1,1,102,0,0.0944484,"\int \frac{a+b x+\frac{b f x^2}{e}}{\sqrt{d+e x+f x^2}} \, dx","Int[(a + b*x + (b*f*x^2)/e)/Sqrt[d + e*x + f*x^2],x]","\frac{\left(8 a f-b \left(\frac{4 d f}{e}+e\right)\right) \tanh ^{-1}\left(\frac{e+2 f x}{2 \sqrt{f} \sqrt{d+e x+f x^2}}\right)}{8 f^{3/2}}+\frac{b x \sqrt{d+e x+f x^2}}{2 e}+\frac{b \sqrt{d+e x+f x^2}}{4 f}","\frac{\left(8 a f-b \left(\frac{4 d f}{e}+e\right)\right) \tanh ^{-1}\left(\frac{e+2 f x}{2 \sqrt{f} \sqrt{d+e x+f x^2}}\right)}{8 f^{3/2}}+\frac{b x \sqrt{d+e x+f x^2}}{2 e}+\frac{b \sqrt{d+e x+f x^2}}{4 f}",1,"(b*Sqrt[d + e*x + f*x^2])/(4*f) + (b*x*Sqrt[d + e*x + f*x^2])/(2*e) + ((8*a*f - b*(e + (4*d*f)/e))*ArcTanh[(e + 2*f*x)/(2*Sqrt[f]*Sqrt[d + e*x + f*x^2])])/(8*f^(3/2))","A",4,4,29,0.1379,1,"{1661, 640, 621, 206}"
2,1,82,0,0.1106227,"\int \frac{1}{\sqrt{d+e x+f x^2} \left(a+b x+\frac{b f x^2}{e}\right)} \, dx","Int[1/(Sqrt[d + e*x + f*x^2]*(a + b*x + (b*f*x^2)/e)),x]","-\frac{2 \sqrt{e} \tanh ^{-1}\left(\frac{(e+2 f x) \sqrt{b d-a e}}{\sqrt{e} \sqrt{b e-4 a f} \sqrt{d+e x+f x^2}}\right)}{\sqrt{b d-a e} \sqrt{b e-4 a f}}","-\frac{2 \sqrt{e} \tanh ^{-1}\left(\frac{(e+2 f x) \sqrt{b d-a e}}{\sqrt{e} \sqrt{b e-4 a f} \sqrt{d+e x+f x^2}}\right)}{\sqrt{b d-a e} \sqrt{b e-4 a f}}",1,"(-2*Sqrt[e]*ArcTanh[(Sqrt[b*d - a*e]*(e + 2*f*x))/(Sqrt[e]*Sqrt[b*e - 4*a*f]*Sqrt[d + e*x + f*x^2])])/(Sqrt[b*d - a*e]*Sqrt[b*e - 4*a*f])","A",2,2,31,0.06452,1,"{982, 208}"
3,1,66,0,0.0790939,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+b x+c x^2\right)} \, dx","Int[1/(Sqrt[a + b*x + c*x^2]*(d + b*x + c*x^2)),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a-d} (b+2 c x)}{\sqrt{b^2-4 c d} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a-d} \sqrt{b^2-4 c d}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a-d} (b+2 c x)}{\sqrt{b^2-4 c d} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a-d} \sqrt{b^2-4 c d}}",1,"(-2*ArcTanh[(Sqrt[a - d]*(b + 2*c*x))/(Sqrt[b^2 - 4*c*d]*Sqrt[a + b*x + c*x^2])])/(Sqrt[a - d]*Sqrt[b^2 - 4*c*d])","A",2,2,27,0.07407,1,"{982, 208}"
4,1,129,0,0.1690223,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+b x+c x^2\right)^2} \, dx","Int[1/(Sqrt[a + b*x + c*x^2]*(d + b*x + c*x^2)^2),x]","\frac{\left(4 c (a-2 d)+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-d} (b+2 c x)}{\sqrt{b^2-4 c d} \sqrt{a+b x+c x^2}}\right)}{(a-d)^{3/2} \left(b^2-4 c d\right)^{3/2}}-\frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(a-d) \left(b^2-4 c d\right) \left(b x+c x^2+d\right)}","\frac{\left(4 c (a-2 d)+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-d} (b+2 c x)}{\sqrt{b^2-4 c d} \sqrt{a+b x+c x^2}}\right)}{(a-d)^{3/2} \left(b^2-4 c d\right)^{3/2}}-\frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(a-d) \left(b^2-4 c d\right) \left(b x+c x^2+d\right)}",1,"-(((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/((a - d)*(b^2 - 4*c*d)*(d + b*x + c*x^2))) + ((b^2 + 4*c*(a - 2*d))*ArcTanh[(Sqrt[a - d]*(b + 2*c*x))/(Sqrt[b^2 - 4*c*d]*Sqrt[a + b*x + c*x^2])])/((a - d)^(3/2)*(b^2 - 4*c*d)^(3/2))","A",4,4,27,0.1481,1,"{974, 12, 982, 208}"
5,1,224,0,0.4268717,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+b x+c x^2\right)^3} \, dx","Int[1/(Sqrt[a + b*x + c*x^2]*(d + b*x + c*x^2)^3),x]","-\frac{\left(16 c^2 \left(3 a^2-8 a d+8 d^2\right)+8 b^2 c (a-4 d)+3 b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a-d} (b+2 c x)}{\sqrt{b^2-4 c d} \sqrt{a+b x+c x^2}}\right)}{4 (a-d)^{5/2} \left(b^2-4 c d\right)^{5/2}}+\frac{3 (b+2 c x) \left(4 c (a-2 d)+b^2\right) \sqrt{a+b x+c x^2}}{4 (a-d)^2 \left(b^2-4 c d\right)^2 \left(b x+c x^2+d\right)}-\frac{(b+2 c x) \sqrt{a+b x+c x^2}}{2 (a-d) \left(b^2-4 c d\right) \left(b x+c x^2+d\right)^2}","-\frac{\left(16 c^2 \left(3 a^2-8 a d+8 d^2\right)+8 b^2 c (a-4 d)+3 b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a-d} (b+2 c x)}{\sqrt{b^2-4 c d} \sqrt{a+b x+c x^2}}\right)}{4 (a-d)^{5/2} \left(b^2-4 c d\right)^{5/2}}+\frac{3 (b+2 c x) \left(4 c (a-2 d)+b^2\right) \sqrt{a+b x+c x^2}}{4 (a-d)^2 \left(b^2-4 c d\right)^2 \left(b x+c x^2+d\right)}-\frac{(b+2 c x) \sqrt{a+b x+c x^2}}{2 (a-d) \left(b^2-4 c d\right) \left(b x+c x^2+d\right)^2}",1,"-((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(2*(a - d)*(b^2 - 4*c*d)*(d + b*x + c*x^2)^2) + (3*(b^2 + 4*c*(a - 2*d))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(4*(a - d)^2*(b^2 - 4*c*d)^2*(d + b*x + c*x^2)) - ((3*b^4 + 8*b^2*c*(a - 4*d) + 16*c^2*(3*a^2 - 8*a*d + 8*d^2))*ArcTanh[(Sqrt[a - d]*(b + 2*c*x))/(Sqrt[b^2 - 4*c*d]*Sqrt[a + b*x + c*x^2])])/(4*(a - d)^(5/2)*(b^2 - 4*c*d)^(5/2))","A",5,5,27,0.1852,1,"{974, 1060, 12, 982, 208}"
6,1,328,0,0.9704839,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+b x+c x^2\right)^4} \, dx","Int[1/(Sqrt[a + b*x + c*x^2]*(d + b*x + c*x^2)^4),x]","-\frac{(b+2 c x) \left(16 c^2 \left(15 a^2-44 a d+44 d^2\right)+8 b^2 c (7 a-22 d)+15 b^4\right) \sqrt{a+b x+c x^2}}{24 (a-d)^3 \left(b^2-4 c d\right)^3 \left(b x+c x^2+d\right)}+\frac{\left(4 c (a-2 d)+b^2\right) \left(16 c^2 \left(5 a^2-8 a d+8 d^2\right)-8 b^2 c (a+4 d)+5 b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a-d} (b+2 c x)}{\sqrt{b^2-4 c d} \sqrt{a+b x+c x^2}}\right)}{8 (a-d)^{7/2} \left(b^2-4 c d\right)^{7/2}}+\frac{5 (b+2 c x) \left(4 c (a-2 d)+b^2\right) \sqrt{a+b x+c x^2}}{12 (a-d)^2 \left(b^2-4 c d\right)^2 \left(b x+c x^2+d\right)^2}-\frac{(b+2 c x) \sqrt{a+b x+c x^2}}{3 (a-d) \left(b^2-4 c d\right) \left(b x+c x^2+d\right)^3}","-\frac{(b+2 c x) \left(16 c^2 \left(15 a^2-44 a d+44 d^2\right)+8 b^2 c (7 a-22 d)+15 b^4\right) \sqrt{a+b x+c x^2}}{24 (a-d)^3 \left(b^2-4 c d\right)^3 \left(b x+c x^2+d\right)}+\frac{\left(4 c (a-2 d)+b^2\right) \left(16 c^2 \left(5 a^2-8 a d+8 d^2\right)-8 b^2 c (a+4 d)+5 b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a-d} (b+2 c x)}{\sqrt{b^2-4 c d} \sqrt{a+b x+c x^2}}\right)}{8 (a-d)^{7/2} \left(b^2-4 c d\right)^{7/2}}+\frac{5 (b+2 c x) \left(4 c (a-2 d)+b^2\right) \sqrt{a+b x+c x^2}}{12 (a-d)^2 \left(b^2-4 c d\right)^2 \left(b x+c x^2+d\right)^2}-\frac{(b+2 c x) \sqrt{a+b x+c x^2}}{3 (a-d) \left(b^2-4 c d\right) \left(b x+c x^2+d\right)^3}",1,"-((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(3*(a - d)*(b^2 - 4*c*d)*(d + b*x + c*x^2)^3) + (5*(b^2 + 4*c*(a - 2*d))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(12*(a - d)^2*(b^2 - 4*c*d)^2*(d + b*x + c*x^2)^2) - ((15*b^4 + 8*b^2*c*(7*a - 22*d) + 16*c^2*(15*a^2 - 44*a*d + 44*d^2))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(24*(a - d)^3*(b^2 - 4*c*d)^3*(d + b*x + c*x^2)) + ((b^2 + 4*c*(a - 2*d))*(5*b^4 - 8*b^2*c*(a + 4*d) + 16*c^2*(5*a^2 - 8*a*d + 8*d^2))*ArcTanh[(Sqrt[a - d]*(b + 2*c*x))/(Sqrt[b^2 - 4*c*d]*Sqrt[a + b*x + c*x^2])])/(8*(a - d)^(7/2)*(b^2 - 4*c*d)^(7/2))","A",6,5,27,0.1852,1,"{974, 1060, 12, 982, 208}"
7,1,162,0,0.3056814,"\int \frac{1}{\sqrt{d+e x+f x^2} \left(a e+b e x+b f x^2\right)^2} \, dx","Int[1/(Sqrt[d + e*x + f*x^2]*(a*e + b*e*x + b*f*x^2)^2),x]","-\frac{\left(8 a e f-b \left(4 d f+e^2\right)\right) \tanh ^{-1}\left(\frac{(e+2 f x) \sqrt{b d-a e}}{\sqrt{e} \sqrt{b e-4 a f} \sqrt{d+e x+f x^2}}\right)}{e^{3/2} (b d-a e)^{3/2} (b e-4 a f)^{3/2}}-\frac{b (e+2 f x) \sqrt{d+e x+f x^2}}{e (b d-a e) (b e-4 a f) \left(a e+b e x+b f x^2\right)}","-\frac{\left(8 a e f-b \left(4 d f+e^2\right)\right) \tanh ^{-1}\left(\frac{(e+2 f x) \sqrt{b d-a e}}{\sqrt{e} \sqrt{b e-4 a f} \sqrt{d+e x+f x^2}}\right)}{e^{3/2} (b d-a e)^{3/2} (b e-4 a f)^{3/2}}-\frac{b (e+2 f x) \sqrt{d+e x+f x^2}}{e (b d-a e) (b e-4 a f) \left(a e+b e x+b f x^2\right)}",1,"-((b*(e + 2*f*x)*Sqrt[d + e*x + f*x^2])/(e*(b*d - a*e)*(b*e - 4*a*f)*(a*e + b*e*x + b*f*x^2))) - ((8*a*e*f - b*(e^2 + 4*d*f))*ArcTanh[(Sqrt[b*d - a*e]*(e + 2*f*x))/(Sqrt[e]*Sqrt[b*e - 4*a*f]*Sqrt[d + e*x + f*x^2])])/(e^(3/2)*(b*d - a*e)^(3/2)*(b*e - 4*a*f)^(3/2))","A",4,4,31,0.1290,1,"{974, 12, 982, 208}"
8,1,28,0,0.0172824,"\int \frac{1}{\left(4+2 x+x^2\right) \sqrt{5+2 x+x^2}} \, dx","Int[1/((4 + 2*x + x^2)*Sqrt[5 + 2*x + x^2]),x]","\frac{\tan ^{-1}\left(\frac{x+1}{\sqrt{3} \sqrt{x^2+2 x+5}}\right)}{\sqrt{3}}","\frac{\tan ^{-1}\left(\frac{x+1}{\sqrt{3} \sqrt{x^2+2 x+5}}\right)}{\sqrt{3}}",1,"ArcTan[(1 + x)/(Sqrt[3]*Sqrt[5 + 2*x + x^2])]/Sqrt[3]","A",2,2,23,0.08696,1,"{982, 204}"
9,1,136,0,0.1029878,"\int \left(a+\frac{e x}{2}+c x^2\right)^p \left(2 a+e x+2 c x^2\right)^q \, dx","Int[(a + (e*x)/2 + c*x^2)^p*(2*a + e*x + 2*c*x^2)^q,x]","-\frac{2^{q+1} \left(-\frac{-\sqrt{e^2-16 a c}+4 c x+e}{\sqrt{e^2-16 a c}}\right)^{-p-q-1} \left(2 a+2 c x^2+e x\right)^{p+q+1} \, _2F_1\left(-p-q,p+q+1;p+q+2;\frac{e+4 c x+\sqrt{e^2-16 a c}}{2 \sqrt{e^2-16 a c}}\right)}{(p+q+1) \sqrt{e^2-16 a c}}","-\frac{2^{q+1} \left(-\frac{-\sqrt{e^2-16 a c}+4 c x+e}{\sqrt{e^2-16 a c}}\right)^{-p-q-1} \left(2 a+2 c x^2+e x\right)^{p+q+1} \, _2F_1\left(-p-q,p+q+1;p+q+2;\frac{e+4 c x+\sqrt{e^2-16 a c}}{2 \sqrt{e^2-16 a c}}\right)}{(p+q+1) \sqrt{e^2-16 a c}}",1,"-((2^(1 + q)*(-((e - Sqrt[-16*a*c + e^2] + 4*c*x)/Sqrt[-16*a*c + e^2]))^(-1 - p - q)*(2*a + e*x + 2*c*x^2)^(1 + p + q)*Hypergeometric2F1[-p - q, 1 + p + q, 2 + p + q, (e + Sqrt[-16*a*c + e^2] + 4*c*x)/(2*Sqrt[-16*a*c + e^2])])/(Sqrt[-16*a*c + e^2]*(1 + p + q)))","A",2,2,31,0.06452,1,"{967, 624}"
10,1,200,0,0.1340285,"\int \left(a+\frac{c e x}{f}+c x^2\right)^p \left(\frac{a f}{c}+e x+f x^2\right)^q \, dx","Int[(a + (c*e*x)/f + c*x^2)^p*((a*f)/c + e*x + f*x^2)^q,x]","-\frac{\sqrt{c} 2^{p+q+1} \left(a+\frac{c e x}{f}+c x^2\right)^p \left(\frac{a f}{c}+e x+f x^2\right)^{q+1} \left(-\frac{\sqrt{c} \left(-\frac{\sqrt{c e^2-4 a f^2}}{\sqrt{c}}+e+2 f x\right)}{\sqrt{c e^2-4 a f^2}}\right)^{-p-q-1} \, _2F_1\left(-p-q,p+q+1;p+q+2;\frac{\sqrt{c} \left(e+2 f x+\frac{\sqrt{c e^2-4 a f^2}}{\sqrt{c}}\right)}{2 \sqrt{c e^2-4 a f^2}}\right)}{(p+q+1) \sqrt{c e^2-4 a f^2}}","-\frac{\sqrt{c} 2^{p+q+1} \left(a+\frac{c e x}{f}+c x^2\right)^p \left(\frac{a f}{c}+e x+f x^2\right)^{q+1} \left(-\frac{\sqrt{c} \left(-\frac{\sqrt{c e^2-4 a f^2}}{\sqrt{c}}+e+2 f x\right)}{\sqrt{c e^2-4 a f^2}}\right)^{-p-q-1} \, _2F_1\left(-p-q,p+q+1;p+q+2;\frac{\sqrt{c} \left(e+2 f x+\frac{\sqrt{c e^2-4 a f^2}}{\sqrt{c}}\right)}{2 \sqrt{c e^2-4 a f^2}}\right)}{(p+q+1) \sqrt{c e^2-4 a f^2}}",1,"-((2^(1 + p + q)*Sqrt[c]*(-((Sqrt[c]*(e - Sqrt[c*e^2 - 4*a*f^2]/Sqrt[c] + 2*f*x))/Sqrt[c*e^2 - 4*a*f^2]))^(-1 - p - q)*(a + (c*e*x)/f + c*x^2)^p*((a*f)/c + e*x + f*x^2)^(1 + q)*Hypergeometric2F1[-p - q, 1 + p + q, 2 + p + q, (Sqrt[c]*(e + Sqrt[c*e^2 - 4*a*f^2]/Sqrt[c] + 2*f*x))/(2*Sqrt[c*e^2 - 4*a*f^2])])/(Sqrt[c*e^2 - 4*a*f^2]*(1 + p + q)))","A",2,2,34,0.05882,1,"{968, 624}"
11,1,48,0,0.0153268,"\int \frac{\sqrt{1+2 x+x^2}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[1 + 2*x + x^2]/Sqrt[1 + x^2],x]","\frac{\sqrt{x^2+1} \sqrt{x^2+2 x+1}}{x+1}+\frac{\sqrt{x^2+2 x+1} \sinh ^{-1}(x)}{x+1}","\frac{\sqrt{x^2+1} \sqrt{x^2+2 x+1}}{x+1}+\frac{\sqrt{x^2+2 x+1} \sinh ^{-1}(x)}{x+1}",1,"(Sqrt[1 + x^2]*Sqrt[1 + 2*x + x^2])/(1 + x) + (Sqrt[1 + 2*x + x^2]*ArcSinh[x])/(1 + x)","A",3,3,22,0.1364,1,"{970, 641, 215}"
12,1,70,0,0.0514388,"\int \frac{1}{\left(-1+x^2\right)^2 \sqrt{-1+x+x^2}} \, dx","Int[1/((-1 + x^2)^2*Sqrt[-1 + x + x^2]),x]","\frac{\sqrt{x^2+x-1}}{2 \left(1-x^2\right)}-\frac{1}{8} \tan ^{-1}\left(\frac{x+3}{2 \sqrt{x^2+x-1}}\right)-\frac{5}{8} \tanh ^{-1}\left(\frac{1-3 x}{2 \sqrt{x^2+x-1}}\right)","\frac{\sqrt{x^2+x-1}}{2 \left(1-x^2\right)}-\frac{1}{8} \tan ^{-1}\left(\frac{x+3}{2 \sqrt{x^2+x-1}}\right)-\frac{5}{8} \tanh ^{-1}\left(\frac{1-3 x}{2 \sqrt{x^2+x-1}}\right)",1,"Sqrt[-1 + x + x^2]/(2*(1 - x^2)) - ArcTan[(3 + x)/(2*Sqrt[-1 + x + x^2])]/8 - (5*ArcTanh[(1 - 3*x)/(2*Sqrt[-1 + x + x^2])])/8","A",6,5,18,0.2778,1,"{976, 1033, 724, 206, 204}"
13,1,1077,0,3.0989873,"\int \frac{1}{\sqrt{a+b x+c x^2} \sqrt{d+f x^2}} \, dx","Int[1/(Sqrt[a + b*x + c*x^2]*Sqrt[d + f*x^2]),x]","-\frac{\sqrt[4]{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)^{3/2} \sqrt{2 a+\left(b+\sqrt{b^2-4 a c}\right) x} \sqrt{\frac{\left(4 a c-\left(b+\sqrt{b^2-4 a c}\right)^2\right)^2 \left(f x^2+d\right)}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}} \left(\frac{\sqrt{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\sqrt{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1\right) \sqrt{\frac{\frac{\left(4 d c^2+\left(b+\sqrt{b^2-4 a c}\right)^2 f\right) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)^2}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}-\frac{4 \left(b+\sqrt{b^2-4 a c}\right) (c d+a f) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1}{\left(\frac{\sqrt{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\sqrt{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \sqrt{2 a+\left(b+\sqrt{b^2-4 a c}\right) x}}{\sqrt[4]{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)} \sqrt{b+2 c x+\sqrt{b^2-4 a c}}}\right)|\frac{1}{2} \left(\frac{\left(b+\sqrt{b^2-4 a c}\right) (c d+a f)}{\sqrt{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \sqrt{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)}}+1\right)\right)}{\left(4 a c-\left(b+\sqrt{b^2-4 a c}\right)^2\right) \sqrt[4]{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \sqrt{c x^2+b x+a} \sqrt{f x^2+d} \sqrt{\frac{\left(4 d c^2+\left(b+\sqrt{b^2-4 a c}\right)^2 f\right) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)^2}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}-\frac{4 \left(b+\sqrt{b^2-4 a c}\right) (c d+a f) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1}}","-\frac{\sqrt[4]{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)^{3/2} \sqrt{2 a+\left(b+\sqrt{b^2-4 a c}\right) x} \sqrt{\frac{\left(4 a c-\left(b+\sqrt{b^2-4 a c}\right)^2\right)^2 \left(f x^2+d\right)}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}} \left(\frac{\sqrt{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\sqrt{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1\right) \sqrt{\frac{\frac{\left(4 d c^2+\left(b+\sqrt{b^2-4 a c}\right)^2 f\right) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)^2}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}-\frac{4 \left(b+\sqrt{b^2-4 a c}\right) (c d+a f) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1}{\left(\frac{\sqrt{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\sqrt{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \sqrt{2 a+\left(b+\sqrt{b^2-4 a c}\right) x}}{\sqrt[4]{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)} \sqrt{b+2 c x+\sqrt{b^2-4 a c}}}\right)|\frac{1}{2} \left(\frac{\left(b+\sqrt{b^2-4 a c}\right) (c d+a f)}{\sqrt{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \sqrt{d b^2+\sqrt{b^2-4 a c} d b-2 a (c d-a f)}}+1\right)\right)}{\left(4 a c-\left(b+\sqrt{b^2-4 a c}\right)^2\right) \sqrt[4]{2 d c^2-2 a f c+b \left(b+\sqrt{b^2-4 a c}\right) f} \sqrt{c x^2+b x+a} \sqrt{f x^2+d} \sqrt{\frac{\left(4 d c^2+\left(b+\sqrt{b^2-4 a c}\right)^2 f\right) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)^2}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}-\frac{4 \left(b+\sqrt{b^2-4 a c}\right) (c d+a f) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\left(4 f a^2+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1}}",1,"-(((b^2*d + b*Sqrt[b^2 - 4*a*c]*d - 2*a*(c*d - a*f))^(1/4)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)^(3/2)*Sqrt[2*a + (b + Sqrt[b^2 - 4*a*c])*x]*Sqrt[((4*a*c - (b + Sqrt[b^2 - 4*a*c])^2)^2*(d + f*x^2))/(((b + Sqrt[b^2 - 4*a*c])^2*d + 4*a^2*f)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)^2)]*(1 + (Sqrt[2*c^2*d - 2*a*c*f + b*(b + Sqrt[b^2 - 4*a*c])*f]*(2*a + (b + Sqrt[b^2 - 4*a*c])*x))/(Sqrt[b^2*d + b*Sqrt[b^2 - 4*a*c]*d - 2*a*(c*d - a*f)]*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)))*Sqrt[(1 - (4*(b + Sqrt[b^2 - 4*a*c])*(c*d + a*f)*(2*a + (b + Sqrt[b^2 - 4*a*c])*x))/(((b + Sqrt[b^2 - 4*a*c])^2*d + 4*a^2*f)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)) + ((4*c^2*d + (b + Sqrt[b^2 - 4*a*c])^2*f)*(2*a + (b + Sqrt[b^2 - 4*a*c])*x)^2)/(((b + Sqrt[b^2 - 4*a*c])^2*d + 4*a^2*f)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)^2))/(1 + (Sqrt[2*c^2*d - 2*a*c*f + b*(b + Sqrt[b^2 - 4*a*c])*f]*(2*a + (b + Sqrt[b^2 - 4*a*c])*x))/(Sqrt[b^2*d + b*Sqrt[b^2 - 4*a*c]*d - 2*a*(c*d - a*f)]*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)))^2]*EllipticF[2*ArcTan[((2*c^2*d - 2*a*c*f + b*(b + Sqrt[b^2 - 4*a*c])*f)^(1/4)*Sqrt[2*a + (b + Sqrt[b^2 - 4*a*c])*x])/((b^2*d + b*Sqrt[b^2 - 4*a*c]*d - 2*a*(c*d - a*f))^(1/4)*Sqrt[b + Sqrt[b^2 - 4*a*c] + 2*c*x])], (1 + ((b + Sqrt[b^2 - 4*a*c])*(c*d + a*f))/(Sqrt[2*c^2*d - 2*a*c*f + b*(b + Sqrt[b^2 - 4*a*c])*f]*Sqrt[b^2*d + b*Sqrt[b^2 - 4*a*c]*d - 2*a*(c*d - a*f)]))/2])/((4*a*c - (b + Sqrt[b^2 - 4*a*c])^2)*(2*c^2*d - 2*a*c*f + b*(b + Sqrt[b^2 - 4*a*c])*f)^(1/4)*Sqrt[a + b*x + c*x^2]*Sqrt[d + f*x^2]*Sqrt[1 - (4*(b + Sqrt[b^2 - 4*a*c])*(c*d + a*f)*(2*a + (b + Sqrt[b^2 - 4*a*c])*x))/(((b + Sqrt[b^2 - 4*a*c])^2*d + 4*a^2*f)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)) + ((4*c^2*d + (b + Sqrt[b^2 - 4*a*c])^2*f)*(2*a + (b + Sqrt[b^2 - 4*a*c])*x)^2)/(((b + Sqrt[b^2 - 4*a*c])^2*d + 4*a^2*f)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)^2)]))","A",3,3,26,0.1154,1,"{993, 936, 1103}"
14,1,98,0,0.2096482,"\int \frac{\sqrt{-3-4 x-x^2}}{3+4 x+2 x^2} \, dx","Int[Sqrt[-3 - 4*x - x^2]/(3 + 4*x + 2*x^2),x]","-\frac{\tan ^{-1}\left(\frac{1-\frac{x+3}{\sqrt{-x^2-4 x-3}}}{\sqrt{2}}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\frac{\frac{x+3}{\sqrt{-x^2-4 x-3}}+1}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{-x^2-4 x-3}}\right)-\frac{1}{2} \sin ^{-1}(x+2)","-\frac{\tan ^{-1}\left(\frac{1-\frac{x+3}{\sqrt{-x^2-4 x-3}}}{\sqrt{2}}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\frac{\frac{x+3}{\sqrt{-x^2-4 x-3}}+1}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{-x^2-4 x-3}}\right)-\frac{1}{2} \sin ^{-1}(x+2)",1,"-ArcSin[2 + x]/2 - ArcTan[(1 - (3 + x)/Sqrt[-3 - 4*x - x^2])/Sqrt[2]]/Sqrt[2] + ArcTan[(1 + (3 + x)/Sqrt[-3 - 4*x - x^2])/Sqrt[2]]/Sqrt[2] - ArcTanh[x/Sqrt[-3 - 4*x - x^2]]/2","A",16,12,27,0.4444,1,"{989, 619, 216, 1028, 986, 12, 1026, 1161, 618, 204, 1027, 206}"
15,1,68,0,0.0491625,"\int \left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^4 \, dx","Int[(3 - x + 2*x^2)*(2 + 3*x + 5*x^2)^4,x]","\frac{1250 x^{11}}{11}+\frac{475 x^{10}}{2}+\frac{5075 x^9}{9}+\frac{3415 x^8}{4}+1176 x^7+\frac{2377 x^6}{2}+\frac{5099 x^5}{5}+656 x^4+\frac{1064 x^3}{3}+136 x^2+48 x","\frac{1250 x^{11}}{11}+\frac{475 x^{10}}{2}+\frac{5075 x^9}{9}+\frac{3415 x^8}{4}+1176 x^7+\frac{2377 x^6}{2}+\frac{5099 x^5}{5}+656 x^4+\frac{1064 x^3}{3}+136 x^2+48 x",1,"48*x + 136*x^2 + (1064*x^3)/3 + 656*x^4 + (5099*x^5)/5 + (2377*x^6)/2 + 1176*x^7 + (3415*x^8)/4 + (5075*x^9)/9 + (475*x^10)/2 + (1250*x^11)/11","A",2,1,23,0.04348,1,"{1657}"
16,1,56,0,0.0377753,"\int \left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^3 \, dx","Int[(3 - x + 2*x^2)*(2 + 3*x + 5*x^2)^3,x]","\frac{250 x^9}{9}+\frac{325 x^8}{8}+\frac{720 x^7}{7}+134 x^6+\frac{876 x^5}{5}+\frac{579 x^4}{4}+\frac{322 x^3}{3}+50 x^2+24 x","\frac{250 x^9}{9}+\frac{325 x^8}{8}+\frac{720 x^7}{7}+134 x^6+\frac{876 x^5}{5}+\frac{579 x^4}{4}+\frac{322 x^3}{3}+50 x^2+24 x",1,"24*x + 50*x^2 + (322*x^3)/3 + (579*x^4)/4 + (876*x^5)/5 + 134*x^6 + (720*x^7)/7 + (325*x^8)/8 + (250*x^9)/9","A",2,1,23,0.04348,1,"{1657}"
17,1,44,0,0.0285789,"\int \left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^2 \, dx","Int[(3 - x + 2*x^2)*(2 + 3*x + 5*x^2)^2,x]","\frac{50 x^7}{7}+\frac{35 x^6}{6}+\frac{103 x^5}{5}+\frac{85 x^4}{4}+\frac{83 x^3}{3}+16 x^2+12 x","\frac{50 x^7}{7}+\frac{35 x^6}{6}+\frac{103 x^5}{5}+\frac{85 x^4}{4}+\frac{83 x^3}{3}+16 x^2+12 x",1,"12*x + 16*x^2 + (83*x^3)/3 + (85*x^4)/4 + (103*x^5)/5 + (35*x^6)/6 + (50*x^7)/7","A",2,1,23,0.04348,1,"{1657}"
18,1,30,0,0.0161242,"\int \left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right) \, dx","Int[(3 - x + 2*x^2)*(2 + 3*x + 5*x^2),x]","2 x^5+\frac{x^4}{4}+\frac{16 x^3}{3}+\frac{7 x^2}{2}+6 x","2 x^5+\frac{x^4}{4}+\frac{16 x^3}{3}+\frac{7 x^2}{2}+6 x",1,"6*x + (7*x^2)/2 + (16*x^3)/3 + x^4/4 + 2*x^5","A",2,1,21,0.04762,1,"{1657}"
19,1,42,0,0.0402874,"\int \frac{3-x+2 x^2}{2+3 x+5 x^2} \, dx","Int[(3 - x + 2*x^2)/(2 + 3*x + 5*x^2),x]","-\frac{11}{50} \log \left(5 x^2+3 x+2\right)+\frac{2 x}{5}+\frac{143 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{25 \sqrt{31}}","-\frac{11}{50} \log \left(5 x^2+3 x+2\right)+\frac{2 x}{5}+\frac{143 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{25 \sqrt{31}}",1,"(2*x)/5 + (143*ArcTan[(3 + 10*x)/Sqrt[31]])/(25*Sqrt[31]) - (11*Log[2 + 3*x + 5*x^2])/50","A",6,5,23,0.2174,1,"{1657, 634, 618, 204, 628}"
20,1,43,0,0.0267706,"\int \frac{3-x+2 x^2}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[(3 - x + 2*x^2)/(2 + 3*x + 5*x^2)^2,x]","\frac{11 (13 x+7)}{155 \left(5 x^2+3 x+2\right)}+\frac{82 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{31 \sqrt{31}}","\frac{11 (13 x+7)}{155 \left(5 x^2+3 x+2\right)}+\frac{82 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{31 \sqrt{31}}",1,"(11*(7 + 13*x))/(155*(2 + 3*x + 5*x^2)) + (82*ArcTan[(3 + 10*x)/Sqrt[31]])/(31*Sqrt[31])","A",4,4,23,0.1739,1,"{1660, 12, 618, 204}"
21,1,64,0,0.0370305,"\int \frac{3-x+2 x^2}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[(3 - x + 2*x^2)/(2 + 3*x + 5*x^2)^3,x]","\frac{553 (10 x+3)}{9610 \left(5 x^2+3 x+2\right)}+\frac{11 (13 x+7)}{310 \left(5 x^2+3 x+2\right)^2}+\frac{1106 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{961 \sqrt{31}}","\frac{553 (10 x+3)}{9610 \left(5 x^2+3 x+2\right)}+\frac{11 (13 x+7)}{310 \left(5 x^2+3 x+2\right)^2}+\frac{1106 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{961 \sqrt{31}}",1,"(11*(7 + 13*x))/(310*(2 + 3*x + 5*x^2)^2) + (553*(3 + 10*x))/(9610*(2 + 3*x + 5*x^2)) + (1106*ArcTan[(3 + 10*x)/Sqrt[31]])/(961*Sqrt[31])","A",5,5,23,0.2174,1,"{1660, 12, 614, 618, 204}"
22,1,80,0,0.0599792,"\int \left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^4 \, dx","Int[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^4,x]","\frac{2500 x^{13}}{13}+\frac{875 x^{12}}{3}+\frac{11525 x^{11}}{11}+1571 x^{10}+\frac{24859 x^9}{9}+3315 x^8+\frac{27763 x^7}{7}+\frac{10771 x^6}{3}+\frac{14801 x^5}{5}+1838 x^4+\frac{3016 x^3}{3}+384 x^2+144 x","\frac{2500 x^{13}}{13}+\frac{875 x^{12}}{3}+\frac{11525 x^{11}}{11}+1571 x^{10}+\frac{24859 x^9}{9}+3315 x^8+\frac{27763 x^7}{7}+\frac{10771 x^6}{3}+\frac{14801 x^5}{5}+1838 x^4+\frac{3016 x^3}{3}+384 x^2+144 x",1,"144*x + 384*x^2 + (3016*x^3)/3 + 1838*x^4 + (14801*x^5)/5 + (10771*x^6)/3 + (27763*x^7)/7 + 3315*x^8 + (24859*x^9)/9 + 1571*x^10 + (11525*x^11)/11 + (875*x^12)/3 + (2500*x^13)/13","A",2,1,25,0.04000,1,"{1657}"
