1,1,236,0,0.4698679,"\int (d+e x)^2 \left(A+B x+C x^2\right) \sqrt{d^2-e^2 x^2} \, dx","Int[(d + e*x)^2*(A + B*x + C*x^2)*Sqrt[d^2 - e^2*x^2],x]","\frac{d^2 x \sqrt{d^2-e^2 x^2} \left(10 A e^2+4 B d e+3 C d^2\right)}{16 e^2}-\frac{d \left(d^2-e^2 x^2\right)^{3/2} \left(e (10 A e+7 B d)+4 C d^2\right)}{15 e^3}-\frac{x \left(d^2-e^2 x^2\right)^{3/2} \left(2 e (A e+2 B d)+3 C d^2\right)}{8 e^2}+\frac{d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(10 A e^2+4 B d e+3 C d^2\right)}{16 e^3}-\frac{x^2 \left(d^2-e^2 x^2\right)^{3/2} (B e+2 C d)}{5 e}-\frac{1}{6} C x^3 \left(d^2-e^2 x^2\right)^{3/2}","\frac{d^2 x \sqrt{d^2-e^2 x^2} \left(10 A e^2+4 B d e+3 C d^2\right)}{16 e^2}-\frac{d \left(d^2-e^2 x^2\right)^{3/2} \left(e (10 A e+7 B d)+4 C d^2\right)}{15 e^3}-\frac{x \left(d^2-e^2 x^2\right)^{3/2} \left(2 e (A e+2 B d)+3 C d^2\right)}{8 e^2}+\frac{d^4 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(10 A e^2+4 B d e+3 C d^2\right)}{16 e^3}-\frac{x^2 \left(d^2-e^2 x^2\right)^{3/2} (B e+2 C d)}{5 e}-\frac{1}{6} C x^3 \left(d^2-e^2 x^2\right)^{3/2}",1,"(d^2*(3*C*d^2 + 4*B*d*e + 10*A*e^2)*x*Sqrt[d^2 - e^2*x^2])/(16*e^2) - (d*(4*C*d^2 + e*(7*B*d + 10*A*e))*(d^2 - e^2*x^2)^(3/2))/(15*e^3) - ((3*C*d^2 + 2*e*(2*B*d + A*e))*x*(d^2 - e^2*x^2)^(3/2))/(8*e^2) - ((2*C*d + B*e)*x^2*(d^2 - e^2*x^2)^(3/2))/(5*e) - (C*x^3*(d^2 - e^2*x^2)^(3/2))/6 + (d^4*(3*C*d^2 + 4*B*d*e + 10*A*e^2)*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(16*e^3)","A",7,5,34,0.1471,1,"{1815, 641, 195, 217, 203}"
2,1,186,0,0.2273343,"\int (d+e x) \left(A+B x+C x^2\right) \sqrt{d^2-e^2 x^2} \, dx","Int[(d + e*x)*(A + B*x + C*x^2)*Sqrt[d^2 - e^2*x^2],x]","\frac{d x \sqrt{d^2-e^2 x^2} \left(e (4 A e+B d)+C d^2\right)}{8 e^2}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(5 e (A e+B d)+2 C d^2\right)}{15 e^3}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(e (4 A e+B d)+C d^2\right)}{8 e^3}-\frac{x \left(d^2-e^2 x^2\right)^{3/2} (B e+C d)}{4 e^2}-\frac{C x^2 \left(d^2-e^2 x^2\right)^{3/2}}{5 e}","\frac{d x \sqrt{d^2-e^2 x^2} \left(e (4 A e+B d)+C d^2\right)}{8 e^2}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(5 e (A e+B d)+2 C d^2\right)}{15 e^3}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(e (4 A e+B d)+C d^2\right)}{8 e^3}-\frac{x \left(d^2-e^2 x^2\right)^{3/2} (B e+C d)}{4 e^2}-\frac{C x^2 \left(d^2-e^2 x^2\right)^{3/2}}{5 e}",1,"(d*(C*d^2 + e*(B*d + 4*A*e))*x*Sqrt[d^2 - e^2*x^2])/(8*e^2) - ((2*C*d^2 + 5*e*(B*d + A*e))*(d^2 - e^2*x^2)^(3/2))/(15*e^3) - ((C*d + B*e)*x*(d^2 - e^2*x^2)^(3/2))/(4*e^2) - (C*x^2*(d^2 - e^2*x^2)^(3/2))/(5*e) + (d^3*(C*d^2 + e*(B*d + 4*A*e))*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^3)","A",6,5,32,0.1562,1,"{1815, 641, 195, 217, 203}"
3,1,125,0,0.068973,"\int \left(A+B x+C x^2\right) \sqrt{d^2-e^2 x^2} \, dx","Int[(A + B*x + C*x^2)*Sqrt[d^2 - e^2*x^2],x]","\frac{1}{8} x \sqrt{d^2-e^2 x^2} \left(4 A+\frac{C d^2}{e^2}\right)+\frac{d^2 \left(4 A e^2+C d^2\right) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}-\frac{B \left(d^2-e^2 x^2\right)^{3/2}}{3 e^2}-\frac{C x \left(d^2-e^2 x^2\right)^{3/2}}{4 e^2}","\frac{1}{8} x \sqrt{d^2-e^2 x^2} \left(4 A+\frac{C d^2}{e^2}\right)+\frac{d^2 \left(4 A e^2+C d^2\right) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{8 e^3}-\frac{B \left(d^2-e^2 x^2\right)^{3/2}}{3 e^2}-\frac{C x \left(d^2-e^2 x^2\right)^{3/2}}{4 e^2}",1,"((4*A + (C*d^2)/e^2)*x*Sqrt[d^2 - e^2*x^2])/8 - (B*(d^2 - e^2*x^2)^(3/2))/(3*e^2) - (C*x*(d^2 - e^2*x^2)^(3/2))/(4*e^2) + (d^2*(C*d^2 + 4*A*e^2)*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^3)","A",5,5,27,0.1852,1,"{1815, 641, 195, 217, 203}"
4,1,148,0,0.1763001,"\int \frac{\left(A+B x+C x^2\right) \sqrt{d^2-e^2 x^2}}{d+e x} \, dx","Int[((A + B*x + C*x^2)*Sqrt[d^2 - e^2*x^2])/(d + e*x),x]","\frac{\sqrt{d^2-e^2 x^2} \left(C d^2-e (B d-2 A e)\right)}{2 e^3}+\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(C d^2-e (B d-2 A e)\right)}{2 e^3}+\frac{\left(d^2-e^2 x^2\right)^{3/2} (C d-B e)}{2 e^3 (d+e x)}-\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{3 e^3}","\frac{\sqrt{d^2-e^2 x^2} \left(C d^2-e (B d-2 A e)\right)}{2 e^3}+\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(C d^2-e (B d-2 A e)\right)}{2 e^3}+\frac{\left(d^2-e^2 x^2\right)^{3/2} (C d-B e)}{2 e^3 (d+e x)}-\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{3 e^3}",1,"((C*d^2 - e*(B*d - 2*A*e))*Sqrt[d^2 - e^2*x^2])/(2*e^3) - (C*(d^2 - e^2*x^2)^(3/2))/(3*e^3) + ((C*d - B*e)*(d^2 - e^2*x^2)^(3/2))/(2*e^3*(d + e*x)) + (d*(C*d^2 - e*(B*d - 2*A*e))*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^3)","A",5,5,34,0.1471,1,"{1639, 795, 665, 217, 203}"
5,1,170,0,0.2025952,"\int \frac{\left(A+B x+C x^2\right) \sqrt{d^2-e^2 x^2}}{(d+e x)^2} \, dx","Int[((A + B*x + C*x^2)*Sqrt[d^2 - e^2*x^2])/(d + e*x)^2,x]","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{d e^3 (d+e x)^2}-\frac{\sqrt{d^2-e^2 x^2} \left(5 C d^2-2 e (2 B d-A e)\right)}{2 d e^3}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(5 C d^2-2 e (2 B d-A e)\right)}{2 e^3}-\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{2 e^3 (d+e x)}","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{d e^3 (d+e x)^2}-\frac{\sqrt{d^2-e^2 x^2} \left(5 C d^2-2 e (2 B d-A e)\right)}{2 d e^3}-\frac{\tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(5 C d^2-2 e (2 B d-A e)\right)}{2 e^3}-\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{2 e^3 (d+e x)}",1,"-((5*C*d^2 - 2*e*(2*B*d - A*e))*Sqrt[d^2 - e^2*x^2])/(2*d*e^3) - ((C*d^2 - B*d*e + A*e^2)*(d^2 - e^2*x^2)^(3/2))/(d*e^3*(d + e*x)^2) - (C*(d^2 - e^2*x^2)^(3/2))/(2*e^3*(d + e*x)) - ((5*C*d^2 - 2*e*(2*B*d - A*e))*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^3)","A",5,5,34,0.1471,1,"{1639, 793, 665, 217, 203}"
6,1,149,0,0.1885418,"\int \frac{\left(A+B x+C x^2\right) \sqrt{d^2-e^2 x^2}}{(d+e x)^3} \, dx","Int[((A + B*x + C*x^2)*Sqrt[d^2 - e^2*x^2])/(d + e*x)^3,x]","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{3 d e^3 (d+e x)^3}+\frac{2 \sqrt{d^2-e^2 x^2} (3 C d-B e)}{e^3 (d+e x)}+\frac{(3 C d-B e) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}-\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{e^3 (d+e x)^2}","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{3 d e^3 (d+e x)^3}+\frac{2 \sqrt{d^2-e^2 x^2} (3 C d-B e)}{e^3 (d+e x)}+\frac{(3 C d-B e) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}-\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{e^3 (d+e x)^2}",1,"(2*(3*C*d - B*e)*Sqrt[d^2 - e^2*x^2])/(e^3*(d + e*x)) - ((C*d^2 - B*d*e + A*e^2)*(d^2 - e^2*x^2)^(3/2))/(3*d*e^3*(d + e*x)^3) - (C*(d^2 - e^2*x^2)^(3/2))/(e^3*(d + e*x)^2) + ((3*C*d - B*e)*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^3","A",5,5,34,0.1471,1,"{1639, 793, 663, 217, 203}"
7,1,196,0,0.1839458,"\int \frac{\left(A+B x+C x^2\right) \sqrt{d^2-e^2 x^2}}{(d+e x)^4} \, dx","Int[((A + B*x + C*x^2)*Sqrt[d^2 - e^2*x^2])/(d + e*x)^4,x]","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{15 d^2 e^3 (d+e x)^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{5 d e^3 (d+e x)^4}+\frac{\left(d^2-e^2 x^2\right)^{3/2} (2 C d-B e)}{3 d e^3 (d+e x)^3}-\frac{2 C \sqrt{d^2-e^2 x^2}}{e^3 (d+e x)}-\frac{C \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{15 d^2 e^3 (d+e x)^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{5 d e^3 (d+e x)^4}+\frac{\left(d^2-e^2 x^2\right)^{3/2} (2 C d-B e)}{3 d e^3 (d+e x)^3}-\frac{2 C \sqrt{d^2-e^2 x^2}}{e^3 (d+e x)}-\frac{C \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}",1,"(-2*C*Sqrt[d^2 - e^2*x^2])/(e^3*(d + e*x)) - ((C*d^2 - B*d*e + A*e^2)*(d^2 - e^2*x^2)^(3/2))/(5*d*e^3*(d + e*x)^4) + ((2*C*d - B*e)*(d^2 - e^2*x^2)^(3/2))/(3*d*e^3*(d + e*x)^3) - ((C*d^2 - B*d*e + A*e^2)*(d^2 - e^2*x^2)^(3/2))/(15*d^2*e^3*(d + e*x)^3) - (C*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^3","A",8,6,34,0.1765,1,"{1637, 659, 651, 663, 217, 203}"
8,1,180,0,0.210378,"\int \frac{\left(A+B x+C x^2\right) \sqrt{d^2-e^2 x^2}}{(d+e x)^5} \, dx","Int[((A + B*x + C*x^2)*Sqrt[d^2 - e^2*x^2])/(d + e*x)^5,x]","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(e (2 A e+5 B d)+23 C d^2\right)}{105 d^3 e^3 (d+e x)^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(e (2 A e+5 B d)+23 C d^2\right)}{35 d^2 e^3 (d+e x)^4}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{7 d e^3 (d+e x)^5}+\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{e^3 (d+e x)^4}","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(e (2 A e+5 B d)+23 C d^2\right)}{105 d^3 e^3 (d+e x)^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(e (2 A e+5 B d)+23 C d^2\right)}{35 d^2 e^3 (d+e x)^4}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{7 d e^3 (d+e x)^5}+\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{e^3 (d+e x)^4}",1,"-((C*d^2 - B*d*e + A*e^2)*(d^2 - e^2*x^2)^(3/2))/(7*d*e^3*(d + e*x)^5) + (C*(d^2 - e^2*x^2)^(3/2))/(e^3*(d + e*x)^4) - ((23*C*d^2 + e*(5*B*d + 2*A*e))*(d^2 - e^2*x^2)^(3/2))/(35*d^2*e^3*(d + e*x)^4) - ((23*C*d^2 + e*(5*B*d + 2*A*e))*(d^2 - e^2*x^2)^(3/2))/(105*d^3*e^3*(d + e*x)^3)","A",4,4,34,0.1176,1,"{1639, 793, 659, 651}"
9,1,234,0,0.2642163,"\int \frac{\left(A+B x+C x^2\right) \sqrt{d^2-e^2 x^2}}{(d+e x)^6} \, dx","Int[((A + B*x + C*x^2)*Sqrt[d^2 - e^2*x^2])/(d + e*x)^6,x]","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(2 e (A e+2 B d)+11 C d^2\right)}{315 d^4 e^3 (d+e x)^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(2 e (A e+2 B d)+11 C d^2\right)}{105 d^3 e^3 (d+e x)^4}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(2 e (A e+2 B d)+11 C d^2\right)}{42 d^2 e^3 (d+e x)^5}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{9 d e^3 (d+e x)^6}+\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{2 e^3 (d+e x)^5}","-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(2 e (A e+2 B d)+11 C d^2\right)}{315 d^4 e^3 (d+e x)^3}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(2 e (A e+2 B d)+11 C d^2\right)}{105 d^3 e^3 (d+e x)^4}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(2 e (A e+2 B d)+11 C d^2\right)}{42 d^2 e^3 (d+e x)^5}-\frac{\left(d^2-e^2 x^2\right)^{3/2} \left(A e^2-B d e+C d^2\right)}{9 d e^3 (d+e x)^6}+\frac{C \left(d^2-e^2 x^2\right)^{3/2}}{2 e^3 (d+e x)^5}",1,"-((C*d^2 - B*d*e + A*e^2)*(d^2 - e^2*x^2)^(3/2))/(9*d*e^3*(d + e*x)^6) + (C*(d^2 - e^2*x^2)^(3/2))/(2*e^3*(d + e*x)^5) - ((11*C*d^2 + 2*e*(2*B*d + A*e))*(d^2 - e^2*x^2)^(3/2))/(42*d^2*e^3*(d + e*x)^5) - ((11*C*d^2 + 2*e*(2*B*d + A*e))*(d^2 - e^2*x^2)^(3/2))/(105*d^3*e^3*(d + e*x)^4) - ((11*C*d^2 + 2*e*(2*B*d + A*e))*(d^2 - e^2*x^2)^(3/2))/(315*d^4*e^3*(d + e*x)^3)","A",5,4,34,0.1176,1,"{1639, 793, 659, 651}"
10,1,236,0,0.6565432,"\int \frac{(d+e x)^3 \left(A+B x+C x^2\right)}{\sqrt{d^2-e^2 x^2}} \, dx","Int[((d + e*x)^3*(A + B*x + C*x^2))/Sqrt[d^2 - e^2*x^2],x]","-\frac{x^2 \sqrt{d^2-e^2 x^2} \left(5 e (A e+3 B d)+19 C d^2\right)}{15 e}-\frac{d x \sqrt{d^2-e^2 x^2} \left(12 A e^2+15 B d e+13 C d^2\right)}{8 e^2}-\frac{d^2 \sqrt{d^2-e^2 x^2} \left(55 A e^2+45 B d e+38 C d^2\right)}{15 e^3}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(20 A e^2+15 B d e+13 C d^2\right)}{8 e^3}-\frac{1}{4} x^3 \sqrt{d^2-e^2 x^2} (B e+3 C d)-\frac{1}{5} C e x^4 \sqrt{d^2-e^2 x^2}","-\frac{x^2 \sqrt{d^2-e^2 x^2} \left(5 e (A e+3 B d)+19 C d^2\right)}{15 e}-\frac{d x \sqrt{d^2-e^2 x^2} \left(12 A e^2+15 B d e+13 C d^2\right)}{8 e^2}-\frac{d^2 \sqrt{d^2-e^2 x^2} \left(55 A e^2+45 B d e+38 C d^2\right)}{15 e^3}+\frac{d^3 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(20 A e^2+15 B d e+13 C d^2\right)}{8 e^3}-\frac{1}{4} x^3 \sqrt{d^2-e^2 x^2} (B e+3 C d)-\frac{1}{5} C e x^4 \sqrt{d^2-e^2 x^2}",1,"-(d^2*(38*C*d^2 + 45*B*d*e + 55*A*e^2)*Sqrt[d^2 - e^2*x^2])/(15*e^3) - (d*(13*C*d^2 + 15*B*d*e + 12*A*e^2)*x*Sqrt[d^2 - e^2*x^2])/(8*e^2) - ((19*C*d^2 + 5*e*(3*B*d + A*e))*x^2*Sqrt[d^2 - e^2*x^2])/(15*e) - ((3*C*d + B*e)*x^3*Sqrt[d^2 - e^2*x^2])/4 - (C*e*x^4*Sqrt[d^2 - e^2*x^2])/5 + (d^3*(13*C*d^2 + 15*B*d*e + 20*A*e^2)*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^3)","A",7,4,34,0.1176,1,"{1815, 641, 217, 203}"
11,1,191,0,0.3781946,"\int \frac{(d+e x)^2 \left(A+B x+C x^2\right)}{\sqrt{d^2-e^2 x^2}} \, dx","Int[((d + e*x)^2*(A + B*x + C*x^2))/Sqrt[d^2 - e^2*x^2],x]","-\frac{x \sqrt{d^2-e^2 x^2} \left(4 e (A e+2 B d)+7 C d^2\right)}{8 e^2}-\frac{d \sqrt{d^2-e^2 x^2} \left(e (6 A e+5 B d)+4 C d^2\right)}{3 e^3}+\frac{d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(12 A e^2+8 B d e+7 C d^2\right)}{8 e^3}-\frac{x^2 \sqrt{d^2-e^2 x^2} (B e+2 C d)}{3 e}-\frac{1}{4} C x^3 \sqrt{d^2-e^2 x^2}","-\frac{x \sqrt{d^2-e^2 x^2} \left(4 e (A e+2 B d)+7 C d^2\right)}{8 e^2}-\frac{d \sqrt{d^2-e^2 x^2} \left(e (6 A e+5 B d)+4 C d^2\right)}{3 e^3}+\frac{d^2 \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(12 A e^2+8 B d e+7 C d^2\right)}{8 e^3}-\frac{x^2 \sqrt{d^2-e^2 x^2} (B e+2 C d)}{3 e}-\frac{1}{4} C x^3 \sqrt{d^2-e^2 x^2}",1,"-(d*(4*C*d^2 + e*(5*B*d + 6*A*e))*Sqrt[d^2 - e^2*x^2])/(3*e^3) - ((7*C*d^2 + 4*e*(2*B*d + A*e))*x*Sqrt[d^2 - e^2*x^2])/(8*e^2) - ((2*C*d + B*e)*x^2*Sqrt[d^2 - e^2*x^2])/(3*e) - (C*x^3*Sqrt[d^2 - e^2*x^2])/4 + (d^2*(7*C*d^2 + 8*B*d*e + 12*A*e^2)*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(8*e^3)","A",6,4,34,0.1176,1,"{1815, 641, 217, 203}"
12,1,143,0,0.1989749,"\int \frac{(d+e x) \left(A+B x+C x^2\right)}{\sqrt{d^2-e^2 x^2}} \, dx","Int[((d + e*x)*(A + B*x + C*x^2))/Sqrt[d^2 - e^2*x^2],x]","-\frac{\sqrt{d^2-e^2 x^2} \left(3 e (A e+B d)+2 C d^2\right)}{3 e^3}+\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(e (2 A e+B d)+C d^2\right)}{2 e^3}-\frac{x \sqrt{d^2-e^2 x^2} (B e+C d)}{2 e^2}-\frac{C x^2 \sqrt{d^2-e^2 x^2}}{3 e}","-\frac{\sqrt{d^2-e^2 x^2} \left(3 e (A e+B d)+2 C d^2\right)}{3 e^3}+\frac{d \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right) \left(e (2 A e+B d)+C d^2\right)}{2 e^3}-\frac{x \sqrt{d^2-e^2 x^2} (B e+C d)}{2 e^2}-\frac{C x^2 \sqrt{d^2-e^2 x^2}}{3 e}",1,"-((2*C*d^2 + 3*e*(B*d + A*e))*Sqrt[d^2 - e^2*x^2])/(3*e^3) - ((C*d + B*e)*x*Sqrt[d^2 - e^2*x^2])/(2*e^2) - (C*x^2*Sqrt[d^2 - e^2*x^2])/(3*e) + (d*(C*d^2 + e*(B*d + 2*A*e))*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^3)","A",5,4,32,0.1250,1,"{1815, 641, 217, 203}"
13,1,87,0,0.0510074,"\int \frac{A+B x+C x^2}{\sqrt{d^2-e^2 x^2}} \, dx","Int[(A + B*x + C*x^2)/Sqrt[d^2 - e^2*x^2],x]","\frac{\left(2 A e^2+C d^2\right) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^3}-\frac{B \sqrt{d^2-e^2 x^2}}{e^2}-\frac{C x \sqrt{d^2-e^2 x^2}}{2 e^2}","\frac{\left(2 A e^2+C d^2\right) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{2 e^3}-\frac{B \sqrt{d^2-e^2 x^2}}{e^2}-\frac{C x \sqrt{d^2-e^2 x^2}}{2 e^2}",1,"-((B*Sqrt[d^2 - e^2*x^2])/e^2) - (C*x*Sqrt[d^2 - e^2*x^2])/(2*e^2) + ((C*d^2 + 2*A*e^2)*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/(2*e^3)","A",4,4,27,0.1481,1,"{1815, 641, 217, 203}"
14,1,103,0,0.1209304,"\int \frac{A+B x+C x^2}{(d+e x) \sqrt{d^2-e^2 x^2}} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)*Sqrt[d^2 - e^2*x^2]),x]","-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{d e^3 (d+e x)}-\frac{(C d-B e) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}-\frac{C \sqrt{d^2-e^2 x^2}}{e^3}","-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{d e^3 (d+e x)}-\frac{(C d-B e) \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}-\frac{C \sqrt{d^2-e^2 x^2}}{e^3}",1,"-((C*Sqrt[d^2 - e^2*x^2])/e^3) - ((C*d^2 - B*d*e + A*e^2)*Sqrt[d^2 - e^2*x^2])/(d*e^3*(d + e*x)) - ((C*d - B*e)*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^3","A",4,4,34,0.1176,1,"{1639, 793, 217, 203}"
15,1,163,0,0.1694274,"\int \frac{A+B x+C x^2}{(d+e x)^2 \sqrt{d^2-e^2 x^2}} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^2*Sqrt[d^2 - e^2*x^2]),x]","-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{3 d^2 e^3 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{3 d e^3 (d+e x)^2}+\frac{\sqrt{d^2-e^2 x^2} (2 C d-B e)}{d e^3 (d+e x)}+\frac{C \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}","-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{3 d^2 e^3 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{3 d e^3 (d+e x)^2}+\frac{\sqrt{d^2-e^2 x^2} (2 C d-B e)}{d e^3 (d+e x)}+\frac{C \tan ^{-1}\left(\frac{e x}{\sqrt{d^2-e^2 x^2}}\right)}{e^3}",1,"-((C*d^2 - B*d*e + A*e^2)*Sqrt[d^2 - e^2*x^2])/(3*d*e^3*(d + e*x)^2) + ((2*C*d - B*e)*Sqrt[d^2 - e^2*x^2])/(d*e^3*(d + e*x)) - ((C*d^2 - B*d*e + A*e^2)*Sqrt[d^2 - e^2*x^2])/(3*d^2*e^3*(d + e*x)) + (C*ArcTan[(e*x)/Sqrt[d^2 - e^2*x^2]])/e^3","A",7,5,34,0.1471,1,"{1637, 217, 203, 659, 651}"
16,1,180,0,0.2051405,"\int \frac{A+B x+C x^2}{(d+e x)^3 \sqrt{d^2-e^2 x^2}} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^3*Sqrt[d^2 - e^2*x^2]),x]","-\frac{\sqrt{d^2-e^2 x^2} \left(e (2 A e+3 B d)+7 C d^2\right)}{15 d^3 e^3 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2} \left(e (2 A e+3 B d)+7 C d^2\right)}{15 d^2 e^3 (d+e x)^2}-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{5 d e^3 (d+e x)^3}+\frac{C \sqrt{d^2-e^2 x^2}}{e^3 (d+e x)^2}","-\frac{\sqrt{d^2-e^2 x^2} \left(e (2 A e+3 B d)+7 C d^2\right)}{15 d^3 e^3 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2} \left(e (2 A e+3 B d)+7 C d^2\right)}{15 d^2 e^3 (d+e x)^2}-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{5 d e^3 (d+e x)^3}+\frac{C \sqrt{d^2-e^2 x^2}}{e^3 (d+e x)^2}",1,"-((C*d^2 - B*d*e + A*e^2)*Sqrt[d^2 - e^2*x^2])/(5*d*e^3*(d + e*x)^3) + (C*Sqrt[d^2 - e^2*x^2])/(e^3*(d + e*x)^2) - ((7*C*d^2 + e*(3*B*d + 2*A*e))*Sqrt[d^2 - e^2*x^2])/(15*d^2*e^3*(d + e*x)^2) - ((7*C*d^2 + e*(3*B*d + 2*A*e))*Sqrt[d^2 - e^2*x^2])/(15*d^3*e^3*(d + e*x))","A",4,4,34,0.1176,1,"{1639, 793, 659, 651}"
17,1,234,0,0.2485221,"\int \frac{A+B x+C x^2}{(d+e x)^4 \sqrt{d^2-e^2 x^2}} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^4*Sqrt[d^2 - e^2*x^2]),x]","-\frac{\sqrt{d^2-e^2 x^2} \left(6 A e^2+8 B d e+13 C d^2\right)}{105 d^4 e^3 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2} \left(6 A e^2+8 B d e+13 C d^2\right)}{105 d^3 e^3 (d+e x)^2}-\frac{\sqrt{d^2-e^2 x^2} \left(6 A e^2+8 B d e+13 C d^2\right)}{70 d^2 e^3 (d+e x)^3}-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{7 d e^3 (d+e x)^4}+\frac{C \sqrt{d^2-e^2 x^2}}{2 e^3 (d+e x)^3}","-\frac{\sqrt{d^2-e^2 x^2} \left(6 A e^2+8 B d e+13 C d^2\right)}{105 d^4 e^3 (d+e x)}-\frac{\sqrt{d^2-e^2 x^2} \left(6 A e^2+8 B d e+13 C d^2\right)}{105 d^3 e^3 (d+e x)^2}-\frac{\sqrt{d^2-e^2 x^2} \left(6 A e^2+8 B d e+13 C d^2\right)}{70 d^2 e^3 (d+e x)^3}-\frac{\sqrt{d^2-e^2 x^2} \left(A e^2-B d e+C d^2\right)}{7 d e^3 (d+e x)^4}+\frac{C \sqrt{d^2-e^2 x^2}}{2 e^3 (d+e x)^3}",1,"-((C*d^2 - B*d*e + A*e^2)*Sqrt[d^2 - e^2*x^2])/(7*d*e^3*(d + e*x)^4) + (C*Sqrt[d^2 - e^2*x^2])/(2*e^3*(d + e*x)^3) - ((13*C*d^2 + 8*B*d*e + 6*A*e^2)*Sqrt[d^2 - e^2*x^2])/(70*d^2*e^3*(d + e*x)^3) - ((13*C*d^2 + 8*B*d*e + 6*A*e^2)*Sqrt[d^2 - e^2*x^2])/(105*d^3*e^3*(d + e*x)^2) - ((13*C*d^2 + 8*B*d*e + 6*A*e^2)*Sqrt[d^2 - e^2*x^2])/(105*d^4*e^3*(d + e*x))","A",5,4,34,0.1176,1,"{1639, 793, 659, 651}"
18,1,173,0,0.3131781,"\int (d+e x)^3 \left(a+c x^2\right) \left(A+B x+C x^2\right) \, dx","Int[(d + e*x)^3*(a + c*x^2)*(A + B*x + C*x^2),x]","\frac{(d+e x)^6 \left(a C e^2-c e (3 B d-A e)+6 c C d^2\right)}{6 e^5}-\frac{(d+e x)^5 \left(a e^2 (2 C d-B e)-c d e (3 B d-2 A e)+4 c C d^3\right)}{5 e^5}+\frac{(d+e x)^4 \left(a e^2+c d^2\right) \left(A e^2-B d e+C d^2\right)}{4 e^5}-\frac{c (d+e x)^7 (4 C d-B e)}{7 e^5}+\frac{c C (d+e x)^8}{8 e^5}","\frac{(d+e x)^6 \left(a C e^2+c \left(6 C d^2-e (3 B d-A e)\right)\right)}{6 e^5}-\frac{(d+e x)^5 \left(a e^2 (2 C d-B e)+c d \left(4 C d^2-e (3 B d-2 A e)\right)\right)}{5 e^5}+\frac{(d+e x)^4 \left(a e^2+c d^2\right) \left(A e^2-B d e+C d^2\right)}{4 e^5}-\frac{c (d+e x)^7 (4 C d-B e)}{7 e^5}+\frac{c C (d+e x)^8}{8 e^5}",1,"((c*d^2 + a*e^2)*(C*d^2 - B*d*e + A*e^2)*(d + e*x)^4)/(4*e^5) - ((4*c*C*d^3 - c*d*e*(3*B*d - 2*A*e) + a*e^2*(2*C*d - B*e))*(d + e*x)^5)/(5*e^5) + ((6*c*C*d^2 + a*C*e^2 - c*e*(3*B*d - A*e))*(d + e*x)^6)/(6*e^5) - (c*(4*C*d - B*e)*(d + e*x)^7)/(7*e^5) + (c*C*(d + e*x)^8)/(8*e^5)","A",2,1,25,0.04000,1,"{1628}"
19,1,173,0,0.2162729,"\int (d+e x)^2 \left(a+c x^2\right) \left(A+B x+C x^2\right) \, dx","Int[(d + e*x)^2*(a + c*x^2)*(A + B*x + C*x^2),x]","\frac{(d+e x)^5 \left(a C e^2-c e (3 B d-A e)+6 c C d^2\right)}{5 e^5}-\frac{(d+e x)^4 \left(a e^2 (2 C d-B e)-c d e (3 B d-2 A e)+4 c C d^3\right)}{4 e^5}+\frac{(d+e x)^3 \left(a e^2+c d^2\right) \left(A e^2-B d e+C d^2\right)}{3 e^5}-\frac{c (d+e x)^6 (4 C d-B e)}{6 e^5}+\frac{c C (d+e x)^7}{7 e^5}","\frac{(d+e x)^5 \left(a C e^2+c \left(6 C d^2-e (3 B d-A e)\right)\right)}{5 e^5}-\frac{(d+e x)^4 \left(a e^2 (2 C d-B e)+c d \left(4 C d^2-e (3 B d-2 A e)\right)\right)}{4 e^5}+\frac{(d+e x)^3 \left(a e^2+c d^2\right) \left(A e^2-B d e+C d^2\right)}{3 e^5}-\frac{c (d+e x)^6 (4 C d-B e)}{6 e^5}+\frac{c C (d+e x)^7}{7 e^5}",1,"((c*d^2 + a*e^2)*(C*d^2 - B*d*e + A*e^2)*(d + e*x)^3)/(3*e^5) - ((4*c*C*d^3 - c*d*e*(3*B*d - 2*A*e) + a*e^2*(2*C*d - B*e))*(d + e*x)^4)/(4*e^5) + ((6*c*C*d^2 + a*C*e^2 - c*e*(3*B*d - A*e))*(d + e*x)^5)/(5*e^5) - (c*(4*C*d - B*e)*(d + e*x)^6)/(6*e^5) + (c*C*(d + e*x)^7)/(7*e^5)","A",2,1,25,0.04000,1,"{1628}"
20,1,86,0,0.1064893,"\int (d+e x) \left(a+c x^2\right) \left(A+B x+C x^2\right) \, dx","Int[(d + e*x)*(a + c*x^2)*(A + B*x + C*x^2),x]","\frac{1}{4} x^4 (a C e+A c e+B c d)+\frac{1}{3} x^3 (a B e+a C d+A c d)+\frac{1}{2} a x^2 (A e+B d)+a A d x+\frac{1}{5} c x^5 (B e+C d)+\frac{1}{6} c C e x^6","\frac{1}{4} x^4 (a C e+A c e+B c d)+\frac{1}{3} x^3 (a B e+a C d+A c d)+\frac{1}{2} a x^2 (A e+B d)+a A d x+\frac{1}{5} c x^5 (B e+C d)+\frac{1}{6} c C e x^6",1,"a*A*d*x + (a*(B*d + A*e)*x^2)/2 + ((A*c*d + a*C*d + a*B*e)*x^3)/3 + ((B*c*d + A*c*e + a*C*e)*x^4)/4 + (c*(C*d + B*e)*x^5)/5 + (c*C*e*x^6)/6","A",2,1,23,0.04348,1,"{1628}"
21,1,46,0,0.028997,"\int \left(a+c x^2\right) \left(A+B x+C x^2\right) \, dx","Int[(a + c*x^2)*(A + B*x + C*x^2),x]","\frac{1}{3} x^3 (a C+A c)+a A x+\frac{1}{2} a B x^2+\frac{1}{4} B c x^4+\frac{1}{5} c C x^5","\frac{1}{3} x^3 (a C+A c)+a A x+\frac{1}{2} a B x^2+\frac{1}{4} B c x^4+\frac{1}{5} c C x^5",1,"a*A*x + (a*B*x^2)/2 + ((A*c + a*C)*x^3)/3 + (B*c*x^4)/4 + (c*C*x^5)/5","A",2,1,18,0.05556,1,"{1657}"
22,1,143,0,0.2451677,"\int \frac{\left(a+c x^2\right) \left(A+B x+C x^2\right)}{d+e x} \, dx","Int[((a + c*x^2)*(A + B*x + C*x^2))/(d + e*x),x]","\frac{x^2 \left(a C e^2-c e (B d-A e)+c C d^2\right)}{2 e^3}-\frac{x \left(a e^2 (C d-B e)-c d e (B d-A e)+c C d^3\right)}{e^4}+\frac{\left(a e^2+c d^2\right) \log (d+e x) \left(A e^2-B d e+C d^2\right)}{e^5}-\frac{c x^3 (C d-B e)}{3 e^2}+\frac{c C x^4}{4 e}","\frac{x^2 \left(a C e^2+c \left(C d^2-e (B d-A e)\right)\right)}{2 e^3}-\frac{x \left(a e^2 (C d-B e)+c d \left(C d^2-e (B d-A e)\right)\right)}{e^4}+\frac{\left(a e^2+c d^2\right) \log (d+e x) \left(A e^2-B d e+C d^2\right)}{e^5}-\frac{c x^3 (C d-B e)}{3 e^2}+\frac{c C x^4}{4 e}",1,"-(((c*C*d^3 - c*d*e*(B*d - A*e) + a*e^2*(C*d - B*e))*x)/e^4) + ((c*C*d^2 + a*C*e^2 - c*e*(B*d - A*e))*x^2)/(2*e^3) - (c*(C*d - B*e)*x^3)/(3*e^2) + (c*C*x^4)/(4*e) + ((c*d^2 + a*e^2)*(C*d^2 - B*d*e + A*e^2)*Log[d + e*x])/e^5","A",2,1,25,0.04000,1,"{1628}"
23,1,151,0,0.2048973,"\int \frac{\left(a+c x^2\right) \left(A+B x+C x^2\right)}{(d+e x)^2} \, dx","Int[((a + c*x^2)*(A + B*x + C*x^2))/(d + e*x)^2,x]","\frac{x \left(a C e^2-c e (2 B d-A e)+3 c C d^2\right)}{e^4}-\frac{\left(a e^2+c d^2\right) \left(A e^2-B d e+C d^2\right)}{e^5 (d+e x)}-\frac{\log (d+e x) \left(a e^2 (2 C d-B e)-c d e (3 B d-2 A e)+4 c C d^3\right)}{e^5}-\frac{c x^2 (2 C d-B e)}{2 e^3}+\frac{c C x^3}{3 e^2}","\frac{x \left(a C e^2+c \left(3 C d^2-e (2 B d-A e)\right)\right)}{e^4}-\frac{\left(a e^2+c d^2\right) \left(A e^2-B d e+C d^2\right)}{e^5 (d+e x)}-\frac{\log (d+e x) \left(a e^2 (2 C d-B e)+c d \left(4 C d^2-e (3 B d-2 A e)\right)\right)}{e^5}-\frac{c x^2 (2 C d-B e)}{2 e^3}+\frac{c C x^3}{3 e^2}",1,"((3*c*C*d^2 + a*C*e^2 - c*e*(2*B*d - A*e))*x)/e^4 - (c*(2*C*d - B*e)*x^2)/(2*e^3) + (c*C*x^3)/(3*e^2) - ((c*d^2 + a*e^2)*(C*d^2 - B*d*e + A*e^2))/(e^5*(d + e*x)) - ((4*c*C*d^3 - c*d*e*(3*B*d - 2*A*e) + a*e^2*(2*C*d - B*e))*Log[d + e*x])/e^5","A",2,1,25,0.04000,1,"{1628}"
24,1,154,0,0.1985738,"\int \frac{\left(a+c x^2\right) \left(A+B x+C x^2\right)}{(d+e x)^3} \, dx","Int[((a + c*x^2)*(A + B*x + C*x^2))/(d + e*x)^3,x]","\frac{a e^2 (2 C d-B e)-c d e (3 B d-2 A e)+4 c C d^3}{e^5 (d+e x)}-\frac{\left(a e^2+c d^2\right) \left(A e^2-B d e+C d^2\right)}{2 e^5 (d+e x)^2}+\frac{\log (d+e x) \left(a C e^2-c e (3 B d-A e)+6 c C d^2\right)}{e^5}-\frac{c x (3 C d-B e)}{e^4}+\frac{c C x^2}{2 e^3}","\frac{a e^2 (2 C d-B e)+c d \left(4 C d^2-e (3 B d-2 A e)\right)}{e^5 (d+e x)}-\frac{\left(a e^2+c d^2\right) \left(A e^2-B d e+C d^2\right)}{2 e^5 (d+e x)^2}+\frac{\log (d+e x) \left(a C e^2+c \left(6 C d^2-e (3 B d-A e)\right)\right)}{e^5}-\frac{c x (3 C d-B e)}{e^4}+\frac{c C x^2}{2 e^3}",1,"-((c*(3*C*d - B*e)*x)/e^4) + (c*C*x^2)/(2*e^3) - ((c*d^2 + a*e^2)*(C*d^2 - B*d*e + A*e^2))/(2*e^5*(d + e*x)^2) + (4*c*C*d^3 - c*d*e*(3*B*d - 2*A*e) + a*e^2*(2*C*d - B*e))/(e^5*(d + e*x)) + ((6*c*C*d^2 + a*C*e^2 - c*e*(3*B*d - A*e))*Log[d + e*x])/e^5","A",2,1,25,0.04000,1,"{1628}"
25,1,301,0,0.534531,"\int (d+e x)^3 \left(a+c x^2\right)^2 \left(A+B x+C x^2\right) \, dx","Int[(d + e*x)^3*(a + c*x^2)^2*(A + B*x + C*x^2),x]","\frac{1}{4} a^2 e x^4 \left(e (A e+3 B d)+3 C d^2\right)+a^2 A d^3 x+\frac{1}{8} c e x^8 \left(2 a C e^2+c e (A e+3 B d)+3 c C d^2\right)+\frac{1}{7} c x^7 \left(2 a e^2 (B e+3 C d)+3 c d e (A e+B d)+c C d^3\right)+\frac{1}{6} a e x^6 \left(a C e^2+2 c e (A e+3 B d)+6 c C d^2\right)+\frac{1}{5} x^5 \left(A c d \left(6 a e^2+c d^2\right)+a \left(a e^2 (B e+3 C d)+2 c d^2 (3 B e+C d)\right)\right)+\frac{1}{3} a d x^3 \left(A \left(3 a e^2+2 c d^2\right)+a d (3 B e+C d)\right)+\frac{d^2 \left(a+c x^2\right)^3 (3 A e+B d)}{6 c}+\frac{1}{9} c^2 e^2 x^9 (B e+3 C d)+\frac{1}{10} c^2 C e^3 x^{10}","\frac{1}{4} a^2 e x^4 \left(e (A e+3 B d)+3 C d^2\right)+a^2 A d^3 x+\frac{1}{8} c e x^8 \left(2 a C e^2+c \left(e (A e+3 B d)+3 C d^2\right)\right)+\frac{1}{7} c x^7 \left(2 a e^2 (B e+3 C d)+c d \left(3 e (A e+B d)+C d^2\right)\right)+\frac{1}{6} a e x^6 \left(a C e^2+2 c \left(e (A e+3 B d)+3 C d^2\right)\right)+\frac{1}{5} x^5 \left(A c d \left(6 a e^2+c d^2\right)+a \left(a e^2 (B e+3 C d)+2 c d^2 (3 B e+C d)\right)\right)+\frac{1}{3} a d x^3 \left(A \left(3 a e^2+2 c d^2\right)+a d (3 B e+C d)\right)+\frac{d^2 \left(a+c x^2\right)^3 (3 A e+B d)}{6 c}+\frac{1}{9} c^2 e^2 x^9 (B e+3 C d)+\frac{1}{10} c^2 C e^3 x^{10}",1,"a^2*A*d^3*x + (a*d*(a*d*(C*d + 3*B*e) + A*(2*c*d^2 + 3*a*e^2))*x^3)/3 + (a^2*e*(3*C*d^2 + e*(3*B*d + A*e))*x^4)/4 + ((A*c*d*(c*d^2 + 6*a*e^2) + a*(a*e^2*(3*C*d + B*e) + 2*c*d^2*(C*d + 3*B*e)))*x^5)/5 + (a*e*(6*c*C*d^2 + a*C*e^2 + 2*c*e*(3*B*d + A*e))*x^6)/6 + (c*(c*C*d^3 + 3*c*d*e*(B*d + A*e) + 2*a*e^2*(3*C*d + B*e))*x^7)/7 + (c*e*(3*c*C*d^2 + 2*a*C*e^2 + c*e*(3*B*d + A*e))*x^8)/8 + (c^2*e^2*(3*C*d + B*e)*x^9)/9 + (c^2*C*e^3*x^10)/10 + (d^2*(B*d + 3*A*e)*(a + c*x^2)^3)/(6*c)","A",3,2,27,0.07407,1,"{1582, 1810}"
26,1,216,0,0.313161,"\int (d+e x)^2 \left(a+c x^2\right)^2 \left(A+B x+C x^2\right) \, dx","Int[(d + e*x)^2*(a + c*x^2)^2*(A + B*x + C*x^2),x]","a^2 A d^2 x+\frac{1}{4} a^2 e x^4 (B e+2 C d)+\frac{1}{7} c x^7 \left(2 a C e^2+c e (A e+2 B d)+c C d^2\right)+\frac{1}{5} x^5 \left(A c \left(2 a e^2+c d^2\right)+a \left(a C e^2+2 c d (2 B e+C d)\right)\right)+\frac{1}{3} a x^3 \left(A \left(a e^2+2 c d^2\right)+a d (2 B e+C d)\right)+\frac{d \left(a+c x^2\right)^3 (2 A e+B d)}{6 c}+\frac{1}{3} a c e x^6 (B e+2 C d)+\frac{1}{8} c^2 e x^8 (B e+2 C d)+\frac{1}{9} c^2 C e^2 x^9","a^2 A d^2 x+\frac{1}{4} a^2 e x^4 (B e+2 C d)+\frac{1}{7} c x^7 \left(2 a C e^2+c \left(e (A e+2 B d)+C d^2\right)\right)+\frac{1}{5} x^5 \left(A c \left(2 a e^2+c d^2\right)+a \left(a C e^2+2 c d (2 B e+C d)\right)\right)+\frac{1}{3} a x^3 \left(A \left(a e^2+2 c d^2\right)+a d (2 B e+C d)\right)+\frac{d \left(a+c x^2\right)^3 (2 A e+B d)}{6 c}+\frac{1}{3} a c e x^6 (B e+2 C d)+\frac{1}{8} c^2 e x^8 (B e+2 C d)+\frac{1}{9} c^2 C e^2 x^9",1,"a^2*A*d^2*x + (a*(a*d*(C*d + 2*B*e) + A*(2*c*d^2 + a*e^2))*x^3)/3 + (a^2*e*(2*C*d + B*e)*x^4)/4 + ((A*c*(c*d^2 + 2*a*e^2) + a*(a*C*e^2 + 2*c*d*(C*d + 2*B*e)))*x^5)/5 + (a*c*e*(2*C*d + B*e)*x^6)/3 + (c*(c*C*d^2 + 2*a*C*e^2 + c*e*(2*B*d + A*e))*x^7)/7 + (c^2*e*(2*C*d + B*e)*x^8)/8 + (c^2*C*e^2*x^9)/9 + (d*(B*d + 2*A*e)*(a + c*x^2)^3)/(6*c)","A",3,2,27,0.07407,1,"{1582, 1810}"
27,1,128,0,0.1586801,"\int (d+e x) \left(a+c x^2\right)^2 \left(A+B x+C x^2\right) \, dx","Int[(d + e*x)*(a + c*x^2)^2*(A + B*x + C*x^2),x]","a^2 A d x+\frac{1}{4} a^2 C e x^4+\frac{1}{5} c x^5 (2 a (B e+C d)+A c d)+\frac{1}{3} a x^3 (a B e+a C d+2 A c d)+\frac{\left(a+c x^2\right)^3 (A e+B d)}{6 c}+\frac{1}{3} a c C e x^6+\frac{1}{7} c^2 x^7 (B e+C d)+\frac{1}{8} c^2 C e x^8","a^2 A d x+\frac{1}{4} a^2 C e x^4+\frac{1}{5} c x^5 (2 a (B e+C d)+A c d)+\frac{1}{3} a x^3 (a B e+a C d+2 A c d)+\frac{\left(a+c x^2\right)^3 (A e+B d)}{6 c}+\frac{1}{3} a c C e x^6+\frac{1}{7} c^2 x^7 (B e+C d)+\frac{1}{8} c^2 C e x^8",1,"a^2*A*d*x + (a*(2*A*c*d + a*C*d + a*B*e)*x^3)/3 + (a^2*C*e*x^4)/4 + (c*(A*c*d + 2*a*(C*d + B*e))*x^5)/5 + (a*c*C*e*x^6)/3 + (c^2*(C*d + B*e)*x^7)/7 + (c^2*C*e*x^8)/8 + ((B*d + A*e)*(a + c*x^2)^3)/(6*c)","A",3,2,25,0.08000,1,"{1582, 1810}"
28,1,67,0,0.040093,"\int \left(a+c x^2\right)^2 \left(A+B x+C x^2\right) \, dx","Int[(a + c*x^2)^2*(A + B*x + C*x^2),x]","a^2 A x+\frac{1}{5} c x^5 (2 a C+A c)+\frac{1}{3} a x^3 (a C+2 A c)+\frac{B \left(a+c x^2\right)^3}{6 c}+\frac{1}{7} c^2 C x^7","a^2 A x+\frac{1}{5} c x^5 (2 a C+A c)+\frac{1}{3} a x^3 (a C+2 A c)+\frac{B \left(a+c x^2\right)^3}{6 c}+\frac{1}{7} c^2 C x^7",1,"a^2*A*x + (a*(2*A*c + a*C)*x^3)/3 + (c*(A*c + 2*a*C)*x^5)/5 + (c^2*C*x^7)/7 + (B*(a + c*x^2)^3)/(6*c)","A",3,2,20,0.1000,1,"{1582, 373}"
29,1,295,0,0.6399001,"\int \frac{\left(a+c x^2\right)^2 \left(A+B x+C x^2\right)}{d+e x} \, dx","Int[((a + c*x^2)^2*(A + B*x + C*x^2))/(d + e*x),x]","\frac{x^2 \left(a^2 C e^4+2 a c e^2 \left(C d^2-e (B d-A e)\right)+c^2 \left(C d^4-d^2 e (B d-A e)\right)\right)}{2 e^5}-\frac{x \left(a^2 e^4 (C d-B e)+2 a c d e^2 \left(C d^2-e (B d-A e)\right)+c^2 \left(C d^5-d^3 e (B d-A e)\right)\right)}{e^6}+\frac{c x^4 \left(2 a C e^2-c e (B d-A e)+c C d^2\right)}{4 e^3}-\frac{c x^3 \left(2 a e^2 (C d-B e)-c d e (B d-A e)+c C d^3\right)}{3 e^4}+\frac{\left(a e^2+c d^2\right)^2 \log (d+e x) \left(A e^2-B d e+C d^2\right)}{e^7}-\frac{c^2 x^5 (C d-B e)}{5 e^2}+\frac{c^2 C x^6}{6 e}","\frac{x^2 \left(a^2 C e^4+2 a c e^2 \left(C d^2-e (B d-A e)\right)+c^2 d^2 \left(C d^2-e (B d-A e)\right)\right)}{2 e^5}-\frac{x \left(a^2 e^4 (C d-B e)+2 a c d e^2 \left(C d^2-e (B d-A e)\right)+c^2 d^3 \left(C d^2-e (B d-A e)\right)\right)}{e^6}+\frac{c x^4 \left(2 a C e^2+c \left(C d^2-e (B d-A e)\right)\right)}{4 e^3}-\frac{c x^3 \left(2 a e^2 (C d-B e)+c d \left(C d^2-e (B d-A e)\right)\right)}{3 e^4}+\frac{\left(a e^2+c d^2\right)^2 \log (d+e x) \left(A e^2-B d e+C d^2\right)}{e^7}-\frac{c^2 x^5 (C d-B e)}{5 e^2}+\frac{c^2 C x^6}{6 e}",1,"-(((a^2*e^4*(C*d - B*e) + 2*a*c*d*e^2*(C*d^2 - e*(B*d - A*e)) + c^2*(C*d^5 - d^3*e*(B*d - A*e)))*x)/e^6) + ((a^2*C*e^4 + 2*a*c*e^2*(C*d^2 - e*(B*d - A*e)) + c^2*(C*d^4 - d^2*e*(B*d - A*e)))*x^2)/(2*e^5) - (c*(c*C*d^3 - c*d*e*(B*d - A*e) + 2*a*e^2*(C*d - B*e))*x^3)/(3*e^4) + (c*(c*C*d^2 + 2*a*C*e^2 - c*e*(B*d - A*e))*x^4)/(4*e^3) - (c^2*(C*d - B*e)*x^5)/(5*e^2) + (c^2*C*x^6)/(6*e) + ((c*d^2 + a*e^2)^2*(C*d^2 - B*d*e + A*e^2)*Log[d + e*x])/e^7","A",2,1,27,0.03704,1,"{1628}"
30,1,289,0,0.5254283,"\int \frac{\left(a+c x^2\right)^2 \left(A+B x+C x^2\right)}{(d+e x)^2} \, dx","Int[((a + c*x^2)^2*(A + B*x + C*x^2))/(d + e*x)^2,x]","\frac{x \left(a^2 C e^4+2 a c e^2 \left(3 C d^2-e (2 B d-A e)\right)+c^2 \left(5 C d^4-d^2 e (4 B d-3 A e)\right)\right)}{e^6}+\frac{c x^3 \left(2 a C e^2-c e (2 B d-A e)+3 c C d^2\right)}{3 e^4}-\frac{c x^2 \left(2 a e^2 (2 C d-B e)-c d e (3 B d-2 A e)+4 c C d^3\right)}{2 e^5}-\frac{\left(a e^2+c d^2\right)^2 \left(A e^2-B d e+C d^2\right)}{e^7 (d+e x)}-\frac{\left(a e^2+c d^2\right) \log (d+e x) \left(a e^2 (2 C d-B e)-c d e (5 B d-4 A e)+6 c C d^3\right)}{e^7}-\frac{c^2 x^4 (2 C d-B e)}{4 e^3}+\frac{c^2 C x^5}{5 e^2}","\frac{x \left(a^2 C e^4+2 a c e^2 \left(3 C d^2-e (2 B d-A e)\right)+c^2 d^2 \left(5 C d^2-e (4 B d-3 A e)\right)\right)}{e^6}+\frac{c x^3 \left(2 a C e^2+c \left(3 C d^2-e (2 B d-A e)\right)\right)}{3 e^4}-\frac{c x^2 \left(2 a e^2 (2 C d-B e)+c d \left(4 C d^2-e (3 B d-2 A e)\right)\right)}{2 e^5}-\frac{\left(a e^2+c d^2\right)^2 \left(A e^2-B d e+C d^2\right)}{e^7 (d+e x)}-\frac{\left(a e^2+c d^2\right) \log (d+e x) \left(a e^2 (2 C d-B e)+c d \left(6 C d^2-e (5 B d-4 A e)\right)\right)}{e^7}-\frac{c^2 x^4 (2 C d-B e)}{4 e^3}+\frac{c^2 C x^5}{5 e^2}",1,"((a^2*C*e^4 + c^2*(5*C*d^4 - d^2*e*(4*B*d - 3*A*e)) + 2*a*c*e^2*(3*C*d^2 - e*(2*B*d - A*e)))*x)/e^6 - (c*(4*c*C*d^3 - c*d*e*(3*B*d - 2*A*e) + 2*a*e^2*(2*C*d - B*e))*x^2)/(2*e^5) + (c*(3*c*C*d^2 + 2*a*C*e^2 - c*e*(2*B*d - A*e))*x^3)/(3*e^4) - (c^2*(2*C*d - B*e)*x^4)/(4*e^3) + (c^2*C*x^5)/(5*e^2) - ((c*d^2 + a*e^2)^2*(C*d^2 - B*d*e + A*e^2))/(e^7*(d + e*x)) - ((c*d^2 + a*e^2)*(6*c*C*d^3 - c*d*e*(5*B*d - 4*A*e) + a*e^2*(2*C*d - B*e))*Log[d + e*x])/e^7","A",2,1,27,0.03704,1,"{1628}"
31,1,292,0,0.4945679,"\int \frac{\left(a+c x^2\right)^2 \left(A+B x+C x^2\right)}{(d+e x)^3} \, dx","Int[((a + c*x^2)^2*(A + B*x + C*x^2))/(d + e*x)^3,x]","\frac{\log (d+e x) \left(a^2 C e^4+2 a c e^2 \left(6 C d^2-e (3 B d-A e)\right)+c^2 \left(15 C d^4-2 d^2 e (5 B d-3 A e)\right)\right)}{e^7}+\frac{c x^2 \left(2 a C e^2-c e (3 B d-A e)+6 c C d^2\right)}{2 e^5}-\frac{c x \left(2 a e^2 (3 C d-B e)-3 c d e (2 B d-A e)+10 c C d^3\right)}{e^6}+\frac{\left(a e^2+c d^2\right) \left(a e^2 (2 C d-B e)-c d e (5 B d-4 A e)+6 c C d^3\right)}{e^7 (d+e x)}-\frac{\left(a e^2+c d^2\right)^2 \left(A e^2-B d e+C d^2\right)}{2 e^7 (d+e x)^2}-\frac{c^2 x^3 (3 C d-B e)}{3 e^4}+\frac{c^2 C x^4}{4 e^3}","\frac{\log (d+e x) \left(a^2 C e^4+2 a c e^2 \left(6 C d^2-e (3 B d-A e)\right)+c^2 d^2 \left(15 C d^2-2 e (5 B d-3 A e)\right)\right)}{e^7}+\frac{c x^2 \left(2 a C e^2+c \left(6 C d^2-e (3 B d-A e)\right)\right)}{2 e^5}-\frac{c x \left(2 a e^2 (3 C d-B e)+c d \left(10 C d^2-3 e (2 B d-A e)\right)\right)}{e^6}+\frac{\left(a e^2+c d^2\right) \left(a e^2 (2 C d-B e)+c d \left(6 C d^2-e (5 B d-4 A e)\right)\right)}{e^7 (d+e x)}-\frac{\left(a e^2+c d^2\right)^2 \left(A e^2-B d e+C d^2\right)}{2 e^7 (d+e x)^2}-\frac{c^2 x^3 (3 C d-B e)}{3 e^4}+\frac{c^2 C x^4}{4 e^3}",1,"-((c*(10*c*C*d^3 - 3*c*d*e*(2*B*d - A*e) + 2*a*e^2*(3*C*d - B*e))*x)/e^6) + (c*(6*c*C*d^2 + 2*a*C*e^2 - c*e*(3*B*d - A*e))*x^2)/(2*e^5) - (c^2*(3*C*d - B*e)*x^3)/(3*e^4) + (c^2*C*x^4)/(4*e^3) - ((c*d^2 + a*e^2)^2*(C*d^2 - B*d*e + A*e^2))/(2*e^7*(d + e*x)^2) + ((c*d^2 + a*e^2)*(6*c*C*d^3 - c*d*e*(5*B*d - 4*A*e) + a*e^2*(2*C*d - B*e)))/(e^7*(d + e*x)) + ((a^2*C*e^4 + c^2*(15*C*d^4 - 2*d^2*e*(5*B*d - 3*A*e)) + 2*a*c*e^2*(6*C*d^2 - e*(3*B*d - A*e)))*Log[d + e*x])/e^7","A",2,1,27,0.03704,1,"{1628}"
32,1,400,0,0.6913941,"\int (d+e x)^3 \left(a+c x^2\right)^3 \left(A+B x+C x^2\right) \, dx","Int[(d + e*x)^3*(a + c*x^2)^3*(A + B*x + C*x^2),x]","\frac{1}{6} a^2 e x^6 \left(a C e^2+3 c e (A e+3 B d)+9 c C d^2\right)+\frac{1}{3} a^2 d x^3 \left(3 A \left(a e^2+c d^2\right)+a d (3 B e+C d)\right)+\frac{1}{4} a^3 e x^4 \left(e (A e+3 B d)+3 C d^2\right)+a^3 A d^3 x+\frac{1}{10} c^2 e x^{10} \left(3 a C e^2+c e (A e+3 B d)+3 c C d^2\right)+\frac{1}{9} c^2 x^9 \left(3 a e^2 (B e+3 C d)+3 c d e (A e+B d)+c C d^3\right)+\frac{3}{8} a c e x^8 \left(a C e^2+c e (A e+3 B d)+3 c C d^2\right)+\frac{1}{7} c x^7 \left(A c d \left(9 a e^2+c d^2\right)+3 a \left(a e^2 (B e+3 C d)+c d^2 (3 B e+C d)\right)\right)+\frac{1}{5} a x^5 \left(3 A c d \left(3 a e^2+c d^2\right)+a \left(a e^2 (B e+3 C d)+3 c d^2 (3 B e+C d)\right)\right)+\frac{d^2 \left(a+c x^2\right)^4 (3 A e+B d)}{8 c}+\frac{1}{11} c^3 e^2 x^{11} (B e+3 C d)+\frac{1}{12} c^3 C e^3 x^{12}","\frac{1}{6} a^2 e x^6 \left(a C e^2+3 c \left(e (A e+3 B d)+3 C d^2\right)\right)+\frac{1}{3} a^2 d x^3 \left(3 A \left(a e^2+c d^2\right)+a d (3 B e+C d)\right)+\frac{1}{4} a^3 e x^4 \left(e (A e+3 B d)+3 C d^2\right)+a^3 A d^3 x+\frac{1}{10} c^2 e x^{10} \left(3 a C e^2+c \left(e (A e+3 B d)+3 C d^2\right)\right)+\frac{1}{9} c^2 x^9 \left(3 a e^2 (B e+3 C d)+c d \left(3 e (A e+B d)+C d^2\right)\right)+\frac{3}{8} a c e x^8 \left(a C e^2+c \left(e (A e+3 B d)+3 C d^2\right)\right)+\frac{1}{7} c x^7 \left(A c d \left(9 a e^2+c d^2\right)+3 a \left(a e^2 (B e+3 C d)+c d^2 (3 B e+C d)\right)\right)+\frac{1}{5} a x^5 \left(3 A c d \left(3 a e^2+c d^2\right)+a \left(a e^2 (B e+3 C d)+3 c d^2 (3 B e+C d)\right)\right)+\frac{d^2 \left(a+c x^2\right)^4 (3 A e+B d)}{8 c}+\frac{1}{11} c^3 e^2 x^{11} (B e+3 C d)+\frac{1}{12} c^3 C e^3 x^{12}",1,"a^3*A*d^3*x + (a^2*d*(a*d*(C*d + 3*B*e) + 3*A*(c*d^2 + a*e^2))*x^3)/3 + (a^3*e*(3*C*d^2 + e*(3*B*d + A*e))*x^4)/4 + (a*(3*A*c*d*(c*d^2 + 3*a*e^2) + a*(a*e^2*(3*C*d + B*e) + 3*c*d^2*(C*d + 3*B*e)))*x^5)/5 + (a^2*e*(9*c*C*d^2 + a*C*e^2 + 3*c*e*(3*B*d + A*e))*x^6)/6 + (c*(A*c*d*(c*d^2 + 9*a*e^2) + 3*a*(a*e^2*(3*C*d + B*e) + c*d^2*(C*d + 3*B*e)))*x^7)/7 + (3*a*c*e*(3*c*C*d^2 + a*C*e^2 + c*e*(3*B*d + A*e))*x^8)/8 + (c^2*(c*C*d^3 + 3*c*d*e*(B*d + A*e) + 3*a*e^2*(3*C*d + B*e))*x^9)/9 + (c^2*e*(3*c*C*d^2 + 3*a*C*e^2 + c*e*(3*B*d + A*e))*x^10)/10 + (c^3*e^2*(3*C*d + B*e)*x^11)/11 + (c^3*C*e^3*x^12)/12 + (d^2*(B*d + 3*A*e)*(a + c*x^2)^4)/(8*c)","A",3,2,27,0.07407,1,"{1582, 1810}"
33,1,288,0,0.4241411,"\int (d+e x)^2 \left(a+c x^2\right)^3 \left(A+B x+C x^2\right) \, dx","Int[(d + e*x)^2*(a + c*x^2)^3*(A + B*x + C*x^2),x]","\frac{1}{3} a^2 x^3 \left(A \left(a e^2+3 c d^2\right)+a d (2 B e+C d)\right)+a^3 A d^2 x+\frac{1}{2} a^2 c e x^6 (B e+2 C d)+\frac{1}{4} a^3 e x^4 (B e+2 C d)+\frac{1}{9} c^2 x^9 \left(3 a C e^2+c e (A e+2 B d)+c C d^2\right)+\frac{1}{7} c x^7 \left(A c \left(3 a e^2+c d^2\right)+3 a \left(a C e^2+c d (2 B e+C d)\right)\right)+\frac{1}{5} a x^5 \left(3 A c \left(a e^2+c d^2\right)+a \left(a C e^2+3 c d (2 B e+C d)\right)\right)+\frac{d \left(a+c x^2\right)^4 (2 A e+B d)}{8 c}+\frac{3}{8} a c^2 e x^8 (B e+2 C d)+\frac{1}{10} c^3 e x^{10} (B e+2 C d)+\frac{1}{11} c^3 C e^2 x^{11}","\frac{1}{3} a^2 x^3 \left(A \left(a e^2+3 c d^2\right)+a d (2 B e+C d)\right)+a^3 A d^2 x+\frac{1}{2} a^2 c e x^6 (B e+2 C d)+\frac{1}{4} a^3 e x^4 (B e+2 C d)+\frac{1}{9} c^2 x^9 \left(3 a C e^2+c \left(e (A e+2 B d)+C d^2\right)\right)+\frac{1}{7} c x^7 \left(A c \left(3 a e^2+c d^2\right)+3 a \left(a C e^2+c d (2 B e+C d)\right)\right)+\frac{1}{5} a x^5 \left(3 A c \left(a e^2+c d^2\right)+a \left(a C e^2+3 c d (2 B e+C d)\right)\right)+\frac{d \left(a+c x^2\right)^4 (2 A e+B d)}{8 c}+\frac{3}{8} a c^2 e x^8 (B e+2 C d)+\frac{1}{10} c^3 e x^{10} (B e+2 C d)+\frac{1}{11} c^3 C e^2 x^{11}",1,"a^3*A*d^2*x + (a^2*(a*d*(C*d + 2*B*e) + A*(3*c*d^2 + a*e^2))*x^3)/3 + (a^3*e*(2*C*d + B*e)*x^4)/4 + (a*(3*A*c*(c*d^2 + a*e^2) + a*(a*C*e^2 + 3*c*d*(C*d + 2*B*e)))*x^5)/5 + (a^2*c*e*(2*C*d + B*e)*x^6)/2 + (c*(A*c*(c*d^2 + 3*a*e^2) + 3*a*(a*C*e^2 + c*d*(C*d + 2*B*e)))*x^7)/7 + (3*a*c^2*e*(2*C*d + B*e)*x^8)/8 + (c^2*(c*C*d^2 + 3*a*C*e^2 + c*e*(2*B*d + A*e))*x^9)/9 + (c^3*e*(2*C*d + B*e)*x^10)/10 + (c^3*C*e^2*x^11)/11 + (d*(B*d + 2*A*e)*(a + c*x^2)^4)/(8*c)","A",3,2,27,0.07407,1,"{1582, 1810}"
34,1,169,0,0.1870311,"\int (d+e x) \left(a+c x^2\right)^3 \left(A+B x+C x^2\right) \, dx","Int[(d + e*x)*(a + c*x^2)^3*(A + B*x + C*x^2),x]","\frac{1}{3} a^2 x^3 (a B e+a C d+3 A c d)+a^3 A d x+\frac{1}{2} a^2 c C e x^6+\frac{1}{4} a^3 C e x^4+\frac{1}{7} c^2 x^7 (3 a (B e+C d)+A c d)+\frac{3}{5} a c x^5 (a B e+a C d+A c d)+\frac{\left(a+c x^2\right)^4 (A e+B d)}{8 c}+\frac{3}{8} a c^2 C e x^8+\frac{1}{9} c^3 x^9 (B e+C d)+\frac{1}{10} c^3 C e x^{10}","\frac{1}{3} a^2 x^3 (a B e+a C d+3 A c d)+a^3 A d x+\frac{1}{2} a^2 c C e x^6+\frac{1}{4} a^3 C e x^4+\frac{1}{7} c^2 x^7 (3 a (B e+C d)+A c d)+\frac{3}{5} a c x^5 (a B e+a C d+A c d)+\frac{\left(a+c x^2\right)^4 (A e+B d)}{8 c}+\frac{3}{8} a c^2 C e x^8+\frac{1}{9} c^3 x^9 (B e+C d)+\frac{1}{10} c^3 C e x^{10}",1,"a^3*A*d*x + (a^2*(3*A*c*d + a*C*d + a*B*e)*x^3)/3 + (a^3*C*e*x^4)/4 + (3*a*c*(A*c*d + a*C*d + a*B*e)*x^5)/5 + (a^2*c*C*e*x^6)/2 + (c^2*(A*c*d + 3*a*(C*d + B*e))*x^7)/7 + (3*a*c^2*C*e*x^8)/8 + (c^3*(C*d + B*e)*x^9)/9 + (c^3*C*e*x^10)/10 + ((B*d + A*e)*(a + c*x^2)^4)/(8*c)","A",3,2,25,0.08000,1,"{1582, 1810}"
35,1,87,0,0.0578149,"\int \left(a+c x^2\right)^3 \left(A+B x+C x^2\right) \, dx","Int[(a + c*x^2)^3*(A + B*x + C*x^2),x]","\frac{1}{3} a^2 x^3 (a C+3 A c)+a^3 A x+\frac{1}{7} c^2 x^7 (3 a C+A c)+\frac{3}{5} a c x^5 (a C+A c)+\frac{B \left(a+c x^2\right)^4}{8 c}+\frac{1}{9} c^3 C x^9","\frac{1}{3} a^2 x^3 (a C+3 A c)+a^3 A x+\frac{1}{7} c^2 x^7 (3 a C+A c)+\frac{3}{5} a c x^5 (a C+A c)+\frac{B \left(a+c x^2\right)^4}{8 c}+\frac{1}{9} c^3 C x^9",1,"a^3*A*x + (a^2*(3*A*c + a*C)*x^3)/3 + (3*a*c*(A*c + a*C)*x^5)/5 + (c^2*(A*c + 3*a*C)*x^7)/7 + (c^3*C*x^9)/9 + (B*(a + c*x^2)^4)/(8*c)","A",3,2,20,0.1000,1,"{1582, 373}"
36,1,487,0,1.0975842,"\int \frac{\left(a+c x^2\right)^3 \left(A+B x+C x^2\right)}{d+e x} \, dx","Int[((a + c*x^2)^3*(A + B*x + C*x^2))/(d + e*x),x]","\frac{c (d+e x)^4 \left(3 a^2 C e^4+3 a c e^2 \left(15 C d^2-e (5 B d-A e)\right)+5 c^2 \left(14 C d^4-d^2 e (7 B d-3 A e)\right)\right)}{4 e^9}-\frac{c (d+e x)^3 \left(3 a^2 e^4 (4 C d-B e)+6 a c d e^2 \left(10 C d^2-e (5 B d-2 A e)\right)+c^2 \left(56 C d^5-5 d^3 e (7 B d-4 A e)\right)\right)}{3 e^9}+\frac{(d+e x)^2 \left(a e^2+c d^2\right) \left(a^2 C e^4+a c e^2 \left(17 C d^2-3 e (3 B d-A e)\right)+c^2 \left(28 C d^4-3 d^2 e (7 B d-5 A e)\right)\right)}{2 e^9}+\frac{c^2 (d+e x)^6 \left(3 a C e^2-c e (7 B d-A e)+28 c C d^2\right)}{6 e^9}-\frac{c^2 (d+e x)^5 \left(3 a e^2 (6 C d-B e)-3 c d e (7 B d-2 A e)+56 c C d^3\right)}{5 e^9}-\frac{x \left(a e^2+c d^2\right)^2 \left(a e^2 (2 C d-B e)-c d e (7 B d-6 A e)+8 c C d^3\right)}{e^8}+\frac{\left(a e^2+c d^2\right)^3 \log (d+e x) \left(A e^2-B d e+C d^2\right)}{e^9}-\frac{c^3 (d+e x)^7 (8 C d-B e)}{7 e^9}+\frac{c^3 C (d+e x)^8}{8 e^9}","\frac{c (d+e x)^4 \left(3 a^2 C e^4+3 a c e^2 \left(15 C d^2-e (5 B d-A e)\right)+5 c^2 d^2 \left(14 C d^2-e (7 B d-3 A e)\right)\right)}{4 e^9}-\frac{c (d+e x)^3 \left(3 a^2 e^4 (4 C d-B e)+6 a c d e^2 \left(10 C d^2-e (5 B d-2 A e)\right)+c^2 d^3 \left(56 C d^2-5 e (7 B d-4 A e)\right)\right)}{3 e^9}+\frac{(d+e x)^2 \left(a e^2+c d^2\right) \left(a^2 C e^4+a c e^2 \left(17 C d^2-3 e (3 B d-A e)\right)+c^2 d^2 \left(28 C d^2-3 e (7 B d-5 A e)\right)\right)}{2 e^9}+\frac{c^2 (d+e x)^6 \left(3 a C e^2+c \left(28 C d^2-e (7 B d-A e)\right)\right)}{6 e^9}-\frac{c^2 (d+e x)^5 \left(3 a e^2 (6 C d-B e)+c d \left(56 C d^2-3 e (7 B d-2 A e)\right)\right)}{5 e^9}-\frac{x \left(a e^2+c d^2\right)^2 \left(a e^2 (2 C d-B e)+c d \left(8 C d^2-e (7 B d-6 A e)\right)\right)}{e^8}+\frac{\left(a e^2+c d^2\right)^3 \log (d+e x) \left(A e^2-B d e+C d^2\right)}{e^9}-\frac{c^3 (d+e x)^7 (8 C d-B e)}{7 e^9}+\frac{c^3 C (d+e x)^8}{8 e^9}",1,"-(((c*d^2 + a*e^2)^2*(8*c*C*d^3 - c*d*e*(7*B*d - 6*A*e) + a*e^2*(2*C*d - B*e))*x)/e^8) + ((c*d^2 + a*e^2)*(a^2*C*e^4 + c^2*(28*C*d^4 - 3*d^2*e*(7*B*d - 5*A*e)) + a*c*e^2*(17*C*d^2 - 3*e*(3*B*d - A*e)))*(d + e*x)^2)/(2*e^9) - (c*(3*a^2*e^4*(4*C*d - B*e) + c^2*(56*C*d^5 - 5*d^3*e*(7*B*d - 4*A*e)) + 6*a*c*d*e^2*(10*C*d^2 - e*(5*B*d - 2*A*e)))*(d + e*x)^3)/(3*e^9) + (c*(3*a^2*C*e^4 + 5*c^2*(14*C*d^4 - d^2*e*(7*B*d - 3*A*e)) + 3*a*c*e^2*(15*C*d^2 - e*(5*B*d - A*e)))*(d + e*x)^4)/(4*e^9) - (c^2*(56*c*C*d^3 - 3*c*d*e*(7*B*d - 2*A*e) + 3*a*e^2*(6*C*d - B*e))*(d + e*x)^5)/(5*e^9) + (c^2*(28*c*C*d^2 + 3*a*C*e^2 - c*e*(7*B*d - A*e))*(d + e*x)^6)/(6*e^9) - (c^3*(8*C*d - B*e)*(d + e*x)^7)/(7*e^9) + (c^3*C*(d + e*x)^8)/(8*e^9) + ((c*d^2 + a*e^2)^3*(C*d^2 - B*d*e + A*e^2)*Log[d + e*x])/e^9","A",2,1,27,0.03704,1,"{1628}"
37,1,483,0,0.9803817,"\int \frac{\left(a+c x^2\right)^3 \left(A+B x+C x^2\right)}{(d+e x)^2} \, dx","Int[((a + c*x^2)^3*(A + B*x + C*x^2))/(d + e*x)^2,x]","\frac{c x^3 \left(3 a^2 C e^4+3 a c e^2 \left(3 C d^2-e (2 B d-A e)\right)+c^2 \left(5 C d^4-d^2 e (4 B d-3 A e)\right)\right)}{3 e^6}-\frac{c x^2 \left(3 a^2 e^4 (2 C d-B e)+3 a c d e^2 \left(4 C d^2-e (3 B d-2 A e)\right)+c^2 \left(6 C d^5-d^3 e (5 B d-4 A e)\right)\right)}{2 e^7}+\frac{x \left(3 a^2 c e^4 \left(3 C d^2-e (2 B d-A e)\right)+a^3 C e^6+3 a c^2 d^2 e^2 \left(5 C d^2-e (4 B d-3 A e)\right)+c^3 \left(7 C d^6-d^4 e (6 B d-5 A e)\right)\right)}{e^8}+\frac{c^2 x^5 \left(3 a C e^2-c e (2 B d-A e)+3 c C d^2\right)}{5 e^4}-\frac{c^2 x^4 \left(3 a e^2 (2 C d-B e)-c d e (3 B d-2 A e)+4 c C d^3\right)}{4 e^5}-\frac{\left(a e^2+c d^2\right)^3 \left(A e^2-B d e+C d^2\right)}{e^9 (d+e x)}-\frac{\left(a e^2+c d^2\right)^2 \log (d+e x) \left(a e^2 (2 C d-B e)-c d e (7 B d-6 A e)+8 c C d^3\right)}{e^9}-\frac{c^3 x^6 (2 C d-B e)}{6 e^3}+\frac{c^3 C x^7}{7 e^2}","\frac{c x^3 \left(3 a^2 C e^4+3 a c e^2 \left(3 C d^2-e (2 B d-A e)\right)+c^2 d^2 \left(5 C d^2-e (4 B d-3 A e)\right)\right)}{3 e^6}-\frac{c x^2 \left(3 a^2 e^4 (2 C d-B e)+3 a c d e^2 \left(4 C d^2-e (3 B d-2 A e)\right)+c^2 d^3 \left(6 C d^2-e (5 B d-4 A e)\right)\right)}{2 e^7}+\frac{x \left(3 a^2 c e^4 \left(3 C d^2-e (2 B d-A e)\right)+a^3 C e^6+3 a c^2 d^2 e^2 \left(5 C d^2-e (4 B d-3 A e)\right)+c^3 d^4 \left(7 C d^2-e (6 B d-5 A e)\right)\right)}{e^8}+\frac{c^2 x^5 \left(3 a C e^2+c \left(3 C d^2-e (2 B d-A e)\right)\right)}{5 e^4}-\frac{c^2 x^4 \left(3 a e^2 (2 C d-B e)+c d \left(4 C d^2-e (3 B d-2 A e)\right)\right)}{4 e^5}-\frac{\left(a e^2+c d^2\right)^3 \left(A e^2-B d e+C d^2\right)}{e^9 (d+e x)}-\frac{\left(a e^2+c d^2\right)^2 \log (d+e x) \left(a e^2 (2 C d-B e)+c d \left(8 C d^2-e (7 B d-6 A e)\right)\right)}{e^9}-\frac{c^3 x^6 (2 C d-B e)}{6 e^3}+\frac{c^3 C x^7}{7 e^2}",1,"((a^3*C*e^6 + c^3*(7*C*d^6 - d^4*e*(6*B*d - 5*A*e)) + 3*a*c^2*d^2*e^2*(5*C*d^2 - e*(4*B*d - 3*A*e)) + 3*a^2*c*e^4*(3*C*d^2 - e*(2*B*d - A*e)))*x)/e^8 - (c*(3*a^2*e^4*(2*C*d - B*e) + c^2*(6*C*d^5 - d^3*e*(5*B*d - 4*A*e)) + 3*a*c*d*e^2*(4*C*d^2 - e*(3*B*d - 2*A*e)))*x^2)/(2*e^7) + (c*(3*a^2*C*e^4 + c^2*(5*C*d^4 - d^2*e*(4*B*d - 3*A*e)) + 3*a*c*e^2*(3*C*d^2 - e*(2*B*d - A*e)))*x^3)/(3*e^6) - (c^2*(4*c*C*d^3 - c*d*e*(3*B*d - 2*A*e) + 3*a*e^2*(2*C*d - B*e))*x^4)/(4*e^5) + (c^2*(3*c*C*d^2 + 3*a*C*e^2 - c*e*(2*B*d - A*e))*x^5)/(5*e^4) - (c^3*(2*C*d - B*e)*x^6)/(6*e^3) + (c^3*C*x^7)/(7*e^2) - ((c*d^2 + a*e^2)^3*(C*d^2 - B*d*e + A*e^2))/(e^9*(d + e*x)) - ((c*d^2 + a*e^2)^2*(8*c*C*d^3 - c*d*e*(7*B*d - 6*A*e) + a*e^2*(2*C*d - B*e))*Log[d + e*x])/e^9","A",2,1,27,0.03704,1,"{1628}"
38,1,463,0,0.9666446,"\int \frac{\left(a+c x^2\right)^3 \left(A+B x+C x^2\right)}{(d+e x)^3} \, dx","Int[((a + c*x^2)^3*(A + B*x + C*x^2))/(d + e*x)^3,x]","\frac{c x^2 \left(3 a^2 C e^4+3 a c e^2 \left(6 C d^2-e (3 B d-A e)\right)+c^2 \left(15 C d^4-2 d^2 e (5 B d-3 A e)\right)\right)}{2 e^7}-\frac{c x \left(3 a^2 e^4 (3 C d-B e)+3 a c d e^2 \left(10 C d^2-3 e (2 B d-A e)\right)+c^2 \left(21 C d^5-5 d^3 e (3 B d-2 A e)\right)\right)}{e^8}+\frac{\left(a e^2+c d^2\right) \log (d+e x) \left(a^2 C e^4+a c e^2 \left(17 C d^2-3 e (3 B d-A e)\right)+c^2 \left(28 C d^4-3 d^2 e (7 B d-5 A e)\right)\right)}{e^9}+\frac{c^2 x^4 \left(3 a C e^2-c e (3 B d-A e)+6 c C d^2\right)}{4 e^5}-\frac{c^2 x^3 \left(3 a e^2 (3 C d-B e)-3 c d e (2 B d-A e)+10 c C d^3\right)}{3 e^6}+\frac{\left(a e^2+c d^2\right)^2 \left(a e^2 (2 C d-B e)-c d e (7 B d-6 A e)+8 c C d^3\right)}{e^9 (d+e x)}-\frac{\left(a e^2+c d^2\right)^3 \left(A e^2-B d e+C d^2\right)}{2 e^9 (d+e x)^2}-\frac{c^3 x^5 (3 C d-B e)}{5 e^4}+\frac{c^3 C x^6}{6 e^3}","\frac{c x^2 \left(3 a^2 C e^4+3 a c e^2 \left(6 C d^2-e (3 B d-A e)\right)+c^2 d^2 \left(15 C d^2-2 e (5 B d-3 A e)\right)\right)}{2 e^7}-\frac{c x \left(3 a^2 e^4 (3 C d-B e)+3 a c d e^2 \left(10 C d^2-3 e (2 B d-A e)\right)+c^2 d^3 \left(21 C d^2-5 e (3 B d-2 A e)\right)\right)}{e^8}+\frac{\left(a e^2+c d^2\right) \log (d+e x) \left(a^2 C e^4+a c e^2 \left(17 C d^2-3 e (3 B d-A e)\right)+c^2 d^2 \left(28 C d^2-3 e (7 B d-5 A e)\right)\right)}{e^9}+\frac{c^2 x^4 \left(3 a C e^2+c \left(6 C d^2-e (3 B d-A e)\right)\right)}{4 e^5}-\frac{c^2 x^3 \left(3 a e^2 (3 C d-B e)+c d \left(10 C d^2-3 e (2 B d-A e)\right)\right)}{3 e^6}+\frac{\left(a e^2+c d^2\right)^2 \left(a e^2 (2 C d-B e)+c d \left(8 C d^2-e (7 B d-6 A e)\right)\right)}{e^9 (d+e x)}-\frac{\left(a e^2+c d^2\right)^3 \left(A e^2-B d e+C d^2\right)}{2 e^9 (d+e x)^2}-\frac{c^3 x^5 (3 C d-B e)}{5 e^4}+\frac{c^3 C x^6}{6 e^3}",1,"-((c*(3*a^2*e^4*(3*C*d - B*e) + c^2*(21*C*d^5 - 5*d^3*e*(3*B*d - 2*A*e)) + 3*a*c*d*e^2*(10*C*d^2 - 3*e*(2*B*d - A*e)))*x)/e^8) + (c*(3*a^2*C*e^4 + c^2*(15*C*d^4 - 2*d^2*e*(5*B*d - 3*A*e)) + 3*a*c*e^2*(6*C*d^2 - e*(3*B*d - A*e)))*x^2)/(2*e^7) - (c^2*(10*c*C*d^3 - 3*c*d*e*(2*B*d - A*e) + 3*a*e^2*(3*C*d - B*e))*x^3)/(3*e^6) + (c^2*(6*c*C*d^2 + 3*a*C*e^2 - c*e*(3*B*d - A*e))*x^4)/(4*e^5) - (c^3*(3*C*d - B*e)*x^5)/(5*e^4) + (c^3*C*x^6)/(6*e^3) - ((c*d^2 + a*e^2)^3*(C*d^2 - B*d*e + A*e^2))/(2*e^9*(d + e*x)^2) + ((c*d^2 + a*e^2)^2*(8*c*C*d^3 - c*d*e*(7*B*d - 6*A*e) + a*e^2*(2*C*d - B*e)))/(e^9*(d + e*x)) + ((c*d^2 + a*e^2)*(a^2*C*e^4 + c^2*(28*C*d^4 - 3*d^2*e*(7*B*d - 5*A*e)) + a*c*e^2*(17*C*d^2 - 3*e*(3*B*d - A*e)))*Log[d + e*x])/e^9","A",2,1,27,0.03704,1,"{1628}"
39,1,17,0,0.0319914,"\int \frac{\left(a+b x^2\right) \left(-a d+4 b c x+3 b d x^2\right)}{(c+d x)^2} \, dx","Int[((a + b*x^2)*(-(a*d) + 4*b*c*x + 3*b*d*x^2))/(c + d*x)^2,x]","\frac{\left(a+b x^2\right)^2}{c+d x}","\frac{\left(a+b x^2\right)^2}{c+d x}",1,"(a + b*x^2)^2/(c + d*x)","A",1,1,32,0.03125,1,"{1590}"
40,1,17,0,0.0188685,"\int \frac{\left(a+b x^2\right) (-a d+b x (4 c+3 d x))}{(c+d x)^2} \, dx","Int[((a + b*x^2)*(-(a*d) + b*x*(4*c + 3*d*x)))/(c + d*x)^2,x]","\frac{\left(a+b x^2\right)^2}{c+d x}","\frac{\left(a+b x^2\right)^2}{c+d x}",1,"(a + b*x^2)^2/(c + d*x)","A",1,1,31,0.03226,1,"{1590}"
41,1,17,0,0.0459761,"\int \frac{\left(a+b x^2\right)^2 \left(-a d+6 b c x+5 b d x^2\right)}{(c+d x)^2} \, dx","Int[((a + b*x^2)^2*(-(a*d) + 6*b*c*x + 5*b*d*x^2))/(c + d*x)^2,x]","\frac{\left(a+b x^2\right)^3}{c+d x}","\frac{\left(a+b x^2\right)^3}{c+d x}",1,"(a + b*x^2)^3/(c + d*x)","A",1,1,34,0.02941,1,"{1590}"
42,1,17,0,0.0249113,"\int \frac{\left(a+b x^2\right)^2 (-a d+b x (6 c+5 d x))}{(c+d x)^2} \, dx","Int[((a + b*x^2)^2*(-(a*d) + b*x*(6*c + 5*d*x)))/(c + d*x)^2,x]","\frac{\left(a+b x^2\right)^3}{c+d x}","\frac{\left(a+b x^2\right)^3}{c+d x}",1,"(a + b*x^2)^3/(c + d*x)","A",1,1,33,0.03030,1,"{1590}"
43,1,237,0,0.4712169,"\int \frac{(d+e x)^3 \left(A+B x+C x^2\right)}{a+c x^2} \, dx","Int[((d + e*x)^3*(A + B*x + C*x^2))/(a + c*x^2),x]","\frac{e x^2 \left(-a C e^2+c e (A e+3 B d)+3 c C d^2\right)}{2 c^2}+\frac{\log \left(a+c x^2\right) \left(e (A c-a C) \left(3 c d^2-a e^2\right)+B c d \left(c d^2-3 a e^2\right)\right)}{2 c^3}+\frac{x \left(-a e^2 (B e+3 C d)+3 c d e (A e+B d)+c C d^3\right)}{c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(c d^2-3 a e^2\right)+a \left(a e^2 (B e+3 C d)-c d^2 (3 B e+C d)\right)\right)}{\sqrt{a} c^{5/2}}+\frac{e^2 x^3 (B e+3 C d)}{3 c}+\frac{C e^3 x^4}{4 c}","-\frac{e x^2 \left(a C e^2-c \left(e (A e+3 B d)+3 C d^2\right)\right)}{2 c^2}+\frac{\log \left(a+c x^2\right) \left(e (A c-a C) \left(3 c d^2-a e^2\right)+B c d \left(c d^2-3 a e^2\right)\right)}{2 c^3}-\frac{x \left(a e^2 (B e+3 C d)-c d \left(3 e (A e+B d)+C d^2\right)\right)}{c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(c d^2-3 a e^2\right)+a \left(a e^2 (B e+3 C d)-c d^2 (3 B e+C d)\right)\right)}{\sqrt{a} c^{5/2}}+\frac{e^2 x^3 (B e+3 C d)}{3 c}+\frac{C e^3 x^4}{4 c}",1,"((c*C*d^3 + 3*c*d*e*(B*d + A*e) - a*e^2*(3*C*d + B*e))*x)/c^2 + (e*(3*c*C*d^2 - a*C*e^2 + c*e*(3*B*d + A*e))*x^2)/(2*c^2) + (e^2*(3*C*d + B*e)*x^3)/(3*c) + (C*e^3*x^4)/(4*c) + ((A*c*d*(c*d^2 - 3*a*e^2) + a*(a*e^2*(3*C*d + B*e) - c*d^2*(C*d + 3*B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(5/2)) + ((B*c*d*(c*d^2 - 3*a*e^2) + (A*c - a*C)*e*(3*c*d^2 - a*e^2))*Log[a + c*x^2])/(2*c^3)","A",5,4,27,0.1481,1,"{1629, 635, 205, 260}"
44,1,166,0,0.2615736,"\int \frac{(d+e x)^2 \left(A+B x+C x^2\right)}{a+c x^2} \, dx","Int[((d + e*x)^2*(A + B*x + C*x^2))/(a + c*x^2),x]","\frac{\log \left(a+c x^2\right) \left(-a B e^2-2 a C d e+2 A c d e+B c d^2\right)}{2 c^2}+\frac{x \left(-a C e^2+c e (A e+2 B d)+c C d^2\right)}{c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c \left(c d^2-a e^2\right)+a \left(a C e^2-c d (2 B e+C d)\right)\right)}{\sqrt{a} c^{5/2}}+\frac{e x^2 (B e+2 C d)}{2 c}+\frac{C e^2 x^3}{3 c}","\frac{\log \left(a+c x^2\right) \left(-a B e^2-2 a C d e+2 A c d e+B c d^2\right)}{2 c^2}-\frac{x \left(a C e^2-c \left(e (A e+2 B d)+C d^2\right)\right)}{c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c \left(c d^2-a e^2\right)+a \left(a C e^2-c d (2 B e+C d)\right)\right)}{\sqrt{a} c^{5/2}}+\frac{e x^2 (B e+2 C d)}{2 c}+\frac{C e^2 x^3}{3 c}",1,"((c*C*d^2 - a*C*e^2 + c*e*(2*B*d + A*e))*x)/c^2 + (e*(2*C*d + B*e)*x^2)/(2*c) + (C*e^2*x^3)/(3*c) + ((A*c*(c*d^2 - a*e^2) + a*(a*C*e^2 - c*d*(C*d + 2*B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(5/2)) + ((B*c*d^2 + 2*A*c*d*e - 2*a*C*d*e - a*B*e^2)*Log[a + c*x^2])/(2*c^2)","A",5,4,27,0.1481,1,"{1629, 635, 205, 260}"
45,1,93,0,0.1173074,"\int \frac{(d+e x) \left(A+B x+C x^2\right)}{a+c x^2} \, dx","Int[((d + e*x)*(A + B*x + C*x^2))/(a + c*x^2),x]","\frac{\log \left(a+c x^2\right) (-a C e+A c e+B c d)}{2 c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (A c d-a (B e+C d))}{\sqrt{a} c^{3/2}}+\frac{x (B e+C d)}{c}+\frac{C e x^2}{2 c}","\frac{\log \left(a+c x^2\right) (-a C e+A c e+B c d)}{2 c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (A c d-a (B e+C d))}{\sqrt{a} c^{3/2}}+\frac{x (B e+C d)}{c}+\frac{C e x^2}{2 c}",1,"((C*d + B*e)*x)/c + (C*e*x^2)/(2*c) + ((A*c*d - a*(C*d + B*e))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(3/2)) + ((B*c*d + A*c*e - a*C*e)*Log[a + c*x^2])/(2*c^2)","A",5,4,25,0.1600,1,"{1629, 635, 205, 260}"
46,1,55,0,0.0525633,"\int \frac{A+B x+C x^2}{a+c x^2} \, dx","Int[(A + B*x + C*x^2)/(a + c*x^2),x]","\frac{(A c-a C) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} c^{3/2}}+\frac{B \log \left(a+c x^2\right)}{2 c}+\frac{C x}{c}","\frac{(A c-a C) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} c^{3/2}}+\frac{B \log \left(a+c x^2\right)}{2 c}+\frac{C x}{c}",1,"(C*x)/c + ((A*c - a*C)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(3/2)) + (B*Log[a + c*x^2])/(2*c)","A",5,4,20,0.2000,1,"{1810, 635, 205, 260}"
47,1,133,0,0.1623955,"\int \frac{A+B x+C x^2}{(d+e x) \left(a+c x^2\right)} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)*(a + c*x^2)),x]","\frac{\log \left(a+c x^2\right) (a C e-A c e+B c d)}{2 c \left(a e^2+c d^2\right)}+\frac{\log (d+e x) \left(A e^2-B d e+C d^2\right)}{e \left(a e^2+c d^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e-a C d+A c d)}{\sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)}","\frac{\log \left(a+c x^2\right) (a C e-A c e+B c d)}{2 c \left(a e^2+c d^2\right)}+\frac{\log (d+e x) \left(A e^2-B d e+C d^2\right)}{e \left(a e^2+c d^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e-a C d+A c d)}{\sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)}",1,"((A*c*d - a*C*d + a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[c]*(c*d^2 + a*e^2)) + ((C*d^2 - B*d*e + A*e^2)*Log[d + e*x])/(e*(c*d^2 + a*e^2)) + ((B*c*d - A*c*e + a*C*e)*Log[a + c*x^2])/(2*c*(c*d^2 + a*e^2))","A",5,4,27,0.1481,1,"{1629, 635, 205, 260}"
48,1,214,0,0.3554508,"\int \frac{A+B x+C x^2}{(d+e x)^2 \left(a+c x^2\right)} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^2*(a + c*x^2)),x]","\frac{\log \left(a+c x^2\right) \left(-a B e^2+2 a C d e-2 A c d e+B c d^2\right)}{2 \left(a e^2+c d^2\right)^2}-\frac{A e^2-B d e+C d^2}{e (d+e x) \left(a e^2+c d^2\right)}-\frac{\log (d+e x) \left(-a B e^2+2 a C d e-2 A c d e+B c d^2\right)}{\left(a e^2+c d^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c \left(c d^2-a e^2\right)+a \left(a C e^2-c d (C d-2 B e)\right)\right)}{\sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)^2}","\frac{\log \left(a+c x^2\right) \left(-a B e^2+2 a C d e-2 A c d e+B c d^2\right)}{2 \left(a e^2+c d^2\right)^2}-\frac{A e^2-B d e+C d^2}{e (d+e x) \left(a e^2+c d^2\right)}-\frac{\log (d+e x) \left(-a B e^2+2 a C d e-2 A c d e+B c d^2\right)}{\left(a e^2+c d^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c \left(c d^2-a e^2\right)+a \left(a C e^2-c d (C d-2 B e)\right)\right)}{\sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)^2}",1,"-((C*d^2 - B*d*e + A*e^2)/(e*(c*d^2 + a*e^2)*(d + e*x))) + ((A*c*(c*d^2 - a*e^2) + a*(a*C*e^2 - c*d*(C*d - 2*B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[c]*(c*d^2 + a*e^2)^2) - ((B*c*d^2 - 2*A*c*d*e + 2*a*C*d*e - a*B*e^2)*Log[d + e*x])/(c*d^2 + a*e^2)^2 + ((B*c*d^2 - 2*A*c*d*e + 2*a*C*d*e - a*B*e^2)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^2)","A",5,4,27,0.1481,1,"{1629, 635, 205, 260}"
49,1,305,0,0.6509463,"\int \frac{A+B x+C x^2}{(d+e x)^3 \left(a+c x^2\right)} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^3*(a + c*x^2)),x]","\frac{\log \left(a+c x^2\right) \left(B c d \left(c d^2-3 a e^2\right)-e (A c-a C) \left(3 c d^2-a e^2\right)\right)}{2 \left(a e^2+c d^2\right)^3}-\frac{A e^2-B d e+C d^2}{2 e (d+e x)^2 \left(a e^2+c d^2\right)}+\frac{-a B e^2+2 a C d e-2 A c d e+B c d^2}{(d+e x) \left(a e^2+c d^2\right)^2}-\frac{\log (d+e x) \left(B c d \left(c d^2-3 a e^2\right)-e (A c-a C) \left(3 c d^2-a e^2\right)\right)}{\left(a e^2+c d^2\right)^3}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(c d^2-3 a e^2\right)-a \left(c d^2 (C d-3 B e)-a e^2 (3 C d-B e)\right)\right)}{\sqrt{a} \left(a e^2+c d^2\right)^3}","\frac{\log \left(a+c x^2\right) \left(B c d \left(c d^2-3 a e^2\right)-e (A c-a C) \left(3 c d^2-a e^2\right)\right)}{2 \left(a e^2+c d^2\right)^3}-\frac{A e^2-B d e+C d^2}{2 e (d+e x)^2 \left(a e^2+c d^2\right)}+\frac{-a B e^2+2 a C d e-2 A c d e+B c d^2}{(d+e x) \left(a e^2+c d^2\right)^2}-\frac{\log (d+e x) \left(B c d \left(c d^2-3 a e^2\right)-e (A c-a C) \left(3 c d^2-a e^2\right)\right)}{\left(a e^2+c d^2\right)^3}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(c d^2-3 a e^2\right)-a \left(c d^2 (C d-3 B e)-a e^2 (3 C d-B e)\right)\right)}{\sqrt{a} \left(a e^2+c d^2\right)^3}",1,"-(C*d^2 - B*d*e + A*e^2)/(2*e*(c*d^2 + a*e^2)*(d + e*x)^2) + (B*c*d^2 - 2*A*c*d*e + 2*a*C*d*e - a*B*e^2)/((c*d^2 + a*e^2)^2*(d + e*x)) + (Sqrt[c]*(A*c*d*(c*d^2 - 3*a*e^2) - a*(c*d^2*(C*d - 3*B*e) - a*e^2*(3*C*d - B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*(c*d^2 + a*e^2)^3) - ((B*c*d*(c*d^2 - 3*a*e^2) - (A*c - a*C)*e*(3*c*d^2 - a*e^2))*Log[d + e*x])/(c*d^2 + a*e^2)^3 + ((B*c*d*(c*d^2 - 3*a*e^2) - (A*c - a*C)*e*(3*c*d^2 - a*e^2))*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^3)","A",5,4,27,0.1481,1,"{1629, 635, 205, 260}"
50,1,216,0,0.504723,"\int \frac{(d+e x)^3 \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^2} \, dx","Int[((d + e*x)^3*(A + B*x + C*x^2))/(a + c*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(3 a e^2+c d^2\right)-a \left(3 a e^2 (B e+3 C d)-c d^2 (3 B e+C d)\right)\right)}{2 a^{3/2} c^{5/2}}-\frac{e \log \left(a+c x^2\right) \left(2 a C e^2-c \left(e (A e+3 B d)+3 C d^2\right)\right)}{2 c^3}-\frac{3 e^2 x (A c d-a (B e+3 C d))}{2 a c^2}-\frac{(d+e x)^3 (a B-x (A c-a C))}{2 a c \left(a+c x^2\right)}-\frac{e^3 x^2 (A c-2 a C)}{2 a c^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(3 a e^2+c d^2\right)-a \left(3 a e^2 (B e+3 C d)-c d^2 (3 B e+C d)\right)\right)}{2 a^{3/2} c^{5/2}}-\frac{e \log \left(a+c x^2\right) \left(2 a C e^2-c \left(e (A e+3 B d)+3 C d^2\right)\right)}{2 c^3}-\frac{3 e^2 x (A c d-a (B e+3 C d))}{2 a c^2}-\frac{(d+e x)^3 (a B-x (A c-a C))}{2 a c \left(a+c x^2\right)}-\frac{e^3 x^2 (A c-2 a C)}{2 a c^2}",1,"(-3*e^2*(A*c*d - a*(3*C*d + B*e))*x)/(2*a*c^2) - ((A*c - 2*a*C)*e^3*x^2)/(2*a*c^2) - ((a*B - (A*c - a*C)*x)*(d + e*x)^3)/(2*a*c*(a + c*x^2)) + ((A*c*d*(c*d^2 + 3*a*e^2) - a*(3*a*e^2*(3*C*d + B*e) - c*d^2*(C*d + 3*B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(5/2)) - (e*(2*a*C*e^2 - c*(3*C*d^2 + e*(3*B*d + A*e)))*Log[a + c*x^2])/(2*c^3)","A",6,5,27,0.1852,1,"{1645, 801, 635, 205, 260}"
51,1,146,0,0.245414,"\int \frac{(d+e x)^2 \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^2} \, dx","Int[((d + e*x)^2*(A + B*x + C*x^2))/(a + c*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d (2 a B e+a C d+A c d)+a e^2 (A c-3 a C)\right)}{2 a^{3/2} c^{5/2}}-\frac{(d+e x)^2 (a B-x (A c-a C))}{2 a c \left(a+c x^2\right)}-\frac{e^2 x (A c-3 a C)}{2 a c^2}+\frac{e \log \left(a+c x^2\right) (B e+2 C d)}{2 c^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d (2 a B e+a C d+A c d)+a e^2 (A c-3 a C)\right)}{2 a^{3/2} c^{5/2}}-\frac{(d+e x)^2 (a B-x (A c-a C))}{2 a c \left(a+c x^2\right)}-\frac{e^2 x (A c-3 a C)}{2 a c^2}+\frac{e \log \left(a+c x^2\right) (B e+2 C d)}{2 c^2}",1,"-((A*c - 3*a*C)*e^2*x)/(2*a*c^2) - ((a*B - (A*c - a*C)*x)*(d + e*x)^2)/(2*a*c*(a + c*x^2)) + ((a*(A*c - 3*a*C)*e^2 + c*d*(A*c*d + a*C*d + 2*a*B*e))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(5/2)) + (e*(2*C*d + B*e)*Log[a + c*x^2])/(2*c^2)","A",5,5,27,0.1852,1,"{1645, 774, 635, 205, 260}"
52,1,97,0,0.0824126,"\int \frac{(d+e x) \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^2} \, dx","Int[((d + e*x)*(A + B*x + C*x^2))/(a + c*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+a C d+A c d)}{2 a^{3/2} c^{3/2}}-\frac{(d+e x) (a B-x (A c-a C))}{2 a c \left(a+c x^2\right)}+\frac{C e \log \left(a+c x^2\right)}{2 c^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+a C d+A c d)}{2 a^{3/2} c^{3/2}}-\frac{(d+e x) (a B-x (A c-a C))}{2 a c \left(a+c x^2\right)}+\frac{C e \log \left(a+c x^2\right)}{2 c^2}",1,"-((a*B - (A*c - a*C)*x)*(d + e*x))/(2*a*c*(a + c*x^2)) + ((A*c*d + a*C*d + a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(3/2)) + (C*e*Log[a + c*x^2])/(2*c^2)","A",4,4,25,0.1600,1,"{1645, 635, 205, 260}"
53,1,69,0,0.0431747,"\int \frac{A+B x+C x^2}{\left(a+c x^2\right)^2} \, dx","Int[(A + B*x + C*x^2)/(a + c*x^2)^2,x]","\frac{(a C+A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{3/2}}-\frac{a B-x (A c-a C)}{2 a c \left(a+c x^2\right)}","\frac{(a C+A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} c^{3/2}}-\frac{a B-x (A c-a C)}{2 a c \left(a+c x^2\right)}",1,"-(a*B - (A*c - a*C)*x)/(2*a*c*(a + c*x^2)) + ((A*c + a*C)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(3/2))","A",3,3,20,0.1500,1,"{1814, 12, 205}"
54,1,226,0,0.4349964,"\int \frac{A+B x+C x^2}{(d+e x) \left(a+c x^2\right)^2} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)*(a + c*x^2)^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(3 a e^2+c d^2\right)+a \left(c d^2-a e^2\right) (C d-B e)\right)}{2 a^{3/2} \sqrt{c} \left(a e^2+c d^2\right)^2}-\frac{a (a C e-A c e+B c d)-c x (a B e-a C d+A c d)}{2 a c \left(a+c x^2\right) \left(a e^2+c d^2\right)}-\frac{e \log \left(a+c x^2\right) \left(A e^2-B d e+C d^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{e \log (d+e x) \left(A e^2-B d e+C d^2\right)}{\left(a e^2+c d^2\right)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(3 a e^2+c d^2\right)+a \left(c d^2-a e^2\right) (C d-B e)\right)}{2 a^{3/2} \sqrt{c} \left(a e^2+c d^2\right)^2}-\frac{a (a C e-A c e+B c d)-c x (a B e-a C d+A c d)}{2 a c \left(a+c x^2\right) \left(a e^2+c d^2\right)}-\frac{e \log \left(a+c x^2\right) \left(A e^2-B d e+C d^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{e \log (d+e x) \left(A e^2-B d e+C d^2\right)}{\left(a e^2+c d^2\right)^2}",1,"-(a*(B*c*d - A*c*e + a*C*e) - c*(A*c*d - a*C*d + a*B*e)*x)/(2*a*c*(c*d^2 + a*e^2)*(a + c*x^2)) + ((a*(C*d - B*e)*(c*d^2 - a*e^2) + A*c*d*(c*d^2 + 3*a*e^2))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[c]*(c*d^2 + a*e^2)^2) + (e*(C*d^2 - B*d*e + A*e^2)*Log[d + e*x])/(c*d^2 + a*e^2)^2 - (e*(C*d^2 - B*d*e + A*e^2)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^2)","A",6,5,27,0.1852,1,"{1647, 801, 635, 205, 260}"
55,1,371,0,0.9504036,"\int \frac{A+B x+C x^2}{(d+e x)^2 \left(a+c x^2\right)^2} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^2*(a + c*x^2)^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)+a \left(a^2 C e^4-6 a c d e^2 (C d-B e)+c^2 d^3 (C d-2 B e)\right)\right)}{2 a^{3/2} \sqrt{c} \left(a e^2+c d^2\right)^3}-\frac{a \left(-a B e^2+2 a C d e-2 A c d e+B c d^2\right)-x \left(A c \left(c d^2-a e^2\right)+a \left(a C e^2-c d (C d-2 B e)\right)\right)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}-\frac{e \log \left(a+c x^2\right) \left(-a e^2 (2 C d-B e)-c d e (3 B d-4 A e)+2 c C d^3\right)}{2 \left(a e^2+c d^2\right)^3}-\frac{e \left(A e^2-B d e+C d^2\right)}{(d+e x) \left(a e^2+c d^2\right)^2}+\frac{e \log (d+e x) \left(-a e^2 (2 C d-B e)-c d e (3 B d-4 A e)+2 c C d^3\right)}{\left(a e^2+c d^2\right)^3}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)+a \left(a^2 C e^4-6 a c d e^2 (C d-B e)+c^2 d^3 (C d-2 B e)\right)\right)}{2 a^{3/2} \sqrt{c} \left(a e^2+c d^2\right)^3}-\frac{a \left(-a B e^2+2 a C d e-2 A c d e+B c d^2\right)-x \left(A c \left(c d^2-a e^2\right)+a \left(a C e^2-c d (C d-2 B e)\right)\right)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}+\frac{e \log \left(a+c x^2\right) \left(a e^2 (2 C d-B e)-c d \left(2 C d^2-e (3 B d-4 A e)\right)\right)}{2 \left(a e^2+c d^2\right)^3}-\frac{e \left(A e^2-B d e+C d^2\right)}{(d+e x) \left(a e^2+c d^2\right)^2}-\frac{e \log (d+e x) \left(a e^2 (2 C d-B e)-c d \left(2 C d^2-e (3 B d-4 A e)\right)\right)}{\left(a e^2+c d^2\right)^3}",1,"-((e*(C*d^2 - B*d*e + A*e^2))/((c*d^2 + a*e^2)^2*(d + e*x))) - (a*(B*c*d^2 - 2*A*c*d*e + 2*a*C*d*e - a*B*e^2) - (A*c*(c*d^2 - a*e^2) + a*(a*C*e^2 - c*d*(C*d - 2*B*e)))*x)/(2*a*(c*d^2 + a*e^2)^2*(a + c*x^2)) + ((A*c*(c^2*d^4 + 6*a*c*d^2*e^2 - 3*a^2*e^4) + a*(a^2*C*e^4 + c^2*d^3*(C*d - 2*B*e) - 6*a*c*d*e^2*(C*d - B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[c]*(c*d^2 + a*e^2)^3) + (e*(2*c*C*d^3 - c*d*e*(3*B*d - 4*A*e) - a*e^2*(2*C*d - B*e))*Log[d + e*x])/(c*d^2 + a*e^2)^3 - (e*(2*c*C*d^3 - c*d*e*(3*B*d - 4*A*e) - a*e^2*(2*C*d - B*e))*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^3)","A",6,5,27,0.1852,1,"{1647, 1629, 635, 205, 260}"
56,1,524,0,1.5522313,"\int \frac{A+B x+C x^2}{(d+e x)^3 \left(a+c x^2\right)^2} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^3*(a + c*x^2)^2),x]","-\frac{e \log \left(a+c x^2\right) \left(a^2 C e^4-2 a c e^2 \left(4 C d^2-e (3 B d-A e)\right)+c^2 \left(3 C d^4-2 d^2 e (3 B d-5 A e)\right)\right)}{2 \left(a e^2+c d^2\right)^4}+\frac{e \log (d+e x) \left(a^2 C e^4-2 a c e^2 \left(4 C d^2-e (3 B d-A e)\right)+c^2 \left(3 C d^4-2 d^2 e (3 B d-5 A e)\right)\right)}{\left(a e^2+c d^2\right)^4}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(-15 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right)-a \left(-3 a^2 e^4 (3 C d-B e)+2 a c d^2 e^2 (7 C d-9 B e)-c^2 d^4 (C d-3 B e)\right)\right)}{2 a^{3/2} \left(a e^2+c d^2\right)^4}-\frac{a \left(B c d \left(c d^2-3 a e^2\right)-e (A c-a C) \left(3 c d^2-a e^2\right)\right)-c x \left(A c d \left(c d^2-3 a e^2\right)-a \left(c d^2 (C d-3 B e)-a e^2 (3 C d-B e)\right)\right)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)^3}-\frac{e \left(A e^2-B d e+C d^2\right)}{2 (d+e x)^2 \left(a e^2+c d^2\right)^2}-\frac{e \left(-a e^2 (2 C d-B e)-c d e (3 B d-4 A e)+2 c C d^3\right)}{(d+e x) \left(a e^2+c d^2\right)^3}","-\frac{e \log \left(a+c x^2\right) \left(a^2 C e^4-2 a c e^2 \left(4 C d^2-e (3 B d-A e)\right)+c^2 d^2 \left(3 C d^2-2 e (3 B d-5 A e)\right)\right)}{2 \left(a e^2+c d^2\right)^4}+\frac{e \log (d+e x) \left(a^2 C e^4-2 a c e^2 \left(4 C d^2-e (3 B d-A e)\right)+c^2 d^2 \left(3 C d^2-2 e (3 B d-5 A e)\right)\right)}{\left(a e^2+c d^2\right)^4}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(-15 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right)-a \left(-3 a^2 e^4 (3 C d-B e)+2 a c d^2 e^2 (7 C d-9 B e)-c^2 d^4 (C d-3 B e)\right)\right)}{2 a^{3/2} \left(a e^2+c d^2\right)^4}-\frac{a \left(B c d \left(c d^2-3 a e^2\right)-e (A c-a C) \left(3 c d^2-a e^2\right)\right)-c x \left(A c d \left(c d^2-3 a e^2\right)-a \left(c d^2 (C d-3 B e)-a e^2 (3 C d-B e)\right)\right)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)^3}-\frac{e \left(A e^2-B d e+C d^2\right)}{2 (d+e x)^2 \left(a e^2+c d^2\right)^2}+\frac{e \left(a e^2 (2 C d-B e)-c d \left(2 C d^2-e (3 B d-4 A e)\right)\right)}{(d+e x) \left(a e^2+c d^2\right)^3}",1,"-(e*(C*d^2 - B*d*e + A*e^2))/(2*(c*d^2 + a*e^2)^2*(d + e*x)^2) - (e*(2*c*C*d^3 - c*d*e*(3*B*d - 4*A*e) - a*e^2*(2*C*d - B*e)))/((c*d^2 + a*e^2)^3*(d + e*x)) - (a*(B*c*d*(c*d^2 - 3*a*e^2) - (A*c - a*C)*e*(3*c*d^2 - a*e^2)) - c*(A*c*d*(c*d^2 - 3*a*e^2) - a*(c*d^2*(C*d - 3*B*e) - a*e^2*(3*C*d - B*e)))*x)/(2*a*(c*d^2 + a*e^2)^3*(a + c*x^2)) + (Sqrt[c]*(A*c*d*(c^2*d^4 + 10*a*c*d^2*e^2 - 15*a^2*e^4) - a*(2*a*c*d^2*e^2*(7*C*d - 9*B*e) - c^2*d^4*(C*d - 3*B*e) - 3*a^2*e^4*(3*C*d - B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*(c*d^2 + a*e^2)^4) + (e*(a^2*C*e^4 + c^2*(3*C*d^4 - 2*d^2*e*(3*B*d - 5*A*e)) - 2*a*c*e^2*(4*C*d^2 - e*(3*B*d - A*e)))*Log[d + e*x])/(c*d^2 + a*e^2)^4 - (e*(a^2*C*e^4 + c^2*(3*C*d^4 - 2*d^2*e*(3*B*d - 5*A*e)) - 2*a*c*e^2*(4*C*d^2 - e*(3*B*d - A*e)))*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^4)","A",6,5,27,0.1852,1,"{1647, 1629, 635, 205, 260}"
57,1,209,0,0.3044232,"\int \frac{(d+e x)^3 \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^3} \, dx","Int[((d + e*x)^3*(A + B*x + C*x^2))/(a + c*x^2)^3,x]","-\frac{(d+e x) \left(a e (3 a B e+5 a C d+3 A c d)-x \left(3 A c^2 d^2-a \left(4 a C e^2-c d (3 B e+C d)\right)\right)\right)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d^2 (3 a B e+a C d+3 A c d)+3 a e^2 (a B e+3 a C d+A c d)\right)}{8 a^{5/2} c^{5/2}}-\frac{(d+e x)^3 (a B-x (A c-a C))}{4 a c \left(a+c x^2\right)^2}+\frac{C e^3 \log \left(a+c x^2\right)}{2 c^3}","-\frac{(d+e x) \left(a e (3 a B e+5 a C d+3 A c d)-x \left(3 A c^2 d^2-a \left(4 a C e^2-c d (3 B e+C d)\right)\right)\right)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d^2 (3 a B e+a C d+3 A c d)+3 a e^2 (a B e+3 a C d+A c d)\right)}{8 a^{5/2} c^{5/2}}-\frac{(d+e x)^3 (a B-x (A c-a C))}{4 a c \left(a+c x^2\right)^2}+\frac{C e^3 \log \left(a+c x^2\right)}{2 c^3}",1,"-((a*B - (A*c - a*C)*x)*(d + e*x)^3)/(4*a*c*(a + c*x^2)^2) - ((d + e*x)*(a*e*(3*A*c*d + 5*a*C*d + 3*a*B*e) - (3*A*c^2*d^2 - a*(4*a*C*e^2 - c*d*(C*d + 3*B*e)))*x))/(8*a^2*c^2*(a + c*x^2)) + ((3*a*e^2*(A*c*d + 3*a*C*d + a*B*e) + c*d^2*(3*A*c*d + a*C*d + 3*a*B*e))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(5/2)) + (C*e^3*Log[a + c*x^2])/(2*c^3)","A",5,5,27,0.1852,1,"{1645, 819, 635, 205, 260}"
58,1,175,0,0.2306753,"\int \frac{(d+e x)^2 \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^3} \, dx","Int[((d + e*x)^2*(A + B*x + C*x^2))/(a + c*x^2)^3,x]","-\frac{x \left(a e^2 (3 a C+A c)-c d (2 a B e+a C d+3 A c d)\right)+2 a e (a B e+2 a C d+2 A c d)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d (2 a B e+a C d+3 A c d)+a e^2 (3 a C+A c)\right)}{8 a^{5/2} c^{5/2}}-\frac{(d+e x)^2 (a B-x (A c-a C))}{4 a c \left(a+c x^2\right)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d (2 a B e+a C d+3 A c d)+a e^2 (3 a C+A c)\right)}{8 a^{5/2} c^{5/2}}-\frac{(d+e x) (a e (3 a C+A c)-c x (2 a B e+a C d+3 A c d))}{8 a^2 c^2 \left(a+c x^2\right)}-\frac{(d+e x)^2 (a B-x (A c-a C))}{4 a c \left(a+c x^2\right)^2}",1,"-((a*B - (A*c - a*C)*x)*(d + e*x)^2)/(4*a*c*(a + c*x^2)^2) - (2*a*e*(2*A*c*d + 2*a*C*d + a*B*e) + (a*(A*c + 3*a*C)*e^2 - c*d*(3*A*c*d + a*C*d + 2*a*B*e))*x)/(8*a^2*c^2*(a + c*x^2)) + ((a*(A*c + 3*a*C)*e^2 + c*d*(3*A*c*d + a*C*d + 2*a*B*e))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(5/2))","A",3,3,27,0.1111,1,"{1645, 778, 205}"
59,1,130,0,0.107909,"\int \frac{(d+e x) \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^3} \, dx","Int[((d + e*x)*(A + B*x + C*x^2))/(a + c*x^2)^3,x]","-\frac{2 a e (a C+A c)-c x (a B e+a C d+3 A c d)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+a C d+3 A c d)}{8 a^{5/2} c^{3/2}}-\frac{(d+e x) (a B-x (A c-a C))}{4 a c \left(a+c x^2\right)^2}","-\frac{2 a e (a C+A c)-c x (a B e+a C d+3 A c d)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+a C d+3 A c d)}{8 a^{5/2} c^{3/2}}-\frac{(d+e x) (a B-x (A c-a C))}{4 a c \left(a+c x^2\right)^2}",1,"-((a*B - (A*c - a*C)*x)*(d + e*x))/(4*a*c*(a + c*x^2)^2) - (2*a*(A*c + a*C)*e - c*(3*A*c*d + a*C*d + a*B*e)*x)/(8*a^2*c^2*(a + c*x^2)) + ((3*A*c*d + a*C*d + a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(3/2))","A",3,3,25,0.1200,1,"{1645, 639, 205}"
60,1,98,0,0.0630782,"\int \frac{A+B x+C x^2}{\left(a+c x^2\right)^3} \, dx","Int[(A + B*x + C*x^2)/(a + c*x^2)^3,x]","\frac{(a C+3 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{3/2}}+\frac{x (a C+3 A c)}{8 a^2 c \left(a+c x^2\right)}-\frac{a B-x (A c-a C)}{4 a c \left(a+c x^2\right)^2}","\frac{(a C+3 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} c^{3/2}}+\frac{x (a C+3 A c)}{8 a^2 c \left(a+c x^2\right)}-\frac{a B-x (A c-a C)}{4 a c \left(a+c x^2\right)^2}",1,"-(a*B - (A*c - a*C)*x)/(4*a*c*(a + c*x^2)^2) + ((3*A*c + a*C)*x)/(8*a^2*c*(a + c*x^2)) + ((3*A*c + a*C)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(3/2))","A",4,4,20,0.2000,1,"{1814, 12, 199, 205}"
61,1,353,0,0.7343475,"\int \frac{A+B x+C x^2}{(d+e x) \left(a+c x^2\right)^3} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)*(a + c*x^2)^3),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right)+a \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right) (C d-B e)\right)}{8 a^{5/2} \sqrt{c} \left(a e^2+c d^2\right)^3}+\frac{4 a^2 e \left(A e^2-B d e+C d^2\right)+x \left(A c d \left(7 a e^2+3 c d^2\right)+a \left(c d^2-3 a e^2\right) (C d-B e)\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}-\frac{a (a C e-A c e+B c d)-c x (a B e-a C d+A c d)}{4 a c \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)}-\frac{e^3 \log \left(a+c x^2\right) \left(A e^2-B d e+C d^2\right)}{2 \left(a e^2+c d^2\right)^3}+\frac{e^3 \log (d+e x) \left(A e^2-B d e+C d^2\right)}{\left(a e^2+c d^2\right)^3}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right)+a \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right) (C d-B e)\right)}{8 a^{5/2} \sqrt{c} \left(a e^2+c d^2\right)^3}+\frac{4 a^2 e \left(A e^2-B d e+C d^2\right)+x \left(A c d \left(7 a e^2+3 c d^2\right)+a \left(c d^2-3 a e^2\right) (C d-B e)\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}-\frac{a (a C e-A c e+B c d)-c x (a B e-a C d+A c d)}{4 a c \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)}-\frac{e^3 \log \left(a+c x^2\right) \left(A e^2-B d e+C d^2\right)}{2 \left(a e^2+c d^2\right)^3}+\frac{e^3 \log (d+e x) \left(A e^2-B d e+C d^2\right)}{\left(a e^2+c d^2\right)^3}",1,"-(a*(B*c*d - A*c*e + a*C*e) - c*(A*c*d - a*C*d + a*B*e)*x)/(4*a*c*(c*d^2 + a*e^2)*(a + c*x^2)^2) + (4*a^2*e*(C*d^2 - B*d*e + A*e^2) + (a*(C*d - B*e)*(c*d^2 - 3*a*e^2) + A*c*d*(3*c*d^2 + 7*a*e^2))*x)/(8*a^2*(c*d^2 + a*e^2)^2*(a + c*x^2)) + ((a*(C*d - B*e)*(c^2*d^4 + 6*a*c*d^2*e^2 - 3*a^2*e^4) + A*c*d*(3*c^2*d^4 + 10*a*c*d^2*e^2 + 15*a^2*e^4))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[c]*(c*d^2 + a*e^2)^3) + (e^3*(C*d^2 - B*d*e + A*e^2)*Log[d + e*x])/(c*d^2 + a*e^2)^3 - (e^3*(C*d^2 - B*d*e + A*e^2)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^3)","A",7,6,27,0.2222,1,"{1647, 823, 801, 635, 205, 260}"
