1,1,112,0,0.1579488,"\int (a+b x) (c+d x) (e+f x) (g+h x) \, dx","Int[(a + b*x)*(c + d*x)*(e + f*x)*(g + h*x),x]","\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","\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,"a*c*e*g*x + ((b*c*e*g + a*(d*e*g + c*f*g + c*e*h))*x^2)/2 + ((b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h))*x^3)/3 + ((a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*x^4)/4 + (b*d*f*h*x^5)/5","A",2,1,21,0.04762,1,"{142}"
2,1,126,0,0.211189,"\int \frac{(a+b x) (c+d x) (e+f x)}{g+h x} \, dx","Int[((a + b*x)*(c + d*x)*(e + f*x))/(g + h*x),x]","\frac{x^2 (a d f h-b (-c f h-d e h+d f g))}{2 h^2}+\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{(b g-a h) (d g-c h) (f g-e h) \log (g+h x)}{h^4}+\frac{b d f x^3}{3 h}","\frac{x^2 (a d f h-b (-c f h-d e h+d f g))}{2 h^2}+\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{(b g-a h) (d g-c h) (f g-e h) \log (g+h x)}{h^4}+\frac{b d f x^3}{3 h}",1,"((b*(d*g - c*h)*(f*g - e*h) - a*h*(d*f*g - d*e*h - c*f*h))*x)/h^3 + ((a*d*f*h - b*(d*f*g - d*e*h - c*f*h))*x^2)/(2*h^2) + (b*d*f*x^3)/(3*h) - ((b*g - a*h)*(d*g - c*h)*(f*g - e*h)*Log[g + h*x])/h^4","A",2,1,23,0.04348,1,"{142}"
3,1,84,0,0.0860184,"\int \frac{(a+b x) (c+d x)}{(e+f x) (g+h x)} \, dx","Int[((a + b*x)*(c + d*x))/((e + f*x)*(g + h*x)),x]","\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}","\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*e - a*f)*(d*e - c*f)*Log[e + f*x])/(f^2*(f*g - e*h)) - ((b*g - a*h)*(d*g - c*h)*Log[g + h*x])/(h^2*(f*g - e*h))","A",2,1,25,0.04000,1,"{142}"
4,1,108,0,0.1103417,"\int \frac{a+b x}{(c+d x) (e+f x) (g+h x)} \, dx","Int[(a + b*x)/((c + d*x)*(e + f*x)*(g + h*x)),x]","-\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)}","-\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",2,1,27,0.03704,1,"{148}"
5,1,163,0,0.2119107,"\int \frac{1}{(a+b x) (c+d x) (e+f x) (g+h x)} \, dx","Int[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) (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)}","\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",2,1,29,0.03448,1,"{180}"
6,1,23,0,0.0107876,"\int \frac{x}{(1+x) (2+x) (3+x)} \, dx","Int[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,"-Log[1 + x]/2 + 2*Log[2 + x] - (3*Log[3 + x])/2","A",2,1,17,0.05882,1,"{148}"
7,1,43,0,0.0366784,"\int \frac{-x^2+x^3}{(-6+x) (3+5 x)^3} \, dx","Int[(-x^2 + x^3)/((-6 + x)*(3 + 5*x)^3),x]","\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}","\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,"-12/(1375*(3 + 5*x)^2) + 201/(15125*(3 + 5*x)) + (20*Log[6 - x])/3993 + (1493*Log[3 + 5*x])/499125","A",3,2,22,0.09091,1,"{1593, 148}"
8,1,227,0,0.2572365,"\int \frac{(a+b x)^3 \sqrt{c+d x} (e+f x)}{x} \, dx","Int[((a + b*x)^3*Sqrt[c + d*x]*(e + f*x))/x,x]","\frac{2 (c+d x)^{3/2} \left(2 \left(3 a^2 b d^2 (45 d e-16 c f)+20 a^3 d^3 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}+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 (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}","\frac{2 (c+d x)^{3/2} \left(2 \left(3 a^2 b d^2 (45 d e-16 c f)+20 a^3 d^3 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}+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 (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*a^3*e*Sqrt[c + d*x] + (2*(3*b*d*e - 2*b*c*f + 2*a*d*f)*(a + b*x)^2*(c + d*x)^(3/2))/(21*d^2) + (2*f*(a + b*x)^3*(c + d*x)^(3/2))/(9*d) + (2*(c + d*x)^(3/2)*(2*(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)) + 3*b*d*(21*a*b*d^2*e - 4*(b*c - a*d)*(3*b*d*e - 2*b*c*f + 2*a*d*f))*x))/(315*d^4) - 2*a^3*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]","A",6,5,25,0.2000,1,"{153, 147, 50, 63, 208}"
9,1,146,0,0.0981034,"\int \frac{(a+b x)^2 \sqrt{c+d x} (e+f x)}{x} \, dx","Int[((a + b*x)^2*Sqrt[c + d*x]*(e + f*x))/x,x]","\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}","\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*a^2*e*Sqrt[c + d*x] + (2*f*(a + b*x)^2*(c + d*x)^(3/2))/(7*d) + (2*(c + d*x)^(3/2)*(2*(10*a^2*d^2*f - b^2*c*(7*d*e - 4*c*f) + 7*a*b*d*(5*d*e - 2*c*f)) + 3*b*d*(7*b*d*e - 4*b*c*f + 4*a*d*f)*x))/(105*d^3) - 2*a^2*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]","A",5,5,25,0.2000,1,"{153, 147, 50, 63, 208}"
10,1,77,0,0.0244644,"\int \frac{(a+b x) \sqrt{c+d x} (e+f x)}{x} \, dx","Int[((a + b*x)*Sqrt[c + d*x]*(e + f*x))/x,x]","-\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)","-\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*a*e*Sqrt[c + d*x] - (2*(c + d*x)^(3/2)*(2*b*c*f - 5*d*(b*e + a*f) - 3*b*d*f*x))/(15*d^2) - 2*a*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]","A",4,4,23,0.1739,1,"{147, 50, 63, 208}"
11,1,54,0,0.0165239,"\int \frac{\sqrt{c+d x} (e+f x)}{x} \, dx","Int[(Sqrt[c + d*x]*(e + f*x))/x,x]","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}","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*e*Sqrt[c + d*x] + (2*f*(c + d*x)^(3/2))/(3*d) - 2*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]","A",4,4,18,0.2222,1,"{80, 50, 63, 208}"
12,1,101,0,0.1135314,"\int \frac{\sqrt{c+d x} (e+f x)}{x (a+b x)} \, dx","Int[(Sqrt[c + d*x]*(e + f*x))/(x*(a + b*x)),x]","\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}","\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[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a + (2*Sqrt[b*c - a*d]*(b*e - a*f)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(a*b^(3/2))","A",6,4,25,0.1600,1,"{154, 156, 63, 208}"
13,1,127,0,0.1093066,"\int \frac{\sqrt{c+d x} (e+f x)}{x (a+b x)^2} \, dx","Int[(Sqrt[c + d*x]*(e + f*x))/(x*(a + b*x)^2),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)}","\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*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a^2 + ((2*b^2*c*e - a*d*(b*e + a*f))*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(a^2*b^(3/2)*Sqrt[b*c - a*d])","A",6,4,25,0.1600,1,"{149, 156, 63, 208}"
14,1,208,0,0.2737706,"\int \frac{\sqrt{c+d x} (e+f x)}{x (a+b x)^3} \, dx","Int[(Sqrt[c + d*x]*(e + f*x))/(x*(a + b*x)^3),x]","\frac{\left(3 a^2 b d^2 e+a^3 d^2 f-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} \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{2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3}+\frac{\sqrt{c+d x} (b e-a f)}{2 a b (a+b x)^2}","\frac{\left(3 a^2 b d^2 e+a^3 d^2 f-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} \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{2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^3}+\frac{\sqrt{c+d x} (b e-a f)}{2 a b (a+b x)^2}",1,"((b*e - a*f)*Sqrt[c + d*x])/(2*a*b*(a + b*x)^2) + ((4*b^2*c*e - 3*a*b*d*e - a^2*d*f)*Sqrt[c + d*x])/(4*a^2*b*(b*c - a*d)*(a + b*x)) - (2*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/a^3 + ((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)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(4*a^3*b^(3/2)*(b*c - a*d)^(3/2))","A",7,5,25,0.2000,1,"{149, 151, 156, 63, 208}"
15,1,226,0,0.2517776,"\int \frac{\sqrt{a+b x} (c+d x)^3 (e+f x)}{x} \, dx","Int[(Sqrt[a + b*x]*(c + d*x)^3*(e + f*x))/x,x]","-\frac{2 (a+b x)^{3/2} \left(2 \left(-12 a^2 b d^2 (3 c f+d e)+8 a^3 d^3 f+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}","-\frac{2 (a+b x)^{3/2} \left(2 \left(-12 a^2 b d^2 (3 c f+d e)+8 a^3 d^3 f+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*c^3*e*Sqrt[a + b*x] + (2*(3*b*d*e + 2*b*c*f - 2*a*d*f)*(a + b*x)^(3/2)*(c + d*x)^2)/(21*b^2) + (2*f*(a + b*x)^(3/2)*(c + d*x)^3)/(9*b) - (2*(a + b*x)^(3/2)*(2*(8*a^3*d^3*f - 12*a^2*b*d^2*(d*e + 3*c*f) - 5*b^3*c^2*(27*d*e + 4*c*f) + 3*a*b^2*c*d*(21*d*e + 16*c*f)) - 3*b*d*(21*b^2*c*d*e + 4*(b*c - a*d)*(3*b*d*e + 2*b*c*f - 2*a*d*f))*x))/(315*b^4) - 2*Sqrt[a]*c^3*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",6,5,25,0.2000,1,"{153, 147, 50, 63, 208}"
16,1,145,0,0.0938083,"\int \frac{\sqrt{a+b x} (c+d x)^2 (e+f x)}{x} \, dx","Int[(Sqrt[a + b*x]*(c + d*x)^2*(e + f*x))/x,x]","\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}","\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*c^2*e*Sqrt[a + b*x] + (2*f*(a + b*x)^(3/2)*(c + d*x)^2)/(7*b) + (2*(a + b*x)^(3/2)*(2*(4*a^2*d^2*f - 7*a*b*d*(d*e + 2*c*f) + 5*b^2*c*(7*d*e + 2*c*f)) + 3*b*d*(7*b*d*e + 4*b*c*f - 4*a*d*f)*x))/(105*b^3) - 2*Sqrt[a]*c^2*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",5,5,25,0.2000,1,"{153, 147, 50, 63, 208}"
17,1,77,0,0.0235912,"\int \frac{\sqrt{a+b x} (c+d x) (e+f x)}{x} \, dx","Int[(Sqrt[a + b*x]*(c + d*x)*(e + f*x))/x,x]","-\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)","-\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*c*e*Sqrt[a + b*x] - (2*(a + b*x)^(3/2)*(2*a*d*f - 5*b*(d*e + c*f) - 3*b*d*f*x))/(15*b^2) - 2*Sqrt[a]*c*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",4,4,23,0.1739,1,"{147, 50, 63, 208}"
18,1,54,0,0.0158209,"\int \frac{\sqrt{a+b x} (e+f x)}{x} \, dx","Int[(Sqrt[a + b*x]*(e + f*x))/x,x]","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}","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*e*Sqrt[a + b*x] + (2*f*(a + b*x)^(3/2))/(3*b) - 2*Sqrt[a]*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",4,4,18,0.2222,1,"{80, 50, 63, 208}"
19,1,101,0,0.1189696,"\int \frac{\sqrt{a+b x} (e+f x)}{x (c+d x)} \, dx","Int[(Sqrt[a + b*x]*(e + f*x))/(x*(c + d*x)),x]","\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}","\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",6,5,25,0.2000,1,"{154, 156, 63, 208, 205}"
20,1,128,0,0.1159982,"\int \frac{\sqrt{a+b x} (e+f x)}{x (c+d x)^2} \, dx","Int[(Sqrt[a + b*x]*(e + f*x))/(x*(c + d*x)^2),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)}","-\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)) - ((2*a*d^2*e - b*c*(d*e + c*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",6,5,25,0.2000,1,"{149, 156, 63, 208, 205}"
21,1,205,0,0.2794626,"\int \frac{\sqrt{a+b x} (e+f x)}{x (c+d x)^3} \, dx","Int[(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^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{\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{2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c^3}+\frac{\sqrt{a+b x} (d e-c f)}{2 c d (c+d x)^2}","-\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{\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{2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c^3}+\frac{\sqrt{a+b x} (d e-c f)}{2 c d (c+d x)^2}",1,"((d*e - c*f)*Sqrt[a + b*x])/(2*c*d*(c + d*x)^2) - ((4*a*d^2*e - b*c*(3*d*e + c*f))*Sqrt[a + b*x])/(4*c^2*d*(b*c - a*d)*(c + d*x)) - ((12*a*b*c*d^2*e - 8*a^2*d^3*e - b^2*c^2*(3*d*e + c*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",7,6,25,0.2400,1,"{149, 151, 156, 63, 208, 205}"
22,1,111,0,0.0448675,"\int \frac{x^3 (1+a x)}{\sqrt{a x} \sqrt{1-a x}} \, dx","Int[(x^3*(1 + a*x))/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\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}","-\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,"(-75*Sqrt[a*x]*Sqrt[1 - a*x])/(64*a^4) - (25*(a*x)^(3/2)*Sqrt[1 - a*x])/(32*a^4) - (5*(a*x)^(5/2)*Sqrt[1 - a*x])/(8*a^4) - ((a*x)^(7/2)*Sqrt[1 - a*x])/(4*a^4) - (75*ArcSin[1 - 2*a*x])/(128*a^4)","A",8,6,26,0.2308,1,"{16, 80, 50, 53, 619, 216}"
23,1,87,0,0.0335764,"\int \frac{x^2 (1+a x)}{\sqrt{a x} \sqrt{1-a x}} \, dx","Int[(x^2*(1 + a*x))/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\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}","-\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,"(-11*Sqrt[a*x]*Sqrt[1 - a*x])/(8*a^3) - (11*(a*x)^(3/2)*Sqrt[1 - a*x])/(12*a^3) - ((a*x)^(5/2)*Sqrt[1 - a*x])/(3*a^3) - (11*ArcSin[1 - 2*a*x])/(16*a^3)","A",7,6,26,0.2308,1,"{16, 80, 50, 53, 619, 216}"
24,1,63,0,0.0232313,"\int \frac{x (1+a x)}{\sqrt{a x} \sqrt{1-a x}} \, dx","Int[(x*(1 + a*x))/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\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}","-\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,"(-7*Sqrt[a*x]*Sqrt[1 - a*x])/(4*a^2) - ((a*x)^(3/2)*Sqrt[1 - a*x])/(2*a^2) - (7*ArcSin[1 - 2*a*x])/(8*a^2)","A",6,6,24,0.2500,1,"{16, 80, 50, 53, 619, 216}"
25,1,37,0,0.0125165,"\int \frac{1+a x}{\sqrt{a x} \sqrt{1-a x}} \, dx","Int[(1 + a*x)/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\frac{\sqrt{a x} \sqrt{1-a x}}{a}-\frac{3 \sin ^{-1}(1-2 a x)}{2 a}","-\frac{\sqrt{a x} \sqrt{1-a x}}{a}-\frac{3 \sin ^{-1}(1-2 a x)}{2 a}",1,"-((Sqrt[a*x]*Sqrt[1 - a*x])/a) - (3*ArcSin[1 - 2*a*x])/(2*a)","A",4,4,23,0.1739,1,"{80, 53, 619, 216}"
26,1,29,0,0.0160123,"\int \frac{1+a x}{x \sqrt{a x} \sqrt{1-a x}} \, dx","Int[(1 + a*x)/(x*Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\frac{2 \sqrt{1-a x}}{\sqrt{a x}}-\sin ^{-1}(1-2 a x)","-\frac{2 \sqrt{1-a x}}{\sqrt{a x}}-\sin ^{-1}(1-2 a x)",1,"(-2*Sqrt[1 - a*x])/Sqrt[a*x] - ArcSin[1 - 2*a*x]","A",5,5,26,0.1923,1,"{16, 78, 53, 619, 216}"
27,1,45,0,0.0098901,"\int \frac{1+a x}{x^2 \sqrt{a x} \sqrt{1-a x}} \, dx","Int[(1 + a*x)/(x^2*Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\frac{10 a \sqrt{1-a x}}{3 \sqrt{a x}}-\frac{2 a \sqrt{1-a x}}{3 (a x)^{3/2}}","-\frac{10 a \sqrt{1-a x}}{3 \sqrt{a x}}-\frac{2 a \sqrt{1-a x}}{3 (a x)^{3/2}}",1,"(-2*a*Sqrt[1 - a*x])/(3*(a*x)^(3/2)) - (10*a*Sqrt[1 - a*x])/(3*Sqrt[a*x])","A",3,3,26,0.1154,1,"{16, 78, 37}"
28,1,73,0,0.0190258,"\int \frac{1+a x}{x^3 \sqrt{a x} \sqrt{1-a x}} \, dx","Int[(1 + a*x)/(x^3*Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\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}}","-\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,"(-2*a^2*Sqrt[1 - a*x])/(5*(a*x)^(5/2)) - (6*a^2*Sqrt[1 - a*x])/(5*(a*x)^(3/2)) - (12*a^2*Sqrt[1 - a*x])/(5*Sqrt[a*x])","A",4,4,26,0.1538,1,"{16, 78, 45, 37}"
29,1,97,0,0.0266511,"\int \frac{1+a x}{x^4 \sqrt{a x} \sqrt{1-a x}} \, dx","Int[(1 + a*x)/(x^4*Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\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}}","-\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,"(-2*a^3*Sqrt[1 - a*x])/(7*(a*x)^(7/2)) - (26*a^3*Sqrt[1 - a*x])/(35*(a*x)^(5/2)) - (104*a^3*Sqrt[1 - a*x])/(105*(a*x)^(3/2)) - (208*a^3*Sqrt[1 - a*x])/(105*Sqrt[a*x])","A",5,4,26,0.1538,1,"{16, 78, 45, 37}"
