1,1,147,112,0.1322888,"\int (a+b x) (c+d x) (e+f x) (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)*(e + f*x)*(g + h*x),x]","\frac{1}{60} \left(60 a c e g x+30 a c e h x^2+30 a c f g x^2+20 a c f h x^3+30 a d e g x^2+20 a d e h x^3+20 a d f g x^3+15 a d f h x^4+30 b c e g x^2+20 b c e h x^3+20 b c f g x^3+15 b c f h x^4+20 b d e g x^3+15 b d e h x^4+15 b d f g x^4+12 b d f h x^5\right)","\frac{1}{4} x^4 (a d f h+b (c f h+d e h+d f g))+\frac{1}{3} x^3 (a (c f h+d e h+d f g)+b (c e h+c f g+d e g))+\frac{1}{2} x^2 (a (c e h+c f g+d e g)+b c e g)+a c e g x+\frac{1}{5} b d f h x^5",1,"(60*a*c*e*g*x + 30*b*c*e*g*x^2 + 30*a*d*e*g*x^2 + 30*a*c*f*g*x^2 + 30*a*c*e*h*x^2 + 20*b*d*e*g*x^3 + 20*b*c*f*g*x^3 + 20*a*d*f*g*x^3 + 20*b*c*e*h*x^3 + 20*a*d*e*h*x^3 + 20*a*c*f*h*x^3 + 15*b*d*f*g*x^4 + 15*b*d*e*h*x^4 + 15*b*c*f*h*x^4 + 15*a*d*f*h*x^4 + 12*b*d*f*h*x^5)/60","A",1
2,1,186,126,0.1560524,"\int \frac{(a+b x) (c+d x) (e+f x)}{g+h x} \, dx","IntegrateAlgebraic[((a + b*x)*(c + d*x)*(e + f*x))/(g + h*x),x]","\frac{x \left(6 a c f h^2+6 a d e h^2-6 a d f g h+3 a d f h^2 x+6 b c e h^2-6 b c f g h+3 b c f h^2 x-6 b d e g h+3 b d e h^2 x+6 b d f g^2-3 b d f g h x+2 b d f h^2 x^2\right)}{6 h^3}+\frac{\log (g+h x) \left(a c e h^3-a c f g h^2-a d e g h^2+a d f g^2 h-b c e g h^2+b c f g^2 h+b d e g^2 h-b d f g^3\right)}{h^4}","-\frac{(b g-a h) (d g-c h) (f g-e h) \log (g+h x)}{h^4}+\frac{x (b (d g-c h) (f g-e h)-a h (-c f h-d e h+d f g))}{h^3}+\frac{x^2 (a d f h-b (-c f h-d e h+d f g))}{2 h^2}+\frac{b d f x^3}{3 h}",1,"(x*(6*b*d*f*g^2 - 6*b*d*e*g*h - 6*b*c*f*g*h - 6*a*d*f*g*h + 6*b*c*e*h^2 + 6*a*d*e*h^2 + 6*a*c*f*h^2 - 3*b*d*f*g*h*x + 3*b*d*e*h^2*x + 3*b*c*f*h^2*x + 3*a*d*f*h^2*x + 2*b*d*f*h^2*x^2))/(6*h^3) + ((-(b*d*f*g^3) + b*d*e*g^2*h + b*c*f*g^2*h + a*d*f*g^2*h - b*c*e*g*h^2 - a*d*e*g*h^2 - a*c*f*g*h^2 + a*c*e*h^3)*Log[g + h*x])/h^4","A",1
3,1,102,84,0.0939296,"\int \frac{(a+b x) (c+d x)}{(e+f x) (g+h x)} \, dx","IntegrateAlgebraic[((a + b*x)*(c + d*x))/((e + f*x)*(g + h*x)),x]","\frac{\log (e+f x) \left(a c f^2-a d e f-b c e f+b d e^2\right)}{f^2 (f g-e h)}-\frac{\log (g+h x) \left(-a c h^2+a d g h+b c g h-b d g^2\right)}{h^2 (e h-f g)}+\frac{b d x}{f h}","\frac{(b e-a f) (d e-c f) \log (e+f x)}{f^2 (f g-e h)}-\frac{(b g-a h) (d g-c h) \log (g+h x)}{h^2 (f g-e h)}+\frac{b d x}{f h}",1,"(b*d*x)/(f*h) + ((b*d*e^2 - b*c*e*f - a*d*e*f + a*c*f^2)*Log[e + f*x])/(f^2*(f*g - e*h)) - ((-(b*d*g^2) + b*c*g*h + a*d*g*h - a*c*h^2)*Log[g + h*x])/(h^2*(-(f*g) + e*h))","A",1
4,1,106,108,0.17663,"\int \frac{a+b x}{(c+d x) (e+f x) (g+h x)} \, dx","IntegrateAlgebraic[(a + b*x)/((c + d*x)*(e + f*x)*(g + h*x)),x]","\frac{(a d-b c) \log (c+d x)}{(d e-c f) (d g-c h)}+\frac{(a f-b e) \log (e+f x)}{(d e-c f) (e h-f g)}+\frac{(a h-b g) \log (g+h x)}{(d g-c h) (f g-e h)}","-\frac{(b c-a d) \log (c+d x)}{(d e-c f) (d g-c h)}+\frac{(b e-a f) \log (e+f x)}{(d e-c f) (f g-e h)}-\frac{(b g-a h) \log (g+h x)}{(d g-c h) (f g-e h)}",1,"((-(b*c) + a*d)*Log[c + d*x])/((d*e - c*f)*(d*g - c*h)) + ((-(b*e) + a*f)*Log[e + f*x])/((d*e - c*f)*(-(f*g) + e*h)) + ((-(b*g) + a*h)*Log[g + h*x])/((d*g - c*h)*(f*g - e*h))","A",1
5,1,164,163,0.2511787,"\int \frac{1}{(a+b x) (c+d x) (e+f x) (g+h x)} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)*(e + f*x)*(g + h*x)),x]","\frac{b^2 \log (a+b x)}{(b c-a d) (b e-a f) (b g-a h)}-\frac{d^2 \log (c+d x)}{(b c-a d) (c f-d e) (c h-d g)}-\frac{f^2 \log (e+f x)}{(b e-a f) (d e-c f) (e h-f g)}-\frac{h^2 \log (g+h x)}{(b g-a h) (d g-c h) (f g-e h)}","\frac{b^2 \log (a+b x)}{(b c-a d) (b e-a f) (b g-a h)}-\frac{d^2 \log (c+d x)}{(b c-a d) (d e-c f) (d g-c h)}+\frac{f^2 \log (e+f x)}{(b e-a f) (d e-c f) (f g-e h)}-\frac{h^2 \log (g+h x)}{(b g-a h) (d g-c h) (f g-e h)}",1,"(b^2*Log[a + b*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)) - (d^2*Log[c + d*x])/((b*c - a*d)*(-(d*e) + c*f)*(-(d*g) + c*h)) - (f^2*Log[e + f*x])/((b*e - a*f)*(d*e - c*f)*(-(f*g) + e*h)) - (h^2*Log[g + h*x])/((b*g - a*h)*(d*g - c*h)*(f*g - e*h))","A",1
6,1,23,23,0.0108718,"\int \frac{x}{(1+x) (2+x) (3+x)} \, dx","IntegrateAlgebraic[x/((1 + x)*(2 + x)*(3 + x)),x]","-\frac{1}{2} \log (x+1)+2 \log (x+2)-\frac{3}{2} \log (x+3)","-\frac{1}{2} \log (x+1)+2 \log (x+2)-\frac{3}{2} \log (x+3)",1,"-1/2*Log[1 + x] + 2*Log[2 + x] - (3*Log[3 + x])/2","A",1
7,1,35,43,0.0313402,"\int \frac{-x^2+x^3}{(-6+x) (3+5 x)^3} \, dx","IntegrateAlgebraic[(-x^2 + x^3)/((-6 + x)*(3 + 5*x)^3),x]","\frac{3 (335 x+157)}{15125 (5 x+3)^2}+\frac{20 \log (x-6)}{3993}+\frac{1493 \log (5 x+3)}{499125}","\frac{201}{15125 (5 x+3)}-\frac{12}{1375 (5 x+3)^2}+\frac{20 \log (6-x)}{3993}+\frac{1493 \log (5 x+3)}{499125}",1,"(3*(157 + 335*x))/(15125*(3 + 5*x)^2) + (20*Log[-6 + x])/3993 + (1493*Log[3 + 5*x])/499125","A",1
8,1,332,227,0.284999,"\int \frac{(a+b x)^3 \sqrt{c+d x} (e+f x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)^3*Sqrt[c + d*x]*(e + f*x))/x,x]","\frac{2 \sqrt{c+d x} \left(105 a^3 c d^3 f+315 a^3 d^4 e+105 a^3 d^4 f x-126 a^2 b c^2 d^2 f+315 a^2 b c d^3 e+63 a^2 b c d^3 f x+315 a^2 b d^4 e x+189 a^2 b d^4 f x^2+72 a b^2 c^3 d f-126 a b^2 c^2 d^2 e-36 a b^2 c^2 d^2 f x+63 a b^2 c d^3 e x+27 a b^2 c d^3 f x^2+189 a b^2 d^4 e x^2+135 a b^2 d^4 f x^3-16 b^3 c^4 f+24 b^3 c^3 d e+8 b^3 c^3 d f x-12 b^3 c^2 d^2 e x-6 b^3 c^2 d^2 f x^2+9 b^3 c d^3 e x^2+5 b^3 c d^3 f x^3+45 b^3 d^4 e x^3+35 b^3 d^4 f x^4\right)}{315 d^4}-2 a^3 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)","2 a^3 e \sqrt{c+d x}-2 a^3 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)+\frac{2 (c+d x)^{3/2} \left(2 \left(20 a^3 d^3 f+3 a^2 b d^2 (45 d e-16 c f)-9 a b^2 c d (7 d e-4 c f)+4 b^3 c^2 (3 d e-2 c f)\right)+3 b d x \left(21 a b d^2 e-4 (b c-a d) (2 a d f-2 b c f+3 b d e)\right)\right)}{315 d^4}+\frac{2 (a+b x)^2 (c+d x)^{3/2} (2 a d f-2 b c f+3 b d e)}{21 d^2}+\frac{2 f (a+b x)^3 (c+d x)^{3/2}}{9 d}",1,"(2*Sqrt[c + d*x]*(24*b^3*c^3*d*e - 126*a*b^2*c^2*d^2*e + 315*a^2*b*c*d^3*e + 315*a^3*d^4*e - 16*b^3*c^4*f + 72*a*b^2*c^3*d*f - 126*a^2*b*c^2*d^2*f + 105*a^3*c*d^3*f - 12*b^3*c^2*d^2*e*x + 63*a*b^2*c*d^3*e*x + 315*a^2*b*d^4*e*x + 8*b^3*c^3*d*f*x - 36*a*b^2*c^2*d^2*f*x + 63*a^2*b*c*d^3*f*x + 105*a^3*d^4*f*x + 9*b^3*c*d^3*e*x^2 + 189*a*b^2*d^4*e*x^2 - 6*b^3*c^2*d^2*f*x^2 + 27*a*b^2*c*d^3*f*x^2 + 189*a^2*b*d^4*f*x^2 + 45*b^3*d^4*e*x^3 + 5*b^3*c*d^3*f*x^3 + 135*a*b^2*d^4*f*x^3 + 35*b^3*d^4*f*x^4))/(315*d^4) - 2*a^3*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]","A",1
9,1,200,146,0.1502059,"\int \frac{(a+b x)^2 \sqrt{c+d x} (e+f x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)^2*Sqrt[c + d*x]*(e + f*x))/x,x]","\frac{2 \sqrt{c+d x} \left(35 a^2 c d^2 f+105 a^2 d^3 e+35 a^2 d^3 f x-28 a b c^2 d f+70 a b c d^2 e+14 a b c d^2 f x+70 a b d^3 e x+42 a b d^3 f x^2+8 b^2 c^3 f-14 b^2 c^2 d e-4 b^2 c^2 d f x+7 b^2 c d^2 e x+3 b^2 c d^2 f x^2+21 b^2 d^3 e x^2+15 b^2 d^3 f x^3\right)}{105 d^3}-2 a^2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)","\frac{2 (c+d x)^{3/2} \left(2 \left(10 a^2 d^2 f+7 a b d (5 d e-2 c f)+b^2 (-c) (7 d e-4 c f)\right)+3 b d x (4 a d f-4 b c f+7 b d e)\right)}{105 d^3}+2 a^2 e \sqrt{c+d x}-2 a^2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)+\frac{2 f (a+b x)^2 (c+d x)^{3/2}}{7 d}",1,"(2*Sqrt[c + d*x]*(-14*b^2*c^2*d*e + 70*a*b*c*d^2*e + 105*a^2*d^3*e + 8*b^2*c^3*f - 28*a*b*c^2*d*f + 35*a^2*c*d^2*f + 7*b^2*c*d^2*e*x + 70*a*b*d^3*e*x - 4*b^2*c^2*d*f*x + 14*a*b*c*d^2*f*x + 35*a^2*d^3*f*x + 21*b^2*d^3*e*x^2 + 3*b^2*c*d^2*f*x^2 + 42*a*b*d^3*f*x^2 + 15*b^2*d^3*f*x^3))/(105*d^3) - 2*a^2*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]","A",1
10,1,101,77,0.0753875,"\int \frac{(a+b x) \sqrt{c+d x} (e+f x)}{x} \, dx","IntegrateAlgebraic[((a + b*x)*Sqrt[c + d*x]*(e + f*x))/x,x]","\frac{2 \sqrt{c+d x} \left(5 a c d f+15 a d^2 e+5 a d^2 f x-2 b c^2 f+5 b c d e+b c d f x+5 b d^2 e x+3 b d^2 f x^2\right)}{15 d^2}-2 a \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)","-\frac{2 (c+d x)^{3/2} (-5 d (a f+b e)+2 b c f-3 b d f x)}{15 d^2}+2 a e \sqrt{c+d x}-2 a \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)",1,"(2*Sqrt[c + d*x]*(5*b*c*d*e + 15*a*d^2*e - 2*b*c^2*f + 5*a*c*d*f + 5*b*d^2*e*x + b*c*d*f*x + 5*a*d^2*f*x + 3*b*d^2*f*x^2))/(15*d^2) - 2*a*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]","A",1
11,1,53,54,0.0409775,"\int \frac{\sqrt{c+d x} (e+f x)}{x} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(e + f*x))/x,x]","\frac{2 \sqrt{c+d x} (c f+3 d e+d f x)}{3 d}-2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)","2 e \sqrt{c+d x}-2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)+\frac{2 f (c+d x)^{3/2}}{3 d}",1,"(2*Sqrt[c + d*x]*(3*d*e + c*f + d*f*x))/(3*d) - 2*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]","A",1
12,1,111,101,0.1685119,"\int \frac{\sqrt{c+d x} (e+f x)}{x (a+b x)} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(e + f*x))/(x*(a + b*x)),x]","-\frac{2 \sqrt{a d-b c} (b e-a f) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a b^{3/2}}-\frac{2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a}+\frac{2 f \sqrt{c+d x}}{b}","\frac{2 \sqrt{b c-a d} (b e-a f) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a b^{3/2}}-\frac{2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a}+\frac{2 f \sqrt{c+d x}}{b}",1,"(2*f*Sqrt[c + d*x])/b - (2*Sqrt[-(b*c) + a*d]*(b*e - a*f)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a*b^(3/2)) - (2*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a","A",1
13,1,139,127,0.3288864,"\int \frac{\sqrt{c+d x} (e+f x)}{x (a+b x)^2} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(e + f*x))/(x*(a + b*x)^2),x]","\frac{\left(a^2 (-d) f-a b d e+2 b^2 c e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{a^2 b^{3/2} \sqrt{a d-b c}}-\frac{2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}+\frac{\sqrt{c+d x} (b e-a f)}{a b (a+b x)}","\frac{\left(2 b^2 c e-a d (a f+b e)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{a^2 b^{3/2} \sqrt{b c-a d}}-\frac{2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}+\frac{\sqrt{c+d x} (b e-a f)}{a b (a+b x)}",1,"((b*e - a*f)*Sqrt[c + d*x])/(a*b*(a + b*x)) + ((2*b^2*c*e - a*b*d*e - a^2*d*f)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(a^2*b^(3/2)*Sqrt[-(b*c) + a*d]) - (2*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a^2","A",1
14,1,221,208,1.0087187,"\int \frac{\sqrt{c+d x} (e+f x)}{x (a+b x)^3} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*(e + f*x))/(x*(a + b*x)^3),x]","-\frac{2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3}+\frac{\sqrt{c+d x} \left(a^3 (-d) f+2 a^2 b c f+5 a^2 b d e+a^2 b d f x-6 a b^2 c e+3 a b^2 d e x-4 b^3 c e x\right)}{4 a^2 b (a+b x)^2 (a d-b c)}+\frac{\left(a^3 \left(-d^2\right) f-3 a^2 b d^2 e+12 a b^2 c d e-8 b^3 c^2 e\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x} \sqrt{a d-b c}}{b c-a d}\right)}{4 a^3 b^{3/2} (a d-b c)^{3/2}}","-\frac{2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3}+\frac{\sqrt{c+d x} \left(a^2 (-d) f-3 a b d e+4 b^2 c e\right)}{4 a^2 b (a+b x) (b c-a d)}+\frac{\left(a^3 d^2 f+3 a^2 b d^2 e-12 a b^2 c d e+8 b^3 c^2 e\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 a^3 b^{3/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x} (b e-a f)}{2 a b (a+b x)^2}",1,"(Sqrt[c + d*x]*(-6*a*b^2*c*e + 5*a^2*b*d*e + 2*a^2*b*c*f - a^3*d*f - 4*b^3*c*e*x + 3*a*b^2*d*e*x + a^2*b*d*f*x))/(4*a^2*b*(-(b*c) + a*d)*(a + b*x)^2) + ((-8*b^3*c^2*e + 12*a*b^2*c*d*e - 3*a^2*b*d^2*e - a^3*d^2*f)*ArcTan[(Sqrt[b]*Sqrt[-(b*c) + a*d]*Sqrt[c + d*x])/(b*c - a*d)])/(4*a^3*b^(3/2)*(-(b*c) + a*d)^(3/2)) - (2*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a^3","A",1
15,1,332,226,0.3076227,"\int \frac{\sqrt{a+b x} (c+d x)^3 (e+f x)}{x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^3*(e + f*x))/x,x]","\frac{2 \sqrt{a+b x} \left(-16 a^4 d^3 f+72 a^3 b c d^2 f+24 a^3 b d^3 e+8 a^3 b d^3 f x-126 a^2 b^2 c^2 d f-126 a^2 b^2 c d^2 e-36 a^2 b^2 c d^2 f x-12 a^2 b^2 d^3 e x-6 a^2 b^2 d^3 f x^2+105 a b^3 c^3 f+315 a b^3 c^2 d e+63 a b^3 c^2 d f x+63 a b^3 c d^2 e x+27 a b^3 c d^2 f x^2+9 a b^3 d^3 e x^2+5 a b^3 d^3 f x^3+315 b^4 c^3 e+105 b^4 c^3 f x+315 b^4 c^2 d e x+189 b^4 c^2 d f x^2+189 b^4 c d^2 e x^2+135 b^4 c d^2 f x^3+45 b^4 d^3 e x^3+35 b^4 d^3 f x^4\right)}{315 b^4}-2 \sqrt{a} c^3 e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-\frac{2 (a+b x)^{3/2} \left(2 \left(8 a^3 d^3 f-12 a^2 b d^2 (3 c f+d e)+3 a b^2 c d (16 c f+21 d e)-5 b^3 c^2 (4 c f+27 d e)\right)-3 b d x \left(4 (b c-a d) (-2 a d f+2 b c f+3 b d e)+21 b^2 c d e\right)\right)}{315 b^4}+\frac{2 (a+b x)^{3/2} (c+d x)^2 (-2 a d f+2 b c f+3 b d e)}{21 b^2}+2 c^3 e \sqrt{a+b x}-2 \sqrt{a} c^3 e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2 f (a+b x)^{3/2} (c+d x)^3}{9 b}",1,"(2*Sqrt[a + b*x]*(315*b^4*c^3*e + 315*a*b^3*c^2*d*e - 126*a^2*b^2*c*d^2*e + 24*a^3*b*d^3*e + 105*a*b^3*c^3*f - 126*a^2*b^2*c^2*d*f + 72*a^3*b*c*d^2*f - 16*a^4*d^3*f + 315*b^4*c^2*d*e*x + 63*a*b^3*c*d^2*e*x - 12*a^2*b^2*d^3*e*x + 105*b^4*c^3*f*x + 63*a*b^3*c^2*d*f*x - 36*a^2*b^2*c*d^2*f*x + 8*a^3*b*d^3*f*x + 189*b^4*c*d^2*e*x^2 + 9*a*b^3*d^3*e*x^2 + 189*b^4*c^2*d*f*x^2 + 27*a*b^3*c*d^2*f*x^2 - 6*a^2*b^2*d^3*f*x^2 + 45*b^4*d^3*e*x^3 + 135*b^4*c*d^2*f*x^3 + 5*a*b^3*d^3*f*x^3 + 35*b^4*d^3*f*x^4))/(315*b^4) - 2*Sqrt[a]*c^3*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
