1,1,415,0,0.6727618,"\int \sqrt{1-d x} \sqrt{1+d x} (e+f x)^3 \left(A+B x+C x^2\right) \, dx","Int[Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^3*(A + B*x + C*x^2),x]","-\frac{\left(1-d^2 x^2\right)^{3/2} (e+f x)^2 \left(7 d^2 f (2 A f+B e)-C \left(3 d^2 e^2-8 f^2\right)\right)}{70 d^4 f}+\frac{\left(1-d^2 x^2\right)^{3/2} \left(3 d^2 f x \left(-98 A d^2 e f^2-14 B d^2 e^2 f-35 B f^3+6 C d^2 e^3-41 C e f^2\right)+8 \left(C \left(-30 d^2 e^2 f^2+3 d^4 e^4-8 f^4\right)-7 d^2 f \left(2 A f \left(6 d^2 e^2+f^2\right)+B \left(d^2 e^3+6 e f^2\right)\right)\right)\right)}{840 d^6 f}+\frac{x \sqrt{1-d^2 x^2} \left(8 A d^4 e^3+6 A d^2 e f^2+6 B d^2 e^2 f+B f^3+2 C d^2 e^3+3 C e f^2\right)}{16 d^4}+\frac{\sin ^{-1}(d x) \left(8 A d^4 e^3+6 A d^2 e f^2+6 B d^2 e^2 f+B f^3+2 C d^2 e^3+3 C e f^2\right)}{16 d^5}+\frac{\left(1-d^2 x^2\right)^{3/2} (e+f x)^3 (3 C e-7 B f)}{42 d^2 f}-\frac{C \left(1-d^2 x^2\right)^{3/2} (e+f x)^4}{7 d^2 f}","-\frac{\left(1-d^2 x^2\right)^{3/2} (e+f x)^2 \left(7 d^2 f (2 A f+B e)-C \left(3 d^2 e^2-8 f^2\right)\right)}{70 d^4 f}+\frac{\left(1-d^2 x^2\right)^{3/2} \left(3 d^2 f x \left(-98 A d^2 e f^2-14 B d^2 e^2 f-35 B f^3+6 C d^2 e^3-41 C e f^2\right)+8 \left(C \left(-30 d^2 e^2 f^2+3 d^4 e^4-8 f^4\right)-7 d^2 f \left(2 A f \left(6 d^2 e^2+f^2\right)+B \left(d^2 e^3+6 e f^2\right)\right)\right)\right)}{840 d^6 f}+\frac{x \sqrt{1-d^2 x^2} \left(8 A d^4 e^3+6 A d^2 e f^2+6 B d^2 e^2 f+B f^3+2 C d^2 e^3+3 C e f^2\right)}{16 d^4}+\frac{\sin ^{-1}(d x) \left(8 A d^4 e^3+6 A d^2 e f^2+6 B d^2 e^2 f+B f^3+2 C d^2 e^3+3 C e f^2\right)}{16 d^5}+\frac{\left(1-d^2 x^2\right)^{3/2} (e+f x)^3 (3 C e-7 B f)}{42 d^2 f}-\frac{C \left(1-d^2 x^2\right)^{3/2} (e+f x)^4}{7 d^2 f}",1,"((2*C*d^2*e^3 + 8*A*d^4*e^3 + 6*B*d^2*e^2*f + 3*C*e*f^2 + 6*A*d^2*e*f^2 + B*f^3)*x*Sqrt[1 - d^2*x^2])/(16*d^4) - ((7*d^2*f*(B*e + 2*A*f) - C*(3*d^2*e^2 - 8*f^2))*(e + f*x)^2*(1 - d^2*x^2)^(3/2))/(70*d^4*f) + ((3*C*e - 7*B*f)*(e + f*x)^3*(1 - d^2*x^2)^(3/2))/(42*d^2*f) - (C*(e + f*x)^4*(1 - d^2*x^2)^(3/2))/(7*d^2*f) + ((8*(C*(3*d^4*e^4 - 30*d^2*e^2*f^2 - 8*f^4) - 7*d^2*f*(2*A*f*(6*d^2*e^2 + f^2) + B*(d^2*e^3 + 6*e*f^2))) + 3*d^2*f*(6*C*d^2*e^3 - 14*B*d^2*e^2*f - 41*C*e*f^2 - 98*A*d^2*e*f^2 - 35*B*f^3)*x)*(1 - d^2*x^2)^(3/2))/(840*d^6*f) + ((2*C*d^2*e^3 + 8*A*d^4*e^3 + 6*B*d^2*e^2*f + 3*C*e*f^2 + 6*A*d^2*e*f^2 + B*f^3)*ArcSin[d*x])/(16*d^5)","A",7,6,37,0.1622,1,"{1609, 1654, 833, 780, 195, 216}"
2,1,286,0,0.5632793,"\int \sqrt{1-d x} \sqrt{1+d x} (e+f x)^2 \left(A+B x+C x^2\right) \, dx","Int[Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^2*(A + B*x + C*x^2),x]","\frac{\left(1-d^2 x^2\right)^{3/2} \left(8 \left(C \left(d^2 e^3-4 e f^2\right)-2 f \left(5 A d^2 e f+B \left(d^2 e^2+f^2\right)\right)\right)-3 f x \left(5 f^2 \left(2 A d^2+C\right)-2 d^2 e (C e-2 B f)\right)\right)}{120 d^4 f}+\frac{x \sqrt{1-d^2 x^2} \left(2 d^2 \left(A \left(4 d^2 e^2+f^2\right)+2 B e f\right)+C \left(2 d^2 e^2+f^2\right)\right)}{16 d^4}+\frac{\sin ^{-1}(d x) \left(2 d^2 \left(A \left(4 d^2 e^2+f^2\right)+2 B e f\right)+C \left(2 d^2 e^2+f^2\right)\right)}{16 d^5}+\frac{\left(1-d^2 x^2\right)^{3/2} (e+f x)^2 (C e-2 B f)}{10 d^2 f}-\frac{C \left(1-d^2 x^2\right)^{3/2} (e+f x)^3}{6 d^2 f}","\frac{\left(1-d^2 x^2\right)^{3/2} \left(8 \left(C \left(d^2 e^3-4 e f^2\right)-2 f \left(5 A d^2 e f+B \left(d^2 e^2+f^2\right)\right)\right)-3 f x \left(5 f^2 \left(2 A d^2+C\right)-2 d^2 e (C e-2 B f)\right)\right)}{120 d^4 f}+\frac{x \sqrt{1-d^2 x^2} \left(2 d^2 \left(A \left(4 d^2 e^2+f^2\right)+2 B e f\right)+C \left(2 d^2 e^2+f^2\right)\right)}{16 d^4}+\frac{\sin ^{-1}(d x) \left(2 d^2 \left(A \left(4 d^2 e^2+f^2\right)+2 B e f\right)+C \left(2 d^2 e^2+f^2\right)\right)}{16 d^5}+\frac{\left(1-d^2 x^2\right)^{3/2} (e+f x)^2 (C e-2 B f)}{10 d^2 f}-\frac{C \left(1-d^2 x^2\right)^{3/2} (e+f x)^3}{6 d^2 f}",1,"((C*(2*d^2*e^2 + f^2) + 2*d^2*(2*B*e*f + A*(4*d^2*e^2 + f^2)))*x*Sqrt[1 - d^2*x^2])/(16*d^4) + ((C*e - 2*B*f)*(e + f*x)^2*(1 - d^2*x^2)^(3/2))/(10*d^2*f) - (C*(e + f*x)^3*(1 - d^2*x^2)^(3/2))/(6*d^2*f) + ((8*(C*(d^2*e^3 - 4*e*f^2) - 2*f*(5*A*d^2*e*f + B*(d^2*e^2 + f^2))) - 3*f*(5*(C + 2*A*d^2)*f^2 - 2*d^2*e*(C*e - 2*B*f))*x)*(1 - d^2*x^2)^(3/2))/(120*d^4*f) + ((C*(2*d^2*e^2 + f^2) + 2*d^2*(2*B*e*f + A*(4*d^2*e^2 + f^2)))*ArcSin[d*x])/(16*d^5)","A",6,6,37,0.1622,1,"{1609, 1654, 833, 780, 195, 216}"
3,1,170,0,0.250389,"\int \sqrt{1-d x} \sqrt{1+d x} (e+f x) \left(A+B x+C x^2\right) \, dx","Int[Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)*(A + B*x + C*x^2),x]","-\frac{\left(1-d^2 x^2\right)^{3/2} \left(4 \left(5 d^2 f (A f+B e)-\frac{1}{4} C \left(12 d^2 e^2-8 f^2\right)\right)-3 d^2 f x (3 C e-5 B f)\right)}{60 d^4 f}+\frac{x \sqrt{1-d^2 x^2} \left(4 A d^2 e+B f+C e\right)}{8 d^2}+\frac{\sin ^{-1}(d x) \left(4 A d^2 e+B f+C e\right)}{8 d^3}-\frac{C \left(1-d^2 x^2\right)^{3/2} (e+f x)^2}{5 d^2 f}","-\frac{\left(1-d^2 x^2\right)^{3/2} \left(4 \left(5 d^2 f (A f+B e)-C \left(3 d^2 e^2-2 f^2\right)\right)-3 d^2 f x (3 C e-5 B f)\right)}{60 d^4 f}+\frac{x \sqrt{1-d^2 x^2} \left(4 A d^2 e+B f+C e\right)}{8 d^2}+\frac{\sin ^{-1}(d x) \left(4 A d^2 e+B f+C e\right)}{8 d^3}-\frac{C \left(1-d^2 x^2\right)^{3/2} (e+f x)^2}{5 d^2 f}",1,"((C*e + 4*A*d^2*e + B*f)*x*Sqrt[1 - d^2*x^2])/(8*d^2) - (C*(e + f*x)^2*(1 - d^2*x^2)^(3/2))/(5*d^2*f) - ((4*(5*d^2*f*(B*e + A*f) - (C*(12*d^2*e^2 - 8*f^2))/4) - 3*d^2*f*(3*C*e - 5*B*f)*x)*(1 - d^2*x^2)^(3/2))/(60*d^4*f) + ((C*e + 4*A*d^2*e + B*f)*ArcSin[d*x])/(8*d^3)","A",5,5,35,0.1429,1,"{1609, 1654, 780, 195, 216}"
4,1,95,0,0.0729961,"\int \sqrt{1-d x} \sqrt{1+d x} \left(A+B x+C x^2\right) \, dx","Int[Sqrt[1 - d*x]*Sqrt[1 + d*x]*(A + B*x + C*x^2),x]","\frac{x \sqrt{1-d^2 x^2} \left(4 A d^2+C\right)}{8 d^2}+\frac{\left(4 A d^2+C\right) \sin ^{-1}(d x)}{8 d^3}-\frac{B \left(1-d^2 x^2\right)^{3/2}}{3 d^2}-\frac{C x \left(1-d^2 x^2\right)^{3/2}}{4 d^2}","\frac{x \sqrt{1-d^2 x^2} \left(4 A d^2+C\right)}{8 d^2}+\frac{\left(4 A d^2+C\right) \sin ^{-1}(d x)}{8 d^3}-\frac{B \left(1-d^2 x^2\right)^{3/2}}{3 d^2}-\frac{C x \left(1-d^2 x^2\right)^{3/2}}{4 d^2}",1,"((C + 4*A*d^2)*x*Sqrt[1 - d^2*x^2])/(8*d^2) - (B*(1 - d^2*x^2)^(3/2))/(3*d^2) - (C*x*(1 - d^2*x^2)^(3/2))/(4*d^2) + ((C + 4*A*d^2)*ArcSin[d*x])/(8*d^3)","A",5,5,30,0.1667,1,"{899, 1815, 641, 195, 216}"
5,1,122,0,0.3107792,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)),x]","\frac{\left(A f^2-B e f+C e^2\right) \tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right)}{f^2 \sqrt{d^2 e^2-f^2}}-\frac{\sin ^{-1}(d x) (C e-B f)}{d f^2}-\frac{C \sqrt{1-d^2 x^2}}{d^2 f}","\frac{\left(A f^2-B e f+C e^2\right) \tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right)}{f^2 \sqrt{d^2 e^2-f^2}}-\frac{\sin ^{-1}(d x) (C e-B f)}{d f^2}-\frac{C \sqrt{1-d^2 x^2}}{d^2 f}",1,"-((C*Sqrt[1 - d^2*x^2])/(d^2*f)) - ((C*e - B*f)*ArcSin[d*x])/(d*f^2) + ((C*e^2 - B*e*f + A*f^2)*ArcTan[(f + d^2*e*x)/(Sqrt[d^2*e^2 - f^2]*Sqrt[1 - d^2*x^2])])/(f^2*Sqrt[d^2*e^2 - f^2])","A",6,6,37,0.1622,1,"{1609, 1654, 844, 216, 725, 204}"
6,1,163,0,0.3305824,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^2} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^2),x]","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{f \left(d^2 e^2-f^2\right) (e+f x)}-\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(-A d^2 e f^2+B f^3+C d^2 e^3-2 C e f^2\right)}{f^2 \left(d^2 e^2-f^2\right)^{3/2}}+\frac{C \sin ^{-1}(d x)}{d f^2}","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{f \left(d^2 e^2-f^2\right) (e+f x)}-\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(-A d^2 e f^2+B f^3+C d^2 e^3-2 C e f^2\right)}{f^2 \left(d^2 e^2-f^2\right)^{3/2}}+\frac{C \sin ^{-1}(d x)}{d f^2}",1,"((C*e^2 - B*e*f + A*f^2)*Sqrt[1 - d^2*x^2])/(f*(d^2*e^2 - f^2)*(e + f*x)) + (C*ArcSin[d*x])/(d*f^2) - ((C*d^2*e^3 - 2*C*e*f^2 - A*d^2*e*f^2 + B*f^3)*ArcTan[(f + d^2*e*x)/(Sqrt[d^2*e^2 - f^2]*Sqrt[1 - d^2*x^2])])/(f^2*(d^2*e^2 - f^2)^(3/2))","A",6,6,37,0.1622,1,"{1609, 1651, 844, 216, 725, 204}"
7,1,248,0,0.3551883,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^3} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^3),x]","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{2 f \left(d^2 e^2-f^2\right) (e+f x)^2}-\frac{\sqrt{1-d^2 x^2} \left(-3 A d^2 e f^2+B d^2 e^2 f+2 B f^3+C d^2 e^3-4 C e f^2\right)}{2 f \left(d^2 e^2-f^2\right)^2 (e+f x)}+\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(C \left(d^2 e^2+2 f^2\right)-d^2 \left(3 B e f-A \left(2 d^2 e^2+f^2\right)\right)\right)}{2 \left(d^2 e^2-f^2\right)^{5/2}}","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{2 f \left(d^2 e^2-f^2\right) (e+f x)^2}-\frac{\sqrt{1-d^2 x^2} \left(-3 A d^2 e f^2+B d^2 e^2 f+2 B f^3+C d^2 e^3-4 C e f^2\right)}{2 f \left(d^2 e^2-f^2\right)^2 (e+f x)}+\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(C \left(d^2 e^2+2 f^2\right)-d^2 \left(3 B e f-A \left(2 d^2 e^2+f^2\right)\right)\right)}{2 \left(d^2 e^2-f^2\right)^{5/2}}",1,"((C*e^2 - B*e*f + A*f^2)*Sqrt[1 - d^2*x^2])/(2*f*(d^2*e^2 - f^2)*(e + f*x)^2) - ((C*d^2*e^3 + B*d^2*e^2*f - 4*C*e*f^2 - 3*A*d^2*e*f^2 + 2*B*f^3)*Sqrt[1 - d^2*x^2])/(2*f*(d^2*e^2 - f^2)^2*(e + f*x)) + ((C*(d^2*e^2 + 2*f^2) - d^2*(3*B*e*f - A*(2*d^2*e^2 + f^2)))*ArcTan[(f + d^2*e*x)/(Sqrt[d^2*e^2 - f^2]*Sqrt[1 - d^2*x^2])])/(2*(d^2*e^2 - f^2)^(5/2))","A",5,5,37,0.1351,1,"{1609, 1651, 807, 725, 204}"
8,1,340,0,0.6329665,"\int \frac{(e+f x)^3 \left(A+B x+C x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[((e + f*x)^3*(A + B*x + C*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{\sqrt{1-d^2 x^2} (e+f x)^2 \left(5 f (4 A f+3 B e)-C \left(3 e^2-\frac{16 f^2}{d^2}\right)\right)}{60 d^2 f}+\frac{\sqrt{1-d^2 x^2} \left(d^2 f x \left(-100 A d^2 e f^2-30 B d^2 e^2 f-45 B f^3+6 C d^2 e^3-71 C e f^2\right)+4 \left(C \left(-52 d^2 e^2 f^2+3 d^4 e^4-16 f^4\right)-5 d^2 f \left(4 A f \left(4 d^2 e^2+f^2\right)+3 B \left(d^2 e^3+4 e f^2\right)\right)\right)\right)}{120 d^6 f}+\frac{\sin ^{-1}(d x) \left(8 A d^4 e^3+12 A d^2 e f^2+12 B d^2 e^2 f+3 B f^3+4 C d^2 e^3+9 C e f^2\right)}{8 d^5}+\frac{\sqrt{1-d^2 x^2} (e+f x)^3 (C e-5 B f)}{20 d^2 f}-\frac{C \sqrt{1-d^2 x^2} (e+f x)^4}{5 d^2 f}","\frac{\sqrt{1-d^2 x^2} \left(d^2 f x \left(-100 A d^2 e f^2-30 B d^2 e^2 f-45 B f^3+6 C d^2 e^3-71 C e f^2\right)+4 \left(C \left(-52 d^2 e^2 f^2+3 d^4 e^4-16 f^4\right)-5 d^2 f \left(4 A f \left(4 d^2 e^2+f^2\right)+3 B \left(d^2 e^3+4 e f^2\right)\right)\right)\right)}{120 d^6 f}+\frac{\sin ^{-1}(d x) \left(8 A d^4 e^3+12 A d^2 e f^2+12 B d^2 e^2 f+3 B f^3+4 C d^2 e^3+9 C e f^2\right)}{8 d^5}-\frac{\sqrt{1-d^2 x^2} (e+f x)^2 \left(4 f^2 \left(5 A d^2+4 C\right)-3 d^2 e (C e-5 B f)\right)}{60 d^4 f}+\frac{\sqrt{1-d^2 x^2} (e+f x)^3 (C e-5 B f)}{20 d^2 f}-\frac{C \sqrt{1-d^2 x^2} (e+f x)^4}{5 d^2 f}",1,"-((5*f*(3*B*e + 4*A*f) - C*(3*e^2 - (16*f^2)/d^2))*(e + f*x)^2*Sqrt[1 - d^2*x^2])/(60*d^2*f) + ((C*e - 5*B*f)*(e + f*x)^3*Sqrt[1 - d^2*x^2])/(20*d^2*f) - (C*(e + f*x)^4*Sqrt[1 - d^2*x^2])/(5*d^2*f) + ((4*(C*(3*d^4*e^4 - 52*d^2*e^2*f^2 - 16*f^4) - 5*d^2*f*(4*A*f*(4*d^2*e^2 + f^2) + 3*B*(d^2*e^3 + 4*e*f^2))) + d^2*f*(6*C*d^2*e^3 - 30*B*d^2*e^2*f - 71*C*e*f^2 - 100*A*d^2*e*f^2 - 45*B*f^3)*x)*Sqrt[1 - d^2*x^2])/(120*d^6*f) + ((4*C*d^2*e^3 + 8*A*d^4*e^3 + 12*B*d^2*e^2*f + 9*C*e*f^2 + 12*A*d^2*e*f^2 + 3*B*f^3)*ArcSin[d*x])/(8*d^5)","A",6,5,37,0.1351,1,"{1609, 1654, 833, 780, 216}"
9,1,228,0,0.4926056,"\int \frac{(e+f x)^2 \left(A+B x+C x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[((e + f*x)^2*(A + B*x + C*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\frac{\sqrt{1-d^2 x^2} \left(4 \left(C \left(d^2 e^3-8 e f^2\right)-4 f \left(3 A d^2 e f+B \left(d^2 e^2+f^2\right)\right)\right)-f x \left(3 f^2 \left(4 A d^2+3 C\right)-2 d^2 e (C e-4 B f)\right)\right)}{24 d^4 f}+\frac{\sin ^{-1}(d x) \left(4 d^2 \left(A \left(2 d^2 e^2+f^2\right)+2 B e f\right)+C \left(4 d^2 e^2+3 f^2\right)\right)}{8 d^5}+\frac{\sqrt{1-d^2 x^2} (e+f x)^2 (C e-4 B f)}{12 d^2 f}-\frac{C \sqrt{1-d^2 x^2} (e+f x)^3}{4 d^2 f}","\frac{\sqrt{1-d^2 x^2} \left(4 \left(C \left(d^2 e^3-8 e f^2\right)-4 f \left(3 A d^2 e f+B \left(d^2 e^2+f^2\right)\right)\right)-f x \left(3 f^2 \left(4 A d^2+3 C\right)-2 d^2 e (C e-4 B f)\right)\right)}{24 d^4 f}+\frac{\sin ^{-1}(d x) \left(4 d^2 \left(A \left(2 d^2 e^2+f^2\right)+2 B e f\right)+C \left(4 d^2 e^2+3 f^2\right)\right)}{8 d^5}+\frac{\sqrt{1-d^2 x^2} (e+f x)^2 (C e-4 B f)}{12 d^2 f}-\frac{C \sqrt{1-d^2 x^2} (e+f x)^3}{4 d^2 f}",1,"((C*e - 4*B*f)*(e + f*x)^2*Sqrt[1 - d^2*x^2])/(12*d^2*f) - (C*(e + f*x)^3*Sqrt[1 - d^2*x^2])/(4*d^2*f) + ((4*(C*(d^2*e^3 - 8*e*f^2) - 4*f*(3*A*d^2*e*f + B*(d^2*e^2 + f^2))) - f*(3*(3*C + 4*A*d^2)*f^2 - 2*d^2*e*(C*e - 4*B*f))*x)*Sqrt[1 - d^2*x^2])/(24*d^4*f) + ((C*(4*d^2*e^2 + 3*f^2) + 4*d^2*(2*B*e*f + A*(2*d^2*e^2 + f^2)))*ArcSin[d*x])/(8*d^5)","A",5,5,37,0.1351,1,"{1609, 1654, 833, 780, 216}"
10,1,133,0,0.2297766,"\int \frac{(e+f x) \left(A+B x+C x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[((e + f*x)*(A + B*x + C*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{\sqrt{1-d^2 x^2} \left(2 \left(3 d^2 f (A f+B e)-\frac{1}{2} C \left(2 d^2 e^2-4 f^2\right)\right)-d^2 f x (C e-3 B f)\right)}{6 d^4 f}+\frac{\sin ^{-1}(d x) \left(2 A d^2 e+B f+C e\right)}{2 d^3}-\frac{C \sqrt{1-d^2 x^2} (e+f x)^2}{3 d^2 f}","-\frac{\sqrt{1-d^2 x^2} \left(2 \left(3 d^2 f (A f+B e)-C \left(d^2 e^2-2 f^2\right)\right)-d^2 f x (C e-3 B f)\right)}{6 d^4 f}+\frac{\sin ^{-1}(d x) \left(2 A d^2 e+B f+C e\right)}{2 d^3}-\frac{C \sqrt{1-d^2 x^2} (e+f x)^2}{3 d^2 f}",1,"-(C*(e + f*x)^2*Sqrt[1 - d^2*x^2])/(3*d^2*f) - ((2*(3*d^2*f*(B*e + A*f) - (C*(2*d^2*e^2 - 4*f^2))/2) - d^2*f*(C*e - 3*B*f)*x)*Sqrt[1 - d^2*x^2])/(6*d^4*f) + ((C*e + 2*A*d^2*e + B*f)*ArcSin[d*x])/(2*d^3)","A",4,4,35,0.1143,1,"{1609, 1654, 780, 216}"
11,1,63,0,0.0608195,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\frac{\left(2 A d^2+C\right) \sin ^{-1}(d x)}{2 d^3}-\frac{B \sqrt{1-d^2 x^2}}{d^2}-\frac{C x \sqrt{1-d^2 x^2}}{2 d^2}","\frac{\left(2 A d^2+C\right) \sin ^{-1}(d x)}{2 d^3}-\frac{B \sqrt{1-d^2 x^2}}{d^2}-\frac{C x \sqrt{1-d^2 x^2}}{2 d^2}",1,"-((B*Sqrt[1 - d^2*x^2])/d^2) - (C*x*Sqrt[1 - d^2*x^2])/(2*d^2) + ((C + 2*A*d^2)*ArcSin[d*x])/(2*d^3)","A",4,4,30,0.1333,1,"{899, 1815, 641, 216}"
12,1,122,0,0.2826605,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)),x]","\frac{\left(A f^2-B e f+C e^2\right) \tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right)}{f^2 \sqrt{d^2 e^2-f^2}}-\frac{\sin ^{-1}(d x) (C e-B f)}{d f^2}-\frac{C \sqrt{1-d^2 x^2}}{d^2 f}","\frac{\left(A f^2-B e f+C e^2\right) \tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right)}{f^2 \sqrt{d^2 e^2-f^2}}-\frac{\sin ^{-1}(d x) (C e-B f)}{d f^2}-\frac{C \sqrt{1-d^2 x^2}}{d^2 f}",1,"-((C*Sqrt[1 - d^2*x^2])/(d^2*f)) - ((C*e - B*f)*ArcSin[d*x])/(d*f^2) + ((C*e^2 - B*e*f + A*f^2)*ArcTan[(f + d^2*e*x)/(Sqrt[d^2*e^2 - f^2]*Sqrt[1 - d^2*x^2])])/(f^2*Sqrt[d^2*e^2 - f^2])","A",6,6,37,0.1622,1,"{1609, 1654, 844, 216, 725, 204}"
13,1,163,0,0.2954647,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^2} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^2),x]","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{f \left(d^2 e^2-f^2\right) (e+f x)}-\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(-A d^2 e f^2+B f^3+C d^2 e^3-2 C e f^2\right)}{f^2 \left(d^2 e^2-f^2\right)^{3/2}}+\frac{C \sin ^{-1}(d x)}{d f^2}","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{f \left(d^2 e^2-f^2\right) (e+f x)}-\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(-A d^2 e f^2+B f^3+C d^2 e^3-2 C e f^2\right)}{f^2 \left(d^2 e^2-f^2\right)^{3/2}}+\frac{C \sin ^{-1}(d x)}{d f^2}",1,"((C*e^2 - B*e*f + A*f^2)*Sqrt[1 - d^2*x^2])/(f*(d^2*e^2 - f^2)*(e + f*x)) + (C*ArcSin[d*x])/(d*f^2) - ((C*d^2*e^3 - 2*C*e*f^2 - A*d^2*e*f^2 + B*f^3)*ArcTan[(f + d^2*e*x)/(Sqrt[d^2*e^2 - f^2]*Sqrt[1 - d^2*x^2])])/(f^2*(d^2*e^2 - f^2)^(3/2))","A",6,6,37,0.1622,1,"{1609, 1651, 844, 216, 725, 204}"
14,1,248,0,0.3289478,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^3} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^3),x]","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{2 f \left(d^2 e^2-f^2\right) (e+f x)^2}-\frac{\sqrt{1-d^2 x^2} \left(-3 A d^2 e f^2+B d^2 e^2 f+2 B f^3+C d^2 e^3-4 C e f^2\right)}{2 f \left(d^2 e^2-f^2\right)^2 (e+f x)}+\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(C \left(d^2 e^2+2 f^2\right)-d^2 \left(3 B e f-A \left(2 d^2 e^2+f^2\right)\right)\right)}{2 \left(d^2 e^2-f^2\right)^{5/2}}","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{2 f \left(d^2 e^2-f^2\right) (e+f x)^2}-\frac{\sqrt{1-d^2 x^2} \left(-3 A d^2 e f^2+B d^2 e^2 f+2 B f^3+C d^2 e^3-4 C e f^2\right)}{2 f \left(d^2 e^2-f^2\right)^2 (e+f x)}+\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(C \left(d^2 e^2+2 f^2\right)-d^2 \left(3 B e f-A \left(2 d^2 e^2+f^2\right)\right)\right)}{2 \left(d^2 e^2-f^2\right)^{5/2}}",1,"((C*e^2 - B*e*f + A*f^2)*Sqrt[1 - d^2*x^2])/(2*f*(d^2*e^2 - f^2)*(e + f*x)^2) - ((C*d^2*e^3 + B*d^2*e^2*f - 4*C*e*f^2 - 3*A*d^2*e*f^2 + 2*B*f^3)*Sqrt[1 - d^2*x^2])/(2*f*(d^2*e^2 - f^2)^2*(e + f*x)) + ((C*(d^2*e^2 + 2*f^2) - d^2*(3*B*e*f - A*(2*d^2*e^2 + f^2)))*ArcTan[(f + d^2*e*x)/(Sqrt[d^2*e^2 - f^2]*Sqrt[1 - d^2*x^2])])/(2*(d^2*e^2 - f^2)^(5/2))","A",5,5,37,0.1351,1,"{1609, 1651, 807, 725, 204}"
15,1,79,0,0.1387126,"\int \frac{x \left(a+b x+c x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(x*(a + b*x + c*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{\sqrt{1-d^2 x^2} \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4}+\frac{b \sin ^{-1}(d x)}{2 d^3}-\frac{c x^2 \sqrt{1-d^2 x^2}}{3 d^2}","-\frac{\sqrt{1-d^2 x^2} \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4}+\frac{b \sin ^{-1}(d x)}{2 d^3}-\frac{c x^2 \sqrt{1-d^2 x^2}}{3 d^2}",1,"-(c*x^2*Sqrt[1 - d^2*x^2])/(3*d^2) - ((2*(2*c + 3*a*d^2) + 3*b*d^2*x)*Sqrt[1 - d^2*x^2])/(6*d^4) + (b*ArcSin[d*x])/(2*d^3)","A",4,4,31,0.1290,1,"{1609, 1809, 780, 216}"
16,1,63,0,0.060904,"\int \frac{a+b x+c x^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\frac{\left(2 a d^2+c\right) \sin ^{-1}(d x)}{2 d^3}-\frac{b \sqrt{1-d^2 x^2}}{d^2}-\frac{c x \sqrt{1-d^2 x^2}}{2 d^2}","\frac{\left(2 a d^2+c\right) \sin ^{-1}(d x)}{2 d^3}-\frac{b \sqrt{1-d^2 x^2}}{d^2}-\frac{c x \sqrt{1-d^2 x^2}}{2 d^2}",1,"-((b*Sqrt[1 - d^2*x^2])/d^2) - (c*x*Sqrt[1 - d^2*x^2])/(2*d^2) + ((c + 2*a*d^2)*ArcSin[d*x])/(2*d^3)","A",4,4,30,0.1333,1,"{899, 1815, 641, 216}"
17,1,48,0,0.1834705,"\int \frac{a+b x+c x^2}{x \sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-a \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)+\frac{b \sin ^{-1}(d x)}{d}-\frac{c \sqrt{1-d^2 x^2}}{d^2}","-a \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)+\frac{b \sin ^{-1}(d x)}{d}-\frac{c \sqrt{1-d^2 x^2}}{d^2}",1,"-((c*Sqrt[1 - d^2*x^2])/d^2) + (b*ArcSin[d*x])/d - a*ArcTanh[Sqrt[1 - d^2*x^2]]","A",7,7,33,0.2121,1,"{1609, 1809, 844, 216, 266, 63, 208}"
18,1,48,0,0.1755334,"\int \frac{a+b x+c x^2}{x^2 \sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^2*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{a \sqrt{1-d^2 x^2}}{x}-b \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)+\frac{c \sin ^{-1}(d x)}{d}","-\frac{a \sqrt{1-d^2 x^2}}{x}-b \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)+\frac{c \sin ^{-1}(d x)}{d}",1,"-((a*Sqrt[1 - d^2*x^2])/x) + (c*ArcSin[d*x])/d - b*ArcTanh[Sqrt[1 - d^2*x^2]]","A",7,7,33,0.2121,1,"{1609, 1807, 844, 216, 266, 63, 208}"
19,1,71,0,0.1840148,"\int \frac{a+b x+c x^2}{x^3 \sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^3*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{1}{2} \left(a d^2+2 c\right) \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)-\frac{a \sqrt{1-d^2 x^2}}{2 x^2}-\frac{b \sqrt{1-d^2 x^2}}{x}","-\frac{1}{2} \left(a d^2+2 c\right) \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)-\frac{a \sqrt{1-d^2 x^2}}{2 x^2}-\frac{b \sqrt{1-d^2 x^2}}{x}",1,"-(a*Sqrt[1 - d^2*x^2])/(2*x^2) - (b*Sqrt[1 - d^2*x^2])/x - ((2*c + a*d^2)*ArcTanh[Sqrt[1 - d^2*x^2]])/2","A",6,6,33,0.1818,1,"{1609, 1807, 807, 266, 63, 208}"
20,1,584,0,1.5174027,"\int \sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^3 \left(A+B x+C x^2\right) \, dx","Int[Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^3*(A + B*x + C*x^2),x]","\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^2 \sqrt{a c-b c x} \left(-\frac{8 a^2 C f^2}{b^2}-7 f (2 A f+B e)+3 C e^2\right)}{70 b^2 f}-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x} \left(3 b^2 f x \left(a^2 f^2 (35 B f+41 C e)-b^2 \left(6 C e^3-14 e f (7 A f+B e)\right)\right)+8 \left(2 a^2 b^2 f^2 \left(7 f (A f+3 B e)+15 C e^2\right)+8 a^4 C f^4+b^4 \left(-\left(3 C e^4-7 e^2 f (12 A f+B e)\right)\right)\right)\right)}{840 b^6 f}+\frac{a^2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(A \left(6 a^2 b^2 e f^2+8 b^4 e^3\right)+2 a^2 b^2 e^2 (3 B f+C e)+a^4 f^2 (B f+3 C e)\right)}{16 b^5 \sqrt{a^2 c-b^2 c x^2}}+\frac{x \sqrt{a+b x} \sqrt{a c-b c x} \left(A \left(6 a^2 b^2 e f^2+8 b^4 e^3\right)+2 a^2 b^2 e^2 (3 B f+C e)+a^4 f^2 (B f+3 C e)\right)}{16 b^4}+\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^3 \sqrt{a c-b c x} (3 C e-7 B f)}{42 b^2 f}-\frac{C \sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^4 \sqrt{a c-b c x}}{7 b^2 f}","-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^2 \sqrt{a c-b c x} \left(8 a^2 C f^2-b^2 \left(3 C e^2-7 f (2 A f+B e)\right)\right)}{70 b^4 f}-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x} \left(3 b^2 f x \left(a^2 f^2 (35 B f+41 C e)-2 b^2 e \left(3 C e^2-7 f (7 A f+B e)\right)\right)+8 \left(2 a^2 b^2 f^2 \left(7 f (A f+3 B e)+15 C e^2\right)+8 a^4 C f^4+b^4 \left(-e^2\right) \left(3 C e^2-7 f (12 A f+B e)\right)\right)\right)}{840 b^6 f}+\frac{a^2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(A \left(6 a^2 b^2 e f^2+8 b^4 e^3\right)+a^2 \left(a^2 f^2 (B f+3 C e)+2 b^2 e^2 (3 B f+C e)\right)\right)}{16 b^5 \sqrt{a^2 c-b^2 c x^2}}+\frac{x \sqrt{a+b x} \sqrt{a c-b c x} \left(A \left(6 a^2 b^2 e f^2+8 b^4 e^3\right)+a^2 \left(a^2 f^2 (B f+3 C e)+2 b^2 e^2 (3 B f+C e)\right)\right)}{16 b^4}+\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^3 \sqrt{a c-b c x} (3 C e-7 B f)}{42 b^2 f}-\frac{C \sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^4 \sqrt{a c-b c x}}{7 b^2 f}",1,"((a^4*f^2*(3*C*e + B*f) + 2*a^2*b^2*e^2*(C*e + 3*B*f) + A*(8*b^4*e^3 + 6*a^2*b^2*e*f^2))*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])/(16*b^4) + ((3*C*e^2 - (8*a^2*C*f^2)/b^2 - 7*f*(B*e + 2*A*f))*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2*(a^2 - b^2*x^2))/(70*b^2*f) + ((3*C*e - 7*B*f)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^3*(a^2 - b^2*x^2))/(42*b^2*f) - (C*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^4*(a^2 - b^2*x^2))/(7*b^2*f) - (Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(8*(8*a^4*C*f^4 + 2*a^2*b^2*f^2*(15*C*e^2 + 7*f*(3*B*e + A*f)) - b^4*(3*C*e^4 - 7*e^2*f*(B*e + 12*A*f))) + 3*b^2*f*(a^2*f^2*(41*C*e + 35*B*f) - b^2*(6*C*e^3 - 14*e*f*(B*e + 7*A*f)))*x)*(a^2 - b^2*x^2))/(840*b^6*f) + (a^2*Sqrt[c]*(a^4*f^2*(3*C*e + B*f) + 2*a^2*b^2*e^2*(C*e + 3*B*f) + A*(8*b^4*e^3 + 6*a^2*b^2*e*f^2))*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(16*b^5*Sqrt[a^2*c - b^2*c*x^2])","A",8,7,40,0.1750,1,"{1610, 1654, 833, 780, 195, 217, 203}"