30,1,121,0,0.0384211,"\int \frac{1+a x}{x^5 \sqrt{a x} \sqrt{1-a x}} \, dx","Int[(1 + a*x)/(x^5*Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\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}}","-\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,"(-2*a^4*Sqrt[1 - a*x])/(9*(a*x)^(9/2)) - (34*a^4*Sqrt[1 - a*x])/(63*(a*x)^(7/2)) - (68*a^4*Sqrt[1 - a*x])/(105*(a*x)^(5/2)) - (272*a^4*Sqrt[1 - a*x])/(315*(a*x)^(3/2)) - (544*a^4*Sqrt[1 - a*x])/(315*Sqrt[a*x])","A",6,4,26,0.1538,1,"{16, 78, 45, 37}"
31,1,39,0,0.0074949,"\int \frac{-1+2 a x}{\sqrt{-1+x} x^2 \sqrt{1+x}} \, dx","Int[(-1 + 2*a*x)/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]","2 a \tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}","2 a \tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"-((Sqrt[-1 + x]*Sqrt[1 + x])/x) + 2*a*ArcTan[Sqrt[-1 + x]*Sqrt[1 + x]]","A",4,4,24,0.1667,1,"{151, 12, 92, 203}"
32,1,39,0,0.0114988,"\int \frac{a^2 x^2-(1-a x)^2}{\sqrt{-1+x} x^2 \sqrt{1+x}} \, dx","Int[(a^2*x^2 - (1 - a*x)^2)/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]","2 a \tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}","2 a \tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"-((Sqrt[-1 + x]*Sqrt[1 + x])/x) + 2*a*ArcTan[Sqrt[-1 + x]*Sqrt[1 + x]]","A",5,5,36,0.1389,1,"{188, 151, 12, 92, 203}"
33,1,145,0,0.1080708,"\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","Int[(A + B*x)/(Sqrt[a + b*x]*Sqrt[c + (b*(-1 + c)*x)/a]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","\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)}","\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,"(-2*a^(3/2)*B*EllipticE[ArcSin[(Sqrt[1 - c]*Sqrt[a + b*x])/Sqrt[a]], (1 - e)/(1 - c)])/(b^2*Sqrt[1 - c]*(1 - e)) + (2*Sqrt[a]*(a*B*e + A*(b - b*e))*EllipticF[ArcSin[(Sqrt[1 - c]*Sqrt[a + b*x])/Sqrt[a]], (1 - e)/(1 - c)])/(b^2*Sqrt[1 - c]*(1 - e))","A",3,3,45,0.06667,1,"{158, 113, 119}"
34,1,221,0,0.1994311,"\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","Int[(A + B*x)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","\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}}","\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,"(-2*a*B*Sqrt[-(b*c) + a*d]*Sqrt[(b*(c + d*x))/(b*c - a*d)]*EllipticE[ArcSin[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[-(b*c) + a*d]], -(((b*c - a*d)*(1 - e))/(a*d))])/(b^2*Sqrt[d]*(1 - e)*Sqrt[c + d*x]) + (2*Sqrt[a]*(a*B*e + A*(b - b*e))*Sqrt[(b*(c + d*x))/(b*c - a*d)]*EllipticF[ArcSin[(Sqrt[1 - e]*Sqrt[a + b*x])/Sqrt[a]], -((a*d)/((b*c - a*d)*(1 - e)))])/(b^2*(1 - e)^(3/2)*Sqrt[c + d*x])","A",5,5,39,0.1282,1,"{158, 114, 113, 121, 119}"
35,1,281,0,0.3894251,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3 \, dx","Int[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3,x]","\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}}","\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,"(-1182926269*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/1603800 - (12243139*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x))/356400 - (17561*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2)/8910 - (427*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3)/2970 + (2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^4)/55 - (6489123157*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(699840*Sqrt[5 - 2*x]) + (522167393*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(23328*Sqrt[-5 + 2*x])","A",10,8,35,0.2286,1,"{161, 1600, 1615, 158, 114, 113, 121, 119}"
36,1,243,0,0.2998774,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2 \, dx","Int[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2,x]","\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}}","\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,"(-5256763*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/97200 - (8141*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x))/2700 - (61*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2)/270 + (2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3)/45 - (17746949*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(29160*Sqrt[5 - 2*x]) + (5592499*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(3888*Sqrt[-5 + 2*x])","A",9,8,35,0.2286,1,"{161, 1600, 1615, 158, 114, 113, 121, 119}"
37,1,193,0,0.0774144,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x) \, dx","Int[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x),x]","\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}}","\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,"(-20911*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/3780 + (136*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*(1 + 4*x)^(3/2))/105 + (5*Sqrt[2 - 3*x]*(-5 + 2*x)^(3/2)*(1 + 4*x)^(3/2))/28 - (954811*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(22680*Sqrt[5 - 2*x]) + (72479*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(756*Sqrt[-5 + 2*x])","A",8,6,33,0.1818,1,"{154, 158, 114, 113, 121, 119}"
38,1,162,0,0.0627527,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \, dx","Int[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x],x]","\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}}","\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,"(-22*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/45 + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*(1 + 4*x)^(3/2))/10 - (847*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(270*Sqrt[5 - 2*x]) + (121*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(18*Sqrt[-5 + 2*x])","A",7,7,28,0.2500,1,"{101, 154, 158, 114, 113, 121, 119}"
39,1,182,0,0.2125192,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{7+5 x} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x),x]","\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}}","\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,"(2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/15 - (427*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(225*Sqrt[5 - 2*x]) - (1253*Sqrt[2/33]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(375*Sqrt[-5 + 2*x]) - (2691*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(125*Sqrt[11]*Sqrt[-5 + 2*x])","A",10,10,35,0.2857,1,"{161, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
40,1,189,0,0.21081,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^2} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^2,x]","-\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}}","-\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,"-(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(5*(7 + 5*x)) + (6*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(25*Sqrt[5 - 2*x]) + (152*Sqrt[2/33]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(125*Sqrt[-5 + 2*x]) + (26859*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(7750*Sqrt[11]*Sqrt[-5 + 2*x])","A",10,10,35,0.2857,1,"{160, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
41,1,227,0,0.3085334,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^3} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^3,x]","\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}}","\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,"-(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(10*(7 + 5*x)^2) + (8953*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(556140*(7 + 5*x)) - (8953*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(1390350*Sqrt[5 - 2*x]) + (397*Sqrt[3/22]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(89125*Sqrt[-5 + 2*x]) - (14832503*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(287339000*Sqrt[11]*Sqrt[-5 + 2*x])","A",11,11,35,0.3143,1,"{160, 1604, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
42,1,263,0,0.3970134,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^4} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^4,x]","\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}}","\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,"-(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(15*(7 + 5*x)^3) + (8953*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(1668420*(7 + 5*x)^2) + (16830401*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(30929169960*(7 + 5*x)) - (16830401*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(77322924900*Sqrt[5 - 2*x]) + (24957247*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(4956597750*Sqrt[66]*Sqrt[-5 + 2*x]) + (15664616449*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(15980071146000*Sqrt[11]*Sqrt[-5 + 2*x])","A",12,11,35,0.3143,1,"{160, 1604, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
43,1,570,0,1.2858375,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{a+b x} \, dx","Int[(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(a + b*x),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}} \left(3 a^2 d f h^2-3 a b h^2 (c f+d e)+b^2 (-(d g (f g-e h)-c h (2 e h+f g)))\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 \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 (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{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 b}","\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)+b^2 (-(d g (f g-e h)-c h (2 e h+f g)))\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 \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 (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{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 b}",1,"(2*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*b) - (2*Sqrt[-(d*e) + c*f]*(3*a*d*f*h - b*(d*f*g + d*e*h + c*f*h))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*b^2*d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) + (2*Sqrt[-(d*e) + c*f]*(3*a^2*d*f*h^2 - 3*a*b*(d*e + c*f)*h^2 - b^2*(d*g*(f*g - e*h) - c*h*(f*g + 2*e*h)))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*b^3*d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[g + h*x]) - (2*(b*e - a*f)*Sqrt[-(d*e) + c*f]*(b*g - a*h)*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b^3*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x])","A",12,10,35,0.2857,1,"{161, 1607, 169, 538, 537, 158, 114, 113, 121, 120}"
44,1,243,0,0.2965468,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^3}{\sqrt{-5+2 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3)/Sqrt[-5 + 2*x],x]","\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}}","\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,"(46134551*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/38880 + (26291*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x))/540 + (1679*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2)/756 + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3)/9 + (2629157597*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(163296*Sqrt[5 - 2*x]) - (2161804579*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(54432*Sqrt[-5 + 2*x])","A",9,8,35,0.2286,1,"{162, 1600, 1615, 158, 114, 113, 121, 119}"
45,1,205,0,0.2130088,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^2}{\sqrt{-5+2 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2)/Sqrt[-5 + 2*x],x]","\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}}","\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,"(73207*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/1080 + (173*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x))/60 + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2)/7 + (8198333*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(9072*Sqrt[5 - 2*x]) - (1679161*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(756*Sqrt[-5 + 2*x])","A",8,8,35,0.2286,1,"{162, 1600, 1615, 158, 114, 113, 121, 119}"
46,1,162,0,0.0624533,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)}{\sqrt{-5+2 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x))/Sqrt[-5 + 2*x],x]","\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}}","\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,"(95*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/18 + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*(1 + 4*x)^(3/2))/4 + (1397*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(27*Sqrt[5 - 2*x]) - (4543*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(36*Sqrt[-5 + 2*x])","A",7,6,33,0.1818,1,"{154, 158, 114, 113, 121, 119}"
47,1,131,0,0.0513602,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x],x]","\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}}","\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,"(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/3 + (55*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(18*Sqrt[5 - 2*x]) - (11*Sqrt[22/3]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(3*Sqrt[-5 + 2*x])","A",6,6,28,0.2143,1,"{101, 158, 114, 113, 121, 119}"
48,1,151,0,0.1210938,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)),x]","-\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}}","-\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,"(2*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(5*Sqrt[5 - 2*x]) - (41*Sqrt[2/33]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(25*Sqrt[-5 + 2*x]) + (69*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(25*Sqrt[11]*Sqrt[-5 + 2*x])","A",9,9,35,0.2571,1,"{163, 168, 538, 537, 158, 114, 113, 121, 119}"
49,1,189,0,0.2142341,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^2} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^2),x]","\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}}","\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,"(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(39*(7 + 5*x)) - (2*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(195*Sqrt[5 - 2*x]) - (2*Sqrt[6/11]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(25*Sqrt[-5 + 2*x]) - (6101*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(20150*Sqrt[11]*Sqrt[-5 + 2*x])","A",10,10,35,0.2857,1,"{164, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
50,1,225,0,0.3008106,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^3} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^3),x]","-\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}}","-\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,"(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(78*(7 + 5*x)^2) - (361*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(481988*(7 + 5*x)) + (361*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(1204970*Sqrt[5 - 2*x]) - (6101*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(231725*Sqrt[66]*Sqrt[-5 + 2*x]) - (6655867*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(747081400*Sqrt[11]*Sqrt[-5 + 2*x])","A",11,11,35,0.3143,1,"{164, 1604, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
