d]*Sqrt[c*d^2 - a*e^2])","A",3,3,37,0.08108,1,"{626, 63, 208}"
2005,1,91,0,0.0830422,"\int \frac{1}{\sqrt{d+e x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)),x]","\frac{2}{\sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{2 \sqrt{c} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{3/2}}","\frac{2}{\sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{2 \sqrt{c} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{3/2}}",1,"2/((c*d^2 - a*e^2)*Sqrt[d + e*x]) - (2*Sqrt[c]*Sqrt[d]*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c*d^2 - a*e^2)^(3/2)","A",4,4,37,0.1081,1,"{626, 51, 63, 208}"
2006,1,120,0,0.0947309,"\int \frac{1}{(d+e x)^{3/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)} \, dx","Int[1/((d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)),x]","-\frac{2 c^{3/2} d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{5/2}}+\frac{2 c d}{\sqrt{d+e x} \left(c d^2-a e^2\right)^2}+\frac{2}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)}","-\frac{2 c^{3/2} d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{5/2}}+\frac{2 c d}{\sqrt{d+e x} \left(c d^2-a e^2\right)^2}+\frac{2}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)}",1,"2/(3*(c*d^2 - a*e^2)*(d + e*x)^(3/2)) + (2*c*d)/((c*d^2 - a*e^2)^2*Sqrt[d + e*x]) - (2*c^(3/2)*d^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c*d^2 - a*e^2)^(5/2)","A",5,4,37,0.1081,1,"{626, 51, 63, 208}"
2007,1,153,0,0.1295548,"\int \frac{1}{(d+e x)^{5/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)} \, dx","Int[1/((d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)),x]","\frac{2 c^2 d^2}{\sqrt{d+e x} \left(c d^2-a e^2\right)^3}-\frac{2 c^{5/2} d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{7/2}}+\frac{2 c d}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}+\frac{2}{5 (d+e x)^{5/2} \left(c d^2-a e^2\right)}","\frac{2 c^2 d^2}{\sqrt{d+e x} \left(c d^2-a e^2\right)^3}-\frac{2 c^{5/2} d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{7/2}}+\frac{2 c d}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}+\frac{2}{5 (d+e x)^{5/2} \left(c d^2-a e^2\right)}",1,"2/(5*(c*d^2 - a*e^2)*(d + e*x)^(5/2)) + (2*c*d)/(3*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) + (2*c^2*d^2)/((c*d^2 - a*e^2)^3*Sqrt[d + e*x]) - (2*c^(5/2)*d^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c*d^2 - a*e^2)^(7/2)","A",6,4,37,0.1081,1,"{626, 51, 63, 208}"
2008,1,186,0,0.1636539,"\int \frac{1}{(d+e x)^{7/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)} \, dx","Int[1/((d + e*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)),x]","\frac{2 c^3 d^3}{\sqrt{d+e x} \left(c d^2-a e^2\right)^4}+\frac{2 c^2 d^2}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}-\frac{2 c^{7/2} d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{9/2}}+\frac{2 c d}{5 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}+\frac{2}{7 (d+e x)^{7/2} \left(c d^2-a e^2\right)}","\frac{2 c^3 d^3}{\sqrt{d+e x} \left(c d^2-a e^2\right)^4}+\frac{2 c^2 d^2}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}-\frac{2 c^{7/2} d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{9/2}}+\frac{2 c d}{5 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}+\frac{2}{7 (d+e x)^{7/2} \left(c d^2-a e^2\right)}",1,"2/(7*(c*d^2 - a*e^2)*(d + e*x)^(7/2)) + (2*c*d)/(5*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2)) + (2*c^2*d^2)/(3*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)) + (2*c^3*d^3)/((c*d^2 - a*e^2)^4*Sqrt[d + e*x]) - (2*c^(7/2)*d^(7/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c*d^2 - a*e^2)^(9/2)","A",7,4,37,0.1081,1,"{626, 51, 63, 208}"
2009,1,210,0,0.1761131,"\int \frac{(d+e x)^{13/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^(13/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{9 e (d+e x)^{5/2} \left(c d^2-a e^2\right)}{5 c^3 d^3}+\frac{3 e (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}{c^4 d^4}+\frac{9 e \sqrt{d+e x} \left(c d^2-a e^2\right)^3}{c^5 d^5}-\frac{9 e \left(c d^2-a e^2\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{11/2} d^{11/2}}-\frac{(d+e x)^{9/2}}{c d (a e+c d x)}+\frac{9 e (d+e x)^{7/2}}{7 c^2 d^2}","\frac{9 e (d+e x)^{5/2} \left(c d^2-a e^2\right)}{5 c^3 d^3}+\frac{3 e (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}{c^4 d^4}+\frac{9 e \sqrt{d+e x} \left(c d^2-a e^2\right)^3}{c^5 d^5}-\frac{9 e \left(c d^2-a e^2\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{11/2} d^{11/2}}-\frac{(d+e x)^{9/2}}{c d (a e+c d x)}+\frac{9 e (d+e x)^{7/2}}{7 c^2 d^2}",1,"(9*e*(c*d^2 - a*e^2)^3*Sqrt[d + e*x])/(c^5*d^5) + (3*e*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2))/(c^4*d^4) + (9*e*(c*d^2 - a*e^2)*(d + e*x)^(5/2))/(5*c^3*d^3) + (9*e*(d + e*x)^(7/2))/(7*c^2*d^2) - (d + e*x)^(9/2)/(c*d*(a*e + c*d*x)) - (9*e*(c*d^2 - a*e^2)^(7/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(11/2)*d^(11/2))","A",8,5,37,0.1351,1,"{626, 47, 50, 63, 208}"
2010,1,178,0,0.1347652,"\int \frac{(d+e x)^{11/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^(11/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{7 e (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 c^3 d^3}+\frac{7 e \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{c^4 d^4}-\frac{7 e \left(c d^2-a e^2\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{9/2} d^{9/2}}-\frac{(d+e x)^{7/2}}{c d (a e+c d x)}+\frac{7 e (d+e x)^{5/2}}{5 c^2 d^2}","\frac{7 e (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 c^3 d^3}+\frac{7 e \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{c^4 d^4}-\frac{7 e \left(c d^2-a e^2\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{9/2} d^{9/2}}-\frac{(d+e x)^{7/2}}{c d (a e+c d x)}+\frac{7 e (d+e x)^{5/2}}{5 c^2 d^2}",1,"(7*e*(c*d^2 - a*e^2)^2*Sqrt[d + e*x])/(c^4*d^4) + (7*e*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(3*c^3*d^3) + (7*e*(d + e*x)^(5/2))/(5*c^2*d^2) - (d + e*x)^(7/2)/(c*d*(a*e + c*d*x)) - (7*e*(c*d^2 - a*e^2)^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(9/2)*d^(9/2))","A",7,5,37,0.1351,1,"{626, 47, 50, 63, 208}"
2011,1,144,0,0.0953684,"\int \frac{(d+e x)^{9/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^(9/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{5 e \sqrt{d+e x} \left(c d^2-a e^2\right)}{c^3 d^3}-\frac{5 e \left(c d^2-a e^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{7/2} d^{7/2}}-\frac{(d+e x)^{5/2}}{c d (a e+c d x)}+\frac{5 e (d+e x)^{3/2}}{3 c^2 d^2}","\frac{5 e \sqrt{d+e x} \left(c d^2-a e^2\right)}{c^3 d^3}-\frac{5 e \left(c d^2-a e^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{7/2} d^{7/2}}-\frac{(d+e x)^{5/2}}{c d (a e+c d x)}+\frac{5 e (d+e x)^{3/2}}{3 c^2 d^2}",1,"(5*e*(c*d^2 - a*e^2)*Sqrt[d + e*x])/(c^3*d^3) + (5*e*(d + e*x)^(3/2))/(3*c^2*d^2) - (d + e*x)^(5/2)/(c*d*(a*e + c*d*x)) - (5*e*(c*d^2 - a*e^2)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(7/2)*d^(7/2))","A",6,5,37,0.1351,1,"{626, 47, 50, 63, 208}"
2012,1,112,0,0.0699287,"\int \frac{(d+e x)^{7/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{3 e \sqrt{c d^2-a e^2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{5/2} d^{5/2}}-\frac{(d+e x)^{3/2}}{c d (a e+c d x)}+\frac{3 e \sqrt{d+e x}}{c^2 d^2}","-\frac{3 e \sqrt{c d^2-a e^2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{5/2} d^{5/2}}-\frac{(d+e x)^{3/2}}{c d (a e+c d x)}+\frac{3 e \sqrt{d+e x}}{c^2 d^2}",1,"(3*e*Sqrt[d + e*x])/(c^2*d^2) - (d + e*x)^(3/2)/(c*d*(a*e + c*d*x)) - (3*e*Sqrt[c*d^2 - a*e^2]*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(5/2)*d^(5/2))","A",5,5,37,0.1351,1,"{626, 47, 50, 63, 208}"
2013,1,94,0,0.0571539,"\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)^2} \, dx","Int[(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{3/2} d^{3/2} \sqrt{c d^2-a e^2}}-\frac{\sqrt{d+e x}}{c d (a e+c d x)}","-\frac{e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{c^{3/2} d^{3/2} \sqrt{c d^2-a e^2}}-\frac{\sqrt{d+e x}}{c d (a e+c d x)}",1,"-(Sqrt[d + e*x]/(c*d*(a*e + c*d*x))) - (e*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c^(3/2)*d^(3/2)*Sqrt[c*d^2 - a*e^2])","A",4,4,37,0.1081,1,"{626, 47, 63, 208}"
2014,1,101,0,0.0565612,"\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)^2} \, dx","Int[(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\sqrt{c} \sqrt{d} \left(c d^2-a e^2\right)^{3/2}}-\frac{\sqrt{d+e x}}{\left(c d^2-a e^2\right) (a e+c d x)}","\frac{e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\sqrt{c} \sqrt{d} \left(c d^2-a e^2\right)^{3/2}}-\frac{\sqrt{d+e x}}{\left(c d^2-a e^2\right) (a e+c d x)}",1,"-(Sqrt[d + e*x]/((c*d^2 - a*e^2)*(a*e + c*d*x))) + (e*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(Sqrt[c]*Sqrt[d]*(c*d^2 - a*e^2)^(3/2))","A",4,4,37,0.1081,1,"{626, 51, 63, 208}"
2015,1,128,0,0.0640229,"\int \frac{\sqrt{d+e x}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[Sqrt[d + e*x]/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{3 e}{\sqrt{d+e x} \left(c d^2-a e^2\right)^2}-\frac{1}{\sqrt{d+e x} \left(c d^2-a e^2\right) (a e+c d x)}+\frac{3 \sqrt{c} \sqrt{d} e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{5/2}}","-\frac{3 e}{\sqrt{d+e x} \left(c d^2-a e^2\right)^2}-\frac{1}{\sqrt{d+e x} \left(c d^2-a e^2\right) (a e+c d x)}+\frac{3 \sqrt{c} \sqrt{d} e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{5/2}}",1,"(-3*e)/((c*d^2 - a*e^2)^2*Sqrt[d + e*x]) - 1/((c*d^2 - a*e^2)*(a*e + c*d*x)*Sqrt[d + e*x]) + (3*Sqrt[c]*Sqrt[d]*e*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c*d^2 - a*e^2)^(5/2)","A",5,4,37,0.1081,1,"{626, 51, 63, 208}"
2016,1,158,0,0.0927356,"\int \frac{1}{\sqrt{d+e x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[1/(Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2),x]","\frac{5 c^{3/2} d^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{7/2}}-\frac{5 c d e}{\sqrt{d+e x} \left(c d^2-a e^2\right)^3}-\frac{1}{(d+e x)^{3/2} \left(c d^2-a e^2\right) (a e+c d x)}-\frac{5 e}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}","\frac{5 c^{3/2} d^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{7/2}}-\frac{5 c d e}{\sqrt{d+e x} \left(c d^2-a e^2\right)^3}-\frac{1}{(d+e x)^{3/2} \left(c d^2-a e^2\right) (a e+c d x)}-\frac{5 e}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}",1,"(-5*e)/(3*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) - 1/((c*d^2 - a*e^2)*(a*e + c*d*x)*(d + e*x)^(3/2)) - (5*c*d*e)/((c*d^2 - a*e^2)^3*Sqrt[d + e*x]) + (5*c^(3/2)*d^(3/2)*e*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c*d^2 - a*e^2)^(7/2)","A",6,4,37,0.1081,1,"{626, 51, 63, 208}"
2017,1,192,0,0.1286078,"\int \frac{1}{(d+e x)^{3/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2} \, dx","Int[1/((d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2),x]","-\frac{7 c^2 d^2 e}{\sqrt{d+e x} \left(c d^2-a e^2\right)^4}+\frac{7 c^{5/2} d^{5/2} e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{9/2}}-\frac{7 c d e}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}-\frac{1}{(d+e x)^{5/2} \left(c d^2-a e^2\right) (a e+c d x)}-\frac{7 e}{5 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}","-\frac{7 c^2 d^2 e}{\sqrt{d+e x} \left(c d^2-a e^2\right)^4}+\frac{7 c^{5/2} d^{5/2} e \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{9/2}}-\frac{7 c d e}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}-\frac{1}{(d+e x)^{5/2} \left(c d^2-a e^2\right) (a e+c d x)}-\frac{7 e}{5 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}",1,"(-7*e)/(5*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2)) - 1/((c*d^2 - a*e^2)*(a*e + c*d*x)*(d + e*x)^(5/2)) - (7*c*d*e)/(3*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)) - (7*c^2*d^2*e)/((c*d^2 - a*e^2)^4*Sqrt[d + e*x]) + (7*c^(5/2)*d^(5/2)*e*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(c*d^2 - a*e^2)^(9/2)","A",7,4,37,0.1081,1,"{626, 51, 63, 208}"
2018,1,222,0,0.1859032,"\int \frac{(d+e x)^{15/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^(15/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{21 e^2 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{4 c^4 d^4}+\frac{63 e^2 \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{4 c^5 d^5}-\frac{63 e^2 \left(c d^2-a e^2\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{11/2} d^{11/2}}-\frac{9 e (d+e x)^{7/2}}{4 c^2 d^2 (a e+c d x)}-\frac{(d+e x)^{9/2}}{2 c d (a e+c d x)^2}+\frac{63 e^2 (d+e x)^{5/2}}{20 c^3 d^3}","\frac{21 e^2 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{4 c^4 d^4}+\frac{63 e^2 \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{4 c^5 d^5}-\frac{63 e^2 \left(c d^2-a e^2\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{11/2} d^{11/2}}-\frac{9 e (d+e x)^{7/2}}{4 c^2 d^2 (a e+c d x)}-\frac{(d+e x)^{9/2}}{2 c d (a e+c d x)^2}+\frac{63 e^2 (d+e x)^{5/2}}{20 c^3 d^3}",1,"(63*e^2*(c*d^2 - a*e^2)^2*Sqrt[d + e*x])/(4*c^5*d^5) + (21*e^2*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(4*c^4*d^4) + (63*e^2*(d + e*x)^(5/2))/(20*c^3*d^3) - (9*e*(d + e*x)^(7/2))/(4*c^2*d^2*(a*e + c*d*x)) - (d + e*x)^(9/2)/(2*c*d*(a*e + c*d*x)^2) - (63*e^2*(c*d^2 - a*e^2)^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(4*c^(11/2)*d^(11/2))","A",8,5,37,0.1351,1,"{626, 47, 50, 63, 208}"
2019,1,186,0,0.1377836,"\int \frac{(d+e x)^{13/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^(13/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{35 e^2 \sqrt{d+e x} \left(c d^2-a e^2\right)}{4 c^4 d^4}-\frac{35 e^2 \left(c d^2-a e^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{9/2} d^{9/2}}-\frac{7 e (d+e x)^{5/2}}{4 c^2 d^2 (a e+c d x)}-\frac{(d+e x)^{7/2}}{2 c d (a e+c d x)^2}+\frac{35 e^2 (d+e x)^{3/2}}{12 c^3 d^3}","\frac{35 e^2 \sqrt{d+e x} \left(c d^2-a e^2\right)}{4 c^4 d^4}-\frac{35 e^2 \left(c d^2-a e^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{9/2} d^{9/2}}-\frac{7 e (d+e x)^{5/2}}{4 c^2 d^2 (a e+c d x)}-\frac{(d+e x)^{7/2}}{2 c d (a e+c d x)^2}+\frac{35 e^2 (d+e x)^{3/2}}{12 c^3 d^3}",1,"(35*e^2*(c*d^2 - a*e^2)*Sqrt[d + e*x])/(4*c^4*d^4) + (35*e^2*(d + e*x)^(3/2))/(12*c^3*d^3) - (7*e*(d + e*x)^(5/2))/(4*c^2*d^2*(a*e + c*d*x)) - (d + e*x)^(7/2)/(2*c*d*(a*e + c*d*x)^2) - (35*e^2*(c*d^2 - a*e^2)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(4*c^(9/2)*d^(9/2))","A",7,5,37,0.1351,1,"{626, 47, 50, 63, 208}"
2020,1,152,0,0.1000753,"\int \frac{(d+e x)^{11/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^(11/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{15 e^2 \sqrt{c d^2-a e^2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{7/2} d^{7/2}}-\frac{5 e (d+e x)^{3/2}}{4 c^2 d^2 (a e+c d x)}-\frac{(d+e x)^{5/2}}{2 c d (a e+c d x)^2}+\frac{15 e^2 \sqrt{d+e x}}{4 c^3 d^3}","-\frac{15 e^2 \sqrt{c d^2-a e^2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{7/2} d^{7/2}}-\frac{5 e (d+e x)^{3/2}}{4 c^2 d^2 (a e+c d x)}-\frac{(d+e x)^{5/2}}{2 c d (a e+c d x)^2}+\frac{15 e^2 \sqrt{d+e x}}{4 c^3 d^3}",1,"(15*e^2*Sqrt[d + e*x])/(4*c^3*d^3) - (5*e*(d + e*x)^(3/2))/(4*c^2*d^2*(a*e + c*d*x)) - (d + e*x)^(5/2)/(2*c*d*(a*e + c*d*x)^2) - (15*e^2*Sqrt[c*d^2 - a*e^2]*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(4*c^(7/2)*d^(7/2))","A",6,5,37,0.1351,1,"{626, 47, 50, 63, 208}"
2021,1,130,0,0.0809901,"\int \frac{(d+e x)^{9/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^(9/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{5/2} d^{5/2} \sqrt{c d^2-a e^2}}-\frac{3 e \sqrt{d+e x}}{4 c^2 d^2 (a e+c d x)}-\frac{(d+e x)^{3/2}}{2 c d (a e+c d x)^2}","-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{5/2} d^{5/2} \sqrt{c d^2-a e^2}}-\frac{3 e \sqrt{d+e x}}{4 c^2 d^2 (a e+c d x)}-\frac{(d+e x)^{3/2}}{2 c d (a e+c d x)^2}",1,"(-3*e*Sqrt[d + e*x])/(4*c^2*d^2*(a*e + c*d*x)) - (d + e*x)^(3/2)/(2*c*d*(a*e + c*d*x)^2) - (3*e^2*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(4*c^(5/2)*d^(5/2)*Sqrt[c*d^2 - a*e^2])","A",5,4,37,0.1081,1,"{626, 47, 63, 208}"
2022,1,144,0,0.0882176,"\int \frac{(d+e x)^{7/2}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{3/2} d^{3/2} \left(c d^2-a e^2\right)^{3/2}}-\frac{e \sqrt{d+e x}}{4 c d \left(c d^2-a e^2\right) (a e+c d x)}-\frac{\sqrt{d+e x}}{2 c d (a e+c d x)^2}","\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 c^{3/2} d^{3/2} \left(c d^2-a e^2\right)^{3/2}}-\frac{e \sqrt{d+e x}}{4 c d \left(c d^2-a e^2\right) (a e+c d x)}-\frac{\sqrt{d+e x}}{2 c d (a e+c d x)^2}",1,"-Sqrt[d + e*x]/(2*c*d*(a*e + c*d*x)^2) - (e*Sqrt[d + e*x])/(4*c*d*(c*d^2 - a*e^2)*(a*e + c*d*x)) + (e^2*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(4*c^(3/2)*d^(3/2)*(c*d^2 - a*e^2)^(3/2))","A",5,5,37,0.1351,1,"{626, 47, 51, 63, 208}"
2023,1,146,0,0.0856611,"\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)^3} \, dx","Int[(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{3 e \sqrt{d+e x}}{4 \left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{\sqrt{d+e x}}{2 \left(c d^2-a e^2\right) (a e+c d x)^2}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 \sqrt{c} \sqrt{d} \left(c d^2-a e^2\right)^{5/2}}","\frac{3 e \sqrt{d+e x}}{4 \left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{\sqrt{d+e x}}{2 \left(c d^2-a e^2\right) (a e+c d x)^2}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 \sqrt{c} \sqrt{d} \left(c d^2-a e^2\right)^{5/2}}",1,"-Sqrt[d + e*x]/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2) + (3*e*Sqrt[d + e*x])/(4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)) - (3*e^2*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(4*Sqrt[c]*Sqrt[d]*(c*d^2 - a*e^2)^(5/2))","A",5,4,37,0.1081,1,"{626, 51, 63, 208}"
2024,1,176,0,0.1190632,"\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} \, dx","Int[(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{15 e^2}{4 \sqrt{d+e x} \left(c d^2-a e^2\right)^3}+\frac{5 e}{4 \sqrt{d+e x} \left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{1}{2 \sqrt{d+e x} \left(c d^2-a e^2\right) (a e+c d x)^2}-\frac{15 \sqrt{c} \sqrt{d} e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{7/2}}","\frac{15 e^2}{4 \sqrt{d+e x} \left(c d^2-a e^2\right)^3}+\frac{5 e}{4 \sqrt{d+e x} \left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{1}{2 \sqrt{d+e x} \left(c d^2-a e^2\right) (a e+c d x)^2}-\frac{15 \sqrt{c} \sqrt{d} e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{7/2}}",1,"(15*e^2)/(4*(c*d^2 - a*e^2)^3*Sqrt[d + e*x]) - 1/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2*Sqrt[d + e*x]) + (5*e)/(4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)*Sqrt[d + e*x]) - (15*Sqrt[c]*Sqrt[d]*e^2*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(4*(c*d^2 - a*e^2)^(7/2))","A",6,4,37,0.1081,1,"{626, 51, 63, 208}"
2025,1,208,0,0.1377049,"\int \frac{\sqrt{d+e x}}{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[Sqrt[d + e*x]/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{35 c^{3/2} d^{3/2} e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{9/2}}+\frac{35 c d e^2}{4 \sqrt{d+e x} \left(c d^2-a e^2\right)^4}+\frac{35 e^2}{12 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}+\frac{7 e}{4 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{1}{2 (d+e x)^{3/2} \left(c d^2-a e^2\right) (a e+c d x)^2}","-\frac{35 c^{3/2} d^{3/2} e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{9/2}}+\frac{35 c d e^2}{4 \sqrt{d+e x} \left(c d^2-a e^2\right)^4}+\frac{35 e^2}{12 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}+\frac{7 e}{4 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{1}{2 (d+e x)^{3/2} \left(c d^2-a e^2\right) (a e+c d x)^2}",1,"(35*e^2)/(12*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)) - 1/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2*(d + e*x)^(3/2)) + (7*e)/(4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)*(d + e*x)^(3/2)) + (35*c*d*e^2)/(4*(c*d^2 - a*e^2)^4*Sqrt[d + e*x]) - (35*c^(3/2)*d^(3/2)*e^2*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(4*(c*d^2 - a*e^2)^(9/2))","A",7,4,37,0.1081,1,"{626, 51, 63, 208}"
2026,1,244,0,0.222973,"\int \frac{1}{\sqrt{d+e x} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3} \, dx","Int[1/(Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3),x]","\frac{63 c^2 d^2 e^2}{4 \sqrt{d+e x} \left(c d^2-a e^2\right)^5}-\frac{63 c^{5/2} d^{5/2} e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{11/2}}+\frac{21 c d e^2}{4 (d+e x)^{3/2} \left(c d^2-a e^2\right)^4}+\frac{9 e}{4 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{1}{2 (d+e x)^{5/2} \left(c d^2-a e^2\right) (a e+c d x)^2}+\frac{63 e^2}{20 (d+e x)^{5/2} \left(c d^2-a e^2\right)^3}","\frac{63 c^2 d^2 e^2}{4 \sqrt{d+e x} \left(c d^2-a e^2\right)^5}-\frac{63 c^{5/2} d^{5/2} e^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d} \sqrt{d+e x}}{\sqrt{c d^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{11/2}}+\frac{21 c d e^2}{4 (d+e x)^{3/2} \left(c d^2-a e^2\right)^4}+\frac{9 e}{4 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2 (a e+c d x)}-\frac{1}{2 (d+e x)^{5/2} \left(c d^2-a e^2\right) (a e+c d x)^2}+\frac{63 e^2}{20 (d+e x)^{5/2} \left(c d^2-a e^2\right)^3}",1,"(63*e^2)/(20*(c*d^2 - a*e^2)^3*(d + e*x)^(5/2)) - 1/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2*(d + e*x)^(5/2)) + (9*e)/(4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)*(d + e*x)^(5/2)) + (21*c*d*e^2)/(4*(c*d^2 - a*e^2)^4*(d + e*x)^(3/2)) + (63*c^2*d^2*e^2)/(4*(c*d^2 - a*e^2)^5*Sqrt[d + e*x]) - (63*c^(5/2)*d^(5/2)*e^2*ArcTanh[(Sqrt[c]*Sqrt[d]*Sqrt[d + e*x])/Sqrt[c*d^2 - a*e^2]])/(4*(c*d^2 - a*e^2)^(11/2))","A",8,4,37,0.1081,1,"{626, 51, 63, 208}"
2027,1,295,0,0.2628228,"\int (d+e x)^{7/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{256 \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}}{3465 c^5 d^5 (d+e x)^{3/2}}+\frac{128 \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)^{3/2}}{1155 c^4 d^4 \sqrt{d+e x}}+\frac{32 \sqrt{d+e x} \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}}{231 c^3 d^3}+\frac{16 (d+e x)^{3/2} \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}}{99 c^2 d^2}+\frac{2 (d+e x)^{5/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{11 c d}","\frac{256 \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}}{3465 c^5 d^5 (d+e x)^{3/2}}+\frac{128 \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)^{3/2}}{1155 c^4 d^4 \sqrt{d+e x}}+\frac{32 \sqrt{d+e x} \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}}{231 c^3 d^3}+\frac{16 (d+e x)^{3/2} \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}}{99 c^2 d^2}+\frac{2 (d+e x)^{5/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{11 c d}",1,"(256*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3465*c^5*d^5*(d + e*x)^(3/2)) + (128*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(1155*c^4*d^4*Sqrt[d + e*x]) + (32*(c*d^2 - a*e^2)^2*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(231*c^3*d^3) + (16*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(99*c^2*d^2) + (2*(d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(11*c*d)","A",5,2,39,0.05128,1,"{656, 648}"
2028,1,233,0,0.1886514,"\int (d+e x)^{5/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{32 \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)^{3/2}}{315 c^4 d^4 (d+e x)^{3/2}}+\frac{16 \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}}{105 c^3 d^3 \sqrt{d+e x}}+\frac{4 \sqrt{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}}{21 c^2 d^2}+\frac{2 (d+e x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{9 c d}","\frac{32 \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)^{3/2}}{315 c^4 d^4 (d+e x)^{3/2}}+\frac{16 \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}}{105 c^3 d^3 \sqrt{d+e x}}+\frac{4 \sqrt{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}}{21 c^2 d^2}+\frac{2 (d+e x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{9 c d}",1,"(32*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(315*c^4*d^4*(d + e*x)^(3/2)) + (16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*c^3*d^3*Sqrt[d + e*x]) + (4*(c*d^2 - a*e^2)*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(21*c^2*d^2) + (2*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(9*c*d)","A",4,2,39,0.05128,1,"{656, 648}"
2029,1,171,0,0.1128507,"\int (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{16 \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}}{105 c^3 d^3 (d+e x)^{3/2}}+\frac{8 \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}}{35 c^2 d^2 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{7 c d}","\frac{16 \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}}{105 c^3 d^3 (d+e x)^{3/2}}+\frac{8 \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}}{35 c^2 d^2 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{7 c d}",1,"(16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*c^3*d^3*(d + e*x)^(3/2)) + (8*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(35*c^2*d^2*Sqrt[d + e*x]) + (2*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(7*c*d)","A",3,2,39,0.05128,1,"{656, 648}"
2030,1,109,0,0.0602184,"\int \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{4 \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}}{15 c^2 d^2 (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}}{5 c d \sqrt{d+e x}}","\frac{4 \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}}{15 c^2 d^2 (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}}{5 c d \sqrt{d+e x}}",1,"(4*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(15*c^2*d^2*(d + e*x)^(3/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(5*c*d*Sqrt[d + e*x])","A",2,2,39,0.05128,1,"{656, 648}"
2031,1,48,0,0.0214836,"\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}"
2032,1,128,0,0.0978779,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{(d+e x)^{3/2}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^(3/2),x]","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e \sqrt{d+e x}}-\frac{2 \sqrt{c d^2-a e^2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{3/2}}","\frac{2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e \sqrt{d+e x}}-\frac{2 \sqrt{c d^2-a e^2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{3/2}}",1,"(2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(e*Sqrt[d + e*x]) - (2*Sqrt[c*d^2 - a*e^2]*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/e^(3/2)","A",3,3,39,0.07692,1,"{664, 660, 205}"
2033,1,129,0,0.0732543,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{(d+e x)^{5/2}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^(5/2),x]","\frac{c d \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{3/2} \sqrt{c d^2-a e^2}}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e (d+e x)^{3/2}}","\frac{c d \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{3/2} \sqrt{c d^2-a e^2}}-\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e (d+e x)^{3/2}}",1,"-(Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(e*(d + e*x)^(3/2))) + (c*d*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(e^(3/2)*Sqrt[c*d^2 - a*e^2])","A",3,3,39,0.07692,1,"{662, 660, 205}"
2034,1,199,0,0.131257,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{(d+e x)^{7/2}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^(7/2),x]","\frac{c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 e^{3/2} \left(c d^2-a e^2\right)^{3/2}}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e (d+e x)^{3/2} \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}}{2 e (d+e x)^{5/2}}","\frac{c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 e^{3/2} \left(c d^2-a e^2\right)^{3/2}}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e (d+e x)^{3/2} \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}}{2 e (d+e x)^{5/2}}",1,"-Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(2*e*(d + e*x)^(5/2)) + (c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*e*(c*d^2 - a*e^2)*(d + e*x)^(3/2)) + (c^2*d^2*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(4*e^(3/2)*(c*d^2 - a*e^2)^(3/2))","A",4,4,39,0.1026,1,"{662, 672, 660, 205}"
2035,1,264,0,0.1767742,"\int \frac{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}}{(d+e x)^{9/2}} \, dx","Int[Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(d + e*x)^(9/2),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 e (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}+\frac{c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 e^{3/2} \left(c d^2-a e^2\right)^{5/2}}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 e (d+e x)^{5/2} \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}}{3 e (d+e x)^{7/2}}","\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 e (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}+\frac{c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 e^{3/2} \left(c d^2-a e^2\right)^{5/2}}+\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{12 e (d+e x)^{5/2} \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}}{3 e (d+e x)^{7/2}}",1,"-Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(3*e*(d + e*x)^(7/2)) + (c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*e*(c*d^2 - a*e^2)*(d + e*x)^(5/2)) + (c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*e*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) + (c^3*d^3*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(8*e^(3/2)*(c*d^2 - a*e^2)^(5/2))","A",5,4,39,0.1026,1,"{662, 672, 660, 205}"
2036,1,295,0,0.2964656,"\int (d+e 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)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{256 \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)^{5/2}}{15015 c^5 d^5 (d+e x)^{5/2}}+\frac{128 \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}}{3003 c^4 d^4 (d+e x)^{3/2}}+\frac{32 \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)^{5/2}}{429 c^3 d^3 \sqrt{d+e x}}+\frac{16 \sqrt{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}}{143 c^2 d^2}+\frac{2 (d+e x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{13 c d}","\frac{256 \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)^{5/2}}{15015 c^5 d^5 (d+e x)^{5/2}}+\frac{128 \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}}{3003 c^4 d^4 (d+e x)^{3/2}}+\frac{32 \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)^{5/2}}{429 c^3 d^3 \sqrt{d+e x}}+\frac{16 \sqrt{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}}{143 c^2 d^2}+\frac{2 (d+e x)^{3/2} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{13 c d}",1,"(256*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(15015*c^5*d^5*(d + e*x)^(5/2)) + (128*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(3003*c^4*d^4*(d + e*x)^(3/2)) + (32*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(429*c^3*d^3*Sqrt[d + e*x]) + (16*(c*d^2 - a*e^2)*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(143*c^2*d^2) + (2*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(13*c*d)","A",5,2,39,0.05128,1,"{656, 648}"
2037,1,233,0,0.2079858,"\int (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{32 \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}}{1155 c^4 d^4 (d+e x)^{5/2}}+\frac{16 \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)^{5/2}}{231 c^3 d^3 (d+e x)^{3/2}}+\frac{4 \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}}{33 c^2 d^2 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{11 c d}","\frac{32 \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}}{1155 c^4 d^4 (d+e x)^{5/2}}+\frac{16 \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)^{5/2}}{231 c^3 d^3 (d+e x)^{3/2}}+\frac{4 \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}}{33 c^2 d^2 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{11 c d}",1,"(32*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(1155*c^4*d^4*(d + e*x)^(5/2)) + (16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(231*c^3*d^3*(d + e*x)^(3/2)) + (4*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(33*c^2*d^2*Sqrt[d + e*x]) + (2*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(11*c*d)","A",4,2,39,0.05128,1,"{656, 648}"
2038,1,171,0,0.1219923,"\int \sqrt{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[Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{8 \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}}{63 c^2 d^2 (d+e x)^{3/2}}+\frac{16 \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)^{5/2}}{315 c^3 d^3 (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}}{9 c d \sqrt{d+e x}}","\frac{8 \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}}{63 c^2 d^2 (d+e x)^{3/2}}+\frac{16 \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)^{5/2}}{315 c^3 d^3 (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}}{9 c d \sqrt{d+e x}}",1,"(16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(315*c^3*d^3*(d + e*x)^(5/2)) + (8*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(63*c^2*d^2*(d + e*x)^(3/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(9*c*d*Sqrt[d + e*x])","A",3,2,39,0.05128,1,"{656, 648}"
2039,1,109,0,0.0610188,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/Sqrt[d + e*x],x]","\frac{4 \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}}{35 c^2 d^2 (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}}{7 c d (d+e x)^{3/2}}","\frac{4 \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}}{35 c^2 d^2 (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}}{7 c d (d+e x)^{3/2}}",1,"(4*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(35*c^2*d^2*(d + e*x)^(5/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(7*c*d*(d + e*x)^(3/2))","A",2,2,39,0.05128,1,"{656, 648}"
2040,1,48,0,0.0245674,"\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}"
2041,1,181,0,0.1629497,"\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)^{5/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(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)^{3/2}}{3 e (d+e x)^{3/2}}+\frac{2 \left(a-\frac{c d^2}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x}}+\frac{2 \left(c d^2-a e^2\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{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 e (d+e x)^{3/2}}+\frac{2 \left(a-\frac{c d^2}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{\sqrt{d+e x}}+\frac{2 \left(c d^2-a e^2\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{5/2}}",1,"(2*(a - (c*d^2)/e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/Sqrt[d + e*x] + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) + (2*(c*d^2 - a*e^2)^(3/2)*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/e^(5/2)","A",4,3,39,0.07692,1,"{664, 660, 205}"
2042,1,175,0,0.1192595,"\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)^{7/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(7/2),x]","-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{e (d+e x)^{5/2}}+\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^2 \sqrt{d+e x}}-\frac{3 c d \sqrt{c d^2-a e^2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{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}}{e (d+e x)^{5/2}}+\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e^2 \sqrt{d+e x}}-\frac{3 c d \sqrt{c d^2-a e^2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{5/2}}",1,"(3*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(e^2*Sqrt[d + e*x]) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(e*(d + e*x)^(5/2)) - (3*c*d*Sqrt[c*d^2 - a*e^2]*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/e^(5/2)","A",4,4,39,0.1026,1,"{662, 664, 660, 205}"
2043,1,185,0,0.117634,"\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)^{9/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(9/2),x]","\frac{3 c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 e^{5/2} \sqrt{c d^2-a e^2}}-\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e^2 (d+e x)^{3/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 e (d+e x)^{7/2}}","\frac{3 c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 e^{5/2} \sqrt{c d^2-a e^2}}-\frac{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e^2 (d+e x)^{3/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{2 e (d+e x)^{7/2}}",1,"(-3*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*e^2*(d + e*x)^(3/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(2*e*(d + e*x)^(7/2)) + (3*c^2*d^2*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(4*e^(5/2)*Sqrt[c*d^2 - a*e^2])","A",4,3,39,0.07692,1,"{662, 660, 205}"
2044,1,250,0,0.1844246,"\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)^{11/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(11/2),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 e^2 (d+e x)^{3/2} \left(c d^2-a e^2\right)}+\frac{c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 e^{5/2} \left(c d^2-a e^2\right)^{3/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e^2 (d+e x)^{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 (d+e x)^{9/2}}","\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 e^2 (d+e x)^{3/2} \left(c d^2-a e^2\right)}+\frac{c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 e^{5/2} \left(c d^2-a e^2\right)^{3/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{4 e^2 (d+e x)^{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 (d+e x)^{9/2}}",1,"-(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*e^2*(d + e*x)^(5/2)) + (c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*e^2*(c*d^2 - a*e^2)*(d + e*x)^(3/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(3*e*(d + e*x)^(9/2)) + (c^3*d^3*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(8*e^(5/2)*(c*d^2 - a*e^2)^(3/2))","A",5,4,39,0.1026,1,"{662, 672, 660, 205}"
2045,1,315,0,0.2229802,"\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)^{13/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(13/2),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 e^2 (d+e x)^{3/2} \left(c d^2-a e^2\right)^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 e^2 (d+e x)^{5/2} \left(c d^2-a e^2\right)}+\frac{3 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{64 e^{5/2} \left(c d^2-a e^2\right)^{5/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 e^2 (d+e x)^{7/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 e (d+e x)^{11/2}}","\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 e^2 (d+e x)^{3/2} \left(c d^2-a e^2\right)^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 e^2 (d+e x)^{5/2} \left(c d^2-a e^2\right)}+\frac{3 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{64 e^{5/2} \left(c d^2-a e^2\right)^{5/2}}-\frac{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{8 e^2 (d+e x)^{7/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}{4 e (d+e x)^{11/2}}",1,"-(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*e^2*(d + e*x)^(7/2)) + (c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(32*e^2*(c*d^2 - a*e^2)*(d + e*x)^(5/2)) + (3*c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*e^2*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(4*e*(d + e*x)^(11/2)) + (3*c^4*d^4*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(64*e^(5/2)*(c*d^2 - a*e^2)^(5/2))","A",6,4,39,0.1026,1,"{662, 672, 660, 205}"
2046,1,295,0,0.2650033,"\int (d+e 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)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{256 \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)^{7/2}}{45045 c^5 d^5 (d+e x)^{7/2}}+\frac{128 \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)^{7/2}}{6435 c^4 d^4 (d+e x)^{5/2}}+\frac{32 \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)^{7/2}}{715 c^3 d^3 (d+e x)^{3/2}}+\frac{16 \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)^{7/2}}{195 c^2 d^2 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{15 c d}","\frac{256 \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)^{7/2}}{45045 c^5 d^5 (d+e x)^{7/2}}+\frac{128 \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)^{7/2}}{6435 c^4 d^4 (d+e x)^{5/2}}+\frac{32 \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)^{7/2}}{715 c^3 d^3 (d+e x)^{3/2}}+\frac{16 \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)^{7/2}}{195 c^2 d^2 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{7/2}}{15 c d}",1,"(256*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(45045*c^5*d^5*(d + e*x)^(7/2)) + (128*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(6435*c^4*d^4*(d + e*x)^(5/2)) + (32*(c*d^2 - a*e^2)^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)^(3/2)) + (16*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(195*c^2*d^2*Sqrt[d + e*x]) + (2*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(15*c*d)","A",5,2,39,0.05128,1,"{656, 648}"
2047,1,233,0,0.1794613,"\int \sqrt{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[Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{12 \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)^{7/2}}{143 c^2 d^2 (d+e x)^{3/2}}+\frac{16 \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)^{7/2}}{429 c^3 d^3 (d+e x)^{5/2}}+\frac{32 \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)^{7/2}}{3003 c^4 d^4 (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}}{13 c d \sqrt{d+e x}}","\frac{12 \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)^{7/2}}{143 c^2 d^2 (d+e x)^{3/2}}+\frac{16 \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)^{7/2}}{429 c^3 d^3 (d+e x)^{5/2}}+\frac{32 \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)^{7/2}}{3003 c^4 d^4 (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}}{13 c d \sqrt{d+e x}}",1,"(32*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(3003*c^4*d^4*(d + e*x)^(7/2)) + (16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(429*c^3*d^3*(d + e*x)^(5/2)) + (12*(c*d^2 - a*e^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)^(3/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(13*c*d*Sqrt[d + e*x])","A",4,2,39,0.05128,1,"{656, 648}"
2048,1,171,0,0.1140859,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/Sqrt[d + e*x],x]","\frac{8 \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)^{7/2}}{99 c^2 d^2 (d+e x)^{5/2}}+\frac{16 \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)^{7/2}}{693 c^3 d^3 (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}}{11 c d (d+e x)^{3/2}}","\frac{8 \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)^{7/2}}{99 c^2 d^2 (d+e x)^{5/2}}+\frac{16 \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)^{7/2}}{693 c^3 d^3 (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}}{11 c d (d+e x)^{3/2}}",1,"(16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(693*c^3*d^3*(d + e*x)^(7/2)) + (8*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(99*c^2*d^2*(d + e*x)^(5/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(11*c*d*(d + e*x)^(3/2))","A",3,2,39,0.05128,1,"{656, 648}"
2049,1,109,0,0.0572526,"\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)^{3/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(3/2),x]","\frac{4 \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)^{7/2}}{63 c^2 d^2 (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}}{9 c d (d+e x)^{5/2}}","\frac{4 \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)^{7/2}}{63 c^2 d^2 (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}}{9 c d (d+e x)^{5/2}}",1,"(4*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(63*c^2*d^2*(d + e*x)^(7/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(9*c*d*(d + e*x)^(5/2))","A",2,2,39,0.05128,1,"{656, 648}"
2050,1,48,0,0.0213256,"\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}"
2051,1,240,0,0.2135783,"\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)^{7/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(7/2),x]","\frac{2 \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}}{e^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)^{5/2}}{5 e (d+e x)^{5/2}}+\frac{2 \left(a-\frac{c d^2}{e^2}\right) \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}}-\frac{2 \left(c d^2-a e^2\right)^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{7/2}}","\frac{2 \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}}{e^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)^{5/2}}{5 e (d+e x)^{5/2}}+\frac{2 \left(a-\frac{c d^2}{e^2}\right) \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}}-\frac{2 \left(c d^2-a e^2\right)^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{7/2}}",1,"(2*(c*d^2 - a*e^2)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(e^3*Sqrt[d + e*x]) + (2*(a - (c*d^2)/e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*(d + e*x)^(3/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*e*(d + e*x)^(5/2)) - (2*(c*d^2 - a*e^2)^(5/2)*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/e^(7/2)","A",5,3,39,0.07692,1,"{664, 660, 205}"
2052,1,233,0,0.1817686,"\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)^{9/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(9/2),x]","-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{e (d+e x)^{7/2}}+\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}}{3 e^2 (d+e x)^{3/2}}+\frac{5 c d \left(a-\frac{c d^2}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e \sqrt{d+e x}}+\frac{5 c d \left(c d^2-a e^2\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{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}}{e (d+e x)^{7/2}}+\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}}{3 e^2 (d+e x)^{3/2}}+\frac{5 c d \left(a-\frac{c d^2}{e^2}\right) \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{e \sqrt{d+e x}}+\frac{5 c d \left(c d^2-a e^2\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{e^{7/2}}",1,"(5*c*d*(a - (c*d^2)/e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(e*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*e^2*(d + e*x)^(3/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(e*(d + e*x)^(7/2)) + (5*c*d*(c*d^2 - a*e^2)^(3/2)*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/e^(7/2)","A",5,4,39,0.1026,1,"{662, 664, 660, 205}"
2053,1,236,0,0.1544522,"\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)^{11/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(11/2),x]","\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 e^3 \sqrt{d+e x}}-\frac{15 c^2 d^2 \sqrt{c d^2-a e^2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 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}}{2 e (d+e x)^{9/2}}-\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}}{4 e^2 (d+e x)^{5/2}}","\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 e^3 \sqrt{d+e x}}-\frac{15 c^2 d^2 \sqrt{c d^2-a e^2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 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}}{2 e (d+e x)^{9/2}}-\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}}{4 e^2 (d+e x)^{5/2}}",1,"(15*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*e^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*e^2*(d + e*x)^(5/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(2*e*(d + e*x)^(9/2)) - (15*c^2*d^2*Sqrt[c*d^2 - a*e^2]*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(4*e^(7/2))","A",5,4,39,0.1026,1,"{662, 664, 660, 205}"
2054,1,236,0,0.1517885,"\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)^{13/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(13/2),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 e^3 (d+e x)^{3/2}}+\frac{5 c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 e^{7/2} \sqrt{c d^2-a e^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}}{12 e^2 (d+e x)^{7/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{3 e (d+e x)^{11/2}}","-\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 e^3 (d+e x)^{3/2}}+\frac{5 c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 e^{7/2} \sqrt{c d^2-a e^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}}{12 e^2 (d+e x)^{7/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{3 e (d+e x)^{11/2}}",1,"(-5*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*e^3*(d + e*x)^(3/2)) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(12*e^2*(d + e*x)^(7/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(3*e*(d + e*x)^(11/2)) + (5*c^3*d^3*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(8*e^(7/2)*Sqrt[c*d^2 - a*e^2])","A",5,3,39,0.07692,1,"{662, 660, 205}"
2055,1,301,0,0.2341589,"\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)^{15/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(15/2),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 e^3 (d+e x)^{3/2} \left(c d^2-a e^2\right)}-\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 e^3 (d+e x)^{5/2}}+\frac{5 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{64 e^{7/2} \left(c d^2-a e^2\right)^{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 e^2 (d+e x)^{9/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4 e (d+e x)^{13/2}}","\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 e^3 (d+e x)^{3/2} \left(c d^2-a e^2\right)}-\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 e^3 (d+e x)^{5/2}}+\frac{5 c^4 d^4 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{64 e^{7/2} \left(c d^2-a e^2\right)^{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 e^2 (d+e x)^{9/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{4 e (d+e x)^{13/2}}",1,"(-5*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(32*e^3*(d + e*x)^(5/2)) + (5*c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*e^3*(c*d^2 - a*e^2)*(d + e*x)^(3/2)) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(24*e^2*(d + e*x)^(9/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(4*e*(d + e*x)^(13/2)) + (5*c^4*d^4*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(64*e^(7/2)*(c*d^2 - a*e^2)^(3/2))","A",6,4,39,0.1026,1,"{662, 672, 660, 205}"
2056,1,366,0,0.279515,"\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)^{17/2}} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(17/2),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 e^3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^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 e^3 (d+e x)^{5/2} \left(c d^2-a e^2\right)}-\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{16 e^3 (d+e x)^{7/2}}+\frac{3 c^5 d^5 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{128 e^{7/2} \left(c d^2-a e^2\right)^{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 e^2 (d+e x)^{11/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 e (d+e x)^{15/2}}","\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 e^3 (d+e x)^{3/2} \left(c d^2-a e^2\right)^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 e^3 (d+e x)^{5/2} \left(c d^2-a e^2\right)}-\frac{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{16 e^3 (d+e x)^{7/2}}+\frac{3 c^5 d^5 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{128 e^{7/2} \left(c d^2-a e^2\right)^{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 e^2 (d+e x)^{11/2}}-\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{5/2}}{5 e (d+e x)^{15/2}}",1,"-(c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(16*e^3*(d + e*x)^(7/2)) + (c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(64*e^3*(c*d^2 - a*e^2)*(d + e*x)^(5/2)) + (3*c^4*d^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(128*e^3*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) - (c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(8*e^2*(d + e*x)^(11/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(5*e*(d + e*x)^(15/2)) + (3*c^5*d^5*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(128*e^(7/2)*(c*d^2 - a*e^2)^(5/2))","A",7,4,39,0.1026,1,"{662, 672, 660, 205}"
2057,1,233,0,0.1781818,"\int \frac{(d+e x)^{7/2}}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)^(7/2)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{32 \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}}{35 c^4 d^4 \sqrt{d+e x}}+\frac{16 \sqrt{d+e x} \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}}{35 c^3 d^3}+\frac{12 (d+e x)^{3/2} \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}}{35 c^2 d^2}+\frac{2 (d+e x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 c d}","\frac{32 \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}}{35 c^4 d^4 \sqrt{d+e x}}+\frac{16 \sqrt{d+e x} \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}}{35 c^3 d^3}+\frac{12 (d+e x)^{3/2} \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}}{35 c^2 d^2}+\frac{2 (d+e x)^{5/2} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{7 c d}",1,"(32*(c*d^2 - a*e^2)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*c^4*d^4*Sqrt[d + e*x]) + (16*(c*d^2 - a*e^2)^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) + (12*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(35*c^2*d^2) + (2*(d + e*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(7*c*d)","A",4,2,39,0.05128,1,"{656, 648}"
2058,1,171,0,0.1138255,"\int \frac{(d+e x)^{5/2}}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)^(5/2)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{16 \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}}{15 c^3 d^3 \sqrt{d+e x}}+\frac{8 \sqrt{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}}{15 c^2 d^2}+\frac{2 (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}","\frac{16 \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}}{15 c^3 d^3 \sqrt{d+e x}}+\frac{8 \sqrt{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}}{15 c^2 d^2}+\frac{2 (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}",1,"(16*(c*d^2 - a*e^2)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(15*c^3*d^3*Sqrt[d + e*x]) + (8*(c*d^2 - a*e^2)*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) + (2*(d + e*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(5*c*d)","A",3,2,39,0.05128,1,"{656, 648}"
2059,1,109,0,0.055953,"\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}"
2060,1,46,0,0.019753,"\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}"
2061,1,84,0,0.0411245,"\int \frac{1}{\sqrt{d+e x} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/(Sqrt[d + e*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{e} \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^2-a e^2}}\right)}{\sqrt{e} \sqrt{c d^2-a e^2}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\sqrt{e} \sqrt{c d^2-a e^2}}",1,"(2*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(Sqrt[e]*Sqrt[c*d^2 - a*e^2])","A",2,2,39,0.05128,1,"{660, 205}"
2062,1,139,0,0.0766746,"\int \frac{1}{(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[1/((d + e*x)^(3/2)*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}}{(d+e x)^{3/2} \left(c d^2-a e^2\right)}+\frac{c d \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\sqrt{e} \left(c d^2-a e^2\right)^{3/2}}","\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{(d+e x)^{3/2} \left(c d^2-a e^2\right)}+\frac{c d \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\sqrt{e} \left(c d^2-a e^2\right)^{3/2}}",1,"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)^(3/2)) + (c*d*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(Sqrt[e]*(c*d^2 - a*e^2)^(3/2))","A",3,3,39,0.07692,1,"{672, 660, 205}"
2063,1,207,0,0.1133088,"\int \frac{1}{(d+e x)^{5/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/((d + e*x)^(5/2)*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{e} \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^2-a e^2}}\right)}{4 \sqrt{e} \left(c d^2-a e^2\right)^{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 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 (d+e x)^{5/2} \left(c d^2-a e^2\right)}","\frac{3 c^2 d^2 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 \sqrt{e} \left(c d^2-a e^2\right)^{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 (d+e x)^{3/2} \left(c d^2-a e^2\right)^2}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{2 (d+e x)^{5/2} \left(c d^2-a e^2\right)}",1,"Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(2*(c*d^2 - a*e^2)*(d + e*x)^(5/2)) + (3*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(4*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) + (3*c^2*d^2*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(4*Sqrt[e]*(c*d^2 - a*e^2)^(5/2))","A",4,3,39,0.07692,1,"{672, 660, 205}"
2064,1,269,0,0.1660553,"\int \frac{1}{(d+e x)^{7/2} \sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[1/((d + e*x)^(7/2)*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 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}+\frac{5 c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 \sqrt{e} \left(c d^2-a e^2\right)^{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 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 (d+e x)^{7/2} \left(c d^2-a e^2\right)}","\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 (d+e x)^{3/2} \left(c d^2-a e^2\right)^3}+\frac{5 c^3 d^3 \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 \sqrt{e} \left(c d^2-a e^2\right)^{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 (d+e x)^{5/2} \left(c d^2-a e^2\right)^2}+\frac{\sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}{3 (d+e x)^{7/2} \left(c d^2-a e^2\right)}",1,"Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]/(3*(c*d^2 - a*e^2)*(d + e*x)^(7/2)) + (5*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(12*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2)) + (5*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(8*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)) + (5*c^3*d^3*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(8*Sqrt[e]*(c*d^2 - a*e^2)^(7/2))","A",5,3,39,0.07692,1,"{672, 660, 205}"
2065,1,171,0,0.116254,"\int \frac{(d+e 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)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{8 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{16 \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{3 c^3 d^3 \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}}{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{8 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{16 \sqrt{d+e x} \left(c d^2-a e^2\right)^2}{3 c^3 d^3 \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}}{3 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-16*(c*d^2 - a*e^2)^2*Sqrt[d + e*x])/(3*c^3*d^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (8*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(3*c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (2*(d + e*x)^(5/2))/(3*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",3,2,39,0.05128,1,"{656, 648}"
2066,1,105,0,0.0581765,"\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)^{3/2}} \, dx","Int[(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2),x]","\frac{2 (d+e x)^{3/2}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{4 \sqrt{d+e x} \left(c d^2-a e^2\right)}{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}}{c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{4 \sqrt{d+e x} \left(c d^2-a e^2\right)}{c^2 d^2 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(-4*(c*d^2 - a*e^2)*Sqrt[d + e*x])/(c^2*d^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (2*(d + e*x)^(3/2))/(c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])","A",2,2,39,0.05128,1,"{656, 648}"
2067,1,46,0,0.0205415,"\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}"
2068,1,139,0,0.0941894,"\int \frac{\sqrt{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[Sqrt[d + e*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}}{\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{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{3/2}}","-\frac{2 \sqrt{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 \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{3/2}}",1,"(-2*Sqrt[d + e*x])/((c*d^2 - a*e^2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (2*Sqrt[e]*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(c*d^2 - a*e^2)^(3/2)","A",3,3,39,0.07692,1,"{666, 660, 205}"
2069,1,196,0,0.1315108,"\int \frac{1}{\sqrt{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/(Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{3 c d \sqrt{d+e x}}{\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{1}{\sqrt{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{3 c d \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{5/2}}","-\frac{3 c d \sqrt{d+e x}}{\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{1}{\sqrt{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{3 c d \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{5/2}}",1,"1/((c*d^2 - a*e^2)*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (3*c*d*Sqrt[d + e*x])/((c*d^2 - a*e^2)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (3*c*d*Sqrt[e]*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(c*d^2 - a*e^2)^(5/2)","A",4,4,39,0.1026,1,"{672, 666, 660, 205}"
2070,1,269,0,0.1774902,"\int \frac{1}{(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[1/((d + e*x)^(3/2)*(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{d+e x}}{4 \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{15 c^2 d^2 \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{7/2}}+\frac{5 c d}{4 \sqrt{d+e x} \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{1}{2 (d+e x)^{3/2} \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{15 c^2 d^2 \sqrt{d+e x}}{4 \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{15 c^2 d^2 \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{7/2}}+\frac{5 c d}{4 \sqrt{d+e x} \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{1}{2 (d+e x)^{3/2} \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,"1/(2*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (5*c*d)/(4*(c*d^2 - a*e^2)^2*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*Sqrt[d + e*x])/(4*(c*d^2 - a*e^2)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (15*c^2*d^2*Sqrt[e]*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(4*(c*d^2 - a*e^2)^(7/2))","A",5,4,39,0.1026,1,"{672, 666, 660, 205}"
2071,1,331,0,0.2464893,"\int \frac{1}{(d+e 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[1/((d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{35 c^3 d^3 \sqrt{d+e x}}{8 \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{35 c^2 d^2}{24 \sqrt{d+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{35 c^3 d^3 \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 \left(c d^2-a e^2\right)^{9/2}}+\frac{7 c d}{12 (d+e x)^{3/2} \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{1}{3 (d+e x)^{5/2} \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{35 c^3 d^3 \sqrt{d+e x}}{8 \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{35 c^2 d^2}{24 \sqrt{d+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{35 c^3 d^3 \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 \left(c d^2-a e^2\right)^{9/2}}+\frac{7 c d}{12 (d+e x)^{3/2} \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{1}{3 (d+e x)^{5/2} \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,"1/(3*(c*d^2 - a*e^2)*(d + e*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (7*c*d)/(12*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (35*c^2*d^2)/(24*(c*d^2 - a*e^2)^3*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*Sqrt[d + e*x])/(8*(c*d^2 - a*e^2)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (35*c^3*d^3*Sqrt[e]*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(8*(c*d^2 - a*e^2)^(9/2))","A",6,4,39,0.1026,1,"{672, 666, 660, 205}"
2072,1,393,0,0.3195703,"\int \frac{1}{(d+e 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[1/((d + e*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)),x]","-\frac{315 c^4 d^4 \sqrt{d+e x}}{64 \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{105 c^3 d^3}{64 \sqrt{d+e x} \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{21 c^2 d^2}{32 (d+e x)^{3/2} \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{315 c^4 d^4 \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{64 \left(c d^2-a e^2\right)^{11/2}}+\frac{3 c d}{8 (d+e x)^{5/2} \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{1}{4 (d+e x)^{7/2} \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{315 c^4 d^4 \sqrt{d+e x}}{64 \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{105 c^3 d^3}{64 \sqrt{d+e x} \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{21 c^2 d^2}{32 (d+e x)^{3/2} \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{315 c^4 d^4 \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{64 \left(c d^2-a e^2\right)^{11/2}}+\frac{3 c d}{8 (d+e x)^{5/2} \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{1}{4 (d+e x)^{7/2} \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,"1/(4*(c*d^2 - a*e^2)*(d + e*x)^(7/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (3*c*d)/(8*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (21*c^2*d^2)/(32*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (105*c^3*d^3)/(64*(c*d^2 - a*e^2)^4*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*Sqrt[d + e*x])/(64*(c*d^2 - a*e^2)^5*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) - (315*c^4*d^4*Sqrt[e]*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(64*(c*d^2 - a*e^2)^(11/2))","A",7,4,39,0.1026,1,"{672, 666, 660, 205}"
2073,1,107,0,0.0650133,"\int \frac{(d+e x)^{7/2}}{\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)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{4 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 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}}-\frac{2 (d+e x)^{5/2}}{c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}","\frac{4 (d+e x)^{3/2} \left(c d^2-a e^2\right)}{3 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}}-\frac{2 (d+e x)^{5/2}}{c d \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{3/2}}",1,"(4*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(3*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (2*(d + e*x)^(5/2))/(c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))","A",2,2,39,0.05128,1,"{656, 648}"
2074,1,48,0,0.0217219,"\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}"
2075,1,251,0,0.17421,"\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)^{5/2}} \, dx","Int[(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{2 e \sqrt{d+e x}}{\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{2 e}{3 c d \sqrt{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 \sqrt{d+e x}}{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 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{5/2}}","\frac{2 e \sqrt{d+e x}}{\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{2 e}{3 c d \sqrt{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 \sqrt{d+e x}}{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 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{5/2}}",1,"(-2*Sqrt[d + e*x])/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (2*e)/(3*c*d*(c*d^2 - a*e^2)*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (2*e*Sqrt[d + e*x])/((c*d^2 - a*e^2)^2*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (2*e^(3/2)*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(c*d^2 - a*e^2)^(5/2)","A",5,5,39,0.1282,1,"{668, 672, 666, 660, 205}"
2076,1,257,0,0.2092538,"\int \frac{\sqrt{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[Sqrt[d + e*x]/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2),x]","\frac{5 c d e \sqrt{d+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{5 e}{3 \sqrt{d+e x} \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{2 \sqrt{d+e 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{5 c d e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{7/2}}","\frac{5 c d e \sqrt{d+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{5 e}{3 \sqrt{d+e x} \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{2 \sqrt{d+e 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{5 c d e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{\left(c d^2-a e^2\right)^{7/2}}",1,"(-2*Sqrt[d + e*x])/(3*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (5*e)/(3*(c*d^2 - a*e^2)^2*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (5*c*d*e*Sqrt[d + e*x])/((c*d^2 - a*e^2)^3*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (5*c*d*e^(3/2)*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(c*d^2 - a*e^2)^(7/2)","A",5,4,39,0.1026,1,"{666, 672, 660, 205}"
2077,1,329,0,0.2806586,"\int \frac{1}{\sqrt{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[1/(Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{35 c^2 d^2 e \sqrt{d+e x}}{4 \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{35 c^2 d^2 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{9/2}}-\frac{35 c d e}{12 \sqrt{d+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{7 c d \sqrt{d+e x}}{6 \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{1}{2 \sqrt{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{35 c^2 d^2 e \sqrt{d+e x}}{4 \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{35 c^2 d^2 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{4 \left(c d^2-a e^2\right)^{9/2}}-\frac{35 c d e}{12 \sqrt{d+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{7 c d \sqrt{d+e x}}{6 \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{1}{2 \sqrt{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,"1/(2*(c*d^2 - a*e^2)*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (7*c*d*Sqrt[d + e*x])/(6*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (35*c*d*e)/(12*(c*d^2 - a*e^2)^3*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (35*c^2*d^2*e*Sqrt[d + e*x])/(4*(c*d^2 - a*e^2)^4*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (35*c^2*d^2*e^(3/2)*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(4*(c*d^2 - a*e^2)^(9/2))","A",6,4,39,0.1026,1,"{672, 666, 660, 205}"
2078,1,395,0,0.3488353,"\int \frac{1}{(d+e 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[1/((d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{105 c^3 d^3 e \sqrt{d+e x}}{8 \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{35 c^2 d^2 e}{8 \sqrt{d+e x} \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{7 c^2 d^2 \sqrt{d+e x}}{4 \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)^{3/2}}+\frac{105 c^3 d^3 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 \left(c d^2-a e^2\right)^{11/2}}+\frac{3 c d}{4 \sqrt{d+e x} \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{1}{3 (d+e x)^{3/2} \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{105 c^3 d^3 e \sqrt{d+e x}}{8 \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{35 c^2 d^2 e}{8 \sqrt{d+e x} \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{7 c^2 d^2 \sqrt{d+e x}}{4 \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)^{3/2}}+\frac{105 c^3 d^3 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{8 \left(c d^2-a e^2\right)^{11/2}}+\frac{3 c d}{4 \sqrt{d+e x} \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{1}{3 (d+e x)^{3/2} \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,"1/(3*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (3*c*d)/(4*(c*d^2 - a*e^2)^2*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (7*c^2*d^2*Sqrt[d + e*x])/(4*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (35*c^2*d^2*e)/(8*(c*d^2 - a*e^2)^4*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*Sqrt[d + e*x])/(8*(c*d^2 - a*e^2)^5*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (105*c^3*d^3*e^(3/2)*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(8*(c*d^2 - a*e^2)^(11/2))","A",7,4,39,0.1026,1,"{672, 666, 660, 205}"
2079,1,457,0,0.5011981,"\int \frac{1}{(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[1/((d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{1155 c^4 d^4 e \sqrt{d+e x}}{64 \left(c d^2-a e^2\right)^6 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{385 c^3 d^3 e}{64 \sqrt{d+e x} \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{77 c^3 d^3 \sqrt{d+e x}}{32 \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{33 c^2 d^2}{32 \sqrt{d+e x} \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)^{3/2}}+\frac{1155 c^4 d^4 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{64 \left(c d^2-a e^2\right)^{13/2}}+\frac{11 c d}{24 (d+e x)^{3/2} \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{1}{4 (d+e x)^{5/2} \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{1155 c^4 d^4 e \sqrt{d+e x}}{64 \left(c d^2-a e^2\right)^6 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{385 c^3 d^3 e}{64 \sqrt{d+e x} \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{77 c^3 d^3 \sqrt{d+e x}}{32 \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{33 c^2 d^2}{32 \sqrt{d+e x} \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)^{3/2}}+\frac{1155 c^4 d^4 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{64 \left(c d^2-a e^2\right)^{13/2}}+\frac{11 c d}{24 (d+e x)^{3/2} \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{1}{4 (d+e x)^{5/2} \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,"1/(4*(c*d^2 - a*e^2)*(d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (11*c*d)/(24*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (33*c^2*d^2)/(32*(c*d^2 - a*e^2)^3*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (77*c^3*d^3*Sqrt[d + e*x])/(32*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (385*c^3*d^3*e)/(64*(c*d^2 - a*e^2)^5*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (1155*c^4*d^4*e*Sqrt[d + e*x])/(64*(c*d^2 - a*e^2)^6*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (1155*c^4*d^4*e^(3/2)*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(64*(c*d^2 - a*e^2)^(13/2))","A",8,4,39,0.1026,1,"{672, 666, 660, 205}"
2080,1,519,0,0.5983392,"\int \frac{1}{(d+e x)^{7/2} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)),x]","\frac{3003 c^5 d^5 e \sqrt{d+e x}}{128 \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{1001 c^4 d^4 e}{128 \sqrt{d+e x} \left(c d^2-a e^2\right)^6 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{1001 c^4 d^4 \sqrt{d+e x}}{320 \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{429 c^3 d^3}{320 \sqrt{d+e x} \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{143 c^2 d^2}{240 (d+e x)^{3/2} \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)^{3/2}}+\frac{3003 c^5 d^5 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{128 \left(c d^2-a e^2\right)^{15/2}}+\frac{13 c d}{40 (d+e x)^{5/2} \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{1}{5 (d+e x)^{7/2} \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{3003 c^5 d^5 e \sqrt{d+e x}}{128 \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{1001 c^4 d^4 e}{128 \sqrt{d+e x} \left(c d^2-a e^2\right)^6 \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}-\frac{1001 c^4 d^4 \sqrt{d+e x}}{320 \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{429 c^3 d^3}{320 \sqrt{d+e x} \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{143 c^2 d^2}{240 (d+e x)^{3/2} \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)^{3/2}}+\frac{3003 c^5 d^5 e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} \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^2-a e^2}}\right)}{128 \left(c d^2-a e^2\right)^{15/2}}+\frac{13 c d}{40 (d+e x)^{5/2} \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{1}{5 (d+e x)^{7/2} \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,"1/(5*(c*d^2 - a*e^2)*(d + e*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (13*c*d)/(40*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (143*c^2*d^2)/(240*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (429*c^3*d^3)/(320*(c*d^2 - a*e^2)^4*Sqrt[d + e*x]*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (1001*c^4*d^4*Sqrt[d + e*x])/(320*(c*d^2 - a*e^2)^5*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (1001*c^4*d^4*e)/(128*(c*d^2 - a*e^2)^6*Sqrt[d + e*x]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (3003*c^5*d^5*e*Sqrt[d + e*x])/(128*(c*d^2 - a*e^2)^7*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (3003*c^5*d^5*e^(3/2)*ArcTan[(Sqrt[e]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2])/(Sqrt[c*d^2 - a*e^2]*Sqrt[d + e*x])])/(128*(c*d^2 - a*e^2)^(15/2))","A",9,4,39,0.1026,1,"{672, 666, 660, 205}"
2081,1,52,0,0.0241019,"\int \frac{1}{\sqrt{d+e x} \sqrt{d^2-e^2 x^2}} \, dx","Int[1/(Sqrt[d + e*x]*Sqrt[d^2 - e^2*x^2]),x]","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{\sqrt{2} \sqrt{d} \sqrt{d+e x}}\right)}{\sqrt{d} e}","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{\sqrt{2} \sqrt{d} \sqrt{d+e x}}\right)}{\sqrt{d} e}",1,"-((Sqrt[2]*ArcTanh[Sqrt[d^2 - e^2*x^2]/(Sqrt[2]*Sqrt[d]*Sqrt[d + e*x])])/(Sqrt[d]*e))","A",2,2,26,0.07692,1,"{661, 208}"
2082,1,53,0,0.02212,"\int \frac{1}{\sqrt{-d+e x} \sqrt{d^2-e^2 x^2}} \, dx","Int[1/(Sqrt[-d + e*x]*Sqrt[d^2 - e^2*x^2]),x]","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{\sqrt{2} \sqrt{d} \sqrt{e x-d}}\right)}{\sqrt{d} e}","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{d^2-e^2 x^2}}{\sqrt{2} \sqrt{d} \sqrt{e x-d}}\right)}{\sqrt{d} e}",1,"(Sqrt[2]*ArcTan[Sqrt[d^2 - e^2*x^2]/(Sqrt[2]*Sqrt[d]*Sqrt[-d + e*x])])/(Sqrt[d]*e)","A",2,2,28,0.07143,1,"{661, 205}"
2083,1,566,0,0.7652032,"\int \frac{(d+e x)^{2/3}}{\sqrt{a d e+\left(c d^2+a e^2\right) x+c d e x^2}} \, dx","Int[(d + e*x)^(2/3)/Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2],x]","\frac{3^{3/4} (d+e x)^{2/3} \left(c d^2-a e^2\right)^{2/3} \sqrt{a d e+c d^2 x} \left(\sqrt[3]{c d^2-a e^2}-\sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}\right) \sqrt{\frac{\sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1} \sqrt[3]{c d^2-a e^2}+\left(c d^2-a e^2\right)^{2/3}+c^{2/3} d^{4/3} \left(\frac{e x}{d}+1\right)^{2/3}}{\left(\sqrt[3]{c d^2-a e^2}-\left(1+\sqrt{3}\right) \sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{c d^2-a e^2}-\left(1-\sqrt{3}\right) \sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}}{\sqrt[3]{c d^2-a e^2}-\left(1+\sqrt{3}\right) \sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 c d e \sqrt{d (a e+c d x)} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \sqrt{-\frac{\sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1} \left(\sqrt[3]{c d^2-a e^2}-\sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}\right)}{\left(\sqrt[3]{c d^2-a e^2}-\left(1+\sqrt{3}\right) \sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}\right)^2}}}+\frac{3 (d+e x)^{2/3} (a e+c d x)}{2 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}","\frac{3^{3/4} (d+e x)^{2/3} \left(c d^2-a e^2\right)^{2/3} \sqrt{a d e+c d^2 x} \left(\sqrt[3]{c d^2-a e^2}-\sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}\right) \sqrt{\frac{\sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1} \sqrt[3]{c d^2-a e^2}+\left(c d^2-a e^2\right)^{2/3}+c^{2/3} d^{4/3} \left(\frac{e x}{d}+1\right)^{2/3}}{\left(\sqrt[3]{c d^2-a e^2}-\left(1+\sqrt{3}\right) \sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}\right)^2}} F\left(\cos ^{-1}\left(\frac{\sqrt[3]{c d^2-a e^2}-\left(1-\sqrt{3}\right) \sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}}{\sqrt[3]{c d^2-a e^2}-\left(1+\sqrt{3}\right) \sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 c d e \sqrt{d (a e+c d x)} \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2} \sqrt{-\frac{\sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1} \left(\sqrt[3]{c d^2-a e^2}-\sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}\right)}{\left(\sqrt[3]{c d^2-a e^2}-\left(1+\sqrt{3}\right) \sqrt[3]{c} d^{2/3} \sqrt[3]{\frac{e x}{d}+1}\right)^2}}}+\frac{3 (d+e x)^{2/3} (a e+c d x)}{2 c d \sqrt{x \left(a e^2+c d^2\right)+a d e+c d e x^2}}",1,"(3*(a*e + c*d*x)*(d + e*x)^(2/3))/(2*c*d*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]) + (3^(3/4)*(c*d^2 - a*e^2)^(2/3)*Sqrt[a*d*e + c*d^2*x]*(d + e*x)^(2/3)*((c*d^2 - a*e^2)^(1/3) - c^(1/3)*d^(2/3)*(1 + (e*x)/d)^(1/3))*Sqrt[((c*d^2 - a*e^2)^(2/3) + c^(1/3)*d^(2/3)*(c*d^2 - a*e^2)^(1/3)*(1 + (e*x)/d)^(1/3) + c^(2/3)*d^(4/3)*(1 + (e*x)/d)^(2/3))/((c*d^2 - a*e^2)^(1/3) - (1 + Sqrt[3])*c^(1/3)*d^(2/3)*(1 + (e*x)/d)^(1/3))^2]*EllipticF[ArcCos[((c*d^2 - a*e^2)^(1/3) - (1 - Sqrt[3])*c^(1/3)*d^(2/3)*(1 + (e*x)/d)^(1/3))/((c*d^2 - a*e^2)^(1/3) - (1 + Sqrt[3])*c^(1/3)*d^(2/3)*(1 + (e*x)/d)^(1/3))], (2 + Sqrt[3])/4])/(4*c*d*e*Sqrt[d*(a*e + c*d*x)]*Sqrt[a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2]*Sqrt[-((c^(1/3)*d^(2/3)*(1 + (e*x)/d)^(1/3)*((c*d^2 - a*e^2)^(1/3) - c^(1/3)*d^(2/3)*(1 + (e*x)/d)^(1/3)))/((c*d^2 - a*e^2)^(1/3) - (1 + Sqrt[3])*c^(1/3)*d^(2/3)*(1 + (e*x)/d)^(1/3))^2)])","A",5,5,39,0.1282,1,"{679, 677, 50, 63, 225}"
2084,1,130,0,0.0765587,"\int (d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^3 \, dx","Int[(d + e*x)^m*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","-\frac{3 c^2 d^2 \left(c d^2-a e^2\right) (d+e x)^{m+6}}{e^4 (m+6)}-\frac{\left(c d^2-a e^2\right)^3 (d+e x)^{m+4}}{e^4 (m+4)}+\frac{3 c d \left(c d^2-a e^2\right)^2 (d+e x)^{m+5}}{e^4 (m+5)}+\frac{c^3 d^3 (d+e x)^{m+7}}{e^4 (m+7)}","-\frac{3 c^2 d^2 \left(c d^2-a e^2\right) (d+e x)^{m+6}}{e^4 (m+6)}-\frac{\left(c d^2-a e^2\right)^3 (d+e x)^{m+4}}{e^4 (m+4)}+\frac{3 c d \left(c d^2-a e^2\right)^2 (d+e x)^{m+5}}{e^4 (m+5)}+\frac{c^3 d^3 (d+e x)^{m+7}}{e^4 (m+7)}",1,"-(((c*d^2 - a*e^2)^3*(d + e*x)^(4 + m))/(e^4*(4 + m))) + (3*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^(5 + m))/(e^4*(5 + m)) - (3*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^(6 + m))/(e^4*(6 + m)) + (c^3*d^3*(d + e*x)^(7 + m))/(e^4*(7 + m))","A",3,2,35,0.05714,1,"{626, 43}"
2085,1,90,0,0.0503699,"\int (d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^2 \, dx","Int[(d + e*x)^m*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","\frac{\left(c d^2-a e^2\right)^2 (d+e x)^{m+3}}{e^3 (m+3)}-\frac{2 c d \left(c d^2-a e^2\right) (d+e x)^{m+4}}{e^3 (m+4)}+\frac{c^2 d^2 (d+e x)^{m+5}}{e^3 (m+5)}","\frac{\left(c d^2-a e^2\right)^2 (d+e x)^{m+3}}{e^3 (m+3)}-\frac{2 c d \left(c d^2-a e^2\right) (d+e x)^{m+4}}{e^3 (m+4)}+\frac{c^2 d^2 (d+e x)^{m+5}}{e^3 (m+5)}",1,"((c*d^2 - a*e^2)^2*(d + e*x)^(3 + m))/(e^3*(3 + m)) - (2*c*d*(c*d^2 - a*e^2)*(d + e*x)^(4 + m))/(e^3*(4 + m)) + (c^2*d^2*(d + e*x)^(5 + m))/(e^3*(5 + m))","A",3,2,35,0.05714,1,"{626, 43}"
2086,1,52,0,0.025133,"\int (d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right) \, dx","Int[(d + e*x)^m*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","\frac{c d (d+e x)^{m+3}}{e^2 (m+3)}-\frac{\left(c d^2-a e^2\right) (d+e x)^{m+2}}{e^2 (m+2)}","\frac{c d (d+e x)^{m+3}}{e^2 (m+3)}-\frac{\left(c d^2-a e^2\right) (d+e x)^{m+2}}{e^2 (m+2)}",1,"-(((c*d^2 - a*e^2)*(d + e*x)^(2 + m))/(e^2*(2 + m))) + (c*d*(d + e*x)^(3 + m))/(e^2*(3 + m))","A",3,2,33,0.06061,1,"{626, 43}"
2087,1,54,0,0.0243076,"\int \frac{(d+e x)^m}{a d e+\left(c d^2+a e^2\right) x+c d e x^2} \, dx","Int[(d + e*x)^m/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]","-\frac{(d+e x)^m \, _2F_1\left(1,m;m+1;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{m \left(c d^2-a e^2\right)}","-\frac{(d+e x)^m \, _2F_1\left(1,m;m+1;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{m \left(c d^2-a e^2\right)}",1,"-(((d + e*x)^m*Hypergeometric2F1[1, m, 1 + m, (c*d*(d + e*x))/(c*d^2 - a*e^2)])/((c*d^2 - a*e^2)*m))","A",2,2,35,0.05714,1,"{626, 68}"
2088,1,61,0,0.0223567,"\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)^2} \, dx","Int[(d + e*x)^m/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2,x]","-\frac{e (d+e x)^{m-1} \, _2F_1\left(2,m-1;m;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(1-m) \left(c d^2-a e^2\right)^2}","-\frac{e (d+e x)^{m-1} \, _2F_1\left(2,m-1;m;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(1-m) \left(c d^2-a e^2\right)^2}",1,"-((e*(d + e*x)^(-1 + m)*Hypergeometric2F1[2, -1 + m, m, (c*d*(d + e*x))/(c*d^2 - a*e^2)])/((c*d^2 - a*e^2)^2*(1 - m)))","A",2,2,35,0.05714,1,"{626, 68}"
2089,1,64,0,0.0272594,"\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)^3} \, dx","Int[(d + e*x)^m/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3,x]","\frac{e^2 (d+e x)^{m-2} \, _2F_1\left(3,m-2;m-1;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(2-m) \left(c d^2-a e^2\right)^3}","\frac{e^2 (d+e x)^{m-2} \, _2F_1\left(3,m-2;m-1;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(2-m) \left(c d^2-a e^2\right)^3}",1,"(e^2*(d + e*x)^(-2 + m)*Hypergeometric2F1[3, -2 + m, -1 + m, (c*d*(d + e*x))/(c*d^2 - a*e^2)])/((c*d^2 - a*e^2)^3*(2 - m))","A",2,2,35,0.05714,1,"{626, 68}"
2090,1,65,0,0.0262358,"\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)^4} \, dx","Int[(d + e*x)^m/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4,x]","-\frac{e^3 (d+e x)^{m-3} \, _2F_1\left(4,m-3;m-2;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(3-m) \left(c d^2-a e^2\right)^4}","-\frac{e^3 (d+e x)^{m-3} \, _2F_1\left(4,m-3;m-2;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(3-m) \left(c d^2-a e^2\right)^4}",1,"-((e^3*(d + e*x)^(-3 + m)*Hypergeometric2F1[4, -3 + m, -2 + m, (c*d*(d + e*x))/(c*d^2 - a*e^2)])/((c*d^2 - a*e^2)^4*(3 - m)))","A",2,2,35,0.05714,1,"{626, 68}"
2091,1,123,0,0.1048224,"\int (d+e x)^m \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(d + e*x)^m*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,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)^p \left(\frac{c d (d+e x)}{c d^2-a e^2}\right)^{-m-p} \, _2F_1\left(-m-p,p+1;p+2;-\frac{e (a e+c d x)}{c d^2-a e^2}\right)}{c d (p+1)}","-\frac{(d+e x)^{m+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)^p \, _2F_1\left(1,m+2 p+2;m+p+2;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(m+p+1) \left(c d^2-a e^2\right)}",1,"((a*e + c*d*x)*(d + e*x)^m*((c*d*(d + e*x))/(c*d^2 - a*e^2))^(-m - p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p*Hypergeometric2F1[-m - p, 1 + p, 2 + p, -((e*(a*e + c*d*x))/(c*d^2 - a*e^2))])/(c*d*(1 + p))","A",4,4,35,0.1143,1,"{679, 677, 70, 69}"
2092,1,124,0,0.0811374,"\int (d+e x)^3 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,x]","\frac{\left(c d^2-a e^2\right)^3 (a e+c d x) \left(\frac{c d (d+e x)}{c d^2-a e^2}\right)^{-p} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(-p-3,p+1;p+2;-\frac{e (a e+c d x)}{c d^2-a e^2}\right)}{c^4 d^4 (p+1)}","-\frac{(d+e x)^4 (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(1,2 p+5;p+5;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(p+4) \left(c d^2-a e^2\right)}",1,"((c*d^2 - a*e^2)^3*(a*e + c*d*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p*Hypergeometric2F1[-3 - p, 1 + p, 2 + p, -((e*(a*e + c*d*x))/(c*d^2 - a*e^2))])/(c^4*d^4*(1 + p)*((c*d*(d + e*x))/(c*d^2 - a*e^2))^p)","A",3,3,35,0.08571,1,"{677, 70, 69}"