62,1,566,0,1.9247694,"\int \frac{A+B x+C x^2}{(d+e x)^2 \left(a+c x^2\right)^3} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^2*(a + c*x^2)^3),x]","\frac{x \left(A c \left(-7 a^2 e^4+12 a c d^2 e^2+3 c^2 d^4\right)+a \left(3 a^2 C e^4-2 a c d e^2 (6 C d-7 B e)+c^2 d^3 (C d-2 B e)\right)\right)+4 a^2 e \left(-a e^2 (2 C d-B e)-c d e (3 B d-4 A e)+2 c C d^3\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(3 A c \left(15 a^2 c d^2 e^4-5 a^3 e^6+5 a c^2 d^4 e^2+c^3 d^6\right)+a \left(-3 a^2 c d e^4 (11 C d-10 B e)+3 a^3 C e^6+a c^2 d^3 e^2 (13 C d-20 B e)+c^3 d^5 (C d-2 B e)\right)\right)}{8 a^{5/2} \sqrt{c} \left(a e^2+c d^2\right)^4}-\frac{a \left(-a B e^2+2 a C d e-2 A c d e+B c d^2\right)-x \left(A c \left(c d^2-a e^2\right)+a \left(a C e^2-c d (C d-2 B e)\right)\right)}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)^2}-\frac{e^3 \log \left(a+c x^2\right) \left(-a e^2 (2 C d-B e)-c d e (5 B d-6 A e)+4 c C d^3\right)}{2 \left(a e^2+c d^2\right)^4}-\frac{e^3 \left(A e^2-B d e+C d^2\right)}{(d+e x) \left(a e^2+c d^2\right)^3}+\frac{e^3 \log (d+e x) \left(-a e^2 (2 C d-B e)-c d e (5 B d-6 A e)+4 c C d^3\right)}{\left(a e^2+c d^2\right)^4}","-\frac{4 a^2 e \left(a e^2 (2 C d-B e)-c d \left(2 C d^2-e (3 B d-4 A e)\right)\right)-x \left(A c \left(-7 a^2 e^4+12 a c d^2 e^2+3 c^2 d^4\right)+a \left(3 a^2 C e^4-2 a c d e^2 (6 C d-7 B e)+c^2 d^3 (C d-2 B e)\right)\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(3 A c \left(15 a^2 c d^2 e^4-5 a^3 e^6+5 a c^2 d^4 e^2+c^3 d^6\right)+a \left(-3 a^2 c d e^4 (11 C d-10 B e)+3 a^3 C e^6+a c^2 d^3 e^2 (13 C d-20 B e)+c^3 d^5 (C d-2 B e)\right)\right)}{8 a^{5/2} \sqrt{c} \left(a e^2+c d^2\right)^4}-\frac{a \left(-a B e^2+2 a C d e-2 A c d e+B c d^2\right)-x \left(A c \left(c d^2-a e^2\right)+a \left(a C e^2-c d (C d-2 B e)\right)\right)}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)^2}+\frac{e^3 \log \left(a+c x^2\right) \left(a e^2 (2 C d-B e)-c d \left(4 C d^2-e (5 B d-6 A e)\right)\right)}{2 \left(a e^2+c d^2\right)^4}-\frac{e^3 \left(A e^2-B d e+C d^2\right)}{(d+e x) \left(a e^2+c d^2\right)^3}-\frac{e^3 \log (d+e x) \left(a e^2 (2 C d-B e)-c d \left(4 C d^2-e (5 B d-6 A e)\right)\right)}{\left(a e^2+c d^2\right)^4}",1,"-((e^3*(C*d^2 - B*d*e + A*e^2))/((c*d^2 + a*e^2)^3*(d + e*x))) - (a*(B*c*d^2 - 2*A*c*d*e + 2*a*C*d*e - a*B*e^2) - (A*c*(c*d^2 - a*e^2) + a*(a*C*e^2 - c*d*(C*d - 2*B*e)))*x)/(4*a*(c*d^2 + a*e^2)^2*(a + c*x^2)^2) + (4*a^2*e*(2*c*C*d^3 - c*d*e*(3*B*d - 4*A*e) - a*e^2*(2*C*d - B*e)) + (A*c*(3*c^2*d^4 + 12*a*c*d^2*e^2 - 7*a^2*e^4) + a*(3*a^2*C*e^4 - 2*a*c*d*e^2*(6*C*d - 7*B*e) + c^2*d^3*(C*d - 2*B*e)))*x)/(8*a^2*(c*d^2 + a*e^2)^3*(a + c*x^2)) + ((3*A*c*(c^3*d^6 + 5*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - 5*a^3*e^6) + a*(3*a^3*C*e^6 + a*c^2*d^3*e^2*(13*C*d - 20*B*e) - 3*a^2*c*d*e^4*(11*C*d - 10*B*e) + c^3*d^5*(C*d - 2*B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[c]*(c*d^2 + a*e^2)^4) + (e^3*(4*c*C*d^3 - c*d*e*(5*B*d - 6*A*e) - a*e^2*(2*C*d - B*e))*Log[d + e*x])/(c*d^2 + a*e^2)^4 - (e^3*(4*c*C*d^3 - c*d*e*(5*B*d - 6*A*e) - a*e^2*(2*C*d - B*e))*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^4)","A",7,5,27,0.1852,1,"{1647, 1629, 635, 205, 260}"
63,1,753,0,3.1425631,"\int \frac{A+B x+C x^2}{(d+e x)^3 \left(a+c x^2\right)^3} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^3*(a + c*x^2)^3),x]","\frac{c x \left(3 A c d \left(-11 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)-a \left(-7 a^2 e^4 (3 C d-B e)+2 a c d^2 e^2 (13 C d-19 B e)-c^2 d^4 (C d-3 B e)\right)\right)+4 a^2 e \left(a^2 C e^4-2 a c e^2 \left(4 C d^2-e (3 B d-A e)\right)+c^2 \left(3 C d^4-2 d^2 e (3 B d-5 A e)\right)\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^4}-\frac{e^3 \log \left(a+c x^2\right) \left(a^2 C e^4-a c e^2 \left(3 A e^2-9 B d e+13 C d^2\right)+c^2 \left(10 C d^4-3 d^2 e (5 B d-7 A e)\right)\right)}{2 \left(a e^2+c d^2\right)^5}+\frac{e^3 \log (d+e x) \left(a^2 C e^4-a c e^2 \left(3 A e^2-9 B d e+13 C d^2\right)+c^2 \left(10 C d^4-3 d^2 e (5 B d-7 A e)\right)\right)}{\left(a e^2+c d^2\right)^5}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(3 A c d \left(35 a^2 c d^2 e^4-35 a^3 e^6+7 a c^2 d^4 e^2+c^3 d^6\right)+a \left(-5 a^2 c d^2 e^4 (25 C d-27 B e)+15 a^3 e^6 (3 C d-B e)+a c^2 d^4 e^2 (23 C d-45 B e)+c^3 d^6 (C d-3 B e)\right)\right)}{8 a^{5/2} \left(a e^2+c d^2\right)^5}-\frac{a \left(B c d \left(c d^2-3 a e^2\right)-e (A c-a C) \left(3 c d^2-a e^2\right)\right)-c x \left(A c d \left(c d^2-3 a e^2\right)-a \left(c d^2 (C d-3 B e)-a e^2 (3 C d-B e)\right)\right)}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)^3}-\frac{e^3 \left(-a e^2 (2 C d-B e)-c d e (5 B d-6 A e)+4 c C d^3\right)}{(d+e x) \left(a e^2+c d^2\right)^4}-\frac{e^3 \left(A e^2-B d e+C d^2\right)}{2 (d+e x)^2 \left(a e^2+c d^2\right)^3}","\frac{c x \left(3 A c d \left(-11 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)-a \left(-7 a^2 e^4 (3 C d-B e)+2 a c d^2 e^2 (13 C d-19 B e)-c^2 d^4 (C d-3 B e)\right)\right)+4 a^2 e \left(a^2 C e^4-2 a c e^2 \left(4 C d^2-e (3 B d-A e)\right)+c^2 d^2 \left(3 C d^2-2 e (3 B d-5 A e)\right)\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^4}-\frac{e^3 \log \left(a+c x^2\right) \left(a^2 C e^4-a c e^2 \left(3 A e^2-9 B d e+13 C d^2\right)+c^2 d^2 \left(10 C d^2-3 e (5 B d-7 A e)\right)\right)}{2 \left(a e^2+c d^2\right)^5}+\frac{e^3 \log (d+e x) \left(a^2 C e^4-a c e^2 \left(3 A e^2-9 B d e+13 C d^2\right)+c^2 d^2 \left(10 C d^2-3 e (5 B d-7 A e)\right)\right)}{\left(a e^2+c d^2\right)^5}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(3 A c d \left(35 a^2 c d^2 e^4-35 a^3 e^6+7 a c^2 d^4 e^2+c^3 d^6\right)+a \left(-5 a^2 c d^2 e^4 (25 C d-27 B e)+15 a^3 e^6 (3 C d-B e)+a c^2 d^4 e^2 (23 C d-45 B e)+c^3 d^6 (C d-3 B e)\right)\right)}{8 a^{5/2} \left(a e^2+c d^2\right)^5}-\frac{a \left(B c d \left(c d^2-3 a e^2\right)-e (A c-a C) \left(3 c d^2-a e^2\right)\right)-c x \left(A c d \left(c d^2-3 a e^2\right)-a \left(c d^2 (C d-3 B e)-a e^2 (3 C d-B e)\right)\right)}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)^3}+\frac{e^3 \left(a e^2 (2 C d-B e)-c d \left(4 C d^2-e (5 B d-6 A e)\right)\right)}{(d+e x) \left(a e^2+c d^2\right)^4}-\frac{e^3 \left(A e^2-B d e+C d^2\right)}{2 (d+e x)^2 \left(a e^2+c d^2\right)^3}",1,"-(e^3*(C*d^2 - B*d*e + A*e^2))/(2*(c*d^2 + a*e^2)^3*(d + e*x)^2) - (e^3*(4*c*C*d^3 - c*d*e*(5*B*d - 6*A*e) - a*e^2*(2*C*d - B*e)))/((c*d^2 + a*e^2)^4*(d + e*x)) - (a*(B*c*d*(c*d^2 - 3*a*e^2) - (A*c - a*C)*e*(3*c*d^2 - a*e^2)) - c*(A*c*d*(c*d^2 - 3*a*e^2) - a*(c*d^2*(C*d - 3*B*e) - a*e^2*(3*C*d - B*e)))*x)/(4*a*(c*d^2 + a*e^2)^3*(a + c*x^2)^2) + (4*a^2*e*(a^2*C*e^4 + c^2*(3*C*d^4 - 2*d^2*e*(3*B*d - 5*A*e)) - 2*a*c*e^2*(4*C*d^2 - e*(3*B*d - A*e))) + c*(3*A*c*d*(c^2*d^4 + 6*a*c*d^2*e^2 - 11*a^2*e^4) - a*(2*a*c*d^2*e^2*(13*C*d - 19*B*e) - c^2*d^4*(C*d - 3*B*e) - 7*a^2*e^4*(3*C*d - B*e)))*x)/(8*a^2*(c*d^2 + a*e^2)^4*(a + c*x^2)) + (Sqrt[c]*(3*A*c*d*(c^3*d^6 + 7*a*c^2*d^4*e^2 + 35*a^2*c*d^2*e^4 - 35*a^3*e^6) + a*(a*c^2*d^4*e^2*(23*C*d - 45*B*e) - 5*a^2*c*d^2*e^4*(25*C*d - 27*B*e) + c^3*d^6*(C*d - 3*B*e) + 15*a^3*e^6*(3*C*d - B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*(c*d^2 + a*e^2)^5) + (e^3*(a^2*C*e^4 - a*c*e^2*(13*C*d^2 - 9*B*d*e + 3*A*e^2) + c^2*(10*C*d^4 - 3*d^2*e*(5*B*d - 7*A*e)))*Log[d + e*x])/(c*d^2 + a*e^2)^5 - (e^3*(a^2*C*e^4 - a*c*e^2*(13*C*d^2 - 9*B*d*e + 3*A*e^2) + c^2*(10*C*d^4 - 3*d^2*e*(5*B*d - 7*A*e)))*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^5)","A",7,5,27,0.1852,1,"{1647, 1629, 635, 205, 260}"
64,1,234,0,0.2914448,"\int \frac{(d+e x)^4 \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^4} \, dx","Int[((d + e*x)^4*(A + B*x + C*x^2))/(a + c*x^2)^4,x]","\frac{\left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d (4 a B e+a C d+5 A c d)+a e^2 (5 a C+A c)\right)}{16 a^{7/2} c^{7/2}}-\frac{(d+e x) (a e-c d x) \left(c d (4 a B e+a C d+5 A c d)+a e^2 (5 a C+A c)\right)}{16 a^3 c^3 \left(a+c x^2\right)}-\frac{(d+e x)^3 (a e (5 a C+A c)-c x (4 a B e+a C d+5 A c d))}{24 a^2 c^2 \left(a+c x^2\right)^2}-\frac{(d+e x)^4 (a B-x (A c-a C))}{6 a c \left(a+c x^2\right)^3}","\frac{\left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d (4 a B e+a C d+5 A c d)+a e^2 (5 a C+A c)\right)}{16 a^{7/2} c^{7/2}}-\frac{(d+e x) (a e-c d x) \left(c d (4 a B e+a C d+5 A c d)+a e^2 (5 a C+A c)\right)}{16 a^3 c^3 \left(a+c x^2\right)}-\frac{(d+e x)^3 (a e (5 a C+A c)-c x (4 a B e+a C d+5 A c d))}{24 a^2 c^2 \left(a+c x^2\right)^2}-\frac{(d+e x)^4 (a B-x (A c-a C))}{6 a c \left(a+c x^2\right)^3}",1,"-((a*B - (A*c - a*C)*x)*(d + e*x)^4)/(6*a*c*(a + c*x^2)^3) - ((d + e*x)^3*(a*(A*c + 5*a*C)*e - c*(5*A*c*d + a*C*d + 4*a*B*e)*x))/(24*a^2*c^2*(a + c*x^2)^2) - ((a*(A*c + 5*a*C)*e^2 + c*d*(5*A*c*d + a*C*d + 4*a*B*e))*(a*e - c*d*x)*(d + e*x))/(16*a^3*c^3*(a + c*x^2)) + ((c*d^2 + a*e^2)*(a*(A*c + 5*a*C)*e^2 + c*d*(5*A*c*d + a*C*d + 4*a*B*e))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*c^(7/2))","A",4,4,27,0.1481,1,"{1645, 805, 723, 205}"
65,1,288,0,0.541702,"\int \frac{(d+e x)^3 \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^4} \, dx","Int[((d + e*x)^3*(A + B*x + C*x^2))/(a + c*x^2)^4,x]","-\frac{4 a e \left(A c \left(a e^2+5 c d^2\right)+a \left(2 a C e^2+c d (3 B e+C d)\right)\right)-c x \left(A c d \left(15 c d^2-a e^2\right)+a \left(a e^2 (7 C d-3 B e)+3 c d^2 (3 B e+C d)\right)\right)}{48 a^3 c^3 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(3 a e^2+5 c d^2\right)+a \left(a e^2 (B e+3 C d)+c d^2 (3 B e+C d)\right)\right)}{16 a^{7/2} c^{5/2}}-\frac{(d+e x)^2 (2 a e (2 a C+A c)-c x (3 a B e+a C d+5 A c d))}{24 a^2 c^2 \left(a+c x^2\right)^2}-\frac{(d+e x)^3 (a B-x (A c-a C))}{6 a c \left(a+c x^2\right)^3}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(3 a e^2+5 c d^2\right)+a \left(a e^2 (B e+3 C d)+c d^2 (3 B e+C d)\right)\right)}{16 a^{7/2} c^{5/2}}-\frac{(d+e x) \left(a e (3 a B e+a C d+5 A c d)-x \left(3 c d (3 a B e+a C d+5 A c d)+4 a e^2 (2 a C+A c)\right)\right)}{48 a^3 c^2 \left(a+c x^2\right)}-\frac{(d+e x)^2 (2 a e (2 a C+A c)-c x (3 a B e+a C d+5 A c d))}{24 a^2 c^2 \left(a+c x^2\right)^2}-\frac{(d+e x)^3 (a B-x (A c-a C))}{6 a c \left(a+c x^2\right)^3}",1,"-((a*B - (A*c - a*C)*x)*(d + e*x)^3)/(6*a*c*(a + c*x^2)^3) - ((d + e*x)^2*(2*a*(A*c + 2*a*C)*e - c*(5*A*c*d + a*C*d + 3*a*B*e)*x))/(24*a^2*c^2*(a + c*x^2)^2) - (4*a*e*(A*c*(5*c*d^2 + a*e^2) + a*(2*a*C*e^2 + c*d*(C*d + 3*B*e))) - c*(A*c*d*(15*c*d^2 - a*e^2) + a*(a*e^2*(7*C*d - 3*B*e) + 3*c*d^2*(C*d + 3*B*e)))*x)/(48*a^3*c^3*(a + c*x^2)) + ((A*c*d*(5*c*d^2 + 3*a*e^2) + a*(a*e^2*(3*C*d + B*e) + c*d^2*(C*d + 3*B*e)))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*c^(5/2))","A",4,4,27,0.1481,1,"{1645, 821, 778, 205}"
66,1,225,0,0.3975081,"\int \frac{(d+e x)^2 \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^4} \, dx","Int[((d + e*x)^2*(A + B*x + C*x^2))/(a + c*x^2)^4,x]","\frac{x \left(c d (2 a B e+a C d+5 A c d)+a e^2 (a C+A c)\right)}{16 a^3 c^2 \left(a+c x^2\right)}-\frac{x \left(3 a e^2 (a C+A c)-c d (2 a B e+a C d+5 A c d)\right)+2 a e (a B e+2 a C d+4 A c d)}{24 a^2 c^2 \left(a+c x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d (2 a B e+a C d+5 A c d)+a e^2 (a C+A c)\right)}{16 a^{7/2} c^{5/2}}-\frac{(d+e x)^2 (a B-x (A c-a C))}{6 a c \left(a+c x^2\right)^3}","\frac{x \left(c d (2 a B e+a C d+5 A c d)+a e^2 (a C+A c)\right)}{16 a^3 c^2 \left(a+c x^2\right)}-\frac{x \left(3 a e^2 (a C+A c)-c d (2 a B e+a C d+5 A c d)\right)+2 a e (a B e+2 a C d+4 A c d)}{24 a^2 c^2 \left(a+c x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(c d (2 a B e+a C d+5 A c d)+a e^2 (a C+A c)\right)}{16 a^{7/2} c^{5/2}}-\frac{(d+e x)^2 (a B-x (A c-a C))}{6 a c \left(a+c x^2\right)^3}",1,"-((a*B - (A*c - a*C)*x)*(d + e*x)^2)/(6*a*c*(a + c*x^2)^3) - (2*a*e*(4*A*c*d + 2*a*C*d + a*B*e) + (3*a*(A*c + a*C)*e^2 - c*d*(5*A*c*d + a*C*d + 2*a*B*e))*x)/(24*a^2*c^2*(a + c*x^2)^2) + ((a*(A*c + a*C)*e^2 + c*d*(5*A*c*d + a*C*d + 2*a*B*e))*x)/(16*a^3*c^2*(a + c*x^2)) + ((a*(A*c + a*C)*e^2 + c*d*(5*A*c*d + a*C*d + 2*a*B*e))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*c^(5/2))","A",4,4,27,0.1481,1,"{1645, 778, 199, 205}"
67,1,165,0,0.1358093,"\int \frac{(d+e x) \left(A+B x+C x^2\right)}{\left(a+c x^2\right)^4} \, dx","Int[((d + e*x)*(A + B*x + C*x^2))/(a + c*x^2)^4,x]","-\frac{2 a e (a C+2 A c)-c x (a B e+a C d+5 A c d)}{24 a^2 c^2 \left(a+c x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+a C d+5 A c d)}{16 a^{7/2} c^{3/2}}+\frac{x (a B e+a C d+5 A c d)}{16 a^3 c \left(a+c x^2\right)}-\frac{(d+e x) (a B-x (A c-a C))}{6 a c \left(a+c x^2\right)^3}","-\frac{2 a e (a C+2 A c)-c x (a B e+a C d+5 A c d)}{24 a^2 c^2 \left(a+c x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+a C d+5 A c d)}{16 a^{7/2} c^{3/2}}+\frac{x (a B e+a C d+5 A c d)}{16 a^3 c \left(a+c x^2\right)}-\frac{(d+e x) (a B-x (A c-a C))}{6 a c \left(a+c x^2\right)^3}",1,"-((a*B - (A*c - a*C)*x)*(d + e*x))/(6*a*c*(a + c*x^2)^3) - (2*a*(2*A*c + a*C)*e - c*(5*A*c*d + a*C*d + a*B*e)*x)/(24*a^2*c^2*(a + c*x^2)^2) + ((5*A*c*d + a*C*d + a*B*e)*x)/(16*a^3*c*(a + c*x^2)) + ((5*A*c*d + a*C*d + a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*c^(3/2))","A",4,4,25,0.1600,1,"{1645, 639, 199, 205}"
68,1,126,0,0.078232,"\int \frac{A+B x+C x^2}{\left(a+c x^2\right)^4} \, dx","Int[(A + B*x + C*x^2)/(a + c*x^2)^4,x]","\frac{(a C+5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} c^{3/2}}+\frac{x (a C+5 A c)}{16 a^3 c \left(a+c x^2\right)}+\frac{x (a C+5 A c)}{24 a^2 c \left(a+c x^2\right)^2}-\frac{a B-x (A c-a C)}{6 a c \left(a+c x^2\right)^3}","\frac{(a C+5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{16 a^{7/2} c^{3/2}}+\frac{x (a C+5 A c)}{16 a^3 c \left(a+c x^2\right)}+\frac{x (a C+5 A c)}{24 a^2 c \left(a+c x^2\right)^2}-\frac{a B-x (A c-a C)}{6 a c \left(a+c x^2\right)^3}",1,"-(a*B - (A*c - a*C)*x)/(6*a*c*(a + c*x^2)^3) + ((5*A*c + a*C)*x)/(24*a^2*c*(a + c*x^2)^2) + ((5*A*c + a*C)*x)/(16*a^3*c*(a + c*x^2)) + ((5*A*c + a*C)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(16*a^(7/2)*c^(3/2))","A",5,4,20,0.2000,1,"{1814, 12, 199, 205}"
69,1,43,0,0.0500244,"\int \frac{x^3 \left(1+x+x^2\right)}{\left(1+x^2\right)^2} \, dx","Int[(x^3*(1 + x + x^2))/(1 + x^2)^2,x]","-\frac{x^3}{2 \left(x^2+1\right)}+\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+1\right)+\frac{3 x}{2}-\frac{3}{2} \tan ^{-1}(x)","-\frac{x^3}{2 \left(x^2+1\right)}+\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+1\right)+\frac{3 x}{2}-\frac{3}{2} \tan ^{-1}(x)",1,"(3*x)/2 + x^2/2 - x^3/(2*(1 + x^2)) - (3*ArcTan[x])/2 - Log[1 + x^2]/2","A",6,5,17,0.2941,1,"{1804, 801, 635, 203, 260}"
70,1,30,0,0.0395859,"\int \frac{x^2 \left(1+x+x^2\right)}{\left(1+x^2\right)^2} \, dx","Int[(x^2*(1 + x + x^2))/(1 + x^2)^2,x]","-\frac{x^2}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)+x-\tan ^{-1}(x)","-\frac{x^2}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)+x-\tan ^{-1}(x)",1,"x - x^2/(2*(1 + x^2)) - ArcTan[x] + Log[1 + x^2]/2","A",5,5,17,0.2941,1,"{1804, 774, 635, 203, 260}"
71,1,29,0,0.0247806,"\int \frac{x \left(1+x+x^2\right)}{\left(1+x^2\right)^2} \, dx","Int[(x*(1 + x + x^2))/(1 + x^2)^2,x]","-\frac{x}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{2} \tan ^{-1}(x)","-\frac{x}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{2} \tan ^{-1}(x)",1,"-x/(2*(1 + x^2)) + ArcTan[x]/2 + Log[1 + x^2]/2","A",4,4,15,0.2667,1,"{1804, 635, 203, 260}"
72,1,14,0,0.0109896,"\int \frac{1+x+x^2}{\left(1+x^2\right)^2} \, dx","Int[(1 + x + x^2)/(1 + x^2)^2,x]","\tan ^{-1}(x)-\frac{1}{2 \left(x^2+1\right)}","\tan ^{-1}(x)-\frac{1}{2 \left(x^2+1\right)}",1,"-1/(2*(1 + x^2)) + ArcTan[x]","A",3,3,14,0.2143,1,"{1814, 12, 203}"
73,1,31,0,0.0389849,"\int \frac{1+x+x^2}{x \left(1+x^2\right)^2} \, dx","Int[(1 + x + x^2)/(x*(1 + x^2)^2),x]","\frac{x}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)+\frac{1}{2} \tan ^{-1}(x)","\frac{x}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)+\frac{1}{2} \tan ^{-1}(x)",1,"x/(2*(1 + x^2)) + ArcTan[x]/2 + Log[x] - Log[1 + x^2]/2","A",6,5,17,0.2941,1,"{1805, 801, 635, 203, 260}"
74,1,33,0,0.0447255,"\int \frac{1+x+x^2}{x^2 \left(1+x^2\right)^2} \, dx","Int[(1 + x + x^2)/(x^2*(1 + x^2)^2),x]","\frac{1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{x}+\log (x)-\tan ^{-1}(x)","\frac{1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{x}+\log (x)-\tan ^{-1}(x)",1,"-x^(-1) + 1/(2*(1 + x^2)) - ArcTan[x] + Log[x] - Log[1 + x^2]/2","A",6,5,17,0.2941,1,"{1805, 801, 635, 203, 260}"
75,1,45,0,0.0633532,"\int \frac{1+x+x^2}{x^3 \left(1+x^2\right)^2} \, dx","Int[(1 + x + x^2)/(x^3*(1 + x^2)^2),x]","-\frac{x}{2 \left(x^2+1\right)}-\frac{1}{2 x^2}+\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{x}-\log (x)-\frac{3}{2} \tan ^{-1}(x)","-\frac{x}{2 \left(x^2+1\right)}-\frac{1}{2 x^2}+\frac{1}{2} \log \left(x^2+1\right)-\frac{1}{x}-\log (x)-\frac{3}{2} \tan ^{-1}(x)",1,"-1/(2*x^2) - x^(-1) - x/(2*(1 + x^2)) - (3*ArcTan[x])/2 - Log[x] + Log[1 + x^2]/2","A",6,5,17,0.2941,1,"{1805, 1802, 635, 203, 260}"
76,1,22,0,0.0071213,"\int \frac{1+2 x+x^2}{\left(1+x^2\right)^2} \, dx","Int[(1 + 2*x + x^2)/(1 + x^2)^2,x]","\tan ^{-1}(x)-\frac{(1-x) (x+1)}{2 \left(x^2+1\right)}","\tan ^{-1}(x)-\frac{1}{x^2+1}",1,"-((1 - x)*(1 + x))/(2*(1 + x^2)) + ArcTan[x]","A",3,3,16,0.1875,1,"{27, 723, 203}"
77,1,27,0,0.0139091,"\int \frac{2+12 x+3 x^2}{\left(4+x^2\right)^2} \, dx","Int[(2 + 12*x + 3*x^2)/(4 + x^2)^2,x]","\frac{7}{8} \tan ^{-1}\left(\frac{x}{2}\right)-\frac{5 x+24}{4 \left(x^2+4\right)}","\frac{7}{8} \tan ^{-1}\left(\frac{x}{2}\right)-\frac{5 x+24}{4 \left(x^2+4\right)}",1,"-(24 + 5*x)/(4*(4 + x^2)) + (7*ArcTan[x/2])/8","A",3,3,18,0.1667,1,"{1814, 12, 203}"
78,1,387,0,0.8296766,"\int (g+h x)^3 \sqrt{a+c x^2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^3*Sqrt[a + c*x^2]*(d + e*x + f*x^2),x]","\frac{\left(a+c x^2\right)^{3/2} \left(8 \left(8 a^2 f h^4-2 a c h^2 \left(7 h (d h+3 e g)+15 f g^2\right)-c^2 \left(3 f g^4-7 g^2 h (12 d h+e g)\right)\right)-3 c h x \left(a h^2 (35 e h+41 f g)-14 c g h (7 d h+e g)+6 c f g^3\right)\right)}{840 c^3 h}+\frac{x \sqrt{a+c x^2} \left(a^2 h^2 (e h+3 f g)-2 a c g \left(3 h (d h+e g)+f g^2\right)+8 c^2 d g^3\right)}{16 c^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(a^2 h^2 (e h+3 f g)-2 a c g \left(3 h (d h+e g)+f g^2\right)+8 c^2 d g^3\right)}{16 c^{5/2}}-\frac{\left(a+c x^2\right)^{3/2} (g+h x)^2 \left(8 a f h^2-7 c h (2 d h+e g)+3 c f g^2\right)}{70 c^2 h}-\frac{\left(a+c x^2\right)^{3/2} (g+h x)^3 (3 f g-7 e h)}{42 c h}+\frac{f \left(a+c x^2\right)^{3/2} (g+h x)^4}{7 c h}","\frac{\left(a+c x^2\right)^{3/2} \left(8 \left(8 a^2 f h^4-2 a c h^2 \left(7 h (d h+3 e g)+15 f g^2\right)-c^2 g^2 \left(3 f g^2-7 h (12 d h+e g)\right)\right)-3 c h x \left(a h^2 (35 e h+41 f g)+2 c g \left(3 f g^2-7 h (7 d h+e g)\right)\right)\right)}{840 c^3 h}+\frac{x \sqrt{a+c x^2} \left(a^2 h^2 (e h+3 f g)-2 a c g \left(3 h (d h+e g)+f g^2\right)+8 c^2 d g^3\right)}{16 c^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(a^2 h^2 (e h+3 f g)-2 a c g \left(3 h (d h+e g)+f g^2\right)+8 c^2 d g^3\right)}{16 c^{5/2}}-\frac{\left(a+c x^2\right)^{3/2} (g+h x)^2 \left(8 a f h^2+c \left(3 f g^2-7 h (2 d h+e g)\right)\right)}{70 c^2 h}-\frac{\left(a+c x^2\right)^{3/2} (g+h x)^3 (3 f g-7 e h)}{42 c h}+\frac{f \left(a+c x^2\right)^{3/2} (g+h x)^4}{7 c h}",1,"((8*c^2*d*g^3 + a^2*h^2*(3*f*g + e*h) - 2*a*c*g*(f*g^2 + 3*h*(e*g + d*h)))*x*Sqrt[a + c*x^2])/(16*c^2) - ((3*c*f*g^2 + 8*a*f*h^2 - 7*c*h*(e*g + 2*d*h))*(g + h*x)^2*(a + c*x^2)^(3/2))/(70*c^2*h) - ((3*f*g - 7*e*h)*(g + h*x)^3*(a + c*x^2)^(3/2))/(42*c*h) + (f*(g + h*x)^4*(a + c*x^2)^(3/2))/(7*c*h) + ((8*(8*a^2*f*h^4 - 2*a*c*h^2*(15*f*g^2 + 7*h*(3*e*g + d*h)) - c^2*(3*f*g^4 - 7*g^2*h*(e*g + 12*d*h))) - 3*c*h*(6*c*f*g^3 - 14*c*g*h*(e*g + 7*d*h) + a*h^2*(41*f*g + 35*e*h))*x)*(a + c*x^2)^(3/2))/(840*c^3*h) + (a*(8*c^2*d*g^3 + a^2*h^2*(3*f*g + e*h) - 2*a*c*g*(f*g^2 + 3*h*(e*g + d*h)))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(5/2))","A",7,6,29,0.2069,1,"{1654, 833, 780, 195, 217, 206}"
79,1,279,0,0.4980832,"\int (g+h x)^2 \sqrt{a+c x^2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^2*Sqrt[a + c*x^2]*(d + e*x + f*x^2),x]","\frac{x \sqrt{a+c x^2} \left(a^2 f h^2-2 a c \left(h (d h+2 e g)+f g^2\right)+8 c^2 d g^2\right)}{16 c^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(a^2 f h^2-2 a c \left(h (d h+2 e g)+f g^2\right)+8 c^2 d g^2\right)}{16 c^{5/2}}-\frac{\left(a+c x^2\right)^{3/2} \left(8 \left(2 a h^2 (e h+2 f g)-2 c g h (5 d h+e g)+c f g^3\right)-3 h x \left(5 h^2 (2 c d-a f)-2 c g (f g-2 e h)\right)\right)}{120 c^2 h}-\frac{\left(a+c x^2\right)^{3/2} (g+h x)^2 (f g-2 e h)}{10 c h}+\frac{f \left(a+c x^2\right)^{3/2} (g+h x)^3}{6 c h}","\frac{x \sqrt{a+c x^2} \left(a^2 f h^2-2 a c \left(h (d h+2 e g)+f g^2\right)+8 c^2 d g^2\right)}{16 c^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(a^2 f h^2-2 a c \left(h (d h+2 e g)+f g^2\right)+8 c^2 d g^2\right)}{16 c^{5/2}}-\frac{\left(a+c x^2\right)^{3/2} \left(8 \left(2 a h^2 (e h+2 f g)+c g \left(f g^2-2 h (5 d h+e g)\right)\right)-3 h x \left(5 h^2 (2 c d-a f)-2 c g (f g-2 e h)\right)\right)}{120 c^2 h}-\frac{\left(a+c x^2\right)^{3/2} (g+h x)^2 (f g-2 e h)}{10 c h}+\frac{f \left(a+c x^2\right)^{3/2} (g+h x)^3}{6 c h}",1,"((8*c^2*d*g^2 + a^2*f*h^2 - 2*a*c*(f*g^2 + h*(2*e*g + d*h)))*x*Sqrt[a + c*x^2])/(16*c^2) - ((f*g - 2*e*h)*(g + h*x)^2*(a + c*x^2)^(3/2))/(10*c*h) + (f*(g + h*x)^3*(a + c*x^2)^(3/2))/(6*c*h) - ((8*(c*f*g^3 - 2*c*g*h*(e*g + 5*d*h) + 2*a*h^2*(2*f*g + e*h)) - 3*h*(5*(2*c*d - a*f)*h^2 - 2*c*g*(f*g - 2*e*h))*x)*(a + c*x^2)^(3/2))/(120*c^2*h) + (a*(8*c^2*d*g^2 + a^2*f*h^2 - 2*a*c*(f*g^2 + h*(2*e*g + d*h)))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(5/2))","A",6,6,29,0.2069,1,"{1654, 833, 780, 195, 217, 206}"
80,1,175,0,0.2680633,"\int (g+h x) \sqrt{a+c x^2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)*Sqrt[a + c*x^2]*(d + e*x + f*x^2),x]","-\frac{\left(a+c x^2\right)^{3/2} \left(4 \left(2 a f h^2+c \left(3 f g^2-5 h (d h+e g)\right)\right)+3 c h x (3 f g-5 e h)\right)}{60 c^2 h}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (-a e h-a f g+4 c d g)}{8 c^{3/2}}+\frac{x \sqrt{a+c x^2} (4 c d g-a (e h+f g))}{8 c}+\frac{f \left(a+c x^2\right)^{3/2} (g+h x)^2}{5 c h}","-\frac{\left(a+c x^2\right)^{3/2} \left(4 \left(2 a f h^2+c \left(3 f g^2-5 h (d h+e g)\right)\right)+3 c h x (3 f g-5 e h)\right)}{60 c^2 h}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (-a e h-a f g+4 c d g)}{8 c^{3/2}}+\frac{x \sqrt{a+c x^2} (4 c d g-a (e h+f g))}{8 c}+\frac{f \left(a+c x^2\right)^{3/2} (g+h x)^2}{5 c h}",1,"((4*c*d*g - a*(f*g + e*h))*x*Sqrt[a + c*x^2])/(8*c) + (f*(g + h*x)^2*(a + c*x^2)^(3/2))/(5*c*h) - ((4*(2*a*f*h^2 + c*(3*f*g^2 - 5*h*(e*g + d*h))) + 3*c*h*(3*f*g - 5*e*h)*x)*(a + c*x^2)^(3/2))/(60*c^2*h) + (a*(4*c*d*g - a*f*g - a*e*h)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(3/2))","A",5,5,27,0.1852,1,"{1654, 780, 195, 217, 206}"
81,1,106,0,0.0642928,"\int \sqrt{a+c x^2} \left(d+e x+f x^2\right) \, dx","Int[Sqrt[a + c*x^2]*(d + e*x + f*x^2),x]","\frac{a (4 c d-a f) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}+\frac{x \sqrt{a+c x^2} (4 c d-a f)}{8 c}+\frac{e \left(a+c x^2\right)^{3/2}}{3 c}+\frac{f x \left(a+c x^2\right)^{3/2}}{4 c}","\frac{a (4 c d-a f) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}+\frac{x \sqrt{a+c x^2} (4 c d-a f)}{8 c}+\frac{e \left(a+c x^2\right)^{3/2}}{3 c}+\frac{f x \left(a+c x^2\right)^{3/2}}{4 c}",1,"((4*c*d - a*f)*x*Sqrt[a + c*x^2])/(8*c) + (e*(a + c*x^2)^(3/2))/(3*c) + (f*x*(a + c*x^2)^(3/2))/(4*c) + (a*(4*c*d - a*f)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(3/2))","A",5,5,22,0.2273,1,"{1815, 641, 195, 217, 206}"
82,1,206,0,0.3915783,"\int \frac{\sqrt{a+c x^2} \left(d+e x+f x^2\right)}{g+h x} \, dx","Int[(Sqrt[a + c*x^2]*(d + e*x + f*x^2))/(g + h*x),x]","\frac{\sqrt{a+c x^2} \left(2 \left(d h^2-e g h+f g^2\right)-h x (f g-e h)\right)}{2 h^3}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(\left(a h^2+2 c g^2\right) (f g-e h)+2 c d g h^2\right)}{2 \sqrt{c} h^4}-\frac{\sqrt{a h^2+c g^2} \left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right)}{h^4}+\frac{f \left(a+c x^2\right)^{3/2}}{3 c h}","\frac{\sqrt{a+c x^2} \left(2 \left(d h^2-e g h+f g^2\right)-h x (f g-e h)\right)}{2 h^3}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(\left(a h^2+2 c g^2\right) (f g-e h)+2 c d g h^2\right)}{2 \sqrt{c} h^4}-\frac{\sqrt{a h^2+c g^2} \left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right)}{h^4}+\frac{f \left(a+c x^2\right)^{3/2}}{3 c h}",1,"((2*(f*g^2 - e*g*h + d*h^2) - h*(f*g - e*h)*x)*Sqrt[a + c*x^2])/(2*h^3) + (f*(a + c*x^2)^(3/2))/(3*c*h) - ((2*c*d*g*h^2 + (f*g - e*h)*(2*c*g^2 + a*h^2))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*Sqrt[c]*h^4) - (Sqrt[c*g^2 + a*h^2]*(f*g^2 - e*g*h + d*h^2)*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/h^4","A",7,6,29,0.2069,1,"{1654, 815, 844, 217, 206, 725}"
83,1,303,0,0.5094023,"\int \frac{\sqrt{a+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^2} \, dx","Int[(Sqrt[a + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^2,x]","-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{h (g+h x) \left(a h^2+c g^2\right)}-\frac{\sqrt{a+c x^2} \left(2 \left(a h^2 (2 f g-e h)-c g h (2 e g-d h)+3 c f g^3\right)-h x \left(a f h^2-2 c h (e g-d h)+3 c f g^2\right)\right)}{2 h^3 \left(a h^2+c g^2\right)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(a f h^2-2 c h (2 e g-d h)+6 c f g^2\right)}{2 \sqrt{c} h^4}+\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a h^2 (2 f g-e h)-c g h (2 e g-d h)+3 c f g^3\right)}{h^4 \sqrt{a h^2+c g^2}}","-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{h (g+h x) \left(a h^2+c g^2\right)}-\frac{\sqrt{a+c x^2} \left(2 \left(a h^2 (2 f g-e h)+c g \left(3 f g^2-h (2 e g-d h)\right)\right)-h x \left(a f h^2+c \left(3 f g^2-2 h (e g-d h)\right)\right)\right)}{2 h^3 \left(a h^2+c g^2\right)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(a f h^2+2 c \left(3 f g^2-h (2 e g-d h)\right)\right)}{2 \sqrt{c} h^4}+\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a h^2 (2 f g-e h)+c g \left(3 f g^2-h (2 e g-d h)\right)\right)}{h^4 \sqrt{a h^2+c g^2}}",1,"-((2*(3*c*f*g^3 - c*g*h*(2*e*g - d*h) + a*h^2*(2*f*g - e*h)) - h*(3*c*f*g^2 + a*f*h^2 - 2*c*h*(e*g - d*h))*x)*Sqrt[a + c*x^2])/(2*h^3*(c*g^2 + a*h^2)) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(3/2))/(h*(c*g^2 + a*h^2)*(g + h*x)) + ((6*c*f*g^2 + a*f*h^2 - 2*c*h*(2*e*g - d*h))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*Sqrt[c]*h^4) + ((3*c*f*g^3 - c*g*h*(2*e*g - d*h) + a*h^2*(2*f*g - e*h))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(h^4*Sqrt[c*g^2 + a*h^2])","A",7,6,29,0.2069,1,"{1651, 815, 844, 217, 206, 725}"
84,1,295,0,0.5456893,"\int \frac{\sqrt{a+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^3} \, dx","Int[(Sqrt[a + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^3,x]","-\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(2 a^2 f h^4+a c h^2 \left(9 f g^2-h (3 e g-d h)\right)+2 c^2 g^3 (3 f g-e h)\right)}{2 h^4 \left(a h^2+c g^2\right)^{3/2}}-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{2 h (g+h x)^2 \left(a h^2+c g^2\right)}+\frac{\sqrt{a+c x^2} \left(h x \left(2 a f h^2-c h (e g-d h)+3 c f g^2\right)+2 \left(a h^2+c g^2\right) (3 f g-e h)\right)}{2 h^3 (g+h x) \left(a h^2+c g^2\right)}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (3 f g-e h)}{h^4}","-\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(2 a^2 f h^4+a c h^2 \left(9 f g^2-h (3 e g-d h)\right)+2 c^2 g^3 (3 f g-e h)\right)}{2 h^4 \left(a h^2+c g^2\right)^{3/2}}-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{2 h (g+h x)^2 \left(a h^2+c g^2\right)}+\frac{\sqrt{a+c x^2} \left(h x \left(2 a f h^2+c \left(3 f g^2-h (e g-d h)\right)\right)+2 \left(a h^2+c g^2\right) (3 f g-e h)\right)}{2 h^3 (g+h x) \left(a h^2+c g^2\right)}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (3 f g-e h)}{h^4}",1,"((2*(3*f*g - e*h)*(c*g^2 + a*h^2) + h*(3*c*f*g^2 + 2*a*f*h^2 - c*h*(e*g - d*h))*x)*Sqrt[a + c*x^2])/(2*h^3*(c*g^2 + a*h^2)*(g + h*x)) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(3/2))/(2*h*(c*g^2 + a*h^2)*(g + h*x)^2) - (Sqrt[c]*(3*f*g - e*h)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/h^4 - ((2*a^2*f*h^4 + 2*c^2*g^3*(3*f*g - e*h) + a*c*h^2*(9*f*g^2 - h*(3*e*g - d*h)))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(2*h^4*(c*g^2 + a*h^2)^(3/2))","A",7,6,29,0.2069,1,"{1651, 813, 844, 217, 206, 725}"
85,1,314,0,0.5054506,"\int \frac{\sqrt{a+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^4} \, dx","Int[(Sqrt[a + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^4,x]","-\frac{\sqrt{a+c x^2} \left(h x \left(2 a^2 f h^4+a c g h^2 (6 f g-e h)+c^2 \left(3 f g^4-d g^2 h^2\right)\right)+a^2 e h^5+a c g h^2 \left(d h^2+3 f g^2\right)+2 c^2 f g^5\right)}{2 h^3 (g+h x)^2 \left(a h^2+c g^2\right)^2}+\frac{c \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a^2 h^4 (4 f g-e h)+a c g h^2 \left(5 f g^2-d h^2\right)+2 c^2 f g^5\right)}{2 h^4 \left(a h^2+c g^2\right)^{5/2}}-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{3 h (g+h x)^3 \left(a h^2+c g^2\right)}+\frac{\sqrt{c} f \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{h^4}","-\frac{\sqrt{a+c x^2} \left(h x \left(2 a^2 f h^4+a c g h^2 (6 f g-e h)+c^2 \left(3 f g^4-d g^2 h^2\right)\right)+a^2 e h^5+a c g h^2 \left(d h^2+3 f g^2\right)+2 c^2 f g^5\right)}{2 h^3 (g+h x)^2 \left(a h^2+c g^2\right)^2}+\frac{c \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a^2 h^4 (4 f g-e h)+a c g h^2 \left(5 f g^2-d h^2\right)+2 c^2 f g^5\right)}{2 h^4 \left(a h^2+c g^2\right)^{5/2}}-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{3 h (g+h x)^3 \left(a h^2+c g^2\right)}+\frac{\sqrt{c} f \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{h^4}",1,"-((2*c^2*f*g^5 + a^2*e*h^5 + a*c*g*h^2*(3*f*g^2 + d*h^2) + h*(2*a^2*f*h^4 + a*c*g*h^2*(6*f*g - e*h) + c^2*(3*f*g^4 - d*g^2*h^2))*x)*Sqrt[a + c*x^2])/(2*h^3*(c*g^2 + a*h^2)^2*(g + h*x)^2) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(3/2))/(3*h*(c*g^2 + a*h^2)*(g + h*x)^3) + (Sqrt[c]*f*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/h^4 + (c*(2*c^2*f*g^5 + a^2*h^4*(4*f*g - e*h) + a*c*g*h^2*(5*f*g^2 - d*h^2))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(2*h^4*(c*g^2 + a*h^2)^(5/2))","A",7,6,29,0.2069,1,"{1651, 811, 844, 217, 206, 725}"
86,1,312,0,0.4288102,"\int \frac{\sqrt{a+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^5} \, dx","Int[(Sqrt[a + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^5,x]","-\frac{\sqrt{a+c x^2} (a h-c g x) \left(4 a^2 f h^2-a c \left(f g^2-h (5 e g-d h)\right)+4 c^2 d g^2\right)}{8 (g+h x)^2 \left(a h^2+c g^2\right)^3}-\frac{a c \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(4 a^2 f h^2-a c \left(f g^2-h (5 e g-d h)\right)+4 c^2 d g^2\right)}{8 \left(a h^2+c g^2\right)^{7/2}}+\frac{\left(a+c x^2\right)^{3/2} \left(4 a h^2 (2 f g-e h)+c g h (e g-5 d h)+3 c f g^3\right)}{12 h (g+h x)^3 \left(a h^2+c g^2\right)^2}-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{4 h (g+h x)^4 \left(a h^2+c g^2\right)}","-\frac{\sqrt{a+c x^2} (a h-c g x) \left(4 a^2 f h^2-a c \left(f g^2-h (5 e g-d h)\right)+4 c^2 d g^2\right)}{8 (g+h x)^2 \left(a h^2+c g^2\right)^3}-\frac{a c \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(4 a^2 f h^2-a c \left(f g^2-h (5 e g-d h)\right)+4 c^2 d g^2\right)}{8 \left(a h^2+c g^2\right)^{7/2}}+\frac{\left(a+c x^2\right)^{3/2} \left(4 a h^2 (2 f g-e h)+c g \left(h (e g-5 d h)+3 f g^2\right)\right)}{12 h (g+h x)^3 \left(a h^2+c g^2\right)^2}-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{4 h (g+h x)^4 \left(a h^2+c g^2\right)}",1,"-((4*c^2*d*g^2 + 4*a^2*f*h^2 - a*c*(f*g^2 - h*(5*e*g - d*h)))*(a*h - c*g*x)*Sqrt[a + c*x^2])/(8*(c*g^2 + a*h^2)^3*(g + h*x)^2) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(3/2))/(4*h*(c*g^2 + a*h^2)*(g + h*x)^4) + ((3*c*f*g^3 + c*g*h*(e*g - 5*d*h) + 4*a*h^2*(2*f*g - e*h))*(a + c*x^2)^(3/2))/(12*h*(c*g^2 + a*h^2)^2*(g + h*x)^3) - (a*c*(4*c^2*d*g^2 + 4*a^2*f*h^2 - a*c*(f*g^2 - h*(5*e*g - d*h)))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(8*(c*g^2 + a*h^2)^(7/2))","A",5,5,29,0.1724,1,"{1651, 807, 721, 725, 206}"
87,1,432,0,0.7426435,"\int \frac{\sqrt{a+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^6} \, dx","Int[(Sqrt[a + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^6,x]","-\frac{c \sqrt{a+c x^2} (a h-c g x) \left(a^2 h^2 (6 f g-e h)-a c g \left(f g^2-3 h (2 e g-d h)\right)+4 c^2 d g^3\right)}{8 (g+h x)^2 \left(a h^2+c g^2\right)^4}-\frac{\left(a+c x^2\right)^{3/2} \left(20 a^2 f h^4-a c h^2 \left(18 f g^2-h (33 e g-8 d h)\right)-c^2 \left(g^2 h (2 e g-27 d h)+3 f g^4\right)\right)}{60 h (g+h x)^3 \left(a h^2+c g^2\right)^3}-\frac{a c^2 \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a^2 h^2 (6 f g-e h)-a c g \left(f g^2-3 h (2 e g-d h)\right)+4 c^2 d g^3\right)}{8 \left(a h^2+c g^2\right)^{9/2}}+\frac{\left(a+c x^2\right)^{3/2} \left(5 a h^2 (2 f g-e h)+c g h (2 e g-7 d h)+3 c f g^3\right)}{20 h (g+h x)^4 \left(a h^2+c g^2\right)^2}-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{5 h (g+h x)^5 \left(a h^2+c g^2\right)}","-\frac{c \sqrt{a+c x^2} (a h-c g x) \left(a^2 h^2 (6 f g-e h)-a c g \left(f g^2-3 h (2 e g-d h)\right)+4 c^2 d g^3\right)}{8 (g+h x)^2 \left(a h^2+c g^2\right)^4}-\frac{\left(a+c x^2\right)^{3/2} \left(20 a^2 f h^4-a c h^2 \left(18 f g^2-h (33 e g-8 d h)\right)-c^2 g^2 \left(h (2 e g-27 d h)+3 f g^2\right)\right)}{60 h (g+h x)^3 \left(a h^2+c g^2\right)^3}-\frac{a c^2 \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a^2 h^2 (6 f g-e h)-a c g \left(f g^2-3 h (2 e g-d h)\right)+4 c^2 d g^3\right)}{8 \left(a h^2+c g^2\right)^{9/2}}+\frac{\left(a+c x^2\right)^{3/2} \left(5 a h^2 (2 f g-e h)+c g \left(h (2 e g-7 d h)+3 f g^2\right)\right)}{20 h (g+h x)^4 \left(a h^2+c g^2\right)^2}-\frac{\left(a+c x^2\right)^{3/2} \left(d h^2-e g h+f g^2\right)}{5 h (g+h x)^5 \left(a h^2+c g^2\right)}",1,"-(c*(4*c^2*d*g^3 + a^2*h^2*(6*f*g - e*h) - a*c*g*(f*g^2 - 3*h*(2*e*g - d*h)))*(a*h - c*g*x)*Sqrt[a + c*x^2])/(8*(c*g^2 + a*h^2)^4*(g + h*x)^2) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(3/2))/(5*h*(c*g^2 + a*h^2)*(g + h*x)^5) + ((3*c*f*g^3 + c*g*h*(2*e*g - 7*d*h) + 5*a*h^2*(2*f*g - e*h))*(a + c*x^2)^(3/2))/(20*h*(c*g^2 + a*h^2)^2*(g + h*x)^4) - ((20*a^2*f*h^4 - c^2*(3*f*g^4 + g^2*h*(2*e*g - 27*d*h)) - a*c*h^2*(18*f*g^2 - h*(33*e*g - 8*d*h)))*(a + c*x^2)^(3/2))/(60*h*(c*g^2 + a*h^2)^3*(g + h*x)^3) - (a*c^2*(4*c^2*d*g^3 + a^2*h^2*(6*f*g - e*h) - a*c*g*(f*g^2 - 3*h*(2*e*g - d*h)))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(8*(c*g^2 + a*h^2)^(9/2))","A",6,6,29,0.2069,1,"{1651, 835, 807, 721, 725, 206}"
88,1,462,0,1.1344299,"\int (g+h x)^3 \left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^3*(a + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{\left(a+c x^2\right)^{5/2} \left(4 \left(32 a^2 f h^4-8 a c h^2 \left(9 h (d h+3 e g)+17 f g^2\right)-c^2 \left(15 f g^4-9 g^2 h (64 d h+3 e g)\right)\right)-5 c h x \left(a h^2 (63 e h+61 f g)+2 c \left(5 f g^3-9 g h (12 d h+e g)\right)\right)\right)}{5040 c^3 h}+\frac{x \left(a+c x^2\right)^{3/2} \left(3 a^2 h^2 (e h+3 f g)-8 a c g \left(3 h (d h+e g)+f g^2\right)+48 c^2 d g^3\right)}{192 c^2}+\frac{a x \sqrt{a+c x^2} \left(3 a^2 h^2 (e h+3 f g)-8 a c g \left(3 h (d h+e g)+f g^2\right)+48 c^2 d g^3\right)}{128 c^2}+\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 h^2 (e h+3 f g)-8 a c g \left(3 h (d h+e g)+f g^2\right)+48 c^2 d g^3\right)}{128 c^{5/2}}+\frac{\left(a+c x^2\right)^{5/2} (g+h x)^2 \left(8 h^2 (9 c d-4 a f)-3 c g (5 f g-9 e h)\right)}{504 c^2 h}-\frac{\left(a+c x^2\right)^{5/2} (g+h x)^3 (5 f g-9 e h)}{72 c h}+\frac{f \left(a+c x^2\right)^{5/2} (g+h x)^4}{9 c h}","\frac{\left(a+c x^2\right)^{5/2} \left(4 \left(32 a^2 f h^4-8 a c h^2 \left(9 h (d h+3 e g)+17 f g^2\right)-3 c^2 g^2 \left(5 f g^2-3 h (64 d h+3 e g)\right)\right)-5 c h x \left(a h^2 (63 e h+61 f g)+2 c g \left(5 f g^2-9 h (12 d h+e g)\right)\right)\right)}{5040 c^3 h}+\frac{x \left(a+c x^2\right)^{3/2} \left(3 a^2 h^2 (e h+3 f g)-8 a c g \left(3 h (d h+e g)+f g^2\right)+48 c^2 d g^3\right)}{192 c^2}+\frac{a x \sqrt{a+c x^2} \left(3 a^2 h^2 (e h+3 f g)-8 a c g \left(3 h (d h+e g)+f g^2\right)+48 c^2 d g^3\right)}{128 c^2}+\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 h^2 (e h+3 f g)-8 a c g \left(3 h (d h+e g)+f g^2\right)+48 c^2 d g^3\right)}{128 c^{5/2}}+\frac{\left(a+c x^2\right)^{5/2} (g+h x)^2 \left(8 h^2 (9 c d-4 a f)-3 c g (5 f g-9 e h)\right)}{504 c^2 h}-\frac{\left(a+c x^2\right)^{5/2} (g+h x)^3 (5 f g-9 e h)}{72 c h}+\frac{f \left(a+c x^2\right)^{5/2} (g+h x)^4}{9 c h}",1,"(a*(48*c^2*d*g^3 + 3*a^2*h^2*(3*f*g + e*h) - 8*a*c*g*(f*g^2 + 3*h*(e*g + d*h)))*x*Sqrt[a + c*x^2])/(128*c^2) + ((48*c^2*d*g^3 + 3*a^2*h^2*(3*f*g + e*h) - 8*a*c*g*(f*g^2 + 3*h*(e*g + d*h)))*x*(a + c*x^2)^(3/2))/(192*c^2) + ((8*(9*c*d - 4*a*f)*h^2 - 3*c*g*(5*f*g - 9*e*h))*(g + h*x)^2*(a + c*x^2)^(5/2))/(504*c^2*h) - ((5*f*g - 9*e*h)*(g + h*x)^3*(a + c*x^2)^(5/2))/(72*c*h) + (f*(g + h*x)^4*(a + c*x^2)^(5/2))/(9*c*h) + ((4*(32*a^2*f*h^4 - 8*a*c*h^2*(17*f*g^2 + 9*h*(3*e*g + d*h)) - c^2*(15*f*g^4 - 9*g^2*h*(3*e*g + 64*d*h))) - 5*c*h*(a*h^2*(61*f*g + 63*e*h) + 2*c*(5*f*g^3 - 9*g*h*(e*g + 12*d*h)))*x)*(a + c*x^2)^(5/2))/(5040*c^3*h) + (a^2*(48*c^2*d*g^3 + 3*a^2*h^2*(3*f*g + e*h) - 8*a*c*g*(f*g^2 + 3*h*(e*g + d*h)))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(5/2))","A",8,6,29,0.2069,1,"{1654, 833, 780, 195, 217, 206}"
89,1,345,0,0.5243363,"\int (g+h x)^2 \left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^2*(a + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{x \left(a+c x^2\right)^{3/2} \left(3 a^2 f h^2-8 a c \left(h (d h+2 e g)+f g^2\right)+48 c^2 d g^2\right)}{192 c^2}+\frac{a x \sqrt{a+c x^2} \left(3 a^2 f h^2-8 a c \left(h (d h+2 e g)+f g^2\right)+48 c^2 d g^2\right)}{128 c^2}+\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 f h^2-8 a c \left(h (d h+2 e g)+f g^2\right)+48 c^2 d g^2\right)}{128 c^{5/2}}-\frac{\left(a+c x^2\right)^{5/2} \left(12 \left(8 a h^2 (e h+2 f g)-8 c g h (7 d h+e g)+5 c f g^3\right)-5 h x \left(7 h^2 (8 c d-3 a f)-2 c g (5 f g-8 e h)\right)\right)}{1680 c^2 h}-\frac{\left(a+c x^2\right)^{5/2} (g+h x)^2 (5 f g-8 e h)}{56 c h}+\frac{f \left(a+c x^2\right)^{5/2} (g+h x)^3}{8 c h}","\frac{x \left(a+c x^2\right)^{3/2} \left(3 a^2 f h^2-8 a c \left(h (d h+2 e g)+f g^2\right)+48 c^2 d g^2\right)}{192 c^2}+\frac{a x \sqrt{a+c x^2} \left(3 a^2 f h^2-8 a c \left(h (d h+2 e g)+f g^2\right)+48 c^2 d g^2\right)}{128 c^2}+\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 f h^2-8 a c \left(h (d h+2 e g)+f g^2\right)+48 c^2 d g^2\right)}{128 c^{5/2}}-\frac{\left(a+c x^2\right)^{5/2} \left(12 \left(8 a h^2 (e h+2 f g)+c g \left(5 f g^2-8 h (7 d h+e g)\right)\right)-5 h x \left(7 h^2 (8 c d-3 a f)-2 c g (5 f g-8 e h)\right)\right)}{1680 c^2 h}-\frac{\left(a+c x^2\right)^{5/2} (g+h x)^2 (5 f g-8 e h)}{56 c h}+\frac{f \left(a+c x^2\right)^{5/2} (g+h x)^3}{8 c h}",1,"(a*(48*c^2*d*g^2 + 3*a^2*f*h^2 - 8*a*c*(f*g^2 + h*(2*e*g + d*h)))*x*Sqrt[a + c*x^2])/(128*c^2) + ((48*c^2*d*g^2 + 3*a^2*f*h^2 - 8*a*c*(f*g^2 + h*(2*e*g + d*h)))*x*(a + c*x^2)^(3/2))/(192*c^2) - ((5*f*g - 8*e*h)*(g + h*x)^2*(a + c*x^2)^(5/2))/(56*c*h) + (f*(g + h*x)^3*(a + c*x^2)^(5/2))/(8*c*h) - ((12*(5*c*f*g^3 - 8*c*g*h*(e*g + 7*d*h) + 8*a*h^2*(2*f*g + e*h)) - 5*h*(7*(8*c*d - 3*a*f)*h^2 - 2*c*g*(5*f*g - 8*e*h))*x)*(a + c*x^2)^(5/2))/(1680*c^2*h) + (a^2*(48*c^2*d*g^2 + 3*a^2*f*h^2 - 8*a*c*(f*g^2 + h*(2*e*g + d*h)))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(5/2))","A",7,6,29,0.2069,1,"{1654, 833, 780, 195, 217, 206}"
90,1,212,0,0.2709137,"\int (g+h x) \left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)*(a + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (-a e h-a f g+6 c d g)}{16 c^{3/2}}-\frac{\left(a+c x^2\right)^{5/2} \left(6 \left(2 a f h^2-7 c h (d h+e g)+5 c f g^2\right)+5 c h x (5 f g-7 e h)\right)}{210 c^2 h}+\frac{x \left(a+c x^2\right)^{3/2} (6 c d g-a (e h+f g))}{24 c}+\frac{a x \sqrt{a+c x^2} (-a e h-a f g+6 c d g)}{16 c}+\frac{f \left(a+c x^2\right)^{5/2} (g+h x)^2}{7 c h}","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (-a e h-a f g+6 c d g)}{16 c^{3/2}}-\frac{\left(a+c x^2\right)^{5/2} \left(6 \left(2 a f h^2+c \left(5 f g^2-7 h (d h+e g)\right)\right)+5 c h x (5 f g-7 e h)\right)}{210 c^2 h}+\frac{x \left(a+c x^2\right)^{3/2} (6 c d g-a (e h+f g))}{24 c}+\frac{a x \sqrt{a+c x^2} (-a e h-a f g+6 c d g)}{16 c}+\frac{f \left(a+c x^2\right)^{5/2} (g+h x)^2}{7 c h}",1,"(a*(6*c*d*g - a*f*g - a*e*h)*x*Sqrt[a + c*x^2])/(16*c) + ((6*c*d*g - a*(f*g + e*h))*x*(a + c*x^2)^(3/2))/(24*c) + (f*(g + h*x)^2*(a + c*x^2)^(5/2))/(7*c*h) - ((6*(5*c*f*g^2 + 2*a*f*h^2 - 7*c*h*(e*g + d*h)) + 5*c*h*(5*f*g - 7*e*h)*x)*(a + c*x^2)^(5/2))/(210*c^2*h) + (a^2*(6*c*d*g - a*f*g - a*e*h)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(3/2))","A",6,5,27,0.1852,1,"{1654, 780, 195, 217, 206}"
91,1,137,0,0.0834329,"\int \left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Int[(a + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{a^2 (6 c d-a f) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}+\frac{x \left(a+c x^2\right)^{3/2} (6 c d-a f)}{24 c}+\frac{a x \sqrt{a+c x^2} (6 c d-a f)}{16 c}+\frac{e \left(a+c x^2\right)^{5/2}}{5 c}+\frac{f x \left(a+c x^2\right)^{5/2}}{6 c}","\frac{a^2 (6 c d-a f) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}+\frac{x \left(a+c x^2\right)^{3/2} (6 c d-a f)}{24 c}+\frac{a x \sqrt{a+c x^2} (6 c d-a f)}{16 c}+\frac{e \left(a+c x^2\right)^{5/2}}{5 c}+\frac{f x \left(a+c x^2\right)^{5/2}}{6 c}",1,"(a*(6*c*d - a*f)*x*Sqrt[a + c*x^2])/(16*c) + ((6*c*d - a*f)*x*(a + c*x^2)^(3/2))/(24*c) + (e*(a + c*x^2)^(5/2))/(5*c) + (f*x*(a + c*x^2)^(5/2))/(6*c) + (a^2*(6*c*d - a*f)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(3/2))","A",6,5,22,0.2273,1,"{1815, 641, 195, 217, 206}"
92,1,326,0,0.7661901,"\int \frac{\left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{g+h x} \, dx","Int[((a + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 h^4 (f g-e h)+12 a c g h^2 \left(f g^2-h (e g-d h)\right)+8 c^2 \left(f g^5-g^3 h (e g-d h)\right)\right)}{8 \sqrt{c} h^6}+\frac{\left(a+c x^2\right)^{3/2} \left(4 \left(d h^2-e g h+f g^2\right)-3 h x (f g-e h)\right)}{12 h^3}+\frac{\sqrt{a+c x^2} \left(8 \left(a h^2+c g^2\right) \left(d h^2-e g h+f g^2\right)-h x \left(\left(3 a h^2+4 c g^2\right) (f g-e h)+4 c d g h^2\right)\right)}{8 h^5}-\frac{\left(a h^2+c g^2\right)^{3/2} \left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right)}{h^6}+\frac{f \left(a+c x^2\right)^{5/2}}{5 c h}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 h^4 (f g-e h)+12 a c g h^2 \left(f g^2-h (e g-d h)\right)+8 c^2 g^3 \left(f g^2-h (e g-d h)\right)\right)}{8 \sqrt{c} h^6}+\frac{\left(a+c x^2\right)^{3/2} \left(4 \left(d h^2-e g h+f g^2\right)-3 h x (f g-e h)\right)}{12 h^3}+\frac{\sqrt{a+c x^2} \left(8 \left(a h^2+c g^2\right) \left(d h^2-e g h+f g^2\right)-h x \left(\left(3 a h^2+4 c g^2\right) (f g-e h)+4 c d g h^2\right)\right)}{8 h^5}-\frac{\left(a h^2+c g^2\right)^{3/2} \left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right)}{h^6}+\frac{f \left(a+c x^2\right)^{5/2}}{5 c h}",1,"((8*(c*g^2 + a*h^2)*(f*g^2 - e*g*h + d*h^2) - h*(4*c*d*g*h^2 + (f*g - e*h)*(4*c*g^2 + 3*a*h^2))*x)*Sqrt[a + c*x^2])/(8*h^5) + ((4*(f*g^2 - e*g*h + d*h^2) - 3*h*(f*g - e*h)*x)*(a + c*x^2)^(3/2))/(12*h^3) + (f*(a + c*x^2)^(5/2))/(5*c*h) - ((3*a^2*h^4*(f*g - e*h) + 12*a*c*g*h^2*(f*g^2 - h*(e*g - d*h)) + 8*c^2*(f*g^5 - g^3*h*(e*g - d*h)))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*Sqrt[c]*h^6) - ((c*g^2 + a*h^2)^(3/2)*(f*g^2 - e*g*h + d*h^2)*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/h^6","A",8,6,29,0.2069,1,"{1654, 815, 844, 217, 206, 725}"
93,1,428,0,0.9013897,"\int \frac{\left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^2} \, dx","Int[((a + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^2,x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 f h^4+12 a c h^2 \left(3 f g^2-h (2 e g-d h)\right)+8 c^2 \left(5 f g^4-g^2 h (4 e g-3 d h)\right)\right)}{8 \sqrt{c} h^6}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{h (g+h x) \left(a h^2+c g^2\right)}-\frac{\left(a+c x^2\right)^{3/2} \left(4 \left(a h^2 (2 f g-e h)-c g h (4 e g-3 d h)+5 c f g^3\right)-3 h x \left(a f h^2-4 c h (e g-d h)+5 c f g^2\right)\right)}{12 h^3 \left(a h^2+c g^2\right)}-\frac{\sqrt{a+c x^2} \left(8 \left(a h^2 (2 f g-e h)-c g h (4 e g-3 d h)+5 c f g^3\right)-h x \left(3 a f h^2+12 c d h^2-16 c e g h+20 c f g^2\right)\right)}{8 h^5}+\frac{\sqrt{a h^2+c g^2} \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a h^2 (2 f g-e h)-c g h (4 e g-3 d h)+5 c f g^3\right)}{h^6}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 f h^4+12 a c h^2 \left(3 f g^2-h (2 e g-d h)\right)+8 c^2 g^2 \left(5 f g^2-h (4 e g-3 d h)\right)\right)}{8 \sqrt{c} h^6}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{h (g+h x) \left(a h^2+c g^2\right)}-\frac{\left(a+c x^2\right)^{3/2} \left(4 \left(a h^2 (2 f g-e h)+c g \left(5 f g^2-h (4 e g-3 d h)\right)\right)-3 h x \left(a f h^2+c \left(5 f g^2-4 h (e g-d h)\right)\right)\right)}{12 h^3 \left(a h^2+c g^2\right)}-\frac{\sqrt{a+c x^2} \left(8 \left(a h^2 (2 f g-e h)+c g \left(5 f g^2-h (4 e g-3 d h)\right)\right)-h x \left(3 a f h^2+12 c d h^2-16 c e g h+20 c f g^2\right)\right)}{8 h^5}+\frac{\sqrt{a h^2+c g^2} \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a h^2 (2 f g-e h)+c g \left(5 f g^2-h (4 e g-3 d h)\right)\right)}{h^6}",1,"-((8*(5*c*f*g^3 - c*g*h*(4*e*g - 3*d*h) + a*h^2*(2*f*g - e*h)) - h*(20*c*f*g^2 - 16*c*e*g*h + 12*c*d*h^2 + 3*a*f*h^2)*x)*Sqrt[a + c*x^2])/(8*h^5) - ((4*(5*c*f*g^3 - c*g*h*(4*e*g - 3*d*h) + a*h^2*(2*f*g - e*h)) - 3*h*(5*c*f*g^2 + a*f*h^2 - 4*c*h*(e*g - d*h))*x)*(a + c*x^2)^(3/2))/(12*h^3*(c*g^2 + a*h^2)) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(5/2))/(h*(c*g^2 + a*h^2)*(g + h*x)) + ((3*a^2*f*h^4 + 8*c^2*(5*f*g^4 - g^2*h*(4*e*g - 3*d*h)) + 12*a*c*h^2*(3*f*g^2 - h*(2*e*g - d*h)))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*Sqrt[c]*h^6) + (Sqrt[c*g^2 + a*h^2]*(5*c*f*g^3 - c*g*h*(4*e*g - 3*d*h) + a*h^2*(2*f*g - e*h))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/h^6","A",8,6,29,0.2069,1,"{1651, 815, 844, 217, 206, 725}"
94,1,480,0,0.9210433,"\int \frac{\left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^3} \, dx","Int[((a + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^3,x]","\frac{\sqrt{a+c x^2} \left(2 a^2 f h^3-c x \left(a h^2 (7 f g-3 e h)-3 c g h (2 e g-d h)+10 c f g^3\right)+a c h \left(19 f g^2-3 h (3 e g-d h)\right)-2 c^2 g^2 \left(-3 d h+6 e g-\frac{10 f g^2}{h}\right)\right)}{2 h^4 \left(a h^2+c g^2\right)}-\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(2 a^2 f h^4+a c h^2 \left(19 f g^2-3 h (3 e g-d h)\right)+2 c^2 \left(10 f g^4-3 g^2 h (2 e g-d h)\right)\right)}{2 h^6 \sqrt{a h^2+c g^2}}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{2 h (g+h x)^2 \left(a h^2+c g^2\right)}-\frac{\left(a+c x^2\right)^{3/2} \left(2 \left(c g \left(-3 d h+6 e g-\frac{10 f g^2}{h}\right)-a h (7 f g-3 e h)\right)-x \left(2 a f h^2-3 c h (e g-d h)+5 c f g^2\right)\right)}{6 h^2 (g+h x) \left(a h^2+c g^2\right)}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a h^2 (3 f g-e h)-6 c g h (2 e g-d h)+20 c f g^3\right)}{2 h^6}","\frac{\sqrt{a+c x^2} \left(2 a^2 f h^4-c h x \left(a h^2 (7 f g-3 e h)+c g \left(10 f g^2-3 h (2 e g-d h)\right)\right)+a c h^2 \left(19 f g^2-3 h (3 e g-d h)\right)+2 c^2 g^2 \left(10 f g^2-3 h (2 e g-d h)\right)\right)}{2 h^5 \left(a h^2+c g^2\right)}-\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(2 a^2 f h^4+a c h^2 \left(19 f g^2-3 h (3 e g-d h)\right)+2 c^2 g^2 \left(10 f g^2-3 h (2 e g-d h)\right)\right)}{2 h^6 \sqrt{a h^2+c g^2}}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{2 h (g+h x)^2 \left(a h^2+c g^2\right)}-\frac{\left(a+c x^2\right)^{3/2} \left(2 \left(c g \left(-3 d h+6 e g-\frac{10 f g^2}{h}\right)-a h (7 f g-3 e h)\right)-x \left(2 a f h^2+c \left(5 f g^2-3 h (e g-d h)\right)\right)\right)}{6 h^2 (g+h x) \left(a h^2+c g^2\right)}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a h^2 (3 f g-e h)+2 c g \left(10 f g^2-3 h (2 e g-d h)\right)\right)}{2 h^6}",1,"((2*a^2*f*h^3 - 2*c^2*g^2*(6*e*g - (10*f*g^2)/h - 3*d*h) + a*c*h*(19*f*g^2 - 3*h*(3*e*g - d*h)) - c*(10*c*f*g^3 - 3*c*g*h*(2*e*g - d*h) + a*h^2*(7*f*g - 3*e*h))*x)*Sqrt[a + c*x^2])/(2*h^4*(c*g^2 + a*h^2)) - ((2*(c*g*(6*e*g - (10*f*g^2)/h - 3*d*h) - a*h*(7*f*g - 3*e*h)) - (5*c*f*g^2 + 2*a*f*h^2 - 3*c*h*(e*g - d*h))*x)*(a + c*x^2)^(3/2))/(6*h^2*(c*g^2 + a*h^2)*(g + h*x)) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(5/2))/(2*h*(c*g^2 + a*h^2)*(g + h*x)^2) - (Sqrt[c]*(20*c*f*g^3 - 6*c*g*h*(2*e*g - d*h) + 3*a*h^2*(3*f*g - e*h))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*h^6) - ((2*a^2*f*h^4 + 2*c^2*(10*f*g^4 - 3*g^2*h*(2*e*g - d*h)) + a*c*h^2*(19*f*g^2 - 3*h*(3*e*g - d*h)))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(2*h^6*Sqrt[c*g^2 + a*h^2])","A",8,7,29,0.2414,1,"{1651, 813, 815, 844, 217, 206, 725}"
95,1,469,0,0.844642,"\int \frac{\left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^4} \, dx","Int[((a + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^4,x]","\frac{c \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(3 a^2 h^4 (4 f g-e h)+3 a c g h^2 \left(11 f g^2-h (4 e g-d h)\right)+2 c^2 \left(10 f g^5-g^3 h (4 e g-d h)\right)\right)}{2 h^6 \left(a h^2+c g^2\right)^{3/2}}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{3 h (g+h x)^3 \left(a h^2+c g^2\right)}-\frac{\left(a+c x^2\right)^{3/2} \left(-x \left(3 a f h^2-2 c h (e g-d h)+5 c f g^2\right)-3 a h (3 f g-e h)+c g \left(-d h+4 e g-\frac{10 f g^2}{h}\right)\right)}{6 h^2 (g+h x)^2 \left(a h^2+c g^2\right)}-\frac{\sqrt{a+c x^2} \left(c h x \left(3 a h^2 (3 f g-e h)-c g h (4 e g-d h)+10 c f g^3\right)+\left(a h^2+c g^2\right) \left(3 a f h^2-2 c h (4 e g-d h)+20 c f g^2\right)\right)}{2 h^5 (g+h x) \left(a h^2+c g^2\right)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a f h^2-2 c h (4 e g-d h)+20 c f g^2\right)}{2 h^6}","\frac{c \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(3 a^2 h^4 (4 f g-e h)+3 a c g h^2 \left(11 f g^2-h (4 e g-d h)\right)+2 c^2 g^3 \left(10 f g^2-h (4 e g-d h)\right)\right)}{2 h^6 \left(a h^2+c g^2\right)^{3/2}}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{3 h (g+h x)^3 \left(a h^2+c g^2\right)}-\frac{\left(a+c x^2\right)^{3/2} \left(-x \left(3 a f h^2+c \left(5 f g^2-2 h (e g-d h)\right)\right)-3 a h (3 f g-e h)+c g \left(-d h+4 e g-\frac{10 f g^2}{h}\right)\right)}{6 h^2 (g+h x)^2 \left(a h^2+c g^2\right)}-\frac{\sqrt{a+c x^2} \left(c h x \left(3 a h^2 (3 f g-e h)+c g \left(10 f g^2-h (4 e g-d h)\right)\right)+\left(a h^2+c g^2\right) \left(3 a f h^2+2 c \left(10 f g^2-h (4 e g-d h)\right)\right)\right)}{2 h^5 (g+h x) \left(a h^2+c g^2\right)}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a f h^2+2 c \left(10 f g^2-h (4 e g-d h)\right)\right)}{2 h^6}",1,"-(((c*g^2 + a*h^2)*(20*c*f*g^2 + 3*a*f*h^2 - 2*c*h*(4*e*g - d*h)) + c*h*(10*c*f*g^3 - c*g*h*(4*e*g - d*h) + 3*a*h^2*(3*f*g - e*h))*x)*Sqrt[a + c*x^2])/(2*h^5*(c*g^2 + a*h^2)*(g + h*x)) - ((c*g*(4*e*g - (10*f*g^2)/h - d*h) - 3*a*h*(3*f*g - e*h) - (5*c*f*g^2 + 3*a*f*h^2 - 2*c*h*(e*g - d*h))*x)*(a + c*x^2)^(3/2))/(6*h^2*(c*g^2 + a*h^2)*(g + h*x)^2) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(5/2))/(3*h*(c*g^2 + a*h^2)*(g + h*x)^3) + (Sqrt[c]*(20*c*f*g^2 + 3*a*f*h^2 - 2*c*h*(4*e*g - d*h))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*h^6) + (c*(3*a^2*h^4*(4*f*g - e*h) + 3*a*c*g*h^2*(11*f*g^2 - h*(4*e*g - d*h)) + 2*c^2*(10*f*g^5 - g^3*h*(4*e*g - d*h)))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(2*h^6*(c*g^2 + a*h^2)^(3/2))","A",8,6,29,0.2069,1,"{1651, 813, 844, 217, 206, 725}"
96,1,511,0,1.0918985,"\int \frac{\left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^5} \, dx","Int[((a + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^5,x]","\frac{\left(a+c x^2\right)^{3/2} \left(-3 x \left(4 a^2 f h^4+a c h^2 \left(17 f g^2-h (5 e g-d h)\right)+2 c^2 \left(5 f g^4-g^2 h (d h+e g)\right)\right)+4 a^2 h^3 (f g-2 e h)-a c g h \left(25 f g^2-h (5 e g-9 d h)\right)-\frac{4 c^2 g^4 (5 f g-e h)}{h}\right)}{24 h^2 (g+h x)^3 \left(a h^2+c g^2\right)^2}+\frac{c \sqrt{a+c x^2} \left(h x \left(12 a^2 f h^4+a c h^2 \left(35 f g^2-h (7 e g-3 d h)\right)+4 c^2 g^3 (5 f g-e h)\right)+8 \left(a h^2+c g^2\right)^2 (5 f g-e h)\right)}{8 h^5 (g+h x) \left(a h^2+c g^2\right)^2}-\frac{c \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(3 a^2 c h^4 \left(25 f g^2-h (5 e g-d h)\right)+12 a^3 f h^6+20 a c^2 g^3 h^2 (5 f g-e h)+8 c^3 g^5 (5 f g-e h)\right)}{8 h^6 \left(a h^2+c g^2\right)^{5/2}}-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (5 f g-e h)}{h^6}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{4 h (g+h x)^4 \left(a h^2+c g^2\right)}","\frac{\left(a+c x^2\right)^{3/2} \left(-3 h x \left(4 a^2 f h^4+a c h^2 \left(17 f g^2-h (5 e g-d h)\right)+2 c^2 g^2 \left(5 f g^2-h (d h+e g)\right)\right)+4 a^2 h^4 (f g-2 e h)-a c g h^2 \left(25 f g^2-h (5 e g-9 d h)\right)-4 c^2 g^4 (5 f g-e h)\right)}{24 h^3 (g+h x)^3 \left(a h^2+c g^2\right)^2}+\frac{c \sqrt{a+c x^2} \left(h x \left(12 a^2 f h^4+a c h^2 \left(35 f g^2-h (7 e g-3 d h)\right)+4 c^2 g^3 (5 f g-e h)\right)+8 \left(a h^2+c g^2\right)^2 (5 f g-e h)\right)}{8 h^5 (g+h x) \left(a h^2+c g^2\right)^2}-\frac{c \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(3 a^2 c h^4 \left(25 f g^2-h (5 e g-d h)\right)+12 a^3 f h^6+20 a c^2 g^3 h^2 (5 f g-e h)+8 c^3 g^5 (5 f g-e h)\right)}{8 h^6 \left(a h^2+c g^2\right)^{5/2}}-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (5 f g-e h)}{h^6}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{4 h (g+h x)^4 \left(a h^2+c g^2\right)}",1,"(c*(8*(5*f*g - e*h)*(c*g^2 + a*h^2)^2 + h*(12*a^2*f*h^4 + 4*c^2*g^3*(5*f*g - e*h) + a*c*h^2*(35*f*g^2 - h*(7*e*g - 3*d*h)))*x)*Sqrt[a + c*x^2])/(8*h^5*(c*g^2 + a*h^2)^2*(g + h*x)) + ((4*a^2*h^3*(f*g - 2*e*h) - (4*c^2*g^4*(5*f*g - e*h))/h - a*c*g*h*(25*f*g^2 - h*(5*e*g - 9*d*h)) - 3*(4*a^2*f*h^4 + a*c*h^2*(17*f*g^2 - h*(5*e*g - d*h)) + 2*c^2*(5*f*g^4 - g^2*h*(e*g + d*h)))*x)*(a + c*x^2)^(3/2))/(24*h^2*(c*g^2 + a*h^2)^2*(g + h*x)^3) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(5/2))/(4*h*(c*g^2 + a*h^2)*(g + h*x)^4) - (c^(3/2)*(5*f*g - e*h)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/h^6 - (c*(12*a^3*f*h^6 + 8*c^3*g^5*(5*f*g - e*h) + 20*a*c^2*g^3*h^2*(5*f*g - e*h) + 3*a^2*c*h^4*(25*f*g^2 - h*(5*e*g - d*h)))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(8*h^6*(c*g^2 + a*h^2)^(5/2))","A",8,7,29,0.2414,1,"{1651, 811, 813, 844, 217, 206, 725}"
97,1,507,0,0.8599683,"\int \frac{\left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^6} \, dx","Int[((a + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^6,x]","-\frac{\left(a+c x^2\right)^{3/2} \left(h x \left(4 a^2 f h^4+a c g h^2 (14 f g-3 e h)+c^2 \left(7 f g^4-3 d g^2 h^2\right)\right)-a^2 h^4 (2 f g-3 e h)+a c g h^2 \left(3 d h^2+5 f g^2\right)+4 c^2 f g^5\right)}{12 h^3 (g+h x)^4 \left(a h^2+c g^2\right)^2}-\frac{c \sqrt{a+c x^2} \left(h x \left(a^2 c g h^4 (34 f g-3 e h)+8 a^3 f h^6+a c^2 g^2 h^2 \left(35 f g^2-3 d h^2\right)+12 c^3 f g^6\right)+a^2 c g h^4 \left(3 d h^2+13 f g^2\right)-a^3 h^6 (2 f g-3 e h)+20 a c^2 f g^5 h^2+8 c^3 f g^7\right)}{8 h^5 (g+h x)^2 \left(a h^2+c g^2\right)^3}+\frac{c^2 \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a^2 c g h^4 \left(35 f g^2-3 d h^2\right)+3 a^3 h^6 (6 f g-e h)+28 a c^2 f g^5 h^2+8 c^3 f g^7\right)}{8 h^6 \left(a h^2+c g^2\right)^{7/2}}+\frac{c^{3/2} f \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{h^6}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{5 h (g+h x)^5 \left(a h^2+c g^2\right)}","-\frac{\left(a+c x^2\right)^{3/2} \left(h x \left(4 a^2 f h^4+a c g h^2 (14 f g-3 e h)+c^2 \left(7 f g^4-3 d g^2 h^2\right)\right)-a^2 h^4 (2 f g-3 e h)+a c g h^2 \left(3 d h^2+5 f g^2\right)+4 c^2 f g^5\right)}{12 h^3 (g+h x)^4 \left(a h^2+c g^2\right)^2}-\frac{c \sqrt{a+c x^2} \left(h x \left(a^2 c g h^4 (34 f g-3 e h)+8 a^3 f h^6+a c^2 g^2 h^2 \left(35 f g^2-3 d h^2\right)+12 c^3 f g^6\right)+a^2 c g h^4 \left(3 d h^2+13 f g^2\right)-a^3 h^6 (2 f g-3 e h)+20 a c^2 f g^5 h^2+8 c^3 f g^7\right)}{8 h^5 (g+h x)^2 \left(a h^2+c g^2\right)^3}+\frac{c^2 \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a^2 c g h^4 \left(35 f g^2-3 d h^2\right)+3 a^3 h^6 (6 f g-e h)+28 a c^2 f g^5 h^2+8 c^3 f g^7\right)}{8 h^6 \left(a h^2+c g^2\right)^{7/2}}+\frac{c^{3/2} f \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{h^6}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{5 h (g+h x)^5 \left(a h^2+c g^2\right)}",1,"-(c*(8*c^3*f*g^7 + 20*a*c^2*f*g^5*h^2 - a^3*h^6*(2*f*g - 3*e*h) + a^2*c*g*h^4*(13*f*g^2 + 3*d*h^2) + h*(12*c^3*f*g^6 + 8*a^3*f*h^6 + a^2*c*g*h^4*(34*f*g - 3*e*h) + a*c^2*g^2*h^2*(35*f*g^2 - 3*d*h^2))*x)*Sqrt[a + c*x^2])/(8*h^5*(c*g^2 + a*h^2)^3*(g + h*x)^2) - ((4*c^2*f*g^5 - a^2*h^4*(2*f*g - 3*e*h) + a*c*g*h^2*(5*f*g^2 + 3*d*h^2) + h*(4*a^2*f*h^4 + a*c*g*h^2*(14*f*g - 3*e*h) + c^2*(7*f*g^4 - 3*d*g^2*h^2))*x)*(a + c*x^2)^(3/2))/(12*h^3*(c*g^2 + a*h^2)^2*(g + h*x)^4) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(5/2))/(5*h*(c*g^2 + a*h^2)*(g + h*x)^5) + (c^(3/2)*f*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/h^6 + (c^2*(8*c^3*f*g^7 + 28*a*c^2*f*g^5*h^2 + 3*a^3*h^6*(6*f*g - e*h) + a^2*c*g*h^4*(35*f*g^2 - 3*d*h^2))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(8*h^6*(c*g^2 + a*h^2)^(7/2))","A",8,6,29,0.2069,1,"{1651, 811, 844, 217, 206, 725}"
98,1,403,0,0.5522424,"\int \frac{\left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^7} \, dx","Int[((a + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^7,x]","-\frac{\left(a+c x^2\right)^{3/2} (a h-c g x) \left(6 a^2 f h^2-a c \left(f g^2-h (7 e g-d h)\right)+6 c^2 d g^2\right)}{24 (g+h x)^4 \left(a h^2+c g^2\right)^3}-\frac{a c \sqrt{a+c x^2} (a h-c g x) \left(6 a^2 f h^2-a c \left(f g^2-h (7 e g-d h)\right)+6 c^2 d g^2\right)}{16 (g+h x)^2 \left(a h^2+c g^2\right)^4}-\frac{a^2 c^2 \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(6 a^2 f h^2-a c \left(f g^2-h (7 e g-d h)\right)+6 c^2 d g^2\right)}{16 \left(a h^2+c g^2\right)^{9/2}}+\frac{\left(a+c x^2\right)^{5/2} \left(6 a h^2 (2 f g-e h)+c g h (e g-7 d h)+5 c f g^3\right)}{30 h (g+h x)^5 \left(a h^2+c g^2\right)^2}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{6 h (g+h x)^6 \left(a h^2+c g^2\right)}","-\frac{\left(a+c x^2\right)^{3/2} (a h-c g x) \left(6 a^2 f h^2-a c \left(f g^2-h (7 e g-d h)\right)+6 c^2 d g^2\right)}{24 (g+h x)^4 \left(a h^2+c g^2\right)^3}-\frac{a c \sqrt{a+c x^2} (a h-c g x) \left(6 a^2 f h^2-a c \left(f g^2-h (7 e g-d h)\right)+6 c^2 d g^2\right)}{16 (g+h x)^2 \left(a h^2+c g^2\right)^4}-\frac{a^2 c^2 \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(6 a^2 f h^2-a c \left(f g^2-h (7 e g-d h)\right)+6 c^2 d g^2\right)}{16 \left(a h^2+c g^2\right)^{9/2}}+\frac{\left(a+c x^2\right)^{5/2} \left(6 a h^2 (2 f g-e h)+c g \left(h (e g-7 d h)+5 f g^2\right)\right)}{30 h (g+h x)^5 \left(a h^2+c g^2\right)^2}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{6 h (g+h x)^6 \left(a h^2+c g^2\right)}",1,"-(a*c*(6*c^2*d*g^2 + 6*a^2*f*h^2 - a*c*(f*g^2 - h*(7*e*g - d*h)))*(a*h - c*g*x)*Sqrt[a + c*x^2])/(16*(c*g^2 + a*h^2)^4*(g + h*x)^2) - ((6*c^2*d*g^2 + 6*a^2*f*h^2 - a*c*(f*g^2 - h*(7*e*g - d*h)))*(a*h - c*g*x)*(a + c*x^2)^(3/2))/(24*(c*g^2 + a*h^2)^3*(g + h*x)^4) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(5/2))/(6*h*(c*g^2 + a*h^2)*(g + h*x)^6) + ((5*c*f*g^3 + c*g*h*(e*g - 7*d*h) + 6*a*h^2*(2*f*g - e*h))*(a + c*x^2)^(5/2))/(30*h*(c*g^2 + a*h^2)^2*(g + h*x)^5) - (a^2*c^2*(6*c^2*d*g^2 + 6*a^2*f*h^2 - a*c*(f*g^2 - h*(7*e*g - d*h)))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(16*(c*g^2 + a*h^2)^(9/2))","A",6,5,29,0.1724,1,"{1651, 807, 721, 725, 206}"
99,1,531,0,0.8887461,"\int \frac{\left(a+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^8} \, dx","Int[((a + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^8,x]","-\frac{a c^2 \sqrt{a+c x^2} (a h-c g x) \left(a^2 h^2 (8 f g-e h)-a c g \left(f g^2-h (8 e g-3 d h)\right)+6 c^2 d g^3\right)}{16 (g+h x)^2 \left(a h^2+c g^2\right)^5}-\frac{c \left(a+c x^2\right)^{3/2} (a h-c g x) \left(a^2 h^2 (8 f g-e h)-a c g \left(f g^2-h (8 e g-3 d h)\right)+6 c^2 d g^3\right)}{24 (g+h x)^4 \left(a h^2+c g^2\right)^4}-\frac{\left(a+c x^2\right)^{5/2} \left(42 a^2 f h^4-a c h^2 \left(26 f g^2-h (61 e g-12 d h)\right)-c^2 \left(g^2 h (2 e g-51 d h)+5 f g^4\right)\right)}{210 h (g+h x)^5 \left(a h^2+c g^2\right)^3}-\frac{a^2 c^3 \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a^2 h^2 (8 f g-e h)-a c g \left(f g^2-h (8 e g-3 d h)\right)+6 c^2 d g^3\right)}{16 \left(a h^2+c g^2\right)^{11/2}}+\frac{\left(a+c x^2\right)^{5/2} \left(7 a h^2 (2 f g-e h)+c g h (2 e g-9 d h)+5 c f g^3\right)}{42 h (g+h x)^6 \left(a h^2+c g^2\right)^2}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{7 h (g+h x)^7 \left(a h^2+c g^2\right)}","-\frac{a c^2 \sqrt{a+c x^2} (a h-c g x) \left(a^2 h^2 (8 f g-e h)-a c g \left(f g^2-h (8 e g-3 d h)\right)+6 c^2 d g^3\right)}{16 (g+h x)^2 \left(a h^2+c g^2\right)^5}-\frac{c \left(a+c x^2\right)^{3/2} (a h-c g x) \left(a^2 h^2 (8 f g-e h)-a c g \left(f g^2-h (8 e g-3 d h)\right)+6 c^2 d g^3\right)}{24 (g+h x)^4 \left(a h^2+c g^2\right)^4}-\frac{\left(a+c x^2\right)^{5/2} \left(42 a^2 f h^4-a c h^2 \left(26 f g^2-h (61 e g-12 d h)\right)-c^2 g^2 \left(h (2 e g-51 d h)+5 f g^2\right)\right)}{210 h (g+h x)^5 \left(a h^2+c g^2\right)^3}-\frac{a^2 c^3 \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a^2 h^2 (8 f g-e h)-a c g \left(f g^2-h (8 e g-3 d h)\right)+6 c^2 d g^3\right)}{16 \left(a h^2+c g^2\right)^{11/2}}+\frac{\left(a+c x^2\right)^{5/2} \left(7 a h^2 (2 f g-e h)+c g \left(h (2 e g-9 d h)+5 f g^2\right)\right)}{42 h (g+h x)^6 \left(a h^2+c g^2\right)^2}-\frac{\left(a+c x^2\right)^{5/2} \left(d h^2-e g h+f g^2\right)}{7 h (g+h x)^7 \left(a h^2+c g^2\right)}",1,"-(a*c^2*(6*c^2*d*g^3 + a^2*h^2*(8*f*g - e*h) - a*c*g*(f*g^2 - h*(8*e*g - 3*d*h)))*(a*h - c*g*x)*Sqrt[a + c*x^2])/(16*(c*g^2 + a*h^2)^5*(g + h*x)^2) - (c*(6*c^2*d*g^3 + a^2*h^2*(8*f*g - e*h) - a*c*g*(f*g^2 - h*(8*e*g - 3*d*h)))*(a*h - c*g*x)*(a + c*x^2)^(3/2))/(24*(c*g^2 + a*h^2)^4*(g + h*x)^4) - ((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(5/2))/(7*h*(c*g^2 + a*h^2)*(g + h*x)^7) + ((5*c*f*g^3 + c*g*h*(2*e*g - 9*d*h) + 7*a*h^2*(2*f*g - e*h))*(a + c*x^2)^(5/2))/(42*h*(c*g^2 + a*h^2)^2*(g + h*x)^6) - ((42*a^2*f*h^4 - c^2*(5*f*g^4 + g^2*h*(2*e*g - 51*d*h)) - a*c*h^2*(26*f*g^2 - h*(61*e*g - 12*d*h)))*(a + c*x^2)^(5/2))/(210*h*(c*g^2 + a*h^2)^3*(g + h*x)^5) - (a^2*c^3*(6*c^2*d*g^3 + a^2*h^2*(8*f*g - e*h) - a*c*g*(f*g^2 - h*(8*e*g - 3*d*h)))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(16*(c*g^2 + a*h^2)^(11/2))","A",7,6,29,0.2069,1,"{1651, 835, 807, 721, 725, 206}"
100,1,168,0,0.1016822,"\int \left(a+c x^2\right)^{5/2} \left(A+B x+C x^2\right) \, dx","Int[(a + c*x^2)^(5/2)*(A + B*x + C*x^2),x]","\frac{5 a^3 (8 A c-a C) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}+\frac{5 a^2 x \sqrt{a+c x^2} (8 A c-a C)}{128 c}+\frac{x \left(a+c x^2\right)^{5/2} (8 A c-a C)}{48 c}+\frac{5 a x \left(a+c x^2\right)^{3/2} (8 A c-a C)}{192 c}+\frac{B \left(a+c x^2\right)^{7/2}}{7 c}+\frac{C x \left(a+c x^2\right)^{7/2}}{8 c}","\frac{5 a^3 (8 A c-a C) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}+\frac{5 a^2 x \sqrt{a+c x^2} (8 A c-a C)}{128 c}+\frac{x \left(a+c x^2\right)^{5/2} (8 A c-a C)}{48 c}+\frac{5 a x \left(a+c x^2\right)^{3/2} (8 A c-a C)}{192 c}+\frac{B \left(a+c x^2\right)^{7/2}}{7 c}+\frac{C x \left(a+c x^2\right)^{7/2}}{8 c}",1,"(5*a^2*(8*A*c - a*C)*x*Sqrt[a + c*x^2])/(128*c) + (5*a*(8*A*c - a*C)*x*(a + c*x^2)^(3/2))/(192*c) + ((8*A*c - a*C)*x*(a + c*x^2)^(5/2))/(48*c) + (B*(a + c*x^2)^(7/2))/(7*c) + (C*x*(a + c*x^2)^(7/2))/(8*c) + (5*a^3*(8*A*c - a*C)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(3/2))","A",7,5,22,0.2273,1,"{1815, 641, 195, 217, 206}"
101,1,323,0,0.6643877,"\int \frac{(g+h x)^3 \left(d+e x+f x^2\right)}{\sqrt{a+c x^2}} \, dx","Int[((g + h*x)^3*(d + e*x + f*x^2))/Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} \left(4 \left(16 a^2 f h^4-4 a c h^2 \left(5 h (d h+3 e g)+13 f g^2\right)-c^2 g^2 \left(3 f g^2-5 h (16 d h+3 e g)\right)\right)-c h x \left(a h^2 (45 e h+71 f g)-10 c g h (10 d h+3 e g)+6 c f g^3\right)\right)}{120 c^3 h}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 h^2 (e h+3 f g)-4 a c g \left(3 h (d h+e g)+f g^2\right)+8 c^2 d g^3\right)}{8 c^{5/2}}+\frac{\sqrt{a+c x^2} (g+h x)^2 \left(4 h^2 (5 c d-4 a f)-3 c g (f g-5 e h)\right)}{60 c^2 h}-\frac{\sqrt{a+c x^2} (g+h x)^3 (f g-5 e h)}{20 c h}+\frac{f \sqrt{a+c x^2} (g+h x)^4}{5 c h}","\frac{\sqrt{a+c x^2} \left(4 \left(16 a^2 f h^4-4 a c h^2 \left(5 h (d h+3 e g)+13 f g^2\right)-c^2 g^2 \left(3 f g^2-5 h (16 d h+3 e g)\right)\right)-c h x \left(a h^2 (45 e h+71 f g)+2 c g \left(3 f g^2-5 h (10 d h+3 e g)\right)\right)\right)}{120 c^3 h}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 h^2 (e h+3 f g)-4 a c g \left(3 h (d h+e g)+f g^2\right)+8 c^2 d g^3\right)}{8 c^{5/2}}+\frac{\sqrt{a+c x^2} (g+h x)^2 \left(4 h^2 (5 c d-4 a f)-3 c g (f g-5 e h)\right)}{60 c^2 h}-\frac{\sqrt{a+c x^2} (g+h x)^3 (f g-5 e h)}{20 c h}+\frac{f \sqrt{a+c x^2} (g+h x)^4}{5 c h}",1,"((4*(5*c*d - 4*a*f)*h^2 - 3*c*g*(f*g - 5*e*h))*(g + h*x)^2*Sqrt[a + c*x^2])/(60*c^2*h) - ((f*g - 5*e*h)*(g + h*x)^3*Sqrt[a + c*x^2])/(20*c*h) + (f*(g + h*x)^4*Sqrt[a + c*x^2])/(5*c*h) + ((4*(16*a^2*f*h^4 - 4*a*c*h^2*(13*f*g^2 + 5*h*(3*e*g + d*h)) - c^2*g^2*(3*f*g^2 - 5*h*(3*e*g + 16*d*h))) - c*h*(6*c*f*g^3 - 10*c*g*h*(3*e*g + 10*d*h) + a*h^2*(71*f*g + 45*e*h))*x)*Sqrt[a + c*x^2])/(120*c^3*h) + ((8*c^2*d*g^3 + 3*a^2*h^2*(3*f*g + e*h) - 4*a*c*g*(f*g^2 + 3*h*(e*g + d*h)))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(5/2))","A",6,5,29,0.1724,1,"{1654, 833, 780, 217, 206}"
102,1,222,0,0.3720309,"\int \frac{(g+h x)^2 \left(d+e x+f x^2\right)}{\sqrt{a+c x^2}} \, dx","Int[((g + h*x)^2*(d + e*x + f*x^2))/Sqrt[a + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 f h^2-4 a c \left(h (d h+2 e g)+f g^2\right)+8 c^2 d g^2\right)}{8 c^{5/2}}-\frac{\sqrt{a+c x^2} \left(4 \left(4 a h^2 (e h+2 f g)-4 c g h (3 d h+e g)+c f g^3\right)-h x \left(3 h^2 (4 c d-3 a f)-2 c g (f g-4 e h)\right)\right)}{24 c^2 h}-\frac{\sqrt{a+c x^2} (g+h x)^2 (f g-4 e h)}{12 c h}+\frac{f \sqrt{a+c x^2} (g+h x)^3}{4 c h}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a^2 f h^2-4 a c \left(h (d h+2 e g)+f g^2\right)+8 c^2 d g^2\right)}{8 c^{5/2}}-\frac{\sqrt{a+c x^2} \left(4 \left(4 a h^2 (e h+2 f g)+c g \left(f g^2-4 h (3 d h+e g)\right)\right)-h x \left(3 h^2 (4 c d-3 a f)-2 c g (f g-4 e h)\right)\right)}{24 c^2 h}-\frac{\sqrt{a+c x^2} (g+h x)^2 (f g-4 e h)}{12 c h}+\frac{f \sqrt{a+c x^2} (g+h x)^3}{4 c h}",1,"-((f*g - 4*e*h)*(g + h*x)^2*Sqrt[a + c*x^2])/(12*c*h) + (f*(g + h*x)^3*Sqrt[a + c*x^2])/(4*c*h) - ((4*(c*f*g^3 - 4*c*g*h*(e*g + 3*d*h) + 4*a*h^2*(2*f*g + e*h)) - h*(3*(4*c*d - 3*a*f)*h^2 - 2*c*g*(f*g - 4*e*h))*x)*Sqrt[a + c*x^2])/(24*c^2*h) + ((8*c^2*d*g^2 + 3*a^2*f*h^2 - 4*a*c*(f*g^2 + h*(2*e*g + d*h)))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(5/2))","A",5,5,29,0.1724,1,"{1654, 833, 780, 217, 206}"
103,1,135,0,0.1787726,"\int \frac{(g+h x) \left(d+e x+f x^2\right)}{\sqrt{a+c x^2}} \, dx","Int[((g + h*x)*(d + e*x + f*x^2))/Sqrt[a + c*x^2],x]","-\frac{\sqrt{a+c x^2} \left(2 \left(2 a f h^2-3 c h (d h+e g)+c f g^2\right)+c h x (f g-3 e h)\right)}{6 c^2 h}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (2 c d g-a (e h+f g))}{2 c^{3/2}}+\frac{f \sqrt{a+c x^2} (g+h x)^2}{3 c h}","-\frac{\sqrt{a+c x^2} \left(2 \left(2 a f h^2+c \left(f g^2-3 h (d h+e g)\right)\right)+c h x (f g-3 e h)\right)}{6 c^2 h}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (2 c d g-a (e h+f g))}{2 c^{3/2}}+\frac{f \sqrt{a+c x^2} (g+h x)^2}{3 c h}",1,"(f*(g + h*x)^2*Sqrt[a + c*x^2])/(3*c*h) - ((2*(c*f*g^2 + 2*a*f*h^2 - 3*c*h*(e*g + d*h)) + c*h*(f*g - 3*e*h)*x)*Sqrt[a + c*x^2])/(6*c^2*h) + ((2*c*d*g - a*(f*g + e*h))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2))","A",4,4,27,0.1481,1,"{1654, 780, 217, 206}"
104,1,74,0,0.0483364,"\int \frac{d+e x+f x^2}{\sqrt{a+c x^2}} \, dx","Int[(d + e*x + f*x^2)/Sqrt[a + c*x^2],x]","\frac{(2 c d-a f) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2}}+\frac{e \sqrt{a+c x^2}}{c}+\frac{f x \sqrt{a+c x^2}}{2 c}","\frac{(2 c d-a f) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2}}+\frac{e \sqrt{a+c x^2}}{c}+\frac{f x \sqrt{a+c x^2}}{2 c}",1,"(e*Sqrt[a + c*x^2])/c + (f*x*Sqrt[a + c*x^2])/(2*c) + ((2*c*d - a*f)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2))","A",4,4,22,0.1818,1,"{1815, 641, 217, 206}"
105,1,130,0,0.1743463,"\int \frac{d+e x+f x^2}{(g+h x) \sqrt{a+c x^2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)*Sqrt[a + c*x^2]),x]","-\frac{\left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right)}{h^2 \sqrt{a h^2+c g^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (f g-e h)}{\sqrt{c} h^2}+\frac{f \sqrt{a+c x^2}}{c h}","-\frac{\left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right)}{h^2 \sqrt{a h^2+c g^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (f g-e h)}{\sqrt{c} h^2}+\frac{f \sqrt{a+c x^2}}{c h}",1,"(f*Sqrt[a + c*x^2])/(c*h) - ((f*g - e*h)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(Sqrt[c]*h^2) - ((f*g^2 - e*g*h + d*h^2)*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(h^2*Sqrt[c*g^2 + a*h^2])","A",6,5,29,0.1724,1,"{1654, 844, 217, 206, 725}"
106,1,168,0,0.2348862,"\int \frac{d+e x+f x^2}{(g+h x)^2 \sqrt{a+c x^2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)^2*Sqrt[a + c*x^2]),x]","-\frac{\sqrt{a+c x^2} \left(d h^2-e g h+f g^2\right)}{h (g+h x) \left(a h^2+c g^2\right)}+\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a h^2 (2 f g-e h)+c \left(f g^3-d g h^2\right)\right)}{h^2 \left(a h^2+c g^2\right)^{3/2}}+\frac{f \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} h^2}","-\frac{\sqrt{a+c x^2} \left(d h^2-e g h+f g^2\right)}{h (g+h x) \left(a h^2+c g^2\right)}+\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a h^2 (2 f g-e h)+c \left(f g^3-d g h^2\right)\right)}{h^2 \left(a h^2+c g^2\right)^{3/2}}+\frac{f \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c} h^2}",1,"-(((f*g^2 - e*g*h + d*h^2)*Sqrt[a + c*x^2])/(h*(c*g^2 + a*h^2)*(g + h*x))) + (f*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(Sqrt[c]*h^2) + ((a*h^2*(2*f*g - e*h) + c*(f*g^3 - d*g*h^2))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(h^2*(c*g^2 + a*h^2)^(3/2))","A",6,5,29,0.1724,1,"{1651, 844, 217, 206, 725}"
107,1,224,0,0.292261,"\int \frac{d+e x+f x^2}{(g+h x)^3 \sqrt{a+c x^2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)^3*Sqrt[a + c*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(2 a^2 f h^2-a c \left(f g^2-h (3 e g-d h)\right)+2 c^2 d g^2\right)}{2 \left(a h^2+c g^2\right)^{5/2}}-\frac{\sqrt{a+c x^2} \left(d h^2-e g h+f g^2\right)}{2 h (g+h x)^2 \left(a h^2+c g^2\right)}+\frac{\sqrt{a+c x^2} \left(2 a h^2 (2 f g-e h)+c g h (e g-3 d h)+c f g^3\right)}{2 h (g+h x) \left(a h^2+c g^2\right)^2}","-\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(2 a^2 f h^2-a c \left(f g^2-h (3 e g-d h)\right)+2 c^2 d g^2\right)}{2 \left(a h^2+c g^2\right)^{5/2}}-\frac{\sqrt{a+c x^2} \left(d h^2-e g h+f g^2\right)}{2 h (g+h x)^2 \left(a h^2+c g^2\right)}+\frac{\sqrt{a+c x^2} \left(2 a h^2 (2 f g-e h)+c g \left(h (e g-3 d h)+f g^2\right)\right)}{2 h (g+h x) \left(a h^2+c g^2\right)^2}",1,"-((f*g^2 - e*g*h + d*h^2)*Sqrt[a + c*x^2])/(2*h*(c*g^2 + a*h^2)*(g + h*x)^2) + ((c*f*g^3 + c*g*h*(e*g - 3*d*h) + 2*a*h^2*(2*f*g - e*h))*Sqrt[a + c*x^2])/(2*h*(c*g^2 + a*h^2)^2*(g + h*x)) - ((2*c^2*d*g^2 + 2*a^2*f*h^2 - a*c*(f*g^2 - h*(3*e*g - d*h)))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(2*(c*g^2 + a*h^2)^(5/2))","A",4,4,29,0.1379,1,"{1651, 807, 725, 206}"
108,1,228,0,0.3247725,"\int \frac{(g+h x)^3 \left(d+e x+f x^2\right)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[((g + h*x)^3*(d + e*x + f*x^2))/(a + c*x^2)^(3/2),x]","-\frac{h \sqrt{a+c x^2} \left(4 \left(4 a^2 f h^2-a c \left(3 h (d h+3 e g)+7 f g^2\right)+3 c^2 d g^2\right)+c h x (-9 a e h-11 a f g+6 c d g)\right)}{6 a c^3}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(-3 a h^2 (e h+3 f g)+6 c g h (d h+e g)+2 c f g^3\right)}{2 c^{5/2}}-\frac{h \sqrt{a+c x^2} (g+h x)^2 (3 c d-4 a f)}{3 a c^2}-\frac{(g+h x)^3 (a e-x (c d-a f))}{a c \sqrt{a+c x^2}}","-\frac{h \sqrt{a+c x^2} \left(4 \left(4 a^2 f h^2-a c \left(3 h (d h+3 e g)+7 f g^2\right)+3 c^2 d g^2\right)+c h x (-9 a e h-11 a f g+6 c d g)\right)}{6 a c^3}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(3 a h^2 (e h+3 f g)-2 c g \left(3 h (d h+e g)+f g^2\right)\right)}{2 c^{5/2}}-\frac{h \sqrt{a+c x^2} (g+h x)^2 (3 c d-4 a f)}{3 a c^2}-\frac{(g+h x)^3 (a e-x (c d-a f))}{a c \sqrt{a+c x^2}}",1,"-(((a*e - (c*d - a*f)*x)*(g + h*x)^3)/(a*c*Sqrt[a + c*x^2])) - ((3*c*d - 4*a*f)*h*(g + h*x)^2*Sqrt[a + c*x^2])/(3*a*c^2) - (h*(4*(3*c^2*d*g^2 + 4*a^2*f*h^2 - a*c*(7*f*g^2 + 3*h*(3*e*g + d*h))) + c*h*(6*c*d*g - 11*a*f*g - 9*a*e*h)*x)*Sqrt[a + c*x^2])/(6*a*c^3) + ((2*c*f*g^3 + 6*c*g*h*(e*g + d*h) - 3*a*h^2*(3*f*g + e*h))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(5/2))","A",5,5,29,0.1724,1,"{1645, 833, 780, 217, 206}"
109,1,149,0,0.1839021,"\int \frac{(g+h x)^2 \left(d+e x+f x^2\right)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[((g + h*x)^2*(d + e*x + f*x^2))/(a + c*x^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(h^2 (2 c d-3 a f)+2 c g (2 e h+f g)\right)}{2 c^{5/2}}-\frac{h \sqrt{a+c x^2} (4 (c d g-a (e h+2 f g))+h x (2 c d-3 a f))}{2 a c^2}-\frac{(g+h x)^2 (a e-x (c d-a f))}{a c \sqrt{a+c x^2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) \left(h^2 (2 c d-3 a f)+2 c g (2 e h+f g)\right)}{2 c^{5/2}}-\frac{h \sqrt{a+c x^2} (4 (c d g-a (e h+2 f g))+h x (2 c d-3 a f))}{2 a c^2}-\frac{(g+h x)^2 (a e-x (c d-a f))}{a c \sqrt{a+c x^2}}",1,"-(((a*e - (c*d - a*f)*x)*(g + h*x)^2)/(a*c*Sqrt[a + c*x^2])) - (h*(4*(c*d*g - a*(2*f*g + e*h)) + (2*c*d - 3*a*f)*h*x)*Sqrt[a + c*x^2])/(2*a*c^2) + (((2*c*d - 3*a*f)*h^2 + 2*c*g*(f*g + 2*e*h))*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(5/2))","A",4,4,29,0.1379,1,"{1645, 780, 217, 206}"