23,1,66,0,0.0481998,"\int \left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^3 \, dx","Int[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^3,x]","\frac{500 x^{11}}{11}+40 x^{10}+\frac{1865 x^9}{9}+\frac{1863 x^8}{8}+444 x^7+449 x^6+\frac{2693 x^5}{5}+\frac{1615 x^4}{4}+\frac{914 x^3}{3}+138 x^2+72 x","\frac{500 x^{11}}{11}+40 x^{10}+\frac{1865 x^9}{9}+\frac{1863 x^8}{8}+444 x^7+449 x^6+\frac{2693 x^5}{5}+\frac{1615 x^4}{4}+\frac{914 x^3}{3}+138 x^2+72 x",1,"72*x + 138*x^2 + (914*x^3)/3 + (1615*x^4)/4 + (2693*x^5)/5 + 449*x^6 + 444*x^7 + (1863*x^8)/8 + (1865*x^9)/9 + 40*x^10 + (500*x^11)/11","A",2,1,25,0.04000,1,"{1657}"
24,1,54,0,0.042492,"\int \left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^2 \, dx","Int[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^2,x]","\frac{100 x^9}{9}+\frac{5 x^8}{2}+\frac{321 x^7}{7}+\frac{86 x^6}{3}+78 x^5+59 x^4+\frac{241 x^3}{3}+42 x^2+36 x","\frac{100 x^9}{9}+\frac{5 x^8}{2}+\frac{321 x^7}{7}+\frac{86 x^6}{3}+78 x^5+59 x^4+\frac{241 x^3}{3}+42 x^2+36 x",1,"36*x + 42*x^2 + (241*x^3)/3 + 59*x^4 + 78*x^5 + (86*x^6)/3 + (321*x^7)/7 + (5*x^8)/2 + (100*x^9)/9","A",2,1,25,0.04000,1,"{1657}"
25,1,46,0,0.0296107,"\int \left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right) \, dx","Int[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2),x]","\frac{20 x^7}{7}-\frac{4 x^6}{3}+\frac{61 x^5}{5}+\frac{x^4}{4}+\frac{53 x^3}{3}+\frac{15 x^2}{2}+18 x","\frac{20 x^7}{7}-\frac{4 x^6}{3}+\frac{61 x^5}{5}+\frac{x^4}{4}+\frac{53 x^3}{3}+\frac{15 x^2}{2}+18 x",1,"18*x + (15*x^2)/2 + (53*x^3)/3 + x^4/4 + (61*x^5)/5 - (4*x^6)/3 + (20*x^7)/7","A",2,1,23,0.04348,1,"{1657}"
26,1,56,0,0.0513899,"\int \frac{\left(3-x+2 x^2\right)^2}{2+3 x+5 x^2} \, dx","Int[(3 - x + 2*x^2)^2/(2 + 3*x + 5*x^2),x]","\frac{4 x^3}{15}-\frac{16 x^2}{25}-\frac{1573 \log \left(5 x^2+3 x+2\right)}{1250}+\frac{381 x}{125}+\frac{8349 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{625 \sqrt{31}}","\frac{4 x^3}{15}-\frac{16 x^2}{25}-\frac{1573 \log \left(5 x^2+3 x+2\right)}{1250}+\frac{381 x}{125}+\frac{8349 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{625 \sqrt{31}}",1,"(381*x)/125 - (16*x^2)/25 + (4*x^3)/15 + (8349*ArcTan[(3 + 10*x)/Sqrt[31]])/(625*Sqrt[31]) - (1573*Log[2 + 3*x + 5*x^2])/1250","A",6,5,25,0.2000,1,"{1657, 634, 618, 204, 628}"
27,1,63,0,0.0608414,"\int \frac{\left(3-x+2 x^2\right)^2}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[(3 - x + 2*x^2)^2/(2 + 3*x + 5*x^2)^2,x]","\frac{121 (69 x+61)}{3875 \left(5 x^2+3 x+2\right)}-\frac{22}{125} \log \left(5 x^2+3 x+2\right)+\frac{4 x}{25}+\frac{41932 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{3875 \sqrt{31}}","\frac{121 (69 x+61)}{3875 \left(5 x^2+3 x+2\right)}-\frac{22}{125} \log \left(5 x^2+3 x+2\right)+\frac{4 x}{25}+\frac{41932 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{3875 \sqrt{31}}",1,"(4*x)/25 + (121*(61 + 69*x))/(3875*(2 + 3*x + 5*x^2)) + (41932*ArcTan[(3 + 10*x)/Sqrt[31]])/(3875*Sqrt[31]) - (22*Log[2 + 3*x + 5*x^2])/125","A",7,6,25,0.2400,1,"{1660, 1657, 634, 618, 204, 628}"
28,1,64,0,0.0516227,"\int \frac{\left(3-x+2 x^2\right)^2}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[(3 - x + 2*x^2)^2/(2 + 3*x + 5*x^2)^3,x]","\frac{121 (69 x+61)}{7750 \left(5 x^2+3 x+2\right)^2}+\frac{11 (45710 x+17557)}{240250 \left(5 x^2+3 x+2\right)}+\frac{4330 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{961 \sqrt{31}}","\frac{121 (69 x+61)}{7750 \left(5 x^2+3 x+2\right)^2}+\frac{11 (45710 x+17557)}{240250 \left(5 x^2+3 x+2\right)}+\frac{4330 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{961 \sqrt{31}}",1,"(121*(61 + 69*x))/(7750*(2 + 3*x + 5*x^2)^2) + (11*(17557 + 45710*x))/(240250*(2 + 3*x + 5*x^2)) + (4330*ArcTan[(3 + 10*x)/Sqrt[31]])/(961*Sqrt[31])","A",5,4,25,0.1600,1,"{1660, 12, 618, 204}"
29,1,85,0,0.0633293,"\int \frac{\left(3-x+2 x^2\right)^2}{\left(2+3 x+5 x^2\right)^4} \, dx","Int[(3 - x + 2*x^2)^2/(2 + 3*x + 5*x^2)^4,x]","\frac{16688 (10 x+3)}{148955 \left(5 x^2+3 x+2\right)}+\frac{11 (12060 x+4579)}{120125 \left(5 x^2+3 x+2\right)^2}+\frac{121 (69 x+61)}{11625 \left(5 x^2+3 x+2\right)^3}+\frac{66752 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{29791 \sqrt{31}}","\frac{16688 (10 x+3)}{148955 \left(5 x^2+3 x+2\right)}+\frac{11 (12060 x+4579)}{120125 \left(5 x^2+3 x+2\right)^2}+\frac{121 (69 x+61)}{11625 \left(5 x^2+3 x+2\right)^3}+\frac{66752 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{29791 \sqrt{31}}",1,"(121*(61 + 69*x))/(11625*(2 + 3*x + 5*x^2)^3) + (11*(4579 + 12060*x))/(120125*(2 + 3*x + 5*x^2)^2) + (16688*(3 + 10*x))/(148955*(2 + 3*x + 5*x^2)) + (66752*ArcTan[(3 + 10*x)/Sqrt[31]])/(29791*Sqrt[31])","A",6,5,25,0.2000,1,"{1660, 12, 614, 618, 204}"
30,1,96,0,0.0705267,"\int \left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^4 \, dx","Int[(3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)^4,x]","\frac{1000 x^{15}}{3}+\frac{2250 x^{14}}{7}+\frac{27050 x^{13}}{13}+\frac{30395 x^{12}}{12}+\frac{68583 x^{11}}{11}+\frac{75311 x^{10}}{10}+\frac{103583 x^9}{9}+\frac{94881 x^8}{8}+\frac{91349 x^7}{7}+\frac{64529 x^6}{6}+\frac{43083 x^5}{5}+5144 x^4+2856 x^3+1080 x^2+432 x","\frac{1000 x^{15}}{3}+\frac{2250 x^{14}}{7}+\frac{27050 x^{13}}{13}+\frac{30395 x^{12}}{12}+\frac{68583 x^{11}}{11}+\frac{75311 x^{10}}{10}+\frac{103583 x^9}{9}+\frac{94881 x^8}{8}+\frac{91349 x^7}{7}+\frac{64529 x^6}{6}+\frac{43083 x^5}{5}+5144 x^4+2856 x^3+1080 x^2+432 x",1,"432*x + 1080*x^2 + 2856*x^3 + 5144*x^4 + (43083*x^5)/5 + (64529*x^6)/6 + (91349*x^7)/7 + (94881*x^8)/8 + (103583*x^9)/9 + (75311*x^10)/10 + (68583*x^11)/11 + (30395*x^12)/12 + (27050*x^13)/13 + (2250*x^14)/7 + (1000*x^15)/3","A",2,1,25,0.04000,1,"{1657}"
31,1,82,0,0.0555126,"\int \left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^3 \, dx","Int[(3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)^3,x]","\frac{1000 x^{13}}{13}+25 x^{12}+\frac{4830 x^{11}}{11}+\frac{3061 x^{10}}{10}+\frac{3316 x^9}{3}+\frac{7869 x^8}{8}+\frac{12016 x^7}{7}+\frac{2873 x^6}{2}+\frac{8292 x^5}{5}+\frac{4483 x^4}{4}+870 x^3+378 x^2+216 x","\frac{1000 x^{13}}{13}+25 x^{12}+\frac{4830 x^{11}}{11}+\frac{3061 x^{10}}{10}+\frac{3316 x^9}{3}+\frac{7869 x^8}{8}+\frac{12016 x^7}{7}+\frac{2873 x^6}{2}+\frac{8292 x^5}{5}+\frac{4483 x^4}{4}+870 x^3+378 x^2+216 x",1,"216*x + 378*x^2 + 870*x^3 + (4483*x^4)/4 + (8292*x^5)/5 + (2873*x^6)/2 + (12016*x^7)/7 + (7869*x^8)/8 + (3316*x^9)/3 + (3061*x^10)/10 + (4830*x^11)/11 + 25*x^12 + (1000*x^13)/13","A",2,1,25,0.04000,1,"{1657}"
32,1,68,0,0.0505835,"\int \left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^2 \, dx","Int[(3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)^2,x]","\frac{200 x^{11}}{11}-6 x^{10}+\frac{922 x^9}{9}+\frac{83 x^8}{8}+\frac{1571 x^7}{7}+\frac{299 x^6}{3}+\frac{1416 x^5}{5}+\frac{635 x^4}{4}+237 x^3+108 x^2+108 x","\frac{200 x^{11}}{11}-6 x^{10}+\frac{922 x^9}{9}+\frac{83 x^8}{8}+\frac{1571 x^7}{7}+\frac{299 x^6}{3}+\frac{1416 x^5}{5}+\frac{635 x^4}{4}+237 x^3+108 x^2+108 x",1,"108*x + 108*x^2 + 237*x^3 + (635*x^4)/4 + (1416*x^5)/5 + (299*x^6)/3 + (1571*x^7)/7 + (83*x^8)/8 + (922*x^9)/9 - 6*x^10 + (200*x^11)/11","A",2,1,25,0.04000,1,"{1657}"
33,1,56,0,0.0318655,"\int \left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right) \, dx","Int[(3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2),x]","\frac{40 x^9}{9}-\frac{9 x^8}{2}+\frac{190 x^7}{7}-\frac{83 x^6}{6}+\frac{288 x^5}{5}-5 x^4+60 x^3+\frac{27 x^2}{2}+54 x","\frac{40 x^9}{9}-\frac{9 x^8}{2}+\frac{190 x^7}{7}-\frac{83 x^6}{6}+\frac{288 x^5}{5}-5 x^4+60 x^3+\frac{27 x^2}{2}+54 x",1,"54*x + (27*x^2)/2 + 60*x^3 - 5*x^4 + (288*x^5)/5 - (83*x^6)/6 + (190*x^7)/7 - (9*x^8)/2 + (40*x^9)/9","A",2,1,23,0.04348,1,"{1657}"
34,1,70,0,0.0529201,"\int \frac{\left(3-x+2 x^2\right)^3}{2+3 x+5 x^2} \, dx","Int[(3 - x + 2*x^2)^3/(2 + 3*x + 5*x^2),x]","\frac{8 x^5}{25}-\frac{21 x^4}{25}+\frac{1222 x^3}{375}-\frac{7451 x^2}{1250}-\frac{158389 \log \left(5 x^2+3 x+2\right)}{31250}+\frac{49508 x}{3125}+\frac{328757 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{15625 \sqrt{31}}","\frac{8 x^5}{25}-\frac{21 x^4}{25}+\frac{1222 x^3}{375}-\frac{7451 x^2}{1250}-\frac{158389 \log \left(5 x^2+3 x+2\right)}{31250}+\frac{49508 x}{3125}+\frac{328757 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{15625 \sqrt{31}}",1,"(49508*x)/3125 - (7451*x^2)/1250 + (1222*x^3)/375 - (21*x^4)/25 + (8*x^5)/25 + (328757*ArcTan[(3 + 10*x)/Sqrt[31]])/(15625*Sqrt[31]) - (158389*Log[2 + 3*x + 5*x^2])/31250","A",6,5,25,0.2000,1,"{1657, 634, 618, 204, 628}"
35,1,77,0,0.0722482,"\int \frac{\left(3-x+2 x^2\right)^3}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[(3 - x + 2*x^2)^3/(2 + 3*x + 5*x^2)^2,x]","\frac{8 x^3}{75}-\frac{54 x^2}{125}+\frac{1331 (247 x+443)}{96875 \left(5 x^2+3 x+2\right)}-\frac{10769 \log \left(5 x^2+3 x+2\right)}{6250}+\frac{1466 x}{625}+\frac{3819607 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{96875 \sqrt{31}}","\frac{8 x^3}{75}-\frac{54 x^2}{125}+\frac{1331 (247 x+443)}{96875 \left(5 x^2+3 x+2\right)}-\frac{10769 \log \left(5 x^2+3 x+2\right)}{6250}+\frac{1466 x}{625}+\frac{3819607 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{96875 \sqrt{31}}",1,"(1466*x)/625 - (54*x^2)/125 + (8*x^3)/75 + (1331*(443 + 247*x))/(96875*(2 + 3*x + 5*x^2)) + (3819607*ArcTan[(3 + 10*x)/Sqrt[31]])/(96875*Sqrt[31]) - (10769*Log[2 + 3*x + 5*x^2])/6250","A",7,6,25,0.2400,1,"{1660, 1657, 634, 618, 204, 628}"
36,1,84,0,0.0865293,"\int \frac{\left(3-x+2 x^2\right)^3}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[(3 - x + 2*x^2)^3/(2 + 3*x + 5*x^2)^3,x]","\frac{121 (342840 x+188381)}{6006250 \left(5 x^2+3 x+2\right)}+\frac{1331 (247 x+443)}{193750 \left(5 x^2+3 x+2\right)^2}-\frac{66}{625} \log \left(5 x^2+3 x+2\right)+\frac{8 x}{125}+\frac{11341176 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{600625 \sqrt{31}}","\frac{121 (342840 x+188381)}{6006250 \left(5 x^2+3 x+2\right)}+\frac{1331 (247 x+443)}{193750 \left(5 x^2+3 x+2\right)^2}-\frac{66}{625} \log \left(5 x^2+3 x+2\right)+\frac{8 x}{125}+\frac{11341176 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{600625 \sqrt{31}}",1,"(8*x)/125 + (1331*(443 + 247*x))/(193750*(2 + 3*x + 5*x^2)^2) + (121*(188381 + 342840*x))/(6006250*(2 + 3*x + 5*x^2)) + (11341176*ArcTan[(3 + 10*x)/Sqrt[31]])/(600625*Sqrt[31]) - (66*Log[2 + 3*x + 5*x^2])/625","A",8,6,25,0.2400,1,"{1660, 1657, 634, 618, 204, 628}"
37,1,84,0,0.056764,"\int \frac{\left(2+3 x+5 x^2\right)^4}{3-x+2 x^2} \, dx","Int[(2 + 3*x + 5*x^2)^4/(3 - x + 2*x^2),x]","\frac{625 x^7}{14}+\frac{3625 x^6}{24}+\frac{1855 x^5}{8}+\frac{6245 x^4}{64}-\frac{21229 x^3}{96}-\frac{28747 x^2}{128}+\frac{307461}{512} \log \left(2 x^2-x+3\right)+\frac{122691 x}{128}+\frac{1156639 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{256 \sqrt{23}}","\frac{625 x^7}{14}+\frac{3625 x^6}{24}+\frac{1855 x^5}{8}+\frac{6245 x^4}{64}-\frac{21229 x^3}{96}-\frac{28747 x^2}{128}+\frac{307461}{512} \log \left(2 x^2-x+3\right)+\frac{122691 x}{128}+\frac{1156639 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{256 \sqrt{23}}",1,"(122691*x)/128 - (28747*x^2)/128 - (21229*x^3)/96 + (6245*x^4)/64 + (1855*x^5)/8 + (3625*x^6)/24 + (625*x^7)/14 + (1156639*ArcTan[(1 - 4*x)/Sqrt[23]])/(256*Sqrt[23]) + (307461*Log[3 - x + 2*x^2])/512","A",6,5,25,0.2000,1,"{1657, 634, 618, 204, 628}"
38,1,70,0,0.0560196,"\int \frac{\left(2+3 x+5 x^2\right)^3}{3-x+2 x^2} \, dx","Int[(2 + 3*x + 5*x^2)^3/(3 - x + 2*x^2),x]","\frac{25 x^5}{2}+\frac{575 x^4}{16}+\frac{965 x^3}{24}-\frac{829 x^2}{32}+\frac{1331}{128} \log \left(2 x^2-x+3\right)-\frac{4795 x}{32}-\frac{59895 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{23}}","\frac{25 x^5}{2}+\frac{575 x^4}{16}+\frac{965 x^3}{24}-\frac{829 x^2}{32}+\frac{1331}{128} \log \left(2 x^2-x+3\right)-\frac{4795 x}{32}-\frac{59895 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{23}}",1,"(-4795*x)/32 - (829*x^2)/32 + (965*x^3)/24 + (575*x^4)/16 + (25*x^5)/2 - (59895*ArcTan[(1 - 4*x)/Sqrt[23]])/(64*Sqrt[23]) + (1331*Log[3 - x + 2*x^2])/128","A",6,5,25,0.2000,1,"{1657, 634, 618, 204, 628}"
39,1,56,0,0.0503026,"\int \frac{\left(2+3 x+5 x^2\right)^2}{3-x+2 x^2} \, dx","Int[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2),x]","\frac{25 x^3}{6}+\frac{85 x^2}{8}-\frac{363}{32} \log \left(2 x^2-x+3\right)+\frac{51 x}{8}+\frac{847 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16 \sqrt{23}}","\frac{25 x^3}{6}+\frac{85 x^2}{8}-\frac{363}{32} \log \left(2 x^2-x+3\right)+\frac{51 x}{8}+\frac{847 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16 \sqrt{23}}",1,"(51*x)/8 + (85*x^2)/8 + (25*x^3)/6 + (847*ArcTan[(1 - 4*x)/Sqrt[23]])/(16*Sqrt[23]) - (363*Log[3 - x + 2*x^2])/32","A",6,5,25,0.2000,1,"{1657, 634, 618, 204, 628}"
40,1,42,0,0.0348584,"\int \frac{2+3 x+5 x^2}{3-x+2 x^2} \, dx","Int[(2 + 3*x + 5*x^2)/(3 - x + 2*x^2),x]","\frac{11}{8} \log \left(2 x^2-x+3\right)+\frac{5 x}{2}+\frac{33 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4 \sqrt{23}}","\frac{11}{8} \log \left(2 x^2-x+3\right)+\frac{5 x}{2}+\frac{33 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4 \sqrt{23}}",1,"(5*x)/2 + (33*ArcTan[(1 - 4*x)/Sqrt[23]])/(4*Sqrt[23]) + (11*Log[3 - x + 2*x^2])/8","A",6,5,23,0.2174,1,"{1657, 634, 618, 204, 628}"
41,1,73,0,0.0533335,"\int \frac{1}{\left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)} \, dx","Int[1/((3 - x + 2*x^2)*(2 + 3*x + 5*x^2)),x]","-\frac{1}{44} \log \left(2 x^2-x+3\right)+\frac{1}{44} \log \left(5 x^2+3 x+2\right)+\frac{3 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{22 \sqrt{23}}+\frac{13 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{22 \sqrt{31}}","-\frac{1}{44} \log \left(2 x^2-x+3\right)+\frac{1}{44} \log \left(5 x^2+3 x+2\right)+\frac{3 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{22 \sqrt{23}}+\frac{13 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{22 \sqrt{31}}",1,"(3*ArcTan[(1 - 4*x)/Sqrt[23]])/(22*Sqrt[23]) + (13*ArcTan[(3 + 10*x)/Sqrt[31]])/(22*Sqrt[31]) - Log[3 - x + 2*x^2]/44 + Log[2 + 3*x + 5*x^2]/44","A",9,5,25,0.2000,1,"{980, 634, 618, 204, 628}"
42,1,94,0,0.0886149,"\int \frac{1}{\left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^2} \, dx","Int[1/((3 - x + 2*x^2)*(2 + 3*x + 5*x^2)^2),x]","\frac{65 x+4}{682 \left(5 x^2+3 x+2\right)}+\frac{3}{968} \log \left(2 x^2-x+3\right)-\frac{3}{968} \log \left(5 x^2+3 x+2\right)+\frac{7 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{484 \sqrt{23}}+\frac{2891 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{15004 \sqrt{31}}","\frac{65 x+4}{682 \left(5 x^2+3 x+2\right)}+\frac{3}{968} \log \left(2 x^2-x+3\right)-\frac{3}{968} \log \left(5 x^2+3 x+2\right)+\frac{7 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{484 \sqrt{23}}+\frac{2891 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{15004 \sqrt{31}}",1,"(4 + 65*x)/(682*(2 + 3*x + 5*x^2)) + (7*ArcTan[(1 - 4*x)/Sqrt[23]])/(484*Sqrt[23]) + (2891*ArcTan[(3 + 10*x)/Sqrt[31]])/(15004*Sqrt[31]) + (3*Log[3 - x + 2*x^2])/968 - (3*Log[2 + 3*x + 5*x^2])/968","A",10,6,25,0.2400,1,"{974, 1072, 634, 618, 204, 628}"
43,1,115,0,0.1241782,"\int \frac{1}{\left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/((3 - x + 2*x^2)*(2 + 3*x + 5*x^2)^3),x]","\frac{65 x+4}{1364 \left(5 x^2+3 x+2\right)^2}+\frac{21605 x+7923}{465124 \left(5 x^2+3 x+2\right)}-\frac{\log \left(2 x^2-x+3\right)}{21296}+\frac{\log \left(5 x^2+3 x+2\right)}{21296}-\frac{45 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{10648 \sqrt{23}}+\frac{847793 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{10232728 \sqrt{31}}","\frac{65 x+4}{1364 \left(5 x^2+3 x+2\right)^2}+\frac{21605 x+7923}{465124 \left(5 x^2+3 x+2\right)}-\frac{\log \left(2 x^2-x+3\right)}{21296}+\frac{\log \left(5 x^2+3 x+2\right)}{21296}-\frac{45 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{10648 \sqrt{23}}+\frac{847793 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{10232728 \sqrt{31}}",1,"(4 + 65*x)/(1364*(2 + 3*x + 5*x^2)^2) + (7923 + 21605*x)/(465124*(2 + 3*x + 5*x^2)) - (45*ArcTan[(1 - 4*x)/Sqrt[23]])/(10648*Sqrt[23]) + (847793*ArcTan[(3 + 10*x)/Sqrt[31]])/(10232728*Sqrt[31]) - Log[3 - x + 2*x^2]/21296 + Log[2 + 3*x + 5*x^2]/21296","A",11,7,25,0.2800,1,"{974, 1060, 1072, 634, 618, 204, 628}"
44,1,91,0,0.0863451,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\left(3-x+2 x^2\right)^2} \, dx","Int[(2 + 3*x + 5*x^2)^4/(3 - x + 2*x^2)^2,x]","\frac{125 x^5}{4}+\frac{2125 x^4}{16}+\frac{9775 x^3}{48}-\frac{1185 x^2}{8}-\frac{14641 (79 x+101)}{2944 \left(2 x^2-x+3\right)}-\frac{30613}{128} \log \left(2 x^2-x+3\right)-\frac{89359 x}{64}-\frac{13292697 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1472 \sqrt{23}}","\frac{125 x^5}{4}+\frac{2125 x^4}{16}+\frac{9775 x^3}{48}-\frac{1185 x^2}{8}-\frac{14641 (79 x+101)}{2944 \left(2 x^2-x+3\right)}-\frac{30613}{128} \log \left(2 x^2-x+3\right)-\frac{89359 x}{64}-\frac{13292697 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1472 \sqrt{23}}",1,"(-89359*x)/64 - (1185*x^2)/8 + (9775*x^3)/48 + (2125*x^4)/16 + (125*x^5)/4 - (14641*(101 + 79*x))/(2944*(3 - x + 2*x^2)) - (13292697*ArcTan[(1 - 4*x)/Sqrt[23]])/(1472*Sqrt[23]) - (30613*Log[3 - x + 2*x^2])/128","A",7,6,25,0.2400,1,"{1660, 1657, 634, 618, 204, 628}"
45,1,77,0,0.0725653,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\left(3-x+2 x^2\right)^2} \, dx","Int[(2 + 3*x + 5*x^2)^3/(3 - x + 2*x^2)^2,x]","\frac{125 x^3}{12}+\frac{175 x^2}{4}-\frac{1331 (17-45 x)}{736 \left(2 x^2-x+3\right)}-\frac{2057}{32} \log \left(2 x^2-x+3\right)+\frac{915 x}{16}+\frac{223971 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{368 \sqrt{23}}","\frac{125 x^3}{12}+\frac{175 x^2}{4}-\frac{1331 (17-45 x)}{736 \left(2 x^2-x+3\right)}-\frac{2057}{32} \log \left(2 x^2-x+3\right)+\frac{915 x}{16}+\frac{223971 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{368 \sqrt{23}}",1,"(915*x)/16 + (175*x^2)/4 + (125*x^3)/12 - (1331*(17 - 45*x))/(736*(3 - x + 2*x^2)) + (223971*ArcTan[(1 - 4*x)/Sqrt[23]])/(368*Sqrt[23]) - (2057*Log[3 - x + 2*x^2])/32","A",7,6,25,0.2400,1,"{1660, 1657, 634, 618, 204, 628}"
46,1,63,0,0.0629492,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\left(3-x+2 x^2\right)^2} \, dx","Int[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2)^2,x]","\frac{121 (19-7 x)}{184 \left(2 x^2-x+3\right)}+\frac{55}{8} \log \left(2 x^2-x+3\right)+\frac{25 x}{4}+\frac{1859 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{92 \sqrt{23}}","\frac{121 (19-7 x)}{184 \left(2 x^2-x+3\right)}+\frac{55}{8} \log \left(2 x^2-x+3\right)+\frac{25 x}{4}+\frac{1859 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{92 \sqrt{23}}",1,"(25*x)/4 + (121*(19 - 7*x))/(184*(3 - x + 2*x^2)) + (1859*ArcTan[(1 - 4*x)/Sqrt[23]])/(92*Sqrt[23]) + (55*Log[3 - x + 2*x^2])/8","A",7,6,25,0.2400,1,"{1660, 1657, 634, 618, 204, 628}"
47,1,43,0,0.0260438,"\int \frac{2+3 x+5 x^2}{\left(3-x+2 x^2\right)^2} \, dx","Int[(2 + 3*x + 5*x^2)/(3 - x + 2*x^2)^2,x]","-\frac{11 (3 x+5)}{46 \left(2 x^2-x+3\right)}-\frac{82 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{23 \sqrt{23}}","-\frac{11 (3 x+5)}{46 \left(2 x^2-x+3\right)}-\frac{82 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{23 \sqrt{23}}",1,"(-11*(5 + 3*x))/(46*(3 - x + 2*x^2)) - (82*ArcTan[(1 - 4*x)/Sqrt[23]])/(23*Sqrt[23])","A",4,4,23,0.1739,1,"{1660, 12, 618, 204}"
48,1,94,0,0.0884198,"\int \frac{1}{\left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)} \, dx","Int[1/((3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)),x]","\frac{13-6 x}{506 \left(2 x^2-x+3\right)}-\frac{13}{968} \log \left(2 x^2-x+3\right)+\frac{13}{968} \log \left(5 x^2+3 x+2\right)+\frac{241 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{11132 \sqrt{23}}+\frac{69 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{484 \sqrt{31}}","\frac{13-6 x}{506 \left(2 x^2-x+3\right)}-\frac{13}{968} \log \left(2 x^2-x+3\right)+\frac{13}{968} \log \left(5 x^2+3 x+2\right)+\frac{241 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{11132 \sqrt{23}}+\frac{69 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{484 \sqrt{31}}",1,"(13 - 6*x)/(506*(3 - x + 2*x^2)) + (241*ArcTan[(1 - 4*x)/Sqrt[23]])/(11132*Sqrt[23]) + (69*ArcTan[(3 + 10*x)/Sqrt[31]])/(484*Sqrt[31]) - (13*Log[3 - x + 2*x^2])/968 + (13*Log[2 + 3*x + 5*x^2])/968","A",10,6,25,0.2400,1,"{974, 1072, 634, 618, 204, 628}"
49,1,127,0,0.122755,"\int \frac{1}{\left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^2} \, dx","Int[1/((3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^2),x]","-\frac{25 (117-137 x)}{172546 \left(5 x^2+3 x+2\right)}+\frac{13-6 x}{506 \left(2 x^2-x+3\right) \left(5 x^2+3 x+2\right)}+\frac{19 \log \left(2 x^2-x+3\right)}{10648}-\frac{19 \log \left(5 x^2+3 x+2\right)}{10648}+\frac{2769 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{122452 \sqrt{23}}+\frac{12643 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{165044 \sqrt{31}}","-\frac{25 (117-137 x)}{172546 \left(5 x^2+3 x+2\right)}+\frac{13-6 x}{506 \left(2 x^2-x+3\right) \left(5 x^2+3 x+2\right)}+\frac{19 \log \left(2 x^2-x+3\right)}{10648}-\frac{19 \log \left(5 x^2+3 x+2\right)}{10648}+\frac{2769 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{122452 \sqrt{23}}+\frac{12643 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{165044 \sqrt{31}}",1,"(-25*(117 - 137*x))/(172546*(2 + 3*x + 5*x^2)) + (13 - 6*x)/(506*(3 - x + 2*x^2)*(2 + 3*x + 5*x^2)) + (2769*ArcTan[(1 - 4*x)/Sqrt[23]])/(122452*Sqrt[23]) + (12643*ArcTan[(3 + 10*x)/Sqrt[31]])/(165044*Sqrt[31]) + (19*Log[3 - x + 2*x^2])/10648 - (19*Log[2 + 3*x + 5*x^2])/10648","A",11,7,25,0.2800,1,"{974, 1060, 1072, 634, 618, 204, 628}"
50,1,148,0,0.1614577,"\int \frac{1}{\left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/((3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^3),x]","-\frac{9446-5765 x}{690184 \left(5 x^2+3 x+2\right)^2}+\frac{3996965 x+1765599}{235352744 \left(5 x^2+3 x+2\right)}+\frac{13-6 x}{506 \left(2 x^2-x+3\right) \left(5 x^2+3 x+2\right)^2}+\frac{97 \log \left(2 x^2-x+3\right)}{468512}-\frac{97 \log \left(5 x^2+3 x+2\right)}{468512}-\frac{25557 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{5387888 \sqrt{23}}+\frac{4464079 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{225120016 \sqrt{31}}","-\frac{9446-5765 x}{690184 \left(5 x^2+3 x+2\right)^2}+\frac{3996965 x+1765599}{235352744 \left(5 x^2+3 x+2\right)}+\frac{13-6 x}{506 \left(2 x^2-x+3\right) \left(5 x^2+3 x+2\right)^2}+\frac{97 \log \left(2 x^2-x+3\right)}{468512}-\frac{97 \log \left(5 x^2+3 x+2\right)}{468512}-\frac{25557 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{5387888 \sqrt{23}}+\frac{4464079 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{225120016 \sqrt{31}}",1,"-(9446 - 5765*x)/(690184*(2 + 3*x + 5*x^2)^2) + (13 - 6*x)/(506*(3 - x + 2*x^2)*(2 + 3*x + 5*x^2)^2) + (1765599 + 3996965*x)/(235352744*(2 + 3*x + 5*x^2)) - (25557*ArcTan[(1 - 4*x)/Sqrt[23]])/(5387888*Sqrt[23]) + (4464079*ArcTan[(3 + 10*x)/Sqrt[31]])/(225120016*Sqrt[31]) + (97*Log[3 - x + 2*x^2])/468512 - (97*Log[2 + 3*x + 5*x^2])/468512","A",12,7,25,0.2800,1,"{974, 1060, 1072, 634, 618, 204, 628}"