51,1,205,0,0.2123805,"\int \frac{\sqrt{2-3 x} (7+5 x)^3}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(Sqrt[2 - 3*x]*(7 + 5*x)^3)/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(110743*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/864 + (121*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x))/24 + (5*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2)/28 + (15629623*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(9072*Sqrt[5 - 2*x]) - (25260049*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(6048*Sqrt[-5 + 2*x])","A",8,8,35,0.2286,1,"{174, 1600, 1615, 158, 114, 113, 121, 119}"
52,1,167,0,0.1454216,"\int \frac{\sqrt{2-3 x} (7+5 x)^2}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(Sqrt[2 - 3*x]*(7 + 5*x)^2)/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(68*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/9 + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x))/4 + (44569*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(432*Sqrt[5 - 2*x]) - (17533*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(72*Sqrt[-5 + 2*x])","A",7,7,35,0.2000,1,"{174, 1615, 158, 114, 113, 121, 119}"
53,1,131,0,0.0510921,"\int \frac{\sqrt{2-3 x} (7+5 x)}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(Sqrt[2 - 3*x]*(7 + 5*x))/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(5*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/12 + (241*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(36*Sqrt[5 - 2*x]) - (179*Sqrt[11/6]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(12*Sqrt[-5 + 2*x])","A",6,6,33,0.1818,1,"{154, 158, 114, 113, 121, 119}"
54,1,47,0,0.0148583,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(Sqrt[11/2]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[1 + 4*x]/Sqrt[11]], 3])/(2*Sqrt[-5 + 2*x])","A",2,2,28,0.07143,1,"{114, 113}"
55,1,103,0,0.0957722,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)} \, dx","Int[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)),x]","-\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}}","-\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,"-(Sqrt[6/11]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(5*Sqrt[-5 + 2*x]) - (3*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(5*Sqrt[11]*Sqrt[-5 + 2*x])","A",6,6,35,0.1714,1,"{175, 121, 119, 168, 538, 537}"
56,1,189,0,0.2096794,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2} \, dx","Int[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2),x]","-\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}}","-\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,"(-5*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(897*(7 + 5*x)) + (2*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(897*Sqrt[5 - 2*x]) - (2*Sqrt[6/11]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(115*Sqrt[-5 + 2*x]) - (3571*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(92690*Sqrt[11]*Sqrt[-5 + 2*x])","A",10,10,35,0.2857,1,"{177, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
57,1,225,0,0.3104024,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3} \, dx","Int[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3),x]","-\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}}","-\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,"(-5*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(1794*(7 + 5*x)^2) - (26825*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(33257172*(7 + 5*x)) + (5365*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(16628586*Sqrt[5 - 2*x]) - (13243*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(1065935*Sqrt[66]*Sqrt[-5 + 2*x]) - (16369941*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(3436574440*Sqrt[11]*Sqrt[-5 + 2*x])","A",11,11,35,0.3143,1,"{177, 1604, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
58,1,293,0,0.5044314,"\int \frac{\sqrt{c+d x}}{(a+b x) \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[Sqrt[c + d*x]/((a + b*x)*Sqrt[e + f*x]*Sqrt[g + h*x]),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}} 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}}","\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,"(2*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x]) - (2*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x])","A",8,6,35,0.1714,1,"{175, 121, 120, 169, 538, 537}"
59,1,449,0,0.6719681,"\int \frac{(c+d x)^{3/2}}{(a+b x) \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(c + d*x)^(3/2)/((a + b*x)*Sqrt[e + f*x]*Sqrt[g + h*x]),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}} 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}}}","\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,"(2*d*Sqrt[-(f*g) + e*h]*Sqrt[c + d*x]*Sqrt[(f*(g + h*x))/(f*g - e*h)]*EllipticE[ArcSin[(Sqrt[h]*Sqrt[e + f*x])/Sqrt[-(f*g) + e*h]], -((d*(f*g - e*h))/((d*e - c*f)*h))])/(b*f*Sqrt[h]*Sqrt[-((f*(c + d*x))/(d*e - c*f))]*Sqrt[g + h*x]) + (2*(b*c - a*d)*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b^2*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x]) - (2*(b*c - a*d)*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b^2*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x])","A",11,8,35,0.2286,1,"{179, 121, 120, 169, 538, 537, 114, 113}"
60,1,203,0,0.2158176,"\int \frac{(7+5 x)^4}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(7 + 5*x)^4/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\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}}","-\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,"(-120355*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/288 - (305*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x))/24 - (25*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2)/84 - (5109835*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(756*Sqrt[5 - 2*x]) + (392989907*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(2016*Sqrt[66]*Sqrt[-5 + 2*x])","A",8,8,35,0.2286,1,"{167, 1600, 1615, 158, 114, 113, 121, 119}"
61,1,165,0,0.1525295,"\int \frac{(7+5 x)^3}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(7 + 5*x)^3/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\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}}","-\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,"(-2135*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/108 - (5*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x))/12 - (487585*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(1296*Sqrt[5 - 2*x]) + (2474201*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(216*Sqrt[66]*Sqrt[-5 + 2*x])","A",7,7,35,0.2000,1,"{167, 1615, 158, 114, 113, 121, 119}"
62,1,129,0,0.0627385,"\int \frac{(7+5 x)^2}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(7 + 5*x)^2/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\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}}","-\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,"(-25*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/36 - (2135*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(108*Sqrt[5 - 2*x]) + (24353*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(36*Sqrt[66]*Sqrt[-5 + 2*x])","A",7,7,35,0.2000,1,"{167, 24, 158, 114, 113, 121, 119}"
63,1,98,0,0.0368844,"\int \frac{7+5 x}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(7 + 5*x)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(-5*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(6*Sqrt[5 - 2*x]) + (13*Sqrt[3/22]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/Sqrt[-5 + 2*x]","A",5,5,33,0.1515,1,"{158, 114, 113, 121, 119}"
64,1,48,0,0.0139663,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(Sqrt[2/33]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/Sqrt[-5 + 2*x]","A",2,2,28,0.07143,1,"{121, 119}"
65,1,51,0,0.0700453,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)} \, dx","Int[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)),x]","-\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}}","-\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,"(-3*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(31*Sqrt[11]*Sqrt[-5 + 2*x])","A",3,3,35,0.08571,1,"{168, 538, 537}"
66,1,189,0,0.220147,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2} \, dx","Int[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2),x]","-\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}}","-\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,"(-25*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(27807*(7 + 5*x)) + (10*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(27807*Sqrt[5 - 2*x]) - (2*Sqrt[6/11]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(713*Sqrt[-5 + 2*x]) - (8953*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(574678*Sqrt[11]*Sqrt[-5 + 2*x])","A",10,10,35,0.2857,1,"{172, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
67,1,225,0,0.3097061,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3} \, dx","Int[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3),x]","-\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}}","-\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,"(-25*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(55614*(7 + 5*x)^2) - (223825*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(1030972332*(7 + 5*x)) + (44765*Sqrt[11]*Sqrt[-5 + 2*x]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(515486166*Sqrt[5 - 2*x]) - (24007*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(6608797*Sqrt[66]*Sqrt[-5 + 2*x]) - (48493305*Sqrt[5 - 2*x]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2])/(21306761528*Sqrt[11]*Sqrt[-5 + 2*x])","A",11,11,35,0.3143,1,"{172, 1604, 1607, 168, 538, 537, 158, 114, 113, 121, 119}"
68,1,137,0,0.0612999,"\int \frac{c i+d i x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(c*i + d*i*x)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\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}}}","\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,"(2*Sqrt[-(f*g) + e*h]*i*Sqrt[c + d*x]*Sqrt[(f*(g + h*x))/(f*g - e*h)]*EllipticE[ArcSin[(Sqrt[h]*Sqrt[e + f*x])/Sqrt[-(f*g) + e*h]], -((d*(f*g - e*h))/((d*e - c*f)*h))])/(f*Sqrt[h]*Sqrt[-((f*(c + d*x))/(d*e - c*f))]*Sqrt[g + h*x])","A",3,3,36,0.08333,1,"{21, 114, 113}"
69,1,284,0,0.1689158,"\int \frac{a+b x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a + b*x)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\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}}","\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,"(2*b*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - (2*Sqrt[-(d*e) + c*f]*(b*g - a*h)*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[g + h*x])","A",6,5,33,0.1515,1,"{158, 114, 113, 121, 120}"
70,1,165,0,0.3739403,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),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)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)}","-\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,"(-2*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x])","A",4,3,35,0.08571,1,"{169, 538, 537}"
71,1,393,0,0.6236359,"\int \frac{1}{(a+b x) (c+d x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[1/((a + b*x)*(c + d*x)^(3/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\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}","\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,"(2*d^2*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(d*e - c*f)*(d*g - c*h)*Sqrt[c + d*x]) - (2*d*Sqrt[h]*Sqrt[-(f*g) + e*h]*Sqrt[c + d*x]*Sqrt[(f*(g + h*x))/(f*g - e*h)]*EllipticE[ArcSin[(Sqrt[h]*Sqrt[e + f*x])/Sqrt[-(f*g) + e*h]], -((d*(f*g - e*h))/((d*e - c*f)*h))])/((b*c - a*d)*(d*e - c*f)*(d*g - c*h)*Sqrt[-((f*(c + d*x))/(d*e - c*f))]*Sqrt[g + h*x]) - (2*b*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)^2*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x])","A",10,8,35,0.2286,1,"{179, 104, 21, 114, 113, 169, 538, 537}"
72,1,875,0,1.3391909,"\int \frac{1}{(a+b x) (c+d x)^{5/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[1/((a + b*x)*(c + d*x)^(5/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),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^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}}","-\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,"(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)) + (2*b*d^2*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)^2*(d*e - c*f)*(d*g - c*h)*Sqrt[c + d*x]) - (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]) + (4*d*Sqrt[f]*(d*f*g + d*e*h - 2*c*f*h)*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*(b*c - a*d)*(-(d*e) + c*f)^(3/2)*(d*g - c*h)^2*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - (2*b*d*Sqrt[h]*Sqrt[-(f*g) + e*h]*Sqrt[c + d*x]*Sqrt[(f*(g + h*x))/(f*g - e*h)]*EllipticE[ArcSin[(Sqrt[h]*Sqrt[e + f*x])/Sqrt[-(f*g) + e*h]], -((d*(f*g - e*h))/((d*e - c*f)*h))])/((b*c - a*d)^2*(d*e - c*f)*(d*g - c*h)*Sqrt[-((f*(c + d*x))/(d*e - c*f))]*Sqrt[g + h*x]) - (2*Sqrt[f]*(2*d*f*g + d*e*h - 3*c*f*h)*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*(b*c - a*d)*(-(d*e) + c*f)^(3/2)*(d*g - c*h)*Sqrt[e + f*x]*Sqrt[g + h*x]) - (2*b^2*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)^3*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x])","A",18,12,35,0.3429,1,"{179, 104, 152, 158, 114, 113, 121, 120, 21, 169, 538, 537}"
73,1,74,0,0.159653,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f x} \sqrt{1+f x}} \, dx","Int[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f*x]*Sqrt[1 + f*x]),x]","-\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}}","-\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,"(-2*Sqrt[(f*(c + d*x))/(d + c*f)]*EllipticPi[(2*b)/(b + a*f), ArcSin[Sqrt[1 - f*x]/Sqrt[2]], (2*d)/(d + c*f)])/((b + a*f)*Sqrt[c + d*x])","A",3,3,36,0.08333,1,"{168, 538, 537}"
74,1,74,0,0.1758837,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^2 x^2}} \, dx","Int[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f^2*x^2]),x]","-\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}}","-\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,"(-2*Sqrt[(f*(c + d*x))/(d + c*f)]*EllipticPi[(2*b)/(b + a*f), ArcSin[Sqrt[1 - f*x]/Sqrt[2]], (2*d)/(d + c*f)])/((b + a*f)*Sqrt[c + d*x])","A",4,4,31,0.1290,1,"{932, 168, 538, 537}"