2093,1,124,0,0.0679863,"\int (d+e x)^2 \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,x]","\frac{\left(c d^2-a e^2\right)^2 (a e+c d x) \left(\frac{c d (d+e x)}{c d^2-a e^2}\right)^{-p} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(-p-2,p+1;p+2;-\frac{e (a e+c d x)}{c d^2-a e^2}\right)}{c^3 d^3 (p+1)}","-\frac{(d+e x)^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)^p \, _2F_1\left(1,2 (p+2);p+4;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(p+3) \left(c d^2-a e^2\right)}",1,"((c*d^2 - a*e^2)^2*(a*e + c*d*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p*Hypergeometric2F1[-2 - p, 1 + p, 2 + p, -((e*(a*e + c*d*x))/(c*d^2 - a*e^2))])/(c^3*d^3*(1 + p)*((c*d*(d + e*x))/(c*d^2 - a*e^2))^p)","A",3,3,35,0.08571,1,"{677, 70, 69}"
2094,1,152,0,0.0576793,"\int (d+e x) \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,x]","\frac{\left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{2 c d (p+1)}-\frac{\left(-\frac{e (a e+c d x)}{c d^2-a e^2}\right)^{-p-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{2 c d (p+1)}","-\frac{(d+e x)^2 (a e+c d x) \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(1,2 p+3;p+3;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(p+2) \left(c d^2-a e^2\right)}",1,"(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p)/(2*c*d*(1 + p)) - ((-((e*(a*e + c*d*x))/(c*d^2 - a*e^2)))^(-1 - p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (c*d*(d + e*x))/(c*d^2 - a*e^2)])/(2*c*d*(1 + p))","A",2,2,33,0.06061,1,"{640, 624}"
2095,1,113,0,0.017553,"\int \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,x]","-\frac{\left(-\frac{e (a e+c d x)}{c d^2-a e^2}\right)^{-p-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(p+1) \left(c d^2-a e^2\right)}","-\frac{\left(-\frac{e (a e+c d x)}{c d^2-a e^2}\right)^{-p-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(p+1) \left(c d^2-a e^2\right)}",1,"-(((-((e*(a*e + c*d*x))/(c*d^2 - a*e^2)))^(-1 - p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (c*d*(d + e*x))/(c*d^2 - a*e^2)])/((c*d^2 - a*e^2)*(1 + p)))","A",1,1,27,0.03704,1,"{624}"
2096,1,93,0,0.0683955,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p}{d+e x} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p/(d + e*x),x]","\frac{\left(-\frac{e (a e+c d x)}{c d^2-a e^2}\right)^{-p} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(-p,p;p+1;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{e p}","\frac{\left(-\frac{e (a e+c d x)}{c d^2-a e^2}\right)^{-p} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(-p,p;p+1;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{e p}",1,"((a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p*Hypergeometric2F1[-p, p, 1 + p, (c*d*(d + e*x))/(c*d^2 - a*e^2)])/(e*p*(-((e*(a*e + c*d*x))/(c*d^2 - a*e^2)))^p)","A",3,3,35,0.08571,1,"{677, 70, 69}"
2097,1,120,0,0.0700642,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p}{(d+e x)^2} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p/(d + e*x)^2,x]","\frac{c d (a e+c d x) \left(\frac{c d (d+e x)}{c d^2-a e^2}\right)^{-p} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(2-p,p+1;p+2;-\frac{e (a e+c d x)}{c d^2-a e^2}\right)}{(p+1) \left(c d^2-a e^2\right)^2}","\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)^p \, _2F_1\left(1,2 p;p;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(1-p) (d+e x) \left(c d^2-a e^2\right)}",1,"(c*d*(a*e + c*d*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p*Hypergeometric2F1[2 - p, 1 + p, 2 + p, -((e*(a*e + c*d*x))/(c*d^2 - a*e^2))])/((c*d^2 - a*e^2)^2*(1 + p)*((c*d*(d + e*x))/(c*d^2 - a*e^2))^p)","A",3,3,35,0.08571,1,"{677, 70, 69}"
2098,1,124,0,0.0684541,"\int \frac{\left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p}{(d+e x)^3} \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p/(d + e*x)^3,x]","\frac{c^2 d^2 (a e+c d x) \left(\frac{c d (d+e x)}{c d^2-a e^2}\right)^{-p} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(3-p,p+1;p+2;-\frac{e (a e+c d x)}{c d^2-a e^2}\right)}{(p+1) \left(c d^2-a e^2\right)^3}","\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)^p \, _2F_1\left(1,2 p-1;p-1;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{(2-p) (d+e x)^2 \left(c d^2-a e^2\right)}",1,"(c^2*d^2*(a*e + c*d*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p*Hypergeometric2F1[3 - p, 1 + p, 2 + p, -((e*(a*e + c*d*x))/(c*d^2 - a*e^2))])/((c*d^2 - a*e^2)^3*(1 + p)*((c*d*(d + e*x))/(c*d^2 - a*e^2))^p)","A",3,3,35,0.08571,1,"{677, 70, 69}"
2099,1,113,0,0.0940342,"\int (d+e x)^{-2 p} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p/(d + e*x)^(2*p),x]","\frac{(d+e x)^{-2 p} (a e+c d x) \left(\frac{c d (d+e x)}{c d^2-a e^2}\right)^p \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(p,p+1;p+2;-\frac{e (a e+c d x)}{c d^2-a e^2}\right)}{c d (p+1)}","\frac{(d+e x)^{-2 p} (a e+c d x) \left(\frac{c d (d+e x)}{c d^2-a e^2}\right)^p \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(p,p+1;p+2;-\frac{e (a e+c d x)}{c d^2-a e^2}\right)}{c d (p+1)}",1,"((a*e + c*d*x)*((c*d*(d + e*x))/(c*d^2 - a*e^2))^p*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p*Hypergeometric2F1[p, 1 + p, 2 + p, -((e*(a*e + c*d*x))/(c*d^2 - a*e^2))])/(c*d*(1 + p)*(d + e*x)^(2*p))","A",4,4,37,0.1081,1,"{679, 677, 70, 69}"
2100,1,107,0,0.095885,"\int (d+e x)^{-1-2 p} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(d + e*x)^(-1 - 2*p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,x]","-\frac{(d+e x)^{-2 p} \left(-\frac{e (a e+c d x)}{c d^2-a e^2}\right)^{-p} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(-p,-p;1-p;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{e p}","-\frac{(d+e x)^{-2 p} \left(-\frac{e (a e+c d x)}{c d^2-a e^2}\right)^{-p} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^p \, _2F_1\left(-p,-p;1-p;\frac{c d (d+e x)}{c d^2-a e^2}\right)}{e p}",1,"-(((a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p*Hypergeometric2F1[-p, -p, 1 - p, (c*d*(d + e*x))/(c*d^2 - a*e^2)])/(e*p*(-((e*(a*e + c*d*x))/(c*d^2 - a*e^2)))^p*(d + e*x)^(2*p)))","A",4,4,39,0.1026,1,"{679, 677, 70, 69}"
2101,1,60,0,0.0162893,"\int (d+e x)^{-2-2 p} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(d + e*x)^(-2 - 2*p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,x]","\frac{(d+e x)^{-2 (p+1)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+1) \left(c d^2-a e^2\right)}","\frac{(d+e x)^{-2 (p+1)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+1) \left(c d^2-a e^2\right)}",1,"(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p)/((c*d^2 - a*e^2)*(1 + p)*(d + e*x)^(2*(1 + p)))","A",1,1,39,0.02564,1,"{650}"
2102,1,128,0,0.0524983,"\int (d+e x)^{-3-2 p} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(d + e*x)^(-3 - 2*p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,x]","\frac{(d+e x)^{-2 p-3} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+2) \left(c d^2-a e^2\right)}+\frac{c d (d+e x)^{-2 (p+1)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+1) (p+2) \left(c d^2-a e^2\right)^2}","\frac{(d+e x)^{-2 p-3} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+2) \left(c d^2-a e^2\right)}+\frac{c d (d+e x)^{-2 (p+1)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+1) (p+2) \left(c d^2-a e^2\right)^2}",1,"((d + e*x)^(-3 - 2*p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p))/((c*d^2 - a*e^2)*(2 + p)) + (c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p))/((c*d^2 - a*e^2)^2*(1 + p)*(2 + p)*(d + e*x)^(2*(1 + p)))","A",2,2,39,0.05128,1,"{658, 650}"
2103,1,206,0,0.0931066,"\int (d+e x)^{-4-2 p} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(d + e*x)^(-4 - 2*p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,x]","\frac{2 c^2 d^2 (d+e x)^{-2 (p+1)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+1) (p+2) (p+3) \left(c d^2-a e^2\right)^3}+\frac{2 c d (d+e x)^{-2 p-3} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+2) (p+3) \left(c d^2-a e^2\right)^2}+\frac{(d+e x)^{-2 (p+2)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+3) \left(c d^2-a e^2\right)}","\frac{2 c^2 d^2 (d+e x)^{-2 (p+1)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+1) (p+2) (p+3) \left(c d^2-a e^2\right)^3}+\frac{2 c d (d+e x)^{-2 p-3} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+2) (p+3) \left(c d^2-a e^2\right)^2}+\frac{(d+e x)^{-2 (p+2)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+3) \left(c d^2-a e^2\right)}",1,"(2*c*d*(d + e*x)^(-3 - 2*p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p))/((c*d^2 - a*e^2)^2*(2 + p)*(3 + p)) + (2*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p))/((c*d^2 - a*e^2)^3*(1 + p)*(2 + p)*(3 + p)*(d + e*x)^(2*(1 + p))) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p)/((c*d^2 - a*e^2)*(3 + p)*(d + e*x)^(2*(2 + p)))","A",3,2,39,0.05128,1,"{658, 650}"
2104,1,288,0,0.1640645,"\int (d+e x)^{-5-2 p} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(d + e*x)^(-5 - 2*p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p,x]","\frac{6 c^2 d^2 (d+e x)^{-2 p-3} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+2) (p+3) (p+4) \left(c d^2-a e^2\right)^3}+\frac{6 c^3 d^3 (d+e x)^{-2 (p+1)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+1) (p+2) (p+3) (p+4) \left(c d^2-a e^2\right)^4}+\frac{(d+e x)^{-2 p-5} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+4) \left(c d^2-a e^2\right)}+\frac{3 c d (d+e x)^{-2 (p+2)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+3) (p+4) \left(c d^2-a e^2\right)^2}","\frac{6 c^2 d^2 (d+e x)^{-2 p-3} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+2) (p+3) (p+4) \left(c d^2-a e^2\right)^3}+\frac{6 c^3 d^3 (d+e x)^{-2 (p+1)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+1) (p+2) (p+3) (p+4) \left(c d^2-a e^2\right)^4}+\frac{(d+e x)^{-2 p-5} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+4) \left(c d^2-a e^2\right)}+\frac{3 c d (d+e x)^{-2 (p+2)} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{(p+3) (p+4) \left(c d^2-a e^2\right)^2}",1,"((d + e*x)^(-5 - 2*p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p))/((c*d^2 - a*e^2)*(4 + p)) + (6*c^2*d^2*(d + e*x)^(-3 - 2*p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p))/((c*d^2 - a*e^2)^3*(2 + p)*(3 + p)*(4 + p)) + (6*c^3*d^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p))/((c*d^2 - a*e^2)^4*(1 + p)*(2 + p)*(3 + p)*(4 + p)*(d + e*x)^(2*(1 + p))) + (3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p))/((c*d^2 - a*e^2)^2*(3 + p)*(4 + p)*(d + e*x)^(2*(2 + p)))","A",4,2,39,0.05128,1,"{658, 650}"
2105,1,54,0,0.018182,"\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}"
2106,1,52,0,0.0160988,"\int (d+e x)^{-p} \left(a d e+\left(c d^2+a e^2\right) x+c d e x^2\right)^p \, dx","Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^p/(d + e*x)^p,x]","\frac{(d+e x)^{-p-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{c d (p+1)}","\frac{(d+e x)^{-p-1} \left(x \left(a e^2+c d^2\right)+a d e+c d e x^2\right)^{p+1}}{c d (p+1)}",1,"((d + e*x)^(-1 - p)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1 + p))/(c*d*(1 + p))","A",1,1,37,0.02703,1,"{648}"
2107,1,69,0,0.0982364,"\int (d+e x)^4 \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^4*(a + b*x + c*x^2),x]","\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)}{5 e^3}-\frac{(d+e x)^6 (2 c d-b e)}{6 e^3}+\frac{c (d+e x)^7}{7 e^3}","\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)}{5 e^3}-\frac{(d+e x)^6 (2 c d-b e)}{6 e^3}+\frac{c (d+e x)^7}{7 e^3}",1,"((c*d^2 - b*d*e + a*e^2)*(d + e*x)^5)/(5*e^3) - ((2*c*d - b*e)*(d + e*x)^6)/(6*e^3) + (c*(d + e*x)^7)/(7*e^3)","A",2,1,18,0.05556,1,"{698}"
2108,1,69,0,0.0691618,"\int (d+e x)^3 \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2),x]","\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)}{4 e^3}-\frac{(d+e x)^5 (2 c d-b e)}{5 e^3}+\frac{c (d+e x)^6}{6 e^3}","\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)}{4 e^3}-\frac{(d+e x)^5 (2 c d-b e)}{5 e^3}+\frac{c (d+e x)^6}{6 e^3}",1,"((c*d^2 - b*d*e + a*e^2)*(d + e*x)^4)/(4*e^3) - ((2*c*d - b*e)*(d + e*x)^5)/(5*e^3) + (c*(d + e*x)^6)/(6*e^3)","A",2,1,18,0.05556,1,"{698}"
2109,1,69,0,0.0538831,"\int (d+e x)^2 \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2),x]","\frac{(d+e x)^3 \left(a e^2-b d e+c d^2\right)}{3 e^3}-\frac{(d+e x)^4 (2 c d-b e)}{4 e^3}+\frac{c (d+e x)^5}{5 e^3}","\frac{(d+e x)^3 \left(a e^2-b d e+c d^2\right)}{3 e^3}-\frac{(d+e x)^4 (2 c d-b e)}{4 e^3}+\frac{c (d+e x)^5}{5 e^3}",1,"((c*d^2 - b*d*e + a*e^2)*(d + e*x)^3)/(3*e^3) - ((2*c*d - b*e)*(d + e*x)^4)/(4*e^3) + (c*(d + e*x)^5)/(5*e^3)","A",2,1,18,0.05556,1,"{698}"
2110,1,42,0,0.028922,"\int (d+e x) \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)*(a + b*x + c*x^2),x]","\frac{1}{2} x^2 (a e+b d)+a d x+\frac{1}{3} x^3 (b e+c d)+\frac{1}{4} c e x^4","\frac{1}{2} x^2 (a e+b d)+a d x+\frac{1}{3} x^3 (b e+c d)+\frac{1}{4} c e x^4",1,"a*d*x + ((b*d + a*e)*x^2)/2 + ((c*d + b*e)*x^3)/3 + (c*e*x^4)/4","A",2,1,16,0.06250,1,"{631}"
2111,1,20,0,0.0039018,"\int \left(a+b x+c x^2\right) \, dx","Int[a + b*x + c*x^2,x]","a x+\frac{b x^2}{2}+\frac{c x^3}{3}","a x+\frac{b x^2}{2}+\frac{c x^3}{3}",1,"a*x + (b*x^2)/2 + (c*x^3)/3","A",1,0,10,0,1,"{}"
2112,1,52,0,0.043259,"\int \frac{a+b x+c x^2}{d+e x} \, dx","Int[(a + b*x + c*x^2)/(d + e*x),x]","\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^3}-\frac{x (c d-b e)}{e^2}+\frac{c x^2}{2 e}","\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^3}-\frac{x (c d-b e)}{e^2}+\frac{c x^2}{2 e}",1,"-(((c*d - b*e)*x)/e^2) + (c*x^2)/(2*e) + ((c*d^2 - b*d*e + a*e^2)*Log[d + e*x])/e^3","A",2,1,18,0.05556,1,"{698}"
2113,1,55,0,0.0454211,"\int \frac{a+b x+c x^2}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)/(d + e*x)^2,x]","-\frac{a e^2-b d e+c d^2}{e^3 (d+e x)}-\frac{(2 c d-b e) \log (d+e x)}{e^3}+\frac{c x}{e^2}","-\frac{a e^2-b d e+c d^2}{e^3 (d+e x)}-\frac{(2 c d-b e) \log (d+e x)}{e^3}+\frac{c x}{e^2}",1,"(c*x)/e^2 - (c*d^2 - b*d*e + a*e^2)/(e^3*(d + e*x)) - ((2*c*d - b*e)*Log[d + e*x])/e^3","A",2,1,18,0.05556,1,"{698}"
2114,1,62,0,0.045073,"\int \frac{a+b x+c x^2}{(d+e x)^3} \, dx","Int[(a + b*x + c*x^2)/(d + e*x)^3,x]","-\frac{a e^2-b d e+c d^2}{2 e^3 (d+e x)^2}+\frac{2 c d-b e}{e^3 (d+e x)}+\frac{c \log (d+e x)}{e^3}","-\frac{a e^2-b d e+c d^2}{2 e^3 (d+e x)^2}+\frac{2 c d-b e}{e^3 (d+e x)}+\frac{c \log (d+e x)}{e^3}",1,"-(c*d^2 - b*d*e + a*e^2)/(2*e^3*(d + e*x)^2) + (2*c*d - b*e)/(e^3*(d + e*x)) + (c*Log[d + e*x])/e^3","A",2,1,18,0.05556,1,"{698}"
2115,1,67,0,0.0443593,"\int \frac{a+b x+c x^2}{(d+e x)^4} \, dx","Int[(a + b*x + c*x^2)/(d + e*x)^4,x]","-\frac{a e^2-b d e+c d^2}{3 e^3 (d+e x)^3}+\frac{2 c d-b e}{2 e^3 (d+e x)^2}-\frac{c}{e^3 (d+e x)}","-\frac{a e^2-b d e+c d^2}{3 e^3 (d+e x)^3}+\frac{2 c d-b e}{2 e^3 (d+e x)^2}-\frac{c}{e^3 (d+e x)}",1,"-(c*d^2 - b*d*e + a*e^2)/(3*e^3*(d + e*x)^3) + (2*c*d - b*e)/(2*e^3*(d + e*x)^2) - c/(e^3*(d + e*x))","A",2,1,18,0.05556,1,"{698}"
2116,1,69,0,0.0464884,"\int \frac{a+b x+c x^2}{(d+e x)^5} \, dx","Int[(a + b*x + c*x^2)/(d + e*x)^5,x]","-\frac{a e^2-b d e+c d^2}{4 e^3 (d+e x)^4}+\frac{2 c d-b e}{3 e^3 (d+e x)^3}-\frac{c}{2 e^3 (d+e x)^2}","-\frac{a e^2-b d e+c d^2}{4 e^3 (d+e x)^4}+\frac{2 c d-b e}{3 e^3 (d+e x)^3}-\frac{c}{2 e^3 (d+e x)^2}",1,"-(c*d^2 - b*d*e + a*e^2)/(4*e^3*(d + e*x)^4) + (2*c*d - b*e)/(3*e^3*(d + e*x)^3) - c/(2*e^3*(d + e*x)^2)","A",2,1,18,0.05556,1,"{698}"
2117,1,69,0,0.0442678,"\int \frac{a+b x+c x^2}{(d+e x)^6} \, dx","Int[(a + b*x + c*x^2)/(d + e*x)^6,x]","-\frac{a e^2-b d e+c d^2}{5 e^3 (d+e x)^5}+\frac{2 c d-b e}{4 e^3 (d+e x)^4}-\frac{c}{3 e^3 (d+e x)^3}","-\frac{a e^2-b d e+c d^2}{5 e^3 (d+e x)^5}+\frac{2 c d-b e}{4 e^3 (d+e x)^4}-\frac{c}{3 e^3 (d+e x)^3}",1,"-(c*d^2 - b*d*e + a*e^2)/(5*e^3*(d + e*x)^5) + (2*c*d - b*e)/(4*e^3*(d + e*x)^4) - c/(3*e^3*(d + e*x)^3)","A",2,1,18,0.05556,1,"{698}"
2118,1,156,0,0.2497005,"\int (d+e x)^4 \left(a+b x+c x^2\right)^2 \, dx","Int[(d + e*x)^4*(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^7 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{7 e^5}-\frac{(d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^2}{5 e^5}-\frac{c (d+e x)^8 (2 c d-b e)}{4 e^5}+\frac{c^2 (d+e x)^9}{9 e^5}","\frac{(d+e x)^7 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{7 e^5}-\frac{(d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^2}{5 e^5}-\frac{c (d+e x)^8 (2 c d-b e)}{4 e^5}+\frac{c^2 (d+e x)^9}{9 e^5}",1,"((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^5)/(5*e^5) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^6)/(3*e^5) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^7)/(7*e^5) - (c*(2*c*d - b*e)*(d + e*x)^8)/(4*e^5) + (c^2*(d + e*x)^9)/(9*e^5)","A",2,1,20,0.05000,1,"{698}"
2119,1,156,0,0.1742318,"\int (d+e x)^3 \left(a+b x+c x^2\right)^2 \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^6 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{6 e^5}-\frac{2 (d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^5}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^2}{4 e^5}-\frac{2 c (d+e x)^7 (2 c d-b e)}{7 e^5}+\frac{c^2 (d+e x)^8}{8 e^5}","\frac{(d+e x)^6 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{6 e^5}-\frac{2 (d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^5}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^2}{4 e^5}-\frac{2 c (d+e x)^7 (2 c d-b e)}{7 e^5}+\frac{c^2 (d+e x)^8}{8 e^5}",1,"((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4)/(4*e^5) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^5)/(5*e^5) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^6)/(6*e^5) - (2*c*(2*c*d - b*e)*(d + e*x)^7)/(7*e^5) + (c^2*(d + e*x)^8)/(8*e^5)","A",2,1,20,0.05000,1,"{698}"
2120,1,156,0,0.1404048,"\int (d+e x)^2 \left(a+b x+c x^2\right)^2 \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^5 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^5}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{2 e^5}+\frac{(d+e x)^3 \left(a e^2-b d e+c d^2\right)^2}{3 e^5}-\frac{c (d+e x)^6 (2 c d-b e)}{3 e^5}+\frac{c^2 (d+e x)^7}{7 e^5}","\frac{(d+e x)^5 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^5}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{2 e^5}+\frac{(d+e x)^3 \left(a e^2-b d e+c d^2\right)^2}{3 e^5}-\frac{c (d+e x)^6 (2 c d-b e)}{3 e^5}+\frac{c^2 (d+e x)^7}{7 e^5}",1,"((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^3)/(3*e^5) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4)/(2*e^5) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^5)/(5*e^5) - (c*(2*c*d - b*e)*(d + e*x)^6)/(3*e^5) + (c^2*(d + e*x)^7)/(7*e^5)","A",2,1,20,0.05000,1,"{698}"
2121,1,96,0,0.0748955,"\int (d+e x) \left(a+b x+c x^2\right)^2 \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^2,x]","a^2 d x+\frac{1}{4} x^4 \left(2 a c e+b^2 e+2 b c d\right)+\frac{1}{3} x^3 \left(2 a b e+2 a c d+b^2 d\right)+\frac{1}{2} a x^2 (a e+2 b d)+\frac{1}{5} c x^5 (2 b e+c d)+\frac{1}{6} c^2 e x^6","a^2 d x+\frac{1}{4} x^4 \left(2 a c e+b^2 e+2 b c d\right)+\frac{1}{3} x^3 \left(2 a b e+2 a c d+b^2 d\right)+\frac{1}{2} a x^2 (a e+2 b d)+\frac{1}{5} c x^5 (2 b e+c d)+\frac{1}{6} c^2 e x^6",1,"a^2*d*x + (a*(2*b*d + a*e)*x^2)/2 + ((b^2*d + 2*a*c*d + 2*a*b*e)*x^3)/3 + ((2*b*c*d + b^2*e + 2*a*c*e)*x^4)/4 + (c*(c*d + 2*b*e)*x^5)/5 + (c^2*e*x^6)/6","A",2,1,18,0.05556,1,"{631}"
2122,1,46,0,0.0229114,"\int \left(a+b x+c x^2\right)^2 \, dx","Int[(a + b*x + c*x^2)^2,x]","a^2 x+\frac{1}{3} x^3 \left(2 a c+b^2\right)+a b x^2+\frac{1}{2} b c x^4+\frac{c^2 x^5}{5}","a^2 x+\frac{1}{3} x^3 \left(2 a c+b^2\right)+a b x^2+\frac{1}{2} b c x^4+\frac{c^2 x^5}{5}",1,"a^2*x + a*b*x^2 + ((b^2 + 2*a*c)*x^3)/3 + (b*c*x^4)/2 + (c^2*x^5)/5","A",2,1,12,0.08333,1,"{611}"
2123,1,129,0,0.155409,"\int \frac{\left(a+b x+c x^2\right)^2}{d+e x} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x),x]","\frac{x^2 \left(-2 c e (b d-a e)+b^2 e^2+c^2 d^2\right)}{2 e^3}-\frac{x (c d-b e) \left(c d^2-e (b d-2 a e)\right)}{e^4}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^5}-\frac{c x^3 (c d-2 b e)}{3 e^2}+\frac{c^2 x^4}{4 e}","\frac{x^2 \left(-2 c e (b d-a e)+b^2 e^2+c^2 d^2\right)}{2 e^3}-\frac{x (c d-b e) \left(c d^2-e (b d-2 a e)\right)}{e^4}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^5}-\frac{c x^3 (c d-2 b e)}{3 e^2}+\frac{c^2 x^4}{4 e}",1,"-(((c*d - b*e)*(c*d^2 - e*(b*d - 2*a*e))*x)/e^4) + ((c^2*d^2 + b^2*e^2 - 2*c*e*(b*d - a*e))*x^2)/(2*e^3) - (c*(c*d - 2*b*e)*x^3)/(3*e^2) + (c^2*x^4)/(4*e) + ((c*d^2 - b*d*e + a*e^2)^2*Log[d + e*x])/e^5","A",2,1,20,0.05000,1,"{698}"
2124,1,131,0,0.1414591,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^2,x]","\frac{x \left(-2 c e (2 b d-a e)+b^2 e^2+3 c^2 d^2\right)}{e^4}-\frac{\left(a e^2-b d e+c d^2\right)^2}{e^5 (d+e x)}-\frac{2 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^5}-\frac{c x^2 (c d-b e)}{e^3}+\frac{c^2 x^3}{3 e^2}","\frac{x \left(-2 c e (2 b d-a e)+b^2 e^2+3 c^2 d^2\right)}{e^4}-\frac{\left(a e^2-b d e+c d^2\right)^2}{e^5 (d+e x)}-\frac{2 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^5}-\frac{c x^2 (c d-b e)}{e^3}+\frac{c^2 x^3}{3 e^2}",1,"((3*c^2*d^2 + b^2*e^2 - 2*c*e*(2*b*d - a*e))*x)/e^4 - (c*(c*d - b*e)*x^2)/e^3 + (c^2*x^3)/(3*e^2) - (c*d^2 - b*d*e + a*e^2)^2/(e^5*(d + e*x)) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Log[d + e*x])/e^5","A",2,1,20,0.05000,1,"{698}"
2125,1,138,0,0.1355456,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^3} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^3,x]","\frac{\log (d+e x) \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^5}-\frac{\left(a e^2-b d e+c d^2\right)^2}{2 e^5 (d+e x)^2}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^5 (d+e x)}-\frac{c x (3 c d-2 b e)}{e^4}+\frac{c^2 x^2}{2 e^3}","\frac{\log (d+e x) \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^5}-\frac{\left(a e^2-b d e+c d^2\right)^2}{2 e^5 (d+e x)^2}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^5 (d+e x)}-\frac{c x (3 c d-2 b e)}{e^4}+\frac{c^2 x^2}{2 e^3}",1,"-((c*(3*c*d - 2*b*e)*x)/e^4) + (c^2*x^2)/(2*e^3) - (c*d^2 - b*d*e + a*e^2)^2/(2*e^5*(d + e*x)^2) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(e^5*(d + e*x)) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*Log[d + e*x])/e^5","A",2,1,20,0.05000,1,"{698}"
2126,1,139,0,0.1226139,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^4} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^4,x]","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{e^5 (d+e x)}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^5 (d+e x)^2}-\frac{\left(a e^2-b d e+c d^2\right)^2}{3 e^5 (d+e x)^3}-\frac{2 c (2 c d-b e) \log (d+e x)}{e^5}+\frac{c^2 x}{e^4}","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{e^5 (d+e x)}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^5 (d+e x)^2}-\frac{\left(a e^2-b d e+c d^2\right)^2}{3 e^5 (d+e x)^3}-\frac{2 c (2 c d-b e) \log (d+e x)}{e^5}+\frac{c^2 x}{e^4}",1,"(c^2*x)/e^4 - (c*d^2 - b*d*e + a*e^2)^2/(3*e^5*(d + e*x)^3) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(e^5*(d + e*x)^2) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))/(e^5*(d + e*x)) - (2*c*(2*c*d - b*e)*Log[d + e*x])/e^5","A",2,1,20,0.05000,1,"{698}"
2127,1,150,0,0.1216795,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^5} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^5,x]","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{2 e^5 (d+e x)^2}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5 (d+e x)^3}-\frac{\left(a e^2-b d e+c d^2\right)^2}{4 e^5 (d+e x)^4}+\frac{2 c (2 c d-b e)}{e^5 (d+e x)}+\frac{c^2 \log (d+e x)}{e^5}","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{2 e^5 (d+e x)^2}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5 (d+e x)^3}-\frac{\left(a e^2-b d e+c d^2\right)^2}{4 e^5 (d+e x)^4}+\frac{2 c (2 c d-b e)}{e^5 (d+e x)}+\frac{c^2 \log (d+e x)}{e^5}",1,"-(c*d^2 - b*d*e + a*e^2)^2/(4*e^5*(d + e*x)^4) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(3*e^5*(d + e*x)^3) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))/(2*e^5*(d + e*x)^2) + (2*c*(2*c*d - b*e))/(e^5*(d + e*x)) + (c^2*Log[d + e*x])/e^5","A",2,1,20,0.05000,1,"{698}"
2128,1,151,0,0.1114218,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^6} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^6,x]","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{3 e^5 (d+e x)^3}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{2 e^5 (d+e x)^4}-\frac{\left(a e^2-b d e+c d^2\right)^2}{5 e^5 (d+e x)^5}+\frac{c (2 c d-b e)}{e^5 (d+e x)^2}-\frac{c^2}{e^5 (d+e x)}","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{3 e^5 (d+e x)^3}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{2 e^5 (d+e x)^4}-\frac{\left(a e^2-b d e+c d^2\right)^2}{5 e^5 (d+e x)^5}+\frac{c (2 c d-b e)}{e^5 (d+e x)^2}-\frac{c^2}{e^5 (d+e x)}",1,"-(c*d^2 - b*d*e + a*e^2)^2/(5*e^5*(d + e*x)^5) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(2*e^5*(d + e*x)^4) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))/(3*e^5*(d + e*x)^3) + (c*(2*c*d - b*e))/(e^5*(d + e*x)^2) - c^2/(e^5*(d + e*x))","A",2,1,20,0.05000,1,"{698}"
2129,1,156,0,0.1090254,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^7} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^7,x]","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{4 e^5 (d+e x)^4}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^5 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right)^2}{6 e^5 (d+e x)^6}+\frac{2 c (2 c d-b e)}{3 e^5 (d+e x)^3}-\frac{c^2}{2 e^5 (d+e x)^2}","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{4 e^5 (d+e x)^4}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^5 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right)^2}{6 e^5 (d+e x)^6}+\frac{2 c (2 c d-b e)}{3 e^5 (d+e x)^3}-\frac{c^2}{2 e^5 (d+e x)^2}",1,"-(c*d^2 - b*d*e + a*e^2)^2/(6*e^5*(d + e*x)^6) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(5*e^5*(d + e*x)^5) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))/(4*e^5*(d + e*x)^4) + (2*c*(2*c*d - b*e))/(3*e^5*(d + e*x)^3) - c^2/(2*e^5*(d + e*x)^2)","A",2,1,20,0.05000,1,"{698}"
2130,1,156,0,0.1080998,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^8} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^8,x]","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{5 e^5 (d+e x)^5}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5 (d+e x)^6}-\frac{\left(a e^2-b d e+c d^2\right)^2}{7 e^5 (d+e x)^7}+\frac{c (2 c d-b e)}{2 e^5 (d+e x)^4}-\frac{c^2}{3 e^5 (d+e x)^3}","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{5 e^5 (d+e x)^5}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5 (d+e x)^6}-\frac{\left(a e^2-b d e+c d^2\right)^2}{7 e^5 (d+e x)^7}+\frac{c (2 c d-b e)}{2 e^5 (d+e x)^4}-\frac{c^2}{3 e^5 (d+e x)^3}",1,"-(c*d^2 - b*d*e + a*e^2)^2/(7*e^5*(d + e*x)^7) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(3*e^5*(d + e*x)^6) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))/(5*e^5*(d + e*x)^5) + (c*(2*c*d - b*e))/(2*e^5*(d + e*x)^4) - c^2/(3*e^5*(d + e*x)^3)","A",2,1,20,0.05000,1,"{698}"
2131,1,272,0,0.5089218,"\int (d+e x)^4 \left(a+b x+c x^2\right)^3 \, dx","Int[(d + e*x)^4*(a + b*x + c*x^2)^3,x]","\frac{c (d+e x)^9 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^7}-\frac{(d+e x)^8 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{8 e^7}+\frac{3 (d+e x)^7 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7}-\frac{(d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{2 e^7}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^3}{5 e^7}-\frac{3 c^2 (d+e x)^{10} (2 c d-b e)}{10 e^7}+\frac{c^3 (d+e x)^{11}}{11 e^7}","\frac{c (d+e x)^9 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^7}-\frac{(d+e x)^8 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{8 e^7}+\frac{3 (d+e x)^7 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7}-\frac{(d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{2 e^7}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^3}{5 e^7}-\frac{3 c^2 (d+e x)^{10} (2 c d-b e)}{10 e^7}+\frac{c^3 (d+e x)^{11}}{11 e^7}",1,"((c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^5)/(5*e^7) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^6)/(2*e^7) + (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^7)/(7*e^7) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^8)/(8*e^7) + (c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^9)/(3*e^7) - (3*c^2*(2*c*d - b*e)*(d + e*x)^10)/(10*e^7) + (c^3*(d + e*x)^11)/(11*e^7)","A",2,1,20,0.05000,1,"{698}"
2132,1,272,0,0.3676238,"\int (d+e x)^3 \left(a+b x+c x^2\right)^3 \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^3,x]","\frac{3 c (d+e x)^8 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{8 e^7}-\frac{(d+e x)^7 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{7 e^7}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7}-\frac{3 (d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^7}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^3}{4 e^7}-\frac{c^2 (d+e x)^9 (2 c d-b e)}{3 e^7}+\frac{c^3 (d+e x)^{10}}{10 e^7}","\frac{3 c (d+e x)^8 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{8 e^7}-\frac{(d+e x)^7 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{7 e^7}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7}-\frac{3 (d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^7}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^3}{4 e^7}-\frac{c^2 (d+e x)^9 (2 c d-b e)}{3 e^7}+\frac{c^3 (d+e x)^{10}}{10 e^7}",1,"((c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4)/(4*e^7) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^5)/(5*e^7) + ((c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^6)/(2*e^7) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^7)/(7*e^7) + (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^8)/(8*e^7) - (c^2*(2*c*d - b*e)*(d + e*x)^9)/(3*e^7) + (c^3*(d + e*x)^10)/(10*e^7)","A",2,1,20,0.05000,1,"{698}"
2133,1,272,0,0.2712276,"\int (d+e x)^2 \left(a+b x+c x^2\right)^3 \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^3,x]","\frac{3 c (d+e x)^7 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7}-\frac{(d+e x)^6 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{6 e^7}+\frac{3 (d+e x)^5 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7}-\frac{3 (d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{4 e^7}+\frac{(d+e x)^3 \left(a e^2-b d e+c d^2\right)^3}{3 e^7}-\frac{3 c^2 (d+e x)^8 (2 c d-b e)}{8 e^7}+\frac{c^3 (d+e x)^9}{9 e^7}","\frac{3 c (d+e x)^7 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7}-\frac{(d+e x)^6 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{6 e^7}+\frac{3 (d+e x)^5 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7}-\frac{3 (d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{4 e^7}+\frac{(d+e x)^3 \left(a e^2-b d e+c d^2\right)^3}{3 e^7}-\frac{3 c^2 (d+e x)^8 (2 c d-b e)}{8 e^7}+\frac{c^3 (d+e x)^9}{9 e^7}",1,"((c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^3)/(3*e^7) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4)/(4*e^7) + (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^5)/(5*e^7) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^6)/(6*e^7) + (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^7)/(7*e^7) - (3*c^2*(2*c*d - b*e)*(d + e*x)^8)/(8*e^7) + (c^3*(d + e*x)^9)/(9*e^7)","A",2,1,20,0.05000,1,"{698}"
2134,1,161,0,0.1574834,"\int (d+e x) \left(a+b x+c x^2\right)^3 \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{4} x^4 \left(3 a^2 c e+3 a b^2 e+6 a b c d+b^3 d\right)+\frac{1}{2} a^2 x^2 (a e+3 b d)+a^3 d x+\frac{1}{5} x^5 \left(6 a b c e+3 a c^2 d+3 b^2 c d+b^3 e\right)+\frac{1}{2} c x^6 \left(a c e+b^2 e+b c d\right)+a x^3 \left(a b e+a c d+b^2 d\right)+\frac{1}{7} c^2 x^7 (3 b e+c d)+\frac{1}{8} c^3 e x^8","\frac{1}{4} x^4 \left(3 a^2 c e+3 a b^2 e+6 a b c d+b^3 d\right)+\frac{1}{2} a^2 x^2 (a e+3 b d)+a^3 d x+\frac{1}{5} x^5 \left(6 a b c e+3 a c^2 d+3 b^2 c d+b^3 e\right)+\frac{1}{2} c x^6 \left(a c e+b^2 e+b c d\right)+a x^3 \left(a b e+a c d+b^2 d\right)+\frac{1}{7} c^2 x^7 (3 b e+c d)+\frac{1}{8} c^3 e x^8",1,"a^3*d*x + (a^2*(3*b*d + a*e)*x^2)/2 + a*(b^2*d + a*c*d + a*b*e)*x^3 + ((b^3*d + 6*a*b*c*d + 3*a*b^2*e + 3*a^2*c*e)*x^4)/4 + ((3*b^2*c*d + 3*a*c^2*d + b^3*e + 6*a*b*c*e)*x^5)/5 + (c*(b*c*d + b^2*e + a*c*e)*x^6)/2 + (c^2*(c*d + 3*b*e)*x^7)/7 + (c^3*e*x^8)/8","A",2,1,18,0.05556,1,"{631}"
2135,1,81,0,0.0557333,"\int \left(a+b x+c x^2\right)^3 \, dx","Int[(a + b*x + c*x^2)^3,x]","\frac{3}{2} a^2 b x^2+a^3 x+\frac{3}{5} c x^5 \left(a c+b^2\right)+\frac{1}{4} b x^4 \left(6 a c+b^2\right)+a x^3 \left(a c+b^2\right)+\frac{1}{2} b c^2 x^6+\frac{c^3 x^7}{7}","\frac{3}{2} a^2 b x^2+a^3 x+\frac{3}{5} c x^5 \left(a c+b^2\right)+\frac{1}{4} b x^4 \left(6 a c+b^2\right)+a x^3 \left(a c+b^2\right)+\frac{1}{2} b c^2 x^6+\frac{c^3 x^7}{7}",1,"a^3*x + (3*a^2*b*x^2)/2 + a*(b^2 + a*c)*x^3 + (b*(b^2 + 6*a*c)*x^4)/4 + (3*c*(b^2 + a*c)*x^5)/5 + (b*c^2*x^6)/2 + (c^3*x^7)/7","A",2,1,12,0.08333,1,"{611}"
2136,1,260,0,0.3227095,"\int \frac{\left(a+b x+c x^2\right)^3}{d+e x} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x),x]","\frac{3 c (d+e x)^4 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{4 e^7}-\frac{(d+e x)^3 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^7}+\frac{3 (d+e x)^2 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7}-\frac{3 x (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^6}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^7}-\frac{3 c^2 (d+e x)^5 (2 c d-b e)}{5 e^7}+\frac{c^3 (d+e x)^6}{6 e^7}","\frac{3 c (d+e x)^4 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{4 e^7}-\frac{(d+e x)^3 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^7}+\frac{3 (d+e x)^2 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7}-\frac{3 x (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^6}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^7}-\frac{3 c^2 (d+e x)^5 (2 c d-b e)}{5 e^7}+\frac{c^3 (d+e x)^6}{6 e^7}",1,"(-3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*x)/e^6 + (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^2)/(2*e^7) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^3)/(3*e^7) + (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^4)/(4*e^7) - (3*c^2*(2*c*d - b*e)*(d + e*x)^5)/(5*e^7) + (c^3*(d + e*x)^6)/(6*e^7) + ((c*d^2 - b*d*e + a*e^2)^3*Log[d + e*x])/e^7","A",2,1,20,0.05000,1,"{698}"
2137,1,256,0,0.3207979,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^2,x]","\frac{c (d+e x)^3 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}-\frac{(d+e x)^2 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^7}+\frac{3 x \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6}-\frac{\left(a e^2-b d e+c d^2\right)^3}{e^7 (d+e x)}-\frac{3 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^7}-\frac{3 c^2 (d+e x)^4 (2 c d-b e)}{4 e^7}+\frac{c^3 (d+e x)^5}{5 e^7}","\frac{c (d+e x)^3 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}-\frac{(d+e x)^2 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^7}+\frac{3 x \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6}-\frac{\left(a e^2-b d e+c d^2\right)^3}{e^7 (d+e x)}-\frac{3 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^7}-\frac{3 c^2 (d+e x)^4 (2 c d-b e)}{4 e^7}+\frac{c^3 (d+e x)^5}{5 e^7}",1,"(3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*x)/e^6 - (c*d^2 - b*d*e + a*e^2)^3/(e^7*(d + e*x)) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^2)/(2*e^7) + (c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^3)/e^7 - (3*c^2*(2*c*d - b*e)*(d + e*x)^4)/(4*e^7) + (c^3*(d + e*x)^5)/(5*e^7) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*Log[d + e*x])/e^7","A",2,1,20,0.05000,1,"{698}"
2138,1,255,0,0.3430871,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^3} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^3,x]","\frac{3 c x^2 \left(-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right)}{2 e^5}-\frac{x \left(-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right)}{e^6}+\frac{3 \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7 (d+e x)}-\frac{\left(a e^2-b d e+c d^2\right)^3}{2 e^7 (d+e x)^2}-\frac{c^2 x^3 (c d-b e)}{e^4}+\frac{c^3 x^4}{4 e^3}","\frac{3 c x^2 \left(-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right)}{2 e^5}-\frac{x \left(-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right)}{e^6}+\frac{3 \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7 (d+e x)}-\frac{\left(a e^2-b d e+c d^2\right)^3}{2 e^7 (d+e x)^2}-\frac{c^2 x^3 (c d-b e)}{e^4}+\frac{c^3 x^4}{4 e^3}",1,"-(((10*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(3*b*d - 2*a*e) - 9*c^2*d*e*(2*b*d - a*e))*x)/e^6) + (3*c*(2*c^2*d^2 + b^2*e^2 - c*e*(3*b*d - a*e))*x^2)/(2*e^5) - (c^2*(c*d - b*e)*x^3)/e^4 + (c^3*x^4)/(4*e^3) - (c*d^2 - b*d*e + a*e^2)^3/(2*e^7*(d + e*x)^2) + (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(e^7*(d + e*x)) + (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*Log[d + e*x])/e^7","A",2,1,20,0.05000,1,"{698}"
2139,1,251,0,0.2960328,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^4} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^4,x]","-\frac{3 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right) \left(a e^2-b d e+c d^2\right)}{e^7 (d+e x)}+\frac{c x \left(-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right)}{e^6}-\frac{(2 c d-b e) \log (d+e x) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^7}-\frac{\left(a e^2-b d e+c d^2\right)^3}{3 e^7 (d+e x)^3}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{2 e^7 (d+e x)^2}-\frac{c^2 x^2 (4 c d-3 b e)}{2 e^5}+\frac{c^3 x^3}{3 e^4}","-\frac{3 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right) \left(a e^2-b d e+c d^2\right)}{e^7 (d+e x)}+\frac{c x \left(-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right)}{e^6}-\frac{(2 c d-b e) \log (d+e x) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^7}-\frac{\left(a e^2-b d e+c d^2\right)^3}{3 e^7 (d+e x)^3}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{2 e^7 (d+e x)^2}-\frac{c^2 x^2 (4 c d-3 b e)}{2 e^5}+\frac{c^3 x^3}{3 e^4}",1,"(c*(10*c^2*d^2 + 3*b^2*e^2 - 3*c*e*(4*b*d - a*e))*x)/e^6 - (c^2*(4*c*d - 3*b*e)*x^2)/(2*e^5) + (c^3*x^3)/(3*e^4) - (c*d^2 - b*d*e + a*e^2)^3/(3*e^7*(d + e*x)^3) + (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(2*e^7*(d + e*x)^2) - (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^7*(d + e*x)) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*Log[d + e*x])/e^7","A",2,1,20,0.05000,1,"{698}"
2140,1,251,0,0.2741861,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^5} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^5,x]","\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^7 (d+e x)}-\frac{3 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7 (d+e x)^2}+\frac{3 c \log (d+e x) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7 (d+e x)^3}-\frac{\left(a e^2-b d e+c d^2\right)^3}{4 e^7 (d+e x)^4}-\frac{c^2 x (5 c d-3 b e)}{e^6}+\frac{c^3 x^2}{2 e^5}","\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^7 (d+e x)}-\frac{3 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7 (d+e x)^2}+\frac{3 c \log (d+e x) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7 (d+e x)^3}-\frac{\left(a e^2-b d e+c d^2\right)^3}{4 e^7 (d+e x)^4}-\frac{c^2 x (5 c d-3 b e)}{e^6}+\frac{c^3 x^2}{2 e^5}",1,"-((c^2*(5*c*d - 3*b*e)*x)/e^6) + (c^3*x^2)/(2*e^5) - (c*d^2 - b*d*e + a*e^2)^3/(4*e^7*(d + e*x)^4) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(e^7*(d + e*x)^3) - (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(2*e^7*(d + e*x)^2) + ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)))/(e^7*(d + e*x)) + (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*Log[d + e*x])/e^7","A",2,1,20,0.05000,1,"{698}"
2141,1,256,0,0.2446841,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^6} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^6,x]","-\frac{3 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (d+e x)}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^7 (d+e x)^2}-\frac{\left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (d+e x)^3}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{4 e^7 (d+e x)^4}-\frac{\left(a e^2-b d e+c d^2\right)^3}{5 e^7 (d+e x)^5}-\frac{3 c^2 (2 c d-b e) \log (d+e x)}{e^7}+\frac{c^3 x}{e^6}","-\frac{3 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (d+e x)}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^7 (d+e x)^2}-\frac{\left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (d+e x)^3}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{4 e^7 (d+e x)^4}-\frac{\left(a e^2-b d e+c d^2\right)^3}{5 e^7 (d+e x)^5}-\frac{3 c^2 (2 c d-b e) \log (d+e x)}{e^7}+\frac{c^3 x}{e^6}",1,"(c^3*x)/e^6 - (c*d^2 - b*d*e + a*e^2)^3/(5*e^7*(d + e*x)^5) + (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(4*e^7*(d + e*x)^4) - ((c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^7*(d + e*x)^3) + ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)))/(2*e^7*(d + e*x)^2) - (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^7*(d + e*x)) - (3*c^2*(2*c*d - b*e)*Log[d + e*x])/e^7","A",2,1,20,0.05000,1,"{698}"
2142,1,266,0,0.2263919,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^7} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^7,x]","-\frac{3 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7 (d+e x)^2}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^7 (d+e x)^3}-\frac{3 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{4 e^7 (d+e x)^4}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^7 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right)^3}{6 e^7 (d+e x)^6}+\frac{3 c^2 (2 c d-b e)}{e^7 (d+e x)}+\frac{c^3 \log (d+e x)}{e^7}","-\frac{3 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7 (d+e x)^2}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^7 (d+e x)^3}-\frac{3 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{4 e^7 (d+e x)^4}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^7 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right)^3}{6 e^7 (d+e x)^6}+\frac{3 c^2 (2 c d-b e)}{e^7 (d+e x)}+\frac{c^3 \log (d+e x)}{e^7}",1,"-(c*d^2 - b*d*e + a*e^2)^3/(6*e^7*(d + e*x)^6) + (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(5*e^7*(d + e*x)^5) - (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(4*e^7*(d + e*x)^4) + ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)))/(3*e^7*(d + e*x)^3) - (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(2*e^7*(d + e*x)^2) + (3*c^2*(2*c*d - b*e))/(e^7*(d + e*x)) + (c^3*Log[d + e*x])/e^7","A",2,1,20,0.05000,1,"{698}"
2143,1,268,0,0.2074059,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^8} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^8,x]","-\frac{c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (d+e x)^3}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{4 e^7 (d+e x)^4}-\frac{3 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7 (d+e x)^5}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{2 e^7 (d+e x)^6}-\frac{\left(a e^2-b d e+c d^2\right)^3}{7 e^7 (d+e x)^7}+\frac{3 c^2 (2 c d-b e)}{2 e^7 (d+e x)^2}-\frac{c^3}{e^7 (d+e x)}","-\frac{c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (d+e x)^3}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{4 e^7 (d+e x)^4}-\frac{3 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7 (d+e x)^5}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{2 e^7 (d+e x)^6}-\frac{\left(a e^2-b d e+c d^2\right)^3}{7 e^7 (d+e x)^7}+\frac{3 c^2 (2 c d-b e)}{2 e^7 (d+e x)^2}-\frac{c^3}{e^7 (d+e x)}",1,"-(c*d^2 - b*d*e + a*e^2)^3/(7*e^7*(d + e*x)^7) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(2*e^7*(d + e*x)^6) - (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(5*e^7*(d + e*x)^5) + ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)))/(4*e^7*(d + e*x)^4) - (c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^7*(d + e*x)^3) + (3*c^2*(2*c*d - b*e))/(2*e^7*(d + e*x)^2) - c^3/(e^7*(d + e*x))","A",2,1,20,0.05000,1,"{698}"
2144,1,269,0,0.2241302,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^9} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^9,x]","-\frac{3 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{4 e^7 (d+e x)^4}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^7 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7 (d+e x)^6}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{7 e^7 (d+e x)^7}-\frac{\left(a e^2-b d e+c d^2\right)^3}{8 e^7 (d+e x)^8}+\frac{c^2 (2 c d-b e)}{e^7 (d+e x)^3}-\frac{c^3}{2 e^7 (d+e x)^2}","-\frac{3 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{4 e^7 (d+e x)^4}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^7 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^7 (d+e x)^6}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{7 e^7 (d+e x)^7}-\frac{\left(a e^2-b d e+c d^2\right)^3}{8 e^7 (d+e x)^8}+\frac{c^2 (2 c d-b e)}{e^7 (d+e x)^3}-\frac{c^3}{2 e^7 (d+e x)^2}",1,"-(c*d^2 - b*d*e + a*e^2)^3/(8*e^7*(d + e*x)^8) + (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(7*e^7*(d + e*x)^7) - ((c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(2*e^7*(d + e*x)^6) + ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)))/(5*e^7*(d + e*x)^5) - (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(4*e^7*(d + e*x)^4) + (c^2*(2*c*d - b*e))/(e^7*(d + e*x)^3) - c^3/(2*e^7*(d + e*x)^2)","A",2,1,20,0.05000,1,"{698}"
2145,1,272,0,0.2093606,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^{10}} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^10,x]","-\frac{3 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7 (d+e x)^5}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{6 e^7 (d+e x)^6}-\frac{3 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7 (d+e x)^7}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{8 e^7 (d+e x)^8}-\frac{\left(a e^2-b d e+c d^2\right)^3}{9 e^7 (d+e x)^9}+\frac{3 c^2 (2 c d-b e)}{4 e^7 (d+e x)^4}-\frac{c^3}{3 e^7 (d+e x)^3}","-\frac{3 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7 (d+e x)^5}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{6 e^7 (d+e x)^6}-\frac{3 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7 (d+e x)^7}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{8 e^7 (d+e x)^8}-\frac{\left(a e^2-b d e+c d^2\right)^3}{9 e^7 (d+e x)^9}+\frac{3 c^2 (2 c d-b e)}{4 e^7 (d+e x)^4}-\frac{c^3}{3 e^7 (d+e x)^3}",1,"-(c*d^2 - b*d*e + a*e^2)^3/(9*e^7*(d + e*x)^9) + (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(8*e^7*(d + e*x)^8) - (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(7*e^7*(d + e*x)^7) + ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)))/(6*e^7*(d + e*x)^6) - (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(5*e^7*(d + e*x)^5) + (3*c^2*(2*c*d - b*e))/(4*e^7*(d + e*x)^4) - c^3/(3*e^7*(d + e*x)^3)","A",2,1,20,0.05000,1,"{698}"
2146,1,443,0,0.8706154,"\int (d+e x)^4 \left(a+b x+c x^2\right)^4 \, dx","Int[(d + e*x)^4*(a + b*x + c*x^2)^4,x]","\frac{(d+e x)^9 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{9 e^9}+\frac{2 c^2 (d+e x)^{11} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{11 e^9}-\frac{2 c (d+e x)^{10} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^9}-\frac{(d+e x)^8 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^9}+\frac{2 (d+e x)^7 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{7 e^9}-\frac{2 (d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^9}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^4}{5 e^9}-\frac{c^3 (d+e x)^{12} (2 c d-b e)}{3 e^9}+\frac{c^4 (d+e x)^{13}}{13 e^9}","\frac{(d+e x)^9 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{9 e^9}+\frac{2 c^2 (d+e x)^{11} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{11 e^9}-\frac{2 c (d+e x)^{10} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^9}-\frac{(d+e x)^8 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^9}+\frac{2 (d+e x)^7 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{7 e^9}-\frac{2 (d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^9}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^4}{5 e^9}-\frac{c^3 (d+e x)^{12} (2 c d-b e)}{3 e^9}+\frac{c^4 (d+e x)^{13}}{13 e^9}",1,"((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^5)/(5*e^9) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^6)/(3*e^9) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^7)/(7*e^9) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^8)/(2*e^9) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^9)/(9*e^9) - (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^10)/(5*e^9) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^11)/(11*e^9) - (c^3*(2*c*d - b*e)*(d + e*x)^12)/(3*e^9) + (c^4*(d + e*x)^13)/(13*e^9)","A",2,1,20,0.05000,1,"{698}"
2147,1,443,0,0.6735692,"\int (d+e x)^3 \left(a+b x+c x^2\right)^4 \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^4,x]","\frac{(d+e x)^8 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{8 e^9}+\frac{c^2 (d+e x)^{10} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9}-\frac{4 c (d+e x)^9 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{9 e^9}-\frac{4 (d+e x)^7 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^9}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9}-\frac{4 (d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^9}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^4}{4 e^9}-\frac{4 c^3 (d+e x)^{11} (2 c d-b e)}{11 e^9}+\frac{c^4 (d+e x)^{12}}{12 e^9}","\frac{(d+e x)^8 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{8 e^9}+\frac{c^2 (d+e x)^{10} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9}-\frac{4 c (d+e x)^9 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{9 e^9}-\frac{4 (d+e x)^7 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^9}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9}-\frac{4 (d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^9}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^4}{4 e^9}-\frac{4 c^3 (d+e x)^{11} (2 c d-b e)}{11 e^9}+\frac{c^4 (d+e x)^{12}}{12 e^9}",1,"((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^4)/(4*e^9) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^5)/(5*e^9) + ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^6)/(3*e^9) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^7)/(7*e^9) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^8)/(8*e^9) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^9)/(9*e^9) + (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^10)/(5*e^9) - (4*c^3*(2*c*d - b*e)*(d + e*x)^11)/(11*e^9) + (c^4*(d + e*x)^12)/(12*e^9)","A",2,1,20,0.05000,1,"{698}"
2148,1,441,0,0.5230817,"\int (d+e x)^2 \left(a+b x+c x^2\right)^4 \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^4,x]","\frac{(d+e x)^7 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{7 e^9}+\frac{2 c^2 (d+e x)^9 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{9 e^9}-\frac{c (d+e x)^8 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^9}-\frac{2 (d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9}+\frac{2 (d+e x)^5 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^9}+\frac{(d+e x)^3 \left(a e^2-b d e+c d^2\right)^4}{3 e^9}-\frac{2 c^3 (d+e x)^{10} (2 c d-b e)}{5 e^9}+\frac{c^4 (d+e x)^{11}}{11 e^9}","\frac{(d+e x)^7 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{7 e^9}+\frac{2 c^2 (d+e x)^9 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{9 e^9}-\frac{c (d+e x)^8 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^9}-\frac{2 (d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9}+\frac{2 (d+e x)^5 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^9}+\frac{(d+e x)^3 \left(a e^2-b d e+c d^2\right)^4}{3 e^9}-\frac{2 c^3 (d+e x)^{10} (2 c d-b e)}{5 e^9}+\frac{c^4 (d+e x)^{11}}{11 e^9}",1,"((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^3)/(3*e^9) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4)/e^9 + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^5)/(5*e^9) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^6)/(3*e^9) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^7)/(7*e^9) - (c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^8)/(2*e^9) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^9)/(9*e^9) - (2*c^3*(2*c*d - b*e)*(d + e*x)^10)/(5*e^9) + (c^4*(d + e*x)^11)/(11*e^9)","A",2,1,20,0.05000,1,"{698}"
2149,1,268,0,0.2909691,"\int (d+e x) \left(a+b x+c x^2\right)^4 \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^4,x]","\frac{1}{6} x^6 \left(6 a^2 c^2 e+12 a b^2 c e+12 a b c^2 d+4 b^3 c d+b^4 e\right)+\frac{1}{5} x^5 \left(12 a^2 b c e+6 a^2 c^2 d+12 a b^2 c d+4 a b^3 e+b^4 d\right)+\frac{1}{2} a x^4 \left(2 a^2 c e+3 a b^2 e+6 a b c d+2 b^3 d\right)+\frac{2}{3} a^2 x^3 \left(2 a b e+2 a c d+3 b^2 d\right)+\frac{1}{2} a^3 x^2 (a e+4 b d)+a^4 d x+\frac{1}{4} c^2 x^8 \left(2 a c e+3 b^2 e+2 b c d\right)+\frac{2}{7} c x^7 \left(6 a b c e+2 a c^2 d+3 b^2 c d+2 b^3 e\right)+\frac{1}{9} c^3 x^9 (4 b e+c d)+\frac{1}{10} c^4 e x^{10}","\frac{1}{6} x^6 \left(6 a^2 c^2 e+12 a b^2 c e+12 a b c^2 d+4 b^3 c d+b^4 e\right)+\frac{1}{5} x^5 \left(12 a^2 b c e+6 a^2 c^2 d+12 a b^2 c d+4 a b^3 e+b^4 d\right)+\frac{1}{2} a x^4 \left(2 a^2 c e+3 a b^2 e+6 a b c d+2 b^3 d\right)+\frac{2}{3} a^2 x^3 \left(2 a b e+2 a c d+3 b^2 d\right)+\frac{1}{2} a^3 x^2 (a e+4 b d)+a^4 d x+\frac{1}{4} c^2 x^8 \left(2 a c e+3 b^2 e+2 b c d\right)+\frac{2}{7} c x^7 \left(6 a b c e+2 a c^2 d+3 b^2 c d+2 b^3 e\right)+\frac{1}{9} c^3 x^9 (4 b e+c d)+\frac{1}{10} c^4 e x^{10}",1,"a^4*d*x + (a^3*(4*b*d + a*e)*x^2)/2 + (2*a^2*(3*b^2*d + 2*a*c*d + 2*a*b*e)*x^3)/3 + (a*(2*b^3*d + 6*a*b*c*d + 3*a*b^2*e + 2*a^2*c*e)*x^4)/2 + ((b^4*d + 12*a*b^2*c*d + 6*a^2*c^2*d + 4*a*b^3*e + 12*a^2*b*c*e)*x^5)/5 + ((4*b^3*c*d + 12*a*b*c^2*d + b^4*e + 12*a*b^2*c*e + 6*a^2*c^2*e)*x^6)/6 + (2*c*(3*b^2*c*d + 2*a*c^2*d + 2*b^3*e + 6*a*b*c*e)*x^7)/7 + (c^2*(2*b*c*d + 3*b^2*e + 2*a*c*e)*x^8)/4 + (c^3*(c*d + 4*b*e)*x^9)/9 + (c^4*e*x^10)/10","A",2,1,18,0.05556,1,"{631}"
2150,1,133,0,0.1165934,"\int \left(a+b x+c x^2\right)^4 \, dx","Int[(a + b*x + c*x^2)^4,x]","\frac{1}{5} x^5 \left(6 a^2 c^2+12 a b^2 c+b^4\right)+\frac{2}{3} a^2 x^3 \left(2 a c+3 b^2\right)+2 a^3 b x^2+a^4 x+\frac{2}{7} c^2 x^7 \left(2 a c+3 b^2\right)+\frac{2}{3} b c x^6 \left(3 a c+b^2\right)+a b x^4 \left(3 a c+b^2\right)+\frac{1}{2} b c^3 x^8+\frac{c^4 x^9}{9}","\frac{1}{5} x^5 \left(6 a^2 c^2+12 a b^2 c+b^4\right)+\frac{2}{3} a^2 x^3 \left(2 a c+3 b^2\right)+2 a^3 b x^2+a^4 x+\frac{2}{7} c^2 x^7 \left(2 a c+3 b^2\right)+\frac{2}{3} b c x^6 \left(3 a c+b^2\right)+a b x^4 \left(3 a c+b^2\right)+\frac{1}{2} b c^3 x^8+\frac{c^4 x^9}{9}",1,"a^4*x + 2*a^3*b*x^2 + (2*a^2*(3*b^2 + 2*a*c)*x^3)/3 + a*b*(b^2 + 3*a*c)*x^4 + ((b^4 + 12*a*b^2*c + 6*a^2*c^2)*x^5)/5 + (2*b*c*(b^2 + 3*a*c)*x^6)/3 + (2*c^2*(3*b^2 + 2*a*c)*x^7)/7 + (b*c^3*x^8)/2 + (c^4*x^9)/9","A",2,1,12,0.08333,1,"{611}"
2151,1,428,0,0.7083344,"\int \frac{\left(a+b x+c x^2\right)^4}{d+e x} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x),x]","\frac{(d+e x)^4 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{4 e^9}+\frac{c^2 (d+e x)^6 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9}-\frac{4 c (d+e x)^5 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^9}-\frac{4 (d+e x)^3 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9}+\frac{(d+e x)^2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9}-\frac{4 x (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^8}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^4}{e^9}-\frac{4 c^3 (d+e x)^7 (2 c d-b e)}{7 e^9}+\frac{c^4 (d+e x)^8}{8 e^9}","\frac{(d+e x)^4 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{4 e^9}+\frac{c^2 (d+e x)^6 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9}-\frac{4 c (d+e x)^5 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^9}-\frac{4 (d+e x)^3 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9}+\frac{(d+e x)^2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9}-\frac{4 x (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^8}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^4}{e^9}-\frac{4 c^3 (d+e x)^7 (2 c d-b e)}{7 e^9}+\frac{c^4 (d+e x)^8}{8 e^9}",1,"(-4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*x)/e^8 + ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^2)/e^9 - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^3)/(3*e^9) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^4)/(4*e^9) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^5)/(5*e^9) + (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^6)/(3*e^9) - (4*c^3*(2*c*d - b*e)*(d + e*x)^7)/(7*e^9) + (c^4*(d + e*x)^8)/(8*e^9) + ((c*d^2 - b*d*e + a*e^2)^4*Log[d + e*x])/e^9","A",2,1,20,0.05000,1,"{698}"
2152,1,426,0,0.7218563,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^2,x]","\frac{(d+e x)^3 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{3 e^9}+\frac{2 c^2 (d+e x)^5 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9}-\frac{c (d+e x)^4 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9}-\frac{2 (d+e x)^2 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9}+\frac{2 x \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8}-\frac{\left(a e^2-b d e+c d^2\right)^4}{e^9 (d+e x)}-\frac{4 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^9}-\frac{2 c^3 (d+e x)^6 (2 c d-b e)}{3 e^9}+\frac{c^4 (d+e x)^7}{7 e^9}","\frac{(d+e x)^3 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{3 e^9}+\frac{2 c^2 (d+e x)^5 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9}-\frac{c (d+e x)^4 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9}-\frac{2 (d+e x)^2 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9}+\frac{2 x \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8}-\frac{\left(a e^2-b d e+c d^2\right)^4}{e^9 (d+e x)}-\frac{4 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^9}-\frac{2 c^3 (d+e x)^6 (2 c d-b e)}{3 e^9}+\frac{c^4 (d+e x)^7}{7 e^9}",1,"(2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*x)/e^8 - (c*d^2 - b*d*e + a*e^2)^4/(e^9*(d + e*x)) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^2)/e^9 + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^3)/(3*e^9) - (c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^4)/e^9 + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^5)/(5*e^9) - (2*c^3*(2*c*d - b*e)*(d + e*x)^6)/(3*e^9) + (c^4*(d + e*x)^7)/(7*e^9) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*Log[d + e*x])/e^9","A",2,1,20,0.05000,1,"{698}"
2153,1,430,0,0.6667832,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^3} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^3,x]","\frac{(d+e x)^2 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{2 e^9}+\frac{c^2 (d+e x)^4 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 e^9}-\frac{4 c (d+e x)^3 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9}-\frac{4 x (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}+\frac{2 \log (d+e x) \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^9 (d+e x)}-\frac{\left(a e^2-b d e+c d^2\right)^4}{2 e^9 (d+e x)^2}-\frac{4 c^3 (d+e x)^5 (2 c d-b e)}{5 e^9}+\frac{c^4 (d+e x)^6}{6 e^9}","\frac{(d+e x)^2 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{2 e^9}+\frac{c^2 (d+e x)^4 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 e^9}-\frac{4 c (d+e x)^3 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9}-\frac{4 x (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}+\frac{2 \log (d+e x) \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^9 (d+e x)}-\frac{\left(a e^2-b d e+c d^2\right)^4}{2 e^9 (d+e x)^2}-\frac{4 c^3 (d+e x)^5 (2 c d-b e)}{5 e^9}+\frac{c^4 (d+e x)^6}{6 e^9}",1,"(-4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*x)/e^8 - (c*d^2 - b*d*e + a*e^2)^4/(2*e^9*(d + e*x)^2) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(e^9*(d + e*x)) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^2)/(2*e^9) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^3)/(3*e^9) + (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^4)/(2*e^9) - (4*c^3*(2*c*d - b*e)*(d + e*x)^5)/(5*e^9) + (c^4*(d + e*x)^6)/(6*e^9) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*Log[d + e*x])/e^9","A",2,1,20,0.05000,1,"{698}"
2154,1,417,0,0.6515693,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^4} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^4,x]","\frac{x \left(6 c^2 e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-4 b^2 c e^3 (4 b d-3 a e)-40 c^3 d^2 e (2 b d-a e)+b^4 e^4+35 c^4 d^4\right)}{e^8}+\frac{2 c^2 x^3 \left(-2 c e (4 b d-a e)+3 b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{2 c x^2 \left(-2 c^2 d e (5 b d-2 a e)+3 b c e^2 (2 b d-a e)-b^3 e^3+5 c^3 d^3\right)}{e^7}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (d+e x)}-\frac{4 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^9 (d+e x)^2}-\frac{\left(a e^2-b d e+c d^2\right)^4}{3 e^9 (d+e x)^3}-\frac{c^3 x^4 (c d-b e)}{e^5}+\frac{c^4 x^5}{5 e^4}","\frac{x \left(6 c^2 e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-4 b^2 c e^3 (4 b d-3 a e)-40 c^3 d^2 e (2 b d-a e)+b^4 e^4+35 c^4 d^4\right)}{e^8}+\frac{2 c^2 x^3 \left(-2 c e (4 b d-a e)+3 b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{2 c x^2 \left(-2 c^2 d e (5 b d-2 a e)+3 b c e^2 (2 b d-a e)-b^3 e^3+5 c^3 d^3\right)}{e^7}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (d+e x)}-\frac{4 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^9 (d+e x)^2}-\frac{\left(a e^2-b d e+c d^2\right)^4}{3 e^9 (d+e x)^3}-\frac{c^3 x^4 (c d-b e)}{e^5}+\frac{c^4 x^5}{5 e^4}",1,"((35*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(4*b*d - 3*a*e) - 40*c^3*d^2*e*(2*b*d - a*e) + 6*c^2*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2))*x)/e^8 - (2*c*(5*c^3*d^3 - b^3*e^3 - 2*c^2*d*e*(5*b*d - 2*a*e) + 3*b*c*e^2*(2*b*d - a*e))*x^2)/e^7 + (2*c^2*(5*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(4*b*d - a*e))*x^3)/(3*e^6) - (c^3*(c*d - b*e)*x^4)/e^5 + (c^4*x^5)/(5*e^4) - (c*d^2 - b*d*e + a*e^2)^4/(3*e^9*(d + e*x)^3) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(e^9*(d + e*x)^2) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*Log[d + e*x])/e^9","A",2,1,20,0.05000,1,"{698}"
2155,1,426,0,0.6347992,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^5} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^5,x]","\frac{\log (d+e x) \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{e^9}+\frac{c^2 x^2 \left(-4 c e (5 b d-a e)+6 b^2 e^2+15 c^2 d^2\right)}{2 e^7}-\frac{\left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right) \left(a e^2-b d e+c d^2\right)^2}{e^9 (d+e x)^2}+\frac{4 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right) \left(a e^2-b d e+c d^2\right)}{e^9 (d+e x)}-\frac{c x \left(-20 c^2 d e (3 b d-a e)+6 b c e^2 (5 b d-2 a e)-4 b^3 e^3+35 c^3 d^3\right)}{e^8}-\frac{\left(a e^2-b d e+c d^2\right)^4}{4 e^9 (d+e x)^4}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^9 (d+e x)^3}-\frac{c^3 x^3 (5 c d-4 b e)}{3 e^6}+\frac{c^4 x^4}{4 e^5}","\frac{\log (d+e x) \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{e^9}+\frac{c^2 x^2 \left(-4 c e (5 b d-a e)+6 b^2 e^2+15 c^2 d^2\right)}{2 e^7}-\frac{\left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right) \left(a e^2-b d e+c d^2\right)^2}{e^9 (d+e x)^2}+\frac{4 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right) \left(a e^2-b d e+c d^2\right)}{e^9 (d+e x)}-\frac{c x \left(-20 c^2 d e (3 b d-a e)+6 b c e^2 (5 b d-2 a e)-4 b^3 e^3+35 c^3 d^3\right)}{e^8}-\frac{\left(a e^2-b d e+c d^2\right)^4}{4 e^9 (d+e x)^4}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^9 (d+e x)^3}-\frac{c^3 x^3 (5 c d-4 b e)}{3 e^6}+\frac{c^4 x^4}{4 e^5}",1,"-((c*(35*c^3*d^3 - 4*b^3*e^3 + 6*b*c*e^2*(5*b*d - 2*a*e) - 20*c^2*d*e*(3*b*d - a*e))*x)/e^8) + (c^2*(15*c^2*d^2 + 6*b^2*e^2 - 4*c*e*(5*b*d - a*e))*x^2)/(2*e^7) - (c^3*(5*c*d - 4*b*e)*x^3)/(3*e^6) + (c^4*x^4)/(4*e^5) - (c*d^2 - b*d*e + a*e^2)^4/(4*e^9*(d + e*x)^4) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(3*e^9*(d + e*x)^3) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x)^2) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*Log[d + e*x])/e^9","A",2,1,20,0.05000,1,"{698}"
2156,1,414,0,0.557145,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^6} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^6,x]","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{e^9 (d+e x)}+\frac{c^2 x \left(-4 c e (6 b d-a e)+6 b^2 e^2+21 c^2 d^2\right)}{e^8}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)^2}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9 (d+e x)^3}-\frac{4 c (2 c d-b e) \log (d+e x) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^9 (d+e x)^4}-\frac{\left(a e^2-b d e+c d^2\right)^4}{5 e^9 (d+e x)^5}-\frac{c^3 x^2 (3 c d-2 b e)}{e^7}+\frac{c^4 x^3}{3 e^6}","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{e^9 (d+e x)}+\frac{c^2 x \left(-4 c e (6 b d-a e)+6 b^2 e^2+21 c^2 d^2\right)}{e^8}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)^2}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9 (d+e x)^3}-\frac{4 c (2 c d-b e) \log (d+e x) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^9 (d+e x)^4}-\frac{\left(a e^2-b d e+c d^2\right)^4}{5 e^9 (d+e x)^5}-\frac{c^3 x^2 (3 c d-2 b e)}{e^7}+\frac{c^4 x^3}{3 e^6}",1,"(c^2*(21*c^2*d^2 + 6*b^2*e^2 - 4*c*e*(6*b*d - a*e))*x)/e^8 - (c^3*(3*c*d - 2*b*e)*x^2)/e^7 + (c^4*x^3)/(3*e^6) - (c*d^2 - b*d*e + a*e^2)^4/(5*e^9*(d + e*x)^5) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(e^9*(d + e*x)^4) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(3*e^9*(d + e*x)^3) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)^2) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(e^9*(d + e*x)) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*Log[d + e*x])/e^9","A",2,1,20,0.05000,1,"{698}"
2157,1,426,0,0.5071438,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^7} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^7,x]","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{2 e^9 (d+e x)^2}+\frac{4 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9 (d+e x)^3}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 e^9 (d+e x)^4}+\frac{2 c^2 \log (d+e x) \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^9 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right)^4}{6 e^9 (d+e x)^6}-\frac{c^3 x (7 c d-4 b e)}{e^8}+\frac{c^4 x^2}{2 e^7}","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{2 e^9 (d+e x)^2}+\frac{4 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9 (d+e x)^3}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 e^9 (d+e x)^4}+\frac{2 c^2 \log (d+e x) \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^9 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right)^4}{6 e^9 (d+e x)^6}-\frac{c^3 x (7 c d-4 b e)}{e^8}+\frac{c^4 x^2}{2 e^7}",1,"-((c^3*(7*c*d - 4*b*e)*x)/e^8) + (c^4*x^2)/(2*e^7) - (c*d^2 - b*d*e + a*e^2)^4/(6*e^9*(d + e*x)^6) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(5*e^9*(d + e*x)^5) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(2*e^9*(d + e*x)^4) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(3*e^9*(d + e*x)^3) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(2*e^9*(d + e*x)^2) + (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*Log[d + e*x])/e^9","A",2,1,20,0.05000,1,"{698}"
2158,1,424,0,0.481811,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^8} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^8,x]","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{3 e^9 (d+e x)^3}-\frac{2 c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (d+e x)}+\frac{2 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)^2}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)^4}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9 (d+e x)^5}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^9 (d+e x)^6}-\frac{\left(a e^2-b d e+c d^2\right)^4}{7 e^9 (d+e x)^7}-\frac{4 c^3 (2 c d-b e) \log (d+e x)}{e^9}+\frac{c^4 x}{e^8}","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{3 e^9 (d+e x)^3}-\frac{2 c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (d+e x)}+\frac{2 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)^2}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)^4}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9 (d+e x)^5}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^9 (d+e x)^6}-\frac{\left(a e^2-b d e+c d^2\right)^4}{7 e^9 (d+e x)^7}-\frac{4 c^3 (2 c d-b e) \log (d+e x)}{e^9}+\frac{c^4 x}{e^8}",1,"(c^4*x)/e^8 - (c*d^2 - b*d*e + a*e^2)^4/(7*e^9*(d + e*x)^7) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(3*e^9*(d + e*x)^6) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(5*e^9*(d + e*x)^5) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)^4) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(3*e^9*(d + e*x)^3) + (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)^2) - (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x)) - (4*c^3*(2*c*d - b*e)*Log[d + e*x])/e^9","A",2,1,20,0.05000,1,"{698}"
2159,1,435,0,0.4621648,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^9} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^9,x]","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{4 e^9 (d+e x)^4}-\frac{c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (d+e x)^2}+\frac{4 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9 (d+e x)^3}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^9 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9 (d+e x)^6}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{7 e^9 (d+e x)^7}-\frac{\left(a e^2-b d e+c d^2\right)^4}{8 e^9 (d+e x)^8}+\frac{4 c^3 (2 c d-b e)}{e^9 (d+e x)}+\frac{c^4 \log (d+e x)}{e^9}","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{4 e^9 (d+e x)^4}-\frac{c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (d+e x)^2}+\frac{4 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9 (d+e x)^3}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^9 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9 (d+e x)^6}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{7 e^9 (d+e x)^7}-\frac{\left(a e^2-b d e+c d^2\right)^4}{8 e^9 (d+e x)^8}+\frac{4 c^3 (2 c d-b e)}{e^9 (d+e x)}+\frac{c^4 \log (d+e x)}{e^9}",1,"-(c*d^2 - b*d*e + a*e^2)^4/(8*e^9*(d + e*x)^8) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(7*e^9*(d + e*x)^7) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(3*e^9*(d + e*x)^6) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(5*e^9*(d + e*x)^5) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(4*e^9*(d + e*x)^4) + (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(3*e^9*(d + e*x)^3) - (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x)^2) + (4*c^3*(2*c*d - b*e))/(e^9*(d + e*x)) + (c^4*Log[d + e*x])/e^9","A",2,1,20,0.05000,1,"{698}"
2160,1,436,0,0.410188,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^{10}} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^10,x]","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{5 e^9 (d+e x)^5}-\frac{2 c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9 (d+e x)^3}+\frac{c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)^4}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9 (d+e x)^6}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{7 e^9 (d+e x)^7}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{2 e^9 (d+e x)^8}-\frac{\left(a e^2-b d e+c d^2\right)^4}{9 e^9 (d+e x)^9}+\frac{2 c^3 (2 c d-b e)}{e^9 (d+e x)^2}-\frac{c^4}{e^9 (d+e x)}","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{5 e^9 (d+e x)^5}-\frac{2 c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^9 (d+e x)^3}+\frac{c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (d+e x)^4}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9 (d+e x)^6}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{7 e^9 (d+e x)^7}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{2 e^9 (d+e x)^8}-\frac{\left(a e^2-b d e+c d^2\right)^4}{9 e^9 (d+e x)^9}+\frac{2 c^3 (2 c d-b e)}{e^9 (d+e x)^2}-\frac{c^4}{e^9 (d+e x)}",1,"-(c*d^2 - b*d*e + a*e^2)^4/(9*e^9*(d + e*x)^9) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(2*e^9*(d + e*x)^8) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(7*e^9*(d + e*x)^7) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(3*e^9*(d + e*x)^6) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(5*e^9*(d + e*x)^5) + (c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)^4) - (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(3*e^9*(d + e*x)^3) + (2*c^3*(2*c*d - b*e))/(e^9*(d + e*x)^2) - c^4/(e^9*(d + e*x))","A",2,1,20,0.05000,1,"{698}"
2161,1,443,0,0.4008896,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^{11}} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^11,x]","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{6 e^9 (d+e x)^6}-\frac{c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 e^9 (d+e x)^4}+\frac{4 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^9 (d+e x)^5}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^9 (d+e x)^7}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{4 e^9 (d+e x)^8}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{9 e^9 (d+e x)^9}-\frac{\left(a e^2-b d e+c d^2\right)^4}{10 e^9 (d+e x)^{10}}+\frac{4 c^3 (2 c d-b e)}{3 e^9 (d+e x)^3}-\frac{c^4}{2 e^9 (d+e x)^2}","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{6 e^9 (d+e x)^6}-\frac{c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 e^9 (d+e x)^4}+\frac{4 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^9 (d+e x)^5}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^9 (d+e x)^7}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{4 e^9 (d+e x)^8}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{9 e^9 (d+e x)^9}-\frac{\left(a e^2-b d e+c d^2\right)^4}{10 e^9 (d+e x)^{10}}+\frac{4 c^3 (2 c d-b e)}{3 e^9 (d+e x)^3}-\frac{c^4}{2 e^9 (d+e x)^2}",1,"-(c*d^2 - b*d*e + a*e^2)^4/(10*e^9*(d + e*x)^10) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(9*e^9*(d + e*x)^9) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(4*e^9*(d + e*x)^8) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(7*e^9*(d + e*x)^7) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(6*e^9*(d + e*x)^6) + (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(5*e^9*(d + e*x)^5) - (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(2*e^9*(d + e*x)^4) + (4*c^3*(2*c*d - b*e))/(3*e^9*(d + e*x)^3) - c^4/(2*e^9*(d + e*x)^2)","A",2,1,20,0.05000,1,"{698}"
2162,1,440,0,0.3969223,"\int \frac{\left(a+b x+c x^2\right)^4}{(d+e x)^{12}} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x)^12,x]","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{7 e^9 (d+e x)^7}-\frac{2 c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9 (d+e x)^5}+\frac{2 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9 (d+e x)^6}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^9 (d+e x)^8}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{9 e^9 (d+e x)^9}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^9 (d+e x)^{10}}-\frac{\left(a e^2-b d e+c d^2\right)^4}{11 e^9 (d+e x)^{11}}+\frac{c^3 (2 c d-b e)}{e^9 (d+e x)^4}-\frac{c^4}{3 e^9 (d+e x)^3}","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{7 e^9 (d+e x)^7}-\frac{2 c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^9 (d+e x)^5}+\frac{2 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^9 (d+e x)^6}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^9 (d+e x)^8}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{9 e^9 (d+e x)^9}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^9 (d+e x)^{10}}-\frac{\left(a e^2-b d e+c d^2\right)^4}{11 e^9 (d+e x)^{11}}+\frac{c^3 (2 c d-b e)}{e^9 (d+e x)^4}-\frac{c^4}{3 e^9 (d+e x)^3}",1,"-(c*d^2 - b*d*e + a*e^2)^4/(11*e^9*(d + e*x)^11) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(5*e^9*(d + e*x)^10) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(9*e^9*(d + e*x)^9) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(2*e^9*(d + e*x)^8) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(7*e^9*(d + e*x)^7) + (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(3*e^9*(d + e*x)^6) - (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(5*e^9*(d + e*x)^5) + (c^3*(2*c*d - b*e))/(e^9*(d + e*x)^4) - c^4/(3*e^9*(d + e*x)^3)","A",2,1,20,0.05000,1,"{698}"
2163,1,32,0,0.0137426,"\int x^4 \left(3-4 x+x^2\right)^2 \, dx","Int[x^4*(3 - 4*x + x^2)^2,x]","\frac{x^9}{9}-x^8+\frac{22 x^7}{7}-4 x^6+\frac{9 x^5}{5}","\frac{x^9}{9}-x^8+\frac{22 x^7}{7}-4 x^6+\frac{9 x^5}{5}",1,"(9*x^5)/5 - 4*x^6 + (22*x^7)/7 - x^8 + x^9/9","A",2,1,14,0.07143,1,"{698}"
2164,1,36,0,0.0125975,"\int x^3 \left(3-4 x+x^2\right)^2 \, dx","Int[x^3*(3 - 4*x + x^2)^2,x]","\frac{x^8}{8}-\frac{8 x^7}{7}+\frac{11 x^6}{3}-\frac{24 x^5}{5}+\frac{9 x^4}{4}","\frac{x^8}{8}-\frac{8 x^7}{7}+\frac{11 x^6}{3}-\frac{24 x^5}{5}+\frac{9 x^4}{4}",1,"(9*x^4)/4 - (24*x^5)/5 + (11*x^6)/3 - (8*x^7)/7 + x^8/8","A",2,1,14,0.07143,1,"{698}"
2165,1,32,0,0.0128501,"\int x^2 \left(3-4 x+x^2\right)^2 \, dx","Int[x^2*(3 - 4*x + x^2)^2,x]","\frac{x^7}{7}-\frac{4 x^6}{3}+\frac{22 x^5}{5}-6 x^4+3 x^3","\frac{x^7}{7}-\frac{4 x^6}{3}+\frac{22 x^5}{5}-6 x^4+3 x^3",1,"3*x^3 - 6*x^4 + (22*x^5)/5 - (4*x^6)/3 + x^7/7","A",2,1,14,0.07143,1,"{698}"
2166,1,34,0,0.0107675,"\int x \left(3-4 x+x^2\right)^2 \, dx","Int[x*(3 - 4*x + x^2)^2,x]","\frac{x^6}{6}-\frac{8 x^5}{5}+\frac{11 x^4}{2}-8 x^3+\frac{9 x^2}{2}","\frac{x^6}{6}-\frac{8 x^5}{5}+\frac{11 x^4}{2}-8 x^3+\frac{9 x^2}{2}",1,"(9*x^2)/2 - 8*x^3 + (11*x^4)/2 - (8*x^5)/5 + x^6/6","A",2,1,12,0.08333,1,"{631}"
2167,1,28,0,0.0106319,"\int \left(3-4 x+x^2\right)^2 \, dx","Int[(3 - 4*x + x^2)^2,x]","-\frac{1}{5} (3-x)^5-\frac{4}{3} (3-x)^3+(x-3)^4","-\frac{1}{5} (3-x)^5-\frac{4}{3} (3-x)^3+(x-3)^4",1,"(-4*(3 - x)^3)/3 - (3 - x)^5/5 + (-3 + x)^4","A",3,2,10,0.2000,1,"{610, 43}"
2168,1,27,0,0.0092649,"\int \frac{\left(3-4 x+x^2\right)^2}{x} \, dx","Int[(3 - 4*x + x^2)^2/x,x]","\frac{x^4}{4}-\frac{8 x^3}{3}+11 x^2-24 x+9 \log (x)","\frac{x^4}{4}-\frac{8 x^3}{3}+11 x^2-24 x+9 \log (x)",1,"-24*x + 11*x^2 - (8*x^3)/3 + x^4/4 + 9*Log[x]","A",2,1,14,0.07143,1,"{698}"
2169,1,25,0,0.01157,"\int \frac{\left(3-4 x+x^2\right)^2}{x^2} \, dx","Int[(3 - 4*x + x^2)^2/x^2,x]","\frac{x^3}{3}-4 x^2+22 x-\frac{9}{x}-24 \log (x)","\frac{x^3}{3}-4 x^2+22 x-\frac{9}{x}-24 \log (x)",1,"-9/x + 22*x - 4*x^2 + x^3/3 - 24*Log[x]","A",2,1,14,0.07143,1,"{698}"
2170,1,27,0,0.0113032,"\int \frac{\left(3-4 x+x^2\right)^2}{x^3} \, dx","Int[(3 - 4*x + x^2)^2/x^3,x]","\frac{x^2}{2}-\frac{9}{2 x^2}-8 x+\frac{24}{x}+22 \log (x)","\frac{x^2}{2}-\frac{9}{2 x^2}-8 x+\frac{24}{x}+22 \log (x)",1,"-9/(2*x^2) + 24/x - 8*x + x^2/2 + 22*Log[x]","A",2,1,14,0.07143,1,"{698}"
2171,1,21,0,0.0107885,"\int \frac{\left(3-4 x+x^2\right)^2}{x^4} \, dx","Int[(3 - 4*x + x^2)^2/x^4,x]","\frac{12}{x^2}-\frac{3}{x^3}+x-\frac{22}{x}-8 \log (x)","\frac{12}{x^2}-\frac{3}{x^3}+x-\frac{22}{x}-8 \log (x)",1,"-3/x^3 + 12/x^2 - 22/x + x - 8*Log[x]","A",2,1,14,0.07143,1,"{698}"
2172,1,25,0,0.0112481,"\int \frac{\left(3-4 x+x^2\right)^2}{x^5} \, dx","Int[(3 - 4*x + x^2)^2/x^5,x]","-\frac{11}{x^2}+\frac{8}{x^3}-\frac{9}{4 x^4}+\frac{8}{x}+\log (x)","-\frac{11}{x^2}+\frac{8}{x^3}-\frac{9}{4 x^4}+\frac{8}{x}+\log (x)",1,"-9/(4*x^4) + 8/x^3 - 11/x^2 + 8/x + Log[x]","A",2,1,14,0.07143,1,"{698}"
2173,1,30,0,0.0116723,"\int \frac{\left(3-4 x+x^2\right)^2}{x^6} \, dx","Int[(3 - 4*x + x^2)^2/x^6,x]","\frac{4}{x^2}-\frac{22}{3 x^3}+\frac{6}{x^4}-\frac{9}{5 x^5}-\frac{1}{x}","\frac{4}{x^2}-\frac{22}{3 x^3}+\frac{6}{x^4}-\frac{9}{5 x^5}-\frac{1}{x}",1,"-9/(5*x^5) + 6/x^4 - 22/(3*x^3) + 4/x^2 - x^(-1)","A",2,1,14,0.07143,1,"{698}"
2174,1,36,0,0.0116563,"\int \frac{\left(3-4 x+x^2\right)^2}{x^7} \, dx","Int[(3 - 4*x + x^2)^2/x^7,x]","-\frac{1}{2 x^2}+\frac{8}{3 x^3}-\frac{11}{2 x^4}+\frac{24}{5 x^5}-\frac{3}{2 x^6}","-\frac{1}{2 x^2}+\frac{8}{3 x^3}-\frac{11}{2 x^4}+\frac{24}{5 x^5}-\frac{3}{2 x^6}",1,"-3/(2*x^6) + 24/(5*x^5) - 11/(2*x^4) + 8/(3*x^3) - 1/(2*x^2)","A",2,1,14,0.07143,1,"{698}"
2175,1,14,0,0.008025,"\int \frac{2+2 x+x^2}{2+x} \, dx","Int[(2 + 2*x + x^2)/(2 + x),x]","\frac{x^2}{2}+2 \log (x+2)","\frac{x^2}{2}+2 \log (x+2)",1,"x^2/2 + 2*Log[2 + x]","A",2,1,14,0.07143,1,"{698}"
2176,1,19,0,0.009546,"\int \frac{5+4 x+x^2}{-2+x} \, dx","Int[(5 + 4*x + x^2)/(-2 + x),x]","\frac{x^2}{2}+6 x+17 \log (2-x)","\frac{x^2}{2}+6 x+17 \log (2-x)",1,"6*x + x^2/2 + 17*Log[2 - x]","A",2,1,14,0.07143,1,"{698}"
2177,1,14,0,0.0071718,"\int \frac{2+2 x+x^2}{(1+x)^3} \, dx","Int[(2 + 2*x + x^2)/(1 + x)^3,x]","\log (x+1)-\frac{1}{2 (x+1)^2}","\log (x+1)-\frac{1}{2 (x+1)^2}",1,"-1/(2*(1 + x)^2) + Log[1 + x]","A",2,1,14,0.07143,1,"{683}"
2178,1,19,0,0.0110944,"\int \frac{3+3 x+2 x^2}{(1+x)^3} \, dx","Int[(3 + 3*x + 2*x^2)/(1 + x)^3,x]","\frac{1}{x+1}-\frac{1}{(x+1)^2}+2 \log (x+1)","\frac{1}{x+1}-\frac{1}{(x+1)^2}+2 \log (x+1)",1,"-(1 + x)^(-2) + (1 + x)^(-1) + 2*Log[1 + x]","A",2,1,16,0.06250,1,"{698}"
2179,1,11,0,0.0027441,"\int \frac{1+x+x^2}{x} \, dx","Int[(1 + x + x^2)/x,x]","\frac{x^2}{2}+x+\log (x)","\frac{x^2}{2}+x+\log (x)",1,"x + x^2/2 + Log[x]","A",2,1,10,0.1000,1,"{14}"
2180,1,11,0,0.0048209,"\int \frac{9+6 x+x^2}{x^2} \, dx","Int[(9 + 6*x + x^2)/x^2,x]","x-\frac{9}{x}+6 \log (x)","x-\frac{9}{x}+6 \log (x)",1,"-9/x + x + 6*Log[x]","A",2,1,12,0.08333,1,"{14}"
2181,1,18,0,0.0047827,"\int \frac{1+2 x+x^2}{x^4} \, dx","Int[(1 + 2*x + x^2)/x^4,x]","-\frac{1}{x^2}-\frac{1}{3 x^3}-\frac{1}{x}","-\frac{1}{x^2}-\frac{1}{3 x^3}-\frac{1}{x}",1,"-1/(3*x^3) - x^(-2) - x^(-1)","A",2,1,12,0.08333,1,"{14}"
2182,1,243,0,0.4390506,"\int \frac{(d+e x)^4}{a+b x+c x^2} \, dx","Int[(d + e*x)^4/(a + b*x + c*x^2),x]","-\frac{\left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{e (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{e^2 x \left(-c e (a e+4 b d)+b^2 e^2+6 c^2 d^2\right)}{c^3}+\frac{e^3 x^2 (4 c d-b e)}{2 c^2}+\frac{e^4 x^3}{3 c}","-\frac{\left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{e (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{e^2 x \left(-c e (a e+4 b d)+b^2 e^2+6 c^2 d^2\right)}{c^3}+\frac{e^3 x^2 (4 c d-b e)}{2 c^2}+\frac{e^4 x^3}{3 c}",1,"(e^2*(6*c^2*d^2 + b^2*e^2 - c*e*(4*b*d + a*e))*x)/c^3 + (e^3*(4*c*d - b*e)*x^2)/(2*c^2) + (e^4*x^3)/(3*c) - ((2*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(b*d + a*e) - 4*c^3*d^2*e*(b*d + 3*a*e) + 2*c^2*e^2*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*Sqrt[b^2 - 4*a*c]) + (e*(2*c*d - b*e)*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*Log[a + b*x + c*x^2])/(2*c^4)","A",6,5,20,0.2500,1,"{701, 634, 618, 206, 628}"
2183,1,151,0,0.1715656,"\int \frac{(d+e x)^3}{a+b x+c x^2} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2),x]","\frac{e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^3}-\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}+\frac{e^2 x (3 c d-b e)}{c^2}+\frac{e^3 x^2}{2 c}","\frac{e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^3}-\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}+\frac{e^2 x (3 c d-b e)}{c^2}+\frac{e^3 x^2}{2 c}",1,"(e^2*(3*c*d - b*e)*x)/c^2 + (e^3*x^2)/(2*c) - ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]) + (e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*Log[a + b*x + c*x^2])/(2*c^3)","A",6,5,20,0.2500,1,"{701, 634, 618, 206, 628}"
2184,1,101,0,0.1233198,"\int \frac{(d+e x)^2}{a+b x+c x^2} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2),x]","-\frac{\left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{e (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{e^2 x}{c}","-\frac{\left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{e (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{e^2 x}{c}",1,"(e^2*x)/c - ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]) + (e*(2*c*d - b*e)*Log[a + b*x + c*x^2])/(2*c^2)","A",6,5,20,0.2500,1,"{701, 634, 618, 206, 628}"
2185,1,66,0,0.0353811,"\int \frac{d+e x}{a+b x+c x^2} \, dx","Int[(d + e*x)/(a + b*x + c*x^2),x]","\frac{e \log \left(a+b x+c x^2\right)}{2 c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}","\frac{e \log \left(a+b x+c x^2\right)}{2 c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}",1,"-(((2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c])) + (e*Log[a + b*x + c*x^2])/(2*c)","A",4,4,18,0.2222,1,"{634, 618, 206, 628}"
2186,1,34,0,0.0177614,"\int \frac{1}{a+b x+c x^2} \, dx","Int[(a + b*x + c*x^2)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"(-2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",2,2,12,0.1667,1,"{618, 206}"
2187,1,122,0,0.0942328,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)),x]","-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}-\frac{e \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}+\frac{e \log (d+e x)}{a e^2-b d e+c d^2}","-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}-\frac{e \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}+\frac{e \log (d+e x)}{a e^2-b d e+c d^2}",1,"-(((2*c*d - b*e)*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))) + (e*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2) - (e*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2))","A",6,6,20,0.3000,1,"{705, 31, 634, 618, 206, 628}"
2188,1,186,0,0.2853231,"\int \frac{1}{(d+e x)^2 \left(a+b x+c x^2\right)} \, dx","Int[1/((d + e*x)^2*(a + b*x + c*x^2)),x]","-\frac{\left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2}-\frac{e (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e}{(d+e x) \left(a e^2-b d e+c d^2\right)}+\frac{e (2 c d-b e) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^2}","-\frac{\left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2}-\frac{e (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e}{(d+e x) \left(a e^2-b d e+c d^2\right)}+\frac{e (2 c d-b e) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^2}",1,"-(e/((c*d^2 - b*d*e + a*e^2)*(d + e*x))) - ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*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) + (e*(2*c*d - b*e)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^2 - (e*(2*c*d - b*e)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^2)","A",7,6,20,0.3000,1,"{709, 800, 634, 618, 206, 628}"