51,1,98,0,0.1125302,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\left(3-x+2 x^2\right)^3} \, dx","Int[(2 + 3*x + 5*x^2)^4/(3 - x + 2*x^2)^3,x]","\frac{625 x^3}{24}+\frac{4875 x^2}{32}+\frac{1331 (76420 x+5229)}{135424 \left(2 x^2-x+3\right)}-\frac{14641 (79 x+101)}{5888 \left(2 x^2-x+3\right)^2}-\frac{13915}{64} \log \left(2 x^2-x+3\right)+\frac{2725 x}{8}+\frac{63799791 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16928 \sqrt{23}}","\frac{625 x^3}{24}+\frac{4875 x^2}{32}+\frac{1331 (76420 x+5229)}{135424 \left(2 x^2-x+3\right)}-\frac{14641 (79 x+101)}{5888 \left(2 x^2-x+3\right)^2}-\frac{13915}{64} \log \left(2 x^2-x+3\right)+\frac{2725 x}{8}+\frac{63799791 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16928 \sqrt{23}}",1,"(2725*x)/8 + (4875*x^2)/32 + (625*x^3)/24 - (14641*(101 + 79*x))/(5888*(3 - x + 2*x^2)^2) + (1331*(5229 + 76420*x))/(135424*(3 - x + 2*x^2)) + (63799791*ArcTan[(1 - 4*x)/Sqrt[23]])/(16928*Sqrt[23]) - (13915*Log[3 - x + 2*x^2])/64","A",8,6,25,0.2400,1,"{1660, 1657, 634, 618, 204, 628}"
52,1,84,0,0.0865576,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\left(3-x+2 x^2\right)^3} \, dx","Int[(2 + 3*x + 5*x^2)^3/(3 - x + 2*x^2)^3,x]","\frac{121 (21193-12828 x)}{33856 \left(2 x^2-x+3\right)}-\frac{1331 (17-45 x)}{1472 \left(2 x^2-x+3\right)^2}+\frac{825}{32} \log \left(2 x^2-x+3\right)+\frac{125 x}{8}+\frac{165099 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8464 \sqrt{23}}","\frac{121 (21193-12828 x)}{33856 \left(2 x^2-x+3\right)}-\frac{1331 (17-45 x)}{1472 \left(2 x^2-x+3\right)^2}+\frac{825}{32} \log \left(2 x^2-x+3\right)+\frac{125 x}{8}+\frac{165099 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8464 \sqrt{23}}",1,"(125*x)/8 - (1331*(17 - 45*x))/(1472*(3 - x + 2*x^2)^2) + (121*(21193 - 12828*x))/(33856*(3 - x + 2*x^2)) + (165099*ArcTan[(1 - 4*x)/Sqrt[23]])/(8464*Sqrt[23]) + (825*Log[3 - x + 2*x^2])/32","A",8,6,25,0.2400,1,"{1660, 1657, 634, 618, 204, 628}"
53,1,64,0,0.0529804,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\left(3-x+2 x^2\right)^3} \, dx","Int[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2)^3,x]","\frac{121 (19-7 x)}{368 \left(2 x^2-x+3\right)^2}-\frac{55 (332 x+975)}{8464 \left(2 x^2-x+3\right)}-\frac{4330 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{529 \sqrt{23}}","\frac{121 (19-7 x)}{368 \left(2 x^2-x+3\right)^2}-\frac{55 (332 x+975)}{8464 \left(2 x^2-x+3\right)}-\frac{4330 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{529 \sqrt{23}}",1,"(121*(19 - 7*x))/(368*(3 - x + 2*x^2)^2) - (55*(975 + 332*x))/(8464*(3 - x + 2*x^2)) - (4330*ArcTan[(1 - 4*x)/Sqrt[23]])/(529*Sqrt[23])","A",5,4,25,0.1600,1,"{1660, 12, 618, 204}"
54,1,64,0,0.0331539,"\int \frac{2+3 x+5 x^2}{\left(3-x+2 x^2\right)^3} \, dx","Int[(2 + 3*x + 5*x^2)/(3 - x + 2*x^2)^3,x]","-\frac{131 (1-4 x)}{2116 \left(2 x^2-x+3\right)}-\frac{11 (3 x+5)}{92 \left(2 x^2-x+3\right)^2}-\frac{262 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{529 \sqrt{23}}","-\frac{131 (1-4 x)}{2116 \left(2 x^2-x+3\right)}-\frac{11 (3 x+5)}{92 \left(2 x^2-x+3\right)^2}-\frac{262 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{529 \sqrt{23}}",1,"(-11*(5 + 3*x))/(92*(3 - x + 2*x^2)^2) - (131*(1 - 4*x))/(2116*(3 - x + 2*x^2)) - (262*ArcTan[(1 - 4*x)/Sqrt[23]])/(529*Sqrt[23])","A",5,5,23,0.2174,1,"{1660, 12, 614, 618, 204}"
55,1,115,0,0.1235001,"\int \frac{1}{\left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)} \, dx","Int[1/((3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)),x]","\frac{3625-746 x}{256036 \left(2 x^2-x+3\right)}+\frac{13-6 x}{1012 \left(2 x^2-x+3\right)^2}-\frac{119 \log \left(2 x^2-x+3\right)}{21296}+\frac{119 \log \left(5 x^2+3 x+2\right)}{21296}-\frac{53403 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{5632792 \sqrt{23}}+\frac{247 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{10648 \sqrt{31}}","\frac{3625-746 x}{256036 \left(2 x^2-x+3\right)}+\frac{13-6 x}{1012 \left(2 x^2-x+3\right)^2}-\frac{119 \log \left(2 x^2-x+3\right)}{21296}+\frac{119 \log \left(5 x^2+3 x+2\right)}{21296}-\frac{53403 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{5632792 \sqrt{23}}+\frac{247 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{10648 \sqrt{31}}",1,"(13 - 6*x)/(1012*(3 - x + 2*x^2)^2) + (3625 - 746*x)/(256036*(3 - x + 2*x^2)) - (53403*ArcTan[(1 - 4*x)/Sqrt[23]])/(5632792*Sqrt[23]) + (247*ArcTan[(3 + 10*x)/Sqrt[31]])/(10648*Sqrt[31]) - (119*Log[3 - x + 2*x^2])/21296 + (119*Log[2 + 3*x + 5*x^2])/21296","A",11,7,25,0.2800,1,"{974, 1060, 1072, 634, 618, 204, 628}"
56,1,160,0,0.1601393,"\int \frac{1}{\left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^2} \, dx","Int[1/((3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)^2),x]","\frac{9665-1446 x}{512072 \left(2 x^2-x+3\right) \left(5 x^2+3 x+2\right)}-\frac{252815 x+2328909}{174616552 \left(5 x^2+3 x+2\right)}+\frac{13-6 x}{1012 \left(2 x^2-x+3\right)^2 \left(5 x^2+3 x+2\right)}+\frac{181 \log \left(2 x^2-x+3\right)}{468512}-\frac{181 \log \left(5 x^2+3 x+2\right)}{468512}+\frac{2038497 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{123921424 \sqrt{23}}+\frac{246757 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{7261936 \sqrt{31}}","\frac{9665-1446 x}{512072 \left(2 x^2-x+3\right) \left(5 x^2+3 x+2\right)}-\frac{252815 x+2328909}{174616552 \left(5 x^2+3 x+2\right)}+\frac{13-6 x}{1012 \left(2 x^2-x+3\right)^2 \left(5 x^2+3 x+2\right)}+\frac{181 \log \left(2 x^2-x+3\right)}{468512}-\frac{181 \log \left(5 x^2+3 x+2\right)}{468512}+\frac{2038497 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{123921424 \sqrt{23}}+\frac{246757 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{7261936 \sqrt{31}}",1,"-(2328909 + 252815*x)/(174616552*(2 + 3*x + 5*x^2)) + (13 - 6*x)/(1012*(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)) + (9665 - 1446*x)/(512072*(3 - x + 2*x^2)*(2 + 3*x + 5*x^2)) + (2038497*ArcTan[(1 - 4*x)/Sqrt[23]])/(123921424*Sqrt[23]) + (246757*ArcTan[(3 + 10*x)/Sqrt[31]])/(7261936*Sqrt[31]) + (181*Log[3 - x + 2*x^2])/468512 - (181*Log[2 + 3*x + 5*x^2])/468512","A",12,7,25,0.2800,1,"{974, 1060, 1072, 634, 618, 204, 628}"
57,1,181,0,0.2041824,"\int \frac{1}{\left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/((3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)^3),x]","\frac{5 (302-35 x)}{64009 \left(2 x^2-x+3\right) \left(5 x^2+3 x+2\right)^2}+\frac{15 (7140435 x+2618306)}{14886061058 \left(5 x^2+3 x+2\right)}-\frac{5 (77020 x+223707)}{87308276 \left(5 x^2+3 x+2\right)^2}+\frac{13-6 x}{1012 \left(2 x^2-x+3\right)^2 \left(5 x^2+3 x+2\right)^2}+\frac{405 \log \left(2 x^2-x+3\right)}{1288408}-\frac{405 \log \left(5 x^2+3 x+2\right)}{1288408}-\frac{880575 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{340783916 \sqrt{23}}+\frac{2768835 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{619080044 \sqrt{31}}","\frac{5 (302-35 x)}{64009 \left(2 x^2-x+3\right) \left(5 x^2+3 x+2\right)^2}+\frac{15 (7140435 x+2618306)}{14886061058 \left(5 x^2+3 x+2\right)}-\frac{5 (77020 x+223707)}{87308276 \left(5 x^2+3 x+2\right)^2}+\frac{13-6 x}{1012 \left(2 x^2-x+3\right)^2 \left(5 x^2+3 x+2\right)^2}+\frac{405 \log \left(2 x^2-x+3\right)}{1288408}-\frac{405 \log \left(5 x^2+3 x+2\right)}{1288408}-\frac{880575 \tan ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{340783916 \sqrt{23}}+\frac{2768835 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{619080044 \sqrt{31}}",1,"(-5*(223707 + 77020*x))/(87308276*(2 + 3*x + 5*x^2)^2) + (13 - 6*x)/(1012*(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^2) + (5*(302 - 35*x))/(64009*(3 - x + 2*x^2)*(2 + 3*x + 5*x^2)^2) + (15*(2618306 + 7140435*x))/(14886061058*(2 + 3*x + 5*x^2)) - (880575*ArcTan[(1 - 4*x)/Sqrt[23]])/(340783916*Sqrt[23]) + (2768835*ArcTan[(3 + 10*x)/Sqrt[31]])/(619080044*Sqrt[31]) + (405*Log[3 - x + 2*x^2])/1288408 - (405*Log[2 + 3*x + 5*x^2])/1288408","A",13,7,25,0.2800,1,"{974, 1060, 1072, 634, 618, 204, 628}"
58,1,208,0,0.3093215,"\int \sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^4 \, dx","Int[Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^4,x]","\frac{125}{4} \left(2 x^2-x+3\right)^{3/2} x^7+\frac{14125}{144} \left(2 x^2-x+3\right)^{3/2} x^6+\frac{233225 \left(2 x^2-x+3\right)^{3/2} x^5}{1536}+\frac{4796405 \left(2 x^2-x+3\right)^{3/2} x^4}{43008}+\frac{8325631 \left(2 x^2-x+3\right)^{3/2} x^3}{1032192}-\frac{83948353 \left(2 x^2-x+3\right)^{3/2} x^2}{2293760}+\frac{804243809 \left(2 x^2-x+3\right)^{3/2} x}{36700160}+\frac{27185733541 \left(2 x^2-x+3\right)^{3/2}}{440401920}-\frac{359471503 (1-4 x) \sqrt{2 x^2-x+3}}{67108864}-\frac{8267844569 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{134217728 \sqrt{2}}","\frac{125}{4} \left(2 x^2-x+3\right)^{3/2} x^7+\frac{14125}{144} \left(2 x^2-x+3\right)^{3/2} x^6+\frac{233225 \left(2 x^2-x+3\right)^{3/2} x^5}{1536}+\frac{4796405 \left(2 x^2-x+3\right)^{3/2} x^4}{43008}+\frac{8325631 \left(2 x^2-x+3\right)^{3/2} x^3}{1032192}-\frac{83948353 \left(2 x^2-x+3\right)^{3/2} x^2}{2293760}+\frac{804243809 \left(2 x^2-x+3\right)^{3/2} x}{36700160}+\frac{27185733541 \left(2 x^2-x+3\right)^{3/2}}{440401920}-\frac{359471503 (1-4 x) \sqrt{2 x^2-x+3}}{67108864}-\frac{8267844569 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{134217728 \sqrt{2}}",1,"(-359471503*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/67108864 + (27185733541*(3 - x + 2*x^2)^(3/2))/440401920 + (804243809*x*(3 - x + 2*x^2)^(3/2))/36700160 - (83948353*x^2*(3 - x + 2*x^2)^(3/2))/2293760 + (8325631*x^3*(3 - x + 2*x^2)^(3/2))/1032192 + (4796405*x^4*(3 - x + 2*x^2)^(3/2))/43008 + (233225*x^5*(3 - x + 2*x^2)^(3/2))/1536 + (14125*x^6*(3 - x + 2*x^2)^(3/2))/144 + (125*x^7*(3 - x + 2*x^2)^(3/2))/4 - (8267844569*ArcSinh[(1 - 4*x)/Sqrt[23]])/(134217728*Sqrt[2])","A",11,5,27,0.1852,1,"{1661, 640, 612, 619, 215}"
59,1,166,0,0.181374,"\int \sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^3 \, dx","Int[Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^3,x]","\frac{125}{16} \left(2 x^2-x+3\right)^{3/2} x^5+\frac{8825}{448} \left(2 x^2-x+3\right)^{3/2} x^4+\frac{247435 \left(2 x^2-x+3\right)^{3/2} x^3}{10752}+\frac{531681 \left(2 x^2-x+3\right)^{3/2} x^2}{71680}-\frac{9627393 \left(2 x^2-x+3\right)^{3/2} x}{1146880}-\frac{22548119 \left(2 x^2-x+3\right)^{3/2}}{4587520}-\frac{6766097 (1-4 x) \sqrt{2 x^2-x+3}}{2097152}-\frac{155620231 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4194304 \sqrt{2}}","\frac{125}{16} \left(2 x^2-x+3\right)^{3/2} x^5+\frac{8825}{448} \left(2 x^2-x+3\right)^{3/2} x^4+\frac{247435 \left(2 x^2-x+3\right)^{3/2} x^3}{10752}+\frac{531681 \left(2 x^2-x+3\right)^{3/2} x^2}{71680}-\frac{9627393 \left(2 x^2-x+3\right)^{3/2} x}{1146880}-\frac{22548119 \left(2 x^2-x+3\right)^{3/2}}{4587520}-\frac{6766097 (1-4 x) \sqrt{2 x^2-x+3}}{2097152}-\frac{155620231 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4194304 \sqrt{2}}",1,"(-6766097*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/2097152 - (22548119*(3 - x + 2*x^2)^(3/2))/4587520 - (9627393*x*(3 - x + 2*x^2)^(3/2))/1146880 + (531681*x^2*(3 - x + 2*x^2)^(3/2))/71680 + (247435*x^3*(3 - x + 2*x^2)^(3/2))/10752 + (8825*x^4*(3 - x + 2*x^2)^(3/2))/448 + (125*x^5*(3 - x + 2*x^2)^(3/2))/16 - (155620231*ArcSinh[(1 - 4*x)/Sqrt[23]])/(4194304*Sqrt[2])","A",9,5,27,0.1852,1,"{1661, 640, 612, 619, 215}"
60,1,124,0,0.0990913,"\int \sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^2 \, dx","Int[Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^2,x]","\frac{25}{12} \left(2 x^2-x+3\right)^{3/2} x^3+\frac{63}{16} \left(2 x^2-x+3\right)^{3/2} x^2+\frac{769}{256} \left(2 x^2-x+3\right)^{3/2} x-\frac{2107 \left(2 x^2-x+3\right)^{3/2}}{3072}+\frac{12371 (1-4 x) \sqrt{2 x^2-x+3}}{16384}+\frac{284533 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32768 \sqrt{2}}","\frac{25}{12} \left(2 x^2-x+3\right)^{3/2} x^3+\frac{63}{16} \left(2 x^2-x+3\right)^{3/2} x^2+\frac{769}{256} \left(2 x^2-x+3\right)^{3/2} x-\frac{2107 \left(2 x^2-x+3\right)^{3/2}}{3072}+\frac{12371 (1-4 x) \sqrt{2 x^2-x+3}}{16384}+\frac{284533 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32768 \sqrt{2}}",1,"(12371*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/16384 - (2107*(3 - x + 2*x^2)^(3/2))/3072 + (769*x*(3 - x + 2*x^2)^(3/2))/256 + (63*x^2*(3 - x + 2*x^2)^(3/2))/16 + (25*x^3*(3 - x + 2*x^2)^(3/2))/12 + (284533*ArcSinh[(1 - 4*x)/Sqrt[23]])/(32768*Sqrt[2])","A",7,5,27,0.1852,1,"{1661, 640, 612, 619, 215}"
61,1,82,0,0.039791,"\int \sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right) \, dx","Int[Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2),x]","\frac{5}{8} x \left(2 x^2-x+3\right)^{3/2}+\frac{73}{96} \left(2 x^2-x+3\right)^{3/2}-\frac{81}{512} (1-4 x) \sqrt{2 x^2-x+3}-\frac{1863 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1024 \sqrt{2}}","\frac{5}{8} x \left(2 x^2-x+3\right)^{3/2}+\frac{73}{96} \left(2 x^2-x+3\right)^{3/2}-\frac{81}{512} (1-4 x) \sqrt{2 x^2-x+3}-\frac{1863 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1024 \sqrt{2}}",1,"(-81*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/512 + (73*(3 - x + 2*x^2)^(3/2))/96 + (5*x*(3 - x + 2*x^2)^(3/2))/8 - (1863*ArcSinh[(1 - 4*x)/Sqrt[23]])/(1024*Sqrt[2])","A",5,5,25,0.2000,1,"{1661, 640, 612, 619, 215}"
62,1,174,0,0.4412959,"\int \frac{\sqrt{3-x+2 x^2}}{2+3 x+5 x^2} \, dx","Int[Sqrt[3 - x + 2*x^2]/(2 + 3*x + 5*x^2),x]","\frac{1}{5} \sqrt{\frac{11}{31} \left(13+10 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(13+10 \sqrt{2}\right)}} \left(\left(20+13 \sqrt{2}\right) x+7 \sqrt{2}+6\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{5} \sqrt{\frac{11}{31} \left(10 \sqrt{2}-13\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(10 \sqrt{2}-13\right)}} \left(\left(20-13 \sqrt{2}\right) x-7 \sqrt{2}+6\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{5} \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)","\frac{1}{5} \sqrt{\frac{11}{31} \left(13+10 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(13+10 \sqrt{2}\right)}} \left(\left(20+13 \sqrt{2}\right) x+7 \sqrt{2}+6\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{5} \sqrt{\frac{11}{31} \left(10 \sqrt{2}-13\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(10 \sqrt{2}-13\right)}} \left(\left(20-13 \sqrt{2}\right) x-7 \sqrt{2}+6\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{5} \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)",1,"-(Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/5 + (Sqrt[(11*(13 + 10*Sqrt[2]))/31]*ArcTan[(Sqrt[11/(62*(13 + 10*Sqrt[2]))]*(6 + 7*Sqrt[2] + (20 + 13*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/5 - (Sqrt[(11*(-13 + 10*Sqrt[2]))/31]*ArcTanh[(Sqrt[11/(62*(-13 + 10*Sqrt[2]))]*(6 - 7*Sqrt[2] + (20 - 13*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/5","A",8,7,27,0.2593,1,"{989, 619, 215, 1035, 1029, 206, 204}"
63,1,188,0,0.3934924,"\int \frac{\sqrt{3-x+2 x^2}}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[Sqrt[3 - x + 2*x^2]/(2 + 3*x + 5*x^2)^2,x]","\frac{\sqrt{2 x^2-x+3} (10 x+3)}{31 \left(5 x^2+3 x+2\right)}+\frac{1}{62} \sqrt{\frac{1}{682} \left(70517+49942 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(70517+49942 \sqrt{2}\right)}} \left(\left(973+696 \sqrt{2}\right) x+277 \sqrt{2}+419\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{62} \sqrt{\frac{1}{682} \left(49942 \sqrt{2}-70517\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(49942 \sqrt{2}-70517\right)}} \left(\left(973-696 \sqrt{2}\right) x-277 \sqrt{2}+419\right)}{\sqrt{2 x^2-x+3}}\right)","\frac{\sqrt{2 x^2-x+3} (10 x+3)}{31 \left(5 x^2+3 x+2\right)}+\frac{1}{62} \sqrt{\frac{1}{682} \left(70517+49942 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(70517+49942 \sqrt{2}\right)}} \left(\left(973+696 \sqrt{2}\right) x+277 \sqrt{2}+419\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{62} \sqrt{\frac{1}{682} \left(49942 \sqrt{2}-70517\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(49942 \sqrt{2}-70517\right)}} \left(\left(973-696 \sqrt{2}\right) x-277 \sqrt{2}+419\right)}{\sqrt{2 x^2-x+3}}\right)",1,"((3 + 10*x)*Sqrt[3 - x + 2*x^2])/(31*(2 + 3*x + 5*x^2)) + (Sqrt[(70517 + 49942*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(70517 + 49942*Sqrt[2]))]*(419 + 277*Sqrt[2] + (973 + 696*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/62 - (Sqrt[(-70517 + 49942*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-70517 + 49942*Sqrt[2]))]*(419 - 277*Sqrt[2] + (973 - 696*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/62","A",6,5,27,0.1852,1,"{971, 1035, 1029, 206, 204}"
64,1,223,0,0.4586401,"\int \frac{\sqrt{3-x+2 x^2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[Sqrt[3 - x + 2*x^2]/(2 + 3*x + 5*x^2)^3,x]","\frac{\sqrt{2 x^2-x+3} (10 x+3)}{62 \left(5 x^2+3 x+2\right)^2}+\frac{(13665 x+3464) \sqrt{2 x^2-x+3}}{84568 \left(5 x^2+3 x+2\right)}+\frac{\sqrt{\frac{1}{682} \left(112285869463+79399380740 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(112285869463+79399380740 \sqrt{2}\right)}} \left(\left(1235163+872375 \sqrt{2}\right) x+362788 \sqrt{2}+509587\right)}{\sqrt{2 x^2-x+3}}\right)}{169136}-\frac{\sqrt{\frac{1}{682} \left(79399380740 \sqrt{2}-112285869463\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(79399380740 \sqrt{2}-112285869463\right)}} \left(\left(1235163-872375 \sqrt{2}\right) x-362788 \sqrt{2}+509587\right)}{\sqrt{2 x^2-x+3}}\right)}{169136}","\frac{\sqrt{2 x^2-x+3} (10 x+3)}{62 \left(5 x^2+3 x+2\right)^2}+\frac{(13665 x+3464) \sqrt{2 x^2-x+3}}{84568 \left(5 x^2+3 x+2\right)}+\frac{\sqrt{\frac{1}{682} \left(112285869463+79399380740 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(112285869463+79399380740 \sqrt{2}\right)}} \left(\left(1235163+872375 \sqrt{2}\right) x+362788 \sqrt{2}+509587\right)}{\sqrt{2 x^2-x+3}}\right)}{169136}-\frac{\sqrt{\frac{1}{682} \left(79399380740 \sqrt{2}-112285869463\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(79399380740 \sqrt{2}-112285869463\right)}} \left(\left(1235163-872375 \sqrt{2}\right) x-362788 \sqrt{2}+509587\right)}{\sqrt{2 x^2-x+3}}\right)}{169136}",1,"((3 + 10*x)*Sqrt[3 - x + 2*x^2])/(62*(2 + 3*x + 5*x^2)^2) + ((3464 + 13665*x)*Sqrt[3 - x + 2*x^2])/(84568*(2 + 3*x + 5*x^2)) + (Sqrt[(112285869463 + 79399380740*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(112285869463 + 79399380740*Sqrt[2]))]*(509587 + 362788*Sqrt[2] + (1235163 + 872375*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/169136 - (Sqrt[(-112285869463 + 79399380740*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-112285869463 + 79399380740*Sqrt[2]))]*(509587 - 362788*Sqrt[2] + (1235163 - 872375*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/169136","A",7,6,27,0.2222,1,"{971, 1060, 1035, 1029, 206, 204}"
65,1,231,0,0.3424482,"\int \left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^4 \, dx","Int[(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^4,x]","\frac{625}{24} \left(2 x^2-x+3\right)^{5/2} x^7+\frac{7625}{96} \left(2 x^2-x+3\right)^{5/2} x^6+\frac{95165}{768} \left(2 x^2-x+3\right)^{5/2} x^5+\frac{941905 \left(2 x^2-x+3\right)^{5/2} x^4}{9216}+\frac{10444117 \left(2 x^2-x+3\right)^{5/2} x^3}{294912}-\frac{56422489 \left(2 x^2-x+3\right)^{5/2} x^2}{8257536}+\frac{48669967 \left(2 x^2-x+3\right)^{5/2} x}{22020096}+\frac{2124689283 \left(2 x^2-x+3\right)^{5/2}}{146800640}-\frac{382121949 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{134217728}-\frac{26366414481 (1-4 x) \sqrt{2 x^2-x+3}}{2147483648}-\frac{606427533063 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4294967296 \sqrt{2}}","\frac{625}{24} \left(2 x^2-x+3\right)^{5/2} x^7+\frac{7625}{96} \left(2 x^2-x+3\right)^{5/2} x^6+\frac{95165}{768} \left(2 x^2-x+3\right)^{5/2} x^5+\frac{941905 \left(2 x^2-x+3\right)^{5/2} x^4}{9216}+\frac{10444117 \left(2 x^2-x+3\right)^{5/2} x^3}{294912}-\frac{56422489 \left(2 x^2-x+3\right)^{5/2} x^2}{8257536}+\frac{48669967 \left(2 x^2-x+3\right)^{5/2} x}{22020096}+\frac{2124689283 \left(2 x^2-x+3\right)^{5/2}}{146800640}-\frac{382121949 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{134217728}-\frac{26366414481 (1-4 x) \sqrt{2 x^2-x+3}}{2147483648}-\frac{606427533063 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4294967296 \sqrt{2}}",1,"(-26366414481*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/2147483648 - (382121949*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/134217728 + (2124689283*(3 - x + 2*x^2)^(5/2))/146800640 + (48669967*x*(3 - x + 2*x^2)^(5/2))/22020096 - (56422489*x^2*(3 - x + 2*x^2)^(5/2))/8257536 + (10444117*x^3*(3 - x + 2*x^2)^(5/2))/294912 + (941905*x^4*(3 - x + 2*x^2)^(5/2))/9216 + (95165*x^5*(3 - x + 2*x^2)^(5/2))/768 + (7625*x^6*(3 - x + 2*x^2)^(5/2))/96 + (625*x^7*(3 - x + 2*x^2)^(5/2))/24 - (606427533063*ArcSinh[(1 - 4*x)/Sqrt[23]])/(4294967296*Sqrt[2])","A",12,5,27,0.1852,1,"{1661, 640, 612, 619, 215}"
66,1,189,0,0.1897095,"\int \left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^3 \, dx","Int[(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^3,x]","\frac{25}{4} \left(2 x^2-x+3\right)^{5/2} x^5+\frac{725}{48} \left(2 x^2-x+3\right)^{5/2} x^4+\frac{27785 \left(2 x^2-x+3\right)^{5/2} x^3}{1536}+\frac{384739 \left(2 x^2-x+3\right)^{5/2} x^2}{43008}-\frac{81685 \left(2 x^2-x+3\right)^{5/2} x}{114688}-\frac{4625907 \left(2 x^2-x+3\right)^{5/2}}{2293760}-\frac{667795 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{2097152}-\frac{46077855 (1-4 x) \sqrt{2 x^2-x+3}}{33554432}-\frac{1059790665 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{67108864 \sqrt{2}}","\frac{25}{4} \left(2 x^2-x+3\right)^{5/2} x^5+\frac{725}{48} \left(2 x^2-x+3\right)^{5/2} x^4+\frac{27785 \left(2 x^2-x+3\right)^{5/2} x^3}{1536}+\frac{384739 \left(2 x^2-x+3\right)^{5/2} x^2}{43008}-\frac{81685 \left(2 x^2-x+3\right)^{5/2} x}{114688}-\frac{4625907 \left(2 x^2-x+3\right)^{5/2}}{2293760}-\frac{667795 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{2097152}-\frac{46077855 (1-4 x) \sqrt{2 x^2-x+3}}{33554432}-\frac{1059790665 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{67108864 \sqrt{2}}",1,"(-46077855*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/33554432 - (667795*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/2097152 - (4625907*(3 - x + 2*x^2)^(5/2))/2293760 - (81685*x*(3 - x + 2*x^2)^(5/2))/114688 + (384739*x^2*(3 - x + 2*x^2)^(5/2))/43008 + (27785*x^3*(3 - x + 2*x^2)^(5/2))/1536 + (725*x^4*(3 - x + 2*x^2)^(5/2))/48 + (25*x^5*(3 - x + 2*x^2)^(5/2))/4 - (1059790665*ArcSinh[(1 - 4*x)/Sqrt[23]])/(67108864*Sqrt[2])","A",10,5,27,0.1852,1,"{1661, 640, 612, 619, 215}"