75,1,86,0,0.160048,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^2 x} \sqrt{1+f^2 x}} \, dx","Int[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f^2*x]*Sqrt[1 + f^2*x]),x]","-\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}}","-\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,"(-2*Sqrt[(f^2*(c + d*x))/(d + c*f^2)]*EllipticPi[(2*b)/(b + a*f^2), ArcSin[Sqrt[1 - f^2*x]/Sqrt[2]], (2*d)/(d + c*f^2)])/((b + a*f^2)*Sqrt[c + d*x])","A",3,3,40,0.07500,1,"{168, 538, 537}"
76,1,86,0,0.1748574,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^4 x^2}} \, dx","Int[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f^4*x^2]),x]","-\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}}","-\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,"(-2*Sqrt[(f^2*(c + d*x))/(d + c*f^2)]*EllipticPi[(2*b)/(b + a*f^2), ArcSin[Sqrt[1 - f^2*x]/Sqrt[2]], (2*d)/(d + c*f^2)])/((b + a*f^2)*Sqrt[c + d*x])","A",4,4,31,0.1290,1,"{932, 168, 538, 537}"
77,1,471,0,0.6650887,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2} \, dx","Int[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2),x]","\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}}","\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,"(-1450582567*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(3686400*Sqrt[-5 + 2*x]) - (70489981*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/1658880 - (83363*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2))/34560 - (427*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2))/2400 + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(7/2))/25 + (1450582567*Sqrt[143/3]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(2457600*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) - (245264762213*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(99532800*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) - (57691792727443*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(497664000*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",12,10,37,0.2703,1,"{161, 1600, 1602, 1598, 170, 418, 165, 537, 176, 424}"
78,1,429,0,0.5418035,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2} \, dx","Int[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2),x]","\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}}","\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,"(-1471781*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(51200*Sqrt[-5 + 2*x]) - (267029*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/69120 - (427*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2))/1440 + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2))/20 + (1471781*Sqrt[429]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(102400*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) - (982275517*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(4147200*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) - (145131624827*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(20736000*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",11,10,37,0.2703,1,"{161, 1600, 1602, 1598, 170, 418, 165, 537, 176, 424}"
79,1,391,0,0.4286242,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x} \, dx","Int[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x],x]","-\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}}","-\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,"(-13027*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(4800*Sqrt[-5 + 2*x]) + (23*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/240 - ((2 - 3*x)^(3/2)*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/9 + (13027*Sqrt[143/3]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(3200*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) - (1368371*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(43200*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) - (65750101*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(216000*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",10,10,37,0.2703,1,"{161, 1600, 1602, 1598, 170, 418, 165, 537, 176, 424}"
80,1,351,0,0.3238783,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{\sqrt{7+5 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/Sqrt[7 + 5*x],x]","\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}}","\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,"(-427*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(600*Sqrt[-5 + 2*x]) + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/10 + (427*Sqrt[143/3]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(400*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) - (20057*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(1800*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) + (1008833*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(9000*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",9,9,37,0.2432,1,"{161, 1602, 1598, 170, 418, 165, 537, 176, 424}"
81,1,349,0,0.318856,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{3/2}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(3/2),x]","\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}}","\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,"(-2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(5*Sqrt[7 + 5*x]) + (6*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(25*Sqrt[-5 + 2*x]) - (3*Sqrt[429]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(25*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (296*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(75*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) - (26474*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(375*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",9,9,37,0.2432,1,"{160, 1602, 1598, 170, 418, 165, 537, 176, 424}"
82,1,391,0,0.4293855,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{5/2}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(5/2),x]","-\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}}","-\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,"(-2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(15*(7 + 5*x)^(3/2)) + (17906*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(417105*Sqrt[7 + 5*x]) - (35812*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(2085525*Sqrt[-5 + 2*x]) + (17906*Sqrt[11/39]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(53475*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) - (496*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(1725*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) + (496*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(125*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",10,10,37,0.2703,1,"{160, 1604, 1602, 1598, 170, 418, 165, 537, 176, 424}"
83,1,330,0,0.3945049,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{7/2}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(7/2),x]","-\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}}","-\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,"(-2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(25*(7 + 5*x)^(5/2)) + (17906*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(2085525*(7 + 5*x)^(3/2)) + (1426348*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(2319687747*Sqrt[7 + 5*x]) - (2852696*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(11598438735*Sqrt[-5 + 2*x]) + (1426348*Sqrt[11/39]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(297395865*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) - (48884*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(9593415*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)])","A",9,9,37,0.2432,1,"{160, 1604, 1599, 1602, 12, 170, 418, 176, 424}"
84,1,370,0,0.5145798,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{9/2}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(9/2),x]","-\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}}","-\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,"(-2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(35*(7 + 5*x)^(7/2)) + (2558*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(695175*(7 + 5*x)^(5/2)) + (23758016*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(57992193675*(7 + 5*x)^(3/2)) + (32843987836*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(451524900265803*Sqrt[7 + 5*x]) - (65687975672*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(2257624501329015*Sqrt[-5 + 2*x]) + (32843987836*Sqrt[11/39]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(57887807726385*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) - (1212290288*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(1867348636335*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)])","A",10,9,37,0.2432,1,"{160, 1604, 1599, 1602, 12, 170, 418, 176, 424}"
85,1,429,0,0.5258913,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^{5/2}}{\sqrt{-5+2 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2))/Sqrt[-5 + 2*x],x]","\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}}","\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,"(2466927*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(4096*Sqrt[-5 + 2*x]) + (1561915*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/27648 + (1445*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2))/576 + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2))/8 - (2466927*Sqrt[429]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(8192*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (861015607*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(331776*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) + (331574321009*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(1658880*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",11,10,37,0.2703,1,"{162, 1600, 1602, 1598, 170, 418, 165, 537, 176, 424}"
86,1,391,0,0.411787,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^{3/2}}{\sqrt{-5+2 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2))/Sqrt[-5 + 2*x],x]","\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}}","\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,"(66377*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(1920*Sqrt[-5 + 2*x]) + (977*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/288 + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2))/6 - (66377*Sqrt[143/3]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(1280*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (2824441*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(17280*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) + (963142751*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(86400*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",10,10,37,0.2703,1,"{162, 1600, 1602, 1598, 170, 418, 165, 537, 176, 424}"
87,1,351,0,0.3163461,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} \sqrt{7+5 x}}{\sqrt{-5+2 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/Sqrt[-5 + 2*x],x]","\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}}","\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,"(509*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(240*Sqrt[-5 + 2*x]) + (Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/4 - (509*Sqrt[143/3]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(160*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (8959*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(720*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) + (2198489*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(3600*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",9,9,37,0.2432,1,"{161, 1602, 1598, 170, 418, 165, 537, 176, 424}"
88,1,365,0,0.2161432,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} \sqrt{7+5 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*Sqrt[7 + 5*x]),x]","\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}}","\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,"(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(5*Sqrt[-5 + 2*x]) - (Sqrt[429]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(10*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (7*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(10*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) + (41*Sqrt[11/62]*Sqrt[2 - 3*x]*EllipticF[ArcTan[(Sqrt[22/23]*Sqrt[7 + 5*x])/Sqrt[-5 + 2*x]], 39/62])/(20*Sqrt[-((2 - 3*x)/(1 + 4*x))]*Sqrt[1 + 4*x]) + (943*Sqrt[2 - 3*x]*EllipticPi[78/55, ArcTan[(Sqrt[22/23]*Sqrt[7 + 5*x])/Sqrt[-5 + 2*x]], 39/62])/(100*Sqrt[682]*Sqrt[-((2 - 3*x)/(1 + 4*x))]*Sqrt[1 + 4*x])","A",9,8,37,0.2162,1,"{173, 176, 424, 170, 418, 165, 536, 539}"
89,1,279,0,0.194712,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{3/2}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(3/2)),x]","-\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}}","-\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,"(2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(39*Sqrt[7 + 5*x]) - (4*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(195*Sqrt[-5 + 2*x]) + (2*Sqrt[11/39]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(5*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) - (69*Sqrt[2/341]*Sqrt[-((2 - 3*x)/(1 + 4*x))]*Sqrt[-((5 - 2*x)/(1 + 4*x))]*(1 + 4*x)*EllipticPi[78/55, ArcSin[(Sqrt[22/39]*Sqrt[7 + 5*x])/Sqrt[1 + 4*x]], 39/62])/(25*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x])","A",7,7,37,0.1892,1,"{164, 1586, 1595, 165, 537, 176, 424}"
90,1,290,0,0.3199855,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{5/2}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(5/2)),x]","\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}}","\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,"(2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(117*(7 + 5*x)^(3/2)) - (9350*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(3253419*Sqrt[7 + 5*x]) + (3740*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(3253419*Sqrt[-5 + 2*x]) - (1870*Sqrt[11/39]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(83421*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (44*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(2691*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)])","A",8,8,37,0.2162,1,"{164, 1599, 1602, 12, 170, 418, 176, 424}"
