1,1,87,102,0.1946497,"\int \frac{a+b x+\frac{b f x^2}{e}}{\sqrt{d+e x+f x^2}} \, dx","Integrate[(a + b*x + (b*f*x^2)/e)/Sqrt[d + e*x + f*x^2],x]","\frac{2 b \sqrt{f} (e+2 f x) \sqrt{d+x (e+f x)}-\left(b \left(4 d f+e^2\right)-8 a e f\right) \tanh ^{-1}\left(\frac{e+2 f x}{2 \sqrt{f} \sqrt{d+x (e+f x)}}\right)}{8 e f^{3/2}}","\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,"(2*b*Sqrt[f]*(e + 2*f*x)*Sqrt[d + x*(e + f*x)] - (-8*a*e*f + b*(e^2 + 4*d*f))*ArcTanh[(e + 2*f*x)/(2*Sqrt[f]*Sqrt[d + x*(e + f*x)])])/(8*e*f^(3/2))","A",1
2,1,178,82,0.3940349,"\int \frac{1}{\sqrt{d+e x+f x^2} \left(a+b x+\frac{b f x^2}{e}\right)} \, dx","Integrate[1/(Sqrt[d + e*x + f*x^2]*(a + b*x + (b*f*x^2)/e)),x]","\frac{\sqrt{e} \left(\tanh ^{-1}\left(\frac{-\sqrt{e} (e+2 f x) \sqrt{b e-4 a f}-\sqrt{b} \left(e^2-4 d f\right)}{4 f \sqrt{b d-a e} \sqrt{d+x (e+f x)}}\right)+\tanh ^{-1}\left(\frac{\sqrt{b} \left(e^2-4 d f\right)-\sqrt{e} (e+2 f x) \sqrt{b e-4 a f}}{4 f \sqrt{b d-a e} \sqrt{d+x (e+f x)}}\right)\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,"(Sqrt[e]*(ArcTanh[(-(Sqrt[b]*(e^2 - 4*d*f)) - Sqrt[e]*Sqrt[b*e - 4*a*f]*(e + 2*f*x))/(4*Sqrt[b*d - a*e]*f*Sqrt[d + x*(e + f*x)])] + ArcTanh[(Sqrt[b]*(e^2 - 4*d*f) - Sqrt[e]*Sqrt[b*e - 4*a*f]*(e + 2*f*x))/(4*Sqrt[b*d - a*e]*f*Sqrt[d + x*(e + f*x)])]))/(Sqrt[b*d - a*e]*Sqrt[b*e - 4*a*f])","B",1
3,1,161,66,0.2276863,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+b x+c x^2\right)} \, dx","Integrate[1/(Sqrt[a + b*x + c*x^2]*(d + b*x + c*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{4 a c-2 c x \sqrt{b^2-4 c d}-b \left(\sqrt{b^2-4 c d}+b\right)}{4 c \sqrt{a-d} \sqrt{a+x (b+c x)}}\right)+\tanh ^{-1}\left(\frac{-2 c \left(2 a+x \sqrt{b^2-4 c d}\right)-b \sqrt{b^2-4 c d}+b^2}{4 c \sqrt{a-d} \sqrt{a+x (b+c x)}}\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,"(ArcTanh[(4*a*c - b*(b + Sqrt[b^2 - 4*c*d]) - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + x*(b + c*x)])] + ArcTanh[(b^2 - b*Sqrt[b^2 - 4*c*d] - 2*c*(2*a + Sqrt[b^2 - 4*c*d]*x))/(4*c*Sqrt[a - d]*Sqrt[a + x*(b + c*x)])])/(Sqrt[a - d]*Sqrt[b^2 - 4*c*d])","B",1
4,1,296,129,0.922851,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+b x+c x^2\right)^2} \, dx","Integrate[1/(Sqrt[a + b*x + c*x^2]*(d + b*x + c*x^2)^2),x]","\frac{1}{2} \left(-\frac{8 c (b+2 c x) \sqrt{a+x (b+c x)}}{(a-d) \left(4 c d-b^2\right) \left(\sqrt{b^2-4 c d}-b-2 c x\right) \left(\sqrt{b^2-4 c d}+b+2 c x\right)}-\frac{\left(4 c (a-2 d)+b^2\right) \tanh ^{-1}\left(\frac{4 a c-2 c x \sqrt{b^2-4 c d}-b \left(\sqrt{b^2-4 c d}+b\right)}{4 c \sqrt{a-d} \sqrt{a+x (b+c x)}}\right)}{(a-d)^{3/2} \left(b^2-4 c d\right)^{3/2}}-\frac{\left(4 c (a-2 d)+b^2\right) \tanh ^{-1}\left(\frac{-2 c \left(2 a+x \sqrt{b^2-4 c d}\right)-b \sqrt{b^2-4 c d}+b^2}{4 c \sqrt{a-d} \sqrt{a+x (b+c x)}}\right)}{(a-d)^{3/2} \left(b^2-4 c d\right)^{3/2}}\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,"((-8*c*(b + 2*c*x)*Sqrt[a + x*(b + c*x)])/((a - d)*(-b^2 + 4*c*d)*(-b + Sqrt[b^2 - 4*c*d] - 2*c*x)*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)) - ((b^2 + 4*c*(a - 2*d))*ArcTanh[(4*a*c - b*(b + Sqrt[b^2 - 4*c*d]) - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + x*(b + c*x)])])/((a - d)^(3/2)*(b^2 - 4*c*d)^(3/2)) - ((b^2 + 4*c*(a - 2*d))*ArcTanh[(b^2 - b*Sqrt[b^2 - 4*c*d] - 2*c*(2*a + Sqrt[b^2 - 4*c*d]*x))/(4*c*Sqrt[a - d]*Sqrt[a + x*(b + c*x)])])/((a - d)^(3/2)*(b^2 - 4*c*d)^(3/2)))/2","B",1
5,1,1746,224,6.3820578,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+b x+c x^2\right)^3} \, dx","Integrate[1/(Sqrt[a + b*x + c*x^2]*(d + b*x + c*x^2)^3),x]","\frac{4 \sqrt{c x^2+b x+a} \left(\frac{\sqrt{c x^2+b x+a} \left(-2 \left(\sqrt{b^2-4 c d}-b\right) c^2-2 \left(b+2 \sqrt{b^2-4 c d}\right) c^2\right)}{\left(4 a c^2+\left(\sqrt{b^2-4 c d}-b\right)^2 c+2 b \left(\sqrt{b^2-4 c d}-b\right) c\right) \left(-b-2 c x+\sqrt{b^2-4 c d}\right)}+\frac{4 c \sqrt{a-d} \left(b \left(2 c^2 \left(b+2 \sqrt{b^2-4 c d}\right)-2 c^2 \left(\sqrt{b^2-4 c d}-b\right)\right)-2 \left(4 a c^3-c^2 \left(\sqrt{b^2-4 c d}-b\right) \left(b+2 \sqrt{b^2-4 c d}\right)\right)\right) \tanh ^{-1}\left(\frac{-4 a c-b \left(\sqrt{b^2-4 c d}-b\right)-\left(2 b c+2 \left(\sqrt{b^2-4 c d}-b\right) c\right) x}{4 c \sqrt{a-d} \sqrt{c x^2+b x+a}}\right)}{\left(4 a