67,1,147,0,0.1220993,"\int \left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^2 \, dx","Int[(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^2,x]","\frac{25}{16} \left(2 x^2-x+3\right)^{5/2} x^3+\frac{1235}{448} \left(2 x^2-x+3\right)^{5/2} x^2+\frac{24499 \left(2 x^2-x+3\right)^{5/2} x}{10752}+\frac{73861 \left(2 x^2-x+3\right)^{5/2}}{215040}+\frac{24293 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{196608}+\frac{558739 (1-4 x) \sqrt{2 x^2-x+3}}{1048576}+\frac{12850997 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2097152 \sqrt{2}}","\frac{25}{16} \left(2 x^2-x+3\right)^{5/2} x^3+\frac{1235}{448} \left(2 x^2-x+3\right)^{5/2} x^2+\frac{24499 \left(2 x^2-x+3\right)^{5/2} x}{10752}+\frac{73861 \left(2 x^2-x+3\right)^{5/2}}{215040}+\frac{24293 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{196608}+\frac{558739 (1-4 x) \sqrt{2 x^2-x+3}}{1048576}+\frac{12850997 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2097152 \sqrt{2}}",1,"(558739*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/1048576 + (24293*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/196608 + (73861*(3 - x + 2*x^2)^(5/2))/215040 + (24499*x*(3 - x + 2*x^2)^(5/2))/10752 + (1235*x^2*(3 - x + 2*x^2)^(5/2))/448 + (25*x^3*(3 - x + 2*x^2)^(5/2))/16 + (12850997*ArcSinh[(1 - 4*x)/Sqrt[23]])/(2097152*Sqrt[2])","A",8,5,27,0.1852,1,"{1661, 640, 612, 619, 215}"
68,1,105,0,0.0504904,"\int \left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right) \, dx","Int[(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2),x]","\frac{5}{12} x \left(2 x^2-x+3\right)^{5/2}+\frac{107}{240} \left(2 x^2-x+3\right)^{5/2}-\frac{179 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{1536}-\frac{4117 (1-4 x) \sqrt{2 x^2-x+3}}{8192}-\frac{94691 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16384 \sqrt{2}}","\frac{5}{12} x \left(2 x^2-x+3\right)^{5/2}+\frac{107}{240} \left(2 x^2-x+3\right)^{5/2}-\frac{179 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{1536}-\frac{4117 (1-4 x) \sqrt{2 x^2-x+3}}{8192}-\frac{94691 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{16384 \sqrt{2}}",1,"(-4117*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/8192 - (179*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/1536 + (107*(3 - x + 2*x^2)^(5/2))/240 + (5*x*(3 - x + 2*x^2)^(5/2))/12 - (94691*ArcSinh[(1 - 4*x)/Sqrt[23]])/(16384*Sqrt[2])","A",6,5,25,0.2000,1,"{1661, 640, 612, 619, 215}"
69,1,197,0,0.4879107,"\int \frac{\left(3-x+2 x^2\right)^{3/2}}{2+3 x+5 x^2} \, dx","Int[(3 - x + 2*x^2)^(3/2)/(2 + 3*x + 5*x^2),x]","-\frac{1}{100} \sqrt{2 x^2-x+3} (49-20 x)+\frac{11}{125} \sqrt{\frac{11}{31} \left(247+500 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(247+500 \sqrt{2}\right)}} \left(\left(130+69 \sqrt{2}\right) x+61 \sqrt{2}+8\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{11}{125} \sqrt{\frac{11}{31} \left(500 \sqrt{2}-247\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(500 \sqrt{2}-247\right)}} \left(\left(130-69 \sqrt{2}\right) x-61 \sqrt{2}+8\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{2203 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1000 \sqrt{2}}","-\frac{1}{100} \sqrt{2 x^2-x+3} (49-20 x)+\frac{11}{125} \sqrt{\frac{11}{31} \left(247+500 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(247+500 \sqrt{2}\right)}} \left(\left(130+69 \sqrt{2}\right) x+61 \sqrt{2}+8\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{11}{125} \sqrt{\frac{11}{31} \left(500 \sqrt{2}-247\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(500 \sqrt{2}-247\right)}} \left(\left(130-69 \sqrt{2}\right) x-61 \sqrt{2}+8\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{2203 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1000 \sqrt{2}}",1,"-((49 - 20*x)*Sqrt[3 - x + 2*x^2])/100 - (2203*ArcSinh[(1 - 4*x)/Sqrt[23]])/(1000*Sqrt[2]) + (11*Sqrt[(11*(247 + 500*Sqrt[2]))/31]*ArcTan[(Sqrt[11/(62*(247 + 500*Sqrt[2]))]*(8 + 61*Sqrt[2] + (130 + 69*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/125 - (11*Sqrt[(11*(-247 + 500*Sqrt[2]))/31]*ArcTanh[(Sqrt[11/(62*(-247 + 500*Sqrt[2]))]*(8 - 61*Sqrt[2] + (130 - 69*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/125","A",9,8,27,0.2963,1,"{977, 1076, 619, 215, 1035, 1029, 206, 204}"
70,1,232,0,0.5754546,"\int \frac{\left(3-x+2 x^2\right)^{3/2}}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[(3 - x + 2*x^2)^(3/2)/(2 + 3*x + 5*x^2)^2,x]","\frac{(10 x+3) \left(2 x^2-x+3\right)^{3/2}}{31 \left(5 x^2+3 x+2\right)}+\frac{4}{155} (4-5 x) \sqrt{2 x^2-x+3}+\frac{\sqrt{\frac{11}{31} \left(3169333+2265350 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(3169333+2265350 \sqrt{2}\right)}} \left(\left(9440+6477 \sqrt{2}\right) x+2963 \sqrt{2}+3514\right)}{\sqrt{2 x^2-x+3}}\right)}{1550}-\frac{\sqrt{\frac{11}{31} \left(2265350 \sqrt{2}-3169333\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(2265350 \sqrt{2}-3169333\right)}} \left(\left(9440-6477 \sqrt{2}\right) x-2963 \sqrt{2}+3514\right)}{\sqrt{2 x^2-x+3}}\right)}{1550}-\frac{2}{25} \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)","\frac{(10 x+3) \left(2 x^2-x+3\right)^{3/2}}{31 \left(5 x^2+3 x+2\right)}+\frac{4}{155} (4-5 x) \sqrt{2 x^2-x+3}+\frac{\sqrt{\frac{11}{31} \left(3169333+2265350 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(3169333+2265350 \sqrt{2}\right)}} \left(\left(9440+6477 \sqrt{2}\right) x+2963 \sqrt{2}+3514\right)}{\sqrt{2 x^2-x+3}}\right)}{1550}-\frac{\sqrt{\frac{11}{31} \left(2265350 \sqrt{2}-3169333\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(2265350 \sqrt{2}-3169333\right)}} \left(\left(9440-6477 \sqrt{2}\right) x-2963 \sqrt{2}+3514\right)}{\sqrt{2 x^2-x+3}}\right)}{1550}-\frac{2}{25} \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)",1,"(4*(4 - 5*x)*Sqrt[3 - x + 2*x^2])/155 + ((3 + 10*x)*(3 - x + 2*x^2)^(3/2))/(31*(2 + 3*x + 5*x^2)) - (2*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/25 + (Sqrt[(11*(3169333 + 2265350*Sqrt[2]))/31]*ArcTan[(Sqrt[11/(62*(3169333 + 2265350*Sqrt[2]))]*(3514 + 2963*Sqrt[2] + (9440 + 6477*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1550 - (Sqrt[(11*(-3169333 + 2265350*Sqrt[2]))/31]*ArcTanh[(Sqrt[11/(62*(-3169333 + 2265350*Sqrt[2]))]*(3514 - 2963*Sqrt[2] + (9440 - 6477*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1550","A",10,9,27,0.3333,1,"{971, 1066, 1076, 619, 215, 1035, 1029, 206, 204}"
71,1,223,0,0.4329449,"\int \frac{\left(3-x+2 x^2\right)^{3/2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[(3 - x + 2*x^2)^(3/2)/(2 + 3*x + 5*x^2)^3,x]","\frac{(10 x+3) \left(2 x^2-x+3\right)^{3/2}}{62 \left(5 x^2+3 x+2\right)^2}+\frac{3 (696 x+277) \sqrt{2 x^2-x+3}}{3844 \left(5 x^2+3 x+2\right)}+\frac{3 \sqrt{\frac{1}{682} \left(366990269+259509026 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(366990269+259509026 \sqrt{2}\right)}} \left(\left(70517+49942 \sqrt{2}\right) x+20575 \sqrt{2}+29367\right)}{\sqrt{2 x^2-x+3}}\right)}{7688}-\frac{3 \sqrt{\frac{1}{682} \left(259509026 \sqrt{2}-366990269\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(259509026 \sqrt{2}-366990269\right)}} \left(\left(70517-49942 \sqrt{2}\right) x-20575 \sqrt{2}+29367\right)}{\sqrt{2 x^2-x+3}}\right)}{7688}","\frac{(10 x+3) \left(2 x^2-x+3\right)^{3/2}}{62 \left(5 x^2+3 x+2\right)^2}+\frac{3 (696 x+277) \sqrt{2 x^2-x+3}}{3844 \left(5 x^2+3 x+2\right)}+\frac{3 \sqrt{\frac{1}{682} \left(366990269+259509026 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(366990269+259509026 \sqrt{2}\right)}} \left(\left(70517+49942 \sqrt{2}\right) x+20575 \sqrt{2}+29367\right)}{\sqrt{2 x^2-x+3}}\right)}{7688}-\frac{3 \sqrt{\frac{1}{682} \left(259509026 \sqrt{2}-366990269\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(259509026 \sqrt{2}-366990269\right)}} \left(\left(70517-49942 \sqrt{2}\right) x-20575 \sqrt{2}+29367\right)}{\sqrt{2 x^2-x+3}}\right)}{7688}",1,"((3 + 10*x)*(3 - x + 2*x^2)^(3/2))/(62*(2 + 3*x + 5*x^2)^2) + (3*(277 + 696*x)*Sqrt[3 - x + 2*x^2])/(3844*(2 + 3*x + 5*x^2)) + (3*Sqrt[(366990269 + 259509026*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(366990269 + 259509026*Sqrt[2]))]*(29367 + 20575*Sqrt[2] + (70517 + 49942*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/7688 - (3*Sqrt[(-366990269 + 259509026*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-366990269 + 259509026*Sqrt[2]))]*(29367 - 20575*Sqrt[2] + (70517 - 49942*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/7688","A",7,6,27,0.2222,1,"{971, 1013, 1035, 1029, 206, 204}"
72,1,254,0,0.3725564,"\int \left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^4 \, dx","Int[(3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^4,x]","\frac{625}{28} \left(2 x^2-x+3\right)^{7/2} x^7+\frac{13875}{208} \left(2 x^2-x+3\right)^{7/2} x^6+\frac{1046225 \left(2 x^2-x+3\right)^{7/2} x^5}{9984}+\frac{3684995 \left(2 x^2-x+3\right)^{7/2} x^4}{39936}+\frac{23460839 \left(2 x^2-x+3\right)^{7/2} x^3}{532480}+\frac{122595067 \left(2 x^2-x+3\right)^{7/2} x^2}{19169280}+\frac{112244125 \left(2 x^2-x+3\right)^{7/2} x}{122683392}+\frac{25250178739 \left(2 x^2-x+3\right)^{7/2}}{5725224960}-\frac{401135647 (1-4 x) \left(2 x^2-x+3\right)^{5/2}}{335544320}-\frac{9226119881 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{2147483648}-\frac{636602271789 (1-4 x) \sqrt{2 x^2-x+3}}{34359738368}-\frac{14641852251147 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{68719476736 \sqrt{2}}","\frac{625}{28} \left(2 x^2-x+3\right)^{7/2} x^7+\frac{13875}{208} \left(2 x^2-x+3\right)^{7/2} x^6+\frac{1046225 \left(2 x^2-x+3\right)^{7/2} x^5}{9984}+\frac{3684995 \left(2 x^2-x+3\right)^{7/2} x^4}{39936}+\frac{23460839 \left(2 x^2-x+3\right)^{7/2} x^3}{532480}+\frac{122595067 \left(2 x^2-x+3\right)^{7/2} x^2}{19169280}+\frac{112244125 \left(2 x^2-x+3\right)^{7/2} x}{122683392}+\frac{25250178739 \left(2 x^2-x+3\right)^{7/2}}{5725224960}-\frac{401135647 (1-4 x) \left(2 x^2-x+3\right)^{5/2}}{335544320}-\frac{9226119881 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{2147483648}-\frac{636602271789 (1-4 x) \sqrt{2 x^2-x+3}}{34359738368}-\frac{14641852251147 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{68719476736 \sqrt{2}}",1,"(-636602271789*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/34359738368 - (9226119881*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/2147483648 - (401135647*(1 - 4*x)*(3 - x + 2*x^2)^(5/2))/335544320 + (25250178739*(3 - x + 2*x^2)^(7/2))/5725224960 + (112244125*x*(3 - x + 2*x^2)^(7/2))/122683392 + (122595067*x^2*(3 - x + 2*x^2)^(7/2))/19169280 + (23460839*x^3*(3 - x + 2*x^2)^(7/2))/532480 + (3684995*x^4*(3 - x + 2*x^2)^(7/2))/39936 + (1046225*x^5*(3 - x + 2*x^2)^(7/2))/9984 + (13875*x^6*(3 - x + 2*x^2)^(7/2))/208 + (625*x^7*(3 - x + 2*x^2)^(7/2))/28 - (14641852251147*ArcSinh[(1 - 4*x)/Sqrt[23]])/(68719476736*Sqrt[2])","A",13,5,27,0.1852,1,"{1661, 640, 612, 619, 215}"
73,1,212,0,0.2195273,"\int \left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^3 \, dx","Int[(3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^3,x]","\frac{125}{24} \left(2 x^2-x+3\right)^{7/2} x^5+\frac{1175}{96} \left(2 x^2-x+3\right)^{7/2} x^4+\frac{3823}{256} \left(2 x^2-x+3\right)^{7/2} x^3+\frac{80483 \left(2 x^2-x+3\right)^{7/2} x^2}{9216}+\frac{509257 \left(2 x^2-x+3\right)^{7/2} x}{294912}-\frac{1696165 \left(2 x^2-x+3\right)^{7/2}}{2752512}-\frac{57915 (1-4 x) \left(2 x^2-x+3\right)^{5/2}}{2097152}-\frac{6660225 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{67108864}-\frac{459555525 (1-4 x) \sqrt{2 x^2-x+3}}{1073741824}-\frac{10569777075 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2147483648 \sqrt{2}}","\frac{125}{24} \left(2 x^2-x+3\right)^{7/2} x^5+\frac{1175}{96} \left(2 x^2-x+3\right)^{7/2} x^4+\frac{3823}{256} \left(2 x^2-x+3\right)^{7/2} x^3+\frac{80483 \left(2 x^2-x+3\right)^{7/2} x^2}{9216}+\frac{509257 \left(2 x^2-x+3\right)^{7/2} x}{294912}-\frac{1696165 \left(2 x^2-x+3\right)^{7/2}}{2752512}-\frac{57915 (1-4 x) \left(2 x^2-x+3\right)^{5/2}}{2097152}-\frac{6660225 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{67108864}-\frac{459555525 (1-4 x) \sqrt{2 x^2-x+3}}{1073741824}-\frac{10569777075 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2147483648 \sqrt{2}}",1,"(-459555525*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/1073741824 - (6660225*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/67108864 - (57915*(1 - 4*x)*(3 - x + 2*x^2)^(5/2))/2097152 - (1696165*(3 - x + 2*x^2)^(7/2))/2752512 + (509257*x*(3 - x + 2*x^2)^(7/2))/294912 + (80483*x^2*(3 - x + 2*x^2)^(7/2))/9216 + (3823*x^3*(3 - x + 2*x^2)^(7/2))/256 + (1175*x^4*(3 - x + 2*x^2)^(7/2))/96 + (125*x^5*(3 - x + 2*x^2)^(7/2))/24 - (10569777075*ArcSinh[(1 - 4*x)/Sqrt[23]])/(2147483648*Sqrt[2])","A",11,5,27,0.1852,1,"{1661, 640, 612, 619, 215}"
74,1,170,0,0.1303796,"\int \left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^2 \, dx","Int[(3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^2,x]","\frac{5}{4} x^3 \left(2 x^2-x+3\right)^{7/2}+\frac{305}{144} x^2 \left(2 x^2-x+3\right)^{7/2}+\frac{8467 x \left(2 x^2-x+3\right)^{7/2}}{4608}+\frac{23225 \left(2 x^2-x+3\right)^{7/2}}{43008}-\frac{1547 (1-4 x) \left(2 x^2-x+3\right)^{5/2}}{98304}-\frac{177905 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{3145728}-\frac{4091815 (1-4 x) \sqrt{2 x^2-x+3}}{16777216}-\frac{94111745 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{33554432 \sqrt{2}}","\frac{5}{4} x^3 \left(2 x^2-x+3\right)^{7/2}+\frac{305}{144} x^2 \left(2 x^2-x+3\right)^{7/2}+\frac{8467 x \left(2 x^2-x+3\right)^{7/2}}{4608}+\frac{23225 \left(2 x^2-x+3\right)^{7/2}}{43008}-\frac{1547 (1-4 x) \left(2 x^2-x+3\right)^{5/2}}{98304}-\frac{177905 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{3145728}-\frac{4091815 (1-4 x) \sqrt{2 x^2-x+3}}{16777216}-\frac{94111745 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{33554432 \sqrt{2}}",1,"(-4091815*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/16777216 - (177905*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/3145728 - (1547*(1 - 4*x)*(3 - x + 2*x^2)^(5/2))/98304 + (23225*(3 - x + 2*x^2)^(7/2))/43008 + (8467*x*(3 - x + 2*x^2)^(7/2))/4608 + (305*x^2*(3 - x + 2*x^2)^(7/2))/144 + (5*x^3*(3 - x + 2*x^2)^(7/2))/4 - (94111745*ArcSinh[(1 - 4*x)/Sqrt[23]])/(33554432*Sqrt[2])","A",9,5,27,0.1852,1,"{1661, 640, 612, 619, 215}"
75,1,128,0,0.0624409,"\int \left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right) \, dx","Int[(3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2),x]","\frac{5}{16} x \left(2 x^2-x+3\right)^{7/2}+\frac{141}{448} \left(2 x^2-x+3\right)^{7/2}-\frac{277 (1-4 x) \left(2 x^2-x+3\right)^{5/2}}{3072}-\frac{31855 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{98304}-\frac{732665 (1-4 x) \sqrt{2 x^2-x+3}}{524288}-\frac{16851295 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1048576 \sqrt{2}}","\frac{5}{16} x \left(2 x^2-x+3\right)^{7/2}+\frac{141}{448} \left(2 x^2-x+3\right)^{7/2}-\frac{277 (1-4 x) \left(2 x^2-x+3\right)^{5/2}}{3072}-\frac{31855 (1-4 x) \left(2 x^2-x+3\right)^{3/2}}{98304}-\frac{732665 (1-4 x) \sqrt{2 x^2-x+3}}{524288}-\frac{16851295 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{1048576 \sqrt{2}}",1,"(-732665*(1 - 4*x)*Sqrt[3 - x + 2*x^2])/524288 - (31855*(1 - 4*x)*(3 - x + 2*x^2)^(3/2))/98304 - (277*(1 - 4*x)*(3 - x + 2*x^2)^(5/2))/3072 + (141*(3 - x + 2*x^2)^(7/2))/448 + (5*x*(3 - x + 2*x^2)^(7/2))/16 - (16851295*ArcSinh[(1 - 4*x)/Sqrt[23]])/(1048576*Sqrt[2])","A",7,5,25,0.2000,1,"{1661, 640, 612, 619, 215}"
76,1,222,0,0.538982,"\int \frac{\left(3-x+2 x^2\right)^{5/2}}{2+3 x+5 x^2} \, dx","Int[(3 - x + 2*x^2)^(5/2)/(2 + 3*x + 5*x^2),x]","-\frac{1}{600} (103-60 x) \left(2 x^2-x+3\right)^{3/2}-\frac{(226249-99620 x) \sqrt{2 x^2-x+3}}{80000}-\frac{121 \sqrt{\frac{11}{31} \left(25000 \sqrt{2}-15457\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(25000 \sqrt{2}-15457\right)}} \left(-\left(690+247 \sqrt{2}\right) x-443 \sqrt{2}+196\right)}{\sqrt{2 x^2-x+3}}\right)}{3125}+\frac{121 \sqrt{\frac{11}{31} \left(15457+25000 \sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(15457+25000 \sqrt{2}\right)}} \left(-\left(690-247 \sqrt{2}\right) x+443 \sqrt{2}+196\right)}{\sqrt{2 x^2-x+3}}\right)}{3125}-\frac{7216203 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{800000 \sqrt{2}}","-\frac{1}{600} (103-60 x) \left(2 x^2-x+3\right)^{3/2}-\frac{(226249-99620 x) \sqrt{2 x^2-x+3}}{80000}-\frac{121 \sqrt{\frac{11}{31} \left(25000 \sqrt{2}-15457\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(25000 \sqrt{2}-15457\right)}} \left(-\left(690+247 \sqrt{2}\right) x-443 \sqrt{2}+196\right)}{\sqrt{2 x^2-x+3}}\right)}{3125}+\frac{121 \sqrt{\frac{11}{31} \left(15457+25000 \sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(15457+25000 \sqrt{2}\right)}} \left(-\left(690-247 \sqrt{2}\right) x+443 \sqrt{2}+196\right)}{\sqrt{2 x^2-x+3}}\right)}{3125}-\frac{7216203 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{800000 \sqrt{2}}",1,"-((226249 - 99620*x)*Sqrt[3 - x + 2*x^2])/80000 - ((103 - 60*x)*(3 - x + 2*x^2)^(3/2))/600 - (7216203*ArcSinh[(1 - 4*x)/Sqrt[23]])/(800000*Sqrt[2]) - (121*Sqrt[(11*(-15457 + 25000*Sqrt[2]))/31]*ArcTan[(Sqrt[11/(62*(-15457 + 25000*Sqrt[2]))]*(196 - 443*Sqrt[2] - (690 + 247*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/3125 + (121*Sqrt[(11*(15457 + 25000*Sqrt[2]))/31]*ArcTanh[(Sqrt[11/(62*(15457 + 25000*Sqrt[2]))]*(196 + 443*Sqrt[2] - (690 - 247*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/3125","A",10,9,27,0.3333,1,"{977, 1066, 1076, 619, 215, 1035, 1029, 206, 204}"
77,1,255,0,0.6598435,"\int \frac{\left(3-x+2 x^2\right)^{5/2}}{\left(2+3 x+5 x^2\right)^2} \, dx","Int[(3 - x + 2*x^2)^(5/2)/(2 + 3*x + 5*x^2)^2,x]","\frac{(10 x+3) \left(2 x^2-x+3\right)^{5/2}}{31 \left(5 x^2+3 x+2\right)}+\frac{4}{155} (4-5 x) \left(2 x^2-x+3\right)^{3/2}-\frac{(2240 x+1277) \sqrt{2 x^2-x+3}}{7750}+\frac{11 \sqrt{\frac{11}{31} \left(224510383+194487500 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(224510383+194487500 \sqrt{2}\right)}} \left(\left(87710+54423 \sqrt{2}\right) x+33287 \sqrt{2}+21136\right)}{\sqrt{2 x^2-x+3}}\right)}{38750}-\frac{11 \sqrt{\frac{11}{31} \left(194487500 \sqrt{2}-224510383\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(194487500 \sqrt{2}-224510383\right)}} \left(\left(87710-54423 \sqrt{2}\right) x-33287 \sqrt{2}+21136\right)}{\sqrt{2 x^2-x+3}}\right)}{38750}-\frac{4799 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2500 \sqrt{2}}","\frac{(10 x+3) \left(2 x^2-x+3\right)^{5/2}}{31 \left(5 x^2+3 x+2\right)}+\frac{4}{155} (4-5 x) \left(2 x^2-x+3\right)^{3/2}-\frac{(2240 x+1277) \sqrt{2 x^2-x+3}}{7750}+\frac{11 \sqrt{\frac{11}{31} \left(224510383+194487500 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(224510383+194487500 \sqrt{2}\right)}} \left(\left(87710+54423 \sqrt{2}\right) x+33287 \sqrt{2}+21136\right)}{\sqrt{2 x^2-x+3}}\right)}{38750}-\frac{11 \sqrt{\frac{11}{31} \left(194487500 \sqrt{2}-224510383\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(194487500 \sqrt{2}-224510383\right)}} \left(\left(87710-54423 \sqrt{2}\right) x-33287 \sqrt{2}+21136\right)}{\sqrt{2 x^2-x+3}}\right)}{38750}-\frac{4799 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2500 \sqrt{2}}",1,"-((1277 + 2240*x)*Sqrt[3 - x + 2*x^2])/7750 + (4*(4 - 5*x)*(3 - x + 2*x^2)^(3/2))/155 + ((3 + 10*x)*(3 - x + 2*x^2)^(5/2))/(31*(2 + 3*x + 5*x^2)) - (4799*ArcSinh[(1 - 4*x)/Sqrt[23]])/(2500*Sqrt[2]) + (11*Sqrt[(11*(224510383 + 194487500*Sqrt[2]))/31]*ArcTan[(Sqrt[11/(62*(224510383 + 194487500*Sqrt[2]))]*(21136 + 33287*Sqrt[2] + (87710 + 54423*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/38750 - (11*Sqrt[(11*(-224510383 + 194487500*Sqrt[2]))/31]*ArcTanh[(Sqrt[11/(62*(-224510383 + 194487500*Sqrt[2]))]*(21136 - 33287*Sqrt[2] + (87710 - 54423*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/38750","A",11,9,27,0.3333,1,"{971, 1066, 1076, 619, 215, 1035, 1029, 206, 204}"
78,1,281,0,0.6545469,"\int \frac{\left(3-x+2 x^2\right)^{5/2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Int[(3 - x + 2*x^2)^(5/2)/(2 + 3*x + 5*x^2)^3,x]","\frac{(10 x+3) \left(2 x^2-x+3\right)^{5/2}}{62 \left(5 x^2+3 x+2\right)^2}+\frac{(2336 x+769) \left(2 x^2-x+3\right)^{3/2}}{3844 \left(5 x^2+3 x+2\right)}+\frac{(11359-12920 x) \sqrt{2 x^2-x+3}}{48050}+\frac{\sqrt{11 \left(1+4 \sqrt{2}\right)} \left(2937349+1978861 \sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(3531015707557+2498852071250 \sqrt{2}\right)}} \left(\left(9832420+6895071 \sqrt{2}\right) x+2937349 \sqrt{2}+3957722\right)}{\sqrt{2 x^2-x+3}}\right)}{29791000}-\frac{\left(2937349-1978861 \sqrt{2}\right) \sqrt{11 \left(4 \sqrt{2}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(2498852071250 \sqrt{2}-3531015707557\right)}} \left(\left(9832420-6895071 \sqrt{2}\right) x-2937349 \sqrt{2}+3957722\right)}{\sqrt{2 x^2-x+3}}\right)}{29791000}-\frac{4}{125} \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)","\frac{(10 x+3) \left(2 x^2-x+3\right)^{5/2}}{62 \left(5 x^2+3 x+2\right)^2}+\frac{(2336 x+769) \left(2 x^2-x+3\right)^{3/2}}{3844 \left(5 x^2+3 x+2\right)}+\frac{(11359-12920 x) \sqrt{2 x^2-x+3}}{48050}+\frac{\sqrt{11 \left(1+4 \sqrt{2}\right)} \left(2937349+1978861 \sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(3531015707557+2498852071250 \sqrt{2}\right)}} \left(\left(9832420+6895071 \sqrt{2}\right) x+2937349 \sqrt{2}+3957722\right)}{\sqrt{2 x^2-x+3}}\right)}{29791000}-\frac{\left(2937349-1978861 \sqrt{2}\right) \sqrt{11 \left(4 \sqrt{2}-1\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{62 \left(2498852071250 \sqrt{2}-3531015707557\right)}} \left(\left(9832420-6895071 \sqrt{2}\right) x-2937349 \sqrt{2}+3957722\right)}{\sqrt{2 x^2-x+3}}\right)}{29791000}-\frac{4}{125} \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)",1,"((11359 - 12920*x)*Sqrt[3 - x + 2*x^2])/48050 + ((3 + 10*x)*(3 - x + 2*x^2)^(5/2))/(62*(2 + 3*x + 5*x^2)^2) + ((769 + 2336*x)*(3 - x + 2*x^2)^(3/2))/(3844*(2 + 3*x + 5*x^2)) - (4*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/125 + (Sqrt[11*(1 + 4*Sqrt[2])]*(2937349 + 1978861*Sqrt[2])*ArcTan[(Sqrt[11/(62*(3531015707557 + 2498852071250*Sqrt[2]))]*(3957722 + 2937349*Sqrt[2] + (9832420 + 6895071*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/29791000 - ((2937349 - 1978861*Sqrt[2])*Sqrt[11*(-1 + 4*Sqrt[2])]*ArcTanh[(Sqrt[11/(62*(-3531015707557 + 2498852071250*Sqrt[2]))]*(3957722 - 2937349*Sqrt[2] + (9832420 - 6895071*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/29791000","A",11,10,27,0.3704,1,"{971, 1054, 1066, 1076, 619, 215, 1035, 1029, 206, 204}"
