1,1,112,112,0.0518835,"\int (a+b x) (c+d x) (e+f x) (g+h x) \, dx","Integrate[(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+b d e h+b d f g)+\frac{1}{3} x^3 (a c f h+a d e h+a d f g+b c e h+b c f g+b d e g)+\frac{1}{2} x^2 (a c e h+a c f g+a 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 + a*c*f*g + a*c*e*h)*x^2)/2 + ((b*d*e*g + b*c*f*g + a*d*f*g + b*c*e*h + a*d*e*h + a*c*f*h)*x^3)/3 + ((b*d*f*g + b*d*e*h + b*c*f*h + a*d*f*h)*x^4)/4 + (b*d*f*h*x^5)/5","A",1
2,1,123,126,0.0881283,"\int \frac{(a+b x) (c+d x) (e+f x)}{g+h x} \, dx","Integrate[((a + b*x)*(c + d*x)*(e + f*x))/(g + h*x),x]","\frac{h x \left(3 a h (2 c f h+d (2 e h-2 f g+f h x))+b \left(3 c h (2 e h-2 f g+f h x)+3 d e h (h x-2 g)+d f \left(6 g^2-3 g h x+2 h^2 x^2\right)\right)\right)-6 (b g-a h) (d g-c h) (f g-e h) \log (g+h x)}{6 h^4}","-\frac{(b g-a h) (d g-c h) (f g-e h) \log (g+h x)}{h^4}+\frac{x (b (d g-c h) (f g-e h)-a h (-c f h-d e h+d f g))}{h^3}+\frac{x^2 (a d f h-b (-c f h-d e h+d f g))}{2 h^2}+\frac{b d f x^3}{3 h}",1,"(h*x*(3*a*h*(2*c*f*h + d*(-2*f*g + 2*e*h + f*h*x)) + b*(3*d*e*h*(-2*g + h*x) + 3*c*h*(-2*f*g + 2*e*h + f*h*x) + d*f*(6*g^2 - 3*g*h*x + 2*h^2*x^2))) - 6*(b*g - a*h)*(d*g - c*h)*(f*g - e*h)*Log[g + h*x])/(6*h^4)","A",1
3,1,85,84,0.062466,"\int \frac{(a+b x) (c+d x)}{(e+f x) (g+h x)} \, dx","Integrate[((a + b*x)*(c + d*x))/((e + f*x)*(g + h*x)),x]","\frac{f (b d h x (f g-e h)-f (b g-a h) (d g-c h) \log (g+h x))+h^2 (b e-a f) (d e-c f) \log (e+f x)}{f^2 h^2 (f g-e 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*e - a*f)*(d*e - c*f)*h^2*Log[e + f*x] + f*(b*d*h*(f*g - e*h)*x - f*(b*g - a*h)*(d*g - c*h)*Log[g + h*x]))/(f^2*h^2*(f*g - e*h))","A",1
4,1,102,108,0.0817405,"\int \frac{a+b x}{(c+d x) (e+f x) (g+h x)} \, dx","Integrate[(a + b*x)/((c + d*x)*(e + f*x)*(g + h*x)),x]","\frac{(b c-a d) \log (c+d x) (f g-e h)-(b e-a f) (d g-c h) \log (e+f x)+(b g-a h) (d e-c f) \log (g+h x)}{(d e-c f) (d g-c h) (e h-f g)}","-\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)*(f*g - e*h)*Log[c + d*x] - (b*e - a*f)*(d*g - c*h)*Log[e + f*x] + (d*e - c*f)*(b*g - a*h)*Log[g + h*x])/((d*e - c*f)*(d*g - c*h)*(-(f*g) + e*h))","A",1
5,1,164,163,0.2011899,"\int \frac{1}{(a+b x) (c+d x) (e+f x) (g+h x)} \, dx","Integrate[1/((a + b*x)*(c + d*x)*(e + f*x)*(g + h*x)),x]","\frac{b^2 \log (a+b x)}{(b c-a d) (b e-a f) (b g-a h)}-\frac{d^2 \log (c+d x)}{(b c-a d) (c f-d e) (c h-d g)}-\frac{f^2 \log (e+f x)}{(b e-a f) (d e-c f) (e h-f g)}-\frac{h^2 \log (g+h x)}{(b g-a h) (d g-c h) (f g-e h)}","\frac{b^2 \log (a+b x)}{(b c-a d) (b e-a f) (b g-a h)}-\frac{d^2 \log (c+d x)}{(b c-a d) (d e-c f) (d g-c h)}+\frac{f^2 \log (e+f x)}{(b e-a f) (d e-c f) (f g-e h)}-\frac{h^2 \log (g+h x)}{(b g-a h) (d g-c h) (f g-e h)}",1,"(b^2*Log[a + b*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)) - (d^2*Log[c + d*x])/((b*c - a*d)*(-(d*e) + c*f)*(-(d*g) + c*h)) - (f^2*Log[e + f*x])/((b*e - a*f)*(d*e - c*f)*(-(f*g) + e*h)) - (h^2*Log[g + h*x])/((b*g - a*h)*(d*g - c*h)*(f*g - e*h))","A",1
6,1,23,23,0.0064463,"\int \frac{x}{(1+x) (2+x) (3+x)} \, dx","Integrate[x/((1 + x)*(2 + x)*(3 + x)),x]","-\frac{1}{2} \log (x+1)+2 \log (x+2)-\frac{3}{2} \log (x+3)","-\frac{1}{2} \log (x+1)+2 \log (x+2)-\frac{3}{2} \log (x+3)",1,"-1/2*Log[1 + x] + 2*Log[2 + x] - (3*Log[3 + x])/2","A",1
7,1,33,43,0.023979,"\int \frac{-x^2+x^3}{(-6+x) (3+5 x)^3} \, dx","Integrate[(-x^2 + x^3)/((-6 + x)*(3 + 5*x)^3),x]","\frac{\frac{99 (335 x+157)}{(5 x+3)^2}+2500 \log (x-6)+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,"((99*(157 + 335*x))/(3 + 5*x)^2 + 2500*Log[-6 + x] + 1493*Log[3 + 5*x])/499125","A",1
8,1,205,227,0.2750064,"\int \frac{(a+b x)^3 \sqrt{c+d x} (e+f x)}{x} \, dx","Integrate[((a + b*x)^3*Sqrt[c + d*x]*(e + f*x))/x,x]","\frac{2 \left(3 d e \left(105 a^3 d^3 \sqrt{c+d x}-105 a^3 \sqrt{c} d^3 \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)+35 b (c+d x)^{3/2} \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)-21 b^2 (c+d x)^{5/2} (2 b c-3 a d)+15 b^3 (c+d x)^{7/2}\right)-f (c+d x)^{3/2} \left(135 b^2 (c+d x)^2 (b c-a d)-189 b (c+d x) (b c-a d)^2+105 (b c-a d)^3-35 b^3 (c+d x)^3\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 (c+d x)^{3/2} \left(2 \left(20 a^3 d^3 f+3 a^2 b d^2 (45 d e-16 c f)-9 a b^2 c d (7 d e-4 c f)+4 b^3 c^2 (3 d e-2 c f)\right)+3 b d x \left(21 a b d^2 e-4 (b c-a d) (2 a d f-2 b c f+3 b d e)\right)\right)}{315 d^4}+\frac{2 (a+b x)^2 (c+d x)^{3/2} (2 a d f-2 b c f+3 b d e)}{21 d^2}+\frac{2 f (a+b x)^3 (c+d x)^{3/2}}{9 d}",1,"(2*(-(f*(c + d*x)^(3/2)*(105*(b*c - a*d)^3 - 189*b*(b*c - a*d)^2*(c + d*x) + 135*b^2*(b*c - a*d)*(c + d*x)^2 - 35*b^3*(c + d*x)^3)) + 3*d*e*(105*a^3*d^3*Sqrt[c + d*x] + 35*b*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*(c + d*x)^(3/2) - 21*b^2*(2*b*c - 3*a*d)*(c + d*x)^(5/2) + 15*b^3*(c + d*x)^(7/2) - 105*a^3*Sqrt[c]*d^3*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])))/(315*d^4)","A",1
9,1,145,146,0.1825591,"\int \frac{(a+b x)^2 \sqrt{c+d x} (e+f x)}{x} \, dx","Integrate[((a + b*x)^2*Sqrt[c + d*x]*(e + f*x))/x,x]","\frac{2 \left(7 d e \left(\sqrt{c+d x} \left(15 a^2 d^2+10 a b d (c+d x)+b^2 \left(-2 c^2+c d x+3 d^2 x^2\right)\right)-15 a^2 \sqrt{c} d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)\right)+f (c+d x)^{3/2} \left(-42 b (c+d x) (b c-a d)+35 (b c-a d)^2+15 b^2 (c+d x)^2\right)\right)}{105 d^3}","\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*(f*(c + d*x)^(3/2)*(35*(b*c - a*d)^2 - 42*b*(b*c - a*d)*(c + d*x) + 15*b^2*(c + d*x)^2) + 7*d*e*(Sqrt[c + d*x]*(15*a^2*d^2 + 10*a*b*d*(c + d*x) + b^2*(-2*c^2 + c*d*x + 3*d^2*x^2)) - 15*a^2*Sqrt[c]*d^2*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])))/(105*d^3)","A",1
10,1,81,77,0.1590865,"\int \frac{(a+b x) \sqrt{c+d x} (e+f x)}{x} \, dx","Integrate[((a + b*x)*Sqrt[c + d*x]*(e + f*x))/x,x]","\frac{2 \sqrt{c+d x} (5 a d (c f+3 d e+d f x)-b (c+d x) (2 c f-5 d e-3 d f x))}{15 d^2}-2 a \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)","-\frac{2 (c+d x)^{3/2} (-5 d (a f+b e)+2 b c f-3 b d f x)}{15 d^2}+2 a e \sqrt{c+d x}-2 a \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)",1,"(2*Sqrt[c + d*x]*(-(b*(c + d*x)*(-5*d*e + 2*c*f - 3*d*f*x)) + 5*a*d*(3*d*e + c*f + d*f*x)))/(15*d^2) - 2*a*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]","A",1
11,1,55,54,0.0479496,"\int \frac{\sqrt{c+d x} (e+f x)}{x} \, dx","Integrate[(Sqrt[c + d*x]*(e + f*x))/x,x]","e \left(2 \sqrt{c+d x}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)\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*f*(c + d*x)^(3/2))/(3*d) + e*(2*Sqrt[c + d*x] - 2*Sqrt[c]*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])","A",1
12,1,101,101,0.1217006,"\int \frac{\sqrt{c+d x} (e+f x)}{x (a+b x)} \, dx","Integrate[(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",1
13,1,124,127,0.4389615,"\int \frac{\sqrt{c+d x} (e+f x)}{x (a+b x)^2} \, dx","Integrate[(Sqrt[c + d*x]*(e + f*x))/(x*(a + b*x)^2),x]","\frac{-\frac{\left(a^2 d f+a b d e-2 b^2 c e\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{b^{3/2} \sqrt{b c-a d}}+\frac{a \sqrt{c+d x} (b e-a f)}{b (a+b x)}-2 \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2}","\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,"((a*(b*e - a*f)*Sqrt[c + d*x])/(b*(a + b*x)) - 2*Sqrt[c]*e*ArcTanh[Sqrt[c + d*x]/Sqrt[c]] - ((-2*b^2*c*e + a*b*d*e + a^2*d*f)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]])/(b^(3/2)*Sqrt[b*c - a*d]))/a^2","A",1
14,1,260,208,0.602415,"\int \frac{\sqrt{c+d x} (e+f x)}{x (a+b x)^3} \, dx","Integrate[(Sqrt[c + d*x]*(e + f*x))/(x*(a + b*x)^3),x]","\frac{-\frac{(c+d x)^{3/2} \left(a^2 d f-5 a b d e+4 b^2 c e\right)}{2 a (a+b x) (a d-b c)}+\frac{4 e (b c-a d) \left(\sqrt{c+d x}-\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)\right)}{a^2}+\frac{\left(a^3 d^2 f+3 a^2 b d^2 e-12 a b^2 c d e+8 b^3 c^2 e\right) \left(\sqrt{b} \sqrt{c+d x}-\sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)\right)}{2 a^2 b^{3/2} (a d-b c)}+\frac{(c+d x)^{3/2} (b e-a f)}{(a+b x)^2}}{2 a (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} \left(a^2 (-d) f-3 a b d e+4 b^2 c e\right)}{4 a^2 b (a+b x) (b c-a d)}+\frac{\left(a^3 d^2 f+3 a^2 b d^2 e-12 a b^2 c d e+8 b^3 c^2 e\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{b c-a d}}\right)}{4 a^3 b^{3/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x} (b e-a f)}{2 a b (a+b x)^2}",1,"(((b*e - a*f)*(c + d*x)^(3/2))/(a + b*x)^2 - ((4*b^2*c*e - 5*a*b*d*e + a^2*d*f)*(c + d*x)^(3/2))/(2*a*(-(b*c) + a*d)*(a + b*x)) + (4*(b*c - a*d)*e*(Sqrt[c + d*x] - Sqrt[c]*ArcTanh[Sqrt[c + d*x]/Sqrt[c]]))/a^2 + ((8*b^3*c^2*e - 12*a*b^2*c*d*e + 3*a^2*b*d^2*e + a^3*d^2*f)*(Sqrt[b]*Sqrt[c + d*x] - Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[b*c - a*d]]))/(2*a^2*b^(3/2)*(-(b*c) + a*d)))/(2*a*(b*c - a*d))","A",1
15,1,204,226,0.2808634,"\int \frac{\sqrt{a+b x} (c+d x)^3 (e+f x)}{x} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^3*(e + f*x))/x,x]","\frac{2 \left(3 b e \left(35 d (a+b x)^{3/2} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)+105 b^3 c^3 \sqrt{a+b x}-105 \sqrt{a} b^3 c^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+21 d^2 (a+b x)^{5/2} (3 b c-2 a d)+15 d^3 (a+b x)^{7/2}\right)+f (a+b x)^{3/2} \left(135 d^2 (a+b x)^2 (b c-a d)+189 d (a+b x) (b c-a d)^2+105 (b c-a d)^3+35 d^3 (a+b x)^3\right)\right)}{315 b^4}","-\frac{2 (a+b x)^{3/2} \left(2 \left(8 a^3 d^3 f-12 a^2 b d^2 (3 c f+d e)+3 a b^2 c d (16 c f+21 d e)-5 b^3 c^2 (4 c f+27 d e)\right)-3 b d x \left(4 (b c-a d) (-2 a d f+2 b c f+3 b d e)+21 b^2 c d e\right)\right)}{315 b^4}+\frac{2 (a+b x)^{3/2} (c+d x)^2 (-2 a d f+2 b c f+3 b d e)}{21 b^2}+2 c^3 e \sqrt{a+b x}-2 \sqrt{a} c^3 e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+\frac{2 f (a+b x)^{3/2} (c+d x)^3}{9 b}",1,"(2*(f*(a + b*x)^(3/2)*(105*(b*c - a*d)^3 + 189*d*(b*c - a*d)^2*(a + b*x) + 135*d^2*(b*c - a*d)*(a + b*x)^2 + 35*d^3*(a + b*x)^3) + 3*b*e*(105*b^3*c^3*Sqrt[a + b*x] + 35*d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*(a + b*x)^(3/2) + 21*d^2*(3*b*c - 2*a*d)*(a + b*x)^(5/2) + 15*d^3*(a + b*x)^(7/2) - 105*Sqrt[a]*b^3*c^3*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])))/(315*b^4)","A",1
16,1,146,145,0.17946,"\int \frac{\sqrt{a+b x} (c+d x)^2 (e+f x)}{x} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)^2*(e + f*x))/x,x]","\frac{2 \left(7 b e \left(15 b^2 c^2 \sqrt{a+b x}-15 \sqrt{a} b^2 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+5 d (a+b x)^{3/2} (2 b c-a d)+3 d^2 (a+b x)^{5/2}\right)+f (a+b x)^{3/2} \left(42 d (a+b x) (b c-a d)+35 (b c-a d)^2+15 d^2 (a+b x)^2\right)\right)}{105 b^3}","\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*(f*(a + b*x)^(3/2)*(35*(b*c - a*d)^2 + 42*d*(b*c - a*d)*(a + b*x) + 15*d^2*(a + b*x)^2) + 7*b*e*(15*b^2*c^2*Sqrt[a + b*x] + 5*d*(2*b*c - a*d)*(a + b*x)^(3/2) + 3*d^2*(a + b*x)^(5/2) - 15*Sqrt[a]*b^2*c^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])))/(105*b^3)","A",1
17,1,87,77,0.1322196,"\int \frac{\sqrt{a+b x} (c+d x) (e+f x)}{x} \, dx","Integrate[(Sqrt[a + b*x]*(c + d*x)*(e + f*x))/x,x]","\frac{2 (a+b x)^{3/2} (-a d f+b c f+b d e)}{3 b^2}+\frac{2 d f (a+b x)^{5/2}}{5 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*(b*d*e + b*c*f - a*d*f)*(a + b*x)^(3/2))/(3*b^2) + (2*d*f*(a + b*x)^(5/2))/(5*b^2) - 2*Sqrt[a]*c*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]","A",1
18,1,55,54,0.0495676,"\int \frac{\sqrt{a+b x} (e+f x)}{x} \, dx","Integrate[(Sqrt[a + b*x]*(e + f*x))/x,x]","e \left(2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)\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*f*(a + b*x)^(3/2))/(3*b) + e*(2*Sqrt[a + b*x] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])","A",1
19,1,100,101,0.2265447,"\int \frac{\sqrt{a+b x} (e+f x)}{x (c+d x)} \, dx","Integrate[(Sqrt[a + b*x]*(e + f*x))/(x*(c + d*x)),x]","\frac{-\frac{2 \sqrt{b c-a d} (c f-d e) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{3/2}}+\frac{2 c f \sqrt{a+b x}}{d}-2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c}","\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*c*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]])/d^(3/2) - 2*Sqrt[a]*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/c","A",1
20,1,122,128,0.1957791,"\int \frac{\sqrt{a+b x} (e+f x)}{x (c+d x)^2} \, dx","Integrate[(Sqrt[a + b*x]*(e + f*x))/(x*(c + d*x)^2),x]","\frac{\frac{\left(b c (c f+d e)-2 a d^2 e\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{d^{3/2} \sqrt{b c-a d}}+\frac{c \sqrt{a+b x} (d e-c f)}{d (c+d x)}-2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c^2}","-\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,"((c*(d*e - c*f)*Sqrt[a + b*x])/(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]])/(d^(3/2)*Sqrt[b*c - a*d]) - 2*Sqrt[a]*e*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/c^2","A",1
21,1,259,205,0.5317163,"\int \frac{\sqrt{a+b x} (e+f x)}{x (c+d x)^3} \, dx","Integrate[(Sqrt[a + b*x]*(e + f*x))/(x*(c + d*x)^3),x]","\frac{\frac{2 \left(\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) \left(\sqrt{d} \sqrt{a+b x}-\sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)\right)}{4 d^{3/2}}+2 e (b c-a d)^2 \left(\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)-\sqrt{a+b x}\right)\right)}{c^2 (b c-a d)}-\frac{(a+b x)^{3/2} \left(4 a d^2 e+b c (c f-5 d e)\right)}{2 c (c+d x) (b c-a d)}+\frac{(a+b x)^{3/2} (d e-c f)}{(c+d x)^2}}{2 c (a d-b c)}","-\frac{\left(-8 a^2 d^3 e+12 a b c d^2 e-b^2 c^2 (c f+3 d e)\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{b c-a d}}\right)}{4 c^3 d^{3/2} (b c-a d)^{3/2}}-\frac{2 \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{c^3}-\frac{\sqrt{a+b x} \left(4 a d^2 e-b c (c f+3 d e)\right)}{4 c^2 d (c+d x) (b c-a d)}+\frac{\sqrt{a+b x} (d e-c f)}{2 c d (c+d x)^2}",1,"(((d*e - c*f)*(a + b*x)^(3/2))/(c + d*x)^2 - ((4*a*d^2*e + b*c*(-5*d*e + c*f))*(a + b*x)^(3/2))/(2*c*(b*c - a*d)*(c + d*x)) + (2*(((-12*a*b*c*d^2*e + 8*a^2*d^3*e + b^2*c^2*(3*d*e + c*f))*(Sqrt[d]*Sqrt[a + b*x] - Sqrt[b*c - a*d]*ArcTan[(Sqrt[d]*Sqrt[a + b*x])/Sqrt[b*c - a*d]]))/(4*d^(3/2)) + 2*(b*c - a*d)^2*e*(-Sqrt[a + b*x] + Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])))/(c^2*(b*c - a*d)))/(2*c*(-(b*c) + a*d))","A",1
22,1,89,111,0.0894231,"\int \frac{x^3 (1+a x)}{\sqrt{a x} \sqrt{1-a x}} \, dx","Integrate[(x^3*(1 + a*x))/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","\frac{\sqrt{a} x \left(16 a^4 x^4+24 a^3 x^3+10 a^2 x^2+25 a x-75\right)+75 \sqrt{x} \sqrt{1-a x} \sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{64 a^{7/2} \sqrt{-a x (a x-1)}}","-\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,"(Sqrt[a]*x*(-75 + 25*a*x + 10*a^2*x^2 + 24*a^3*x^3 + 16*a^4*x^4) + 75*Sqrt[x]*Sqrt[1 - a*x]*ArcSin[Sqrt[a]*Sqrt[x]])/(64*a^(7/2)*Sqrt[-(a*x*(-1 + a*x))])","A",1
23,1,81,87,0.031437,"\int \frac{x^2 (1+a x)}{\sqrt{a x} \sqrt{1-a x}} \, dx","Integrate[(x^2*(1 + a*x))/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","\frac{\sqrt{a} x \left(8 a^3 x^3+14 a^2 x^2+11 a x-33\right)+33 \sqrt{x} \sqrt{1-a x} \sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{24 a^{5/2} \sqrt{-a x (a x-1)}}","-\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,"(Sqrt[a]*x*(-33 + 11*a*x + 14*a^2*x^2 + 8*a^3*x^3) + 33*Sqrt[x]*Sqrt[1 - a*x]*ArcSin[Sqrt[a]*Sqrt[x]])/(24*a^(5/2)*Sqrt[-(a*x*(-1 + a*x))])","A",1
24,1,73,63,0.0299981,"\int \frac{x (1+a x)}{\sqrt{a x} \sqrt{1-a x}} \, dx","Integrate[(x*(1 + a*x))/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","\frac{\sqrt{a} x \left(2 a^2 x^2+5 a x-7\right)+7 \sqrt{x} \sqrt{1-a x} \sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{4 a^{3/2} \sqrt{-a x (a x-1)}}","-\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,"(Sqrt[a]*x*(-7 + 5*a*x + 2*a^2*x^2) + 7*Sqrt[x]*Sqrt[1 - a*x]*ArcSin[Sqrt[a]*Sqrt[x]])/(4*a^(3/2)*Sqrt[-(a*x*(-1 + a*x))])","A",1
25,1,61,37,0.0262107,"\int \frac{1+a x}{\sqrt{a x} \sqrt{1-a x}} \, dx","Integrate[(1 + a*x)/(Sqrt[a*x]*Sqrt[1 - a*x]),x]","\frac{\sqrt{a} x (a x-1)+3 \sqrt{x} \sqrt{1-a x} \sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{-a x (a x-1)}}","-\frac{\sqrt{a x} \sqrt{1-a x}}{a}-\frac{3 \sin ^{-1}(1-2 a x)}{2 a}",1,"(Sqrt[a]*x*(-1 + a*x) + 3*Sqrt[x]*Sqrt[1 - a*x]*ArcSin[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[-(a*x*(-1 + a*x))])","A",1
26,1,53,29,0.0253601,"\int \frac{1+a x}{x \sqrt{a x} \sqrt{1-a x}} \, dx","Integrate[(1 + a*x)/(x*Sqrt[a*x]*Sqrt[1 - a*x]),x]","\frac{2 \left(a x+\sqrt{a} \sqrt{x} \sqrt{1-a x} \sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)-1\right)}{\sqrt{-a x (a x-1)}}","-\frac{2 \sqrt{1-a x}}{\sqrt{a x}}-\sin ^{-1}(1-2 a x)",1,"(2*(-1 + a*x + Sqrt[a]*Sqrt[x]*Sqrt[1 - a*x]*ArcSin[Sqrt[a]*Sqrt[x]]))/Sqrt[-(a*x*(-1 + a*x))]","A",1
27,1,29,45,0.012826,"\int \frac{1+a x}{x^2 \sqrt{a x} \sqrt{1-a x}} \, dx","Integrate[(1 + a*x)/(x^2*Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\frac{2 \sqrt{-a x (a x-1)} (5 a x+1)}{3 a x^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*Sqrt[-(a*x*(-1 + a*x))]*(1 + 5*a*x))/(3*a*x^2)","A",1
28,1,37,73,0.0164187,"\int \frac{1+a x}{x^3 \sqrt{a x} \sqrt{1-a x}} \, dx","Integrate[(1 + a*x)/(x^3*Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\frac{2 \sqrt{-a x (a x-1)} \left(6 a^2 x^2+3 a x+1\right)}{5 a x^3}","-\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*Sqrt[-(a*x*(-1 + a*x))]*(1 + 3*a*x + 6*a^2*x^2))/(5*a*x^3)","A",1
29,1,45,97,0.0178223,"\int \frac{1+a x}{x^4 \sqrt{a x} \sqrt{1-a x}} \, dx","Integrate[(1 + a*x)/(x^4*Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\frac{2 \sqrt{-a x (a x-1)} \left(104 a^3 x^3+52 a^2 x^2+39 a x+15\right)}{105 a x^4}","-\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*Sqrt[-(a*x*(-1 + a*x))]*(15 + 39*a*x + 52*a^2*x^2 + 104*a^3*x^3))/(105*a*x^4)","A",1
30,1,53,121,0.0189531,"\int \frac{1+a x}{x^5 \sqrt{a x} \sqrt{1-a x}} \, dx","Integrate[(1 + a*x)/(x^5*Sqrt[a*x]*Sqrt[1 - a*x]),x]","-\frac{2 \sqrt{-a x (a x-1)} \left(272 a^4 x^4+136 a^3 x^3+102 a^2 x^2+85 a x+35\right)}{315 a x^5}","-\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*Sqrt[-(a*x*(-1 + a*x))]*(35 + 85*a*x + 102*a^2*x^2 + 136*a^3*x^3 + 272*a^4*x^4))/(315*a*x^5)","A",1
31,1,48,39,0.0162,"\int \frac{-1+2 a x}{\sqrt{-1+x} x^2 \sqrt{1+x}} \, dx","Integrate[(-1 + 2*a*x)/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]","\frac{2 a \sqrt{x^2-1} x \tan ^{-1}\left(\sqrt{x^2-1}\right)-x^2+1}{\sqrt{x-1} x \sqrt{x+1}}","2 a \tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"(1 - x^2 + 2*a*x*Sqrt[-1 + x^2]*ArcTan[Sqrt[-1 + x^2]])/(Sqrt[-1 + x]*x*Sqrt[1 + x])","A",1
32,1,48,39,0.0062496,"\int \frac{a^2 x^2-(1-a x)^2}{\sqrt{-1+x} x^2 \sqrt{1+x}} \, dx","Integrate[(a^2*x^2 - (1 - a*x)^2)/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]","\frac{2 a \sqrt{x^2-1} x \tan ^{-1}\left(\sqrt{x^2-1}\right)-x^2+1}{\sqrt{x-1} x \sqrt{x+1}}","2 a \tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"(1 - x^2 + 2*a*x*Sqrt[-1 + x^2]*ArcTan[Sqrt[-1 + x^2]])/(Sqrt[-1 + x]*x*Sqrt[1 + x])","A",1
33,1,309,145,1.51073,"\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","Integrate[(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{\frac{a}{c-1}} (a+b x)^{3/2} \left(\frac{i (e-1) \sqrt{\frac{\frac{a}{a+b x}+c-1}{c-1}} \sqrt{\frac{\frac{a}{a+b x}+e-1}{e-1}} (a B c+A (b-b c)) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{a}{c-1}}}{\sqrt{a+b x}}\right),\frac{c-1}{e-1}\right)}{\sqrt{a+b x}}-B \sqrt{\frac{a}{c-1}} \left(\frac{a}{a+b x}+c-1\right) \left(\frac{a}{a+b x}+e-1\right)-\frac{i a B (e-1) \sqrt{\frac{\frac{a}{a+b x}+c-1}{c-1}} \sqrt{\frac{\frac{a}{a+b x}+e-1}{e-1}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{a}{c-1}}}{\sqrt{a+b x}}\right)|\frac{c-1}{e-1}\right)}{\sqrt{a+b x}}\right)}{a b^2 (e-1) \sqrt{\frac{b (c-1) x}{a}+c} \sqrt{\frac{b (e-1) x}{a}+e}}","\frac{2 \sqrt{a} (a B e+A (b-b e)) \operatorname{EllipticF}\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*Sqrt[a/(-1 + c)]*(a + b*x)^(3/2)*(-(B*Sqrt[a/(-1 + c)]*(-1 + c + a/(a + b*x))*(-1 + e + a/(a + b*x))) - (I*a*B*(-1 + e)*Sqrt[(-1 + c + a/(a + b*x))/(-1 + c)]*Sqrt[(-1 + e + a/(a + b*x))/(-1 + e)]*EllipticE[I*ArcSinh[Sqrt[a/(-1 + c)]/Sqrt[a + b*x]], (-1 + c)/(-1 + e)])/Sqrt[a + b*x] + (I*(a*B*c + A*(b - b*c))*(-1 + e)*Sqrt[(-1 + c + a/(a + b*x))/(-1 + c)]*Sqrt[(-1 + e + a/(a + b*x))/(-1 + e)]*EllipticF[I*ArcSinh[Sqrt[a/(-1 + c)]/Sqrt[a + b*x]], (-1 + c)/(-1 + e)])/Sqrt[a + b*x]))/(a*b^2*(-1 + e)*Sqrt[c + (b*(-1 + c)*x)/a]*Sqrt[e + (b*(-1 + e)*x)/a])","C",1
