1,1,127,0,0.0819759,"\int x^3 (A+B x) \sqrt{a+b x^2} \, dx","Int[x^3*(A + B*x)*Sqrt[a + b*x^2],x]","\frac{a^2 B x \sqrt{a+b x^2}}{16 b^2}+\frac{a^3 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{5/2}}-\frac{a \left(a+b x^2\right)^{3/2} (16 A+15 B x)}{120 b^2}+\frac{A x^2 \left(a+b x^2\right)^{3/2}}{5 b}+\frac{B x^3 \left(a+b x^2\right)^{3/2}}{6 b}","\frac{a^2 B x \sqrt{a+b x^2}}{16 b^2}+\frac{a^3 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{5/2}}-\frac{a \left(a+b x^2\right)^{3/2} (16 A+15 B x)}{120 b^2}+\frac{A x^2 \left(a+b x^2\right)^{3/2}}{5 b}+\frac{B x^3 \left(a+b x^2\right)^{3/2}}{6 b}",1,"(a^2*B*x*Sqrt[a + b*x^2])/(16*b^2) + (A*x^2*(a + b*x^2)^(3/2))/(5*b) + (B*x^3*(a + b*x^2)^(3/2))/(6*b) - (a*(16*A + 15*B*x)*(a + b*x^2)^(3/2))/(120*b^2) + (a^3*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(5/2))","A",6,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
2,1,104,0,0.0490937,"\int x^2 (A+B x) \sqrt{a+b x^2} \, dx","Int[x^2*(A + B*x)*Sqrt[a + b*x^2],x]","-\frac{a^2 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}-\frac{\left(a+b x^2\right)^{3/2} (8 a B-15 A b x)}{60 b^2}-\frac{a A x \sqrt{a+b x^2}}{8 b}+\frac{B x^2 \left(a+b x^2\right)^{3/2}}{5 b}","-\frac{a^2 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}-\frac{\left(a+b x^2\right)^{3/2} (8 a B-15 A b x)}{60 b^2}-\frac{a A x \sqrt{a+b x^2}}{8 b}+\frac{B x^2 \left(a+b x^2\right)^{3/2}}{5 b}",1,"-(a*A*x*Sqrt[a + b*x^2])/(8*b) + (B*x^2*(a + b*x^2)^(3/2))/(5*b) - ((8*a*B - 15*A*b*x)*(a + b*x^2)^(3/2))/(60*b^2) - (a^2*A*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(3/2))","A",5,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
3,1,80,0,0.0256785,"\int x (A+B x) \sqrt{a+b x^2} \, dx","Int[x*(A + B*x)*Sqrt[a + b*x^2],x]","-\frac{a^2 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}+\frac{\left(a+b x^2\right)^{3/2} (4 A+3 B x)}{12 b}-\frac{a B x \sqrt{a+b x^2}}{8 b}","-\frac{a^2 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}+\frac{\left(a+b x^2\right)^{3/2} (4 A+3 B x)}{12 b}-\frac{a B x \sqrt{a+b x^2}}{8 b}",1,"-(a*B*x*Sqrt[a + b*x^2])/(8*b) + ((4*A + 3*B*x)*(a + b*x^2)^(3/2))/(12*b) - (a^2*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(3/2))","A",4,4,18,0.2222,1,"{780, 195, 217, 206}"
4,1,67,0,0.0193309,"\int (A+B x) \sqrt{a+b x^2} \, dx","Int[(A + B*x)*Sqrt[a + b*x^2],x]","\frac{1}{2} A x \sqrt{a+b x^2}+\frac{a A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b}}+\frac{B \left(a+b x^2\right)^{3/2}}{3 b}","\frac{1}{2} A x \sqrt{a+b x^2}+\frac{a A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b}}+\frac{B \left(a+b x^2\right)^{3/2}}{3 b}",1,"(A*x*Sqrt[a + b*x^2])/2 + (B*(a + b*x^2)^(3/2))/(3*b) + (a*A*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*Sqrt[b])","A",4,4,17,0.2353,1,"{641, 195, 217, 206}"
5,1,79,0,0.0605239,"\int \frac{(A+B x) \sqrt{a+b x^2}}{x} \, dx","Int[((A + B*x)*Sqrt[a + b*x^2])/x,x]","\frac{1}{2} \sqrt{a+b x^2} (2 A+B x)-\sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{a B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b}}","\frac{1}{2} \sqrt{a+b x^2} (2 A+B x)-\sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{a B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b}}",1,"((2*A + B*x)*Sqrt[a + b*x^2])/2 + (a*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*Sqrt[b]) - Sqrt[a]*A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",7,7,20,0.3500,1,"{815, 844, 217, 206, 266, 63, 208}"
6,1,75,0,0.0586444,"\int \frac{(A+B x) \sqrt{a+b x^2}}{x^2} \, dx","Int[((A + B*x)*Sqrt[a + b*x^2])/x^2,x]","-\frac{\sqrt{a+b x^2} (A-B x)}{x}+A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\sqrt{a} B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","-\frac{\sqrt{a+b x^2} (A-B x)}{x}+A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\sqrt{a} B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)",1,"-(((A - B*x)*Sqrt[a + b*x^2])/x) + A*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]] - Sqrt[a]*B*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",7,7,20,0.3500,1,"{813, 844, 217, 206, 266, 63, 208}"
7,1,80,0,0.0604033,"\int \frac{(A+B x) \sqrt{a+b x^2}}{x^3} \, dx","Int[((A + B*x)*Sqrt[a + b*x^2])/x^3,x]","-\frac{\sqrt{a+b x^2} (A+2 B x)}{2 x^2}-\frac{A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}+\sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","-\frac{\sqrt{a+b x^2} (A+2 B x)}{2 x^2}-\frac{A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}+\sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)",1,"-((A + 2*B*x)*Sqrt[a + b*x^2])/(2*x^2) + Sqrt[b]*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]] - (A*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*Sqrt[a])","A",7,7,20,0.3500,1,"{811, 844, 217, 206, 266, 63, 208}"
8,1,150,0,0.0950358,"\int x^3 (A+B x) \left(a+b x^2\right)^{3/2} \, dx","Int[x^3*(A + B*x)*(a + b*x^2)^(3/2),x]","\frac{3 a^3 B x \sqrt{a+b x^2}}{128 b^2}+\frac{a^2 B x \left(a+b x^2\right)^{3/2}}{64 b^2}+\frac{3 a^4 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{5/2}}-\frac{a \left(a+b x^2\right)^{5/2} (32 A+35 B x)}{560 b^2}+\frac{A x^2 \left(a+b x^2\right)^{5/2}}{7 b}+\frac{B x^3 \left(a+b x^2\right)^{5/2}}{8 b}","\frac{3 a^3 B x \sqrt{a+b x^2}}{128 b^2}+\frac{a^2 B x \left(a+b x^2\right)^{3/2}}{64 b^2}+\frac{3 a^4 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{5/2}}-\frac{a \left(a+b x^2\right)^{5/2} (32 A+35 B x)}{560 b^2}+\frac{A x^2 \left(a+b x^2\right)^{5/2}}{7 b}+\frac{B x^3 \left(a+b x^2\right)^{5/2}}{8 b}",1,"(3*a^3*B*x*Sqrt[a + b*x^2])/(128*b^2) + (a^2*B*x*(a + b*x^2)^(3/2))/(64*b^2) + (A*x^2*(a + b*x^2)^(5/2))/(7*b) + (B*x^3*(a + b*x^2)^(5/2))/(8*b) - (a*(32*A + 35*B*x)*(a + b*x^2)^(5/2))/(560*b^2) + (3*a^4*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(5/2))","A",7,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
9,1,127,0,0.0620431,"\int x^2 (A+B x) \left(a+b x^2\right)^{3/2} \, dx","Int[x^2*(A + B*x)*(a + b*x^2)^(3/2),x]","-\frac{a^3 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{3/2}}-\frac{a^2 A x \sqrt{a+b x^2}}{16 b}-\frac{\left(a+b x^2\right)^{5/2} (12 a B-35 A b x)}{210 b^2}-\frac{a A x \left(a+b x^2\right)^{3/2}}{24 b}+\frac{B x^2 \left(a+b x^2\right)^{5/2}}{7 b}","-\frac{a^3 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{3/2}}-\frac{a^2 A x \sqrt{a+b x^2}}{16 b}-\frac{\left(a+b x^2\right)^{5/2} (12 a B-35 A b x)}{210 b^2}-\frac{a A x \left(a+b x^2\right)^{3/2}}{24 b}+\frac{B x^2 \left(a+b x^2\right)^{5/2}}{7 b}",1,"-(a^2*A*x*Sqrt[a + b*x^2])/(16*b) - (a*A*x*(a + b*x^2)^(3/2))/(24*b) + (B*x^2*(a + b*x^2)^(5/2))/(7*b) - ((12*a*B - 35*A*b*x)*(a + b*x^2)^(5/2))/(210*b^2) - (a^3*A*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(3/2))","A",6,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
10,1,103,0,0.0332214,"\int x (A+B x) \left(a+b x^2\right)^{3/2} \, dx","Int[x*(A + B*x)*(a + b*x^2)^(3/2),x]","-\frac{a^3 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{3/2}}-\frac{a^2 B x \sqrt{a+b x^2}}{16 b}+\frac{\left(a+b x^2\right)^{5/2} (6 A+5 B x)}{30 b}-\frac{a B x \left(a+b x^2\right)^{3/2}}{24 b}","-\frac{a^3 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{3/2}}-\frac{a^2 B x \sqrt{a+b x^2}}{16 b}+\frac{\left(a+b x^2\right)^{5/2} (6 A+5 B x)}{30 b}-\frac{a B x \left(a+b x^2\right)^{3/2}}{24 b}",1,"-(a^2*B*x*Sqrt[a + b*x^2])/(16*b) - (a*B*x*(a + b*x^2)^(3/2))/(24*b) + ((6*A + 5*B*x)*(a + b*x^2)^(5/2))/(30*b) - (a^3*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(3/2))","A",5,4,18,0.2222,1,"{780, 195, 217, 206}"
11,1,87,0,0.0261586,"\int (A+B x) \left(a+b x^2\right)^{3/2} \, dx","Int[(A + B*x)*(a + b*x^2)^(3/2),x]","\frac{3 a^2 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b}}+\frac{1}{4} A x \left(a+b x^2\right)^{3/2}+\frac{3}{8} a A x \sqrt{a+b x^2}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b}","\frac{3 a^2 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b}}+\frac{1}{4} A x \left(a+b x^2\right)^{3/2}+\frac{3}{8} a A x \sqrt{a+b x^2}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b}",1,"(3*a*A*x*Sqrt[a + b*x^2])/8 + (A*x*(a + b*x^2)^(3/2))/4 + (B*(a + b*x^2)^(5/2))/(5*b) + (3*a^2*A*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*Sqrt[b])","A",5,4,17,0.2353,1,"{641, 195, 217, 206}"
12,1,106,0,0.0940031,"\int \frac{(A+B x) \left(a+b x^2\right)^{3/2}}{x} \, dx","Int[((A + B*x)*(a + b*x^2)^(3/2))/x,x]","-a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{3 a^2 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b}}+\frac{1}{8} a \sqrt{a+b x^2} (8 A+3 B x)+\frac{1}{12} \left(a+b x^2\right)^{3/2} (4 A+3 B x)","-a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{3 a^2 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b}}+\frac{1}{8} a \sqrt{a+b x^2} (8 A+3 B x)+\frac{1}{12} \left(a+b x^2\right)^{3/2} (4 A+3 B x)",1,"(a*(8*A + 3*B*x)*Sqrt[a + b*x^2])/8 + ((4*A + 3*B*x)*(a + b*x^2)^(3/2))/12 + (3*a^2*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*Sqrt[b]) - a^(3/2)*A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",8,7,20,0.3500,1,"{815, 844, 217, 206, 266, 63, 208}"
13,1,108,0,0.0890723,"\int \frac{(A+B x) \left(a+b x^2\right)^{3/2}}{x^2} \, dx","Int[((A + B*x)*(a + b*x^2)^(3/2))/x^2,x]","a^{3/2} (-B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{3/2} (3 A-B x)}{3 x}+\frac{1}{2} \sqrt{a+b x^2} (2 a B+3 A b x)+\frac{3}{2} a A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","a^{3/2} (-B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{3/2} (3 A-B x)}{3 x}+\frac{1}{2} \sqrt{a+b x^2} (2 a B+3 A b x)+\frac{3}{2} a A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)",1,"((2*a*B + 3*A*b*x)*Sqrt[a + b*x^2])/2 - ((3*A - B*x)*(a + b*x^2)^(3/2))/(3*x) + (3*a*A*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2 - a^(3/2)*B*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",8,8,20,0.4000,1,"{813, 815, 844, 217, 206, 266, 63, 208}"
14,1,111,0,0.0845428,"\int \frac{(A+B x) \left(a+b x^2\right)^{3/2}}{x^3} \, dx","Int[((A + B*x)*(a + b*x^2)^(3/2))/x^3,x]","-\frac{\left(a+b x^2\right)^{3/2} (A-B x)}{2 x^2}-\frac{3 \sqrt{a+b x^2} (a B-A b x)}{2 x}-\frac{3}{2} \sqrt{a} A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{3}{2} a \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","-\frac{\left(a+b x^2\right)^{3/2} (A-B x)}{2 x^2}-\frac{3 \sqrt{a+b x^2} (a B-A b x)}{2 x}-\frac{3}{2} \sqrt{a} A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{3}{2} a \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)",1,"(-3*(a*B - A*b*x)*Sqrt[a + b*x^2])/(2*x) - ((A - B*x)*(a + b*x^2)^(3/2))/(2*x^2) + (3*a*Sqrt[b]*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2 - (3*Sqrt[a]*A*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",8,7,20,0.3500,1,"{813, 844, 217, 206, 266, 63, 208}"
15,1,173,0,0.1045587,"\int x^3 (A+B x) \left(a+b x^2\right)^{5/2} \, dx","Int[x^3*(A + B*x)*(a + b*x^2)^(5/2),x]","\frac{3 a^4 B x \sqrt{a+b x^2}}{256 b^2}+\frac{a^3 B x \left(a+b x^2\right)^{3/2}}{128 b^2}+\frac{a^2 B x \left(a+b x^2\right)^{5/2}}{160 b^2}+\frac{3 a^5 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{5/2}}-\frac{a \left(a+b x^2\right)^{7/2} (160 A+189 B x)}{5040 b^2}+\frac{A x^2 \left(a+b x^2\right)^{7/2}}{9 b}+\frac{B x^3 \left(a+b x^2\right)^{7/2}}{10 b}","\frac{3 a^4 B x \sqrt{a+b x^2}}{256 b^2}+\frac{a^3 B x \left(a+b x^2\right)^{3/2}}{128 b^2}+\frac{a^2 B x \left(a+b x^2\right)^{5/2}}{160 b^2}+\frac{3 a^5 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{5/2}}-\frac{a \left(a+b x^2\right)^{7/2} (160 A+189 B x)}{5040 b^2}+\frac{A x^2 \left(a+b x^2\right)^{7/2}}{9 b}+\frac{B x^3 \left(a+b x^2\right)^{7/2}}{10 b}",1,"(3*a^4*B*x*Sqrt[a + b*x^2])/(256*b^2) + (a^3*B*x*(a + b*x^2)^(3/2))/(128*b^2) + (a^2*B*x*(a + b*x^2)^(5/2))/(160*b^2) + (A*x^2*(a + b*x^2)^(7/2))/(9*b) + (B*x^3*(a + b*x^2)^(7/2))/(10*b) - (a*(160*A + 189*B*x)*(a + b*x^2)^(7/2))/(5040*b^2) + (3*a^5*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(256*b^(5/2))","A",8,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
16,1,150,0,0.0694944,"\int x^2 (A+B x) \left(a+b x^2\right)^{5/2} \, dx","Int[x^2*(A + B*x)*(a + b*x^2)^(5/2),x]","-\frac{5 a^4 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{3/2}}-\frac{5 a^3 A x \sqrt{a+b x^2}}{128 b}-\frac{5 a^2 A x \left(a+b x^2\right)^{3/2}}{192 b}-\frac{\left(a+b x^2\right)^{7/2} (16 a B-63 A b x)}{504 b^2}-\frac{a A x \left(a+b x^2\right)^{5/2}}{48 b}+\frac{B x^2 \left(a+b x^2\right)^{7/2}}{9 b}","-\frac{5 a^4 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{3/2}}-\frac{5 a^3 A x \sqrt{a+b x^2}}{128 b}-\frac{5 a^2 A x \left(a+b x^2\right)^{3/2}}{192 b}-\frac{\left(a+b x^2\right)^{7/2} (16 a B-63 A b x)}{504 b^2}-\frac{a A x \left(a+b x^2\right)^{5/2}}{48 b}+\frac{B x^2 \left(a+b x^2\right)^{7/2}}{9 b}",1,"(-5*a^3*A*x*Sqrt[a + b*x^2])/(128*b) - (5*a^2*A*x*(a + b*x^2)^(3/2))/(192*b) - (a*A*x*(a + b*x^2)^(5/2))/(48*b) + (B*x^2*(a + b*x^2)^(7/2))/(9*b) - ((16*a*B - 63*A*b*x)*(a + b*x^2)^(7/2))/(504*b^2) - (5*a^4*A*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(3/2))","A",7,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
17,1,126,0,0.0435616,"\int x (A+B x) \left(a+b x^2\right)^{5/2} \, dx","Int[x*(A + B*x)*(a + b*x^2)^(5/2),x]","-\frac{5 a^4 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{3/2}}-\frac{5 a^3 B x \sqrt{a+b x^2}}{128 b}-\frac{5 a^2 B x \left(a+b x^2\right)^{3/2}}{192 b}+\frac{\left(a+b x^2\right)^{7/2} (8 A+7 B x)}{56 b}-\frac{a B x \left(a+b x^2\right)^{5/2}}{48 b}","-\frac{5 a^4 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{3/2}}-\frac{5 a^3 B x \sqrt{a+b x^2}}{128 b}-\frac{5 a^2 B x \left(a+b x^2\right)^{3/2}}{192 b}+\frac{\left(a+b x^2\right)^{7/2} (8 A+7 B x)}{56 b}-\frac{a B x \left(a+b x^2\right)^{5/2}}{48 b}",1,"(-5*a^3*B*x*Sqrt[a + b*x^2])/(128*b) - (5*a^2*B*x*(a + b*x^2)^(3/2))/(192*b) - (a*B*x*(a + b*x^2)^(5/2))/(48*b) + ((8*A + 7*B*x)*(a + b*x^2)^(7/2))/(56*b) - (5*a^4*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(3/2))","A",6,4,18,0.2222,1,"{780, 195, 217, 206}"
18,1,107,0,0.0369465,"\int (A+B x) \left(a+b x^2\right)^{5/2} \, dx","Int[(A + B*x)*(a + b*x^2)^(5/2),x]","\frac{5}{16} a^2 A x \sqrt{a+b x^2}+\frac{5 a^3 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{1}{6} A x \left(a+b x^2\right)^{5/2}+\frac{5}{24} a A x \left(a+b x^2\right)^{3/2}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b}","\frac{5}{16} a^2 A x \sqrt{a+b x^2}+\frac{5 a^3 A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{1}{6} A x \left(a+b x^2\right)^{5/2}+\frac{5}{24} a A x \left(a+b x^2\right)^{3/2}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b}",1,"(5*a^2*A*x*Sqrt[a + b*x^2])/16 + (5*a*A*x*(a + b*x^2)^(3/2))/24 + (A*x*(a + b*x^2)^(5/2))/6 + (B*(a + b*x^2)^(7/2))/(7*b) + (5*a^3*A*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*Sqrt[b])","A",6,4,17,0.2353,1,"{641, 195, 217, 206}"
19,1,132,0,0.1588629,"\int \frac{(A+B x) \left(a+b x^2\right)^{5/2}}{x} \, dx","Int[((A + B*x)*(a + b*x^2)^(5/2))/x,x]","\frac{1}{16} a^2 \sqrt{a+b x^2} (16 A+5 B x)-a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{5 a^3 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{1}{24} a \left(a+b x^2\right)^{3/2} (8 A+5 B x)+\frac{1}{30} \left(a+b x^2\right)^{5/2} (6 A+5 B x)","\frac{1}{16} a^2 \sqrt{a+b x^2} (16 A+5 B x)-a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{5 a^3 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{1}{24} a \left(a+b x^2\right)^{3/2} (8 A+5 B x)+\frac{1}{30} \left(a+b x^2\right)^{5/2} (6 A+5 B x)",1,"(a^2*(16*A + 5*B*x)*Sqrt[a + b*x^2])/16 + (a*(8*A + 5*B*x)*(a + b*x^2)^(3/2))/24 + ((6*A + 5*B*x)*(a + b*x^2)^(5/2))/30 + (5*a^3*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*Sqrt[b]) - a^(5/2)*A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",9,7,20,0.3500,1,"{815, 844, 217, 206, 266, 63, 208}"
20,1,136,0,0.1324214,"\int \frac{(A+B x) \left(a+b x^2\right)^{5/2}}{x^2} \, dx","Int[((A + B*x)*(a + b*x^2)^(5/2))/x^2,x]","\frac{15}{8} a^2 A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+a^{5/2} (-B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{1}{8} a \sqrt{a+b x^2} (8 a B+15 A b x)-\frac{\left(a+b x^2\right)^{5/2} (5 A-B x)}{5 x}+\frac{1}{12} \left(a+b x^2\right)^{3/2} (4 a B+15 A b x)","\frac{15}{8} a^2 A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+a^{5/2} (-B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{1}{8} a \sqrt{a+b x^2} (8 a B+15 A b x)-\frac{\left(a+b x^2\right)^{5/2} (5 A-B x)}{5 x}+\frac{1}{12} \left(a+b x^2\right)^{3/2} (4 a B+15 A b x)",1,"(a*(8*a*B + 15*A*b*x)*Sqrt[a + b*x^2])/8 + ((4*a*B + 15*A*b*x)*(a + b*x^2)^(3/2))/12 - ((5*A - B*x)*(a + b*x^2)^(5/2))/(5*x) + (15*a^2*A*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/8 - a^(5/2)*B*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",9,8,20,0.4000,1,"{813, 815, 844, 217, 206, 266, 63, 208}"
21,1,141,0,0.117082,"\int \frac{(A+B x) \left(a+b x^2\right)^{5/2}}{x^3} \, dx","Int[((A + B*x)*(a + b*x^2)^(5/2))/x^3,x]","-\frac{5}{2} a^{3/2} A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{15}{8} a^2 \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{5/2} (2 A-B x)}{4 x^2}-\frac{5 \left(a+b x^2\right)^{3/2} (3 a B-2 A b x)}{12 x}+\frac{5}{8} a b \sqrt{a+b x^2} (4 A+3 B x)","-\frac{5}{2} a^{3/2} A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{15}{8} a^2 \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{5/2} (2 A-B x)}{4 x^2}-\frac{5 \left(a+b x^2\right)^{3/2} (3 a B-2 A b x)}{12 x}+\frac{5}{8} a b \sqrt{a+b x^2} (4 A+3 B x)",1,"(5*a*b*(4*A + 3*B*x)*Sqrt[a + b*x^2])/8 - (5*(3*a*B - 2*A*b*x)*(a + b*x^2)^(3/2))/(12*x) - ((2*A - B*x)*(a + b*x^2)^(5/2))/(4*x^2) + (15*a^2*Sqrt[b]*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/8 - (5*a^(3/2)*A*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",9,8,20,0.4000,1,"{813, 815, 844, 217, 206, 266, 63, 208}"
22,1,104,0,0.0772985,"\int \frac{x^3 (A+B x)}{\sqrt{a+b x^2}} \, dx","Int[(x^3*(A + B*x))/Sqrt[a + b*x^2],x]","\frac{3 a^2 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{5/2}}-\frac{a \sqrt{a+b x^2} (16 A+9 B x)}{24 b^2}+\frac{A x^2 \sqrt{a+b x^2}}{3 b}+\frac{B x^3 \sqrt{a+b x^2}}{4 b}","\frac{3 a^2 B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{5/2}}-\frac{a \sqrt{a+b x^2} (16 A+9 B x)}{24 b^2}+\frac{A x^2 \sqrt{a+b x^2}}{3 b}+\frac{B x^3 \sqrt{a+b x^2}}{4 b}",1,"(A*x^2*Sqrt[a + b*x^2])/(3*b) + (B*x^3*Sqrt[a + b*x^2])/(4*b) - (a*(16*A + 9*B*x)*Sqrt[a + b*x^2])/(24*b^2) + (3*a^2*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(5/2))","A",5,4,20,0.2000,1,"{833, 780, 217, 206}"
23,1,81,0,0.0421102,"\int \frac{x^2 (A+B x)}{\sqrt{a+b x^2}} \, dx","Int[(x^2*(A + B*x))/Sqrt[a + b*x^2],x]","-\frac{\sqrt{a+b x^2} (4 a B-3 A b x)}{6 b^2}-\frac{a A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}+\frac{B x^2 \sqrt{a+b x^2}}{3 b}","-\frac{\sqrt{a+b x^2} (4 a B-3 A b x)}{6 b^2}-\frac{a A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}+\frac{B x^2 \sqrt{a+b x^2}}{3 b}",1,"(B*x^2*Sqrt[a + b*x^2])/(3*b) - ((4*a*B - 3*A*b*x)*Sqrt[a + b*x^2])/(6*b^2) - (a*A*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(3/2))","A",4,4,20,0.2000,1,"{833, 780, 217, 206}"
24,1,56,0,0.0230157,"\int \frac{x (A+B x)}{\sqrt{a+b x^2}} \, dx","Int[(x*(A + B*x))/Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2} (2 A+B x)}{2 b}-\frac{a B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}","\frac{\sqrt{a+b x^2} (2 A+B x)}{2 b}-\frac{a B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}",1,"((2*A + B*x)*Sqrt[a + b*x^2])/(2*b) - (a*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(3/2))","A",3,3,18,0.1667,1,"{780, 217, 206}"
25,1,43,0,0.0149365,"\int \frac{A+B x}{\sqrt{a+b x^2}} \, dx","Int[(A + B*x)/Sqrt[a + b*x^2],x]","\frac{A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}+\frac{B \sqrt{a+b x^2}}{b}","\frac{A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}+\frac{B \sqrt{a+b x^2}}{b}",1,"(B*Sqrt[a + b*x^2])/b + (A*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/Sqrt[b]","A",3,3,17,0.1765,1,"{641, 217, 206}"