c^2+\left(\sqrt{b^2-4 c d}-b\right)^2 c+2 b \left(\sqrt{b^2-4 c d}-b\right) c\right) \left(16 a c^2+4 \left(\sqrt{b^2-4 c d}-b\right)^2 c+8 b \left(\sqrt{b^2-4 c d}-b\right) c\right)}\right) c^3}{\left(b^2-4 c d\right)^{3/2} \left(4 a c^2+\left(\sqrt{b^2-4 c d}-b\right)^2 c+2 b \left(\sqrt{b^2-4 c d}-b\right) c\right) \sqrt{a+x (b+c x)}}+\frac{4 \sqrt{c x^2+b x+a} \left(\frac{\sqrt{c x^2+b x+a} \left(2 c^2 \left(b+\sqrt{b^2-4 c d}\right)-2 c^2 \left(b-2 \sqrt{b^2-4 c d}\right)\right)}{\left(4 a c^2+\left(b+\sqrt{b^2-4 c d}\right)^2 c-2 b \left(b+\sqrt{b^2-4 c d}\right) c\right) \left(b+2 c x+\sqrt{b^2-4 c d}\right)}+\frac{4 c \sqrt{a-d} \left(b \left(2 \left(b-2 \sqrt{b^2-4 c d}\right) c^2+2 \left(b+\sqrt{b^2-4 c d}\right) c^2\right)-2 \left(4 a c^3+\left(b-2 \sqrt{b^2-4 c d}\right) \left(b+\sqrt{b^2-4 c d}\right) c^2\right)\right) \tanh ^{-1}\left(\frac{4 a c-b \left(b+\sqrt{b^2-4 c d}\right)-\left(2 c \left(b+\sqrt{b^2-4 c d}\right)-2 b c\right) x}{4 c \sqrt{a-d} \sqrt{c x^2+b x+a}}\right)}{\left(4 a c^2+\left(b+\sqrt{b^2-4 c d}\right)^2 c-2 b \left(b+\sqrt{b^2-4 c d}\right) c\right) \left(16 a c^2+4 \left(b+\sqrt{b^2-4 c d}\right)^2 c-8 b \left(b+\sqrt{b^2-4 c d}\right) c\right)}\right) c^3}{\left(b^2-4 c d\right)^{3/2} \left(4 a c^2+\left(b+\sqrt{b^2-4 c d}\right)^2 c-2 b \left(b+\sqrt{b^2-4 c d}\right) c\right) \sqrt{a+x (b+c x)}}+\frac{6 \sqrt{c x^2+b x+a} \tanh ^{-1}\left(\frac{b^2-\sqrt{b^2-4 c d} b-4 a c-2 c \sqrt{b^2-4 c d} x}{4 c \sqrt{a-d} \sqrt{c x^2+b x+a}}\right) c^2}{\sqrt{a-d} \left(b^2-4 c d\right)^{5/2} \sqrt{a+x (b+c x)}}+\frac{6 \sqrt{c x^2+b x+a} \tanh ^{-1}\left(\frac{4 a c-2 \sqrt{b^2-4 c d} x c-b \left(b+\sqrt{b^2-4 c d}\right)}{4 c \sqrt{a-d} \sqrt{c x^2+b x+a}}\right) c^2}{\sqrt{a-d} \left(b^2-4 c d\right)^{5/2} \sqrt{a+x (b+c x)}}+\frac{6 \left(c x^2+b x+a\right) c^2}{(a-d) \left(b^2-4 c d\right)^2 \left(b+2 c x-\sqrt{b^2-4 c d}\right) \sqrt{a+x (b+c x)}}+\frac{6 \left(c x^2+b x+a\right) c^2}{(a-d) \left(b^2-4 c d\right)^2 \left(b+2 c x+\sqrt{b^2-4 c d}\right) \sqrt{a+x (b+c x)}}-\frac{2 \left(c x^2+b x+a\right) c^2}{(a-d) \left(b^2-4 c d\right)^{3/2} \left(b+2 c x-\sqrt{b^2-4 c d}\right)^2 \sqrt{a+x (b+c x)}}+\frac{2 \left(c x^2+b x+a\right) c^2}{(a-d) \left(b^2-4 c d\right)^{3/2} \left(b+2 c x+\sqrt{b^2-4 c d}\right)^2 \sqrt{a+x (b+c x)}}+\frac{3 \sqrt{c x^2+b x+a} \tanh ^{-1}\left(\frac{b^2-\sqrt{b^2-4 c d} b-4 a c-2 c \sqrt{b^2-4 c d} x}{4 c \sqrt{a-d} \sqrt{c x^2+b x+a}}\right) c}{2 (a-d)^{3/2} \left(b^2-4 c d\right)^{3/2} \sqrt{a+x (b+c x)}}+\frac{3 \sqrt{c x^2+b x+a} \tanh ^{-1}\left(\frac{4 a c-2 \sqrt{b^2-4 c d} x c-b \left(b+\sqrt{b^2-4 c d}\right)}{4 c \sqrt{a-d} \sqrt{c x^2+b x+a}}\right) c}{2 (a-d)^{3/2} \left(b^2-4 c d\right)^{3/2} \sqrt{a+x (b+c 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}",1,"(-2*c^2*(a + b*x + c*x^2))/((a - d)*(b^2 - 4*c*d)^(3/2)*(b - Sqrt[b^2 - 4*c*d] + 2*c*x)^2*Sqrt[a + x*(b + c*x)]) + (6*c^2*(a + b*x + c*x^2))/((a - d)*(b^2 - 4*c*d)^2*(b - Sqrt[b^2 - 4*c*d] + 2*c*x)*Sqrt[a + x*(b + c*x)]) + (2*c^2*(a + b*x + c*x^2))/((a - d)*(b^2 - 4*c*d)^(3/2)*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)^2*Sqrt[a + x*(b + c*x)]) + (6*c^2*(a + b*x + c*x^2))/((a - d)*(b^2 - 4*c*d)^2*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)*Sqrt[a + x*(b + c*x)]) + (6*c^2*Sqrt[a + b*x + c*x^2]*ArcTanh[(b^2 - 4*a*c - b*Sqrt[b^2 - 4*c*d] - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/(Sqrt[a - d]*(b^2 - 4*c*d)^(5/2)*Sqrt[a + x*(b + c*x)]) + (3*c*Sqrt[a + b*x + c*x^2]*ArcTanh[(b^2 - 4*a*c - b*Sqrt[b^2 - 4*c*d] - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/(2*(a - d)^(3/2)*(b^2 - 4*c*d)^(3/2)*Sqrt[a + x*(b + c*x)]) + (6*c^2*Sqrt[a + b*x + c*x^2]*ArcTanh[(4*a*c - b*(b + Sqrt[b^2 - 4*c*d]) - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/(Sqrt[a - d]*(b^2 - 4*c*d)^(5/2)*Sqrt[a + x*(b + c*x)]) + (3*c*Sqrt[a + b*x + c*x^2]*ArcTanh[(4*a*c - b*(b + Sqrt[b^2 - 4*c*d]) - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/(2*(a - d)^(3/2)*(b^2 - 4*c*d)^(3/2)*Sqrt[a + x*(b + c*x)]) + (4*c^3*Sqrt[a + b*x + c*x^2]*(((-2*c^2*(-b + Sqrt[b^2 - 4*c*d]) - 2*c^2*(b + 2*Sqrt[b^2 - 4*c*d]))*Sqrt[a + b*x + c*x^2])/((4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*(-b + Sqrt[b^2 - 4*c*d] - 2*c*x)) + (4*c*Sqrt[a - d]*(b*(-2*c^2*(-b + Sqrt[b^2 - 4*c*d]) + 2*c^2*(b + 2*Sqrt[b^2 - 4*c*d])) - 2*(4*a*c^3 - c^2*(-b + Sqrt[b^2 - 4*c*d])*(b + 2*Sqrt[b^2 - 4*c*d])))*ArcTanh[(-4*a*c - b*(-b + Sqrt[b^2 - 4*c*d]) - (2*b*c + 2*c*(-b + Sqrt[b^2 - 4*c*d]))*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/((4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*(16*a*c^2 + 8*b*c*(-b + Sqrt[b^2 - 4*c*d]) + 4*c*(-b + Sqrt[b^2 - 4*c*d])^2))))/((b^2 - 4*c*d)^(3/2)*(4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*Sqrt[a + x*(b + c*x)]) + (4*c^3*Sqrt[a + b*x + c*x^2]*(((-2*c^2*(b - 2*Sqrt[b^2 - 4*c*d]) + 2*c^2*(b + Sqrt[b^2 - 4*c*d]))*Sqrt[a + b*x + c*x^2])/((4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)) + (4*c*Sqrt[a - d]*(b*(2*c^2*(b - 2*Sqrt[b^2 - 4*c*d]) + 2*c^2*(b + Sqrt[b^2 - 4*c*d])) - 2*(4*a*c^3 + c^2*(b - 2*Sqrt[b^2 - 4*c*d])*(b + Sqrt[b^2 - 4*c*d])))*ArcTanh[(4*a*c - b*(b + Sqrt[b^2 - 4*c*d]) - (-2*b*c + 2*c*(b + Sqrt[b^2 - 4*c*d]))*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/((4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*(16*a*c^2 - 8*b*c*(b + Sqrt[b^2 - 4*c*d]) + 4*c*(b + Sqrt[b^2 - 4*c*d])^2))))/((b^2 - 4*c*d)^(3/2)*(4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*Sqrt[a + x*(b + c*x)])","B",1
6,1,3382,328,6.6068511,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+b x+c x^2\right)^4} \, dx","Integrate[1/(Sqrt[a + b*x + c*x^2]*(d + b*x + c*x^2)^4),x]","\text{Result too large to show}","-\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,"(-8*c^3*(a + b*x + c*x^2))/(3*(a - d)*(b^2 - 4*c*d)^2*(b - Sqrt[b^2 - 4*c*d] + 2*c*x)^3*Sqrt[a + x*(b + c*x)]) + (8*c^3*(a + b*x + c*x^2))/((a - d)*(b^2 - 4*c*d)^(5/2)*(b - Sqrt[b^2 - 4*c*d] + 2*c*x)^2*Sqrt[a + x*(b + c*x)]) - (20*c^3*(a + b*x + c*x^2))/((a - d)*(b^2 - 4*c*d)^3*(b - Sqrt[b^2 - 4*c*d] + 2*c*x)*Sqrt[a + x*(b + c*x)]) - (8*c^3*(a + b*x + c*x^2))/(3*(a - d)*(b^2 - 4*c*d)^2*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)^3*Sqrt[a + x*(b + c*x)]) - (8*c^3*(a + b*x + c*x^2))/((a - d)*(b^2 - 4*c*d)^(5/2)*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)^2*Sqrt[a + x*(b + c*x)]) - (20*c^3*(a + b*x + c*x^2))/((a - d)*(b^2 - 4*c*d)^3*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)*Sqrt[a + x*(b + c*x)]) - (20*c^3*Sqrt[a + b*x + c*x^2]*ArcTanh[(b^2 - 4*a*c - b*Sqrt[b^2 - 4*c*d] - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/(Sqrt[a - d]*(b^2 - 4*c*d)^(7/2)*Sqrt[a + x*(b + c*x)]) - (5*c^2*Sqrt[a + b*x + c*x^2]*ArcTanh[(b^2 - 4*a*c - b*Sqrt[b^2 - 4*c*d] - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/((a - d)^(3/2)*(b^2 - 4*c*d)^(5/2)*Sqrt[a + x*(b + c*x)]) - (20*c^3*Sqrt[a + b*x + c*x^2]*ArcTanh[(4*a*c - b*(b + Sqrt[b^2 - 4*c*d]) - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/(Sqrt[a - d]*(b^2 - 4*c*d)^(7/2)*Sqrt[a + x*(b + c*x)]) - (5*c^2*Sqrt[a + b*x + c*x^2]*ArcTanh[(4*a*c - b*(b + Sqrt[b^2 - 4*c*d]) - 2*c*Sqrt[b^2 - 4*c*d]*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/((a - d)^(3/2)*(b^2 - 4*c*d)^(5/2)*Sqrt[a + x*(b + c*x)]) - (16*c^4*Sqrt[a + b*x + c*x^2]*(((-2*c^2*(-b + Sqrt[b^2 - 4*c*d]) - 2*c^2*(b + 2*Sqrt[b^2 - 4*c*d]))*Sqrt[a + b*x + c*x^2])/((4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*(-b + Sqrt[b^2 - 4*c*d] - 2*c*x)) + (4*c*Sqrt[a - d]*(b*(-2*c^2*(-b + Sqrt[b^2 - 4*c*d]) + 2*c^2*(b + 2*Sqrt[b^2 - 4*c*d])) - 2*(4*a*c^3 - c^2*(-b + Sqrt[b^2 - 4*c*d])*(b + 2*Sqrt[b^2 - 4*c*d])))*ArcTanh[(-4*a*c - b*(-b + Sqrt[b^2 - 4*c*d]) - (2*b*c + 2*c*(-b + Sqrt[b^2 - 4*c*d]))*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/((4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*(16*a*c^2 + 8*b*c*(-b + Sqrt[b^2 - 4*c*d]) + 4*c*(-b + Sqrt[b^2 - 4*c*d])^2))))/((b^2 - 4*c*d)^(5/2)*(4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*Sqrt[a + x*(b + c*x)]) - (16*c^4*Sqrt[a + b*x + c*x^2]*(-1/2*((4*c^2*(-b + Sqrt[b^2 - 4*c*d]) + 2*c^2*(2*b + 3*Sqrt[b^2 - 4*c*d]))*Sqrt[a + b*x + c*x^2])/((4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*(-b + Sqrt[b^2 - 4*c*d] - 2*c*x)^2) - (((10*c^3*Sqrt[b^2 - 4*c*d]*(-b + Sqrt[b^2 - 4*c*d]) + 2*c^3*(10*b^2 - 16*a*c - 24*c*d + 5*b*Sqrt[b^2 - 4*c*d]))*Sqrt[a + b*x + c*x^2])/((4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*(-b + Sqrt[b^2 - 4*c*d] - 2*c*x)) + (4*c*Sqrt[a - d]*(b*(10*c^3*Sqrt[b^2 - 4*c*d]*(-b + Sqrt[b^2 - 4*c*d]) - 2*c^3*(10*b^2 - 16*a*c - 24*c*d + 5*b*Sqrt[b^2 - 4*c*d])) - 2*(-20*a*c^4*Sqrt[b^2 - 4*c*d] + c^3*(-b + Sqrt[b^2 - 4*c*d])*(10*b^2 - 16*a*c - 24*c*d + 5*b*Sqrt[b^2 - 4*c*d])))*ArcTanh[(-4*a*c - b*(-b + Sqrt[b^2 - 4*c*d]) - (2*b*c + 2*c*(-b + Sqrt[b^2 - 4*c*d]))*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/((4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*(16*a*c^2 + 8*b*c*(-b + Sqrt[b^2 - 4*c*d]) + 4*c*(-b + Sqrt[b^2 - 4*c*d])^2)))/(2*(4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2))))/(3*(b^2 - 4*c*d)^2*(4*a*c^2 + 2*b*c*(-b + Sqrt[b^2 - 4*c*d]) + c*(-b + Sqrt[b^2 - 4*c*d])^2)*Sqrt[a + x*(b + c*x)]) - (16*c^4*Sqrt[a + b*x + c*x^2]*(((-2*c^2*(b - 2*Sqrt[b^2 - 4*c*d]) + 2*c^2*(b + Sqrt[b^2 - 4*c*d]))*Sqrt[a + b*x + c*x^2])/((4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)) + (4*c*Sqrt[a - d]*(b*(2*c^2*(b - 2*Sqrt[b^2 - 4*c*d]) + 2*c^2*(b + Sqrt[b^2 - 4*c*d])) - 2*(4*a*c^3 + c^2*(b - 2*Sqrt[b^2 - 4*c*d])*(b + Sqrt[b^2 - 4*c*d])))*ArcTanh[(4*a*c - b*(b + Sqrt[b^2 - 4*c*d]) - (-2*b*c + 2*c*(b + Sqrt[b^2 - 4*c*d]))*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/((4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*(16*a*c^2 - 8*b*c*(b + Sqrt[b^2 - 4*c*d]) + 4*c*(b + Sqrt[b^2 - 4*c*d])^2))))/((b^2 - 4*c*d)^(5/2)*(4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*Sqrt[a + x*(b + c*x)]) - (16*c^4*Sqrt[a + b*x + c*x^2]*(-1/2*((2*c^2*(2*b - 3*Sqrt[b^2 - 4*c*d]) - 4*c^2*(b + Sqrt[b^2 - 4*c*d]))*Sqrt[a + b*x + c*x^2])/((4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)^2) - (((-10*c^3*Sqrt[b^2 - 4*c*d]*(b + Sqrt[b^2 - 4*c*d]) - 2*c^3*(10*b^2 - 16*a*c - 24*c*d - 5*b*Sqrt[b^2 - 4*c*d]))*Sqrt[a + b*x + c*x^2])/((4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*(b + Sqrt[b^2 - 4*c*d] + 2*c*x)) + (4*c*Sqrt[a - d]*(b*(-10*c^3*Sqrt[b^2 - 4*c*d]*(b + Sqrt[b^2 - 4*c*d]) + 2*c^3*(10*b^2 - 16*a*c - 24*c*d - 5*b*Sqrt[b^2 - 4*c*d])) - 2*(-20*a*c^4*Sqrt[b^2 - 4*c*d] + c^3*(b + Sqrt[b^2 - 4*c*d])*(10*b^2 - 16*a*c - 24*c*d - 5*b*Sqrt[b^2 - 4*c*d])))*ArcTanh[(4*a*c - b*(b + Sqrt[b^2 - 4*c*d]) - (-2*b*c + 2*c*(b + Sqrt[b^2 - 4*c*d]))*x)/(4*c*Sqrt[a - d]*Sqrt[a + b*x + c*x^2])])/((4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*(16*a*c^2 - 8*b*c*(b + Sqrt[b^2 - 4*c*d]) + 4*c*(b + Sqrt[b^2 - 4*c*d])^2)))/(2*(4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2))))/(3*(b^2 - 4*c*d)^2*(4*a*c^2 - 2*b*c*(b + Sqrt[b^2 - 4*c*d]) + c*(b + Sqrt[b^2 - 4*c*d])^2)*Sqrt[a + x*(b + c*x)])","B",0
7,1,490,162,1.9646208,"\int \frac{1}{\sqrt{d+e x+f x^2} \left(a e+b e x+b f x^2\right)^2} \, dx","Integrate[1/(Sqrt[d + e*x + f*x^2]*(a*e + b*e*x + b*f*x^2)^2),x]","\frac{2 f \left(-\frac{\left(b \left(4 d f+e^2\right)-8 a e f\right) \tanh ^{-1}\left(\frac{-\sqrt{e} (e+2 f x) \sqrt{b e-4 a f}-\sqrt{b} \left(e^2-4 d f\right)}{4 f \sqrt{b d-a e} \sqrt{d+x (e+f x)}}\right)}{4 f (b d-a e)^{3/2} (b e-4 a f)^{3/2}}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{b} \left(e^2-4 d f\right)-\sqrt{e} (e+2 f x) \sqrt{b e-4 a f}}{4 f \sqrt{b d-a e} \sqrt{d+x (e+f x)}}\right)}{4 f (b d-a e)^{3/2} \sqrt{b e-4 a f}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} (e+2 f x) \sqrt{b e-4 a f}-\sqrt{b} \left(e^2-4 d f\right)}{4 f \sqrt{b d-a e} \sqrt{d+x (e+f x)}}\right)}{\sqrt{b d-a e} (b e-4 a f)^{3/2}}-\frac{\sqrt{b} \sqrt{e} \sqrt{d+x (e+f x)}}{(b d-a e) (b e-4 a f) \left(\sqrt{b} (e+2 f x)-\sqrt{e} \sqrt{b e-4 a f}\right)}-\frac{\sqrt{b} \sqrt{e} \sqrt{d+x (e+f x)}}{(b d-a e) (b e-4 a f) \left(\sqrt{e} \sqrt{b e-4 a f}+\sqrt{b} (e+2 f x)\right)}\right)}{e^{3/2}}","-\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,"(2*f*(-((Sqrt[b]*Sqrt[e]*Sqrt[d + x*(e + f*x)])/((b*d - a*e)*(b*e - 4*a*f)*(-(Sqrt[e]*Sqrt[b*e - 4*a*f]) + Sqrt[b]*(e + 2*f*x)))) - (Sqrt[b]*Sqrt[e]*Sqrt[d + x*(e + f*x)])/((b*d - a*e)*(b*e - 4*a*f)*(Sqrt[e]*Sqrt[b*e - 4*a*f] + Sqrt[b]*(e + 2*f*x))) - ((-8*a*e*f + b*(e^2 + 4*d*f))*ArcTanh[(-(Sqrt[b]*(e^2 - 4*d*f)) - Sqrt[e]*Sqrt[b*e - 4*a*f]*(e + 2*f*x))/(4*Sqrt[b*d - a*e]*f*Sqrt[d + x*(e + f*x)])])/(4*(b*d - a*e)^(3/2)*f*(b*e - 4*a*f)^(3/2)) - (e*ArcTanh[(Sqrt[b]*(e^2 - 4*d*f) - Sqrt[e]*Sqrt[b*e - 4*a*f]*(e + 2*f*x))/(4*Sqrt[b*d - a*e]*f*Sqrt[d + x*(e + f*x)])])/(4*(b*d - a*e)^(3/2)*f*Sqrt[b*e - 4*a*f]) + ArcTanh[(-(Sqrt[b]*(e^2 - 4*d*f)) + Sqrt[e]*Sqrt[b*e - 4*a*f]*(e + 2*f*x))/(4*Sqrt[b*d - a*e]*f*Sqrt[d + x*(e + f*x)])]/(Sqrt[b*d - a*e]*(b*e - 4*a*f)^(3/2))))/e^(3/2)","B",1