34,1,312,221,2.2493164,"\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+\frac{b (-1+e) x}{a}}} \, dx","Integrate[(A + B*x)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + (b*(-1 + e)*x)/a]),x]","-\frac{2 \sqrt{\frac{a}{e-1}} (a+b x)^{3/2} \left(\frac{i d \sqrt{\frac{\frac{a}{a+b x}+e-1}{e-1}} (a B e+A (b-b e)) \sqrt{\frac{b (c+d x)}{d (a+b x)}} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{a}{e-1}}}{\sqrt{a+b x}}\right),\frac{(e-1) (b c-a d)}{a d}\right)}{\sqrt{a+b x}}-\frac{b B \sqrt{\frac{a}{e-1}} (c+d x) (a e+b (e-1) x)}{(a+b x)^2}-\frac{i a B d \sqrt{\frac{\frac{a}{a+b x}+e-1}{e-1}} \sqrt{\frac{b (c+d x)}{d (a+b x)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{a}{e-1}}}{\sqrt{a+b x}}\right)|\frac{(b c-a d) (e-1)}{a d}\right)}{\sqrt{a+b x}}\right)}{a b^2 d \sqrt{c+d x} \sqrt{\frac{b (e-1) x}{a}+e}}","\frac{2 \sqrt{a} (a B e+A (b-b e)) \sqrt{\frac{b (c+d x)}{b c-a d}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{1-e} \sqrt{a+b x}}{\sqrt{a}}\right),-\frac{a d}{(1-e) (b c-a d)}\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*Sqrt[a/(-1 + e)]*(a + b*x)^(3/2)*(-((b*B*Sqrt[a/(-1 + e)]*(c + d*x)*(a*e + b*(-1 + e)*x))/(a + b*x)^2) - (I*a*B*d*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*Sqrt[(-1 + e + a/(a + b*x))/(-1 + e)]*EllipticE[I*ArcSinh[Sqrt[a/(-1 + e)]/Sqrt[a + b*x]], ((b*c - a*d)*(-1 + e))/(a*d)])/Sqrt[a + b*x] + (I*d*(a*B*e + A*(b - b*e))*Sqrt[(b*(c + d*x))/(d*(a + b*x))]*Sqrt[(-1 + e + a/(a + b*x))/(-1 + e)]*EllipticF[I*ArcSinh[Sqrt[a/(-1 + e)]/Sqrt[a + b*x]], ((b*c - a*d)*(-1 + e))/(a*d)])/Sqrt[a + b*x]))/(a*b^2*d*Sqrt[c + d*x]*Sqrt[e + (b*(-1 + e)*x)/a])","C",1
35,1,135,281,0.4364574,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3 \, dx","Integrate[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3,x]","\frac{57438413230 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+24 \sqrt{2-3 x} \sqrt{4 x+1} \left(29160000 x^5+67338000 x^4-167736600 x^3-670058262 x^2-797747975 x+3325071575\right)-71380354727 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{15396480 \sqrt{2 x-5}}","\frac{522167393 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{23328 \sqrt{2 x-5}}+\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{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,"(24*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(3325071575 - 797747975*x - 670058262*x^2 - 167736600*x^3 + 67338000*x^4 + 29160000*x^5) - 71380354727*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] + 57438413230*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(15396480*Sqrt[-5 + 2*x])","A",1
36,1,130,243,0.2834403,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2 \, dx","Integrate[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2,x]","\frac{27962495 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+6 \sqrt{2-3 x} \sqrt{4 x+1} \left(216000 x^4+147600 x^3-1649952 x^2-2933650 x+6902575\right)-35493898 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{116640 \sqrt{2 x-5}}","\frac{5592499 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{3888 \sqrt{2 x-5}}+\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{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,"(6*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(6902575 - 2933650*x - 1649952*x^2 + 147600*x^3 + 216000*x^4) - 35493898*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] + 27962495*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(116640*Sqrt[-5 + 2*x])","A",1
37,1,125,193,0.2458007,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x) \, dx","Integrate[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x),x]","\frac{724790 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+24 \sqrt{2-3 x} \sqrt{4 x+1} \left(5400 x^3-6066 x^2-37975 x+48475\right)-954811 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{45360 \sqrt{2 x-5}}","\frac{72479 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{756 \sqrt{2 x-5}}+\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{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,"(24*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(48475 - 37975*x - 6066*x^2 + 5400*x^3) - 954811*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] + 724790*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(45360*Sqrt[-5 + 2*x])","A",1
38,1,120,162,0.1800849,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \, dx","Integrate[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x],x]","\frac{605 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+6 \sqrt{2-3 x} \sqrt{4 x+1} \left(72 x^2-250 x+175\right)-847 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{540 \sqrt{2 x-5}}","\frac{121 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{18 \sqrt{2 x-5}}+\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{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,"(6*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(175 - 250*x + 72*x^2) - 847*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] + 605*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(540*Sqrt[-5 + 2*x])","A",1
39,1,139,182,0.8175123,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{7+5 x} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x),x]","\frac{\sqrt{2 x-5} \left(-3759 \sqrt{11} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)+1650 \sqrt{2-3 x} \sqrt{5-2 x} \sqrt{4 x+1}-23485 \sqrt{11} E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)+24219 \sqrt{11} \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)}{12375 \sqrt{5-2 x}}","-\frac{1253 \sqrt{\frac{2}{33}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{375 \sqrt{2 x-5}}+\frac{2}{15} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}-\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,"(Sqrt[-5 + 2*x]*(1650*Sqrt[2 - 3*x]*Sqrt[5 - 2*x]*Sqrt[1 + 4*x] - 23485*Sqrt[11]*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - 3759*Sqrt[11]*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 24219*Sqrt[11]*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/(12375*Sqrt[5 - 2*x])","A",1
40,1,130,189,0.8152825,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^2} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^2,x]","\frac{\sqrt{2 x-5} \left(\frac{3 \sqrt{11} \left(9424 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)+20460 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)-26859 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)}{\sqrt{5-2 x}}-\frac{51150 \sqrt{2-3 x} \sqrt{4 x+1}}{5 x+7}\right)}{255750}","\frac{152 \sqrt{\frac{2}{33}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{125 \sqrt{2 x-5}}-\frac{\sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{5 (5 x+7)}+\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[-5 + 2*x]*((-51150*Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(7 + 5*x) + (3*Sqrt[11]*(20460*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 9424*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - 26859*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/Sqrt[5 - 2*x]))/255750","A",1
41,1,134,227,0.7496097,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^3} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^3,x]","\frac{\sqrt{2 x-5} \left(\frac{\sqrt{11} \left(5759676 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)-61059460 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)+44497509 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)}{\sqrt{5-2 x}}+\frac{17050 \sqrt{2-3 x} \sqrt{4 x+1} (44765 x+7057)}{(5 x+7)^2}\right)}{9482187000}","\frac{397 \sqrt{\frac{3}{22}} \sqrt{5-2 x} \operatorname{EllipticF}\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{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{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[-5 + 2*x]*((17050*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7057 + 44765*x))/(7 + 5*x)^2 + (Sqrt[11]*(-61059460*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 5759676*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 44497509*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/Sqrt[5 - 2*x]))/9482187000","A",1
42,1,139,263,0.786827,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^4} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^4,x]","\frac{\sqrt{2 x-5} \left(\frac{\sqrt{11} \left(120693246492 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)-114783334820 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)-46993849347 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)}{\sqrt{5-2 x}}+\frac{17050 \sqrt{2-3 x} \sqrt{4 x+1} \left(420760025 x^2+2007981640 x-75460017\right)}{(5 x+7)^3}\right)}{527342347818000}","\frac{24957247 \sqrt{5-2 x} \operatorname{EllipticF}\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{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{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[-5 + 2*x]*((17050*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(-75460017 + 2007981640*x + 420760025*x^2))/(7 + 5*x)^3 + (Sqrt[11]*(-114783334820*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 120693246492*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - 46993849347*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/Sqrt[5 - 2*x]))/527342347818000","A",1
43,1,1820,570,14.190896,"\int \frac{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{a+b x} \, dx","Integrate[(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(a + b*x),x]","\frac{\left(\frac{2 b^2 f^2 \sqrt{\frac{d g}{h}-c} h^2 c^3}{(c+d x)^2}-\frac{4 b^2 f^2 \sqrt{\frac{d g}{h}-c} h^2 c^2}{c+d x}-\frac{6 a b d f^2 \sqrt{\frac{d g}{h}-c} h^2 c^2}{(c+d x)^2}+2 b^2 f^2 \sqrt{\frac{d g}{h}-c} h^2 c+\frac{12 a b d f^2 \sqrt{\frac{d g}{h}-c} h^2 c}{c+d x}-\frac{2 b^2 d e f \sqrt{\frac{d g}{h}-c} h^2 c}{c+d x}-\frac{2 b^2 d f^2 g \sqrt{\frac{d g}{h}-c} h c}{c+d x}-\frac{2 b^2 d^2 e^2 \sqrt{\frac{d g}{h}-c} h^2 c}{(c+d x)^2}+\frac{6 a b d^2 e f \sqrt{\frac{d g}{h}-c} h^2 c}{(c+d x)^2}+\frac{6 a b d^2 f^2 g \sqrt{\frac{d g}{h}-c} h c}{(c+d x)^2}-\frac{2 b^2 d^2 e f g \sqrt{\frac{d g}{h}-c} h c}{(c+d x)^2}-\frac{2 b^2 d^2 f^2 g^2 \sqrt{\frac{d g}{h}-c} c}{(c+d x)^2}-6 a b d f^2 \sqrt{\frac{d g}{h}-c} h^2+2 b^2 d e f \sqrt{\frac{d g}{h}-c} h^2+2 b^2 d f^2 g \sqrt{\frac{d g}{h}-c} h-\frac{2 i b f (c h-d g) (b (d f g+d e h+c f h)-3 a d f h) \sqrt{-\frac{c}{c+d x}+\frac{d e}{f (c+d x)}+1} \sqrt{-\frac{c}{c+d x}+\frac{d g}{h (c+d x)}+1} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)}{\sqrt{c+d x}}-\frac{2 i b d f (c h-d g) (-b f g-2 b e h+3 a f h) \sqrt{-\frac{c}{c+d x}+\frac{d e}{f (c+d x)}+1} \sqrt{-\frac{c}{c+d x}+\frac{d g}{h (c+d x)}+1} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right),\frac{d e h-c f h}{d f g-c f h}\right)}{\sqrt{c+d x}}+\frac{6 i a^2 d^2 f^2 h^2 \sqrt{-\frac{c}{c+d x}+\frac{d e}{f (c+d x)}+1} \sqrt{-\frac{c}{c+d x}+\frac{d g}{h (c+d x)}+1} \Pi \left(-\frac{b c h-a d h}{b d g-b c h};i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)}{\sqrt{c+d x}}-\frac{6 i a b d^2 e f h^2 \sqrt{-\frac{c}{c+d x}+\frac{d e}{f (c+d x)}+1} \sqrt{-\frac{c}{c+d x}+\frac{d g}{h (c+d x)}+1} \Pi \left(-\frac{b c h-a d h}{b d g-b c h};i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)}{\sqrt{c+d x}}-\frac{6 i a b d^2 f^2 g h \sqrt{-\frac{c}{c+d x}+\frac{d e}{f (c+d x)}+1} \sqrt{-\frac{c}{c+d x}+\frac{d g}{h (c+d x)}+1} \Pi \left(-\frac{b c h-a d h}{b d g-b c h};i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)}{\sqrt{c+d x}}+\frac{6 i b^2 d^2 e f g h \sqrt{-\frac{c}{c+d x}+\frac{d e}{f (c+d x)}+1} \sqrt{-\frac{c}{c+d x}+\frac{d g}{h (c+d x)}+1} \Pi \left(-\frac{b c h-a d h}{b d g-b c h};i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)}{\sqrt{c+d x}}+\frac{2 b^2 d^2 e^2 \sqrt{\frac{d g}{h}-c} h^2}{c+d x}-\frac{6 a b d^2 e f \sqrt{\frac{d g}{h}-c} h^2}{c+d x}-\frac{6 a b d^2 f^2 g \sqrt{\frac{d g}{h}-c} h}{c+d x}+\frac{4 b^2 d^2 e f g \sqrt{\frac{d g}{h}-c} h}{c+d x}+\frac{2 b^2 d^2 f^2 g^2 \sqrt{\frac{d g}{h}-c}}{c+d x}+\frac{2 b^2 d^3 e^2 g \sqrt{\frac{d g}{h}-c} h}{(c+d x)^2}-\frac{6 a b d^3 e f g \sqrt{\frac{d g}{h}-c} h}{(c+d x)^2}+\frac{2 b^2 d^3 e f g^2 \sqrt{\frac{d g}{h}-c}}{(c+d x)^2}\right) (c+d x)^{3/2}}{3 b^3 d^2 f \sqrt{\frac{d g}{h}-c} h \sqrt{e+\frac{(c+d x) \left(f-\frac{c f}{c+d x}\right)}{d}} \sqrt{g+\frac{(c+d x) \left(h-\frac{c h}{c+d x}\right)}{d}}}+\frac{2 \sqrt{e+f x} \sqrt{g+h x} \sqrt{c+d 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)-\left(b^2 (d g (f g-e h)-c h (2 e h+f g))\right)\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right),\frac{h (d e-c f)}{f (d g-c h)}\right)}{3 b^3 d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 (b e-a f) (b g-a h) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^3 \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} (3 a d f h-b (c f h+d e h+d f g)) E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 b^2 d \sqrt{f} h \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 b}",1,"(2*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*b) + ((c + d*x)^(3/2)*(2*b^2*d*f^2*g*Sqrt[-c + (d*g)/h]*h + 2*b^2*d*e*f*Sqrt[-c + (d*g)/h]*h^2 + 2*b^2*c*f^2*Sqrt[-c + (d*g)/h]*h^2 - 6*a*b*d*f^2*Sqrt[-c + (d*g)/h]*h^2 + (2*b^2*d^3*e*f*g^2*Sqrt[-c + (d*g)/h])/(c + d*x)^2 - (2*b^2*c*d^2*f^2*g^2*Sqrt[-c + (d*g)/h])/(c + d*x)^2 + (2*b^2*d^3*e^2*g*Sqrt[-c + (d*g)/h]*h)/(c + d*x)^2 - (2*b^2*c*d^2*e*f*g*Sqrt[-c + (d*g)/h]*h)/(c + d*x)^2 - (6*a*b*d^3*e*f*g*Sqrt[-c + (d*g)/h]*h)/(c + d*x)^2 + (6*a*b*c*d^2*f^2*g*Sqrt[-c + (d*g)/h]*h)/(c + d*x)^2 - (2*b^2*c*d^2*e^2*Sqrt[-c + (d*g)/h]*h^2)/(c + d*x)^2 + (6*a*b*c*d^2*e*f*Sqrt[-c + (d*g)/h]*h^2)/(c + d*x)^2 + (2*b^2*c^3*f^2*Sqrt[-c + (d*g)/h]*h^2)/(c + d*x)^2 - (6*a*b*c^2*d*f^2*Sqrt[-c + (d*g)/h]*h^2)/(c + d*x)^2 + (2*b^2*d^2*f^2*g^2*Sqrt[-c + (d*g)/h])/(c + d*x) + (4*b^2*d^2*e*f*g*Sqrt[-c + (d*g)/h]*h)/(c + d*x) - (2*b^2*c*d*f^2*g*Sqrt[-c + (d*g)/h]*h)/(c + d*x) - (6*a*b*d^2*f^2*g*Sqrt[-c + (d*g)/h]*h)/(c + d*x) + (2*b^2*d^2*e^2*Sqrt[-c + (d*g)/h]*h^2)/(c + d*x) - (2*b^2*c*d*e*f*Sqrt[-c + (d*g)/h]*h^2)/(c + d*x) - (6*a*b*d^2*e*f*Sqrt[-c + (d*g)/h]*h^2)/(c + d*x) - (4*b^2*c^2*f^2*Sqrt[-c + (d*g)/h]*h^2)/(c + d*x) + (12*a*b*c*d*f^2*Sqrt[-c + (d*g)/h]*h^2)/(c + d*x) - ((2*I)*b*f*(-(d*g) + c*h)*(-3*a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*Sqrt[1 - c/(c + d*x) + (d*e)/(f*(c + d*x))]*Sqrt[1 - c/(c + d*x) + (d*g)/(h*(c + d*x))]*EllipticE[I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)])/Sqrt[c + d*x] - ((2*I)*b*d*f*(-(d*g) + c*h)*(-(b*f*g) - 2*b*e*h + 3*a*f*h)*Sqrt[1 - c/(c + d*x) + (d*e)/(f*(c + d*x))]*Sqrt[1 - c/(c + d*x) + (d*g)/(h*(c + d*x))]*EllipticF[I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)])/Sqrt[c + d*x] + ((6*I)*b^2*d^2*e*f*g*h*Sqrt[1 - c/(c + d*x) + (d*e)/(f*(c + d*x))]*Sqrt[1 - c/(c + d*x) + (d*g)/(h*(c + d*x))]*EllipticPi[-((b*c*h - a*d*h)/(b*d*g - b*c*h)), I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)])/Sqrt[c + d*x] - ((6*I)*a*b*d^2*f^2*g*h*Sqrt[1 - c/(c + d*x) + (d*e)/(f*(c + d*x))]*Sqrt[1 - c/(c + d*x) + (d*g)/(h*(c + d*x))]*EllipticPi[-((b*c*h - a*d*h)/(b*d*g - b*c*h)), I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)])/Sqrt[c + d*x] - ((6*I)*a*b*d^2*e*f*h^2*Sqrt[1 - c/(c + d*x) + (d*e)/(f*(c + d*x))]*Sqrt[1 - c/(c + d*x) + (d*g)/(h*(c + d*x))]*EllipticPi[-((b*c*h - a*d*h)/(b*d*g - b*c*h)), I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)])/Sqrt[c + d*x] + ((6*I)*a^2*d^2*f^2*h^2*Sqrt[1 - c/(c + d*x) + (d*e)/(f*(c + d*x))]*Sqrt[1 - c/(c + d*x) + (d*g)/(h*(c + d*x))]*EllipticPi[-((b*c*h - a*d*h)/(b*d*g - b*c*h)), I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)])/Sqrt[c + d*x]))/(3*b^3*d^2*f*Sqrt[-c + (d*g)/h]*h*Sqrt[e + ((c + d*x)*(f - (c*f)/(c + d*x)))/d]*Sqrt[g + ((c + d*x)*(h - (c*h)/(c + d*x)))/d])","C",1
44,1,130,243,0.388821,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^3}{\sqrt{-5+2 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3)/Sqrt[-5 + 2*x],x]","\frac{-2161804579 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+6 \sqrt{2-3 x} \sqrt{4 x+1} \left(1512000 x^4+8614800 x^3+21329208 x^2+51484034 x-455686385\right)+2629157597 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{326592 \sqrt{2 x-5}}","-\frac{2161804579 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{54432 \sqrt{2 x-5}}+\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{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,"(6*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(-455686385 + 51484034*x + 21329208*x^2 + 8614800*x^3 + 1512000*x^4) + 2629157597*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] - 2161804579*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(326592*Sqrt[-5 + 2*x])","A",1
45,1,125,205,0.3179954,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^2}{\sqrt{-5+2 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2)/Sqrt[-5 + 2*x],x]","\frac{-6716644 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+12 \sqrt{2-3 x} \sqrt{4 x+1} \left(10800 x^3+46836 x^2+102592 x-717955\right)+8198333 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{18144 \sqrt{2 x-5}}","-\frac{1679161 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{756 \sqrt{2 x-5}}+\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{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,"(12*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(-717955 + 102592*x + 46836*x^2 + 10800*x^3) + 8198333*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] - 6716644*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(18144*Sqrt[-5 + 2*x])","A",1
46,1,120,162,0.2057633,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)}{\sqrt{-5+2 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x))/Sqrt[-5 + 2*x],x]","\frac{-4543 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+6 \sqrt{2-3 x} \sqrt{4 x+1} \left(72 x^2+218 x-995\right)+5588 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{216 \sqrt{2 x-5}}","-\frac{4543 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{36 \sqrt{2 x-5}}+\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{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,"(6*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(-995 + 218*x + 72*x^2) + 5588*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] - 4543*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(216*Sqrt[-5 + 2*x])","A",1
47,1,115,131,0.195209,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/Sqrt[-5 + 2*x],x]","\frac{-44 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+12 \sqrt{2-3 x} \sqrt{4 x+1} (2 x-5)+55 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{36 \sqrt{2 x-5}}","-\frac{11 \sqrt{\frac{22}{3}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{3 \sqrt{2 x-5}}+\frac{1}{3} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}+\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,"(12*Sqrt[2 - 3*x]*(-5 + 2*x)*Sqrt[1 + 4*x] + 55*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] - 44*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(36*Sqrt[-5 + 2*x])","A",1