2189,1,272,0,0.4251771,"\int \frac{1}{(d+e x)^3 \left(a+b x+c x^2\right)} \, dx","Int[1/((d + e*x)^3*(a + b*x + c*x^2)),x]","-\frac{e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{e \log (d+e x) \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^3}-\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^3}-\frac{e (2 c d-b e)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{e}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}","-\frac{e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{e \log (d+e x) \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^3}-\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^3}-\frac{e (2 c d-b e)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{e}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}",1,"-e/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (e*(2*c*d - b*e))/((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) - ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*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)^3) + (e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 - (e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^3)","A",7,6,20,0.3000,1,"{709, 800, 634, 618, 206, 628}"
2190,1,374,0,0.7254897,"\int \frac{(d+e x)^5}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)^5/(a + b*x + c*x^2)^2,x]","\frac{(2 c d-b e) \left(-2 c^2 e^2 \left(15 a^2 e^2+10 a b d e+b^2 d^2\right)+4 b^2 c e^3 (5 a e+b d)-4 c^3 d^2 e (b d-5 a e)-3 b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{3/2}}+\frac{e^3 x^2 \left(-2 c e (4 a e+5 b d)+3 b^2 e^2+16 c^2 d^2\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{e^3 \left(-2 c e (a e+5 b d)+3 b^2 e^2+10 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{e^2 x \left(-10 c^2 d e (3 a e+b d)+b c e^2 (11 a e+10 b d)-3 b^3 e^3+12 c^3 d^3\right)}{c^3 \left(b^2-4 a c\right)}+\frac{e^4 x^3 (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{(d+e x)^4 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{(2 c d-b e) \left(-2 c^2 e^2 \left(15 a^2 e^2+10 a b d e+b^2 d^2\right)+4 b^2 c e^3 (5 a e+b d)-4 c^3 d^2 e (b d-5 a e)-3 b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{3/2}}+\frac{e^3 x^2 \left(-2 c e (4 a e+5 b d)+3 b^2 e^2+16 c^2 d^2\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{e^3 \left(-2 c e (a e+5 b d)+3 b^2 e^2+10 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{e^2 x \left(-10 c^2 d e (3 a e+b d)+b c e^2 (11 a e+10 b d)-3 b^3 e^3+12 c^3 d^3\right)}{c^3 \left(b^2-4 a c\right)}+\frac{e^4 x^3 (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{(d+e x)^4 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"(e^2*(12*c^3*d^3 - 3*b^3*e^3 - 10*c^2*d*e*(b*d + 3*a*e) + b*c*e^2*(10*b*d + 11*a*e))*x)/(c^3*(b^2 - 4*a*c)) + (e^3*(16*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(5*b*d + 4*a*e))*x^2)/(2*c^2*(b^2 - 4*a*c)) + (e^4*(2*c*d - b*e)*x^3)/(c*(b^2 - 4*a*c)) - ((d + e*x)^4*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((2*c*d - b*e)*(2*c^4*d^4 - 3*b^4*e^4 - 4*c^3*d^2*e*(b*d - 5*a*e) + 4*b^2*c*e^3*(b*d + 5*a*e) - 2*c^2*e^2*(b^2*d^2 + 10*a*b*d*e + 15*a^2*e^2))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*(b^2 - 4*a*c)^(3/2)) + (e^3*(10*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(5*b*d + a*e))*Log[a + b*x + c*x^2])/(2*c^4)","A",7,6,20,0.3000,1,"{738, 800, 634, 618, 206, 628}"
2191,1,260,0,0.5672807,"\int \frac{(d+e x)^4}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)^4/(a + b*x + c*x^2)^2,x]","\frac{2 e^2 x \left(-c e (3 a e+2 b d)+b^2 e^2+3 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)}+\frac{2 \left(2 b^2 c e^3 (3 a e+b d)-4 c^3 d^2 e (b d-3 a e)-6 a c^2 e^3 (a e+2 b d)-b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{e^3 x^2 (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{(d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e^3 (2 c d-b e) \log \left(a+b x+c x^2\right)}{c^3}","\frac{2 e^2 x \left(-c e (3 a e+2 b d)+b^2 e^2+3 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)}+\frac{2 \left(2 b^2 c e^3 (3 a e+b d)-4 c^3 d^2 e (b d-3 a e)-6 a c^2 e^3 (a e+2 b d)-b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{e^3 x^2 (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{(d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e^3 (2 c d-b e) \log \left(a+b x+c x^2\right)}{c^3}",1,"(2*e^2*(3*c^2*d^2 + b^2*e^2 - c*e*(2*b*d + 3*a*e))*x)/(c^2*(b^2 - 4*a*c)) + (e^3*(2*c*d - b*e)*x^2)/(c*(b^2 - 4*a*c)) - ((d + e*x)^3*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (2*(2*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(b*d - 3*a*e) - 6*a*c^2*e^3*(2*b*d + a*e) + 2*b^2*c*e^3*(b*d + 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(3/2)) + (e^3*(2*c*d - b*e)*Log[a + b*x + c*x^2])/c^3","A",7,6,20,0.3000,1,"{738, 800, 634, 618, 206, 628}"
2192,1,173,0,0.2849768,"\int \frac{(d+e x)^3}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^2,x]","\frac{(2 c d-b e) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{e^2 x (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{(d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e^3 \log \left(a+b x+c x^2\right)}{2 c^2}","\frac{(2 c d-b e) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{e^2 x (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{(d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e^3 \log \left(a+b x+c x^2\right)}{2 c^2}",1,"(e^2*(2*c*d - b*e)*x)/(c*(b^2 - 4*a*c)) - ((d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*(b^2 - 4*a*c)^(3/2)) + (e^3*Log[a + b*x + c*x^2])/(2*c^2)","A",6,6,20,0.3000,1,"{738, 773, 634, 618, 206, 628}"
2193,1,99,0,0.0512849,"\int \frac{(d+e x)^2}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^2,x]","\frac{4 \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{(d+e x) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{4 \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{(d+e x) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-(((d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (4*(c*d^2 - b*d*e + a*e^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",3,3,20,0.1500,1,"{722, 618, 206}"
2194,1,87,0,0.0383568,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^2,x]","\frac{2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{-2 a e+x (2 c d-b e)+b d}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{-2 a e+x (2 c d-b e)+b d}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((b*d - 2*a*e + (2*c*d - b*e)*x)/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (2*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",3,3,18,0.1667,1,"{638, 618, 206}"
2195,1,66,0,0.0278588,"\int \frac{1}{\left(a+b x+c x^2\right)^2} \, dx","Int[(a + b*x + c*x^2)^(-2),x]","\frac{4 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{4 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((b + 2*c*x)/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (4*c*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",3,3,12,0.2500,1,"{614, 618, 206}"
2196,1,224,0,0.3812301,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^2),x]","\frac{(2 c d-b e) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{\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)}-\frac{e^3 \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^2}+\frac{e^3 \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^2}","\frac{(2 c d-b e) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{\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)}-\frac{e^3 \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^2}+\frac{e^3 \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^2}",1,"-((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)*(a + b*x + c*x^2))) + ((2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*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)^2) + (e^3*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^2 - (e^3*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^2)","A",7,6,20,0.3000,1,"{740, 800, 634, 618, 206, 628}"
2197,1,344,0,0.6521937,"\int \frac{1}{(d+e x)^2 \left(a+b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)^2*(a + b*x + c*x^2)^2),x]","-\frac{2 e \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(2 b^2 c e^3 (3 a e+b d)-4 c^3 d^2 e (b d-3 a e)-6 a c^2 e^3 (a e+2 b d)-b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^3}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{\left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{e^3 (2 c d-b e) \log \left(a+b x+c x^2\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{2 e^3 (2 c d-b e) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^3}","-\frac{2 e \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(2 b^2 c e^3 (3 a e+b d)-4 c^3 d^2 e (b d-3 a e)-6 a c^2 e^3 (a e+2 b d)-b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^3}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{\left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{e^3 (2 c d-b e) \log \left(a+b x+c x^2\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{2 e^3 (2 c d-b e) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^3}",1,"(-2*e*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e)))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) - (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)*(d + e*x)*(a + b*x + c*x^2)) + (2*(2*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(b*d - 3*a*e) - 6*a*c^2*e^3*(2*b*d + a*e) + 2*b^2*c*e^3*(b*d + 3*a*e))*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)^3) + (2*e^3*(2*c*d - b*e)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 - (e^3*(2*c*d - b*e)*Log[a + b*x + c*x^2])/(c*d^2 - b*d*e + a*e^2)^3","A",7,6,20,0.3000,1,"{740, 800, 634, 618, 206, 628}"
2198,1,485,0,1.0567857,"\int \frac{1}{(d+e x)^3 \left(a+b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)^3*(a + b*x + c*x^2)^2),x]","\frac{(2 c d-b e) \left(-2 c^2 e^2 \left(15 a^2 e^2+10 a b d e+b^2 d^2\right)+4 b^2 c e^3 (5 a e+b d)-4 c^3 d^2 e (b d-5 a e)-3 b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^4}-\frac{e^3 \left(-2 c e (a e+5 b d)+3 b^2 e^2+10 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^4}-\frac{e (2 c d-b e) \left(-c e (11 a e+b d)+3 b^2 e^2+c^2 d^2\right)}{\left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{e \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{2 \left(b^2-4 a c\right) (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{e^3 \log (d+e x) \left(-2 c e (a e+5 b d)+3 b^2 e^2+10 c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^4}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{\left(b^2-4 a c\right) (d+e x)^2 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}","\frac{(2 c d-b e) \left(-2 c^2 e^2 \left(15 a^2 e^2+10 a b d e+b^2 d^2\right)+4 b^2 c e^3 (5 a e+b d)-4 c^3 d^2 e (b d-5 a e)-3 b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^4}-\frac{e^3 \left(-2 c e (a e+5 b d)+3 b^2 e^2+10 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^4}-\frac{e (2 c d-b e) \left(-c e (11 a e+b d)+3 b^2 e^2+c^2 d^2\right)}{\left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{e \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{2 \left(b^2-4 a c\right) (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{e^3 \log (d+e x) \left(-2 c e (a e+5 b d)+3 b^2 e^2+10 c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^4}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{\left(b^2-4 a c\right) (d+e x)^2 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}",1,"-(e*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e)))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (e*(2*c*d - b*e)*(c^2*d^2 + 3*b^2*e^2 - c*e*(b*d + 11*a*e)))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) - (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)*(d + e*x)^2*(a + b*x + c*x^2)) + ((2*c*d - b*e)*(2*c^4*d^4 - 3*b^4*e^4 - 4*c^3*d^2*e*(b*d - 5*a*e) + 4*b^2*c*e^3*(b*d + 5*a*e) - 2*c^2*e^2*(b^2*d^2 + 10*a*b*d*e + 15*a^2*e^2))*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)^4) + (e^3*(10*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(5*b*d + a*e))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^4 - (e^3*(10*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(5*b*d + a*e))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^4)","A",7,6,20,0.3000,1,"{740, 800, 634, 618, 206, 628}"
2199,1,294,0,0.4245925,"\int \frac{x^7}{\left(a+b x+c x^2\right)^3} \, dx","Int[x^7/(a + b*x + c*x^2)^3,x]","\frac{3 x^2 \left(16 a^2 c^2-13 a b^2 c+2 b^4\right)}{2 c^3 \left(b^2-4 a c\right)^2}+\frac{3 b \left(70 a^2 b^2 c^2-70 a^3 c^3-21 a b^4 c+2 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^5 \left(b^2-4 a c\right)^{5/2}}-\frac{b x^3 \left(2 b^2-11 a c\right)}{c^2 \left(b^2-4 a c\right)^2}+\frac{3 \left(2 b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 c^5}-\frac{3 b x \left(2 b^2-9 a c\right) \left(b^2-3 a c\right)}{c^4 \left(b^2-4 a c\right)^2}+\frac{x^6 (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{3 x^4 \left(b x \left(b^2-6 a c\right)+a \left(b^2-8 a c\right)\right)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}","\frac{3 x^2 \left(16 a^2 c^2-13 a b^2 c+2 b^4\right)}{2 c^3 \left(b^2-4 a c\right)^2}+\frac{3 b \left(70 a^2 b^2 c^2-70 a^3 c^3-21 a b^4 c+2 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^5 \left(b^2-4 a c\right)^{5/2}}-\frac{b x^3 \left(2 b^2-11 a c\right)}{c^2 \left(b^2-4 a c\right)^2}+\frac{3 \left(2 b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 c^5}-\frac{3 b x \left(2 b^2-9 a c\right) \left(b^2-3 a c\right)}{c^4 \left(b^2-4 a c\right)^2}+\frac{x^6 (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{3 x^4 \left(b x \left(b^2-6 a c\right)+a \left(b^2-8 a c\right)\right)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}",1,"(-3*b*(2*b^2 - 9*a*c)*(b^2 - 3*a*c)*x)/(c^4*(b^2 - 4*a*c)^2) + (3*(2*b^4 - 13*a*b^2*c + 16*a^2*c^2)*x^2)/(2*c^3*(b^2 - 4*a*c)^2) - (b*(2*b^2 - 11*a*c)*x^3)/(c^2*(b^2 - 4*a*c)^2) + (x^6*(2*a + b*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*x^4*(a*(b^2 - 8*a*c) + b*(b^2 - 6*a*c)*x))/(2*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (3*b*(2*b^6 - 21*a*b^4*c + 70*a^2*b^2*c^2 - 70*a^3*c^3)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^5*(b^2 - 4*a*c)^(5/2)) + (3*(2*b^2 - a*c)*Log[a + b*x + c*x^2])/(2*c^5)","A",8,7,16,0.4375,1,"{738, 818, 800, 634, 618, 206, 628}"
2200,1,238,0,0.2874178,"\int \frac{x^6}{\left(a+b x+c x^2\right)^3} \, dx","Int[x^6/(a + b*x + c*x^2)^3,x]","\frac{3 x \left(10 a^2 c^2-7 a b^2 c+b^4\right)}{c^3 \left(b^2-4 a c\right)^2}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 b x^2 \left(b^2-6 a c\right)}{2 c^2 \left(b^2-4 a c\right)^2}+\frac{x^5 (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x^3 \left(b x \left(b^2-7 a c\right)+a \left(b^2-10 a c\right)\right)}{c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 b \log \left(a+b x+c x^2\right)}{2 c^4}","\frac{3 x \left(10 a^2 c^2-7 a b^2 c+b^4\right)}{c^3 \left(b^2-4 a c\right)^2}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 b x^2 \left(b^2-6 a c\right)}{2 c^2 \left(b^2-4 a c\right)^2}+\frac{x^5 (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x^3 \left(b x \left(b^2-7 a c\right)+a \left(b^2-10 a c\right)\right)}{c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 b \log \left(a+b x+c x^2\right)}{2 c^4}",1,"(3*(b^4 - 7*a*b^2*c + 10*a^2*c^2)*x)/(c^3*(b^2 - 4*a*c)^2) - (3*b*(b^2 - 6*a*c)*x^2)/(2*c^2*(b^2 - 4*a*c)^2) + (x^5*(2*a + b*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (x^3*(a*(b^2 - 10*a*c) + b*(b^2 - 7*a*c)*x))/(c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*(b^2 - 4*a*c)^(5/2)) - (3*b*Log[a + b*x + c*x^2])/(2*c^4)","A",8,7,16,0.4375,1,"{738, 818, 800, 634, 618, 206, 628}"
2201,1,388,0,1.1100542,"\int \frac{(d+e x)^5}{\left(a+b x+c x^2\right)^3} \, dx","Int[(d + e*x)^5/(a + b*x + c*x^2)^3,x]","-\frac{\left(20 c^3 d e^2 \left(3 a^2 e^2-3 a b d e+b^2 d^2\right)-30 a^2 b c^2 e^5+10 a b^3 c e^5-10 c^4 d^3 e (3 b d-4 a e)-b^5 e^5+12 c^5 d^5\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x)^2 \left(-x (2 c d-b e) \left(-2 c e (3 b d-5 a e)-b^2 e^2+6 c^2 d^2\right)+b^2 \left(7 c d^2 e-a e^3\right)-6 b c d \left(3 a e^2+c d^2\right)+8 a c e \left(2 a e^2+c d^2\right)\right)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{e^2 x (2 c d-b e) \left(-c e (3 b d-7 a e)-b^2 e^2+3 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)^2}-\frac{(d+e x)^4 (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{e^5 \log \left(a+b x+c x^2\right)}{2 c^3}","-\frac{\left(20 c^3 d e^2 \left(3 a^2 e^2-3 a b d e+b^2 d^2\right)-30 a^2 b c^2 e^5+10 a b^3 c e^5-10 c^4 d^3 e (3 b d-4 a e)-b^5 e^5+12 c^5 d^5\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x)^2 \left(-x (2 c d-b e) \left(-2 c e (3 b d-5 a e)-b^2 e^2+6 c^2 d^2\right)+b^2 \left(7 c d^2 e-a e^3\right)-6 b c d \left(3 a e^2+c d^2\right)+8 a c e \left(2 a e^2+c d^2\right)\right)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{e^2 x (2 c d-b e) \left(-c e (3 b d-7 a e)-b^2 e^2+3 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)^2}-\frac{(d+e x)^4 (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{e^5 \log \left(a+b x+c x^2\right)}{2 c^3}",1,"-((e^2*(2*c*d - b*e)*(3*c^2*d^2 - b^2*e^2 - c*e*(3*b*d - 7*a*e))*x)/(c^2*(b^2 - 4*a*c)^2)) - ((d + e*x)^4*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - ((d + e*x)^2*(8*a*c*e*(c*d^2 + 2*a*e^2) - 6*b*c*d*(c*d^2 + 3*a*e^2) + b^2*(7*c*d^2*e - a*e^3) - (2*c*d - b*e)*(6*c^2*d^2 - b^2*e^2 - 2*c*e*(3*b*d - 5*a*e))*x))/(2*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - ((12*c^5*d^5 - b^5*e^5 + 10*a*b^3*c*e^5 - 30*a^2*b*c^2*e^5 - 10*c^4*d^3*e*(3*b*d - 4*a*e) + 20*c^3*d*e^2*(b^2*d^2 - 3*a*b*d*e + 3*a^2*e^2))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(5/2)) + (e^5*Log[a + b*x + c*x^2])/(2*c^3)","A",7,7,20,0.3500,1,"{738, 818, 773, 634, 618, 206, 628}"
2202,1,169,0,0.1227292,"\int \frac{(d+e x)^4}{\left(a+b x+c x^2\right)^3} \, dx","Int[(d + e*x)^4/(a + b*x + c*x^2)^3,x]","\frac{3 (d+e x) \left(a e^2-b d e+c d^2\right) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{12 \left(a e^2-b d e+c d^2\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{3 (d+e x) \left(a e^2-b d e+c d^2\right) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{12 \left(a e^2-b d e+c d^2\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-((d + e*x)^3*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (12*(c*d^2 - b*d*e + a*e^2)^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",4,3,20,0.1500,1,"{722, 618, 206}"
2203,1,158,0,0.0882377,"\int \frac{(d+e x)^3}{\left(a+b x+c x^2\right)^3} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^3,x]","-\frac{6 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(b+2 c x) (d+e x)^3}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{3 (d+e x) (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}","-\frac{6 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(b+2 c x) (d+e x)^3}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{3 (d+e x) (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}",1,"-((b + 2*c*x)*(d + e*x)^3)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*(2*c*d - b*e)*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",4,4,20,0.2000,1,"{728, 722, 618, 206}"
2204,1,198,0,0.2182795,"\int \frac{(d+e x)^2}{\left(a+b x+c x^2\right)^3} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^3,x]","-\frac{-x \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)-3 b \left(a e^2+c d^2\right)+4 a c d e+2 b^2 d e}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{2 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x) (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{-x \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)-3 b \left(a e^2+c d^2\right)+4 a c d e+2 b^2 d e}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{2 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x) (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-((d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - (2*b^2*d*e + 4*a*c*d*e - 3*b*(c*d^2 + a*e^2) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*x)/((b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",4,4,20,0.2000,1,"{738, 638, 618, 206}"
2205,1,131,0,0.0498186,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^3} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^3,x]","\frac{3 (b+2 c x) (2 c d-b e)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{-2 a e+x (2 c d-b e)+b d}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{6 c (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","\frac{3 (b+2 c x) (2 c d-b e)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{-2 a e+x (2 c d-b e)+b d}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{6 c (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"-(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*(2*c*d - b*e)*(b + 2*c*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (6*c*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",4,4,18,0.2222,1,"{638, 614, 618, 206}"
2206,1,101,0,0.0361321,"\int \frac{1}{\left(a+b x+c x^2\right)^3} \, dx","Int[(a + b*x + c*x^2)^(-3),x]","-\frac{12 c^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{3 c (b+2 c x)}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{b+2 c x}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{12 c^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{3 c (b+2 c x)}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{b+2 c x}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-(b + 2*c*x)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*c*(b + 2*c*x))/((b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (12*c^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",4,3,12,0.2500,1,"{614, 618, 206}"
2207,1,429,0,1.0157127,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)^3} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^3),x]","-\frac{\left(20 c^3 d e^2 \left(3 a^2 e^2-3 a b d e+b^2 d^2\right)-30 a^2 b c^2 e^5+10 a b^3 c e^5-10 c^4 d^3 e (3 b d-4 a e)-b^5 e^5+12 c^5 d^5\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2} \left(a e^2-b d e+c d^2\right)^3}-\frac{-2 c x (2 c d-b e) \left(-c e (3 b d-7 a e)-b^2 e^2+3 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-c e (3 b d-8 a e)-2 b^2 e^2+6 c^2 d^2\right)+3 a c e (2 c d-b e)^2}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)}-\frac{e^5 \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{e^5 \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^3}","-\frac{\left(20 c^3 d e^2 \left(3 a^2 e^2-3 a b d e+b^2 d^2\right)-30 a^2 b c^2 e^5+10 a b^3 c e^5-10 c^4 d^3 e (3 b d-4 a e)-b^5 e^5+12 c^5 d^5\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2} \left(a e^2-b d e+c d^2\right)^3}-\frac{-2 c x (2 c d-b e) \left(-c e (3 b d-7 a e)-b^2 e^2+3 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-c e (3 b d-8 a e)-2 b^2 e^2+6 c^2 d^2\right)+3 a c e (2 c d-b e)^2}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)}-\frac{e^5 \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{e^5 \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^3}",1,"-(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (3*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(6*c^2*d^2 - 2*b^2*e^2 - c*e*(3*b*d - 8*a*e)) - 2*c*(2*c*d - b*e)*(3*c^2*d^2 - b^2*e^2 - c*e*(3*b*d - 7*a*e))*x)/(2*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) - ((12*c^5*d^5 - b^5*e^5 + 10*a*b^3*c*e^5 - 30*a^2*b*c^2*e^5 - 10*c^4*d^3*e*(3*b*d - 4*a*e) + 20*c^3*d*e^2*(b^2*d^2 - 3*a*b*d*e + 3*a^2*e^2))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*(c*d^2 - b*d*e + a*e^2)^3) + (e^5*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 - (e^5*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^3)","A",8,7,20,0.3500,1,"{740, 822, 800, 634, 618, 206, 628}"
2208,1,239,0,0.3136307,"\int \frac{1}{x^2 \left(a+b x+c x^2\right)^3} \, dx","Int[1/(x^2*(a + b*x + c*x^2)^3),x]","\frac{20 a^2 c^2+3 b c x \left(b^2-6 a c\right)-20 a b^2 c+3 b^4}{2 a^2 x \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{a^3 x \left(b^2-4 a c\right)^2}+\frac{3 b \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{3 b \log (x)}{a^4}+\frac{-2 a c+b^2+b c x}{2 a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{20 a^2 c^2+3 b c x \left(b^2-6 a c\right)-20 a b^2 c+3 b^4}{2 a^2 x \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{a^3 x \left(b^2-4 a c\right)^2}+\frac{3 b \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{3 b \log (x)}{a^4}+\frac{-2 a c+b^2+b c x}{2 a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"(-3*(b^2 - 5*a*c)*(b^2 - 2*a*c))/(a^3*(b^2 - 4*a*c)^2*x) + (b^2 - 2*a*c + b*c*x)/(2*a*(b^2 - 4*a*c)*x*(a + b*x + c*x^2)^2) + (3*b^4 - 20*a*b^2*c + 20*a^2*c^2 + 3*b*c*(b^2 - 6*a*c)*x)/(2*a^2*(b^2 - 4*a*c)^2*x*(a + b*x + c*x^2)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^4*(b^2 - 4*a*c)^(5/2)) - (3*b*Log[x])/a^4 + (3*b*Log[a + b*x + c*x^2])/(2*a^4)","A",8,7,16,0.4375,1,"{740, 822, 800, 634, 618, 206, 628}"
2209,1,306,0,0.4595143,"\int \frac{1}{x^3 \left(a+b x+c x^2\right)^3} \, dx","Int[1/(x^3*(a + b*x + c*x^2)^3),x]","\frac{24 a^2 c^2+2 b c x \left(2 b^2-11 a c\right)-25 a b^2 c+4 b^4}{2 a^2 x^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \left(16 a^2 c^2-13 a b^2 c+2 b^4\right)}{2 a^3 x^2 \left(b^2-4 a c\right)^2}+\frac{3 b \left(70 a^2 b^2 c^2-70 a^3 c^3-21 a b^4 c+2 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^5 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(2 b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 a^5}+\frac{3 b \left(2 b^2-9 a c\right) \left(b^2-3 a c\right)}{a^4 x \left(b^2-4 a c\right)^2}+\frac{3 \log (x) \left(2 b^2-a c\right)}{a^5}+\frac{-2 a c+b^2+b c x}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{24 a^2 c^2+2 b c x \left(2 b^2-11 a c\right)-25 a b^2 c+4 b^4}{2 a^2 x^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \left(16 a^2 c^2-13 a b^2 c+2 b^4\right)}{2 a^3 x^2 \left(b^2-4 a c\right)^2}+\frac{3 b \left(70 a^2 b^2 c^2-70 a^3 c^3-21 a b^4 c+2 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^5 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(2 b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 a^5}+\frac{3 b \left(2 b^2-9 a c\right) \left(b^2-3 a c\right)}{a^4 x \left(b^2-4 a c\right)^2}+\frac{3 \log (x) \left(2 b^2-a c\right)}{a^5}+\frac{-2 a c+b^2+b c x}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"(-3*(2*b^4 - 13*a*b^2*c + 16*a^2*c^2))/(2*a^3*(b^2 - 4*a*c)^2*x^2) + (3*b*(2*b^2 - 9*a*c)*(b^2 - 3*a*c))/(a^4*(b^2 - 4*a*c)^2*x) + (b^2 - 2*a*c + b*c*x)/(2*a*(b^2 - 4*a*c)*x^2*(a + b*x + c*x^2)^2) + (4*b^4 - 25*a*b^2*c + 24*a^2*c^2 + 2*b*c*(2*b^2 - 11*a*c)*x)/(2*a^2*(b^2 - 4*a*c)^2*x^2*(a + b*x + c*x^2)) + (3*b*(2*b^6 - 21*a*b^4*c + 70*a^2*b^2*c^2 - 70*a^3*c^3)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^5*(b^2 - 4*a*c)^(5/2)) + (3*(2*b^2 - a*c)*Log[x])/a^5 - (3*(2*b^2 - a*c)*Log[a + b*x + c*x^2])/(2*a^5)","A",8,7,16,0.4375,1,"{740, 822, 800, 634, 618, 206, 628}"
2210,1,349,0,0.6399745,"\int \frac{x^8}{\left(a+b x+c x^2\right)^4} \, dx","Int[x^8/(a + b*x + c*x^2)^4,x]","\frac{x^3 \left(b x \left(122 a^2 c^2-39 a b^2 c+4 b^4\right)+4 a \left(35 a^2 c^2-9 a b^2 c+b^4\right)\right)}{3 c^2 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}-\frac{2 b x^2 \left(29 a^2 c^2-10 a b^2 c+b^4\right)}{c^3 \left(b^2-4 a c\right)^3}+\frac{4 x \left(38 a^2 b^2 c^2-35 a^3 c^3-11 a b^4 c+b^6\right)}{c^4 \left(b^2-4 a c\right)^3}-\frac{4 \left(70 a^2 b^4 c^2-140 a^3 b^2 c^3+70 a^4 c^4-14 a b^6 c+b^8\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^5 \left(b^2-4 a c\right)^{7/2}}+\frac{x^7 (2 a+b x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{x^5 \left(b x \left(b^2-9 a c\right)+a \left(b^2-14 a c\right)\right)}{3 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{2 b \log \left(a+b x+c x^2\right)}{c^5}","\frac{x^3 \left(b x \left(122 a^2 c^2-39 a b^2 c+4 b^4\right)+4 a \left(35 a^2 c^2-9 a b^2 c+b^4\right)\right)}{3 c^2 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}-\frac{2 b x^2 \left(29 a^2 c^2-10 a b^2 c+b^4\right)}{c^3 \left(b^2-4 a c\right)^3}+\frac{4 x \left(38 a^2 b^2 c^2-35 a^3 c^3-11 a b^4 c+b^6\right)}{c^4 \left(b^2-4 a c\right)^3}-\frac{4 \left(70 a^2 b^4 c^2-140 a^3 b^2 c^3+70 a^4 c^4-14 a b^6 c+b^8\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^5 \left(b^2-4 a c\right)^{7/2}}+\frac{x^7 (2 a+b x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{x^5 \left(b x \left(b^2-9 a c\right)+a \left(b^2-14 a c\right)\right)}{3 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{2 b \log \left(a+b x+c x^2\right)}{c^5}",1,"(4*(b^6 - 11*a*b^4*c + 38*a^2*b^2*c^2 - 35*a^3*c^3)*x)/(c^4*(b^2 - 4*a*c)^3) - (2*b*(b^4 - 10*a*b^2*c + 29*a^2*c^2)*x^2)/(c^3*(b^2 - 4*a*c)^3) + (x^7*(2*a + b*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + (x^5*(a*(b^2 - 14*a*c) + b*(b^2 - 9*a*c)*x))/(3*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) + (x^3*(4*a*(b^4 - 9*a*b^2*c + 35*a^2*c^2) + b*(4*b^4 - 39*a*b^2*c + 122*a^2*c^2)*x))/(3*c^2*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)) - (4*(b^8 - 14*a*b^6*c + 70*a^2*b^4*c^2 - 140*a^3*b^2*c^3 + 70*a^4*c^4)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^5*(b^2 - 4*a*c)^(7/2)) - (2*b*Log[a + b*x + c*x^2])/c^5","A",9,7,16,0.4375,1,"{738, 818, 800, 634, 618, 206, 628}"
2211,1,291,0,0.5045403,"\int \frac{x^7}{\left(a+b x+c x^2\right)^4} \, dx","Int[x^7/(a + b*x + c*x^2)^4,x]","\frac{x^2 \left(b x \left(140 a^2 c^2-32 a b^2 c+3 b^4\right)+3 a \left(64 a^2 c^2-10 a b^2 c+b^4\right)\right)}{6 c^2 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}-\frac{b x \left(38 a^2 c^2-11 a b^2 c+b^4\right)}{c^3 \left(b^2-4 a c\right)^3}+\frac{b \left(70 a^2 b^2 c^2-140 a^3 c^3-14 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{7/2}}+\frac{x^6 (2 a+b x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{x^4 \left(b x \left(b^2-14 a c\right)+a \left(b^2-24 a c\right)\right)}{6 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}+\frac{\log \left(a+b x+c x^2\right)}{2 c^4}","\frac{x^2 \left(b x \left(140 a^2 c^2-32 a b^2 c+3 b^4\right)+3 a \left(64 a^2 c^2-10 a b^2 c+b^4\right)\right)}{6 c^2 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}-\frac{b x \left(38 a^2 c^2-11 a b^2 c+b^4\right)}{c^3 \left(b^2-4 a c\right)^3}+\frac{b \left(70 a^2 b^2 c^2-140 a^3 c^3-14 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{7/2}}+\frac{x^6 (2 a+b x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{x^4 \left(b x \left(b^2-14 a c\right)+a \left(b^2-24 a c\right)\right)}{6 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}+\frac{\log \left(a+b x+c x^2\right)}{2 c^4}",1,"-((b*(b^4 - 11*a*b^2*c + 38*a^2*c^2)*x)/(c^3*(b^2 - 4*a*c)^3)) + (x^6*(2*a + b*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + (x^4*(a*(b^2 - 24*a*c) + b*(b^2 - 14*a*c)*x))/(6*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) + (x^2*(3*a*(b^4 - 10*a*b^2*c + 64*a^2*c^2) + b*(3*b^4 - 32*a*b^2*c + 140*a^2*c^2)*x))/(6*c^2*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (b*(b^6 - 14*a*b^4*c + 70*a^2*b^2*c^2 - 140*a^3*c^3)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*(b^2 - 4*a*c)^(7/2)) + Log[a + b*x + c*x^2]/(2*c^4)","A",8,7,16,0.4375,1,"{738, 818, 773, 634, 618, 206, 628}"
2212,1,146,0,0.0831933,"\int \frac{x^6}{\left(a+b x+c x^2\right)^4} \, dx","Int[x^6/(a + b*x + c*x^2)^4,x]","\frac{10 a^2 x (2 a+b x)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{40 a^3 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}+\frac{x^5 (2 a+b x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}-\frac{5 a x^3 (2 a+b x)}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}","\frac{10 a^2 x (2 a+b x)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{40 a^3 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}+\frac{x^5 (2 a+b x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}-\frac{5 a x^3 (2 a+b x)}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}",1,"(x^5*(2*a + b*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) - (5*a*x^3*(2*a + b*x))/(3*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) + (10*a^2*x*(2*a + b*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (40*a^3*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(7/2)","A",5,3,16,0.1875,1,"{722, 618, 206}"
2213,1,145,0,0.0638838,"\int \frac{x^5}{\left(a+b x+c x^2\right)^4} \, dx","Int[x^5/(a + b*x + c*x^2)^4,x]","-\frac{20 a^2 b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{x^5 (b+2 c x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{5 b x^3 (2 a+b x)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{5 a b x (2 a+b x)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}","-\frac{20 a^2 b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{x^5 (b+2 c x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{5 b x^3 (2 a+b x)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{5 a b x (2 a+b x)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}",1,"-(x^5*(b + 2*c*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + (5*b*x^3*(2*a + b*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (5*a*b*x*(2*a + b*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) - (20*a^2*b*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(7/2)","A",5,4,16,0.2500,1,"{728, 722, 618, 206}"
2214,1,259,0,0.4522329,"\int \frac{(d+e x)^4}{\left(a+b x+c x^2\right)^4} \, dx","Int[(d + e*x)^4/(a + b*x + c*x^2)^4,x]","-\frac{2 (d+e x) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{8 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{(b+2 c x) (d+e x)^4}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{(d+e x)^3 \left(-2 a c e-2 b^2 e+5 c x (2 c d-b e)+5 b c d\right)}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}","-\frac{2 (d+e x) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{8 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{(b+2 c x) (d+e x)^4}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{(d+e x)^3 \left(-2 a c e-2 b^2 e+5 c x (2 c d-b e)+5 b c d\right)}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}",1,"-((b + 2*c*x)*(d + e*x)^4)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + ((d + e*x)^3*(5*b*c*d - 2*b^2*e - 2*a*c*e + 5*c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (2*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (8*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(7/2)","A",5,5,20,0.2500,1,"{736, 804, 722, 618, 206}"
2215,1,306,0,0.4294867,"\int \frac{(d+e x)^3}{\left(a+b x+c x^2\right)^4} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^4,x]","-\frac{2 x (2 c d-b e) \left(-c e (a e+15 b d)+4 b^2 e^2+15 c^2 d^2\right)-b^2 \left(11 a e^3+25 c d^2 e\right)+6 b c d \left(13 a e^2+5 c d^2\right)-16 a c e \left(a e^2+5 c d^2\right)+3 b^3 d e^2}{3 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{2 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{(b+2 c x) (d+e x)^3}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{(d+e x)^2 \left(-8 a c e-3 b^2 e+10 c x (2 c d-b e)+10 b c d\right)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}","-\frac{2 x (2 c d-b e) \left(-c e (a e+15 b d)+4 b^2 e^2+15 c^2 d^2\right)-b^2 \left(11 a e^3+25 c d^2 e\right)+6 b c d \left(13 a e^2+5 c d^2\right)-16 a c e \left(a e^2+5 c d^2\right)+3 b^3 d e^2}{3 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{2 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{(b+2 c x) (d+e x)^3}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{(d+e x)^2 \left(-8 a c e-3 b^2 e+10 c x (2 c d-b e)+10 b c d\right)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}",1,"-((b + 2*c*x)*(d + e*x)^3)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + ((d + e*x)^2*(10*b*c*d - 3*b^2*e - 8*a*c*e + 10*c*(2*c*d - b*e)*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (3*b^3*d*e^2 - 16*a*c*e*(5*c*d^2 + a*e^2) + 6*b*c*d*(5*c*d^2 + 13*a*e^2) - b^2*(25*c*d^2*e + 11*a*e^3) + 2*(2*c*d - b*e)*(15*c^2*d^2 + 4*b^2*e^2 - c*e*(15*b*d + a*e))*x)/(3*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(7/2)","A",5,5,20,0.2500,1,"{736, 820, 777, 618, 206}"
2216,1,260,0,0.2616814,"\int \frac{(d+e x)^2}{\left(a+b x+c x^2\right)^4} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^4,x]","-\frac{2 (b+2 c x) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}-\frac{-2 x \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)-5 b \left(a e^2+c d^2\right)+8 a c d e+3 b^2 d e}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}+\frac{8 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{(d+e x) (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}","-\frac{2 (b+2 c x) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}-\frac{-2 x \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)-5 b \left(a e^2+c d^2\right)+8 a c d e+3 b^2 d e}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}+\frac{8 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{(d+e x) (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}",1,"-((d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) - (3*b^2*d*e + 8*a*c*d*e - 5*b*(c*d^2 + a*e^2) - 2*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*x)/(3*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (2*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(b + 2*c*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (8*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(7/2)","A",5,5,20,0.2500,1,"{738, 638, 614, 618, 206}"
2217,1,173,0,0.0738182,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^4} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^4,x]","\frac{20 c^2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{5 c (b+2 c x) (2 c d-b e)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{5 (b+2 c x) (2 c d-b e)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{-2 a e+x (2 c d-b e)+b d}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}","\frac{20 c^2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}-\frac{5 c (b+2 c x) (2 c d-b e)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{5 (b+2 c x) (2 c d-b e)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{-2 a e+x (2 c d-b e)+b d}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}",1,"-(b*d - 2*a*e + (2*c*d - b*e)*x)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + (5*(2*c*d - b*e)*(b + 2*c*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (5*c*(2*c*d - b*e)*(b + 2*c*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (20*c^2*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(7/2)","A",5,4,18,0.2222,1,"{638, 614, 618, 206}"
2218,1,136,0,0.050947,"\int \frac{1}{\left(a+b x+c x^2\right)^4} \, dx","Int[(a + b*x + c*x^2)^(-4),x]","-\frac{10 c^2 (b+2 c x)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{40 c^3 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}+\frac{5 c (b+2 c x)}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{b+2 c x}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}","-\frac{10 c^2 (b+2 c x)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{40 c^3 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}+\frac{5 c (b+2 c x)}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{b+2 c x}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}",1,"-(b + 2*c*x)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + (5*c*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (10*c^2*(b + 2*c*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (40*c^3*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(7/2)","A",5,3,12,0.2500,1,"{614, 618, 206}"
2219,1,771,0,7.2998714,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)^4} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^4),x]","\frac{-2 c x (2 c d-b e) \left(c^2 e^2 \left(38 a^2 e^2-32 a b d e+7 b^2 d^2\right)+b^2 c e^3 (3 b d-11 a e)-4 c^3 d^2 e (5 b d-8 a e)+b^4 e^4+10 c^4 d^4\right)+2 b^2 c^2 e \left(43 a^2 e^4+48 a c d^2 e^2+25 c^2 d^4\right)-4 b c^3 d \left(19 a^2 e^4+16 a c d^2 e^2+5 c^2 d^4\right)-64 a^3 c^3 e^5-2 b^3 c^2 d e^2 \left(5 a e^2+17 c d^2\right)+b^4 c e^3 \left(c d^2-23 a e^2\right)+b^5 c d e^4+2 b^6 e^5}{2 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^3}+\frac{\left(28 c^5 d^3 e^2 \left(10 a^2 e^2-15 a b d e+6 b^2 d^2\right)-70 c^4 d e^3 \left(6 a^2 b d e^2-4 a^3 e^3-4 a b^2 d^2 e+b^3 d^3\right)+70 a^2 b^3 c^2 e^7-140 a^3 b c^3 e^7-14 a b^5 c e^7-28 c^6 d^5 e (5 b d-6 a e)+b^7 e^7+40 c^7 d^7\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2} \left(a e^2-b d e+c d^2\right)^4}-\frac{-c x (2 c d-b e) \left(-2 c e (5 b d-11 a e)-3 b^2 e^2+10 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-c e (5 b d-12 a e)-3 b^2 e^2+10 c^2 d^2\right)+5 a c e (2 c d-b e)^2}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)^2}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3 \left(a e^2-b d e+c d^2\right)}-\frac{e^7 \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^4}+\frac{e^7 \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^4}","\frac{-2 c x (2 c d-b e) \left(c^2 e^2 \left(38 a^2 e^2-32 a b d e+7 b^2 d^2\right)+b^2 c e^3 (3 b d-11 a e)-4 c^3 d^2 e (5 b d-8 a e)+b^4 e^4+10 c^4 d^4\right)+2 b^2 c^2 e \left(43 a^2 e^4+48 a c d^2 e^2+25 c^2 d^4\right)-4 b c^3 d \left(19 a^2 e^4+16 a c d^2 e^2+5 c^2 d^4\right)-64 a^3 c^3 e^5-2 b^3 c^2 d e^2 \left(5 a e^2+17 c d^2\right)+b^4 c e^3 \left(c d^2-23 a e^2\right)+b^5 c d e^4+2 b^6 e^5}{2 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^3}+\frac{\left(28 c^5 d^3 e^2 \left(10 a^2 e^2-15 a b d e+6 b^2 d^2\right)-70 c^4 d e^3 \left(6 a^2 b d e^2-4 a^3 e^3-4 a b^2 d^2 e+b^3 d^3\right)+70 a^2 b^3 c^2 e^7-140 a^3 b c^3 e^7-14 a b^5 c e^7-28 c^6 d^5 e (5 b d-6 a e)+b^7 e^7+40 c^7 d^7\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2} \left(a e^2-b d e+c d^2\right)^4}-\frac{-c x (2 c d-b e) \left(-2 c e (5 b d-11 a e)-3 b^2 e^2+10 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-c e (5 b d-12 a e)-3 b^2 e^2+10 c^2 d^2\right)+5 a c e (2 c d-b e)^2}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)^2}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3 \left(a e^2-b d e+c d^2\right)}-\frac{e^7 \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^4}+\frac{e^7 \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^4}",1,"-(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^3) - (5*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(10*c^2*d^2 - 3*b^2*e^2 - c*e*(5*b*d - 12*a*e)) - c*(2*c*d - b*e)*(10*c^2*d^2 - 3*b^2*e^2 - 2*c*e*(5*b*d - 11*a*e))*x)/(6*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)^2) + (b^5*c*d*e^4 + 2*b^6*e^5 - 64*a^3*c^3*e^5 + b^4*c*e^3*(c*d^2 - 23*a*e^2) - 2*b^3*c^2*d*e^2*(17*c*d^2 + 5*a*e^2) - 4*b*c^3*d*(5*c^2*d^4 + 16*a*c*d^2*e^2 + 19*a^2*e^4) + 2*b^2*c^2*e*(25*c^2*d^4 + 48*a*c*d^2*e^2 + 43*a^2*e^4) - 2*c*(2*c*d - b*e)*(10*c^4*d^4 + b^4*e^4 + b^2*c*e^3*(3*b*d - 11*a*e) - 4*c^3*d^2*e*(5*b*d - 8*a*e) + c^2*e^2*(7*b^2*d^2 - 32*a*b*d*e + 38*a^2*e^2))*x)/(2*(b^2 - 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^3*(a + b*x + c*x^2)) + ((40*c^7*d^7 + b^7*e^7 - 14*a*b^5*c*e^7 + 70*a^2*b^3*c^2*e^7 - 140*a^3*b*c^3*e^7 - 28*c^6*d^5*e*(5*b*d - 6*a*e) + 28*c^5*d^3*e^2*(6*b^2*d^2 - 15*a*b*d*e + 10*a^2*e^2) - 70*c^4*d*e^3*(b^3*d^3 - 4*a*b^2*d^2*e + 6*a^2*b*d*e^2 - 4*a^3*e^3))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(7/2)*(c*d^2 - b*d*e + a*e^2)^4) + (e^7*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^4 - (e^7*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^4)","A",9,7,20,0.3500,1,"{740, 822, 800, 634, 618, 206, 628}"
2220,1,352,0,0.5199095,"\int \frac{1}{x^2 \left(a+b x+c x^2\right)^4} \, dx","Int[1/(x^2*(a + b*x + c*x^2)^4),x]","\frac{2 \left(3 b c x \left(29 a^2 c^2-10 a b^2 c+b^4\right)+105 a^2 b^2 c^2-70 a^3 c^3-32 a b^4 c+3 b^6\right)}{3 a^3 x \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{2 \left(7 a^2 c^2-7 a b^2 c+b^4\right)+b c x \left(2 b^2-13 a c\right)}{3 a^2 x \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{4 \left(38 a^2 b^2 c^2-35 a^3 c^3-11 a b^4 c+b^6\right)}{a^4 x \left(b^2-4 a c\right)^3}-\frac{4 \left(70 a^2 b^4 c^2-140 a^3 b^2 c^3+70 a^4 c^4-14 a b^6 c+b^8\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^5 \left(b^2-4 a c\right)^{7/2}}+\frac{2 b \log \left(a+b x+c x^2\right)}{a^5}-\frac{4 b \log (x)}{a^5}+\frac{-2 a c+b^2+b c x}{3 a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}","\frac{2 \left(3 b c x \left(29 a^2 c^2-10 a b^2 c+b^4\right)+105 a^2 b^2 c^2-70 a^3 c^3-32 a b^4 c+3 b^6\right)}{3 a^3 x \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}+\frac{2 \left(7 a^2 c^2-7 a b^2 c+b^4\right)+b c x \left(2 b^2-13 a c\right)}{3 a^2 x \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}-\frac{4 \left(38 a^2 b^2 c^2-35 a^3 c^3-11 a b^4 c+b^6\right)}{a^4 x \left(b^2-4 a c\right)^3}-\frac{4 \left(70 a^2 b^4 c^2-140 a^3 b^2 c^3+70 a^4 c^4-14 a b^6 c+b^8\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^5 \left(b^2-4 a c\right)^{7/2}}+\frac{2 b \log \left(a+b x+c x^2\right)}{a^5}-\frac{4 b \log (x)}{a^5}+\frac{-2 a c+b^2+b c x}{3 a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}",1,"(-4*(b^6 - 11*a*b^4*c + 38*a^2*b^2*c^2 - 35*a^3*c^3))/(a^4*(b^2 - 4*a*c)^3*x) + (b^2 - 2*a*c + b*c*x)/(3*a*(b^2 - 4*a*c)*x*(a + b*x + c*x^2)^3) + (2*(b^4 - 7*a*b^2*c + 7*a^2*c^2) + b*c*(2*b^2 - 13*a*c)*x)/(3*a^2*(b^2 - 4*a*c)^2*x*(a + b*x + c*x^2)^2) + (2*(3*b^6 - 32*a*b^4*c + 105*a^2*b^2*c^2 - 70*a^3*c^3 + 3*b*c*(b^4 - 10*a*b^2*c + 29*a^2*c^2)*x))/(3*a^3*(b^2 - 4*a*c)^3*x*(a + b*x + c*x^2)) - (4*(b^8 - 14*a*b^6*c + 70*a^2*b^4*c^2 - 140*a^3*b^2*c^3 + 70*a^4*c^4)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^5*(b^2 - 4*a*c)^(7/2)) - (4*b*Log[x])/a^5 + (2*b*Log[a + b*x + c*x^2])/a^5","A",9,7,16,0.4375,1,"{740, 822, 800, 634, 618, 206, 628}"
2221,1,388,0,0.5613691,"\int \frac{(d+e x)^5}{\left(a+b x+c x^2\right)^5} \, dx","Int[(d + e*x)^5/(a + b*x + c*x^2)^5,x]","\frac{(d+e x)^3 \left(-c x \left(-4 c e (35 b d-8 a e)+27 b^2 e^2+140 c^2 d^2\right)-10 b c \left(3 a e^2+7 c d^2\right)+28 a c^2 d e+63 b^2 c d e-10 b^3 e^2\right)}{12 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}+\frac{5 (d+e x) (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{10 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}-\frac{(b+2 c x) (d+e x)^5}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}+\frac{(d+e x)^4 \left(-8 a c e-5 b^2 e+14 c x (2 c d-b e)+14 b c d\right)}{12 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}","\frac{(d+e x)^3 \left(-c x \left(-4 c e (35 b d-8 a e)+27 b^2 e^2+140 c^2 d^2\right)-10 b c \left(3 a e^2+7 c d^2\right)+28 a c^2 d e+63 b^2 c d e-10 b^3 e^2\right)}{12 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}+\frac{5 (d+e x) (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{10 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}-\frac{(b+2 c x) (d+e x)^5}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}+\frac{(d+e x)^4 \left(-8 a c e-5 b^2 e+14 c x (2 c d-b e)+14 b c d\right)}{12 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}",1,"-((b + 2*c*x)*(d + e*x)^5)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4) + ((d + e*x)^4*(14*b*c*d - 5*b^2*e - 8*a*c*e + 14*c*(2*c*d - b*e)*x))/(12*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) + ((d + e*x)^3*(63*b^2*c*d*e + 28*a*c^2*d*e - 10*b^3*e^2 - 10*b*c*(7*c*d^2 + 3*a*e^2) - c*(140*c^2*d^2 + 27*b^2*e^2 - 4*c*e*(35*b*d - 8*a*e))*x))/(12*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (5*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (10*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(9/2)","A",6,6,20,0.3000,1,"{736, 820, 804, 722, 618, 206}"
2222,1,545,0,0.879508,"\int \frac{(d+e x)^4}{\left(a+b x+c x^2\right)^5} \, dx","Int[(d + e*x)^4/(a + b*x + c*x^2)^5,x]","-\frac{-x \left(2 c^2 e^2 \left(-18 a^2 e^2-40 a b d e+305 b^2 d^2\right)-38 b^2 c e^3 (5 b d-a e)-40 c^3 d^2 e (21 b d-2 a e)+19 b^4 e^4+420 c^4 d^4\right)-10 b c \left(11 a^2 e^4+88 a c d^2 e^2+21 c^2 d^4\right)-5 b^3 \left(5 a e^4+19 c d^2 e^2\right)+4 b^2 c d e \left(83 a e^2+70 c d^2\right)+16 a c^2 d e \left(16 a e^2+35 c d^2\right)+6 b^4 d e^3}{6 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{2 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}+\frac{(d+e x)^2 \left(-c x \left(-2 c e (35 b d-9 a e)+13 b^2 e^2+70 c^2 d^2\right)-b c \left(23 a e^2+35 c d^2\right)+28 a c^2 d e+28 b^2 c d e-3 b^3 e^2\right)}{6 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}-\frac{(b+2 c x) (d+e x)^4}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}+\frac{(d+e x)^3 \left(-6 a c e-2 b^2 e+7 c x (2 c d-b e)+7 b c d\right)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}","-\frac{-x \left(2 c^2 e^2 \left(-18 a^2 e^2-40 a b d e+305 b^2 d^2\right)-38 b^2 c e^3 (5 b d-a e)-40 c^3 d^2 e (21 b d-2 a e)+19 b^4 e^4+420 c^4 d^4\right)-10 b c \left(11 a^2 e^4+88 a c d^2 e^2+21 c^2 d^4\right)-5 b^3 \left(5 a e^4+19 c d^2 e^2\right)+4 b^2 c d e \left(83 a e^2+70 c d^2\right)+16 a c^2 d e \left(16 a e^2+35 c d^2\right)+6 b^4 d e^3}{6 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{2 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}+\frac{(d+e x)^2 \left(-c x \left(-2 c e (35 b d-9 a e)+13 b^2 e^2+70 c^2 d^2\right)-b c \left(23 a e^2+35 c d^2\right)+28 a c^2 d e+28 b^2 c d e-3 b^3 e^2\right)}{6 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}-\frac{(b+2 c x) (d+e x)^4}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}+\frac{(d+e x)^3 \left(-6 a c e-2 b^2 e+7 c x (2 c d-b e)+7 b c d\right)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}",1,"-((b + 2*c*x)*(d + e*x)^4)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4) + ((d + e*x)^3*(7*b*c*d - 2*b^2*e - 6*a*c*e + 7*c*(2*c*d - b*e)*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) + ((d + e*x)^2*(28*b^2*c*d*e + 28*a*c^2*d*e - 3*b^3*e^2 - b*c*(35*c*d^2 + 23*a*e^2) - c*(70*c^2*d^2 + 13*b^2*e^2 - 2*c*e*(35*b*d - 9*a*e))*x))/(6*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) - (6*b^4*d*e^3 + 16*a*c^2*d*e*(35*c*d^2 + 16*a*e^2) + 4*b^2*c*d*e*(70*c*d^2 + 83*a*e^2) - 5*b^3*(19*c*d^2*e^2 + 5*a*e^4) - 10*b*c*(21*c^2*d^4 + 88*a*c*d^2*e^2 + 11*a^2*e^4) - (420*c^4*d^4 + 19*b^4*e^4 - 40*c^3*d^2*e*(21*b*d - 2*a*e) - 38*b^2*c*e^3*(5*b*d - a*e) + 2*c^2*e^2*(305*b^2*d^2 - 40*a*b*d*e - 18*a^2*e^2))*x)/(6*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (2*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(9/2)","A",6,5,20,0.2500,1,"{736, 820, 777, 618, 206}"
2223,1,378,0,0.5016092,"\int \frac{(d+e x)^3}{\left(a+b x+c x^2\right)^5} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^5,x]","\frac{5 (b+2 c x) (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{2 x (2 c d-b e) \left(-c e (13 a e+35 b d)+12 b^2 e^2+35 c^2 d^2\right)-b^2 \left(27 a e^3+49 c d^2 e\right)+2 b c d \left(99 a e^2+35 c d^2\right)-32 a c e \left(a e^2+7 c d^2\right)+3 b^3 d e^2}{12 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}-\frac{10 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}-\frac{(b+2 c x) (d+e x)^3}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}+\frac{(d+e x)^2 \left(-16 a c e-3 b^2 e+14 c x (2 c d-b e)+14 b c d\right)}{12 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}","\frac{5 (b+2 c x) (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{2 x (2 c d-b e) \left(-c e (13 a e+35 b d)+12 b^2 e^2+35 c^2 d^2\right)-b^2 \left(27 a e^3+49 c d^2 e\right)+2 b c d \left(99 a e^2+35 c d^2\right)-32 a c e \left(a e^2+7 c d^2\right)+3 b^3 d e^2}{12 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}-\frac{10 c (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}-\frac{(b+2 c x) (d+e x)^3}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}+\frac{(d+e x)^2 \left(-16 a c e-3 b^2 e+14 c x (2 c d-b e)+14 b c d\right)}{12 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}",1,"-((b + 2*c*x)*(d + e*x)^3)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4) + ((d + e*x)^2*(14*b*c*d - 3*b^2*e - 16*a*c*e + 14*c*(2*c*d - b*e)*x))/(12*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) - (3*b^3*d*e^2 - 32*a*c*e*(7*c*d^2 + a*e^2) + 2*b*c*d*(35*c*d^2 + 99*a*e^2) - b^2*(49*c*d^2*e + 27*a*e^3) + 2*(2*c*d - b*e)*(35*c^2*d^2 + 12*b^2*e^2 - c*e*(35*b*d + 13*a*e))*x)/(12*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (5*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(b + 2*c*x))/(2*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (10*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(9/2)","A",6,6,20,0.3000,1,"{736, 820, 777, 614, 618, 206}"
2224,1,330,0,0.386843,"\int \frac{(d+e x)^2}{\left(a+b x+c x^2\right)^5} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^5,x]","\frac{5 c (b+2 c x) \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{5 (b+2 c x) \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{12 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}-\frac{-x \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)-7 b \left(a e^2+c d^2\right)+12 a c d e+4 b^2 d e}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}-\frac{10 c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}-\frac{(d+e x) (-2 a e+x (2 c d-b e)+b d)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}","\frac{5 c (b+2 c x) \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{5 (b+2 c x) \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{12 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}-\frac{-x \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)-7 b \left(a e^2+c d^2\right)+12 a c d e+4 b^2 d e}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}-\frac{10 c^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}-\frac{(d+e x) (-2 a e+x (2 c d-b e)+b d)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}",1,"-((d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4) - (4*b^2*d*e + 12*a*c*d*e - 7*b*(c*d^2 + a*e^2) - (14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*x)/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) - (5*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(b + 2*c*x))/(12*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (5*c*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(b + 2*c*x))/(2*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (10*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(9/2)","A",6,5,20,0.2500,1,"{738, 638, 614, 618, 206}"
2225,1,219,0,0.0963824,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^5} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^5,x]","\frac{35 c^2 (b+2 c x) (2 c d-b e)}{2 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{70 c^3 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}-\frac{35 c (b+2 c x) (2 c d-b e)}{12 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}+\frac{7 (b+2 c x) (2 c d-b e)}{12 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}-\frac{-2 a e+x (2 c d-b e)+b d}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}","\frac{35 c^2 (b+2 c x) (2 c d-b e)}{2 \left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{70 c^3 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}-\frac{35 c (b+2 c x) (2 c d-b e)}{12 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}+\frac{7 (b+2 c x) (2 c d-b e)}{12 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}-\frac{-2 a e+x (2 c d-b e)+b d}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}",1,"-(b*d - 2*a*e + (2*c*d - b*e)*x)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4) + (7*(2*c*d - b*e)*(b + 2*c*x))/(12*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) - (35*c*(2*c*d - b*e)*(b + 2*c*x))/(12*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (35*c^2*(2*c*d - b*e)*(b + 2*c*x))/(2*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (70*c^3*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(9/2)","A",6,4,18,0.2222,1,"{638, 614, 618, 206}"
2226,1,171,0,0.0698263,"\int \frac{1}{\left(a+b x+c x^2\right)^5} \, dx","Int[(a + b*x + c*x^2)^(-5),x]","\frac{35 c^3 (b+2 c x)}{\left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{35 c^2 (b+2 c x)}{6 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}-\frac{140 c^4 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}+\frac{7 c (b+2 c x)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}-\frac{b+2 c x}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}","\frac{35 c^3 (b+2 c x)}{\left(b^2-4 a c\right)^4 \left(a+b x+c x^2\right)}-\frac{35 c^2 (b+2 c x)}{6 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^2}-\frac{140 c^4 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2}}+\frac{7 c (b+2 c x)}{6 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^3}-\frac{b+2 c x}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^4}",1,"-(b + 2*c*x)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4) + (7*c*(b + 2*c*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) - (35*c^2*(b + 2*c*x))/(6*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (35*c^3*(b + 2*c*x))/((b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (140*c^4*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(9/2)","A",6,3,12,0.2500,1,"{614, 618, 206}"
2227,1,1324,0,13.9007968,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)^5} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^5),x]","\frac{\log (d+e x) e^9}{\left(c d^2-b e d+a e^2\right)^5}-\frac{\log \left(c x^2+b x+a\right) e^9}{2 \left(c d^2-b e d+a e^2\right)^5}-\frac{\left(140 c^9 d^9-90 c^8 e (7 b d-8 a e) d^7+72 c^7 e^2 \left(15 b^2 d^2-35 a b e d+21 a^2 e^2\right) d^5-84 c^6 e^3 \left(10 b^3 d^3-36 a b^2 e d^2+45 a^2 b e^2 d-20 a^3 e^3\right) d^3+252 c^5 e^4 \left(b^4 d^4-5 a b^3 e d^3+10 a^2 b^2 e^2 d^2-10 a^3 b e^3 d+5 a^4 e^4\right) d-b^9 e^9-630 a^4 b c^4 e^9+420 a^3 b^3 c^3 e^9-126 a^2 b^5 c^2 e^9+18 a b^7 c e^9\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2} \left(c d^2-e (b d-a e)\right)^5}+\frac{2 e^7 b^8+c d e^6 b^7+c e^5 \left(c d^2-31 a e^2\right) b^6+c^2 d e^4 \left(c d^2-14 a e^2\right) b^5-c^2 e^3 \left(125 c^2 d^4+13 a c e^2 d^2-178 a^2 e^4\right) b^4+c^3 d e^2 \left(295 c^2 d^4+492 a c e^2 d^2+69 a^2 e^4\right) b^3-c^3 e \left(245 c^3 d^6+725 a c^2 e^2 d^4+699 a^2 c e^4 d^2+443 a^3 e^6\right) b^2+2 c^4 d \left(35 c^3 d^6+145 a c^2 e^2 d^4+233 a^2 c e^4 d^2+187 a^3 e^6\right) b+256 a^4 c^4 e^7+2 c (2 c d-b e) \left(35 c^6 d^6-5 c^5 e (21 b d-29 a e) d^4+c^4 e^2 \left(95 b^2 d^2-290 a b e d+233 a^2 e^2\right) d^2-b^6 e^6-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left(7 b^2 d^2-44 a b e d+82 a^2 e^2\right)-c^3 e^3 \left(15 b^3 d^3-101 a b^2 e d^2+233 a^2 b e^2 d-187 a^3 e^3\right)\right) x}{2 \left(b^2-4 a c\right)^4 \left(c d^2-b e d+a e^2\right)^4 \left(c x^2+b x+a\right)}+\frac{5 a c e \left(7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right) (2 c d-b e)^2-2 c \left(35 c^4 d^4-10 c^3 e (7 b d-11 a e) d^2+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)+c^2 e^2 \left(25 b^2 d^2-110 a b e d+123 a^2 e^2\right)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(70 c^4 d^4-15 c^3 e (7 b d-10 a e) d^2+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)+3 c^2 e^2 \left(5 b^2 d^2-25 a b e d+32 a^2 e^2\right)\right)}{12 \left(b^2-4 a c\right)^3 \left(c d^2-b e d+a e^2\right)^3 \left(c x^2+b x+a\right)^2}-\frac{7 a c e (2 c d-b e)^2-2 c \left(7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right)}{12 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 \left(c x^2+b x+a\right)^3}-\frac{-e b^2+c d b+2 a c e+c (2 c d-b e) x}{4 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \left(c x^2+b x+a\right)^4}","\frac{\log (d+e x) e^9}{\left(c d^2-b e d+a e^2\right)^5}-\frac{\log \left(c x^2+b x+a\right) e^9}{2 \left(c d^2-b e d+a e^2\right)^5}-\frac{\left(140 c^9 d^9-90 c^8 e (7 b d-8 a e) d^7+72 c^7 e^2 \left(15 b^2 d^2-35 a b e d+21 a^2 e^2\right) d^5-84 c^6 e^3 \left(10 b^3 d^3-36 a b^2 e d^2+45 a^2 b e^2 d-20 a^3 e^3\right) d^3+252 c^5 e^4 \left(b^4 d^4-5 a b^3 e d^3+10 a^2 b^2 e^2 d^2-10 a^3 b e^3 d+5 a^4 e^4\right) d-b^9 e^9-630 a^4 b c^4 e^9+420 a^3 b^3 c^3 e^9-126 a^2 b^5 c^2 e^9+18 a b^7 c e^9\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2} \left(c d^2-e (b d-a e)\right)^5}+\frac{2 e^7 b^8+c d e^6 b^7+c e^5 \left(c d^2-31 a e^2\right) b^6+c^2 d e^4 \left(c d^2-14 a e^2\right) b^5-c^2 e^3 \left(125 c^2 d^4+13 a c e^2 d^2-178 a^2 e^4\right) b^4+c^3 d e^2 \left(295 c^2 d^4+492 a c e^2 d^2+69 a^2 e^4\right) b^3-c^3 e \left(245 c^3 d^6+725 a c^2 e^2 d^4+699 a^2 c e^4 d^2+443 a^3 e^6\right) b^2+2 c^4 d \left(35 c^3 d^6+145 a c^2 e^2 d^4+233 a^2 c e^4 d^2+187 a^3 e^6\right) b+256 a^4 c^4 e^7+2 c (2 c d-b e) \left(35 c^6 d^6-5 c^5 e (21 b d-29 a e) d^4+c^4 e^2 \left(95 b^2 d^2-290 a b e d+233 a^2 e^2\right) d^2-b^6 e^6-3 b^4 c e^5 (b d-5 a e)-b^2 c^2 e^4 \left(7 b^2 d^2-44 a b e d+82 a^2 e^2\right)-c^3 e^3 \left(15 b^3 d^3-101 a b^2 e d^2+233 a^2 b e^2 d-187 a^3 e^3\right)\right) x}{2 \left(b^2-4 a c\right)^4 \left(c d^2-b e d+a e^2\right)^4 \left(c x^2+b x+a\right)}+\frac{5 a c e \left(7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right) (2 c d-b e)^2-2 c \left(35 c^4 d^4-10 c^3 e (7 b d-11 a e) d^2+3 b^4 e^4+2 b^2 c e^3 (5 b d-17 a e)+c^2 e^2 \left(25 b^2 d^2-110 a b e d+123 a^2 e^2\right)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(70 c^4 d^4-15 c^3 e (7 b d-10 a e) d^2+6 b^4 e^4+2 b^2 c e^3 (5 b d-24 a e)+3 c^2 e^2 \left(5 b^2 d^2-25 a b e d+32 a^2 e^2\right)\right)}{12 \left(b^2-4 a c\right)^3 \left(c d^2-b e d+a e^2\right)^3 \left(c x^2+b x+a\right)^2}-\frac{7 a c e (2 c d-b e)^2-2 c \left(7 c^2 d^2-2 b^2 e^2-c e (7 b d-15 a e)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(14 c^2 d^2-4 b^2 e^2-c e (7 b d-16 a e)\right)}{12 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 \left(c x^2+b x+a\right)^3}-\frac{-e b^2+c d b+2 a c e+c (2 c d-b e) x}{4 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \left(c x^2+b x+a\right)^4}",1,"-(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^4) - (7*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(14*c^2*d^2 - 4*b^2*e^2 - c*e*(7*b*d - 16*a*e)) - 2*c*(2*c*d - b*e)*(7*c^2*d^2 - 2*b^2*e^2 - c*e*(7*b*d - 15*a*e))*x)/(12*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)^3) + (5*a*c*e*(2*c*d - b*e)^2*(7*c^2*d^2 - 2*b^2*e^2 - c*e*(7*b*d - 15*a*e)) - (b*c*d - b^2*e + 2*a*c*e)*(70*c^4*d^4 + 6*b^4*e^4 + 2*b^2*c*e^3*(5*b*d - 24*a*e) - 15*c^3*d^2*e*(7*b*d - 10*a*e) + 3*c^2*e^2*(5*b^2*d^2 - 25*a*b*d*e + 32*a^2*e^2)) - 2*c*(2*c*d - b*e)*(35*c^4*d^4 + 3*b^4*e^4 + 2*b^2*c*e^3*(5*b*d - 17*a*e) - 10*c^3*d^2*e*(7*b*d - 11*a*e) + c^2*e^2*(25*b^2*d^2 - 110*a*b*d*e + 123*a^2*e^2))*x)/(12*(b^2 - 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^3*(a + b*x + c*x^2)^2) + (b^7*c*d*e^6 + 2*b^8*e^7 + 256*a^4*c^4*e^7 + b^6*c*e^5*(c*d^2 - 31*a*e^2) + b^5*c^2*d*e^4*(c*d^2 - 14*a*e^2) - b^4*c^2*e^3*(125*c^2*d^4 + 13*a*c*d^2*e^2 - 178*a^2*e^4) + b^3*c^3*d*e^2*(295*c^2*d^4 + 492*a*c*d^2*e^2 + 69*a^2*e^4) + 2*b*c^4*d*(35*c^3*d^6 + 145*a*c^2*d^4*e^2 + 233*a^2*c*d^2*e^4 + 187*a^3*e^6) - b^2*c^3*e*(245*c^3*d^6 + 725*a*c^2*d^4*e^2 + 699*a^2*c*d^2*e^4 + 443*a^3*e^6) + 2*c*(2*c*d - b*e)*(35*c^6*d^6 - b^6*e^6 - 5*c^5*d^4*e*(21*b*d - 29*a*e) - 3*b^4*c*e^5*(b*d - 5*a*e) - b^2*c^2*e^4*(7*b^2*d^2 - 44*a*b*d*e + 82*a^2*e^2) + c^4*d^2*e^2*(95*b^2*d^2 - 290*a*b*d*e + 233*a^2*e^2) - c^3*e^3*(15*b^3*d^3 - 101*a*b^2*d^2*e + 233*a^2*b*d*e^2 - 187*a^3*e^3))*x)/(2*(b^2 - 4*a*c)^4*(c*d^2 - b*d*e + a*e^2)^4*(a + b*x + c*x^2)) - ((140*c^9*d^9 - b^9*e^9 + 18*a*b^7*c*e^9 - 126*a^2*b^5*c^2*e^9 + 420*a^3*b^3*c^3*e^9 - 630*a^4*b*c^4*e^9 - 90*c^8*d^7*e*(7*b*d - 8*a*e) + 72*c^7*d^5*e^2*(15*b^2*d^2 - 35*a*b*d*e + 21*a^2*e^2) - 84*c^6*d^3*e^3*(10*b^3*d^3 - 36*a*b^2*d^2*e + 45*a^2*b*d*e^2 - 20*a^3*e^3) + 252*c^5*d*e^4*(b^4*d^4 - 5*a*b^3*d^3*e + 10*a^2*b^2*d^2*e^2 - 10*a^3*b*d*e^3 + 5*a^4*e^4))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(9/2)*(c*d^2 - e*(b*d - a*e))^5) + (e^9*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^5 - (e^9*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^5)","A",10,7,20,0.3500,1,"{740, 822, 800, 634, 618, 206, 628}"
2228,1,1761,0,15.1958743,"\int \frac{1}{(d+e x)^2 \left(a+b x+c x^2\right)^5} \, dx","Int[1/((d + e*x)^2*(a + b*x + c*x^2)^5),x]","\frac{5 (2 c d-b e) \log (d+e x) e^9}{\left(c d^2-b e d+a e^2\right)^6}-\frac{5 (2 c d-b e) \log \left(c x^2+b x+a\right) e^9}{2 \left(c d^2-b e d+a e^2\right)^6}+\frac{5 \left(14 c^8 d^8-4 c^7 e (14 b d-19 a e) d^6+c^6 e^2 \left(79 b^2 d^2-228 a b e d+176 a^2 e^2\right) d^4-c^5 e^3 \left(41 b^3 d^3-197 a b^2 e d^2+352 a^2 b e^2 d-244 a^3 e^3\right) d^2-b^8 e^8+b^6 c e^7 (b d+15 a e)+b^4 c^2 e^6 \left(b^2 d^2-16 a b e d-82 a^2 e^2\right)+b^2 c^3 e^5 \left(b^3 d^3-15 a b^2 e d^2+95 a^2 b e^2 d+187 a^3 e^3\right)+c^4 e^4 \left(b^4 d^4-14 a b^3 e d^3+81 a^2 b^2 e^2 d^2-244 a^3 b e^3 d-126 a^4 e^4\right)\right) e}{\left(b^2-4 a c\right)^4 \left(c d^2-b e d+a e^2\right)^5 (d+e x)}-\frac{5 \left(28 c^{10} d^{10}-20 c^9 e (7 b d-9 a e) d^8+18 c^8 e^2 \left(15 b^2 d^2-40 a b e d+28 a^2 e^2\right) d^6-24 c^7 e^3 \left(10 b^3 d^3-42 a b^2 e d^2+63 a^2 b e^2 d-35 a^3 e^3\right) d^4+84 c^6 e^4 \left(b^4 d^4-6 a b^3 e d^3+15 a^2 b^2 e^2 d^2-20 a^3 b e^3 d+15 a^4 e^4\right) d^2+b^{10} e^{10}-252 a^4 c^5 e^9 (5 b d+a e)+210 a^3 b^2 c^4 e^9 (4 b d+3 a e)-84 a^2 b^4 c^3 e^9 (3 b d+5 a e)+18 a b^6 c^2 e^9 (2 b d+7 a e)-2 b^8 c e^9 (b d+9 a e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2} \left(c d^2-e (b d-a e)\right)^6}-\frac{5 \left(2 a c e \left(14 c^4 d^4-4 c^3 e (7 b d-12 a e) d^2+2 b^4 e^4+b^2 c e^3 (5 b d-21 a e)+3 c^2 e^2 \left(3 b^2 d^2-16 a b e d+22 a^2 e^2\right)\right) (2 c d-b e)^2-3 c \left(14 c^6 d^6-2 c^5 e (21 b d-31 a e) d^4+c^4 e^2 \left(37 b^2 d^2-124 a b e d+114 a^2 e^2\right) d^2-b^6 e^6-2 b^4 c e^5 (b d-7 a e)-b^2 c^2 e^4 \left(3 b^2 d^2-26 a b e d+69 a^2 e^2\right)-2 c^3 e^3 \left(2 b^3 d^3-18 a b^2 e d^2+57 a^2 b e^2 d-65 a^3 e^3\right)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(42 c^6 d^6-2 c^5 e (49 b d-65 a e) d^4+c^4 e^2 \left(55 b^2 d^2-164 a b e d+150 a^2 e^2\right) d^2-3 b^6 e^6-2 b^4 c e^5 (b d-17 a e)+b^2 c^2 e^4 \left(b^2 d^2+16 a b e d-123 a^2 e^2\right)+6 c^3 e^3 \left(b^3 d^3-4 a b^2 e d^2-3 a^2 b e^2 d+21 a^3 e^3\right)\right)\right)}{6 \left(b^2-4 a c\right)^4 \left(c d^2-b e d+a e^2\right)^4 (d+e x) \left(c x^2+b x+a\right)}+\frac{3 a c e \left(14 c^2 d^2-5 b^2 e^2-2 c e (7 b d-17 a e)\right) (2 c d-b e)^2-5 c \left(14 c^4 d^4-4 c^3 e (7 b d-12 a e) d^2+2 b^4 e^4+b^2 c e^3 (5 b d-21 a e)+3 c^2 e^2 \left(3 b^2 d^2-16 a b e d+22 a^2 e^2\right)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(70 c^4 d^4-2 c^3 e (49 b d-78 a e) d^2+10 b^4 e^4+5 b^2 c e^3 (2 b d-15 a e)+3 c^2 e^2 \left(b^2 d^2-18 a b e d+42 a^2 e^2\right)\right)}{12 \left(b^2-4 a c\right)^3 \left(c d^2-b e d+a e^2\right)^3 (d+e x) \left(c x^2+b x+a\right)^2}-\frac{8 a c e (2 c d-b e)^2-c \left(14 c^2 d^2-5 b^2 e^2-2 c e (7 b d-17 a e)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(14 c^2 d^2-5 b^2 e^2-6 c e (b d-3 a e)\right)}{12 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 (d+e x) \left(c x^2+b x+a\right)^3}-\frac{-e b^2+c d b+2 a c e+c (2 c d-b e) x}{4 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (d+e x) \left(c x^2+b x+a\right)^4}","\frac{5 (2 c d-b e) \log (d+e x) e^9}{\left(c d^2-b e d+a e^2\right)^6}-\frac{5 (2 c d-b e) \log \left(c x^2+b x+a\right) e^9}{2 \left(c d^2-b e d+a e^2\right)^6}+\frac{5 \left(14 c^8 d^8-4 c^7 e (14 b d-19 a e) d^6+c^6 e^2 \left(79 b^2 d^2-228 a b e d+176 a^2 e^2\right) d^4-c^5 e^3 \left(41 b^3 d^3-197 a b^2 e d^2+352 a^2 b e^2 d-244 a^3 e^3\right) d^2-b^8 e^8+b^6 c e^7 (b d+15 a e)+b^4 c^2 e^6 \left(b^2 d^2-16 a b e d-82 a^2 e^2\right)+b^2 c^3 e^5 \left(b^3 d^3-15 a b^2 e d^2+95 a^2 b e^2 d+187 a^3 e^3\right)+c^4 e^4 \left(b^4 d^4-14 a b^3 e d^3+81 a^2 b^2 e^2 d^2-244 a^3 b e^3 d-126 a^4 e^4\right)\right) e}{\left(b^2-4 a c\right)^4 \left(c d^2-b e d+a e^2\right)^5 (d+e x)}-\frac{5 \left(28 c^{10} d^{10}-20 c^9 e (7 b d-9 a e) d^8+18 c^8 e^2 \left(15 b^2 d^2-40 a b e d+28 a^2 e^2\right) d^6-24 c^7 e^3 \left(10 b^3 d^3-42 a b^2 e d^2+63 a^2 b e^2 d-35 a^3 e^3\right) d^4+84 c^6 e^4 \left(b^4 d^4-6 a b^3 e d^3+15 a^2 b^2 e^2 d^2-20 a^3 b e^3 d+15 a^4 e^4\right) d^2+b^{10} e^{10}-252 a^4 c^5 e^9 (5 b d+a e)+210 a^3 b^2 c^4 e^9 (4 b d+3 a e)-84 a^2 b^4 c^3 e^9 (3 b d+5 a e)+18 a b^6 c^2 e^9 (2 b d+7 a e)-2 b^8 c e^9 (b d+9 a e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{9/2} \left(c d^2-e (b d-a e)\right)^6}-\frac{5 \left(2 a c e \left(14 c^4 d^4-4 c^3 e (7 b d-12 a e) d^2+2 b^4 e^4+b^2 c e^3 (5 b d-21 a e)+3 c^2 e^2 \left(3 b^2 d^2-16 a b e d+22 a^2 e^2\right)\right) (2 c d-b e)^2-3 c \left(14 c^6 d^6-2 c^5 e (21 b d-31 a e) d^4+c^4 e^2 \left(37 b^2 d^2-124 a b e d+114 a^2 e^2\right) d^2-b^6 e^6-2 b^4 c e^5 (b d-7 a e)-b^2 c^2 e^4 \left(3 b^2 d^2-26 a b e d+69 a^2 e^2\right)-2 c^3 e^3 \left(2 b^3 d^3-18 a b^2 e d^2+57 a^2 b e^2 d-65 a^3 e^3\right)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(42 c^6 d^6-2 c^5 e (49 b d-65 a e) d^4+c^4 e^2 \left(55 b^2 d^2-164 a b e d+150 a^2 e^2\right) d^2-3 b^6 e^6-2 b^4 c e^5 (b d-17 a e)+b^2 c^2 e^4 \left(b^2 d^2+16 a b e d-123 a^2 e^2\right)+6 c^3 e^3 \left(b^3 d^3-4 a b^2 e d^2-3 a^2 b e^2 d+21 a^3 e^3\right)\right)\right)}{6 \left(b^2-4 a c\right)^4 \left(c d^2-b e d+a e^2\right)^4 (d+e x) \left(c x^2+b x+a\right)}+\frac{3 a c e \left(14 c^2 d^2-5 b^2 e^2-2 c e (7 b d-17 a e)\right) (2 c d-b e)^2-5 c \left(14 c^4 d^4-4 c^3 e (7 b d-12 a e) d^2+2 b^4 e^4+b^2 c e^3 (5 b d-21 a e)+3 c^2 e^2 \left(3 b^2 d^2-16 a b e d+22 a^2 e^2\right)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(70 c^4 d^4-2 c^3 e (49 b d-78 a e) d^2+10 b^4 e^4+5 b^2 c e^3 (2 b d-15 a e)+3 c^2 e^2 \left(b^2 d^2-18 a b e d+42 a^2 e^2\right)\right)}{12 \left(b^2-4 a c\right)^3 \left(c d^2-b e d+a e^2\right)^3 (d+e x) \left(c x^2+b x+a\right)^2}-\frac{8 a c e (2 c d-b e)^2-c \left(14 c^2 d^2-5 b^2 e^2-2 c e (7 b d-17 a e)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(14 c^2 d^2-5 b^2 e^2-6 c e (b d-3 a e)\right)}{12 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 (d+e x) \left(c x^2+b x+a\right)^3}-\frac{-e b^2+c d b+2 a c e+c (2 c d-b e) x}{4 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (d+e x) \left(c x^2+b x+a\right)^4}",1,"(5*e*(14*c^8*d^8 - b^8*e^8 - 4*c^7*d^6*e*(14*b*d - 19*a*e) + b^6*c*e^7*(b*d + 15*a*e) + b^4*c^2*e^6*(b^2*d^2 - 16*a*b*d*e - 82*a^2*e^2) + c^6*d^4*e^2*(79*b^2*d^2 - 228*a*b*d*e + 176*a^2*e^2) - c^5*d^2*e^3*(41*b^3*d^3 - 197*a*b^2*d^2*e + 352*a^2*b*d*e^2 - 244*a^3*e^3) + b^2*c^3*e^5*(b^3*d^3 - 15*a*b^2*d^2*e + 95*a^2*b*d*e^2 + 187*a^3*e^3) + c^4*e^4*(b^4*d^4 - 14*a*b^3*d^3*e + 81*a^2*b^2*d^2*e^2 - 244*a^3*b*d*e^3 - 126*a^4*e^4)))/((b^2 - 4*a*c)^4*(c*d^2 - b*d*e + a*e^2)^5*(d + e*x)) - (b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^4) - (8*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(14*c^2*d^2 - 5*b^2*e^2 - 6*c*e*(b*d - 3*a*e)) - c*(2*c*d - b*e)*(14*c^2*d^2 - 5*b^2*e^2 - 2*c*e*(7*b*d - 17*a*e))*x)/(12*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*(a + b*x + c*x^2)^3) + (3*a*c*e*(2*c*d - b*e)^2*(14*c^2*d^2 - 5*b^2*e^2 - 2*c*e*(7*b*d - 17*a*e)) - (b*c*d - b^2*e + 2*a*c*e)*(70*c^4*d^4 + 10*b^4*e^4 - 2*c^3*d^2*e*(49*b*d - 78*a*e) + 5*b^2*c*e^3*(2*b*d - 15*a*e) + 3*c^2*e^2*(b^2*d^2 - 18*a*b*d*e + 42*a^2*e^2)) - 5*c*(2*c*d - b*e)*(14*c^4*d^4 + 2*b^4*e^4 + b^2*c*e^3*(5*b*d - 21*a*e) - 4*c^3*d^2*e*(7*b*d - 12*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 16*a*b*d*e + 22*a^2*e^2))*x)/(12*(b^2 - 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)*(a + b*x + c*x^2)^2) - (5*(2*a*c*e*(2*c*d - b*e)^2*(14*c^4*d^4 + 2*b^4*e^4 + b^2*c*e^3*(5*b*d - 21*a*e) - 4*c^3*d^2*e*(7*b*d - 12*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 16*a*b*d*e + 22*a^2*e^2)) - (b*c*d - b^2*e + 2*a*c*e)*(42*c^6*d^6 - 3*b^6*e^6 - 2*c^5*d^4*e*(49*b*d - 65*a*e) - 2*b^4*c*e^5*(b*d - 17*a*e) + b^2*c^2*e^4*(b^2*d^2 + 16*a*b*d*e - 123*a^2*e^2) + c^4*d^2*e^2*(55*b^2*d^2 - 164*a*b*d*e + 150*a^2*e^2) + 6*c^3*e^3*(b^3*d^3 - 4*a*b^2*d^2*e - 3*a^2*b*d*e^2 + 21*a^3*e^3)) - 3*c*(2*c*d - b*e)*(14*c^6*d^6 - b^6*e^6 - 2*c^5*d^4*e*(21*b*d - 31*a*e) - 2*b^4*c*e^5*(b*d - 7*a*e) - b^2*c^2*e^4*(3*b^2*d^2 - 26*a*b*d*e + 69*a^2*e^2) + c^4*d^2*e^2*(37*b^2*d^2 - 124*a*b*d*e + 114*a^2*e^2) - 2*c^3*e^3*(2*b^3*d^3 - 18*a*b^2*d^2*e + 57*a^2*b*d*e^2 - 65*a^3*e^3))*x))/(6*(b^2 - 4*a*c)^4*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)*(a + b*x + c*x^2)) - (5*(28*c^10*d^10 + b^10*e^10 - 20*c^9*d^8*e*(7*b*d - 9*a*e) - 252*a^4*c^5*e^9*(5*b*d + a*e) + 210*a^3*b^2*c^4*e^9*(4*b*d + 3*a*e) - 84*a^2*b^4*c^3*e^9*(3*b*d + 5*a*e) + 18*a*b^6*c^2*e^9*(2*b*d + 7*a*e) - 2*b^8*c*e^9*(b*d + 9*a*e) + 18*c^8*d^6*e^2*(15*b^2*d^2 - 40*a*b*d*e + 28*a^2*e^2) - 24*c^7*d^4*e^3*(10*b^3*d^3 - 42*a*b^2*d^2*e + 63*a^2*b*d*e^2 - 35*a^3*e^3) + 84*c^6*d^2*e^4*(b^4*d^4 - 6*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^2 - 20*a^3*b*d*e^3 + 15*a^4*e^4))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(9/2)*(c*d^2 - e*(b*d - a*e))^6) + (5*e^9*(2*c*d - b*e)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^6 - (5*e^9*(2*c*d - b*e)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^6)","A",10,7,20,0.3500,1,"{740, 822, 800, 634, 618, 206, 628}"
2229,1,89,0,0.0825689,"\int \frac{1}{(1+2 x) \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/((1 + 2*x)*(2 + 3*x + 5*x^2)^3),x]","\frac{20 x+37}{434 \left(5 x^2+3 x+2\right)^2}+\frac{2 (2290 x+2609)}{47089 \left(5 x^2+3 x+2\right)}-\frac{16}{343} \log \left(5 x^2+3 x+2\right)+\frac{32}{343} \log (2 x+1)+\frac{125624 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{329623 \sqrt{31}}","\frac{20 x+37}{434 \left(5 x^2+3 x+2\right)^2}+\frac{2 (2290 x+2609)}{47089 \left(5 x^2+3 x+2\right)}-\frac{16}{343} \log \left(5 x^2+3 x+2\right)+\frac{32}{343} \log (2 x+1)+\frac{125624 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{329623 \sqrt{31}}",1,"(37 + 20*x)/(434*(2 + 3*x + 5*x^2)^2) + (2*(2609 + 2290*x))/(47089*(2 + 3*x + 5*x^2)) + (125624*ArcTan[(3 + 10*x)/Sqrt[31]])/(329623*Sqrt[31]) + (32*Log[1 + 2*x])/343 - (16*Log[2 + 3*x + 5*x^2])/343","A",8,7,20,0.3500,1,"{740, 822, 800, 634, 618, 204, 628}"
2230,1,114,0,0.0882789,"\int \frac{1}{(1+2 x)^2 \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/((1 + 2*x)^2*(2 + 3*x + 5*x^2)^3),x]","\frac{20 x+37}{434 (2 x+1) \left(5 x^2+3 x+2\right)^2}+\frac{5820 x+6427}{47089 (2 x+1) \left(5 x^2+3 x+2\right)}-\frac{192 \log \left(5 x^2+3 x+2\right)}{2401}-\frac{51516}{329623 (2 x+1)}+\frac{384 \log (2 x+1)}{2401}-\frac{1065012 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{2307361 \sqrt{31}}","\frac{20 x+37}{434 (2 x+1) \left(5 x^2+3 x+2\right)^2}+\frac{5820 x+6427}{47089 (2 x+1) \left(5 x^2+3 x+2\right)}-\frac{192 \log \left(5 x^2+3 x+2\right)}{2401}-\frac{51516}{329623 (2 x+1)}+\frac{384 \log (2 x+1)}{2401}-\frac{1065012 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{2307361 \sqrt{31}}",1,"-51516/(329623*(1 + 2*x)) + (37 + 20*x)/(434*(1 + 2*x)*(2 + 3*x + 5*x^2)^2) + (6427 + 5820*x)/(47089*(1 + 2*x)*(2 + 3*x + 5*x^2)) - (1065012*ArcTan[(3 + 10*x)/Sqrt[31]])/(2307361*Sqrt[31]) + (384*Log[1 + 2*x])/2401 - (192*Log[2 + 3*x + 5*x^2])/2401","A",8,7,20,0.3500,1,"{740, 822, 800, 634, 618, 204, 628}"
2231,1,110,0,0.0992217,"\int \frac{1}{(1+2 x) \left(2+3 x+5 x^2\right)^4} \, dx","Int[1/((1 + 2*x)*(2 + 3*x + 5*x^2)^4),x]","\frac{20 x+37}{651 \left(5 x^2+3 x+2\right)^3}+\frac{4 (203230 x+180133)}{10218313 \left(5 x^2+3 x+2\right)}+\frac{4 (1805 x+1983)}{141267 \left(5 x^2+3 x+2\right)^2}-\frac{64 \log \left(5 x^2+3 x+2\right)}{2401}+\frac{128 \log (2 x+1)}{2401}+\frac{19007376 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{71528191 \sqrt{31}}","\frac{20 x+37}{651 \left(5 x^2+3 x+2\right)^3}+\frac{4 (203230 x+180133)}{10218313 \left(5 x^2+3 x+2\right)}+\frac{4 (1805 x+1983)}{141267 \left(5 x^2+3 x+2\right)^2}-\frac{64 \log \left(5 x^2+3 x+2\right)}{2401}+\frac{128 \log (2 x+1)}{2401}+\frac{19007376 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{71528191 \sqrt{31}}",1,"(37 + 20*x)/(651*(2 + 3*x + 5*x^2)^3) + (4*(1983 + 1805*x))/(141267*(2 + 3*x + 5*x^2)^2) + (4*(180133 + 203230*x))/(10218313*(2 + 3*x + 5*x^2)) + (19007376*ArcTan[(3 + 10*x)/Sqrt[31]])/(71528191*Sqrt[31]) + (128*Log[1 + 2*x])/2401 - (64*Log[2 + 3*x + 5*x^2])/2401","A",9,7,20,0.3500,1,"{740, 822, 800, 634, 618, 204, 628}"
2232,1,142,0,0.1085021,"\int \frac{1}{(1+2 x)^2 \left(2+3 x+5 x^2\right)^4} \, dx","Int[1/((1 + 2*x)^2*(2 + 3*x + 5*x^2)^4),x]","\frac{20 x+37}{651 (2 x+1) \left(5 x^2+3 x+2\right)^3}+\frac{2 (603620 x+504757)}{10218313 (2 x+1) \left(5 x^2+3 x+2\right)}+\frac{2820 x+3047}{47089 (2 x+1) \left(5 x^2+3 x+2\right)^2}-\frac{1024 \log \left(5 x^2+3 x+2\right)}{16807}-\frac{6802312}{71528191 (2 x+1)}+\frac{2048 \log (2 x+1)}{16807}-\frac{116056984 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{500697337 \sqrt{31}}","\frac{20 x+37}{651 (2 x+1) \left(5 x^2+3 x+2\right)^3}+\frac{2 (603620 x+504757)}{10218313 (2 x+1) \left(5 x^2+3 x+2\right)}+\frac{2820 x+3047}{47089 (2 x+1) \left(5 x^2+3 x+2\right)^2}-\frac{1024 \log \left(5 x^2+3 x+2\right)}{16807}-\frac{6802312}{71528191 (2 x+1)}+\frac{2048 \log (2 x+1)}{16807}-\frac{116056984 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{500697337 \sqrt{31}}",1,"-6802312/(71528191*(1 + 2*x)) + (37 + 20*x)/(651*(1 + 2*x)*(2 + 3*x + 5*x^2)^3) + (3047 + 2820*x)/(47089*(1 + 2*x)*(2 + 3*x + 5*x^2)^2) + (2*(504757 + 603620*x))/(10218313*(1 + 2*x)*(2 + 3*x + 5*x^2)) - (116056984*ArcTan[(3 + 10*x)/Sqrt[31]])/(500697337*Sqrt[31]) + (2048*Log[1 + 2*x])/16807 - (1024*Log[2 + 3*x + 5*x^2])/16807","A",9,7,20,0.3500,1,"{740, 822, 800, 634, 618, 204, 628}"
2233,1,47,0,0.026857,"\int \frac{7-3 x}{-5+2 x+x^2} \, dx","Int[(7 - 3*x)/(-5 + 2*x + x^2),x]","-\frac{1}{6} \left(9-5 \sqrt{6}\right) \log \left(x-\sqrt{6}+1\right)-\frac{1}{6} \left(9+5 \sqrt{6}\right) \log \left(x+\sqrt{6}+1\right)","-\frac{1}{6} \left(9-5 \sqrt{6}\right) \log \left(x-\sqrt{6}+1\right)-\frac{1}{6} \left(9+5 \sqrt{6}\right) \log \left(x+\sqrt{6}+1\right)",1,"-((9 - 5*Sqrt[6])*Log[1 - Sqrt[6] + x])/6 - ((9 + 5*Sqrt[6])*Log[1 + Sqrt[6] + x])/6","A",3,2,16,0.1250,1,"{632, 31}"
2234,1,41,0,0.0274052,"\int \frac{1}{(-1+x) \left(1+x+x^2\right)} \, dx","Int[1/((-1 + x)*(1 + x + x^2)),x]","-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[1 - x]/3 - Log[1 + x + x^2]/6","A",6,6,14,0.4286,1,"{705, 31, 634, 618, 204, 628}"
2235,1,114,0,0.2615963,"\int \frac{2 \left(\left(\frac{a}{b}\right)^{\frac{1}{n}}-x \cos \left(\frac{(-1+2 k) \pi }{n}\right)\right)}{\left(\frac{a}{b}\right)^{2/n}+x^2-2 \left(\frac{a}{b}\right)^{\frac{1}{n}} x \cos \left(\frac{(-1+2 k) \pi }{n}\right)} \, dx","Int[(2*((a/b)^n^(-1) - x*Cos[((-1 + 2*k)*Pi)/n]))/((a/b)^(2/n) + x^2 - 2*(a/b)^n^(-1)*x*Cos[((-1 + 2*k)*Pi)/n]),x]","2 \sin \left(\frac{\pi -2 \pi  k}{n}\right) \tan ^{-1}\left(\left(\frac{a}{b}\right)^{-1/n} \csc \left(\frac{\pi -2 \pi  k}{n}\right) \left(x-\left(\frac{a}{b}\right)^{\frac{1}{n}} \cos \left(\frac{\pi -2 \pi  k}{n}\right)\right)\right)-\cos \left(\frac{\pi -2 \pi  k}{n}\right) \log \left(-2 x \left(\frac{a}{b}\right)^{\frac{1}{n}} \cos \left(\frac{\pi -2 \pi  k}{n}\right)+\left(\frac{a}{b}\right)^{2/n}+x^2\right)","2 \sin \left(\frac{\pi -2 \pi  k}{n}\right) \tan ^{-1}\left(\left(\frac{a}{b}\right)^{-1/n} \csc \left(\frac{\pi -2 \pi  k}{n}\right) \left(x-\left(\frac{a}{b}\right)^{\frac{1}{n}} \cos \left(\frac{\pi -2 \pi  k}{n}\right)\right)\right)-\cos \left(\frac{\pi -2 \pi  k}{n}\right) \log \left(-2 x \left(\frac{a}{b}\right)^{\frac{1}{n}} \cos \left(\frac{\pi -2 \pi  k}{n}\right)+\left(\frac{a}{b}\right)^{2/n}+x^2\right)",1,"-(Cos[(Pi - 2*k*Pi)/n]*Log[(a/b)^(2/n) + x^2 - 2*(a/b)^n^(-1)*x*Cos[(Pi - 2*k*Pi)/n]]) + 2*ArcTan[((x - (a/b)^n^(-1)*Cos[(Pi - 2*k*Pi)/n])*Csc[(Pi - 2*k*Pi)/n])/(a/b)^n^(-1)]*Sin[(Pi - 2*k*Pi)/n]","A",5,5,66,0.07576,1,"{12, 634, 618, 204, 628}"
2236,1,40,0,0.0172645,"\int \frac{x^4}{2+13 x+15 x^2} \, dx","Int[x^4/(2 + 13*x + 15*x^2),x]","\frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375}","\frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375}",1,"(139*x)/3375 - (13*x^2)/450 + x^3/45 - (16*Log[2 + 3*x])/567 + Log[1 + 5*x]/4375","A",5,3,16,0.1875,1,"{701, 632, 31}"
2237,1,33,0,0.0161926,"\int \frac{x^3}{2+13 x+15 x^2} \, dx","Int[x^3/(2 + 13*x + 15*x^2),x]","\frac{x^2}{30}-\frac{13 x}{225}+\frac{8}{189} \log (3 x+2)-\frac{1}{875} \log (5 x+1)","\frac{x^2}{30}-\frac{13 x}{225}+\frac{8}{189} \log (3 x+2)-\frac{1}{875} \log (5 x+1)",1,"(-13*x)/225 + x^2/30 + (8*Log[2 + 3*x])/189 - Log[1 + 5*x]/875","A",5,3,16,0.1875,1,"{701, 632, 31}"
2238,1,26,0,0.0124871,"\int \frac{x^2}{2+13 x+15 x^2} \, dx","Int[x^2/(2 + 13*x + 15*x^2),x]","\frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1)","\frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1)",1,"x/15 - (4*Log[2 + 3*x])/63 + Log[1 + 5*x]/175","A",4,3,16,0.1875,1,"{703, 632, 31}"
2239,1,21,0,0.0058873,"\int \frac{x}{2+13 x+15 x^2} \, dx","Int[x/(2 + 13*x + 15*x^2),x]","\frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1)","\frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1)",1,"(2*Log[2 + 3*x])/21 - Log[1 + 5*x]/35","A",3,2,14,0.1429,1,"{632, 31}"
2240,1,21,0,0.0058359,"\int \frac{1}{2+13 x+15 x^2} \, dx","Int[(2 + 13*x + 15*x^2)^(-1),x]","\frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2)","\frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2)",1,"-Log[2 + 3*x]/7 + Log[1 + 5*x]/7","A",3,2,12,0.1667,1,"{616, 31}"
2241,1,27,0,0.0119905,"\int \frac{1}{x \left(2+13 x+15 x^2\right)} \, dx","Int[1/(x*(2 + 13*x + 15*x^2)),x]","\frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1)","\frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1)",1,"Log[x]/2 + (3*Log[2 + 3*x])/14 - (5*Log[1 + 5*x])/7","A",5,4,16,0.2500,1,"{705, 29, 632, 31}"
2242,1,34,0,0.0259163,"\int \frac{1}{x^2 \left(2+13 x+15 x^2\right)} \, dx","Int[1/(x^2*(2 + 13*x + 15*x^2)),x]","-\frac{1}{2 x}-\frac{13 \log (x)}{4}-\frac{9}{28} \log (3 x+2)+\frac{25}{7} \log (5 x+1)","-\frac{1}{2 x}-\frac{13 \log (x)}{4}-\frac{9}{28} \log (3 x+2)+\frac{25}{7} \log (5 x+1)",1,"-1/(2*x) - (13*Log[x])/4 - (9*Log[2 + 3*x])/28 + (25*Log[1 + 5*x])/7","A",3,2,16,0.1250,1,"{709, 800}"
2243,1,41,0,0.0283698,"\int \frac{1}{x^3 \left(2+13 x+15 x^2\right)} \, dx","Int[1/(x^3*(2 + 13*x + 15*x^2)),x]","-\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1)","-\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1)",1,"-1/(4*x^2) + 13/(4*x) + (139*Log[x])/8 + (27*Log[2 + 3*x])/56 - (125*Log[1 + 5*x])/7","A",3,2,16,0.1250,1,"{709, 800}"
2244,1,48,0,0.0374681,"\int \frac{1}{x^4 \left(2+13 x+15 x^2\right)} \, dx","Int[1/(x^4*(2 + 13*x + 15*x^2)),x]","\frac{13}{8 x^2}-\frac{1}{6 x^3}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1)","\frac{13}{8 x^2}-\frac{1}{6 x^3}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1)",1,"-1/(6*x^3) + 13/(8*x^2) - 139/(8*x) - (1417*Log[x])/16 - (81*Log[2 + 3*x])/112 + (625*Log[1 + 5*x])/7","A",3,2,16,0.1250,1,"{709, 800}"
2245,1,40,0,0.0253351,"\int \frac{x^5}{2 x+13 x^2+15 x^3} \, dx","Int[x^5/(2*x + 13*x^2 + 15*x^3),x]","\frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375}","\frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375}",1,"(139*x)/3375 - (13*x^2)/450 + x^3/45 - (16*Log[2 + 3*x])/567 + Log[1 + 5*x]/4375","A",6,4,20,0.2000,1,"{1585, 701, 632, 31}"
2246,1,33,0,0.0233262,"\int \frac{x^4}{2 x+13 x^2+15 x^3} \, dx","Int[x^4/(2*x + 13*x^2 + 15*x^3),x]","\frac{x^2}{30}-\frac{13 x}{225}+\frac{8}{189} \log (3 x+2)-\frac{1}{875} \log (5 x+1)","\frac{x^2}{30}-\frac{13 x}{225}+\frac{8}{189} \log (3 x+2)-\frac{1}{875} \log (5 x+1)",1,"(-13*x)/225 + x^2/30 + (8*Log[2 + 3*x])/189 - Log[1 + 5*x]/875","A",6,4,20,0.2000,1,"{1585, 701, 632, 31}"
2247,1,26,0,0.0191958,"\int \frac{x^3}{2 x+13 x^2+15 x^3} \, dx","Int[x^3/(2*x + 13*x^2 + 15*x^3),x]","\frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1)","\frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1)",1,"x/15 - (4*Log[2 + 3*x])/63 + Log[1 + 5*x]/175","A",5,4,20,0.2000,1,"{1585, 703, 632, 31}"
2248,1,21,0,0.0132027,"\int \frac{x^2}{2 x+13 x^2+15 x^3} \, dx","Int[x^2/(2*x + 13*x^2 + 15*x^3),x]","\frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1)","\frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1)",1,"(2*Log[2 + 3*x])/21 - Log[1 + 5*x]/35","A",4,3,20,0.1500,1,"{1585, 632, 31}"
2249,1,21,0,0.0106777,"\int \frac{x}{2 x+13 x^2+15 x^3} \, dx","Int[x/(2*x + 13*x^2 + 15*x^3),x]","\frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2)","\frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2)",1,"-Log[2 + 3*x]/7 + Log[1 + 5*x]/7","A",4,3,18,0.1667,1,"{1585, 616, 31}"
2250,1,27,0,0.0139869,"\int \frac{1}{2 x+13 x^2+15 x^3} \, dx","Int[(2*x + 13*x^2 + 15*x^3)^(-1),x]","\frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1)","\frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1)",1,"Log[x]/2 + (3*Log[2 + 3*x])/14 - (5*Log[1 + 5*x])/7","A",6,5,16,0.3125,1,"{1594, 705, 29, 632, 31}"
2251,1,34,0,0.0281488,"\int \frac{1}{x \left(2 x+13 x^2+15 x^3\right)} \, dx","Int[1/(x*(2*x + 13*x^2 + 15*x^3)),x]","-\frac{1}{2 x}-\frac{13 \log (x)}{4}-\frac{9}{28} \log (3 x+2)+\frac{25}{7} \log (5 x+1)","-\frac{1}{2 x}-\frac{13 \log (x)}{4}-\frac{9}{28} \log (3 x+2)+\frac{25}{7} \log (5 x+1)",1,"-1/(2*x) - (13*Log[x])/4 - (9*Log[2 + 3*x])/28 + (25*Log[1 + 5*x])/7","A",4,3,20,0.1500,1,"{1585, 709, 800}"
2252,1,41,0,0.0314923,"\int \frac{1}{x^2 \left(2 x+13 x^2+15 x^3\right)} \, dx","Int[1/(x^2*(2*x + 13*x^2 + 15*x^3)),x]","-\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1)","-\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1)",1,"-1/(4*x^2) + 13/(4*x) + (139*Log[x])/8 + (27*Log[2 + 3*x])/56 - (125*Log[1 + 5*x])/7","A",4,3,20,0.1500,1,"{1585, 709, 800}"
2253,1,48,0,0.034138,"\int \frac{1}{x^3 \left(2 x+13 x^2+15 x^3\right)} \, dx","Int[1/(x^3*(2*x + 13*x^2 + 15*x^3)),x]","\frac{13}{8 x^2}-\frac{1}{6 x^3}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1)","\frac{13}{8 x^2}-\frac{1}{6 x^3}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1)",1,"-1/(6*x^3) + 13/(8*x^2) - 139/(8*x) - (1417*Log[x])/16 - (81*Log[2 + 3*x])/112 + (625*Log[1 + 5*x])/7","A",4,3,20,0.1500,1,"{1585, 709, 800}"
2254,1,12,0,0.0064843,"\int \frac{x}{4+4 x+x^2} \, dx","Int[x/(4 + 4*x + x^2),x]","\frac{2}{x+2}+\log (x+2)","\frac{2}{x+2}+\log (x+2)",1,"2/(2 + x) + Log[2 + x]","A",3,2,12,0.1667,1,"{27, 43}"