21,1,450,0,1.0096746,"\int \sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^2 \left(A+B x+C x^2\right) \, dx","Int[Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2*(A + B*x + C*x^2),x]","-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x} \left(3 f x \left(5 a^2 C f^2-b^2 \left(2 C e^2-2 f (5 A f+2 B e)\right)\right)+8 \left(2 a^2 f^2 (B f+2 C e)-\frac{1}{8} b^2 \left(8 C e^3-16 e f (5 A f+B e)\right)\right)\right)}{120 b^4 f}+\frac{a^2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(2 A \left(a^2 b^2 f^2+4 b^4 e^2\right)+2 a^2 b^2 e (2 B f+C e)+a^4 C f^2\right)}{16 b^5 \sqrt{a^2 c-b^2 c x^2}}+\frac{x \sqrt{a+b x} \sqrt{a c-b c x} \left(2 A \left(a^2 b^2 f^2+4 b^4 e^2\right)+2 a^2 b^2 e (2 B f+C e)+a^4 C f^2\right)}{16 b^4}+\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^2 \sqrt{a c-b c x} (C e-2 B f)}{10 b^2 f}-\frac{C \sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^3 \sqrt{a c-b c x}}{6 b^2 f}","-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x} \left(3 f x \left(5 a^2 C f^2-b^2 \left(2 C e^2-2 f (5 A f+2 B e)\right)\right)+8 \left(2 a^2 f^2 (B f+2 C e)-b^2 e \left(C e^2-2 f (5 A f+B e)\right)\right)\right)}{120 b^4 f}+\frac{a^2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(2 A \left(a^2 b^2 f^2+4 b^4 e^2\right)+a^2 \left(a^2 C f^2+2 b^2 e (2 B f+C e)\right)\right)}{16 b^5 \sqrt{a^2 c-b^2 c x^2}}+\frac{x \sqrt{a+b x} \sqrt{a c-b c x} \left(2 A \left(a^2 b^2 f^2+4 b^4 e^2\right)+a^2 \left(a^2 C f^2+2 b^2 e (2 B f+C e)\right)\right)}{16 b^4}+\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^2 \sqrt{a c-b c x} (C e-2 B f)}{10 b^2 f}-\frac{C \sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^3 \sqrt{a c-b c x}}{6 b^2 f}",1,"((a^4*C*f^2 + 2*a^2*b^2*e*(C*e + 2*B*f) + 2*A*(4*b^4*e^2 + a^2*b^2*f^2))*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])/(16*b^4) + ((C*e - 2*B*f)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2*(a^2 - b^2*x^2))/(10*b^2*f) - (C*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^3*(a^2 - b^2*x^2))/(6*b^2*f) - (Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(8*(2*a^2*f^2*(2*C*e + B*f) - (b^2*(8*C*e^3 - 16*e*f*(B*e + 5*A*f)))/8) + 3*f*(5*a^2*C*f^2 - b^2*(2*C*e^2 - 2*f*(2*B*e + 5*A*f)))*x)*(a^2 - b^2*x^2))/(120*b^4*f) + (a^2*Sqrt[c]*(a^4*C*f^2 + 2*a^2*b^2*e*(C*e + 2*B*f) + 2*A*(4*b^4*e^2 + a^2*b^2*f^2))*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(16*b^5*Sqrt[a^2*c - b^2*c*x^2])","A",7,7,40,0.1750,1,"{1610, 1654, 833, 780, 195, 217, 203}"
22,1,297,0,0.4459621,"\int \sqrt{a+b x} \sqrt{a c-b c x} (e+f x) \left(A+B x+C x^2\right) \, dx","Int[Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)*(A + B*x + C*x^2),x]","-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x} \left(4 \left(2 a^2 C f^2-b^2 \left(3 C e^2-5 f (A f+B e)\right)\right)-3 b^2 f x (3 C e-5 B f)\right)}{60 b^4 f}+\frac{a^2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(a^2 (B f+C e)+4 A b^2 e\right)}{8 b^3 \sqrt{a^2 c-b^2 c x^2}}+\frac{1}{8} x \sqrt{a+b x} \sqrt{a c-b c x} \left(\frac{a^2 (B f+C e)}{b^2}+4 A e\right)-\frac{C \sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^2 \sqrt{a c-b c x}}{5 b^2 f}","-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x} \left(4 \left(2 a^2 C f^2-b^2 \left(3 C e^2-5 f (A f+B e)\right)\right)-3 b^2 f x (3 C e-5 B f)\right)}{60 b^4 f}+\frac{a^2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(a^2 (B f+C e)+4 A b^2 e\right)}{8 b^3 \sqrt{a^2 c-b^2 c x^2}}+\frac{x \sqrt{a+b x} \sqrt{a c-b c x} \left(a^2 (B f+C e)+4 A b^2 e\right)}{8 b^2}-\frac{C \sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^2 \sqrt{a c-b c x}}{5 b^2 f}",1,"((4*A*e + (a^2*(C*e + B*f))/b^2)*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])/8 - (C*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2*(a^2 - b^2*x^2))/(5*b^2*f) - (Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(4*(2*a^2*C*f^2 - b^2*(3*C*e^2 - 5*f*(B*e + A*f))) - 3*b^2*f*(3*C*e - 5*B*f)*x)*(a^2 - b^2*x^2))/(60*b^4*f) + (a^2*Sqrt[c]*(4*A*b^2*e + a^2*(C*e + B*f))*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(8*b^3*Sqrt[a^2*c - b^2*c*x^2])","A",6,6,38,0.1579,1,"{1610, 1654, 780, 195, 217, 203}"
23,1,221,0,0.1469674,"\int \sqrt{a+b x} \sqrt{a c-b c x} \left(A+B x+C x^2\right) \, dx","Int[Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(A + B*x + C*x^2),x]","\frac{a^2 \sqrt{c} \sqrt{a+b x} \left(a^2 C+4 A b^2\right) \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{8 b^3 \sqrt{a^2 c-b^2 c x^2}}+\frac{1}{8} x \sqrt{a+b x} \left(\frac{a^2 C}{b^2}+4 A\right) \sqrt{a c-b c x}-\frac{B \sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x}}{3 b^2}-\frac{C x \sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x}}{4 b^2}","\frac{a^2 \sqrt{c} \sqrt{a+b x} \left(a^2 C+4 A b^2\right) \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{8 b^3 \sqrt{a^2 c-b^2 c x^2}}+\frac{1}{8} x \sqrt{a+b x} \left(\frac{a^2 C}{b^2}+4 A\right) \sqrt{a c-b c x}-\frac{B \sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x}}{3 b^2}-\frac{C x \sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x}}{4 b^2}",1,"((4*A + (a^2*C)/b^2)*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])/8 - (B*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(a^2 - b^2*x^2))/(3*b^2) - (C*x*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(a^2 - b^2*x^2))/(4*b^2) + (a^2*Sqrt[c]*(4*A*b^2 + a^2*C)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(8*b^3*Sqrt[a^2*c - b^2*c*x^2])","A",6,6,33,0.1818,1,"{901, 1815, 641, 195, 217, 203}"
24,1,278,0,0.4895793,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)),x]","\frac{\sqrt{a^2 c-b^2 c x^2} \left(A f^2-B e f+C e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{\sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x} \sqrt{b^2 e^2-a^2 f^2}}-\frac{\sqrt{a^2 c-b^2 c x^2} (C e-B f) \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{b \sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right)}{b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}","\frac{\sqrt{a^2 c-b^2 c x^2} \left(A f^2-B e f+C e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{\sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x} \sqrt{b^2 e^2-a^2 f^2}}-\frac{\sqrt{a^2 c-b^2 c x^2} (C e-B f) \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{b \sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right)}{b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}",1,"-((C*(a^2 - b^2*x^2))/(b^2*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])) - ((C*e - B*f)*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(b*Sqrt[c]*f^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) + ((C*e^2 - B*e*f + A*f^2)*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(Sqrt[c]*(a^2*f + b^2*e*x))/(Sqrt[b^2*e^2 - a^2*f^2]*Sqrt[a^2*c - b^2*c*x^2])])/(Sqrt[c]*f^2*Sqrt[b^2*e^2 - a^2*f^2]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",7,7,40,0.1750,1,"{1610, 1654, 844, 217, 203, 725, 204}"
25,1,322,0,0.5794395,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^2} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2),x]","\frac{f \left(a^2-b^2 x^2\right) \left(A+\frac{e (C e-B f)}{f^2}\right)}{\sqrt{a+b x} (e+f x) \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)}+\frac{\sqrt{a^2 c-b^2 c x^2} \left(a^2 f^2 (2 C e-B f)-b^2 \left(C e^3-A e f^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{\sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^{3/2}}+\frac{C \sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{b \sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x}}","\frac{f \left(a^2-b^2 x^2\right) \left(A+\frac{e (C e-B f)}{f^2}\right)}{\sqrt{a+b x} (e+f x) \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)}+\frac{\sqrt{a^2 c-b^2 c x^2} \left(a^2 f^2 (2 C e-B f)-b^2 \left(C e^3-A e f^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{\sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^{3/2}}+\frac{C \sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{b \sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x}}",1,"(f*(A + (e*(C*e - B*f))/f^2)*(a^2 - b^2*x^2))/((b^2*e^2 - a^2*f^2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)) + (C*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(b*Sqrt[c]*f^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) + ((a^2*f^2*(2*C*e - B*f) - b^2*(C*e^3 - A*e*f^2))*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(Sqrt[c]*(a^2*f + b^2*e*x))/(Sqrt[b^2*e^2 - a^2*f^2]*Sqrt[a^2*c - b^2*c*x^2])])/(Sqrt[c]*f^2*(b^2*e^2 - a^2*f^2)^(3/2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",7,7,40,0.1750,1,"{1610, 1651, 844, 217, 203, 725, 204}"
26,1,361,0,0.6769154,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^3} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^3),x]","\frac{\left(a^2-b^2 x^2\right) \left(2 a^2 f^2 (2 C e-B f)-b^2 \left(e f (B e-3 A f)+C e^3\right)\right)}{2 f \sqrt{a+b x} (e+f x) \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^2}+\frac{f \left(a^2-b^2 x^2\right) \left(A+\frac{e (C e-B f)}{f^2}\right)}{2 \sqrt{a+b x} (e+f x)^2 \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)}+\frac{\sqrt{a^2 c-b^2 c x^2} \left(A \left(a^2 b^2 f^2+2 b^4 e^2\right)+a^2 b^2 e (C e-3 B f)+2 a^4 C f^2\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^{5/2}}","\frac{\left(a^2-b^2 x^2\right) \left(2 a^2 f^2 (2 C e-B f)-b^2 e \left(f (B e-3 A f)+C e^2\right)\right)}{2 f \sqrt{a+b x} (e+f x) \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^2}+\frac{f \left(a^2-b^2 x^2\right) \left(A+\frac{e (C e-B f)}{f^2}\right)}{2 \sqrt{a+b x} (e+f x)^2 \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)}+\frac{\sqrt{a^2 c-b^2 c x^2} \left(A \left(a^2 b^2 f^2+2 b^4 e^2\right)+a^2 \left(2 a^2 C f^2+b^2 e (C e-3 B f)\right)\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^{5/2}}",1,"(f*(A + (e*(C*e - B*f))/f^2)*(a^2 - b^2*x^2))/(2*(b^2*e^2 - a^2*f^2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2) + ((2*a^2*f^2*(2*C*e - B*f) - b^2*(C*e^3 + e*f*(B*e - 3*A*f)))*(a^2 - b^2*x^2))/(2*f*(b^2*e^2 - a^2*f^2)^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)) + ((2*a^4*C*f^2 + a^2*b^2*e*(C*e - 3*B*f) + A*(2*b^4*e^2 + a^2*b^2*f^2))*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(Sqrt[c]*(a^2*f + b^2*e*x))/(Sqrt[b^2*e^2 - a^2*f^2]*Sqrt[a^2*c - b^2*c*x^2])])/(2*Sqrt[c]*(b^2*e^2 - a^2*f^2)^(5/2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",5,5,40,0.1250,1,"{1610, 1651, 807, 725, 204}"
27,1,496,0,1.2811074,"\int \frac{(e+f x)^3 \left(A+B x+C x^2\right)}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","Int[((e + f*x)^3*(A + B*x + C*x^2))/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","\frac{\left(a^2-b^2 x^2\right) (e+f x)^2 \left(-\frac{16 a^2 C f^2}{b^2}-5 f (4 A f+3 B e)+3 C e^2\right)}{60 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{\left(a^2-b^2 x^2\right) \left(b^2 f x \left(a^2 f^2 (45 B f+71 C e)-b^2 \left(6 C e^3-10 e f (10 A f+3 B e)\right)\right)+4 \left(4 a^2 b^2 f^2 \left(5 f (A f+3 B e)+13 C e^2\right)+16 a^4 C f^4+b^4 \left(-e^2\right) \left(3 C e^2-5 f (16 A f+3 B e)\right)\right)\right)}{120 b^6 f \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(4 A \left(3 a^2 b^2 e f^2+2 b^4 e^3\right)+4 a^2 b^2 e^2 (3 B f+C e)+3 a^4 f^2 (B f+3 C e)\right)}{8 b^5 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\left(a^2-b^2 x^2\right) (e+f x)^3 (C e-5 B f)}{20 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right) (e+f x)^4}{5 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}","-\frac{\left(a^2-b^2 x^2\right) (e+f x)^2 \left(16 a^2 C f^2-b^2 \left(3 C e^2-5 f (4 A f+3 B e)\right)\right)}{60 b^4 f \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{\left(a^2-b^2 x^2\right) \left(b^2 f x \left(a^2 f^2 (45 B f+71 C e)-2 b^2 e \left(3 C e^2-5 f (10 A f+3 B e)\right)\right)+4 \left(4 a^2 b^2 f^2 \left(5 f (A f+3 B e)+13 C e^2\right)+16 a^4 C f^4+b^4 \left(-e^2\right) \left(3 C e^2-5 f (16 A f+3 B e)\right)\right)\right)}{120 b^6 f \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(4 A \left(3 a^2 b^2 e f^2+2 b^4 e^3\right)+a^2 \left(3 a^2 f^2 (B f+3 C e)+4 b^2 e^2 (3 B f+C e)\right)\right)}{8 b^5 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\left(a^2-b^2 x^2\right) (e+f x)^3 (C e-5 B f)}{20 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right) (e+f x)^4}{5 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}",1,"((3*C*e^2 - (16*a^2*C*f^2)/b^2 - 5*f*(3*B*e + 4*A*f))*(e + f*x)^2*(a^2 - b^2*x^2))/(60*b^2*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) + ((C*e - 5*B*f)*(e + f*x)^3*(a^2 - b^2*x^2))/(20*b^2*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) - (C*(e + f*x)^4*(a^2 - b^2*x^2))/(5*b^2*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) - ((4*(16*a^4*C*f^4 + 4*a^2*b^2*f^2*(13*C*e^2 + 5*f*(3*B*e + A*f)) - b^4*e^2*(3*C*e^2 - 5*f*(3*B*e + 16*A*f))) + b^2*f*(a^2*f^2*(71*C*e + 45*B*f) - b^2*(6*C*e^3 - 10*e*f*(3*B*e + 10*A*f)))*x)*(a^2 - b^2*x^2))/(120*b^6*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) + ((3*a^4*f^2*(3*C*e + B*f) + 4*a^2*b^2*e^2*(C*e + 3*B*f) + 4*A*(2*b^4*e^3 + 3*a^2*b^2*e*f^2))*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(8*b^5*Sqrt[c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",7,6,40,0.1500,1,"{1610, 1654, 833, 780, 217, 203}"
28,1,369,0,0.8750559,"\int \frac{(e+f x)^2 \left(A+B x+C x^2\right)}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","Int[((e + f*x)^2*(A + B*x + C*x^2))/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","-\frac{\left(a^2-b^2 x^2\right) \left(f x \left(9 a^2 C f^2-b^2 \left(2 C e^2-4 f (3 A f+2 B e)\right)\right)+4 \left(4 a^2 f^2 (B f+2 C e)-\frac{1}{4} b^2 \left(4 C e^3-16 e f (3 A f+B e)\right)\right)\right)}{24 b^4 f \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(4 A \left(a^2 b^2 f^2+2 b^4 e^2\right)+4 a^2 b^2 e (2 B f+C e)+3 a^4 C f^2\right)}{8 b^5 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\left(a^2-b^2 x^2\right) (e+f x)^2 (C e-4 B f)}{12 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right) (e+f x)^3}{4 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}","-\frac{\left(a^2-b^2 x^2\right) \left(f x \left(9 a^2 C f^2-b^2 \left(2 C e^2-4 f (3 A f+2 B e)\right)\right)+4 \left(4 a^2 f^2 (B f+2 C e)-b^2 e \left(C e^2-4 f (3 A f+B e)\right)\right)\right)}{24 b^4 f \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(4 A \left(a^2 b^2 f^2+2 b^4 e^2\right)+a^2 \left(3 a^2 C f^2+4 b^2 e (2 B f+C e)\right)\right)}{8 b^5 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\left(a^2-b^2 x^2\right) (e+f x)^2 (C e-4 B f)}{12 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right) (e+f x)^3}{4 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}",1,"((C*e - 4*B*f)*(e + f*x)^2*(a^2 - b^2*x^2))/(12*b^2*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) - (C*(e + f*x)^3*(a^2 - b^2*x^2))/(4*b^2*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) - ((4*(4*a^2*f^2*(2*C*e + B*f) - (b^2*(4*C*e^3 - 16*e*f*(B*e + 3*A*f)))/4) + f*(9*a^2*C*f^2 - b^2*(2*C*e^2 - 4*f*(2*B*e + 3*A*f)))*x)*(a^2 - b^2*x^2))/(24*b^4*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) + ((3*a^4*C*f^2 + 4*a^2*b^2*e*(C*e + 2*B*f) + 4*A*(2*b^4*e^2 + a^2*b^2*f^2))*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(8*b^5*Sqrt[c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",6,6,40,0.1500,1,"{1610, 1654, 833, 780, 217, 203}"
29,1,249,0,0.4002786,"\int \frac{(e+f x) \left(A+B x+C x^2\right)}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","Int[((e + f*x)*(A + B*x + C*x^2))/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","-\frac{\left(a^2-b^2 x^2\right) \left(2 \left(2 a^2 C f^2-\frac{1}{2} b^2 \left(2 C e^2-6 f (A f+B e)\right)\right)-b^2 f x (C e-3 B f)\right)}{6 b^4 f \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(a^2 (B f+C e)+2 A b^2 e\right)}{2 b^3 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right) (e+f x)^2}{3 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}","-\frac{\left(a^2-b^2 x^2\right) \left(2 \left(2 a^2 C f^2-b^2 \left(C e^2-3 f (A f+B e)\right)\right)-b^2 f x (C e-3 B f)\right)}{6 b^4 f \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(a^2 (B f+C e)+2 A b^2 e\right)}{2 b^3 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right) (e+f x)^2}{3 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}",1,"-(C*(e + f*x)^2*(a^2 - b^2*x^2))/(3*b^2*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) - ((2*(2*a^2*C*f^2 - (b^2*(2*C*e^2 - 6*f*(B*e + A*f)))/2) - b^2*f*(C*e - 3*B*f)*x)*(a^2 - b^2*x^2))/(6*b^4*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) + ((2*A*b^2*e + a^2*(C*e + B*f))*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(2*b^3*Sqrt[c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",5,5,38,0.1316,1,"{1610, 1654, 780, 217, 203}"
30,1,177,0,0.1243756,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","\frac{\left(a^2 C+2 A b^2\right) \sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{2 b^3 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{B \left(a^2-b^2 x^2\right)}{b^2 \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C x \left(a^2-b^2 x^2\right)}{2 b^2 \sqrt{a+b x} \sqrt{a c-b c x}}","\frac{\left(a^2 C+2 A b^2\right) \sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{2 b^3 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{B \left(a^2-b^2 x^2\right)}{b^2 \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C x \left(a^2-b^2 x^2\right)}{2 b^2 \sqrt{a+b x} \sqrt{a c-b c x}}",1,"-((B*(a^2 - b^2*x^2))/(b^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])) - (C*x*(a^2 - b^2*x^2))/(2*b^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) + ((2*A*b^2 + a^2*C)*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(2*b^3*Sqrt[c]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",5,5,33,0.1515,1,"{901, 1815, 641, 217, 203}"
31,1,278,0,0.4641243,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)),x]","\frac{\sqrt{a^2 c-b^2 c x^2} \left(A f^2-B e f+C e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{\sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x} \sqrt{b^2 e^2-a^2 f^2}}-\frac{\sqrt{a^2 c-b^2 c x^2} (C e-B f) \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{b \sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right)}{b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}","\frac{\sqrt{a^2 c-b^2 c x^2} \left(A f^2-B e f+C e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{\sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x} \sqrt{b^2 e^2-a^2 f^2}}-\frac{\sqrt{a^2 c-b^2 c x^2} (C e-B f) \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{b \sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right)}{b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}",1,"-((C*(a^2 - b^2*x^2))/(b^2*f*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])) - ((C*e - B*f)*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(b*Sqrt[c]*f^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) + ((C*e^2 - B*e*f + A*f^2)*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(Sqrt[c]*(a^2*f + b^2*e*x))/(Sqrt[b^2*e^2 - a^2*f^2]*Sqrt[a^2*c - b^2*c*x^2])])/(Sqrt[c]*f^2*Sqrt[b^2*e^2 - a^2*f^2]*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",7,7,40,0.1750,1,"{1610, 1654, 844, 217, 203, 725, 204}"
32,1,322,0,0.5304347,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^2} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2),x]","\frac{f \left(a^2-b^2 x^2\right) \left(A+\frac{e (C e-B f)}{f^2}\right)}{\sqrt{a+b x} (e+f x) \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)}+\frac{\sqrt{a^2 c-b^2 c x^2} \left(a^2 f^2 (2 C e-B f)-b^2 \left(C e^3-A e f^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{\sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^{3/2}}+\frac{C \sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{b \sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x}}","\frac{f \left(a^2-b^2 x^2\right) \left(A+\frac{e (C e-B f)}{f^2}\right)}{\sqrt{a+b x} (e+f x) \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)}+\frac{\sqrt{a^2 c-b^2 c x^2} \left(a^2 f^2 (2 C e-B f)-b^2 \left(C e^3-A e f^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{\sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^{3/2}}+\frac{C \sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right)}{b \sqrt{c} f^2 \sqrt{a+b x} \sqrt{a c-b c x}}",1,"(f*(A + (e*(C*e - B*f))/f^2)*(a^2 - b^2*x^2))/((b^2*e^2 - a^2*f^2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)) + (C*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(b*Sqrt[c]*x)/Sqrt[a^2*c - b^2*c*x^2]])/(b*Sqrt[c]*f^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]) + ((a^2*f^2*(2*C*e - B*f) - b^2*(C*e^3 - A*e*f^2))*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(Sqrt[c]*(a^2*f + b^2*e*x))/(Sqrt[b^2*e^2 - a^2*f^2]*Sqrt[a^2*c - b^2*c*x^2])])/(Sqrt[c]*f^2*(b^2*e^2 - a^2*f^2)^(3/2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",7,7,40,0.1750,1,"{1610, 1651, 844, 217, 203, 725, 204}"