26,1,53,0,0.0397549,"\int \frac{A+B x}{x \sqrt{a+b x^2}} \, dx","Int[(A + B*x)/(x*Sqrt[a + b*x^2]),x]","\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/Sqrt[b] - (A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/Sqrt[a]","A",6,6,20,0.3000,1,"{844, 217, 206, 266, 63, 208}"
27,1,47,0,0.0325682,"\int \frac{A+B x}{x^2 \sqrt{a+b x^2}} \, dx","Int[(A + B*x)/(x^2*Sqrt[a + b*x^2]),x]","-\frac{A \sqrt{a+b x^2}}{a x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{A \sqrt{a+b x^2}}{a x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-((A*Sqrt[a + b*x^2])/(a*x)) - (B*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/Sqrt[a]","A",4,4,20,0.2000,1,"{807, 266, 63, 208}"
28,1,72,0,0.0531302,"\int \frac{A+B x}{x^3 \sqrt{a+b x^2}} \, dx","Int[(A + B*x)/(x^3*Sqrt[a + b*x^2]),x]","\frac{A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+b x^2}}{2 a x^2}-\frac{B \sqrt{a+b x^2}}{a x}","\frac{A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+b x^2}}{2 a x^2}-\frac{B \sqrt{a+b x^2}}{a x}",1,"-(A*Sqrt[a + b*x^2])/(2*a*x^2) - (B*Sqrt[a + b*x^2])/(a*x) + (A*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(3/2))","A",5,5,20,0.2500,1,"{835, 807, 266, 63, 208}"
29,1,81,0,0.0434866,"\int \frac{x^3 (A+B x)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x^3*(A + B*x))/(a + b*x^2)^(3/2),x]","\frac{\sqrt{a+b x^2} (4 A+3 B x)}{2 b^2}-\frac{x^2 (A+B x)}{b \sqrt{a+b x^2}}-\frac{3 a B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{5/2}}","\frac{\sqrt{a+b x^2} (4 A+3 B x)}{2 b^2}-\frac{x^2 (A+B x)}{b \sqrt{a+b x^2}}-\frac{3 a B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{5/2}}",1,"-((x^2*(A + B*x))/(b*Sqrt[a + b*x^2])) + ((4*A + 3*B*x)*Sqrt[a + b*x^2])/(2*b^2) - (3*a*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(5/2))","A",4,4,20,0.2000,1,"{819, 780, 217, 206}"
30,1,66,0,0.0363449,"\int \frac{x^2 (A+B x)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x^2*(A + B*x))/(a + b*x^2)^(3/2),x]","\frac{A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2}}-\frac{x (A+B x)}{b \sqrt{a+b x^2}}+\frac{2 B \sqrt{a+b x^2}}{b^2}","\frac{A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2}}-\frac{x (A+B x)}{b \sqrt{a+b x^2}}+\frac{2 B \sqrt{a+b x^2}}{b^2}",1,"-((x*(A + B*x))/(b*Sqrt[a + b*x^2])) + (2*B*Sqrt[a + b*x^2])/b^2 + (A*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(3/2)","A",4,4,20,0.2000,1,"{819, 641, 217, 206}"
31,1,48,0,0.0201247,"\int \frac{x (A+B x)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x*(A + B*x))/(a + b*x^2)^(3/2),x]","\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2}}-\frac{A+B x}{b \sqrt{a+b x^2}}","\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2}}-\frac{A+B x}{b \sqrt{a+b x^2}}",1,"-((A + B*x)/(b*Sqrt[a + b*x^2])) + (B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(3/2)","A",3,3,18,0.1667,1,"{778, 217, 206}"
32,1,28,0,0.006717,"\int \frac{A+B x}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(a + b*x^2)^(3/2),x]","-\frac{a B-A b x}{a b \sqrt{a+b x^2}}","-\frac{a B-A b x}{a b \sqrt{a+b x^2}}",1,"-((a*B - A*b*x)/(a*b*Sqrt[a + b*x^2]))","A",1,1,17,0.05882,1,"{637}"
33,1,47,0,0.0380149,"\int \frac{A+B x}{x \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x*(a + b*x^2)^(3/2)),x]","\frac{A+B x}{a \sqrt{a+b x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{A+B x}{a \sqrt{a+b x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{3/2}}",1,"(A + B*x)/(a*Sqrt[a + b*x^2]) - (A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/a^(3/2)","A",5,5,20,0.2500,1,"{823, 12, 266, 63, 208}"
34,1,70,0,0.0570752,"\int \frac{A+B x}{x^2 \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^2*(a + b*x^2)^(3/2)),x]","-\frac{2 A \sqrt{a+b x^2}}{a^2 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{A+B x}{a x \sqrt{a+b x^2}}","-\frac{2 A \sqrt{a+b x^2}}{a^2 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{A+B x}{a x \sqrt{a+b x^2}}",1,"(A + B*x)/(a*x*Sqrt[a + b*x^2]) - (2*A*Sqrt[a + b*x^2])/(a^2*x) - (B*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/a^(3/2)","A",5,5,20,0.2500,1,"{823, 807, 266, 63, 208}"
35,1,95,0,0.0783209,"\int \frac{A+B x}{x^3 \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^3*(a + b*x^2)^(3/2)),x]","-\frac{3 A \sqrt{a+b x^2}}{2 a^2 x^2}+\frac{3 A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{2 B \sqrt{a+b x^2}}{a^2 x}+\frac{A+B x}{a x^2 \sqrt{a+b x^2}}","-\frac{3 A \sqrt{a+b x^2}}{2 a^2 x^2}+\frac{3 A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{2 B \sqrt{a+b x^2}}{a^2 x}+\frac{A+B x}{a x^2 \sqrt{a+b x^2}}",1,"(A + B*x)/(a*x^2*Sqrt[a + b*x^2]) - (3*A*Sqrt[a + b*x^2])/(2*a^2*x^2) - (2*B*Sqrt[a + b*x^2])/(a^2*x) + (3*A*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(5/2))","A",6,6,20,0.3000,1,"{823, 835, 807, 266, 63, 208}"
36,1,79,0,0.042459,"\int \frac{x^3 (A+B x)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x^3*(A + B*x))/(a + b*x^2)^(5/2),x]","-\frac{2 A+3 B x}{3 b^2 \sqrt{a+b x^2}}-\frac{x^2 (A+B x)}{3 b \left(a+b x^2\right)^{3/2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{5/2}}","-\frac{2 A+3 B x}{3 b^2 \sqrt{a+b x^2}}-\frac{x^2 (A+B x)}{3 b \left(a+b x^2\right)^{3/2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{5/2}}",1,"-(x^2*(A + B*x))/(3*b*(a + b*x^2)^(3/2)) - (2*A + 3*B*x)/(3*b^2*Sqrt[a + b*x^2]) + (B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(5/2)","A",4,4,20,0.2000,1,"{819, 778, 217, 206}"
37,1,53,0,0.0217641,"\int \frac{x^2 (A+B x)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x^2*(A + B*x))/(a + b*x^2)^(5/2),x]","-\frac{x^2 (a B-A b x)}{3 a b \left(a+b x^2\right)^{3/2}}-\frac{2 B}{3 b^2 \sqrt{a+b x^2}}","-\frac{x^2 (a B-A b x)}{3 a b \left(a+b x^2\right)^{3/2}}-\frac{2 B}{3 b^2 \sqrt{a+b x^2}}",1,"-(x^2*(a*B - A*b*x))/(3*a*b*(a + b*x^2)^(3/2)) - (2*B)/(3*b^2*Sqrt[a + b*x^2])","A",2,2,20,0.1000,1,"{805, 261}"
38,1,47,0,0.0144857,"\int \frac{x (A+B x)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x*(A + B*x))/(a + b*x^2)^(5/2),x]","\frac{B x}{3 a b \sqrt{a+b x^2}}-\frac{A+B x}{3 b \left(a+b x^2\right)^{3/2}}","\frac{B x}{3 a b \sqrt{a+b x^2}}-\frac{A+B x}{3 b \left(a+b x^2\right)^{3/2}}",1,"-(A + B*x)/(3*b*(a + b*x^2)^(3/2)) + (B*x)/(3*a*b*Sqrt[a + b*x^2])","A",2,2,18,0.1111,1,"{778, 191}"
39,1,51,0,0.0104064,"\int \frac{A+B x}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(a + b*x^2)^(5/2),x]","\frac{2 A x}{3 a^2 \sqrt{a+b x^2}}-\frac{a B-A b x}{3 a b \left(a+b x^2\right)^{3/2}}","\frac{2 A x}{3 a^2 \sqrt{a+b x^2}}-\frac{a B-A b x}{3 a b \left(a+b x^2\right)^{3/2}}",1,"-(a*B - A*b*x)/(3*a*b*(a + b*x^2)^(3/2)) + (2*A*x)/(3*a^2*Sqrt[a + b*x^2])","A",2,2,17,0.1176,1,"{639, 191}"
40,1,76,0,0.0634318,"\int \frac{A+B x}{x \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x*(a + b*x^2)^(5/2)),x]","\frac{3 A+2 B x}{3 a^2 \sqrt{a+b x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A+B x}{3 a \left(a+b x^2\right)^{3/2}}","\frac{3 A+2 B x}{3 a^2 \sqrt{a+b x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A+B x}{3 a \left(a+b x^2\right)^{3/2}}",1,"(A + B*x)/(3*a*(a + b*x^2)^(3/2)) + (3*A + 2*B*x)/(3*a^2*Sqrt[a + b*x^2]) - (A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/a^(5/2)","A",6,5,20,0.2500,1,"{823, 12, 266, 63, 208}"
41,1,104,0,0.0880568,"\int \frac{A+B x}{x^2 \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^2*(a + b*x^2)^(5/2)),x]","\frac{4 A+3 B x}{3 a^2 x \sqrt{a+b x^2}}-\frac{8 A \sqrt{a+b x^2}}{3 a^3 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A+B x}{3 a x \left(a+b x^2\right)^{3/2}}","\frac{4 A+3 B x}{3 a^2 x \sqrt{a+b x^2}}-\frac{8 A \sqrt{a+b x^2}}{3 a^3 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A+B x}{3 a x \left(a+b x^2\right)^{3/2}}",1,"(A + B*x)/(3*a*x*(a + b*x^2)^(3/2)) + (4*A + 3*B*x)/(3*a^2*x*Sqrt[a + b*x^2]) - (8*A*Sqrt[a + b*x^2])/(3*a^3*x) - (B*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/a^(5/2)","A",6,5,20,0.2500,1,"{823, 807, 266, 63, 208}"
42,1,129,0,0.1194399,"\int \frac{A+B x}{x^3 \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^3*(a + b*x^2)^(5/2)),x]","\frac{5 A+4 B x}{3 a^2 x^2 \sqrt{a+b x^2}}-\frac{5 A \sqrt{a+b x^2}}{2 a^3 x^2}+\frac{5 A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{8 B \sqrt{a+b x^2}}{3 a^3 x}+\frac{A+B x}{3 a x^2 \left(a+b x^2\right)^{3/2}}","\frac{5 A+4 B x}{3 a^2 x^2 \sqrt{a+b x^2}}-\frac{5 A \sqrt{a+b x^2}}{2 a^3 x^2}+\frac{5 A b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{8 B \sqrt{a+b x^2}}{3 a^3 x}+\frac{A+B x}{3 a x^2 \left(a+b x^2\right)^{3/2}}",1,"(A + B*x)/(3*a*x^2*(a + b*x^2)^(3/2)) + (5*A + 4*B*x)/(3*a^2*x^2*Sqrt[a + b*x^2]) - (5*A*Sqrt[a + b*x^2])/(2*a^3*x^2) - (8*B*Sqrt[a + b*x^2])/(3*a^3*x) + (5*A*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(7/2))","A",7,6,20,0.3000,1,"{823, 835, 807, 266, 63, 208}"
43,1,27,0,0.007999,"\int \frac{(1-x) x}{\sqrt{1-x^2}} \, dx","Int[((1 - x)*x)/Sqrt[1 - x^2],x]","-\frac{1}{2} \sqrt{1-x^2} (2-x)-\frac{1}{2} \sin ^{-1}(x)","-\frac{1}{2} \sqrt{1-x^2} (2-x)-\frac{1}{2} \sin ^{-1}(x)",1,"-((2 - x)*Sqrt[1 - x^2])/2 - ArcSin[x]/2","A",2,2,18,0.1111,1,"{780, 216}"
44,1,27,0,0.0170198,"\int \frac{x-x^2}{\sqrt{1-x^2}} \, dx","Int[(x - x^2)/Sqrt[1 - x^2],x]","-\frac{1}{2} \sqrt{1-x^2} (2-x)-\frac{1}{2} \sin ^{-1}(x)","-\frac{1}{2} \sqrt{1-x^2} (2-x)-\frac{1}{2} \sin ^{-1}(x)",1,"-((2 - x)*Sqrt[1 - x^2])/2 - ArcSin[x]/2","A",3,3,19,0.1579,1,"{1593, 780, 216}"
45,1,17,0,0.0057999,"\int \frac{3+x^2}{-3+x^2} \, dx","Int[(3 + x^2)/(-3 + x^2),x]","x-2 \sqrt{3} \tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)","x-2 \sqrt{3} \tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)",1,"x - 2*Sqrt[3]*ArcTanh[x/Sqrt[3]]","A",2,2,13,0.1538,1,"{388, 207}"
46,1,6,0,0.0034794,"\int \frac{-1+x^2}{1+x^2} \, dx","Int[(-1 + x^2)/(1 + x^2),x]","x-2 \tan ^{-1}(x)","x-2 \tan ^{-1}(x)",1,"x - 2*ArcTan[x]","A",2,2,13,0.1538,1,"{388, 203}"
47,1,213,0,0.3242912,"\int \frac{x^7 \left(A+B x+C x^2\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^7*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x]","-\frac{x^5 (7 a B-x (A b-8 a C))}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^3 (35 a B-6 x (A b-8 a C))}{105 a b^3 \left(a+b x^2\right)^{3/2}}-\frac{x (35 a B-8 x (A b-8 a C))}{35 a b^4 \sqrt{a+b x^2}}-\frac{16 \sqrt{a+b x^2} (A b-8 a C)}{35 a b^5}-\frac{x^7 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}","-\frac{x^5 (7 a B-x (A b-8 a C))}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^3 (35 a B-6 x (A b-8 a C))}{105 a b^3 \left(a+b x^2\right)^{3/2}}-\frac{x (35 a B-8 x (A b-8 a C))}{35 a b^4 \sqrt{a+b x^2}}-\frac{16 \sqrt{a+b x^2} (A b-8 a C)}{35 a b^5}-\frac{x^7 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}",1,"-(x^7*(a*B - (A*b - a*C)*x))/(7*a*b*(a + b*x^2)^(7/2)) - (x^5*(7*a*B - (A*b - 8*a*C)*x))/(35*a*b^2*(a + b*x^2)^(5/2)) - (x^3*(35*a*B - 6*(A*b - 8*a*C)*x))/(105*a*b^3*(a + b*x^2)^(3/2)) - (x*(35*a*B - 8*(A*b - 8*a*C)*x))/(35*a*b^4*Sqrt[a + b*x^2]) - (16*(A*b - 8*a*C)*Sqrt[a + b*x^2])/(35*a*b^5) + (B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(9/2)","A",7,5,25,0.2000,1,"{1804, 819, 641, 217, 206}"
48,1,150,0,0.165252,"\int \frac{x^6 \left(A+B x+C x^2\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^6*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x]","-\frac{x^6 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}-\frac{x^4 (6 B+7 C x)}{35 b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^2 (24 B+35 C x)}{105 b^3 \left(a+b x^2\right)^{3/2}}-\frac{16 B+35 C x}{35 b^4 \sqrt{a+b x^2}}+\frac{C \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}","-\frac{x^6 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}-\frac{x^4 (6 B+7 C x)}{35 b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^2 (24 B+35 C x)}{105 b^3 \left(a+b x^2\right)^{3/2}}-\frac{16 B+35 C x}{35 b^4 \sqrt{a+b x^2}}+\frac{C \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}",1,"-(x^6*(a*B - (A*b - a*C)*x))/(7*a*b*(a + b*x^2)^(7/2)) - (x^4*(6*B + 7*C*x))/(35*b^2*(a + b*x^2)^(5/2)) - (x^2*(24*B + 35*C*x))/(105*b^3*(a + b*x^2)^(3/2)) - (16*B + 35*C*x)/(35*b^4*Sqrt[a + b*x^2]) + (C*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(9/2)","A",6,5,25,0.2000,1,"{1804, 819, 778, 217, 206}"
49,1,132,0,0.1662225,"\int \frac{x^5 \left(A+B x+C x^2\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^5*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x]","-\frac{x^4 (6 a C+A b-5 b B x)}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{4 (6 a C+A b)}{35 a b^4 \sqrt{a+b x^2}}+\frac{4 (6 a C+A b)}{105 b^4 \left(a+b x^2\right)^{3/2}}-\frac{x^5 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}","-\frac{x^4 (6 a C+A b-5 b B x)}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{4 (6 a C+A b)}{35 a b^4 \sqrt{a+b x^2}}+\frac{4 (6 a C+A b)}{105 b^4 \left(a+b x^2\right)^{3/2}}-\frac{x^5 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}",1,"-(x^5*(a*B - (A*b - a*C)*x))/(7*a*b*(a + b*x^2)^(7/2)) - (x^4*(A*b + 6*a*C - 5*b*B*x))/(35*a*b^2*(a + b*x^2)^(5/2)) + (4*(A*b + 6*a*C))/(105*b^4*(a + b*x^2)^(3/2)) - (4*(A*b + 6*a*C))/(35*a*b^4*Sqrt[a + b*x^2])","A",5,4,25,0.1600,1,"{1804, 805, 266, 43}"
50,1,149,0,0.1813024,"\int \frac{x^4 \left(A+B x+C x^2\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^4*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x]","\frac{x (5 a C+2 A b)}{35 a^2 b^3 \sqrt{a+b x^2}}-\frac{x^2 (x (5 a C+2 A b)+4 a B)}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{3 x (5 a C+2 A b)+8 a B}{105 a b^3 \left(a+b x^2\right)^{3/2}}-\frac{x^4 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}","\frac{x (5 a C+2 A b)}{35 a^2 b^3 \sqrt{a+b x^2}}-\frac{x^2 (x (5 a C+2 A b)+4 a B)}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{3 x (5 a C+2 A b)+8 a B}{105 a b^3 \left(a+b x^2\right)^{3/2}}-\frac{x^4 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}",1,"-(x^4*(a*B - (A*b - a*C)*x))/(7*a*b*(a + b*x^2)^(7/2)) - (x^2*(4*a*B + (2*A*b + 5*a*C)*x))/(35*a*b^2*(a + b*x^2)^(5/2)) - (8*a*B + 3*(2*A*b + 5*a*C)*x)/(105*a*b^3*(a + b*x^2)^(3/2)) + ((2*A*b + 5*a*C)*x)/(35*a^2*b^3*Sqrt[a + b*x^2])","A",4,4,25,0.1600,1,"{1804, 819, 778, 191}"
51,1,139,0,0.1512642,"\int \frac{x^3 \left(A+B x+C x^2\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^3*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x]","\frac{2 B x}{35 a^2 b^2 \sqrt{a+b x^2}}-\frac{x (x (4 a C+3 A b)+3 a B)}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{2 (4 a C+3 A b)-3 b B x}{105 a b^3 \left(a+b x^2\right)^{3/2}}-\frac{x^3 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}","\frac{2 B x}{35 a^2 b^2 \sqrt{a+b x^2}}-\frac{x (x (4 a C+3 A b)+3 a B)}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{2 (4 a C+3 A b)-3 b B x}{105 a b^3 \left(a+b x^2\right)^{3/2}}-\frac{x^3 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}",1,"-(x^3*(a*B - (A*b - a*C)*x))/(7*a*b*(a + b*x^2)^(7/2)) - (x*(3*a*B + (3*A*b + 4*a*C)*x))/(35*a*b^2*(a + b*x^2)^(5/2)) - (2*(3*A*b + 4*a*C) - 3*b*B*x)/(105*a*b^3*(a + b*x^2)^(3/2)) + (2*B*x)/(35*a^2*b^2*Sqrt[a + b*x^2])","A",4,4,25,0.1600,1,"{1804, 819, 639, 191}"
52,1,139,0,0.1310297,"\int \frac{x^2 \left(A+B x+C x^2\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^2*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x]","\frac{2 x (3 a C+4 A b)}{105 a^3 b^2 \sqrt{a+b x^2}}+\frac{x (3 a C+4 A b)}{105 a^2 b^2 \left(a+b x^2\right)^{3/2}}-\frac{x (3 a C+4 A b)+2 a B}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^2 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}","\frac{2 x (3 a C+4 A b)}{105 a^3 b^2 \sqrt{a+b x^2}}+\frac{x (3 a C+4 A b)}{105 a^2 b^2 \left(a+b x^2\right)^{3/2}}-\frac{x (3 a C+4 A b)+2 a B}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^2 (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}",1,"-(x^2*(a*B - (A*b - a*C)*x))/(7*a*b*(a + b*x^2)^(7/2)) - (2*a*B + (4*A*b + 3*a*C)*x)/(35*a*b^2*(a + b*x^2)^(5/2)) + ((4*A*b + 3*a*C)*x)/(105*a^2*b^2*(a + b*x^2)^(3/2)) + (2*(4*A*b + 3*a*C)*x)/(105*a^3*b^2*Sqrt[a + b*x^2])","A",4,4,25,0.1600,1,"{1804, 778, 192, 191}"
53,1,119,0,0.0876955,"\int \frac{x \left(A+B x+C x^2\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x]","\frac{8 B x}{105 a^3 b \sqrt{a+b x^2}}+\frac{4 B x}{105 a^2 b \left(a+b x^2\right)^{3/2}}-\frac{2 a C+5 A b-b B x}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{x (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}","\frac{8 B x}{105 a^3 b \sqrt{a+b x^2}}+\frac{4 B x}{105 a^2 b \left(a+b x^2\right)^{3/2}}-\frac{2 a C+5 A b-b B x}{35 a b^2 \left(a+b x^2\right)^{5/2}}-\frac{x (a B-x (A b-a C))}{7 a b \left(a+b x^2\right)^{7/2}}",1,"-(x*(a*B - (A*b - a*C)*x))/(7*a*b*(a + b*x^2)^(7/2)) - (5*A*b + 2*a*C - b*B*x)/(35*a*b^2*(a + b*x^2)^(5/2)) + (4*B*x)/(105*a^2*b*(a + b*x^2)^(3/2)) + (8*B*x)/(105*a^3*b*Sqrt[a + b*x^2])","A",4,4,23,0.1739,1,"{1804, 639, 192, 191}"
54,1,127,0,0.0686267,"\int \frac{A+B x+C x^2}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x + C*x^2)/(a + b*x^2)^(9/2),x]","\frac{8 x (a C+6 A b)}{105 a^4 b \sqrt{a+b x^2}}+\frac{4 x (a C+6 A b)}{105 a^3 b \left(a+b x^2\right)^{3/2}}+\frac{x (a C+6 A b)}{35 a^2 b \left(a+b x^2\right)^{5/2}}-\frac{a B-x (A b-a C)}{7 a b \left(a+b x^2\right)^{7/2}}","\frac{8 x (a C+6 A b)}{105 a^4 b \sqrt{a+b x^2}}+\frac{4 x (a C+6 A b)}{105 a^3 b \left(a+b x^2\right)^{3/2}}+\frac{x (a C+6 A b)}{35 a^2 b \left(a+b x^2\right)^{5/2}}-\frac{a B-x (A b-a C)}{7 a b \left(a+b x^2\right)^{7/2}}",1,"-(a*B - (A*b - a*C)*x)/(7*a*b*(a + b*x^2)^(7/2)) + ((6*A*b + a*C)*x)/(35*a^2*b*(a + b*x^2)^(5/2)) + (4*(6*A*b + a*C)*x)/(105*a^3*b*(a + b*x^2)^(3/2)) + (8*(6*A*b + a*C)*x)/(105*a^4*b*Sqrt[a + b*x^2])","A",5,4,22,0.1818,1,"{1814, 12, 192, 191}"
55,1,138,0,0.1620655,"\int \frac{A+B x+C x^2}{x \left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x + C*x^2)/(x*(a + b*x^2)^(9/2)),x]","\frac{7 A+6 B x}{35 a^2 \left(a+b x^2\right)^{5/2}}+\frac{35 A+16 B x}{35 a^4 \sqrt{a+b x^2}}+\frac{35 A+24 B x}{105 a^3 \left(a+b x^2\right)^{3/2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{-a C+A b+b B x}{7 a b \left(a+b x^2\right)^{7/2}}","\frac{7 A+6 B x}{35 a^2 \left(a+b x^2\right)^{5/2}}+\frac{35 A+16 B x}{35 a^4 \sqrt{a+b x^2}}+\frac{35 A+24 B x}{105 a^3 \left(a+b x^2\right)^{3/2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{-a C+A b+b B x}{7 a b \left(a+b x^2\right)^{7/2}}",1,"(A*b - a*C + b*B*x)/(7*a*b*(a + b*x^2)^(7/2)) + (7*A + 6*B*x)/(35*a^2*(a + b*x^2)^(5/2)) + (35*A + 24*B*x)/(105*a^3*(a + b*x^2)^(3/2)) + (35*A + 16*B*x)/(35*a^4*Sqrt[a + b*x^2]) - (A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/a^(9/2)","A",8,6,25,0.2400,1,"{1805, 823, 12, 266, 63, 208}"
56,1,188,0,0.3813143,"\int \frac{A+B x+C x^2}{x^2 \left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x + C*x^2)/(x^2*(a + b*x^2)^(9/2)),x]","\frac{35 B-x \left(\frac{93 A b}{a}-16 C\right)}{35 a^4 \sqrt{a+b x^2}}+\frac{35 B-3 x \left(\frac{29 A b}{a}-8 C\right)}{105 a^3 \left(a+b x^2\right)^{3/2}}+\frac{7 B-x \left(\frac{13 A b}{a}-6 C\right)}{35 a^2 \left(a+b x^2\right)^{5/2}}-\frac{A \sqrt{a+b x^2}}{a^5 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{B-x \left(\frac{A b}{a}-C\right)}{7 a \left(a+b x^2\right)^{7/2}}","\frac{35 B-x \left(\frac{93 A b}{a}-16 C\right)}{35 a^4 \sqrt{a+b x^2}}+\frac{35 B-3 x \left(\frac{29 A b}{a}-8 C\right)}{105 a^3 \left(a+b x^2\right)^{3/2}}+\frac{7 B-x \left(\frac{13 A b}{a}-6 C\right)}{35 a^2 \left(a+b x^2\right)^{5/2}}-\frac{A \sqrt{a+b x^2}}{a^5 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{B-x \left(\frac{A b}{a}-C\right)}{7 a \left(a+b x^2\right)^{7/2}}",1,"(B - ((A*b)/a - C)*x)/(7*a*(a + b*x^2)^(7/2)) + (7*B - ((13*A*b)/a - 6*C)*x)/(35*a^2*(a + b*x^2)^(5/2)) + (35*B - 3*((29*A*b)/a - 8*C)*x)/(105*a^3*(a + b*x^2)^(3/2)) + (35*B - ((93*A*b)/a - 16*C)*x)/(35*a^4*Sqrt[a + b*x^2]) - (A*Sqrt[a + b*x^2])/(a^5*x) - (B*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/a^(9/2)","A",8,5,25,0.2000,1,"{1805, 807, 266, 63, 208}"