16,1,200,145,0.1606849,"\int \frac{\sqrt{a+b x} (c+d x)^2 (e+f x)}{x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)^2*(e + f*x))/x,x]","\frac{2 \sqrt{a+b x} \left(8 a^3 d^2 f-28 a^2 b c d f-14 a^2 b d^2 e-4 a^2 b d^2 f x+35 a b^2 c^2 f+70 a b^2 c d e+14 a b^2 c d f x+7 a b^2 d^2 e x+3 a b^2 d^2 f x^2+105 b^3 c^2 e+35 b^3 c^2 f x+70 b^3 c d e x+42 b^3 c d f x^2+21 b^3 d^2 e x^2+15 b^3 d^2 f x^3\right)}{105 b^3}-2 \sqrt{a} c^2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","\frac{2 (a+b x)^{3/2} \left(2 \left(4 a^2 d^2 f-7 a b d (2 c f+d e)+5 b^2 c (2 c f+7 d e)\right)+3 b d x (-4 a d f+4 b c f+7 b d e)\right)}{105 b^3}+2 c^2 e \sqrt{a+b x}-2 \sqrt{a} c^2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2 f (a+b x)^{3/2} (c+d x)^2}{7 b}",1,"(2*Sqrt[a + b*x]*(105*b^3*c^2*e + 70*a*b^2*c*d*e - 14*a^2*b*d^2*e + 35*a*b^2*c^2*f - 28*a^2*b*c*d*f + 8*a^3*d^2*f + 70*b^3*c*d*e*x + 7*a*b^2*d^2*e*x + 35*b^3*c^2*f*x + 14*a*b^2*c*d*f*x - 4*a^2*b*d^2*f*x + 21*b^3*d^2*e*x^2 + 42*b^3*c*d*f*x^2 + 3*a*b^2*d^2*f*x^2 + 15*b^3*d^2*f*x^3))/(105*b^3) - 2*Sqrt[a]*c^2*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
17,1,101,77,0.0817289,"\int \frac{\sqrt{a+b x} (c+d x) (e+f x)}{x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(c + d*x)*(e + f*x))/x,x]","\frac{2 \sqrt{a+b x} \left(-2 a^2 d f+5 a b c f+5 a b d e+a b d f x+15 b^2 c e+5 b^2 c f x+5 b^2 d e x+3 b^2 d f x^2\right)}{15 b^2}-2 \sqrt{a} c e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","-\frac{2 (a+b x)^{3/2} (2 a d f-5 b (c f+d e)-3 b d f x)}{15 b^2}+2 c e \sqrt{a+b x}-2 \sqrt{a} c e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)",1,"(2*Sqrt[a + b*x]*(15*b^2*c*e + 5*a*b*d*e + 5*a*b*c*f - 2*a^2*d*f + 5*b^2*d*e*x + 5*b^2*c*f*x + a*b*d*f*x + 3*b^2*d*f*x^2))/(15*b^2) - 2*Sqrt[a]*c*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
18,1,53,54,0.0413551,"\int \frac{\sqrt{a+b x} (e+f x)}{x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(e + f*x))/x,x]","\frac{2 \sqrt{a+b x} (a f+3 b e+b f x)}{3 b}-2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)","2 e \sqrt{a+b x}-2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2 f (a+b x)^{3/2}}{3 b}",1,"(2*Sqrt[a + b*x]*(3*b*e + a*f + b*f*x))/(3*b) - 2*Sqrt[a]*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
19,1,101,101,0.1572456,"\int \frac{\sqrt{a+b x} (e+f x)}{x (c+d x)} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(e + f*x))/(x*(c + d*x)),x]","-\frac{2 \sqrt{b c-a d} (c f-d e) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{c d^{3/2}}-\frac{2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c}+\frac{2 f \sqrt{a+b x}}{d}","\frac{2 \sqrt{b c-a d} (d e-c f) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{c d^{3/2}}-\frac{2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c}+\frac{2 f \sqrt{a+b x}}{d}",1,"(2*f*Sqrt[a + b*x])/d - (2*Sqrt[b*c - a*d]*(-(d*e) + c*f)*ArcTan[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c*d^(3/2)) - (2*Sqrt[a]*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/c","A",1
20,1,127,128,0.3435796,"\int \frac{\sqrt{a+b x} (e+f x)}{x (c+d x)^2} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(e + f*x))/(x*(c + d*x)^2),x]","\frac{\left(-2 a d^2 e+b c^2 f+b c d e\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{c^2 d^{3/2} \sqrt{b c-a d}}-\frac{2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c^2}+\frac{\sqrt{a+b x} (d e-c f)}{c d (c+d x)}","-\frac{\left(2 a d^2 e-b c (c f+d e)\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{c^2 d^{3/2} \sqrt{b c-a d}}-\frac{2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c^2}+\frac{\sqrt{a+b x} (d e-c f)}{c d (c+d x)}",1,"((d*e - c*f)*Sqrt[a + b*x])/(c*d*(c + d*x)) + ((b*c*d*e - 2*a*d^2*e + b*c^2*f)*ArcTan[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(c^2*d^(3/2)*Sqrt[b*c - a*d]) - (2*Sqrt[a]*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/c^2","A",1
21,1,210,205,0.8557981,"\int \frac{\sqrt{a+b x} (e+f x)}{x (c+d x)^3} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(e + f*x))/(x*(c + d*x)^3),x]","\frac{\left(8 a^2 d^3 e-12 a b c d^2 e+b^2 c^3 f+3 b^2 c^2 d e\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 c^3 d^{3/2} (b c-a d)^{3/2}}-\frac{2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c^3}+\frac{\sqrt{a+b x} \left(2 a c^2 d f-6 a c d^2 e-4 a d^3 e x-b c^3 f+5 b c^2 d e+b c^2 d f x+3 b c d^2 e x\right)}{4 c^2 d (c+d x)^2 (b c-a d)}","-\frac{\left(-8 a^2 d^3 e+12 a b c d^2 e-b^2 c^2 (c f+3 d e)\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 c^3 d^{3/2} (b c-a d)^{3/2}}-\frac{2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c^3}-\frac{\sqrt{a+b x} \left(4 a d^2 e-b c (c f+3 d e)\right)}{4 c^2 d (c+d x) (b c-a d)}+\frac{\sqrt{a+b x} (d e-c f)}{2 c d (c+d x)^2}",1,"(Sqrt[a + b*x]*(5*b*c^2*d*e - 6*a*c*d^2*e - b*c^3*f + 2*a*c^2*d*f + 3*b*c*d^2*e*x - 4*a*d^3*e*x + b*c^2*d*f*x))/(4*c^2*d*(b*c - a*d)*(c + d*x)^2) + ((3*b^2*c^2*d*e - 12*a*b*c*d^2*e + 8*a^2*d^3*e + b^2*c^3*f)*ArcTan[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]])/(4*c^3*d^(3/2)*(b*c - a*d)^(3/2)) - (2*Sqrt[a]*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/c^3","A",1
22,-1,0,111,180.0050176,"\int \frac{x^3 (1+a x)}{\sqrt{a x} \sqrt{1-a x}} \, dx","IntegrateAlgebraic[(x^3*(1 + a*x))/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","\text{\$Aborted}","-\frac{\sqrt{1-a x} (a x)^{7/2}}{4 a^4}-\frac{5 \sqrt{1-a x} (a x)^{5/2}}{8 a^4}-\frac{25 \sqrt{1-a x} (a x)^{3/2}}{32 a^4}-\frac{75 \sqrt{1-a x} \sqrt{a x}}{64 a^4}-\frac{75 \sin ^{-1}(1-2 a x)}{128 a^4}",1,"$Aborted","F",-1
23,-1,0,87,180.7519877,"\int \frac{x^2 (1+a x)}{\sqrt{a x} \sqrt{1-a x}} \, dx","IntegrateAlgebraic[(x^2*(1 + a*x))/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","\text{\$Aborted}","-\frac{\sqrt{1-a x} (a x)^{5/2}}{3 a^3}-\frac{11 \sqrt{1-a x} (a x)^{3/2}}{12 a^3}-\frac{11 \sqrt{1-a x} \sqrt{a x}}{8 a^3}-\frac{11 \sin ^{-1}(1-2 a x)}{16 a^3}",1,"$Aborted","F",-1
24,-1,0,63,180.197171,"\int \frac{x (1+a x)}{\sqrt{a x} \sqrt{1-a x}} \, dx","IntegrateAlgebraic[(x*(1 + a*x))/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","\text{\$Aborted}","-\frac{\sqrt{1-a x} (a x)^{3/2}}{2 a^2}-\frac{7 \sqrt{1-a x} \sqrt{a x}}{4 a^2}-\frac{7 \sin ^{-1}(1-2 a x)}{8 a^2}",1,"$Aborted","F",-1
25,-1,0,37,180.0331476,"\int \frac{1+a x}{\sqrt{a x} \sqrt{1-a x}} \, dx","IntegrateAlgebraic[(1 + a*x)/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","\text{\$Aborted}","-\frac{\sqrt{a x} \sqrt{1-a x}}{a}-\frac{3 \sin ^{-1}(1-2 a x)}{2 a}",1,"$Aborted","F",-1
26,-1,0,29,180.1119152,"\int \frac{1+a x}{x \sqrt{a x} \sqrt{1-a x}} \, dx","IntegrateAlgebraic[(1 + a*x)/(x*Sqrt[a*x]*Sqrt[1 - a*x]),x]","\text{\$Aborted}","-\frac{2 \sqrt{1-a x}}{\sqrt{a x}}-\sin ^{-1}(1-2 a x)",1,"$Aborted","F",-1
27,-1,0,45,180.0111011,"\int \frac{1+a x}{x^2 \sqrt{a x} \sqrt{1-a x}} \, dx","IntegrateAlgebraic[(1 + a*x)/(x^2*Sqrt[a*x]*Sqrt[1 - a*x]),x]","\text{\$Aborted}","-\frac{10 a \sqrt{1-a x}}{3 \sqrt{a x}}-\frac{2 a \sqrt{1-a x}}{3 (a x)^{3/2}}",1,"$Aborted","F",-1
28,0,0,73,129.8122468,"\int \frac{1+a x}{x^3 \sqrt{a x} \sqrt{1-a x}} \, dx","IntegrateAlgebraic[(1 + a*x)/(x^3*Sqrt[a*x]*Sqrt[1 - a*x]),x]","\int \frac{1+a x}{x^3 \sqrt{a x} \sqrt{1-a x}} \, dx","-\frac{12 a^2 \sqrt{1-a x}}{5 \sqrt{a x}}-\frac{6 a^2 \sqrt{1-a x}}{5 (a x)^{3/2}}-\frac{2 a^2 \sqrt{1-a x}}{5 (a x)^{5/2}}",1,"Could not integrate","F",-1
29,-1,0,97,180.020841,"\int \frac{1+a x}{x^4 \sqrt{a x} \sqrt{1-a x}} \, dx","IntegrateAlgebraic[(1 + a*x)/(x^4*Sqrt[a*x]*Sqrt[1 - a*x]),x]","\text{\$Aborted}","-\frac{208 a^3 \sqrt{1-a x}}{105 \sqrt{a x}}-\frac{104 a^3 \sqrt{1-a x}}{105 (a x)^{3/2}}-\frac{26 a^3 \sqrt{1-a x}}{35 (a x)^{5/2}}-\frac{2 a^3 \sqrt{1-a x}}{7 (a x)^{7/2}}",1,"$Aborted","F",-1
30,-1,0,121,180.0033842,"\int \frac{1+a x}{x^5 \sqrt{a x} \sqrt{1-a x}} \, dx","IntegrateAlgebraic[(1 + a*x)/(x^5*Sqrt[a*x]*Sqrt[1 - a*x]),x]","\text{\$Aborted}","-\frac{544 a^4 \sqrt{1-a x}}{315 \sqrt{a x}}-\frac{272 a^4 \sqrt{1-a x}}{315 (a x)^{3/2}}-\frac{68 a^4 \sqrt{1-a x}}{105 (a x)^{5/2}}-\frac{34 a^4 \sqrt{1-a x}}{63 (a x)^{7/2}}-\frac{2 a^4 \sqrt{1-a x}}{9 (a x)^{9/2}}",1,"$Aborted","F",-1
31,1,202,39,1.6362638,"\int \frac{-1+2 a x}{\sqrt{-1+x} x^2 \sqrt{1+x}} \, dx","IntegrateAlgebraic[(-1 + 2*a*x)/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]","\frac{\left(\frac{\sqrt{x-1}}{2}-\frac{1}{2}\right) \left(\sqrt{3}-\sqrt{x+1}\right) \left(-x+\sqrt{x-1}+\sqrt{3} \sqrt{x+1}-2\right)}{x \left(-2 x-2 \sqrt{x-1}+\sqrt{3} \sqrt{x-1} \sqrt{x+1}+2 \sqrt{3} \sqrt{x+1}-3\right)}-4 a \tan ^{-1}\left(\frac{-2 x+\sqrt{x-1} \left(\sqrt{3} \sqrt{x+1}-1\right)+\sqrt{3} \sqrt{x+1}-1}{-\sqrt{x+1} \sqrt{x-1}+\sqrt{3} \sqrt{x-1}+\sqrt{x+1}-\sqrt{3}}\right)","2 a \tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"((-1/2 + Sqrt[-1 + x]/2)*(Sqrt[3] - Sqrt[1 + x])*(-2 + Sqrt[-1 + x] - x + Sqrt[3]*Sqrt[1 + x]))/(x*(-3 - 2*Sqrt[-1 + x] - 2*x + 2*Sqrt[3]*Sqrt[1 + x] + Sqrt[3]*Sqrt[-1 + x]*Sqrt[1 + x])) - 4*a*ArcTan[(-1 - 2*x + Sqrt[3]*Sqrt[1 + x] + Sqrt[-1 + x]*(-1 + Sqrt[3]*Sqrt[1 + x]))/(-Sqrt[3] + Sqrt[3]*Sqrt[-1 + x] + Sqrt[1 + x] - Sqrt[-1 + x]*Sqrt[1 + x])]","B",1
32,1,202,39,1.275316,"\int \frac{a^2 x^2-(1-a x)^2}{\sqrt{-1+x} x^2 \sqrt{1+x}} \, dx","IntegrateAlgebraic[(a^2*x^2 - (1 - a*x)^2)/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]","\frac{\left(\frac{\sqrt{x-1}}{2}-\frac{1}{2}\right) \left(\sqrt{3}-\sqrt{x+1}\right) \left(-x+\sqrt{x-1}+\sqrt{3} \sqrt{x+1}-2\right)}{x \left(-2 x-2 \sqrt{x-1}+\sqrt{3} \sqrt{x-1} \sqrt{x+1}+2 \sqrt{3} \sqrt{x+1}-3\right)}-4 a \tan ^{-1}\left(\frac{-2 x+\sqrt{x-1} \left(\sqrt{3} \sqrt{x+1}-1\right)+\sqrt{3} \sqrt{x+1}-1}{-\sqrt{x+1} \sqrt{x-1}+\sqrt{3} \sqrt{x-1}+\sqrt{x+1}-\sqrt{3}}\right)","2 a \tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"((-1/2 + Sqrt[-1 + x]/2)*(Sqrt[3] - Sqrt[1 + x])*(-2 + Sqrt[-1 + x] - x + Sqrt[3]*Sqrt[1 + x]))/(x*(-3 - 2*Sqrt[-1 + x] - 2*x + 2*Sqrt[3]*Sqrt[1 + x] + Sqrt[3]*Sqrt[-1 + x]*Sqrt[1 + x])) - 4*a*ArcTan[(-1 - 2*x + Sqrt[3]*Sqrt[1 + x] + Sqrt[-1 + x]*(-1 + Sqrt[3]*Sqrt[1 + x]))/(-Sqrt[3] + Sqrt[3]*Sqrt[-1 + x] + Sqrt[1 + x] - Sqrt[-1 + x]*Sqrt[1 + x])]","B",1
33,0,0,145,2.3357998,"\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+\frac{b (-1+c) x}{a}} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[a + b*x]*Sqrt[c + (b*(-1 + c)*x)/a]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+\frac{b (-1+c) x}{a}} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","\frac{2 \sqrt{a} (a B e+A (b-b e)) F\left(\sin ^{-1}\left(\frac{\sqrt{1-c} \sqrt{a+b x}}{\sqrt{a}}\right)|\frac{1-e}{1-c}\right)}{b^2 \sqrt{1-c} (1-e)}-\frac{2 a^{3/2} B E\left(\sin ^{-1}\left(\frac{\sqrt{1-c} \sqrt{a+b x}}{\sqrt{a}}\right)|\frac{1-e}{1-c}\right)}{b^2 \sqrt{1-c} (1-e)}",1,"Could not integrate","F",-1
34,0,0,221,2.321758,"\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","\frac{2 \sqrt{a} (a B e+A (b-b e)) \sqrt{\frac{b (c+d x)}{b c-a d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-e} \sqrt{a+b x}}{\sqrt{a}}\right)|-\frac{a d}{(b c-a d) (1-e)}\right)}{b^2 (1-e)^{3/2} \sqrt{c+d x}}-\frac{2 a B \sqrt{a d-b c} \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) (1-e)}{a d}\right)}{b^2 \sqrt{d} (1-e) \sqrt{c+d x}}",1,"Could not integrate","F",-1
35,0,0,281,0.6459186,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3 \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3,x]","\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3 \, dx","\frac{2}{55} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^4-\frac{427 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^3}{2970}-\frac{17561 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^2}{8910}-\frac{12243139 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)}{356400}-\frac{1182926269 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{1603800}+\frac{522167393 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{23328 \sqrt{2 x-5}}-\frac{6489123157 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{699840 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
36,0,0,243,0.6390809,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2 \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2,x]","\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2 \, dx","\frac{2}{45} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^3-\frac{61}{270} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^2-\frac{8141 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)}{2700}-\frac{5256763 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{97200}+\frac{5592499 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{3888 \sqrt{2 x-5}}-\frac{17746949 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{29160 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