48,1,95,151,0.4177748,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)),x]","\frac{\sqrt{5-2 x} \left(41 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)-110 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)+69 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)}{25 \sqrt{22 x-55}}","-\frac{41 \sqrt{\frac{2}{33}} \sqrt{5-2 x} \operatorname{EllipticF}\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,"(Sqrt[5 - 2*x]*(-110*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 41*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 69*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/(25*Sqrt[-55 + 22*x])","A",1
49,1,130,189,0.6587705,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^2} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^2),x]","\frac{3 \sqrt{55-22 x} \left(14508 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)+6820 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)-18303 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)+\frac{51150 \sqrt{2-3 x} \sqrt{4 x+1} (2 x-5)}{5 x+7}}{1994850 \sqrt{2 x-5}}","-\frac{2 \sqrt{\frac{6}{11}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{25 \sqrt{2 x-5}}+\frac{\sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{39 (5 x+7)}-\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,"((51150*Sqrt[2 - 3*x]*(-5 + 2*x)*Sqrt[1 + 4*x])/(7 + 5*x) + 3*Sqrt[55 - 22*x]*(6820*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 14508*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - 18303*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/(1994850*Sqrt[-5 + 2*x])","A",1
50,1,135,225,0.5798901,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^3} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^3),x]","\frac{-3 \sqrt{55-22 x} \left(-9834812 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)+2462020 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)+6655867 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)-\frac{17050 \sqrt{2-3 x} (2 x-5) \sqrt{4 x+1} (5415 x-10957)}{(5 x+7)^2}}{24653686200 \sqrt{2 x-5}}","-\frac{6101 \sqrt{5-2 x} \operatorname{EllipticF}\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{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{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,"((-17050*Sqrt[2 - 3*x]*(-5 + 2*x)*Sqrt[1 + 4*x]*(-10957 + 5415*x))/(7 + 5*x)^2 - 3*Sqrt[55 - 22*x]*(2462020*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - 9834812*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 6655867*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/(24653686200*Sqrt[-5 + 2*x])","A",1
51,1,125,205,0.3728577,"\int \frac{\sqrt{2-3 x} (7+5 x)^3}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*(7 + 5*x)^3)/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{-25260049 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+30 \sqrt{2-3 x} \sqrt{4 x+1} \left(10800 x^3+64224 x^2+188566 x-1041565\right)+31259246 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{36288 \sqrt{2 x-5}}","-\frac{25260049 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{6048 \sqrt{2 x-5}}+\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{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,"(30*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(-1041565 + 188566*x + 64224*x^2 + 10800*x^3) + 31259246*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] - 25260049*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(36288*Sqrt[-5 + 2*x])","A",1
52,1,120,167,0.3000879,"\int \frac{\sqrt{2-3 x} (7+5 x)^2}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*(7 + 5*x)^2)/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{-35066 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+120 \sqrt{2-3 x} \sqrt{4 x+1} \left(18 x^2+89 x-335\right)+44569 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{864 \sqrt{2 x-5}}","-\frac{17533 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{72 \sqrt{2 x-5}}+\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{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,"(120*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(-335 + 89*x + 18*x^2) + 44569*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] - 35066*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(864*Sqrt[-5 + 2*x])","A",1
53,1,115,131,0.1925814,"\int \frac{\sqrt{2-3 x} (7+5 x)}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*(7 + 5*x))/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{-179 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+30 \sqrt{2-3 x} \sqrt{4 x+1} (2 x-5)+241 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{72 \sqrt{2 x-5}}","-\frac{179 \sqrt{\frac{11}{6}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{12 \sqrt{2 x-5}}+\frac{5}{12} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}+\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,"(30*Sqrt[2 - 3*x]*(-5 + 2*x)*Sqrt[1 + 4*x] + 241*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] - 179*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(72*Sqrt[-5 + 2*x])","A",1
54,1,111,47,0.3637878,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\frac{\frac{2 (2 x-5) (3 x-2)}{\sqrt{2 x+\frac{1}{2}}}+\sqrt{11} \sqrt{\frac{2 x-5}{4 x+1}} \sqrt{\frac{3 x-2}{4 x+1}} (4 x+1) E\left(\left.\sin ^{-1}\left(\frac{\sqrt{\frac{11}{3}}}{\sqrt{4 x+1}}\right)\right|3\right)}{2 \sqrt{2-3 x} \sqrt{4 x-10}}","\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,"-1/2*((2*(-5 + 2*x)*(-2 + 3*x))/Sqrt[1/2 + 2*x] + Sqrt[11]*Sqrt[(-5 + 2*x)/(1 + 4*x)]*Sqrt[(-2 + 3*x)/(1 + 4*x)]*(1 + 4*x)*EllipticE[ArcSin[Sqrt[11/3]/Sqrt[1 + 4*x]], 3])/(Sqrt[2 - 3*x]*Sqrt[-10 + 4*x])","B",1
55,1,70,103,0.4243862,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)} \, dx","Integrate[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)),x]","\frac{3 \sqrt{5-2 x} \left(\operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)-\Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)}{5 \sqrt{22 x-55}}","-\frac{\sqrt{\frac{6}{11}} \sqrt{5-2 x} \operatorname{EllipticF}\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,"(3*Sqrt[5 - 2*x]*(EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/(5*Sqrt[-55 + 22*x])","A",1
56,1,130,189,0.6908594,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2} \, dx","Integrate[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2),x]","\frac{-3 \sqrt{55-22 x} \left(-14508 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)+6820 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)+10713 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)-\frac{51150 \sqrt{2-3 x} \sqrt{4 x+1} (2 x-5)}{5 x+7}}{9176310 \sqrt{2 x-5}}","-\frac{2 \sqrt{\frac{6}{11}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{115 \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{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,"((-51150*Sqrt[2 - 3*x]*(-5 + 2*x)*Sqrt[1 + 4*x])/(7 + 5*x) - 3*Sqrt[55 - 22*x]*(6820*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - 14508*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 10713*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/(9176310*Sqrt[-5 + 2*x])","A",1
57,1,142,225,0.4611483,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3} \, dx","Integrate[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3),x]","\frac{-\sqrt{55-22 x} (5 x+7)^2 \left(-64043148 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)+36589300 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)+49109823 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)-17050 \sqrt{2-3 x} (2 x-5) \sqrt{4 x+1} (26825 x+56093)}{113406956520 \sqrt{2 x-5} (5 x+7)^2}","-\frac{13243 \sqrt{5-2 x} \operatorname{EllipticF}\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{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{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,"(-17050*Sqrt[2 - 3*x]*(-5 + 2*x)*Sqrt[1 + 4*x]*(56093 + 26825*x) - Sqrt[55 - 22*x]*(7 + 5*x)^2*(36589300*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - 64043148*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 49109823*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/(113406956520*Sqrt[-5 + 2*x]*(7 + 5*x)^2)","A",1
58,1,202,293,1.7698373,"\int \frac{\sqrt{c+d x}}{(a+b x) \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[Sqrt[c + d*x]/((a + b*x)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 i \sqrt{c+d x} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt{\frac{f (c+d x)}{d e-c f}}\right),\frac{d e h-c f h}{d f g-c f h}\right)-\Pi \left(\frac{b (c f-d e)}{(b c-a d) f};i \sinh ^{-1}\left(\sqrt{\frac{f (c+d x)}{d e-c f}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)\right)}{b \sqrt{e+f x} \sqrt{g+h x} \sqrt{\frac{f (c+d x)}{d (e+f 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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right),\frac{h (d e-c f)}{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*I)*Sqrt[c + d*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*(EllipticF[I*ArcSinh[Sqrt[(f*(c + d*x))/(d*e - c*f)]], (d*e*h - c*f*h)/(d*f*g - c*f*h)] - EllipticPi[(b*(-(d*e) + c*f))/((b*c - a*d)*f), I*ArcSinh[Sqrt[(f*(c + d*x))/(d*e - c*f)]], (d*e*h - c*f*h)/(d*f*g - c*f*h)]))/(b*Sqrt[(f*(c + d*x))/(d*(e + f*x))]*Sqrt[e + f*x]*Sqrt[g + h*x])","C",1
59,1,1198,449,7.7442359,"\int \frac{(c+d x)^{3/2}}{(a+b x) \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[(c + d*x)^(3/2)/((a + b*x)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \left(b^2 d^2 \sqrt{\frac{f g}{h}-e} h e^3-a b d^2 f \sqrt{\frac{f g}{h}-e} h e^2-b^2 c d f \sqrt{\frac{f g}{h}-e} h e^2-2 b^2 d^2 \sqrt{\frac{f g}{h}-e} h (e+f x) e^2-b^2 d^2 f g \sqrt{\frac{f g}{h}-e} e^2+b^2 d^2 \sqrt{\frac{f g}{h}-e} h (e+f x)^2 e+a b c d f^2 \sqrt{\frac{f g}{h}-e} h e+2 a b d^2 f \sqrt{\frac{f g}{h}-e} h (e+f x) e+b^2 c d f \sqrt{\frac{f g}{h}-e} h (e+f x) e+b^2 d^2 f g \sqrt{\frac{f g}{h}-e} (e+f x) e+a b d^2 f^2 g \sqrt{\frac{f g}{h}-e} e+b^2 c d f^2 g \sqrt{\frac{f g}{h}-e} e-a b d^2 f \sqrt{\frac{f g}{h}-e} h (e+f x)^2-a b c d f^2 \sqrt{\frac{f g}{h}-e} h (e+f x)-a b d^2 f^2 g \sqrt{\frac{f g}{h}-e} (e+f x)+i b d^2 (b e-a f) (f g-e h) \sqrt{\frac{f (c+d x)}{d (e+f x)}} (e+f x)^{3/2} \sqrt{\frac{f (g+h x)}{h (e+f x)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{f g}{h}-e}}{\sqrt{e+f x}}\right)|\frac{(d e-c f) h}{d (e h-f g)}\right)-i b f \left(a (e h-f g) d^2+b \left(f h c^2-2 d e h c+d^2 e g\right)\right) \sqrt{\frac{f (c+d x)}{d (e+f x)}} (e+f x)^{3/2} \sqrt{\frac{f (g+h x)}{h (e+f x)}} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{f g}{h}-e}}{\sqrt{e+f x}}\right),\frac{(d e-c f) h}{d (e h-f g)}\right)+i b^2 c^2 f^2 h \sqrt{\frac{f (c+d x)}{d (e+f x)}} (e+f x)^{3/2} \sqrt{\frac{f (g+h x)}{h (e+f x)}} \Pi \left(-\frac{b e h-a f h}{b f g-b e h};i \sinh ^{-1}\left(\frac{\sqrt{\frac{f g}{h}-e}}{\sqrt{e+f x}}\right)|\frac{(d e-c f) h}{d (e h-f g)}\right)+i a^2 d^2 f^2 h \sqrt{\frac{f (c+d x)}{d (e+f x)}} (e+f x)^{3/2} \sqrt{\frac{f (g+h x)}{h (e+f x)}} \Pi \left(-\frac{b e h-a f h}{b f g-b e h};i \sinh ^{-1}\left(\frac{\sqrt{\frac{f g}{h}-e}}{\sqrt{e+f x}}\right)|\frac{(d e-c f) h}{d (e h-f g)}\right)-2 i a b c d f^2 h \sqrt{\frac{f (c+d x)}{d (e+f x)}} (e+f x)^{3/2} \sqrt{\frac{f (g+h x)}{h (e+f x)}} \Pi \left(-\frac{b e h-a f h}{b f g-b e h};i \sinh ^{-1}\left(\frac{\sqrt{\frac{f g}{h}-e}}{\sqrt{e+f x}}\right)|\frac{(d e-c f) h}{d (e h-f g)}\right)-a b c d f^3 g \sqrt{\frac{f g}{h}-e}\right)}{b^2 f^2 (a f-b e) \sqrt{\frac{f g}{h}-e} h \sqrt{c+d x} \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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right),\frac{h (d e-c f)}{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*(-(b^2*d^2*e^2*f*g*Sqrt[-e + (f*g)/h]) + b^2*c*d*e*f^2*g*Sqrt[-e + (f*g)/h] + a*b*d^2*e*f^2*g*Sqrt[-e + (f*g)/h] - a*b*c*d*f^3*g*Sqrt[-e + (f*g)/h] + b^2*d^2*e^3*Sqrt[-e + (f*g)/h]*h - b^2*c*d*e^2*f*Sqrt[-e + (f*g)/h]*h - a*b*d^2*e^2*f*Sqrt[-e + (f*g)/h]*h + a*b*c*d*e*f^2*Sqrt[-e + (f*g)/h]*h + b^2*d^2*e*f*g*Sqrt[-e + (f*g)/h]*(e + f*x) - a*b*d^2*f^2*g*Sqrt[-e + (f*g)/h]*(e + f*x) - 2*b^2*d^2*e^2*Sqrt[-e + (f*g)/h]*h*(e + f*x) + b^2*c*d*e*f*Sqrt[-e + (f*g)/h]*h*(e + f*x) + 2*a*b*d^2*e*f*Sqrt[-e + (f*g)/h]*h*(e + f*x) - a*b*c*d*f^2*Sqrt[-e + (f*g)/h]*h*(e + f*x) + b^2*d^2*e*Sqrt[-e + (f*g)/h]*h*(e + f*x)^2 - a*b*d^2*f*Sqrt[-e + (f*g)/h]*h*(e + f*x)^2 + I*b*d^2*(b*e - a*f)*(f*g - e*h)*Sqrt[(f*(c + d*x))/(d*(e + f*x))]*(e + f*x)^(3/2)*Sqrt[(f*(g + h*x))/(h*(e + f*x))]*EllipticE[I*ArcSinh[Sqrt[-e + (f*g)/h]/Sqrt[e + f*x]], ((d*e - c*f)*h)/(d*(-(f*g) + e*h))] - I*b*f*(a*d^2*(-(f*g) + e*h) + b*(d^2*e*g - 2*c*d*e*h + c^2*f*h))*Sqrt[(f*(c + d*x))/(d*(e + f*x))]*(e + f*x)^(3/2)*Sqrt[(f*(g + h*x))/(h*(e + f*x))]*EllipticF[I*ArcSinh[Sqrt[-e + (f*g)/h]/Sqrt[e + f*x]], ((d*e - c*f)*h)/(d*(-(f*g) + e*h))] + I*b^2*c^2*f^2*h*Sqrt[(f*(c + d*x))/(d*(e + f*x))]*(e + f*x)^(3/2)*Sqrt[(f*(g + h*x))/(h*(e + f*x))]*EllipticPi[-((b*e*h - a*f*h)/(b*f*g - b*e*h)), I*ArcSinh[Sqrt[-e + (f*g)/h]/Sqrt[e + f*x]], ((d*e - c*f)*h)/(d*(-(f*g) + e*h))] - (2*I)*a*b*c*d*f^2*h*Sqrt[(f*(c + d*x))/(d*(e + f*x))]*(e + f*x)^(3/2)*Sqrt[(f*(g + h*x))/(h*(e + f*x))]*EllipticPi[-((b*e*h - a*f*h)/(b*f*g - b*e*h)), I*ArcSinh[Sqrt[-e + (f*g)/h]/Sqrt[e + f*x]], ((d*e - c*f)*h)/(d*(-(f*g) + e*h))] + I*a^2*d^2*f^2*h*Sqrt[(f*(c + d*x))/(d*(e + f*x))]*(e + f*x)^(3/2)*Sqrt[(f*(g + h*x))/(h*(e + f*x))]*EllipticPi[-((b*e*h - a*f*h)/(b*f*g - b*e*h)), I*ArcSinh[Sqrt[-e + (f*g)/h]/Sqrt[e + f*x]], ((d*e - c*f)*h)/(d*(-(f*g) + e*h))]))/(b^2*f^2*(-(b*e) + a*f)*Sqrt[-e + (f*g)/h]*h*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])","C",1
60,1,125,203,0.5300817,"\int \frac{(7+5 x)^4}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(7 + 5*x)^4/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{392989907 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)-1650 \sqrt{2-3 x} \sqrt{4 x+1} \left(1200 x^3+10608 x^2+50078 x-210245\right)-449665480 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{133056 \sqrt{2 x-5}}","\frac{392989907 \sqrt{5-2 x} \operatorname{EllipticF}\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{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{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,"(-1650*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(-210245 + 50078*x + 10608*x^2 + 1200*x^3) - 449665480*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] + 392989907*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(133056*Sqrt[-5 + 2*x])","A",1
61,1,120,165,0.3720259,"\int \frac{(7+5 x)^3}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(7 + 5*x)^3/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{4948402 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)-6600 \sqrt{2-3 x} \sqrt{4 x+1} \left(18 x^2+151 x-490\right)-5363435 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{28512 \sqrt{2 x-5}}","\frac{2474201 \sqrt{5-2 x} \operatorname{EllipticF}\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{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{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,"(-6600*Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(-490 + 151*x + 18*x^2) - 5363435*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] + 4948402*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(28512*Sqrt[-5 + 2*x])","A",1
62,1,115,129,0.2567325,"\int \frac{(7+5 x)^2}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(7 + 5*x)^2/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{24353 \sqrt{66} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)+1650 \sqrt{2-3 x} \sqrt{4 x+1} (5-2 x)-23485 \sqrt{66} \sqrt{5-2 x} E\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right)|\frac{1}{3}\right)}{2376 \sqrt{2 x-5}}","\frac{24353 \sqrt{5-2 x} \operatorname{EllipticF}\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{25}{36} \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}-\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,"(1650*Sqrt[2 - 3*x]*(5 - 2*x)*Sqrt[1 + 4*x] - 23485*Sqrt[66]*Sqrt[5 - 2*x]*EllipticE[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3] + 24353*Sqrt[66]*Sqrt[5 - 2*x]*EllipticF[ArcSin[Sqrt[3/11]*Sqrt[1 + 4*x]], 1/3])/(2376*Sqrt[-5 + 2*x])","A",1
63,1,187,98,0.4781094,"\int \frac{7+5 x}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(7 + 5*x)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{-124 \sqrt{22} \sqrt{\frac{2 x-5}{4 x+1}} \sqrt{\frac{3 x-2}{4 x+1}} (4 x+1)^2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{\frac{11}{3}}}{\sqrt{4 x+1}}\right),3\right)+220 \left(6 x^2-19 x+10\right) \sqrt{4 x+1}+55 \sqrt{22} \sqrt{\frac{2 x-5}{4 x+1}} \sqrt{\frac{3 x-2}{4 x+1}} (4 x+1)^2 E\left(\left.\sin ^{-1}\left(\frac{\sqrt{\frac{11}{3}}}{\sqrt{4 x+1}}\right)\right|3\right)}{132 \sqrt{2-3 x} \sqrt{2 x-5} (4 x+1)}","\frac{13 \sqrt{\frac{3}{22}} \sqrt{5-2 x} \operatorname{EllipticF}\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,"(220*Sqrt[1 + 4*x]*(10 - 19*x + 6*x^2) + 55*Sqrt[22]*Sqrt[(-5 + 2*x)/(1 + 4*x)]*Sqrt[(-2 + 3*x)/(1 + 4*x)]*(1 + 4*x)^2*EllipticE[ArcSin[Sqrt[11/3]/Sqrt[1 + 4*x]], 3] - 124*Sqrt[22]*Sqrt[(-5 + 2*x)/(1 + 4*x)]*Sqrt[(-2 + 3*x)/(1 + 4*x)]*(1 + 4*x)^2*EllipticF[ArcSin[Sqrt[11/3]/Sqrt[1 + 4*x]], 3])/(132*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*(1 + 4*x))","A",1
64,1,79,48,0.1117381,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\frac{\sqrt{\frac{3 x-2}{4 x+1}} (4 x+1) \sqrt{\frac{4 x-10}{44 x+11}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{\frac{11}{3}}}{\sqrt{4 x+1}}\right),3\right)}{\sqrt{2-3 x} \sqrt{2 x-5}}","\frac{\sqrt{\frac{2}{33}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{\sqrt{2 x-5}}",1,"-((Sqrt[(-2 + 3*x)/(1 + 4*x)]*(1 + 4*x)*Sqrt[(-10 + 4*x)/(11 + 44*x)]*EllipticF[ArcSin[Sqrt[11/3]/Sqrt[1 + 4*x]], 3])/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]))","A",1
65,1,99,51,0.4874427,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)),x]","-\frac{3 (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(\operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{11}}{2 \sqrt{2-3 x}}\right),-2\right)-\Pi \left(\frac{124}{55};\left.\sin ^{-1}\left(\frac{\sqrt{11}}{2 \sqrt{2-3 x}}\right)\right|-2\right)\right)}{31 \sqrt{4 x+1} \sqrt{11 x-\frac{55}{2}}}","-\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*(-2 + 3*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(EllipticF[ArcSin[Sqrt[11]/(2*Sqrt[2 - 3*x])], -2] - EllipticPi[124/55, ArcSin[Sqrt[11]/(2*Sqrt[2 - 3*x])], -2]))/(31*Sqrt[1 + 4*x]*Sqrt[-55/2 + 11*x])","A",1
66,1,130,189,0.7033793,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^2} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^2),x]","\frac{-3 \sqrt{55-22 x} \left(-14508 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)+6820 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)+26859 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)-\frac{51150 \sqrt{2-3 x} \sqrt{4 x+1} (2 x-5)}{5 x+7}}{56893122 \sqrt{2 x-5}}","-\frac{2 \sqrt{\frac{6}{11}} \sqrt{5-2 x} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right),\frac{1}{3}\right)}{713 \sqrt{2 x-5}}-\frac{25 \sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1}}{27807 (5 x+7)}+\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,"((-51150*Sqrt[2 - 3*x]*(-5 + 2*x)*Sqrt[1 + 4*x])/(7 + 5*x) - 3*Sqrt[55 - 22*x]*(6820*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - 14508*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 26859*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/(56893122*Sqrt[-5 + 2*x])","A",1