57,1,219,0,0.4803103,"\int \frac{A+B x+C x^2}{x^3 \left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x + C*x^2)/(x^3*(a + b*x^2)^(9/2)),x]","-\frac{35 (4 A b-a C)+93 b B x}{35 a^5 \sqrt{a+b x^2}}-\frac{35 (3 A b-a C)+87 b B x}{105 a^4 \left(a+b x^2\right)^{3/2}}-\frac{7 (2 A b-a C)+13 b B x}{35 a^3 \left(a+b x^2\right)^{5/2}}-\frac{a \left(\frac{A b}{a}-C\right)+b B x}{7 a^2 \left(a+b x^2\right)^{7/2}}+\frac{(9 A b-2 a C) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{11/2}}-\frac{A \sqrt{a+b x^2}}{2 a^5 x^2}-\frac{B \sqrt{a+b x^2}}{a^5 x}","-\frac{35 (4 A b-a C)+93 b B x}{35 a^5 \sqrt{a+b x^2}}-\frac{35 (3 A b-a C)+87 b B x}{105 a^4 \left(a+b x^2\right)^{3/2}}-\frac{7 (2 A b-a C)+13 b B x}{35 a^3 \left(a+b x^2\right)^{5/2}}-\frac{a \left(\frac{A b}{a}-C\right)+b B x}{7 a^2 \left(a+b x^2\right)^{7/2}}+\frac{(9 A b-2 a C) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{11/2}}-\frac{A \sqrt{a+b x^2}}{2 a^5 x^2}-\frac{B \sqrt{a+b x^2}}{a^5 x}",1,"-(a*((A*b)/a - C) + b*B*x)/(7*a^2*(a + b*x^2)^(7/2)) - (7*(2*A*b - a*C) + 13*b*B*x)/(35*a^3*(a + b*x^2)^(5/2)) - (35*(3*A*b - a*C) + 87*b*B*x)/(105*a^4*(a + b*x^2)^(3/2)) - (35*(4*A*b - a*C) + 93*b*B*x)/(35*a^5*Sqrt[a + b*x^2]) - (A*Sqrt[a + b*x^2])/(2*a^5*x^2) - (B*Sqrt[a + b*x^2])/(a^5*x) + ((9*A*b - 2*a*C)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(11/2))","A",9,6,25,0.2400,1,"{1805, 1807, 807, 266, 63, 208}"
58,1,45,0,0.0166907,"\int \frac{A (c x)^m}{a+b x^2} \, dx","Int[(A*(c*x)^m)/(a + b*x^2),x]","\frac{A (c x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a c (m+1)}","\frac{A (c x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a c (m+1)}",1,"(A*(c*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*c*(1 + m))","A",2,2,16,0.1250,1,"{12, 364}"
59,1,91,0,0.0427198,"\int \frac{(c x)^m (A+B x)}{a+b x^2} \, dx","Int[((c*x)^m*(A + B*x))/(a + b*x^2),x]","\frac{A (c x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a c (m+1)}+\frac{B (c x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{a c^2 (m+2)}","\frac{A (c x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a c (m+1)}+\frac{B (c x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{a c^2 (m+2)}",1,"(A*(c*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*c*(1 + m)) + (B*(c*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -((b*x^2)/a)])/(a*c^2*(2 + m))","A",3,2,20,0.1000,1,"{808, 364}"
60,1,76,0,0.0386468,"\int \frac{(c x)^m \left(A+C x^2\right)}{a+b x^2} \, dx","Int[((c*x)^m*(A + C*x^2))/(a + b*x^2),x]","\frac{(c x)^{m+1} (A b-a C) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b c (m+1)}+\frac{C (c x)^{m+1}}{b c (m+1)}","\frac{(c x)^{m+1} (A b-a C) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b c (m+1)}+\frac{C (c x)^{m+1}}{b c (m+1)}",1,"(C*(c*x)^(1 + m))/(b*c*(1 + m)) + ((A*b - a*C)*(c*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*b*c*(1 + m))","A",2,2,22,0.09091,1,"{459, 364}"
61,1,121,0,0.1224736,"\int \frac{(c x)^m \left(A+B x+C x^2\right)}{a+b x^2} \, dx","Int[((c*x)^m*(A + B*x + C*x^2))/(a + b*x^2),x]","\frac{(c x)^{m+1} (A b-a C) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b c (m+1)}+\frac{B (c x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{a c^2 (m+2)}+\frac{C (c x)^{m+1}}{b c (m+1)}","\frac{(c x)^{m+1} (A b-a C) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b c (m+1)}+\frac{B (c x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{a c^2 (m+2)}+\frac{C (c x)^{m+1}}{b c (m+1)}",1,"(C*(c*x)^(1 + m))/(b*c*(1 + m)) + ((A*b - a*C)*(c*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*b*c*(1 + m)) + (B*(c*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -((b*x^2)/a)])/(a*c^2*(2 + m))","A",5,3,25,0.1200,1,"{1802, 808, 364}"
62,1,65,0,0.0742998,"\int x^3 \left(a+b x^2\right) \left(A+B x+C x^2+D x^3\right) \, dx","Int[x^3*(a + b*x^2)*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{6} x^6 (a C+A b)+\frac{1}{4} a A x^4+\frac{1}{7} x^7 (a D+b B)+\frac{1}{5} a B x^5+\frac{1}{8} b C x^8+\frac{1}{9} b D x^9","\frac{1}{6} x^6 (a C+A b)+\frac{1}{4} a A x^4+\frac{1}{7} x^7 (a D+b B)+\frac{1}{5} a B x^5+\frac{1}{8} b C x^8+\frac{1}{9} b D x^9",1,"(a*A*x^4)/4 + (a*B*x^5)/5 + ((A*b + a*C)*x^6)/6 + ((b*B + a*D)*x^7)/7 + (b*C*x^8)/8 + (b*D*x^9)/9","A",2,1,26,0.03846,1,"{1802}"
63,1,65,0,0.0764878,"\int x^2 \left(a+b x^2\right) \left(A+B x+C x^2+D x^3\right) \, dx","Int[x^2*(a + b*x^2)*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{6} x^6 (a D+b B)+\frac{1}{4} a B x^4+\frac{1}{7} b C x^7+\frac{1}{8} b D x^8","\frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{6} x^6 (a D+b B)+\frac{1}{4} a B x^4+\frac{1}{7} b C x^7+\frac{1}{8} b D x^8",1,"(a*A*x^3)/3 + (a*B*x^4)/4 + ((A*b + a*C)*x^5)/5 + ((b*B + a*D)*x^6)/6 + (b*C*x^7)/7 + (b*D*x^8)/8","A",2,1,26,0.03846,1,"{1802}"
64,1,65,0,0.0609981,"\int x \left(a+b x^2\right) \left(A+B x+C x^2+D x^3\right) \, dx","Int[x*(a + b*x^2)*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{4} x^4 (a C+A b)+\frac{1}{2} a A x^2+\frac{1}{5} x^5 (a D+b B)+\frac{1}{3} a B x^3+\frac{1}{6} b C x^6+\frac{1}{7} b D x^7","\frac{1}{4} x^4 (a C+A b)+\frac{1}{2} a A x^2+\frac{1}{5} x^5 (a D+b B)+\frac{1}{3} a B x^3+\frac{1}{6} b C x^6+\frac{1}{7} b D x^7",1,"(a*A*x^2)/2 + (a*B*x^3)/3 + ((A*b + a*C)*x^4)/4 + ((b*B + a*D)*x^5)/5 + (b*C*x^6)/6 + (b*D*x^7)/7","A",2,1,24,0.04167,1,"{1802}"
65,1,60,0,0.0411648,"\int \left(a+b x^2\right) \left(A+B x+C x^2+D x^3\right) \, dx","Int[(a + b*x^2)*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{3} x^3 (a C+A b)+a A x+\frac{1}{4} x^4 (a D+b B)+\frac{1}{2} a B x^2+\frac{1}{5} b C x^5+\frac{1}{6} b D x^6","\frac{1}{3} x^3 (a C+A b)+a A x+\frac{1}{4} x^4 (a D+b B)+\frac{1}{2} a B x^2+\frac{1}{5} b C x^5+\frac{1}{6} b D x^6",1,"a*A*x + (a*B*x^2)/2 + ((A*b + a*C)*x^3)/3 + ((b*B + a*D)*x^4)/4 + (b*C*x^5)/5 + (b*D*x^6)/6","A",2,1,23,0.04348,1,"{1810}"
66,1,56,0,0.0400955,"\int \frac{\left(a+b x^2\right) \left(A+B x+C x^2+D x^3\right)}{x} \, dx","Int[((a + b*x^2)*(A + B*x + C*x^2 + D*x^3))/x,x]","\frac{1}{2} x^2 (a C+A b)+a A \log (x)+\frac{1}{3} x^3 (a D+b B)+a B x+\frac{1}{4} b C x^4+\frac{1}{5} b D x^5","\frac{1}{2} x^2 (a C+A b)+a A \log (x)+\frac{1}{3} x^3 (a D+b B)+a B x+\frac{1}{4} b C x^4+\frac{1}{5} b D x^5",1,"a*B*x + ((A*b + a*C)*x^2)/2 + ((b*B + a*D)*x^3)/3 + (b*C*x^4)/4 + (b*D*x^5)/5 + a*A*Log[x]","A",2,1,26,0.03846,1,"{1802}"
67,1,54,0,0.0481677,"\int \frac{\left(a+b x^2\right) \left(A+B x+C x^2+D x^3\right)}{x^2} \, dx","Int[((a + b*x^2)*(A + B*x + C*x^2 + D*x^3))/x^2,x]","x (a C+A b)-\frac{a A}{x}+\frac{1}{2} x^2 (a D+b B)+a B \log (x)+\frac{1}{3} b C x^3+\frac{1}{4} b D x^4","x (a C+A b)-\frac{a A}{x}+\frac{1}{2} x^2 (a D+b B)+a B \log (x)+\frac{1}{3} b C x^3+\frac{1}{4} b D x^4",1,"-((a*A)/x) + (A*b + a*C)*x + ((b*B + a*D)*x^2)/2 + (b*C*x^3)/3 + (b*D*x^4)/4 + a*B*Log[x]","A",2,1,26,0.03846,1,"{1802}"
68,1,54,0,0.048458,"\int \frac{\left(a+b x^2\right) \left(A+B x+C x^2+D x^3\right)}{x^3} \, dx","Int[((a + b*x^2)*(A + B*x + C*x^2 + D*x^3))/x^3,x]","\log (x) (a C+A b)-\frac{a A}{2 x^2}+x (a D+b B)-\frac{a B}{x}+\frac{1}{2} b C x^2+\frac{1}{3} b D x^3","\log (x) (a C+A b)-\frac{a A}{2 x^2}+x (a D+b B)-\frac{a B}{x}+\frac{1}{2} b C x^2+\frac{1}{3} b D x^3",1,"-(a*A)/(2*x^2) - (a*B)/x + (b*B + a*D)*x + (b*C*x^2)/2 + (b*D*x^3)/3 + (A*b + a*C)*Log[x]","A",2,1,26,0.03846,1,"{1802}"
69,1,54,0,0.0487032,"\int \frac{\left(a+b x^2\right) \left(A+B x+C x^2+D x^3\right)}{x^4} \, dx","Int[((a + b*x^2)*(A + B*x + C*x^2 + D*x^3))/x^4,x]","-\frac{a C+A b}{x}-\frac{a A}{3 x^3}+\log (x) (a D+b B)-\frac{a B}{2 x^2}+b C x+\frac{1}{2} b D x^2","-\frac{a C+A b}{x}-\frac{a A}{3 x^3}+\log (x) (a D+b B)-\frac{a B}{2 x^2}+b C x+\frac{1}{2} b D x^2",1,"-(a*A)/(3*x^3) - (a*B)/(2*x^2) - (A*b + a*C)/x + b*C*x + (b*D*x^2)/2 + (b*B + a*D)*Log[x]","A",2,1,26,0.03846,1,"{1802}"
70,1,109,0,0.1241716,"\int x^3 \left(a+b x^2\right)^2 \left(A+B x+C x^2+D x^3\right) \, dx","Int[x^3*(a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{4} a^2 A x^4+\frac{1}{5} a^2 B x^5+\frac{1}{8} b x^8 (2 a C+A b)+\frac{1}{6} a x^6 (a C+2 A b)+\frac{1}{9} b x^9 (2 a D+b B)+\frac{1}{7} a x^7 (a D+2 b B)+\frac{1}{10} b^2 C x^{10}+\frac{1}{11} b^2 D x^{11}","\frac{1}{4} a^2 A x^4+\frac{1}{5} a^2 B x^5+\frac{1}{8} b x^8 (2 a C+A b)+\frac{1}{6} a x^6 (a C+2 A b)+\frac{1}{9} b x^9 (2 a D+b B)+\frac{1}{7} a x^7 (a D+2 b B)+\frac{1}{10} b^2 C x^{10}+\frac{1}{11} b^2 D x^{11}",1,"(a^2*A*x^4)/4 + (a^2*B*x^5)/5 + (a*(2*A*b + a*C)*x^6)/6 + (a*(2*b*B + a*D)*x^7)/7 + (b*(A*b + 2*a*C)*x^8)/8 + (b*(b*B + 2*a*D)*x^9)/9 + (b^2*C*x^10)/10 + (b^2*D*x^11)/11","A",2,1,28,0.03571,1,"{1802}"
71,1,109,0,0.1117172,"\int x^2 \left(a+b x^2\right)^2 \left(A+B x+C x^2+D x^3\right) \, dx","Int[x^2*(a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{3} a^2 A x^3+\frac{1}{4} a^2 B x^4+\frac{1}{7} b x^7 (2 a C+A b)+\frac{1}{5} a x^5 (a C+2 A b)+\frac{1}{8} b x^8 (2 a D+b B)+\frac{1}{6} a x^6 (a D+2 b B)+\frac{1}{9} b^2 C x^9+\frac{1}{10} b^2 D x^{10}","\frac{1}{3} a^2 A x^3+\frac{1}{4} a^2 B x^4+\frac{1}{7} b x^7 (2 a C+A b)+\frac{1}{5} a x^5 (a C+2 A b)+\frac{1}{8} b x^8 (2 a D+b B)+\frac{1}{6} a x^6 (a D+2 b B)+\frac{1}{9} b^2 C x^9+\frac{1}{10} b^2 D x^{10}",1,"(a^2*A*x^3)/3 + (a^2*B*x^4)/4 + (a*(2*A*b + a*C)*x^5)/5 + (a*(2*b*B + a*D)*x^6)/6 + (b*(A*b + 2*a*C)*x^7)/7 + (b*(b*B + 2*a*D)*x^8)/8 + (b^2*C*x^9)/9 + (b^2*D*x^10)/10","A",2,1,28,0.03571,1,"{1802}"
72,1,104,0,0.0738811,"\int x \left(a+b x^2\right)^2 \left(A+B x+C x^2+D x^3\right) \, dx","Int[x*(a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{3} a^2 B x^3+\frac{1}{4} a^2 C x^4+\frac{A \left(a+b x^2\right)^3}{6 b}+\frac{1}{7} b x^7 (2 a D+b B)+\frac{1}{5} a x^5 (a D+2 b B)+\frac{1}{3} a b C x^6+\frac{1}{8} b^2 C x^8+\frac{1}{9} b^2 D x^9","\frac{1}{3} a^2 B x^3+\frac{1}{4} a^2 C x^4+\frac{A \left(a+b x^2\right)^3}{6 b}+\frac{1}{7} b x^7 (2 a D+b B)+\frac{1}{5} a x^5 (a D+2 b B)+\frac{1}{3} a b C x^6+\frac{1}{8} b^2 C x^8+\frac{1}{9} b^2 D x^9",1,"(a^2*B*x^3)/3 + (a^2*C*x^4)/4 + (a*(2*b*B + a*D)*x^5)/5 + (a*b*C*x^6)/3 + (b*(b*B + 2*a*D)*x^7)/7 + (b^2*C*x^8)/8 + (b^2*D*x^9)/9 + (A*(a + b*x^2)^3)/(6*b)","A",3,2,26,0.07692,1,"{1582, 1810}"
73,1,99,0,0.0723119,"\int \left(a+b x^2\right)^2 \left(A+B x+C x^2+D x^3\right) \, dx","Int[(a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3),x]","a^2 A x+\frac{1}{4} a^2 D x^4+\frac{1}{5} b x^5 (2 a C+A b)+\frac{1}{3} a x^3 (a C+2 A b)+\frac{B \left(a+b x^2\right)^3}{6 b}+\frac{1}{3} a b D x^6+\frac{1}{7} b^2 C x^7+\frac{1}{8} b^2 D x^8","a^2 A x+\frac{1}{4} a^2 D x^4+\frac{1}{5} b x^5 (2 a C+A b)+\frac{1}{3} a x^3 (a C+2 A b)+\frac{B \left(a+b x^2\right)^3}{6 b}+\frac{1}{3} a b D x^6+\frac{1}{7} b^2 C x^7+\frac{1}{8} b^2 D x^8",1,"a^2*A*x + (a*(2*A*b + a*C)*x^3)/3 + (a^2*D*x^4)/4 + (b*(A*b + 2*a*C)*x^5)/5 + (a*b*D*x^6)/3 + (b^2*C*x^7)/7 + (b^2*D*x^8)/8 + (B*(a + b*x^2)^3)/(6*b)","A",3,2,25,0.08000,1,"{1582, 1810}"
74,1,92,0,0.0685905,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x+C x^2+D x^3\right)}{x} \, dx","Int[((a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3))/x,x]","a^2 A \log (x)+a^2 B x+a A b x^2+\frac{1}{5} b x^5 (2 a D+b B)+\frac{1}{3} a x^3 (a D+2 b B)+\frac{C \left(a+b x^2\right)^3}{6 b}+\frac{1}{4} A b^2 x^4+\frac{1}{7} b^2 D x^7","a^2 A \log (x)+a^2 B x+a A b x^2+\frac{1}{5} b x^5 (2 a D+b B)+\frac{1}{3} a x^3 (a D+2 b B)+\frac{C \left(a+b x^2\right)^3}{6 b}+\frac{1}{4} A b^2 x^4+\frac{1}{7} b^2 D x^7",1,"a^2*B*x + a*A*b*x^2 + (a*(2*b*B + a*D)*x^3)/3 + (A*b^2*x^4)/4 + (b*(b*B + 2*a*D)*x^5)/5 + (b^2*D*x^7)/7 + (C*(a + b*x^2)^3)/(6*b) + a^2*A*Log[x]","A",3,2,28,0.07143,1,"{1583, 1802}"
75,1,90,0,0.080234,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x+C x^2+D x^3\right)}{x^2} \, dx","Int[((a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3))/x^2,x]","-\frac{a^2 A}{x}+a^2 B \log (x)+\frac{1}{3} b x^3 (2 a C+A b)+a x (a C+2 A b)+a b B x^2+\frac{D \left(a+b x^2\right)^3}{6 b}+\frac{1}{4} b^2 B x^4+\frac{1}{5} b^2 C x^5","-\frac{a^2 A}{x}+a^2 B \log (x)+\frac{1}{3} b x^3 (2 a C+A b)+a x (a C+2 A b)+a b B x^2+\frac{D \left(a+b x^2\right)^3}{6 b}+\frac{1}{4} b^2 B x^4+\frac{1}{5} b^2 C x^5",1,"-((a^2*A)/x) + a*(2*A*b + a*C)*x + a*b*B*x^2 + (b*(A*b + 2*a*C)*x^3)/3 + (b^2*B*x^4)/4 + (b^2*C*x^5)/5 + (D*(a + b*x^2)^3)/(6*b) + a^2*B*Log[x]","A",3,2,28,0.07143,1,"{1583, 1628}"
76,1,98,0,0.0863914,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x+C x^2+D x^3\right)}{x^3} \, dx","Int[((a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3))/x^3,x]","-\frac{a^2 A}{2 x^2}-\frac{a^2 B}{x}+\frac{1}{2} b x^2 (2 a C+A b)+a \log (x) (a C+2 A b)+\frac{1}{3} b x^3 (2 a D+b B)+a x (a D+2 b B)+\frac{1}{4} b^2 C x^4+\frac{1}{5} b^2 D x^5","-\frac{a^2 A}{2 x^2}-\frac{a^2 B}{x}+\frac{1}{2} b x^2 (2 a C+A b)+a \log (x) (a C+2 A b)+\frac{1}{3} b x^3 (2 a D+b B)+a x (a D+2 b B)+\frac{1}{4} b^2 C x^4+\frac{1}{5} b^2 D x^5",1,"-(a^2*A)/(2*x^2) - (a^2*B)/x + a*(2*b*B + a*D)*x + (b*(A*b + 2*a*C)*x^2)/2 + (b*(b*B + 2*a*D)*x^3)/3 + (b^2*C*x^4)/4 + (b^2*D*x^5)/5 + a*(2*A*b + a*C)*Log[x]","A",2,1,28,0.03571,1,"{1802}"
77,1,98,0,0.0857923,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x+C x^2+D x^3\right)}{x^4} \, dx","Int[((a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3))/x^4,x]","-\frac{a^2 A}{3 x^3}-\frac{a^2 B}{2 x^2}+b x (2 a C+A b)-\frac{a (a C+2 A b)}{x}+\frac{1}{2} b x^2 (2 a D+b B)+a \log (x) (a D+2 b B)+\frac{1}{3} b^2 C x^3+\frac{1}{4} b^2 D x^4","-\frac{a^2 A}{3 x^3}-\frac{a^2 B}{2 x^2}+b x (2 a C+A b)-\frac{a (a C+2 A b)}{x}+\frac{1}{2} b x^2 (2 a D+b B)+a \log (x) (a D+2 b B)+\frac{1}{3} b^2 C x^3+\frac{1}{4} b^2 D x^4",1,"-(a^2*A)/(3*x^3) - (a^2*B)/(2*x^2) - (a*(2*A*b + a*C))/x + b*(A*b + 2*a*C)*x + (b*(b*B + 2*a*D)*x^2)/2 + (b^2*C*x^3)/3 + (b^2*D*x^4)/4 + a*(2*b*B + a*D)*Log[x]","A",2,1,28,0.03571,1,"{1802}"
78,1,149,0,0.1861612,"\int x^3 \left(a+b x^2\right)^3 \left(A+B x+C x^2+D x^3\right) \, dx","Int[x^3*(a + b*x^2)^3*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{6} a^2 x^6 (a C+3 A b)+\frac{1}{4} a^3 A x^4+\frac{1}{7} a^2 x^7 (a D+3 b B)+\frac{1}{5} a^3 B x^5+\frac{1}{10} b^2 x^{10} (3 a C+A b)+\frac{3}{8} a b x^8 (a C+A b)+\frac{1}{11} b^2 x^{11} (3 a D+b B)+\frac{1}{3} a b x^9 (a D+b B)+\frac{1}{12} b^3 C x^{12}+\frac{1}{13} b^3 D x^{13}","\frac{1}{6} a^2 x^6 (a C+3 A b)+\frac{1}{4} a^3 A x^4+\frac{1}{7} a^2 x^7 (a D+3 b B)+\frac{1}{5} a^3 B x^5+\frac{1}{10} b^2 x^{10} (3 a C+A b)+\frac{3}{8} a b x^8 (a C+A b)+\frac{1}{11} b^2 x^{11} (3 a D+b B)+\frac{1}{3} a b x^9 (a D+b B)+\frac{1}{12} b^3 C x^{12}+\frac{1}{13} b^3 D x^{13}",1,"(a^3*A*x^4)/4 + (a^3*B*x^5)/5 + (a^2*(3*A*b + a*C)*x^6)/6 + (a^2*(3*b*B + a*D)*x^7)/7 + (3*a*b*(A*b + a*C)*x^8)/8 + (a*b*(b*B + a*D)*x^9)/3 + (b^2*(A*b + 3*a*C)*x^10)/10 + (b^2*(b*B + 3*a*D)*x^11)/11 + (b^3*C*x^12)/12 + (b^3*D*x^13)/13","A",2,1,28,0.03571,1,"{1802}"
79,1,149,0,0.1410606,"\int x^2 \left(a+b x^2\right)^3 \left(A+B x+C x^2+D x^3\right) \, dx","Int[x^2*(a + b*x^2)^3*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{5} a^2 x^5 (a C+3 A b)+\frac{1}{3} a^3 A x^3+\frac{1}{6} a^2 x^6 (a D+3 b B)+\frac{1}{4} a^3 B x^4+\frac{1}{9} b^2 x^9 (3 a C+A b)+\frac{3}{7} a b x^7 (a C+A b)+\frac{1}{10} b^2 x^{10} (3 a D+b B)+\frac{3}{8} a b x^8 (a D+b B)+\frac{1}{11} b^3 C x^{11}+\frac{1}{12} b^3 D x^{12}","\frac{1}{5} a^2 x^5 (a C+3 A b)+\frac{1}{3} a^3 A x^3+\frac{1}{6} a^2 x^6 (a D+3 b B)+\frac{1}{4} a^3 B x^4+\frac{1}{9} b^2 x^9 (3 a C+A b)+\frac{3}{7} a b x^7 (a C+A b)+\frac{1}{10} b^2 x^{10} (3 a D+b B)+\frac{3}{8} a b x^8 (a D+b B)+\frac{1}{11} b^3 C x^{11}+\frac{1}{12} b^3 D x^{12}",1,"(a^3*A*x^3)/3 + (a^3*B*x^4)/4 + (a^2*(3*A*b + a*C)*x^5)/5 + (a^2*(3*b*B + a*D)*x^6)/6 + (3*a*b*(A*b + a*C)*x^7)/7 + (3*a*b*(b*B + a*D)*x^8)/8 + (b^2*(A*b + 3*a*C)*x^9)/9 + (b^2*(b*B + 3*a*D)*x^10)/10 + (b^3*C*x^11)/11 + (b^3*D*x^12)/12","A",2,1,28,0.03571,1,"{1802}"
80,1,138,0,0.0947486,"\int x \left(a+b x^2\right)^3 \left(A+B x+C x^2+D x^3\right) \, dx","Int[x*(a + b*x^2)^3*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{5} a^2 x^5 (a D+3 b B)+\frac{1}{2} a^2 b C x^6+\frac{1}{3} a^3 B x^3+\frac{1}{4} a^3 C x^4+\frac{A \left(a+b x^2\right)^4}{8 b}+\frac{1}{9} b^2 x^9 (3 a D+b B)+\frac{3}{8} a b^2 C x^8+\frac{3}{7} a b x^7 (a D+b B)+\frac{1}{10} b^3 C x^{10}+\frac{1}{11} b^3 D x^{11}","\frac{1}{5} a^2 x^5 (a D+3 b B)+\frac{1}{2} a^2 b C x^6+\frac{1}{3} a^3 B x^3+\frac{1}{4} a^3 C x^4+\frac{A \left(a+b x^2\right)^4}{8 b}+\frac{1}{9} b^2 x^9 (3 a D+b B)+\frac{3}{8} a b^2 C x^8+\frac{3}{7} a b x^7 (a D+b B)+\frac{1}{10} b^3 C x^{10}+\frac{1}{11} b^3 D x^{11}",1,"(a^3*B*x^3)/3 + (a^3*C*x^4)/4 + (a^2*(3*b*B + a*D)*x^5)/5 + (a^2*b*C*x^6)/2 + (3*a*b*(b*B + a*D)*x^7)/7 + (3*a*b^2*C*x^8)/8 + (b^2*(b*B + 3*a*D)*x^9)/9 + (b^3*C*x^10)/10 + (b^3*D*x^11)/11 + (A*(a + b*x^2)^4)/(8*b)","A",3,2,26,0.07692,1,"{1582, 1810}"
81,1,133,0,0.0926051,"\int \left(a+b x^2\right)^3 \left(A+B x+C x^2+D x^3\right) \, dx","Int[(a + b*x^2)^3*(A + B*x + C*x^2 + D*x^3),x]","\frac{1}{3} a^2 x^3 (a C+3 A b)+a^3 A x+\frac{1}{2} a^2 b D x^6+\frac{1}{4} a^3 D x^4+\frac{1}{7} b^2 x^7 (3 a C+A b)+\frac{3}{5} a b x^5 (a C+A b)+\frac{3}{8} a b^2 D x^8+\frac{B \left(a+b x^2\right)^4}{8 b}+\frac{1}{9} b^3 C x^9+\frac{1}{10} b^3 D x^{10}","\frac{1}{3} a^2 x^3 (a C+3 A b)+a^3 A x+\frac{1}{2} a^2 b D x^6+\frac{1}{4} a^3 D x^4+\frac{1}{7} b^2 x^7 (3 a C+A b)+\frac{3}{5} a b x^5 (a C+A b)+\frac{3}{8} a b^2 D x^8+\frac{B \left(a+b x^2\right)^4}{8 b}+\frac{1}{9} b^3 C x^9+\frac{1}{10} b^3 D x^{10}",1,"a^3*A*x + (a^2*(3*A*b + a*C)*x^3)/3 + (a^3*D*x^4)/4 + (3*a*b*(A*b + a*C)*x^5)/5 + (a^2*b*D*x^6)/2 + (b^2*(A*b + 3*a*C)*x^7)/7 + (3*a*b^2*D*x^8)/8 + (b^3*C*x^9)/9 + (b^3*D*x^10)/10 + (B*(a + b*x^2)^4)/(8*b)","A",3,2,25,0.08000,1,"{1582, 1810}"
82,1,129,0,0.0904408,"\int \frac{\left(a+b x^2\right)^3 \left(A+B x+C x^2+D x^3\right)}{x} \, dx","Int[((a + b*x^2)^3*(A + B*x + C*x^2 + D*x^3))/x,x]","\frac{3}{2} a^2 A b x^2+a^3 A \log (x)+\frac{1}{3} a^2 x^3 (a D+3 b B)+a^3 B x+\frac{3}{4} a A b^2 x^4+\frac{1}{7} b^2 x^7 (3 a D+b B)+\frac{3}{5} a b x^5 (a D+b B)+\frac{C \left(a+b x^2\right)^4}{8 b}+\frac{1}{6} A b^3 x^6+\frac{1}{9} b^3 D x^9","\frac{3}{2} a^2 A b x^2+a^3 A \log (x)+\frac{1}{3} a^2 x^3 (a D+3 b B)+a^3 B x+\frac{3}{4} a A b^2 x^4+\frac{1}{7} b^2 x^7 (3 a D+b B)+\frac{3}{5} a b x^5 (a D+b B)+\frac{C \left(a+b x^2\right)^4}{8 b}+\frac{1}{6} A b^3 x^6+\frac{1}{9} b^3 D x^9",1,"a^3*B*x + (3*a^2*A*b*x^2)/2 + (a^2*(3*b*B + a*D)*x^3)/3 + (3*a*A*b^2*x^4)/4 + (3*a*b*(b*B + a*D)*x^5)/5 + (A*b^3*x^6)/6 + (b^2*(b*B + 3*a*D)*x^7)/7 + (b^3*D*x^9)/9 + (C*(a + b*x^2)^4)/(8*b) + a^3*A*Log[x]","A",3,2,28,0.07143,1,"{1583, 1802}"
83,1,124,0,0.1093203,"\int \frac{\left(a+b x^2\right)^3 \left(A+B x+C x^2+D x^3\right)}{x^2} \, dx","Int[((a + b*x^2)^3*(A + B*x + C*x^2 + D*x^3))/x^2,x]","a^2 x (a C+3 A b)-\frac{a^3 A}{x}+\frac{3}{2} a^2 b B x^2+a^3 B \log (x)+\frac{1}{5} b^2 x^5 (3 a C+A b)+a b x^3 (a C+A b)+\frac{3}{4} a b^2 B x^4+\frac{D \left(a+b x^2\right)^4}{8 b}+\frac{1}{6} b^3 B x^6+\frac{1}{7} b^3 C x^7","a^2 x (a C+3 A b)-\frac{a^3 A}{x}+\frac{3}{2} a^2 b B x^2+a^3 B \log (x)+\frac{1}{5} b^2 x^5 (3 a C+A b)+a b x^3 (a C+A b)+\frac{3}{4} a b^2 B x^4+\frac{D \left(a+b x^2\right)^4}{8 b}+\frac{1}{6} b^3 B x^6+\frac{1}{7} b^3 C x^7",1,"-((a^3*A)/x) + a^2*(3*A*b + a*C)*x + (3*a^2*b*B*x^2)/2 + a*b*(A*b + a*C)*x^3 + (3*a*b^2*B*x^4)/4 + (b^2*(A*b + 3*a*C)*x^5)/5 + (b^3*B*x^6)/6 + (b^3*C*x^7)/7 + (D*(a + b*x^2)^4)/(8*b) + a^3*B*Log[x]","A",3,2,28,0.07143,1,"{1583, 1628}"