79,1,185,0,0.3122076,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\sqrt{3-x+2 x^2}} \, dx","Int[(2 + 3*x + 5*x^2)^4/Sqrt[3 - x + 2*x^2],x]","\frac{625}{16} \sqrt{2 x^2-x+3} x^7+\frac{57375}{448} \sqrt{2 x^2-x+3} x^6+\frac{2116475 \sqrt{2 x^2-x+3} x^5}{10752}+\frac{686531 \sqrt{2 x^2-x+3} x^4}{6144}-\frac{19750457 \sqrt{2 x^2-x+3} x^3}{229376}-\frac{15428243 \sqrt{2 x^2-x+3} x^2}{131072}+\frac{1572007407 \sqrt{2 x^2-x+3} x}{7340032}+\frac{16493087661 \sqrt{2 x^2-x+3}}{29360128}+\frac{2899366573 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8388608 \sqrt{2}}","\frac{625}{16} \sqrt{2 x^2-x+3} x^7+\frac{57375}{448} \sqrt{2 x^2-x+3} x^6+\frac{2116475 \sqrt{2 x^2-x+3} x^5}{10752}+\frac{686531 \sqrt{2 x^2-x+3} x^4}{6144}-\frac{19750457 \sqrt{2 x^2-x+3} x^3}{229376}-\frac{15428243 \sqrt{2 x^2-x+3} x^2}{131072}+\frac{1572007407 \sqrt{2 x^2-x+3} x}{7340032}+\frac{16493087661 \sqrt{2 x^2-x+3}}{29360128}+\frac{2899366573 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8388608 \sqrt{2}}",1,"(16493087661*Sqrt[3 - x + 2*x^2])/29360128 + (1572007407*x*Sqrt[3 - x + 2*x^2])/7340032 - (15428243*x^2*Sqrt[3 - x + 2*x^2])/131072 - (19750457*x^3*Sqrt[3 - x + 2*x^2])/229376 + (686531*x^4*Sqrt[3 - x + 2*x^2])/6144 + (2116475*x^5*Sqrt[3 - x + 2*x^2])/10752 + (57375*x^6*Sqrt[3 - x + 2*x^2])/448 + (625*x^7*Sqrt[3 - x + 2*x^2])/16 + (2899366573*ArcSinh[(1 - 4*x)/Sqrt[23]])/(8388608*Sqrt[2])","A",10,4,27,0.1481,1,"{1661, 640, 619, 215}"
80,1,143,0,0.1681617,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\sqrt{3-x+2 x^2}} \, dx","Int[(2 + 3*x + 5*x^2)^3/Sqrt[3 - x + 2*x^2],x]","\frac{125}{12} \sqrt{2 x^2-x+3} x^5+\frac{1355}{48} \sqrt{2 x^2-x+3} x^4+\frac{8185}{256} \sqrt{2 x^2-x+3} x^3-\frac{3387 \sqrt{2 x^2-x+3} x^2}{1024}-\frac{372783 \sqrt{2 x^2-x+3} x}{8192}-\frac{203373 \sqrt{2 x^2-x+3}}{32768}-\frac{9267707 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{65536 \sqrt{2}}","\frac{125}{12} \sqrt{2 x^2-x+3} x^5+\frac{1355}{48} \sqrt{2 x^2-x+3} x^4+\frac{8185}{256} \sqrt{2 x^2-x+3} x^3-\frac{3387 \sqrt{2 x^2-x+3} x^2}{1024}-\frac{372783 \sqrt{2 x^2-x+3} x}{8192}-\frac{203373 \sqrt{2 x^2-x+3}}{32768}-\frac{9267707 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{65536 \sqrt{2}}",1,"(-203373*Sqrt[3 - x + 2*x^2])/32768 - (372783*x*Sqrt[3 - x + 2*x^2])/8192 - (3387*x^2*Sqrt[3 - x + 2*x^2])/1024 + (8185*x^3*Sqrt[3 - x + 2*x^2])/256 + (1355*x^4*Sqrt[3 - x + 2*x^2])/48 + (125*x^5*Sqrt[3 - x + 2*x^2])/12 - (9267707*ArcSinh[(1 - 4*x)/Sqrt[23]])/(65536*Sqrt[2])","A",8,4,27,0.1481,1,"{1661, 640, 619, 215}"
81,1,101,0,0.0883339,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\sqrt{3-x+2 x^2}} \, dx","Int[(2 + 3*x + 5*x^2)^2/Sqrt[3 - x + 2*x^2],x]","\frac{25}{8} \sqrt{2 x^2-x+3} x^3+\frac{655}{96} \sqrt{2 x^2-x+3} x^2+\frac{3443}{768} \sqrt{2 x^2-x+3} x-\frac{11373 \sqrt{2 x^2-x+3}}{1024}+\frac{30725 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2048 \sqrt{2}}","\frac{25}{8} \sqrt{2 x^2-x+3} x^3+\frac{655}{96} \sqrt{2 x^2-x+3} x^2+\frac{3443}{768} \sqrt{2 x^2-x+3} x-\frac{11373 \sqrt{2 x^2-x+3}}{1024}+\frac{30725 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2048 \sqrt{2}}",1,"(-11373*Sqrt[3 - x + 2*x^2])/1024 + (3443*x*Sqrt[3 - x + 2*x^2])/768 + (655*x^2*Sqrt[3 - x + 2*x^2])/96 + (25*x^3*Sqrt[3 - x + 2*x^2])/8 + (30725*ArcSinh[(1 - 4*x)/Sqrt[23]])/(2048*Sqrt[2])","A",6,4,27,0.1481,1,"{1661, 640, 619, 215}"
82,1,59,0,0.032932,"\int \frac{2+3 x+5 x^2}{\sqrt{3-x+2 x^2}} \, dx","Int[(2 + 3*x + 5*x^2)/Sqrt[3 - x + 2*x^2],x]","\frac{5}{4} \sqrt{2 x^2-x+3} x+\frac{39}{16} \sqrt{2 x^2-x+3}+\frac{17 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32 \sqrt{2}}","\frac{5}{4} \sqrt{2 x^2-x+3} x+\frac{39}{16} \sqrt{2 x^2-x+3}+\frac{17 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32 \sqrt{2}}",1,"(39*Sqrt[3 - x + 2*x^2])/16 + (5*x*Sqrt[3 - x + 2*x^2])/4 + (17*ArcSinh[(1 - 4*x)/Sqrt[23]])/(32*Sqrt[2])","A",4,4,25,0.1600,1,"{1661, 640, 619, 215}"
83,1,148,0,0.3143587,"\int \frac{1}{\sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)} \, dx","Int[1/(Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)),x]","\sqrt{\frac{1}{682} \left(13+10 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(13+10 \sqrt{2}\right)}} \left(\left(13+10 \sqrt{2}\right) x+3 \sqrt{2}+7\right)}{\sqrt{2 x^2-x+3}}\right)-\sqrt{\frac{1}{682} \left(10 \sqrt{2}-13\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(10 \sqrt{2}-13\right)}} \left(\left(13-10 \sqrt{2}\right) x-3 \sqrt{2}+7\right)}{\sqrt{2 x^2-x+3}}\right)","\sqrt{\frac{1}{682} \left(13+10 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(13+10 \sqrt{2}\right)}} \left(\left(13+10 \sqrt{2}\right) x+3 \sqrt{2}+7\right)}{\sqrt{2 x^2-x+3}}\right)-\sqrt{\frac{1}{682} \left(10 \sqrt{2}-13\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(10 \sqrt{2}-13\right)}} \left(\left(13-10 \sqrt{2}\right) x-3 \sqrt{2}+7\right)}{\sqrt{2 x^2-x+3}}\right)",1,"Sqrt[(13 + 10*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(13 + 10*Sqrt[2]))]*(7 + 3*Sqrt[2] + (13 + 10*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]] - Sqrt[(-13 + 10*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-13 + 10*Sqrt[2]))]*(7 - 3*Sqrt[2] + (13 - 10*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]]","A",5,4,27,0.1481,1,"{986, 1029, 204, 206}"
84,1,188,0,0.4288406,"\int \frac{1}{\sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^2} \, dx","Int[1/(Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^2),x]","\frac{\sqrt{2 x^2-x+3} (65 x+4)}{682 \left(5 x^2+3 x+2\right)}+\frac{\sqrt{\frac{1}{682} \left(2343727+1678700 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(2343727+1678700 \sqrt{2}\right)}} \left(\left(5751+3935 \sqrt{2}\right) x+1816 \sqrt{2}+2119\right)}{\sqrt{2 x^2-x+3}}\right)}{1364}-\frac{\sqrt{\frac{1}{682} \left(1678700 \sqrt{2}-2343727\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(1678700 \sqrt{2}-2343727\right)}} \left(\left(5751-3935 \sqrt{2}\right) x-1816 \sqrt{2}+2119\right)}{\sqrt{2 x^2-x+3}}\right)}{1364}","\frac{\sqrt{2 x^2-x+3} (65 x+4)}{682 \left(5 x^2+3 x+2\right)}+\frac{\sqrt{\frac{1}{682} \left(2343727+1678700 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(2343727+1678700 \sqrt{2}\right)}} \left(\left(5751+3935 \sqrt{2}\right) x+1816 \sqrt{2}+2119\right)}{\sqrt{2 x^2-x+3}}\right)}{1364}-\frac{\sqrt{\frac{1}{682} \left(1678700 \sqrt{2}-2343727\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(1678700 \sqrt{2}-2343727\right)}} \left(\left(5751-3935 \sqrt{2}\right) x-1816 \sqrt{2}+2119\right)}{\sqrt{2 x^2-x+3}}\right)}{1364}",1,"((4 + 65*x)*Sqrt[3 - x + 2*x^2])/(682*(2 + 3*x + 5*x^2)) + (Sqrt[(2343727 + 1678700*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(2343727 + 1678700*Sqrt[2]))]*(2119 + 1816*Sqrt[2] + (5751 + 3935*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1364 - (Sqrt[(-2343727 + 1678700*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-2343727 + 1678700*Sqrt[2]))]*(2119 - 1816*Sqrt[2] + (5751 - 3935*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1364","A",6,5,27,0.1852,1,"{974, 1035, 1029, 206, 204}"
85,1,223,0,0.4694534,"\int \frac{1}{\sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/(Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^3),x]","\frac{\sqrt{2 x^2-x+3} (65 x+4)}{1364 \left(5 x^2+3 x+2\right)^2}+\frac{(86265 x+26794) \sqrt{2 x^2-x+3}}{1860496 \left(5 x^2+3 x+2\right)}+\frac{25 \sqrt{\frac{1}{682} \left(6414867847+4536374600 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(6414867847+4536374600 \sqrt{2}\right)}} \left(\left(294669+208915 \sqrt{2}\right) x+85754 \sqrt{2}+123161\right)}{\sqrt{2 x^2-x+3}}\right)}{3720992}-\frac{25 \sqrt{\frac{1}{682} \left(4536374600 \sqrt{2}-6414867847\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(4536374600 \sqrt{2}-6414867847\right)}} \left(\left(294669-208915 \sqrt{2}\right) x-85754 \sqrt{2}+123161\right)}{\sqrt{2 x^2-x+3}}\right)}{3720992}","\frac{\sqrt{2 x^2-x+3} (65 x+4)}{1364 \left(5 x^2+3 x+2\right)^2}+\frac{(86265 x+26794) \sqrt{2 x^2-x+3}}{1860496 \left(5 x^2+3 x+2\right)}+\frac{25 \sqrt{\frac{1}{682} \left(6414867847+4536374600 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(6414867847+4536374600 \sqrt{2}\right)}} \left(\left(294669+208915 \sqrt{2}\right) x+85754 \sqrt{2}+123161\right)}{\sqrt{2 x^2-x+3}}\right)}{3720992}-\frac{25 \sqrt{\frac{1}{682} \left(4536374600 \sqrt{2}-6414867847\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(4536374600 \sqrt{2}-6414867847\right)}} \left(\left(294669-208915 \sqrt{2}\right) x-85754 \sqrt{2}+123161\right)}{\sqrt{2 x^2-x+3}}\right)}{3720992}",1,"((4 + 65*x)*Sqrt[3 - x + 2*x^2])/(1364*(2 + 3*x + 5*x^2)^2) + ((26794 + 86265*x)*Sqrt[3 - x + 2*x^2])/(1860496*(2 + 3*x + 5*x^2)) + (25*Sqrt[(6414867847 + 4536374600*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(6414867847 + 4536374600*Sqrt[2]))]*(123161 + 85754*Sqrt[2] + (294669 + 208915*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/3720992 - (25*Sqrt[(-6414867847 + 4536374600*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-6414867847 + 4536374600*Sqrt[2]))]*(123161 - 85754*Sqrt[2] + (294669 - 208915*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/3720992","A",7,6,27,0.2222,1,"{974, 1060, 1035, 1029, 206, 204}"
86,1,166,0,0.2039455,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Int[(2 + 3*x + 5*x^2)^4/(3 - x + 2*x^2)^(3/2),x]","\frac{625}{24} \sqrt{2 x^2-x+3} x^5+\frac{10075}{96} \sqrt{2 x^2-x+3} x^4+\frac{79425}{512} \sqrt{2 x^2-x+3} x^3-\frac{111315 \sqrt{2 x^2-x+3} x^2}{2048}-\frac{8992487 \sqrt{2 x^2-x+3} x}{16384}-\frac{31009685 \sqrt{2 x^2-x+3}}{65536}-\frac{14641 (79 x+101)}{1472 \sqrt{2 x^2-x+3}}-\frac{310445587 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{131072 \sqrt{2}}","\frac{625}{24} \sqrt{2 x^2-x+3} x^5+\frac{10075}{96} \sqrt{2 x^2-x+3} x^4+\frac{79425}{512} \sqrt{2 x^2-x+3} x^3-\frac{111315 \sqrt{2 x^2-x+3} x^2}{2048}-\frac{8992487 \sqrt{2 x^2-x+3} x}{16384}-\frac{31009685 \sqrt{2 x^2-x+3}}{65536}-\frac{14641 (79 x+101)}{1472 \sqrt{2 x^2-x+3}}-\frac{310445587 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{131072 \sqrt{2}}",1,"(-14641*(101 + 79*x))/(1472*Sqrt[3 - x + 2*x^2]) - (31009685*Sqrt[3 - x + 2*x^2])/65536 - (8992487*x*Sqrt[3 - x + 2*x^2])/16384 - (111315*x^2*Sqrt[3 - x + 2*x^2])/2048 + (79425*x^3*Sqrt[3 - x + 2*x^2])/512 + (10075*x^4*Sqrt[3 - x + 2*x^2])/96 + (625*x^5*Sqrt[3 - x + 2*x^2])/24 - (310445587*ArcSinh[(1 - 4*x)/Sqrt[23]])/(131072*Sqrt[2])","A",9,5,27,0.1852,1,"{1660, 1661, 640, 619, 215}"
87,1,124,0,0.1270946,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Int[(2 + 3*x + 5*x^2)^3/(3 - x + 2*x^2)^(3/2),x]","\frac{125}{16} \sqrt{2 x^2-x+3} x^3+\frac{1825}{64} \sqrt{2 x^2-x+3} x^2+\frac{15565}{512} \sqrt{2 x^2-x+3} x-\frac{181561 \sqrt{2 x^2-x+3}}{2048}-\frac{1331 (17-45 x)}{368 \sqrt{2 x^2-x+3}}+\frac{1168881 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4096 \sqrt{2}}","\frac{125}{16} \sqrt{2 x^2-x+3} x^3+\frac{1825}{64} \sqrt{2 x^2-x+3} x^2+\frac{15565}{512} \sqrt{2 x^2-x+3} x-\frac{181561 \sqrt{2 x^2-x+3}}{2048}-\frac{1331 (17-45 x)}{368 \sqrt{2 x^2-x+3}}+\frac{1168881 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4096 \sqrt{2}}",1,"(-1331*(17 - 45*x))/(368*Sqrt[3 - x + 2*x^2]) - (181561*Sqrt[3 - x + 2*x^2])/2048 + (15565*x*Sqrt[3 - x + 2*x^2])/512 + (1825*x^2*Sqrt[3 - x + 2*x^2])/64 + (125*x^3*Sqrt[3 - x + 2*x^2])/16 + (1168881*ArcSinh[(1 - 4*x)/Sqrt[23]])/(4096*Sqrt[2])","A",7,5,27,0.1852,1,"{1660, 1661, 640, 619, 215}"
88,1,82,0,0.0708539,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Int[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2)^(3/2),x]","\frac{121 (19-7 x)}{92 \sqrt{2 x^2-x+3}}+\frac{25}{8} x \sqrt{2 x^2-x+3}+\frac{415}{32} \sqrt{2 x^2-x+3}-\frac{223 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{2}}","\frac{121 (19-7 x)}{92 \sqrt{2 x^2-x+3}}+\frac{25}{8} x \sqrt{2 x^2-x+3}+\frac{415}{32} \sqrt{2 x^2-x+3}-\frac{223 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{64 \sqrt{2}}",1,"(121*(19 - 7*x))/(92*Sqrt[3 - x + 2*x^2]) + (415*Sqrt[3 - x + 2*x^2])/32 + (25*x*Sqrt[3 - x + 2*x^2])/8 - (223*ArcSinh[(1 - 4*x)/Sqrt[23]])/(64*Sqrt[2])","A",5,5,27,0.1852,1,"{1660, 1661, 640, 619, 215}"
89,1,45,0,0.0291616,"\int \frac{2+3 x+5 x^2}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Int[(2 + 3*x + 5*x^2)/(3 - x + 2*x^2)^(3/2),x]","-\frac{11 (3 x+5)}{23 \sqrt{2 x^2-x+3}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2 \sqrt{2}}","-\frac{11 (3 x+5)}{23 \sqrt{2 x^2-x+3}}-\frac{5 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2 \sqrt{2}}",1,"(-11*(5 + 3*x))/(23*Sqrt[3 - x + 2*x^2]) - (5*ArcSinh[(1 - 4*x)/Sqrt[23]])/(2*Sqrt[2])","A",4,4,25,0.1600,1,"{1660, 12, 619, 215}"
90,1,176,0,0.4078758,"\int \frac{1}{\left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)} \, dx","Int[1/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)),x]","\frac{13-6 x}{253 \sqrt{2 x^2-x+3}}+\frac{1}{22} \sqrt{\frac{1}{682} \left(247+500 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(247+500 \sqrt{2}\right)}} \left(\left(69+65 \sqrt{2}\right) x+4 \sqrt{2}+61\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{22} \sqrt{\frac{1}{682} \left(500 \sqrt{2}-247\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(500 \sqrt{2}-247\right)}} \left(\left(69-65 \sqrt{2}\right) x-4 \sqrt{2}+61\right)}{\sqrt{2 x^2-x+3}}\right)","\frac{13-6 x}{253 \sqrt{2 x^2-x+3}}+\frac{1}{22} \sqrt{\frac{1}{682} \left(247+500 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(247+500 \sqrt{2}\right)}} \left(\left(69+65 \sqrt{2}\right) x+4 \sqrt{2}+61\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{22} \sqrt{\frac{1}{682} \left(500 \sqrt{2}-247\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(500 \sqrt{2}-247\right)}} \left(\left(69-65 \sqrt{2}\right) x-4 \sqrt{2}+61\right)}{\sqrt{2 x^2-x+3}}\right)",1,"(13 - 6*x)/(253*Sqrt[3 - x + 2*x^2]) + (Sqrt[(247 + 500*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(247 + 500*Sqrt[2]))]*(61 + 4*Sqrt[2] + (69 + 65*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/22 - (Sqrt[(-247 + 500*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-247 + 500*Sqrt[2]))]*(61 - 4*Sqrt[2] + (69 - 65*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/22","A",6,5,27,0.1852,1,"{974, 1035, 1029, 206, 204}"
91,1,211,0,0.4732255,"\int \frac{1}{\left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^2} \, dx","Int[1/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^2),x]","-\frac{6315-2306 x}{345092 \sqrt{2 x^2-x+3}}+\frac{65 x+4}{682 \sqrt{2 x^2-x+3} \left(5 x^2+3 x+2\right)}+\frac{\sqrt{\frac{1}{682} \left(129694447+103775000 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(129694447+103775000 \sqrt{2}\right)}} \left(\left(45519+29065 \sqrt{2}\right) x+16454 \sqrt{2}+12611\right)}{\sqrt{2 x^2-x+3}}\right)}{30008}-\frac{\sqrt{\frac{1}{682} \left(103775000 \sqrt{2}-129694447\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(103775000 \sqrt{2}-129694447\right)}} \left(\left(45519-29065 \sqrt{2}\right) x-16454 \sqrt{2}+12611\right)}{\sqrt{2 x^2-x+3}}\right)}{30008}","-\frac{6315-2306 x}{345092 \sqrt{2 x^2-x+3}}+\frac{65 x+4}{682 \sqrt{2 x^2-x+3} \left(5 x^2+3 x+2\right)}+\frac{\sqrt{\frac{1}{682} \left(129694447+103775000 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(129694447+103775000 \sqrt{2}\right)}} \left(\left(45519+29065 \sqrt{2}\right) x+16454 \sqrt{2}+12611\right)}{\sqrt{2 x^2-x+3}}\right)}{30008}-\frac{\sqrt{\frac{1}{682} \left(103775000 \sqrt{2}-129694447\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(103775000 \sqrt{2}-129694447\right)}} \left(\left(45519-29065 \sqrt{2}\right) x-16454 \sqrt{2}+12611\right)}{\sqrt{2 x^2-x+3}}\right)}{30008}",1,"-(6315 - 2306*x)/(345092*Sqrt[3 - x + 2*x^2]) + (4 + 65*x)/(682*Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)) + (Sqrt[(129694447 + 103775000*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(129694447 + 103775000*Sqrt[2]))]*(12611 + 16454*Sqrt[2] + (45519 + 29065*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/30008 - (Sqrt[(-129694447 + 103775000*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-129694447 + 103775000*Sqrt[2]))]*(12611 - 16454*Sqrt[2] + (45519 - 29065*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/30008","A",7,6,27,0.2222,1,"{974, 1060, 1035, 1029, 206, 204}"
92,1,246,0,0.5252461,"\int \frac{1}{\left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^3),x]","-\frac{4353943-6508666 x}{941410976 \sqrt{2 x^2-x+3}}+\frac{5 (17315 x+7318)}{1860496 \sqrt{2 x^2-x+3} \left(5 x^2+3 x+2\right)}+\frac{65 x+4}{1364 \sqrt{2 x^2-x+3} \left(5 x^2+3 x+2\right)^2}+\frac{3 \sqrt{\frac{1}{682} \left(13874275807943+9819738650000 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(13874275807943+9819738650000 \sqrt{2}\right)}} \left(\left(13785797+9662095 \sqrt{2}\right) x+4123702 \sqrt{2}+5538393\right)}{\sqrt{2 x^2-x+3}}\right)}{81861824}-\frac{3 \sqrt{\frac{1}{682} \left(9819738650000 \sqrt{2}-13874275807943\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(9819738650000 \sqrt{2}-13874275807943\right)}} \left(\left(13785797-9662095 \sqrt{2}\right) x-4123702 \sqrt{2}+5538393\right)}{\sqrt{2 x^2-x+3}}\right)}{81861824}","-\frac{4353943-6508666 x}{941410976 \sqrt{2 x^2-x+3}}+\frac{5 (17315 x+7318)}{1860496 \sqrt{2 x^2-x+3} \left(5 x^2+3 x+2\right)}+\frac{65 x+4}{1364 \sqrt{2 x^2-x+3} \left(5 x^2+3 x+2\right)^2}+\frac{3 \sqrt{\frac{1}{682} \left(13874275807943+9819738650000 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(13874275807943+9819738650000 \sqrt{2}\right)}} \left(\left(13785797+9662095 \sqrt{2}\right) x+4123702 \sqrt{2}+5538393\right)}{\sqrt{2 x^2-x+3}}\right)}{81861824}-\frac{3 \sqrt{\frac{1}{682} \left(9819738650000 \sqrt{2}-13874275807943\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(9819738650000 \sqrt{2}-13874275807943\right)}} \left(\left(13785797-9662095 \sqrt{2}\right) x-4123702 \sqrt{2}+5538393\right)}{\sqrt{2 x^2-x+3}}\right)}{81861824}",1,"-(4353943 - 6508666*x)/(941410976*Sqrt[3 - x + 2*x^2]) + (4 + 65*x)/(1364*Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^2) + (5*(7318 + 17315*x))/(1860496*Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)) + (3*Sqrt[(13874275807943 + 9819738650000*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(13874275807943 + 9819738650000*Sqrt[2]))]*(5538393 + 4123702*Sqrt[2] + (13785797 + 9662095*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/81861824 - (3*Sqrt[(-13874275807943 + 9819738650000*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-13874275807943 + 9819738650000*Sqrt[2]))]*(5538393 - 4123702*Sqrt[2] + (13785797 - 9662095*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/81861824","A",8,6,27,0.2222,1,"{974, 1060, 1035, 1029, 206, 204}"
93,1,147,0,0.1674032,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Int[(2 + 3*x + 5*x^2)^4/(3 - x + 2*x^2)^(5/2),x]","\frac{625}{32} \sqrt{2 x^2-x+3} x^3+\frac{38375}{384} \sqrt{2 x^2-x+3} x^2+\frac{526075 \sqrt{2 x^2-x+3} x}{3072}-\frac{1308645 \sqrt{2 x^2-x+3}}{4096}+\frac{1331 (116368 x+7409)}{101568 \sqrt{2 x^2-x+3}}-\frac{14641 (79 x+101)}{4416 \left(2 x^2-x+3\right)^{3/2}}+\frac{16955197 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8192 \sqrt{2}}","\frac{625}{32} \sqrt{2 x^2-x+3} x^3+\frac{38375}{384} \sqrt{2 x^2-x+3} x^2+\frac{526075 \sqrt{2 x^2-x+3} x}{3072}-\frac{1308645 \sqrt{2 x^2-x+3}}{4096}+\frac{1331 (116368 x+7409)}{101568 \sqrt{2 x^2-x+3}}-\frac{14641 (79 x+101)}{4416 \left(2 x^2-x+3\right)^{3/2}}+\frac{16955197 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8192 \sqrt{2}}",1,"(-14641*(101 + 79*x))/(4416*(3 - x + 2*x^2)^(3/2)) + (1331*(7409 + 116368*x))/(101568*Sqrt[3 - x + 2*x^2]) - (1308645*Sqrt[3 - x + 2*x^2])/4096 + (526075*x*Sqrt[3 - x + 2*x^2])/3072 + (38375*x^2*Sqrt[3 - x + 2*x^2])/384 + (625*x^3*Sqrt[3 - x + 2*x^2])/32 + (16955197*ArcSinh[(1 - 4*x)/Sqrt[23]])/(8192*Sqrt[2])","A",8,5,27,0.1852,1,"{1660, 1661, 640, 619, 215}"
94,1,105,0,0.1053663,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Int[(2 + 3*x + 5*x^2)^3/(3 - x + 2*x^2)^(5/2),x]","\frac{121 (10679-6744 x)}{8464 \sqrt{2 x^2-x+3}}+\frac{125}{16} x \sqrt{2 x^2-x+3}+\frac{3175}{64} \sqrt{2 x^2-x+3}-\frac{1331 (17-45 x)}{1104 \left(2 x^2-x+3\right)^{3/2}}-\frac{7495 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{128 \sqrt{2}}","\frac{121 (10679-6744 x)}{8464 \sqrt{2 x^2-x+3}}+\frac{125}{16} x \sqrt{2 x^2-x+3}+\frac{3175}{64} \sqrt{2 x^2-x+3}-\frac{1331 (17-45 x)}{1104 \left(2 x^2-x+3\right)^{3/2}}-\frac{7495 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{128 \sqrt{2}}",1,"(-1331*(17 - 45*x))/(1104*(3 - x + 2*x^2)^(3/2)) + (121*(10679 - 6744*x))/(8464*Sqrt[3 - x + 2*x^2]) + (3175*Sqrt[3 - x + 2*x^2])/64 + (125*x*Sqrt[3 - x + 2*x^2])/16 - (7495*ArcSinh[(1 - 4*x)/Sqrt[23]])/(128*Sqrt[2])","A",6,5,27,0.1852,1,"{1660, 1661, 640, 619, 215}"
95,1,68,0,0.0612398,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Int[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2)^(5/2),x]","\frac{121 (19-7 x)}{276 \left(2 x^2-x+3\right)^{3/2}}-\frac{11 (2336 x+7351)}{6348 \sqrt{2 x^2-x+3}}-\frac{25 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4 \sqrt{2}}","\frac{121 (19-7 x)}{276 \left(2 x^2-x+3\right)^{3/2}}-\frac{11 (2336 x+7351)}{6348 \sqrt{2 x^2-x+3}}-\frac{25 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4 \sqrt{2}}",1,"(121*(19 - 7*x))/(276*(3 - x + 2*x^2)^(3/2)) - (11*(7351 + 2336*x))/(6348*Sqrt[3 - x + 2*x^2]) - (25*ArcSinh[(1 - 4*x)/Sqrt[23]])/(4*Sqrt[2])","A",5,4,27,0.1481,1,"{1660, 12, 619, 215}"
96,1,47,0,0.0223468,"\int \frac{2+3 x+5 x^2}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Int[(2 + 3*x + 5*x^2)/(3 - x + 2*x^2)^(5/2),x]","-\frac{71 (1-4 x)}{529 \sqrt{2 x^2-x+3}}-\frac{11 (3 x+5)}{69 \left(2 x^2-x+3\right)^{3/2}}","-\frac{71 (1-4 x)}{529 \sqrt{2 x^2-x+3}}-\frac{11 (3 x+5)}{69 \left(2 x^2-x+3\right)^{3/2}}",1,"(-11*(5 + 3*x))/(69*(3 - x + 2*x^2)^(3/2)) - (71*(1 - 4*x))/(529*Sqrt[3 - x + 2*x^2])","A",3,3,25,0.1200,1,"{1660, 12, 613}"
