1,-1,0,415,180.0594473,"\int \sqrt{1-d x} \sqrt{1+d x} (e+f x)^3 \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^3*(A + B*x + C*x^2),x]","\text{\$Aborted}","-\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{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{\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(3 d^4 e^4-30 d^2 e^2 f^2-8 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{\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,"$Aborted","F",-1
2,-1,0,286,180.0354369,"\int \sqrt{1-d x} \sqrt{1+d x} (e+f x)^2 \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^2*(A + B*x + C*x^2),x]","\text{\$Aborted}","\frac{\sin ^{-1}(d x) \left(2 d^2 \left(A \left(4 d^2 e^2+f^2\right)+2 B e f\right)+C \left(2 d^2 e^2+f^2\right)\right)}{16 d^5}+\frac{x \sqrt{1-d^2 x^2} \left(2 d^2 \left(A \left(4 d^2 e^2+f^2\right)+2 B e f\right)+C \left(2 d^2 e^2+f^2\right)\right)}{16 d^4}+\frac{\left(1-d^2 x^2\right)^{3/2} \left(8 \left(C \left(d^2 e^3-4 e f^2\right)-2 f \left(5 A d^2 e f+B \left(d^2 e^2+f^2\right)\right)\right)-3 f x \left(5 f^2 \left(2 A d^2+C\right)-2 d^2 e (C e-2 B f)\right)\right)}{120 d^4 f}+\frac{\left(1-d^2 x^2\right)^{3/2} (e+f x)^2 (C e-2 B f)}{10 d^2 f}-\frac{C \left(1-d^2 x^2\right)^{3/2} (e+f x)^3}{6 d^2 f}",1,"$Aborted","F",-1
3,-1,0,168,180.0230976,"\int \sqrt{1-d x} \sqrt{1+d x} (e+f x) \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)*(A + B*x + C*x^2),x]","\text{\$Aborted}","\frac{x \sqrt{1-d^2 x^2} \left(4 A d^2 e+B f+C e\right)}{8 d^2}-\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{\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,"$Aborted","F",-1
4,-1,0,95,180.0078433,"\int \sqrt{1-d x} \sqrt{1+d x} \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[1 - d*x]*Sqrt[1 + d*x]*(A + B*x + C*x^2),x]","\text{\$Aborted}","\frac{x \sqrt{1-d^2 x^2} \left(4 A d^2+C\right)}{8 d^2}+\frac{\left(4 A d^2+C\right) \sin ^{-1}(d x)}{8 d^3}-\frac{B \left(1-d^2 x^2\right)^{3/2}}{3 d^2}-\frac{C x \left(1-d^2 x^2\right)^{3/2}}{4 d^2}",1,"$Aborted","F",-1
5,-1,0,122,180.7216859,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
6,-1,0,163,182.3524248,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^2} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^2),x]","\text{\$Aborted}","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{f \left(d^2 e^2-f^2\right) (e+f x)}-\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(-A d^2 e f^2+B f^3+C d^2 e^3-2 C e f^2\right)}{f^2 \left(d^2 e^2-f^2\right)^{3/2}}+\frac{C \sin ^{-1}(d x)}{d f^2}",1,"$Aborted","F",-1
7,-1,0,248,180.0295712,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^3} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^3),x]","\text{\$Aborted}","\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{\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(-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)}",1,"$Aborted","F",-1
8,-1,0,340,180.0572609,"\int \frac{(e+f x)^3 \left(A+B x+C x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[((e + f*x)^3*(A + B*x + C*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","-\frac{\sqrt{1-d^2 x^2} (e+f x)^2 \left(4 f^2 \left(5 A d^2+4 C\right)-3 d^2 e (C e-5 B f)\right)}{60 d^4 f}+\frac{\sqrt{1-d^2 x^2} \left(d^2 f x \left(-100 A d^2 e f^2-30 B d^2 e^2 f-45 B f^3+6 C d^2 e^3-71 C e f^2\right)+4 \left(C \left(3 d^4 e^4-52 d^2 e^2 f^2-16 f^4\right)-5 d^2 f \left(4 A f \left(4 d^2 e^2+f^2\right)+3 B \left(d^2 e^3+4 e f^2\right)\right)\right)\right)}{120 d^6 f}+\frac{\sin ^{-1}(d x) \left(8 A d^4 e^3+12 A d^2 e f^2+12 B d^2 e^2 f+3 B f^3+4 C d^2 e^3+9 C e f^2\right)}{8 d^5}+\frac{\sqrt{1-d^2 x^2} (e+f x)^3 (C e-5 B f)}{20 d^2 f}-\frac{C \sqrt{1-d^2 x^2} (e+f x)^4}{5 d^2 f}",1,"$Aborted","F",-1
9,-1,0,228,180.0196189,"\int \frac{(e+f x)^2 \left(A+B x+C x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[((e + f*x)^2*(A + B*x + C*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","\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} \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{\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,"$Aborted","F",-1
10,-1,0,130,180.0088573,"\int \frac{(e+f x) \left(A+B x+C x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[((e + f*x)*(A + B*x + C*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","-\frac{\sqrt{1-d^2 x^2} \left(2 \left(3 d^2 f (A f+B e)-C \left(d^2 e^2-2 f^2\right)\right)-d^2 f x (C e-3 B f)\right)}{6 d^4 f}+\frac{\sin ^{-1}(d x) \left(2 A d^2 e+B f+C e\right)}{2 d^3}-\frac{C \sqrt{1-d^2 x^2} (e+f x)^2}{3 d^2 f}",1,"$Aborted","F",-1
11,1,1107,63,5.9124474,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\frac{\left(\frac{2 B \sqrt{1-d x}}{d^2}-\frac{2 B \sqrt{1-d}}{d^2}\right) \left(\sqrt{d+1}-\sqrt{d x+1}\right) \left(x d^2+d^2+\sqrt{1-d} \sqrt{1-d x} d-\sqrt{d+1} \sqrt{d x+1} d+\sqrt{1-d} \sqrt{d+1} \sqrt{1-d^2}-\sqrt{d+1} \sqrt{1-d^2} \sqrt{1-d x}-\sqrt{1-d} \sqrt{1-d^2} \sqrt{d x+1}+\sqrt{1-d^2} \sqrt{1-d x} \sqrt{d x+1}\right)}{\left(\sqrt{1-d} \sqrt{1-d x}+\sqrt{d+1} \sqrt{d x+1}-2\right)^2}+\frac{\left(\frac{2 C \sqrt{1-d x}}{d^3}-\frac{2 C \sqrt{1-d}}{d^3}\right) \left(\sqrt{d+1}-\sqrt{d x+1}\right) \left(x d+d+\sqrt{1-d} \sqrt{1-d x}-\sqrt{d+1} \sqrt{d x+1}\right) \left(2 x^2 d^4+6 x d^4+2 d^4+4 \sqrt{1-d} x \sqrt{1-d x} d^3+4 \sqrt{1-d} \sqrt{1-d x} d^3-4 \sqrt{d+1} x \sqrt{d x+1} d^3-4 \sqrt{d+1} \sqrt{d x+1} d^3-x^2 d^2+6 \sqrt{1-d} \sqrt{d+1} \sqrt{1-d^2} x d^2-3 x d^2+2 \sqrt{1-d} \sqrt{d+1} \sqrt{1-d^2} d^2-4 \sqrt{d+1} \sqrt{1-d^2} x \sqrt{1-d x} d^2+4 \sqrt{1-d} \sqrt{1-d x} d^2-4 \sqrt{d+1} \sqrt{1-d^2} \sqrt{1-d x} d^2-4 \sqrt{1-d} \sqrt{1-d^2} x \sqrt{d x+1} d^2+4 \sqrt{d+1} \sqrt{d x+1} d^2-4 \sqrt{1-d} \sqrt{1-d^2} \sqrt{d x+1} d^2+2 \sqrt{1-d^2} x \sqrt{1-d x} \sqrt{d x+1} d^2-6 \sqrt{1-d} \sqrt{d+1} \sqrt{1-d x} \sqrt{d x+1} d^2+6 \sqrt{1-d^2} \sqrt{1-d x} \sqrt{d x+1} d^2-3 d^2-2 \sqrt{1-d} x \sqrt{1-d x} d-2 \sqrt{1-d} \sqrt{1-d x} d+2 \sqrt{d+1} x \sqrt{d x+1} d+2 \sqrt{d+1} \sqrt{d x+1} d-2 \sqrt{1-d} \sqrt{1-d x}-2 \sqrt{d+1} \sqrt{d x+1}+3 \sqrt{1-d} \sqrt{d+1} \sqrt{1-d x} \sqrt{d x+1}+1\right)}{\left(\sqrt{1-d} \sqrt{1-d x}+\sqrt{d+1} \sqrt{d x+1}-2\right)^4}+\left(-\frac{4 A}{d}-\frac{2 C}{d^3}\right) \tan ^{-1}\left(\frac{\sqrt{1-d}-\sqrt{1-d x}}{\sqrt{d+1}-\sqrt{d x+1}}\right)","\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,"(((-2*B*Sqrt[1 - d])/d^2 + (2*B*Sqrt[1 - d*x])/d^2)*(Sqrt[1 + d] - Sqrt[1 + d*x])*(d^2 + Sqrt[1 - d]*Sqrt[1 + d]*Sqrt[1 - d^2] + d^2*x + Sqrt[1 - d]*d*Sqrt[1 - d*x] - Sqrt[1 + d]*Sqrt[1 - d^2]*Sqrt[1 - d*x] - d*Sqrt[1 + d]*Sqrt[1 + d*x] - Sqrt[1 - d]*Sqrt[1 - d^2]*Sqrt[1 + d*x] + Sqrt[1 - d^2]*Sqrt[1 - d*x]*Sqrt[1 + d*x]))/(-2 + Sqrt[1 - d]*Sqrt[1 - d*x] + Sqrt[1 + d]*Sqrt[1 + d*x])^2 + (((-2*C*Sqrt[1 - d])/d^3 + (2*C*Sqrt[1 - d*x])/d^3)*(Sqrt[1 + d] - Sqrt[1 + d*x])*(d + d*x + Sqrt[1 - d]*Sqrt[1 - d*x] - Sqrt[1 + d]*Sqrt[1 + d*x])*(1 - 3*d^2 + 2*d^4 + 2*Sqrt[1 - d]*d^2*Sqrt[1 + d]*Sqrt[1 - d^2] - 3*d^2*x + 6*d^4*x + 6*Sqrt[1 - d]*d^2*Sqrt[1 + d]*Sqrt[1 - d^2]*x - d^2*x^2 + 2*d^4*x^2 - 2*Sqrt[1 - d]*Sqrt[1 - d*x] - 2*Sqrt[1 - d]*d*Sqrt[1 - d*x] + 4*Sqrt[1 - d]*d^2*Sqrt[1 - d*x] + 4*Sqrt[1 - d]*d^3*Sqrt[1 - d*x] - 4*d^2*Sqrt[1 + d]*Sqrt[1 - d^2]*Sqrt[1 - d*x] - 2*Sqrt[1 - d]*d*x*Sqrt[1 - d*x] + 4*Sqrt[1 - d]*d^3*x*Sqrt[1 - d*x] - 4*d^2*Sqrt[1 + d]*Sqrt[1 - d^2]*x*Sqrt[1 - d*x] - 2*Sqrt[1 + d]*Sqrt[1 + d*x] + 2*d*Sqrt[1 + d]*Sqrt[1 + d*x] + 4*d^2*Sqrt[1 + d]*Sqrt[1 + d*x] - 4*d^3*Sqrt[1 + d]*Sqrt[1 + d*x] - 4*Sqrt[1 - d]*d^2*Sqrt[1 - d^2]*Sqrt[1 + d*x] + 2*d*Sqrt[1 + d]*x*Sqrt[1 + d*x] - 4*d^3*Sqrt[1 + d]*x*Sqrt[1 + d*x] - 4*Sqrt[1 - d]*d^2*Sqrt[1 - d^2]*x*Sqrt[1 + d*x] + 3*Sqrt[1 - d]*Sqrt[1 + d]*Sqrt[1 - d*x]*Sqrt[1 + d*x] - 6*Sqrt[1 - d]*d^2*Sqrt[1 + d]*Sqrt[1 - d*x]*Sqrt[1 + d*x] + 6*d^2*Sqrt[1 - d^2]*Sqrt[1 - d*x]*Sqrt[1 + d*x] + 2*d^2*Sqrt[1 - d^2]*x*Sqrt[1 - d*x]*Sqrt[1 + d*x]))/(-2 + Sqrt[1 - d]*Sqrt[1 - d*x] + Sqrt[1 + d]*Sqrt[1 + d*x])^4 + ((-2*C)/d^3 - (4*A)/d)*ArcTan[(Sqrt[1 - d] - Sqrt[1 - d*x])/(Sqrt[1 + d] - Sqrt[1 + d*x])]","B",0
12,-1,0,122,180.0161481,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
13,-1,0,163,180.034515,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^2} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^2),x]","\text{\$Aborted}","\frac{\sqrt{1-d^2 x^2} \left(A f^2-B e f+C e^2\right)}{f \left(d^2 e^2-f^2\right) (e+f x)}-\frac{\tan ^{-1}\left(\frac{d^2 e x+f}{\sqrt{1-d^2 x^2} \sqrt{d^2 e^2-f^2}}\right) \left(-A d^2 e f^2+B f^3+C d^2 e^3-2 C e f^2\right)}{f^2 \left(d^2 e^2-f^2\right)^{3/2}}+\frac{C \sin ^{-1}(d x)}{d f^2}",1,"$Aborted","F",-1
14,-1,0,248,180.0337059,"\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^3} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]*(e + f*x)^3),x]","\text{\$Aborted}","\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{\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(-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)}",1,"$Aborted","F",-1
15,-1,0,79,180.0162435,"\int \frac{x \left(a+b x+c x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(x*(a + b*x + c*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","-\frac{\sqrt{1-d^2 x^2} \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4}+\frac{b \sin ^{-1}(d x)}{2 d^3}-\frac{c x^2 \sqrt{1-d^2 x^2}}{3 d^2}",1,"$Aborted","F",-1
16,1,1107,63,0.0007357,"\int \frac{a+b x+c x^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\frac{\left(\frac{2 b \sqrt{1-d x}}{d^2}-\frac{2 b \sqrt{1-d}}{d^2}\right) \left(\sqrt{d+1}-\sqrt{d x+1}\right) \left(x d^2+d^2+\sqrt{1-d} \sqrt{1-d x} d-\sqrt{d+1} \sqrt{d x+1} d+\sqrt{1-d} \sqrt{d+1} \sqrt{1-d^2}-\sqrt{d+1} \sqrt{1-d^2} \sqrt{1-d x}-\sqrt{1-d} \sqrt{1-d^2} \sqrt{d x+1}+\sqrt{1-d^2} \sqrt{1-d x} \sqrt{d x+1}\right)}{\left(\sqrt{1-d} \sqrt{1-d x}+\sqrt{d+1} \sqrt{d x+1}-2\right)^2}+\frac{\left(\frac{2 c \sqrt{1-d x}}{d^3}-\frac{2 c \sqrt{1-d}}{d^3}\right) \left(\sqrt{d+1}-\sqrt{d x+1}\right) \left(x d+d+\sqrt{1-d} \sqrt{1-d x}-\sqrt{d+1} \sqrt{d x+1}\right) \left(2 x^2 d^4+6 x d^4+2 d^4+4 \sqrt{1-d} x \sqrt{1-d x} d^3+4 \sqrt{1-d} \sqrt{1-d x} d^3-4 \sqrt{d+1} x \sqrt{d x+1} d^3-4 \sqrt{d+1} \sqrt{d x+1} d^3-x^2 d^2+6 \sqrt{1-d} \sqrt{d+1} \sqrt{1-d^2} x d^2-3 x d^2+2 \sqrt{1-d} \sqrt{d+1} \sqrt{1-d^2} d^2-4 \sqrt{d+1} \sqrt{1-d^2} x \sqrt{1-d x} d^2+4 \sqrt{1-d} \sqrt{1-d x} d^2-4 \sqrt{d+1} \sqrt{1-d^2} \sqrt{1-d x} d^2-4 \sqrt{1-d} \sqrt{1-d^2} x \sqrt{d x+1} d^2+4 \sqrt{d+1} \sqrt{d x+1} d^2-4 \sqrt{1-d} \sqrt{1-d^2} \sqrt{d x+1} d^2+2 \sqrt{1-d^2} x \sqrt{1-d x} \sqrt{d x+1} d^2-6 \sqrt{1-d} \sqrt{d+1} \sqrt{1-d x} \sqrt{d x+1} d^2+6 \sqrt{1-d^2} \sqrt{1-d x} \sqrt{d x+1} d^2-3 d^2-2 \sqrt{1-d} x \sqrt{1-d x} d-2 \sqrt{1-d} \sqrt{1-d x} d+2 \sqrt{d+1} x \sqrt{d x+1} d+2 \sqrt{d+1} \sqrt{d x+1} d-2 \sqrt{1-d} \sqrt{1-d x}-2 \sqrt{d+1} \sqrt{d x+1}+3 \sqrt{1-d} \sqrt{d+1} \sqrt{1-d x} \sqrt{d x+1}+1\right)}{\left(\sqrt{1-d} \sqrt{1-d x}+\sqrt{d+1} \sqrt{d x+1}-2\right)^4}+\left(-\frac{4 a}{d}-\frac{2 c}{d^3}\right) \tan ^{-1}\left(\frac{\sqrt{1-d}-\sqrt{1-d x}}{\sqrt{d+1}-\sqrt{d x+1}}\right)","\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,"(((-2*b*Sqrt[1 - d])/d^2 + (2*b*Sqrt[1 - d*x])/d^2)*(Sqrt[1 + d] - Sqrt[1 + d*x])*(d^2 + Sqrt[1 - d]*Sqrt[1 + d]*Sqrt[1 - d^2] + d^2*x + Sqrt[1 - d]*d*Sqrt[1 - d*x] - Sqrt[1 + d]*Sqrt[1 - d^2]*Sqrt[1 - d*x] - d*Sqrt[1 + d]*Sqrt[1 + d*x] - Sqrt[1 - d]*Sqrt[1 - d^2]*Sqrt[1 + d*x] + Sqrt[1 - d^2]*Sqrt[1 - d*x]*Sqrt[1 + d*x]))/(-2 + Sqrt[1 - d]*Sqrt[1 - d*x] + Sqrt[1 + d]*Sqrt[1 + d*x])^2 + (((-2*c*Sqrt[1 - d])/d^3 + (2*c*Sqrt[1 - d*x])/d^3)*(Sqrt[1 + d] - Sqrt[1 + d*x])*(d + d*x + Sqrt[1 - d]*Sqrt[1 - d*x] - Sqrt[1 + d]*Sqrt[1 + d*x])*(1 - 3*d^2 + 2*d^4 + 2*Sqrt[1 - d]*d^2*Sqrt[1 + d]*Sqrt[1 - d^2] - 3*d^2*x + 6*d^4*x + 6*Sqrt[1 - d]*d^2*Sqrt[1 + d]*Sqrt[1 - d^2]*x - d^2*x^2 + 2*d^4*x^2 - 2*Sqrt[1 - d]*Sqrt[1 - d*x] - 2*Sqrt[1 - d]*d*Sqrt[1 - d*x] + 4*Sqrt[1 - d]*d^2*Sqrt[1 - d*x] + 4*Sqrt[1 - d]*d^3*Sqrt[1 - d*x] - 4*d^2*Sqrt[1 + d]*Sqrt[1 - d^2]*Sqrt[1 - d*x] - 2*Sqrt[1 - d]*d*x*Sqrt[1 - d*x] + 4*Sqrt[1 - d]*d^3*x*Sqrt[1 - d*x] - 4*d^2*Sqrt[1 + d]*Sqrt[1 - d^2]*x*Sqrt[1 - d*x] - 2*Sqrt[1 + d]*Sqrt[1 + d*x] + 2*d*Sqrt[1 + d]*Sqrt[1 + d*x] + 4*d^2*Sqrt[1 + d]*Sqrt[1 + d*x] - 4*d^3*Sqrt[1 + d]*Sqrt[1 + d*x] - 4*Sqrt[1 - d]*d^2*Sqrt[1 - d^2]*Sqrt[1 + d*x] + 2*d*Sqrt[1 + d]*x*Sqrt[1 + d*x] - 4*d^3*Sqrt[1 + d]*x*Sqrt[1 + d*x] - 4*Sqrt[1 - d]*d^2*Sqrt[1 - d^2]*x*Sqrt[1 + d*x] + 3*Sqrt[1 - d]*Sqrt[1 + d]*Sqrt[1 - d*x]*Sqrt[1 + d*x] - 6*Sqrt[1 - d]*d^2*Sqrt[1 + d]*Sqrt[1 - d*x]*Sqrt[1 + d*x] + 6*d^2*Sqrt[1 - d^2]*Sqrt[1 - d*x]*Sqrt[1 + d*x] + 2*d^2*Sqrt[1 - d^2]*x*Sqrt[1 - d*x]*Sqrt[1 + d*x]))/(-2 + Sqrt[1 - d]*Sqrt[1 - d*x] + Sqrt[1 + d]*Sqrt[1 + d*x])^4 + ((-2*c)/d^3 - (4*a)/d)*ArcTan[(Sqrt[1 - d] - Sqrt[1 - d*x])/(Sqrt[1 + d] - Sqrt[1 + d*x])]","B",0