67,1,142,225,0.4598404,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^3} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^3),x]","\frac{-\sqrt{55-22 x} (5 x+7)^2 \left(-116097852 \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right),-\frac{1}{2}\right)+61059460 E\left(\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)+145479915 \Pi \left(\frac{55}{124};\sin ^{-1}\left(\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right)|-\frac{1}{2}\right)\right)-17050 \sqrt{2-3 x} (2 x-5) \sqrt{4 x+1} (44765 x+81209)}{703123130424 \sqrt{2 x-5} (5 x+7)^2}","-\frac{24007 \sqrt{5-2 x} \operatorname{EllipticF}\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{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{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,"(-17050*Sqrt[2 - 3*x]*(-5 + 2*x)*Sqrt[1 + 4*x]*(81209 + 44765*x) - Sqrt[55 - 22*x]*(7 + 5*x)^2*(61059460*EllipticE[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] - 116097852*EllipticF[ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2] + 145479915*EllipticPi[55/124, ArcSin[(2*Sqrt[2 - 3*x])/Sqrt[11]], -1/2]))/(703123130424*Sqrt[-5 + 2*x]*(7 + 5*x)^2)","A",1
68,1,180,137,0.5992655,"\int \frac{c i+d i x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[(c*i + d*i*x)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 i i \sqrt{c+d x} \sqrt{g+h x} \left(E\left(i \sinh ^{-1}\left(\sqrt{\frac{f (c+d x)}{d e-c f}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)-\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\sqrt{\frac{f (c+d x)}{d e-c f}}\right),\frac{d e h-c f h}{d f g-c f h}\right)\right)}{h \sqrt{e+f x} \sqrt{\frac{f (c+d x)}{d (e+f x)}} \sqrt{\frac{d (g+h x)}{d g-c h}}}","\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*I)*i*Sqrt[c + d*x]*Sqrt[g + h*x]*(EllipticE[I*ArcSinh[Sqrt[(f*(c + d*x))/(d*e - c*f)]], (d*e*h - c*f*h)/(d*f*g - c*f*h)] - EllipticF[I*ArcSinh[Sqrt[(f*(c + d*x))/(d*e - c*f)]], (d*e*h - c*f*h)/(d*f*g - c*f*h)]))/(h*Sqrt[(f*(c + d*x))/(d*(e + f*x))]*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)])","C",1
69,1,319,284,1.9741304,"\int \frac{a+b x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[(a + b*x)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \left(i d h (c+d x)^{3/2} (b e-a f) \sqrt{\frac{d (e+f x)}{f (c+d x)}} \sqrt{\frac{d (g+h x)}{h (c+d x)}} \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{d e}{f}-c}}{\sqrt{c+d x}}\right),\frac{d f g-c f h}{d e h-c f h}\right)-b d^2 (e+f x) (g+h x) \sqrt{\frac{d e}{f}-c}-i b h (c+d x)^{3/2} (d e-c f) \sqrt{\frac{d (e+f x)}{f (c+d x)}} \sqrt{\frac{d (g+h x)}{h (c+d x)}} E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{d e}{f}-c}}{\sqrt{c+d x}}\right)|\frac{d f g-c f h}{d e h-c f h}\right)\right)}{d^2 f h \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \sqrt{\frac{d e}{f}-c}}","\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}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right),\frac{h (d e-c f)}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}",1,"(-2*(-(b*d^2*Sqrt[-c + (d*e)/f]*(e + f*x)*(g + h*x)) - I*b*(d*e - c*f)*h*(c + d*x)^(3/2)*Sqrt[(d*(e + f*x))/(f*(c + d*x))]*Sqrt[(d*(g + h*x))/(h*(c + d*x))]*EllipticE[I*ArcSinh[Sqrt[-c + (d*e)/f]/Sqrt[c + d*x]], (d*f*g - c*f*h)/(d*e*h - c*f*h)] + I*d*(b*e - a*f)*h*(c + d*x)^(3/2)*Sqrt[(d*(e + f*x))/(f*(c + d*x))]*Sqrt[(d*(g + h*x))/(h*(c + d*x))]*EllipticF[I*ArcSinh[Sqrt[-c + (d*e)/f]/Sqrt[c + d*x]], (d*f*g - c*f*h)/(d*e*h - c*f*h)]))/(d^2*Sqrt[-c + (d*e)/f]*f*h*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])","C",1
70,1,226,165,1.4046853,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 i (c+d x) \sqrt{\frac{d (e+f x)}{f (c+d x)}} \sqrt{\frac{d (g+h x)}{h (c+d x)}} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{d e}{f}-c}}{\sqrt{c+d x}}\right),\frac{d f g-c f h}{d e h-c f h}\right)-\Pi \left(-\frac{b c f-a d f}{b d e-b c f};i \sinh ^{-1}\left(\frac{\sqrt{\frac{d e}{f}-c}}{\sqrt{c+d x}}\right)|\frac{d f g-c f h}{d e h-c f h}\right)\right)}{\sqrt{e+f x} \sqrt{g+h x} (a d-b c) \sqrt{\frac{d e}{f}-c}}","-\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*I)*(c + d*x)*Sqrt[(d*(e + f*x))/(f*(c + d*x))]*Sqrt[(d*(g + h*x))/(h*(c + d*x))]*(EllipticF[I*ArcSinh[Sqrt[-c + (d*e)/f]/Sqrt[c + d*x]], (d*f*g - c*f*h)/(d*e*h - c*f*h)] - EllipticPi[-((b*c*f - a*d*f)/(b*d*e - b*c*f)), I*ArcSinh[Sqrt[-c + (d*e)/f]/Sqrt[c + d*x]], (d*f*g - c*f*h)/(d*e*h - c*f*h)]))/((-(b*c) + a*d)*Sqrt[-c + (d*e)/f]*Sqrt[e + f*x]*Sqrt[g + h*x])","C",1
71,1,322,393,4.0510911,"\int \frac{1}{(a+b x) (c+d x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[1/((a + b*x)*(c + d*x)^(3/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 i (c+d x) \sqrt{\frac{d (e+f x)}{f (c+d x)}} \sqrt{\frac{d (g+h x)}{h (c+d x)}} \left((a d f-2 b c f+b d e) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right),\frac{d e h-c f h}{d f g-c f h}\right)+f (b c-a d) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)+b (c f-d e) \Pi \left(-\frac{b c h-a d h}{b d g-b c h};i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)\right)}{\sqrt{e+f x} \sqrt{g+h x} (b c-a d)^2 (c f-d e) \sqrt{\frac{d g}{h}-c}}","\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*I)*(c + d*x)*Sqrt[(d*(e + f*x))/(f*(c + d*x))]*Sqrt[(d*(g + h*x))/(h*(c + d*x))]*((b*c - a*d)*f*EllipticE[I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)] + (b*d*e - 2*b*c*f + a*d*f)*EllipticF[I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)] + b*(-(d*e) + c*f)*EllipticPi[-((b*c*h - a*d*h)/(b*d*g - b*c*h)), I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)]))/((b*c - a*d)^2*(-(d*e) + c*f)*Sqrt[-c + (d*g)/h]*Sqrt[e + f*x]*Sqrt[g + h*x])","C",1
72,1,721,875,15.7678424,"\int \frac{1}{(a+b x) (c+d x)^{5/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[1/((a + b*x)*(c + d*x)^(5/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 \left(d^2 (e+f x) (g+h x) (b c-a d) \sqrt{\frac{d g}{h}-c} \left((c+d x) \left(2 a d (-2 c f h+d e h+d f g)+b \left(7 c^2 f h-5 c d (e h+f g)+3 d^2 e g\right)\right)+(b c-a d) (c f-d e) (c h-d g)\right)-(c+d x) \left(d^2 (e+f x) (g+h x) (b c-a d) \sqrt{\frac{d g}{h}-c} \left(2 a d (-2 c f h+d e h+d f g)+b \left(7 c^2 f h-5 c d (e h+f g)+3 d^2 e g\right)\right)+i (c+d x)^{3/2} (d g-c h) \sqrt{\frac{d (e+f x)}{f (c+d x)}} \sqrt{\frac{d (g+h x)}{h (c+d x)}} \left(\left(a^2 d^2 f (-3 c f h+d e h+2 d f g)+a b d f \left(9 c^2 f h-c d (5 e h+7 f g)+3 d^2 e g\right)+b^2 \left(-9 c^3 f^2 h+2 c^2 d f (5 e h+4 f g)-3 c d^2 e (e h+3 f g)+3 d^3 e^2 g\right)\right) \operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right),\frac{d e h-c f h}{d f g-c f h}\right)-3 b^2 (d e-c f)^2 (d g-c h) \Pi \left(-\frac{b c h-a d h}{b d g-b c h};i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)+f (b c-a d) \left(2 a d (-2 c f h+d e h+d f g)+b \left(7 c^2 f h-5 c d (e h+f g)+3 d^2 e g\right)\right) E\left(i \sinh ^{-1}\left(\frac{\sqrt{\frac{d g}{h}-c}}{\sqrt{c+d x}}\right)|\frac{d e h-c f h}{d f g-c f h}\right)\right)\right)\right)}{3 (c+d x)^{3/2} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)^3 (d e-c f)^2 \sqrt{\frac{d g}{h}-c} (d g-c h)^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}} \operatorname{EllipticF}\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*(b*c - a*d)*Sqrt[-c + (d*g)/h]*(e + f*x)*(g + h*x)*((b*c - a*d)*(-(d*e) + c*f)*(-(d*g) + c*h) + (2*a*d*(d*f*g + d*e*h - 2*c*f*h) + b*(3*d^2*e*g + 7*c^2*f*h - 5*c*d*(f*g + e*h)))*(c + d*x)) - (c + d*x)*(d^2*(b*c - a*d)*Sqrt[-c + (d*g)/h]*(2*a*d*(d*f*g + d*e*h - 2*c*f*h) + b*(3*d^2*e*g + 7*c^2*f*h - 5*c*d*(f*g + e*h)))*(e + f*x)*(g + h*x) + I*(d*g - c*h)*(c + d*x)^(3/2)*Sqrt[(d*(e + f*x))/(f*(c + d*x))]*Sqrt[(d*(g + h*x))/(h*(c + d*x))]*((b*c - a*d)*f*(2*a*d*(d*f*g + d*e*h - 2*c*f*h) + b*(3*d^2*e*g + 7*c^2*f*h - 5*c*d*(f*g + e*h)))*EllipticE[I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)] + (a^2*d^2*f*(2*d*f*g + d*e*h - 3*c*f*h) + b^2*(3*d^3*e^2*g - 9*c^3*f^2*h - 3*c*d^2*e*(3*f*g + e*h) + 2*c^2*d*f*(4*f*g + 5*e*h)) + a*b*d*f*(3*d^2*e*g + 9*c^2*f*h - c*d*(7*f*g + 5*e*h)))*EllipticF[I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)] - 3*b^2*(d*e - c*f)^2*(d*g - c*h)*EllipticPi[-((b*c*h - a*d*h)/(b*d*g - b*c*h)), I*ArcSinh[Sqrt[-c + (d*g)/h]/Sqrt[c + d*x]], (d*e*h - c*f*h)/(d*f*g - c*f*h)]))))/(3*(b*c - a*d)^3*(d*e - c*f)^2*Sqrt[-c + (d*g)/h]*(d*g - c*h)^2*(c + d*x)^(3/2)*Sqrt[e + f*x]*Sqrt[g + h*x])","C",1
73,1,203,74,0.9052921,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f x} \sqrt{1+f x}} \, dx","Integrate[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f*x]*Sqrt[1 + f*x]),x]","\frac{2 i (c+d x) \sqrt{\frac{d (f x-1)}{f (c+d x)}} \sqrt{\frac{d f x+d}{c f+d f x}} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{c f+d}{f}}}{\sqrt{c+d x}}\right),\frac{c f-d}{c f+d}\right)-\Pi \left(\frac{b c f-a d f}{b d+b c f};i \sinh ^{-1}\left(\frac{\sqrt{-\frac{d+c f}{f}}}{\sqrt{c+d x}}\right)|\frac{c f-d}{d+c f}\right)\right)}{\sqrt{1-f^2 x^2} \sqrt{-\frac{c f+d}{f}} (a d-b c)}","-\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*I)*(c + d*x)*Sqrt[(d*(-1 + f*x))/(f*(c + d*x))]*Sqrt[(d + d*f*x)/(c*f + d*f*x)]*(EllipticF[I*ArcSinh[Sqrt[-((d + c*f)/f)]/Sqrt[c + d*x]], (-d + c*f)/(d + c*f)] - EllipticPi[(b*c*f - a*d*f)/(b*d + b*c*f), I*ArcSinh[Sqrt[-((d + c*f)/f)]/Sqrt[c + d*x]], (-d + c*f)/(d + c*f)]))/((-(b*c) + a*d)*Sqrt[-((d + c*f)/f)]*Sqrt[1 - f^2*x^2])","C",1
74,1,203,74,0.1681921,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^2 x^2}} \, dx","Integrate[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f^2*x^2]),x]","\frac{2 i (c+d x) \sqrt{\frac{d (f x-1)}{f (c+d x)}} \sqrt{\frac{d f x+d}{c f+d f x}} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{-\frac{c f+d}{f}}}{\sqrt{c+d x}}\right),\frac{c f-d}{c f+d}\right)-\Pi \left(\frac{b c f-a d f}{b d+b c f};i \sinh ^{-1}\left(\frac{\sqrt{-\frac{d+c f}{f}}}{\sqrt{c+d x}}\right)|\frac{c f-d}{d+c f}\right)\right)}{\sqrt{1-f^2 x^2} \sqrt{-\frac{c f+d}{f}} (a d-b c)}","-\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*I)*(c + d*x)*Sqrt[(d*(-1 + f*x))/(f*(c + d*x))]*Sqrt[(d + d*f*x)/(c*f + d*f*x)]*(EllipticF[I*ArcSinh[Sqrt[-((d + c*f)/f)]/Sqrt[c + d*x]], (-d + c*f)/(d + c*f)] - EllipticPi[(b*c*f - a*d*f)/(b*d + b*c*f), I*ArcSinh[Sqrt[-((d + c*f)/f)]/Sqrt[c + d*x]], (-d + c*f)/(d + c*f)]))/((-(b*c) + a*d)*Sqrt[-((d + c*f)/f)]*Sqrt[1 - f^2*x^2])","C",1
75,1,218,86,0.8579452,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^2 x} \sqrt{1+f^2 x}} \, dx","Integrate[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f^2*x]*Sqrt[1 + f^2*x]),x]","\frac{2 i (c+d x) \sqrt{\frac{d \left(f^2 x-1\right)}{f^2 (c+d x)}} \sqrt{\frac{d \left(f^2 x+1\right)}{f^2 (c+d x)}} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{-c-\frac{d}{f^2}}}{\sqrt{c+d x}}\right),\frac{c f^2-d}{c f^2+d}\right)-\Pi \left(\frac{(b c-a d) f^2}{b \left(c f^2+d\right)};i \sinh ^{-1}\left(\frac{\sqrt{-c-\frac{d}{f^2}}}{\sqrt{c+d x}}\right)|\frac{c f^2-d}{c f^2+d}\right)\right)}{\sqrt{1-f^4 x^2} \sqrt{-c-\frac{d}{f^2}} (a d-b c)}","-\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*I)*(c + d*x)*Sqrt[(d*(-1 + f^2*x))/(f^2*(c + d*x))]*Sqrt[(d*(1 + f^2*x))/(f^2*(c + d*x))]*(EllipticF[I*ArcSinh[Sqrt[-c - d/f^2]/Sqrt[c + d*x]], (-d + c*f^2)/(d + c*f^2)] - EllipticPi[((b*c - a*d)*f^2)/(b*(d + c*f^2)), I*ArcSinh[Sqrt[-c - d/f^2]/Sqrt[c + d*x]], (-d + c*f^2)/(d + c*f^2)]))/((-(b*c) + a*d)*Sqrt[-c - d/f^2]*Sqrt[1 - f^4*x^2])","C",1
76,1,218,86,0.1619766,"\int \frac{1}{(a+b x) \sqrt{c+d x} \sqrt{1-f^4 x^2}} \, dx","Integrate[1/((a + b*x)*Sqrt[c + d*x]*Sqrt[1 - f^4*x^2]),x]","\frac{2 i (c+d x) \sqrt{\frac{d \left(f^2 x-1\right)}{f^2 (c+d x)}} \sqrt{\frac{d \left(f^2 x+1\right)}{f^2 (c+d x)}} \left(\operatorname{EllipticF}\left(i \sinh ^{-1}\left(\frac{\sqrt{-c-\frac{d}{f^2}}}{\sqrt{c+d x}}\right),\frac{c f^2-d}{c f^2+d}\right)-\Pi \left(\frac{(b c-a d) f^2}{b \left(c f^2+d\right)};i \sinh ^{-1}\left(\frac{\sqrt{-c-\frac{d}{f^2}}}{\sqrt{c+d x}}\right)|\frac{c f^2-d}{c f^2+d}\right)\right)}{\sqrt{1-f^4 x^2} \sqrt{-c-\frac{d}{f^2}} (a d-b c)}","-\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*I)*(c + d*x)*Sqrt[(d*(-1 + f^2*x))/(f^2*(c + d*x))]*Sqrt[(d*(1 + f^2*x))/(f^2*(c + d*x))]*(EllipticF[I*ArcSinh[Sqrt[-c - d/f^2]/Sqrt[c + d*x]], (-d + c*f^2)/(d + c*f^2)] - EllipticPi[((b*c - a*d)*f^2)/(b*(d + c*f^2)), I*ArcSinh[Sqrt[-c - d/f^2]/Sqrt[c + d*x]], (-d + c*f^2)/(d + c*f^2)]))/((-(b*c) + a*d)*Sqrt[-c - d/f^2]*Sqrt[1 - f^4*x^2])","C",1
77,1,350,471,4.5987612,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2} \, dx","Integrate[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2),x]","-\frac{\sqrt{2 x-5} \sqrt{4 x+1} \left(-62507925572 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+78331458618 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(6 \left(39813120000 x^7+71414784000 x^6-288728294400 x^5-849459145920 x^4-795166559320 x^3+2861488598626 x^2+5225923788019 x+1118234665415\right)-60033082963 \sqrt{682} (2-3 x)^2 \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)\right)\right)}{398131200 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","-\frac{245264762213 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"-1/398131200*(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(78331458618*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 62507925572*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + Sqrt[(7 + 5*x)/(-2 + 3*x)]*(6*(1118234665415 + 5225923788019*x + 2861488598626*x^2 - 795166559320*x^3 - 849459145920*x^4 - 288728294400*x^5 + 71414784000*x^6 + 39813120000*x^7) - 60033082963*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",0
78,1,345,429,4.3306498,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2} \, dx","Integrate[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2),x]","-\frac{\sqrt{2 x-5} \sqrt{4 x+1} \left(-5426733148 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+7391284182 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(186 \left(414720000 x^6+40320000 x^5-3503236800 x^4-4479491480 x^3+9107809874 x^2+16491468251 x+3497259535\right)-4681665317 \sqrt{682} (2-3 x)^2 \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)\right)\right)}{514252800 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","-\frac{982275517 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"-1/514252800*(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7391284182*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 5426733148*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + Sqrt[(7 + 5*x)/(-2 + 3*x)]*(186*(3497259535 + 16491468251*x + 9107809874*x^2 - 4479491480*x^3 - 3503236800*x^4 + 40320000*x^5 + 414720000*x^6) - 4681665317*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",0
79,1,340,391,4.2666158,"\int \sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x} \, dx","Integrate[Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x],x]","-\frac{\sqrt{2 x-5} \sqrt{4 x+1} \left(-4532324 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+7269066 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(186 \left(1152000 x^5-2184000 x^4-7723240 x^3+7278862 x^2+17658613 x+3848705\right)-2120971 \sqrt{682} (2-3 x)^2 \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)\right)\right)}{5356800 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","-\frac{1368371 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"-1/5356800*(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7269066*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 4532324*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + Sqrt[(7 + 5*x)/(-2 + 3*x)]*(186*(3848705 + 17658613*x + 7278862*x^2 - 7723240*x^3 - 2184000*x^4 + 1152000*x^5) - 2120971*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",0
80,1,347,351,3.0692862,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{\sqrt{7+5 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/Sqrt[7 + 5*x],x]","\frac{\sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7} \left(\frac{117924 \sqrt{682} (3 x-2) (5 x+7) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-238266 \sqrt{682} (3 x-2) (5 x+7) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)-7 \sqrt{\frac{5 x+7}{3 x-2}} \left(13947 \sqrt{682} (2-3 x)^2 \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)-102114 \left(40 x^3-34 x^2-151 x-35\right)\right)}{\left(\frac{5 x+7}{3 x-2}\right)^{3/2} \left(-8 x^2+18 x+5\right) (2-3 x)}+66960 (2-3 x)\right)}{669600 \sqrt{2-3 x}}","-\frac{20057 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]*(66960*(2 - 3*x) + (-238266*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 117924*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 7*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-102114*(-35 - 151*x - 34*x^2 + 40*x^3) + 13947*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/((2 - 3*x)*((7 + 5*x)/(-2 + 3*x))^(3/2)*(5 + 18*x - 8*x^2))))/(669600*Sqrt[2 - 3*x])","A",0
81,1,330,349,2.9770666,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{3/2}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(3/2),x]","-\frac{\sqrt{2 x-5} \sqrt{4 x+1} \left(262 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-558 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(186 \left(120 x^3+394 x^2-1569 x-415\right)-427 \sqrt{682} (2-3 x)^2 \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)\right)\right)}{4650 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\frac{296 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"-1/4650*(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(-558*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 262*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + Sqrt[(7 + 5*x)/(-2 + 3*x)]*(186*(-415 - 1569*x + 394*x^2 + 120*x^3) - 427*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",0
82,1,366,391,3.226453,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{5/2}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(5/2),x]","\frac{\sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7} \left(\frac{30 \sqrt{6-9 x} (44765 x+34864)}{(5 x+7)^2}-\frac{2 \left(-37053 \sqrt{682} (3 x-2) (5 x+7) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+80577 \sqrt{682} (3 x-2) (5 x+7) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(48438 \sqrt{682} (2-3 x)^2 \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)-241731 \left(40 x^3-34 x^2-151 x-35\right)\right)\right)}{\sqrt{3} (2-3 x)^{3/2} \left(\frac{5 x+7}{3 x-2}\right)^{3/2} \left(-8 x^2+18 x+5\right)}\right)}{6256575 \sqrt{3}}","-\frac{496 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]*((30*Sqrt[6 - 9*x]*(34864 + 44765*x))/(7 + 5*x)^2 - (2*(80577*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 37053*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-241731*(-35 - 151*x - 34*x^2 + 40*x^3) + 48438*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(Sqrt[3]*(2 - 3*x)^(3/2)*((7 + 5*x)/(-2 + 3*x))^(3/2)*(5 + 18*x - 8*x^2))))/(6256575*Sqrt[3])","A",0
83,1,251,330,2.4583286,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{7/2}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(7/2),x]","-\frac{2 \sqrt{2 x-5} \sqrt{4 x+1} \left(-236555 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} (5 x+7)^3 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+713174 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} (5 x+7)^3 E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+31 \sqrt{\frac{5 x+7}{3 x-2}} \left(50105384 x^4-729949210 x^3+1137407943 x^2+880765228 x+137502130\right)\right)}{11598438735 \sqrt{2-3 x} (5 x+7)^{5/2} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","-\frac{48884 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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[-5 + 2*x]*Sqrt[1 + 4*x]*(31*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(137502130 + 880765228*x + 1137407943*x^2 - 729949210*x^3 + 50105384*x^4) + 713174*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^3*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 236555*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^3*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/(11598438735*Sqrt[2 - 3*x]*(7 + 5*x)^(5/2)*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",1