97,1,199,0,0.4555977,"\int \frac{1}{\left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)} \, dx","Int[1/((3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)),x]","\frac{3603-658 x}{128018 \sqrt{2 x^2-x+3}}+\frac{13-6 x}{759 \left(2 x^2-x+3\right)^{3/2}}+\frac{1}{484} \sqrt{\frac{1}{682} \left(25000 \sqrt{2}-15457\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(25000 \sqrt{2}-15457\right)}} \left(\left(247+345 \sqrt{2}\right) x-98 \sqrt{2}+443\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{484} \sqrt{\frac{1}{682} \left(15457+25000 \sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(15457+25000 \sqrt{2}\right)}} \left(\left(247-345 \sqrt{2}\right) x+98 \sqrt{2}+443\right)}{\sqrt{2 x^2-x+3}}\right)","\frac{3603-658 x}{128018 \sqrt{2 x^2-x+3}}+\frac{13-6 x}{759 \left(2 x^2-x+3\right)^{3/2}}+\frac{1}{484} \sqrt{\frac{1}{682} \left(25000 \sqrt{2}-15457\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(25000 \sqrt{2}-15457\right)}} \left(\left(247+345 \sqrt{2}\right) x-98 \sqrt{2}+443\right)}{\sqrt{2 x^2-x+3}}\right)-\frac{1}{484} \sqrt{\frac{1}{682} \left(15457+25000 \sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(15457+25000 \sqrt{2}\right)}} \left(\left(247-345 \sqrt{2}\right) x+98 \sqrt{2}+443\right)}{\sqrt{2 x^2-x+3}}\right)",1,"(13 - 6*x)/(759*(3 - x + 2*x^2)^(3/2)) + (3603 - 658*x)/(128018*Sqrt[3 - x + 2*x^2]) + (Sqrt[(-15457 + 25000*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(-15457 + 25000*Sqrt[2]))]*(443 - 98*Sqrt[2] + (247 + 345*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/484 - (Sqrt[(15457 + 25000*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(15457 + 25000*Sqrt[2]))]*(443 + 98*Sqrt[2] + (247 - 345*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/484","A",7,6,27,0.2222,1,"{974, 1060, 1035, 1029, 206, 204}"
98,1,234,0,0.5430072,"\int \frac{1}{\left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^2} \, dx","Int[1/((3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^2),x]","-\frac{15101-8654 x}{1035276 \left(2 x^2-x+3\right)^{3/2}}-\frac{1352542 x+3133427}{523849656 \sqrt{2 x^2-x+3}}+\frac{65 x+4}{682 \left(2 x^2-x+3\right)^{3/2} \left(5 x^2+3 x+2\right)}+\frac{625 \sqrt{\frac{1}{682} \left(30463+23600 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(30463+23600 \sqrt{2}\right)}} \left(\left(687+445 \sqrt{2}\right) x+242 \sqrt{2}+203\right)}{\sqrt{2 x^2-x+3}}\right)}{660176}-\frac{625 \sqrt{\frac{1}{682} \left(23600 \sqrt{2}-30463\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(23600 \sqrt{2}-30463\right)}} \left(\left(687-445 \sqrt{2}\right) x-242 \sqrt{2}+203\right)}{\sqrt{2 x^2-x+3}}\right)}{660176}","-\frac{15101-8654 x}{1035276 \left(2 x^2-x+3\right)^{3/2}}-\frac{1352542 x+3133427}{523849656 \sqrt{2 x^2-x+3}}+\frac{65 x+4}{682 \left(2 x^2-x+3\right)^{3/2} \left(5 x^2+3 x+2\right)}+\frac{625 \sqrt{\frac{1}{682} \left(30463+23600 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(30463+23600 \sqrt{2}\right)}} \left(\left(687+445 \sqrt{2}\right) x+242 \sqrt{2}+203\right)}{\sqrt{2 x^2-x+3}}\right)}{660176}-\frac{625 \sqrt{\frac{1}{682} \left(23600 \sqrt{2}-30463\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(23600 \sqrt{2}-30463\right)}} \left(\left(687-445 \sqrt{2}\right) x-242 \sqrt{2}+203\right)}{\sqrt{2 x^2-x+3}}\right)}{660176}",1,"-(15101 - 8654*x)/(1035276*(3 - x + 2*x^2)^(3/2)) - (3133427 + 1352542*x)/(523849656*Sqrt[3 - x + 2*x^2]) + (4 + 65*x)/(682*(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)) + (625*Sqrt[(30463 + 23600*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(30463 + 23600*Sqrt[2]))]*(203 + 242*Sqrt[2] + (687 + 445*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/660176 - (625*Sqrt[(-30463 + 23600*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-30463 + 23600*Sqrt[2]))]*(203 - 242*Sqrt[2] + (687 - 445*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/660176","A",8,6,27,0.2222,1,"{974, 1060, 1035, 1029, 206, 204}"
99,1,269,0,0.5894352,"\int \frac{1}{\left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^3} \, dx","Int[1/((3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^3),x]","-\frac{1134826571-1504660754 x}{476353953856 \sqrt{2 x^2-x+3}}+\frac{86885 x+46386}{1860496 \left(2 x^2-x+3\right)^{3/2} \left(5 x^2+3 x+2\right)}-\frac{12280939-19536786 x}{2824232928 \left(2 x^2-x+3\right)^{3/2}}+\frac{65 x+4}{1364 \left(2 x^2-x+3\right)^{3/2} \left(5 x^2+3 x+2\right)^2}+\frac{35 \sqrt{\frac{1}{682} \left(2243059557247+2011748500000 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(2243059557247+2011748500000 \sqrt{2}\right)}} \left(\left(6290431+3861685 \sqrt{2}\right) x+2428746 \sqrt{2}+1432939\right)}{\sqrt{2 x^2-x+3}}\right)}{1800960128}-\frac{35 \sqrt{\frac{1}{682} \left(2011748500000 \sqrt{2}-2243059557247\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(2011748500000 \sqrt{2}-2243059557247\right)}} \left(\left(6290431-3861685 \sqrt{2}\right) x-2428746 \sqrt{2}+1432939\right)}{\sqrt{2 x^2-x+3}}\right)}{1800960128}","-\frac{1134826571-1504660754 x}{476353953856 \sqrt{2 x^2-x+3}}+\frac{86885 x+46386}{1860496 \left(2 x^2-x+3\right)^{3/2} \left(5 x^2+3 x+2\right)}-\frac{12280939-19536786 x}{2824232928 \left(2 x^2-x+3\right)^{3/2}}+\frac{65 x+4}{1364 \left(2 x^2-x+3\right)^{3/2} \left(5 x^2+3 x+2\right)^2}+\frac{35 \sqrt{\frac{1}{682} \left(2243059557247+2011748500000 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(2243059557247+2011748500000 \sqrt{2}\right)}} \left(\left(6290431+3861685 \sqrt{2}\right) x+2428746 \sqrt{2}+1432939\right)}{\sqrt{2 x^2-x+3}}\right)}{1800960128}-\frac{35 \sqrt{\frac{1}{682} \left(2011748500000 \sqrt{2}-2243059557247\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{11}{31 \left(2011748500000 \sqrt{2}-2243059557247\right)}} \left(\left(6290431-3861685 \sqrt{2}\right) x-2428746 \sqrt{2}+1432939\right)}{\sqrt{2 x^2-x+3}}\right)}{1800960128}",1,"-(12280939 - 19536786*x)/(2824232928*(3 - x + 2*x^2)^(3/2)) - (1134826571 - 1504660754*x)/(476353953856*Sqrt[3 - x + 2*x^2]) + (4 + 65*x)/(1364*(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^2) + (46386 + 86885*x)/(1860496*(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)) + (35*Sqrt[(2243059557247 + 2011748500000*Sqrt[2])/682]*ArcTan[(Sqrt[11/(31*(2243059557247 + 2011748500000*Sqrt[2]))]*(1432939 + 2428746*Sqrt[2] + (6290431 + 3861685*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1800960128 - (35*Sqrt[(-2243059557247 + 2011748500000*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-2243059557247 + 2011748500000*Sqrt[2]))]*(1432939 - 2428746*Sqrt[2] + (6290431 - 3861685*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/1800960128","A",9,6,27,0.2222,1,"{974, 1060, 1035, 1029, 206, 204}"
100,1,436,0,0.7893734,"\int \sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)^2 \, dx","Int[Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2)^2,x]","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(8 c^2 \left(2 a^2 f^2+12 a b e f+5 b^2 \left(2 d f+e^2\right)\right)-56 b^2 c f (a f+b e)-32 c^3 \left(a \left(2 d f+e^2\right)+4 b d e\right)+21 b^4 f^2+128 c^4 d^2\right)}{512 c^5}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(8 c^2 \left(2 a^2 f^2+12 a b e f+5 b^2 \left(2 d f+e^2\right)\right)-56 b^2 c f (a f+b e)-32 c^3 \left(a \left(2 d f+e^2\right)+4 b d e\right)+21 b^4 f^2+128 c^4 d^2\right)}{1024 c^{11/2}}+\frac{x \left(a+b x+c x^2\right)^{3/2} \left(-4 c f (5 a f+14 b e)+21 b^2 f^2+40 c^2 \left(2 d f+e^2\right)\right)}{160 c^3}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(-8 c^2 \left(32 a e f+25 b \left(2 d f+e^2\right)\right)+28 b c f (7 a f+10 b e)-105 b^3 f^2+640 c^3 d e\right)}{960 c^4}+\frac{f x^2 \left(a+b x+c x^2\right)^{3/2} (8 c e-3 b f)}{20 c^2}+\frac{f^2 x^3 \left(a+b x+c x^2\right)^{3/2}}{6 c}","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(8 c^2 \left(2 a^2 f^2+12 a b e f+5 b^2 \left(2 d f+e^2\right)\right)-56 b^2 c f (a f+b e)-32 c^3 \left(a \left(2 d f+e^2\right)+4 b d e\right)+21 b^4 f^2+128 c^4 d^2\right)}{512 c^5}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(8 c^2 \left(2 a^2 f^2+12 a b e f+5 b^2 \left(2 d f+e^2\right)\right)-56 b^2 c f (a f+b e)-32 c^3 \left(a \left(2 d f+e^2\right)+4 b d e\right)+21 b^4 f^2+128 c^4 d^2\right)}{1024 c^{11/2}}+\frac{x \left(a+b x+c x^2\right)^{3/2} \left(-4 c f (5 a f+14 b e)+21 b^2 f^2+40 c^2 \left(2 d f+e^2\right)\right)}{160 c^3}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(-8 c^2 \left(32 a e f+25 b \left(2 d f+e^2\right)\right)+28 b c f (7 a f+10 b e)-105 b^3 f^2+640 c^3 d e\right)}{960 c^4}+\frac{f x^2 \left(a+b x+c x^2\right)^{3/2} (8 c e-3 b f)}{20 c^2}+\frac{f^2 x^3 \left(a+b x+c x^2\right)^{3/2}}{6 c}",1,"((128*c^4*d^2 + 21*b^4*f^2 - 56*b^2*c*f*(b*e + a*f) - 32*c^3*(4*b*d*e + a*(e^2 + 2*d*f)) + 8*c^2*(12*a*b*e*f + 2*a^2*f^2 + 5*b^2*(e^2 + 2*d*f)))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^5) + ((640*c^3*d*e - 105*b^3*f^2 + 28*b*c*f*(10*b*e + 7*a*f) - 8*c^2*(32*a*e*f + 25*b*(e^2 + 2*d*f)))*(a + b*x + c*x^2)^(3/2))/(960*c^4) + ((21*b^2*f^2 - 4*c*f*(14*b*e + 5*a*f) + 40*c^2*(e^2 + 2*d*f))*x*(a + b*x + c*x^2)^(3/2))/(160*c^3) + (f*(8*c*e - 3*b*f)*x^2*(a + b*x + c*x^2)^(3/2))/(20*c^2) + (f^2*x^3*(a + b*x + c*x^2)^(3/2))/(6*c) - ((b^2 - 4*a*c)*(128*c^4*d^2 + 21*b^4*f^2 - 56*b^2*c*f*(b*e + a*f) - 32*c^3*(4*b*d*e + a*(e^2 + 2*d*f)) + 8*c^2*(12*a*b*e*f + 2*a^2*f^2 + 5*b^2*(e^2 + 2*d*f)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(11/2))","A",7,5,27,0.1852,1,"{1661, 640, 612, 621, 206}"
101,1,175,0,0.1637769,"\int \sqrt{a+b x+c x^2} \left(d+e x+f x^2\right) \, dx","Int[Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2),x]","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c f+5 b^2 f-8 b c e+16 c^2 d\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+2 b e)+5 b^2 f+16 c^2 d\right)}{128 c^{7/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (8 c e-5 b f)}{24 c^2}+\frac{f x \left(a+b x+c x^2\right)^{3/2}}{4 c}","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a c f+5 b^2 f-8 b c e+16 c^2 d\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+2 b e)+5 b^2 f+16 c^2 d\right)}{128 c^{7/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (8 c e-5 b f)}{24 c^2}+\frac{f x \left(a+b x+c x^2\right)^{3/2}}{4 c}",1,"((16*c^2*d - 8*b*c*e + 5*b^2*f - 4*a*c*f)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(64*c^3) + ((8*c*e - 5*b*f)*(a + b*x + c*x^2)^(3/2))/(24*c^2) + (f*x*(a + b*x + c*x^2)^(3/2))/(4*c) - ((b^2 - 4*a*c)*(16*c^2*d + 5*b^2*f - 4*c*(2*b*e + a*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(7/2))","A",5,5,25,0.2000,1,"{1661, 640, 612, 621, 206}"
102,1,431,0,1.0513295,"\int \frac{\sqrt{a+b x+c x^2}}{d+e x+f x^2} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x + f*x^2),x]","-\frac{\sqrt{f \left(2 a f-b \left(e-\sqrt{e^2-4 d f}\right)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)} \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} f \sqrt{e^2-4 d f}}+\frac{\sqrt{f \left(2 a f-b \left(\sqrt{e^2-4 d f}+e\right)\right)+c \left(e \sqrt{e^2-4 d f}-2 d f+e^2\right)} \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} f \sqrt{e^2-4 d f}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{f}","-\frac{\sqrt{f \left(2 a f-b \left(e-\sqrt{e^2-4 d f}\right)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)} \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} f \sqrt{e^2-4 d f}}+\frac{\sqrt{f \left(2 a f-b \left(\sqrt{e^2-4 d f}+e\right)\right)+c \left(e \sqrt{e^2-4 d f}-2 d f+e^2\right)} \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} f \sqrt{e^2-4 d f}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{f}",1,"(Sqrt[c]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/f - (Sqrt[c*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) + f*(2*a*f - b*(e - Sqrt[e^2 - 4*d*f]))]*ArcTanh[(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[2]*f*Sqrt[e^2 - 4*d*f]) + (Sqrt[c*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) + f*(2*a*f - b*(e + Sqrt[e^2 - 4*d*f]))]*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[2]*f*Sqrt[e^2 - 4*d*f])","A",8,5,27,0.1852,1,"{989, 621, 206, 1032, 724}"
103,1,488,0,2.92941,"\int \frac{\sqrt{a+b x+c x^2}}{\left(d+e x+f x^2\right)^2} \, dx","Int[Sqrt[a + b*x + c*x^2]/(d + e*x + f*x^2)^2,x]","-\frac{\left(f (b e-4 a f)-\left(e-\sqrt{e^2-4 d f}\right) (c e-b f)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} \left(e^2-4 d f\right)^{3/2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{\left(f (b e-4 a f)-\left(\sqrt{e^2-4 d f}+e\right) (c e-b f)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} \left(e^2-4 d f\right)^{3/2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}-\frac{(e+2 f x) \sqrt{a+b x+c x^2}}{\left(e^2-4 d f\right) \left(d+e x+f x^2\right)}","-\frac{\left(f (b e-4 a f)-\left(e-\sqrt{e^2-4 d f}\right) (c e-b f)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} \left(e^2-4 d f\right)^{3/2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{\left(f (b e-4 a f)-\left(\sqrt{e^2-4 d f}+e\right) (c e-b f)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} \left(e^2-4 d f\right)^{3/2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}-\frac{(e+2 f x) \sqrt{a+b x+c x^2}}{\left(e^2-4 d f\right) \left(d+e x+f x^2\right)}",1,"-(((e + 2*f*x)*Sqrt[a + b*x + c*x^2])/((e^2 - 4*d*f)*(d + e*x + f*x^2))) - ((f*(b*e - 4*a*f) - (c*e - b*f)*(e - Sqrt[e^2 - 4*d*f]))*ArcTanh[(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[2]*(e^2 - 4*d*f)^(3/2)*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]) + ((f*(b*e - 4*a*f) - (c*e - b*f)*(e + Sqrt[e^2 - 4*d*f]))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[2]*(e^2 - 4*d*f)^(3/2)*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]])","A",6,4,27,0.1481,1,"{971, 1032, 724, 206}"
104,1,564,0,0.9348471,"\int \left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)^2 \, dx","Int[(a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2)^2,x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(16 c^2 \left(3 a^2 f^2+24 a b e f+14 b^2 \left(2 d f+e^2\right)\right)-72 b^2 c f (3 a f+4 b e)-128 c^3 \left(a \left(2 d f+e^2\right)+6 b d e\right)+99 b^4 f^2+768 c^4 d^2\right)}{6144 c^5}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(16 c^2 \left(3 a^2 f^2+24 a b e f+14 b^2 \left(2 d f+e^2\right)\right)-72 b^2 c f (3 a f+4 b e)-128 c^3 \left(a \left(2 d f+e^2\right)+6 b d e\right)+99 b^4 f^2+768 c^4 d^2\right)}{16384 c^6}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(16 c^2 \left(3 a^2 f^2+24 a b e f+14 b^2 \left(2 d f+e^2\right)\right)-72 b^2 c f (3 a f+4 b e)-128 c^3 \left(a \left(2 d f+e^2\right)+6 b d e\right)+99 b^4 f^2+768 c^4 d^2\right)}{32768 c^{13/2}}+\frac{x \left(a+b x+c x^2\right)^{5/2} \left(-12 c f (7 a f+24 b e)+99 b^2 f^2+224 c^2 \left(2 d f+e^2\right)\right)}{1344 c^3}+\frac{\left(a+b x+c x^2\right)^{5/2} \left(-32 c^2 \left(48 a e f+49 b \left(2 d f+e^2\right)\right)+36 b c f (31 a f+56 b e)-693 b^3 f^2+5376 c^3 d e\right)}{13440 c^4}+\frac{f x^2 \left(a+b x+c x^2\right)^{5/2} (32 c e-11 b f)}{112 c^2}+\frac{f^2 x^3 \left(a+b x+c x^2\right)^{5/2}}{8 c}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(16 c^2 \left(3 a^2 f^2+24 a b e f+14 b^2 \left(2 d f+e^2\right)\right)-72 b^2 c f (3 a f+4 b e)-128 c^3 \left(a \left(2 d f+e^2\right)+6 b d e\right)+99 b^4 f^2+768 c^4 d^2\right)}{6144 c^5}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(16 c^2 \left(3 a^2 f^2+24 a b e f+14 b^2 \left(2 d f+e^2\right)\right)-72 b^2 c f (3 a f+4 b e)-128 c^3 \left(a \left(2 d f+e^2\right)+6 b d e\right)+99 b^4 f^2+768 c^4 d^2\right)}{16384 c^6}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(16 c^2 \left(3 a^2 f^2+24 a b e f+14 b^2 \left(2 d f+e^2\right)\right)-72 b^2 c f (3 a f+4 b e)-128 c^3 \left(a \left(2 d f+e^2\right)+6 b d e\right)+99 b^4 f^2+768 c^4 d^2\right)}{32768 c^{13/2}}+\frac{x \left(a+b x+c x^2\right)^{5/2} \left(-12 c f (7 a f+24 b e)+99 b^2 f^2+224 c^2 \left(2 d f+e^2\right)\right)}{1344 c^3}+\frac{\left(a+b x+c x^2\right)^{5/2} \left(-32 c^2 \left(48 a e f+49 b \left(2 d f+e^2\right)\right)+36 b c f (31 a f+56 b e)-693 b^3 f^2+5376 c^3 d e\right)}{13440 c^4}+\frac{f x^2 \left(a+b x+c x^2\right)^{5/2} (32 c e-11 b f)}{112 c^2}+\frac{f^2 x^3 \left(a+b x+c x^2\right)^{5/2}}{8 c}",1,"-((b^2 - 4*a*c)*(768*c^4*d^2 + 99*b^4*f^2 - 72*b^2*c*f*(4*b*e + 3*a*f) - 128*c^3*(6*b*d*e + a*(e^2 + 2*d*f)) + 16*c^2*(24*a*b*e*f + 3*a^2*f^2 + 14*b^2*(e^2 + 2*d*f)))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(16384*c^6) + ((768*c^4*d^2 + 99*b^4*f^2 - 72*b^2*c*f*(4*b*e + 3*a*f) - 128*c^3*(6*b*d*e + a*(e^2 + 2*d*f)) + 16*c^2*(24*a*b*e*f + 3*a^2*f^2 + 14*b^2*(e^2 + 2*d*f)))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(6144*c^5) + ((5376*c^3*d*e - 693*b^3*f^2 + 36*b*c*f*(56*b*e + 31*a*f) - 32*c^2*(48*a*e*f + 49*b*(e^2 + 2*d*f)))*(a + b*x + c*x^2)^(5/2))/(13440*c^4) + ((99*b^2*f^2 - 12*c*f*(24*b*e + 7*a*f) + 224*c^2*(e^2 + 2*d*f))*x*(a + b*x + c*x^2)^(5/2))/(1344*c^3) + (f*(32*c*e - 11*b*f)*x^2*(a + b*x + c*x^2)^(5/2))/(112*c^2) + (f^2*x^3*(a + b*x + c*x^2)^(5/2))/(8*c) + ((b^2 - 4*a*c)^2*(768*c^4*d^2 + 99*b^4*f^2 - 72*b^2*c*f*(4*b*e + 3*a*f) - 128*c^3*(6*b*d*e + a*(e^2 + 2*d*f)) + 16*c^2*(24*a*b*e*f + 3*a^2*f^2 + 14*b^2*(e^2 + 2*d*f)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32768*c^(13/2))","A",8,5,27,0.1852,1,"{1661, 640, 612, 621, 206}"
105,1,236,0,0.230253,"\int \left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Int[(a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a c f+7 b^2 f-12 b c e+24 c^2 d\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c (a f+3 b e)+7 b^2 f+24 c^2 d\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+3 b e)+7 b^2 f+24 c^2 d\right)}{1024 c^{9/2}}+\frac{\left(a+b x+c x^2\right)^{5/2} (12 c e-7 b f)}{60 c^2}+\frac{f x \left(a+b x+c x^2\right)^{5/2}}{6 c}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a c f+7 b^2 f-12 b c e+24 c^2 d\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c (a f+3 b e)+7 b^2 f+24 c^2 d\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+3 b e)+7 b^2 f+24 c^2 d\right)}{1024 c^{9/2}}+\frac{\left(a+b x+c x^2\right)^{5/2} (12 c e-7 b f)}{60 c^2}+\frac{f x \left(a+b x+c x^2\right)^{5/2}}{6 c}",1,"-((b^2 - 4*a*c)*(24*c^2*d + 7*b^2*f - 4*c*(3*b*e + a*f))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^4) + ((24*c^2*d - 12*b*c*e + 7*b^2*f - 4*a*c*f)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(192*c^3) + ((12*c*e - 7*b*f)*(a + b*x + c*x^2)^(5/2))/(60*c^2) + (f*x*(a + b*x + c*x^2)^(5/2))/(6*c) + ((b^2 - 4*a*c)^2*(24*c^2*d + 7*b^2*f - 4*c*(3*b*e + a*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(9/2))","A",6,5,25,0.2000,1,"{1661, 640, 612, 621, 206}"
106,1,678,0,11.0326541,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{d+e x+f x^2} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x + f*x^2),x]","\frac{\left(\left(e-\sqrt{e^2-4 d f}\right) (c e-b f) \left(f (b e-2 a f)-c \left(e^2-2 d f\right)\right)-2 f \left(-f^2 \left(b^2 d-a^2 f\right)+2 c d f (b e-a f)+c^2 (-d) \left(e^2-d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} f^3 \sqrt{e^2-4 d f} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{\left(-2 f^3 \left(b^2 d-a^2 f\right)-\left(\sqrt{e^2-4 d f}+e\right) (c e-b f) \left(f (b e-2 a f)-c \left(e^2-2 d f\right)\right)+4 c d f^2 (b e-a f)-2 c^2 d f \left(e^2-d f\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} f^3 \sqrt{e^2-4 d f} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-12 c f (b e-a f)+3 b^2 f^2+8 c^2 \left(e^2-d f\right)\right)}{8 \sqrt{c} f^3}-\frac{\sqrt{a+b x+c x^2} (-5 b f+4 c e-2 c f x)}{4 f^2}","\frac{\left(\left(e-\sqrt{e^2-4 d f}\right) (c e-b f) \left(f (b e-2 a f)-c \left(e^2-2 d f\right)\right)-2 f \left(-f^2 \left(b^2 d-a^2 f\right)+2 c d f (b e-a f)+c^2 (-d) \left(e^2-d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} f^3 \sqrt{e^2-4 d f} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}-\frac{\left(\left(\sqrt{e^2-4 d f}+e\right) (c e-b f) \left(f (b e-2 a f)-c \left(e^2-2 d f\right)\right)-2 f \left(-f^2 \left(b^2 d-a^2 f\right)+2 c d f (b e-a f)+c^2 (-d) \left(e^2-d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} f^3 \sqrt{e^2-4 d f} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-12 c f (b e-a f)+3 b^2 f^2+8 c^2 \left(e^2-d f\right)\right)}{8 \sqrt{c} f^3}-\frac{\sqrt{a+b x+c x^2} (-5 b f+4 c e-2 c f x)}{4 f^2}",1,"-((4*c*e - 5*b*f - 2*c*f*x)*Sqrt[a + b*x + c*x^2])/(4*f^2) + ((3*b^2*f^2 - 12*c*f*(b*e - a*f) + 8*c^2*(e^2 - d*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[c]*f^3) + (((c*e - b*f)*(e - Sqrt[e^2 - 4*d*f])*(f*(b*e - 2*a*f) - c*(e^2 - 2*d*f)) - 2*f*(2*c*d*f*(b*e - a*f) - f^2*(b^2*d - a^2*f) - c^2*d*(e^2 - d*f)))*ArcTanh[(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[2]*f^3*Sqrt[e^2 - 4*d*f]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]) + ((4*c*d*f^2*(b*e - a*f) - 2*f^3*(b^2*d - a^2*f) - 2*c^2*d*f*(e^2 - d*f) - (c*e - b*f)*(e + Sqrt[e^2 - 4*d*f])*(f*(b*e - 2*a*f) - c*(e^2 - 2*d*f)))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[2]*f^3*Sqrt[e^2 - 4*d*f]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]])","A",9,6,27,0.2222,1,"{977, 1076, 621, 206, 1032, 724}"
107,1,704,0,11.9496052,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{\left(d+e x+f x^2\right)^2} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x + f*x^2)^2,x]","-\frac{\left(\left(e-\sqrt{e^2-4 d f}\right) (c e-b f) \left(f (b e-2 a f)+2 c \left(e^2-5 d f\right)\right)-2 f \left(f \left(-b e (3 a f+c d)+4 a f (a f+c d)+2 b^2 d f\right)+2 c^2 d \left(e^2-4 d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{2 \sqrt{2} f^2 \left(e^2-4 d f\right)^{3/2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{\left(\left(\sqrt{e^2-4 d f}+e\right) (c e-b f) \left(f (b e-2 a f)+2 c \left(e^2-5 d f\right)\right)-2 f \left(f \left(-b e (3 a f+c d)+4 a f (a f+c d)+2 b^2 d f\right)+2 c^2 d \left(e^2-4 d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{2 \sqrt{2} f^2 \left(e^2-4 d f\right)^{3/2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{f^2}-\frac{\sqrt{a+b x+c x^2} (-2 b f+c e-2 c f x)}{f \left(e^2-4 d f\right)}-\frac{(e+2 f x) \left(a+b x+c x^2\right)^{3/2}}{\left(e^2-4 d f\right) \left(d+e x+f x^2\right)}","-\frac{\left(\left(e-\sqrt{e^2-4 d f}\right) (c e-b f) \left(f (b e-2 a f)+2 c \left(e^2-5 d f\right)\right)-2 f \left(f \left(-b e (3 a f+c d)+4 a f (a f+c d)+2 b^2 d f\right)+2 c^2 d \left(e^2-4 d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{2 \sqrt{2} f^2 \left(e^2-4 d f\right)^{3/2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{\left(\left(\sqrt{e^2-4 d f}+e\right) (c e-b f) \left(f (b e-2 a f)+2 c \left(e^2-5 d f\right)\right)-2 f \left(f \left(-b e (3 a f+c d)+4 a f (a f+c d)+2 b^2 d f\right)+2 c^2 d \left(e^2-4 d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{2 \sqrt{2} f^2 \left(e^2-4 d f\right)^{3/2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{f^2}-\frac{\sqrt{a+b x+c x^2} (-2 b f+c e-2 c f x)}{f \left(e^2-4 d f\right)}-\frac{(e+2 f x) \left(a+b x+c x^2\right)^{3/2}}{\left(e^2-4 d f\right) \left(d+e x+f x^2\right)}",1,"-(((c*e - 2*b*f - 2*c*f*x)*Sqrt[a + b*x + c*x^2])/(f*(e^2 - 4*d*f))) - ((e + 2*f*x)*(a + b*x + c*x^2)^(3/2))/((e^2 - 4*d*f)*(d + e*x + f*x^2)) + (c^(3/2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/f^2 - (((c*e - b*f)*(f*(b*e - 2*a*f) + 2*c*(e^2 - 5*d*f))*(e - Sqrt[e^2 - 4*d*f]) - 2*f*(2*c^2*d*(e^2 - 4*d*f) + f*(2*b^2*d*f + 4*a*f*(c*d + a*f) - b*e*(c*d + 3*a*f))))*ArcTanh[(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[2]*f^2*(e^2 - 4*d*f)^(3/2)*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]) + (((c*e - b*f)*(f*(b*e - 2*a*f) + 2*c*(e^2 - 5*d*f))*(e + Sqrt[e^2 - 4*d*f]) - 2*f*(2*c^2*d*(e^2 - 4*d*f) + f*(2*b^2*d*f + 4*a*f*(c*d + a*f) - b*e*(c*d + 3*a*f))))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[2]*f^2*(e^2 - 4*d*f)^(3/2)*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]])","A",10,7,27,0.2593,1,"{971, 1066, 1076, 621, 206, 1032, 724}"