37,0,0,193,0.3569131,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x) \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x),x]","\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x) \, dx","\frac{5}{28} \sqrt{2-3 x} (2 x-5)^{3/2} (4 x+1)^{3/2}+\frac{136}{105} \sqrt{2-3 x} \sqrt{2 x-5} (4 x+1)^{3/2}-\frac{20911 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{3780}+\frac{72479 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{756 \sqrt{2 x-5}}-\frac{954811 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{22680 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
38,0,0,162,0.292807,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x],x]","\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \, dx","\frac{1}{10} \sqrt{2-3 x} \sqrt{2 x-5} (4 x+1)^{3/2}-\frac{22}{45} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}+\frac{121 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{18 \sqrt{2 x-5}}-\frac{847 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{270 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
39,0,0,182,0.5667618,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{7+5 x} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x),x]","\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{7+5 x} \, dx","\frac{2}{15} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}-\frac{1253 \sqrt{\frac{2}{33}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{375 \sqrt{2 x-5}}-\frac{427 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{225 \sqrt{5-2 x}}-\frac{2691 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{125 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
40,0,0,189,0.8909054,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^2,x]","\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^2} \, dx","-\frac{\sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{5 (5 x+7)}+\frac{152 \sqrt{\frac{2}{33}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{125 \sqrt{2 x-5}}+\frac{6 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{25 \sqrt{5-2 x}}+\frac{26859 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{7750 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
41,0,0,227,0.9024015,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^3,x]","\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^3} \, dx","\frac{8953 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{556140 (5 x+7)}-\frac{\sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{10 (5 x+7)^2}+\frac{397 \sqrt{\frac{3}{22}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{89125 \sqrt{2 x-5}}-\frac{8953 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{1390350 \sqrt{5-2 x}}-\frac{14832503 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{287339000 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
42,0,0,263,1.0137182,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^4} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^4,x]","\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^4} \, dx","\frac{16830401 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{30929169960 (5 x+7)}+\frac{8953 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{1668420 (5 x+7)^2}-\frac{\sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{15 (5 x+7)^3}+\frac{24957247 \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{4956597750 \sqrt{66} \sqrt{2 x-5}}-\frac{16830401 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{77322924900 \sqrt{5-2 x}}+\frac{15664616449 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{15980071146000 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
43,0,0,570,2.2738538,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{a+b x} \, dx","IntegrateAlgebraic[(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(a + b*x),x]","\int \frac{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{a+b x} \, dx","\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(3 a^2 d f h^2-3 a b h^2 (c f+d e)-\left(b^2 (d g (f g-e h)-c h (2 e h+f g))\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 b^3 d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 (b e-a f) (b g-a h) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^3 \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} (3 a d f h-b (c f h+d e h+d f g)) E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 b^2 d \sqrt{f} h \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 b}",1,"Could not integrate","F",-1
44,0,0,243,0.7410631,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^3}{\sqrt{-5+2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3)/Sqrt[-5 + 2*x],x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^3}{\sqrt{-5+2 x}} \, dx","\frac{1}{9} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^3+\frac{1679}{756} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^2+\frac{26291}{540} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)+\frac{46134551 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{38880}-\frac{2161804579 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{54432 \sqrt{2 x-5}}+\frac{2629157597 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{163296 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
45,0,0,205,0.6883356,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^2}{\sqrt{-5+2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2)/Sqrt[-5 + 2*x],x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^2}{\sqrt{-5+2 x}} \, dx","\frac{1}{7} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^2+\frac{173}{60} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)+\frac{73207 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{1080}-\frac{1679161 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{756 \sqrt{2 x-5}}+\frac{8198333 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{9072 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
46,0,0,162,0.4381583,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)}{\sqrt{-5+2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x))/Sqrt[-5 + 2*x],x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)}{\sqrt{-5+2 x}} \, dx","\frac{1}{4} \sqrt{2-3 x} \sqrt{2 x-5} (4 x+1)^{3/2}+\frac{95}{18} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}-\frac{4543 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{36 \sqrt{2 x-5}}+\frac{1397 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{27 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
47,0,0,131,0.2811105,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x],x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x}} \, dx","\frac{1}{3} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}-\frac{11 \sqrt{\frac{22}{3}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{3 \sqrt{2 x-5}}+\frac{55 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{18 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
48,0,0,151,0.6639063,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)),x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)} \, dx","-\frac{41 \sqrt{\frac{2}{33}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{25 \sqrt{2 x-5}}+\frac{2 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{5 \sqrt{5-2 x}}+\frac{69 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{25 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
49,0,0,189,0.9682429,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^2} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^2),x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^2} \, dx","\frac{\sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{39 (5 x+7)}-\frac{2 \sqrt{\frac{6}{11}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{25 \sqrt{2 x-5}}-\frac{2 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{195 \sqrt{5-2 x}}-\frac{6101 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{20150 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
50,0,0,225,1.0699605,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^3} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^3),x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^3} \, dx","-\frac{361 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{481988 (5 x+7)}+\frac{\sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{78 (5 x+7)^2}-\frac{6101 \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{231725 \sqrt{66} \sqrt{2 x-5}}+\frac{361 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{1204970 \sqrt{5-2 x}}-\frac{6655867 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{747081400 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
51,0,0,205,0.7573426,"\int \frac{\sqrt{2-3 x} (7+5 x)^3}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*(7 + 5*x)^3)/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{\sqrt{2-3 x} (7+5 x)^3}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{5}{28} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^2+\frac{121}{24} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)+\frac{110743}{864} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}-\frac{25260049 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{6048 \sqrt{2 x-5}}+\frac{15629623 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{9072 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
52,0,0,167,0.7076917,"\int \frac{\sqrt{2-3 x} (7+5 x)^2}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*(7 + 5*x)^2)/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{\sqrt{2-3 x} (7+5 x)^2}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{1}{4} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)+\frac{68}{9} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}-\frac{17533 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{72 \sqrt{2 x-5}}+\frac{44569 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{432 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
53,0,0,131,0.4444853,"\int \frac{\sqrt{2-3 x} (7+5 x)}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*(7 + 5*x))/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{\sqrt{2-3 x} (7+5 x)}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{5}{12} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}-\frac{179 \sqrt{\frac{11}{6}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{12 \sqrt{2 x-5}}+\frac{241 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{36 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
54,0,0,47,0.2824533,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{\sqrt{\frac{11}{2}} \sqrt{5-2 x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{11}}\right)\right|3\right)}{2 \sqrt{2 x-5}}",1,"Could not integrate","F",-1
55,0,0,103,0.6181643,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)),x]","\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)} \, dx","-\frac{\sqrt{\frac{6}{11}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{5 \sqrt{2 x-5}}-\frac{3 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{5 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
56,0,0,189,0.9224471,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2),x]","\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2} \, dx","-\frac{5 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{897 (5 x+7)}-\frac{2 \sqrt{\frac{6}{11}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{115 \sqrt{2 x-5}}+\frac{2 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{897 \sqrt{5-2 x}}-\frac{3571 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{92690 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
57,0,0,225,1.0441656,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3),x]","\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3} \, dx","-\frac{26825 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{33257172 (5 x+7)}-\frac{5 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{1794 (5 x+7)^2}-\frac{13243 \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{1065935 \sqrt{66} \sqrt{2 x-5}}+\frac{5365 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{16628586 \sqrt{5-2 x}}-\frac{16369941 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{3436574440 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
58,0,0,293,2.2366919,"\int \frac{\sqrt{c+d x}}{(a+b x) \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/((a + b*x)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{\sqrt{c+d x}}{(a+b x) \sqrt{e+f x} \sqrt{g+h x}} \, dx","\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}",1,"Could not integrate","F",-1
59,0,0,449,2.6076394,"\int \frac{(c+d x)^{3/2}}{(a+b x) \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(c + d*x)^(3/2)/((a + b*x)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{(c+d x)^{3/2}}{(a+b x) \sqrt{e+f x} \sqrt{g+h x}} \, dx","\frac{2 (b c-a d) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^2 \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 (b c-a d) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^2 \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 d \sqrt{c+d x} \sqrt{e h-f g} \sqrt{\frac{f (g+h x)}{f g-e h}} E\left(\sin ^{-1}\left(\frac{\sqrt{h} \sqrt{e+f x}}{\sqrt{e h-f g}}\right)|-\frac{d (f g-e h)}{(d e-c f) h}\right)}{b f \sqrt{h} \sqrt{g+h x} \sqrt{-\frac{f (c+d x)}{d e-c f}}}",1,"Could not integrate","F",-1