110,1,100,0,0.0869532,"\int \frac{(g+h x) \left(d+e x+f x^2\right)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[((g + h*x)*(d + e*x + f*x^2))/(a + c*x^2)^(3/2),x]","-\frac{h \sqrt{a+c x^2} (c d-2 a f)}{a c^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (e h+f g)}{c^{3/2}}-\frac{(g+h x) (a e-x (c d-a f))}{a c \sqrt{a+c x^2}}","-\frac{h \sqrt{a+c x^2} (c d-2 a f)}{a c^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right) (e h+f g)}{c^{3/2}}-\frac{(g+h x) (a e-x (c d-a f))}{a c \sqrt{a+c x^2}}",1,"-(((a*e - (c*d - a*f)*x)*(g + h*x))/(a*c*Sqrt[a + c*x^2])) - ((c*d - 2*a*f)*h*Sqrt[a + c*x^2])/(a*c^2) + ((f*g + e*h)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(3/2)","A",4,4,27,0.1481,1,"{1645, 641, 217, 206}"
111,1,61,0,0.0357731,"\int \frac{d+e x+f x^2}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/(a + c*x^2)^(3/2),x]","\frac{f \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}-\frac{a e-x (c d-a f)}{a c \sqrt{a+c x^2}}","\frac{f \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}-\frac{a e-x (c d-a f)}{a c \sqrt{a+c x^2}}",1,"-((a*e - (c*d - a*f)*x)/(a*c*Sqrt[a + c*x^2])) + (f*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(3/2)","A",4,4,22,0.1818,1,"{1814, 12, 217, 206}"
112,1,138,0,0.1413564,"\int \frac{d+e x+f x^2}{(g+h x) \left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)*(a + c*x^2)^(3/2)),x]","-\frac{a (a f h-c d h+c e g)-c x (a e h-a f g+c d g)}{a c \sqrt{a+c x^2} \left(a h^2+c g^2\right)}-\frac{\left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right)}{\left(a h^2+c g^2\right)^{3/2}}","-\frac{a (a f h-c d h+c e g)-c x (a e h-a f g+c d g)}{a c \sqrt{a+c x^2} \left(a h^2+c g^2\right)}-\frac{\left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right)}{\left(a h^2+c g^2\right)^{3/2}}",1,"-((a*(c*e*g - c*d*h + a*f*h) - c*(c*d*g - a*f*g + a*e*h)*x)/(a*c*(c*g^2 + a*h^2)*Sqrt[a + c*x^2])) - ((f*g^2 - e*g*h + d*h^2)*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(c*g^2 + a*h^2)^(3/2)","A",4,4,29,0.1379,1,"{1647, 12, 725, 206}"
113,1,239,0,0.4181309,"\int \frac{d+e x+f x^2}{(g+h x)^2 \left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)^2*(a + c*x^2)^(3/2)),x]","-\frac{a (a h (2 f g-e h)+c g (e g-2 d h))-x \left(a^2 f h^2-a c \left(f g^2-h (2 e g-d h)\right)+c^2 d g^2\right)}{a \sqrt{a+c x^2} \left(a h^2+c g^2\right)^2}-\frac{h \sqrt{a+c x^2} \left(d h^2-e g h+f g^2\right)}{(g+h x) \left(a h^2+c g^2\right)^2}-\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(-a h^2 (2 f g-e h)-c g h (2 e g-3 d h)+c f g^3\right)}{\left(a h^2+c g^2\right)^{5/2}}","-\frac{a (a h (2 f g-e h)+c g (e g-2 d h))-x \left(a^2 f h^2-a c \left(f g^2-h (2 e g-d h)\right)+c^2 d g^2\right)}{a \sqrt{a+c x^2} \left(a h^2+c g^2\right)^2}-\frac{h \sqrt{a+c x^2} \left(d h^2-e g h+f g^2\right)}{(g+h x) \left(a h^2+c g^2\right)^2}+\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(a h^2 (2 f g-e h)-c g \left(f g^2-h (2 e g-3 d h)\right)\right)}{\left(a h^2+c g^2\right)^{5/2}}",1,"-((a*(c*g*(e*g - 2*d*h) + a*h*(2*f*g - e*h)) - (c^2*d*g^2 + a^2*f*h^2 - a*c*(f*g^2 - h*(2*e*g - d*h)))*x)/(a*(c*g^2 + a*h^2)^2*Sqrt[a + c*x^2])) - (h*(f*g^2 - e*g*h + d*h^2)*Sqrt[a + c*x^2])/((c*g^2 + a*h^2)^2*(g + h*x)) - ((c*f*g^3 - c*g*h*(2*e*g - 3*d*h) - a*h^2*(2*f*g - e*h))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(c*g^2 + a*h^2)^(5/2)","A",4,4,29,0.1379,1,"{1647, 807, 725, 206}"
114,1,372,0,1.027857,"\int \frac{d+e x+f x^2}{(g+h x)^3 \left(a+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)^3*(a + c*x^2)^(3/2)),x]","\frac{c x \left(a^2 h^2 (3 f g-e h)-a c g \left(f g^2-3 h (e g-d h)\right)+c^2 d g^3\right)+a \left(a^2 f h^3-a c h \left(3 f g^2-h (3 e g-d h)\right)-c^2 g^2 (e g-3 d h)\right)}{a \sqrt{a+c x^2} \left(a h^2+c g^2\right)^3}-\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(2 a^2 f h^4-a c h^2 \left(3 d h^2-9 e g h+11 f g^2\right)+2 c^2 g^2 \left(6 d h^2-3 e g h+f g^2\right)\right)}{2 \left(a h^2+c g^2\right)^{7/2}}-\frac{h \sqrt{a+c x^2} \left(d h^2-e g h+f g^2\right)}{2 (g+h x)^2 \left(a h^2+c g^2\right)^2}-\frac{h \sqrt{a+c x^2} \left(-2 a h^2 (2 f g-e h)-c g h (5 e g-7 d h)+3 c f g^3\right)}{2 (g+h x) \left(a h^2+c g^2\right)^3}","\frac{c x \left(a^2 h^2 (3 f g-e h)-a c g \left(f g^2-3 h (e g-d h)\right)+c^2 d g^3\right)+a \left(a^2 f h^3-a c h \left(3 f g^2-h (3 e g-d h)\right)-c^2 g^2 (e g-3 d h)\right)}{a \sqrt{a+c x^2} \left(a h^2+c g^2\right)^3}-\frac{\tanh ^{-1}\left(\frac{a h-c g x}{\sqrt{a+c x^2} \sqrt{a h^2+c g^2}}\right) \left(2 a^2 f h^4-a c h^2 \left(3 d h^2-9 e g h+11 f g^2\right)+2 c^2 g^2 \left(6 d h^2-3 e g h+f g^2\right)\right)}{2 \left(a h^2+c g^2\right)^{7/2}}-\frac{h \sqrt{a+c x^2} \left(d h^2-e g h+f g^2\right)}{2 (g+h x)^2 \left(a h^2+c g^2\right)^2}+\frac{h \sqrt{a+c x^2} \left(2 a h^2 (2 f g-e h)-c g \left(3 f g^2-h (5 e g-7 d h)\right)\right)}{2 (g+h x) \left(a h^2+c g^2\right)^3}",1,"(a*(a^2*f*h^3 - c^2*g^2*(e*g - 3*d*h) - a*c*h*(3*f*g^2 - h*(3*e*g - d*h))) + c*(c^2*d*g^3 + a^2*h^2*(3*f*g - e*h) - a*c*g*(f*g^2 - 3*h*(e*g - d*h)))*x)/(a*(c*g^2 + a*h^2)^3*Sqrt[a + c*x^2]) - (h*(f*g^2 - e*g*h + d*h^2)*Sqrt[a + c*x^2])/(2*(c*g^2 + a*h^2)^2*(g + h*x)^2) - (h*(3*c*f*g^3 - c*g*h*(5*e*g - 7*d*h) - 2*a*h^2*(2*f*g - e*h))*Sqrt[a + c*x^2])/(2*(c*g^2 + a*h^2)^3*(g + h*x)) - ((2*a^2*f*h^4 - a*c*h^2*(11*f*g^2 - 9*e*g*h + 3*d*h^2) + 2*c^2*g^2*(f*g^2 - 3*e*g*h + 6*d*h^2))*ArcTanh[(a*h - c*g*x)/(Sqrt[c*g^2 + a*h^2]*Sqrt[a + c*x^2])])/(2*(c*g^2 + a*h^2)^(7/2))","A",5,5,29,0.1724,1,"{1647, 1651, 807, 725, 206}"
115,1,67,0,0.0422141,"\int \frac{A+B x+C x^2}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(A + B*x + C*x^2)/(a + c*x^2)^(5/2),x]","\frac{x (a C+2 A c)}{3 a^2 c \sqrt{a+c x^2}}-\frac{a B-x (A c-a C)}{3 a c \left(a+c x^2\right)^{3/2}}","\frac{x (a C+2 A c)}{3 a^2 c \sqrt{a+c x^2}}-\frac{a B-x (A c-a C)}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-(a*B - (A*c - a*C)*x)/(3*a*c*(a + c*x^2)^(3/2)) + ((2*A*c + a*C)*x)/(3*a^2*c*Sqrt[a + c*x^2])","A",3,3,22,0.1364,1,"{1814, 12, 191}"
116,1,97,0,0.0573023,"\int \frac{A+B x+C x^2}{\left(a+c x^2\right)^{7/2}} \, dx","Int[(A + B*x + C*x^2)/(a + c*x^2)^(7/2),x]","\frac{2 x (a C+4 A c)}{15 a^3 c \sqrt{a+c x^2}}+\frac{x (a C+4 A c)}{15 a^2 c \left(a+c x^2\right)^{3/2}}-\frac{a B-x (A c-a C)}{5 a c \left(a+c x^2\right)^{5/2}}","\frac{2 x (a C+4 A c)}{15 a^3 c \sqrt{a+c x^2}}+\frac{x (a C+4 A c)}{15 a^2 c \left(a+c x^2\right)^{3/2}}-\frac{a B-x (A c-a C)}{5 a c \left(a+c x^2\right)^{5/2}}",1,"-(a*B - (A*c - a*C)*x)/(5*a*c*(a + c*x^2)^(5/2)) + ((4*A*c + a*C)*x)/(15*a^2*c*(a + c*x^2)^(3/2)) + (2*(4*A*c + a*C)*x)/(15*a^3*c*Sqrt[a + c*x^2])","A",4,4,22,0.1818,1,"{1814, 12, 192, 191}"
117,1,127,0,0.0871571,"\int \frac{A+B x+C x^2}{\left(a+c x^2\right)^{9/2}} \, dx","Int[(A + B*x + C*x^2)/(a + c*x^2)^(9/2),x]","\frac{8 x (a C+6 A c)}{105 a^4 c \sqrt{a+c x^2}}+\frac{4 x (a C+6 A c)}{105 a^3 c \left(a+c x^2\right)^{3/2}}+\frac{x (a C+6 A c)}{35 a^2 c \left(a+c x^2\right)^{5/2}}-\frac{a B-x (A c-a C)}{7 a c \left(a+c x^2\right)^{7/2}}","\frac{8 x (a C+6 A c)}{105 a^4 c \sqrt{a+c x^2}}+\frac{4 x (a C+6 A c)}{105 a^3 c \left(a+c x^2\right)^{3/2}}+\frac{x (a C+6 A c)}{35 a^2 c \left(a+c x^2\right)^{5/2}}-\frac{a B-x (A c-a C)}{7 a c \left(a+c x^2\right)^{7/2}}",1,"-(a*B - (A*c - a*C)*x)/(7*a*c*(a + c*x^2)^(7/2)) + ((6*A*c + a*C)*x)/(35*a^2*c*(a + c*x^2)^(5/2)) + (4*(6*A*c + a*C)*x)/(105*a^3*c*(a + c*x^2)^(3/2)) + (8*(6*A*c + a*C)*x)/(105*a^4*c*Sqrt[a + c*x^2])","A",5,4,22,0.1818,1,"{1814, 12, 192, 191}"
118,1,106,0,0.1140041,"\int \frac{(1+2 x)^3 \left(1+3 x+4 x^2\right)}{\sqrt{2+3 x^2}} \, dx","Int[((1 + 2*x)^3*(1 + 3*x + 4*x^2))/Sqrt[2 + 3*x^2],x]","\frac{2}{15} \sqrt{3 x^2+2} (2 x+1)^4+\frac{13}{60} \sqrt{3 x^2+2} (2 x+1)^3-\frac{19}{540} \sqrt{3 x^2+2} (2 x+1)^2-\frac{1}{810} (2073 x+3937) \sqrt{3 x^2+2}+\frac{5 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","\frac{2}{15} \sqrt{3 x^2+2} (2 x+1)^4+\frac{13}{60} \sqrt{3 x^2+2} (2 x+1)^3-\frac{19}{540} \sqrt{3 x^2+2} (2 x+1)^2-\frac{1}{810} (2073 x+3937) \sqrt{3 x^2+2}+\frac{5 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(-19*(1 + 2*x)^2*Sqrt[2 + 3*x^2])/540 + (13*(1 + 2*x)^3*Sqrt[2 + 3*x^2])/60 + (2*(1 + 2*x)^4*Sqrt[2 + 3*x^2])/15 - ((3937 + 2073*x)*Sqrt[2 + 3*x^2])/810 + (5*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",5,4,29,0.1379,1,"{1654, 833, 780, 215}"
119,1,82,0,0.0884072,"\int \frac{(1+2 x)^2 \left(1+3 x+4 x^2\right)}{\sqrt{2+3 x^2}} \, dx","Int[((1 + 2*x)^2*(1 + 3*x + 4*x^2))/Sqrt[2 + 3*x^2],x]","\frac{1}{6} \sqrt{3 x^2+2} (2 x+1)^3+\frac{5}{18} \sqrt{3 x^2+2} (2 x+1)^2-\frac{1}{27} (3 x+61) \sqrt{3 x^2+2}-\sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","\frac{1}{6} \sqrt{3 x^2+2} (2 x+1)^3+\frac{5}{18} \sqrt{3 x^2+2} (2 x+1)^2-\frac{1}{27} (3 x+61) \sqrt{3 x^2+2}-\sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(5*(1 + 2*x)^2*Sqrt[2 + 3*x^2])/18 + ((1 + 2*x)^3*Sqrt[2 + 3*x^2])/6 - ((61 + 3*x)*Sqrt[2 + 3*x^2])/27 - Sqrt[3]*ArcSinh[Sqrt[3/2]*x]","A",4,4,29,0.1379,1,"{1654, 833, 780, 215}"
120,1,62,0,0.0516871,"\int \frac{(1+2 x) \left(1+3 x+4 x^2\right)}{\sqrt{2+3 x^2}} \, dx","Int[((1 + 2*x)*(1 + 3*x + 4*x^2))/Sqrt[2 + 3*x^2],x]","\frac{2}{9} \sqrt{3 x^2+2} (2 x+1)^2+\frac{7}{27} (3 x+1) \sqrt{3 x^2+2}-\frac{7 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","\frac{2}{9} \sqrt{3 x^2+2} (2 x+1)^2+\frac{7}{27} (3 x+1) \sqrt{3 x^2+2}-\frac{7 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(2*(1 + 2*x)^2*Sqrt[2 + 3*x^2])/9 + (7*(1 + 3*x)*Sqrt[2 + 3*x^2])/27 - (7*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",3,3,27,0.1111,1,"{1654, 780, 215}"
121,1,67,0,0.0806947,"\int \frac{1+3 x+4 x^2}{(1+2 x) \sqrt{2+3 x^2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)*Sqrt[2 + 3*x^2]),x]","\frac{2}{3} \sqrt{3 x^2+2}-\frac{\tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{2 \sqrt{11}}+\frac{\sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{2 \sqrt{3}}","\frac{2}{3} \sqrt{3 x^2+2}-\frac{\tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{2 \sqrt{11}}+\frac{\sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{2 \sqrt{3}}",1,"(2*Sqrt[2 + 3*x^2])/3 + ArcSinh[Sqrt[3/2]*x]/(2*Sqrt[3]) - ArcTanh[(4 - 3*x)/(Sqrt[11]*Sqrt[2 + 3*x^2])]/(2*Sqrt[11])","A",5,5,29,0.1724,1,"{1654, 844, 215, 725, 206}"
122,1,71,0,0.069962,"\int \frac{1+3 x+4 x^2}{(1+2 x)^2 \sqrt{2+3 x^2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^2*Sqrt[2 + 3*x^2]),x]","-\frac{\sqrt{3 x^2+2}}{11 (2 x+1)}+\frac{4 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{11 \sqrt{11}}+\frac{\sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{3}}","-\frac{\sqrt{3 x^2+2}}{11 (2 x+1)}+\frac{4 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{11 \sqrt{11}}+\frac{\sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{3}}",1,"-Sqrt[2 + 3*x^2]/(11*(1 + 2*x)) + ArcSinh[Sqrt[3/2]*x]/Sqrt[3] + (4*ArcTanh[(4 - 3*x)/(Sqrt[11]*Sqrt[2 + 3*x^2])])/(11*Sqrt[11])","A",5,5,29,0.1724,1,"{1651, 844, 215, 725, 206}"
123,1,77,0,0.066702,"\int \frac{1+3 x+4 x^2}{(1+2 x)^3 \sqrt{2+3 x^2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^3*Sqrt[2 + 3*x^2]),x]","\frac{13 \sqrt{3 x^2+2}}{242 (2 x+1)}-\frac{\sqrt{3 x^2+2}}{22 (2 x+1)^2}-\frac{103 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{121 \sqrt{11}}","\frac{13 \sqrt{3 x^2+2}}{242 (2 x+1)}-\frac{\sqrt{3 x^2+2}}{22 (2 x+1)^2}-\frac{103 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{121 \sqrt{11}}",1,"-Sqrt[2 + 3*x^2]/(22*(1 + 2*x)^2) + (13*Sqrt[2 + 3*x^2])/(242*(1 + 2*x)) - (103*ArcTanh[(4 - 3*x)/(Sqrt[11]*Sqrt[2 + 3*x^2])])/(121*Sqrt[11])","A",4,4,29,0.1379,1,"{1651, 807, 725, 206}"
124,1,87,0,0.103597,"\int \frac{(1+2 x)^3 \left(1+3 x+4 x^2\right)}{\left(2+3 x^2\right)^{3/2}} \, dx","Int[((1 + 2*x)^3*(1 + 3*x + 4*x^2))/(2 + 3*x^2)^(3/2),x]","\frac{32}{27} \sqrt{3 x^2+2} x^2+4 \sqrt{3 x^2+2} x+\frac{292}{81} \sqrt{3 x^2+2}+\frac{279 x+398}{54 \sqrt{3 x^2+2}}-\frac{38 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","\frac{32}{27} \sqrt{3 x^2+2} x^2+4 \sqrt{3 x^2+2} x+\frac{292}{81} \sqrt{3 x^2+2}+\frac{279 x+398}{54 \sqrt{3 x^2+2}}-\frac{38 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(398 + 279*x)/(54*Sqrt[2 + 3*x^2]) + (292*Sqrt[2 + 3*x^2])/81 + 4*x*Sqrt[2 + 3*x^2] + (32*x^2*Sqrt[2 + 3*x^2])/27 - (38*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",5,4,29,0.1379,1,"{1814, 1815, 641, 215}"
125,1,71,0,0.0840017,"\int \frac{(1+2 x)^2 \left(1+3 x+4 x^2\right)}{\left(2+3 x^2\right)^{3/2}} \, dx","Int[((1 + 2*x)^2*(1 + 3*x + 4*x^2))/(2 + 3*x^2)^(3/2),x]","\frac{70-47 x}{18 \sqrt{3 x^2+2}}+\frac{8}{9} x \sqrt{3 x^2+2}+\frac{28}{9} \sqrt{3 x^2+2}+\frac{4 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","\frac{70-47 x}{18 \sqrt{3 x^2+2}}+\frac{8}{9} x \sqrt{3 x^2+2}+\frac{28}{9} \sqrt{3 x^2+2}+\frac{4 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(70 - 47*x)/(18*Sqrt[2 + 3*x^2]) + (28*Sqrt[2 + 3*x^2])/9 + (8*x*Sqrt[2 + 3*x^2])/9 + (4*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",4,4,29,0.1379,1,"{1814, 1815, 641, 215}"
126,1,55,0,0.0444929,"\int \frac{(1+2 x) \left(1+3 x+4 x^2\right)}{\left(2+3 x^2\right)^{3/2}} \, dx","Int[((1 + 2*x)*(1 + 3*x + 4*x^2))/(2 + 3*x^2)^(3/2),x]","\frac{2-51 x}{18 \sqrt{3 x^2+2}}+\frac{8}{9} \sqrt{3 x^2+2}+\frac{10 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","\frac{2-51 x}{18 \sqrt{3 x^2+2}}+\frac{8}{9} \sqrt{3 x^2+2}+\frac{10 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(2 - 51*x)/(18*Sqrt[2 + 3*x^2]) + (8*Sqrt[2 + 3*x^2])/9 + (10*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",3,3,27,0.1111,1,"{1814, 641, 215}"
127,1,53,0,0.0599846,"\int \frac{1+3 x+4 x^2}{(1+2 x) \left(2+3 x^2\right)^{3/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)*(2 + 3*x^2)^(3/2)),x]","-\frac{38-21 x}{66 \sqrt{3 x^2+2}}-\frac{2 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{11 \sqrt{11}}","-\frac{38-21 x}{66 \sqrt{3 x^2+2}}-\frac{2 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{11 \sqrt{11}}",1,"-(38 - 21*x)/(66*Sqrt[2 + 3*x^2]) - (2*ArcTanh[(4 - 3*x)/(Sqrt[11]*Sqrt[2 + 3*x^2])])/(11*Sqrt[11])","A",4,4,29,0.1379,1,"{1647, 12, 725, 206}"
128,1,75,0,0.0772505,"\int \frac{1+3 x+4 x^2}{(1+2 x)^2 \left(2+3 x^2\right)^{3/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^2*(2 + 3*x^2)^(3/2)),x]","-\frac{10-97 x}{242 \sqrt{3 x^2+2}}-\frac{4 \sqrt{3 x^2+2}}{121 (2 x+1)}+\frac{4 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{121 \sqrt{11}}","-\frac{10-97 x}{242 \sqrt{3 x^2+2}}-\frac{4 \sqrt{3 x^2+2}}{121 (2 x+1)}+\frac{4 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{121 \sqrt{11}}",1,"-(10 - 97*x)/(242*Sqrt[2 + 3*x^2]) - (4*Sqrt[2 + 3*x^2])/(121*(1 + 2*x)) + (4*ArcTanh[(4 - 3*x)/(Sqrt[11]*Sqrt[2 + 3*x^2])])/(121*Sqrt[11])","A",4,4,29,0.1379,1,"{1647, 807, 725, 206}"
129,1,97,0,0.122966,"\int \frac{1+3 x+4 x^2}{(1+2 x)^3 \left(2+3 x^2\right)^{3/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^3*(2 + 3*x^2)^(3/2)),x]","\frac{351 x+358}{2662 \sqrt{3 x^2+2}}+\frac{2 \sqrt{3 x^2+2}}{1331 (2 x+1)}-\frac{2 \sqrt{3 x^2+2}}{121 (2 x+1)^2}-\frac{322 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{1331 \sqrt{11}}","\frac{351 x+358}{2662 \sqrt{3 x^2+2}}+\frac{2 \sqrt{3 x^2+2}}{1331 (2 x+1)}-\frac{2 \sqrt{3 x^2+2}}{121 (2 x+1)^2}-\frac{322 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{1331 \sqrt{11}}",1,"(358 + 351*x)/(2662*Sqrt[2 + 3*x^2]) - (2*Sqrt[2 + 3*x^2])/(121*(1 + 2*x)^2) + (2*Sqrt[2 + 3*x^2])/(1331*(1 + 2*x)) - (322*ArcTanh[(4 - 3*x)/(Sqrt[11]*Sqrt[2 + 3*x^2])])/(1331*Sqrt[11])","A",5,5,29,0.1724,1,"{1647, 1651, 807, 725, 206}"
130,1,73,0,0.0849701,"\int \frac{(1+2 x)^3 \left(1+3 x+4 x^2\right)}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[((1 + 2*x)^3*(1 + 3*x + 4*x^2))/(2 + 3*x^2)^(5/2),x]","\frac{279 x+398}{162 \left(3 x^2+2\right)^{3/2}}+\frac{32}{27} \sqrt{3 x^2+2}-\frac{465 x+152}{54 \sqrt{3 x^2+2}}+\frac{8 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{3}}","\frac{279 x+398}{162 \left(3 x^2+2\right)^{3/2}}+\frac{32}{27} \sqrt{3 x^2+2}-\frac{465 x+152}{54 \sqrt{3 x^2+2}}+\frac{8 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{3}}",1,"(398 + 279*x)/(162*(2 + 3*x^2)^(3/2)) - (152 + 465*x)/(54*Sqrt[2 + 3*x^2]) + (32*Sqrt[2 + 3*x^2])/27 + (8*ArcSinh[Sqrt[3/2]*x])/Sqrt[3]","A",4,3,29,0.1034,1,"{1814, 641, 215}"
131,1,60,0,0.0752021,"\int \frac{(1+2 x)^2 \left(1+3 x+4 x^2\right)}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[((1 + 2*x)^2*(1 + 3*x + 4*x^2))/(2 + 3*x^2)^(5/2),x]","\frac{70-47 x}{54 \left(3 x^2+2\right)^{3/2}}-\frac{59 x+168}{54 \sqrt{3 x^2+2}}+\frac{16 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}","\frac{70-47 x}{54 \left(3 x^2+2\right)^{3/2}}-\frac{59 x+168}{54 \sqrt{3 x^2+2}}+\frac{16 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}",1,"(70 - 47*x)/(54*(2 + 3*x^2)^(3/2)) - (168 + 59*x)/(54*Sqrt[2 + 3*x^2]) + (16*ArcSinh[Sqrt[3/2]*x])/(9*Sqrt[3])","A",4,3,29,0.1034,1,"{1814, 12, 215}"
132,1,41,0,0.0533089,"\int \frac{(1+2 x) \left(1+3 x+4 x^2\right)}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[((1 + 2*x)*(1 + 3*x + 4*x^2))/(2 + 3*x^2)^(5/2),x]","\frac{2-51 x}{54 \left(3 x^2+2\right)^{3/2}}-\frac{16-13 x}{18 \sqrt{3 x^2+2}}","\frac{2-51 x}{54 \left(3 x^2+2\right)^{3/2}}-\frac{16-13 x}{18 \sqrt{3 x^2+2}}",1,"(2 - 51*x)/(54*(2 + 3*x^2)^(3/2)) - (16 - 13*x)/(18*Sqrt[2 + 3*x^2])","A",2,2,27,0.07407,1,"{1814, 637}"
133,1,73,0,0.0850621,"\int \frac{1+3 x+4 x^2}{(1+2 x) \left(2+3 x^2\right)^{5/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)*(2 + 3*x^2)^(5/2)),x]","-\frac{38-21 x}{198 \left(3 x^2+2\right)^{3/2}}+\frac{95 x+24}{726 \sqrt{3 x^2+2}}-\frac{8 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{121 \sqrt{11}}","-\frac{38-21 x}{198 \left(3 x^2+2\right)^{3/2}}+\frac{95 x+24}{726 \sqrt{3 x^2+2}}-\frac{8 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{121 \sqrt{11}}",1,"-(38 - 21*x)/(198*(2 + 3*x^2)^(3/2)) + (24 + 95*x)/(726*Sqrt[2 + 3*x^2]) - (8*ArcTanh[(4 - 3*x)/(Sqrt[11]*Sqrt[2 + 3*x^2])])/(121*Sqrt[11])","A",5,5,29,0.1724,1,"{1647, 823, 12, 725, 206}"
134,1,95,0,0.1690626,"\int \frac{1+3 x+4 x^2}{(1+2 x)^2 \left(2+3 x^2\right)^{5/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^2*(2 + 3*x^2)^(5/2)),x]","-\frac{10-97 x}{726 \left(3 x^2+2\right)^{3/2}}-\frac{16 \sqrt{3 x^2+2}}{1331 (2 x+1)}+\frac{887 x+24}{7986 \sqrt{3 x^2+2}}-\frac{32 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{1331 \sqrt{11}}","-\frac{10-97 x}{726 \left(3 x^2+2\right)^{3/2}}-\frac{16 \sqrt{3 x^2+2}}{1331 (2 x+1)}+\frac{887 x+24}{7986 \sqrt{3 x^2+2}}-\frac{32 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{1331 \sqrt{11}}",1,"-(10 - 97*x)/(726*(2 + 3*x^2)^(3/2)) + (24 + 887*x)/(7986*Sqrt[2 + 3*x^2]) - (16*Sqrt[2 + 3*x^2])/(1331*(1 + 2*x)) - (32*ArcTanh[(4 - 3*x)/(Sqrt[11]*Sqrt[2 + 3*x^2])])/(1331*Sqrt[11])","A",5,4,29,0.1379,1,"{1647, 807, 725, 206}"
135,1,117,0,0.2062795,"\int \frac{1+3 x+4 x^2}{(1+2 x)^3 \left(2+3 x^2\right)^{5/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^3*(2 + 3*x^2)^(5/2)),x]","\frac{351 x+358}{7986 \left(3 x^2+2\right)^{3/2}}-\frac{8 \sqrt{3 x^2+2}}{1331 (2 x+1)}-\frac{8 \sqrt{3 x^2+2}}{1331 (2 x+1)^2}+\frac{2133 x+1216}{29282 \sqrt{3 x^2+2}}-\frac{1216 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{14641 \sqrt{11}}","\frac{351 x+358}{7986 \left(3 x^2+2\right)^{3/2}}-\frac{8 \sqrt{3 x^2+2}}{1331 (2 x+1)}-\frac{8 \sqrt{3 x^2+2}}{1331 (2 x+1)^2}+\frac{2133 x+1216}{29282 \sqrt{3 x^2+2}}-\frac{1216 \tanh ^{-1}\left(\frac{4-3 x}{\sqrt{11} \sqrt{3 x^2+2}}\right)}{14641 \sqrt{11}}",1,"(358 + 351*x)/(7986*(2 + 3*x^2)^(3/2)) + (1216 + 2133*x)/(29282*Sqrt[2 + 3*x^2]) - (8*Sqrt[2 + 3*x^2])/(1331*(1 + 2*x)^2) - (8*Sqrt[2 + 3*x^2])/(1331*(1 + 2*x)) - (1216*ArcTanh[(4 - 3*x)/(Sqrt[11]*Sqrt[2 + 3*x^2])])/(14641*Sqrt[11])","A",6,5,29,0.1724,1,"{1647, 1651, 807, 725, 206}"
136,1,417,0,0.604235,"\int (g+h x)^m \left(a+c x^2\right)^p \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^m*(a + c*x^2)^p*(d + e*x + f*x^2),x]","-\frac{\left(a+c x^2\right)^p (g+h x)^{m+1} \left(1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}\right)^{-p} \left(1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right) \left(a f h^2 (m+1)+c h (m+2 p+3) (e g-d h)-2 c f g^2 (p+1)\right)}{c h^3 (m+1) (m+2 p+3)}-\frac{\left(a+c x^2\right)^p (g+h x)^{m+2} \left(1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}\right)^{-p} \left(1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}\right)^{-p} (2 f g (p+1)-e h (m+2 p+3)) F_1\left(m+2;-p,-p;m+3;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right)}{h^3 (m+2) (m+2 p+3)}+\frac{f \left(a+c x^2\right)^{p+1} (g+h x)^{m+1}}{c h (m+2 p+3)}","-\frac{\left(a+c x^2\right)^p (g+h x)^{m+1} \left(1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}\right)^{-p} \left(1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right) \left(a f h^2 (m+1)-c \left(2 f g^2 (p+1)-h (m+2 p+3) (e g-d h)\right)\right)}{c h^3 (m+1) (m+2 p+3)}-\frac{\left(a+c x^2\right)^p (g+h x)^{m+2} \left(1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}\right)^{-p} \left(1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}\right)^{-p} (2 f g (p+1)-e h (m+2 p+3)) F_1\left(m+2;-p,-p;m+3;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right)}{h^3 (m+2) (m+2 p+3)}+\frac{f \left(a+c x^2\right)^{p+1} (g+h x)^{m+1}}{c h (m+2 p+3)}",1,"(f*(g + h*x)^(1 + m)*(a + c*x^2)^(1 + p))/(c*h*(3 + m + 2*p)) - ((a*f*h^2*(1 + m) - 2*c*f*g^2*(1 + p) + c*h*(e*g - d*h)*(3 + m + 2*p))*(g + h*x)^(1 + m)*(a + c*x^2)^p*AppellF1[1 + m, -p, -p, 2 + m, (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c]), (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c])])/(c*h^3*(1 + m)*(3 + m + 2*p)*(1 - (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c]))^p*(1 - (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c]))^p) - ((2*f*g*(1 + p) - e*h*(3 + m + 2*p))*(g + h*x)^(2 + m)*(a + c*x^2)^p*AppellF1[2 + m, -p, -p, 3 + m, (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c]), (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c])])/(h^3*(2 + m)*(3 + m + 2*p)*(1 - (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c]))^p*(1 - (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c]))^p)","A",6,4,27,0.1481,1,"{1654, 844, 760, 133}"
137,1,401,0,0.4532141,"\int (g+h x)^m \sqrt{a+c x^2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^m*Sqrt[a + c*x^2]*(d + e*x + f*x^2),x]","\frac{\sqrt{a+c x^2} (g+h x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right) \left(-a f h^2 (m+1)-c h (m+4) (e g-d h)+3 c f g^2\right)}{c h^3 (m+1) (m+4) \sqrt{1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}} \sqrt{1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}}}-\frac{\sqrt{a+c x^2} (g+h x)^{m+2} (3 f g-e h (m+4)) F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right)}{h^3 (m+2) (m+4) \sqrt{1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}} \sqrt{1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}}}+\frac{f \left(a+c x^2\right)^{3/2} (g+h x)^{m+1}}{c h (m+4)}","-\frac{\sqrt{a+c x^2} (g+h x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right) \left(a f h^2 (m+1)-c \left(3 f g^2-h (m+4) (e g-d h)\right)\right)}{c h^3 (m+1) (m+4) \sqrt{1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}} \sqrt{1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}}}-\frac{\sqrt{a+c x^2} (g+h x)^{m+2} (3 f g-e h (m+4)) F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right)}{h^3 (m+2) (m+4) \sqrt{1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}} \sqrt{1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}}}+\frac{f \left(a+c x^2\right)^{3/2} (g+h x)^{m+1}}{c h (m+4)}",1,"(f*(g + h*x)^(1 + m)*(a + c*x^2)^(3/2))/(c*h*(4 + m)) + ((3*c*f*g^2 - a*f*h^2*(1 + m) - c*h*(e*g - d*h)*(4 + m))*(g + h*x)^(1 + m)*Sqrt[a + c*x^2]*AppellF1[1 + m, -1/2, -1/2, 2 + m, (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c]), (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c])])/(c*h^3*(1 + m)*(4 + m)*Sqrt[1 - (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c])]*Sqrt[1 - (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c])]) - ((3*f*g - e*h*(4 + m))*(g + h*x)^(2 + m)*Sqrt[a + c*x^2]*AppellF1[2 + m, -1/2, -1/2, 3 + m, (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c]), (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c])])/(h^3*(2 + m)*(4 + m)*Sqrt[1 - (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c])]*Sqrt[1 - (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c])])","A",6,4,29,0.1379,1,"{1654, 844, 760, 133}"
138,1,474,0,0.5190976,"\int (g+h x)^{-3-2 p} \left(a+c x^2\right)^p \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^(-3 - 2*p)*(a + c*x^2)^p*(d + e*x + f*x^2),x]","-\frac{f \left(a+c x^2\right)^p (g+h x)^{-2 p} \left(1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}\right)^{-p} \left(1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}\right)^{-p} F_1\left(-2 p;-p,-p;1-2 p;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right)}{2 h^3 p}+\frac{\left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (g+h x)^{-2 p-1} \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} h+\sqrt{c} g\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} g-\sqrt{-a} h\right)}\right)^{-p} \left(a h^2 (2 f g-e h)+c \left(f g^3-d g h^2\right)\right) \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (g+h x)}{\left(\sqrt{c} g-\sqrt{-a} h\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{h^2 (2 p+1) \left(\sqrt{-a} h+\sqrt{c} g\right) \left(a h^2+c g^2\right)}-\frac{\left(a+c x^2\right)^{p+1} (g+h x)^{-2 (p+1)} \left(d h^2-e g h+f g^2\right)}{2 h (p+1) \left(a h^2+c g^2\right)}","-\frac{f \left(a+c x^2\right)^p (g+h x)^{-2 p} \left(1-\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}}\right)^{-p} \left(1-\frac{g+h x}{\frac{\sqrt{-a} h}{\sqrt{c}}+g}\right)^{-p} F_1\left(-2 p;-p,-p;1-2 p;\frac{g+h x}{g-\frac{\sqrt{-a} h}{\sqrt{c}}},\frac{g+h x}{g+\frac{\sqrt{-a} h}{\sqrt{c}}}\right)}{2 h^3 p}+\frac{\left(\sqrt{-a}-\sqrt{c} x\right) \left(a+c x^2\right)^p (g+h x)^{-2 p-1} \left(-\frac{\left(\sqrt{-a}+\sqrt{c} x\right) \left(\sqrt{-a} h+\sqrt{c} g\right)}{\left(\sqrt{-a}-\sqrt{c} x\right) \left(\sqrt{c} g-\sqrt{-a} h\right)}\right)^{-p} \left(a h^2 (2 f g-e h)+c \left(f g^3-d g h^2\right)\right) \, _2F_1\left(-2 p-1,-p;-2 p;\frac{2 \sqrt{-a} \sqrt{c} (g+h x)}{\left(\sqrt{c} g-\sqrt{-a} h\right) \left(\sqrt{-a}-\sqrt{c} x\right)}\right)}{h^2 (2 p+1) \left(\sqrt{-a} h+\sqrt{c} g\right) \left(a h^2+c g^2\right)}-\frac{\left(a+c x^2\right)^{p+1} (g+h x)^{-2 (p+1)} \left(d h^2-e g h+f g^2\right)}{2 h (p+1) \left(a h^2+c g^2\right)}",1,"-((f*g^2 - e*g*h + d*h^2)*(a + c*x^2)^(1 + p))/(2*h*(c*g^2 + a*h^2)*(1 + p)*(g + h*x)^(2*(1 + p))) - (f*(a + c*x^2)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c]), (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c])])/(2*h^3*p*(g + h*x)^(2*p)*(1 - (g + h*x)/(g - (Sqrt[-a]*h)/Sqrt[c]))^p*(1 - (g + h*x)/(g + (Sqrt[-a]*h)/Sqrt[c]))^p) + ((a*h^2*(2*f*g - e*h) + c*(f*g^3 - d*g*h^2))*(Sqrt[-a] - Sqrt[c]*x)*(g + h*x)^(-1 - 2*p)*(a + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (2*Sqrt[-a]*Sqrt[c]*(g + h*x))/((Sqrt[c]*g - Sqrt[-a]*h)*(Sqrt[-a] - Sqrt[c]*x))])/(h^2*(Sqrt[c]*g + Sqrt[-a]*h)*(c*g^2 + a*h^2)*(1 + 2*p)*(-(((Sqrt[c]*g + Sqrt[-a]*h)*(Sqrt[-a] + Sqrt[c]*x))/((Sqrt[c]*g - Sqrt[-a]*h)*(Sqrt[-a] - Sqrt[c]*x))))^p)","A",5,5,31,0.1613,1,"{1656, 760, 133, 807, 727}"
139,1,222,0,0.4073903,"\int (d+e x)^m \left(-c d^2+b d e+b e^2 x+c e^2 x^2\right)^p \left(-(c d-b e) f+(c e f-c d g+b e g) x+c e g x^2\right) \, dx","Int[(d + e*x)^m*(-(c*d^2) + b*d*e + b*e^2*x + c*e^2*x^2)^p*(-((c*d - b*e)*f) + (c*e*f - c*d*g + b*e*g)*x + c*e*g*x^2),x]","\frac{g (d+e x)^{m-1} \left(-d (c d-b e)+b e^2 x+c e^2 x^2\right)^{p+2}}{c e^2 (m+2 p+3)}-\frac{(d+e x)^m (-b e+c d-c e x)^2 \left(-d (c d-b e)+b e^2 x+c e^2 x^2\right)^p \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-p} (b e g (m+p+1)+c (d g (1-m)-e f (m+2 p+3))) \, _2F_1\left(-m-p,p+2;p+3;\frac{c d-b e-c e x}{2 c d-b e}\right)}{c^2 e^2 (p+2) (m+2 p+3)}","\frac{g (d+e x)^{m-1} \left(-d (c d-b e)+b e^2 x+c e^2 x^2\right)^{p+2}}{c e^2 (m+2 p+3)}-\frac{(d+e x)^m (-b e+c d-c e x)^2 \left(-d (c d-b e)+b e^2 x+c e^2 x^2\right)^p \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-p} (b e g (m+p+1)+c (d g (1-m)-e f (m+2 p+3))) \, _2F_1\left(-m-p,p+2;p+3;\frac{c d-b e-c e x}{2 c d-b e}\right)}{c^2 e^2 (p+2) (m+2 p+3)}",1,"(g*(d + e*x)^(-1 + m)*(-(d*(c*d - b*e)) + b*e^2*x + c*e^2*x^2)^(2 + p))/(c*e^2*(3 + m + 2*p)) - ((b*e*g*(1 + m + p) + c*(d*g*(1 - m) - e*f*(3 + m + 2*p)))*(d + e*x)^m*((c*(d + e*x))/(2*c*d - b*e))^(-m - p)*(c*d - b*e - c*e*x)^2*(-(d*(c*d - b*e)) + b*e^2*x + c*e^2*x^2)^p*Hypergeometric2F1[-m - p, 2 + p, 3 + p, (c*d - b*e - c*e*x)/(2*c*d - b*e)])/(c^2*e^2*(2 + p)*(3 + m + 2*p))","A",6,6,70,0.08571,1,"{1632, 794, 679, 677, 70, 69}"
140,1,254,0,0.3255649,"\int \left(a+b x+c x^2\right)^4 \left(A+C x^2\right) \, dx","Int[(a + b*x + c*x^2)^4*(A + C*x^2),x]","\frac{1}{7} x^7 \left(C \left(6 a^2 c^2+12 a b^2 c+b^4\right)+2 A c^2 \left(2 a c+3 b^2\right)\right)+\frac{1}{5} x^5 \left(A \left(6 a^2 c^2+12 a b^2 c+b^4\right)+2 a^2 C \left(2 a c+3 b^2\right)\right)+a b x^4 \left(a^2 C+A \left(3 a c+b^2\right)\right)+\frac{1}{3} a^2 x^3 \left(a^2 C+4 a A c+6 A b^2\right)+2 a^3 A b x^2+a^4 A x+\frac{1}{9} c^2 x^9 \left(4 a c C+A c^2+6 b^2 C\right)+\frac{1}{2} b c x^8 \left(C \left(3 a c+b^2\right)+A c^2\right)+\frac{2}{3} b x^6 \left(3 a c+b^2\right) (a C+A c)+\frac{2}{5} b c^3 C x^{10}+\frac{1}{11} c^4 C x^{11}","\frac{1}{7} x^7 \left(C \left(6 a^2 c^2+12 a b^2 c+b^4\right)+2 A c^2 \left(2 a c+3 b^2\right)\right)+\frac{1}{5} x^5 \left(A \left(6 a^2 c^2+12 a b^2 c+b^4\right)+2 a^2 C \left(2 a c+3 b^2\right)\right)+a b x^4 \left(a^2 C+A \left(3 a c+b^2\right)\right)+\frac{1}{3} a^2 x^3 \left(a^2 C+4 a A c+6 A b^2\right)+2 a^3 A b x^2+a^4 A x+\frac{1}{9} c^2 x^9 \left(4 a c C+A c^2+6 b^2 C\right)+\frac{1}{2} b c x^8 \left(C \left(3 a c+b^2\right)+A c^2\right)+\frac{2}{3} b x^6 \left(3 a c+b^2\right) (a C+A c)+\frac{2}{5} b c^3 C x^{10}+\frac{1}{11} c^4 C x^{11}",1,"a^4*A*x + 2*a^3*A*b*x^2 + (a^2*(6*A*b^2 + 4*a*A*c + a^2*C)*x^3)/3 + a*b*(A*(b^2 + 3*a*c) + a^2*C)*x^4 + ((A*(b^4 + 12*a*b^2*c + 6*a^2*c^2) + 2*a^2*(3*b^2 + 2*a*c)*C)*x^5)/5 + (2*b*(b^2 + 3*a*c)*(A*c + a*C)*x^6)/3 + ((2*A*c^2*(3*b^2 + 2*a*c) + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*C)*x^7)/7 + (b*c*(A*c^2 + (b^2 + 3*a*c)*C)*x^8)/2 + (c^2*(A*c^2 + 6*b^2*C + 4*a*c*C)*x^9)/9 + (2*b*c^3*C*x^10)/5 + (c^4*C*x^11)/11","A",2,1,20,0.05000,1,"{1657}"
141,1,161,0,0.1930146,"\int \left(a+b x+c x^2\right)^3 \left(A+C x^2\right) \, dx","Int[(a + b*x + c*x^2)^3*(A + C*x^2),x]","\frac{1}{4} b x^4 \left(3 a^2 C+A \left(6 a c+b^2\right)\right)+\frac{1}{3} a x^3 \left(a^2 C+3 A \left(a c+b^2\right)\right)+\frac{3}{2} a^2 A b x^2+a^3 A x+\frac{1}{7} c x^7 \left(3 C \left(a c+b^2\right)+A c^2\right)+\frac{1}{6} b x^6 \left(C \left(6 a c+b^2\right)+3 A c^2\right)+\frac{3}{5} x^5 \left(a c+b^2\right) (a C+A c)+\frac{3}{8} b c^2 C x^8+\frac{1}{9} c^3 C x^9","\frac{1}{4} b x^4 \left(3 a^2 C+A \left(6 a c+b^2\right)\right)+\frac{1}{3} a x^3 \left(a^2 C+3 A \left(a c+b^2\right)\right)+\frac{3}{2} a^2 A b x^2+a^3 A x+\frac{1}{7} c x^7 \left(3 C \left(a c+b^2\right)+A c^2\right)+\frac{1}{6} b x^6 \left(C \left(6 a c+b^2\right)+3 A c^2\right)+\frac{3}{5} x^5 \left(a c+b^2\right) (a C+A c)+\frac{3}{8} b c^2 C x^8+\frac{1}{9} c^3 C x^9",1,"a^3*A*x + (3*a^2*A*b*x^2)/2 + (a*(3*A*(b^2 + a*c) + a^2*C)*x^3)/3 + (b*(A*(b^2 + 6*a*c) + 3*a^2*C)*x^4)/4 + (3*(b^2 + a*c)*(A*c + a*C)*x^5)/5 + (b*(3*A*c^2 + (b^2 + 6*a*c)*C)*x^6)/6 + (c*(A*c^2 + 3*(b^2 + a*c)*C)*x^7)/7 + (3*b*c^2*C*x^8)/8 + (c^3*C*x^9)/9","A",2,1,20,0.05000,1,"{1657}"
142,1,96,0,0.0994486,"\int \left(a+b x+c x^2\right)^2 \left(A+C x^2\right) \, dx","Int[(a + b*x + c*x^2)^2*(A + C*x^2),x]","\frac{1}{3} x^3 \left(a^2 C+A \left(2 a c+b^2\right)\right)+a^2 A x+\frac{1}{5} x^5 \left(C \left(2 a c+b^2\right)+A c^2\right)+\frac{1}{2} b x^4 (a C+A c)+a A b x^2+\frac{1}{3} b c C x^6+\frac{1}{7} c^2 C x^7","\frac{1}{3} x^3 \left(a^2 C+A \left(2 a c+b^2\right)\right)+a^2 A x+\frac{1}{5} x^5 \left(C \left(2 a c+b^2\right)+A c^2\right)+\frac{1}{2} b x^4 (a C+A c)+a A b x^2+\frac{1}{3} b c C x^6+\frac{1}{7} c^2 C x^7",1,"a^2*A*x + a*A*b*x^2 + ((A*(b^2 + 2*a*c) + a^2*C)*x^3)/3 + (b*(A*c + a*C)*x^4)/2 + ((A*c^2 + (b^2 + 2*a*c)*C)*x^5)/5 + (b*c*C*x^6)/3 + (c^2*C*x^7)/7","A",2,1,20,0.05000,1,"{1657}"
143,1,46,0,0.0295376,"\int \left(a+b x+c x^2\right) \left(A+C x^2\right) \, dx","Int[(a + b*x + c*x^2)*(A + C*x^2),x]","\frac{1}{3} x^3 (a C+A c)+a A x+\frac{1}{2} A b x^2+\frac{1}{4} b C x^4+\frac{1}{5} c C x^5","\frac{1}{3} x^3 (a C+A c)+a A x+\frac{1}{2} A b x^2+\frac{1}{4} b C x^4+\frac{1}{5} c C x^5",1,"a*A*x + (A*b*x^2)/2 + ((A*c + a*C)*x^3)/3 + (b*C*x^4)/4 + (c*C*x^5)/5","A",2,1,18,0.05556,1,"{1657}"
144,1,81,0,0.100283,"\int \frac{A+C x^2}{a+b x+c x^2} \, dx","Int[(A + C*x^2)/(a + b*x + c*x^2),x]","-\frac{\left(C \left(b^2-2 a c\right)+2 A c^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}-\frac{b C \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{C x}{c}","-\frac{\left(C \left(b^2-2 a c\right)+2 A c^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}-\frac{b C \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{C x}{c}",1,"(C*x)/c - ((2*A*c^2 + (b^2 - 2*a*c)*C)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]) - (b*C*Log[a + b*x + c*x^2])/(2*c^2)","A",6,5,20,0.2500,1,"{1657, 634, 618, 206, 628}"
145,1,100,0,0.0682772,"\int \frac{A+C x^2}{\left(a+b x+c x^2\right)^2} \, dx","Int[(A + C*x^2)/(a + b*x + c*x^2)^2,x]","\frac{4 (a C+A c) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{4 (a C+A c) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((b*c*(A + (a*C)/c) + (2*A*c^2 + (b^2 - 2*a*c)*C)*x)/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2))) + (4*(A*c + a*C)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,20,0.2000,1,"{1660, 12, 618, 206}"
146,1,161,0,0.1139234,"\int \frac{A+C x^2}{\left(a+b x+c x^2\right)^3} \, dx","Int[(A + C*x^2)/(a + b*x + c*x^2)^3,x]","-\frac{x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{2 \left(C \left(2 a c+b^2\right)+6 A c^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{(b+2 c x) \left(2 a C+6 A c+\frac{b^2 C}{c}\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}","-\frac{x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{2 \left(C \left(2 a c+b^2\right)+6 A c^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{(b+2 c x) \left(2 a C+6 A c+\frac{b^2 C}{c}\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}",1,"-(b*c*(A + (a*C)/c) + (2*A*c^2 + (b^2 - 2*a*c)*C)*x)/(2*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + ((6*A*c + 2*a*C + (b^2*C)/c)*(b + 2*c*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (2*(6*A*c^2 + (b^2 + 2*a*c)*C)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,20,0.2500,1,"{1660, 12, 614, 618, 206}"
147,1,206,0,0.1901334,"\int \frac{A+C x^2}{\left(a+b x+c x^2\right)^4} \, dx","Int[(A + C*x^2)/(a + b*x + c*x^2)^4,x]","-\frac{2 (b+2 c x) \left(C \left(a c+b^2\right)+5 A c^2\right)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}-\frac{x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{8 c \left(C \left(a c+b^2\right)+5 A c^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}+\frac{(b+2 c x) \left(C \left(a+\frac{b^2}{c}\right)+5 A c\right)}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}","-\frac{2 (b+2 c x) \left(C \left(a c+b^2\right)+5 A c^2\right)}{\left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)}-\frac{x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^3}+\frac{8 c \left(C \left(a c+b^2\right)+5 A c^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{7/2}}+\frac{(b+2 c x) \left(C \left(a+\frac{b^2}{c}\right)+5 A c\right)}{3 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^2}",1,"-(b*c*(A + (a*C)/c) + (2*A*c^2 + (b^2 - 2*a*c)*C)*x)/(3*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + ((5*A*c + (a + b^2/c)*C)*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (2*(5*A*c^2 + (b^2 + a*c)*C)*(b + 2*c*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (8*c*(5*A*c^2 + (b^2 + a*c)*C)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(7/2)","A",6,5,20,0.2500,1,"{1660, 12, 614, 618, 206}"
148,1,591,0,1.4281086,"\int \frac{(d+e x)^3 \left(f+g x+h x^2\right)}{a+b x+c x^2} \, dx","Int[((d + e*x)^3*(f + g*x + h*x^2))/(a + b*x + c*x^2),x]","\frac{\log \left(a+b x+c x^2\right) \left(c^2 e \left(a^2 e^2 h+2 a b e (3 d h+e g)+b^2 \left(3 d^2 h+3 d e g+e^2 f\right)\right)-b^2 c e^2 (3 a e h+3 b d h+b e g)-c^3 \left(a e \left(3 d^2 h+3 d e g+e^2 f\right)+b d \left(d^2 h+3 d e g+3 e^2 f\right)\right)+b^4 e^3 h+c^4 d^2 (d g+3 e f)\right)}{2 c^5}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-b c^2 e \left(5 a^2 e^2 h+4 a b e (3 d h+e g)+b^2 \left(3 d^2 h+3 d e g+e^2 f\right)\right)+c^3 \left(2 a^2 e^2 (3 d h+e g)+3 a b e \left(3 d^2 h+3 d e g+e^2 f\right)+b^2 d \left(d^2 h+3 d e g+3 e^2 f\right)\right)+b^3 c e^2 (5 a e h+3 b d h+b e g)-c^4 d \left(2 a \left(d^2 h+3 d e g+3 e^2 f\right)+b d (d g+3 e f)\right)+b^5 \left(-e^3\right) h+2 c^5 d^3 f\right)}{c^5 \sqrt{b^2-4 a c}}+\frac{e x^2 \left(-c e (a e h+3 b d h+b e g)+b^2 e^2 h+c^2 \left(3 d^2 h+3 d e g+e^2 f\right)\right)}{2 c^3}-\frac{x \left(c^2 e \left(a e (3 d h+e g)+b \left(3 d^2 h+3 d e g+e^2 f\right)\right)-b c e^2 (2 a e h+3 b d h+b e g)+b^3 e^3 h+c^3 (-d) \left(d^2 h+3 d e g+3 e^2 f\right)\right)}{c^4}+\frac{e^2 x^3 (-b e h+3 c d h+c e g)}{3 c^2}+\frac{e^3 h x^4}{4 c}","\frac{\log \left(a+b x+c x^2\right) \left(c^2 e \left(a^2 e^2 h+2 a b e (3 d h+e g)+b^2 \left(3 d^2 h+3 d e g+e^2 f\right)\right)-b^2 c e^2 (3 a e h+3 b d h+b e g)-c^3 \left(a e \left(3 d^2 h+3 d e g+e^2 f\right)+b d \left(d^2 h+3 d e g+3 e^2 f\right)\right)+b^4 e^3 h+c^4 d^2 (d g+3 e f)\right)}{2 c^5}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-b c^2 e \left(5 a^2 e^2 h+4 a b e (3 d h+e g)+b^2 \left(3 d^2 h+3 d e g+e^2 f\right)\right)+c^3 \left(2 a^2 e^2 (3 d h+e g)+3 a b e \left(3 d^2 h+3 d e g+e^2 f\right)+b^2 d \left(d^2 h+3 d e g+3 e^2 f\right)\right)+b^3 c e^2 (5 a e h+3 b d h+b e g)-c^4 d \left(2 a \left(d^2 h+3 d e g+3 e^2 f\right)+b d (d g+3 e f)\right)+b^5 \left(-e^3\right) h+2 c^5 d^3 f\right)}{c^5 \sqrt{b^2-4 a c}}+\frac{e x^2 \left(-c e (a e h+3 b d h+b e g)+b^2 e^2 h+c^2 \left(3 d^2 h+3 d e g+e^2 f\right)\right)}{2 c^3}-\frac{x \left(c^2 e \left(a e (3 d h+e g)+b \left(3 d^2 h+3 d e g+e^2 f\right)\right)-b c e^2 (2 a e h+3 b d h+b e g)+b^3 e^3 h+c^3 (-d) \left(d^2 h+3 d e g+3 e^2 f\right)\right)}{c^4}+\frac{e^2 x^3 (-b e h+3 c d h+c e g)}{3 c^2}+\frac{e^3 h x^4}{4 c}",1,"-(((b^3*e^3*h - c^3*d*(3*e^2*f + 3*d*e*g + d^2*h) - b*c*e^2*(b*e*g + 3*b*d*h + 2*a*e*h) + c^2*e*(a*e*(e*g + 3*d*h) + b*(e^2*f + 3*d*e*g + 3*d^2*h)))*x)/c^4) + (e*(b^2*e^2*h + c^2*(e^2*f + 3*d*e*g + 3*d^2*h) - c*e*(b*e*g + 3*b*d*h + a*e*h))*x^2)/(2*c^3) + (e^2*(c*e*g + 3*c*d*h - b*e*h)*x^3)/(3*c^2) + (e^3*h*x^4)/(4*c) - ((2*c^5*d^3*f - b^5*e^3*h + b^3*c*e^2*(b*e*g + 3*b*d*h + 5*a*e*h) - c^4*d*(b*d*(3*e*f + d*g) + 2*a*(3*e^2*f + 3*d*e*g + d^2*h)) - b*c^2*e*(5*a^2*e^2*h + 4*a*b*e*(e*g + 3*d*h) + b^2*(e^2*f + 3*d*e*g + 3*d^2*h)) + c^3*(2*a^2*e^2*(e*g + 3*d*h) + b^2*d*(3*e^2*f + 3*d*e*g + d^2*h) + 3*a*b*e*(e^2*f + 3*d*e*g + 3*d^2*h)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^5*Sqrt[b^2 - 4*a*c]) + ((c^4*d^2*(3*e*f + d*g) + b^4*e^3*h - b^2*c*e^2*(b*e*g + 3*b*d*h + 3*a*e*h) + c^2*e*(a^2*e^2*h + 2*a*b*e*(e*g + 3*d*h) + b^2*(e^2*f + 3*d*e*g + 3*d^2*h)) - c^3*(b*d*(3*e^2*f + 3*d*e*g + d^2*h) + a*e*(e^2*f + 3*d*e*g + 3*d^2*h)))*Log[a + b*x + c*x^2])/(2*c^5)","A",6,5,30,0.1667,1,"{1628, 634, 618, 206, 628}"
149,1,348,0,0.6768357,"\int \frac{(d+e x)^2 \left(f+g x+h x^2\right)}{a+b x+c x^2} \, dx","Int[((d + e*x)^2*(f + g*x + h*x^2))/(a + b*x + c*x^2),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(c^2 \left(2 a^2 e^2 h+3 a b e (2 d h+e g)+b^2 \left(d^2 h+2 d e g+e^2 f\right)\right)-b^2 c e (4 a e h+2 b d h+b e g)-c^3 \left(2 a \left(d^2 h+2 d e g+e^2 f\right)+b d (d g+2 e f)\right)+b^4 e^2 h+2 c^4 d^2 f\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right) \left(-c^2 \left(a e (2 d h+e g)+b \left(d^2 h+2 d e g+e^2 f\right)\right)+b c e (2 a e h+2 b d h+b e g)+b^3 \left(-e^2\right) h+c^3 d (d g+2 e f)\right)}{2 c^4}+\frac{x \left(-c e (a e h+2 b d h+b e g)+b^2 e^2 h+c^2 \left(d^2 h+2 d e g+e^2 f\right)\right)}{c^3}+\frac{e x^2 (-b e h+2 c d h+c e g)}{2 c^2}+\frac{e^2 h x^3}{3 c}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(c^2 \left(2 a^2 e^2 h+3 a b e (2 d h+e g)+b^2 \left(d^2 h+2 d e g+e^2 f\right)\right)-b^2 c e (4 a e h+2 b d h+b e g)-c^3 \left(2 a \left(d^2 h+2 d e g+e^2 f\right)+b d (d g+2 e f)\right)+b^4 e^2 h+2 c^4 d^2 f\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right) \left(-c^2 \left(a e (2 d h+e g)+b \left(d^2 h+2 d e g+e^2 f\right)\right)+b c e (2 a e h+2 b d h+b e g)+b^3 \left(-e^2\right) h+c^3 d (d g+2 e f)\right)}{2 c^4}+\frac{x \left(-c e (a e h+2 b d h+b e g)+b^2 e^2 h+c^2 \left(d^2 h+2 d e g+e^2 f\right)\right)}{c^3}+\frac{e x^2 (-b e h+2 c d h+c e g)}{2 c^2}+\frac{e^2 h x^3}{3 c}",1,"((b^2*e^2*h + c^2*(e^2*f + 2*d*e*g + d^2*h) - c*e*(b*e*g + 2*b*d*h + a*e*h))*x)/c^3 + (e*(c*e*g + 2*c*d*h - b*e*h)*x^2)/(2*c^2) + (e^2*h*x^3)/(3*c) - ((2*c^4*d^2*f + b^4*e^2*h - b^2*c*e*(b*e*g + 2*b*d*h + 4*a*e*h) - c^3*(b*d*(2*e*f + d*g) + 2*a*(e^2*f + 2*d*e*g + d^2*h)) + c^2*(2*a^2*e^2*h + 3*a*b*e*(e*g + 2*d*h) + b^2*(e^2*f + 2*d*e*g + d^2*h)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*Sqrt[b^2 - 4*a*c]) + ((c^3*d*(2*e*f + d*g) - b^3*e^2*h + b*c*e*(b*e*g + 2*b*d*h + 2*a*e*h) - c^2*(a*e*(e*g + 2*d*h) + b*(e^2*f + 2*d*e*g + d^2*h)))*Log[a + b*x + c*x^2])/(2*c^4)","A",6,5,30,0.1667,1,"{1628, 634, 618, 206, 628}"
150,1,177,0,0.349583,"\int \frac{(d+e x) \left(f+g x+h x^2\right)}{a+b x+c x^2} \, dx","Int[((d + e*x)*(f + g*x + h*x^2))/(a + b*x + c*x^2),x]","\frac{\log \left(a+b x+c x^2\right) \left(-c (a e h+b d h+b e g)+b^2 e h+c^2 (d g+e f)\right)}{2 c^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 a d h+2 a e g+b d g+b e f)+b c (3 a e h+b d h+b e g)+b^3 (-e) h+2 c^3 d f\right)}{c^3 \sqrt{b^2-4 a c}}+\frac{x (-b e h+c d h+c e g)}{c^2}+\frac{e h x^2}{2 c}","\frac{\log \left(a+b x+c x^2\right) \left(-c (a e h+b d h+b e g)+b^2 e h+c^2 (d g+e f)\right)}{2 c^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 a d h+2 a e g+b d g+b e f)+b c (3 a e h+b d h+b e g)+b^3 (-e) h+2 c^3 d f\right)}{c^3 \sqrt{b^2-4 a c}}+\frac{x (-b e h+c d h+c e g)}{c^2}+\frac{e h x^2}{2 c}",1,"((c*e*g + c*d*h - b*e*h)*x)/c^2 + (e*h*x^2)/(2*c) - ((2*c^3*d*f - b^3*e*h - c^2*(b*e*f + b*d*g + 2*a*e*g + 2*a*d*h) + b*c*(b*e*g + b*d*h + 3*a*e*h))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]) + ((c^2*(e*f + d*g) + b^2*e*h - c*(b*e*g + b*d*h + a*e*h))*Log[a + b*x + c*x^2])/(2*c^3)","A",6,5,28,0.1786,1,"{1628, 634, 618, 206, 628}"
151,1,92,0,0.1561625,"\int \frac{f+g x+h x^2}{a+b x+c x^2} \, dx","Int[(f + g*x + h*x^2)/(a + b*x + c*x^2),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-2 a c h+b^2 h-b c g+2 c^2 f\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{(c g-b h) \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{h x}{c}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-2 a c h+b^2 h-b c g+2 c^2 f\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{(c g-b h) \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{h x}{c}",1,"(h*x)/c - ((2*c^2*f - b*c*g + b^2*h - 2*a*c*h)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]) + ((c*g - b*h)*Log[a + b*x + c*x^2])/(2*c^2)","A",6,5,23,0.2174,1,"{1657, 634, 618, 206, 628}"
152,1,196,0,0.348852,"\int \frac{f+g x+h x^2}{(d+e x) \left(a+b x+c x^2\right)} \, dx","Int[(f + g*x + h*x^2)/((d + e*x)*(a + b*x + c*x^2)),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c (2 a d h-2 a e g+b d g+b e f)+b h (b d-a e)+2 c^2 d f\right)}{c \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(a+b x+c x^2\right) (-a e h+b d h-c d g+c e f)}{2 c \left(a e^2-b d e+c d^2\right)}+\frac{\log (d+e x) \left(d^2 h-d e g+e^2 f\right)}{e \left(a e^2-b d e+c d^2\right)}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c (2 a d h-2 a e g+b d g+b e f)+b h (b d-a e)+2 c^2 d f\right)}{c \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}-\frac{\log \left(a+b x+c x^2\right) (-a e h+b d h-c d g+c e f)}{2 c \left(a e^2-b d e+c d^2\right)}+\frac{\log (d+e x) \left(d^2 h-d e g+e^2 f\right)}{e \left(a e^2-b d e+c d^2\right)}",1,"-(((2*c^2*d*f + b*(b*d - a*e)*h - c*(b*e*f + b*d*g - 2*a*e*g + 2*a*d*h))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2))) + ((e^2*f - d*e*g + d^2*h)*Log[d + e*x])/(e*(c*d^2 - b*d*e + a*e^2)) - ((c*e*f - c*d*g + b*d*h - a*e*h)*Log[a + b*x + c*x^2])/(2*c*(c*d^2 - b*d*e + a*e^2))","A",6,5,30,0.1667,1,"{1628, 634, 618, 206, 628}"
153,1,316,0,0.7606741,"\int \frac{f+g x+h x^2}{(d+e x)^2 \left(a+b x+c x^2\right)} \, dx","Int[(f + g*x + h*x^2)/((d + e*x)^2*(a + b*x + c*x^2)),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 a^2 e^2 h-c \left(2 a \left(d^2 h-2 d e g+e^2 f\right)+b d (d g+2 e f)\right)-a b e (2 d h+e g)+b^2 \left(d^2 h+e^2 f\right)+2 c^2 d^2 f\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2}-\frac{\log \left(a+b x+c x^2\right) \left(a e (e g-2 d h)-b \left(e^2 f-d^2 h\right)+c d (2 e f-d g)\right)}{2 \left(a e^2-b d e+c d^2\right)^2}-\frac{d^2 h-d e g+e^2 f}{e (d+e x) \left(a e^2-b d e+c d^2\right)}+\frac{\log (d+e x) \left(a e (e g-2 d h)-b \left(e^2 f-d^2 h\right)+c d (2 e f-d g)\right)}{\left(a e^2-b d e+c d^2\right)^2}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 a^2 e^2 h-c \left(2 a \left(d^2 h-2 d e g+e^2 f\right)+b d (d g+2 e f)\right)-a b e (2 d h+e g)+b^2 \left(d^2 h+e^2 f\right)+2 c^2 d^2 f\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2}-\frac{\log \left(a+b x+c x^2\right) \left(a e (e g-2 d h)-b \left(e^2 f-d^2 h\right)+c d (2 e f-d g)\right)}{2 \left(a e^2-b d e+c d^2\right)^2}-\frac{d^2 h-d e g+e^2 f}{e (d+e x) \left(a e^2-b d e+c d^2\right)}+\frac{\log (d+e x) \left(a e (e g-2 d h)-b \left(e^2 f-d^2 h\right)+c d (2 e f-d g)\right)}{\left(a e^2-b d e+c d^2\right)^2}",1,"-((e^2*f - d*e*g + d^2*h)/(e*(c*d^2 - b*d*e + a*e^2)*(d + e*x))) - ((2*c^2*d^2*f + 2*a^2*e^2*h - a*b*e*(e*g + 2*d*h) + b^2*(e^2*f + d^2*h) - c*(b*d*(2*e*f + d*g) + 2*a*(e^2*f - 2*d*e*g + d^2*h)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2) + ((c*d*(2*e*f - d*g) + a*e*(e*g - 2*d*h) - b*(e^2*f - d^2*h))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^2 - ((c*d*(2*e*f - d*g) + a*e*(e*g - 2*d*h) - b*(e^2*f - d^2*h))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^2)","A",6,5,30,0.1667,1,"{1628, 634, 618, 206, 628}"
154,1,509,0,1.2507832,"\int \frac{f+g x+h x^2}{(d+e x)^3 \left(a+b x+c x^2\right)} \, dx","Int[(f + g*x + h*x^2)/((d + e*x)^3*(a + b*x + c*x^2)),x]","-\frac{\log \left(a+b x+c x^2\right) \left(e^3 \left(a^2 h-a b g+b^2 f\right)-a c e \left(3 d^2 h-3 d e g+e^2 f\right)-b c \left(3 d e^2 f-d^3 h\right)+c^2 d^2 (3 e f-d g)\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{\log (d+e x) \left(e^3 \left(a^2 h-a b g+b^2 f\right)-a c e \left(3 d^2 h-3 d e g+e^2 f\right)-b c \left(3 d e^2 f-d^3 h\right)+c^2 d^2 (3 e f-d g)\right)}{\left(a e^2-b d e+c d^2\right)^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c \left(2 a^2 e^2 (e g-3 d h)-3 a b e \left(d^2 (-h)-d e g+e^2 f\right)+b^2 \left(-\left(d^3 h+3 d e^2 f\right)\right)\right)-b e^3 \left(a^2 h-a b g+b^2 f\right)-c^2 d \left(2 a \left(d^2 h-3 d e g+3 e^2 f\right)+b d (d g+3 e f)\right)+2 c^3 d^3 f\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^3}-\frac{d^2 h-d e g+e^2 f}{2 e (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{a e (e g-2 d h)-b \left(e^2 f-d^2 h\right)+c d (2 e f-d g)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}","-\frac{\log \left(a+b x+c x^2\right) \left(e^3 \left(a^2 h-a b g+b^2 f\right)-c \left(a e \left(3 d^2 h-3 d e g+e^2 f\right)+b \left(3 d e^2 f-d^3 h\right)\right)+c^2 d^2 (3 e f-d g)\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{\log (d+e x) \left(e^3 \left(a^2 h-a b g+b^2 f\right)-c \left(a e \left(3 d^2 h-3 d e g+e^2 f\right)+b \left(3 d e^2 f-d^3 h\right)\right)+c^2 d^2 (3 e f-d g)\right)}{\left(a e^2-b d e+c d^2\right)^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c \left(2 a^2 e^2 (e g-3 d h)-3 a b e \left(d^2 (-h)-d e g+e^2 f\right)+b^2 \left(-\left(d^3 h+3 d e^2 f\right)\right)\right)-b e^3 \left(a^2 h-a b g+b^2 f\right)-c^2 d \left(2 a \left(d^2 h-3 d e g+3 e^2 f\right)+b d (d g+3 e f)\right)+2 c^3 d^3 f\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^3}-\frac{d^2 h-d e g+e^2 f}{2 e (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{a e (e g-2 d h)-b \left(e^2 f-d^2 h\right)+c d (2 e f-d g)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}",1,"-(e^2*f - d*e*g + d^2*h)/(2*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (c*d*(2*e*f - d*g) + a*e*(e*g - 2*d*h) - b*(e^2*f - d^2*h))/((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) - ((2*c^3*d^3*f - b*e^3*(b^2*f - a*b*g + a^2*h) - c^2*d*(b*d*(3*e*f + d*g) + 2*a*(3*e^2*f - 3*d*e*g + d^2*h)) - c*(2*a^2*e^2*(e*g - 3*d*h) - 3*a*b*e*(e^2*f - d*e*g - d^2*h) - b^2*(3*d*e^2*f + d^3*h)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^3) + ((c^2*d^2*(3*e*f - d*g) + e^3*(b^2*f - a*b*g + a^2*h) - a*c*e*(e^2*f - 3*d*e*g + 3*d^2*h) - b*c*(3*d*e^2*f - d^3*h))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 - ((c^2*d^2*(3*e*f - d*g) + e^3*(b^2*f - a*b*g + a^2*h) - a*c*e*(e^2*f - 3*d*e*g + 3*d^2*h) - b*c*(3*d*e^2*f - d^3*h))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^3)","A",6,5,30,0.1667,1,"{1628, 634, 618, 206, 628}"
155,1,288,0,0.700316,"\int \frac{(d+e x)^2 \left(f+g x+h x^2\right)}{\left(a+b x+c x^2\right)^2} \, dx","Int[((d + e*x)^2*(f + g*x + h*x^2))/(a + b*x + c*x^2)^2,x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(b^2 c e (12 a e h+2 b d h+b e g)-c^3 \left(2 b d (d g+2 e f)-4 a \left(d^2 h+2 d e g+e^2 f\right)\right)-6 a c^2 e (2 a e h+2 b d h+b e g)-2 b^4 e^2 h+4 c^4 d^2 f\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{(d+e x)^2 \left(c \left(2 a g-b \left(\frac{a h}{c}+f\right)\right)-x \left(-2 a c h+b^2 h-b c g+2 c^2 f\right)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e^2 x \left(-6 a c h+2 b^2 h-b c g+2 c^2 f\right)}{c^2 \left(b^2-4 a c\right)}+\frac{e \log \left(a+b x+c x^2\right) (-2 b e h+2 c d h+c e g)}{2 c^3}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(b^2 c e (12 a e h+2 b d h+b e g)-c^3 \left(2 b d (d g+2 e f)-4 a \left(d^2 h+2 d e g+e^2 f\right)\right)-6 a c^2 e (2 a e h+2 b d h+b e g)-2 b^4 e^2 h+4 c^4 d^2 f\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{(d+e x)^2 \left(c \left(2 a g-b \left(\frac{a h}{c}+f\right)\right)-x \left(-2 a c h+b^2 h-b c g+2 c^2 f\right)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e^2 x \left(-6 a c h+2 b^2 h-b c g+2 c^2 f\right)}{c^2 \left(b^2-4 a c\right)}+\frac{e \log \left(a+b x+c x^2\right) (-2 b e h+2 c d h+c e g)}{2 c^3}",1,"(e^2*(2*c^2*f - b*c*g + 2*b^2*h - 6*a*c*h)*x)/(c^2*(b^2 - 4*a*c)) + ((d + e*x)^2*(c*(2*a*g - b*(f + (a*h)/c)) - (2*c^2*f - b*c*g + b^2*h - 2*a*c*h)*x))/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((4*c^4*d^2*f - 2*b^4*e^2*h - 6*a*c^2*e*(b*e*g + 2*b*d*h + 2*a*e*h) + b^2*c*e*(b*e*g + 2*b*d*h + 12*a*e*h) - c^3*(2*b*d*(2*e*f + d*g) - 4*a*(e^2*f + 2*d*e*g + d^2*h)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(3/2)) + (e*(c*e*g + 2*c*d*h - 2*b*e*h)*Log[a + b*x + c*x^2])/(2*c^3)","A",6,6,30,0.2000,1,"{1644, 773, 634, 618, 206, 628}"
156,1,178,0,0.2658626,"\int \frac{(d+e x) \left(f+g x+h x^2\right)}{\left(a+b x+c x^2\right)^2} \, dx","Int[((d + e*x)*(f + g*x + h*x^2))/(a + b*x + c*x^2)^2,x]","\frac{(d+e x) \left(c \left(2 a g-b \left(\frac{a h}{c}+f\right)\right)-x \left(-2 a c h+b^2 h-b c g+2 c^2 f\right)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-2 c^2 (b (d g+e f)-2 a (d h+e g))-6 a b c e h+b^3 e h+4 c^3 d f\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{e h \log \left(a+b x+c x^2\right)}{2 c^2}","\frac{(d+e x) \left(c \left(2 a g-b \left(\frac{a h}{c}+f\right)\right)-x \left(-2 a c h+b^2 h-b c g+2 c^2 f\right)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-2 c^2 (b (d g+e f)-2 a (d h+e g))-6 a b c e h+b^3 e h+4 c^3 d f\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{e h \log \left(a+b x+c x^2\right)}{2 c^2}",1,"((d + e*x)*(c*(2*a*g - b*(f + (a*h)/c)) - (2*c^2*f - b*c*g + b^2*h - 2*a*c*h)*x))/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((4*c^3*d*f + b^3*e*h - 6*a*b*c*e*h - 2*c^2*(b*(e*f + d*g) - 2*a*(e*g + d*h)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*(b^2 - 4*a*c)^(3/2)) + (e*h*Log[a + b*x + c*x^2])/(2*c^2)","A",5,5,28,0.1786,1,"{1644, 634, 618, 206, 628}"
157,1,118,0,0.0979572,"\int \frac{f+g x+h x^2}{\left(a+b x+c x^2\right)^2} \, dx","Int[(f + g*x + h*x^2)/(a + b*x + c*x^2)^2,x]","\frac{c \left(2 a g-b \left(\frac{a h}{c}+f\right)\right)-x \left(-2 a c h+b^2 h-b c g+2 c^2 f\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) (2 a h-b g+2 c f)}{\left(b^2-4 a c\right)^{3/2}}","\frac{c \left(2 a g-b \left(\frac{a h}{c}+f\right)\right)-x \left(-2 a c h+b^2 h-b c g+2 c^2 f\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) (2 a h-b g+2 c f)}{\left(b^2-4 a c\right)^{3/2}}",1,"(c*(2*a*g - b*(f + (a*h)/c)) - (2*c^2*f - b*c*g + b^2*h - 2*a*c*h)*x)/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (2*(2*c*f - b*g + 2*a*h)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,23,0.1739,1,"{1660, 12, 618, 206}"
158,1,407,0,1.086735,"\int \frac{f+g x+h x^2}{(d+e x) \left(a+b x+c x^2\right)^2} \, dx","Int[(f + g*x + h*x^2)/((d + e*x)*(a + b*x + c*x^2)^2),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 c e \left(2 a^2 e (e g-d h)-a b \left(d^2 h+d e g+3 e^2 f\right)+2 b^2 d^2 g\right)+b e \left(-2 a^2 e^2 h+4 a b d e h+b^2 \left(d^2 (-h)-d e g+e^2 f\right)\right)-2 c^2 d \left(b d (d g+3 e f)-2 a \left(d^2 h-d e g+3 e^2 f\right)\right)+4 c^3 d^3 f\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^2}+\frac{-x \left(-c (2 a d h-2 a e g+b d g+b e f)+b h (b d-a e)+2 c^2 d f\right)-b (a d h+a e g+c d f)-2 a (-a e h-c d g+c e f)+b^2 e f}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{e \log \left(a+b x+c x^2\right) \left(d^2 h-d e g+e^2 f\right)}{2 \left(a e^2-b d e+c d^2\right)^2}+\frac{e \log (d+e x) \left(d^2 h-d e g+e^2 f\right)}{\left(a e^2-b d e+c d^2\right)^2}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 c e \left(2 a^2 e (e g-d h)-a b \left(d^2 h+d e g+3 e^2 f\right)+2 b^2 d^2 g\right)+b e \left(-2 a^2 e^2 h+4 a b d e h+b^2 \left(d^2 (-h)-d e g+e^2 f\right)\right)-2 c^2 d \left(b d (d g+3 e f)-2 a \left(d^2 h-d e g+3 e^2 f\right)\right)+4 c^3 d^3 f\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^2}+\frac{-x \left(-c (2 a d h-2 a e g+b d g+b e f)+b h (b d-a e)+2 c^2 d f\right)-b (a d h+a e g+c d f)-2 a (-a e h-c d g+c e f)+b^2 e f}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{e \log \left(a+b x+c x^2\right) \left(d^2 h-d e g+e^2 f\right)}{2 \left(a e^2-b d e+c d^2\right)^2}+\frac{e \log (d+e x) \left(d^2 h-d e g+e^2 f\right)}{\left(a e^2-b d e+c d^2\right)^2}",1,"(b^2*e*f - b*(c*d*f + a*e*g + a*d*h) - 2*a*(c*e*f - c*d*g - a*e*h) - (2*c^2*d*f + b*(b*d - a*e)*h - c*(b*e*f + b*d*g - 2*a*e*g + 2*a*d*h))*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)) + ((4*c^3*d^3*f + b*e*(4*a*b*d*e*h - 2*a^2*e^2*h + b^2*(e^2*f - d*e*g - d^2*h)) - 2*c^2*d*(b*d*(3*e*f + d*g) - 2*a*(3*e^2*f - d*e*g + d^2*h)) + 2*c*e*(2*b^2*d^2*g + 2*a^2*e*(e*g - d*h) - a*b*(3*e^2*f + d*e*g + d^2*h)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^2) + (e*(e^2*f - d*e*g + d^2*h)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^2 - (e*(e^2*f - d*e*g + d^2*h)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^2)","A",7,6,30,0.2000,1,"{1646, 800, 634, 618, 206, 628}"
159,1,673,0,2.5585849,"\int \frac{f+g x+h x^2}{(d+e x)^2 \left(a+b x+c x^2\right)^2} \, dx","Int[(f + g*x + h*x^2)/((d + e*x)^2*(a + b*x + c*x^2)^2),x]","-\frac{c x \left(2 a^2 e^2 h-c \left(2 a \left(d^2 h-2 d e g+e^2 f\right)+b d (d g+2 e f)\right)-a b e (2 d h+e g)+b^2 \left(d^2 h+e^2 f\right)+2 c^2 d^2 f\right)+b \left(a^2 e^2 h-a c \left(d^2 (-h)-2 d e g+3 e^2 f\right)+c^2 d^2 f\right)-b^2 e (a e g+2 c d f)+2 a c (a e (e g-2 d h)+c d (2 e f-d g))+b^3 e^2 f}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-6 c^2 e \left(2 a^2 e \left(2 d^2 h-2 d e g+e^2 f\right)+4 a b d e^2 f-b^2 d^3 g\right)-c e \left(6 a^2 b e^3 g-4 a^3 e^3 h-6 a b^2 e \left(2 d^2 h-d e g+2 e^2 f\right)+b^3 (-d) \left(-2 d^2 h-3 d e g+4 e^2 f\right)\right)-b^3 e^3 (2 a d h-a e g-b d g+2 b e f)-2 c^3 d^2 \left(b d (d g+4 e f)-2 a \left(d^2 h-2 d e g+6 e^2 f\right)\right)+4 c^4 d^4 f\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^3}+\frac{e \log \left(a+b x+c x^2\right) \left(e^2 (2 a d h-a e g-b d g+2 b e f)-c d \left(2 d^2 h-3 d e g+4 e^2 f\right)\right)}{2 \left(a e^2-b d e+c d^2\right)^3}-\frac{e \left(d^2 h-d e g+e^2 f\right)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{e \log (d+e x) \left(e^2 (2 a d h-a e g-b d g+2 b e f)-c d \left(2 d^2 h-3 d e g+4 e^2 f\right)\right)}{\left(a e^2-b d e+c d^2\right)^3}","-\frac{c x \left(2 a^2 e^2 h-c \left(2 a \left(d^2 h-2 d e g+e^2 f\right)+b d (d g+2 e f)\right)-a b e (2 d h+e g)+b^2 \left(d^2 h+e^2 f\right)+2 c^2 d^2 f\right)+b \left(a^2 e^2 h-a c \left(d^2 (-h)-2 d e g+3 e^2 f\right)+c^2 d^2 f\right)-b^2 e (a e g+2 c d f)+2 a c (a e (e g-2 d h)+c d (2 e f-d g))+b^3 e^2 f}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-6 c^2 e \left(2 a^2 e \left(2 d^2 h-2 d e g+e^2 f\right)+4 a b d e^2 f-b^2 d^3 g\right)-c e \left(6 a^2 b e^3 g-4 a^3 e^3 h-6 a b^2 e \left(2 d^2 h-d e g+2 e^2 f\right)+b^3 (-d) \left(-2 d^2 h-3 d e g+4 e^2 f\right)\right)-b^3 e^3 (2 a d h-a e g-b d g+2 b e f)-2 c^3 d^2 \left(b d (d g+4 e f)-2 a \left(d^2 h-2 d e g+6 e^2 f\right)\right)+4 c^4 d^4 f\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^3}+\frac{e \log \left(a+b x+c x^2\right) \left(e^2 (2 a d h-a e g-b d g+2 b e f)-c d \left(2 d^2 h-3 d e g+4 e^2 f\right)\right)}{2 \left(a e^2-b d e+c d^2\right)^3}-\frac{e \left(d^2 h-d e g+e^2 f\right)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{e \log (d+e x) \left(e^2 (2 a d h-a e g-b d g+2 b e f)-c d \left(2 d^2 h-3 d e g+4 e^2 f\right)\right)}{\left(a e^2-b d e+c d^2\right)^3}",1,"-((e*(e^2*f - d*e*g + d^2*h))/((c*d^2 - b*d*e + a*e^2)^2*(d + e*x))) - (b^3*e^2*f - b^2*e*(2*c*d*f + a*e*g) + 2*a*c*(c*d*(2*e*f - d*g) + a*e*(e*g - 2*d*h)) + b*(c^2*d^2*f + a^2*e^2*h - a*c*(3*e^2*f - 2*d*e*g - d^2*h)) + c*(2*c^2*d^2*f + 2*a^2*e^2*h - a*b*e*(e*g + 2*d*h) + b^2*(e^2*f + d^2*h) - c*(b*d*(2*e*f + d*g) + 2*a*(e^2*f - 2*d*e*g + d^2*h)))*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) + ((4*c^4*d^4*f - b^3*e^3*(2*b*e*f - b*d*g - a*e*g + 2*a*d*h) - 2*c^3*d^2*(b*d*(4*e*f + d*g) - 2*a*(6*e^2*f - 2*d*e*g + d^2*h)) - 6*c^2*e*(4*a*b*d*e^2*f - b^2*d^3*g + 2*a^2*e*(e^2*f - 2*d*e*g + 2*d^2*h)) - c*e*(6*a^2*b*e^3*g - 4*a^3*e^3*h - b^3*d*(4*e^2*f - 3*d*e*g - 2*d^2*h) - 6*a*b^2*e*(2*e^2*f - d*e*g + 2*d^2*h)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^3) - (e*(e^2*(2*b*e*f - b*d*g - a*e*g + 2*a*d*h) - c*d*(4*e^2*f - 3*d*e*g + 2*d^2*h))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 + (e*(e^2*(2*b*e*f - b*d*g - a*e*g + 2*a*d*h) - c*d*(4*e^2*f - 3*d*e*g + 2*d^2*h))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^3)","A",7,6,30,0.2000,1,"{1646, 1628, 634, 618, 206, 628}"
160,1,62,0,0.0743509,"\int \frac{x^3 \left(1+x+x^2\right)}{\left(1-x+x^2\right)^2} \, dx","Int[(x^3*(1 + x + x^2))/(1 - x + x^2)^2,x]","\frac{x^2}{2}+\frac{2 (2-x)}{3 \left(x^2-x+1\right)}+2 \log \left(x^2-x+1\right)+3 x+\frac{10 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x^2}{2}+\frac{2 (2-x)}{3 \left(x^2-x+1\right)}+2 \log \left(x^2-x+1\right)+3 x+\frac{10 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"3*x + x^2/2 + (2*(2 - x))/(3*(1 - x + x^2)) + (10*ArcTan[(1 - 2*x)/Sqrt[3]])/(3*Sqrt[3]) + 2*Log[1 - x + x^2]","A",7,6,20,0.3000,1,"{1660, 1657, 634, 618, 204, 628}"
161,1,55,0,0.0662584,"\int \frac{x^2 \left(1+x+x^2\right)}{\left(1-x+x^2\right)^2} \, dx","Int[(x^2*(1 + x + x^2))/(1 - x + x^2)^2,x]","\frac{2 (1-2 x)}{3 \left(x^2-x+1\right)}+\frac{3}{2} \log \left(x^2-x+1\right)+x-\frac{7 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{2 (1-2 x)}{3 \left(x^2-x+1\right)}+\frac{3}{2} \log \left(x^2-x+1\right)+x-\frac{7 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"x + (2*(1 - 2*x))/(3*(1 - x + x^2)) - (7*ArcTan[(1 - 2*x)/Sqrt[3]])/(3*Sqrt[3]) + (3*Log[1 - x + x^2])/2","A",7,6,20,0.3000,1,"{1660, 1657, 634, 618, 204, 628}"
162,1,52,0,0.0515259,"\int \frac{x \left(1+x+x^2\right)}{\left(1-x+x^2\right)^2} \, dx","Int[(x*(1 + x + x^2))/(1 - x + x^2)^2,x]","-\frac{2 (x+1)}{3 \left(x^2-x+1\right)}+\frac{1}{2} \log \left(x^2-x+1\right)-\frac{11 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{2 (x+1)}{3 \left(x^2-x+1\right)}+\frac{1}{2} \log \left(x^2-x+1\right)-\frac{11 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(-2*(1 + x))/(3*(1 - x + x^2)) - (11*ArcTan[(1 - 2*x)/Sqrt[3]])/(3*Sqrt[3]) + Log[1 - x + x^2]/2","A",5,5,18,0.2778,1,"{1660, 634, 618, 204, 628}"
163,1,41,0,0.0329209,"\int \frac{1+x+x^2}{\left(1-x+x^2\right)^2} \, dx","Int[(1 + x + x^2)/(1 - x + x^2)^2,x]","-\frac{2 (2-x)}{3 \left(x^2-x+1\right)}-\frac{10 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{2 (2-x)}{3 \left(x^2-x+1\right)}-\frac{10 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(-2*(2 - x))/(3*(1 - x + x^2)) - (10*ArcTan[(1 - 2*x)/Sqrt[3]])/(3*Sqrt[3])","A",4,4,17,0.2353,1,"{1660, 12, 618, 204}"
164,1,56,0,0.0894687,"\int \frac{1+x+x^2}{x \left(1-x+x^2\right)^2} \, dx","Int[(1 + x + x^2)/(x*(1 - x + x^2)^2),x]","-\frac{2 (1-2 x)}{3 \left(x^2-x+1\right)}-\frac{1}{2} \log \left(x^2-x+1\right)+\log (x)-\frac{11 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{2 (1-2 x)}{3 \left(x^2-x+1\right)}-\frac{1}{2} \log \left(x^2-x+1\right)+\log (x)-\frac{11 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(-2*(1 - 2*x))/(3*(1 - x + x^2)) - (11*ArcTan[(1 - 2*x)/Sqrt[3]])/(3*Sqrt[3]) + Log[x] - Log[1 - x + x^2]/2","A",7,6,20,0.3000,1,"{1646, 800, 634, 618, 204, 628}"
165,1,61,0,0.1280979,"\int \frac{1+x+x^2}{x^2 \left(1-x+x^2\right)^2} \, dx","Int[(1 + x + x^2)/(x^2*(1 - x + x^2)^2),x]","\frac{2 (x+1)}{3 \left(x^2-x+1\right)}-\frac{3}{2} \log \left(x^2-x+1\right)-\frac{1}{x}+3 \log (x)-\frac{7 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{2 (x+1)}{3 \left(x^2-x+1\right)}-\frac{3}{2} \log \left(x^2-x+1\right)-\frac{1}{x}+3 \log (x)-\frac{7 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-x^(-1) + (2*(1 + x))/(3*(1 - x + x^2)) - (7*ArcTan[(1 - 2*x)/Sqrt[3]])/(3*Sqrt[3]) + 3*Log[x] - (3*Log[1 - x + x^2])/2","A",7,6,20,0.3000,1,"{1646, 1628, 634, 618, 204, 628}"
166,1,68,0,0.1095815,"\int \frac{1+x+x^2}{x^3 \left(1-x+x^2\right)^2} \, dx","Int[(1 + x + x^2)/(x^3*(1 - x + x^2)^2),x]","\frac{2 (2-x)}{3 \left(x^2-x+1\right)}-\frac{1}{2 x^2}-2 \log \left(x^2-x+1\right)-\frac{3}{x}+4 \log (x)+\frac{10 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{2 (2-x)}{3 \left(x^2-x+1\right)}-\frac{1}{2 x^2}-2 \log \left(x^2-x+1\right)-\frac{3}{x}+4 \log (x)+\frac{10 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-1/(2*x^2) - 3/x + (2*(2 - x))/(3*(1 - x + x^2)) + (10*ArcTan[(1 - 2*x)/Sqrt[3]])/(3*Sqrt[3]) + 4*Log[x] - 2*Log[1 - x + x^2]","A",7,6,20,0.3000,1,"{1646, 1628, 634, 618, 204, 628}"
167,1,10,0,0.0107474,"\int \frac{1-x^2}{\left(1+x+x^2\right)^2} \, dx","Int[(1 - x^2)/(1 + x + x^2)^2,x]","\frac{x}{x^2+x+1}","\frac{x}{x^2+x+1}",1,"x/(1 + x + x^2)","A",1,1,16,0.06250,1,"{1588}"
168,1,31,0,0.0318015,"\int \frac{1+x^2}{1+x+x^2} \, dx","Int[(1 + x^2)/(1 + x + x^2),x]","-\frac{1}{2} \log \left(x^2+x+1\right)+x+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{2} \log \left(x^2+x+1\right)+x+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"x + ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3] - Log[1 + x + x^2]/2","A",6,5,14,0.3571,1,"{1657, 634, 618, 204, 628}"
169,1,23,0,0.0349412,"\int \frac{-1+x^2}{25-6 x+x^2} \, dx","Int[(-1 + x^2)/(25 - 6*x + x^2),x]","3 \log \left(x^2-6 x+25\right)+x-2 \tan ^{-1}\left(\frac{x-3}{4}\right)","3 \log \left(x^2-6 x+25\right)+x-2 \tan ^{-1}\left(\frac{x-3}{4}\right)",1,"x - 2*ArcTan[(-3 + x)/4] + 3*Log[25 - 6*x + x^2]","A",6,5,16,0.3125,1,"{1657, 634, 618, 204, 628}"
170,1,21,0,0.0132023,"\int \frac{-10+3 x^2}{4-4 x+x^2} \, dx","Int[(-10 + 3*x^2)/(4 - 4*x + x^2),x]","3 x+\frac{2}{2-x}+12 \log (2-x)","3 x+\frac{2}{2-x}+12 \log (2-x)",1,"2/(2 - x) + 3*x + 12*Log[2 - x]","A",3,2,18,0.1111,1,"{27, 697}"
171,1,18,0,0.017693,"\int \frac{8+x^2}{6-5 x+x^2} \, dx","Int[(8 + x^2)/(6 - 5*x + x^2),x]","x-12 \log (2-x)+17 \log (3-x)","x-12 \log (2-x)+17 \log (3-x)",1,"x - 12*Log[2 - x] + 17*Log[3 - x]","A",5,3,16,0.1875,1,"{1657, 632, 31}"
172,1,14,0,0.0165158,"\int \frac{-4+3 x+x^2}{-8-2 x+x^2} \, dx","Int[(-4 + 3*x + x^2)/(-8 - 2*x + x^2),x]","x+4 \log (4-x)+\log (x+2)","x+4 \log (4-x)+\log (x+2)",1,"x + 4*Log[4 - x] + Log[2 + x]","A",5,3,19,0.1579,1,"{1657, 632, 31}"
173,1,27,0,0.0276561,"\int \frac{7+5 x+4 x^2}{5+4 x+4 x^2} \, dx","Int[(7 + 5*x + 4*x^2)/(5 + 4*x + 4*x^2),x]","\frac{1}{8} \log \left(4 x^2+4 x+5\right)+x+\frac{3}{8} \tan ^{-1}\left(x+\frac{1}{2}\right)","\frac{1}{8} \log \left(4 x^2+4 x+5\right)+x+\frac{3}{8} \tan ^{-1}\left(x+\frac{1}{2}\right)",1,"x + (3*ArcTan[1/2 + x])/8 + Log[5 + 4*x + 4*x^2]/8","A",6,5,23,0.2174,1,"{1657, 634, 618, 204, 628}"
174,1,48,0,0.0446019,"\int \frac{2-x+x^2}{-5+2 x+x^2} \, dx","Int[(2 - x + x^2)/(-5 + 2*x + x^2),x]","x-\frac{1}{6} \left(9-5 \sqrt{6}\right) \log \left(x-\sqrt{6}+1\right)-\frac{1}{6} \left(9+5 \sqrt{6}\right) \log \left(x+\sqrt{6}+1\right)","x-\frac{1}{6} \left(9-5 \sqrt{6}\right) \log \left(x-\sqrt{6}+1\right)-\frac{1}{6} \left(9+5 \sqrt{6}\right) \log \left(x+\sqrt{6}+1\right)",1,"x - ((9 - 5*Sqrt[6])*Log[1 - Sqrt[6] + x])/6 - ((9 + 5*Sqrt[6])*Log[1 + Sqrt[6] + x])/6","A",5,3,19,0.1579,1,"{1657, 632, 31}"
175,1,21,0,0.0119356,"\int \frac{1+4 x+3 x^2}{\left(4+7 x+2 x^2\right)^2} \, dx","Int[(1 + 4*x + 3*x^2)/(4 + 7*x + 2*x^2)^2,x]","-\frac{3 x+2}{2 \left(2 x^2+7 x+4\right)}","-\frac{3 x+2}{2 \left(2 x^2+7 x+4\right)}",1,"-(2 + 3*x)/(2*(4 + 7*x + 2*x^2))","A",2,2,23,0.08696,1,"{1660, 8}"
176,1,39,0,0.0233002,"\int \frac{1+x+x^2}{\left(3+2 x+x^2\right)^2} \, dx","Int[(1 + x + x^2)/(3 + 2*x + x^2)^2,x]","\frac{1-x}{4 \left(x^2+2 x+3\right)}+\frac{3 \tan ^{-1}\left(\frac{x+1}{\sqrt{2}}\right)}{4 \sqrt{2}}","\frac{1-x}{4 \left(x^2+2 x+3\right)}+\frac{3 \tan ^{-1}\left(\frac{x+1}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"(1 - x)/(4*(3 + 2*x + x^2)) + (3*ArcTan[(1 + x)/Sqrt[2]])/(4*Sqrt[2])","A",4,4,17,0.2353,1,"{1660, 12, 618, 204}"
177,1,11,0,0.0076456,"\int \frac{-1+2 x+5 x^2}{\left(1+x+x^2\right)^4} \, dx","Int[(-1 + 2*x + 5*x^2)/(1 + x + x^2)^4,x]","-\frac{x}{\left(x^2+x+1\right)^3}","-\frac{x}{\left(x^2+x+1\right)^3}",1,"-(x/(1 + x + x^2)^3)","A",1,1,19,0.05263,1,"{1588}"
178,1,267,0,0.2380799,"\int \left(a+b x+c x^2\right)^{5/2} \left(A+C x^2\right) \, dx","Int[(a + b*x + c*x^2)^(5/2)*(A + C*x^2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-4 a c C+32 A c^2+9 b^2 C\right)}{384 c^3}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a c C+32 A c^2+9 b^2 C\right)}{6144 c^4}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c C+32 A c^2+9 b^2 C\right)}{16384 c^5}-\frac{5 \left(b^2-4 a c\right)^3 \left(-4 a c C+32 A c^2+9 b^2 C\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{11/2}}-\frac{9 b C \left(a+b x+c x^2\right)^{7/2}}{112 c^2}+\frac{C x \left(a+b x+c x^2\right)^{7/2}}{8 c}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-4 a c C+32 A c^2+9 b^2 C\right)}{384 c^3}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a c C+32 A c^2+9 b^2 C\right)}{6144 c^4}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c C+32 A c^2+9 b^2 C\right)}{16384 c^5}-\frac{5 \left(b^2-4 a c\right)^3 \left(-4 a c C+32 A c^2+9 b^2 C\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{11/2}}-\frac{9 b C \left(a+b x+c x^2\right)^{7/2}}{112 c^2}+\frac{C x \left(a+b x+c x^2\right)^{7/2}}{8 c}",1,"(5*(b^2 - 4*a*c)^2*(32*A*c^2 + 9*b^2*C - 4*a*c*C)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(16384*c^5) - (5*(b^2 - 4*a*c)*(32*A*c^2 + 9*b^2*C - 4*a*c*C)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(6144*c^4) + ((32*A*c^2 + 9*b^2*C - 4*a*c*C)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(384*c^3) - (9*b*C*(a + b*x + c*x^2)^(7/2))/(112*c^2) + (C*x*(a + b*x + c*x^2)^(7/2))/(8*c) - (5*(b^2 - 4*a*c)^3*(32*A*c^2 + 9*b^2*C - 4*a*c*C)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32768*c^(11/2))","A",7,5,22,0.2273,1,"{1661, 640, 612, 621, 206}"
179,1,212,0,0.1833743,"\int \left(a+b x+c x^2\right)^{3/2} \left(A+C x^2\right) \, dx","Int[(a + b*x + c*x^2)^(3/2)*(A + C*x^2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a c C+24 A c^2+7 b^2 C\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c C+24 A c^2+7 b^2 C\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(-4 a c C+24 A c^2+7 b^2 C\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{9/2}}-\frac{7 b C \left(a+b x+c x^2\right)^{5/2}}{60 c^2}+\frac{C x \left(a+b x+c x^2\right)^{5/2}}{6 c}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a c C+24 A c^2+7 b^2 C\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c C+24 A c^2+7 b^2 C\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(-4 a c C+24 A c^2+7 b^2 C\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{9/2}}-\frac{7 b C \left(a+b x+c x^2\right)^{5/2}}{60 c^2}+\frac{C x \left(a+b x+c x^2\right)^{5/2}}{6 c}",1,"-((b^2 - 4*a*c)*(24*A*c^2 + 7*b^2*C - 4*a*c*C)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^4) + ((24*A*c^2 + 7*b^2*C - 4*a*c*C)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(192*c^3) - (7*b*C*(a + b*x + c*x^2)^(5/2))/(60*c^2) + (C*x*(a + b*x + c*x^2)^(5/2))/(6*c) + ((b^2 - 4*a*c)^2*(24*A*c^2 + 7*b^2*C - 4*a*c*C)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(9/2))","A",6,5,22,0.2273,1,"{1661, 640, 612, 621, 206}"
180,1,157,0,0.1238953,"\int \sqrt{a+b x+c x^2} \left(A+C x^2\right) \, dx","Int[Sqrt[a + b*x + c*x^2]*(A + C*x^2),x]","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c C+16 A c^2+5 b^2 C\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \left(-4 a c C+16 A c^2+5 b^2 C\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2}}-\frac{5 b C \left(a+b x+c x^2\right)^{3/2}}{24 c^2}+\frac{C x \left(a+b x+c x^2\right)^{3/2}}{4 c}","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c C+16 A c^2+5 b^2 C\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \left(-4 a c C+16 A c^2+5 b^2 C\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2}}-\frac{5 b C \left(a+b x+c x^2\right)^{3/2}}{24 c^2}+\frac{C x \left(a+b x+c x^2\right)^{3/2}}{4 c}",1,"((16*A*c^2 + 5*b^2*C - 4*a*c*C)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(64*c^3) - (5*b*C*(a + b*x + c*x^2)^(3/2))/(24*c^2) + (C*x*(a + b*x + c*x^2)^(3/2))/(4*c) - ((b^2 - 4*a*c)*(16*A*c^2 + 5*b^2*C - 4*a*c*C)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(7/2))","A",5,5,22,0.2273,1,"{1661, 640, 612, 621, 206}"
181,1,104,0,0.0795335,"\int \frac{A+C x^2}{\sqrt{a+b x+c x^2}} \, dx","Int[(A + C*x^2)/Sqrt[a + b*x + c*x^2],x]","\frac{\left(-4 a c C+8 A c^2+3 b^2 C\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{5/2}}-\frac{3 b C \sqrt{a+b x+c x^2}}{4 c^2}+\frac{C x \sqrt{a+b x+c x^2}}{2 c}","\frac{\left(-4 a c C+8 A c^2+3 b^2 C\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{5/2}}-\frac{3 b C \sqrt{a+b x+c x^2}}{4 c^2}+\frac{C x \sqrt{a+b x+c x^2}}{2 c}",1,"(-3*b*C*Sqrt[a + b*x + c*x^2])/(4*c^2) + (C*x*Sqrt[a + b*x + c*x^2])/(2*c) + ((8*A*c^2 + 3*b^2*C - 4*a*c*C)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(5/2))","A",4,4,22,0.1818,1,"{1661, 640, 621, 206}"
182,1,98,0,0.0770029,"\int \frac{A+C x^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + C*x^2)/(a + b*x + c*x^2)^(3/2),x]","\frac{C \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}-\frac{2 \left(x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","\frac{C \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}-\frac{2 \left(x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(-2*(b*c*(A + (a*C)/c) + (2*A*c^2 + (b^2 - 2*a*c)*C)*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (C*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(3/2)","A",4,4,22,0.1818,1,"{1660, 12, 621, 206}"
183,1,114,0,0.093144,"\int \frac{A+C x^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(A + C*x^2)/(a + b*x + c*x^2)^(5/2),x]","\frac{2 (b+2 c x) \left(4 a C+8 A c+\frac{b^2 C}{c}\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 \left(x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{2 (b+2 c x) \left(4 a C+8 A c+\frac{b^2 C}{c}\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 \left(x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(b*c*(A + (a*C)/c) + (2*A*c^2 + (b^2 - 2*a*c)*C)*x))/(3*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (2*(8*A*c + 4*a*C + (b^2*C)/c)*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",3,3,22,0.1364,1,"{1660, 12, 613}"
184,1,167,0,0.1065908,"\int \frac{A+C x^2}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[(A + C*x^2)/(a + b*x + c*x^2)^(7/2),x]","-\frac{16 (b+2 c x) \left(4 a c C+16 A c^2+3 b^2 C\right)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{2 \left(x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)\right)}{5 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}+\frac{2 (b+2 c x) \left(4 a C+16 A c+\frac{3 b^2 C}{c}\right)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}","-\frac{16 (b+2 c x) \left(4 a c C+16 A c^2+3 b^2 C\right)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{2 \left(x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)\right)}{5 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}+\frac{2 (b+2 c x) \left(4 a C+16 A c+\frac{3 b^2 C}{c}\right)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(b*c*(A + (a*C)/c) + (2*A*c^2 + (b^2 - 2*a*c)*C)*x))/(5*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) + (2*(16*A*c + 4*a*C + (3*b^2*C)/c)*(b + 2*c*x))/(15*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)) - (16*(16*A*c^2 + 3*b^2*C + 4*a*c*C)*(b + 2*c*x))/(15*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2])","A",4,4,22,0.1818,1,"{1660, 12, 614, 613}"