33,1,361,0,0.5876299,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^3} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^3),x]","\frac{\left(a^2-b^2 x^2\right) \left(2 a^2 f^2 (2 C e-B f)-b^2 \left(e f (B e-3 A f)+C e^3\right)\right)}{2 f \sqrt{a+b x} (e+f x) \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^2}+\frac{f \left(a^2-b^2 x^2\right) \left(A+\frac{e (C e-B f)}{f^2}\right)}{2 \sqrt{a+b x} (e+f x)^2 \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)}+\frac{\sqrt{a^2 c-b^2 c x^2} \left(A \left(a^2 b^2 f^2+2 b^4 e^2\right)+a^2 b^2 e (C e-3 B f)+2 a^4 C f^2\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^{5/2}}","\frac{\left(a^2-b^2 x^2\right) \left(2 a^2 f^2 (2 C e-B f)-b^2 e \left(f (B e-3 A f)+C e^2\right)\right)}{2 f \sqrt{a+b x} (e+f x) \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^2}+\frac{f \left(a^2-b^2 x^2\right) \left(A+\frac{e (C e-B f)}{f^2}\right)}{2 \sqrt{a+b x} (e+f x)^2 \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)}+\frac{\sqrt{a^2 c-b^2 c x^2} \left(A \left(a^2 b^2 f^2+2 b^4 e^2\right)+a^2 \left(2 a^2 C f^2+b^2 e (C e-3 B f)\right)\right) \tan ^{-1}\left(\frac{\sqrt{c} \left(a^2 f+b^2 e x\right)}{\sqrt{a^2 c-b^2 c x^2} \sqrt{b^2 e^2-a^2 f^2}}\right)}{2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \left(b^2 e^2-a^2 f^2\right)^{5/2}}",1,"(f*(A + (e*(C*e - B*f))/f^2)*(a^2 - b^2*x^2))/(2*(b^2*e^2 - a^2*f^2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2) + ((2*a^2*f^2*(2*C*e - B*f) - b^2*(C*e^3 + e*f*(B*e - 3*A*f)))*(a^2 - b^2*x^2))/(2*f*(b^2*e^2 - a^2*f^2)^2*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)) + ((2*a^4*C*f^2 + a^2*b^2*e*(C*e - 3*B*f) + A*(2*b^4*e^2 + a^2*b^2*f^2))*Sqrt[a^2*c - b^2*c*x^2]*ArcTan[(Sqrt[c]*(a^2*f + b^2*e*x))/(Sqrt[b^2*e^2 - a^2*f^2]*Sqrt[a^2*c - b^2*c*x^2])])/(2*Sqrt[c]*(b^2*e^2 - a^2*f^2)^(5/2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x])","A",5,5,40,0.1250,1,"{1610, 1651, 807, 725, 204}"
34,1,151,0,0.1461051,"\int \frac{x \left(a+b x+c x^2\right)}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(x*(a + b*x + c*x^2))/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","-\frac{\left(1-d^2 x^2\right) \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4 \sqrt{d x-1} \sqrt{d x+1}}+\frac{b \sqrt{d^2 x^2-1} \tanh ^{-1}\left(\frac{d x}{\sqrt{d^2 x^2-1}}\right)}{2 d^3 \sqrt{d x-1} \sqrt{d x+1}}-\frac{c x^2 \left(1-d^2 x^2\right)}{3 d^2 \sqrt{d x-1} \sqrt{d x+1}}","\frac{\sqrt{d x-1} \sqrt{d x+1} \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4}+\frac{b \cosh ^{-1}(d x)}{2 d^3}+\frac{c x^2 \sqrt{d x-1} \sqrt{d x+1}}{3 d^2}",1,"-(c*x^2*(1 - d^2*x^2))/(3*d^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) - ((2*(2*c + 3*a*d^2) + 3*b*d^2*x)*(1 - d^2*x^2))/(6*d^4*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + (b*Sqrt[-1 + d^2*x^2]*ArcTanh[(d*x)/Sqrt[-1 + d^2*x^2]])/(2*d^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","A",5,5,30,0.1667,1,"{1610, 1809, 780, 217, 206}"
35,1,135,0,0.0706656,"\int \frac{a+b x+c x^2}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{\sqrt{d^2 x^2-1} \left(2 a d^2+c\right) \tanh ^{-1}\left(\frac{d x}{\sqrt{d^2 x^2-1}}\right)}{2 d^3 \sqrt{d x-1} \sqrt{d x+1}}-\frac{b \left(1-d^2 x^2\right)}{d^2 \sqrt{d x-1} \sqrt{d x+1}}-\frac{c x \left(1-d^2 x^2\right)}{2 d^2 \sqrt{d x-1} \sqrt{d x+1}}","\frac{\left(2 a d^2+c\right) \cosh ^{-1}(d x)}{2 d^3}+\frac{\sqrt{d x-1} \sqrt{d x+1} (2 b+c x)}{2 d^2}",1,"-((b*(1 - d^2*x^2))/(d^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x])) - (c*x*(1 - d^2*x^2))/(2*d^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + ((c + 2*a*d^2)*Sqrt[-1 + d^2*x^2]*ArcTanh[(d*x)/Sqrt[-1 + d^2*x^2]])/(2*d^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","B",5,5,29,0.1724,1,"{901, 1815, 641, 217, 206}"
36,1,135,0,0.1846662,"\int \frac{a+b x+c x^2}{x \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{a \sqrt{d^2 x^2-1} \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{\sqrt{d x-1} \sqrt{d x+1}}+\frac{b \sqrt{d^2 x^2-1} \tanh ^{-1}\left(\frac{d x}{\sqrt{d^2 x^2-1}}\right)}{d \sqrt{d x-1} \sqrt{d x+1}}-\frac{c \left(1-d^2 x^2\right)}{d^2 \sqrt{d x-1} \sqrt{d x+1}}","a \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{b \cosh ^{-1}(d x)}{d}+\frac{c \sqrt{d x-1} \sqrt{d x+1}}{d^2}",1,"-((c*(1 - d^2*x^2))/(d^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x])) + (a*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + (b*Sqrt[-1 + d^2*x^2]*ArcTanh[(d*x)/Sqrt[-1 + d^2*x^2]])/(d*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","B",8,8,32,0.2500,1,"{1610, 1809, 844, 217, 206, 266, 63, 205}"
37,1,135,0,0.1796833,"\int \frac{a+b x+c x^2}{x^2 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","-\frac{a \left(1-d^2 x^2\right)}{x \sqrt{d x-1} \sqrt{d x+1}}+\frac{b \sqrt{d^2 x^2-1} \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{\sqrt{d x-1} \sqrt{d x+1}}+\frac{c \sqrt{d^2 x^2-1} \tanh ^{-1}\left(\frac{d x}{\sqrt{d^2 x^2-1}}\right)}{d \sqrt{d x-1} \sqrt{d x+1}}","\frac{a \sqrt{d x-1} \sqrt{d x+1}}{x}+b \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{c \cosh ^{-1}(d x)}{d}",1,"-((a*(1 - d^2*x^2))/(x*Sqrt[-1 + d*x]*Sqrt[1 + d*x])) + (b*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + (c*Sqrt[-1 + d^2*x^2]*ArcTanh[(d*x)/Sqrt[-1 + d^2*x^2]])/(d*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","B",8,8,32,0.2500,1,"{1610, 1807, 844, 217, 206, 266, 63, 205}"
38,1,129,0,0.1912475,"\int \frac{a+b x+c x^2}{x^3 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{\sqrt{d^2 x^2-1} \left(a d^2+2 c\right) \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{2 \sqrt{d x-1} \sqrt{d x+1}}-\frac{a \left(1-d^2 x^2\right)}{2 x^2 \sqrt{d x-1} \sqrt{d x+1}}-\frac{b \left(1-d^2 x^2\right)}{x \sqrt{d x-1} \sqrt{d x+1}}","\frac{1}{2} \left(a d^2+2 c\right) \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{a \sqrt{d x-1} \sqrt{d x+1}}{2 x^2}+\frac{b \sqrt{d x-1} \sqrt{d x+1}}{x}",1,"-(a*(1 - d^2*x^2))/(2*x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) - (b*(1 - d^2*x^2))/(x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + ((2*c + a*d^2)*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(2*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","A",6,6,32,0.1875,1,"{1610, 1807, 807, 266, 63, 205}"
39,1,171,0,0.2171632,"\int \frac{a+b x+c x^2}{x^4 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^4*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","-\frac{\left(1-d^2 x^2\right) \left(2 a d^2+3 c\right)}{3 x \sqrt{d x-1} \sqrt{d x+1}}-\frac{a \left(1-d^2 x^2\right)}{3 x^3 \sqrt{d x-1} \sqrt{d x+1}}-\frac{b \left(1-d^2 x^2\right)}{2 x^2 \sqrt{d x-1} \sqrt{d x+1}}+\frac{b d^2 \sqrt{d^2 x^2-1} \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{2 \sqrt{d x-1} \sqrt{d x+1}}","\frac{\sqrt{d x-1} \sqrt{d x+1} \left(2 a d^2+3 c\right)}{3 x}+\frac{a \sqrt{d x-1} \sqrt{d x+1}}{3 x^3}+\frac{1}{2} b d^2 \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{b \sqrt{d x-1} \sqrt{d x+1}}{2 x^2}",1,"-(a*(1 - d^2*x^2))/(3*x^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) - (b*(1 - d^2*x^2))/(2*x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) - ((3*c + 2*a*d^2)*(1 - d^2*x^2))/(3*x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + (b*d^2*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(2*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","A",7,7,32,0.2188,1,"{1610, 1807, 835, 807, 266, 63, 205}"
40,1,242,0,0.3282907,"\int \frac{a+b x+c x^2}{\sqrt{-1+x} \sqrt{1+x} (d+e x)^3} \, dx","Int[(a + b*x + c*x^2)/(Sqrt[-1 + x]*Sqrt[1 + x]*(d + e*x)^3),x]","-\frac{\left(1-x^2\right) \left(c \left(d^3-4 d e^2\right)-e \left(3 a d e-b \left(d^2+2 e^2\right)\right)\right)}{2 e \sqrt{x-1} \sqrt{x+1} \left(d^2-e^2\right)^2 (d+e x)}+\frac{\left(1-x^2\right) \left(a e^2-b d e+c d^2\right)}{2 e \sqrt{x-1} \sqrt{x+1} \left(d^2-e^2\right) (d+e x)^2}-\frac{\sqrt{x^2-1} \tanh ^{-1}\left(\frac{d x+e}{\sqrt{x^2-1} \sqrt{d^2-e^2}}\right) \left(-a \left(2 d^2+e^2\right)+3 b d e-c \left(d^2+2 e^2\right)\right)}{2 \sqrt{x-1} \sqrt{x+1} \left(d^2-e^2\right)^{5/2}}","-\frac{\sqrt{x-1} \sqrt{x+1} \left(a e^2-b d e+c d^2\right)}{2 e \left(d^2-e^2\right) (d+e x)^2}+\frac{\sqrt{x-1} \sqrt{x+1} \left(-d e^2 (3 a+4 c)+b d^2 e+2 b e^3+c d^3\right)}{2 e \left(d^2-e^2\right)^2 (d+e x)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{x+1} \sqrt{d+e}}{\sqrt{x-1} \sqrt{d-e}}\right) \left(d^2 (2 a+c)+e^2 (a+2 c)-3 b d e\right)}{(d-e)^{5/2} (d+e)^{5/2}}",1,"((c*d^2 - b*d*e + a*e^2)*(1 - x^2))/(2*e*(d^2 - e^2)*Sqrt[-1 + x]*Sqrt[1 + x]*(d + e*x)^2) - ((c*(d^3 - 4*d*e^2) - e*(3*a*d*e - b*(d^2 + 2*e^2)))*(1 - x^2))/(2*e*(d^2 - e^2)^2*Sqrt[-1 + x]*Sqrt[1 + x]*(d + e*x)) - ((3*b*d*e - a*(2*d^2 + e^2) - c*(d^2 + 2*e^2))*Sqrt[-1 + x^2]*ArcTanh[(e + d*x)/(Sqrt[d^2 - e^2]*Sqrt[-1 + x^2])])/(2*(d^2 - e^2)^(5/2)*Sqrt[-1 + x]*Sqrt[1 + x])","A",5,5,32,0.1562,1,"{1610, 1651, 807, 725, 206}"
41,1,1345,0,2.3663906,"\int (a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right) \, dx","Int[(a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2),x]","\frac{C (c+d x)^{3/2} (e+f x)^{3/2} (a+b x)^3}{6 b d f}+\frac{(4 b B d f-2 a C d f-3 b C (d e+c f)) (c+d x)^{3/2} (e+f x)^{3/2} (a+b x)^2}{20 b d^2 f^2}-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(\left(7 C \left(15 d^3 e^3+17 c d^2 f e^2+17 c^2 d f^2 e+15 c^3 f^3\right)+4 d f \left(50 A d f (d e+c f)-B \left(35 d^2 e^2+38 c d f e+35 c^2 f^2\right)\right)\right) b^3-8 a d f \left(C \left(35 d^2 e^2+38 c d f e+35 c^2 f^2\right)+10 d f (8 A d f-5 B (d e+c f))\right) b^2-8 a^2 d^2 f^2 (16 B d f-7 C (d e+c f)) b+6 d f (10 b d f (2 b c C e+a C d e+a c C f-4 A b d f)-(4 a d f-7 b (d e+c f)) (4 b B d f-2 a C d f-3 b C (d e+c f))) x b+64 a^3 C d^3 f^3\right)}{960 b d^4 f^4}-\frac{(d e-c f)^2 \left(\left(C \left(21 d^4 e^4+28 c d^3 f e^3+30 c^2 d^2 f^2 e^2+28 c^3 d f^3 e+21 c^4 f^4\right)+4 d f \left(2 A d f \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)-B \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)\right)\right) b^2-8 a d f \left(C \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)+2 d f \left(8 A d f (d e+c f)-B \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)\right)\right) b+8 a^2 d^2 f^2 \left(C \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)+8 d f (2 A d f-B (d e+c f))\right)\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right)}{512 d^{11/2} f^{11/2}}+\frac{\left(\left(C \left(21 d^4 e^4+28 c d^3 f e^3+30 c^2 d^2 f^2 e^2+28 c^3 d f^3 e+21 c^4 f^4\right)+4 d f \left(2 A d f \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)-B \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)\right)\right) b^2-8 a d f \left(C \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)+2 d f \left(8 A d f (d e+c f)-B \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)\right)\right) b+8 a^2 d^2 f^2 \left(C \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)+8 d f (2 A d f-B (d e+c f))\right)\right) (c+d x)^{3/2} \sqrt{e+f x}}{256 d^5 f^4}+\frac{(d e-c f) \left(\left(C \left(21 d^4 e^4+28 c d^3 f e^3+30 c^2 d^2 f^2 e^2+28 c^3 d f^3 e+21 c^4 f^4\right)+4 d f \left(2 A d f \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)-B \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)\right)\right) b^2-8 a d f \left(C \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)+2 d f \left(8 A d f (d e+c f)-B \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)\right)\right) b+8 a^2 d^2 f^2 \left(C \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)+8 d f (2 A d f-B (d e+c f))\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{512 d^5 f^5}","\frac{C (c+d x)^{3/2} (e+f x)^{3/2} (a+b x)^3}{6 b d f}-\frac{(2 a C d f-b (4 B d f-3 C (d e+c f))) (c+d x)^{3/2} (e+f x)^{3/2} (a+b x)^2}{20 b d^2 f^2}-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(\left(7 C \left(15 d^3 e^3+17 c d^2 f e^2+17 c^2 d f^2 e+15 c^3 f^3\right)+4 d f \left(50 A d f (d e+c f)-B \left(35 d^2 e^2+38 c d f e+35 c^2 f^2\right)\right)\right) b^3-8 a d f \left(C \left(35 d^2 e^2+38 c d f e+35 c^2 f^2\right)+10 d f (8 A d f-5 B (d e+c f))\right) b^2-8 a^2 d^2 f^2 (16 B d f-7 C (d e+c f)) b+6 d f (10 b d f (2 b c C e+a C d e+a c C f-4 A b d f)+(4 a d f-7 b (d e+c f)) (2 a C d f-b (4 B d f-3 C (d e+c f)))) x b+64 a^3 C d^3 f^3\right)}{960 b d^4 f^4}-\frac{(d e-c f)^2 \left(\left(C \left(21 d^4 e^4+28 c d^3 f e^3+30 c^2 d^2 f^2 e^2+28 c^3 d f^3 e+21 c^4 f^4\right)+4 d f \left(2 A d f \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)-B \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)\right)\right) b^2-8 a d f \left(C \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)+2 d f \left(8 A d f (d e+c f)-B \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)\right)\right) b+8 a^2 d^2 f^2 \left(C \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)+8 d f (2 A d f-B (d e+c f))\right)\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right)}{512 d^{11/2} f^{11/2}}+\frac{\left(\left(C \left(21 d^4 e^4+28 c d^3 f e^3+30 c^2 d^2 f^2 e^2+28 c^3 d f^3 e+21 c^4 f^4\right)+4 d f \left(2 A d f \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)-B \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)\right)\right) b^2-8 a d f \left(C \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)+2 d f \left(8 A d f (d e+c f)-B \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)\right)\right) b+8 a^2 d^2 f^2 \left(C \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)+8 d f (2 A d f-B (d e+c f))\right)\right) (c+d x)^{3/2} \sqrt{e+f x}}{256 d^5 f^4}+\frac{(d e-c f) \left(\left(C \left(21 d^4 e^4+28 c d^3 f e^3+30 c^2 d^2 f^2 e^2+28 c^3 d f^3 e+21 c^4 f^4\right)+4 d f \left(2 A d f \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)-B \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)\right)\right) b^2-8 a d f \left(C \left(7 d^3 e^3+9 c d^2 f e^2+9 c^2 d f^2 e+7 c^3 f^3\right)+2 d f \left(8 A d f (d e+c f)-B \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)\right)\right) b+8 a^2 d^2 f^2 \left(C \left(5 d^2 e^2+6 c d f e+5 c^2 f^2\right)+8 d f (2 A d f-B (d e+c f))\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{512 d^5 f^5}",1,"((d*e - c*f)*(8*a^2*d^2*f^2*(C*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) + 8*d*f*(2*A*d*f - B*(d*e + c*f))) - 8*a*b*d*f*(C*(7*d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 7*c^3*f^3) + 2*d*f*(8*A*d*f*(d*e + c*f) - B*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2))) + b^2*(C*(21*d^4*e^4 + 28*c*d^3*e^3*f + 30*c^2*d^2*e^2*f^2 + 28*c^3*d*e*f^3 + 21*c^4*f^4) + 4*d*f*(2*A*d*f*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) - B*(7*d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 7*c^3*f^3))))*Sqrt[c + d*x]*Sqrt[e + f*x])/(512*d^5*f^5) + ((8*a^2*d^2*f^2*(C*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) + 8*d*f*(2*A*d*f - B*(d*e + c*f))) - 8*a*b*d*f*(C*(7*d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 7*c^3*f^3) + 2*d*f*(8*A*d*f*(d*e + c*f) - B*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2))) + b^2*(C*(21*d^4*e^4 + 28*c*d^3*e^3*f + 30*c^2*d^2*e^2*f^2 + 28*c^3*d*e*f^3 + 21*c^4*f^4) + 4*d*f*(2*A*d*f*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) - B*(7*d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 7*c^3*f^3))))*(c + d*x)^(3/2)*Sqrt[e + f*x])/(256*d^5*f^4) + ((4*b*B*d*f - 2*a*C*d*f - 3*b*C*(d*e + c*f))*(a + b*x)^2*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(20*b*d^2*f^2) + (C*(a + b*x)^3*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(6*b*d*f) - ((c + d*x)^(3/2)*(e + f*x)^(3/2)*(64*a^3*C*d^3*f^3 - 8*a^2*b*d^2*f^2*(16*B*d*f - 7*C*(d*e + c*f)) - 8*a*b^2*d*f*(C*(35*d^2*e^2 + 38*c*d*e*f + 35*c^2*f^2) + 10*d*f*(8*A*d*f - 5*B*(d*e + c*f))) + b^3*(7*C*(15*d^3*e^3 + 17*c*d^2*e^2*f + 17*c^2*d*e*f^2 + 15*c^3*f^3) + 4*d*f*(50*A*d*f*(d*e + c*f) - B*(35*d^2*e^2 + 38*c*d*e*f + 35*c^2*f^2))) + 6*b*d*f*(10*b*d*f*(2*b*c*C*e + a*C*d*e + a*c*C*f - 4*A*b*d*f) - (4*a*d*f - 7*b*(d*e + c*f))*(4*b*B*d*f - 2*a*C*d*f - 3*b*C*(d*e + c*f)))*x))/(960*b*d^4*f^4) - ((d*e - c*f)^2*(8*a^2*d^2*f^2*(C*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) + 8*d*f*(2*A*d*f - B*(d*e + c*f))) - 8*a*b*d*f*(C*(7*d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 7*c^3*f^3) + 2*d*f*(8*A*d*f*(d*e + c*f) - B*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2))) + b^2*(C*(21*d^4*e^4 + 28*c*d^3*e^3*f + 30*c^2*d^2*e^2*f^2 + 28*c^3*d*e*f^3 + 21*c^4*f^4) + 4*d*f*(2*A*d*f*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) - B*(7*d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 7*c^3*f^3))))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(512*d^(11/2)*f^(11/2))","A",8,7,36,0.1944,1,"{1615, 153, 147, 50, 63, 217, 206}"
42,1,719,0,0.9631882,"\int (a+b x) \sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right) \, dx","Int[(a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2),x]","-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(48 a^2 C d^2 f^2-6 b d f x (-6 a C d f+10 b B d f-7 b C (c f+d e))-10 a b d f (8 B d f-5 C (c f+d e))+b^2 \left(-\left(10 d f (8 A d f-5 B (c f+d e))+C \left(35 c^2 f^2+38 c d e f+35 d^2 e^2\right)\right)\right)\right)}{240 b d^3 f^3}+\frac{\sqrt{c+d x} \sqrt{e+f x} (d e-c f) \left(2 a d f \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)-b \left(2 d f \left(8 A d f (c f+d e)-B \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+7 c^3 f^3+9 c d^2 e^2 f+7 d^3 e^3\right)\right)\right)}{128 d^4 f^4}+\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(2 a d f \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)-b \left(2 d f \left(8 A d f (c f+d e)-B \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+7 c^3 f^3+9 c d^2 e^2 f+7 d^3 e^3\right)\right)\right)}{64 d^4 f^3}-\frac{(d e-c f)^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(2 a d f \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)-b \left(2 d f \left(8 A d f (c f+d e)-B \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+7 c^3 f^3+9 c d^2 e^2 f+7 d^3 e^3\right)\right)\right)}{128 d^{9/2} f^{9/2}}+\frac{C (a+b x)^2 (c+d x)^{3/2} (e+f x)^{3/2}}{5 b d f}","-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(48 a^2 C d^2 f^2+6 b d f x (6 a C d f-b (10 B d f-7 C (c f+d e)))-10 a b d f (8 B d f-5 C (c f+d e))+b^2 \left(-\left(10 d f (8 A d f-5 B (c f+d e))+C \left(35 c^2 f^2+38 c d e f+35 d^2 e^2\right)\right)\right)\right)}{240 b d^3 f^3}+\frac{\sqrt{c+d x} \sqrt{e+f x} (d e-c f) \left(2 a d f \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)-b \left(2 d f \left(8 A d f (c f+d e)-B \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+7 c^3 f^3+9 c d^2 e^2 f+7 d^3 e^3\right)\right)\right)}{128 d^4 f^4}+\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(2 a d f \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)-b \left(2 d f \left(8 A d f (c f+d e)-B \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+7 c^3 f^3+9 c d^2 e^2 f+7 d^3 e^3\right)\right)\right)}{64 d^4 f^3}-\frac{(d e-c f)^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(2 a d f \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)-b \left(2 d f \left(8 A d f (c f+d e)-B \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+7 c^3 f^3+9 c d^2 e^2 f+7 d^3 e^3\right)\right)\right)}{128 d^{9/2} f^{9/2}}+\frac{C (a+b x)^2 (c+d x)^{3/2} (e+f x)^{3/2}}{5 b d f}",1,"((d*e - c*f)*(2*a*d*f*(C*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) + 8*d*f*(2*A*d*f - B*(d*e + c*f))) - b*(C*(7*d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 7*c^3*f^3) + 2*d*f*(8*A*d*f*(d*e + c*f) - B*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2))))*Sqrt[c + d*x]*Sqrt[e + f*x])/(128*d^4*f^4) + ((2*a*d*f*(C*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) + 8*d*f*(2*A*d*f - B*(d*e + c*f))) - b*(C*(7*d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 7*c^3*f^3) + 2*d*f*(8*A*d*f*(d*e + c*f) - B*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2))))*(c + d*x)^(3/2)*Sqrt[e + f*x])/(64*d^4*f^3) + (C*(a + b*x)^2*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(5*b*d*f) - ((c + d*x)^(3/2)*(e + f*x)^(3/2)*(48*a^2*C*d^2*f^2 - 10*a*b*d*f*(8*B*d*f - 5*C*(d*e + c*f)) - b^2*(C*(35*d^2*e^2 + 38*c*d*e*f + 35*c^2*f^2) + 10*d*f*(8*A*d*f - 5*B*(d*e + c*f))) - 6*b*d*f*(10*b*B*d*f - 6*a*C*d*f - 7*b*C*(d*e + c*f))*x))/(240*b*d^3*f^3) - ((d*e - c*f)^2*(2*a*d*f*(C*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) + 8*d*f*(2*A*d*f - B*(d*e + c*f))) - b*(C*(7*d^3*e^3 + 9*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 7*c^3*f^3) + 2*d*f*(8*A*d*f*(d*e + c*f) - B*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2))))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(128*d^(9/2)*f^(9/2))","A",7,6,34,0.1765,1,"{1615, 147, 50, 63, 217, 206}"
43,1,330,0,0.2975922,"\int \sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right) \, dx","Int[Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2),x]","\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)}{32 d^3 f^2}+\frac{\sqrt{c+d x} \sqrt{e+f x} (d e-c f) \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)}{64 d^3 f^3}-\frac{(d e-c f)^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)}{64 d^{7/2} f^{7/2}}-\frac{(c+d x)^{3/2} (e+f x)^{3/2} (-8 B d f+11 c C f+5 C d e)}{24 d^2 f^2}+\frac{C (c+d x)^{5/2} (e+f x)^{3/2}}{4 d^2 f}","\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)}{32 d^3 f^2}+\frac{\sqrt{c+d x} \sqrt{e+f x} (d e-c f) \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)}{64 d^3 f^3}-\frac{(d e-c f)^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)}{64 d^{7/2} f^{7/2}}-\frac{(c+d x)^{3/2} (e+f x)^{3/2} (-8 B d f+11 c C f+5 C d e)}{24 d^2 f^2}+\frac{C (c+d x)^{5/2} (e+f x)^{3/2}}{4 d^2 f}",1,"((d*e - c*f)*(C*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) + 8*d*f*(2*A*d*f - B*(d*e + c*f)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(64*d^3*f^3) + ((C*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) + 8*d*f*(2*A*d*f - B*(d*e + c*f)))*(c + d*x)^(3/2)*Sqrt[e + f*x])/(32*d^3*f^2) - ((5*C*d*e + 11*c*C*f - 8*B*d*f)*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(24*d^2*f^2) + (C*(c + d*x)^(5/2)*(e + f*x)^(3/2))/(4*d^2*f) - ((d*e - c*f)^2*(C*(5*d^2*e^2 + 6*c*d*e*f + 5*c^2*f^2) + 8*d*f*(2*A*d*f - B*(d*e + c*f)))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(64*d^(7/2)*f^(7/2))","A",7,6,29,0.2069,1,"{951, 80, 50, 63, 217, 206}"