8,1,84,28,0.0736418,"\int \frac{1}{\left(4+2 x+x^2\right) \sqrt{5+2 x+x^2}} \, dx","Integrate[1/((4 + 2*x + x^2)*Sqrt[5 + 2*x + x^2]),x]","-\frac{i \left(\tanh ^{-1}\left(\frac{-i \sqrt{3} x-i \sqrt{3}+4}{\sqrt{x^2+2 x+5}}\right)-\tanh ^{-1}\left(\frac{i \sqrt{3} x+i \sqrt{3}+4}{\sqrt{x^2+2 x+5}}\right)\right)}{2 \sqrt{3}}","\frac{\tan ^{-1}\left(\frac{x+1}{\sqrt{3} \sqrt{x^2+2 x+5}}\right)}{\sqrt{3}}",1,"((-1/2*I)*(ArcTanh[(4 - I*Sqrt[3] - I*Sqrt[3]*x)/Sqrt[5 + 2*x + x^2]] - ArcTanh[(4 + I*Sqrt[3] + I*Sqrt[3]*x)/Sqrt[5 + 2*x + x^2]]))/Sqrt[3]","C",1
9,1,142,136,0.1433607,"\int \left(a+\frac{e x}{2}+c x^2\right)^p \left(2 a+e x+2 c x^2\right)^q \, dx","Integrate[(a + (e*x)/2 + c*x^2)^p*(2*a + e*x + 2*c*x^2)^q,x]","\frac{2^{q-2} \left(-\sqrt{e^2-16 a c}+4 c x+e\right) \left(\frac{\sqrt{e^2-16 a c}+4 c x+e}{\sqrt{e^2-16 a c}}\right)^{-p-q} (2 a+x (2 c x+e))^{p+q} \, _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)}{c (p+q+1)}","-\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^(-2 + q)*(e - Sqrt[-16*a*c + e^2] + 4*c*x)*((e + Sqrt[-16*a*c + e^2] + 4*c*x)/Sqrt[-16*a*c + e^2])^(-p - q)*(2*a + x*(e + 2*c*x))^(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])])/(c*(1 + p + q))","A",1
10,1,172,200,0.2431072,"\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","Integrate[(a + (c*e*x)/f + c*x^2)^p*((a*f)/c + e*x + f*x^2)^q,x]","\frac{2^{p+q-1} \left(\sqrt{c} (e+2 f x)-\sqrt{c e^2-4 a f^2}\right) \left(a+\frac{c x (e+f x)}{f}\right)^p \left(\frac{a f}{c}+x (e+f x)\right)^q \left(\frac{\sqrt{c} (e+2 f x)}{\sqrt{c e^2-4 a f^2}}+1\right)^{-p-q} \, _2F_1\left(-p-q,p+q+1;p+q+2;\frac{1}{2}-\frac{\sqrt{c} (e+2 f x)}{2 \sqrt{c e^2-4 a f^2}}\right)}{\sqrt{c} f (p+q+1)}","-\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)*((a*f)/c + x*(e + f*x))^q*(a + (c*x*(e + f*x))/f)^p*(-Sqrt[c*e^2 - 4*a*f^2] + Sqrt[c]*(e + 2*f*x))*(1 + (Sqrt[c]*(e + 2*f*x))/Sqrt[c*e^2 - 4*a*f^2])^(-p - q)*Hypergeometric2F1[-p - q, 1 + p + q, 2 + p + q, 1/2 - (Sqrt[c]*(e + 2*f*x))/(2*Sqrt[c*e^2 - 4*a*f^2])])/(Sqrt[c]*f*(1 + p + q))","A",1
11,1,27,48,0.0201257,"\int \frac{\sqrt{1+2 x+x^2}}{\sqrt{1+x^2}} \, dx","Integrate[Sqrt[1 + 2*x + x^2]/Sqrt[1 + x^2],x]","\frac{\sqrt{(x+1)^2} \left(\sqrt{x^2+1}+\sinh ^{-1}(x)\right)}{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 + x^2] + ArcSinh[x]))/(1 + x)","A",1
12,1,66,70,0.0875261,"\int \frac{1}{\left(-1+x^2\right)^2 \sqrt{-1+x+x^2}} \, dx","Integrate[1/((-1 + x^2)^2*Sqrt[-1 + x + x^2]),x]","\frac{1}{8} \left(-\frac{4 \sqrt{x^2+x-1}}{x^2-1}-\tan ^{-1}\left(\frac{x+3}{2 \sqrt{x^2+x-1}}\right)-5 \tanh ^{-1}\left(\frac{1-3 x}{2 \sqrt{x^2+x-1}}\right)\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,"((-4*Sqrt[-1 + x + x^2])/(-1 + x^2) - ArcTan[(3 + x)/(2*Sqrt[-1 + x + x^2])] - 5*ArcTanh[(1 - 3*x)/(2*Sqrt[-1 + x + x^2])])/8","A",1
13,1,600,1077,1.6394814,"\int \frac{1}{\sqrt{a+b x+c x^2} \sqrt{d+f x^2}} \, dx","Integrate[1/(Sqrt[a + b*x + c*x^2]*Sqrt[d + f*x^2]),x]","-\frac{2 \sqrt{2} \left(\sqrt{f} x-i \sqrt{d}\right) \left(\sqrt{b^2-4 a c}-b-2 c x\right) \sqrt{-\frac{c \sqrt{b^2-4 a c} \left(\sqrt{f} x+i \sqrt{d}\right)}{\left(\sqrt{b^2-4 a c}-b-2 c x\right) \left(\sqrt{f} \left(\sqrt{b^2-4 a c}+b\right)-2 i c \sqrt{d}\right)}} \sqrt{\frac{c \left(-i \sqrt{d} \left(\sqrt{b^2-4 a c}+2 c x\right)+\sqrt{f} \left(x \sqrt{b^2-4 a c}-2 a\right)+b \left(-\sqrt{f} x-i \sqrt{d}\right)\right)}{\left(\sqrt{b^2-4 a c}-b-2 c x\right) \left(\sqrt{f} \left(\sqrt{b^2-4 a c}+b\right)+2 i c \sqrt{d}\right)}} F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\left(\sqrt{b^2-4 a c}-b\right) \sqrt{f}-2 i c \sqrt{d}\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{\left(2 i \sqrt{d} c+\left(b+\sqrt{b^2-4 a c}\right) \sqrt{f}\right) \left(-b-2 c x+\sqrt{b^2-4 a c}\right)}}\right)|\frac{c d-i \sqrt{b^2-4 a c} \sqrt{f} \sqrt{d}+a f}{c d+i \sqrt{b^2-4 a c} \sqrt{f} \sqrt{d}+a f}\right)}{\sqrt{d+f x^2} \sqrt{a+x (b+c x)} \left(\sqrt{f} \left(\sqrt{b^2-4 a c}-b\right)-2 i c \sqrt{d}\right) \sqrt{\frac{i c \sqrt{b^2-4 a c} \left(\sqrt{d}+i \sqrt{f} x\right)}{\left(\sqrt{b^2-4 a c}-b-2 c x\right) \left(\sqrt{f} \left(\sqrt{b^2-4 a c}+b\right)+2 i c \sqrt{d}\right)}}}","-\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,"(-2*Sqrt[2]*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x)*((-I)*Sqrt[d] + Sqrt[f]*x)*Sqrt[-((c*Sqrt[b^2 - 4*a*c]*(I*Sqrt[d] + Sqrt[f]*x))/(((-2*I)*c*Sqrt[d] + (b + Sqrt[b^2 - 4*a*c])*Sqrt[f])*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x)))]*Sqrt[(c*((-I)*Sqrt[d]*(Sqrt[b^2 - 4*a*c] + 2*c*x) + Sqrt[f]*(-2*a + Sqrt[b^2 - 4*a*c]*x) + b*((-I)*Sqrt[d] - Sqrt[f]*x)))/(((2*I)*c*Sqrt[d] + (b + Sqrt[b^2 - 4*a*c])*Sqrt[f])*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x))]*EllipticF[ArcSin[Sqrt[(((-2*I)*c*Sqrt[d] + (-b + Sqrt[b^2 - 4*a*c])*Sqrt[f])*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(((2*I)*c*Sqrt[d] + (b + Sqrt[b^2 - 4*a*c])*Sqrt[f])*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x))]], (c*d - I*Sqrt[b^2 - 4*a*c]*Sqrt[d]*Sqrt[f] + a*f)/(c*d + I*Sqrt[b^2 - 4*a*c]*Sqrt[d]*Sqrt[f] + a*f)])/(((-2*I)*c*Sqrt[d] + (-b + Sqrt[b^2 - 4*a*c])*Sqrt[f])*Sqrt[(I*c*Sqrt[b^2 - 4*a*c]*(Sqrt[d] + I*Sqrt[f]*x))/(((2*I)*c*Sqrt[d] + (b + Sqrt[b^2 - 4*a*c])*Sqrt[f])*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x))]*Sqrt[d + f*x^2]*Sqrt[a + x*(b + c*x)])","C",1
14,1,159,98,0.3949925,"\int \frac{\sqrt{-3-4 x-x^2}}{3+4 x+2 x^2} \, dx","Integrate[Sqrt[-3 - 4*x - x^2]/(3 + 4*x + 2*x^2),x]","\frac{1}{4} \left(-i \sqrt{1-2 i \sqrt{2}} \tanh ^{-1}\left(\frac{i \sqrt{2} x+2 x+2 i \sqrt{2}+2}{\sqrt{2-4 i \sqrt{2}} \sqrt{-x^2-4 x-3}}\right)+i \sqrt{1+2 i \sqrt{2}} \tanh ^{-1}\left(\frac{\left(2-i \sqrt{2}\right) x-2 i \sqrt{2}+2}{\sqrt{2+4 i \sqrt{2}} \sqrt{-x^2-4 x-3}}\right)-2 \sin ^{-1}(x+2)\right)","-\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,"(-2*ArcSin[2 + x] - I*Sqrt[1 - (2*I)*Sqrt[2]]*ArcTanh[(2 + (2*I)*Sqrt[2] + 2*x + I*Sqrt[2]*x)/(Sqrt[2 - (4*I)*Sqrt[2]]*Sqrt[-3 - 4*x - x^2])] + I*Sqrt[1 + (2*I)*Sqrt[2]]*ArcTanh[(2 - (2*I)*Sqrt[2] + (2 - I*Sqrt[2])*x)/(Sqrt[2 + (4*I)*Sqrt[2]]*Sqrt[-3 - 4*x - x^2])])/4","C",1
15,1,68,68,0.0028037,"\int \left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^4 \, dx","Integrate[(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",1
16,1,56,56,0.00164,"\int \left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^3 \, dx","Integrate[(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",1
17,1,44,44,0.0010496,"\int \left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^2 \, dx","Integrate[(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",1
18,1,30,30,0.0011217,"\int \left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right) \, dx","Integrate[(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",1
19,1,42,42,0.0160952,"\int \frac{3-x+2 x^2}{2+3 x+5 x^2} \, dx","Integrate[(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",1
20,1,43,43,0.0152197,"\int \frac{3-x+2 x^2}{\left(2+3 x+5 x^2\right)^2} \, dx","Integrate[(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",1
21,1,53,64,0.0257738,"\int \frac{3-x+2 x^2}{\left(2+3 x+5 x^2\right)^3} \, dx","Integrate[(3 - x + 2*x^2)/(2 + 3*x + 5*x^2)^3,x]","\frac{\frac{31 \left(5530 x^3+4977 x^2+4094 x+1141\right)}{\left(5 x^2+3 x+2\right)^2}+2212 \sqrt{31} \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{59582}","\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,"((31*(1141 + 4094*x + 4977*x^2 + 5530*x^3))/(2 + 3*x + 5*x^2)^2 + 2212*Sqrt[31]*ArcTan[(3 + 10*x)/Sqrt[31]])/59582","A",1
22,1,80,80,0.0030611,"\int \left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^4 \, dx","Integrate[(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",1
23,1,66,66,0.0021628,"\int \left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^3 \, dx","Integrate[(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",1
24,1,54,54,0.0017218,"\int \left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^2 \, dx","Integrate[(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",1
25,1,46,46,0.0009552,"\int \left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right) \, dx","Integrate[(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",1
26,1,53,56,0.0195105,"\int \frac{\left(3-x+2 x^2\right)^2}{2+3 x+5 x^2} \, dx","Integrate[(3 - x + 2*x^2)^2/(2 + 3*x + 5*x^2),x]","\frac{10 x \left(100 x^2-240 x+1143\right)-4719 \log \left(5 x^2+3 x+2\right)}{3750}+\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,"(8349*ArcTan[(3 + 10*x)/Sqrt[31]])/(625*Sqrt[31]) + (10*x*(1143 - 240*x + 100*x^2) - 4719*Log[2 + 3*x + 5*x^2])/3750","A",1