60,0,0,203,0.984724,"\int \frac{(7+5 x)^4}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(7 + 5*x)^4/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{(7+5 x)^4}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","-\frac{25}{84} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^2-\frac{305}{24} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)-\frac{120355}{288} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}+\frac{392989907 \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{2016 \sqrt{66} \sqrt{2 x-5}}-\frac{5109835 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{756 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
61,0,0,165,0.8570441,"\int \frac{(7+5 x)^3}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(7 + 5*x)^3/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{(7+5 x)^3}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","-\frac{5}{12} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)-\frac{2135}{108} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}+\frac{2474201 \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{216 \sqrt{66} \sqrt{2 x-5}}-\frac{487585 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{1296 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
62,0,0,129,0.7762836,"\int \frac{(7+5 x)^2}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(7 + 5*x)^2/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{(7+5 x)^2}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","-\frac{25}{36} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}+\frac{24353 \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{36 \sqrt{66} \sqrt{2 x-5}}-\frac{2135 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{108 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
63,0,0,98,0.4584598,"\int \frac{7+5 x}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(7 + 5*x)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{7+5 x}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{13 \sqrt{\frac{3}{22}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{\sqrt{2 x-5}}-\frac{5 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{6 \sqrt{5-2 x}}",1,"Could not integrate","F",-1
64,0,0,48,0.308266,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{\sqrt{\frac{2}{33}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{\sqrt{2 x-5}}",1,"Could not integrate","F",-1
65,0,0,51,0.7205944,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)} \, dx","-\frac{3 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{31 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
66,0,0,189,1.1498054,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2} \, dx","-\frac{25 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{27807 (5 x+7)}-\frac{2 \sqrt{\frac{6}{11}} \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{713 \sqrt{2 x-5}}+\frac{10 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{27807 \sqrt{5-2 x}}-\frac{8953 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{574678 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
67,0,0,225,1.3083401,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3} \, dx","-\frac{223825 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{1030972332 (5 x+7)}-\frac{25 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{55614 (5 x+7)^2}-\frac{24007 \sqrt{5-2 x} F\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{6608797 \sqrt{66} \sqrt{2 x-5}}+\frac{44765 \sqrt{11} \sqrt{2 x-5} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{515486166 \sqrt{5-2 x}}-\frac{48493305 \sqrt{5-2 x} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)}{21306761528 \sqrt{11} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
68,0,0,137,1.4540321,"\int \frac{c i+d i x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(c*i + d*i*x)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{c i+d i x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\frac{2 i \sqrt{c+d x} \sqrt{e h-f g} \sqrt{\frac{f (g+h x)}{f g-e h}} E\left(\sin ^{-1}\left(\frac{\sqrt{h} \sqrt{e+f x}}{\sqrt{e h-f g}}\right)|-\frac{d (f g-e h)}{(d e-c f) h}\right)}{f \sqrt{h} \sqrt{g+h x} \sqrt{-\frac{f (c+d x)}{d e-c f}}}",1,"Could not integrate","F",-1
69,0,0,284,1.8458526,"\int \frac{a+b x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(a + b*x)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{a+b x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\frac{2 b \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}-\frac{2 (b g-a h) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}",1,"Could not integrate","F",-1
70,0,0,165,2.3384789,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)}",1,"Could not integrate","F",-1
71,0,0,393,2.7590613,"\int \frac{1}{(a+b x) (c+d x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^(3/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{1}{(a+b x) (c+d x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\frac{2 d^2 \sqrt{e+f x} \sqrt{g+h x}}{\sqrt{c+d x} (b c-a d) (d e-c f) (d g-c h)}-\frac{2 d \sqrt{h} \sqrt{c+d x} \sqrt{e h-f g} \sqrt{\frac{f (g+h x)}{f g-e h}} E\left(\sin ^{-1}\left(\frac{\sqrt{h} \sqrt{e+f x}}{\sqrt{e h-f g}}\right)|-\frac{d (f g-e h)}{(d e-c f) h}\right)}{\sqrt{g+h x} (b c-a d) (d e-c f) (d g-c h) \sqrt{-\frac{f (c+d x)}{d e-c f}}}-\frac{2 b \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)^2}",1,"Could not integrate","F",-1
72,0,0,875,2.7812622,"\int \frac{1}{(a+b x) (c+d x)^{5/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[1/((a + b*x)*(c + d*x)^(5/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{1}{(a+b x) (c+d x)^{5/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) b^2}{(b c-a d)^3 \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 d \sqrt{h} \sqrt{e h-f g} \sqrt{c+d x} \sqrt{\frac{f (g+h x)}{f g-e h}} E\left(\sin ^{-1}\left(\frac{\sqrt{h} \sqrt{e+f x}}{\sqrt{e h-f g}}\right)|-\frac{d (f g-e h)}{(d e-c f) h}\right) b}{(b c-a d)^2 (d e-c f) (d g-c h) \sqrt{-\frac{f (c+d x)}{d e-c f}} \sqrt{g+h x}}+\frac{2 d^2 \sqrt{e+f x} \sqrt{g+h x} b}{(b c-a d)^2 (d e-c f) (d g-c h) \sqrt{c+d x}}+\frac{4 d \sqrt{f} (d f g+d e h-2 c f h) \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{g+h x} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 (b c-a d) (c f-d e)^{3/2} (d g-c h)^2 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}-\frac{2 \sqrt{f} (2 d f g+d e h-3 c f h) \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 (b c-a d) (c f-d e)^{3/2} (d g-c h) \sqrt{e+f x} \sqrt{g+h x}}-\frac{4 d^2 (d f g+d e h-2 c f h) \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d) (d e-c f)^2 (d g-c h)^2 \sqrt{c+d x}}+\frac{2 d^2 \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d) (d e-c f) (d g-c h) (c+d x)^{3/2}}",1,"Could not integrate","F",-1
73,0,0,74,2.1227465,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f x} \sqrt{1+f x}} \, dx","IntegrateAlgebraic[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f*x]*Sqrt[1 + f*x]),x]","\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f x} \sqrt{1+f x}} \, dx","-\frac{2 \sqrt{\frac{f (c+d x)}{c f+d}} \Pi \left(\frac{2 b}{b+a f};\sin ^{-1}\left(\frac{\sqrt{1-f x}}{\sqrt{2}}\right)|\frac{2 d}{d+c f}\right)}{(a f+b) \sqrt{c+d x}}",1,"Could not integrate","F",-1
74,0,0,74,43.698827,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^2 x^2}} \, dx","IntegrateAlgebraic[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f^2*x^2]),x]","\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^2 x^2}} \, dx","-\frac{2 \sqrt{\frac{f (c+d x)}{c f+d}} \Pi \left(\frac{2 b}{b+a f};\sin ^{-1}\left(\frac{\sqrt{1-f x}}{\sqrt{2}}\right)|\frac{2 d}{d+c f}\right)}{(a f+b) \sqrt{c+d x}}",1,"Could not integrate","F",-1
75,0,0,86,2.2605099,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^2 x} \sqrt{1+f^2 x}} \, dx","IntegrateAlgebraic[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f^2*x]*Sqrt[1 + f^2*x]),x]","\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^2 x} \sqrt{1+f^2 x}} \, dx","-\frac{2 \sqrt{\frac{f^2 (c+d x)}{c f^2+d}} \Pi \left(\frac{2 b}{a f^2+b};\sin ^{-1}\left(\frac{\sqrt{1-f^2 x}}{\sqrt{2}}\right)|\frac{2 d}{c f^2+d}\right)}{\left(a f^2+b\right) \sqrt{c+d x}}",1,"Could not integrate","F",-1
76,0,0,86,43.7531725,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^4 x^2}} \, dx","IntegrateAlgebraic[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f^4*x^2]),x]","\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^4 x^2}} \, dx","-\frac{2 \sqrt{\frac{f^2 (c+d x)}{c f^2+d}} \Pi \left(\frac{2 b}{a f^2+b};\sin ^{-1}\left(\frac{\sqrt{1-f^2 x}}{\sqrt{2}}\right)|\frac{2 d}{c f^2+d}\right)}{\left(a f^2+b\right) \sqrt{c+d x}}",1,"Could not integrate","F",-1
77,0,0,471,1.2449603,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2),x]","\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2} \, dx","\frac{1}{25} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^{7/2}-\frac{427 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^{5/2}}{2400}-\frac{83363 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^{3/2}}{34560}-\frac{70489981 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7}}{1658880}-\frac{1450582567 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{3686400 \sqrt{2 x-5}}-\frac{245264762213 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{99532800 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{1450582567 \sqrt{\frac{143}{3}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{2457600 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}-\frac{57691792727443 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{497664000 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
78,0,0,429,1.0800598,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2),x]","\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2} \, dx","\frac{1}{20} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^{5/2}-\frac{427 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^{3/2}}{1440}-\frac{267029 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7}}{69120}-\frac{1471781 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{51200 \sqrt{2 x-5}}-\frac{982275517 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{4147200 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{1471781 \sqrt{429} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{102400 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}-\frac{145131624827 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{20736000 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
79,0,0,391,0.6077147,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x],x]","\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x} \, dx","-\frac{1}{9} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7} (2-3 x)^{3/2}+\frac{23}{240} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7} \sqrt{2-3 x}-\frac{13027 \sqrt{4 x+1} \sqrt{5 x+7} \sqrt{2-3 x}}{4800 \sqrt{2 x-5}}-\frac{1368371 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{43200 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{13027 \sqrt{\frac{143}{3}} \sqrt{\frac{5 x+7}{5-2 x}} \sqrt{2-3 x} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{3200 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}-\frac{65750101 \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} (2-3 x) \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{216000 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
80,0,0,351,0.6890814,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{\sqrt{7+5 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/Sqrt[7 + 5*x],x]","\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{\sqrt{7+5 x}} \, dx","\frac{1}{10} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7}-\frac{427 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{600 \sqrt{2 x-5}}-\frac{20057 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{1800 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{427 \sqrt{\frac{143}{3}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{400 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{1008833 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{9000 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
81,0,0,349,1.046209,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(3/2),x]","\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{3/2}} \, dx","\frac{6 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{25 \sqrt{2 x-5}}-\frac{2 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{5 \sqrt{5 x+7}}+\frac{296 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{75 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{3 \sqrt{429} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{25 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}-\frac{26474 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{375 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