2255,1,26,0,0.0134394,"\int \frac{x}{5+2 x+x^2} \, dx","Int[x/(5 + 2*x + x^2),x]","\frac{1}{2} \log \left(x^2+2 x+5\right)-\frac{1}{2} \tan ^{-1}\left(\frac{x+1}{2}\right)","\frac{1}{2} \log \left(x^2+2 x+5\right)-\frac{1}{2} \tan ^{-1}\left(\frac{x+1}{2}\right)",1,"-ArcTan[(1 + x)/2]/2 + Log[5 + 2*x + x^2]/2","A",4,4,12,0.3333,1,"{634, 618, 204, 628}"
2256,1,17,0,0.00531,"\int \frac{x}{6-5 x+x^2} \, dx","Int[x/(6 - 5*x + x^2),x]","3 \log (3-x)-2 \log (2-x)","3 \log (3-x)-2 \log (2-x)",1,"-2*Log[2 - x] + 3*Log[3 - x]","A",3,2,12,0.1667,1,"{632, 31}"
2257,1,26,0,0.0065948,"\int \frac{x}{\left(2+2 x+x^2\right)^2} \, dx","Int[x/(2 + 2*x + x^2)^2,x]","-\frac{x+2}{2 \left(x^2+2 x+2\right)}-\frac{1}{2} \tan ^{-1}(x+1)","-\frac{x+2}{2 \left(x^2+2 x+2\right)}-\frac{1}{2} \tan ^{-1}(x+1)",1,"-(2 + x)/(2*(2 + 2*x + x^2)) - ArcTan[1 + x]/2","A",3,3,12,0.2500,1,"{638, 617, 204}"
2258,1,54,0,0.0205593,"\int \frac{x}{\left(1+x+x^2\right)^3} \, dx","Int[x/(1 + x + x^2)^3,x]","-\frac{x+2}{6 \left(x^2+x+1\right)^2}-\frac{2 x+1}{6 \left(x^2+x+1\right)}-\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{x+2}{6 \left(x^2+x+1\right)^2}-\frac{2 x+1}{6 \left(x^2+x+1\right)}-\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-(2 + x)/(6*(1 + x + x^2)^2) - (1 + 2*x)/(6*(1 + x + x^2)) - (2*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3])","A",4,4,10,0.4000,1,"{638, 614, 618, 204}"
2259,1,32,0,0.0192937,"\int \frac{x^2}{1+x+x^2} \, dx","Int[x^2/(1 + x + x^2),x]","-\frac{1}{2} \log \left(x^2+x+1\right)+x-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{2} \log \left(x^2+x+1\right)+x-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"x - ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3] - Log[1 + x + x^2]/2","A",5,5,12,0.4167,1,"{703, 634, 618, 204, 628}"
2260,1,18,0,0.0079984,"\int \frac{x^2}{2-3 x+x^2} \, dx","Int[x^2/(2 - 3*x + x^2),x]","x-\log (1-x)+4 \log (2-x)","x-\log (1-x)+4 \log (2-x)",1,"x - Log[1 - x] + 4*Log[2 - x]","A",4,3,14,0.2143,1,"{703, 632, 31}"
2261,1,20,0,0.0082817,"\int \frac{x^2}{-6+x+x^2} \, dx","Int[x^2/(-6 + x + x^2),x]","x+\frac{4}{5} \log (2-x)-\frac{9}{5} \log (x+3)","x+\frac{4}{5} \log (2-x)-\frac{9}{5} \log (x+3)",1,"x + (4*Log[2 - x])/5 - (9*Log[3 + x])/5","A",4,3,12,0.2500,1,"{703, 632, 31}"
2262,1,23,0,0.0076848,"\int \frac{x^2}{\left(2+2 x+x^2\right)^2} \, dx","Int[x^2/(2 + 2*x + x^2)^2,x]","\tan ^{-1}(x+1)-\frac{x (x+2)}{2 \left(x^2+2 x+2\right)}","\frac{1}{x^2+2 x+2}+\tan ^{-1}(x+1)",1,"-(x*(2 + x))/(2*(2 + 2*x + x^2)) + ArcTan[1 + x]","A",3,3,14,0.2143,1,"{722, 617, 204}"
2263,1,27,0,0.0121766,"\int \frac{x^3}{2-3 x+x^2} \, dx","Int[x^3/(2 - 3*x + x^2),x]","\frac{x^2}{2}+3 x-\log (1-x)+8 \log (2-x)","\frac{x^2}{2}+3 x-\log (1-x)+8 \log (2-x)",1,"3*x + x^2/2 - Log[1 - x] + 8*Log[2 - x]","A",5,3,14,0.2143,1,"{701, 632, 31}"
2264,1,22,0,0.0100248,"\int \frac{x^3}{1+2 x+x^2} \, dx","Int[x^3/(1 + 2*x + x^2),x]","\frac{x^2}{2}-2 x+\frac{1}{x+1}+3 \log (x+1)","\frac{x^2}{2}-2 x+\frac{1}{x+1}+3 \log (x+1)",1,"-2*x + x^2/2 + (1 + x)^(-1) + 3*Log[1 + x]","A",3,2,14,0.1429,1,"{27, 43}"
2265,1,26,0,0.0101849,"\int \frac{x^3}{1-2 x+x^2} \, dx","Int[x^3/(1 - 2*x + x^2),x]","\frac{x^2}{2}+2 x+\frac{1}{1-x}+3 \log (1-x)","\frac{x^2}{2}+2 x+\frac{1}{1-x}+3 \log (1-x)",1,"(1 - x)^(-1) + 2*x + x^2/2 + 3*Log[1 - x]","A",3,2,14,0.1429,1,"{27, 43}"
2266,1,29,0,0.0147971,"\int \frac{x^4}{4+4 x+x^2} \, dx","Int[x^4/(4 + 4*x + x^2),x]","\frac{x^3}{3}-2 x^2+12 x-\frac{16}{x+2}-32 \log (x+2)","\frac{x^3}{3}-2 x^2+12 x-\frac{16}{x+2}-32 \log (x+2)",1,"12*x - 2*x^2 + x^3/3 - 16/(2 + x) - 32*Log[2 + x]","A",3,2,14,0.1429,1,"{27, 43}"
2267,1,33,0,0.0186396,"\int \frac{1}{x \left(1+x+x^2\right)} \, dx","Int[1/(x*(1 + x + x^2)),x]","-\frac{1}{2} \log \left(x^2+x+1\right)+\log (x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{2} \log \left(x^2+x+1\right)+\log (x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[x] - Log[1 + x + x^2]/2","A",6,6,12,0.5000,1,"{705, 29, 634, 618, 204, 628}"
2268,1,75,0,0.0381153,"\int (d+e x)^{5/2} \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^(5/2)*(a + b*x + c*x^2),x]","\frac{2 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right)}{7 e^3}-\frac{2 (d+e x)^{9/2} (2 c d-b e)}{9 e^3}+\frac{2 c (d+e x)^{11/2}}{11 e^3}","\frac{2 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right)}{7 e^3}-\frac{2 (d+e x)^{9/2} (2 c d-b e)}{9 e^3}+\frac{2 c (d+e x)^{11/2}}{11 e^3}",1,"(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(7/2))/(7*e^3) - (2*(2*c*d - b*e)*(d + e*x)^(9/2))/(9*e^3) + (2*c*(d + e*x)^(11/2))/(11*e^3)","A",2,1,20,0.05000,1,"{698}"
2269,1,75,0,0.0291398,"\int (d+e x)^{3/2} \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^(3/2)*(a + b*x + c*x^2),x]","\frac{2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}{5 e^3}-\frac{2 (d+e x)^{7/2} (2 c d-b e)}{7 e^3}+\frac{2 c (d+e x)^{9/2}}{9 e^3}","\frac{2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}{5 e^3}-\frac{2 (d+e x)^{7/2} (2 c d-b e)}{7 e^3}+\frac{2 c (d+e x)^{9/2}}{9 e^3}",1,"(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2))/(5*e^3) - (2*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^3) + (2*c*(d + e*x)^(9/2))/(9*e^3)","A",2,1,20,0.05000,1,"{698}"
2270,1,75,0,0.0296745,"\int \sqrt{d+e x} \left(a+b x+c x^2\right) \, dx","Int[Sqrt[d + e*x]*(a + b*x + c*x^2),x]","\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}{3 e^3}-\frac{2 (d+e x)^{5/2} (2 c d-b e)}{5 e^3}+\frac{2 c (d+e x)^{7/2}}{7 e^3}","\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}{3 e^3}-\frac{2 (d+e x)^{5/2} (2 c d-b e)}{5 e^3}+\frac{2 c (d+e x)^{7/2}}{7 e^3}",1,"(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2))/(3*e^3) - (2*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^3) + (2*c*(d + e*x)^(7/2))/(7*e^3)","A",2,1,20,0.05000,1,"{698}"
2271,1,73,0,0.0299421,"\int \frac{a+b x+c x^2}{\sqrt{d+e x}} \, dx","Int[(a + b*x + c*x^2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}{e^3}-\frac{2 (d+e x)^{3/2} (2 c d-b e)}{3 e^3}+\frac{2 c (d+e x)^{5/2}}{5 e^3}","\frac{2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}{e^3}-\frac{2 (d+e x)^{3/2} (2 c d-b e)}{3 e^3}+\frac{2 c (d+e x)^{5/2}}{5 e^3}",1,"(2*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x])/e^3 - (2*(2*c*d - b*e)*(d + e*x)^(3/2))/(3*e^3) + (2*c*(d + e*x)^(5/2))/(5*e^3)","A",2,1,20,0.05000,1,"{698}"
2272,1,71,0,0.0306339,"\int \frac{a+b x+c x^2}{(d+e x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)/(d + e*x)^(3/2),x]","-\frac{2 \left(a e^2-b d e+c d^2\right)}{e^3 \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} (2 c d-b e)}{e^3}+\frac{2 c (d+e x)^{3/2}}{3 e^3}","-\frac{2 \left(a e^2-b d e+c d^2\right)}{e^3 \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} (2 c d-b e)}{e^3}+\frac{2 c (d+e x)^{3/2}}{3 e^3}",1,"(-2*(c*d^2 - b*d*e + a*e^2))/(e^3*Sqrt[d + e*x]) - (2*(2*c*d - b*e)*Sqrt[d + e*x])/e^3 + (2*c*(d + e*x)^(3/2))/(3*e^3)","A",2,1,20,0.05000,1,"{698}"
2273,1,71,0,0.0321167,"\int \frac{a+b x+c x^2}{(d+e x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)/(d + e*x)^(5/2),x]","-\frac{2 \left(a e^2-b d e+c d^2\right)}{3 e^3 (d+e x)^{3/2}}+\frac{2 (2 c d-b e)}{e^3 \sqrt{d+e x}}+\frac{2 c \sqrt{d+e x}}{e^3}","-\frac{2 \left(a e^2-b d e+c d^2\right)}{3 e^3 (d+e x)^{3/2}}+\frac{2 (2 c d-b e)}{e^3 \sqrt{d+e x}}+\frac{2 c \sqrt{d+e x}}{e^3}",1,"(-2*(c*d^2 - b*d*e + a*e^2))/(3*e^3*(d + e*x)^(3/2)) + (2*(2*c*d - b*e))/(e^3*Sqrt[d + e*x]) + (2*c*Sqrt[d + e*x])/e^3","A",2,1,20,0.05000,1,"{698}"
2274,1,73,0,0.029924,"\int \frac{a+b x+c x^2}{(d+e x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)/(d + e*x)^(7/2),x]","-\frac{2 \left(a e^2-b d e+c d^2\right)}{5 e^3 (d+e x)^{5/2}}+\frac{2 (2 c d-b e)}{3 e^3 (d+e x)^{3/2}}-\frac{2 c}{e^3 \sqrt{d+e x}}","-\frac{2 \left(a e^2-b d e+c d^2\right)}{5 e^3 (d+e x)^{5/2}}+\frac{2 (2 c d-b e)}{3 e^3 (d+e x)^{3/2}}-\frac{2 c}{e^3 \sqrt{d+e x}}",1,"(-2*(c*d^2 - b*d*e + a*e^2))/(5*e^3*(d + e*x)^(5/2)) + (2*(2*c*d - b*e))/(3*e^3*(d + e*x)^(3/2)) - (2*c)/(e^3*Sqrt[d + e*x])","A",2,1,20,0.05000,1,"{698}"
2275,1,166,0,0.092938,"\int (d+e x)^{5/2} \left(a+b x+c x^2\right)^2 \, dx","Int[(d + e*x)^(5/2)*(a + b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{11/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{11 e^5}-\frac{4 (d+e x)^{9/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{9 e^5}+\frac{2 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right)^2}{7 e^5}-\frac{4 c (d+e x)^{13/2} (2 c d-b e)}{13 e^5}+\frac{2 c^2 (d+e x)^{15/2}}{15 e^5}","\frac{2 (d+e x)^{11/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{11 e^5}-\frac{4 (d+e x)^{9/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{9 e^5}+\frac{2 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right)^2}{7 e^5}-\frac{4 c (d+e x)^{13/2} (2 c d-b e)}{13 e^5}+\frac{2 c^2 (d+e x)^{15/2}}{15 e^5}",1,"(2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(7/2))/(7*e^5) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(9/2))/(9*e^5) + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(11/2))/(11*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(13/2))/(13*e^5) + (2*c^2*(d + e*x)^(15/2))/(15*e^5)","A",2,1,22,0.04545,1,"{698}"
2276,1,166,0,0.0733657,"\int (d+e x)^{3/2} \left(a+b x+c x^2\right)^2 \, dx","Int[(d + e*x)^(3/2)*(a + b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{9/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{9 e^5}-\frac{4 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{7 e^5}+\frac{2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)^2}{5 e^5}-\frac{4 c (d+e x)^{11/2} (2 c d-b e)}{11 e^5}+\frac{2 c^2 (d+e x)^{13/2}}{13 e^5}","\frac{2 (d+e x)^{9/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{9 e^5}-\frac{4 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{7 e^5}+\frac{2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)^2}{5 e^5}-\frac{4 c (d+e x)^{11/2} (2 c d-b e)}{11 e^5}+\frac{2 c^2 (d+e x)^{13/2}}{13 e^5}",1,"(2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(5/2))/(5*e^5) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(7/2))/(7*e^5) + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(9/2))/(9*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^5) + (2*c^2*(d + e*x)^(13/2))/(13*e^5)","A",2,1,22,0.04545,1,"{698}"
2277,1,166,0,0.0724684,"\int \sqrt{d+e x} \left(a+b x+c x^2\right)^2 \, dx","Int[Sqrt[d + e*x]*(a + b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{7/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{7 e^5}-\frac{4 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^5}+\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^2}{3 e^5}-\frac{4 c (d+e x)^{9/2} (2 c d-b e)}{9 e^5}+\frac{2 c^2 (d+e x)^{11/2}}{11 e^5}","\frac{2 (d+e x)^{7/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{7 e^5}-\frac{4 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^5}+\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^2}{3 e^5}-\frac{4 c (d+e x)^{9/2} (2 c d-b e)}{9 e^5}+\frac{2 c^2 (d+e x)^{11/2}}{11 e^5}",1,"(2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2))/(3*e^5) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2))/(5*e^5) + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(7/2))/(7*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(9/2))/(9*e^5) + (2*c^2*(d + e*x)^(11/2))/(11*e^5)","A",2,1,22,0.04545,1,"{698}"
2278,1,164,0,0.0727377,"\int \frac{\left(a+b x+c x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[(a + b*x + c*x^2)^2/Sqrt[d + e*x],x]","\frac{2 (d+e x)^{5/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^5}-\frac{4 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5}+\frac{2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}{e^5}-\frac{4 c (d+e x)^{7/2} (2 c d-b e)}{7 e^5}+\frac{2 c^2 (d+e x)^{9/2}}{9 e^5}","\frac{2 (d+e x)^{5/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^5}-\frac{4 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5}+\frac{2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}{e^5}-\frac{4 c (d+e x)^{7/2} (2 c d-b e)}{7 e^5}+\frac{2 c^2 (d+e x)^{9/2}}{9 e^5}",1,"(2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x])/e^5 - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2))/(3*e^5) + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(5/2))/(5*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^5) + (2*c^2*(d + e*x)^(9/2))/(9*e^5)","A",2,1,22,0.04545,1,"{698}"
2279,1,162,0,0.0700174,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^(3/2),x]","\frac{2 (d+e x)^{3/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{3 e^5}-\frac{4 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^5}-\frac{2 \left(a e^2-b d e+c d^2\right)^2}{e^5 \sqrt{d+e x}}-\frac{4 c (d+e x)^{5/2} (2 c d-b e)}{5 e^5}+\frac{2 c^2 (d+e x)^{7/2}}{7 e^5}","\frac{2 (d+e x)^{3/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{3 e^5}-\frac{4 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^5}-\frac{2 \left(a e^2-b d e+c d^2\right)^2}{e^5 \sqrt{d+e x}}-\frac{4 c (d+e x)^{5/2} (2 c d-b e)}{5 e^5}+\frac{2 c^2 (d+e x)^{7/2}}{7 e^5}",1,"(-2*(c*d^2 - b*d*e + a*e^2)^2)/(e^5*Sqrt[d + e*x]) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x])/e^5 + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(3/2))/(3*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^5) + (2*c^2*(d + e*x)^(7/2))/(7*e^5)","A",2,1,22,0.04545,1,"{698}"
2280,1,162,0,0.0745995,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^5}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^5 \sqrt{d+e x}}-\frac{2 \left(a e^2-b d e+c d^2\right)^2}{3 e^5 (d+e x)^{3/2}}-\frac{4 c (d+e x)^{3/2} (2 c d-b e)}{3 e^5}+\frac{2 c^2 (d+e x)^{5/2}}{5 e^5}","\frac{2 \sqrt{d+e x} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^5}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^5 \sqrt{d+e x}}-\frac{2 \left(a e^2-b d e+c d^2\right)^2}{3 e^5 (d+e x)^{3/2}}-\frac{4 c (d+e x)^{3/2} (2 c d-b e)}{3 e^5}+\frac{2 c^2 (d+e x)^{5/2}}{5 e^5}",1,"(-2*(c*d^2 - b*d*e + a*e^2)^2)/(3*e^5*(d + e*x)^(3/2)) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(e^5*Sqrt[d + e*x]) + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*Sqrt[d + e*x])/e^5 - (4*c*(2*c*d - b*e)*(d + e*x)^(3/2))/(3*e^5) + (2*c^2*(d + e*x)^(5/2))/(5*e^5)","A",2,1,22,0.04545,1,"{698}"
2281,1,162,0,0.0708952,"\int \frac{\left(a+b x+c x^2\right)^2}{(d+e x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x)^(7/2),x]","-\frac{2 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^5 \sqrt{d+e x}}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5 (d+e x)^{3/2}}-\frac{2 \left(a e^2-b d e+c d^2\right)^2}{5 e^5 (d+e x)^{5/2}}-\frac{4 c \sqrt{d+e x} (2 c d-b e)}{e^5}+\frac{2 c^2 (d+e x)^{3/2}}{3 e^5}","-\frac{2 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^5 \sqrt{d+e x}}+\frac{4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^5 (d+e x)^{3/2}}-\frac{2 \left(a e^2-b d e+c d^2\right)^2}{5 e^5 (d+e x)^{5/2}}-\frac{4 c \sqrt{d+e x} (2 c d-b e)}{e^5}+\frac{2 c^2 (d+e x)^{3/2}}{3 e^5}",1,"(-2*(c*d^2 - b*d*e + a*e^2)^2)/(5*e^5*(d + e*x)^(5/2)) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(3*e^5*(d + e*x)^(3/2)) - (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))/(e^5*Sqrt[d + e*x]) - (4*c*(2*c*d - b*e)*Sqrt[d + e*x])/e^5 + (2*c^2*(d + e*x)^(3/2))/(3*e^5)","A",2,1,22,0.04545,1,"{698}"
2282,1,286,0,0.1809409,"\int (d+e x)^{5/2} \left(a+b x+c x^2\right)^3 \, dx","Int[(d + e*x)^(5/2)*(a + b*x + c*x^2)^3,x]","\frac{2 c (d+e x)^{15/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{13/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{13 e^7}+\frac{6 (d+e x)^{11/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{11 e^7}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^7}+\frac{2 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right)^3}{7 e^7}-\frac{6 c^2 (d+e x)^{17/2} (2 c d-b e)}{17 e^7}+\frac{2 c^3 (d+e x)^{19/2}}{19 e^7}","\frac{2 c (d+e x)^{15/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{13/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{13 e^7}+\frac{6 (d+e x)^{11/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{11 e^7}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^7}+\frac{2 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right)^3}{7 e^7}-\frac{6 c^2 (d+e x)^{17/2} (2 c d-b e)}{17 e^7}+\frac{2 c^3 (d+e x)^{19/2}}{19 e^7}",1,"(2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(7/2))/(7*e^7) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(9/2))/(3*e^7) + (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(11/2))/(11*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(13/2))/(13*e^7) + (2*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(15/2))/(5*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(17/2))/(17*e^7) + (2*c^3*(d + e*x)^(19/2))/(19*e^7)","A",2,1,22,0.04545,1,"{698}"
2283,1,286,0,0.1291179,"\int (d+e x)^{3/2} \left(a+b x+c x^2\right)^3 \, dx","Int[(d + e*x)^(3/2)*(a + b*x + c*x^2)^3,x]","\frac{6 c (d+e x)^{13/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{13 e^7}-\frac{2 (d+e x)^{11/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{11 e^7}+\frac{2 (d+e x)^{9/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^7}-\frac{6 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{7 e^7}+\frac{2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)^3}{5 e^7}-\frac{2 c^2 (d+e x)^{15/2} (2 c d-b e)}{5 e^7}+\frac{2 c^3 (d+e x)^{17/2}}{17 e^7}","\frac{6 c (d+e x)^{13/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{13 e^7}-\frac{2 (d+e x)^{11/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{11 e^7}+\frac{2 (d+e x)^{9/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^7}-\frac{6 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{7 e^7}+\frac{2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)^3}{5 e^7}-\frac{2 c^2 (d+e x)^{15/2} (2 c d-b e)}{5 e^7}+\frac{2 c^3 (d+e x)^{17/2}}{17 e^7}",1,"(2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(5/2))/(5*e^7) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(7/2))/(7*e^7) + (2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(9/2))/(3*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(11/2))/(11*e^7) + (6*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(13/2))/(13*e^7) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(15/2))/(5*e^7) + (2*c^3*(d + e*x)^(17/2))/(17*e^7)","A",2,1,22,0.04545,1,"{698}"
2284,1,286,0,0.129942,"\int \sqrt{d+e x} \left(a+b x+c x^2\right)^3 \, dx","Int[Sqrt[d + e*x]*(a + b*x + c*x^2)^3,x]","\frac{6 c (d+e x)^{11/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{11 e^7}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{9 e^7}+\frac{6 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7}-\frac{6 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^7}+\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^3}{3 e^7}-\frac{6 c^2 (d+e x)^{13/2} (2 c d-b e)}{13 e^7}+\frac{2 c^3 (d+e x)^{15/2}}{15 e^7}","\frac{6 c (d+e x)^{11/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{11 e^7}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{9 e^7}+\frac{6 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7}-\frac{6 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^7}+\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^3}{3 e^7}-\frac{6 c^2 (d+e x)^{13/2} (2 c d-b e)}{13 e^7}+\frac{2 c^3 (d+e x)^{15/2}}{15 e^7}",1,"(2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(3/2))/(3*e^7) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(5/2))/(5*e^7) + (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(7/2))/(7*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(9/2))/(9*e^7) + (6*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(11/2))/(11*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(13/2))/(13*e^7) + (2*c^3*(d + e*x)^(15/2))/(15*e^7)","A",2,1,22,0.04545,1,"{698}"
2285,1,282,0,0.1278723,"\int \frac{\left(a+b x+c x^2\right)^3}{\sqrt{d+e x}} \, dx","Int[(a + b*x + c*x^2)^3/Sqrt[d + e*x],x]","\frac{2 c (d+e x)^{9/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^7}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{7 e^7}+\frac{6 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7}+\frac{2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^3}{e^7}-\frac{6 c^2 (d+e x)^{11/2} (2 c d-b e)}{11 e^7}+\frac{2 c^3 (d+e x)^{13/2}}{13 e^7}","\frac{2 c (d+e x)^{9/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^7}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{7 e^7}+\frac{6 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7}+\frac{2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^3}{e^7}-\frac{6 c^2 (d+e x)^{11/2} (2 c d-b e)}{11 e^7}+\frac{2 c^3 (d+e x)^{13/2}}{13 e^7}",1,"(2*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[d + e*x])/e^7 - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2))/e^7 + (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(5/2))/(5*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(7/2))/(7*e^7) + (2*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(9/2))/(3*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^7) + (2*c^3*(d + e*x)^(13/2))/(13*e^7)","A",2,1,22,0.04545,1,"{698}"
2286,1,280,0,0.127591,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^(3/2),x]","\frac{6 c (d+e x)^{7/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^7}+\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}-\frac{6 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7}-\frac{2 \left(a e^2-b d e+c d^2\right)^3}{e^7 \sqrt{d+e x}}-\frac{2 c^2 (d+e x)^{9/2} (2 c d-b e)}{3 e^7}+\frac{2 c^3 (d+e x)^{11/2}}{11 e^7}","\frac{6 c (d+e x)^{7/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^7}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^7}+\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}-\frac{6 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7}-\frac{2 \left(a e^2-b d e+c d^2\right)^3}{e^7 \sqrt{d+e x}}-\frac{2 c^2 (d+e x)^{9/2} (2 c d-b e)}{3 e^7}+\frac{2 c^3 (d+e x)^{11/2}}{11 e^7}",1,"(-2*(c*d^2 - b*d*e + a*e^2)^3)/(e^7*Sqrt[d + e*x]) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x])/e^7 + (2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(3/2))/e^7 - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(5/2))/(5*e^7) + (6*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(7/2))/(7*e^7) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(9/2))/(3*e^7) + (2*c^3*(d + e*x)^(11/2))/(11*e^7)","A",2,1,22,0.04545,1,"{698}"
2287,1,282,0,0.1315646,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^(5/2),x]","\frac{6 c (d+e x)^{5/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^7}+\frac{6 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}+\frac{6 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7 \sqrt{d+e x}}-\frac{2 \left(a e^2-b d e+c d^2\right)^3}{3 e^7 (d+e x)^{3/2}}-\frac{6 c^2 (d+e x)^{7/2} (2 c d-b e)}{7 e^7}+\frac{2 c^3 (d+e x)^{9/2}}{9 e^7}","\frac{6 c (d+e x)^{5/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^7}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^7}+\frac{6 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}+\frac{6 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7 \sqrt{d+e x}}-\frac{2 \left(a e^2-b d e+c d^2\right)^3}{3 e^7 (d+e x)^{3/2}}-\frac{6 c^2 (d+e x)^{7/2} (2 c d-b e)}{7 e^7}+\frac{2 c^3 (d+e x)^{9/2}}{9 e^7}",1,"(-2*(c*d^2 - b*d*e + a*e^2)^3)/(3*e^7*(d + e*x)^(3/2)) + (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(e^7*Sqrt[d + e*x]) + (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*Sqrt[d + e*x])/e^7 - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(3/2))/(3*e^7) + (6*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(5/2))/(5*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^7) + (2*c^3*(d + e*x)^(9/2))/(9*e^7)","A",2,1,22,0.04545,1,"{698}"
2288,1,278,0,0.1341663,"\int \frac{\left(a+b x+c x^2\right)^3}{(d+e x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x)^(7/2),x]","\frac{2 c (d+e x)^{3/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^7}-\frac{6 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 \sqrt{d+e x}}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7 (d+e x)^{3/2}}-\frac{2 \left(a e^2-b d e+c d^2\right)^3}{5 e^7 (d+e x)^{5/2}}-\frac{6 c^2 (d+e x)^{5/2} (2 c d-b e)}{5 e^7}+\frac{2 c^3 (d+e x)^{7/2}}{7 e^7}","\frac{2 c (d+e x)^{3/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^7}-\frac{6 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 \sqrt{d+e x}}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^7 (d+e x)^{3/2}}-\frac{2 \left(a e^2-b d e+c d^2\right)^3}{5 e^7 (d+e x)^{5/2}}-\frac{6 c^2 (d+e x)^{5/2} (2 c d-b e)}{5 e^7}+\frac{2 c^3 (d+e x)^{7/2}}{7 e^7}",1,"(-2*(c*d^2 - b*d*e + a*e^2)^3)/(5*e^7*(d + e*x)^(5/2)) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(e^7*(d + e*x)^(3/2)) - (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^7*Sqrt[d + e*x]) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*Sqrt[d + e*x])/e^7 + (2*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(3/2))/e^7 - (6*c^2*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^7) + (2*c^3*(d + e*x)^(7/2))/(7*e^7)","A",2,1,22,0.04545,1,"{698}"
2289,1,459,0,4.4319095,"\int \frac{(d+e x)^{5/2}}{a+b x+c x^2} \, dx","Int[(d + e*x)^(5/2)/(a + b*x + c*x^2),x]","-\frac{\sqrt{2} \left(-3 c^2 d e \left(-d \sqrt{b^2-4 a c}+2 a e+b d\right)+c e^2 \left(-3 b d \sqrt{b^2-4 a c}-a e \sqrt{b^2-4 a c}+3 a b e+3 b^2 d\right)-b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+2 c^3 d^3\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(-3 c^2 d e \left(d \sqrt{b^2-4 a c}+2 a e+b d\right)+c e^2 \left(3 b \left(d \sqrt{b^2-4 a c}+a e\right)+a e \sqrt{b^2-4 a c}+3 b^2 d\right)-b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+2 c^3 d^3\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 e \sqrt{d+e x} (2 c d-b e)}{c^2}+\frac{2 e (d+e x)^{3/2}}{3 c}","-\frac{\sqrt{2} \left(-3 c^2 d e \left(-d \sqrt{b^2-4 a c}+2 a e+b d\right)+c e^2 \left(-3 b d \sqrt{b^2-4 a c}-a e \sqrt{b^2-4 a c}+3 a b e+3 b^2 d\right)-b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+2 c^3 d^3\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(-3 c^2 d e \left(d \sqrt{b^2-4 a c}+2 a e+b d\right)+c e^2 \left(3 b \left(d \sqrt{b^2-4 a c}+a e\right)+a e \sqrt{b^2-4 a c}+3 b^2 d\right)-b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+2 c^3 d^3\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 e \sqrt{d+e x} (2 c d-b e)}{c^2}+\frac{2 e (d+e x)^{3/2}}{3 c}",1,"(2*e*(2*c*d - b*e)*Sqrt[d + e*x])/c^2 + (2*e*(d + e*x)^(3/2))/(3*c) - (Sqrt[2]*(2*c^3*d^3 - b^2*(b - Sqrt[b^2 - 4*a*c])*e^3 - 3*c^2*d*e*(b*d - Sqrt[b^2 - 4*a*c]*d + 2*a*e) + c*e^2*(3*b^2*d - 3*b*Sqrt[b^2 - 4*a*c]*d + 3*a*b*e - a*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]])/(c^(5/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*(2*c^3*d^3 - b^2*(b + Sqrt[b^2 - 4*a*c])*e^3 - 3*c^2*d*e*(b*d + Sqrt[b^2 - 4*a*c]*d + 2*a*e) + c*e^2*(3*b^2*d + a*Sqrt[b^2 - 4*a*c]*e + 3*b*(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^(5/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,22,0.2273,1,"{703, 824, 826, 1166, 208}"
2290,1,322,0,1.2158711,"\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}"
2291,1,198,0,0.2885921,"\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}"
2292,1,199,0,0.2957396,"\int \frac{1}{\sqrt{d+e x} \left(a+b x+c x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*(a + b*x + c*x^2)),x]","\frac{2 \sqrt{2} \sqrt{c} \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{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{2} \sqrt{c} \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{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}","\frac{2 \sqrt{2} \sqrt{c} \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{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 \sqrt{2} \sqrt{c} \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{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}",1,"(-2*Sqrt[2]*Sqrt[c]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (2*Sqrt[2]*Sqrt[c]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",4,3,22,0.1364,1,"{707, 1093, 208}"
2293,1,310,0,0.7287916,"\int \frac{1}{(d+e x)^{3/2} \left(a+b x+c x^2\right)} \, dx","Int[1/((d + e*x)^(3/2)*(a + b*x + c*x^2)),x]","-\frac{\sqrt{2} \sqrt{c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\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)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{2} \sqrt{c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\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)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{2 e}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}","-\frac{\sqrt{2} \sqrt{c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\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)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{2} \sqrt{c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\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)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{2 e}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}",1,"(-2*e)/((c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[c]*(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[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) + (Sqrt[2]*Sqrt[c]*(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[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",5,4,22,0.1818,1,"{709, 826, 1166, 208}"
2294,1,414,0,1.54601,"\int \frac{1}{(d+e x)^{5/2} \left(a+b x+c x^2\right)} \, dx","Int[1/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x]","-\frac{\sqrt{2} \sqrt{c} \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(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)} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{2} \sqrt{c} \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(\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)} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}","-\frac{\sqrt{2} \sqrt{c} \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(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)} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{2} \sqrt{c} \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(\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)} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}",1,"(-2*e)/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) - (2*e*(2*c*d - b*e))/((c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[c]*(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]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2) + (Sqrt[2]*Sqrt[c]*(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]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2)","A",6,5,22,0.2273,1,"{709, 828, 826, 1166, 208}"
2295,1,691,0,15.9623205,"\int \frac{(d+e x)^{7/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)^(7/2)/(a + b*x + c*x^2)^2,x]","\frac{e \sqrt{d+e x} \left(-2 c e (5 a e+b d)+3 b^2 e^2+2 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)}+\frac{\left(c^2 e^2 \left(-3 b d \left(d \sqrt{b^2-4 a c}+12 a e\right)+2 a e \left(13 d \sqrt{b^2-4 a c}-10 a e\right)+3 b^2 d^2\right)-2 c^3 d^2 e \left(-d \sqrt{b^2-4 a c}-18 a e+8 b d\right)+b c e^3 \left(-5 b d \sqrt{b^2-4 a c}-13 a e \sqrt{b^2-4 a c}+19 a b e+5 b^2 d\right)-3 b^3 e^4 \left(b-\sqrt{b^2-4 a c}\right)+8 c^4 d^4\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^{5/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(c^2 e^2 \left(3 b d \left(d \sqrt{b^2-4 a c}-12 a e\right)-2 a e \left(13 d \sqrt{b^2-4 a c}+10 a e\right)+3 b^2 d^2\right)-2 c^3 d^2 e \left(d \sqrt{b^2-4 a c}-18 a e+8 b d\right)+b c e^3 \left(5 b d \sqrt{b^2-4 a c}+13 a e \sqrt{b^2-4 a c}+19 a b e+5 b^2 d\right)-3 b^3 e^4 \left(\sqrt{b^2-4 a c}+b\right)+8 c^4 d^4\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^{5/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{5/2} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e (d+e x)^{3/2} (2 c d-b e)}{c \left(b^2-4 a c\right)}","\frac{e \sqrt{d+e x} \left(-2 c e (5 a e+b d)+3 b^2 e^2+2 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)}+\frac{\left(c^2 e^2 \left(-3 b d \left(d \sqrt{b^2-4 a c}+12 a e\right)+2 a e \left(13 d \sqrt{b^2-4 a c}-10 a e\right)+3 b^2 d^2\right)-2 c^3 d^2 e \left(-d \sqrt{b^2-4 a c}-18 a e+8 b d\right)+b c e^3 \left(-5 b d \sqrt{b^2-4 a c}-13 a e \sqrt{b^2-4 a c}+19 a b e+5 b^2 d\right)-3 b^3 e^4 \left(b-\sqrt{b^2-4 a c}\right)+8 c^4 d^4\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^{5/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(c^2 e^2 \left(3 b d \left(d \sqrt{b^2-4 a c}-12 a e\right)-2 a e \left(13 d \sqrt{b^2-4 a c}+10 a e\right)+3 b^2 d^2\right)-2 c^3 d^2 e \left(d \sqrt{b^2-4 a c}-18 a e+8 b d\right)+b c e^3 \left(5 b d \sqrt{b^2-4 a c}+13 a e \sqrt{b^2-4 a c}+19 a b e+5 b^2 d\right)-3 b^3 e^4 \left(\sqrt{b^2-4 a c}+b\right)+8 c^4 d^4\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^{5/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{5/2} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e (d+e x)^{3/2} (2 c d-b e)}{c \left(b^2-4 a c\right)}",1,"(e*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))*Sqrt[d + e*x])/(c^2*(b^2 - 4*a*c)) + (e*(2*c*d - b*e)*(d + e*x)^(3/2))/(c*(b^2 - 4*a*c)) - ((d + e*x)^(5/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((8*c^4*d^4 - 3*b^3*(b - Sqrt[b^2 - 4*a*c])*e^4 - 2*c^3*d^2*e*(8*b*d - Sqrt[b^2 - 4*a*c]*d - 18*a*e) + b*c*e^3*(5*b^2*d - 5*b*Sqrt[b^2 - 4*a*c]*d + 19*a*b*e - 13*a*Sqrt[b^2 - 4*a*c]*e) + c^2*e^2*(3*b^2*d^2 + 2*a*e*(13*Sqrt[b^2 - 4*a*c]*d - 10*a*e) - 3*b*d*(Sqrt[b^2 - 4*a*c]*d + 12*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((8*c^4*d^4 - 3*b^3*(b + Sqrt[b^2 - 4*a*c])*e^4 - 2*c^3*d^2*e*(8*b*d + Sqrt[b^2 - 4*a*c]*d - 18*a*e) + b*c*e^3*(5*b^2*d + 5*b*Sqrt[b^2 - 4*a*c]*d + 19*a*b*e + 13*a*Sqrt[b^2 - 4*a*c]*e) + c^2*e^2*(3*b^2*d^2 + 3*b*d*(Sqrt[b^2 - 4*a*c]*d - 12*a*e) - 2*a*e*(13*Sqrt[b^2 - 4*a*c]*d + 10*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",7,5,22,0.2273,1,"{738, 824, 826, 1166, 208}"
2296,1,504,0,4.6180587,"\int \frac{(d+e x)^{5/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)^(5/2)/(a + b*x + c*x^2)^2,x]","\frac{\left(-2 c^2 d e \left(-d \sqrt{b^2-4 a c}-8 a e+6 b d\right)+2 c e^2 \left(-b \left(d \sqrt{b^2-4 a c}+4 a e\right)+3 a e \sqrt{b^2-4 a c}+b^2 d\right)+b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+8 c^3 d^3\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^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(-2 c^2 d e \left(d \sqrt{b^2-4 a c}-8 a e+6 b d\right)+2 c e^2 \left(b d \sqrt{b^2-4 a c}-3 a e \sqrt{b^2-4 a c}-4 a b e+b^2 d\right)+b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+8 c^3 d^3\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^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e \sqrt{d+e x} (2 c d-b e)}{c \left(b^2-4 a c\right)}","\frac{\left(-2 c^2 d e \left(-d \sqrt{b^2-4 a c}-8 a e+6 b d\right)+2 c e^2 \left(-b \left(d \sqrt{b^2-4 a c}+4 a e\right)+3 a e \sqrt{b^2-4 a c}+b^2 d\right)+b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+8 c^3 d^3\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^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(-2 c^2 d e \left(d \sqrt{b^2-4 a c}-8 a e+6 b d\right)+2 c e^2 \left(b d \sqrt{b^2-4 a c}-3 a e \sqrt{b^2-4 a c}-4 a b e+b^2 d\right)+b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+8 c^3 d^3\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^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e \sqrt{d+e x} (2 c d-b e)}{c \left(b^2-4 a c\right)}",1,"(e*(2*c*d - b*e)*Sqrt[d + e*x])/(c*(b^2 - 4*a*c)) - ((d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((8*c^3*d^3 + b^2*(b - Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e*(6*b*d - Sqrt[b^2 - 4*a*c]*d - 8*a*e) + 2*c*e^2*(b^2*d + 3*a*Sqrt[b^2 - 4*a*c]*e - b*(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]])/(Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((8*c^3*d^3 + b^2*(b + Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e*(6*b*d + Sqrt[b^2 - 4*a*c]*d - 8*a*e) + 2*c*e^2*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d - 4*a*b*e - 3*a*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[2]*c^(3/2)*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,22,0.2273,1,"{738, 824, 826, 1166, 208}"
2297,1,363,0,1.2929553,"\int \frac{(d+e x)^{3/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)^(3/2)/(a + b*x + c*x^2)^2,x]","\frac{\left(-2 c e \left(-d \sqrt{b^2-4 a c}-2 a e+4 b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+8 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)}{\sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(-2 c e \left(d \sqrt{b^2-4 a c}-2 a e+4 b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+8 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)}{\sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{\left(-2 c e \left(-d \sqrt{b^2-4 a c}-2 a e+4 b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+8 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)}{\sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(-2 c e \left(d \sqrt{b^2-4 a c}-2 a e+4 b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+8 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)}{\sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((Sqrt[d + e*x]*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + ((8*c^2*d^2 + b*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(4*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]])/(Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((8*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(4*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]])/(Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",5,4,22,0.1818,1,"{738, 826, 1166, 208}"
2298,1,287,0,0.6711108,"\int \frac{\sqrt{d+e x}}{\left(a+b x+c x^2\right)^2} \, dx","Int[Sqrt[d + e*x]/(a + b*x + c*x^2)^2,x]","-\frac{(b+2 c x) \sqrt{d+e x}}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{\sqrt{2} \sqrt{c} \left(4 c d-e \left(2 b-\sqrt{b^2-4 a c}\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)}{\left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \sqrt{c} \left(4 c d-e \left(\sqrt{b^2-4 a c}+2 b\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)}{\left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}","-\frac{(b+2 c x) \sqrt{d+e x}}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{\sqrt{2} \sqrt{c} \left(4 c d-e \left(2 b-\sqrt{b^2-4 a c}\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)}{\left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \sqrt{c} \left(4 c d-e \left(\sqrt{b^2-4 a c}+2 b\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)}{\left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}",1,"-(((b + 2*c*x)*Sqrt[d + e*x])/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (Sqrt[2]*Sqrt[c]*(4*c*d - (2*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]])/((b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*Sqrt[c]*(4*c*d - (2*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]])/((b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",5,4,22,0.1818,1,"{736, 826, 1166, 208}"
2299,1,428,0,1.472124,"\int \frac{1}{\sqrt{d+e x} \left(a+b x+c x^2\right)^2} \, dx","Int[1/(Sqrt[d + e*x]*(a + b*x + c*x^2)^2),x]","\frac{\sqrt{c} \left(-2 c e \left(-d \sqrt{b^2-4 a c}-6 a e+4 b d\right)-b e^2 \left(\sqrt{b^2-4 a c}+b\right)+8 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)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} \left(-2 c e \left(d \sqrt{b^2-4 a c}-6 a e+4 b d\right)-b e^2 \left(b-\sqrt{b^2-4 a c}\right)+8 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)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{d+e x} \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) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}","\frac{\sqrt{c} \left(-2 c e \left(-d \sqrt{b^2-4 a c}-6 a e+4 b d\right)-b e^2 \left(\sqrt{b^2-4 a c}+b\right)+8 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)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} \left(-2 c e \left(d \sqrt{b^2-4 a c}-6 a e+4 b d\right)-b e^2 \left(b-\sqrt{b^2-4 a c}\right)+8 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)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{d+e x} \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) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}",1,"-((Sqrt[d + e*x]*(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)*(a + b*x + c*x^2))) + (Sqrt[c]*(8*c^2*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(4*b*d - Sqrt[b^2 - 4*a*c]*d - 6*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) - (Sqrt[c]*(8*c^2*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(4*b*d + Sqrt[b^2 - 4*a*c]*d - 6*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",5,4,22,0.1818,1,"{740, 826, 1166, 208}"
2300,1,604,0,4.9426735,"\int \frac{1}{(d+e x)^{3/2} \left(a+b x+c x^2\right)^2} \, dx","Int[1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^2),x]","-\frac{e \left(-2 c e (5 a e+b d)+3 b^2 e^2+2 c^2 d^2\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{c} \left(-2 c^2 d e \left(-d \sqrt{b^2-4 a c}-16 a e+6 b d\right)-2 c e^2 \left(b d \sqrt{b^2-4 a c}+5 a e \sqrt{b^2-4 a c}+8 a b e+b^2 d\right)+3 b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+8 c^3 d^3\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} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{c} \left(-2 c^2 d e \left(d \sqrt{b^2-4 a c}-16 a e+6 b d\right)-2 c e^2 \left(-b d \sqrt{b^2-4 a c}-5 a e \sqrt{b^2-4 a c}+8 a b e+b^2 d\right)+3 b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+8 c^3 d^3\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} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}","-\frac{e \left(-2 c e (5 a e+b d)+3 b^2 e^2+2 c^2 d^2\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{c} \left(-2 c^2 d e \left(-d \sqrt{b^2-4 a c}-16 a e+6 b d\right)-2 c e^2 \left(b d \sqrt{b^2-4 a c}+5 a e \sqrt{b^2-4 a c}+8 a b e+b^2 d\right)+3 b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+8 c^3 d^3\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} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{c} \left(-2 c^2 d e \left(d \sqrt{b^2-4 a c}-16 a e+6 b d\right)-2 c e^2 \left(-b d \sqrt{b^2-4 a c}-5 a e \sqrt{b^2-4 a c}+8 a b e+b^2 d\right)+3 b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+8 c^3 d^3\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} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}",1,"-((e*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e)))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x])) - (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[d + e*x]*(a + b*x + c*x^2)) + (Sqrt[c]*(8*c^3*d^3 + 3*b^2*(b + Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e*(6*b*d - Sqrt[b^2 - 4*a*c]*d - 16*a*e) - 2*c*e^2*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d + 8*a*b*e + 5*a*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[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2) - (Sqrt[c]*(8*c^3*d^3 + 3*b^2*(b - Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e*(6*b*d + Sqrt[b^2 - 4*a*c]*d - 16*a*e) - 2*c*e^2*(b^2*d - b*Sqrt[b^2 - 4*a*c]*d + 8*a*b*e - 5*a*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[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2)","A",6,5,22,0.2273,1,"{740, 828, 826, 1166, 208}"
2301,1,360,0,3.6934424,"\int \frac{1}{x^{5/2} \left(a+b x+c x^2\right)^2} \, dx","Int[1/(x^(5/2)*(a + b*x + c*x^2)^2),x]","\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c+b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c-b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{5 b^2-14 a c}{3 a^2 x^{3/2} \left(b^2-4 a c\right)}+\frac{b \left(5 b^2-19 a c\right)}{a^3 \sqrt{x} \left(b^2-4 a c\right)}+\frac{-2 a c+b^2+b c x}{a x^{3/2} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c+b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c-b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{5 b^2-14 a c}{3 a^2 x^{3/2} \left(b^2-4 a c\right)}+\frac{b \left(5 b^2-19 a c\right)}{a^3 \sqrt{x} \left(b^2-4 a c\right)}+\frac{-2 a c+b^2+b c x}{a x^{3/2} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-(5*b^2 - 14*a*c)/(3*a^2*(b^2 - 4*a*c)*x^(3/2)) + (b*(5*b^2 - 19*a*c))/(a^3*(b^2 - 4*a*c)*Sqrt[x]) + (b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*x^(3/2)*(a + b*x + c*x^2)) + (Sqrt[c]*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 + b*(5*b^2 - 19*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 - b*(5*b^2 - 19*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,5,18,0.2778,1,"{740, 828, 826, 1166, 205}"
2302,1,751,0,13.5123112,"\int \frac{(d+e x)^{7/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(d + e*x)^(7/2)/(a + b*x + c*x^2)^3,x]","\frac{\sqrt{d+e x} \left(x (2 c d-b e) \left(-4 c e (3 b d-2 a e)+b^2 e^2+12 c^2 d^2\right)+b^2 \left(-\left(a e^3+11 c d^2 e\right)\right)+12 b c d \left(3 a e^2+c d^2\right)-4 a c e \left(5 a e^2+7 c d^2\right)\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{\left(2 c^2 e^2 \left(-2 b d \left(9 d \sqrt{b^2-4 a c}+38 a e\right)+4 a e \left(4 d \sqrt{b^2-4 a c}+5 a e\right)+53 b^2 d^2\right)-8 c^3 d^2 e \left(-3 d \sqrt{b^2-4 a c}-19 a e+24 b d\right)-2 b c e^3 \left(-5 b d \sqrt{b^2-4 a c}+8 a e \sqrt{b^2-4 a c}-9 a b e+5 b^2 d\right)-b^3 e^4 \left(b-\sqrt{b^2-4 a c}\right)+96 c^4 d^4\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)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\left(2 c^2 e^2 \left(2 b d \left(9 d \sqrt{b^2-4 a c}-38 a e\right)-4 a e \left(4 d \sqrt{b^2-4 a c}-5 a e\right)+53 b^2 d^2\right)-8 c^3 d^2 e \left(3 d \sqrt{b^2-4 a c}-19 a e+24 b d\right)-2 b c e^3 \left(5 b d \sqrt{b^2-4 a c}-8 a e \sqrt{b^2-4 a c}-9 a b e+5 b^2 d\right)-b^3 e^4 \left(\sqrt{b^2-4 a c}+b\right)+96 c^4 d^4\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)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{5/2} (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{\sqrt{d+e x} \left(x (2 c d-b e) \left(-4 c e (3 b d-2 a e)+b^2 e^2+12 c^2 d^2\right)+b^2 \left(-\left(a e^3+11 c d^2 e\right)\right)+12 b c d \left(3 a e^2+c d^2\right)-4 a c e \left(5 a e^2+7 c d^2\right)\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{\left(2 c^2 e^2 \left(-2 b d \left(9 d \sqrt{b^2-4 a c}+38 a e\right)+4 a e \left(4 d \sqrt{b^2-4 a c}+5 a e\right)+53 b^2 d^2\right)-8 c^3 d^2 e \left(-3 d \sqrt{b^2-4 a c}-19 a e+24 b d\right)-2 b c e^3 \left(-5 b d \sqrt{b^2-4 a c}+8 a e \sqrt{b^2-4 a c}-9 a b e+5 b^2 d\right)-b^3 e^4 \left(b-\sqrt{b^2-4 a c}\right)+96 c^4 d^4\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)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\left(2 c^2 e^2 \left(2 b d \left(9 d \sqrt{b^2-4 a c}-38 a e\right)-4 a e \left(4 d \sqrt{b^2-4 a c}-5 a e\right)+53 b^2 d^2\right)-8 c^3 d^2 e \left(3 d \sqrt{b^2-4 a c}-19 a e+24 b d\right)-2 b c e^3 \left(5 b d \sqrt{b^2-4 a c}-8 a e \sqrt{b^2-4 a c}-9 a b e+5 b^2 d\right)-b^3 e^4 \left(\sqrt{b^2-4 a c}+b\right)+96 c^4 d^4\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)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{5/2} (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-((d + e*x)^(5/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (Sqrt[d + e*x]*(12*b*c*d*(c*d^2 + 3*a*e^2) - 4*a*c*e*(7*c*d^2 + 5*a*e^2) - b^2*(11*c*d^2*e + a*e^3) + (2*c*d - b*e)*(12*c^2*d^2 + b^2*e^2 - 4*c*e*(3*b*d - 2*a*e))*x))/(4*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - ((96*c^4*d^4 - b^3*(b - Sqrt[b^2 - 4*a*c])*e^4 - 8*c^3*d^2*e*(24*b*d - 3*Sqrt[b^2 - 4*a*c]*d - 19*a*e) - 2*b*c*e^3*(5*b^2*d - 5*b*Sqrt[b^2 - 4*a*c]*d - 9*a*b*e + 8*a*Sqrt[b^2 - 4*a*c]*e) + 2*c^2*e^2*(53*b^2*d^2 + 4*a*e*(4*Sqrt[b^2 - 4*a*c]*d + 5*a*e) - 2*b*d*(9*Sqrt[b^2 - 4*a*c]*d + 38*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + ((96*c^4*d^4 - b^3*(b + Sqrt[b^2 - 4*a*c])*e^4 - 8*c^3*d^2*e*(24*b*d + 3*Sqrt[b^2 - 4*a*c]*d - 19*a*e) - 2*b*c*e^3*(5*b^2*d + 5*b*Sqrt[b^2 - 4*a*c]*d - 9*a*b*e - 8*a*Sqrt[b^2 - 4*a*c]*e) + 2*c^2*e^2*(53*b^2*d^2 + 2*b*d*(9*Sqrt[b^2 - 4*a*c]*d - 38*a*e) - 4*a*e*(4*Sqrt[b^2 - 4*a*c]*d - 5*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,22,0.2273,1,"{738, 818, 826, 1166, 208}"
2303,1,577,0,5.056836,"\int \frac{(d+e x)^{5/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(d + e*x)^(5/2)/(a + b*x + c*x^2)^3,x]","-\frac{3 \sqrt{d+e x} \left(-x \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right)-4 b \left(a e^2+c d^2\right)+4 a c d e+3 b^2 d e\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \left(-8 c^2 d e \left(-d \sqrt{b^2-4 a c}-3 a e+6 b d\right)+2 c e^2 \left(-4 b d \sqrt{b^2-4 a c}+2 a e \sqrt{b^2-4 a c}-6 a b e+9 b^2 d\right)-b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+32 c^3 d^3\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)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{3 \left(-8 c^2 d e \left(d \sqrt{b^2-4 a c}-3 a e+6 b d\right)+2 c e^2 \left(4 b d \sqrt{b^2-4 a c}-2 a e \sqrt{b^2-4 a c}-6 a b e+9 b^2 d\right)-b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+32 c^3 d^3\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)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{3 \sqrt{d+e x} \left(-x \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right)-4 b \left(a e^2+c d^2\right)+4 a c d e+3 b^2 d e\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \left(-8 c^2 d e \left(-d \sqrt{b^2-4 a c}-3 a e+6 b d\right)+2 c e^2 \left(-4 b d \sqrt{b^2-4 a c}+2 a e \sqrt{b^2-4 a c}-6 a b e+9 b^2 d\right)-b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+32 c^3 d^3\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)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{3 \left(-8 c^2 d e \left(d \sqrt{b^2-4 a c}-3 a e+6 b d\right)+2 c e^2 \left(4 b d \sqrt{b^2-4 a c}-2 a e \sqrt{b^2-4 a c}-6 a b e+9 b^2 d\right)-b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+32 c^3 d^3\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)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-((d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - (3*Sqrt[d + e*x]*(3*b^2*d*e + 4*a*c*d*e - 4*b*(c*d^2 + a*e^2) - (8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*x))/(4*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (3*(32*c^3*d^3 - b^2*(b - Sqrt[b^2 - 4*a*c])*e^3 - 8*c^2*d*e*(6*b*d - Sqrt[b^2 - 4*a*c]*d - 3*a*e) + 2*c*e^2*(9*b^2*d - 4*b*Sqrt[b^2 - 4*a*c]*d - 6*a*b*e + 2*a*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]])/(4*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (3*(32*c^3*d^3 - b^2*(b + Sqrt[b^2 - 4*a*c])*e^3 - 8*c^2*d*e*(6*b*d + Sqrt[b^2 - 4*a*c]*d - 3*a*e) + 2*c*e^2*(9*b^2*d + 4*b*Sqrt[b^2 - 4*a*c]*d - 6*a*b*e - 2*a*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]])/(4*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,22,0.2273,1,"{738, 820, 826, 1166, 208}"
2304,1,441,0,1.9424865,"\int \frac{(d+e x)^{3/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[(d + e*x)^(3/2)/(a + b*x + c*x^2)^3,x]","-\frac{3 \sqrt{c} \left(-4 c e \left(-d \sqrt{b^2-4 a c}-a e+4 b d\right)+b e^2 \left(3 b-2 \sqrt{b^2-4 a c}\right)+16 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)}{2 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{3 \sqrt{c} \left(-4 c e \left(d \sqrt{b^2-4 a c}-a e+4 b d\right)+b e^2 \left(2 \sqrt{b^2-4 a c}+3 b\right)+16 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)}{2 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{\sqrt{d+e x} \left(4 a c e-7 b^2 e+12 c x (2 c d-b e)+12 b c d\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}","-\frac{3 \sqrt{c} \left(-4 c e \left(-d \sqrt{b^2-4 a c}-a e+4 b d\right)+b e^2 \left(3 b-2 \sqrt{b^2-4 a c}\right)+16 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)}{2 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{3 \sqrt{c} \left(-4 c e \left(d \sqrt{b^2-4 a c}-a e+4 b d\right)+b e^2 \left(2 \sqrt{b^2-4 a c}+3 b\right)+16 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)}{2 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{\sqrt{d+e x} \left(4 a c e-7 b^2 e+12 c x (2 c d-b e)+12 b c d\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}",1,"-(Sqrt[d + e*x]*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (Sqrt[d + e*x]*(12*b*c*d - 7*b^2*e + 4*a*c*e + 12*c*(2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (3*Sqrt[c]*(16*c^2*d^2 + b*(3*b - 2*Sqrt[b^2 - 4*a*c])*e^2 - 4*c*e*(4*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]])/(2*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (3*Sqrt[c]*(16*c^2*d^2 + b*(3*b + 2*Sqrt[b^2 - 4*a*c])*e^2 - 4*c*e*(4*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]])/(2*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,22,0.2273,1,"{738, 822, 826, 1166, 208}"
2305,1,634,0,4.9737457,"\int \frac{\sqrt{d+e x}}{\left(a+b x+c x^2\right)^3} \, dx","Int[Sqrt[d + e*x]/(a + b*x + c*x^2)^3,x]","-\frac{\sqrt{d+e x} \left(-c x \left(-4 c e (6 b d-5 a e)+b^2 e^2+24 c^2 d^2\right)-4 b c \left(2 a e^2+3 c d^2\right)-4 a c^2 d e+13 b^2 c d e+b^3 \left(-e^2\right)\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} \left(-8 c^2 d e \left(-3 d \sqrt{b^2-4 a c}-13 a e+18 b d\right)+2 c e^2 \left(-2 b \left(6 d \sqrt{b^2-4 a c}+13 a e\right)+10 a e \sqrt{b^2-4 a c}+23 b^2 d\right)+b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+96 c^3 d^3\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)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{c} \left(-8 c^2 d e \left(3 d \sqrt{b^2-4 a c}-13 a e+18 b d\right)+2 c e^2 \left(12 b d \sqrt{b^2-4 a c}-10 a e \sqrt{b^2-4 a c}-26 a b e+23 b^2 d\right)+b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+96 c^3 d^3\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)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{(b+2 c x) \sqrt{d+e x}}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{\sqrt{d+e x} \left(-c x \left(-4 c e (6 b d-5 a e)+b^2 e^2+24 c^2 d^2\right)-4 b c \left(2 a e^2+3 c d^2\right)-4 a c^2 d e+13 b^2 c d e+b^3 \left(-e^2\right)\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} \left(-8 c^2 d e \left(-3 d \sqrt{b^2-4 a c}-13 a e+18 b d\right)+2 c e^2 \left(-2 b \left(6 d \sqrt{b^2-4 a c}+13 a e\right)+10 a e \sqrt{b^2-4 a c}+23 b^2 d\right)+b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+96 c^3 d^3\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)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{c} \left(-8 c^2 d e \left(3 d \sqrt{b^2-4 a c}-13 a e+18 b d\right)+2 c e^2 \left(12 b d \sqrt{b^2-4 a c}-10 a e \sqrt{b^2-4 a c}-26 a b e+23 b^2 d\right)+b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+96 c^3 d^3\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)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{(b+2 c x) \sqrt{d+e x}}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-((b + 2*c*x)*Sqrt[d + e*x])/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - (Sqrt[d + e*x]*(13*b^2*c*d*e - 4*a*c^2*d*e - b^3*e^2 - 4*b*c*(3*c*d^2 + 2*a*e^2) - c*(24*c^2*d^2 + b^2*e^2 - 4*c*e*(6*b*d - 5*a*e))*x))/(4*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)) - (Sqrt[c]*(96*c^3*d^3 + b^2*(b + Sqrt[b^2 - 4*a*c])*e^3 - 8*c^2*d*e*(18*b*d - 3*Sqrt[b^2 - 4*a*c]*d - 13*a*e) + 2*c*e^2*(23*b^2*d + 10*a*Sqrt[b^2 - 4*a*c]*e - 2*b*(6*Sqrt[b^2 - 4*a*c]*d + 13*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) + (Sqrt[c]*(96*c^3*d^3 + b^2*(b - Sqrt[b^2 - 4*a*c])*e^3 - 8*c^2*d*e*(18*b*d + 3*Sqrt[b^2 - 4*a*c]*d - 13*a*e) + 2*c*e^2*(23*b^2*d + 12*b*Sqrt[b^2 - 4*a*c]*d - 26*a*b*e - 10*a*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]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",6,5,22,0.2273,1,"{736, 822, 826, 1166, 208}"
2306,1,834,0,13.9194131,"\int \frac{1}{\sqrt{d+e x} \left(a+b x+c x^2\right)^3} \, dx","Int[1/(Sqrt[d + e*x]*(a + b*x + c*x^2)^3),x]","-\frac{\sqrt{d+e x} \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right)}{2 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \left(c x^2+b x+a\right)^2}-\frac{3 \sqrt{c} \left(32 c^4 d^4-8 c^3 e \left(8 b d-\sqrt{b^2-4 a c} d-9 a e\right) d^2+b^3 \left(b+\sqrt{b^2-4 a c}\right) e^4+2 b c e^3 \left(d b^2+\sqrt{b^2-4 a c} d b-5 a e b-4 a \sqrt{b^2-4 a c} e\right)+2 c^2 e^2 \left(15 b^2 d^2-6 b \left(\sqrt{b^2-4 a c} d+6 a e\right) d+4 a e \left(2 \sqrt{b^2-4 a c} d+7 a e\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e} \left(c d^2-b e d+a e^2\right)^2}+\frac{3 \sqrt{c} \left(32 c^4 d^4-8 c^3 e \left(8 b d+\sqrt{b^2-4 a c} d-9 a e\right) d^2+b^3 \left(b-\sqrt{b^2-4 a c}\right) e^4+2 c^2 e^2 \left(15 b^2 d^2+6 b \left(\sqrt{b^2-4 a c} d-6 a e\right) d-4 a e \left(2 \sqrt{b^2-4 a c} d-7 a e\right)\right)+2 b c e^3 \left(d b^2-\left(\sqrt{b^2-4 a c} d+5 a e\right) b+4 a \sqrt{b^2-4 a c} e\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e} \left(c d^2-b e d+a e^2\right)^2}-\frac{\sqrt{d+e x} \left(5 a c e (2 c d-b e)^2-3 c \left(4 c^2 d^2-b^2 e^2-4 c e (b d-2 a e)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(12 c^2 d^2-3 b^2 e^2-7 c e (b d-2 a e)\right)\right)}{4 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 \left(c x^2+b x+a\right)}","-\frac{\sqrt{d+e x} \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right)}{2 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \left(c x^2+b x+a\right)^2}-\frac{3 \sqrt{c} \left(32 c^4 d^4-8 c^3 e \left(8 b d-\sqrt{b^2-4 a c} d-9 a e\right) d^2+b^3 \left(b+\sqrt{b^2-4 a c}\right) e^4+2 b c e^3 \left(d b^2+\sqrt{b^2-4 a c} d b-5 a e b-4 a \sqrt{b^2-4 a c} e\right)+2 c^2 e^2 \left(15 b^2 d^2-6 b \left(\sqrt{b^2-4 a c} d+6 a e\right) d+4 a e \left(2 \sqrt{b^2-4 a c} d+7 a e\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e} \left(c d^2-b e d+a e^2\right)^2}+\frac{3 \sqrt{c} \left(32 c^4 d^4-8 c^3 e \left(8 b d+\sqrt{b^2-4 a c} d-9 a e\right) d^2+b^3 \left(b-\sqrt{b^2-4 a c}\right) e^4+2 c^2 e^2 \left(15 b^2 d^2+6 b \left(\sqrt{b^2-4 a c} d-6 a e\right) d-4 a e \left(2 \sqrt{b^2-4 a c} d-7 a e\right)\right)+2 b c e^3 \left(d b^2-\left(\sqrt{b^2-4 a c} d+5 a e\right) b+4 a \sqrt{b^2-4 a c} e\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e} \left(c d^2-e (b d-a e)\right)^2}-\frac{\sqrt{d+e x} \left(5 a c e (2 c d-b e)^2-3 c \left(4 c^2 d^2-b^2 e^2-4 c e (b d-2 a e)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(12 c^2 d^2-3 b^2 e^2-7 c e (b d-2 a e)\right)\right)}{4 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 \left(c x^2+b x+a\right)}",1,"-(Sqrt[d + e*x]*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (Sqrt[d + e*x]*(5*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(12*c^2*d^2 - 3*b^2*e^2 - 7*c*e*(b*d - 2*a*e)) - 3*c*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*x))/(4*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) - (3*Sqrt[c]*(32*c^4*d^4 + b^3*(b + Sqrt[b^2 - 4*a*c])*e^4 - 8*c^3*d^2*e*(8*b*d - Sqrt[b^2 - 4*a*c]*d - 9*a*e) + 2*b*c*e^3*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d - 5*a*b*e - 4*a*Sqrt[b^2 - 4*a*c]*e) + 2*c^2*e^2*(15*b^2*d^2 - 6*b*d*(Sqrt[b^2 - 4*a*c]*d + 6*a*e) + 4*a*e*(2*Sqrt[b^2 - 4*a*c]*d + 7*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2) + (3*Sqrt[c]*(32*c^4*d^4 + b^3*(b - Sqrt[b^2 - 4*a*c])*e^4 - 8*c^3*d^2*e*(8*b*d + Sqrt[b^2 - 4*a*c]*d - 9*a*e) + 2*c^2*e^2*(15*b^2*d^2 - 4*a*e*(2*Sqrt[b^2 - 4*a*c]*d - 7*a*e) + 6*b*d*(Sqrt[b^2 - 4*a*c]*d - 6*a*e)) + 2*b*c*e^3*(b^2*d + 4*a*Sqrt[b^2 - 4*a*c]*e - b*(Sqrt[b^2 - 4*a*c]*d + 5*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2)","A",6,5,22,0.2273,1,"{740, 822, 826, 1166, 208}"
2307,1,629,0,1.2270652,"\int \frac{\sqrt{d+e x}}{a+i b x+c x^2} \, dx","Int[Sqrt[d + e*x]/(a + I*b*x + c*x^2),x]","\frac{e \log \left(-\sqrt{d+e x} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}+\sqrt{c d^2-e (-a e+i b d)}+\sqrt{c} (d+e x)\right)}{2 \sqrt{c} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}-\frac{e \log \left(\sqrt{d+e x} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}+\sqrt{c d^2-e (-a e+i b d)}+\sqrt{c} (d+e x)\right)}{2 \sqrt{c} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}+\frac{e \tanh ^{-1}\left(\frac{-2 \sqrt{c} \sqrt{d+e x}+\sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}{\sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}\right)}{\sqrt{c} \sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}-\frac{e \tanh ^{-1}\left(\frac{2 \sqrt{c} \sqrt{d+e x}+\sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}{\sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}\right)}{\sqrt{c} \sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}","\frac{e \log \left(-\sqrt{d+e x} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}+\sqrt{c d^2-e (-a e+i b d)}+\sqrt{c} (d+e x)\right)}{2 \sqrt{c} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}-\frac{e \log \left(\sqrt{d+e x} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}+\sqrt{c d^2-e (-a e+i b d)}+\sqrt{c} (d+e x)\right)}{2 \sqrt{c} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}+\frac{e \tanh ^{-1}\left(\frac{-2 \sqrt{c} \sqrt{d+e x}+\sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}{\sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}\right)}{\sqrt{c} \sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}-\frac{e \tanh ^{-1}\left(\frac{2 \sqrt{c} \sqrt{d+e x}+\sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}{\sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}\right)}{\sqrt{c} \sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}",1,"(e*ArcTanh[(Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]] - 2*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - I*b*e - 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]])/(Sqrt[c]*Sqrt[2*c*d - I*b*e - 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]) - (e*ArcTanh[(Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]] + 2*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - I*b*e - 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]])/(Sqrt[c]*Sqrt[2*c*d - I*b*e - 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]) + (e*Log[Sqrt[c*d^2 - e*(I*b*d - a*e)] - Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[c]*Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]) - (e*Log[Sqrt[c*d^2 - e*(I*b*d - a*e)] + Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[c]*Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]])","A",10,6,25,0.2400,1,"{699, 1129, 634, 618, 206, 628}"
2308,1,705,0,0.7914805,"\int \frac{1}{\sqrt{d+e x} \left(a+i b x+c x^2\right)} \, dx","Int[1/(Sqrt[d + e*x]*(a + I*b*x + c*x^2)),x]","-\frac{e \log \left(-\sqrt{d+e x} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}+\sqrt{c d^2-e (-a e+i b d)}+\sqrt{c} (d+e x)\right)}{2 \sqrt{c d^2-e (-a e+i b d)} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}+\frac{e \log \left(\sqrt{d+e x} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}+\sqrt{c d^2-e (-a e+i b d)}+\sqrt{c} (d+e x)\right)}{2 \sqrt{c d^2-e (-a e+i b d)} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}+\frac{e \tanh ^{-1}\left(\frac{-2 \sqrt{c} \sqrt{d+e x}+\sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}{\sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}\right)}{\sqrt{c d^2-e (-a e+i b d)} \sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}-\frac{e \tanh ^{-1}\left(\frac{2 \sqrt{c} \sqrt{d+e x}+\sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}{\sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}\right)}{\sqrt{c d^2-e (-a e+i b d)} \sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}","-\frac{e \log \left(-\sqrt{d+e x} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}+\sqrt{c d^2-e (-a e+i b d)}+\sqrt{c} (d+e x)\right)}{2 \sqrt{c d^2-e (-a e+i b d)} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}+\frac{e \log \left(\sqrt{d+e x} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}+\sqrt{c d^2-e (-a e+i b d)}+\sqrt{c} (d+e x)\right)}{2 \sqrt{c d^2-e (-a e+i b d)} \sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}+\frac{e \tanh ^{-1}\left(\frac{-2 \sqrt{c} \sqrt{d+e x}+\sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}{\sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}\right)}{\sqrt{c d^2-e (-a e+i b d)} \sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}-\frac{e \tanh ^{-1}\left(\frac{2 \sqrt{c} \sqrt{d+e x}+\sqrt{2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}{\sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}\right)}{\sqrt{c d^2-e (-a e+i b d)} \sqrt{-2 \sqrt{c} \sqrt{c d^2-e (-a e+i b d)}-i b e+2 c d}}",1,"(e*ArcTanh[(Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]] - 2*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - I*b*e - 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]])/(Sqrt[c*d^2 - e*(I*b*d - a*e)]*Sqrt[2*c*d - I*b*e - 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]) - (e*ArcTanh[(Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]] + 2*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - I*b*e - 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]])/(Sqrt[c*d^2 - e*(I*b*d - a*e)]*Sqrt[2*c*d - I*b*e - 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]) - (e*Log[Sqrt[c*d^2 - e*(I*b*d - a*e)] - Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[c*d^2 - e*(I*b*d - a*e)]*Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]) + (e*Log[Sqrt[c*d^2 - e*(I*b*d - a*e)] + Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]]*Sqrt[d + e*x] + Sqrt[c]*(d + e*x)])/(2*Sqrt[c*d^2 - e*(I*b*d - a*e)]*Sqrt[2*c*d - I*b*e + 2*Sqrt[c]*Sqrt[c*d^2 - e*(I*b*d - a*e)]])","A",10,6,25,0.2400,1,"{707, 1094, 634, 618, 206, 628}"
2309,1,279,0,0.6075799,"\int \frac{(1+2 x)^{7/2}}{2+3 x+5 x^2} \, dx","Int[(1 + 2*x)^(7/2)/(2 + 3*x + 5*x^2),x]","\frac{4}{25} (2 x+1)^{5/2}+\frac{16}{75} (2 x+1)^{3/2}-\frac{76}{125} \sqrt{2 x+1}-\frac{1}{125} \sqrt{\frac{1}{310} \left(168698+42875 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{125} \sqrt{\frac{1}{310} \left(168698+42875 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{125} \sqrt{\frac{2}{155} \left(42875 \sqrt{35}-168698\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{125} \sqrt{\frac{2}{155} \left(42875 \sqrt{35}-168698\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","\frac{4}{25} (2 x+1)^{5/2}+\frac{16}{75} (2 x+1)^{3/2}-\frac{76}{125} \sqrt{2 x+1}-\frac{1}{125} \sqrt{\frac{1}{310} \left(168698+42875 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{125} \sqrt{\frac{1}{310} \left(168698+42875 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{125} \sqrt{\frac{2}{155} \left(42875 \sqrt{35}-168698\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{125} \sqrt{\frac{2}{155} \left(42875 \sqrt{35}-168698\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"(-76*Sqrt[1 + 2*x])/125 + (16*(1 + 2*x)^(3/2))/75 + (4*(1 + 2*x)^(5/2))/25 + (Sqrt[(2*(-168698 + 42875*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/125 - (Sqrt[(2*(-168698 + 42875*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/125 - (Sqrt[(168698 + 42875*Sqrt[35])/310]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/125 + (Sqrt[(168698 + 42875*Sqrt[35])/310]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/125","A",13,8,22,0.3636,1,"{703, 824, 826, 1169, 634, 618, 204, 628}"
2310,1,266,0,0.4362008,"\int \frac{(1+2 x)^{5/2}}{2+3 x+5 x^2} \, dx","Int[(1 + 2*x)^(5/2)/(2 + 3*x + 5*x^2),x]","\frac{4}{15} (2 x+1)^{3/2}+\frac{16}{25} \sqrt{2 x+1}+\frac{1}{25} \sqrt{\frac{1}{310} \left(1225 \sqrt{35}-7162\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{25} \sqrt{\frac{1}{310} \left(1225 \sqrt{35}-7162\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{25} \sqrt{\frac{2}{155} \left(7162+1225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{25} \sqrt{\frac{2}{155} \left(7162+1225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","\frac{4}{15} (2 x+1)^{3/2}+\frac{16}{25} \sqrt{2 x+1}+\frac{1}{25} \sqrt{\frac{1}{310} \left(1225 \sqrt{35}-7162\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{25} \sqrt{\frac{1}{310} \left(1225 \sqrt{35}-7162\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{25} \sqrt{\frac{2}{155} \left(7162+1225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{25} \sqrt{\frac{2}{155} \left(7162+1225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"(16*Sqrt[1 + 2*x])/25 + (4*(1 + 2*x)^(3/2))/15 + (Sqrt[(2*(7162 + 1225*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/25 - (Sqrt[(2*(7162 + 1225*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/25 + (Sqrt[(-7162 + 1225*Sqrt[35])/310]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/25 - (Sqrt[(-7162 + 1225*Sqrt[35])/310]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/25","A",12,8,22,0.3636,1,"{703, 824, 826, 1169, 634, 618, 204, 628}"
2311,1,253,0,0.3579225,"\int \frac{(1+2 x)^{3/2}}{2+3 x+5 x^2} \, dx","Int[(1 + 2*x)^(3/2)/(2 + 3*x + 5*x^2),x]","\frac{4}{5} \sqrt{2 x+1}+\frac{1}{5} \sqrt{\frac{1}{310} \left(178+35 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{5} \sqrt{\frac{1}{310} \left(178+35 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{5} \sqrt{\frac{2}{155} \left(35 \sqrt{35}-178\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{5} \sqrt{\frac{2}{155} \left(35 \sqrt{35}-178\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","\frac{4}{5} \sqrt{2 x+1}+\frac{1}{5} \sqrt{\frac{1}{310} \left(178+35 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{5} \sqrt{\frac{1}{310} \left(178+35 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{5} \sqrt{\frac{2}{155} \left(35 \sqrt{35}-178\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{5} \sqrt{\frac{2}{155} \left(35 \sqrt{35}-178\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"(4*Sqrt[1 + 2*x])/5 + (Sqrt[(2*(-178 + 35*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/5 - (Sqrt[(2*(-178 + 35*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/5 + (Sqrt[(178 + 35*Sqrt[35])/310]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/5 - (Sqrt[(178 + 35*Sqrt[35])/310]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/5","A",11,7,22,0.3182,1,"{703, 826, 1169, 634, 618, 204, 628}"
2312,1,222,0,0.2470471,"\int \frac{\sqrt{1+2 x}}{2+3 x+5 x^2} \, dx","Int[Sqrt[1 + 2*x]/(2 + 3*x + 5*x^2),x]","\frac{\log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{\sqrt{10 \left(2+\sqrt{35}\right)}}-\frac{\log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{\sqrt{10 \left(2+\sqrt{35}\right)}}-\sqrt{\frac{2}{5 \left(\sqrt{35}-2\right)}} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\sqrt{\frac{2}{5 \left(\sqrt{35}-2\right)}} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","\frac{\log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{\sqrt{10 \left(2+\sqrt{35}\right)}}-\frac{\log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{\sqrt{10 \left(2+\sqrt{35}\right)}}-\sqrt{\frac{2}{5 \left(\sqrt{35}-2\right)}} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\sqrt{\frac{2}{5 \left(\sqrt{35}-2\right)}} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"-(Sqrt[2/(5*(-2 + Sqrt[35]))]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]]) + Sqrt[2/(5*(-2 + Sqrt[35]))]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]] + Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)]/Sqrt[10*(2 + Sqrt[35])] - Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)]/Sqrt[10*(2 + Sqrt[35])]","A",10,7,22,0.3182,1,"{699, 1127, 1161, 618, 204, 1164, 628}"
2313,1,218,0,0.2719726,"\int \frac{1}{\sqrt{1+2 x} \left(2+3 x+5 x^2\right)} \, dx","Int[1/(Sqrt[1 + 2*x]*(2 + 3*x + 5*x^2)),x]","-\frac{\log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{\sqrt{14 \left(2+\sqrt{35}\right)}}+\frac{\log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{\sqrt{14 \left(2+\sqrt{35}\right)}}-\sqrt{\frac{2}{217} \left(2+\sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\sqrt{\frac{2}{217} \left(2+\sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","-\frac{\log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{\sqrt{14 \left(2+\sqrt{35}\right)}}+\frac{\log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{\sqrt{14 \left(2+\sqrt{35}\right)}}-\sqrt{\frac{2}{217} \left(2+\sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\sqrt{\frac{2}{217} \left(2+\sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"-(Sqrt[(2*(2 + Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]]) + Sqrt[(2*(2 + Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]] - Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)]/Sqrt[14*(2 + Sqrt[35])] + Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)]/Sqrt[14*(2 + Sqrt[35])]","A",10,6,22,0.2727,1,"{707, 1094, 634, 618, 204, 628}"
2314,1,253,0,0.3374023,"\int \frac{1}{(1+2 x)^{3/2} \left(2+3 x+5 x^2\right)} \, dx","Int[1/((1 + 2*x)^(3/2)*(2 + 3*x + 5*x^2)),x]","-\frac{4}{7 \sqrt{2 x+1}}-\frac{1}{7} \sqrt{\frac{1}{434} \left(178+35 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{7} \sqrt{\frac{1}{434} \left(178+35 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{7} \sqrt{\frac{2}{217} \left(35 \sqrt{35}-178\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{7} \sqrt{\frac{2}{217} \left(35 \sqrt{35}-178\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","-\frac{4}{7 \sqrt{2 x+1}}-\frac{1}{7} \sqrt{\frac{1}{434} \left(178+35 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{7} \sqrt{\frac{1}{434} \left(178+35 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{7} \sqrt{\frac{2}{217} \left(35 \sqrt{35}-178\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{7} \sqrt{\frac{2}{217} \left(35 \sqrt{35}-178\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"-4/(7*Sqrt[1 + 2*x]) + (Sqrt[(2*(-178 + 35*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/7 - (Sqrt[(2*(-178 + 35*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/7 - (Sqrt[(178 + 35*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/7 + (Sqrt[(178 + 35*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/7","A",11,7,22,0.3182,1,"{709, 826, 1169, 634, 618, 204, 628}"
2315,1,266,0,0.3821565,"\int \frac{1}{(1+2 x)^{5/2} \left(2+3 x+5 x^2\right)} \, dx","Int[1/((1 + 2*x)^(5/2)*(2 + 3*x + 5*x^2)),x]","-\frac{16}{49 \sqrt{2 x+1}}-\frac{4}{21 (2 x+1)^{3/2}}-\frac{1}{49} \sqrt{\frac{1}{434} \left(1225 \sqrt{35}-7162\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{49} \sqrt{\frac{1}{434} \left(1225 \sqrt{35}-7162\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{49} \sqrt{\frac{2}{217} \left(7162+1225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{49} \sqrt{\frac{2}{217} \left(7162+1225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","-\frac{16}{49 \sqrt{2 x+1}}-\frac{4}{21 (2 x+1)^{3/2}}-\frac{1}{49} \sqrt{\frac{1}{434} \left(1225 \sqrt{35}-7162\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{49} \sqrt{\frac{1}{434} \left(1225 \sqrt{35}-7162\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{49} \sqrt{\frac{2}{217} \left(7162+1225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{49} \sqrt{\frac{2}{217} \left(7162+1225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"-4/(21*(1 + 2*x)^(3/2)) - 16/(49*Sqrt[1 + 2*x]) + (Sqrt[(2*(7162 + 1225*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/49 - (Sqrt[(2*(7162 + 1225*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/49 - (Sqrt[(-7162 + 1225*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/49 + (Sqrt[(-7162 + 1225*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/49","A",12,8,22,0.3636,1,"{709, 828, 826, 1169, 634, 618, 204, 628}"
2316,1,296,0,0.4456665,"\int \frac{(1+2 x)^{7/2}}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[(1 + 2*x)^(7/2)/(2 + 3*x + 5*x^2)^2,x]","-\frac{(5-4 x) (2 x+1)^{5/2}}{31 \left(5 x^2+3 x+2\right)}-\frac{8}{155} (2 x+1)^{3/2}+\frac{604}{775} \sqrt{2 x+1}+\frac{1}{775} \sqrt{\frac{1}{310} \left(5682718+968975 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{775} \sqrt{\frac{1}{310} \left(5682718+968975 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{775} \sqrt{\frac{2}{155} \left(968975 \sqrt{35}-5682718\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{775} \sqrt{\frac{2}{155} \left(968975 \sqrt{35}-5682718\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","-\frac{(5-4 x) (2 x+1)^{5/2}}{31 \left(5 x^2+3 x+2\right)}-\frac{8}{155} (2 x+1)^{3/2}+\frac{604}{775} \sqrt{2 x+1}+\frac{1}{775} \sqrt{\frac{1}{310} \left(5682718+968975 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{775} \sqrt{\frac{1}{310} \left(5682718+968975 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{775} \sqrt{\frac{2}{155} \left(968975 \sqrt{35}-5682718\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-\frac{1}{775} \sqrt{\frac{2}{155} \left(968975 \sqrt{35}-5682718\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"(604*Sqrt[1 + 2*x])/775 - (8*(1 + 2*x)^(3/2))/155 - ((5 - 4*x)*(1 + 2*x)^(5/2))/(31*(2 + 3*x + 5*x^2)) + (Sqrt[(2*(-5682718 + 968975*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/775 - (Sqrt[(2*(-5682718 + 968975*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/775 + (Sqrt[(5682718 + 968975*Sqrt[35])/310]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/775 - (Sqrt[(5682718 + 968975*Sqrt[35])/310]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/775","A",13,8,22,0.3636,1,"{738, 824, 826, 1169, 634, 618, 204, 628}"
2317,1,283,0,0.4101166,"\int \frac{(1+2 x)^{5/2}}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[(1 + 2*x)^(5/2)/(2 + 3*x + 5*x^2)^2,x]","-\frac{(5-4 x) (2 x+1)^{3/2}}{31 \left(5 x^2+3 x+2\right)}-\frac{8}{155} \sqrt{2 x+1}+\frac{1}{155} \sqrt{\frac{1}{310} \left(10325 \sqrt{35}-32678\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{155} \sqrt{\frac{1}{310} \left(10325 \sqrt{35}-32678\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{155} \sqrt{\frac{2}{155} \left(32678+10325 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{1}{155} \sqrt{\frac{2}{155} \left(32678+10325 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","-\frac{(5-4 x) (2 x+1)^{3/2}}{31 \left(5 x^2+3 x+2\right)}-\frac{8}{155} \sqrt{2 x+1}+\frac{1}{155} \sqrt{\frac{1}{310} \left(10325 \sqrt{35}-32678\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{155} \sqrt{\frac{1}{310} \left(10325 \sqrt{35}-32678\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{155} \sqrt{\frac{2}{155} \left(32678+10325 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{1}{155} \sqrt{\frac{2}{155} \left(32678+10325 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"(-8*Sqrt[1 + 2*x])/155 - ((5 - 4*x)*(1 + 2*x)^(3/2))/(31*(2 + 3*x + 5*x^2)) - (Sqrt[(2*(32678 + 10325*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/155 + (Sqrt[(2*(32678 + 10325*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/155 + (Sqrt[(-32678 + 10325*Sqrt[35])/310]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/155 - (Sqrt[(-32678 + 10325*Sqrt[35])/310]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/155","A",12,8,22,0.3636,1,"{738, 824, 826, 1169, 634, 618, 204, 628}"
2318,1,270,0,0.3635688,"\int \frac{(1+2 x)^{3/2}}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[(1 + 2*x)^(3/2)/(2 + 3*x + 5*x^2)^2,x]","-\frac{\sqrt{2 x+1} (5-4 x)}{31 \left(5 x^2+3 x+2\right)}-\frac{1}{31} \sqrt{\frac{1}{310} \left(47 \sqrt{35}-218\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{31} \sqrt{\frac{1}{310} \left(47 \sqrt{35}-218\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{31} \sqrt{\frac{2}{155} \left(218+47 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{1}{31} \sqrt{\frac{2}{155} \left(218+47 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","-\frac{\sqrt{2 x+1} (5-4 x)}{31 \left(5 x^2+3 x+2\right)}-\frac{1}{31} \sqrt{\frac{1}{310} \left(47 \sqrt{35}-218\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{31} \sqrt{\frac{1}{310} \left(47 \sqrt{35}-218\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{31} \sqrt{\frac{2}{155} \left(218+47 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{1}{31} \sqrt{\frac{2}{155} \left(218+47 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"-((5 - 4*x)*Sqrt[1 + 2*x])/(31*(2 + 3*x + 5*x^2)) - (Sqrt[(2*(218 + 47*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/31 + (Sqrt[(2*(218 + 47*Sqrt[35]))/155]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/31 - (Sqrt[(-218 + 47*Sqrt[35])/310]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/31 + (Sqrt[(-218 + 47*Sqrt[35])/310]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/31","A",11,7,22,0.3182,1,"{738, 826, 1169, 634, 618, 204, 628}"
2319,1,270,0,0.3404295,"\int \frac{\sqrt{1+2 x}}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[Sqrt[1 + 2*x]/(2 + 3*x + 5*x^2)^2,x]","\frac{\sqrt{2 x+1} (10 x+3)}{31 \left(5 x^2+3 x+2\right)}+\frac{1}{31} \sqrt{\frac{1}{434} \left(47 \sqrt{35}-218\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{31} \sqrt{\frac{1}{434} \left(47 \sqrt{35}-218\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{31} \sqrt{\frac{2}{217} \left(218+47 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{1}{31} \sqrt{\frac{2}{217} \left(218+47 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","\frac{\sqrt{2 x+1} (10 x+3)}{31 \left(5 x^2+3 x+2\right)}+\frac{1}{31} \sqrt{\frac{1}{434} \left(47 \sqrt{35}-218\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{31} \sqrt{\frac{1}{434} \left(47 \sqrt{35}-218\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{31} \sqrt{\frac{2}{217} \left(218+47 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{1}{31} \sqrt{\frac{2}{217} \left(218+47 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"(Sqrt[1 + 2*x]*(3 + 10*x))/(31*(2 + 3*x + 5*x^2)) - (Sqrt[(2*(218 + 47*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/31 + (Sqrt[(2*(218 + 47*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/31 + (Sqrt[(-218 + 47*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/31 - (Sqrt[(-218 + 47*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/31","A",11,7,22,0.3182,1,"{736, 826, 1169, 634, 618, 204, 628}"
2320,1,270,0,0.3237512,"\int \frac{1}{\sqrt{1+2 x} \left(2+3 x+5 x^2\right)^2} \, dx","Int[1/(Sqrt[1 + 2*x]*(2 + 3*x + 5*x^2)^2),x]","\frac{\sqrt{2 x+1} (20 x+37)}{217 \left(5 x^2+3 x+2\right)}-\frac{1}{217} \sqrt{\frac{1}{434} \left(10325 \sqrt{35}-32678\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{217} \sqrt{\frac{1}{434} \left(10325 \sqrt{35}-32678\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{217} \sqrt{\frac{2}{217} \left(32678+10325 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{1}{217} \sqrt{\frac{2}{217} \left(32678+10325 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","\frac{\sqrt{2 x+1} (20 x+37)}{217 \left(5 x^2+3 x+2\right)}-\frac{1}{217} \sqrt{\frac{1}{434} \left(10325 \sqrt{35}-32678\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)+\frac{1}{217} \sqrt{\frac{1}{434} \left(10325 \sqrt{35}-32678\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)-\frac{1}{217} \sqrt{\frac{2}{217} \left(32678+10325 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{1}{217} \sqrt{\frac{2}{217} \left(32678+10325 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"(Sqrt[1 + 2*x]*(37 + 20*x))/(217*(2 + 3*x + 5*x^2)) - (Sqrt[(2*(32678 + 10325*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/217 + (Sqrt[(2*(32678 + 10325*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/217 - (Sqrt[(-32678 + 10325*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/217 + (Sqrt[(-32678 + 10325*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/217","A",11,7,22,0.3182,1,"{740, 826, 1169, 634, 618, 204, 628}"
2321,1,283,0,0.3668287,"\int \frac{1}{(1+2 x)^{3/2} \left(2+3 x+5 x^2\right)^2} \, dx","Int[1/((1 + 2*x)^(3/2)*(2 + 3*x + 5*x^2)^2),x]","\frac{20 x+37}{217 \sqrt{2 x+1} \left(5 x^2+3 x+2\right)}-\frac{604}{1519 \sqrt{2 x+1}}-\frac{\sqrt{\frac{1}{434} \left(5682718+968975 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1519}+\frac{\sqrt{\frac{1}{434} \left(5682718+968975 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1519}+\frac{\sqrt{\frac{2}{217} \left(968975 \sqrt{35}-5682718\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{1519}-\frac{\sqrt{\frac{2}{217} \left(968975 \sqrt{35}-5682718\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{1519}","\frac{20 x+37}{217 \sqrt{2 x+1} \left(5 x^2+3 x+2\right)}-\frac{604}{1519 \sqrt{2 x+1}}-\frac{\sqrt{\frac{1}{434} \left(5682718+968975 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1519}+\frac{\sqrt{\frac{1}{434} \left(5682718+968975 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1519}+\frac{\sqrt{\frac{2}{217} \left(968975 \sqrt{35}-5682718\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{1519}-\frac{\sqrt{\frac{2}{217} \left(968975 \sqrt{35}-5682718\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{1519}",1,"-604/(1519*Sqrt[1 + 2*x]) + (37 + 20*x)/(217*Sqrt[1 + 2*x]*(2 + 3*x + 5*x^2)) + (Sqrt[(2*(-5682718 + 968975*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/1519 - (Sqrt[(2*(-5682718 + 968975*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/1519 - (Sqrt[(5682718 + 968975*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/1519 + (Sqrt[(5682718 + 968975*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/1519","A",12,8,22,0.3636,1,"{740, 828, 826, 1169, 634, 618, 204, 628}"
2322,1,296,0,0.4431796,"\int \frac{1}{(1+2 x)^{5/2} \left(2+3 x+5 x^2\right)^2} \, dx","Int[1/((1 + 2*x)^(5/2)*(2 + 3*x + 5*x^2)^2),x]","\frac{20 x+37}{217 (2 x+1)^{3/2} \left(5 x^2+3 x+2\right)}-\frac{4680}{10633 \sqrt{2 x+1}}-\frac{820}{4557 (2 x+1)^{3/2}}-\frac{5 \sqrt{\frac{1}{434} \left(2632525 \sqrt{35}-12504542\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{10633}+\frac{5 \sqrt{\frac{1}{434} \left(2632525 \sqrt{35}-12504542\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{10633}+\frac{5 \sqrt{\frac{2}{217} \left(12504542+2632525 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{10633}-\frac{5 \sqrt{\frac{2}{217} \left(12504542+2632525 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{10633}","\frac{20 x+37}{217 (2 x+1)^{3/2} \left(5 x^2+3 x+2\right)}-\frac{4680}{10633 \sqrt{2 x+1}}-\frac{820}{4557 (2 x+1)^{3/2}}-\frac{5 \sqrt{\frac{1}{434} \left(2632525 \sqrt{35}-12504542\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{10633}+\frac{5 \sqrt{\frac{1}{434} \left(2632525 \sqrt{35}-12504542\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{10633}+\frac{5 \sqrt{\frac{2}{217} \left(12504542+2632525 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{10633}-\frac{5 \sqrt{\frac{2}{217} \left(12504542+2632525 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{10633}",1,"-820/(4557*(1 + 2*x)^(3/2)) - 4680/(10633*Sqrt[1 + 2*x]) + (37 + 20*x)/(217*(1 + 2*x)^(3/2)*(2 + 3*x + 5*x^2)) + (5*Sqrt[(2*(12504542 + 2632525*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/10633 - (5*Sqrt[(2*(12504542 + 2632525*Sqrt[35]))/217]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/10633 - (5*Sqrt[(-12504542 + 2632525*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/10633 + (5*Sqrt[(-12504542 + 2632525*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/10633","A",13,8,22,0.3636,1,"{740, 828, 826, 1169, 634, 618, 204, 628}"