185,1,220,0,0.1418162,"\int \frac{A+C x^2}{\left(a+b x+c x^2\right)^{9/2}} \, dx","Int[(A + C*x^2)/(a + b*x + c*x^2)^(9/2),x]","\frac{256 c (b+2 c x) \left(4 a c C+24 A c^2+5 b^2 C\right)}{105 \left(b^2-4 a c\right)^4 \sqrt{a+b x+c x^2}}-\frac{32 (b+2 c x) \left(4 a c C+24 A c^2+5 b^2 C\right)}{105 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^{3/2}}-\frac{2 \left(x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)\right)}{7 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{7/2}}+\frac{2 (b+2 c x) \left(4 a C+24 A c+\frac{5 b^2 C}{c}\right)}{35 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{5/2}}","\frac{256 c (b+2 c x) \left(4 a c C+24 A c^2+5 b^2 C\right)}{105 \left(b^2-4 a c\right)^4 \sqrt{a+b x+c x^2}}-\frac{32 (b+2 c x) \left(4 a c C+24 A c^2+5 b^2 C\right)}{105 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^{3/2}}-\frac{2 \left(x \left(C \left(b^2-2 a c\right)+2 A c^2\right)+b c \left(\frac{a C}{c}+A\right)\right)}{7 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{7/2}}+\frac{2 (b+2 c x) \left(4 a C+24 A c+\frac{5 b^2 C}{c}\right)}{35 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{5/2}}",1,"(-2*(b*c*(A + (a*C)/c) + (2*A*c^2 + (b^2 - 2*a*c)*C)*x))/(7*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(7/2)) + (2*(24*A*c + 4*a*C + (5*b^2*C)/c)*(b + 2*c*x))/(35*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(5/2)) - (32*(24*A*c^2 + 5*b^2*C + 4*a*c*C)*(b + 2*c*x))/(105*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^(3/2)) + (256*c*(24*A*c^2 + 5*b^2*C + 4*a*c*C)*(b + 2*c*x))/(105*(b^2 - 4*a*c)^4*Sqrt[a + b*x + c*x^2])","A",5,4,22,0.1818,1,"{1660, 12, 614, 613}"
186,1,927,0,3.0127179,"\int (g+h x)^3 \sqrt{a+b x+c x^2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^3*Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2),x]","\frac{f \left(c x^2+b x+a\right)^{3/2} (g+h x)^4}{7 c h}-\frac{(6 c f g-14 c e h+11 b f h) \left(c x^2+b x+a\right)^{3/2} (g+h x)^3}{84 c^2 h}+\frac{\left(-4 \left(3 f g^2-7 h (e g+2 d h)\right) c^2-2 h (8 b f g+21 b e h+16 a f h) c+33 b^2 f h^2\right) \left(c x^2+b x+a\right)^{3/2} (g+h x)^2}{280 c^3 h}+\frac{\left(-128 \left(3 f g^4-7 g^2 h (e g+12 d h)\right) c^4-16 h \left(16 a h \left(15 f g^2+7 h (3 e g+d h)\right)+b g \left(17 f g^2+21 h (19 e g+25 d h)\right)\right) c^3+8 h^2 \left(\left(537 f g^2+245 h (3 e g+d h)\right) b^2+343 a h (3 f g+e h) b+128 a^2 f h^2\right) c^2-42 b^2 h^3 (78 a f h+35 b (3 f g+e h)) c-6 h \left(16 \left(3 f g^3-7 g h (e g+7 d h)\right) c^3+8 h \left(5 b f g^2+7 b h (9 e g+7 d h)+a h (41 f g+35 e h)\right) c^2-6 b h^2 (59 b f g+49 b e h+74 a f h) c+231 b^3 f h^3\right) x c+1155 b^4 f h^4\right) \left(c x^2+b x+a\right)^{3/2}}{13440 c^5 h}-\frac{\left(b^2-4 a c\right) \left(-33 f h^3 b^5+6 c h^2 (20 a f h+7 b (3 f g+e h)) b^3-8 c^2 h \left(7 \left(3 f g^2+3 e h g+d h^2\right) b^2+14 a h (3 f g+e h) b+10 a^2 f h^2\right) b+256 c^5 d g^3-64 c^4 g \left(a f g^2+2 b (e g+3 d h) g+3 a h (e g+d h)\right)+16 c^3 \left(5 g \left(f g^2+3 h (e g+d h)\right) b^2+6 a h \left(3 f g^2+h (3 e g+d h)\right) b+2 a^2 h^2 (3 f g+e h)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{2048 c^{13/2}}+\frac{\left(-33 f h^3 b^5+6 c h^2 (20 a f h+7 b (3 f g+e h)) b^3-8 c^2 h \left(7 \left(3 f g^2+3 e h g+d h^2\right) b^2+14 a h (3 f g+e h) b+10 a^2 f h^2\right) b+256 c^5 d g^3-64 c^4 g \left(a f g^2+2 b (e g+3 d h) g+3 a h (e g+d h)\right)+16 c^3 \left(5 g \left(f g^2+3 h (e g+d h)\right) b^2+6 a h \left(3 f g^2+h (3 e g+d h)\right) b+2 a^2 h^2 (3 f g+e h)\right)\right) (b+2 c x) \sqrt{c x^2+b x+a}}{1024 c^6}","\frac{f \left(c x^2+b x+a\right)^{3/2} (g+h x)^4}{7 c h}-\frac{(6 c f g-14 c e h+11 b f h) \left(c x^2+b x+a\right)^{3/2} (g+h x)^3}{84 c^2 h}+\frac{\left(-4 \left(3 f g^2-7 h (e g+2 d h)\right) c^2-2 h (8 b f g+21 b e h+16 a f h) c+33 b^2 f h^2\right) \left(c x^2+b x+a\right)^{3/2} (g+h x)^2}{280 c^3 h}+\frac{\left(-128 g^2 \left(3 f g^2-7 h (e g+12 d h)\right) c^4-16 h \left(16 a h \left(15 f g^2+7 h (3 e g+d h)\right)+b g \left(17 f g^2+21 h (19 e g+25 d h)\right)\right) c^3+8 h^2 \left(\left(537 f g^2+245 h (3 e g+d h)\right) b^2+343 a h (3 f g+e h) b+128 a^2 f h^2\right) c^2-42 b^2 h^3 (78 a f h+35 b (3 f g+e h)) c-6 h \left(16 g \left(3 f g^2-7 h (e g+7 d h)\right) c^3+8 h \left(a h (41 f g+35 e h)+b \left(5 f g^2+7 h (9 e g+7 d h)\right)\right) c^2-6 b h^2 (59 b f g+49 b e h+74 a f h) c+231 b^3 f h^3\right) x c+1155 b^4 f h^4\right) \left(c x^2+b x+a\right)^{3/2}}{13440 c^5 h}-\frac{\left(b^2-4 a c\right) \left(-33 f h^3 b^5+6 c h^2 (20 a f h+7 b (3 f g+e h)) b^3-8 c^2 h \left(7 \left(3 f g^2+3 e h g+d h^2\right) b^2+14 a h (3 f g+e h) b+10 a^2 f h^2\right) b+256 c^5 d g^3-64 c^4 g \left(2 b g (e g+3 d h)+a \left(f g^2+3 h (e g+d h)\right)\right)+16 c^3 \left(5 g \left(f g^2+3 h (e g+d h)\right) b^2+6 a h \left(3 f g^2+h (3 e g+d h)\right) b+2 a^2 h^2 (3 f g+e h)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{2048 c^{13/2}}+\frac{\left(-33 f h^3 b^5+6 c h^2 (20 a f h+7 b (3 f g+e h)) b^3-8 c^2 h \left(7 \left(3 f g^2+3 e h g+d h^2\right) b^2+14 a h (3 f g+e h) b+10 a^2 f h^2\right) b+256 c^5 d g^3-64 c^4 g \left(2 b g (e g+3 d h)+a \left(f g^2+3 h (e g+d h)\right)\right)+16 c^3 \left(5 g \left(f g^2+3 h (e g+d h)\right) b^2+6 a h \left(3 f g^2+h (3 e g+d h)\right) b+2 a^2 h^2 (3 f g+e h)\right)\right) (b+2 c x) \sqrt{c x^2+b x+a}}{1024 c^6}",1,"((256*c^5*d*g^3 - 33*b^5*f*h^3 - 64*c^4*g*(a*f*g^2 + 3*a*h*(e*g + d*h) + 2*b*g*(e*g + 3*d*h)) + 6*b^3*c*h^2*(20*a*f*h + 7*b*(3*f*g + e*h)) - 8*b*c^2*h*(10*a^2*f*h^2 + 14*a*b*h*(3*f*g + e*h) + 7*b^2*(3*f*g^2 + 3*e*g*h + d*h^2)) + 16*c^3*(2*a^2*h^2*(3*f*g + e*h) + 5*b^2*g*(f*g^2 + 3*h*(e*g + d*h)) + 6*a*b*h*(3*f*g^2 + h*(3*e*g + d*h))))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^6) + ((33*b^2*f*h^2 - 2*c*h*(8*b*f*g + 21*b*e*h + 16*a*f*h) - 4*c^2*(3*f*g^2 - 7*h*(e*g + 2*d*h)))*(g + h*x)^2*(a + b*x + c*x^2)^(3/2))/(280*c^3*h) - ((6*c*f*g - 14*c*e*h + 11*b*f*h)*(g + h*x)^3*(a + b*x + c*x^2)^(3/2))/(84*c^2*h) + (f*(g + h*x)^4*(a + b*x + c*x^2)^(3/2))/(7*c*h) + ((1155*b^4*f*h^4 - 128*c^4*(3*f*g^4 - 7*g^2*h*(e*g + 12*d*h)) - 42*b^2*c*h^3*(78*a*f*h + 35*b*(3*f*g + e*h)) + 8*c^2*h^2*(128*a^2*f*h^2 + 343*a*b*h*(3*f*g + e*h) + b^2*(537*f*g^2 + 245*h*(3*e*g + d*h))) - 16*c^3*h*(16*a*h*(15*f*g^2 + 7*h*(3*e*g + d*h)) + b*g*(17*f*g^2 + 21*h*(19*e*g + 25*d*h))) - 6*c*h*(231*b^3*f*h^3 - 6*b*c*h^2*(59*b*f*g + 49*b*e*h + 74*a*f*h) + 16*c^3*(3*f*g^3 - 7*g*h*(e*g + 7*d*h)) + 8*c^2*h*(5*b*f*g^2 + 7*b*h*(9*e*g + 7*d*h) + a*h*(41*f*g + 35*e*h)))*x)*(a + b*x + c*x^2)^(3/2))/(13440*c^5*h) - ((b^2 - 4*a*c)*(256*c^5*d*g^3 - 33*b^5*f*h^3 - 64*c^4*g*(a*f*g^2 + 3*a*h*(e*g + d*h) + 2*b*g*(e*g + 3*d*h)) + 6*b^3*c*h^2*(20*a*f*h + 7*b*(3*f*g + e*h)) - 8*b*c^2*h*(10*a^2*f*h^2 + 14*a*b*h*(3*f*g + e*h) + 7*b^2*(3*f*g^2 + 3*e*g*h + d*h^2)) + 16*c^3*(2*a^2*h^2*(3*f*g + e*h) + 5*b^2*g*(f*g^2 + 3*h*(e*g + d*h)) + 6*a*b*h*(3*f*g^2 + h*(3*e*g + d*h))))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(13/2))","A",7,6,32,0.1875,1,"{1653, 832, 779, 612, 621, 206}"
187,1,581,0,1.4400138,"\int (g+h x)^2 \sqrt{a+b x+c x^2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^2*Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2),x]","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(8 c^2 \left(2 a^2 f h^2+6 a b h (e h+2 f g)+5 b^2 \left(h (d h+2 e g)+f g^2\right)\right)-28 b^2 c h (2 a f h+b e h+2 b f g)-32 c^3 \left(a h (d h+2 e g)+a f g^2+2 b g (2 d h+e g)\right)+21 b^4 f h^2+128 c^4 d g^2\right)}{512 c^5}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(8 c^2 \left(2 a^2 f h^2+6 a b h (e h+2 f g)+5 b^2 \left(h (d h+2 e g)+f g^2\right)\right)-28 b^2 c h (2 a f h+b e h+2 b f g)-32 c^3 \left(a h (d h+2 e g)+a f g^2+2 b g (2 d h+e g)\right)+21 b^4 f h^2+128 c^4 d g^2\right)}{1024 c^{11/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-6 c h x \left(-4 c h (5 a f h+7 b e h+2 b f g)+21 b^2 f h^2-8 c^2 \left(f g^2-h (5 d h+2 e g)\right)\right)+8 c^2 h \left(16 a h (e h+2 f g)+25 b h (d h+2 e g)+7 b f g^2\right)-28 b c h^2 (7 a f h+5 b (e h+2 f g))+105 b^3 f h^3+64 c^3 \left(f g^3-2 g h (5 d h+e g)\right)\right)}{960 c^4 h}-\frac{(g+h x)^2 \left(a+b x+c x^2\right)^{3/2} (3 b f h-4 c e h+2 c f g)}{20 c^2 h}+\frac{f (g+h x)^3 \left(a+b x+c x^2\right)^{3/2}}{6 c h}","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(8 c^2 \left(2 a^2 f h^2+6 a b h (e h+2 f g)+5 b^2 \left(d h^2+2 e g h+f g^2\right)\right)-28 b^2 c h (2 a f h+b e h+2 b f g)-32 c^3 \left(a \left(d h^2+2 e g h+f g^2\right)+2 b g (2 d h+e g)\right)+21 b^4 f h^2+128 c^4 d g^2\right)}{512 c^5}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(8 c^2 \left(2 a^2 f h^2+6 a b h (e h+2 f g)+5 b^2 \left(d h^2+2 e g h+f g^2\right)\right)-28 b^2 c h (2 a f h+b e h+2 b f g)-32 c^3 \left(a \left(d h^2+2 e g h+f g^2\right)+2 b g (2 d h+e g)\right)+21 b^4 f h^2+128 c^4 d g^2\right)}{1024 c^{11/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-6 c h x \left(-4 c h (5 a f h+7 b e h+2 b f g)+21 b^2 f h^2-8 c^2 \left(f g^2-h (5 d h+2 e g)\right)\right)+8 c^2 h \left(16 a h (e h+2 f g)+b \left(25 h (d h+2 e g)+7 f g^2\right)\right)-28 b c h^2 (7 a f h+5 b (e h+2 f g))+105 b^3 f h^3+64 c^3 g \left(f g^2-2 h (5 d h+e g)\right)\right)}{960 c^4 h}-\frac{(g+h x)^2 \left(a+b x+c x^2\right)^{3/2} (3 b f h-4 c e h+2 c f g)}{20 c^2 h}+\frac{f (g+h x)^3 \left(a+b x+c x^2\right)^{3/2}}{6 c h}",1,"((128*c^4*d*g^2 + 21*b^4*f*h^2 - 28*b^2*c*h*(2*b*f*g + b*e*h + 2*a*f*h) - 32*c^3*(a*f*g^2 + a*h*(2*e*g + d*h) + 2*b*g*(e*g + 2*d*h)) + 8*c^2*(2*a^2*f*h^2 + 6*a*b*h*(2*f*g + e*h) + 5*b^2*(f*g^2 + h*(2*e*g + d*h))))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^5) - ((2*c*f*g - 4*c*e*h + 3*b*f*h)*(g + h*x)^2*(a + b*x + c*x^2)^(3/2))/(20*c^2*h) + (f*(g + h*x)^3*(a + b*x + c*x^2)^(3/2))/(6*c*h) - ((105*b^3*f*h^3 + 64*c^3*(f*g^3 - 2*g*h*(e*g + 5*d*h)) - 28*b*c*h^2*(7*a*f*h + 5*b*(2*f*g + e*h)) + 8*c^2*h*(7*b*f*g^2 + 25*b*h*(2*e*g + d*h) + 16*a*h*(2*f*g + e*h)) - 6*c*h*(21*b^2*f*h^2 - 4*c*h*(2*b*f*g + 7*b*e*h + 5*a*f*h) - 8*c^2*(f*g^2 - h*(2*e*g + 5*d*h)))*x)*(a + b*x + c*x^2)^(3/2))/(960*c^4*h) - ((b^2 - 4*a*c)*(128*c^4*d*g^2 + 21*b^4*f*h^2 - 28*b^2*c*h*(2*b*f*g + b*e*h + 2*a*f*h) - 32*c^3*(a*f*g^2 + a*h*(2*e*g + d*h) + 2*b*g*(e*g + 2*d*h)) + 8*c^2*(2*a^2*f*h^2 + 6*a*b*h*(2*f*g + e*h) + 5*b^2*(f*g^2 + h*(2*e*g + d*h))))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(11/2))","A",6,6,32,0.1875,1,"{1653, 832, 779, 612, 621, 206}"
188,1,322,0,0.503646,"\int (g+h x) \sqrt{a+b x+c x^2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)*Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2),x]","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-2 c h (16 a f h+25 b (e h+f g))+35 b^2 f h^2-6 c h x (7 b f h-10 c e h+6 c f g)+c^2 \left(-\left(48 f g^2-80 h (d h+e g)\right)\right)\right)}{240 c^3 h}+\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-8 c^2 (a e h+a f g+2 b d h+2 b e g)+2 b c (6 a f h+5 b (e h+f g))-7 b^3 f h+32 c^3 d g\right)}{128 c^4}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-8 c^2 (a e h+a f g+2 b d h+2 b e g)+2 b c (6 a f h+5 b (e h+f g))-7 b^3 f h+32 c^3 d g\right)}{256 c^{9/2}}+\frac{f (g+h x)^2 \left(a+b x+c x^2\right)^{3/2}}{5 c h}","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-2 c h (16 a f h+25 b (e h+f g))+35 b^2 f h^2-6 c h x (7 b f h-10 c e h+6 c f g)-16 c^2 \left(3 f g^2-5 h (d h+e g)\right)\right)}{240 c^3 h}+\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-8 c^2 (a e h+a f g+2 b d h+2 b e g)+2 b c (6 a f h+5 b (e h+f g))-7 b^3 f h+32 c^3 d g\right)}{128 c^4}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-8 c^2 (a e h+a f g+2 b d h+2 b e g)+2 b c (6 a f h+5 b (e h+f g))-7 b^3 f h+32 c^3 d g\right)}{256 c^{9/2}}+\frac{f (g+h x)^2 \left(a+b x+c x^2\right)^{3/2}}{5 c h}",1,"((32*c^3*d*g - 7*b^3*f*h - 8*c^2*(2*b*e*g + a*f*g + 2*b*d*h + a*e*h) + 2*b*c*(6*a*f*h + 5*b*(f*g + e*h)))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(128*c^4) + (f*(g + h*x)^2*(a + b*x + c*x^2)^(3/2))/(5*c*h) + ((35*b^2*f*h^2 - c^2*(48*f*g^2 - 80*h*(e*g + d*h)) - 2*c*h*(16*a*f*h + 25*b*(f*g + e*h)) - 6*c*h*(6*c*f*g - 10*c*e*h + 7*b*f*h)*x)*(a + b*x + c*x^2)^(3/2))/(240*c^3*h) - ((b^2 - 4*a*c)*(32*c^3*d*g - 7*b^3*f*h - 8*c^2*(2*b*e*g + a*f*g + 2*b*d*h + a*e*h) + 2*b*c*(6*a*f*h + 5*b*(f*g + e*h)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(9/2))","A",5,5,30,0.1667,1,"{1653, 779, 612, 621, 206}"
189,1,175,0,0.1669759,"\int \sqrt{a+b x+c x^2} \left(d+e x+f x^2\right) \, dx","Int[Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2),x]","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c f+5 b^2 f-8 b c e+16 c^2 d\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+2 b e)+5 b^2 f+16 c^2 d\right)}{128 c^{7/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (8 c e-5 b f)}{24 c^2}+\frac{f x \left(a+b x+c x^2\right)^{3/2}}{4 c}","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c f+5 b^2 f-8 b c e+16 c^2 d\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+2 b e)+5 b^2 f+16 c^2 d\right)}{128 c^{7/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (8 c e-5 b f)}{24 c^2}+\frac{f x \left(a+b x+c x^2\right)^{3/2}}{4 c}",1,"((16*c^2*d - 8*b*c*e + 5*b^2*f - 4*a*c*f)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(64*c^3) + ((8*c*e - 5*b*f)*(a + b*x + c*x^2)^(3/2))/(24*c^2) + (f*x*(a + b*x + c*x^2)^(3/2))/(4*c) - ((b^2 - 4*a*c)*(16*c^2*d + 5*b^2*f - 4*c*(2*b*e + a*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(7/2))","A",5,5,25,0.2000,1,"{1661, 640, 612, 621, 206}"
190,1,321,0,0.7781524,"\int \frac{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)}{g+h x} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2))/(g + h*x),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 c h (2 c g-b h) (b f g-2 c d h)-\left(-4 c h (b g-a h)-b^2 h^2+8 c^2 g^2\right) (b f h-2 c e h+2 c f g)\right)}{16 c^{5/2} h^4}-\frac{\sqrt{a+b x+c x^2} (4 c h (b f g-2 c d h)+2 c h x (b f h-2 c e h+2 c f g)-(4 c g-b h) (b f h-2 c e h+2 c f g))}{8 c^2 h^3}+\frac{\sqrt{a h^2-b g h+c g^2} \left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right)}{h^4}+\frac{f \left(a+b x+c x^2\right)^{3/2}}{3 c h}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 c h (2 c g-b h) (b f g-2 c d h)-\left(-4 c h (b g-a h)-b^2 h^2+8 c^2 g^2\right) (b f h-2 c e h+2 c f g)\right)}{16 c^{5/2} h^4}-\frac{\sqrt{a+b x+c x^2} (4 c h (b f g-2 c d h)+2 c h x (b f h-2 c e h+2 c f g)-(4 c g-b h) (b f h-2 c e h+2 c f g))}{8 c^2 h^3}+\frac{\sqrt{a h^2-b g h+c g^2} \left(d h^2-e g h+f g^2\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right)}{h^4}+\frac{f \left(a+b x+c x^2\right)^{3/2}}{3 c h}",1,"-((4*c*h*(b*f*g - 2*c*d*h) - (4*c*g - b*h)*(2*c*f*g - 2*c*e*h + b*f*h) + 2*c*h*(2*c*f*g - 2*c*e*h + b*f*h)*x)*Sqrt[a + b*x + c*x^2])/(8*c^2*h^3) + (f*(a + b*x + c*x^2)^(3/2))/(3*c*h) + ((4*c*h*(2*c*g - b*h)*(b*f*g - 2*c*d*h) - (2*c*f*g - 2*c*e*h + b*f*h)*(8*c^2*g^2 - b^2*h^2 - 4*c*h*(b*g - a*h)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(5/2)*h^4) + (Sqrt[c*g^2 - b*g*h + a*h^2]*(f*g^2 - e*g*h + d*h^2)*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/h^4","A",7,6,32,0.1875,1,"{1653, 814, 843, 621, 206, 724}"
191,1,453,0,1.100229,"\int \frac{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^2} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^2,x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 c h (-a f h-b e h+2 b f g)+b^2 f h^2-8 c^2 \left(3 f g^2-h (2 e g-d h)\right)\right)}{8 c^{3/2} h^4}-\frac{\sqrt{a+b x+c x^2} \left(2 c h x \left(-a f h+b f g-2 c d h+2 c e g-\frac{3 c f g^2}{h}\right)+b f h (b g-a h)+4 a c h (2 f g-e h)-b c \left(4 d h^2-8 e g h+13 f g^2\right)-4 c^2 g \left(-d h+2 e g-\frac{3 f g^2}{h}\right)\right)}{4 c h^2 \left(a h^2-b g h+c g^2\right)}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(f g^2-h (e g-d h)\right)}{h (g+h x) \left(a h^2-b g h+c g^2\right)}-\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(2 c \left(3 f g^3-g h (2 e g-d h)\right)-h \left(-2 a h (2 f g-e h)-b h (3 e g-d h)+5 b f g^2\right)\right)}{2 h^4 \sqrt{a h^2-b g h+c g^2}}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 c h (-a f h-b e h+2 b f g)+b^2 f h^2-8 c^2 \left(3 f g^2-h (2 e g-d h)\right)\right)}{8 c^{3/2} h^4}-\frac{\sqrt{a+b x+c x^2} \left(2 c h^2 x \left(-a f h+b f g-2 c d h+2 c e g-\frac{3 c f g^2}{h}\right)+c h \left(4 a h (2 f g-e h)-b \left(4 d h^2-8 e g h+13 f g^2\right)\right)+b f h^2 (b g-a h)+4 c^2 g \left(3 f g^2-h (2 e g-d h)\right)\right)}{4 c h^3 \left(a h^2-b g h+c g^2\right)}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(f g^2-h (e g-d h)\right)}{h (g+h x) \left(a h^2-b g h+c g^2\right)}-\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(h \left(2 a h (2 f g-e h)-b \left(d h^2-3 e g h+5 f g^2\right)\right)+2 c g \left(3 f g^2-h (2 e g-d h)\right)\right)}{2 h^4 \sqrt{a h^2-b g h+c g^2}}",1,"-((b*f*h*(b*g - a*h) - 4*c^2*g*(2*e*g - (3*f*g^2)/h - d*h) + 4*a*c*h*(2*f*g - e*h) - b*c*(13*f*g^2 - 8*e*g*h + 4*d*h^2) + 2*c*h*(2*c*e*g + b*f*g - (3*c*f*g^2)/h - 2*c*d*h - a*f*h)*x)*Sqrt[a + b*x + c*x^2])/(4*c*h^2*(c*g^2 - b*g*h + a*h^2)) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(3/2))/(h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)) - ((b^2*f*h^2 + 4*c*h*(2*b*f*g - b*e*h - a*f*h) - 8*c^2*(3*f*g^2 - h*(2*e*g - d*h)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(3/2)*h^4) - ((2*c*(3*f*g^3 - g*h*(2*e*g - d*h)) - h*(5*b*f*g^2 - b*h*(3*e*g - d*h) - 2*a*h*(2*f*g - e*h)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(2*h^4*Sqrt[c*g^2 - b*g*h + a*h^2])","A",7,6,32,0.1875,1,"{1650, 814, 843, 621, 206, 724}"
192,1,446,0,0.8749617,"\int \frac{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^3} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^3,x]","\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(h^2 \left(8 a^2 f h^2-4 a b h (6 f g-e h)+b^2 \left(15 f g^2-h (d h+3 e g)\right)\right)-4 c h \left(b g^2 (10 f g-3 e h)-a h \left(d h^2-3 e g h+9 f g^2\right)\right)+8 c^2 g^3 (3 f g-e h)\right)}{8 h^4 \left(a h^2-b g h+c g^2\right)^{3/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(f g^2-h (e g-d h)\right)}{2 h (g+h x)^2 \left(a h^2-b g h+c g^2\right)}-\frac{\sqrt{a+b x+c x^2} \left(2 h x \left(-2 a f h+2 b f g-c d h+c e g-\frac{3 c f g^2}{h}\right)-4 a h (3 f g-e h)-b h (d h+3 e g)+11 b f g^2-\frac{4 c g^2 (3 f g-e h)}{h}\right)}{4 h^2 (g+h x) \left(a h^2-b g h+c g^2\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (-b f h-2 c e h+6 c f g)}{2 \sqrt{c} h^4}","\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(h^2 \left(8 a^2 f h^2-4 a b h (6 f g-e h)+b^2 \left(15 f g^2-h (d h+3 e g)\right)\right)-4 c h \left(b g^2 (10 f g-3 e h)-a h \left(d h^2-3 e g h+9 f g^2\right)\right)+8 c^2 g^3 (3 f g-e h)\right)}{8 h^4 \left(a h^2-b g h+c g^2\right)^{3/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(f g^2-h (e g-d h)\right)}{2 h (g+h x)^2 \left(a h^2-b g h+c g^2\right)}+\frac{\sqrt{a+b x+c x^2} \left(-2 h x \left(-2 a f h+2 b f g-c d h+c e g-\frac{3 c f g^2}{h}\right)+4 a h (3 f g-e h)-b \left(-d h^2-3 e g h+11 f g^2\right)+\frac{4 c g^2 (3 f g-e h)}{h}\right)}{4 h^2 (g+h x) \left(a h^2-b g h+c g^2\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (-b f h-2 c e h+6 c f g)}{2 \sqrt{c} h^4}",1,"-((11*b*f*g^2 - b*h*(3*e*g + d*h) - (4*c*g^2*(3*f*g - e*h))/h - 4*a*h*(3*f*g - e*h) + 2*h*(c*e*g + 2*b*f*g - (3*c*f*g^2)/h - c*d*h - 2*a*f*h)*x)*Sqrt[a + b*x + c*x^2])/(4*h^2*(c*g^2 - b*g*h + a*h^2)*(g + h*x)) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(3/2))/(2*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^2) - ((6*c*f*g - 2*c*e*h - b*f*h)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c]*h^4) + ((8*c^2*g^3*(3*f*g - e*h) - 4*c*h*(b*g^2*(10*f*g - 3*e*h) - a*h*(9*f*g^2 - 3*e*g*h + d*h^2)) + h^2*(8*a^2*f*h^2 - 4*a*b*h*(6*f*g - e*h) + b^2*(15*f*g^2 - h*(3*e*g + d*h))))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(8*h^4*(c*g^2 - b*g*h + a*h^2)^(3/2))","A",7,6,32,0.1875,1,"{1650, 812, 843, 621, 206, 724}"
193,1,601,0,1.4487677,"\int \frac{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^4} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^4,x]","-\frac{\sqrt{a+b x+c x^2} \left(h x \left(8 a^2 f h^3-2 b \left(a h^2 (10 f g-e h)-c g h (2 d h+e g)+12 c f g^3\right)+4 a c g h (6 f g-e h)+b^2 h \left(11 f g^2-h (d h+e g)\right)+c^2 \left(\frac{12 f g^4}{h}-4 d g^2 h\right)\right)+4 a^2 e h^4-2 b \left(a h^2 \left(d h^2+2 e g h+3 f g^2\right)+c \left(d g^2 h^2+7 f g^4\right)\right)+4 a c g h \left(d h^2+3 f g^2\right)+b^2 g h \left(h (d h+e g)+5 f g^2\right)+\frac{8 c^2 f g^5}{h}\right)}{8 h^2 (g+h x)^2 \left(a h^2-b g h+c g^2\right)^2}-\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(2 c h^2 \left(4 a^2 h^2 (4 f g-e h)-2 a b h \left(-d h^2-e g h+15 f g^2\right)+b^2 \left(d g h^2+15 f g^3\right)\right)-b h^3 \left(8 a^2 f h^2-2 a b h (e h+6 f g)+b^2 \left(d h^2+e g h+5 f g^2\right)\right)-8 c^2 g h \left(a d h^3-5 a f g^2 h+5 b f g^3\right)+16 c^3 f g^5\right)}{16 h^4 \left(a h^2-b g h+c g^2\right)^{5/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(f g^2-h (e g-d h)\right)}{3 h (g+h x)^3 \left(a h^2-b g h+c g^2\right)}+\frac{\sqrt{c} f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{h^4}","-\frac{\sqrt{a+b x+c x^2} \left(h x \left(h^2 \left(8 a^2 f h^2-2 a b h (10 f g-e h)+b^2 \left(11 f g^2-h (d h+e g)\right)\right)+2 c g h \left(2 a h (6 f g-e h)-b \left(12 f g^2-h (2 d h+e g)\right)\right)+4 c^2 \left(3 f g^4-d g^2 h^2\right)\right)+h^2 \left(4 a^2 e h^3-2 a b h \left(d h^2+2 e g h+3 f g^2\right)+b^2 g \left(d h^2+e g h+5 f g^2\right)\right)-2 c g h \left(-2 a d h^3-6 a f g^2 h+b d g h^2+7 b f g^3\right)+8 c^2 f g^5\right)}{8 h^3 (g+h x)^2 \left(a h^2-b g h+c g^2\right)^2}-\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(2 c h^2 \left(4 a^2 h^2 (4 f g-e h)-2 a b h \left(-d h^2-e g h+15 f g^2\right)+b^2 \left(d g h^2+15 f g^3\right)\right)-b h^3 \left(8 a^2 f h^2-2 a b h (e h+6 f g)+b^2 \left(d h^2+e g h+5 f g^2\right)\right)-8 c^2 g h \left(a d h^3-5 a f g^2 h+5 b f g^3\right)+16 c^3 f g^5\right)}{16 h^4 \left(a h^2-b g h+c g^2\right)^{5/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(f g^2-h (e g-d h)\right)}{3 h (g+h x)^3 \left(a h^2-b g h+c g^2\right)}+\frac{\sqrt{c} f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{h^4}",1,"-(((8*c^2*f*g^5)/h + 4*a^2*e*h^4 + 4*a*c*g*h*(3*f*g^2 + d*h^2) + b^2*g*h*(5*f*g^2 + h*(e*g + d*h)) - 2*b*(a*h^2*(3*f*g^2 + 2*e*g*h + d*h^2) + c*(7*f*g^4 + d*g^2*h^2)) + h*(8*a^2*f*h^3 + 4*a*c*g*h*(6*f*g - e*h) + c^2*((12*f*g^4)/h - 4*d*g^2*h) + b^2*h*(11*f*g^2 - h*(e*g + d*h)) - 2*b*(12*c*f*g^3 - c*g*h*(e*g + 2*d*h) + a*h^2*(10*f*g - e*h)))*x)*Sqrt[a + b*x + c*x^2])/(8*h^2*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)^2) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(3/2))/(3*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^3) + (Sqrt[c]*f*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/h^4 - ((16*c^3*f*g^5 - 8*c^2*g*h*(5*b*f*g^3 - 5*a*f*g^2*h + a*d*h^3) - b*h^3*(8*a^2*f*h^2 - 2*a*b*h*(6*f*g + e*h) + b^2*(5*f*g^2 + e*g*h + d*h^2)) + 2*c*h^2*(4*a^2*h^2*(4*f*g - e*h) - 2*a*b*h*(15*f*g^2 - e*g*h - d*h^2) + b^2*(15*f*g^3 + d*g*h^2)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(16*h^4*(c*g^2 - b*g*h + a*h^2)^(5/2))","A",7,6,32,0.1875,1,"{1650, 810, 843, 621, 206, 724}"
194,1,499,0,0.8554503,"\int \frac{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^5} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^5,x]","\frac{\sqrt{a+b x+c x^2} (-2 a h+x (2 c g-b h)+b g) \left(16 a^2 f h^2-4 c \left(-a h (5 e g-d h)+a f g^2+2 b g (2 d h+e g)\right)-8 a b h (e h+2 f g)+b^2 \left(h (5 d h+3 e g)+5 f g^2\right)+16 c^2 d g^2\right)}{64 (g+h x)^2 \left(a h^2-b g h+c g^2\right)^3}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(16 a^2 f h^2-4 c \left(-a h (5 e g-d h)+a f g^2+2 b g (2 d h+e g)\right)-8 a b h (e h+2 f g)+b^2 \left(h (5 d h+3 e g)+5 f g^2\right)+16 c^2 d g^2\right)}{128 \left(a h^2-b g h+c g^2\right)^{7/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(8 a h^2 (2 f g-e h)-b h \left(11 f g^2-h (5 d h+3 e g)\right)+2 c g h (e g-5 d h)+6 c f g^3\right)}{24 h (g+h x)^3 \left(a h^2-b g h+c g^2\right)^2}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(f g^2-h (e g-d h)\right)}{4 h (g+h x)^4 \left(a h^2-b g h+c g^2\right)}","\frac{\sqrt{a+b x+c x^2} (-2 a h+x (2 c g-b h)+b g) \left(16 a^2 f h^2-4 c \left(a \left(d h^2-5 e g h+f g^2\right)+2 b g (2 d h+e g)\right)-8 a b h (e h+2 f g)+b^2 \left(5 d h^2+3 e g h+5 f g^2\right)+16 c^2 d g^2\right)}{64 (g+h x)^2 \left(a h^2-b g h+c g^2\right)^3}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(16 a^2 f h^2-4 c \left(a \left(d h^2-5 e g h+f g^2\right)+2 b g (2 d h+e g)\right)-8 a b h (e h+2 f g)+b^2 \left(5 d h^2+3 e g h+5 f g^2\right)+16 c^2 d g^2\right)}{128 \left(a h^2-b g h+c g^2\right)^{7/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(h \left(8 a h (2 f g-e h)-b \left(-5 d h^2-3 e g h+11 f g^2\right)\right)+2 c g \left(h (e g-5 d h)+3 f g^2\right)\right)}{24 h (g+h x)^3 \left(a h^2-b g h+c g^2\right)^2}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(f g^2-h (e g-d h)\right)}{4 h (g+h x)^4 \left(a h^2-b g h+c g^2\right)}",1,"((16*c^2*d*g^2 + 16*a^2*f*h^2 - 8*a*b*h*(2*f*g + e*h) - 4*c*(a*f*g^2 - a*h*(5*e*g - d*h) + 2*b*g*(e*g + 2*d*h)) + b^2*(5*f*g^2 + h*(3*e*g + 5*d*h)))*(b*g - 2*a*h + (2*c*g - b*h)*x)*Sqrt[a + b*x + c*x^2])/(64*(c*g^2 - b*g*h + a*h^2)^3*(g + h*x)^2) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(3/2))/(4*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^4) + ((6*c*f*g^3 + 2*c*g*h*(e*g - 5*d*h) + 8*a*h^2*(2*f*g - e*h) - b*h*(11*f*g^2 - h*(3*e*g + 5*d*h)))*(a + b*x + c*x^2)^(3/2))/(24*h*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)^3) - ((b^2 - 4*a*c)*(16*c^2*d*g^2 + 16*a^2*f*h^2 - 8*a*b*h*(2*f*g + e*h) - 4*c*(a*f*g^2 - a*h*(5*e*g - d*h) + 2*b*g*(e*g + 2*d*h)) + b^2*(5*f*g^2 + h*(3*e*g + 5*d*h)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(128*(c*g^2 - b*g*h + a*h^2)^(7/2))","A",5,5,32,0.1562,1,"{1650, 806, 720, 724, 206}"
195,1,826,0,2.3347387,"\int \frac{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)}{(g+h x)^6} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2))/(g + h*x)^6,x]","\frac{\left(4 \left(3 f g^4+h (2 e g-27 d h) g^2\right) c^2-2 h \left(b g \left(16 f g^2-21 e h g-54 d h^2\right)-2 a h \left(18 f g^2-33 e h g+8 d h^2\right)\right) c-5 h^2 \left(\left(3 f g^2+3 e h g+7 d h^2\right) b^2-2 a h (6 f g+5 e h) b+16 a^2 f h^2\right)\right) \left(c x^2+b x+a\right)^{3/2}}{240 h \left(c g^2-b h g+a h^2\right)^3 (g+h x)^3}+\frac{\left(6 c f g^3+2 c h (2 e g-7 d h) g+10 a h^2 (2 f g-e h)-b h \left(13 f g^2-h (3 e g+7 d h)\right)\right) \left(c x^2+b x+a\right)^{3/2}}{40 h \left(c g^2-b h g+a h^2\right)^2 (g+h x)^4}-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{3/2}}{5 h \left(c g^2-b h g+a h^2\right) (g+h x)^5}+\frac{\left(32 c^3 d g^3-8 c^2 \left(a f g^2+2 b (e g+3 d h) g-3 a h (2 e g-d h)\right) g+2 c \left(\left(5 f g^3+3 h (2 e g+5 d h) g\right) b^2-6 a h \left(3 f g^2+h (3 e g-d h)\right) b+4 a^2 h^2 (6 f g-e h)\right)-b h \left(\left(3 f g^2+h (3 e g+7 d h)\right) b^2-2 a h (6 f g+5 e h) b+16 a^2 f h^2\right)\right) (b g-2 a h+(2 c g-b h) x) \sqrt{c x^2+b x+a}}{128 \left(c g^2-b h g+a h^2\right)^4 (g+h x)^2}-\frac{\left(b^2-4 a c\right) \left(32 c^3 d g^3-8 c^2 \left(a f g^2+2 b (e g+3 d h) g-3 a h (2 e g-d h)\right) g+2 c \left(\left(5 f g^3+3 h (2 e g+5 d h) g\right) b^2-6 a h \left(3 f g^2+h (3 e g-d h)\right) b+4 a^2 h^2 (6 f g-e h)\right)-b h \left(\left(3 f g^2+h (3 e g+7 d h)\right) b^2-2 a h (6 f g+5 e h) b+16 a^2 f h^2\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{256 \left(c g^2-b h g+a h^2\right)^{9/2}}","\frac{\left(4 c^2 \left(3 f g^2+h (2 e g-27 d h)\right) g^2-5 h^2 \left(\left(3 f g^2+3 e h g+7 d h^2\right) b^2-2 a h (6 f g+5 e h) b+16 a^2 f h^2\right)-2 c h \left(b g \left(16 f g^2-21 e h g-54 d h^2\right)-2 a h \left(18 f g^2-33 e h g+8 d h^2\right)\right)\right) \left(c x^2+b x+a\right)^{3/2}}{240 h \left(c g^2-b h g+a h^2\right)^3 (g+h x)^3}+\frac{\left(2 c g \left(3 f g^2+h (2 e g-7 d h)\right)+h \left(10 a h (2 f g-e h)-b \left(13 f g^2-3 e h g-7 d h^2\right)\right)\right) \left(c x^2+b x+a\right)^{3/2}}{40 h \left(c g^2-b h g+a h^2\right)^2 (g+h x)^4}-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{3/2}}{5 h \left(c g^2-b h g+a h^2\right) (g+h x)^5}+\frac{\left(32 c^3 d g^3-8 c^2 \left(2 b g (e g+3 d h)+a \left(f g^2-6 e h g+3 d h^2\right)\right) g-b h \left(\left(3 f g^2+3 e h g+7 d h^2\right) b^2-2 a h (6 f g+5 e h) b+16 a^2 f h^2\right)+2 c \left(g \left(5 f g^2+6 e h g+15 d h^2\right) b^2-6 a h \left(3 f g^2+3 e h g-d h^2\right) b+4 a^2 h^2 (6 f g-e h)\right)\right) (b g-2 a h+(2 c g-b h) x) \sqrt{c x^2+b x+a}}{128 \left(c g^2-b h g+a h^2\right)^4 (g+h x)^2}-\frac{\left(b^2-4 a c\right) \left(32 c^3 d g^3-8 c^2 \left(2 b g (e g+3 d h)+a \left(f g^2-6 e h g+3 d h^2\right)\right) g-b h \left(\left(3 f g^2+3 e h g+7 d h^2\right) b^2-2 a h (6 f g+5 e h) b+16 a^2 f h^2\right)+2 c \left(g \left(5 f g^2+6 e h g+15 d h^2\right) b^2-6 a h \left(3 f g^2+3 e h g-d h^2\right) b+4 a^2 h^2 (6 f g-e h)\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{256 \left(c g^2-b h g+a h^2\right)^{9/2}}",1,"((32*c^3*d*g^3 - 8*c^2*g*(a*f*g^2 - 3*a*h*(2*e*g - d*h) + 2*b*g*(e*g + 3*d*h)) + 2*c*(4*a^2*h^2*(6*f*g - e*h) - 6*a*b*h*(3*f*g^2 + h*(3*e*g - d*h)) + b^2*(5*f*g^3 + 3*g*h*(2*e*g + 5*d*h))) - b*h*(16*a^2*f*h^2 - 2*a*b*h*(6*f*g + 5*e*h) + b^2*(3*f*g^2 + h*(3*e*g + 7*d*h))))*(b*g - 2*a*h + (2*c*g - b*h)*x)*Sqrt[a + b*x + c*x^2])/(128*(c*g^2 - b*g*h + a*h^2)^4*(g + h*x)^2) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(3/2))/(5*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^5) + ((6*c*f*g^3 + 2*c*g*h*(2*e*g - 7*d*h) + 10*a*h^2*(2*f*g - e*h) - b*h*(13*f*g^2 - h*(3*e*g + 7*d*h)))*(a + b*x + c*x^2)^(3/2))/(40*h*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)^4) + ((4*c^2*(3*f*g^4 + g^2*h*(2*e*g - 27*d*h)) - 5*h^2*(16*a^2*f*h^2 - 2*a*b*h*(6*f*g + 5*e*h) + b^2*(3*f*g^2 + 3*e*g*h + 7*d*h^2)) - 2*c*h*(b*g*(16*f*g^2 - 21*e*g*h - 54*d*h^2) - 2*a*h*(18*f*g^2 - 33*e*g*h + 8*d*h^2)))*(a + b*x + c*x^2)^(3/2))/(240*h*(c*g^2 - b*g*h + a*h^2)^3*(g + h*x)^3) - ((b^2 - 4*a*c)*(32*c^3*d*g^3 - 8*c^2*g*(a*f*g^2 - 3*a*h*(2*e*g - d*h) + 2*b*g*(e*g + 3*d*h)) + 2*c*(4*a^2*h^2*(6*f*g - e*h) - 6*a*b*h*(3*f*g^2 + h*(3*e*g - d*h)) + b^2*(5*f*g^3 + 3*g*h*(2*e*g + 5*d*h))) - b*h*(16*a^2*f*h^2 - 2*a*b*h*(6*f*g + 5*e*h) + b^2*(3*f*g^2 + h*(3*e*g + 7*d*h))))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(256*(c*g^2 - b*g*h + a*h^2)^(9/2))","A",6,6,32,0.1875,1,"{1650, 834, 806, 720, 724, 206}"
196,1,1166,0,3.697658,"\int (g+h x)^3 \left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^3*(a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{f \left(c x^2+b x+a\right)^{5/2} (g+h x)^4}{9 c h}-\frac{(10 c f g-18 c e h+13 b f h) \left(c x^2+b x+a\right)^{5/2} (g+h x)^3}{144 c^2 h}+\frac{\left(-12 \left(5 f g^2-3 h (3 e g+8 d h)\right) c^2-2 h (24 b f g+99 b e h+64 a f h) c+143 b^2 f h^2\right) \left(c x^2+b x+a\right)^{5/2} (g+h x)^2}{2016 c^3 h}+\frac{\left(-192 \left(5 f g^4-3 g^2 h (3 e g+64 d h)\right) c^4-16 h \left(32 a h \left(17 f g^2+9 h (3 e g+d h)\right)+b g \left(13 f g^2+9 h (141 e g+196 d h)\right)\right) c^3+8 h^2 \left(\left(1553 f g^2+756 h (3 e g+d h)\right) b^2+837 a h (3 f g+e h) b+256 a^2 f h^2\right) c^2-198 b^2 h^3 (38 a f h+21 b (3 f g+e h)) c-10 h \left(16 \left(5 f g^3-9 g h (e g+12 d h)\right) c^3+8 h \left(a h (61 f g+63 e h)+3 b \left(f g^2+6 h (7 e g+6 d h)\right)\right) c^2-22 b h^2 (29 b f g+27 b e h+34 a f h) c+429 b^3 f h^3\right) x c+3003 b^4 f h^4\right) \left(c x^2+b x+a\right)^{5/2}}{80640 c^5 h}+\frac{\left(-143 f h^3 b^5+22 c h^2 (20 a f h+9 b (3 f g+e h)) b^3-48 c^2 h \left(6 \left(3 f g^2+3 e h g+d h^2\right) b^2+9 a h (3 f g+e h) b+5 a^2 f h^2\right) b+1536 c^5 d g^3-256 c^4 g \left(a f g^2+3 b (e g+3 d h) g+3 a h (e g+d h)\right)+32 c^3 \left(14 g \left(f g^2+3 h (e g+d h)\right) b^2+12 a h \left(3 f g^2+h (3 e g+d h)\right) b+3 a^2 h^2 (3 f g+e h)\right)\right) (b+2 c x) \left(c x^2+b x+a\right)^{3/2}}{12288 c^6}+\frac{\left(b^2-4 a c\right)^2 \left(-143 f h^3 b^5+22 c h^2 (20 a f h+9 b (3 f g+e h)) b^3-48 c^2 h \left(6 \left(3 f g^2+3 e h g+d h^2\right) b^2+9 a h (3 f g+e h) b+5 a^2 f h^2\right) b+1536 c^5 d g^3-256 c^4 g \left(a f g^2+3 b (e g+3 d h) g+3 a h (e g+d h)\right)+32 c^3 \left(14 g \left(f g^2+3 h (e g+d h)\right) b^2+12 a h \left(3 f g^2+h (3 e g+d h)\right) b+3 a^2 h^2 (3 f g+e h)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{65536 c^{15/2}}-\frac{\left(b^2-4 a c\right) \left(-143 f h^3 b^5+22 c h^2 (20 a f h+9 b (3 f g+e h)) b^3-48 c^2 h \left(6 \left(3 f g^2+3 e h g+d h^2\right) b^2+9 a h (3 f g+e h) b+5 a^2 f h^2\right) b+1536 c^5 d g^3-256 c^4 g \left(a f g^2+3 b (e g+3 d h) g+3 a h (e g+d h)\right)+32 c^3 \left(14 g \left(f g^2+3 h (e g+d h)\right) b^2+12 a h \left(3 f g^2+h (3 e g+d h)\right) b+3 a^2 h^2 (3 f g+e h)\right)\right) (b+2 c x) \sqrt{c x^2+b x+a}}{32768 c^7}","\frac{f \left(c x^2+b x+a\right)^{5/2} (g+h x)^4}{9 c h}-\frac{(10 c f g-18 c e h+13 b f h) \left(c x^2+b x+a\right)^{5/2} (g+h x)^3}{144 c^2 h}+\frac{\left(-12 \left(5 f g^2-3 h (3 e g+8 d h)\right) c^2-2 h (24 b f g+99 b e h+64 a f h) c+143 b^2 f h^2\right) \left(c x^2+b x+a\right)^{5/2} (g+h x)^2}{2016 c^3 h}+\frac{\left(-192 g^2 \left(5 f g^2-3 h (3 e g+64 d h)\right) c^4-16 h \left(32 a h \left(17 f g^2+9 h (3 e g+d h)\right)+b g \left(13 f g^2+9 h (141 e g+196 d h)\right)\right) c^3+8 h^2 \left(\left(1553 f g^2+756 h (3 e g+d h)\right) b^2+837 a h (3 f g+e h) b+256 a^2 f h^2\right) c^2-198 b^2 h^3 (38 a f h+21 b (3 f g+e h)) c-10 h \left(16 g \left(5 f g^2-9 h (e g+12 d h)\right) c^3+8 h \left(a h (61 f g+63 e h)+3 b \left(f g^2+6 h (7 e g+6 d h)\right)\right) c^2-22 b h^2 (29 b f g+27 b e h+34 a f h) c+429 b^3 f h^3\right) x c+3003 b^4 f h^4\right) \left(c x^2+b x+a\right)^{5/2}}{80640 c^5 h}+\frac{\left(-143 f h^3 b^5+22 c h^2 (20 a f h+9 b (3 f g+e h)) b^3-48 c^2 h \left(6 \left(3 f g^2+3 e h g+d h^2\right) b^2+9 a h (3 f g+e h) b+5 a^2 f h^2\right) b+1536 c^5 d g^3-256 c^4 g \left(3 b g (e g+3 d h)+a \left(f g^2+3 h (e g+d h)\right)\right)+32 c^3 \left(14 g \left(f g^2+3 h (e g+d h)\right) b^2+12 a h \left(3 f g^2+h (3 e g+d h)\right) b+3 a^2 h^2 (3 f g+e h)\right)\right) (b+2 c x) \left(c x^2+b x+a\right)^{3/2}}{12288 c^6}+\frac{\left(b^2-4 a c\right)^2 \left(-143 f h^3 b^5+22 c h^2 (20 a f h+9 b (3 f g+e h)) b^3-48 c^2 h \left(6 \left(3 f g^2+3 e h g+d h^2\right) b^2+9 a h (3 f g+e h) b+5 a^2 f h^2\right) b+1536 c^5 d g^3-256 c^4 g \left(3 b g (e g+3 d h)+a \left(f g^2+3 h (e g+d h)\right)\right)+32 c^3 \left(14 g \left(f g^2+3 h (e g+d h)\right) b^2+12 a h \left(3 f g^2+h (3 e g+d h)\right) b+3 a^2 h^2 (3 f g+e h)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{65536 c^{15/2}}-\frac{\left(b^2-4 a c\right) \left(-143 f h^3 b^5+22 c h^2 (20 a f h+9 b (3 f g+e h)) b^3-48 c^2 h \left(6 \left(3 f g^2+3 e h g+d h^2\right) b^2+9 a h (3 f g+e h) b+5 a^2 f h^2\right) b+1536 c^5 d g^3-256 c^4 g \left(3 b g (e g+3 d h)+a \left(f g^2+3 h (e g+d h)\right)\right)+32 c^3 \left(14 g \left(f g^2+3 h (e g+d h)\right) b^2+12 a h \left(3 f g^2+h (3 e g+d h)\right) b+3 a^2 h^2 (3 f g+e h)\right)\right) (b+2 c x) \sqrt{c x^2+b x+a}}{32768 c^7}",1,"-((b^2 - 4*a*c)*(1536*c^5*d*g^3 - 143*b^5*f*h^3 - 256*c^4*g*(a*f*g^2 + 3*a*h*(e*g + d*h) + 3*b*g*(e*g + 3*d*h)) + 22*b^3*c*h^2*(20*a*f*h + 9*b*(3*f*g + e*h)) - 48*b*c^2*h*(5*a^2*f*h^2 + 9*a*b*h*(3*f*g + e*h) + 6*b^2*(3*f*g^2 + 3*e*g*h + d*h^2)) + 32*c^3*(3*a^2*h^2*(3*f*g + e*h) + 14*b^2*g*(f*g^2 + 3*h*(e*g + d*h)) + 12*a*b*h*(3*f*g^2 + h*(3*e*g + d*h))))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(32768*c^7) + ((1536*c^5*d*g^3 - 143*b^5*f*h^3 - 256*c^4*g*(a*f*g^2 + 3*a*h*(e*g + d*h) + 3*b*g*(e*g + 3*d*h)) + 22*b^3*c*h^2*(20*a*f*h + 9*b*(3*f*g + e*h)) - 48*b*c^2*h*(5*a^2*f*h^2 + 9*a*b*h*(3*f*g + e*h) + 6*b^2*(3*f*g^2 + 3*e*g*h + d*h^2)) + 32*c^3*(3*a^2*h^2*(3*f*g + e*h) + 14*b^2*g*(f*g^2 + 3*h*(e*g + d*h)) + 12*a*b*h*(3*f*g^2 + h*(3*e*g + d*h))))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(12288*c^6) + ((143*b^2*f*h^2 - 2*c*h*(24*b*f*g + 99*b*e*h + 64*a*f*h) - 12*c^2*(5*f*g^2 - 3*h*(3*e*g + 8*d*h)))*(g + h*x)^2*(a + b*x + c*x^2)^(5/2))/(2016*c^3*h) - ((10*c*f*g - 18*c*e*h + 13*b*f*h)*(g + h*x)^3*(a + b*x + c*x^2)^(5/2))/(144*c^2*h) + (f*(g + h*x)^4*(a + b*x + c*x^2)^(5/2))/(9*c*h) + ((3003*b^4*f*h^4 - 192*c^4*(5*f*g^4 - 3*g^2*h*(3*e*g + 64*d*h)) - 198*b^2*c*h^3*(38*a*f*h + 21*b*(3*f*g + e*h)) + 8*c^2*h^2*(256*a^2*f*h^2 + 837*a*b*h*(3*f*g + e*h) + b^2*(1553*f*g^2 + 756*h*(3*e*g + d*h))) - 16*c^3*h*(32*a*h*(17*f*g^2 + 9*h*(3*e*g + d*h)) + b*g*(13*f*g^2 + 9*h*(141*e*g + 196*d*h))) - 10*c*h*(429*b^3*f*h^3 - 22*b*c*h^2*(29*b*f*g + 27*b*e*h + 34*a*f*h) + 16*c^3*(5*f*g^3 - 9*g*h*(e*g + 12*d*h)) + 8*c^2*h*(a*h*(61*f*g + 63*e*h) + 3*b*(f*g^2 + 6*h*(7*e*g + 6*d*h))))*x)*(a + b*x + c*x^2)^(5/2))/(80640*c^5*h) + ((b^2 - 4*a*c)^2*(1536*c^5*d*g^3 - 143*b^5*f*h^3 - 256*c^4*g*(a*f*g^2 + 3*a*h*(e*g + d*h) + 3*b*g*(e*g + 3*d*h)) + 22*b^3*c*h^2*(20*a*f*h + 9*b*(3*f*g + e*h)) - 48*b*c^2*h*(5*a^2*f*h^2 + 9*a*b*h*(3*f*g + e*h) + 6*b^2*(3*f*g^2 + 3*e*g*h + d*h^2)) + 32*c^3*(3*a^2*h^2*(3*f*g + e*h) + 14*b^2*g*(f*g^2 + 3*h*(e*g + d*h)) + 12*a*b*h*(3*f*g^2 + h*(3*e*g + d*h))))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(65536*c^(15/2))","A",8,6,32,0.1875,1,"{1653, 832, 779, 612, 621, 206}"
197,1,749,0,2.1036872,"\int (g+h x)^2 \left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^2*(a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(16 c^2 \left(3 a^2 f h^2+12 a b h (e h+2 f g)+14 b^2 \left(h (d h+2 e g)+f g^2\right)\right)-72 b^2 c h (3 a f h+2 b e h+4 b f g)-128 c^3 \left(a h (d h+2 e g)+a f g^2+3 b g (2 d h+e g)\right)+99 b^4 f h^2+768 c^4 d g^2\right)}{6144 c^5}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(16 c^2 \left(3 a^2 f h^2+12 a b h (e h+2 f g)+14 b^2 \left(h (d h+2 e g)+f g^2\right)\right)-72 b^2 c h (3 a f h+2 b e h+4 b f g)-128 c^3 \left(a h (d h+2 e g)+a f g^2+3 b g (2 d h+e g)\right)+99 b^4 f h^2+768 c^4 d g^2\right)}{16384 c^6}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(16 c^2 \left(3 a^2 f h^2+12 a b h (e h+2 f g)+14 b^2 \left(h (d h+2 e g)+f g^2\right)\right)-72 b^2 c h (3 a f h+2 b e h+4 b f g)-128 c^3 \left(a h (d h+2 e g)+a f g^2+3 b g (2 d h+e g)\right)+99 b^4 f h^2+768 c^4 d g^2\right)}{32768 c^{13/2}}-\frac{\left(a+b x+c x^2\right)^{5/2} \left(-10 c h x \left(-12 c h (7 a f h+2 b (6 e h+f g))+99 b^2 f h^2-8 c^2 \left(5 f g^2-4 h (7 d h+2 e g)\right)\right)+8 c^2 h \left(96 a h (e h+2 f g)+196 b h (d h+2 e g)+31 b f g^2\right)-36 b c h^2 (31 a f h+28 b (e h+2 f g))+693 b^3 f h^3+96 c^3 \left(5 f g^3-8 g h (7 d h+e g)\right)\right)}{13440 c^4 h}-\frac{(g+h x)^2 \left(a+b x+c x^2\right)^{5/2} (11 b f h-16 c e h+10 c f g)}{112 c^2 h}+\frac{f (g+h x)^3 \left(a+b x+c x^2\right)^{5/2}}{8 c h}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(16 c^2 \left(3 a^2 f h^2+12 a b h (e h+2 f g)+14 b^2 \left(d h^2+2 e g h+f g^2\right)\right)-72 b^2 c h (3 a f h+2 b e h+4 b f g)-128 c^3 \left(a \left(d h^2+2 e g h+f g^2\right)+3 b g (2 d h+e g)\right)+99 b^4 f h^2+768 c^4 d g^2\right)}{6144 c^5}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(16 c^2 \left(3 a^2 f h^2+12 a b h (e h+2 f g)+14 b^2 \left(d h^2+2 e g h+f g^2\right)\right)-72 b^2 c h (3 a f h+2 b e h+4 b f g)-128 c^3 \left(a \left(d h^2+2 e g h+f g^2\right)+3 b g (2 d h+e g)\right)+99 b^4 f h^2+768 c^4 d g^2\right)}{16384 c^6}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(16 c^2 \left(3 a^2 f h^2+12 a b h (e h+2 f g)+14 b^2 \left(d h^2+2 e g h+f g^2\right)\right)-72 b^2 c h (3 a f h+2 b e h+4 b f g)-128 c^3 \left(a \left(d h^2+2 e g h+f g^2\right)+3 b g (2 d h+e g)\right)+99 b^4 f h^2+768 c^4 d g^2\right)}{32768 c^{13/2}}-\frac{\left(a+b x+c x^2\right)^{5/2} \left(-10 c h x \left(-12 c h (7 a f h+2 b (6 e h+f g))+99 b^2 f h^2-8 c^2 \left(5 f g^2-4 h (7 d h+2 e g)\right)\right)+8 c^2 h \left(96 a h (e h+2 f g)+b \left(196 h (d h+2 e g)+31 f g^2\right)\right)-36 b c h^2 (31 a f h+28 b (e h+2 f g))+693 b^3 f h^3+96 c^3 g \left(5 f g^2-8 h (7 d h+e g)\right)\right)}{13440 c^4 h}-\frac{(g+h x)^2 \left(a+b x+c x^2\right)^{5/2} (11 b f h-16 c e h+10 c f g)}{112 c^2 h}+\frac{f (g+h x)^3 \left(a+b x+c x^2\right)^{5/2}}{8 c h}",1,"-((b^2 - 4*a*c)*(768*c^4*d*g^2 + 99*b^4*f*h^2 - 72*b^2*c*h*(4*b*f*g + 2*b*e*h + 3*a*f*h) - 128*c^3*(a*f*g^2 + a*h*(2*e*g + d*h) + 3*b*g*(e*g + 2*d*h)) + 16*c^2*(3*a^2*f*h^2 + 12*a*b*h*(2*f*g + e*h) + 14*b^2*(f*g^2 + h*(2*e*g + d*h))))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(16384*c^6) + ((768*c^4*d*g^2 + 99*b^4*f*h^2 - 72*b^2*c*h*(4*b*f*g + 2*b*e*h + 3*a*f*h) - 128*c^3*(a*f*g^2 + a*h*(2*e*g + d*h) + 3*b*g*(e*g + 2*d*h)) + 16*c^2*(3*a^2*f*h^2 + 12*a*b*h*(2*f*g + e*h) + 14*b^2*(f*g^2 + h*(2*e*g + d*h))))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(6144*c^5) - ((10*c*f*g - 16*c*e*h + 11*b*f*h)*(g + h*x)^2*(a + b*x + c*x^2)^(5/2))/(112*c^2*h) + (f*(g + h*x)^3*(a + b*x + c*x^2)^(5/2))/(8*c*h) - ((693*b^3*f*h^3 + 96*c^3*(5*f*g^3 - 8*g*h*(e*g + 7*d*h)) - 36*b*c*h^2*(31*a*f*h + 28*b*(2*f*g + e*h)) + 8*c^2*h*(31*b*f*g^2 + 196*b*h*(2*e*g + d*h) + 96*a*h*(2*f*g + e*h)) - 10*c*h*(99*b^2*f*h^2 - 8*c^2*(5*f*g^2 - 4*h*(2*e*g + 7*d*h)) - 12*c*h*(7*a*f*h + 2*b*(f*g + 6*e*h)))*x)*(a + b*x + c*x^2)^(5/2))/(13440*c^4*h) + ((b^2 - 4*a*c)^2*(768*c^4*d*g^2 + 99*b^4*f*h^2 - 72*b^2*c*h*(4*b*f*g + 2*b*e*h + 3*a*f*h) - 128*c^3*(a*f*g^2 + a*h*(2*e*g + d*h) + 3*b*g*(e*g + 2*d*h)) + 16*c^2*(3*a^2*f*h^2 + 12*a*b*h*(2*f*g + e*h) + 14*b^2*(f*g^2 + h*(2*e*g + d*h))))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32768*c^(13/2))","A",7,6,32,0.1875,1,"{1653, 832, 779, 612, 621, 206}"
198,1,418,0,0.6454295,"\int (g+h x) \left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)*(a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{\left(a+b x+c x^2\right)^{5/2} \left(-2 c h (24 a f h+49 b (e h+f g))+63 b^2 f h^2-10 c h x (9 b f h-14 c e h+10 c f g)-24 c^2 \left(5 f g^2-7 h (d h+e g)\right)\right)}{840 c^3 h}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-8 c^2 (a e h+a f g+3 b d h+3 b e g)+2 b c (6 a f h+7 b (e h+f g))-9 b^3 f h+48 c^3 d g\right)}{384 c^4}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-8 c^2 (a e h+a f g+3 b d h+3 b e g)+2 b c (6 a f h+7 b (e h+f g))-9 b^3 f h+48 c^3 d g\right)}{1024 c^5}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-8 c^2 (a e h+a f g+3 b d h+3 b e g)+2 b c (6 a f h+7 b (e h+f g))-9 b^3 f h+48 c^3 d g\right)}{2048 c^{11/2}}+\frac{f (g+h x)^2 \left(a+b x+c x^2\right)^{5/2}}{7 c h}","\frac{\left(a+b x+c x^2\right)^{5/2} \left(-2 c h (24 a f h+49 b (e h+f g))+63 b^2 f h^2-10 c h x (9 b f h-14 c e h+10 c f g)-24 c^2 \left(5 f g^2-7 h (d h+e g)\right)\right)}{840 c^3 h}+\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-8 c^2 (a e h+a f g+3 b d h+3 b e g)+2 b c (6 a f h+7 b (e h+f g))-9 b^3 f h+48 c^3 d g\right)}{384 c^4}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-8 c^2 (a e h+a f g+3 b d h+3 b e g)+2 b c (6 a f h+7 b (e h+f g))-9 b^3 f h+48 c^3 d g\right)}{1024 c^5}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-8 c^2 (a e h+a f g+3 b d h+3 b e g)+2 b c (6 a f h+7 b (e h+f g))-9 b^3 f h+48 c^3 d g\right)}{2048 c^{11/2}}+\frac{f (g+h x)^2 \left(a+b x+c x^2\right)^{5/2}}{7 c h}",1,"-((b^2 - 4*a*c)*(48*c^3*d*g - 9*b^3*f*h - 8*c^2*(3*b*e*g + a*f*g + 3*b*d*h + a*e*h) + 2*b*c*(6*a*f*h + 7*b*(f*g + e*h)))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^5) + ((48*c^3*d*g - 9*b^3*f*h - 8*c^2*(3*b*e*g + a*f*g + 3*b*d*h + a*e*h) + 2*b*c*(6*a*f*h + 7*b*(f*g + e*h)))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(384*c^4) + (f*(g + h*x)^2*(a + b*x + c*x^2)^(5/2))/(7*c*h) + ((63*b^2*f*h^2 - 24*c^2*(5*f*g^2 - 7*h*(e*g + d*h)) - 2*c*h*(24*a*f*h + 49*b*(f*g + e*h)) - 10*c*h*(10*c*f*g - 14*c*e*h + 9*b*f*h)*x)*(a + b*x + c*x^2)^(5/2))/(840*c^3*h) + ((b^2 - 4*a*c)^2*(48*c^3*d*g - 9*b^3*f*h - 8*c^2*(3*b*e*g + a*f*g + 3*b*d*h + a*e*h) + 2*b*c*(6*a*f*h + 7*b*(f*g + e*h)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(11/2))","A",6,5,30,0.1667,1,"{1653, 779, 612, 621, 206}"
199,1,236,0,0.2419522,"\int \left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Int[(a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a c f+7 b^2 f-12 b c e+24 c^2 d\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c (a f+3 b e)+7 b^2 f+24 c^2 d\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+3 b e)+7 b^2 f+24 c^2 d\right)}{1024 c^{9/2}}+\frac{\left(a+b x+c x^2\right)^{5/2} (12 c e-7 b f)}{60 c^2}+\frac{f x \left(a+b x+c x^2\right)^{5/2}}{6 c}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a c f+7 b^2 f-12 b c e+24 c^2 d\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c (a f+3 b e)+7 b^2 f+24 c^2 d\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+3 b e)+7 b^2 f+24 c^2 d\right)}{1024 c^{9/2}}+\frac{\left(a+b x+c x^2\right)^{5/2} (12 c e-7 b f)}{60 c^2}+\frac{f x \left(a+b x+c x^2\right)^{5/2}}{6 c}",1,"-((b^2 - 4*a*c)*(24*c^2*d + 7*b^2*f - 4*c*(3*b*e + a*f))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^4) + ((24*c^2*d - 12*b*c*e + 7*b^2*f - 4*a*c*f)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(192*c^3) + ((12*c*e - 7*b*f)*(a + b*x + c*x^2)^(5/2))/(60*c^2) + (f*x*(a + b*x + c*x^2)^(5/2))/(6*c) + ((b^2 - 4*a*c)^2*(24*c^2*d + 7*b^2*f - 4*c*(3*b*e + a*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(9/2))","A",6,5,25,0.2000,1,"{1661, 640, 612, 621, 206}"
200,1,660,0,1.8250612,"\int \frac{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{g+h x} \, dx","Int[((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x),x]","\frac{\sqrt{a+b x+c x^2} \left(2 c h x \left(8 c h (2 c g-b h) (b f g-2 c d h)-\left(-4 c h (2 b g-3 a h)-3 b^2 h^2+16 c^2 g^2\right) (b f h-2 c e h+2 c f g)\right)+6 b^2 c h^3 (-2 a f h-b e h+b f g)-8 b c^2 h^2 \left(3 a h (f g-e h)-2 b \left(d h^2-e g h+f g^2\right)\right)-32 c^3 h (5 b g-4 a h) \left(f g^2-h (e g-d h)\right)+3 b^4 f h^4+128 c^4 \left(f g^4-g^2 h (e g-d h)\right)\right)}{128 c^3 h^5}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 c h (2 c g-b h) \left(8 c h (b g-2 a h) (b f g-2 c d h)-g \left(-4 a c h-3 b^2 h+8 b c g\right) (b f h-2 c e h+2 c f g)\right)-2 \left(-2 c h (b g-a h)-\frac{b^2 h^2}{2}+4 c^2 g^2\right) \left(8 c h (2 c g-b h) (b f g-2 c d h)-\left(-4 c h (2 b g-3 a h)-3 b^2 h^2+16 c^2 g^2\right) (b f h-2 c e h+2 c f g)\right)\right)}{256 c^{7/2} h^6}-\frac{\left(a+b x+c x^2\right)^{3/2} (8 c h (b f g-2 c d h)+6 c h x (b f h-2 c e h+2 c f g)-(8 c g-3 b h) (b f h-2 c e h+2 c f g))}{48 c^2 h^3}+\frac{\left(a h^2-b g h+c g^2\right)^{3/2} \left(f g^2-h (e g-d h)\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right)}{h^6}+\frac{f \left(a+b x+c x^2\right)^{5/2}}{5 c h}","\frac{\sqrt{a+b x+c x^2} \left(2 c h x \left(8 c h (2 c g-b h) (b f g-2 c d h)-\left(-4 c h (2 b g-3 a h)-3 b^2 h^2+16 c^2 g^2\right) (b f h-2 c e h+2 c f g)\right)+6 b^2 c h^3 (-2 a f h-b e h+b f g)-8 b c^2 h^2 \left(3 a h (f g-e h)-2 b \left(d h^2-e g h+f g^2\right)\right)-32 c^3 h (5 b g-4 a h) \left(f g^2-h (e g-d h)\right)+3 b^4 f h^4+128 c^4 g^2 \left(f g^2-h (e g-d h)\right)\right)}{128 c^3 h^5}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 c h (2 c g-b h) \left(8 c h (b g-2 a h) (b f g-2 c d h)-g \left(-4 a c h-3 b^2 h+8 b c g\right) (b f h-2 c e h+2 c f g)\right)-2 \left(-2 c h (b g-a h)-\frac{b^2 h^2}{2}+4 c^2 g^2\right) \left(8 c h (2 c g-b h) (b f g-2 c d h)-\left(-4 c h (2 b g-3 a h)-3 b^2 h^2+16 c^2 g^2\right) (b f h-2 c e h+2 c f g)\right)\right)}{256 c^{7/2} h^6}-\frac{\left(a+b x+c x^2\right)^{3/2} (8 c h (b f g-2 c d h)+6 c h x (b f h-2 c e h+2 c f g)-(8 c g-3 b h) (b f h-2 c e h+2 c f g))}{48 c^2 h^3}+\frac{\left(a h^2-b g h+c g^2\right)^{3/2} \left(f g^2-h (e g-d h)\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right)}{h^6}+\frac{f \left(a+b x+c x^2\right)^{5/2}}{5 c h}",1,"((3*b^4*f*h^4 + 6*b^2*c*h^3*(b*f*g - b*e*h - 2*a*f*h) - 32*c^3*h*(5*b*g - 4*a*h)*(f*g^2 - h*(e*g - d*h)) + 128*c^4*(f*g^4 - g^2*h*(e*g - d*h)) - 8*b*c^2*h^2*(3*a*h*(f*g - e*h) - 2*b*(f*g^2 - e*g*h + d*h^2)) + 2*c*h*(8*c*h*(2*c*g - b*h)*(b*f*g - 2*c*d*h) - (2*c*f*g - 2*c*e*h + b*f*h)*(16*c^2*g^2 - 3*b^2*h^2 - 4*c*h*(2*b*g - 3*a*h)))*x)*Sqrt[a + b*x + c*x^2])/(128*c^3*h^5) - ((8*c*h*(b*f*g - 2*c*d*h) - (8*c*g - 3*b*h)*(2*c*f*g - 2*c*e*h + b*f*h) + 6*c*h*(2*c*f*g - 2*c*e*h + b*f*h)*x)*(a + b*x + c*x^2)^(3/2))/(48*c^2*h^3) + (f*(a + b*x + c*x^2)^(5/2))/(5*c*h) - ((4*c*h*(2*c*g - b*h)*(8*c*h*(b*g - 2*a*h)*(b*f*g - 2*c*d*h) - g*(8*b*c*g - 3*b^2*h - 4*a*c*h)*(2*c*f*g - 2*c*e*h + b*f*h)) - 2*(4*c^2*g^2 - (b^2*h^2)/2 - 2*c*h*(b*g - a*h))*(8*c*h*(2*c*g - b*h)*(b*f*g - 2*c*d*h) - (2*c*f*g - 2*c*e*h + b*f*h)*(16*c^2*g^2 - 3*b^2*h^2 - 4*c*h*(2*b*g - 3*a*h))))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(7/2)*h^6) + ((c*g^2 - b*g*h + a*h^2)^(3/2)*(f*g^2 - h*(e*g - d*h))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/h^6","A",8,6,32,0.1875,1,"{1653, 814, 843, 621, 206, 724}"
201,1,750,0,2.5032745,"\int \frac{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^2} \, dx","Int[((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^2,x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 c^2 h^2 \left(a^2 f h^2-2 a b h (2 f g-e h)+b^2 \left(d h^2-2 e g h+3 f g^2\right)\right)+8 b^2 c h^3 (-3 a f h-b e h+2 b f g)+192 c^3 h \left(a h \left(d h^2-2 e g h+3 f g^2\right)-b g \left(2 d h^2-3 e g h+4 f g^2\right)\right)+3 b^4 f h^4+128 c^4 \left(5 f g^4-g^2 h (4 e g-3 d h)\right)\right)}{128 c^{5/2} h^6}-\frac{\sqrt{a+b x+c x^2} \left(2 c h x \left(4 c h (-3 a f h-2 b e h+4 b f g)+3 b^2 f h^2-16 c^2 \left(5 f g^2-h (4 e g-3 d h)\right)\right)-16 c^2 h \left(-4 a h (2 f g-e h)-b h (14 e g-9 d h)+19 b f g^2\right)+4 b c h^2 (-3 a f h-2 b e h+4 b f g)+3 b^3 f h^3+64 c^3 \left(5 f g^3-g h (4 e g-3 d h)\right)\right)}{64 c^2 h^5}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(6 c h x \left(-a f h+b f g-4 c d h+4 c e g-\frac{5 c f g^2}{h}\right)-c \left(-8 a h (2 f g-e h)-8 b h (4 e g-3 d h)+43 b f g^2\right)+3 b f h (b g-a h)+\frac{8 c^2 \left(5 f g^3-g h (4 e g-3 d h)\right)}{h}\right)}{24 c h^2 \left(a h^2-b g h+c g^2\right)}-\frac{\left(a+b x+c x^2\right)^{5/2} \left(f g^2-h (e g-d h)\right)}{h (g+h x) \left(a h^2-b g h+c g^2\right)}-\frac{\sqrt{a h^2-b g h+c g^2} \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(2 c \left(5 f g^3-g h (4 e g-3 d h)\right)-h \left(-2 a h (2 f g-e h)-b h (5 e g-3 d h)+7 b f g^2\right)\right)}{2 h^6}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 c^2 h^2 \left(a^2 f h^2-2 a b h (2 f g-e h)+b^2 \left(d h^2-2 e g h+3 f g^2\right)\right)+8 b^2 c h^3 (-3 a f h-b e h+2 b f g)+192 c^3 h \left(a h \left(d h^2-2 e g h+3 f g^2\right)-b g \left(2 d h^2-3 e g h+4 f g^2\right)\right)+3 b^4 f h^4+128 c^4 g^2 \left(5 f g^2-h (4 e g-3 d h)\right)\right)}{128 c^{5/2} h^6}-\frac{\sqrt{a+b x+c x^2} \left(2 c h x \left(4 c h (-3 a f h-2 b e h+4 b f g)+3 b^2 f h^2-16 c^2 \left(5 f g^2-h (4 e g-3 d h)\right)\right)+16 c^2 h \left(4 a h (2 f g-e h)-b \left(9 d h^2-14 e g h+19 f g^2\right)\right)+4 b c h^2 (-3 a f h-2 b e h+4 b f g)+3 b^3 f h^3+64 c^3 g \left(5 f g^2-h (4 e g-3 d h)\right)\right)}{64 c^2 h^5}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(6 c h^2 x \left(-a f h+b f g-4 c d h+4 c e g-\frac{5 c f g^2}{h}\right)+c h \left(8 a h (2 f g-e h)-b \left(43 f g^2-8 h (4 e g-3 d h)\right)\right)+3 b f h^2 (b g-a h)+8 c^2 g \left(5 f g^2-h (4 e g-3 d h)\right)\right)}{24 c h^3 \left(a h^2-b g h+c g^2\right)}-\frac{\left(a+b x+c x^2\right)^{5/2} \left(f g^2-h (e g-d h)\right)}{h (g+h x) \left(a h^2-b g h+c g^2\right)}-\frac{\sqrt{a h^2-b g h+c g^2} \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(h \left(2 a h (2 f g-e h)-b \left(3 d h^2-5 e g h+7 f g^2\right)\right)+2 c g \left(5 f g^2-h (4 e g-3 d h)\right)\right)}{2 h^6}",1,"-((3*b^3*f*h^3 + 4*b*c*h^2*(4*b*f*g - 2*b*e*h - 3*a*f*h) + 64*c^3*(5*f*g^3 - g*h*(4*e*g - 3*d*h)) - 16*c^2*h*(19*b*f*g^2 - b*h*(14*e*g - 9*d*h) - 4*a*h*(2*f*g - e*h)) + 2*c*h*(3*b^2*f*h^2 + 4*c*h*(4*b*f*g - 2*b*e*h - 3*a*f*h) - 16*c^2*(5*f*g^2 - h*(4*e*g - 3*d*h)))*x)*Sqrt[a + b*x + c*x^2])/(64*c^2*h^5) - ((3*b*f*h*(b*g - a*h) + (8*c^2*(5*f*g^3 - g*h*(4*e*g - 3*d*h)))/h - c*(43*b*f*g^2 - 8*b*h*(4*e*g - 3*d*h) - 8*a*h*(2*f*g - e*h)) + 6*c*h*(4*c*e*g + b*f*g - (5*c*f*g^2)/h - 4*c*d*h - a*f*h)*x)*(a + b*x + c*x^2)^(3/2))/(24*c*h^2*(c*g^2 - b*g*h + a*h^2)) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(5/2))/(h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)) + ((3*b^4*f*h^4 + 8*b^2*c*h^3*(2*b*f*g - b*e*h - 3*a*f*h) + 128*c^4*(5*f*g^4 - g^2*h*(4*e*g - 3*d*h)) + 48*c^2*h^2*(a^2*f*h^2 - 2*a*b*h*(2*f*g - e*h) + b^2*(3*f*g^2 - 2*e*g*h + d*h^2)) + 192*c^3*h*(a*h*(3*f*g^2 - 2*e*g*h + d*h^2) - b*g*(4*f*g^2 - 3*e*g*h + 2*d*h^2)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(5/2)*h^6) - (Sqrt[c*g^2 - b*g*h + a*h^2]*(2*c*(5*f*g^3 - g*h*(4*e*g - 3*d*h)) - h*(7*b*f*g^2 - b*h*(5*e*g - 3*d*h) - 2*a*h*(2*f*g - e*h)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(2*h^6)","A",8,6,32,0.1875,1,"{1650, 814, 843, 621, 206, 724}"
202,1,819,0,2.1410701,"\int \frac{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^3} \, dx","Int[((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^3,x]","-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{2 h \left(c g^2-b h g+a h^2\right) (g+h x)^2}-\frac{\left(31 b f g^2+4 c \left(-\frac{10 f g^2}{h}+6 e g-3 d h\right) g-3 b h (5 e g-d h)-4 a h (7 f g-3 e h)+2 h \left(-\frac{5 c f g^2}{h}+3 c e g+2 b f g-3 c d h-2 a f h\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{12 h^2 \left(c g^2-b h g+a h^2\right) (g+h x)}-\frac{\left(8 g^2 \left(-\frac{10 f g^2}{h}+6 e g-3 d h\right) c^3-2 \left(2 a h \left(19 f g^2-9 e h g+3 d h^2\right)-3 b g \left(22 f g^2-12 e h g+5 d h^2\right)\right) c^2-h \left(\left(53 f g^2-6 h (4 e g-d h)\right) b^2-18 a h (3 f g-e h) b+8 a^2 f h^2\right) c+2 \left(2 \left(10 f g^3-3 g h (2 e g-d h)\right) c^2+h \left(2 a h (7 f g-3 e h)-3 b \left(6 f g^2-3 e h g+d h^2\right)\right) c+b f h^2 (b g-a h)\right) x c+b^2 f h^2 (b g-a h)\right) \sqrt{c x^2+b x+a}}{8 c h^4 \left(c g^2-b h g+a h^2\right)}-\frac{\left(16 \left(10 f g^3-3 g h (2 e g-d h)\right) c^3-24 h \left(6 b f g^2-b h (3 e g-d h)-a h (3 f g-e h)\right) c^2+6 b h^2 (3 b f g-b e h-2 a f h) c+b^3 f h^3\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{16 c^{3/2} h^6}+\frac{\left(8 \left(10 f g^4-3 g^2 h (2 e g-d h)\right) c^2-4 h \left(28 b f g^3-3 b h (5 e g-2 d h) g-a h \left(19 f g^2-9 e h g+3 d h^2\right)\right) c+h^2 \left(\left(35 f g^2-3 h (5 e g-d h)\right) b^2-4 a h (10 f g-3 e h) b+8 a^2 f h^2\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{8 h^6 \sqrt{c g^2-b h g+a h^2}}","-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{2 h \left(c g^2-b h g+a h^2\right) (g+h x)^2}-\frac{\left(4 c g \left(-\frac{10 f g^2}{h}+6 e g-3 d h\right)-4 a h (7 f g-3 e h)+b \left(31 f g^2-3 h (5 e g-d h)\right)+2 h \left(-\frac{5 c f g^2}{h}+3 c e g+2 b f g-3 c d h-2 a f h\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{12 h^2 \left(c g^2-b h g+a h^2\right) (g+h x)}-\frac{\left(-8 g^2 \left(10 f g^2-3 h (2 e g-d h)\right) c^3-2 h \left(2 a h \left(19 f g^2-9 e h g+3 d h^2\right)-3 b g \left(22 f g^2-12 e h g+5 d h^2\right)\right) c^2-h^2 \left(\left(53 f g^2-6 h (4 e g-d h)\right) b^2-18 a h (3 f g-e h) b+8 a^2 f h^2\right) c+2 h \left(2 g \left(10 f g^2-3 h (2 e g-d h)\right) c^2+h \left(2 a h (7 f g-3 e h)-3 b \left(6 f g^2-3 e h g+d h^2\right)\right) c+b f h^2 (b g-a h)\right) x c+b^2 f h^3 (b g-a h)\right) \sqrt{c x^2+b x+a}}{8 c h^5 \left(c g^2-b h g+a h^2\right)}-\frac{\left(16 g \left(10 f g^2-3 h (2 e g-d h)\right) c^3+24 h \left(a h (3 f g-e h)-b \left(6 f g^2-3 e h g+d h^2\right)\right) c^2+6 b h^2 (3 b f g-b e h-2 a f h) c+b^3 f h^3\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{16 c^{3/2} h^6}+\frac{\left(8 c^2 \left(10 f g^2-3 h (2 e g-d h)\right) g^2+4 c h \left(a h \left(19 f g^2-9 e h g+3 d h^2\right)-b g \left(28 f g^2-15 e h g+6 d h^2\right)\right)+h^2 \left(\left(35 f g^2-3 h (5 e g-d h)\right) b^2-4 a h (10 f g-3 e h) b+8 a^2 f h^2\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{8 h^6 \sqrt{c g^2-b h g+a h^2}}",1,"-((b^2*f*h^2*(b*g - a*h) + 8*c^3*g^2*(6*e*g - (10*f*g^2)/h - 3*d*h) - 2*c^2*(2*a*h*(19*f*g^2 - 9*e*g*h + 3*d*h^2) - 3*b*g*(22*f*g^2 - 12*e*g*h + 5*d*h^2)) - c*h*(8*a^2*f*h^2 - 18*a*b*h*(3*f*g - e*h) + b^2*(53*f*g^2 - 6*h*(4*e*g - d*h))) + 2*c*(b*f*h^2*(b*g - a*h) + 2*c^2*(10*f*g^3 - 3*g*h*(2*e*g - d*h)) + c*h*(2*a*h*(7*f*g - 3*e*h) - 3*b*(6*f*g^2 - 3*e*g*h + d*h^2)))*x)*Sqrt[a + b*x + c*x^2])/(8*c*h^4*(c*g^2 - b*g*h + a*h^2)) - ((31*b*f*g^2 + 4*c*g*(6*e*g - (10*f*g^2)/h - 3*d*h) - 3*b*h*(5*e*g - d*h) - 4*a*h*(7*f*g - 3*e*h) + 2*h*(3*c*e*g + 2*b*f*g - (5*c*f*g^2)/h - 3*c*d*h - 2*a*f*h)*x)*(a + b*x + c*x^2)^(3/2))/(12*h^2*(c*g^2 - b*g*h + a*h^2)*(g + h*x)) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(5/2))/(2*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^2) - ((b^3*f*h^3 + 6*b*c*h^2*(3*b*f*g - b*e*h - 2*a*f*h) + 16*c^3*(10*f*g^3 - 3*g*h*(2*e*g - d*h)) - 24*c^2*h*(6*b*f*g^2 - b*h*(3*e*g - d*h) - a*h*(3*f*g - e*h)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2)*h^6) + ((8*c^2*(10*f*g^4 - 3*g^2*h*(2*e*g - d*h)) - 4*c*h*(28*b*f*g^3 - 3*b*g*h*(5*e*g - 2*d*h) - a*h*(19*f*g^2 - 9*e*g*h + 3*d*h^2)) + h^2*(8*a^2*f*h^2 - 4*a*b*h*(10*f*g - 3*e*h) + b^2*(35*f*g^2 - 3*h*(5*e*g - d*h))))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(8*h^6*Sqrt[c*g^2 - b*g*h + a*h^2])","A",8,7,32,0.2188,1,"{1650, 812, 814, 843, 621, 206, 724}"
203,1,829,0,2.2643806,"\int \frac{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^4} \, dx","Int[((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^4,x]","-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{3 h \left(c g^2-b h g+a h^2\right) (g+h x)^3}-\frac{\left(17 b f g^2+2 c \left(-\frac{10 f g^2}{h}+4 e g-d h\right) g-b h (5 e g+d h)-6 a h (3 f g-e h)+2 h \left(-\frac{5 c f g^2}{h}+2 c e g+3 b f g-2 c d h-3 a f h\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{12 h^2 \left(c g^2-b h g+a h^2\right) (g+h x)^2}-\frac{\left(12 a^2 f h^3-6 a b (7 f g-e h) h^2+4 a c \left(23 f g^2-2 h (4 e g-d h)\right) h+b^2 \left(29 f g^2-h (5 e g+d h)\right) h-8 c^2 g^2 \left(-\frac{10 f g^2}{h}+4 e g-d h\right)-6 b c g \left(18 f g^2-h (6 e g-d h)\right)+2 \left(2 \left(10 f g^3-g h (4 e g-d h)\right) c^2-h \left(22 b f g^2-b h (7 e g-d h)-6 a h (3 f g-e h)\right) c+3 b f h^2 (b g-a h)\right) x\right) \sqrt{c x^2+b x+a}}{8 h^4 \left(c g^2-b h g+a h^2\right) (g+h x)}+\frac{\left(8 \left(10 f g^2-h (4 e g-d h)\right) c^2-12 h (4 b f g-b e h-a f h) c+3 b^2 f h^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{8 \sqrt{c} h^6}-\frac{\left(16 \left(10 f g^5-g^3 h (4 e g-d h)\right) c^3-24 g h \left(b g \left(14 f g^2-5 e h g+d h^2\right)-a h \left(11 f g^2-4 e h g+d h^2\right)\right) c^2+6 h^2 \left(g \left(35 f g^2-10 e h g+d h^2\right) b^2-2 a h \left(25 f g^2-7 e h g+d h^2\right) b+4 a^2 h^2 (4 f g-e h)\right) c-b h^3 \left(\left(35 f g^2-5 e h g-d h^2\right) b^2-6 a h (10 f g-e h) b+24 a^2 f h^2\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{16 h^6 \left(c g^2-b h g+a h^2\right)^{3/2}}","-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{3 h \left(c g^2-b h g+a h^2\right) (g+h x)^3}-\frac{\left(2 c g \left(-\frac{10 f g^2}{h}+4 e g-d h\right)-6 a h (3 f g-e h)+b \left(17 f g^2-h (5 e g+d h)\right)+2 h \left(-\frac{5 c f g^2}{h}+2 c e g+3 b f g-2 c d h-3 a f h\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{12 h^2 \left(c g^2-b h g+a h^2\right) (g+h x)^2}-\frac{\left(8 c^2 \left(10 f g^2-h (4 e g-d h)\right) g^2-2 c h \left(3 b g \left(18 f g^2-6 e h g+d h^2\right)-2 a h \left(23 f g^2-8 e h g+2 d h^2\right)\right)+h^2 \left(\left(29 f g^2-h (5 e g+d h)\right) b^2-6 a h (7 f g-e h) b+12 a^2 f h^2\right)+2 h \left(2 g \left(10 f g^2-h (4 e g-d h)\right) c^2+h \left(6 a h (3 f g-e h)-b \left(22 f g^2-7 e h g+d h^2\right)\right) c+3 b f h^2 (b g-a h)\right) x\right) \sqrt{c x^2+b x+a}}{8 h^5 \left(c g^2-b h g+a h^2\right) (g+h x)}+\frac{\left(8 \left(10 f g^2-h (4 e g-d h)\right) c^2-12 h (4 b f g-b e h-a f h) c+3 b^2 f h^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{8 \sqrt{c} h^6}-\frac{\left(16 c^3 \left(10 f g^2-h (4 e g-d h)\right) g^3-24 c^2 h \left(b g \left(14 f g^2-5 e h g+d h^2\right)-a h \left(11 f g^2-4 e h g+d h^2\right)\right) g-b h^3 \left(\left(35 f g^2-5 e h g-d h^2\right) b^2-6 a h (10 f g-e h) b+24 a^2 f h^2\right)+6 c h^2 \left(g \left(35 f g^2-10 e h g+d h^2\right) b^2-2 a h \left(25 f g^2-7 e h g+d h^2\right) b+4 a^2 h^2 (4 f g-e h)\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{16 h^6 \left(c g^2-b h g+a h^2\right)^{3/2}}",1,"-((12*a^2*f*h^3 - 8*c^2*g^2*(4*e*g - (10*f*g^2)/h - d*h) - 6*a*b*h^2*(7*f*g - e*h) + 4*a*c*h*(23*f*g^2 - 2*h*(4*e*g - d*h)) - 6*b*c*g*(18*f*g^2 - h*(6*e*g - d*h)) + b^2*h*(29*f*g^2 - h*(5*e*g + d*h)) + 2*(3*b*f*h^2*(b*g - a*h) + 2*c^2*(10*f*g^3 - g*h*(4*e*g - d*h)) - c*h*(22*b*f*g^2 - b*h*(7*e*g - d*h) - 6*a*h*(3*f*g - e*h)))*x)*Sqrt[a + b*x + c*x^2])/(8*h^4*(c*g^2 - b*g*h + a*h^2)*(g + h*x)) - ((17*b*f*g^2 + 2*c*g*(4*e*g - (10*f*g^2)/h - d*h) - b*h*(5*e*g + d*h) - 6*a*h*(3*f*g - e*h) + 2*h*(2*c*e*g + 3*b*f*g - (5*c*f*g^2)/h - 2*c*d*h - 3*a*f*h)*x)*(a + b*x + c*x^2)^(3/2))/(12*h^2*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^2) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(5/2))/(3*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^3) + ((3*b^2*f*h^2 - 12*c*h*(4*b*f*g - b*e*h - a*f*h) + 8*c^2*(10*f*g^2 - h*(4*e*g - d*h)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[c]*h^6) - ((16*c^3*(10*f*g^5 - g^3*h*(4*e*g - d*h)) - b*h^3*(24*a^2*f*h^2 - 6*a*b*h*(10*f*g - e*h) + b^2*(35*f*g^2 - 5*e*g*h - d*h^2)) + 6*c*h^2*(4*a^2*h^2*(4*f*g - e*h) + b^2*g*(35*f*g^2 - 10*e*g*h + d*h^2) - 2*a*b*h*(25*f*g^2 - 7*e*g*h + d*h^2)) - 24*c^2*g*h*(b*g*(14*f*g^2 - 5*e*g*h + d*h^2) - a*h*(11*f*g^2 - 4*e*g*h + d*h^2)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(16*h^6*(c*g^2 - b*g*h + a*h^2)^(3/2))","A",8,6,32,0.1875,1,"{1650, 812, 843, 621, 206, 724}"
204,1,1096,0,3.1227298,"\int \frac{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^5} \, dx","Int[((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^5,x]","-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{4 h \left(c g^2-b h g+a h^2\right) (g+h x)^4}-\frac{\left(\frac{16 c^2 (5 f g-e h) g^4}{h}-4 c \left(b g \left(31 f g^2-5 e h g+3 d h^2\right)-a h \left(25 f g^2-5 e h g+9 d h^2\right)\right) g-h \left(-g \left(35 f g^2+5 e h g+3 d h^2\right) b^2+4 a h \left(7 f g^2+7 e h g+3 d h^2\right) b+16 a^2 h^2 (f g-2 e h)\right)+3 h \left(\frac{40 c^2 f g^4}{h}-8 c^2 (e g+d h) g^2-8 b c \left(9 f g^2-h (2 e g+d h)\right) g+16 a^2 f h^3-8 a b h^2 (6 f g-e h)+4 a c h \left(17 f g^2-h (5 e g-d h)\right)+b^2 h \left(29 f g^2-h (5 e g+3 d h)\right)\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{96 h^2 \left(c g^2-b h g+a h^2\right)^2 (g+h x)^3}+\frac{\left(\frac{64 c^3 (5 f g-e h) g^4}{h}-16 c^2 (b g (41 f g-7 e h)-8 a h (5 f g-e h)) g^2+4 c h \left(2 b^2 (46 f g-5 e h) g^2+16 a^2 h^2 (5 f g-e h)-a b h \left(173 f g^2-25 e h g-3 d h^2\right)\right)-b h^2 \left(\left(35 f g^2+5 e h g+3 d h^2\right) b^2-8 a h (10 f g+e h) b+48 a^2 f h^2\right)+2 c \left(16 c^2 (5 f g-e h) g^3-4 c h \left(6 b g^2 (6 f g-e h)-a h \left(35 f g^2-h (7 e g-3 d h)\right)\right)+h^2 \left(\left(61 f g^2-h (5 e g+3 d h)\right) b^2-8 a h (14 f g-e h) b+48 a^2 f h^2\right)\right) x\right) \sqrt{c x^2+b x+a}}{64 h^4 \left(c g^2-b h g+a h^2\right)^2 (g+h x)}-\frac{\sqrt{c} (10 c f g-2 c e h-3 b f h) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{2 h^6}+\frac{\left(128 c^4 (5 f g-e h) g^5-64 c^3 h (b g (28 f g-5 e h)-5 a h (5 f g-e h)) g^3+8 c h^3 \left(-5 g^2 (14 f g-e h) b^3+3 a h \left(55 f g^2-5 e h g-d h^2\right) b^2-12 a^2 h^2 (10 f g-e h) b+24 a^3 f h^3\right)-48 c^2 h^2 \left(-5 b^2 (7 f g-e h) g^3+10 a b h (6 f g-e h) g^2-a^2 h^2 \left(25 f g^2-5 e h g+d h^2\right)\right)+b^2 h^4 \left(\left(35 f g^2+5 e h g+3 d h^2\right) b^2-8 a h (10 f g+e h) b+48 a^2 f h^2\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{128 h^6 \left(c g^2-b h g+a h^2\right)^{5/2}}","-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{4 h \left(c g^2-b h g+a h^2\right) (g+h x)^4}-\frac{\left(16 c^2 (5 f g-e h) g^4-4 c h \left(b g \left(31 f g^2-5 e h g+3 d h^2\right)-a h \left(25 f g^2-5 e h g+9 d h^2\right)\right) g-h^2 \left(-g \left(35 f g^2+5 e h g+3 d h^2\right) b^2+4 a h \left(7 f g^2+7 e h g+3 d h^2\right) b+16 a^2 h^2 (f g-2 e h)\right)+3 h \left(8 c^2 \left(5 f g^2-h (e g+d h)\right) g^2+h^2 \left(\left(29 f g^2-5 e h g-3 d h^2\right) b^2-8 a h (6 f g-e h) b+16 a^2 f h^2\right)-4 c h \left(2 b g \left(9 f g^2-2 e h g-d h^2\right)-a h \left(17 f g^2-5 e h g+d h^2\right)\right)\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{96 h^3 \left(c g^2-b h g+a h^2\right)^2 (g+h x)^3}+\frac{\left(64 c^3 (5 f g-e h) g^4-16 c^2 h (b g (41 f g-7 e h)-8 a h (5 f g-e h)) g^2+4 c h^2 \left(2 b^2 (46 f g-5 e h) g^2+16 a^2 h^2 (5 f g-e h)-a b h \left(173 f g^2-25 e h g-3 d h^2\right)\right)-b h^3 \left(\left(35 f g^2+5 e h g+3 d h^2\right) b^2-8 a h (10 f g+e h) b+48 a^2 f h^2\right)+2 c h \left(16 c^2 (5 f g-e h) g^3-4 c h \left(6 b g^2 (6 f g-e h)-a h \left(35 f g^2-h (7 e g-3 d h)\right)\right)+h^2 \left(\left(61 f g^2-h (5 e g+3 d h)\right) b^2-8 a h (14 f g-e h) b+48 a^2 f h^2\right)\right) x\right) \sqrt{c x^2+b x+a}}{64 h^5 \left(c g^2-b h g+a h^2\right)^2 (g+h x)}-\frac{\sqrt{c} (10 c f g-2 c e h-3 b f h) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{2 h^6}+\frac{\left(128 c^4 (5 f g-e h) g^5-64 c^3 h (b g (28 f g-5 e h)-5 a h (5 f g-e h)) g^3+8 c h^3 \left(-5 g^2 (14 f g-e h) b^3+3 a h \left(55 f g^2-5 e h g-d h^2\right) b^2-12 a^2 h^2 (10 f g-e h) b+24 a^3 f h^3\right)-48 c^2 h^2 \left(-5 b^2 (7 f g-e h) g^3+10 a b h (6 f g-e h) g^2-a^2 h^2 \left(25 f g^2-5 e h g+d h^2\right)\right)+b^2 h^4 \left(\left(35 f g^2+5 e h g+3 d h^2\right) b^2-8 a h (10 f g+e h) b+48 a^2 f h^2\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{128 h^6 \left(c g^2-b h g+a h^2\right)^{5/2}}",1,"(((64*c^3*g^4*(5*f*g - e*h))/h - 16*c^2*g^2*(b*g*(41*f*g - 7*e*h) - 8*a*h*(5*f*g - e*h)) + 4*c*h*(2*b^2*g^2*(46*f*g - 5*e*h) + 16*a^2*h^2*(5*f*g - e*h) - a*b*h*(173*f*g^2 - 25*e*g*h - 3*d*h^2)) - b*h^2*(48*a^2*f*h^2 - 8*a*b*h*(10*f*g + e*h) + b^2*(35*f*g^2 + 5*e*g*h + 3*d*h^2)) + 2*c*(16*c^2*g^3*(5*f*g - e*h) - 4*c*h*(6*b*g^2*(6*f*g - e*h) - a*h*(35*f*g^2 - h*(7*e*g - 3*d*h))) + h^2*(48*a^2*f*h^2 - 8*a*b*h*(14*f*g - e*h) + b^2*(61*f*g^2 - h*(5*e*g + 3*d*h))))*x)*Sqrt[a + b*x + c*x^2])/(64*h^4*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)) - (((16*c^2*g^4*(5*f*g - e*h))/h - h*(16*a^2*h^2*(f*g - 2*e*h) - b^2*g*(35*f*g^2 + 5*e*g*h + 3*d*h^2) + 4*a*b*h*(7*f*g^2 + 7*e*g*h + 3*d*h^2)) - 4*c*g*(b*g*(31*f*g^2 - 5*e*g*h + 3*d*h^2) - a*h*(25*f*g^2 - 5*e*g*h + 9*d*h^2)) + 3*h*((40*c^2*f*g^4)/h + 16*a^2*f*h^3 - 8*c^2*g^2*(e*g + d*h) - 8*a*b*h^2*(6*f*g - e*h) + 4*a*c*h*(17*f*g^2 - h*(5*e*g - d*h)) - 8*b*c*g*(9*f*g^2 - h*(2*e*g + d*h)) + b^2*h*(29*f*g^2 - h*(5*e*g + 3*d*h)))*x)*(a + b*x + c*x^2)^(3/2))/(96*h^2*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)^3) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(5/2))/(4*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^4) - (Sqrt[c]*(10*c*f*g - 2*c*e*h - 3*b*f*h)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*h^6) + ((128*c^4*g^5*(5*f*g - e*h) - 64*c^3*g^3*h*(b*g*(28*f*g - 5*e*h) - 5*a*h*(5*f*g - e*h)) + 8*c*h^3*(24*a^3*f*h^3 - 12*a^2*b*h^2*(10*f*g - e*h) - 5*b^3*g^2*(14*f*g - e*h) + 3*a*b^2*h*(55*f*g^2 - 5*e*g*h - d*h^2)) - 48*c^2*h^2*(10*a*b*g^2*h*(6*f*g - e*h) - 5*b^2*g^3*(7*f*g - e*h) - a^2*h^2*(25*f*g^2 - 5*e*g*h + d*h^2)) + b^2*h^4*(48*a^2*f*h^2 - 8*a*b*h*(10*f*g + e*h) + b^2*(35*f*g^2 + 5*e*g*h + 3*d*h^2)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(128*h^6*(c*g^2 - b*g*h + a*h^2)^(5/2))","A",8,7,32,0.2188,1,"{1650, 810, 812, 843, 621, 206, 724}"
205,1,1223,0,3.9972791,"\int \frac{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^6} \, dx","Int[((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^6,x]","-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{5 h \left(c g^2-b h g+a h^2\right) (g+h x)^5}-\frac{\left(16 c^2 f g^5-2 c h \left(13 b f g^3-10 a f h g^2+3 b d h^2 g-6 a d h^3\right) g-h^2 \left(-g \left(7 f g^2+3 h (e g+d h)\right) b^2+2 a h \left(f g^2+3 h (2 e g+d h)\right) b+4 a^2 h^2 (2 f g-3 e h)\right)+h^2 \left(16 a^2 f h^3+4 a c g (14 f g-3 e h) h+b^2 \left(25 f g^2-3 h (e g+d h)\right) h+c^2 \left(\frac{28 f g^4}{h}-12 d g^2 h\right)-b \left(56 c f g^3-6 c h (e g+2 d h) g+2 a h^2 (22 f g-3 e h)\right)\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{48 h^3 \left(c g^2-b h g+a h^2\right)^2 (g+h x)^4}-\frac{\left(\frac{128 c^4 f g^7}{h}-32 c^3 f (11 b g-10 a h) g^5+8 c^2 h \left(38 b^2 f g^4-a b h \left(65 f g^2+3 d h^2\right) g+2 a^2 h^2 \left(13 f g^2+3 d h^2\right)\right) g-b h^3 (b g-2 a h) \left(\left(7 f g^2+3 h (e g+d h)\right) b^2-2 a h (10 f g+3 e h) b+16 a^2 f h^2\right)-2 c h^2 \left(\left(35 f g^4-3 d g^2 h^2\right) b^3-2 a g^2 h (34 f g+3 e h) b^2+4 a^2 h^2 \left(5 f g^2+3 h (2 e g+d h)\right) b+8 a^3 h^3 (2 f g-3 e h)\right)+\left(128 c f \left(c g^2-h (b g-a h)\right)^3+(2 c g-b h) \left(32 c^3 f g^5-8 c^2 h \left(10 b f g^3-11 a f h g^2+3 a d h^3\right) g+2 c h^2 \left(\left(29 f g^3+3 d h^2 g\right) b^2-6 a h \left(11 f g^2-e h g-d h^2\right) b+4 a^2 h^2 (10 f g-3 e h)\right)-b h^3 \left(\left(7 f g^2+3 h (e g+d h)\right) b^2-2 a h (10 f g+3 e h) b+16 a^2 f h^2\right)\right)\right) x\right) \sqrt{c x^2+b x+a}}{128 h^4 \left(c g^2-b h g+a h^2\right)^3 (g+h x)^2}+\frac{c^{3/2} f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{h^6}-\frac{\left(256 c^5 f g^7-896 c^4 f h (b g-a h) g^5+32 c^3 h^2 \left(35 b^2 f g^4-70 a b f h g^3+a^2 h^2 \left(35 f g^2-3 d h^2\right)\right) g-16 c^2 h^3 \left(35 b^3 f g^4-3 a b^2 h \left(35 f g^2+d h^2\right) g-6 a^3 h^3 (6 f g-e h)+3 a^2 b h^2 \left(35 f g^2-e h g-d h^2\right)\right)+b^3 h^5 \left(\left(7 f g^2+3 h (e g+d h)\right) b^2-2 a h (10 f g+3 e h) b+16 a^2 f h^2\right)-2 b c h^4 \left(-\left(35 f g^3-3 d g h^2\right) b^3+4 a h \left(35 f g^2+3 h (e g+d h)\right) b^2-24 a^2 h^2 (8 f g+e h) b+96 a^3 f h^3\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{256 h^6 \left(c g^2-b h g+a h^2\right)^{7/2}}","-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{5 h \left(c g^2-b h g+a h^2\right) (g+h x)^5}-\frac{\left(16 c^2 f g^5-2 c h \left(13 b f g^3-10 a f h g^2+3 b d h^2 g-6 a d h^3\right) g-h^2 \left(-g \left(7 f g^2+3 h (e g+d h)\right) b^2+2 a h \left(f g^2+3 h (2 e g+d h)\right) b+4 a^2 h^2 (2 f g-3 e h)\right)+h \left(4 \left(7 f g^4-3 d g^2 h^2\right) c^2+2 g h \left(2 a h (14 f g-3 e h)-b \left(28 f g^2-3 e h g-6 d h^2\right)\right) c+h^2 \left(\left(25 f g^2-3 h (e g+d h)\right) b^2-2 a h (22 f g-3 e h) b+16 a^2 f h^2\right)\right) x\right) \left(c x^2+b x+a\right)^{3/2}}{48 h^3 \left(c g^2-b h g+a h^2\right)^2 (g+h x)^4}-\frac{\left(128 c^4 f g^7-32 c^3 f h (11 b g-10 a h) g^5+8 c^2 h^2 \left(38 b^2 f g^4-a b h \left(65 f g^2+3 d h^2\right) g+2 a^2 h^2 \left(13 f g^2+3 d h^2\right)\right) g-2 c h^3 \left(\left(35 f g^4-3 d g^2 h^2\right) b^3-2 a g^2 h (34 f g+3 e h) b^2+4 a^2 h^2 \left(5 f g^2+6 e h g+3 d h^2\right) b+8 a^3 h^3 (2 f g-3 e h)\right)-b h^4 (b g-2 a h) \left(\left(7 f g^2+3 h (e g+d h)\right) b^2-2 a h (10 f g+3 e h) b+16 a^2 f h^2\right)+h \left(128 c f \left(c g^2-h (b g-a h)\right)^3+(2 c g-b h) \left(32 c^3 f g^5-8 c^2 h \left(10 b f g^3-11 a f h g^2+3 a d h^3\right) g+2 c h^2 \left(\left(29 f g^3+3 d h^2 g\right) b^2-6 a h \left(11 f g^2-e h g-d h^2\right) b+4 a^2 h^2 (10 f g-3 e h)\right)-b h^3 \left(\left(7 f g^2+3 h (e g+d h)\right) b^2-2 a h (10 f g+3 e h) b+16 a^2 f h^2\right)\right)\right) x\right) \sqrt{c x^2+b x+a}}{128 h^5 \left(c g^2-b h g+a h^2\right)^3 (g+h x)^2}+\frac{c^{3/2} f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right)}{h^6}-\frac{\left(256 c^5 f g^7-896 c^4 f h (b g-a h) g^5+32 c^3 h^2 \left(35 b^2 f g^4-70 a b f h g^3+a^2 h^2 \left(35 f g^2-3 d h^2\right)\right) g-16 c^2 h^3 \left(35 b^3 f g^4-3 a b^2 h \left(35 f g^2+d h^2\right) g-6 a^3 h^3 (6 f g-e h)+3 a^2 b h^2 \left(35 f g^2-e h g-d h^2\right)\right)+b^3 h^5 \left(\left(7 f g^2+3 h (e g+d h)\right) b^2-2 a h (10 f g+3 e h) b+16 a^2 f h^2\right)-2 b c h^4 \left(-\left(35 f g^3-3 d g h^2\right) b^3+4 a h \left(35 f g^2+3 h (e g+d h)\right) b^2-24 a^2 h^2 (8 f g+e h) b+96 a^3 f h^3\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{256 h^6 \left(c g^2-b h g+a h^2\right)^{7/2}}",1,"-(((128*c^4*f*g^7)/h - 32*c^3*f*g^5*(11*b*g - 10*a*h) + 8*c^2*g*h*(38*b^2*f*g^4 + 2*a^2*h^2*(13*f*g^2 + 3*d*h^2) - a*b*g*h*(65*f*g^2 + 3*d*h^2)) - b*h^3*(b*g - 2*a*h)*(16*a^2*f*h^2 - 2*a*b*h*(10*f*g + 3*e*h) + b^2*(7*f*g^2 + 3*h*(e*g + d*h))) - 2*c*h^2*(8*a^3*h^3*(2*f*g - 3*e*h) - 2*a*b^2*g^2*h*(34*f*g + 3*e*h) + b^3*(35*f*g^4 - 3*d*g^2*h^2) + 4*a^2*b*h^2*(5*f*g^2 + 3*h*(2*e*g + d*h))) + (128*c*f*(c*g^2 - h*(b*g - a*h))^3 + (2*c*g - b*h)*(32*c^3*f*g^5 - 8*c^2*g*h*(10*b*f*g^3 - 11*a*f*g^2*h + 3*a*d*h^3) + 2*c*h^2*(4*a^2*h^2*(10*f*g - 3*e*h) - 6*a*b*h*(11*f*g^2 - e*g*h - d*h^2) + b^2*(29*f*g^3 + 3*d*g*h^2)) - b*h^3*(16*a^2*f*h^2 - 2*a*b*h*(10*f*g + 3*e*h) + b^2*(7*f*g^2 + 3*h*(e*g + d*h)))))*x)*Sqrt[a + b*x + c*x^2])/(128*h^4*(c*g^2 - b*g*h + a*h^2)^3*(g + h*x)^2) - ((16*c^2*f*g^5 - 2*c*g*h*(13*b*f*g^3 - 10*a*f*g^2*h + 3*b*d*g*h^2 - 6*a*d*h^3) - h^2*(4*a^2*h^2*(2*f*g - 3*e*h) - b^2*g*(7*f*g^2 + 3*h*(e*g + d*h)) + 2*a*b*h*(f*g^2 + 3*h*(2*e*g + d*h))) + h^2*(16*a^2*f*h^3 + 4*a*c*g*h*(14*f*g - 3*e*h) + c^2*((28*f*g^4)/h - 12*d*g^2*h) + b^2*h*(25*f*g^2 - 3*h*(e*g + d*h)) - b*(56*c*f*g^3 - 6*c*g*h*(e*g + 2*d*h) + 2*a*h^2*(22*f*g - 3*e*h)))*x)*(a + b*x + c*x^2)^(3/2))/(48*h^3*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)^4) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(5/2))/(5*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^5) + (c^(3/2)*f*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/h^6 - ((256*c^5*f*g^7 - 896*c^4*f*g^5*h*(b*g - a*h) + 32*c^3*g*h^2*(35*b^2*f*g^4 - 70*a*b*f*g^3*h + a^2*h^2*(35*f*g^2 - 3*d*h^2)) - 16*c^2*h^3*(35*b^3*f*g^4 - 6*a^3*h^3*(6*f*g - e*h) + 3*a^2*b*h^2*(35*f*g^2 - e*g*h - d*h^2) - 3*a*b^2*g*h*(35*f*g^2 + d*h^2)) + b^3*h^5*(16*a^2*f*h^2 - 2*a*b*h*(10*f*g + 3*e*h) + b^2*(7*f*g^2 + 3*h*(e*g + d*h))) - 2*b*c*h^4*(96*a^3*f*h^3 - 24*a^2*b*h^2*(8*f*g + e*h) - b^3*(35*f*g^3 - 3*d*g*h^2) + 4*a*b^2*h*(35*f*g^2 + 3*h*(e*g + d*h))))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(256*h^6*(c*g^2 - b*g*h + a*h^2)^(7/2))","A",8,6,32,0.1875,1,"{1650, 810, 843, 621, 206, 724}"