44,1,453,0,1.3694473,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{a+b x} \, dx","Int[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(-8 a^2 b d^2 f^2 (2 B d f+c C f+C d e)+16 a^3 C d^3 f^3-2 a b^2 d f \left(C (d e-c f)^2-4 d f (2 A d f+B c f+B d e)\right)+b^3 \left(-\left(C (d e-c f)^2 (c f+d e)-2 d f \left(B (d e-c f)^2-4 A d f (c f+d e)\right)\right)\right)\right)}{8 b^4 d^{5/2} f^{5/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(\frac{(4 a d f-b c f+b d e) (2 a C d f+b (-2 B d f+c C f+C d e))}{b d f}-4 a C (c f+d e)+8 A b d f\right)}{8 b^2 d f}-\frac{2 \sqrt{b c-a d} \sqrt{b e-a f} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right)}{b^4}-\frac{\sqrt{c+d x} (e+f x)^{3/2} (2 a C d f+b (-2 B d f+c C f+C d e))}{4 b^2 d f^2}+\frac{C (c+d x)^{3/2} (e+f x)^{3/2}}{3 b d f}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(-8 a^2 b d^2 f^2 (2 B d f+c C f+C d e)+16 a^3 C d^3 f^3-2 a b^2 d f \left(C (d e-c f)^2-4 d f (2 A d f+B c f+B d e)\right)+b^3 \left(-\left(C (d e-c f)^2 (c f+d e)-2 d f \left(B (d e-c f)^2-4 A d f (c f+d e)\right)\right)\right)\right)}{8 b^4 d^{5/2} f^{5/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} (4 b d f (2 A b d f-a C (c f+d e))+(4 a d f-b c f+b d e) (2 a C d f+b (-2 B d f+c C f+C d e)))}{8 b^3 d^2 f^2}-\frac{2 \sqrt{b c-a d} \sqrt{b e-a f} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right)}{b^4}-\frac{\sqrt{c+d x} (e+f x)^{3/2} (2 a C d f+b (-2 B d f+c C f+C d e))}{4 b^2 d f^2}+\frac{C (c+d x)^{3/2} (e+f x)^{3/2}}{3 b d f}",1,"((8*A*b*d*f - 4*a*C*(d*e + c*f) + ((b*d*e - b*c*f + 4*a*d*f)*(2*a*C*d*f + b*(C*d*e + c*C*f - 2*B*d*f)))/(b*d*f))*Sqrt[c + d*x]*Sqrt[e + f*x])/(8*b^2*d*f) - ((2*a*C*d*f + b*(C*d*e + c*C*f - 2*B*d*f))*Sqrt[c + d*x]*(e + f*x)^(3/2))/(4*b^2*d*f^2) + (C*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(3*b*d*f) - ((16*a^3*C*d^3*f^3 - 8*a^2*b*d^2*f^2*(C*d*e + c*C*f + 2*B*d*f) - 2*a*b^2*d*f*(C*(d*e - c*f)^2 - 4*d*f*(B*d*e + B*c*f + 2*A*d*f)) - b^3*(C*(d*e - c*f)^2*(d*e + c*f) - 2*d*f*(B*(d*e - c*f)^2 - 4*A*d*f*(d*e + c*f))))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(8*b^4*d^(5/2)*f^(5/2)) - (2*(A*b^2 - a*(b*B - a*C))*Sqrt[b*c - a*d]*Sqrt[b*e - a*f]*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/b^4","A",9,8,36,0.2222,1,"{1615, 154, 157, 63, 217, 206, 93, 208}"
45,1,521,0,1.6957627,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^2} \, dx","Int[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^2,x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(24 a^2 C d^2 f^2-8 a b d f (2 B d f+c C f+C d e)+b^2 \left(-\left(C (d e-c f)^2-4 d f (2 A d f+B c f+B d e)\right)\right)\right)}{4 b^4 d^{3/2} f^{3/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(12 a^2 C d f^2-a b f (8 B d f+c C f+7 C d e)+b^2 (4 d f (A f+B e)-C e (d e-c f))\right)}{4 b^3 d f (b e-a f)}+\frac{\sqrt{c+d x} (e+f x)^{3/2} \left(3 a^2 C d f-a b (2 B d f+c C f+C d e)+b^2 (2 A d f+c C e)\right)}{2 b^2 f (b c-a d) (b e-a f)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(-a^2 b (4 B d f+5 C (c f+d e))+6 a^3 C d f+a b^2 (2 A d f+3 B c f+3 B d e+4 c C e)-b^3 (A c f+A d e+2 B c e)\right)}{b^4 \sqrt{b c-a d} \sqrt{b e-a f}}-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(A b^2-a (b B-a C)\right)}{b (a+b x) (b c-a d) (b e-a f)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(24 a^2 C d^2 f^2-8 a b d f (2 B d f+c C f+C d e)+b^2 \left(-\left(C (d e-c f)^2-4 d f (2 A d f+B c f+B d e)\right)\right)\right)}{4 b^4 d^{3/2} f^{3/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(12 a^2 C d f^2-a b f (8 B d f+c C f+7 C d e)+b^2 (4 d f (A f+B e)-C e (d e-c f))\right)}{4 b^3 d f (b e-a f)}+\frac{\sqrt{c+d x} (e+f x)^{3/2} \left(3 a^2 C d f-a b (2 B d f+c C f+C d e)+b^2 (2 A d f+c C e)\right)}{2 b^2 f (b c-a d) (b e-a f)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(-a^2 b (4 B d f+5 C (c f+d e))+6 a^3 C d f+a b^2 (2 A d f+3 B c f+3 B d e+4 c C e)-b^3 (A c f+A d e+2 B c e)\right)}{b^4 \sqrt{b c-a d} \sqrt{b e-a f}}-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(A b^2-a (b B-a C)\right)}{b (a+b x) (b c-a d) (b e-a f)}",1,"((12*a^2*C*d*f^2 - a*b*f*(7*C*d*e + c*C*f + 8*B*d*f) + b^2*(4*d*f*(B*e + A*f) - C*e*(d*e - c*f)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(4*b^3*d*f*(b*e - a*f)) + ((3*a^2*C*d*f + b^2*(c*C*e + 2*A*d*f) - a*b*(C*d*e + c*C*f + 2*B*d*f))*Sqrt[c + d*x]*(e + f*x)^(3/2))/(2*b^2*(b*c - a*d)*f*(b*e - a*f)) - ((A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(b*(b*c - a*d)*(b*e - a*f)*(a + b*x)) + ((24*a^2*C*d^2*f^2 - 8*a*b*d*f*(C*d*e + c*C*f + 2*B*d*f) - b^2*(C*(d*e - c*f)^2 - 4*d*f*(B*d*e + B*c*f + 2*A*d*f)))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(4*b^4*d^(3/2)*f^(3/2)) + ((6*a^3*C*d*f - b^3*(2*B*c*e + A*d*e + A*c*f) + a*b^2*(4*c*C*e + 3*B*d*e + 3*B*c*f + 2*A*d*f) - a^2*b*(4*B*d*f + 5*C*(d*e + c*f)))*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(b^4*Sqrt[b*c - a*d]*Sqrt[b*e - a*f])","A",9,8,36,0.2222,1,"{1613, 154, 157, 63, 217, 206, 93, 208}"
46,1,657,0,2.6795113,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^3} \, dx","Int[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^3,x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(3 a^2 b^2 \left(4 B d f (c f+d e)+C \left(5 c^2 f^2+22 c d e f+5 d^2 e^2\right)\right)-8 a^3 b d f (B d f+5 C (c f+d e))+24 a^4 C d^2 f^2-3 a b^3 \left(c^2 f (B f+8 C e)+2 c d e (3 B f+4 C e)+B d^2 e^2\right)-b^4 \left(c^2 \left(-\left(-A f^2+4 B e f+8 C e^2\right)\right)-2 c d e (A f+2 B e)+A d^2 e^2\right)\right)}{4 b^4 (b c-a d)^{3/2} (b e-a f)^{3/2}}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-a^2 b f (4 B d f+11 c C f+17 C d e)+12 a^3 C d f^2+a b^2 (B f (3 c f+5 d e)+4 C e (4 c f+d e))-b^3 \left(c f (4 B e-A f)+A d e f+4 c C e^2\right)\right)}{4 b^3 (b c-a d) (b e-a f)^2}+\frac{\sqrt{c+d x} (e+f x)^{3/2} \left(-a^2 b (2 B d f+7 C (c f+d e))+6 a^3 C d f+a b^2 (-2 A d f+3 B c f+3 B d e+8 c C e)-b^3 (-A c f-A d e+4 B c e)\right)}{4 b^2 (a+b x) (b c-a d) (b e-a f)^2}-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(A b^2-a (b B-a C)\right)}{2 b (a+b x)^2 (b c-a d) (b e-a f)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (6 a C d f-b (2 B d f+c C f+C d e))}{b^4 \sqrt{d} \sqrt{f}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(3 a^2 b^2 \left(4 B d f (c f+d e)+C \left(5 c^2 f^2+22 c d e f+5 d^2 e^2\right)\right)-8 a^3 b d f (B d f+5 C (c f+d e))+24 a^4 C d^2 f^2-3 a b^3 \left(c^2 f (B f+8 C e)+2 c d e (3 B f+4 C e)+B d^2 e^2\right)-b^4 \left(c^2 \left(-\left(-A f^2+4 B e f+8 C e^2\right)\right)-2 c d e (A f+2 B e)+A d^2 e^2\right)\right)}{4 b^4 (b c-a d)^{3/2} (b e-a f)^{3/2}}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-a^2 b f (4 B d f+11 c C f+17 C d e)+12 a^3 C d f^2+a b^2 (B f (3 c f+5 d e)+4 C e (4 c f+d e))-b^3 \left(c \left(-A f^2+4 B e f+4 C e^2\right)+A d e f\right)\right)}{4 b^3 (b c-a d) (b e-a f)^2}+\frac{\sqrt{c+d x} (e+f x)^{3/2} \left(-a^2 b (2 B d f+7 C (c f+d e))+6 a^3 C d f+a b^2 (-2 A d f+3 B c f+3 B d e+8 c C e)-b^3 (-A c f-A d e+4 B c e)\right)}{4 b^2 (a+b x) (b c-a d) (b e-a f)^2}-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(A b^2-a (b B-a C)\right)}{2 b (a+b x)^2 (b c-a d) (b e-a f)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (6 a C d f-b (2 B d f+c C f+C d e))}{b^4 \sqrt{d} \sqrt{f}}",1,"-((12*a^3*C*d*f^2 - a^2*b*f*(17*C*d*e + 11*c*C*f + 4*B*d*f) - b^3*(4*c*C*e^2 + A*d*e*f + c*f*(4*B*e - A*f)) + a*b^2*(B*f*(5*d*e + 3*c*f) + 4*C*e*(d*e + 4*c*f)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(4*b^3*(b*c - a*d)*(b*e - a*f)^2) + ((6*a^3*C*d*f - b^3*(4*B*c*e - A*d*e - A*c*f) + a*b^2*(8*c*C*e + 3*B*d*e + 3*B*c*f - 2*A*d*f) - a^2*b*(2*B*d*f + 7*C*(d*e + c*f)))*Sqrt[c + d*x]*(e + f*x)^(3/2))/(4*b^2*(b*c - a*d)*(b*e - a*f)^2*(a + b*x)) - ((A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(2*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^2) - ((6*a*C*d*f - b*(C*d*e + c*C*f + 2*B*d*f))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(b^4*Sqrt[d]*Sqrt[f]) - ((24*a^4*C*d^2*f^2 - 3*a*b^3*(B*d^2*e^2 + c^2*f*(8*C*e + B*f) + 2*c*d*e*(4*C*e + 3*B*f)) - 8*a^3*b*d*f*(B*d*f + 5*C*(d*e + c*f)) - b^4*(A*d^2*e^2 - 2*c*d*e*(2*B*e + A*f) - c^2*(8*C*e^2 + 4*B*e*f - A*f^2)) + 3*a^2*b^2*(4*B*d*f*(d*e + c*f) + C*(5*d^2*e^2 + 22*c*d*e*f + 5*c^2*f^2)))*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(4*b^4*(b*c - a*d)^(3/2)*(b*e - a*f)^(3/2))","A",9,9,36,0.2500,1,"{1613, 149, 154, 157, 63, 217, 206, 93, 208}"
47,1,1032,0,1.7876846,"\int \frac{(a+b x)^2 \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","Int[((a + b*x)^2*Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","\frac{C (c+d x)^{3/2} \sqrt{e+f x} (a+b x)^3}{5 b d f}-\frac{(4 a C d f+b (9 C d e+7 c C f-10 B d f)) (c+d x)^{3/2} \sqrt{e+f x} (a+b x)^2}{40 b d^2 f^2}-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(\left(C \left(315 d^3 e^3+203 c d^2 f e^2+145 c^2 d f^2 e+105 c^3 f^3\right)+10 d f \left(8 A d f (5 d e+3 c f)-B \left(35 d^2 e^2+22 c d f e+15 c^2 f^2\right)\right)\right) b^3+20 a d f \left(8 d f (5 B d e+3 B c f-6 A d f)-C \left(35 d^2 e^2+22 c d f e+15 c^2 f^2\right)\right) b^2+8 a^2 d^2 f^2 (23 C d e+9 c C f-30 B d f) b+4 d f (8 b d f (6 b c C e+3 a C d e+a c C f-10 A b d f)-(7 b d e+5 b c f-4 a d f) (4 a C d f+b (9 C d e+7 c C f-10 B d f))) x b+96 a^3 C d^3 f^3\right)}{960 b d^4 f^4}+\frac{(d e-c f) \left(-\left(C \left(63 d^4 e^4+28 c d^3 f e^3+18 c^2 d^2 f^2 e^2+12 c^3 d f^3 e+7 c^4 f^4\right)+2 d f \left(8 A d f \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)-B \left(35 d^3 e^3+15 c d^2 f e^2+9 c^2 d f^2 e+5 c^3 f^3\right)\right)\right) b^2+4 a d f \left(C \left(35 d^3 e^3+15 c d^2 f e^2+9 c^2 d f^2 e+5 c^3 f^3\right)+8 d f \left(2 A d f (3 d e+c f)-B \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) b+16 a^2 d^2 f^2 \left(2 d f (3 B d e+B c f-4 A d f)-C \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right)}{128 d^{9/2} f^{11/2}}-\frac{\left(-\left(C \left(63 d^4 e^4+28 c d^3 f e^3+18 c^2 d^2 f^2 e^2+12 c^3 d f^3 e+7 c^4 f^4\right)+2 d f \left(8 A d f \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)-B \left(35 d^3 e^3+15 c d^2 f e^2+9 c^2 d f^2 e+5 c^3 f^3\right)\right)\right) b^2+4 a d f \left(C \left(35 d^3 e^3+15 c d^2 f e^2+9 c^2 d f^2 e+5 c^3 f^3\right)+8 d f \left(2 A d f (3 d e+c f)-B \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) b+16 a^2 d^2 f^2 \left(2 d f (3 B d e+B c f-4 A d f)-C \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{128 d^4 f^5}","\frac{C (c+d x)^{3/2} \sqrt{e+f x} (a+b x)^3}{5 b d f}-\frac{(4 a C d f+b (9 C d e+7 c C f-10 B d f)) (c+d x)^{3/2} \sqrt{e+f x} (a+b x)^2}{40 b d^2 f^2}-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(\left(C \left(315 d^3 e^3+203 c d^2 f e^2+145 c^2 d f^2 e+105 c^3 f^3\right)+10 d f \left(8 A d f (5 d e+3 c f)-B \left(35 d^2 e^2+22 c d f e+15 c^2 f^2\right)\right)\right) b^3+20 a d f \left(8 d f (5 B d e+3 B c f-6 A d f)-C \left(35 d^2 e^2+22 c d f e+15 c^2 f^2\right)\right) b^2+8 a^2 d^2 f^2 (23 C d e+9 c C f-30 B d f) b+4 d f (8 b d f (6 b c C e+3 a C d e+a c C f-10 A b d f)-(7 b d e+5 b c f-4 a d f) (4 a C d f+b (9 C d e+7 c C f-10 B d f))) x b+96 a^3 C d^3 f^3\right)}{960 b d^4 f^4}+\frac{(d e-c f) \left(-\left(C \left(63 d^4 e^4+28 c d^3 f e^3+18 c^2 d^2 f^2 e^2+12 c^3 d f^3 e+7 c^4 f^4\right)+2 d f \left(8 A d f \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)-B \left(35 d^3 e^3+15 c d^2 f e^2+9 c^2 d f^2 e+5 c^3 f^3\right)\right)\right) b^2+4 a d f \left(C \left(35 d^3 e^3+15 c d^2 f e^2+9 c^2 d f^2 e+5 c^3 f^3\right)+8 d f \left(2 A d f (3 d e+c f)-B \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) b+16 a^2 d^2 f^2 \left(2 d f (3 B d e+B c f-4 A d f)-C \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right)}{128 d^{9/2} f^{11/2}}-\frac{\left(-\left(C \left(63 d^4 e^4+28 c d^3 f e^3+18 c^2 d^2 f^2 e^2+12 c^3 d f^3 e+7 c^4 f^4\right)+2 d f \left(8 A d f \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)-B \left(35 d^3 e^3+15 c d^2 f e^2+9 c^2 d f^2 e+5 c^3 f^3\right)\right)\right) b^2+4 a d f \left(C \left(35 d^3 e^3+15 c d^2 f e^2+9 c^2 d f^2 e+5 c^3 f^3\right)+8 d f \left(2 A d f (3 d e+c f)-B \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) b+16 a^2 d^2 f^2 \left(2 d f (3 B d e+B c f-4 A d f)-C \left(5 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{128 d^4 f^5}",1,"-((16*a^2*d^2*f^2*(2*d*f*(3*B*d*e + B*c*f - 4*A*d*f) - C*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2)) + 4*a*b*d*f*(C*(35*d^3*e^3 + 15*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 5*c^3*f^3) + 8*d*f*(2*A*d*f*(3*d*e + c*f) - B*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2))) - b^2*(C*(63*d^4*e^4 + 28*c*d^3*e^3*f + 18*c^2*d^2*e^2*f^2 + 12*c^3*d*e*f^3 + 7*c^4*f^4) + 2*d*f*(8*A*d*f*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2) - B*(35*d^3*e^3 + 15*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 5*c^3*f^3))))*Sqrt[c + d*x]*Sqrt[e + f*x])/(128*d^4*f^5) - ((4*a*C*d*f + b*(9*C*d*e + 7*c*C*f - 10*B*d*f))*(a + b*x)^2*(c + d*x)^(3/2)*Sqrt[e + f*x])/(40*b*d^2*f^2) + (C*(a + b*x)^3*(c + d*x)^(3/2)*Sqrt[e + f*x])/(5*b*d*f) - ((c + d*x)^(3/2)*Sqrt[e + f*x]*(96*a^3*C*d^3*f^3 + 8*a^2*b*d^2*f^2*(23*C*d*e + 9*c*C*f - 30*B*d*f) + 20*a*b^2*d*f*(8*d*f*(5*B*d*e + 3*B*c*f - 6*A*d*f) - C*(35*d^2*e^2 + 22*c*d*e*f + 15*c^2*f^2)) + b^3*(C*(315*d^3*e^3 + 203*c*d^2*e^2*f + 145*c^2*d*e*f^2 + 105*c^3*f^3) + 10*d*f*(8*A*d*f*(5*d*e + 3*c*f) - B*(35*d^2*e^2 + 22*c*d*e*f + 15*c^2*f^2))) + 4*b*d*f*(8*b*d*f*(6*b*c*C*e + 3*a*C*d*e + a*c*C*f - 10*A*b*d*f) - (7*b*d*e + 5*b*c*f - 4*a*d*f)*(4*a*C*d*f + b*(9*C*d*e + 7*c*C*f - 10*B*d*f)))*x))/(960*b*d^4*f^4) + ((d*e - c*f)*(16*a^2*d^2*f^2*(2*d*f*(3*B*d*e + B*c*f - 4*A*d*f) - C*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2)) + 4*a*b*d*f*(C*(35*d^3*e^3 + 15*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 5*c^3*f^3) + 8*d*f*(2*A*d*f*(3*d*e + c*f) - B*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2))) - b^2*(C*(63*d^4*e^4 + 28*c*d^3*e^3*f + 18*c^2*d^2*e^2*f^2 + 12*c^3*d*e*f^3 + 7*c^4*f^4) + 2*d*f*(8*A*d*f*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2) - B*(35*d^3*e^3 + 15*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 5*c^3*f^3))))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(128*d^(9/2)*f^(11/2))","A",7,7,36,0.1944,1,"{1615, 153, 147, 50, 63, 217, 206}"
48,1,540,0,0.7125299,"\int \frac{(a+b x) \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","Int[((a + b*x)*Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(24 a^2 C d^2 f^2+4 b d f x (4 a C d f+b (-8 B d f+5 c C f+7 C d e))+8 a b d f (-6 B d f+3 c C f+5 C d e)+b^2 \left(8 d f (-6 A d f+3 B c f+5 B d e)-C \left(15 c^2 f^2+22 c d e f+35 d^2 e^2\right)\right)\right)}{96 b d^3 f^3}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(8 a d f \left(2 d f (-4 A d f+B c f+3 B d e)-C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+b \left(8 d f \left(2 A d f (c f+3 d e)-B \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+5 c^3 f^3+15 c d^2 e^2 f+35 d^3 e^3\right)\right)\right)}{64 d^3 f^4}+\frac{(d e-c f) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(8 a d f \left(2 d f (-4 A d f+B c f+3 B d e)-C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+b \left(8 d f \left(2 A d f (c f+3 d e)-B \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+5 c^3 f^3+15 c d^2 e^2 f+35 d^3 e^3\right)\right)\right)}{64 d^{7/2} f^{9/2}}+\frac{C (a+b x)^2 (c+d x)^{3/2} \sqrt{e+f x}}{4 b d f}","-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(24 a^2 C d^2 f^2+4 b d f x (4 a C d f+b (-8 B d f+5 c C f+7 C d e))+8 a b d f (-6 B d f+3 c C f+5 C d e)+b^2 \left(8 d f (-6 A d f+3 B c f+5 B d e)-C \left(15 c^2 f^2+22 c d e f+35 d^2 e^2\right)\right)\right)}{96 b d^3 f^3}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(8 a d f \left(2 d f (-4 A d f+B c f+3 B d e)-C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+b \left(8 d f \left(2 A d f (c f+3 d e)-B \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+5 c^3 f^3+15 c d^2 e^2 f+35 d^3 e^3\right)\right)\right)}{64 d^3 f^4}+\frac{(d e-c f) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(8 a d f \left(2 d f (-4 A d f+B c f+3 B d e)-C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+b \left(8 d f \left(2 A d f (c f+3 d e)-B \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+C \left(9 c^2 d e f^2+5 c^3 f^3+15 c d^2 e^2 f+35 d^3 e^3\right)\right)\right)}{64 d^{7/2} f^{9/2}}+\frac{C (a+b x)^2 (c+d x)^{3/2} \sqrt{e+f x}}{4 b d f}",1,"-((8*a*d*f*(2*d*f*(3*B*d*e + B*c*f - 4*A*d*f) - C*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2)) + b*(C*(35*d^3*e^3 + 15*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 5*c^3*f^3) + 8*d*f*(2*A*d*f*(3*d*e + c*f) - B*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2))))*Sqrt[c + d*x]*Sqrt[e + f*x])/(64*d^3*f^4) + (C*(a + b*x)^2*(c + d*x)^(3/2)*Sqrt[e + f*x])/(4*b*d*f) - ((c + d*x)^(3/2)*Sqrt[e + f*x]*(24*a^2*C*d^2*f^2 + 8*a*b*d*f*(5*C*d*e + 3*c*C*f - 6*B*d*f) + b^2*(8*d*f*(5*B*d*e + 3*B*c*f - 6*A*d*f) - C*(35*d^2*e^2 + 22*c*d*e*f + 15*c^2*f^2)) + 4*b*d*f*(4*a*C*d*f + b*(7*C*d*e + 5*c*C*f - 8*B*d*f))*x))/(96*b*d^3*f^3) + ((d*e - c*f)*(8*a*d*f*(2*d*f*(3*B*d*e + B*c*f - 4*A*d*f) - C*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2)) + b*(C*(35*d^3*e^3 + 15*c*d^2*e^2*f + 9*c^2*d*e*f^2 + 5*c^3*f^3) + 8*d*f*(2*A*d*f*(3*d*e + c*f) - B*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2))))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(64*d^(7/2)*f^(9/2))","A",6,6,34,0.1765,1,"{1615, 147, 50, 63, 217, 206}"
49,1,246,0,0.2303146,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","Int[(Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","\frac{\sqrt{c+d x} \sqrt{e+f x} \left(2 d f (4 A d f-B (c f+3 d e))+C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)}{8 d^2 f^3}-\frac{(d e-c f) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(2 d f (4 A d f-B (c f+3 d e))+C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)}{8 d^{5/2} f^{7/2}}-\frac{(c+d x)^{3/2} \sqrt{e+f x} (-6 B d f+7 c C f+5 C d e)}{12 d^2 f^2}+\frac{C (c+d x)^{5/2} \sqrt{e+f x}}{3 d^2 f}","\frac{\sqrt{c+d x} \sqrt{e+f x} \left(2 d f (4 A d f-B (c f+3 d e))+C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)}{8 d^2 f^3}-\frac{(d e-c f) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(2 d f (4 A d f-B (c f+3 d e))+C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)}{8 d^{5/2} f^{7/2}}-\frac{(c+d x)^{3/2} \sqrt{e+f x} (-6 B d f+7 c C f+5 C d e)}{12 d^2 f^2}+\frac{C (c+d x)^{5/2} \sqrt{e+f x}}{3 d^2 f}",1,"((C*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2) + 2*d*f*(4*A*d*f - B*(3*d*e + c*f)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(8*d^2*f^3) - ((5*C*d*e + 7*c*C*f - 6*B*d*f)*(c + d*x)^(3/2)*Sqrt[e + f*x])/(12*d^2*f^2) + (C*(c + d*x)^(5/2)*Sqrt[e + f*x])/(3*d^2*f) - ((d*e - c*f)*(C*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2) + 2*d*f*(4*A*d*f - B*(3*d*e + c*f)))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(8*d^(5/2)*f^(7/2))","A",6,6,29,0.2069,1,"{951, 80, 50, 63, 217, 206}"
50,1,290,0,0.6723547,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x) \sqrt{e+f x}} \, dx","Int[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)*Sqrt[e + f*x]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (2 b d f (4 A b d f-a C (c f+3 d e))+(2 a d f-b c f+b d e) (4 a C d f+b (-4 B d f+c C f+3 C d e)))}{4 b^3 d^{3/2} f^{5/2}}-\frac{2 \sqrt{b c-a d} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right)}{b^3 \sqrt{b e-a f}}-\frac{\sqrt{c+d x} \sqrt{e+f x} (4 a C d f+b (-4 B d f+c C f+3 C d e))}{4 b^2 d f^2}+\frac{C (c+d x)^{3/2} \sqrt{e+f x}}{2 b d f}","\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (2 b d f (4 A b d f-a C (c f+3 d e))+(2 a d f-b c f+b d e) (4 a C d f+b (-4 B d f+c C f+3 C d e)))}{4 b^3 d^{3/2} f^{5/2}}-\frac{2 \sqrt{b c-a d} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right)}{b^3 \sqrt{b e-a f}}-\frac{\sqrt{c+d x} \sqrt{e+f x} (4 a C d f+b (-4 B d f+c C f+3 C d e))}{4 b^2 d f^2}+\frac{C (c+d x)^{3/2} \sqrt{e+f x}}{2 b d f}",1,"-((4*a*C*d*f + b*(3*C*d*e + c*C*f - 4*B*d*f))*Sqrt[c + d*x]*Sqrt[e + f*x])/(4*b^2*d*f^2) + (C*(c + d*x)^(3/2)*Sqrt[e + f*x])/(2*b*d*f) + ((2*b*d*f*(4*A*b*d*f - a*C*(3*d*e + c*f)) + (b*d*e - b*c*f + 2*a*d*f)*(4*a*C*d*f + b*(3*C*d*e + c*C*f - 4*B*d*f)))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(4*b^3*d^(3/2)*f^(5/2)) - (2*(A*b^2 - a*(b*B - a*C))*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(b^3*Sqrt[b*e - a*f])","A",8,8,36,0.2222,1,"{1615, 154, 157, 63, 217, 206, 93, 208}"
51,1,364,0,1.0974771,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^2 \sqrt{e+f x}} \, dx","Int[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^2*Sqrt[e + f*x]),x]","\frac{\sqrt{c+d x} \sqrt{e+f x} \left(2 a^2 C d f-a b (B d f+c C f+C d e)+b^2 (A d f+c C e)\right)}{b^2 f (b c-a d) (b e-a f)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(-a^2 b (2 B d f+3 c C f+5 C d e)+4 a^3 C d f+a b^2 (B c f+3 B d e+4 c C e)-b^3 (-A c f+A d e+2 B c e)\right)}{b^3 \sqrt{b c-a d} (b e-a f)^{3/2}}-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{b (a+b x) (b c-a d) (b e-a f)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (4 a C d f+b (-2 B d f-c C f+C d e))}{b^3 \sqrt{d} f^{3/2}}","\frac{\sqrt{c+d x} \sqrt{e+f x} \left(2 a^2 C d f-a b (B d f+c C f+C d e)+b^2 (A d f+c C e)\right)}{b^2 f (b c-a d) (b e-a f)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(-a^2 b (2 B d f+3 c C f+5 C d e)+4 a^3 C d f+a b^2 (B c f+3 B d e+4 c C e)-b^3 (-A c f+A d e+2 B c e)\right)}{b^3 \sqrt{b c-a d} (b e-a f)^{3/2}}-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{b (a+b x) (b c-a d) (b e-a f)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (4 a C d f+b (-2 B d f-c C f+C d e))}{b^3 \sqrt{d} f^{3/2}}",1,"((2*a^2*C*d*f + b^2*(c*C*e + A*d*f) - a*b*(C*d*e + c*C*f + B*d*f))*Sqrt[c + d*x]*Sqrt[e + f*x])/(b^2*(b*c - a*d)*f*(b*e - a*f)) - ((A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*Sqrt[e + f*x])/(b*(b*c - a*d)*(b*e - a*f)*(a + b*x)) - ((4*a*C*d*f + b*(C*d*e - c*C*f - 2*B*d*f))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(b^3*Sqrt[d]*f^(3/2)) + ((4*a^3*C*d*f - b^3*(2*B*c*e + A*d*e - A*c*f) + a*b^2*(4*c*C*e + 3*B*d*e + B*c*f) - a^2*b*(5*C*d*e + 3*c*C*f + 2*B*d*f))*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(b^3*Sqrt[b*c - a*d]*(b*e - a*f)^(3/2))","A",8,8,36,0.2222,1,"{1613, 154, 157, 63, 217, 206, 93, 208}"