2323,1,313,0,0.5215328,"\int \frac{(1+2 x)^{9/2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[(1 + 2*x)^(9/2)/(2 + 3*x + 5*x^2)^3,x]","-\frac{(5-4 x) (2 x+1)^{7/2}}{62 \left(5 x^2+3 x+2\right)^2}-\frac{(1143-1088 x) (2 x+1)^{3/2}}{9610 \left(5 x^2+3 x+2\right)}-\frac{1584 \sqrt{2 x+1}}{24025}+\frac{3 \sqrt{\frac{1}{310} \left(64681225 \sqrt{35}-250141922\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{48050}-\frac{3 \sqrt{\frac{1}{310} \left(64681225 \sqrt{35}-250141922\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{48050}-\frac{3 \sqrt{\frac{1}{310} \left(250141922+64681225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{24025}+\frac{3 \sqrt{\frac{1}{310} \left(250141922+64681225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{24025}","-\frac{(5-4 x) (2 x+1)^{7/2}}{62 \left(5 x^2+3 x+2\right)^2}-\frac{(1143-1088 x) (2 x+1)^{3/2}}{9610 \left(5 x^2+3 x+2\right)}-\frac{1584 \sqrt{2 x+1}}{24025}+\frac{3 \sqrt{\frac{1}{310} \left(64681225 \sqrt{35}-250141922\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{48050}-\frac{3 \sqrt{\frac{1}{310} \left(64681225 \sqrt{35}-250141922\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{48050}-\frac{3 \sqrt{\frac{1}{310} \left(250141922+64681225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{24025}+\frac{3 \sqrt{\frac{1}{310} \left(250141922+64681225 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{24025}",1,"(-1584*Sqrt[1 + 2*x])/24025 - ((5 - 4*x)*(1 + 2*x)^(7/2))/(62*(2 + 3*x + 5*x^2)^2) - ((1143 - 1088*x)*(1 + 2*x)^(3/2))/(9610*(2 + 3*x + 5*x^2)) - (3*Sqrt[(250141922 + 64681225*Sqrt[35])/310]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/24025 + (3*Sqrt[(250141922 + 64681225*Sqrt[35])/310]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/24025 + (3*Sqrt[(-250141922 + 64681225*Sqrt[35])/310]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/48050 - (3*Sqrt[(-250141922 + 64681225*Sqrt[35])/310]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/48050","A",13,9,22,0.4091,1,"{738, 818, 824, 826, 1169, 634, 618, 204, 628}"
2324,1,300,0,0.4382872,"\int \frac{(1+2 x)^{7/2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[(1 + 2*x)^(7/2)/(2 + 3*x + 5*x^2)^3,x]","-\frac{(5-4 x) (2 x+1)^{5/2}}{62 \left(5 x^2+3 x+2\right)^2}-\frac{(957-592 x) \sqrt{2 x+1}}{9610 \left(5 x^2+3 x+2\right)}-\frac{\sqrt{\frac{1}{310} \left(1806875 \sqrt{35}-9651062\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{9610}+\frac{\sqrt{\frac{1}{310} \left(1806875 \sqrt{35}-9651062\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{9610}-\frac{\sqrt{\frac{1}{310} \left(9651062+1806875 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{4805}+\frac{\sqrt{\frac{1}{310} \left(9651062+1806875 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{4805}","-\frac{(5-4 x) (2 x+1)^{5/2}}{62 \left(5 x^2+3 x+2\right)^2}-\frac{(957-592 x) \sqrt{2 x+1}}{9610 \left(5 x^2+3 x+2\right)}-\frac{\sqrt{\frac{1}{310} \left(1806875 \sqrt{35}-9651062\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{9610}+\frac{\sqrt{\frac{1}{310} \left(1806875 \sqrt{35}-9651062\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{9610}-\frac{\sqrt{\frac{1}{310} \left(9651062+1806875 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{4805}+\frac{\sqrt{\frac{1}{310} \left(9651062+1806875 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{4805}",1,"-((5 - 4*x)*(1 + 2*x)^(5/2))/(62*(2 + 3*x + 5*x^2)^2) - ((957 - 592*x)*Sqrt[1 + 2*x])/(9610*(2 + 3*x + 5*x^2)) - (Sqrt[(9651062 + 1806875*Sqrt[35])/310]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/4805 + (Sqrt[(9651062 + 1806875*Sqrt[35])/310]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/4805 - (Sqrt[(-9651062 + 1806875*Sqrt[35])/310]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/9610 + (Sqrt[(-9651062 + 1806875*Sqrt[35])/310]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/9610","A",12,8,22,0.3636,1,"{738, 818, 826, 1169, 634, 618, 204, 628}"
2325,1,300,0,0.4350214,"\int \frac{(1+2 x)^{5/2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[(1 + 2*x)^(5/2)/(2 + 3*x + 5*x^2)^3,x]","-\frac{(5-4 x) (2 x+1)^{3/2}}{62 \left(5 x^2+3 x+2\right)^2}+\frac{3 (78 x+11) \sqrt{2 x+1}}{1922 \left(5 x^2+3 x+2\right)}+\frac{3 \sqrt{\frac{1}{310} \left(2705 \sqrt{35}-15082\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1922}-\frac{3 \sqrt{\frac{1}{310} \left(2705 \sqrt{35}-15082\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1922}-\frac{3}{961} \sqrt{\frac{1}{310} \left(15082+2705 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{3}{961} \sqrt{\frac{1}{310} \left(15082+2705 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","-\frac{(5-4 x) (2 x+1)^{3/2}}{62 \left(5 x^2+3 x+2\right)^2}+\frac{3 (78 x+11) \sqrt{2 x+1}}{1922 \left(5 x^2+3 x+2\right)}+\frac{3 \sqrt{\frac{1}{310} \left(2705 \sqrt{35}-15082\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1922}-\frac{3 \sqrt{\frac{1}{310} \left(2705 \sqrt{35}-15082\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1922}-\frac{3}{961} \sqrt{\frac{1}{310} \left(15082+2705 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{3}{961} \sqrt{\frac{1}{310} \left(15082+2705 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"-((5 - 4*x)*(1 + 2*x)^(3/2))/(62*(2 + 3*x + 5*x^2)^2) + (3*Sqrt[1 + 2*x]*(11 + 78*x))/(1922*(2 + 3*x + 5*x^2)) - (3*Sqrt[(15082 + 2705*Sqrt[35])/310]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/961 + (3*Sqrt[(15082 + 2705*Sqrt[35])/310]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/961 + (3*Sqrt[(-15082 + 2705*Sqrt[35])/310]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/1922 - (3*Sqrt[(-15082 + 2705*Sqrt[35])/310]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/1922","A",12,8,22,0.3636,1,"{738, 820, 826, 1169, 634, 618, 204, 628}"
2326,1,300,0,0.4219292,"\int \frac{(1+2 x)^{3/2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[(1 + 2*x)^(3/2)/(2 + 3*x + 5*x^2)^3,x]","-\frac{\sqrt{2 x+1} (5-4 x)}{62 \left(5 x^2+3 x+2\right)^2}+\frac{\sqrt{2 x+1} (120 x+67)}{1922 \left(5 x^2+3 x+2\right)}-\frac{3 \sqrt{\frac{1}{434} \left(2705 \sqrt{35}-15082\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1922}+\frac{3 \sqrt{\frac{1}{434} \left(2705 \sqrt{35}-15082\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1922}-\frac{3}{961} \sqrt{\frac{1}{434} \left(15082+2705 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{3}{961} \sqrt{\frac{1}{434} \left(15082+2705 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","-\frac{\sqrt{2 x+1} (5-4 x)}{62 \left(5 x^2+3 x+2\right)^2}+\frac{\sqrt{2 x+1} (120 x+67)}{1922 \left(5 x^2+3 x+2\right)}-\frac{3 \sqrt{\frac{1}{434} \left(2705 \sqrt{35}-15082\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1922}+\frac{3 \sqrt{\frac{1}{434} \left(2705 \sqrt{35}-15082\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{1922}-\frac{3}{961} \sqrt{\frac{1}{434} \left(15082+2705 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)+\frac{3}{961} \sqrt{\frac{1}{434} \left(15082+2705 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)",1,"-((5 - 4*x)*Sqrt[1 + 2*x])/(62*(2 + 3*x + 5*x^2)^2) + (Sqrt[1 + 2*x]*(67 + 120*x))/(1922*(2 + 3*x + 5*x^2)) - (3*Sqrt[(15082 + 2705*Sqrt[35])/434]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/961 + (3*Sqrt[(15082 + 2705*Sqrt[35])/434]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/961 - (3*Sqrt[(-15082 + 2705*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/1922 + (3*Sqrt[(-15082 + 2705*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/1922","A",12,8,22,0.3636,1,"{738, 822, 826, 1169, 634, 618, 204, 628}"
2327,1,300,0,0.3845675,"\int \frac{\sqrt{1+2 x}}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[Sqrt[1 + 2*x]/(2 + 3*x + 5*x^2)^3,x]","\frac{\sqrt{2 x+1} (10 x+3)}{62 \left(5 x^2+3 x+2\right)^2}+\frac{\sqrt{2 x+1} (1790 x+599)}{13454 \left(5 x^2+3 x+2\right)}+\frac{\sqrt{\frac{1}{434} \left(1806875 \sqrt{35}-9651062\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{13454}-\frac{\sqrt{\frac{1}{434} \left(1806875 \sqrt{35}-9651062\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{13454}-\frac{\sqrt{\frac{1}{434} \left(9651062+1806875 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{6727}+\frac{\sqrt{\frac{1}{434} \left(9651062+1806875 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{6727}","\frac{\sqrt{2 x+1} (10 x+3)}{62 \left(5 x^2+3 x+2\right)^2}+\frac{\sqrt{2 x+1} (1790 x+599)}{13454 \left(5 x^2+3 x+2\right)}+\frac{\sqrt{\frac{1}{434} \left(1806875 \sqrt{35}-9651062\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{13454}-\frac{\sqrt{\frac{1}{434} \left(1806875 \sqrt{35}-9651062\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{13454}-\frac{\sqrt{\frac{1}{434} \left(9651062+1806875 \sqrt{35}\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{6727}+\frac{\sqrt{\frac{1}{434} \left(9651062+1806875 \sqrt{35}\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{6727}",1,"(Sqrt[1 + 2*x]*(3 + 10*x))/(62*(2 + 3*x + 5*x^2)^2) + (Sqrt[1 + 2*x]*(599 + 1790*x))/(13454*(2 + 3*x + 5*x^2)) - (Sqrt[(9651062 + 1806875*Sqrt[35])/434]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/6727 + (Sqrt[(9651062 + 1806875*Sqrt[35])/434]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/6727 + (Sqrt[(-9651062 + 1806875*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/13454 - (Sqrt[(-9651062 + 1806875*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/13454","A",12,8,22,0.3636,1,"{736, 822, 826, 1169, 634, 618, 204, 628}"
2328,1,314,0,0.3861571,"\int \frac{1}{\sqrt{1+2 x} \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/(Sqrt[1 + 2*x]*(2 + 3*x + 5*x^2)^3),x]","\frac{\sqrt{2 x+1} (20 x+37)}{434 \left(5 x^2+3 x+2\right)^2}+\frac{\sqrt{2 x+1} (7920 x+9227)}{94178 \left(5 x^2+3 x+2\right)}-\frac{3 \sqrt{\frac{1}{434} \left(64681225 \sqrt{35}-250141922\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{94178}+\frac{3 \sqrt{\frac{1}{434} \left(64681225 \sqrt{35}-250141922\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{94178}-\frac{3 \sqrt{\frac{1}{434} \left(2+\sqrt{35}\right)} \left(7379+264 \sqrt{35}\right) \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{47089}+\frac{3 \sqrt{\frac{1}{434} \left(2+\sqrt{35}\right)} \left(7379+264 \sqrt{35}\right) \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{47089}","\frac{\sqrt{2 x+1} (20 x+37)}{434 \left(5 x^2+3 x+2\right)^2}+\frac{\sqrt{2 x+1} (7920 x+9227)}{94178 \left(5 x^2+3 x+2\right)}-\frac{3 \sqrt{\frac{1}{434} \left(64681225 \sqrt{35}-250141922\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{94178}+\frac{3 \sqrt{\frac{1}{434} \left(64681225 \sqrt{35}-250141922\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{94178}-\frac{3 \sqrt{\frac{1}{434} \left(2+\sqrt{35}\right)} \left(7379+264 \sqrt{35}\right) \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{47089}+\frac{3 \sqrt{\frac{1}{434} \left(2+\sqrt{35}\right)} \left(7379+264 \sqrt{35}\right) \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{47089}",1,"(Sqrt[1 + 2*x]*(37 + 20*x))/(434*(2 + 3*x + 5*x^2)^2) + (Sqrt[1 + 2*x]*(9227 + 7920*x))/(94178*(2 + 3*x + 5*x^2)) - (3*Sqrt[(2 + Sqrt[35])/434]*(7379 + 264*Sqrt[35])*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/47089 + (3*Sqrt[(2 + Sqrt[35])/434]*(7379 + 264*Sqrt[35])*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/47089 - (3*Sqrt[(-250141922 + 64681225*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/94178 + (3*Sqrt[(-250141922 + 64681225*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/94178","A",12,8,22,0.3636,1,"{740, 822, 826, 1169, 634, 618, 204, 628}"
2329,1,313,0,0.423517,"\int \frac{1}{(1+2 x)^{3/2} \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/((1 + 2*x)^(3/2)*(2 + 3*x + 5*x^2)^3),x]","\frac{20 x+37}{434 \sqrt{2 x+1} \left(5 x^2+3 x+2\right)^2}+\frac{5 (2080 x+2329)}{94178 \sqrt{2 x+1} \left(5 x^2+3 x+2\right)}-\frac{81090}{329623 \sqrt{2 x+1}}-\frac{15 \sqrt{\frac{1}{434} \left(2257111762+387427075 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{659246}+\frac{15 \sqrt{\frac{1}{434} \left(2257111762+387427075 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{659246}-\frac{15 \sqrt{\frac{1}{434} \left(387427075 \sqrt{35}-2257111762\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{329623}+\frac{15 \sqrt{\frac{1}{434} \left(387427075 \sqrt{35}-2257111762\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{329623}","\frac{20 x+37}{434 \sqrt{2 x+1} \left(5 x^2+3 x+2\right)^2}+\frac{5 (2080 x+2329)}{94178 \sqrt{2 x+1} \left(5 x^2+3 x+2\right)}-\frac{81090}{329623 \sqrt{2 x+1}}-\frac{15 \sqrt{\frac{1}{434} \left(2257111762+387427075 \sqrt{35}\right)} \log \left(5 (2 x+1)-\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{659246}+\frac{15 \sqrt{\frac{1}{434} \left(2257111762+387427075 \sqrt{35}\right)} \log \left(5 (2 x+1)+\sqrt{10 \left(2+\sqrt{35}\right)} \sqrt{2 x+1}+\sqrt{35}\right)}{659246}-\frac{15 \sqrt{\frac{1}{434} \left(387427075 \sqrt{35}-2257111762\right)} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{329623}+\frac{15 \sqrt{\frac{1}{434} \left(387427075 \sqrt{35}-2257111762\right)} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)}{329623}",1,"-81090/(329623*Sqrt[1 + 2*x]) + (37 + 20*x)/(434*Sqrt[1 + 2*x]*(2 + 3*x + 5*x^2)^2) + (5*(2329 + 2080*x))/(94178*Sqrt[1 + 2*x]*(2 + 3*x + 5*x^2)) - (15*Sqrt[(-2257111762 + 387427075*Sqrt[35])/434]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/329623 + (15*Sqrt[(-2257111762 + 387427075*Sqrt[35])/434]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]])/329623 - (15*Sqrt[(2257111762 + 387427075*Sqrt[35])/434]*Log[Sqrt[35] - Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/659246 + (15*Sqrt[(2257111762 + 387427075*Sqrt[35])/434]*Log[Sqrt[35] + Sqrt[10*(2 + Sqrt[35])]*Sqrt[1 + 2*x] + 5*(1 + 2*x)])/659246","A",13,9,22,0.4091,1,"{740, 822, 828, 826, 1169, 634, 618, 204, 628}"
2330,1,389,0,1.7629638,"\int \frac{x^{9/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[x^(9/2)/(a + b*x + c*x^2)^3,x]","\frac{3 \left(-\frac{44 a^2 b c^2-11 a b^3 c+b^5}{\sqrt{b^2-4 a c}}+28 a^2 c^2-9 a b^2 c+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{44 a^2 b c^2-11 a b^3 c+b^5}{\sqrt{b^2-4 a c}}+28 a^2 c^2-9 a b^2 c+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 b \sqrt{x} \left(b^2-8 a c\right)}{4 c^2 \left(b^2-4 a c\right)^2}+\frac{x^{7/2} (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x^{3/2} \left(b x \left(b^2-16 a c\right)+a \left(b^2-28 a c\right)\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}","\frac{3 \left(-\frac{44 a^2 b c^2-11 a b^3 c+b^5}{\sqrt{b^2-4 a c}}+28 a^2 c^2-9 a b^2 c+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{44 a^2 b c^2-11 a b^3 c+b^5}{\sqrt{b^2-4 a c}}+28 a^2 c^2-9 a b^2 c+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 b \sqrt{x} \left(b^2-8 a c\right)}{4 c^2 \left(b^2-4 a c\right)^2}+\frac{x^{7/2} (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x^{3/2} \left(b x \left(b^2-16 a c\right)+a \left(b^2-28 a c\right)\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}",1,"(-3*b*(b^2 - 8*a*c)*Sqrt[x])/(4*c^2*(b^2 - 4*a*c)^2) + (x^(7/2)*(2*a + b*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (x^(3/2)*(a*(b^2 - 28*a*c) + b*(b^2 - 16*a*c)*x))/(4*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (3*(b^4 - 9*a*b^2*c + 28*a^2*c^2 - (b^5 - 11*a*b^3*c + 44*a^2*b*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (3*(b^4 - 9*a*b^2*c + 28*a^2*c^2 + (b^5 - 11*a*b^3*c + 44*a^2*b*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,6,18,0.3333,1,"{738, 818, 824, 826, 1166, 205}"
2331,1,458,0,9.7215661,"\int \frac{1}{x^{3/2} \left(a+b x+c x^2\right)^3} \, dx","Int[1/(x^(3/2)*(a + b*x + c*x^2)^3),x]","\frac{36 a^2 c^2+b c x \left(5 b^2-32 a c\right)-35 a b^2 c+5 b^4}{4 a^2 \sqrt{x} \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \sqrt{c} \left(\sqrt{b^2-4 a c} \left(60 a^2 c^2-37 a b^2 c+5 b^4\right)+124 a^2 b c^2-47 a b^3 c+5 b^5\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} a^3 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \sqrt{c} \left(-60 a^2 c^2 \sqrt{b^2-4 a c}+124 a^2 b c^2-5 b^4 \sqrt{b^2-4 a c}-47 a b^3 c+37 a b^2 c \sqrt{b^2-4 a c}+5 b^5\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} a^3 \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 \left(5 b^2-12 a c\right) \left(b^2-5 a c\right)}{4 a^3 \sqrt{x} \left(b^2-4 a c\right)^2}+\frac{-2 a c+b^2+b c x}{2 a \sqrt{x} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{36 a^2 c^2+b c x \left(5 b^2-32 a c\right)-35 a b^2 c+5 b^4}{4 a^2 \sqrt{x} \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \sqrt{c} \left(\sqrt{b^2-4 a c} \left(60 a^2 c^2-37 a b^2 c+5 b^4\right)+124 a^2 b c^2-47 a b^3 c+5 b^5\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} a^3 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \sqrt{c} \left(-60 a^2 c^2 \sqrt{b^2-4 a c}+124 a^2 b c^2-5 b^4 \sqrt{b^2-4 a c}-47 a b^3 c+37 a b^2 c \sqrt{b^2-4 a c}+5 b^5\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} a^3 \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 \left(5 b^2-12 a c\right) \left(b^2-5 a c\right)}{4 a^3 \sqrt{x} \left(b^2-4 a c\right)^2}+\frac{-2 a c+b^2+b c x}{2 a \sqrt{x} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"(-3*(5*b^2 - 12*a*c)*(b^2 - 5*a*c))/(4*a^3*(b^2 - 4*a*c)^2*Sqrt[x]) + (b^2 - 2*a*c + b*c*x)/(2*a*(b^2 - 4*a*c)*Sqrt[x]*(a + b*x + c*x^2)^2) + (5*b^4 - 35*a*b^2*c + 36*a^2*c^2 + b*c*(5*b^2 - 32*a*c)*x)/(4*a^2*(b^2 - 4*a*c)^2*Sqrt[x]*(a + b*x + c*x^2)) - (3*Sqrt[c]*(5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2 + Sqrt[b^2 - 4*a*c]*(5*b^4 - 37*a*b^2*c + 60*a^2*c^2))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*a^3*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (3*Sqrt[c]*(5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2 - 5*b^4*Sqrt[b^2 - 4*a*c] + 37*a*b^2*c*Sqrt[b^2 - 4*a*c] - 60*a^2*c^2*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*a^3*(b^2 - 4*a*c)^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,6,18,0.3333,1,"{740, 822, 828, 826, 1166, 205}"
2332,1,28,0,0.0044893,"\int \frac{3-x+x^2}{\sqrt[3]{x}} \, dx","Int[(3 - x + x^2)/x^(1/3),x]","\frac{3 x^{8/3}}{8}-\frac{3 x^{5/3}}{5}+\frac{9 x^{2/3}}{2}","\frac{3 x^{8/3}}{8}-\frac{3 x^{5/3}}{5}+\frac{9 x^{2/3}}{2}",1,"(9*x^(2/3))/2 - (3*x^(5/3))/5 + (3*x^(8/3))/8","A",2,1,14,0.07143,1,"{14}"
2333,1,248,0,0.2549031,"\int (d+e x)^3 \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)^3*Sqrt[a + b*x + c*x^2],x]","\frac{e \left(a+b x+c x^2\right)^{3/2} \left(-2 c e (16 a e+75 b d)+35 b^2 e^2+42 c e x (2 c d-b e)+192 c^2 d^2\right)}{240 c^3}+\frac{(b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right)}{128 c^4}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{9/2}}+\frac{e (d+e x)^2 \left(a+b x+c x^2\right)^{3/2}}{5 c}","\frac{e \left(a+b x+c x^2\right)^{3/2} \left(-2 c e (16 a e+75 b d)+35 b^2 e^2+42 c e x (2 c d-b e)+192 c^2 d^2\right)}{240 c^3}+\frac{(b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right)}{128 c^4}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{9/2}}+\frac{e (d+e x)^2 \left(a+b x+c x^2\right)^{3/2}}{5 c}",1,"((2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(128*c^4) + (e*(d + e*x)^2*(a + b*x + c*x^2)^(3/2))/(5*c) + (e*(192*c^2*d^2 + 35*b^2*e^2 - 2*c*e*(75*b*d + 16*a*e) + 42*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(240*c^3) - ((b^2 - 4*a*c)*(2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(9/2))","A",5,5,22,0.2273,1,"{742, 779, 612, 621, 206}"
2334,1,191,0,0.2344117,"\int (d+e x)^2 \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)^2*Sqrt[a + b*x + c*x^2],x]","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2}}+\frac{5 e \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{24 c^2}+\frac{e (d+e x) \left(a+b x+c x^2\right)^{3/2}}{4 c}","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2}}+\frac{5 e \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{24 c^2}+\frac{e (d+e x) \left(a+b x+c x^2\right)^{3/2}}{4 c}",1,"((16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(64*c^3) + (5*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/2))/(24*c^2) + (e*(d + e*x)*(a + b*x + c*x^2)^(3/2))/(4*c) - ((b^2 - 4*a*c)*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(7/2))","A",5,5,22,0.2273,1,"{742, 640, 612, 621, 206}"
2335,1,115,0,0.0428137,"\int (d+e x) \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)*Sqrt[a + b*x + c*x^2],x]","-\frac{\left(b^2-4 a c\right) (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{5/2}}+\frac{(b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{8 c^2}+\frac{e \left(a+b x+c x^2\right)^{3/2}}{3 c}","-\frac{\left(b^2-4 a c\right) (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{5/2}}+\frac{(b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{8 c^2}+\frac{e \left(a+b x+c x^2\right)^{3/2}}{3 c}",1,"((2*c*d - b*e)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(8*c^2) + (e*(a + b*x + c*x^2)^(3/2))/(3*c) - ((b^2 - 4*a*c)*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(5/2))","A",4,4,20,0.2000,1,"{640, 612, 621, 206}"
2336,1,75,0,0.0196978,"\int \sqrt{a+b x+c x^2} \, dx","Int[Sqrt[a + b*x + c*x^2],x]","\frac{(b+2 c x) \sqrt{a+b x+c x^2}}{4 c}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{3/2}}","\frac{(b+2 c x) \sqrt{a+b x+c x^2}}{4 c}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{3/2}}",1,"((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(4*c) - ((b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(3/2))","A",3,3,14,0.2143,1,"{612, 621, 206}"
2337,1,152,0,0.1674018,"\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}"
2338,1,160,0,0.1268273,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^2} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x)^2,x]","-\frac{(2 c d-b 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)}{2 e^2 \sqrt{a e^2-b d e+c d^2}}-\frac{\sqrt{a+b x+c x^2}}{e (d+e x)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^2}","-\frac{(2 c d-b 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)}{2 e^2 \sqrt{a e^2-b d e+c d^2}}-\frac{\sqrt{a+b x+c x^2}}{e (d+e x)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^2}",1,"-(Sqrt[a + b*x + c*x^2]/(e*(d + e*x))) + (Sqrt[c]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/e^2 - ((2*c*d - b*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])])/(2*e^2*Sqrt[c*d^2 - b*d*e + a*e^2])","A",6,5,22,0.2273,1,"{732, 843, 621, 206, 724}"
2339,1,153,0,0.0979662,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^3} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x)^3,x]","\frac{\sqrt{a+b x+c x^2} (-2 a e+x (2 c d-b e)+b d)}{4 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{\left(b^2-4 a c\right) \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)}{8 \left(a e^2-b d e+c d^2\right)^{3/2}}","\frac{\sqrt{a+b x+c x^2} (-2 a e+x (2 c d-b e)+b d)}{4 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{\left(b^2-4 a c\right) \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)}{8 \left(a e^2-b d e+c d^2\right)^{3/2}}",1,"((b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(4*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - ((b^2 - 4*a*c)*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])])/(8*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",3,3,22,0.1364,1,"{720, 724, 206}"
2340,1,215,0,0.1475031,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^4} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x)^4,x]","-\frac{\left(b^2-4 a c\right) (2 c d-b 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)}{16 \left(a e^2-b d e+c d^2\right)^{5/2}}-\frac{e \left(a+b x+c x^2\right)^{3/2}}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{a+b x+c x^2} (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{8 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}","-\frac{\left(b^2-4 a c\right) (2 c d-b 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)}{16 \left(a e^2-b d e+c d^2\right)^{5/2}}-\frac{e \left(a+b x+c x^2\right)^{3/2}}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{a+b x+c x^2} (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{8 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}",1,"((2*c*d - b*e)*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (e*(a + b*x + c*x^2)^(3/2))/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) - ((b^2 - 4*a*c)*(2*c*d - b*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])])/(16*(c*d^2 - b*d*e + a*e^2)^(5/2))","A",4,4,22,0.1818,1,"{730, 720, 724, 206}"
2341,1,308,0,0.4153269,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^5} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x)^5,x]","\frac{\sqrt{a+b x+c x^2} \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{64 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(b^2-4 a c\right) \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \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)}{128 \left(a e^2-b d e+c d^2\right)^{7/2}}-\frac{5 e \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{24 (d+e x)^3 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(a+b x+c x^2\right)^{3/2}}{4 (d+e x)^4 \left(a e^2-b d e+c d^2\right)}","\frac{\sqrt{a+b x+c x^2} \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{64 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(b^2-4 a c\right) \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \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)}{128 \left(a e^2-b d e+c d^2\right)^{7/2}}-\frac{5 e \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{24 (d+e x)^3 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(a+b x+c x^2\right)^{3/2}}{4 (d+e x)^4 \left(a e^2-b d e+c d^2\right)}",1,"((16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(64*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) - (e*(a + b*x + c*x^2)^(3/2))/(4*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4) - (5*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/2))/(24*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^3) - ((b^2 - 4*a*c)*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*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])])/(128*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,5,22,0.2273,1,"{744, 806, 720, 724, 206}"
2342,1,402,0,0.5247293,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^6} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x)^6,x]","-\frac{e \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (8 a e+27 b d)+35 b^2 e^2+108 c^2 d^2\right)}{240 (d+e x)^3 \left(a e^2-b d e+c d^2\right)^3}+\frac{\sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{128 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^4}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right) \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)}{256 \left(a e^2-b d e+c d^2\right)^{9/2}}-\frac{7 e \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{40 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(a+b x+c x^2\right)^{3/2}}{5 (d+e x)^5 \left(a e^2-b d e+c d^2\right)}","-\frac{e \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (8 a e+27 b d)+35 b^2 e^2+108 c^2 d^2\right)}{240 (d+e x)^3 \left(a e^2-b d e+c d^2\right)^3}+\frac{\sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{128 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^4}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right) \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)}{256 \left(a e^2-b d e+c d^2\right)^{9/2}}-\frac{7 e \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{40 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(a+b x+c x^2\right)^{3/2}}{5 (d+e x)^5 \left(a e^2-b d e+c d^2\right)}",1,"((2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(128*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^2) - (e*(a + b*x + c*x^2)^(3/2))/(5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^5) - (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/2))/(40*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4) - (e*(108*c^2*d^2 + 35*b^2*e^2 - 4*c*e*(27*b*d + 8*a*e))*(a + b*x + c*x^2)^(3/2))/(240*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^3) - ((b^2 - 4*a*c)*(2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*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])])/(256*(c*d^2 - b*d*e + a*e^2)^(9/2))","A",6,6,22,0.2727,1,"{744, 834, 806, 720, 724, 206}"
2343,1,321,0,0.3469599,"\int (d+e x)^3 \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^(3/2),x]","\frac{e \left(a+b x+c x^2\right)^{5/2} \left(-2 c e (8 a e+49 b d)+21 b^2 e^2+30 c e x (2 c d-b e)+128 c^2 d^2\right)}{280 c^3}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right)}{128 c^4}-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right)}{1024 c^5}+\frac{3 \left(b^2-4 a c\right)^2 (2 c d-b e) \left(-4 c e (a e+2 b d)+3 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)}{2048 c^{11/2}}+\frac{e (d+e x)^2 \left(a+b x+c x^2\right)^{5/2}}{7 c}","\frac{e \left(a+b x+c x^2\right)^{5/2} \left(-2 c e (8 a e+49 b d)+21 b^2 e^2+30 c e x (2 c d-b e)+128 c^2 d^2\right)}{280 c^3}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right)}{128 c^4}-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right)}{1024 c^5}+\frac{3 \left(b^2-4 a c\right)^2 (2 c d-b e) \left(-4 c e (a e+2 b d)+3 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)}{2048 c^{11/2}}+\frac{e (d+e x)^2 \left(a+b x+c x^2\right)^{5/2}}{7 c}",1,"(-3*(b^2 - 4*a*c)*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^5) + ((2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(128*c^4) + (e*(d + e*x)^2*(a + b*x + c*x^2)^(5/2))/(7*c) + (e*(128*c^2*d^2 + 21*b^2*e^2 - 2*c*e*(49*b*d + 8*a*e) + 30*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2))/(280*c^3) + (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(11/2))","A",6,5,22,0.2273,1,"{742, 779, 612, 621, 206}"
2344,1,257,0,0.332935,"\int (d+e x)^2 \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^(3/2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{9/2}}+\frac{7 e \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{60 c^2}+\frac{e (d+e x) \left(a+b x+c x^2\right)^{5/2}}{6 c}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{9/2}}+\frac{7 e \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{60 c^2}+\frac{e (d+e x) \left(a+b x+c x^2\right)^{5/2}}{6 c}",1,"-((b^2 - 4*a*c)*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^4) + ((24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(192*c^3) + (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(5/2))/(60*c^2) + (e*(d + e*x)*(a + b*x + c*x^2)^(5/2))/(6*c) + ((b^2 - 4*a*c)^2*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(9/2))","A",6,5,22,0.2273,1,"{742, 640, 612, 621, 206}"
2345,1,161,0,0.0623502,"\int (d+e x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^(3/2),x]","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{128 c^3}+\frac{3 \left(b^2-4 a c\right)^2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{7/2}}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{16 c^2}+\frac{e \left(a+b x+c x^2\right)^{5/2}}{5 c}","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{128 c^3}+\frac{3 \left(b^2-4 a c\right)^2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{7/2}}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{16 c^2}+\frac{e \left(a+b x+c x^2\right)^{5/2}}{5 c}",1,"(-3*(b^2 - 4*a*c)*(2*c*d - b*e)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(128*c^3) + ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(16*c^2) + (e*(a + b*x + c*x^2)^(5/2))/(5*c) + (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(7/2))","A",5,4,20,0.2000,1,"{640, 612, 621, 206}"
2346,1,112,0,0.0331895,"\int \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(a + b*x + c*x^2)^(3/2),x]","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}{64 c^2}+\frac{3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{5/2}}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{8 c}","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}{64 c^2}+\frac{3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{5/2}}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{8 c}",1,"(-3*(b^2 - 4*a*c)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(64*c^2) + ((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(8*c) + (3*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(5/2))","A",4,3,14,0.2143,1,"{612, 621, 206}"
2347,1,252,0,0.3428798,"\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}"
2348,1,227,0,0.2747554,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^2,x]","\frac{3 \left(-4 c e (2 b d-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)}{8 \sqrt{c} e^4}-\frac{3 (2 c d-b 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)}{2 e^4}-\frac{3 \sqrt{a+b x+c x^2} (-3 b e+4 c d-2 c e x)}{4 e^3}-\frac{\left(a+b x+c x^2\right)^{3/2}}{e (d+e x)}","\frac{3 \left(-4 c e (2 b d-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)}{8 \sqrt{c} e^4}-\frac{3 (2 c d-b 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)}{2 e^4}-\frac{3 \sqrt{a+b x+c x^2} (-3 b e+4 c d-2 c e x)}{4 e^3}-\frac{\left(a+b x+c x^2\right)^{3/2}}{e (d+e x)}",1,"(-3*(4*c*d - 3*b*e - 2*c*e*x)*Sqrt[a + b*x + c*x^2])/(4*e^3) - (a + b*x + c*x^2)^(3/2)/(e*(d + e*x)) + (3*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[c]*e^4) - (3*(2*c*d - b*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])])/(2*e^4)","A",7,6,22,0.2727,1,"{732, 814, 843, 621, 206, 724}"
2349,1,236,0,0.2520686,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^3,x]","\frac{3 \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \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)}{8 e^4 \sqrt{a e^2-b d e+c d^2}}+\frac{3 \sqrt{a+b x+c x^2} (-b e+4 c d+2 c e x)}{4 e^3 (d+e x)}-\frac{3 \sqrt{c} (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 e^4}-\frac{\left(a+b x+c x^2\right)^{3/2}}{2 e (d+e x)^2}","\frac{3 \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \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)}{8 e^4 \sqrt{a e^2-b d e+c d^2}}+\frac{3 \sqrt{a+b x+c x^2} (-b e+4 c d+2 c e x)}{4 e^3 (d+e x)}-\frac{3 \sqrt{c} (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 e^4}-\frac{\left(a+b x+c x^2\right)^{3/2}}{2 e (d+e x)^2}",1,"(3*(4*c*d - b*e + 2*c*e*x)*Sqrt[a + b*x + c*x^2])/(4*e^3*(d + e*x)) - (a + b*x + c*x^2)^(3/2)/(2*e*(d + e*x)^2) - (3*Sqrt[c]*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*e^4) + (3*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*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])])/(8*e^4*Sqrt[c*d^2 - b*d*e + a*e^2])","A",7,6,22,0.2727,1,"{732, 812, 843, 621, 206, 724}"
2350,1,307,0,0.3553877,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^4} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^4,x]","-\frac{\sqrt{a+b x+c x^2} \left(e x \left(-4 c e (3 b d-2 a e)+b^2 e^2+12 c^2 d^2\right)-2 c d e (3 b d-2 a e)-b e^2 (b d-2 a e)+8 c^2 d^3\right)}{8 e^3 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\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{-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)}{16 e^4 \left(a e^2-b d e+c d^2\right)^{3/2}}+\frac{c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^4}-\frac{\left(a+b x+c x^2\right)^{3/2}}{3 e (d+e x)^3}","-\frac{\sqrt{a+b x+c x^2} \left(e x \left(-4 c e (3 b d-2 a e)+b^2 e^2+12 c^2 d^2\right)-2 c d e (3 b d-2 a e)-b e^2 (b d-2 a e)+8 c^2 d^3\right)}{8 e^3 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\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{-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)}{16 e^4 \left(a e^2-b d e+c d^2\right)^{3/2}}+\frac{c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^4}-\frac{\left(a+b x+c x^2\right)^{3/2}}{3 e (d+e x)^3}",1,"-((8*c^2*d^3 - b*e^2*(b*d - 2*a*e) - 2*c*d*e*(3*b*d - 2*a*e) + e*(12*c^2*d^2 + b^2*e^2 - 4*c*e*(3*b*d - 2*a*e))*x)*Sqrt[a + b*x + c*x^2])/(8*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (a + b*x + c*x^2)^(3/2)/(3*e*(d + e*x)^3) + (c^(3/2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/e^4 - ((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*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])])/(16*e^4*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",7,6,22,0.2727,1,"{732, 810, 843, 621, 206, 724}"
2351,1,225,0,0.1502745,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^5} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^5,x]","-\frac{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (-2 a e+x (2 c d-b e)+b d)}{64 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{3 \left(b^2-4 a c\right)^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)}{128 \left(a e^2-b d e+c d^2\right)^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{8 (d+e x)^4 \left(a e^2-b d e+c d^2\right)}","-\frac{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (-2 a e+x (2 c d-b e)+b d)}{64 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{3 \left(b^2-4 a c\right)^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)}{128 \left(a e^2-b d e+c d^2\right)^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{8 (d+e x)^4 \left(a e^2-b d e+c d^2\right)}",1,"(-3*(b^2 - 4*a*c)*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(64*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) + ((b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(8*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4) + (3*(b^2 - 4*a*c)^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])])/(128*(c*d^2 - b*d*e + a*e^2)^(5/2))","A",4,3,22,0.1364,1,"{720, 724, 206}"
2352,1,296,0,0.2347949,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^6} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^6,x]","-\frac{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{128 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}+\frac{3 \left(b^2-4 a c\right)^2 (2 c d-b 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)}{256 \left(a e^2-b d e+c d^2\right)^{7/2}}-\frac{e \left(a+b x+c x^2\right)^{5/2}}{5 (d+e x)^5 \left(a e^2-b d e+c d^2\right)}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{16 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^2}","-\frac{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{128 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}+\frac{3 \left(b^2-4 a c\right)^2 (2 c d-b 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)}{256 \left(a e^2-b d e+c d^2\right)^{7/2}}-\frac{e \left(a+b x+c x^2\right)^{5/2}}{5 (d+e x)^5 \left(a e^2-b d e+c d^2\right)}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{16 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^2}",1,"(-3*(b^2 - 4*a*c)*(2*c*d - b*e)*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(128*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) + ((2*c*d - b*e)*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(16*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4) - (e*(a + b*x + c*x^2)^(5/2))/(5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^5) + (3*(b^2 - 4*a*c)^2*(2*c*d - b*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])])/(256*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,4,22,0.1818,1,"{730, 720, 724, 206}"
2353,1,409,0,0.5959259,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^7} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^7,x]","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{192 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{512 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^4}+\frac{\left(b^2-4 a c\right)^2 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \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)}{1024 \left(a e^2-b d e+c d^2\right)^{9/2}}-\frac{7 e \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{60 (d+e x)^5 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(a+b x+c x^2\right)^{5/2}}{6 (d+e x)^6 \left(a e^2-b d e+c d^2\right)}","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{192 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{512 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^4}+\frac{\left(b^2-4 a c\right)^2 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \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)}{1024 \left(a e^2-b d e+c d^2\right)^{9/2}}-\frac{7 e \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{60 (d+e x)^5 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(a+b x+c x^2\right)^{5/2}}{6 (d+e x)^6 \left(a e^2-b d e+c d^2\right)}",1,"-((b^2 - 4*a*c)*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(512*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^2) + ((24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(192*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4) - (e*(a + b*x + c*x^2)^(5/2))/(6*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^6) - (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(5/2))/(60*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^5) + ((b^2 - 4*a*c)^2*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*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])])/(1024*(c*d^2 - b*d*e + a*e^2)^(9/2))","A",6,5,22,0.2273,1,"{744, 806, 720, 724, 206}"
2354,1,510,0,0.7659075,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^8} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^8,x]","-\frac{e \left(a+b x+c x^2\right)^{5/2} \left(-4 c e (4 a e+17 b d)+21 b^2 e^2+68 c^2 d^2\right)}{280 (d+e x)^5 \left(a e^2-b d e+c d^2\right)^3}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{128 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^4}-\frac{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{1024 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^5}+\frac{3 \left(b^2-4 a c\right)^2 (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \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)}{2048 \left(a e^2-b d e+c d^2\right)^{11/2}}-\frac{3 e \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{28 (d+e x)^6 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(a+b x+c x^2\right)^{5/2}}{7 (d+e x)^7 \left(a e^2-b d e+c d^2\right)}","-\frac{e \left(a+b x+c x^2\right)^{5/2} \left(-4 c e (4 a e+17 b d)+21 b^2 e^2+68 c^2 d^2\right)}{280 (d+e x)^5 \left(a e^2-b d e+c d^2\right)^3}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{128 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^4}-\frac{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{1024 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^5}+\frac{3 \left(b^2-4 a c\right)^2 (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \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)}{2048 \left(a e^2-b d e+c d^2\right)^{11/2}}-\frac{3 e \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{28 (d+e x)^6 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(a+b x+c x^2\right)^{5/2}}{7 (d+e x)^7 \left(a e^2-b d e+c d^2\right)}",1,"(-3*(b^2 - 4*a*c)*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(1024*(c*d^2 - b*d*e + a*e^2)^5*(d + e*x)^2) + ((2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(128*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^4) - (e*(a + b*x + c*x^2)^(5/2))/(7*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^7) - (3*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(5/2))/(28*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^6) - (e*(68*c^2*d^2 + 21*b^2*e^2 - 4*c*e*(17*b*d + 4*a*e))*(a + b*x + c*x^2)^(5/2))/(280*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^5) + (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*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])])/(2048*(c*d^2 - b*d*e + a*e^2)^(11/2))","A",7,6,22,0.2727,1,"{744, 834, 806, 720, 724, 206}"
2355,1,400,0,0.4399295,"\int (d+e x)^3 \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^(5/2),x]","\frac{e \left(a+b x+c x^2\right)^{7/2} \left(-2 c e (32 a e+243 b d)+99 b^2 e^2+154 c e x (2 c d-b e)+640 c^2 d^2\right)}{2016 c^3}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} (2 c d-b e) \left(-4 c e (3 a e+8 b d)+11 b^2 e^2+32 c^2 d^2\right)}{768 c^4}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e) \left(-4 c e (3 a e+8 b d)+11 b^2 e^2+32 c^2 d^2\right)}{12288 c^5}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (3 a e+8 b d)+11 b^2 e^2+32 c^2 d^2\right)}{32768 c^6}-\frac{5 \left(b^2-4 a c\right)^3 (2 c d-b e) \left(-4 c e (3 a e+8 b d)+11 b^2 e^2+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{65536 c^{13/2}}+\frac{e (d+e x)^2 \left(a+b x+c x^2\right)^{7/2}}{9 c}","\frac{e \left(a+b x+c x^2\right)^{7/2} \left(-2 c e (32 a e+243 b d)+99 b^2 e^2+154 c e x (2 c d-b e)+640 c^2 d^2\right)}{2016 c^3}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} (2 c d-b e) \left(-4 c e (3 a e+8 b d)+11 b^2 e^2+32 c^2 d^2\right)}{768 c^4}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e) \left(-4 c e (3 a e+8 b d)+11 b^2 e^2+32 c^2 d^2\right)}{12288 c^5}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (3 a e+8 b d)+11 b^2 e^2+32 c^2 d^2\right)}{32768 c^6}-\frac{5 \left(b^2-4 a c\right)^3 (2 c d-b e) \left(-4 c e (3 a e+8 b d)+11 b^2 e^2+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{65536 c^{13/2}}+\frac{e (d+e x)^2 \left(a+b x+c x^2\right)^{7/2}}{9 c}",1,"(5*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(32*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(8*b*d + 3*a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(32768*c^6) - (5*(b^2 - 4*a*c)*(2*c*d - b*e)*(32*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(8*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(12288*c^5) + ((2*c*d - b*e)*(32*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(8*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(768*c^4) + (e*(d + e*x)^2*(a + b*x + c*x^2)^(7/2))/(9*c) + (e*(640*c^2*d^2 + 99*b^2*e^2 - 2*c*e*(243*b*d + 32*a*e) + 154*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/2))/(2016*c^3) - (5*(b^2 - 4*a*c)^3*(2*c*d - b*e)*(32*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(8*b*d + 3*a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(65536*c^(13/2))","A",7,5,22,0.2273,1,"{742, 779, 612, 621, 206}"
2356,1,323,0,0.4398598,"\int (d+e x)^2 \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^(5/2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{384 c^3}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{6144 c^4}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{16384 c^5}-\frac{5 \left(b^2-4 a c\right)^3 \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{11/2}}+\frac{9 e \left(a+b x+c x^2\right)^{7/2} (2 c d-b e)}{112 c^2}+\frac{e (d+e x) \left(a+b x+c x^2\right)^{7/2}}{8 c}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{384 c^3}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{6144 c^4}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{16384 c^5}-\frac{5 \left(b^2-4 a c\right)^3 \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{11/2}}+\frac{9 e \left(a+b x+c x^2\right)^{7/2} (2 c d-b e)}{112 c^2}+\frac{e (d+e x) \left(a+b x+c x^2\right)^{7/2}}{8 c}",1,"(5*(b^2 - 4*a*c)^2*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(16384*c^5) - (5*(b^2 - 4*a*c)*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(6144*c^4) + ((32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(384*c^3) + (9*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(7/2))/(112*c^2) + (e*(d + e*x)*(a + b*x + c*x^2)^(7/2))/(8*c) - (5*(b^2 - 4*a*c)^3*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32768*c^(11/2))","A",7,5,22,0.2273,1,"{742, 640, 612, 621, 206}"
2357,1,207,0,0.0885637,"\int (d+e x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^(5/2),x]","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{384 c^3}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{1024 c^4}-\frac{5 \left(b^2-4 a c\right)^3 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{9/2}}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{24 c^2}+\frac{e \left(a+b x+c x^2\right)^{7/2}}{7 c}","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{384 c^3}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{1024 c^4}-\frac{5 \left(b^2-4 a c\right)^3 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{9/2}}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{24 c^2}+\frac{e \left(a+b x+c x^2\right)^{7/2}}{7 c}",1,"(5*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^4) - (5*(b^2 - 4*a*c)*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(384*c^3) + ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(24*c^2) + (e*(a + b*x + c*x^2)^(7/2))/(7*c) - (5*(b^2 - 4*a*c)^3*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(9/2))","A",6,4,20,0.2000,1,"{640, 612, 621, 206}"
2358,1,149,0,0.0503224,"\int \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(a + b*x + c*x^2)^(5/2),x]","\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}{512 c^3}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{192 c^2}-\frac{5 \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{7/2}}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{12 c}","\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}{512 c^3}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{192 c^2}-\frac{5 \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{7/2}}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{12 c}",1,"(5*(b^2 - 4*a*c)^2*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^3) - (5*(b^2 - 4*a*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(192*c^2) + ((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(12*c) - (5*(b^2 - 4*a*c)^3*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(7/2))","A",5,3,14,0.2143,1,"{612, 621, 206}"
2359,1,459,0,0.7496411,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{d+e x} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x),x]","\frac{\sqrt{a+b x+c x^2} \left(8 c^2 e^2 \left(16 a^2 e^2-39 a b d e+22 b^2 d^2\right)-2 c e x (2 c d-b e) \left(-4 c e (4 b d-7 a e)-3 b^2 e^2+16 c^2 d^2\right)-2 b^2 c e^3 (5 b d-14 a e)-32 c^3 d^2 e (9 b d-8 a e)-3 b^4 e^4+128 c^4 d^4\right)}{128 c^2 e^5}-\frac{(2 c d-b e) \left(16 c^2 e^2 \left(15 a^2 e^2-20 a b d e+7 b^2 d^2\right)+8 b^2 c e^3 (2 b d-5 a e)-64 c^3 d^2 e (4 b d-5 a e)+3 b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{5/2} e^6}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(-2 c e (11 b d-8 a e)+3 b^2 e^2-6 c e x (2 c d-b e)+16 c^2 d^2\right)}{48 c e^3}+\frac{\left(a e^2-b d e+c d^2\right)^{5/2} \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{\left(a+b x+c x^2\right)^{5/2}}{5 e}","\frac{\sqrt{a+b x+c x^2} \left(8 c^2 e^2 \left(16 a^2 e^2-39 a b d e+22 b^2 d^2\right)-2 c e x (2 c d-b e) \left(-4 c e (4 b d-7 a e)-3 b^2 e^2+16 c^2 d^2\right)-2 b^2 c e^3 (5 b d-14 a e)-32 c^3 d^2 e (9 b d-8 a e)-3 b^4 e^4+128 c^4 d^4\right)}{128 c^2 e^5}-\frac{(2 c d-b e) \left(16 c^2 e^2 \left(15 a^2 e^2-20 a b d e+7 b^2 d^2\right)+8 b^2 c e^3 (2 b d-5 a e)-64 c^3 d^2 e (4 b d-5 a e)+3 b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{5/2} e^6}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(-2 c e (11 b d-8 a e)+3 b^2 e^2-6 c e x (2 c d-b e)+16 c^2 d^2\right)}{48 c e^3}+\frac{\left(a e^2-b d e+c d^2\right)^{5/2} \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{\left(a+b x+c x^2\right)^{5/2}}{5 e}",1,"((128*c^4*d^4 - 3*b^4*e^4 - 2*b^2*c*e^3*(5*b*d - 14*a*e) - 32*c^3*d^2*e*(9*b*d - 8*a*e) + 8*c^2*e^2*(22*b^2*d^2 - 39*a*b*d*e + 16*a^2*e^2) - 2*c*e*(2*c*d - b*e)*(16*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(4*b*d - 7*a*e))*x)*Sqrt[a + b*x + c*x^2])/(128*c^2*e^5) + ((16*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(11*b*d - 8*a*e) - 6*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(48*c*e^3) + (a + b*x + c*x^2)^(5/2)/(5*e) - ((2*c*d - b*e)*(128*c^4*d^4 + 3*b^4*e^4 + 8*b^2*c*e^3*(2*b*d - 5*a*e) - 64*c^3*d^2*e*(4*b*d - 5*a*e) + 16*c^2*e^2*(7*b^2*d^2 - 20*a*b*d*e + 15*a^2*e^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(5/2)*e^6) + ((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^6","A",8,6,22,0.2727,1,"{734, 814, 843, 621, 206, 724}"
2360,1,388,0,0.6632178,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x)^2,x]","\frac{5 \left(48 c^2 e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-8 b^2 c e^3 (2 b d-3 a e)-64 c^3 d^2 e (4 b d-3 a e)-b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{3/2} e^6}-\frac{5 \sqrt{a+b x+c x^2} \left(-2 c e x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (7 b d-4 a e)+4 b c e^2 (12 b d-11 a e)-b^3 e^3+64 c^3 d^3\right)}{64 c e^5}-\frac{5 (2 c d-b e) \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)}{2 e^6}-\frac{5 \left(a+b x+c x^2\right)^{3/2} (-7 b e+8 c d-6 c e x)}{24 e^3}-\frac{\left(a+b x+c x^2\right)^{5/2}}{e (d+e x)}","\frac{5 \left(48 c^2 e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-8 b^2 c e^3 (2 b d-3 a e)-64 c^3 d^2 e (4 b d-3 a e)-b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{3/2} e^6}-\frac{5 \sqrt{a+b x+c x^2} \left(-2 c e x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (7 b d-4 a e)+4 b c e^2 (12 b d-11 a e)-b^3 e^3+64 c^3 d^3\right)}{64 c e^5}-\frac{5 (2 c d-b e) \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)}{2 e^6}-\frac{5 \left(a+b x+c x^2\right)^{3/2} (-7 b e+8 c d-6 c e x)}{24 e^3}-\frac{\left(a+b x+c x^2\right)^{5/2}}{e (d+e x)}",1,"(-5*(64*c^3*d^3 - b^3*e^3 + 4*b*c*e^2*(12*b*d - 11*a*e) - 16*c^2*d*e*(7*b*d - 4*a*e) - 2*c*e*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x)*Sqrt[a + b*x + c*x^2])/(64*c*e^5) - (5*(8*c*d - 7*b*e - 6*c*e*x)*(a + b*x + c*x^2)^(3/2))/(24*e^3) - (a + b*x + c*x^2)^(5/2)/(e*(d + e*x)) + (5*(128*c^4*d^4 - b^4*e^4 - 8*b^2*c*e^3*(2*b*d - 3*a*e) - 64*c^3*d^2*e*(4*b*d - 3*a*e) + 48*c^2*e^2*(3*b^2*d^2 - 4*a*b*d*e + a^2*e^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(3/2)*e^6) - (5*(2*c*d - b*e)*(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])])/(2*e^6)","A",8,6,22,0.2727,1,"{732, 814, 843, 621, 206, 724}"
2361,1,331,0,0.5481457,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x)^3,x]","\frac{5 \sqrt{a+b x+c x^2} \left(-4 c e (5 b d-a e)+5 b^2 e^2-4 c e x (2 c d-b e)+16 c^2 d^2\right)}{8 e^5}-\frac{5 (2 c d-b e) \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 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 \sqrt{c} e^6}+\frac{5 \sqrt{a e^2-b d e+c d^2} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \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)}{8 e^6}+\frac{5 \left(a+b x+c x^2\right)^{3/2} (-3 b e+8 c d+2 c e x)}{12 e^3 (d+e x)}-\frac{\left(a+b x+c x^2\right)^{5/2}}{2 e (d+e x)^2}","\frac{5 \sqrt{a+b x+c x^2} \left(-4 c e (5 b d-a e)+5 b^2 e^2-4 c e x (2 c d-b e)+16 c^2 d^2\right)}{8 e^5}-\frac{5 (2 c d-b e) \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 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 \sqrt{c} e^6}+\frac{5 \sqrt{a e^2-b d e+c d^2} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \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)}{8 e^6}+\frac{5 \left(a+b x+c x^2\right)^{3/2} (-3 b e+8 c d+2 c e x)}{12 e^3 (d+e x)}-\frac{\left(a+b x+c x^2\right)^{5/2}}{2 e (d+e x)^2}",1,"(5*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(5*b*d - a*e) - 4*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*e^5) + (5*(8*c*d - 3*b*e + 2*c*e*x)*(a + b*x + c*x^2)^(3/2))/(12*e^3*(d + e*x)) - (a + b*x + c*x^2)^(5/2)/(2*e*(d + e*x)^2) - (5*(2*c*d - b*e)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*Sqrt[c]*e^6) + (5*Sqrt[c*d^2 - b*d*e + a*e^2]*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*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])])/(8*e^6)","A",8,7,22,0.3182,1,"{732, 812, 814, 843, 621, 206, 724}"
2362,1,337,0,0.4288502,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x)^4,x]","-\frac{5 \sqrt{a+b x+c x^2} \left(-4 c e (3 b d-a e)+b^2 e^2+4 c e x (2 c d-b e)+16 c^2 d^2\right)}{8 e^5 (d+e x)}+\frac{5 \sqrt{c} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 e^6}-\frac{5 (2 c d-b e) \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) \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)}{16 e^6 \sqrt{a e^2-b d e+c d^2}}+\frac{5 \left(a+b x+c x^2\right)^{3/2} (-b e+4 c d+2 c e x)}{12 e^3 (d+e x)^2}-\frac{\left(a+b x+c x^2\right)^{5/2}}{3 e (d+e x)^3}","-\frac{5 \sqrt{a+b x+c x^2} \left(-4 c e (3 b d-a e)+b^2 e^2+4 c e x (2 c d-b e)+16 c^2 d^2\right)}{8 e^5 (d+e x)}+\frac{5 \sqrt{c} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 e^6}-\frac{5 (2 c d-b e) \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) \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)}{16 e^6 \sqrt{a e^2-b d e+c d^2}}+\frac{5 \left(a+b x+c x^2\right)^{3/2} (-b e+4 c d+2 c e x)}{12 e^3 (d+e x)^2}-\frac{\left(a+b x+c x^2\right)^{5/2}}{3 e (d+e x)^3}",1,"(-5*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(3*b*d - a*e) + 4*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*e^5*(d + e*x)) + (5*(4*c*d - b*e + 2*c*e*x)*(a + b*x + c*x^2)^(3/2))/(12*e^3*(d + e*x)^2) - (a + b*x + c*x^2)^(5/2)/(3*e*(d + e*x)^3) + (5*Sqrt[c]*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*e^6) - (5*(2*c*d - b*e)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*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])])/(16*e^6*Sqrt[c*d^2 - b*d*e + a*e^2])","A",8,6,22,0.2727,1,"{732, 812, 843, 621, 206, 724}"
2363,1,492,0,0.7347627,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x)^5} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x)^5,x]","\frac{5 \left(48 c^2 e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-8 b^2 c e^3 (2 b d-3 a e)-64 c^3 d^2 e (4 b d-3 a e)-b^4 e^4+128 c^4 d^4\right) \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)}{128 e^6 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2} \left(3 e x \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right)-4 c d e (3 b d-a e)-b e^2 (b d-4 a e)+16 c^2 d^3\right)}{96 e^3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}+\frac{5 \sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (5 b d-4 a e)+4 b c e^2 (4 b d-5 a e)+b^3 e^3+64 c^3 d^3\right)}{64 e^5 (d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{5 c^{3/2} (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 e^6}-\frac{\left(a+b x+c x^2\right)^{5/2}}{4 e (d+e x)^4}","\frac{5 \left(48 c^2 e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-8 b^2 c e^3 (2 b d-3 a e)-64 c^3 d^2 e (4 b d-3 a e)-b^4 e^4+128 c^4 d^4\right) \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)}{128 e^6 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2} \left(3 e x \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right)-4 c d e (3 b d-a e)-b e^2 (b d-4 a e)+16 c^2 d^3\right)}{96 e^3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}+\frac{5 \sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (5 b d-4 a e)+4 b c e^2 (4 b d-5 a e)+b^3 e^3+64 c^3 d^3\right)}{64 e^5 (d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{5 c^{3/2} (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 e^6}-\frac{\left(a+b x+c x^2\right)^{5/2}}{4 e (d+e x)^4}",1,"(5*(64*c^3*d^3 + b^3*e^3 + 4*b*c*e^2*(4*b*d - 5*a*e) - 16*c^2*d*e*(5*b*d - 4*a*e) + 2*c*e*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x)*Sqrt[a + b*x + c*x^2])/(64*e^5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)) - (5*(16*c^2*d^3 - b*e^2*(b*d - 4*a*e) - 4*c*d*e*(3*b*d - a*e) + 3*e*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*x)*(a + b*x + c*x^2)^(3/2))/(96*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) - (a + b*x + c*x^2)^(5/2)/(4*e*(d + e*x)^4) - (5*c^(3/2)*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*e^6) + (5*(128*c^4*d^4 - b^4*e^4 - 8*b^2*c*e^3*(2*b*d - 3*a*e) - 64*c^3*d^2*e*(4*b*d - 3*a*e) + 48*c^2*e^2*(3*b^2*d^2 - 4*a*b*d*e + a^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])])/(128*e^6*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",8,7,22,0.3182,1,"{732, 810, 812, 843, 621, 206, 724}"
2364,1,88,0,0.0487672,"\int \frac{\sqrt{-2-3 x+5 x^2}}{x} \, dx","Int[Sqrt[-2 - 3*x + 5*x^2]/x,x]","\sqrt{5 x^2-3 x-2}+\sqrt{2} \tan ^{-1}\left(\frac{3 x+4}{2 \sqrt{2} \sqrt{5 x^2-3 x-2}}\right)+\frac{3 \tanh ^{-1}\left(\frac{3-10 x}{2 \sqrt{5} \sqrt{5 x^2-3 x-2}}\right)}{2 \sqrt{5}}","\sqrt{5 x^2-3 x-2}+\sqrt{2} \tan ^{-1}\left(\frac{3 x+4}{2 \sqrt{2} \sqrt{5 x^2-3 x-2}}\right)+\frac{3 \tanh ^{-1}\left(\frac{3-10 x}{2 \sqrt{5} \sqrt{5 x^2-3 x-2}}\right)}{2 \sqrt{5}}",1,"Sqrt[-2 - 3*x + 5*x^2] + Sqrt[2]*ArcTan[(4 + 3*x)/(2*Sqrt[2]*Sqrt[-2 - 3*x + 5*x^2])] + (3*ArcTanh[(3 - 10*x)/(2*Sqrt[5]*Sqrt[-2 - 3*x + 5*x^2])])/(2*Sqrt[5])","A",6,6,18,0.3333,1,"{734, 843, 621, 206, 724, 204}"
2365,1,68,0,0.0406899,"\int \frac{\sqrt{2-x-x^2}}{x^2} \, dx","Int[Sqrt[2 - x - x^2]/x^2,x]","-\frac{\sqrt{-x^2-x+2}}{x}+\frac{\tanh ^{-1}\left(\frac{4-x}{2 \sqrt{2} \sqrt{-x^2-x+2}}\right)}{2 \sqrt{2}}+\sin ^{-1}\left(\frac{1}{3} (-2 x-1)\right)","-\frac{\sqrt{-x^2-x+2}}{x}+\frac{\tanh ^{-1}\left(\frac{4-x}{2 \sqrt{2} \sqrt{-x^2-x+2}}\right)}{2 \sqrt{2}}+\sin ^{-1}\left(\frac{1}{3} (-2 x-1)\right)",1,"-(Sqrt[2 - x - x^2]/x) + ArcSin[(-1 - 2*x)/3] + ArcTanh[(4 - x)/(2*Sqrt[2]*Sqrt[2 - x - x^2])]/(2*Sqrt[2])","A",6,6,18,0.3333,1,"{732, 843, 619, 216, 724, 206}"
2366,1,38,0,0.0118175,"\int (1+x)^3 \sqrt{2+2 x+x^2} \, dx","Int[(1 + x)^3*Sqrt[2 + 2*x + x^2],x]","\frac{1}{5} (x+1)^2 \left(x^2+2 x+2\right)^{3/2}-\frac{2}{15} \left(x^2+2 x+2\right)^{3/2}","\frac{1}{5} (x+1)^2 \left(x^2+2 x+2\right)^{3/2}-\frac{2}{15} \left(x^2+2 x+2\right)^{3/2}",1,"(-2*(2 + 2*x + x^2)^(3/2))/15 + ((1 + x)^2*(2 + 2*x + x^2)^(3/2))/5","A",2,2,18,0.1111,1,"{692, 629}"
2367,1,54,0,0.0180984,"\int (-2+3 x) \sqrt{8+12 x+9 x^2} \, dx","Int[(-2 + 3*x)*Sqrt[8 + 12*x + 9*x^2],x]","\frac{1}{9} \left(9 x^2+12 x+8\right)^{3/2}-\frac{2}{3} (3 x+2) \sqrt{9 x^2+12 x+8}-\frac{8}{3} \sinh ^{-1}\left(\frac{3 x}{2}+1\right)","\frac{1}{9} \left(9 x^2+12 x+8\right)^{3/2}-\frac{2}{3} (3 x+2) \sqrt{9 x^2+12 x+8}-\frac{8}{3} \sinh ^{-1}\left(\frac{3 x}{2}+1\right)",1,"(-2*(2 + 3*x)*Sqrt[8 + 12*x + 9*x^2])/3 + (8 + 12*x + 9*x^2)^(3/2)/9 - (8*ArcSinh[1 + (3*x)/2])/3","A",4,4,20,0.2000,1,"{640, 612, 619, 215}"
2368,1,56,0,0.0171845,"\int (7-2 x) \sqrt{9+16 x-4 x^2} \, dx","Int[(7 - 2*x)*Sqrt[9 + 16*x - 4*x^2],x]","\frac{1}{6} \left(-4 x^2+16 x+9\right)^{3/2}-\frac{3}{2} (2-x) \sqrt{-4 x^2+16 x+9}-\frac{75}{4} \sin ^{-1}\left(\frac{2 (2-x)}{5}\right)","\frac{1}{6} \left(-4 x^2+16 x+9\right)^{3/2}-\frac{3}{2} (2-x) \sqrt{-4 x^2+16 x+9}-\frac{75}{4} \sin ^{-1}\left(\frac{2 (2-x)}{5}\right)",1,"(-3*(2 - x)*Sqrt[9 + 16*x - 4*x^2])/2 + (9 + 16*x - 4*x^2)^(3/2)/6 - (75*ArcSin[(2*(2 - x))/5])/4","A",4,4,20,0.2000,1,"{640, 612, 619, 216}"
2369,1,61,0,0.0425961,"\int \frac{\sqrt{-1-x+x^2}}{1+x} \, dx","Int[Sqrt[-1 - x + x^2]/(1 + x),x]","\sqrt{x^2-x-1}+\frac{3}{2} \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)+\tanh ^{-1}\left(\frac{3 x+1}{2 \sqrt{x^2-x-1}}\right)","\sqrt{x^2-x-1}+\frac{3}{2} \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)+\tanh ^{-1}\left(\frac{3 x+1}{2 \sqrt{x^2-x-1}}\right)",1,"Sqrt[-1 - x + x^2] + (3*ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])])/2 + ArcTanh[(1 + 3*x)/(2*Sqrt[-1 - x + x^2])]","A",6,5,18,0.2778,1,"{734, 843, 621, 206, 724}"
2370,1,65,0,0.0428585,"\int \frac{\sqrt{-1-x+x^2}}{1-x} \, dx","Int[Sqrt[-1 - x + x^2]/(1 - x),x]","-\sqrt{x^2-x-1}-\tan ^{-1}\left(\frac{3-x}{2 \sqrt{x^2-x-1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)","-\sqrt{x^2-x-1}-\tan ^{-1}\left(\frac{3-x}{2 \sqrt{x^2-x-1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)",1,"-Sqrt[-1 - x + x^2] - ArcTan[(3 - x)/(2*Sqrt[-1 - x + x^2])] + ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])]/2","A",6,6,20,0.3000,1,"{734, 843, 621, 206, 724, 204}"
2371,1,261,0,0.3818299,"\int \frac{x^6}{\sqrt{a+b x+c x^2}} \, dx","Int[x^6/Sqrt[a + b*x + c*x^2],x]","-\frac{\left(7 b \left(528 a^2 c^2-680 a b^2 c+165 b^4\right)-2 c x \left(400 a^2 c^2-1176 a b^2 c+385 b^4\right)\right) \sqrt{a+b x+c x^2}}{2560 c^6}+\frac{\left(1680 a^2 b^2 c^2-320 a^3 c^3-1260 a b^4 c+231 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{13/2}}+\frac{x^3 \left(99 b^2-100 a c\right) \sqrt{a+b x+c x^2}}{480 c^3}-\frac{b x^2 \left(77 b^2-156 a c\right) \sqrt{a+b x+c x^2}}{320 c^4}-\frac{11 b x^4 \sqrt{a+b x+c x^2}}{60 c^2}+\frac{x^5 \sqrt{a+b x+c x^2}}{6 c}","-\frac{\left(7 b \left(528 a^2 c^2-680 a b^2 c+165 b^4\right)-2 c x \left(400 a^2 c^2-1176 a b^2 c+385 b^4\right)\right) \sqrt{a+b x+c x^2}}{2560 c^6}+\frac{\left(1680 a^2 b^2 c^2-320 a^3 c^3-1260 a b^4 c+231 b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{13/2}}+\frac{x^3 \left(99 b^2-100 a c\right) \sqrt{a+b x+c x^2}}{480 c^3}-\frac{b x^2 \left(77 b^2-156 a c\right) \sqrt{a+b x+c x^2}}{320 c^4}-\frac{11 b x^4 \sqrt{a+b x+c x^2}}{60 c^2}+\frac{x^5 \sqrt{a+b x+c x^2}}{6 c}",1,"-(b*(77*b^2 - 156*a*c)*x^2*Sqrt[a + b*x + c*x^2])/(320*c^4) + ((99*b^2 - 100*a*c)*x^3*Sqrt[a + b*x + c*x^2])/(480*c^3) - (11*b*x^4*Sqrt[a + b*x + c*x^2])/(60*c^2) + (x^5*Sqrt[a + b*x + c*x^2])/(6*c) - ((7*b*(165*b^4 - 680*a*b^2*c + 528*a^2*c^2) - 2*c*(385*b^4 - 1176*a*b^2*c + 400*a^2*c^2)*x)*Sqrt[a + b*x + c*x^2])/(2560*c^6) + ((231*b^6 - 1260*a*b^4*c + 1680*a^2*b^2*c^2 - 320*a^3*c^3)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(13/2))","A",7,5,18,0.2778,1,"{742, 832, 779, 621, 206}"
2372,1,202,0,0.2165003,"\int \frac{x^5}{\sqrt{a+b x+c x^2}} \, dx","Int[x^5/Sqrt[a + b*x + c*x^2],x]","\frac{\left(1024 a^2 c^2-14 b c x \left(45 b^2-92 a c\right)-2940 a b^2 c+945 b^4\right) \sqrt{a+b x+c x^2}}{1920 c^5}-\frac{b \left(240 a^2 c^2-280 a b^2 c+63 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{11/2}}+\frac{x^2 \left(63 b^2-64 a c\right) \sqrt{a+b x+c x^2}}{240 c^3}-\frac{9 b x^3 \sqrt{a+b x+c x^2}}{40 c^2}+\frac{x^4 \sqrt{a+b x+c x^2}}{5 c}","\frac{\left(1024 a^2 c^2-14 b c x \left(45 b^2-92 a c\right)-2940 a b^2 c+945 b^4\right) \sqrt{a+b x+c x^2}}{1920 c^5}-\frac{b \left(240 a^2 c^2-280 a b^2 c+63 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{11/2}}+\frac{x^2 \left(63 b^2-64 a c\right) \sqrt{a+b x+c x^2}}{240 c^3}-\frac{9 b x^3 \sqrt{a+b x+c x^2}}{40 c^2}+\frac{x^4 \sqrt{a+b x+c x^2}}{5 c}",1,"((63*b^2 - 64*a*c)*x^2*Sqrt[a + b*x + c*x^2])/(240*c^3) - (9*b*x^3*Sqrt[a + b*x + c*x^2])/(40*c^2) + (x^4*Sqrt[a + b*x + c*x^2])/(5*c) + ((945*b^4 - 2940*a*b^2*c + 1024*a^2*c^2 - 14*b*c*(45*b^2 - 92*a*c)*x)*Sqrt[a + b*x + c*x^2])/(1920*c^5) - (b*(63*b^4 - 280*a*b^2*c + 240*a^2*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(11/2))","A",6,5,18,0.2778,1,"{742, 832, 779, 621, 206}"
2373,1,296,0,0.3772915,"\int \frac{(d+e x)^4}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^4/Sqrt[a + b*x + c*x^2],x]","\frac{\left(48 c^2 e^2 \left(a^2 e^2+8 a b d e+6 b^2 d^2\right)-40 b^2 c e^3 (3 a e+4 b d)-128 c^3 d^2 e (3 a e+2 b d)+35 b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{9/2}}+\frac{e \sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (9 a e+26 b d)+35 b^2 e^2+104 c^2 d^2\right)-8 c^2 d e (64 a e+101 b d)+20 b c e^2 (11 a e+24 b d)-105 b^3 e^3+608 c^3 d^3\right)}{192 c^4}+\frac{7 e (d+e x)^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{24 c^2}+\frac{e (d+e x)^3 \sqrt{a+b x+c x^2}}{4 c}","\frac{\left(48 c^2 e^2 \left(a^2 e^2+8 a b d e+6 b^2 d^2\right)-40 b^2 c e^3 (3 a e+4 b d)-128 c^3 d^2 e (3 a e+2 b d)+35 b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{9/2}}+\frac{e \sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (9 a e+26 b d)+35 b^2 e^2+104 c^2 d^2\right)-8 c^2 d e (64 a e+101 b d)+20 b c e^2 (11 a e+24 b d)-105 b^3 e^3+608 c^3 d^3\right)}{192 c^4}+\frac{7 e (d+e x)^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{24 c^2}+\frac{e (d+e x)^3 \sqrt{a+b x+c x^2}}{4 c}",1,"(7*e*(2*c*d - b*e)*(d + e*x)^2*Sqrt[a + b*x + c*x^2])/(24*c^2) + (e*(d + e*x)^3*Sqrt[a + b*x + c*x^2])/(4*c) + (e*(608*c^3*d^3 - 105*b^3*e^3 + 20*b*c*e^2*(24*b*d + 11*a*e) - 8*c^2*d*e*(101*b*d + 64*a*e) + 2*c*e*(104*c^2*d^2 + 35*b^2*e^2 - 4*c*e*(26*b*d + 9*a*e))*x)*Sqrt[a + b*x + c*x^2])/(192*c^4) + ((128*c^4*d^4 + 35*b^4*e^4 - 128*c^3*d^2*e*(2*b*d + 3*a*e) - 40*b^2*c*e^3*(4*b*d + 3*a*e) + 48*c^2*e^2*(6*b^2*d^2 + 8*a*b*d*e + a^2*e^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(9/2))","A",5,5,22,0.2273,1,"{742, 832, 779, 621, 206}"
2374,1,174,0,0.1510029,"\int \frac{(d+e x)^3}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^3/Sqrt[a + b*x + c*x^2],x]","\frac{e \sqrt{a+b x+c x^2} \left(-2 c e (8 a e+27 b d)+15 b^2 e^2+10 c e x (2 c d-b e)+64 c^2 d^2\right)}{24 c^3}+\frac{(2 c d-b e) \left(-4 c e (3 a e+2 b d)+5 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^{7/2}}+\frac{e (d+e x)^2 \sqrt{a+b x+c x^2}}{3 c}","\frac{e \sqrt{a+b x+c x^2} \left(-2 c e (8 a e+27 b d)+15 b^2 e^2+10 c e x (2 c d-b e)+64 c^2 d^2\right)}{24 c^3}+\frac{(2 c d-b e) \left(-4 c e (3 a e+2 b d)+5 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^{7/2}}+\frac{e (d+e x)^2 \sqrt{a+b x+c x^2}}{3 c}",1,"(e*(d + e*x)^2*Sqrt[a + b*x + c*x^2])/(3*c) + (e*(64*c^2*d^2 + 15*b^2*e^2 - 2*c*e*(27*b*d + 8*a*e) + 10*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(24*c^3) + ((2*c*d - b*e)*(8*c^2*d^2 + 5*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^(7/2))","A",4,4,22,0.1818,1,"{742, 779, 621, 206}"
2375,1,127,0,0.1163122,"\int \frac{(d+e x)^2}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^2/Sqrt[a + b*x + c*x^2],x]","\frac{\left(-4 c e (a e+2 b d)+3 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)}{8 c^{5/2}}+\frac{3 e \sqrt{a+b x+c x^2} (2 c d-b e)}{4 c^2}+\frac{e (d+e x) \sqrt{a+b x+c x^2}}{2 c}","\frac{\left(-4 c e (a e+2 b d)+3 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)}{8 c^{5/2}}+\frac{3 e \sqrt{a+b x+c x^2} (2 c d-b e)}{4 c^2}+\frac{e (d+e x) \sqrt{a+b x+c x^2}}{2 c}",1,"(3*e*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(4*c^2) + (e*(d + e*x)*Sqrt[a + b*x + c*x^2])/(2*c) + ((8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(5/2))","A",4,4,22,0.1818,1,"{742, 640, 621, 206}"
2376,1,68,0,0.0242194,"\int \frac{d+e x}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)/Sqrt[a + b*x + c*x^2],x]","\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 c^{3/2}}+\frac{e \sqrt{a+b x+c x^2}}{c}","\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 c^{3/2}}+\frac{e \sqrt{a+b x+c x^2}}{c}",1,"(e*Sqrt[a + b*x + c*x^2])/c + ((2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(3/2))","A",3,3,20,0.1500,1,"{640, 621, 206}"
2377,1,36,0,0.0105089,"\int \frac{1}{\sqrt{a+b x+c x^2}} \, dx","Int[1/Sqrt[a + b*x + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c}}",1,"ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]/Sqrt[c]","A",2,2,14,0.1429,1,"{621, 206}"
2378,1,79,0,0.0386044,"\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}"
2379,1,134,0,0.0784632,"\int \frac{1}{(d+e x)^2 \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^2*Sqrt[a + b*x + c*x^2]),x]","\frac{(2 c d-b 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)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{e \sqrt{a+b x+c x^2}}{(d+e x) \left(a e^2-b d e+c d^2\right)}","\frac{(2 c d-b 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)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{e \sqrt{a+b x+c x^2}}{(d+e x) \left(a e^2-b d e+c d^2\right)}",1,"-((e*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)*(d + e*x))) + ((2*c*d - b*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])])/(2*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",3,3,22,0.1364,1,"{730, 724, 206}"
2380,1,209,0,0.2189339,"\int \frac{1}{(d+e x)^3 \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^3*Sqrt[a + b*x + c*x^2]),x]","\frac{\left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \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)}{8 \left(a e^2-b d e+c d^2\right)^{5/2}}-\frac{3 e \sqrt{a+b x+c x^2} (2 c d-b e)}{4 (d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{e \sqrt{a+b x+c x^2}}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}","\frac{\left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \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)}{8 \left(a e^2-b d e+c d^2\right)^{5/2}}-\frac{3 e \sqrt{a+b x+c x^2} (2 c d-b e)}{4 (d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{e \sqrt{a+b x+c x^2}}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}",1,"-(e*Sqrt[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (3*e*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(4*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + ((8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*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])])/(8*(c*d^2 - b*d*e + a*e^2)^(5/2))","A",4,4,22,0.1818,1,"{744, 806, 724, 206}"
2381,1,293,0,0.3594751,"\int \frac{1}{(d+e x)^4 \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^4*Sqrt[a + b*x + c*x^2]),x]","-\frac{e \sqrt{a+b x+c x^2} \left(-4 c e (4 a e+11 b d)+15 b^2 e^2+44 c^2 d^2\right)}{24 (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{(2 c d-b e) \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right) \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)}{16 \left(a e^2-b d e+c d^2\right)^{7/2}}-\frac{5 e \sqrt{a+b x+c x^2} (2 c d-b e)}{12 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \sqrt{a+b x+c x^2}}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}","-\frac{e \sqrt{a+b x+c x^2} \left(-4 c e (4 a e+11 b d)+15 b^2 e^2+44 c^2 d^2\right)}{24 (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{(2 c d-b e) \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right) \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)}{16 \left(a e^2-b d e+c d^2\right)^{7/2}}-\frac{5 e \sqrt{a+b x+c x^2} (2 c d-b e)}{12 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \sqrt{a+b x+c x^2}}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}",1,"-(e*Sqrt[a + b*x + c*x^2])/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) - (5*e*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(12*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (e*(44*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(11*b*d + 4*a*e))*Sqrt[a + b*x + c*x^2])/(24*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) + ((2*c*d - b*e)*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*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])])/(16*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,5,22,0.2273,1,"{744, 834, 806, 724, 206}"
2382,1,286,0,0.3177872,"\int \frac{(d+e x)^4}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^4/(a + b*x + c*x^2)^(3/2),x]","\frac{e \sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)-8 c^2 d e (16 a e+5 b d)+4 b c e^2 (13 a e+12 b d)-15 b^3 e^3+32 c^3 d^3\right)}{4 c^3 \left(b^2-4 a c\right)}+\frac{3 e^2 \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{7/2}}-\frac{2 (d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 e (d+e x)^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}","\frac{e \sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)-8 c^2 d e (16 a e+5 b d)+4 b c e^2 (13 a e+12 b d)-15 b^3 e^3+32 c^3 d^3\right)}{4 c^3 \left(b^2-4 a c\right)}+\frac{3 e^2 \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{7/2}}-\frac{2 (d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 e (d+e x)^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}",1,"(-2*(d + e*x)^3*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (2*e*(2*c*d - b*e)*(d + e*x)^2*Sqrt[a + b*x + c*x^2])/(c*(b^2 - 4*a*c)) + (e*(32*c^3*d^3 - 15*b^3*e^3 + 4*b*c*e^2*(12*b*d + 13*a*e) - 8*c^2*d*e*(5*b*d + 16*a*e) + 2*c*e*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*x)*Sqrt[a + b*x + c*x^2])/(4*c^3*(b^2 - 4*a*c)) + (3*e^2*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(7/2))","A",5,5,22,0.2273,1,"{738, 832, 779, 621, 206}"
2383,1,177,0,0.1779961,"\int \frac{(d+e x)^3}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^(3/2),x]","\frac{e \sqrt{a+b x+c x^2} \left(-2 c e (4 a e+3 b d)+3 b^2 e^2+2 c e x (2 c d-b e)+8 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)}-\frac{2 (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{3 e^2 (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 c^{5/2}}","\frac{e \sqrt{a+b x+c x^2} \left(-2 c e (4 a e+3 b d)+3 b^2 e^2+2 c e x (2 c d-b e)+8 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)}-\frac{2 (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{3 e^2 (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 c^{5/2}}",1,"(-2*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (e*(8*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(3*b*d + 4*a*e) + 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(c^2*(b^2 - 4*a*c)) + (3*e^2*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(5/2))","A",4,4,22,0.1818,1,"{738, 779, 621, 206}"
2384,1,129,0,0.0796547,"\int \frac{(d+e x)^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^(3/2),x]","\frac{2 e \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{2 (d+e x) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{e^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}","\frac{2 e \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{2 (d+e x) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{e^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}",1,"(-2*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (2*e*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(c*(b^2 - 4*a*c)) + (e^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(3/2)","A",4,4,22,0.1818,1,"{738, 640, 621, 206}"
2385,1,45,0,0.0110652,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(-2*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2])","A",1,1,20,0.05000,1,"{636}"
2386,1,32,0,0.0042317,"\int \frac{1}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^(-3/2),x]","-\frac{2 (b+2 c x)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{2 (b+2 c x)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(-2*(b + 2*c*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2])","A",1,1,14,0.07143,1,"{613}"
2387,1,155,0,0.1004439,"\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}"
2388,1,255,0,0.2753757,"\int \frac{1}{(d+e x)^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^2*(a + b*x + c*x^2)^(3/2)),x]","-\frac{e \sqrt{a+b x+c x^2} \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{\left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^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) (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{3 e^2 (2 c d-b 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)}{2 \left(a e^2-b d e+c d^2\right)^{5/2}}","-\frac{e \sqrt{a+b x+c x^2} \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{\left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^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) (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{3 e^2 (2 c d-b 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)}{2 \left(a e^2-b d e+c d^2\right)^{5/2}}",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)*(d + e*x)*Sqrt[a + b*x + c*x^2]) - (e*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + (3*e^2*(2*c*d - b*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])])/(2*(c*d^2 - b*d*e + a*e^2)^(5/2))","A",4,4,22,0.1818,1,"{740, 806, 724, 206}"
2389,1,371,0,0.4755235,"\int \frac{1}{(d+e x)^3 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^3*(a + b*x + c*x^2)^(3/2)),x]","-\frac{e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (13 a e+2 b d)+15 b^2 e^2+8 c^2 d^2\right)}{4 \left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{e \sqrt{a+b x+c x^2} \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)}{2 \left(b^2-4 a c\right) (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{3 e^2 \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \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)}{8 \left(a e^2-b d e+c d^2\right)^{7/2}}-\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) (d+e x)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}","-\frac{e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (13 a e+2 b d)+15 b^2 e^2+8 c^2 d^2\right)}{4 \left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{e \sqrt{a+b x+c x^2} \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)}{2 \left(b^2-4 a c\right) (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{3 e^2 \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \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)}{8 \left(a e^2-b d e+c d^2\right)^{7/2}}-\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) (d+e x)^2 \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)*(d + e*x)^2*Sqrt[a + b*x + c*x^2]) - (e*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*Sqrt[a + b*x + c*x^2])/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (e*(2*c*d - b*e)*(8*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(2*b*d + 13*a*e))*Sqrt[a + b*x + c*x^2])/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) + (3*e^2*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*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])])/(8*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,5,22,0.2273,1,"{740, 834, 806, 724, 206}"
2390,1,519,0,0.8576263,"\int \frac{1}{(d+e x)^4 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^4*(a + b*x + c*x^2)^(3/2)),x]","-\frac{e \sqrt{a+b x+c x^2} \left(4 c^2 e^2 \left(64 a^2 e^2+332 a b d e+119 b^2 d^2\right)-20 b^2 c e^3 (23 a e+19 b d)-16 c^3 d^2 e (83 a e+12 b d)+105 b^4 e^4+96 c^4 d^4\right)}{24 \left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^4}-\frac{e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (29 a e+6 b d)+35 b^2 e^2+24 c^2 d^2\right)}{12 \left(b^2-4 a c\right) (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}-\frac{e \sqrt{a+b x+c x^2} \left(-4 c e (4 a e+3 b d)+7 b^2 e^2+12 c^2 d^2\right)}{3 \left(b^2-4 a c\right) (d+e x)^3 \left(a e^2-b d e+c d^2\right)^2}+\frac{5 e^2 (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right) \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)}{16 \left(a e^2-b d e+c d^2\right)^{9/2}}-\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) (d+e x)^3 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}","-\frac{e \sqrt{a+b x+c x^2} \left(4 c^2 e^2 \left(64 a^2 e^2+332 a b d e+119 b^2 d^2\right)-20 b^2 c e^3 (23 a e+19 b d)-16 c^3 d^2 e (83 a e+12 b d)+105 b^4 e^4+96 c^4 d^4\right)}{24 \left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^4}-\frac{e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (29 a e+6 b d)+35 b^2 e^2+24 c^2 d^2\right)}{12 \left(b^2-4 a c\right) (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}-\frac{e \sqrt{a+b x+c x^2} \left(-4 c e (4 a e+3 b d)+7 b^2 e^2+12 c^2 d^2\right)}{3 \left(b^2-4 a c\right) (d+e x)^3 \left(a e^2-b d e+c d^2\right)^2}+\frac{5 e^2 (2 c d-b e) \left(-4 c e (3 a e+4 b d)+7 b^2 e^2+16 c^2 d^2\right) \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)}{16 \left(a e^2-b d e+c d^2\right)^{9/2}}-\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) (d+e x)^3 \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)*(d + e*x)^3*Sqrt[a + b*x + c*x^2]) - (e*(12*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(3*b*d + 4*a*e))*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^3) - (e*(2*c*d - b*e)*(24*c^2*d^2 + 35*b^2*e^2 - 4*c*e*(6*b*d + 29*a*e))*Sqrt[a + b*x + c*x^2])/(12*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) - (e*(96*c^4*d^4 + 105*b^4*e^4 - 20*b^2*c*e^3*(19*b*d + 23*a*e) - 16*c^3*d^2*e*(12*b*d + 83*a*e) + 4*c^2*e^2*(119*b^2*d^2 + 332*a*b*d*e + 64*a^2*e^2))*Sqrt[a + b*x + c*x^2])/(24*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)) + (5*e^2*(2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*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])])/(16*(c*d^2 - b*d*e + a*e^2)^(9/2))","A",6,5,22,0.2273,1,"{740, 834, 806, 724, 206}"
2391,1,389,0,0.4651864,"\int \frac{(d+e x)^5}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^5/(a + b*x + c*x^2)^(5/2),x]","-\frac{e \sqrt{a+b x+c x^2} \left(8 c^2 e^2 \left(-16 a^2 e^2-25 a b d e+b^2 d^2\right)+2 c e x (2 c d-b e) \left(-4 c e (2 b d-7 a e)-5 b^2 e^2+8 c^2 d^2\right)+10 b^2 c e^3 (10 a e+3 b d)-16 c^3 d^2 e (7 b d-16 a e)-15 b^4 e^4+64 c^4 d^4\right)}{3 c^3 \left(b^2-4 a c\right)^2}-\frac{8 (d+e x)^2 \left(8 a^2 c e^3-x (2 c d-b e) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right)+b^2 \left(3 c d^2 e-a e^3\right)-2 b c d \left(3 a e^2+c d^2\right)\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^4 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{5 e^4 (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 c^{7/2}}","-\frac{e \sqrt{a+b x+c x^2} \left(8 c^2 e^2 \left(-16 a^2 e^2-25 a b d e+b^2 d^2\right)+2 c e x (2 c d-b e) \left(-4 c e (2 b d-7 a e)-5 b^2 e^2+8 c^2 d^2\right)+10 b^2 c e^3 (10 a e+3 b d)-16 c^3 d^2 e (7 b d-16 a e)-15 b^4 e^4+64 c^4 d^4\right)}{3 c^3 \left(b^2-4 a c\right)^2}-\frac{8 (d+e x)^2 \left(8 a^2 c e^3-x (2 c d-b e) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right)+b^2 \left(3 c d^2 e-a e^3\right)-2 b c d \left(3 a e^2+c d^2\right)\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^4 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{5 e^4 (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 c^{7/2}}",1,"(-2*(d + e*x)^4*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (8*(d + e*x)^2*(8*a^2*c*e^3 - 2*b*c*d*(c*d^2 + 3*a*e^2) + b^2*(3*c*d^2*e - a*e^3) - (2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*x))/(3*c*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) - (e*(64*c^4*d^4 - 15*b^4*e^4 - 16*c^3*d^2*e*(7*b*d - 16*a*e) + 10*b^2*c*e^3*(3*b*d + 10*a*e) + 8*c^2*e^2*(b^2*d^2 - 25*a*b*d*e - 16*a^2*e^2) + 2*c*e*(2*c*d - b*e)*(8*c^2*d^2 - 5*b^2*e^2 - 4*c*e*(2*b*d - 7*a*e))*x)*Sqrt[a + b*x + c*x^2])/(3*c^3*(b^2 - 4*a*c)^2) + (5*e^4*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(7/2))","A",5,5,22,0.2273,1,"{738, 818, 779, 621, 206}"