206,1,660,0,1.2164408,"\int \frac{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^7} \, dx","Int[((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^7,x]","\frac{\left(a+b x+c x^2\right)^{3/2} (-2 a h+x (2 c g-b h)+b g) \left(24 a^2 f h^2-4 c \left(-a h (7 e g-d h)+a f g^2+3 b g (2 d h+e g)\right)-12 a b h (e h+2 f g)+b^2 \left(h (7 d h+5 e g)+7 f g^2\right)+24 c^2 d g^2\right)}{192 (g+h x)^4 \left(a h^2-b g h+c g^2\right)^3}-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (-2 a h+x (2 c g-b h)+b g) \left(24 a^2 f h^2-4 c \left(-a h (7 e g-d h)+a f g^2+3 b g (2 d h+e g)\right)-12 a b h (e h+2 f g)+b^2 \left(h (7 d h+5 e g)+7 f g^2\right)+24 c^2 d g^2\right)}{512 (g+h x)^2 \left(a h^2-b g h+c g^2\right)^4}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(24 a^2 f h^2-4 c \left(-a h (7 e g-d h)+a f g^2+3 b g (2 d h+e g)\right)-12 a b h (e h+2 f g)+b^2 \left(h (7 d h+5 e g)+7 f g^2\right)+24 c^2 d g^2\right)}{1024 \left(a h^2-b g h+c g^2\right)^{9/2}}+\frac{\left(a+b x+c x^2\right)^{5/2} \left(2 c \left(g h (e g-7 d h)+5 f g^3\right)-h \left(-12 a h (2 f g-e h)-b h (7 d h+5 e g)+17 b f g^2\right)\right)}{60 h (g+h x)^5 \left(a h^2-b g h+c g^2\right)^2}-\frac{\left(a+b x+c x^2\right)^{5/2} \left(f g^2-h (e g-d h)\right)}{6 h (g+h x)^6 \left(a h^2-b g h+c g^2\right)}","\frac{\left(a+b x+c x^2\right)^{3/2} (-2 a h+x (2 c g-b h)+b g) \left(24 a^2 f h^2-4 c \left(a \left(d h^2-7 e g h+f g^2\right)+3 b g (2 d h+e g)\right)-12 a b h (e h+2 f g)+b^2 \left(7 d h^2+5 e g h+7 f g^2\right)+24 c^2 d g^2\right)}{192 (g+h x)^4 \left(a h^2-b g h+c g^2\right)^3}-\frac{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (-2 a h+x (2 c g-b h)+b g) \left(24 a^2 f h^2-4 c \left(a \left(d h^2-7 e g h+f g^2\right)+3 b g (2 d h+e g)\right)-12 a b h (e h+2 f g)+b^2 \left(7 d h^2+5 e g h+7 f g^2\right)+24 c^2 d g^2\right)}{512 (g+h x)^2 \left(a h^2-b g h+c g^2\right)^4}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(24 a^2 f h^2-4 c \left(a \left(d h^2-7 e g h+f g^2\right)+3 b g (2 d h+e g)\right)-12 a b h (e h+2 f g)+b^2 \left(7 d h^2+5 e g h+7 f g^2\right)+24 c^2 d g^2\right)}{1024 \left(a h^2-b g h+c g^2\right)^{9/2}}+\frac{\left(a+b x+c x^2\right)^{5/2} \left(h \left(12 a h (2 f g-e h)-b \left(-7 d h^2-5 e g h+17 f g^2\right)\right)+2 c g \left(h (e g-7 d h)+5 f g^2\right)\right)}{60 h (g+h x)^5 \left(a h^2-b g h+c g^2\right)^2}-\frac{\left(a+b x+c x^2\right)^{5/2} \left(f g^2-h (e g-d h)\right)}{6 h (g+h x)^6 \left(a h^2-b g h+c g^2\right)}",1,"-((b^2 - 4*a*c)*(24*c^2*d*g^2 + 24*a^2*f*h^2 - 12*a*b*h*(2*f*g + e*h) - 4*c*(a*f*g^2 - a*h*(7*e*g - d*h) + 3*b*g*(e*g + 2*d*h)) + b^2*(7*f*g^2 + h*(5*e*g + 7*d*h)))*(b*g - 2*a*h + (2*c*g - b*h)*x)*Sqrt[a + b*x + c*x^2])/(512*(c*g^2 - b*g*h + a*h^2)^4*(g + h*x)^2) + ((24*c^2*d*g^2 + 24*a^2*f*h^2 - 12*a*b*h*(2*f*g + e*h) - 4*c*(a*f*g^2 - a*h*(7*e*g - d*h) + 3*b*g*(e*g + 2*d*h)) + b^2*(7*f*g^2 + h*(5*e*g + 7*d*h)))*(b*g - 2*a*h + (2*c*g - b*h)*x)*(a + b*x + c*x^2)^(3/2))/(192*(c*g^2 - b*g*h + a*h^2)^3*(g + h*x)^4) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(5/2))/(6*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^6) + ((2*c*(5*f*g^3 + g*h*(e*g - 7*d*h)) - h*(17*b*f*g^2 - b*h*(5*e*g + 7*d*h) - 12*a*h*(2*f*g - e*h)))*(a + b*x + c*x^2)^(5/2))/(60*h*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)^5) + ((b^2 - 4*a*c)^2*(24*c^2*d*g^2 + 24*a^2*f*h^2 - 12*a*b*h*(2*f*g + e*h) - 4*c*(a*f*g^2 - a*h*(7*e*g - d*h) + 3*b*g*(e*g + 2*d*h)) + b^2*(7*f*g^2 + h*(5*e*g + 7*d*h)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(1024*(c*g^2 - b*g*h + a*h^2)^(9/2))","A",6,5,32,0.1562,1,"{1650, 806, 720, 724, 206}"
207,1,1062,0,3.0035674,"\int \frac{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)}{(g+h x)^8} \, dx","Int[((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2))/(g + h*x)^8,x]","\frac{\left(4 \left(5 f g^4+h (2 e g-51 d h) g^2\right) c^2-2 h \left(3 b g \left(8 f g^2-15 e h g-34 d h^2\right)-2 a h \left(26 f g^2-61 e h g+12 d h^2\right)\right) c-7 h^2 \left(\left(5 f g^2+5 e h g+9 d h^2\right) b^2-2 a h (10 f g+7 e h) b+24 a^2 f h^2\right)\right) \left(c x^2+b x+a\right)^{5/2}}{840 h \left(c g^2-b h g+a h^2\right)^3 (g+h x)^5}+\frac{\left(2 c \left(5 f g^3+h (2 e g-9 d h) g\right)-h \left(19 b f g^2-b h (5 e g+9 d h)-14 a h (2 f g-e h)\right)\right) \left(c x^2+b x+a\right)^{5/2}}{84 h \left(c g^2-b h g+a h^2\right)^2 (g+h x)^6}-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{7 h \left(c g^2-b h g+a h^2\right) (g+h x)^7}+\frac{\left(48 c^3 d g^3-8 c^2 \left(a f g^2+3 b (e g+3 d h) g-a h (8 e g-3 d h)\right) g-b h \left(\left(5 f g^2+h (5 e g+9 d h)\right) b^2-2 a h (10 f g+7 e h) b+24 a^2 f h^2\right)+2 c \left(\left(7 f g^3+h (10 e g+21 d h) g\right) b^2-2 a h \left(13 f g^2+h (13 e g-3 d h)\right) b+4 a^2 h^2 (8 f g-e h)\right)\right) (b g-2 a h+(2 c g-b h) x) \left(c x^2+b x+a\right)^{3/2}}{384 \left(c g^2-b h g+a h^2\right)^4 (g+h x)^4}-\frac{\left(b^2-4 a c\right) \left(48 c^3 d g^3-8 c^2 \left(a f g^2+3 b (e g+3 d h) g-a h (8 e g-3 d h)\right) g-b h \left(\left(5 f g^2+h (5 e g+9 d h)\right) b^2-2 a h (10 f g+7 e h) b+24 a^2 f h^2\right)+2 c \left(\left(7 f g^3+h (10 e g+21 d h) g\right) b^2-2 a h \left(13 f g^2+h (13 e g-3 d h)\right) b+4 a^2 h^2 (8 f g-e h)\right)\right) (b g-2 a h+(2 c g-b h) x) \sqrt{c x^2+b x+a}}{1024 \left(c g^2-b h g+a h^2\right)^5 (g+h x)^2}+\frac{\left(b^2-4 a c\right)^2 \left(48 c^3 d g^3-8 c^2 \left(a f g^2+3 b (e g+3 d h) g-a h (8 e g-3 d h)\right) g-b h \left(\left(5 f g^2+h (5 e g+9 d h)\right) b^2-2 a h (10 f g+7 e h) b+24 a^2 f h^2\right)+2 c \left(\left(7 f g^3+h (10 e g+21 d h) g\right) b^2-2 a h \left(13 f g^2+h (13 e g-3 d h)\right) b+4 a^2 h^2 (8 f g-e h)\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{2048 \left(c g^2-b h g+a h^2\right)^{11/2}}","\frac{\left(4 c^2 \left(5 f g^2+h (2 e g-51 d h)\right) g^2-7 h^2 \left(\left(5 f g^2+5 e h g+9 d h^2\right) b^2-2 a h (10 f g+7 e h) b+24 a^2 f h^2\right)-2 c h \left(3 b g \left(8 f g^2-15 e h g-34 d h^2\right)-2 a h \left(26 f g^2-61 e h g+12 d h^2\right)\right)\right) \left(c x^2+b x+a\right)^{5/2}}{840 h \left(c g^2-b h g+a h^2\right)^3 (g+h x)^5}+\frac{\left(2 c g \left(5 f g^2+h (2 e g-9 d h)\right)+h \left(14 a h (2 f g-e h)-b \left(19 f g^2-5 e h g-9 d h^2\right)\right)\right) \left(c x^2+b x+a\right)^{5/2}}{84 h \left(c g^2-b h g+a h^2\right)^2 (g+h x)^6}-\frac{\left(f g^2-h (e g-d h)\right) \left(c x^2+b x+a\right)^{5/2}}{7 h \left(c g^2-b h g+a h^2\right) (g+h x)^7}+\frac{\left(48 c^3 d g^3-8 c^2 \left(3 b g (e g+3 d h)+a \left(f g^2-8 e h g+3 d h^2\right)\right) g-b h \left(\left(5 f g^2+5 e h g+9 d h^2\right) b^2-2 a h (10 f g+7 e h) b+24 a^2 f h^2\right)+2 c \left(g \left(7 f g^2+10 e h g+21 d h^2\right) b^2-2 a h \left(13 f g^2+13 e h g-3 d h^2\right) b+4 a^2 h^2 (8 f g-e h)\right)\right) (b g-2 a h+(2 c g-b h) x) \left(c x^2+b x+a\right)^{3/2}}{384 \left(c g^2-b h g+a h^2\right)^4 (g+h x)^4}-\frac{\left(b^2-4 a c\right) \left(48 c^3 d g^3-8 c^2 \left(3 b g (e g+3 d h)+a \left(f g^2-8 e h g+3 d h^2\right)\right) g-b h \left(\left(5 f g^2+5 e h g+9 d h^2\right) b^2-2 a h (10 f g+7 e h) b+24 a^2 f h^2\right)+2 c \left(g \left(7 f g^2+10 e h g+21 d h^2\right) b^2-2 a h \left(13 f g^2+13 e h g-3 d h^2\right) b+4 a^2 h^2 (8 f g-e h)\right)\right) (b g-2 a h+(2 c g-b h) x) \sqrt{c x^2+b x+a}}{1024 \left(c g^2-b h g+a h^2\right)^5 (g+h x)^2}+\frac{\left(b^2-4 a c\right)^2 \left(48 c^3 d g^3-8 c^2 \left(3 b g (e g+3 d h)+a \left(f g^2-8 e h g+3 d h^2\right)\right) g-b h \left(\left(5 f g^2+5 e h g+9 d h^2\right) b^2-2 a h (10 f g+7 e h) b+24 a^2 f h^2\right)+2 c \left(g \left(7 f g^2+10 e h g+21 d h^2\right) b^2-2 a h \left(13 f g^2+13 e h g-3 d h^2\right) b+4 a^2 h^2 (8 f g-e h)\right)\right) \tanh ^{-1}\left(\frac{b g-2 a h+(2 c g-b h) x}{2 \sqrt{c g^2-b h g+a h^2} \sqrt{c x^2+b x+a}}\right)}{2048 \left(c g^2-b h g+a h^2\right)^{11/2}}",1,"-((b^2 - 4*a*c)*(48*c^3*d*g^3 - 8*c^2*g*(a*f*g^2 - a*h*(8*e*g - 3*d*h) + 3*b*g*(e*g + 3*d*h)) - b*h*(24*a^2*f*h^2 - 2*a*b*h*(10*f*g + 7*e*h) + b^2*(5*f*g^2 + h*(5*e*g + 9*d*h))) + 2*c*(4*a^2*h^2*(8*f*g - e*h) - 2*a*b*h*(13*f*g^2 + h*(13*e*g - 3*d*h)) + b^2*(7*f*g^3 + g*h*(10*e*g + 21*d*h))))*(b*g - 2*a*h + (2*c*g - b*h)*x)*Sqrt[a + b*x + c*x^2])/(1024*(c*g^2 - b*g*h + a*h^2)^5*(g + h*x)^2) + ((48*c^3*d*g^3 - 8*c^2*g*(a*f*g^2 - a*h*(8*e*g - 3*d*h) + 3*b*g*(e*g + 3*d*h)) - b*h*(24*a^2*f*h^2 - 2*a*b*h*(10*f*g + 7*e*h) + b^2*(5*f*g^2 + h*(5*e*g + 9*d*h))) + 2*c*(4*a^2*h^2*(8*f*g - e*h) - 2*a*b*h*(13*f*g^2 + h*(13*e*g - 3*d*h)) + b^2*(7*f*g^3 + g*h*(10*e*g + 21*d*h))))*(b*g - 2*a*h + (2*c*g - b*h)*x)*(a + b*x + c*x^2)^(3/2))/(384*(c*g^2 - b*g*h + a*h^2)^4*(g + h*x)^4) - ((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(5/2))/(7*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^7) + ((2*c*(5*f*g^3 + g*h*(2*e*g - 9*d*h)) - h*(19*b*f*g^2 - b*h*(5*e*g + 9*d*h) - 14*a*h*(2*f*g - e*h)))*(a + b*x + c*x^2)^(5/2))/(84*h*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)^6) + ((4*c^2*(5*f*g^4 + g^2*h*(2*e*g - 51*d*h)) - 7*h^2*(24*a^2*f*h^2 - 2*a*b*h*(10*f*g + 7*e*h) + b^2*(5*f*g^2 + 5*e*g*h + 9*d*h^2)) - 2*c*h*(3*b*g*(8*f*g^2 - 15*e*g*h - 34*d*h^2) - 2*a*h*(26*f*g^2 - 61*e*g*h + 12*d*h^2)))*(a + b*x + c*x^2)^(5/2))/(840*h*(c*g^2 - b*g*h + a*h^2)^3*(g + h*x)^5) + ((b^2 - 4*a*c)^2*(48*c^3*d*g^3 - 8*c^2*g*(a*f*g^2 - a*h*(8*e*g - 3*d*h) + 3*b*g*(e*g + 3*d*h)) - b*h*(24*a^2*f*h^2 - 2*a*b*h*(10*f*g + 7*e*h) + b^2*(5*f*g^2 + h*(5*e*g + 9*d*h))) + 2*c*(4*a^2*h^2*(8*f*g - e*h) - 2*a*b*h*(13*f*g^2 + h*(13*e*g - 3*d*h)) + b^2*(7*f*g^3 + g*h*(10*e*g + 21*d*h))))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(2048*(c*g^2 - b*g*h + a*h^2)^(11/2))","A",7,6,32,0.1875,1,"{1650, 834, 806, 720, 724, 206}"
208,1,143,0,0.1383622,"\int (1+2 x)^3 \sqrt{2-x+3 x^2} \left(1+3 x+4 x^2\right) \, dx","Int[(1 + 2*x)^3*Sqrt[2 - x + 3*x^2]*(1 + 3*x + 4*x^2),x]","\frac{2}{21} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^4+\frac{67}{378} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^3+\frac{17}{105} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^2-\frac{(26982 x+75295) \left(3 x^2-x+2\right)^{3/2}}{68040}+\frac{5393 (1-6 x) \sqrt{3 x^2-x+2}}{15552}+\frac{124039 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{31104 \sqrt{3}}","\frac{2}{21} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^4+\frac{67}{378} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^3+\frac{17}{105} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^2-\frac{(26982 x+75295) \left(3 x^2-x+2\right)^{3/2}}{68040}+\frac{5393 (1-6 x) \sqrt{3 x^2-x+2}}{15552}+\frac{124039 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{31104 \sqrt{3}}",1,"(5393*(1 - 6*x)*Sqrt[2 - x + 3*x^2])/15552 + (17*(1 + 2*x)^2*(2 - x + 3*x^2)^(3/2))/105 + (67*(1 + 2*x)^3*(2 - x + 3*x^2)^(3/2))/378 + (2*(1 + 2*x)^4*(2 - x + 3*x^2)^(3/2))/21 - ((75295 + 26982*x)*(2 - x + 3*x^2)^(3/2))/68040 + (124039*ArcSinh[(1 - 6*x)/Sqrt[23]])/(31104*Sqrt[3])","A",7,6,32,0.1875,1,"{1653, 832, 779, 612, 619, 215}"
209,1,118,0,0.111741,"\int (1+2 x)^2 \sqrt{2-x+3 x^2} \left(1+3 x+4 x^2\right) \, dx","Int[(1 + 2*x)^2*Sqrt[2 - x + 3*x^2]*(1 + 3*x + 4*x^2),x]","\frac{1}{9} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^3+\frac{1}{5} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^2+\frac{1}{810} (306 x+25) \left(3 x^2-x+2\right)^{3/2}+\frac{235 (1-6 x) \sqrt{3 x^2-x+2}}{1296}+\frac{5405 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{2592 \sqrt{3}}","\frac{1}{9} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^3+\frac{1}{5} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^2+\frac{1}{810} (306 x+25) \left(3 x^2-x+2\right)^{3/2}+\frac{235 (1-6 x) \sqrt{3 x^2-x+2}}{1296}+\frac{5405 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{2592 \sqrt{3}}",1,"(235*(1 - 6*x)*Sqrt[2 - x + 3*x^2])/1296 + ((1 + 2*x)^2*(2 - x + 3*x^2)^(3/2))/5 + ((1 + 2*x)^3*(2 - x + 3*x^2)^(3/2))/9 + ((25 + 306*x)*(2 - x + 3*x^2)^(3/2))/810 + (5405*ArcSinh[(1 - 6*x)/Sqrt[23]])/(2592*Sqrt[3])","A",6,6,32,0.1875,1,"{1653, 832, 779, 612, 619, 215}"
210,1,93,0,0.0657437,"\int (1+2 x) \sqrt{2-x+3 x^2} \left(1+3 x+4 x^2\right) \, dx","Int[(1 + 2*x)*Sqrt[2 - x + 3*x^2]*(1 + 3*x + 4*x^2),x]","\frac{2}{15} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^2+\frac{(738 x+745) \left(3 x^2-x+2\right)^{3/2}}{1620}+\frac{19 (1-6 x) \sqrt{3 x^2-x+2}}{2592}+\frac{437 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{5184 \sqrt{3}}","\frac{2}{15} \left(3 x^2-x+2\right)^{3/2} (2 x+1)^2+\frac{(738 x+745) \left(3 x^2-x+2\right)^{3/2}}{1620}+\frac{19 (1-6 x) \sqrt{3 x^2-x+2}}{2592}+\frac{437 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{5184 \sqrt{3}}",1,"(19*(1 - 6*x)*Sqrt[2 - x + 3*x^2])/2592 + (2*(1 + 2*x)^2*(2 - x + 3*x^2)^(3/2))/15 + ((745 + 738*x)*(2 - x + 3*x^2)^(3/2))/1620 + (437*ArcSinh[(1 - 6*x)/Sqrt[23]])/(5184*Sqrt[3])","A",5,5,30,0.1667,1,"{1653, 779, 612, 619, 215}"
211,1,101,0,0.1168989,"\int \frac{\sqrt{2-x+3 x^2} \left(1+3 x+4 x^2\right)}{1+2 x} \, dx","Int[(Sqrt[2 - x + 3*x^2]*(1 + 3*x + 4*x^2))/(1 + 2*x),x]","\frac{2}{9} \left(3 x^2-x+2\right)^{3/2}+\frac{1}{72} (30 x+13) \sqrt{3 x^2-x+2}-\frac{1}{8} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)-\frac{43 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{144 \sqrt{3}}","\frac{2}{9} \left(3 x^2-x+2\right)^{3/2}+\frac{1}{72} (30 x+13) \sqrt{3 x^2-x+2}-\frac{1}{8} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)-\frac{43 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{144 \sqrt{3}}",1,"((13 + 30*x)*Sqrt[2 - x + 3*x^2])/72 + (2*(2 - x + 3*x^2)^(3/2))/9 - (43*ArcSinh[(1 - 6*x)/Sqrt[23]])/(144*Sqrt[3]) - (Sqrt[13]*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/8","A",7,7,32,0.2188,1,"{1653, 814, 843, 619, 215, 724, 206}"
212,1,108,0,0.1164136,"\int \frac{\sqrt{2-x+3 x^2} \left(1+3 x+4 x^2\right)}{(1+2 x)^2} \, dx","Int[(Sqrt[2 - x + 3*x^2]*(1 + 3*x + 4*x^2))/(1 + 2*x)^2,x]","-\frac{\left(3 x^2-x+2\right)^{3/2}}{13 (2 x+1)}-\frac{1}{156} (67-96 x) \sqrt{3 x^2-x+2}+\frac{17 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{8 \sqrt{13}}-\frac{11 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{6 \sqrt{3}}","-\frac{\left(3 x^2-x+2\right)^{3/2}}{13 (2 x+1)}-\frac{1}{156} (67-96 x) \sqrt{3 x^2-x+2}+\frac{17 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{8 \sqrt{13}}-\frac{11 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{6 \sqrt{3}}",1,"-((67 - 96*x)*Sqrt[2 - x + 3*x^2])/156 - (2 - x + 3*x^2)^(3/2)/(13*(1 + 2*x)) - (11*ArcSinh[(1 - 6*x)/Sqrt[23]])/(6*Sqrt[3]) + (17*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(8*Sqrt[13])","A",7,7,32,0.2188,1,"{1650, 814, 843, 619, 215, 724, 206}"
213,1,115,0,0.1168742,"\int \frac{\sqrt{2-x+3 x^2} \left(1+3 x+4 x^2\right)}{(1+2 x)^3} \, dx","Int[(Sqrt[2 - x + 3*x^2]*(1 + 3*x + 4*x^2))/(1 + 2*x)^3,x]","-\frac{\left(3 x^2-x+2\right)^{3/2}}{26 (2 x+1)^2}+\frac{11 (10 x+7) \sqrt{3 x^2-x+2}}{104 (2 x+1)}-\frac{803 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{208 \sqrt{13}}+\frac{11 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{8 \sqrt{3}}","-\frac{\left(3 x^2-x+2\right)^{3/2}}{26 (2 x+1)^2}+\frac{11 (10 x+7) \sqrt{3 x^2-x+2}}{104 (2 x+1)}-\frac{803 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{208 \sqrt{13}}+\frac{11 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{8 \sqrt{3}}",1,"(11*(7 + 10*x)*Sqrt[2 - x + 3*x^2])/(104*(1 + 2*x)) - (2 - x + 3*x^2)^(3/2)/(26*(1 + 2*x)^2) + (11*ArcSinh[(1 - 6*x)/Sqrt[23]])/(8*Sqrt[3]) - (803*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(208*Sqrt[13])","A",7,7,32,0.2188,1,"{1650, 812, 843, 619, 215, 724, 206}"
214,1,158,0,0.2006349,"\int (1+2 x)^3 \left(2-x+3 x^2\right)^{3/2} \left(1+3 x+4 x^2\right) \, dx","Int[(1 + 2*x)^3*(2 - x + 3*x^2)^(3/2)*(1 + 3*x + 4*x^2),x]","\frac{2}{27} \left(3 x^2-x+2\right)^{5/2} (2 x+1)^4+\frac{77}{81} x^3 \left(3 x^2-x+2\right)^{5/2}+\frac{913}{486} x^2 \left(3 x^2-x+2\right)^{5/2}-\frac{11 (283-5850 x) \left(3 x^2-x+2\right)^{5/2}}{58320}+\frac{54593 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{559872}+\frac{1255639 (1-6 x) \sqrt{3 x^2-x+2}}{4478976}+\frac{28879697 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{8957952 \sqrt{3}}","\frac{2}{27} \left(3 x^2-x+2\right)^{5/2} (2 x+1)^4+\frac{77}{81} x^3 \left(3 x^2-x+2\right)^{5/2}+\frac{913}{486} x^2 \left(3 x^2-x+2\right)^{5/2}-\frac{11 (283-5850 x) \left(3 x^2-x+2\right)^{5/2}}{58320}+\frac{54593 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{559872}+\frac{1255639 (1-6 x) \sqrt{3 x^2-x+2}}{4478976}+\frac{28879697 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{8957952 \sqrt{3}}",1,"(1255639*(1 - 6*x)*Sqrt[2 - x + 3*x^2])/4478976 + (54593*(1 - 6*x)*(2 - x + 3*x^2)^(3/2))/559872 - (11*(283 - 5850*x)*(2 - x + 3*x^2)^(5/2))/58320 + (913*x^2*(2 - x + 3*x^2)^(5/2))/486 + (77*x^3*(2 - x + 3*x^2)^(5/2))/81 + (2*(1 + 2*x)^4*(2 - x + 3*x^2)^(5/2))/27 + (28879697*ArcSinh[(1 - 6*x)/Sqrt[23]])/(8957952*Sqrt[3])","A",9,6,32,0.1875,1,"{1653, 12, 779, 612, 619, 215}"
215,1,141,0,0.1209504,"\int (1+2 x)^2 \left(2-x+3 x^2\right)^{3/2} \left(1+3 x+4 x^2\right) \, dx","Int[(1 + 2*x)^2*(2 - x + 3*x^2)^(3/2)*(1 + 3*x + 4*x^2),x]","\frac{1}{12} \left(3 x^2-x+2\right)^{5/2} (2 x+1)^3+\frac{8}{63} \left(3 x^2-x+2\right)^{5/2} (2 x+1)^2+\frac{13 (50 x+29) \left(3 x^2-x+2\right)^{5/2}}{2520}+\frac{91 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{3456}+\frac{2093 (1-6 x) \sqrt{3 x^2-x+2}}{27648}+\frac{48139 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{55296 \sqrt{3}}","\frac{1}{12} \left(3 x^2-x+2\right)^{5/2} (2 x+1)^3+\frac{8}{63} \left(3 x^2-x+2\right)^{5/2} (2 x+1)^2+\frac{13 (50 x+29) \left(3 x^2-x+2\right)^{5/2}}{2520}+\frac{91 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{3456}+\frac{2093 (1-6 x) \sqrt{3 x^2-x+2}}{27648}+\frac{48139 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{55296 \sqrt{3}}",1,"(2093*(1 - 6*x)*Sqrt[2 - x + 3*x^2])/27648 + (91*(1 - 6*x)*(2 - x + 3*x^2)^(3/2))/3456 + (8*(1 + 2*x)^2*(2 - x + 3*x^2)^(5/2))/63 + ((1 + 2*x)^3*(2 - x + 3*x^2)^(5/2))/12 + (13*(29 + 50*x)*(2 - x + 3*x^2)^(5/2))/2520 + (48139*ArcSinh[(1 - 6*x)/Sqrt[23]])/(55296*Sqrt[3])","A",7,6,32,0.1875,1,"{1653, 832, 779, 612, 619, 215}"
216,1,116,0,0.0822707,"\int (1+2 x) \left(2-x+3 x^2\right)^{3/2} \left(1+3 x+4 x^2\right) \, dx","Int[(1 + 2*x)*(2 - x + 3*x^2)^(3/2)*(1 + 3*x + 4*x^2),x]","\frac{2}{21} (2 x+1)^2 \left(3 x^2-x+2\right)^{5/2}+\frac{1}{378} (102 x+109) \left(3 x^2-x+2\right)^{5/2}-\frac{71 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{2592}-\frac{1633 (1-6 x) \sqrt{3 x^2-x+2}}{20736}-\frac{37559 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{41472 \sqrt{3}}","\frac{2}{21} (2 x+1)^2 \left(3 x^2-x+2\right)^{5/2}+\frac{1}{378} (102 x+109) \left(3 x^2-x+2\right)^{5/2}-\frac{71 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{2592}-\frac{1633 (1-6 x) \sqrt{3 x^2-x+2}}{20736}-\frac{37559 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{41472 \sqrt{3}}",1,"(-1633*(1 - 6*x)*Sqrt[2 - x + 3*x^2])/20736 - (71*(1 - 6*x)*(2 - x + 3*x^2)^(3/2))/2592 + (2*(1 + 2*x)^2*(2 - x + 3*x^2)^(5/2))/21 + ((109 + 102*x)*(2 - x + 3*x^2)^(5/2))/378 - (37559*ArcSinh[(1 - 6*x)/Sqrt[23]])/(41472*Sqrt[3])","A",6,5,30,0.1667,1,"{1653, 779, 612, 619, 215}"
217,1,124,0,0.1441688,"\int \frac{\left(2-x+3 x^2\right)^{3/2} \left(1+3 x+4 x^2\right)}{1+2 x} \, dx","Int[((2 - x + 3*x^2)^(3/2)*(1 + 3*x + 4*x^2))/(1 + 2*x),x]","\frac{2}{15} \left(3 x^2-x+2\right)^{5/2}+\frac{1}{144} (30 x+7) \left(3 x^2-x+2\right)^{3/2}+\frac{(402 x+869) \sqrt{3 x^2-x+2}}{1152}-\frac{13}{32} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)+\frac{2203 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{2304 \sqrt{3}}","\frac{2}{15} \left(3 x^2-x+2\right)^{5/2}+\frac{1}{144} (30 x+7) \left(3 x^2-x+2\right)^{3/2}+\frac{(402 x+869) \sqrt{3 x^2-x+2}}{1152}-\frac{13}{32} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)+\frac{2203 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{2304 \sqrt{3}}",1,"((869 + 402*x)*Sqrt[2 - x + 3*x^2])/1152 + ((7 + 30*x)*(2 - x + 3*x^2)^(3/2))/144 + (2*(2 - x + 3*x^2)^(5/2))/15 + (2203*ArcSinh[(1 - 6*x)/Sqrt[23]])/(2304*Sqrt[3]) - (13*Sqrt[13]*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/32","A",8,7,32,0.2188,1,"{1653, 814, 843, 619, 215, 724, 206}"
218,1,131,0,0.140166,"\int \frac{\left(2-x+3 x^2\right)^{3/2} \left(1+3 x+4 x^2\right)}{(1+2 x)^2} \, dx","Int[((2 - x + 3*x^2)^(3/2)*(1 + 3*x + 4*x^2))/(1 + 2*x)^2,x]","-\frac{\left(3 x^2-x+2\right)^{5/2}}{13 (2 x+1)}-\frac{1}{104} (23-38 x) \left(3 x^2-x+2\right)^{3/2}-\frac{1}{192} (349-294 x) \sqrt{3 x^2-x+2}+\frac{25}{32} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)-\frac{2327 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{384 \sqrt{3}}","-\frac{\left(3 x^2-x+2\right)^{5/2}}{13 (2 x+1)}-\frac{1}{104} (23-38 x) \left(3 x^2-x+2\right)^{3/2}-\frac{1}{192} (349-294 x) \sqrt{3 x^2-x+2}+\frac{25}{32} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)-\frac{2327 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{384 \sqrt{3}}",1,"-((349 - 294*x)*Sqrt[2 - x + 3*x^2])/192 - ((23 - 38*x)*(2 - x + 3*x^2)^(3/2))/104 - (2 - x + 3*x^2)^(5/2)/(13*(1 + 2*x)) - (2327*ArcSinh[(1 - 6*x)/Sqrt[23]])/(384*Sqrt[3]) + (25*Sqrt[13]*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/32","A",8,7,32,0.2188,1,"{1650, 814, 843, 619, 215, 724, 206}"
219,1,138,0,0.1391584,"\int \frac{\left(2-x+3 x^2\right)^{3/2} \left(1+3 x+4 x^2\right)}{(1+2 x)^3} \, dx","Int[((2 - x + 3*x^2)^(3/2)*(1 + 3*x + 4*x^2))/(1 + 2*x)^3,x]","-\frac{\left(3 x^2-x+2\right)^{5/2}}{26 (2 x+1)^2}+\frac{(122 x+151) \left(3 x^2-x+2\right)^{3/2}}{312 (2 x+1)}+\frac{1}{624} (1858-771 x) \sqrt{3 x^2-x+2}-\frac{1153 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{64 \sqrt{13}}+\frac{1519 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{192 \sqrt{3}}","-\frac{\left(3 x^2-x+2\right)^{5/2}}{26 (2 x+1)^2}+\frac{(122 x+151) \left(3 x^2-x+2\right)^{3/2}}{312 (2 x+1)}+\frac{1}{624} (1858-771 x) \sqrt{3 x^2-x+2}-\frac{1153 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{64 \sqrt{13}}+\frac{1519 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{192 \sqrt{3}}",1,"((1858 - 771*x)*Sqrt[2 - x + 3*x^2])/624 + ((151 + 122*x)*(2 - x + 3*x^2)^(3/2))/(312*(1 + 2*x)) - (2 - x + 3*x^2)^(5/2)/(26*(1 + 2*x)^2) + (1519*ArcSinh[(1 - 6*x)/Sqrt[23]])/(192*Sqrt[3]) - (1153*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(64*Sqrt[13])","A",8,8,32,0.2500,1,"{1650, 812, 814, 843, 619, 215, 724, 206}"
220,1,189,0,0.1559517,"\int (1+2 x)^3 \left(2-x+3 x^2\right)^{5/2} \left(1+3 x+4 x^2\right) \, dx","Int[(1 + 2*x)^3*(2 - x + 3*x^2)^(5/2)*(1 + 3*x + 4*x^2),x]","\frac{2}{33} \left(3 x^2-x+2\right)^{7/2} (2 x+1)^4+\frac{29}{330} \left(3 x^2-x+2\right)^{7/2} (2 x+1)^3+\frac{133 \left(3 x^2-x+2\right)^{7/2} (2 x+1)^2}{1485}-\frac{(26353-21350 x) \left(3 x^2-x+2\right)^{7/2}}{498960}+\frac{5089 (1-6 x) \left(3 x^2-x+2\right)^{5/2}}{155520}+\frac{117047 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{1492992}+\frac{2692081 (1-6 x) \sqrt{3 x^2-x+2}}{11943936}+\frac{61917863 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{23887872 \sqrt{3}}","\frac{2}{33} \left(3 x^2-x+2\right)^{7/2} (2 x+1)^4+\frac{29}{330} \left(3 x^2-x+2\right)^{7/2} (2 x+1)^3+\frac{133 \left(3 x^2-x+2\right)^{7/2} (2 x+1)^2}{1485}-\frac{(26353-21350 x) \left(3 x^2-x+2\right)^{7/2}}{498960}+\frac{5089 (1-6 x) \left(3 x^2-x+2\right)^{5/2}}{155520}+\frac{117047 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{1492992}+\frac{2692081 (1-6 x) \sqrt{3 x^2-x+2}}{11943936}+\frac{61917863 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{23887872 \sqrt{3}}",1,"(2692081*(1 - 6*x)*Sqrt[2 - x + 3*x^2])/11943936 + (117047*(1 - 6*x)*(2 - x + 3*x^2)^(3/2))/1492992 + (5089*(1 - 6*x)*(2 - x + 3*x^2)^(5/2))/155520 - ((26353 - 21350*x)*(2 - x + 3*x^2)^(7/2))/498960 + (133*(1 + 2*x)^2*(2 - x + 3*x^2)^(7/2))/1485 + (29*(1 + 2*x)^3*(2 - x + 3*x^2)^(7/2))/330 + (2*(1 + 2*x)^4*(2 - x + 3*x^2)^(7/2))/33 + (61917863*ArcSinh[(1 - 6*x)/Sqrt[23]])/(23887872*Sqrt[3])","A",9,6,32,0.1875,1,"{1653, 832, 779, 612, 619, 215}"
221,1,164,0,0.132842,"\int (1+2 x)^2 \left(2-x+3 x^2\right)^{5/2} \left(1+3 x+4 x^2\right) \, dx","Int[(1 + 2*x)^2*(2 - x + 3*x^2)^(5/2)*(1 + 3*x + 4*x^2),x]","\frac{1}{15} (2 x+1)^3 \left(3 x^2-x+2\right)^{7/2}+\frac{37}{405} (2 x+1)^2 \left(3 x^2-x+2\right)^{7/2}+\frac{(3430 x+2731) \left(3 x^2-x+2\right)^{7/2}}{17010}-\frac{293 (1-6 x) \left(3 x^2-x+2\right)^{5/2}}{58320}-\frac{6739 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{559872}-\frac{154997 (1-6 x) \sqrt{3 x^2-x+2}}{4478976}-\frac{3564931 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{8957952 \sqrt{3}}","\frac{1}{15} (2 x+1)^3 \left(3 x^2-x+2\right)^{7/2}+\frac{37}{405} (2 x+1)^2 \left(3 x^2-x+2\right)^{7/2}+\frac{(3430 x+2731) \left(3 x^2-x+2\right)^{7/2}}{17010}-\frac{293 (1-6 x) \left(3 x^2-x+2\right)^{5/2}}{58320}-\frac{6739 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{559872}-\frac{154997 (1-6 x) \sqrt{3 x^2-x+2}}{4478976}-\frac{3564931 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{8957952 \sqrt{3}}",1,"(-154997*(1 - 6*x)*Sqrt[2 - x + 3*x^2])/4478976 - (6739*(1 - 6*x)*(2 - x + 3*x^2)^(3/2))/559872 - (293*(1 - 6*x)*(2 - x + 3*x^2)^(5/2))/58320 + (37*(1 + 2*x)^2*(2 - x + 3*x^2)^(7/2))/405 + ((1 + 2*x)^3*(2 - x + 3*x^2)^(7/2))/15 + ((2731 + 3430*x)*(2 - x + 3*x^2)^(7/2))/17010 - (3564931*ArcSinh[(1 - 6*x)/Sqrt[23]])/(8957952*Sqrt[3])","A",8,6,32,0.1875,1,"{1653, 832, 779, 612, 619, 215}"
222,1,139,0,0.0917934,"\int (1+2 x) \left(2-x+3 x^2\right)^{5/2} \left(1+3 x+4 x^2\right) \, dx","Int[(1 + 2*x)*(2 - x + 3*x^2)^(5/2)*(1 + 3*x + 4*x^2),x]","\frac{2}{27} (2 x+1)^2 \left(3 x^2-x+2\right)^{7/2}+\frac{1}{648} (122 x+137) \left(3 x^2-x+2\right)^{7/2}-\frac{445 (1-6 x) \left(3 x^2-x+2\right)^{5/2}}{15552}-\frac{51175 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{746496}-\frac{1177025 (1-6 x) \sqrt{3 x^2-x+2}}{5971968}-\frac{27071575 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{11943936 \sqrt{3}}","\frac{2}{27} (2 x+1)^2 \left(3 x^2-x+2\right)^{7/2}+\frac{1}{648} (122 x+137) \left(3 x^2-x+2\right)^{7/2}-\frac{445 (1-6 x) \left(3 x^2-x+2\right)^{5/2}}{15552}-\frac{51175 (1-6 x) \left(3 x^2-x+2\right)^{3/2}}{746496}-\frac{1177025 (1-6 x) \sqrt{3 x^2-x+2}}{5971968}-\frac{27071575 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{11943936 \sqrt{3}}",1,"(-1177025*(1 - 6*x)*Sqrt[2 - x + 3*x^2])/5971968 - (51175*(1 - 6*x)*(2 - x + 3*x^2)^(3/2))/746496 - (445*(1 - 6*x)*(2 - x + 3*x^2)^(5/2))/15552 + (2*(1 + 2*x)^2*(2 - x + 3*x^2)^(7/2))/27 + ((137 + 122*x)*(2 - x + 3*x^2)^(7/2))/648 - (27071575*ArcSinh[(1 - 6*x)/Sqrt[23]])/(11943936*Sqrt[3])","A",7,5,30,0.1667,1,"{1653, 779, 612, 619, 215}"
223,1,147,0,0.1595248,"\int \frac{\left(2-x+3 x^2\right)^{5/2} \left(1+3 x+4 x^2\right)}{1+2 x} \, dx","Int[((2 - x + 3*x^2)^(5/2)*(1 + 3*x + 4*x^2))/(1 + 2*x),x]","\frac{2}{21} \left(3 x^2-x+2\right)^{7/2}+\frac{(150 x+29) \left(3 x^2-x+2\right)^{5/2}}{1080}+\frac{(2154 x+2449) \left(3 x^2-x+2\right)^{3/2}}{10368}+\frac{(221999-17850 x) \sqrt{3 x^2-x+2}}{82944}-\frac{169}{128} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)+\frac{944521 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{165888 \sqrt{3}}","\frac{2}{21} \left(3 x^2-x+2\right)^{7/2}+\frac{(150 x+29) \left(3 x^2-x+2\right)^{5/2}}{1080}+\frac{(2154 x+2449) \left(3 x^2-x+2\right)^{3/2}}{10368}+\frac{(221999-17850 x) \sqrt{3 x^2-x+2}}{82944}-\frac{169}{128} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)+\frac{944521 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{165888 \sqrt{3}}",1,"((221999 - 17850*x)*Sqrt[2 - x + 3*x^2])/82944 + ((2449 + 2154*x)*(2 - x + 3*x^2)^(3/2))/10368 + ((29 + 150*x)*(2 - x + 3*x^2)^(5/2))/1080 + (2*(2 - x + 3*x^2)^(7/2))/21 + (944521*ArcSinh[(1 - 6*x)/Sqrt[23]])/(165888*Sqrt[3]) - (169*Sqrt[13]*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/128","A",9,7,32,0.2188,1,"{1653, 814, 843, 619, 215, 724, 206}"
224,1,154,0,0.1630714,"\int \frac{\left(2-x+3 x^2\right)^{5/2} \left(1+3 x+4 x^2\right)}{(1+2 x)^2} \, dx","Int[((2 - x + 3*x^2)^(5/2)*(1 + 3*x + 4*x^2))/(1 + 2*x)^2,x]","-\frac{\left(3 x^2-x+2\right)^{7/2}}{13 (2 x+1)}-\frac{11 (37-60 x) \left(3 x^2-x+2\right)^{5/2}}{2340}-\frac{11}{864} (67-78 x) \left(3 x^2-x+2\right)^{3/2}-\frac{11 (4727-3090 x) \sqrt{3 x^2-x+2}}{6912}+\frac{429}{128} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)-\frac{315623 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{13824 \sqrt{3}}","-\frac{\left(3 x^2-x+2\right)^{7/2}}{13 (2 x+1)}-\frac{11 (37-60 x) \left(3 x^2-x+2\right)^{5/2}}{2340}-\frac{11}{864} (67-78 x) \left(3 x^2-x+2\right)^{3/2}-\frac{11 (4727-3090 x) \sqrt{3 x^2-x+2}}{6912}+\frac{429}{128} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)-\frac{315623 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{13824 \sqrt{3}}",1,"(-11*(4727 - 3090*x)*Sqrt[2 - x + 3*x^2])/6912 - (11*(67 - 78*x)*(2 - x + 3*x^2)^(3/2))/864 - (11*(37 - 60*x)*(2 - x + 3*x^2)^(5/2))/2340 - (2 - x + 3*x^2)^(7/2)/(13*(1 + 2*x)) - (315623*ArcSinh[(1 - 6*x)/Sqrt[23]])/(13824*Sqrt[3]) + (429*Sqrt[13]*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/128","A",9,7,32,0.2188,1,"{1650, 814, 843, 619, 215, 724, 206}"
225,1,161,0,0.1627843,"\int \frac{\left(2-x+3 x^2\right)^{5/2} \left(1+3 x+4 x^2\right)}{(1+2 x)^3} \, dx","Int[((2 - x + 3*x^2)^(5/2)*(1 + 3*x + 4*x^2))/(1 + 2*x)^3,x]","-\frac{\left(3 x^2-x+2\right)^{7/2}}{26 (2 x+1)^2}+\frac{(134 x+257) \left(3 x^2-x+2\right)^{5/2}}{520 (2 x+1)}+\frac{1}{832} (1227-838 x) \left(3 x^2-x+2\right)^{3/2}+\frac{(21317-10470 x) \sqrt{3 x^2-x+2}}{1536}-\frac{1631}{256} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)+\frac{118423 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{3072 \sqrt{3}}","-\frac{\left(3 x^2-x+2\right)^{7/2}}{26 (2 x+1)^2}+\frac{(134 x+257) \left(3 x^2-x+2\right)^{5/2}}{520 (2 x+1)}+\frac{1}{832} (1227-838 x) \left(3 x^2-x+2\right)^{3/2}+\frac{(21317-10470 x) \sqrt{3 x^2-x+2}}{1536}-\frac{1631}{256} \sqrt{13} \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)+\frac{118423 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{3072 \sqrt{3}}",1,"((21317 - 10470*x)*Sqrt[2 - x + 3*x^2])/1536 + ((1227 - 838*x)*(2 - x + 3*x^2)^(3/2))/832 + ((257 + 134*x)*(2 - x + 3*x^2)^(5/2))/(520*(1 + 2*x)) - (2 - x + 3*x^2)^(7/2)/(26*(1 + 2*x)^2) + (118423*ArcSinh[(1 - 6*x)/Sqrt[23]])/(3072*Sqrt[3]) - (1631*Sqrt[13]*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/256","A",9,8,32,0.2500,1,"{1650, 812, 814, 843, 619, 215, 724, 206}"
226,1,692,0,2.1022142,"\int \frac{(g+h x)^3 \left(d+e x+f x^2\right)}{\sqrt{a+b x+c x^2}} \, dx","Int[((g + h*x)^3*(d + e*x + f*x^2))/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(8 c^2 h^2 \left(128 a^2 f h^2+275 a b h (e h+3 f g)+3 b^2 \left(50 h (d h+3 e g)+129 f g^2\right)\right)-2 c h x \left(8 c^2 h \left(a h (45 e h+71 f g)+10 b h (5 d h+8 e g)+21 b f g^2\right)-14 b c h^2 (46 a f h+25 b e h+39 b f g)+315 b^3 f h^3+16 c^3 \left(3 f g^3-5 g h (10 d h+3 e g)\right)\right)-210 b^2 c h^3 (14 a f h+5 b (e h+3 f g))-16 c^3 h \left(16 a h \left(5 h (d h+3 e g)+13 f g^2\right)+b g \left(5 h (54 d h+47 e g)+39 f g^2\right)\right)+945 b^4 f h^4-64 c^4 \left(3 f g^4-5 g^2 h (16 d h+3 e g)\right)\right)}{1920 c^5 h}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-80 b c^2 h \left(3 a^2 f h^2+3 a b h (e h+3 f g)+b^2 \left(d h^2+3 e g h+3 f g^2\right)\right)+96 c^3 \left(a^2 h^2 (e h+3 f g)+2 a b h \left(h (d h+3 e g)+3 f g^2\right)+b^2 g \left(3 h (d h+e g)+f g^2\right)\right)+70 b^3 c h^2 (4 a f h+b e h+3 b f g)-128 c^4 g \left(3 a h (d h+e g)+a f g^2+b g (3 d h+e g)\right)-63 b^5 f h^3+256 c^5 d g^3\right)}{256 c^{11/2}}+\frac{(g+h x)^2 \sqrt{a+b x+c x^2} \left(-2 c h (32 a f h+35 b e h+24 b f g)+63 b^2 f h^2+c^2 \left(-\left(12 f g^2-20 h (4 d h+3 e g)\right)\right)\right)}{240 c^3 h}-\frac{(g+h x)^3 \sqrt{a+b x+c x^2} (9 b f h+2 c (f g-5 e h))}{40 c^2 h}+\frac{f (g+h x)^4 \sqrt{a+b x+c x^2}}{5 c h}","\frac{\sqrt{a+b x+c x^2} \left(8 c^2 h^2 \left(128 a^2 f h^2+275 a b h (e h+3 f g)+3 b^2 \left(50 h (d h+3 e g)+129 f g^2\right)\right)-2 c h x \left(8 c^2 h \left(a h (45 e h+71 f g)+b \left(50 d h^2+80 e g h+21 f g^2\right)\right)-14 b c h^2 (46 a f h+25 b e h+39 b f g)+315 b^3 f h^3+16 c^3 g \left(3 f g^2-5 h (10 d h+3 e g)\right)\right)-210 b^2 c h^3 (14 a f h+5 b (e h+3 f g))-16 c^3 h \left(16 a h \left(5 h (d h+3 e g)+13 f g^2\right)+b g \left(5 h (54 d h+47 e g)+39 f g^2\right)\right)+945 b^4 f h^4-64 c^4 g^2 \left(3 f g^2-5 h (16 d h+3 e g)\right)\right)}{1920 c^5 h}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-80 b c^2 h \left(3 a^2 f h^2+3 a b h (e h+3 f g)+b^2 \left(d h^2+3 e g h+3 f g^2\right)\right)+96 c^3 \left(a^2 h^2 (e h+3 f g)+2 a b h \left(h (d h+3 e g)+3 f g^2\right)+b^2 g \left(3 h (d h+e g)+f g^2\right)\right)+70 b^3 c h^2 (4 a f h+b e h+3 b f g)-128 c^4 g \left(a \left(3 h (d h+e g)+f g^2\right)+b g (3 d h+e g)\right)-63 b^5 f h^3+256 c^5 d g^3\right)}{256 c^{11/2}}+\frac{(g+h x)^2 \sqrt{a+b x+c x^2} \left(-2 c h (32 a f h+35 b e h+24 b f g)+63 b^2 f h^2+c^2 \left(-\left(12 f g^2-20 h (4 d h+3 e g)\right)\right)\right)}{240 c^3 h}-\frac{(g+h x)^3 \sqrt{a+b x+c x^2} (9 b f h+2 c (f g-5 e h))}{40 c^2 h}+\frac{f (g+h x)^4 \sqrt{a+b x+c x^2}}{5 c h}",1,"((63*b^2*f*h^2 - 2*c*h*(24*b*f*g + 35*b*e*h + 32*a*f*h) - c^2*(12*f*g^2 - 20*h*(3*e*g + 4*d*h)))*(g + h*x)^2*Sqrt[a + b*x + c*x^2])/(240*c^3*h) - ((9*b*f*h + 2*c*(f*g - 5*e*h))*(g + h*x)^3*Sqrt[a + b*x + c*x^2])/(40*c^2*h) + (f*(g + h*x)^4*Sqrt[a + b*x + c*x^2])/(5*c*h) + ((945*b^4*f*h^4 - 64*c^4*(3*f*g^4 - 5*g^2*h*(3*e*g + 16*d*h)) - 210*b^2*c*h^3*(14*a*f*h + 5*b*(3*f*g + e*h)) + 8*c^2*h^2*(128*a^2*f*h^2 + 275*a*b*h*(3*f*g + e*h) + 3*b^2*(129*f*g^2 + 50*h*(3*e*g + d*h))) - 16*c^3*h*(16*a*h*(13*f*g^2 + 5*h*(3*e*g + d*h)) + b*g*(39*f*g^2 + 5*h*(47*e*g + 54*d*h))) - 2*c*h*(315*b^3*f*h^3 - 14*b*c*h^2*(39*b*f*g + 25*b*e*h + 46*a*f*h) + 16*c^3*(3*f*g^3 - 5*g*h*(3*e*g + 10*d*h)) + 8*c^2*h*(21*b*f*g^2 + 10*b*h*(8*e*g + 5*d*h) + a*h*(71*f*g + 45*e*h)))*x)*Sqrt[a + b*x + c*x^2])/(1920*c^5*h) + ((256*c^5*d*g^3 - 63*b^5*f*h^3 + 70*b^3*c*h^2*(3*b*f*g + b*e*h + 4*a*f*h) - 128*c^4*g*(a*f*g^2 + 3*a*h*(e*g + d*h) + b*g*(e*g + 3*d*h)) - 80*b*c^2*h*(3*a^2*f*h^2 + 3*a*b*h*(3*f*g + e*h) + b^2*(3*f*g^2 + 3*e*g*h + d*h^2)) + 96*c^3*(a^2*h^2*(3*f*g + e*h) + b^2*g*(f*g^2 + 3*h*(e*g + d*h)) + 2*a*b*h*(3*f*g^2 + h*(3*e*g + d*h))))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(11/2))","A",6,5,32,0.1562,1,"{1653, 832, 779, 621, 206}"
227,1,418,0,1.0110901,"\int \frac{(g+h x)^2 \left(d+e x+f x^2\right)}{\sqrt{a+b x+c x^2}} \, dx","Int[((g + h*x)^2*(d + e*x + f*x^2))/Sqrt[a + b*x + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 c^2 \left(a^2 f h^2+2 a b h (e h+2 f g)+b^2 \left(h (d h+2 e g)+f g^2\right)\right)-40 b^2 c h (3 a f h+b e h+2 b f g)-64 c^3 \left(a h (d h+2 e g)+a f g^2+b g (2 d h+e g)\right)+35 b^4 f h^2+128 c^4 d g^2\right)}{128 c^{9/2}}-\frac{\sqrt{a+b x+c x^2} \left(-2 c h x \left(-4 c h (9 a f h+10 b e h+6 b f g)+35 b^2 f h^2-8 c^2 \left(f g^2-2 h (3 d h+2 e g)\right)\right)+8 c^2 h \left(16 a h (e h+2 f g)+18 b h (d h+2 e g)+11 b f g^2\right)-20 b c h^2 (11 a f h+6 b (e h+2 f g))+105 b^3 f h^3+32 c^3 \left(f g^3-4 g h (3 d h+e g)\right)\right)}{192 c^4 h}-\frac{(g+h x)^2 \sqrt{a+b x+c x^2} (7 b f h-8 c e h+2 c f g)}{24 c^2 h}+\frac{f (g+h x)^3 \sqrt{a+b x+c x^2}}{4 c h}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 c^2 \left(a^2 f h^2+2 a b h (e h+2 f g)+b^2 \left(d h^2+2 e g h+f g^2\right)\right)-40 b^2 c h (3 a f h+b e h+2 b f g)-64 c^3 \left(a \left(d h^2+2 e g h+f g^2\right)+b g (2 d h+e g)\right)+35 b^4 f h^2+128 c^4 d g^2\right)}{128 c^{9/2}}-\frac{\sqrt{a+b x+c x^2} \left(-2 c h x \left(-4 c h (9 a f h+10 b e h+6 b f g)+35 b^2 f h^2-8 c^2 \left(f g^2-2 h (3 d h+2 e g)\right)\right)+8 c^2 h \left(16 a h (e h+2 f g)+b \left(18 h (d h+2 e g)+11 f g^2\right)\right)-20 b c h^2 (11 a f h+6 b (e h+2 f g))+105 b^3 f h^3+32 c^3 g \left(f g^2-4 h (3 d h+e g)\right)\right)}{192 c^4 h}-\frac{(g+h x)^2 \sqrt{a+b x+c x^2} (7 b f h-8 c e h+2 c f g)}{24 c^2 h}+\frac{f (g+h x)^3 \sqrt{a+b x+c x^2}}{4 c h}",1,"-((2*c*f*g - 8*c*e*h + 7*b*f*h)*(g + h*x)^2*Sqrt[a + b*x + c*x^2])/(24*c^2*h) + (f*(g + h*x)^3*Sqrt[a + b*x + c*x^2])/(4*c*h) - ((105*b^3*f*h^3 + 32*c^3*(f*g^3 - 4*g*h*(e*g + 3*d*h)) - 20*b*c*h^2*(11*a*f*h + 6*b*(2*f*g + e*h)) + 8*c^2*h*(11*b*f*g^2 + 18*b*h*(2*e*g + d*h) + 16*a*h*(2*f*g + e*h)) - 2*c*h*(35*b^2*f*h^2 - 4*c*h*(6*b*f*g + 10*b*e*h + 9*a*f*h) - 8*c^2*(f*g^2 - 2*h*(2*e*g + 3*d*h)))*x)*Sqrt[a + b*x + c*x^2])/(192*c^4*h) + ((128*c^4*d*g^2 + 35*b^4*f*h^2 - 40*b^2*c*h*(2*b*f*g + b*e*h + 3*a*f*h) - 64*c^3*(a*f*g^2 + a*h*(2*e*g + d*h) + b*g*(e*g + 2*d*h)) + 48*c^2*(a^2*f*h^2 + 2*a*b*h*(2*f*g + e*h) + b^2*(f*g^2 + h*(2*e*g + d*h))))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(9/2))","A",5,5,32,0.1562,1,"{1653, 832, 779, 621, 206}"
228,1,223,0,0.3031924,"\int \frac{(g+h x) \left(d+e x+f x^2\right)}{\sqrt{a+b x+c x^2}} \, dx","Int[((g + h*x)*(d + e*x + f*x^2))/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(-2 c h (8 a f h+9 b (e h+f g))+15 b^2 f h^2-2 c h x (5 b f h-6 c e h+2 c f g)-8 c^2 \left(f g^2-3 h (d h+e g)\right)\right)}{24 c^3 h}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-8 c^2 (a e h+a f g+b d h+b e g)+6 b c (2 a f h+b e h+b f g)-5 b^3 f h+16 c^3 d g\right)}{16 c^{7/2}}+\frac{f (g+h x)^2 \sqrt{a+b x+c x^2}}{3 c h}","\frac{\sqrt{a+b x+c x^2} \left(-2 c h (8 a f h+9 b (e h+f g))+15 b^2 f h^2-2 c h x (5 b f h-6 c e h+2 c f g)-8 c^2 \left(f g^2-3 h (d h+e g)\right)\right)}{24 c^3 h}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-8 c^2 (a e h+a f g+b d h+b e g)+6 b c (2 a f h+b e h+b f g)-5 b^3 f h+16 c^3 d g\right)}{16 c^{7/2}}+\frac{f (g+h x)^2 \sqrt{a+b x+c x^2}}{3 c h}",1,"(f*(g + h*x)^2*Sqrt[a + b*x + c*x^2])/(3*c*h) + ((15*b^2*f*h^2 - 8*c^2*(f*g^2 - 3*h*(e*g + d*h)) - 2*c*h*(8*a*f*h + 9*b*(f*g + e*h)) - 2*c*h*(2*c*f*g - 6*c*e*h + 5*b*f*h)*x)*Sqrt[a + b*x + c*x^2])/(24*c^3*h) + ((16*c^3*d*g - 5*b^3*f*h - 8*c^2*(b*e*g + a*f*g + b*d*h + a*e*h) + 6*b*c*(b*f*g + b*e*h + 2*a*f*h))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(7/2))","A",4,4,30,0.1333,1,"{1653, 779, 621, 206}"
229,1,116,0,0.1060521,"\int \frac{d+e x+f x^2}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2)/Sqrt[a + b*x + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+b e)+3 b^2 f+8 c^2 d\right)}{8 c^{5/2}}+\frac{\sqrt{a+b x+c x^2} (4 c e-3 b f)}{4 c^2}+\frac{f x \sqrt{a+b x+c x^2}}{2 c}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+b e)+3 b^2 f+8 c^2 d\right)}{8 c^{5/2}}+\frac{\sqrt{a+b x+c x^2} (4 c e-3 b f)}{4 c^2}+\frac{f x \sqrt{a+b x+c x^2}}{2 c}",1,"((4*c*e - 3*b*f)*Sqrt[a + b*x + c*x^2])/(4*c^2) + (f*x*Sqrt[a + b*x + c*x^2])/(2*c) + ((8*c^2*d + 3*b^2*f - 4*c*(b*e + a*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(5/2))","A",4,4,25,0.1600,1,"{1661, 640, 621, 206}"
230,1,179,0,0.293372,"\int \frac{d+e x+f x^2}{(g+h x) \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)*Sqrt[a + b*x + c*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (b f h-2 c e h+2 c f g)}{2 c^{3/2} h^2}+\frac{\left(f g^2-h (e g-d h)\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right)}{h^2 \sqrt{a h^2-b g h+c g^2}}+\frac{f \sqrt{a+b x+c x^2}}{c h}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (b f h-2 c e h+2 c f g)}{2 c^{3/2} h^2}+\frac{\left(f g^2-h (e g-d h)\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right)}{h^2 \sqrt{a h^2-b g h+c g^2}}+\frac{f \sqrt{a+b x+c x^2}}{c h}",1,"(f*Sqrt[a + b*x + c*x^2])/(c*h) - ((2*c*f*g - 2*c*e*h + b*f*h)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(3/2)*h^2) + ((f*g^2 - h*(e*g - d*h))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(h^2*Sqrt[c*g^2 - b*g*h + a*h^2])","A",6,5,32,0.1562,1,"{1653, 843, 621, 206, 724}"
231,1,239,0,0.3711197,"\int \frac{d+e x+f x^2}{(g+h x)^2 \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)^2*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{a+b x+c x^2} \left(f g^2-h (e g-d h)\right)}{h (g+h x) \left(a h^2-b g h+c g^2\right)}-\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(2 c \left(f g^3-d g h^2\right)-h \left(-2 a h (2 f g-e h)-b h (d h+e g)+3 b f g^2\right)\right)}{2 h^2 \left(a h^2-b g h+c g^2\right)^{3/2}}+\frac{f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c} h^2}","-\frac{\sqrt{a+b x+c x^2} \left(f g^2-h (e g-d h)\right)}{h (g+h x) \left(a h^2-b g h+c g^2\right)}-\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(h \left(2 a h (2 f g-e h)-b \left(-d h^2-e g h+3 f g^2\right)\right)+2 c \left(f g^3-d g h^2\right)\right)}{2 h^2 \left(a h^2-b g h+c g^2\right)^{3/2}}+\frac{f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c} h^2}",1,"-(((f*g^2 - h*(e*g - d*h))*Sqrt[a + b*x + c*x^2])/(h*(c*g^2 - b*g*h + a*h^2)*(g + h*x))) + (f*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c]*h^2) - ((2*c*(f*g^3 - d*g*h^2) - h*(3*b*f*g^2 - b*h*(e*g + d*h) - 2*a*h*(2*f*g - e*h)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(2*h^2*(c*g^2 - b*g*h + a*h^2)^(3/2))","A",6,5,32,0.1562,1,"{1650, 843, 621, 206, 724}"
232,1,336,0,0.6562205,"\int \frac{d+e x+f x^2}{(g+h x)^3 \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)^3*Sqrt[a + b*x + c*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(8 a^2 f h^2-4 c \left(-a h (3 e g-d h)+a f g^2+b g (2 d h+e g)\right)-4 a b h (e h+2 f g)+b^2 \left(h (3 d h+e g)+3 f g^2\right)+8 c^2 d g^2\right)}{8 \left(a h^2-b g h+c g^2\right)^{5/2}}-\frac{\sqrt{a+b x+c x^2} \left(f g^2-h (e g-d h)\right)}{2 h (g+h x)^2 \left(a h^2-b g h+c g^2\right)}+\frac{\sqrt{a+b x+c x^2} \left(2 c \left(g h (e g-3 d h)+f g^3\right)-h \left(-4 a h (2 f g-e h)-b h (3 d h+e g)+5 b f g^2\right)\right)}{4 h (g+h x) \left(a h^2-b g h+c g^2\right)^2}","\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(8 a^2 f h^2-4 c \left(a \left(d h^2-3 e g h+f g^2\right)+b g (2 d h+e g)\right)-4 a b h (e h+2 f g)+b^2 \left(3 d h^2+e g h+3 f g^2\right)+8 c^2 d g^2\right)}{8 \left(a h^2-b g h+c g^2\right)^{5/2}}-\frac{\sqrt{a+b x+c x^2} \left(f g^2-h (e g-d h)\right)}{2 h (g+h x)^2 \left(a h^2-b g h+c g^2\right)}+\frac{\sqrt{a+b x+c x^2} \left(h \left(4 a h (2 f g-e h)-b \left(-3 d h^2-e g h+5 f g^2\right)\right)+2 c g \left(h (e g-3 d h)+f g^2\right)\right)}{4 h (g+h x) \left(a h^2-b g h+c g^2\right)^2}",1,"-((f*g^2 - h*(e*g - d*h))*Sqrt[a + b*x + c*x^2])/(2*h*(c*g^2 - b*g*h + a*h^2)*(g + h*x)^2) + ((2*c*(f*g^3 + g*h*(e*g - 3*d*h)) - h*(5*b*f*g^2 - b*h*(e*g + 3*d*h) - 4*a*h*(2*f*g - e*h)))*Sqrt[a + b*x + c*x^2])/(4*h*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)) + ((8*c^2*d*g^2 + 8*a^2*f*h^2 - 4*a*b*h*(2*f*g + e*h) - 4*c*(a*f*g^2 - a*h*(3*e*g - d*h) + b*g*(e*g + 2*d*h)) + b^2*(3*f*g^2 + h*(e*g + 3*d*h)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(8*(c*g^2 - b*g*h + a*h^2)^(5/2))","A",4,4,32,0.1250,1,"{1650, 806, 724, 206}"
233,1,502,0,1.1756011,"\int \frac{(g+h x)^3 \left(d+e x+f x^2\right)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((g + h*x)^3*(d + e*x + f*x^2))/(a + b*x + c*x^2)^(3/2),x]","\frac{h \sqrt{a+b x+c x^2} \left(8 c \left(32 a^2 f h^2+39 a b h (e h+3 f g)+b^2 \left(9 h (d h+3 e g)+20 f g^2\right)\right)+2 h x \left(-8 c^2 (9 a e h+11 a f g+3 b d h+3 b e g)+2 b c (58 a f h+15 b e h+17 b f g)-35 b^3 f h+48 c^3 d g\right)-10 b^2 h (46 a f h+9 b (e h+3 f g))-16 c^2 \left(4 a \left(3 d h^2+9 e g h+7 f g^2\right)+3 b g (3 d h+2 e g)\right)+\frac{105 b^4 f h^2}{c}+192 c^3 d g^2\right)}{24 c^3 \left(b^2-4 a c\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(24 c^2 h \left(a h (e h+3 f g)+b h (d h+3 e g)+3 b f g^2\right)-30 b c h^2 (2 a f h+b e h+3 b f g)+35 b^3 f h^3-16 c^3 \left(3 g h (d h+e g)+f g^3\right)\right)}{16 c^{9/2}}+\frac{2 (g+h x)^3 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{h (g+h x)^2 \sqrt{a+b x+c x^2} \left(-16 a c f+7 b^2 f-6 b c e+12 c^2 d\right)}{3 c^2 \left(b^2-4 a c\right)}","\frac{h \sqrt{a+b x+c x^2} \left(8 c^2 \left(32 a^2 f h^2+39 a b h (e h+3 f g)+b^2 \left(9 h (d h+3 e g)+20 f g^2\right)\right)+2 c h x \left(-8 c^2 (9 a e h+11 a f g+3 b d h+3 b e g)+2 b c (58 a f h+15 b e h+17 b f g)-35 b^3 f h+48 c^3 d g\right)-10 b^2 c h (46 a f h+9 b (e h+3 f g))-16 c^3 \left(4 a \left(3 d h^2+9 e g h+7 f g^2\right)+3 b g (3 d h+2 e g)\right)+105 b^4 f h^2+192 c^4 d g^2\right)}{24 c^4 \left(b^2-4 a c\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(24 c^2 h \left(a h (e h+3 f g)+b \left(d h^2+3 e g h+3 f g^2\right)\right)-30 b c h^2 (2 a f h+b e h+3 b f g)+35 b^3 f h^3-16 c^3 g \left(3 h (d h+e g)+f g^2\right)\right)}{16 c^{9/2}}+\frac{2 (g+h x)^3 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{h (g+h x)^2 \sqrt{a+b x+c x^2} \left(-16 a c f+7 b^2 f-6 b c e+12 c^2 d\right)}{3 c^2 \left(b^2-4 a c\right)}",1,"(2*(c*(2*a*e - b*(d + (a*f)/c)) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x)*(g + h*x)^3)/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + ((12*c^2*d - 6*b*c*e + 7*b^2*f - 16*a*c*f)*h*(g + h*x)^2*Sqrt[a + b*x + c*x^2])/(3*c^2*(b^2 - 4*a*c)) + (h*(192*c^3*d*g^2 + (105*b^4*f*h^2)/c - 10*b^2*h*(46*a*f*h + 9*b*(3*f*g + e*h)) - 16*c^2*(3*b*g*(2*e*g + 3*d*h) + 4*a*(7*f*g^2 + 9*e*g*h + 3*d*h^2)) + 8*c*(32*a^2*f*h^2 + 39*a*b*h*(3*f*g + e*h) + b^2*(20*f*g^2 + 9*h*(3*e*g + d*h))) + 2*h*(48*c^3*d*g - 35*b^3*f*h - 8*c^2*(3*b*e*g + 11*a*f*g + 3*b*d*h + 9*a*e*h) + 2*b*c*(17*b*f*g + 15*b*e*h + 58*a*f*h))*x)*Sqrt[a + b*x + c*x^2])/(24*c^3*(b^2 - 4*a*c)) - ((35*b^3*f*h^3 - 30*b*c*h^2*(3*b*f*g + b*e*h + 2*a*f*h) - 16*c^3*(f*g^3 + 3*g*h*(e*g + d*h)) + 24*c^2*h*(3*b*f*g^2 + b*h*(3*e*g + d*h) + a*h*(3*f*g + e*h)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(9/2))","A",5,5,32,0.1562,1,"{1644, 832, 779, 621, 206}"
234,1,288,0,0.3916575,"\int \frac{(g+h x)^2 \left(d+e x+f x^2\right)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((g + h*x)^2*(d + e*x + f*x^2))/(a + b*x + c*x^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-12 c h (a f h+b e h+2 b f g)+15 b^2 f h^2+8 c^2 \left(h (d h+2 e g)+f g^2\right)\right)}{8 c^{7/2}}+\frac{2 (g+h x)^2 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{h \sqrt{a+b x+c x^2} \left(2 h x \left(-12 a c f+5 b^2 f-4 b c e+8 c^2 d\right)-8 c (4 a e h+8 a f g+b d h+2 b e g)+4 b (13 a f h+3 b e h+6 b f g)-\frac{15 b^3 f h}{c}+32 c^2 d g\right)}{4 c^2 \left(b^2-4 a c\right)}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-12 c h (a f h+b e h+2 b f g)+15 b^2 f h^2+8 c^2 \left(h (d h+2 e g)+f g^2\right)\right)}{8 c^{7/2}}+\frac{2 (g+h x)^2 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{h \sqrt{a+b x+c x^2} \left(2 c h x \left(-12 a c f+5 b^2 f-4 b c e+8 c^2 d\right)-8 c^2 (4 a e h+8 a f g+b d h+2 b e g)+4 b c (13 a f h+3 b e h+6 b f g)-15 b^3 f h+32 c^3 d g\right)}{4 c^3 \left(b^2-4 a c\right)}",1,"(2*(c*(2*a*e - b*(d + (a*f)/c)) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x)*(g + h*x)^2)/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (h*(32*c^2*d*g - (15*b^3*f*h)/c - 8*c*(2*b*e*g + 8*a*f*g + b*d*h + 4*a*e*h) + 4*b*(6*b*f*g + 3*b*e*h + 13*a*f*h) + 2*(8*c^2*d - 4*b*c*e + 5*b^2*f - 12*a*c*f)*h*x)*Sqrt[a + b*x + c*x^2])/(4*c^2*(b^2 - 4*a*c)) + ((15*b^2*f*h^2 - 12*c*h*(2*b*f*g + b*e*h + a*f*h) + 8*c^2*(f*g^2 + h*(2*e*g + d*h)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(7/2))","A",4,4,32,0.1250,1,"{1644, 779, 621, 206}"
235,1,186,0,0.2268166,"\int \frac{(g+h x) \left(d+e x+f x^2\right)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((g + h*x)*(d + e*x + f*x^2))/(a + b*x + c*x^2)^(3/2),x]","\frac{2 (g+h x) \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{h \sqrt{a+b x+c x^2} \left(-8 a c f+3 b^2 f-2 b c e+4 c^2 d\right)}{c^2 \left(b^2-4 a c\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (3 b f h-2 c (e h+f g))}{2 c^{5/2}}","\frac{2 (g+h x) \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{h \sqrt{a+b x+c x^2} \left(-8 a c f+3 b^2 f-2 b c e+4 c^2 d\right)}{c^2 \left(b^2-4 a c\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (3 b f h-2 c (e h+f g))}{2 c^{5/2}}",1,"(2*(c*(2*a*e - b*(d + (a*f)/c)) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x)*(g + h*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + ((4*c^2*d - 2*b*c*e + 3*b^2*f - 8*a*c*f)*h*Sqrt[a + b*x + c*x^2])/(c^2*(b^2 - 4*a*c)) - ((3*b*f*h - 2*c*(f*g + e*h))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(5/2))","A",4,4,30,0.1333,1,"{1644, 640, 621, 206}"
236,1,111,0,0.0658969,"\int \frac{d+e x+f x^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}","\frac{2 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}",1,"(2*(c*(2*a*e - b*(d + (a*f)/c)) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (f*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(3/2)","A",4,4,25,0.1600,1,"{1660, 12, 621, 206}"
237,1,225,0,0.2656582,"\int \frac{d+e x+f x^2}{(g+h x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \left(-x \left(-c (-2 a e h+2 a f g+b d h+b e g)+b f (b g-a h)+2 c^2 d g\right)-b (a e h+a f g+c d g)+2 a (a f h-c d h+c e g)+b^2 d h\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a h^2-b g h+c g^2\right)}+\frac{\left(f g^2-h (e g-d h)\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right)}{\left(a h^2-b g h+c g^2\right)^{3/2}}","\frac{2 \left(-x \left(-c (-2 a e h+2 a f g+b d h+b e g)+b f (b g-a h)+2 c^2 d g\right)-b (a e h+a f g+c d g)+2 a (a f h-c d h+c e g)+b^2 d h\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a h^2-b g h+c g^2\right)}+\frac{\left(f g^2-h (e g-d h)\right) \tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right)}{\left(a h^2-b g h+c g^2\right)^{3/2}}",1,"(2*(b^2*d*h - b*(c*d*g + a*f*g + a*e*h) + 2*a*(c*e*g - c*d*h + a*f*h) - (2*c^2*d*g + b*f*(b*g - a*h) - c*(b*e*g + 2*a*f*g + b*d*h - 2*a*e*h))*x))/((b^2 - 4*a*c)*(c*g^2 - b*g*h + a*h^2)*Sqrt[a + b*x + c*x^2]) + ((f*g^2 - h*(e*g - d*h))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(c*g^2 - b*g*h + a*h^2)^(3/2)","A",4,4,32,0.1250,1,"{1646, 12, 724, 206}"
238,1,418,0,0.796687,"\int \frac{d+e x+f x^2}{(g+h x)^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)^2*(a + b*x + c*x^2)^(3/2)),x]","-\frac{2 \left(c x \left(2 a^2 f h^2-c \left(2 a \left(d h^2-2 e g h+f g^2\right)+b g (2 d h+e g)\right)-a b h (e h+2 f g)+b^2 \left(d h^2+f g^2\right)+2 c^2 d g^2\right)+b \left(a^2 f h^2+a c \left(-3 d h^2+2 e g h+f g^2\right)+c^2 d g^2\right)-b^2 h (a e h+2 c d g)-2 a c (a h (2 f g-e h)+c g (e g-2 d h))+b^3 d h^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a h^2-b g h+c g^2\right)^2}-\frac{h \sqrt{a+b x+c x^2} \left(f g^2-h (e g-d h)\right)}{(g+h x) \left(a h^2-b g h+c g^2\right)^2}+\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(h \left(-2 a h (2 f g-e h)+b h (e g-3 d h)+b f g^2\right)+2 c \left(f g^3-g h (2 e g-3 d h)\right)\right)}{2 \left(a h^2-b g h+c g^2\right)^{5/2}}","-\frac{2 \left(c x \left(2 a^2 f h^2-c \left(2 a \left(d h^2-2 e g h+f g^2\right)+b g (2 d h+e g)\right)-a b h (e h+2 f g)+b^2 \left(d h^2+f g^2\right)+2 c^2 d g^2\right)+b \left(a^2 f h^2+a c \left(-3 d h^2+2 e g h+f g^2\right)+c^2 d g^2\right)-b^2 h (a e h+2 c d g)-2 a c (a h (2 f g-e h)+c g (e g-2 d h))+b^3 d h^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a h^2-b g h+c g^2\right)^2}-\frac{h \sqrt{a+b x+c x^2} \left(f g^2-h (e g-d h)\right)}{(g+h x) \left(a h^2-b g h+c g^2\right)^2}+\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(2 c g \left(f g^2-h (2 e g-3 d h)\right)-h \left(2 a h (2 f g-e h)-b \left(-3 d h^2+e g h+f g^2\right)\right)\right)}{2 \left(a h^2-b g h+c g^2\right)^{5/2}}",1,"(-2*(b^3*d*h^2 - b^2*h*(2*c*d*g + a*e*h) - 2*a*c*(c*g*(e*g - 2*d*h) + a*h*(2*f*g - e*h)) + b*(c^2*d*g^2 + a^2*f*h^2 + a*c*(f*g^2 + 2*e*g*h - 3*d*h^2)) + c*(2*c^2*d*g^2 + 2*a^2*f*h^2 - a*b*h*(2*f*g + e*h) + b^2*(f*g^2 + d*h^2) - c*(b*g*(e*g + 2*d*h) + 2*a*(f*g^2 - 2*e*g*h + d*h^2)))*x))/((b^2 - 4*a*c)*(c*g^2 - b*g*h + a*h^2)^2*Sqrt[a + b*x + c*x^2]) - (h*(f*g^2 - h*(e*g - d*h))*Sqrt[a + b*x + c*x^2])/((c*g^2 - b*g*h + a*h^2)^2*(g + h*x)) + ((2*c*(f*g^3 - g*h*(2*e*g - 3*d*h)) + h*(b*f*g^2 + b*h*(e*g - 3*d*h) - 2*a*h*(2*f*g - e*h)))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(2*(c*g^2 - b*g*h + a*h^2)^(5/2))","A",4,4,32,0.1250,1,"{1646, 806, 724, 206}"
239,1,707,0,2.6696093,"\int \frac{d+e x+f x^2}{(g+h x)^3 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)^3*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \left(-c x \left(c \left(2 a^2 h^2 (3 f g-e h)-3 a b h \left(h (e g-d h)+f g^2\right)+b^2 \left(3 d g h^2+f g^3\right)\right)-b h^3 \left(a^2 f-a b e+b^2 d\right)-c^2 g \left(-6 a h (e g-d h)+2 a f g^2+b g (3 d h+e g)\right)+2 c^3 d g^3\right)+b^2 h \left(a^2 f h^2+a c h (3 e g-4 d h)+3 c^2 d g^2\right)-b c \left(3 a^2 h^2 (f g-e h)+a c g \left(-9 d h^2+3 e g h+f g^2\right)+c^2 d g^3\right)-2 a c \left(a^2 f h^3-a c h \left(d h^2-3 e g h+3 f g^2\right)-c^2 g^2 (e g-3 d h)\right)-b^3 h^2 (a e h+3 c d g)+b^4 d h^3\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a h^2-b g h+c g^2\right)^3}+\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(h^2 \left(8 a^2 f h^2+4 a b h (2 f g-3 e h)+b^2 \left(-\left(3 h (e g-5 d h)+f g^2\right)\right)\right)+4 c h \left(-a h \left(3 d h^2-9 e g h+11 f g^2\right)+3 b g h (e g-4 d h)+2 b f g^3\right)+8 c^2 g^2 \left(6 d h^2-3 e g h+f g^2\right)\right)}{8 \left(a h^2-b g h+c g^2\right)^{7/2}}-\frac{h \sqrt{a+b x+c x^2} \left(f g^2-h (e g-d h)\right)}{2 (g+h x)^2 \left(a h^2-b g h+c g^2\right)^2}-\frac{h \sqrt{a+b x+c x^2} \left(-4 a h^2 (2 f g-e h)+b h \left(h (3 e g-7 d h)+f g^2\right)-2 c g h (5 e g-7 d h)+6 c f g^3\right)}{4 (g+h x) \left(a h^2-b g h+c g^2\right)^3}","\frac{2 \left(-c x \left(c \left(2 a^2 h^2 (3 f g-e h)-3 a b h \left(-d h^2+e g h+f g^2\right)+b^2 \left(3 d g h^2+f g^3\right)\right)-b h^3 \left(a^2 f-a b e+b^2 d\right)-c^2 g \left(2 a \left(3 d h^2-3 e g h+f g^2\right)+b g (3 d h+e g)\right)+2 c^3 d g^3\right)+b^2 h \left(a^2 f h^2+a c h (3 e g-4 d h)+3 c^2 d g^2\right)-b c \left(3 a^2 h^2 (f g-e h)+a c g \left(-9 d h^2+3 e g h+f g^2\right)+c^2 d g^3\right)-2 a c \left(a^2 f h^3-a c h \left(d h^2-3 e g h+3 f g^2\right)-c^2 g^2 (e g-3 d h)\right)-b^3 h^2 (a e h+3 c d g)+b^4 d h^3\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a h^2-b g h+c g^2\right)^3}+\frac{\tanh ^{-1}\left(\frac{-2 a h+x (2 c g-b h)+b g}{2 \sqrt{a+b x+c x^2} \sqrt{a h^2-b g h+c g^2}}\right) \left(h^2 \left(8 a^2 f h^2+4 a b h (2 f g-3 e h)+b^2 \left(-\left(3 h (e g-5 d h)+f g^2\right)\right)\right)-4 c h \left(a h \left(3 d h^2-9 e g h+11 f g^2\right)-b g \left(3 h (e g-4 d h)+2 f g^2\right)\right)+8 c^2 g^2 \left(6 d h^2-3 e g h+f g^2\right)\right)}{8 \left(a h^2-b g h+c g^2\right)^{7/2}}-\frac{h \sqrt{a+b x+c x^2} \left(f g^2-h (e g-d h)\right)}{2 (g+h x)^2 \left(a h^2-b g h+c g^2\right)^2}-\frac{h \sqrt{a+b x+c x^2} \left(2 c g \left(3 f g^2-h (5 e g-7 d h)\right)-h \left(4 a h (2 f g-e h)-b \left(-7 d h^2+3 e g h+f g^2\right)\right)\right)}{4 (g+h x) \left(a h^2-b g h+c g^2\right)^3}",1,"(2*(b^4*d*h^3 - b^3*h^2*(3*c*d*g + a*e*h) + b^2*h*(3*c^2*d*g^2 + a^2*f*h^2 + a*c*h*(3*e*g - 4*d*h)) - b*c*(c^2*d*g^3 + 3*a^2*h^2*(f*g - e*h) + a*c*g*(f*g^2 + 3*e*g*h - 9*d*h^2)) - 2*a*c*(a^2*f*h^3 - c^2*g^2*(e*g - 3*d*h) - a*c*h*(3*f*g^2 - 3*e*g*h + d*h^2)) - c*(2*c^3*d*g^3 - b*(b^2*d - a*b*e + a^2*f)*h^3 - c^2*g*(2*a*f*g^2 - 6*a*h*(e*g - d*h) + b*g*(e*g + 3*d*h)) + c*(2*a^2*h^2*(3*f*g - e*h) + b^2*(f*g^3 + 3*d*g*h^2) - 3*a*b*h*(f*g^2 + h*(e*g - d*h))))*x))/((b^2 - 4*a*c)*(c*g^2 - b*g*h + a*h^2)^3*Sqrt[a + b*x + c*x^2]) - (h*(f*g^2 - h*(e*g - d*h))*Sqrt[a + b*x + c*x^2])/(2*(c*g^2 - b*g*h + a*h^2)^2*(g + h*x)^2) - (h*(6*c*f*g^3 - 2*c*g*h*(5*e*g - 7*d*h) - 4*a*h^2*(2*f*g - e*h) + b*h*(f*g^2 + h*(3*e*g - 7*d*h)))*Sqrt[a + b*x + c*x^2])/(4*(c*g^2 - b*g*h + a*h^2)^3*(g + h*x)) + ((8*c^2*g^2*(f*g^2 - 3*e*g*h + 6*d*h^2) + 4*c*h*(2*b*f*g^3 + 3*b*g*h*(e*g - 4*d*h) - a*h*(11*f*g^2 - 9*e*g*h + 3*d*h^2)) + h^2*(8*a^2*f*h^2 + 4*a*b*h*(2*f*g - 3*e*h) - b^2*(f*g^2 + 3*h*(e*g - 5*d*h))))*ArcTanh[(b*g - 2*a*h + (2*c*g - b*h)*x)/(2*Sqrt[c*g^2 - b*g*h + a*h^2]*Sqrt[a + b*x + c*x^2])])/(8*(c*g^2 - b*g*h + a*h^2)^(7/2))","A",5,5,32,0.1562,1,"{1646, 1650, 806, 724, 206}"
240,1,120,0,0.1348771,"\int \frac{(1+2 x)^3 \left(1+3 x+4 x^2\right)}{\sqrt{2-x+3 x^2}} \, dx","Int[((1 + 2*x)^3*(1 + 3*x + 4*x^2))/Sqrt[2 - x + 3*x^2],x]","\frac{2}{15} \sqrt{3 x^2-x+2} (2 x+1)^4+\frac{19}{60} \sqrt{3 x^2-x+2} (2 x+1)^3+\frac{44}{135} \sqrt{3 x^2-x+2} (2 x+1)^2-\frac{(6298 x+24897) \sqrt{3 x^2-x+2}}{3240}+\frac{9211 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{1296 \sqrt{3}}","\frac{2}{15} \sqrt{3 x^2-x+2} (2 x+1)^4+\frac{19}{60} \sqrt{3 x^2-x+2} (2 x+1)^3+\frac{44}{135} \sqrt{3 x^2-x+2} (2 x+1)^2-\frac{(6298 x+24897) \sqrt{3 x^2-x+2}}{3240}+\frac{9211 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{1296 \sqrt{3}}",1,"(44*(1 + 2*x)^2*Sqrt[2 - x + 3*x^2])/135 + (19*(1 + 2*x)^3*Sqrt[2 - x + 3*x^2])/60 + (2*(1 + 2*x)^4*Sqrt[2 - x + 3*x^2])/15 - ((24897 + 6298*x)*Sqrt[2 - x + 3*x^2])/3240 + (9211*ArcSinh[(1 - 6*x)/Sqrt[23]])/(1296*Sqrt[3])","A",6,5,32,0.1562,1,"{1653, 832, 779, 619, 215}"
241,1,95,0,0.0989095,"\int \frac{(1+2 x)^2 \left(1+3 x+4 x^2\right)}{\sqrt{2-x+3 x^2}} \, dx","Int[((1 + 2*x)^2*(1 + 3*x + 4*x^2))/Sqrt[2 - x + 3*x^2],x]","\frac{1}{6} \sqrt{3 x^2-x+2} (2 x+1)^3+\frac{11}{27} \sqrt{3 x^2-x+2} (2 x+1)^2-\frac{143}{324} (3-2 x) \sqrt{3 x^2-x+2}+\frac{4147 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{648 \sqrt{3}}","\frac{1}{6} \sqrt{3 x^2-x+2} (2 x+1)^3+\frac{11}{27} \sqrt{3 x^2-x+2} (2 x+1)^2-\frac{143}{324} (3-2 x) \sqrt{3 x^2-x+2}+\frac{4147 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{648 \sqrt{3}}",1,"(-143*(3 - 2*x)*Sqrt[2 - x + 3*x^2])/324 + (11*(1 + 2*x)^2*Sqrt[2 - x + 3*x^2])/27 + ((1 + 2*x)^3*Sqrt[2 - x + 3*x^2])/6 + (4147*ArcSinh[(1 - 6*x)/Sqrt[23]])/(648*Sqrt[3])","A",5,5,32,0.1562,1,"{1653, 832, 779, 619, 215}"
242,1,70,0,0.0580893,"\int \frac{(1+2 x) \left(1+3 x+4 x^2\right)}{\sqrt{2-x+3 x^2}} \, dx","Int[((1 + 2*x)*(1 + 3*x + 4*x^2))/Sqrt[2 - x + 3*x^2],x]","\frac{2}{9} \sqrt{3 x^2-x+2} (2 x+1)^2+\frac{1}{54} (62 x+69) \sqrt{3 x^2-x+2}+\frac{251 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{108 \sqrt{3}}","\frac{2}{9} \sqrt{3 x^2-x+2} (2 x+1)^2+\frac{1}{54} (62 x+69) \sqrt{3 x^2-x+2}+\frac{251 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{108 \sqrt{3}}",1,"(2*(1 + 2*x)^2*Sqrt[2 - x + 3*x^2])/9 + ((69 + 62*x)*Sqrt[2 - x + 3*x^2])/54 + (251*ArcSinh[(1 - 6*x)/Sqrt[23]])/(108*Sqrt[3])","A",4,4,30,0.1333,1,"{1653, 779, 619, 215}"
243,1,78,0,0.0969312,"\int \frac{1+3 x+4 x^2}{(1+2 x) \sqrt{2-x+3 x^2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)*Sqrt[2 - x + 3*x^2]),x]","\frac{2}{3} \sqrt{3 x^2-x+2}-\frac{\tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{2 \sqrt{13}}-\frac{5 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{6 \sqrt{3}}","\frac{2}{3} \sqrt{3 x^2-x+2}-\frac{\tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{2 \sqrt{13}}-\frac{5 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{6 \sqrt{3}}",1,"(2*Sqrt[2 - x + 3*x^2])/3 - (5*ArcSinh[(1 - 6*x)/Sqrt[23]])/(6*Sqrt[3]) - ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])]/(2*Sqrt[13])","A",6,6,32,0.1875,1,"{1653, 843, 619, 215, 724, 206}"
244,1,83,0,0.0950249,"\int \frac{1+3 x+4 x^2}{(1+2 x)^2 \sqrt{2-x+3 x^2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^2*Sqrt[2 - x + 3*x^2]),x]","-\frac{\sqrt{3 x^2-x+2}}{13 (2 x+1)}+\frac{9 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{26 \sqrt{13}}-\frac{\sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{\sqrt{3}}","-\frac{\sqrt{3 x^2-x+2}}{13 (2 x+1)}+\frac{9 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{26 \sqrt{13}}-\frac{\sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{\sqrt{3}}",1,"-Sqrt[2 - x + 3*x^2]/(13*(1 + 2*x)) - ArcSinh[(1 - 6*x)/Sqrt[23]]/Sqrt[3] + (9*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(26*Sqrt[13])","A",6,6,32,0.1875,1,"{1650, 843, 619, 215, 724, 206}"
245,1,89,0,0.0882716,"\int \frac{1+3 x+4 x^2}{(1+2 x)^3 \sqrt{2-x+3 x^2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^3*Sqrt[2 - x + 3*x^2]),x]","\frac{7 \sqrt{3 x^2-x+2}}{169 (2 x+1)}-\frac{\sqrt{3 x^2-x+2}}{26 (2 x+1)^2}-\frac{581 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{676 \sqrt{13}}","\frac{7 \sqrt{3 x^2-x+2}}{169 (2 x+1)}-\frac{\sqrt{3 x^2-x+2}}{26 (2 x+1)^2}-\frac{581 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{676 \sqrt{13}}",1,"-Sqrt[2 - x + 3*x^2]/(26*(1 + 2*x)^2) + (7*Sqrt[2 - x + 3*x^2])/(169*(1 + 2*x)) - (581*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(676*Sqrt[13])","A",4,4,32,0.1250,1,"{1650, 806, 724, 206}"
246,1,103,0,0.1242102,"\int \frac{(1+2 x)^3 \left(1+3 x+4 x^2\right)}{\left(2-x+3 x^2\right)^{3/2}} \, dx","Int[((1 + 2*x)^3*(1 + 3*x + 4*x^2))/(2 - x + 3*x^2)^(3/2),x]","\frac{32}{27} \sqrt{3 x^2-x+2} x^2+\frac{412}{81} \sqrt{3 x^2-x+2} x+\frac{746}{81} \sqrt{3 x^2-x+2}+\frac{2 (12839-3871 x)}{1863 \sqrt{3 x^2-x+2}}+\frac{353 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{81 \sqrt{3}}","\frac{32}{27} \sqrt{3 x^2-x+2} x^2+\frac{412}{81} \sqrt{3 x^2-x+2} x+\frac{746}{81} \sqrt{3 x^2-x+2}+\frac{2 (12839-3871 x)}{1863 \sqrt{3 x^2-x+2}}+\frac{353 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{81 \sqrt{3}}",1,"(2*(12839 - 3871*x))/(1863*Sqrt[2 - x + 3*x^2]) + (746*Sqrt[2 - x + 3*x^2])/81 + (412*x*Sqrt[2 - x + 3*x^2])/81 + (32*x^2*Sqrt[2 - x + 3*x^2])/27 + (353*ArcSinh[(1 - 6*x)/Sqrt[23]])/(81*Sqrt[3])","A",6,5,32,0.1562,1,"{1660, 1661, 640, 619, 215}"
247,1,82,0,0.1081177,"\int \frac{(1+2 x)^2 \left(1+3 x+4 x^2\right)}{\left(2-x+3 x^2\right)^{3/2}} \, dx","Int[((1 + 2*x)^2*(1 + 3*x + 4*x^2))/(2 - x + 3*x^2)^(3/2),x]","\frac{2 (1249-2273 x)}{621 \sqrt{3 x^2-x+2}}+\frac{8}{9} x \sqrt{3 x^2-x+2}+\frac{112}{27} \sqrt{3 x^2-x+2}-\frac{64 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{9 \sqrt{3}}","\frac{2 (1249-2273 x)}{621 \sqrt{3 x^2-x+2}}+\frac{8}{9} x \sqrt{3 x^2-x+2}+\frac{112}{27} \sqrt{3 x^2-x+2}-\frac{64 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{9 \sqrt{3}}",1,"(2*(1249 - 2273*x))/(621*Sqrt[2 - x + 3*x^2]) + (112*Sqrt[2 - x + 3*x^2])/27 + (8*x*Sqrt[2 - x + 3*x^2])/9 - (64*ArcSinh[(1 - 6*x)/Sqrt[23]])/(9*Sqrt[3])","A",5,5,32,0.1562,1,"{1660, 1661, 640, 619, 215}"
248,1,63,0,0.0596095,"\int \frac{(1+2 x) \left(1+3 x+4 x^2\right)}{\left(2-x+3 x^2\right)^{3/2}} \, dx","Int[((1 + 2*x)*(1 + 3*x + 4*x^2))/(2 - x + 3*x^2)^(3/2),x]","-\frac{2 (367 x+73)}{207 \sqrt{3 x^2-x+2}}+\frac{8}{9} \sqrt{3 x^2-x+2}-\frac{14 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{3 \sqrt{3}}","-\frac{2 (367 x+73)}{207 \sqrt{3 x^2-x+2}}+\frac{8}{9} \sqrt{3 x^2-x+2}-\frac{14 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{3 \sqrt{3}}",1,"(-2*(73 + 367*x))/(207*Sqrt[2 - x + 3*x^2]) + (8*Sqrt[2 - x + 3*x^2])/9 - (14*ArcSinh[(1 - 6*x)/Sqrt[23]])/(3*Sqrt[3])","A",4,4,30,0.1333,1,"{1660, 640, 619, 215}"
249,1,62,0,0.0736133,"\int \frac{1+3 x+4 x^2}{(1+2 x) \left(2-x+3 x^2\right)^{3/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)*(2 - x + 3*x^2)^(3/2)),x]","-\frac{2 (101-77 x)}{299 \sqrt{3 x^2-x+2}}-\frac{2 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{13 \sqrt{13}}","-\frac{2 (101-77 x)}{299 \sqrt{3 x^2-x+2}}-\frac{2 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{13 \sqrt{13}}",1,"(-2*(101 - 77*x))/(299*Sqrt[2 - x + 3*x^2]) - (2*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(13*Sqrt[13])","A",4,4,32,0.1250,1,"{1646, 12, 724, 206}"
250,1,87,0,0.092342,"\int \frac{1+3 x+4 x^2}{(1+2 x)^2 \left(2-x+3 x^2\right)^{3/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^2*(2 - x + 3*x^2)^(3/2)),x]","-\frac{2 (197-837 x)}{3887 \sqrt{3 x^2-x+2}}-\frac{4 \sqrt{3 x^2-x+2}}{169 (2 x+1)}+\frac{2 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{169 \sqrt{13}}","-\frac{2 (197-837 x)}{3887 \sqrt{3 x^2-x+2}}-\frac{4 \sqrt{3 x^2-x+2}}{169 (2 x+1)}+\frac{2 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{169 \sqrt{13}}",1,"(-2*(197 - 837*x))/(3887*Sqrt[2 - x + 3*x^2]) - (4*Sqrt[2 - x + 3*x^2])/(169*(1 + 2*x)) + (2*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(169*Sqrt[13])","A",4,4,32,0.1250,1,"{1646, 806, 724, 206}"
251,1,112,0,0.1547977,"\int \frac{1+3 x+4 x^2}{(1+2 x)^3 \left(2-x+3 x^2\right)^{3/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^3*(2 - x + 3*x^2)^(3/2)),x]","\frac{2 (3693 x+2363)}{50531 \sqrt{3 x^2-x+2}}-\frac{4 \sqrt{3 x^2-x+2}}{2197 (2 x+1)}-\frac{2 \sqrt{3 x^2-x+2}}{169 (2 x+1)^2}-\frac{487 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{2197 \sqrt{13}}","\frac{2 (3693 x+2363)}{50531 \sqrt{3 x^2-x+2}}-\frac{4 \sqrt{3 x^2-x+2}}{2197 (2 x+1)}-\frac{2 \sqrt{3 x^2-x+2}}{169 (2 x+1)^2}-\frac{487 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{2197 \sqrt{13}}",1,"(2*(2363 + 3693*x))/(50531*Sqrt[2 - x + 3*x^2]) - (2*Sqrt[2 - x + 3*x^2])/(169*(1 + 2*x)^2) - (4*Sqrt[2 - x + 3*x^2])/(2197*(1 + 2*x)) - (487*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(2197*Sqrt[13])","A",5,5,32,0.1562,1,"{1646, 1650, 806, 724, 206}"
252,1,86,0,0.1125693,"\int \frac{(1+2 x)^3 \left(1+3 x+4 x^2\right)}{\left(2-x+3 x^2\right)^{5/2}} \, dx","Int[((1 + 2*x)^3*(1 + 3*x + 4*x^2))/(2 - x + 3*x^2)^(5/2),x]","\frac{2 (12839-3871 x)}{5589 \left(3 x^2-x+2\right)^{3/2}}+\frac{32}{27} \sqrt{3 x^2-x+2}-\frac{28 (42240 x+35809)}{128547 \sqrt{3 x^2-x+2}}-\frac{296 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{27 \sqrt{3}}","\frac{2 (12839-3871 x)}{5589 \left(3 x^2-x+2\right)^{3/2}}+\frac{32}{27} \sqrt{3 x^2-x+2}-\frac{28 (42240 x+35809)}{128547 \sqrt{3 x^2-x+2}}-\frac{296 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{27 \sqrt{3}}",1,"(2*(12839 - 3871*x))/(5589*(2 - x + 3*x^2)^(3/2)) - (28*(35809 + 42240*x))/(128547*Sqrt[2 - x + 3*x^2]) + (32*Sqrt[2 - x + 3*x^2])/27 - (296*ArcSinh[(1 - 6*x)/Sqrt[23]])/(27*Sqrt[3])","A",5,4,32,0.1250,1,"{1660, 640, 619, 215}"
253,1,68,0,0.0946948,"\int \frac{(1+2 x)^2 \left(1+3 x+4 x^2\right)}{\left(2-x+3 x^2\right)^{5/2}} \, dx","Int[((1 + 2*x)^2*(1 + 3*x + 4*x^2))/(2 - x + 3*x^2)^(5/2),x]","\frac{2 (1249-2273 x)}{1863 \left(3 x^2-x+2\right)^{3/2}}-\frac{8 (23257-1473 x)}{42849 \sqrt{3 x^2-x+2}}-\frac{16 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{9 \sqrt{3}}","\frac{2 (1249-2273 x)}{1863 \left(3 x^2-x+2\right)^{3/2}}-\frac{8 (23257-1473 x)}{42849 \sqrt{3 x^2-x+2}}-\frac{16 \sinh ^{-1}\left(\frac{1-6 x}{\sqrt{23}}\right)}{9 \sqrt{3}}",1,"(2*(1249 - 2273*x))/(1863*(2 - x + 3*x^2)^(3/2)) - (8*(23257 - 1473*x))/(42849*Sqrt[2 - x + 3*x^2]) - (16*ArcSinh[(1 - 6*x)/Sqrt[23]])/(9*Sqrt[3])","A",5,4,32,0.1250,1,"{1660, 12, 619, 215}"
254,1,47,0,0.0476253,"\int \frac{(1+2 x) \left(1+3 x+4 x^2\right)}{\left(2-x+3 x^2\right)^{5/2}} \, dx","Int[((1 + 2*x)*(1 + 3*x + 4*x^2))/(2 - x + 3*x^2)^(5/2),x]","-\frac{4 (3889-4290 x)}{14283 \sqrt{3 x^2-x+2}}-\frac{2 (367 x+73)}{621 \left(3 x^2-x+2\right)^{3/2}}","-\frac{4 (3889-4290 x)}{14283 \sqrt{3 x^2-x+2}}-\frac{2 (367 x+73)}{621 \left(3 x^2-x+2\right)^{3/2}}",1,"(-2*(73 + 367*x))/(621*(2 - x + 3*x^2)^(3/2)) - (4*(3889 - 4290*x))/(14283*Sqrt[2 - x + 3*x^2])","A",2,2,30,0.06667,1,"{1660, 636}"
255,1,85,0,0.0944011,"\int \frac{1+3 x+4 x^2}{(1+2 x) \left(2-x+3 x^2\right)^{5/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)*(2 - x + 3*x^2)^(5/2)),x]","-\frac{4 (691-13668 x)}{268203 \sqrt{3 x^2-x+2}}-\frac{2 (101-77 x)}{897 \left(3 x^2-x+2\right)^{3/2}}-\frac{8 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{169 \sqrt{13}}","-\frac{4 (691-13668 x)}{268203 \sqrt{3 x^2-x+2}}-\frac{2 (101-77 x)}{897 \left(3 x^2-x+2\right)^{3/2}}-\frac{8 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{169 \sqrt{13}}",1,"(-2*(101 - 77*x))/(897*(2 - x + 3*x^2)^(3/2)) - (4*(691 - 13668*x))/(268203*Sqrt[2 - x + 3*x^2]) - (8*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(169*Sqrt[13])","A",5,5,32,0.1562,1,"{1646, 822, 12, 724, 206}"
256,1,110,0,0.1505618,"\int \frac{1+3 x+4 x^2}{(1+2 x)^2 \left(2-x+3 x^2\right)^{5/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^2*(2 - x + 3*x^2)^(5/2)),x]","-\frac{24 (841-6633 x)}{1162213 \sqrt{3 x^2-x+2}}-\frac{16 \sqrt{3 x^2-x+2}}{2197 (2 x+1)}-\frac{2 (197-837 x)}{11661 \left(3 x^2-x+2\right)^{3/2}}-\frac{56 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{2197 \sqrt{13}}","-\frac{24 (841-6633 x)}{1162213 \sqrt{3 x^2-x+2}}-\frac{16 \sqrt{3 x^2-x+2}}{2197 (2 x+1)}-\frac{2 (197-837 x)}{11661 \left(3 x^2-x+2\right)^{3/2}}-\frac{56 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{2197 \sqrt{13}}",1,"(-2*(197 - 837*x))/(11661*(2 - x + 3*x^2)^(3/2)) - (24*(841 - 6633*x))/(1162213*Sqrt[2 - x + 3*x^2]) - (16*Sqrt[2 - x + 3*x^2])/(2197*(1 + 2*x)) - (56*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(2197*Sqrt[13])","A",5,4,32,0.1250,1,"{1646, 806, 724, 206}"
257,1,135,0,0.2125562,"\int \frac{1+3 x+4 x^2}{(1+2 x)^3 \left(2-x+3 x^2\right)^{5/2}} \, dx","Int[(1 + 3*x + 4*x^2)/((1 + 2*x)^3*(2 - x + 3*x^2)^(5/2)),x]","\frac{2 (3693 x+2363)}{151593 \left(3 x^2-x+2\right)^{3/2}}-\frac{144 \sqrt{3 x^2-x+2}}{28561 (2 x+1)}-\frac{8 \sqrt{3 x^2-x+2}}{2197 (2 x+1)^2}+\frac{12 (103526 x+25771)}{15108769 \sqrt{3 x^2-x+2}}-\frac{2084 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{28561 \sqrt{13}}","\frac{2 (3693 x+2363)}{151593 \left(3 x^2-x+2\right)^{3/2}}-\frac{144 \sqrt{3 x^2-x+2}}{28561 (2 x+1)}-\frac{8 \sqrt{3 x^2-x+2}}{2197 (2 x+1)^2}+\frac{12 (103526 x+25771)}{15108769 \sqrt{3 x^2-x+2}}-\frac{2084 \tanh ^{-1}\left(\frac{9-8 x}{2 \sqrt{13} \sqrt{3 x^2-x+2}}\right)}{28561 \sqrt{13}}",1,"(2*(2363 + 3693*x))/(151593*(2 - x + 3*x^2)^(3/2)) + (12*(25771 + 103526*x))/(15108769*Sqrt[2 - x + 3*x^2]) - (8*Sqrt[2 - x + 3*x^2])/(2197*(1 + 2*x)^2) - (144*Sqrt[2 - x + 3*x^2])/(28561*(1 + 2*x)) - (2084*ArcTanh[(9 - 8*x)/(2*Sqrt[13]*Sqrt[2 - x + 3*x^2])])/(28561*Sqrt[13])","A",6,5,32,0.1562,1,"{1646, 1650, 806, 724, 206}"
258,1,208,0,0.4242054,"\int \frac{d+e x+f x^2}{(g+h x) \left(-c g^2+b g h+b h^2 x+c h^2 x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/((g + h*x)*(-(c*g^2) + b*g*h + b*h^2*x + c*h^2*x^2)^(3/2)),x]","\frac{(b+2 c x) \left(-3 b^2 f h^2+6 b c e h^2+4 c^2 \left(f g^2-h (2 d h+e g)\right)\right)}{3 c h^2 (2 c g-b h)^3 \sqrt{-g (c g-b h)+b h^2 x+c h^2 x^2}}+\frac{2 \left(d h^2-e g h+f g^2\right)}{3 h^3 (g+h x) (2 c g-b h) \sqrt{-g (c g-b h)+b h^2 x+c h^2 x^2}}-\frac{f}{c h^3 \sqrt{-g (c g-b h)+b h^2 x+c h^2 x^2}}","\frac{(b+2 c x) \left(-3 b^2 f h^2+6 b c e h^2+4 c^2 \left(f g^2-h (2 d h+e g)\right)\right)}{3 c h^2 (2 c g-b h)^3 \sqrt{-g (c g-b h)+b h^2 x+c h^2 x^2}}+\frac{2 \left(d h^2-e g h+f g^2\right)}{3 h^3 (g+h x) (2 c g-b h) \sqrt{-g (c g-b h)+b h^2 x+c h^2 x^2}}-\frac{f}{c h^3 \sqrt{-g (c g-b h)+b h^2 x+c h^2 x^2}}",1,"-(f/(c*h^3*Sqrt[-(g*(c*g - b*h)) + b*h^2*x + c*h^2*x^2])) + ((6*b*c*e*h^2 - 3*b^2*f*h^2 + 4*c^2*(f*g^2 - h*(e*g + 2*d*h)))*(b + 2*c*x))/(3*c*h^2*(2*c*g - b*h)^3*Sqrt[-(g*(c*g - b*h)) + b*h^2*x + c*h^2*x^2]) + (2*(f*g^2 - e*g*h + d*h^2))/(3*h^3*(2*c*g - b*h)*(g + h*x)*Sqrt[-(g*(c*g - b*h)) + b*h^2*x + c*h^2*x^2])","A",3,3,47,0.06383,1,"{1638, 792, 613}"
259,1,905,0,2.7003836,"\int \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(A+B x+C x^2\right) \, dx","Int[Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2]*(A + B*x + C*x^2),x]","\frac{2 C (d+e x)^{3/2} \left(c x^2+b x+a\right)^{3/2}}{9 c e}-\frac{2 (2 c C d-3 B c e+2 b C e) \sqrt{d+e x} \left(c x^2+b x+a\right)^{3/2}}{21 c^2 e}+\frac{2 \sqrt{d+e x} \left(\left(8 C d^3-3 d e (4 B d-7 A e)\right) c^3-3 e \left(b C d^2-b e (2 B d+7 A e)-a e (C d-5 B e)\right) c^2-3 b e^2 (b C d+4 b B e-a C e) c+3 e \left(-\left(2 C d^2-3 e (B d+7 A e)\right) c^2-e (b C d+12 b B e+7 a C e) c+8 b^2 C e^2\right) x c+8 b^3 C e^3\right) \sqrt{c x^2+b x+a}}{315 c^3 e^3}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(5 c e (2 c d-b e) \left(6 C d e b^2+2 a C e^2 b-c d (C d+9 B e) b+c e (21 A c d-5 a C d-3 a B e)\right)-2 \left(4 c^2 d^2-b^2 e^2-\frac{3}{2} c e (b d-2 a e)\right) \left(-\left(2 C d^2-3 e (B d+7 A e)\right) c^2-e (b C d+12 b B e+7 a C e) c+8 b^2 C e^2\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^4 e^4 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right) \left(-2 \left(8 C d^3-3 d e (4 B d-7 A e)\right) c^3-3 e^2 (b B d+2 a C d-7 A b e-10 a B e) c^2+3 b e^2 (b C d-4 b B e-9 a C e) c+8 b^3 C e^3\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^4 e^4 \sqrt{d+e x} \sqrt{c x^2+b x+a}}","\frac{2 C (d+e x)^{3/2} \left(c x^2+b x+a\right)^{3/2}}{9 c e}-\frac{2 (2 c C d-3 B c e+2 b C e) \sqrt{d+e x} \left(c x^2+b x+a\right)^{3/2}}{21 c^2 e}+\frac{2 \sqrt{d+e x} \left(d \left(8 C d^2-3 e (4 B d-7 A e)\right) c^3+3 e \left(a e (C d-5 B e)-b \left(C d^2-2 B e d-7 A e^2\right)\right) c^2-3 b e^2 (b C d+4 b B e-a C e) c+3 e \left(-\left(2 C d^2-3 e (B d+7 A e)\right) c^2-e (b C d+12 b B e+7 a C e) c+8 b^2 C e^2\right) x c+8 b^3 C e^3\right) \sqrt{c x^2+b x+a}}{315 c^3 e^3}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(2 \left(4 c^2 d^2-b^2 e^2-\frac{3}{2} c e (b d-2 a e)\right) \left(-\left(2 C d^2-3 e (B d+7 A e)\right) c^2-e (b C d+12 b B e+7 a C e) c+8 b^2 C e^2\right)-5 c e (2 c d-b e) \left(6 C d e b^2+\left(2 a C e^2-c d (C d+9 B e)\right) b+c e (21 A c d-5 a C d-3 a B e)\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^4 e^4 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c d^2-b e d+a e^2\right) \left(-2 d \left(8 C d^2-3 e (4 B d-7 A e)\right) c^3-3 e^2 (b B d+2 a C d-7 A b e-10 a B e) c^2+3 b e^2 (b C d-4 b B e-9 a C e) c+8 b^3 C e^3\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^4 e^4 \sqrt{d+e x} \sqrt{c x^2+b x+a}}",1,"(2*Sqrt[d + e*x]*(8*b^3*C*e^3 - 3*b*c*e^2*(b*C*d + 4*b*B*e - a*C*e) + c^3*(8*C*d^3 - 3*d*e*(4*B*d - 7*A*e)) - 3*c^2*e*(b*C*d^2 - b*e*(2*B*d + 7*A*e) - a*e*(C*d - 5*B*e)) + 3*c*e*(8*b^2*C*e^2 - c*e*(b*C*d + 12*b*B*e + 7*a*C*e) - c^2*(2*C*d^2 - 3*e*(B*d + 7*A*e)))*x)*Sqrt[a + b*x + c*x^2])/(315*c^3*e^3) - (2*(2*c*C*d - 3*B*c*e + 2*b*C*e)*Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2))/(21*c^2*e) + (2*C*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(9*c*e) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(5*c*e*(2*c*d - b*e)*(6*b^2*C*d*e + 2*a*b*C*e^2 - b*c*d*(C*d + 9*B*e) + c*e*(21*A*c*d - 5*a*C*d - 3*a*B*e)) - 2*(4*c^2*d^2 - b^2*e^2 - (3*c*e*(b*d - 2*a*e))/2)*(8*b^2*C*e^2 - c*e*(b*C*d + 12*b*B*e + 7*a*C*e) - c^2*(2*C*d^2 - 3*e*(B*d + 7*A*e))))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*c^4*e^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(8*b^3*C*e^3 - 3*c^2*e^2*(b*B*d + 2*a*C*d - 7*A*b*e - 10*a*B*e) + 3*b*c*e^2*(b*C*d - 4*b*B*e - 9*a*C*e) - 2*c^3*(8*C*d^3 - 3*d*e*(4*B*d - 7*A*e)))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*c^4*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,7,34,0.2059,1,"{1653, 832, 814, 843, 718, 424, 419}"