84,1,135,0,0.1118279,"\int \frac{\left(a+b x^2\right)^3 \left(A+B x+C x^2+D x^3\right)}{x^3} \, dx","Int[((a + b*x^2)^3*(A + B*x + C*x^2 + D*x^3))/x^3,x]","a^2 \log (x) (a C+3 A b)-\frac{a^3 A}{2 x^2}+a^2 x (a D+3 b B)-\frac{a^3 B}{x}+\frac{1}{4} b^2 x^4 (3 a C+A b)+\frac{3}{2} a b x^2 (a C+A b)+\frac{1}{5} b^2 x^5 (3 a D+b B)+a b x^3 (a D+b B)+\frac{1}{6} b^3 C x^6+\frac{1}{7} b^3 D x^7","a^2 \log (x) (a C+3 A b)-\frac{a^3 A}{2 x^2}+a^2 x (a D+3 b B)-\frac{a^3 B}{x}+\frac{1}{4} b^2 x^4 (3 a C+A b)+\frac{3}{2} a b x^2 (a C+A b)+\frac{1}{5} b^2 x^5 (3 a D+b B)+a b x^3 (a D+b B)+\frac{1}{6} b^3 C x^6+\frac{1}{7} b^3 D x^7",1,"-(a^3*A)/(2*x^2) - (a^3*B)/x + a^2*(3*b*B + a*D)*x + (3*a*b*(A*b + a*C)*x^2)/2 + a*b*(b*B + a*D)*x^3 + (b^2*(A*b + 3*a*C)*x^4)/4 + (b^2*(b*B + 3*a*D)*x^5)/5 + (b^3*C*x^6)/6 + (b^3*D*x^7)/7 + a^2*(3*A*b + a*C)*Log[x]","A",2,1,28,0.03571,1,"{1802}"
85,1,139,0,0.1139006,"\int \frac{\left(a+b x^2\right)^3 \left(A+B x+C x^2+D x^3\right)}{x^4} \, dx","Int[((a + b*x^2)^3*(A + B*x + C*x^2 + D*x^3))/x^4,x]","-\frac{a^2 (a C+3 A b)}{x}-\frac{a^3 A}{3 x^3}+a^2 \log (x) (a D+3 b B)-\frac{a^3 B}{2 x^2}+\frac{1}{3} b^2 x^3 (3 a C+A b)+3 a b x (a C+A b)+\frac{1}{4} b^2 x^4 (3 a D+b B)+\frac{3}{2} a b x^2 (a D+b B)+\frac{1}{5} b^3 C x^5+\frac{1}{6} b^3 D x^6","-\frac{a^2 (a C+3 A b)}{x}-\frac{a^3 A}{3 x^3}+a^2 \log (x) (a D+3 b B)-\frac{a^3 B}{2 x^2}+\frac{1}{3} b^2 x^3 (3 a C+A b)+3 a b x (a C+A b)+\frac{1}{4} b^2 x^4 (3 a D+b B)+\frac{3}{2} a b x^2 (a D+b B)+\frac{1}{5} b^3 C x^5+\frac{1}{6} b^3 D x^6",1,"-(a^3*A)/(3*x^3) - (a^3*B)/(2*x^2) - (a^2*(3*A*b + a*C))/x + 3*a*b*(A*b + a*C)*x + (3*a*b*(b*B + a*D)*x^2)/2 + (b^2*(A*b + 3*a*C)*x^3)/3 + (b^2*(b*B + 3*a*D)*x^4)/4 + (b^3*C*x^5)/5 + (b^3*D*x^6)/6 + a^2*(3*b*B + a*D)*Log[x]","A",2,1,28,0.03571,1,"{1802}"
86,1,151,0,0.1449339,"\int \frac{x^4 \left(A+B x+C x^2+D x^3\right)}{a+b x^2} \, dx","Int[(x^4*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2),x]","\frac{a^{3/2} (A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{a^2 (b B-a D) \log \left(a+b x^2\right)}{2 b^4}+\frac{x^3 (A b-a C)}{3 b^2}-\frac{a x (A b-a C)}{b^3}+\frac{x^4 (b B-a D)}{4 b^2}-\frac{a x^2 (b B-a D)}{2 b^3}+\frac{C x^5}{5 b}+\frac{D x^6}{6 b}","\frac{a^{3/2} (A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{a^2 (b B-a D) \log \left(a+b x^2\right)}{2 b^4}+\frac{x^3 (A b-a C)}{3 b^2}-\frac{a x (A b-a C)}{b^3}+\frac{x^4 (b B-a D)}{4 b^2}-\frac{a x^2 (b B-a D)}{2 b^3}+\frac{C x^5}{5 b}+\frac{D x^6}{6 b}",1,"-((a*(A*b - a*C)*x)/b^3) - (a*(b*B - a*D)*x^2)/(2*b^3) + ((A*b - a*C)*x^3)/(3*b^2) + ((b*B - a*D)*x^4)/(4*b^2) + (C*x^5)/(5*b) + (D*x^6)/(6*b) + (a^(3/2)*(A*b - a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(7/2) + (a^2*(b*B - a*D)*Log[a + b*x^2])/(2*b^4)","A",5,4,28,0.1429,1,"{1802, 635, 205, 260}"
87,1,130,0,0.1237916,"\int \frac{x^3 \left(A+B x+C x^2+D x^3\right)}{a+b x^2} \, dx","Int[(x^3*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2),x]","\frac{a^{3/2} (b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{x^2 (A b-a C)}{2 b^2}-\frac{a (A b-a C) \log \left(a+b x^2\right)}{2 b^3}+\frac{x^3 (b B-a D)}{3 b^2}-\frac{a x (b B-a D)}{b^3}+\frac{C x^4}{4 b}+\frac{D x^5}{5 b}","\frac{a^{3/2} (b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{x^2 (A b-a C)}{2 b^2}-\frac{a (A b-a C) \log \left(a+b x^2\right)}{2 b^3}+\frac{x^3 (b B-a D)}{3 b^2}-\frac{a x (b B-a D)}{b^3}+\frac{C x^4}{4 b}+\frac{D x^5}{5 b}",1,"-((a*(b*B - a*D)*x)/b^3) + ((A*b - a*C)*x^2)/(2*b^2) + ((b*B - a*D)*x^3)/(3*b^2) + (C*x^4)/(4*b) + (D*x^5)/(5*b) + (a^(3/2)*(b*B - a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(7/2) - (a*(A*b - a*C)*Log[a + b*x^2])/(2*b^3)","A",5,4,28,0.1429,1,"{1802, 635, 205, 260}"
88,1,111,0,0.1131188,"\int \frac{x^2 \left(A+B x+C x^2+D x^3\right)}{a+b x^2} \, dx","Int[(x^2*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2),x]","\frac{x (A b-a C)}{b^2}-\frac{\sqrt{a} (A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}+\frac{x^2 (b B-a D)}{2 b^2}-\frac{a (b B-a D) \log \left(a+b x^2\right)}{2 b^3}+\frac{C x^3}{3 b}+\frac{D x^4}{4 b}","\frac{x (A b-a C)}{b^2}-\frac{\sqrt{a} (A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}+\frac{x^2 (b B-a D)}{2 b^2}-\frac{a (b B-a D) \log \left(a+b x^2\right)}{2 b^3}+\frac{C x^3}{3 b}+\frac{D x^4}{4 b}",1,"((A*b - a*C)*x)/b^2 + ((b*B - a*D)*x^2)/(2*b^2) + (C*x^3)/(3*b) + (D*x^4)/(4*b) - (Sqrt[a]*(A*b - a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(5/2) - (a*(b*B - a*D)*Log[a + b*x^2])/(2*b^3)","A",5,4,28,0.1429,1,"{1802, 635, 205, 260}"
89,1,92,0,0.0846149,"\int \frac{x \left(A+B x+C x^2+D x^3\right)}{a+b x^2} \, dx","Int[(x*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2),x]","\frac{(A b-a C) \log \left(a+b x^2\right)}{2 b^2}+\frac{x (b B-a D)}{b^2}-\frac{\sqrt{a} (b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}+\frac{C x^2}{2 b}+\frac{D x^3}{3 b}","\frac{(A b-a C) \log \left(a+b x^2\right)}{2 b^2}+\frac{x (b B-a D)}{b^2}-\frac{\sqrt{a} (b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}+\frac{C x^2}{2 b}+\frac{D x^3}{3 b}",1,"((b*B - a*D)*x)/b^2 + (C*x^2)/(2*b) + (D*x^3)/(3*b) - (Sqrt[a]*(b*B - a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(5/2) + ((A*b - a*C)*Log[a + b*x^2])/(2*b^2)","A",5,4,26,0.1538,1,"{1802, 635, 205, 260}"
90,1,73,0,0.0650568,"\int \frac{A+B x+C x^2+D x^3}{a+b x^2} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(a + b*x^2),x]","\frac{(A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}+\frac{(b B-a D) \log \left(a+b x^2\right)}{2 b^2}+\frac{C x}{b}+\frac{D x^2}{2 b}","\frac{(A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}+\frac{(b B-a D) \log \left(a+b x^2\right)}{2 b^2}+\frac{C x}{b}+\frac{D x^2}{2 b}",1,"(C*x)/b + (D*x^2)/(2*b) + ((A*b - a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*b^(3/2)) + ((b*B - a*D)*Log[a + b*x^2])/(2*b^2)","A",5,4,25,0.1600,1,"{1810, 635, 205, 260}"
91,1,72,0,0.0977419,"\int \frac{A+B x+C x^2+D x^3}{x \left(a+b x^2\right)} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(x*(a + b*x^2)),x]","-\frac{(A b-a C) \log \left(a+b x^2\right)}{2 a b}+\frac{A \log (x)}{a}+\frac{(b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}+\frac{D x}{b}","-\frac{(A b-a C) \log \left(a+b x^2\right)}{2 a b}+\frac{A \log (x)}{a}+\frac{(b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}+\frac{D x}{b}",1,"(D*x)/b + ((b*B - a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*b^(3/2)) + (A*Log[x])/a - ((A*b - a*C)*Log[a + b*x^2])/(2*a*b)","A",5,4,28,0.1429,1,"{1802, 635, 205, 260}"
92,1,76,0,0.0984595,"\int \frac{A+B x+C x^2+D x^3}{x^2 \left(a+b x^2\right)} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(x^2*(a + b*x^2)),x]","-\frac{(A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{A}{a x}-\frac{(b B-a D) \log \left(a+b x^2\right)}{2 a b}+\frac{B \log (x)}{a}","-\frac{(A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{A}{a x}-\frac{(b B-a D) \log \left(a+b x^2\right)}{2 a b}+\frac{B \log (x)}{a}",1,"-(A/(a*x)) - ((A*b - a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]) + (B*Log[x])/a - ((b*B - a*D)*Log[a + b*x^2])/(2*a*b)","A",5,4,28,0.1429,1,"{1802, 635, 205, 260}"
93,1,92,0,0.1086232,"\int \frac{A+B x+C x^2+D x^3}{x^3 \left(a+b x^2\right)} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(x^3*(a + b*x^2)),x]","\frac{(A b-a C) \log \left(a+b x^2\right)}{2 a^2}-\frac{\log (x) (A b-a C)}{a^2}-\frac{(b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{A}{2 a x^2}-\frac{B}{a x}","\frac{(A b-a C) \log \left(a+b x^2\right)}{2 a^2}-\frac{\log (x) (A b-a C)}{a^2}-\frac{(b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{A}{2 a x^2}-\frac{B}{a x}",1,"-A/(2*a*x^2) - B/(a*x) - ((b*B - a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]) - ((A*b - a*C)*Log[x])/a^2 + ((A*b - a*C)*Log[a + b*x^2])/(2*a^2)","A",5,4,28,0.1429,1,"{1802, 635, 205, 260}"
94,1,176,0,0.2679268,"\int \frac{x^4 \left(A+B x+C x^2+D x^3\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2)^2,x]","-\frac{x^3 (3 A b-5 a C)}{6 a b^2}+\frac{x (3 A b-5 a C)}{2 b^3}-\frac{\sqrt{a} (3 A b-5 a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}-\frac{x^4 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{2 a b \left(a+b x^2\right)}+\frac{x^2 (2 b B-3 a D)}{2 b^3}-\frac{a (2 b B-3 a D) \log \left(a+b x^2\right)}{2 b^4}+\frac{D x^4}{4 b^2}","-\frac{x^3 (3 A b-5 a C)}{6 a b^2}+\frac{x (3 A b-5 a C)}{2 b^3}-\frac{\sqrt{a} (3 A b-5 a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}-\frac{x^4 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{2 a b \left(a+b x^2\right)}+\frac{x^2 (2 b B-3 a D)}{2 b^3}-\frac{a (2 b B-3 a D) \log \left(a+b x^2\right)}{2 b^4}+\frac{D x^4}{4 b^2}",1,"((3*A*b - 5*a*C)*x)/(2*b^3) + ((2*b*B - 3*a*D)*x^2)/(2*b^3) - ((3*A*b - 5*a*C)*x^3)/(6*a*b^2) + (D*x^4)/(4*b^2) - (x^4*(a*(B - (a*D)/b) - (A*b - a*C)*x))/(2*a*b*(a + b*x^2)) - (Sqrt[a]*(3*A*b - 5*a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(7/2)) - (a*(2*b*B - 3*a*D)*Log[a + b*x^2])/(2*b^4)","A",6,5,28,0.1786,1,"{1804, 1802, 635, 205, 260}"
95,1,154,0,0.2413221,"\int \frac{x^3 \left(A+B x+C x^2+D x^3\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2)^2,x]","-\frac{x^2 (A b-2 a C)}{2 a b^2}+\frac{(A b-2 a C) \log \left(a+b x^2\right)}{2 b^3}-\frac{x^3 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{2 a b \left(a+b x^2\right)}+\frac{x (3 b B-5 a D)}{2 b^3}-\frac{\sqrt{a} (3 b B-5 a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}+\frac{D x^3}{3 b^2}","-\frac{x^2 (A b-2 a C)}{2 a b^2}+\frac{(A b-2 a C) \log \left(a+b x^2\right)}{2 b^3}-\frac{x^3 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{2 a b \left(a+b x^2\right)}+\frac{x (3 b B-5 a D)}{2 b^3}-\frac{\sqrt{a} (3 b B-5 a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}+\frac{D x^3}{3 b^2}",1,"((3*b*B - 5*a*D)*x)/(2*b^3) - ((A*b - 2*a*C)*x^2)/(2*a*b^2) + (D*x^3)/(3*b^2) - (x^3*(a*(B - (a*D)/b) - (A*b - a*C)*x))/(2*a*b*(a + b*x^2)) - (Sqrt[a]*(3*b*B - 5*a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(7/2)) + ((A*b - 2*a*C)*Log[a + b*x^2])/(2*b^3)","A",6,5,28,0.1786,1,"{1804, 1802, 635, 205, 260}"
96,1,134,0,0.2263884,"\int \frac{x^2 \left(A+B x+C x^2+D x^3\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2)^2,x]","-\frac{x (A b-3 a C)}{2 a b^2}+\frac{(A b-3 a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{5/2}}-\frac{x^2 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{2 a b \left(a+b x^2\right)}+\frac{(b B-2 a D) \log \left(a+b x^2\right)}{2 b^3}+\frac{D x^2}{2 b^2}","-\frac{x (A b-3 a C)}{2 a b^2}+\frac{(A b-3 a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{5/2}}-\frac{x^2 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{2 a b \left(a+b x^2\right)}+\frac{(b B-2 a D) \log \left(a+b x^2\right)}{2 b^3}+\frac{D x^2}{2 b^2}",1,"-((A*b - 3*a*C)*x)/(2*a*b^2) + (D*x^2)/(2*b^2) - (x^2*(a*(B - (a*D)/b) - (A*b - a*C)*x))/(2*a*b*(a + b*x^2)) + ((A*b - 3*a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*b^(5/2)) + ((b*B - 2*a*D)*Log[a + b*x^2])/(2*b^3)","A",6,5,28,0.1786,1,"{1804, 1802, 635, 205, 260}"
97,1,101,0,0.117818,"\int \frac{x \left(A+B x+C x^2+D x^3\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2)^2,x]","-\frac{x \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{2 a b \left(a+b x^2\right)}+\frac{(b B-3 a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{5/2}}+\frac{C \log \left(a+b x^2\right)}{2 b^2}+\frac{D x}{b^2}","-\frac{x \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{2 a b \left(a+b x^2\right)}+\frac{(b B-3 a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{5/2}}+\frac{C \log \left(a+b x^2\right)}{2 b^2}+\frac{D x}{b^2}",1,"(D*x)/b^2 - (x*(a*(B - (a*D)/b) - (A*b - a*C)*x))/(2*a*b*(a + b*x^2)) + ((b*B - 3*a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*b^(5/2)) + (C*Log[a + b*x^2])/(2*b^2)","A",6,5,26,0.1923,1,"{1804, 1810, 635, 205, 260}"
98,1,93,0,0.0654198,"\int \frac{A+B x+C x^2+D x^3}{\left(a+b x^2\right)^2} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(a + b*x^2)^2,x]","\frac{(a C+A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2}}-\frac{a \left(B-\frac{a D}{b}\right)-x (A b-a C)}{2 a b \left(a+b x^2\right)}+\frac{D \log \left(a+b x^2\right)}{2 b^2}","\frac{(a C+A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2}}-\frac{a \left(B-\frac{a D}{b}\right)-x (A b-a C)}{2 a b \left(a+b x^2\right)}+\frac{D \log \left(a+b x^2\right)}{2 b^2}",1,"-(a*(B - (a*D)/b) - (A*b - a*C)*x)/(2*a*b*(a + b*x^2)) + ((A*b + a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*b^(3/2)) + (D*Log[a + b*x^2])/(2*b^2)","A",4,4,25,0.1600,1,"{1814, 635, 205, 260}"
99,1,95,0,0.1216478,"\int \frac{A+B x+C x^2+D x^3}{x \left(a+b x^2\right)^2} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(x*(a + b*x^2)^2),x]","-\frac{A \log \left(a+b x^2\right)}{2 a^2}+\frac{A \log (x)}{a^2}+\frac{(a D+b B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2}}+\frac{x (b B-a D)-a C+A b}{2 a b \left(a+b x^2\right)}","-\frac{A \log \left(a+b x^2\right)}{2 a^2}+\frac{A \log (x)}{a^2}+\frac{(a D+b B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2}}+\frac{x (b B-a D)-a C+A b}{2 a b \left(a+b x^2\right)}",1,"(A*b - a*C + (b*B - a*D)*x)/(2*a*b*(a + b*x^2)) + ((b*B + a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*b^(3/2)) + (A*Log[x])/a^2 - (A*Log[a + b*x^2])/(2*a^2)","A",6,5,28,0.1786,1,"{1805, 801, 635, 205, 260}"
100,1,110,0,0.141581,"\int \frac{A+B x+C x^2+D x^3}{x^2 \left(a+b x^2\right)^2} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(x^2*(a + b*x^2)^2),x]","-\frac{(3 A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b}}-\frac{A}{a^2 x}-\frac{B \log \left(a+b x^2\right)}{2 a^2}+\frac{B \log (x)}{a^2}+\frac{-b x \left(\frac{A b}{a}-C\right)-a D+b B}{2 a b \left(a+b x^2\right)}","-\frac{(3 A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b}}-\frac{A}{a^2 x}-\frac{B \log \left(a+b x^2\right)}{2 a^2}+\frac{B \log (x)}{a^2}+\frac{-b x \left(\frac{A b}{a}-C\right)-a D+b B}{2 a b \left(a+b x^2\right)}",1,"-(A/(a^2*x)) + (b*B - a*D - b*((A*b)/a - C)*x)/(2*a*b*(a + b*x^2)) - ((3*A*b - a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*Sqrt[b]) + (B*Log[x])/a^2 - (B*Log[a + b*x^2])/(2*a^2)","A",6,5,28,0.1786,1,"{1805, 1802, 635, 205, 260}"
101,1,135,0,0.2040274,"\int \frac{A+B x+C x^2+D x^3}{x^3 \left(a+b x^2\right)^2} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(x^3*(a + b*x^2)^2),x]","\frac{(2 A b-a C) \log \left(a+b x^2\right)}{2 a^3}-\frac{\log (x) (2 A b-a C)}{a^3}-\frac{A}{2 a^2 x^2}-\frac{(3 b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b}}-\frac{B}{a^2 x}-\frac{\frac{A b}{a}+x \left(\frac{b B}{a}-D\right)-C}{2 a \left(a+b x^2\right)}","\frac{(2 A b-a C) \log \left(a+b x^2\right)}{2 a^3}-\frac{\log (x) (2 A b-a C)}{a^3}-\frac{A}{2 a^2 x^2}-\frac{(3 b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b}}-\frac{B}{a^2 x}-\frac{\frac{A b}{a}+x \left(\frac{b B}{a}-D\right)-C}{2 a \left(a+b x^2\right)}",1,"-A/(2*a^2*x^2) - B/(a^2*x) - ((A*b)/a - C + ((b*B)/a - D)*x)/(2*a*(a + b*x^2)) - ((3*b*B - a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*Sqrt[b]) - ((2*A*b - a*C)*Log[x])/a^3 + ((2*A*b - a*C)*Log[a + b*x^2])/(2*a^3)","A",6,5,28,0.1786,1,"{1805, 1802, 635, 205, 260}"
102,1,185,0,0.3381833,"\int \frac{x^4 \left(A+B x+C x^2+D x^3\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^4*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2)^3,x]","\frac{x^3 (4 x (b B-2 a D)-5 a C+A b)}{8 a b^2 \left(a+b x^2\right)}-\frac{3 x (A b-5 a C)}{8 a b^3}+\frac{3 (A b-5 a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{7/2}}-\frac{x^4 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{4 a b \left(a+b x^2\right)^2}-\frac{x^2 (b B-3 a D)}{2 a b^3}+\frac{(b B-3 a D) \log \left(a+b x^2\right)}{2 b^4}","\frac{x^3 (4 x (b B-2 a D)-5 a C+A b)}{8 a b^2 \left(a+b x^2\right)}-\frac{3 x (A b-5 a C)}{8 a b^3}+\frac{3 (A b-5 a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{7/2}}-\frac{x^4 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{4 a b \left(a+b x^2\right)^2}-\frac{x^2 (b B-3 a D)}{2 a b^3}+\frac{(b B-3 a D) \log \left(a+b x^2\right)}{2 b^4}",1,"(-3*(A*b - 5*a*C)*x)/(8*a*b^3) - ((b*B - 3*a*D)*x^2)/(2*a*b^3) - (x^4*(a*(B - (a*D)/b) - (A*b - a*C)*x))/(4*a*b*(a + b*x^2)^2) + (x^3*(A*b - 5*a*C + 4*(b*B - 2*a*D)*x))/(8*a*b^2*(a + b*x^2)) + (3*(A*b - 5*a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*Sqrt[a]*b^(7/2)) + ((b*B - 3*a*D)*Log[a + b*x^2])/(2*b^4)","A",7,5,28,0.1786,1,"{1804, 801, 635, 205, 260}"
103,1,155,0,0.2324435,"\int \frac{x^3 \left(A+B x+C x^2+D x^3\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^3*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2)^3,x]","-\frac{x^3 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{4 a b \left(a+b x^2\right)^2}-\frac{x^2 (4 a C-x (3 b B-7 a D))}{8 a b^2 \left(a+b x^2\right)}-\frac{3 x (b B-5 a D)}{8 a b^3}+\frac{3 (b B-5 a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{7/2}}+\frac{C \log \left(a+b x^2\right)}{2 b^3}","-\frac{x^3 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{4 a b \left(a+b x^2\right)^2}-\frac{x^2 (4 a C-x (3 b B-7 a D))}{8 a b^2 \left(a+b x^2\right)}-\frac{3 x (b B-5 a D)}{8 a b^3}+\frac{3 (b B-5 a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{7/2}}+\frac{C \log \left(a+b x^2\right)}{2 b^3}",1,"(-3*(b*B - 5*a*D)*x)/(8*a*b^3) - (x^3*(a*(B - (a*D)/b) - (A*b - a*C)*x))/(4*a*b*(a + b*x^2)^2) - (x^2*(4*a*C - (3*b*B - 7*a*D)*x))/(8*a*b^2*(a + b*x^2)) + (3*(b*B - 5*a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*Sqrt[a]*b^(7/2)) + (C*Log[a + b*x^2])/(2*b^3)","A",6,5,28,0.1786,1,"{1804, 774, 635, 205, 260}"
104,1,136,0,0.1584623,"\int \frac{x^2 \left(A+B x+C x^2+D x^3\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^2*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2)^3,x]","\frac{(3 a C+A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{5/2}}-\frac{x (-2 x (b B-3 a D)+3 a C+A b)}{8 a b^2 \left(a+b x^2\right)}-\frac{x^2 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{4 a b \left(a+b x^2\right)^2}+\frac{D \log \left(a+b x^2\right)}{2 b^3}","\frac{(3 a C+A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{5/2}}-\frac{x (-2 x (b B-3 a D)+3 a C+A b)}{8 a b^2 \left(a+b x^2\right)}-\frac{x^2 \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{4 a b \left(a+b x^2\right)^2}+\frac{D \log \left(a+b x^2\right)}{2 b^3}",1,"-(x^2*(a*(B - (a*D)/b) - (A*b - a*C)*x))/(4*a*b*(a + b*x^2)^2) - (x*(A*b + 3*a*C - 2*(b*B - 3*a*D)*x))/(8*a*b^2*(a + b*x^2)) + ((A*b + 3*a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(3/2)*b^(5/2)) + (D*Log[a + b*x^2])/(2*b^3)","A",5,4,28,0.1429,1,"{1804, 635, 205, 260}"
105,1,119,0,0.1141078,"\int \frac{x \left(A+B x+C x^2+D x^3\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x*(A + B*x + C*x^2 + D*x^3))/(a + b*x^2)^3,x]","\frac{(3 a D+b B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{5/2}}-\frac{2 (a C+A b)-x (b B-5 a D)}{8 a b^2 \left(a+b x^2\right)}-\frac{x \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{4 a b \left(a+b x^2\right)^2}","\frac{(3 a D+b B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{5/2}}-\frac{2 (a C+A b)-x (b B-5 a D)}{8 a b^2 \left(a+b x^2\right)}-\frac{x \left(a \left(B-\frac{a D}{b}\right)-x (A b-a C)\right)}{4 a b \left(a+b x^2\right)^2}",1,"-(x*(a*(B - (a*D)/b) - (A*b - a*C)*x))/(4*a*b*(a + b*x^2)^2) - (2*(A*b + a*C) - (b*B - 5*a*D)*x)/(8*a*b^2*(a + b*x^2)) + ((b*B + 3*a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(3/2)*b^(5/2))","A",4,4,26,0.1538,1,"{1804, 1814, 12, 205}"
106,1,116,0,0.0682323,"\int \frac{A+B x+C x^2+D x^3}{\left(a+b x^2\right)^3} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(a + b*x^2)^3,x]","-\frac{4 a^2 D-b x (a C+3 A b)}{8 a^2 b^2 \left(a+b x^2\right)}+\frac{(a C+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2}}-\frac{a \left(B-\frac{a D}{b}\right)-x (A b-a C)}{4 a b \left(a+b x^2\right)^2}","-\frac{4 a^2 D-b x (a C+3 A b)}{8 a^2 b^2 \left(a+b x^2\right)}+\frac{(a C+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2}}-\frac{a \left(B-\frac{a D}{b}\right)-x (A b-a C)}{4 a b \left(a+b x^2\right)^2}",1,"-(a*(B - (a*D)/b) - (A*b - a*C)*x)/(4*a*b*(a + b*x^2)^2) - (4*a^2*D - b*(3*A*b + a*C)*x)/(8*a^2*b^2*(a + b*x^2)) + ((3*A*b + a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*b^(3/2))","A",3,3,25,0.1200,1,"{1814, 639, 205}"