52,1,484,0,1.5632638,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^3 \sqrt{e+f x}} \, dx","Int[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^3*Sqrt[e + f*x]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(3 a^2 b^2 C \left(c^2 f^2+10 c d e f+5 d^2 e^2\right)-4 a^3 b C d f (3 c f+5 d e)+8 a^4 C d^2 f^2-a b^3 \left(2 c d \left(2 A f^2-B e f+12 C e^2\right)+d^2 e (3 B e-4 A f)+c^2 f (8 C e-B f)\right)-b^4 \left(c^2 \left(-\left(3 A f^2-4 B e f+8 C e^2\right)\right)-2 c d e (2 B e-A f)+A d^2 e^2\right)\right)}{4 b^3 (b c-a d)^{3/2} (b e-a f)^{5/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-a^2 b C (5 c f+7 d e)+4 a^3 C d f+a b^2 (-4 A d f+B c f+3 B d e+8 c C e)-b^3 (-3 A c f-A d e+4 B c e)\right)}{4 b^2 (a+b x) (b c-a d) (b e-a f)^2}-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{2 b (a+b x)^2 (b c-a d) (b e-a f)}+\frac{2 C \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right)}{b^3 \sqrt{f}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(3 a^2 b^2 C \left(c^2 f^2+10 c d e f+5 d^2 e^2\right)-4 a^3 b C d f (3 c f+5 d e)+8 a^4 C d^2 f^2-a b^3 \left(2 c d \left(2 A f^2-B e f+12 C e^2\right)+d^2 e (3 B e-4 A f)+c^2 f (8 C e-B f)\right)-b^4 \left(c^2 \left(-\left(3 A f^2-4 B e f+8 C e^2\right)\right)-2 c d e (2 B e-A f)+A d^2 e^2\right)\right)}{4 b^3 (b c-a d)^{3/2} (b e-a f)^{5/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-a^2 b C (5 c f+7 d e)+4 a^3 C d f+a b^2 (-4 A d f+B c f+3 B d e+8 c C e)-b^3 (-3 A c f-A d e+4 B c e)\right)}{4 b^2 (a+b x) (b c-a d) (b e-a f)^2}-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{2 b (a+b x)^2 (b c-a d) (b e-a f)}+\frac{2 C \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right)}{b^3 \sqrt{f}}",1,"((4*a^3*C*d*f - a^2*b*C*(7*d*e + 5*c*f) - b^3*(4*B*c*e - A*d*e - 3*A*c*f) + a*b^2*(8*c*C*e + 3*B*d*e + B*c*f - 4*A*d*f))*Sqrt[c + d*x]*Sqrt[e + f*x])/(4*b^2*(b*c - a*d)*(b*e - a*f)^2*(a + b*x)) - ((A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*Sqrt[e + f*x])/(2*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^2) + (2*C*Sqrt[d]*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(b^3*Sqrt[f]) - ((8*a^4*C*d^2*f^2 - 4*a^3*b*C*d*f*(5*d*e + 3*c*f) + 3*a^2*b^2*C*(5*d^2*e^2 + 10*c*d*e*f + c^2*f^2) - a*b^3*(d^2*e*(3*B*e - 4*A*f) + c^2*f*(8*C*e - B*f) + 2*c*d*(12*C*e^2 - B*e*f + 2*A*f^2)) - b^4*(A*d^2*e^2 - 2*c*d*e*(2*B*e - A*f) - c^2*(8*C*e^2 - 4*B*e*f + 3*A*f^2)))*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(4*b^3*(b*c - a*d)^(3/2)*(b*e - a*f)^(5/2))","A",8,8,36,0.2222,1,"{1613, 149, 157, 63, 217, 206, 93, 208}"
53,1,685,0,1.7778796,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^4 \sqrt{e+f x}} \, dx","Int[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^4*Sqrt[e + f*x]),x]","-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-a^2 b^2 \left(4 d f (-2 A d f+B c f+4 B d e)-C \left(3 c^2 f^2+44 c d e f+33 d^2 e^2\right)\right)-2 a^3 b d f (-2 B d f+7 c C f+13 C d e)+8 a^4 C d^2 f^2-a b^3 \left(2 c d \left(13 A f^2-14 B e f+30 C e^2\right)+d^2 e (3 B e-10 A f)+3 c^2 f (4 C e-B f)\right)-b^4 \left(-3 c^2 \left(5 A f^2-6 B e f+8 C e^2\right)-2 c d e (3 B e-2 A f)+3 A d^2 e^2\right)\right)}{24 b^2 (a+b x) (b c-a d)^2 (b e-a f)^3}-\frac{(d e-c f) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(a^2 \left(-\left(2 d f (-4 A d f+B c f+3 B d e)-C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)\right)+a b \left(-2 c d \left(6 A f^2-7 B e f+6 C e^2\right)+d^2 e (B e-4 A f)+c^2 (-f) (4 C e-B f)\right)+b^2 \left(c^2 \left(5 A f^2-6 B e f+8 C e^2\right)-2 c d e (B e-A f)+A d^2 e^2\right)\right)}{8 (b c-a d)^{5/2} (b e-a f)^{7/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-a^2 b (-2 B d f+7 c C f+9 C d e)+4 a^3 C d f+a b^2 (-8 A d f+B c f+3 B d e+12 c C e)-b^3 (-5 A c f-3 A d e+6 B c e)\right)}{12 b^2 (a+b x)^2 (b c-a d) (b e-a f)^2}-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{3 b (a+b x)^3 (b c-a d) (b e-a f)}","-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-a^2 b^2 \left(4 d f (-2 A d f+B c f+4 B d e)-C \left(3 c^2 f^2+44 c d e f+33 d^2 e^2\right)\right)-2 a^3 b d f (-2 B d f+7 c C f+13 C d e)+8 a^4 C d^2 f^2-a b^3 \left(2 c d \left(13 A f^2-14 B e f+30 C e^2\right)+d^2 e (3 B e-10 A f)+3 c^2 f (4 C e-B f)\right)-b^4 \left(-3 c^2 \left(5 A f^2-6 B e f+8 C e^2\right)-2 c d e (3 B e-2 A f)+3 A d^2 e^2\right)\right)}{24 b^2 (a+b x) (b c-a d)^2 (b e-a f)^3}-\frac{(d e-c f) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(a^2 \left(-\left(2 d f (-4 A d f+B c f+3 B d e)-C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)\right)+a b \left(-2 c d \left(6 A f^2-7 B e f+6 C e^2\right)+d^2 e (B e-4 A f)+c^2 (-f) (4 C e-B f)\right)+b^2 \left(c^2 \left(5 A f^2-6 B e f+8 C e^2\right)-2 c d e (B e-A f)+A d^2 e^2\right)\right)}{8 (b c-a d)^{5/2} (b e-a f)^{7/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-a^2 b (-2 B d f+7 c C f+9 C d e)+4 a^3 C d f+a b^2 (-8 A d f+B c f+3 B d e+12 c C e)-b^3 (-5 A c f-3 A d e+6 B c e)\right)}{12 b^2 (a+b x)^2 (b c-a d) (b e-a f)^2}-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{3 b (a+b x)^3 (b c-a d) (b e-a f)}",1,"((4*a^3*C*d*f - b^3*(6*B*c*e - 3*A*d*e - 5*A*c*f) + a*b^2*(12*c*C*e + 3*B*d*e + B*c*f - 8*A*d*f) - a^2*b*(9*C*d*e + 7*c*C*f - 2*B*d*f))*Sqrt[c + d*x]*Sqrt[e + f*x])/(12*b^2*(b*c - a*d)*(b*e - a*f)^2*(a + b*x)^2) - ((8*a^4*C*d^2*f^2 - 2*a^3*b*d*f*(13*C*d*e + 7*c*C*f - 2*B*d*f) - b^4*(3*A*d^2*e^2 - 2*c*d*e*(3*B*e - 2*A*f) - 3*c^2*(8*C*e^2 - 6*B*e*f + 5*A*f^2)) - a*b^3*(d^2*e*(3*B*e - 10*A*f) + 3*c^2*f*(4*C*e - B*f) + 2*c*d*(30*C*e^2 - 14*B*e*f + 13*A*f^2)) - a^2*b^2*(4*d*f*(4*B*d*e + B*c*f - 2*A*d*f) - C*(33*d^2*e^2 + 44*c*d*e*f + 3*c^2*f^2)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(24*b^2*(b*c - a*d)^2*(b*e - a*f)^3*(a + b*x)) - ((A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*Sqrt[e + f*x])/(3*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^3) - ((d*e - c*f)*(b^2*(A*d^2*e^2 - 2*c*d*e*(B*e - A*f) + c^2*(8*C*e^2 - 6*B*e*f + 5*A*f^2)) + a*b*(d^2*e*(B*e - 4*A*f) - c^2*f*(4*C*e - B*f) - 2*c*d*(6*C*e^2 - 7*B*e*f + 6*A*f^2)) - a^2*(2*d*f*(3*B*d*e + B*c*f - 4*A*d*f) - C*(5*d^2*e^2 + 2*c*d*e*f + c^2*f^2)))*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(8*(b*c - a*d)^(5/2)*(b*e - a*f)^(7/2))","A",6,6,36,0.1667,1,"{1613, 149, 151, 12, 93, 208}"
54,1,715,0,1.3355201,"\int \frac{(a+b x)^2 \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[((a + b*x)^2*(A + B*x + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-8 a^2 b d^2 f^2 (16 B d f-11 C (c f+d e))+32 a^3 C d^3 f^3-16 a b^2 d f \left(6 d f (4 A d f-3 B (c f+d e))+C \left(15 c^2 f^2+14 c d e f+15 d^2 e^2\right)\right)+2 b d f x (6 b d f (a c C f+a C d e-8 A b d f+6 b c C e)-(4 a d f-5 b (c f+d e)) (-2 a C d f+8 b B d f-7 b C (c f+d e)))+b^3 \left(8 d f \left(18 A d f (c f+d e)-B \left(15 c^2 f^2+14 c d e f+15 d^2 e^2\right)\right)+5 C \left(19 c^2 d e f^2+21 c^3 f^3+19 c d^2 e^2 f+21 d^3 e^3\right)\right)\right)}{192 b d^4 f^4}+\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(16 a^2 d^2 f^2 \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)-16 a b d f \left(2 d f \left(4 A d f (c f+d e)-B \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)+C \left(3 c^2 d e f^2+5 c^3 f^3+3 c d^2 e^2 f+5 d^3 e^3\right)\right)+b^2 \left(8 d f \left(2 A d f \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)-B \left(3 c^2 d e f^2+5 c^3 f^3+3 c d^2 e^2 f+5 d^3 e^3\right)\right)+C \left(18 c^2 d^2 e^2 f^2+20 c^3 d e f^3+35 c^4 f^4+20 c d^3 e^3 f+35 d^4 e^4\right)\right)\right)}{64 d^{9/2} f^{9/2}}+\frac{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} (-2 a C d f+8 b B d f-7 b C (c f+d e))}{24 b d^2 f^2}+\frac{C (a+b x)^3 \sqrt{c+d x} \sqrt{e+f x}}{4 b d f}","-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(-8 a^2 b d^2 f^2 (16 B d f-11 C (c f+d e))+32 a^3 C d^3 f^3-16 a b^2 d f \left(6 d f (4 A d f-3 B (c f+d e))+C \left(15 c^2 f^2+14 c d e f+15 d^2 e^2\right)\right)+2 b d f x (6 b d f (a c C f+a C d e-8 A b d f+6 b c C e)+(4 a d f-5 b (c f+d e)) (2 a C d f-b (8 B d f-7 C (c f+d e))))+b^3 \left(8 d f \left(18 A d f (c f+d e)-B \left(15 c^2 f^2+14 c d e f+15 d^2 e^2\right)\right)+5 C \left(19 c^2 d e f^2+21 c^3 f^3+19 c d^2 e^2 f+21 d^3 e^3\right)\right)\right)}{192 b d^4 f^4}+\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(16 a^2 d^2 f^2 \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)-16 a b d f \left(2 d f \left(4 A d f (c f+d e)-B \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)+C \left(3 c^2 d e f^2+5 c^3 f^3+3 c d^2 e^2 f+5 d^3 e^3\right)\right)+b^2 \left(8 d f \left(2 A d f \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)-B \left(3 c^2 d e f^2+5 c^3 f^3+3 c d^2 e^2 f+5 d^3 e^3\right)\right)+C \left(18 c^2 d^2 e^2 f^2+20 c^3 d e f^3+35 c^4 f^4+20 c d^3 e^3 f+35 d^4 e^4\right)\right)\right)}{64 d^{9/2} f^{9/2}}-\frac{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} (2 a C d f-b (8 B d f-7 C (c f+d e)))}{24 b d^2 f^2}+\frac{C (a+b x)^3 \sqrt{c+d x} \sqrt{e+f x}}{4 b d f}",1,"((8*b*B*d*f - 2*a*C*d*f - 7*b*C*(d*e + c*f))*(a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x])/(24*b*d^2*f^2) + (C*(a + b*x)^3*Sqrt[c + d*x]*Sqrt[e + f*x])/(4*b*d*f) - (Sqrt[c + d*x]*Sqrt[e + f*x]*(32*a^3*C*d^3*f^3 - 8*a^2*b*d^2*f^2*(16*B*d*f - 11*C*(d*e + c*f)) - 16*a*b^2*d*f*(C*(15*d^2*e^2 + 14*c*d*e*f + 15*c^2*f^2) + 6*d*f*(4*A*d*f - 3*B*(d*e + c*f))) + b^3*(5*C*(21*d^3*e^3 + 19*c*d^2*e^2*f + 19*c^2*d*e*f^2 + 21*c^3*f^3) + 8*d*f*(18*A*d*f*(d*e + c*f) - B*(15*d^2*e^2 + 14*c*d*e*f + 15*c^2*f^2))) + 2*b*d*f*(6*b*d*f*(6*b*c*C*e + a*C*d*e + a*c*C*f - 8*A*b*d*f) - (4*a*d*f - 5*b*(d*e + c*f))*(8*b*B*d*f - 2*a*C*d*f - 7*b*C*(d*e + c*f)))*x))/(192*b*d^4*f^4) + ((16*a^2*d^2*f^2*(C*(3*d^2*e^2 + 2*c*d*e*f + 3*c^2*f^2) + 4*d*f*(2*A*d*f - B*(d*e + c*f))) - 16*a*b*d*f*(C*(5*d^3*e^3 + 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 + 5*c^3*f^3) + 2*d*f*(4*A*d*f*(d*e + c*f) - B*(3*d^2*e^2 + 2*c*d*e*f + 3*c^2*f^2))) + b^2*(C*(35*d^4*e^4 + 20*c*d^3*e^3*f + 18*c^2*d^2*e^2*f^2 + 20*c^3*d*e*f^3 + 35*c^4*f^4) + 8*d*f*(2*A*d*f*(3*d^2*e^2 + 2*c*d*e*f + 3*c^2*f^2) - B*(5*d^3*e^3 + 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 + 5*c^3*f^3))))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(64*d^(9/2)*f^(9/2))","A",6,6,36,0.1667,1,"{1615, 153, 147, 63, 217, 206}"
55,1,369,0,0.5094004,"\int \frac{(a+b x) \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[((a + b*x)*(A + B*x + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(8 a^2 C d^2 f^2-2 b d f x (-2 a C d f+6 b B d f-5 b C (c f+d e))-6 a b d f (4 B d f-3 C (c f+d e))+b^2 \left(-\left(6 d f (4 A d f-3 B (c f+d e))+C \left(15 c^2 f^2+14 c d e f+15 d^2 e^2\right)\right)\right)\right)}{24 b d^3 f^3}+\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(2 a d f \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)-b \left(2 d f \left(4 A d f (c f+d e)-B \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)+C \left(3 c^2 d e f^2+5 c^3 f^3+3 c d^2 e^2 f+5 d^3 e^3\right)\right)\right)}{8 d^{7/2} f^{7/2}}+\frac{C (a+b x)^2 \sqrt{c+d x} \sqrt{e+f x}}{3 b d f}","-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(8 a^2 C d^2 f^2+2 b d f x (2 a C d f-b (6 B d f-5 C (c f+d e)))-6 a b d f (4 B d f-3 C (c f+d e))+b^2 \left(-\left(6 d f (4 A d f-3 B (c f+d e))+C \left(15 c^2 f^2+14 c d e f+15 d^2 e^2\right)\right)\right)\right)}{24 b d^3 f^3}+\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(2 a d f \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)-b \left(2 d f \left(4 A d f (c f+d e)-B \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)+C \left(3 c^2 d e f^2+5 c^3 f^3+3 c d^2 e^2 f+5 d^3 e^3\right)\right)\right)}{8 d^{7/2} f^{7/2}}+\frac{C (a+b x)^2 \sqrt{c+d x} \sqrt{e+f x}}{3 b d f}",1,"(C*(a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x])/(3*b*d*f) - (Sqrt[c + d*x]*Sqrt[e + f*x]*(8*a^2*C*d^2*f^2 - 6*a*b*d*f*(4*B*d*f - 3*C*(d*e + c*f)) - b^2*(C*(15*d^2*e^2 + 14*c*d*e*f + 15*c^2*f^2) + 6*d*f*(4*A*d*f - 3*B*(d*e + c*f))) - 2*b*d*f*(6*b*B*d*f - 2*a*C*d*f - 5*b*C*(d*e + c*f))*x))/(24*b*d^3*f^3) + ((2*a*d*f*(C*(3*d^2*e^2 + 2*c*d*e*f + 3*c^2*f^2) + 4*d*f*(2*A*d*f - B*(d*e + c*f))) - b*(C*(5*d^3*e^3 + 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 + 5*c^3*f^3) + 2*d*f*(4*A*d*f*(d*e + c*f) - B*(3*d^2*e^2 + 2*c*d*e*f + 3*c^2*f^2))))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(8*d^(7/2)*f^(7/2))","A",5,5,34,0.1471,1,"{1615, 147, 63, 217, 206}"
56,1,164,0,0.149335,"\int \frac{A+B x+C x^2}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)}{4 d^{5/2} f^{5/2}}-\frac{\sqrt{c+d x} \sqrt{e+f x} (-4 B d f+5 c C f+3 C d e)}{4 d^2 f^2}+\frac{C (c+d x)^{3/2} \sqrt{e+f x}}{2 d^2 f}","\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)}{4 d^{5/2} f^{5/2}}-\frac{\sqrt{c+d x} \sqrt{e+f x} (-4 B d f+5 c C f+3 C d e)}{4 d^2 f^2}+\frac{C (c+d x)^{3/2} \sqrt{e+f x}}{2 d^2 f}",1,"-((3*C*d*e + 5*c*C*f - 4*B*d*f)*Sqrt[c + d*x]*Sqrt[e + f*x])/(4*d^2*f^2) + (C*(c + d*x)^(3/2)*Sqrt[e + f*x])/(2*d^2*f) + ((C*(3*d^2*e^2 + 2*c*d*e*f + 3*c^2*f^2) + 4*d*f*(2*A*d*f - B*(d*e + c*f)))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(4*d^(5/2)*f^(5/2))","A",5,5,29,0.1724,1,"{951, 80, 63, 217, 206}"
57,1,188,0,0.3409166,"\int \frac{A+B x+C x^2}{(a+b x) \sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(A + B*x + C*x^2)/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right)}{b^2 \sqrt{b c-a d} \sqrt{b e-a f}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (2 a C d f+b (-2 B d f+c C f+C d e))}{b^2 d^{3/2} f^{3/2}}+\frac{C \sqrt{c+d x} \sqrt{e+f x}}{b d f}","-\frac{2 \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right)}{b^2 \sqrt{b c-a d} \sqrt{b e-a f}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (2 a C d f+b (-2 B d f+c C f+C d e))}{b^2 d^{3/2} f^{3/2}}+\frac{C \sqrt{c+d x} \sqrt{e+f x}}{b d f}",1,"(C*Sqrt[c + d*x]*Sqrt[e + f*x])/(b*d*f) - ((2*a*C*d*f + b*(C*d*e + c*C*f - 2*B*d*f))*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(b^2*d^(3/2)*f^(3/2)) - (2*(A*b^2 - a*(b*B - a*C))*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(b^2*Sqrt[b*c - a*d]*Sqrt[b*e - a*f])","A",7,7,36,0.1944,1,"{1615, 157, 63, 217, 206, 93, 208}"
58,1,254,0,0.6384894,"\int \frac{A+B x+C x^2}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(A + B*x + C*x^2)/((a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(-3 a^2 b C (c f+d e)+2 a^3 C d f+a b^2 (-2 A d f+B c f+B d e+4 c C e)-b^3 (-A c f-A d e+2 B c e)\right)}{b^2 (b c-a d)^{3/2} (b e-a f)^{3/2}}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{b (a+b x) (b c-a d) (b e-a f)}+\frac{2 C \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right)}{b^2 \sqrt{d} \sqrt{f}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(-3 a^2 b C (c f+d e)+2 a^3 C d f+a b^2 (-2 A d f+B c f+B d e+4 c C e)-b^3 (-A c f-A d e+2 B c e)\right)}{b^2 (b c-a d)^{3/2} (b e-a f)^{3/2}}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{b (a+b x) (b c-a d) (b e-a f)}+\frac{2 C \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right)}{b^2 \sqrt{d} \sqrt{f}}",1,"-(((A*b^2 - a*(b*B - a*C))*Sqrt[c + d*x]*Sqrt[e + f*x])/(b*(b*c - a*d)*(b*e - a*f)*(a + b*x))) + (2*C*ArcTanh[(Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[e + f*x])])/(b^2*Sqrt[d]*Sqrt[f]) + ((2*a^3*C*d*f - 3*a^2*b*C*(d*e + c*f) - b^3*(2*B*c*e - A*d*e - A*c*f) + a*b^2*(4*c*C*e + B*d*e + B*c*f - 2*A*d*f))*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(b^2*(b*c - a*d)^(3/2)*(b*e - a*f)^(3/2))","A",7,7,36,0.1944,1,"{1613, 157, 63, 217, 206, 93, 208}"
59,1,424,0,0.9673716,"\int \frac{A+B x+C x^2}{(a+b x)^3 \sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(A + B*x + C*x^2)/((a + b*x)^3*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(a^2 \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)+a b \left(-2 c d \left(4 A f^2-7 B e f+4 C e^2\right)+d^2 e (B e-8 A f)+c^2 (-f) (8 C e-B f)\right)+b^2 \left(c^2 \left(3 A f^2-4 B e f+8 C e^2\right)-2 c d e (2 B e-A f)+3 A d^2 e^2\right)\right)}{4 (b c-a d)^{5/2} (b e-a f)^{5/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(a^2 b (2 B d f-5 C (c f+d e))+2 a^3 C d f+a b^2 (-6 A d f+B c f+B d e+8 c C e)-b^3 (4 B c e-3 A (c f+d e))\right)}{4 b (a+b x) (b c-a d)^2 (b e-a f)^2}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{2 b (a+b x)^2 (b c-a d) (b e-a f)}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(a^2 \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)+a b \left(-2 c d \left(4 A f^2-7 B e f+4 C e^2\right)+d^2 e (B e-8 A f)+c^2 (-f) (8 C e-B f)\right)+b^2 \left(c^2 \left(3 A f^2-4 B e f+8 C e^2\right)-2 c d e (2 B e-A f)+3 A d^2 e^2\right)\right)}{4 (b c-a d)^{5/2} (b e-a f)^{5/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(a^2 b (2 B d f-5 C (c f+d e))+2 a^3 C d f+a b^2 (-6 A d f+B c f+B d e+8 c C e)-b^3 (4 B c e-3 A (c f+d e))\right)}{4 b (a+b x) (b c-a d)^2 (b e-a f)^2}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{2 b (a+b x)^2 (b c-a d) (b e-a f)}",1,"-((A*b^2 - a*(b*B - a*C))*Sqrt[c + d*x]*Sqrt[e + f*x])/(2*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^2) + ((2*a^3*C*d*f + a*b^2*(8*c*C*e + B*d*e + B*c*f - 6*A*d*f) - b^3*(4*B*c*e - 3*A*(d*e + c*f)) + a^2*b*(2*B*d*f - 5*C*(d*e + c*f)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(4*b*(b*c - a*d)^2*(b*e - a*f)^2*(a + b*x)) - ((b^2*(3*A*d^2*e^2 - 2*c*d*e*(2*B*e - A*f) + c^2*(8*C*e^2 - 4*B*e*f + 3*A*f^2)) + a*b*(d^2*e*(B*e - 8*A*f) - c^2*f*(8*C*e - B*f) - 2*c*d*(4*C*e^2 - 7*B*e*f + 4*A*f^2)) + a^2*(C*(3*d^2*e^2 + 2*c*d*e*f + 3*c^2*f^2) + 4*d*f*(2*A*d*f - B*(d*e + c*f))))*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(4*(b*c - a*d)^(5/2)*(b*e - a*f)^(5/2))","A",5,5,36,0.1389,1,"{1613, 151, 12, 93, 208}"
60,1,826,0,2.4333434,"\int \frac{A+B x+C x^2}{(a+b x)^4 \sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(A + B*x + C*x^2)/((a + b*x)^4*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{3 b (b c-a d) (b e-a f) (a+b x)^3}+\frac{\left(-2 d f \left(C \left(3 d^2 e^2+2 c d f e+3 c^2 f^2\right)+4 d f (2 A d f-B (d e+c f))\right) a^3+b \left(C \left(d^3 e^3+23 c d^2 f e^2+23 c^2 d f^2 e+c^3 f^3\right)+4 d f \left(6 A d f (d e+c f)-B \left(d^2 e^2+10 c d f e+c^2 f^2\right)\right)\right) a^2+b^2 \left(-f^2 (4 C e-B f) c^3-d f \left(40 C e^2-23 B f e+18 A f^2\right) c^2-d^2 e \left(4 C e^2-23 B f e+12 A f^2\right) c+d^3 e^2 (B e-18 A f)\right) a+b^3 \left(f \left(8 C e^2-6 B f e+5 A f^2\right) c^3+d e \left(8 C e^2-4 B f e+3 A f^2\right) c^2-3 d^2 e^2 (2 B e-A f) c+5 A d^3 e^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b e-a f} \sqrt{c+d x}}{\sqrt{b c-a d} \sqrt{e+f x}}\right)}{8 (b c-a d)^{7/2} (b e-a f)^{7/2}}+\frac{\left(4 C d^2 f^2 a^4+8 b d f (B d f-2 C (d e+c f)) a^3-b^2 \left(C \left(3 d^2 e^2-34 c d f e+3 c^2 f^2\right)+2 d f (22 A d f-5 B (d e+c f))\right) a^2-b^3 \left(-3 f (4 C e-B f) c^2-2 d \left(6 C e^2-29 B f e+22 A f^2\right) c+d^2 e (3 B e-44 A f)\right) a-b^4 \left(3 \left(8 C e^2-6 B f e+5 A f^2\right) c^2-2 d e (9 B e-7 A f) c+15 A d^2 e^2\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{24 b (b c-a d)^3 (b e-a f)^3 (a+b x)}+\frac{\left(2 C d f a^3+b (4 B d f-7 C (d e+c f)) a^2+b^2 (12 c C e+B d e+B c f-10 A d f) a-b^3 (6 B c e-5 A (d e+c f))\right) \sqrt{c+d x} \sqrt{e+f x}}{12 b (b c-a d)^2 (b e-a f)^2 (a+b x)^2}","-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{3 b (b c-a d) (b e-a f) (a+b x)^3}+\frac{\left(-2 d f \left(C \left(3 d^2 e^2+2 c d f e+3 c^2 f^2\right)+4 d f (2 A d f-B (d e+c f))\right) a^3+b \left(C \left(d^3 e^3+23 c d^2 f e^2+23 c^2 d f^2 e+c^3 f^3\right)+4 d f \left(6 A d f (d e+c f)-B \left(d^2 e^2+10 c d f e+c^2 f^2\right)\right)\right) a^2+b^2 \left(-f^2 (4 C e-B f) c^3-d f \left(40 C e^2-23 B f e+18 A f^2\right) c^2-d^2 e \left(4 C e^2-23 B f e+12 A f^2\right) c+d^3 e^2 (B e-18 A f)\right) a+b^3 \left(f \left(8 C e^2-6 B f e+5 A f^2\right) c^3+d e \left(8 C e^2-4 B f e+3 A f^2\right) c^2-3 d^2 e^2 (2 B e-A f) c+5 A d^3 e^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b e-a f} \sqrt{c+d x}}{\sqrt{b c-a d} \sqrt{e+f x}}\right)}{8 (b c-a d)^{7/2} (b e-a f)^{7/2}}+\frac{\left(4 C d^2 f^2 a^4+8 b d f (B d f-2 C (d e+c f)) a^3-b^2 \left(C \left(3 d^2 e^2-34 c d f e+3 c^2 f^2\right)+2 d f (22 A d f-5 B (d e+c f))\right) a^2-b^3 \left(-3 f (4 C e-B f) c^2-2 d \left(6 C e^2-29 B f e+22 A f^2\right) c+d^2 e (3 B e-44 A f)\right) a-b^4 \left(3 \left(8 C e^2-6 B f e+5 A f^2\right) c^2-2 d e (9 B e-7 A f) c+15 A d^2 e^2\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{24 b (b c-a d)^3 (b e-a f)^3 (a+b x)}+\frac{\left(2 C d f a^3+b (4 B d f-7 C (d e+c f)) a^2+b^2 (12 c C e+B d e+B c f-10 A d f) a-b^3 (6 B c e-5 A (d e+c f))\right) \sqrt{c+d x} \sqrt{e+f x}}{12 b (b c-a d)^2 (b e-a f)^2 (a+b x)^2}",1,"-((A*b^2 - a*(b*B - a*C))*Sqrt[c + d*x]*Sqrt[e + f*x])/(3*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^3) + ((2*a^3*C*d*f + a*b^2*(12*c*C*e + B*d*e + B*c*f - 10*A*d*f) - b^3*(6*B*c*e - 5*A*(d*e + c*f)) + a^2*b*(4*B*d*f - 7*C*(d*e + c*f)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(12*b*(b*c - a*d)^2*(b*e - a*f)^2*(a + b*x)^2) + ((4*a^4*C*d^2*f^2 + 8*a^3*b*d*f*(B*d*f - 2*C*(d*e + c*f)) - b^4*(15*A*d^2*e^2 - 2*c*d*e*(9*B*e - 7*A*f) + 3*c^2*(8*C*e^2 - 6*B*e*f + 5*A*f^2)) - a*b^3*(d^2*e*(3*B*e - 44*A*f) - 3*c^2*f*(4*C*e - B*f) - 2*c*d*(6*C*e^2 - 29*B*e*f + 22*A*f^2)) - a^2*b^2*(C*(3*d^2*e^2 - 34*c*d*e*f + 3*c^2*f^2) + 2*d*f*(22*A*d*f - 5*B*(d*e + c*f))))*Sqrt[c + d*x]*Sqrt[e + f*x])/(24*b*(b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)) + ((b^3*(5*A*d^3*e^3 - 3*c*d^2*e^2*(2*B*e - A*f) + c^2*d*e*(8*C*e^2 - 4*B*e*f + 3*A*f^2) + c^3*f*(8*C*e^2 - 6*B*e*f + 5*A*f^2)) + a*b^2*(d^3*e^2*(B*e - 18*A*f) - c^3*f^2*(4*C*e - B*f) - c*d^2*e*(4*C*e^2 - 23*B*e*f + 12*A*f^2) - c^2*d*f*(40*C*e^2 - 23*B*e*f + 18*A*f^2)) - 2*a^3*d*f*(C*(3*d^2*e^2 + 2*c*d*e*f + 3*c^2*f^2) + 4*d*f*(2*A*d*f - B*(d*e + c*f))) + a^2*b*(C*(d^3*e^3 + 23*c*d^2*e^2*f + 23*c^2*d*e*f^2 + c^3*f^3) + 4*d*f*(6*A*d*f*(d*e + c*f) - B*(d^2*e^2 + 10*c*d*e*f + c^2*f^2))))*ArcTanh[(Sqrt[b*e - a*f]*Sqrt[c + d*x])/(Sqrt[b*c - a*d]*Sqrt[e + f*x])])/(8*(b*c - a*d)^(7/2)*(b*e - a*f)^(7/2))","A",6,5,36,0.1389,1,"{1613, 151, 12, 93, 208}"