260,1,668,0,1.1884649,"\int \frac{\sqrt{a+b x+c x^2} \left(A+B x+C x^2\right)}{\sqrt{d+e x}} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(A + B*x + C*x^2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(c e (-10 a C e-7 b B e+8 b C d)+c^2 \left(48 C d^2-14 e (4 B d-5 A e)\right)+4 b^2 C e^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^3 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(5 c e (2 c d-b e) (a C e-7 A c e+3 b C d)-\left(-3 c e (b d-2 a e)-2 b^2 e^2+8 c^2 d^2\right) (4 b C e-7 B c e+6 c C d)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^3 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (5 c e (a C e-7 A c e+3 b C d)+3 c e x (4 b C e-7 B c e+6 c C d)-(4 c d-b e) (4 b C e-7 B c e+6 c C d))}{105 c^2 e^3}+\frac{2 C \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}}{7 c e}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(c e (-10 a C e-7 b B e+8 b C d)+c^2 \left(48 C d^2-14 e (4 B d-5 A e)\right)+4 b^2 C e^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^3 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(5 c e (2 c d-b e) (a C e-7 A c e+3 b C d)-\left(-3 c e (b d-2 a e)-2 b^2 e^2+8 c^2 d^2\right) (4 b C e-7 B c e+6 c C d)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^3 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (5 c e (a C e-7 A c e+3 b C d)+3 c e x (4 b C e-7 B c e+6 c C d)-(4 c d-b e) (4 b C e-7 B c e+6 c C d))}{105 c^2 e^3}+\frac{2 C \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}}{7 c e}",1,"(-2*Sqrt[d + e*x]*(5*c*e*(3*b*C*d - 7*A*c*e + a*C*e) - (4*c*d - b*e)*(6*c*C*d - 7*B*c*e + 4*b*C*e) + 3*c*e*(6*c*C*d - 7*B*c*e + 4*b*C*e)*x)*Sqrt[a + b*x + c*x^2])/(105*c^2*e^3) + (2*C*Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2))/(7*c*e) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(5*c*e*(2*c*d - b*e)*(3*b*C*d - 7*A*c*e + a*C*e) - (6*c*C*d - 7*B*c*e + 4*b*C*e)*(8*c^2*d^2 - 2*b^2*e^2 - 3*c*e*(b*d - 2*a*e)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^3*e^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(4*b^2*C*e^2 + c*e*(8*b*C*d - 7*b*B*e - 10*a*C*e) + c^2*(48*C*d^2 - 14*e*(4*B*d - 5*A*e)))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^3*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,34,0.1765,1,"{1653, 814, 843, 718, 424, 419}"
261,1,746,0,1.5184546,"\int \frac{\sqrt{a+b x+c x^2} \left(A+B x+C x^2\right)}{(d+e x)^{3/2}} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(A + B*x + C*x^2))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(c e \left(-2 a e (9 C d-5 B e)-5 b e (5 B d-3 A e)+32 b C d^2\right)+b C e^2 (b d-a e)-2 c^2 d \left(24 C d^2-5 e (4 B d-3 A e)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^2 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c e (-6 a C e-5 b B e+8 b C d)+c^2 \left(-\left(48 C d^2-10 e (4 B d-3 A e)\right)\right)+2 b^2 C e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^2 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(3 c e^2 x \left(-a C e-5 A c e+b C d+5 B c d-\frac{6 c C d^2}{e}\right)+c e \left(a e (9 C d-5 B e)-5 b \left(3 A e^2-4 B d e+5 C d^2\right)\right)+b C e^2 (b d-a e)+c^2 \left(24 C d^3-5 d e (4 B d-3 A e)\right)\right)}{15 c e^3 \left(a e^2-b d e+c d^2\right)}-\frac{2 \left(a+b x+c x^2\right)^{3/2} \left(C d^2-e (B d-A e)\right)}{e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(-c e \left(2 a e (9 C d-5 B e)-b \left(32 C d^2-5 e (5 B d-3 A e)\right)\right)+b C e^2 (b d-a e)-2 c^2 d \left(24 C d^2-5 e (4 B d-3 A e)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^2 e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c e (-6 a C e-5 b B e+8 b C d)+c^2 \left(-\left(48 C d^2-10 e (4 B d-3 A e)\right)\right)+2 b^2 C e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^2 e^4 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(3 c e^2 x \left(-a C e-5 A c e+b C d+5 B c d-\frac{6 c C d^2}{e}\right)+c e \left(a e (9 C d-5 B e)-5 b \left(3 A e^2-4 B d e+5 C d^2\right)\right)+b C e^2 (b d-a e)+c^2 d \left(24 C d^2-5 e (4 B d-3 A e)\right)\right)}{15 c e^3 \left(a e^2-b d e+c d^2\right)}-\frac{2 \left(a+b x+c x^2\right)^{3/2} \left(C d^2-e (B d-A e)\right)}{e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}",1,"(-2*Sqrt[d + e*x]*(b*C*e^2*(b*d - a*e) + c^2*(24*C*d^3 - 5*d*e*(4*B*d - 3*A*e)) + c*e*(a*e*(9*C*d - 5*B*e) - 5*b*(5*C*d^2 - 4*B*d*e + 3*A*e^2)) + 3*c*e^2*(5*B*c*d + b*C*d - (6*c*C*d^2)/e - 5*A*c*e - a*C*e)*x)*Sqrt[a + b*x + c*x^2])/(15*c*e^3*(c*d^2 - b*d*e + a*e^2)) - (2*(C*d^2 - e*(B*d - A*e))*(a + b*x + c*x^2)^(3/2))/(e*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*b^2*C*e^2 + c*e*(8*b*C*d - 5*b*B*e - 6*a*C*e) - c^2*(48*C*d^2 - 10*e*(4*B*d - 3*A*e)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^2*e^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(b*C*e^2*(b*d - a*e) - 2*c^2*d*(24*C*d^2 - 5*e*(4*B*d - 3*A*e)) + c*e*(32*b*C*d^2 - 5*b*e*(5*B*d - 3*A*e) - 2*a*e*(9*C*d - 5*B*e)))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^2*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,34,0.1765,1,"{1650, 814, 843, 718, 424, 419}"
262,1,711,0,1.2710654,"\int \frac{\sqrt{a+b x+c x^2} \left(A+B x+C x^2\right)}{(d+e x)^{5/2}} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(A + B*x + C*x^2))/(d + e*x)^(5/2),x]","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(e (-2 a C e-3 b B e+8 b C d)-2 c \left(8 C d^2-e (4 B d-A e)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(2 \left(4 c d-\frac{b e}{2}\right) \left(-a C e-A c e+b C d+B c d-\frac{2 c C d^2}{e}\right)+6 c (e (a B e-a C d+A c d)+b d (C d-B e))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^3 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \left(a+b x+c x^2\right)^{3/2} \left(C d^2-e (B d-A e)\right)}{3 e (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{a+b x+c x^2} \left(-e x \left(-a C e-A c e+b C d+B c d-\frac{2 c C d^2}{e}\right)-(b d-a e) (7 C d-3 B e)-c d (4 B d-A e)+\frac{8 c C d^3}{e}\right)}{3 e^2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(e (-2 a C e-3 b B e+8 b C d)-2 c \left(8 C d^2-e (4 B d-A e)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^4 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(2 \left(4 c d-\frac{b e}{2}\right) \left(-a C e-A c e+b C d+B c d-\frac{2 c C d^2}{e}\right)+6 c (e (a B e-a C d+A c d)+b d (C d-B e))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^3 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \left(a+b x+c x^2\right)^{3/2} \left(C d^2-e (B d-A e)\right)}{3 e (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{a+b x+c x^2} \left(e^2 x \left(-a C e-A c e+b C d+B c d-\frac{2 c C d^2}{e}\right)+e (b d-a e) (7 C d-3 B e)-c d \left(8 C d^2-e (4 B d-A e)\right)\right)}{3 e^3 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}",1,"(2*((8*c*C*d^3)/e - c*d*(4*B*d - A*e) - (b*d - a*e)*(7*C*d - 3*B*e) - e*(B*c*d + b*C*d - (2*c*C*d^2)/e - A*c*e - a*C*e)*x)*Sqrt[a + b*x + c*x^2])/(3*e^2*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) - (2*(C*d^2 - e*(B*d - A*e))*(a + b*x + c*x^2)^(3/2))/(3*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*(4*c*d - (b*e)/2)*(B*c*d + b*C*d - (2*c*C*d^2)/e - A*c*e - a*C*e) + 6*c*(b*d*(C*d - B*e) + e*(A*c*d - a*C*d + a*B*e)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*e^3*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(e*(8*b*C*d - 3*b*B*e - 2*a*C*e) - 2*c*(8*C*d^2 - e*(4*B*d - A*e)))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*e^4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,34,0.1765,1,"{1650, 812, 843, 718, 424, 419}"
263,1,989,0,1.916332,"\int \frac{\sqrt{a+b x+c x^2} \left(A+B x+C x^2\right)}{(d+e x)^{7/2}} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(A + B*x + C*x^2))/(d + e*x)^(7/2),x]","-\frac{2 \left(C d^2-e (B d-A e)\right) \left(c x^2+b x+a\right)^{3/2}}{5 e \left(c d^2-b e d+a e^2\right) (d+e x)^{5/2}}-\frac{2 \left(\left(24 C d^5-d^3 e (4 B d+A e)\right) c^2-d e \left(b d \left(41 C d^2-6 B e d+A e^2\right)-a e \left(37 C d^2-7 B e d+7 A e^2\right)\right) c+e^2 \left(15 b^2 C d^3+5 a^2 e^2 (C d+B e)-a b e \left(22 C d^2+3 B e d+2 A e^2\right)\right)+e^2 \left(\frac{30 c^2 C d^4}{e}-5 c^2 (B d+A e) d^2-5 b c \left(11 C d^2-e (2 B d+A e)\right) d+15 a^2 C e^3-5 a b e^2 (8 C d-B e)+a c e \left(53 C d^2-e (13 B d-3 A e)\right)+b^2 e \left(23 C d^2-e (3 B d+2 A e)\right)\right) x\right) \sqrt{c x^2+b x+a}}{15 e^3 \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{3/2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(\left(48 C d^4-2 d^2 e (4 B d+A e)\right) c^2-e \left(b d \left(88 C d^2-13 B e d-2 A e^2\right)-2 a e \left(43 C d^2-8 B e d+3 A e^2\right)\right) c+e^2 \left(\left(38 C d^2-3 B e d-2 A e^2\right) b^2-5 a e (14 C d-B e) b+30 a^2 C e^2\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^4 \left(c d^2-b e d+a e^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(\left(48 C d^3-2 d e (4 B d+A e)\right) c^2-e \left(64 b C d^2-b e (9 B d+A e)-10 a e (5 C d-B e)\right) c+15 b C e^2 (b d-a e)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^4 \left(c d^2-b e d+a e^2\right) \sqrt{d+e x} \sqrt{c x^2+b x+a}}","-\frac{2 \left(C d^2-e (B d-A e)\right) \left(c x^2+b x+a\right)^{3/2}}{5 e \left(c d^2-b e d+a e^2\right) (d+e x)^{5/2}}-\frac{2 \left(c^2 \left(24 C d^2-e (4 B d+A e)\right) d^3-c e \left(b d \left(41 C d^2-6 B e d+A e^2\right)-a e \left(37 C d^2-7 B e d+7 A e^2\right)\right) d+e^2 \left(15 b^2 C d^3+5 a^2 e^2 (C d+B e)-a b e \left(22 C d^2+3 B e d+2 A e^2\right)\right)+e \left(5 c^2 \left(6 C d^2-e (B d+A e)\right) d^2+e^2 \left(\left(23 C d^2-3 B e d-2 A e^2\right) b^2-5 a e (8 C d-B e) b+15 a^2 C e^2\right)-c e \left(5 b d \left(11 C d^2-2 B e d-A e^2\right)-a e \left(53 C d^2-13 B e d+3 A e^2\right)\right)\right) x\right) \sqrt{c x^2+b x+a}}{15 e^3 \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{3/2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(2 c^2 \left(24 C d^2-e (4 B d+A e)\right) d^2+e^2 \left(\left(38 C d^2-3 B e d-2 A e^2\right) b^2-5 a e (14 C d-B e) b+30 a^2 C e^2\right)-c e \left(b d \left(88 C d^2-13 B e d-2 A e^2\right)-2 a e \left(43 C d^2-8 B e d+3 A e^2\right)\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^4 \left(c d^2-b e d+a e^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(2 d \left(24 C d^2-e (4 B d+A e)\right) c^2+e \left(10 a e (5 C d-B e)-b \left(64 C d^2-9 B e d-A e^2\right)\right) c+15 b C e^2 (b d-a e)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^4 \left(c d^2-b e d+a e^2\right) \sqrt{d+e x} \sqrt{c x^2+b x+a}}",1,"(-2*(c^2*(24*C*d^5 - d^3*e*(4*B*d + A*e)) + e^2*(15*b^2*C*d^3 + 5*a^2*e^2*(C*d + B*e) - a*b*e*(22*C*d^2 + 3*B*d*e + 2*A*e^2)) - c*d*e*(b*d*(41*C*d^2 - 6*B*d*e + A*e^2) - a*e*(37*C*d^2 - 7*B*d*e + 7*A*e^2)) + e^2*((30*c^2*C*d^4)/e + 15*a^2*C*e^3 - 5*c^2*d^2*(B*d + A*e) - 5*a*b*e^2*(8*C*d - B*e) + a*c*e*(53*C*d^2 - e*(13*B*d - 3*A*e)) - 5*b*c*d*(11*C*d^2 - e*(2*B*d + A*e)) + b^2*e*(23*C*d^2 - e*(3*B*d + 2*A*e)))*x)*Sqrt[a + b*x + c*x^2])/(15*e^3*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2)) - (2*(C*d^2 - e*(B*d - A*e))*(a + b*x + c*x^2)^(3/2))/(5*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c^2*(48*C*d^4 - 2*d^2*e*(4*B*d + A*e)) + e^2*(30*a^2*C*e^2 - 5*a*b*e*(14*C*d - B*e) + b^2*(38*C*d^2 - 3*B*d*e - 2*A*e^2)) - c*e*(b*d*(88*C*d^2 - 13*B*d*e - 2*A*e^2) - 2*a*e*(43*C*d^2 - 8*B*d*e + 3*A*e^2)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^4*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(15*b*C*e^2*(b*d - a*e) + c^2*(48*C*d^3 - 2*d*e*(4*B*d + A*e)) - c*e*(64*b*C*d^2 - b*e*(9*B*d + A*e) - 10*a*e*(5*C*d - B*e)))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c*e^4*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,34,0.1765,1,"{1650, 810, 843, 718, 424, 419}"
264,1,1363,0,4.199987,"\int \frac{\sqrt{a+b x+c x^2} \left(A+B x+C x^2\right)}{(d+e x)^{9/2}} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(A + B*x + C*x^2))/(d + e*x)^(9/2),x]","-\frac{2 \left(C d^2-e (B d-A e)\right) \left(c x^2+b x+a\right)^{3/2}}{7 e \left(c d^2-b e d+a e^2\right) (d+e x)^{7/2}}-\frac{2 \left(\left(24 C d^5+e (4 B d+3 A e) d^3\right) c^2-d e \left(b d \left(43 C d^2+6 B e d+15 A e^2\right)-a e \left(33 C d^2+9 B e d+19 A e^2\right)\right) c-e^2 \left(-d \left(15 C d^2+6 B e d+8 A e^2\right) b^2+a e \left(12 C d^2+23 B e d+12 A e^2\right) b+7 a^2 e^2 (C d-3 B e)\right)+e \left(7 \left(6 C d^4+e (B d-3 A e) d^2\right) c^2+e \left(a e \left(93 C d^2-9 B e d-5 A e^2\right)-b \left(91 C d^3-21 A d e^2\right)\right) c+e^2 \left(\left(45 C d^2-3 B e d-4 A e^2\right) b^2-7 a e (12 C d-B e) b+35 a^2 C e^2\right)\right) x\right) \sqrt{c x^2+b x+a}}{105 e^3 \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{5/2}}+\frac{2 \left(\left(48 C d^5+2 e (4 B d+3 A e) d^3\right) c^3+d e \left(2 a e \left(69 C d^2+e (15 B d-29 A e)\right)-b \left(128 C d^3+e (19 B d+9 A e) d\right)\right) c^2+e^2 \left(\left(103 C d^3+e (9 B d+19 A e) d\right) b^2-a e \left(237 C d^2+e (B d-29 A e)\right) b+14 a^2 e^2 (11 C d-3 B e)\right) c-b e^3 \left(\left(15 C d^2+6 B e d+8 A e^2\right) b^2-14 a e (3 C d+B e) b+35 a^2 C e^2\right)\right) \sqrt{c x^2+b x+a}}{105 e^3 \left(c d^2-b e d+a e^2\right)^3 \sqrt{d+e x}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(2 \left(24 C d^5+e (4 B d+3 A e) d^3\right) c^3+d e \left(2 a e \left(69 C d^2+e (15 B d-29 A e)\right)-b \left(128 C d^3+e (19 B d+9 A e) d\right)\right) c^2+e^2 \left(\left(103 C d^3+e (9 B d+19 A e) d\right) b^2-a e \left(237 C d^2+e (B d-29 A e)\right) b+14 a^2 e^2 (11 C d-3 B e)\right) c-b e^3 \left(\left(15 C d^2+6 B e d+8 A e^2\right) b^2-14 a e (3 C d+B e) b+35 a^2 C e^2\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 e^4 \left(c d^2-b e d+a e^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(\left(48 C d^4+2 e (4 B d+3 A e) d^2\right) c^2+e \left(2 a e \left(51 C d^2+e (12 B d-5 A e)\right)-b \left(104 C d^3+3 e (5 B d+2 A e) d\right)\right) c+e^2 \left(\left(60 C d^2+e (3 B d+4 A e)\right) b^2-7 a e (18 C d+B e) b+70 a^2 C e^2\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 e^4 \left(c d^2-b e d+a e^2\right)^2 \sqrt{d+e x} \sqrt{c x^2+b x+a}}","-\frac{2 \left(C d^2-e (B d-A e)\right) \left(c x^2+b x+a\right)^{3/2}}{7 e \left(c d^2-b e d+a e^2\right) (d+e x)^{7/2}}-\frac{2 \left(c^2 \left(24 C d^2+e (4 B d+3 A e)\right) d^3-c e \left(b d \left(43 C d^2+6 B e d+15 A e^2\right)-a e \left(33 C d^2+9 B e d+19 A e^2\right)\right) d-e^2 \left(-d \left(15 C d^2+6 B e d+8 A e^2\right) b^2+a e \left(12 C d^2+23 B e d+12 A e^2\right) b+7 a^2 e^2 (C d-3 B e)\right)+e \left(7 c^2 \left(6 C d^2+e (B d-3 A e)\right) d^2+e^2 \left(\left(45 C d^2-3 B e d-4 A e^2\right) b^2-7 a e (12 C d-B e) b+35 a^2 C e^2\right)+c e \left(a e \left(93 C d^2-9 B e d-5 A e^2\right)-b \left(91 C d^3-21 A d e^2\right)\right)\right) x\right) \sqrt{c x^2+b x+a}}{105 e^3 \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{5/2}}+\frac{2 \left(2 c^3 \left(24 C d^2+e (4 B d+3 A e)\right) d^3+c^2 e \left(2 a e \left(69 C d^2+e (15 B d-29 A e)\right)-b d \left(128 C d^2+e (19 B d+9 A e)\right)\right) d-b e^3 \left(\left(15 C d^2+6 B e d+8 A e^2\right) b^2-14 a e (3 C d+B e) b+35 a^2 C e^2\right)+c e^2 \left(d \left(103 C d^2+e (9 B d+19 A e)\right) b^2-a e \left(237 C d^2+e (B d-29 A e)\right) b+14 a^2 e^2 (11 C d-3 B e)\right)\right) \sqrt{c x^2+b x+a}}{105 e^3 \left(c d^2-b e d+a e^2\right)^3 \sqrt{d+e x}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(2 c^3 \left(24 C d^2+e (4 B d+3 A e)\right) d^3+c^2 e \left(2 a e \left(69 C d^2+e (15 B d-29 A e)\right)-b d \left(128 C d^2+e (19 B d+9 A e)\right)\right) d-b e^3 \left(\left(15 C d^2+6 B e d+8 A e^2\right) b^2-14 a e (3 C d+B e) b+35 a^2 C e^2\right)+c e^2 \left(d \left(103 C d^2+e (9 B d+19 A e)\right) b^2-a e \left(237 C d^2+e (B d-29 A e)\right) b+14 a^2 e^2 (11 C d-3 B e)\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 e^4 \left(c d^2-b e d+a e^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(2 c^2 \left(24 C d^2+e (4 B d+3 A e)\right) d^2+c e \left(2 a e \left(51 C d^2+e (12 B d-5 A e)\right)-b d \left(104 C d^2+3 e (5 B d+2 A e)\right)\right)+e^2 \left(\left(60 C d^2+e (3 B d+4 A e)\right) b^2-7 a e (18 C d+B e) b+70 a^2 C e^2\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 e^4 \left(c d^2-b e d+a e^2\right)^2 \sqrt{d+e x} \sqrt{c x^2+b x+a}}",1,"(2*(c^3*(48*C*d^5 + 2*d^3*e*(4*B*d + 3*A*e)) - b*e^3*(35*a^2*C*e^2 - 14*a*b*e*(3*C*d + B*e) + b^2*(15*C*d^2 + 6*B*d*e + 8*A*e^2)) + c^2*d*e*(2*a*e*(69*C*d^2 + e*(15*B*d - 29*A*e)) - b*(128*C*d^3 + d*e*(19*B*d + 9*A*e))) + c*e^2*(14*a^2*e^2*(11*C*d - 3*B*e) - a*b*e*(237*C*d^2 + e*(B*d - 29*A*e)) + b^2*(103*C*d^3 + d*e*(9*B*d + 19*A*e))))*Sqrt[a + b*x + c*x^2])/(105*e^3*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[d + e*x]) - (2*(c^2*(24*C*d^5 + d^3*e*(4*B*d + 3*A*e)) - e^2*(7*a^2*e^2*(C*d - 3*B*e) - b^2*d*(15*C*d^2 + 6*B*d*e + 8*A*e^2) + a*b*e*(12*C*d^2 + 23*B*d*e + 12*A*e^2)) - c*d*e*(b*d*(43*C*d^2 + 6*B*d*e + 15*A*e^2) - a*e*(33*C*d^2 + 9*B*d*e + 19*A*e^2)) + e*(7*c^2*(6*C*d^4 + d^2*e*(B*d - 3*A*e)) + e^2*(35*a^2*C*e^2 - 7*a*b*e*(12*C*d - B*e) + b^2*(45*C*d^2 - 3*B*d*e - 4*A*e^2)) + c*e*(a*e*(93*C*d^2 - 9*B*d*e - 5*A*e^2) - b*(91*C*d^3 - 21*A*d*e^2)))*x)*Sqrt[a + b*x + c*x^2])/(105*e^3*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(5/2)) - (2*(C*d^2 - e*(B*d - A*e))*(a + b*x + c*x^2)^(3/2))/(7*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(7/2)) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c^3*(24*C*d^5 + d^3*e*(4*B*d + 3*A*e)) - b*e^3*(35*a^2*C*e^2 - 14*a*b*e*(3*C*d + B*e) + b^2*(15*C*d^2 + 6*B*d*e + 8*A*e^2)) + c^2*d*e*(2*a*e*(69*C*d^2 + e*(15*B*d - 29*A*e)) - b*(128*C*d^3 + d*e*(19*B*d + 9*A*e))) + c*e^2*(14*a^2*e^2*(11*C*d - 3*B*e) - a*b*e*(237*C*d^2 + e*(B*d - 29*A*e)) + b^2*(103*C*d^3 + d*e*(9*B*d + 19*A*e))))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*e^4*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c^2*(48*C*d^4 + 2*d^2*e*(4*B*d + 3*A*e)) + c*e*(2*a*e*(51*C*d^2 + e*(12*B*d - 5*A*e)) - b*(104*C*d^3 + 3*d*e*(5*B*d + 2*A*e))) + e^2*(70*a^2*C*e^2 - 7*a*b*e*(18*C*d + B*e) + b^2*(60*C*d^2 + e*(3*B*d + 4*A*e))))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*e^4*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,7,34,0.2059,1,"{1650, 810, 834, 843, 718, 424, 419}"
265,1,1904,0,6.2431257,"\int \frac{\sqrt{a+b x+c x^2} \left(A+B x+C x^2\right)}{(d+e x)^{11/2}} \, dx","Int[(Sqrt[a + b*x + c*x^2]*(A + B*x + C*x^2))/(d + e*x)^(11/2),x]","-\frac{2 \left(C d^2-e (B d-A e)\right) \left(c x^2+b x+a\right)^{3/2}}{9 e \left(c d^2-b e d+a e^2\right) (d+e x)^{9/2}}-\frac{2 \left(\left(8 C d^5+e (4 B d+5 A e) d^3\right) c^2-d e \left(3 b d \left(5 C d^2+2 B e d+5 A e^2\right)-a e \left(7 C d^2+11 B e d+13 A e^2\right)\right) c-e^2 \left(-d \left(5 C d^2+4 B e d+8 A e^2\right) b^2-a e \left(2 C d^2-17 B e d-10 A e^2\right) b+3 a^2 e^2 (3 C d-5 B e)\right)+e^2 \left(\frac{3 \left(6 C d^4+e (3 B d-5 A e) d^2\right) c^2}{e}+\left(a e \left(47 C d^2+e (B d-7 A e)\right)-3 b \left(15 C d^3+e (2 B d-5 A e) d\right)\right) c+e \left(\left(25 C d^2-e (B d+2 A e)\right) b^2-3 a e (16 C d-B e) b+21 a^2 C e^2\right)\right) x\right) \sqrt{c x^2+b x+a}}{105 e^3 \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{7/2}}+\frac{2 \left(2 \left(8 C d^6+e (4 B d+5 A e) d^4\right) c^4-d^2 e \left(56 b C d^3+5 b e (5 B d+4 A e) d-6 a e \left(11 C d^2+8 B e d-34 A e^2\right)\right) c^3-6 e^2 \left(-b^2 \left(11 C d^2+3 B e d+11 A e^2\right) d^2+a b e \left(30 C d^2-5 B e d-34 A e^2\right) d-a^2 e^2 \left(30 C d^2-36 B e d+7 A e^2\right)\right) c^2-e^3 \left(d \left(20 C d^2+25 B e d+56 A e^2\right) b^3-6 a e \left(5 C d^2+7 B e d-12 A e^2\right) b^2-3 a^2 e^2 (12 C d+29 B e) b+126 a^3 C e^3\right) c+2 b^2 e^4 \left(\left(5 C d^2+4 B e d+8 A e^2\right) b^2-6 a e (3 C d+2 B e) b+21 a^2 C e^2\right)\right) \sqrt{c x^2+b x+a}}{315 e^3 \left(c d^2-b e d+a e^2\right)^4 \sqrt{d+e x}}+\frac{2 \left(2 \left(8 C d^5+e (4 B d+5 A e) d^3\right) c^3+3 d e \left(2 a e \left(9 C d^2+7 B e d-9 A e^2\right)-b d \left(16 C d^2+7 B e d+5 A e^2\right)\right) c^2+3 e^2 \left(d \left(15 C d^2+3 B e d+7 A e^2\right) b^2-a e \left(41 C d^2+5 B e d-9 A e^2\right) b+2 a^2 e^2 (17 C d-5 B e)\right) c-b e^3 \left(\left(5 C d^2+4 B e d+8 A e^2\right) b^2-6 a e (3 C d+2 B e) b+21 a^2 C e^2\right)\right) \sqrt{c x^2+b x+a}}{315 e^3 \left(c d^2-b e d+a e^2\right)^3 (d+e x)^{3/2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(2 \left(8 C d^6+e (4 B d+5 A e) d^4\right) c^4-d^2 e \left(56 b C d^3+5 b e (5 B d+4 A e) d-6 a e \left(11 C d^2+8 B e d-34 A e^2\right)\right) c^3-6 e^2 \left(-b^2 \left(11 C d^2+3 B e d+11 A e^2\right) d^2+a b e \left(30 C d^2-5 B e d-34 A e^2\right) d-a^2 e^2 \left(30 C d^2-36 B e d+7 A e^2\right)\right) c^2-e^3 \left(d \left(20 C d^2+25 B e d+56 A e^2\right) b^3-6 a e \left(5 C d^2+7 B e d-12 A e^2\right) b^2-3 a^2 e^2 (12 C d+29 B e) b+126 a^3 C e^3\right) c+2 b^2 e^4 \left(\left(5 C d^2+4 B e d+8 A e^2\right) b^2-6 a e (3 C d+2 B e) b+21 a^2 C e^2\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 e^4 \left(c d^2-b e d+a e^2\right)^4 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(2 \left(8 C d^5+e (4 B d+5 A e) d^3\right) c^3+3 d e \left(2 a e \left(9 C d^2+7 B e d-9 A e^2\right)-b d \left(16 C d^2+7 B e d+5 A e^2\right)\right) c^2+3 e^2 \left(d \left(15 C d^2+3 B e d+7 A e^2\right) b^2-a e \left(41 C d^2+5 B e d-9 A e^2\right) b+2 a^2 e^2 (17 C d-5 B e)\right) c-b e^3 \left(\left(5 C d^2+4 B e d+8 A e^2\right) b^2-6 a e (3 C d+2 B e) b+21 a^2 C e^2\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 e^4 \left(c d^2-b e d+a e^2\right)^3 \sqrt{d+e x} \sqrt{c x^2+b x+a}}","-\frac{2 \left(C d^2-e (B d-A e)\right) \left(c x^2+b x+a\right)^{3/2}}{9 e \left(c d^2-b e d+a e^2\right) (d+e x)^{9/2}}-\frac{2 \left(c^2 \left(8 C d^2+e (4 B d+5 A e)\right) d^3-c e \left(3 b d \left(5 C d^2+2 B e d+5 A e^2\right)-a e \left(7 C d^2+11 B e d+13 A e^2\right)\right) d-e^2 \left(-d \left(5 C d^2+4 B e d+8 A e^2\right) b^2-a e \left(2 C d^2-17 B e d-10 A e^2\right) b+3 a^2 e^2 (3 C d-5 B e)\right)+e \left(3 c^2 \left(6 C d^2+e (3 B d-5 A e)\right) d^2+c e \left(a e \left(47 C d^2+B e d-7 A e^2\right)-3 b d \left(15 C d^2+2 B e d-5 A e^2\right)\right)+e^2 \left(\left(25 C d^2-e (B d+2 A e)\right) b^2-3 a e (16 C d-B e) b+21 a^2 C e^2\right)\right) x\right) \sqrt{c x^2+b x+a}}{105 e^3 \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{7/2}}+\frac{2 \left(2 c^4 \left(8 C d^2+e (4 B d+5 A e)\right) d^4+c^3 e \left(6 a e \left(11 C d^2+8 B e d-34 A e^2\right)-b d \left(56 C d^2+5 e (5 B d+4 A e)\right)\right) d^2+2 b^2 e^4 \left(\left(5 C d^2+4 B e d+8 A e^2\right) b^2-6 a e (3 C d+2 B e) b+21 a^2 C e^2\right)-6 c^2 e^2 \left(-b^2 \left(11 C d^2+3 B e d+11 A e^2\right) d^2+a b e \left(30 C d^2-5 B e d-34 A e^2\right) d-a^2 e^2 \left(30 C d^2-36 B e d+7 A e^2\right)\right)-c e^3 \left(d \left(20 C d^2+25 B e d+56 A e^2\right) b^3-6 a e \left(5 C d^2+7 B e d-12 A e^2\right) b^2-3 a^2 e^2 (12 C d+29 B e) b+126 a^3 C e^3\right)\right) \sqrt{c x^2+b x+a}}{315 e^3 \left(c d^2-b e d+a e^2\right)^4 \sqrt{d+e x}}+\frac{2 \left(2 c^3 \left(8 C d^2+e (4 B d+5 A e)\right) d^3+3 c^2 e \left(2 a e \left(9 C d^2+7 B e d-9 A e^2\right)-b d \left(16 C d^2+7 B e d+5 A e^2\right)\right) d+3 c e^2 \left(d \left(15 C d^2+3 B e d+7 A e^2\right) b^2-a e \left(41 C d^2+5 B e d-9 A e^2\right) b+2 a^2 e^2 (17 C d-5 B e)\right)-b e^3 \left(\left(5 C d^2+4 B e d+8 A e^2\right) b^2-6 a e (3 C d+2 B e) b+21 a^2 C e^2\right)\right) \sqrt{c x^2+b x+a}}{315 e^3 \left(c d^2-b e d+a e^2\right)^3 (d+e x)^{3/2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(2 c^4 \left(8 C d^2+e (4 B d+5 A e)\right) d^4+c^3 e \left(6 a e \left(11 C d^2+8 B e d-34 A e^2\right)-b d \left(56 C d^2+5 e (5 B d+4 A e)\right)\right) d^2+2 b^2 e^4 \left(\left(5 C d^2+4 B e d+8 A e^2\right) b^2-6 a e (3 C d+2 B e) b+21 a^2 C e^2\right)-6 c^2 e^2 \left(-b^2 \left(11 C d^2+3 B e d+11 A e^2\right) d^2+a b e \left(30 C d^2-5 B e d-34 A e^2\right) d-a^2 e^2 \left(30 C d^2-36 B e d+7 A e^2\right)\right)-c e^3 \left(d \left(20 C d^2+25 B e d+56 A e^2\right) b^3-6 a e \left(5 C d^2+7 B e d-12 A e^2\right) b^2-3 a^2 e^2 (12 C d+29 B e) b+126 a^3 C e^3\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 e^4 \left(c d^2-b e d+a e^2\right)^4 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(2 c^3 \left(8 C d^2+e (4 B d+5 A e)\right) d^3+3 c^2 e \left(2 a e \left(9 C d^2+7 B e d-9 A e^2\right)-b d \left(16 C d^2+7 B e d+5 A e^2\right)\right) d+3 c e^2 \left(d \left(15 C d^2+3 B e d+7 A e^2\right) b^2-a e \left(41 C d^2+5 B e d-9 A e^2\right) b+2 a^2 e^2 (17 C d-5 B e)\right)-b e^3 \left(\left(5 C d^2+4 B e d+8 A e^2\right) b^2-6 a e (3 C d+2 B e) b+21 a^2 C e^2\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 e^4 \left(c d^2-b e d+a e^2\right)^3 \sqrt{d+e x} \sqrt{c x^2+b x+a}}",1,"(2*(2*c^3*(8*C*d^5 + d^3*e*(4*B*d + 5*A*e)) + 3*c^2*d*e*(2*a*e*(9*C*d^2 + 7*B*d*e - 9*A*e^2) - b*d*(16*C*d^2 + 7*B*d*e + 5*A*e^2)) + 3*c*e^2*(2*a^2*e^2*(17*C*d - 5*B*e) - a*b*e*(41*C*d^2 + 5*B*d*e - 9*A*e^2) + b^2*d*(15*C*d^2 + 3*B*d*e + 7*A*e^2)) - b*e^3*(21*a^2*C*e^2 - 6*a*b*e*(3*C*d + 2*B*e) + b^2*(5*C*d^2 + 4*B*d*e + 8*A*e^2)))*Sqrt[a + b*x + c*x^2])/(315*e^3*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(3/2)) + (2*(2*c^4*(8*C*d^6 + d^4*e*(4*B*d + 5*A*e)) - c^3*d^2*e*(56*b*C*d^3 + 5*b*d*e*(5*B*d + 4*A*e) - 6*a*e*(11*C*d^2 + 8*B*d*e - 34*A*e^2)) + 2*b^2*e^4*(21*a^2*C*e^2 - 6*a*b*e*(3*C*d + 2*B*e) + b^2*(5*C*d^2 + 4*B*d*e + 8*A*e^2)) - 6*c^2*e^2*(a*b*d*e*(30*C*d^2 - 5*B*d*e - 34*A*e^2) - a^2*e^2*(30*C*d^2 - 36*B*d*e + 7*A*e^2) - b^2*d^2*(11*C*d^2 + 3*B*d*e + 11*A*e^2)) - c*e^3*(126*a^3*C*e^3 - 3*a^2*b*e^2*(12*C*d + 29*B*e) - 6*a*b^2*e*(5*C*d^2 + 7*B*d*e - 12*A*e^2) + b^3*d*(20*C*d^2 + 25*B*d*e + 56*A*e^2)))*Sqrt[a + b*x + c*x^2])/(315*e^3*(c*d^2 - b*d*e + a*e^2)^4*Sqrt[d + e*x]) - (2*(c^2*(8*C*d^5 + d^3*e*(4*B*d + 5*A*e)) - e^2*(3*a^2*e^2*(3*C*d - 5*B*e) - a*b*e*(2*C*d^2 - 17*B*d*e - 10*A*e^2) - b^2*d*(5*C*d^2 + 4*B*d*e + 8*A*e^2)) - c*d*e*(3*b*d*(5*C*d^2 + 2*B*d*e + 5*A*e^2) - a*e*(7*C*d^2 + 11*B*d*e + 13*A*e^2)) + e^2*((3*c^2*(6*C*d^4 + d^2*e*(3*B*d - 5*A*e)))/e + c*(a*e*(47*C*d^2 + e*(B*d - 7*A*e)) - 3*b*(15*C*d^3 + d*e*(2*B*d - 5*A*e))) + e*(21*a^2*C*e^2 - 3*a*b*e*(16*C*d - B*e) + b^2*(25*C*d^2 - e*(B*d + 2*A*e))))*x)*Sqrt[a + b*x + c*x^2])/(105*e^3*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(7/2)) - (2*(C*d^2 - e*(B*d - A*e))*(a + b*x + c*x^2)^(3/2))/(9*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(9/2)) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c^4*(8*C*d^6 + d^4*e*(4*B*d + 5*A*e)) - c^3*d^2*e*(56*b*C*d^3 + 5*b*d*e*(5*B*d + 4*A*e) - 6*a*e*(11*C*d^2 + 8*B*d*e - 34*A*e^2)) + 2*b^2*e^4*(21*a^2*C*e^2 - 6*a*b*e*(3*C*d + 2*B*e) + b^2*(5*C*d^2 + 4*B*d*e + 8*A*e^2)) - 6*c^2*e^2*(a*b*d*e*(30*C*d^2 - 5*B*d*e - 34*A*e^2) - a^2*e^2*(30*C*d^2 - 36*B*d*e + 7*A*e^2) - b^2*d^2*(11*C*d^2 + 3*B*d*e + 11*A*e^2)) - c*e^3*(126*a^3*C*e^3 - 3*a^2*b*e^2*(12*C*d + 29*B*e) - 6*a*b^2*e*(5*C*d^2 + 7*B*d*e - 12*A*e^2) + b^3*d*(20*C*d^2 + 25*B*d*e + 56*A*e^2)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*e^4*(c*d^2 - b*d*e + a*e^2)^4*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c^3*(8*C*d^5 + d^3*e*(4*B*d + 5*A*e)) + 3*c^2*d*e*(2*a*e*(9*C*d^2 + 7*B*d*e - 9*A*e^2) - b*d*(16*C*d^2 + 7*B*d*e + 5*A*e^2)) + 3*c*e^2*(2*a^2*e^2*(17*C*d - 5*B*e) - a*b*e*(41*C*d^2 + 5*B*d*e - 9*A*e^2) + b^2*d*(15*C*d^2 + 3*B*d*e + 7*A*e^2)) - b*e^3*(21*a^2*C*e^2 - 6*a*b*e*(3*C*d + 2*B*e) + b^2*(5*C*d^2 + 4*B*d*e + 8*A*e^2)))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*e^4*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",9,7,34,0.2059,1,"{1650, 810, 834, 843, 718, 424, 419}"
266,1,724,0,1.7785382,"\int \frac{(d+e x)^{3/2} \left(A+B x+C x^2\right)}{\sqrt{a+b x+c x^2}} \, dx","Int[((d + e*x)^(3/2)*(A + B*x + C*x^2))/Sqrt[a + b*x + c*x^2],x]","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (25 a C e+28 b B e+15 b C d)+c^2 \left(-\left(6 C d^2-7 e (5 A e+3 B d)\right)\right)+24 b^2 C e^2\right)}{105 c^3 e}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(-c e (25 a C e+28 b B e+15 b C d)+c^2 \left(-\left(6 C d^2-7 e (5 A e+3 B d)\right)\right)+24 b^2 C e^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^4 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c^2 e \left(a e (63 B e+82 C d)+b \left(70 A e^2+91 B d e+12 C d^2\right)\right)-8 b c e^2 (13 a C e+7 b B e+9 b C d)+c^3 \left(6 C d^3-7 d e (20 A e+3 B d)\right)+48 b^3 C e^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^4 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{3/2} \sqrt{a+b x+c x^2} (6 b C e-7 B c e+2 c C d)}{35 c^2 e}+\frac{2 C (d+e x)^{5/2} \sqrt{a+b x+c x^2}}{7 c e}","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (25 a C e+28 b B e+15 b C d)+c^2 \left(-\left(6 C d^2-7 e (5 A e+3 B d)\right)\right)+24 b^2 C e^2\right)}{105 c^3 e}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(-c e (25 a C e+28 b B e+15 b C d)+c^2 \left(-\left(6 C d^2-7 e (5 A e+3 B d)\right)\right)+24 b^2 C e^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^4 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(c^2 e \left(a e (63 B e+82 C d)+b \left(70 A e^2+91 B d e+12 C d^2\right)\right)-8 b c e^2 (13 a C e+7 b B e+9 b C d)+c^3 d \left(6 C d^2-7 e (20 A e+3 B d)\right)+48 b^3 C e^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^4 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{3/2} \sqrt{a+b x+c x^2} (6 b C e-7 B c e+2 c C d)}{35 c^2 e}+\frac{2 C (d+e x)^{5/2} \sqrt{a+b x+c x^2}}{7 c e}",1,"(2*(24*b^2*C*e^2 - c*e*(15*b*C*d + 28*b*B*e + 25*a*C*e) - c^2*(6*C*d^2 - 7*e*(3*B*d + 5*A*e)))*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(105*c^3*e) - (2*(2*c*C*d - 7*B*c*e + 6*b*C*e)*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(35*c^2*e) + (2*C*(d + e*x)^(5/2)*Sqrt[a + b*x + c*x^2])/(7*c*e) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(48*b^3*C*e^3 - 8*b*c*e^2*(9*b*C*d + 7*b*B*e + 13*a*C*e) + c^3*(6*C*d^3 - 7*d*e*(3*B*d + 20*A*e)) + c^2*e*(a*e*(82*C*d + 63*B*e) + b*(12*C*d^2 + 91*B*d*e + 70*A*e^2)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^4*e^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(24*b^2*C*e^2 - c*e*(15*b*C*d + 28*b*B*e + 25*a*C*e) - c^2*(6*C*d^2 - 7*e*(3*B*d + 5*A*e)))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^4*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,34,0.1765,1,"{1653, 832, 843, 718, 424, 419}"
267,1,557,0,0.8888353,"\int \frac{\sqrt{d+e x} \left(A+B x+C x^2\right)}{\sqrt{a+b x+c x^2}} \, dx","Int[(Sqrt[d + e*x]*(A + B*x + C*x^2))/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (9 a C e+10 b B e+3 b C d)+c^2 \left(-\left(2 C d^2-5 e (3 A e+B d)\right)\right)+8 b^2 C e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (4 b C e-5 B c e+2 c C d) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (4 b C e-5 B c e+2 c C d)}{15 c^2 e}+\frac{2 C (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 c e}","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (9 a C e+10 b B e+3 b C d)+c^2 \left(-\left(2 C d^2-5 e (3 A e+B d)\right)\right)+8 b^2 C e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (4 b C e-5 B c e+2 c C d) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (4 b C e-5 B c e+2 c C d)}{15 c^2 e}+\frac{2 C (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 c e}",1,"(-2*(2*c*C*d - 5*B*c*e + 4*b*C*e)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(15*c^2*e) + (2*C*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(5*c*e) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(8*b^2*C*e^2 - c*e*(3*b*C*d + 10*b*B*e + 9*a*C*e) - c^2*(2*C*d^2 - 5*e*(B*d + 3*A*e)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^3*e^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*C*d - 5*B*c*e + 4*b*C*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^3*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,34,0.1765,1,"{1653, 832, 843, 718, 424, 419}"
268,1,470,0,0.4818547,"\int \frac{A+B x+C x^2}{\sqrt{d+e x} \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(C e (b d-a e)-3 c e (B d-A e)+2 c C d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 b C e-3 B c e+2 c C d) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 C \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 c e}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(C e (b d-a e)+c \left(2 C d^2-3 e (B d-A e)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 b C e-3 B c e+2 c C d) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 e^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 C \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 c e}",1,"(2*C*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(3*c*e) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*C*d - 3*B*c*e + 2*b*C*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*e^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*C*d^2 + C*e*(b*d - a*e) - 3*c*e*(B*d - A*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,34,0.1471,1,"{1653, 843, 718, 424, 419}"
269,1,506,0,0.6489221,"\int \frac{A+B x+C x^2}{(d+e x)^{3/2} \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-C e (b d-a e)-c e (B d-A e)+2 c C d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{a+b x+c x^2} \left(C d^2-e (B d-A e)\right)}{e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 C d-B e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}","-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(C e (b d-a e)-c \left(2 C d^2-e (B d-A e)\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{a+b x+c x^2} \left(C d^2-e (B d-A e)\right)}{e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 C d-B e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}",1,"(-2*(C*d^2 - e*(B*d - A*e))*Sqrt[a + b*x + c*x^2])/(e*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*C*d^2 - C*e*(b*d - a*e) - c*e*(B*d - A*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e^2*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*C*d - B*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,34,0.1471,1,"{1650, 843, 718, 424, 419}"
270,1,680,0,1.1920528,"\int \frac{A+B x+C x^2}{(d+e x)^{5/2} \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^(5/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(-3 C e (b d-a e)+c e (B d-A e)+2 c C d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(3 a e^2 (2 C d-B e)-b e \left(4 C d^2-e (2 A e+B d)\right)+c d e (B d-4 A e)+2 c C d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{a+b x+c x^2} \left(C d^2-e (B d-A e)\right)}{3 e (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{a+b x+c x^2} \left(3 a e^2 (2 C d-B e)-b e \left(4 C d^2-e (2 A e+B d)\right)+c d e (B d-4 A e)+2 c C d^3\right)}{3 e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(3 C e (b d-a e)-c \left(e (B d-A e)+2 C d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(e \left(3 a e (2 C d-B e)-b \left(-2 A e^2-B d e+4 C d^2\right)\right)+c d \left(e (B d-4 A e)+2 C d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{a+b x+c x^2} \left(C d^2-e (B d-A e)\right)}{3 e (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{a+b x+c x^2} \left(e \left(3 a e (2 C d-B e)-b \left(-2 A e^2-B d e+4 C d^2\right)\right)+c d \left(e (B d-4 A e)+2 C d^2\right)\right)}{3 e \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}",1,"(-2*(C*d^2 - e*(B*d - A*e))*Sqrt[a + b*x + c*x^2])/(3*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) + (2*(2*c*C*d^3 + c*d*e*(B*d - 4*A*e) + 3*a*e^2*(2*C*d - B*e) - b*e*(4*C*d^2 - e*(B*d + 2*A*e)))*Sqrt[a + b*x + c*x^2])/(3*e*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*C*d^3 + c*d*e*(B*d - 4*A*e) + 3*a*e^2*(2*C*d - B*e) - b*e*(4*C*d^2 - e*(B*d + 2*A*e)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e^2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*C*d^2 - 3*C*e*(b*d - a*e) + c*e*(B*d - A*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*e^2*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,34,0.1765,1,"{1650, 834, 843, 718, 424, 419}"
271,1,942,0,2.2557526,"\int \frac{A+B x+C x^2}{(d+e x)^{7/2} \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x + C*x^2)/((d + e*x)^(7/2)*Sqrt[a + b*x + c*x^2]),x]","-\frac{2 \sqrt{c x^2+b x+a} \left(C d^2-e (B d-A e)\right)}{5 e \left(c d^2-b e d+a e^2\right) (d+e x)^{5/2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(\left(2 C d^4+e (3 B d-23 A e) d^2\right) c^2-e \left(b d \left(7 C d^2-7 B e d-23 A e^2\right)-a e \left(19 C d^2-29 B e d+9 A e^2\right)\right) c-e^2 \left(\left(3 C d^2+2 B e d+8 A e^2\right) b^2-10 a e (C d+B e) b+15 a^2 C e^2\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^2 \left(c d^2-b e d+a e^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(2 c C d^3+c e (3 B d-8 A e) d+5 a e^2 (2 C d-B e)-b e \left(6 C d^2-e (B d+4 A e)\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^2 \left(c d^2-b e d+a e^2\right)^2 \sqrt{d+e x} \sqrt{c x^2+b x+a}}+\frac{2 \left(\left(2 C d^4+e (3 B d-23 A e) d^2\right) c^2-e \left(b d \left(7 C d^2-7 B e d-23 A e^2\right)-a e \left(19 C d^2-29 B e d+9 A e^2\right)\right) c-e^2 \left(\left(3 C d^2+2 B e d+8 A e^2\right) b^2-10 a e (C d+B e) b+15 a^2 C e^2\right)\right) \sqrt{c x^2+b x+a}}{15 e \left(c d^2-b e d+a e^2\right)^3 \sqrt{d+e x}}+\frac{2 \left(2 c C d^3+c e (3 B d-8 A e) d+5 a e^2 (2 C d-B e)-b e \left(6 C d^2-e (B d+4 A e)\right)\right) \sqrt{c x^2+b x+a}}{15 e \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{3/2}}","-\frac{2 \sqrt{c x^2+b x+a} \left(C d^2-e (B d-A e)\right)}{5 e \left(c d^2-b e d+a e^2\right) (d+e x)^{5/2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \left(c^2 \left(2 C d^2+e (3 B d-23 A e)\right) d^2-e^2 \left(\left(3 C d^2+2 B e d+8 A e^2\right) b^2-10 a e (C d+B e) b+15 a^2 C e^2\right)-c e \left(b d \left(7 C d^2-7 B e d-23 A e^2\right)-a e \left(19 C d^2-29 B e d+9 A e^2\right)\right)\right) \sqrt{d+e x} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^2 \left(c d^2-b e d+a e^2\right)^3 \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{c x^2+b x+a}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \left(c d \left(2 C d^2+e (3 B d-8 A e)\right)+e \left(5 a e (2 C d-B e)-b \left(6 C d^2-B e d-4 A e^2\right)\right)\right) \sqrt{\frac{c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}} \sqrt{-\frac{c \left(c x^2+b x+a\right)}{b^2-4 a c}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^2 \left(c d^2-b e d+a e^2\right)^2 \sqrt{d+e x} \sqrt{c x^2+b x+a}}+\frac{2 \left(c^2 \left(2 C d^2+e (3 B d-23 A e)\right) d^2-e^2 \left(\left(3 C d^2+2 B e d+8 A e^2\right) b^2-10 a e (C d+B e) b+15 a^2 C e^2\right)-c e \left(b d \left(7 C d^2-7 B e d-23 A e^2\right)-a e \left(19 C d^2-29 B e d+9 A e^2\right)\right)\right) \sqrt{c x^2+b x+a}}{15 e \left(c d^2-b e d+a e^2\right)^3 \sqrt{d+e x}}+\frac{2 \left(c d \left(2 C d^2+e (3 B d-8 A e)\right)+e \left(5 a e (2 C d-B e)-b \left(6 C d^2-B e d-4 A e^2\right)\right)\right) \sqrt{c x^2+b x+a}}{15 e \left(c d^2-b e d+a e^2\right)^2 (d+e x)^{3/2}}",1,"(-2*(C*d^2 - e*(B*d - A*e))*Sqrt[a + b*x + c*x^2])/(5*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) + (2*(2*c*C*d^3 + c*d*e*(3*B*d - 8*A*e) + 5*a*e^2*(2*C*d - B*e) - b*e*(6*C*d^2 - e*(B*d + 4*A*e)))*Sqrt[a + b*x + c*x^2])/(15*e*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2)) + (2*(c^2*(2*C*d^4 + d^2*e*(3*B*d - 23*A*e)) - e^2*(15*a^2*C*e^2 - 10*a*b*e*(C*d + B*e) + b^2*(3*C*d^2 + 2*B*d*e + 8*A*e^2)) - c*e*(b*d*(7*C*d^2 - 7*B*d*e - 23*A*e^2) - a*e*(19*C*d^2 - 29*B*d*e + 9*A*e^2)))*Sqrt[a + b*x + c*x^2])/(15*e*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c^2*(2*C*d^4 + d^2*e*(3*B*d - 23*A*e)) - e^2*(15*a^2*C*e^2 - 10*a*b*e*(C*d + B*e) + b^2*(3*C*d^2 + 2*B*d*e + 8*A*e^2)) - c*e*(b*d*(7*C*d^2 - 7*B*d*e - 23*A*e^2) - a*e*(19*C*d^2 - 29*B*d*e + 9*A*e^2)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^2*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*C*d^3 + c*d*e*(3*B*d - 8*A*e) + 5*a*e^2*(2*C*d - B*e) - b*e*(6*C*d^2 - e*(B*d + 4*A*e)))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,6,34,0.1765,1,"{1650, 834, 843, 718, 424, 419}"
272,1,508,0,0.8330574,"\int (g+h x)^m \left(a+b x+c x^2\right)^p \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^m*(a + b*x + c*x^2)^p*(d + e*x + f*x^2),x]","\frac{(g+h x)^{m+1} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right) \left(f h (m+1) (b g-a h)-c h (m+2 p+3) (e g-d h)+2 c f g^2 (p+1)\right)}{c h^3 (m+1) (m+2 p+3)}-\frac{(g+h x)^{m+2} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} (b f h (m+p+2)-c e h (m+2 p+3)+2 c f g (p+1)) F_1\left(m+2;-p,-p;m+3;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right)}{c h^3 (m+2) (m+2 p+3)}+\frac{f (g+h x)^{m+1} \left(a+b x+c x^2\right)^{p+1}}{c h (m+2 p+3)}","\frac{(g+h x)^{m+1} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(m+1;-p,-p;m+2;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right) \left(f h (m+1) (b g-a h)+c \left(2 f g^2 (p+1)-h (m+2 p+3) (e g-d h)\right)\right)}{c h^3 (m+1) (m+2 p+3)}-\frac{(g+h x)^{m+2} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} (b f h (m+p+2)+c (2 f g (p+1)-e h (m+2 p+3))) F_1\left(m+2;-p,-p;m+3;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right)}{c h^3 (m+2) (m+2 p+3)}+\frac{f (g+h x)^{m+1} \left(a+b x+c x^2\right)^{p+1}}{c h (m+2 p+3)}",1,"(f*(g + h*x)^(1 + m)*(a + b*x + c*x^2)^(1 + p))/(c*h*(3 + m + 2*p)) + ((f*h*(b*g - a*h)*(1 + m) + 2*c*f*g^2*(1 + p) - c*h*(e*g - d*h)*(3 + m + 2*p))*(g + h*x)^(1 + m)*(a + b*x + c*x^2)^p*AppellF1[1 + m, -p, -p, 2 + m, (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h), (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h)])/(c*h^3*(1 + m)*(3 + m + 2*p)*(1 - (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h))^p*(1 - (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h))^p) - ((2*c*f*g*(1 + p) + b*f*h*(2 + m + p) - c*e*h*(3 + m + 2*p))*(g + h*x)^(2 + m)*(a + b*x + c*x^2)^p*AppellF1[2 + m, -p, -p, 3 + m, (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h), (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h)])/(c*h^3*(2 + m)*(3 + m + 2*p)*(1 - (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h))^p*(1 - (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h))^p)","A",6,4,30,0.1333,1,"{1653, 843, 759, 133}"
273,1,494,0,0.6723793,"\int (g+h x)^m \sqrt{a+b x+c x^2} \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^m*Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2),x]","\frac{\sqrt{a+b x+c x^2} (g+h x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right) \left(f h (m+1) (b g-a h)-c h (m+4) (e g-d h)+3 c f g^2\right)}{c h^3 (m+1) (m+4) \sqrt{1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{\sqrt{a+b x+c x^2} (g+h x)^{m+2} (b f h (2 m+5)-2 c e h (m+4)+6 c f g) F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right)}{2 c h^3 (m+2) (m+4) \sqrt{1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{f \left(a+b x+c x^2\right)^{3/2} (g+h x)^{m+1}}{c h (m+4)}","\frac{\sqrt{a+b x+c x^2} (g+h x)^{m+1} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right) \left(f h (m+1) (b g-a h)+c \left(3 f g^2-h (m+4) (e g-d h)\right)\right)}{c h^3 (m+1) (m+4) \sqrt{1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{\sqrt{a+b x+c x^2} (g+h x)^{m+2} (b f h (2 m+5)+c (6 f g-2 e h (m+4))) F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right)}{2 c h^3 (m+2) (m+4) \sqrt{1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}} \sqrt{1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{f \left(a+b x+c x^2\right)^{3/2} (g+h x)^{m+1}}{c h (m+4)}",1,"(f*(g + h*x)^(1 + m)*(a + b*x + c*x^2)^(3/2))/(c*h*(4 + m)) + ((3*c*f*g^2 + f*h*(b*g - a*h)*(1 + m) - c*h*(e*g - d*h)*(4 + m))*(g + h*x)^(1 + m)*Sqrt[a + b*x + c*x^2]*AppellF1[1 + m, -1/2, -1/2, 2 + m, (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h), (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h)])/(c*h^3*(1 + m)*(4 + m)*Sqrt[1 - (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h)]*Sqrt[1 - (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h)]) - ((6*c*f*g - 2*c*e*h*(4 + m) + b*f*h*(5 + 2*m))*(g + h*x)^(2 + m)*Sqrt[a + b*x + c*x^2]*AppellF1[2 + m, -1/2, -1/2, 3 + m, (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h), (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h)])/(2*c*h^3*(2 + m)*(4 + m)*Sqrt[1 - (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h)]*Sqrt[1 - (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h)])","A",6,4,32,0.1250,1,"{1653, 843, 759, 133}"
274,1,588,0,0.7552472,"\int (g+h x)^{-3-2 p} \left(a+b x+c x^2\right)^p \left(d+e x+f x^2\right) \, dx","Int[(g + h*x)^(-3 - 2*p)*(a + b*x + c*x^2)^p*(d + e*x + f*x^2),x]","-\frac{f (g+h x)^{-2 p} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(-2 p;-p,-p;1-2 p;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right)}{2 h^3 p}-\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (g+h x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c g-h \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c g-h \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \left(2 c \left(f g^3-d g h^2\right)-h \left(-2 a h (2 f g-e h)-b h (d h+e g)+3 b f g^2\right)\right) \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (g+h x)}{\left(2 c g-\left(b+\sqrt{b^2-4 a c}\right) h\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{2 h^2 (2 p+1) \left(2 c g-h \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a h^2-b g h+c g^2\right)}-\frac{(g+h x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1} \left(f g^2-h (e g-d h)\right)}{2 h (p+1) \left(a h^2-b g h+c g^2\right)}","-\frac{f (g+h x)^{-2 p} \left(a+b x+c x^2\right)^p \left(1-\frac{2 c (g+h x)}{2 c g-h \left(b-\sqrt{b^2-4 a c}\right)}\right)^{-p} \left(1-\frac{2 c (g+h x)}{2 c g-h \left(\sqrt{b^2-4 a c}+b\right)}\right)^{-p} F_1\left(-2 p;-p,-p;1-2 p;\frac{2 c (g+h x)}{2 c g-\left(b-\sqrt{b^2-4 a c}\right) h},\frac{2 c (g+h x)}{2 c g-\left(b+\sqrt{b^2-4 a c}\right) h}\right)}{2 h^3 p}-\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (g+h x)^{-2 p-1} \left(a+b x+c x^2\right)^p \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c g-h \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c g-h \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \left(h \left(2 a h (2 f g-e h)-b \left(-d h^2-e g h+3 f g^2\right)\right)+2 c \left(f g^3-d g h^2\right)\right) \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (g+h x)}{\left(2 c g-\left(b+\sqrt{b^2-4 a c}\right) h\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{2 h^2 (2 p+1) \left(2 c g-h \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a h^2-b g h+c g^2\right)}-\frac{(g+h x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1} \left(f g^2-h (e g-d h)\right)}{2 h (p+1) \left(a h^2-b g h+c g^2\right)}",1,"-((f*g^2 - h*(e*g - d*h))*(a + b*x + c*x^2)^(1 + p))/(2*h*(c*g^2 - b*g*h + a*h^2)*(1 + p)*(g + h*x)^(2*(1 + p))) - (f*(a + b*x + c*x^2)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h), (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h)])/(2*h^3*p*(g + h*x)^(2*p)*(1 - (2*c*(g + h*x))/(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h))^p*(1 - (2*c*(g + h*x))/(2*c*g - (b + Sqrt[b^2 - 4*a*c])*h))^p) - ((2*c*(f*g^3 - d*g*h^2) - h*(3*b*f*g^2 - b*h*(e*g + d*h) - 2*a*h*(2*f*g - e*h)))*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*(g + h*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (-4*c*Sqrt[b^2 - 4*a*c]*(g + h*x))/((2*c*g - (b + Sqrt[b^2 - 4*a*c])*h)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))])/(2*h^2*(2*c*g - (b - Sqrt[b^2 - 4*a*c])*h)*(c*g^2 - b*g*h + a*h^2)*(1 + 2*p)*(((2*c*g - (b - Sqrt[b^2 - 4*a*c])*h)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*g - (b + Sqrt[b^2 - 4*a*c])*h)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)))^p)","A",5,5,34,0.1471,1,"{1655, 759, 133, 806, 726}"
275,1,41,0,0.0515075,"\int \left(d+f x^2\right)^p \left(2 c d f+2 b f^2 (3+2 p) x+2 c f^2 (3+2 p) x^2\right) \, dx","Int[(d + f*x^2)^p*(2*c*d*f + 2*b*f^2*(3 + 2*p)*x + 2*c*f^2*(3 + 2*p)*x^2),x]","\frac{b f (2 p+3) \left(d+f x^2\right)^{p+1}}{p+1}+2 c f x \left(d+f x^2\right)^{p+1}","\frac{b f (2 p+3) \left(d+f x^2\right)^{p+1}}{p+1}+2 c f x \left(d+f x^2\right)^{p+1}",1,"(b*f*(3 + 2*p)*(d + f*x^2)^(1 + p))/(1 + p) + 2*c*f*x*(d + f*x^2)^(1 + p)","A",3,3,42,0.07143,1,"{1815, 12, 261}"
276,1,46,0,0.0721821,"\int \left(d+e x+f x^2\right)^p \left(-2 c e^2+2 c d f-c e^2 p+2 c f^2 (3+2 p) x^2\right) \, dx","Int[(d + e*x + f*x^2)^p*(-2*c*e^2 + 2*c*d*f - c*e^2*p + 2*c*f^2*(3 + 2*p)*x^2),x]","2 c f x \left(d+e x+f x^2\right)^{p+1}-\frac{c e (p+2) \left(d+e x+f x^2\right)^{p+1}}{p+1}","2 c f x \left(d+e x+f x^2\right)^{p+1}-\frac{c e (p+2) \left(d+e x+f x^2\right)^{p+1}}{p+1}",1,"-((c*e*(2 + p)*(d + e*x + f*x^2)^(1 + p))/(1 + p)) + 2*c*f*x*(d + e*x + f*x^2)^(1 + p)","A",2,2,46,0.04348,1,"{1661, 629}"
277,1,57,0,0.1212347,"\int \left(d+e x+f x^2\right)^p \left(-2 c e^2+2 c d f+3 b e f-c e^2 p+2 b e f p+2 b f^2 (3+2 p) x+2 c f^2 (3+2 p) x^2\right) \, dx","Int[(d + e*x + f*x^2)^p*(-2*c*e^2 + 2*c*d*f + 3*b*e*f - c*e^2*p + 2*b*e*f*p + 2*b*f^2*(3 + 2*p)*x + 2*c*f^2*(3 + 2*p)*x^2),x]","2 c f x \left(d+e x+f x^2\right)^{p+1}-\frac{(c e (p+2)-b f (2 p+3)) \left(d+e x+f x^2\right)^{p+1}}{p+1}","2 c f x \left(d+e x+f x^2\right)^{p+1}-\frac{(c e (p+2)-b f (2 p+3)) \left(d+e x+f x^2\right)^{p+1}}{p+1}",1,"-(((c*e*(2 + p) - b*f*(3 + 2*p))*(d + e*x + f*x^2)^(1 + p))/(1 + p)) + 2*c*f*x*(d + e*x + f*x^2)^(1 + p)","A",2,2,69,0.02899,1,"{1661, 629}"
278,1,20,0,0.4200429,"\int (d+e x)^3 \left(a+b x+c x^2\right)^5 \left(d (6 b d+5 a e)+\left(12 c d^2+17 b d e+5 a e^2\right) x+e (29 c d+11 b e) x^2+17 c e^2 x^3\right) \, dx","Int[(d + e*x)^3*(a + b*x + c*x^2)^5*(d*(6*b*d + 5*a*e) + (12*c*d^2 + 17*b*d*e + 5*a*e^2)*x + e*(29*c*d + 11*b*e)*x^2 + 17*c*e^2*x^3),x]","(d+e x)^5 \left(a+b x+c x^2\right)^6","(d+e x)^5 \left(a+b x+c x^2\right)^6",1,"(d + e*x)^5*(a + b*x + c*x^2)^6","A",2,2,75,0.02667,1,"{1624, 1590}"
279,1,26,0,0.0245635,"\int \frac{x^2+x^3}{-2+x+x^2} \, dx","Int[(x^2 + x^3)/(-2 + x + x^2),x]","\frac{x^2}{2}+\frac{2}{3} \log (1-x)+\frac{4}{3} \log (x+2)","\frac{x^2}{2}+\frac{2}{3} \log (1-x)+\frac{4}{3} \log (x+2)",1,"x^2/2 + (2*Log[1 - x])/3 + (4*Log[2 + x])/3","A",6,4,16,0.2500,1,"{1593, 800, 632, 31}"
280,1,346,0,0.8116774,"\int \frac{x^2 \left(d+e x+f x^2+g x^3\right)}{\sqrt{a+b x+c x^2}} \, dx","Int[(x^2*(d + e*x + f*x^2 + g*x^3))/Sqrt[a + b*x + c*x^2],x]","-\frac{\sqrt{a+b x+c x^2} \left(-2 c x \left(-40 c^2 (9 a f+10 b e)+14 b c (46 a g+25 b f)-315 b^3 g+480 c^3 d\right)-60 b^2 c (20 c e-49 a g)+40 b c^2 (36 c d-55 a f)+256 a c^2 (5 c e-4 a g)+1050 b^3 c f-945 b^4 g\right)}{1920 c^5}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 b^2 c^2 (2 c d-5 a f)-40 b^3 c (2 c e-7 a g)+48 a b c^2 (4 c e-5 a g)-32 a c^3 (4 c d-3 a f)+70 b^4 c f-63 b^5 g\right)}{256 c^{11/2}}+\frac{x^2 \sqrt{a+b x+c x^2} \left(-64 a c g+63 b^2 g-70 b c f+80 c^2 e\right)}{240 c^3}+\frac{x^3 \sqrt{a+b x+c x^2} (10 c f-9 b g)}{40 c^2}+\frac{g x^4 \sqrt{a+b x+c x^2}}{5 c}","-\frac{\sqrt{a+b x+c x^2} \left(-2 c x \left(-40 c^2 (9 a f+10 b e)+14 b c (46 a g+25 b f)-315 b^3 g+480 c^3 d\right)-60 b^2 c (20 c e-49 a g)+40 b c^2 (36 c d-55 a f)+256 a c^2 (5 c e-4 a g)+1050 b^3 c f-945 b^4 g\right)}{1920 c^5}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 b^2 c^2 (2 c d-5 a f)-40 b^3 c (2 c e-7 a g)+48 a b c^2 (4 c e-5 a g)-32 a c^3 (4 c d-3 a f)+70 b^4 c f-63 b^5 g\right)}{256 c^{11/2}}+\frac{x^2 \sqrt{a+b x+c x^2} \left(-64 a c g+63 b^2 g-70 b c f+80 c^2 e\right)}{240 c^3}+\frac{x^3 \sqrt{a+b x+c x^2} (10 c f-9 b g)}{40 c^2}+\frac{g x^4 \sqrt{a+b x+c x^2}}{5 c}",1,"((80*c^2*e - 70*b*c*f + 63*b^2*g - 64*a*c*g)*x^2*Sqrt[a + b*x + c*x^2])/(240*c^3) + ((10*c*f - 9*b*g)*x^3*Sqrt[a + b*x + c*x^2])/(40*c^2) + (g*x^4*Sqrt[a + b*x + c*x^2])/(5*c) - ((1050*b^3*c*f + 40*b*c^2*(36*c*d - 55*a*f) - 945*b^4*g - 60*b^2*c*(20*c*e - 49*a*g) + 256*a*c^2*(5*c*e - 4*a*g) - 2*c*(480*c^3*d - 40*c^2*(10*b*e + 9*a*f) - 315*b^3*g + 14*b*c*(25*b*f + 46*a*g))*x)*Sqrt[a + b*x + c*x^2])/(1920*c^5) + ((70*b^4*c*f + 48*b^2*c^2*(2*c*d - 5*a*f) - 32*a*c^3*(4*c*d - 3*a*f) - 63*b^5*g - 40*b^3*c*(2*c*e - 7*a*g) + 48*a*b*c^2*(4*c*e - 5*a*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(11/2))","A",6,5,33,0.1515,1,"{1653, 832, 779, 621, 206}"
281,1,245,0,0.4375468,"\int \frac{x \left(d+e x+f x^2+g x^3\right)}{\sqrt{a+b x+c x^2}} \, dx","Int[(x*(d + e*x + f*x^2 + g*x^3))/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(2 c x \left(-36 a c g+35 b^2 g-40 b c f+48 c^2 e\right)-16 c^2 (8 a f+9 b e)+20 b c (11 a g+6 b f)-105 b^3 g+192 c^3 d\right)}{192 c^4}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-24 b^2 c (2 c e-5 a g)+32 b c^2 (2 c d-3 a f)+16 a c^2 (4 c e-3 a g)+40 b^3 c f-35 b^4 g\right)}{128 c^{9/2}}+\frac{x^2 \sqrt{a+b x+c x^2} (8 c f-7 b g)}{24 c^2}+\frac{g x^3 \sqrt{a+b x+c x^2}}{4 c}","\frac{\sqrt{a+b x+c x^2} \left(2 c x \left(-36 a c g+35 b^2 g-40 b c f+48 c^2 e\right)-16 c^2 (8 a f+9 b e)+20 b c (11 a g+6 b f)-105 b^3 g+192 c^3 d\right)}{192 c^4}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-24 b^2 c (2 c e-5 a g)+32 b c^2 (2 c d-3 a f)+16 a c^2 (4 c e-3 a g)+40 b^3 c f-35 b^4 g\right)}{128 c^{9/2}}+\frac{x^2 \sqrt{a+b x+c x^2} (8 c f-7 b g)}{24 c^2}+\frac{g x^3 \sqrt{a+b x+c x^2}}{4 c}",1,"((8*c*f - 7*b*g)*x^2*Sqrt[a + b*x + c*x^2])/(24*c^2) + (g*x^3*Sqrt[a + b*x + c*x^2])/(4*c) + ((192*c^3*d - 16*c^2*(9*b*e + 8*a*f) - 105*b^3*g + 20*b*c*(6*b*f + 11*a*g) + 2*c*(48*c^2*e - 40*b*c*f + 35*b^2*g - 36*a*c*g)*x)*Sqrt[a + b*x + c*x^2])/(192*c^4) - ((40*b^3*c*f + 32*b*c^2*(2*c*d - 3*a*f) - 35*b^4*g - 24*b^2*c*(2*c*e - 5*a*g) + 16*a*c^2*(4*c*e - 3*a*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(9/2))","A",5,4,31,0.1290,1,"{1653, 779, 621, 206}"
282,1,177,0,0.2351673,"\int \frac{d+e x+f x^2+g x^3}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/Sqrt[a + b*x + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-8 c^2 (a f+b e)+6 b c (2 a g+b f)-5 b^3 g+16 c^3 d\right)}{16 c^{7/2}}+\frac{\sqrt{a+b x+c x^2} \left(-16 a c g+15 b^2 g-18 b c f+24 c^2 e\right)}{24 c^3}+\frac{x \sqrt{a+b x+c x^2} (6 c f-5 b g)}{12 c^2}+\frac{g x^2 \sqrt{a+b x+c x^2}}{3 c}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-8 c^2 (a f+b e)+6 b c (2 a g+b f)-5 b^3 g+16 c^3 d\right)}{16 c^{7/2}}+\frac{\sqrt{a+b x+c x^2} \left(-16 a c g+15 b^2 g-18 b c f+24 c^2 e\right)}{24 c^3}+\frac{x \sqrt{a+b x+c x^2} (6 c f-5 b g)}{12 c^2}+\frac{g x^2 \sqrt{a+b x+c x^2}}{3 c}",1,"((24*c^2*e - 18*b*c*f + 15*b^2*g - 16*a*c*g)*Sqrt[a + b*x + c*x^2])/(24*c^3) + ((6*c*f - 5*b*g)*x*Sqrt[a + b*x + c*x^2])/(12*c^2) + (g*x^2*Sqrt[a + b*x + c*x^2])/(3*c) + ((16*c^3*d - 8*c^2*(b*e + a*f) - 5*b^3*g + 6*b*c*(b*f + 2*a*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(7/2))","A",5,4,30,0.1333,1,"{1661, 640, 621, 206}"
283,1,155,0,0.2563075,"\int \frac{d+e x+f x^2+g x^3}{x \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(x*Sqrt[a + b*x + c*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a g+b f)+3 b^2 g+8 c^2 e\right)}{8 c^{5/2}}+\frac{\sqrt{a+b x+c x^2} (4 c f-3 b g)}{4 c^2}-\frac{d \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a}}+\frac{g x \sqrt{a+b x+c x^2}}{2 c}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a g+b f)+3 b^2 g+8 c^2 e\right)}{8 c^{5/2}}+\frac{\sqrt{a+b x+c x^2} (4 c f-3 b g)}{4 c^2}-\frac{d \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a}}+\frac{g x \sqrt{a+b x+c x^2}}{2 c}",1,"((4*c*f - 3*b*g)*Sqrt[a + b*x + c*x^2])/(4*c^2) + (g*x*Sqrt[a + b*x + c*x^2])/(2*c) - (d*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/Sqrt[a] + ((8*c^2*e + 3*b^2*g - 4*c*(b*f + a*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(5/2))","A",7,5,33,0.1515,1,"{1653, 843, 621, 206, 724}"
284,1,139,0,0.2352711,"\int \frac{d+e x+f x^2+g x^3}{x^2 \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(x^2*Sqrt[a + b*x + c*x^2]),x]","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 a^{3/2}}+\frac{(2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{3/2}}-\frac{d \sqrt{a+b x+c x^2}}{a x}+\frac{g \sqrt{a+b x+c x^2}}{c}","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 a^{3/2}}+\frac{(2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{3/2}}-\frac{d \sqrt{a+b x+c x^2}}{a x}+\frac{g \sqrt{a+b x+c x^2}}{c}",1,"(g*Sqrt[a + b*x + c*x^2])/c - (d*Sqrt[a + b*x + c*x^2])/(a*x) + ((b*d - 2*a*e)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(2*a^(3/2)) + ((2*c*f - b*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(3/2))","A",7,6,33,0.1818,1,"{1650, 1653, 843, 621, 206, 724}"
285,1,159,0,0.2443069,"\int \frac{d+e x+f x^2+g x^3}{x^3 \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(x^3*Sqrt[a + b*x + c*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right) \left(8 a^2 f-4 a b e-4 a c d+3 b^2 d\right)}{8 a^{5/2}}+\frac{\sqrt{a+b x+c x^2} (3 b d-4 a e)}{4 a^2 x}-\frac{d \sqrt{a+b x+c x^2}}{2 a x^2}+\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c}}","-\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right) \left(8 a^2 f-4 a b e-4 a c d+3 b^2 d\right)}{8 a^{5/2}}+\frac{\sqrt{a+b x+c x^2} (3 b d-4 a e)}{4 a^2 x}-\frac{d \sqrt{a+b x+c x^2}}{2 a x^2}+\frac{g \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c}}",1,"-(d*Sqrt[a + b*x + c*x^2])/(2*a*x^2) + ((3*b*d - 4*a*e)*Sqrt[a + b*x + c*x^2])/(4*a^2*x) - ((3*b^2*d - 4*a*c*d - 4*a*b*e + 8*a^2*f)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(8*a^(5/2)) + (g*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/Sqrt[c]","A",7,5,33,0.1515,1,"{1650, 843, 621, 206, 724}"
286,1,186,0,0.3199216,"\int \frac{d+e x+f x^2+g x^3}{x^4 \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(x^4*Sqrt[a + b*x + c*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right) \left(8 a^2 (c e-2 a g)-6 a b^2 e-4 a b (3 c d-2 a f)+5 b^3 d\right)}{16 a^{7/2}}-\frac{\sqrt{a+b x+c x^2} \left(24 a^2 f-18 a b e-16 a c d+15 b^2 d\right)}{24 a^3 x}+\frac{\sqrt{a+b x+c x^2} (5 b d-6 a e)}{12 a^2 x^2}-\frac{d \sqrt{a+b x+c x^2}}{3 a x^3}","\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right) \left(8 a^2 (c e-2 a g)-6 a b^2 e-4 a b (3 c d-2 a f)+5 b^3 d\right)}{16 a^{7/2}}-\frac{\sqrt{a+b x+c x^2} \left(24 a^2 f-18 a b e-16 a c d+15 b^2 d\right)}{24 a^3 x}+\frac{\sqrt{a+b x+c x^2} (5 b d-6 a e)}{12 a^2 x^2}-\frac{d \sqrt{a+b x+c x^2}}{3 a x^3}",1,"-(d*Sqrt[a + b*x + c*x^2])/(3*a*x^3) + ((5*b*d - 6*a*e)*Sqrt[a + b*x + c*x^2])/(12*a^2*x^2) - ((15*b^2*d - 16*a*c*d - 18*a*b*e + 24*a^2*f)*Sqrt[a + b*x + c*x^2])/(24*a^3*x) + ((5*b^3*d - 6*a*b^2*e - 4*a*b*(3*c*d - 2*a*f) + 8*a^2*(c*e - 2*a*g))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(16*a^(7/2))","A",5,4,33,0.1212,1,"{1650, 806, 724, 206}"
287,1,270,0,0.4877953,"\int \frac{d+e x+f x^2+g x^3}{x^5 \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(x^5*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+b x+c x^2} \left(64 a^2 (2 c e-3 a g)-120 a b^2 e-4 a b (55 c d-36 a f)+105 b^3 d\right)}{192 a^4 x}-\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right) \left(32 a^2 b (3 c e-2 a g)+16 a^2 c (3 c d-4 a f)-24 a b^2 (5 c d-2 a f)-40 a b^3 e+35 b^4 d\right)}{128 a^{9/2}}-\frac{\sqrt{a+b x+c x^2} \left(48 a^2 f-40 a b e-36 a c d+35 b^2 d\right)}{96 a^3 x^2}+\frac{\sqrt{a+b x+c x^2} (7 b d-8 a e)}{24 a^2 x^3}-\frac{d \sqrt{a+b x+c x^2}}{4 a x^4}","\frac{\sqrt{a+b x+c x^2} \left(64 a^2 (2 c e-3 a g)-120 a b^2 e-4 a b (55 c d-36 a f)+105 b^3 d\right)}{192 a^4 x}-\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right) \left(32 a^2 b (3 c e-2 a g)+16 a^2 c (3 c d-4 a f)-24 a b^2 (5 c d-2 a f)-40 a b^3 e+35 b^4 d\right)}{128 a^{9/2}}-\frac{\sqrt{a+b x+c x^2} \left(48 a^2 f-40 a b e-36 a c d+35 b^2 d\right)}{96 a^3 x^2}+\frac{\sqrt{a+b x+c x^2} (7 b d-8 a e)}{24 a^2 x^3}-\frac{d \sqrt{a+b x+c x^2}}{4 a x^4}",1,"-(d*Sqrt[a + b*x + c*x^2])/(4*a*x^4) + ((7*b*d - 8*a*e)*Sqrt[a + b*x + c*x^2])/(24*a^2*x^3) - ((35*b^2*d - 36*a*c*d - 40*a*b*e + 48*a^2*f)*Sqrt[a + b*x + c*x^2])/(96*a^3*x^2) + ((105*b^3*d - 120*a*b^2*e - 4*a*b*(55*c*d - 36*a*f) + 64*a^2*(2*c*e - 3*a*g))*Sqrt[a + b*x + c*x^2])/(192*a^4*x) - ((35*b^4*d - 40*a*b^3*e + 16*a^2*c*(3*c*d - 4*a*f) - 24*a*b^2*(5*c*d - 2*a*f) + 32*a^2*b*(3*c*e - 2*a*g))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(128*a^(9/2))","A",6,5,33,0.1515,1,"{1650, 834, 806, 724, 206}"
288,1,371,0,0.8171701,"\int \frac{d+e x+f x^2+g x^3}{x^6 \sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(x^6*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{a+b x+c x^2} \left(40 a^2 b (55 c e-36 a g)+256 a^2 c (4 c d-5 a f)-60 a b^2 (49 c d-20 a f)-1050 a b^3 e+945 b^4 d\right)}{1920 a^5 x}+\frac{\sqrt{a+b x+c x^2} \left(120 a^2 (3 c e-4 a g)-350 a b^2 e-4 a b (161 c d-100 a f)+315 b^3 d\right)}{960 a^4 x^2}+\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right) \left(48 a^2 b^2 (5 c e-2 a g)+48 a^2 b c (5 c d-4 a f)-32 a^3 c (3 c e-4 a g)-40 a b^3 (7 c d-2 a f)-70 a b^4 e+63 b^5 d\right)}{256 a^{11/2}}-\frac{\sqrt{a+b x+c x^2} \left(80 a^2 f-70 a b e-64 a c d+63 b^2 d\right)}{240 a^3 x^3}+\frac{\sqrt{a+b x+c x^2} (9 b d-10 a e)}{40 a^2 x^4}-\frac{d \sqrt{a+b x+c x^2}}{5 a x^5}","-\frac{\sqrt{a+b x+c x^2} \left(40 a^2 b (55 c e-36 a g)+256 a^2 c (4 c d-5 a f)-60 a b^2 (49 c d-20 a f)-1050 a b^3 e+945 b^4 d\right)}{1920 a^5 x}+\frac{\sqrt{a+b x+c x^2} \left(120 a^2 (3 c e-4 a g)-350 a b^2 e-4 a b (161 c d-100 a f)+315 b^3 d\right)}{960 a^4 x^2}+\frac{\tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right) \left(48 a^2 b^2 (5 c e-2 a g)+48 a^2 b c (5 c d-4 a f)-32 a^3 c (3 c e-4 a g)-40 a b^3 (7 c d-2 a f)-70 a b^4 e+63 b^5 d\right)}{256 a^{11/2}}-\frac{\sqrt{a+b x+c x^2} \left(80 a^2 f-70 a b e-64 a c d+63 b^2 d\right)}{240 a^3 x^3}+\frac{\sqrt{a+b x+c x^2} (9 b d-10 a e)}{40 a^2 x^4}-\frac{d \sqrt{a+b x+c x^2}}{5 a x^5}",1,"-(d*Sqrt[a + b*x + c*x^2])/(5*a*x^5) + ((9*b*d - 10*a*e)*Sqrt[a + b*x + c*x^2])/(40*a^2*x^4) - ((63*b^2*d - 64*a*c*d - 70*a*b*e + 80*a^2*f)*Sqrt[a + b*x + c*x^2])/(240*a^3*x^3) + ((315*b^3*d - 350*a*b^2*e - 4*a*b*(161*c*d - 100*a*f) + 120*a^2*(3*c*e - 4*a*g))*Sqrt[a + b*x + c*x^2])/(960*a^4*x^2) - ((945*b^4*d - 1050*a*b^3*e - 60*a*b^2*(49*c*d - 20*a*f) + 256*a^2*c*(4*c*d - 5*a*f) + 40*a^2*b*(55*c*e - 36*a*g))*Sqrt[a + b*x + c*x^2])/(1920*a^5*x) + ((63*b^5*d - 70*a*b^4*e + 48*a^2*b*c*(5*c*d - 4*a*f) - 40*a*b^3*(7*c*d - 2*a*f) - 32*a^3*c*(3*c*e - 4*a*g) + 48*a^2*b^2*(5*c*e - 2*a*g))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(256*a^(11/2))","A",7,5,33,0.1515,1,"{1650, 834, 806, 724, 206}"
289,1,258,0,0.2566234,"\int (d+e x)^3 \left(3+2 x+5 x^2\right) \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(d + e*x)^3*(3 + 2*x + 5*x^2)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{\left(300 d^2+85 d e+17 e^2\right) (d+e x)^8}{8 e^7}-\frac{2 \left(85 d^2 e+200 d^3+34 d e^2+2 e^3\right) (d+e x)^7}{7 e^7}+\frac{\left(102 d^2 e^2+170 d^3 e+300 d^4+12 d e^3+21 e^4\right) (d+e x)^6}{6 e^7}-\frac{\left(68 d^3 e^2+12 d^2 e^3+85 d^4 e+120 d^5+42 d e^4-7 e^5\right) (d+e x)^5}{5 e^7}+\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^4}{4 e^7}+\frac{2 (d+e x)^{10}}{e^7}-\frac{(120 d+17 e) (d+e x)^9}{9 e^7}","\frac{\left(300 d^2+85 d e+17 e^2\right) (d+e x)^8}{8 e^7}-\frac{2 \left(85 d^2 e+200 d^3+34 d e^2+2 e^3\right) (d+e x)^7}{7 e^7}+\frac{\left(102 d^2 e^2+170 d^3 e+300 d^4+12 d e^3+21 e^4\right) (d+e x)^6}{6 e^7}-\frac{\left(68 d^3 e^2+12 d^2 e^3+85 d^4 e+120 d^5+42 d e^4-7 e^5\right) (d+e x)^5}{5 e^7}+\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^4}{4 e^7}+\frac{2 (d+e x)^{10}}{e^7}-\frac{(120 d+17 e) (d+e x)^9}{9 e^7}",1,"((5*d^2 - 2*d*e + 3*e^2)*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*(d + e*x)^4)/(4*e^7) - ((120*d^5 + 85*d^4*e + 68*d^3*e^2 + 12*d^2*e^3 + 42*d*e^4 - 7*e^5)*(d + e*x)^5)/(5*e^7) + ((300*d^4 + 170*d^3*e + 102*d^2*e^2 + 12*d*e^3 + 21*e^4)*(d + e*x)^6)/(6*e^7) - (2*(200*d^3 + 85*d^2*e + 34*d*e^2 + 2*e^3)*(d + e*x)^7)/(7*e^7) + ((300*d^2 + 85*d*e + 17*e^2)*(d + e*x)^8)/(8*e^7) - ((120*d + 17*e)*(d + e*x)^9)/(9*e^7) + (2*(d + e*x)^10)/e^7","A",2,1,36,0.02778,1,"{1628}"
290,1,157,0,0.1660517,"\int (d+e x)^2 \left(3+2 x+5 x^2\right) \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(d + e*x)^2*(3 + 2*x + 5*x^2)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{1}{7} x^7 \left(20 d^2-34 d e+17 e^2\right)-\frac{1}{6} x^6 \left(17 d^2-34 d e+4 e^2\right)+\frac{1}{5} x^5 \left(17 d^2-8 d e+21 e^2\right)-\frac{1}{4} x^4 \left(4 d^2-42 d e-7 e^2\right)+\frac{1}{3} x^3 \left(21 d^2+14 d e+6 e^2\right)+6 d^2 x+\frac{1}{8} e x^8 (40 d-17 e)+\frac{1}{2} d x^2 (7 d+12 e)+\frac{20 e^2 x^9}{9}","\frac{1}{7} x^7 \left(20 d^2-34 d e+17 e^2\right)-\frac{1}{6} x^6 \left(17 d^2-34 d e+4 e^2\right)+\frac{1}{5} x^5 \left(17 d^2-8 d e+21 e^2\right)-\frac{1}{4} x^4 \left(4 d^2-42 d e-7 e^2\right)+\frac{1}{3} x^3 \left(21 d^2+14 d e+6 e^2\right)+6 d^2 x+\frac{1}{8} e x^8 (40 d-17 e)+\frac{1}{2} d x^2 (7 d+12 e)+\frac{20 e^2 x^9}{9}",1,"6*d^2*x + (d*(7*d + 12*e)*x^2)/2 + ((21*d^2 + 14*d*e + 6*e^2)*x^3)/3 - ((4*d^2 - 42*d*e - 7*e^2)*x^4)/4 + ((17*d^2 - 8*d*e + 21*e^2)*x^5)/5 - ((17*d^2 - 34*d*e + 4*e^2)*x^6)/6 + ((20*d^2 - 34*d*e + 17*e^2)*x^7)/7 + ((40*d - 17*e)*e*x^8)/8 + (20*e^2*x^9)/9","A",2,1,36,0.02778,1,"{1628}"
291,1,93,0,0.1075987,"\int (d+e x) \left(3+2 x+5 x^2\right) \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(d + e*x)*(3 + 2*x + 5*x^2)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{1}{7} x^7 (20 d-17 e)-\frac{17}{6} x^6 (d-e)+\frac{1}{5} x^5 (17 d-4 e)-\frac{1}{4} x^4 (4 d-21 e)+\frac{7}{3} x^3 (3 d+e)+\frac{1}{2} x^2 (7 d+6 e)+6 d x+\frac{5 e x^8}{2}","\frac{1}{7} x^7 (20 d-17 e)-\frac{17}{6} x^6 (d-e)+\frac{1}{5} x^5 (17 d-4 e)-\frac{1}{4} x^4 (4 d-21 e)+\frac{7}{3} x^3 (3 d+e)+\frac{1}{2} x^2 (7 d+6 e)+6 d x+\frac{5 e x^8}{2}",1,"6*d*x + ((7*d + 6*e)*x^2)/2 + (7*(3*d + e)*x^3)/3 - ((4*d - 21*e)*x^4)/4 + ((17*d - 4*e)*x^5)/5 - (17*(d - e)*x^6)/6 + ((20*d - 17*e)*x^7)/7 + (5*e*x^8)/2","A",2,1,34,0.02941,1,"{1628}"
292,1,42,0,0.0248029,"\int \left(3+2 x+5 x^2\right) \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(3 + 2*x + 5*x^2)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{20 x^7}{7}-\frac{17 x^6}{6}+\frac{17 x^5}{5}-x^4+7 x^3+\frac{7 x^2}{2}+6 x","\frac{20 x^7}{7}-\frac{17 x^6}{6}+\frac{17 x^5}{5}-x^4+7 x^3+\frac{7 x^2}{2}+6 x",1,"6*x + (7*x^2)/2 + 7*x^3 - x^4 + (17*x^5)/5 - (17*x^6)/6 + (20*x^7)/7","A",2,1,29,0.03448,1,"{1657}"
293,1,228,0,0.1934993,"\int \frac{\left(3+2 x+5 x^2\right) \left(2+x+3 x^2-5 x^3+4 x^4\right)}{d+e x} \, dx","Int[((3 + 2*x + 5*x^2)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(d + e*x),x]","\frac{x^4 \left(20 d^2+17 d e+17 e^2\right)}{4 e^3}-\frac{x^3 \left(17 d^2 e+20 d^3+17 d e^2+4 e^3\right)}{3 e^4}+\frac{x^2 \left(17 d^2 e^2+17 d^3 e+20 d^4+4 d e^3+21 e^4\right)}{2 e^5}-\frac{x \left(17 d^3 e^2+4 d^2 e^3+17 d^4 e+20 d^5+21 d e^4-7 e^5\right)}{e^6}+\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{e^7}-\frac{x^5 (20 d+17 e)}{5 e^2}+\frac{10 x^6}{3 e}","\frac{x^4 \left(20 d^2+17 d e+17 e^2\right)}{4 e^3}-\frac{x^3 \left(17 d^2 e+20 d^3+17 d e^2+4 e^3\right)}{3 e^4}+\frac{x^2 \left(17 d^2 e^2+17 d^3 e+20 d^4+4 d e^3+21 e^4\right)}{2 e^5}-\frac{x \left(17 d^3 e^2+4 d^2 e^3+17 d^4 e+20 d^5+21 d e^4-7 e^5\right)}{e^6}+\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{e^7}-\frac{x^5 (20 d+17 e)}{5 e^2}+\frac{10 x^6}{3 e}",1,"-(((20*d^5 + 17*d^4*e + 17*d^3*e^2 + 4*d^2*e^3 + 21*d*e^4 - 7*e^5)*x)/e^6) + ((20*d^4 + 17*d^3*e + 17*d^2*e^2 + 4*d*e^3 + 21*e^4)*x^2)/(2*e^5) - ((20*d^3 + 17*d^2*e + 17*d*e^2 + 4*e^3)*x^3)/(3*e^4) + ((20*d^2 + 17*d*e + 17*e^2)*x^4)/(4*e^3) - ((20*d + 17*e)*x^5)/(5*e^2) + (10*x^6)/(3*e) + ((5*d^2 - 2*d*e + 3*e^2)*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*Log[d + e*x])/e^7","A",2,1,36,0.02778,1,"{1628}"
294,1,228,0,0.1912749,"\int \frac{\left(3+2 x+5 x^2\right) \left(2+x+3 x^2-5 x^3+4 x^4\right)}{(d+e x)^2} \, dx","Int[((3 + 2*x + 5*x^2)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(d + e*x)^2,x]","\frac{x^3 \left(60 d^2+34 d e+17 e^2\right)}{3 e^4}-\frac{x^2 \left(51 d^2 e+80 d^3+34 d e^2+4 e^3\right)}{2 e^5}+\frac{x \left(51 d^2 e^2+68 d^3 e+100 d^4+8 d e^3+21 e^4\right)}{e^6}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{e^7 (d+e x)}-\frac{\left(68 d^3 e^2+12 d^2 e^3+85 d^4 e+120 d^5+42 d e^4-7 e^5\right) \log (d+e x)}{e^7}-\frac{x^4 (40 d+17 e)}{4 e^3}+\frac{4 x^5}{e^2}","\frac{x^3 \left(60 d^2+34 d e+17 e^2\right)}{3 e^4}-\frac{x^2 \left(51 d^2 e+80 d^3+34 d e^2+4 e^3\right)}{2 e^5}+\frac{x \left(51 d^2 e^2+68 d^3 e+100 d^4+8 d e^3+21 e^4\right)}{e^6}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{e^7 (d+e x)}-\frac{\left(68 d^3 e^2+12 d^2 e^3+85 d^4 e+120 d^5+42 d e^4-7 e^5\right) \log (d+e x)}{e^7}-\frac{x^4 (40 d+17 e)}{4 e^3}+\frac{4 x^5}{e^2}",1,"((100*d^4 + 68*d^3*e + 51*d^2*e^2 + 8*d*e^3 + 21*e^4)*x)/e^6 - ((80*d^3 + 51*d^2*e + 34*d*e^2 + 4*e^3)*x^2)/(2*e^5) + ((60*d^2 + 34*d*e + 17*e^2)*x^3)/(3*e^4) - ((40*d + 17*e)*x^4)/(4*e^3) + (4*x^5)/e^2 - ((5*d^2 - 2*d*e + 3*e^2)*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4))/(e^7*(d + e*x)) - ((120*d^5 + 85*d^4*e + 68*d^3*e^2 + 12*d^2*e^3 + 42*d*e^4 - 7*e^5)*Log[d + e*x])/e^7","A",2,1,36,0.02778,1,"{1628}"
295,1,231,0,0.2037439,"\int \frac{\left(3+2 x+5 x^2\right) \left(2+x+3 x^2-5 x^3+4 x^4\right)}{(d+e x)^3} \, dx","Int[((3 + 2*x + 5*x^2)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(d + e*x)^3,x]","\frac{x^2 \left(120 d^2+51 d e+17 e^2\right)}{2 e^5}-\frac{x \left(102 d^2 e+200 d^3+51 d e^2+4 e^3\right)}{e^6}+\frac{68 d^3 e^2+12 d^2 e^3+85 d^4 e+120 d^5+42 d e^4-7 e^5}{e^7 (d+e x)}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{2 e^7 (d+e x)^2}+\frac{\left(102 d^2 e^2+170 d^3 e+300 d^4+12 d e^3+21 e^4\right) \log (d+e x)}{e^7}-\frac{x^3 (60 d+17 e)}{3 e^4}+\frac{5 x^4}{e^3}","\frac{x^2 \left(120 d^2+51 d e+17 e^2\right)}{2 e^5}-\frac{x \left(102 d^2 e+200 d^3+51 d e^2+4 e^3\right)}{e^6}+\frac{68 d^3 e^2+12 d^2 e^3+85 d^4 e+120 d^5+42 d e^4-7 e^5}{e^7 (d+e x)}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{2 e^7 (d+e x)^2}+\frac{\left(102 d^2 e^2+170 d^3 e+300 d^4+12 d e^3+21 e^4\right) \log (d+e x)}{e^7}-\frac{x^3 (60 d+17 e)}{3 e^4}+\frac{5 x^4}{e^3}",1,"-(((200*d^3 + 102*d^2*e + 51*d*e^2 + 4*e^3)*x)/e^6) + ((120*d^2 + 51*d*e + 17*e^2)*x^2)/(2*e^5) - ((60*d + 17*e)*x^3)/(3*e^4) + (5*x^4)/e^3 - ((5*d^2 - 2*d*e + 3*e^2)*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4))/(2*e^7*(d + e*x)^2) + (120*d^5 + 85*d^4*e + 68*d^3*e^2 + 12*d^2*e^3 + 42*d*e^4 - 7*e^5)/(e^7*(d + e*x)) + ((300*d^4 + 170*d^3*e + 102*d^2*e^2 + 12*d*e^3 + 21*e^4)*Log[d + e*x])/e^7","A",2,1,36,0.02778,1,"{1628}"
296,1,391,0,0.3855545,"\int (d+e x)^3 \left(3+2 x+5 x^2\right)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(d + e*x)^3*(3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{\left(2800 d^2+315 d e+111 e^2\right) (d+e x)^{10}}{10 e^9}-\frac{\left(945 d^2 e+5600 d^3+666 d e^2+37 e^3\right) (d+e x)^9}{9 e^9}+\frac{\left(1665 d^2 e^2+1575 d^3 e+7000 d^4+185 d e^3+148 e^4\right) (d+e x)^8}{8 e^9}-\frac{\left(2220 d^3 e^2+370 d^2 e^3+1575 d^4 e+5600 d^5+592 d e^4-65 e^5\right) (d+e x)^7}{7 e^9}+\frac{\left(1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6\right) (d+e x)^6}{6 e^9}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right) (d+e x)^5}{5 e^9}+\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^4}{4 e^9}+\frac{25 (d+e x)^{12}}{3 e^9}-\frac{5 (160 d+9 e) (d+e x)^{11}}{11 e^9}","\frac{\left(2800 d^2+315 d e+111 e^2\right) (d+e x)^{10}}{10 e^9}-\frac{\left(945 d^2 e+5600 d^3+666 d e^2+37 e^3\right) (d+e x)^9}{9 e^9}+\frac{\left(1665 d^2 e^2+1575 d^3 e+7000 d^4+185 d e^3+148 e^4\right) (d+e x)^8}{8 e^9}-\frac{\left(2220 d^3 e^2+370 d^2 e^3+1575 d^4 e+5600 d^5+592 d e^4-65 e^5\right) (d+e x)^7}{7 e^9}+\frac{\left(1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6\right) (d+e x)^6}{6 e^9}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right) (d+e x)^5}{5 e^9}+\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^4}{4 e^9}+\frac{25 (d+e x)^{12}}{3 e^9}-\frac{5 (160 d+9 e) (d+e x)^{11}}{11 e^9}",1,"((5*d^2 - 2*d*e + 3*e^2)^2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*(d + e*x)^4)/(4*e^9) - ((5*d^2 - 2*d*e + 3*e^2)*(160*d^5 + 127*d^4*e + 88*d^3*e^2 - 4*d^2*e^3 + 64*d*e^4 - 11*e^5)*(d + e*x)^5)/(5*e^9) + ((2800*d^6 + 945*d^5*e + 1665*d^4*e^2 + 370*d^3*e^3 + 888*d^2*e^4 - 195*d*e^5 + 107*e^6)*(d + e*x)^6)/(6*e^9) - ((5600*d^5 + 1575*d^4*e + 2220*d^3*e^2 + 370*d^2*e^3 + 592*d*e^4 - 65*e^5)*(d + e*x)^7)/(7*e^9) + ((7000*d^4 + 1575*d^3*e + 1665*d^2*e^2 + 185*d*e^3 + 148*e^4)*(d + e*x)^8)/(8*e^9) - ((5600*d^3 + 945*d^2*e + 666*d*e^2 + 37*e^3)*(d + e*x)^9)/(9*e^9) + ((2800*d^2 + 315*d*e + 111*e^2)*(d + e*x)^10)/(10*e^9) - (5*(160*d + 9*e)*(d + e*x)^11)/(11*e^9) + (25*(d + e*x)^12)/(3*e^9)","A",2,1,38,0.02632,1,"{1628}"
297,1,201,0,0.2402337,"\int (d+e x)^2 \left(3+2 x+5 x^2\right)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(d + e*x)^2*(3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{1}{9} x^9 \left(100 d^2-90 d e+111 e^2\right)-\frac{1}{8} x^8 \left(45 d^2-222 d e+37 e^2\right)+\frac{37}{7} x^7 \left(3 d^2-2 d e+4 e^2\right)-\frac{1}{6} x^6 \left(37 d^2-296 d e-65 e^2\right)+\frac{1}{5} x^5 \left(148 d^2+130 d e+107 e^2\right)+\frac{1}{4} x^4 \left(65 d^2+214 d e+33 e^2\right)+\frac{1}{3} x^3 \left(107 d^2+66 d e+18 e^2\right)+18 d^2 x+\frac{1}{2} e x^{10} (40 d-9 e)+\frac{3}{2} d x^2 (11 d+12 e)+\frac{100 e^2 x^{11}}{11}","\frac{1}{9} x^9 \left(100 d^2-90 d e+111 e^2\right)-\frac{1}{8} x^8 \left(45 d^2-222 d e+37 e^2\right)+\frac{37}{7} x^7 \left(3 d^2-2 d e+4 e^2\right)-\frac{1}{6} x^6 \left(37 d^2-296 d e-65 e^2\right)+\frac{1}{5} x^5 \left(148 d^2+130 d e+107 e^2\right)+\frac{1}{4} x^4 \left(65 d^2+214 d e+33 e^2\right)+\frac{1}{3} x^3 \left(107 d^2+66 d e+18 e^2\right)+18 d^2 x+\frac{1}{2} e x^{10} (40 d-9 e)+\frac{3}{2} d x^2 (11 d+12 e)+\frac{100 e^2 x^{11}}{11}",1,"18*d^2*x + (3*d*(11*d + 12*e)*x^2)/2 + ((107*d^2 + 66*d*e + 18*e^2)*x^3)/3 + ((65*d^2 + 214*d*e + 33*e^2)*x^4)/4 + ((148*d^2 + 130*d*e + 107*e^2)*x^5)/5 - ((37*d^2 - 296*d*e - 65*e^2)*x^6)/6 + (37*(3*d^2 - 2*d*e + 4*e^2)*x^7)/7 - ((45*d^2 - 222*d*e + 37*e^2)*x^8)/8 + ((100*d^2 - 90*d*e + 111*e^2)*x^9)/9 + ((40*d - 9*e)*e*x^10)/2 + (100*e^2*x^11)/11","A",2,1,38,0.02632,1,"{1628}"
298,1,121,0,0.1603464,"\int (d+e x) \left(3+2 x+5 x^2\right)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(d + e*x)*(3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{5}{9} x^9 (20 d-9 e)-\frac{3}{8} x^8 (15 d-37 e)+\frac{37}{7} x^7 (3 d-e)-\frac{37}{6} x^6 (d-4 e)+\frac{1}{5} x^5 (148 d+65 e)+\frac{1}{4} x^4 (65 d+107 e)+\frac{1}{3} x^3 (107 d+33 e)+\frac{3}{2} x^2 (11 d+6 e)+18 d x+10 e x^{10}","\frac{5}{9} x^9 (20 d-9 e)-\frac{3}{8} x^8 (15 d-37 e)+\frac{37}{7} x^7 (3 d-e)-\frac{37}{6} x^6 (d-4 e)+\frac{1}{5} x^5 (148 d+65 e)+\frac{1}{4} x^4 (65 d+107 e)+\frac{1}{3} x^3 (107 d+33 e)+\frac{3}{2} x^2 (11 d+6 e)+18 d x+10 e x^{10}",1,"18*d*x + (3*(11*d + 6*e)*x^2)/2 + ((107*d + 33*e)*x^3)/3 + ((65*d + 107*e)*x^4)/4 + ((148*d + 65*e)*x^5)/5 - (37*(d - 4*e)*x^6)/6 + (37*(3*d - e)*x^7)/7 - (3*(15*d - 37*e)*x^8)/8 + (5*(20*d - 9*e)*x^9)/9 + 10*e*x^10","A",2,1,36,0.02778,1,"{1628}"