27,1,59,63,0.0317045,"\int \frac{\left(3-x+2 x^2\right)^2}{\left(2+3 x+5 x^2\right)^2} \, dx","Integrate[(3 - x + 2*x^2)^2/(2 + 3*x + 5*x^2)^2,x]","\frac{\frac{3751 (69 x+61)}{5 x^2+3 x+2}-21142 \log \left(5 x^2+3 x+2\right)+19220 x+41932 \sqrt{31} \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{120125}","\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,"(19220*x + (3751*(61 + 69*x))/(2 + 3*x + 5*x^2) + 41932*Sqrt[31]*ArcTan[(3 + 10*x)/Sqrt[31]] - 21142*Log[2 + 3*x + 5*x^2])/120125","A",1
28,1,53,64,0.0240563,"\int \frac{\left(3-x+2 x^2\right)^2}{\left(2+3 x+5 x^2\right)^3} \, dx","Integrate[(3 - x + 2*x^2)^2/(2 + 3*x + 5*x^2)^3,x]","\frac{11 \left(45710 x^3+44983 x^2+33524 x+11183\right)}{48050 \left(5 x^2+3 x+2\right)^2}+\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,"(11*(11183 + 33524*x + 44983*x^2 + 45710*x^3))/(48050*(2 + 3*x + 5*x^2)^2) + (4330*ArcTan[(3 + 10*x)/Sqrt[31]])/(961*Sqrt[31])","A",1
29,1,63,85,0.0436188,"\int \frac{\left(3-x+2 x^2\right)^2}{\left(2+3 x+5 x^2\right)^4} \, dx","Integrate[(3 - x + 2*x^2)^2/(2 + 3*x + 5*x^2)^4,x]","\frac{12516000 x^5+18774000 x^4+21491796 x^3+12780597 x^2+5674908 x+1259239}{446865 \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,"(1259239 + 5674908*x + 12780597*x^2 + 21491796*x^3 + 18774000*x^4 + 12516000*x^5)/(446865*(2 + 3*x + 5*x^2)^3) + (66752*ArcTan[(3 + 10*x)/Sqrt[31]])/(29791*Sqrt[31])","A",1
30,1,96,96,0.0044427,"\int \left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^4 \, dx","Integrate[(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",1
31,1,82,82,0.0017185,"\int \left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^3 \, dx","Integrate[(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",1
32,1,68,68,0.0021763,"\int \left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^2 \, dx","Integrate[(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",1
33,1,56,56,0.0012105,"\int \left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right) \, dx","Integrate[(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",1
34,1,63,70,0.0227639,"\int \frac{\left(3-x+2 x^2\right)^3}{2+3 x+5 x^2} \, dx","Integrate[(3 - x + 2*x^2)^3/(2 + 3*x + 5*x^2),x]","\frac{31 \left(5 x \left(6000 x^4-15750 x^3+61100 x^2-111765 x+297048\right)-475167 \log \left(5 x^2+3 x+2\right)\right)+1972542 \sqrt{31} \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{2906250}","\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,"(1972542*Sqrt[31]*ArcTan[(3 + 10*x)/Sqrt[31]] + 31*(5*x*(297048 - 111765*x + 61100*x^2 - 15750*x^3 + 6000*x^4) - 475167*Log[2 + 3*x + 5*x^2]))/2906250","A",1
35,1,77,77,0.0271809,"\int \frac{\left(3-x+2 x^2\right)^3}{\left(2+3 x+5 x^2\right)^2} \, dx","Integrate[(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",1
36,1,78,84,0.0370058,"\int \frac{\left(3-x+2 x^2\right)^3}{\left(2+3 x+5 x^2\right)^3} \, dx","Integrate[(3 - x + 2*x^2)^3/(2 + 3*x + 5*x^2)^3,x]","\frac{\frac{3751 (342840 x+188381)}{5 x^2+3 x+2}+\frac{1279091 (247 x+443)}{\left(5 x^2+3 x+2\right)^2}-19662060 \log \left(5 x^2+3 x+2\right)+11916400 x+113411760 \sqrt{31} \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{186193750}","\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,"(11916400*x + (1279091*(443 + 247*x))/(2 + 3*x + 5*x^2)^2 + (3751*(188381 + 342840*x))/(2 + 3*x + 5*x^2) + 113411760*Sqrt[31]*ArcTan[(3 + 10*x)/Sqrt[31]] - 19662060*Log[2 + 3*x + 5*x^2])/186193750","A",1
37,1,72,84,0.0279565,"\int \frac{\left(2+3 x+5 x^2\right)^4}{3-x+2 x^2} \, dx","Integrate[(2 + 3*x + 5*x^2)^4/(3 - x + 2*x^2),x]","\frac{307461}{512} \log \left(2 x^2-x+3\right)+\frac{x \left(120000 x^6+406000 x^5+623280 x^4+262290 x^3-594412 x^2-603687 x+2576511\right)}{2688}-\frac{1156639 \tan ^{-1}\left(\frac{4 x-1}{\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,"(x*(2576511 - 603687*x - 594412*x^2 + 262290*x^3 + 623280*x^4 + 406000*x^5 + 120000*x^6))/2688 - (1156639*ArcTan[(-1 + 4*x)/Sqrt[23]])/(256*Sqrt[23]) + (307461*Log[3 - x + 2*x^2])/512","A",1