107,1,130,0,0.134627,"\int \frac{A+B x+C x^2+D x^3}{x \left(a+b x^2\right)^3} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(x*(a + b*x^2)^3),x]","\frac{x (a D+3 b B)+4 A b}{8 a^2 b \left(a+b x^2\right)}-\frac{A \log \left(a+b x^2\right)}{2 a^3}+\frac{A \log (x)}{a^3}+\frac{(a D+3 b B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2}}+\frac{x (b B-a D)-a C+A b}{4 a b \left(a+b x^2\right)^2}","\frac{x (a D+3 b B)+4 A b}{8 a^2 b \left(a+b x^2\right)}-\frac{A \log \left(a+b x^2\right)}{2 a^3}+\frac{A \log (x)}{a^3}+\frac{(a D+3 b B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2}}+\frac{x (b B-a D)-a C+A b}{4 a b \left(a+b x^2\right)^2}",1,"(A*b - a*C + (b*B - a*D)*x)/(4*a*b*(a + b*x^2)^2) + (4*A*b + (3*b*B + a*D)*x)/(8*a^2*b*(a + b*x^2)) + ((3*b*B + a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*b^(3/2)) + (A*Log[x])/a^3 - (A*Log[a + b*x^2])/(2*a^3)","A",7,6,28,0.2143,1,"{1805, 823, 801, 635, 205, 260}"
108,1,144,0,0.2281485,"\int \frac{A+B x+C x^2+D x^3}{x^2 \left(a+b x^2\right)^3} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(x^2*(a + b*x^2)^3),x]","\frac{4 B-x \left(\frac{7 A b}{a}-3 C\right)}{8 a^2 \left(a+b x^2\right)}-\frac{3 (5 A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{b}}-\frac{A}{a^3 x}-\frac{B \log \left(a+b x^2\right)}{2 a^3}+\frac{B \log (x)}{a^3}+\frac{-b x \left(\frac{A b}{a}-C\right)-a D+b B}{4 a b \left(a+b x^2\right)^2}","\frac{4 B-x \left(\frac{7 A b}{a}-3 C\right)}{8 a^2 \left(a+b x^2\right)}-\frac{3 (5 A b-a C) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{b}}-\frac{A}{a^3 x}-\frac{B \log \left(a+b x^2\right)}{2 a^3}+\frac{B \log (x)}{a^3}+\frac{-b x \left(\frac{A b}{a}-C\right)-a D+b B}{4 a b \left(a+b x^2\right)^2}",1,"-(A/(a^3*x)) + (b*B - a*D - b*((A*b)/a - C)*x)/(4*a*b*(a + b*x^2)^2) + (4*B - ((7*A*b)/a - 3*C)*x)/(8*a^2*(a + b*x^2)) - (3*(5*A*b - a*C)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2)*Sqrt[b]) + (B*Log[x])/a^3 - (B*Log[a + b*x^2])/(2*a^3)","A",7,5,28,0.1786,1,"{1805, 1802, 635, 205, 260}"
109,1,174,0,0.3110106,"\int \frac{A+B x+C x^2+D x^3}{x^3 \left(a+b x^2\right)^3} \, dx","Int[(A + B*x + C*x^2 + D*x^3)/(x^3*(a + b*x^2)^3),x]","-\frac{4 (2 A b-a C)+x (7 b B-3 a D)}{8 a^3 \left(a+b x^2\right)}+\frac{(3 A b-a C) \log \left(a+b x^2\right)}{2 a^4}-\frac{\log (x) (3 A b-a C)}{a^4}-\frac{A}{2 a^3 x^2}-\frac{3 (5 b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{b}}-\frac{B}{a^3 x}-\frac{\frac{A b}{a}+x \left(\frac{b B}{a}-D\right)-C}{4 a \left(a+b x^2\right)^2}","-\frac{4 (2 A b-a C)+x (7 b B-3 a D)}{8 a^3 \left(a+b x^2\right)}+\frac{(3 A b-a C) \log \left(a+b x^2\right)}{2 a^4}-\frac{\log (x) (3 A b-a C)}{a^4}-\frac{A}{2 a^3 x^2}-\frac{3 (5 b B-a D) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{b}}-\frac{B}{a^3 x}-\frac{\frac{A b}{a}+x \left(\frac{b B}{a}-D\right)-C}{4 a \left(a+b x^2\right)^2}",1,"-A/(2*a^3*x^2) - B/(a^3*x) - ((A*b)/a - C + ((b*B)/a - D)*x)/(4*a*(a + b*x^2)^2) - (4*(2*A*b - a*C) + (7*b*B - 3*a*D)*x)/(8*a^3*(a + b*x^2)) - (3*(5*b*B - a*D)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2)*Sqrt[b]) - ((3*A*b - a*C)*Log[x])/a^4 + ((3*A*b - a*C)*Log[a + b*x^2])/(2*a^4)","A",7,5,28,0.1786,1,"{1805, 1802, 635, 205, 260}"
110,1,20,0,0.0230683,"\int \frac{-x+4 x^3}{\left(5+x^2\right)^2} \, dx","Int[(-x + 4*x^3)/(5 + x^2)^2,x]","\frac{21}{2 \left(x^2+5\right)}+2 \log \left(x^2+5\right)","\frac{21}{2 \left(x^2+5\right)}+2 \log \left(x^2+5\right)",1,"21/(2*(5 + x^2)) + 2*Log[5 + x^2]","A",4,3,17,0.1765,1,"{1593, 444, 43}"
111,1,23,0,0.0211766,"\int \frac{-x+x^3}{\sqrt{-2+x^2}} \, dx","Int[(-x + x^3)/Sqrt[-2 + x^2],x]","\frac{1}{3} \left(x^2-2\right)^{3/2}+\sqrt{x^2-2}","\frac{1}{3} \left(x^2-2\right)^{3/2}+\sqrt{x^2-2}",1,"Sqrt[-2 + x^2] + (-2 + x^2)^(3/2)/3","A",4,3,17,0.1765,1,"{1593, 444, 43}"
112,1,25,0,0.0241169,"\int \frac{-x^2+2 x^4}{1+2 x^2} \, dx","Int[(-x^2 + 2*x^4)/(1 + 2*x^2),x]","\frac{x^3}{3}-x+\frac{\tan ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}","\frac{x^3}{3}-x+\frac{\tan ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}",1,"-x + x^3/3 + ArcTan[Sqrt[2]*x]/Sqrt[2]","A",4,4,21,0.1905,1,"{1593, 459, 321, 203}"
113,1,30,0,0.0252424,"\int \frac{x^3+x^4}{1+x^2} \, dx","Int[(x^3 + x^4)/(1 + x^2),x]","\frac{x^3}{3}+\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+1\right)-x+\tan ^{-1}(x)","\frac{x^3}{3}+\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+1\right)-x+\tan ^{-1}(x)",1,"-x + x^2/2 + x^3/3 + ArcTan[x] - Log[1 + x^2]/2","A",6,5,15,0.3333,1,"{1593, 801, 635, 203, 260}"
114,1,210,0,0.161395,"\int \frac{x^6 \left(c+d x^2+e x^4+f x^6\right)}{a+b x^2} \, dx","Int[(x^6*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2),x]","\frac{x^5 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{5 b^4}-\frac{a x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5}+\frac{a^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^6}-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^{13/2}}+\frac{x^7 \left(a^2 f-a b e+b^2 d\right)}{7 b^3}+\frac{x^9 (b e-a f)}{9 b^2}+\frac{f x^{11}}{11 b}","\frac{x^5 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{5 b^4}-\frac{a x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5}+\frac{a^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^6}-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^{13/2}}+\frac{x^7 \left(a^2 f-a b e+b^2 d\right)}{7 b^3}+\frac{x^9 (b e-a f)}{9 b^2}+\frac{f x^{11}}{11 b}",1,"(a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^6 - (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(3*b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^5)/(5*b^4) + ((b^2*d - a*b*e + a^2*f)*x^7)/(7*b^3) + ((b*e - a*f)*x^9)/(9*b^2) + (f*x^11)/(11*b) - (a^(5/2)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(13/2)","A",3,2,30,0.06667,1,"{1802, 205}"
115,1,172,0,0.1227127,"\int \frac{x^4 \left(c+d x^2+e x^4+f x^6\right)}{a+b x^2} \, dx","Int[(x^4*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2),x]","\frac{x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4}-\frac{a x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^5}+\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^{11/2}}+\frac{x^5 \left(a^2 f-a b e+b^2 d\right)}{5 b^3}+\frac{x^7 (b e-a f)}{7 b^2}+\frac{f x^9}{9 b}","\frac{x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4}-\frac{a x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^5}+\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^{11/2}}+\frac{x^5 \left(a^2 f-a b e+b^2 d\right)}{5 b^3}+\frac{x^7 (b e-a f)}{7 b^2}+\frac{f x^9}{9 b}",1,"-((a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(3*b^4) + ((b^2*d - a*b*e + a^2*f)*x^5)/(5*b^3) + ((b*e - a*f)*x^7)/(7*b^2) + (f*x^9)/(9*b) + (a^(3/2)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(11/2)","A",3,2,30,0.06667,1,"{1802, 205}"
116,1,136,0,0.1053738,"\int \frac{x^2 \left(c+d x^2+e x^4+f x^6\right)}{a+b x^2} \, dx","Int[(x^2*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2),x]","\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^{9/2}}+\frac{x^3 \left(a^2 f-a b e+b^2 d\right)}{3 b^3}+\frac{x^5 (b e-a f)}{5 b^2}+\frac{f x^7}{7 b}","\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^{9/2}}+\frac{x^3 \left(a^2 f-a b e+b^2 d\right)}{3 b^3}+\frac{x^5 (b e-a f)}{5 b^2}+\frac{f x^7}{7 b}",1,"((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^4 + ((b^2*d - a*b*e + a^2*f)*x^3)/(3*b^3) + ((b*e - a*f)*x^5)/(5*b^2) + (f*x^7)/(7*b) - (Sqrt[a]*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(9/2)","A",3,2,30,0.06667,1,"{1802, 205}"
117,1,100,0,0.0615987,"\int \frac{c+d x^2+e x^4+f x^6}{a+b x^2} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(a + b*x^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{a} b^{7/2}}+\frac{x \left(a^2 f-a b e+b^2 d\right)}{b^3}+\frac{x^3 (b e-a f)}{3 b^2}+\frac{f x^5}{5 b}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{a} b^{7/2}}+\frac{x \left(a^2 f-a b e+b^2 d\right)}{b^3}+\frac{x^3 (b e-a f)}{3 b^2}+\frac{f x^5}{5 b}",1,"((b^2*d - a*b*e + a^2*f)*x)/b^3 + ((b*e - a*f)*x^3)/(3*b^2) + (f*x^5)/(5*b) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*b^(7/2))","A",3,2,27,0.07407,1,"{1810, 205}"
118,1,84,0,0.0940384,"\int \frac{c+d x^2+e x^4+f x^6}{x^2 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^2*(a + b*x^2)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{3/2} b^{5/2}}+\frac{x (b e-a f)}{b^2}-\frac{c}{a x}+\frac{f x^3}{3 b}","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{3/2} b^{5/2}}+\frac{x (b e-a f)}{b^2}-\frac{c}{a x}+\frac{f x^3}{3 b}",1,"-(c/(a*x)) + ((b*e - a*f)*x)/b^2 + (f*x^3)/(3*b) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*b^(5/2))","A",3,2,30,0.06667,1,"{1802, 205}"
119,1,82,0,0.087426,"\int \frac{c+d x^2+e x^4+f x^6}{x^4 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^4*(a + b*x^2)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{5/2} b^{3/2}}+\frac{b c-a d}{a^2 x}-\frac{c}{3 a x^3}+\frac{f x}{b}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{5/2} b^{3/2}}+\frac{b c-a d}{a^2 x}-\frac{c}{3 a x^3}+\frac{f x}{b}",1,"-c/(3*a*x^3) + (b*c - a*d)/(a^2*x) + (f*x)/b + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(5/2)*b^(3/2))","A",3,2,30,0.06667,1,"{1802, 205}"
120,1,104,0,0.1023928,"\int \frac{c+d x^2+e x^4+f x^6}{x^6 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^6*(a + b*x^2)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{7/2} \sqrt{b}}-\frac{a^2 e-a b d+b^2 c}{a^3 x}+\frac{b c-a d}{3 a^2 x^3}-\frac{c}{5 a x^5}","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{7/2} \sqrt{b}}-\frac{a^2 e-a b d+b^2 c}{a^3 x}+\frac{b c-a d}{3 a^2 x^3}-\frac{c}{5 a x^5}",1,"-c/(5*a*x^5) + (b*c - a*d)/(3*a^2*x^3) - (b^2*c - a*b*d + a^2*e)/(a^3*x) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(7/2)*Sqrt[b])","A",3,2,30,0.06667,1,"{1802, 205}"
121,1,137,0,0.1303515,"\int \frac{c+d x^2+e x^4+f x^6}{x^8 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^8*(a + b*x^2)),x]","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{a^4 x}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{9/2}}-\frac{a^2 e-a b d+b^2 c}{3 a^3 x^3}+\frac{b c-a d}{5 a^2 x^5}-\frac{c}{7 a x^7}","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{a^4 x}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{9/2}}-\frac{a^2 e-a b d+b^2 c}{3 a^3 x^3}+\frac{b c-a d}{5 a^2 x^5}-\frac{c}{7 a x^7}",1,"-c/(7*a*x^7) + (b*c - a*d)/(5*a^2*x^5) - (b^2*c - a*b*d + a^2*e)/(3*a^3*x^3) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(a^4*x) + (Sqrt[b]*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(9/2)","A",3,2,30,0.06667,1,"{1802, 205}"
122,1,175,0,0.1459239,"\int \frac{c+d x^2+e x^4+f x^6}{x^{10} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^10*(a + b*x^2)),x]","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^4 x^3}-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^5 x}-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{11/2}}-\frac{a^2 e-a b d+b^2 c}{5 a^3 x^5}+\frac{b c-a d}{7 a^2 x^7}-\frac{c}{9 a x^9}","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^4 x^3}-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^5 x}-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{11/2}}-\frac{a^2 e-a b d+b^2 c}{5 a^3 x^5}+\frac{b c-a d}{7 a^2 x^7}-\frac{c}{9 a x^9}",1,"-c/(9*a*x^9) + (b*c - a*d)/(7*a^2*x^7) - (b^2*c - a*b*d + a^2*e)/(5*a^3*x^5) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a^4*x^3) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(a^5*x) - (b^(3/2)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(11/2)","A",3,2,30,0.06667,1,"{1802, 205}"
123,1,211,0,0.1751879,"\int \frac{c+d x^2+e x^4+f x^6}{x^{12} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^12*(a + b*x^2)),x]","-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 x^3}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{5 a^4 x^5}+\frac{b^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^6 x}+\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{13/2}}-\frac{a^2 e-a b d+b^2 c}{7 a^3 x^7}+\frac{b c-a d}{9 a^2 x^9}-\frac{c}{11 a x^{11}}","-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 x^3}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{5 a^4 x^5}+\frac{b^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^6 x}+\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^{13/2}}-\frac{a^2 e-a b d+b^2 c}{7 a^3 x^7}+\frac{b c-a d}{9 a^2 x^9}-\frac{c}{11 a x^{11}}",1,"-c/(11*a*x^11) + (b*c - a*d)/(9*a^2*x^9) - (b^2*c - a*b*d + a^2*e)/(7*a^3*x^7) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(5*a^4*x^5) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*a^5*x^3) + (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(a^6*x) + (b^(5/2)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(13/2)","A",3,2,30,0.06667,1,"{1802, 205}"
124,1,240,0,0.2942878,"\int \frac{x^6 \left(c+d x^2+e x^4+f x^6\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^6*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^2,x]","\frac{x^7 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{2 a \left(a+b x^2\right)}-\frac{x^5 \left(9 a^2 b e-11 a^3 f-7 a b^2 d+5 b^3 c\right)}{10 a b^4}+\frac{x^3 \left(9 a^2 b e-11 a^3 f-7 a b^2 d+5 b^3 c\right)}{6 b^5}-\frac{a x \left(9 a^2 b e-11 a^3 f-7 a b^2 d+5 b^3 c\right)}{2 b^6}+\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(9 a^2 b e-11 a^3 f-7 a b^2 d+5 b^3 c\right)}{2 b^{13/2}}+\frac{x^7 (b e-2 a f)}{7 b^3}+\frac{f x^9}{9 b^2}","\frac{x^7 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{2 a \left(a+b x^2\right)}-\frac{x^5 \left(9 a^2 b e-11 a^3 f-7 a b^2 d+5 b^3 c\right)}{10 a b^4}+\frac{x^3 \left(9 a^2 b e-11 a^3 f-7 a b^2 d+5 b^3 c\right)}{6 b^5}-\frac{a x \left(9 a^2 b e-11 a^3 f-7 a b^2 d+5 b^3 c\right)}{2 b^6}+\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(9 a^2 b e-11 a^3 f-7 a b^2 d+5 b^3 c\right)}{2 b^{13/2}}+\frac{x^7 (b e-2 a f)}{7 b^3}+\frac{f x^9}{9 b^2}",1,"-(a*(5*b^3*c - 7*a*b^2*d + 9*a^2*b*e - 11*a^3*f)*x)/(2*b^6) + ((5*b^3*c - 7*a*b^2*d + 9*a^2*b*e - 11*a^3*f)*x^3)/(6*b^5) - ((5*b^3*c - 7*a*b^2*d + 9*a^2*b*e - 11*a^3*f)*x^5)/(10*a*b^4) + ((b*e - 2*a*f)*x^7)/(7*b^3) + (f*x^9)/(9*b^2) + ((c - (a*(b^2*d - a*b*e + a^2*f))/b^3)*x^7)/(2*a*(a + b*x^2)) + (a^(3/2)*(5*b^3*c - 7*a*b^2*d + 9*a^2*b*e - 11*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(13/2))","A",5,4,30,0.1333,1,"{1804, 1585, 1261, 205}"
125,1,202,0,0.2348744,"\int \frac{x^4 \left(c+d x^2+e x^4+f x^6\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^2,x]","\frac{x^5 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{2 a \left(a+b x^2\right)}-\frac{x^3 \left(7 a^2 b e-9 a^3 f-5 a b^2 d+3 b^3 c\right)}{6 a b^4}+\frac{x \left(7 a^2 b e-9 a^3 f-5 a b^2 d+3 b^3 c\right)}{2 b^5}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(7 a^2 b e-9 a^3 f-5 a b^2 d+3 b^3 c\right)}{2 b^{11/2}}+\frac{x^5 (b e-2 a f)}{5 b^3}+\frac{f x^7}{7 b^2}","\frac{x^5 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{2 a \left(a+b x^2\right)}-\frac{x^3 \left(7 a^2 b e-9 a^3 f-5 a b^2 d+3 b^3 c\right)}{6 a b^4}+\frac{x \left(7 a^2 b e-9 a^3 f-5 a b^2 d+3 b^3 c\right)}{2 b^5}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(7 a^2 b e-9 a^3 f-5 a b^2 d+3 b^3 c\right)}{2 b^{11/2}}+\frac{x^5 (b e-2 a f)}{5 b^3}+\frac{f x^7}{7 b^2}",1,"((3*b^3*c - 5*a*b^2*d + 7*a^2*b*e - 9*a^3*f)*x)/(2*b^5) - ((3*b^3*c - 5*a*b^2*d + 7*a^2*b*e - 9*a^3*f)*x^3)/(6*a*b^4) + ((b*e - 2*a*f)*x^5)/(5*b^3) + (f*x^7)/(7*b^2) + ((c - (a*(b^2*d - a*b*e + a^2*f))/b^3)*x^5)/(2*a*(a + b*x^2)) - (Sqrt[a]*(3*b^3*c - 5*a*b^2*d + 7*a^2*b*e - 9*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(11/2))","A",5,4,30,0.1333,1,"{1804, 1585, 1261, 205}"
126,1,163,0,0.2287939,"\int \frac{x^2 \left(c+d x^2+e x^4+f x^6\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^2,x]","\frac{x^3 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{2 a \left(a+b x^2\right)}-\frac{x \left(5 a^2 b e-7 a^3 f-3 a b^2 d+b^3 c\right)}{2 a b^4}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(5 a^2 b e-7 a^3 f-3 a b^2 d+b^3 c\right)}{2 \sqrt{a} b^{9/2}}+\frac{x^3 (b e-2 a f)}{3 b^3}+\frac{f x^5}{5 b^2}","\frac{x^3 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{2 a \left(a+b x^2\right)}-\frac{x \left(5 a^2 b e-7 a^3 f-3 a b^2 d+b^3 c\right)}{2 a b^4}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(5 a^2 b e-7 a^3 f-3 a b^2 d+b^3 c\right)}{2 \sqrt{a} b^{9/2}}+\frac{x^3 (b e-2 a f)}{3 b^3}+\frac{f x^5}{5 b^2}",1,"-((b^3*c - 3*a*b^2*d + 5*a^2*b*e - 7*a^3*f)*x)/(2*a*b^4) + ((b*e - 2*a*f)*x^3)/(3*b^3) + (f*x^5)/(5*b^2) + ((c - (a*(b^2*d - a*b*e + a^2*f))/b^3)*x^3)/(2*a*(a + b*x^2)) + ((b^3*c - 3*a*b^2*d + 5*a^2*b*e - 7*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*b^(9/2))","A",5,4,30,0.1333,1,"{1804, 1585, 1261, 205}"
127,1,118,0,0.1198564,"\int \frac{c+d x^2+e x^4+f x^6}{\left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(a + b*x^2)^2,x]","\frac{x \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{2 a \left(a+b x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(-3 a^2 b e+5 a^3 f+a b^2 d+b^3 c\right)}{2 a^{3/2} b^{7/2}}+\frac{x (b e-2 a f)}{b^3}+\frac{f x^3}{3 b^2}","\frac{x \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{2 a \left(a+b x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(-3 a^2 b e+5 a^3 f+a b^2 d+b^3 c\right)}{2 a^{3/2} b^{7/2}}+\frac{x (b e-2 a f)}{b^3}+\frac{f x^3}{3 b^2}",1,"((b*e - 2*a*f)*x)/b^3 + (f*x^3)/(3*b^2) + ((c - (a*(b^2*d - a*b*e + a^2*f))/b^3)*x)/(2*a*(a + b*x^2)) + ((b^3*c + a*b^2*d - 3*a^2*b*e + 5*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*b^(7/2))","A",4,3,27,0.1111,1,"{1814, 1153, 205}"
128,1,112,0,0.1318822,"\int \frac{c+d x^2+e x^4+f x^6}{x^2 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^2*(a + b*x^2)^2),x]","-\frac{x \left(-\frac{a^2 f}{b^2}+\frac{b c}{a}+\frac{a e}{b}-d\right)}{2 a \left(a+b x^2\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(-a^2 b e+3 a^3 f-a b^2 d+3 b^3 c\right)}{2 a^{5/2} b^{5/2}}-\frac{c}{a^2 x}+\frac{f x}{b^2}","-\frac{x \left(-\frac{a^2 f}{b^2}+\frac{b c}{a}+\frac{a e}{b}-d\right)}{2 a \left(a+b x^2\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(-a^2 b e+3 a^3 f-a b^2 d+3 b^3 c\right)}{2 a^{5/2} b^{5/2}}-\frac{c}{a^2 x}+\frac{f x}{b^2}",1,"-(c/(a^2*x)) + (f*x)/b^2 - (((b*c)/a - d + (a*e)/b - (a^2*f)/b^2)*x)/(2*a*(a + b*x^2)) - ((3*b^3*c - a*b^2*d - a^2*b*e + 3*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*b^(5/2))","A",4,3,30,0.1000,1,"{1805, 1261, 205}"
129,1,121,0,0.1575491,"\int \frac{c+d x^2+e x^4+f x^6}{x^4 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^4*(a + b*x^2)^2),x]","\frac{x \left(\frac{b^2 c}{a^2}-\frac{b d}{a}-\frac{a f}{b}+e\right)}{2 a \left(a+b x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 f-3 a b^2 d+5 b^3 c\right)}{2 a^{7/2} b^{3/2}}+\frac{2 b c-a d}{a^3 x}-\frac{c}{3 a^2 x^3}","\frac{x \left(\frac{b^2 c}{a^2}-\frac{b d}{a}-\frac{a f}{b}+e\right)}{2 a \left(a+b x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(a^2 b e+a^3 f-3 a b^2 d+5 b^3 c\right)}{2 a^{7/2} b^{3/2}}+\frac{2 b c-a d}{a^3 x}-\frac{c}{3 a^2 x^3}",1,"-c/(3*a^2*x^3) + (2*b*c - a*d)/(a^3*x) + (((b^2*c)/a^2 - (b*d)/a + e - (a*f)/b)*x)/(2*a*(a + b*x^2)) + ((5*b^3*c - 3*a*b^2*d + a^2*b*e + a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2)*b^(3/2))","A",4,3,30,0.1000,1,"{1805, 1261, 205}"