84,1,259,370,2.8064821,"\int \frac{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}}{(7+5 x)^{9/2}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])/(7 + 5*x)^(9/2),x]","\frac{2 \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7} \left(\frac{242 \left(19017205 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+203578437 \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)-67859479 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)\right)}{\sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}-\frac{(3 x-2) \left(10263746198750 x^3+54668919175710 x^2+113490310442229 x+15395515423270\right)}{(5 x+7)^4}\right)}{2257624501329015 \sqrt{2-3 x}}","-\frac{1212290288 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]*(-(((-2 + 3*x)*(15395515423270 + 113490310442229*x + 54668919175710*x^2 + 10263746198750*x^3))/(7 + 5*x)^4) + (242*(203578437*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2) - 67859479*Sqrt[682]*(-2 + 3*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 19017205*Sqrt[682]*(-2 + 3*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/(Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))))/(2257624501329015*Sqrt[2 - 3*x])","A",1
85,1,345,429,3.8518711,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^{5/2}}{\sqrt{-5+2 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2))/Sqrt[-5 + 2*x],x]","-\frac{\sqrt{2 x-5} \sqrt{4 x+1} \left(10666876180 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-12388907394 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(10695945839 \sqrt{682} \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} (2-3 x)^2 \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+186 \left(82944000 x^6+439372800 x^5+1004819520 x^4+3088122056 x^3-12645389558 x^2-26349657233 x-5752341805\right)\right)\right)}{41140224 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\frac{861015607 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"-1/41140224*(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(-12388907394*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 10666876180*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + Sqrt[(7 + 5*x)/(-2 + 3*x)]*(186*(-5752341805 - 26349657233*x - 12645389558*x^2 + 3088122056*x^3 + 1004819520*x^4 + 439372800*x^5 + 82944000*x^6) + 10695945839*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",0
86,1,340,391,3.7712717,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} (7+5 x)^{3/2}}{\sqrt{-5+2 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2))/Sqrt[-5 + 2*x],x]","-\frac{\sqrt{2 x-5} \sqrt{4 x+1} \left(31389484 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-37038366 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(31069121 \sqrt{682} \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} (2-3 x)^2 \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+186 \left(1152000 x^5+4555200 x^4+10641080 x^3-38640362 x^2-79187903 x-17232355\right)\right)\right)}{2142720 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\frac{2824441 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"-1/2142720*(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(-37038366*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 31389484*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + Sqrt[(7 + 5*x)/(-2 + 3*x)]*(186*(-17232355 - 79187903*x - 38640362*x^2 + 10641080*x^3 + 4555200*x^4 + 1152000*x^5) + 31069121*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",0
87,1,347,351,4.2136457,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x} \sqrt{7+5 x}}{\sqrt{-5+2 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])/Sqrt[-5 + 2*x],x]","\frac{\sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7} \left(66960 (2-3 x)-\frac{3 \left(76756 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+94674 \sqrt{682} (2-3 x) (5 x+7) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(70919 \sqrt{682} \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} (2-3 x)^2 \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+284022 \left(40 x^3-34 x^2-151 x-35\right)\right)\right)}{(2-3 x) \left(\frac{5 x+7}{3 x-2}\right)^{3/2} \left(-8 x^2+18 x+5\right)}\right)}{267840 \sqrt{2-3 x}}","\frac{8959 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]*(66960*(2 - 3*x) - (3*(94674*Sqrt[682]*(2 - 3*x)*(7 + 5*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 76756*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + Sqrt[(7 + 5*x)/(-2 + 3*x)]*(284022*(-35 - 151*x - 34*x^2 + 40*x^3) + 70919*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/((2 - 3*x)*((7 + 5*x)/(-2 + 3*x))^(3/2)*(5 + 18*x - 8*x^2))))/(267840*Sqrt[2 - 3*x])","A",0
88,1,318,365,1.289478,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} \sqrt{7+5 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*Sqrt[7 + 5*x]),x]","\frac{\sqrt{2-3 x} \left(1984 \sqrt{682} \sqrt{\frac{5-2 x}{5 x+7}} \sqrt{\frac{4 x+1}{5 x+7}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{155-62 x}{55 x+77}}\right),\frac{23}{62}\right)-3410 \sqrt{682} \sqrt{\frac{5-2 x}{5 x+7}} \sqrt{\frac{4 x+1}{5 x+7}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{155-62 x}{55 x+77}}\right)|\frac{23}{62}\right)+\sqrt{\frac{3 x-2}{5 x+7}} \left(17050 \left(24 x^3-70 x^2+21 x+10\right)-1599 \sqrt{682} \sqrt{\frac{4 x+1}{5 x+7}} (5 x+7)^2 \sqrt{\frac{-6 x^2+19 x-10}{(5 x+7)^2}} \Pi \left(-\frac{55}{62};\sin ^{-1}\left(\sqrt{\frac{155-62 x}{55 x+77}}\right)|\frac{23}{62}\right)\right)\right)}{34100 \sqrt{2 x-5} \sqrt{4 x+1} \left(\frac{3 x-2}{5 x+7}\right)^{3/2} (5 x+7)^{3/2}}","\frac{7 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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} \operatorname{EllipticF}\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{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{5 \sqrt{2 x-5}}-\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]*(-3410*Sqrt[682]*Sqrt[(5 - 2*x)/(7 + 5*x)]*Sqrt[(1 + 4*x)/(7 + 5*x)]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[(155 - 62*x)/(77 + 55*x)]], 23/62] + 1984*Sqrt[682]*Sqrt[(5 - 2*x)/(7 + 5*x)]*Sqrt[(1 + 4*x)/(7 + 5*x)]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[(155 - 62*x)/(77 + 55*x)]], 23/62] + Sqrt[(-2 + 3*x)/(7 + 5*x)]*(17050*(10 + 21*x - 70*x^2 + 24*x^3) - 1599*Sqrt[682]*Sqrt[(1 + 4*x)/(7 + 5*x)]*(7 + 5*x)^2*Sqrt[(-10 + 19*x - 6*x^2)/(7 + 5*x)^2]*EllipticPi[-55/62, ArcSin[Sqrt[(155 - 62*x)/(77 + 55*x)]], 23/62])))/(34100*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*((-2 + 3*x)/(7 + 5*x))^(3/2)*(7 + 5*x)^(3/2))","A",0
89,1,326,279,2.4669572,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{3/2}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(3/2)),x]","\frac{\sqrt{2 x-5} \sqrt{4 x+1} \left(23 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-62 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)-2 \sqrt{\frac{5 x+7}{3 x-2}} \left(39 \sqrt{682} (2-3 x)^2 \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)-961 \left(8 x^2-18 x-5\right)\right)\right)}{6045 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","-\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,"(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(-62*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 23*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 2*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-961*(-5 - 18*x + 8*x^2) + 39*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(6045*Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",0
90,1,246,290,1.9500501,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{5/2}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(5/2)),x]","-\frac{2 \sqrt{2 x-5} \sqrt{4 x+1} \left(506 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} (5 x+7)^2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-935 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} (5 x+7)^2 E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+31 \sqrt{\frac{5 x+7}{3 x-2}} \left(58928 x^3-94580 x^2-122348 x-23755\right)\right)}{3253419 \sqrt{2-3 x} (5 x+7)^{3/2} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\frac{44 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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[-5 + 2*x]*Sqrt[1 + 4*x]*(31*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-23755 - 122348*x - 94580*x^2 + 58928*x^3) - 935*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^2*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 506*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^2*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/(3253419*Sqrt[2 - 3*x]*(7 + 5*x)^(3/2)*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",1
91,1,251,330,1.8678973,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{7/2}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(7/2)),x]","-\frac{2 \sqrt{2 x-5} \sqrt{4 x+1} \left(958111 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} (5 x+7)^3 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-2046484 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} (5 x+7)^3 E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+31 \sqrt{\frac{5 x+7}{3 x-2}} \left(370051256 x^4+643813106 x^3-2953846743 x^2-2271416114 x-374624540\right)\right)}{90467822133 \sqrt{2-3 x} (5 x+7)^{5/2} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\frac{111628 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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[-5 + 2*x]*Sqrt[1 + 4*x]*(31*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-374624540 - 2271416114*x - 2953846743*x^2 + 643813106*x^3 + 370051256*x^4) - 2046484*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^3*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 958111*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^3*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/(90467822133*Sqrt[2 - 3*x]*(7 + 5*x)^(5/2)*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",1
92,1,258,370,2.4512325,"\int \frac{\sqrt{2-3 x} \sqrt{1+4 x}}{\sqrt{-5+2 x} (7+5 x)^{9/2}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[1 + 4*x])/(Sqrt[-5 + 2*x]*(7 + 5*x)^(9/2)),x]","\frac{2 \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7} \left(\frac{(3 x-2) \left(2559027583750 x^3+12313608173580 x^2+19165803061167 x+2552362046246\right)}{(5 x+7)^4}-\frac{22 \left(71545594 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+558333291 \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)-186111097 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)\right)}{\sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}\right)}{1956607901151813 \sqrt{2-3 x}}","\frac{258506776 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]*(((-2 + 3*x)*(2552362046246 + 19165803061167*x + 12313608173580*x^2 + 2559027583750*x^3))/(7 + 5*x)^4 - (22*(558333291*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2) - 186111097*Sqrt[682]*(-2 + 3*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 71545594*Sqrt[682]*(-2 + 3*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/(Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))))/(1956607901151813*Sqrt[2 - 3*x])","A",1
93,1,340,391,2.6173882,"\int \frac{\sqrt{2-3 x} (7+5 x)^{5/2}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*(7 + 5*x)^(5/2))/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\frac{\sqrt{2 x-5} \sqrt{4 x+1} \left(46704724 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-57187746 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(47673695 \sqrt{682} \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} (2-3 x)^2 \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+186 \left(1152000 x^5+6542400 x^4+20626760 x^3-56065622 x^2-124999073 x-27447805\right)\right)\right)}{1714176 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\frac{5241511 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"-1/1714176*(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(-57187746*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 46704724*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + Sqrt[(7 + 5*x)/(-2 + 3*x)]*(186*(-27447805 - 124999073*x - 56065622*x^2 + 20626760*x^3 + 6542400*x^4 + 1152000*x^5) + 47673695*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",0
94,1,349,351,3.3409083,"\int \frac{\sqrt{2-3 x} (7+5 x)^{3/2}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*(7 + 5*x)^(3/2))/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{\sqrt{2-3 x} \sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7} \left(\frac{(2-3 x) \left(\frac{998820 \sqrt{682} (5 x+7) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)}{(2-3 x)^2}-\frac{1314090 \sqrt{682} (5 x+7) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)}{(2-3 x)^2}+\sqrt{\frac{5 x+7}{3 x-2}} \left(\frac{1082907 \sqrt{682} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} \left(\frac{4 x+1}{3 x-2}\right)^{3/2} \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)}{4 x+1}+\frac{3942270 \left(40 x^3-34 x^2-151 x-35\right)}{(3 x-2)^3}\right)\right)}{\left(\frac{5 x+7}{3 x-2}\right)^{3/2} \left(-8 x^2+18 x+5\right)}+200880\right)}{642816}","\frac{17515 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]*(200880 + ((2 - 3*x)*((-1314090*Sqrt[682]*(7 + 5*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])/(2 - 3*x)^2 + (998820*Sqrt[682]*(7 + 5*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])/(2 - 3*x)^2 + Sqrt[(7 + 5*x)/(-2 + 3*x)]*((3942270*(-35 - 151*x - 34*x^2 + 40*x^3))/(-2 + 3*x)^3 + (1082907*Sqrt[682]*((1 + 4*x)/(-2 + 3*x))^(3/2)*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])/(1 + 4*x))))/(((7 + 5*x)/(-2 + 3*x))^(3/2)*(5 + 18*x - 8*x^2))))/642816","A",0
95,1,347,365,1.4723597,"\int \frac{\sqrt{2-3 x} \sqrt{7+5 x}}{\sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(Sqrt[2 - 3*x]*Sqrt[7 + 5*x])/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\frac{-1265 \sqrt{341} \sqrt{\frac{3 x-2}{4 x+1}} \sqrt{\frac{5 x+7}{4 x+1}} \left(8 x^2-18 x-5\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{22}{39}} \sqrt{\frac{5 x+7}{4 x+1}}\right),\frac{39}{62}\right)+6820 \sqrt{341} \sqrt{\frac{3 x-2}{4 x+1}} \sqrt{\frac{5 x+7}{4 x+1}} \left(8 x^2-18 x-5\right) E\left(\sin ^{-1}\left(\sqrt{\frac{22}{39}} \sqrt{\frac{5 x+7}{4 x+1}}\right)|\frac{39}{62}\right)+\sqrt{\frac{2 x-5}{4 x+1}} \left(4117 \sqrt{341} \sqrt{\frac{3 x-2}{4 x+1}} \sqrt{\frac{10 x^2-11 x-35}{(4 x+1)^2}} (4 x+1)^2 \Pi \left(\frac{78}{55};\sin ^{-1}\left(\sqrt{\frac{22}{39}} \sqrt{\frac{5 x+7}{4 x+1}}\right)|\frac{39}{62}\right)+13640 \sqrt{2} \left(30 x^3-53 x^2-83 x+70\right)\right)}{27280 \sqrt{2-3 x} \sqrt{4 x-10} \sqrt{\frac{2 x-5}{4 x+1}} \sqrt{4 x+1} \sqrt{5 x+7}}","-\frac{39 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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} \operatorname{EllipticF}\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{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{4 \sqrt{2 x-5}}-\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,"-1/27280*(6820*Sqrt[341]*Sqrt[(-2 + 3*x)/(1 + 4*x)]*Sqrt[(7 + 5*x)/(1 + 4*x)]*(-5 - 18*x + 8*x^2)*EllipticE[ArcSin[Sqrt[22/39]*Sqrt[(7 + 5*x)/(1 + 4*x)]], 39/62] - 1265*Sqrt[341]*Sqrt[(-2 + 3*x)/(1 + 4*x)]*Sqrt[(7 + 5*x)/(1 + 4*x)]*(-5 - 18*x + 8*x^2)*EllipticF[ArcSin[Sqrt[22/39]*Sqrt[(7 + 5*x)/(1 + 4*x)]], 39/62] + Sqrt[(-5 + 2*x)/(1 + 4*x)]*(13640*Sqrt[2]*(70 - 83*x - 53*x^2 + 30*x^3) + 4117*Sqrt[341]*Sqrt[(-2 + 3*x)/(1 + 4*x)]*(1 + 4*x)^2*Sqrt[(-35 - 11*x + 10*x^2)/(1 + 4*x)^2]*EllipticPi[78/55, ArcSin[Sqrt[22/39]*Sqrt[(7 + 5*x)/(1 + 4*x)]], 39/62]))/(Sqrt[2 - 3*x]*Sqrt[-10 + 4*x]*Sqrt[(-5 + 2*x)/(1 + 4*x)]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x])","A",0
96,1,170,101,0.5884901,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x}} \, dx","Integrate[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]),x]","\frac{\sqrt{\frac{4 x+1}{5 x+7}} (5 x+7)^{3/2} \left(117 \sqrt{\frac{-6 x^2+19 x-10}{(5 x+7)^2}} \Pi \left(-\frac{55}{62};\sin ^{-1}\left(\sqrt{\frac{155-62 x}{55 x+77}}\right)|\frac{23}{62}\right)-62 \sqrt{\frac{5-2 x}{5 x+7}} \sqrt{\frac{3 x-2}{5 x+7}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{155-62 x}{55 x+77}}\right),\frac{23}{62}\right)\right)}{5 \sqrt{682} \sqrt{2-3 x} \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,"(Sqrt[(1 + 4*x)/(7 + 5*x)]*(7 + 5*x)^(3/2)*(-62*Sqrt[(5 - 2*x)/(7 + 5*x)]*Sqrt[(-2 + 3*x)/(7 + 5*x)]*EllipticF[ArcSin[Sqrt[(155 - 62*x)/(77 + 55*x)]], 23/62] + 117*Sqrt[(-10 + 19*x - 6*x^2)/(7 + 5*x)^2]*EllipticPi[-55/62, ArcSin[Sqrt[(155 - 62*x)/(77 + 55*x)]], 23/62]))/(5*Sqrt[682]*Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x])","A",0
97,1,237,60,1.8598606,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2}} \, dx","Integrate[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2)),x]","\frac{\sqrt{2 x-5} \sqrt{4 x+1} \left(-23 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-1922 \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)+62 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)\right)}{27807 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\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,"(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(-1922*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2) + 62*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 23*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/(27807*Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","B",1
98,1,248,290,1.915828,"\int \frac{\sqrt{2-3 x}}{\sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2}} \, dx","Integrate[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2)),x]","-\frac{2 \sqrt{2 x-5} \sqrt{4 x+1} \left(31 \left(92 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} (5 x+7)^2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+\sqrt{\frac{5 x+7}{3 x-2}} \left(285680 x^3-20372 x^2-1578968 x-389005\right)\right)-9833 \sqrt{682} (3 x-2) (5 x+7)^2 \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)\right)}{74828637 \sqrt{2-3 x} (5 x+7)^{3/2} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\frac{716 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"(-2*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(-9833*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^2*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 31*(Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-389005 - 1578968*x - 20372*x^2 + 285680*x^3) + 92*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^2*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62])))/(74828637*Sqrt[2 - 3*x]*(7 + 5*x)^(3/2)*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",1
99,1,6667,721,15.0463009,"\int \frac{\sqrt{a+b x} \sqrt{c+d x}}{\sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[(Sqrt[a + b*x]*Sqrt[c + d*x])/(Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\text{Result too large to show}","\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)}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{e+f x} \sqrt{b g-a h}}{\sqrt{a+b x} \sqrt{f g-e h}}\right),-\frac{(b c-a d) (f g-e h)}{(b g-a h) (d e-c f)}\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{(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{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,"Result too large to show","B",0
100,1,206,161,5.2060379,"\int \frac{\sqrt{c+d x}}{(a+b x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[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{e+f x} \sqrt{g+h x} E\left(\sin ^{-1}\left(\sqrt{\frac{(a f-b e) (g+h x)}{(f g-e h) (a+b x)}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{(a+b x)^{3/2} (e h-f g) \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{-\frac{(e+f x) (g+h x) (b e-a f) (b g-a h)}{(a+b x)^2 (f g-e h)^2}}}","-\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[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]*EllipticE[ArcSin[Sqrt[((-(b*e) + a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))]], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/((-(f*g) + e*h)*(a + b*x)^(3/2)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[-(((b*e - a*f)*(b*g - a*h)*(e + f*x)*(g + h*x))/((f*g - e*h)^2*(a + b*x)^2))])","A",1