82,0,0,391,1.1051621,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(5/2),x]","\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{5/2}} \, dx","-\frac{35812 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{2085525 \sqrt{2 x-5}}+\frac{17906 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{417105 \sqrt{5 x+7}}-\frac{2 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{15 (5 x+7)^{3/2}}-\frac{496 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{1725 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{17906 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{53475 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{496 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{125 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
83,0,0,330,1.2462052,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{7/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(7/2),x]","\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{7/2}} \, dx","-\frac{2852696 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{11598438735 \sqrt{2 x-5}}+\frac{1426348 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{2319687747 \sqrt{5 x+7}}+\frac{17906 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{2085525 (5 x+7)^{3/2}}-\frac{2 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{25 (5 x+7)^{5/2}}-\frac{48884 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{9593415 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{1426348 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{297395865 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}",1,"Could not integrate","F",-1
84,0,0,370,1.4017618,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{9/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(9/2),x]","\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{9/2}} \, dx","-\frac{65687975672 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{2257624501329015 \sqrt{2 x-5}}+\frac{32843987836 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{451524900265803 \sqrt{5 x+7}}+\frac{23758016 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{57992193675 (5 x+7)^{3/2}}+\frac{2558 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{695175 (5 x+7)^{5/2}}-\frac{2 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{35 (5 x+7)^{7/2}}-\frac{1212290288 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{1867348636335 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{32843987836 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{57887807726385 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}",1,"Could not integrate","F",-1
85,0,0,429,1.2743686,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^{5/2}}{\sqrt{-5+2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2))/Sqrt[-5 + 2*x],x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^{5/2}}{\sqrt{-5+2 x}} \, dx","\frac{1}{8} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^{5/2}+\frac{1445}{576} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^{3/2}+\frac{1561915 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7}}{27648}+\frac{2466927 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{4096 \sqrt{2 x-5}}+\frac{861015607 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{331776 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{2466927 \sqrt{429} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{8192 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{331574321009 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{1658880 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
86,0,0,391,1.0886296,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^{3/2}}{\sqrt{-5+2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2))/Sqrt[-5 + 2*x],x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^{3/2}}{\sqrt{-5+2 x}} \, dx","\frac{1}{6} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^{3/2}+\frac{977}{288} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7}+\frac{66377 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{1920 \sqrt{2 x-5}}+\frac{2824441 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{17280 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{66377 \sqrt{\frac{143}{3}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{1280 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{963142751 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{86400 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
87,0,0,351,0.6515081,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} \sqrt{7+5 x}}{\sqrt{-5+2 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/Sqrt[-5 + 2*x],x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} \sqrt{7+5 x}}{\sqrt{-5+2 x}} \, dx","\frac{1}{4} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7}+\frac{509 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{240 \sqrt{2 x-5}}+\frac{8959 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{720 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{509 \sqrt{\frac{143}{3}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{160 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{2198489 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{3600 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
88,0,0,365,0.6473524,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} \sqrt{7+5 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*Sqrt[7 + 5*x]),x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} \sqrt{7+5 x}} \, dx","\frac{\sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{5 \sqrt{2 x-5}}+\frac{7 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{10 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{41 \sqrt{\frac{11}{62}} \sqrt{2-3 x} F\left(\tan ^{-1}\left(\frac{\sqrt{\frac{22}{23}} \sqrt{5 x+7}}{\sqrt{2 x-5}}\right)|\frac{39}{62}\right)}{20 \sqrt{-\frac{2-3 x}{4 x+1}} \sqrt{4 x+1}}-\frac{\sqrt{429} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{10 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{943 \sqrt{2-3 x} \Pi \left(\frac{78}{55};\tan ^{-1}\left(\frac{\sqrt{\frac{22}{23}} \sqrt{5 x+7}}{\sqrt{2 x-5}}\right)|\frac{39}{62}\right)}{100 \sqrt{682} \sqrt{-\frac{2-3 x}{4 x+1}} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
89,0,0,279,1.2625023,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{3/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(3/2)),x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{3/2}} \, dx","-\frac{4 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{195 \sqrt{2 x-5}}+\frac{2 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{39 \sqrt{5 x+7}}+\frac{2 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{5 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}-\frac{69 \sqrt{\frac{2}{341}} \sqrt{-\frac{2-3 x}{4 x+1}} \sqrt{-\frac{5-2 x}{4 x+1}} (4 x+1) \Pi \left(\frac{78}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{22}{39}} \sqrt{5 x+7}}{\sqrt{4 x+1}}\right)|\frac{39}{62}\right)}{25 \sqrt{2-3 x} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
90,0,0,290,1.359563,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{5/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(5/2)),x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{5/2}} \, dx","\frac{3740 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{3253419 \sqrt{2 x-5}}-\frac{9350 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{3253419 \sqrt{5 x+7}}+\frac{2 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{117 (5 x+7)^{3/2}}+\frac{44 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{2691 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{1870 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{83421 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}",1,"Could not integrate","F",-1
91,0,0,330,1.5453171,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{7/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(7/2)),x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{7/2}} \, dx","\frac{8185936 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{90467822133 \sqrt{2 x-5}}-\frac{20464840 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{90467822133 \sqrt{5 x+7}}-\frac{3646 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{16267095 (5 x+7)^{3/2}}+\frac{2 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{195 (5 x+7)^{5/2}}+\frac{111628 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{74828637 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{4092968 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{2319687747 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}",1,"Could not integrate","F",-1
92,0,0,370,1.7057241,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{9/2}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(9/2)),x]","\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{9/2}} \, dx","\frac{16377776536 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{1956607901151813 \sqrt{2 x-5}}-\frac{40944441340 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{1956607901151813 \sqrt{5 x+7}}-\frac{3217468 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{50259901185 (5 x+7)^{3/2}}+\frac{98 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{1807455 (5 x+7)^{5/2}}+\frac{2 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{273 (5 x+7)^{7/2}}+\frac{258506776 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{1618368818157 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{8188888268 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{50169433362867 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}",1,"Could not integrate","F",-1
93,0,0,391,1.1071402,"\int \frac{\sqrt{2-3 x} (7+5 x)^{5/2}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*(7 + 5*x)^(5/2))/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{\sqrt{2-3 x} (7+5 x)^{5/2}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{5}{24} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} (5 x+7)^{3/2}+\frac{6955 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7}}{1152}+\frac{102487 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{1536 \sqrt{2 x-5}}+\frac{5241511 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{13824 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{102487 \sqrt{\frac{143}{3}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{1024 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{295576909 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{13824 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
94,0,0,351,0.9594165,"\int \frac{\sqrt{2-3 x} (7+5 x)^{3/2}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*(7 + 5*x)^(3/2))/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{\sqrt{2-3 x} (7+5 x)^{3/2}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{5}{16} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7}+\frac{785 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{192 \sqrt{2 x-5}}+\frac{17515 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{576 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{785 \sqrt{\frac{143}{3}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{128 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{3730013 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{2880 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
95,0,0,365,0.7098334,"\int \frac{\sqrt{2-3 x} \sqrt{7+5 x}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(Sqrt[2 - 3*x]*Sqrt[7 + 5*x])/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{\sqrt{2-3 x} \sqrt{7+5 x}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{\sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{4 \sqrt{2 x-5}}-\frac{39 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{8 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{179 \sqrt{\frac{11}{62}} \sqrt{2-3 x} F\left(\tan ^{-1}\left(\frac{\sqrt{\frac{22}{23}} \sqrt{5 x+7}}{\sqrt{2 x-5}}\right)|\frac{39}{62}\right)}{16 \sqrt{-\frac{2-3 x}{4 x+1}} \sqrt{4 x+1}}-\frac{\sqrt{429} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{8 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{4117 \sqrt{2-3 x} \Pi \left(\frac{78}{55};\tan ^{-1}\left(\frac{\sqrt{\frac{22}{23}} \sqrt{5 x+7}}{\sqrt{2 x-5}}\right)|\frac{39}{62}\right)}{80 \sqrt{682} \sqrt{-\frac{2-3 x}{4 x+1}} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
96,0,0,101,0.7191955,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x}} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]),x]","\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x}} \, dx","\frac{62 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{5 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
97,0,0,60,1.2164636,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2)),x]","\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2}} \, dx","\frac{2 \sqrt{\frac{11}{39}} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{22}} \sqrt{4 x+1}}{\sqrt{5 x+7}}\right)|\frac{62}{39}\right)}{23 \sqrt{2 x-5}}",1,"Could not integrate","F",-1