2392,1,295,0,0.3446031,"\int \frac{(d+e x)^4}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^4/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (2 b d-5 a e)-3 b^2 e^2+8 c^2 d^2\right)}{3 c^2 \left(b^2-4 a c\right)^2}+\frac{4 (d+e x) \left(x (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right)+b^2 \left(-\left(5 c d^2 e-a e^3\right)\right)+4 b c d \left(3 a e^2+c d^2\right)-4 a c e \left(3 a e^2+c d^2\right)\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{e^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}","-\frac{2 e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (2 b d-5 a e)-3 b^2 e^2+8 c^2 d^2\right)}{3 c^2 \left(b^2-4 a c\right)^2}+\frac{4 (d+e x) \left(x (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right)+b^2 \left(-\left(5 c d^2 e-a e^3\right)\right)+4 b c d \left(3 a e^2+c d^2\right)-4 a c e \left(3 a e^2+c d^2\right)\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{e^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}",1,"(-2*(d + e*x)^3*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (4*(d + e*x)*(4*b*c*d*(c*d^2 + 3*a*e^2) - 4*a*c*e*(c*d^2 + 3*a*e^2) - b^2*(5*c*d^2*e - a*e^3) + (2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*x))/(3*c*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) - (2*e*(2*c*d - b*e)*(8*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(2*b*d - 5*a*e))*Sqrt[a + b*x + c*x^2])/(3*c^2*(b^2 - 4*a*c)^2) + (e^4*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(5/2)","A",5,5,22,0.2273,1,"{738, 818, 640, 621, 206}"
2393,1,118,0,0.0416106,"\int \frac{(d+e x)^3}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^(5/2),x]","\frac{16 \left(a e^2-b d e+c d^2\right) (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{16 \left(a e^2-b d e+c d^2\right) (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (16*(c*d^2 - b*d*e + a*e^2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,22,0.09091,1,"{722, 636}"
2394,1,98,0,0.0374289,"\int \frac{(d+e x)^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^(5/2),x]","\frac{8 (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (b+2 c x) (d+e x)^2}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{8 (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (b+2 c x) (d+e x)^2}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(b + 2*c*x)*(d + e*x)^2)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (8*(2*c*d - b*e)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,22,0.09091,1,"{728, 636}"
2395,1,91,0,0.0213004,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^(5/2),x]","\frac{8 (b+2 c x) (2 c d-b e)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{8 (b+2 c x) (2 c d-b e)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (8*(2*c*d - b*e)*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,20,0.1000,1,"{638, 613}"
2396,1,70,0,0.0118909,"\int \frac{1}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(a + b*x + c*x^2)^(-5/2),x]","\frac{16 c (b+2 c x)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (b+2 c x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{16 c (b+2 c x)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (b+2 c x)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(b + 2*c*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (16*c*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,14,0.1429,1,"{614, 613}"
2397,1,310,0,0.27333,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^(5/2)),x]","-\frac{2 \left(-c x (2 c d-b e) \left(-4 c e (2 b d-5 a e)-3 b^2 e^2+8 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-4 c e (b d-3 a e)-3 b^2 e^2+8 c^2 d^2\right)+4 a c e (2 c d-b e)^2\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^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)}{\left(a e^2-b d e+c d^2\right)^{5/2}}","-\frac{2 \left(-c x (2 c d-b e) \left(-4 c e (2 b d-5 a e)-3 b^2 e^2+8 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-4 c e (b d-3 a e)-3 b^2 e^2+8 c^2 d^2\right)+4 a c e (2 c d-b e)^2\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^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)}{\left(a e^2-b d e+c d^2\right)^{5/2}}",1,"(-2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(3/2)) - (2*(4*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(b*d - 3*a*e)) - c*(2*c*d - b*e)*(8*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(2*b*d - 5*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[a + b*x + c*x^2]) + (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)^(5/2)","A",5,5,22,0.2273,1,"{740, 822, 12, 724, 206}"
2398,1,473,0,0.6141577,"\int \frac{1}{(d+e x)^2 \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^2*(a + b*x + c*x^2)^(5/2)),x]","\frac{e \sqrt{a+b x+c x^2} \left(4 c^2 e^2 \left(-32 a^2 e^2-36 a b d e+3 b^2 d^2\right)+20 b^2 c e^3 (5 a e+b d)-16 c^3 d^2 e (4 b d-9 a e)-15 b^4 e^4+32 c^4 d^4\right)}{3 \left(b^2-4 a c\right)^2 (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{2 \left(-c x (2 c d-b e) \left(-4 c e (2 b d-7 a e)-5 b^2 e^2+8 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-2 c e (b d-8 a e)-5 b^2 e^2+8 c^2 d^2\right)+6 a c e (2 c d-b e)^2\right)}{3 \left(b^2-4 a c\right)^2 (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{5 e^4 (2 c d-b 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)}{2 \left(a e^2-b d e+c d^2\right)^{7/2}}","\frac{e \sqrt{a+b x+c x^2} \left(4 c^2 e^2 \left(-32 a^2 e^2-36 a b d e+3 b^2 d^2\right)+20 b^2 c e^3 (5 a e+b d)-16 c^3 d^2 e (4 b d-9 a e)-15 b^4 e^4+32 c^4 d^4\right)}{3 \left(b^2-4 a c\right)^2 (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{2 \left(-c x (2 c d-b e) \left(-4 c e (2 b d-7 a e)-5 b^2 e^2+8 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-2 c e (b d-8 a e)-5 b^2 e^2+8 c^2 d^2\right)+6 a c e (2 c d-b e)^2\right)}{3 \left(b^2-4 a c\right)^2 (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{5 e^4 (2 c d-b 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)}{2 \left(a e^2-b d e+c d^2\right)^{7/2}}",1,"(-2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^(3/2)) - (2*(6*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 5*b^2*e^2 - 2*c*e*(b*d - 8*a*e)) - c*(2*c*d - b*e)*(8*c^2*d^2 - 5*b^2*e^2 - 4*c*e*(2*b*d - 7*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*Sqrt[a + b*x + c*x^2]) + (e*(32*c^4*d^4 - 15*b^4*e^4 - 16*c^3*d^2*e*(4*b*d - 9*a*e) + 20*b^2*c*e^3*(b*d + 5*a*e) + 4*c^2*e^2*(3*b^2*d^2 - 36*a*b*d*e - 32*a^2*e^2))*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) + (5*e^4*(2*c*d - b*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])])/(2*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,5,22,0.2273,1,"{740, 822, 806, 724, 206}"
2399,1,621,0,1.0410948,"\int \frac{1}{(d+e x)^3 \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^3*(a + b*x + c*x^2)^(5/2)),x]","\frac{e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-16 c^2 e^2 \left(81 a^2 e^2+28 a b d e+b^2 d^2\right)+40 b^2 c e^3 (19 a e+2 b d)-64 c^3 d^2 e (2 b d-7 a e)-105 b^4 e^4+64 c^4 d^4\right)}{12 \left(b^2-4 a c\right)^2 (d+e x) \left(a e^2-b d e+c d^2\right)^4}+\frac{e \sqrt{a+b x+c x^2} \left(8 b^2 c e^3 (27 a e+8 b d)-128 c^3 d^2 e (b d-3 a e)-48 a c^2 e^3 (5 a e+8 b d)-35 b^4 e^4+64 c^4 d^4\right)}{6 \left(b^2-4 a c\right)^2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}-\frac{2 \left(-c x (2 c d-b e) \left(-4 c e (2 b d-9 a e)-7 b^2 e^2+8 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(20 a c e^2-7 b^2 e^2+8 c^2 d^2\right)+8 a c e (2 c d-b e)^2\right)}{3 \left(b^2-4 a c\right)^2 (d+e x)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{5 e^4 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \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)}{8 \left(a e^2-b d e+c d^2\right)^{9/2}}-\frac{2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) (d+e x)^2 \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}","\frac{e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-16 c^2 e^2 \left(81 a^2 e^2+28 a b d e+b^2 d^2\right)+40 b^2 c e^3 (19 a e+2 b d)-64 c^3 d^2 e (2 b d-7 a e)-105 b^4 e^4+64 c^4 d^4\right)}{12 \left(b^2-4 a c\right)^2 (d+e x) \left(a e^2-b d e+c d^2\right)^4}+\frac{e \sqrt{a+b x+c x^2} \left(8 b^2 c e^3 (27 a e+8 b d)-128 c^3 d^2 e (b d-3 a e)-48 a c^2 e^3 (5 a e+8 b d)-35 b^4 e^4+64 c^4 d^4\right)}{6 \left(b^2-4 a c\right)^2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}-\frac{2 \left(-c x (2 c d-b e) \left(-4 c e (2 b d-9 a e)-7 b^2 e^2+8 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(20 a c e^2-7 b^2 e^2+8 c^2 d^2\right)+8 a c e (2 c d-b e)^2\right)}{3 \left(b^2-4 a c\right)^2 (d+e x)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{5 e^4 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \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)}{8 \left(a e^2-b d e+c d^2\right)^{9/2}}-\frac{2 \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) (d+e x)^2 \left(a+b x+c x^2\right)^{3/2} \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))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2*(a + b*x + c*x^2)^(3/2)) - (2*(8*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 7*b^2*e^2 + 20*a*c*e^2) - c*(2*c*d - b*e)*(8*c^2*d^2 - 7*b^2*e^2 - 4*c*e*(2*b*d - 9*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2*Sqrt[a + b*x + c*x^2]) + (e*(64*c^4*d^4 - 35*b^4*e^4 - 128*c^3*d^2*e*(b*d - 3*a*e) - 48*a*c^2*e^3*(8*b*d + 5*a*e) + 8*b^2*c*e^3*(8*b*d + 27*a*e))*Sqrt[a + b*x + c*x^2])/(6*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) + (e*(2*c*d - b*e)*(64*c^4*d^4 - 105*b^4*e^4 - 64*c^3*d^2*e*(2*b*d - 7*a*e) + 40*b^2*c*e^3*(2*b*d + 19*a*e) - 16*c^2*e^2*(b^2*d^2 + 28*a*b*d*e + 81*a^2*e^2))*Sqrt[a + b*x + c*x^2])/(12*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)) + (5*e^4*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*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])])/(8*(c*d^2 - b*d*e + a*e^2)^(9/2))","A",6,6,22,0.2727,1,"{740, 822, 834, 806, 724, 206}"
2400,1,29,0,0.0129247,"\int \frac{3+x}{\sqrt{5-4 x-x^2}} \, dx","Int[(3 + x)/Sqrt[5 - 4*x - x^2],x]","-\sqrt{-x^2-4 x+5}-\sin ^{-1}\left(\frac{1}{3} (-x-2)\right)","-\sqrt{-x^2-4 x+5}-\sin ^{-1}\left(\frac{1}{3} (-x-2)\right)",1,"-Sqrt[5 - 4*x - x^2] - ArcSin[(-2 - x)/3]","A",3,3,18,0.1667,1,"{640, 619, 216}"
2401,1,25,0,0.0107881,"\int \frac{5-4 x}{\sqrt{-8+12 x-4 x^2}} \, dx","Int[(5 - 4*x)/Sqrt[-8 + 12*x - 4*x^2],x]","\sqrt{-4 x^2+12 x-8}+\frac{1}{2} \sin ^{-1}(3-2 x)","\sqrt{-4 x^2+12 x-8}+\frac{1}{2} \sin ^{-1}(3-2 x)",1,"Sqrt[-8 + 12*x - 4*x^2] + ArcSin[3 - 2*x]/2","A",3,3,20,0.1500,1,"{640, 619, 216}"
2402,1,23,0,0.0110523,"\int \frac{3+2 x}{\sqrt{5+2 x+x^2}} \, dx","Int[(3 + 2*x)/Sqrt[5 + 2*x + x^2],x]","2 \sqrt{x^2+2 x+5}+\sinh ^{-1}\left(\frac{x+1}{2}\right)","2 \sqrt{x^2+2 x+5}+\sinh ^{-1}\left(\frac{x+1}{2}\right)",1,"2*Sqrt[5 + 2*x + x^2] + ArcSinh[(1 + x)/2]","A",3,3,18,0.1667,1,"{640, 619, 215}"
2403,1,34,0,0.009237,"\int \frac{-1+x}{\sqrt{3-4 x+x^2}} \, dx","Int[(-1 + x)/Sqrt[3 - 4*x + x^2],x]","\sqrt{x^2-4 x+3}-\tanh ^{-1}\left(\frac{2-x}{\sqrt{x^2-4 x+3}}\right)","\sqrt{x^2-4 x+3}-\tanh ^{-1}\left(\frac{2-x}{\sqrt{x^2-4 x+3}}\right)",1,"Sqrt[3 - 4*x + x^2] - ArcTanh[(2 - x)/Sqrt[3 - 4*x + x^2]]","A",3,3,16,0.1875,1,"{640, 621, 206}"
2404,1,19,0,0.0118567,"\int \frac{1}{(1-x) \sqrt{-4+2 x+x^2}} \, dx","Int[1/((1 - x)*Sqrt[-4 + 2*x + x^2]),x]","\tan ^{-1}\left(\frac{3-2 x}{\sqrt{x^2+2 x-4}}\right)","\tan ^{-1}\left(\frac{3-2 x}{\sqrt{x^2+2 x-4}}\right)",1,"ArcTan[(3 - 2*x)/Sqrt[-4 + 2*x + x^2]]","A",2,2,20,0.1000,1,"{724, 204}"
2405,1,13,0,0.008268,"\int \frac{1}{(-2+x) \sqrt{3-4 x+x^2}} \, dx","Int[1/((-2 + x)*Sqrt[3 - 4*x + x^2]),x]","\tan ^{-1}\left(\sqrt{x^2-4 x+3}\right)","\tan ^{-1}\left(\sqrt{x^2-4 x+3}\right)",1,"ArcTan[Sqrt[3 - 4*x + x^2]]","A",2,2,18,0.1111,1,"{688, 203}"
2406,1,17,0,0.0045294,"\int \frac{1+x}{\left(2+3 x+x^2\right)^{3/2}} \, dx","Int[(1 + x)/(2 + 3*x + x^2)^(3/2),x]","\frac{2 (x+1)}{\sqrt{x^2+3 x+2}}","\frac{2 (x+1)}{\sqrt{x^2+3 x+2}}",1,"(2*(1 + x))/Sqrt[2 + 3*x + x^2]","A",1,1,16,0.06250,1,"{636}"
2407,1,96,0,0.034538,"\int \frac{1}{(d+e x) \sqrt{\frac{b^2}{4 c}+b x+c x^2}} \, dx","Int[1/((d + e*x)*Sqrt[b^2/(4*c) + b*x + c*x^2]),x]","\frac{2 (b+2 c x) \log (b+2 c x)}{\sqrt{\frac{b^2}{c}+4 b x+4 c x^2} (2 c d-b e)}-\frac{2 (b+2 c x) \log (d+e x)}{\sqrt{\frac{b^2}{c}+4 b x+4 c x^2} (2 c d-b e)}","\frac{2 (b+2 c x) \log (b+2 c x)}{\sqrt{\frac{b^2}{c}+4 b x+4 c x^2} (2 c d-b e)}-\frac{2 (b+2 c x) \log (d+e x)}{\sqrt{\frac{b^2}{c}+4 b x+4 c x^2} (2 c d-b e)}",1,"(2*(b + 2*c*x)*Log[b + 2*c*x])/((2*c*d - b*e)*Sqrt[b^2/c + 4*b*x + 4*c*x^2]) - (2*(b + 2*c*x)*Log[d + e*x])/((2*c*d - b*e)*Sqrt[b^2/c + 4*b*x + 4*c*x^2])","A",4,3,31,0.09677,1,"{646, 36, 31}"
2408,1,56,0,0.0530509,"\int \frac{1}{\left(\frac{b e}{2 c}+e x\right) \sqrt{a+b x+c x^2}} \, dx","Int[1/(((b*e)/(2*c) + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{e \sqrt{b^2-4 a c}}","\frac{2 \sqrt{c} \tan ^{-1}\left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}\right)}{e \sqrt{b^2-4 a c}}",1,"(2*Sqrt[c]*ArcTan[(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*e)","A",2,2,30,0.06667,1,"{688, 205}"
2409,1,48,0,0.0268307,"\int \frac{1}{(d+e x) \sqrt{\frac{-c d^2+b d e}{e^2}+b x+c x^2}} \, dx","Int[1/((d + e*x)*Sqrt[(-(c*d^2) + b*d*e)/e^2 + b*x + c*x^2]),x]","\frac{2 e \sqrt{-\frac{d (c d-b e)}{e^2}+b x+c x^2}}{(d+e x) (2 c d-b e)}","\frac{2 e \sqrt{-\frac{d (c d-b e)}{e^2}+b x+c x^2}}{(d+e x) (2 c d-b e)}",1,"(2*e*Sqrt[-((d*(c*d - b*e))/e^2) + b*x + c*x^2])/((2*c*d - b*e)*(d + e*x))","A",1,1,36,0.02778,1,"{650}"
2410,1,27,0,0.0284133,"\int \frac{1}{\left(\frac{b e}{2 c}+e x\right) \sqrt{\frac{b^2}{4 c}+b x+c x^2}} \, dx","Int[1/(((b*e)/(2*c) + e*x)*Sqrt[b^2/(4*c) + b*x + c*x^2]),x]","-\frac{2}{e \sqrt{\frac{b^2}{c}+4 b x+4 c x^2}}","-\frac{2}{e \sqrt{\frac{b^2}{c}+4 b x+4 c x^2}}",1,"-2/(e*Sqrt[b^2/c + 4*b*x + 4*c*x^2])","A",2,2,39,0.05128,1,"{643, 629}"
2411,1,40,0,0.0177499,"\int \frac{x}{\sqrt{2+4 x+3 x^2}} \, dx","Int[x/Sqrt[2 + 4*x + 3*x^2],x]","\frac{1}{3} \sqrt{3 x^2+4 x+2}-\frac{2 \sinh ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{3 \sqrt{3}}","\frac{1}{3} \sqrt{3 x^2+4 x+2}-\frac{2 \sinh ^{-1}\left(\frac{3 x+2}{\sqrt{2}}\right)}{3 \sqrt{3}}",1,"Sqrt[2 + 4*x + 3*x^2]/3 - (2*ArcSinh[(2 + 3*x)/Sqrt[2]])/(3*Sqrt[3])","A",3,3,16,0.1875,1,"{640, 619, 215}"
2412,1,40,0,0.0225357,"\int \frac{x}{\sqrt{2+4 x-3 x^2}} \, dx","Int[x/Sqrt[2 + 4*x - 3*x^2],x]","-\frac{1}{3} \sqrt{-3 x^2+4 x+2}-\frac{2 \sin ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{3 \sqrt{3}}","-\frac{1}{3} \sqrt{-3 x^2+4 x+2}-\frac{2 \sin ^{-1}\left(\frac{2-3 x}{\sqrt{10}}\right)}{3 \sqrt{3}}",1,"-Sqrt[2 + 4*x - 3*x^2]/3 - (2*ArcSin[(2 - 3*x)/Sqrt[10]])/(3*Sqrt[3])","A",3,3,16,0.1875,1,"{640, 619, 216}"
2413,1,57,0,0.014573,"\int \frac{x}{\sqrt{2+5 x+3 x^2}} \, dx","Int[x/Sqrt[2 + 5*x + 3*x^2],x]","\frac{1}{3} \sqrt{3 x^2+5 x+2}-\frac{5 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{6 \sqrt{3}}","\frac{1}{3} \sqrt{3 x^2+5 x+2}-\frac{5 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{6 \sqrt{3}}",1,"Sqrt[2 + 5*x + 3*x^2]/3 - (5*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(6*Sqrt[3])","A",3,3,16,0.1875,1,"{640, 621, 206}"
2414,1,38,0,0.0127859,"\int \frac{x}{\sqrt{2+5 x-3 x^2}} \, dx","Int[x/Sqrt[2 + 5*x - 3*x^2],x]","-\frac{1}{3} \sqrt{-3 x^2+5 x+2}-\frac{5 \sin ^{-1}\left(\frac{1}{7} (5-6 x)\right)}{6 \sqrt{3}}","-\frac{1}{3} \sqrt{-3 x^2+5 x+2}-\frac{5 \sin ^{-1}\left(\frac{1}{7} (5-6 x)\right)}{6 \sqrt{3}}",1,"-Sqrt[2 + 5*x - 3*x^2]/3 - (5*ArcSin[(5 - 6*x)/7])/(6*Sqrt[3])","A",3,3,16,0.1875,1,"{640, 619, 216}"
2415,1,54,0,0.015042,"\int \frac{x}{\sqrt{-2+4 x+3 x^2}} \, dx","Int[x/Sqrt[-2 + 4*x + 3*x^2],x]","\frac{1}{3} \sqrt{3 x^2+4 x-2}-\frac{2 \tanh ^{-1}\left(\frac{3 x+2}{\sqrt{3} \sqrt{3 x^2+4 x-2}}\right)}{3 \sqrt{3}}","\frac{1}{3} \sqrt{3 x^2+4 x-2}-\frac{2 \tanh ^{-1}\left(\frac{3 x+2}{\sqrt{3} \sqrt{3 x^2+4 x-2}}\right)}{3 \sqrt{3}}",1,"Sqrt[-2 + 4*x + 3*x^2]/3 - (2*ArcTanh[(2 + 3*x)/(Sqrt[3]*Sqrt[-2 + 4*x + 3*x^2])])/(3*Sqrt[3])","A",3,3,16,0.1875,1,"{640, 621, 206}"
2416,1,54,0,0.0152533,"\int \frac{x}{\sqrt{-2+4 x-3 x^2}} \, dx","Int[x/Sqrt[-2 + 4*x - 3*x^2],x]","-\frac{1}{3} \sqrt{-3 x^2+4 x-2}-\frac{2 \tan ^{-1}\left(\frac{2-3 x}{\sqrt{3} \sqrt{-3 x^2+4 x-2}}\right)}{3 \sqrt{3}}","-\frac{1}{3} \sqrt{-3 x^2+4 x-2}-\frac{2 \tan ^{-1}\left(\frac{2-3 x}{\sqrt{3} \sqrt{-3 x^2+4 x-2}}\right)}{3 \sqrt{3}}",1,"-Sqrt[-2 + 4*x - 3*x^2]/3 - (2*ArcTan[(2 - 3*x)/(Sqrt[3]*Sqrt[-2 + 4*x - 3*x^2])])/(3*Sqrt[3])","A",3,3,16,0.1875,1,"{640, 621, 204}"
2417,1,57,0,0.0145413,"\int \frac{x}{\sqrt{-2+5 x+3 x^2}} \, dx","Int[x/Sqrt[-2 + 5*x + 3*x^2],x]","\frac{1}{3} \sqrt{3 x^2+5 x-2}-\frac{5 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x-2}}\right)}{6 \sqrt{3}}","\frac{1}{3} \sqrt{3 x^2+5 x-2}-\frac{5 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x-2}}\right)}{6 \sqrt{3}}",1,"Sqrt[-2 + 5*x + 3*x^2]/3 - (5*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[-2 + 5*x + 3*x^2])])/(6*Sqrt[3])","A",3,3,16,0.1875,1,"{640, 621, 206}"
2418,1,34,0,0.0091497,"\int \frac{x}{\sqrt{-2+5 x-3 x^2}} \, dx","Int[x/Sqrt[-2 + 5*x - 3*x^2],x]","-\frac{1}{3} \sqrt{-3 x^2+5 x-2}-\frac{5 \sin ^{-1}(5-6 x)}{6 \sqrt{3}}","-\frac{1}{3} \sqrt{-3 x^2+5 x-2}-\frac{5 \sin ^{-1}(5-6 x)}{6 \sqrt{3}}",1,"-Sqrt[-2 + 5*x - 3*x^2]/3 - (5*ArcSin[5 - 6*x])/(6*Sqrt[3])","A",3,3,16,0.1875,1,"{640, 619, 216}"
2419,1,55,0,0.0123664,"\int \frac{1}{x \sqrt{4+12 x+9 x^2}} \, dx","Int[1/(x*Sqrt[4 + 12*x + 9*x^2]),x]","\frac{(3 x+2) \log (x)}{2 \sqrt{9 x^2+12 x+4}}-\frac{(3 x+2) \log (3 x+2)}{2 \sqrt{9 x^2+12 x+4}}","-\frac{(3 x+2) \tanh ^{-1}(3 x+1)}{\sqrt{9 x^2+12 x+4}}",1,"((2 + 3*x)*Log[x])/(2*Sqrt[4 + 12*x + 9*x^2]) - ((2 + 3*x)*Log[2 + 3*x])/(2*Sqrt[4 + 12*x + 9*x^2])","B",4,4,18,0.2222,1,"{646, 36, 29, 31}"
2420,1,55,0,0.0157698,"\int \frac{1}{x \sqrt{4-12 x+9 x^2}} \, dx","Int[1/(x*Sqrt[4 - 12*x + 9*x^2]),x]","\frac{(2-3 x) \log (x)}{2 \sqrt{9 x^2-12 x+4}}-\frac{(2-3 x) \log (2-3 x)}{2 \sqrt{9 x^2-12 x+4}}","-\frac{(2-3 x) \tanh ^{-1}(1-3 x)}{\sqrt{9 x^2-12 x+4}}",1,"-((2 - 3*x)*Log[2 - 3*x])/(2*Sqrt[4 - 12*x + 9*x^2]) + ((2 - 3*x)*Log[x])/(2*Sqrt[4 - 12*x + 9*x^2])","B",4,4,18,0.2222,1,"{646, 36, 29, 31}"
2421,1,55,0,0.0129094,"\int \frac{1}{x \sqrt{-4+12 x-9 x^2}} \, dx","Int[1/(x*Sqrt[-4 + 12*x - 9*x^2]),x]","\frac{(2-3 x) \log (x)}{2 \sqrt{-9 x^2+12 x-4}}-\frac{(2-3 x) \log (2-3 x)}{2 \sqrt{-9 x^2+12 x-4}}","-\frac{(2-3 x) \tanh ^{-1}(1-3 x)}{\sqrt{-9 x^2+12 x-4}}",1,"-((2 - 3*x)*Log[2 - 3*x])/(2*Sqrt[-4 + 12*x - 9*x^2]) + ((2 - 3*x)*Log[x])/(2*Sqrt[-4 + 12*x - 9*x^2])","B",4,4,18,0.2222,1,"{646, 36, 31, 29}"
2422,1,55,0,0.0137119,"\int \frac{1}{x \sqrt{-4-12 x-9 x^2}} \, dx","Int[1/(x*Sqrt[-4 - 12*x - 9*x^2]),x]","\frac{(3 x+2) \log (x)}{2 \sqrt{-9 x^2-12 x-4}}-\frac{(3 x+2) \log (3 x+2)}{2 \sqrt{-9 x^2-12 x-4}}","-\frac{(3 x+2) \tanh ^{-1}(3 x+1)}{\sqrt{-9 x^2-12 x-4}}",1,"((2 + 3*x)*Log[x])/(2*Sqrt[-4 - 12*x - 9*x^2]) - ((2 + 3*x)*Log[2 + 3*x])/(2*Sqrt[-4 - 12*x - 9*x^2])","B",4,4,18,0.2222,1,"{646, 36, 31, 29}"
2423,1,68,0,0.0224197,"\int \frac{1}{x \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[1/(x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{\log (x) (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{\log (x) (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*Log[x])/(a*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((a + b*x)*Log[a + b*x])/(a*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,24,0.1667,1,"{646, 36, 29, 31}"
2424,1,71,0,0.0241426,"\int \frac{1}{x \sqrt{a^2-2 a b x+b^2 x^2}} \, dx","Int[1/(x*Sqrt[a^2 - 2*a*b*x + b^2*x^2]),x]","\frac{\log (x) (a-b x)}{a \sqrt{a^2-2 a b x+b^2 x^2}}-\frac{(a-b x) \log (a-b x)}{a \sqrt{a^2-2 a b x+b^2 x^2}}","\frac{\log (x) (a-b x)}{a \sqrt{a^2-2 a b x+b^2 x^2}}-\frac{(a-b x) \log (a-b x)}{a \sqrt{a^2-2 a b x+b^2 x^2}}",1,"((a - b*x)*Log[x])/(a*Sqrt[a^2 - 2*a*b*x + b^2*x^2]) - ((a - b*x)*Log[a - b*x])/(a*Sqrt[a^2 - 2*a*b*x + b^2*x^2])","A",4,4,24,0.1667,1,"{646, 36, 29, 31}"
2425,1,77,0,0.0240125,"\int \frac{1}{x \sqrt{-a^2+2 a b x-b^2 x^2}} \, dx","Int[1/(x*Sqrt[-a^2 + 2*a*b*x - b^2*x^2]),x]","\frac{\log (x) (a-b x)}{a \sqrt{-a^2+2 a b x-b^2 x^2}}-\frac{(a-b x) \log (a-b x)}{a \sqrt{-a^2+2 a b x-b^2 x^2}}","\frac{\log (x) (a-b x)}{a \sqrt{-a^2+2 a b x-b^2 x^2}}-\frac{(a-b x) \log (a-b x)}{a \sqrt{-a^2+2 a b x-b^2 x^2}}",1,"((a - b*x)*Log[x])/(a*Sqrt[-a^2 + 2*a*b*x - b^2*x^2]) - ((a - b*x)*Log[a - b*x])/(a*Sqrt[-a^2 + 2*a*b*x - b^2*x^2])","A",4,4,27,0.1481,1,"{646, 36, 29, 31}"
2426,1,74,0,0.0264302,"\int \frac{1}{x \sqrt{-a^2-2 a b x-b^2 x^2}} \, dx","Int[1/(x*Sqrt[-a^2 - 2*a*b*x - b^2*x^2]),x]","\frac{\log (x) (a+b x)}{a \sqrt{-a^2-2 a b x-b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a \sqrt{-a^2-2 a b x-b^2 x^2}}","\frac{\log (x) (a+b x)}{a \sqrt{-a^2-2 a b x-b^2 x^2}}-\frac{(a+b x) \log (a+b x)}{a \sqrt{-a^2-2 a b x-b^2 x^2}}",1,"((a + b*x)*Log[x])/(a*Sqrt[-a^2 - 2*a*b*x - b^2*x^2]) - ((a + b*x)*Log[a + b*x])/(a*Sqrt[-a^2 - 2*a*b*x - b^2*x^2])","A",4,4,27,0.1481,1,"{646, 36, 29, 31}"
2427,1,52,0,0.0137335,"\int x \sqrt{3-2 x-x^2} \, dx","Int[x*Sqrt[3 - 2*x - x^2],x]","-\frac{1}{3} \left(-x^2-2 x+3\right)^{3/2}-\frac{1}{2} (x+1) \sqrt{-x^2-2 x+3}+2 \sin ^{-1}\left(\frac{1}{2} (-x-1)\right)","-\frac{1}{3} \left(-x^2-2 x+3\right)^{3/2}-\frac{1}{2} (x+1) \sqrt{-x^2-2 x+3}+2 \sin ^{-1}\left(\frac{1}{2} (-x-1)\right)",1,"-((1 + x)*Sqrt[3 - 2*x - x^2])/2 - (3 - 2*x - x^2)^(3/2)/3 + 2*ArcSin[(-1 - x)/2]","A",4,4,16,0.2500,1,"{640, 612, 619, 216}"
2428,1,56,0,0.0137811,"\int x \sqrt{8+2 x-x^2} \, dx","Int[x*Sqrt[8 + 2*x - x^2],x]","-\frac{1}{3} \left(-x^2+2 x+8\right)^{3/2}-\frac{1}{2} (1-x) \sqrt{-x^2+2 x+8}-\frac{9}{2} \sin ^{-1}\left(\frac{1-x}{3}\right)","-\frac{1}{3} \left(-x^2+2 x+8\right)^{3/2}-\frac{1}{2} (1-x) \sqrt{-x^2+2 x+8}-\frac{9}{2} \sin ^{-1}\left(\frac{1-x}{3}\right)",1,"-((1 - x)*Sqrt[8 + 2*x - x^2])/2 - (8 + 2*x - x^2)^(3/2)/3 - (9*ArcSin[(1 - x)/3])/2","A",4,4,16,0.2500,1,"{640, 612, 619, 216}"
2429,1,50,0,0.0154104,"\int x \sqrt{4+2 x+x^2} \, dx","Int[x*Sqrt[4 + 2*x + x^2],x]","\frac{1}{3} \left(x^2+2 x+4\right)^{3/2}-\frac{1}{2} (x+1) \sqrt{x^2+2 x+4}-\frac{3}{2} \sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)","\frac{1}{3} \left(x^2+2 x+4\right)^{3/2}-\frac{1}{2} (x+1) \sqrt{x^2+2 x+4}-\frac{3}{2} \sinh ^{-1}\left(\frac{x+1}{\sqrt{3}}\right)",1,"-((1 + x)*Sqrt[4 + 2*x + x^2])/2 + (4 + 2*x + x^2)^(3/2)/3 - (3*ArcSinh[(1 + x)/Sqrt[3]])/2","A",4,4,14,0.2857,1,"{640, 612, 619, 215}"
2430,1,31,0,0.0117503,"\int \frac{1}{x \sqrt{2+4 x+3 x^2}} \, dx","Int[1/(x*Sqrt[2 + 4*x + 3*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} (x+1)}{\sqrt{3 x^2+4 x+2}}\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} (x+1)}{\sqrt{3 x^2+4 x+2}}\right)}{\sqrt{2}}",1,"-(ArcTanh[(Sqrt[2]*(1 + x))/Sqrt[2 + 4*x + 3*x^2]]/Sqrt[2])","A",2,2,18,0.1111,1,"{724, 206}"
2431,1,31,0,0.0109847,"\int \frac{1}{x \sqrt{2+4 x-3 x^2}} \, dx","Int[1/(x*Sqrt[2 + 4*x - 3*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} (x+1)}{\sqrt{-3 x^2+4 x+2}}\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} (x+1)}{\sqrt{-3 x^2+4 x+2}}\right)}{\sqrt{2}}",1,"-(ArcTanh[(Sqrt[2]*(1 + x))/Sqrt[2 + 4*x - 3*x^2]]/Sqrt[2])","A",2,2,18,0.1111,1,"{724, 206}"
2432,1,36,0,0.0110107,"\int \frac{1}{x \sqrt{2+5 x+3 x^2}} \, dx","Int[1/(x*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{5 x+4}{2 \sqrt{2} \sqrt{3 x^2+5 x+2}}\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{5 x+4}{2 \sqrt{2} \sqrt{3 x^2+5 x+2}}\right)}{\sqrt{2}}",1,"-(ArcTanh[(4 + 5*x)/(2*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])]/Sqrt[2])","A",2,2,18,0.1111,1,"{724, 206}"
2433,1,36,0,0.0126804,"\int \frac{1}{x \sqrt{2+5 x-3 x^2}} \, dx","Int[1/(x*Sqrt[2 + 5*x - 3*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{5 x+4}{2 \sqrt{2} \sqrt{-3 x^2+5 x+2}}\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{5 x+4}{2 \sqrt{2} \sqrt{-3 x^2+5 x+2}}\right)}{\sqrt{2}}",1,"-(ArcTanh[(4 + 5*x)/(2*Sqrt[2]*Sqrt[2 + 5*x - 3*x^2])]/Sqrt[2])","A",2,2,18,0.1111,1,"{724, 206}"
2434,1,33,0,0.0106804,"\int \frac{1}{x \sqrt{-2+4 x+3 x^2}} \, dx","Int[1/(x*Sqrt[-2 + 4*x + 3*x^2]),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} (1-x)}{\sqrt{3 x^2+4 x-2}}\right)}{\sqrt{2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} (1-x)}{\sqrt{3 x^2+4 x-2}}\right)}{\sqrt{2}}",1,"-(ArcTan[(Sqrt[2]*(1 - x))/Sqrt[-2 + 4*x + 3*x^2]]/Sqrt[2])","A",2,2,18,0.1111,1,"{724, 204}"
2435,1,33,0,0.011465,"\int \frac{1}{x \sqrt{-2+4 x-3 x^2}} \, dx","Int[1/(x*Sqrt[-2 + 4*x - 3*x^2]),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} (1-x)}{\sqrt{-3 x^2+4 x-2}}\right)}{\sqrt{2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} (1-x)}{\sqrt{-3 x^2+4 x-2}}\right)}{\sqrt{2}}",1,"-(ArcTan[(Sqrt[2]*(1 - x))/Sqrt[-2 + 4*x - 3*x^2]]/Sqrt[2])","A",2,2,18,0.1111,1,"{724, 204}"
2436,1,36,0,0.0108348,"\int \frac{1}{x \sqrt{-2+5 x+3 x^2}} \, dx","Int[1/(x*Sqrt[-2 + 5*x + 3*x^2]),x]","-\frac{\tan ^{-1}\left(\frac{4-5 x}{2 \sqrt{2} \sqrt{3 x^2+5 x-2}}\right)}{\sqrt{2}}","-\frac{\tan ^{-1}\left(\frac{4-5 x}{2 \sqrt{2} \sqrt{3 x^2+5 x-2}}\right)}{\sqrt{2}}",1,"-(ArcTan[(4 - 5*x)/(2*Sqrt[2]*Sqrt[-2 + 5*x + 3*x^2])]/Sqrt[2])","A",2,2,18,0.1111,1,"{724, 204}"
2437,1,36,0,0.0108753,"\int \frac{1}{x \sqrt{-2+5 x-3 x^2}} \, dx","Int[1/(x*Sqrt[-2 + 5*x - 3*x^2]),x]","-\frac{\tan ^{-1}\left(\frac{4-5 x}{2 \sqrt{2} \sqrt{-3 x^2+5 x-2}}\right)}{\sqrt{2}}","-\frac{\tan ^{-1}\left(\frac{4-5 x}{2 \sqrt{2} \sqrt{-3 x^2+5 x-2}}\right)}{\sqrt{2}}",1,"-(ArcTan[(4 - 5*x)/(2*Sqrt[2]*Sqrt[-2 + 5*x - 3*x^2])]/Sqrt[2])","A",2,2,18,0.1111,1,"{724, 204}"
2438,1,57,0,0.0240948,"\int \frac{1}{x^3 \sqrt{1+x+x^2}} \, dx","Int[1/(x^3*Sqrt[1 + x + x^2]),x]","\frac{3 \sqrt{x^2+x+1}}{4 x}-\frac{\sqrt{x^2+x+1}}{2 x^2}+\frac{1}{8} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)","\frac{3 \sqrt{x^2+x+1}}{4 x}-\frac{\sqrt{x^2+x+1}}{2 x^2}+\frac{1}{8} \tanh ^{-1}\left(\frac{x+2}{2 \sqrt{x^2+x+1}}\right)",1,"-Sqrt[1 + x + x^2]/(2*x^2) + (3*Sqrt[1 + x + x^2])/(4*x) + ArcTanh[(2 + x)/(2*Sqrt[1 + x + x^2])]/8","A",4,4,14,0.2857,1,"{744, 806, 724, 206}"
2439,1,27,0,0.0146442,"\int \left(\frac{1}{x}-\frac{1}{x \sqrt{1+b x+c x^2}}\right) \, dx","Int[x^(-1) - 1/(x*Sqrt[1 + b*x + c*x^2]),x]","\tanh ^{-1}\left(\frac{b x+2}{2 \sqrt{b x+c x^2+1}}\right)+\log (x)","\log \left(-2 \sqrt{b x+c x^2+1}-b x-2\right)",1,"ArcTanh[(2 + b*x)/(2*Sqrt[1 + b*x + c*x^2])] + Log[x]","A",3,2,23,0.08696,1,"{724, 206}"
2440,1,504,0,0.6452281,"\int (d x)^{5/2} \sqrt{a+b x+c x^2} \, dx","Int[(d*x)^(5/2)*Sqrt[a + b*x + c*x^2],x]","-\frac{4 d^3 x \left(21 a^2 c^2-36 a b^2 c+8 b^4\right) \sqrt{a+b x+c x^2}}{315 c^{7/2} \sqrt{d x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{\sqrt[4]{a} d^3 \sqrt{x} \left(42 a^2 c^2-72 a b^2 c+\sqrt{a} b \sqrt{c} \left(8 b^2-27 a c\right)+16 b^4\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{315 c^{15/4} \sqrt{d x} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt[4]{a} d^3 \sqrt{x} \left(21 a^2 c^2-36 a b^2 c+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{315 c^{15/4} \sqrt{d x} \sqrt{a+b x+c x^2}}+\frac{2 d^2 \sqrt{d x} \left(3 c x \left(8 b^2-7 a c\right)+b \left(3 a c+8 b^2\right)\right) \sqrt{a+b x+c x^2}}{315 c^3}-\frac{4 b d^2 \sqrt{d x} \left(a+b x+c x^2\right)^{3/2}}{21 c^2}+\frac{2 d (d x)^{3/2} \left(a+b x+c x^2\right)^{3/2}}{9 c}","-\frac{4 d^3 x \left(21 a^2 c^2-36 a b^2 c+8 b^4\right) \sqrt{a+b x+c x^2}}{315 c^{7/2} \sqrt{d x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{\sqrt[4]{a} d^3 \sqrt{x} \left(42 a^2 c^2-72 a b^2 c+\sqrt{a} b \sqrt{c} \left(8 b^2-27 a c\right)+16 b^4\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{315 c^{15/4} \sqrt{d x} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt[4]{a} d^3 \sqrt{x} \left(21 a^2 c^2-36 a b^2 c+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{315 c^{15/4} \sqrt{d x} \sqrt{a+b x+c x^2}}+\frac{2 d^2 \sqrt{d x} \left(3 c x \left(8 b^2-7 a c\right)+b \left(3 a c+8 b^2\right)\right) \sqrt{a+b x+c x^2}}{315 c^3}-\frac{4 b d^2 \sqrt{d x} \left(a+b x+c x^2\right)^{3/2}}{21 c^2}+\frac{2 d (d x)^{3/2} \left(a+b x+c x^2\right)^{3/2}}{9 c}",1,"(-4*(8*b^4 - 36*a*b^2*c + 21*a^2*c^2)*d^3*x*Sqrt[a + b*x + c*x^2])/(315*c^(7/2)*Sqrt[d*x]*(Sqrt[a] + Sqrt[c]*x)) + (2*d^2*Sqrt[d*x]*(b*(8*b^2 + 3*a*c) + 3*c*(8*b^2 - 7*a*c)*x)*Sqrt[a + b*x + c*x^2])/(315*c^3) - (4*b*d^2*Sqrt[d*x]*(a + b*x + c*x^2)^(3/2))/(21*c^2) + (2*d*(d*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(9*c) + (4*a^(1/4)*(8*b^4 - 36*a*b^2*c + 21*a^2*c^2)*d^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(315*c^(15/4)*Sqrt[d*x]*Sqrt[a + b*x + c*x^2]) - (a^(1/4)*(16*b^4 - 72*a*b^2*c + 42*a^2*c^2 + Sqrt[a]*b*Sqrt[c]*(8*b^2 - 27*a*c))*d^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(315*c^(15/4)*Sqrt[d*x]*Sqrt[a + b*x + c*x^2])","A",8,8,22,0.3636,1,"{742, 832, 814, 841, 839, 1197, 1103, 1195}"
2441,1,581,0,0.8681457,"\int (d+e x)^{3/2} \sqrt{a+b x+c x^2} \, dx","Int[(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(c e (9 b d-5 a e)-4 b^2 e^2+12 c e x (2 c d-b e)+3 c^2 d^2\right)}{105 c^2 e}+\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 e^2-b d e+c d^2\right) \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^3 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^3 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}}{7 c}","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(c e (9 b d-5 a e)-4 b^2 e^2+12 c e x (2 c d-b e)+3 c^2 d^2\right)}{105 c^2 e}+\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 e^2-b d e+c d^2\right) \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^3 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^3 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}}{7 c}",1,"(2*Sqrt[d + e*x]*(3*c^2*d^2 - 4*b^2*e^2 + c*e*(9*b*d - 5*a*e) + 12*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(105*c^2*e) + (2*e*Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2))/(7*c) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^3*e^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^3*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{742, 814, 843, 718, 424, 419}"
2442,1,513,0,0.4916603,"\int \sqrt{d+e x} \sqrt{a+b x+c x^2} \, dx","Int[Sqrt[d + e*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 d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^2 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^2 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 e}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{15 c e}","\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 d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^2 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^2 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 e}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{15 c e}",1,"(-2*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(15*c*e) + (2*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(5*e) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^2*e^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^2*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{734, 832, 843, 718, 424, 419}"
2443,1,444,0,0.3075368,"\int \frac{\sqrt{a+b x+c x^2}}{\sqrt{d+e x}} \, dx","Int[Sqrt[a + b*x + c*x^2]/Sqrt[d + e*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 e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 e}","\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 e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 e}",1,"(2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(3*e) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*e^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,24,0.2083,1,"{734, 843, 718, 424, 419}"
2444,1,419,0,0.266012,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^{3/2}} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x)^(3/2),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 d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{a+b x+c x^2}}{e \sqrt{d+e 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 d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{a+b x+c x^2}}{e \sqrt{d+e x}}",1,"(-2*Sqrt[a + b*x + c*x^2])/(e*Sqrt[d + e*x]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,24,0.2083,1,"{732, 843, 718, 424, 419}"
2445,1,497,0,0.3938711,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^{5/2}} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x)^(5/2),x]","-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\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}} \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{a+b x+c x^2} (2 c d-b e)}{3 e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{a+b x+c x^2}}{3 e (d+e x)^{3/2}}","-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\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}} \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{a+b x+c x^2} (2 c d-b e)}{3 e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{a+b x+c x^2}}{3 e (d+e x)^{3/2}}",1,"(-2*Sqrt[a + b*x + c*x^2])/(3*e*(d + e*x)^(3/2)) + (2*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(3*e*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e^2*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{732, 834, 843, 718, 424, 419}"
2446,1,617,0,0.6252718,"\int \frac{\sqrt{a+b x+c x^2}}{(d+e x)^{7/2}} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x)^(7/2),x]","\frac{4 \sqrt{a+b x+c x^2} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{15 e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \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}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{a+b x+c x^2} (2 c d-b e)}{15 e (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{a+b x+c x^2}}{5 e (d+e x)^{5/2}}","\frac{4 \sqrt{a+b x+c x^2} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{15 e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \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}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{a+b x+c x^2} (2 c d-b e)}{15 e (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{a+b x+c x^2}}{5 e (d+e x)^{5/2}}",1,"(-2*Sqrt[a + b*x + c*x^2])/(5*e*(d + e*x)^(5/2)) + (2*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(15*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) + (4*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[a + b*x + c*x^2])/(15*e*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^2*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{732, 834, 843, 718, 424, 419}"
2447,1,816,0,2.8359631,"\int (d+e x)^{3/2} \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2),x]","\frac{2 e \sqrt{d+e x} \left(c x^2+b x+a\right)^{5/2}}{11 c}+\frac{2 \sqrt{d+e x} \left(c^2 d^2-6 b^2 e^2+c e (13 b d-3 a e)+14 c e (2 c d-b e) x\right) \left(c x^2+b x+a\right)^{3/2}}{231 c^2 e}+\frac{2 \sqrt{d+e x} \left(8 c^4 d^4-c^3 e (19 b d-42 a e) d^2+8 b^4 e^4-b^2 c e^3 (19 b d+21 a e)+3 c^2 e^2 \left(2 b^2 d^2+17 a b e d-10 a^2 e^2\right)-3 c e (2 c d-b e) \left(c^2 d^2+8 b^2 e^2-c e (b d+31 a e)\right) x\right) \sqrt{c x^2+b x+a}}{1155 c^3 e^3}-\frac{8 \sqrt{2} \sqrt{b^2-4 a c} (2 c d-b e) \left(c^2 d^2-2 b^2 e^2-c e (b d-9 a e)\right) \left(c^2 d^2+b^2 e^2-c e (b d+3 a e)\right) \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{1155 c^4 e^4 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right) \left(16 c^4 d^4-4 c^3 e (8 b d-21 a e) d^2-8 b^4 e^4+b^2 c e^3 (13 b d+51 a e)+3 c^2 e^2 \left(b^2 d^2-28 a b e d-20 a^2 e^2\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{1155 c^4 e^4 \sqrt{d+e x} \sqrt{c x^2+b x+a}}","\frac{2 e \sqrt{d+e x} \left(c x^2+b x+a\right)^{5/2}}{11 c}+\frac{2 \sqrt{d+e x} \left(c^2 d^2-6 b^2 e^2+c e (13 b d-3 a e)+14 c e (2 c d-b e) x\right) \left(c x^2+b x+a\right)^{3/2}}{231 c^2 e}+\frac{2 \sqrt{d+e x} \left(8 c^4 d^4-c^3 e (19 b d-42 a e) d^2+8 b^4 e^4-b^2 c e^3 (19 b d+21 a e)+3 c^2 e^2 \left(2 b^2 d^2+17 a b e d-10 a^2 e^2\right)-3 c e (2 c d-b e) \left(c^2 d^2+8 b^2 e^2-c e (b d+31 a e)\right) x\right) \sqrt{c x^2+b x+a}}{1155 c^3 e^3}-\frac{8 \sqrt{2} \sqrt{b^2-4 a c} (2 c d-b e) \left(c^2 d^2-2 b^2 e^2-c e (b d-9 a e)\right) \left(c^2 d^2+b^2 e^2-c e (b d+3 a e)\right) \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{1155 c^4 e^4 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right) \left(16 c^4 d^4-4 c^3 e (8 b d-21 a e) d^2-8 b^4 e^4+b^2 c e^3 (13 b d+51 a e)+3 c^2 e^2 \left(b^2 d^2-28 a b e d-20 a^2 e^2\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{1155 c^4 e^4 \sqrt{d+e x} \sqrt{c x^2+b x+a}}",1,"(2*Sqrt[d + e*x]*(8*c^4*d^4 + 8*b^4*e^4 - c^3*d^2*e*(19*b*d - 42*a*e) - b^2*c*e^3*(19*b*d + 21*a*e) + 3*c^2*e^2*(2*b^2*d^2 + 17*a*b*d*e - 10*a^2*e^2) - 3*c*e*(2*c*d - b*e)*(c^2*d^2 + 8*b^2*e^2 - c*e*(b*d + 31*a*e))*x)*Sqrt[a + b*x + c*x^2])/(1155*c^3*e^3) + (2*Sqrt[d + e*x]*(c^2*d^2 - 6*b^2*e^2 + c*e*(13*b*d - 3*a*e) + 14*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(231*c^2*e) + (2*e*Sqrt[d + e*x]*(a + b*x + c*x^2)^(5/2))/(11*c) - (8*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(c^2*d^2 - 2*b^2*e^2 - c*e*(b*d - 9*a*e))*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(1155*c^4*e^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(16*c^4*d^4 - 8*b^4*e^4 - 4*c^3*d^2*e*(8*b*d - 21*a*e) + b^2*c*e^3*(13*b*d + 51*a*e) + 3*c^2*e^2*(b^2*d^2 - 28*a*b*d*e - 20*a^2*e^2))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(1155*c^4*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{742, 814, 843, 718, 424, 419}"
2448,1,712,0,1.2727689,"\int \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2} \, dx","Int[Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2),x]","-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(3 c^2 e^2 \left(-28 a^2 e^2-20 a b d e+3 b^2 d^2\right)+b^2 c e^3 (57 a e+7 b d)-4 c^3 d^2 e (8 b d-15 a e)-8 b^4 e^4+16 c^4 d^4\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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^3 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-6 c e x \left(-c e (7 a e+b d)+2 b^2 e^2+c^2 d^2\right)-3 c^2 d e (5 b d-8 a e)+3 b c e^2 (3 a e+b d)-4 b^3 e^3+8 c^3 d^3\right)}{315 c^2 e^3}+\frac{8 \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 d-b e) \left(a e^2-b d e+c d^2\right) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^3 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 (d+e x)^{3/2} \left(a+b x+c x^2\right)^{3/2}}{9 e}-\frac{2 \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{21 c e}","-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(3 c^2 e^2 \left(-28 a^2 e^2-20 a b d e+3 b^2 d^2\right)+b^2 c e^3 (57 a e+7 b d)-4 c^3 d^2 e (8 b d-15 a e)-8 b^4 e^4+16 c^4 d^4\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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^3 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-6 c e x \left(-c e (7 a e+b d)+2 b^2 e^2+c^2 d^2\right)-3 c^2 d e (5 b d-8 a e)+3 b c e^2 (3 a e+b d)-4 b^3 e^3+8 c^3 d^3\right)}{315 c^2 e^3}+\frac{8 \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 d-b e) \left(a e^2-b d e+c d^2\right) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^3 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 (d+e x)^{3/2} \left(a+b x+c x^2\right)^{3/2}}{9 e}-\frac{2 \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{21 c e}",1,"(2*Sqrt[d + e*x]*(8*c^3*d^3 - 4*b^3*e^3 - 3*c^2*d*e*(5*b*d - 8*a*e) + 3*b*c*e^2*(b*d + 3*a*e) - 6*c*e*(c^2*d^2 + 2*b^2*e^2 - c*e*(b*d + 7*a*e))*x)*Sqrt[a + b*x + c*x^2])/(315*c^2*e^3) - (2*(2*c*d - b*e)*Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2))/(21*c*e) + (2*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(9*e) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*c^4*d^4 - 8*b^4*e^4 - 4*c^3*d^2*e*(8*b*d - 15*a*e) + b^2*c*e^3*(7*b*d + 57*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 20*a*b*d*e - 28*a^2*e^2))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*c^3*e^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (8*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*c^3*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,7,24,0.2917,1,"{734, 832, 814, 843, 718, 424, 419}"
2449,1,579,0,0.6723287,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (11 b d-10 a e)+b^2 e^2-3 c e x (2 c d-b e)+8 c^2 d^2\right)}{35 c e^3}+\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 e^2-b d e+c d^2\right) \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 c^2 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 c^2 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}}{7 e}","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (11 b d-10 a e)+b^2 e^2-3 c e x (2 c d-b e)+8 c^2 d^2\right)}{35 c e^3}+\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 e^2-b d e+c d^2\right) \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 c^2 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 c^2 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}}{7 e}",1,"(2*Sqrt[d + e*x]*(8*c^2*d^2 + b^2*e^2 - c*e*(11*b*d - 10*a*e) - 3*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(35*c*e^3) + (2*Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2))/(7*e) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(35*c^2*e^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(35*c^2*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{734, 814, 843, 718, 424, 419}"
2450,1,515,0,0.521268,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^(3/2),x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 c e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{16 \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 d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 c e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (-7 b e+8 c d-6 c e x)}{5 e^3}-\frac{2 \left(a+b x+c x^2\right)^{3/2}}{e \sqrt{d+e x}}","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 c e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{16 \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 d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 c e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (-7 b e+8 c d-6 c e x)}{5 e^3}-\frac{2 \left(a+b x+c x^2\right)^{3/2}}{e \sqrt{d+e x}}",1,"(-2*Sqrt[d + e*x]*(8*c*d - 7*b*e - 6*c*e*x)*Sqrt[a + b*x + c*x^2])/(5*e^3) - (2*(a + b*x + c*x^2)^(3/2))/(e*Sqrt[d + e*x]) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(5*c*e^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (16*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(5*c*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{732, 814, 843, 718, 424, 419}"
2451,1,499,0,0.4521329,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^(5/2),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(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{8 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{a+b x+c x^2} (-3 b e+8 c d+2 c e x)}{3 e^3 \sqrt{d+e x}}-\frac{2 \left(a+b x+c x^2\right)^{3/2}}{3 e (d+e x)^{3/2}}","\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(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{8 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{a+b x+c x^2} (-3 b e+8 c d+2 c e x)}{3 e^3 \sqrt{d+e x}}-\frac{2 \left(a+b x+c x^2\right)^{3/2}}{3 e (d+e x)^{3/2}}",1,"(2*(8*c*d - 3*b*e + 2*c*e*x)*Sqrt[a + b*x + c*x^2])/(3*e^3*Sqrt[d + e*x]) - (2*(a + b*x + c*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) - (8*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{732, 812, 843, 718, 424, 419}"
2452,1,578,0,0.5188931,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{a+b x+c x^2} \left(e x \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-c d e (7 b d-4 a e)+a b e^3+8 c^2 d^3\right)}{5 e^3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 e^4 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{16 \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 d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \left(a+b x+c x^2\right)^{3/2}}{5 e (d+e x)^{5/2}}","-\frac{2 \sqrt{a+b x+c x^2} \left(e x \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-c d e (7 b d-4 a e)+a b e^3+8 c^2 d^3\right)}{5 e^3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 e^4 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{16 \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 d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \left(a+b x+c x^2\right)^{3/2}}{5 e (d+e x)^{5/2}}",1,"(-2*(8*c^2*d^3 + a*b*e^3 - c*d*e*(7*b*d - 4*a*e) + e*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*x)*Sqrt[a + b*x + c*x^2])/(5*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) - (2*(a + b*x + c*x^2)^(3/2))/(5*e*(d + e*x)^(5/2)) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(5*e^4*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (16*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(5*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{732, 810, 843, 718, 424, 419}"
2453,1,721,0,0.8813754,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{9/2}} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^(9/2),x]","-\frac{2 \sqrt{a+b x+c x^2} \left(e x \left(-2 c e (7 b d-5 a e)+b^2 e^2+14 c^2 d^2\right)-c d e (5 b d-4 a e)-b e^2 (2 b d-3 a e)+8 c^2 d^3\right)}{35 e^3 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}+\frac{4 \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right)}{35 e^3 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^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(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 e^4 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \left(a+b x+c x^2\right)^{3/2}}{7 e (d+e x)^{7/2}}","-\frac{2 \sqrt{a+b x+c x^2} \left(e x \left(-2 c e (7 b d-5 a e)+b^2 e^2+14 c^2 d^2\right)-c d e (5 b d-4 a e)-b e^2 (2 b d-3 a e)+8 c^2 d^3\right)}{35 e^3 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}+\frac{4 \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right)}{35 e^3 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^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(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 e^4 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \left(a+b x+c x^2\right)^{3/2}}{7 e (d+e x)^{7/2}}",1,"(4*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*Sqrt[a + b*x + c*x^2])/(35*e^3*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (2*(8*c^2*d^3 - c*d*e*(5*b*d - 4*a*e) - b*e^2*(2*b*d - 3*a*e) + e*(14*c^2*d^2 + b^2*e^2 - 2*c*e*(7*b*d - 5*a*e))*x)*Sqrt[a + b*x + c*x^2])/(35*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) - (2*(a + b*x + c*x^2)^(3/2))/(7*e*(d + e*x)^(7/2)) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(35*e^4*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(35*e^4*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,7,24,0.2917,1,"{732, 810, 834, 843, 718, 424, 419}"
2454,1,616,0,0.959471,"\int \sqrt{d x} \left(a+b x+c x^2\right)^{5/2} \, dx","Int[Sqrt[d*x]*(a + b*x + c*x^2)^(5/2),x]","\frac{2 \sqrt{d x} \left(3 c x \left(308 a^2 c^2-181 a b^2 c+24 b^4\right)+b \left(108 a^2 c^2-151 a b^2 c+24 b^4\right)\right) \sqrt{a+b x+c x^2}}{9009 c^3}-\frac{4 d x \left(951 a^2 b^2 c^2-924 a^3 c^3-268 a b^4 c+24 b^6\right) \sqrt{a+b x+c x^2}}{9009 c^{7/2} \sqrt{d x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{\sqrt[4]{a} d \sqrt{x} \left(\sqrt{a} b \sqrt{c} \left(708 a^2 c^2-241 a b^2 c+24 b^4\right)+2 \left(951 a^2 b^2 c^2-924 a^3 c^3-268 a b^4 c+24 b^6\right)\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{9009 c^{15/4} \sqrt{d x} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt[4]{a} d \sqrt{x} \left(951 a^2 b^2 c^2-924 a^3 c^3-268 a b^4 c+24 b^6\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{9009 c^{15/4} \sqrt{d x} \sqrt{a+b x+c x^2}}-\frac{10 \sqrt{d x} \left(14 c x \left(3 b^2-11 a c\right)+3 b \left(6 b^2-19 a c\right)\right) \left(a+b x+c x^2\right)^{3/2}}{9009 c^2}+\frac{2 (d x)^{3/2} \left(a+b x+c x^2\right)^{5/2}}{13 d}+\frac{10 b \sqrt{d x} \left(a+b x+c x^2\right)^{5/2}}{143 c}","\frac{2 \sqrt{d x} \left(3 c x \left(308 a^2 c^2-181 a b^2 c+24 b^4\right)+b \left(108 a^2 c^2-151 a b^2 c+24 b^4\right)\right) \sqrt{a+b x+c x^2}}{9009 c^3}-\frac{4 d x \left(951 a^2 b^2 c^2-924 a^3 c^3-268 a b^4 c+24 b^6\right) \sqrt{a+b x+c x^2}}{9009 c^{7/2} \sqrt{d x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{\sqrt[4]{a} d \sqrt{x} \left(\sqrt{a} b \sqrt{c} \left(708 a^2 c^2-241 a b^2 c+24 b^4\right)+2 \left(951 a^2 b^2 c^2-924 a^3 c^3-268 a b^4 c+24 b^6\right)\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{9009 c^{15/4} \sqrt{d x} \sqrt{a+b x+c x^2}}+\frac{4 \sqrt[4]{a} d \sqrt{x} \left(951 a^2 b^2 c^2-924 a^3 c^3-268 a b^4 c+24 b^6\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{9009 c^{15/4} \sqrt{d x} \sqrt{a+b x+c x^2}}-\frac{10 \sqrt{d x} \left(14 c x \left(3 b^2-11 a c\right)+3 b \left(6 b^2-19 a c\right)\right) \left(a+b x+c x^2\right)^{3/2}}{9009 c^2}+\frac{2 (d x)^{3/2} \left(a+b x+c x^2\right)^{5/2}}{13 d}+\frac{10 b \sqrt{d x} \left(a+b x+c x^2\right)^{5/2}}{143 c}",1,"(-4*(24*b^6 - 268*a*b^4*c + 951*a^2*b^2*c^2 - 924*a^3*c^3)*d*x*Sqrt[a + b*x + c*x^2])/(9009*c^(7/2)*Sqrt[d*x]*(Sqrt[a] + Sqrt[c]*x)) + (2*Sqrt[d*x]*(b*(24*b^4 - 151*a*b^2*c + 108*a^2*c^2) + 3*c*(24*b^4 - 181*a*b^2*c + 308*a^2*c^2)*x)*Sqrt[a + b*x + c*x^2])/(9009*c^3) - (10*Sqrt[d*x]*(3*b*(6*b^2 - 19*a*c) + 14*c*(3*b^2 - 11*a*c)*x)*(a + b*x + c*x^2)^(3/2))/(9009*c^2) + (10*b*Sqrt[d*x]*(a + b*x + c*x^2)^(5/2))/(143*c) + (2*(d*x)^(3/2)*(a + b*x + c*x^2)^(5/2))/(13*d) + (4*a^(1/4)*(24*b^6 - 268*a*b^4*c + 951*a^2*b^2*c^2 - 924*a^3*c^3)*d*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(9009*c^(15/4)*Sqrt[d*x]*Sqrt[a + b*x + c*x^2]) - (a^(1/4)*(Sqrt[a]*b*Sqrt[c]*(24*b^4 - 241*a*b^2*c + 708*a^2*c^2) + 2*(24*b^6 - 268*a*b^4*c + 951*a^2*b^2*c^2 - 924*a^3*c^3))*d*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(9009*c^(15/4)*Sqrt[d*x]*Sqrt[a + b*x + c*x^2])","A",9,8,22,0.3636,1,"{734, 832, 814, 841, 839, 1197, 1103, 1195}"
2455,1,847,0,2.7007053,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(c x^2+b x+a\right)^{5/2}}{11 e}+\frac{10 \sqrt{d+e x} \left(16 c^2 d^2+3 b^2 e^2-c e (23 b d-18 a e)-7 c e (2 c d-b e) x\right) \left(c x^2+b x+a\right)^{3/2}}{693 c e^3}+\frac{2 \sqrt{d+e x} \left(128 c^4 d^4-4 c^3 e (76 b d-69 a e) d^2-4 b^4 e^4-b^2 c e^3 (7 b d-27 a e)+3 c^2 e^2 \left(65 b^2 d^2-124 a b e d+60 a^2 e^2\right)-12 c e (2 c d-b e) \left(4 c^2 d^2-b^2 e^2-4 c e (b d-2 a e)\right) x\right) \sqrt{c x^2+b x+a}}{693 c^2 e^5}-\frac{\sqrt{2} \sqrt{b^2-4 a c} (2 c d-b e) \left(128 c^4 d^4-4 c^3 e (64 b d-93 a e) d^2+8 b^4 e^4+b^2 c e^3 (29 b d-93 a e)+3 c^2 e^2 \left(33 b^2 d^2-124 a b e d+124 a^2 e^2\right)\right) \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{693 c^3 e^6 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right) \left(128 c^4 d^4-4 c^3 e (64 b d-69 a e) d^2+2 b^4 e^4+b^2 c e^3 (5 b d-21 a e)+3 c^2 e^2 \left(41 b^2 d^2-92 a b e d+60 a^2 e^2\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{693 c^3 e^6 \sqrt{d+e x} \sqrt{c x^2+b x+a}}","\frac{2 \sqrt{d+e x} \left(c x^2+b x+a\right)^{5/2}}{11 e}+\frac{10 \sqrt{d+e x} \left(16 c^2 d^2+3 b^2 e^2-c e (23 b d-18 a e)-7 c e (2 c d-b e) x\right) \left(c x^2+b x+a\right)^{3/2}}{693 c e^3}+\frac{2 \sqrt{d+e x} \left(128 c^4 d^4-4 c^3 e (76 b d-69 a e) d^2-4 b^4 e^4-b^2 c e^3 (7 b d-27 a e)+3 c^2 e^2 \left(65 b^2 d^2-124 a b e d+60 a^2 e^2\right)-12 c e (2 c d-b e) \left(4 c^2 d^2-b^2 e^2-4 c e (b d-2 a e)\right) x\right) \sqrt{c x^2+b x+a}}{693 c^2 e^5}-\frac{\sqrt{2} \sqrt{b^2-4 a c} (2 c d-b e) \left(128 c^4 d^4-4 c^3 e (64 b d-93 a e) d^2+8 b^4 e^4+b^2 c e^3 (29 b d-93 a e)+3 c^2 e^2 \left(33 b^2 d^2-124 a b e d+124 a^2 e^2\right)\right) \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{693 c^3 e^6 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right) \left(128 c^4 d^4-4 c^3 e (64 b d-69 a e) d^2+2 b^4 e^4+b^2 c e^3 (5 b d-21 a e)+3 c^2 e^2 \left(41 b^2 d^2-92 a b e d+60 a^2 e^2\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{693 c^3 e^6 \sqrt{d+e x} \sqrt{c x^2+b x+a}}",1,"(2*Sqrt[d + e*x]*(128*c^4*d^4 - 4*b^4*e^4 - 4*c^3*d^2*e*(76*b*d - 69*a*e) - b^2*c*e^3*(7*b*d - 27*a*e) + 3*c^2*e^2*(65*b^2*d^2 - 124*a*b*d*e + 60*a^2*e^2) - 12*c*e*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*x)*Sqrt[a + b*x + c*x^2])/(693*c^2*e^5) + (10*Sqrt[d + e*x]*(16*c^2*d^2 + 3*b^2*e^2 - c*e*(23*b*d - 18*a*e) - 7*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(693*c*e^3) + (2*Sqrt[d + e*x]*(a + b*x + c*x^2)^(5/2))/(11*e) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(128*c^4*d^4 + 8*b^4*e^4 + b^2*c*e^3*(29*b*d - 93*a*e) - 4*c^3*d^2*e*(64*b*d - 93*a*e) + 3*c^2*e^2*(33*b^2*d^2 - 124*a*b*d*e + 124*a^2*e^2))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(693*c^3*e^6*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(128*c^4*d^4 + 2*b^4*e^4 - 4*c^3*d^2*e*(64*b*d - 69*a*e) + b^2*c*e^3*(5*b*d - 21*a*e) + 3*c^2*e^2*(41*b^2*d^2 - 92*a*b*d*e + 60*a^2*e^2))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(693*c^3*e^6*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{734, 814, 843, 718, 424, 419}"
2456,1,716,0,1.1410043,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x)^(3/2),x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(3 c^2 e^2 \left(28 a^2 e^2-76 a b d e+45 b^2 d^2\right)-b^2 c e^3 (7 b d-15 a e)-4 c^3 d^2 e (64 b d-57 a e)-b^4 e^4+128 c^4 d^4\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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{63 c^2 e^6 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-3 c e x \left(-4 c e (8 b d-7 a e)+b^2 e^2+32 c^2 d^2\right)-12 c^2 d e (20 b d-11 a e)+3 b c e^2 (37 b d-36 a e)-b^3 e^3+128 c^3 d^3\right)}{63 c e^5}-\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 d-b e) \left(a e^2-b d e+c d^2\right) \left(-4 c e (32 b d-33 a e)-b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{63 c^2 e^6 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{10 \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2} (-15 b e+16 c d-14 c e x)}{63 e^3}-\frac{2 \left(a+b x+c x^2\right)^{5/2}}{e \sqrt{d+e x}}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(3 c^2 e^2 \left(28 a^2 e^2-76 a b d e+45 b^2 d^2\right)-b^2 c e^3 (7 b d-15 a e)-4 c^3 d^2 e (64 b d-57 a e)-b^4 e^4+128 c^4 d^4\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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{63 c^2 e^6 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-3 c e x \left(-4 c e (8 b d-7 a e)+b^2 e^2+32 c^2 d^2\right)-12 c^2 d e (20 b d-11 a e)+3 b c e^2 (37 b d-36 a e)-b^3 e^3+128 c^3 d^3\right)}{63 c e^5}-\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 d-b e) \left(a e^2-b d e+c d^2\right) \left(-4 c e (32 b d-33 a e)-b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{63 c^2 e^6 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{10 \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2} (-15 b e+16 c d-14 c e x)}{63 e^3}-\frac{2 \left(a+b x+c x^2\right)^{5/2}}{e \sqrt{d+e x}}",1,"(-2*Sqrt[d + e*x]*(128*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(37*b*d - 36*a*e) - 12*c^2*d*e*(20*b*d - 11*a*e) - 3*c*e*(32*c^2*d^2 + b^2*e^2 - 4*c*e*(8*b*d - 7*a*e))*x)*Sqrt[a + b*x + c*x^2])/(63*c*e^5) - (10*Sqrt[d + e*x]*(16*c*d - 15*b*e - 14*c*e*x)*(a + b*x + c*x^2)^(3/2))/(63*e^3) - (2*(a + b*x + c*x^2)^(5/2))/(e*Sqrt[d + e*x]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(128*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(64*b*d - 57*a*e) - b^2*c*e^3*(7*b*d - 15*a*e) + 3*c^2*e^2*(45*b^2*d^2 - 76*a*b*d*e + 28*a^2*e^2))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(63*c^2*e^6*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(128*c^2*d^2 - b^2*e^2 - 4*c*e*(32*b*d - 33*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(63*c^2*e^6*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{732, 814, 843, 718, 424, 419}"
2457,1,622,0,0.8054145,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x)^(5/2),x]","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-4 c e (44 b d-5 a e)+51 b^2 e^2-48 c e x (2 c d-b e)+128 c^2 d^2\right)}{21 e^5}+\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 e^2-b d e+c d^2\right) \left(-4 c e (32 b d-5 a e)+27 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 c e^6 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-29 a e)+3 b^2 e^2+128 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 c e^6 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{10 \left(a+b x+c x^2\right)^{3/2} (-7 b e+16 c d+2 c e x)}{21 e^3 \sqrt{d+e x}}-\frac{2 \left(a+b x+c x^2\right)^{5/2}}{3 e (d+e x)^{3/2}}","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-4 c e (44 b d-5 a e)+51 b^2 e^2-48 c e x (2 c d-b e)+128 c^2 d^2\right)}{21 e^5}+\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 e^2-b d e+c d^2\right) \left(-4 c e (32 b d-5 a e)+27 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 c e^6 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-29 a e)+3 b^2 e^2+128 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 c e^6 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{10 \left(a+b x+c x^2\right)^{3/2} (-7 b e+16 c d+2 c e x)}{21 e^3 \sqrt{d+e x}}-\frac{2 \left(a+b x+c x^2\right)^{5/2}}{3 e (d+e x)^{3/2}}",1,"(2*Sqrt[d + e*x]*(128*c^2*d^2 + 51*b^2*e^2 - 4*c*e*(44*b*d - 5*a*e) - 48*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(21*e^5) + (10*(16*c*d - 7*b*e + 2*c*e*x)*(a + b*x + c*x^2)^(3/2))/(21*e^3*Sqrt[d + e*x]) - (2*(a + b*x + c*x^2)^(5/2))/(3*e*(d + e*x)^(3/2)) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(128*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(32*b*d - 29*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(21*c*e^6*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(128*c^2*d^2 + 27*b^2*e^2 - 4*c*e*(32*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(21*c*e^6*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,7,24,0.2917,1,"{732, 812, 814, 843, 718, 424, 419}"
2458,1,603,0,0.6894546,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x)^{7/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{a+b x+c x^2} \left(-4 c e (28 b d-9 a e)+15 b^2 e^2+16 c e x (2 c d-b e)+128 c^2 d^2\right)}{15 e^5 \sqrt{d+e 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 d-b e) \left(-4 c e (32 b d-17 a e)+15 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^6 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (32 b d-9 a e)+23 b^2 e^2+128 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^6 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \left(a+b x+c x^2\right)^{3/2} (-5 b e+16 c d+6 c e x)}{15 e^3 (d+e x)^{3/2}}-\frac{2 \left(a+b x+c x^2\right)^{5/2}}{5 e (d+e x)^{5/2}}","-\frac{2 \sqrt{a+b x+c x^2} \left(-4 c e (28 b d-9 a e)+15 b^2 e^2+16 c e x (2 c d-b e)+128 c^2 d^2\right)}{15 e^5 \sqrt{d+e 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 d-b e) \left(-4 c e (32 b d-17 a e)+15 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^6 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (32 b d-9 a e)+23 b^2 e^2+128 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^6 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \left(a+b x+c x^2\right)^{3/2} (-5 b e+16 c d+6 c e x)}{15 e^3 (d+e x)^{3/2}}-\frac{2 \left(a+b x+c x^2\right)^{5/2}}{5 e (d+e x)^{5/2}}",1,"(-2*(128*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(28*b*d - 9*a*e) + 16*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(15*e^5*Sqrt[d + e*x]) + (2*(16*c*d - 5*b*e + 6*c*e*x)*(a + b*x + c*x^2)^(3/2))/(15*e^3*(d + e*x)^(3/2)) - (2*(a + b*x + c*x^2)^(5/2))/(5*e*(d + e*x)^(5/2)) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(128*c^2*d^2 + 23*b^2*e^2 - 4*c*e*(32*b*d - 9*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^6*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(128*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(32*b*d - 17*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c*e^6*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{732, 812, 843, 718, 424, 419}"
2459,1,731,0,0.8870405,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x)^{9/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x)^(9/2),x]","-\frac{2 \left(a+b x+c x^2\right)^{3/2} \left(e x \left(-2 c e (11 b d-5 a e)+3 b^2 e^2+22 c^2 d^2\right)-c d e (13 b d-4 a e)+3 a b e^3+16 c^2 d^3\right)}{21 e^3 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 c \sqrt{a+b x+c x^2} \left(e x \left(-4 c e (8 b d-5 a e)+3 b^2 e^2+32 c^2 d^2\right)-4 c d e (44 b d-29 a e)+3 b e^2 (17 b d-16 a e)+128 c^2 d^3\right)}{21 e^5 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}+\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(-4 c e (32 b d-5 a e)+27 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 e^6 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-29 a e)+3 b^2 e^2+128 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 e^6 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \left(a+b x+c x^2\right)^{5/2}}{7 e (d+e x)^{7/2}}","-\frac{2 \left(a+b x+c x^2\right)^{3/2} \left(e x \left(-2 c e (11 b d-5 a e)+3 b^2 e^2+22 c^2 d^2\right)-c d e (13 b d-4 a e)+3 a b e^3+16 c^2 d^3\right)}{21 e^3 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 c \sqrt{a+b x+c x^2} \left(e x \left(-4 c e (8 b d-5 a e)+3 b^2 e^2+32 c^2 d^2\right)-4 c d e (44 b d-29 a e)+3 b e^2 (17 b d-16 a e)+128 c^2 d^3\right)}{21 e^5 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}+\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(-4 c e (32 b d-5 a e)+27 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 e^6 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-29 a e)+3 b^2 e^2+128 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 e^6 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \left(a+b x+c x^2\right)^{5/2}}{7 e (d+e x)^{7/2}}",1,"(2*c*(128*c^2*d^3 - 4*c*d*e*(44*b*d - 29*a*e) + 3*b*e^2*(17*b*d - 16*a*e) + e*(32*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(8*b*d - 5*a*e))*x)*Sqrt[a + b*x + c*x^2])/(21*e^5*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) - (2*(16*c^2*d^3 + 3*a*b*e^3 - c*d*e*(13*b*d - 4*a*e) + e*(22*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(11*b*d - 5*a*e))*x)*(a + b*x + c*x^2)^(3/2))/(21*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) - (2*(a + b*x + c*x^2)^(5/2))/(7*e*(d + e*x)^(7/2)) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(128*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(32*b*d - 29*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(21*e^6*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(128*c^2*d^2 + 27*b^2*e^2 - 4*c*e*(32*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(21*e^6*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,7,24,0.2917,1,"{732, 810, 812, 843, 718, 424, 419}"
2460,1,923,0,1.188265,"\int \frac{\left(a+b x+c x^2\right)^{5/2}}{(d+e x)^{11/2}} \, dx","Int[(a + b*x + c*x^2)^(5/2)/(d + e*x)^(11/2),x]","-\frac{2 \left(c x^2+b x+a\right)^{5/2}}{9 e (d+e x)^{9/2}}-\frac{2 \left(16 c^2 d^3-c e (11 b d-4 a e) d-b e^2 (2 b d-5 a e)+e \left(26 c^2 d^2+3 b^2 e^2-2 c e (13 b d-7 a e)\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{63 e^3 \left(c d^2-b e d+a e^2\right) (d+e x)^{7/2}}-\frac{2 \left(128 c^4 d^5-4 c^3 e (60 b d-49 a e) d^3+3 c^2 e^2 \left(37 b^2 d^2-52 a b e d+12 a^2 e^2\right) d-2 a b^3 e^5-b c e^3 \left(b^2 d^2+9 a b e d-24 a^2 e^2\right)+e \left(160 c^4 d^4-4 c^3 e (80 b d-69 a e) d^2-2 b^4 e^4-b^2 c e^3 (11 b d-27 a e)+3 c^2 e^2 \left(57 b^2 d^2-92 a b e d+28 a^2 e^2\right)\right) x\right) \sqrt{c x^2+b x+a}}{63 e^5 \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{3/2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(128 c^4 d^4-4 c^3 e (64 b d-57 a e) d^2-b^4 e^4-b^2 c e^3 (7 b d-15 a e)+3 c^2 e^2 \left(45 b^2 d^2-76 a b e d+28 a^2 e^2\right)\right) \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{63 e^6 \left(c d^2-b e d+a e^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} (2 c d-b e) \left(128 c^2 d^2-b^2 e^2-4 c e (32 b d-33 a e)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{63 e^6 \left(c d^2-b e d+a e^2\right) \sqrt{d+e x} \sqrt{c x^2+b x+a}}","-\frac{2 \left(c x^2+b x+a\right)^{5/2}}{9 e (d+e x)^{9/2}}-\frac{2 \left(16 c^2 d^3-c e (11 b d-4 a e) d-b e^2 (2 b d-5 a e)+e \left(26 c^2 d^2+3 b^2 e^2-2 c e (13 b d-7 a e)\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{63 e^3 \left(c d^2-b e d+a e^2\right) (d+e x)^{7/2}}-\frac{2 \left(128 c^4 d^5-4 c^3 e (60 b d-49 a e) d^3+3 c^2 e^2 \left(37 b^2 d^2-52 a b e d+12 a^2 e^2\right) d-2 a b^3 e^5-b c e^3 \left(b^2 d^2+9 a b e d-24 a^2 e^2\right)+e \left(160 c^4 d^4-4 c^3 e (80 b d-69 a e) d^2-2 b^4 e^4-b^2 c e^3 (11 b d-27 a e)+3 c^2 e^2 \left(57 b^2 d^2-92 a b e d+28 a^2 e^2\right)\right) x\right) \sqrt{c x^2+b x+a}}{63 e^5 \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{3/2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(128 c^4 d^4-4 c^3 e (64 b d-57 a e) d^2-b^4 e^4-b^2 c e^3 (7 b d-15 a e)+3 c^2 e^2 \left(45 b^2 d^2-76 a b e d+28 a^2 e^2\right)\right) \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{63 e^6 \left(c d^2-b e d+a e^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} (2 c d-b e) \left(128 c^2 d^2-b^2 e^2-4 c e (32 b d-33 a e)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{63 e^6 \left(c d^2-b e d+a e^2\right) \sqrt{d+e x} \sqrt{c x^2+b x+a}}",1,"(-2*(128*c^4*d^5 - 2*a*b^3*e^5 - 4*c^3*d^3*e*(60*b*d - 49*a*e) - b*c*e^3*(b^2*d^2 + 9*a*b*d*e - 24*a^2*e^2) + 3*c^2*d*e^2*(37*b^2*d^2 - 52*a*b*d*e + 12*a^2*e^2) + e*(160*c^4*d^4 - 2*b^4*e^4 - 4*c^3*d^2*e*(80*b*d - 69*a*e) - b^2*c*e^3*(11*b*d - 27*a*e) + 3*c^2*e^2*(57*b^2*d^2 - 92*a*b*d*e + 28*a^2*e^2))*x)*Sqrt[a + b*x + c*x^2])/(63*e^5*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2)) - (2*(16*c^2*d^3 - b*e^2*(2*b*d - 5*a*e) - c*d*e*(11*b*d - 4*a*e) + e*(26*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(13*b*d - 7*a*e))*x)*(a + b*x + c*x^2)^(3/2))/(63*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(7/2)) - (2*(a + b*x + c*x^2)^(5/2))/(9*e*(d + e*x)^(9/2)) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(128*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(64*b*d - 57*a*e) - b^2*c*e^3*(7*b*d - 15*a*e) + 3*c^2*e^2*(45*b^2*d^2 - 76*a*b*d*e + 28*a^2*e^2))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(63*e^6*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(128*c^2*d^2 - b^2*e^2 - 4*c*e*(32*b*d - 33*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(63*e^6*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{732, 810, 843, 718, 424, 419}"
2461,1,600,0,0.8488734,"\int \frac{(d+e x)^{7/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^(7/2)/Sqrt[a + b*x + c*x^2],x]","\frac{2 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (25 a e+71 b d)+24 b^2 e^2+71 c^2 d^2\right)}{105 c^3}-\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 e^2-b d e+c d^2\right) \left(-c e (25 a e+71 b d)+24 b^2 e^2+71 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{8 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (13 a e+11 b d)+6 b^2 e^2+11 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{12 e (d+e x)^{3/2} \sqrt{a+b x+c x^2} (2 c d-b e)}{35 c^2}+\frac{2 e (d+e x)^{5/2} \sqrt{a+b x+c x^2}}{7 c}","\frac{2 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (25 a e+71 b d)+24 b^2 e^2+71 c^2 d^2\right)}{105 c^3}-\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 e^2-b d e+c d^2\right) \left(-c e (25 a e+71 b d)+24 b^2 e^2+71 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{8 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (13 a e+11 b d)+6 b^2 e^2+11 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{12 e (d+e x)^{3/2} \sqrt{a+b x+c x^2} (2 c d-b e)}{35 c^2}+\frac{2 e (d+e x)^{5/2} \sqrt{a+b x+c x^2}}{7 c}",1,"(2*e*(71*c^2*d^2 + 24*b^2*e^2 - c*e*(71*b*d + 25*a*e))*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(105*c^3) + (12*e*(2*c*d - b*e)*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(35*c^2) + (2*e*(d + e*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(7*c) + (8*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(11*c^2*d^2 + 6*b^2*e^2 - c*e*(11*b*d + 13*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(71*c^2*d^2 + 24*b^2*e^2 - c*e*(71*b*d + 25*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{742, 832, 843, 718, 424, 419}"
2462,1,509,0,0.5411354,"\int \frac{(d+e x)^{5/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^(5/2)/Sqrt[a + b*x + c*x^2],x]","-\frac{8 \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 d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (9 a e+23 b d)+8 b^2 e^2+23 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{8 e \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{15 c^2}+\frac{2 e (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 c}","-\frac{8 \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 d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (9 a e+23 b d)+8 b^2 e^2+23 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{8 e \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{15 c^2}+\frac{2 e (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 c}",1,"(8*e*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(15*c^2) + (2*e*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(5*c) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(23*c^2*d^2 + 8*b^2*e^2 - c*e*(23*b*d + 9*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (8*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^3*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{742, 832, 843, 718, 424, 419}"
2463,1,439,0,0.320669,"\int \frac{(d+e x)^{3/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x)^(3/2)/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 e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 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 e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 c}",1,"(2*e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(3*c) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,24,0.2083,1,"{742, 843, 718, 424, 419}"
2464,1,188,0,0.0686928,"\int \frac{\sqrt{d+e x}}{\sqrt{a+b x+c x^2}} \, dx","Int[Sqrt[d + e*x]/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2])","A",2,2,24,0.08333,1,"{718, 424}"
2465,1,189,0,0.0711155,"\int \frac{1}{\sqrt{d+e x} \sqrt{a+b x+c x^2}} \, dx","Int[1/(Sqrt[d + e*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 (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{d+e 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 (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{d+e x} \sqrt{a+b x+c x^2}}",1,"(2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",2,2,24,0.08333,1,"{718, 419}"
2466,1,248,0,0.129045,"\int \frac{1}{(d+e x)^{3/2} \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 e \sqrt{a+b x+c x^2}}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 e \sqrt{a+b x+c x^2}}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}",1,"(-2*e*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/((c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2])","A",4,4,24,0.1667,1,"{744, 21, 718, 424}"
2467,1,523,0,0.4120848,"\int \frac{1}{(d+e x)^{5/2} \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^(5/2)*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 (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{4 e \sqrt{a+b x+c x^2} (2 c d-b e)}{3 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e \sqrt{a+b x+c x^2}}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\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}} \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{4 e \sqrt{a+b x+c x^2} (2 c d-b e)}{3 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e \sqrt{a+b x+c x^2}}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}",1,"(-2*e*Sqrt[a + b*x + c*x^2])/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) - (4*e*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(3*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{744, 834, 843, 718, 424, 419}"
2468,1,629,0,0.6866615,"\int \frac{1}{(d+e x)^{7/2} \sqrt{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^(7/2)*Sqrt[a + b*x + c*x^2]),x]","-\frac{2 e \sqrt{a+b x+c x^2} \left(-c e (9 a e+23 b d)+8 b^2 e^2+23 c^2 d^2\right)}{15 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^3}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (9 a e+23 b d)+8 b^2 e^2+23 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{8 \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 d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{8 e \sqrt{a+b x+c x^2} (2 c d-b e)}{15 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e \sqrt{a+b x+c x^2}}{5 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}","-\frac{2 e \sqrt{a+b x+c x^2} \left(-c e (9 a e+23 b d)+8 b^2 e^2+23 c^2 d^2\right)}{15 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^3}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (9 a e+23 b d)+8 b^2 e^2+23 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{8 \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 d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{8 e \sqrt{a+b x+c x^2} (2 c d-b e)}{15 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e \sqrt{a+b x+c x^2}}{5 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}",1,"(-2*e*Sqrt[a + b*x + c*x^2])/(5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) - (8*e*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(15*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2)) - (2*e*(23*c^2*d^2 + 8*b^2*e^2 - c*e*(23*b*d + 9*a*e))*Sqrt[a + b*x + c*x^2])/(15*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[d + e*x]) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(23*c^2*d^2 + 8*b^2*e^2 - c*e*(23*b*d + 9*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (8*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{744, 834, 843, 718, 424, 419}"
2469,1,641,0,0.949103,"\int \frac{(d+e x)^{7/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(7/2)/(a + b*x + c*x^2)^(3/2),x]","\frac{4 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right)}{3 c^2 \left(b^2-4 a c\right)}-\frac{4 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{5/2} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 e (d+e x)^{3/2} \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}","\frac{4 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right)}{3 c^2 \left(b^2-4 a c\right)}-\frac{4 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{5/2} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 e (d+e x)^{3/2} \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}",1,"(-2*(d + e*x)^(5/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (4*e*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(3*c^2*(b^2 - 4*a*c)) + (2*e*(2*c*d - b*e)*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(c*(b^2 - 4*a*c)) + (Sqrt[2]*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^3*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^3*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{738, 832, 843, 718, 424, 419}"
2470,1,533,0,0.5121005,"\int \frac{(d+e x)^{5/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(5/2)/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c^2 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c^2 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 e \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}","-\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c^2 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c^2 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 e \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}",1,"(-2*(d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (2*e*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(c*(b^2 - 4*a*c)) + (2*Sqrt[2]*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c^2*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c^2*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{738, 832, 843, 718, 424, 419}"
2471,1,457,0,0.3291536,"\int \frac{(d+e x)^{3/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^(3/2)/(a + b*x + c*x^2)^(3/2),x]","-\frac{4 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","-\frac{4 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(-2*Sqrt[d + e*x]*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (Sqrt[2]*(2*c*d - b*e)*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,24,0.2083,1,"{738, 843, 718, 424, 419}"
2472,1,426,0,0.2491957,"\int \frac{\sqrt{d+e x}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[Sqrt[d + e*x]/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 (b+2 c x) \sqrt{d+e x}}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","-\frac{2 (b+2 c x) \sqrt{d+e x}}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(-2*(b + 2*c*x)*Sqrt[d + e*x])/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,24,0.2083,1,"{736, 843, 718, 424, 419}"
2473,1,480,0,0.3204675,"\int \frac{1}{\sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2)),x]","-\frac{2 \sqrt{d+e x} \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{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{4 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}","-\frac{2 \sqrt{d+e x} \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{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{4 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}",1,"(-2*Sqrt[d + e*x]*(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]) + (Sqrt[2]*(2*c*d - b*e)*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[2]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,24,0.2083,1,"{740, 843, 718, 424, 419}"
2474,1,607,0,0.5285594,"\int \frac{1}{(d+e x)^{3/2} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{4 e \sqrt{a+b x+c x^2} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\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{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}","-\frac{4 e \sqrt{a+b x+c x^2} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\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{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{d+e x} \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[d + e*x]*Sqrt[a + b*x + c*x^2]) - (4*e*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) + (2*Sqrt[2]*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{740, 834, 843, 718, 424, 419}"
2475,1,744,0,0.9111967,"\int \frac{1}{(d+e x)^{5/2} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[1/((d + e*x)^(5/2)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{4 e \sqrt{a+b x+c x^2} \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right)}{3 \left(b^2-4 a c\right) (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^2\right)}{3 \left(b^2-4 a c\right) \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^3}-\frac{4 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\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) (d+e x)^{3/2} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}","-\frac{4 e \sqrt{a+b x+c x^2} \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right)}{3 \left(b^2-4 a c\right) (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 e \sqrt{a+b x+c x^2} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^2\right)}{3 \left(b^2-4 a c\right) \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^3}-\frac{4 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\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) (d+e x)^{3/2} \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)*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2]) - (4*e*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2)) - (2*e*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[d + e*x]) + (Sqrt[2]*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[2]*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,24,0.2500,1,"{740, 834, 843, 718, 424, 419}"
2476,1,659,0,0.8105075,"\int \frac{(d+e x)^{7/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(7/2)/(a + b*x + c*x^2)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(x (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)+b^2 \left(-\left(9 c d^2 e-a e^3\right)\right)+8 b c d \left(3 a e^2+c d^2\right)-4 a c e \left(5 a e^2+3 c d^2\right)\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{5/2} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{2 \sqrt{d+e x} \left(x (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)+b^2 \left(-\left(9 c d^2 e-a e^3\right)\right)+8 b c d \left(3 a e^2+c d^2\right)-4 a c e \left(5 a e^2+3 c d^2\right)\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{5/2} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(5/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(8*b*c*d*(c*d^2 + 3*a*e^2) - 4*a*c*e*(3*c*d^2 + 5*a*e^2) - b^2*(9*c*d^2*e - a*e^3) + (2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*x))/(3*c*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*(b^2 - 4*a*c)^(3/2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*(b^2 - 4*a*c)^(3/2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{738, 818, 843, 718, 424, 419}"
2477,1,590,0,0.5876743,"\int \frac{(d+e x)^{5/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(5/2)/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \sqrt{d+e x} \left(-x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-8 b \left(a e^2+c d^2\right)+4 a c d e+7 b^2 d e\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{16 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","-\frac{2 \sqrt{d+e x} \left(-x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-8 b \left(a e^2+c d^2\right)+4 a c d e+7 b^2 d e\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{16 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*Sqrt[d + e*x]*(7*b^2*d*e + 4*a*c*d*e - 8*b*(c*d^2 + a*e^2) - (16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*(b^2 - 4*a*c)^(3/2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (16*Sqrt[2]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*(b^2 - 4*a*c)^(3/2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{738, 820, 843, 718, 424, 419}"
2478,1,542,0,0.5637031,"\int \frac{(d+e x)^{3/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^(3/2)/(a + b*x + c*x^2)^(5/2),x]","\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{2 \sqrt{d+e x} \left(4 a c e-5 b^2 e+8 c x (2 c d-b e)+8 b c d\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{8 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{2 \sqrt{d+e x} \left(4 a c e-5 b^2 e+8 c x (2 c d-b e)+8 b c d\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{8 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(-2*Sqrt[d + e*x]*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(8*b*c*d - 5*b^2*e + 4*a*c*e + 8*c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) - (8*Sqrt[2]*(2*c*d - b*e)*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*(b^2 - 4*a*c)^(3/2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*(b^2 - 4*a*c)^(3/2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{738, 822, 843, 718, 424, 419}"
2479,1,605,0,0.5756146,"\int \frac{\sqrt{d+e x}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[Sqrt[d + e*x]/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \sqrt{d+e x} \left(-c x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-4 b c \left(a e^2+2 c d^2\right)-4 a c^2 d e+9 b^2 c d e+b^3 \left(-e^2\right)\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (b+2 c x) \sqrt{d+e x}}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{16 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2}}","-\frac{2 \sqrt{d+e x} \left(-c x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-4 b c \left(a e^2+2 c d^2\right)-4 a c^2 d e+9 b^2 c d e+b^3 \left(-e^2\right)\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (b+2 c x) \sqrt{d+e x}}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{16 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2}}",1,"(-2*(b + 2*c*x)*Sqrt[d + e*x])/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*Sqrt[d + e*x]*(9*b^2*c*d*e - 4*a*c^2*d*e - b^3*e^2 - 4*b*c*(2*c*d^2 + a*e^2) - c*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (16*Sqrt[2]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*(b^2 - 4*a*c)^(3/2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{736, 822, 843, 718, 424, 419}"
2480,1,725,0,0.7359364,"\int \frac{1}{\sqrt{d+e x} \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/(Sqrt[d + e*x]*(a + b*x + c*x^2)^(5/2)),x]","-\frac{2 \sqrt{d+e x} \left(-2 c x (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-5 c e (b d-2 a e)-2 b^2 e^2+8 c^2 d^2\right)+3 a c e (2 c d-b e)^2\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}","-\frac{2 \sqrt{d+e x} \left(-2 c x (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(-5 c e (b d-2 a e)-2 b^2 e^2+8 c^2 d^2\right)+3 a c e (2 c d-b e)^2\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}",1,"(-2*Sqrt[d + e*x]*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(3/2)) - (2*Sqrt[d + e*x]*(3*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 2*b^2*e^2 - 5*c*e*(b*d - 2*a*e)) - 2*c*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,24,0.2500,1,"{740, 822, 843, 718, 424, 419}"