130,1,152,0,0.2131069,"\int \frac{c+d x^2+e x^4+f x^6}{x^6 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^6*(a + b*x^2)^2),x]","-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 a^4 \left(a+b x^2\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(3 a^2 b e+a^3 (-f)-5 a b^2 d+7 b^3 c\right)}{2 a^{9/2} \sqrt{b}}-\frac{a^2 e-2 a b d+3 b^2 c}{a^4 x}+\frac{2 b c-a d}{3 a^3 x^3}-\frac{c}{5 a^2 x^5}","-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 a^4 \left(a+b x^2\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(3 a^2 b e+a^3 (-f)-5 a b^2 d+7 b^3 c\right)}{2 a^{9/2} \sqrt{b}}-\frac{a^2 e-2 a b d+3 b^2 c}{a^4 x}+\frac{2 b c-a d}{3 a^3 x^3}-\frac{c}{5 a^2 x^5}",1,"-c/(5*a^2*x^5) + (2*b*c - a*d)/(3*a^3*x^3) - (3*b^2*c - 2*a*b*d + a^2*e)/(a^4*x) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(2*a^4*(a + b*x^2)) - ((7*b^3*c - 5*a*b^2*d + 3*a^2*b*e - a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(9/2)*Sqrt[b])","A",4,3,30,0.1000,1,"{1805, 1802, 205}"
131,1,189,0,0.2933508,"\int \frac{c+d x^2+e x^4+f x^6}{x^8 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^8*(a + b*x^2)^2),x]","\frac{b x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 a^5 \left(a+b x^2\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{a^5 x}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(5 a^2 b e-3 a^3 f-7 a b^2 d+9 b^3 c\right)}{2 a^{11/2}}-\frac{a^2 e-2 a b d+3 b^2 c}{3 a^4 x^3}+\frac{2 b c-a d}{5 a^3 x^5}-\frac{c}{7 a^2 x^7}","\frac{b x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 a^5 \left(a+b x^2\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{a^5 x}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(5 a^2 b e-3 a^3 f-7 a b^2 d+9 b^3 c\right)}{2 a^{11/2}}-\frac{a^2 e-2 a b d+3 b^2 c}{3 a^4 x^3}+\frac{2 b c-a d}{5 a^3 x^5}-\frac{c}{7 a^2 x^7}",1,"-c/(7*a^2*x^7) + (2*b*c - a*d)/(5*a^3*x^5) - (3*b^2*c - 2*a*b*d + a^2*e)/(3*a^4*x^3) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(a^5*x) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(2*a^5*(a + b*x^2)) + (Sqrt[b]*(9*b^3*c - 7*a*b^2*d + 5*a^2*b*e - 3*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(11/2))","A",4,3,30,0.1000,1,"{1805, 1802, 205}"
132,1,230,0,0.3760654,"\int \frac{c+d x^2+e x^4+f x^6}{x^{10} \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^10*(a + b*x^2)^2),x]","-\frac{b^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 a^6 \left(a+b x^2\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{3 a^5 x^3}-\frac{b \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{a^6 x}-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(7 a^2 b e-5 a^3 f-9 a b^2 d+11 b^3 c\right)}{2 a^{13/2}}-\frac{a^2 e-2 a b d+3 b^2 c}{5 a^4 x^5}+\frac{2 b c-a d}{7 a^3 x^7}-\frac{c}{9 a^2 x^9}","-\frac{b^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 a^6 \left(a+b x^2\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{3 a^5 x^3}-\frac{b \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{a^6 x}-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(7 a^2 b e-5 a^3 f-9 a b^2 d+11 b^3 c\right)}{2 a^{13/2}}-\frac{a^2 e-2 a b d+3 b^2 c}{5 a^4 x^5}+\frac{2 b c-a d}{7 a^3 x^7}-\frac{c}{9 a^2 x^9}",1,"-c/(9*a^2*x^9) + (2*b*c - a*d)/(7*a^3*x^7) - (3*b^2*c - 2*a*b*d + a^2*e)/(5*a^4*x^5) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(3*a^5*x^3) - (b*(5*b^3*c - 4*a*b^2*d + 3*a^2*b*e - 2*a^3*f))/(a^6*x) - (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(2*a^6*(a + b*x^2)) - (b^(3/2)*(11*b^3*c - 9*a*b^2*d + 7*a^2*b*e - 5*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(13/2))","A",4,3,30,0.1000,1,"{1805, 1802, 205}"
133,1,287,0,0.492374,"\int \frac{x^8 \left(c+d x^2+e x^4+f x^6\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^8*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^3,x]","\frac{x^9 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}-\frac{x^5 \left(17 a^2 b e-29 a^3 f-9 a b^2 d+5 b^3 c\right)}{20 a b^5}+\frac{x^3 \left(15 a^2 b e-23 a^3 f-9 a b^2 d+5 b^3 c\right)}{6 b^6}-\frac{a^2 x \left(13 a^2 b e-17 a^3 f-9 a b^2 d+5 b^3 c\right)}{8 b^7 \left(a+b x^2\right)}-\frac{a x \left(43 a^2 b e-63 a^3 f-27 a b^2 d+15 b^3 c\right)}{4 b^7}+\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(99 a^2 b e-143 a^3 f-63 a b^2 d+35 b^3 c\right)}{8 b^{15/2}}+\frac{x^7 (b e-3 a f)}{7 b^4}+\frac{f x^9}{9 b^3}","\frac{x^9 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}-\frac{x^5 \left(17 a^2 b e-29 a^3 f-9 a b^2 d+5 b^3 c\right)}{20 a b^5}+\frac{x^3 \left(15 a^2 b e-23 a^3 f-9 a b^2 d+5 b^3 c\right)}{6 b^6}-\frac{a^2 x \left(13 a^2 b e-17 a^3 f-9 a b^2 d+5 b^3 c\right)}{8 b^7 \left(a+b x^2\right)}-\frac{a x \left(43 a^2 b e-63 a^3 f-27 a b^2 d+15 b^3 c\right)}{4 b^7}+\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(99 a^2 b e-143 a^3 f-63 a b^2 d+35 b^3 c\right)}{8 b^{15/2}}+\frac{x^7 (b e-3 a f)}{7 b^4}+\frac{f x^9}{9 b^3}",1,"-(a*(15*b^3*c - 27*a*b^2*d + 43*a^2*b*e - 63*a^3*f)*x)/(4*b^7) + ((5*b^3*c - 9*a*b^2*d + 15*a^2*b*e - 23*a^3*f)*x^3)/(6*b^6) - ((5*b^3*c - 9*a*b^2*d + 17*a^2*b*e - 29*a^3*f)*x^5)/(20*a*b^5) + ((b*e - 3*a*f)*x^7)/(7*b^4) + (f*x^9)/(9*b^3) + ((c - (a*(b^2*d - a*b*e + a^2*f))/b^3)*x^9)/(4*a*(a + b*x^2)^2) - (a^2*(5*b^3*c - 9*a*b^2*d + 13*a^2*b*e - 17*a^3*f)*x)/(8*b^7*(a + b*x^2)) + (a^(3/2)*(35*b^3*c - 63*a*b^2*d + 99*a^2*b*e - 143*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(15/2))","A",6,5,30,0.1667,1,"{1804, 1585, 1257, 1810, 205}"
134,1,247,0,0.411223,"\int \frac{x^6 \left(c+d x^2+e x^4+f x^6\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^6*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^3,x]","\frac{x^7 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}-\frac{x^3 \left(15 a^2 b e-27 a^3 f-7 a b^2 d+3 b^3 c\right)}{12 a b^5}+\frac{a x \left(11 a^2 b e-15 a^3 f-7 a b^2 d+3 b^3 c\right)}{8 b^6 \left(a+b x^2\right)}+\frac{x \left(13 a^2 b e-21 a^3 f-7 a b^2 d+3 b^3 c\right)}{2 b^6}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(63 a^2 b e-99 a^3 f-35 a b^2 d+15 b^3 c\right)}{8 b^{13/2}}+\frac{x^5 (b e-3 a f)}{5 b^4}+\frac{f x^7}{7 b^3}","\frac{x^7 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}-\frac{x^3 \left(15 a^2 b e-27 a^3 f-7 a b^2 d+3 b^3 c\right)}{12 a b^5}+\frac{a x \left(11 a^2 b e-15 a^3 f-7 a b^2 d+3 b^3 c\right)}{8 b^6 \left(a+b x^2\right)}+\frac{x \left(13 a^2 b e-21 a^3 f-7 a b^2 d+3 b^3 c\right)}{2 b^6}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(63 a^2 b e-99 a^3 f-35 a b^2 d+15 b^3 c\right)}{8 b^{13/2}}+\frac{x^5 (b e-3 a f)}{5 b^4}+\frac{f x^7}{7 b^3}",1,"((3*b^3*c - 7*a*b^2*d + 13*a^2*b*e - 21*a^3*f)*x)/(2*b^6) - ((3*b^3*c - 7*a*b^2*d + 15*a^2*b*e - 27*a^3*f)*x^3)/(12*a*b^5) + ((b*e - 3*a*f)*x^5)/(5*b^4) + (f*x^7)/(7*b^3) + ((c - (a*(b^2*d - a*b*e + a^2*f))/b^3)*x^7)/(4*a*(a + b*x^2)^2) + (a*(3*b^3*c - 7*a*b^2*d + 11*a^2*b*e - 15*a^3*f)*x)/(8*b^6*(a + b*x^2)) - (Sqrt[a]*(15*b^3*c - 35*a*b^2*d + 63*a^2*b*e - 99*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(13/2))","A",6,5,30,0.1667,1,"{1804, 1585, 1257, 1810, 205}"
135,1,207,0,0.333674,"\int \frac{x^4 \left(c+d x^2+e x^4+f x^6\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^4*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^3,x]","\frac{x^5 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}-\frac{x \left(9 a^2 b e-13 a^3 f-5 a b^2 d+b^3 c\right)}{8 b^5 \left(a+b x^2\right)}-\frac{x \left(13 a^2 b e-25 a^3 f-5 a b^2 d+b^3 c\right)}{4 a b^5}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(35 a^2 b e-63 a^3 f-15 a b^2 d+3 b^3 c\right)}{8 \sqrt{a} b^{11/2}}+\frac{x^3 (b e-3 a f)}{3 b^4}+\frac{f x^5}{5 b^3}","\frac{x^5 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}-\frac{x \left(9 a^2 b e-13 a^3 f-5 a b^2 d+b^3 c\right)}{8 b^5 \left(a+b x^2\right)}-\frac{x \left(13 a^2 b e-25 a^3 f-5 a b^2 d+b^3 c\right)}{4 a b^5}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(35 a^2 b e-63 a^3 f-15 a b^2 d+3 b^3 c\right)}{8 \sqrt{a} b^{11/2}}+\frac{x^3 (b e-3 a f)}{3 b^4}+\frac{f x^5}{5 b^3}",1,"-((b^3*c - 5*a*b^2*d + 13*a^2*b*e - 25*a^3*f)*x)/(4*a*b^5) + ((b*e - 3*a*f)*x^3)/(3*b^4) + (f*x^5)/(5*b^3) + ((c - (a*(b^2*d - a*b*e + a^2*f))/b^3)*x^5)/(4*a*(a + b*x^2)^2) - ((b^3*c - 5*a*b^2*d + 9*a^2*b*e - 13*a^3*f)*x)/(8*b^5*(a + b*x^2)) + ((3*b^3*c - 15*a*b^2*d + 35*a^2*b*e - 63*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*Sqrt[a]*b^(11/2))","A",6,5,30,0.1667,1,"{1804, 1585, 1257, 1810, 205}"
136,1,167,0,0.2621146,"\int \frac{x^2 \left(c+d x^2+e x^4+f x^6\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^2*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^3,x]","\frac{x^3 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}-\frac{x \left(-7 a^2 b e+11 a^3 f+3 a b^2 d+b^3 c\right)}{8 a b^4 \left(a+b x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(-15 a^2 b e+35 a^3 f+3 a b^2 d+b^3 c\right)}{8 a^{3/2} b^{9/2}}+\frac{x (b e-3 a f)}{b^4}+\frac{f x^3}{3 b^3}","\frac{x^3 \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}-\frac{x \left(-7 a^2 b e+11 a^3 f+3 a b^2 d+b^3 c\right)}{8 a b^4 \left(a+b x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(-15 a^2 b e+35 a^3 f+3 a b^2 d+b^3 c\right)}{8 a^{3/2} b^{9/2}}+\frac{x (b e-3 a f)}{b^4}+\frac{f x^3}{3 b^3}",1,"((b*e - 3*a*f)*x)/b^4 + (f*x^3)/(3*b^3) + ((c - (a*(b^2*d - a*b*e + a^2*f))/b^3)*x^3)/(4*a*(a + b*x^2)^2) - ((b^3*c + 3*a*b^2*d - 7*a^2*b*e + 11*a^3*f)*x)/(8*a*b^4*(a + b*x^2)) + ((b^3*c + 3*a*b^2*d - 15*a^2*b*e + 35*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(3/2)*b^(9/2))","A",6,5,30,0.1667,1,"{1804, 1585, 1257, 1153, 205}"
137,1,147,0,0.1502058,"\int \frac{c+d x^2+e x^4+f x^6}{\left(a+b x^2\right)^3} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(a + b*x^2)^3,x]","\frac{x \left(-5 a^2 b e+9 a^3 f+a b^2 d+3 b^3 c\right)}{8 a^2 b^3 \left(a+b x^2\right)}+\frac{x \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(3 a^2 b e-15 a^3 f+a b^2 d+3 b^3 c\right)}{8 a^{5/2} b^{7/2}}+\frac{f x}{b^3}","\frac{x \left(-5 a^2 b e+9 a^3 f+a b^2 d+3 b^3 c\right)}{8 a^2 b^3 \left(a+b x^2\right)}+\frac{x \left(c-\frac{a \left(a^2 f-a b e+b^2 d\right)}{b^3}\right)}{4 a \left(a+b x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(3 a^2 b e-15 a^3 f+a b^2 d+3 b^3 c\right)}{8 a^{5/2} b^{7/2}}+\frac{f x}{b^3}",1,"(f*x)/b^3 + ((c - (a*(b^2*d - a*b*e + a^2*f))/b^3)*x)/(4*a*(a + b*x^2)^2) + ((3*b^3*c + a*b^2*d - 5*a^2*b*e + 9*a^3*f)*x)/(8*a^2*b^3*(a + b*x^2)) + ((3*b^3*c + a*b^2*d + 3*a^2*b*e - 15*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*b^(7/2))","A",4,4,27,0.1481,1,"{1814, 1157, 388, 205}"
138,1,153,0,0.1761844,"\int \frac{c+d x^2+e x^4+f x^6}{x^2 \left(a+b x^2\right)^3} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^2*(a + b*x^2)^3),x]","-\frac{x \left(-a^2 b e+5 a^3 f-3 a b^2 d+7 b^3 c\right)}{8 a^3 b^2 \left(a+b x^2\right)}-\frac{x \left(-\frac{a^2 f}{b^2}+\frac{b c}{a}+\frac{a e}{b}-d\right)}{4 a \left(a+b x^2\right)^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(-a^2 b e-3 a^3 f-3 a b^2 d+15 b^3 c\right)}{8 a^{7/2} b^{5/2}}-\frac{c}{a^3 x}","-\frac{x \left(-a^2 b e+5 a^3 f-3 a b^2 d+7 b^3 c\right)}{8 a^3 b^2 \left(a+b x^2\right)}-\frac{x \left(-\frac{a^2 f}{b^2}+\frac{b c}{a}+\frac{a e}{b}-d\right)}{4 a \left(a+b x^2\right)^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(-a^2 b e-3 a^3 f-3 a b^2 d+15 b^3 c\right)}{8 a^{7/2} b^{5/2}}-\frac{c}{a^3 x}",1,"-(c/(a^3*x)) - (((b*c)/a - d + (a*e)/b - (a^2*f)/b^2)*x)/(4*a*(a + b*x^2)^2) - ((7*b^3*c - 3*a*b^2*d - a^2*b*e + 5*a^3*f)*x)/(8*a^3*b^2*(a + b*x^2)) - ((15*b^3*c - 3*a*b^2*d - a^2*b*e - 3*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2)*b^(5/2))","A",4,4,30,0.1333,1,"{1805, 1259, 453, 205}"
139,1,168,0,0.2424448,"\int \frac{c+d x^2+e x^4+f x^6}{x^4 \left(a+b x^2\right)^3} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^4*(a + b*x^2)^3),x]","\frac{x \left(3 a^2 b e+a^3 f-7 a b^2 d+11 b^3 c\right)}{8 a^4 b \left(a+b x^2\right)}+\frac{x \left(\frac{b^2 c}{a^2}-\frac{b d}{a}-\frac{a f}{b}+e\right)}{4 a \left(a+b x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(3 a^2 b e+a^3 f-15 a b^2 d+35 b^3 c\right)}{8 a^{9/2} b^{3/2}}+\frac{3 b c-a d}{a^4 x}-\frac{c}{3 a^3 x^3}","\frac{x \left(3 a^2 b e+a^3 f-7 a b^2 d+11 b^3 c\right)}{8 a^4 b \left(a+b x^2\right)}+\frac{x \left(\frac{b^2 c}{a^2}-\frac{b d}{a}-\frac{a f}{b}+e\right)}{4 a \left(a+b x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(3 a^2 b e+a^3 f-15 a b^2 d+35 b^3 c\right)}{8 a^{9/2} b^{3/2}}+\frac{3 b c-a d}{a^4 x}-\frac{c}{3 a^3 x^3}",1,"-c/(3*a^3*x^3) + (3*b*c - a*d)/(a^4*x) + (((b^2*c)/a^2 - (b*d)/a + e - (a*f)/b)*x)/(4*a*(a + b*x^2)^2) + ((11*b^3*c - 7*a*b^2*d + 3*a^2*b*e + a^3*f)*x)/(8*a^4*b*(a + b*x^2)) + ((35*b^3*c - 15*a*b^2*d + 3*a^2*b*e + a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(9/2)*b^(3/2))","A",5,4,30,0.1333,1,"{1805, 1259, 1261, 205}"
140,1,196,0,0.3502033,"\int \frac{c+d x^2+e x^4+f x^6}{x^6 \left(a+b x^2\right)^3} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^6*(a + b*x^2)^3),x]","-\frac{x \left(7 a^2 b e-3 a^3 f-11 a b^2 d+15 b^3 c\right)}{8 a^5 \left(a+b x^2\right)}-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 a^4 \left(a+b x^2\right)^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(15 a^2 b e-3 a^3 f-35 a b^2 d+63 b^3 c\right)}{8 a^{11/2} \sqrt{b}}-\frac{a^2 e-3 a b d+6 b^2 c}{a^5 x}+\frac{3 b c-a d}{3 a^4 x^3}-\frac{c}{5 a^3 x^5}","-\frac{x \left(7 a^2 b e-3 a^3 f-11 a b^2 d+15 b^3 c\right)}{8 a^5 \left(a+b x^2\right)}-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 a^4 \left(a+b x^2\right)^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(15 a^2 b e-3 a^3 f-35 a b^2 d+63 b^3 c\right)}{8 a^{11/2} \sqrt{b}}-\frac{a^2 e-3 a b d+6 b^2 c}{a^5 x}+\frac{3 b c-a d}{3 a^4 x^3}-\frac{c}{5 a^3 x^5}",1,"-c/(5*a^3*x^5) + (3*b*c - a*d)/(3*a^4*x^3) - (6*b^2*c - 3*a*b*d + a^2*e)/(a^5*x) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(4*a^4*(a + b*x^2)^2) - ((15*b^3*c - 11*a*b^2*d + 7*a^2*b*e - 3*a^3*f)*x)/(8*a^5*(a + b*x^2)) - ((63*b^3*c - 35*a*b^2*d + 15*a^2*b*e - 3*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(11/2)*Sqrt[b])","A",5,3,30,0.1000,1,"{1805, 1802, 205}"
141,1,234,0,0.4864561,"\int \frac{c+d x^2+e x^4+f x^6}{x^8 \left(a+b x^2\right)^3} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^8*(a + b*x^2)^3),x]","\frac{b x \left(11 a^2 b e-7 a^3 f-15 a b^2 d+19 b^3 c\right)}{8 a^6 \left(a+b x^2\right)}+\frac{b x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 a^5 \left(a+b x^2\right)^2}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{a^6 x}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(35 a^2 b e-15 a^3 f-63 a b^2 d+99 b^3 c\right)}{8 a^{13/2}}-\frac{a^2 e-3 a b d+6 b^2 c}{3 a^5 x^3}+\frac{3 b c-a d}{5 a^4 x^5}-\frac{c}{7 a^3 x^7}","\frac{b x \left(11 a^2 b e-7 a^3 f-15 a b^2 d+19 b^3 c\right)}{8 a^6 \left(a+b x^2\right)}+\frac{b x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 a^5 \left(a+b x^2\right)^2}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{a^6 x}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(35 a^2 b e-15 a^3 f-63 a b^2 d+99 b^3 c\right)}{8 a^{13/2}}-\frac{a^2 e-3 a b d+6 b^2 c}{3 a^5 x^3}+\frac{3 b c-a d}{5 a^4 x^5}-\frac{c}{7 a^3 x^7}",1,"-c/(7*a^3*x^7) + (3*b*c - a*d)/(5*a^4*x^5) - (6*b^2*c - 3*a*b*d + a^2*e)/(3*a^5*x^3) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(a^6*x) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(4*a^5*(a + b*x^2)^2) + (b*(19*b^3*c - 15*a*b^2*d + 11*a^2*b*e - 7*a^3*f)*x)/(8*a^6*(a + b*x^2)) + (Sqrt[b]*(99*b^3*c - 63*a*b^2*d + 35*a^2*b*e - 15*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(13/2))","A",5,3,30,0.1000,1,"{1805, 1802, 205}"
142,1,277,0,0.603401,"\int \frac{c+d x^2+e x^4+f x^6}{x^{10} \left(a+b x^2\right)^3} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^10*(a + b*x^2)^3),x]","-\frac{b^2 x \left(15 a^2 b e-11 a^3 f-19 a b^2 d+23 b^3 c\right)}{8 a^7 \left(a+b x^2\right)}-\frac{b^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 a^6 \left(a+b x^2\right)^2}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{3 a^6 x^3}-\frac{b \left(6 a^2 b e-3 a^3 f-10 a b^2 d+15 b^3 c\right)}{a^7 x}-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(63 a^2 b e-35 a^3 f-99 a b^2 d+143 b^3 c\right)}{8 a^{15/2}}-\frac{a^2 e-3 a b d+6 b^2 c}{5 a^5 x^5}+\frac{3 b c-a d}{7 a^4 x^7}-\frac{c}{9 a^3 x^9}","-\frac{b^2 x \left(15 a^2 b e-11 a^3 f-19 a b^2 d+23 b^3 c\right)}{8 a^7 \left(a+b x^2\right)}-\frac{b^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 a^6 \left(a+b x^2\right)^2}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{3 a^6 x^3}-\frac{b \left(6 a^2 b e-3 a^3 f-10 a b^2 d+15 b^3 c\right)}{a^7 x}-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(63 a^2 b e-35 a^3 f-99 a b^2 d+143 b^3 c\right)}{8 a^{15/2}}-\frac{a^2 e-3 a b d+6 b^2 c}{5 a^5 x^5}+\frac{3 b c-a d}{7 a^4 x^7}-\frac{c}{9 a^3 x^9}",1,"-c/(9*a^3*x^9) + (3*b*c - a*d)/(7*a^4*x^7) - (6*b^2*c - 3*a*b*d + a^2*e)/(5*a^5*x^5) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(3*a^6*x^3) - (b*(15*b^3*c - 10*a*b^2*d + 6*a^2*b*e - 3*a^3*f))/(a^7*x) - (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(4*a^6*(a + b*x^2)^2) - (b^2*(23*b^3*c - 19*a*b^2*d + 15*a^2*b*e - 11*a^3*f)*x)/(8*a^7*(a + b*x^2)) - (b^(3/2)*(143*b^3*c - 99*a*b^2*d + 63*a^2*b*e - 35*a^3*f)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(15/2))","A",5,3,30,0.1000,1,"{1805, 1802, 205}"
143,1,214,0,0.2515746,"\int \frac{x^5 \left(c+d x^2+e x^4+f x^6\right)}{\sqrt{a+b x^2}} \, dx","Int[(x^5*(c + d*x^2 + e*x^4 + f*x^6))/Sqrt[a + b*x^2],x]","\frac{\left(a+b x^2\right)^{5/2} \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{5 b^6}-\frac{a \left(a+b x^2\right)^{3/2} \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6}+\frac{a^2 \sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^6}+\frac{\left(a+b x^2\right)^{7/2} \left(10 a^2 f-4 a b e+b^2 d\right)}{7 b^6}+\frac{\left(a+b x^2\right)^{9/2} (b e-5 a f)}{9 b^6}+\frac{f \left(a+b x^2\right)^{11/2}}{11 b^6}","\frac{\left(a+b x^2\right)^{5/2} \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{5 b^6}-\frac{a \left(a+b x^2\right)^{3/2} \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6}+\frac{a^2 \sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^6}+\frac{\left(a+b x^2\right)^{7/2} \left(10 a^2 f-4 a b e+b^2 d\right)}{7 b^6}+\frac{\left(a+b x^2\right)^{9/2} (b e-5 a f)}{9 b^6}+\frac{f \left(a+b x^2\right)^{11/2}}{11 b^6}",1,"(a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Sqrt[a + b*x^2])/b^6 - (a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f)*(a + b*x^2)^(3/2))/(3*b^6) + ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*(a + b*x^2)^(5/2))/(5*b^6) + ((b^2*d - 4*a*b*e + 10*a^2*f)*(a + b*x^2)^(7/2))/(7*b^6) + ((b*e - 5*a*f)*(a + b*x^2)^(9/2))/(9*b^6) + (f*(a + b*x^2)^(11/2))/(11*b^6)","A",3,2,32,0.06250,1,"{1799, 1620}"
144,1,167,0,0.1940131,"\int \frac{x^3 \left(c+d x^2+e x^4+f x^6\right)}{\sqrt{a+b x^2}} \, dx","Int[(x^3*(c + d*x^2 + e*x^4 + f*x^6))/Sqrt[a + b*x^2],x]","\frac{\left(a+b x^2\right)^{3/2} \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{3 b^5}-\frac{a \sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^5}+\frac{\left(a+b x^2\right)^{5/2} \left(6 a^2 f-3 a b e+b^2 d\right)}{5 b^5}+\frac{\left(a+b x^2\right)^{7/2} (b e-4 a f)}{7 b^5}+\frac{f \left(a+b x^2\right)^{9/2}}{9 b^5}","\frac{\left(a+b x^2\right)^{3/2} \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{3 b^5}-\frac{a \sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^5}+\frac{\left(a+b x^2\right)^{5/2} \left(6 a^2 f-3 a b e+b^2 d\right)}{5 b^5}+\frac{\left(a+b x^2\right)^{7/2} (b e-4 a f)}{7 b^5}+\frac{f \left(a+b x^2\right)^{9/2}}{9 b^5}",1,"-((a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Sqrt[a + b*x^2])/b^5) + ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*(a + b*x^2)^(3/2))/(3*b^5) + ((b^2*d - 3*a*b*e + 6*a^2*f)*(a + b*x^2)^(5/2))/(5*b^5) + ((b*e - 4*a*f)*(a + b*x^2)^(7/2))/(7*b^5) + (f*(a + b*x^2)^(9/2))/(9*b^5)","A",3,2,32,0.06250,1,"{1799, 1620}"