98,0,0,290,1.3847423,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2)),x]","\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2}} \, dx","\frac{39332 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{74828637 \sqrt{2 x-5}}-\frac{98330 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{74828637 \sqrt{5 x+7}}-\frac{10 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{2691 (5 x+7)^{3/2}}+\frac{716 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{61893 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{19666 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{1918683 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}",1,"Could not integrate","F",-1
99,0,0,721,2.3168276,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{\sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*Sqrt[c + d*x])/(Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{\sqrt{e+f x} \sqrt{g+h x}} \, dx","\frac{(e+f x) \sqrt{b g-a h} \sqrt{\frac{(a+b x) (f g-e h)}{(e+f x) (b g-a h)}} \sqrt{\frac{(c+d x) (f g-e h)}{(e+f x) (d g-c h)}} (a d f h-b (-c f h+d e h+d f g)) \Pi \left(\frac{f (b g-a h)}{(b e-a f) h};\sin ^{-1}\left(\frac{\sqrt{b e-a f} \sqrt{g+h x}}{\sqrt{b g-a h} \sqrt{e+f x}}\right)|\frac{(d e-c f) (b g-a h)}{(b e-a f) (d g-c h)}\right)}{f^2 h^2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{b e-a f}}+\frac{\sqrt{g+h x} (d e-c f) (-2 a f h+b e h+b f g) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{f^2 h \sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \sqrt{g+h x}}{h \sqrt{e+f x}}-\frac{\sqrt{a+b x} \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{\frac{(g+h x) (d e-c f)}{(e+f x) (d g-c h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{f g-e h} \sqrt{c+d x}}{\sqrt{d g-c h} \sqrt{e+f x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{f h \sqrt{g+h x} \sqrt{-\frac{(a+b x) (d e-c f)}{(e+f x) (b c-a d)}}}",1,"Could not integrate","F",-1
100,0,0,161,2.8608822,"\int \frac{\sqrt{c+d x}}{(a+b x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[Sqrt[c + d*x]/((a + b*x)^(3/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{\sqrt{c+d x}}{(a+b x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\frac{2 \sqrt{c+d x} E\left(\tan ^{-1}\left(\frac{\sqrt{a f-b e} \sqrt{g+h x}}{\sqrt{b g-a h} \sqrt{e+f x}}\right)|\frac{(a d-b c) (f g-e h)}{(a f-b e) (d g-c h)}\right)}{\sqrt{a+b x} \sqrt{a f-b e} \sqrt{b g-a h} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}}}",1,"Could not integrate","F",-1
101,0,0,351,1.2117674,"\int \frac{(7+5 x)^{5/2}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(7 + 5*x)^(5/2)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{(7+5 x)^{5/2}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","-\frac{25}{48} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7}-\frac{2135 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{192 \sqrt{2 x-5}}+\frac{29047 \sqrt{\frac{23}{11}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{576 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}+\frac{2135 \sqrt{\frac{143}{3}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{128 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}-\frac{3431855 (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} \Pi \left(-\frac{69}{55};\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{576 \sqrt{429} \sqrt{2 x-5} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
102,0,0,469,1.0265456,"\int \frac{(7+5 x)^{3/2}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[(7 + 5*x)^(3/2)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{(7+5 x)^{3/2}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","-\frac{5 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{12 \sqrt{2 x-5}}+\frac{65 \sqrt{\frac{11}{23}} \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{8 \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{895 \sqrt{\frac{11}{62}} \sqrt{2-3 x} F\left(\tan ^{-1}\left(\frac{\sqrt{\frac{22}{23}} \sqrt{5 x+7}}{\sqrt{2 x-5}}\right)|\frac{39}{62}\right)}{48 \sqrt{-\frac{2-3 x}{4 x+1}} \sqrt{4 x+1}}+\frac{5 \sqrt{\frac{143}{3}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{8 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}+\frac{23 \sqrt{\frac{31}{22}} \sqrt{\frac{2-3 x}{5 x+7}} \sqrt{\frac{5-2 x}{5 x+7}} (5 x+7) \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{\sqrt{\frac{31}{11}} \sqrt{4 x+1}}{\sqrt{5 x+7}}\right)|\frac{39}{62}\right)}{6 \sqrt{2-3 x} \sqrt{2 x-5}}-\frac{4117 \sqrt{2-3 x} \Pi \left(\frac{78}{55};\tan ^{-1}\left(\frac{\sqrt{\frac{22}{23}} \sqrt{5 x+7}}{\sqrt{2 x-5}}\right)|\frac{39}{62}\right)}{48 \sqrt{682} \sqrt{-\frac{2-3 x}{4 x+1}} \sqrt{4 x+1}}",1,"Could not integrate","F",-1
103,0,0,100,0.927513,"\int \frac{\sqrt{7+5 x}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","IntegrateAlgebraic[Sqrt[7 + 5*x]/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\int \frac{\sqrt{7+5 x}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","\frac{23 \sqrt{\frac{2-3 x}{5 x+7}} \sqrt{\frac{5-2 x}{5 x+7}} (5 x+7) \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{\sqrt{\frac{31}{11}} \sqrt{4 x+1}}{\sqrt{5 x+7}}\right)|\frac{39}{62}\right)}{2 \sqrt{682} \sqrt{2-3 x} \sqrt{2 x-5}}",1,"Could not integrate","F",-1
104,0,0,71,0.7858784,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x}} \, dx","\frac{2 \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{\sqrt{253} \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}",1,"Could not integrate","F",-1
105,0,0,195,1.5797879,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2)),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2}} \, dx","\frac{2 \sqrt{\frac{3}{143}} (2-3 x) \sqrt{\frac{5-2 x}{2-3 x}} \sqrt{-\frac{4 x+1}{2-3 x}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{11}{23}} \sqrt{5 x+7}}{\sqrt{2-3 x}}\right)|-\frac{23}{39}\right)}{31 \sqrt{2 x-5} \sqrt{4 x+1}}+\frac{10 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5-2 x}{5 x+7}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{22}} \sqrt{4 x+1}}{\sqrt{5 x+7}}\right)|\frac{62}{39}\right)}{713 \sqrt{2 x-5} \sqrt{\frac{2-3 x}{5 x+7}}}",1,"Could not integrate","F",-1
106,0,0,288,1.7355057,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2)),x]","\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2}} \, dx","\frac{358120 \sqrt{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{2319687747 \sqrt{2 x-5}}-\frac{895300 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{2319687747 \sqrt{5 x+7}}-\frac{50 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{83421 (5 x+7)^{3/2}}+\frac{103964 \sqrt{5 x+7} F\left(\tan ^{-1}\left(\frac{\sqrt{4 x+1}}{\sqrt{2} \sqrt{2-3 x}}\right)|-\frac{39}{23}\right)}{1918683 \sqrt{253} \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{179060 \sqrt{\frac{11}{39}} \sqrt{2-3 x} \sqrt{\frac{5 x+7}{5-2 x}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{39}{23}} \sqrt{4 x+1}}{\sqrt{2 x-5}}\right)|-\frac{23}{39}\right)}{59479173 \sqrt{\frac{2-3 x}{5-2 x}} \sqrt{5 x+7}}",1,"Could not integrate","F",-1
107,0,0,968,3.028369,"\int \frac{(a+b x)^{3/2}}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(a + b*x)^(3/2)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{(a+b x)^{3/2}}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\frac{\sqrt{d g-c h} \sqrt{f g-e h} \sqrt{a+b x} \sqrt{\frac{(d e-c f) (g+h x)}{(d g-c h) (e+f x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{f g-e h} \sqrt{c+d x}}{\sqrt{d g-c h} \sqrt{e+f x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right) b}{d f h \sqrt{-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}} \sqrt{g+h x}}+\frac{(d e-c f) (b f g+b e h-2 a f h) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right) b}{d f^2 h \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}+\frac{\sqrt{b g-a h} (a d f h-b (d f g+d e h-c f h)) \sqrt{\frac{(f g-e h) (a+b x)}{(b g-a h) (e+f x)}} \sqrt{\frac{(f g-e h) (c+d x)}{(d g-c h) (e+f x)}} (e+f x) \Pi \left(\frac{f (b g-a h)}{(b e-a f) h};\sin ^{-1}\left(\frac{\sqrt{b e-a f} \sqrt{g+h x}}{\sqrt{b g-a h} \sqrt{e+f x}}\right)|\frac{(d e-c f) (b g-a h)}{(b e-a f) (d g-c h)}\right) b}{d f^2 \sqrt{b e-a f} h^2 \sqrt{a+b x} \sqrt{c+d x}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \sqrt{g+h x} b}{d h \sqrt{e+f x}}-\frac{2 \sqrt{b c-a d} \sqrt{c h-d g} (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{d h \sqrt{c+d x} \sqrt{e+f x}}",1,"Could not integrate","F",-1
108,0,0,228,2.4099353,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x]/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{\sqrt{a+b x}}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\frac{2 (a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{h \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}",1,"Could not integrate","F",-1
109,0,0,161,2.6158896,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[1/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\frac{2 \sqrt{e+f x} \sqrt{\frac{(c+d x) (f g-e h)}{(e+f x) (d g-c h)}} F\left(\tan ^{-1}\left(\frac{\sqrt{b e-a f} \sqrt{g+h x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|\frac{(d e-c f) (b g-a h)}{(b e-a f) (d g-c h)}\right)}{\sqrt{c+d x} \sqrt{b e-a f} \sqrt{f g-e h}}",1,"Could not integrate","F",-1
110,0,0,429,3.0498522,"\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\frac{2 d \sqrt{g+h x} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} (b c-a d) \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{2 b \sqrt{c+d x} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{g+h x} (b c-a d) (b e-a f) \sqrt{b g-a h} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}}}",1,"Could not integrate","F",-1
111,0,0,786,3.3031169,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[1/((a + b*x)^(3/2)*(c + d*x)^(3/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \left(a^2 d^2 f h-a b d^2 (e h+f g)+b^2 \left(c^2 f h-c d (e h+f g)+2 d^2 e g\right)\right)}{\sqrt{a+b x} (b c-a d)^2 (b e-a f) (b g-a h) (d e-c f) (d g-c h)}-\frac{2 \sqrt{c+d x} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}} \left(a^2 d^2 f h-a b d^2 (e h+f g)+b^2 \left(c^2 f h-c d (e h+f g)+2 d^2 e g\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{g+h x} (b c-a d)^2 (b e-a f) \sqrt{b g-a h} (d e-c f) (d g-c h) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}}}-\frac{2 b^3 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{\sqrt{a+b x} (b c-a d)^2 (b e-a f) (b g-a h)}-\frac{2 d^3 \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{\sqrt{c+d x} (b c-a d)^2 (d e-c f) (d g-c h)}-\frac{4 b d \sqrt{g+h x} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} (b c-a d)^2 \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}",1,"Could not integrate","F",-1
112,0,0,319,0.3508099,"\int \frac{x^4 (e+f x)^n}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[(x^4*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\int \frac{x^4 (e+f x)^n}{(a+b x) (c+d x)} \, dx","-\frac{a^4 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{b^3 (n+1) (b c-a d) (b e-a f)}+\frac{\left(a^2 d^2+a b c d+b^2 c^2\right) (e+f x)^{n+1}}{b^3 d^3 f (n+1)}+\frac{e (a d+b c) (e+f x)^{n+1}}{b^2 d^2 f^2 (n+1)}-\frac{(a d+b c) (e+f x)^{n+2}}{b^2 d^2 f^2 (n+2)}+\frac{c^4 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{d^3 (n+1) (b c-a d) (d e-c f)}+\frac{e^2 (e+f x)^{n+1}}{b d f^3 (n+1)}-\frac{2 e (e+f x)^{n+2}}{b d f^3 (n+2)}+\frac{(e+f x)^{n+3}}{b d f^3 (n+3)}",1,"Could not integrate","F",-1
113,0,0,216,0.1886193,"\int \frac{x^3 (e+f x)^n}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[(x^3*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\int \frac{x^3 (e+f x)^n}{(a+b x) (c+d x)} \, dx","\frac{a^3 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{b^2 (n+1) (b c-a d) (b e-a f)}-\frac{(a d+b c) (e+f x)^{n+1}}{b^2 d^2 f (n+1)}-\frac{c^3 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{d^2 (n+1) (b c-a d) (d e-c f)}-\frac{e (e+f x)^{n+1}}{b d f^2 (n+1)}+\frac{(e+f x)^{n+2}}{b d f^2 (n+2)}",1,"Could not integrate","F",-1
114,0,0,158,0.1901668,"\int \frac{x^2 (e+f x)^n}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[(x^2*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\int \frac{x^2 (e+f x)^n}{(a+b x) (c+d x)} \, dx","-\frac{a^2 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{b (n+1) (b c-a d) (b e-a f)}+\frac{c^2 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{d (n+1) (b c-a d) (d e-c f)}+\frac{(e+f x)^{n+1}}{b d f (n+1)}",1,"Could not integrate","F",-1
115,0,0,124,0.1131157,"\int \frac{x (e+f x)^n}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[(x*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\int \frac{x (e+f x)^n}{(a+b x) (c+d x)} \, dx","\frac{a (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{(n+1) (b c-a d) (b e-a f)}-\frac{c (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{(n+1) (b c-a d) (d e-c f)}",1,"Could not integrate","F",-1