91,1,330,0,0.3982227,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{7/2}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(7/2)),x]","\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}}","\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,"(2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(195*(7 + 5*x)^(5/2)) - (3646*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(16267095*(7 + 5*x)^(3/2)) - (20464840*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(90467822133*Sqrt[7 + 5*x]) + (8185936*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(90467822133*Sqrt[-5 + 2*x]) - (4092968*Sqrt[11/39]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(2319687747*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (111628*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(74828637*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)])","A",9,9,37,0.2432,1,"{164, 1604, 1599, 1602, 12, 170, 418, 176, 424}"
92,1,370,0,0.5212918,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{9/2}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(9/2)),x]","\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}}","\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,"(2*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(273*(7 + 5*x)^(7/2)) + (98*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(1807455*(7 + 5*x)^(5/2)) - (3217468*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(50259901185*(7 + 5*x)^(3/2)) - (40944441340*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(1956607901151813*Sqrt[7 + 5*x]) + (16377776536*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(1956607901151813*Sqrt[-5 + 2*x]) - (8188888268*Sqrt[11/39]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(50169433362867*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (258506776*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(1618368818157*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)])","A",10,9,37,0.2432,1,"{164, 1604, 1599, 1602, 12, 170, 418, 176, 424}"
93,1,391,0,0.420862,"\int \frac{\sqrt{2-3 x} (7+5 x)^{5/2}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(Sqrt[2 - 3*x]*(7 + 5*x)^(5/2))/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(102487*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(1536*Sqrt[-5 + 2*x]) + (6955*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/1152 + (5*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2))/24 - (102487*Sqrt[143/3]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(1024*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (5241511*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(13824*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) + (295576909*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(13824*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",10,10,37,0.2703,1,"{174, 1600, 1602, 1598, 170, 418, 165, 537, 176, 424}"
94,1,351,0,0.3216508,"\int \frac{\sqrt{2-3 x} (7+5 x)^{3/2}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(Sqrt[2 - 3*x]*(7 + 5*x)^(3/2))/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(785*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(192*Sqrt[-5 + 2*x]) + (5*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/16 - (785*Sqrt[143/3]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(128*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (17515*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(576*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) + (3730013*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(2880*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",9,9,37,0.2432,1,"{174, 1602, 1598, 170, 418, 165, 537, 176, 424}"
95,1,365,0,0.2019785,"\int \frac{\sqrt{2-3 x} \sqrt{7+5 x}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(Sqrt[2 - 3*x]*Sqrt[7 + 5*x])/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(4*Sqrt[-5 + 2*x]) - (Sqrt[429]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(8*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) - (39*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(8*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) + (179*Sqrt[11/62]*Sqrt[2 - 3*x]*EllipticF[ArcTan[(Sqrt[22/23]*Sqrt[7 + 5*x])/Sqrt[-5 + 2*x]], 39/62])/(16*Sqrt[-((2 - 3*x)/(1 + 4*x))]*Sqrt[1 + 4*x]) + (4117*Sqrt[2 - 3*x]*EllipticPi[78/55, ArcTan[(Sqrt[22/23]*Sqrt[7 + 5*x])/Sqrt[-5 + 2*x]], 39/62])/(80*Sqrt[682]*Sqrt[-((2 - 3*x)/(1 + 4*x))]*Sqrt[1 + 4*x])","A",9,8,37,0.2162,1,"{173, 176, 424, 170, 418, 165, 536, 539}"
96,1,101,0,0.0371325,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x}} \, dx","Int[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]),x]","\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}}","\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,"(62*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(5*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",2,2,37,0.05405,1,"{165, 537}"
97,1,195,0,0.1308837,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2}} \, dx","Int[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2)),x]","-\frac{62 \sqrt{2 x-5} \sqrt{4 x+1}}{897 \sqrt{2-3 x} \sqrt{5 x+7}}-\frac{\sqrt{\frac{22}{31}} \sqrt{4 x+1} F\left(\tan ^{-1}\left(\frac{\sqrt{\frac{31}{11}} \sqrt{2 x-5}}{\sqrt{5 x+7}}\right)|\frac{39}{62}\right)}{39 \sqrt{2-3 x} \sqrt{-\frac{4 x+1}{2-3 x}}}+\frac{2 \sqrt{682} \sqrt{4 x+1} E\left(\tan ^{-1}\left(\frac{\sqrt{\frac{31}{11}} \sqrt{2 x-5}}{\sqrt{5 x+7}}\right)|\frac{39}{62}\right)}{897 \sqrt{2-3 x} \sqrt{-\frac{4 x+1}{2-3 x}}}","\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,"(-62*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(897*Sqrt[2 - 3*x]*Sqrt[7 + 5*x]) + (2*Sqrt[682]*Sqrt[1 + 4*x]*EllipticE[ArcTan[(Sqrt[31/11]*Sqrt[-5 + 2*x])/Sqrt[7 + 5*x]], 39/62])/(897*Sqrt[2 - 3*x]*Sqrt[-((1 + 4*x)/(2 - 3*x))]) - (Sqrt[22/31]*Sqrt[1 + 4*x]*EllipticF[ArcTan[(Sqrt[31/11]*Sqrt[-5 + 2*x])/Sqrt[7 + 5*x]], 39/62])/(39*Sqrt[2 - 3*x]*Sqrt[-((1 + 4*x)/(2 - 3*x))])","B",5,5,37,0.1351,1,"{176, 422, 418, 492, 411}"
98,1,290,0,0.2960522,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2}} \, dx","Int[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2)),x]","\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}}","\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,"(-10*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(2691*(7 + 5*x)^(3/2)) - (98330*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(74828637*Sqrt[7 + 5*x]) + (39332*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(74828637*Sqrt[-5 + 2*x]) - (19666*Sqrt[11/39]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(1918683*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (716*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(61893*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)])","A",8,8,37,0.2162,1,"{177, 1599, 1602, 12, 170, 418, 176, 424}"
99,1,721,0,0.6748451,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{\sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(Sqrt[a + b*x]*Sqrt[c + d*x])/(Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\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)}}}","\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,"(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[g + h*x])/(h*Sqrt[e + f*x]) - (Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*Sqrt[a + b*x]*Sqrt[((d*e - c*f)*(g + h*x))/((d*g - c*h)*(e + f*x))]*EllipticE[ArcSin[(Sqrt[f*g - e*h]*Sqrt[c + d*x])/(Sqrt[d*g - c*h]*Sqrt[e + f*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(f*h*Sqrt[-(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))]*Sqrt[g + h*x]) + ((d*e - c*f)*(b*f*g + b*e*h - 2*a*f*h)*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(f^2*h*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) + (Sqrt[b*g - a*h]*(a*d*f*h - b*(d*f*g + d*e*h - c*f*h))*Sqrt[((f*g - e*h)*(a + b*x))/((b*g - a*h)*(e + f*x))]*Sqrt[((f*g - e*h)*(c + d*x))/((d*g - c*h)*(e + f*x))]*(e + f*x)*EllipticPi[(f*(b*g - a*h))/((b*e - a*f)*h), ArcSin[(Sqrt[b*e - a*f]*Sqrt[g + h*x])/(Sqrt[b*g - a*h]*Sqrt[e + f*x])], ((d*e - c*f)*(b*g - a*h))/((b*e - a*f)*(d*g - c*h))])/(f^2*Sqrt[b*e - a*f]*h^2*Sqrt[a + b*x]*Sqrt[c + d*x])","A",7,7,37,0.1892,1,"{173, 176, 424, 170, 419, 165, 537}"
100,1,208,0,0.0925571,"\int \frac{\sqrt{c+d x}}{(a+b x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[Sqrt[c + d*x]/((a + b*x)^(3/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\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)}} 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 e-a f) \sqrt{b g-a h} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}}}","-\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,"(-2*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]*EllipticE[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/((b*e - a*f)*Sqrt[b*g - a*h]*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x])","A",2,2,37,0.05405,1,"{176, 424}"
101,1,351,0,0.3188935,"\int \frac{(7+5 x)^{5/2}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(7 + 5*x)^(5/2)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\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}}","-\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,"(-2135*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(192*Sqrt[-5 + 2*x]) - (25*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/48 + (2135*Sqrt[143/3]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(128*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (29047*Sqrt[23/11]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(576*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) - (3431855*(2 - 3*x)*Sqrt[(5 - 2*x)/(2 - 3*x)]*Sqrt[-((1 + 4*x)/(2 - 3*x))]*EllipticPi[-69/55, ArcSin[(Sqrt[11/23]*Sqrt[7 + 5*x])/Sqrt[2 - 3*x]], -23/39])/(576*Sqrt[429]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",9,9,37,0.2432,1,"{167, 1602, 1598, 170, 418, 165, 537, 176, 424}"
102,1,469,0,0.2803475,"\int \frac{(7+5 x)^{3/2}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[(7 + 5*x)^(3/2)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\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}}","-\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,"(-5*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(12*Sqrt[-5 + 2*x]) + (5*Sqrt[143/3]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(8*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (65*Sqrt[11/23]*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(8*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) - (895*Sqrt[11/62]*Sqrt[2 - 3*x]*EllipticF[ArcTan[(Sqrt[22/23]*Sqrt[7 + 5*x])/Sqrt[-5 + 2*x]], 39/62])/(48*Sqrt[-((2 - 3*x)/(1 + 4*x))]*Sqrt[1 + 4*x]) + (23*Sqrt[31/22]*Sqrt[(2 - 3*x)/(7 + 5*x)]*Sqrt[(5 - 2*x)/(7 + 5*x)]*(7 + 5*x)*EllipticPi[55/124, ArcSin[(Sqrt[31/11]*Sqrt[1 + 4*x])/Sqrt[7 + 5*x]], 39/62])/(6*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]) - (4117*Sqrt[2 - 3*x]*EllipticPi[78/55, ArcTan[(Sqrt[22/23]*Sqrt[7 + 5*x])/Sqrt[-5 + 2*x]], 39/62])/(48*Sqrt[682]*Sqrt[-((2 - 3*x)/(1 + 4*x))]*Sqrt[1 + 4*x])","A",12,10,37,0.2703,1,"{166, 173, 176, 424, 170, 418, 165, 536, 539, 537}"
103,1,100,0,0.0383713,"\int \frac{\sqrt{7+5 x}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Int[Sqrt[7 + 5*x]/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\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}}","\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,"(23*Sqrt[(2 - 3*x)/(7 + 5*x)]*Sqrt[(5 - 2*x)/(7 + 5*x)]*(7 + 5*x)*EllipticPi[55/124, ArcSin[(Sqrt[31/11]*Sqrt[1 + 4*x])/Sqrt[7 + 5*x]], 39/62])/(2*Sqrt[682]*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x])","A",2,2,37,0.05405,1,"{165, 537}"
104,1,71,0,0.0428364,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x}} \, dx","Int[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]),x]","\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}}}","\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,"(2*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(Sqrt[253]*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)])","A",2,2,37,0.05405,1,"{170, 418}"
105,1,270,0,0.182889,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2}} \, dx","Int[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2)),x]","-\frac{10 \sqrt{2 x-5} \sqrt{4 x+1}}{897 \sqrt{2-3 x} \sqrt{5 x+7}}+\frac{6 \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)}{31 \sqrt{253} \sqrt{2 x-5} \sqrt{\frac{5 x+7}{5-2 x}}}-\frac{5 \sqrt{\frac{22}{31}} \sqrt{4 x+1} F\left(\tan ^{-1}\left(\frac{\sqrt{\frac{31}{11}} \sqrt{2 x-5}}{\sqrt{5 x+7}}\right)|\frac{39}{62}\right)}{1209 \sqrt{2-3 x} \sqrt{-\frac{4 x+1}{2-3 x}}}+\frac{10 \sqrt{\frac{22}{31}} \sqrt{4 x+1} E\left(\tan ^{-1}\left(\frac{\sqrt{\frac{31}{11}} \sqrt{2 x-5}}{\sqrt{5 x+7}}\right)|\frac{39}{62}\right)}{897 \sqrt{2-3 x} \sqrt{-\frac{4 x+1}{2-3 x}}}","\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,"(-10*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(897*Sqrt[2 - 3*x]*Sqrt[7 + 5*x]) + (10*Sqrt[22/31]*Sqrt[1 + 4*x]*EllipticE[ArcTan[(Sqrt[31/11]*Sqrt[-5 + 2*x])/Sqrt[7 + 5*x]], 39/62])/(897*Sqrt[2 - 3*x]*Sqrt[-((1 + 4*x)/(2 - 3*x))]) + (6*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(31*Sqrt[253]*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]) - (5*Sqrt[22/31]*Sqrt[1 + 4*x]*EllipticF[ArcTan[(Sqrt[31/11]*Sqrt[-5 + 2*x])/Sqrt[7 + 5*x]], 39/62])/(1209*Sqrt[2 - 3*x]*Sqrt[-((1 + 4*x)/(2 - 3*x))])","A",8,7,37,0.1892,1,"{171, 170, 418, 176, 422, 492, 411}"
106,1,288,0,0.3029177,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2}} \, dx","Int[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2)),x]","\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}}","\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,"(-50*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(83421*(7 + 5*x)^(3/2)) - (895300*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(2319687747*Sqrt[7 + 5*x]) + (358120*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/(2319687747*Sqrt[-5 + 2*x]) - (179060*Sqrt[11/39]*Sqrt[2 - 3*x]*Sqrt[(7 + 5*x)/(5 - 2*x)]*EllipticE[ArcSin[(Sqrt[39/23]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x]], -23/39])/(59479173*Sqrt[(2 - 3*x)/(5 - 2*x)]*Sqrt[7 + 5*x]) + (103964*Sqrt[7 + 5*x]*EllipticF[ArcTan[Sqrt[1 + 4*x]/(Sqrt[2]*Sqrt[2 - 3*x])], -39/23])/(1918683*Sqrt[253]*Sqrt[-5 + 2*x]*Sqrt[(7 + 5*x)/(5 - 2*x)])","A",8,8,37,0.2162,1,"{172, 1599, 1602, 12, 170, 418, 176, 424}"