108,1,669,0,11.5970426,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{\left(d+e x+f x^2\right)^3} \, dx","Int[(a + b*x + c*x^2)^(3/2)/(d + e*x + f*x^2)^3,x]","\frac{3 \left(-2 \left(e-\sqrt{e^2-4 d f}\right) (c e-b f) (2 a f-b e+2 c d)+4 b e f (3 a f+c d)-4 a f \left(4 a f^2+c e^2\right)+b^2 (-f) \left(4 d f+e^2\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{4 \sqrt{2} \left(e^2-4 d f\right)^{5/2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}-\frac{3 \left(-2 \left(\sqrt{e^2-4 d f}+e\right) (c e-b f) (2 a f-b e+2 c d)+4 b e f (3 a f+c d)-4 a f \left(4 a f^2+c e^2\right)+b^2 (-f) \left(4 d f+e^2\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{4 \sqrt{2} \left(e^2-4 d f\right)^{5/2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{3 \sqrt{a+b x+c x^2} \left(2 x \left(4 a f^2-2 b e f+c e^2\right)+4 a e f-b \left(4 d f+e^2\right)+4 c d e\right)}{4 \left(e^2-4 d f\right)^2 \left(d+e x+f x^2\right)}-\frac{(e+2 f x) \left(a+b x+c x^2\right)^{3/2}}{2 \left(e^2-4 d f\right) \left(d+e x+f x^2\right)^2}","-\frac{3 \left(2 \left(e-\sqrt{e^2-4 d f}\right) (c e-b f) (2 a f-b e+2 c d)-f \left(4 b e (3 a f+c d)-4 a \left(4 a f^2+c e^2\right)+b^2 \left(-\left(4 d f+e^2\right)\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{4 \sqrt{2} \left(e^2-4 d f\right)^{5/2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{3 \left(2 \left(\sqrt{e^2-4 d f}+e\right) (c e-b f) (2 a f-b e+2 c d)-f \left(4 b e (3 a f+c d)-4 a \left(4 a f^2+c e^2\right)+b^2 \left(-\left(4 d f+e^2\right)\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{4 \sqrt{2} \left(e^2-4 d f\right)^{5/2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{3 \sqrt{a+b x+c x^2} \left(2 x \left(4 a f^2-2 b e f+c e^2\right)+4 a e f-b \left(4 d f+e^2\right)+4 c d e\right)}{4 \left(e^2-4 d f\right)^2 \left(d+e x+f x^2\right)}-\frac{(e+2 f x) \left(a+b x+c x^2\right)^{3/2}}{2 \left(e^2-4 d f\right) \left(d+e x+f x^2\right)^2}",1,"-((e + 2*f*x)*(a + b*x + c*x^2)^(3/2))/(2*(e^2 - 4*d*f)*(d + e*x + f*x^2)^2) + (3*(4*c*d*e + 4*a*e*f - b*(e^2 + 4*d*f) + 2*(c*e^2 - 2*b*e*f + 4*a*f^2)*x)*Sqrt[a + b*x + c*x^2])/(4*(e^2 - 4*d*f)^2*(d + e*x + f*x^2)) + (3*(4*b*e*f*(c*d + 3*a*f) - b^2*f*(e^2 + 4*d*f) - 4*a*f*(c*e^2 + 4*a*f^2) - 2*(2*c*d - b*e + 2*a*f)*(c*e - b*f)*(e - Sqrt[e^2 - 4*d*f]))*ArcTanh[(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(4*Sqrt[2]*(e^2 - 4*d*f)^(5/2)*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]) - (3*(4*b*e*f*(c*d + 3*a*f) - b^2*f*(e^2 + 4*d*f) - 4*a*f*(c*e^2 + 4*a*f^2) - 2*(2*c*d - b*e + 2*a*f)*(c*e - b*f)*(e + Sqrt[e^2 - 4*d*f]))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(4*Sqrt[2]*(e^2 - 4*d*f)^(5/2)*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]])","A",7,5,27,0.1852,1,"{971, 1013, 1032, 724, 206}"
109,1,717,0,2.7096449,"\int \frac{\left(d+e x+f x^2\right)^3}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2)^3/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(-504 b c^2 f \left(22 a^2 f^2+70 a b e f+25 b^2 \left(d f+e^2\right)\right)+96 c^3 \left(128 a^2 e f^2+275 a b f \left(d f+e^2\right)+50 b^2 \left(6 d e f+e^3\right)\right)+420 b^3 c f^2 (34 a f+27 b e)-640 c^4 \left(8 a e \left(6 d f+e^2\right)+27 b d \left(d f+e^2\right)\right)-3465 b^5 f^3+23040 c^5 d^2 e\right)}{7680 c^6}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(840 b^2 c^2 f \left(2 a^2 f^2+4 a b e f+b^2 \left(d f+e^2\right)\right)-320 c^3 \left(9 a^2 b e f^2+a^3 f^3+9 a b^2 f \left(d f+e^2\right)+b^3 \left(6 d e f+e^3\right)\right)+384 c^4 \left(3 a^2 f \left(d f+e^2\right)+2 a b e \left(6 d f+e^2\right)+3 b^2 d \left(d f+e^2\right)\right)-252 b^4 c f^2 (5 a f+3 b e)-1536 c^5 d \left(a \left(d f+e^2\right)+b d e\right)+231 b^6 f^3+1024 c^6 d^3\right)}{1024 c^{13/2}}+\frac{x \sqrt{a+b x+c x^2} \left(24 c^2 f \left(50 a^2 f^2+322 a b e f+175 b^2 \left(d f+e^2\right)\right)-252 b^2 c f^2 (14 a f+15 b e)-160 c^3 \left(27 a f \left(d f+e^2\right)+10 b \left(6 d e f+e^3\right)\right)+1155 b^4 f^3+5760 c^4 d \left(d f+e^2\right)\right)}{3840 c^5}+\frac{f x^3 \sqrt{a+b x+c x^2} \left(-4 c f (25 a f+81 b e)+99 b^2 f^2+360 c^2 \left(d f+e^2\right)\right)}{480 c^3}-\frac{x^2 \sqrt{a+b x+c x^2} \left(24 c^2 f \left(32 a e f+35 b \left(d f+e^2\right)\right)-36 b c f^2 (13 a f+21 b e)+231 b^3 f^3-320 c^3 \left(6 d e f+e^3\right)\right)}{960 c^4}+\frac{f^2 x^4 \sqrt{a+b x+c x^2} (36 c e-11 b f)}{60 c^2}+\frac{f^3 x^5 \sqrt{a+b x+c x^2}}{6 c}","\frac{\sqrt{a+b x+c x^2} \left(-504 b c^2 f \left(22 a^2 f^2+70 a b e f+25 b^2 \left(d f+e^2\right)\right)+96 c^3 \left(128 a^2 e f^2+275 a b f \left(d f+e^2\right)+50 b^2 \left(6 d e f+e^3\right)\right)+420 b^3 c f^2 (34 a f+27 b e)-640 c^4 \left(8 a e \left(6 d f+e^2\right)+27 b d \left(d f+e^2\right)\right)-3465 b^5 f^3+23040 c^5 d^2 e\right)}{7680 c^6}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(840 b^2 c^2 f \left(2 a^2 f^2+4 a b e f+b^2 \left(d f+e^2\right)\right)-320 c^3 \left(9 a^2 b e f^2+a^3 f^3+9 a b^2 f \left(d f+e^2\right)+b^3 \left(6 d e f+e^3\right)\right)+384 c^4 \left(3 a^2 f \left(d f+e^2\right)+2 a b e \left(6 d f+e^2\right)+3 b^2 d \left(d f+e^2\right)\right)-252 b^4 c f^2 (5 a f+3 b e)-1536 c^5 d \left(a \left(d f+e^2\right)+b d e\right)+231 b^6 f^3+1024 c^6 d^3\right)}{1024 c^{13/2}}+\frac{x \sqrt{a+b x+c x^2} \left(24 c^2 f \left(50 a^2 f^2+322 a b e f+175 b^2 \left(d f+e^2\right)\right)-252 b^2 c f^2 (14 a f+15 b e)-160 c^3 \left(27 a f \left(d f+e^2\right)+10 b \left(6 d e f+e^3\right)\right)+1155 b^4 f^3+5760 c^4 d \left(d f+e^2\right)\right)}{3840 c^5}+\frac{f x^3 \sqrt{a+b x+c x^2} \left(-4 c f (25 a f+81 b e)+99 b^2 f^2+360 c^2 \left(d f+e^2\right)\right)}{480 c^3}-\frac{x^2 \sqrt{a+b x+c x^2} \left(24 c^2 f \left(32 a e f+35 b \left(d f+e^2\right)\right)-36 b c f^2 (13 a f+21 b e)+231 b^3 f^3-320 c^3 \left(6 d e f+e^3\right)\right)}{960 c^4}+\frac{f^2 x^4 \sqrt{a+b x+c x^2} (36 c e-11 b f)}{60 c^2}+\frac{f^3 x^5 \sqrt{a+b x+c x^2}}{6 c}",1,"((23040*c^5*d^2*e - 3465*b^5*f^3 + 420*b^3*c*f^2*(27*b*e + 34*a*f) - 504*b*c^2*f*(70*a*b*e*f + 22*a^2*f^2 + 25*b^2*(e^2 + d*f)) - 640*c^4*(27*b*d*(e^2 + d*f) + 8*a*e*(e^2 + 6*d*f)) + 96*c^3*(128*a^2*e*f^2 + 275*a*b*f*(e^2 + d*f) + 50*b^2*(e^3 + 6*d*e*f)))*Sqrt[a + b*x + c*x^2])/(7680*c^6) + ((1155*b^4*f^3 - 252*b^2*c*f^2*(15*b*e + 14*a*f) + 5760*c^4*d*(e^2 + d*f) + 24*c^2*f*(322*a*b*e*f + 50*a^2*f^2 + 175*b^2*(e^2 + d*f)) - 160*c^3*(27*a*f*(e^2 + d*f) + 10*b*(e^3 + 6*d*e*f)))*x*Sqrt[a + b*x + c*x^2])/(3840*c^5) - ((231*b^3*f^3 - 36*b*c*f^2*(21*b*e + 13*a*f) - 320*c^3*(e^3 + 6*d*e*f) + 24*c^2*f*(32*a*e*f + 35*b*(e^2 + d*f)))*x^2*Sqrt[a + b*x + c*x^2])/(960*c^4) + (f*(99*b^2*f^2 - 4*c*f*(81*b*e + 25*a*f) + 360*c^2*(e^2 + d*f))*x^3*Sqrt[a + b*x + c*x^2])/(480*c^3) + (f^2*(36*c*e - 11*b*f)*x^4*Sqrt[a + b*x + c*x^2])/(60*c^2) + (f^3*x^5*Sqrt[a + b*x + c*x^2])/(6*c) + ((1024*c^6*d^3 + 231*b^6*f^3 - 252*b^4*c*f^2*(3*b*e + 5*a*f) - 1536*c^5*d*(b*d*e + a*(e^2 + d*f)) + 840*b^2*c^2*f*(4*a*b*e*f + 2*a^2*f^2 + b^2*(e^2 + d*f)) + 384*c^4*(3*b^2*d*(e^2 + d*f) + 3*a^2*f*(e^2 + d*f) + 2*a*b*e*(e^2 + 6*d*f)) - 320*c^3*(9*a^2*b*e*f^2 + a^3*f^3 + 9*a*b^2*f*(e^2 + d*f) + b^3*(e^3 + 6*d*e*f)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(13/2))","A",8,4,27,0.1481,1,"{1661, 640, 621, 206}"
110,1,316,0,0.6262103,"\int \frac{\left(d+e x+f x^2\right)^2}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2)^2/Sqrt[a + b*x + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 c^2 \left(a^2 f^2+4 a b e f+b^2 \left(2 d f+e^2\right)\right)-40 b^2 c f (3 a f+2 b e)-64 c^3 \left(a \left(2 d f+e^2\right)+2 b d e\right)+35 b^4 f^2+128 c^4 d^2\right)}{128 c^{9/2}}+\frac{x \sqrt{a+b x+c x^2} \left(-4 c f (9 a f+20 b e)+35 b^2 f^2+48 c^2 \left(2 d f+e^2\right)\right)}{96 c^3}+\frac{\sqrt{a+b x+c x^2} \left(-16 c^2 \left(16 a e f+9 b \left(2 d f+e^2\right)\right)+20 b c f (11 a f+12 b e)-105 b^3 f^2+384 c^3 d e\right)}{192 c^4}+\frac{f x^2 \sqrt{a+b x+c x^2} (16 c e-7 b f)}{24 c^2}+\frac{f^2 x^3 \sqrt{a+b x+c x^2}}{4 c}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(48 c^2 \left(a^2 f^2+4 a b e f+b^2 \left(2 d f+e^2\right)\right)-40 b^2 c f (3 a f+2 b e)-64 c^3 \left(a \left(2 d f+e^2\right)+2 b d e\right)+35 b^4 f^2+128 c^4 d^2\right)}{128 c^{9/2}}+\frac{x \sqrt{a+b x+c x^2} \left(-4 c f (9 a f+20 b e)+35 b^2 f^2+48 c^2 \left(2 d f+e^2\right)\right)}{96 c^3}+\frac{\sqrt{a+b x+c x^2} \left(-16 c^2 \left(16 a e f+9 b \left(2 d f+e^2\right)\right)+20 b c f (11 a f+12 b e)-105 b^3 f^2+384 c^3 d e\right)}{192 c^4}+\frac{f x^2 \sqrt{a+b x+c x^2} (16 c e-7 b f)}{24 c^2}+\frac{f^2 x^3 \sqrt{a+b x+c x^2}}{4 c}",1,"((384*c^3*d*e - 105*b^3*f^2 + 20*b*c*f*(12*b*e + 11*a*f) - 16*c^2*(16*a*e*f + 9*b*(e^2 + 2*d*f)))*Sqrt[a + b*x + c*x^2])/(192*c^4) + ((35*b^2*f^2 - 4*c*f*(20*b*e + 9*a*f) + 48*c^2*(e^2 + 2*d*f))*x*Sqrt[a + b*x + c*x^2])/(96*c^3) + (f*(16*c*e - 7*b*f)*x^2*Sqrt[a + b*x + c*x^2])/(24*c^2) + (f^2*x^3*Sqrt[a + b*x + c*x^2])/(4*c) + ((128*c^4*d^2 + 35*b^4*f^2 - 40*b^2*c*f*(2*b*e + 3*a*f) - 64*c^3*(2*b*d*e + a*(e^2 + 2*d*f)) + 48*c^2*(4*a*b*e*f + a^2*f^2 + b^2*(e^2 + 2*d*f)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(9/2))","A",6,4,27,0.1481,1,"{1661, 640, 621, 206}"
111,1,116,0,0.1107692,"\int \frac{d+e x+f x^2}{\sqrt{a+b x+c x^2}} \, dx","Int[(d + e*x + f*x^2)/Sqrt[a + b*x + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+b e)+3 b^2 f+8 c^2 d\right)}{8 c^{5/2}}+\frac{\sqrt{a+b x+c x^2} (4 c e-3 b f)}{4 c^2}+\frac{f x \sqrt{a+b x+c x^2}}{2 c}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 c (a f+b e)+3 b^2 f+8 c^2 d\right)}{8 c^{5/2}}+\frac{\sqrt{a+b x+c x^2} (4 c e-3 b f)}{4 c^2}+\frac{f x \sqrt{a+b x+c x^2}}{2 c}",1,"((4*c*e - 3*b*f)*Sqrt[a + b*x + c*x^2])/(4*c^2) + (f*x*Sqrt[a + b*x + c*x^2])/(2*c) + ((8*c^2*d + 3*b^2*f - 4*c*(b*e + a*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(5/2))","A",4,4,25,0.1600,1,"{1661, 640, 621, 206}"
112,1,374,0,0.5788299,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)} \, dx","Int[1/(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2)),x]","\frac{\sqrt{2} f \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{e^2-4 d f} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}-\frac{\sqrt{2} f \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{e^2-4 d f} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}","\frac{\sqrt{2} f \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{e^2-4 d f} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}-\frac{\sqrt{2} f \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{e^2-4 d f} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}",1,"-((Sqrt[2]*f*ArcTanh[(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[e^2 - 4*d*f]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]])) + (Sqrt[2]*f*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[e^2 - 4*d*f]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]])","A",5,3,27,0.1111,1,"{983, 724, 206}"
113,1,787,0,8.209727,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)^2} \, dx","Int[1/(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2)^2),x]","\frac{\left(f \left(e-\sqrt{e^2-4 d f}\right) (c e-b f) (2 a f-b e+2 c d)-2 f \left(-4 a^2 f^3+3 a b e f^2-4 a c f \left(e^2-3 d f\right)+b^2 f \left(e^2-6 d f\right)-b c \left(e^3-5 d e f\right)+2 c^2 d \left(e^2-4 d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{2 \sqrt{2} \left(e^2-4 d f\right)^{3/2} \left((c d-a f)^2-(b d-a e) (c e-b f)\right) \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}-\frac{\left(f \left(\sqrt{e^2-4 d f}+e\right) (c e-b f) (2 a f-b e+2 c d)-2 f \left(-4 a^2 f^3+3 a b e f^2-4 a c f \left(e^2-3 d f\right)+b^2 f \left(e^2-6 d f\right)-b c \left(e^3-5 d e f\right)+2 c^2 d \left(e^2-4 d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{2 \sqrt{2} \left(e^2-4 d f\right)^{3/2} \left((c d-a f)^2-(b d-a e) (c e-b f)\right) \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{\sqrt{a+b x+c x^2} \left(f x \left(f (b e-2 a f)-c \left(e^2-2 d f\right)\right)+f \left(-a e f-2 b d f+b e^2\right)-c \left(e^3-3 d e f\right)\right)}{\left(e^2-4 d f\right) \left(d+e x+f x^2\right) \left((c d-a f)^2-(b d-a e) (c e-b f)\right)}","\frac{\left(f \left(e-\sqrt{e^2-4 d f}\right) (c e-b f) (2 a f-b e+2 c d)-2 f \left(f \left(-4 a^2 f^2+3 a b e f+b^2 \left(e^2-6 d f\right)\right)-c \left(4 a f \left(e^2-3 d f\right)+b \left(e^3-5 d e f\right)\right)+2 c^2 d \left(e^2-4 d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{2 \sqrt{2} \left(e^2-4 d f\right)^{3/2} \left((c d-a f)^2-(b d-a e) (c e-b f)\right) \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}-\frac{\left(f \left(\sqrt{e^2-4 d f}+e\right) (c e-b f) (2 a f-b e+2 c d)-2 f \left(f \left(-4 a^2 f^2+3 a b e f+b^2 \left(e^2-6 d f\right)\right)-c \left(4 a f \left(e^2-3 d f\right)+b \left(e^3-5 d e f\right)\right)+2 c^2 d \left(e^2-4 d f\right)\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{2 \sqrt{2} \left(e^2-4 d f\right)^{3/2} \left((c d-a f)^2-(b d-a e) (c e-b f)\right) \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}+\frac{\sqrt{a+b x+c x^2} \left(f x \left(f (b e-2 a f)-c \left(e^2-2 d f\right)\right)+f \left(-a e f-2 b d f+b e^2\right)-c \left(e^3-3 d e f\right)\right)}{\left(e^2-4 d f\right) \left(d+e x+f x^2\right) \left((c d-a f)^2-(b d-a e) (c e-b f)\right)}",1,"((f*(b*e^2 - 2*b*d*f - a*e*f) - c*(e^3 - 3*d*e*f) + f*(f*(b*e - 2*a*f) - c*(e^2 - 2*d*f))*x)*Sqrt[a + b*x + c*x^2])/((e^2 - 4*d*f)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(d + e*x + f*x^2)) + ((f*(2*c*d - b*e + 2*a*f)*(c*e - b*f)*(e - Sqrt[e^2 - 4*d*f]) - 2*f*(3*a*b*e*f^2 - 4*a^2*f^3 + b^2*f*(e^2 - 6*d*f) + 2*c^2*d*(e^2 - 4*d*f) - 4*a*c*f*(e^2 - 3*d*f) - b*c*(e^3 - 5*d*e*f)))*ArcTanh[(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[2]*(e^2 - 4*d*f)^(3/2)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]) - ((f*(2*c*d - b*e + 2*a*f)*(c*e - b*f)*(e + Sqrt[e^2 - 4*d*f]) - 2*f*(3*a*b*e*f^2 - 4*a^2*f^3 + b^2*f*(e^2 - 6*d*f) + 2*c^2*d*(e^2 - 4*d*f) - 4*a*c*f*(e^2 - 3*d*f) - b*c*(e^3 - 5*d*e*f)))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[2]*(e^2 - 4*d*f)^(3/2)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]])","A",6,4,27,0.1481,1,"{974, 1032, 724, 206}"
114,1,649,0,2.1055689,"\int \frac{\left(d+e x+f x^2\right)^3}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)^3/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \left(-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right) \left(a^2 c^2 f^2-4 a b^2 c f^2+7 a b c^2 e f-2 a c^3 d f-3 a c^3 e^2+b^2 c^2 d f+b^2 c^2 e^2-2 b^3 c e f+b^4 f^2-b c^3 d e+c^4 d^2\right)-b c^2 \left(-9 a^2 c f \left(d f+e^2\right)+5 a^3 f^3+3 a c^2 d \left(d f+e^2\right)+c^3 d^3\right)+2 a c^3 e \left(3 a^2 f^2-a c \left(6 d f+e^2\right)+3 c^2 d^2\right)-a b^2 c^2 e \left(12 a f^2-c \left(6 d f+e^2\right)\right)+a b^3 c f \left(5 a f^2-3 c \left(d f+e^2\right)\right)+3 a b^4 c e f^2-a b^5 f^3\right)}{c^5 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(80 c^2 f \left(a^2 f^2+6 a b e f+3 b^2 \left(d f+e^2\right)\right)-280 b^2 c f^2 (a f+b e)-64 c^3 \left(3 a f \left(d f+e^2\right)+b \left(6 d e f+e^3\right)\right)+105 b^4 f^3+128 c^4 d \left(d f+e^2\right)\right)}{128 c^{11/2}}+\frac{f x \sqrt{a+b x+c x^2} \left(-4 c f (7 a f+22 b e)+41 b^2 f^2+48 c^2 \left(d f+e^2\right)\right)}{32 c^4}-\frac{\sqrt{a+b x+c x^2} \left(16 c^2 f \left(20 a e f+21 b \left(d f+e^2\right)\right)-4 b c f^2 (73 a f+114 b e)+187 b^3 f^3-64 c^3 \left(6 d e f+e^3\right)\right)}{64 c^5}+\frac{f^2 x^2 \sqrt{a+b x+c x^2} (8 c e-5 b f)}{8 c^3}+\frac{f^3 x^3 \sqrt{a+b x+c x^2}}{4 c^2}","\frac{2 \left(-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right) \left(a^2 c^2 f^2-4 a b^2 c f^2+7 a b c^2 e f-2 a c^3 d f-3 a c^3 e^2+b^2 c^2 d f+b^2 c^2 e^2-2 b^3 c e f+b^4 f^2-b c^3 d e+c^4 d^2\right)-b c^2 \left(-9 a^2 c f \left(d f+e^2\right)+5 a^3 f^3+3 a c^2 d \left(d f+e^2\right)+c^3 d^3\right)+2 a c^3 e \left(3 a^2 f^2-a c \left(6 d f+e^2\right)+3 c^2 d^2\right)-a b^2 c^2 e \left(12 a f^2-c \left(6 d f+e^2\right)\right)+a b^3 c f \left(5 a f^2-3 c \left(d f+e^2\right)\right)+3 a b^4 c e f^2-a b^5 f^3\right)}{c^5 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(80 c^2 f \left(a^2 f^2+6 a b e f+3 b^2 \left(d f+e^2\right)\right)-280 b^2 c f^2 (a f+b e)-64 c^3 \left(3 a f \left(d f+e^2\right)+b \left(6 d e f+e^3\right)\right)+105 b^4 f^3+128 c^4 d \left(d f+e^2\right)\right)}{128 c^{11/2}}+\frac{f x \sqrt{a+b x+c x^2} \left(-4 c f (7 a f+22 b e)+41 b^2 f^2+48 c^2 \left(d f+e^2\right)\right)}{32 c^4}-\frac{\sqrt{a+b x+c x^2} \left(16 c^2 f \left(20 a e f+21 b \left(d f+e^2\right)\right)-4 b c f^2 (73 a f+114 b e)+187 b^3 f^3-64 c^3 \left(6 d e f+e^3\right)\right)}{64 c^5}+\frac{f^2 x^2 \sqrt{a+b x+c x^2} (8 c e-5 b f)}{8 c^3}+\frac{f^3 x^3 \sqrt{a+b x+c x^2}}{4 c^2}",1,"(2*(3*a*b^4*c*e*f^2 - a*b^5*f^3 + a*b^3*c*f*(5*a*f^2 - 3*c*(e^2 + d*f)) - b*c^2*(c^3*d^3 + 5*a^3*f^3 + 3*a*c^2*d*(e^2 + d*f) - 9*a^2*c*f*(e^2 + d*f)) - a*b^2*c^2*e*(12*a*f^2 - c*(e^2 + 6*d*f)) + 2*a*c^3*e*(3*c^2*d^2 + 3*a^2*f^2 - a*c*(e^2 + 6*d*f)) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*(c^4*d^2 - b*c^3*d*e + b^2*c^2*e^2 - 3*a*c^3*e^2 + b^2*c^2*d*f - 2*a*c^3*d*f - 2*b^3*c*e*f + 7*a*b*c^2*e*f + b^4*f^2 - 4*a*b^2*c*f^2 + a^2*c^2*f^2)*x))/(c^5*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) - ((187*b^3*f^3 - 4*b*c*f^2*(114*b*e + 73*a*f) - 64*c^3*(e^3 + 6*d*e*f) + 16*c^2*f*(20*a*e*f + 21*b*(e^2 + d*f)))*Sqrt[a + b*x + c*x^2])/(64*c^5) + (f*(41*b^2*f^2 - 4*c*f*(22*b*e + 7*a*f) + 48*c^2*(e^2 + d*f))*x*Sqrt[a + b*x + c*x^2])/(32*c^4) + (f^2*(8*c*e - 5*b*f)*x^2*Sqrt[a + b*x + c*x^2])/(8*c^3) + (f^3*x^3*Sqrt[a + b*x + c*x^2])/(4*c^2) + (3*(105*b^4*f^3 - 280*b^2*c*f^2*(b*e + a*f) + 128*c^4*d*(e^2 + d*f) + 80*c^2*f*(6*a*b*e*f + a^2*f^2 + 3*b^2*(e^2 + d*f)) - 64*c^3*(3*a*f*(e^2 + d*f) + b*(e^3 + 6*d*e*f)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(11/2))","A",7,5,27,0.1852,1,"{1660, 1661, 640, 621, 206}"
115,1,309,0,0.4466536,"\int \frac{\left(d+e x+f x^2\right)^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)^2/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \left(-x \left(c^2 \left(2 a^2 f^2+6 a b e f+b^2 \left(2 d f+e^2\right)\right)-2 b^2 c f (2 a f+b e)-2 c^3 \left(a \left(2 d f+e^2\right)+b d e\right)+b^4 f^2+2 c^4 d^2\right)-b c \left(-3 a^2 f^2+a c \left(2 d f+e^2\right)+c^2 d^2\right)+2 a b^2 c e f-a b^3 f^2+4 a c^2 e (c d-a f)\right)}{c^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-12 c f (a f+2 b e)+15 b^2 f^2+8 c^2 \left(2 d f+e^2\right)\right)}{8 c^{7/2}}+\frac{f \sqrt{a+b x+c x^2} (8 c e-7 b f)}{4 c^3}+\frac{f^2 x \sqrt{a+b x+c x^2}}{2 c^2}","\frac{2 \left(-x \left(c^2 \left(2 a^2 f^2+6 a b e f+b^2 \left(2 d f+e^2\right)\right)-2 b^2 c f (2 a f+b e)-2 c^3 \left(a \left(2 d f+e^2\right)+b d e\right)+b^4 f^2+2 c^4 d^2\right)-b c \left(-3 a^2 f^2+a c \left(2 d f+e^2\right)+c^2 d^2\right)+2 a b^2 c e f-a b^3 f^2+4 a c^2 e (c d-a f)\right)}{c^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-12 c f (a f+2 b e)+15 b^2 f^2+8 c^2 \left(2 d f+e^2\right)\right)}{8 c^{7/2}}+\frac{f \sqrt{a+b x+c x^2} (8 c e-7 b f)}{4 c^3}+\frac{f^2 x \sqrt{a+b x+c x^2}}{2 c^2}",1,"(2*(2*a*b^2*c*e*f - a*b^3*f^2 + 4*a*c^2*e*(c*d - a*f) - b*c*(c^2*d^2 - 3*a^2*f^2 + a*c*(e^2 + 2*d*f)) - (2*c^4*d^2 + b^4*f^2 - 2*b^2*c*f*(b*e + 2*a*f) - 2*c^3*(b*d*e + a*(e^2 + 2*d*f)) + c^2*(6*a*b*e*f + 2*a^2*f^2 + b^2*(e^2 + 2*d*f)))*x))/(c^3*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (f*(8*c*e - 7*b*f)*Sqrt[a + b*x + c*x^2])/(4*c^3) + (f^2*x*Sqrt[a + b*x + c*x^2])/(2*c^2) + ((15*b^2*f^2 - 12*c*f*(2*b*e + a*f) + 8*c^2*(e^2 + 2*d*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(7/2))","A",5,5,27,0.1852,1,"{1660, 1661, 640, 621, 206}"
116,1,111,0,0.0797038,"\int \frac{d+e x+f x^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2)/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}","\frac{2 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{f \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}",1,"(2*(c*(2*a*e - b*(d + (a*f)/c)) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (f*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(3/2)","A",4,4,25,0.1600,1,"{1660, 12, 621, 206}"