116,0,0,124,0.1627261,"\int \frac{(e+f x)^n}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[(e + f*x)^n/((a + b*x)*(c + d*x)),x]","\int \frac{(e+f x)^n}{(a+b x) (c+d x)} \, dx","\frac{d (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{(n+1) (b c-a d) (d e-c f)}-\frac{b (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{(n+1) (b c-a d) (b e-a f)}",1,"Could not integrate","F",-1
117,0,0,175,0.1720457,"\int \frac{(e+f x)^n}{x (a+b x) (c+d x)} \, dx","IntegrateAlgebraic[(e + f*x)^n/(x*(a + b*x)*(c + d*x)),x]","\int \frac{(e+f x)^n}{x (a+b x) (c+d x)} \, dx","\frac{b^2 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{a (n+1) (b c-a d) (b e-a f)}-\frac{d^2 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{c (n+1) (b c-a d) (d e-c f)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)}{a c e (n+1)}",1,"Could not integrate","F",-1
118,0,0,222,0.2025171,"\int \frac{(e+f x)^n}{x^2 (a+b x) (c+d x)} \, dx","IntegrateAlgebraic[(e + f*x)^n/(x^2*(a + b*x)*(c + d*x)),x]","\int \frac{(e+f x)^n}{x^2 (a+b x) (c+d x)} \, dx","-\frac{b^3 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{a^2 (n+1) (b c-a d) (b e-a f)}+\frac{(a d+b c) (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)}{a^2 c^2 e (n+1)}+\frac{d^3 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{c^2 (n+1) (b c-a d) (d e-c f)}+\frac{f (e+f x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{f x}{e}+1\right)}{a c e^2 (n+1)}",1,"Could not integrate","F",-1
119,0,0,167,0.0911816,"\int (a+b x)^m (c+d x) (e+f x) (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)*(e + f*x)*(g + h*x),x]","\int (a+b x)^m (c+d x) (e+f x) (g+h x) \, dx","\frac{(a+b x)^{m+2} \left(3 a^2 d f h-2 a b (c f h+d e h+d f g)+b^2 (c e h+c f g+d e g)\right)}{b^4 (m+2)}+\frac{(b c-a d) (b e-a f) (b g-a h) (a+b x)^{m+1}}{b^4 (m+1)}-\frac{(a+b x)^{m+3} (3 a d f h-b (c f h+d e h+d f g))}{b^4 (m+3)}+\frac{d f h (a+b x)^{m+4}}{b^4 (m+4)}",1,"Could not integrate","F",-1
120,0,0,134,0.1606745,"\int \frac{(a+b x)^m (c+d x) (e+f x)}{g+h x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)*(e + f*x))/(g + h*x),x]","\int \frac{(a+b x)^m (c+d x) (e+f x)}{g+h x} \, dx","\frac{(a+b x)^{m+1} (d g-c h) (f g-e h) \, _2F_1\left(1,m+1;m+2;-\frac{h (a+b x)}{b g-a h}\right)}{h^2 (m+1) (b g-a h)}-\frac{(a+b x)^{m+1} (a d f h+b (m+2) (-c f h-d e h+d f g)-b d f h (m+1) x)}{b^2 h^2 (m+1) (m+2)}",1,"Could not integrate","F",-1
121,0,0,140,0.1753693,"\int \frac{(a+b x)^m (c+d x)}{(e+f x) (g+h x)} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x))/((e + f*x)*(g + h*x)),x]","\int \frac{(a+b x)^m (c+d x)}{(e+f x) (g+h x)} \, dx","\frac{(a+b x)^{m+1} (d g-c h) \, _2F_1\left(1,m+1;m+2;-\frac{h (a+b x)}{b g-a h}\right)}{(m+1) (b g-a h) (f g-e h)}-\frac{(a+b x)^{m+1} (d e-c f) \, _2F_1\left(1,m+1;m+2;-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f) (f g-e h)}",1,"Could not integrate","F",-1
122,0,0,224,0.2470799,"\int \frac{(a+b x)^m}{(c+d x) (e+f x) (g+h x)} \, dx","IntegrateAlgebraic[(a + b*x)^m/((c + d*x)*(e + f*x)*(g + h*x)),x]","\int \frac{(a+b x)^m}{(c+d x) (e+f x) (g+h x)} \, dx","\frac{d^2 (a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right)}{(m+1) (b c-a d) (d e-c f) (d g-c h)}-\frac{f^2 (a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{f (a+b x)}{b e-a f}\right)}{(m+1) (b e-a f) (d e-c f) (f g-e h)}+\frac{h^2 (a+b x)^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{h (a+b x)}{b g-a h}\right)}{(m+1) (b g-a h) (d g-c h) (f g-e h)}",1,"Could not integrate","F",-1
123,0,0,140,0.1004665,"\int \frac{x^m (e+f x)^n}{(a+b x) (c+d x)} \, dx","IntegrateAlgebraic[(x^m*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\int \frac{x^m (e+f x)^n}{(a+b x) (c+d x)} \, dx","\frac{b x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{b x}{a}\right)}{a (m+1) (b c-a d)}-\frac{d x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{d x}{c}\right)}{c (m+1) (b c-a d)}",1,"Could not integrate","F",-1
124,0,0,266,0.0704407,"\int (a+b x)^m (c+d x)^n (e+f x) (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)*(g + h*x),x]","\int (a+b x)^m (c+d x)^n (e+f x) (g+h x) \, dx","\frac{(a+b x)^{m+1} (c+d x)^n \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{d (a+b x)}{b c-a d}\right) \left(a^2 d^2 f h (n+1) (n+2)+a b d (n+1) (2 c f h (m+1)-d (m+n+3) (e h+f g))+b^2 \left(c^2 f h (m+1) (m+2)-c d (m+1) (m+n+3) (e h+f g)+d^2 e g (m+n+2) (m+n+3)\right)\right)}{b^3 d^2 (m+1) (m+n+2) (m+n+3)}-\frac{(a+b x)^{m+1} (c+d x)^{n+1} (a d f h (n+2)+b c f h (m+2)-b d (m+n+3) (e h+f g)-b d f h x (m+n+2))}{b^2 d^2 (m+n+2) (m+n+3)}",1,"Could not integrate","F",-1
125,0,0,245,0.1340266,"\int (a+b x)^m (c+d x)^{1-m} (e+f x) (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x)*(g + h*x),x]","\int (a+b x)^m (c+d x)^{1-m} (e+f x) (g+h x) \, dx","\frac{(b c-a d) (a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m-1,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right) \left(a^2 d^2 f h \left(m^2-5 m+6\right)-2 a b d (2-m) (2 d (e h+f g)-c f h (m+1))+b^2 \left(c^2 f h \left(m^2+3 m+2\right)-4 c d (m+1) (e h+f g)+12 d^2 e g\right)\right)}{12 b^4 d^2 (m+1)}+\frac{(a+b x)^{m+1} (c+d x)^{2-m} (-a d f h (3-m)-b c f h (m+2)+4 b d (e h+f g)+3 b d f h x)}{12 b^2 d^2}",1,"Could not integrate","F",-1
126,0,0,235,0.0738028,"\int (a+b x)^m (c+d x)^{-m} (e+f x) (g+h x) \, dx","IntegrateAlgebraic[((a + b*x)^m*(e + f*x)*(g + h*x))/(c + d*x)^m,x]","\int (a+b x)^m (c+d x)^{-m} (e+f x) (g+h x) \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right) \left(a^2 d^2 f h \left(m^2-3 m+2\right)-a b d (1-m) (3 d (e h+f g)-2 c f h (m+1))+b^2 \left(c^2 f h \left(m^2+3 m+2\right)-3 c d (m+1) (e h+f g)+6 d^2 e g\right)\right)}{6 b^3 d^2 (m+1)}+\frac{(a+b x)^{m+1} (c+d x)^{1-m} (-a d f h (2-m)-b c f h (m+2)+3 b d (e h+f g)+2 b d f h x)}{6 b^2 d^2}",1,"Could not integrate","F",-1
127,0,0,261,0.0966565,"\int (a+b x)^m (c+d x)^{-1-m} (e+f x) (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-1 - m)*(e + f*x)*(g + h*x),x]","\int (a+b x)^m (c+d x)^{-1-m} (e+f x) (g+h x) \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(-c d (a f h m+2 b (e h+f g))+d f h m x (b c-a d)+b c^2 f h (m+2)+2 b d^2 e g\right)}{2 b d^2 m (b c-a d)}-\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right) \left(d^2 \left(a^2 (-f) h (1-m) m+2 a b m (e h+f g)+2 b^2 e g\right)-2 b c d (m+1) (a f h m+b e h+b f g)+b^2 c^2 f h (m+1) (m+2)\right)}{2 b^2 d^2 m (m+1) (b c-a d)}",1,"Could not integrate","F",-1
128,0,0,203,0.0929103,"\int (a+b x)^m (c+d x)^{-2-m} (e+f x) (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-2 - m)*(e + f*x)*(g + h*x),x]","\int (a+b x)^m (c+d x)^{-2-m} (e+f x) (g+h x) \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(-c d (a f h (m+1)+b (e h+f g))+d f h (m+1) x (b c-a d)+b c^2 f h (m+2)+b d^2 e g\right)}{b d^2 (m+1) (b c-a d)}-\frac{(a+b x)^m (c+d x)^{-m} \left(-\frac{d (a+b x)}{b c-a d}\right)^{-m} \, _2F_1\left(-m,-m;1-m;\frac{b (c+d x)}{b c-a d}\right) (a d f h m+b (d (e h+f g)-c f h (m+2)))}{b d^3 m}",1,"Could not integrate","F",-1
129,0,0,246,0.0926801,"\int (a+b x)^m (c+d x)^{-3-m} (e+f x) (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-3 - m)*(e + f*x)*(g + h*x),x]","\int (a+b x)^m (c+d x)^{-3-m} (e+f x) (g+h x) \, dx","\frac{f h (a+b x)^{m+3} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m+3,m+3;m+4;-\frac{d (a+b x)}{b c-a d}\right)}{(m+3) (b c-a d)^3}-\frac{(a+b x)^{m+1} (c+d x)^{-m-2} \left(a^3 (-d) f h (m+1)-b x \left(a^2 d f h (2 m+3)-a b (2 c f h (m+1)+d (m+2) (e h+f g))+b^2 (c (m+1) (e h+f g)+d e g)\right)+a^2 b c f h m+a b^2 (c (e h+f g)+d e g (m+1))-b^3 c e g (m+2)\right)}{b^2 (m+1) (m+2) (b c-a d)^2}",1,"Could not integrate","F",-1
130,0,0,362,0.096277,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x) (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x)*(g + h*x),x]","\int (a+b x)^m (c+d x)^{-4-m} (e+f x) (g+h x) \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-2} \left(a^2 d^2 f h \left(m^2+5 m+6\right)-a b d (m+3) (2 c f h (m+1)+d (e h+f g))+b^2 \left(c^2 f h \left(m^2+3 m+2\right)+c d (m+1) (e h+f g)+2 d^2 e g\right)\right)}{b d^2 (m+2) (m+3) (b c-a d)^2}+\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(a^2 d^2 f h \left(m^2+5 m+6\right)-a b d (m+3) (2 c f h (m+1)+d (e h+f g))+b^2 \left(c^2 f h \left(m^2+3 m+2\right)+c d (m+1) (e h+f g)+2 d^2 e g\right)\right)}{d^2 (m+1) (m+2) (m+3) (b c-a d)^3}+\frac{(a+b x)^{m+1} (c+d x)^{-m-3} \left(-d f h (m+3) x (b c-a d)+a c d f h (m+3)+b \left(c^2 (-f) h (m+2)-c d (e h+f g)+d^2 e g\right)\right)}{b d^2 (m+3) (b c-a d)}",1,"Could not integrate","F",-1
131,0,0,507,0.095177,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x) (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)*(g + h*x),x]","\int (a+b x)^m (c+d x)^{-5-m} (e+f x) (g+h x) \, dx","\frac{(a+b x)^{m+1} (c+d x)^{-m-3} \left(a^2 d^2 f h \left(m^2+7 m+12\right)-2 a b d (m+4) (c f h (m+1)+d (e h+f g))+b^2 \left(c^2 f h \left(m^2+3 m+2\right)+2 c d (m+1) (e h+f g)+6 d^2 e g\right)\right)}{2 b d^2 (m+3) (m+4) (b c-a d)^2}+\frac{(a+b x)^{m+1} (c+d x)^{-m-2} \left(a^2 d^2 f h \left(m^2+7 m+12\right)-2 a b d (m+4) (c f h (m+1)+d (e h+f g))+b^2 \left(c^2 f h \left(m^2+3 m+2\right)+2 c d (m+1) (e h+f g)+6 d^2 e g\right)\right)}{d^2 (m+2) (m+3) (m+4) (b c-a d)^3}+\frac{b (a+b x)^{m+1} (c+d x)^{-m-1} \left(a^2 d^2 f h \left(m^2+7 m+12\right)-2 a b d (m+4) (c f h (m+1)+d (e h+f g))+b^2 \left(c^2 f h \left(m^2+3 m+2\right)+2 c d (m+1) (e h+f g)+6 d^2 e g\right)\right)}{d^2 (m+1) (m+2) (m+3) (m+4) (b c-a d)^4}+\frac{(a+b x)^{m+1} (c+d x)^{-m-4} \left(-d f h (m+4) x (b c-a d)+a c d f h (m+4)+b \left(c^2 (-f) h (m+2)-2 c d (e h+f g)+2 d^2 e g\right)\right)}{2 b d^2 (m+4) (b c-a d)}",1,"Could not integrate","F",-1
132,0,0,815,0.1183463,"\int (a+b x)^3 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^3*(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","\int (a+b x)^3 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","\frac{h (a+b x)^3 (e+f x)^{m+1} (c+d x)^{-m-3}}{d f}+\frac{(b c-a d)^2 (a d f+b (c f (m+2)-d e (m+3))) (c f h (m+4)-d (f g+e h (m+3))) (e+f x)^{m+1} (c+d x)^{-m-3}}{d^4 f^2 (d e-c f) (m+3)}-\frac{b (b c-a d) (c f h (m+4)-d (f g+e h (m+3))) (a+b x) (e+f x)^{m+1} (c+d x)^{-m-3}}{d^3 f^2}-\frac{(b c-a d)^2 (3 a d f h-b (c f h (m+4)-d (f g+e h m))) (e+f x)^{m+1} (c+d x)^{-m-2}}{d^4 f (d e-c f) (m+2)}+\frac{(b c-a d) (c f h (m+4)-d (f g+e h (m+3))) \left(\left(d^2 \left(m^2+5 m+6\right) e^2-2 c d f \left(m^2+4 m+3\right) e+c^2 f^2 \left(m^2+3 m+2\right)\right) b^2+2 a d f (c f (m+1)-d e (m+3)) b+2 a^2 d^2 f^2\right) (e+f x)^{m+1} (c+d x)^{-m-2}}{d^4 f^2 (d e-c f)^2 (m+2) (m+3)}-\frac{(b c-a d) (a d f-b (2 d e (m+2)-c f (2 m+3))) (3 a d f h-b (c f h (m+4)-d (f g+e h m))) (e+f x)^{m+1} (c+d x)^{-m-1}}{d^4 f (d e-c f)^2 (m+1) (m+2)}-\frac{(b c-a d) (c f h (m+4)-d (f g+e h (m+3))) \left(\left(d^2 \left(m^2+5 m+6\right) e^2-2 c d f \left(m^2+4 m+3\right) e+c^2 f^2 \left(m^2+3 m+2\right)\right) b^2+2 a d f (c f (m+1)-d e (m+3)) b+2 a^2 d^2 f^2\right) (e+f x)^{m+1} (c+d x)^{-m-1}}{d^4 f (d e-c f)^3 (m+1) (m+2) (m+3)}-\frac{b^2 (3 a d f h-b (c f h (m+4)-d (f g+e h m))) (e+f x)^m \left(\frac{d (e+f x)}{d e-c f}\right)^{-m} \, _2F_1\left(-m,-m;1-m;-\frac{f (c+d x)}{d e-c f}\right) (c+d x)^{-m}}{d^5 f m}",1,"Could not integrate","F",-1
133,0,0,572,0.1093041,"\int (a+b x)^2 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^2*(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","\int (a+b x)^2 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","-\frac{(d g-c h) (c+d x)^{-m-2} (e+f x)^{m+1} \left(b^2 (m+2) (d e-c f) (c f (m+1)-d e (m+3))-2 d f \left(a^2 d f+a b (c f (m+1)-d e (m+3))+b^2 c e\right)\right)}{d^3 f (m+2) (m+3) (d e-c f)^2}+\frac{(d g-c h) (c+d x)^{-m-1} (e+f x)^{m+1} \left(b^2 (m+2) (d e-c f) (c f (m+1)-d e (m+3))-2 d f \left(a^2 d f+a b (c f (m+1)-d e (m+3))+b^2 c e\right)\right)}{d^3 (m+1) (m+2) (m+3) (d e-c f)^3}+\frac{(b c-a d) (d g-c h) (c+d x)^{-m-3} (e+f x)^{m+1} (a d f+b (c f (m+2)-d e (m+3)))}{d^3 f (m+3) (d e-c f)}-\frac{h (b c-a d)^2 (c+d x)^{-m-2} (e+f x)^{m+1}}{d^3 (m+2) (d e-c f)}-\frac{h (b c-a d) (c+d x)^{-m-1} (e+f x)^{m+1} (a d f-b (2 d e (m+2)-c f (2 m+3)))}{d^3 (m+1) (m+2) (d e-c f)^2}-\frac{b (a+b x) (d g-c h) (c+d x)^{-m-3} (e+f x)^{m+1}}{d^2 f}-\frac{b^2 h (c+d x)^{-m} (e+f x)^m \left(\frac{d (e+f x)}{d e-c f}\right)^{-m} \, _2F_1\left(-m,-m;1-m;-\frac{f (c+d x)}{d e-c f}\right)}{d^4 m}",1,"Could not integrate","F",-1
134,0,0,363,0.0980691,"\int (a+b x) (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)*(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","\int (a+b x) (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","\frac{(c+d x)^{-m-2} (e+f x)^{m+1} \left(a d f (c f h (m+1)+d (2 f g-e h (m+3)))+b \left(c^2 f^2 h \left(m^2+3 m+2\right)+c d f (m+1) (f g-2 e h (m+3))+d^2 (-e) (m+3) (f g-e h (m+2))\right)\right)}{d^2 f (m+2) (m+3) (d e-c f)^2}-\frac{(c+d x)^{-m-1} (e+f x)^{m+1} \left(a d f (c f h (m+1)+d (2 f g-e h (m+3)))+b \left(c^2 f^2 h \left(m^2+3 m+2\right)+c d f (m+1) (f g-2 e h (m+3))+d^2 (-e) (m+3) (f g-e h (m+2))\right)\right)}{d^2 (m+1) (m+2) (m+3) (d e-c f)^3}-\frac{(c+d x)^{-m-3} (e+f x)^{m+1} (a d f (d g-c h)-b c (c f h (m+2)+d (f g-e h (m+3)))+b d h (m+3) x (d e-c f))}{d^2 f (m+3) (d e-c f)}",1,"Could not integrate","F",-1