145,1,121,0,0.133137,"\int \frac{x \left(c+d x^2+e x^4+f x^6\right)}{\sqrt{a+b x^2}} \, dx","Int[(x*(c + d*x^2 + e*x^4 + f*x^6))/Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}+\frac{\left(a+b x^2\right)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{\left(a+b x^2\right)^{5/2} (b e-3 a f)}{5 b^4}+\frac{f \left(a+b x^2\right)^{7/2}}{7 b^4}","\frac{\sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}+\frac{\left(a+b x^2\right)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{\left(a+b x^2\right)^{5/2} (b e-3 a f)}{5 b^4}+\frac{f \left(a+b x^2\right)^{7/2}}{7 b^4}",1,"((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Sqrt[a + b*x^2])/b^4 + ((b^2*d - 2*a*b*e + 3*a^2*f)*(a + b*x^2)^(3/2))/(3*b^4) + ((b*e - 3*a*f)*(a + b*x^2)^(5/2))/(5*b^4) + (f*(a + b*x^2)^(7/2))/(7*b^4)","A",3,2,30,0.06667,1,"{1799, 1850}"
146,1,103,0,0.1402657,"\int \frac{c+d x^2+e x^4+f x^6}{x \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x*Sqrt[a + b*x^2]),x]","\frac{\sqrt{a+b x^2} \left(a^2 f-a b e+b^2 d\right)}{b^3}+\frac{\left(a+b x^2\right)^{3/2} (b e-2 a f)}{3 b^3}+\frac{f \left(a+b x^2\right)^{5/2}}{5 b^3}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\sqrt{a+b x^2} \left(a^2 f-a b e+b^2 d\right)}{b^3}+\frac{\left(a+b x^2\right)^{3/2} (b e-2 a f)}{3 b^3}+\frac{f \left(a+b x^2\right)^{5/2}}{5 b^3}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"((b^2*d - a*b*e + a^2*f)*Sqrt[a + b*x^2])/b^3 + ((b*e - 2*a*f)*(a + b*x^2)^(3/2))/(3*b^3) + (f*(a + b*x^2)^(5/2))/(5*b^3) - (c*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/Sqrt[a]","A",5,4,32,0.1250,1,"{1799, 1620, 63, 208}"
147,1,100,0,0.2029963,"\int \frac{c+d x^2+e x^4+f x^6}{x^3 \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^3*Sqrt[a + b*x^2]),x]","\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}+\frac{\sqrt{a+b x^2} (b e-a f)}{b^2}+\frac{f \left(a+b x^2\right)^{3/2}}{3 b^2}-\frac{c \sqrt{a+b x^2}}{2 a x^2}","\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}+\frac{\sqrt{a+b x^2} (b e-a f)}{b^2}+\frac{f \left(a+b x^2\right)^{3/2}}{3 b^2}-\frac{c \sqrt{a+b x^2}}{2 a x^2}",1,"((b*e - a*f)*Sqrt[a + b*x^2])/b^2 - (c*Sqrt[a + b*x^2])/(2*a*x^2) + (f*(a + b*x^2)^(3/2))/(3*b^2) + ((b*c - 2*a*d)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(3/2))","A",6,5,32,0.1562,1,"{1799, 1621, 897, 1153, 208}"
148,1,114,0,0.2326877,"\int \frac{c+d x^2+e x^4+f x^6}{x^5 \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^5*Sqrt[a + b*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right) \left(8 a^2 e-4 a b d+3 b^2 c\right)}{8 a^{5/2}}+\frac{\sqrt{a+b x^2} (3 b c-4 a d)}{8 a^2 x^2}-\frac{c \sqrt{a+b x^2}}{4 a x^4}+\frac{f \sqrt{a+b x^2}}{b}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right) \left(8 a^2 e-4 a b d+3 b^2 c\right)}{8 a^{5/2}}+\frac{\sqrt{a+b x^2} (3 b c-4 a d)}{8 a^2 x^2}-\frac{c \sqrt{a+b x^2}}{4 a x^4}+\frac{f \sqrt{a+b x^2}}{b}",1,"(f*Sqrt[a + b*x^2])/b - (c*Sqrt[a + b*x^2])/(4*a*x^4) + ((3*b*c - 4*a*d)*Sqrt[a + b*x^2])/(8*a^2*x^2) - ((3*b^2*c - 4*a*b*d + 8*a^2*e)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*a^(5/2))","A",6,6,32,0.1875,1,"{1799, 1621, 897, 1157, 388, 208}"
149,1,146,0,0.276366,"\int \frac{c+d x^2+e x^4+f x^6}{x^7 \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^7*Sqrt[a + b*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right) \left(8 a^2 b e-16 a^3 f-6 a b^2 d+5 b^3 c\right)}{16 a^{7/2}}-\frac{\sqrt{a+b x^2} \left(8 a^2 e-6 a b d+5 b^2 c\right)}{16 a^3 x^2}+\frac{\sqrt{a+b x^2} (5 b c-6 a d)}{24 a^2 x^4}-\frac{c \sqrt{a+b x^2}}{6 a x^6}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right) \left(8 a^2 b e-16 a^3 f-6 a b^2 d+5 b^3 c\right)}{16 a^{7/2}}-\frac{\sqrt{a+b x^2} \left(8 a^2 e-6 a b d+5 b^2 c\right)}{16 a^3 x^2}+\frac{\sqrt{a+b x^2} (5 b c-6 a d)}{24 a^2 x^4}-\frac{c \sqrt{a+b x^2}}{6 a x^6}",1,"-(c*Sqrt[a + b*x^2])/(6*a*x^6) + ((5*b*c - 6*a*d)*Sqrt[a + b*x^2])/(24*a^2*x^4) - ((5*b^2*c - 6*a*b*d + 8*a^2*e)*Sqrt[a + b*x^2])/(16*a^3*x^2) + ((5*b^3*c - 6*a*b^2*d + 8*a^2*b*e - 16*a^3*f)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*a^(7/2))","A",6,6,32,0.1875,1,"{1799, 1621, 897, 1157, 385, 208}"
150,1,195,0,0.3500108,"\int \frac{c+d x^2+e x^4+f x^6}{x^9 \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^9*Sqrt[a + b*x^2]),x]","\frac{\sqrt{a+b x^2} \left(48 a^2 b e-64 a^3 f-40 a b^2 d+35 b^3 c\right)}{128 a^4 x^2}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right) \left(48 a^2 b e-64 a^3 f-40 a b^2 d+35 b^3 c\right)}{128 a^{9/2}}-\frac{\sqrt{a+b x^2} \left(48 a^2 e-40 a b d+35 b^2 c\right)}{192 a^3 x^4}+\frac{\sqrt{a+b x^2} (7 b c-8 a d)}{48 a^2 x^6}-\frac{c \sqrt{a+b x^2}}{8 a x^8}","\frac{\sqrt{a+b x^2} \left(48 a^2 b e-64 a^3 f-40 a b^2 d+35 b^3 c\right)}{128 a^4 x^2}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right) \left(48 a^2 b e-64 a^3 f-40 a b^2 d+35 b^3 c\right)}{128 a^{9/2}}-\frac{\sqrt{a+b x^2} \left(48 a^2 e-40 a b d+35 b^2 c\right)}{192 a^3 x^4}+\frac{\sqrt{a+b x^2} (7 b c-8 a d)}{48 a^2 x^6}-\frac{c \sqrt{a+b x^2}}{8 a x^8}",1,"-(c*Sqrt[a + b*x^2])/(8*a*x^8) + ((7*b*c - 8*a*d)*Sqrt[a + b*x^2])/(48*a^2*x^6) - ((35*b^2*c - 40*a*b*d + 48*a^2*e)*Sqrt[a + b*x^2])/(192*a^3*x^4) + ((35*b^3*c - 40*a*b^2*d + 48*a^2*b*e - 64*a^3*f)*Sqrt[a + b*x^2])/(128*a^4*x^2) - (b*(35*b^3*c - 40*a*b^2*d + 48*a^2*b*e - 64*a^3*f)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(128*a^(9/2))","A",7,7,32,0.2188,1,"{1799, 1621, 897, 1157, 385, 199, 208}"
151,1,245,0,0.2584888,"\int \frac{x^4 \left(c+d x^2+e x^4+f x^6\right)}{\sqrt{a+b x^2}} \, dx","Int[(x^4*(c + d*x^2 + e*x^4 + f*x^6))/Sqrt[a + b*x^2],x]","\frac{x^3 \sqrt{a+b x^2} \left(70 a^2 b e-63 a^3 f-80 a b^2 d+96 b^3 c\right)}{384 b^4}-\frac{a x \sqrt{a+b x^2} \left(70 a^2 b e-63 a^3 f-80 a b^2 d+96 b^3 c\right)}{256 b^5}+\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(70 a^2 b e-63 a^3 f-80 a b^2 d+96 b^3 c\right)}{256 b^{11/2}}+\frac{x^5 \sqrt{a+b x^2} \left(63 a^2 f-70 a b e+80 b^2 d\right)}{480 b^3}+\frac{x^7 \sqrt{a+b x^2} (10 b e-9 a f)}{80 b^2}+\frac{f x^9 \sqrt{a+b x^2}}{10 b}","\frac{x^3 \sqrt{a+b x^2} \left(70 a^2 b e-63 a^3 f-80 a b^2 d+96 b^3 c\right)}{384 b^4}-\frac{a x \sqrt{a+b x^2} \left(70 a^2 b e-63 a^3 f-80 a b^2 d+96 b^3 c\right)}{256 b^5}+\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(70 a^2 b e-63 a^3 f-80 a b^2 d+96 b^3 c\right)}{256 b^{11/2}}+\frac{x^5 \sqrt{a+b x^2} \left(63 a^2 f-70 a b e+80 b^2 d\right)}{480 b^3}+\frac{x^7 \sqrt{a+b x^2} (10 b e-9 a f)}{80 b^2}+\frac{f x^9 \sqrt{a+b x^2}}{10 b}",1,"-(a*(96*b^3*c - 80*a*b^2*d + 70*a^2*b*e - 63*a^3*f)*x*Sqrt[a + b*x^2])/(256*b^5) + ((96*b^3*c - 80*a*b^2*d + 70*a^2*b*e - 63*a^3*f)*x^3*Sqrt[a + b*x^2])/(384*b^4) + ((80*b^2*d - 70*a*b*e + 63*a^2*f)*x^5*Sqrt[a + b*x^2])/(480*b^3) + ((10*b*e - 9*a*f)*x^7*Sqrt[a + b*x^2])/(80*b^2) + (f*x^9*Sqrt[a + b*x^2])/(10*b) + (a^2*(96*b^3*c - 80*a*b^2*d + 70*a^2*b*e - 63*a^3*f)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(256*b^(11/2))","A",7,6,32,0.1875,1,"{1809, 1267, 459, 321, 217, 206}"
152,1,194,0,0.2076437,"\int \frac{x^2 \left(c+d x^2+e x^4+f x^6\right)}{\sqrt{a+b x^2}} \, dx","Int[(x^2*(c + d*x^2 + e*x^4 + f*x^6))/Sqrt[a + b*x^2],x]","\frac{x \sqrt{a+b x^2} \left(40 a^2 b e-35 a^3 f-48 a b^2 d+64 b^3 c\right)}{128 b^4}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(40 a^2 b e-35 a^3 f-48 a b^2 d+64 b^3 c\right)}{128 b^{9/2}}+\frac{x^3 \sqrt{a+b x^2} \left(35 a^2 f-40 a b e+48 b^2 d\right)}{192 b^3}+\frac{x^5 \sqrt{a+b x^2} (8 b e-7 a f)}{48 b^2}+\frac{f x^7 \sqrt{a+b x^2}}{8 b}","\frac{x \sqrt{a+b x^2} \left(40 a^2 b e-35 a^3 f-48 a b^2 d+64 b^3 c\right)}{128 b^4}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(40 a^2 b e-35 a^3 f-48 a b^2 d+64 b^3 c\right)}{128 b^{9/2}}+\frac{x^3 \sqrt{a+b x^2} \left(35 a^2 f-40 a b e+48 b^2 d\right)}{192 b^3}+\frac{x^5 \sqrt{a+b x^2} (8 b e-7 a f)}{48 b^2}+\frac{f x^7 \sqrt{a+b x^2}}{8 b}",1,"((64*b^3*c - 48*a*b^2*d + 40*a^2*b*e - 35*a^3*f)*x*Sqrt[a + b*x^2])/(128*b^4) + ((48*b^2*d - 40*a*b*e + 35*a^2*f)*x^3*Sqrt[a + b*x^2])/(192*b^3) + ((8*b*e - 7*a*f)*x^5*Sqrt[a + b*x^2])/(48*b^2) + (f*x^7*Sqrt[a + b*x^2])/(8*b) - (a*(64*b^3*c - 48*a*b^2*d + 40*a^2*b*e - 35*a^3*f)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(9/2))","A",6,6,32,0.1875,1,"{1809, 1267, 459, 321, 217, 206}"
153,1,145,0,0.1192889,"\int \frac{c+d x^2+e x^4+f x^6}{\sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/Sqrt[a + b*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(6 a^2 b e-5 a^3 f-8 a b^2 d+16 b^3 c\right)}{16 b^{7/2}}+\frac{x \sqrt{a+b x^2} \left(5 a^2 f-6 a b e+8 b^2 d\right)}{16 b^3}+\frac{x^3 \sqrt{a+b x^2} (6 b e-5 a f)}{24 b^2}+\frac{f x^5 \sqrt{a+b x^2}}{6 b}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(6 a^2 b e-5 a^3 f-8 a b^2 d+16 b^3 c\right)}{16 b^{7/2}}+\frac{x \sqrt{a+b x^2} \left(5 a^2 f-6 a b e+8 b^2 d\right)}{16 b^3}+\frac{x^3 \sqrt{a+b x^2} (6 b e-5 a f)}{24 b^2}+\frac{f x^5 \sqrt{a+b x^2}}{6 b}",1,"((8*b^2*d - 6*a*b*e + 5*a^2*f)*x*Sqrt[a + b*x^2])/(16*b^3) + ((6*b*e - 5*a*f)*x^3*Sqrt[a + b*x^2])/(24*b^2) + (f*x^5*Sqrt[a + b*x^2])/(6*b) + ((16*b^3*c - 8*a*b^2*d + 6*a^2*b*e - 5*a^3*f)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(7/2))","A",5,5,29,0.1724,1,"{1815, 1159, 388, 217, 206}"
154,1,117,0,0.1359765,"\int \frac{c+d x^2+e x^4+f x^6}{x^2 \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^2*Sqrt[a + b*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(3 a^2 f-4 a b e+8 b^2 d\right)}{8 b^{5/2}}+\frac{x \sqrt{a+b x^2} (4 b e-3 a f)}{8 b^2}-\frac{c \sqrt{a+b x^2}}{a x}+\frac{f x^3 \sqrt{a+b x^2}}{4 b}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(3 a^2 f-4 a b e+8 b^2 d\right)}{8 b^{5/2}}+\frac{x \sqrt{a+b x^2} (4 b e-3 a f)}{8 b^2}-\frac{c \sqrt{a+b x^2}}{a x}+\frac{f x^3 \sqrt{a+b x^2}}{4 b}",1,"-((c*Sqrt[a + b*x^2])/(a*x)) + ((4*b*e - 3*a*f)*x*Sqrt[a + b*x^2])/(8*b^2) + (f*x^3*Sqrt[a + b*x^2])/(4*b) + ((8*b^2*d - 4*a*b*e + 3*a^2*f)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(5/2))","A",6,6,32,0.1875,1,"{1807, 1585, 1159, 388, 217, 206}"
155,1,110,0,0.1271047,"\int \frac{c+d x^2+e x^4+f x^6}{x^4 \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^4*Sqrt[a + b*x^2]),x]","\frac{\sqrt{a+b x^2} (2 b c-3 a d)}{3 a^2 x}+\frac{(2 b e-a f) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}-\frac{c \sqrt{a+b x^2}}{3 a x^3}+\frac{f x \sqrt{a+b x^2}}{2 b}","\frac{\sqrt{a+b x^2} (2 b c-3 a d)}{3 a^2 x}+\frac{(2 b e-a f) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}-\frac{c \sqrt{a+b x^2}}{3 a x^3}+\frac{f x \sqrt{a+b x^2}}{2 b}",1,"-(c*Sqrt[a + b*x^2])/(3*a*x^3) + ((2*b*c - 3*a*d)*Sqrt[a + b*x^2])/(3*a^2*x) + (f*x*Sqrt[a + b*x^2])/(2*b) + ((2*b*e - a*f)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(3/2))","A",6,6,32,0.1875,1,"{1807, 1585, 1265, 388, 217, 206}"
156,1,118,0,0.1330009,"\int \frac{c+d x^2+e x^4+f x^6}{x^6 \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^6*Sqrt[a + b*x^2]),x]","-\frac{\sqrt{a+b x^2} \left(15 a^2 e-10 a b d+8 b^2 c\right)}{15 a^3 x}+\frac{\sqrt{a+b x^2} (4 b c-5 a d)}{15 a^2 x^3}-\frac{c \sqrt{a+b x^2}}{5 a x^5}+\frac{f \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}","-\frac{\sqrt{a+b x^2} \left(15 a^2 e-10 a b d+8 b^2 c\right)}{15 a^3 x}+\frac{\sqrt{a+b x^2} (4 b c-5 a d)}{15 a^2 x^3}-\frac{c \sqrt{a+b x^2}}{5 a x^5}+\frac{f \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}",1,"-(c*Sqrt[a + b*x^2])/(5*a*x^5) + ((4*b*c - 5*a*d)*Sqrt[a + b*x^2])/(15*a^2*x^3) - ((8*b^2*c - 10*a*b*d + 15*a^2*e)*Sqrt[a + b*x^2])/(15*a^3*x) + (f*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/Sqrt[b]","A",6,6,32,0.1875,1,"{1807, 1585, 1265, 451, 217, 206}"
157,1,140,0,0.1842846,"\int \frac{c+d x^2+e x^4+f x^6}{x^8 \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^8*Sqrt[a + b*x^2]),x]","\frac{\sqrt{a+b x^2} \left(70 a^2 b e-105 a^3 f-56 a b^2 d+48 b^3 c\right)}{105 a^4 x}-\frac{\sqrt{a+b x^2} \left(35 a^2 e-28 a b d+24 b^2 c\right)}{105 a^3 x^3}+\frac{\sqrt{a+b x^2} (6 b c-7 a d)}{35 a^2 x^5}-\frac{c \sqrt{a+b x^2}}{7 a x^7}","\frac{\sqrt{a+b x^2} \left(70 a^2 b e-105 a^3 f-56 a b^2 d+48 b^3 c\right)}{105 a^4 x}-\frac{\sqrt{a+b x^2} \left(35 a^2 e-28 a b d+24 b^2 c\right)}{105 a^3 x^3}+\frac{\sqrt{a+b x^2} (6 b c-7 a d)}{35 a^2 x^5}-\frac{c \sqrt{a+b x^2}}{7 a x^7}",1,"-(c*Sqrt[a + b*x^2])/(7*a*x^7) + ((6*b*c - 7*a*d)*Sqrt[a + b*x^2])/(35*a^2*x^5) - ((24*b^2*c - 28*a*b*d + 35*a^2*e)*Sqrt[a + b*x^2])/(105*a^3*x^3) + ((48*b^3*c - 56*a*b^2*d + 70*a^2*b*e - 105*a^3*f)*Sqrt[a + b*x^2])/(105*a^4*x)","A",5,3,32,0.09375,1,"{1803, 12, 264}"
158,1,189,0,0.2543145,"\int \frac{c+d x^2+e x^4+f x^6}{x^{10} \sqrt{a+b x^2}} \, dx","Int[(c + d*x^2 + e*x^4 + f*x^6)/(x^10*Sqrt[a + b*x^2]),x]","-\frac{2 b \sqrt{a+b x^2} \left(84 a^2 b e-105 a^3 f-72 a b^2 d+64 b^3 c\right)}{315 a^5 x}+\frac{\sqrt{a+b x^2} \left(84 a^2 b e-105 a^3 f-72 a b^2 d+64 b^3 c\right)}{315 a^4 x^3}-\frac{\sqrt{a+b x^2} \left(21 a^2 e-18 a b d+16 b^2 c\right)}{105 a^3 x^5}+\frac{\sqrt{a+b x^2} (8 b c-9 a d)}{63 a^2 x^7}-\frac{c \sqrt{a+b x^2}}{9 a x^9}","-\frac{2 b \sqrt{a+b x^2} \left(84 a^2 b e-105 a^3 f-72 a b^2 d+64 b^3 c\right)}{315 a^5 x}+\frac{\sqrt{a+b x^2} \left(84 a^2 b e-105 a^3 f-72 a b^2 d+64 b^3 c\right)}{315 a^4 x^3}-\frac{\sqrt{a+b x^2} \left(21 a^2 e-18 a b d+16 b^2 c\right)}{105 a^3 x^5}+\frac{\sqrt{a+b x^2} (8 b c-9 a d)}{63 a^2 x^7}-\frac{c \sqrt{a+b x^2}}{9 a x^9}",1,"-(c*Sqrt[a + b*x^2])/(9*a*x^9) + ((8*b*c - 9*a*d)*Sqrt[a + b*x^2])/(63*a^2*x^7) - ((16*b^2*c - 18*a*b*d + 21*a^2*e)*Sqrt[a + b*x^2])/(105*a^3*x^5) + ((64*b^3*c - 72*a*b^2*d + 84*a^2*b*e - 105*a^3*f)*Sqrt[a + b*x^2])/(315*a^4*x^3) - (2*b*(64*b^3*c - 72*a*b^2*d + 84*a^2*b*e - 105*a^3*f)*Sqrt[a + b*x^2])/(315*a^5*x)","A",6,4,32,0.1250,1,"{1803, 12, 271, 264}"
159,1,381,0,0.6623345,"\int \frac{x^8 \left(A+B x^2+C x^4+D x^6\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^8*(A + B*x^2 + C*x^4 + D*x^6))/(a + b*x^2)^(9/2),x]","-\frac{x^9 \left(2 A b^3-a \left(23 a^2 D-16 a b C+9 b^2 B\right)\right)}{35 a^2 b^3 \left(a+b x^2\right)^{5/2}}+\frac{x^9 \left(A-\frac{a \left(a^2 D-a b C+b^2 B\right)}{b^3}\right)}{7 a \left(a+b x^2\right)^{7/2}}-\frac{x^7 \left(16 A b^3-3 a \left(143 a^2 D-66 a b C+24 b^2 B\right)\right)}{210 a^2 b^4 \left(a+b x^2\right)^{3/2}}-\frac{x^5 \left(16 A b^3-3 a \left(143 a^2 D-66 a b C+24 b^2 B\right)\right)}{30 a^2 b^5 \sqrt{a+b x^2}}+\frac{x^3 \sqrt{a+b x^2} \left(16 A b^3-3 a \left(143 a^2 D-66 a b C+24 b^2 B\right)\right)}{24 a^2 b^6}-\frac{x \sqrt{a+b x^2} \left(16 A b^3-3 a \left(143 a^2 D-66 a b C+24 b^2 B\right)\right)}{16 a b^7}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(198 a^2 b C-429 a^3 D-72 a b^2 B+16 A b^3\right)}{16 b^{15/2}}+\frac{D x^9}{6 b^3 \left(a+b x^2\right)^{3/2}}","-\frac{x^9 \left(2 A b^3-a \left(23 a^2 D-16 a b C+9 b^2 B\right)\right)}{35 a^2 b^3 \left(a+b x^2\right)^{5/2}}+\frac{x^9 \left(A-\frac{a \left(a^2 D-a b C+b^2 B\right)}{b^3}\right)}{7 a \left(a+b x^2\right)^{7/2}}-\frac{x^7 \left(16 A b^3-3 a \left(143 a^2 D-66 a b C+24 b^2 B\right)\right)}{210 a^2 b^4 \left(a+b x^2\right)^{3/2}}-\frac{x^5 \left(16 A b^3-3 a \left(143 a^2 D-66 a b C+24 b^2 B\right)\right)}{30 a^2 b^5 \sqrt{a+b x^2}}+\frac{x^3 \sqrt{a+b x^2} \left(16 A b^3-3 a \left(143 a^2 D-66 a b C+24 b^2 B\right)\right)}{24 a^2 b^6}-\frac{x \sqrt{a+b x^2} \left(16 A b^3-3 a \left(143 a^2 D-66 a b C+24 b^2 B\right)\right)}{16 a b^7}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(198 a^2 b C-429 a^3 D-72 a b^2 B+16 A b^3\right)}{16 b^{15/2}}+\frac{D x^9}{6 b^3 \left(a+b x^2\right)^{3/2}}",1,"((A - (a*(b^2*B - a*b*C + a^2*D))/b^3)*x^9)/(7*a*(a + b*x^2)^(7/2)) - ((2*A*b^3 - a*(9*b^2*B - 16*a*b*C + 23*a^2*D))*x^9)/(35*a^2*b^3*(a + b*x^2)^(5/2)) - ((16*A*b^3 - 3*a*(24*b^2*B - 66*a*b*C + 143*a^2*D))*x^7)/(210*a^2*b^4*(a + b*x^2)^(3/2)) + (D*x^9)/(6*b^3*(a + b*x^2)^(3/2)) - ((16*A*b^3 - 3*a*(24*b^2*B - 66*a*b*C + 143*a^2*D))*x^5)/(30*a^2*b^5*Sqrt[a + b*x^2]) - ((16*A*b^3 - 3*a*(24*b^2*B - 66*a*b*C + 143*a^2*D))*x*Sqrt[a + b*x^2])/(16*a*b^7) + ((16*A*b^3 - 3*a*(24*b^2*B - 66*a*b*C + 143*a^2*D))*x^3*Sqrt[a + b*x^2])/(24*a^2*b^6) + ((16*A*b^3 - 72*a*b^2*B + 198*a^2*b*C - 429*a^3*D)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(15/2))","A",11,9,32,0.2812,1,"{1804, 1585, 1263, 1584, 459, 288, 321, 217, 206}"
160,1,279,0,0.4549095,"\int \frac{x^6 \left(A+B x^2+C x^4+D x^6\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^6*(A + B*x^2 + C*x^4 + D*x^6))/(a + b*x^2)^(9/2),x]","\frac{x^7 \left(A-\frac{a \left(a^2 D-a b C+b^2 B\right)}{b^3}\right)}{7 a \left(a+b x^2\right)^{7/2}}+\frac{x^7 \left(3 a^2 D-2 a b C+b^2 B\right)}{5 a b^3 \left(a+b x^2\right)^{5/2}}+\frac{x^5 \left(99 a^2 D-36 a b C+8 b^2 B\right)}{60 a b^4 \left(a+b x^2\right)^{3/2}}+\frac{x^3 \left(99 a^2 D-36 a b C+8 b^2 B\right)}{12 a b^5 \sqrt{a+b x^2}}-\frac{x \sqrt{a+b x^2} \left(99 a^2 D-36 a b C+8 b^2 B\right)}{8 a b^6}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(99 a^2 D-36 a b C+8 b^2 B\right)}{8 b^{13/2}}+\frac{D x^7}{4 b^3 \left(a+b x^2\right)^{3/2}}","\frac{x^7 \left(A-\frac{a \left(a^2 D-a b C+b^2 B\right)}{b^3}\right)}{7 a \left(a+b x^2\right)^{7/2}}+\frac{x^7 \left(3 a^2 D-2 a b C+b^2 B\right)}{5 a b^3 \left(a+b x^2\right)^{5/2}}+\frac{x^5 \left(99 a^2 D-36 a b C+8 b^2 B\right)}{60 a b^4 \left(a+b x^2\right)^{3/2}}+\frac{x^3 \left(99 a^2 D-36 a b C+8 b^2 B\right)}{12 a b^5 \sqrt{a+b x^2}}-\frac{x \sqrt{a+b x^2} \left(99 a^2 D-36 a b C+8 b^2 B\right)}{8 a b^6}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right) \left(99 a^2 D-36 a b C+8 b^2 B\right)}{8 b^{13/2}}+\frac{D x^7}{4 b^3 \left(a+b x^2\right)^{3/2}}",1,"((A - (a*(b^2*B - a*b*C + a^2*D))/b^3)*x^7)/(7*a*(a + b*x^2)^(7/2)) + ((b^2*B - 2*a*b*C + 3*a^2*D)*x^7)/(5*a*b^3*(a + b*x^2)^(5/2)) + ((8*b^2*B - 36*a*b*C + 99*a^2*D)*x^5)/(60*a*b^4*(a + b*x^2)^(3/2)) + (D*x^7)/(4*b^3*(a + b*x^2)^(3/2)) + ((8*b^2*B - 36*a*b*C + 99*a^2*D)*x^3)/(12*a*b^5*Sqrt[a + b*x^2]) - ((8*b^2*B - 36*a*b*C + 99*a^2*D)*x*Sqrt[a + b*x^2])/(8*a*b^6) + ((8*b^2*B - 36*a*b*C + 99*a^2*D)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(13/2))","A",10,9,32,0.2812,1,"{1804, 1585, 1263, 1584, 459, 288, 321, 217, 206}"
161,1,210,0,0.387121,"\int \frac{x^4 \left(A+B x^2+C x^4+D x^6\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^4*(A + B*x^2 + C*x^4 + D*x^6))/(a + b*x^2)^(9/2),x]","\frac{x^5 \left(a \left(19 a^2 D-12 a b C+5 b^2 B\right)+2 A b^3\right)}{35 a^2 b^3 \left(a+b x^2\right)^{5/2}}+\frac{x^5 \left(A-\frac{a \left(a^2 D-a b C+b^2 B\right)}{b^3}\right)}{7 a \left(a+b x^2\right)^{7/2}}-\frac{x (4 b C-15 a D)}{3 b^5 \sqrt{a+b x^2}}+\frac{a x (b C-3 a D)}{3 b^5 \left(a+b x^2\right)^{3/2}}+\frac{(2 b C-9 a D) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{11/2}}+\frac{D x \sqrt{a+b x^2}}{2 b^5}","\frac{x^5 \left(a \left(19 a^2 D-12 a b C+5 b^2 B\right)+2 A b^3\right)}{35 a^2 b^3 \left(a+b x^2\right)^{5/2}}+\frac{x^5 \left(A-\frac{a \left(a^2 D-a b C+b^2 B\right)}{b^3}\right)}{7 a \left(a+b x^2\right)^{7/2}}-\frac{x (4 b C-15 a D)}{3 b^5 \sqrt{a+b x^2}}+\frac{a x (b C-3 a D)}{3 b^5 \left(a+b x^2\right)^{3/2}}+\frac{(2 b C-9 a D) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{11/2}}+\frac{D x \sqrt{a+b x^2}}{2 b^5}",1,"((A - (a*(b^2*B - a*b*C + a^2*D))/b^3)*x^5)/(7*a*(a + b*x^2)^(7/2)) + ((2*A*b^3 + a*(5*b^2*B - 12*a*b*C + 19*a^2*D))*x^5)/(35*a^2*b^3*(a + b*x^2)^(5/2)) + (a*(b*C - 3*a*D)*x)/(3*b^5*(a + b*x^2)^(3/2)) - ((4*b*C - 15*a*D)*x)/(3*b^5*Sqrt[a + b*x^2]) + (D*x*Sqrt[a + b*x^2])/(2*b^5) + ((2*b*C - 9*a*D)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(11/2))","A",9,9,32,0.2812,1,"{1804, 1585, 1263, 1584, 455, 1157, 388, 217, 206}"