107,1,968,0,0.8820661,"\int \frac{(a+b x)^{3/2}}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a + b*x)^(3/2)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\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}}","-\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,"(b*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[g + h*x])/(d*h*Sqrt[e + f*x]) - (b*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*Sqrt[a + b*x]*Sqrt[((d*e - c*f)*(g + h*x))/((d*g - c*h)*(e + f*x))]*EllipticE[ArcSin[(Sqrt[f*g - e*h]*Sqrt[c + d*x])/(Sqrt[d*g - c*h]*Sqrt[e + f*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(d*f*h*Sqrt[-(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))]*Sqrt[g + h*x]) + (b*(d*e - c*f)*(b*f*g + b*e*h - 2*a*f*h)*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(d*f^2*h*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) + (b*Sqrt[b*g - a*h]*(a*d*f*h - b*(d*f*g + d*e*h - c*f*h))*Sqrt[((f*g - e*h)*(a + b*x))/((b*g - a*h)*(e + f*x))]*Sqrt[((f*g - e*h)*(c + d*x))/((d*g - c*h)*(e + f*x))]*(e + f*x)*EllipticPi[(f*(b*g - a*h))/((b*e - a*f)*h), ArcSin[(Sqrt[b*e - a*f]*Sqrt[g + h*x])/(Sqrt[b*g - a*h]*Sqrt[e + f*x])], ((d*e - c*f)*(b*g - a*h))/((b*e - a*f)*(d*g - c*h))])/(d*f^2*Sqrt[b*e - a*f]*h^2*Sqrt[a + b*x]*Sqrt[c + d*x]) - (2*Sqrt[b*c - a*d]*Sqrt[-(d*g) + c*h]*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(d*h*Sqrt[c + d*x]*Sqrt[e + f*x])","A",10,8,37,0.2162,1,"{166, 173, 176, 424, 170, 419, 165, 537}"
108,1,228,0,0.1497606,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[Sqrt[a + b*x]/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\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}}","\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,"(2*Sqrt[-(d*g) + c*h]*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(Sqrt[b*c - a*d]*h*Sqrt[c + d*x]*Sqrt[e + f*x])","A",2,2,37,0.05405,1,"{165, 537}"
109,1,198,0,0.0820603,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[1/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 \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} \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 \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,"(2*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))])","A",2,2,37,0.05405,1,"{170, 419}"
110,1,429,0,0.2563458,"\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[1/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\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)}}}","-\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,"(-2*b*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]*EllipticE[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/((b*c - a*d)*(b*e - a*f)*Sqrt[b*g - a*h]*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]) - (2*d*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/((b*c - a*d)*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))])","A",5,5,37,0.1351,1,"{171, 170, 419, 176, 424}"
111,0,0,0,0.010114,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[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,"Defer[Int][1/((a + b*x)^(3/2)*(c + d*x)^(3/2)*Sqrt[e + f*x]*Sqrt[g + h*x]), x]","F",0,0,0,0,-1,"{}"
112,1,319,0,0.279362,"\int \frac{x^4 (e+f x)^n}{(a+b x) (c+d x)} \, dx","Int[(x^4*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\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{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{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)}","\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{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{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,"(e^2*(e + f*x)^(1 + n))/(b*d*f^3*(1 + n)) + ((b*c + a*d)*e*(e + f*x)^(1 + n))/(b^2*d^2*f^2*(1 + n)) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*(e + f*x)^(1 + n))/(b^3*d^3*f*(1 + n)) - (2*e*(e + f*x)^(2 + n))/(b*d*f^3*(2 + n)) - ((b*c + a*d)*(e + f*x)^(2 + n))/(b^2*d^2*f^2*(2 + n)) + (e + f*x)^(3 + n)/(b*d*f^3*(3 + n)) - (a^4*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/(b^3*(b*c - a*d)*(b*e - a*f)*(1 + n)) + (c^4*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/(d^3*(b*c - a*d)*(d*e - c*f)*(1 + n))","A",8,3,25,0.1200,1,"{180, 43, 68}"
113,1,216,0,0.1541596,"\int \frac{x^3 (e+f x)^n}{(a+b x) (c+d x)} \, dx","Int[(x^3*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\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)}","\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,"-((e*(e + f*x)^(1 + n))/(b*d*f^2*(1 + n))) - ((b*c + a*d)*(e + f*x)^(1 + n))/(b^2*d^2*f*(1 + n)) + (e + f*x)^(2 + n)/(b*d*f^2*(2 + n)) + (a^3*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/(b^2*(b*c - a*d)*(b*e - a*f)*(1 + n)) - (c^3*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/(d^2*(b*c - a*d)*(d*e - c*f)*(1 + n))","A",6,3,25,0.1200,1,"{180, 43, 68}"
114,1,158,0,0.107468,"\int \frac{x^2 (e+f x)^n}{(a+b x) (c+d x)} \, dx","Int[(x^2*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","-\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)}","-\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,"(e + f*x)^(1 + n)/(b*d*f*(1 + n)) - (a^2*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/(b*(b*c - a*d)*(b*e - a*f)*(1 + n)) + (c^2*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/(d*(b*c - a*d)*(d*e - c*f)*(1 + n))","A",4,2,25,0.08000,1,"{180, 68}"
115,1,124,0,0.0385097,"\int \frac{x (e+f x)^n}{(a+b x) (c+d x)} \, dx","Int[(x*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\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)}","\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,"(a*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/((b*c - a*d)*(b*e - a*f)*(1 + n)) - (c*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/((b*c - a*d)*(d*e - c*f)*(1 + n))","A",3,2,23,0.08696,1,"{156, 68}"
116,1,124,0,0.0331753,"\int \frac{(e+f x)^n}{(a+b x) (c+d x)} \, dx","Int[(e + f*x)^n/((a + b*x)*(c + d*x)),x]","\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)}","\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,"-((b*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/((b*c - a*d)*(b*e - a*f)*(1 + n))) + (d*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/((b*c - a*d)*(d*e - c*f)*(1 + n))","A",3,2,22,0.09091,1,"{86, 68}"
117,1,175,0,0.1194873,"\int \frac{(e+f x)^n}{x (a+b x) (c+d x)} \, dx","Int[(e + f*x)^n/(x*(a + b*x)*(c + d*x)),x]","\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)}","\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,"(b^2*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/(a*(b*c - a*d)*(b*e - a*f)*(1 + n)) - (d^2*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/(c*(b*c - a*d)*(d*e - c*f)*(1 + n)) - ((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (f*x)/e])/(a*c*e*(1 + n))","A",5,3,25,0.1200,1,"{180, 65, 68}"
118,1,222,0,0.1512564,"\int \frac{(e+f x)^n}{x^2 (a+b x) (c+d x)} \, dx","Int[(e + f*x)^n/(x^2*(a + b*x)*(c + d*x)),x]","-\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)}","-\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,"-((b^3*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/(a^2*(b*c - a*d)*(b*e - a*f)*(1 + n))) + (d^3*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/(c^2*(b*c - a*d)*(d*e - c*f)*(1 + n)) + ((b*c + a*d)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (f*x)/e])/(a^2*c^2*e*(1 + n)) + (f*(e + f*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (f*x)/e])/(a*c*e^2*(1 + n))","A",6,3,25,0.1200,1,"{180, 65, 68}"
119,1,167,0,0.1305652,"\int (a+b x)^m (c+d x) (e+f x) (g+h x) \, dx","Int[(a + b*x)^m*(c + d*x)*(e + f*x)*(g + h*x),x]","\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)}","\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,"((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x)^(1 + m))/(b^4*(1 + m)) + ((3*a^2*d*f*h + b^2*(d*e*g + c*f*g + c*e*h) - 2*a*b*(d*f*g + d*e*h + c*f*h))*(a + b*x)^(2 + m))/(b^4*(2 + m)) - ((3*a*d*f*h - b*(d*f*g + d*e*h + c*f*h))*(a + b*x)^(3 + m))/(b^4*(3 + m)) + (d*f*h*(a + b*x)^(4 + m))/(b^4*(4 + m))","A",2,1,23,0.04348,1,"{142}"
120,1,134,0,0.0860064,"\int \frac{(a+b x)^m (c+d x) (e+f x)}{g+h x} \, dx","Int[((a + b*x)^m*(c + d*x)*(e + f*x))/(g + h*x),x]","\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)}","\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,"-(((a + b*x)^(1 + m)*(a*d*f*h + b*(d*f*g - d*e*h - c*f*h)*(2 + m) - b*d*f*h*(1 + m)*x))/(b^2*h^2*(1 + m)*(2 + m))) + ((d*g - c*h)*(f*g - e*h)*(a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((h*(a + b*x))/(b*g - a*h))])/(h^2*(b*g - a*h)*(1 + m))","A",2,2,25,0.08000,1,"{147, 68}"
121,1,140,0,0.0591633,"\int \frac{(a+b x)^m (c+d x)}{(e+f x) (g+h x)} \, dx","Int[((a + b*x)^m*(c + d*x))/((e + f*x)*(g + h*x)),x]","\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)}","\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,"-(((d*e - c*f)*(a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((f*(a + b*x))/(b*e - a*f))])/((b*e - a*f)*(f*g - e*h)*(1 + m))) + ((d*g - c*h)*(a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((h*(a + b*x))/(b*g - a*h))])/((b*g - a*h)*(f*g - e*h)*(1 + m))","A",3,2,27,0.07407,1,"{156, 68}"
122,1,224,0,0.1949515,"\int \frac{(a+b x)^m}{(c+d x) (e+f x) (g+h x)} \, dx","Int[(a + b*x)^m/((c + d*x)*(e + f*x)*(g + h*x)),x]","\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)}","\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,"(d^2*(a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)*(d*e - c*f)*(d*g - c*h)*(1 + m)) - (f^2*(a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((f*(a + b*x))/(b*e - a*f))])/((b*e - a*f)*(d*e - c*f)*(f*g - e*h)*(1 + m)) + (h^2*(a + b*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((h*(a + b*x))/(b*g - a*h))])/((b*g - a*h)*(d*g - c*h)*(f*g - e*h)*(1 + m))","A",5,2,29,0.06897,1,"{180, 68}"
123,1,140,0,0.1227731,"\int \frac{x^m (e+f x)^n}{(a+b x) (c+d x)} \, dx","Int[(x^m*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\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)}","\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,"(b*x^(1 + m)*(e + f*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((f*x)/e), -((b*x)/a)])/(a*(b*c - a*d)*(1 + m)*(1 + (f*x)/e)^n) - (d*x^(1 + m)*(e + f*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((f*x)/e), -((d*x)/c)])/(c*(b*c - a*d)*(1 + m)*(1 + (f*x)/e)^n)","A",6,3,25,0.1200,1,"{180, 135, 133}"
124,1,266,0,0.1651178,"\int (a+b x)^m (c+d x)^n (e+f x) (g+h x) \, dx","Int[(a + b*x)^m*(c + d*x)^n*(e + f*x)*(g + h*x),x]","\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)}","\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,"-(((a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(b*c*f*h*(2 + m) + a*d*f*h*(2 + n) - b*d*(f*g + e*h)*(3 + m + n) - b*d*f*h*(2 + m + n)*x))/(b^2*d^2*(2 + m + n)*(3 + m + n))) + ((a^2*d^2*f*h*(1 + n)*(2 + n) + a*b*d*(1 + n)*(2*c*f*h*(1 + m) - d*(f*g + e*h)*(3 + m + n)) + b^2*(c^2*f*h*(1 + m)*(2 + m) - c*d*(f*g + e*h)*(1 + m)*(3 + m + n) + d^2*e*g*(2 + m + n)*(3 + m + n)))*(a + b*x)^(1 + m)*(c + d*x)^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/(b^3*d^2*(1 + m)*(2 + m + n)*(3 + m + n)*((b*(c + d*x))/(b*c - a*d))^n)","A",3,3,25,0.1200,1,"{147, 70, 69}"
125,1,245,0,0.1546409,"\int (a+b x)^m (c+d x)^{1-m} (e+f x) (g+h x) \, dx","Int[(a + b*x)^m*(c + d*x)^(1 - m)*(e + f*x)*(g + h*x),x]","\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}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(2 - m)*(4*b*d*(f*g + e*h) - a*d*f*h*(3 - m) - b*c*f*h*(2 + m) + 3*b*d*f*h*x))/(12*b^2*d^2) + ((b*c - a*d)*(a^2*d^2*f*h*(6 - 5*m + m^2) - 2*a*b*d*(2 - m)*(2*d*(f*g + e*h) - c*f*h*(1 + m)) + b^2*(12*d^2*e*g - 4*c*d*(f*g + e*h)*(1 + m) + c^2*f*h*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/(12*b^4*d^2*(1 + m)*(c + d*x)^m)","A",3,3,29,0.1034,1,"{147, 70, 69}"
126,1,235,0,0.1375099,"\int (a+b x)^m (c+d x)^{-m} (e+f x) (g+h x) \, dx","Int[((a + b*x)^m*(e + f*x)*(g + h*x))/(c + d*x)^m,x]","\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}","\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,"((a + b*x)^(1 + m)*(c + d*x)^(1 - m)*(3*b*d*(f*g + e*h) - a*d*f*h*(2 - m) - b*c*f*h*(2 + m) + 2*b*d*f*h*x))/(6*b^2*d^2) + ((a^2*d^2*f*h*(2 - 3*m + m^2) - a*b*d*(1 - m)*(3*d*(f*g + e*h) - 2*c*f*h*(1 + m)) + b^2*(6*d^2*e*g - 3*c*d*(f*g + e*h)*(1 + m) + c^2*f*h*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/(6*b^3*d^2*(1 + m)*(c + d*x)^m)","A",3,3,27,0.1111,1,"{147, 70, 69}"
127,1,261,0,0.1861994,"\int (a+b x)^m (c+d x)^{-1-m} (e+f x) (g+h x) \, dx","Int[(a + b*x)^m*(c + d*x)^(-1 - m)*(e + f*x)*(g + h*x),x]","\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)}","\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,"((a + b*x)^(1 + m)*(2*b*d^2*e*g + b*c^2*f*h*(2 + m) - c*d*(2*b*(f*g + e*h) + a*f*h*m) + d*(b*c - a*d)*f*h*m*x))/(2*b*d^2*(b*c - a*d)*m*(c + d*x)^m) - ((b^2*c^2*f*h*(1 + m)*(2 + m) - 2*b*c*d*(1 + m)*(b*f*g + b*e*h + a*f*h*m) + d^2*(2*b^2*e*g + 2*a*b*(f*g + e*h)*m - a^2*f*h*(1 - m)*m))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/(2*b^2*d^2*(b*c - a*d)*m*(1 + m)*(c + d*x)^m)","A",3,3,29,0.1034,1,"{146, 70, 69}"
128,1,205,0,0.1067246,"\int (a+b x)^m (c+d x)^{-2-m} (e+f x) (g+h x) \, dx","Int[(a + b*x)^m*(c + d*x)^(-2 - m)*(e + f*x)*(g + h*x),x]","-\frac{(a+b x)^{m+1} (c+d x)^{-m-1} \left(-d f h (m+1) x (b c-a d)+a c d f h (m+1)-b \left(c^2 f h (m+2)-c d (e h+f g)+d^2 e g\right)\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 c f h (m+2)+b d (e h+f g))}{b d^3 m}","\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,"-(((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*(a*c*d*f*h*(1 + m) - b*(d^2*e*g - c*d*(f*g + e*h) + c^2*f*h*(2 + m)) - d*(b*c - a*d)*f*h*(1 + m)*x))/(b*d^2*(b*c - a*d)*(1 + m))) - ((b*d*(f*g + e*h) + a*d*f*h*m - b*c*f*h*(2 + m))*(a + b*x)^m*Hypergeometric2F1[-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)])/(b*d^3*m*(-((d*(a + b*x))/(b*c - a*d)))^m*(c + d*x)^m)","A",3,3,29,0.1034,1,"{143, 70, 69}"