17,-1,0,48,181.9468212,"\int \frac{a+b x+c x^2}{x \sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","-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,"$Aborted","F",-1
18,-1,0,48,180.0115843,"\int \frac{a+b x+c x^2}{x^2 \sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x^2*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","-\frac{a \sqrt{1-d^2 x^2}}{x}-b \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)+\frac{c \sin ^{-1}(d x)}{d}",1,"$Aborted","F",-1
19,-1,0,71,182.3990863,"\int \frac{a+b x+c x^2}{x^3 \sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x^3*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
20,-1,0,591,180.0670564,"\int \sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^3 \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^3*(A + B*x + C*x^2),x]","\text{\$Aborted}","-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^2 \sqrt{a c-b c x} \left(8 a^2 C f^2-b^2 \left(3 C e^2-7 f (2 A f+B e)\right)\right)}{70 b^4 f}+\frac{x \sqrt{a+b x} \sqrt{a c-b c x} \left(A \left(6 a^2 b^2 e f^2+8 b^4 e^3\right)+a^2 \left(a^2 f^2 (B f+3 C e)+2 b^2 e^2 (3 B f+C e)\right)\right)}{16 b^4}+\frac{a^2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(A \left(6 a^2 b^2 e f^2+8 b^4 e^3\right)+a^2 \left(a^2 f^2 (B f+3 C e)+2 b^2 e^2 (3 B f+C e)\right)\right)}{16 b^5 \sqrt{a^2 c-b^2 c x^2}}+\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^3 \sqrt{a c-b c x} (3 C e-7 B f)}{42 b^2 f}-\frac{C \sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^4 \sqrt{a c-b c x}}{7 b^2 f}-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x} \left(3 b^2 f x \left(a^2 f^2 (35 B f+41 C e)-2 b^2 e \left(3 C e^2-7 f (7 A f+B e)\right)\right)+8 \left(8 a^4 C f^4+2 a^2 b^2 f^2 \left(7 f (A f+3 B e)+15 C e^2\right)+b^4 \left(-e^2\right) \left(3 C e^2-7 f (12 A f+B e)\right)\right)\right)}{840 b^6 f}",1,"$Aborted","F",-1
21,-1,0,451,180.1255483,"\int \sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^2 \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2*(A + B*x + C*x^2),x]","\text{\$Aborted}","-\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{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{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{\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,"$Aborted","F",-1
22,-1,0,300,180.0132714,"\int \sqrt{a+b x} \sqrt{a c-b c x} (e+f x) \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)*(A + B*x + C*x^2),x]","\text{\$Aborted}","\frac{x \sqrt{a+b x} \sqrt{a c-b c x} \left(a^2 (B f+C e)+4 A b^2 e\right)}{8 b^2}-\frac{\sqrt{a+b x} \left(a^2-b^2 x^2\right) \sqrt{a c-b c x} \left(4 \left(2 a^2 C f^2-b^2 \left(3 C e^2-5 f (A f+B e)\right)\right)-3 b^2 f x (3 C e-5 B f)\right)}{60 b^4 f}+\frac{a^2 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(a^2 (B f+C e)+4 A b^2 e\right)}{8 b^3 \sqrt{a^2 c-b^2 c x^2}}-\frac{C \sqrt{a+b x} \left(a^2-b^2 x^2\right) (e+f x)^2 \sqrt{a c-b c x}}{5 b^2 f}",1,"$Aborted","F",-1
23,1,4771,221,63.1532193,"\int \sqrt{a+b x} \sqrt{a c-b c x} \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(A + B*x + C*x^2),x]","\text{Result too large to show}","\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{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{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,"(-(c*Sqrt[a*c - b*c]*Sqrt[a + b*x]*(12288*a^8*A*b^2 + 6528*a^7*A*b^3 - 7488*a^6*A*b^4 - 1632*a^5*A*b^5 + 96*a^4*A*b^6 - 16384*a^10*B - 8192*a^9*b*B + 14336*a^8*b^2*B + 5504*a^7*b^3*B - 5056*a^6*b^4*B - 1088*a^5*b^5*B + 64*a^4*b^6*B - 3072*a^10*C - 1632*a^9*b*C + 8016*a^8*b^2*C + 3672*a^7*b^3*C - 3768*a^6*b^4*C - 816*a^5*b^5*C + 48*a^4*b^6*C + 12288*a^8*A*b^2*x + 7488*a^6*A*b^4*x + 11712*a^5*A*b^5*x - 3552*a^4*A*b^6*x - 384*a^3*A*b^7*x + 8192*a^9*b*B*x - 12288*a^8*b^2*B*x - 14976*a^7*b^3*B*x + 8704*a^6*b^4*B*x + 8128*a^5*b^5*B*x - 2368*a^4*b^6*B*x - 256*a^3*b^7*B*x - 3072*a^10*C*x - 1872*a^8*b^2*C*x - 5808*a^7*b^3*C*x + 5496*a^6*b^4*C*x + 6000*a^5*b^5*C*x - 1776*a^4*b^6*C*x - 192*a^3*b^7*C*x - 6528*a^7*A*b^3*x^2 + 7488*a^6*A*b^4*x^2 + 3456*a^4*A*b^6*x^2 + 6528*a^3*A*b^7*x^2 - 384*a^2*A*b^8*x^2 + 14336*a^8*b^2*B*x^2 + 14976*a^7*b^3*B*x^2 - 7296*a^6*b^4*B*x^2 - 8192*a^5*b^5*B*x^2 + 2752*a^4*b^6*B*x^2 + 4352*a^3*b^7*B*x^2 - 256*a^2*b^8*B*x^2 + 1632*a^9*b*C*x^2 - 1872*a^8*b^2*C*x^2 - 1728*a^6*b^4*C*x^2 - 4080*a^5*b^5*C*x^2 + 1968*a^4*b^6*C*x^2 + 3264*a^3*b^7*C*x^2 - 192*a^2*b^8*C*x^2 - 7488*a^6*A*b^4*x^3 - 11712*a^5*A*b^5*x^3 + 3456*a^4*A*b^6*x^3 + 384*a^2*A*b^8*x^3 + 768*a*A*b^9*x^3 - 5504*a^7*b^3*B*x^3 + 8704*a^6*b^4*B*x^3 + 8192*a^5*b^5*B*x^3 - 896*a^4*b^6*B*x^3 - 1024*a^3*b^7*B*x^3 + 256*a^2*b^8*B*x^3 + 512*a*b^9*B*x^3 + 8016*a^8*b^2*C*x^3 + 5808*a^7*b^3*C*x^3 - 1728*a^6*b^4*C*x^3 - 240*a^4*b^6*C*x^3 - 576*a^3*b^7*C*x^3 + 192*a^2*b^8*C*x^3 + 384*a*b^9*C*x^3 + 1632*a^5*A*b^5*x^4 - 3552*a^4*A*b^6*x^4 - 6528*a^3*A*b^7*x^4 + 384*a^2*A*b^8*x^4 - 5056*a^6*b^4*B*x^4 - 8128*a^5*b^5*B*x^4 + 2752*a^4*b^6*B*x^4 + 1024*a^3*b^7*B*x^4 - 3672*a^7*b^3*C*x^4 + 5496*a^6*b^4*C*x^4 + 4080*a^5*b^5*C*x^4 - 240*a^4*b^6*C*x^4 + 96*a^4*A*b^6*x^5 + 384*a^3*A*b^7*x^5 - 384*a^2*A*b^8*x^5 - 768*a*A*b^9*x^5 + 1088*a^5*b^5*B*x^5 - 2368*a^4*b^6*B*x^5 - 4352*a^3*b^7*B*x^5 + 256*a^2*b^8*B*x^5 - 3768*a^6*b^4*C*x^5 - 6000*a^5*b^5*C*x^5 + 1968*a^4*b^6*C*x^5 + 576*a^3*b^7*C*x^5 + 64*a^4*b^6*B*x^6 + 256*a^3*b^7*B*x^6 - 256*a^2*b^8*B*x^6 - 512*a*b^9*B*x^6 + 816*a^5*b^5*C*x^6 - 1776*a^4*b^6*C*x^6 - 3264*a^3*b^7*C*x^6 + 192*a^2*b^8*C*x^6 + 48*a^4*b^6*C*x^7 + 192*a^3*b^7*C*x^7 - 192*a^2*b^8*C*x^7 - 384*a*b^9*C*x^7)) - c*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(-12192*a^8*A*b^2 + 12912*a^6*A*b^4 - 720*a^4*A*b^6 + 16384*a^10*B - 20384*a^8*b^2*B + 9096*a^6*b^4*B - 480*a^4*b^6*B + 3048*a^10*C - 9324*a^8*b^2*C + 6636*a^6*b^4*C - 360*a^4*b^6*C - 12384*a^8*A*b^2*x - 5472*a^6*A*b^4*x + 10980*a^4*A*b^6*x - 48*a^2*A*b^8*x + 16384*a^8*b^2*B*x - 16064*a^6*b^4*B*x + 7360*a^4*b^6*B*x - 32*a^2*b^8*B*x + 3096*a^10*C*x + 1368*a^8*b^2*C*x - 8217*a^6*b^4*C*x + 5508*a^4*b^6*C*x - 24*a^2*b^8*C*x - 12912*a^6*A*b^4*x^2 - 1440*a^4*A*b^6*x^2 + 2880*a^2*A*b^8*x^2 - 12384*a^8*b^2*B*x^2 + 13872*a^6*b^4*B*x^2 - 4392*a^4*b^6*B*x^2 + 1920*a^2*b^8*B*x^2 + 3228*a^8*b^2*C*x^2 + 720*a^6*b^4*C*x^2 - 2520*a^4*b^6*C*x^2 + 1440*a^2*b^8*C*x^2 + 5472*a^6*A*b^4*x^3 - 10968*a^4*A*b^6*x^3 - 48*a^2*A*b^8*x^3 + 96*A*b^10*x^3 - 10560*a^6*b^4*B*x^3 + 3488*a^4*b^6*B*x^3 - 160*a^2*b^8*B*x^3 + 64*b^10*B*x^3 - 7560*a^8*b^2*C*x^3 + 5478*a^6*b^4*C*x^3 + 30*a^4*b^6*C*x^3 - 96*a^2*b^8*C*x^3 + 48*b^10*C*x^3 + 2160*a^4*A*b^6*x^4 - 2880*a^2*A*b^8*x^4 + 3656*a^6*b^4*B*x^4 - 7408*a^4*b^6*B*x^4 + 128*a^2*b^8*B*x^4 - 7356*a^6*b^4*C*x^4 + 1800*a^4*b^6*C*x^4 - 12*a^4*A*b^6*x^5 + 96*a^2*A*b^8*x^5 - 96*A*b^10*x^5 + 1440*a^4*b^6*B*x^5 - 1920*a^2*b^8*B*x^5 + 2739*a^6*b^4*C*x^5 - 5532*a^4*b^6*C*x^5 + 72*a^2*b^8*C*x^5 - 8*a^4*b^6*B*x^6 + 64*a^2*b^8*B*x^6 - 64*b^10*B*x^6 + 1080*a^4*b^6*C*x^6 - 1440*a^2*b^8*C*x^6 - 6*a^4*b^6*C*x^7 + 48*a^2*b^8*C*x^7 - 48*b^10*C*x^7) + Sqrt[a + b]*(-(c*Sqrt[a*c - b*c*x]*(12288*a^8*A*b^2 - 6528*a^7*A*b^3 - 7488*a^6*A*b^4 + 1632*a^5*A*b^5 + 96*a^4*A*b^6 - 16384*a^10*B + 8192*a^9*b*B + 14336*a^8*b^2*B - 5504*a^7*b^3*B - 5056*a^6*b^4*B + 1088*a^5*b^5*B + 64*a^4*b^6*B - 3072*a^10*C + 1632*a^9*b*C + 8016*a^8*b^2*C - 3672*a^7*b^3*C - 3768*a^6*b^4*C + 816*a^5*b^5*C + 48*a^4*b^6*C + 12288*a^8*A*b^2*x + 7488*a^6*A*b^4*x - 11712*a^5*A*b^5*x - 3552*a^4*A*b^6*x + 384*a^3*A*b^7*x - 8192*a^9*b*B*x - 12288*a^8*b^2*B*x + 14976*a^7*b^3*B*x + 8704*a^6*b^4*B*x - 8128*a^5*b^5*B*x - 2368*a^4*b^6*B*x + 256*a^3*b^7*B*x - 3072*a^10*C*x - 1872*a^8*b^2*C*x + 5808*a^7*b^3*C*x + 5496*a^6*b^4*C*x - 6000*a^5*b^5*C*x - 1776*a^4*b^6*C*x + 192*a^3*b^7*C*x + 6528*a^7*A*b^3*x^2 + 7488*a^6*A*b^4*x^2 + 3456*a^4*A*b^6*x^2 - 6528*a^3*A*b^7*x^2 - 384*a^2*A*b^8*x^2 + 14336*a^8*b^2*B*x^2 - 14976*a^7*b^3*B*x^2 - 7296*a^6*b^4*B*x^2 + 8192*a^5*b^5*B*x^2 + 2752*a^4*b^6*B*x^2 - 4352*a^3*b^7*B*x^2 - 256*a^2*b^8*B*x^2 - 1632*a^9*b*C*x^2 - 1872*a^8*b^2*C*x^2 - 1728*a^6*b^4*C*x^2 + 4080*a^5*b^5*C*x^2 + 1968*a^4*b^6*C*x^2 - 3264*a^3*b^7*C*x^2 - 192*a^2*b^8*C*x^2 - 7488*a^6*A*b^4*x^3 + 11712*a^5*A*b^5*x^3 + 3456*a^4*A*b^6*x^3 + 384*a^2*A*b^8*x^3 - 768*a*A*b^9*x^3 + 5504*a^7*b^3*B*x^3 + 8704*a^6*b^4*B*x^3 - 8192*a^5*b^5*B*x^3 - 896*a^4*b^6*B*x^3 + 1024*a^3*b^7*B*x^3 + 256*a^2*b^8*B*x^3 - 512*a*b^9*B*x^3 + 8016*a^8*b^2*C*x^3 - 5808*a^7*b^3*C*x^3 - 1728*a^6*b^4*C*x^3 - 240*a^4*b^6*C*x^3 + 576*a^3*b^7*C*x^3 + 192*a^2*b^8*C*x^3 - 384*a*b^9*C*x^3 - 1632*a^5*A*b^5*x^4 - 3552*a^4*A*b^6*x^4 + 6528*a^3*A*b^7*x^4 + 384*a^2*A*b^8*x^4 - 5056*a^6*b^4*B*x^4 + 8128*a^5*b^5*B*x^4 + 2752*a^4*b^6*B*x^4 - 1024*a^3*b^7*B*x^4 + 3672*a^7*b^3*C*x^4 + 5496*a^6*b^4*C*x^4 - 4080*a^5*b^5*C*x^4 - 240*a^4*b^6*C*x^4 + 96*a^4*A*b^6*x^5 - 384*a^3*A*b^7*x^5 - 384*a^2*A*b^8*x^5 + 768*a*A*b^9*x^5 - 1088*a^5*b^5*B*x^5 - 2368*a^4*b^6*B*x^5 + 4352*a^3*b^7*B*x^5 + 256*a^2*b^8*B*x^5 - 3768*a^6*b^4*C*x^5 + 6000*a^5*b^5*C*x^5 + 1968*a^4*b^6*C*x^5 - 576*a^3*b^7*C*x^5 + 64*a^4*b^6*B*x^6 - 256*a^3*b^7*B*x^6 - 256*a^2*b^8*B*x^6 + 512*a*b^9*B*x^6 - 816*a^5*b^5*C*x^6 - 1776*a^4*b^6*C*x^6 + 3264*a^3*b^7*C*x^6 + 192*a^2*b^8*C*x^6 + 48*a^4*b^6*C*x^7 - 192*a^3*b^7*C*x^7 - 192*a^2*b^8*C*x^7 + 384*a*b^9*C*x^7)) - c*Sqrt[a*c - b*c]*(-12384*a^8*A*b^2 + 5472*a^6*A*b^4 - 12*a^4*A*b^6 + 16384*a^10*B - 12384*a^8*b^2*B + 3656*a^6*b^4*B - 8*a^4*b^6*B + 3096*a^10*C - 7560*a^8*b^2*C + 2739*a^6*b^4*C - 6*a^4*b^6*C - 12192*a^8*A*b^2*x - 12912*a^6*A*b^4*x + 2160*a^4*A*b^6*x + 16384*a^8*b^2*B*x - 10560*a^6*b^4*B*x + 1440*a^4*b^6*B*x + 3048*a^10*C*x + 3228*a^8*b^2*C*x - 7356*a^6*b^4*C*x + 1080*a^4*b^6*C*x - 5472*a^6*A*b^4*x^2 - 10968*a^4*A*b^6*x^2 + 96*a^2*A*b^8*x^2 - 20384*a^8*b^2*B*x^2 + 13872*a^6*b^4*B*x^2 - 7408*a^4*b^6*B*x^2 + 64*a^2*b^8*B*x^2 + 1368*a^8*b^2*C*x^2 + 5478*a^6*b^4*C*x^2 - 5532*a^4*b^6*C*x^2 + 48*a^2*b^8*C*x^2 + 12912*a^6*A*b^4*x^3 - 