61,1,1154,0,4.1658964,"\int \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right) \, dx","Int[Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2),x]","\frac{2 C (a+b x)^{3/2} (c+d x)^{3/2} (e+f x)^{3/2}}{9 b d f}+\frac{2 (3 b B d f-2 a C d f-2 b C (d e+c f)) \sqrt{a+b x} (c+d x)^{3/2} (e+f x)^{3/2}}{21 b d^2 f^2}-\frac{2 (7 b d f (b c C e+a C d e+a c C f-3 A b d f)-(a d f-4 b (d e+c f)) (3 b B d f-2 a C d f-2 b C (d e+c f))) \sqrt{a+b x} \sqrt{c+d x} (e+f x)^{3/2}}{105 b^2 d^2 f^3}-\frac{2 \sqrt{a d-b c} \left(\left(2 C \left(8 d^4 e^4-4 c d^3 f e^3-3 c^2 d^2 f^2 e^2-4 c^3 d f^3 e+8 c^4 f^4\right)+3 d f \left(14 A d f \left(d^2 e^2-c d f e+c^2 f^2\right)-B \left(8 d^3 e^3-5 c d^2 f e^2-5 c^2 d f^2 e+8 c^3 f^3\right)\right)\right) b^4-a d f \left(C \left(8 d^3 e^3-6 c d^2 f e^2-6 c^2 d f^2 e+8 c^3 f^3\right)+3 d f \left(14 A d f (d e+c f)-B \left(5 d^2 e^2-6 c d f e+5 c^2 f^2\right)\right)\right) b^3+3 a^2 d^2 f^2 \left(d f (5 B d e+5 B c f+14 A d f)-2 C \left(d^2 e^2-c d f e+c^2 f^2\right)\right) b^2-8 a^3 d^3 f^3 (C d e+c C f+3 B d f) b+16 a^4 C d^4 f^4\right) \sqrt{\frac{b (c+d x)}{b c-a d}} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right) \sqrt{e+f x}}{315 b^4 d^{7/2} f^4 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \left(\frac{8 C d f a^3}{b}+3 (C d e-c C f-4 B d f) a^2-3 b \left(\frac{C f c^2}{d}-2 B f c+B d e-7 A d f\right) a+b^2 \left(\frac{8 C f c^3}{d^2}+\frac{3 C e c^2}{d}+21 A f c-42 A d e-B \left(\frac{12 f c^2}{d}+3 e c-\frac{24 d e^2}{f}\right)-\frac{16 C d e^3}{f^2}\right)\right) \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}}{315 b^2 d f}-\frac{2 \sqrt{a d-b c} (b e-a f) (d e-c f) \left(-\left(C \left(16 d^3 e^3-3 c^2 d f^2 e-8 c^3 f^3\right)+3 d f \left(7 A d f (2 d e-c f)-B \left(8 d^2 e^2-c d f e-4 c^2 f^2\right)\right)\right) b^3-3 a d f^2 \left(\left(c^2 C-7 A d^2\right) f+B d (d e-2 c f)\right) b^2+3 a^2 d^2 f^2 (C d e-c C f-4 B d f) b+8 a^3 C d^3 f^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{315 b^4 d^{7/2} f^4 \sqrt{c+d x} \sqrt{e+f x}}","\frac{2 C (a+b x)^{3/2} (c+d x)^{3/2} (e+f x)^{3/2}}{9 b d f}-\frac{2 (2 a C d f-b (3 B d f-2 C (d e+c f))) \sqrt{a+b x} (c+d x)^{3/2} (e+f x)^{3/2}}{21 b d^2 f^2}-\frac{2 (7 b d f (b c C e+a C d e+a c C f-3 A b d f)+(a d f-4 b (d e+c f)) (2 a C d f-b (3 B d f-2 C (d e+c f)))) \sqrt{a+b x} \sqrt{c+d x} (e+f x)^{3/2}}{105 b^2 d^2 f^3}-\frac{2 \sqrt{a d-b c} \left(\left(2 C \left(8 d^4 e^4-4 c d^3 f e^3-3 c^2 d^2 f^2 e^2-4 c^3 d f^3 e+8 c^4 f^4\right)+3 d f \left(14 A d f \left(d^2 e^2-c d f e+c^2 f^2\right)-B \left(8 d^3 e^3-5 c d^2 f e^2-5 c^2 d f^2 e+8 c^3 f^3\right)\right)\right) b^4-a d f \left(C \left(8 d^3 e^3-6 c d^2 f e^2-6 c^2 d f^2 e+8 c^3 f^3\right)+3 d f \left(14 A d f (d e+c f)-B \left(5 d^2 e^2-6 c d f e+5 c^2 f^2\right)\right)\right) b^3+3 a^2 d^2 f^2 \left(d f (5 B d e+5 B c f+14 A d f)-2 C \left(d^2 e^2-c d f e+c^2 f^2\right)\right) b^2-8 a^3 d^3 f^3 (C d e+c C f+3 B d f) b+16 a^4 C d^4 f^4\right) \sqrt{\frac{b (c+d x)}{b c-a d}} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right) \sqrt{e+f x}}{315 b^4 d^{7/2} f^4 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \left(-\left(C \left(16 d^3 e^3-3 c^2 d f^2 e-8 c^3 f^3\right)+3 d f \left(7 A d f (2 d e-c f)-B \left(8 d^2 e^2-c d f e-4 c^2 f^2\right)\right)\right) b^3-3 a d f^2 \left(\left(c^2 C-7 A d^2\right) f+B d (d e-2 c f)\right) b^2+3 a^2 d^2 f^2 (C d e-c C f-4 B d f) b+8 a^3 C d^3 f^3\right) \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}}{315 b^3 d^3 f^3}-\frac{2 \sqrt{a d-b c} (b e-a f) (d e-c f) \left(-\left(C \left(16 d^3 e^3-3 c^2 d f^2 e-8 c^3 f^3\right)+3 d f \left(7 A d f (2 d e-c f)-B \left(8 d^2 e^2-c d f e-4 c^2 f^2\right)\right)\right) b^3-3 a d f^2 \left(\left(c^2 C-7 A d^2\right) f+B d (d e-2 c f)\right) b^2+3 a^2 d^2 f^2 (C d e-c C f-4 B d f) b+8 a^3 C d^3 f^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{315 b^4 d^{7/2} f^4 \sqrt{c+d x} \sqrt{e+f x}}",1,"(2*((8*a^3*C*d*f)/b - 3*a*b*(B*d*e - 2*B*c*f + (c^2*C*f)/d - 7*A*d*f) + 3*a^2*(C*d*e - c*C*f - 4*B*d*f) + b^2*((3*c^2*C*e)/d - 42*A*d*e - (16*C*d*e^3)/f^2 + 21*A*c*f + (8*c^3*C*f)/d^2 - B*(3*c*e - (24*d*e^2)/f + (12*c^2*f)/d)))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(315*b^2*d*f) - (2*(7*b*d*f*(b*c*C*e + a*C*d*e + a*c*C*f - 3*A*b*d*f) - (a*d*f - 4*b*(d*e + c*f))*(3*b*B*d*f - 2*a*C*d*f - 2*b*C*(d*e + c*f)))*Sqrt[a + b*x]*Sqrt[c + d*x]*(e + f*x)^(3/2))/(105*b^2*d^2*f^3) + (2*(3*b*B*d*f - 2*a*C*d*f - 2*b*C*(d*e + c*f))*Sqrt[a + b*x]*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(21*b*d^2*f^2) + (2*C*(a + b*x)^(3/2)*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(9*b*d*f) - (2*Sqrt[-(b*c) + a*d]*(16*a^4*C*d^4*f^4 - 8*a^3*b*d^3*f^3*(C*d*e + c*C*f + 3*B*d*f) + 3*a^2*b^2*d^2*f^2*(d*f*(5*B*d*e + 5*B*c*f + 14*A*d*f) - 2*C*(d^2*e^2 - c*d*e*f + c^2*f^2)) - a*b^3*d*f*(C*(8*d^3*e^3 - 6*c*d^2*e^2*f - 6*c^2*d*e*f^2 + 8*c^3*f^3) + 3*d*f*(14*A*d*f*(d*e + c*f) - B*(5*d^2*e^2 - 6*c*d*e*f + 5*c^2*f^2))) + b^4*(2*C*(8*d^4*e^4 - 4*c*d^3*e^3*f - 3*c^2*d^2*e^2*f^2 - 4*c^3*d*e*f^3 + 8*c^4*f^4) + 3*d*f*(14*A*d*f*(d^2*e^2 - c*d*e*f + c^2*f^2) - B*(8*d^3*e^3 - 5*c*d^2*e^2*f - 5*c^2*d*e*f^2 + 8*c^3*f^3))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(315*b^4*d^(7/2)*f^4*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) - (2*Sqrt[-(b*c) + a*d]*(b*e - a*f)*(d*e - c*f)*(8*a^3*C*d^3*f^3 + 3*a^2*b*d^2*f^2*(C*d*e - c*C*f - 4*B*d*f) - 3*a*b^2*d*f^2*((c^2*C - 7*A*d^2)*f + B*d*(d*e - 2*c*f)) - b^3*(C*(16*d^3*e^3 - 3*c^2*d*e*f^2 - 8*c^3*f^3) + 3*d*f*(7*A*d*f*(2*d*e - c*f) - B*(8*d^2*e^2 - c*d*e*f - 4*c^2*f^2))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(315*b^4*d^(7/2)*f^4*Sqrt[c + d*x]*Sqrt[e + f*x])","A",10,7,38,0.1842,1,"{1615, 154, 158, 114, 113, 121, 120}"
62,1,769,0,2.2300838,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{\sqrt{a+b x}} \, dx","Int[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/Sqrt[a + b*x],x]","-\frac{2 \sqrt{a d-b c} (b e-a f) (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(24 a^2 C d^2 f^2+a b d f (-28 B d f-5 c C f+13 C d e)+b^2 \left(-\left(7 d f (-5 A d f-B c f+2 B d e)-C \left(-4 c^2 f^2-c d e f+8 d^2 e^2\right)\right)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^4 d^{5/2} f^3 \sqrt{c+d x} \sqrt{e+f x}}-\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(3 b d f (5 b c f (3 a C (c f+d e)+b (c C e-7 A d f))+(3 a c f+a d e+b c e) (-6 a C d f+7 b B d f-4 b C (c f+d e)))+2 \left(\frac{b d e}{2}-f (a d+b c)\right) (5 b d f (3 a C (c f+d e)+b (c C e-7 A d f))+(4 a d f-b c f+2 b d e) (-6 a C d f+7 b B d f-4 b C (c f+d e)))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^4 d^{5/2} f^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(5 (3 a C (c f+d e)+b (c C e-7 A d f))+\frac{(4 a d f-b c f+2 b d e) (-6 a C d f+7 b B d f-4 b C (c f+d e))}{b d f}\right)}{105 b^2 d f}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} (e+f x)^{3/2} (-6 a C d f+7 b B d f-4 b C (c f+d e))}{35 b^2 d f^2}+\frac{2 C \sqrt{a+b x} (c+d x)^{3/2} (e+f x)^{3/2}}{7 b d f}","-\frac{2 \sqrt{a d-b c} (b e-a f) (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(24 a^2 C d^2 f^2+a b d f (-28 B d f-5 c C f+13 C d e)+b^2 \left(-\left(7 d f (-5 A d f-B c f+2 B d e)-C \left(-4 c^2 f^2-c d e f+8 d^2 e^2\right)\right)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^4 d^{5/2} f^3 \sqrt{c+d x} \sqrt{e+f x}}-\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} (5 b d f (3 a C (c f+d e)+b (c C e-7 A d f))-(4 a d f-b c f+2 b d e) (6 a C d f-b (7 B d f-4 C (c f+d e))))}{105 b^3 d^2 f^2}-\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(3 b d f (5 b c f (3 a C (c f+d e)+b (c C e-7 A d f))-(3 a c f+a d e+b c e) (6 a C d f-b (7 B d f-4 C (c f+d e))))+2 \left(\frac{b d e}{2}-f (a d+b c)\right) (5 b d f (3 a C (c f+d e)+b (c C e-7 A d f))-(4 a d f-b c f+2 b d e) (6 a C d f-b (7 B d f-4 C (c f+d e))))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^4 d^{5/2} f^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a+b x} \sqrt{c+d x} (e+f x)^{3/2} (6 a C d f-b (7 B d f-4 C (c f+d e)))}{35 b^2 d f^2}+\frac{2 C \sqrt{a+b x} (c+d x)^{3/2} (e+f x)^{3/2}}{7 b d f}",1,"(-2*(((2*b*d*e - b*c*f + 4*a*d*f)*(7*b*B*d*f - 6*a*C*d*f - 4*b*C*(d*e + c*f)))/(b*d*f) + 5*(3*a*C*(d*e + c*f) + b*(c*C*e - 7*A*d*f)))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(105*b^2*d*f) + (2*(7*b*B*d*f - 6*a*C*d*f - 4*b*C*(d*e + c*f))*Sqrt[a + b*x]*Sqrt[c + d*x]*(e + f*x)^(3/2))/(35*b^2*d*f^2) + (2*C*Sqrt[a + b*x]*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(7*b*d*f) - (2*Sqrt[-(b*c) + a*d]*(3*b*d*f*((b*c*e + a*d*e + 3*a*c*f)*(7*b*B*d*f - 6*a*C*d*f - 4*b*C*(d*e + c*f)) + 5*b*c*f*(3*a*C*(d*e + c*f) + b*(c*C*e - 7*A*d*f))) + 2*((b*d*e)/2 - (b*c + a*d)*f)*((2*b*d*e - b*c*f + 4*a*d*f)*(7*b*B*d*f - 6*a*C*d*f - 4*b*C*(d*e + c*f)) + 5*b*d*f*(3*a*C*(d*e + c*f) + b*(c*C*e - 7*A*d*f))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(105*b^4*d^(5/2)*f^3*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) - (2*Sqrt[-(b*c) + a*d]*(b*e - a*f)*(d*e - c*f)*(24*a^2*C*d^2*f^2 + a*b*d*f*(13*C*d*e - 5*c*C*f - 28*B*d*f) - b^2*(7*d*f*(2*B*d*e - B*c*f - 5*A*d*f) - C*(8*d^2*e^2 - c*d*e*f - 4*c^2*f^2)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(105*b^4*d^(5/2)*f^3*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,7,38,0.1842,1,"{1615, 154, 158, 114, 113, 121, 120}"
63,1,706,0,1.8446517,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{3/2}} \, dx","Int[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^(3/2),x]","\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(48 a^2 C d^2 f^2-8 a b d f (5 B d f+c C f+C d e)+b^2 \left(5 d f (6 A d f+B c f+B d e)-2 C \left(c^2 f^2-c d e f+d^2 e^2\right)\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^4 d^{3/2} f^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a d-b c} (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(24 a^2 C d f^2-a b f (20 B d f+c C f+7 C d e)+b^2 (5 d f (3 A f+B e)-C e (2 d e-c f))\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^4 d^{3/2} f^2 \sqrt{c+d x} \sqrt{e+f x}}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(24 a^2 C d f^2-a b f (20 B d f+c C f+7 C d e)+b^2 (5 d f (3 A f+B e)-C e (2 d e-c f))\right)}{15 b^3 d f (b e-a f)}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} (e+f x)^{3/2} \left(6 a^2 C d f-a b (5 B d f+c C f+C d e)+b^2 (5 A d f+c C e)\right)}{5 b^2 f (b c-a d) (b e-a f)}-\frac{2 (c+d x)^{3/2} (e+f x)^{3/2} \left(A b^2-a (b B-a C)\right)}{b \sqrt{a+b x} (b c-a d) (b e-a f)}","\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(48 a^2 C d^2 f^2-8 a b d f (5 B d f+c C f+C d e)+b^2 \left(5 d f (6 A d f+B c f+B d e)-2 C \left(c^2 f^2-c d e f+d^2 e^2\right)\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^4 d^{3/2} f^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a d-b c} (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(24 a^2 C d f^2-a b f (20 B d f+c C f+7 C d e)+b^2 (5 d f (3 A f+B e)-C e (2 d e-c f))\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^4 d^{3/2} f^2 \sqrt{c+d x} \sqrt{e+f x}}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(24 a^2 C d f^2-a b f (20 B d f+c C f+7 C d e)+b^2 (5 d f (3 A f+B e)-C e (2 d e-c f))\right)}{15 b^3 d f (b e-a f)}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} (e+f x)^{3/2} \left(6 a^2 C d f-a b (5 B d f+c C f+C d e)+b^2 (5 A d f+c C e)\right)}{5 b^2 f (b c-a d) (b e-a f)}-\frac{2 (c+d x)^{3/2} (e+f x)^{3/2} \left(A b^2-a (b B-a C)\right)}{b \sqrt{a+b x} (b c-a d) (b e-a f)}",1,"(2*(24*a^2*C*d*f^2 - a*b*f*(7*C*d*e + c*C*f + 20*B*d*f) + b^2*(5*d*f*(B*e + 3*A*f) - C*e*(2*d*e - c*f)))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(15*b^3*d*f*(b*e - a*f)) + (2*(6*a^2*C*d*f + b^2*(c*C*e + 5*A*d*f) - a*b*(C*d*e + c*C*f + 5*B*d*f))*Sqrt[a + b*x]*Sqrt[c + d*x]*(e + f*x)^(3/2))/(5*b^2*(b*c - a*d)*f*(b*e - a*f)) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(b*(b*c - a*d)*(b*e - a*f)*Sqrt[a + b*x]) + (2*Sqrt[-(b*c) + a*d]*(48*a^2*C*d^2*f^2 - 8*a*b*d*f*(C*d*e + c*C*f + 5*B*d*f) + b^2*(5*d*f*(B*d*e + B*c*f + 6*A*d*f) - 2*C*(d^2*e^2 - c*d*e*f + c^2*f^2)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^4*d^(3/2)*f^2*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) - (2*Sqrt[-(b*c) + a*d]*(d*e - c*f)*(24*a^2*C*d*f^2 - a*b*f*(7*C*d*e + c*C*f + 20*B*d*f) + b^2*(5*d*f*(B*e + 3*A*f) - C*e*(2*d*e - c*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^4*d^(3/2)*f^2*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,7,38,0.1842,1,"{1614, 154, 158, 114, 113, 121, 120}"
64,1,687,0,1.9027607,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{5/2}} \, dx","Int[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^(5/2),x]","\frac{2 \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(-8 a^2 b d f (B d f+2 C (c f+d e))+16 a^3 C d^2 f^2+a b^2 \left(d f (2 A d f+7 B c f+7 B d e)+C \left(c^2 f^2+16 c d e f+d^2 e^2\right)\right)-b^3 \left(c d \left(A f^2+6 B e f+C e^2\right)+A d^2 e f+c^2 C e f\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^4 \sqrt{d} f \sqrt{c+d x} \sqrt{a d-b c} (b e-a f) \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(8 a^2 C d f-a b (4 B d f+7 c C f+C d e)+b^2 (A d f+3 B c f+c C e)\right)}{3 b^3 (b c-a d) (b e-a f)}+\frac{2 (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(8 a^2 C d f-a b (4 B d f+7 c C f+C d e)+b^2 (A d f+3 B c f+c C e)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^4 \sqrt{d} f \sqrt{c+d x} \sqrt{e+f x} \sqrt{a d-b c}}-\frac{2 (c+d x)^{3/2} (e+f x)^{3/2} \left(A b^2-a (b B-a C)\right)}{3 b (a+b x)^{3/2} (b c-a d) (b e-a f)}-\frac{2 \sqrt{c+d x} (e+f x)^{3/2} (b B-2 a C)}{b^2 \sqrt{a+b x} (b e-a f)}","\frac{2 \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(-8 a^2 b d f (B d f+2 C (c f+d e))+16 a^3 C d^2 f^2+a b^2 \left(d f (2 A d f+7 B c f+7 B d e)+C \left(c^2 f^2+16 c d e f+d^2 e^2\right)\right)-b^3 \left(c d \left(A f^2+6 B e f+C e^2\right)+A d^2 e f+c^2 C e f\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^4 \sqrt{d} f \sqrt{c+d x} \sqrt{a d-b c} (b e-a f) \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(8 a^2 C d f-a b (4 B d f+7 c C f+C d e)+b^2 (A d f+3 B c f+c C e)\right)}{3 b^3 (b c-a d) (b e-a f)}+\frac{2 (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(8 a^2 C d f-a b (4 B d f+7 c C f+C d e)+b^2 (A d f+3 B c f+c C e)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^4 \sqrt{d} f \sqrt{c+d x} \sqrt{e+f x} \sqrt{a d-b c}}-\frac{2 (c+d x)^{3/2} (e+f x)^{3/2} \left(A b^2-a (b B-a C)\right)}{3 b (a+b x)^{3/2} (b c-a d) (b e-a f)}-\frac{2 \sqrt{c+d x} (e+f x)^{3/2} (b B-2 a C)}{b^2 \sqrt{a+b x} (b e-a f)}",1,"(2*(8*a^2*C*d*f + b^2*(c*C*e + 3*B*c*f + A*d*f) - a*b*(C*d*e + 7*c*C*f + 4*B*d*f))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(3*b^3*(b*c - a*d)*(b*e - a*f)) - (2*(b*B - 2*a*C)*Sqrt[c + d*x]*(e + f*x)^(3/2))/(b^2*(b*e - a*f)*Sqrt[a + b*x]) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(3*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^(3/2)) + (2*(16*a^3*C*d^2*f^2 - 8*a^2*b*d*f*(B*d*f + 2*C*(d*e + c*f)) - b^3*(c^2*C*e*f + A*d^2*e*f + c*d*(C*e^2 + 6*B*e*f + A*f^2)) + a*b^2*(d*f*(7*B*d*e + 7*B*c*f + 2*A*d*f) + C*(d^2*e^2 + 16*c*d*e*f + c^2*f^2)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^4*Sqrt[d]*Sqrt[-(b*c) + a*d]*f*(b*e - a*f)*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) + (2*(d*e - c*f)*(8*a^2*C*d*f + b^2*(c*C*e + 3*B*c*f + A*d*f) - a*b*(C*d*e + 7*c*C*f + 4*B*d*f))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^4*Sqrt[d]*Sqrt[-(b*c) + a*d]*f*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,8,38,0.2105,1,"{1614, 150, 154, 158, 114, 113, 121, 120}"
65,1,964,0,3.1158644,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{7/2}} \, dx","Int[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^(7/2),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{2 \left(6 C d f a^3-b (B d f+8 C (d e+c f)) a^2+b^2 (10 c C e+3 B d e+3 B c f-4 A d f) a-b^3 (5 B c e-2 A (d e+c f))\right) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}+\frac{2 \sqrt{d} \left(48 C d^2 f^2 a^4-8 b d f (B d f+11 C (d e+c f)) a^3+b^2 \left(2 C \left(19 d^2 e^2+81 c d f e+19 c^2 f^2\right)-d f (2 A d f-13 B (d e+c f))\right) a^2-b^3 \left(f (70 C e+3 B f) c^2+2 d \left(35 C e^2+11 B f e-A f^2\right) c+d^2 e (3 B e-2 A f)\right) a-b^4 \left(-\left(30 C e^2+5 B f e-2 A f^2\right) c^2-d e (5 B e+2 A f) c+2 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right) \sqrt{e+f x}}{15 b^4 (a d-b c)^{3/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \left(24 C d^2 f a^3-b d (23 C d e+41 c C f+4 B d f) a^2+b^2 \left(15 C f c^2+(40 C d e+6 B d f) c+d^2 (3 B e-A f)\right) a-b^3 \left(15 C e c^2+d (5 B e+A f) c-2 A d^2 e\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{a+b x}}+\frac{2 (d e-c f) \left(24 C d^2 f a^3-b d (23 C d e+41 c C f+4 B d f) a^2+b^2 \left(15 C f c^2+(40 C d e+6 B d f) c+d^2 (3 B e-A f)\right) a-b^3 \left(15 C e c^2+d (5 B e+A f) c-2 A d^2 e\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^4 \sqrt{d} (a d-b c)^{3/2} (b e-a f) \sqrt{c+d x} \sqrt{e+f x}}","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{2 \left(6 C d f a^3-b (B d f+8 C (d e+c f)) a^2+b^2 (10 c C e+3 B d e+3 B c f-4 A d f) a-b^3 (5 B c e-2 A (d e+c f))\right) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}+\frac{2 \sqrt{d} \left(48 C d^2 f^2 a^4-8 b d f (B d f+11 C (d e+c f)) a^3+b^2 \left(2 C \left(19 d^2 e^2+81 c d f e+19 c^2 f^2\right)-d f (2 A d f-13 B (d e+c f))\right) a^2-b^3 \left(f (70 C e+3 B f) c^2+2 d \left(35 C e^2+11 B f e-A f^2\right) c+d^2 e (3 B e-2 A f)\right) a-b^4 \left(-\left(30 C e^2+5 B f e-2 A f^2\right) c^2-d e (5 B e+2 A f) c+2 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right) \sqrt{e+f x}}{15 b^4 (a d-b c)^{3/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \left(24 C d^2 f a^3-b d (23 C d e+41 c C f+4 B d f) a^2+b^2 \left(15 C f c^2+(40 C d e+6 B d f) c+d^2 (3 B e-A f)\right) a-b^3 \left(15 C e c^2+d (5 B e+A f) c-2 A d^2 e\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{a+b x}}+\frac{2 (d e-c f) \left(24 C d^2 f a^3-b d (23 C d e+41 c C f+4 B d f) a^2+b^2 \left(15 C f c^2+(40 C d e+6 B d f) c+d^2 (3 B e-A f)\right) a-b^3 \left(15 C e c^2+d (5 B e+A f) c-2 A d^2 e\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^4 \sqrt{d} (a d-b c)^{3/2} (b e-a f) \sqrt{c+d x} \sqrt{e+f x}}",1,"(2*(24*a^3*C*d^2*f - a^2*b*d*(23*C*d*e + 41*c*C*f + 4*B*d*f) - b^3*(15*c^2*C*e - 2*A*d^2*e + c*d*(5*B*e + A*f)) + a*b^2*(15*c^2*C*f + d^2*(3*B*e - A*f) + c*(40*C*d*e + 6*B*d*f)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(15*b^3*(b*c - a*d)^2*(b*e - a*f)*Sqrt[a + b*x]) + (2*(6*a^3*C*d*f + a*b^2*(10*c*C*e + 3*B*d*e + 3*B*c*f - 4*A*d*f) - b^3*(5*B*c*e - 2*A*(d*e + c*f)) - a^2*b*(B*d*f + 8*C*(d*e + c*f)))*Sqrt[c + d*x]*(e + f*x)^(3/2))/(15*b^2*(b*c - a*d)*(b*e - a*f)^2*(a + b*x)^(3/2)) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(5*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^(5/2)) + (2*Sqrt[d]*(48*a^4*C*d^2*f^2 - 8*a^3*b*d*f*(B*d*f + 11*C*(d*e + c*f)) - b^4*(2*A*d^2*e^2 - c*d*e*(5*B*e + 2*A*f) - c^2*(30*C*e^2 + 5*B*e*f - 2*A*f^2)) - a*b^3*(d^2*e*(3*B*e - 2*A*f) + c^2*f*(70*C*e + 3*B*f) + 2*c*d*(35*C*e^2 + 11*B*e*f - A*f^2)) + a^2*b^2*(2*C*(19*d^2*e^2 + 81*c*d*e*f + 19*c^2*f^2) - d*f*(2*A*d*f - 13*B*(d*e + c*f))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^4*(-(b*c) + a*d)^(3/2)*(b*e - a*f)^2*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) + (2*(d*e - c*f)*(24*a^3*C*d^2*f - a^2*b*d*(23*C*d*e + 41*c*C*f + 4*B*d*f) - b^3*(15*c^2*C*e - 2*A*d^2*e + c*d*(5*B*e + A*f)) + a*b^2*(15*c^2*C*f + d^2*(3*B*e - A*f) + c*(40*C*d*e + 6*B*d*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^4*Sqrt[d]*(-(b*c) + a*d)^(3/2)*(b*e - a*f)*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,7,38,0.1842,1,"{1614, 150, 158, 114, 113, 121, 120}"
66,1,1716,0,7.0453513,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{9/2}} \, dx","Int[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^(9/2),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d x)^{3/2} (e+f x)^{3/2}}{7 b (b c-a d) (b e-a f) (a+b x)^{7/2}}+\frac{2 \left(6 C d f a^3+b (B d f-10 C (d e+c f)) a^2+b^2 (14 c C e+3 B d e+3 B c f-8 A d f) a-b^3 (7 B c e-4 A (d e+c f))\right) \sqrt{c+d x} (e+f x)^{3/2}}{35 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{5/2}}+\frac{2 \sqrt{d} \left(48 C d^3 f^3 a^5+8 b d^2 f^2 (B d f-16 C (d e+c f)) a^4+b^2 d f \left(C \left(103 d^2 e^2+344 c d f e+103 c^2 f^2\right)+d f (6 A d f-19 B (d e+c f))\right) a^3-3 b^3 \left(C \left(5 d^3 e^3+94 c d^2 f e^2+94 c^2 d f^2 e+5 c^3 f^3\right)+d f \left(3 A d f (d e+c f)-B \left(3 d^2 e^2+16 c d f e+3 c^2 f^2\right)\right)\right) a^2-b^4 \left(-6 f^2 (7 C e-B f) c^3-d f \left(238 C e^2-19 f (B e-A f)\right) c^2-d^2 e \left(42 C e^2-f (19 B e+20 A f)\right) c+d^3 e^2 (6 B e-19 A f)\right) a-b^5 \left(f \left(35 C e^2-14 B f e+8 A f^2\right) c^3+d e \left(35 C e^2+14 B f e-5 A f^2\right) c^2-d^2 e^2 (14 B e+5 A f) c+8 A d^3 e^3\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right) \sqrt{e+f x}}{105 b^4 (a d-b c)^{5/2} (b e-a f)^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \left(48 C d^3 f^3 a^5+8 b d^2 f^2 (B d f-16 C (d e+c f)) a^4+b^2 d f \left(C \left(103 d^2 e^2+344 c d f e+103 c^2 f^2\right)+d f (6 A d f-19 B (d e+c f))\right) a^3-3 b^3 \left(C \left(5 d^3 e^3+94 c d^2 f e^2+94 c^2 d f^2 e+5 c^3 f^3\right)+d f \left(3 A d f (d e+c f)-B \left(3 d^2 e^2+16 c d f e+3 c^2 f^2\right)\right)\right) a^2-b^4 \left(-6 f^2 (7 C e-B f) c^3-d f \left(238 C e^2-19 f (B e-A f)\right) c^2-d^2 e \left(42 C e^2-f (19 B e+20 A f)\right) c+d^3 e^2 (6 B e-19 A f)\right) a-b^5 \left(f \left(35 C e^2-14 B f e+8 A f^2\right) c^3+d e \left(35 C e^2+14 B f e-5 A f^2\right) c^2-d^2 e^2 (14 B e+5 A f) c+8 A d^3 e^3\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{105 b^3 (b c-a d)^3 (b e-a f)^3 \sqrt{a+b x}}-\frac{2 \left(24 C d^2 f^2 a^4-b d f (61 C d e+43 c C f-4 B d f) a^3-3 b^2 \left(d f (3 B d e+2 B c f-A d f)-C \left(15 d^2 e^2+37 c d f e+5 c^2 f^2\right)\right) a^2-3 b^3 \left(2 f (7 C e-B f) c^2+d \left(28 C e^2-5 B f e+5 A f^2\right) c+d^2 e (B e-3 A f)\right) a-b^4 \left(-\left(35 C e^2-14 B f e+8 A f^2\right) c^2-d e (7 B e-A f) c+4 A d^2 e^2\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{105 b^3 (b c-a d)^2 (b e-a f)^2 (a+b x)^{3/2}}+\frac{2 \sqrt{d} (d e-c f) \left(24 C d^2 f^2 a^4-b d f (43 C d e+61 c C f-4 B d f) a^3-3 b^2 \left(d f (2 B d e+3 B c f-A d f)-C \left(5 d^2 e^2+37 c d f e+15 c^2 f^2\right)\right) a^2+3 b^3 \left(-f (28 C e+B f) c^2-d \left(14 C e^2-5 B f e-3 A f^2\right) c+d^2 e (2 B e-5 A f)\right) a+b^4 \left(\left(35 C e^2+7 B f e-4 A f^2\right) c^2-d e (14 B e+A f) c+8 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^4 (a d-b c)^{5/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{e+f x}}","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d x)^{3/2} (e+f x)^{3/2}}{7 b (b c-a d) (b e-a f) (a+b x)^{7/2}}+\frac{2 \left(6 C d f a^3+b (B d f-10 C (d e+c f)) a^2+b^2 (14 c C e+3 B d e+3 B c f-8 A d f) a-b^3 (7 B c e-4 A (d e+c f))\right) \sqrt{c+d x} (e+f x)^{3/2}}{35 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{5/2}}+\frac{2 \sqrt{d} \left(48 C d^3 f^3 a^5+8 b d^2 f^2 (B d f-16 C (d e+c f)) a^4+b^2 d f \left(C \left(103 d^2 e^2+344 