299,1,60,0,0.0362729,"\int \left(3+2 x+5 x^2\right)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{100 x^9}{9}-\frac{45 x^8}{8}+\frac{111 x^7}{7}-\frac{37 x^6}{6}+\frac{148 x^5}{5}+\frac{65 x^4}{4}+\frac{107 x^3}{3}+\frac{33 x^2}{2}+18 x","\frac{100 x^9}{9}-\frac{45 x^8}{8}+\frac{111 x^7}{7}-\frac{37 x^6}{6}+\frac{148 x^5}{5}+\frac{65 x^4}{4}+\frac{107 x^3}{3}+\frac{33 x^2}{2}+18 x",1,"18*x + (33*x^2)/2 + (107*x^3)/3 + (65*x^4)/4 + (148*x^5)/5 - (37*x^6)/6 + (111*x^7)/7 - (45*x^8)/8 + (100*x^9)/9","A",2,1,31,0.03226,1,"{1657}"
300,1,352,0,0.3164755,"\int \frac{\left(3+2 x+5 x^2\right)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{d+e x} \, dx","Int[((3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(d + e*x),x]","\frac{x^6 \left(100 d^2+45 d e+111 e^2\right)}{6 e^3}-\frac{x^5 \left(45 d^2 e+100 d^3+111 d e^2+37 e^3\right)}{5 e^4}+\frac{x^4 \left(111 d^2 e^2+45 d^3 e+100 d^4+37 d e^3+148 e^4\right)}{4 e^5}-\frac{x^3 \left(111 d^3 e^2+37 d^2 e^3+45 d^4 e+100 d^5+148 d e^4-65 e^5\right)}{3 e^6}+\frac{x^2 \left(111 d^4 e^2+37 d^3 e^3+148 d^2 e^4+45 d^5 e+100 d^6-65 d e^5+107 e^6\right)}{2 e^7}-\frac{x \left(111 d^5 e^2+37 d^4 e^3+148 d^3 e^4-65 d^2 e^5+45 d^6 e+100 d^7+107 d e^6-33 e^7\right)}{e^8}+\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{e^9}-\frac{5 x^7 (20 d+9 e)}{7 e^2}+\frac{25 x^8}{2 e}","\frac{x^6 \left(100 d^2+45 d e+111 e^2\right)}{6 e^3}-\frac{x^5 \left(45 d^2 e+100 d^3+111 d e^2+37 e^3\right)}{5 e^4}+\frac{x^4 \left(111 d^2 e^2+45 d^3 e+100 d^4+37 d e^3+148 e^4\right)}{4 e^5}-\frac{x^3 \left(111 d^3 e^2+37 d^2 e^3+45 d^4 e+100 d^5+148 d e^4-65 e^5\right)}{3 e^6}+\frac{x^2 \left(111 d^4 e^2+37 d^3 e^3+148 d^2 e^4+45 d^5 e+100 d^6-65 d e^5+107 e^6\right)}{2 e^7}-\frac{x \left(111 d^5 e^2+37 d^4 e^3+148 d^3 e^4-65 d^2 e^5+45 d^6 e+100 d^7+107 d e^6-33 e^7\right)}{e^8}+\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{e^9}-\frac{5 x^7 (20 d+9 e)}{7 e^2}+\frac{25 x^8}{2 e}",1,"-(((100*d^7 + 45*d^6*e + 111*d^5*e^2 + 37*d^4*e^3 + 148*d^3*e^4 - 65*d^2*e^5 + 107*d*e^6 - 33*e^7)*x)/e^8) + ((100*d^6 + 45*d^5*e + 111*d^4*e^2 + 37*d^3*e^3 + 148*d^2*e^4 - 65*d*e^5 + 107*e^6)*x^2)/(2*e^7) - ((100*d^5 + 45*d^4*e + 111*d^3*e^2 + 37*d^2*e^3 + 148*d*e^4 - 65*e^5)*x^3)/(3*e^6) + ((100*d^4 + 45*d^3*e + 111*d^2*e^2 + 37*d*e^3 + 148*e^4)*x^4)/(4*e^5) - ((100*d^3 + 45*d^2*e + 111*d*e^2 + 37*e^3)*x^5)/(5*e^4) + ((100*d^2 + 45*d*e + 111*e^2)*x^6)/(6*e^3) - (5*(20*d + 9*e)*x^7)/(7*e^2) + (25*x^8)/(2*e) + ((5*d^2 - 2*d*e + 3*e^2)^2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*Log[d + e*x])/e^9","A",2,1,38,0.02632,1,"{1628}"
301,1,353,0,0.3280503,"\int \frac{\left(3+2 x+5 x^2\right)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{(d+e x)^2} \, dx","Int[((3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(d + e*x)^2,x]","\frac{3 x^5 \left(100 d^2+30 d e+37 e^2\right)}{5 e^4}-\frac{x^4 \left(135 d^2 e+400 d^3+222 d e^2+37 e^3\right)}{4 e^5}+\frac{x^3 \left(333 d^2 e^2+180 d^3 e+500 d^4+74 d e^3+148 e^4\right)}{3 e^6}-\frac{x^2 \left(444 d^3 e^2+111 d^2 e^3+225 d^4 e+600 d^5+296 d e^4-65 e^5\right)}{2 e^7}+\frac{x \left(555 d^4 e^2+148 d^3 e^3+444 d^2 e^4+270 d^5 e+700 d^6-130 d e^5+107 e^6\right)}{e^8}-\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{e^9 (d+e x)}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right) \log (d+e x)}{e^9}-\frac{5 x^6 (40 d+9 e)}{6 e^3}+\frac{100 x^7}{7 e^2}","\frac{3 x^5 \left(100 d^2+30 d e+37 e^2\right)}{5 e^4}-\frac{x^4 \left(135 d^2 e+400 d^3+222 d e^2+37 e^3\right)}{4 e^5}+\frac{x^3 \left(333 d^2 e^2+180 d^3 e+500 d^4+74 d e^3+148 e^4\right)}{3 e^6}-\frac{x^2 \left(444 d^3 e^2+111 d^2 e^3+225 d^4 e+600 d^5+296 d e^4-65 e^5\right)}{2 e^7}+\frac{x \left(555 d^4 e^2+148 d^3 e^3+444 d^2 e^4+270 d^5 e+700 d^6-130 d e^5+107 e^6\right)}{e^8}-\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{e^9 (d+e x)}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right) \log (d+e x)}{e^9}-\frac{5 x^6 (40 d+9 e)}{6 e^3}+\frac{100 x^7}{7 e^2}",1,"((700*d^6 + 270*d^5*e + 555*d^4*e^2 + 148*d^3*e^3 + 444*d^2*e^4 - 130*d*e^5 + 107*e^6)*x)/e^8 - ((600*d^5 + 225*d^4*e + 444*d^3*e^2 + 111*d^2*e^3 + 296*d*e^4 - 65*e^5)*x^2)/(2*e^7) + ((500*d^4 + 180*d^3*e + 333*d^2*e^2 + 74*d*e^3 + 148*e^4)*x^3)/(3*e^6) - ((400*d^3 + 135*d^2*e + 222*d*e^2 + 37*e^3)*x^4)/(4*e^5) + (3*(100*d^2 + 30*d*e + 37*e^2)*x^5)/(5*e^4) - (5*(40*d + 9*e)*x^6)/(6*e^3) + (100*x^7)/(7*e^2) - ((5*d^2 - 2*d*e + 3*e^2)^2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4))/(e^9*(d + e*x)) - ((5*d^2 - 2*d*e + 3*e^2)*(160*d^5 + 127*d^4*e + 88*d^3*e^2 - 4*d^2*e^3 + 64*d*e^4 - 11*e^5)*Log[d + e*x])/e^9","A",2,1,38,0.02632,1,"{1628}"
302,1,354,0,0.3433367,"\int \frac{\left(3+2 x+5 x^2\right)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{(d+e x)^3} \, dx","Int[((3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(d + e*x)^3,x]","\frac{3 x^4 \left(200 d^2+45 d e+37 e^2\right)}{4 e^5}-\frac{x^3 \left(270 d^2 e+1000 d^3+333 d e^2+37 e^3\right)}{3 e^6}+\frac{x^2 \left(666 d^2 e^2+450 d^3 e+1500 d^4+111 d e^3+148 e^4\right)}{2 e^7}-\frac{x \left(1110 d^3 e^2+222 d^2 e^3+675 d^4 e+2100 d^5+444 d e^4-65 e^5\right)}{e^8}+\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right)}{e^9 (d+e x)}-\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{2 e^9 (d+e x)^2}+\frac{\left(1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6\right) \log (d+e x)}{e^9}-\frac{3 x^5 (20 d+3 e)}{e^4}+\frac{50 x^6}{3 e^3}","\frac{3 x^4 \left(200 d^2+45 d e+37 e^2\right)}{4 e^5}-\frac{x^3 \left(270 d^2 e+1000 d^3+333 d e^2+37 e^3\right)}{3 e^6}+\frac{x^2 \left(666 d^2 e^2+450 d^3 e+1500 d^4+111 d e^3+148 e^4\right)}{2 e^7}-\frac{x \left(1110 d^3 e^2+222 d^2 e^3+675 d^4 e+2100 d^5+444 d e^4-65 e^5\right)}{e^8}+\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right)}{e^9 (d+e x)}-\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{2 e^9 (d+e x)^2}+\frac{\left(1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6\right) \log (d+e x)}{e^9}-\frac{3 x^5 (20 d+3 e)}{e^4}+\frac{50 x^6}{3 e^3}",1,"-(((2100*d^5 + 675*d^4*e + 1110*d^3*e^2 + 222*d^2*e^3 + 444*d*e^4 - 65*e^5)*x)/e^8) + ((1500*d^4 + 450*d^3*e + 666*d^2*e^2 + 111*d*e^3 + 148*e^4)*x^2)/(2*e^7) - ((1000*d^3 + 270*d^2*e + 333*d*e^2 + 37*e^3)*x^3)/(3*e^6) + (3*(200*d^2 + 45*d*e + 37*e^2)*x^4)/(4*e^5) - (3*(20*d + 3*e)*x^5)/e^4 + (50*x^6)/(3*e^3) - ((5*d^2 - 2*d*e + 3*e^2)^2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4))/(2*e^9*(d + e*x)^2) + ((5*d^2 - 2*d*e + 3*e^2)*(160*d^5 + 127*d^4*e + 88*d^3*e^2 - 4*d^2*e^3 + 64*d*e^4 - 11*e^5))/(e^9*(d + e*x)) + ((2800*d^6 + 945*d^5*e + 1665*d^4*e^2 + 370*d^3*e^3 + 888*d^2*e^4 - 195*d*e^5 + 107*e^6)*Log[d + e*x])/e^9","A",2,1,38,0.02632,1,"{1628}"
303,1,360,0,0.3582924,"\int \frac{\left(3+2 x+5 x^2\right)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{(d+e x)^4} \, dx","Int[((3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(d + e*x)^4,x]","\frac{x^3 \left(1000 d^2+180 d e+111 e^2\right)}{3 e^6}-\frac{x^2 \left(450 d^2 e+2000 d^3+444 d e^2+37 e^3\right)}{2 e^7}+\frac{2 x \left(555 d^2 e^2+450 d^3 e+1750 d^4+74 d e^3+74 e^4\right)}{e^8}-\frac{1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6}{e^9 (d+e x)}+\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right)}{2 e^9 (d+e x)^2}-\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{3 e^9 (d+e x)^3}-\frac{\left(2220 d^3 e^2+370 d^2 e^3+1575 d^4 e+5600 d^5+592 d e^4-65 e^5\right) \log (d+e x)}{e^9}-\frac{5 x^4 (80 d+9 e)}{4 e^5}+\frac{20 x^5}{e^4}","\frac{x^3 \left(1000 d^2+180 d e+111 e^2\right)}{3 e^6}-\frac{x^2 \left(450 d^2 e+2000 d^3+444 d e^2+37 e^3\right)}{2 e^7}+\frac{2 x \left(555 d^2 e^2+450 d^3 e+1750 d^4+74 d e^3+74 e^4\right)}{e^8}-\frac{1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6}{e^9 (d+e x)}+\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right)}{2 e^9 (d+e x)^2}-\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{3 e^9 (d+e x)^3}-\frac{\left(2220 d^3 e^2+370 d^2 e^3+1575 d^4 e+5600 d^5+592 d e^4-65 e^5\right) \log (d+e x)}{e^9}-\frac{5 x^4 (80 d+9 e)}{4 e^5}+\frac{20 x^5}{e^4}",1,"(2*(1750*d^4 + 450*d^3*e + 555*d^2*e^2 + 74*d*e^3 + 74*e^4)*x)/e^8 - ((2000*d^3 + 450*d^2*e + 444*d*e^2 + 37*e^3)*x^2)/(2*e^7) + ((1000*d^2 + 180*d*e + 111*e^2)*x^3)/(3*e^6) - (5*(80*d + 9*e)*x^4)/(4*e^5) + (20*x^5)/e^4 - ((5*d^2 - 2*d*e + 3*e^2)^2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4))/(3*e^9*(d + e*x)^3) + ((5*d^2 - 2*d*e + 3*e^2)*(160*d^5 + 127*d^4*e + 88*d^3*e^2 - 4*d^2*e^3 + 64*d*e^4 - 11*e^5))/(2*e^9*(d + e*x)^2) - (2800*d^6 + 945*d^5*e + 1665*d^4*e^2 + 370*d^3*e^3 + 888*d^2*e^4 - 195*d*e^5 + 107*e^6)/(e^9*(d + e*x)) - ((5600*d^5 + 1575*d^4*e + 2220*d^3*e^2 + 370*d^2*e^3 + 592*d*e^4 - 65*e^5)*Log[d + e*x])/e^9","A",2,1,38,0.02632,1,"{1628}"
304,1,221,0,0.1901294,"\int \frac{(d+e x)^3 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{3+2 x+5 x^2} \, dx","Int[((d + e*x)^3*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2),x]","\frac{3}{500} e x^4 \left(100 d^2-165 d e+27 e^2\right)+\frac{x^3 \left(-2475 d^2 e+500 d^3+1215 d e^2+458 e^3\right)}{1875}-\frac{x^2 \left(-6075 d^2 e+4125 d^3-6870 d e^2+881 e^3\right)}{6250}+\frac{\left(-66075 d^2 e+57250 d^3-76620 d e^2+23431 e^3\right) \log \left(5 x^2+2 x+3\right)}{156250}+\frac{x \left(34350 d^2 e+10125 d^3-13215 d e^2-5108 e^3\right)}{15625}-\frac{\left(449175 d^2 e+52875 d^3-274845 d e^2-53189 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{78125 \sqrt{14}}+\frac{3}{125} e^2 x^5 (20 d-11 e)+\frac{2 e^3 x^6}{15}","\frac{3}{500} e x^4 \left(100 d^2-165 d e+27 e^2\right)+\frac{x^3 \left(-2475 d^2 e+500 d^3+1215 d e^2+458 e^3\right)}{1875}-\frac{x^2 \left(-6075 d^2 e+4125 d^3-6870 d e^2+881 e^3\right)}{6250}+\frac{\left(-66075 d^2 e+57250 d^3-76620 d e^2+23431 e^3\right) \log \left(5 x^2+2 x+3\right)}{156250}+\frac{x \left(34350 d^2 e+10125 d^3-13215 d e^2-5108 e^3\right)}{15625}-\frac{\left(449175 d^2 e+52875 d^3-274845 d e^2-53189 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{78125 \sqrt{14}}+\frac{3}{125} e^2 x^5 (20 d-11 e)+\frac{2 e^3 x^6}{15}",1,"((10125*d^3 + 34350*d^2*e - 13215*d*e^2 - 5108*e^3)*x)/15625 - ((4125*d^3 - 6075*d^2*e - 6870*d*e^2 + 881*e^3)*x^2)/6250 + ((500*d^3 - 2475*d^2*e + 1215*d*e^2 + 458*e^3)*x^3)/1875 + (3*e*(100*d^2 - 165*d*e + 27*e^2)*x^4)/500 + (3*(20*d - 11*e)*e^2*x^5)/125 + (2*e^3*x^6)/15 - ((52875*d^3 + 449175*d^2*e - 274845*d*e^2 - 53189*e^3)*ArcTan[(1 + 5*x)/Sqrt[14]])/(78125*Sqrt[14]) + ((57250*d^3 - 66075*d^2*e - 76620*d*e^2 + 23431*e^3)*Log[3 + 2*x + 5*x^2])/156250","A",6,5,38,0.1316,1,"{1628, 634, 618, 204, 628}"
305,1,156,0,0.1621306,"\int \frac{(d+e x)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{3+2 x+5 x^2} \, dx","Int[((d + e*x)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2),x]","\frac{1}{375} x^3 \left(100 d^2-330 d e+81 e^2\right)-\frac{x^2 \left(825 d^2-810 d e-458 e^2\right)}{1250}+\frac{\left(5725 d^2-4405 d e-2554 e^2\right) \log \left(5 x^2+2 x+3\right)}{15625}+\frac{x \left(2025 d^2+4580 d e-881 e^2\right)}{3125}-\frac{\left(10575 d^2+59890 d e-18323 e^2\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{15625 \sqrt{14}}+\frac{1}{100} e x^4 (40 d-33 e)+\frac{4 e^2 x^5}{25}","\frac{1}{375} x^3 \left(100 d^2-330 d e+81 e^2\right)-\frac{x^2 \left(825 d^2-810 d e-458 e^2\right)}{1250}+\frac{\left(5725 d^2-4405 d e-2554 e^2\right) \log \left(5 x^2+2 x+3\right)}{15625}+\frac{x \left(2025 d^2+4580 d e-881 e^2\right)}{3125}-\frac{\left(10575 d^2+59890 d e-18323 e^2\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{15625 \sqrt{14}}+\frac{1}{100} e x^4 (40 d-33 e)+\frac{4 e^2 x^5}{25}",1,"((2025*d^2 + 4580*d*e - 881*e^2)*x)/3125 - ((825*d^2 - 810*d*e - 458*e^2)*x^2)/1250 + ((100*d^2 - 330*d*e + 81*e^2)*x^3)/375 + ((40*d - 33*e)*e*x^4)/100 + (4*e^2*x^5)/25 - ((10575*d^2 + 59890*d*e - 18323*e^2)*ArcTan[(1 + 5*x)/Sqrt[14]])/(15625*Sqrt[14]) + ((5725*d^2 - 4405*d*e - 2554*e^2)*Log[3 + 2*x + 5*x^2])/15625","A",6,5,38,0.1316,1,"{1628, 634, 618, 204, 628}"
306,1,99,0,0.1082656,"\int \frac{(d+e x) \left(2+x+3 x^2-5 x^3+4 x^4\right)}{3+2 x+5 x^2} \, dx","Int[((d + e*x)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2),x]","\frac{1}{75} x^3 (20 d-33 e)-\frac{3}{250} x^2 (55 d-27 e)+\frac{(2290 d-881 e) \log \left(5 x^2+2 x+3\right)}{6250}+\frac{1}{625} x (405 d+458 e)-\frac{(2115 d+5989 e) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{3125 \sqrt{14}}+\frac{e x^4}{5}","\frac{1}{75} x^3 (20 d-33 e)-\frac{3}{250} x^2 (55 d-27 e)+\frac{(2290 d-881 e) \log \left(5 x^2+2 x+3\right)}{6250}+\frac{1}{625} x (405 d+458 e)-\frac{(2115 d+5989 e) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{3125 \sqrt{14}}+\frac{e x^4}{5}",1,"((405*d + 458*e)*x)/625 - (3*(55*d - 27*e)*x^2)/250 + ((20*d - 33*e)*x^3)/75 + (e*x^4)/5 - ((2115*d + 5989*e)*ArcTan[(1 + 5*x)/Sqrt[14]])/(3125*Sqrt[14]) + ((2290*d - 881*e)*Log[3 + 2*x + 5*x^2])/6250","A",6,5,36,0.1389,1,"{1628, 634, 618, 204, 628}"
307,1,56,0,0.0486828,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{3+2 x+5 x^2} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/(3 + 2*x + 5*x^2),x]","\frac{4 x^3}{15}-\frac{33 x^2}{50}+\frac{229}{625} \log \left(5 x^2+2 x+3\right)+\frac{81 x}{125}-\frac{423 \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{625 \sqrt{14}}","\frac{4 x^3}{15}-\frac{33 x^2}{50}+\frac{229}{625} \log \left(5 x^2+2 x+3\right)+\frac{81 x}{125}-\frac{423 \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{625 \sqrt{14}}",1,"(81*x)/125 - (33*x^2)/50 + (4*x^3)/15 - (423*ArcTan[(1 + 5*x)/Sqrt[14]])/(625*Sqrt[14]) + (229*Log[3 + 2*x + 5*x^2])/625","A",6,5,31,0.1613,1,"{1657, 634, 618, 204, 628}"
308,1,168,0,0.1936783,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{(d+e x) \left(3+2 x+5 x^2\right)} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/((d + e*x)*(3 + 2*x + 5*x^2)),x]","\frac{(458 d-7 e) \log \left(5 x^2+2 x+3\right)}{250 \left(5 d^2-2 d e+3 e^2\right)}+\frac{\left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{e^3 \left(5 d^2-2 d e+3 e^2\right)}-\frac{(423 d-1367 e) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{125 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)}-\frac{x (20 d+33 e)}{25 e^2}+\frac{2 x^2}{5 e}","\frac{(458 d-7 e) \log \left(5 x^2+2 x+3\right)}{250 \left(5 d^2-2 d e+3 e^2\right)}+\frac{\left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{e^3 \left(5 d^2-2 d e+3 e^2\right)}-\frac{(423 d-1367 e) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{125 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)}-\frac{x (20 d+33 e)}{25 e^2}+\frac{2 x^2}{5 e}",1,"-((20*d + 33*e)*x)/(25*e^2) + (2*x^2)/(5*e) - ((423*d - 1367*e)*ArcTan[(1 + 5*x)/Sqrt[14]])/(125*Sqrt[14]*(5*d^2 - 2*d*e + 3*e^2)) + ((4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*Log[d + e*x])/(e^3*(5*d^2 - 2*d*e + 3*e^2)) + ((458*d - 7*e)*Log[3 + 2*x + 5*x^2])/(250*(5*d^2 - 2*d*e + 3*e^2))","A",6,5,38,0.1316,1,"{1628, 634, 618, 204, 628}"
309,1,233,0,0.2511819,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{(d+e x)^2 \left(3+2 x+5 x^2\right)} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/((d + e*x)^2*(3 + 2*x + 5*x^2)),x]","\frac{\left(229 d^2-7 d e-136 e^2\right) \log \left(5 x^2+2 x+3\right)}{25 \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4}{e^3 \left(5 d^2-2 d e+3 e^2\right) (d+e x)}-\frac{\left(28 d^3 e^2+44 d^2 e^3+d^4 e+40 d^5-2 d e^4+e^5\right) \log (d+e x)}{e^3 \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{\left(423 d^2-2734 d e+293 e^2\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{25 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^2}+\frac{4 x}{5 e^2}","\frac{\left(229 d^2-7 d e-136 e^2\right) \log \left(5 x^2+2 x+3\right)}{25 \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4}{e^3 \left(5 d^2-2 d e+3 e^2\right) (d+e x)}-\frac{\left(28 d^3 e^2+44 d^2 e^3+d^4 e+40 d^5-2 d e^4+e^5\right) \log (d+e x)}{e^3 \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{\left(423 d^2-2734 d e+293 e^2\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{25 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^2}+\frac{4 x}{5 e^2}",1,"(4*x)/(5*e^2) - (4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)/(e^3*(5*d^2 - 2*d*e + 3*e^2)*(d + e*x)) - ((423*d^2 - 2734*d*e + 293*e^2)*ArcTan[(1 + 5*x)/Sqrt[14]])/(25*Sqrt[14]*(5*d^2 - 2*d*e + 3*e^2)^2) - ((40*d^5 + d^4*e + 28*d^3*e^2 + 44*d^2*e^3 - 2*d*e^4 + e^5)*Log[d + e*x])/(e^3*(5*d^2 - 2*d*e + 3*e^2)^2) + ((229*d^2 - 7*d*e - 136*e^2)*Log[3 + 2*x + 5*x^2])/(25*(5*d^2 - 2*d*e + 3*e^2)^2)","A",6,5,38,0.1316,1,"{1628, 634, 618, 204, 628}"
310,1,317,0,0.2900283,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{(d+e x)^3 \left(3+2 x+5 x^2\right)} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/((d + e*x)^3*(3 + 2*x + 5*x^2)),x]","\frac{\left(-21 d^2 e+458 d^3-816 d e^2+113 e^3\right) \log \left(5 x^2+2 x+3\right)}{10 \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4}{2 e^3 \left(5 d^2-2 d e+3 e^2\right) (d+e x)^2}+\frac{28 d^3 e^2+44 d^2 e^3+d^4 e+40 d^5-2 d e^4+e^5}{e^3 \left(5 d^2-2 d e+3 e^2\right)^2 (d+e x)}+\frac{\left(228 d^4 e^2-242 d^3 e^3+141 d^2 e^4-120 d^5 e+100 d^6+120 d e^5-e^6\right) \log (d+e x)}{e^3 \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{\left(-4101 d^2 e+423 d^3+879 d e^2+703 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{5 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^3}","\frac{\left(-21 d^2 e+458 d^3-816 d e^2+113 e^3\right) \log \left(5 x^2+2 x+3\right)}{10 \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4}{2 e^3 \left(5 d^2-2 d e+3 e^2\right) (d+e x)^2}+\frac{28 d^3 e^2+44 d^2 e^3+d^4 e+40 d^5-2 d e^4+e^5}{e^3 \left(5 d^2-2 d e+3 e^2\right)^2 (d+e x)}+\frac{\left(228 d^4 e^2-242 d^3 e^3+141 d^2 e^4-120 d^5 e+100 d^6+120 d e^5-e^6\right) \log (d+e x)}{e^3 \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{\left(-4101 d^2 e+423 d^3+879 d e^2+703 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{5 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^3}",1,"-(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)/(2*e^3*(5*d^2 - 2*d*e + 3*e^2)*(d + e*x)^2) + (40*d^5 + d^4*e + 28*d^3*e^2 + 44*d^2*e^3 - 2*d*e^4 + e^5)/(e^3*(5*d^2 - 2*d*e + 3*e^2)^2*(d + e*x)) - ((423*d^3 - 4101*d^2*e + 879*d*e^2 + 703*e^3)*ArcTan[(1 + 5*x)/Sqrt[14]])/(5*Sqrt[14]*(5*d^2 - 2*d*e + 3*e^2)^3) + ((100*d^6 - 120*d^5*e + 228*d^4*e^2 - 242*d^3*e^3 + 141*d^2*e^4 + 120*d*e^5 - e^6)*Log[d + e*x])/(e^3*(5*d^2 - 2*d*e + 3*e^2)^3) + ((458*d^3 - 21*d^2*e - 816*d*e^2 + 113*e^3)*Log[3 + 2*x + 5*x^2])/(10*(5*d^2 - 2*d*e + 3*e^2)^3)","A",6,5,38,0.1316,1,"{1628, 634, 618, 204, 628}"
311,1,189,0,0.255334,"\int \frac{(d+e x)^3 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{\left(3+2 x+5 x^2\right)^2} \, dx","Int[((d + e*x)^3*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2)^2,x]","\frac{e x^2 \left(840 d^2-1722 d e+373 e^2\right)}{3500}-\frac{\left(-1545 d^2 e+1025 d^3-2601 d e^2+832 e^3\right) \log \left(5 x^2+2 x+3\right)}{6250}+\frac{x \left(-17220 d^2 e+2800 d^3+9921 d e^2+6053 e^3\right)}{17500}+\frac{\left(317565 d^2 e+32825 d^3-221643 d e^2-67499 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{87500 \sqrt{14}}+\frac{1}{375} e^2 x^3 (60 d-41 e)-\frac{(423 x+1367) (d+e x)^3}{3500 \left(5 x^2+2 x+3\right)}+\frac{e^3 x^4}{25}","\frac{e x^2 \left(840 d^2-1722 d e+373 e^2\right)}{3500}-\frac{\left(-1545 d^2 e+1025 d^3-2601 d e^2+832 e^3\right) \log \left(5 x^2+2 x+3\right)}{6250}+\frac{x \left(-17220 d^2 e+2800 d^3+9921 d e^2+6053 e^3\right)}{17500}+\frac{\left(317565 d^2 e+32825 d^3-221643 d e^2-67499 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{87500 \sqrt{14}}+\frac{1}{375} e^2 x^3 (60 d-41 e)-\frac{(423 x+1367) (d+e x)^3}{3500 \left(5 x^2+2 x+3\right)}+\frac{e^3 x^4}{25}",1,"((2800*d^3 - 17220*d^2*e + 9921*d*e^2 + 6053*e^3)*x)/17500 + (e*(840*d^2 - 1722*d*e + 373*e^2)*x^2)/3500 + ((60*d - 41*e)*e^2*x^3)/375 + (e^3*x^4)/25 - ((1367 + 423*x)*(d + e*x)^3)/(3500*(3 + 2*x + 5*x^2)) + ((32825*d^3 + 317565*d^2*e - 221643*d*e^2 - 67499*e^3)*ArcTan[(1 + 5*x)/Sqrt[14]])/(87500*Sqrt[14]) - ((1025*d^3 - 1545*d^2*e - 2601*d*e^2 + 832*e^3)*Log[3 + 2*x + 5*x^2])/6250","A",7,6,38,0.1579,1,"{1644, 1628, 634, 618, 204, 628}"
312,1,140,0,0.208256,"\int \frac{(d+e x)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{\left(3+2 x+5 x^2\right)^2} \, dx","Int[((d + e*x)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2)^2,x]","-\frac{\left(1025 d^2-1030 d e-867 e^2\right) \log \left(5 x^2+2 x+3\right)}{6250}+\frac{x \left(2800 d^2-11480 d e+3307 e^2\right)}{17500}+\frac{\left(32825 d^2+211710 d e-73881 e^2\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{87500 \sqrt{14}}+\frac{1}{250} e x^2 (40 d-41 e)-\frac{(423 x+1367) (d+e x)^2}{3500 \left(5 x^2+2 x+3\right)}+\frac{4 e^2 x^3}{75}","-\frac{\left(1025 d^2-1030 d e-867 e^2\right) \log \left(5 x^2+2 x+3\right)}{6250}+\frac{x \left(2800 d^2-11480 d e+3307 e^2\right)}{17500}+\frac{\left(32825 d^2+211710 d e-73881 e^2\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{87500 \sqrt{14}}+\frac{1}{250} e x^2 (40 d-41 e)-\frac{(423 x+1367) (d+e x)^2}{3500 \left(5 x^2+2 x+3\right)}+\frac{4 e^2 x^3}{75}",1,"((2800*d^2 - 11480*d*e + 3307*e^2)*x)/17500 + ((40*d - 41*e)*e*x^2)/250 + (4*e^2*x^3)/75 - ((1367 + 423*x)*(d + e*x)^2)/(3500*(3 + 2*x + 5*x^2)) + ((32825*d^2 + 211710*d*e - 73881*e^2)*ArcTan[(1 + 5*x)/Sqrt[14]])/(87500*Sqrt[14]) - ((1025*d^2 - 1030*d*e - 867*e^2)*Log[3 + 2*x + 5*x^2])/6250","A",7,6,38,0.1579,1,"{1644, 1628, 634, 618, 204, 628}"
313,1,97,0,0.1934612,"\int \frac{(d+e x) \left(2+x+3 x^2-5 x^3+4 x^4\right)}{\left(3+2 x+5 x^2\right)^2} \, dx","Int[((d + e*x)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2)^2,x]","-\frac{(423 x+1367) (d+e x)}{3500 \left(5 x^2+2 x+3\right)}-\frac{(205 d-103 e) \log \left(5 x^2+2 x+3\right)}{1250}+\frac{1}{125} x (20 d-41 e)+\frac{(6565 d+21171 e) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{17500 \sqrt{14}}+\frac{2 e x^2}{25}","-\frac{(423 x+1367) (d+e x)}{3500 \left(5 x^2+2 x+3\right)}-\frac{(205 d-103 e) \log \left(5 x^2+2 x+3\right)}{1250}+\frac{1}{125} x (20 d-41 e)+\frac{(6565 d+21171 e) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{17500 \sqrt{14}}+\frac{2 e x^2}{25}",1,"((20*d - 41*e)*x)/125 + (2*e*x^2)/25 - ((1367 + 423*x)*(d + e*x))/(3500*(3 + 2*x + 5*x^2)) + ((6565*d + 21171*e)*ArcTan[(1 + 5*x)/Sqrt[14]])/(17500*Sqrt[14]) - ((205*d - 103*e)*Log[3 + 2*x + 5*x^2])/1250","A",7,6,36,0.1667,1,"{1644, 1657, 634, 618, 204, 628}"
314,1,63,0,0.0773302,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{\left(3+2 x+5 x^2\right)^2} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/(3 + 2*x + 5*x^2)^2,x]","-\frac{423 x+1367}{3500 \left(5 x^2+2 x+3\right)}-\frac{41}{250} \log \left(5 x^2+2 x+3\right)+\frac{4 x}{25}+\frac{1313 \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{3500 \sqrt{14}}","-\frac{423 x+1367}{3500 \left(5 x^2+2 x+3\right)}-\frac{41}{250} \log \left(5 x^2+2 x+3\right)+\frac{4 x}{25}+\frac{1313 \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{3500 \sqrt{14}}",1,"(4*x)/25 - (1367 + 423*x)/(3500*(3 + 2*x + 5*x^2)) + (1313*ArcTan[(1 + 5*x)/Sqrt[14]])/(3500*Sqrt[14]) - (41*Log[3 + 2*x + 5*x^2])/250","A",7,6,31,0.1935,1,"{1660, 1657, 634, 618, 204, 628}"
315,1,224,0,0.3402748,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{(d+e x) \left(3+2 x+5 x^2\right)^2} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/((d + e*x)*(3 + 2*x + 5*x^2)^2),x]","-\frac{x (423 d-1367 e)+1367 d-293 e}{700 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)}-\frac{\left(-61 d^2 e+205 d^3+23 d e^2+14 e^3\right) \log \left(5 x^2+2 x+3\right)}{50 \left(5 d^2-2 d e+3 e^2\right)^2}+\frac{\left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{e \left(5 d^2-2 d e+3 e^2\right)^2}+\frac{\left(-26423 d^2 e+6565 d^3+11089 d e^2-6623 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{700 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^2}","-\frac{x (423 d-1367 e)+1367 d-293 e}{700 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)}-\frac{\left(-61 d^2 e+205 d^3+23 d e^2+14 e^3\right) \log \left(5 x^2+2 x+3\right)}{50 \left(5 d^2-2 d e+3 e^2\right)^2}+\frac{\left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{e \left(5 d^2-2 d e+3 e^2\right)^2}+\frac{\left(-26423 d^2 e+6565 d^3+11089 d e^2-6623 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{700 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^2}",1,"-(1367*d - 293*e + (423*d - 1367*e)*x)/(700*(5*d^2 - 2*d*e + 3*e^2)*(3 + 2*x + 5*x^2)) + ((6565*d^3 - 26423*d^2*e + 11089*d*e^2 - 6623*e^3)*ArcTan[(1 + 5*x)/Sqrt[14]])/(700*Sqrt[14]*(5*d^2 - 2*d*e + 3*e^2)^2) + ((4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*Log[d + e*x])/(e*(5*d^2 - 2*d*e + 3*e^2)^2) - ((205*d^3 - 61*d^2*e + 23*d*e^2 + 14*e^3)*Log[3 + 2*x + 5*x^2])/(50*(5*d^2 - 2*d*e + 3*e^2)^2)","A",7,6,38,0.1579,1,"{1646, 1628, 634, 618, 204, 628}"
316,1,313,0,0.4979719,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{(d+e x)^2 \left(3+2 x+5 x^2\right)^2} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/((d + e*x)^2*(3 + 2*x + 5*x^2)^2),x]","-\frac{x \left(423 d^2-2734 d e+293 e^2\right)+1367 d^2-586 d e-703 e^2}{140 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{\left(-60 d^2 e^2-8 d^3 e+41 d^4+24 d e^3-5 e^4\right) \log \left(5 x^2+2 x+3\right)}{2 \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4}{e \left(5 d^2-2 d e+3 e^2\right)^2 (d+e x)}+\frac{\left(-60 d^2 e^2-8 d^3 e+41 d^4+24 d e^3-5 e^4\right) \log (d+e x)}{\left(5 d^2-2 d e+3 e^2\right)^3}+\frac{\left(4290 d^2 e^2-10044 d^3 e+1313 d^4+156 d e^3-271 e^4\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{28 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^3}","-\frac{x \left(423 d^2-2734 d e+293 e^2\right)+1367 d^2-586 d e-703 e^2}{140 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{\left(-60 d^2 e^2-8 d^3 e+41 d^4+24 d e^3-5 e^4\right) \log \left(5 x^2+2 x+3\right)}{2 \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4}{e \left(5 d^2-2 d e+3 e^2\right)^2 (d+e x)}+\frac{\left(-60 d^2 e^2-8 d^3 e+41 d^4+24 d e^3-5 e^4\right) \log (d+e x)}{\left(5 d^2-2 d e+3 e^2\right)^3}+\frac{\left(4290 d^2 e^2-10044 d^3 e+1313 d^4+156 d e^3-271 e^4\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{28 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^3}",1,"-((4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)/(e*(5*d^2 - 2*d*e + 3*e^2)^2*(d + e*x))) - (1367*d^2 - 586*d*e - 703*e^2 + (423*d^2 - 2734*d*e + 293*e^2)*x)/(140*(5*d^2 - 2*d*e + 3*e^2)^2*(3 + 2*x + 5*x^2)) + ((1313*d^4 - 10044*d^3*e + 4290*d^2*e^2 + 156*d*e^3 - 271*e^4)*ArcTan[(1 + 5*x)/Sqrt[14]])/(28*Sqrt[14]*(5*d^2 - 2*d*e + 3*e^2)^3) + ((41*d^4 - 8*d^3*e - 60*d^2*e^2 + 24*d*e^3 - 5*e^4)*Log[d + e*x])/(5*d^2 - 2*d*e + 3*e^2)^3 - ((41*d^4 - 8*d^3*e - 60*d^2*e^2 + 24*d*e^3 - 5*e^4)*Log[3 + 2*x + 5*x^2])/(2*(5*d^2 - 2*d*e + 3*e^2)^3)","A",7,6,38,0.1579,1,"{1646, 1628, 634, 618, 204, 628}"
317,1,412,0,0.7147535,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{(d+e x)^3 \left(3+2 x+5 x^2\right)^2} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/((d + e*x)^3*(3 + 2*x + 5*x^2)^2),x]","-\frac{x \left(-4101 d^2 e+423 d^3+879 d e^2+703 e^3\right)-879 d^2 e+1367 d^3-2109 d e^2+457 e^3}{28 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{\left(-846 d^3 e^2+396 d^2 e^3-19 d^4 e+205 d^5+57 d e^4-21 e^5\right) \log \left(5 x^2+2 x+3\right)}{2 \left(5 d^2-2 d e+3 e^2\right)^4}-\frac{-60 d^2 e^2-8 d^3 e+41 d^4+24 d e^3-5 e^4}{\left(5 d^2-2 d e+3 e^2\right)^3 (d+e x)}-\frac{3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4}{2 e \left(5 d^2-2 d e+3 e^2\right)^2 (d+e x)^2}+\frac{\left(-846 d^3 e^2+396 d^2 e^3-19 d^4 e+205 d^5+57 d e^4-21 e^5\right) \log (d+e x)}{\left(5 d^2-2 d e+3 e^2\right)^4}+\frac{\left(35022 d^3 e^2+42858 d^2 e^3-74017 d^4 e+6565 d^5-17247 d e^4+579 e^5\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{28 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^4}","-\frac{x \left(-4101 d^2 e+423 d^3+879 d e^2+703 e^3\right)-879 d^2 e+1367 d^3-2109 d e^2+457 e^3}{28 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{\left(-846 d^3 e^2+396 d^2 e^3-19 d^4 e+205 d^5+57 d e^4-21 e^5\right) \log \left(5 x^2+2 x+3\right)}{2 \left(5 d^2-2 d e+3 e^2\right)^4}-\frac{-60 d^2 e^2-8 d^3 e+41 d^4+24 d e^3-5 e^4}{\left(5 d^2-2 d e+3 e^2\right)^3 (d+e x)}-\frac{3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4}{2 e \left(5 d^2-2 d e+3 e^2\right)^2 (d+e x)^2}+\frac{\left(-846 d^3 e^2+396 d^2 e^3-19 d^4 e+205 d^5+57 d e^4-21 e^5\right) \log (d+e x)}{\left(5 d^2-2 d e+3 e^2\right)^4}+\frac{\left(35022 d^3 e^2+42858 d^2 e^3-74017 d^4 e+6565 d^5-17247 d e^4+579 e^5\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{28 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^4}",1,"-(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)/(2*e*(5*d^2 - 2*d*e + 3*e^2)^2*(d + e*x)^2) - (41*d^4 - 8*d^3*e - 60*d^2*e^2 + 24*d*e^3 - 5*e^4)/((5*d^2 - 2*d*e + 3*e^2)^3*(d + e*x)) - (1367*d^3 - 879*d^2*e - 2109*d*e^2 + 457*e^3 + (423*d^3 - 4101*d^2*e + 879*d*e^2 + 703*e^3)*x)/(28*(5*d^2 - 2*d*e + 3*e^2)^3*(3 + 2*x + 5*x^2)) + ((6565*d^5 - 74017*d^4*e + 35022*d^3*e^2 + 42858*d^2*e^3 - 17247*d*e^4 + 579*e^5)*ArcTan[(1 + 5*x)/Sqrt[14]])/(28*Sqrt[14]*(5*d^2 - 2*d*e + 3*e^2)^4) + ((205*d^5 - 19*d^4*e - 846*d^3*e^2 + 396*d^2*e^3 + 57*d*e^4 - 21*e^5)*Log[d + e*x])/(5*d^2 - 2*d*e + 3*e^2)^4 - ((205*d^5 - 19*d^4*e - 846*d^3*e^2 + 396*d^2*e^3 + 57*d*e^4 - 21*e^5)*Log[3 + 2*x + 5*x^2])/(2*(5*d^2 - 2*d*e + 3*e^2)^4)","A",7,6,38,0.1579,1,"{1646, 1628, 634, 618, 204, 628}"
318,1,171,0,0.3360161,"\int \frac{(d+e x)^3 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{\left(3+2 x+5 x^2\right)^3} \, dx","Int[((d + e*x)^3*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2)^3,x]","\frac{3 e \left(100 d^2-245 d e+47 e^2\right) \log \left(5 x^2+2 x+3\right)}{6250}+\frac{3 \left(-855175 d^2 e+353125 d^3+74085 d e^2+556349 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{4900000 \sqrt{14}}+\frac{e^2 x (83065 d-126009 e)}{980000}+\frac{(d+e x)^2 (x (11015 d+49177 e)+3 (11449 d-2105 e))}{196000 \left(5 x^2+2 x+3\right)}-\frac{(423 x+1367) (d+e x)^3}{7000 \left(5 x^2+2 x+3\right)^2}+\frac{2 e^3 x^2}{125}","\frac{3 e \left(100 d^2-245 d e+47 e^2\right) \log \left(5 x^2+2 x+3\right)}{6250}+\frac{3 \left(-855175 d^2 e+353125 d^3+74085 d e^2+556349 e^3\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{4900000 \sqrt{14}}+\frac{e^2 x (83065 d-126009 e)}{980000}+\frac{(d+e x)^2 (x (11015 d+49177 e)+3 (11449 d-2105 e))}{196000 \left(5 x^2+2 x+3\right)}-\frac{(423 x+1367) (d+e x)^3}{7000 \left(5 x^2+2 x+3\right)^2}+\frac{2 e^3 x^2}{125}",1,"((83065*d - 126009*e)*e^2*x)/980000 + (2*e^3*x^2)/125 - ((1367 + 423*x)*(d + e*x)^3)/(7000*(3 + 2*x + 5*x^2)^2) + ((d + e*x)^2*(3*(11449*d - 2105*e) + (11015*d + 49177*e)*x))/(196000*(3 + 2*x + 5*x^2)) + (3*(353125*d^3 - 855175*d^2*e + 74085*d*e^2 + 556349*e^3)*ArcTan[(1 + 5*x)/Sqrt[14]])/(4900000*Sqrt[14]) + (3*e*(100*d^2 - 245*d*e + 47*e^2)*Log[3 + 2*x + 5*x^2])/6250","A",8,6,38,0.1579,1,"{1644, 1628, 634, 618, 204, 628}"
319,1,134,0,0.2387416,"\int \frac{(d+e x)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right)}{\left(3+2 x+5 x^2\right)^3} \, dx","Int[((d + e*x)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2)^3,x]","\frac{\left(211875 d^2-342070 d e+14817 e^2\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{980000 \sqrt{14}}+\frac{(d+e x) (5 x (2203 d+8553 e)+34347 d-6413 e)}{196000 \left(5 x^2+2 x+3\right)}-\frac{(423 x+1367) (d+e x)^2}{7000 \left(5 x^2+2 x+3\right)^2}+\frac{e (40 d-49 e) \log \left(5 x^2+2 x+3\right)}{1250}+\frac{4 e^2 x}{125}","\frac{\left(211875 d^2-342070 d e+14817 e^2\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{980000 \sqrt{14}}+\frac{(d+e x) (5 x (2203 d+8553 e)+34347 d-6413 e)}{196000 \left(5 x^2+2 x+3\right)}-\frac{(423 x+1367) (d+e x)^2}{7000 \left(5 x^2+2 x+3\right)^2}+\frac{e (40 d-49 e) \log \left(5 x^2+2 x+3\right)}{1250}+\frac{4 e^2 x}{125}",1,"(4*e^2*x)/125 - ((1367 + 423*x)*(d + e*x)^2)/(7000*(3 + 2*x + 5*x^2)^2) + ((d + e*x)*(34347*d - 6413*e + 5*(2203*d + 8553*e)*x))/(196000*(3 + 2*x + 5*x^2)) + ((211875*d^2 - 342070*d*e + 14817*e^2)*ArcTan[(1 + 5*x)/Sqrt[14]])/(980000*Sqrt[14]) + ((40*d - 49*e)*e*Log[3 + 2*x + 5*x^2])/1250","A",8,6,38,0.1579,1,"{1644, 1657, 634, 618, 204, 628}"
320,1,103,0,0.1453505,"\int \frac{(d+e x) \left(2+x+3 x^2-5 x^3+4 x^4\right)}{\left(3+2 x+5 x^2\right)^3} \, dx","Int[((d + e*x)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2)^3,x]","-\frac{(423 x+1367) (d+e x)}{7000 \left(5 x^2+2 x+3\right)^2}+\frac{x (11015 d+36353 e)+34347 d-6511 e}{196000 \left(5 x^2+2 x+3\right)}+\frac{(42375 d-34207 e) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{196000 \sqrt{14}}+\frac{2}{125} e \log \left(5 x^2+2 x+3\right)","-\frac{(423 x+1367) (d+e x)}{7000 \left(5 x^2+2 x+3\right)^2}+\frac{x (11015 d+36353 e)+34347 d-6511 e}{196000 \left(5 x^2+2 x+3\right)}+\frac{(42375 d-34207 e) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{196000 \sqrt{14}}+\frac{2}{125} e \log \left(5 x^2+2 x+3\right)",1,"-((1367 + 423*x)*(d + e*x))/(7000*(3 + 2*x + 5*x^2)^2) + (34347*d - 6511*e + (11015*d + 36353*e)*x)/(196000*(3 + 2*x + 5*x^2)) + ((42375*d - 34207*e)*ArcTan[(1 + 5*x)/Sqrt[14]])/(196000*Sqrt[14]) + (2*e*Log[3 + 2*x + 5*x^2])/125","A",6,6,36,0.1667,1,"{1644, 1660, 634, 618, 204, 628}"
321,1,64,0,0.0497837,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{\left(3+2 x+5 x^2\right)^3} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/(3 + 2*x + 5*x^2)^3,x]","-\frac{423 x+1367}{7000 \left(5 x^2+2 x+3\right)^2}+\frac{11015 x+34347}{196000 \left(5 x^2+2 x+3\right)}+\frac{339 \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1568 \sqrt{14}}","-\frac{423 x+1367}{7000 \left(5 x^2+2 x+3\right)^2}+\frac{11015 x+34347}{196000 \left(5 x^2+2 x+3\right)}+\frac{339 \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1568 \sqrt{14}}",1,"-(1367 + 423*x)/(7000*(3 + 2*x + 5*x^2)^2) + (34347 + 11015*x)/(196000*(3 + 2*x + 5*x^2)) + (339*ArcTan[(1 + 5*x)/Sqrt[14]])/(1568*Sqrt[14])","A",5,4,31,0.1290,1,"{1660, 12, 618, 204}"
322,1,329,0,0.4960075,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{(d+e x) \left(3+2 x+5 x^2\right)^3} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/((d + e*x)*(3 + 2*x + 5*x^2)^3),x]","-\frac{x (423 d-1367 e)+1367 d-293 e}{1400 \left(5 x^2+2 x+3\right)^2 \left(5 d^2-2 d e+3 e^2\right)}+\frac{25 x \left(-9033 d^2 e+2203 d^3+3635 d e^2-1829 e^3\right)-92989 d^2 e+171735 d^3+36207 d e^2+1831 e^3}{39200 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{e \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log \left(5 x^2+2 x+3\right)}{2 \left(5 d^2-2 d e+3 e^2\right)^3}+\frac{e \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{\left(5 d^2-2 d e+3 e^2\right)^3}+\frac{\left(58530 d^3 e^2-56058 d^2 e^3-16643 d^4 e+42375 d^5+31811 d e^4-8623 e^5\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1568 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^3}","-\frac{x (423 d-1367 e)+1367 d-293 e}{1400 \left(5 x^2+2 x+3\right)^2 \left(5 d^2-2 d e+3 e^2\right)}+\frac{25 x \left(-9033 d^2 e+2203 d^3+3635 d e^2-1829 e^3\right)-92989 d^2 e+171735 d^3+36207 d e^2+1831 e^3}{39200 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{e \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log \left(5 x^2+2 x+3\right)}{2 \left(5 d^2-2 d e+3 e^2\right)^3}+\frac{e \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) \log (d+e x)}{\left(5 d^2-2 d e+3 e^2\right)^3}+\frac{\left(58530 d^3 e^2-56058 d^2 e^3-16643 d^4 e+42375 d^5+31811 d e^4-8623 e^5\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1568 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^3}",1,"-(1367*d - 293*e + (423*d - 1367*e)*x)/(1400*(5*d^2 - 2*d*e + 3*e^2)*(3 + 2*x + 5*x^2)^2) + (171735*d^3 - 92989*d^2*e + 36207*d*e^2 + 1831*e^3 + 25*(2203*d^3 - 9033*d^2*e + 3635*d*e^2 - 1829*e^3)*x)/(39200*(5*d^2 - 2*d*e + 3*e^2)^2*(3 + 2*x + 5*x^2)) + ((42375*d^5 - 16643*d^4*e + 58530*d^3*e^2 - 56058*d^2*e^3 + 31811*d*e^4 - 8623*e^5)*ArcTan[(1 + 5*x)/Sqrt[14]])/(1568*Sqrt[14]*(5*d^2 - 2*d*e + 3*e^2)^3) + (e*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*Log[d + e*x])/(5*d^2 - 2*d*e + 3*e^2)^3 - (e*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*Log[3 + 2*x + 5*x^2])/(2*(5*d^2 - 2*d*e + 3*e^2)^3)","A",8,6,38,0.1579,1,"{1646, 800, 634, 618, 204, 628}"
323,1,443,0,0.8926803,"\int \frac{2+x+3 x^2-5 x^3+4 x^4}{(d+e x)^2 \left(3+2 x+5 x^2\right)^3} \, dx","Int[(2 + x + 3*x^2 - 5*x^3 + 4*x^4)/((d + e*x)^2*(3 + 2*x + 5*x^2)^3),x]","\frac{5 x \left(34698 d^2 e^2-85924 d^3 e+11015 d^4+10348 d e^3-3589 e^4\right)-200502 d^2 e^2-117284 d^3 e+171735 d^4+104428 d e^3-23189 e^4}{7840 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{x \left(423 d^2-2734 d e+293 e^2\right)+1367 d^2-586 d e-703 e^2}{280 \left(5 x^2+2 x+3\right)^2 \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{e \left(12 d^3 e^2-76 d^2 e^3+83 d^4 e+40 d^5+46 d e^4-9 e^5\right) \log \left(5 x^2+2 x+3\right)}{2 \left(5 d^2-2 d e+3 e^2\right)^4}-\frac{e \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{\left(5 d^2-2 d e+3 e^2\right)^3 (d+e x)}+\frac{e \left(12 d^3 e^2-76 d^2 e^3+83 d^4 e+40 d^5+46 d e^4-9 e^5\right) \log (d+e x)}{\left(5 d^2-2 d e+3 e^2\right)^4}+\frac{\left(209039 d^4 e^2-921444 d^3 e^3+380621 d^2 e^4+3070 d^5 e+211875 d^6-49586 d e^5-43695 e^6\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1568 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^4}","\frac{5 x \left(34698 d^2 e^2-85924 d^3 e+11015 d^4+10348 d e^3-3589 e^4\right)-200502 d^2 e^2-117284 d^3 e+171735 d^4+104428 d e^3-23189 e^4}{7840 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)^3}-\frac{x \left(423 d^2-2734 d e+293 e^2\right)+1367 d^2-586 d e-703 e^2}{280 \left(5 x^2+2 x+3\right)^2 \left(5 d^2-2 d e+3 e^2\right)^2}-\frac{e \left(12 d^3 e^2-76 d^2 e^3+83 d^4 e+40 d^5+46 d e^4-9 e^5\right) \log \left(5 x^2+2 x+3\right)}{2 \left(5 d^2-2 d e+3 e^2\right)^4}-\frac{e \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right)}{\left(5 d^2-2 d e+3 e^2\right)^3 (d+e x)}+\frac{e \left(12 d^3 e^2-76 d^2 e^3+83 d^4 e+40 d^5+46 d e^4-9 e^5\right) \log (d+e x)}{\left(5 d^2-2 d e+3 e^2\right)^4}+\frac{\left(209039 d^4 e^2-921444 d^3 e^3+380621 d^2 e^4+3070 d^5 e+211875 d^6-49586 d e^5-43695 e^6\right) \tan ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1568 \sqrt{14} \left(5 d^2-2 d e+3 e^2\right)^4}",1,"-((e*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4))/((5*d^2 - 2*d*e + 3*e^2)^3*(d + e*x))) - (1367*d^2 - 586*d*e - 703*e^2 + (423*d^2 - 2734*d*e + 293*e^2)*x)/(280*(5*d^2 - 2*d*e + 3*e^2)^2*(3 + 2*x + 5*x^2)^2) + (171735*d^4 - 117284*d^3*e - 200502*d^2*e^2 + 104428*d*e^3 - 23189*e^4 + 5*(11015*d^4 - 85924*d^3*e + 34698*d^2*e^2 + 10348*d*e^3 - 3589*e^4)*x)/(7840*(5*d^2 - 2*d*e + 3*e^2)^3*(3 + 2*x + 5*x^2)) + ((211875*d^6 + 3070*d^5*e + 209039*d^4*e^2 - 921444*d^3*e^3 + 380621*d^2*e^4 - 49586*d*e^5 - 43695*e^6)*ArcTan[(1 + 5*x)/Sqrt[14]])/(1568*Sqrt[14]*(5*d^2 - 2*d*e + 3*e^2)^4) + (e*(40*d^5 + 83*d^4*e + 12*d^3*e^2 - 76*d^2*e^3 + 46*d*e^4 - 9*e^5)*Log[d + e*x])/(5*d^2 - 2*d*e + 3*e^2)^4 - (e*(40*d^5 + 83*d^4*e + 12*d^3*e^2 - 76*d^2*e^3 + 46*d*e^4 - 9*e^5)*Log[3 + 2*x + 5*x^2])/(2*(5*d^2 - 2*d*e + 3*e^2)^4)","A",8,6,38,0.1579,1,"{1646, 1628, 634, 618, 204, 628}"
324,1,143,0,0.1554204,"\int (5+2 x) \sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right) \, dx","Int[(5 + 2*x)*Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4),x]","\frac{5}{112} \left(2 x^2-x+3\right)^{3/2} (2 x+5)^4-\frac{823 \left(2 x^2-x+3\right)^{3/2} (2 x+5)^3}{1344}+\frac{11433 \left(2 x^2-x+3\right)^{3/2} (2 x+5)^2}{4480}-\frac{(295276 x+1005757) \left(2 x^2-x+3\right)^{3/2}}{71680}-\frac{51435 (1-4 x) \sqrt{2 x^2-x+3}}{32768}-\frac{1183005 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{65536 \sqrt{2}}","\frac{5}{112} \left(2 x^2-x+3\right)^{3/2} (2 x+5)^4-\frac{823 \left(2 x^2-x+3\right)^{3/2} (2 x+5)^3}{1344}+\frac{11433 \left(2 x^2-x+3\right)^{3/2} (2 x+5)^2}{4480}-\frac{(295276 x+1005757) \left(2 x^2-x+3\right)^{3/2}}{71680}-\frac{51435 (1-4 x) \sqrt{2 x^2-x+3}}{32768}-\frac{1183005 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{65536 \sqrt{2}}",1,"(-51435*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/32768 + (11433*(5 + 2*x)^2*(3 - x + 2*x^2)^(3/2))/4480 - (823*(5 + 2*x)^3*(3 - x + 2*x^2)^(3/2))/1344 + (5*(5 + 2*x)^4*(3 - x + 2*x^2)^(3/2))/112 - ((1005757 + 295276*x)*(3 - x + 2*x^2)^(3/2))/71680 - (1183005*ArcSinh[(1 - 4*x)/Sqrt[23]])/(65536*Sqrt[2])","A",7,5,38,0.1316,1,"{1653, 779, 612, 619, 215}"
325,1,124,0,0.0921227,"\int \sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right) \, dx","Int[Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4),x]","\frac{5}{12} \left(2 x^2-x+3\right)^{3/2} x^3+\frac{7}{80} \left(2 x^2-x+3\right)^{3/2} x^2-\frac{71 \left(2 x^2-x+3\right)^{3/2} x}{1280}+\frac{287 \left(2 x^2-x+3\right)^{3/2}}{5120}-\frac{4609 (1-4 x) \sqrt{2 x^2-x+3}}{16384}-\frac{106007 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32768 \sqrt{2}}","\frac{5}{12} \left(2 x^2-x+3\right)^{3/2} x^3+\frac{7}{80} \left(2 x^2-x+3\right)^{3/2} x^2-\frac{71 \left(2 x^2-x+3\right)^{3/2} x}{1280}+\frac{287 \left(2 x^2-x+3\right)^{3/2}}{5120}-\frac{4609 (1-4 x) \sqrt{2 x^2-x+3}}{16384}-\frac{106007 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32768 \sqrt{2}}",1,"(-4609*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/16384 + (287*(3 - x + 2*x^2)^(3/2))/5120 - (71*x*(3 - x + 2*x^2)^(3/2))/1280 + (7*x^2*(3 - x + 2*x^2)^(3/2))/80 + (5*x^3*(3 - x + 2*x^2)^(3/2))/12 - (106007*ArcSinh[(1 - 4*x)/Sqrt[23]])/(32768*Sqrt[2])","A",7,5,33,0.1515,1,"{1661, 640, 612, 619, 215}"
326,1,149,0,0.2404358,"\int \frac{\sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right)}{5+2 x} \, dx","Int[(Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x),x]","\frac{1}{16} \left(2 x^2-x+3\right)^{3/2} (2 x+5)^2-\frac{127}{128} \left(2 x^2-x+3\right)^{3/2} (2 x+5)+\frac{4535}{768} \left(2 x^2-x+3\right)^{3/2}+\frac{(489587-80844 x) \sqrt{2 x^2-x+3}}{4096}-\frac{11001 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{16 \sqrt{2}}+\frac{5627989 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8192 \sqrt{2}}","\frac{1}{16} \left(2 x^2-x+3\right)^{3/2} (2 x+5)^2-\frac{127}{128} \left(2 x^2-x+3\right)^{3/2} (2 x+5)+\frac{4535}{768} \left(2 x^2-x+3\right)^{3/2}+\frac{(489587-80844 x) \sqrt{2 x^2-x+3}}{4096}-\frac{11001 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{16 \sqrt{2}}+\frac{5627989 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8192 \sqrt{2}}",1,"((489587 - 80844*x)*Sqrt[3 - x + 2*x^2])/4096 + (4535*(3 - x + 2*x^2)^(3/2))/768 - (127*(5 + 2*x)*(3 - x + 2*x^2)^(3/2))/128 + ((5 + 2*x)^2*(3 - x + 2*x^2)^(3/2))/16 + (5627989*ArcSinh[(1 - 4*x)/Sqrt[23]])/(8192*Sqrt[2]) - (11001*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(16*Sqrt[2])","A",9,7,40,0.1750,1,"{1653, 814, 843, 619, 215, 724, 206}"
327,1,149,0,0.2366454,"\int \frac{\sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^2} \, dx","Int[(Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^2,x]","\frac{5}{64} (2 x+5) \left(2 x^2-x+3\right)^{3/2}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{576 (2 x+5)}-\frac{541}{384} \left(2 x^2-x+3\right)^{3/2}-\frac{(1996953-333380 x) \sqrt{2 x^2-x+3}}{18432}+\frac{239201 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{384 \sqrt{2}}-\frac{2551847 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4096 \sqrt{2}}","\frac{5}{64} (2 x+5) \left(2 x^2-x+3\right)^{3/2}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{576 (2 x+5)}-\frac{541}{384} \left(2 x^2-x+3\right)^{3/2}-\frac{(1996953-333380 x) \sqrt{2 x^2-x+3}}{18432}+\frac{239201 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{384 \sqrt{2}}-\frac{2551847 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4096 \sqrt{2}}",1,"-((1996953 - 333380*x)*Sqrt[3 - x + 2*x^2])/18432 - (541*(3 - x + 2*x^2)^(3/2))/384 - (3667*(3 - x + 2*x^2)^(3/2))/(576*(5 + 2*x)) + (5*(5 + 2*x)*(3 - x + 2*x^2)^(3/2))/64 - (2551847*ArcSinh[(1 - 4*x)/Sqrt[23]])/(4096*Sqrt[2]) + (239201*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(384*Sqrt[2])","A",9,8,40,0.2000,1,"{1650, 1653, 814, 843, 619, 215, 724, 206}"
328,1,151,0,0.2283585,"\int \frac{\sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^3} \, dx","Int[(Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^3,x]","\frac{357391 \left(2 x^2-x+3\right)^{3/2}}{82944 (2 x+5)}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{1152 (2 x+5)^2}+\frac{5}{48} \left(2 x^2-x+3\right)^{3/2}+\frac{5 (661065-110099 x) \sqrt{2 x^2-x+3}}{82944}-\frac{12670805 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{55296 \sqrt{2}}+\frac{117315 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{512 \sqrt{2}}","\frac{357391 \left(2 x^2-x+3\right)^{3/2}}{82944 (2 x+5)}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{1152 (2 x+5)^2}+\frac{5}{48} \left(2 x^2-x+3\right)^{3/2}+\frac{5 (661065-110099 x) \sqrt{2 x^2-x+3}}{82944}-\frac{12670805 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{55296 \sqrt{2}}+\frac{117315 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{512 \sqrt{2}}",1,"(5*(661065 - 110099*x)*Sqrt[3 - x + 2*x^2])/82944 + (5*(3 - x + 2*x^2)^(3/2))/48 - (3667*(3 - x + 2*x^2)^(3/2))/(1152*(5 + 2*x)^2) + (357391*(3 - x + 2*x^2)^(3/2))/(82944*(5 + 2*x)) + (117315*ArcSinh[(1 - 4*x)/Sqrt[23]])/(512*Sqrt[2]) - (12670805*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(55296*Sqrt[2])","A",9,8,40,0.2000,1,"{1650, 1653, 814, 843, 619, 215, 724, 206}"
329,1,158,0,0.2258102,"\int \frac{\sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^4} \, dx","Int[(Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^4,x]","-\frac{6467659 \left(2 x^2-x+3\right)^{3/2}}{5971968 (2 x+5)}+\frac{158527 \left(2 x^2-x+3\right)^{3/2}}{82944 (2 x+5)^2}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{1728 (2 x+5)^3}-\frac{(44378877-7400779 x) \sqrt{2 x^2-x+3}}{5971968}+\frac{170114729 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{3981312 \sqrt{2}}-\frac{10939 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{256 \sqrt{2}}","-\frac{6467659 \left(2 x^2-x+3\right)^{3/2}}{5971968 (2 x+5)}+\frac{158527 \left(2 x^2-x+3\right)^{3/2}}{82944 (2 x+5)^2}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{1728 (2 x+5)^3}-\frac{(44378877-7400779 x) \sqrt{2 x^2-x+3}}{5971968}+\frac{170114729 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{3981312 \sqrt{2}}-\frac{10939 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{256 \sqrt{2}}",1,"-((44378877 - 7400779*x)*Sqrt[3 - x + 2*x^2])/5971968 - (3667*(3 - x + 2*x^2)^(3/2))/(1728*(5 + 2*x)^3) + (158527*(3 - x + 2*x^2)^(3/2))/(82944*(5 + 2*x)^2) - (6467659*(3 - x + 2*x^2)^(3/2))/(5971968*(5 + 2*x)) - (10939*ArcSinh[(1 - 4*x)/Sqrt[23]])/(256*Sqrt[2]) + (170114729*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(3981312*Sqrt[2])","A",9,7,40,0.1750,1,"{1650, 814, 843, 619, 215, 724, 206}"
330,1,165,0,0.2340987,"\int \frac{\sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^5} \, dx","Int[(Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^5,x]","-\frac{9363383 \left(2 x^2-x+3\right)^{3/2}}{23887872 (2 x+5)^2}+\frac{593771 \left(2 x^2-x+3\right)^{3/2}}{497664 (2 x+5)^3}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{2304 (2 x+5)^4}+\frac{7 (9616196 x+52836655) \sqrt{2 x^2-x+3}}{95551488 (2 x+5)}-\frac{4640586097 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1146617856 \sqrt{2}}+\frac{259 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{2}}","-\frac{9363383 \left(2 x^2-x+3\right)^{3/2}}{23887872 (2 x+5)^2}+\frac{593771 \left(2 x^2-x+3\right)^{3/2}}{497664 (2 x+5)^3}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{2304 (2 x+5)^4}+\frac{7 (9616196 x+52836655) \sqrt{2 x^2-x+3}}{95551488 (2 x+5)}-\frac{4640586097 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1146617856 \sqrt{2}}+\frac{259 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{2}}",1,"(7*(52836655 + 9616196*x)*Sqrt[3 - x + 2*x^2])/(95551488*(5 + 2*x)) - (3667*(3 - x + 2*x^2)^(3/2))/(2304*(5 + 2*x)^4) + (593771*(3 - x + 2*x^2)^(3/2))/(497664*(5 + 2*x)^3) - (9363383*(3 - x + 2*x^2)^(3/2))/(23887872*(5 + 2*x)^2) + (259*ArcSinh[(1 - 4*x)/Sqrt[23]])/(64*Sqrt[2]) - (4640586097*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(1146617856*Sqrt[2])","A",9,7,40,0.1750,1,"{1650, 812, 843, 619, 215, 724, 206}"
331,1,165,0,0.2285302,"\int \frac{\sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^6} \, dx","Int[(Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^6,x]","-\frac{38732321 \left(2 x^2-x+3\right)^{3/2}}{179159040 (2 x+5)^3}+\frac{711961 \left(2 x^2-x+3\right)^{3/2}}{829440 (2 x+5)^4}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{2880 (2 x+5)^5}-\frac{(3174439702 x+4583087983) \sqrt{2 x^2-x+3}}{6879707136 (2 x+5)^2}+\frac{12895597463 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{82556485632 \sqrt{2}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32 \sqrt{2}}","-\frac{38732321 \left(2 x^2-x+3\right)^{3/2}}{179159040 (2 x+5)^3}+\frac{711961 \left(2 x^2-x+3\right)^{3/2}}{829440 (2 x+5)^4}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{2880 (2 x+5)^5}-\frac{(3174439702 x+4583087983) \sqrt{2 x^2-x+3}}{6879707136 (2 x+5)^2}+\frac{12895597463 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{82556485632 \sqrt{2}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32 \sqrt{2}}",1,"-((4583087983 + 3174439702*x)*Sqrt[3 - x + 2*x^2])/(6879707136*(5 + 2*x)^2) - (3667*(3 - x + 2*x^2)^(3/2))/(2880*(5 + 2*x)^5) + (711961*(3 - x + 2*x^2)^(3/2))/(829440*(5 + 2*x)^4) - (38732321*(3 - x + 2*x^2)^(3/2))/(179159040*(5 + 2*x)^3) - (5*ArcSinh[(1 - 4*x)/Sqrt[23]])/(32*Sqrt[2]) + (12895597463*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(82556485632*Sqrt[2])","A",9,7,40,0.1750,1,"{1650, 810, 843, 619, 215, 724, 206}"
332,1,169,0,0.2182436,"\int \frac{\sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^7} \, dx","Int[(Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^7,x]","\frac{87677717 \left(2 x^2-x+3\right)^{3/2}}{8599633920 (2 x+5)^3}-\frac{5703277 \left(2 x^2-x+3\right)^{3/2}}{39813120 (2 x+5)^4}+\frac{92239 \left(2 x^2-x+3\right)^{3/2}}{138240 (2 x+5)^5}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{3456 (2 x+5)^6}-\frac{1172725 (17-22 x) \sqrt{2 x^2-x+3}}{330225942528 (2 x+5)^2}-\frac{26972675 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{3962711310336 \sqrt{2}}","\frac{87677717 \left(2 x^2-x+3\right)^{3/2}}{8599633920 (2 x+5)^3}-\frac{5703277 \left(2 x^2-x+3\right)^{3/2}}{39813120 (2 x+5)^4}+\frac{92239 \left(2 x^2-x+3\right)^{3/2}}{138240 (2 x+5)^5}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{3456 (2 x+5)^6}-\frac{1172725 (17-22 x) \sqrt{2 x^2-x+3}}{330225942528 (2 x+5)^2}-\frac{26972675 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{3962711310336 \sqrt{2}}",1,"(-1172725*(17 - 22*x)*Sqrt[3 - x + 2*x^2])/(330225942528*(5 + 2*x)^2) - (3667*(3 - x + 2*x^2)^(3/2))/(3456*(5 + 2*x)^6) + (92239*(3 - x + 2*x^2)^(3/2))/(138240*(5 + 2*x)^5) - (5703277*(3 - x + 2*x^2)^(3/2))/(39813120*(5 + 2*x)^4) + (87677717*(3 - x + 2*x^2)^(3/2))/(8599633920*(5 + 2*x)^3) - (26972675*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(3962711310336*Sqrt[2])","A",7,5,40,0.1250,1,"{1650, 806, 720, 724, 206}"
333,1,194,0,0.2675029,"\int \frac{\sqrt{3-x+2 x^2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^8} \, dx","Int[(Sqrt[3 - x + 2*x^2]*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^8,x]","\frac{246159769 \left(2 x^2-x+3\right)^{3/2}}{866843099136 (2 x+5)^3}+\frac{19414831 \left(2 x^2-x+3\right)^{3/2}}{4013162496 (2 x+5)^4}-\frac{1464037 \left(2 x^2-x+3\right)^{3/2}}{13934592 (2 x+5)^5}+\frac{948341 \left(2 x^2-x+3\right)^{3/2}}{1741824 (2 x+5)^6}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{4032 (2 x+5)^7}-\frac{12568315 (17-22 x) \sqrt{2 x^2-x+3}}{23776267862016 (2 x+5)^2}-\frac{289071245 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{285315214344192 \sqrt{2}}","\frac{246159769 \left(2 x^2-x+3\right)^{3/2}}{866843099136 (2 x+5)^3}+\frac{19414831 \left(2 x^2-x+3\right)^{3/2}}{4013162496 (2 x+5)^4}-\frac{1464037 \left(2 x^2-x+3\right)^{3/2}}{13934592 (2 x+5)^5}+\frac{948341 \left(2 x^2-x+3\right)^{3/2}}{1741824 (2 x+5)^6}-\frac{3667 \left(2 x^2-x+3\right)^{3/2}}{4032 (2 x+5)^7}-\frac{12568315 (17-22 x) \sqrt{2 x^2-x+3}}{23776267862016 (2 x+5)^2}-\frac{289071245 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{285315214344192 \sqrt{2}}",1,"(-12568315*(17 - 22*x)*Sqrt[3 - x + 2*x^2])/(23776267862016*(5 + 2*x)^2) - (3667*(3 - x + 2*x^2)^(3/2))/(4032*(5 + 2*x)^7) + (948341*(3 - x + 2*x^2)^(3/2))/(1741824*(5 + 2*x)^6) - (1464037*(3 - x + 2*x^2)^(3/2))/(13934592*(5 + 2*x)^5) + (19414831*(3 - x + 2*x^2)^(3/2))/(4013162496*(5 + 2*x)^4) + (246159769*(3 - x + 2*x^2)^(3/2))/(866843099136*(5 + 2*x)^3) - (289071245*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(285315214344192*Sqrt[2])","A",8,6,40,0.1500,1,"{1650, 834, 806, 720, 724, 206}"
334,1,166,0,0.1944053,"\int (5+2 x) \left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right) \, dx","Int[(5 + 2*x)*(3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4),x]","\frac{5}{144} \left(2 x^2-x+3\right)^{5/2} (2 x+5)^4-\frac{1121 \left(2 x^2-x+3\right)^{5/2} (2 x+5)^3}{2304}+\frac{69415 \left(2 x^2-x+3\right)^{5/2} (2 x+5)^2}{32256}-\frac{3 (215900 x+661397) \left(2 x^2-x+3\right)^{5/2}}{143360}-\frac{92727 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{131072}-\frac{6398163 (1-4 x) \sqrt{2 x^2-x+3}}{2097152}-\frac{147157749 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4194304 \sqrt{2}}","\frac{5}{144} \left(2 x^2-x+3\right)^{5/2} (2 x+5)^4-\frac{1121 \left(2 x^2-x+3\right)^{5/2} (2 x+5)^3}{2304}+\frac{69415 \left(2 x^2-x+3\right)^{5/2} (2 x+5)^2}{32256}-\frac{3 (215900 x+661397) \left(2 x^2-x+3\right)^{5/2}}{143360}-\frac{92727 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{131072}-\frac{6398163 (1-4 x) \sqrt{2 x^2-x+3}}{2097152}-\frac{147157749 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4194304 \sqrt{2}}",1,"(-6398163*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/2097152 - (92727*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/131072 + (69415*(5 + 2*x)^2*(3 - x + 2*x^2)^(5/2))/32256 - (1121*(5 + 2*x)^3*(3 - x + 2*x^2)^(5/2))/2304 + (5*(5 + 2*x)^4*(3 - x + 2*x^2)^(5/2))/144 - (3*(661397 + 215900*x)*(3 - x + 2*x^2)^(5/2))/143360 - (147157749*ArcSinh[(1 - 4*x)/Sqrt[23]])/(4194304*Sqrt[2])","A",8,5,38,0.1316,1,"{1653, 779, 612, 619, 215}"
335,1,147,0,0.1214558,"\int \left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right) \, dx","Int[(3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4),x]","\frac{5}{16} \left(2 x^2-x+3\right)^{5/2} x^3+\frac{23}{448} \left(2 x^2-x+3\right)^{5/2} x^2+\frac{125 \left(2 x^2-x+3\right)^{5/2} x}{3584}+\frac{1167 \left(2 x^2-x+3\right)^{5/2}}{14336}-\frac{8597 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{65536}-\frac{593193 (1-4 x) \sqrt{2 x^2-x+3}}{1048576}-\frac{13643439 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2097152 \sqrt{2}}","\frac{5}{16} \left(2 x^2-x+3\right)^{5/2} x^3+\frac{23}{448} \left(2 x^2-x+3\right)^{5/2} x^2+\frac{125 \left(2 x^2-x+3\right)^{5/2} x}{3584}+\frac{1167 \left(2 x^2-x+3\right)^{5/2}}{14336}-\frac{8597 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{65536}-\frac{593193 (1-4 x) \sqrt{2 x^2-x+3}}{1048576}-\frac{13643439 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2097152 \sqrt{2}}",1,"(-593193*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/1048576 - (8597*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/65536 + (1167*(3 - x + 2*x^2)^(5/2))/14336 + (125*x*(3 - x + 2*x^2)^(5/2))/3584 + (23*x^2*(3 - x + 2*x^2)^(5/2))/448 + (5*x^3*(3 - x + 2*x^2)^(5/2))/16 - (13643439*ArcSinh[(1 - 4*x)/Sqrt[23]])/(2097152*Sqrt[2])","A",8,5,33,0.1515,1,"{1661, 640, 612, 619, 215}"
336,1,172,0,0.2681629,"\int \frac{\left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right)}{5+2 x} \, dx","Int[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x),x]","\frac{5}{112} (2 x+5)^2 \left(2 x^2-x+3\right)^{5/2}-\frac{311}{448} (2 x+5) \left(2 x^2-x+3\right)^{5/2}+\frac{3505}{896} \left(2 x^2-x+3\right)^{5/2}+\frac{(500141-123060 x) \left(2 x^2-x+3\right)^{3/2}}{12288}+\frac{(141051019-23482924 x) \sqrt{2 x^2-x+3}}{65536}-\frac{99009 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{8 \sqrt{2}}+\frac{1622009981 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{131072 \sqrt{2}}","\frac{5}{112} (2 x+5)^2 \left(2 x^2-x+3\right)^{5/2}-\frac{311}{448} (2 x+5) \left(2 x^2-x+3\right)^{5/2}+\frac{3505}{896} \left(2 x^2-x+3\right)^{5/2}+\frac{(500141-123060 x) \left(2 x^2-x+3\right)^{3/2}}{12288}+\frac{(141051019-23482924 x) \sqrt{2 x^2-x+3}}{65536}-\frac{99009 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{8 \sqrt{2}}+\frac{1622009981 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{131072 \sqrt{2}}",1,"((141051019 - 23482924*x)*Sqrt[3 - x + 2*x^2])/65536 + ((500141 - 123060*x)*(3 - x + 2*x^2)^(3/2))/12288 + (3505*(3 - x + 2*x^2)^(5/2))/896 - (311*(5 + 2*x)*(3 - x + 2*x^2)^(5/2))/448 + (5*(5 + 2*x)^2*(3 - x + 2*x^2)^(5/2))/112 + (1622009981*ArcSinh[(1 - 4*x)/Sqrt[23]])/(131072*Sqrt[2]) - (99009*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(8*Sqrt[2])","A",10,7,40,0.1750,1,"{1653, 814, 843, 619, 215, 724, 206}"
337,1,172,0,0.2816928,"\int \frac{\left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^2} \, dx","Int[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^2,x]","\frac{5}{96} (2 x+5) \left(2 x^2-x+3\right)^{5/2}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{576 (2 x+5)}-\frac{839}{960} \left(2 x^2-x+3\right)^{5/2}-\frac{(909513-226052 x) \left(2 x^2-x+3\right)^{3/2}}{18432}-\frac{(85448933-14243732 x) \sqrt{2 x^2-x+3}}{32768}+\frac{959625 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{64 \sqrt{2}}-\frac{982669459 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{65536 \sqrt{2}}","\frac{5}{96} (2 x+5) \left(2 x^2-x+3\right)^{5/2}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{576 (2 x+5)}-\frac{839}{960} \left(2 x^2-x+3\right)^{5/2}-\frac{(909513-226052 x) \left(2 x^2-x+3\right)^{3/2}}{18432}-\frac{(85448933-14243732 x) \sqrt{2 x^2-x+3}}{32768}+\frac{959625 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{64 \sqrt{2}}-\frac{982669459 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{65536 \sqrt{2}}",1,"-((85448933 - 14243732*x)*Sqrt[3 - x + 2*x^2])/32768 - ((909513 - 226052*x)*(3 - x + 2*x^2)^(3/2))/18432 - (839*(3 - x + 2*x^2)^(5/2))/960 - (3667*(3 - x + 2*x^2)^(5/2))/(576*(5 + 2*x)) + (5*(5 + 2*x)*(3 - x + 2*x^2)^(5/2))/96 - (982669459*ArcSinh[(1 - 4*x)/Sqrt[23]])/(65536*Sqrt[2]) + (959625*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(64*Sqrt[2])","A",10,8,40,0.2000,1,"{1650, 1653, 814, 843, 619, 215, 724, 206}"
338,1,174,0,0.2727232,"\int \frac{\left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^3} \, dx","Int[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^3,x]","\frac{438065 \left(2 x^2-x+3\right)^{5/2}}{82944 (2 x+5)}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{1152 (2 x+5)^2}+\frac{1}{16} \left(2 x^2-x+3\right)^{5/2}+\frac{(2154633-534617 x) \left(2 x^2-x+3\right)^{3/2}}{82944}+\frac{(33741483-5623292 x) \sqrt{2 x^2-x+3}}{24576}-\frac{8083915 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1024 \sqrt{2}}+\frac{129342063 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16384 \sqrt{2}}","\frac{438065 \left(2 x^2-x+3\right)^{5/2}}{82944 (2 x+5)}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{1152 (2 x+5)^2}+\frac{1}{16} \left(2 x^2-x+3\right)^{5/2}+\frac{(2154633-534617 x) \left(2 x^2-x+3\right)^{3/2}}{82944}+\frac{(33741483-5623292 x) \sqrt{2 x^2-x+3}}{24576}-\frac{8083915 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1024 \sqrt{2}}+\frac{129342063 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16384 \sqrt{2}}",1,"((33741483 - 5623292*x)*Sqrt[3 - x + 2*x^2])/24576 + ((2154633 - 534617*x)*(3 - x + 2*x^2)^(3/2))/82944 + (3 - x + 2*x^2)^(5/2)/16 - (3667*(3 - x + 2*x^2)^(5/2))/(1152*(5 + 2*x)^2) + (438065*(3 - x + 2*x^2)^(5/2))/(82944*(5 + 2*x)) + (129342063*ArcSinh[(1 - 4*x)/Sqrt[23]])/(16384*Sqrt[2]) - (8083915*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(1024*Sqrt[2])","A",10,8,40,0.2000,1,"{1650, 1653, 814, 843, 619, 215, 724, 206}"
339,1,181,0,0.2671448,"\int \frac{\left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^4} \, dx","Int[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^4,x]","-\frac{32865365 \left(2 x^2-x+3\right)^{5/2}}{17915904 (2 x+5)}+\frac{556255 \left(2 x^2-x+3\right)^{5/2}}{248832 (2 x+5)^2}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{1728 (2 x+5)^3}-\frac{(138006843-34265045 x) \left(2 x^2-x+3\right)^{3/2}}{17915904}-\frac{(135068604-22512089 x) \sqrt{2 x^2-x+3}}{331776}+\frac{517762327 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{221184 \sqrt{2}}-\frac{19176431 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8192 \sqrt{2}}","-\frac{32865365 \left(2 x^2-x+3\right)^{5/2}}{17915904 (2 x+5)}+\frac{556255 \left(2 x^2-x+3\right)^{5/2}}{248832 (2 x+5)^2}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{1728 (2 x+5)^3}-\frac{(138006843-34265045 x) \left(2 x^2-x+3\right)^{3/2}}{17915904}-\frac{(135068604-22512089 x) \sqrt{2 x^2-x+3}}{331776}+\frac{517762327 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{221184 \sqrt{2}}-\frac{19176431 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8192 \sqrt{2}}",1,"-((135068604 - 22512089*x)*Sqrt[3 - x + 2*x^2])/331776 - ((138006843 - 34265045*x)*(3 - x + 2*x^2)^(3/2))/17915904 - (3667*(3 - x + 2*x^2)^(5/2))/(1728*(5 + 2*x)^3) + (556255*(3 - x + 2*x^2)^(5/2))/(248832*(5 + 2*x)^2) - (32865365*(3 - x + 2*x^2)^(5/2))/(17915904*(5 + 2*x)) - (19176431*ArcSinh[(1 - 4*x)/Sqrt[23]])/(8192*Sqrt[2]) + (517762327*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(221184*Sqrt[2])","A",10,7,40,0.1750,1,"{1650, 814, 843, 619, 215, 724, 206}"
340,1,188,0,0.2654785,"\int \frac{\left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^5} \, dx","Int[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^5,x]","-\frac{14477995 \left(2 x^2-x+3\right)^{5/2}}{23887872 (2 x+5)^2}+\frac{224815 \left(2 x^2-x+3\right)^{5/2}}{165888 (2 x+5)^3}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{2304 (2 x+5)^4}+\frac{(67865260 x+762984903) \left(2 x^2-x+3\right)^{3/2}}{95551488 (2 x+5)}+\frac{(2339916063-389975609 x) \sqrt{2 x^2-x+3}}{31850496}-\frac{8969688643 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{21233664 \sqrt{2}}+\frac{432565 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1024 \sqrt{2}}","-\frac{14477995 \left(2 x^2-x+3\right)^{5/2}}{23887872 (2 x+5)^2}+\frac{224815 \left(2 x^2-x+3\right)^{5/2}}{165888 (2 x+5)^3}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{2304 (2 x+5)^4}+\frac{(67865260 x+762984903) \left(2 x^2-x+3\right)^{3/2}}{95551488 (2 x+5)}+\frac{(2339916063-389975609 x) \sqrt{2 x^2-x+3}}{31850496}-\frac{8969688643 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{21233664 \sqrt{2}}+\frac{432565 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1024 \sqrt{2}}",1,"((2339916063 - 389975609*x)*Sqrt[3 - x + 2*x^2])/31850496 + ((762984903 + 67865260*x)*(3 - x + 2*x^2)^(3/2))/(95551488*(5 + 2*x)) - (3667*(3 - x + 2*x^2)^(5/2))/(2304*(5 + 2*x)^4) + (224815*(3 - x + 2*x^2)^(5/2))/(165888*(5 + 2*x)^3) - (14477995*(3 - x + 2*x^2)^(5/2))/(23887872*(5 + 2*x)^2) + (432565*ArcSinh[(1 - 4*x)/Sqrt[23]])/(1024*Sqrt[2]) - (8969688643*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(21233664*Sqrt[2])","A",10,8,40,0.2000,1,"{1650, 812, 814, 843, 619, 215, 724, 206}"
341,1,195,0,0.2628749,"\int \frac{\left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^6} \, dx","Int[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^6,x]","-\frac{3730507 \left(2 x^2-x+3\right)^{5/2}}{11943936 (2 x+5)^3}+\frac{158527 \left(2 x^2-x+3\right)^{5/2}}{165888 (2 x+5)^4}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{2880 (2 x+5)^5}+\frac{(44773976 x+246012435) \left(2 x^2-x+3\right)^{3/2}}{95551488 (2 x+5)^2}-\frac{(1028823716 x+5658774871) \sqrt{2 x^2-x+3}}{127401984 (2 x+5)}+\frac{70991525167 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1528823808 \sqrt{2}}-\frac{23775 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{512 \sqrt{2}}","-\frac{3730507 \left(2 x^2-x+3\right)^{5/2}}{11943936 (2 x+5)^3}+\frac{158527 \left(2 x^2-x+3\right)^{5/2}}{165888 (2 x+5)^4}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{2880 (2 x+5)^5}+\frac{(44773976 x+246012435) \left(2 x^2-x+3\right)^{3/2}}{95551488 (2 x+5)^2}-\frac{(1028823716 x+5658774871) \sqrt{2 x^2-x+3}}{127401984 (2 x+5)}+\frac{70991525167 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1528823808 \sqrt{2}}-\frac{23775 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{512 \sqrt{2}}",1,"-((5658774871 + 1028823716*x)*Sqrt[3 - x + 2*x^2])/(127401984*(5 + 2*x)) + ((246012435 + 44773976*x)*(3 - x + 2*x^2)^(3/2))/(95551488*(5 + 2*x)^2) - (3667*(3 - x + 2*x^2)^(5/2))/(2880*(5 + 2*x)^5) + (158527*(3 - x + 2*x^2)^(5/2))/(165888*(5 + 2*x)^4) - (3730507*(3 - x + 2*x^2)^(5/2))/(11943936*(5 + 2*x)^3) - (23775*ArcSinh[(1 - 4*x)/Sqrt[23]])/(512*Sqrt[2]) + (70991525167*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(1528823808*Sqrt[2])","A",10,7,40,0.1750,1,"{1650, 812, 843, 619, 215, 724, 206}"
342,1,195,0,0.2675464,"\int \frac{\left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^7} \, dx","Int[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^7,x]","-\frac{14087245 \left(2 x^2-x+3\right)^{5/2}}{71663616 (2 x+5)^4}+\frac{182165 \left(2 x^2-x+3\right)^{5/2}}{248832 (2 x+5)^5}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{3456 (2 x+5)^6}-\frac{(6793718806 x+9802984711) \left(2 x^2-x+3\right)^{3/2}}{13759414272 (2 x+5)^3}+\frac{(27596573612 x+151764102421) \sqrt{2 x^2-x+3}}{55037657088 (2 x+5)}-\frac{1903976002333 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{660451885056 \sqrt{2}}+\frac{369 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{128 \sqrt{2}}","-\frac{14087245 \left(2 x^2-x+3\right)^{5/2}}{71663616 (2 x+5)^4}+\frac{182165 \left(2 x^2-x+3\right)^{5/2}}{248832 (2 x+5)^5}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{3456 (2 x+5)^6}-\frac{(6793718806 x+9802984711) \left(2 x^2-x+3\right)^{3/2}}{13759414272 (2 x+5)^3}+\frac{(27596573612 x+151764102421) \sqrt{2 x^2-x+3}}{55037657088 (2 x+5)}-\frac{1903976002333 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{660451885056 \sqrt{2}}+\frac{369 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{128 \sqrt{2}}",1,"((151764102421 + 27596573612*x)*Sqrt[3 - x + 2*x^2])/(55037657088*(5 + 2*x)) - ((9802984711 + 6793718806*x)*(3 - x + 2*x^2)^(3/2))/(13759414272*(5 + 2*x)^3) - (3667*(3 - x + 2*x^2)^(5/2))/(3456*(5 + 2*x)^6) + (182165*(3 - x + 2*x^2)^(5/2))/(248832*(5 + 2*x)^5) - (14087245*(3 - x + 2*x^2)^(5/2))/(71663616*(5 + 2*x)^4) + (369*ArcSinh[(1 - 4*x)/Sqrt[23]])/(128*Sqrt[2]) - (1903976002333*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(660451885056*Sqrt[2])","A",10,8,40,0.2000,1,"{1650, 810, 812, 843, 619, 215, 724, 206}"
343,1,195,0,0.2619814,"\int \frac{\left(3-x+2 x^2\right)^{3/2} \left(2+x+3 x^2-x^3+5 x^4\right)}{(5+2 x)^8} \, dx","Int[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x)^8,x]","-\frac{1930441 \left(2 x^2-x+3\right)^{5/2}}{13934592 (2 x+5)^5}+\frac{114335 \left(2 x^2-x+3\right)^{5/2}}{193536 (2 x+5)^6}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{4032 (2 x+5)^7}-\frac{(411822458 x+463558457) \left(2 x^2-x+3\right)^{3/2}}{2293235712 (2 x+5)^4}-\frac{(101679102454 x+146583836191) \sqrt{2 x^2-x+3}}{440301256704 (2 x+5)^2}+\frac{412760561351 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{5283615080448 \sqrt{2}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{2}}","-\frac{1930441 \left(2 x^2-x+3\right)^{5/2}}{13934592 (2 x+5)^5}+\frac{114335 \left(2 x^2-x+3\right)^{5/2}}{193536 (2 x+5)^6}-\frac{3667 \left(2 x^2-x+3\right)^{5/2}}{4032 (2 x+5)^7}-\frac{(411822458 x+463558457) \left(2 x^2-x+3\right)^{3/2}}{2293235712 (2 x+5)^4}-\frac{(101679102454 x+146583836191) \sqrt{2 x^2-x+3}}{440301256704 (2 x+5)^2}+\frac{412760561351 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{5283615080448 \sqrt{2}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{2}}",1,"-((146583836191 + 101679102454*x)*Sqrt[3 - x + 2*x^2])/(440301256704*(5 + 2*x)^2) - ((463558457 + 411822458*x)*(3 - x + 2*x^2)^(3/2))/(2293235712*(5 + 2*x)^4) - (3667*(3 - x + 2*x^2)^(5/2))/(4032*(5 + 2*x)^7) + (114335*(3 - x + 2*x^2)^(5/2))/(193536*(5 + 2*x)^6) - (1930441*(3 - x + 2*x^2)^(5/2))/(13934592*(5 + 2*x)^5) - (5*ArcSinh[(1 - 4*x)/Sqrt[23]])/(64*Sqrt[2]) + (412760561351*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(5283615080448*Sqrt[2])","A",10,7,40,0.1750,1,"{1650, 810, 843, 619, 215, 724, 206}"
344,1,120,0,0.1357344,"\int \frac{(5+2 x) \left(2+x+3 x^2-x^3+5 x^4\right)}{\sqrt{3-x+2 x^2}} \, dx","Int[((5 + 2*x)*(2 + x + 3*x^2 - x^3 + 5*x^4))/Sqrt[3 - x + 2*x^2],x]","\frac{1}{16} \sqrt{2 x^2-x+3} (2 x+5)^4-\frac{105}{128} \sqrt{2 x^2-x+3} (2 x+5)^3+\frac{761}{256} \sqrt{2 x^2-x+3} (2 x+5)^2-\frac{(4676 x+19227) \sqrt{2 x^2-x+3}}{2048}-\frac{85429 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4096 \sqrt{2}}","\frac{1}{16} \sqrt{2 x^2-x+3} (2 x+5)^4-\frac{105}{128} \sqrt{2 x^2-x+3} (2 x+5)^3+\frac{761}{256} \sqrt{2 x^2-x+3} (2 x+5)^2-\frac{(4676 x+19227) \sqrt{2 x^2-x+3}}{2048}-\frac{85429 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4096 \sqrt{2}}",1,"(761*(5 + 2*x)^2*Sqrt[3 - x + 2*x^2])/256 - (105*(5 + 2*x)^3*Sqrt[3 - x + 2*x^2])/128 + ((5 + 2*x)^4*Sqrt[3 - x + 2*x^2])/16 - ((19227 + 4676*x)*Sqrt[3 - x + 2*x^2])/2048 - (85429*ArcSinh[(1 - 4*x)/Sqrt[23]])/(4096*Sqrt[2])","A",6,4,38,0.1053,1,"{1653, 779, 619, 215}"
345,1,101,0,0.0801967,"\int \frac{2+x+3 x^2-x^3+5 x^4}{\sqrt{3-x+2 x^2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/Sqrt[3 - x + 2*x^2],x]","\frac{5}{8} \sqrt{2 x^2-x+3} x^3+\frac{19}{96} \sqrt{2 x^2-x+3} x^2-\frac{409}{768} \sqrt{2 x^2-x+3} x-\frac{505 \sqrt{2 x^2-x+3}}{1024}-\frac{6863 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2048 \sqrt{2}}","\frac{5}{8} \sqrt{2 x^2-x+3} x^3+\frac{19}{96} \sqrt{2 x^2-x+3} x^2-\frac{409}{768} \sqrt{2 x^2-x+3} x-\frac{505 \sqrt{2 x^2-x+3}}{1024}-\frac{6863 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2048 \sqrt{2}}",1,"(-505*Sqrt[3 - x + 2*x^2])/1024 - (409*x*Sqrt[3 - x + 2*x^2])/768 + (19*x^2*Sqrt[3 - x + 2*x^2])/96 + (5*x^3*Sqrt[3 - x + 2*x^2])/8 - (6863*ArcSinh[(1 - 4*x)/Sqrt[23]])/(2048*Sqrt[2])","A",6,4,33,0.1212,1,"{1661, 640, 619, 215}"
346,1,126,0,0.210483,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x) \sqrt{3-x+2 x^2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)*Sqrt[3 - x + 2*x^2]),x]","\frac{5}{48} \sqrt{2 x^2-x+3} (2 x+5)^2-\frac{337}{192} \sqrt{2 x^2-x+3} (2 x+5)+\frac{1669}{128} \sqrt{2 x^2-x+3}-\frac{3667 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{96 \sqrt{2}}+\frac{9657 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{256 \sqrt{2}}","\frac{5}{48} \sqrt{2 x^2-x+3} (2 x+5)^2-\frac{337}{192} \sqrt{2 x^2-x+3} (2 x+5)+\frac{1669}{128} \sqrt{2 x^2-x+3}-\frac{3667 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{96 \sqrt{2}}+\frac{9657 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{256 \sqrt{2}}",1,"(1669*Sqrt[3 - x + 2*x^2])/128 - (337*(5 + 2*x)*Sqrt[3 - x + 2*x^2])/192 + (5*(5 + 2*x)^2*Sqrt[3 - x + 2*x^2])/48 + (9657*ArcSinh[(1 - 4*x)/Sqrt[23]])/(256*Sqrt[2]) - (3667*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(96*Sqrt[2])","A",8,6,40,0.1500,1,"{1653, 843, 619, 215, 724, 206}"
347,1,126,0,0.2020462,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^2 \sqrt{3-x+2 x^2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^2*Sqrt[3 - x + 2*x^2]),x]","\frac{5}{32} \sqrt{2 x^2-x+3} (2 x+5)-\frac{243}{64} \sqrt{2 x^2-x+3}-\frac{3667 \sqrt{2 x^2-x+3}}{576 (2 x+5)}+\frac{158527 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{6912 \sqrt{2}}-\frac{2943 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{128 \sqrt{2}}","\frac{5}{32} \sqrt{2 x^2-x+3} (2 x+5)-\frac{243}{64} \sqrt{2 x^2-x+3}-\frac{3667 \sqrt{2 x^2-x+3}}{576 (2 x+5)}+\frac{158527 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{6912 \sqrt{2}}-\frac{2943 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{128 \sqrt{2}}",1,"(-243*Sqrt[3 - x + 2*x^2])/64 - (3667*Sqrt[3 - x + 2*x^2])/(576*(5 + 2*x)) + (5*(5 + 2*x)*Sqrt[3 - x + 2*x^2])/32 - (2943*ArcSinh[(1 - 4*x)/Sqrt[23]])/(128*Sqrt[2]) + (158527*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(6912*Sqrt[2])","A",8,7,40,0.1750,1,"{1650, 1653, 843, 619, 215, 724, 206}"
348,1,128,0,0.2076311,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^3 \sqrt{3-x+2 x^2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^3*Sqrt[3 - x + 2*x^2]),x]","\frac{92239 \sqrt{2 x^2-x+3}}{27648 (2 x+5)}-\frac{3667 \sqrt{2 x^2-x+3}}{1152 (2 x+5)^2}+\frac{5}{16} \sqrt{2 x^2-x+3}-\frac{1546507 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{331776 \sqrt{2}}+\frac{149 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32 \sqrt{2}}","\frac{92239 \sqrt{2 x^2-x+3}}{27648 (2 x+5)}-\frac{3667 \sqrt{2 x^2-x+3}}{1152 (2 x+5)^2}+\frac{5}{16} \sqrt{2 x^2-x+3}-\frac{1546507 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{331776 \sqrt{2}}+\frac{149 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32 \sqrt{2}}",1,"(5*Sqrt[3 - x + 2*x^2])/16 - (3667*Sqrt[3 - x + 2*x^2])/(1152*(5 + 2*x)^2) + (92239*Sqrt[3 - x + 2*x^2])/(27648*(5 + 2*x)) + (149*ArcSinh[(1 - 4*x)/Sqrt[23]])/(32*Sqrt[2]) - (1546507*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(331776*Sqrt[2])","A",8,7,40,0.1750,1,"{1650, 1653, 843, 619, 215, 724, 206}"
349,1,135,0,0.2047156,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^4 \sqrt{3-x+2 x^2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^4*Sqrt[3 - x + 2*x^2]),x]","-\frac{3163415 \sqrt{2 x^2-x+3}}{5971968 (2 x+5)}+\frac{394907 \sqrt{2 x^2-x+3}}{248832 (2 x+5)^2}-\frac{3667 \sqrt{2 x^2-x+3}}{1728 (2 x+5)^3}+\frac{22389491 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{71663616 \sqrt{2}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16 \sqrt{2}}","-\frac{3163415 \sqrt{2 x^2-x+3}}{5971968 (2 x+5)}+\frac{394907 \sqrt{2 x^2-x+3}}{248832 (2 x+5)^2}-\frac{3667 \sqrt{2 x^2-x+3}}{1728 (2 x+5)^3}+\frac{22389491 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{71663616 \sqrt{2}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16 \sqrt{2}}",1,"(-3667*Sqrt[3 - x + 2*x^2])/(1728*(5 + 2*x)^3) + (394907*Sqrt[3 - x + 2*x^2])/(248832*(5 + 2*x)^2) - (3163415*Sqrt[3 - x + 2*x^2])/(5971968*(5 + 2*x)) - (5*ArcSinh[(1 - 4*x)/Sqrt[23]])/(16*Sqrt[2]) + (22389491*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(71663616*Sqrt[2])","A",8,6,40,0.1500,1,"{1650, 843, 619, 215, 724, 206}"