1440*a^4*A*b^6*x^3 - 2880*a^2*A*b^8*x^3 - 16064*a^6*b^4*B*x^3 + 3488*a^4*b^6*B*x^3 - 1920*a^2*b^8*B*x^3 - 9324*a^8*b^2*C*x^3 + 720*a^6*b^4*C*x^3 + 1800*a^4*b^6*C*x^3 - 1440*a^2*b^8*C*x^3 + 10980*a^4*A*b^6*x^4 - 48*a^2*A*b^8*x^4 - 96*A*b^10*x^4 + 9096*a^6*b^4*B*x^4 - 4392*a^4*b^6*B*x^4 + 128*a^2*b^8*B*x^4 - 64*b^10*B*x^4 - 8217*a^6*b^4*C*x^4 + 30*a^4*b^6*C*x^4 + 72*a^2*b^8*C*x^4 - 48*b^10*C*x^4 - 720*a^4*A*b^6*x^5 + 2880*a^2*A*b^8*x^5 + 7360*a^4*b^6*B*x^5 - 160*a^2*b^8*B*x^5 + 6636*a^6*b^4*C*x^5 - 2520*a^4*b^6*C*x^5 - 48*a^2*A*b^8*x^6 + 96*A*b^10*x^6 - 480*a^4*b^6*B*x^6 + 1920*a^2*b^8*B*x^6 + 5508*a^4*b^6*C*x^6 - 96*a^2*b^8*C*x^6 - 32*a^2*b^8*B*x^7 + 64*b^10*B*x^7 - 360*a^4*b^6*C*x^7 + 1440*a^2*b^8*C*x^7 - 24*a^2*b^8*C*x^8 + 48*b^10*C*x^8)))/(24*b^2*Sqrt[a + b]*Sqrt[a + b*x]*(-1024*a^7*c + 480*a^6*b*c + 144*a^5*b^2*c - 8*a^4*b^3*c + 480*a^6*b*c*x - 1248*a^5*b^2*c*x + 264*a^4*b^3*c*x + 32*a^3*b^4*c*x + 144*a^5*b^2*c*x^2 + 264*a^4*b^3*c*x^2 - 576*a^3*b^4*c*x^2 + 32*a^2*b^5*c*x^2 - 8*a^4*b^3*c*x^3 + 32*a^3*b^4*c*x^3 + 32*a^2*b^5*c*x^3 - 64*a*b^6*c*x^3) + 24*b^2*(1032*a^8*c - 456*a^6*b^2*c + a^4*b^4*c + 1136*a^6*b^2*c*x - 180*a^4*b^4*c*x - 456*a^6*b^2*c*x^2 + 918*a^4*b^4*c*x^2 - 8*a^2*b^6*c*x^2 - 180*a^4*b^4*c*x^3 + 240*a^2*b^6*c*x^3 + a^4*b^4*c*x^4 - 8*a^2*b^6*c*x^4 + 8*b^8*c*x^4) + Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x]*(24*b^2*Sqrt[a + b]*Sqrt[a + b*x]*(1016*a^6 - 60*a^4*b^2 + 912*a^4*b^2*x - 4*a^2*b^4*x - 60*a^4*b^2*x^2 + 240*a^2*b^4*x^2 - 4*a^2*b^4*x^3 + 8*b^6*x^3) + 24*b^2*(-1024*a^7 - 480*a^6*b + 144*a^5*b^2 + 8*a^4*b^3 - 480*a^6*b*x - 1248*a^5*b^2*x - 264*a^4*b^3*x + 32*a^3*b^4*x + 144*a^5*b^2*x^2 - 264*a^4*b^3*x^2 - 576*a^3*b^4*x^2 - 32*a^2*b^5*x^2 + 8*a^4*b^3*x^3 + 32*a^3*b^4*x^3 - 32*a^2*b^5*x^3 - 64*a*b^6*x^3))) + ((2*a^2*A*Sqrt[c])/b + (a^4*Sqrt[c]*C)/(2*b^3))*ArcTan[(Sqrt[a + b]*Sqrt[c] - Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])]","B",1
24,-1,0,278,180.0430897,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
25,1,1164,322,87.6964752,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^2} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2),x]","\frac{\sqrt{a+b} \left(C e^2-B f e+A f^2\right) \sqrt{a+b x} \left(4 c e a^3+2 c f a^3+2 c f x a^3-2 b c e a^2-2 b c f a^2-2 b c e x a^2-2 b c f x a^2-2 b^2 c e a+2 b^2 c e x a\right)+\left(C e^2-B f e+A f^2\right) \left(-4 c e a^4-c f a^4-3 c f x a^4+b^2 c e x^2 a^2+4 b^2 c e a^2+b^2 c f a^2-b^2 c e x a^2+3 b^2 c f x a^2-b^4 c e x^2+b^4 c e x\right)+\sqrt{a c-b c} \sqrt{a c-b c x} \left(\sqrt{a+b} \left(C e^2-B f e+A f^2\right) \sqrt{a+b x} \left(-4 e a^2-3 f a^2-f x a^2+b^2 e-b^2 e x\right)+\left(C e^2-B f e+A f^2\right) \left(4 e a^3+2 f a^3+2 f x a^3+2 b e a^2+2 b f a^2+2 b e x a^2+2 b f x a^2-2 b^2 e a+2 b^2 e x a\right)\right)}{\left(-2 a^2-2 b a\right) c \sqrt{a c-b c} f (e+f) \left(a^2 f^2-b^2 e^2\right) \sqrt{a+b x} (e+f x)+\left(a^2-b^2\right) c f (e+f) \left(a^2 f^2-b^2 e^2\right) \sqrt{a+b x} \sqrt{a c-b c x} (e+f x)+\sqrt{a+b} \left(c \sqrt{a c-b c} f (e+f) \left(a^2 f^2-b^2 e^2\right) \left(3 a^2+b^2 x\right) (e+f x)+\left(2 a b-2 a^2\right) c f (e+f) \left(a^2 f^2-b^2 e^2\right) \sqrt{a c-b c x} (e+f x)\right)}+\frac{4 C \tan ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c}-\sqrt{c} \sqrt{a+b x}}{\sqrt{a c-b c}-\sqrt{a c-b c x}}\right)}{b \sqrt{c} f^2}+\left(\frac{b^2 C e^3}{f^2 \left(a^2 f^2-b^2 e^2\right)}-\frac{A b^2 e}{a^2 f^2-b^2 e^2}-\frac{2 a^2 C e}{a^2 f^2-b^2 e^2}+\frac{a^2 B f}{a^2 f^2-b^2 e^2}\right) \text{RootSum}\left[b c^2 e \text{$\#$1}^4+b c^2 f \text{$\#$1}^4+4 \sqrt{a+b} c \sqrt{-((b-a) c)} f \text{$\#$1}^3+2 b c e \text{$\#$1}^2-6 b c f \text{$\#$1}^2-4 \sqrt{a+b} \sqrt{-((b-a) c)} f \text{$\#$1}+b e+b f\&,\frac{-c \log \left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right) \text{$\#$1}^2+c \log \left(-\sqrt{a c-b c} \text{$\#$1}+\sqrt{a c-b c x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-\log \left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)+\log \left(-\sqrt{a c-b c} \text{$\#$1}+\sqrt{a c-b c x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{b c^2 e \text{$\#$1}^3+b c^2 f \text{$\#$1}^3+3 \sqrt{a+b} c \sqrt{(a-b) c} f \text{$\#$1}^2+b c e \text{$\#$1}-3 b c f \text{$\#$1}-\sqrt{a+b} \sqrt{(a-b) c} f}\&\right]","\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,"(Sqrt[a + b]*(C*e^2 - B*e*f + A*f^2)*Sqrt[a + b*x]*(4*a^3*c*e - 2*a^2*b*c*e - 2*a*b^2*c*e + 2*a^3*c*f - 2*a^2*b*c*f - 2*a^2*b*c*e*x + 2*a*b^2*c*e*x + 2*a^3*c*f*x - 2*a^2*b*c*f*x) + (C*e^2 - B*e*f + A*f^2)*(-4*a^4*c*e + 4*a^2*b^2*c*e - a^4*c*f + a^2*b^2*c*f - a^2*b^2*c*e*x + b^4*c*e*x - 3*a^4*c*f*x + 3*a^2*b^2*c*f*x + a^2*b^2*c*e*x^2 - b^4*c*e*x^2) + Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x]*(Sqrt[a + b]*(C*e^2 - B*e*f + A*f^2)*Sqrt[a + b*x]*(-4*a^2*e + b^2*e - 3*a^2*f - b^2*e*x - a^2*f*x) + (C*e^2 - B*e*f + A*f^2)*(4*a^3*e + 2*a^2*b*e - 2*a*b^2*e + 2*a^3*f + 2*a^2*b*f + 2*a^2*b*e*x + 2*a*b^2*e*x + 2*a^3*f*x + 2*a^2*b*f*x)))/((-2*a^2 - 2*a*b)*c*Sqrt[a*c - b*c]*f*(e + f)*(-(b^2*e^2) + a^2*f^2)*Sqrt[a + b*x]*(e + f*x) + (a^2 - b^2)*c*f*(e + f)*(-(b^2*e^2) + a^2*f^2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x) + Sqrt[a + b]*(c*Sqrt[a*c - b*c]*f*(e + f)*(-(b^2*e^2) + a^2*f^2)*(3*a^2 + b^2*x)*(e + f*x) + (-2*a^2 + 2*a*b)*c*f*(e + f)*(-(b^2*e^2) + a^2*f^2)*Sqrt[a*c - b*c*x]*(e + f*x))) + (4*C*ArcTan[(Sqrt[a + b]*Sqrt[c] - Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])])/(b*Sqrt[c]*f^2) + (-((A*b^2*e)/(-(b^2*e^2) + a^2*f^2)) - (2*a^2*C*e)/(-(b^2*e^2) + a^2*f^2) + (b^2*C*e^3)/(f^2*(-(b^2*e^2) + a^2*f^2)) + (a^2*B*f)/(-(b^2*e^2) + a^2*f^2))*RootSum[b*e + b*f - 4*Sqrt[a + b]*Sqrt[-((-a + b)*c)]*f*#1 + 2*b*c*e*#1^2 - 6*b*c*f*#1^2 + 4*Sqrt[a + b]*c*Sqrt[-((-a + b)*c)]*f*#1^3 + b*c^2*e*#1^4 + b*c^2*f*#1^4 & , (-Log[Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x]] + Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[a*c - b*c]*#1 + Sqrt[a*c - b*c*x]*#1] - c*Log[Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x]]*#1^2 + c*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[a*c - b*c]*#1 + Sqrt[a*c - b*c*x]*#1]*#1^2)/(-(Sqrt[a + b]*Sqrt[(a - b)*c]*f) + b*c*e*#1 - 3*b*c*f*#1 + 3*Sqrt[a + b]*c*Sqrt[(a - b)*c]*f*#1^2 + b*c^2*e*#1^3 + b*c^2*f*#1^3) & ]","C",1
26,-1,0,363,180.2616812,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^3} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^3),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
27,-1,0,501,180.0196062,"\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","IntegrateAlgebraic[((e + f*x)^3*(A + B*x + C*x^2))/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","\text{\$Aborted}","-\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{\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}}-\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(16 a^4 C f^4+4 a^2 b^2 f^2 \left(5 f (A f+3 B e)+13 C e^2\right)+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}}",1,"$Aborted","F",-1
28,-1,0,368,180.0069782,"\int \frac{(e+f x)^2 \left(A+B x+C x^2\right)}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","IntegrateAlgebraic[((e + f*x)^2*(A + B*x + C*x^2))/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","\text{\$Aborted}","-\frac{\left(a^2-b^2 x^2\right) \left(f x \left(9 a^2 C f^2-b^2 \left(2 C e^2-4 f (3 A f+2 B e)\right)\right)+4 \left(4 a^2 f^2 (B f+2 C e)-b^2 e \left(C e^2-4 f (3 A f+B e)\right)\right)\right)}{24 b^4 f \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\sqrt{a^2 c-b^2 c x^2} \tan ^{-1}\left(\frac{b \sqrt{c} x}{\sqrt{a^2 c-b^2 c x^2}}\right) \left(4 A \left(a^2 b^2 f^2+2 b^4 e^2\right)+a^2 \left(3 a^2 C f^2+4 b^2 e (2 B f+C e)\right)\right)}{8 b^5 \sqrt{c} \sqrt{a+b x} \sqrt{a c-b c x}}+\frac{\left(a^2-b^2 x^2\right) (e+f x)^2 (C e-4 B f)}{12 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}-\frac{C \left(a^2-b^2 x^2\right) (e+f x)^3}{4 b^2 f \sqrt{a+b x} \sqrt{a c-b c x}}",1,"$Aborted","F",-1
29,1,4097,246,44.9008266,"\int \frac{(e+f x) \left(A+B x+C x^2\right)}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","IntegrateAlgebraic[((e + f*x)*(A + B*x + C*x^2))/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","\text{Result too large to show}","-\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,"(Sqrt[a*c - b*c]*Sqrt[a + b*x]*(1536*a^6*b^2*B*e + 768*a^5*b^3*B*e - 384*a^4*b^4*B*e - 36*a^3*b^5*B*e + 384*a^6*b^2*C*e + 228*a^5*b^3*C*e - 174*a^4*b^4*C*e - 18*a^3*b^5*C*e + 1536*a^6*A*b^2*f + 768*a^5*A*b^3*f - 384*a^4*A*b^4*f - 36*a^3*A*b^5*f + 384*a^6*b^2*B*f + 228*a^5*b^3*B*f - 174*a^4*b^4*B*f - 18*a^3*b^5*B*f + 1024*a^8*C*f + 512*a^7*b*C*f + 128*a^5*b^3*C*f - 116*a^4*b^4*C*f - 12*a^3*b^5*C*f - 768*a^5*b^3*B*e*x + 768*a^4*b^4*B*e*x + 732*a^3*b^5*B*e*x - 72*a^2*b^6*B*e*x + 384*a^6*b^2*C*e*x + 174*a^4*b^4*C*e*x + 312*a^3*b^5*C*e*x - 36*a^2*b^6*C*e*x - 768*a^5*A*b^3*f*x + 768*a^4*A*b^4*f*x + 732*a^3*A*b^5*f*x - 72*a^2*A*b^6*f*x + 384*a^6*b^2*B*f*x + 174*a^4*b^4*B*f*x + 312*a^3*b^5*B*f*x - 36*a^2*b^6*B*f*x - 512*a^7*b*C*f*x + 512*a^6*b^2*C*f*x + 384*a^5*b^3*C*f*x + 80*a^4*b^4*C*f*x + 208*a^3*b^5*C*f*x - 24*a^2*b^6*C*f*x - 384*a^4*b^4*B*e*x^2 - 732*a^3*b^5*B*e*x^2 + 144*a^2*b^6*B*e*x^2 + 144*a*b^7*B*e*x^2 - 228*a^5*b^3*C*e*x^2 + 174*a^4*b^4*C*e*x^2 + 36*a^2*b^6*C*e*x^2 + 72*a*b^7*C*e*x^2 - 384*a^4*A*b^4*f*x^2 - 732*a^3*A*b^5*f*x^2 + 144*a^2*A*b^6*f*x^2 + 144*a*A*b^7*f*x^2 - 228*a^5*b^3*B*f*x^2 + 174*a^4*b^4*B*f*x^2 + 36*a^2*b^6*B*f*x^2 + 72*a*b^7*B*f*x^2 - 384*a^5*b^3*C*f*x^2 + 72*a^4*b^4*C*f*x^2 + 60*a^3*b^5*C*f*x^2 + 24*a^2*b^6*C*f*x^2 + 48*a*b^7*C*f*x^2 + 36*a^3*b^5*B*e*x^3 - 72*a^2*b^6*B*e*x^3 - 144*a*b^7*B*e*x^3 - 174*a^4*b^4*C*e*x^3 - 312*a^3*b^5*C*e*x^3 + 36*a^2*b^6*C*e*x^3 + 36*a^3*A*b^5*f*x^3 - 72*a^2*A*b^6*f*x^3 - 144*a*A*b^7*f*x^3 - 174*a^4*b^4*B*f*x^3 - 312*a^3*b^5*B*f*x^3 + 36*a^2*b^6*B*f*x^3 - 128*a^5*b^3*C*f*x^3 + 80*a^4*b^4*C*f*x^3 - 60*a^3*b^5*C*f*x^3 + 18*a^3*b^5*C*e*x^4 - 36*a^2*b^6*C*e*x^4 - 72*a*b^7*C*e*x^4 + 18*a^3*b^5*B*f*x^4 - 36*a^2*b^6*B*f*x^4 - 72*a*b^7*B*f*x^4 - 116*a^4*b^4*C*f*x^4 - 208*a^3*b^5*C*f*x^4 + 24*a^2*b^6*C*f*x^4 + 12*a^3*b^5*C*f*x^5 - 24*a^2*b^6*C*f*x^5 - 48*a*b^7*C*f*x^5) + Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(-1536*a^6*b^2*B*e + 948*a^4*b^4*B*e - 6*a^2*b^6*B*e - 372*a^6*b^2*C*e + 375*a^4*b^4*C*e - 3*a^2*b^6*C*e - 1536*a^6*A*b^2*f + 948*a^4*A*b^4*f - 6*a^2*A*b^6*f - 372*a^6*b^2*B*f + 375*a^4*b^4*B*f - 3*a^2*b^6*B*f - 1024*a^8*C*f + 384*a^6*b^2*C*f + 246*a^4*b^4*C*f - 2*a^2*b^6*C*f - 1152*a^4*b^4*B*e*x + 414*a^2*b^6*B*e*x - 396*a^6*b^2*C*e*x - 99*a^4*b^4*C*e*x + 198*a^2*b^6*C*e*x - 1152*a^4*A*b^4*f*x + 414*a^2*A*b^6*f*x - 396*a^6*b^2*B*f*x - 99*a^4*b^4*B*f*x + 198*a^2*b^6*B*f*x - 768*a^6*b^2*C*f*x + 144*a^4*b^4*C*f*x + 132*a^2*b^6*C*f*x + 204*a^4*b^4*B*e*x^2 - 426*a^2*b^6*B*e*x^2 + 24*b^8*B*e*x^2 - 375*a^4*b^4*C*e*x^2 - 6*a^2*b^6*C*e*x^2 + 12*b^8*C*e*x^2 + 204*a^4*A*b^4*f*x^2 - 426*a^2*A*b^6*f*x^2 + 24*A*b^8*f*x^2 - 375*a^4*b^4*B*f*x^2 - 6*a^2*b^6*B*f*x^2 + 12*b^8*B*f*x^2 - 128*a^6*b^2*C*f*x^2 - 216*a^4*b^4*C*f*x^2 + 6*a^2*b^6*C*f*x^2 + 8*b^8*C*f*x^2 + 18*a^2*b^6*B*e*x^3 - 24*b^8*B*e*x^3 + 99*a^4*b^4*C*e*x^3 - 198*a^2*b^6*C*e*x^3 + 18*a^2*A*b^6*f*x^3 - 24*A*b^8*f*x^3 + 99*a^4*b^4*B*f*x^3 - 198*a^2*b^6*B*f*x^3 - 240*a^4*b^4*C*f*x^3 - 10*a^2*b^6*C*f*x^3 + 9*a^2*b^6*C*e*x^4 - 12*b^8*C*e*x^4 + 9*a^2*b^6*B*f*x^4 - 12*b^8*B*f*x^4 + 66*a^4*b^4*C*f*x^4 - 132*a^2*b^6*C*f*x^4 + 6*a^2*b^6*C*f*x^5 - 8*b^8*C*f*x^5) + Sqrt[a + b]*(Sqrt[a*c - b*c*x]*(1536*a^6*b^2*B*e - 768*a^5*b^3*B*e - 384*a^4*b^4*B*e + 36*a^3*b^5*B*e + 384*a^6*b^2*C*e - 228*a^5*b^3*C*e - 174*a^4*b^4*C*e + 18*a^3*b^5*C*e + 1536*a^6*A*b^2*f - 768*a^5*A*b^3*f - 384*a^4*A*b^4*f + 36*a^3*A*b^5*f + 384*a^6*b^2*B*f - 228*a^5*b^3*B*f - 174*a^4*b^4*B*f + 18*a^3*b^5*B*f + 1024*a^8*C*f - 512*a^7*b*C*f - 128*a^5*b^3*C*f - 116*a^4*b^4*C*f + 12*a^3*b^5*C*f + 768*a^5*b^3*B*e*x + 768*a^4*b^4*B*e*x - 732*a^3*b^5*B*e*x - 72*a^2*b^6*B*e*x + 384*a^6*b^2*C*e*x + 174*a^4*b^4*C*e*x - 312*a^3*b^5*C*e*x - 36*a^2*b^6*C*e*x + 768*a^5*A*b^3*f*x + 768*a^4*A*b^4*f*x - 732*a^3*A*b^5*f*x - 72*a^2*A*b^6*f*x + 384*a^6*b^2*B*f*x + 174*a^4*b^4*B*f*x - 312*a^3*b^5*B*f*x - 36*a^2*b^6*B*f*x + 512*a^7*b*C*f*x + 512*a^6*b^2*C*f*x - 384*a^5*b^3*C*f*x + 80*a^4*b^4*C*f*x - 208*a^3*b^5*C*f*x - 24*a^2*b^6*C*f*x - 384*a^4*b^4*B*e*x^2 + 732*a^3*b^5*B*e*x^2 + 144*a^2*b^6*B*e*x^2 - 144*a*b^7*B*e*x^2 + 228*a^5*b^3*C*e*x^2 + 174*a^4*b^4*C*e*x^2 + 36*a^2*b^6*C*e*x^2 - 72*a*b^7*C*e*x^2 - 384*a^4*A*b^4*f*x^2 + 732*a^3*A*b^5*f*x^2 + 144*a^2*A*b^6*f*x^2 - 144*a*A*b^7*f*x^2 + 228*a^5*b^3*B*f*x^2 + 174*a^4*b^4*B*f*x^2 + 36*a^2*b^6*B*f*x^2 - 72*a*b^7*B*f*x^2 + 384*a^5*b^3*C*f*x^2 + 72*a^4*b^4*C*f*x^2 - 60*a^3*b^5*C*f*x^2 + 24*a^2*b^6*C*f*x^2 - 48*a*b^7*C*f*x^2 - 36*a^3*b^5*B*e*x^3 - 72*a^2*b^6*B*e*x^3 + 144*a*b^7*B*e*x^3 - 174*a^4*b^4*C*e*x^3 + 312*a^3*b^5*C*e*x^3 + 36*a^2*b^6*C*e*x^3 - 36*a^3*A*b^5*f*x^3 - 72*a^2*A*b^6*f*x^3 + 144*a*A*b^7*f*x^3 - 174*a^4*b^4*B*f*x^3 + 312*a^3*b^5*B*f*x^3 + 36*a^2*b^6*B*f*x^3 + 128*a^5*b^3*C*f*x^3 + 80*a^4*b^4*C*f*x^3 + 60*a^3*b^5*C*f*x^3 - 18*a^3*b^5*C*e*x^4 - 36*a^2*b^6*C*e*x^4 + 72*a*b^7*C*e*x^4 - 18*a^3*b^5*B*f*x^4 - 36*a^2*b^6*B*f*x^4 + 72*a*b^7*B*f*x^4 - 116*a^4*b^4*C*f*x^4 + 208*a^3*b^5*C*f*x^4 + 24*a^2*b^6*C*f*x^4 - 12*a^3*b^5*C*f*x^5 - 24*a^2*b^6*C*f*x^5 + 48*a*b^7*C*f*x^5) + Sqrt[a*c - b*c]*(-1536*a^6*b^2*B*e + 204*a^4*b^4*B*e - 396*a^6*b^2*C*e + 99*a^4*b^4*C*e - 1536*a^6*A*b^2*f + 204*a^4*A*b^4*f - 396*a^6*b^2*B*f + 99*a^4*b^4*B*f - 1024*a^8*C*f - 128*a^6*b^2*C*f + 66*a^4*b^4*C*f - 1152*a^4*b^4*B*e*x + 18*a^2*b^6*B*e*x - 372*a^6*b^2*C*e*x - 375*a^4*b^4*C*e*x + 9*a^2*b^6*C*e*x - 1152*a^4*A*b^4*f*x + 18*a^2*A*b^6*f*x - 372*a^6*b^2*B*f*x - 375*a^4*b^4*B*f*x + 9*a^2*b^6*B*f*x - 768*a^6*b^2*C*f*x - 240*a^4*b^4*C*f*x + 6*a^2*b^6*C*f*x + 948*a^4*b^4*B*e*x^2 - 426*a^2*b^6*B*e*x^2 - 99*a^4*b^4*C*e*x^2 - 198*a^2*b^6*C*e*x^2 + 948*a^4*A*b^4*f*x^2 - 426*a^2*A*b^6*f*x^2 - 99*a^4*b^4*B*f*x^2 - 198*a^2*b^6*B*f*x^2 + 384*a^6*b^2*C*f*x^2 - 216*a^4*b^4*C*f*x^2 - 132*a^2*b^6*C*f*x^2 + 414*a^2*b^6*B*e*x^3 - 24*b^8*B*e*x^3 + 375*a^4*b^4*C*e*x^3 - 6*a^2*b^6*C*e*x^3 - 12*b^8*C*e*x^3 + 414*a^2*A*b^6*f*x^3 - 24*A*b^8*f*x^3 + 375*a^4*b^4*B*f*x^3 - 6*a^2*b^6*B*f*x^3 - 12*b^8*B*f*x^3 + 144*a^4*b^4*C*f*x^3 - 10*a^2*b^6*C*f*x^3 - 8*b^8*C*f*x^3 - 6*a^2*b^6*B*e*x^4 + 24*b^8*B*e*x^4 + 198*a^2*b^6*C*e*x^4 - 6*a^2*A*b^6*f*x^4 + 24*A*b^8*f*x^4 + 198*a^2*b^6*B*f*x^4 + 246*a^4*b^4*C*f*x^4 + 6*a^2*b^6*C*f*x^4 - 3*a^2*b^6*C*e*x^5 + 12*b^8*C*e*x^5 - 3*a^2*b^6*B*f*x^5 + 12*b^8*B*f*x^5 + 132*a^2*b^6*C*f*x^5 - 2*a^2*b^6*C*f*x^6 + 8*b^8*C*f*x^6)))/(6*b^4*Sqrt[a + b]*Sqrt[a + b*x]*(-128*a^5*c + 52*a^4*b*c + 6*a^3*b^2*c + 52*a^4*b*c*x - 116*a^3*b^2*c*x + 12*a^2*b^3*c*x + 6*a^3*b^2*c*x^2 + 12*a^2*b^3*c*x^2 - 24*a*b^4*c*x^2) + 6*b^4*(132*a^6*c - 33*a^4*b^2*c + 126*a^4*b^2*c*x - 3*a^2*b^4*c*x - 33*a^4*b^2*c*x^2 + 66*a^2*b^4*c*x^2 - 3*a^2*b^4*c*x^3 + 4*b^6*c*x^3) + Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x]*(6*b^4*Sqrt[a + b]*Sqrt[a + b*x]*(124*a^4 - a^2*b^2 + 66*a^2*b^2*x - a^2*b^2*x^2 + 4*b^4*x^2) + 6*b^4*(-128*a^5 - 52*a^4*b + 6*a^3*b^2 - 52*a^4*b*x - 116*a^3*b^2*x - 12*a^2*b^3*x + 6*a^3*b^2*x^2 - 12*a^2*b^3*x^2 - 24*a*b^4*x^2))) + ((4*A*e)/(b*Sqrt[c]) + (2*a^2*C*e)/(b^3*Sqrt[c]) + (2*a^2*B*f)/(b^3*Sqrt[c]))*ArcTan[(Sqrt[a + b]*Sqrt[c] - Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])]","B",1
30,1,948,177,6.326234,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]),x]","\frac{\sqrt{a c-b c} \sqrt{a+b x} \left(64 B a^4+16 C a^4+16 C x a^4-12 b C x^2 a^3+32 b B a^3+12 b C a^3-32 b B x a^3-4 b^2 C x^3 a^2-8 b^2 B x^2 a^2+4 b^2 C x^2 a^2-8 b^2 B a^2-4 b^2 C a^2+16 b^2 B x a^2+4 b^2 C x a^2-8 b^3 C x^3 a-16 b^3 B x^2 a+16 b^3 B x a+8 b^3 C x a\right)+\sqrt{a+b x} \sqrt{a c-b c x} \left(-64 B a^4-14 C a^4-18 C x a^4+b^2 C x^3 a^2+2 b^2 B x^2 a^2-14 b^2 C x^2 a^2+30 b^2 B a^2+14 b^2 C a^2-32 b^2 B x a^2-b^2 C x a^2-2 b^4 C x^3-4 b^4 B x^2+4 b^4 B x+2 b^4 C x\right)+\sqrt{a+b} \left(\sqrt{a c-b c x} \left(64 B a^4+16 C a^4+16 C x a^4+12 b C x^2 a^3-32 b B a^3-12 b C a^3+32 b B x a^3-4 b^2 C x^3 a^2-8 b^2 B x^2 a^2+4 b^2 C x^2 a^2-8 b^2 B a^2-4 b^2 C a^2+16 b^2 B x a^2+4 b^2 C x a^2+8 b^3 C x^3 a+16 b^3 B x^2 a-16 b^3 B x a-8 b^3 C x a\right)+\sqrt{a c-b c} \left(-64 B a^4-18 C a^4-14 C x a^4+14 b^2 C x^3 a^2+30 b^2 B x^2 a^2-b^2 C x^2 a^2+2 b^2 B a^2+b^2 C a^2-32 b^2 B x a^2-14 b^2 C x a^2+2 b^4 C x^4+4 b^4 B x^3-4 b^4 B x^2-2 b^4 C x^2\right)\right)}{2 \sqrt{a+b} \sqrt{a+b x} \left(-16 c a^3+4 b c a^2+4 b c x a^2-8 b^2 c x a\right) b^2+2 \left(18 c a^4-b^2 c x^2 a^2-b^2 c a^2+14 b^2 c x a^2+2 b^4 c x^2\right) b^2+\sqrt{a c-b c} \sqrt{a c-b c x} \left(2 \sqrt{a+b} \sqrt{a+b x} \left(14 a^2+2 b^2 x\right) b^2+2 \left(-16 a^3-4 b a^2-4 b x a^2-8 b^2 x a\right) b^2\right)}+\left(\frac{2 C a^2}{b^3 \sqrt{c}}+\frac{4 A}{b \sqrt{c}}\right) \tan ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c}-\sqrt{c} \sqrt{a+b x}}{\sqrt{a c-b c}-\sqrt{a c-b c x}}\right)","\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,"(Sqrt[a*c - b*c]*Sqrt[a + b*x]*(64*a^4*B + 32*a^3*b*B - 8*a^2*b^2*B + 16*a^4*C + 12*a^3*b*C - 4*a^2*b^2*C - 32*a^3*b*B*x + 16*a^2*b^2*B*x + 16*a*b^3*B*x + 16*a^4*C*x + 4*a^2*b^2*C*x + 8*a*b^3*C*x - 8*a^2*b^2*B*x^2 - 16*a*b^3*B*x^2 - 12*a^3*b*C*x^2 + 4*a^2*b^2*C*x^2 - 4*a^2*b^2*C*x^3 - 8*a*b^3*C*x^3) + Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(-64*a^4*B + 30*a^2*b^2*B - 14*a^4*C + 14*a^2*b^2*C - 32*a^2*b^2*B*x + 4*b^4*B*x - 18*a^4*C*x - a^2*b^2*C*x + 2*b^4*C*x + 2*a^2*b^2*B*x^2 - 4*b^4*B*x^2 - 14*a^2*b^2*C*x^2 + a^2*b^2*C*x^3 - 2*b^4*C*x^3) + Sqrt[a + b]*(Sqrt[a*c - b*c*x]*(64*a^4*B - 32*a^3*b*B - 8*a^2*b^2*B + 16*a^4*C - 12*a^3*b*C - 4*a^2*b^2*C + 32*a^3*b*B*x + 16*a^2*b^2*B*x - 16*a*b^3*B*x + 16*a^4*C*x + 4*a^2*b^2*C*x - 8*a*b^3*C*x - 8*a^2*b^2*B*x^2 + 16*a*b^3*B*x^2 + 12*a^3*b*C*x^2 + 4*a^2*b^2*C*x^2 - 4*a^2*b^2*C*x^3 + 8*a*b^3*C*x^3) + Sqrt[a*c - b*c]*(-64*a^4*B + 2*a^2*b^2*B - 18*a^4*C + a^2*b^2*C - 32*a^2*b^2*B*x - 14*a^4*C*x - 14*a^2*b^2*C*x + 30*a^2*b^2*B*x^2 - 4*b^4*B*x^2 - a^2*b^2*C*x^2 - 2*b^4*C*x^2 + 4*b^4*B*x^3 + 14*a^2*b^2*C*x^3 + 2*b^4*C*x^4)))/(2*b^2*Sqrt[a + b]*Sqrt[a + b*x]*(-16*a^3*c + 4*a^2*b*c + 4*a^2*b*c*x - 8*a*b^2*c*x) + 2*b^2*(18*a^4*c - a^2*b^2*c + 14*a^2*b^2*c*x - a^2*b^2*c*x^2 + 2*b^4*c*x^2) + Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x]*(2*b^2*Sqrt[a + b]*Sqrt[a + b*x]*(14*a^2 + 2*b^2*x) + 2*b^2*(-16*a^3 - 4*a^2*b - 4*a^2*b*x - 8*a*b^2*x))) + ((4*A)/(b*Sqrt[c]) + (2*a^2*C)/(b^3*Sqrt[c]))*ArcTan[(Sqrt[a + b]*Sqrt[c] - Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])]","B",1
31,-1,0,278,180.0432417,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
32,1,1164,322,0.0008612,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^2} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^2),x]","\frac{\sqrt{a+b} \left(C e^2-B f e+A f^2\right) \sqrt{a+b x} \left(4 c e a^3+2 c f a^3+2 c f x a^3-2 b c e a^2-2 b c f a^2-2 b c e x a^2-2 b c f x a^2-2 b^2 c e a+2 b^2 c e x a\right)+\left(C e^2-B f e+A f^2\right) \left(-4 c e a^4-c f a^4-3 c f x a^4+b^2 c e x^2 a^2+4 b^2 c e a^2+b^2 c f a^2-b^2 c e x a^2+3 b^2 c f x a^2-b^4 c e x^2+b^4 c e x\right)+\sqrt{a c-b c} \sqrt{a c-b c x} \left(\sqrt{a+b} \left(C e^2-B f e+A f^2\right) \sqrt{a+b x} \left(-4 e a^2-3 f a^2-f x a^2+b^2 e-b^2 e x\right)+\left(C e^2-B f e+A f^2\right) \left(4 e a^3+2 f a^3+2 f x a^3+2 b e a^2+2 b f a^2+2 b e x a^2+2 b f x a^2-2 b^2 e a+2 b^2 e x a\right)\right)}{\left(-2 a^2-2 b a\right) c \sqrt{a c-b c} f (e+f) \left(a^2 f^2-b^2 e^2\right) \sqrt{a+b x} (e+f x)+\left(a^2-b^2\right) c f (e+f) \left(a^2 f^2-b^2 e^2\right) \sqrt{a+b x} \sqrt{a c-b c x} (e+f x)+\sqrt{a+b} \left(c \sqrt{a c-b c} f (e+f) \left(a^2 f^2-b^2 e^2\right) \left(3 a^2+b^2 x\right) (e+f x)+\left(2 a b-2 a^2\right) c f (e+f) \left(a^2 f^2-b^2 e^2\right) \sqrt{a c-b c x} (e+f x)\right)}+\frac{4 C \tan ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c}-\sqrt{c} \sqrt{a+b x}}{\sqrt{a c-b c}-\sqrt{a c-b c x}}\right)}{b \sqrt{c} f^2}+\left(\frac{b^2 C e^3}{f^2 \left(a^2 f^2-b^2 e^2\right)}-\frac{A b^2 e}{a^2 f^2-b^2 e^2}-\frac{2 a^2 C e}{a^2 f^2-b^2 e^2}+\frac{a^2 B f}{a^2 f^2-b^2 e^2}\right) \text{RootSum}\left[b c^2 e \text{$\#$1}^4+b c^2 f \text{$\#$1}^4+4 \sqrt{a+b} c \sqrt{-((b-a) c)} f \text{$\#$1}^3+2 b c e \text{$\#$1}^2-6 b c f \text{$\#$1}^2-4 \sqrt{a+b} \sqrt{-((b-a) c)} f \text{$\#$1}+b e+b f\&,\frac{-c \log \left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right) \text{$\#$1}^2+c \log \left(-\sqrt{a c-b c} \text{$\#$1}+\sqrt{a c-b c x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right) \text{$\#$1}^2-\log \left(\sqrt{a c-b c}-\sqrt{a c-b c x}\right)+\log \left(-\sqrt{a c-b c} \text{$\#$1}+\sqrt{a c-b c x} \text{$\#$1}+\sqrt{a+b}-\sqrt{a+b x}\right)}{b c^2 e \text{$\#$1}^3+b c^2 f \text{$\#$1}^3+3 \sqrt{a+b} c \sqrt{(a-b) c} f \text{$\#$1}^2+b c e \text{$\#$1}-3 b c f \text{$\#$1}-\sqrt{a+b} \sqrt{(a-b) c} f}\&\right]","\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,"(Sqrt[a + b]*(C*e^2 - B*e*f + A*f^2)*Sqrt[a + b*x]*(4*a^3*c*e - 2*a^2*b*c*e - 2*a*b^2*c*e + 2*a^3*c*f - 2*a^2*b*c*f - 2*a^2*b*c*e*x + 2*a*b^2*c*e*x + 2*a^3*c*f*x - 2*a^2*b*c*f*x) + (C*e^2 - B*e*f + A*f^2)*(-4*a^4*c*e + 4*a^2*b^2*c*e - a^4*c*f + a^2*b^2*c*f - a^2*b^2*c*e*x + b^4*c*e*x - 3*a^4*c*f*x + 3*a^2*b^2*c*f*x + a^2*b^2*c*e*x^2 - b^4*c*e*x^2) + Sqrt[a*c - b*c]*Sqrt[a*c - b*c*x]*(Sqrt[a + b]*(C*e^2 - B*e*f + A*f^2)*Sqrt[a + b*x]*(-4*a^2*e + b^2*e - 3*a^2*f - b^2*e*x - a^2*f*x) + (C*e^2 - B*e*f + A*f^2)*(4*a^3*e + 2*a^2*b*e - 2*a*b^2*e + 2*a^3*f + 2*a^2*b*f + 2*a^2*b*e*x + 2*a*b^2*e*x + 2*a^3*f*x + 2*a^2*b*f*x)))/((-2*a^2 - 2*a*b)*c*Sqrt[a*c - b*c]*f*(e + f)*(-(b^2*e^2) + a^2*f^2)*Sqrt[a + b*x]*(e + f*x) + (a^2 - b^2)*c*f*(e + f)*(-(b^2*e^2) + a^2*f^2)*Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x) + Sqrt[a + b]*(c*Sqrt[a*c - b*c]*f*(e + f)*(-(b^2*e^2) + a^2*f^2)*(3*a^2 + b^2*x)*(e + f*x) + (-2*a^2 + 2*a*b)*c*f*(e + f)*(-(b^2*e^2) + a^2*f^2)*Sqrt[a*c - b*c*x]*(e + f*x))) + (4*C*ArcTan[(Sqrt[a + b]*Sqrt[c] - Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x])])/(b*Sqrt[c]*f^2) + (-((A*b^2*e)/(-(b^2*e^2) + a^2*f^2)) - (2*a^2*C*e)/(-(b^2*e^2) + a^2*f^2) + (b^2*C*e^3)/(f^2*(-(b^2*e^2) + a^2*f^2)) + (a^2*B*f)/(-(b^2*e^2) + a^2*f^2))*RootSum[b*e + b*f - 4*Sqrt[a + b]*Sqrt[-((-a + b)*c)]*f*#1 + 2*b*c*e*#1^2 - 6*b*c*f*#1^2 + 4*Sqrt[a + b]*c*Sqrt[-((-a + b)*c)]*f*#1^3 + b*c^2*e*#1^4 + b*c^2*f*#1^4 & , (-Log[Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x]] + Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[a*c - b*c]*#1 + Sqrt[a*c - b*c*x]*#1] - c*Log[Sqrt[a*c - b*c] - Sqrt[a*c - b*c*x]]*#1^2 + c*Log[Sqrt[a + b] - Sqrt[a + b*x] - Sqrt[a*c - b*c]*#1 + Sqrt[a*c - b*c*x]*#1]*#1^2)/(-(Sqrt[a + b]*Sqrt[(a - b)*c]*f) + b*c*e*#1 - 3*b*c*f*#1 + 3*Sqrt[a + b]*c*Sqrt[(a - b)*c]*f*#1^2 + b*c^2*e*#1^3 + b*c^2*f*#1^3) & ]","C",1