101,1,347,351,2.6056266,"\int \frac{(7+5 x)^{5/2}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(7 + 5*x)^(5/2)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{\sqrt{2 x-5} \sqrt{4 x+1} \sqrt{5 x+7} \left(\frac{17113116 \sqrt{682} (3 x-2) (5 x+7) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-13104630 \sqrt{682} (3 x-2) (5 x+7) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)-385 \sqrt{\frac{5 x+7}{3 x-2}} \left(-47445 \sqrt{682} \sqrt{\frac{4 x+1}{3 x-2}} \sqrt{\frac{10 x^2-11 x-35}{(2-3 x)^2}} (2-3 x)^2 \Pi \left(\frac{117}{62};\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)-102114 \left(40 x^3-34 x^2-151 x-35\right)\right)}{(2-3 x) \left(\frac{5 x+7}{3 x-2}\right)^{3/2} \left(-8 x^2+18 x+5\right)}+1227600 (3 x-2)\right)}{2356992 \sqrt{2-3 x}}","\frac{29047 \sqrt{\frac{23}{11}} \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]*(1227600*(-2 + 3*x) + (-13104630*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] + 17113116*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 385*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-102114*(-35 - 151*x - 34*x^2 + 40*x^3) - 47445*Sqrt[682]*(2 - 3*x)^2*Sqrt[(1 + 4*x)/(-2 + 3*x)]*Sqrt[(-35 - 11*x + 10*x^2)/(2 - 3*x)^2]*EllipticPi[117/62, ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/((2 - 3*x)*((7 + 5*x)/(-2 + 3*x))^(3/2)*(5 + 18*x - 8*x^2))))/(2356992*Sqrt[2 - 3*x])","A",0
102,1,347,469,1.3228658,"\int \frac{(7+5 x)^{3/2}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[(7 + 5*x)^(3/2)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","\frac{\sqrt{2 x-5} \left(-6969 \sqrt{341} \sqrt{\frac{3 x-2}{4 x+1}} \sqrt{\frac{5 x+7}{4 x+1}} \left(8 x^2-18 x-5\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{22}{39}} \sqrt{\frac{5 x+7}{4 x+1}}\right),\frac{39}{62}\right)+6820 \sqrt{341} \sqrt{\frac{3 x-2}{4 x+1}} \sqrt{\frac{5 x+7}{4 x+1}} \left(8 x^2-18 x-5\right) E\left(\sin ^{-1}\left(\sqrt{\frac{22}{39}} \sqrt{\frac{5 x+7}{4 x+1}}\right)|\frac{39}{62}\right)+\sqrt{\frac{2 x-5}{4 x+1}} \left(9821 \sqrt{341} \sqrt{\frac{3 x-2}{4 x+1}} \sqrt{\frac{10 x^2-11 x-35}{(4 x+1)^2}} (4 x+1)^2 \Pi \left(\frac{78}{55};\sin ^{-1}\left(\sqrt{\frac{22}{39}} \sqrt{\frac{5 x+7}{4 x+1}}\right)|\frac{39}{62}\right)+13640 \sqrt{2} \left(30 x^3-53 x^2-83 x+70\right)\right)\right)}{16368 \sqrt{4-6 x} \left(\frac{2 x-5}{4 x+1}\right)^{3/2} (4 x+1)^{3/2} \sqrt{5 x+7}}","\frac{65 \sqrt{\frac{11}{23}} \sqrt{5 x+7} \operatorname{EllipticF}\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} \operatorname{EllipticF}\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{2-3 x} \sqrt{4 x+1} \sqrt{5 x+7}}{12 \sqrt{2 x-5}}+\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,"(Sqrt[-5 + 2*x]*(6820*Sqrt[341]*Sqrt[(-2 + 3*x)/(1 + 4*x)]*Sqrt[(7 + 5*x)/(1 + 4*x)]*(-5 - 18*x + 8*x^2)*EllipticE[ArcSin[Sqrt[22/39]*Sqrt[(7 + 5*x)/(1 + 4*x)]], 39/62] - 6969*Sqrt[341]*Sqrt[(-2 + 3*x)/(1 + 4*x)]*Sqrt[(7 + 5*x)/(1 + 4*x)]*(-5 - 18*x + 8*x^2)*EllipticF[ArcSin[Sqrt[22/39]*Sqrt[(7 + 5*x)/(1 + 4*x)]], 39/62] + Sqrt[(-5 + 2*x)/(1 + 4*x)]*(13640*Sqrt[2]*(70 - 83*x - 53*x^2 + 30*x^3) + 9821*Sqrt[341]*Sqrt[(-2 + 3*x)/(1 + 4*x)]*(1 + 4*x)^2*Sqrt[(-35 - 11*x + 10*x^2)/(1 + 4*x)^2]*EllipticPi[78/55, ArcSin[Sqrt[22/39]*Sqrt[(7 + 5*x)/(1 + 4*x)]], 39/62])))/(16368*Sqrt[4 - 6*x]*((-5 + 2*x)/(1 + 4*x))^(3/2)*(1 + 4*x)^(3/2)*Sqrt[7 + 5*x])","A",0
103,1,95,100,0.1705025,"\int \frac{\sqrt{7+5 x}}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x}} \, dx","Integrate[Sqrt[7 + 5*x]/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]","-\frac{62 \sqrt{4 x+1} \sqrt{\frac{5-2 x}{5 x+7}} \Pi \left(-\frac{55}{69};\sin ^{-1}\left(\frac{\sqrt{\frac{23}{11}} \sqrt{2-3 x}}{\sqrt{5 x+7}}\right)|-\frac{39}{23}\right)}{3 \sqrt{253} \sqrt{2 x-5} \sqrt{\frac{4 x+1}{5 x+7}}}","\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,"(-62*Sqrt[1 + 4*x]*Sqrt[(5 - 2*x)/(7 + 5*x)]*EllipticPi[-55/69, ArcSin[(Sqrt[23/11]*Sqrt[2 - 3*x])/Sqrt[7 + 5*x]], -39/23])/(3*Sqrt[253]*Sqrt[-5 + 2*x]*Sqrt[(1 + 4*x)/(7 + 5*x)])","A",1
104,1,90,71,0.1631867,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} \sqrt{7+5 x}} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*Sqrt[7 + 5*x]),x]","-\frac{2 \sqrt{4 x+1} \sqrt{\frac{5-2 x}{5 x+7}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{\frac{23}{11}} \sqrt{2-3 x}}{\sqrt{5 x+7}}\right),-\frac{39}{23}\right)}{\sqrt{253} \sqrt{2 x-5} \sqrt{\frac{4 x+1}{5 x+7}}}","\frac{2 \sqrt{5 x+7} \operatorname{EllipticF}\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[1 + 4*x]*Sqrt[(5 - 2*x)/(7 + 5*x)]*EllipticF[ArcSin[(Sqrt[23/11]*Sqrt[2 - 3*x])/Sqrt[7 + 5*x]], -39/23])/(Sqrt[253]*Sqrt[-5 + 2*x]*Sqrt[(1 + 4*x)/(7 + 5*x)])","A",1
105,1,237,195,1.6912735,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{3/2}} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(3/2)),x]","-\frac{2 \sqrt{2 x-5} \sqrt{4 x+1} \left(-23 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)+1705 \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)-55 \sqrt{682} \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} \left(15 x^2+11 x-14\right) E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)\right)}{305877 \sqrt{2-3 x} \sqrt{5 x+7} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\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}} \operatorname{EllipticF}\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,"(-2*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(1705*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2) - 55*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 23*Sqrt[682]*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*(-14 + 11*x + 15*x^2)*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/(305877*Sqrt[2 - 3*x]*Sqrt[7 + 5*x]*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",1
106,1,246,288,1.8261227,"\int \frac{1}{\sqrt{2-3 x} \sqrt{-5+2 x} \sqrt{1+4 x} (7+5 x)^{5/2}} \, dx","Integrate[1/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(7 + 5*x)^(5/2)),x]","-\frac{2 \sqrt{2 x-5} \sqrt{4 x+1} \left(-28819 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} (5 x+7)^2 \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right),\frac{39}{62}\right)-984830 \sqrt{682} (3 x-2) \sqrt{\frac{8 x^2-18 x-5}{(2-3 x)^2}} (5 x+7)^2 E\left(\sin ^{-1}\left(\sqrt{\frac{31}{39}} \sqrt{\frac{2 x-5}{3 x-2}}\right)|\frac{39}{62}\right)+1705 \sqrt{\frac{5 x+7}{3 x-2}} \left(608600 x^3-294854 x^2-2797991 x-671560\right)\right)}{25516565217 \sqrt{2-3 x} (5 x+7)^{3/2} \sqrt{\frac{5 x+7}{3 x-2}} \left(8 x^2-18 x-5\right)}","\frac{103964 \sqrt{5 x+7} \operatorname{EllipticF}\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{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{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,"(-2*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]*(1705*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-671560 - 2797991*x - 294854*x^2 + 608600*x^3) - 984830*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^2*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticE[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62] - 28819*Sqrt[682]*(-2 + 3*x)*(7 + 5*x)^2*Sqrt[(-5 - 18*x + 8*x^2)/(2 - 3*x)^2]*EllipticF[ArcSin[Sqrt[31/39]*Sqrt[(-5 + 2*x)/(-2 + 3*x)]], 39/62]))/(25516565217*Sqrt[2 - 3*x]*(7 + 5*x)^(3/2)*Sqrt[(7 + 5*x)/(-2 + 3*x)]*(-5 - 18*x + 8*x^2))","A",1
107,1,6638,968,14.1578307,"\int \frac{(a+b x)^{3/2}}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[(a + b*x)^(3/2)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\text{Result too large to show}","-\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} \operatorname{EllipticF}\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,"Result too large to show","B",0
108,1,584,228,5.5764114,"\int \frac{\sqrt{a+b x}}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[Sqrt[a + b*x]/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 (c+d x)^{3/2} \sqrt{\frac{(a+b x) (d g-c h)}{(c+d x) (b g-a h)}} \left(\frac{a d (g+h x) \sqrt{\frac{(e+f x) (d g-c h)}{(c+d x) (f g-e h)}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{(g+h x) (c f-d e)}{(c+d x) (f g-e h)}}\right),\frac{(b c-a d) (e h-f g)}{(b g-a h) (d e-c f)}\right)}{(c+d x) (d g-c h) \sqrt{\frac{(g+h x) (c f-d e)}{(c+d x) (f g-e h)}}}+\frac{b c (g+h x) \sqrt{\frac{(e+f x) (d g-c h)}{(c+d x) (f g-e h)}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{(g+h x) (c f-d e)}{(c+d x) (f g-e h)}}\right),\frac{(b c-a d) (e h-f g)}{(b g-a h) (d e-c f)}\right)}{(c+d x) (c h-d g) \sqrt{\frac{(g+h x) (c f-d e)}{(c+d x) (f g-e h)}}}+\frac{b (f g-e h) \sqrt{-\frac{(e+f x) (g+h x) (d e-c f) (d g-c h)}{(c+d x)^2 (f g-e h)^2}} \Pi \left(\frac{d (e h-f g)}{(d e-c f) h};\sin ^{-1}\left(\sqrt{\frac{(c f-d e) (g+h x)}{(f g-e h) (c+d x)}}\right)|\frac{(b c-a d) (e h-f g)}{(d e-c f) (b g-a h)}\right)}{h (d e-c f)}\right)}{d \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h 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}}",1,"(-2*Sqrt[((d*g - c*h)*(a + b*x))/((b*g - a*h)*(c + d*x))]*(c + d*x)^(3/2)*((a*d*Sqrt[((d*g - c*h)*(e + f*x))/((f*g - e*h)*(c + d*x))]*(g + h*x)*EllipticF[ArcSin[Sqrt[((-(d*e) + c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))]], ((b*c - a*d)*(-(f*g) + e*h))/((d*e - c*f)*(b*g - a*h))])/((d*g - c*h)*(c + d*x)*Sqrt[((-(d*e) + c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))]) + (b*c*Sqrt[((d*g - c*h)*(e + f*x))/((f*g - e*h)*(c + d*x))]*(g + h*x)*EllipticF[ArcSin[Sqrt[((-(d*e) + c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))]], ((b*c - a*d)*(-(f*g) + e*h))/((d*e - c*f)*(b*g - a*h))])/((-(d*g) + c*h)*(c + d*x)*Sqrt[((-(d*e) + c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))]) + (b*(f*g - e*h)*Sqrt[-(((d*e - c*f)*(d*g - c*h)*(e + f*x)*(g + h*x))/((f*g - e*h)^2*(c + d*x)^2))]*EllipticPi[(d*(-(f*g) + e*h))/((d*e - c*f)*h), ArcSin[Sqrt[((-(d*e) + c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))]], ((b*c - a*d)*(-(f*g) + e*h))/((d*e - c*f)*(b*g - a*h))])/((d*e - c*f)*h)))/(d*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])","B",1
109,1,227,161,1.3366783,"\int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[1/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \sqrt{a+b x} \sqrt{g+h x} \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)}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\sqrt{\frac{(g+h x) (a f-b e)}{(a+b x) (f g-e h)}}\right),\frac{(a d-b c) (e h-f g)}{(b e-a f) (d g-c h)}\right)}{\sqrt{c+d x} \sqrt{e+f x} (b g-a h) \sqrt{\frac{(g+h x) (a f-b e)}{(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)}} \operatorname{EllipticF}\left(\tan ^{-1}\left(\frac{\sqrt{g+h x} \sqrt{b e-a f}}{\sqrt{a+b x} \sqrt{f g-e h}}\right),\frac{(b g-a h) (d e-c f)}{(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[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))]*Sqrt[g + h*x]*EllipticF[ArcSin[Sqrt[((-(b*e) + a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))]], ((-(b*c) + a*d)*(-(f*g) + e*h))/((b*e - a*f)*(d*g - c*h))])/((b*g - a*h)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[((-(b*e) + a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))])","A",1
110,1,3247,429,14.1419925,"\int \frac{1}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[1/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\text{Result too large to show}","-\frac{2 d \sqrt{g+h x} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{e+f x} \sqrt{b g-a h}}{\sqrt{a+b x} \sqrt{f g-e h}}\right),-\frac{(b c-a d) (f g-e h)}{(b g-a h) (d e-c f)}\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^2*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[a + b*x]) - (2*(-((b*(c + d*x)^(3/2)*(f + (d*e)/(c + d*x) - (c*f)/(c + d*x))*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x))*Sqrt[a + ((c + d*x)*(b - (b*c)/(c + d*x)))/d])/(Sqrt[e + ((c + d*x)*(f - (c*f)/(c + d*x)))/d]*Sqrt[g + ((c + d*x)*(h - (c*h)/(c + d*x)))/d])) + ((b*c - a*d)*f*(b*g - a*h)*(-(d*g) + c*h)*Sqrt[c + d*x]*Sqrt[(b - (b*c)/(c + d*x) + (a*d)/(c + d*x))*(f + (d*e)/(c + d*x) - (c*f)/(c + d*x))*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x))]*Sqrt[a + ((c + d*x)*(b - (b*c)/(c + d*x)))/d]*((d*e*Sqrt[((b*c - a*d)*(-(d*g) + c*h)*(b/(b*c - a*d) - (c + d*x)^(-1)))/(-(b*d*g) + a*d*h)]*(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))*Sqrt[(-(h/(-(d*g) + c*h)) + (c + d*x)^(-1))/(f/(-(d*e) + c*f) - h/(-(d*g) + c*h))]*(((-(b*d*g) + a*d*h)*EllipticE[ArcSin[Sqrt[((d*e - c*f)*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/((b*c - a*d)*(-(d*g) + c*h)) - (b*EllipticF[ArcSin[Sqrt[((d*e - c*f)*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/(b*c - a*d)))/(Sqrt[(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))/(-(f/(-(d*e) + c*f)) + h/(-(d*g) + c*h))]*Sqrt[(b + (-(b*c) + a*d)/(c + d*x))*(f + (d*e - c*f)/(c + d*x))*(h + (d*g - c*h)/(c + d*x))]) - (c*f*Sqrt[((b*c - a*d)*(-(d*g) + c*h)*(b/(b*c - a*d) - (c + d*x)^(-1)))/(-(b*d*g) + a*d*h)]*(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))*Sqrt[(-(h/(-(d*g) + c*h)) + (c + d*x)^(-1))/(f/(-(d*e) + c*f) - h/(-(d*g) + c*h))]*(((-(b*d*g) + a*d*h)*EllipticE[ArcSin[Sqrt[((d*e - c*f)*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/((b*c - a*d)*(-(d*g) + c*h)) - (b*EllipticF[ArcSin[Sqrt[((d*e - c*f)*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/(b*c - a*d)))/(Sqrt[(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))/(-(f/(-(d*e) + c*f)) + h/(-(d*g) + c*h))]*Sqrt[(b + (-(b*c) + a*d)/(c + d*x))*(f + (d*e - c*f)/(c + d*x))*(h + (d*g - c*h)/(c + d*x))]) + (f*Sqrt[(-(b/(b*c - a*d)) + (c + d*x)^(-1))/(-(b/(b*c - a*d)) + h/(-(d*g) + c*h))]*Sqrt[(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))/(-(f/(-(d*e) + c*f)) + h/(-(d*g) + c*h))]*(-(h/(-(d*g) + c*h)) + (c + d*x)^(-1))*EllipticF[ArcSin[Sqrt[((-(d*e) + c*f)*(-h - (d*g)/(c + d*x) + (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/(Sqrt[(-(h/(-(d*g) + c*h)) + (c + d*x)^(-1))/(f/(-(d*e) + c*f) - h/(-(d*g) + c*h))]*Sqrt[(b + (-(b*c) + a*d)/(c + d*x))*(f + (d*e - c*f)/(c + d*x))*(h + (d*g - c*h)/(c + d*x))])))/((f*g - e*h)*(b - (b*c)/(c + d*x) + (a*d)/(c + d*x))*Sqrt[e + ((c + d*x)*(f - (c*f)/(c + d*x)))/d]*Sqrt[g + ((c + d*x)*(h - (c*h)/(c + d*x)))/d]) - ((b*c - a*d)*(b*e - a*f)*(-(d*e) + c*f)*h*Sqrt[c + d*x]*Sqrt[(b - (b*c)/(c + d*x) + (a*d)/(c + d*x))*(f + (d*e)/(c + d*x) - (c*f)/(c + d*x))*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x))]*Sqrt[a + ((c + d*x)*(b - (b*c)/(c + d*x)))/d]*((d*g*Sqrt[((b*c - a*d)*(-(d*g) + c*h)*(b/(b*c - a*d) - (c + d*x)^(-1)))/(-(b*d*g) + a*d*h)]*(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))*Sqrt[(-(h/(-(d*g) + c*h)) + (c + d*x)^(-1))/(f/(-(d*e) + c*f) - h/(-(d*g) + c*h))]*(((-(b*d*g) + a*d*h)*EllipticE[ArcSin[Sqrt[((d*e - c*f)*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/((b*c - a*d)*(-(d*g) + c*h)) - (b*EllipticF[ArcSin[Sqrt[((d*e - c*f)*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/(b*c - a*d)))/(Sqrt[(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))/(-(f/(-(d*e) + c*f)) + h/(-(d*g) + c*h))]*Sqrt[(b + (-(b*c) + a*d)/(c + d*x))*(f + (d*e - c*f)/(c + d*x))*(h + (d*g - c*h)/(c + d*x))]) - (c*h*Sqrt[((b*c - a*d)*(-(d*g) + c*h)*(b/(b*c - a*d) - (c + d*x)^(-1)))/(-(b*d*g) + a*d*h)]*(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))*Sqrt[(-(h/(-(d*g) + c*h)) + (c + d*x)^(-1))/(f/(-(d*e) + c*f) - h/(-(d*g) + c*h))]*(((-(b*d*g) + a*d*h)*EllipticE[ArcSin[Sqrt[((d*e - c*f)*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/((b*c - a*d)*(-(d*g) + c*h)) - (b*EllipticF[ArcSin[Sqrt[((d*e - c*f)*(h + (d*g)/(c + d*x) - (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/(b*c - a*d)))/(Sqrt[(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))/(-(f/(-(d*e) + c*f)) + h/(-(d*g) + c*h))]*Sqrt[(b + (-(b*c) + a*d)/(c + d*x))*(f + (d*e - c*f)/(c + d*x))*(h + (d*g - c*h)/(c + d*x))]) + (h*Sqrt[(-(b/(b*c - a*d)) + (c + d*x)^(-1))/(-(b/(b*c - a*d)) + h/(-(d*g) + c*h))]*Sqrt[(-(f/(-(d*e) + c*f)) + (c + d*x)^(-1))/(-(f/(-(d*e) + c*f)) + h/(-(d*g) + c*h))]*(-(h/(-(d*g) + c*h)) + (c + d*x)^(-1))*EllipticF[ArcSin[Sqrt[((-(d*e) + c*f)*(-h - (d*g)/(c + d*x) + (c*h)/(c + d*x)))/(d*(-(f*g) + e*h))]], ((b*c - a*d)*(-(f*g) + e*h))/((-(d*e) + c*f)*(-(b*g) + a*h))])/(Sqrt[(-(h/(-(d*g) + c*h)) + (c + d*x)^(-1))/(f/(-(d*e) + c*f) - h/(-(d*g) + c*h))]*Sqrt[(b + (-(b*c) + a*d)/(c + d*x))*(f + (d*e - c*f)/(c + d*x))*(h + (d*g - c*h)/(c + d*x))])))/((f*g - e*h)*(b - (b*c)/(c + d*x) + (a*d)/(c + d*x))*Sqrt[e + ((c + d*x)*(f - (c*f)/(c + d*x)))/d]*Sqrt[g + ((c + d*x)*(h - (c*h)/(c + d*x)))/d])))/(d*(b*c - a*d)*(b*e - a*f)*(b*g - a*h))","B",1
111,1,7075,786,17.2873213,"\int \frac{1}{(a+b x)^{3/2} (c+d x)^{3/2} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Integrate[1/((a + b*x)^(3/2)*(c + d*x)^(3/2)*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\text{Result too large to show}","-\frac{4 b d \sqrt{g+h x} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{\sqrt{e+f x} \sqrt{b g-a h}}{\sqrt{a+b x} \sqrt{f g-e h}}\right),-\frac{(b c-a d) (f g-e h)}{(b g-a h) (d e-c f)}\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)}}}+\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)}",1,"Result too large to show","B",0
112,1,285,319,0.986491,"\int \frac{x^4 (e+f x)^n}{(a+b x) (c+d x)} \, dx","Integrate[(x^4*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\frac{(e+f x)^{n+1} \left(\frac{b^3 c^4 f^3 \left(n^2+5 n+6\right) \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)-(b c-a d) (c f-d e) \left(a^2 d^2 f^2 \left(n^2+5 n+6\right)+a b d f (n+3) (c f (n+2)+d (e-f (n+1) x))+b^2 \left(c^2 f^2 \left(n^2+5 n+6\right)+c d f (n+3) (e-f (n+1) x)+d^2 \left(2 e^2-2 e f (n+1) x+f^2 \left(n^2+3 n+2\right) x^2\right)\right)\right)}{f^3 (n+2) (n+3) (a d-b c) (c f-d e)}-\frac{a^4 d^3 \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{(b c-a d) (b e-a f)}\right)}{b^3 d^3 (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{\left(a^2 d^2+a b c d+b^2 c^2\right) (e+f x)^{n+1}}{b^3 d^3 f (n+1)}+\frac{e (a d+b c) (e+f x)^{n+1}}{b^2 d^2 f^2 (n+1)}-\frac{(a d+b c) (e+f x)^{n+2}}{b^2 d^2 f^2 (n+2)}+\frac{c^4 (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{d^3 (n+1) (b c-a d) (d e-c f)}+\frac{e^2 (e+f x)^{n+1}}{b d f^3 (n+1)}-\frac{2 e (e+f x)^{n+2}}{b d f^3 (n+2)}+\frac{(e+f x)^{n+3}}{b d f^3 (n+3)}",1,"((e + f*x)^(1 + n)*(-((a^4*d^3*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/((b*c - a*d)*(b*e - a*f))) + (-((b*c - a*d)*(-(d*e) + c*f)*(a^2*d^2*f^2*(6 + 5*n + n^2) + a*b*d*f*(3 + n)*(c*f*(2 + n) + d*(e - f*(1 + n)*x)) + b^2*(c^2*f^2*(6 + 5*n + n^2) + c*d*f*(3 + n)*(e - f*(1 + n)*x) + d^2*(2*e^2 - 2*e*f*(1 + n)*x + f^2*(2 + 3*n + n^2)*x^2)))) + b^3*c^4*f^3*(6 + 5*n + n^2)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/((-(b*c) + a*d)*f^3*(-(d*e) + c*f)*(2 + n)*(3 + n))))/(b^3*d^3*(1 + n))","A",1
113,1,174,216,0.4267025,"\int \frac{x^3 (e+f x)^n}{(a+b x) (c+d x)} \, dx","Integrate[(x^3*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\frac{(e+f x)^{n+1} \left(\frac{a^3 \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{b e-a f}+\frac{(b c-a d) (c f-d e) (a d f (n+2)+b c f (n+2)+b d (e-f (n+1) x))-b^2 c^3 f^2 (n+2) \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{d^2 f^2 (n+2) (d e-c f)}\right)}{b^2 (n+1) (b c-a d)}","\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 + f*x)^(1 + n)*((a^3*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/(b*e - a*f) + ((b*c - a*d)*(-(d*e) + c*f)*(b*c*f*(2 + n) + a*d*f*(2 + n) + b*d*(e - f*(1 + n)*x)) - b^2*c^3*f^2*(2 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/(d^2*f^2*(d*e - c*f)*(2 + n))))/(b^2*(b*c - a*d)*(1 + n))","A",1