135,0,0,188,0.0586838,"\int (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","IntegrateAlgebraic[(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","\int (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","-\frac{(d g-c h) (c+d x)^{-m-3} (e+f x)^{m+1}}{d (m+3) (d e-c f)}+\frac{(c+d x)^{-m-2} (e+f x)^{m+1} (c f h (m+1)+d (2 f g-e h (m+3)))}{d (m+2) (m+3) (d e-c f)^2}-\frac{f (c+d x)^{-m-1} (e+f x)^{m+1} (c f h (m+1)+d (2 f g-e h (m+3)))}{d (m+1) (m+2) (m+3) (d e-c f)^3}",1,"Could not integrate","F",-1
136,0,0,177,0.1622996,"\int \frac{(A+B x) (c+d x)^n (e+f x)^p}{a+b x} \, dx","IntegrateAlgebraic[((A + B*x)*(c + d*x)^n*(e + f*x)^p)/(a + b*x),x]","\int \frac{(A+B x) (c+d x)^n (e+f x)^p}{a+b x} \, dx","-\frac{(A b-a B) (c+d x)^{n+1} (e+f x)^p \left(\frac{d (e+f x)}{d e-c f}\right)^{-p} F_1\left(n+1;1,-p;n+2;\frac{b (c+d x)}{b c-a d},-\frac{f (c+d x)}{d e-c f}\right)}{b (n+1) (b c-a d)}-\frac{B (c+d x)^{n+1} (e+f x)^{p+1} \, _2F_1\left(1,n+p+2;p+2;\frac{d (e+f x)}{d e-c f}\right)}{b (p+1) (d e-c f)}",1,"Could not integrate","F",-1
137,0,0,233,0.1012835,"\int \frac{(a+b x)^m (A+B x) (c+d x)^{-m}}{e+f x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(A + B*x))/((c + d*x)^m*(e + f*x)),x]","\int \frac{(a+b x)^m (A+B x) (c+d x)^{-m}}{e+f x} \, dx","-\frac{(a+b x)^m (B e-A f) (c+d x)^{-m} \, _2F_1\left(1,-m;1-m;\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}\right)}{f^2 m}-\frac{(a+b x)^{m+1} (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m+1;m+2;-\frac{d (a+b x)}{b c-a d}\right) (a B d f m-b (-A d f+B c f m+B d e))}{b f^2 m (m+1) (b c-a d)}-\frac{d (a+b x)^{m+1} (B e-A f) (c+d x)^{-m}}{f^2 m (b c-a d)}",1,"Could not integrate","F",-1
138,0,0,250,0.1591734,"\int \frac{(A+B x) (c+d x)^n (e+f x)^p}{\sqrt{a+b x}} \, dx","IntegrateAlgebraic[((A + B*x)*(c + d*x)^n*(e + f*x)^p)/Sqrt[a + b*x],x]","\int \frac{(A+B x) (c+d x)^n (e+f x)^p}{\sqrt{a+b x}} \, dx","\frac{2 \sqrt{a+b x} (A b-a B) (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(\frac{1}{2};-n,-p;\frac{3}{2};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2}+\frac{2 B (a+b x)^{3/2} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(\frac{3}{2};-n,-p;\frac{5}{2};-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{3 b^2}",1,"Could not integrate","F",-1
139,0,0,530,0.1325188,"\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^3 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x)^3,x]","\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^3 \, dx","\frac{3 h^2 (b g-a h) (a+b x)^{m+3} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+3;-n,-p;m+4;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^4 (m+3)}+\frac{(b g-a h)^3 (a+b x)^{m+1} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^4 (m+1)}+\frac{3 h (b g-a h)^2 (a+b x)^{m+2} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+2;-n,-p;m+3;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^4 (m+2)}+\frac{h^3 (a+b x)^{m+4} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+4;-n,-p;m+5;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^4 (m+4)}",1,"Could not integrate","F",-1
140,0,0,393,0.083917,"\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^2 \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x)^2,x]","\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^2 \, dx","\frac{(b g-a h)^2 (a+b x)^{m+1} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^3 (m+1)}+\frac{2 h (b g-a h) (a+b x)^{m+2} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+2;-n,-p;m+3;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^3 (m+2)}+\frac{h^2 (a+b x)^{m+3} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+3;-n,-p;m+4;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^3 (m+3)}",1,"Could not integrate","F",-1
141,0,0,256,0.1170528,"\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x) \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x),x]","\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x) \, dx","\frac{(b g-a h) (a+b x)^{m+1} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+1)}+\frac{h (a+b x)^{m+2} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+2;-n,-p;m+3;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+2)}",1,"Could not integrate","F",-1
142,0,0,123,0.0005749,"\int (a+b x)^m (c+d x)^n (e+f x)^p \, dx","IntegrateAlgebraic[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p,x]","\int (a+b x)^m (c+d x)^n (e+f x)^p \, dx","\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b (m+1)}",1,"Could not integrate","F",-1
143,0,0,32,0.0952785,"\int \frac{(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx","IntegrateAlgebraic[((a + b*x)^m*(c + d*x)^n*(e + f*x)^p)/(g + h*x),x]","\int \frac{(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx","\text{Int}\left(\frac{(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x},x\right)",0,"Could not integrate","A",-1
144,0,0,268,0.1231436,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-m - n),x]","\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-m-n} \, dx","\frac{(A b-a B) (a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{m+n} F_1\left(m+1;-n,m+n;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+1)}+\frac{B (a+b x)^{m+2} (c+d x)^n (e+f x)^{-m-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{m+n} F_1\left(m+2;-n,m+n;m+3;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+2)}",1,"Could not integrate","F",-1
145,0,0,283,0.1138696,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-1-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-1 - m - n),x]","\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-1-m-n} \, dx","\frac{B (a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{m+n} F_1\left(m+1;-n,m+n;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b f (m+1)}-\frac{(a+b x)^{m+1} (B e-A f) (c+d x)^n (e+f x)^{-m-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{m+n} F_1\left(m+1;-n,m+n+1;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{f (m+1) (b e-a f)}",1,"Could not integrate","F",-1
146,0,0,277,0.1461844,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-2-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-2 - m - n),x]","\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-2-m-n} \, dx","\frac{B (a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{m+n} F_1\left(m+1;-n,m+n+1;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{f (m+1) (b e-a f)}-\frac{(a+b x)^{m+1} (B e-A f) (c+d x)^n (e+f x)^{-m-n-1} \left(\frac{(c+d x) (b e-a f)}{(e+f x) (b c-a d)}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}\right)}{f (m+1) (b e-a f)}",1,"Could not integrate","F",-1
147,0,0,263,0.1406517,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-3-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-3 - m - n),x]","\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-3-m-n} \, dx","\frac{(a+b x)^{m+1} (B e-A f) (c+d x)^{n+1} (e+f x)^{-m-n-2}}{(m+n+2) (b e-a f) (d e-c f)}-\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-1} \left(\frac{(c+d x) (b e-a f)}{(e+f x) (b c-a d)}\right)^{-n} (a (A d f (m+1)+B (d e (n+1)-c f (m+n+2)))+b (A (c f (n+1)-d e (m+n+2))+B c e (m+1))) \, _2F_1\left(m+1,-n;m+2;-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (m+n+2) (b e-a f)^2 (d e-c f)}",1,"Could not integrate","F",-1
148,0,0,558,0.1170582,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-4-m-n} \, dx","IntegrateAlgebraic[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-4 - m - n),x]","\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-4-m-n} \, dx","\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-1} \left(\frac{(c+d x) (b e-a f)}{(e+f x) (b c-a d)}\right)^{-n} ((m+n+2) (b d e ((m+n+3) (A (-a d f-b c f+b d e)+a B c f)-(B e-A f) (a d (n+1)+b c (m+1)))-f (a d+b c) ((m+n+3) (A (-a d f-b c f+b d e)+a B c f)-(B e-A f) (a d (n+1)+b c (m+1)))+a b c d f (B e-A f))-(a d (n+1)+b c (m+1)) (a f (A d f (m+2)+B (d e (n+1)-c f (m+n+3)))+b (A f (c f (n+2)-d e (m+n+4))+B e (c f (m+1)+d e)))) \, _2F_1\left(m+1,-n;m+2;-\frac{(d e-c f) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (m+n+2) (m+n+3) (b e-a f)^3 (d e-c f)^2}+\frac{(a+b x)^{m+1} (B e-A f) (c+d x)^{n+1} (e+f x)^{-m-n-3}}{(m+n+3) (b e-a f) (d e-c f)}+\frac{(a+b x)^{m+1} (c+d x)^{n+1} (e+f x)^{-m-n-2} (a f (A d f (m+2)+B (d e (n+1)-c f (m+n+3)))+b (A f (c f (n+2)-d e (m+n+4))+B e (c f (m+1)+d e)))}{(m+n+2) (m+n+3) (b e-a f)^2 (d e-c f)^2}",1,"Could not integrate","F",-1
149,-1,0,79,180.0145455,"\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
150,1,1107,63,5.9276807,"\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
151,-1,0,48,181.8937973,"\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
152,-1,0,48,180.0120116,"\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,"$Aborted","F",-1
153,-1,0,71,182.3805168,"\int \frac{a+b x+c x^2}{x^3 \sqrt{1-d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x^3*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","-\frac{1}{2} \left(a d^2+2 c\right) \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)-\frac{a \sqrt{1-d^2 x^2}}{2 x^2}-\frac{b \sqrt{1-d^2 x^2}}{x}",1,"$Aborted","F",-1
154,1,1895,87,20.1643082,"\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
155,1,607,52,2.1768537,"\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
156,1,864,55,15.2158408,"\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{$\#$1}^8-4 d^2 \text{$\#$1}^6+16 \text{$\#$1}^6+6 d^2 \text{$\#$1}^4+32 \text{$\#$1}^4-4 d^2 \text{$\#$1}^2+16 \text{$\#$1}^2+d^2\&,\frac{-d \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}^6+d \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}^6-4 \sqrt{d-1} \sqrt{d+1} \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}^5+4 \sqrt{d-1} \sqrt{d+1} \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}^5-5 d \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}^4+5 d \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}^4+5 d \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}^2-5 d \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}^2+4 \sqrt{d-1} \sqrt{d+1} \log \left(\sqrt{d+1}-\sqrt{d x+1}\right) \text{$\#$1}-4 \sqrt{d-1} \sqrt{d+1} \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right) \text{$\#$1}+d \log \left(\sqrt{d+1}-\sqrt{d x+1}\right)-d \log \left(-\sqrt{d+1} \text{$\#$1}+\sqrt{d x+1} \text{$\#$1}+\sqrt{d-1}-\sqrt{d x-1}\right)}{d^2 \text{$\#$1}^7-3 d^2 \text{$\#$1}^5+12 \text{$\#$1}^5+3 d^2 \text{$\#$1}^3+16 \text{$\#$1}^3-d^2 \text{$\#$1}+4 \text{$\#$1}}\&\right]","a \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{b \cosh ^{-1}(d x)}{d}+\frac{c \sqrt{d x-1} \sqrt{d x+1}}{d^2}",1,"(-(c*Sqrt[1 + d]*Sqrt[-1 + d*x]*(4 - 2*d + 2*d*x)) - c*Sqrt[-1 + d*x]*Sqrt[1 + d*x]*(-4 + d^2 - d^2*x) + Sqrt[-1 + d]*(-(c*(4 + 2*d - 2*d*x)*Sqrt[1 + d*x]) - c*Sqrt[1 + d]*(-4 - d^2*x + d^2*x^2)))/(-2*d^2*Sqrt[1 + d]*Sqrt[1 + d*x] + d^2*(3 + d^2*x) + Sqrt[-1 + d]*Sqrt[-1 + d*x]*(2*d^2 - d^2*Sqrt[1 + d]*Sqrt[1 + d*x])) - (4*b*ArcTanh[(-Sqrt[-1 + d] + Sqrt[-1 + d*x])/(Sqrt[1 + d] - Sqrt[1 + d*x])])/d - (a*RootSum[d^2 + 16*#1^2 - 4*d^2*#1^2 + 32*#1^4 + 6*d^2*#1^4 + 16*#1^6 - 4*d^2*#1^6 + d^2*#1^8 & , (d*Log[Sqrt[1 + d] - Sqrt[1 + d*x]] - d*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1] + 4*Sqrt[-1 + d]*Sqrt[1 + d]*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1 - 4*Sqrt[-1 + d]*Sqrt[1 + d]*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1 + 5*d*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1^2 - 5*d*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1^2 - 5*d*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1^4 + 5*d*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1^4 - 4*Sqrt[-1 + d]*Sqrt[1 + d]*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1^5 + 4*Sqrt[-1 + d]*Sqrt[1 + d]*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1^5 - d*Log[Sqrt[1 + d] - Sqrt[1 + d*x]]*#1^6 + d*Log[Sqrt[-1 + d] - Sqrt[-1 + d*x] - Sqrt[1 + d]*#1 + Sqrt[1 + d*x]*#1]*#1^6)/(4*#1 - d^2*#1 + 16*#1^3 + 3*d^2*#1^3 + 12*#1^5 - 3*d^2*#1^5 + d^2*#1^7) & ])/2","C",1
157,-1,0,55,180.0542049,"\int \frac{a+b x+c x^2}{x^2 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","\frac{a \sqrt{d x-1} \sqrt{d x+1}}{x}+b \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{c \cosh ^{-1}(d x)}{d}",1,"$Aborted","F",-1
158,-1,0,83,180.249037,"\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,"$Aborted","F",-1
159,-1,0,116,180.0113312,"\int \frac{a+b x+c x^2}{x^4 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","IntegrateAlgebraic[(a + b*x + c*x^2)/(x^4*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\text{\$Aborted}","\frac{\sqrt{d x-1} \sqrt{d x+1} \left(2 a d^2+3 c\right)}{3 x}+\frac{a \sqrt{d x-1} \sqrt{d x+1}}{3 x^3}+\frac{1}{2} b d^2 \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{b \sqrt{d x-1} \sqrt{d x+1}}{2 x^2}",1,"$Aborted","F",-1