33,-1,0,363,180.2204643,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^3} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[a*c - b*c*x]*(e + f*x)^3),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
34,1,1895,87,0.0009182,"\int \frac{x \left(a+b x+c x^2\right)}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(x*(a + b*x + c*x^2))/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{\sqrt{d+1} \sqrt{d x-1} \left(-48 c x^5 d^7-72 b x^4 d^7-144 a x^3 d^7+144 a x^2 d^7+72 b x^2 d^7+48 c x^2 d^7+24 c x^5 d^6+36 b x^4 d^6-24 c x^4 d^6+72 a x^3 d^6-36 b x^3 d^6-144 a x^2 d^6-36 b x^2 d^6-24 c x^2 d^6+72 a x d^6+36 b x d^6+24 c x d^6+12 c x^5 d^5+18 b x^4 d^5-208 c x^4 d^5+36 a x^3 d^5-312 b x^3 d^5-60 c x^3 d^5-732 a x^2 d^5+60 c x^2 d^5-36 a d^5-18 b d^5-12 c d^5+732 a x d^5+312 b x d^5+208 c x d^5+116 c x^4 d^4+174 b x^3 d^4-80 c x^3 d^4+384 a x^2 d^4-174 b x^2 d^4-72 c x^2 d^4+384 a d^4+174 b d^4+116 c d^4-768 a x d^4-174 b x d^4-80 c x d^4-128 c x^3 d^3-228 b x^2 d^3-384 c x^2 d^3+768 a d^3+228 b d^3+128 c d^3-768 a x d^3+384 c x d^3-1536 a d^2-384 b d^2-384 b x d^2-512 c x d^2+512 c d-512 c x d-1024 c\right)+\sqrt{d x-1} \sqrt{d x+1} \left(8 c x^5 d^8+12 b x^4 d^8+24 a x^3 d^8-24 a x^2 d^8-12 b x^2 d^8-8 c x^2 d^8-6 c x^5 d^6-9 b x^4 d^6+132 c x^4 d^6-18 a x^3 d^6+198 b x^3 d^6+10 c x^3 d^6+426 a x^2 d^6+6 b x^2 d^6-6 c x^2 d^6+6 a d^6+3 b d^6+2 c d^6-414 a x d^6-198 b x d^6-132 c x d^6-66 c x^4 d^4-99 b x^3 d^4+240 c x^3 d^4-204 a x^2 d^4+375 b x^2 d^4+216 c x^2 d^4-948 a d^4-375 b d^4-246 c d^4+1152 a x d^4+99 b x d^4-144 c x d^4+128 c x^2 d^2+1536 a d^2+372 b d^2-384 c d^2+396 b x d^2+768 c x d^2+1024 c\right)+\sqrt{d-1} \left(\sqrt{d x+1} \left(48 c x^5 d^7+72 b x^4 d^7+144 a x^3 d^7-144 a x^2 d^7-72 b x^2 d^7-48 c x^2 d^7+24 c x^5 d^6+36 b x^4 d^6-24 c x^4 d^6+72 a x^3 d^6-36 b x^3 d^6-144 a x^2 d^6-36 b x^2 d^6-24 c x^2 d^6+72 a x d^6+36 b x d^6+24 c x d^6-12 c x^5 d^5-18 b x^4 d^5+208 c x^4 d^5-36 a x^3 d^5+312 b x^3 d^5+60 c x^3 d^5+732 a x^2 d^5-60 c x^2 d^5+36 a d^5+18 b d^5+12 c d^5-732 a x d^5-312 b x d^5-208 c x d^5+116 c x^4 d^4+174 b x^3 d^4-80 c x^3 d^4+384 a x^2 d^4-174 b x^2 d^4-72 c x^2 d^4+384 a d^4+174 b d^4+116 c d^4-768 a x d^4-174 b x d^4-80 c x d^4+128 c x^3 d^3+228 b x^2 d^3+384 c x^2 d^3-768 a d^3-228 b d^3-128 c d^3+768 a x d^3-384 c x d^3-1536 a d^2-384 b d^2-384 b x d^2-512 c x d^2-512 c d+512 c x d-1024 c\right)+\sqrt{d+1} \left(-8 c x^6 d^8-12 b x^5 d^8-24 a x^4 d^8+24 a x^3 d^8+12 b x^3 d^8+8 c x^3 d^8+2 c x^6 d^6+3 b x^5 d^6-132 c x^5 d^6+6 a x^4 d^6-198 b x^4 d^6-6 c x^4 d^6-414 a x^3 d^6+6 b x^3 d^6+10 c x^3 d^6+426 a x^2 d^6+198 b x^2 d^6+132 c x^2 d^6-18 a x d^6-9 b x d^6-6 c x d^6-246 c x^4 d^4-375 b x^3 d^4-144 c x^3 d^4-948 a x^2 d^4+99 b x^2 d^4+216 c x^2 d^4-204 a d^4-99 b d^4-66 c d^4+1152 a x d^4+375 b x d^4+240 c x d^4-384 c x^2 d^2+1536 a d^2+396 b d^2+128 c d^2+372 b x d^2+768 c x d^2+1024 c\right)\right)}{6 \sqrt{d+1} \sqrt{d x+1} \left(-24 x^2 d^4+12 x^2 d^3+12 x d^3+6 x^2 d^2-116 x d^2+6 d^2+52 x d+52 d-128\right) d^4+6 \left(4 x^3 d^6-3 x^3 d^4+66 x^2 d^4-3 x d^4-33 x^2 d^2+126 x d^2-33 d^2+132\right) d^4+\sqrt{d-1} \sqrt{d x-1} \left(6 \sqrt{d+1} \sqrt{d x+1} \left(-4 x^2 d^4+x^2 d^2-66 x d^2+d^2-124\right) d^4+6 \left(24 x^2 d^4+12 x^2 d^3+12 x d^3-6 x^2 d^2+116 x d^2-6 d^2+52 x d+52 d+128\right) d^4\right)}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{d x-1}-\sqrt{d-1}}{\sqrt{d+1}-\sqrt{d x+1}}\right)}{d^3}","\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,"(Sqrt[1 + d]*Sqrt[-1 + d*x]*(-1024*c + 512*c*d - 1536*a*d^2 - 384*b*d^2 + 768*a*d^3 + 228*b*d^3 + 128*c*d^3 + 384*a*d^4 + 174*b*d^4 + 116*c*d^4 - 36*a*d^5 - 18*b*d^5 - 12*c*d^5 - 512*c*d*x - 384*b*d^2*x - 512*c*d^2*x - 768*a*d^3*x + 384*c*d^3*x - 768*a*d^4*x - 174*b*d^4*x - 80*c*d^4*x + 732*a*d^5*x + 312*b*d^5*x + 208*c*d^5*x + 72*a*d^6*x + 36*b*d^6*x + 24*c*d^6*x - 228*b*d^3*x^2 - 384*c*d^3*x^2 + 384*a*d^4*x^2 - 174*b*d^4*x^2 - 72*c*d^4*x^2 - 732*a*d^5*x^2 + 60*c*d^5*x^2 - 144*a*d^6*x^2 - 36*b*d^6*x^2 - 24*c*d^6*x^2 + 144*a*d^7*x^2 + 72*b*d^7*x^2 + 48*c*d^7*x^2 - 128*c*d^3*x^3 + 174*b*d^4*x^3 - 80*c*d^4*x^3 + 36*a*d^5*x^3 - 312*b*d^5*x^3 - 60*c*d^5*x^3 + 72*a*d^6*x^3 - 36*b*d^6*x^3 - 144*a*d^7*x^3 + 116*c*d^4*x^4 + 18*b*d^5*x^4 - 208*c*d^5*x^4 + 36*b*d^6*x^4 - 24*c*d^6*x^4 - 72*b*d^7*x^4 + 12*c*d^5*x^5 + 24*c*d^6*x^5 - 48*c*d^7*x^5) + Sqrt[-1 + d*x]*Sqrt[1 + d*x]*(1024*c + 1536*a*d^2 + 372*b*d^2 - 384*c*d^2 - 948*a*d^4 - 375*b*d^4 - 246*c*d^4 + 6*a*d^6 + 3*b*d^6 + 2*c*d^6 + 396*b*d^2*x + 768*c*d^2*x + 1152*a*d^4*x + 99*b*d^4*x - 144*c*d^4*x - 414*a*d^6*x - 198*b*d^6*x - 132*c*d^6*x + 128*c*d^2*x^2 - 204*a*d^4*x^2 + 375*b*d^4*x^2 + 216*c*d^4*x^2 + 426*a*d^6*x^2 + 6*b*d^6*x^2 - 6*c*d^6*x^2 - 24*a*d^8*x^2 - 12*b*d^8*x^2 - 8*c*d^8*x^2 - 99*b*d^4*x^3 + 240*c*d^4*x^3 - 18*a*d^6*x^3 + 198*b*d^6*x^3 + 10*c*d^6*x^3 + 24*a*d^8*x^3 - 66*c*d^4*x^4 - 9*b*d^6*x^4 + 132*c*d^6*x^4 + 12*b*d^8*x^4 - 6*c*d^6*x^5 + 8*c*d^8*x^5) + Sqrt[-1 + d]*(Sqrt[1 + d*x]*(-1024*c - 512*c*d - 1536*a*d^2 - 384*b*d^2 - 768*a*d^3 - 228*b*d^3 - 128*c*d^3 + 384*a*d^4 + 174*b*d^4 + 116*c*d^4 + 36*a*d^5 + 18*b*d^5 + 12*c*d^5 + 512*c*d*x - 384*b*d^2*x - 512*c*d^2*x + 768*a*d^3*x - 384*c*d^3*x - 768*a*d^4*x - 174*b*d^4*x - 80*c*d^4*x - 732*a*d^5*x - 312*b*d^5*x - 208*c*d^5*x + 72*a*d^6*x + 36*b*d^6*x + 24*c*d^6*x + 228*b*d^3*x^2 + 384*c*d^3*x^2 + 384*a*d^4*x^2 - 174*b*d^4*x^2 - 72*c*d^4*x^2 + 732*a*d^5*x^2 - 60*c*d^5*x^2 - 144*a*d^6*x^2 - 36*b*d^6*x^2 - 24*c*d^6*x^2 - 144*a*d^7*x^2 - 72*b*d^7*x^2 - 48*c*d^7*x^2 + 128*c*d^3*x^3 + 174*b*d^4*x^3 - 80*c*d^4*x^3 - 36*a*d^5*x^3 + 312*b*d^5*x^3 + 60*c*d^5*x^3 + 72*a*d^6*x^3 - 36*b*d^6*x^3 + 144*a*d^7*x^3 + 116*c*d^4*x^4 - 18*b*d^5*x^4 + 208*c*d^5*x^4 + 36*b*d^6*x^4 - 24*c*d^6*x^4 + 72*b*d^7*x^4 - 12*c*d^5*x^5 + 24*c*d^6*x^5 + 48*c*d^7*x^5) + Sqrt[1 + d]*(1024*c + 1536*a*d^2 + 396*b*d^2 + 128*c*d^2 - 204*a*d^4 - 99*b*d^4 - 66*c*d^4 + 372*b*d^2*x + 768*c*d^2*x + 1152*a*d^4*x + 375*b*d^4*x + 240*c*d^4*x - 18*a*d^6*x - 9*b*d^6*x - 6*c*d^6*x - 384*c*d^2*x^2 - 948*a*d^4*x^2 + 99*b*d^4*x^2 + 216*c*d^4*x^2 + 426*a*d^6*x^2 + 198*b*d^6*x^2 + 132*c*d^6*x^2 - 375*b*d^4*x^3 - 144*c*d^4*x^3 - 414*a*d^6*x^3 + 6*b*d^6*x^3 + 10*c*d^6*x^3 + 24*a*d^8*x^3 + 12*b*d^8*x^3 + 8*c*d^8*x^3 - 246*c*d^4*x^4 + 6*a*d^6*x^4 - 198*b*d^6*x^4 - 6*c*d^6*x^4 - 24*a*d^8*x^4 + 3*b*d^6*x^5 - 132*c*d^6*x^5 - 12*b*d^8*x^5 + 2*c*d^6*x^6 - 8*c*d^8*x^6)))/(6*d^4*Sqrt[1 + d]*Sqrt[1 + d*x]*(-128 + 52*d + 6*d^2 + 52*d*x - 116*d^2*x + 12*d^3*x + 6*d^2*x^2 + 12*d^3*x^2 - 24*d^4*x^2) + 6*d^4*(132 - 33*d^2 + 126*d^2*x - 3*d^4*x - 33*d^2*x^2 + 66*d^4*x^2 - 3*d^4*x^3 + 4*d^6*x^3) + Sqrt[-1 + d]*Sqrt[-1 + d*x]*(6*d^4*Sqrt[1 + d]*Sqrt[1 + d*x]*(-124 + d^2 - 66*d^2*x + d^2*x^2 - 4*d^4*x^2) + 6*d^4*(128 + 52*d - 6*d^2 + 52*d*x + 116*d^2*x + 12*d^3*x - 6*d^2*x^2 + 12*d^3*x^2 + 24*d^4*x^2))) - (2*b*ArcTanh[(-Sqrt[-1 + d] + Sqrt[-1 + d*x])/(Sqrt[1 + d] - Sqrt[1 + d*x])])/d^3","B",1
35,1,607,52,0.0006474,"\int \frac{a+b x+c x^2}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\left(-\frac{4 a}{d}-\frac{2 c}{d^3}\right) \tanh ^{-1}\left(\frac{\sqrt{d x-1}-\sqrt{d-1}}{\sqrt{d+1}-\sqrt{d x+1}}\right)+\frac{\left(\sqrt{d+1}-\sqrt{d x+1}\right) \left(d^2 (-x)-\sqrt{d-1} \sqrt{d x-1}+\sqrt{d+1} \sqrt{d x+1}+\sqrt{d-1} \sqrt{d+1} \sqrt{d x-1} \sqrt{d x+1}-1\right) \left(\frac{2 b \sqrt{d x-1}}{d^2}-\frac{2 b \sqrt{d-1}}{d^2}\right)}{\left(\sqrt{d-1} \sqrt{d x-1}-\sqrt{d+1} \sqrt{d x+1}+2\right)^2}+\frac{\left(\sqrt{d+1}-\sqrt{d x+1}\right) \left(d (-x)+\sqrt{d-1} \sqrt{d x-1}+\sqrt{d+1} \sqrt{d x+1}-d\right) \left(-2 d^4 x^2+d^2 x^2-3 d^2 x-4 \sqrt{d-1} d^2 x \sqrt{d x-1}+4 \sqrt{d+1} d^2 x \sqrt{d x+1}+2 \sqrt{d-1} \sqrt{d+1} d^2 x \sqrt{d x-1} \sqrt{d x+1}+d^2-2 \sqrt{d-1} d x \sqrt{d x-1}-2 \sqrt{d-1} d \sqrt{d x-1}-2 \sqrt{d+1} d x \sqrt{d x+1}-2 \sqrt{d+1} d \sqrt{d x+1}-2 \sqrt{d-1} \sqrt{d x-1}+2 \sqrt{d+1} \sqrt{d x+1}+3 \sqrt{d-1} \sqrt{d+1} \sqrt{d x-1} \sqrt{d x+1}-1\right) \left(\frac{2 c \sqrt{d-1}}{d^3}-\frac{2 c \sqrt{d x-1}}{d^3}\right)}{\left(\sqrt{d-1} \sqrt{d x-1}-\sqrt{d+1} \sqrt{d x+1}+2\right)^4}","\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,"(((-2*b*Sqrt[-1 + d])/d^2 + (2*b*Sqrt[-1 + d*x])/d^2)*(Sqrt[1 + d] - Sqrt[1 + d*x])*(-1 - d^2*x - Sqrt[-1 + d]*Sqrt[-1 + d*x] + Sqrt[1 + d]*Sqrt[1 + d*x] + Sqrt[-1 + d]*Sqrt[1 + d]*Sqrt[-1 + d*x]*Sqrt[1 + d*x]))/(2 + Sqrt[-1 + d]*Sqrt[-1 + d*x] - Sqrt[1 + d]*Sqrt[1 + d*x])^2 + (((2*c*Sqrt[-1 + d])/d^3 - (2*c*Sqrt[-1 + d*x])/d^3)*(Sqrt[1 + d] - Sqrt[1 + d*x])*(-d - d*x + Sqrt[-1 + d]*Sqrt[-1 + d*x] + Sqrt[1 + d]*Sqrt[1 + d*x])*(-1 + d^2 - 3*d^2*x + d^2*x^2 - 2*d^4*x^2 - 2*Sqrt[-1 + d]*Sqrt[-1 + d*x] - 2*Sqrt[-1 + d]*d*Sqrt[-1 + d*x] - 2*Sqrt[-1 + d]*d*x*Sqrt[-1 + d*x] - 4*Sqrt[-1 + d]*d^2*x*Sqrt[-1 + d*x] + 2*Sqrt[1 + d]*Sqrt[1 + d*x] - 2*d*Sqrt[1 + d]*Sqrt[1 + d*x] - 2*d*Sqrt[1 + d]*x*Sqrt[1 + d*x] + 4*d^2*Sqrt[1 + d]*x*Sqrt[1 + d*x] + 3*Sqrt[-1 + d]*Sqrt[1 + d]*Sqrt[-1 + d*x]*Sqrt[1 + d*x] + 2*Sqrt[-1 + d]*d^2*Sqrt[1 + d]*x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]))/(2 + Sqrt[-1 + d]*Sqrt[-1 + d*x] - Sqrt[1 + d]*Sqrt[1 + d*x])^4 + ((-2*c)/d^3 - (4*a)/d)*ArcTanh[(-Sqrt[-1 + d] + Sqrt[-1 + d*x])/(Sqrt[1 + d] - Sqrt[1 + d*x])]","B",1
36,1,864,55,0.0006921,"\int \frac{a+b x+c x^2}{x \sqrt{-1+d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{-c \sqrt{d+1} \sqrt{d x-1} (2 x d-2 d+4)-c \sqrt{d x-1} \sqrt{d x+1} \left(-x d^2+d^2-4\right)+\sqrt{d-1} \left(-c \sqrt{d x+1} (-2 x d+2 d+4)-c \sqrt{d+1} \left(x^2 d^2-x d^2-4\right)\right)}{\left(x d^2+3\right) d^2-2 \sqrt{d+1} \sqrt{d x+1} d^2+\sqrt{d-1} \sqrt{d x-1} \left(2 d^2-d^2 \sqrt{d+1} \sqrt{d x+1}\right)}-\frac{4 b \tanh ^{-1}\left(\frac{\sqrt{d x-1}-\sqrt{d-1}}{\sqrt{d+1}-\sqrt{d x+1}}\right)}{d}-\frac{1}{2} a \text{RootSum}\left[d^2 \text{$\#$1}^8-4 d^2 \text{$\#$1}^6+16 \text{$\#$1}^6+6 d^2 \text{$\#$1}^4+32 \text{$\#$1}^4-4 d^2 \text{$\#$1}^2+16 \text{$\#$1}^2+d^2\&,\frac{-d \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}^6+d \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}^6-4 \sqrt{d-1} \sqrt{d+1} \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}^5+4 \sqrt{d-1} \sqrt{d+1} \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}^5-5 d \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}^4+5 d \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}^4+5 d \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}^2-5 d \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}^2+4 \sqrt{d-1} \sqrt{d+1} \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}-4 \sqrt{d-1} \sqrt{d+1} \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}+d \log \left(\sqrt{d+1}-\sqrt{d x+1}\right)-d \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right)}{d^2 \text{$\#$1}^7-3 d^2 \text{$\#$1}^5+12 \text{$\#$1}^5+3 d^2 \text{$\#$1}^3+16 \text{$\#$1}^3-d^2 \text{$\#$1}+4 \text{$\#$1}}\&\right]","a \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{b \cosh ^{-1}(d x)}{d}+\frac{c \sqrt{d x-1} \sqrt{d x+1}}{d^2}",1,"(-(c*Sqrt[1 + d]*Sqrt[-1 + d*x]*(4 - 2*d + 2*d*x)) - c*Sqrt[-1 + d*x]*Sqrt[1 + d*x]*(-4 + d^2 - d^2*x) + Sqrt[-1 + d]*(-(c*(4 + 2*d - 2*d*x)*Sqrt[1 + d*x]) - c*Sqrt[1 + d]*(-4 - d^2*x + d^2*x^2)))/(-2*d^2*Sqrt[1 + d]*Sqrt[1 + d*x] + d^2*(3 + d^2*x) + Sqrt[-1 + d]*Sqrt[-1 + d*x]*(2*d^2 - d^2*Sqrt[1 + d]*Sqrt[1 + d*x])) - (4*b*ArcTanh[(-Sqrt[-1 + d] + Sqrt[-1 + d*x])/(Sqrt[1 + d] - Sqrt[1 + d*x])])/d - (a*RootSum[d^2 + 16*#1^2 - 4*d^2*#1^2 + 32*#1^4 + 6*d^2*#1^4 + 16*#1^6 - 4*d^2*#1^6 + d^2*#1^8 & , (d*Log[Sqrt[1 + d] - Sqrt[1 + d*x]] - d*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1] + 4*Sqrt[-1 + d]*Sqrt[1 + d]*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1 - 4*Sqrt[-1 + d]*Sqrt[1 + d]*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1 + 5*d*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1^2 - 5*d*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1^2 - 5*d*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1^4 + 5*d*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1^4 - 4*Sqrt[-1 + d]*Sqrt[1 + d]*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1^5 + 4*Sqrt[-1 + d]*Sqrt[1 + d]*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1^5 - d*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1^6 + d*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1^6)/(4*#1 - d^2*#1 + 16*#1^3 + 3*d^2*#1^3 + 12*#1^5 - 3*d^2*#1^5 + d^2*#1^7) & ])/2","C",1