129,1,246,0,0.1597628,"\int (a+b x)^m (c+d x)^{-3-m} (e+f x) (g+h x) \, dx","Int[(a + b*x)^m*(c + d*x)^(-3 - m)*(e + f*x)*(g + h*x),x]","\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(-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^3 (-d) f h (m+1)+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}","\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(-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^3 (-d) f h (m+1)+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,"-(((a + b*x)^(1 + m)*(c + d*x)^(-2 - m)*(a^2*b*c*f*h*m - a^3*d*f*h*(1 + m) - b^3*c*e*g*(2 + m) + a*b^2*(c*(f*g + e*h) + d*e*g*(1 + m)) - b*(a^2*d*f*h*(3 + 2*m) + b^2*(d*e*g + c*(f*g + e*h)*(1 + m)) - a*b*(2*c*f*h*(1 + m) + d*(f*g + e*h)*(2 + m)))*x))/(b^2*(b*c - a*d)^2*(1 + m)*(2 + m))) + (f*h*(a + b*x)^(3 + m)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[3 + m, 3 + m, 4 + m, -((d*(a + b*x))/(b*c - a*d))])/((b*c - a*d)^3*(3 + m)*(c + d*x)^m)","A",3,3,29,0.1034,1,"{145, 70, 69}"
130,1,362,0,0.3618663,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x) (g+h x) \, dx","Int[(a + b*x)^m*(c + d*x)^(-4 - m)*(e + f*x)*(g + h*x),x]","\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)}","\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,"((a^2*d^2*f*h*(6 + 5*m + m^2) - a*b*d*(3 + m)*(d*(f*g + e*h) + 2*c*f*h*(1 + m)) + b^2*(2*d^2*e*g + c*d*(f*g + e*h)*(1 + m) + c^2*f*h*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(b*d^2*(b*c - a*d)^2*(2 + m)*(3 + m)) + ((a^2*d^2*f*h*(6 + 5*m + m^2) - a*b*d*(3 + m)*(d*(f*g + e*h) + 2*c*f*h*(1 + m)) + b^2*(2*d^2*e*g + c*d*(f*g + e*h)*(1 + m) + c^2*f*h*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^2*(b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m)) + ((a + b*x)^(1 + m)*(c + d*x)^(-3 - m)*(a*c*d*f*h*(3 + m) + b*(d^2*e*g - c*d*(f*g + e*h) - c^2*f*h*(2 + m)) - d*(b*c - a*d)*f*h*(3 + m)*x))/(b*d^2*(b*c - a*d)*(3 + m))","A",3,3,29,0.1034,1,"{146, 45, 37}"
131,1,507,0,0.5859288,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x) (g+h x) \, dx","Int[(a + b*x)^m*(c + d*x)^(-5 - m)*(e + f*x)*(g + h*x),x]","\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)}","\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,"((a^2*d^2*f*h*(12 + 7*m + m^2) - 2*a*b*d*(4 + m)*(d*(f*g + e*h) + c*f*h*(1 + m)) + b^2*(6*d^2*e*g + 2*c*d*(f*g + e*h)*(1 + m) + c^2*f*h*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/(2*b*d^2*(b*c - a*d)^2*(3 + m)*(4 + m)) + ((a^2*d^2*f*h*(12 + 7*m + m^2) - 2*a*b*d*(4 + m)*(d*(f*g + e*h) + c*f*h*(1 + m)) + b^2*(6*d^2*e*g + 2*c*d*(f*g + e*h)*(1 + m) + c^2*f*h*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d^2*(b*c - a*d)^3*(2 + m)*(3 + m)*(4 + m)) + (b*(a^2*d^2*f*h*(12 + 7*m + m^2) - 2*a*b*d*(4 + m)*(d*(f*g + e*h) + c*f*h*(1 + m)) + b^2*(6*d^2*e*g + 2*c*d*(f*g + e*h)*(1 + m) + c^2*f*h*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^2*(b*c - a*d)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m)) + ((a + b*x)^(1 + m)*(c + d*x)^(-4 - m)*(a*c*d*f*h*(4 + m) + b*(2*d^2*e*g - 2*c*d*(f*g + e*h) - c^2*f*h*(2 + m)) - d*(b*c - a*d)*f*h*(4 + m)*x))/(2*b*d^2*(b*c - a*d)*(4 + m))","A",4,3,29,0.1034,1,"{146, 45, 37}"
132,1,803,0,1.4346148,"\int (a+b x)^3 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","Int[(a + b*x)^3*(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","\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 (m+2) f-b 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 (b d f g+3 a d f h+b d e h m-b c f h (m+4)) (e+f x)^{m+1} (c+d x)^{-m-2}}{d^4 f (d e-c f) (m+2)}-\frac{(b c-a d) (d f g+d e h (m+3)-c f h (m+4)) \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) (b d f g+3 a d f h+b d e h m-b c f h (m+4)) (a d f+b c (2 m+3) f-2 b d e (m+2)) (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) (d f g+d e h (m+3)-c f h (m+4)) \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 (b d f g+3 a d f h+b d e h m-b c f h (m+4)) (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}","\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,"((b*c - a*d)^2*(a*d*f + b*c*f*(2 + m) - b*d*e*(3 + m))*(c*f*h*(4 + m) - d*(f*g + e*h*(3 + m)))*(c + d*x)^(-3 - m)*(e + f*x)^(1 + m))/(d^4*f^2*(d*e - c*f)*(3 + m)) - (b*(b*c - a*d)*(c*f*h*(4 + m) - d*(f*g + e*h*(3 + m)))*(a + b*x)*(c + d*x)^(-3 - m)*(e + f*x)^(1 + m))/(d^3*f^2) + (h*(a + b*x)^3*(c + d*x)^(-3 - m)*(e + f*x)^(1 + m))/(d*f) - ((b*c - a*d)^2*(b*d*f*g + 3*a*d*f*h + b*d*e*h*m - b*c*f*h*(4 + m))*(c + d*x)^(-2 - m)*(e + f*x)^(1 + m))/(d^4*f*(d*e - c*f)*(2 + m)) - ((b*c - a*d)*(d*f*g + d*e*h*(3 + m) - c*f*h*(4 + m))*(2*a^2*d^2*f^2 + 2*a*b*d*f*(c*f*(1 + m) - d*e*(3 + m)) + b^2*(c^2*f^2*(2 + 3*m + m^2) - 2*c*d*e*f*(3 + 4*m + m^2) + d^2*e^2*(6 + 5*m + m^2)))*(c + d*x)^(-2 - m)*(e + f*x)^(1 + m))/(d^4*f^2*(d*e - c*f)^2*(2 + m)*(3 + m)) - ((b*c - a*d)*(b*d*f*g + 3*a*d*f*h + b*d*e*h*m - b*c*f*h*(4 + m))*(a*d*f - 2*b*d*e*(2 + m) + b*c*f*(3 + 2*m))*(c + d*x)^(-1 - m)*(e + f*x)^(1 + m))/(d^4*f*(d*e - c*f)^2*(1 + m)*(2 + m)) + ((b*c - a*d)*(d*f*g + d*e*h*(3 + m) - c*f*h*(4 + m))*(2*a^2*d^2*f^2 + 2*a*b*d*f*(c*f*(1 + m) - d*e*(3 + m)) + b^2*(c^2*f^2*(2 + 3*m + m^2) - 2*c*d*e*f*(3 + 4*m + m^2) + d^2*e^2*(6 + 5*m + m^2)))*(c + d*x)^(-1 - m)*(e + f*x)^(1 + m))/(d^4*f*(d*e - c*f)^3*(1 + m)*(2 + m)*(3 + m)) - (b^2*(b*d*f*g + 3*a*d*f*h + b*d*e*h*m - b*c*f*h*(4 + m))*(e + f*x)^m*Hypergeometric2F1[-m, -m, 1 - m, -((f*(c + d*x))/(d*e - c*f))])/(d^5*f*m*(c + d*x)^m*((d*(e + f*x))/(d*e - c*f))^m)","A",10,9,31,0.2903,1,"{153, 159, 89, 79, 70, 69, 90, 45, 37}"
133,1,566,0,0.6620167,"\int (a+b x)^2 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","Int[(a + b*x)^2*(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","-\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+b (a c f (m+1)-a d e (m+3)+b 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+b (a c f (m+1)-a d e (m+3)+b 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)-b d e (m+3))}{d^3 f (m+3) (d e-c f)}-\frac{b (a+b x) (d g-c h) (c+d x)^{-m-3} (e+f x)^{m+1}}{d^2 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 c f (2 m+3)-2 b d e (m+2))}{d^3 (m+1) (m+2) (d e-c f)^2}-\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}","-\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{b (a+b x) (d g-c h) (c+d x)^{-m-3} (e+f x)^{m+1}}{d^2 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^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,"((b*c - a*d)*(d*g - c*h)*(a*d*f + b*c*f*(2 + m) - b*d*e*(3 + m))*(c + d*x)^(-3 - m)*(e + f*x)^(1 + m))/(d^3*f*(d*e - c*f)*(3 + m)) - (b*(d*g - c*h)*(a + b*x)*(c + d*x)^(-3 - m)*(e + f*x)^(1 + m))/(d^2*f) - ((b*c - a*d)^2*h*(c + d*x)^(-2 - m)*(e + f*x)^(1 + m))/(d^3*(d*e - c*f)*(2 + m)) - ((d*g - c*h)*(b^2*(d*e - c*f)*(2 + m)*(c*f*(1 + m) - d*e*(3 + m)) - 2*d*f*(a^2*d*f + b*(b*c*e + a*c*f*(1 + m) - a*d*e*(3 + m))))*(c + d*x)^(-2 - m)*(e + f*x)^(1 + m))/(d^3*f*(d*e - c*f)^2*(2 + m)*(3 + m)) - ((b*c - a*d)*h*(a*d*f - 2*b*d*e*(2 + m) + b*c*f*(3 + 2*m))*(c + d*x)^(-1 - m)*(e + f*x)^(1 + m))/(d^3*(d*e - c*f)^2*(1 + m)*(2 + m)) + ((d*g - c*h)*(b^2*(d*e - c*f)*(2 + m)*(c*f*(1 + m) - d*e*(3 + m)) - 2*d*f*(a^2*d*f + b*(b*c*e + a*c*f*(1 + m) - a*d*e*(3 + m))))*(c + d*x)^(-1 - m)*(e + f*x)^(1 + m))/(d^3*(d*e - c*f)^3*(1 + m)*(2 + m)*(3 + m)) - (b^2*h*(e + f*x)^m*Hypergeometric2F1[-m, -m, 1 - m, -((f*(c + d*x))/(d*e - c*f))])/(d^4*m*(c + d*x)^m*((d*(e + f*x))/(d*e - c*f))^m)","A",9,8,31,0.2581,1,"{159, 89, 79, 70, 69, 90, 45, 37}"
134,1,360,0,0.3967076,"\int (a+b x) (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","Int[(a + b*x)*(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","\frac{(c+d x)^{-m-2} (e+f x)^{m+1} \left(a d f (c f h (m+1)-d e h (m+3)+2 d f g)+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 e h (m+3)+2 d f g)+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 e h (m+3)+d f g)+b d h (m+3) x (d e-c f))}{d^2 f (m+3) (d e-c f)}","\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,"((a*d*f*(2*d*f*g + c*f*h*(1 + m) - d*e*h*(3 + m)) + b*(c^2*f^2*h*(2 + 3*m + m^2) - d^2*e*(3 + m)*(f*g - e*h*(2 + m)) + c*d*f*(1 + m)*(f*g - 2*e*h*(3 + m))))*(c + d*x)^(-2 - m)*(e + f*x)^(1 + m))/(d^2*f*(d*e - c*f)^2*(2 + m)*(3 + m)) - ((a*d*f*(2*d*f*g + c*f*h*(1 + m) - d*e*h*(3 + m)) + b*(c^2*f^2*h*(2 + 3*m + m^2) - d^2*e*(3 + m)*(f*g - e*h*(2 + m)) + c*d*f*(1 + m)*(f*g - 2*e*h*(3 + m))))*(c + d*x)^(-1 - m)*(e + f*x)^(1 + m))/(d^2*(d*e - c*f)^3*(1 + m)*(2 + m)*(3 + m)) - ((c + d*x)^(-3 - m)*(e + f*x)^(1 + m)*(a*d*f*(d*g - c*h) - b*c*(d*f*g + c*f*h*(2 + m) - d*e*h*(3 + m)) + b*d*(d*e - c*f)*h*(3 + m)*x))/(d^2*f*(d*e - c*f)*(3 + m))","A",3,3,29,0.1034,1,"{146, 45, 37}"
135,1,186,0,0.0982305,"\int (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","Int[(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","-\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 e h (m+3)+2 d f g)}{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 e h (m+3)+2 d f g)}{d (m+1) (m+2) (m+3) (d e-c f)^3}","-\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,"-(((d*g - c*h)*(c + d*x)^(-3 - m)*(e + f*x)^(1 + m))/(d*(d*e - c*f)*(3 + m))) + ((2*d*f*g + c*f*h*(1 + m) - d*e*h*(3 + m))*(c + d*x)^(-2 - m)*(e + f*x)^(1 + m))/(d*(d*e - c*f)^2*(2 + m)*(3 + m)) - (f*(2*d*f*g + c*f*h*(1 + m) - d*e*h*(3 + m))*(c + d*x)^(-1 - m)*(e + f*x)^(1 + m))/(d*(d*e - c*f)^3*(1 + m)*(2 + m)*(3 + m))","A",3,3,24,0.1250,1,"{79, 45, 37}"
136,1,190,0,0.1185191,"\int \frac{(A+B x) (c+d x)^n (e+f x)^p}{a+b x} \, dx","Int[((A + B*x)*(c + d*x)^n*(e + f*x)^p)/(a + b*x),x]","\frac{B (c+d x)^{n+1} (e+f x)^p \left(\frac{d (e+f x)}{d e-c f}\right)^{-p} \, _2F_1\left(n+1,-p;n+2;-\frac{f (c+d x)}{d e-c f}\right)}{b d (n+1)}-\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;-p,1;n+2;-\frac{f (c+d x)}{d e-c f},\frac{b (c+d x)}{b c-a d}\right)}{b (n+1) (b c-a d)}","-\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,"-(((A*b - a*B)*(c + d*x)^(1 + n)*(e + f*x)^p*AppellF1[1 + n, -p, 1, 2 + n, -((f*(c + d*x))/(d*e - c*f)), (b*(c + d*x))/(b*c - a*d)])/(b*(b*c - a*d)*(1 + n)*((d*(e + f*x))/(d*e - c*f))^p)) + (B*(c + d*x)^(1 + n)*(e + f*x)^p*Hypergeometric2F1[1 + n, -p, 2 + n, -((f*(c + d*x))/(d*e - c*f))])/(b*d*(1 + n)*((d*(e + f*x))/(d*e - c*f))^p)","A",5,5,27,0.1852,0,"{157, 70, 69, 137, 136}"
137,1,220,0,0.1270399,"\int \frac{(a+b x)^m (A+B x) (c+d x)^{-m}}{e+f x} \, dx","Int[((a + b*x)^m*(A + B*x))/((c + d*x)^m*(e + f*x)),x]","\frac{(a+b x)^m (B e-A f) (c+d x)^{-m} \, _2F_1\left(1,m;m+1;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)}{f^2 m}-\frac{(a+b x)^m (B e-A f) (c+d x)^{-m} \left(\frac{b (c+d x)}{b c-a d}\right)^m \, _2F_1\left(m,m;m+1;-\frac{d (a+b x)}{b c-a d}\right)}{f^2 m}+\frac{B (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)}{b f (m+1)}","-\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,"((B*e - A*f)*(a + b*x)^m*Hypergeometric2F1[1, m, 1 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))])/(f^2*m*(c + d*x)^m) - ((B*e - A*f)*(a + b*x)^m*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, m, 1 + m, -((d*(a + b*x))/(b*c - a*d))])/(f^2*m*(c + d*x)^m) + (B*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))])/(b*f*(1 + m)*(c + d*x)^m)","A",7,5,29,0.1724,1,"{157, 70, 69, 105, 131}"
138,1,250,0,0.2171651,"\int \frac{(A+B x) (c+d x)^n (e+f x)^p}{\sqrt{a+b x}} \, dx","Int[((A + B*x)*(c + d*x)^n*(e + f*x)^p)/Sqrt[a + b*x],x]","\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}","\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,"(2*(A*b - a*B)*Sqrt[a + b*x]*(c + d*x)^n*(e + f*x)^p*AppellF1[1/2, -n, -p, 3/2, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^2*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p) + (2*B*(a + b*x)^(3/2)*(c + d*x)^n*(e + f*x)^p*AppellF1[3/2, -n, -p, 5/2, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(3*b^2*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p)","A",7,4,29,0.1379,1,"{159, 140, 139, 138}"
139,1,530,0,1.1786433,"\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^3 \, dx","Int[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x)^3,x]","\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)}","\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,"((b*g - a*h)^3*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[1 + m, -n, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^4*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p) + (3*h*(b*g - a*h)^2*(a + b*x)^(2 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[2 + m, -n, -p, 3 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^4*(2 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p) + (3*h^2*(b*g - a*h)*(a + b*x)^(3 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[3 + m, -n, -p, 4 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^4*(3 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p) + (h^3*(a + b*x)^(4 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[4 + m, -n, -p, 5 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^4*(4 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p)","A",31,5,29,0.1724,1,"{181, 159, 140, 139, 138}"
140,1,393,0,0.492588,"\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^2 \, dx","Int[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x)^2,x]","\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)}","\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,"((b*g - a*h)^2*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[1 + m, -n, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^3*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p) + (2*h*(b*g - a*h)*(a + b*x)^(2 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[2 + m, -n, -p, 3 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^3*(2 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p) + (h^2*(a + b*x)^(3 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[3 + m, -n, -p, 4 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^3*(3 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p)","A",15,5,29,0.1724,1,"{181, 159, 140, 139, 138}"
141,1,256,0,0.2104476,"\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x) \, dx","Int[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x),x]","\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)}","\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,"((b*g - a*h)*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[1 + m, -n, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^2*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p) + (h*(a + b*x)^(2 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[2 + m, -n, -p, 3 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^2*(2 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p)","A",7,4,27,0.1481,1,"{159, 140, 139, 138}"