114,1,153,158,0.073556,"\int \frac{x^2 (e+f x)^n}{(a+b x) (c+d x)} \, dx","Integrate[(x^2*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\frac{(e+f x)^{n+1} \left(a^2 d f (c f-d e) \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)+(b e-a f) \left(b c^2 f \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)-(b c-a d) (c f-d e)\right)\right)}{b d f (n+1) (b c-a d) (b e-a f) (d e-c f)}","-\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)*(a^2*d*f*(-(d*e) + c*f)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)] + (b*e - a*f)*(-((b*c - a*d)*(-(d*e) + c*f)) + b*c^2*f*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])))/(b*d*(b*c - a*d)*f*(b*e - a*f)*(d*e - c*f)*(1 + n))","A",1
115,1,116,124,0.0362339,"\int \frac{x (e+f x)^n}{(a+b x) (c+d x)} \, dx","Integrate[(x*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\frac{(e+f x)^{n+1} \left(a (c f-d e) \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)+c (b e-a f) \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)\right)}{(n+1) (b c-a d) (b e-a f) (c f-d e)}","\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,"((e + f*x)^(1 + n)*(a*(-(d*e) + c*f)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)] + c*(b*e - a*f)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)]))/((b*c - a*d)*(b*e - a*f)*(-(d*e) + c*f)*(1 + n))","A",1
116,1,116,124,0.0330631,"\int \frac{(e+f x)^n}{(a+b x) (c+d x)} \, dx","Integrate[(e + f*x)^n/((a + b*x)*(c + d*x)),x]","\frac{(e+f x)^{n+1} \left(b (d e-c f) \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)+d (a f-b e) \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)\right)}{(n+1) (b c-a d) (b e-a f) (c f-d e)}","\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,"((e + f*x)^(1 + n)*(b*(d*e - c*f)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)] + d*(-(b*e) + a*f)*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)]))/((b*c - a*d)*(b*e - a*f)*(-(d*e) + c*f)*(1 + n))","A",1
117,1,170,175,0.192298,"\int \frac{(e+f x)^n}{x (a+b x) (c+d x)} \, dx","Integrate[(e + f*x)^n/(x*(a + b*x)*(c + d*x)),x]","-\frac{(e+f x)^{n+1} \left(b^2 c e (d e-c f) \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)+(a f-b e) \left(a d^2 e \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)-(b c-a d) (c f-d e) \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)\right)\right)}{a c e (n+1) (a d-b c) (a f-b e) (c f-d e)}","\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,"-(((e + f*x)^(1 + n)*(b^2*c*e*(d*e - c*f)*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)] + (-(b*e) + a*f)*(a*d^2*e*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)] - (b*c - a*d)*(-(d*e) + c*f)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (f*x)/e])))/(a*c*(-(b*c) + a*d)*e*(-(b*e) + a*f)*(-(d*e) + c*f)*(1 + n)))","A",1
118,1,177,222,0.2783819,"\int \frac{(e+f x)^n}{x^2 (a+b x) (c+d x)} \, dx","Integrate[(e + f*x)^n/(x^2*(a + b*x)*(c + d*x)),x]","\frac{(e+f x)^{n+1} \left(\frac{\frac{e (a d+b c) \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)+a c f \, _2F_1\left(2,n+1;n+2;\frac{f x}{e}+1\right)}{a^2 e^2}-\frac{d^3 \, _2F_1\left(1,n+1;n+2;\frac{d (e+f x)}{d e-c f}\right)}{(b c-a d) (c f-d e)}}{c^2}-\frac{b^3 \, _2F_1\left(1,n+1;n+2;\frac{b (e+f x)}{b e-a f}\right)}{a^2 (b c-a d) (b e-a f)}\right)}{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,"((e + f*x)^(1 + n)*(-((b^3*Hypergeometric2F1[1, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)])/(a^2*(b*c - a*d)*(b*e - a*f))) + (-((d^3*Hypergeometric2F1[1, 1 + n, 2 + n, (d*(e + f*x))/(d*e - c*f)])/((b*c - a*d)*(-(d*e) + c*f))) + ((b*c + a*d)*e*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (f*x)/e] + a*c*f*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (f*x)/e])/(a^2*e^2))/c^2))/(1 + n)","A",1
119,1,149,167,0.2314295,"\int (a+b x)^m (c+d x) (e+f x) (g+h x) \, dx","Integrate[(a + b*x)^m*(c + d*x)*(e + f*x)*(g + h*x),x]","\frac{(a+b x)^{m+1} \left(\frac{(a+b x) \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)}{m+2}+\frac{(a+b x)^2 (b (c f h+d e h+d f g)-3 a d f h)}{m+3}+\frac{(b c-a d) (b e-a f) (b g-a h)}{m+1}+\frac{d f h (a+b x)^3}{m+4}\right)}{b^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,"((a + b*x)^(1 + m)*(((b*c - a*d)*(b*e - a*f)*(b*g - a*h))/(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) + ((-3*a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*(a + b*x)^2)/(3 + m) + (d*f*h*(a + b*x)^3)/(4 + m)))/b^4","A",1
120,1,120,134,0.1984269,"\int \frac{(a+b x)^m (c+d x) (e+f x)}{g+h x} \, dx","Integrate[((a + b*x)^m*(c + d*x)*(e + f*x))/(g + h*x),x]","\frac{(a+b x)^{m+1} \left(\frac{b (c f h+d e h-d f g)-a d f h}{b^2 (m+1)}+\frac{d f h (a+b x)}{b^2 (m+2)}+\frac{(d g-c h) (f g-e h) \, _2F_1\left(1,m+1;m+2;\frac{h (a+b x)}{a h-b g}\right)}{(m+1) (b g-a h)}\right)}{h^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))/(b^2*(1 + m)) + (d*f*h*(a + b*x))/(b^2*(2 + m)) + ((d*g - c*h)*(f*g - e*h)*Hypergeometric2F1[1, 1 + m, 2 + m, (h*(a + b*x))/(-(b*g) + a*h)])/((b*g - a*h)*(1 + m))))/h^2","A",1
121,1,115,140,0.078767,"\int \frac{(a+b x)^m (c+d x)}{(e+f x) (g+h x)} \, dx","Integrate[((a + b*x)^m*(c + d*x))/((e + f*x)*(g + h*x)),x]","\frac{(a+b x)^{m+1} \left(\frac{(d g-c h) \, _2F_1\left(1,m+1;m+2;\frac{h (a+b x)}{a h-b g}\right)}{b g-a h}-\frac{(d e-c f) \, _2F_1\left(1,m+1;m+2;\frac{f (a+b x)}{a f-b e}\right)}{b e-a f}\right)}{(m+1) (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,"((a + b*x)^(1 + m)*(-(((d*e - c*f)*Hypergeometric2F1[1, 1 + m, 2 + m, (f*(a + b*x))/(-(b*e) + a*f)])/(b*e - a*f)) + ((d*g - c*h)*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",1
122,1,193,224,0.3687006,"\int \frac{(a+b x)^m}{(c+d x) (e+f x) (g+h x)} \, dx","Integrate[(a + b*x)^m/((c + d*x)*(e + f*x)*(g + h*x)),x]","\frac{(a+b x)^{m+1} \left(\frac{d^2 \, _2F_1\left(1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)}{(b c-a d) (c f-d e) (c h-d g)}+\frac{f^2 \, _2F_1\left(1,m+1;m+2;\frac{f (a+b x)}{a f-b e}\right)}{(b e-a f) (d e-c f) (e h-f g)}+\frac{h^2 \, _2F_1\left(1,m+1;m+2;\frac{h (a+b x)}{a h-b g}\right)}{(b g-a h) (d g-c h) (f g-e h)}\right)}{m+1}","\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,"((a + b*x)^(1 + m)*((d^2*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)) + (f^2*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)) + (h^2*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",1
123,1,104,140,0.2306862,"\int \frac{x^m (e+f x)^n}{(a+b x) (c+d x)} \, dx","Integrate[(x^m*(e + f*x)^n)/((a + b*x)*(c + d*x)),x]","\frac{x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} \left(a d F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{d x}{c}\right)-b c F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{b x}{a}\right)\right)}{a c (m+1) (a d-b c)}","\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,"(x^(1 + m)*(e + f*x)^n*(-(b*c*AppellF1[1 + m, -n, 1, 2 + m, -((f*x)/e), -((b*x)/a)]) + a*d*AppellF1[1 + m, -n, 1, 2 + m, -((f*x)/e), -((d*x)/c)]))/(a*c*(-(b*c) + a*d)*(1 + m)*(1 + (f*x)/e)^n)","A",1
124,1,195,266,0.2403201,"\int (a+b x)^m (c+d x)^n (e+f x) (g+h x) \, dx","Integrate[(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} \left(b \left(b (d e-c f) (d g-c h) \, _2F_1\left(m+1,-n;m+2;\frac{d (a+b x)}{a d-b c}\right)-(b c-a d) (2 c f h-d (e h+f g)) \, _2F_1\left(m+1,-n-1;m+2;\frac{d (a+b x)}{a d-b c}\right)\right)+f h (b c-a d)^2 \, _2F_1\left(m+1,-n-2;m+2;\frac{d (a+b x)}{a d-b c}\right)\right)}{b^3 d^2 (m+1)}","\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)^n*((b*c - a*d)^2*f*h*Hypergeometric2F1[1 + m, -2 - n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] + b*(-((b*c - a*d)*(2*c*f*h - d*(f*g + e*h))*Hypergeometric2F1[1 + m, -1 - n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]) + b*(d*e - c*f)*(d*g - c*h)*Hypergeometric2F1[1 + m, -n, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])))/(b^3*d^2*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
125,1,195,245,0.2647558,"\int (a+b x)^m (c+d x)^{1-m} (e+f x) (g+h x) \, dx","Integrate[(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)^{1-m} \left(\frac{b (c+d x)}{b c-a d}\right)^{m-1} \left(b \left(b (d e-c f) (d g-c h) \, _2F_1\left(m-1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)-(b c-a d) (2 c f h-d (e h+f g)) \, _2F_1\left(m-2,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)\right)+f h (b c-a d)^2 \, _2F_1\left(m-3,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)\right)}{b^3 d^2 (m+1)}","\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)^(1 - m)*((b*(c + d*x))/(b*c - a*d))^(-1 + m)*((b*c - a*d)^2*f*h*Hypergeometric2F1[-3 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] + b*(-((b*c - a*d)*(2*c*f*h - d*(f*g + e*h))*Hypergeometric2F1[-2 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]) + b*(d*e - c*f)*(d*g - c*h)*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])))/(b^3*d^2*(1 + m))","A",1
126,1,189,235,0.2175591,"\int (a+b x)^m (c+d x)^{-m} (e+f x) (g+h x) \, dx","Integrate[((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 \left(b \left(b (d e-c f) (d g-c h) \, _2F_1\left(m,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)-(b c-a d) (2 c f h-d (e h+f g)) \, _2F_1\left(m-1,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)\right)+f h (b c-a d)^2 \, _2F_1\left(m-2,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)\right)}{b^3 d^2 (m+1)}","\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)*((b*(c + d*x))/(b*c - a*d))^m*((b*c - a*d)^2*f*h*Hypergeometric2F1[-2 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)] + b*(-((b*c - a*d)*(2*c*f*h - d*(f*g + e*h))*Hypergeometric2F1[-1 + m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)]) + b*(d*e - c*f)*(d*g - c*h)*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])))/(b^3*d^2*(1 + m)*(c + d*x)^m)","A",1
127,1,221,261,0.2077617,"\int (a+b x)^m (c+d x)^{-1-m} (e+f x) (g+h x) \, dx","Integrate[(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(\frac{\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)}{a d-b c}\right) \left(a^2 d^2 f h (m-1) m+2 a b d m (d (e h+f g)-c f h (m+1))+b^2 \left(c^2 f h \left(m^2+3 m+2\right)-2 c d (m+1) (e h+f g)+2 d^2 e g\right)\right)}{m+1}+b \left(a d f h m (c+d x)-b \left(c^2 f h (m+2)+c d (-2 e h-2 f g+f h m x)+2 d^2 e g\right)\right)\right)}{2 b^2 d^2 m (a d-b c)}","\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)*(b*(a*d*f*h*m*(c + d*x) - b*(2*d^2*e*g + c^2*f*h*(2 + m) + c*d*(-2*f*g - 2*e*h + f*h*m*x))) + ((a^2*d^2*f*h*(-1 + m)*m + 2*a*b*d*m*(d*(f*g + e*h) - c*f*h*(1 + m)) + b^2*(2*d^2*e*g - 2*c*d*(f*g + e*h)*(1 + m) + c^2*f*h*(2 + 3*m + m^2)))*((b*(c + d*x))/(b*c - a*d))^m*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])/(1 + m)))/(2*b^2*d^2*(-(b*c) + a*d)*m*(c + d*x)^m)","A",1
128,1,198,203,0.2314996,"\int (a+b x)^m (c+d x)^{-2-m} (e+f x) (g+h x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-2 - m)*(e + f*x)*(g + h*x),x]","\frac{(a+b x)^m (c+d x)^{-m} \left(\frac{(m+1) (b c-a d) \left(\frac{d (a+b x)}{a d-b c}\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))}{m}-\frac{d (a+b x) \left(a d f h (m+1) (c+d x)-b \left(c^2 f h (m+2)+c d (-e h-f g+f h (m+1) x)+d^2 e g\right)\right)}{c+d x}\right)}{b d^3 (m+1) (b c-a d)}","\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)^m*(-((d*(a + b*x)*(a*d*f*h*(1 + m)*(c + d*x) - b*(d^2*e*g + c^2*f*h*(2 + m) + c*d*(-(f*g) - e*h + f*h*(1 + m)*x))))/(c + d*x)) + ((b*c - a*d)*(1 + m)*(-(b*d*(f*g + e*h)) - a*d*f*h*m + b*c*f*h*(2 + m))*Hypergeometric2F1[-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)])/(m*((d*(a + b*x))/(-(b*c) + a*d))^m)))/(b*d^3*(b*c - a*d)*(1 + m)*(c + d*x)^m)","A",1
129,1,237,246,0.3216153,"\int (a+b x)^m (c+d x)^{-3-m} (e+f x) (g+h x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^(-3 - m)*(e + f*x)*(g + h*x),x]","-\frac{(a+b x)^m (c+d x)^{-m-2} \left(d^3 (a+b x) \left(a^3 (-d) f h (m+1)+a^2 b f h (c m-d (2 m+3) x)+a b^2 (c e h+c f (g+2 h (m+1) x)+d e g (m+1)+d e h (m+2) x+d f g (m+2) x)-b^3 (c (e g (m+2)+e h (m+1) x+f g (m+1) x)+d e g x)\right)+f h (m+1) (b c-a d)^4 \left(\frac{d (a+b x)}{a d-b c}\right)^{-m} \, _2F_1\left(-m-2,-m-2;-m-1;\frac{b (c+d x)}{b c-a d}\right)\right)}{b^2 d^3 (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(a^3 (-d) f h (m+1)-b x \left(a^2 d f h (2 m+3)-a b (2 c f h (m+1)+d (m+2) (e h+f g))+b^2 (c (m+1) (e h+f g)+d e g)\right)+a^2 b c f h m+a b^2 (c (e h+f g)+d e g (m+1))-b^3 c e g (m+2)\right)}{b^2 (m+1) (m+2) (b c-a d)^2}",1,"-(((a + b*x)^m*(c + d*x)^(-2 - m)*(d^3*(a + b*x)*(-(a^3*d*f*h*(1 + m)) + a^2*b*f*h*(c*m - d*(3 + 2*m)*x) + a*b^2*(c*e*h + d*e*g*(1 + m) + d*f*g*(2 + m)*x + d*e*h*(2 + m)*x + c*f*(g + 2*h*(1 + m)*x)) - b^3*(d*e*g*x + c*(e*g*(2 + m) + f*g*(1 + m)*x + e*h*(1 + m)*x))) + ((b*c - a*d)^4*f*h*(1 + m)*Hypergeometric2F1[-2 - m, -2 - m, -1 - m, (b*(c + d*x))/(b*c - a*d)])/((d*(a + b*x))/(-(b*c) + a*d))^m))/(b^2*d^3*(b*c - a*d)^2*(1 + m)*(2 + m)))","A",1
130,1,220,362,0.477943,"\int (a+b x)^m (c+d x)^{-4-m} (e+f x) (g+h x) \, dx","Integrate[(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-3} \left(\frac{(c+d x) (-a d (m+1)+b c (m+2)+b d x) \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)}{(m+1) (m+2) (b c-a d)^2}+a d f h (m+3) (c+d x)+b \left(c^2 (-f) h (m+2)-c d (e h+f (g+h (m+3) x))+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 + b*x)^(1 + m)*(c + d*x)^(-3 - m)*(a*d*f*h*(3 + m)*(c + d*x) + ((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)))*(c + d*x)*(-(a*d*(1 + m)) + b*c*(2 + m) + b*d*x))/((b*c - a*d)^2*(1 + m)*(2 + m)) + b*(d^2*e*g - c^2*f*h*(2 + m) - c*d*(e*h + f*(g + h*(3 + m)*x)))))/(b*d^2*(b*c - a*d)*(3 + m))","A",1
131,1,279,507,0.7016608,"\int (a+b x)^m (c+d x)^{-5-m} (e+f x) (g+h x) \, dx","Integrate[(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-4} \left(\frac{(c+d x) \left(a^2 d^2 \left(m^2+3 m+2\right)-2 a b d (m+1) (c (m+3)+d x)+b^2 \left(c^2 \left(m^2+5 m+6\right)+2 c d (m+3) x+2 d^2 x^2\right)\right) \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)}{(m+1) (m+2) (m+3) (b c-a d)^3}+a d f h (m+4) (c+d x)+b \left(c^2 (-f) h (m+2)-c d (2 e h+2 f g+f h (m+4) x)+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 + b*x)^(1 + m)*(c + d*x)^(-4 - m)*(a*d*f*h*(4 + m)*(c + d*x) + b*(2*d^2*e*g - c^2*f*h*(2 + m) - c*d*(2*f*g + 2*e*h + f*h*(4 + m)*x)) + ((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)))*(c + d*x)*(a^2*d^2*(2 + 3*m + m^2) - 2*a*b*d*(1 + m)*(c*(3 + m) + d*x) + b^2*(c^2*(6 + 5*m + m^2) + 2*c*d*(3 + m)*x + 2*d^2*x^2)))/((b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m))))/(2*b*d^2*(b*c - a*d)*(4 + m))","A",1
132,1,3579,815,44.2423135,"\int (a+b x)^3 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","Integrate[(a + b*x)^3*(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","\text{Result too large to show}","\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,"(3*a*b^2*c^3*g*(c + d*x)^(-7 - m)*((c + d*x)/c)^(4 + m)*(e + f*x)^(3 + m)*(-2*c^3*e^3 - 6*c^2*d*e^3*x - 2*c^2*d*e^3*m*x + 2*c^3*e^2*f*m*x - 6*c*d^2*e^3*x^2 - 5*c*d^2*e^3*m*x^2 + 6*c^2*d*e^2*f*m*x^2 - c^3*e*f^2*m*x^2 - c*d^2*e^3*m^2*x^2 + 2*c^2*d*e^2*f*m^2*x^2 - c^3*e*f^2*m^2*x^2 - 6*c*d^2*e^2*f*x^3 + 6*c^2*d*e*f^2*x^3 - 2*c^3*f^3*x^3 - 5*c*d^2*e^2*f*m*x^3 + 8*c^2*d*e*f^2*m*x^3 - 3*c^3*f^3*m*x^3 - c*d^2*e^2*f*m^2*x^3 + 2*c^2*d*e*f^2*m^2*x^3 - c^3*f^3*m^2*x^3 + 2*c^3*e^3*((c*e + d*e*x)/(c*(e + f*x)))^m + 6*c^2*d*e^3*x*((c*e + d*e*x)/(c*(e + f*x)))^m + 6*c*d^2*e^3*x^2*((c*e + d*e*x)/(c*(e + f*x)))^m + 2*d^3*e^3*x^3*((c*e + d*e*x)/(c*(e + f*x)))^m))/(e^3*(d*e - c*f)^3*(1 + m)*(2 + m)*(3 + m)*((c*e + d*e*x)/(c*(e + f*x)))^m*((e + f*x)/e)^m*(1 + (f*x)/e)^3) + (3*a^2*b*c^3*h*(c + d*x)^(-7 - m)*((c + d*x)/c)^(4 + m)*(e + f*x)^(3 + m)*(-2*c^3*e^3 - 6*c^2*d*e^3*x - 2*c^2*d*e^3*m*x + 2*c^3*e^2*f*m*x - 6*c*d^2*e^3*x^2 - 5*c*d^2*e^3*m*x^2 + 6*c^2*d*e^2*f*m*x^2 - c^3*e*f^2*m*x^2 - c*d^2*e^3*m^2*x^2 + 2*c^2*d*e^2*f*m^2*x^2 - c^3*e*f^2*m^2*x^2 - 6*c*d^2*e^2*f*x^3 + 6*c^2*d*e*f^2*x^3 - 2*c^3*f^3*x^3 - 5*c*d^2*e^2*f*m*x^3 + 8*c^2*d*e*f^2*m*x^3 - 3*c^3*f^3*m*x^3 - c*d^2*e^2*f*m^2*x^3 + 2*c^2*d*e*f^2*m^2*x^3 - c^3*f^3*m^2*x^3 + 2*c^3*e^3*((c*e + d*e*x)/(c*(e + f*x)))^m + 6*c^2*d*e^3*x*((c*e + d*e*x)/(c*(e + f*x)))^m + 6*c*d^2*e^3*x^2*((c*e + d*e*x)/(c*(e + f*x)))^m + 2*d^3*e^3*x^3*((c*e + d*e*x)/(c*(e + f*x)))^m))/(e^3*(d*e - c*f)^3*(1 + m)*(2 + m)*(3 + m)*((c*e + d*e*x)/(c*(e + f*x)))^m*((e + f*x)/e)^m*(1 + (f*x)/e)^3) + (b^3*g*x^4*(c + d*x)^(-4 - m)*((c + d*x)/c)^(4 + m)*(e + f*x)^m*AppellF1[4, 4 + m, -m, 5, -((d*x)/c), -((f*x)/e)])/(4*((e + f*x)/e)^m) + (3*a*b^2*h*x^4*(c + d*x)^(-4 - m)*((c + d*x)/c)^(4 + m)*(e + f*x)^m*AppellF1[4, 4 + m, -m, 5, -((d*x)/c), -((f*x)/e)])/(4*((e + f*x)/e)^m) + (b^3*h*x^5*(c + d*x)^(-4 - m)*((c + d*x)/c)^(4 + m)*(e + f*x)^m*AppellF1[5, 4 + m, -m, 6, -((d*x)/c), -((f*x)/e)])/(5*((e + f*x)/e)^m) + (3*a^2*b*g*(c + d*x)^(-4 - m)*((c + d*x)/c)^(4 + m)*(1 + (d*x)/c)^(-4 - m)*(e + f*x)^m*((c*(e + f*x))/(e*(c + d*x)))^(-1 - m)*(1 + (f*x)/e)^(1 + m)*(c*(4 + m)*(3*e + f*x)*(-2*d^3*e^3*x^3 + c^3*(-2*e^2*f*m*x*((c*(e + f*x))/(e*(c + d*x)))^m + e*f^2*m*(1 + m)*x^2*((c*(e + f*x))/(e*(c + d*x)))^m + f^3*(2 + 3*m + m^2)*x^3*((c*(e + f*x))/(e*(c + d*x)))^m + 2*e^3*(-1 + ((c*(e + f*x))/(e*(c + d*x)))^m)) - 2*c^2*d*e*x*(e*f*m*(3 + m)*x*((c*(e + f*x))/(e*(c + d*x)))^m + f^2*(3 + 4*m + m^2)*x^2*((c*(e + f*x))/(e*(c + d*x)))^m - e^2*(-3 + 3*((c*(e + f*x))/(e*(c + d*x)))^m + m*((c*(e + f*x))/(e*(c + d*x)))^m)) + c*d^2*e^2*x^2*(f*(6 + 5*m + m^2)*x*((c*(e + f*x))/(e*(c + d*x)))^m + e*(-6 + 6*((c*(e + f*x))/(e*(c + d*x)))^m + 5*m*((c*(e + f*x))/(e*(c + d*x)))^m + m^2*((c*(e + f*x))/(e*(c + d*x)))^m)))*Gamma[4 + m] - (2*d^4*e^4*(1 + m)*x^4 - 2*c*d^3*e^3*x^3*(-3*e*m + f*(4 + m)*x) + c^4*(e^2*f^2*(-5 + m)*m*x^2*((c*(e + f*x))/(e*(c + d*x)))^m + 2*e*f^3*m*(1 + m)*x^3*((c*(e + f*x))/(e*(c + d*x)))^m + f^4*(2 + 3*m + m^2)*x^4*((c*(e + f*x))/(e*(c + d*x)))^m + 6*e^4*(-1 + ((c*(e + f*x))/(e*(c + d*x)))^m) - 2*e^3*f*x*(4 + m - 4*((c*(e + f*x))/(e*(c + d*x)))^m + 2*m*((c*(e + f*x))/(e*(c + d*x)))^m)) - 2*c^3*d*e*x*(2*e*f^2*m*(4 + m)*x^2*((c*(e + f*x))/(e*(c + d*x)))^m + f^3*(4 + 5*m + m^2)*x^3*((c*(e + f*x))/(e*(c + d*x)))^m + e^2*f*(4 + m)*x*(3 - 3*((c*(e + f*x))/(e*(c + d*x)))^m + m*((c*(e + f*x))/(e*(c + d*x)))^m) - e^3*(-8 + m + 8*((c*(e + f*x))/(e*(c + d*x)))^m + 2*m*((c*(e + f*x))/(e*(c + d*x)))^m)) + c^2*d^2*e^2*x^2*(f^2*(12 + 7*m + m^2)*x^2*((c*(e + f*x))/(e*(c + d*x)))^m + 2*e*f*(4 + m)*x*(-3 + 3*((c*(e + f*x))/(e*(c + d*x)))^m + m*((c*(e + f*x))/(e*(c + d*x)))^m) + e^2*(m^2*((c*(e + f*x))/(e*(c + d*x)))^m + 12*(-1 + ((c*(e + f*x))/(e*(c + d*x)))^m) + m*(6 + 7*((c*(e + f*x))/(e*(c + d*x)))^m))))*Gamma[5 + m]))/(2*c*e*(-(d*e) + c*f)^3*(1 + m)*(2 + m)*(3 + m)*(4 + m)*x*((e + f*x)/e)^m*Gamma[4 + m]) + (a^3*h*(c + d*x)^(-4 - m)*((c + d*x)/c)^(4 + m)*(1 + (d*x)/c)^(-4 - m)*(e + f*x)^m*((c*(e + f*x))/(e*(c + d*x)))^(-1 - m)*(1 + (f*x)/e)^(1 + m)*(c*(4 + m)*(3*e + f*x)*(-2*d^3*e^3*x^3 + c^3*(-2*e^2*f*m*x*((c*(e + f*x))/(e*(c + d*x)))^m + e*f^2*m*(1 + m)*x^2*((c*(e + f*x))/(e*(c + d*x)))^m + f^3*(2 + 3*m + m^2)*x^3*((c*(e + f*x))/(e*(c + d*x)))^m + 2*e^3*(-1 + ((c*(e + f*x))/(e*(c + d*x)))^m)) - 2*c^2*d*e*x*(e*f*m*(3 + m)*x*((c*(e + f*x))/(e*(c + d*x)))^m + f^2*(3 + 4*m + m^2)*x^2*((c*(e + f*x))/(e*(c + d*x)))^m - e^2*(-3 + 3*((c*(e + f*x))/(e*(c + d*x)))^m + m*((c*(e + f*x))/(e*(c + d*x)))^m)) + c*d^2*e^2*x^2*(f*(6 + 5*m + m^2)*x*((c*(e + f*x))/(e*(c + d*x)))^m + e*(-6 + 6*((c*(e + f*x))/(e*(c + d*x)))^m + 5*m*((c*(e + f*x))/(e*(c + d*x)))^m + m^2*((c*(e + f*x))/(e*(c + d*x)))^m)))*Gamma[4 + m] - (2*d^4*e^4*(1 + m)*x^4 - 2*c*d^3*e^3*x^3*(-3*e*m + f*(4 + m)*x) + c^4*(e^2*f^2*(-5 + m)*m*x^2*((c*(e + f*x))/(e*(c + d*x)))^m + 2*e*f^3*m*(1 + m)*x^3*((c*(e + f*x))/(e*(c + d*x)))^m + f^4*(2 + 3*m + m^2)*x^4*((c*(e + f*x))/(e*(c + d*x)))^m + 6*e^4*(-1 + ((c*(e + f*x))/(e*(c + d*x)))^m) - 2*e^3*f*x*(4 + m - 4*((c*(e + f*x))/(e*(c + d*x)))^m + 2*m*((c*(e + f*x))/(e*(c + d*x)))^m)) - 2*c^3*d*e*x*(2*e*f^2*m*(4 + m)*x^2*((c*(e + f*x))/(e*(c + d*x)))^m + f^3*(4 + 5*m + m^2)*x^3*((c*(e + f*x))/(e*(c + d*x)))^m + e^2*f*(4 + m)*x*(3 - 3*((c*(e + f*x))/(e*(c + d*x)))^m + m*((c*(e + f*x))/(e*(c + d*x)))^m) - e^3*(-8 + m + 8*((c*(e + f*x))/(e*(c + d*x)))^m + 2*m*((c*(e + f*x))/(e*(c + d*x)))^m)) + c^2*d^2*e^2*x^2*(f^2*(12 + 7*m + m^2)*x^2*((c*(e + f*x))/(e*(c + d*x)))^m + 2*e*f*(4 + m)*x*(-3 + 3*((c*(e + f*x))/(e*(c + d*x)))^m + m*((c*(e + f*x))/(e*(c + d*x)))^m) + e^2*(m^2*((c*(e + f*x))/(e*(c + d*x)))^m + 12*(-1 + ((c*(e + f*x))/(e*(c + d*x)))^m) + m*(6 + 7*((c*(e + f*x))/(e*(c + d*x)))^m))))*Gamma[5 + m]))/(2*c*e*(-(d*e) + c*f)^3*(1 + m)*(2 + m)*(3 + m)*(4 + m)*x*((e + f*x)/e)^m*Gamma[4 + m]) + (a^3*f^3*g*(e + f*x)^(1 + m)*(1 + (d*(e + f*x))/((c - (d*e)/f)*f))^m*Hypergeometric2F1[1 + m, 4 + m, 2 + m, -((d*(e + f*x))/((c - (d*e)/f)*f))])/((-(d*e) + c*f)^4*(1 + m)*(c - (d*e)/f + (d*(e + f*x))/f)^m)","C",0