2481,1,918,0,1.4633247,"\int \frac{1}{(d+e x)^{3/2} \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(5/2)),x]","-\frac{\sqrt{2} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) \left(16 c^4 d^4-4 c^3 e (8 b d-15 a e) d^2-8 b^4 e^4+b^2 c e^3 (7 b d+57 a e)+3 c^2 e^2 \left(3 b^2 d^2-20 a b e d-28 a^2 e^2\right)\right)}{3 \left(b^2-4 a c\right)^{3/2} \left(c d^2-b e d+a e^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 e \sqrt{c x^2+b x+a} \left(16 c^4 d^4-4 c^3 e (8 b d-15 a e) d^2-8 b^4 e^4+b^2 c e^3 (7 b d+57 a e)+3 c^2 e^2 \left(3 b^2 d^2-20 a b e d-28 a^2 e^2\right)\right)}{3 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^3 \sqrt{d+e x}}+\frac{8 \sqrt{2} (2 c d-b e) \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \left(c d^2-b e d+a e^2\right)^2 \sqrt{d+e x} \sqrt{c x^2+b x+a}}-\frac{2 \left(5 a c e (2 c d-b e)^2-4 c \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(8 c^2 d^2-4 b^2 e^2-c e (3 b d-14 a e)\right)\right)}{3 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 \sqrt{d+e x} \sqrt{c x^2+b x+a}}-\frac{2 \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right)}{3 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \sqrt{d+e x} \left(c x^2+b x+a\right)^{3/2}}","-\frac{\sqrt{2} \sqrt{d+e 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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right) \left(16 c^4 d^4-4 c^3 e (8 b d-15 a e) d^2-8 b^4 e^4+b^2 c e^3 (7 b d+57 a e)+3 c^2 e^2 \left(3 b^2 d^2-20 a b e d-28 a^2 e^2\right)\right)}{3 \left(b^2-4 a c\right)^{3/2} \left(c d^2-b e d+a e^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 e \sqrt{c x^2+b x+a} \left(16 c^4 d^4-4 c^3 e (8 b d-15 a e) d^2-8 b^4 e^4+b^2 c e^3 (7 b d+57 a e)+3 c^2 e^2 \left(3 b^2 d^2-20 a b e d-28 a^2 e^2\right)\right)}{3 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^3 \sqrt{d+e x}}+\frac{8 \sqrt{2} (2 c d-b e) \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \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} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \left(b^2-4 a c\right)^{3/2} \left(c d^2-b e d+a e^2\right)^2 \sqrt{d+e x} \sqrt{c x^2+b x+a}}-\frac{2 \left(5 a c e (2 c d-b e)^2-4 c \left(2 c^2 d^2-b^2 e^2-2 c e (b d-3 a e)\right) x (2 c d-b e)-\left(-e b^2+c d b+2 a c e\right) \left(8 c^2 d^2-4 b^2 e^2-c e (3 b d-14 a e)\right)\right)}{3 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 \sqrt{d+e x} \sqrt{c x^2+b x+a}}-\frac{2 \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right)}{3 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \sqrt{d+e x} \left(c x^2+b x+a\right)^{3/2}}",1,"(-2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2)) - (2*(5*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 4*b^2*e^2 - c*e*(3*b*d - 14*a*e)) - 4*c*(2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2]) + (2*e*(16*c^4*d^4 - 8*b^4*e^4 - 4*c^3*d^2*e*(8*b*d - 15*a*e) + b^2*c*e^3*(7*b*d + 57*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 20*a*b*d*e - 28*a^2*e^2))*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[d + e*x]) - (Sqrt[2]*(16*c^4*d^4 - 8*b^4*e^4 - 4*c^3*d^2*e*(8*b*d - 15*a*e) + b^2*c*e^3*(7*b*d + 57*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 20*a*b*d*e - 28*a^2*e^2))*Sqrt[d + e*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (8*Sqrt[2]*(2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*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]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,7,24,0.2917,1,"{740, 822, 834, 843, 718, 424, 419}"
2482,1,30,0,0.02086,"\int \frac{\sqrt{3+5 x}}{\sqrt{2+5 x-12 x^2}} \, dx","Int[Sqrt[3 + 5*x]/Sqrt[2 + 5*x - 12*x^2],x]","-\frac{1}{3} \sqrt{19} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|\frac{55}{76}\right)","-\frac{1}{3} \sqrt{19} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|\frac{55}{76}\right)",1,"-(Sqrt[19]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], 55/76])/3","A",2,2,24,0.08333,1,"{718, 424}"
2483,1,638,0,1.0718683,"\int (d+e x)^2 \left(a+b x+c x^2\right)^{4/3} \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^(4/3),x]","\frac{3 (b+2 c x) \left(a+b x+c x^2\right)^{4/3} \left(-c e (3 a e+17 b d)+5 b^2 e^2+17 c^2 d^2\right)}{374 c^3}-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt[3]{a+b x+c x^2} \left(-c e (3 a e+17 b d)+5 b^2 e^2+17 c^2 d^2\right)}{935 c^4}+\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} \left(b^2-4 a c\right)^2 \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right) \sqrt{\frac{-2^{2/3} \sqrt[3]{c} \sqrt[3]{b^2-4 a c} \sqrt[3]{a+b x+c x^2}+\left(b^2-4 a c\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} \left(a+b x+c x^2\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}} \left(-c e (3 a e+17 b d)+5 b^2 e^2+17 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{935 c^{13/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}}}+\frac{15 e \left(a+b x+c x^2\right)^{7/3} (2 c d-b e)}{119 c^2}+\frac{3 e (d+e x) \left(a+b x+c x^2\right)^{7/3}}{17 c}","\frac{3 (b+2 c x) \left(a+b x+c x^2\right)^{4/3} \left(-c e (3 a e+17 b d)+5 b^2 e^2+17 c^2 d^2\right)}{374 c^3}-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt[3]{a+b x+c x^2} \left(-c e (3 a e+17 b d)+5 b^2 e^2+17 c^2 d^2\right)}{935 c^4}+\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} \left(b^2-4 a c\right)^2 \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right) \sqrt{\frac{-2^{2/3} \sqrt[3]{c} \sqrt[3]{b^2-4 a c} \sqrt[3]{a+b x+c x^2}+\left(b^2-4 a c\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} \left(a+b x+c x^2\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}} \left(-c e (3 a e+17 b d)+5 b^2 e^2+17 c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{935 c^{13/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}}}+\frac{15 e \left(a+b x+c x^2\right)^{7/3} (2 c d-b e)}{119 c^2}+\frac{3 e (d+e x) \left(a+b x+c x^2\right)^{7/3}}{17 c}",1,"(-3*(b^2 - 4*a*c)*(17*c^2*d^2 + 5*b^2*e^2 - c*e*(17*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/3))/(935*c^4) + (3*(17*c^2*d^2 + 5*b^2*e^2 - c*e*(17*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(4/3))/(374*c^3) + (15*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(7/3))/(119*c^2) + (3*e*(d + e*x)*(a + b*x + c*x^2)^(7/3))/(17*c) + (2^(1/3)*3^(3/4)*Sqrt[2 + Sqrt[3]]*(b^2 - 4*a*c)^2*(17*c^2*d^2 + 5*b^2*e^2 - c*e*(17*b*d + 3*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(935*c^(13/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2])","A",6,5,22,0.2273,1,"{742, 640, 623, 321, 218}"
2484,1,539,0,0.5137502,"\int (d+e x) \left(a+b x+c x^2\right)^{4/3} \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^(4/3),x]","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt[3]{a+b x+c x^2} (2 c d-b e)}{110 c^3}+\frac{3^{3/4} \sqrt{2+\sqrt{3}} \left(b^2-4 a c\right)^2 \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right) \sqrt{\frac{-2^{2/3} \sqrt[3]{c} \sqrt[3]{b^2-4 a c} \sqrt[3]{a+b x+c x^2}+\left(b^2-4 a c\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} \left(a+b x+c x^2\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{55\ 2^{2/3} c^{10/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}}}+\frac{3 (b+2 c x) \left(a+b x+c x^2\right)^{4/3} (2 c d-b e)}{44 c^2}+\frac{3 e \left(a+b x+c x^2\right)^{7/3}}{14 c}","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt[3]{a+b x+c x^2} (2 c d-b e)}{110 c^3}+\frac{3^{3/4} \sqrt{2+\sqrt{3}} \left(b^2-4 a c\right)^2 \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right) \sqrt{\frac{-2^{2/3} \sqrt[3]{c} \sqrt[3]{b^2-4 a c} \sqrt[3]{a+b x+c x^2}+\left(b^2-4 a c\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} \left(a+b x+c x^2\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}} (2 c d-b e) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{55\ 2^{2/3} c^{10/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}}}+\frac{3 (b+2 c x) \left(a+b x+c x^2\right)^{4/3} (2 c d-b e)}{44 c^2}+\frac{3 e \left(a+b x+c x^2\right)^{7/3}}{14 c}",1,"(-3*(b^2 - 4*a*c)*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/3))/(110*c^3) + (3*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(4/3))/(44*c^2) + (3*e*(a + b*x + c*x^2)^(7/3))/(14*c) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*(b^2 - 4*a*c)^2*(2*c*d - b*e)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(55*2^(2/3)*c^(10/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2])","A",5,4,20,0.2000,1,"{640, 623, 321, 218}"
2485,1,490,0,0.3909915,"\int \left(a+b x+c x^2\right)^{4/3} \, dx","Int[(a + b*x + c*x^2)^(4/3),x]","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt[3]{a+b x+c x^2}}{55 c^2}+\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} \left(b^2-4 a c\right)^2 \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right) \sqrt{\frac{-2^{2/3} \sqrt[3]{c} \sqrt[3]{b^2-4 a c} \sqrt[3]{a+b x+c x^2}+\left(b^2-4 a c\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} \left(a+b x+c x^2\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{55 c^{7/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}}}+\frac{3 (b+2 c x) \left(a+b x+c x^2\right)^{4/3}}{22 c}","-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt[3]{a+b x+c x^2}}{55 c^2}+\frac{\sqrt[3]{2} 3^{3/4} \sqrt{2+\sqrt{3}} \left(b^2-4 a c\right)^2 \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right) \sqrt{\frac{-2^{2/3} \sqrt[3]{c} \sqrt[3]{b^2-4 a c} \sqrt[3]{a+b x+c x^2}+\left(b^2-4 a c\right)^{2/3}+2 \sqrt[3]{2} c^{2/3} \left(a+b x+c x^2\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{55 c^{7/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{a+b x+c x^2}\right)^2}}}+\frac{3 (b+2 c x) \left(a+b x+c x^2\right)^{4/3}}{22 c}",1,"(-3*(b^2 - 4*a*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/3))/(55*c^2) + (3*(b + 2*c*x)*(a + b*x + c*x^2)^(4/3))/(22*c) + (2^(1/3)*3^(3/4)*Sqrt[2 + Sqrt[3]]*(b^2 - 4*a*c)^2*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(55*c^(7/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2])","A",4,3,14,0.2143,1,"{623, 321, 218}"
2486,1,180,0,0.1983093,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{d+e x} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(d + e*x),x]","\frac{3 \left(a+b x+c x^2\right)^{4/3} F_1\left(-\frac{8}{3};-\frac{4}{3},-\frac{4}{3};-\frac{5}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{\sqrt[3]{2} e \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3}}","\frac{3 \left(a+b x+c x^2\right)^{4/3} F_1\left(-\frac{8}{3};-\frac{4}{3},-\frac{4}{3};-\frac{5}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{\sqrt[3]{2} e \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3}}",1,"(3*(a + b*x + c*x^2)^(4/3)*AppellF1[-8/3, -4/3, -4/3, -5/3, (2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)/(2*c*(d + e*x)), (2*d - ((b + Sqrt[b^2 - 4*a*c])*e)/c)/(2*(d + e*x))])/(2^(1/3)*e*((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(4/3)*((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(4/3))","A",2,2,22,0.09091,1,"{758, 133}"
2487,1,189,0,0.0908302,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(d + e*x)^2,x]","\frac{12\ 2^{2/3} \left(a+b x+c x^2\right)^{4/3} F_1\left(-\frac{5}{3};-\frac{4}{3},-\frac{4}{3};-\frac{2}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{5 e (d+e x) \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3}}","\frac{12\ 2^{2/3} \left(a+b x+c x^2\right)^{4/3} F_1\left(-\frac{5}{3};-\frac{4}{3},-\frac{4}{3};-\frac{2}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{5 e (d+e x) \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3}}",1,"(12*2^(2/3)*(a + b*x + c*x^2)^(4/3)*AppellF1[-5/3, -4/3, -4/3, -2/3, (2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)/(2*c*(d + e*x)), (2*d - ((b + Sqrt[b^2 - 4*a*c])*e)/c)/(2*(d + e*x))])/(5*e*((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(4/3)*((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(4/3)*(d + e*x))","A",2,2,22,0.09091,1,"{758, 133}"
2488,1,187,0,0.0885369,"\int \frac{\left(a+b x+c x^2\right)^{4/3}}{(d+e x)^3} \, dx","Int[(a + b*x + c*x^2)^(4/3)/(d + e*x)^3,x]","\frac{6\ 2^{2/3} \left(a+b x+c x^2\right)^{4/3} F_1\left(-\frac{2}{3};-\frac{4}{3},-\frac{4}{3};\frac{1}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{e (d+e x)^2 \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3}}","\frac{6\ 2^{2/3} \left(a+b x+c x^2\right)^{4/3} F_1\left(-\frac{2}{3};-\frac{4}{3},-\frac{4}{3};\frac{1}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{e (d+e x)^2 \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{4/3}}",1,"(6*2^(2/3)*(a + b*x + c*x^2)^(4/3)*AppellF1[-2/3, -4/3, -4/3, 1/3, (2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)/(2*c*(d + e*x)), (2*d - ((b + Sqrt[b^2 - 4*a*c])*e)/c)/(2*(d + e*x))])/(e*((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(4/3)*((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(4/3)*(d + e*x)^2)","A",2,2,22,0.09091,1,"{758, 133}"
2489,1,1224,0,1.5561334,"\int \frac{(d+e x)^3}{\left(a+b x+c x^2\right)^{7/3}} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^(7/3),x]","-\frac{3 (b d-2 a e+(2 c d-b e) x) (d+e x)^2}{4 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{4/3}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (2 c d-b e) \left(5 c^2 d^2-b^2 e^2-c e (5 b d-9 a e)\right) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt[3]{2} c^{5/3} \left(b^2-4 a c\right)^{5/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}}}-\frac{3^{3/4} (2 c d-b e) \left(5 c^2 d^2-b^2 e^2-c e (5 b d-9 a e)\right) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} c^{5/3} \left(b^2-4 a c\right)^{5/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}}}+\frac{3 \left(-\left(11 c d^2 e-a e^3\right) b^2+10 c d \left(c d^2+3 a e^2\right) b-8 a c e \left(2 c d^2+3 a e^2\right)+(2 c d-b e) \left(10 c^2 d^2-b^2 e^2-2 c e (5 b d-7 a e)\right) x\right)}{4 c \left(b^2-4 a c\right)^2 \sqrt[3]{c x^2+b x+a}}-\frac{3 (2 c d-b e) \left(5 c^2 d^2-b^2 e^2-c e (5 b d-9 a e)\right) (b+2 c x)}{2 \sqrt[3]{2} c^{5/3} \left(b^2-4 a c\right)^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}","-\frac{3 (b d-2 a e+(2 c d-b e) x) (d+e x)^2}{4 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{4/3}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (2 c d-b e) \left(5 c^2 d^2-b^2 e^2-c e (5 b d-9 a e)\right) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt[3]{2} c^{5/3} \left(b^2-4 a c\right)^{5/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}}}-\frac{3^{3/4} (2 c d-b e) \left(5 c^2 d^2-b^2 e^2-c e (5 b d-9 a e)\right) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} c^{5/3} \left(b^2-4 a c\right)^{5/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}}}+\frac{3 \left(-\left(11 c d^2 e-a e^3\right) b^2+10 c d \left(c d^2+3 a e^2\right) b-8 a c e \left(2 c d^2+3 a e^2\right)+(2 c d-b e) \left(10 c^2 d^2-b^2 e^2-2 c e (5 b d-7 a e)\right) x\right)}{4 c \left(b^2-4 a c\right)^2 \sqrt[3]{c x^2+b x+a}}-\frac{3 (2 c d-b e) \left(5 c^2 d^2-b^2 e^2-c e (5 b d-9 a e)\right) (b+2 c x)}{2 \sqrt[3]{2} c^{5/3} \left(b^2-4 a c\right)^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}",1,"(-3*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(4/3)) + (3*(10*b*c*d*(c*d^2 + 3*a*e^2) - 8*a*c*e*(2*c*d^2 + 3*a*e^2) - b^2*(11*c*d^2*e - a*e^3) + (2*c*d - b*e)*(10*c^2*d^2 - b^2*e^2 - 2*c*e*(5*b*d - 7*a*e))*x))/(4*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(1/3)) - (3*(2*c*d - b*e)*(5*c^2*d^2 - b^2*e^2 - c*e*(5*b*d - 9*a*e))*(b + 2*c*x))/(2*2^(1/3)*c^(5/3)*(b^2 - 4*a*c)^2*((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(2*c*d - b*e)*(5*c^2*d^2 - b^2*e^2 - c*e*(5*b*d - 9*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(4*2^(1/3)*c^(5/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]) - (3^(3/4)*(2*c*d - b*e)*(5*c^2*d^2 - b^2*e^2 - c*e*(5*b*d - 9*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(2^(5/6)*c^(5/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2])","A",6,6,22,0.2727,1,"{738, 777, 623, 303, 218, 1877}"
2490,1,1153,0,1.3677055,"\int \frac{(d+e x)^2}{\left(a+b x+c x^2\right)^{7/3}} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^(7/3),x]","-\frac{3 \left(10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right) (b+2 c x)}{2 \sqrt[3]{2} c^{2/3} \left(b^2-4 a c\right)^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}-\frac{3 \left(4 d e b^2-5 \left(c d^2+a e^2\right) b+4 a c d e-\left(10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right) x\right)}{2 \left(b^2-4 a c\right)^2 \sqrt[3]{c x^2+b x+a}}-\frac{3 (d+e x) (b d-2 a e+(2 c d-b e) x)}{4 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{4/3}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt[3]{2} c^{2/3} \left(b^2-4 a c\right)^{5/3} \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} (b+2 c x)}-\frac{3^{3/4} \left(10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} c^{2/3} \left(b^2-4 a c\right)^{5/3} \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} (b+2 c x)}","-\frac{3 \left(10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right) (b+2 c x)}{2 \sqrt[3]{2} c^{2/3} \left(b^2-4 a c\right)^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}-\frac{3 \left(4 d e b^2-5 \left(c d^2+a e^2\right) b+4 a c d e-\left(10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right) x\right)}{2 \left(b^2-4 a c\right)^2 \sqrt[3]{c x^2+b x+a}}-\frac{3 (d+e x) (b d-2 a e+(2 c d-b e) x)}{4 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{4/3}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt[3]{2} c^{2/3} \left(b^2-4 a c\right)^{5/3} \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} (b+2 c x)}-\frac{3^{3/4} \left(10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} c^{2/3} \left(b^2-4 a c\right)^{5/3} \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} (b+2 c x)}",1,"(-3*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(4/3)) - (3*(4*b^2*d*e + 4*a*c*d*e - 5*b*(c*d^2 + a*e^2) - (10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(1/3)) - (3*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(b + 2*c*x))/(2*2^(1/3)*c^(2/3)*(b^2 - 4*a*c)^2*((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(4*2^(1/3)*c^(2/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]) - (3^(3/4)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(2^(5/6)*c^(2/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2])","A",6,6,22,0.2727,1,"{738, 638, 623, 303, 218, 1877}"
2491,1,1043,0,0.9886796,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^{7/3}} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^(7/3),x]","\frac{15 (2 c d-b e) (b+2 c x)}{4 \left(b^2-4 a c\right)^2 \sqrt[3]{c x^2+b x+a}}-\frac{15 \sqrt[3]{c} (2 c d-b e) (b+2 c x)}{2 \sqrt[3]{2} \left(b^2-4 a c\right)^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}-\frac{3 (b d-2 a e+(2 c d-b e) x)}{4 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{4/3}}+\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} (2 c d-b e) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt[3]{2} \left(b^2-4 a c\right)^{5/3} \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} (b+2 c x)}-\frac{5\ 3^{3/4} \sqrt[3]{c} (2 c d-b e) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} \left(b^2-4 a c\right)^{5/3} \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} (b+2 c x)}","\frac{15 (2 c d-b e) (b+2 c x)}{4 \left(b^2-4 a c\right)^2 \sqrt[3]{c x^2+b x+a}}-\frac{15 \sqrt[3]{c} (2 c d-b e) (b+2 c x)}{2 \sqrt[3]{2} \left(b^2-4 a c\right)^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}-\frac{3 (b d-2 a e+(2 c d-b e) x)}{4 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{4/3}}+\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} (2 c d-b e) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt[3]{2} \left(b^2-4 a c\right)^{5/3} \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} (b+2 c x)}-\frac{5\ 3^{3/4} \sqrt[3]{c} (2 c d-b e) \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} \left(b^2-4 a c\right)^{5/3} \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} (b+2 c x)}",1,"(-3*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(4/3)) + (15*(2*c*d - b*e)*(b + 2*c*x))/(4*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(1/3)) - (15*c^(1/3)*(2*c*d - b*e)*(b + 2*c*x))/(2*2^(1/3)*(b^2 - 4*a*c)^2*((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))) + (15*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(1/3)*(2*c*d - b*e)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(4*2^(1/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]) - (5*3^(3/4)*c^(1/3)*(2*c*d - b*e)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(2^(5/6)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2])","A",6,6,20,0.3000,1,"{638, 623, 325, 303, 218, 1877}"
2492,1,993,0,0.9539008,"\int \frac{1}{\left(a+b x+c x^2\right)^{7/3}} \, dx","Int[(a + b*x + c*x^2)^(-7/3),x]","\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right) c^{4/3}}{2 \sqrt[3]{2} \left(b^2-4 a c\right)^{5/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}}}-\frac{5 \sqrt[6]{2} 3^{3/4} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right) c^{4/3}}{\left(b^2-4 a c\right)^{5/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}}}-\frac{15 (b+2 c x) c^{4/3}}{\sqrt[3]{2} \left(b^2-4 a c\right)^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}+\frac{15 (b+2 c x) c}{2 \left(b^2-4 a c\right)^2 \sqrt[3]{c x^2+b x+a}}-\frac{3 (b+2 c x)}{4 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{4/3}}","\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right) c^{4/3}}{2 \sqrt[3]{2} \left(b^2-4 a c\right)^{5/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}}}-\frac{5 \sqrt[6]{2} 3^{3/4} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right) \sqrt{\frac{\left(b^2-4 a c\right)^{2/3}-2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a} \sqrt[3]{b^2-4 a c}+2 \sqrt[3]{2} c^{2/3} \left(c x^2+b x+a\right)^{2/3}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}}\right)|-7-4 \sqrt{3}\right) c^{4/3}}{\left(b^2-4 a c\right)^{5/3} (b+2 c x) \sqrt{\frac{\sqrt[3]{b^2-4 a c} \left(\sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)^2}}}-\frac{15 (b+2 c x) c^{4/3}}{\sqrt[3]{2} \left(b^2-4 a c\right)^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{b^2-4 a c}+2^{2/3} \sqrt[3]{c} \sqrt[3]{c x^2+b x+a}\right)}+\frac{15 (b+2 c x) c}{2 \left(b^2-4 a c\right)^2 \sqrt[3]{c x^2+b x+a}}-\frac{3 (b+2 c x)}{4 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{4/3}}",1,"(-3*(b + 2*c*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(4/3)) + (15*c*(b + 2*c*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(1/3)) - (15*c^(4/3)*(b + 2*c*x))/(2^(1/3)*(b^2 - 4*a*c)^2*((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))) + (15*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(4/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/(2*2^(1/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]) - (5*2^(1/6)*3^(3/4)*c^(4/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*Sqrt[((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))], -7 - 4*Sqrt[3]])/((b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*Sqrt[((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + Sqrt[3])*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2])","A",6,5,14,0.3571,1,"{623, 325, 303, 218, 1877}"
2493,1,182,0,0.1097916,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)^{7/3}} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^(7/3)),x]","-\frac{3 \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} F_1\left(\frac{14}{3};\frac{7}{3},\frac{7}{3};\frac{17}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{224\ 2^{2/3} e \left(a+b x+c x^2\right)^{7/3}}","-\frac{3 \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} F_1\left(\frac{14}{3};\frac{7}{3},\frac{7}{3};\frac{17}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{224\ 2^{2/3} e \left(a+b x+c x^2\right)^{7/3}}",1,"(-3*((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(7/3)*((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(7/3)*AppellF1[14/3, 7/3, 7/3, 17/3, (2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)/(2*c*(d + e*x)), (2*d - ((b + Sqrt[b^2 - 4*a*c])*e)/c)/(2*(d + e*x))])/(224*2^(2/3)*e*(a + b*x + c*x^2)^(7/3))","A",2,2,22,0.09091,1,"{758, 133}"
2494,1,189,0,0.0913116,"\int \frac{1}{(d+e x)^2 \left(a+b x+c x^2\right)^{7/3}} \, dx","Int[1/((d + e*x)^2*(a + b*x + c*x^2)^(7/3)),x]","-\frac{3 \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} F_1\left(\frac{17}{3};\frac{7}{3},\frac{7}{3};\frac{20}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{272\ 2^{2/3} e (d+e x) \left(a+b x+c x^2\right)^{7/3}}","-\frac{3 \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} F_1\left(\frac{17}{3};\frac{7}{3},\frac{7}{3};\frac{20}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{272\ 2^{2/3} e (d+e x) \left(a+b x+c x^2\right)^{7/3}}",1,"(-3*((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(7/3)*((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(7/3)*AppellF1[17/3, 7/3, 7/3, 20/3, (2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)/(2*c*(d + e*x)), (2*d - ((b + Sqrt[b^2 - 4*a*c])*e)/c)/(2*(d + e*x))])/(272*2^(2/3)*e*(d + e*x)*(a + b*x + c*x^2)^(7/3))","A",2,2,22,0.09091,1,"{758, 133}"
2495,1,189,0,0.0902785,"\int \frac{1}{(d+e x)^3 \left(a+b x+c x^2\right)^{7/3}} \, dx","Int[1/((d + e*x)^3*(a + b*x + c*x^2)^(7/3)),x]","-\frac{3 \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} F_1\left(\frac{20}{3};\frac{7}{3},\frac{7}{3};\frac{23}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{320\ 2^{2/3} e (d+e x)^2 \left(a+b x+c x^2\right)^{7/3}}","-\frac{3 \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{7/3} F_1\left(\frac{20}{3};\frac{7}{3},\frac{7}{3};\frac{23}{3};\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{320\ 2^{2/3} e (d+e x)^2 \left(a+b x+c x^2\right)^{7/3}}",1,"(-3*((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(7/3)*((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^(7/3)*AppellF1[20/3, 7/3, 7/3, 23/3, (2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)/(2*c*(d + e*x)), (2*d - ((b + Sqrt[b^2 - 4*a*c])*e)/c)/(2*(d + e*x))])/(320*2^(2/3)*e*(d + e*x)^2*(a + b*x + c*x^2)^(7/3))","A",2,2,22,0.09091,1,"{758, 133}"
2496,1,242,0,0.1393107,"\int \frac{1}{(d+e x) \sqrt[3]{c^2 d^2-b c d e+b^2 e^2+3 b c e^2 x+3 c^2 e^2 x^2}} \, dx","Int[1/((d + e*x)*(c^2*d^2 - b*c*d*e + b^2*e^2 + 3*b*c*e^2*x + 3*c^2*e^2*x^2)^(1/3)),x]","\frac{\log \left(-3 c e^2 \sqrt[3]{2 c d-b e} \sqrt[3]{b^2 e^2-b c d e+3 b c e^2 x+c^2 d^2+3 c^2 e^2 x^2}+3 c e^2 (c d-b e)-3 c^2 e^3 x\right)}{2 e (2 c d-b e)^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 (-b e+c d-c e x)}{\sqrt{3} \sqrt[3]{2 c d-b e} \sqrt[3]{b^2 e^2-b c d e+3 b c e^2 x+c^2 d^2+3 c^2 e^2 x^2}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} e (2 c d-b e)^{2/3}}-\frac{\log (d+e x)}{2 e (2 c d-b e)^{2/3}}","\frac{\log \left(-3 c e^2 \sqrt[3]{2 c d-b e} \sqrt[3]{b^2 e^2-b c d e+3 b c e^2 x+c^2 d^2+3 c^2 e^2 x^2}+3 c e^2 (c d-b e)-3 c^2 e^3 x\right)}{2 e (2 c d-b e)^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 (-b e+c d-c e x)}{\sqrt{3} \sqrt[3]{2 c d-b e} \sqrt[3]{b^2 e^2-b c d e+3 b c e^2 x+c^2 d^2+3 c^2 e^2 x^2}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} e (2 c d-b e)^{2/3}}-\frac{\log (d+e x)}{2 e (2 c d-b e)^{2/3}}",1,"-(ArcTan[1/Sqrt[3] + (2*(c*d - b*e - c*e*x))/(Sqrt[3]*(2*c*d - b*e)^(1/3)*(c^2*d^2 - b*c*d*e + b^2*e^2 + 3*b*c*e^2*x + 3*c^2*e^2*x^2)^(1/3))]/(Sqrt[3]*e*(2*c*d - b*e)^(2/3))) - Log[d + e*x]/(2*e*(2*c*d - b*e)^(2/3)) + Log[3*c*e^2*(c*d - b*e) - 3*c^2*e^3*x - 3*c*e^2*(2*c*d - b*e)^(1/3)*(c^2*d^2 - b*c*d*e + b^2*e^2 + 3*b*c*e^2*x + 3*c^2*e^2*x^2)^(1/3)]/(2*e*(2*c*d - b*e)^(2/3))","A",1,1,52,0.01923,1,"{750}"
2497,1,635,0,0.7328424,"\int \frac{(2+3 x)^3}{\sqrt[3]{52-54 x+27 x^2}} \, dx","Int[(2 + 3*x)^3/(52 - 54*x + 27*x^2)^(1/3),x]","\frac{1}{30} \left(27 x^2-54 x+52\right)^{2/3} (3 x+2)^2+\frac{1}{7} (8 x+27) \left(27 x^2-54 x+52\right)^{2/3}+\frac{9000 \sqrt[3]{5} (1-x)}{7 \left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)}+\frac{50\ 5^{5/6} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{189\ 3^{3/4} (1-x) \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}}}-\frac{25\ 5^{5/6} \sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{189 \sqrt{2} \sqrt[4]{3} (1-x) \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}}}","\frac{1}{30} \left(27 x^2-54 x+52\right)^{2/3} (3 x+2)^2+\frac{1}{7} (8 x+27) \left(27 x^2-54 x+52\right)^{2/3}+\frac{9000 \sqrt[3]{5} (1-x)}{7 \left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)}+\frac{50\ 5^{5/6} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{189\ 3^{3/4} (1-x) \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}}}-\frac{25\ 5^{5/6} \sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{189 \sqrt{2} \sqrt[4]{3} (1-x) \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}}}",1,"((2 + 3*x)^2*(52 - 54*x + 27*x^2)^(2/3))/30 + ((27 + 8*x)*(52 - 54*x + 27*x^2)^(2/3))/7 + (9000*5^(1/3)*(1 - x))/(7*(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))) - (25*5^(5/6)*Sqrt[2 + Sqrt[3]]*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(189*Sqrt[2]*3^(1/4)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)]) + (50*5^(5/6)*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(189*3^(3/4)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)])","A",7,7,22,0.3182,1,"{742, 779, 619, 235, 304, 219, 1879}"
2498,1,628,0,0.5414435,"\int \frac{(2+3 x)^2}{\sqrt[3]{52-54 x+27 x^2}} \, dx","Int[(2 + 3*x)^2/(52 - 54*x + 27*x^2)^(1/3),x]","\frac{1}{21} (3 x+2) \left(27 x^2-54 x+52\right)^{2/3}+\frac{25}{42} \left(27 x^2-54 x+52\right)^{2/3}+\frac{2700 \sqrt[3]{5} (1-x)}{7 \left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)}+\frac{5\ 5^{5/6} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{63\ 3^{3/4} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}-\frac{5\ 5^{5/6} \sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{126 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}","\frac{1}{21} (3 x+2) \left(27 x^2-54 x+52\right)^{2/3}+\frac{25}{42} \left(27 x^2-54 x+52\right)^{2/3}+\frac{2700 \sqrt[3]{5} (1-x)}{7 \left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)}+\frac{5\ 5^{5/6} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{63\ 3^{3/4} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}-\frac{5\ 5^{5/6} \sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{126 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}",1,"(25*(52 - 54*x + 27*x^2)^(2/3))/42 + ((2 + 3*x)*(52 - 54*x + 27*x^2)^(2/3))/21 + (2700*5^(1/3)*(1 - x))/(7*(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))) - (5*5^(5/6)*Sqrt[2 + Sqrt[3]]*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(126*Sqrt[2]*3^(1/4)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)]) + (5*5^(5/6)*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(63*3^(3/4)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)])","A",8,8,22,0.3636,1,"{742, 12, 640, 619, 235, 304, 219, 1879}"
2499,1,603,0,0.485279,"\int \frac{2+3 x}{\sqrt[3]{52-54 x+27 x^2}} \, dx","Int[(2 + 3*x)/(52 - 54*x + 27*x^2)^(1/3),x]","\frac{1}{12} \left(27 x^2-54 x+52\right)^{2/3}+\frac{90 \sqrt[3]{5} (1-x)}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}+\frac{5^{5/6} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{54\ 3^{3/4} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}-\frac{5^{5/6} \sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{108 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}","\frac{1}{12} \left(27 x^2-54 x+52\right)^{2/3}+\frac{90 \sqrt[3]{5} (1-x)}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}+\frac{5^{5/6} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{54\ 3^{3/4} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}-\frac{5^{5/6} \sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{108 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}",1,"(52 - 54*x + 27*x^2)^(2/3)/12 + (90*5^(1/3)*(1 - x))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3)) - (5^(5/6)*Sqrt[2 + Sqrt[3]]*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(108*Sqrt[2]*3^(1/4)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)]) + (5^(5/6)*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(54*3^(3/4)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)])","A",6,6,20,0.3000,1,"{640, 619, 235, 304, 219, 1879}"
2500,1,108,0,0.0188848,"\int \frac{1}{(2+3 x) \sqrt[3]{52-54 x+27 x^2}} \, dx","Int[1/((2 + 3*x)*(52 - 54*x + 27*x^2)^(1/3)),x]","\frac{\log \left(-27 \sqrt[3]{10} \sqrt[3]{27 x^2-54 x+52}-81 x+216\right)}{6\ 10^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (8-3 x)}{\sqrt{3} \sqrt[3]{5} \sqrt[3]{27 x^2-54 x+52}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} 10^{2/3}}-\frac{\log (3 x+2)}{6\ 10^{2/3}}","\frac{\log \left(-27 \sqrt[3]{10} \sqrt[3]{27 x^2-54 x+52}-81 x+216\right)}{6\ 10^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (8-3 x)}{\sqrt{3} \sqrt[3]{5} \sqrt[3]{27 x^2-54 x+52}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} 10^{2/3}}-\frac{\log (3 x+2)}{6\ 10^{2/3}}",1,"-ArcTan[1/Sqrt[3] + (2^(2/3)*(8 - 3*x))/(Sqrt[3]*5^(1/3)*(52 - 54*x + 27*x^2)^(1/3))]/(3*Sqrt[3]*10^(2/3)) - Log[2 + 3*x]/(6*10^(2/3)) + Log[216 - 81*x - 27*10^(1/3)*(52 - 54*x + 27*x^2)^(1/3)]/(6*10^(2/3))","A",1,1,22,0.04545,1,"{750}"
2501,1,719,0,0.6052844,"\int \frac{1}{(2+3 x)^2 \sqrt[3]{52-54 x+27 x^2}} \, dx","Int[1/((2 + 3*x)^2*(52 - 54*x + 27*x^2)^(1/3)),x]","-\frac{\left(27 x^2-54 x+52\right)^{2/3}}{300 (3 x+2)}+\frac{\log \left(-27 \sqrt[3]{10} \sqrt[3]{27 x^2-54 x+52}-81 x+216\right)}{60\ 10^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (8-3 x)}{\sqrt{3} \sqrt[3]{5} \sqrt[3]{27 x^2-54 x+52}}+\frac{1}{\sqrt{3}}\right)}{30 \sqrt{3} 10^{2/3}}+\frac{9 (1-x)}{10\ 5^{2/3} \left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)}-\frac{\log (3 x+2)}{60\ 10^{2/3}}+\frac{\left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{5400\ 3^{3/4} \sqrt[6]{5} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}-\frac{\sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{10800 \sqrt{2} \sqrt[4]{3} \sqrt[6]{5} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}","-\frac{\left(27 x^2-54 x+52\right)^{2/3}}{300 (3 x+2)}+\frac{\log \left(-27 \sqrt[3]{10} \sqrt[3]{27 x^2-54 x+52}-81 x+216\right)}{60\ 10^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (8-3 x)}{\sqrt{3} \sqrt[3]{5} \sqrt[3]{27 x^2-54 x+52}}+\frac{1}{\sqrt{3}}\right)}{30 \sqrt{3} 10^{2/3}}+\frac{9 (1-x)}{10\ 5^{2/3} \left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)}-\frac{\log (3 x+2)}{60\ 10^{2/3}}+\frac{\left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{5400\ 3^{3/4} \sqrt[6]{5} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}-\frac{\sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{10800 \sqrt{2} \sqrt[4]{3} \sqrt[6]{5} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}",1,"-(52 - 54*x + 27*x^2)^(2/3)/(300*(2 + 3*x)) + (9*(1 - x))/(10*5^(2/3)*(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))) - ArcTan[1/Sqrt[3] + (2^(2/3)*(8 - 3*x))/(Sqrt[3]*5^(1/3)*(52 - 54*x + 27*x^2)^(1/3))]/(30*Sqrt[3]*10^(2/3)) - (Sqrt[2 + Sqrt[3]]*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(10800*Sqrt[2]*3^(1/4)*5^(1/6)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)]) + ((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(5400*3^(3/4)*5^(1/6)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)]) - Log[2 + 3*x]/(60*10^(2/3)) + Log[216 - 81*x - 27*10^(1/3)*(52 - 54*x + 27*x^2)^(1/3)]/(60*10^(2/3))","A",8,8,22,0.3636,1,"{744, 843, 619, 235, 304, 219, 1879, 750}"
2502,1,744,0,0.6747759,"\int \frac{1}{(2+3 x)^3 \sqrt[3]{52-54 x+27 x^2}} \, dx","Int[1/((2 + 3*x)^3*(52 - 54*x + 27*x^2)^(1/3)),x]","-\frac{\left(27 x^2-54 x+52\right)^{2/3}}{1500 (3 x+2)}-\frac{\left(27 x^2-54 x+52\right)^{2/3}}{600 (3 x+2)^2}+\frac{\log \left(-27 \sqrt[3]{10} \sqrt[3]{27 x^2-54 x+52}-81 x+216\right)}{600\ 10^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (8-3 x)}{\sqrt{3} \sqrt[3]{5} \sqrt[3]{27 x^2-54 x+52}}+\frac{1}{\sqrt{3}}\right)}{300 \sqrt{3} 10^{2/3}}+\frac{9 (1-x)}{50\ 5^{2/3} \left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)}-\frac{\log (3 x+2)}{600\ 10^{2/3}}+\frac{\left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{27000\ 3^{3/4} \sqrt[6]{5} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}-\frac{\sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{54000 \sqrt{2} \sqrt[4]{3} \sqrt[6]{5} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}","-\frac{\left(27 x^2-54 x+52\right)^{2/3}}{1500 (3 x+2)}-\frac{\left(27 x^2-54 x+52\right)^{2/3}}{600 (3 x+2)^2}+\frac{\log \left(-27 \sqrt[3]{10} \sqrt[3]{27 x^2-54 x+52}-81 x+216\right)}{600\ 10^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (8-3 x)}{\sqrt{3} \sqrt[3]{5} \sqrt[3]{27 x^2-54 x+52}}+\frac{1}{\sqrt{3}}\right)}{300 \sqrt{3} 10^{2/3}}+\frac{9 (1-x)}{50\ 5^{2/3} \left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)}-\frac{\log (3 x+2)}{600\ 10^{2/3}}+\frac{\left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} F\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{27000\ 3^{3/4} \sqrt[6]{5} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}-\frac{\sqrt{2+\sqrt{3}} \left(30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right) \sqrt{\frac{10^{2/3} \left((54 x-54)^2+2700\right)^{2/3}+30 \sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}+900}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} E\left(\sin ^{-1}\left(\frac{30 \left(1+\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}\right)|-7+4 \sqrt{3}\right)}{54000 \sqrt{2} \sqrt[4]{3} \sqrt[6]{5} \sqrt{-\frac{30-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}}{\left(30 \left(1-\sqrt{3}\right)-\sqrt[3]{10} \sqrt[3]{(54 x-54)^2+2700}\right)^2}} (1-x)}",1,"-(52 - 54*x + 27*x^2)^(2/3)/(600*(2 + 3*x)^2) - (52 - 54*x + 27*x^2)^(2/3)/(1500*(2 + 3*x)) + (9*(1 - x))/(50*5^(2/3)*(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))) - ArcTan[1/Sqrt[3] + (2^(2/3)*(8 - 3*x))/(Sqrt[3]*5^(1/3)*(52 - 54*x + 27*x^2)^(1/3))]/(300*Sqrt[3]*10^(2/3)) - (Sqrt[2 + Sqrt[3]]*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(54000*Sqrt[2]*3^(1/4)*5^(1/6)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)]) + ((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*Sqrt[(900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(30*(1 + Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(27000*3^(3/4)*5^(1/6)*(1 - x)*Sqrt[-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - Sqrt[3]) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)]) - Log[2 + 3*x]/(600*10^(2/3)) + Log[216 - 81*x - 27*10^(1/3)*(52 - 54*x + 27*x^2)^(1/3)]/(600*10^(2/3))","A",9,9,22,0.4091,1,"{744, 834, 843, 619, 235, 304, 219, 1879, 750}"
2503,1,589,0,0.5631896,"\int \frac{(2+3 x)^3}{\sqrt[3]{28+54 x+27 x^2}} \, dx","Int[(2 + 3*x)^3/(28 + 54*x + 27*x^2)^(1/3),x]","\frac{1}{30} \left(27 x^2+54 x+28\right)^{2/3} (3 x+2)^2-\frac{1}{35} (8 x+1) \left(27 x^2+54 x+28\right)^{2/3}+\frac{4 \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{63\ 3^{3/4} (x+1) \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}}}-\frac{\sqrt{2 \left(2+\sqrt{3}\right)} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{63 \sqrt[4]{3} (x+1) \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}}}+\frac{72 (x+1)}{7 \left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)}","\frac{1}{30} \left(27 x^2+54 x+28\right)^{2/3} (3 x+2)^2-\frac{1}{35} (8 x+1) \left(27 x^2+54 x+28\right)^{2/3}+\frac{4 \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{63\ 3^{3/4} (x+1) \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}}}-\frac{\sqrt{2 \left(2+\sqrt{3}\right)} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{63 \sqrt[4]{3} (x+1) \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}}}+\frac{72 (x+1)}{7 \left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)}",1,"((2 + 3*x)^2*(28 + 54*x + 27*x^2)^(2/3))/30 - ((1 + 8*x)*(28 + 54*x + 27*x^2)^(2/3))/35 + (72*(1 + x))/(7*(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))) - (Sqrt[2*(2 + Sqrt[3])]*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(63*3^(1/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)]) + (4*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(63*3^(3/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)])","A",7,7,22,0.3182,1,"{742, 779, 619, 235, 304, 219, 1879}"
2504,1,585,0,0.4859291,"\int \frac{(2+3 x)^2}{\sqrt[3]{28+54 x+27 x^2}} \, dx","Int[(2 + 3*x)^2/(28 + 54*x + 27*x^2)^(1/3),x]","\frac{1}{21} (3 x+2) \left(27 x^2+54 x+28\right)^{2/3}-\frac{5}{42} \left(27 x^2+54 x+28\right)^{2/3}-\frac{2 \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{21\ 3^{3/4} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}+\frac{\sqrt{2+\sqrt{3}} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{21 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}-\frac{108 (x+1)}{7 \left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)}","\frac{1}{21} (3 x+2) \left(27 x^2+54 x+28\right)^{2/3}-\frac{5}{42} \left(27 x^2+54 x+28\right)^{2/3}-\frac{2 \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{21\ 3^{3/4} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}+\frac{\sqrt{2+\sqrt{3}} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{21 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}-\frac{108 (x+1)}{7 \left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)}",1,"(-5*(28 + 54*x + 27*x^2)^(2/3))/42 + ((2 + 3*x)*(28 + 54*x + 27*x^2)^(2/3))/21 - (108*(1 + x))/(7*(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))) + (Sqrt[2 + Sqrt[3]]*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(21*Sqrt[2]*3^(1/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)]) - (2*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(21*3^(3/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)])","A",7,7,22,0.3182,1,"{742, 640, 619, 235, 304, 219, 1879}"
2505,1,560,0,0.3784519,"\int \frac{2+3 x}{\sqrt[3]{28+54 x+27 x^2}} \, dx","Int[(2 + 3*x)/(28 + 54*x + 27*x^2)^(1/3),x]","\frac{1}{12} \left(27 x^2+54 x+28\right)^{2/3}+\frac{\left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{9\ 3^{3/4} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}-\frac{\sqrt{2+\sqrt{3}} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{18 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}+\frac{18 (x+1)}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}","\frac{1}{12} \left(27 x^2+54 x+28\right)^{2/3}+\frac{\left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{9\ 3^{3/4} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}-\frac{\sqrt{2+\sqrt{3}} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{18 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}+\frac{18 (x+1)}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}",1,"(28 + 54*x + 27*x^2)^(2/3)/12 + (18*(1 + x))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3)) - (Sqrt[2 + Sqrt[3]]*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(18*Sqrt[2]*3^(1/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)]) + ((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(3/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)])","A",6,6,20,0.3000,1,"{640, 619, 235, 304, 219, 1879}"
2506,1,103,0,0.0187359,"\int \frac{1}{(2+3 x) \sqrt[3]{28+54 x+27 x^2}} \, dx","Int[1/((2 + 3*x)*(28 + 54*x + 27*x^2)^(1/3)),x]","\frac{\log \left(27 \sqrt[3]{2} \sqrt[3]{27 x^2+54 x+28}-81 x-108\right)}{6\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (3 x+4)}{\sqrt{3} \sqrt[3]{27 x^2+54 x+28}}+\frac{1}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt{3}}-\frac{\log (3 x+2)}{6\ 2^{2/3}}","\frac{\log \left(27 \sqrt[3]{2} \sqrt[3]{27 x^2+54 x+28}-81 x-108\right)}{6\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (3 x+4)}{\sqrt{3} \sqrt[3]{27 x^2+54 x+28}}+\frac{1}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt{3}}-\frac{\log (3 x+2)}{6\ 2^{2/3}}",1,"-ArcTan[1/Sqrt[3] + (2^(2/3)*(4 + 3*x))/(Sqrt[3]*(28 + 54*x + 27*x^2)^(1/3))]/(3*2^(2/3)*Sqrt[3]) - Log[2 + 3*x]/(6*2^(2/3)) + Log[-108 - 81*x + 27*2^(1/3)*(28 + 54*x + 27*x^2)^(1/3)]/(6*2^(2/3))","A",1,1,22,0.04545,1,"{752}"
2507,1,671,0,0.5949438,"\int \frac{1}{(2+3 x)^2 \sqrt[3]{28+54 x+27 x^2}} \, dx","Int[1/((2 + 3*x)^2*(28 + 54*x + 27*x^2)^(1/3)),x]","-\frac{\left(27 x^2+54 x+28\right)^{2/3}}{12 (3 x+2)}-\frac{\log \left(27 \sqrt[3]{2} \sqrt[3]{27 x^2+54 x+28}-81 x-108\right)}{12\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} (3 x+4)}{\sqrt{3} \sqrt[3]{27 x^2+54 x+28}}+\frac{1}{\sqrt{3}}\right)}{6\ 2^{2/3} \sqrt{3}}-\frac{\left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{36\ 3^{3/4} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}+\frac{\sqrt{2+\sqrt{3}} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{72 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}-\frac{9 (x+1)}{2 \left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)}+\frac{\log (3 x+2)}{12\ 2^{2/3}}","-\frac{\left(27 x^2+54 x+28\right)^{2/3}}{12 (3 x+2)}-\frac{\log \left(27 \sqrt[3]{2} \sqrt[3]{27 x^2+54 x+28}-81 x-108\right)}{12\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} (3 x+4)}{\sqrt{3} \sqrt[3]{27 x^2+54 x+28}}+\frac{1}{\sqrt{3}}\right)}{6\ 2^{2/3} \sqrt{3}}-\frac{\left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{36\ 3^{3/4} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}+\frac{\sqrt{2+\sqrt{3}} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{72 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}-\frac{9 (x+1)}{2 \left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)}+\frac{\log (3 x+2)}{12\ 2^{2/3}}",1,"-(28 + 54*x + 27*x^2)^(2/3)/(12*(2 + 3*x)) - (9*(1 + x))/(2*(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))) + ArcTan[1/Sqrt[3] + (2^(2/3)*(4 + 3*x))/(Sqrt[3]*(28 + 54*x + 27*x^2)^(1/3))]/(6*2^(2/3)*Sqrt[3]) + (Sqrt[2 + Sqrt[3]]*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(72*Sqrt[2]*3^(1/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)]) - ((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(36*3^(3/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)]) + Log[2 + 3*x]/(12*2^(2/3)) - Log[-108 - 81*x + 27*2^(1/3)*(28 + 54*x + 27*x^2)^(1/3)]/(12*2^(2/3))","A",9,9,22,0.4091,1,"{744, 12, 843, 619, 235, 304, 219, 1879, 752}"
2508,1,696,0,0.5959023,"\int \frac{1}{(2+3 x)^3 \sqrt[3]{28+54 x+27 x^2}} \, dx","Int[1/((2 + 3*x)^3*(28 + 54*x + 27*x^2)^(1/3)),x]","\frac{\left(27 x^2+54 x+28\right)^{2/3}}{12 (3 x+2)}-\frac{\left(27 x^2+54 x+28\right)^{2/3}}{24 (3 x+2)^2}+\frac{\log \left(27 \sqrt[3]{2} \sqrt[3]{27 x^2+54 x+28}-81 x-108\right)}{24\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (3 x+4)}{\sqrt{3} \sqrt[3]{27 x^2+54 x+28}}+\frac{1}{\sqrt{3}}\right)}{12\ 2^{2/3} \sqrt{3}}+\frac{\left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{36\ 3^{3/4} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}-\frac{\sqrt{2+\sqrt{3}} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{72 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}+\frac{9 (x+1)}{2 \left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)}-\frac{\log (3 x+2)}{24\ 2^{2/3}}","\frac{\left(27 x^2+54 x+28\right)^{2/3}}{12 (3 x+2)}-\frac{\left(27 x^2+54 x+28\right)^{2/3}}{24 (3 x+2)^2}+\frac{\log \left(27 \sqrt[3]{2} \sqrt[3]{27 x^2+54 x+28}-81 x-108\right)}{24\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (3 x+4)}{\sqrt{3} \sqrt[3]{27 x^2+54 x+28}}+\frac{1}{\sqrt{3}}\right)}{12\ 2^{2/3} \sqrt{3}}+\frac{\left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} F\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{36\ 3^{3/4} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}-\frac{\sqrt{2+\sqrt{3}} \left(6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right) \sqrt{\frac{\left(27 x^2+54 x+28\right)^{2/3}+\sqrt[3]{27 x^2+54 x+28}+1}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} E\left(\sin ^{-1}\left(\frac{6 \left(1+\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}\right)|-7+4 \sqrt{3}\right)}{72 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{6-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}}{\left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)^2}} (x+1)}+\frac{9 (x+1)}{2 \left(6 \left(1-\sqrt{3}\right)-\sqrt[3]{2} \sqrt[3]{(54 x+54)^2+108}\right)}-\frac{\log (3 x+2)}{24\ 2^{2/3}}",1,"-(28 + 54*x + 27*x^2)^(2/3)/(24*(2 + 3*x)^2) + (28 + 54*x + 27*x^2)^(2/3)/(12*(2 + 3*x)) + (9*(1 + x))/(2*(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))) - ArcTan[1/Sqrt[3] + (2^(2/3)*(4 + 3*x))/(Sqrt[3]*(28 + 54*x + 27*x^2)^(1/3))]/(12*2^(2/3)*Sqrt[3]) - (Sqrt[2 + Sqrt[3]]*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticE[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(72*Sqrt[2]*3^(1/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)]) + ((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*Sqrt[(1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2]*EllipticF[ArcSin[(6*(1 + Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))], -7 + 4*Sqrt[3]])/(36*3^(3/4)*(1 + x)*Sqrt[-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - Sqrt[3]) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)]) - Log[2 + 3*x]/(24*2^(2/3)) + Log[-108 - 81*x + 27*2^(1/3)*(28 + 54*x + 27*x^2)^(1/3)]/(24*2^(2/3))","A",9,9,22,0.4091,1,"{744, 834, 843, 619, 235, 304, 219, 1879, 752}"
2509,1,564,0,0.4052836,"\int \frac{1}{(d+e x) \sqrt[3]{-c^2 d^2+b c d e+2 b^2 e^2+9 b c e^2 x+9 c^2 e^2 x^2}} \, dx","Int[1/((d + e*x)*(-(c^2*d^2) + b*c*d*e + 2*b^2*e^2 + 9*b*c*e^2*x + 9*c^2*e^2*x^2)^(1/3)),x]","-\frac{\log (d+e x) \sqrt[3]{3 c^2 e^2 x-c e (c d-2 b e)} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x}}{2 \sqrt[3]{2} c^{2/3} e^{5/3} (2 c d-b e)^{2/3} \sqrt[3]{-(c d-2 b e) (b e+c d)+9 b c e^2 x+9 c^2 e^2 x^2}}+\frac{3 \sqrt[3]{3 c^2 e^2 x-c e (c d-2 b e)} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x} \log \left(-\frac{\sqrt[3]{\frac{3}{2}} \left(3 c^2 e^2 x-c e (c d-2 b e)\right)^{2/3}}{\sqrt[3]{c} \sqrt[3]{e} \sqrt[3]{2 c d-b e}}-\sqrt[3]{6} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x}\right)}{4 \sqrt[3]{2} c^{2/3} e^{5/3} (2 c d-b e)^{2/3} \sqrt[3]{-(c d-2 b e) (b e+c d)+9 b c e^2 x+9 c^2 e^2 x^2}}-\frac{\sqrt{3} \sqrt[3]{3 c^2 e^2 x-c e (c d-2 b e)} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\sqrt[3]{2} \left(3 c^2 e^2 x-c e (c d-2 b e)\right)^{2/3}}{\sqrt{3} \sqrt[3]{c} \sqrt[3]{e} \sqrt[3]{2 c d-b e} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x}}\right)}{2 \sqrt[3]{2} c^{2/3} e^{5/3} (2 c d-b e)^{2/3} \sqrt[3]{-(c d-2 b e) (b e+c d)+9 b c e^2 x+9 c^2 e^2 x^2}}","-\frac{\log (d+e x) \sqrt[3]{3 c^2 e^2 x-c e (c d-2 b e)} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x}}{2 \sqrt[3]{2} c^{2/3} e^{5/3} (2 c d-b e)^{2/3} \sqrt[3]{-(c d-2 b e) (b e+c d)+9 b c e^2 x+9 c^2 e^2 x^2}}+\frac{3 \sqrt[3]{3 c^2 e^2 x-c e (c d-2 b e)} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x} \log \left(-\frac{\sqrt[3]{\frac{3}{2}} \left(3 c^2 e^2 x-c e (c d-2 b e)\right)^{2/3}}{\sqrt[3]{c} \sqrt[3]{e} \sqrt[3]{2 c d-b e}}-\sqrt[3]{6} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x}\right)}{4 \sqrt[3]{2} c^{2/3} e^{5/3} (2 c d-b e)^{2/3} \sqrt[3]{-(c d-2 b e) (b e+c d)+9 b c e^2 x+9 c^2 e^2 x^2}}-\frac{\sqrt{3} \sqrt[3]{3 c^2 e^2 x-c e (c d-2 b e)} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\sqrt[3]{2} \left(3 c^2 e^2 x-c e (c d-2 b e)\right)^{2/3}}{\sqrt{3} \sqrt[3]{c} \sqrt[3]{e} \sqrt[3]{2 c d-b e} \sqrt[3]{c e (b e+c d)+3 c^2 e^2 x}}\right)}{2 \sqrt[3]{2} c^{2/3} e^{5/3} (2 c d-b e)^{2/3} \sqrt[3]{-(c d-2 b e) (b e+c d)+9 b c e^2 x+9 c^2 e^2 x^2}}",1,"-(Sqrt[3]*(-(c*e*(c*d - 2*b*e)) + 3*c^2*e^2*x)^(1/3)*(c*e*(c*d + b*e) + 3*c^2*e^2*x)^(1/3)*ArcTan[1/Sqrt[3] - (2^(1/3)*(-(c*e*(c*d - 2*b*e)) + 3*c^2*e^2*x)^(2/3))/(Sqrt[3]*c^(1/3)*e^(1/3)*(2*c*d - b*e)^(1/3)*(c*e*(c*d + b*e) + 3*c^2*e^2*x)^(1/3))])/(2*2^(1/3)*c^(2/3)*e^(5/3)*(2*c*d - b*e)^(2/3)*(-((c*d - 2*b*e)*(c*d + b*e)) + 9*b*c*e^2*x + 9*c^2*e^2*x^2)^(1/3)) - ((-(c*e*(c*d - 2*b*e)) + 3*c^2*e^2*x)^(1/3)*(c*e*(c*d + b*e) + 3*c^2*e^2*x)^(1/3)*Log[d + e*x])/(2*2^(1/3)*c^(2/3)*e^(5/3)*(2*c*d - b*e)^(2/3)*(-((c*d - 2*b*e)*(c*d + b*e)) + 9*b*c*e^2*x + 9*c^2*e^2*x^2)^(1/3)) + (3*(-(c*e*(c*d - 2*b*e)) + 3*c^2*e^2*x)^(1/3)*(c*e*(c*d + b*e) + 3*c^2*e^2*x)^(1/3)*Log[-(((3/2)^(1/3)*(-(c*e*(c*d - 2*b*e)) + 3*c^2*e^2*x)^(2/3))/(c^(1/3)*e^(1/3)*(2*c*d - b*e)^(1/3))) - 6^(1/3)*(c*e*(c*d + b*e) + 3*c^2*e^2*x)^(1/3)])/(4*2^(1/3)*c^(2/3)*e^(5/3)*(2*c*d - b*e)^(2/3)*(-((c*d - 2*b*e)*(c*d + b*e)) + 9*b*c*e^2*x + 9*c^2*e^2*x^2)^(1/3))","A",2,2,53,0.03774,1,"{755, 123}"
2510,1,374,0,0.5184452,"\int (d+e x)^3 \sqrt[4]{a+b x+c x^2} \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^(1/4),x]","\frac{e \left(a+b x+c x^2\right)^{5/4} \left(-2 c e (56 a e+243 b d)+117 b^2 e^2+130 c e x (2 c d-b e)+616 c^2 d^2\right)}{630 c^3}+\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (6 a e+7 b d)+13 b^2 e^2+28 c^2 d^2\right)}{168 c^4}-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+7 b d)+13 b^2 e^2+28 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{336 \sqrt{2} c^{17/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \left(a+b x+c x^2\right)^{5/4}}{9 c}","\frac{e \left(a+b x+c x^2\right)^{5/4} \left(-2 c e (56 a e+243 b d)+117 b^2 e^2+130 c e x (2 c d-b e)+616 c^2 d^2\right)}{630 c^3}+\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (6 a e+7 b d)+13 b^2 e^2+28 c^2 d^2\right)}{168 c^4}-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+7 b d)+13 b^2 e^2+28 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{336 \sqrt{2} c^{17/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \left(a+b x+c x^2\right)^{5/4}}{9 c}",1,"((2*c*d - b*e)*(28*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(7*b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(168*c^4) + (2*e*(d + e*x)^2*(a + b*x + c*x^2)^(5/4))/(9*c) + (e*(616*c^2*d^2 + 117*b^2*e^2 - 2*c*e*(243*b*d + 56*a*e) + 130*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/4))/(630*c^3) - ((b^2 - 4*a*c)^(5/4)*(2*c*d - b*e)*(28*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(7*b*d + 6*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(336*Sqrt[2]*c^(17/4)*(b + 2*c*x))","A",5,5,22,0.2273,1,"{742, 779, 612, 623, 220}"
2511,1,319,0,0.4231344,"\int (d+e x)^2 \sqrt[4]{a+b x+c x^2} \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^(1/4),x]","\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+7 b d)+9 b^2 e^2+28 c^2 d^2\right)}{84 c^3}-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+7 b d)+9 b^2 e^2+28 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{168 \sqrt{2} c^{13/4} (b+2 c x)}+\frac{9 e \left(a+b x+c x^2\right)^{5/4} (2 c d-b e)}{35 c^2}+\frac{2 e (d+e x) \left(a+b x+c x^2\right)^{5/4}}{7 c}","\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+7 b d)+9 b^2 e^2+28 c^2 d^2\right)}{84 c^3}-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+7 b d)+9 b^2 e^2+28 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{168 \sqrt{2} c^{13/4} (b+2 c x)}+\frac{9 e \left(a+b x+c x^2\right)^{5/4} (2 c d-b e)}{35 c^2}+\frac{2 e (d+e x) \left(a+b x+c x^2\right)^{5/4}}{7 c}",1,"((28*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(7*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(84*c^3) + (9*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(5/4))/(35*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(5/4))/(7*c) - ((b^2 - 4*a*c)^(5/4)*(28*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(7*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(168*Sqrt[2]*c^(13/4)*(b + 2*c*x))","A",5,5,22,0.2273,1,"{742, 640, 612, 623, 220}"
2512,1,241,0,0.1838017,"\int (d+e x) \sqrt[4]{a+b x+c x^2} \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^(1/4),x]","-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{12 \sqrt{2} c^{9/4} (b+2 c x)}+\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{6 c^2}+\frac{2 e \left(a+b x+c x^2\right)^{5/4}}{5 c}","-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{12 \sqrt{2} c^{9/4} (b+2 c x)}+\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{6 c^2}+\frac{2 e \left(a+b x+c x^2\right)^{5/4}}{5 c}",1,"((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(6*c^2) + (2*e*(a + b*x + c*x^2)^(5/4))/(5*c) - ((b^2 - 4*a*c)^(5/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(12*Sqrt[2]*c^(9/4)*(b + 2*c*x))","A",4,4,20,0.2000,1,"{640, 612, 623, 220}"
2513,1,201,0,0.1313184,"\int \sqrt[4]{a+b x+c x^2} \, dx","Int[(a + b*x + c*x^2)^(1/4),x]","\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2}}{3 c}-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} c^{5/4} (b+2 c x)}","\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2}}{3 c}-\frac{\left(b^2-4 a c\right)^{5/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} c^{5/4} (b+2 c x)}",1,"((b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(3*c) - ((b^2 - 4*a*c)^(5/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(6*Sqrt[2]*c^(5/4)*(b + 2*c*x))","A",3,3,14,0.2143,1,"{612, 623, 220}"
2514,1,881,0,2.637606,"\int \frac{\sqrt[4]{a+b x+c x^2}}{d+e x} \, dx","Int[(a + b*x + c*x^2)^(1/4)/(d + e*x),x]","-\frac{\left(4 a c-b^2\right)^{3/4} \sqrt[4]{c d^2-b e d+a e^2} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{c^{3/4} e^{3/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(4 a c-b^2\right)^{3/4} \sqrt[4]{c d^2-b e d+a e^2} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{c^{3/4} e^{3/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\sqrt[4]{b^2-4 a c} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt[4]{c} e^2 (b+2 c x)}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} c e^2 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} c e^2 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{2 \sqrt[4]{c x^2+b x+a}}{e}","-\frac{\left(4 a c-b^2\right)^{3/4} \sqrt[4]{c d^2-b e d+a e^2} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{c^{3/4} e^{3/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(4 a c-b^2\right)^{3/4} \sqrt[4]{c d^2-b e d+a e^2} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{c^{3/4} e^{3/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\sqrt[4]{b^2-4 a c} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt[4]{c} e^2 (b+2 c x)}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} c e^2 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} c e^2 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{2 \sqrt[4]{c x^2+b x+a}}{e}",1,"(2*(a + b*x + c*x^2)^(1/4))/e - ((-b^2 + 4*a*c)^(3/4)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(3/4)*e^(3/2)*(a + b*x + c*x^2)^(3/4)) - ((-b^2 + 4*a*c)^(3/4)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(3/4)*e^(3/2)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*c^(1/4)*e^2*(b + 2*c*x)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*c*e^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*c*e^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))","A",19,17,22,0.7727,1,"{734, 843, 623, 220, 749, 748, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
2515,1,944,0,2.0259233,"\int \frac{\sqrt[4]{a+b x+c x^2}}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^(1/4)/(d + e*x)^2,x]","\frac{\left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c e^2 \left(c d^2-b e d+a e^2\right) (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{\left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c e^2 \left(c d^2-b e d+a e^2\right) (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{\left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} e^{3/2} \left(c d^2-b e d+a e^2\right)^{3/4} \left(c x^2+b x+a\right)^{3/4}}+\frac{\left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} e^{3/2} \left(c d^2-b e d+a e^2\right)^{3/4} \left(c x^2+b x+a\right)^{3/4}}+\frac{c^{3/4} \sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} e^2 (b+2 c x)}-\frac{\sqrt[4]{c x^2+b x+a}}{e (d+e x)}","\frac{\left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c e^2 \left(c d^2-b e d+a e^2\right) (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{\left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c e^2 \left(c d^2-b e d+a e^2\right) (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{\left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} e^{3/2} \left(c d^2-b e d+a e^2\right)^{3/4} \left(c x^2+b x+a\right)^{3/4}}+\frac{\left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} e^{3/2} \left(c d^2-b e d+a e^2\right)^{3/4} \left(c x^2+b x+a\right)^{3/4}}+\frac{c^{3/4} \sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} e^2 (b+2 c x)}-\frac{\sqrt[4]{c x^2+b x+a}}{e (d+e x)}",1,"-((a + b*x + c*x^2)^(1/4)/(e*(d + e*x))) + ((-b^2 + 4*a*c)^(3/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(3/4)*e^(3/2)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(a + b*x + c*x^2)^(3/4)) + ((-b^2 + 4*a*c)^(3/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(3/4)*e^(3/2)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(a + b*x + c*x^2)^(3/4)) + (c^(3/4)*(b^2 - 4*a*c)^(1/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*e^2*(b + 2*c*x)) + ((b^2 - 4*a*c)*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*c*e^2*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) + ((b^2 - 4*a*c)*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*c*e^2*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))","A",19,17,22,0.7727,1,"{732, 843, 623, 220, 749, 748, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
2516,1,703,0,0.8666846,"\int (d+e x)^3 \left(a+b x+c x^2\right)^{3/4} \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^(3/4),x]","\frac{e \left(a+b x+c x^2\right)^{7/4} \left(-2 c e (24 a e+121 b d)+55 b^2 e^2+70 c e x (2 c d-b e)+312 c^2 d^2\right)}{462 c^3}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/4} (2 c d-b e) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right)}{120 c^4}-\frac{\sqrt{b^2-4 a c} (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right)}{80 c^{9/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}-\frac{\left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{160 \sqrt{2} c^{19/4} (b+2 c x)}+\frac{\left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{80 \sqrt{2} c^{19/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \left(a+b x+c x^2\right)^{7/4}}{11 c}","\frac{e \left(a+b x+c x^2\right)^{7/4} \left(-2 c e (24 a e+121 b d)+55 b^2 e^2+70 c e x (2 c d-b e)+312 c^2 d^2\right)}{462 c^3}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/4} (2 c d-b e) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right)}{120 c^4}-\frac{\sqrt{b^2-4 a c} (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right)}{80 c^{9/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}-\frac{\left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{160 \sqrt{2} c^{19/4} (b+2 c x)}+\frac{\left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{80 \sqrt{2} c^{19/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \left(a+b x+c x^2\right)^{7/4}}{11 c}",1,"((2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))/(120*c^4) + (2*e*(d + e*x)^2*(a + b*x + c*x^2)^(7/4))/(11*c) + (e*(312*c^2*d^2 + 55*b^2*e^2 - 2*c*e*(121*b*d + 24*a*e) + 70*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/4))/(462*c^3) - (Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(80*c^(9/2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) + ((b^2 - 4*a*c)^(7/4)*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(80*Sqrt[2]*c^(19/4)*(b + 2*c*x)) - ((b^2 - 4*a*c)^(7/4)*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(160*Sqrt[2]*c^(19/4)*(b + 2*c*x))","A",7,7,22,0.3182,1,"{742, 779, 612, 623, 305, 220, 1196}"
2517,1,630,0,0.8481536,"\int (d+e x)^2 \left(a+b x+c x^2\right)^{3/4} \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^(3/4),x]","-\frac{\sqrt{b^2-4 a c} (b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+9 b d)+11 b^2 e^2+36 c^2 d^2\right)}{120 c^{7/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/4} \left(-4 c e (2 a e+9 b d)+11 b^2 e^2+36 c^2 d^2\right)}{180 c^3}-\frac{\left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+9 b d)+11 b^2 e^2+36 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{240 \sqrt{2} c^{15/4} (b+2 c x)}+\frac{\left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+9 b d)+11 b^2 e^2+36 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{120 \sqrt{2} c^{15/4} (b+2 c x)}+\frac{11 e \left(a+b x+c x^2\right)^{7/4} (2 c d-b e)}{63 c^2}+\frac{2 e (d+e x) \left(a+b x+c x^2\right)^{7/4}}{9 c}","-\frac{\sqrt{b^2-4 a c} (b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+9 b d)+11 b^2 e^2+36 c^2 d^2\right)}{120 c^{7/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/4} \left(-4 c e (2 a e+9 b d)+11 b^2 e^2+36 c^2 d^2\right)}{180 c^3}-\frac{\left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+9 b d)+11 b^2 e^2+36 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{240 \sqrt{2} c^{15/4} (b+2 c x)}+\frac{\left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+9 b d)+11 b^2 e^2+36 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{120 \sqrt{2} c^{15/4} (b+2 c x)}+\frac{11 e \left(a+b x+c x^2\right)^{7/4} (2 c d-b e)}{63 c^2}+\frac{2 e (d+e x) \left(a+b x+c x^2\right)^{7/4}}{9 c}",1,"((36*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(9*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))/(180*c^3) + (11*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(7/4))/(63*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(7/4))/(9*c) - (Sqrt[b^2 - 4*a*c]*(36*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(9*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(120*c^(7/2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) + ((b^2 - 4*a*c)^(7/4)*(36*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(9*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(120*Sqrt[2]*c^(15/4)*(b + 2*c*x)) - ((b^2 - 4*a*c)^(7/4)*(36*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(9*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(240*Sqrt[2]*c^(15/4)*(b + 2*c*x))","A",7,7,22,0.3182,1,"{742, 640, 612, 623, 305, 220, 1196}"
2518,1,510,0,0.4389505,"\int (d+e x) \left(a+b x+c x^2\right)^{3/4} \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^(3/4),x]","-\frac{3 \sqrt{b^2-4 a c} (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{20 c^{5/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}-\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{40 \sqrt{2} c^{11/4} (b+2 c x)}+\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} c^{11/4} (b+2 c x)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/4} (2 c d-b e)}{10 c^2}+\frac{2 e \left(a+b x+c x^2\right)^{7/4}}{7 c}","-\frac{3 \sqrt{b^2-4 a c} (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{20 c^{5/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}-\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{40 \sqrt{2} c^{11/4} (b+2 c x)}+\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} c^{11/4} (b+2 c x)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/4} (2 c d-b e)}{10 c^2}+\frac{2 e \left(a+b x+c x^2\right)^{7/4}}{7 c}",1,"((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))/(10*c^2) + (2*e*(a + b*x + c*x^2)^(7/4))/(7*c) - (3*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(20*c^(5/2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) + (3*(b^2 - 4*a*c)^(7/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(20*Sqrt[2]*c^(11/4)*(b + 2*c*x)) - (3*(b^2 - 4*a*c)^(7/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(40*Sqrt[2]*c^(11/4)*(b + 2*c*x))","A",6,6,20,0.3000,1,"{640, 612, 623, 305, 220, 1196}"
2519,1,452,0,0.3624709,"\int \left(a+b x+c x^2\right)^{3/4} \, dx","Int[(a + b*x + c*x^2)^(3/4),x]","-\frac{3 \sqrt{b^2-4 a c} (b+2 c x) \sqrt[4]{a+b x+c x^2}}{10 c^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}-\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} c^{7/4} (b+2 c x)}+\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{10 \sqrt{2} c^{7/4} (b+2 c x)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/4}}{5 c}","-\frac{3 \sqrt{b^2-4 a c} (b+2 c x) \sqrt[4]{a+b x+c x^2}}{10 c^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}-\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} c^{7/4} (b+2 c x)}+\frac{3 \left(b^2-4 a c\right)^{7/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{10 \sqrt{2} c^{7/4} (b+2 c x)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/4}}{5 c}",1,"((b + 2*c*x)*(a + b*x + c*x^2)^(3/4))/(5*c) - (3*Sqrt[b^2 - 4*a*c]*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(10*c^(3/2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) + (3*(b^2 - 4*a*c)^(7/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(10*Sqrt[2]*c^(7/4)*(b + 2*c*x)) - (3*(b^2 - 4*a*c)^(7/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(20*Sqrt[2]*c^(7/4)*(b + 2*c*x))","A",5,5,14,0.3571,1,"{612, 623, 305, 220, 1196}"
2520,1,1209,0,2.5129144,"\int \frac{\left(a+b x+c x^2\right)^{3/4}}{d+e x} \, dx","Int[(a + b*x + c*x^2)^(3/4)/(d + e*x),x]","-\frac{(2 c d-b e) \sqrt[4]{c x^2+b x+a} (b+2 c x)}{\sqrt{c} \sqrt{b^2-4 a c} e^2 \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\sqrt[4]{4 a c-b^2} \left(c d^2-b e d+a e^2\right)^{3/4} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{\sqrt[4]{c} e^{5/2} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{4 a c-b^2} \left(c d^2-b e d+a e^2\right)^{3/4} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{\sqrt[4]{c} e^{5/2} \sqrt[4]{c x^2+b x+a}}+\frac{2 \left(c x^2+b x+a\right)^{3/4}}{3 e}+\frac{\left(b^2-4 a c\right)^{3/4} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{3/4} e^2 (b+2 c x)}-\frac{\left(b^2-4 a c\right)^{3/4} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} c^{3/4} e^2 (b+2 c x)}-\frac{\sqrt{4 a c-b^2} (2 c d-b e) \sqrt{c d^2-b e d+a e^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} \sqrt{c} e^3 \sqrt[4]{c x^2+b x+a} (b+2 c x)}+\frac{\sqrt{4 a c-b^2} (2 c d-b e) \sqrt{c d^2-b e d+a e^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} \sqrt{c} e^3 \sqrt[4]{c x^2+b x+a} (b+2 c x)}","-\frac{(2 c d-b e) \sqrt[4]{c x^2+b x+a} (b+2 c x)}{\sqrt{c} \sqrt{b^2-4 a c} e^2 \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\sqrt[4]{4 a c-b^2} \left(c d^2-b e d+a e^2\right)^{3/4} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{\sqrt[4]{c} e^{5/2} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{4 a c-b^2} \left(c d^2-b e d+a e^2\right)^{3/4} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{\sqrt[4]{c} e^{5/2} \sqrt[4]{c x^2+b x+a}}+\frac{2 \left(c x^2+b x+a\right)^{3/4}}{3 e}+\frac{\left(b^2-4 a c\right)^{3/4} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{3/4} e^2 (b+2 c x)}-\frac{\left(b^2-4 a c\right)^{3/4} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} c^{3/4} e^2 (b+2 c x)}-\frac{\sqrt{4 a c-b^2} (2 c d-b e) \sqrt{c d^2-b e d+a e^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} \sqrt{c} e^3 \sqrt[4]{c x^2+b x+a} (b+2 c x)}+\frac{\sqrt{4 a c-b^2} (2 c d-b e) \sqrt{c d^2-b e d+a e^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} \sqrt{c} e^3 \sqrt[4]{c x^2+b x+a} (b+2 c x)}",1,"(2*(a + b*x + c*x^2)^(3/4))/(3*e) - ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(Sqrt[c]*Sqrt[b^2 - 4*a*c]*e^2*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) + ((-b^2 + 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(1/4)*e^(5/2)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(1/4)*e^(5/2)*(a + b*x + c*x^2)^(1/4)) + ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*c^(3/4)*e^2*(b + 2*c*x)) - ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(2*Sqrt[2]*c^(3/4)*e^2*(b + 2*c*x)) - (Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*Sqrt[c]*e^3*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*Sqrt[c]*e^3*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))","A",20,18,22,0.8182,1,"{734, 843, 623, 305, 220, 1196, 749, 748, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
2521,1,1220,0,2.179023,"\int \frac{\left(a+b x+c x^2\right)^{3/4}}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^(3/4)/(d + e*x)^2,x]","\frac{3 \sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} e^3 \sqrt{c d^2-b e d+a e^2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}-\frac{3 \sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} e^3 \sqrt{c d^2-b e d+a e^2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}-\frac{3 \sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} e^{5/2} \sqrt[4]{c d^2-b e d+a e^2} \sqrt[4]{c x^2+b x+a}}+\frac{3 \sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} e^{5/2} \sqrt[4]{c d^2-b e d+a e^2} \sqrt[4]{c x^2+b x+a}}-\frac{3 \sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} e^2 (b+2 c x)}+\frac{3 \sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} e^2 (b+2 c x)}-\frac{\left(c x^2+b x+a\right)^{3/4}}{e (d+e x)}+\frac{3 \sqrt{c} (b+2 c x) \sqrt[4]{c x^2+b x+a}}{\sqrt{b^2-4 a c} e^2 \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}","\frac{3 \sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} e^3 \sqrt{c d^2-b e d+a e^2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}-\frac{3 \sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} e^3 \sqrt{c d^2-b e d+a e^2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}-\frac{3 \sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} e^{5/2} \sqrt[4]{c d^2-b e d+a e^2} \sqrt[4]{c x^2+b x+a}}+\frac{3 \sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} e^{5/2} \sqrt[4]{c d^2-b e d+a e^2} \sqrt[4]{c x^2+b x+a}}-\frac{3 \sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} e^2 (b+2 c x)}+\frac{3 \sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} e^2 (b+2 c x)}-\frac{\left(c x^2+b x+a\right)^{3/4}}{e (d+e x)}+\frac{3 \sqrt{c} (b+2 c x) \sqrt[4]{c x^2+b x+a}}{\sqrt{b^2-4 a c} e^2 \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}",1,"-((a + b*x + c*x^2)^(3/4)/(e*(d + e*x))) + (3*Sqrt[c]*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(Sqrt[b^2 - 4*a*c]*e^2*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) - (3*(-b^2 + 4*a*c)^(1/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(1/4)*e^(5/2)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(a + b*x + c*x^2)^(1/4)) + (3*(-b^2 + 4*a*c)^(1/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(1/4)*e^(5/2)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(a + b*x + c*x^2)^(1/4)) - (3*c^(1/4)*(b^2 - 4*a*c)^(3/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*e^2*(b + 2*c*x)) + (3*c^(1/4)*(b^2 - 4*a*c)^(3/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(2*Sqrt[2]*e^2*(b + 2*c*x)) + (3*Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*Sqrt[c]*e^3*Sqrt[c*d^2 - b*d*e + a*e^2]*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) - (3*Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*Sqrt[c]*e^3*Sqrt[c*d^2 - b*d*e + a*e^2]*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))","A",20,18,22,0.8182,1,"{732, 843, 623, 305, 220, 1196, 749, 748, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
2522,1,448,0,0.5590056,"\int (d+e x)^3 \left(a+b x+c x^2\right)^{5/4} \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^(5/4),x]","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (6 a e+11 b d)+17 b^2 e^2+44 c^2 d^2\right)}{7392 c^5}+\frac{e \left(a+b x+c x^2\right)^{9/4} \left(-2 c e (88 a e+507 b d)+221 b^2 e^2+306 c e x (2 c d-b e)+1320 c^2 d^2\right)}{2574 c^3}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/4} (2 c d-b e) \left(-4 c e (6 a e+11 b d)+17 b^2 e^2+44 c^2 d^2\right)}{616 c^4}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+11 b d)+17 b^2 e^2+44 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{14784 \sqrt{2} c^{21/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \left(a+b x+c x^2\right)^{9/4}}{13 c}","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (6 a e+11 b d)+17 b^2 e^2+44 c^2 d^2\right)}{7392 c^5}+\frac{e \left(a+b x+c x^2\right)^{9/4} \left(-2 c e (88 a e+507 b d)+221 b^2 e^2+306 c e x (2 c d-b e)+1320 c^2 d^2\right)}{2574 c^3}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/4} (2 c d-b e) \left(-4 c e (6 a e+11 b d)+17 b^2 e^2+44 c^2 d^2\right)}{616 c^4}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+11 b d)+17 b^2 e^2+44 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{14784 \sqrt{2} c^{21/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \left(a+b x+c x^2\right)^{9/4}}{13 c}",1,"(-5*(b^2 - 4*a*c)*(2*c*d - b*e)*(44*c^2*d^2 + 17*b^2*e^2 - 4*c*e*(11*b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(7392*c^5) + ((2*c*d - b*e)*(44*c^2*d^2 + 17*b^2*e^2 - 4*c*e*(11*b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/4))/(616*c^4) + (2*e*(d + e*x)^2*(a + b*x + c*x^2)^(9/4))/(13*c) + (e*(1320*c^2*d^2 + 221*b^2*e^2 - 2*c*e*(507*b*d + 88*a*e) + 306*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(9/4))/(2574*c^3) + (5*(b^2 - 4*a*c)^(9/4)*(2*c*d - b*e)*(44*c^2*d^2 + 17*b^2*e^2 - 4*c*e*(11*b*d + 6*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(14784*Sqrt[2]*c^(21/4)*(b + 2*c*x))","A",6,5,22,0.2273,1,"{742, 779, 612, 623, 220}"
2523,1,384,0,0.5412752,"\int (d+e x)^2 \left(a+b x+c x^2\right)^{5/4} \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^(5/4),x]","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+11 b d)+13 b^2 e^2+44 c^2 d^2\right)}{3696 c^4}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/4} \left(-4 c e (2 a e+11 b d)+13 b^2 e^2+44 c^2 d^2\right)}{308 c^3}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+11 b d)+13 b^2 e^2+44 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{7392 \sqrt{2} c^{17/4} (b+2 c x)}+\frac{13 e \left(a+b x+c x^2\right)^{9/4} (2 c d-b e)}{99 c^2}+\frac{2 e (d+e x) \left(a+b x+c x^2\right)^{9/4}}{11 c}","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+11 b d)+13 b^2 e^2+44 c^2 d^2\right)}{3696 c^4}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/4} \left(-4 c e (2 a e+11 b d)+13 b^2 e^2+44 c^2 d^2\right)}{308 c^3}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+11 b d)+13 b^2 e^2+44 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{7392 \sqrt{2} c^{17/4} (b+2 c x)}+\frac{13 e \left(a+b x+c x^2\right)^{9/4} (2 c d-b e)}{99 c^2}+\frac{2 e (d+e x) \left(a+b x+c x^2\right)^{9/4}}{11 c}",1,"(-5*(b^2 - 4*a*c)*(44*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(11*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(3696*c^4) + ((44*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(11*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/4))/(308*c^3) + (13*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(9/4))/(99*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(9/4))/(11*c) + (5*(b^2 - 4*a*c)^(9/4)*(44*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(11*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(7392*Sqrt[2]*c^(17/4)*(b + 2*c*x))","A",6,5,22,0.2273,1,"{742, 640, 612, 623, 220}"
2524,1,285,0,0.2121819,"\int (d+e x) \left(a+b x+c x^2\right)^{5/4} \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^(5/4),x]","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{168 c^3}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{336 \sqrt{2} c^{13/4} (b+2 c x)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/4} (2 c d-b e)}{14 c^2}+\frac{2 e \left(a+b x+c x^2\right)^{9/4}}{9 c}","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{168 c^3}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{336 \sqrt{2} c^{13/4} (b+2 c x)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/4} (2 c d-b e)}{14 c^2}+\frac{2 e \left(a+b x+c x^2\right)^{9/4}}{9 c}",1,"(-5*(b^2 - 4*a*c)*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(168*c^3) + ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/4))/(14*c^2) + (2*e*(a + b*x + c*x^2)^(9/4))/(9*c) + (5*(b^2 - 4*a*c)^(9/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(336*Sqrt[2]*c^(13/4)*(b + 2*c*x))","A",5,4,20,0.2000,1,"{640, 612, 623, 220}"
2525,1,236,0,0.1571686,"\int \left(a+b x+c x^2\right)^{5/4} \, dx","Int[(a + b*x + c*x^2)^(5/4),x]","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \sqrt[4]{a+b x+c x^2}}{84 c^2}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{168 \sqrt{2} c^{9/4} (b+2 c x)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/4}}{7 c}","-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \sqrt[4]{a+b x+c x^2}}{84 c^2}+\frac{5 \left(b^2-4 a c\right)^{9/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{168 \sqrt{2} c^{9/4} (b+2 c x)}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/4}}{7 c}",1,"(-5*(b^2 - 4*a*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(84*c^2) + ((b + 2*c*x)*(a + b*x + c*x^2)^(5/4))/(7*c) + (5*(b^2 - 4*a*c)^(9/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(168*Sqrt[2]*c^(9/4)*(b + 2*c*x))","A",4,3,14,0.2143,1,"{612, 623, 220}"
2526,1,1014,0,2.6938953,"\int \frac{\left(a+b x+c x^2\right)^{5/4}}{d+e x} \, dx","Int[(a + b*x + c*x^2)^(5/4)/(d + e*x),x]","-\frac{\left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) \left(c d^2-b e d+a e^2\right)^{5/4}}{c^{3/4} e^{7/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) \left(c d^2-b e d+a e^2\right)^{5/4}}{c^{3/4} e^{7/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) \left(c d^2-b e d+a e^2\right)}{\sqrt{2} c e^4 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) \left(c d^2-b e d+a e^2\right)}{\sqrt{2} c e^4 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{2 \left(c x^2+b x+a\right)^{5/4}}{5 e}-\frac{\sqrt[4]{b^2-4 a c} (2 c d-b e) \left(12 c^2 d^2-b^2 e^2-4 c e (3 b d-4 a e)\right) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{12 \sqrt{2} c^{5/4} e^4 (b+2 c x)}+\frac{\left(12 c^2 d^2+b^2 e^2-2 c e (7 b d-6 a e)-2 c e (2 c d-b e) x\right) \sqrt[4]{c x^2+b x+a}}{6 c e^3}","-\frac{\left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) \left(c d^2-b e d+a e^2\right)^{5/4}}{c^{3/4} e^{7/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) \left(c d^2-b e d+a e^2\right)^{5/4}}{c^{3/4} e^{7/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) \left(c d^2-b e d+a e^2\right)}{\sqrt{2} c e^4 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(b^2-4 a c\right) (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) \left(c d^2-b e d+a e^2\right)}{\sqrt{2} c e^4 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{2 \left(c x^2+b x+a\right)^{5/4}}{5 e}-\frac{\sqrt[4]{b^2-4 a c} (2 c d-b e) \left(12 c^2 d^2-b^2 e^2-4 c e (3 b d-4 a e)\right) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{12 \sqrt{2} c^{5/4} e^4 (b+2 c x)}+\frac{\left(12 c^2 d^2+b^2 e^2-2 c e (7 b d-6 a e)-2 c e (2 c d-b e) x\right) \sqrt[4]{c x^2+b x+a}}{6 c e^3}",1,"((12*c^2*d^2 + b^2*e^2 - 2*c*e*(7*b*d - 6*a*e) - 2*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(1/4))/(6*c*e^3) + (2*(a + b*x + c*x^2)^(5/4))/(5*e) - ((-b^2 + 4*a*c)^(3/4)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(3/4)*e^(7/2)*(a + b*x + c*x^2)^(3/4)) - ((-b^2 + 4*a*c)^(3/4)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(3/4)*e^(7/2)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*(12*c^2*d^2 - b^2*e^2 - 4*c*e*(3*b*d - 4*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(12*Sqrt[2]*c^(5/4)*e^4*(b + 2*c*x)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*c*e^4*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*c*e^4*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))","A",20,18,22,0.8182,1,"{734, 814, 843, 623, 220, 749, 748, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
2527,1,975,0,2.328346,"\int \frac{\left(a+b x+c x^2\right)^{5/4}}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^(5/4)/(d + e*x)^2,x]","\frac{5 \left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c e^4 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{5 \left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c e^4 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{5 \left(4 a c-b^2\right)^{3/4} \sqrt[4]{c d^2-b e d+a e^2} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} e^{7/2} \left(c x^2+b x+a\right)^{3/4}}+\frac{5 \left(4 a c-b^2\right)^{3/4} \sqrt[4]{c d^2-b e d+a e^2} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} e^{7/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(c x^2+b x+a\right)^{5/4}}{e (d+e x)}+\frac{5 \sqrt[4]{b^2-4 a c} \left(6 c^2 d^2+b^2 e^2-2 c e (3 b d-a e)\right) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} \sqrt[4]{c} e^4 (b+2 c x)}-\frac{5 (3 c d-2 b e-c e x) \sqrt[4]{c x^2+b x+a}}{3 e^3}","\frac{5 \left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c e^4 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{5 \left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c e^4 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}+\frac{5 \left(4 a c-b^2\right)^{3/4} \sqrt[4]{c d^2-b e d+a e^2} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} e^{7/2} \left(c x^2+b x+a\right)^{3/4}}+\frac{5 \left(4 a c-b^2\right)^{3/4} \sqrt[4]{c d^2-b e d+a e^2} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} e^{7/2} \left(c x^2+b x+a\right)^{3/4}}-\frac{\left(c x^2+b x+a\right)^{5/4}}{e (d+e x)}+\frac{5 \sqrt[4]{b^2-4 a c} \left(6 c^2 d^2+b^2 e^2-2 c e (3 b d-a e)\right) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} \sqrt[4]{c} e^4 (b+2 c x)}-\frac{5 (3 c d-2 b e-c e x) \sqrt[4]{c x^2+b x+a}}{3 e^3}",1,"(-5*(3*c*d - 2*b*e - c*e*x)*(a + b*x + c*x^2)^(1/4))/(3*e^3) - (a + b*x + c*x^2)^(5/4)/(e*(d + e*x)) + (5*(-b^2 + 4*a*c)^(3/4)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(3/4)*e^(7/2)*(a + b*x + c*x^2)^(3/4)) + (5*(-b^2 + 4*a*c)^(3/4)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(3/4)*e^(7/2)*(a + b*x + c*x^2)^(3/4)) + (5*(b^2 - 4*a*c)^(1/4)*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(6*Sqrt[2]*c^(1/4)*e^4*(b + 2*c*x)) + (5*(b^2 - 4*a*c)*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*c*e^4*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) + (5*(b^2 - 4*a*c)*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*c*e^4*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))","A",20,18,22,0.8182,1,"{732, 814, 843, 623, 220, 749, 748, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