117,1,666,0,1.8291617,"\int \frac{1}{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)} \, dx","Int[1/((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2)),x]","\frac{2 \left(-c x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left((c d-a f)^2-(b d-a e) (c e-b f)\right)}-\frac{f \left(f \left(2 a f-b \left(\sqrt{e^2-4 d f}+e\right)\right)+c \left(e \sqrt{e^2-4 d f}-2 d f+e^2\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} \sqrt{e^2-4 d f} \left((c d-a f)^2-(b d-a e) (c e-b f)\right) \sqrt{f \left(2 a f-b \left(e-\sqrt{e^2-4 d f}\right)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)}}+\frac{f \left(f \left(2 a f-b \left(e-\sqrt{e^2-4 d f}\right)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} \sqrt{e^2-4 d f} \left((c d-a f)^2-(b d-a e) (c e-b f)\right) \sqrt{f \left(2 a f-b \left(\sqrt{e^2-4 d f}+e\right)\right)+c \left(e \sqrt{e^2-4 d f}-2 d f+e^2\right)}}","\frac{2 \left(-c x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)-b c (c d-3 a f)-2 a c^2 e+b^2 c e+b^3 (-f)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left((c d-a f)^2-(b d-a e) (c e-b f)\right)}-\frac{f \left(f \left(2 a f-b \left(\sqrt{e^2-4 d f}+e\right)\right)+c \left(e \sqrt{e^2-4 d f}-2 d f+e^2\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right)-b \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2-\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} \sqrt{e^2-4 d f} \left((c d-a f)^2-(b d-a e) (c e-b f)\right) \sqrt{f \left(2 a f-b \left(e-\sqrt{e^2-4 d f}\right)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)}}+\frac{f \left(f \left(2 a f-b \left(e-\sqrt{e^2-4 d f}\right)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 x \left(b f-c \left(\sqrt{e^2-4 d f}+e\right)\right)-b \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+b x+c x^2} \sqrt{2 a f^2+\sqrt{e^2-4 d f} (c e-b f)-b e f-2 c d f+c e^2}}\right)}{\sqrt{2} \sqrt{e^2-4 d f} \left((c d-a f)^2-(b d-a e) (c e-b f)\right) \sqrt{f \left(2 a f-b \left(\sqrt{e^2-4 d f}+e\right)\right)+c \left(e \sqrt{e^2-4 d f}-2 d f+e^2\right)}}",1,"(2*(b^2*c*e - 2*a*c^2*e - b^3*f - b*c*(c*d - 3*a*f) - c*(2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x))/((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*Sqrt[a + b*x + c*x^2]) - (f*(c*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) + f*(2*a*f - b*(e + Sqrt[e^2 - 4*d*f])))*ArcTanh[(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[2]*Sqrt[e^2 - 4*d*f]*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*Sqrt[c*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) + f*(2*a*f - b*(e - Sqrt[e^2 - 4*d*f]))]) + (f*(c*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) + f*(2*a*f - b*(e - Sqrt[e^2 - 4*d*f])))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)/(2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + (c*e - b*f)*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(Sqrt[2]*Sqrt[e^2 - 4*d*f]*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*Sqrt[c*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) + f*(2*a*f - b*(e + Sqrt[e^2 - 4*d*f]))])","A",6,4,27,0.1481,1,"{974, 1032, 724, 206}"
118,1,891,0,1.7683301,"\int \frac{\left(d+e x+f x^2\right)^3}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x + f*x^2)^3/(a + b*x + c*x^2)^(5/2),x]","\frac{x \sqrt{c x^2+b x+a} f^3}{2 c^3}+\frac{(12 c e-11 b f) \sqrt{c x^2+b x+a} f^2}{4 c^4}+\frac{\left(24 \left(e^2+d f\right) c^2-20 f (3 b e+a f) c+35 b^2 f^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) f}{8 c^{9/2}}-\frac{2 \left(-f^3 b^7+3 c e f^2 b^6+3 c f \left(6 a f^2-c \left(e^2+d f\right)\right) b^5-c^2 e \left(42 a f^2-c \left(e^2+6 d f\right)\right) b^4-3 c^2 \left(29 a^2 f^3-10 a c \left(e^2+d f\right) f+c^2 d \left(e^2+d f\right)\right) b^3+6 c^3 e \left(2 c^2 d^2+28 a^2 f^2-a c \left(e^2+6 d f\right)\right) b^2-4 c^3 \left(2 c^3 d^3+3 a c^2 \left(e^2+d f\right) d-29 a^3 f^3+24 a^2 c f \left(e^2+d f\right)\right) b-24 a^2 c^4 e \left(6 a f^2-c \left(e^2+6 d f\right)\right)-c \left(-10 f^3 b^6+3 c f^2 (7 b e+26 a f) b^4-6 c^2 f \left(2 \left(e^2+d f\right) b^2+25 a e f b+27 a^2 f^2\right) b^2+16 c^6 d^3-24 c^5 d \left(b d e-a \left(e^2+d f\right)\right)+6 c^4 \left(-16 f \left(e^2+d f\right) a^2-2 b e \left(e^2+6 d f\right) a+b^2 d \left(e^2+d f\right)\right)+c^3 \left(\left(e^3+6 d f e\right) b^3+84 a f \left(e^2+d f\right) b^2+240 a^2 e f^2 b+56 a^3 f^3\right)\right) x\right)}{3 c^5 \left(b^2-4 a c\right)^2 \sqrt{c x^2+b x+a}}+\frac{2 \left(-a f^3 b^5+3 a c e f^2 b^4+a c f \left(5 a f^2-3 c \left(e^2+d f\right)\right) b^3-a c^2 e \left(12 a f^2-c \left(e^2+6 d f\right)\right) b^2-c^2 \left(c^3 d^3+3 a c^2 \left(e^2+d f\right) d+5 a^3 f^3-9 a^2 c f \left(e^2+d f\right)\right) b+2 a c^3 e \left(3 c^2 d^2+3 a^2 f^2-a c \left(e^2+6 d f\right)\right)-\left(f b^2-c e b+2 c^2 d-2 a c f\right) \left(f^2 b^4-2 c e f b^3+c^2 e^2 b^2-4 a c f^2 b^2+c^2 d f b^2-c^3 d e b+7 a c^2 e f b+c^4 d^2-3 a c^3 e^2+a^2 c^2 f^2-2 a c^3 d f\right) x\right)}{3 c^5 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{3/2}}","\frac{x \sqrt{c x^2+b x+a} f^3}{2 c^3}+\frac{(12 c e-11 b f) \sqrt{c x^2+b x+a} f^2}{4 c^4}+\frac{\left(24 \left(e^2+d f\right) c^2-20 f (3 b e+a f) c+35 b^2 f^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) f}{8 c^{9/2}}-\frac{2 \left(-f^3 b^7+3 c e f^2 b^6+3 c f \left(6 a f^2-c \left(e^2+d f\right)\right) b^5-c^2 e \left(42 a f^2-c \left(e^2+6 d f\right)\right) b^4-3 c^2 \left(29 a^2 f^3-10 a c \left(e^2+d f\right) f+c^2 d \left(e^2+d f\right)\right) b^3+6 c^3 e \left(2 c^2 d^2+28 a^2 f^2-a c \left(e^2+6 d f\right)\right) b^2-4 c^3 \left(2 c^3 d^3+3 a c^2 \left(e^2+d f\right) d-29 a^3 f^3+24 a^2 c f \left(e^2+d f\right)\right) b-24 a^2 c^4 e \left(6 a f^2-c \left(e^2+6 d f\right)\right)-c \left(-10 f^3 b^6+3 c f^2 (7 b e+26 a f) b^4-6 c^2 f \left(2 \left(e^2+d f\right) b^2+25 a e f b+27 a^2 f^2\right) b^2+16 c^6 d^3-24 c^5 d \left(b d e-a \left(e^2+d f\right)\right)+6 c^4 \left(-16 f \left(e^2+d f\right) a^2-2 b e \left(e^2+6 d f\right) a+b^2 d \left(e^2+d f\right)\right)+c^3 \left(\left(e^3+6 d f e\right) b^3+84 a f \left(e^2+d f\right) b^2+240 a^2 e f^2 b+56 a^3 f^3\right)\right) x\right)}{3 c^5 \left(b^2-4 a c\right)^2 \sqrt{c x^2+b x+a}}+\frac{2 \left(-a f^3 b^5+3 a c e f^2 b^4+a c f \left(5 a f^2-3 c \left(e^2+d f\right)\right) b^3-a c^2 e \left(12 a f^2-c \left(e^2+6 d f\right)\right) b^2-c^2 \left(c^3 d^3+3 a c^2 \left(e^2+d f\right) d+5 a^3 f^3-9 a^2 c f \left(e^2+d f\right)\right) b+2 a c^3 e \left(3 c^2 d^2+3 a^2 f^2-a c \left(e^2+6 d f\right)\right)-\left(f b^2-c e b+2 c^2 d-2 a c f\right) \left(f^2 b^4-2 c e f b^3+c^2 e^2 b^2-4 a c f^2 b^2+c^2 d f b^2-c^3 d e b+7 a c^2 e f b+c^4 d^2-3 a c^3 e^2+a^2 c^2 f^2-2 a c^3 d f\right) x\right)}{3 c^5 \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{3/2}}",1,"(2*(3*a*b^4*c*e*f^2 - a*b^5*f^3 + a*b^3*c*f*(5*a*f^2 - 3*c*(e^2 + d*f)) - b*c^2*(c^3*d^3 + 5*a^3*f^3 + 3*a*c^2*d*(e^2 + d*f) - 9*a^2*c*f*(e^2 + d*f)) - a*b^2*c^2*e*(12*a*f^2 - c*(e^2 + 6*d*f)) + 2*a*c^3*e*(3*c^2*d^2 + 3*a^2*f^2 - a*c*(e^2 + 6*d*f)) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*(c^4*d^2 - b*c^3*d*e + b^2*c^2*e^2 - 3*a*c^3*e^2 + b^2*c^2*d*f - 2*a*c^3*d*f - 2*b^3*c*e*f + 7*a*b*c^2*e*f + b^4*f^2 - 4*a*b^2*c*f^2 + a^2*c^2*f^2)*x))/(3*c^5*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*(3*b^6*c*e*f^2 - b^7*f^3 + 3*b^5*c*f*(6*a*f^2 - c*(e^2 + d*f)) - 3*b^3*c^2*(29*a^2*f^3 + c^2*d*(e^2 + d*f) - 10*a*c*f*(e^2 + d*f)) - 4*b*c^3*(2*c^3*d^3 - 29*a^3*f^3 + 3*a*c^2*d*(e^2 + d*f) + 24*a^2*c*f*(e^2 + d*f)) - 24*a^2*c^4*e*(6*a*f^2 - c*(e^2 + 6*d*f)) - b^4*c^2*e*(42*a*f^2 - c*(e^2 + 6*d*f)) + 6*b^2*c^3*e*(2*c^2*d^2 + 28*a^2*f^2 - a*c*(e^2 + 6*d*f)) - c*(16*c^6*d^3 - 10*b^6*f^3 + 3*b^4*c*f^2*(7*b*e + 26*a*f) - 24*c^5*d*(b*d*e - a*(e^2 + d*f)) - 6*b^2*c^2*f*(25*a*b*e*f + 27*a^2*f^2 + 2*b^2*(e^2 + d*f)) + 6*c^4*(b^2*d*(e^2 + d*f) - 16*a^2*f*(e^2 + d*f) - 2*a*b*e*(e^2 + 6*d*f)) + c^3*(240*a^2*b*e*f^2 + 56*a^3*f^3 + 84*a*b^2*f*(e^2 + d*f) + b^3*(e^3 + 6*d*e*f)))*x))/(3*c^5*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) + (f^2*(12*c*e - 11*b*f)*Sqrt[a + b*x + c*x^2])/(4*c^4) + (f^3*x*Sqrt[a + b*x + c*x^2])/(2*c^3) + (f*(35*b^2*f^2 - 20*c*f*(3*b*e + a*f) + 24*c^2*(e^2 + d*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(9/2))","A",6,5,27,0.1852,1,"{1660, 1661, 640, 621, 206}"
119,1,444,0,0.4507277,"\int \frac{\left(d+e x+f x^2\right)^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x + f*x^2)^2/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \left(-2 c x \left(-c^2 \left(16 a^2 f^2+12 a b e f+b^2 \left(-\left(2 d f+e^2\right)\right)\right)+b^2 c f (14 a f+b e)-c^3 \left(8 b d e-4 a \left(2 d f+e^2\right)\right)-2 b^4 f^2+8 c^4 d^2\right)-4 b c^2 \left(8 a^2 f^2+a c \left(2 d f+e^2\right)+2 c^2 d^2\right)+48 a^2 c^3 e f+4 b^2 c^2 e (2 c d-3 a f)+b^3 c \left(10 a f^2-c \left(2 d f+e^2\right)\right)+2 b^4 c e f+b^5 \left(-f^2\right)\right)}{3 c^3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 \left(-x \left(c^2 \left(2 a^2 f^2+6 a b e f+b^2 \left(2 d f+e^2\right)\right)-2 b^2 c f (2 a f+b e)-2 c^3 \left(a \left(2 d f+e^2\right)+b d e\right)+b^4 f^2+2 c^4 d^2\right)-b c \left(-3 a^2 f^2+a c \left(2 d f+e^2\right)+c^2 d^2\right)+2 a b^2 c e f-a b^3 f^2+4 a c^2 e (c d-a f)\right)}{3 c^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{f^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}","-\frac{2 \left(-2 c x \left(-c^2 \left(16 a^2 f^2+12 a b e f+b^2 \left(-\left(2 d f+e^2\right)\right)\right)+b^2 c f (14 a f+b e)-c^3 \left(8 b d e-4 a \left(2 d f+e^2\right)\right)-2 b^4 f^2+8 c^4 d^2\right)-4 b c^2 \left(8 a^2 f^2+a c \left(2 d f+e^2\right)+2 c^2 d^2\right)+48 a^2 c^3 e f+4 b^2 c^2 e (2 c d-3 a f)+b^3 c \left(10 a f^2-c \left(2 d f+e^2\right)\right)+2 b^4 c e f+b^5 \left(-f^2\right)\right)}{3 c^3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 \left(-x \left(c^2 \left(2 a^2 f^2+6 a b e f+b^2 \left(2 d f+e^2\right)\right)-2 b^2 c f (2 a f+b e)-2 c^3 \left(a \left(2 d f+e^2\right)+b d e\right)+b^4 f^2+2 c^4 d^2\right)-b c \left(-3 a^2 f^2+a c \left(2 d f+e^2\right)+c^2 d^2\right)+2 a b^2 c e f-a b^3 f^2+4 a c^2 e (c d-a f)\right)}{3 c^3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{f^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}",1,"(2*(2*a*b^2*c*e*f - a*b^3*f^2 + 4*a*c^2*e*(c*d - a*f) - b*c*(c^2*d^2 - 3*a^2*f^2 + a*c*(e^2 + 2*d*f)) - (2*c^4*d^2 + b^4*f^2 - 2*b^2*c*f*(b*e + 2*a*f) - 2*c^3*(b*d*e + a*(e^2 + 2*d*f)) + c^2*(6*a*b*e*f + 2*a^2*f^2 + b^2*(e^2 + 2*d*f)))*x))/(3*c^3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*(2*b^4*c*e*f + 48*a^2*c^3*e*f - b^5*f^2 + 4*b^2*c^2*e*(2*c*d - 3*a*f) + b^3*c*(10*a*f^2 - c*(e^2 + 2*d*f)) - 4*b*c^2*(2*c^2*d^2 + 8*a^2*f^2 + a*c*(e^2 + 2*d*f)) - 2*c*(8*c^4*d^2 - 2*b^4*f^2 + b^2*c*f*(b*e + 14*a*f) - c^3*(8*b*d*e - 4*a*(e^2 + 2*d*f)) - c^2*(12*a*b*e*f + 16*a^2*f^2 - b^2*(e^2 + 2*d*f)))*x))/(3*c^3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) + (f^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(5/2)","A",5,4,27,0.1481,1,"{1660, 12, 621, 206}"
120,1,131,0,0.0852556,"\int \frac{d+e x+f x^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(d + e*x + f*x^2)/(a + b*x + c*x^2)^(5/2),x]","\frac{2 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{2 (b+2 c x) \left(4 a f+\frac{b^2 f}{c}-4 b e+8 c d\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}","\frac{2 \left(c \left(2 a e-b \left(\frac{a f}{c}+d\right)\right)-x \left(-2 a c f+b^2 f-b c e+2 c^2 d\right)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{2 (b+2 c x) \left(4 a f+\frac{b^2 f}{c}-4 b e+8 c d\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}",1,"(2*(c*(2*a*e - b*(d + (a*f)/c)) - (2*c^2*d - b*c*e + b^2*f - 2*a*c*f)*x))/(3*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (2*(8*c*d - 4*b*e + 4*a*f + (b^2*f)/c)*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",3,3,25,0.1200,1,"{1660, 12, 613}"
121,1,51,0,0.0656829,"\int \frac{1}{\sqrt{-7+2 x+5 x^2} \left(8+12 x+5 x^2\right)} \, dx","Int[1/(Sqrt[-7 + 2*x + 5*x^2]*(8 + 12*x + 5*x^2)),x]","\frac{1}{10} \tan ^{-1}\left(\frac{5 (x+2)}{2 \sqrt{5 x^2+2 x-7}}\right)+\frac{1}{5} \tanh ^{-1}\left(\frac{5 (x+1)}{\sqrt{5 x^2+2 x-7}}\right)","\frac{1}{10} \tan ^{-1}\left(\frac{5 (x+2)}{2 \sqrt{5 x^2+2 x-7}}\right)+\frac{1}{5} \tanh ^{-1}\left(\frac{5 (x+1)}{\sqrt{5 x^2+2 x-7}}\right)",1,"ArcTan[(5*(2 + x))/(2*Sqrt[-7 + 2*x + 5*x^2])]/10 + ArcTanh[(5*(1 + x))/Sqrt[-7 + 2*x + 5*x^2]]/5","A",5,4,27,0.1481,1,"{986, 1029, 203, 207}"
122,1,1432,0,6.2188129,"\int \frac{1}{\sqrt{a+b x+c x^2} \sqrt{d+e x+f x^2}} \, dx","Int[1/(Sqrt[a + b*x + c*x^2]*Sqrt[d + e*x + f*x^2]),x]","-\frac{\sqrt[4]{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)^{3/2} \sqrt{2 a+\left(b+\sqrt{b^2-4 a c}\right) x} \sqrt{\frac{\left(4 a c-\left(b+\sqrt{b^2-4 a c}\right)^2\right)^2 \left(f x^2+e x+d\right)}{\left(4 f a^2-2 \left(b+\sqrt{b^2-4 a c}\right) e a+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}} \left(\frac{\sqrt{f b^2-c e b+2 c^2 d-2 a c f-\sqrt{b^2-4 a c} (c e-b f)} \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\sqrt{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1\right) \sqrt{\frac{\frac{\left(4 d c^2-2 \left(b+\sqrt{b^2-4 a c}\right) e c+\left(b+\sqrt{b^2-4 a c}\right)^2 f\right) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)^2}{\left(4 f a^2-2 \left(b+\sqrt{b^2-4 a c}\right) e a+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}-\frac{\left(b+\sqrt{b^2-4 a c}\right) (2 c d-b e+2 a f) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\left(d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1}{\left(\frac{\sqrt{f b^2-c e b+2 c^2 d-2 a c f-\sqrt{b^2-4 a c} (c e-b f)} \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\sqrt{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{f b^2-c e b+2 c^2 d-2 a c f-\sqrt{b^2-4 a c} (c e-b f)} \sqrt{2 a+\left(b+\sqrt{b^2-4 a c}\right) x}}{\sqrt[4]{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \sqrt{b+2 c x+\sqrt{b^2-4 a c}}}\right)|\frac{1}{4} \left(\frac{\left(b+\sqrt{b^2-4 a c}\right) (2 c d-b e+2 a f)}{\sqrt{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \sqrt{2 d c^2-\left(b e+\sqrt{b^2-4 a c} e+2 a f\right) c+b \left(b+\sqrt{b^2-4 a c}\right) f}}+2\right)\right)}{\left(4 a c-\left(b+\sqrt{b^2-4 a c}\right)^2\right) \sqrt[4]{f b^2-c e b+2 c^2 d-2 a c f-\sqrt{b^2-4 a c} (c e-b f)} \sqrt{c x^2+b x+a} \sqrt{f x^2+e x+d} \sqrt{\frac{\left(4 d c^2-2 \left(b+\sqrt{b^2-4 a c}\right) e c+\left(b+\sqrt{b^2-4 a c}\right)^2 f\right) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)^2}{\left(4 f a^2-2 \left(b+\sqrt{b^2-4 a c}\right) e a+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}-\frac{\left(b+\sqrt{b^2-4 a c}\right) (2 c d-b e+2 a f) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\left(d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1}}","-\frac{\sqrt[4]{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)^{3/2} \sqrt{2 a+\left(b+\sqrt{b^2-4 a c}\right) x} \sqrt{\frac{\left(4 a c-\left(b+\sqrt{b^2-4 a c}\right)^2\right)^2 \left(f x^2+e x+d\right)}{\left(4 f a^2-2 \left(b+\sqrt{b^2-4 a c}\right) e a+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}} \left(\frac{\sqrt{f b^2-c e b+2 c^2 d-2 a c f-\sqrt{b^2-4 a c} (c e-b f)} \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\sqrt{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1\right) \sqrt{\frac{\frac{\left(4 d c^2-2 \left(b+\sqrt{b^2-4 a c}\right) e c+\left(b+\sqrt{b^2-4 a c}\right)^2 f\right) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)^2}{\left(4 f a^2-2 \left(b+\sqrt{b^2-4 a c}\right) e a+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}-\frac{\left(b+\sqrt{b^2-4 a c}\right) (2 c d-b e+2 a f) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\left(d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1}{\left(\frac{\sqrt{f b^2-c e b+2 c^2 d-2 a c f-\sqrt{b^2-4 a c} (c e-b f)} \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\sqrt{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{f b^2-c e b+2 c^2 d-2 a c f-\sqrt{b^2-4 a c} (c e-b f)} \sqrt{2 a+\left(b+\sqrt{b^2-4 a c}\right) x}}{\sqrt[4]{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \sqrt{b+2 c x+\sqrt{b^2-4 a c}}}\right)|\frac{1}{4} \left(\frac{\left(b+\sqrt{b^2-4 a c}\right) (2 c d-b e+2 a f)}{\sqrt{d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)} \sqrt{2 d c^2-\left(b e+\sqrt{b^2-4 a c} e+2 a f\right) c+b \left(b+\sqrt{b^2-4 a c}\right) f}}+2\right)\right)}{\left(4 a c-\left(b+\sqrt{b^2-4 a c}\right)^2\right) \sqrt[4]{f b^2-c e b+2 c^2 d-2 a c f-\sqrt{b^2-4 a c} (c e-b f)} \sqrt{c x^2+b x+a} \sqrt{f x^2+e x+d} \sqrt{\frac{\left(4 d c^2-2 \left(b+\sqrt{b^2-4 a c}\right) e c+\left(b+\sqrt{b^2-4 a c}\right)^2 f\right) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)^2}{\left(4 f a^2-2 \left(b+\sqrt{b^2-4 a c}\right) e a+\left(b+\sqrt{b^2-4 a c}\right)^2 d\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)^2}-\frac{\left(b+\sqrt{b^2-4 a c}\right) (2 c d-b e+2 a f) \left(2 a+\left(b+\sqrt{b^2-4 a c}\right) x\right)}{\left(d b^2+\left(\sqrt{b^2-4 a c} d-a e\right) b-a \left(2 c d+\sqrt{b^2-4 a c} e-2 a f\right)\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}+1}}",1,"-(((b^2*d + b*(Sqrt[b^2 - 4*a*c]*d - a*e) - a*(2*c*d + Sqrt[b^2 - 4*a*c]*e - 2*a*f))^(1/4)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)^(3/2)*Sqrt[2*a + (b + Sqrt[b^2 - 4*a*c])*x]*Sqrt[((4*a*c - (b + Sqrt[b^2 - 4*a*c])^2)^2*(d + e*x + f*x^2))/(((b + Sqrt[b^2 - 4*a*c])^2*d - 2*a*(b + Sqrt[b^2 - 4*a*c])*e + 4*a^2*f)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)^2)]*(1 + (Sqrt[2*c^2*d - b*c*e + b^2*f - 2*a*c*f - Sqrt[b^2 - 4*a*c]*(c*e - b*f)]*(2*a + (b + Sqrt[b^2 - 4*a*c])*x))/(Sqrt[b^2*d + b*(Sqrt[b^2 - 4*a*c]*d - a*e) - a*(2*c*d + Sqrt[b^2 - 4*a*c]*e - 2*a*f)]*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)))*Sqrt[(1 - ((b + Sqrt[b^2 - 4*a*c])*(2*c*d - b*e + 2*a*f)*(2*a + (b + Sqrt[b^2 - 4*a*c])*x))/((b^2*d + b*(Sqrt[b^2 - 4*a*c]*d - a*e) - a*(2*c*d + Sqrt[b^2 - 4*a*c]*e - 2*a*f))*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)) + ((4*c^2*d - 2*c*(b + Sqrt[b^2 - 4*a*c])*e + (b + Sqrt[b^2 - 4*a*c])^2*f)*(2*a + (b + Sqrt[b^2 - 4*a*c])*x)^2)/(((b + Sqrt[b^2 - 4*a*c])^2*d - 2*a*(b + Sqrt[b^2 - 4*a*c])*e + 4*a^2*f)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)^2))/(1 + (Sqrt[2*c^2*d - b*c*e + b^2*f - 2*a*c*f - Sqrt[b^2 - 4*a*c]*(c*e - b*f)]*(2*a + (b + Sqrt[b^2 - 4*a*c])*x))/(Sqrt[b^2*d + b*(Sqrt[b^2 - 4*a*c]*d - a*e) - a*(2*c*d + Sqrt[b^2 - 4*a*c]*e - 2*a*f)]*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)))^2]*EllipticF[2*ArcTan[((2*c^2*d - b*c*e + b^2*f - 2*a*c*f - Sqrt[b^2 - 4*a*c]*(c*e - b*f))^(1/4)*Sqrt[2*a + (b + Sqrt[b^2 - 4*a*c])*x])/((b^2*d + b*(Sqrt[b^2 - 4*a*c]*d - a*e) - a*(2*c*d + Sqrt[b^2 - 4*a*c]*e - 2*a*f))^(1/4)*Sqrt[b + Sqrt[b^2 - 4*a*c] + 2*c*x])], (2 + ((b + Sqrt[b^2 - 4*a*c])*(2*c*d - b*e + 2*a*f))/(Sqrt[b^2*d + b*(Sqrt[b^2 - 4*a*c]*d - a*e) - a*(2*c*d + Sqrt[b^2 - 4*a*c]*e - 2*a*f)]*Sqrt[2*c^2*d + b*(b + Sqrt[b^2 - 4*a*c])*f - c*(b*e + Sqrt[b^2 - 4*a*c]*e + 2*a*f)]))/4])/((4*a*c - (b + Sqrt[b^2 - 4*a*c])^2)*(2*c^2*d - b*c*e + b^2*f - 2*a*c*f - Sqrt[b^2 - 4*a*c]*(c*e - b*f))^(1/4)*Sqrt[a + b*x + c*x^2]*Sqrt[d + e*x + f*x^2]*Sqrt[1 - ((b + Sqrt[b^2 - 4*a*c])*(2*c*d - b*e + 2*a*f)*(2*a + (b + Sqrt[b^2 - 4*a*c])*x))/((b^2*d + b*(Sqrt[b^2 - 4*a*c]*d - a*e) - a*(2*c*d + Sqrt[b^2 - 4*a*c]*e - 2*a*f))*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)) + ((4*c^2*d - 2*c*(b + Sqrt[b^2 - 4*a*c])*e + (b + Sqrt[b^2 - 4*a*c])^2*f)*(2*a + (b + Sqrt[b^2 - 4*a*c])*x)^2)/(((b + Sqrt[b^2 - 4*a*c])^2*d - 2*a*(b + Sqrt[b^2 - 4*a*c])*e + 4*a^2*f)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x)^2)]))","A",3,3,29,0.1034,1,"{992, 935, 1103}"
123,1,652,0,0.676932,"\int \frac{1}{\sqrt{3-x+2 x^2} \sqrt{2+3 x+5 x^2}} \, dx","Int[1/(Sqrt[3 - x + 2*x^2]*Sqrt[2 + 3*x + 5*x^2]),x]","\frac{\sqrt{\frac{23}{11}} \left(-4 x-i \sqrt{23}+1\right) \sqrt{4 x+i \sqrt{23}-1} \sqrt{6-\left(1-i \sqrt{23}\right) x} \sqrt{\frac{\left(-\sqrt{23}+11 i\right) \left(5 x^2+3 x+2\right)}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)^2}} \left(1-\frac{\sqrt{-\frac{-\sqrt{23}+3 i}{\sqrt{23}+7 i}} \left(6-\left(1-i \sqrt{23}\right) x\right)}{-4 x-i \sqrt{23}+1}\right) \sqrt{\frac{-\frac{11 \left(-\sqrt{23}+3 i\right) \left(6-\left(1-i \sqrt{23}\right) x\right)^2}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)^2}-\frac{41 \left(\sqrt{23}+i\right) \left(6-\left(1-i \sqrt{23}\right) x\right)}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)}+11}{\left(1-\frac{\sqrt{-\frac{-\sqrt{23}+3 i}{\sqrt{23}+7 i}} \left(6-\left(1-i \sqrt{23}\right) x\right)}{-4 x-i \sqrt{23}+1}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{3 i-\sqrt{23}}{7 i+\sqrt{23}}} \sqrt{6-\left(1-i \sqrt{23}\right) x}}{\sqrt{4 x+i \sqrt{23}-1}}\right)|\frac{1}{88} \left(44-\frac{41 \left(i+\sqrt{23}\right)}{\sqrt{11+i \sqrt{23}}}\right)\right)}{\left(23+i \sqrt{23}\right) \sqrt[4]{-\frac{-\sqrt{23}+3 i}{\sqrt{23}+7 i}} \sqrt{2 x^2-x+3} \sqrt{5 x^2+3 x+2} \sqrt{-\frac{11 \left(-\sqrt{23}+3 i\right) \left(6-\left(1-i \sqrt{23}\right) x\right)^2}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)^2}-\frac{41 \left(\sqrt{23}+i\right) \left(6-\left(1-i \sqrt{23}\right) x\right)}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)}+11}}","\frac{\sqrt{\frac{23}{11}} \left(-4 x-i \sqrt{23}+1\right) \sqrt{4 x+i \sqrt{23}-1} \sqrt{6-\left(1-i \sqrt{23}\right) x} \sqrt{\frac{\left(-\sqrt{23}+11 i\right) \left(5 x^2+3 x+2\right)}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)^2}} \left(1-\frac{\sqrt{-\frac{-\sqrt{23}+3 i}{\sqrt{23}+7 i}} \left(6-\left(1-i \sqrt{23}\right) x\right)}{-4 x-i \sqrt{23}+1}\right) \sqrt{\frac{-\frac{11 \left(-\sqrt{23}+3 i\right) \left(6-\left(1-i \sqrt{23}\right) x\right)^2}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)^2}-\frac{41 \left(\sqrt{23}+i\right) \left(6-\left(1-i \sqrt{23}\right) x\right)}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)}+11}{\left(1-\frac{\sqrt{-\frac{-\sqrt{23}+3 i}{\sqrt{23}+7 i}} \left(6-\left(1-i \sqrt{23}\right) x\right)}{-4 x-i \sqrt{23}+1}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{3 i-\sqrt{23}}{7 i+\sqrt{23}}} \sqrt{6-\left(1-i \sqrt{23}\right) x}}{\sqrt{4 x+i \sqrt{23}-1}}\right)|\frac{1}{88} \left(44-\frac{41 \left(i+\sqrt{23}\right)}{\sqrt{11+i \sqrt{23}}}\right)\right)}{\left(23+i \sqrt{23}\right) \sqrt[4]{-\frac{-\sqrt{23}+3 i}{\sqrt{23}+7 i}} \sqrt{2 x^2-x+3} \sqrt{5 x^2+3 x+2} \sqrt{-\frac{11 \left(-\sqrt{23}+3 i\right) \left(6-\left(1-i \sqrt{23}\right) x\right)^2}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)^2}-\frac{41 \left(\sqrt{23}+i\right) \left(6-\left(1-i \sqrt{23}\right) x\right)}{\left(\sqrt{23}+7 i\right) \left(-4 x-i \sqrt{23}+1\right)}+11}}",1,"(Sqrt[23/11]*(1 - I*Sqrt[23] - 4*x)*Sqrt[-1 + I*Sqrt[23] + 4*x]*Sqrt[6 - (1 - I*Sqrt[23])*x]*Sqrt[((11*I - Sqrt[23])*(2 + 3*x + 5*x^2))/((7*I + Sqrt[23])*(1 - I*Sqrt[23] - 4*x)^2)]*(1 - (Sqrt[-((3*I - Sqrt[23])/(7*I + Sqrt[23]))]*(6 - (1 - I*Sqrt[23])*x))/(1 - I*Sqrt[23] - 4*x))*Sqrt[(11 - (41*(I + Sqrt[23])*(6 - (1 - I*Sqrt[23])*x))/((7*I + Sqrt[23])*(1 - I*Sqrt[23] - 4*x)) - (11*(3*I - Sqrt[23])*(6 - (1 - I*Sqrt[23])*x)^2)/((7*I + Sqrt[23])*(1 - I*Sqrt[23] - 4*x)^2))/(1 - (Sqrt[-((3*I - Sqrt[23])/(7*I + Sqrt[23]))]*(6 - (1 - I*Sqrt[23])*x))/(1 - I*Sqrt[23] - 4*x))^2]*EllipticF[2*ArcTan[((-((3*I - Sqrt[23])/(7*I + Sqrt[23])))^(1/4)*Sqrt[6 - (1 - I*Sqrt[23])*x])/Sqrt[-1 + I*Sqrt[23] + 4*x]], (44 - (41*(I + Sqrt[23]))/Sqrt[11 + I*Sqrt[23]])/88])/((23 + I*Sqrt[23])*(-((3*I - Sqrt[23])/(7*I + Sqrt[23])))^(1/4)*Sqrt[3 - x + 2*x^2]*Sqrt[2 + 3*x + 5*x^2]*Sqrt[11 - (41*(I + Sqrt[23])*(6 - (1 - I*Sqrt[23])*x))/((7*I + Sqrt[23])*(1 - I*Sqrt[23] - 4*x)) - (11*(3*I - Sqrt[23])*(6 - (1 - I*Sqrt[23])*x)^2)/((7*I + Sqrt[23])*(1 - I*Sqrt[23] - 4*x)^2)])","A",3,3,29,0.1034,1,"{992, 935, 1103}"