162,1,192,0,0.3138593,"\int \frac{x^2 \left(A+B x^2+C x^4+D x^6\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^2*(A + B*x^2 + C*x^4 + D*x^6))/(a + b*x^2)^(9/2),x]","\frac{x^3 \left(a \left(-71 a^2 D+15 a b C+6 b^2 B\right)+8 A b^3\right)}{105 a^3 b^3 \left(a+b x^2\right)^{3/2}}+\frac{x^3 \left(a \left(17 a^2 D-10 a b C+3 b^2 B\right)+4 A b^3\right)}{35 a^2 b^3 \left(a+b x^2\right)^{5/2}}+\frac{x^3 \left(A-\frac{a \left(a^2 D-a b C+b^2 B\right)}{b^3}\right)}{7 a \left(a+b x^2\right)^{7/2}}-\frac{D x}{b^4 \sqrt{a+b x^2}}+\frac{D \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}","\frac{x^7 \left(15 a^2 b C-176 a^3 D+6 a b^2 B+8 A b^3\right)}{105 a^3 b \left(a+b x^2\right)^{7/2}}+\frac{x^5 \left(-58 a^3 D+3 a b^2 B+4 A b^3\right)}{15 a^2 b^2 \left(a+b x^2\right)^{7/2}}+\frac{x^3 \left(A b^3-10 a^3 D\right)}{3 a b^3 \left(a+b x^2\right)^{7/2}}-\frac{a^3 D x}{b^4 \left(a+b x^2\right)^{7/2}}+\frac{D \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}",1,"((A - (a*(b^2*B - a*b*C + a^2*D))/b^3)*x^3)/(7*a*(a + b*x^2)^(7/2)) + ((4*A*b^3 + a*(3*b^2*B - 10*a*b*C + 17*a^2*D))*x^3)/(35*a^2*b^3*(a + b*x^2)^(5/2)) + ((8*A*b^3 + a*(6*b^2*B + 15*a*b*C - 71*a^2*D))*x^3)/(105*a^3*b^3*(a + b*x^2)^(3/2)) - (D*x)/(b^4*Sqrt[a + b*x^2]) + (D*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(9/2)","A",8,8,32,0.2500,1,"{1804, 1585, 1263, 1584, 452, 288, 217, 206}"
163,1,134,0,0.2104403,"\int \frac{A+B x^2+C x^4+D x^6}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x^2 + C*x^4 + D*x^6)/(a + b*x^2)^(9/2),x]","\frac{x^7 \left(a \left(15 a^2 D+6 a b C+8 b^2 B\right)+48 A b^3\right)}{105 a^4 \left(a+b x^2\right)^{7/2}}+\frac{x^5 \left(a (3 a C+4 b B)+24 A b^2\right)}{15 a^3 \left(a+b x^2\right)^{7/2}}+\frac{x^3 (a B+6 A b)}{3 a^2 \left(a+b x^2\right)^{7/2}}+\frac{A x}{a \left(a+b x^2\right)^{7/2}}","\frac{x^7 \left(a \left(15 a^2 D+6 a b C+8 b^2 B\right)+48 A b^3\right)}{105 a^4 \left(a+b x^2\right)^{7/2}}+\frac{x^5 \left(a (3 a C+4 b B)+24 A b^2\right)}{15 a^3 \left(a+b x^2\right)^{7/2}}+\frac{x^3 (a B+6 A b)}{3 a^2 \left(a+b x^2\right)^{7/2}}+\frac{A x}{a \left(a+b x^2\right)^{7/2}}",1,"(A*x)/(a*(a + b*x^2)^(7/2)) + ((6*A*b + a*B)*x^3)/(3*a^2*(a + b*x^2)^(7/2)) + ((24*A*b^2 + a*(4*b*B + 3*a*C))*x^5)/(15*a^3*(a + b*x^2)^(7/2)) + ((48*A*b^3 + a*(8*b^2*B + 6*a*b*C + 15*a^2*D))*x^7)/(105*a^4*(a + b*x^2)^(7/2))","A",5,4,29,0.1379,1,"{1813, 1803, 12, 264}"
164,1,179,0,0.2463497,"\int \frac{A+B x^2+C x^4+D x^6}{x^2 \left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x^2 + C*x^4 + D*x^6)/(x^2*(a + b*x^2)^(9/2)),x]","-\frac{2 b x^7 \left(-3 a^3 D-4 a b (a C+6 b B)+192 A b^3\right)}{105 a^5 \left(a+b x^2\right)^{7/2}}-\frac{x^5 \left(-3 a^3 D-4 a b (a C+6 b B)+192 A b^3\right)}{15 a^4 \left(a+b x^2\right)^{7/2}}-\frac{x^3 \left(48 A b^2-a (a C+6 b B)\right)}{3 a^3 \left(a+b x^2\right)^{7/2}}-\frac{x (8 A b-a B)}{a^2 \left(a+b x^2\right)^{7/2}}-\frac{A}{a x \left(a+b x^2\right)^{7/2}}","-\frac{2 b x^7 \left(4 b \left(48 A b^2-a (a C+6 b B)\right)-3 a^3 D\right)}{105 a^5 \left(a+b x^2\right)^{7/2}}-\frac{x^5 \left(4 b \left(48 A b^2-a (a C+6 b B)\right)-3 a^3 D\right)}{15 a^4 \left(a+b x^2\right)^{7/2}}-\frac{x^3 \left(48 A b^2-a (a C+6 b B)\right)}{3 a^3 \left(a+b x^2\right)^{7/2}}-\frac{x (8 A b-a B)}{a^2 \left(a+b x^2\right)^{7/2}}-\frac{A}{a x \left(a+b x^2\right)^{7/2}}",1,"-(A/(a*x*(a + b*x^2)^(7/2))) - ((8*A*b - a*B)*x)/(a^2*(a + b*x^2)^(7/2)) - ((48*A*b^2 - a*(6*b*B + a*C))*x^3)/(3*a^3*(a + b*x^2)^(7/2)) - ((192*A*b^3 - 4*a*b*(6*b*B + a*C) - 3*a^3*D)*x^5)/(15*a^4*(a + b*x^2)^(7/2)) - (2*b*(192*A*b^3 - 4*a*b*(6*b*B + a*C) - 3*a^3*D)*x^7)/(105*a^5*(a + b*x^2)^(7/2))","A",6,5,32,0.1562,1,"{1803, 1813, 12, 271, 264}"
165,1,242,0,0.3218032,"\int \frac{A+B x^2+C x^4+D x^6}{x^4 \left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x^2 + C*x^4 + D*x^6)/(x^4*(a + b*x^2)^(9/2)),x]","\frac{8 b^2 x^7 \left(160 A b^3-a \left(a^2 (-D)-6 a b C+48 b^2 B\right)\right)}{105 a^6 \left(a+b x^2\right)^{7/2}}+\frac{4 b x^5 \left(160 A b^3-a \left(a^2 (-D)-6 a b C+48 b^2 B\right)\right)}{15 a^5 \left(a+b x^2\right)^{7/2}}+\frac{x^3 \left(160 A b^3-a \left(a^2 (-D)-6 a b C+48 b^2 B\right)\right)}{3 a^4 \left(a+b x^2\right)^{7/2}}+\frac{x \left(80 A b^2-3 a (8 b B-a C)\right)}{3 a^3 \left(a+b x^2\right)^{7/2}}+\frac{10 A b-3 a B}{3 a^2 x \left(a+b x^2\right)^{7/2}}-\frac{A}{3 a x^3 \left(a+b x^2\right)^{7/2}}","\frac{8 b^2 x^7 \left(160 A b^3-a \left(a^2 (-D)-6 a b C+48 b^2 B\right)\right)}{105 a^6 \left(a+b x^2\right)^{7/2}}+\frac{4 b x^5 \left(160 A b^3-a \left(a^2 (-D)-6 a b C+48 b^2 B\right)\right)}{15 a^5 \left(a+b x^2\right)^{7/2}}+\frac{x^3 \left(160 A b^3-a \left(a^2 (-D)-6 a b C+48 b^2 B\right)\right)}{3 a^4 \left(a+b x^2\right)^{7/2}}+\frac{x \left(80 A b^2-3 a (8 b B-a C)\right)}{3 a^3 \left(a+b x^2\right)^{7/2}}+\frac{10 A b-3 a B}{3 a^2 x \left(a+b x^2\right)^{7/2}}-\frac{A}{3 a x^3 \left(a+b x^2\right)^{7/2}}",1,"-A/(3*a*x^3*(a + b*x^2)^(7/2)) + (10*A*b - 3*a*B)/(3*a^2*x*(a + b*x^2)^(7/2)) + ((80*A*b^2 - 3*a*(8*b*B - a*C))*x)/(3*a^3*(a + b*x^2)^(7/2)) + ((160*A*b^3 - a*(48*b^2*B - 6*a*b*C - a^2*D))*x^3)/(3*a^4*(a + b*x^2)^(7/2)) + (4*b*(160*A*b^3 - a*(48*b^2*B - 6*a*b*C - a^2*D))*x^5)/(15*a^5*(a + b*x^2)^(7/2)) + (8*b^2*(160*A*b^3 - a*(48*b^2*B - 6*a*b*C - a^2*D))*x^7)/(105*a^6*(a + b*x^2)^(7/2))","A",7,5,32,0.1562,1,"{1803, 1813, 12, 271, 264}"
166,1,275,0,0.4289955,"\int \frac{A+B x^2+C x^4+D x^6}{x^6 \left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x^2 + C*x^4 + D*x^6)/(x^6*(a + b*x^2)^(9/2)),x]","-\frac{16 x \left(-3 a^3 D-8 a b (10 b B-3 a C)+192 A b^3\right)}{105 a^7 \sqrt{a+b x^2}}-\frac{8 x \left(192 A b^3-a \left(3 a^2 D-24 a b C+80 b^2 B\right)\right)}{105 a^6 \left(a+b x^2\right)^{3/2}}-\frac{2 x \left(-3 a^3 D-8 a b (10 b B-3 a C)+192 A b^3\right)}{35 a^5 \left(a+b x^2\right)^{5/2}}-\frac{x \left(-3 a^3 D-8 a b (10 b B-3 a C)+192 A b^3\right)}{21 a^4 \left(a+b x^2\right)^{7/2}}-\frac{24 A b^2-a (10 b B-3 a C)}{3 a^3 x \left(a+b x^2\right)^{7/2}}+\frac{12 A b-5 a B}{15 a^2 x^3 \left(a+b x^2\right)^{7/2}}-\frac{A}{5 a x^5 \left(a+b x^2\right)^{7/2}}","-\frac{16 x \left(192 A b^3-a \left(3 a^2 D-24 a b C+80 b^2 B\right)\right)}{105 a^7 \sqrt{a+b x^2}}-\frac{8 x \left(192 A b^3-a \left(3 a^2 D-24 a b C+80 b^2 B\right)\right)}{105 a^6 \left(a+b x^2\right)^{3/2}}-\frac{2 x \left(192 A b^3-a \left(3 a^2 D-24 a b C+80 b^2 B\right)\right)}{35 a^5 \left(a+b x^2\right)^{5/2}}-\frac{x \left(192 A b^3-a \left(3 a^2 D-24 a b C+80 b^2 B\right)\right)}{21 a^4 \left(a+b x^2\right)^{7/2}}-\frac{24 A b^2-a (10 b B-3 a C)}{3 a^3 x \left(a+b x^2\right)^{7/2}}+\frac{12 A b-5 a B}{15 a^2 x^3 \left(a+b x^2\right)^{7/2}}-\frac{A}{5 a x^5 \left(a+b x^2\right)^{7/2}}",1,"-A/(5*a*x^5*(a + b*x^2)^(7/2)) + (12*A*b - 5*a*B)/(15*a^2*x^3*(a + b*x^2)^(7/2)) - (24*A*b^2 - a*(10*b*B - 3*a*C))/(3*a^3*x*(a + b*x^2)^(7/2)) - ((192*A*b^3 - 8*a*b*(10*b*B - 3*a*C) - 3*a^3*D)*x)/(21*a^4*(a + b*x^2)^(7/2)) - (2*(192*A*b^3 - 8*a*b*(10*b*B - 3*a*C) - 3*a^3*D)*x)/(35*a^5*(a + b*x^2)^(5/2)) - (8*(192*A*b^3 - a*(80*b^2*B - 24*a*b*C + 3*a^2*D))*x)/(105*a^6*(a + b*x^2)^(3/2)) - (16*(192*A*b^3 - 8*a*b*(10*b*B - 3*a*C) - 3*a^3*D)*x)/(105*a^7*Sqrt[a + b*x^2])","A",8,4,32,0.1250,1,"{1803, 12, 192, 191}"
167,1,334,0,0.4803113,"\int \frac{A+B x^2+C x^4+D x^6}{x^8 \left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x^2 + C*x^4 + D*x^6)/(x^8*(a + b*x^2)^(9/2)),x]","\frac{128 b x \left(48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)\right)}{105 a^8 \sqrt{a+b x^2}}+\frac{64 b x \left(48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)\right)}{105 a^7 \left(a+b x^2\right)^{3/2}}+\frac{16 b x \left(48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)\right)}{35 a^6 \left(a+b x^2\right)^{5/2}}+\frac{8 b x \left(48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)\right)}{21 a^5 \left(a+b x^2\right)^{7/2}}+\frac{48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)}{3 a^4 x \left(a+b x^2\right)^{7/2}}-\frac{24 A b^2-a (12 b B-5 a C)}{15 a^3 x^3 \left(a+b x^2\right)^{7/2}}+\frac{2 A b-a B}{5 a^2 x^5 \left(a+b x^2\right)^{7/2}}-\frac{A}{7 a x^7 \left(a+b x^2\right)^{7/2}}","\frac{128 b x \left(48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)\right)}{105 a^8 \sqrt{a+b x^2}}+\frac{64 b x \left(48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)\right)}{105 a^7 \left(a+b x^2\right)^{3/2}}+\frac{16 b x \left(48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)\right)}{35 a^6 \left(a+b x^2\right)^{5/2}}+\frac{8 b x \left(48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)\right)}{21 a^5 \left(a+b x^2\right)^{7/2}}+\frac{48 A b^3-a \left(3 a^2 D-10 a b C+24 b^2 B\right)}{3 a^4 x \left(a+b x^2\right)^{7/2}}-\frac{24 A b^2-a (12 b B-5 a C)}{15 a^3 x^3 \left(a+b x^2\right)^{7/2}}+\frac{2 A b-a B}{5 a^2 x^5 \left(a+b x^2\right)^{7/2}}-\frac{A}{7 a x^7 \left(a+b x^2\right)^{7/2}}",1,"-A/(7*a*x^7*(a + b*x^2)^(7/2)) + (2*A*b - a*B)/(5*a^2*x^5*(a + b*x^2)^(7/2)) - (24*A*b^2 - a*(12*b*B - 5*a*C))/(15*a^3*x^3*(a + b*x^2)^(7/2)) + (48*A*b^3 - a*(24*b^2*B - 10*a*b*C + 3*a^2*D))/(3*a^4*x*(a + b*x^2)^(7/2)) + (8*b*(48*A*b^3 - a*(24*b^2*B - 10*a*b*C + 3*a^2*D))*x)/(21*a^5*(a + b*x^2)^(7/2)) + (16*b*(48*A*b^3 - a*(24*b^2*B - 10*a*b*C + 3*a^2*D))*x)/(35*a^6*(a + b*x^2)^(5/2)) + (64*b*(48*A*b^3 - a*(24*b^2*B - 10*a*b*C + 3*a^2*D))*x)/(105*a^7*(a + b*x^2)^(3/2)) + (128*b*(48*A*b^3 - a*(24*b^2*B - 10*a*b*C + 3*a^2*D))*x)/(105*a^8*Sqrt[a + b*x^2])","A",9,5,32,0.1562,1,"{1803, 12, 271, 192, 191}"
168,1,380,0,0.546361,"\int \frac{A+B x^2+C x^4+D x^6}{x^{10} \left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x^2 + C*x^4 + D*x^6)/(x^10*(a + b*x^2)^(9/2)),x]","-\frac{256 b^2 x \left(-15 a^3 D-36 a b (2 b B-a C)+128 A b^3\right)}{315 a^9 \sqrt{a+b x^2}}-\frac{128 b^2 x \left(-15 a^3 D-36 a b (2 b B-a C)+128 A b^3\right)}{315 a^8 \left(a+b x^2\right)^{3/2}}-\frac{32 b^2 x \left(-15 a^3 D-36 a b (2 b B-a C)+128 A b^3\right)}{105 a^7 \left(a+b x^2\right)^{5/2}}-\frac{16 b^2 x \left(-15 a^3 D-36 a b (2 b B-a C)+128 A b^3\right)}{63 a^6 \left(a+b x^2\right)^{7/2}}-\frac{2 b \left(-15 a^3 D-36 a b (2 b B-a C)+128 A b^3\right)}{9 a^5 x \left(a+b x^2\right)^{7/2}}+\frac{-15 a^3 D-36 a b (2 b B-a C)+128 A b^3}{45 a^4 x^3 \left(a+b x^2\right)^{7/2}}-\frac{32 A b^2-9 a (2 b B-a C)}{45 a^3 x^5 \left(a+b x^2\right)^{7/2}}+\frac{16 A b-9 a B}{63 a^2 x^7 \left(a+b x^2\right)^{7/2}}-\frac{A}{9 a x^9 \left(a+b x^2\right)^{7/2}}","-\frac{256 b^2 x \left(128 A b^3-3 a \left(5 a^2 D-12 a b C+24 b^2 B\right)\right)}{315 a^9 \sqrt{a+b x^2}}-\frac{128 b^2 x \left(128 A b^3-3 a \left(5 a^2 D-12 a b C+24 b^2 B\right)\right)}{315 a^8 \left(a+b x^2\right)^{3/2}}-\frac{32 b^2 x \left(128 A b^3-3 a \left(5 a^2 D-12 a b C+24 b^2 B\right)\right)}{105 a^7 \left(a+b x^2\right)^{5/2}}-\frac{16 b^2 x \left(128 A b^3-3 a \left(5 a^2 D-12 a b C+24 b^2 B\right)\right)}{63 a^6 \left(a+b x^2\right)^{7/2}}-\frac{2 b \left(128 A b^3-3 a \left(5 a^2 D-12 a b C+24 b^2 B\right)\right)}{9 a^5 x \left(a+b x^2\right)^{7/2}}+\frac{128 A b^3-3 a \left(5 a^2 D-12 a b C+24 b^2 B\right)}{45 a^4 x^3 \left(a+b x^2\right)^{7/2}}-\frac{32 A b^2-9 a (2 b B-a C)}{45 a^3 x^5 \left(a+b x^2\right)^{7/2}}+\frac{16 A b-9 a B}{63 a^2 x^7 \left(a+b x^2\right)^{7/2}}-\frac{A}{9 a x^9 \left(a+b x^2\right)^{7/2}}",1,"-A/(9*a*x^9*(a + b*x^2)^(7/2)) + (16*A*b - 9*a*B)/(63*a^2*x^7*(a + b*x^2)^(7/2)) - (32*A*b^2 - 9*a*(2*b*B - a*C))/(45*a^3*x^5*(a + b*x^2)^(7/2)) + (128*A*b^3 - 36*a*b*(2*b*B - a*C) - 15*a^3*D)/(45*a^4*x^3*(a + b*x^2)^(7/2)) - (2*b*(128*A*b^3 - 36*a*b*(2*b*B - a*C) - 15*a^3*D))/(9*a^5*x*(a + b*x^2)^(7/2)) - (16*b^2*(128*A*b^3 - 36*a*b*(2*b*B - a*C) - 15*a^3*D)*x)/(63*a^6*(a + b*x^2)^(7/2)) - (32*b^2*(128*A*b^3 - 36*a*b*(2*b*B - a*C) - 15*a^3*D)*x)/(105*a^7*(a + b*x^2)^(5/2)) - (128*b^2*(128*A*b^3 - 36*a*b*(2*b*B - a*C) - 15*a^3*D)*x)/(315*a^8*(a + b*x^2)^(3/2)) - (256*b^2*(128*A*b^3 - 36*a*b*(2*b*B - a*C) - 15*a^3*D)*x)/(315*a^9*Sqrt[a + b*x^2])","A",10,5,32,0.1562,1,"{1803, 12, 271, 192, 191}"
169,1,214,0,0.2223029,"\int \frac{c x^5+d x^7+e x^9+f x^{11}}{\sqrt{a+b x^2}} \, dx","Int[(c*x^5 + d*x^7 + e*x^9 + f*x^11)/Sqrt[a + b*x^2],x]","\frac{\left(a+b x^2\right)^{5/2} \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{5 b^6}-\frac{a \left(a+b x^2\right)^{3/2} \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6}+\frac{a^2 \sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^6}+\frac{\left(a+b x^2\right)^{7/2} \left(10 a^2 f-4 a b e+b^2 d\right)}{7 b^6}+\frac{\left(a+b x^2\right)^{9/2} (b e-5 a f)}{9 b^6}+\frac{f \left(a+b x^2\right)^{11/2}}{11 b^6}","\frac{\left(a+b x^2\right)^{5/2} \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{5 b^6}-\frac{a \left(a+b x^2\right)^{3/2} \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6}+\frac{a^2 \sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^6}+\frac{\left(a+b x^2\right)^{7/2} \left(10 a^2 f-4 a b e+b^2 d\right)}{7 b^6}+\frac{\left(a+b x^2\right)^{9/2} (b e-5 a f)}{9 b^6}+\frac{f \left(a+b x^2\right)^{11/2}}{11 b^6}",1,"(a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Sqrt[a + b*x^2])/b^6 - (a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f)*(a + b*x^2)^(3/2))/(3*b^6) + ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*(a + b*x^2)^(5/2))/(5*b^6) + ((b^2*d - 4*a*b*e + 10*a^2*f)*(a + b*x^2)^(7/2))/(7*b^6) + ((b*e - 5*a*f)*(a + b*x^2)^(9/2))/(9*b^6) + (f*(a + b*x^2)^(11/2))/(11*b^6)","A",4,3,33,0.09091,1,"{1811, 1799, 1850}"
170,1,167,0,0.1747342,"\int \frac{c x^3+d x^5+e x^7+f x^9}{\sqrt{a+b x^2}} \, dx","Int[(c*x^3 + d*x^5 + e*x^7 + f*x^9)/Sqrt[a + b*x^2],x]","\frac{\left(a+b x^2\right)^{3/2} \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{3 b^5}-\frac{a \sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^5}+\frac{\left(a+b x^2\right)^{5/2} \left(6 a^2 f-3 a b e+b^2 d\right)}{5 b^5}+\frac{\left(a+b x^2\right)^{7/2} (b e-4 a f)}{7 b^5}+\frac{f \left(a+b x^2\right)^{9/2}}{9 b^5}","\frac{\left(a+b x^2\right)^{3/2} \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{3 b^5}-\frac{a \sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^5}+\frac{\left(a+b x^2\right)^{5/2} \left(6 a^2 f-3 a b e+b^2 d\right)}{5 b^5}+\frac{\left(a+b x^2\right)^{7/2} (b e-4 a f)}{7 b^5}+\frac{f \left(a+b x^2\right)^{9/2}}{9 b^5}",1,"-((a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Sqrt[a + b*x^2])/b^5) + ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*(a + b*x^2)^(3/2))/(3*b^5) + ((b^2*d - 3*a*b*e + 6*a^2*f)*(a + b*x^2)^(5/2))/(5*b^5) + ((b*e - 4*a*f)*(a + b*x^2)^(7/2))/(7*b^5) + (f*(a + b*x^2)^(9/2))/(9*b^5)","A",4,3,33,0.09091,1,"{1811, 1799, 1850}"
171,1,121,0,0.1500719,"\int \frac{c x+d x^3+e x^5+f x^7}{\sqrt{a+b x^2}} \, dx","Int[(c*x + d*x^3 + e*x^5 + f*x^7)/Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}+\frac{\left(a+b x^2\right)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{\left(a+b x^2\right)^{5/2} (b e-3 a f)}{5 b^4}+\frac{f \left(a+b x^2\right)^{7/2}}{7 b^4}","\frac{\sqrt{a+b x^2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}+\frac{\left(a+b x^2\right)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{\left(a+b x^2\right)^{5/2} (b e-3 a f)}{5 b^4}+\frac{f \left(a+b x^2\right)^{7/2}}{7 b^4}",1,"((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Sqrt[a + b*x^2])/b^4 + ((b^2*d - 2*a*b*e + 3*a^2*f)*(a + b*x^2)^(3/2))/(3*b^4) + ((b*e - 3*a*f)*(a + b*x^2)^(5/2))/(5*b^4) + (f*(a + b*x^2)^(7/2))/(7*b^4)","A",4,3,31,0.09677,1,"{1811, 1799, 1850}"
172,1,257,0,0.7164158,"\int \frac{x^2 \left(A+B x^2+C x^4+D x^6+F x^8\right)}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(x^2*(A + B*x^2 + C*x^4 + D*x^6 + F*x^8))/(a + b*x^2)^(9/2),x]","\frac{x^3 \left(a \left(-71 a^2 b D+162 a^3 F+15 a b^2 C+6 b^3 B\right)+8 A b^4\right)}{105 a^3 b^4 \left(a+b x^2\right)^{3/2}}+\frac{x^3 \left(a \left(17 a^2 b D-24 a^3 F-10 a b^2 C+3 b^3 B\right)+4 A b^4\right)}{35 a^2 b^4 \left(a+b x^2\right)^{5/2}}+\frac{x^3 \left(\frac{A}{a}-\frac{a^2 b D+a^3 (-F)-a b^2 C+b^3 B}{b^4}\right)}{7 \left(a+b x^2\right)^{7/2}}-\frac{x (b D-4 a F)}{b^5 \sqrt{a+b x^2}}+\frac{(2 b D-9 a F) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{11/2}}+\frac{F x \sqrt{a+b x^2}}{2 b^5}","\frac{x^3 \left(a \left(-71 a^2 b D+162 a^3 F+15 a b^2 C+6 b^3 B\right)+8 A b^4\right)}{105 a^3 b^4 \left(a+b x^2\right)^{3/2}}+\frac{x^3 \left(a \left(17 a^2 b D-24 a^3 F-10 a b^2 C+3 b^3 B\right)+4 A b^4\right)}{35 a^2 b^4 \left(a+b x^2\right)^{5/2}}+\frac{x^3 \left(A b^4-a \left(a^2 b D+a^3 (-F)-a b^2 C+b^3 B\right)\right)}{7 a b^4 \left(a+b x^2\right)^{7/2}}-\frac{x (b D-4 a F)}{b^5 \sqrt{a+b x^2}}+\frac{(2 b D-9 a F) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{11/2}}+\frac{F x \sqrt{a+b x^2}}{2 b^5}",1,"((A/a - (b^3*B - a*b^2*C + a^2*b*D - a^3*F)/b^4)*x^3)/(7*(a + b*x^2)^(7/2)) + ((4*A*b^4 + a*(3*b^3*B - 10*a*b^2*C + 17*a^2*b*D - 24*a^3*F))*x^3)/(35*a^2*b^4*(a + b*x^2)^(5/2)) + ((8*A*b^4 + a*(6*b^3*B + 15*a*b^2*C - 71*a^2*b*D + 162*a^3*F))*x^3)/(105*a^3*b^4*(a + b*x^2)^(3/2)) - ((b*D - 4*a*F)*x)/(b^5*Sqrt[a + b*x^2]) + (F*x*Sqrt[a + b*x^2])/(2*b^5) + ((2*b*D - 9*a*F)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(11/2))","A",10,9,37,0.2432,1,"{1804, 1800, 1585, 1263, 1584, 455, 388, 217, 206}"
173,1,250,0,0.4096231,"\int \frac{A+B x^2+C x^4+D x^6+F x^8}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x^2 + C*x^4 + D*x^6 + F*x^8)/(a + b*x^2)^(9/2),x]","\frac{x \left(\frac{15 a^2 b D-176 a^3 F+6 a b^2 C+8 b^3 B}{b^4}+\frac{48 A}{a}\right)}{105 a^3 \sqrt{a+b x^2}}+\frac{x \left(a \left(-45 a^2 b D+122 a^3 F+3 a b^2 C+4 b^3 B\right)+24 A b^4\right)}{105 a^3 b^4 \left(a+b x^2\right)^{3/2}}+\frac{x \left(\frac{15 a^2 b D-22 a^3 F-8 a b^2 C+b^3 B}{b^4}+\frac{6 A}{a}\right)}{35 a \left(a+b x^2\right)^{5/2}}+\frac{x \left(\frac{A}{a}-\frac{a^2 b D+a^3 (-F)-a b^2 C+b^3 B}{b^4}\right)}{7 \left(a+b x^2\right)^{7/2}}+\frac{F \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}","\frac{x^7 \left(a \left(15 a^2 b D-176 a^3 F+6 a b^2 C+8 b^3 B\right)+48 A b^4\right)}{105 a^4 b \left(a+b x^2\right)^{7/2}}+\frac{x^5 \left(a \left(-58 a^3 F+3 a b^2 C+4 b^3 B\right)+24 A b^4\right)}{15 a^3 b^2 \left(a+b x^2\right)^{7/2}}+\frac{x^3 \left(-10 a^4 F+a b^3 B+6 A b^4\right)}{3 a^2 b^3 \left(a+b x^2\right)^{7/2}}+\frac{x \left(A b^4-a^4 F\right)}{a b^4 \left(a+b x^2\right)^{7/2}}+\frac{F \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}",1,"((A/a - (b^3*B - a*b^2*C + a^2*b*D - a^3*F)/b^4)*x)/(7*(a + b*x^2)^(7/2)) + (((6*A)/a + (b^3*B - 8*a*b^2*C + 15*a^2*b*D - 22*a^3*F)/b^4)*x)/(35*a*(a + b*x^2)^(5/2)) + ((24*A*b^4 + a*(4*b^3*B + 3*a*b^2*C - 45*a^2*b*D + 122*a^3*F))*x)/(105*a^3*b^4*(a + b*x^2)^(3/2)) + (((48*A)/a + (8*b^3*B + 6*a*b^2*C + 15*a^2*b*D - 176*a^3*F)/b^4)*x)/(105*a^3*Sqrt[a + b*x^2]) + (F*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(9/2)","A",6,5,34,0.1471,1,"{1814, 1157, 385, 217, 206}"
174,1,193,0,0.3411739,"\int \frac{A+B x^2+C x^4+D x^6+F x^8}{x^2 \left(a+b x^2\right)^{9/2}} \, dx","Int[(A + B*x^2 + C*x^4 + D*x^6 + F*x^8)/(x^2*(a + b*x^2)^(9/2)),x]","-\frac{x^7 \left(384 A b^4-a \left(6 a^2 b D+15 a^3 F+8 a b^2 C+48 b^3 B\right)\right)}{105 a^5 \left(a+b x^2\right)^{7/2}}-\frac{x^5 \left(192 A b^3-a \left(3 a^2 D+4 a b C+24 b^2 B\right)\right)}{15 a^4 \left(a+b x^2\right)^{7/2}}-\frac{x^3 \left(48 A b^2-a (a C+6 b B)\right)}{3 a^3 \left(a+b x^2\right)^{7/2}}-\frac{x (8 A b-a B)}{a^2 \left(a+b x^2\right)^{7/2}}-\frac{A}{a x \left(a+b x^2\right)^{7/2}}","-\frac{x^7 \left(384 A b^4-a \left(6 a^2 b D+15 a^3 F+8 a b^2 C+48 b^3 B\right)\right)}{105 a^5 \left(a+b x^2\right)^{7/2}}-\frac{x^5 \left(192 A b^3-a \left(3 a^2 D+4 a b C+24 b^2 B\right)\right)}{15 a^4 \left(a+b x^2\right)^{7/2}}-\frac{x^3 \left(48 A b^2-a (a C+6 b B)\right)}{3 a^3 \left(a+b x^2\right)^{7/2}}-\frac{x (8 A b-a B)}{a^2 \left(a+b x^2\right)^{7/2}}-\frac{A}{a x \left(a+b x^2\right)^{7/2}}",1,"-(A/(a*x*(a + b*x^2)^(7/2))) - ((8*A*b - a*B)*x)/(a^2*(a + b*x^2)^(7/2)) - ((48*A*b^2 - a*(6*b*B + a*C))*x^3)/(3*a^3*(a + b*x^2)^(7/2)) - ((192*A*b^3 - a*(24*b^2*B + 4*a*b*C + 3*a^2*D))*x^5)/(15*a^4*(a + b*x^2)^(7/2)) - ((384*A*b^4 - a*(48*b^3*B + 8*a*b^2*C + 6*a^2*b*D + 15*a^3*F))*x^7)/(105*a^5*(a + b*x^2)^(7/2))","A",6,4,37,0.1081,1,"{1803, 1813, 12, 264}"