142,1,123,0,0.0830603,"\int (a+b x)^m (c+d x)^n (e+f x)^p \, dx","Int[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p,x]","\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)}","\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,"((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1[1 + m, -n, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p)","A",3,3,22,0.1364,1,"{140, 139, 138}"
143,0,0,0,0.0075481,"\int \frac{(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx","Int[((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,"Defer[Int][((a + b*x)^m*(c + d*x)^n*(e + f*x)^p)/(g + h*x), x]","A",0,0,0,0,-1,"{}"
144,1,268,0,0.211948,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-m-n} \, dx","Int[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-m - n),x]","\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)}","\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,"((A*b - a*B)*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-m - n)*((b*(e + f*x))/(b*e - a*f))^(m + n)*AppellF1[1 + m, -n, m + n, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^2*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n) + (B*(a + b*x)^(2 + m)*(c + d*x)^n*(e + f*x)^(-m - n)*((b*(e + f*x))/(b*e - a*f))^(m + n)*AppellF1[2 + m, -n, m + n, 3 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b^2*(2 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",7,4,33,0.1212,1,"{159, 140, 139, 138}"
145,1,283,0,0.2080655,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-1-m-n} \, dx","Int[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-1 - m - n),x]","\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)}","\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,"(B*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-m - n)*((b*(e + f*x))/(b*e - a*f))^(m + n)*AppellF1[1 + m, -n, m + n, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(b*f*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n) - ((B*e - A*f)*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-m - n)*((b*(e + f*x))/(b*e - a*f))^(m + n)*AppellF1[1 + m, -n, 1 + m + n, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(f*(b*e - a*f)*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",7,4,34,0.1176,1,"{159, 140, 139, 138}"
146,1,277,0,0.1472952,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-2-m-n} \, dx","Int[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-2 - m - n),x]","\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)}","\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,"(B*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-m - n)*((b*(e + f*x))/(b*e - a*f))^(m + n)*AppellF1[1 + m, -n, 1 + m + n, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))])/(f*(b*e - a*f)*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n) - ((B*e - A*f)*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*Hypergeometric2F1[1 + m, -n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))])/(f*(b*e - a*f)*(1 + m)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)","A",5,5,34,0.1471,1,"{159, 140, 139, 138, 132}"
147,1,261,0,0.2265974,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-3-m-n} \, dx","Int[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-3 - m - n),x]","\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 c f (m+n+2)+B d e (n+1))+b (A c f (n+1)-A 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)}","\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,"((B*e - A*f)*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-2 - m - n))/((b*e - a*f)*(d*e - c*f)*(2 + m + n)) - ((b*(B*c*e*(1 + m) + A*c*f*(1 + n) - A*d*e*(2 + m + n)) + a*(A*d*f*(1 + m) + B*d*e*(1 + n) - B*c*f*(2 + m + n)))*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*Hypergeometric2F1[1 + m, -n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))])/((b*e - a*f)^2*(d*e - c*f)*(1 + m)*(2 + m + n)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)","A",3,3,34,0.08824,1,"{155, 12, 132}"
148,1,558,0,0.9808002,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-4-m-n} \, dx","Int[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-4 - m - n),x]","\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 (a (A d f (m+2)-B c f (m+n+3)+B d e (n+1))+b (A c f (n+2)-A d e (m+n+3)+B c e (m+1)))+f (a d+b c) (a (A d f (m+2)-B c f (m+n+3)+B d e (n+1))+b (A c f (n+2)-A d e (m+n+3)+B c e (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 c f (m+n+3)+B d e (n+1))+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 c f (m+n+3)+B d e (n+1))+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}","\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,"((B*e - A*f)*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-3 - m - n))/((b*e - a*f)*(d*e - c*f)*(3 + m + n)) + ((a*f*(A*d*f*(2 + m) + B*d*e*(1 + n) - B*c*f*(3 + m + n)) + b*(B*e*(d*e + c*f*(1 + m)) + A*f*(c*f*(2 + n) - d*e*(4 + m + n))))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-2 - m - n))/((b*e - a*f)^2*(d*e - c*f)^2*(2 + m + n)*(3 + m + n)) + (((2 + m + n)*(a*b*c*d*f*(B*e - A*f) - b*d*e*(b*(B*c*e*(1 + m) + A*c*f*(2 + n) - A*d*e*(3 + m + n)) + a*(A*d*f*(2 + m) + B*d*e*(1 + n) - B*c*f*(3 + m + n))) + (b*c + a*d)*f*(b*(B*c*e*(1 + m) + A*c*f*(2 + n) - A*d*e*(3 + m + n)) + a*(A*d*f*(2 + m) + B*d*e*(1 + n) - B*c*f*(3 + m + n)))) - (b*c*(1 + m) + a*d*(1 + n))*(a*f*(A*d*f*(2 + m) + B*d*e*(1 + n) - B*c*f*(3 + m + n)) + b*(B*e*(d*e + c*f*(1 + m)) + A*f*(c*f*(2 + n) - d*e*(4 + m + n)))))*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*Hypergeometric2F1[1 + m, -n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))])/((b*e - a*f)^3*(d*e - c*f)^2*(1 + m)*(2 + m + n)*(3 + m + n)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)","A",4,3,34,0.08824,1,"{155, 12, 132}"
149,1,79,0,0.1423935,"\int \frac{x \left(a+b x+c x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(x*(a + b*x + c*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{\sqrt{1-d^2 x^2} \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4}+\frac{b \sin ^{-1}(d x)}{2 d^3}-\frac{c x^2 \sqrt{1-d^2 x^2}}{3 d^2}","-\frac{\sqrt{1-d^2 x^2} \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4}+\frac{b \sin ^{-1}(d x)}{2 d^3}-\frac{c x^2 \sqrt{1-d^2 x^2}}{3 d^2}",1,"-(c*x^2*Sqrt[1 - d^2*x^2])/(3*d^2) - ((2*(2*c + 3*a*d^2) + 3*b*d^2*x)*Sqrt[1 - d^2*x^2])/(6*d^4) + (b*ArcSin[d*x])/(2*d^3)","A",4,4,31,0.1290,1,"{1609, 1809, 780, 216}"
150,1,63,0,0.0613671,"\int \frac{a+b x+c x^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\frac{\left(2 a d^2+c\right) \sin ^{-1}(d x)}{2 d^3}-\frac{b \sqrt{1-d^2 x^2}}{d^2}-\frac{c x \sqrt{1-d^2 x^2}}{2 d^2}","\frac{\left(2 a d^2+c\right) \sin ^{-1}(d x)}{2 d^3}-\frac{b \sqrt{1-d^2 x^2}}{d^2}-\frac{c x \sqrt{1-d^2 x^2}}{2 d^2}",1,"-((b*Sqrt[1 - d^2*x^2])/d^2) - (c*x*Sqrt[1 - d^2*x^2])/(2*d^2) + ((c + 2*a*d^2)*ArcSin[d*x])/(2*d^3)","A",4,4,30,0.1333,1,"{899, 1815, 641, 216}"
151,1,48,0,0.1840225,"\int \frac{a+b x+c x^2}{x \sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-a \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)+\frac{b \sin ^{-1}(d x)}{d}-\frac{c \sqrt{1-d^2 x^2}}{d^2}","-a \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)+\frac{b \sin ^{-1}(d x)}{d}-\frac{c \sqrt{1-d^2 x^2}}{d^2}",1,"-((c*Sqrt[1 - d^2*x^2])/d^2) + (b*ArcSin[d*x])/d - a*ArcTanh[Sqrt[1 - d^2*x^2]]","A",7,7,33,0.2121,1,"{1609, 1809, 844, 216, 266, 63, 208}"
152,1,48,0,0.1833127,"\int \frac{a+b x+c x^2}{x^2 \sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^2*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{a \sqrt{1-d^2 x^2}}{x}-b \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)+\frac{c \sin ^{-1}(d x)}{d}","-\frac{a \sqrt{1-d^2 x^2}}{x}-b \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)+\frac{c \sin ^{-1}(d x)}{d}",1,"-((a*Sqrt[1 - d^2*x^2])/x) + (c*ArcSin[d*x])/d - b*ArcTanh[Sqrt[1 - d^2*x^2]]","A",7,7,33,0.2121,1,"{1609, 1807, 844, 216, 266, 63, 208}"
153,1,71,0,0.1880451,"\int \frac{a+b x+c x^2}{x^3 \sqrt{1-d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^3*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{1}{2} \left(a d^2+2 c\right) \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)-\frac{a \sqrt{1-d^2 x^2}}{2 x^2}-\frac{b \sqrt{1-d^2 x^2}}{x}","-\frac{1}{2} \left(a d^2+2 c\right) \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)-\frac{a \sqrt{1-d^2 x^2}}{2 x^2}-\frac{b \sqrt{1-d^2 x^2}}{x}",1,"-(a*Sqrt[1 - d^2*x^2])/(2*x^2) - (b*Sqrt[1 - d^2*x^2])/x - ((2*c + a*d^2)*ArcTanh[Sqrt[1 - d^2*x^2]])/2","A",6,6,33,0.1818,1,"{1609, 1807, 807, 266, 63, 208}"
154,1,151,0,0.1462623,"\int \frac{x \left(a+b x+c x^2\right)}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(x*(a + b*x + c*x^2))/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","-\frac{\left(1-d^2 x^2\right) \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4 \sqrt{d x-1} \sqrt{d x+1}}+\frac{b \sqrt{d^2 x^2-1} \tanh ^{-1}\left(\frac{d x}{\sqrt{d^2 x^2-1}}\right)}{2 d^3 \sqrt{d x-1} \sqrt{d x+1}}-\frac{c x^2 \left(1-d^2 x^2\right)}{3 d^2 \sqrt{d x-1} \sqrt{d x+1}}","\frac{\sqrt{d x-1} \sqrt{d x+1} \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4}+\frac{b \cosh ^{-1}(d x)}{2 d^3}+\frac{c x^2 \sqrt{d x-1} \sqrt{d x+1}}{3 d^2}",1,"-(c*x^2*(1 - d^2*x^2))/(3*d^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) - ((2*(2*c + 3*a*d^2) + 3*b*d^2*x)*(1 - d^2*x^2))/(6*d^4*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + (b*Sqrt[-1 + d^2*x^2]*ArcTanh[(d*x)/Sqrt[-1 + d^2*x^2]])/(2*d^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","A",5,5,30,0.1667,1,"{1610, 1809, 780, 217, 206}"
155,1,135,0,0.0711419,"\int \frac{a+b x+c x^2}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{\sqrt{d^2 x^2-1} \left(2 a d^2+c\right) \tanh ^{-1}\left(\frac{d x}{\sqrt{d^2 x^2-1}}\right)}{2 d^3 \sqrt{d x-1} \sqrt{d x+1}}-\frac{b \left(1-d^2 x^2\right)}{d^2 \sqrt{d x-1} \sqrt{d x+1}}-\frac{c x \left(1-d^2 x^2\right)}{2 d^2 \sqrt{d x-1} \sqrt{d x+1}}","\frac{\left(2 a d^2+c\right) \cosh ^{-1}(d x)}{2 d^3}+\frac{\sqrt{d x-1} \sqrt{d x+1} (2 b+c x)}{2 d^2}",1,"-((b*(1 - d^2*x^2))/(d^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x])) - (c*x*(1 - d^2*x^2))/(2*d^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + ((c + 2*a*d^2)*Sqrt[-1 + d^2*x^2]*ArcTanh[(d*x)/Sqrt[-1 + d^2*x^2]])/(2*d^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","B",5,5,29,0.1724,1,"{901, 1815, 641, 217, 206}"
156,1,135,0,0.1840606,"\int \frac{a+b x+c x^2}{x \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{a \sqrt{d^2 x^2-1} \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{\sqrt{d x-1} \sqrt{d x+1}}+\frac{b \sqrt{d^2 x^2-1} \tanh ^{-1}\left(\frac{d x}{\sqrt{d^2 x^2-1}}\right)}{d \sqrt{d x-1} \sqrt{d x+1}}-\frac{c \left(1-d^2 x^2\right)}{d^2 \sqrt{d x-1} \sqrt{d x+1}}","a \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{b \cosh ^{-1}(d x)}{d}+\frac{c \sqrt{d x-1} \sqrt{d x+1}}{d^2}",1,"-((c*(1 - d^2*x^2))/(d^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x])) + (a*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + (b*Sqrt[-1 + d^2*x^2]*ArcTanh[(d*x)/Sqrt[-1 + d^2*x^2]])/(d*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","B",8,8,32,0.2500,1,"{1610, 1809, 844, 217, 206, 266, 63, 205}"
157,1,135,0,0.182098,"\int \frac{a+b x+c x^2}{x^2 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","-\frac{a \left(1-d^2 x^2\right)}{x \sqrt{d x-1} \sqrt{d x+1}}+\frac{b \sqrt{d^2 x^2-1} \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{\sqrt{d x-1} \sqrt{d x+1}}+\frac{c \sqrt{d^2 x^2-1} \tanh ^{-1}\left(\frac{d x}{\sqrt{d^2 x^2-1}}\right)}{d \sqrt{d x-1} \sqrt{d x+1}}","\frac{a \sqrt{d x-1} \sqrt{d x+1}}{x}+b \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{c \cosh ^{-1}(d x)}{d}",1,"-((a*(1 - d^2*x^2))/(x*Sqrt[-1 + d*x]*Sqrt[1 + d*x])) + (b*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + (c*Sqrt[-1 + d^2*x^2]*ArcTanh[(d*x)/Sqrt[-1 + d^2*x^2]])/(d*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","B",8,8,32,0.2500,1,"{1610, 1807, 844, 217, 206, 266, 63, 205}"
158,1,129,0,0.1888468,"\int \frac{a+b x+c x^2}{x^3 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{\sqrt{d^2 x^2-1} \left(a d^2+2 c\right) \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{2 \sqrt{d x-1} \sqrt{d x+1}}-\frac{a \left(1-d^2 x^2\right)}{2 x^2 \sqrt{d x-1} \sqrt{d x+1}}-\frac{b \left(1-d^2 x^2\right)}{x \sqrt{d x-1} \sqrt{d x+1}}","\frac{1}{2} \left(a d^2+2 c\right) \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{a \sqrt{d x-1} \sqrt{d x+1}}{2 x^2}+\frac{b \sqrt{d x-1} \sqrt{d x+1}}{x}",1,"-(a*(1 - d^2*x^2))/(2*x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) - (b*(1 - d^2*x^2))/(x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + ((2*c + a*d^2)*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(2*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","A",6,6,32,0.1875,1,"{1610, 1807, 807, 266, 63, 205}"
159,1,171,0,0.2208458,"\int \frac{a+b x+c x^2}{x^4 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Int[(a + b*x + c*x^2)/(x^4*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","-\frac{\left(1-d^2 x^2\right) \left(2 a d^2+3 c\right)}{3 x \sqrt{d x-1} \sqrt{d x+1}}-\frac{a \left(1-d^2 x^2\right)}{3 x^3 \sqrt{d x-1} \sqrt{d x+1}}-\frac{b \left(1-d^2 x^2\right)}{2 x^2 \sqrt{d x-1} \sqrt{d x+1}}+\frac{b d^2 \sqrt{d^2 x^2-1} \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{2 \sqrt{d x-1} \sqrt{d x+1}}","\frac{\sqrt{d x-1} \sqrt{d x+1} \left(2 a d^2+3 c\right)}{3 x}+\frac{a \sqrt{d x-1} \sqrt{d x+1}}{3 x^3}+\frac{1}{2} b d^2 \tan ^{-1}\left(\sqrt{d x-1} \sqrt{d x+1}\right)+\frac{b \sqrt{d x-1} \sqrt{d x+1}}{2 x^2}",1,"-(a*(1 - d^2*x^2))/(3*x^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) - (b*(1 - d^2*x^2))/(2*x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) - ((3*c + 2*a*d^2)*(1 - d^2*x^2))/(3*x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + (b*d^2*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(2*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","A",7,7,32,0.2188,1,"{1610, 1807, 835, 807, 266, 63, 205}"