c d f e+103 c^2 f^2\right)+d f (6 A d f-19 B (d e+c f))\right) a^3-3 b^3 \left(C \left(5 d^3 e^3+94 c d^2 f e^2+94 c^2 d f^2 e+5 c^3 f^3\right)+d f \left(3 A d f (d e+c f)-B \left(3 d^2 e^2+16 c d f e+3 c^2 f^2\right)\right)\right) a^2-b^4 \left(-6 f^2 (7 C e-B f) c^3-d f \left(238 C e^2-19 f (B e-A f)\right) c^2-d^2 e \left(42 C e^2-f (19 B e+20 A f)\right) c+d^3 e^2 (6 B e-19 A f)\right) a-b^5 \left(f \left(35 C e^2-14 B f e+8 A f^2\right) c^3+d e \left(35 C e^2+14 B f e-5 A f^2\right) c^2-d^2 e^2 (14 B e+5 A f) c+8 A d^3 e^3\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right) \sqrt{e+f x}}{105 b^4 (a d-b c)^{5/2} (b e-a f)^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \left(48 C d^3 f^3 a^5+8 b d^2 f^2 (B d f-16 C (d e+c f)) a^4+b^2 d f \left(C \left(103 d^2 e^2+344 c d f e+103 c^2 f^2\right)+d f (6 A d f-19 B (d e+c f))\right) a^3-3 b^3 \left(C \left(5 d^3 e^3+94 c d^2 f e^2+94 c^2 d f^2 e+5 c^3 f^3\right)+d f \left(3 A d f (d e+c f)-B \left(3 d^2 e^2+16 c d f e+3 c^2 f^2\right)\right)\right) a^2-b^4 \left(-6 f^2 (7 C e-B f) c^3-d f \left(238 C e^2-19 f (B e-A f)\right) c^2-d^2 e \left(42 C e^2-f (19 B e+20 A f)\right) c+d^3 e^2 (6 B e-19 A f)\right) a-b^5 \left(f \left(35 C e^2-14 B f e+8 A f^2\right) c^3+d e \left(35 C e^2+14 B f e-5 A f^2\right) c^2-d^2 e^2 (14 B e+5 A f) c+8 A d^3 e^3\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{105 b^3 (b c-a d)^3 (b e-a f)^3 \sqrt{a+b x}}-\frac{2 \left(24 C d^2 f^2 a^4-b d f (61 C d e+43 c C f-4 B d f) a^3-3 b^2 \left(d f (3 B d e+2 B c f-A d f)-C \left(15 d^2 e^2+37 c d f e+5 c^2 f^2\right)\right) a^2-3 b^3 \left(2 f (7 C e-B f) c^2+d \left(28 C e^2-5 B f e+5 A f^2\right) c+d^2 e (B e-3 A f)\right) a-b^4 \left(-\left(35 C e^2-14 B f e+8 A f^2\right) c^2-d e (7 B e-A f) c+4 A d^2 e^2\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{105 b^3 (b c-a d)^2 (b e-a f)^2 (a+b x)^{3/2}}+\frac{2 \sqrt{d} (d e-c f) \left(24 C d^2 f^2 a^4-b d f (43 C d e+61 c C f-4 B d f) a^3-3 b^2 \left(d f (2 B d e+3 B c f-A d f)-C \left(5 d^2 e^2+37 c d f e+15 c^2 f^2\right)\right) a^2+3 b^3 \left(-f (28 C e+B f) c^2-d \left(14 C e^2-5 B f e-3 A f^2\right) c+d^2 e (2 B e-5 A f)\right) a+b^4 \left(\left(35 C e^2+7 B f e-4 A f^2\right) c^2-d e (14 B e+A f) c+8 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^4 (a d-b c)^{5/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{e+f x}}",1,"(-2*(24*a^4*C*d^2*f^2 - a^3*b*d*f*(61*C*d*e + 43*c*C*f - 4*B*d*f) - 3*a*b^3*(d^2*e*(B*e - 3*A*f) + 2*c^2*f*(7*C*e - B*f) + c*d*(28*C*e^2 - 5*B*e*f + 5*A*f^2)) - b^4*(4*A*d^2*e^2 - c*d*e*(7*B*e - A*f) - c^2*(35*C*e^2 - 14*B*e*f + 8*A*f^2)) - 3*a^2*b^2*(d*f*(3*B*d*e + 2*B*c*f - A*d*f) - C*(15*d^2*e^2 + 37*c*d*e*f + 5*c^2*f^2)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(105*b^3*(b*c - a*d)^2*(b*e - a*f)^2*(a + b*x)^(3/2)) + (2*(48*a^5*C*d^3*f^3 + 8*a^4*b*d^2*f^2*(B*d*f - 16*C*(d*e + c*f)) - b^5*(8*A*d^3*e^3 - c*d^2*e^2*(14*B*e + 5*A*f) + c^2*d*e*(35*C*e^2 + 14*B*e*f - 5*A*f^2) + c^3*f*(35*C*e^2 - 14*B*e*f + 8*A*f^2)) - a*b^4*(d^3*e^2*(6*B*e - 19*A*f) - 6*c^3*f^2*(7*C*e - B*f) - c^2*d*f*(238*C*e^2 - 19*f*(B*e - A*f)) - c*d^2*e*(42*C*e^2 - f*(19*B*e + 20*A*f))) + a^3*b^2*d*f*(C*(103*d^2*e^2 + 344*c*d*e*f + 103*c^2*f^2) + d*f*(6*A*d*f - 19*B*(d*e + c*f))) - 3*a^2*b^3*(C*(5*d^3*e^3 + 94*c*d^2*e^2*f + 94*c^2*d*e*f^2 + 5*c^3*f^3) + d*f*(3*A*d*f*(d*e + c*f) - B*(3*d^2*e^2 + 16*c*d*e*f + 3*c^2*f^2))))*Sqrt[c + d*x]*Sqrt[e + f*x])/(105*b^3*(b*c - a*d)^3*(b*e - a*f)^3*Sqrt[a + b*x]) + (2*(6*a^3*C*d*f + a*b^2*(14*c*C*e + 3*B*d*e + 3*B*c*f - 8*A*d*f) - b^3*(7*B*c*e - 4*A*(d*e + c*f)) + a^2*b*(B*d*f - 10*C*(d*e + c*f)))*Sqrt[c + d*x]*(e + f*x)^(3/2))/(35*b^2*(b*c - a*d)*(b*e - a*f)^2*(a + b*x)^(5/2)) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*(e + f*x)^(3/2))/(7*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^(7/2)) + (2*Sqrt[d]*(48*a^5*C*d^3*f^3 + 8*a^4*b*d^2*f^2*(B*d*f - 16*C*(d*e + c*f)) - b^5*(8*A*d^3*e^3 - c*d^2*e^2*(14*B*e + 5*A*f) + c^2*d*e*(35*C*e^2 + 14*B*e*f - 5*A*f^2) + c^3*f*(35*C*e^2 - 14*B*e*f + 8*A*f^2)) - a*b^4*(d^3*e^2*(6*B*e - 19*A*f) - 6*c^3*f^2*(7*C*e - B*f) - c^2*d*f*(238*C*e^2 - 19*f*(B*e - A*f)) - c*d^2*e*(42*C*e^2 - f*(19*B*e + 20*A*f))) + a^3*b^2*d*f*(C*(103*d^2*e^2 + 344*c*d*e*f + 103*c^2*f^2) + d*f*(6*A*d*f - 19*B*(d*e + c*f))) - 3*a^2*b^3*(C*(5*d^3*e^3 + 94*c*d^2*e^2*f + 94*c^2*d*e*f^2 + 5*c^3*f^3) + d*f*(3*A*d*f*(d*e + c*f) - B*(3*d^2*e^2 + 16*c*d*e*f + 3*c^2*f^2))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(105*b^4*(-(b*c) + a*d)^(5/2)*(b*e - a*f)^3*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) + (2*Sqrt[d]*(d*e - c*f)*(24*a^4*C*d^2*f^2 - a^3*b*d*f*(43*C*d*e + 61*c*C*f - 4*B*d*f) + b^4*(8*A*d^2*e^2 - c*d*e*(14*B*e + A*f) + c^2*(35*C*e^2 + 7*B*e*f - 4*A*f^2)) + 3*a*b^3*(d^2*e*(2*B*e - 5*A*f) - c^2*f*(28*C*e + B*f) - c*d*(14*C*e^2 - 5*B*e*f - 3*A*f^2)) - 3*a^2*b^2*(d*f*(2*B*d*e + 3*B*c*f - A*d*f) - C*(5*d^2*e^2 + 37*c*d*e*f + 15*c^2*f^2)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(105*b^4*(-(b*c) + a*d)^(5/2)*(b*e - a*f)^2*Sqrt[c + d*x]*Sqrt[e + f*x])","A",10,8,38,0.2105,1,"{1614, 150, 152, 158, 114, 113, 121, 120}"
67,1,1235,0,4.3951496,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","Int[((a + b*x)^(3/2)*Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","\frac{2 C (c+d x)^{3/2} \sqrt{e+f x} (a+b x)^{5/2}}{9 b d f}-\frac{2 (4 a C d f+b (8 C d e+6 c C f-9 B d f)) (c+d x)^{3/2} \sqrt{e+f x} (a+b x)^{3/2}}{63 b d^2 f^2}-\frac{2 (7 b d f (5 b c C e+3 a C d e+a c C f-9 A b d f)-(6 b d e+4 b c f-3 a d f) (4 a C d f+b (8 C d e+6 c C f-9 B d f))) (c+d x)^{3/2} \sqrt{e+f x} \sqrt{a+b x}}{315 b d^3 f^3}-\frac{2 \left(5 b d f (7 a d f (5 b c C e+3 a C d e+a c C f-9 A b d f)-(3 b c e+3 a d e+a c f) (4 a C d f+b (8 C d e+6 c C f-9 B d f)))+2 \left(\frac{a d f}{2}-b (2 d e+c f)\right) (7 b d f (5 b c C e+3 a C d e+a c C f-9 A b d f)-(6 b d e+4 b c f-3 a d f) (4 a C d f+b (8 C d e+6 c C f-9 B d f)))\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{a+b x}}{945 b^2 d^3 f^4}+\frac{2 \sqrt{a d-b c} \left(\left(C \left(128 d^4 e^4-40 c d^3 f e^3-21 c^2 d^2 f^2 e^2-16 c^3 d f^3 e-16 c^4 f^4\right)+3 d f \left(7 A d f \left(8 d^2 e^2-3 c d f e-2 c^2 f^2\right)-B \left(48 d^3 e^3-16 c d^2 f e^2-9 c^2 d f^2 e-8 c^3 f^3\right)\right)\right) b^4-a d f \left(2 C \left(92 d^3 e^3-33 c d^2 f e^2-18 c^2 d f^2 e-16 c^3 f^3\right)+3 d f \left(7 A d f (13 d e-7 c f)-B \left(72 d^2 e^2-29 c d f e-19 c^2 f^2\right)\right)\right) b^3-3 a^2 d^2 f^2 \left(3 d f (4 B d e-3 B c f-7 A d f)-C \left(9 d^2 e^2-5 c d f e-3 c^2 f^2\right)\right) b^2+a^3 d^3 f^3 (11 C d e-7 c C f-18 B d f) b+8 a^4 C d^4 f^4\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{315 b^3 d^{7/2} f^5 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \sqrt{a d-b c} (b e-a f) (d e-c f) \left(-\left(C \left(128 d^3 e^3+24 c d^2 f e^2+15 c^2 d f^2 e+8 c^3 f^3\right)+3 d f \left(7 A d f (8 d e+c f)-4 B \left(12 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) b^3-3 a d f \left(3 d f (16 B d e+3 B c f-21 A d f)-5 C \left(8 d^2 e^2+2 c d f e+c^2 f^2\right)\right) b^2+3 a^2 d^2 f^2 (3 C d e-c C f-3 B d f) b+4 a^3 C d^3 f^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{315 b^3 d^{7/2} f^5 \sqrt{c+d x} \sqrt{e+f x}}","\frac{2 C (c+d x)^{3/2} \sqrt{e+f x} (a+b x)^{5/2}}{9 b d f}-\frac{2 (4 a C d f+b (8 C d e+6 c C f-9 B d f)) (c+d x)^{3/2} \sqrt{e+f x} (a+b x)^{3/2}}{63 b d^2 f^2}-\frac{2 (7 b d f (5 b c C e+3 a C d e+a c C f-9 A b d f)-(6 b d e+4 b c f-3 a d f) (4 a C d f+b (8 C d e+6 c C f-9 B d f))) (c+d x)^{3/2} \sqrt{e+f x} \sqrt{a+b x}}{315 b d^3 f^3}-\frac{2 \left(5 b d f (7 a d f (5 b c C e+3 a C d e+a c C f-9 A b d f)-(3 b c e+3 a d e+a c f) (4 a C d f+b (8 C d e+6 c C f-9 B d f)))+2 \left(\frac{a d f}{2}-b (2 d e+c f)\right) (7 b d f (5 b c C e+3 a C d e+a c C f-9 A b d f)-(6 b d e+4 b c f-3 a d f) (4 a C d f+b (8 C d e+6 c C f-9 B d f)))\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{a+b x}}{945 b^2 d^3 f^4}+\frac{2 \sqrt{a d-b c} \left(\left(C \left(128 d^4 e^4-40 c d^3 f e^3-21 c^2 d^2 f^2 e^2-16 c^3 d f^3 e-16 c^4 f^4\right)+3 d f \left(7 A d f \left(8 d^2 e^2-3 c d f e-2 c^2 f^2\right)-B \left(48 d^3 e^3-16 c d^2 f e^2-9 c^2 d f^2 e-8 c^3 f^3\right)\right)\right) b^4-a d f \left(2 C \left(92 d^3 e^3-33 c d^2 f e^2-18 c^2 d f^2 e-16 c^3 f^3\right)+3 d f \left(7 A d f (13 d e-7 c f)-B \left(72 d^2 e^2-29 c d f e-19 c^2 f^2\right)\right)\right) b^3-3 a^2 d^2 f^2 \left(3 d f (4 B d e-3 B c f-7 A d f)-C \left(9 d^2 e^2-5 c d f e-3 c^2 f^2\right)\right) b^2+a^3 d^3 f^3 (11 C d e-7 c C f-18 B d f) b+8 a^4 C d^4 f^4\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{315 b^3 d^{7/2} f^5 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \sqrt{a d-b c} (b e-a f) (d e-c f) \left(-\left(C \left(128 d^3 e^3+24 c d^2 f e^2+15 c^2 d f^2 e+8 c^3 f^3\right)+3 d f \left(7 A d f (8 d e+c f)-4 B \left(12 d^2 e^2+2 c d f e+c^2 f^2\right)\right)\right) b^3-3 a d f \left(3 d f (16 B d e+3 B c f-21 A d f)-5 C \left(8 d^2 e^2+2 c d f e+c^2 f^2\right)\right) b^2+3 a^2 d^2 f^2 (3 C d e-c C f-3 B d f) b+4 a^3 C d^3 f^3\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{315 b^3 d^{7/2} f^5 \sqrt{c+d x} \sqrt{e+f x}}",1,"(-2*(5*b*d*f*(7*a*d*f*(5*b*c*C*e + 3*a*C*d*e + a*c*C*f - 9*A*b*d*f) - (3*b*c*e + 3*a*d*e + a*c*f)*(4*a*C*d*f + b*(8*C*d*e + 6*c*C*f - 9*B*d*f))) + 2*((a*d*f)/2 - b*(2*d*e + c*f))*(7*b*d*f*(5*b*c*C*e + 3*a*C*d*e + a*c*C*f - 9*A*b*d*f) - (6*b*d*e + 4*b*c*f - 3*a*d*f)*(4*a*C*d*f + b*(8*C*d*e + 6*c*C*f - 9*B*d*f))))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(945*b^2*d^3*f^4) - (2*(7*b*d*f*(5*b*c*C*e + 3*a*C*d*e + a*c*C*f - 9*A*b*d*f) - (6*b*d*e + 4*b*c*f - 3*a*d*f)*(4*a*C*d*f + b*(8*C*d*e + 6*c*C*f - 9*B*d*f)))*Sqrt[a + b*x]*(c + d*x)^(3/2)*Sqrt[e + f*x])/(315*b*d^3*f^3) - (2*(4*a*C*d*f + b*(8*C*d*e + 6*c*C*f - 9*B*d*f))*(a + b*x)^(3/2)*(c + d*x)^(3/2)*Sqrt[e + f*x])/(63*b*d^2*f^2) + (2*C*(a + b*x)^(5/2)*(c + d*x)^(3/2)*Sqrt[e + f*x])/(9*b*d*f) + (2*Sqrt[-(b*c) + a*d]*(8*a^4*C*d^4*f^4 + a^3*b*d^3*f^3*(11*C*d*e - 7*c*C*f - 18*B*d*f) - 3*a^2*b^2*d^2*f^2*(3*d*f*(4*B*d*e - 3*B*c*f - 7*A*d*f) - C*(9*d^2*e^2 - 5*c*d*e*f - 3*c^2*f^2)) - a*b^3*d*f*(2*C*(92*d^3*e^3 - 33*c*d^2*e^2*f - 18*c^2*d*e*f^2 - 16*c^3*f^3) + 3*d*f*(7*A*d*f*(13*d*e - 7*c*f) - B*(72*d^2*e^2 - 29*c*d*e*f - 19*c^2*f^2))) + b^4*(C*(128*d^4*e^4 - 40*c*d^3*e^3*f - 21*c^2*d^2*e^2*f^2 - 16*c^3*d*e*f^3 - 16*c^4*f^4) + 3*d*f*(7*A*d*f*(8*d^2*e^2 - 3*c*d*e*f - 2*c^2*f^2) - B*(48*d^3*e^3 - 16*c*d^2*e^2*f - 9*c^2*d*e*f^2 - 8*c^3*f^3))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(315*b^3*d^(7/2)*f^5*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) + (2*Sqrt[-(b*c) + a*d]*(b*e - a*f)*(d*e - c*f)*(4*a^3*C*d^3*f^3 + 3*a^2*b*d^2*f^2*(3*C*d*e - c*C*f - 3*B*d*f) - 3*a*b^2*d*f*(3*d*f*(16*B*d*e + 3*B*c*f - 21*A*d*f) - 5*C*(8*d^2*e^2 + 2*c*d*e*f + c^2*f^2)) - b^3*(C*(128*d^3*e^3 + 24*c*d^2*e^2*f + 15*c^2*d*e*f^2 + 8*c^3*f^3) + 3*d*f*(7*A*d*f*(8*d*e + c*f) - 4*B*(12*d^2*e^2 + 2*c*d*e*f + c^2*f^2))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(315*b^3*d^(7/2)*f^5*Sqrt[c + d*x]*Sqrt[e + f*x])","A",10,7,38,0.1842,1,"{1615, 154, 158, 114, 113, 121, 120}"
68,1,766,0,2.0614081,"\int \frac{\sqrt{a+b x} \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","Int[(Sqrt[a + b*x]*Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","\frac{2 \sqrt{a d-b c} (b e-a f) (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(4 a^2 C d^2 f^2+a b d f (-7 B d f-2 c C f+8 C d e)+b^2 \left(-\left(7 d f (-10 A d f+B c f+8 B d e)-4 C \left(c^2 f^2+2 c d e f+12 d^2 e^2\right)\right)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^3 d^{5/2} f^4 \sqrt{c+d x} \sqrt{e+f x}}-\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} (5 b d f (a c C f+3 a C d e-7 A b d f+3 b c C e)+(a d f-2 b (c f+2 d e)) (4 a C d f+b (-7 B d f+4 c C f+6 C d e)))}{105 b^2 d^2 f^3}-\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(3 b d f (5 a d f (a c C f+3 a C d e-7 A b d f+3 b c C e)-(a c f+3 a d e+b c e) (4 a C d f+b (-7 B d f+4 c C f+6 C d e)))+2 \left(\frac{b c f}{2}-d (a f+b e)\right) (5 b d f (a c C f+3 a C d e-7 A b d f+3 b c C e)+(a d f-2 b (c f+2 d e)) (4 a C d f+b (-7 B d f+4 c C f+6 C d e)))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^3 d^{5/2} f^4 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a+b x} (c+d x)^{3/2} \sqrt{e+f x} (4 a C d f+b (-7 B d f+4 c C f+6 C d e))}{35 b d^2 f^2}+\frac{2 C (a+b x)^{3/2} (c+d x)^{3/2} \sqrt{e+f x}}{7 b d f}","\frac{2 \sqrt{a d-b c} (b e-a f) (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(4 a^2 C d^2 f^2+a b d f (-7 B d f-2 c C f+8 C d e)+b^2 \left(-\left(7 d f (-10 A d f+B c f+8 B d e)-4 C \left(c^2 f^2+2 c d e f+12 d^2 e^2\right)\right)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^3 d^{5/2} f^4 \sqrt{c+d x} \sqrt{e+f x}}-\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} (5 b d f (a c C f+3 a C d e-7 A b d f+3 b c C e)+(a d f-2 b (c f+2 d e)) (4 a C d f+b (-7 B d f+4 c C f+6 C d e)))}{105 b^2 d^2 f^3}-\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(3 b d f (5 a d f (a c C f+3 a C d e-7 A b d f+3 b c C e)-(a c f+3 a d e+b c e) (4 a C d f+b (-7 B d f+4 c C f+6 C d e)))+2 \left(\frac{b c f}{2}-d (a f+b e)\right) (5 b d f (a c C f+3 a C d e-7 A b d f+3 b c C e)+(a d f-2 b (c f+2 d e)) (4 a C d f+b (-7 B d f+4 c C f+6 C d e)))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^3 d^{5/2} f^4 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a+b x} (c+d x)^{3/2} \sqrt{e+f x} (4 a C d f+b (-7 B d f+4 c C f+6 C d e))}{35 b d^2 f^2}+\frac{2 C (a+b x)^{3/2} (c+d x)^{3/2} \sqrt{e+f x}}{7 b d f}",1,"(-2*(5*b*d*f*(3*b*c*C*e + 3*a*C*d*e + a*c*C*f - 7*A*b*d*f) + (a*d*f - 2*b*(2*d*e + c*f))*(4*a*C*d*f + b*(6*C*d*e + 4*c*C*f - 7*B*d*f)))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(105*b^2*d^2*f^3) - (2*(4*a*C*d*f + b*(6*C*d*e + 4*c*C*f - 7*B*d*f))*Sqrt[a + b*x]*(c + d*x)^(3/2)*Sqrt[e + f*x])/(35*b*d^2*f^2) + (2*C*(a + b*x)^(3/2)*(c + d*x)^(3/2)*Sqrt[e + f*x])/(7*b*d*f) - (2*Sqrt[-(b*c) + a*d]*(3*b*d*f*(5*a*d*f*(3*b*c*C*e + 3*a*C*d*e + a*c*C*f - 7*A*b*d*f) - (b*c*e + 3*a*d*e + a*c*f)*(4*a*C*d*f + b*(6*C*d*e + 4*c*C*f - 7*B*d*f))) + 2*((b*c*f)/2 - d*(b*e + a*f))*(5*b*d*f*(3*b*c*C*e + 3*a*C*d*e + a*c*C*f - 7*A*b*d*f) + (a*d*f - 2*b*(2*d*e + c*f))*(4*a*C*d*f + b*(6*C*d*e + 4*c*C*f - 7*B*d*f))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(105*b^3*d^(5/2)*f^4*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) + (2*Sqrt[-(b*c) + a*d]*(b*e - a*f)*(d*e - c*f)*(4*a^2*C*d^2*f^2 + a*b*d*f*(8*C*d*e - 2*c*C*f - 7*B*d*f) - b^2*(7*d*f*(8*B*d*e + B*c*f - 10*A*d*f) - 4*C*(12*d^2*e^2 + 2*c*d*e*f + c^2*f^2)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(105*b^3*d^(5/2)*f^4*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,7,38,0.1842,1,"{1615, 154, 158, 114, 113, 121, 120}"
69,1,527,0,0.9799134,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{a+b x} \sqrt{e+f x}} \, dx","Int[(Sqrt[c + d*x]*(A + B*x + C*x^2))/(Sqrt[a + b*x]*Sqrt[e + f*x]),x]","-\frac{2 \sqrt{a d-b c} (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(4 a^2 C d f^2+a b f (-5 B d f-c C f+3 C d e)+b^2 (-(5 d f (2 B e-3 A f)-C e (c f+8 d e)))\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^3 d^{3/2} f^3 \sqrt{c+d x} \sqrt{e+f x}}-\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} (3 b d f (a c C f+3 a C d e-5 A b d f+b c C e)-(2 a d f-b c f+2 b d e) (4 a C d f+b (-5 B d f+2 c C f+4 C d e))) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^3 d^{3/2} f^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} (4 a C d f+b (-5 B d f+2 c C f+4 C d e))}{15 b^2 d f^2}+\frac{2 C \sqrt{a+b x} (c+d x)^{3/2} \sqrt{e+f x}}{5 b d f}","-\frac{2 \sqrt{a d-b c} (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(4 a^2 C d f^2+a b f (-5 B d f-c C f+3 C d e)+b^2 (-(5 d f (2 B e-3 A f)-C e (c f+8 d e)))\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^3 d^{3/2} f^3 \sqrt{c+d x} \sqrt{e+f x}}-\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} (3 b d f (a c C f+3 a C d e-5 A b d f+b c C e)-(2 a d f-b c f+2 b d e) (4 a C d f+b (-5 B d f+2 c C f+4 C d e))) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^3 d^{3/2} f^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} (4 a C d f+b (-5 B d f+2 c C f+4 C d e))}{15 b^2 d f^2}+\frac{2 C \sqrt{a+b x} (c+d x)^{3/2} \sqrt{e+f x}}{5 b d f}",1,"(-2*(4*a*C*d*f + b*(4*C*d*e + 2*c*C*f - 5*B*d*f))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(15*b^2*d*f^2) + (2*C*Sqrt[a + b*x]*(c + d*x)^(3/2)*Sqrt[e + f*x])/(5*b*d*f) - (2*Sqrt[-(b*c) + a*d]*(3*b*d*f*(b*c*C*e + 3*a*C*d*e + a*c*C*f - 5*A*b*d*f) - (2*b*d*e - b*c*f + 2*a*d*f)*(4*a*C*d*f + b*(4*C*d*e + 2*c*C*f - 5*B*d*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^3*d^(3/2)*f^3*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) - (2*Sqrt[-(b*c) + a*d]*(d*e - c*f)*(4*a^2*C*d*f^2 + a*b*f*(3*C*d*e - c*C*f - 5*B*d*f) - b^2*(5*d*f*(2*B*e - 3*A*f) - C*e*(8*d*e + c*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^3*d^(3/2)*f^3*Sqrt[c + d*x]*Sqrt[e + f*x])","A",8,7,38,0.1842,1,"{1615, 154, 158, 114, 113, 121, 120}"
70,1,540,0,1.1110668,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^{3/2} \sqrt{e+f x}} \, dx","Int[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^(3/2)*Sqrt[e + f*x]),x]","\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(8 a^2 C d f^2-a b f (6 B d f+c C f+3 C d e)+b^2 (3 d f (A f+B e)-C e (2 d e-c f))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^3 \sqrt{d} f^2 \sqrt{c+d x} (b e-a f) \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(4 a^2 C d f-a b (3 B d f+c C f+C d e)+b^2 (3 A d f+c C e)\right)}{3 b^2 f (b c-a d) (b e-a f)}-\frac{2 (c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{b \sqrt{a+b x} (b c-a d) (b e-a f)}+\frac{2 \sqrt{a d-b c} (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} (4 a C f-3 b B f+2 b C e) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^3 \sqrt{d} f^2 \sqrt{c+d x} \sqrt{e+f x}}","\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(8 a^2 C d f^2-a b f (6 B d f+c C f+3 C d e)+b^2 (3 d f (A f+B e)-C e (2 d e-c f))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^3 \sqrt{d} f^2 \sqrt{c+d x} (b e-a f) \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(4 a^2 C d f-a b (3 B d f+c C f+C d e)+b^2 (3 A d f+c C e)\right)}{3 b^2 f (b c-a d) (b e-a f)}-\frac{2 (c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{b \sqrt{a+b x} (b c-a d) (b e-a f)}+\frac{2 \sqrt{a d-b c} (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} (4 a C f-3 b B f+2 b C e) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^3 \sqrt{d} f^2 \sqrt{c+d x} \sqrt{e+f x}}",1,"(2*(4*a^2*C*d*f + b^2*(c*C*e + 3*A*d*f) - a*b*(C*d*e + c*C*f + 3*B*d*f))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(3*b^2*(b*c - a*d)*f*(b*e - a*f)) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*Sqrt[e + f*x])/(b*(b*c - a*d)*(b*e - a*f)*Sqrt[a + b*x]) + (2*Sqrt[-(b*c) + a*d]*(8*a^2*C*d*f^2 - a*b*f*(3*C*d*e + c*C*f + 6*B*d*f) + b^2*(3*d*f*(B*e + A*f) - C*e*(2*d*e - c*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^3*Sqrt[d]*f^2*(b*e - a*f)*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) + (2*Sqrt[-(b*c) + a*d]*(d*e - c*f)*(2*b*C*e - 3*b*B*f + 4*a*C*f)*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^3*Sqrt[d]*f^2*Sqrt[c + d*x]*Sqrt[e + f*x])","A",8,7,38,0.1842,1,"{1614, 154, 158, 114, 113, 121, 120}"
71,1,596,0,1.3589441,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^{5/2} \sqrt{e+f x}} \, dx","Int[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^(5/2)*Sqrt[e + f*x]),x]","\frac{2 \sqrt{d} \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(-a^2 b f (2 B d f+7 c C f+13 C d e)+8 a^3 C d f^2+a b^2 (f (-A d f+B c f+4 B d e)+3 C e (4 c f+d e))-b^3 \left(c f (3 B e-2 A f)+A d e f+3 c C e^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^3 f \sqrt{c+d x} \sqrt{a d-b c} (b e-a f)^2 \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(4 a^2 C f-a b (B f+6 C e)+b^2 (3 B e-2 A f)\right)}{3 b^2 \sqrt{a+b x} (b e-a f)^2}+\frac{2 (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(4 a^2 C d f-a b (B d f+3 C (c f+d e))+b^2 (A d f+3 c C e)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^3 \sqrt{d} f \sqrt{c+d x} \sqrt{e+f x} \sqrt{a d-b c} (b e-a f)}-\frac{2 (c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{3 b (a+b x)^{3/2} (b c-a d) (b e-a f)}","\frac{2 \sqrt{d} \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(-a^2 b f (2 B d f+7 c C f+13 C d e)+8 a^3 C d f^2+a b^2 (f (-A d f+B c f+4 B d e)+3 C e (4 c f+d e))-b^3 \left(c \left(-2 A f^2+3 B e f+3 C e^2\right)+A d e f\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^3 f \sqrt{c+d x} \sqrt{a d-b c} (b e-a f)^2 \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(4 a^2 C f-a b (B f+6 C e)+b^2 (3 B e-2 A f)\right)}{3 b^2 \sqrt{a+b x} (b e-a f)^2}+\frac{2 (d e-c f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(4 a^2 C d f-a b (B d f+3 C (c f+d e))+b^2 (A d f+3 c C e)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^3 \sqrt{d} f \sqrt{c+d x} \sqrt{e+f x} \sqrt{a d-b c} (b e-a f)}-\frac{2 (c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{3 b (a+b x)^{3/2} (b c-a d) (b e-a f)}",1,"(-2*(4*a^2*C*f + b^2*(3*B*e - 2*A*f) - a*b*(6*C*e + B*f))*Sqrt[c + d*x]*Sqrt[e + f*x])/(3*b^2*(b*e - a*f)^2*Sqrt[a + b*x]) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*Sqrt[e + f*x])/(3*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^(3/2)) + (2*Sqrt[d]*(8*a^3*C*d*f^2 - a^2*b*f*(13*C*d*e + 7*c*C*f + 2*B*d*f) - b^3*(3*c*C*e^2 + A*d*e*f + c*f*(3*B*e - 2*A*f)) + a*b^2*(3*C*e*(d*e + 4*c*f) + f*(4*B*d*e + B*c*f - A*d*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^3*Sqrt[-(b*c) + a*d]*f*(b*e - a*f)^2*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) + (2*(d*e - c*f)*(4*a^2*C*d*f + b^2*(3*c*C*e + A*d*f) - a*b*(B*d*f + 3*C*(d*e + c*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^3*Sqrt[d]*Sqrt[-(b*c) + a*d]*f*(b*e - a*f)*Sqrt[c + d*x]*Sqrt[e + f*x])","A",8,7,38,0.1842,1,"{1614, 150, 158, 114, 113, 121, 120}"