2528,1,637,0,0.7279333,"\int \frac{(d+e x)^3}{\sqrt[4]{a+b x+c x^2}} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^(1/4),x]","\frac{e \left(a+b x+c x^2\right)^{3/4} \left(-2 c e (40 a e+147 b d)+77 b^2 e^2+66 c e x (2 c d-b e)+360 c^2 d^2\right)}{210 c^3}+\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (6 a e+5 b d)+11 b^2 e^2+20 c^2 d^2\right)}{20 c^{7/2} \sqrt{b^2-4 a c} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+5 b d)+11 b^2 e^2+20 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{40 \sqrt{2} c^{15/4} (b+2 c x)}-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+5 b d)+11 b^2 e^2+20 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} c^{15/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \left(a+b x+c x^2\right)^{3/4}}{7 c}","\frac{e \left(a+b x+c x^2\right)^{3/4} \left(-2 c e (40 a e+147 b d)+77 b^2 e^2+66 c e x (2 c d-b e)+360 c^2 d^2\right)}{210 c^3}+\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (6 a e+5 b d)+11 b^2 e^2+20 c^2 d^2\right)}{20 c^{7/2} \sqrt{b^2-4 a c} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+5 b d)+11 b^2 e^2+20 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{40 \sqrt{2} c^{15/4} (b+2 c x)}-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+5 b d)+11 b^2 e^2+20 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} c^{15/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \left(a+b x+c x^2\right)^{3/4}}{7 c}",1,"(2*e*(d + e*x)^2*(a + b*x + c*x^2)^(3/4))/(7*c) + (e*(360*c^2*d^2 + 77*b^2*e^2 - 2*c*e*(147*b*d + 40*a*e) + 66*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/4))/(210*c^3) + ((2*c*d - b*e)*(20*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(5*b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(20*c^(7/2)*Sqrt[b^2 - 4*a*c]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) - ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*(20*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(5*b*d + 6*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(20*Sqrt[2]*c^(15/4)*(b + 2*c*x)) + ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*(20*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(5*b*d + 6*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(40*Sqrt[2]*c^(15/4)*(b + 2*c*x))","A",6,6,22,0.2727,1,"{742, 779, 623, 305, 220, 1196}"
2529,1,573,0,0.7250859,"\int \frac{(d+e x)^2}{\sqrt[4]{a+b x+c x^2}} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^(1/4),x]","\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+5 b d)+7 b^2 e^2+20 c^2 d^2\right)}{10 c^{5/2} \sqrt{b^2-4 a c} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+5 b d)+7 b^2 e^2+20 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} c^{11/4} (b+2 c x)}-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+5 b d)+7 b^2 e^2+20 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{10 \sqrt{2} c^{11/4} (b+2 c x)}+\frac{7 e \left(a+b x+c x^2\right)^{3/4} (2 c d-b e)}{15 c^2}+\frac{2 e (d+e x) \left(a+b x+c x^2\right)^{3/4}}{5 c}","\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+5 b d)+7 b^2 e^2+20 c^2 d^2\right)}{10 c^{5/2} \sqrt{b^2-4 a c} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+5 b d)+7 b^2 e^2+20 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{20 \sqrt{2} c^{11/4} (b+2 c x)}-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+5 b d)+7 b^2 e^2+20 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{10 \sqrt{2} c^{11/4} (b+2 c x)}+\frac{7 e \left(a+b x+c x^2\right)^{3/4} (2 c d-b e)}{15 c^2}+\frac{2 e (d+e x) \left(a+b x+c x^2\right)^{3/4}}{5 c}",1,"(7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/4))/(15*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(3/4))/(5*c) + ((20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(10*c^(5/2)*Sqrt[b^2 - 4*a*c]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) - ((b^2 - 4*a*c)^(3/4)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(10*Sqrt[2]*c^(11/4)*(b + 2*c*x)) + ((b^2 - 4*a*c)^(3/4)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(20*Sqrt[2]*c^(11/4)*(b + 2*c*x))","A",6,6,22,0.2727,1,"{742, 640, 623, 305, 220, 1196}"
2530,1,469,0,0.3812509,"\int \frac{d+e x}{\sqrt[4]{a+b x+c x^2}} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^(1/4),x]","\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{c^{3/2} \sqrt{b^2-4 a c} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} c^{7/4} (b+2 c x)}-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{7/4} (b+2 c x)}+\frac{2 e \left(a+b x+c x^2\right)^{3/4}}{3 c}","\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{c^{3/2} \sqrt{b^2-4 a c} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} c^{7/4} (b+2 c x)}-\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{7/4} (b+2 c x)}+\frac{2 e \left(a+b x+c x^2\right)^{3/4}}{3 c}",1,"(2*e*(a + b*x + c*x^2)^(3/4))/(3*c) + ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(c^(3/2)*Sqrt[b^2 - 4*a*c]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) - ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*c^(7/4)*(b + 2*c*x)) + ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(2*Sqrt[2]*c^(7/4)*(b + 2*c*x))","A",5,5,20,0.2500,1,"{640, 623, 305, 220, 1196}"
2531,1,418,0,0.3054178,"\int \frac{1}{\sqrt[4]{a+b x+c x^2}} \, dx","Int[(a + b*x + c*x^2)^(-1/4),x]","\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{3/4} (b+2 c x)}-\frac{\sqrt{2} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{c^{3/4} (b+2 c x)}+\frac{2 (b+2 c x) \sqrt[4]{a+b x+c x^2}}{\sqrt{c} \sqrt{b^2-4 a c} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}","\frac{\left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{3/4} (b+2 c x)}-\frac{\sqrt{2} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{c^{3/4} (b+2 c x)}+\frac{2 (b+2 c x) \sqrt[4]{a+b x+c x^2}}{\sqrt{c} \sqrt{b^2-4 a c} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}",1,"(2*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(Sqrt[c]*Sqrt[b^2 - 4*a*c]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) - (Sqrt[2]*(b^2 - 4*a*c)^(3/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(c^(3/4)*(b + 2*c*x)) + ((b^2 - 4*a*c)^(3/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*c^(3/4)*(b + 2*c*x))","A",4,4,14,0.2857,1,"{623, 305, 220, 1196}"
2532,1,733,0,1.5599573,"\int \frac{1}{(d+e x) \sqrt[4]{a+b x+c x^2}} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^(1/4)),x]","\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[4]{4 a c-b^2} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{a e^2-b d e+c d^2}}\right)}{\sqrt[4]{c} \sqrt{e} \sqrt[4]{a+b x+c x^2} \sqrt[4]{a e^2-b d e+c d^2}}-\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt[4]{4 a c-b^2} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{a e^2-b d e+c d^2}}\right)}{\sqrt[4]{c} \sqrt{e} \sqrt[4]{a+b x+c x^2} \sqrt[4]{a e^2-b d e+c d^2}}-\frac{\sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} \sqrt{c} e (b+2 c x) \sqrt[4]{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}+\frac{\sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} \sqrt{c} e (b+2 c x) \sqrt[4]{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}","\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[4]{4 a c-b^2} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{a e^2-b d e+c d^2}}\right)}{\sqrt[4]{c} \sqrt{e} \sqrt[4]{a+b x+c x^2} \sqrt[4]{a e^2-b d e+c d^2}}-\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt[4]{4 a c-b^2} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{a e^2-b d e+c d^2}}\right)}{\sqrt[4]{c} \sqrt{e} \sqrt[4]{a+b x+c x^2} \sqrt[4]{a e^2-b d e+c d^2}}-\frac{\sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} \sqrt{c} e (b+2 c x) \sqrt[4]{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}+\frac{\sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} \sqrt{c} e (b+2 c x) \sqrt[4]{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}",1,"((-b^2 + 4*a*c)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(1/4)*Sqrt[e]*(c*d^2 - b*d*e + a*e^2)^(1/4)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(1/4)*Sqrt[e]*(c*d^2 - b*d*e + a*e^2)^(1/4)*(a + b*x + c*x^2)^(1/4)) - (Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*Sqrt[c]*e*Sqrt[c*d^2 - b*d*e + a*e^2]*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*Sqrt[c]*e*Sqrt[c*d^2 - b*d*e + a*e^2]*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))","A",14,12,22,0.5455,1,"{749, 748, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
2533,1,1280,0,2.3937979,"\int \frac{1}{(d+e x)^2 \sqrt[4]{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^2*(a + b*x + c*x^2)^(1/4)),x]","-\frac{\sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} e \left(c d^2-b e d+a e^2\right)^{3/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{\sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} e \left(c d^2-b e d+a e^2\right)^{3/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} \sqrt{e} \left(c d^2-b e d+a e^2\right)^{5/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} \sqrt{e} \left(c d^2-b e d+a e^2\right)^{5/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} \left(c d^2-b e d+a e^2\right) (b+2 c x)}+\frac{\sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \left(c d^2-b e d+a e^2\right) (b+2 c x)}-\frac{e \left(c x^2+b x+a\right)^{3/4}}{\left(c d^2-b e d+a e^2\right) (d+e x)}+\frac{\sqrt{c} (b+2 c x) \sqrt[4]{c x^2+b x+a}}{\sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}","-\frac{\sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} e \left(c d^2-b e d+a e^2\right)^{3/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{\sqrt{4 a c-b^2} \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} e \left(c d^2-b e d+a e^2\right)^{3/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} \sqrt{e} \left(c d^2-b e d+a e^2\right)^{5/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} \sqrt{e} \left(c d^2-b e d+a e^2\right)^{5/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} \left(c d^2-b e d+a e^2\right) (b+2 c x)}+\frac{\sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \left(c d^2-b e d+a e^2\right) (b+2 c x)}-\frac{e \left(c x^2+b x+a\right)^{3/4}}{\left(c d^2-b e d+a e^2\right) (d+e x)}+\frac{\sqrt{c} (b+2 c x) \sqrt[4]{c x^2+b x+a}}{\sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}",1,"-((e*(a + b*x + c*x^2)^(3/4))/((c*d^2 - b*d*e + a*e^2)*(d + e*x))) + (Sqrt[c]*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) + ((-b^2 + 4*a*c)^(1/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(1/4)*Sqrt[e]*(c*d^2 - b*d*e + a*e^2)^(5/4)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(1/4)*Sqrt[e]*(c*d^2 - b*d*e + a*e^2)^(5/4)*(a + b*x + c*x^2)^(1/4)) - (c^(1/4)*(b^2 - 4*a*c)^(3/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) + (c^(1/4)*(b^2 - 4*a*c)^(3/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(2*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) - (Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*Sqrt[c]*e*(c*d^2 - b*d*e + a*e^2)^(3/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*Sqrt[c]*e*(c*d^2 - b*d*e + a*e^2)^(3/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))","A",20,18,22,0.8182,1,"{744, 843, 623, 305, 220, 1196, 749, 748, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
2534,1,1465,0,3.2176348,"\int \frac{1}{(d+e x)^3 \sqrt[4]{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^3*(a + b*x + c*x^2)^(1/4)),x]","-\frac{5 (2 c d-b e) \left(c x^2+b x+a\right)^{3/4} e}{8 \left(c d^2-b e d+a e^2\right)^2 (d+e x)}-\frac{\left(c x^2+b x+a\right)^{3/4} e}{2 \left(c d^2-b e d+a e^2\right) (d+e x)^2}-\frac{5 \sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{8 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}+\frac{5 \sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{16 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}+\frac{5 \sqrt{c} (2 c d-b e) (b+2 c x) \sqrt[4]{c x^2+b x+a}}{8 \sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right)^2 \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\sqrt[4]{4 a c-b^2} \left(12 c^2 d^2+5 b^2 e^2-4 c e (3 b d+2 a e)\right) \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{32 \sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{9/4} \sqrt[4]{c x^2+b x+a} \sqrt{e}}-\frac{\sqrt[4]{4 a c-b^2} \left(12 c^2 d^2+5 b^2 e^2-4 c e (3 b d+2 a e)\right) \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{32 \sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{9/4} \sqrt[4]{c x^2+b x+a} \sqrt{e}}-\frac{\sqrt{4 a c-b^2} (2 c d-b e) \left(12 c^2 d^2+5 b^2 e^2-4 c e (3 b d+2 a e)\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{32 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{5/2} (b+2 c x) \sqrt[4]{c x^2+b x+a} e}+\frac{\sqrt{4 a c-b^2} (2 c d-b e) \left(12 c^2 d^2+5 b^2 e^2-4 c e (3 b d+2 a e)\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{32 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{5/2} (b+2 c x) \sqrt[4]{c x^2+b x+a} e}","-\frac{5 (2 c d-b e) \left(c x^2+b x+a\right)^{3/4} e}{8 \left(c d^2-b e d+a e^2\right)^2 (d+e x)}-\frac{\left(c x^2+b x+a\right)^{3/4} e}{2 \left(c d^2-b e d+a e^2\right) (d+e x)^2}-\frac{5 \sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{8 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}+\frac{5 \sqrt[4]{c} \left(b^2-4 a c\right)^{3/4} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{16 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}+\frac{5 \sqrt{c} (2 c d-b e) (b+2 c x) \sqrt[4]{c x^2+b x+a}}{8 \sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right)^2 \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\sqrt[4]{4 a c-b^2} \left(12 c^2 d^2+5 b^2 e^2-4 c e (3 b d+2 a e)\right) \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{32 \sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{9/4} \sqrt[4]{c x^2+b x+a} \sqrt{e}}-\frac{\sqrt[4]{4 a c-b^2} \left(12 c^2 d^2+5 b^2 e^2-4 c e (3 b d+2 a e)\right) \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right)}{32 \sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{9/4} \sqrt[4]{c x^2+b x+a} \sqrt{e}}-\frac{\sqrt{4 a c-b^2} (2 c d-b e) \left(12 c^2 d^2+5 b^2 e^2-4 c e (3 b d+2 a e)\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{32 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{5/2} (b+2 c x) \sqrt[4]{c x^2+b x+a} e}+\frac{\sqrt{4 a c-b^2} (2 c d-b e) \left(12 c^2 d^2+5 b^2 e^2-4 c e (3 b d+2 a e)\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{32 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{5/2} (b+2 c x) \sqrt[4]{c x^2+b x+a} e}",1,"-(e*(a + b*x + c*x^2)^(3/4))/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (5*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/4))/(8*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + (5*Sqrt[c]*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(8*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) + ((-b^2 + 4*a*c)^(1/4)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(32*c^(1/4)*Sqrt[e]*(c*d^2 - b*d*e + a*e^2)^(9/4)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(32*c^(1/4)*Sqrt[e]*(c*d^2 - b*d*e + a*e^2)^(9/4)*(a + b*x + c*x^2)^(1/4)) - (5*c^(1/4)*(b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(8*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) + (5*c^(1/4)*(b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(16*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) - (Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(32*Sqrt[2]*Sqrt[c]*e*(c*d^2 - b*d*e + a*e^2)^(5/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (Sqrt[-b^2 + 4*a*c]*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(32*Sqrt[2]*Sqrt[c]*e*(c*d^2 - b*d*e + a*e^2)^(5/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))","A",21,19,22,0.8636,1,"{744, 834, 843, 623, 305, 220, 1196, 749, 748, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
2535,1,307,0,0.3299166,"\int \frac{(d+e x)^3}{\left(a+b x+c x^2\right)^{3/4}} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^(3/4),x]","\frac{e \sqrt[4]{a+b x+c x^2} \left(-2 c e (8 a e+25 b d)+15 b^2 e^2+6 c e x (2 c d-b e)+56 c^2 d^2\right)}{10 c^3}+\frac{\sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} c^{13/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \sqrt[4]{a+b x+c x^2}}{5 c}","\frac{e \sqrt[4]{a+b x+c x^2} \left(-2 c e (8 a e+25 b d)+15 b^2 e^2+6 c e x (2 c d-b e)+56 c^2 d^2\right)}{10 c^3}+\frac{\sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} c^{13/4} (b+2 c x)}+\frac{2 e (d+e x)^2 \sqrt[4]{a+b x+c x^2}}{5 c}",1,"(2*e*(d + e*x)^2*(a + b*x + c*x^2)^(1/4))/(5*c) + (e*(56*c^2*d^2 + 15*b^2*e^2 - 2*c*e*(25*b*d + 8*a*e) + 6*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(1/4))/(10*c^3) + ((b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(4*Sqrt[2]*c^(13/4)*(b + 2*c*x))","A",4,4,22,0.1818,1,"{742, 779, 623, 220}"
2536,1,262,0,0.2547947,"\int \frac{(d+e x)^2}{\left(a+b x+c x^2\right)^{3/4}} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^(3/4),x]","\frac{\sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} c^{9/4} (b+2 c x)}+\frac{5 e \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{3 c^2}+\frac{2 e (d+e x) \sqrt[4]{a+b x+c x^2}}{3 c}","\frac{\sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+3 b d)+5 b^2 e^2+12 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{6 \sqrt{2} c^{9/4} (b+2 c x)}+\frac{5 e \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{3 c^2}+\frac{2 e (d+e x) \sqrt[4]{a+b x+c x^2}}{3 c}",1,"(5*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(1/4))/(3*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(1/4))/(3*c) + ((b^2 - 4*a*c)^(1/4)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(6*Sqrt[2]*c^(9/4)*(b + 2*c*x))","A",4,4,22,0.1818,1,"{742, 640, 623, 220}"
2537,1,200,0,0.1421575,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^{3/4}} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^(3/4),x]","\frac{\sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{5/4} (b+2 c x)}+\frac{2 e \sqrt[4]{a+b x+c x^2}}{c}","\frac{\sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{5/4} (b+2 c x)}+\frac{2 e \sqrt[4]{a+b x+c x^2}}{c}",1,"(2*e*(a + b*x + c*x^2)^(1/4))/c + ((b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*c^(5/4)*(b + 2*c*x))","A",3,3,20,0.1500,1,"{640, 623, 220}"
2538,1,170,0,0.1116446,"\int \frac{1}{\left(a+b x+c x^2\right)^{3/4}} \, dx","Int[(a + b*x + c*x^2)^(-3/4),x]","\frac{\sqrt{2} \sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{c} (b+2 c x)}","\frac{\sqrt{2} \sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{c} (b+2 c x)}",1,"(Sqrt[2]*(b^2 - 4*a*c)^(1/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(c^(1/4)*(b + 2*c*x))","A",2,2,14,0.1429,1,"{623, 220}"
2539,1,709,0,1.5742874,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)^{3/4}} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^(3/4)),x]","-\frac{\sqrt{e} \left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[4]{4 a c-b^2} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{a e^2-b d e+c d^2}}\right)}{c^{3/4} \left(a+b x+c x^2\right)^{3/4} \left(a e^2-b d e+c d^2\right)^{3/4}}-\frac{\sqrt{e} \left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt[4]{4 a c-b^2} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{a e^2-b d e+c d^2}}\right)}{c^{3/4} \left(a+b x+c x^2\right)^{3/4} \left(a e^2-b d e+c d^2\right)^{3/4}}-\frac{\left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}\right)^{3/4} (2 c d-b e) \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} c (b+2 c x) \left(a+b x+c x^2\right)^{3/4} \left(a e^2-b d e+c d^2\right)}-\frac{\left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}\right)^{3/4} (2 c d-b e) \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} c (b+2 c x) \left(a+b x+c x^2\right)^{3/4} \left(a e^2-b d e+c d^2\right)}","-\frac{\sqrt{e} \left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[4]{4 a c-b^2} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{a e^2-b d e+c d^2}}\right)}{c^{3/4} \left(a+b x+c x^2\right)^{3/4} \left(a e^2-b d e+c d^2\right)^{3/4}}-\frac{\sqrt{e} \left(4 a c-b^2\right)^{3/4} \left(-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt[4]{4 a c-b^2} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{a e^2-b d e+c d^2}}\right)}{c^{3/4} \left(a+b x+c x^2\right)^{3/4} \left(a e^2-b d e+c d^2\right)^{3/4}}-\frac{\left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}\right)^{3/4} (2 c d-b e) \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} c (b+2 c x) \left(a+b x+c x^2\right)^{3/4} \left(a e^2-b d e+c d^2\right)}-\frac{\left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}\right)^{3/4} (2 c d-b e) \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{\sqrt{2} c (b+2 c x) \left(a+b x+c x^2\right)^{3/4} \left(a e^2-b d e+c d^2\right)}",1,"-(((-b^2 + 4*a*c)^(3/4)*Sqrt[e]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(a + b*x + c*x^2)^(3/4))) - ((-b^2 + 4*a*c)^(3/4)*Sqrt[e]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*c*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*c*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))","A",15,13,22,0.5909,1,"{749, 748, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
2540,1,970,0,2.0138543,"\int \frac{1}{(d+e x)^2 \left(a+b x+c x^2\right)^{3/4}} \, dx","Int[1/((d + e*x)^2*(a + b*x + c*x^2)^(3/4)),x]","-\frac{3 \left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c \left(c d^2-b e d+a e^2\right)^2 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c \left(c d^2-b e d+a e^2\right)^2 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(4 a c-b^2\right)^{3/4} \sqrt{e} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} \left(c d^2-b e d+a e^2\right)^{7/4} \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(4 a c-b^2\right)^{3/4} \sqrt{e} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} \left(c d^2-b e d+a e^2\right)^{7/4} \left(c x^2+b x+a\right)^{3/4}}-\frac{c^{3/4} \sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} \left(c d^2-b e d+a e^2\right) (b+2 c x)}-\frac{e \sqrt[4]{c x^2+b x+a}}{\left(c d^2-b e d+a e^2\right) (d+e x)}","-\frac{3 \left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c \left(c d^2-b e d+a e^2\right)^2 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(b^2-4 a c\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} c \left(c d^2-b e d+a e^2\right)^2 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(4 a c-b^2\right)^{3/4} \sqrt{e} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} \left(c d^2-b e d+a e^2\right)^{7/4} \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(4 a c-b^2\right)^{3/4} \sqrt{e} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 c^{3/4} \left(c d^2-b e d+a e^2\right)^{7/4} \left(c x^2+b x+a\right)^{3/4}}-\frac{c^{3/4} \sqrt[4]{b^2-4 a c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} \left(c d^2-b e d+a e^2\right) (b+2 c x)}-\frac{e \sqrt[4]{c x^2+b x+a}}{\left(c d^2-b e d+a e^2\right) (d+e x)}",1,"-((e*(a + b*x + c*x^2)^(1/4))/((c*d^2 - b*d*e + a*e^2)*(d + e*x))) - (3*(-b^2 + 4*a*c)^(3/4)*Sqrt[e]*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(7/4)*(a + b*x + c*x^2)^(3/4)) - (3*(-b^2 + 4*a*c)^(3/4)*Sqrt[e]*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(7/4)*(a + b*x + c*x^2)^(3/4)) - (c^(3/4)*(b^2 - 4*a*c)^(1/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) - (3*(b^2 - 4*a*c)*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*c*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - (3*(b^2 - 4*a*c)*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*c*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))","A",19,17,22,0.7727,1,"{744, 843, 623, 220, 749, 748, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
2541,1,1134,0,2.5487748,"\int \frac{1}{(d+e x)^3 \left(a+b x+c x^2\right)^{3/4}} \, dx","Int[1/((d + e*x)^3*(a + b*x + c*x^2)^(3/4)),x]","-\frac{7 (2 c d-b e) \sqrt[4]{c x^2+b x+a} e}{8 \left(c d^2-b e d+a e^2\right)^2 (d+e x)}-\frac{\sqrt[4]{c x^2+b x+a} e}{2 \left(c d^2-b e d+a e^2\right) (d+e x)^2}-\frac{3 \left(4 a c-b^2\right)^{3/4} \left(20 c^2 d^2+7 b^2 e^2-4 c e (5 b d+2 a e)\right) \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) \sqrt{e}}{32 c^{3/4} \left(c d^2-b e d+a e^2\right)^{11/4} \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(4 a c-b^2\right)^{3/4} \left(20 c^2 d^2+7 b^2 e^2-4 c e (5 b d+2 a e)\right) \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) \sqrt{e}}{32 c^{3/4} \left(c d^2-b e d+a e^2\right)^{11/4} \left(c x^2+b x+a\right)^{3/4}}-\frac{7 c^{3/4} \sqrt[4]{b^2-4 a c} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{8 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}-\frac{3 \left(b^2-4 a c\right) (2 c d-b e) \left(20 c^2 d^2+7 b^2 e^2-4 c e (5 b d+2 a e)\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{32 \sqrt{2} c \left(c d^2-b e d+a e^2\right)^3 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(b^2-4 a c\right) (2 c d-b e) \left(20 c^2 d^2+7 b^2 e^2-4 c e (5 b d+2 a e)\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{32 \sqrt{2} c \left(c d^2-b e d+a e^2\right)^3 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}","-\frac{7 (2 c d-b e) \sqrt[4]{c x^2+b x+a} e}{8 \left(c d^2-b e d+a e^2\right)^2 (d+e x)}-\frac{\sqrt[4]{c x^2+b x+a} e}{2 \left(c d^2-b e d+a e^2\right) (d+e x)^2}-\frac{3 \left(4 a c-b^2\right)^{3/4} \left(20 c^2 d^2+7 b^2 e^2-4 c e (5 b d+2 a e)\right) \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) \sqrt{e}}{32 c^{3/4} \left(c d^2-b e d+a e^2\right)^{11/4} \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(4 a c-b^2\right)^{3/4} \left(20 c^2 d^2+7 b^2 e^2-4 c e (5 b d+2 a e)\right) \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) \sqrt{e}}{32 c^{3/4} \left(c d^2-b e d+a e^2\right)^{11/4} \left(c x^2+b x+a\right)^{3/4}}-\frac{7 c^{3/4} \sqrt[4]{b^2-4 a c} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{8 \sqrt{2} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}-\frac{3 \left(b^2-4 a c\right) (2 c d-b e) \left(20 c^2 d^2+7 b^2 e^2-4 c e (5 b d+2 a e)\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{32 \sqrt{2} c \left(c d^2-b e d+a e^2\right)^3 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}-\frac{3 \left(b^2-4 a c\right) (2 c d-b e) \left(20 c^2 d^2+7 b^2 e^2-4 c e (5 b d+2 a e)\right) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \left(-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}\right)^{3/4} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right)}{32 \sqrt{2} c \left(c d^2-b e d+a e^2\right)^3 (b+2 c x) \left(c x^2+b x+a\right)^{3/4}}",1,"-(e*(a + b*x + c*x^2)^(1/4))/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(1/4))/(8*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) - (3*(-b^2 + 4*a*c)^(3/4)*Sqrt[e]*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(32*c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(11/4)*(a + b*x + c*x^2)^(3/4)) - (3*(-b^2 + 4*a*c)^(3/4)*Sqrt[e]*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(32*c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(11/4)*(a + b*x + c*x^2)^(3/4)) - (7*c^(3/4)*(b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(8*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) - (3*(b^2 - 4*a*c)*(2*c*d - b*e)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(32*Sqrt[2]*c*(c*d^2 - b*d*e + a*e^2)^3*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - (3*(b^2 - 4*a*c)*(2*c*d - b*e)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(32*Sqrt[2]*c*(c*d^2 - b*d*e + a*e^2)^3*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))","A",20,18,22,0.8182,1,"{744, 834, 843, 623, 220, 749, 748, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
2542,1,662,0,0.7244999,"\int \frac{(d+e x)^3}{\left(a+b x+c x^2\right)^{5/4}} \, dx","Int[(d + e*x)^3/(a + b*x + c*x^2)^(5/4),x]","\frac{2 e \left(a+b x+c x^2\right)^{3/4} \left(-2 c e (8 a e+9 b d)+7 b^2 e^2+6 c e x (2 c d-b e)+24 c^2 d^2\right)}{3 c^2 \left(b^2-4 a c\right)}+\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (6 a e+b d)+7 b^2 e^2+4 c^2 d^2\right)}{c^{5/2} \left(b^2-4 a c\right)^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+b d)+7 b^2 e^2+4 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} c^{11/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{\sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+b d)+7 b^2 e^2+4 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{11/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{4 (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt[4]{a+b x+c x^2}}","\frac{2 e \left(a+b x+c x^2\right)^{3/4} \left(-2 c e (8 a e+9 b d)+7 b^2 e^2+6 c e x (2 c d-b e)+24 c^2 d^2\right)}{3 c^2 \left(b^2-4 a c\right)}+\frac{(b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e) \left(-4 c e (6 a e+b d)+7 b^2 e^2+4 c^2 d^2\right)}{c^{5/2} \left(b^2-4 a c\right)^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+b d)+7 b^2 e^2+4 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} c^{11/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{\sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) \left(-4 c e (6 a e+b d)+7 b^2 e^2+4 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{11/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{4 (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt[4]{a+b x+c x^2}}",1,"(-4*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/4)) + (2*e*(24*c^2*d^2 + 7*b^2*e^2 - 2*c*e*(9*b*d + 8*a*e) + 6*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/4))/(3*c^2*(b^2 - 4*a*c)) + ((2*c*d - b*e)*(4*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(c^(5/2)*(b^2 - 4*a*c)^(3/2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) - ((2*c*d - b*e)*(4*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(b*d + 6*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*c^(11/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x)) + ((2*c*d - b*e)*(4*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(b*d + 6*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(2*Sqrt[2]*c^(11/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x))","A",6,6,22,0.2727,1,"{738, 779, 623, 305, 220, 1196}"
2543,1,594,0,0.7369352,"\int \frac{(d+e x)^2}{\left(a+b x+c x^2\right)^{5/4}} \, dx","Int[(d + e*x)^2/(a + b*x + c*x^2)^(5/4),x]","\frac{2 (b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{c^{3/2} \left(b^2-4 a c\right)^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{7/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{\sqrt{2} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{c^{7/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}+\frac{4 e \left(a+b x+c x^2\right)^{3/4} (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{4 (d+e x) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt[4]{a+b x+c x^2}}","\frac{2 (b+2 c x) \sqrt[4]{a+b x+c x^2} \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{c^{3/2} \left(b^2-4 a c\right)^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{\sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} c^{7/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{\sqrt{2} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{c^{7/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}+\frac{4 e \left(a+b x+c x^2\right)^{3/4} (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{4 (d+e x) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt[4]{a+b x+c x^2}}",1,"(-4*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/4)) + (4*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/4))/(c*(b^2 - 4*a*c)) + (2*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(c^(3/2)*(b^2 - 4*a*c)^(3/2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) - (Sqrt[2]*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(c^(7/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x)) + ((4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*c^(7/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x))","A",6,6,22,0.2727,1,"{738, 640, 623, 305, 220, 1196}"
2544,1,490,0,0.3965418,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^{5/4}} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^(5/4),x]","\frac{\sqrt{2} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{2 \sqrt{2} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}+\frac{4 (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{\sqrt{c} \left(b^2-4 a c\right)^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}-\frac{4 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt[4]{a+b x+c x^2}}","\frac{\sqrt{2} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{2 \sqrt{2} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) (2 c d-b e) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt[4]{b^2-4 a c} (b+2 c x)}+\frac{4 (b+2 c x) \sqrt[4]{a+b x+c x^2} (2 c d-b e)}{\sqrt{c} \left(b^2-4 a c\right)^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}-\frac{4 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt[4]{a+b x+c x^2}}",1,"(-4*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/4)) + (4*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(Sqrt[c]*(b^2 - 4*a*c)^(3/2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) - (2*Sqrt[2]*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(c^(3/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x)) + (Sqrt[2]*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(c^(3/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x))","A",5,5,20,0.2500,1,"{638, 623, 305, 220, 1196}"
2545,1,451,0,0.3607216,"\int \frac{1}{\left(a+b x+c x^2\right)^{5/4}} \, dx","Int[(a + b*x + c*x^2)^(-5/4),x]","-\frac{4 (b+2 c x)}{\left(b^2-4 a c\right) \sqrt[4]{a+b x+c x^2}}+\frac{8 \sqrt{c} (b+2 c x) \sqrt[4]{a+b x+c x^2}}{\left(b^2-4 a c\right)^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{2 \sqrt{2} \sqrt[4]{c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{4 \sqrt{2} \sqrt[4]{c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b^2-4 a c} (b+2 c x)}","-\frac{4 (b+2 c x)}{\left(b^2-4 a c\right) \sqrt[4]{a+b x+c x^2}}+\frac{8 \sqrt{c} (b+2 c x) \sqrt[4]{a+b x+c x^2}}{\left(b^2-4 a c\right)^{3/2} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)}+\frac{2 \sqrt{2} \sqrt[4]{c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b^2-4 a c} (b+2 c x)}-\frac{4 \sqrt{2} \sqrt[4]{c} \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{a+b x+c x^2}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b^2-4 a c} (b+2 c x)}",1,"(-4*(b + 2*c*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/4)) + (8*Sqrt[c]*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/((b^2 - 4*a*c)^(3/2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) - (4*Sqrt[2]*c^(1/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/((b^2 - 4*a*c)^(1/4)*(b + 2*c*x)) + (2*Sqrt[2]*c^(1/4)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/((b^2 - 4*a*c)^(1/4)*(b + 2*c*x))","A",5,5,14,0.3571,1,"{614, 623, 305, 220, 1196}"
2546,1,1299,0,2.5176166,"\int \frac{1}{(d+e x) \left(a+b x+c x^2\right)^{5/4}} \, dx","Int[1/((d + e*x)*(a + b*x + c*x^2)^(5/4)),x]","\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) e^{3/2}}{\sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{5/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) e^{3/2}}{\sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{5/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt{4 a c-b^2} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) e}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{3/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{\sqrt{4 a c-b^2} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) e}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{3/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt[4]{c} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b^2-4 a c} \left(c d^2-b e d+a e^2\right) (b+2 c x)}+\frac{\sqrt{2} \sqrt[4]{c} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b^2-4 a c} \left(c d^2-b e d+a e^2\right) (b+2 c x)}-\frac{4 \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right)}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \sqrt[4]{c x^2+b x+a}}+\frac{4 \sqrt{c} (2 c d-b e) (b+2 c x) \sqrt[4]{c x^2+b x+a}}{\left(b^2-4 a c\right)^{3/2} \left(c d^2-b e d+a e^2\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}","\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) e^{3/2}}{\sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{5/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{4 a c-b^2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) e^{3/2}}{\sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{5/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt{4 a c-b^2} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) e}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{3/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{\sqrt{4 a c-b^2} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) e}{\sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{3/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt[4]{c} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b^2-4 a c} \left(c d^2-b e d+a e^2\right) (b+2 c x)}+\frac{\sqrt{2} \sqrt[4]{c} (2 c d-b e) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b^2-4 a c} \left(c d^2-b e d+a e^2\right) (b+2 c x)}-\frac{4 \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right)}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \sqrt[4]{c x^2+b x+a}}+\frac{4 \sqrt{c} (2 c d-b e) (b+2 c x) \sqrt[4]{c x^2+b x+a}}{\left(b^2-4 a c\right)^{3/2} \left(c d^2-b e d+a e^2\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}",1,"(-4*(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)*(a + b*x + c*x^2)^(1/4)) + (4*Sqrt[c]*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) + ((-b^2 + 4*a*c)^(1/4)*e^(3/2)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*e^(3/2)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(a + b*x + c*x^2)^(1/4)) - (2*Sqrt[2]*c^(1/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/((b^2 - 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) + (Sqrt[2]*c^(1/4)*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/((b^2 - 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) - (Sqrt[-b^2 + 4*a*c]*e*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*Sqrt[c]*(c*d^2 - b*d*e + a*e^2)^(3/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (Sqrt[-b^2 + 4*a*c]*e*(2*c*d - b*e)*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(Sqrt[2]*Sqrt[c]*(c*d^2 - b*d*e + a*e^2)^(3/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))","A",20,18,22,0.8182,1,"{740, 843, 623, 305, 220, 1196, 749, 748, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
2547,1,1485,0,3.1700557,"\int \frac{1}{(d+e x)^2 \left(a+b x+c x^2\right)^{5/4}} \, dx","Int[1/((d + e*x)^2*(a + b*x + c*x^2)^(5/4)),x]","-\frac{5 \sqrt{4 a c-b^2} e \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{5/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{5 \sqrt{4 a c-b^2} e \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{5/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{5 \sqrt[4]{4 a c-b^2} e^{3/2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{9/4} \sqrt[4]{c x^2+b x+a}}-\frac{5 \sqrt[4]{4 a c-b^2} e^{3/2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{9/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{c} \left(8 c^2 d^2+5 b^2 e^2-4 c e (2 b d+3 a e)\right) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt[4]{b^2-4 a c} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}+\frac{\sqrt[4]{c} \left(8 c^2 d^2+5 b^2 e^2-4 c e (2 b d+3 a e)\right) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt[4]{b^2-4 a c} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}-\frac{e \left(8 c^2 d^2+5 b^2 e^2-4 c e (2 b d+3 a e)\right) \left(c x^2+b x+a\right)^{3/4}}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)^2 (d+e x)}-\frac{4 \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right)}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (d+e x) \sqrt[4]{c x^2+b x+a}}+\frac{\sqrt{c} \left(8 c^2 d^2+5 b^2 e^2-4 c e (2 b d+3 a e)\right) (b+2 c x) \sqrt[4]{c x^2+b x+a}}{\left(b^2-4 a c\right)^{3/2} \left(c d^2-b e d+a e^2\right)^2 \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}","-\frac{5 \sqrt{4 a c-b^2} e \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(-\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{5/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{5 \sqrt{4 a c-b^2} e \sqrt{\frac{(b+2 c x)^2}{b^2-4 a c}} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \Pi \left(\frac{\sqrt{4 a c-b^2} e}{2 \sqrt{c} \sqrt{c d^2-b e d+a e^2}};\left.\sin ^{-1}\left(\sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}\right)\right|-1\right) (2 c d-b e)^2}{4 \sqrt{2} \sqrt{c} \left(c d^2-b e d+a e^2\right)^{5/2} (b+2 c x) \sqrt[4]{c x^2+b x+a}}+\frac{5 \sqrt[4]{4 a c-b^2} e^{3/2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{9/4} \sqrt[4]{c x^2+b x+a}}-\frac{5 \sqrt[4]{4 a c-b^2} e^{3/2} \sqrt[4]{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a c-b^2} \sqrt{e} \sqrt[4]{1-\frac{(b+2 c x)^2}{b^2-4 a c}}}{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c d^2-b e d+a e^2}}\right) (2 c d-b e)}{4 \sqrt[4]{c} \left(c d^2-b e d+a e^2\right)^{9/4} \sqrt[4]{c x^2+b x+a}}-\frac{\sqrt[4]{c} \left(8 c^2 d^2+5 b^2 e^2-4 c e (2 b d+3 a e)\right) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt[4]{b^2-4 a c} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}+\frac{\sqrt[4]{c} \left(8 c^2 d^2+5 b^2 e^2-4 c e (2 b d+3 a e)\right) \sqrt{\frac{(b+2 c x)^2}{\left(b^2-4 a c\right) \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)^2}} \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt[4]{c x^2+b x+a}}{\sqrt[4]{b^2-4 a c}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt[4]{b^2-4 a c} \left(c d^2-b e d+a e^2\right)^2 (b+2 c x)}-\frac{e \left(8 c^2 d^2+5 b^2 e^2-4 c e (2 b d+3 a e)\right) \left(c x^2+b x+a\right)^{3/4}}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)^2 (d+e x)}-\frac{4 \left(-e b^2+c d b+2 a c e+c (2 c d-b e) x\right)}{\left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (d+e x) \sqrt[4]{c x^2+b x+a}}+\frac{\sqrt{c} \left(8 c^2 d^2+5 b^2 e^2-4 c e (2 b d+3 a e)\right) (b+2 c x) \sqrt[4]{c x^2+b x+a}}{\left(b^2-4 a c\right)^{3/2} \left(c d^2-b e d+a e^2\right)^2 \left(\frac{2 \sqrt{c} \sqrt{c x^2+b x+a}}{\sqrt{b^2-4 a c}}+1\right)}",1,"(-4*(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)*(d + e*x)*(a + b*x + c*x^2)^(1/4)) - (e*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*(a + b*x + c*x^2)^(3/4))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + (Sqrt[c]*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^2*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])) + (5*(-b^2 + 4*a*c)^(1/4)*e^(3/2)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTan[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(9/4)*(a + b*x + c*x^2)^(1/4)) - (5*(-b^2 + 4*a*c)^(1/4)*e^(3/2)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*ArcTanh[((-b^2 + 4*a*c)^(1/4)*Sqrt[e]*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(Sqrt[2]*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))])/(4*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(9/4)*(a + b*x + c*x^2)^(1/4)) - (c^(1/4)*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticE[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(Sqrt[2]*(b^2 - 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) + (c^(1/4)*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*Sqrt[(b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])^2)]*(1 + (2*Sqrt[c]*Sqrt[a + b*x + c*x^2])/Sqrt[b^2 - 4*a*c])*EllipticF[2*ArcTan[(Sqrt[2]*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)], 1/2])/(2*Sqrt[2]*(b^2 - 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) - (5*Sqrt[-b^2 + 4*a*c]*e*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[-(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*Sqrt[c]*(c*d^2 - b*d*e + a*e^2)^(5/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (5*Sqrt[-b^2 + 4*a*c]*e*(2*c*d - b*e)^2*Sqrt[(b + 2*c*x)^2/(b^2 - 4*a*c)]*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*EllipticPi[(Sqrt[-b^2 + 4*a*c]*e)/(2*Sqrt[c]*Sqrt[c*d^2 - b*d*e + a*e^2]), ArcSin[(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)], -1])/(4*Sqrt[2]*Sqrt[c]*(c*d^2 - b*d*e + a*e^2)^(5/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))","A",21,19,22,0.8636,1,"{740, 834, 843, 623, 305, 220, 1196, 749, 748, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
2548,1,239,0,0.1536446,"\int \frac{1}{(d+e x)^{3/2} \sqrt[4]{a+b x+c x^2}} \, dx","Int[1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(1/4)),x]","\frac{2 \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \sqrt[4]{\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{\sqrt{d+e x} \sqrt[4]{a+b x+c x^2} \left(e \sqrt{b^2-4 a c}-b e+2 c d\right)}","\frac{2 \left(-\sqrt{b^2-4 a c}+b+2 c x\right) \sqrt[4]{\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{\sqrt{d+e x} \sqrt[4]{a+b x+c x^2} \left(e \sqrt{b^2-4 a c}-b e+2 c d\right)}",1,"(2*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*(((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)))^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, (-4*c*Sqrt[b^2 - 4*a*c]*(d + e*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))])/((2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)*Sqrt[d + e*x]*(a + b*x + c*x^2)^(1/4))","A",1,1,24,0.04167,1,"{726}"
2549,1,485,0,0.38575,"\int (d+e x)^m \left(a+b x+c x^2\right)^4 \, dx","Int[(d + e*x)^m*(a + b*x + c*x^2)^4,x]","\frac{(d+e x)^{m+5} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{e^9 (m+5)}+\frac{2 (d+e x)^{m+3} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (m+3)}-\frac{4 (2 c d-b e) (d+e x)^{m+4} \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (m+4)}-\frac{4 c (2 c d-b e) (d+e x)^{m+6} \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (m+6)}+\frac{2 c^2 (d+e x)^{m+7} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (m+7)}+\frac{(d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^4}{e^9 (m+1)}-\frac{4 (2 c d-b e) (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)^3}{e^9 (m+2)}-\frac{4 c^3 (2 c d-b e) (d+e x)^{m+8}}{e^9 (m+8)}+\frac{c^4 (d+e x)^{m+9}}{e^9 (m+9)}","\frac{(d+e x)^{m+5} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{e^9 (m+5)}+\frac{2 (d+e x)^{m+3} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (m+3)}-\frac{4 (2 c d-b e) (d+e x)^{m+4} \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (m+4)}-\frac{4 c (2 c d-b e) (d+e x)^{m+6} \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^9 (m+6)}+\frac{2 c^2 (d+e x)^{m+7} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^9 (m+7)}+\frac{(d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^4}{e^9 (m+1)}-\frac{4 (2 c d-b e) (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)^3}{e^9 (m+2)}-\frac{4 c^3 (2 c d-b e) (d+e x)^{m+8}}{e^9 (m+8)}+\frac{c^4 (d+e x)^{m+9}}{e^9 (m+9)}",1,"((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^(1 + m))/(e^9*(1 + m)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(2 + m))/(e^9*(2 + m)) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(3 + m))/(e^9*(3 + m)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(4 + m))/(e^9*(4 + m)) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(5 + m))/(e^9*(5 + m)) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(6 + m))/(e^9*(6 + m)) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(7 + m))/(e^9*(7 + m)) - (4*c^3*(2*c*d - b*e)*(d + e*x)^(8 + m))/(e^9*(8 + m)) + (c^4*(d + e*x)^(9 + m))/(e^9*(9 + m))","A",2,1,20,0.05000,1,"{698}"
2550,1,305,0,0.2115113,"\int (d+e x)^m \left(a+b x+c x^2\right)^3 \, dx","Int[(d + e*x)^m*(a + b*x + c*x^2)^3,x]","\frac{3 (d+e x)^{m+3} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (m+3)}-\frac{(2 c d-b e) (d+e x)^{m+4} \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^7 (m+4)}+\frac{3 c (d+e x)^{m+5} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (m+5)}+\frac{(d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^3}{e^7 (m+1)}-\frac{3 (2 c d-b e) (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)^2}{e^7 (m+2)}-\frac{3 c^2 (2 c d-b e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{c^3 (d+e x)^{m+7}}{e^7 (m+7)}","\frac{3 (d+e x)^{m+3} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (m+3)}-\frac{(2 c d-b e) (d+e x)^{m+4} \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^7 (m+4)}+\frac{3 c (d+e x)^{m+5} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^7 (m+5)}+\frac{(d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^3}{e^7 (m+1)}-\frac{3 (2 c d-b e) (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)^2}{e^7 (m+2)}-\frac{3 c^2 (2 c d-b e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{c^3 (d+e x)^{m+7}}{e^7 (m+7)}",1,"((c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(3 + m))/(e^7*(3 + m)) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (3*c^2*(2*c*d - b*e)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^7*(7 + m))","A",2,1,20,0.05000,1,"{698}"
2551,1,178,0,0.1137835,"\int (d+e x)^m \left(a+b x+c x^2\right)^2 \, dx","Int[(d + e*x)^m*(a + b*x + c*x^2)^2,x]","\frac{(d+e x)^{m+3} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^5 (m+3)}+\frac{(d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^5 (m+1)}-\frac{2 (2 c d-b e) (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)}{e^5 (m+2)}-\frac{2 c (2 c d-b e) (d+e x)^{m+4}}{e^5 (m+4)}+\frac{c^2 (d+e x)^{m+5}}{e^5 (m+5)}","\frac{(d+e x)^{m+3} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^5 (m+3)}+\frac{(d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^5 (m+1)}-\frac{2 (2 c d-b e) (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)}{e^5 (m+2)}-\frac{2 c (2 c d-b e) (d+e x)^{m+4}}{e^5 (m+4)}+\frac{c^2 (d+e x)^{m+5}}{e^5 (m+5)}",1,"((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(1 + m))/(e^5*(1 + m)) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(2 + m))/(e^5*(2 + m)) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(3 + m))/(e^5*(3 + m)) - (2*c*(2*c*d - b*e)*(d + e*x)^(4 + m))/(e^5*(4 + m)) + (c^2*(d + e*x)^(5 + m))/(e^5*(5 + m))","A",2,1,20,0.05000,1,"{698}"
2552,1,82,0,0.0447129,"\int (d+e x)^m \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^m*(a + b*x + c*x^2),x]","\frac{(d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^3 (m+1)}-\frac{(2 c d-b e) (d+e x)^{m+2}}{e^3 (m+2)}+\frac{c (d+e x)^{m+3}}{e^3 (m+3)}","\frac{(d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^3 (m+1)}-\frac{(2 c d-b e) (d+e x)^{m+2}}{e^3 (m+2)}+\frac{c (d+e x)^{m+3}}{e^3 (m+3)}",1,"((c*d^2 - b*d*e + a*e^2)*(d + e*x)^(1 + m))/(e^3*(1 + m)) - ((2*c*d - b*e)*(d + e*x)^(2 + m))/(e^3*(2 + m)) + (c*(d + e*x)^(3 + m))/(e^3*(3 + m))","A",2,1,18,0.05556,1,"{698}"
2553,1,191,0,0.3835646,"\int \frac{(d+e x)^m}{a+b x+c x^2} \, dx","Int[(d + e*x)^m/(a + b*x + c*x^2),x]","\frac{2 c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{2 c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}","\frac{2 c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{2 c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}",1,"(-2*c*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + m)) + (2*c*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(1 + m))","A",4,2,20,0.1000,1,"{711, 68}"
2554,1,425,0,1.0687295,"\int \frac{(d+e x)^m}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)^m/(a + b*x + c*x^2)^2,x]","\frac{c (d+e x)^{m+1} \left(-2 c e \left(d m \sqrt{b^2-4 a c}-2 a e (1-m)+2 b d\right)+b e^2 m \left(\sqrt{b^2-4 a c}+b\right)+4 c^2 d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(b^2-4 a c\right)^{3/2} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}-\frac{c (d+e x)^{m+1} \left(\frac{-4 c e (b d-a e (1-m))+b^2 e^2 m+4 c^2 d^2}{\sqrt{b^2-4 a c}}+e m (2 c d-b e)\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(b^2-4 a c\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \left(a e^2-b d e+c d^2\right)}-\frac{(d+e x)^{m+1} \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) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}","\frac{c (d+e x)^{m+1} \left(-2 c e \left(d m \sqrt{b^2-4 a c}-2 a e (1-m)+2 b d\right)+b e^2 m \left(\sqrt{b^2-4 a c}+b\right)+4 c^2 d^2\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(b^2-4 a c\right)^{3/2} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}-\frac{c (d+e x)^{m+1} \left(\frac{-4 c e (b d-a e (1-m))+b^2 e^2 m+4 c^2 d^2}{\sqrt{b^2-4 a c}}+e m (2 c d-b e)\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(b^2-4 a c\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \left(a e^2-b d e+c d^2\right)}-\frac{(d+e x)^{m+1} \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) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}",1,"-(((d + e*x)^(1 + m)*(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)*(a + b*x + c*x^2))) + (c*(4*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2*m - 2*c*e*(2*b*d - 2*a*e*(1 - m) + Sqrt[b^2 - 4*a*c]*d*m))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/((b^2 - 4*a*c)^(3/2)*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)*(1 + m)) - (c*(e*(2*c*d - b*e)*m + (4*c^2*d^2 - 4*c*e*(b*d - a*e*(1 - m)) + b^2*e^2*m)/Sqrt[b^2 - 4*a*c])*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/((b^2 - 4*a*c)*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)*(1 + m))","A",5,3,20,0.1500,1,"{740, 830, 68}"
2555,1,189,0,0.2523475,"\int (d+e x)^m \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(d + e*x)^m*(a + b*x + c*x^2)^(5/2),x]","\frac{\left(a+b x+c x^2\right)^{5/2} (d+e x)^{m+1} F_1\left(m+1;-\frac{5}{2},-\frac{5}{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) \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{5/2} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{5/2}}","\frac{\left(a+b x+c x^2\right)^{5/2} (d+e x)^{m+1} F_1\left(m+1;-\frac{5}{2},-\frac{5}{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) \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{5/2} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{5/2}}",1,"((d + e*x)^(1 + m)*(a + b*x + c*x^2)^(5/2)*AppellF1[1 + m, -5/2, -5/2, 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)*(1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))^(5/2)*(1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))^(5/2))","A",2,2,22,0.09091,1,"{759, 133}"
2556,1,189,0,0.1060631,"\int (d+e x)^m \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(d + e*x)^m*(a + b*x + c*x^2)^(3/2),x]","\frac{\left(a+b x+c x^2\right)^{3/2} (d+e x)^{m+1} F_1\left(m+1;-\frac{3}{2},-\frac{3}{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) \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{3/2} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{3/2}}","\frac{\left(a+b x+c x^2\right)^{3/2} (d+e x)^{m+1} F_1\left(m+1;-\frac{3}{2},-\frac{3}{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) \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{3/2} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{3/2}}",1,"((d + e*x)^(1 + m)*(a + b*x + c*x^2)^(3/2)*AppellF1[1 + m, -3/2, -3/2, 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)*(1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))^(3/2)*(1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))^(3/2))","A",2,2,22,0.09091,1,"{759, 133}"
2557,1,189,0,0.1066707,"\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}"
2558,1,189,0,0.1065615,"\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}"
2559,1,189,0,0.1046564,"\int \frac{(d+e x)^m}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x)^m/(a + b*x + c*x^2)^(3/2),x]","\frac{(d+e x)^{m+1} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{3/2} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{3/2} F_1\left(m+1;\frac{3}{2},\frac{3}{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) \left(a+b x+c x^2\right)^{3/2}}","\frac{(d+e x)^{m+1} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{3/2} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{3/2} F_1\left(m+1;\frac{3}{2},\frac{3}{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) \left(a+b x+c x^2\right)^{3/2}}",1,"((d + e*x)^(1 + m)*(1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))^(3/2)*(1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))^(3/2)*AppellF1[1 + m, 3/2, 3/2, 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)*(a + b*x + c*x^2)^(3/2))","A",2,2,22,0.09091,1,"{759, 133}"
2560,1,189,0,0.1101784,"\int \frac{(d+e x)^m}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x)^m/(a + b*x + c*x^2)^(5/2),x]","\frac{(d+e x)^{m+1} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{5/2} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{5/2} F_1\left(m+1;\frac{5}{2},\frac{5}{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) \left(a+b x+c x^2\right)^{5/2}}","\frac{(d+e x)^{m+1} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}\right)^{5/2} \left(1-\frac{2 c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}\right)^{5/2} F_1\left(m+1;\frac{5}{2},\frac{5}{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) \left(a+b x+c x^2\right)^{5/2}}",1,"((d + e*x)^(1 + m)*(1 - (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e))^(5/2)*(1 - (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e))^(5/2)*AppellF1[1 + m, 5/2, 5/2, 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)*(a + b*x + c*x^2)^(5/2))","A",2,2,22,0.09091,1,"{759, 133}"
2561,1,137,0,0.2776542,"\int (d x)^m \left(a+b x+c x^2\right)^p \, dx","Int[(d*x)^m*(a + b*x + c*x^2)^p,x]","\frac{(d x)^{m+1} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(m+1;-p,-p;m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1)}","\frac{(d x)^{m+1} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(m+1;-p,-p;m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1)}",1,"((d*x)^(1 + m)*(a + b*x + c*x^2)^p*AppellF1[1 + m, -p, -p, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,18,0.1111,1,"{759, 133}"
2562,1,187,0,0.1104154,"\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}"
2563,1,327,0,0.4234521,"\int (d+e x)^3 \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^p,x]","-\frac{2^{p-1} (2 c d-b e) \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(-2 c e (3 a e+b d (2 p+3))+b^2 e^2 (p+3)+2 c^2 d^2 (2 p+3)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^3 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{e \left(a+b x+c x^2\right)^{p+1} \left(-2 c (2 p+3) \left(c d^2 (2 p+5)-e (a e+b d (p+2))\right)-2 c e (p+1) (p+3) x (2 c d-b e)+b e (p+2) (p+3) (2 c d-b e)\right)}{4 c^3 (p+1) (p+2) (2 p+3)}+\frac{e (d+e x)^2 \left(a+b x+c x^2\right)^{p+1}}{2 c (p+2)}","-\frac{2^{p-1} (2 c d-b e) \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(-2 c e (3 a e+b d (2 p+3))+b^2 e^2 (p+3)+2 c^2 d^2 (2 p+3)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^3 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{e \left(a+b x+c x^2\right)^{p+1} \left(-2 c (2 p+3) \left(c d^2 (2 p+5)-e (a e+b d (p+2))\right)-2 c e (p+1) (p+3) x (2 c d-b e)+b e (p+2) (p+3) (2 c d-b e)\right)}{4 c^3 (p+1) (p+2) (2 p+3)}+\frac{e (d+e x)^2 \left(a+b x+c x^2\right)^{p+1}}{2 c (p+2)}",1,"(e*(d + e*x)^2*(a + b*x + c*x^2)^(1 + p))/(2*c*(2 + p)) - (e*(b*e*(2*c*d - b*e)*(2 + p)*(3 + p) - 2*c*(3 + 2*p)*(c*d^2*(5 + 2*p) - e*(a*e + b*d*(2 + p))) - 2*c*e*(2*c*d - b*e)*(1 + p)*(3 + p)*x)*(a + b*x + c*x^2)^(1 + p))/(4*c^3*(1 + p)*(2 + p)*(3 + 2*p)) - (2^(-1 + p)*(2*c*d - b*e)*(b^2*e^2*(3 + p) + 2*c^2*d^2*(3 + 2*p) - 2*c*e*(3*a*e + b*d*(3 + 2*p)))*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c^3*Sqrt[b^2 - 4*a*c]*(1 + p)*(3 + 2*p))","A",3,3,20,0.1500,1,"{742, 779, 624}"
2564,1,248,0,0.2093723,"\int (d+e x)^2 \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^2*(a + b*x + c*x^2)^p,x]","-\frac{2^p \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(-2 c e (a e+b d (2 p+3))+b^2 e^2 (p+2)+2 c^2 d^2 (2 p+3)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^2 (p+1) (2 p+3) \sqrt{b^2-4 a c}}+\frac{e (p+2) (2 c d-b e) \left(a+b x+c x^2\right)^{p+1}}{2 c^2 (p+1) (2 p+3)}+\frac{e (d+e x) \left(a+b x+c x^2\right)^{p+1}}{c (2 p+3)}","-\frac{2^p \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(-2 c e (a e+b d (2 p+3))+b^2 e^2 (p+2)+2 c^2 d^2 (2 p+3)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^2 (p+1) (2 p+3) \sqrt{b^2-4 a c}}+\frac{e (p+2) (2 c d-b e) \left(a+b x+c x^2\right)^{p+1}}{2 c^2 (p+1) (2 p+3)}+\frac{e (d+e x) \left(a+b x+c x^2\right)^{p+1}}{c (2 p+3)}",1,"(e*(2*c*d - b*e)*(2 + p)*(a + b*x + c*x^2)^(1 + p))/(2*c^2*(1 + p)*(3 + 2*p)) + (e*(d + e*x)*(a + b*x + c*x^2)^(1 + p))/(c*(3 + 2*p)) - (2^p*(b^2*e^2*(2 + p) + 2*c^2*d^2*(3 + 2*p) - 2*c*e*(a*e + b*d*(3 + 2*p)))*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c^2*Sqrt[b^2 - 4*a*c]*(1 + p)*(3 + 2*p))","A",3,3,20,0.1500,1,"{742, 640, 624}"
2565,1,160,0,0.0451696,"\int (d+e x) \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)*(a + b*x + c*x^2)^p,x]","\frac{e \left(a+b x+c x^2\right)^{p+1}}{2 c (p+1)}-\frac{2^p (2 c d-b e) \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c (p+1) \sqrt{b^2-4 a c}}","\frac{e \left(a+b x+c x^2\right)^{p+1}}{2 c (p+1)}-\frac{2^p (2 c d-b e) \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c (p+1) \sqrt{b^2-4 a c}}",1,"(e*(a + b*x + c*x^2)^(1 + p))/(2*c*(1 + p)) - (2^p*(2*c*d - b*e)*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c*Sqrt[b^2 - 4*a*c]*(1 + p))","A",2,2,18,0.1111,1,"{640, 624}"
2566,1,122,0,0.0149388,"\int \left(a+b x+c x^2\right)^p \, dx","Int[(a + b*x + c*x^2)^p,x]","-\frac{2^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{(p+1) \sqrt{b^2-4 a c}}","-\frac{2^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{(p+1) \sqrt{b^2-4 a c}}",1,"-((2^(1 + p)*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(1 + p)))","A",1,1,12,0.08333,1,"{624}"
2567,1,184,0,0.1844561,"\int \frac{\left(a+b x+c x^2\right)^p}{d+e x} \, dx","Int[(a + b*x + c*x^2)^p/(d + e*x),x]","\frac{2^{2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} F_1\left(-2 p;-p,-p;1-2 p;\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{e p}","\frac{2^{2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} F_1\left(-2 p;-p,-p;1-2 p;\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{e p}",1,"(2^(-1 + 2*p)*(a + b*x + c*x^2)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, (2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)/(2*c*(d + e*x)), (2*d - ((b + Sqrt[b^2 - 4*a*c])*e)/c)/(2*(d + e*x))])/(e*p*((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^p*((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^p)","A",2,2,20,0.1000,1,"{758, 133}"
2568,1,196,0,0.1092191,"\int \frac{\left(a+b x+c x^2\right)^p}{(d+e x)^2} \, dx","Int[(a + b*x + c*x^2)^p/(d + e*x)^2,x]","-\frac{4^p \left(a+b x+c x^2\right)^p \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} F_1\left(1-2 p;-p,-p;2 (1-p);\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{e (1-2 p) (d+e x)}","-\frac{4^p \left(a+b x+c x^2\right)^p \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} F_1\left(1-2 p;-p,-p;2 (1-p);\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{e (1-2 p) (d+e x)}",1,"-((4^p*(a + b*x + c*x^2)^p*AppellF1[1 - 2*p, -p, -p, 2*(1 - p), (2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)/(2*c*(d + e*x)), (2*d - ((b + Sqrt[b^2 - 4*a*c])*e)/c)/(2*(d + e*x))])/(e*(1 - 2*p)*((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^p*((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^p*(d + e*x)))","A",2,2,20,0.1000,1,"{758, 133}"
2569,1,200,0,0.1140279,"\int \frac{\left(a+b x+c x^2\right)^p}{(d+e x)^3} \, dx","Int[(a + b*x + c*x^2)^p/(d + e*x)^3,x]","-\frac{2^{2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} F_1\left(2 (1-p);-p,-p;3-2 p;\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{e (1-p) (d+e x)^2}","-\frac{2^{2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} \left(\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{c (d+e x)}\right)^{-p} F_1\left(2 (1-p);-p,-p;3-2 p;\frac{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}{2 c (d+e x)},\frac{2 d-\frac{\left(b+\sqrt{b^2-4 a c}\right) e}{c}}{2 (d+e x)}\right)}{e (1-p) (d+e x)^2}",1,"-((2^(-1 + 2*p)*(a + b*x + c*x^2)^p*AppellF1[2*(1 - p), -p, -p, 3 - 2*p, (2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)/(2*c*(d + e*x)), (2*d - ((b + Sqrt[b^2 - 4*a*c])*e)/c)/(2*(d + e*x))])/(e*(1 - p)*((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^p*((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(c*(d + e*x)))^p*(d + e*x)^2))","A",2,2,20,0.1000,1,"{758, 133}"
2570,1,185,0,0.1502116,"\int (d+e x)^{3/2} \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^(3/2)*(a + b*x + c*x^2)^p,x]","\frac{2 (d+e x)^{5/2} \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(\frac{5}{2};-p,-p;\frac{7}{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)}{5 e}","\frac{2 (d+e x)^{5/2} \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(\frac{5}{2};-p,-p;\frac{7}{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)}{5 e}",1,"(2*(d + e*x)^(5/2)*(a + b*x + c*x^2)^p*AppellF1[5/2, -p, -p, 7/2, (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)])/(5*e*(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",2,2,22,0.09091,1,"{759, 133}"
2571,1,185,0,0.1062695,"\int \sqrt{d+e x} \left(a+b x+c x^2\right)^p \, dx","Int[Sqrt[d + e*x]*(a + b*x + c*x^2)^p,x]","\frac{2 (d+e x)^{3/2} \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(\frac{3}{2};-p,-p;\frac{5}{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)}{3 e}","\frac{2 (d+e x)^{3/2} \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(\frac{3}{2};-p,-p;\frac{5}{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)}{3 e}",1,"(2*(d + e*x)^(3/2)*(a + b*x + c*x^2)^p*AppellF1[3/2, -p, -p, 5/2, (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)])/(3*e*(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",2,2,22,0.09091,1,"{759, 133}"
2572,1,183,0,0.1045999,"\int \frac{\left(a+b x+c x^2\right)^p}{\sqrt{d+e x}} \, dx","Int[(a + b*x + c*x^2)^p/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \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(\frac{1}{2};-p,-p;\frac{3}{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}","\frac{2 \sqrt{d+e x} \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(\frac{1}{2};-p,-p;\frac{3}{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}",1,"(2*Sqrt[d + e*x]*(a + b*x + c*x^2)^p*AppellF1[1/2, -p, -p, 3/2, (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 - (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",2,2,22,0.09091,1,"{759, 133}"
2573,1,183,0,0.1046663,"\int \frac{\left(a+b x+c x^2\right)^p}{(d+e x)^{3/2}} \, dx","Int[(a + b*x + c*x^2)^p/(d + e*x)^(3/2),x]","-\frac{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(-\frac{1}{2};-p,-p;\frac{1}{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 \sqrt{d+e x}}","-\frac{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(-\frac{1}{2};-p,-p;\frac{1}{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 \sqrt{d+e x}}",1,"(-2*(a + b*x + c*x^2)^p*AppellF1[-1/2, -p, -p, 1/2, (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*Sqrt[d + e*x]*(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",2,2,22,0.09091,1,"{759, 133}"
2574,1,195,0,0.1052123,"\int (d+e x)^{-2 p} \left(a+b x+c x^2\right)^p \, dx","Int[(a + b*x + c*x^2)^p/(d + e*x)^(2*p),x]","\frac{(d+e x)^{1-2 p} \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(1-2 p;-p,-p;2-2 p;\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 (1-2 p)}","\frac{(d+e x)^{1-2 p} \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(1-2 p;-p,-p;2-2 p;\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 (1-2 p)}",1,"((d + e*x)^(1 - 2*p)*(a + b*x + c*x^2)^p*AppellF1[1 - 2*p, -p, -p, 2 - 2*p, (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 - 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",2,2,22,0.09091,1,"{759, 133}"
2575,1,190,0,0.1059361,"\int (d+e x)^{-1-2 p} \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p,x]","-\frac{(d+e x)^{-2 p} \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(-2 p;-p,-p;1-2 p;\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 e p}","-\frac{(d+e x)^{-2 p} \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(-2 p;-p,-p;1-2 p;\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 e p}",1,"-((a + b*x + c*x^2)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, (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*e*p*(d + e*x)^(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",2,2,24,0.08333,1,"{759, 133}"
2576,1,248,0,0.1218298,"\int (d+e x)^{-2-2 p} \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^(-2 - 2*p)*(a + b*x + c*x^2)^p,x]","\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{(2 p+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}","\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{(2 p+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}",1,"((b - Sqrt[b^2 - 4*a*c] + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (-4*c*Sqrt[b^2 - 4*a*c]*(d + e*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))])/((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + 2*p)*(((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)))^p)","A",1,1,24,0.04167,1,"{726}"
2577,1,332,0,0.1357401,"\int (d+e x)^{-3-2 p} \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^(-3 - 2*p)*(a + b*x + c*x^2)^p,x]","\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (2 c d-b e) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{2 (2 p+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}-\frac{e (d+e x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1}}{2 (p+1) \left(a e^2-b d e+c d^2\right)}","\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (2 c d-b e) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{2 (2 p+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}-\frac{e (d+e x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1}}{2 (p+1) \left(a e^2-b d e+c d^2\right)}",1,"-(e*(a + b*x + c*x^2)^(1 + p))/(2*(c*d^2 - b*d*e + a*e^2)*(1 + p)*(d + e*x)^(2*(1 + p))) + ((2*c*d - b*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (-4*c*Sqrt[b^2 - 4*a*c]*(d + e*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))])/(2*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)*(1 + 2*p)*(((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)))^p)","A",2,2,24,0.08333,1,"{730, 726}"
2578,1,442,0,0.3525568,"\int (d+e x)^{-4-2 p} \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^(-4 - 2*p)*(a + b*x + c*x^2)^p,x]","\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(-2 c e (a e+b d (2 p+3))+b^2 e^2 (p+2)+2 c^2 d^2 (2 p+3)\right) \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{2 (2 p+1) (2 p+3) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{e (d+e x)^{-2 p-3} \left(a+b x+c x^2\right)^{p+1}}{(2 p+3) \left(a e^2-b d e+c d^2\right)}-\frac{e (p+2) (2 c d-b e) (d+e x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1}}{2 (p+1) (2 p+3) \left(a e^2-b d e+c d^2\right)^2}","\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(-2 c e (a e+b d (2 p+3))+b^2 e^2 (p+2)+2 c^2 d^2 (2 p+3)\right) \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{2 (2 p+1) (2 p+3) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{e (d+e x)^{-2 p-3} \left(a+b x+c x^2\right)^{p+1}}{(2 p+3) \left(a e^2-b d e+c d^2\right)}-\frac{e (p+2) (2 c d-b e) (d+e x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1}}{2 (p+1) (2 p+3) \left(a e^2-b d e+c d^2\right)^2}",1,"-((e*(d + e*x)^(-3 - 2*p)*(a + b*x + c*x^2)^(1 + p))/((c*d^2 - b*d*e + a*e^2)*(3 + 2*p))) - (e*(2*c*d - b*e)*(2 + p)*(a + b*x + c*x^2)^(1 + p))/(2*(c*d^2 - b*d*e + a*e^2)^2*(1 + p)*(3 + 2*p)*(d + e*x)^(2*(1 + p))) + ((b^2*e^2*(2 + p) + 2*c^2*d^2*(3 + 2*p) - 2*c*e*(a*e + b*d*(3 + 2*p)))*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (-4*c*Sqrt[b^2 - 4*a*c]*(d + e*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))])/(2*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)^2*(1 + 2*p)*(3 + 2*p)*(((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)))^p)","A",3,3,24,0.1250,1,"{744, 806, 726}"
2579,1,577,0,0.8677371,"\int (d+e x)^{-5-2 p} \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^(-5 - 2*p)*(a + b*x + c*x^2)^p,x]","\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (2 c d-b e) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(-2 c e (3 a e+b d (2 p+3))+b^2 e^2 (p+3)+2 c^2 d^2 (2 p+3)\right) \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{4 (2 p+1) (2 p+3) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)^3}-\frac{e (d+e x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1} \left(-2 c e \left(a e (2 p+3)+b d \left(2 p^2+8 p+9\right)\right)+b^2 e^2 \left(p^2+5 p+6\right)+2 c^2 d^2 \left(2 p^2+8 p+9\right)\right)}{4 (p+1) (p+2) (2 p+3) \left(a e^2-b d e+c d^2\right)^3}-\frac{e (p+3) (2 c d-b e) (d+e x)^{-2 p-3} \left(a+b x+c x^2\right)^{p+1}}{2 (p+2) (2 p+3) \left(a e^2-b d e+c d^2\right)^2}-\frac{e (d+e x)^{-2 (p+2)} \left(a+b x+c x^2\right)^{p+1}}{2 (p+2) \left(a e^2-b d e+c d^2\right)}","\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (2 c d-b e) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(-2 c e (3 a e+b d (2 p+3))+b^2 e^2 (p+3)+2 c^2 d^2 (2 p+3)\right) \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{4 (2 p+1) (2 p+3) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)^3}-\frac{e (d+e x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1} \left(-2 c e \left(a e (2 p+3)+b d \left(2 p^2+8 p+9\right)\right)+b^2 e^2 \left(p^2+5 p+6\right)+2 c^2 d^2 \left(2 p^2+8 p+9\right)\right)}{4 (p+1) (p+2) (2 p+3) \left(a e^2-b d e+c d^2\right)^3}-\frac{e (p+3) (2 c d-b e) (d+e x)^{-2 p-3} \left(a+b x+c x^2\right)^{p+1}}{2 (p+2) (2 p+3) \left(a e^2-b d e+c d^2\right)^2}-\frac{e (d+e x)^{-2 (p+2)} \left(a+b x+c x^2\right)^{p+1}}{2 (p+2) \left(a e^2-b d e+c d^2\right)}",1,"-(e*(2*c*d - b*e)*(3 + p)*(d + e*x)^(-3 - 2*p)*(a + b*x + c*x^2)^(1 + p))/(2*(c*d^2 - b*d*e + a*e^2)^2*(2 + p)*(3 + 2*p)) - (e*(b^2*e^2*(6 + 5*p + p^2) + 2*c^2*d^2*(9 + 8*p + 2*p^2) - 2*c*e*(a*e*(3 + 2*p) + b*d*(9 + 8*p + 2*p^2)))*(a + b*x + c*x^2)^(1 + p))/(4*(c*d^2 - b*d*e + a*e^2)^3*(1 + p)*(2 + p)*(3 + 2*p)*(d + e*x)^(2*(1 + p))) - (e*(a + b*x + c*x^2)^(1 + p))/(2*(c*d^2 - b*d*e + a*e^2)*(2 + p)*(d + e*x)^(2*(2 + p))) + ((2*c*d - b*e)*(b^2*e^2*(3 + p) + 2*c^2*d^2*(3 + 2*p) - 2*c*e*(3*a*e + b*d*(3 + 2*p)))*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (-4*c*Sqrt[b^2 - 4*a*c]*(d + e*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))])/(4*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)^3*(1 + 2*p)*(3 + 2*p)*(((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)))^p)","A",4,4,24,0.1667,1,"{744, 836, 806, 726}"
2580,1,809,0,1.7199562,"\int (d+e x)^{-6-2 p} \left(a+b x+c x^2\right)^p \, dx","Int[(d + e*x)^(-6 - 2*p)*(a + b*x + c*x^2)^p,x]","-\frac{e \left(c x^2+b x+a\right)^{p+1} (d+e x)^{-2 p-5}}{\left(c d^2-b e d+a e^2\right) (2 p+5)}-\frac{e \left(2 c^2 \left(2 p^2+11 p+18\right) d^2+b^2 e^2 \left(p^2+7 p+12\right)-2 c e \left(3 a e (p+2)+b d \left(2 p^2+11 p+18\right)\right)\right) \left(c x^2+b x+a\right)^{p+1} (d+e x)^{-2 p-3}}{2 \left(c d^2-b e d+a e^2\right)^3 (p+2) (2 p+3) (2 p+5)}+\frac{\left(4 c^4 \left(4 p^2+16 p+15\right) d^4-8 c^3 e (2 p+5) (3 a e+b d (2 p+3)) d^2+b^4 e^4 \left(p^2+7 p+12\right)-4 b^2 c e^3 (p+3) (3 a e+b d (2 p+5))+12 c^2 e^2 \left(b^2 \left(2 p^2+9 p+10\right) d^2+2 a b e (2 p+5) d+a^2 e^2\right)\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right) \left(\frac{\left(2 c d-\left(b-\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(c x^2+b x+a\right)^p \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right) (d+e x)^{-2 p-1}}{4 \left(2 c d-\left(b-\sqrt{b^2-4 a c}\right) e\right) \left(c d^2-b e d+a e^2\right)^4 (2 p+1) (2 p+3) (2 p+5)}-\frac{e (2 c d-b e) (p+3) \left(2 c^2 \left(2 p^2+7 p+8\right) d^2+b^2 e^2 \left(p^2+6 p+8\right)-2 c e \left(a e (5 p+8)+b d \left(2 p^2+7 p+8\right)\right)\right) \left(c x^2+b x+a\right)^{p+1} (d+e x)^{-2 (p+1)}}{4 \left(c d^2-b e d+a e^2\right)^4 (p+1) (p+2) (2 p+3) (2 p+5)}-\frac{e (2 c d-b e) (p+4) \left(c x^2+b x+a\right)^{p+1} (d+e x)^{-2 (p+2)}}{2 \left(c d^2-b e d+a e^2\right)^2 (p+2) (2 p+5)}","-\frac{e \left(c x^2+b x+a\right)^{p+1} (d+e x)^{-2 p-5}}{\left(c d^2-b e d+a e^2\right) (2 p+5)}-\frac{e \left(2 c^2 \left(2 p^2+11 p+18\right) d^2+b^2 e^2 \left(p^2+7 p+12\right)-2 c e \left(3 a e (p+2)+b d \left(2 p^2+11 p+18\right)\right)\right) \left(c x^2+b x+a\right)^{p+1} (d+e x)^{-2 p-3}}{2 \left(c d^2-b e d+a e^2\right)^3 (p+2) (2 p+3) (2 p+5)}+\frac{\left(4 c^4 \left(4 p^2+16 p+15\right) d^4-8 c^3 e (2 p+5) (3 a e+b d (2 p+3)) d^2+b^4 e^4 \left(p^2+7 p+12\right)-4 b^2 c e^3 (p+3) (3 a e+b d (2 p+5))+12 c^2 e^2 \left(b^2 \left(2 p^2+9 p+10\right) d^2+2 a b e (2 p+5) d+a^2 e^2\right)\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right) \left(\frac{\left(2 c d-\left(b-\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(c x^2+b x+a\right)^p \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right) (d+e x)^{-2 p-1}}{4 \left(2 c d-\left(b-\sqrt{b^2-4 a c}\right) e\right) \left(c d^2-b e d+a e^2\right)^4 (2 p+1) (2 p+3) (2 p+5)}-\frac{e (2 c d-b e) (p+3) \left(2 c^2 \left(2 p^2+7 p+8\right) d^2+b^2 e^2 \left(p^2+6 p+8\right)-2 c e \left(a e (5 p+8)+b d \left(2 p^2+7 p+8\right)\right)\right) \left(c x^2+b x+a\right)^{p+1} (d+e x)^{-2 (p+1)}}{4 \left(c d^2-b e d+a e^2\right)^4 (p+1) (p+2) (2 p+3) (2 p+5)}-\frac{e (2 c d-b e) (p+4) \left(c x^2+b x+a\right)^{p+1} (d+e x)^{-2 (p+2)}}{2 \left(c d^2-b e d+a e^2\right)^2 (p+2) (2 p+5)}",1,"-((e*(d + e*x)^(-5 - 2*p)*(a + b*x + c*x^2)^(1 + p))/((c*d^2 - b*d*e + a*e^2)*(5 + 2*p))) - (e*(b^2*e^2*(12 + 7*p + p^2) + 2*c^2*d^2*(18 + 11*p + 2*p^2) - 2*c*e*(3*a*e*(2 + p) + b*d*(18 + 11*p + 2*p^2)))*(d + e*x)^(-3 - 2*p)*(a + b*x + c*x^2)^(1 + p))/(2*(c*d^2 - b*d*e + a*e^2)^3*(2 + p)*(3 + 2*p)*(5 + 2*p)) - (e*(2*c*d - b*e)*(3 + p)*(b^2*e^2*(8 + 6*p + p^2) + 2*c^2*d^2*(8 + 7*p + 2*p^2) - 2*c*e*(a*e*(8 + 5*p) + b*d*(8 + 7*p + 2*p^2)))*(a + b*x + c*x^2)^(1 + p))/(4*(c*d^2 - b*d*e + a*e^2)^4*(1 + p)*(2 + p)*(3 + 2*p)*(5 + 2*p)*(d + e*x)^(2*(1 + p))) - (e*(2*c*d - b*e)*(4 + p)*(a + b*x + c*x^2)^(1 + p))/(2*(c*d^2 - b*d*e + a*e^2)^2*(2 + p)*(5 + 2*p)*(d + e*x)^(2*(2 + p))) + ((b^4*e^4*(12 + 7*p + p^2) + 4*c^4*d^4*(15 + 16*p + 4*p^2) - 8*c^3*d^2*e*(5 + 2*p)*(3*a*e + b*d*(3 + 2*p)) - 4*b^2*c*e^3*(3 + p)*(3*a*e + b*d*(5 + 2*p)) + 12*c^2*e^2*(a^2*e^2 + 2*a*b*d*e*(5 + 2*p) + b^2*d^2*(10 + 9*p + 2*p^2)))*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (-4*c*Sqrt[b^2 - 4*a*c]*(d + e*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))])/(4*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)^4*(1 + 2*p)*(3 + 2*p)*(5 + 2*p)*(((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)))^p)","A",5,4,24,0.1667,1,"{744, 836, 806, 726}"
2581,1,440,0,0.3850769,"\int (d+e x)^m \left(a+b x+c x^2\right)^{-2-\frac{m}{2}} \, dx","Int[(d + e*x)^m*(a + b*x + c*x^2)^(-2 - m/2),x]","-\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (d+e x)^{m+3} \left(a+b x+c x^2\right)^{-\frac{m}{2}-2} \left(4 c e (a e-b d (m+1))+b^2 e^2 m+4 c^2 d^2 (m+1)\right) \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{\frac{m+4}{2}} \, _2F_1\left(m+3,\frac{m+4}{2};m+4;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{4 (m+1) (m+3) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)^2}+\frac{e (d+e x)^{m+1} \left(a+b x+c x^2\right)^{-\frac{m}{2}-1}}{(m+1) \left(a e^2-b d e+c d^2\right)}+\frac{e m (2 c d-b e) (d+e x)^{m+2} \left(a+b x+c x^2\right)^{-\frac{m}{2}-1}}{2 (m+1) (m+2) \left(a e^2-b d e+c d^2\right)^2}","-\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (d+e x)^{m+3} \left(a+b x+c x^2\right)^{-\frac{m}{2}-2} \left(4 c e (a e-b d (m+1))+b^2 e^2 m+4 c^2 d^2 (m+1)\right) \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{\frac{m+4}{2}} \, _2F_1\left(m+3,\frac{m+4}{2};m+4;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{4 (m+1) (m+3) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)^2}+\frac{e (d+e x)^{m+1} \left(a+b x+c x^2\right)^{-\frac{m}{2}-1}}{(m+1) \left(a e^2-b d e+c d^2\right)}+\frac{e m (2 c d-b e) (d+e x)^{m+2} \left(a+b x+c x^2\right)^{-\frac{m}{2}-1}}{2 (m+1) (m+2) \left(a e^2-b d e+c d^2\right)^2}",1,"(e*(d + e*x)^(1 + m)*(a + b*x + c*x^2)^(-1 - m/2))/((c*d^2 - b*d*e + a*e^2)*(1 + m)) + (e*(2*c*d - b*e)*m*(d + e*x)^(2 + m)*(a + b*x + c*x^2)^(-1 - m/2))/(2*(c*d^2 - b*d*e + a*e^2)^2*(1 + m)*(2 + m)) - ((b^2*e^2*m + 4*c^2*d^2*(1 + m) + 4*c*e*(a*e - b*d*(1 + m)))*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*(((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)))^((4 + m)/2)*(d + e*x)^(3 + m)*(a + b*x + c*x^2)^(-2 - m/2)*Hypergeometric2F1[3 + m, (4 + m)/2, 4 + m, (-4*c*Sqrt[b^2 - 4*a*c]*(d + e*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))])/(4*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)^2*(1 + m)*(3 + m))","A",3,3,26,0.1154,1,"{744, 806, 726}"
2582,1,102,0,0.0171366,"\int \frac{1}{\sqrt[3]{1+x} \sqrt[3]{1-x+x^2}} \, dx","Int[1/((1 + x)^(1/3)*(1 - x + x^2)^(1/3)),x]","\frac{\sqrt[3]{x^3+1} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{x+1} \sqrt[3]{x^2-x+1}}-\frac{\sqrt[3]{x^3+1} \log \left(\sqrt[3]{x^3+1}-x\right)}{2 \sqrt[3]{x+1} \sqrt[3]{x^2-x+1}}","\frac{\sqrt[3]{x^3+1} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{x+1} \sqrt[3]{x^2-x+1}}-\frac{\sqrt[3]{x^3+1} \log \left(\sqrt[3]{x^3+1}-x\right)}{2 \sqrt[3]{x+1} \sqrt[3]{x^2-x+1}}",1,"((1 + x^3)^(1/3)*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*(1 + x)^(1/3)*(1 - x + x^2)^(1/3)) - ((1 + x^3)^(1/3)*Log[-x + (1 + x^3)^(1/3)])/(2*(1 + x)^(1/3)*(1 - x + x^2)^(1/3))","A",2,2,20,0.1000,1,"{713, 239}"
2583,1,45,0,0.0152849,"\int \frac{1}{(1+x)^{2/3} \left(1-x+x^2\right)^{2/3}} \, dx","Int[1/((1 + x)^(2/3)*(1 - x + x^2)^(2/3)),x]","\frac{x \left(x^3+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-x^3\right)}{(x+1)^{2/3} \left(x^2-x+1\right)^{2/3}}","\frac{x \left(x^3+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-x^3\right)}{(x+1)^{2/3} \left(x^2-x+1\right)^{2/3}}",1,"(x*(1 + x^3)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -x^3])/((1 + x)^(2/3)*(1 - x + x^2)^(2/3))","A",2,2,20,0.1000,1,"{713, 245}"
2584,1,41,0,0.0122855,"\int (1+x)^p \left(1-x+x^2\right)^p \, dx","Int[(1 + x)^p*(1 - x + x^2)^p,x]","x (x+1)^p \left(x^2-x+1\right)^p \left(x^3+1\right)^{-p} \, _2F_1\left(\frac{1}{3},-p;\frac{4}{3};-x^3\right)","x (x+1)^p \left(x^2-x+1\right)^p \left(x^3+1\right)^{-p} \, _2F_1\left(\frac{1}{3},-p;\frac{4}{3};-x^3\right)",1,"(x*(1 + x)^p*(1 - x + x^2)^p*Hypergeometric2F1[1/3, -p, 4/3, -x^3])/(1 + x^3)^p","A",2,2,16,0.1250,1,"{713, 245}"
2585,1,109,0,0.0187458,"\int \frac{1}{\sqrt[3]{1-x} \sqrt[3]{1+x+x^2}} \, dx","Int[1/((1 - x)^(1/3)*(1 + x + x^2)^(1/3)),x]","\frac{\sqrt[3]{1-x^3} \log \left(\sqrt[3]{1-x^3}+x\right)}{2 \sqrt[3]{1-x} \sqrt[3]{x^2+x+1}}-\frac{\sqrt[3]{1-x^3} \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1-x} \sqrt[3]{x^2+x+1}}","\frac{\sqrt[3]{1-x^3} \log \left(\sqrt[3]{1-x^3}+x\right)}{2 \sqrt[3]{1-x} \sqrt[3]{x^2+x+1}}-\frac{\sqrt[3]{1-x^3} \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1-x} \sqrt[3]{x^2+x+1}}",1,"-(((1 - x^3)^(1/3)*ArcTan[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*(1 - x)^(1/3)*(1 + x + x^2)^(1/3))) + ((1 - x^3)^(1/3)*Log[x + (1 - x^3)^(1/3)])/(2*(1 - x)^(1/3)*(1 + x + x^2)^(1/3))","A",2,2,20,0.1000,1,"{713, 239}"
2586,1,45,0,0.016428,"\int \frac{1}{(1-x)^{2/3} \left(1+x+x^2\right)^{2/3}} \, dx","Int[1/((1 - x)^(2/3)*(1 + x + x^2)^(2/3)),x]","\frac{x \left(1-x^3\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};x^3\right)}{(1-x)^{2/3} \left(x^2+x+1\right)^{2/3}}","\frac{x \left(1-x^3\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};x^3\right)}{(1-x)^{2/3} \left(x^2+x+1\right)^{2/3}}",1,"(x*(1 - x^3)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, x^3])/((1 - x)^(2/3)*(1 + x + x^2)^(2/3))","A",2,2,20,0.1000,1,"{713, 245}"
2587,1,41,0,0.0122532,"\int (1-x)^p \left(1+x+x^2\right)^p \, dx","Int[(1 - x)^p*(1 + x + x^2)^p,x]","x (1-x)^p \left(x^2+x+1\right)^p \left(1-x^3\right)^{-p} \, _2F_1\left(\frac{1}{3},-p;\frac{4}{3};x^3\right)","x (1-x)^p \left(x^2+x+1\right)^p \left(1-x^3\right)^{-p} \, _2F_1\left(\frac{1}{3},-p;\frac{4}{3};x^3\right)",1,"((1 - x)^p*x*(1 + x + x^2)^p*Hypergeometric2F1[1/3, -p, 4/3, x^3])/(1 - x^3)^p","A",2,2,16,0.1250,1,"{713, 245}"
2588,1,196,0,0.0585334,"\int \frac{1}{\sqrt[3]{b e-c e x} \sqrt[3]{b^2+b c x+c^2 x^2}} \, dx","Int[1/((b*e - c*e*x)^(1/3)*(b^2 + b*c*x + c^2*x^2)^(1/3)),x]","\frac{\sqrt[3]{b^3 e-c^3 e x^3} \log \left(\sqrt[3]{b^3 e-c^3 e x^3}+c \sqrt[3]{e} x\right)}{2 c \sqrt[3]{e} \sqrt[3]{b^2+b c x+c^2 x^2} \sqrt[3]{b e-c e x}}-\frac{\sqrt[3]{b^3 e-c^3 e x^3} \tan ^{-1}\left(\frac{1-\frac{2 c \sqrt[3]{e} x}{\sqrt[3]{b^3 e-c^3 e x^3}}}{\sqrt{3}}\right)}{\sqrt{3} c \sqrt[3]{e} \sqrt[3]{b^2+b c x+c^2 x^2} \sqrt[3]{b e-c e x}}","\frac{\sqrt[3]{b^3 e-c^3 e x^3} \log \left(\sqrt[3]{b^3 e-c^3 e x^3}+c \sqrt[3]{e} x\right)}{2 c \sqrt[3]{e} \sqrt[3]{b^2+b c x+c^2 x^2} \sqrt[3]{b e-c e x}}-\frac{\sqrt[3]{b^3 e-c^3 e x^3} \tan ^{-1}\left(\frac{1-\frac{2 c \sqrt[3]{e} x}{\sqrt[3]{b^3 e-c^3 e x^3}}}{\sqrt{3}}\right)}{\sqrt{3} c \sqrt[3]{e} \sqrt[3]{b^2+b c x+c^2 x^2} \sqrt[3]{b e-c e x}}",1,"-(((b^3*e - c^3*e*x^3)^(1/3)*ArcTan[(1 - (2*c*e^(1/3)*x)/(b^3*e - c^3*e*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*c*e^(1/3)*(b*e - c*e*x)^(1/3)*(b^2 + b*c*x + c^2*x^2)^(1/3))) + ((b^3*e - c^3*e*x^3)^(1/3)*Log[c*e^(1/3)*x + (b^3*e - c^3*e*x^3)^(1/3)])/(2*c*e^(1/3)*(b*e - c*e*x)^(1/3)*(b^2 + b*c*x + c^2*x^2)^(1/3))","A",2,2,33,0.06061,1,"{713, 239}"
2589,1,71,0,0.0391936,"\int \frac{1}{(b e-c e x)^{2/3} \left(b^2+b c x+c^2 x^2\right)^{2/3}} \, dx","Int[1/((b*e - c*e*x)^(2/3)*(b^2 + b*c*x + c^2*x^2)^(2/3)),x]","\frac{x \left(1-\frac{c^3 x^3}{b^3}\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{c^3 x^3}{b^3}\right)}{\left(b^2+b c x+c^2 x^2\right)^{2/3} (b e-c e x)^{2/3}}","\frac{x \left(1-\frac{c^3 x^3}{b^3}\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{c^3 x^3}{b^3}\right)}{\left(b^2+b c x+c^2 x^2\right)^{2/3} (b e-c e x)^{2/3}}",1,"(x*(1 - (c^3*x^3)/b^3)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, (c^3*x^3)/b^3])/((b*e - c*e*x)^(2/3)*(b^2 + b*c*x + c^2*x^2)^(2/3))","A",3,3,33,0.09091,1,"{713, 246, 245}"
2590,1,67,0,0.0334323,"\int (b e-c e x)^p \left(b^2+b c x+c^2 x^2\right)^p \, dx","Int[(b*e - c*e*x)^p*(b^2 + b*c*x + c^2*x^2)^p,x]","x \left(b^2+b c x+c^2 x^2\right)^p \left(1-\frac{c^3 x^3}{b^3}\right)^{-p} (b e-c e x)^p \, _2F_1\left(\frac{1}{3},-p;\frac{4}{3};\frac{c^3 x^3}{b^3}\right)","x \left(b^2+b c x+c^2 x^2\right)^p \left(1-\frac{c^3 x^3}{b^3}\right)^{-p} (b e-c e x)^p \, _2F_1\left(\frac{1}{3},-p;\frac{4}{3};\frac{c^3 x^3}{b^3}\right)",1,"(x*(b*e - c*e*x)^p*(b^2 + b*c*x + c^2*x^2)^p*Hypergeometric2F1[1/3, -p, 4/3, (c^3*x^3)/b^3])/(1 - (c^3*x^3)/b^3)^p","A",3,3,29,0.1034,1,"{713, 246, 245}"