37,-1,0,55,180.0549529,"\int \frac{a+b x+c x^2}{x^2 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","\frac{a \sqrt{d x-1} \sqrt{d x+1}}{x}+b \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{c \cosh ^{-1}(d x)}{d}",1,"$Aborted","F",-1
38,-1,0,83,180.2457735,"\int \frac{a+b x+c x^2}{x^3 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
39,-1,0,116,180.0131701,"\int \frac{a+b x+c x^2}{x^4 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x^4*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","\frac{\sqrt{d x-1} \sqrt{d x+1} \left(2 a d^2+3 c\right)}{3 x}+\frac{a \sqrt{d x-1} \sqrt{d x+1}}{3 x^3}+\frac{1}{2} b d^2 \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{b \sqrt{d x-1} \sqrt{d x+1}}{2 x^2}",1,"$Aborted","F",-1
40,1,2897,199,27.2151265,"\int \frac{a+b x+c x^2}{\sqrt{-1+x} \sqrt{1+x} (d+e x)^3} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(Sqrt[-1 + x]*Sqrt[1 + x]*(d + e*x)^3),x]","\text{Result too large to show}","-\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{\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}}+\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)}",1,"(Sqrt[-1 + x]*Sqrt[1 + x]*(-56*b*d^5 - 84*c*d^5 + 112*a*d^4*e + 28*b*d^4*e + 84*c*d^4*e + 28*a*d^3*e^2 + 84*b*d^3*e^2 + 168*c*d^3*e^2 - 252*a*d^2*e^3 - 112*b*d^2*e^3 - 168*c*d^2*e^3 + 56*a*d*e^4 + 56*b*d*e^4 + 56*a*e^5 + 32*b*d^5*x - 10*c*d^5*x - 64*a*d^4*e*x + 46*b*d^4*e*x - 160*c*d^4*e*x - 82*a*d^3*e^2*x + 128*b*d^3*e^2*x + 12*c*d^3*e^2*x - 96*a*d^2*e^3*x + 64*b*d^2*e^3*x + 112*c*d^2*e^3*x - 140*a*d*e^4*x - 112*b*d*e^4*x - 224*c*d*e^4*x + 112*a*e^5*x + 112*b*e^5*x + 14*b*d^5*x^2 + 28*c*d^5*x^2 - 28*a*d^4*e*x^2 + 36*b*d^4*e*x^2 + 43*c*d^4*e*x^2 - 100*a*d^3*e^2*x^2 + 43*b*d^3*e^2*x^2 - 96*c*d^3*e^2*x^2 - 129*a*d^2*e^3*x^2 + 88*b*d^2*e^3*x^2 - 214*c*d^2*e^3*x^2 - 80*a*d*e^4*x^2 + 114*b*d*e^4*x^2 - 112*c*d*e^4*x^2 - 14*a*e^5*x^2 + 56*b*e^5*x^2 + 7*c*d^5*x^3 + 7*b*d^4*e*x^3 + 28*c*d^4*e*x^3 - 21*a*d^3*e^2*x^3 + 4*b*d^3*e^2*x^3 - 24*c*d^3*e^2*x^3 - 36*a*d^2*e^3*x^3 + 18*b*d^2*e^3*x^3 - 76*c*d^2*e^3*x^3 - 12*a*d*e^4*x^3 + 44*b*d*e^4*x^3 - 16*c*d*e^4*x^3 - 12*a*e^5*x^3 + 8*b*e^5*x^3) + Sqrt[1 + x]*(-96*b*d^5 - 48*c*d^5 + 192*a*d^4*e - 240*b*d^4*e + 144*c*d^4*e + 528*a*d^3*e^2 - 240*b*d^3*e^2 + 480*c*d^3*e^2 + 336*a*d^2*e^3 - 192*b*d^2*e^3 + 288*c*d^2*e^3 - 96*a*d*e^4 - 96*b*d*e^4 - 96*a*e^5 - 64*b*d^5*x - 96*c*d^5*x + 128*a*d^4*e*x - 160*b*d^4*e*x - 96*c*d^4*e*x + 416*a*d^3*e^2*x - 192*b*d^3*e^2*x + 384*c*d^3*e^2*x + 480*a*d^2*e^3*x - 320*b*d^2*e^3*x + 720*c*d^2*e^3*x + 256*a*d*e^4*x - 368*b*d*e^4*x + 384*c*d*e^4*x + 16*a*e^5*x - 192*b*e^5*x + 40*b*d^5*x^2 + 4*c*d^5*x^2 - 80*a*d^4*e*x^2 + 20*b*d^4*e*x^2 - 188*c*d^4*e*x^2 - 44*a*d^3*e^2*x^2 + 4*b*d^3*e^2*x^2 - 72*c*d^3*e^2*x^2 + 180*a*d^2*e^3*x^2 - 16*b*d^2*e^3*x^2 + 344*c*d^2*e^3*x^2 + 104*a*d*e^4*x^2 - 200*b*d*e^4*x^2 + 128*c*d*e^4*x^2 + 56*a*e^5*x^2 - 64*b*e^5*x^2 + 20*c*d^5*x^3 + 20*b*d^4*e*x^3 + 80*c*d^4*e*x^3 - 60*a*d^3*e^2*x^3 + 8*b*d^3*e^2*x^3 - 72*c*d^3*e^2*x^3 - 96*a*d^2*e^3*x^3 + 48*b*d^2*e^3*x^3 - 212*c*d^2*e^3*x^3 - 24*a*d*e^4*x^3 + 124*b*d*e^4*x^3 - 32*c*d*e^4*x^3 - 36*a*e^5*x^3 + 16*b*e^5*x^3) + Sqrt[3]*(56*b*d^5 + 28*c*d^5 - 112*a*d^4*e + 140*b*d^4*e - 84*c*d^4*e - 308*a*d^3*e^2 + 140*b*d^3*e^2 - 280*c*d^3*e^2 - 196*a*d^2*e^3 + 112*b*d^2*e^3 - 168*c*d^2*e^3 + 56*a*d*e^4 + 56*b*d*e^4 + 56*a*e^5 + 64*b*d^5*x + 70*c*d^5*x - 128*a*d^4*e*x + 158*b*d^4*e*x + 16*c*d^4*e*x - 386*a*d^3*e^2*x + 176*b*d^3*e^2*x - 356*c*d^3*e^2*x - 368*a*d^2*e^3*x + 240*b*d^2*e^3*x - 496*c*d^2*e^3*x - 124*a*d*e^4*x + 240*b*d*e^4*x - 224*c*d*e^4*x + 16*a*e^5*x + 112*b*e^5*x - 14*b*d^5*x^2 + 18*c*d^5*x^2 + 28*a*d^4*e*x^2 + 18*b*d^4*e*x^2 + 149*c*d^4*e*x^2 - 54*a*d^3*e^2*x^2 + 37*b*d^3*e^2*x^2 - 28*c*d^3*e^2*x^2 - 223*a*d^2*e^3*x^2 + 80*b*d^2*e^3*x^2 - 386*c*d^2*e^3*x^2 - 132*a*d*e^4*x^2 + 214*b*d*e^4*x^2 - 176*c*d*e^4*x^2 - 42*a*e^5*x^2 + 88*b*e^5*x^2 - 8*b*d^5*x^3 - 14*c*d^5*x^3 + 16*a*d^4*e*x^3 - 18*b*d^4*e*x^3 - 16*c*d^4*e*x^3 + 50*a*d^3*e^2*x^3 - 8*b*d^3*e^2*x^3 + 62*c*d^3*e^2*x^3 + 32*a*d^2*e^3*x^3 - 30*b*d^2*e^3*x^3 + 76*c*d^2*e^3*x^3 - 2*a*d*e^4*x^3 - 44*b*d*e^4*x^3 + 12*a*e^5*x^3 - 4*c*d^5*x^4 - 4*b*d^4*e*x^4 - 16*c*d^4*e*x^4 + 12*a*d^3*e^2*x^4 - 2*b*d^3*e^2*x^4 + 14*c*d^3*e^2*x^4 + 20*a*d^2*e^3*x^4 - 10*b*d^2*e^3*x^4 + 43*c*d^2*e^3*x^4 + 6*a*d*e^4*x^4 - 25*b*d*e^4*x^4 + 8*c*d*e^4*x^4 + 7*a*e^5*x^4 - 4*b*e^5*x^4 + Sqrt[-1 + x]*(32*b*d^5 + 48*c*d^5 - 64*a*d^4*e - 16*b*d^4*e - 48*c*d^4*e - 16*a*d^3*e^2 - 48*b*d^3*e^2 - 96*c*d^3*e^2 + 144*a*d^2*e^3 + 64*b*d^2*e^3 + 96*c*d^2*e^3 - 32*a*d*e^4 - 32*b*d*e^4 - 32*a*e^5 + 32*c*d^5*x - 32*b*d^4*e*x + 64*c*d^4*e*x + 32*a*d^3*e^2*x - 96*b*d^3*e^2*x - 64*c*d^3*e^2*x + 128*a*d^2*e^3*x - 16*c*d^2*e^3*x + 64*a*d*e^4*x + 48*b*d*e^4*x + 128*c*d*e^4*x - 80*a*e^5*x - 64*b*e^5*x - 24*b*d^5*x^2 - 20*c*d^5*x^2 + 48*a*d^4*e*x^2 - 36*b*d^4*e*x^2 + 36*c*d^4*e*x^2 + 92*a*d^3*e^2*x^2 - 60*b*d^3*e^2*x^2 + 72*c*d^3*e^2*x^2 + 84*a*d^2*e^3*x^2 - 80*b*d^2*e^3*x^2 + 72*c*d^2*e^3*x^2 + 88*a*d*e^4*x^2 - 24*b*d*e^4*x^2 + 128*c*d*e^4*x^2 - 24*a*e^5*x^2 - 64*b*e^5*x^2 - 12*c*d^5*x^3 - 12*b*d^4*e*x^3 - 48*c*d^4*e*x^3 + 36*a*d^3*e^2*x^3 - 8*b*d^3*e^2*x^3 + 40*c*d^3*e^2*x^3 + 64*a*d^2*e^3*x^3 - 32*b*d^2*e^3*x^3 + 132*c*d^2*e^3*x^3 + 24*a*d*e^4*x^3 - 76*b*d*e^4*x^3 + 32*c*d*e^4*x^3 + 20*a*e^5*x^3 - 16*b*e^5*x^3)))/(2*Sqrt[3]*(d^3 + 2*d^2*e - d*e^2 - 2*e^3)^2*(-8 - 12*x)*Sqrt[1 + x]*(d + e*x)^2 + 2*(d^3 + 2*d^2*e - d*e^2 - 2*e^3)^2*(d + e*x)^2*(14 + 28*x + 7*x^2) + Sqrt[-1 + x]*(2*Sqrt[3]*(d^3 + 2*d^2*e - d*e^2 - 2*e^3)^2*(-14 - 4*x)*Sqrt[1 + x]*(d + e*x)^2 + 2*(d^3 + 2*d^2*e - d*e^2 - 2*e^3)^2*(24 + 20*x)*(d + e*x)^2)) + (-((a*d^2)/(d^2 - e^2)^2) - (c*d^2)/(2*(d^2 - e^2)^2) + (3*b*d*e)/(2*(d^2 - e^2)^2) - (a*e^2)/(2*(d^2 - e^2)^2) - (c*e^2)/(d^2 - e^2)^2)*RootSum[d + 2*e - 4*Sqrt[3]*e*#1 - 2*d*#1^2 + 12*e*#1^2 - 4*Sqrt[3]*e*#1^3 + d*#1^4 + 2*e*#1^4 & , (Log[Sqrt[3] - Sqrt[1 + x]] - Log[-1 + Sqrt[-1 + x] + Sqrt[3]*#1 - Sqrt[1 + x]*#1] - Log[Sqrt[3] - Sqrt[1 + x]]*#1^2 + Log[-1 + Sqrt[-1 + x] + Sqrt[3]*#1 - Sqrt[1 + x]*#1]*#1^2)/(-(Sqrt[3]*e) - d*#1 + 6*e*#1 - 3*Sqrt[3]*e*#1^2 + d*#1^3 + 2*e*#1^3) & ]","C",1
41,-1,0,1348,180.1679951,"\int (a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[(a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2),x]","\text{\$Aborted}","\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,"$Aborted","F",-1
42,-1,0,721,180.0589897,"\int (a+b x) \sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[(a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2),x]","\text{\$Aborted}","-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(48 a^2 C d^2 f^2+6 b d f x (6 a C d f-b (10 B d f-7 C (c f+d e)))-10 a b d f (8 B d f-5 C (c f+d e))-\left(b^2 \left(10 d f (8 A d f-5 B (c f+d e))+C \left(35 c^2 f^2+38 c d e f+35 d^2 e^2\right)\right)\right)\right)}{240 b d^3 f^3}-\frac{(d e-c f)^2 \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(2 a d f \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)-b \left(2 d f \left(8 A d f (c f+d e)-B \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)+C \left(7 c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+7 d^3 e^3\right)\right)\right)}{128 d^{9/2} f^{9/2}}+\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(2 a d f \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)-b \left(2 d f \left(8 A d f (c f+d e)-B \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)+C \left(7 c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+7 d^3 e^3\right)\right)\right)}{64 d^4 f^3}+\frac{\sqrt{c+d x} \sqrt{e+f x} (d e-c f) \left(2 a d f \left(8 d f (2 A d f-B (c f+d e))+C \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)-b \left(2 d f \left(8 A d f (c f+d e)-B \left(5 c^2 f^2+6 c d e f+5 d^2 e^2\right)\right)+C \left(7 c^3 f^3+9 c^2 d e f^2+9 c d^2 e^2 f+7 d^3 e^3\right)\right)\right)}{128 d^4 f^4}+\frac{C (a+b x)^2 (c+d x)^{3/2} (e+f x)^{3/2}}{5 b d f}",1,"$Aborted","F",-1
43,-1,0,330,180.0201357,"\int \sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2),x]","\text{\$Aborted}","-\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} \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{(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,"$Aborted","F",-1
44,-1,0,450,180.0288887,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{a+b x} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x),x]","\text{\$Aborted}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(16 a^3 C d^3 f^3-8 a^2 b d^2 f^2 (2 B d f+c C f+C d e)-2 a b^2 d f \left(C (d e-c f)^2-4 d f (2 A d f+B c f+B d e)\right)-\left(b^3 \left(C (d e-c f)^2 (c f+d e)-2 d f \left(B (d e-c f)^2-4 A d f (c f+d e)\right)\right)\right)\right)}{8 b^4 d^{5/2} f^{5/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} (4 b d f (2 A b d f-a C (c f+d e))+(4 a d f-b c f+b d e) (2 a C d f+b (-2 B d f+c C f+C d e)))}{8 b^3 d^2 f^2}-\frac{2 \sqrt{b c-a d} \sqrt{b e-a f} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right)}{b^4}-\frac{\sqrt{c+d x} (e+f x)^{3/2} (2 a C d f+b (-2 B d f+c C f+C d e))}{4 b^2 d f^2}+\frac{C (c+d x)^{3/2} (e+f x)^{3/2}}{3 b d f}",1,"$Aborted","F",-1
45,-1,0,521,180.0806113,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^2} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^2,x]","\text{\$Aborted}","\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{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)-\left(b^2 \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{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(6 a^3 C d f-a^2 b (4 B d f+5 C (c f+d e))+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,"$Aborted","F",-1