72,1,1034,0,3.1597932,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^{7/2} \sqrt{e+f x}} \, dx","Int[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^(7/2)*Sqrt[e + f*x]),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{e+f x} (c+d x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}-\frac{2 \left(8 C d^2 f^2 a^4-b d f (23 C d e+13 c C f-2 B d f) a^3-b^2 \left(d f (7 B d e+2 B c f-3 A d f)-C \left(23 d^2 e^2+37 c d f e+3 c^2 f^2\right)\right) a^2-b^3 \left(2 f (5 C e-B f) c^2+d \left(40 C e^2-13 f (B e-A f)\right) c+d^2 e (3 B e-7 A f)\right) a-b^4 \left(-\left(15 C e^2-10 B f e+8 A f^2\right) c^2-d e (5 B e-3 A f) c+2 A d^2 e^2\right)\right) \sqrt{e+f x} \sqrt{c+d x}}{15 b^2 (b c-a d)^2 (b e-a f)^3 \sqrt{a+b x}}+\frac{2 \left(4 C d f a^3-b (8 C d e+6 c C f-B d f) a^2+b^2 (10 c C e+3 B d e+B c f-6 A d f) a-b^3 (5 B c e-2 A d e-4 A c f)\right) \sqrt{e+f x} \sqrt{c+d x}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}+\frac{2 \sqrt{d} \left(8 C d^2 f^2 a^4-b d f (23 C d e+13 c C f-2 B d f) a^3-b^2 \left(d f (7 B d e+2 B c f-3 A d f)-C \left(23 d^2 e^2+37 c d f e+3 c^2 f^2\right)\right) a^2-b^3 \left(2 f (5 C e-B f) c^2+d \left(40 C e^2-13 f (B e-A f)\right) c+d^2 e (3 B e-7 A f)\right) a-b^4 \left(-\left(15 C e^2-10 B f e+8 A f^2\right) c^2-d e (5 B e-3 A f) c+2 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^3 (a d-b c)^{3/2} (b e-a f)^3 \sqrt{\frac{b (e+f x)}{b e-a f}} \sqrt{c+d x}}+\frac{2 \sqrt{d} (d e-c f) \left(4 C d f a^3-b (8 C d e+6 c C f-B d f) a^2+b^2 (10 c C e+3 B d e+B c f-6 A d f) a-b^3 (5 B c e-2 A d e-4 A c f)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^3 (a d-b c)^{3/2} (b e-a f)^2 \sqrt{e+f x} \sqrt{c+d x}}","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{e+f x} (c+d x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}-\frac{2 \left(8 C d^2 f^2 a^4-b d f (23 C d e+13 c C f-2 B d f) a^3-b^2 \left(d f (7 B d e+2 B c f-3 A d f)-C \left(23 d^2 e^2+37 c d f e+3 c^2 f^2\right)\right) a^2-b^3 \left(2 f (5 C e-B f) c^2+d \left(40 C e^2-13 f (B e-A f)\right) c+d^2 e (3 B e-7 A f)\right) a-b^4 \left(-\left(15 C e^2-10 B f e+8 A f^2\right) c^2-d e (5 B e-3 A f) c+2 A d^2 e^2\right)\right) \sqrt{e+f x} \sqrt{c+d x}}{15 b^2 (b c-a d)^2 (b e-a f)^3 \sqrt{a+b x}}+\frac{2 \left(4 C d f a^3-b (8 C d e+6 c C f-B d f) a^2+b^2 (10 c C e+3 B d e+B c f-6 A d f) a-b^3 (5 B c e-2 A d e-4 A c f)\right) \sqrt{e+f x} \sqrt{c+d x}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}+\frac{2 \sqrt{d} \left(8 C d^2 f^2 a^4-b d f (23 C d e+13 c C f-2 B d f) a^3-b^2 \left(d f (7 B d e+2 B c f-3 A d f)-C \left(23 d^2 e^2+37 c d f e+3 c^2 f^2\right)\right) a^2-b^3 \left(2 f (5 C e-B f) c^2+d \left(40 C e^2-13 f (B e-A f)\right) c+d^2 e (3 B e-7 A f)\right) a-b^4 \left(-\left(15 C e^2-10 B f e+8 A f^2\right) c^2-d e (5 B e-3 A f) c+2 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^3 (a d-b c)^{3/2} (b e-a f)^3 \sqrt{\frac{b (e+f x)}{b e-a f}} \sqrt{c+d x}}+\frac{2 \sqrt{d} (d e-c f) \left(4 C d f a^3-b (8 C d e+6 c C f-B d f) a^2+b^2 (10 c C e+3 B d e+B c f-6 A d f) a-b^3 (5 B c e-2 A d e-4 A c f)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^3 (a d-b c)^{3/2} (b e-a f)^2 \sqrt{e+f x} \sqrt{c+d x}}",1,"(2*(4*a^3*C*d*f - b^3*(5*B*c*e - 2*A*d*e - 4*A*c*f) + a*b^2*(10*c*C*e + 3*B*d*e + B*c*f - 6*A*d*f) - a^2*b*(8*C*d*e + 6*c*C*f - B*d*f))*Sqrt[c + d*x]*Sqrt[e + f*x])/(15*b^2*(b*c - a*d)*(b*e - a*f)^2*(a + b*x)^(3/2)) - (2*(8*a^4*C*d^2*f^2 - a^3*b*d*f*(23*C*d*e + 13*c*C*f - 2*B*d*f) - b^4*(2*A*d^2*e^2 - c*d*e*(5*B*e - 3*A*f) - c^2*(15*C*e^2 - 10*B*e*f + 8*A*f^2)) - a^2*b^2*(d*f*(7*B*d*e + 2*B*c*f - 3*A*d*f) - C*(23*d^2*e^2 + 37*c*d*e*f + 3*c^2*f^2)) - a*b^3*(d^2*e*(3*B*e - 7*A*f) + 2*c^2*f*(5*C*e - B*f) + c*d*(40*C*e^2 - 13*f*(B*e - A*f))))*Sqrt[c + d*x]*Sqrt[e + f*x])/(15*b^2*(b*c - a*d)^2*(b*e - a*f)^3*Sqrt[a + b*x]) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*x)^(3/2)*Sqrt[e + f*x])/(5*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^(5/2)) + (2*Sqrt[d]*(8*a^4*C*d^2*f^2 - a^3*b*d*f*(23*C*d*e + 13*c*C*f - 2*B*d*f) - b^4*(2*A*d^2*e^2 - c*d*e*(5*B*e - 3*A*f) - c^2*(15*C*e^2 - 10*B*e*f + 8*A*f^2)) - a^2*b^2*(d*f*(7*B*d*e + 2*B*c*f - 3*A*d*f) - C*(23*d^2*e^2 + 37*c*d*e*f + 3*c^2*f^2)) - a*b^3*(d^2*e*(3*B*e - 7*A*f) + 2*c^2*f*(5*C*e - B*f) + c*d*(40*C*e^2 - 13*f*(B*e - A*f))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^3*(-(b*c) + a*d)^(3/2)*(b*e - a*f)^3*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) + (2*Sqrt[d]*(d*e - c*f)*(4*a^3*C*d*f - b^3*(5*B*c*e - 2*A*d*e - 4*A*c*f) + a*b^2*(10*c*C*e + 3*B*d*e + B*c*f - 6*A*d*f) - a^2*b*(8*C*d*e + 6*c*C*f - B*d*f))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^3*(-(b*c) + a*d)^(3/2)*(b*e - a*f)^2*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,8,38,0.2105,1,"{1614, 150, 152, 158, 114, 113, 121, 120}"
73,1,831,0,2.1667788,"\int \frac{(a+b x)^{3/2} \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[((a + b*x)^(3/2)*(A + B*x + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\frac{2 C \sqrt{c+d x} \sqrt{e+f x} (a+b x)^{5/2}}{7 b d f}+\frac{2 (7 b B d f-2 a C d f-6 b C (d e+c f)) \sqrt{c+d x} \sqrt{e+f x} (a+b x)^{3/2}}{35 b d^2 f^2}-\frac{2 (5 b d f (5 b c C e+a C d e+a c C f-7 A b d f)-(3 a d f-4 b (d e+c f)) (7 b B d f-2 a C d f-6 b C (d e+c f))) \sqrt{c+d x} \sqrt{e+f x} \sqrt{a+b x}}{105 b d^3 f^3}-\frac{2 \sqrt{a d-b c} \left(3 b d f (5 a d f (5 b c C e+a C d e+a c C f-7 A b d f)+(3 b c e+a d e+a c f) (7 b B d f-2 a C d f-6 b C (d e+c f)))+2 \left(\frac{a d f}{2}-b (d e+c f)\right) (5 b d f (5 b c C e+a C d e+a c C f-7 A b d f)-(3 a d f-4 b (d e+c f)) (7 b B d f-2 a C d f-6 b C (d e+c f)))\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^2 d^{7/2} f^4 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a d-b c} (b e-a f) \left(-\left(C \left(48 d^3 e^3+16 c d^2 f e^2+17 c^2 d f^2 e+24 c^3 f^3\right)+7 d f \left(5 A d f (2 d e+c f)-B \left(8 d^2 e^2+3 c d f e+4 c^2 f^2\right)\right)\right) b^2-3 a d f \left(7 d f (3 B d e+2 B c f-5 A d f)-C \left(16 d^2 e^2+8 c d f e+11 c^2 f^2\right)\right) b+3 a^2 C d^2 f^2 (d e-c f)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^2 d^{7/2} f^4 \sqrt{c+d x} \sqrt{e+f x}}","\frac{2 C \sqrt{c+d x} \sqrt{e+f x} (a+b x)^{5/2}}{7 b d f}-\frac{2 (2 a C d f-b (7 B d f-6 C (d e+c f))) \sqrt{c+d x} \sqrt{e+f x} (a+b x)^{3/2}}{35 b d^2 f^2}-\frac{2 (5 b d f (5 b c C e+a C d e+a c C f-7 A b d f)+(3 a d f-4 b (d e+c f)) (2 a C d f-b (7 B d f-6 C (d e+c f)))) \sqrt{c+d x} \sqrt{e+f x} \sqrt{a+b x}}{105 b d^3 f^3}-\frac{2 \sqrt{a d-b c} \left(3 b d f (5 a d f (5 b c C e+a C d e+a c C f-7 A b d f)-(3 b c e+a d e+a c f) (2 a C d f-b (7 B d f-6 C (d e+c f))))+2 \left(\frac{a d f}{2}-b (d e+c f)\right) (5 b d f (5 b c C e+a C d e+a c C f-7 A b d f)+(3 a d f-4 b (d e+c f)) (2 a C d f-b (7 B d f-6 C (d e+c f))))\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^2 d^{7/2} f^4 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a d-b c} (b e-a f) \left(-\left(C \left(48 d^3 e^3+16 c d^2 f e^2+17 c^2 d f^2 e+24 c^3 f^3\right)+7 d f \left(5 A d f (2 d e+c f)-B \left(8 d^2 e^2+3 c d f e+4 c^2 f^2\right)\right)\right) b^2-3 a d f \left(7 d f (3 B d e+2 B c f-5 A d f)-C \left(16 d^2 e^2+8 c d f e+11 c^2 f^2\right)\right) b+3 a^2 C d^2 f^2 (d e-c f)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{105 b^2 d^{7/2} f^4 \sqrt{c+d x} \sqrt{e+f x}}",1,"(-2*(5*b*d*f*(5*b*c*C*e + a*C*d*e + a*c*C*f - 7*A*b*d*f) - (3*a*d*f - 4*b*(d*e + c*f))*(7*b*B*d*f - 2*a*C*d*f - 6*b*C*(d*e + c*f)))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(105*b*d^3*f^3) + (2*(7*b*B*d*f - 2*a*C*d*f - 6*b*C*(d*e + c*f))*(a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x])/(35*b*d^2*f^2) + (2*C*(a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x])/(7*b*d*f) - (2*Sqrt[-(b*c) + a*d]*(3*b*d*f*(5*a*d*f*(5*b*c*C*e + a*C*d*e + a*c*C*f - 7*A*b*d*f) + (3*b*c*e + a*d*e + a*c*f)*(7*b*B*d*f - 2*a*C*d*f - 6*b*C*(d*e + c*f))) + 2*((a*d*f)/2 - b*(d*e + c*f))*(5*b*d*f*(5*b*c*C*e + a*C*d*e + a*c*C*f - 7*A*b*d*f) - (3*a*d*f - 4*b*(d*e + c*f))*(7*b*B*d*f - 2*a*C*d*f - 6*b*C*(d*e + c*f))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(105*b^2*d^(7/2)*f^4*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) - (2*Sqrt[-(b*c) + a*d]*(b*e - a*f)*(3*a^2*C*d^2*f^2*(d*e - c*f) - 3*a*b*d*f*(7*d*f*(3*B*d*e + 2*B*c*f - 5*A*d*f) - C*(16*d^2*e^2 + 8*c*d*e*f + 11*c^2*f^2)) - b^2*(C*(48*d^3*e^3 + 16*c*d^2*e^2*f + 17*c^2*d*e*f^2 + 24*c^3*f^3) + 7*d*f*(5*A*d*f*(2*d*e + c*f) - B*(8*d^2*e^2 + 3*c*d*e*f + 4*c^2*f^2))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(105*b^2*d^(7/2)*f^4*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,7,38,0.1842,1,"{1615, 154, 158, 114, 113, 121, 120}"
74,1,524,0,1.0275872,"\int \frac{\sqrt{a+b x} \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(Sqrt[a + b*x]*(A + B*x + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{2 \sqrt{a d-b c} (b e-a f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(a C d f (d e-c f)+5 b d f (3 A d f-B (c f+2 d e))+b C \left(4 c^2 f^2+3 c d e f+8 d^2 e^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^2 d^{5/2} f^3 \sqrt{c+d x} \sqrt{e+f x}}-\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} (3 b d f (a c C f+a C d e-5 A b d f+3 b c C e)-(a d f-2 b (c f+d e)) (-2 a C d f+5 b B d f-4 b C (c f+d e))) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^2 d^{5/2} f^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} (-2 a C d f+5 b B d f-4 b C (c f+d e))}{15 b d^2 f^2}+\frac{2 C (a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x}}{5 b d f}","-\frac{2 \sqrt{a d-b c} (b e-a f) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(a C d f (d e-c f)-b \left(5 d f (-3 A d f+B c f+2 B d e)-C \left(4 c^2 f^2+3 c d e f+8 d^2 e^2\right)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^2 d^{5/2} f^3 \sqrt{c+d x} \sqrt{e+f x}}-\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} (3 b d f (a c C f+a C d e-5 A b d f+3 b c C e)+(a d f-2 b (c f+d e)) (2 a C d f-b (5 B d f-4 C (c f+d e)))) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^2 d^{5/2} f^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} (2 a C d f-b (5 B d f-4 C (c f+d e)))}{15 b d^2 f^2}+\frac{2 C (a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x}}{5 b d f}",1,"(2*(5*b*B*d*f - 2*a*C*d*f - 4*b*C*(d*e + c*f))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(15*b*d^2*f^2) + (2*C*(a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x])/(5*b*d*f) - (2*Sqrt[-(b*c) + a*d]*(3*b*d*f*(3*b*c*C*e + a*C*d*e + a*c*C*f - 5*A*b*d*f) - (a*d*f - 2*b*(d*e + c*f))*(5*b*B*d*f - 2*a*C*d*f - 4*b*C*(d*e + c*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^2*d^(5/2)*f^3*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) - (2*Sqrt[-(b*c) + a*d]*(b*e - a*f)*(a*C*d*f*(d*e - c*f) + b*C*(8*d^2*e^2 + 3*c*d*e*f + 4*c^2*f^2) + 5*b*d*f*(3*A*d*f - B*(2*d*e + c*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^2*d^(5/2)*f^3*Sqrt[c + d*x]*Sqrt[e + f*x])","A",8,7,38,0.1842,1,"{1615, 154, 158, 114, 113, 121, 120}"
75,1,384,0,0.5052089,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{2 \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} (-a C f (d e-c f)+3 b d f (B e-A f)-b C e (c f+2 d e)) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^2 d^{3/2} f^2 \sqrt{c+d x} \sqrt{e+f x}}+\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} (-2 a C d f+3 b B d f-2 b C (c f+d e)) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^2 d^{3/2} f^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 C \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}}{3 b d f}","\frac{2 \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} (a C f (d e-c f)-b (3 d f (B e-A f)-C e (c f+2 d e))) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^2 d^{3/2} f^2 \sqrt{c+d x} \sqrt{e+f x}}-\frac{2 \sqrt{e+f x} \sqrt{a d-b c} \sqrt{\frac{b (c+d x)}{b c-a d}} (2 a C d f-b (3 B d f-2 C (c f+d e))) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^2 d^{3/2} f^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 C \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}}{3 b d f}",1,"(2*C*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x])/(3*b*d*f) + (2*Sqrt[-(b*c) + a*d]*(3*b*B*d*f - 2*a*C*d*f - 2*b*C*(d*e + c*f))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^2*d^(3/2)*f^2*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) - (2*Sqrt[-(b*c) + a*d]*(3*b*d*f*(B*e - A*f) - a*C*f*(d*e - c*f) - b*C*e*(2*d*e + c*f))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^2*d^(3/2)*f^2*Sqrt[c + d*x]*Sqrt[e + f*x])","A",7,6,38,0.1579,1,"{1615, 158, 114, 113, 121, 120}"
76,1,422,0,0.6910095,"\int \frac{A+B x+C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(A + B*x + C*x^2)/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{2 \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(2 a^2 C d f-a b (B d f+c C f+C d e)+b^2 (A d f+c C e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{b^2 \sqrt{d} f \sqrt{c+d x} \sqrt{a d-b c} (b e-a f) \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{b \sqrt{a+b x} (b c-a d) (b e-a f)}-\frac{2 \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} (a C (d e-c f)-b (A d f-B c f+c C e)) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{b^2 \sqrt{d} f \sqrt{c+d x} \sqrt{e+f x} \sqrt{a d-b c}}","-\frac{2 \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(2 a^2 C d f-a b (B d f+c C f+C d e)+b^2 (A d f+c C e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{b^2 \sqrt{d} f \sqrt{c+d x} \sqrt{a d-b c} (b e-a f) \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{b \sqrt{a+b x} (b c-a d) (b e-a f)}-\frac{2 \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} (a C (d e-c f)-b (A d f-B c f+c C e)) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{b^2 \sqrt{d} f \sqrt{c+d x} \sqrt{e+f x} \sqrt{a d-b c}}",1,"(-2*(A*b^2 - a*(b*B - a*C))*Sqrt[c + d*x]*Sqrt[e + f*x])/(b*(b*c - a*d)*(b*e - a*f)*Sqrt[a + b*x]) - (2*(2*a^2*C*d*f + b^2*(c*C*e + A*d*f) - a*b*(C*d*e + c*C*f + B*d*f))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(b^2*Sqrt[d]*Sqrt[-(b*c) + a*d]*f*(b*e - a*f)*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) - (2*(a*C*(d*e - c*f) - b*(c*C*e - B*c*f + A*d*f))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(b^2*Sqrt[d]*Sqrt[-(b*c) + a*d]*f*Sqrt[c + d*x]*Sqrt[e + f*x])","A",7,6,38,0.1579,1,"{1614, 158, 114, 113, 121, 120}"
77,1,642,0,1.5166555,"\int \frac{A+B x+C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(A + B*x + C*x^2)/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{2 \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(a^2 C d (d e-c f)+a b \left(3 f \left(A d^2+c^2 C\right)-B d (2 c f+d e)\right)-b^2 \left(A c d f+2 A d^2 e-3 B c d e+3 c^2 C e\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^2 \sqrt{d} \sqrt{c+d x} \sqrt{e+f x} (a d-b c)^{3/2} (b e-a f)}+\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(a^2 b (B d f-4 C (c f+d e))+2 a^3 C d f+a b^2 (-4 A d f+B c f+B d e+6 c C e)-b^3 (3 B c e-2 A (c f+d e))\right)}{3 b \sqrt{a+b x} (b c-a d)^2 (b e-a f)^2}-\frac{2 \sqrt{d} \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(a^2 b (B d f-4 C (c f+d e))+2 a^3 C d f+a b^2 (-4 A d f+B c f+B d e+6 c C e)-b^3 (3 B c e-2 A (c f+d e))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^2 \sqrt{c+d x} (a d-b c)^{3/2} (b e-a f)^2 \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{3 b (a+b x)^{3/2} (b c-a d) (b e-a f)}","-\frac{2 \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \left(a^2 C d (d e-c f)+a b \left(3 f \left(A d^2+c^2 C\right)-B d (2 c f+d e)\right)-b^2 \left(A c d f+2 A d^2 e-3 B c d e+3 c^2 C e\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^2 \sqrt{d} \sqrt{c+d x} \sqrt{e+f x} (a d-b c)^{3/2} (b e-a f)}+\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(a^2 b (B d f-4 C (c f+d e))+2 a^3 C d f+a b^2 (-4 A d f+B c f+B d e+6 c C e)-b^3 (3 B c e-2 A (c f+d e))\right)}{3 b \sqrt{a+b x} (b c-a d)^2 (b e-a f)^2}-\frac{2 \sqrt{d} \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(a^2 b (B d f-4 C (c f+d e))+2 a^3 C d f+a b^2 (-4 A d f+B c f+B d e+6 c C e)-b^3 (3 B c e-2 A (c f+d e))\right) E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{3 b^2 \sqrt{c+d x} (a d-b c)^{3/2} (b e-a f)^2 \sqrt{\frac{b (e+f x)}{b e-a f}}}-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{3 b (a+b x)^{3/2} (b c-a d) (b e-a f)}",1,"(-2*(A*b^2 - a*(b*B - a*C))*Sqrt[c + d*x]*Sqrt[e + f*x])/(3*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^(3/2)) + (2*(2*a^3*C*d*f + a*b^2*(6*c*C*e + B*d*e + B*c*f - 4*A*d*f) - b^3*(3*B*c*e - 2*A*(d*e + c*f)) + a^2*b*(B*d*f - 4*C*(d*e + c*f)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(3*b*(b*c - a*d)^2*(b*e - a*f)^2*Sqrt[a + b*x]) - (2*Sqrt[d]*(2*a^3*C*d*f + a*b^2*(6*c*C*e + B*d*e + B*c*f - 4*A*d*f) - b^3*(3*B*c*e - 2*A*(d*e + c*f)) + a^2*b*(B*d*f - 4*C*(d*e + c*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^2*(-(b*c) + a*d)^(3/2)*(b*e - a*f)^2*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) - (2*(a^2*C*d*(d*e - c*f) - b^2*(3*c^2*C*e - 3*B*c*d*e + 2*A*d^2*e + A*c*d*f) + a*b*(3*(c^2*C + A*d^2)*f - B*d*(d*e + 2*c*f)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(3*b^2*Sqrt[d]*(-(b*c) + a*d)^(3/2)*(b*e - a*f)*Sqrt[c + d*x]*Sqrt[e + f*x])","A",8,7,38,0.1842,1,"{1614, 152, 158, 114, 113, 121, 120}"
78,1,1116,0,3.3418617,"\int \frac{A+B x+C x^2}{(a+b x)^{7/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","Int[(A + B*x + C*x^2)/((a + b*x)^(7/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{2 \sqrt{d} \left(2 C d^2 f^2 a^4+b d f (3 B d f-7 C (d e+c f)) a^3-b^2 \left(C \left(3 d^2 e^2-13 c d f e+3 c^2 f^2\right)+d f (23 A d f-7 B (d e+c f))\right) a^2-b^3 \left(-2 f (5 C e-B f) c^2-d \left(10 C e^2-33 B f e+23 A f^2\right) c+d^2 e (2 B e-23 A f)\right) a-b^4 \left(\left(15 C e^2-10 B f e+8 A f^2\right) c^2-d e (10 B e-7 A f) c+8 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^2 (a d-b c)^{5/2} (b e-a f)^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \sqrt{d} \left(C d f (d e-c f) a^3-3 b \left(d f (2 B d e+3 B c f-5 A d f)-C \left(d^2 e^2+c d f e+3 c^2 f^2\right)\right) a^2+b^2 \left(-f (20 C e-B f) c^2-d \left(10 C e^2-27 B f e+11 A f^2\right) c+d^2 e (2 B e-19 A f)\right) a+b^3 \left(\left(15 C e^2-5 B f e+4 A f^2\right) c^2-d e (10 B e-3 A f) c+8 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^2 (a d-b c)^{5/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{e+f x}}+\frac{2 \left(2 C d^2 f^2 a^4+b d f (3 B d f-7 C (d e+c f)) a^3-b^2 \left(C \left(3 d^2 e^2-13 c d f e+3 c^2 f^2\right)+d f (23 A d f-7 B (d e+c f))\right) a^2-b^3 \left(-2 f (5 C e-B f) c^2-d \left(10 C e^2-33 B f e+23 A f^2\right) c+d^2 e (2 B e-23 A f)\right) a-b^4 \left(\left(15 C e^2-10 B f e+8 A f^2\right) c^2-d e (10 B e-7 A f) c+8 A d^2 e^2\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{15 b (b c-a d)^3 (b e-a f)^3 \sqrt{a+b x}}+\frac{2 \left(2 C d f a^3+3 b (B d f-2 C (d e+c f)) a^2+b^2 (10 c C e+B d e+B c f-8 A d f) a-b^3 (5 B c e-4 A (d e+c f))\right) \sqrt{c+d x} \sqrt{e+f x}}{15 b (b c-a d)^2 (b e-a f)^2 (a+b x)^{3/2}}","-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{2 \sqrt{d} \left(2 C d^2 f^2 a^4+b d f (3 B d f-7 C (d e+c f)) a^3-b^2 \left(C \left(3 d^2 e^2-13 c d f e+3 c^2 f^2\right)+d f (23 A d f-7 B (d e+c f))\right) a^2-b^3 \left(-2 f (5 C e-B f) c^2-d \left(10 C e^2-33 B f e+23 A f^2\right) c+d^2 e (2 B e-23 A f)\right) a-b^4 \left(\left(15 C e^2-10 B f e+8 A f^2\right) c^2-d e (10 B e-7 A f) c+8 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^2 (a d-b c)^{5/2} (b e-a f)^3 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \sqrt{d} \left(C d f (d e-c f) a^3-3 b \left(d f (2 B d e+3 B c f-5 A d f)-C \left(d^2 e^2+c d f e+3 c^2 f^2\right)\right) a^2+b^2 \left(-f (20 C e-B f) c^2-d \left(10 C e^2-27 B f e+11 A f^2\right) c+d^2 e (2 B e-19 A f)\right) a+b^3 \left(\left(15 C e^2-5 B f e+4 A f^2\right) c^2-d e (10 B e-3 A f) c+8 A d^2 e^2\right)\right) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left(\sin ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right)|\frac{(b c-a d) f}{d (b e-a f)}\right)}{15 b^2 (a d-b c)^{5/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{e+f x}}+\frac{2 \left(2 C d^2 f^2 a^4+b d f (3 B d f-7 C (d e+c f)) a^3-b^2 \left(C \left(3 d^2 e^2-13 c d f e+3 c^2 f^2\right)+d f (23 A d f-7 B (d e+c f))\right) a^2-b^3 \left(-2 f (5 C e-B f) c^2-d \left(10 C e^2-33 B f e+23 A f^2\right) c+d^2 e (2 B e-23 A f)\right) a-b^4 \left(\left(15 C e^2-10 B f e+8 A f^2\right) c^2-d e (10 B e-7 A f) c+8 A d^2 e^2\right)\right) \sqrt{c+d x} \sqrt{e+f x}}{15 b (b c-a d)^3 (b e-a f)^3 \sqrt{a+b x}}+\frac{2 \left(2 C d f a^3+3 b (B d f-2 C (d e+c f)) a^2+b^2 (10 c C e+B d e+B c f-8 A d f) a-b^3 (5 B c e-4 A (d e+c f))\right) \sqrt{c+d x} \sqrt{e+f x}}{15 b (b c-a d)^2 (b e-a f)^2 (a+b x)^{3/2}}",1,"(-2*(A*b^2 - a*(b*B - a*C))*Sqrt[c + d*x]*Sqrt[e + f*x])/(5*b*(b*c - a*d)*(b*e - a*f)*(a + b*x)^(5/2)) + (2*(2*a^3*C*d*f + a*b^2*(10*c*C*e + B*d*e + B*c*f - 8*A*d*f) - b^3*(5*B*c*e - 4*A*(d*e + c*f)) + 3*a^2*b*(B*d*f - 2*C*(d*e + c*f)))*Sqrt[c + d*x]*Sqrt[e + f*x])/(15*b*(b*c - a*d)^2*(b*e - a*f)^2*(a + b*x)^(3/2)) + (2*(2*a^4*C*d^2*f^2 + a^3*b*d*f*(3*B*d*f - 7*C*(d*e + c*f)) - b^4*(8*A*d^2*e^2 - c*d*e*(10*B*e - 7*A*f) + c^2*(15*C*e^2 - 10*B*e*f + 8*A*f^2)) - a*b^3*(d^2*e*(2*B*e - 23*A*f) - 2*c^2*f*(5*C*e - B*f) - c*d*(10*C*e^2 - 33*B*e*f + 23*A*f^2)) - a^2*b^2*(C*(3*d^2*e^2 - 13*c*d*e*f + 3*c^2*f^2) + d*f*(23*A*d*f - 7*B*(d*e + c*f))))*Sqrt[c + d*x]*Sqrt[e + f*x])/(15*b*(b*c - a*d)^3*(b*e - a*f)^3*Sqrt[a + b*x]) + (2*Sqrt[d]*(2*a^4*C*d^2*f^2 + a^3*b*d*f*(3*B*d*f - 7*C*(d*e + c*f)) - b^4*(8*A*d^2*e^2 - c*d*e*(10*B*e - 7*A*f) + c^2*(15*C*e^2 - 10*B*e*f + 8*A*f^2)) - a*b^3*(d^2*e*(2*B*e - 23*A*f) - 2*c^2*f*(5*C*e - B*f) - c*d*(10*C*e^2 - 33*B*e*f + 23*A*f^2)) - a^2*b^2*(C*(3*d^2*e^2 - 13*c*d*e*f + 3*c^2*f^2) + d*f*(23*A*d*f - 7*B*(d*e + c*f))))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[e + f*x]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^2*(-(b*c) + a*d)^(5/2)*(b*e - a*f)^3*Sqrt[c + d*x]*Sqrt[(b*(e + f*x))/(b*e - a*f)]) + (2*Sqrt[d]*(a^3*C*d*f*(d*e - c*f) + b^3*(8*A*d^2*e^2 - c*d*e*(10*B*e - 3*A*f) + c^2*(15*C*e^2 - 5*B*e*f + 4*A*f^2)) + a*b^2*(d^2*e*(2*B*e - 19*A*f) - c^2*f*(20*C*e - B*f) - c*d*(10*C*e^2 - 27*B*e*f + 11*A*f^2)) - 3*a^2*b*(d*f*(2*B*d*e + 3*B*c*f - 5*A*d*f) - C*(d^2*e^2 + c*d*e*f + 3*c^2*f^2)))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*Sqrt[(b*(e + f*x))/(b*e - a*f)]*EllipticF[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], ((b*c - a*d)*f)/(d*(b*e - a*f))])/(15*b^2*(-(b*c) + a*d)^(5/2)*(b*e - a*f)^2*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,7,38,0.1842,1,"{1614, 152, 158, 114, 113, 121, 120}"