133,1,422,572,1.9065924,"\int (a+b x)^2 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","Integrate[(a + b*x)^2*(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","\frac{(c+d x)^{-m-3} (e+f x)^m \left(-h (m+3) (c+d x) (d e-c f) \left(d f (m+1) (e+f x) (b c-a d)^2 (d e-c f)-(c+d x) \left(d (e+f x) \left(a^2 d^2 f^2+2 a b d f (c f (m+1)-d e (m+2))+b^2 \left(d^2 e^2 (m+2)-c^2 f^2 (m+1)\right)\right)-b^2 (m+2) (d e-c f)^3 \left(\frac{d (e+f x)}{d e-c f}\right)^{-m} \, _2F_1\left(-m-1,-m-1;-m;\frac{f (c+d x)}{c f-d e}\right)\right)\right)-d (e+f x) (d g-c h) \left((c+d x) (d (e m+e-f x)-c f (m+2)) \left(2 d f \left(a^2 (-d) f-b (a c f (m+1)-a d e (m+3)+b c e)\right)+b^2 (m+2) (d e-c f) (c f (m+1)-d e (m+3))\right)+b d (m+1) (m+2) (m+3) (a+b x) (d e-c f)^3-(m+1) (m+2) (b c-a d) (d e-c f)^2 (a d f+b c f (m+2)-b d e (m+3))\right)\right)}{d^4 f (m+1) (m+2) (m+3) (d e-c f)^3}","-\frac{(d g-c h) (c+d x)^{-m-2} (e+f x)^{m+1} \left(b^2 (m+2) (d e-c f) (c f (m+1)-d e (m+3))-2 d f \left(a^2 d f+a b (c f (m+1)-d e (m+3))+b^2 c e\right)\right)}{d^3 f (m+2) (m+3) (d e-c f)^2}+\frac{(d g-c h) (c+d x)^{-m-1} (e+f x)^{m+1} \left(b^2 (m+2) (d e-c f) (c f (m+1)-d e (m+3))-2 d f \left(a^2 d f+a b (c f (m+1)-d e (m+3))+b^2 c e\right)\right)}{d^3 (m+1) (m+2) (m+3) (d e-c f)^3}+\frac{(b c-a d) (d g-c h) (c+d x)^{-m-3} (e+f x)^{m+1} (a d f+b (c f (m+2)-d e (m+3)))}{d^3 f (m+3) (d e-c f)}-\frac{h (b c-a d)^2 (c+d x)^{-m-2} (e+f x)^{m+1}}{d^3 (m+2) (d e-c f)}-\frac{h (b c-a d) (c+d x)^{-m-1} (e+f x)^{m+1} (a d f-b (2 d e (m+2)-c f (2 m+3)))}{d^3 (m+1) (m+2) (d e-c f)^2}-\frac{b (a+b x) (d g-c h) (c+d x)^{-m-3} (e+f x)^{m+1}}{d^2 f}-\frac{b^2 h (c+d x)^{-m} (e+f x)^m \left(\frac{d (e+f x)}{d e-c f}\right)^{-m} \, _2F_1\left(-m,-m;1-m;-\frac{f (c+d x)}{d e-c f}\right)}{d^4 m}",1,"((c + d*x)^(-3 - m)*(e + f*x)^m*(-(d*(d*g - c*h)*(e + f*x)*(-((b*c - a*d)*(d*e - c*f)^2*(1 + m)*(2 + m)*(a*d*f + b*c*f*(2 + m) - b*d*e*(3 + m))) + b*d*(d*e - c*f)^3*(1 + m)*(2 + m)*(3 + m)*(a + b*x) + (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)*(-(c*f*(2 + m)) + d*(e + e*m - f*x)))) - (d*e - c*f)*h*(3 + m)*(c + d*x)*(d*(b*c - a*d)^2*f*(d*e - c*f)*(1 + m)*(e + f*x) - (c + d*x)*(d*(a^2*d^2*f^2 + 2*a*b*d*f*(c*f*(1 + m) - d*e*(2 + m)) + b^2*(-(c^2*f^2*(1 + m)) + d^2*e^2*(2 + m)))*(e + f*x) - (b^2*(d*e - c*f)^3*(2 + m)*Hypergeometric2F1[-1 - m, -1 - m, -m, (f*(c + d*x))/(-(d*e) + c*f)])/((d*(e + f*x))/(d*e - c*f))^m))))/(d^4*f*(d*e - c*f)^3*(1 + m)*(2 + m)*(3 + m))","A",1
134,1,227,363,0.5479915,"\int (a+b x) (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","Integrate[(a + b*x)*(c + d*x)^(-4 - m)*(e + f*x)^m*(g + h*x),x]","\frac{(c+d x)^{-m-3} (e+f x)^{m+1} \left(\frac{(c+d x) (c f (m+2)-d (e m+e-f x)) \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) (e h (m+2)-f g)\right)\right)}{(m+1) (m+2) (d e-c f)^2}+a d f (d g-c h)-b \left(c^2 f h (m+2)+c d (f (g+h (m+3) x)-e h (m+3))-d^2 e h (m+3) x\right)\right)}{d^2 f (m+3) (c f-d e)}","\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,"((c + d*x)^(-3 - m)*(e + f*x)^(1 + m)*(a*d*f*(d*g - c*h) + ((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)*(c*f*(2 + m) - d*(e + e*m - f*x)))/((d*e - c*f)^2*(1 + m)*(2 + m)) - b*(c^2*f*h*(2 + m) - d^2*e*h*(3 + m)*x + c*d*(-(e*h*(3 + m)) + f*(g + h*(3 + m)*x)))))/(d^2*f*(-(d*e) + c*f)*(3 + m))","A",1
135,1,181,188,0.127661,"\int (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx","Integrate[(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{\left(\frac{(c+d x)^{-m-2} (e+f x)^{m+1}}{(-m-2) (d e-c f)}+\frac{f (c+d x)^{-m-1} (e+f x)^{m+1}}{(-m-2) (-m-1) (d e-c f)^2}\right) (-h (c f (m+1)+d e (-m-3))-2 d f g)}{d (-m-3) (d e-c f)}","-\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 - h*(d*e*(-3 - m) + c*f*(1 + m)))*(((c + d*x)^(-2 - m)*(e + f*x)^(1 + m))/((d*e - c*f)*(-2 - m)) + (f*(c + d*x)^(-1 - m)*(e + f*x)^(1 + m))/((d*e - c*f)^2*(-2 - m)*(-1 - m))))/(d*(d*e - c*f)*(-3 - m))","A",1
136,1,199,177,0.3991337,"\int \frac{(A+B x) (c+d x)^n (e+f x)^p}{a+b x} \, dx","Integrate[((A + B*x)*(c + d*x)^n*(e + f*x)^p)/(a + b*x),x]","\frac{(c+d x)^n (e+f x)^p \left(\frac{(A b-a B) \left(\frac{b (c+d x)}{d (a+b x)}\right)^{-n} \left(\frac{b (e+f x)}{f (a+b x)}\right)^{-p} F_1\left(-n-p;-n,-p;-n-p+1;\frac{a d-b c}{d (a+b x)},\frac{a f-b e}{f (a+b x)}\right)}{n+p}+\frac{b B (e+f x) \left(\frac{f (c+d x)}{c f-d e}\right)^{-n} \, _2F_1\left(-n,p+1;p+2;\frac{d (e+f x)}{d e-c f}\right)}{f (p+1)}\right)}{b^2}","-\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,"((c + d*x)^n*(e + f*x)^p*(((A*b - a*B)*AppellF1[-n - p, -n, -p, 1 - n - p, (-(b*c) + a*d)/(d*(a + b*x)), (-(b*e) + a*f)/(f*(a + b*x))])/((n + p)*((b*(c + d*x))/(d*(a + b*x)))^n*((b*(e + f*x))/(f*(a + b*x)))^p) + (b*B*(e + f*x)*Hypergeometric2F1[-n, 1 + p, 2 + p, (d*(e + f*x))/(d*e - c*f)])/(f*(1 + p)*((f*(c + d*x))/(-(d*e) + c*f))^n)))/b^2","A",0
137,1,174,233,0.1402754,"\int \frac{(a+b x)^m (A+B x) (c+d x)^{-m}}{e+f x} \, dx","Integrate[((a + b*x)^m*(A + B*x))/((c + d*x)^m*(e + f*x)),x]","\frac{(a+b x)^m (c+d x)^{-m} \left(\left(\frac{b (c+d x)}{b c-a d}\right)^m \left(B f m (a+b x) \, _2F_1\left(m,m+1;m+2;\frac{d (a+b x)}{a d-b c}\right)-b (m+1) (B e-A f) \, _2F_1\left(m,m;m+1;\frac{d (a+b x)}{a d-b c}\right)\right)+b (m+1) (B e-A f) \, _2F_1\left(1,m;m+1;\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}\right)\right)}{b f^2 m (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,"((a + b*x)^m*(b*(B*e - A*f)*(1 + m)*Hypergeometric2F1[1, m, 1 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))] + ((b*(c + d*x))/(b*c - a*d))^m*(-(b*(B*e - A*f)*(1 + m)*Hypergeometric2F1[m, m, 1 + m, (d*(a + b*x))/(-(b*c) + a*d)]) + B*f*m*(a + b*x)*Hypergeometric2F1[m, 1 + m, 2 + m, (d*(a + b*x))/(-(b*c) + a*d)])))/(b*f^2*m*(1 + m)*(c + d*x)^m)","A",1
138,1,184,250,0.2255358,"\int \frac{(A+B x) (c+d x)^n (e+f x)^p}{\sqrt{a+b x}} \, dx","Integrate[((A + B*x)*(c + d*x)^n*(e + f*x)^p)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} (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} \left(3 (A b-a B) F_1\left(\frac{1}{2};-n,-p;\frac{3}{2};\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)+B (a+b x) F_1\left(\frac{3}{2};-n,-p;\frac{5}{2};\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)\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*Sqrt[a + b*x]*(c + d*x)^n*(e + f*x)^p*(3*(A*b - a*B)*AppellF1[1/2, -n, -p, 3/2, (d*(a + b*x))/(-(b*c) + a*d), (f*(a + b*x))/(-(b*e) + a*f)] + B*(a + b*x)*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",1
139,0,0,530,4.5321696,"\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^3 \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x)^3,x]","\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^3 \, dx","\frac{3 h^2 (b g-a h) (a+b x)^{m+3} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+3;-n,-p;m+4;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^4 (m+3)}+\frac{(b g-a h)^3 (a+b x)^{m+1} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^4 (m+1)}+\frac{3 h (b g-a h)^2 (a+b x)^{m+2} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+2;-n,-p;m+3;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^4 (m+2)}+\frac{h^3 (a+b x)^{m+4} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+4;-n,-p;m+5;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^4 (m+4)}",1,"Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x)^3, x]","F",-1
140,0,0,393,1.5294023,"\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^2 \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x)^2,x]","\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^2 \, dx","\frac{(b g-a h)^2 (a+b x)^{m+1} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^3 (m+1)}+\frac{2 h (b g-a h) (a+b x)^{m+2} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+2;-n,-p;m+3;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^3 (m+2)}+\frac{h^2 (a+b x)^{m+3} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+3;-n,-p;m+4;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^3 (m+3)}",1,"Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x)^2, x]","F",-1
141,0,0,256,0.8335406,"\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x) \, dx","Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x),x]","\int (a+b x)^m (c+d x)^n (e+f x)^p (g+h x) \, dx","\frac{(b g-a h) (a+b x)^{m+1} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+1;-n,-p;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+1)}+\frac{h (a+b x)^{m+2} (c+d x)^n (e+f x)^p \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{-p} F_1\left(m+2;-n,-p;m+3;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+2)}",1,"Integrate[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x), x]","F",-1
142,1,121,123,0.1328837,"\int (a+b x)^m (c+d x)^n (e+f x)^p \, dx","Integrate[(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)}{a d-b c},\frac{f (a+b x)}{a f-b e}\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",1
143,0,0,32,0.2518083,"\int \frac{(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx","Integrate[((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,"Integrate[((a + b*x)^m*(c + d*x)^n*(e + f*x)^p)/(g + h*x), x]","A",-1
144,0,0,268,0.6461668,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-m-n} \, dx","Integrate[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-m - n),x]","\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-m-n} \, dx","\frac{(A b-a B) (a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{m+n} F_1\left(m+1;-n,m+n;m+2;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+1)}+\frac{B (a+b x)^{m+2} (c+d x)^n (e+f x)^{-m-n} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^{m+n} F_1\left(m+2;-n,m+n;m+3;-\frac{d (a+b x)}{b c-a d},-\frac{f (a+b x)}{b e-a f}\right)}{b^2 (m+2)}",1,"Integrate[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-m - n), x]","F",-1
145,1,208,283,0.3258108,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-1-m-n} \, dx","Integrate[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-1 - m - n),x]","\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n+1} \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-1} \left(b (A f-B e) F_1\left(m+1;-n,m+n+1;m+2;\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)+B (b e-a f) F_1\left(m+1;-n,m+n;m+2;\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)\right)}{f (m+1) (b e-a f)^2}","\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,"((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(1 - m - n)*((b*(e + f*x))/(b*e - a*f))^(-1 + m + n)*(B*(b*e - a*f)*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*(-(B*e) + A*f)*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)^2*(1 + m)*((b*(c + d*x))/(b*c - a*d))^n)","A",1
146,1,215,277,0.4353948,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-2-m-n} \, dx","Integrate[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-2 - m - n),x]","-\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-1} \left(\frac{b (c+d x)}{b c-a d}\right)^{-n} \left(\frac{b (e+f x)}{b e-a f}\right)^n \left((A f-B e) \, _2F_1\left(m+1,-n;m+2;\frac{(c f-d e) (a+b x)}{(b c-a d) (e+f x)}\right)+B (e+f x) \left(\frac{b (e+f x)}{b e-a f}\right)^m F_1\left(m+1;-n,m+n+1;m+2;\frac{d (a+b x)}{a d-b c},\frac{f (a+b x)}{a f-b e}\right)\right)}{f (m+1) (a f-b e)}","\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,"-(((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*((b*(e + f*x))/(b*e - a*f))^n*(B*(e + f*x)*((b*(e + f*x))/(b*e - a*f))^m*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)] + (-(B*e) + A*f)*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*(c + d*x))/(b*c - a*d))^n))","A",0
147,1,223,263,0.2711145,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-3-m-n} \, dx","Integrate[(a + b*x)^m*(A + B*x)*(c + d*x)^n*(e + f*x)^(-3 - m - n),x]","-\frac{(a+b x)^{m+1} (c+d x)^n (e+f x)^{-m-n-2} \left(\frac{(e+f x) \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{(c f-d e) (a+b x)}{(b c-a d) (e+f x)}\right)}{(m+1) (b e-a f)}+(c+d x) (A f-B e)\right)}{(m+n+2) (b e-a f) (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,"-(((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-2 - m - n)*((-(B*e) + A*f)*(c + d*x) + ((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)))*(e + f*x)*Hypergeometric2F1[1 + m, -n, 2 + m, ((-(d*e) + c*f)*(a + b*x))/((b*c - a*d)*(e + f*x))])/((b*e - a*f)*(1 + m)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)))/((b*e - a*f)*(d*e - c*f)*(2 + m + n)))","A",1
148,1,508,558,1.941963,"\int (a+b x)^m (A+B x) (c+d x)^n (e+f x)^{-4-m-n} \, dx","Integrate[(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-3} \left(-\frac{(e+f x)^2 \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{(c f-d e) (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{(c+d x) (e+f x) (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) (b e-a f) (d e-c f)}-(c+d x) (B e-A f)\right)}{(m+n+3) (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} ((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,"-(((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-3 - m - n)*(-((B*e - A*f)*(c + d*x)) - ((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))))*(c + d*x)*(e + f*x))/((b*e - a*f)*(d*e - c*f)*(2 + 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)))))*(e + f*x)^2*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)))/((b*e - a*f)*(d*e - c*f)*(3 + m + n)))","A",1
149,1,57,79,0.0662533,"\int \frac{x \left(a+b x+c x^2\right)}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Integrate[(x*(a + b*x + c*x^2))/(Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","\frac{3 b d \sin ^{-1}(d x)-\sqrt{1-d^2 x^2} \left(3 d^2 (2 a+b x)+2 c \left(d^2 x^2+2\right)\right)}{6 d^4}","-\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,"(-(Sqrt[1 - d^2*x^2]*(3*d^2*(2*a + b*x) + 2*c*(2 + d^2*x^2))) + 3*b*d*ArcSin[d*x])/(6*d^4)","A",1
150,1,45,63,0.0350136,"\int \frac{a+b x+c x^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx","Integrate[(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)-d \sqrt{1-d^2 x^2} (2 b+c x)}{2 d^3}","\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,"(-(d*(2*b + c*x)*Sqrt[1 - d^2*x^2]) + (c + 2*a*d^2)*ArcSin[d*x])/(2*d^3)","A",1
151,1,48,48,0.0602163,"\int \frac{a+b x+c x^2}{x \sqrt{1-d x} \sqrt{1+d x}} \, dx","Integrate[(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",1
152,1,48,48,0.0595165,"\int \frac{a+b x+c x^2}{x^2 \sqrt{1-d x} \sqrt{1+d x}} \, dx","Integrate[(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",1
153,1,56,71,0.0504254,"\int \frac{a+b x+c x^2}{x^3 \sqrt{1-d x} \sqrt{1+d x}} \, dx","Integrate[(a + b*x + c*x^2)/(x^3*Sqrt[1 - d*x]*Sqrt[1 + d*x]),x]","-\frac{\sqrt{1-d^2 x^2} (a+2 b x)}{2 x^2}-\frac{1}{2} \left(a d^2+2 c\right) \tanh ^{-1}\left(\sqrt{1-d^2 x^2}\right)","-\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,"-1/2*((a + 2*b*x)*Sqrt[1 - d^2*x^2])/x^2 - ((2*c + a*d^2)*ArcTanh[Sqrt[1 - d^2*x^2]])/2","A",1
154,1,149,87,0.3485834,"\int \frac{x \left(a+b x+c x^2\right)}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx","Integrate[(x*(a + b*x + c*x^2))/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{\sqrt{-(d x-1)^2} \sqrt{d x+1} \left(3 d^2 (2 a+b x)+2 c \left(d^2 x^2+2\right)\right)+6 \sqrt{d x-1} \sin ^{-1}\left(\frac{\sqrt{1-d x}}{\sqrt{2}}\right) (d (2 a d-b)+2 c)-12 \sqrt{1-d x} \tanh ^{-1}\left(\sqrt{\frac{d x-1}{d x+1}}\right) (d (a d-b)+c)}{6 d^4 \sqrt{1-d x}}","\frac{\sqrt{d x-1} \sqrt{d x+1} \left(2 \left(3 a d^2+2 c\right)+3 b d^2 x\right)}{6 d^4}+\frac{b \cosh ^{-1}(d x)}{2 d^3}+\frac{c x^2 \sqrt{d x-1} \sqrt{d x+1}}{3 d^2}",1,"(Sqrt[-(-1 + d*x)^2]*Sqrt[1 + d*x]*(3*d^2*(2*a + b*x) + 2*c*(2 + d^2*x^2)) + 6*(2*c + d*(-b + 2*a*d))*Sqrt[-1 + d*x]*ArcSin[Sqrt[1 - d*x]/Sqrt[2]] - 12*(c + d*(-b + a*d))*Sqrt[1 - d*x]*ArcTanh[Sqrt[(-1 + d*x)/(1 + d*x)]])/(6*d^4*Sqrt[1 - d*x])","A",0
155,1,126,52,0.2248546,"\int \frac{a+b x+c x^2}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx","Integrate[(a + b*x + c*x^2)/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{4 \sqrt{1-d x} \tanh ^{-1}\left(\sqrt{\frac{d x-1}{d x+1}}\right) (d (a d-b)+c)+d \sqrt{-(d x-1)^2} \sqrt{d x+1} (2 b+c x)+2 \sqrt{d x-1} (2 b d-c) \sin ^{-1}\left(\frac{\sqrt{1-d x}}{\sqrt{2}}\right)}{2 d^3 \sqrt{1-d x}}","\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,"(d*(2*b + c*x)*Sqrt[-(-1 + d*x)^2]*Sqrt[1 + d*x] + 2*(-c + 2*b*d)*Sqrt[-1 + d*x]*ArcSin[Sqrt[1 - d*x]/Sqrt[2]] + 4*(c + d*(-b + a*d))*Sqrt[1 - d*x]*ArcTanh[Sqrt[(-1 + d*x)/(1 + d*x)]])/(2*d^3*Sqrt[1 - d*x])","B",0
156,1,128,55,0.4184647,"\int \frac{a+b x+c x^2}{x \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Integrate[(a + b*x + c*x^2)/(x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{\frac{a d^2 \sqrt{d^2 x^2-1} \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)+c d^2 x^2-2 c \sqrt{1-d^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-d x}}{\sqrt{2}}\right)-c}{\sqrt{d x-1} \sqrt{d x+1}}-2 (c-b d) \tanh ^{-1}\left(\sqrt{\frac{d x-1}{d x+1}}\right)}{d^2}","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 + c*d^2*x^2 - 2*c*Sqrt[1 - d^2*x^2]*ArcSin[Sqrt[1 - d*x]/Sqrt[2]] + a*d^2*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(Sqrt[-1 + d*x]*Sqrt[1 + d*x]) - 2*(c - b*d)*ArcTanh[Sqrt[(-1 + d*x)/(1 + d*x)]])/d^2","B",0
157,1,89,55,0.185216,"\int \frac{a+b x+c x^2}{x^2 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Integrate[(a + b*x + c*x^2)/(x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{a \left(d^2 x^2-1\right)+b x \sqrt{d^2 x^2-1} \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{x \sqrt{d x-1} \sqrt{d x+1}}+\frac{2 c \tanh ^{-1}\left(\sqrt{\frac{d x-1}{d x+1}}\right)}{d}","\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) + b*x*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(x*Sqrt[-1 + d*x]*Sqrt[1 + d*x]) + (2*c*ArcTanh[Sqrt[(-1 + d*x)/(1 + d*x)]])/d","A",0
158,1,82,83,0.1438946,"\int \frac{a+b x+c x^2}{x^3 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Integrate[(a + b*x + c*x^2)/(x^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{\left(d^2 x^2-1\right) (a+2 b x)+x^2 \sqrt{d^2 x^2-1} \left(a d^2+2 c\right) \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{2 x^2 \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 + 2*b*x)*(-1 + d^2*x^2) + (2*c + a*d^2)*x^2*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(2*x^2*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","A",1
159,1,94,116,0.1333958,"\int \frac{a+b x+c x^2}{x^4 \sqrt{-1+d x} \sqrt{1+d x}} \, dx","Integrate[(a + b*x + c*x^2)/(x^4*Sqrt[-1 + d*x]*Sqrt[1 + d*x]),x]","\frac{\left(d^2 x^2-1\right) \left(a \left(4 d^2 x^2+2\right)+3 x (b+2 c x)\right)+3 b d^2 x^3 \sqrt{d^2 x^2-1} \tan ^{-1}\left(\sqrt{d^2 x^2-1}\right)}{6 x^3 \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,"((-1 + d^2*x^2)*(3*x*(b + 2*c*x) + a*(2 + 4*d^2*x^2)) + 3*b*d^2*x^3*Sqrt[-1 + d^2*x^2]*ArcTan[Sqrt[-1 + d^2*x^2]])/(6*x^3*Sqrt[-1 + d*x]*Sqrt[1 + d*x])","A",1