46,-1,0,658,180.0366684,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^3} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^3,x]","\text{\$Aborted}","-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(12 a^3 C d f^2-a^2 b f (4 B d f+11 c C f+17 C d e)+a b^2 (B f (3 c f+5 d e)+4 C e (4 c f+d e))-b^3 \left(c \left(-A f^2+4 B e f+4 C e^2\right)+A d e f\right)\right)}{4 b^3 (b c-a d) (b e-a f)^2}+\frac{\sqrt{c+d x} (e+f x)^{3/2} \left(6 a^3 C d f-a^2 b (2 B d f+7 C (c f+d e))+a b^2 (-2 A d f+3 B c f+3 B d e+8 c C e)-b^3 (-A c f-A d e+4 B c e)\right)}{4 b^2 (a+b x) (b c-a d) (b e-a f)^2}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(24 a^4 C d^2 f^2-8 a^3 b d f (B d f+5 C (c f+d e))+3 a^2 b^2 \left(4 B d f (c f+d e)+C \left(5 c^2 f^2+22 c d e f+5 d^2 e^2\right)\right)-3 a b^3 \left(c^2 f (B f+8 C e)+2 c d e (3 B f+4 C e)+B d^2 e^2\right)-b^4 \left(-\left(c^2 \left(-A f^2+4 B e f+8 C e^2\right)\right)-2 c d e (A f+2 B e)+A d^2 e^2\right)\right)}{4 b^4 (b c-a d)^{3/2} (b e-a f)^{3/2}}-\frac{(c+d x)^{3/2} (e+f x)^{3/2} \left(A b^2-a (b B-a C)\right)}{2 b (a+b x)^2 (b c-a d) (b e-a f)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (6 a C d f-b (2 B d f+c C f+C d e))}{b^4 \sqrt{d} \sqrt{f}}",1,"$Aborted","F",-1
47,-1,0,1032,180.0660621,"\int \frac{(a+b x)^2 \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","IntegrateAlgebraic[((a + b*x)^2*Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","\text{\$Aborted}","\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(\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\right)+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(\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\right)+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,"$Aborted","F",-1
48,-1,0,540,180.0195157,"\int \frac{(a+b x) \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","IntegrateAlgebraic[((a + b*x)*Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","\text{\$Aborted}","-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(24 a^2 C d^2 f^2+4 b d f x (4 a C d f+b (-8 B d f+5 c C f+7 C d e))+8 a b d f (-6 B d f+3 c C f+5 C d e)+b^2 \left(8 d f (-6 A d f+3 B c f+5 B d e)-C \left(15 c^2 f^2+22 c d e f+35 d^2 e^2\right)\right)\right)}{96 b d^3 f^3}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(8 a d f \left(2 d f (-4 A d f+B c f+3 B d e)-C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+b \left(8 d f \left(2 A d f (c f+3 d e)-B \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+C \left(5 c^3 f^3+9 c^2 d e f^2+15 c d^2 e^2 f+35 d^3 e^3\right)\right)\right)}{64 d^3 f^4}+\frac{(d e-c f) \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(8 a d f \left(2 d f (-4 A d f+B c f+3 B d e)-C \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+b \left(8 d f \left(2 A d f (c f+3 d e)-B \left(c^2 f^2+2 c d e f+5 d^2 e^2\right)\right)+C \left(5 c^3 f^3+9 c^2 d e f^2+15 c d^2 e^2 f+35 d^3 e^3\right)\right)\right)}{64 d^{7/2} f^{9/2}}+\frac{C (a+b x)^2 (c+d x)^{3/2} \sqrt{e+f x}}{4 b d f}",1,"$Aborted","F",-1
49,-1,0,246,180.0139034,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","\text{\$Aborted}","\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,"$Aborted","F",-1
50,-1,0,290,180.045417,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x) \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)*Sqrt[e + f*x]),x]","\text{\$Aborted}","\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) (2 b d f (4 A b d f-a C (c f+3 d e))+(2 a d f-b c f+b d e) (4 a C d f+b (-4 B d f+c C f+3 C d e)))}{4 b^3 d^{3/2} f^{5/2}}-\frac{2 \sqrt{b c-a d} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right)}{b^3 \sqrt{b e-a f}}-\frac{\sqrt{c+d x} \sqrt{e+f x} (4 a C d f+b (-4 B d f+c C f+3 C d e))}{4 b^2 d f^2}+\frac{C (c+d x)^{3/2} \sqrt{e+f x}}{2 b d f}",1,"$Aborted","F",-1
51,-1,0,364,180.0530932,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^2 \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^2*Sqrt[e + f*x]),x]","\text{\$Aborted}","\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(4 a^3 C d f-a^2 b (2 B d f+3 c C f+5 C d e)+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,"$Aborted","F",-1
52,-1,0,484,180.0819193,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^3 \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^3*Sqrt[e + f*x]),x]","\text{\$Aborted}","\frac{\sqrt{c+d x} \sqrt{e+f x} \left(4 a^3 C d f-a^2 b C (5 c f+7 d e)+a b^2 (-4 A d f+B c f+3 B d e+8 c C e)-b^3 (-3 A c f-A d e+4 B c e)\right)}{4 b^2 (a+b x) (b c-a d) (b e-a f)^2}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(8 a^4 C d^2 f^2-4 a^3 b C d f (3 c f+5 d e)+3 a^2 b^2 C \left(c^2 f^2+10 c d e f+5 d^2 e^2\right)-a b^3 \left(2 c d \left(2 A f^2-B e f+12 C e^2\right)+d^2 e (3 B e-4 A f)+c^2 f (8 C e-B f)\right)-b^4 \left(-\left(c^2 \left(3 A f^2-4 B e f+8 C e^2\right)\right)-2 c d e (2 B e-A f)+A d^2 e^2\right)\right)}{4 b^3 (b c-a d)^{3/2} (b e-a f)^{5/2}}-\frac{(c+d x)^{3/2} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{2 b (a+b x)^2 (b c-a d) (b e-a f)}+\frac{2 C \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right)}{b^3 \sqrt{f}}",1,"$Aborted","F",-1
53,-1,0,685,180.0468906,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^4 \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^4*Sqrt[e + f*x]),x]","\text{\$Aborted}","-\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(-\left(a^2 \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(4 a^3 C d f-a^2 b (-2 B d f+7 c C f+9 C d e)+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{\sqrt{c+d x} \sqrt{e+f x} \left(8 a^4 C d^2 f^2-2 a^3 b d f (-2 B d f+7 c C f+13 C d e)-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)-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{(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,"$Aborted","F",-1
54,-1,0,718,180.0239772,"\int \frac{(a+b x)^2 \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\text{\$Aborted}","\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \sqrt{e+f x}}\right) \left(16 a^2 d^2 f^2 \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)-16 a b d f \left(2 d f \left(4 A d f (c f+d e)-B \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)+C \left(5 c^3 f^3+3 c^2 d e f^2+3 c d^2 e^2 f+5 d^3 e^3\right)\right)+b^2 \left(8 d f \left(2 A d f \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)-B \left(5 c^3 f^3+3 c^2 d e f^2+3 c d^2 e^2 f+5 d^3 e^3\right)\right)+C \left(35 c^4 f^4+20 c^3 d e f^3+18 c^2 d^2 e^2 f^2+20 c d^3 e^3 f+35 d^4 e^4\right)\right)\right)}{64 d^{9/2} f^{9/2}}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(32 a^3 C d^3 f^3-8 a^2 b d^2 f^2 (16 B d f-11 C (c f+d e))-16 a b^2 d f \left(6 d f (4 A d f-3 B (c f+d e))+C \left(15 c^2 f^2+14 c d e f+15 d^2 e^2\right)\right)+2 b d f x (6 b d f (a c C f+a C d e-8 A b d f+6 b c C e)+(4 a d f-5 b (c f+d e)) (2 a C d f-b (8 B d f-7 C (c f+d e))))+b^3 \left(8 d f \left(18 A d f (c f+d e)-B \left(15 c^2 f^2+14 c d e f+15 d^2 e^2\right)\right)+5 C \left(21 c^3 f^3+19 c^2 d e f^2+19 c d^2 e^2 f+21 d^3 e^3\right)\right)\right)}{192 b d^4 f^4}-\frac{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} (2 a C d f-b (8 B d f-7 C (c f+d e)))}{24 b d^2 f^2}+\frac{C (a+b x)^3 \sqrt{c+d x} \sqrt{e+f x}}{4 b d f}",1,"$Aborted","F",-1
55,-1,0,371,180.0261136,"\int \frac{(a+b x) \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\text{\$Aborted}","-\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))-\left(b^2 \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(5 c^3 f^3+3 c^2 d e f^2+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,"$Aborted","F",-1
56,1,1714,164,15.3165891,"\int \frac{A+B x+C x^2}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\frac{\left(-4 C \sqrt{c+d x} d^3-\frac{4 C e \sqrt{c+d x} d^3}{f}-\frac{C e^2 \sqrt{c+d x} d^3}{2 f^2}+\frac{4 C \sqrt{c+d} \sqrt{e+f} \sqrt{e+f x} d^3}{f}+\frac{2 C \sqrt{c+d} e \sqrt{e+f} \sqrt{e+f x} d^3}{f^2}-\frac{2 C \sqrt{c+d} e d^3}{f}-\frac{3 C \sqrt{c+d} e^2 d^3}{2 f^2}+2 c C \sqrt{c+d} d^2-4 c C \sqrt{c+d x} d^2-\frac{3 c C e \sqrt{c+d x} d^2}{f}+\frac{2 c C \sqrt{c+d} \sqrt{e+f} \sqrt{e+f x} d^2}{f}+\frac{c C \sqrt{c+d} e d^2}{f}+\frac{1}{2} c^2 C \sqrt{c+d} d-\frac{1}{2} c^2 C \sqrt{c+d x} d\right) \left(\sqrt{e+f}-\sqrt{e+f x}\right)^7}{\left(-e d+\sqrt{e+f} \sqrt{e+f x} d+c f-\sqrt{c+d} f \sqrt{c+d x}\right)^4}+\frac{\left(\frac{3}{2} C \sqrt{c+d} c^2-\frac{3}{2} C \sqrt{c+d x} c^2+4 C d \sqrt{c+d} c-12 C d \sqrt{c+d x} c-\frac{9 C d e \sqrt{c+d x} c}{f}+\frac{8 C d \sqrt{c+d} \sqrt{e+f} \sqrt{e+f x} c}{f}+\frac{C d \sqrt{c+d} e c}{f}-4 C d^2 \sqrt{c+d}-12 C d^2 \sqrt{c+d x}-\frac{12 C d^2 e \sqrt{c+d x}}{f}-\frac{3 C d^2 e^2 \sqrt{c+d x}}{2 f^2}+\frac{16 C d^2 \sqrt{c+d} \sqrt{e+f} \sqrt{e+f x}}{f}+\frac{8 C d^2 \sqrt{c+d} e \sqrt{e+f} \sqrt{e+f x}}{f^2}-\frac{12 C d^2 \sqrt{c+d} e}{f}-\frac{13 C d^2 \sqrt{c+d} e^2}{2 f^2}\right) \left(\sqrt{e+f}-\sqrt{e+f x}\right)^5}{\left(-e d+\sqrt{e+f} \sqrt{e+f x} d+c f-\sqrt{c+d} f \sqrt{c+d x}\right)^3}+\frac{\left(\frac{C \sqrt{c+d} c^2}{4 d}-\frac{C \sqrt{c+d x} c^2}{4 d}+B \sqrt{c+d} c-B \sqrt{c+d x} c-8 C \sqrt{c+d x} c-\frac{11 C e \sqrt{c+d x} c}{2 f}+\frac{8 C \sqrt{c+d} \sqrt{e+f} \sqrt{e+f x} c}{f}-\frac{5 C \sqrt{c+d} e c}{2 f}-10 C d \sqrt{c+d}-2 B d \sqrt{c+d x}-10 C d \sqrt{c+d x}-\frac{B d e \sqrt{c+d x}}{f}-\frac{8 C d e \sqrt{c+d x}}{f}-\frac{C d e^2 \sqrt{c+d x}}{4 f^2}+\frac{2 B d \sqrt{c+d} \sqrt{e+f} \sqrt{e+f x}}{f}+\frac{20 C d \sqrt{c+d} \sqrt{e+f} \sqrt{e+f x}}{f}+\frac{8 C d \sqrt{c+d} e \sqrt{e+f} \sqrt{e+f x}}{f^2}-\frac{B d \sqrt{c+d} e}{f}-\frac{20 C d \sqrt{c+d} e}{f}-\frac{31 C d \sqrt{c+d} e^2}{4 f^2}\right) \left(\sqrt{e+f}-\sqrt{e+f x}\right)^3}{\left(-e d+\sqrt{e+f} \sqrt{e+f x} d+c f-\sqrt{c+d} f \sqrt{c+d x}\right)^2}+\frac{\left(\frac{\sqrt{e+f}}{4 d^2 f^2}-\frac{\sqrt{e+f x}}{4 d^2 f^2}\right) \left(-3 C \sqrt{c+d} e^2 d^2-8 B \sqrt{c+d} f^2 d^2-24 C \sqrt{c+d} f^2 d^2-12 B \sqrt{c+d} e f d^2-32 C \sqrt{c+d} e f d^2+3 C e^2 \sqrt{c+d x} d^2-8 B f^2 \sqrt{c+d x} d^2-8 C f^2 \sqrt{c+d x} d^2-4 B e f \sqrt{c+d x} d^2+16 B \sqrt{c+d} f \sqrt{e+f} \sqrt{e+f x} d^2+32 C \sqrt{c+d} f \sqrt{e+f} \sqrt{e+f x} d^2+4 B c \sqrt{c+d} f^2 d-2 c C \sqrt{c+d} e f d-4 B c f^2 \sqrt{c+d x} d+2 c C e f \sqrt{c+d x} d-3 c^2 C \sqrt{c+d} f^2+3 c^2 C f^2 \sqrt{c+d x}\right)}{-e d+\sqrt{e+f} \sqrt{e+f x} d+c f-\sqrt{c+d} f \sqrt{c+d x}}+\left(\frac{3 C c^2}{2 d^{5/2} \sqrt{f}}-\frac{2 B c}{d^{3/2} \sqrt{f}}+\frac{C e c}{d^{3/2} f^{3/2}}+\frac{4 A}{\sqrt{d} \sqrt{f}}-\frac{2 B e}{\sqrt{d} f^{3/2}}+\frac{3 C e^2}{2 \sqrt{d} f^{5/2}}\right) \tanh ^{-1}\left(\frac{\sqrt{c+d} \sqrt{f}-\sqrt{f} \sqrt{c+d x}}{\sqrt{d} \left(\sqrt{e+f}-\sqrt{e+f x}\right)}\right)","\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,"((Sqrt[e + f] - Sqrt[e + f*x])^3*(B*c*Sqrt[c + d] + (c^2*C*Sqrt[c + d])/(4*d) - 10*C*d*Sqrt[c + d] - (31*C*d*Sqrt[c + d]*e^2)/(4*f^2) - (5*c*C*Sqrt[c + d]*e)/(2*f) - (B*d*Sqrt[c + d]*e)/f - (20*C*d*Sqrt[c + d]*e)/f - B*c*Sqrt[c + d*x] - 8*c*C*Sqrt[c + d*x] - (c^2*C*Sqrt[c + d*x])/(4*d) - 2*B*d*Sqrt[c + d*x] - 10*C*d*Sqrt[c + d*x] - (C*d*e^2*Sqrt[c + d*x])/(4*f^2) - (11*c*C*e*Sqrt[c + d*x])/(2*f) - (B*d*e*Sqrt[c + d*x])/f - (8*C*d*e*Sqrt[c + d*x])/f + (8*C*d*Sqrt[c + d]*e*Sqrt[e + f]*Sqrt[e + f*x])/f^2 + (8*c*C*Sqrt[c + d]*Sqrt[e + f]*Sqrt[e + f*x])/f + (2*B*d*Sqrt[c + d]*Sqrt[e + f]*Sqrt[e + f*x])/f + (20*C*d*Sqrt[c + d]*Sqrt[e + f]*Sqrt[e + f*x])/f))/(-(d*e) + c*f - Sqrt[c + d]*f*Sqrt[c + d*x] + d*Sqrt[e + f]*Sqrt[e + f*x])^2 + ((Sqrt[e + f] - Sqrt[e + f*x])^5*((3*c^2*C*Sqrt[c + d])/2 + 4*c*C*d*Sqrt[c + d] - 4*C*d^2*Sqrt[c + d] - (13*C*d^2*Sqrt[c + d]*e^2)/(2*f^2) + (c*C*d*Sqrt[c + d]*e)/f - (12*C*d^2*Sqrt[c + d]*e)/f - (3*c^2*C*Sqrt[c + d*x])/2 - 12*c*C*d*Sqrt[c + d*x] - 12*C*d^2*Sqrt[c + d*x] - (3*C*d^2*e^2*Sqrt[c + d*x])/(2*f^2) - (9*c*C*d*e*Sqrt[c + d*x])/f - (12*C*d^2*e*Sqrt[c + d*x])/f + (8*C*d^2*Sqrt[c + d]*e*Sqrt[e + f]*Sqrt[e + f*x])/f^2 + (8*c*C*d*Sqrt[c + d]*Sqrt[e + f]*Sqrt[e + f*x])/f + (16*C*d^2*Sqrt[c + d]*Sqrt[e + f]*Sqrt[e + f*x])/f))/(-(d*e) + c*f - Sqrt[c + d]*f*Sqrt[c + d*x] + d*Sqrt[e + f]*Sqrt[e + f*x])^3 + ((Sqrt[e + f] - Sqrt[e + f*x])^7*((c^2*C*d*Sqrt[c + d])/2 + 2*c*C*d^2*Sqrt[c + d] - (3*C*d^3*Sqrt[c + d]*e^2)/(2*f^2) + (c*C*d^2*Sqrt[c + d]*e)/f - (2*C*d^3*Sqrt[c + d]*e)/f - (c^2*C*d*Sqrt[c + d*x])/2 - 4*c*C*d^2*Sqrt[c + d*x] - 4*C*d^3*Sqrt[c + d*x] - (C*d^3*e^2*Sqrt[c + d*x])/(2*f^2) - (3*c*C*d^2*e*Sqrt[c + d*x])/f - (4*C*d^3*e*Sqrt[c + d*x])/f + (2*C*d^3*Sqrt[c + d]*e*Sqrt[e + f]*Sqrt[e + f*x])/f^2 + (2*c*C*d^2*Sqrt[c + d]*Sqrt[e + f]*Sqrt[e + f*x])/f + (4*C*d^3*Sqrt[c + d]*Sqrt[e + f]*Sqrt[e + f*x])/f))/(-(d*e) + c*f - Sqrt[c + d]*f*Sqrt[c + d*x] + d*Sqrt[e + f]*Sqrt[e + f*x])^4 + ((Sqrt[e + f]/(4*d^2*f^2) - Sqrt[e + f*x]/(4*d^2*f^2))*(-3*C*d^2*Sqrt[c + d]*e^2 - 2*c*C*d*Sqrt[c + d]*e*f - 12*B*d^2*Sqrt[c + d]*e*f - 32*C*d^2*Sqrt[c + d]*e*f - 3*c^2*C*Sqrt[c + d]*f^2 + 4*B*c*d*Sqrt[c + d]*f^2 - 8*B*d^2*Sqrt[c + d]*f^2 - 24*C*d^2*Sqrt[c + d]*f^2 + 3*C*d^2*e^2*Sqrt[c + d*x] + 2*c*C*d*e*f*Sqrt[c + d*x] - 4*B*d^2*e*f*Sqrt[c + d*x] + 3*c^2*C*f^2*Sqrt[c + d*x] - 4*B*c*d*f^2*Sqrt[c + d*x] - 8*B*d^2*f^2*Sqrt[c + d*x] - 8*C*d^2*f^2*Sqrt[c + d*x] + 16*B*d^2*Sqrt[c + d]*f*Sqrt[e + f]*Sqrt[e + f*x] + 32*C*d^2*Sqrt[c + d]*f*Sqrt[e + f]*Sqrt[e + f*x]))/(-(d*e) + c*f - Sqrt[c + d]*f*Sqrt[c + d*x] + d*Sqrt[e + f]*Sqrt[e + f*x]) + ((3*C*e^2)/(2*Sqrt[d]*f^(5/2)) + (c*C*e)/(d^(3/2)*f^(3/2)) - (2*B*e)/(Sqrt[d]*f^(3/2)) + (3*c^2*C)/(2*d^(5/2)*Sqrt[f]) - (2*B*c)/(d^(3/2)*Sqrt[f]) + (4*A)/(Sqrt[d]*Sqrt[f]))*ArcTanh[(Sqrt[c + d]*Sqrt[f] - Sqrt[f]*Sqrt[c + d*x])/(Sqrt[d]*(Sqrt[e + f] - Sqrt[e + f*x]))]","B",1
57,-1,0,188,180.0320147,"\int \frac{A+B x+C x^2}{(a+b x) \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
58,-1,0,254,180.0596839,"\int \frac{A+B x+C x^2}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/((a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\text{\$Aborted}","\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(2 a^3 C d f-3 a^2 b C (c f+d e)+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,"$Aborted","F",-1
59,-1,0,424,180.0538852,"\int \frac{A+B x+C x^2}{(a+b x)^3 \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/((a + b*x)^3*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\text{\$Aborted}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x} \sqrt{b e-a f}}{\sqrt{e+f x} \sqrt{b c-a d}}\right) \left(a^2 \left(4 d f (2 A d f-B (c f+d e))+C \left(3 c^2 f^2+2 c d e f+3 d^2 e^2\right)\right)+a b \left(-2 c d \left(4 A f^2-7 B e f+4 C e^2\right)+d^2 e (B e-8 A f)+c^2 (-f) (8 C e-B f)\right)+b^2 \left(c^2 \left(3 A f^2-4 B e f+8 C e^2\right)-2 c d e (2 B e-A f)+3 A d^2 e^2\right)\right)}{4 (b c-a d)^{5/2} (b e-a f)^{5/2}}+\frac{\sqrt{c+d x} \sqrt{e+f x} \left(2 a^3 C d f+a^2 b (2 B d f-5 C (c f+d e))+a b^2 (-6 A d f+B c f+B d e+8 c C e)-b^3 (4 B c e-3 A (c f+d e))\right)}{4 b (a+b x) (b c-a d)^2 (b e-a f)^2}-\frac{\sqrt{c+d x} \sqrt{e+f x} \left(A b^2-a (b B-a C)\right)}{2 b (a+b x)^2 (b c-a d) (b e-a f)}",1,"$Aborted","F",-1
60,-1,0,826,180.0600084,"\int \frac{A+B x+C x^2}{(a+b x)^4 \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/((a + b*x)^4*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\text{\$Aborted}","-\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,"$Aborted","F",-1
61,0,0,1182,2.5028381,"\int \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right) \, dx","IntegrateAlgebraic[Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2),x]","\int \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right) \, dx","\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(\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\right)-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(\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\right)-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,"Could not integrate","F",-1
62,0,0,774,2.5297363,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/Sqrt[a + b*x],x]","\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{\sqrt{a+b x}} \, dx","-\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)-\left(b^2 \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-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} \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{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,"Could not integrate","F",-1
63,0,0,706,2.7949237,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^(3/2),x]","\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{3/2}} \, dx","\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 \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 (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,"Could not integrate","F",-1
64,0,0,687,2.7955936,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^(5/2),x]","\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{5/2}} \, dx","\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 \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 \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(16 a^3 C d^2 f^2-8 a^2 b d f (B d f+2 C (c f+d e))+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 (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,"Could not integrate","F",-1
65,0,0,964,2.8032939,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{7/2}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^(7/2),x]","\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{7/2}} \, dx","-\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(\left(30 C e^2+5 B f e-2 A f^2\right) c^2\right)-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,"Could not integrate","F",-1
66,0,0,1716,2.8044638,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{9/2}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*Sqrt[e + f*x]*(A + B*x + C*x^2))/(a + b*x)^(9/2),x]","\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left(A+B x+C x^2\right)}{(a+b x)^{9/2}} \, dx","-\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(\left(35 C e^2-14 B f e+8 A f^2\right) c^2\right)-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,"Could not integrate","F",-1
67,0,0,1235,2.7695973,"\int \frac{(a+b x)^{3/2} \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","\int \frac{(a+b x)^{3/2} \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","\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(\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\right)-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,"Could not integrate","F",-1
68,0,0,766,2.4773663,"\int \frac{\sqrt{a+b x} \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*Sqrt[c + d*x]*(A + B*x + C*x^2))/Sqrt[e + f*x],x]","\int \frac{\sqrt{a+b x} \sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{e+f x}} \, dx","\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)-\left(b^2 \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{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} \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{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,"Could not integrate","F",-1
69,0,0,527,2.5098017,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{a+b x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(A + B*x + C*x^2))/(Sqrt[a + b*x]*Sqrt[e + f*x]),x]","\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{\sqrt{a+b x} \sqrt{e+f x}} \, dx","-\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)-\left(b^2 (5 d f (2 B e-3 A f)-C e (c f+8 d 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)}{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,"Could not integrate","F",-1
70,0,0,540,2.7749757,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^{3/2} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^(3/2)*Sqrt[e + f*x]),x]","\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^{3/2} \sqrt{e+f x}} \, dx","\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 \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 (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,"Could not integrate","F",-1
71,0,0,597,2.7913523,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^{5/2} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^(5/2)*Sqrt[e + f*x]),x]","\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^{5/2} \sqrt{e+f x}} \, dx","-\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 \sqrt{d} \sqrt{e+f x} \sqrt{\frac{b (c+d x)}{b c-a d}} \left(8 a^3 C d f^2-a^2 b f (2 B d f+7 c C f+13 C d e)+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 (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,"Could not integrate","F",-1
72,0,0,1034,2.8022267,"\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^{7/2} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(A + B*x + C*x^2))/((a + b*x)^(7/2)*Sqrt[e + f*x]),x]","\int \frac{\sqrt{c+d x} \left(A+B x+C x^2\right)}{(a+b x)^{7/2} \sqrt{e+f x}} \, dx","-\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(\left(15 C e^2-10 B f e+8 A f^2\right) c^2\right)-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(\left(15 C e^2-10 B f e+8 A f^2\right) c^2\right)-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,"Could not integrate","F",-1
73,0,0,838,2.8056328,"\int \frac{(a+b x)^{3/2} \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{(a+b x)^{3/2} \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","\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(\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\right)-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,"Could not integrate","F",-1
74,0,0,528,2.5100407,"\int \frac{\sqrt{a+b x} \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{\sqrt{a+b x} \left(A+B x+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x}} \, dx","-\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,"Could not integrate","F",-1
75,0,0,387,2.5536911,"\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}} \, dx","\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,"Could not integrate","F",-1
76,0,0,422,2.8060698,"\int \frac{A+B x+C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{A+B x+C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","-\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,"Could not integrate","F",-1
77,0,0,642,2.8180065,"\int \frac{A+B x+C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{A+B x+C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","-\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(2 a^3 C d f+a^2 b (B d f-4 C (c f+d e))+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(2 a^3 C d f+a^2 b (B d f-4 C (c f+d e))+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,"Could not integrate","F",-1
78,0,0,1116,2.8221841,"\int \frac{A+B x+C x^2}{(a+b x)^{7/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","IntegrateAlgebraic[(A + B*x + C*x^2)/((a + b*x)^(7/2)*Sqrt[c + d*x]*Sqrt[e + f*x]),x]","\int \frac{A+B x+C x^2}{(a+b x)^{7/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx","-\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,"Could not integrate","F",-1