350,1,139,0,0.1914783,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^5 \sqrt{3-x+2 x^2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^5*Sqrt[3 - x + 2*x^2]),x]","\frac{26800085 \sqrt{2 x^2-x+3}}{1719926784 (2 x+5)}-\frac{16295969 \sqrt{2 x^2-x+3}}{71663616 (2 x+5)^2}+\frac{513097 \sqrt{2 x^2-x+3}}{497664 (2 x+5)^3}-\frac{3667 \sqrt{2 x^2-x+3}}{2304 (2 x+5)^4}+\frac{2053207 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{20639121408 \sqrt{2}}","\frac{26800085 \sqrt{2 x^2-x+3}}{1719926784 (2 x+5)}-\frac{16295969 \sqrt{2 x^2-x+3}}{71663616 (2 x+5)^2}+\frac{513097 \sqrt{2 x^2-x+3}}{497664 (2 x+5)^3}-\frac{3667 \sqrt{2 x^2-x+3}}{2304 (2 x+5)^4}+\frac{2053207 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{20639121408 \sqrt{2}}",1,"(-3667*Sqrt[3 - x + 2*x^2])/(2304*(5 + 2*x)^4) + (513097*Sqrt[3 - x + 2*x^2])/(497664*(5 + 2*x)^3) - (16295969*Sqrt[3 - x + 2*x^2])/(71663616*(5 + 2*x)^2) + (26800085*Sqrt[3 - x + 2*x^2])/(1719926784*(5 + 2*x)) + (2053207*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(20639121408*Sqrt[2])","A",6,4,40,0.1000,1,"{1650, 806, 724, 206}"
351,1,124,0,0.1522518,"\int \frac{(5+2 x)^2 \left(2+x+3 x^2-x^3+5 x^4\right)}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Int[((5 + 2*x)^2*(2 + x + 3*x^2 - x^3 + 5*x^4))/(3 - x + 2*x^2)^(3/2),x]","\frac{5}{4} \sqrt{2 x^2-x+3} x^3+\frac{153}{16} \sqrt{2 x^2-x+3} x^2+\frac{2645}{128} \sqrt{2 x^2-x+3} x-\frac{13153}{512} \sqrt{2 x^2-x+3}-\frac{4 (346-533 x)}{23 \sqrt{2 x^2-x+3}}+\frac{144217 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1024 \sqrt{2}}","\frac{5}{4} \sqrt{2 x^2-x+3} x^3+\frac{153}{16} \sqrt{2 x^2-x+3} x^2+\frac{2645}{128} \sqrt{2 x^2-x+3} x-\frac{13153}{512} \sqrt{2 x^2-x+3}-\frac{4 (346-533 x)}{23 \sqrt{2 x^2-x+3}}+\frac{144217 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1024 \sqrt{2}}",1,"(-4*(346 - 533*x))/(23*Sqrt[3 - x + 2*x^2]) - (13153*Sqrt[3 - x + 2*x^2])/512 + (2645*x*Sqrt[3 - x + 2*x^2])/128 + (153*x^2*Sqrt[3 - x + 2*x^2])/16 + (5*x^3*Sqrt[3 - x + 2*x^2])/4 + (144217*ArcSinh[(1 - 4*x)/Sqrt[23]])/(1024*Sqrt[2])","A",7,5,40,0.1250,1,"{1660, 1661, 640, 619, 215}"
352,1,103,0,0.1016657,"\int \frac{(5+2 x) \left(2+x+3 x^2-x^3+5 x^4\right)}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Int[((5 + 2*x)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(3 - x + 2*x^2)^(3/2),x]","\frac{5}{6} \sqrt{2 x^2-x+3} x^2+\frac{193}{48} \sqrt{2 x^2-x+3} x+\frac{33}{64} \sqrt{2 x^2-x+3}-\frac{53-373 x}{23 \sqrt{2 x^2-x+3}}+\frac{3111 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{128 \sqrt{2}}","\frac{5}{6} \sqrt{2 x^2-x+3} x^2+\frac{193}{48} \sqrt{2 x^2-x+3} x+\frac{33}{64} \sqrt{2 x^2-x+3}-\frac{53-373 x}{23 \sqrt{2 x^2-x+3}}+\frac{3111 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{128 \sqrt{2}}",1,"-(53 - 373*x)/(23*Sqrt[3 - x + 2*x^2]) + (33*Sqrt[3 - x + 2*x^2])/64 + (193*x*Sqrt[3 - x + 2*x^2])/48 + (5*x^2*Sqrt[3 - x + 2*x^2])/6 + (3111*ArcSinh[(1 - 4*x)/Sqrt[23]])/(128*Sqrt[2])","A",6,5,38,0.1316,1,"{1660, 1661, 640, 619, 215}"
353,1,82,0,0.0551878,"\int \frac{2+x+3 x^2-x^3+5 x^4}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/(3 - x + 2*x^2)^(3/2),x]","\frac{5}{8} \sqrt{2 x^2-x+3} x+\frac{27}{32} \sqrt{2 x^2-x+3}+\frac{219 x+89}{92 \sqrt{2 x^2-x+3}}+\frac{213 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{2}}","\frac{5}{8} \sqrt{2 x^2-x+3} x+\frac{27}{32} \sqrt{2 x^2-x+3}+\frac{219 x+89}{92 \sqrt{2 x^2-x+3}}+\frac{213 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{2}}",1,"(89 + 219*x)/(92*Sqrt[3 - x + 2*x^2]) + (27*Sqrt[3 - x + 2*x^2])/32 + (5*x*Sqrt[3 - x + 2*x^2])/8 + (213*ArcSinh[(1 - 4*x)/Sqrt[23]])/(64*Sqrt[2])","A",5,5,33,0.1515,1,"{1660, 1661, 640, 619, 215}"
354,1,101,0,0.1512455,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x) \left(3-x+2 x^2\right)^{3/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)*(3 - x + 2*x^2)^(3/2)),x]","\frac{917 x+1191}{3312 \sqrt{2 x^2-x+3}}+\frac{5}{8} \sqrt{2 x^2-x+3}-\frac{3667 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1728 \sqrt{2}}+\frac{39 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16 \sqrt{2}}","\frac{917 x+1191}{3312 \sqrt{2 x^2-x+3}}+\frac{5}{8} \sqrt{2 x^2-x+3}-\frac{3667 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1728 \sqrt{2}}+\frac{39 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16 \sqrt{2}}",1,"(1191 + 917*x)/(3312*Sqrt[3 - x + 2*x^2]) + (5*Sqrt[3 - x + 2*x^2])/8 + (39*ArcSinh[(1 - 4*x)/Sqrt[23]])/(16*Sqrt[2]) - (3667*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(1728*Sqrt[2])","A",7,7,40,0.1750,1,"{1646, 1653, 843, 619, 215, 724, 206}"
355,1,108,0,0.1527432,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^2 \left(3-x+2 x^2\right)^{3/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^2*(3 - x + 2*x^2)^(3/2)),x]","\frac{2203 x+9897}{119232 \sqrt{2 x^2-x+3}}-\frac{3667 \sqrt{2 x^2-x+3}}{10368 (2 x+5)}+\frac{25951 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{41472 \sqrt{2}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8 \sqrt{2}}","\frac{2203 x+9897}{119232 \sqrt{2 x^2-x+3}}-\frac{3667 \sqrt{2 x^2-x+3}}{10368 (2 x+5)}+\frac{25951 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{41472 \sqrt{2}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8 \sqrt{2}}",1,"(9897 + 2203*x)/(119232*Sqrt[3 - x + 2*x^2]) - (3667*Sqrt[3 - x + 2*x^2])/(10368*(5 + 2*x)) - (5*ArcSinh[(1 - 4*x)/Sqrt[23]])/(8*Sqrt[2]) + (25951*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(41472*Sqrt[2])","A",7,7,40,0.1750,1,"{1646, 1650, 843, 619, 215, 724, 206}"
356,1,112,0,0.1458849,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^3 \left(3-x+2 x^2\right)^{3/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^3*(3 - x + 2*x^2)^(3/2)),x]","\frac{65991-8779 x}{4292352 \sqrt{2 x^2-x+3}}+\frac{115369 \sqrt{2 x^2-x+3}}{1492992 (2 x+5)}-\frac{3667 \sqrt{2 x^2-x+3}}{20736 (2 x+5)^2}-\frac{52631 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{5971968 \sqrt{2}}","\frac{65991-8779 x}{4292352 \sqrt{2 x^2-x+3}}+\frac{115369 \sqrt{2 x^2-x+3}}{1492992 (2 x+5)}-\frac{3667 \sqrt{2 x^2-x+3}}{20736 (2 x+5)^2}-\frac{52631 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{5971968 \sqrt{2}}",1,"(65991 - 8779*x)/(4292352*Sqrt[3 - x + 2*x^2]) - (3667*Sqrt[3 - x + 2*x^2])/(20736*(5 + 2*x)^2) + (115369*Sqrt[3 - x + 2*x^2])/(1492992*(5 + 2*x)) - (52631*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(5971968*Sqrt[2])","A",5,5,40,0.1250,1,"{1646, 1650, 806, 724, 206}"
357,1,137,0,0.2035116,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^4 \left(3-x+2 x^2\right)^{3/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^4*(3 - x + 2*x^2)^(3/2)),x]","\frac{369609-175877 x}{154524672 \sqrt{2 x^2-x+3}}+\frac{430799 \sqrt{2 x^2-x+3}}{107495424 (2 x+5)}+\frac{152885 \sqrt{2 x^2-x+3}}{4478976 (2 x+5)^2}-\frac{3667 \sqrt{2 x^2-x+3}}{31104 (2 x+5)^3}-\frac{3505819 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1289945088 \sqrt{2}}","\frac{369609-175877 x}{154524672 \sqrt{2 x^2-x+3}}+\frac{430799 \sqrt{2 x^2-x+3}}{107495424 (2 x+5)}+\frac{152885 \sqrt{2 x^2-x+3}}{4478976 (2 x+5)^2}-\frac{3667 \sqrt{2 x^2-x+3}}{31104 (2 x+5)^3}-\frac{3505819 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{1289945088 \sqrt{2}}",1,"(369609 - 175877*x)/(154524672*Sqrt[3 - x + 2*x^2]) - (3667*Sqrt[3 - x + 2*x^2])/(31104*(5 + 2*x)^3) + (152885*Sqrt[3 - x + 2*x^2])/(4478976*(5 + 2*x)^2) + (430799*Sqrt[3 - x + 2*x^2])/(107495424*(5 + 2*x)) - (3505819*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(1289945088*Sqrt[2])","A",6,5,40,0.1250,1,"{1646, 1650, 806, 724, 206}"
358,1,105,0,0.1307733,"\int \frac{(5+2 x)^2 \left(2+x+3 x^2-x^3+5 x^4\right)}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Int[((5 + 2*x)^2*(2 + x + 3*x^2 - x^3 + 5*x^4))/(3 - x + 2*x^2)^(5/2),x]","\frac{4 (18982-20383 x)}{1587 \sqrt{2 x^2-x+3}}+\frac{5}{4} x \sqrt{2 x^2-x+3}+\frac{247}{16} \sqrt{2 x^2-x+3}-\frac{4 (346-533 x)}{69 \left(2 x^2-x+3\right)^{3/2}}-\frac{1471 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32 \sqrt{2}}","\frac{4 (18982-20383 x)}{1587 \sqrt{2 x^2-x+3}}+\frac{5}{4} x \sqrt{2 x^2-x+3}+\frac{247}{16} \sqrt{2 x^2-x+3}-\frac{4 (346-533 x)}{69 \left(2 x^2-x+3\right)^{3/2}}-\frac{1471 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32 \sqrt{2}}",1,"(-4*(346 - 533*x))/(69*(3 - x + 2*x^2)^(3/2)) + (4*(18982 - 20383*x))/(1587*Sqrt[3 - x + 2*x^2]) + (247*Sqrt[3 - x + 2*x^2])/16 + (5*x*Sqrt[3 - x + 2*x^2])/4 - (1471*ArcSinh[(1 - 4*x)/Sqrt[23]])/(32*Sqrt[2])","A",6,5,40,0.1250,1,"{1660, 1661, 640, 619, 215}"
359,1,86,0,0.0822592,"\int \frac{(5+2 x) \left(2+x+3 x^2-x^3+5 x^4\right)}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Int[((5 + 2*x)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(3 - x + 2*x^2)^(5/2),x]","\frac{6055-28981 x}{3174 \sqrt{2 x^2-x+3}}+\frac{5}{4} \sqrt{2 x^2-x+3}-\frac{53-373 x}{69 \left(2 x^2-x+3\right)^{3/2}}-\frac{71 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8 \sqrt{2}}","\frac{6055-28981 x}{3174 \sqrt{2 x^2-x+3}}+\frac{5}{4} \sqrt{2 x^2-x+3}-\frac{53-373 x}{69 \left(2 x^2-x+3\right)^{3/2}}-\frac{71 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8 \sqrt{2}}",1,"-(53 - 373*x)/(69*(3 - x + 2*x^2)^(3/2)) + (6055 - 28981*x)/(3174*Sqrt[3 - x + 2*x^2]) + (5*Sqrt[3 - x + 2*x^2])/4 - (71*ArcSinh[(1 - 4*x)/Sqrt[23]])/(8*Sqrt[2])","A",5,4,38,0.1053,1,"{1660, 640, 619, 215}"
360,1,68,0,0.0518717,"\int \frac{2+x+3 x^2-x^3+5 x^4}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/(3 - x + 2*x^2)^(5/2),x]","\frac{219 x+89}{276 \left(2 x^2-x+3\right)^{3/2}}-\frac{2604 x+1465}{2116 \sqrt{2 x^2-x+3}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4 \sqrt{2}}","\frac{219 x+89}{276 \left(2 x^2-x+3\right)^{3/2}}-\frac{2604 x+1465}{2116 \sqrt{2 x^2-x+3}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4 \sqrt{2}}",1,"(89 + 219*x)/(276*(3 - x + 2*x^2)^(3/2)) - (1465 + 2604*x)/(2116*Sqrt[3 - x + 2*x^2]) - (5*ArcSinh[(1 - 4*x)/Sqrt[23]])/(4*Sqrt[2])","A",5,4,33,0.1212,1,"{1660, 12, 619, 215}"
361,1,85,0,0.1282614,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x) \left(3-x+2 x^2\right)^{5/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)*(3 - x + 2*x^2)^(5/2)),x]","\frac{917 x+1191}{9936 \left(2 x^2-x+3\right)^{3/2}}-\frac{146729 x+335337}{1371168 \sqrt{2 x^2-x+3}}-\frac{3667 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{31104 \sqrt{2}}","\frac{917 x+1191}{9936 \left(2 x^2-x+3\right)^{3/2}}-\frac{146729 x+335337}{1371168 \sqrt{2 x^2-x+3}}-\frac{3667 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{31104 \sqrt{2}}",1,"(1191 + 917*x)/(9936*(3 - x + 2*x^2)^(3/2)) - (335337 + 146729*x)/(1371168*Sqrt[3 - x + 2*x^2]) - (3667*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(31104*Sqrt[2])","A",5,4,40,0.1000,1,"{1646, 12, 724, 206}"
362,1,110,0,0.1529123,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^2 \left(3-x+2 x^2\right)^{5/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^2*(3 - x + 2*x^2)^(5/2)),x]","-\frac{1255878-62021 x}{24681024 \sqrt{2 x^2-x+3}}-\frac{3667 \sqrt{2 x^2-x+3}}{186624 (2 x+5)}+\frac{2203 x+9897}{357696 \left(2 x^2-x+3\right)^{3/2}}-\frac{2821 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{2239488 \sqrt{2}}","-\frac{1255878-62021 x}{24681024 \sqrt{2 x^2-x+3}}-\frac{3667 \sqrt{2 x^2-x+3}}{186624 (2 x+5)}+\frac{2203 x+9897}{357696 \left(2 x^2-x+3\right)^{3/2}}-\frac{2821 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{2239488 \sqrt{2}}",1,"(9897 + 2203*x)/(357696*(3 - x + 2*x^2)^(3/2)) - (1255878 - 62021*x)/(24681024*Sqrt[3 - x + 2*x^2]) - (3667*Sqrt[3 - x + 2*x^2])/(186624*(5 + 2*x)) - (2821*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(2239488*Sqrt[2])","A",5,4,40,0.1000,1,"{1646, 806, 724, 206}"
363,1,135,0,0.2208955,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^3 \left(3-x+2 x^2\right)^{5/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^3*(3 - x + 2*x^2)^(5/2)),x]","-\frac{4679797-2148263 x}{592344576 \sqrt{2 x^2-x+3}}-\frac{45979 \sqrt{2 x^2-x+3}}{26873856 (2 x+5)}-\frac{3667 \sqrt{2 x^2-x+3}}{373248 (2 x+5)^2}+\frac{65991-8779 x}{12877056 \left(2 x^2-x+3\right)^{3/2}}+\frac{774079 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{322486272 \sqrt{2}}","-\frac{4679797-2148263 x}{592344576 \sqrt{2 x^2-x+3}}-\frac{45979 \sqrt{2 x^2-x+3}}{26873856 (2 x+5)}-\frac{3667 \sqrt{2 x^2-x+3}}{373248 (2 x+5)^2}+\frac{65991-8779 x}{12877056 \left(2 x^2-x+3\right)^{3/2}}+\frac{774079 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{322486272 \sqrt{2}}",1,"(65991 - 8779*x)/(12877056*(3 - x + 2*x^2)^(3/2)) - (4679797 - 2148263*x)/(592344576*Sqrt[3 - x + 2*x^2]) - (3667*Sqrt[3 - x + 2*x^2])/(373248*(5 + 2*x)^2) - (45979*Sqrt[3 - x + 2*x^2])/(26873856*(5 + 2*x)) + (774079*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(322486272*Sqrt[2])","A",6,5,40,0.1250,1,"{1646, 1650, 806, 724, 206}"
364,1,160,0,0.2829993,"\int \frac{2+x+3 x^2-x^3+5 x^4}{(5+2 x)^4 \left(3-x+2 x^2\right)^{5/2}} \, dx","Int[(2 + x + 3*x^2 - x^3 + 5*x^4)/((5 + 2*x)^4*(3 - x + 2*x^2)^(5/2)),x]","-\frac{27754539-31190998 x}{31986607104 \sqrt{2 x^2-x+3}}+\frac{475357 \sqrt{2 x^2-x+3}}{1934917632 (2 x+5)}-\frac{89137 \sqrt{2 x^2-x+3}}{80621568 (2 x+5)^2}-\frac{3667 \sqrt{2 x^2-x+3}}{559872 (2 x+5)^3}+\frac{369609-175877 x}{463574016 \left(2 x^2-x+3\right)^{3/2}}+\frac{4778789 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{7739670528 \sqrt{2}}","-\frac{27754539-31190998 x}{31986607104 \sqrt{2 x^2-x+3}}+\frac{475357 \sqrt{2 x^2-x+3}}{1934917632 (2 x+5)}-\frac{89137 \sqrt{2 x^2-x+3}}{80621568 (2 x+5)^2}-\frac{3667 \sqrt{2 x^2-x+3}}{559872 (2 x+5)^3}+\frac{369609-175877 x}{463574016 \left(2 x^2-x+3\right)^{3/2}}+\frac{4778789 \tanh ^{-1}\left(\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right)}{7739670528 \sqrt{2}}",1,"(369609 - 175877*x)/(463574016*(3 - x + 2*x^2)^(3/2)) - (27754539 - 31190998*x)/(31986607104*Sqrt[3 - x + 2*x^2]) - (3667*Sqrt[3 - x + 2*x^2])/(559872*(5 + 2*x)^3) - (89137*Sqrt[3 - x + 2*x^2])/(80621568*(5 + 2*x)^2) + (475357*Sqrt[3 - x + 2*x^2])/(1934917632*(5 + 2*x)) + (4778789*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*Sqrt[3 - x + 2*x^2])])/(7739670528*Sqrt[2])","A",7,5,40,0.1250,1,"{1646, 1650, 806, 724, 206}"
365,1,354,0,0.377244,"\int \frac{f+g x+h x^2+i x^3+j x^4}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(f + g*x + h*x^2 + i*x^3 + j*x^4)/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \left(-c x \left(2 c^2 \left(-16 a^2 j-6 a b i+b^2 h\right)+b^2 c (28 a j+b i)-c^3 (8 b g-8 a h)-4 b^4 j+16 c^4 f\right)-4 b c^2 \left(8 a^2 j+a c h+2 c^2 f\right)+24 a^2 c^3 i+2 b^2 c^2 (2 c g-3 a i)-b^3 c (c h-10 a j)+b^4 c i+b^5 (-j)\right)}{3 c^3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 \left(-x \left(c^2 \left(2 a^2 j+3 a b i+b^2 h\right)-b^2 c (4 a j+b i)-c^3 (2 a h+b g)+b^4 j+2 c^4 f\right)-b c \left(-3 a^2 j+a c h+c^2 f\right)+a b^2 c i-a b^3 j+2 a c^2 (c g-a i)\right)}{3 c^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{j \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}","-\frac{2 \left(-c x \left(2 c^2 \left(-16 a^2 j-6 a b i+b^2 h\right)+b^2 c (28 a j+b i)-c^3 (8 b g-8 a h)-4 b^4 j+16 c^4 f\right)-4 b c^2 \left(8 a^2 j+a c h+2 c^2 f\right)+24 a^2 c^3 i+2 b^2 c^2 (2 c g-3 a i)-b^3 c (c h-10 a j)+b^4 c i+b^5 (-j)\right)}{3 c^3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 \left(-x \left(c^2 \left(2 a^2 j+3 a b i+b^2 h\right)-b^2 c (4 a j+b i)-c^3 (2 a h+b g)+b^4 j+2 c^4 f\right)-b c \left(-3 a^2 j+a c h+c^2 f\right)+a b^2 c i-a b^3 j+2 a c^2 (c g-a i)\right)}{3 c^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{j \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}",1,"(2*(a*b^2*c*i + 2*a*c^2*(c*g - a*i) - a*b^3*j - b*c*(c^2*f + a*c*h - 3*a^2*j) - (2*c^4*f - c^3*(b*g + 2*a*h) + b^4*j - b^2*c*(b*i + 4*a*j) + c^2*(b^2*h + 3*a*b*i + 2*a^2*j))*x))/(3*c^3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*(b^4*c*i + 24*a^2*c^3*i + 2*b^2*c^2*(2*c*g - 3*a*i) - b^5*j - b^3*c*(c*h - 10*a*j) - 4*b*c^2*(2*c^2*f + a*c*h + 8*a^2*j) - c*(16*c^4*f - c^3*(8*b*g - 8*a*h) - 4*b^4*j + b^2*c*(b*i + 28*a*j) + 2*c^2*(b^2*h - 6*a*b*i - 16*a^2*j))*x))/(3*c^3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) + (j*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(5/2)","A",5,4,35,0.1143,1,"{1660, 12, 621, 206}"
366,1,353,0,0.3857002,"\int \frac{f+g x+h x^2+i x^3+j x^4}{\left(a+b x-c x^2\right)^{5/2}} \, dx","Int[(f + g*x + h*x^2 + i*x^3 + j*x^4)/(a + b*x - c*x^2)^(5/2),x]","-\frac{2 \left(-c x \left(2 c^2 \left(-16 a^2 j-6 a b i+b^2 h\right)-b^2 c (28 a j+b i)+8 c^3 (b g-a h)-4 b^4 j+16 c^4 f\right)+4 b c^2 \left(8 a^2 j-a c h+2 c^2 f\right)+24 a^2 c^3 i+2 b^2 c^2 (3 a i+2 c g)+b^3 c (10 a j+c h)+b^4 c i+b^5 j\right)}{3 c^3 \left(4 a c+b^2\right)^2 \sqrt{a+b x-c x^2}}+\frac{2 \left(x \left(c^2 \left(2 a^2 j+3 a b i+b^2 h\right)+b^2 c (4 a j+b i)+c^3 (2 a h+b g)+b^4 j+2 c^4 f\right)-b c \left(-3 a^2 j-a c h+c^2 f\right)+a b^2 c i+a b^3 j+2 a c^2 (a i+c g)\right)}{3 c^3 \left(4 a c+b^2\right) \left(a+b x-c x^2\right)^{3/2}}-\frac{j \tan ^{-1}\left(\frac{b-2 c x}{2 \sqrt{c} \sqrt{a+b x-c x^2}}\right)}{c^{5/2}}","-\frac{2 \left(-c x \left(2 c^2 \left(-16 a^2 j-6 a b i+b^2 h\right)-b^2 c (28 a j+b i)+8 c^3 (b g-a h)-4 b^4 j+16 c^4 f\right)+4 b c^2 \left(8 a^2 j-a c h+2 c^2 f\right)+24 a^2 c^3 i+2 b^2 c^2 (3 a i+2 c g)+b^3 c (10 a j+c h)+b^4 c i+b^5 j\right)}{3 c^3 \left(4 a c+b^2\right)^2 \sqrt{a+b x-c x^2}}+\frac{2 \left(x \left(c^2 \left(2 a^2 j+3 a b i+b^2 h\right)+b^2 c (4 a j+b i)+c^3 (2 a h+b g)+b^4 j+2 c^4 f\right)-b c \left(-3 a^2 j-a c h+c^2 f\right)+a b^2 c i+a b^3 j+2 a c^2 (a i+c g)\right)}{3 c^3 \left(4 a c+b^2\right) \left(a+b x-c x^2\right)^{3/2}}-\frac{j \tan ^{-1}\left(\frac{b-2 c x}{2 \sqrt{c} \sqrt{a+b x-c x^2}}\right)}{c^{5/2}}",1,"(2*(a*b^2*c*i + 2*a*c^2*(c*g + a*i) + a*b^3*j - b*c*(c^2*f - a*c*h - 3*a^2*j) + (2*c^4*f + c^3*(b*g + 2*a*h) + b^4*j + b^2*c*(b*i + 4*a*j) + c^2*(b^2*h + 3*a*b*i + 2*a^2*j))*x))/(3*c^3*(b^2 + 4*a*c)*(a + b*x - c*x^2)^(3/2)) - (2*(b^4*c*i + 24*a^2*c^3*i + 2*b^2*c^2*(2*c*g + 3*a*i) + b^5*j + b^3*c*(c*h + 10*a*j) + 4*b*c^2*(2*c^2*f - a*c*h + 8*a^2*j) - c*(16*c^4*f + 8*c^3*(b*g - a*h) - 4*b^4*j - b^2*c*(b*i + 28*a*j) + 2*c^2*(b^2*h - 6*a*b*i - 16*a^2*j))*x))/(3*c^3*(b^2 + 4*a*c)^2*Sqrt[a + b*x - c*x^2]) - (j*ArcTan[(b - 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x - c*x^2])])/c^(5/2)","A",5,4,36,0.1111,1,"{1660, 12, 621, 204}"
367,1,588,0,0.364184,"\int (d+e x)^m \left(3+2 x+5 x^2\right)^3 \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(d + e*x)^m*(3 + 2*x + 5*x^2)^3*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{\left(5 d^2-2 d e+3 e^2\right)^3 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^{m+1}}{e^{11} (m+1)}-\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(108 d^3 e^2-20 d^2 e^3+169 d^4 e+200 d^5+86 d e^4-15 e^5\right) (d+e x)^{m+2}}{e^{11} (m+2)}+\frac{3 \left(5 d^2-2 d e+3 e^2\right) \left(792 d^4 e^2+58 d^3 e^3+547 d^2 e^4+660 d^5 e+1500 d^6-156 d e^5+53 e^6\right) (d+e x)^{m+3}}{e^{11} (m+3)}-\frac{2 \left(21420 d^5 e^2+1715 d^4 e^3+9990 d^3 e^4-2550 d^2 e^5+1050 d^6 e+30000 d^7+2218 d e^6-287 e^7\right) (d+e x)^{m+4}}{e^{11} (m+4)}+\frac{\left(53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4+3150 d^5 e+105000 d^6-2550 d e^5+1109 e^6\right) (d+e x)^{m+5}}{e^{11} (m+5)}-\frac{6 \left(7140 d^3 e^2+343 d^2 e^3+525 d^4 e+21000 d^5+999 d e^4-85 e^5\right) (d+e x)^{m+6}}{e^{11} (m+6)}+\frac{\left(21420 d^2 e^2+2100 d^3 e+105000 d^4+686 d e^3+999 e^4\right) (d+e x)^{m+7}}{e^{11} (m+7)}-\frac{2 \left(450 d^2 e+30000 d^3+3060 d e^2+49 e^3\right) (d+e x)^{m+8}}{e^{11} (m+8)}+\frac{45 \left(500 d^2+5 d e+17 e^2\right) (d+e x)^{m+9}}{e^{11} (m+9)}-\frac{25 (200 d+e) (d+e x)^{m+10}}{e^{11} (m+10)}+\frac{500 (d+e x)^{m+11}}{e^{11} (m+11)}","\frac{\left(5 d^2-2 d e+3 e^2\right)^3 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^{m+1}}{e^{11} (m+1)}-\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(108 d^3 e^2-20 d^2 e^3+169 d^4 e+200 d^5+86 d e^4-15 e^5\right) (d+e x)^{m+2}}{e^{11} (m+2)}+\frac{3 \left(5 d^2-2 d e+3 e^2\right) \left(792 d^4 e^2+58 d^3 e^3+547 d^2 e^4+660 d^5 e+1500 d^6-156 d e^5+53 e^6\right) (d+e x)^{m+3}}{e^{11} (m+3)}-\frac{2 \left(21420 d^5 e^2+1715 d^4 e^3+9990 d^3 e^4-2550 d^2 e^5+1050 d^6 e+30000 d^7+2218 d e^6-287 e^7\right) (d+e x)^{m+4}}{e^{11} (m+4)}+\frac{\left(53550 d^4 e^2+3430 d^3 e^3+14985 d^2 e^4+3150 d^5 e+105000 d^6-2550 d e^5+1109 e^6\right) (d+e x)^{m+5}}{e^{11} (m+5)}-\frac{6 \left(7140 d^3 e^2+343 d^2 e^3+525 d^4 e+21000 d^5+999 d e^4-85 e^5\right) (d+e x)^{m+6}}{e^{11} (m+6)}+\frac{\left(21420 d^2 e^2+2100 d^3 e+105000 d^4+686 d e^3+999 e^4\right) (d+e x)^{m+7}}{e^{11} (m+7)}-\frac{2 \left(450 d^2 e+30000 d^3+3060 d e^2+49 e^3\right) (d+e x)^{m+8}}{e^{11} (m+8)}+\frac{45 \left(500 d^2+5 d e+17 e^2\right) (d+e x)^{m+9}}{e^{11} (m+9)}-\frac{25 (200 d+e) (d+e x)^{m+10}}{e^{11} (m+10)}+\frac{500 (d+e x)^{m+11}}{e^{11} (m+11)}",1,"((5*d^2 - 2*d*e + 3*e^2)^3*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*(d + e*x)^(1 + m))/(e^11*(1 + m)) - ((5*d^2 - 2*d*e + 3*e^2)^2*(200*d^5 + 169*d^4*e + 108*d^3*e^2 - 20*d^2*e^3 + 86*d*e^4 - 15*e^5)*(d + e*x)^(2 + m))/(e^11*(2 + m)) + (3*(5*d^2 - 2*d*e + 3*e^2)*(1500*d^6 + 660*d^5*e + 792*d^4*e^2 + 58*d^3*e^3 + 547*d^2*e^4 - 156*d*e^5 + 53*e^6)*(d + e*x)^(3 + m))/(e^11*(3 + m)) - (2*(30000*d^7 + 1050*d^6*e + 21420*d^5*e^2 + 1715*d^4*e^3 + 9990*d^3*e^4 - 2550*d^2*e^5 + 2218*d*e^6 - 287*e^7)*(d + e*x)^(4 + m))/(e^11*(4 + m)) + ((105000*d^6 + 3150*d^5*e + 53550*d^4*e^2 + 3430*d^3*e^3 + 14985*d^2*e^4 - 2550*d*e^5 + 1109*e^6)*(d + e*x)^(5 + m))/(e^11*(5 + m)) - (6*(21000*d^5 + 525*d^4*e + 7140*d^3*e^2 + 343*d^2*e^3 + 999*d*e^4 - 85*e^5)*(d + e*x)^(6 + m))/(e^11*(6 + m)) + ((105000*d^4 + 2100*d^3*e + 21420*d^2*e^2 + 686*d*e^3 + 999*e^4)*(d + e*x)^(7 + m))/(e^11*(7 + m)) - (2*(30000*d^3 + 450*d^2*e + 3060*d*e^2 + 49*e^3)*(d + e*x)^(8 + m))/(e^11*(8 + m)) + (45*(500*d^2 + 5*d*e + 17*e^2)*(d + e*x)^(9 + m))/(e^11*(9 + m)) - (25*(200*d + e)*(d + e*x)^(10 + m))/(e^11*(10 + m)) + (500*(d + e*x)^(11 + m))/(e^11*(11 + m))","A",2,1,38,0.02632,1,"{1628}"
368,1,432,0,0.2427947,"\int (d+e x)^m \left(3+2 x+5 x^2\right)^2 \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(d + e*x)^m*(3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^{m+1}}{e^9 (m+1)}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right) (d+e x)^{m+2}}{e^9 (m+2)}+\frac{\left(1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6\right) (d+e x)^{m+3}}{e^9 (m+3)}-\frac{\left(2220 d^3 e^2+370 d^2 e^3+1575 d^4 e+5600 d^5+592 d e^4-65 e^5\right) (d+e x)^{m+4}}{e^9 (m+4)}+\frac{\left(1665 d^2 e^2+1575 d^3 e+7000 d^4+185 d e^3+148 e^4\right) (d+e x)^{m+5}}{e^9 (m+5)}-\frac{\left(945 d^2 e+5600 d^3+666 d e^2+37 e^3\right) (d+e x)^{m+6}}{e^9 (m+6)}+\frac{\left(2800 d^2+315 d e+111 e^2\right) (d+e x)^{m+7}}{e^9 (m+7)}-\frac{5 (160 d+9 e) (d+e x)^{m+8}}{e^9 (m+8)}+\frac{100 (d+e x)^{m+9}}{e^9 (m+9)}","\frac{\left(5 d^2-2 d e+3 e^2\right)^2 \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^{m+1}}{e^9 (m+1)}-\frac{\left(5 d^2-2 d e+3 e^2\right) \left(88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right) (d+e x)^{m+2}}{e^9 (m+2)}+\frac{\left(1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6\right) (d+e x)^{m+3}}{e^9 (m+3)}-\frac{\left(2220 d^3 e^2+370 d^2 e^3+1575 d^4 e+5600 d^5+592 d e^4-65 e^5\right) (d+e x)^{m+4}}{e^9 (m+4)}+\frac{\left(1665 d^2 e^2+1575 d^3 e+7000 d^4+185 d e^3+148 e^4\right) (d+e x)^{m+5}}{e^9 (m+5)}-\frac{\left(945 d^2 e+5600 d^3+666 d e^2+37 e^3\right) (d+e x)^{m+6}}{e^9 (m+6)}+\frac{\left(2800 d^2+315 d e+111 e^2\right) (d+e x)^{m+7}}{e^9 (m+7)}-\frac{5 (160 d+9 e) (d+e x)^{m+8}}{e^9 (m+8)}+\frac{100 (d+e x)^{m+9}}{e^9 (m+9)}",1,"((5*d^2 - 2*d*e + 3*e^2)^2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*(d + e*x)^(1 + m))/(e^9*(1 + m)) - ((5*d^2 - 2*d*e + 3*e^2)*(160*d^5 + 127*d^4*e + 88*d^3*e^2 - 4*d^2*e^3 + 64*d*e^4 - 11*e^5)*(d + e*x)^(2 + m))/(e^9*(2 + m)) + ((2800*d^6 + 945*d^5*e + 1665*d^4*e^2 + 370*d^3*e^3 + 888*d^2*e^4 - 195*d*e^5 + 107*e^6)*(d + e*x)^(3 + m))/(e^9*(3 + m)) - ((5600*d^5 + 1575*d^4*e + 2220*d^3*e^2 + 370*d^2*e^3 + 592*d*e^4 - 65*e^5)*(d + e*x)^(4 + m))/(e^9*(4 + m)) + ((7000*d^4 + 1575*d^3*e + 1665*d^2*e^2 + 185*d*e^3 + 148*e^4)*(d + e*x)^(5 + m))/(e^9*(5 + m)) - ((5600*d^3 + 945*d^2*e + 666*d*e^2 + 37*e^3)*(d + e*x)^(6 + m))/(e^9*(6 + m)) + ((2800*d^2 + 315*d*e + 111*e^2)*(d + e*x)^(7 + m))/(e^9*(7 + m)) - (5*(160*d + 9*e)*(d + e*x)^(8 + m))/(e^9*(8 + m)) + (100*(d + e*x)^(9 + m))/(e^9*(9 + m))","A",2,1,38,0.02632,1,"{1628}"
369,1,292,0,0.1890027,"\int (d+e x)^m \left(3+2 x+5 x^2\right) \left(2+x+3 x^2-5 x^3+4 x^4\right) \, dx","Int[(d + e*x)^m*(3 + 2*x + 5*x^2)*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]","\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^{m+1}}{e^7 (m+1)}-\frac{\left(68 d^3 e^2+12 d^2 e^3+85 d^4 e+120 d^5+42 d e^4-7 e^5\right) (d+e x)^{m+2}}{e^7 (m+2)}+\frac{\left(102 d^2 e^2+170 d^3 e+300 d^4+12 d e^3+21 e^4\right) (d+e x)^{m+3}}{e^7 (m+3)}-\frac{2 \left(85 d^2 e+200 d^3+34 d e^2+2 e^3\right) (d+e x)^{m+4}}{e^7 (m+4)}+\frac{\left(300 d^2+85 d e+17 e^2\right) (d+e x)^{m+5}}{e^7 (m+5)}-\frac{(120 d+17 e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{20 (d+e x)^{m+7}}{e^7 (m+7)}","\frac{\left(5 d^2-2 d e+3 e^2\right) \left(3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right) (d+e x)^{m+1}}{e^7 (m+1)}-\frac{\left(68 d^3 e^2+12 d^2 e^3+85 d^4 e+120 d^5+42 d e^4-7 e^5\right) (d+e x)^{m+2}}{e^7 (m+2)}+\frac{\left(102 d^2 e^2+170 d^3 e+300 d^4+12 d e^3+21 e^4\right) (d+e x)^{m+3}}{e^7 (m+3)}-\frac{2 \left(85 d^2 e+200 d^3+34 d e^2+2 e^3\right) (d+e x)^{m+4}}{e^7 (m+4)}+\frac{\left(300 d^2+85 d e+17 e^2\right) (d+e x)^{m+5}}{e^7 (m+5)}-\frac{(120 d+17 e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{20 (d+e x)^{m+7}}{e^7 (m+7)}",1,"((5*d^2 - 2*d*e + 3*e^2)*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*(d + e*x)^(1 + m))/(e^7*(1 + m)) - ((120*d^5 + 85*d^4*e + 68*d^3*e^2 + 12*d^2*e^3 + 42*d*e^4 - 7*e^5)*(d + e*x)^(2 + m))/(e^7*(2 + m)) + ((300*d^4 + 170*d^3*e + 102*d^2*e^2 + 12*d*e^3 + 21*e^4)*(d + e*x)^(3 + m))/(e^7*(3 + m)) - (2*(200*d^3 + 85*d^2*e + 34*d*e^2 + 2*e^3)*(d + e*x)^(4 + m))/(e^7*(4 + m)) + ((300*d^2 + 85*d*e + 17*e^2)*(d + e*x)^(5 + m))/(e^7*(5 + m)) - ((120*d + 17*e)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (20*(d + e*x)^(7 + m))/(e^7*(7 + m))","A",2,1,36,0.02778,1,"{1628}"
370,1,255,0,0.4807408,"\int \frac{(d+e x)^m \left(2+x+3 x^2-5 x^3+4 x^4\right)}{3+2 x+5 x^2} \, dx","Int[((d + e*x)^m*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2),x]","\frac{\left(100 d^2+165 d e+81 e^2\right) (d+e x)^{m+1}}{125 e^3 (m+1)}-\frac{(40 d+33 e) (d+e x)^{m+2}}{25 e^3 (m+2)}+\frac{4 (d+e x)^{m+3}}{5 e^3 (m+3)}-\frac{\left(-423 \sqrt{14}+6412 i\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{5 (d+e x)}{5 d+i \sqrt{14} e-e}\right)}{3500 (m+1) \left(5 i d-\left(\sqrt{14}+i\right) e\right)}-\frac{\left(423 \sqrt{14}+6412 i\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{5 (d+e x)}{5 d-\left(1+i \sqrt{14}\right) e}\right)}{3500 (m+1) \left(5 i d-\left(-\sqrt{14}+i\right) e\right)}","\frac{\left(100 d^2+165 d e+81 e^2\right) (d+e x)^{m+1}}{125 e^3 (m+1)}-\frac{(40 d+33 e) (d+e x)^{m+2}}{25 e^3 (m+2)}+\frac{4 (d+e x)^{m+3}}{5 e^3 (m+3)}-\frac{\left(-423 \sqrt{14}+6412 i\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{5 (d+e x)}{5 d+i \sqrt{14} e-e}\right)}{3500 (m+1) \left(5 i d-\left(\sqrt{14}+i\right) e\right)}-\frac{\left(423 \sqrt{14}+6412 i\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{5 (d+e x)}{5 d-\left(1+i \sqrt{14}\right) e}\right)}{3500 (m+1) \left(5 i d-\left(-\sqrt{14}+i\right) e\right)}",1,"((100*d^2 + 165*d*e + 81*e^2)*(d + e*x)^(1 + m))/(125*e^3*(1 + m)) - ((40*d + 33*e)*(d + e*x)^(2 + m))/(25*e^3*(2 + m)) + (4*(d + e*x)^(3 + m))/(5*e^3*(3 + m)) - ((6412*I - 423*Sqrt[14])*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (5*(d + e*x))/(5*d - e + I*Sqrt[14]*e)])/(3500*((5*I)*d - (I + Sqrt[14])*e)*(1 + m)) - ((6412*I + 423*Sqrt[14])*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (5*(d + e*x))/(5*d - (1 + I*Sqrt[14])*e)])/(3500*((5*I)*d - (I - Sqrt[14])*e)*(1 + m))","A",4,2,38,0.05263,1,"{1628, 68}"
371,1,377,0,0.8998619,"\int \frac{(d+e x)^m \left(2+x+3 x^2-5 x^3+4 x^4\right)}{\left(3+2 x+5 x^2\right)^2} \, dx","Int[((d + e*x)^m*(2 + x + 3*x^2 - 5*x^3 + 4*x^4))/(3 + 2*x + 5*x^2)^2,x]","\frac{\left(i \sqrt{14} \left(6565 d^2-2 d e (1313-3206 m)+e^2 (3939-98 m)\right)+80360 d^2-5922 d e m-32144 d e+19138 e^2 m+48216 e^2\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{5 (d+e x)}{5 d+i \sqrt{14} e-e}\right)}{19600 (m+1) \left(5 d+i \left(\sqrt{14}+i\right) e\right) \left(5 d^2-2 d e+3 e^2\right)}+\frac{\left(-i \sqrt{14} \left(6565 d^2-2 d e (1313-3206 m)+e^2 (3939-98 m)\right)+80360 d^2-5922 d e m-32144 d e+19138 e^2 m+48216 e^2\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{5 (d+e x)}{5 d-\left(1+i \sqrt{14}\right) e}\right)}{19600 (m+1) \left(5 d-\left(1+i \sqrt{14}\right) e\right) \left(5 d^2-2 d e+3 e^2\right)}-\frac{(x (423 d-1367 e)+1367 d-293 e) (d+e x)^{m+1}}{700 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)}+\frac{4 (d+e x)^{m+1}}{25 e (m+1)}","\frac{\left(i \sqrt{14} \left(6565 d^2-2 d e (1313-3206 m)+e^2 (3939-98 m)\right)+80360 d^2-5922 d e m-32144 d e+19138 e^2 m+48216 e^2\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{5 (d+e x)}{5 d+i \sqrt{14} e-e}\right)}{19600 (m+1) \left(5 d+i \left(\sqrt{14}+i\right) e\right) \left(5 d^2-2 d e+3 e^2\right)}+\frac{\left(-i \sqrt{14} \left(6565 d^2-2 d e (1313-3206 m)+e^2 (3939-98 m)\right)+80360 d^2-5922 d e m-32144 d e+19138 e^2 m+48216 e^2\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{5 (d+e x)}{5 d-\left(1+i \sqrt{14}\right) e}\right)}{19600 (m+1) \left(5 d-\left(1+i \sqrt{14}\right) e\right) \left(5 d^2-2 d e+3 e^2\right)}-\frac{(x (423 d-1367 e)+1367 d-293 e) (d+e x)^{m+1}}{700 \left(5 x^2+2 x+3\right) \left(5 d^2-2 d e+3 e^2\right)}+\frac{4 (d+e x)^{m+1}}{25 e (m+1)}",1,"(4*(d + e*x)^(1 + m))/(25*e*(1 + m)) - ((1367*d - 293*e + (423*d - 1367*e)*x)*(d + e*x)^(1 + m))/(700*(5*d^2 - 2*d*e + 3*e^2)*(3 + 2*x + 5*x^2)) + ((80360*d^2 - 32144*d*e + 48216*e^2 + I*Sqrt[14]*(6565*d^2 - 2*d*e*(1313 - 3206*m) + e^2*(3939 - 98*m)) - 5922*d*e*m + 19138*e^2*m)*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (5*(d + e*x))/(5*d - e + I*Sqrt[14]*e)])/(19600*(5*d + I*(I + Sqrt[14])*e)*(5*d^2 - 2*d*e + 3*e^2)*(1 + m)) + ((80360*d^2 - 32144*d*e + 48216*e^2 - I*Sqrt[14]*(6565*d^2 - 2*d*e*(1313 - 3206*m) + e^2*(3939 - 98*m)) - 5922*d*e*m + 19138*e^2*m)*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (5*(d + e*x))/(5*d - (1 + I*Sqrt[14])*e)])/(19600*(5*d - (1 + I*Sqrt[14])*e)*(5*d^2 - 2*d*e + 3*e^2)*(1 + m))","A",5,3,38,0.07895,1,"{1648, 1628, 68}"
372,1,528,0,1.31158,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left(a+b x+c x^2\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(a + b*x + c*x^2)^3,x]","\frac{2 c x \left(c^3 \left(-10 a^2 h-3 a b g+b^2 f\right)-b^3 c (15 a i+b h)-c^4 (3 b e-2 a f)+a b c^2 (25 a i+8 b h)+2 b^5 i+6 c^5 d\right)-b^2 c^2 \left(39 a^2 i-5 a c g+3 c^2 e\right)+2 b c^3 \left(11 a^2 h+a c f+3 c^2 d\right)-16 a^2 c^3 (c g-2 a i)+b^3 c^2 (c f-8 a h)-b^4 c (c g-11 a i)+b^5 c h+b^6 (-i)}{2 c^4 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{x \left(c^3 \left(2 a^2 h+3 a b g+b^2 f\right)-b c^2 \left(5 a^2 i+4 a b h+b^2 g\right)+b^3 c (5 a i+b h)-c^4 (2 a f+b e)+b^5 (-i)+2 c^5 d\right)+b c^2 \left(-3 a^2 h+a c f+c^2 d\right)-2 a c^2 \left(a^2 i-a c g+c^2 e\right)-a b^2 c (c g-4 a i)+a b^3 c h-a b^4 i}{2 c^4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 c^3 \left(6 a^2 h-3 a b g+b^2 f\right)-30 a^2 b c^2 i+10 a b^3 c i-c^4 (6 b e-4 a f)+b^5 (-i)+12 c^5 d\right)}{c^3 \left(b^2-4 a c\right)^{5/2}}+\frac{i \log \left(a+b x+c x^2\right)}{2 c^3}","\frac{2 c x \left(c^3 \left(-10 a^2 h-3 a b g+b^2 f\right)-b^3 c (15 a i+b h)-c^4 (3 b e-2 a f)+a b c^2 (25 a i+8 b h)+2 b^5 i+6 c^5 d\right)-b^2 c^2 \left(39 a^2 i-5 a c g+3 c^2 e\right)+2 b c^3 \left(11 a^2 h+a c f+3 c^2 d\right)-16 a^2 c^3 (c g-2 a i)+b^3 c^2 (c f-8 a h)-b^4 c (c g-11 a i)+b^5 c h+b^6 (-i)}{2 c^4 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{x \left(c^3 \left(2 a^2 h+3 a b g+b^2 f\right)-b c^2 \left(5 a^2 i+4 a b h+b^2 g\right)+b^3 c (5 a i+b h)-c^4 (2 a f+b e)+b^5 (-i)+2 c^5 d\right)+b c^2 \left(-3 a^2 h+a c f+c^2 d\right)-2 a c^2 \left(a^2 i-a c g+c^2 e\right)-a b^2 c (c g-4 a i)+a b^3 c h-a b^4 i}{2 c^4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 c^3 \left(6 a^2 h-3 a b g+b^2 f\right)-30 a^2 b c^2 i+10 a b^3 c i-c^4 (6 b e-4 a f)+b^5 (-i)+12 c^5 d\right)}{c^3 \left(b^2-4 a c\right)^{5/2}}+\frac{i \log \left(a+b x+c x^2\right)}{2 c^3}",1,"-(a*b^3*c*h + b*c^2*(c^2*d + a*c*f - 3*a^2*h) - a*b^4*i - a*b^2*c*(c*g - 4*a*i) - 2*a*c^2*(c^2*e - a*c*g + a^2*i) + (2*c^5*d - c^4*(b*e + 2*a*f) + c^3*(b^2*f + 3*a*b*g + 2*a^2*h) - b^5*i + b^3*c*(b*h + 5*a*i) - b*c^2*(b^2*g + 4*a*b*h + 5*a^2*i))*x)/(2*c^4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (b^5*c*h + b^3*c^2*(c*f - 8*a*h) + 2*b*c^3*(3*c^2*d + a*c*f + 11*a^2*h) - b^6*i - b^4*c*(c*g - 11*a*i) - 16*a^2*c^3*(c*g - 2*a*i) - b^2*c^2*(3*c^2*e - 5*a*c*g + 39*a^2*i) + 2*c*(6*c^5*d - c^4*(3*b*e - 2*a*f) + c^3*(b^2*f - 3*a*b*g - 10*a^2*h) + 2*b^5*i - b^3*c*(b*h + 15*a*i) + a*b*c^2*(8*b*h + 25*a*i))*x)/(2*c^4*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - ((12*c^5*d - c^4*(6*b*e - 4*a*f) + 2*c^3*(b^2*f - 3*a*b*g + 6*a^2*h) - b^5*i + 10*a*b^3*c*i - 30*a^2*b*c^2*i)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(5/2)) + (i*Log[a + b*x + c*x^2])/(2*c^3)","A",6,5,38,0.1316,1,"{1660, 634, 618, 206, 628}"
373,1,765,0,5.8251879,"\int \frac{d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{a+b x+c x^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + j*x^5 + k*x^6 + l*x^7 + m*x^8)/(a + b*x + c*x^2),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(c^6 \left(2 a^2 h+3 a b g+b^2 f\right)-c^5 \left(5 a^2 b j+2 a^3 k+4 a b^2 h+b^3 g\right)+c^4 \left(9 a^2 b^2 k+7 a^3 b l+2 a^4 m+5 a b^3 j+b^4 h\right)-b^2 c^3 \left(14 a^2 b l+16 a^3 m+6 a b^2 k+b^3 j\right)+b^4 c^2 \left(20 a^2 m+7 a b l+b^2 k\right)-b^6 c (8 a m+b l)-c^7 (2 a f+b e)+b^8 m+2 c^8 d\right)}{c^8 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right) \left(c^5 \left(a^2 j+2 a b h+b^2 g\right)-c^4 \left(3 a^2 b k+a^3 l+3 a b^2 j+b^3 h\right)+b c^3 \left(6 a^2 b l+4 a^3 m+4 a b^2 k+b^3 j\right)-b^3 c^2 \left(10 a^2 m+5 a b l+b^2 k\right)+b^5 c (6 a m+b l)-c^6 (a g+b f)+b^7 (-m)+c^7 e\right)}{2 c^8}+\frac{x \left(c^4 \left(a^2 k+2 a b j+b^2 h\right)-c^3 \left(3 a^2 b l+a^3 m+3 a b^2 k+b^3 j\right)+b^2 c^2 \left(6 a^2 m+4 a b l+b^2 k\right)-b^4 c (5 a m+b l)-c^5 (a h+b g)+b^6 m+c^6 f\right)}{c^7}+\frac{x^2 \left(c^3 \left(a^2 l+2 a b k+b^2 j\right)-b c^2 \left(3 a^2 m+3 a b l+b^2 k\right)+b^3 c (4 a m+b l)-c^4 (a j+b h)+b^5 (-m)+c^5 g\right)}{2 c^6}+\frac{x^3 \left(c^2 \left(a^2 m+2 a b l+b^2 k\right)-b^2 c (3 a m+b l)-c^3 (a k+b j)+b^4 m+c^4 h\right)}{3 c^5}+\frac{x^4 \left(-c^2 (a l+b k)+b c (2 a m+b l)+b^3 (-m)+c^3 j\right)}{4 c^4}+\frac{x^5 \left(-c (a m+b l)+b^2 m+c^2 k\right)}{5 c^3}+\frac{x^6 (c l-b m)}{6 c^2}+\frac{m x^7}{7 c}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(c^6 \left(2 a^2 h+3 a b g+b^2 f\right)-c^5 \left(5 a^2 b j+2 a^3 k+4 a b^2 h+b^3 g\right)+c^4 \left(9 a^2 b^2 k+7 a^3 b l+2 a^4 m+5 a b^3 j+b^4 h\right)-b^2 c^3 \left(14 a^2 b l+16 a^3 m+6 a b^2 k+b^3 j\right)+b^4 c^2 \left(20 a^2 m+7 a b l+b^2 k\right)-b^6 c (8 a m+b l)-c^7 (2 a f+b e)+b^8 m+2 c^8 d\right)}{c^8 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right) \left(c^5 \left(a^2 j+2 a b h+b^2 g\right)-c^4 \left(3 a^2 b k+a^3 l+3 a b^2 j+b^3 h\right)+b c^3 \left(6 a^2 b l+4 a^3 m+4 a b^2 k+b^3 j\right)-b^3 c^2 \left(10 a^2 m+5 a b l+b^2 k\right)+b^5 c (6 a m+b l)-c^6 (a g+b f)+b^7 (-m)+c^7 e\right)}{2 c^8}+\frac{x \left(c^4 \left(a^2 k+2 a b j+b^2 h\right)-c^3 \left(3 a^2 b l+a^3 m+3 a b^2 k+b^3 j\right)+b^2 c^2 \left(6 a^2 m+4 a b l+b^2 k\right)-b^4 c (5 a m+b l)-c^5 (a h+b g)+b^6 m+c^6 f\right)}{c^7}+\frac{x^2 \left(c^3 \left(a^2 l+2 a b k+b^2 j\right)-b c^2 \left(3 a^2 m+3 a b l+b^2 k\right)+b^3 c (4 a m+b l)-c^4 (a j+b h)+b^5 (-m)+c^5 g\right)}{2 c^6}+\frac{x^3 \left(c^2 \left(a^2 m+2 a b l+b^2 k\right)-b^2 c (3 a m+b l)-c^3 (a k+b j)+b^4 m+c^4 h\right)}{3 c^5}+\frac{x^4 \left(-c^2 (a l+b k)+b c (2 a m+b l)+b^3 (-m)+c^3 j\right)}{4 c^4}+\frac{x^5 \left(-c (a m+b l)+b^2 m+c^2 k\right)}{5 c^3}+\frac{x^6 (c l-b m)}{6 c^2}+\frac{m x^7}{7 c}",1,"((c^6*f - c^5*(b*g + a*h) + c^4*(b^2*h + 2*a*b*j + a^2*k) + b^6*m - b^4*c*(b*l + 5*a*m) + b^2*c^2*(b^2*k + 4*a*b*l + 6*a^2*m) - c^3*(b^3*j + 3*a*b^2*k + 3*a^2*b*l + a^3*m))*x)/c^7 + ((c^5*g - c^4*(b*h + a*j) + c^3*(b^2*j + 2*a*b*k + a^2*l) - b^5*m + b^3*c*(b*l + 4*a*m) - b*c^2*(b^2*k + 3*a*b*l + 3*a^2*m))*x^2)/(2*c^6) + ((c^4*h - c^3*(b*j + a*k) + b^4*m - b^2*c*(b*l + 3*a*m) + c^2*(b^2*k + 2*a*b*l + a^2*m))*x^3)/(3*c^5) + ((c^3*j - c^2*(b*k + a*l) - b^3*m + b*c*(b*l + 2*a*m))*x^4)/(4*c^4) + ((c^2*k + b^2*m - c*(b*l + a*m))*x^5)/(5*c^3) + ((c*l - b*m)*x^6)/(6*c^2) + (m*x^7)/(7*c) - ((2*c^8*d - c^7*(b*e + 2*a*f) + c^6*(b^2*f + 3*a*b*g + 2*a^2*h) - c^5*(b^3*g + 4*a*b^2*h + 5*a^2*b*j + 2*a^3*k) + b^8*m - b^6*c*(b*l + 8*a*m) + b^4*c^2*(b^2*k + 7*a*b*l + 20*a^2*m) - b^2*c^3*(b^3*j + 6*a*b^2*k + 14*a^2*b*l + 16*a^3*m) + c^4*(b^4*h + 5*a*b^3*j + 9*a^2*b^2*k + 7*a^3*b*l + 2*a^4*m))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^8*Sqrt[b^2 - 4*a*c]) + ((c^7*e - c^6*(b*f + a*g) + c^5*(b^2*g + 2*a*b*h + a^2*j) - c^4*(b^3*h + 3*a*b^2*j + 3*a^2*b*k + a^3*l) - b^7*m + b^5*c*(b*l + 6*a*m) - b^3*c^2*(b^2*k + 5*a*b*l + 10*a^2*m) + b*c^3*(b^3*j + 4*a*b^2*k + 6*a^2*b*l + 4*a^3*m))*Log[a + b*x + c*x^2])/(2*c^8)","A",6,5,53,0.09434,1,"{1657, 634, 618, 206, 628}"
374,1,208,0,0.3523476,"\int \left(1+4 x-7 x^2\right)^3 \left(2+5 x+x^2\right) \sqrt{3+2 x+5 x^2} \, dx","Int[(1 + 4*x - 7*x^2)^3*(2 + 5*x + x^2)*Sqrt[3 + 2*x + 5*x^2],x]","-\frac{343}{50} \left(5 x^2+2 x+3\right)^{3/2} x^7-\frac{50519 \left(5 x^2+2 x+3\right)^{3/2} x^6}{2250}+\frac{190939 \left(5 x^2+2 x+3\right)^{3/2} x^5}{3000}-\frac{888751 \left(5 x^2+2 x+3\right)^{3/2} x^4}{105000}-\frac{90960857 \left(5 x^2+2 x+3\right)^{3/2} x^3}{1575000}+\frac{98060877 \left(5 x^2+2 x+3\right)^{3/2} x^2}{4375000}+\frac{1045360143 \left(5 x^2+2 x+3\right)^{3/2} x}{43750000}-\frac{1968340667 \left(5 x^2+2 x+3\right)^{3/2}}{131250000}-\frac{77159983 (5 x+1) \sqrt{5 x^2+2 x+3}}{31250000}-\frac{540119881 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{15625000 \sqrt{5}}","-\frac{343}{50} \left(5 x^2+2 x+3\right)^{3/2} x^7-\frac{50519 \left(5 x^2+2 x+3\right)^{3/2} x^6}{2250}+\frac{190939 \left(5 x^2+2 x+3\right)^{3/2} x^5}{3000}-\frac{888751 \left(5 x^2+2 x+3\right)^{3/2} x^4}{105000}-\frac{90960857 \left(5 x^2+2 x+3\right)^{3/2} x^3}{1575000}+\frac{98060877 \left(5 x^2+2 x+3\right)^{3/2} x^2}{4375000}+\frac{1045360143 \left(5 x^2+2 x+3\right)^{3/2} x}{43750000}-\frac{1968340667 \left(5 x^2+2 x+3\right)^{3/2}}{131250000}-\frac{77159983 (5 x+1) \sqrt{5 x^2+2 x+3}}{31250000}-\frac{540119881 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{15625000 \sqrt{5}}",1,"(-77159983*(1 + 5*x)*Sqrt[3 + 2*x + 5*x^2])/31250000 - (1968340667*(3 + 2*x + 5*x^2)^(3/2))/131250000 + (1045360143*x*(3 + 2*x + 5*x^2)^(3/2))/43750000 + (98060877*x^2*(3 + 2*x + 5*x^2)^(3/2))/4375000 - (90960857*x^3*(3 + 2*x + 5*x^2)^(3/2))/1575000 - (888751*x^4*(3 + 2*x + 5*x^2)^(3/2))/105000 + (190939*x^5*(3 + 2*x + 5*x^2)^(3/2))/3000 - (50519*x^6*(3 + 2*x + 5*x^2)^(3/2))/2250 - (343*x^7*(3 + 2*x + 5*x^2)^(3/2))/50 - (540119881*ArcSinh[(1 + 5*x)/Sqrt[14]])/(15625000*Sqrt[5])","A",11,5,35,0.1429,1,"{1661, 640, 612, 619, 215}"
375,1,166,0,0.203479,"\int \left(1+4 x-7 x^2\right)^2 \left(2+5 x+x^2\right) \sqrt{3+2 x+5 x^2} \, dx","Int[(1 + 4*x - 7*x^2)^2*(2 + 5*x + x^2)*Sqrt[3 + 2*x + 5*x^2],x]","\frac{49}{40} \left(5 x^2+2 x+3\right)^{3/2} x^5+\frac{989}{200} \left(5 x^2+2 x+3\right)^{3/2} x^4-\frac{25277 \left(5 x^2+2 x+3\right)^{3/2} x^3}{3000}-\frac{77509 \left(5 x^2+2 x+3\right)^{3/2} x^2}{25000}+\frac{1781669 \left(5 x^2+2 x+3\right)^{3/2} x}{250000}+\frac{198439 \left(5 x^2+2 x+3\right)^{3/2}}{750000}-\frac{2521723 (5 x+1) \sqrt{5 x^2+2 x+3}}{1250000}-\frac{17652061 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{625000 \sqrt{5}}","\frac{49}{40} \left(5 x^2+2 x+3\right)^{3/2} x^5+\frac{989}{200} \left(5 x^2+2 x+3\right)^{3/2} x^4-\frac{25277 \left(5 x^2+2 x+3\right)^{3/2} x^3}{3000}-\frac{77509 \left(5 x^2+2 x+3\right)^{3/2} x^2}{25000}+\frac{1781669 \left(5 x^2+2 x+3\right)^{3/2} x}{250000}+\frac{198439 \left(5 x^2+2 x+3\right)^{3/2}}{750000}-\frac{2521723 (5 x+1) \sqrt{5 x^2+2 x+3}}{1250000}-\frac{17652061 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{625000 \sqrt{5}}",1,"(-2521723*(1 + 5*x)*Sqrt[3 + 2*x + 5*x^2])/1250000 + (198439*(3 + 2*x + 5*x^2)^(3/2))/750000 + (1781669*x*(3 + 2*x + 5*x^2)^(3/2))/250000 - (77509*x^2*(3 + 2*x + 5*x^2)^(3/2))/25000 - (25277*x^3*(3 + 2*x + 5*x^2)^(3/2))/3000 + (989*x^4*(3 + 2*x + 5*x^2)^(3/2))/200 + (49*x^5*(3 + 2*x + 5*x^2)^(3/2))/40 - (17652061*ArcSinh[(1 + 5*x)/Sqrt[14]])/(625000*Sqrt[5])","A",9,5,35,0.1429,1,"{1661, 640, 612, 619, 215}"
376,1,124,0,0.1157721,"\int \left(1+4 x-7 x^2\right) \left(2+5 x+x^2\right) \sqrt{3+2 x+5 x^2} \, dx","Int[(1 + 4*x - 7*x^2)*(2 + 5*x + x^2)*Sqrt[3 + 2*x + 5*x^2],x]","-\frac{7}{30} \left(5 x^2+2 x+3\right)^{3/2} x^3-\frac{289}{250} \left(5 x^2+2 x+3\right)^{3/2} x^2+\frac{2149 \left(5 x^2+2 x+3\right)^{3/2} x}{2500}+\frac{7819 \left(5 x^2+2 x+3\right)^{3/2}}{7500}-\frac{4633 (5 x+1) \sqrt{5 x^2+2 x+3}}{12500}-\frac{32431 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{6250 \sqrt{5}}","-\frac{7}{30} \left(5 x^2+2 x+3\right)^{3/2} x^3-\frac{289}{250} \left(5 x^2+2 x+3\right)^{3/2} x^2+\frac{2149 \left(5 x^2+2 x+3\right)^{3/2} x}{2500}+\frac{7819 \left(5 x^2+2 x+3\right)^{3/2}}{7500}-\frac{4633 (5 x+1) \sqrt{5 x^2+2 x+3}}{12500}-\frac{32431 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{6250 \sqrt{5}}",1,"(-4633*(1 + 5*x)*Sqrt[3 + 2*x + 5*x^2])/12500 + (7819*(3 + 2*x + 5*x^2)^(3/2))/7500 + (2149*x*(3 + 2*x + 5*x^2)^(3/2))/2500 - (289*x^2*(3 + 2*x + 5*x^2)^(3/2))/250 - (7*x^3*(3 + 2*x + 5*x^2)^(3/2))/30 - (32431*ArcSinh[(1 + 5*x)/Sqrt[14]])/(6250*Sqrt[5])","A",7,5,33,0.1515,1,"{1661, 640, 612, 619, 215}"
377,1,187,0,0.3547199,"\int \frac{\left(2+5 x+x^2\right) \sqrt{3+2 x+5 x^2}}{1+4 x-7 x^2} \, dx","Int[((2 + 5*x + x^2)*Sqrt[3 + 2*x + 5*x^2])/(1 + 4*x - 7*x^2),x]","-\frac{1}{490} \sqrt{5 x^2+2 x+3} (35 x+397)-\frac{3}{343} \sqrt{\frac{1}{11} \left(497041-146555 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)+\frac{3}{343} \sqrt{\frac{1}{11} \left(497041+146555 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)-\frac{8233 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1715 \sqrt{5}}","-\frac{1}{490} \sqrt{5 x^2+2 x+3} (35 x+397)-\frac{3}{343} \sqrt{\frac{1}{11} \left(497041-146555 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)+\frac{3}{343} \sqrt{\frac{1}{11} \left(497041+146555 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)-\frac{8233 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1715 \sqrt{5}}",1,"-((397 + 35*x)*Sqrt[3 + 2*x + 5*x^2])/490 - (8233*ArcSinh[(1 + 5*x)/Sqrt[14]])/(1715*Sqrt[5]) - (3*Sqrt[(497041 - 146555*Sqrt[11])/11]*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/343 + (3*Sqrt[(497041 + 146555*Sqrt[11])/11]*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/343","A",9,7,35,0.2000,1,"{1066, 1076, 619, 215, 1032, 724, 206}"
378,1,199,0,0.2500701,"\int \frac{\left(2+5 x+x^2\right) \sqrt{3+2 x+5 x^2}}{\left(1+4 x-7 x^2\right)^2} \, dx","Int[((2 + 5*x + x^2)*Sqrt[3 + 2*x + 5*x^2])/(1 + 4*x - 7*x^2)^2,x]","\frac{3 \sqrt{5 x^2+2 x+3} (61 x+3)}{154 \left(-7 x^2+4 x+1\right)}-\frac{\sqrt{\frac{325022311+39132731 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{2156}+\frac{\sqrt{\frac{325022311-39132731 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{2156}+\frac{1}{49} \sqrt{5} \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)","\frac{3 \sqrt{5 x^2+2 x+3} (61 x+3)}{154 \left(-7 x^2+4 x+1\right)}-\frac{\sqrt{\frac{325022311+39132731 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{2156}+\frac{\sqrt{\frac{325022311-39132731 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{2156}+\frac{1}{49} \sqrt{5} \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)",1,"(3*(3 + 61*x)*Sqrt[3 + 2*x + 5*x^2])/(154*(1 + 4*x - 7*x^2)) + (Sqrt[5]*ArcSinh[(1 + 5*x)/Sqrt[14]])/49 - (Sqrt[(325022311 + 39132731*Sqrt[11])/1397]*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/2156 + (Sqrt[(325022311 - 39132731*Sqrt[11])/1397]*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/2156","A",9,7,35,0.2000,1,"{1054, 1076, 619, 215, 1032, 724, 206}"
379,1,213,0,0.2365512,"\int \frac{\left(2+5 x+x^2\right) \sqrt{3+2 x+5 x^2}}{\left(1+4 x-7 x^2\right)^3} \, dx","Int[((2 + 5*x + x^2)*Sqrt[3 + 2*x + 5*x^2])/(1 + 4*x - 7*x^2)^3,x]","-\frac{\sqrt{5 x^2+2 x+3} (272941-813113 x)}{1721104 \left(-7 x^2+4 x+1\right)}+\frac{3 (61 x+3) \sqrt{5 x^2+2 x+3}}{308 \left(-7 x^2+4 x+1\right)^2}-\frac{\sqrt{\frac{6492253020949-11879169071 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{491744}+\frac{\sqrt{\frac{6492253020949+11879169071 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{491744}","-\frac{\sqrt{5 x^2+2 x+3} (272941-813113 x)}{1721104 \left(-7 x^2+4 x+1\right)}+\frac{3 (61 x+3) \sqrt{5 x^2+2 x+3}}{308 \left(-7 x^2+4 x+1\right)^2}-\frac{\sqrt{\frac{6492253020949-11879169071 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{491744}+\frac{\sqrt{\frac{6492253020949+11879169071 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{491744}",1,"(3*(3 + 61*x)*Sqrt[3 + 2*x + 5*x^2])/(308*(1 + 4*x - 7*x^2)^2) - ((272941 - 813113*x)*Sqrt[3 + 2*x + 5*x^2])/(1721104*(1 + 4*x - 7*x^2)) - (Sqrt[(6492253020949 - 11879169071*Sqrt[11])/1397]*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/491744 + (Sqrt[(6492253020949 + 11879169071*Sqrt[11])/1397]*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/491744","A",7,5,35,0.1429,1,"{1054, 1060, 1032, 724, 206}"
380,1,231,0,0.3638434,"\int \left(1+4 x-7 x^2\right)^3 \left(2+5 x+x^2\right) \left(3+2 x+5 x^2\right)^{3/2} \, dx","Int[(1 + 4*x - 7*x^2)^3*(2 + 5*x + x^2)*(3 + 2*x + 5*x^2)^(3/2),x]","-\frac{343}{60} \left(5 x^2+2 x+3\right)^{5/2} x^7-\frac{61103 \left(5 x^2+2 x+3\right)^{5/2} x^6}{3300}+\frac{1031177 \left(5 x^2+2 x+3\right)^{5/2} x^5}{20625}-\frac{796559 \left(5 x^2+2 x+3\right)^{5/2} x^4}{123750}-\frac{190236913 \left(5 x^2+2 x+3\right)^{5/2} x^3}{4950000}+\frac{2173004363 \left(5 x^2+2 x+3\right)^{5/2} x^2}{173250000}+\frac{837379699 \left(5 x^2+2 x+3\right)^{5/2} x}{72187500}-\frac{6133820867 \left(5 x^2+2 x+3\right)^{5/2}}{1203125000}-\frac{22840599 (5 x+1) \left(5 x^2+2 x+3\right)^{3/2}}{62500000}-\frac{479652579 (5 x+1) \sqrt{5 x^2+2 x+3}}{312500000}-\frac{3357568053 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{156250000 \sqrt{5}}","-\frac{343}{60} \left(5 x^2+2 x+3\right)^{5/2} x^7-\frac{61103 \left(5 x^2+2 x+3\right)^{5/2} x^6}{3300}+\frac{1031177 \left(5 x^2+2 x+3\right)^{5/2} x^5}{20625}-\frac{796559 \left(5 x^2+2 x+3\right)^{5/2} x^4}{123750}-\frac{190236913 \left(5 x^2+2 x+3\right)^{5/2} x^3}{4950000}+\frac{2173004363 \left(5 x^2+2 x+3\right)^{5/2} x^2}{173250000}+\frac{837379699 \left(5 x^2+2 x+3\right)^{5/2} x}{72187500}-\frac{6133820867 \left(5 x^2+2 x+3\right)^{5/2}}{1203125000}-\frac{22840599 (5 x+1) \left(5 x^2+2 x+3\right)^{3/2}}{62500000}-\frac{479652579 (5 x+1) \sqrt{5 x^2+2 x+3}}{312500000}-\frac{3357568053 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{156250000 \sqrt{5}}",1,"(-479652579*(1 + 5*x)*Sqrt[3 + 2*x + 5*x^2])/312500000 - (22840599*(1 + 5*x)*(3 + 2*x + 5*x^2)^(3/2))/62500000 - (6133820867*(3 + 2*x + 5*x^2)^(5/2))/1203125000 + (837379699*x*(3 + 2*x + 5*x^2)^(5/2))/72187500 + (2173004363*x^2*(3 + 2*x + 5*x^2)^(5/2))/173250000 - (190236913*x^3*(3 + 2*x + 5*x^2)^(5/2))/4950000 - (796559*x^4*(3 + 2*x + 5*x^2)^(5/2))/123750 + (1031177*x^5*(3 + 2*x + 5*x^2)^(5/2))/20625 - (61103*x^6*(3 + 2*x + 5*x^2)^(5/2))/3300 - (343*x^7*(3 + 2*x + 5*x^2)^(5/2))/60 - (3357568053*ArcSinh[(1 + 5*x)/Sqrt[14]])/(156250000*Sqrt[5])","A",12,5,35,0.1429,1,"{1661, 640, 612, 619, 215}"
381,1,189,0,0.2265317,"\int \left(1+4 x-7 x^2\right)^2 \left(2+5 x+x^2\right) \left(3+2 x+5 x^2\right)^{3/2} \, dx","Int[(1 + 4*x - 7*x^2)^2*(2 + 5*x + x^2)*(3 + 2*x + 5*x^2)^(3/2),x]","\frac{49}{50} \left(5 x^2+2 x+3\right)^{5/2} x^5+\frac{581}{150} \left(5 x^2+2 x+3\right)^{5/2} x^4-\frac{18379 \left(5 x^2+2 x+3\right)^{5/2} x^3}{3000}-\frac{219271 \left(5 x^2+2 x+3\right)^{5/2} x^2}{105000}+\frac{86721 \left(5 x^2+2 x+3\right)^{5/2} x}{21875}+\frac{505667 \left(5 x^2+2 x+3\right)^{5/2}}{2187500}-\frac{690561 (5 x+1) \left(5 x^2+2 x+3\right)^{3/2}}{1250000}-\frac{14501781 (5 x+1) \sqrt{5 x^2+2 x+3}}{6250000}-\frac{101512467 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{3125000 \sqrt{5}}","\frac{49}{50} \left(5 x^2+2 x+3\right)^{5/2} x^5+\frac{581}{150} \left(5 x^2+2 x+3\right)^{5/2} x^4-\frac{18379 \left(5 x^2+2 x+3\right)^{5/2} x^3}{3000}-\frac{219271 \left(5 x^2+2 x+3\right)^{5/2} x^2}{105000}+\frac{86721 \left(5 x^2+2 x+3\right)^{5/2} x}{21875}+\frac{505667 \left(5 x^2+2 x+3\right)^{5/2}}{2187500}-\frac{690561 (5 x+1) \left(5 x^2+2 x+3\right)^{3/2}}{1250000}-\frac{14501781 (5 x+1) \sqrt{5 x^2+2 x+3}}{6250000}-\frac{101512467 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{3125000 \sqrt{5}}",1,"(-14501781*(1 + 5*x)*Sqrt[3 + 2*x + 5*x^2])/6250000 - (690561*(1 + 5*x)*(3 + 2*x + 5*x^2)^(3/2))/1250000 + (505667*(3 + 2*x + 5*x^2)^(5/2))/2187500 + (86721*x*(3 + 2*x + 5*x^2)^(5/2))/21875 - (219271*x^2*(3 + 2*x + 5*x^2)^(5/2))/105000 - (18379*x^3*(3 + 2*x + 5*x^2)^(5/2))/3000 + (581*x^4*(3 + 2*x + 5*x^2)^(5/2))/150 + (49*x^5*(3 + 2*x + 5*x^2)^(5/2))/50 - (101512467*ArcSinh[(1 + 5*x)/Sqrt[14]])/(3125000*Sqrt[5])","A",10,5,35,0.1429,1,"{1661, 640, 612, 619, 215}"
382,1,147,0,0.1297807,"\int \left(1+4 x-7 x^2\right) \left(2+5 x+x^2\right) \left(3+2 x+5 x^2\right)^{3/2} \, dx","Int[(1 + 4*x - 7*x^2)*(2 + 5*x + x^2)*(3 + 2*x + 5*x^2)^(3/2),x]","-\frac{7}{40} \left(5 x^2+2 x+3\right)^{5/2} x^3-\frac{1163 \left(5 x^2+2 x+3\right)^{5/2} x^2}{1400}+\frac{2809 \left(5 x^2+2 x+3\right)^{5/2} x}{5250}+\frac{149509 \left(5 x^2+2 x+3\right)^{5/2}}{262500}-\frac{18397 (5 x+1) \left(5 x^2+2 x+3\right)^{3/2}}{150000}-\frac{128779 (5 x+1) \sqrt{5 x^2+2 x+3}}{250000}-\frac{901453 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{125000 \sqrt{5}}","-\frac{7}{40} \left(5 x^2+2 x+3\right)^{5/2} x^3-\frac{1163 \left(5 x^2+2 x+3\right)^{5/2} x^2}{1400}+\frac{2809 \left(5 x^2+2 x+3\right)^{5/2} x}{5250}+\frac{149509 \left(5 x^2+2 x+3\right)^{5/2}}{262500}-\frac{18397 (5 x+1) \left(5 x^2+2 x+3\right)^{3/2}}{150000}-\frac{128779 (5 x+1) \sqrt{5 x^2+2 x+3}}{250000}-\frac{901453 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{125000 \sqrt{5}}",1,"(-128779*(1 + 5*x)*Sqrt[3 + 2*x + 5*x^2])/250000 - (18397*(1 + 5*x)*(3 + 2*x + 5*x^2)^(3/2))/150000 + (149509*(3 + 2*x + 5*x^2)^(5/2))/262500 + (2809*x*(3 + 2*x + 5*x^2)^(5/2))/5250 - (1163*x^2*(3 + 2*x + 5*x^2)^(5/2))/1400 - (7*x^3*(3 + 2*x + 5*x^2)^(5/2))/40 - (901453*ArcSinh[(1 + 5*x)/Sqrt[14]])/(125000*Sqrt[5])","A",8,5,33,0.1515,1,"{1661, 640, 612, 619, 215}"
383,1,210,0,0.3040758,"\int \frac{\left(2+5 x+x^2\right) \left(3+2 x+5 x^2\right)^{3/2}}{1+4 x-7 x^2} \, dx","Int[((2 + 5*x + x^2)*(3 + 2*x + 5*x^2)^(3/2))/(1 + 4*x - 7*x^2),x]","-\frac{1}{980} (35 x+267) \left(5 x^2+2 x+3\right)^{3/2}-\frac{3 (196105 x+571621) \sqrt{5 x^2+2 x+3}}{240100}-\frac{6 \sqrt{\frac{2}{11} \left(8098902607-2434122235 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{16807}+\frac{6 \sqrt{\frac{2}{11} \left(8098902607+2434122235 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{16807}-\frac{34425687 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{840350 \sqrt{5}}","-\frac{1}{980} (35 x+267) \left(5 x^2+2 x+3\right)^{3/2}-\frac{3 (196105 x+571621) \sqrt{5 x^2+2 x+3}}{240100}-\frac{6 \sqrt{\frac{2}{11} \left(8098902607-2434122235 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{16807}+\frac{6 \sqrt{\frac{2}{11} \left(8098902607+2434122235 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{16807}-\frac{34425687 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{840350 \sqrt{5}}",1,"(-3*(571621 + 196105*x)*Sqrt[3 + 2*x + 5*x^2])/240100 - ((267 + 35*x)*(3 + 2*x + 5*x^2)^(3/2))/980 - (34425687*ArcSinh[(1 + 5*x)/Sqrt[14]])/(840350*Sqrt[5]) - (6*Sqrt[(2*(8098902607 - 2434122235*Sqrt[11]))/11]*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/16807 + (6*Sqrt[(2*(8098902607 + 2434122235*Sqrt[11]))/11]*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/16807","A",10,7,35,0.2000,1,"{1066, 1076, 619, 215, 1032, 724, 206}"
384,1,222,0,0.3215995,"\int \frac{\left(2+5 x+x^2\right) \left(3+2 x+5 x^2\right)^{3/2}}{\left(1+4 x-7 x^2\right)^2} \, dx","Int[((2 + 5*x + x^2)*(3 + 2*x + 5*x^2)^(3/2))/(1 + 4*x - 7*x^2)^2,x]","\frac{3 (61 x+3) \left(5 x^2+2 x+3\right)^{3/2}}{154 \left(-7 x^2+4 x+1\right)}+\frac{(3395 x+5826) \sqrt{5 x^2+2 x+3}}{3773}-\frac{\sqrt{\frac{1}{22} \left(52175400311-13155376531 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{26411}-\frac{\sqrt{\frac{1}{22} \left(52175400311+13155376531 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{26411}+\frac{16691 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{2401 \sqrt{5}}","\frac{3 (61 x+3) \left(5 x^2+2 x+3\right)^{3/2}}{154 \left(-7 x^2+4 x+1\right)}+\frac{(3395 x+5826) \sqrt{5 x^2+2 x+3}}{3773}-\frac{\sqrt{\frac{1}{22} \left(52175400311-13155376531 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{26411}-\frac{\sqrt{\frac{1}{22} \left(52175400311+13155376531 \sqrt{11}\right)} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{26411}+\frac{16691 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{2401 \sqrt{5}}",1,"((5826 + 3395*x)*Sqrt[3 + 2*x + 5*x^2])/3773 + (3*(3 + 61*x)*(3 + 2*x + 5*x^2)^(3/2))/(154*(1 + 4*x - 7*x^2)) + (16691*ArcSinh[(1 + 5*x)/Sqrt[14]])/(2401*Sqrt[5]) - (Sqrt[(52175400311 - 13155376531*Sqrt[11])/22]*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/26411 - (Sqrt[(52175400311 + 13155376531*Sqrt[11])/22]*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/26411","A",10,8,35,0.2286,1,"{1054, 1066, 1076, 619, 215, 1032, 724, 206}"
385,1,234,0,0.3186174,"\int \frac{\left(2+5 x+x^2\right) \left(3+2 x+5 x^2\right)^{3/2}}{\left(1+4 x-7 x^2\right)^3} \, dx","Int[((2 + 5*x + x^2)*(3 + 2*x + 5*x^2)^(3/2))/(1 + 4*x - 7*x^2)^3,x]","\frac{3 (61 x+3) \left(5 x^2+2 x+3\right)^{3/2}}{308 \left(-7 x^2+4 x+1\right)^2}-\frac{(9495-37088 x) \sqrt{5 x^2+2 x+3}}{23716 \left(-7 x^2+4 x+1\right)}-\frac{\sqrt{\frac{62294197250171-2085440742055 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{332024}+\frac{\sqrt{\frac{62294197250171+2085440742055 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{332024}-\frac{5}{343} \sqrt{5} \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)","\frac{3 (61 x+3) \left(5 x^2+2 x+3\right)^{3/2}}{308 \left(-7 x^2+4 x+1\right)^2}-\frac{(9495-37088 x) \sqrt{5 x^2+2 x+3}}{23716 \left(-7 x^2+4 x+1\right)}-\frac{\sqrt{\frac{62294197250171-2085440742055 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{332024}+\frac{\sqrt{\frac{62294197250171+2085440742055 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{332024}-\frac{5}{343} \sqrt{5} \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)",1,"-((9495 - 37088*x)*Sqrt[3 + 2*x + 5*x^2])/(23716*(1 + 4*x - 7*x^2)) + (3*(3 + 61*x)*(3 + 2*x + 5*x^2)^(3/2))/(308*(1 + 4*x - 7*x^2)^2) - (5*Sqrt[5]*ArcSinh[(1 + 5*x)/Sqrt[14]])/343 - (Sqrt[(62294197250171 - 2085440742055*Sqrt[11])/2794]*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/332024 + (Sqrt[(62294197250171 + 2085440742055*Sqrt[11])/2794]*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/332024","A",10,7,35,0.2000,1,"{1054, 1076, 619, 215, 1032, 724, 206}"
386,1,185,0,0.3123317,"\int \frac{\left(1+4 x-7 x^2\right)^3 \left(2+5 x+x^2\right)}{\sqrt{3+2 x+5 x^2}} \, dx","Int[((1 + 4*x - 7*x^2)^3*(2 + 5*x + x^2))/Sqrt[3 + 2*x + 5*x^2],x]","-\frac{343}{40} \sqrt{5 x^2+2 x+3} x^7-\frac{1141}{40} \sqrt{5 x^2+2 x+3} x^6+\frac{26159}{300} \sqrt{5 x^2+2 x+3} x^5-\frac{47807 \sqrt{5 x^2+2 x+3} x^4}{3750}-\frac{5160533 \sqrt{5 x^2+2 x+3} x^3}{50000}+\frac{40722851 \sqrt{5 x^2+2 x+3} x^2}{750000}+\frac{5793077 \sqrt{5 x^2+2 x+3} x}{75000}-\frac{16515809 \sqrt{5 x^2+2 x+3}}{156250}-\frac{77513689 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{625000 \sqrt{5}}","-\frac{343}{40} \sqrt{5 x^2+2 x+3} x^7-\frac{1141}{40} \sqrt{5 x^2+2 x+3} x^6+\frac{26159}{300} \sqrt{5 x^2+2 x+3} x^5-\frac{47807 \sqrt{5 x^2+2 x+3} x^4}{3750}-\frac{5160533 \sqrt{5 x^2+2 x+3} x^3}{50000}+\frac{40722851 \sqrt{5 x^2+2 x+3} x^2}{750000}+\frac{5793077 \sqrt{5 x^2+2 x+3} x}{75000}-\frac{16515809 \sqrt{5 x^2+2 x+3}}{156250}-\frac{77513689 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{625000 \sqrt{5}}",1,"(-16515809*Sqrt[3 + 2*x + 5*x^2])/156250 + (5793077*x*Sqrt[3 + 2*x + 5*x^2])/75000 + (40722851*x^2*Sqrt[3 + 2*x + 5*x^2])/750000 - (5160533*x^3*Sqrt[3 + 2*x + 5*x^2])/50000 - (47807*x^4*Sqrt[3 + 2*x + 5*x^2])/3750 + (26159*x^5*Sqrt[3 + 2*x + 5*x^2])/300 - (1141*x^6*Sqrt[3 + 2*x + 5*x^2])/40 - (343*x^7*Sqrt[3 + 2*x + 5*x^2])/40 - (77513689*ArcSinh[(1 + 5*x)/Sqrt[14]])/(625000*Sqrt[5])","A",10,4,35,0.1143,1,"{1661, 640, 619, 215}"
387,1,143,0,0.2028133,"\int \frac{\left(1+4 x-7 x^2\right)^2 \left(2+5 x+x^2\right)}{\sqrt{3+2 x+5 x^2}} \, dx","Int[((1 + 4*x - 7*x^2)^2*(2 + 5*x + x^2))/Sqrt[3 + 2*x + 5*x^2],x]","\frac{49}{30} \sqrt{5 x^2+2 x+3} x^5+\frac{5131}{750} \sqrt{5 x^2+2 x+3} x^4-\frac{33259 \sqrt{5 x^2+2 x+3} x^3}{2500}-\frac{207427 \sqrt{5 x^2+2 x+3} x^2}{37500}+\frac{36073 \sqrt{5 x^2+2 x+3} x}{1875}-\frac{22053 \sqrt{5 x^2+2 x+3}}{31250}-\frac{1719097 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{31250 \sqrt{5}}","\frac{49}{30} \sqrt{5 x^2+2 x+3} x^5+\frac{5131}{750} \sqrt{5 x^2+2 x+3} x^4-\frac{33259 \sqrt{5 x^2+2 x+3} x^3}{2500}-\frac{207427 \sqrt{5 x^2+2 x+3} x^2}{37500}+\frac{36073 \sqrt{5 x^2+2 x+3} x}{1875}-\frac{22053 \sqrt{5 x^2+2 x+3}}{31250}-\frac{1719097 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{31250 \sqrt{5}}",1,"(-22053*Sqrt[3 + 2*x + 5*x^2])/31250 + (36073*x*Sqrt[3 + 2*x + 5*x^2])/1875 - (207427*x^2*Sqrt[3 + 2*x + 5*x^2])/37500 - (33259*x^3*Sqrt[3 + 2*x + 5*x^2])/2500 + (5131*x^4*Sqrt[3 + 2*x + 5*x^2])/750 + (49*x^5*Sqrt[3 + 2*x + 5*x^2])/30 - (1719097*ArcSinh[(1 + 5*x)/Sqrt[14]])/(31250*Sqrt[5])","A",8,4,35,0.1143,1,"{1661, 640, 619, 215}"
388,1,101,0,0.1450734,"\int \frac{\left(1+4 x-7 x^2\right) \left(2+5 x+x^2\right)}{\sqrt{3+2 x+5 x^2}} \, dx","Int[((1 + 4*x - 7*x^2)*(2 + 5*x + x^2))/Sqrt[3 + 2*x + 5*x^2],x]","-\frac{7}{20} \sqrt{5 x^2+2 x+3} x^3-\frac{571}{300} \sqrt{5 x^2+2 x+3} x^2+\frac{59}{30} \sqrt{5 x^2+2 x+3} x+\frac{463}{125} \sqrt{5 x^2+2 x+3}-\frac{1901 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{250 \sqrt{5}}","-\frac{7}{20} \sqrt{5 x^2+2 x+3} x^3-\frac{571}{300} \sqrt{5 x^2+2 x+3} x^2+\frac{59}{30} \sqrt{5 x^2+2 x+3} x+\frac{463}{125} \sqrt{5 x^2+2 x+3}-\frac{1901 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{250 \sqrt{5}}",1,"(463*Sqrt[3 + 2*x + 5*x^2])/125 + (59*x*Sqrt[3 + 2*x + 5*x^2])/30 - (571*x^2*Sqrt[3 + 2*x + 5*x^2])/300 - (7*x^3*Sqrt[3 + 2*x + 5*x^2])/20 - (1901*ArcSinh[(1 + 5*x)/Sqrt[14]])/(250*Sqrt[5])","A",6,4,33,0.1212,1,"{1661, 640, 619, 215}"
389,1,164,0,0.2301324,"\int \frac{2+5 x+x^2}{\left(1+4 x-7 x^2\right) \sqrt{3+2 x+5 x^2}} \, dx","Int[(2 + 5*x + x^2)/((1 + 4*x - 7*x^2)*Sqrt[3 + 2*x + 5*x^2]),x]","-\frac{3}{14} \sqrt{\frac{4091-1055 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)+\frac{3}{14} \sqrt{\frac{4091+1055 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)-\frac{\sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{7 \sqrt{5}}","-\frac{3}{14} \sqrt{\frac{4091-1055 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)+\frac{3}{14} \sqrt{\frac{4091+1055 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)-\frac{\sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{7 \sqrt{5}}",1,"-ArcSinh[(1 + 5*x)/Sqrt[14]]/(7*Sqrt[5]) - (3*Sqrt[(4091 - 1055*Sqrt[11])/2794]*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/14 + (3*Sqrt[(4091 + 1055*Sqrt[11])/2794]*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/14","A",8,6,35,0.1714,1,"{1076, 619, 215, 1032, 724, 206}"
390,1,178,0,0.1959384,"\int \frac{2+5 x+x^2}{\left(1+4 x-7 x^2\right)^2 \sqrt{3+2 x+5 x^2}} \, dx","Int[(2 + 5*x + x^2)/((1 + 4*x - 7*x^2)^2*Sqrt[3 + 2*x + 5*x^2]),x]","-\frac{3 \sqrt{5 x^2+2 x+3} (40-371 x)}{5588 \left(-7 x^2+4 x+1\right)}-\frac{\sqrt{\frac{3027900955+14035681 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{11176}+\frac{\sqrt{\frac{3027900955-14035681 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{11176}","-\frac{3 \sqrt{5 x^2+2 x+3} (40-371 x)}{5588 \left(-7 x^2+4 x+1\right)}-\frac{\sqrt{\frac{3027900955+14035681 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{11176}+\frac{\sqrt{\frac{3027900955-14035681 \sqrt{11}}{2794}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{11176}",1,"(-3*(40 - 371*x)*Sqrt[3 + 2*x + 5*x^2])/(5588*(1 + 4*x - 7*x^2)) - (Sqrt[(3027900955 + 14035681*Sqrt[11])/2794]*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/11176 + (Sqrt[(3027900955 - 14035681*Sqrt[11])/2794]*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/11176","A",6,4,35,0.1143,1,"{1060, 1032, 724, 206}"
391,1,227,0,0.2711384,"\int \frac{2+5 x+x^2}{\left(1+4 x-7 x^2\right)^3 \sqrt{3+2 x+5 x^2}} \, dx","Int[(2 + 5*x + x^2)/((1 + 4*x - 7*x^2)^3*Sqrt[3 + 2*x + 5*x^2]),x]","-\frac{7 \sqrt{5 x^2+2 x+3} (409769-1189370 x)}{62451488 \left(-7 x^2+4 x+1\right)}-\frac{3 (40-371 x) \sqrt{5 x^2+2 x+3}}{11176 \left(-7 x^2+4 x+1\right)^2}-\frac{7 \left(39370231-2538725 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{124902976 \sqrt{22 \left(125-17 \sqrt{11}\right)}}+\frac{7 \left(39370231+2538725 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{124902976 \sqrt{22 \left(125+17 \sqrt{11}\right)}}","-\frac{7 \sqrt{5 x^2+2 x+3} (409769-1189370 x)}{62451488 \left(-7 x^2+4 x+1\right)}-\frac{3 (40-371 x) \sqrt{5 x^2+2 x+3}}{11176 \left(-7 x^2+4 x+1\right)^2}-\frac{7 \left(39370231-2538725 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{124902976 \sqrt{22 \left(125-17 \sqrt{11}\right)}}+\frac{7 \left(39370231+2538725 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{124902976 \sqrt{22 \left(125+17 \sqrt{11}\right)}}",1,"(-3*(40 - 371*x)*Sqrt[3 + 2*x + 5*x^2])/(11176*(1 + 4*x - 7*x^2)^2) - (7*(409769 - 1189370*x)*Sqrt[3 + 2*x + 5*x^2])/(62451488*(1 + 4*x - 7*x^2)) - (7*(39370231 - 2538725*Sqrt[11])*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/(124902976*Sqrt[22*(125 - 17*Sqrt[11])]) + (7*(39370231 + 2538725*Sqrt[11])*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/(124902976*Sqrt[22*(125 + 17*Sqrt[11])])","A",7,4,35,0.1143,1,"{1060, 1032, 724, 206}"
392,1,166,0,0.2410015,"\int \frac{\left(1+4 x-7 x^2\right)^3 \left(2+5 x+x^2\right)}{\left(3+2 x+5 x^2\right)^{3/2}} \, dx","Int[((1 + 4*x - 7*x^2)^3*(2 + 5*x + x^2))/(3 + 2*x + 5*x^2)^(3/2),x]","-\frac{343}{150} \sqrt{5 x^2+2 x+3} x^5-\frac{25921 \sqrt{5 x^2+2 x+3} x^4}{3750}+\frac{393659 \sqrt{5 x^2+2 x+3} x^3}{12500}-\frac{2583293 \sqrt{5 x^2+2 x+3} x^2}{187500}-\frac{3192602 \sqrt{5 x^2+2 x+3} x}{46875}+\frac{15715799 \sqrt{5 x^2+2 x+3}}{156250}+\frac{16 (6122807-5338217 x)}{546875 \sqrt{5 x^2+2 x+3}}+\frac{50047657 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{156250 \sqrt{5}}","-\frac{343}{150} \sqrt{5 x^2+2 x+3} x^5-\frac{25921 \sqrt{5 x^2+2 x+3} x^4}{3750}+\frac{393659 \sqrt{5 x^2+2 x+3} x^3}{12500}-\frac{2583293 \sqrt{5 x^2+2 x+3} x^2}{187500}-\frac{3192602 \sqrt{5 x^2+2 x+3} x}{46875}+\frac{15715799 \sqrt{5 x^2+2 x+3}}{156250}+\frac{16 (6122807-5338217 x)}{546875 \sqrt{5 x^2+2 x+3}}+\frac{50047657 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{156250 \sqrt{5}}",1,"(16*(6122807 - 5338217*x))/(546875*Sqrt[3 + 2*x + 5*x^2]) + (15715799*Sqrt[3 + 2*x + 5*x^2])/156250 - (3192602*x*Sqrt[3 + 2*x + 5*x^2])/46875 - (2583293*x^2*Sqrt[3 + 2*x + 5*x^2])/187500 + (393659*x^3*Sqrt[3 + 2*x + 5*x^2])/12500 - (25921*x^4*Sqrt[3 + 2*x + 5*x^2])/3750 - (343*x^5*Sqrt[3 + 2*x + 5*x^2])/150 + (50047657*ArcSinh[(1 + 5*x)/Sqrt[14]])/(156250*Sqrt[5])","A",9,5,35,0.1429,1,"{1660, 1661, 640, 619, 215}"
393,1,124,0,0.1608347,"\int \frac{\left(1+4 x-7 x^2\right)^2 \left(2+5 x+x^2\right)}{\left(3+2 x+5 x^2\right)^{3/2}} \, dx","Int[((1 + 4*x - 7*x^2)^2*(2 + 5*x + x^2))/(3 + 2*x + 5*x^2)^(3/2),x]","\frac{49}{100} \sqrt{5 x^2+2 x+3} x^3+\frac{203}{100} \sqrt{5 x^2+2 x+3} x^2-\frac{8749 \sqrt{5 x^2+2 x+3} x}{1250}-\frac{5086 \sqrt{5 x^2+2 x+3}}{3125}-\frac{8 (136602 x+12983)}{21875 \sqrt{5 x^2+2 x+3}}+\frac{89583 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1250 \sqrt{5}}","\frac{49}{100} \sqrt{5 x^2+2 x+3} x^3+\frac{203}{100} \sqrt{5 x^2+2 x+3} x^2-\frac{8749 \sqrt{5 x^2+2 x+3} x}{1250}-\frac{5086 \sqrt{5 x^2+2 x+3}}{3125}-\frac{8 (136602 x+12983)}{21875 \sqrt{5 x^2+2 x+3}}+\frac{89583 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{1250 \sqrt{5}}",1,"(-8*(12983 + 136602*x))/(21875*Sqrt[3 + 2*x + 5*x^2]) - (5086*Sqrt[3 + 2*x + 5*x^2])/3125 - (8749*x*Sqrt[3 + 2*x + 5*x^2])/1250 + (203*x^2*Sqrt[3 + 2*x + 5*x^2])/100 + (49*x^3*Sqrt[3 + 2*x + 5*x^2])/100 + (89583*ArcSinh[(1 + 5*x)/Sqrt[14]])/(1250*Sqrt[5])","A",7,5,35,0.1429,1,"{1660, 1661, 640, 619, 215}"
394,1,82,0,0.0865919,"\int \frac{\left(1+4 x-7 x^2\right) \left(2+5 x+x^2\right)}{\left(3+2 x+5 x^2\right)^{3/2}} \, dx","Int[((1 + 4*x - 7*x^2)*(2 + 5*x + x^2))/(3 + 2*x + 5*x^2)^(3/2),x]","-\frac{7}{50} \sqrt{5 x^2+2 x+3} x-\frac{261}{250} \sqrt{5 x^2+2 x+3}-\frac{2 (2449 x+2321)}{875 \sqrt{5 x^2+2 x+3}}+\frac{149 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{25 \sqrt{5}}","-\frac{7}{50} \sqrt{5 x^2+2 x+3} x-\frac{261}{250} \sqrt{5 x^2+2 x+3}-\frac{2 (2449 x+2321)}{875 \sqrt{5 x^2+2 x+3}}+\frac{149 \sinh ^{-1}\left(\frac{5 x+1}{\sqrt{14}}\right)}{25 \sqrt{5}}",1,"(-2*(2321 + 2449*x))/(875*Sqrt[3 + 2*x + 5*x^2]) - (261*Sqrt[3 + 2*x + 5*x^2])/250 - (7*x*Sqrt[3 + 2*x + 5*x^2])/50 + (149*ArcSinh[(1 + 5*x)/Sqrt[14]])/(25*Sqrt[5])","A",5,5,33,0.1515,1,"{1660, 1661, 640, 619, 215}"
395,1,166,0,0.2157548,"\int \frac{2+5 x+x^2}{\left(1+4 x-7 x^2\right) \left(3+2 x+5 x^2\right)^{3/2}} \, dx","Int[(2 + 5*x + x^2)/((1 + 4*x - 7*x^2)*(3 + 2*x + 5*x^2)^(3/2)),x]","-\frac{131-605 x}{3556 \sqrt{5 x^2+2 x+3}}-\frac{3 \sqrt{\frac{281693-25015 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{1016}+\frac{3 \sqrt{\frac{281693+25015 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{1016}","-\frac{131-605 x}{3556 \sqrt{5 x^2+2 x+3}}-\frac{3 \sqrt{\frac{281693-25015 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{1016}+\frac{3 \sqrt{\frac{281693+25015 \sqrt{11}}{1397}} \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{1016}",1,"-(131 - 605*x)/(3556*Sqrt[3 + 2*x + 5*x^2]) - (3*Sqrt[(281693 - 25015*Sqrt[11])/1397]*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/1016 + (3*Sqrt[(281693 + 25015*Sqrt[11])/1397]*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/1016","A",6,4,35,0.1143,1,"{1060, 1032, 724, 206}"
396,1,215,0,0.3163056,"\int \frac{2+5 x+x^2}{\left(1+4 x-7 x^2\right)^2 \left(3+2 x+5 x^2\right)^{3/2}} \, dx","Int[(2 + 5*x + x^2)/((1 + 4*x - 7*x^2)^2*(3 + 2*x + 5*x^2)^(3/2)),x]","-\frac{3 (40-371 x)}{5588 \left(-7 x^2+4 x+1\right) \sqrt{5 x^2+2 x+3}}-\frac{22755 x+76567}{19870928 \sqrt{5 x^2+2 x+3}}-\frac{7 \left(541543-5144 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{2838704 \sqrt{22 \left(125-17 \sqrt{11}\right)}}+\frac{7 \left(541543+5144 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{2838704 \sqrt{22 \left(125+17 \sqrt{11}\right)}}","-\frac{3 (40-371 x)}{5588 \left(-7 x^2+4 x+1\right) \sqrt{5 x^2+2 x+3}}-\frac{22755 x+76567}{19870928 \sqrt{5 x^2+2 x+3}}-\frac{7 \left(541543-5144 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{2838704 \sqrt{22 \left(125-17 \sqrt{11}\right)}}+\frac{7 \left(541543+5144 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{2838704 \sqrt{22 \left(125+17 \sqrt{11}\right)}}",1,"-(76567 + 22755*x)/(19870928*Sqrt[3 + 2*x + 5*x^2]) - (3*(40 - 371*x))/(5588*(1 + 4*x - 7*x^2)*Sqrt[3 + 2*x + 5*x^2]) - (7*(541543 - 5144*Sqrt[11])*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/(2838704*Sqrt[22*(125 - 17*Sqrt[11])]) + (7*(541543 + 5144*Sqrt[11])*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/(2838704*Sqrt[22*(125 + 17*Sqrt[11])])","A",7,4,35,0.1143,1,"{1060, 1032, 724, 206}"
397,1,250,0,0.3239719,"\int \frac{2+5 x+x^2}{\left(1+4 x-7 x^2\right)^3 \left(3+2 x+5 x^2\right)^{3/2}} \, dx","Int[(2 + 5*x + x^2)/((1 + 4*x - 7*x^2)^3*(3 + 2*x + 5*x^2)^(3/2)),x]","-\frac{2701733-9148874 x}{62451488 \left(-7 x^2+4 x+1\right) \sqrt{5 x^2+2 x+3}}-\frac{5 (1118731375 x+461370781)}{222077491328 \sqrt{5 x^2+2 x+3}}-\frac{3 (40-371 x)}{11176 \left(-7 x^2+4 x+1\right)^2 \sqrt{5 x^2+2 x+3}}-\frac{7 \left(2792860024-84865895 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{31725355904 \sqrt{22 \left(125-17 \sqrt{11}\right)}}+\frac{7 \left(2792860024+84865895 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{31725355904 \sqrt{22 \left(125+17 \sqrt{11}\right)}}","-\frac{2701733-9148874 x}{62451488 \left(-7 x^2+4 x+1\right) \sqrt{5 x^2+2 x+3}}-\frac{5 (1118731375 x+461370781)}{222077491328 \sqrt{5 x^2+2 x+3}}-\frac{3 (40-371 x)}{11176 \left(-7 x^2+4 x+1\right)^2 \sqrt{5 x^2+2 x+3}}-\frac{7 \left(2792860024-84865895 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17-5 \sqrt{11}\right) x-\sqrt{11}+23}{\sqrt{2 \left(125-17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{31725355904 \sqrt{22 \left(125-17 \sqrt{11}\right)}}+\frac{7 \left(2792860024+84865895 \sqrt{11}\right) \tanh ^{-1}\left(\frac{\left(17+5 \sqrt{11}\right) x+\sqrt{11}+23}{\sqrt{2 \left(125+17 \sqrt{11}\right)} \sqrt{5 x^2+2 x+3}}\right)}{31725355904 \sqrt{22 \left(125+17 \sqrt{11}\right)}}",1,"(-5*(461370781 + 1118731375*x))/(222077491328*Sqrt[3 + 2*x + 5*x^2]) - (3*(40 - 371*x))/(11176*(1 + 4*x - 7*x^2)^2*Sqrt[3 + 2*x + 5*x^2]) - (2701733 - 9148874*x)/(62451488*(1 + 4*x - 7*x^2)*Sqrt[3 + 2*x + 5*x^2]) - (7*(2792860024 - 84865895*Sqrt[11])*ArcTanh[(23 - Sqrt[11] + (17 - 5*Sqrt[11])*x)/(Sqrt[2*(125 - 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/(31725355904*Sqrt[22*(125 - 17*Sqrt[11])]) + (7*(2792860024 + 84865895*Sqrt[11])*ArcTanh[(23 + Sqrt[11] + (17 + 5*Sqrt[11])*x)/(Sqrt[2*(125 + 17*Sqrt[11])]*Sqrt[3 + 2*x + 5*x^2])])/(31725355904*Sqrt[22*(125 + 17*Sqrt[11])])","A",8,4,35,0.1143,1,"{1060, 1032, 724, 206}"
398,1,166,0,0.1465896,"\int \left(a+c x^2\right)^p \left(A+C x^2\right) \left(d+f x^2\right)^q \, dx","Int[(a + c*x^2)^p*(A + C*x^2)*(d + f*x^2)^q,x]","A x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)+\frac{1}{3} C x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{3}{2};-p,-q;\frac{5}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)","A x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)+\frac{1}{3} C x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{3}{2};-p,-q;\frac{5}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)",1,"(A*x*(a + c*x^2)^p*(d + f*x^2)^q*AppellF1[1/2, -p, -q, 3/2, -((c*x^2)/a), -((f*x^2)/d)])/((1 + (c*x^2)/a)^p*(1 + (f*x^2)/d)^q) + (C*x^3*(a + c*x^2)^p*(d + f*x^2)^q*AppellF1[3/2, -p, -q, 5/2, -((c*x^2)/a), -((f*x^2)/d)])/(3*(1 + (c*x^2)/a)^p*(1 + (f*x^2)/d)^q)","A",7,5,26,0.1923,1,"{531, 430, 429, 511, 510}"
399,1,167,0,0.152508,"\int (A+B x) \left(a+c x^2\right)^p \left(d+f x^2\right)^q \, dx","Int[(A + B*x)*(a + c*x^2)^p*(d + f*x^2)^q,x]","A x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)+\frac{B \left(a+c x^2\right)^{p+1} \left(d+f x^2\right)^q \left(\frac{c \left(d+f x^2\right)}{c d-a f}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{f \left(c x^2+a\right)}{c d-a f}\right)}{2 c (p+1)}","A x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)+\frac{B \left(a+c x^2\right)^{p+1} \left(d+f x^2\right)^q \left(\frac{c \left(d+f x^2\right)}{c d-a f}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{f \left(c x^2+a\right)}{c d-a f}\right)}{2 c (p+1)}",1,"(A*x*(a + c*x^2)^p*(d + f*x^2)^q*AppellF1[1/2, -p, -q, 3/2, -((c*x^2)/a), -((f*x^2)/d)])/((1 + (c*x^2)/a)^p*(1 + (f*x^2)/d)^q) + (B*(a + c*x^2)^(1 + p)*(d + f*x^2)^q*Hypergeometric2F1[1 + p, -q, 2 + p, -((f*(a + c*x^2))/(c*d - a*f))])/(2*c*(1 + p)*((c*(d + f*x^2))/(c*d - a*f))^q)","A",7,6,24,0.2500,1,"{1010, 430, 429, 444, 70, 69}"
400,1,252,0,0.4806778,"\int \left(a+c x^2\right)^p \left(A+B x+C x^2\right) \left(d+f x^2\right)^q \, dx","Int[(a + c*x^2)^p*(A + B*x + C*x^2)*(d + f*x^2)^q,x]","A x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)+\frac{1}{3} C x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{3}{2};-p,-q;\frac{5}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)+\frac{B \left(a+c x^2\right)^{p+1} \left(d+f x^2\right)^q \left(\frac{c \left(d+f x^2\right)}{c d-a f}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{f \left(c x^2+a\right)}{c d-a f}\right)}{2 c (p+1)}","A x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)+\frac{1}{3} C x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \left(d+f x^2\right)^q \left(\frac{f x^2}{d}+1\right)^{-q} F_1\left(\frac{3}{2};-p,-q;\frac{5}{2};-\frac{c x^2}{a},-\frac{f x^2}{d}\right)+\frac{B \left(a+c x^2\right)^{p+1} \left(d+f x^2\right)^q \left(\frac{c \left(d+f x^2\right)}{c d-a f}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{f \left(c x^2+a\right)}{c d-a f}\right)}{2 c (p+1)}",1,"(A*x*(a + c*x^2)^p*(d + f*x^2)^q*AppellF1[1/2, -p, -q, 3/2, -((c*x^2)/a), -((f*x^2)/d)])/((1 + (c*x^2)/a)^p*(1 + (f*x^2)/d)^q) + (C*x^3*(a + c*x^2)^p*(d + f*x^2)^q*AppellF1[3/2, -p, -q, 5/2, -((c*x^2)/a), -((f*x^2)/d)])/(3*(1 + (c*x^2)/a)^p*(1 + (f*x^2)/d)^q) + (B*(a + c*x^2)^(1 + p)*(d + f*x^2)^q*Hypergeometric2F1[1 + p, -q, 2 + p, -((f*(a + c*x^2))/(c*d - a*f))])/(2*c*(1 + p)*((c*(d + f*x^2))/(c*d - a*f))^q)","A",11,8,29,0.2759,1,"{6742, 430, 429, 444, 70, 69, 511, 510}"