38,1,63,70,0.0209448,"\int \frac{\left(2+3 x+5 x^2\right)^3}{3-x+2 x^2} \, dx","Integrate[(2 + 3*x + 5*x^2)^3/(3 - x + 2*x^2),x]","\frac{1}{384} \left(3993 \log \left(2 x^2-x+3\right)+4 x \left(1200 x^4+3450 x^3+3860 x^2-2487 x-14385\right)\right)+\frac{59895 \tan ^{-1}\left(\frac{4 x-1}{\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,"(59895*ArcTan[(-1 + 4*x)/Sqrt[23]])/(64*Sqrt[23]) + (4*x*(-14385 - 2487*x + 3860*x^2 + 3450*x^3 + 1200*x^4) + 3993*Log[3 - x + 2*x^2])/384","A",1
39,1,52,56,0.017165,"\int \frac{\left(2+3 x+5 x^2\right)^2}{3-x+2 x^2} \, dx","Integrate[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2),x]","\frac{1}{24} x \left(100 x^2+255 x+153\right)-\frac{363}{32} \log \left(2 x^2-x+3\right)-\frac{847 \tan ^{-1}\left(\frac{4 x-1}{\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,"(x*(153 + 255*x + 100*x^2))/24 - (847*ArcTan[(-1 + 4*x)/Sqrt[23]])/(16*Sqrt[23]) - (363*Log[3 - x + 2*x^2])/32","A",1
40,1,42,42,0.0098017,"\int \frac{2+3 x+5 x^2}{3-x+2 x^2} \, dx","Integrate[(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{4 x-1}{\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",1
41,1,73,73,0.0316928,"\int \frac{1}{\left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)} \, dx","Integrate[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{4 x-1}{\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",1
42,1,94,94,0.0828722,"\int \frac{1}{\left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^2} \, dx","Integrate[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{4 x-1}{\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",1
43,1,104,115,0.1553601,"\int \frac{1}{\left(3-x+2 x^2\right) \left(2+3 x+5 x^2\right)^3} \, dx","Integrate[1/((3 - x + 2*x^2)*(2 + 3*x + 5*x^2)^3),x]","\frac{31 \left(-961 \log \left(2 x^2-x+3\right)+961 \log \left(5 x^2+3 x+2\right)+\frac{44 \left(108025 x^3+104430 x^2+89144 x+17210\right)}{\left(5 x^2+3 x+2\right)^2}\right)+1695586 \sqrt{31} \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{634429136}+\frac{45 \tan ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{10648 \sqrt{23}}","\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,"(45*ArcTan[(-1 + 4*x)/Sqrt[23]])/(10648*Sqrt[23]) + (1695586*Sqrt[31]*ArcTan[(3 + 10*x)/Sqrt[31]] + 31*((44*(17210 + 89144*x + 104430*x^2 + 108025*x^3))/(2 + 3*x + 5*x^2)^2 - 961*Log[3 - x + 2*x^2] + 961*Log[2 + 3*x + 5*x^2]))/634429136","A",1
44,1,91,91,0.0515098,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\left(3-x+2 x^2\right)^2} \, dx","Integrate[(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{4 x-1}{\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",1
45,1,77,77,0.0275698,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\left(3-x+2 x^2\right)^2} \, dx","Integrate[(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 (45 x-17)}{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{4 x-1}{\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",1
46,1,63,63,0.030857,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\left(3-x+2 x^2\right)^2} \, dx","Integrate[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2)^2,x]","-\frac{121 (7 x-19)}{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{4 x-1}{\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",1
47,1,43,43,0.0146179,"\int \frac{2+3 x+5 x^2}{\left(3-x+2 x^2\right)^2} \, dx","Integrate[(2 + 3*x + 5*x^2)/(3 - x + 2*x^2)^2,x]","\frac{82 \tan ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{23 \sqrt{23}}-\frac{11 (3 x+5)}{46 \left(2 x^2-x+3\right)}","-\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",1
48,1,94,94,0.061067,"\int \frac{1}{\left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)} \, dx","Integrate[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{4 x-1}{\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",1
49,1,106,127,0.057328,"\int \frac{1}{\left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^2} \, dx","Integrate[1/((3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^2),x]","\frac{9659011 \log \left(2 x^2-x+3\right)-9659011 \log \left(5 x^2+3 x+2\right)+\frac{31372 \left(6850 x^3-9275 x^2+11154 x-4342\right)}{10 x^4+x^3+16 x^2+7 x+6}-5322018 \sqrt{23} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)+13376294 \sqrt{31} \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{5413113112}","-\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,"((31372*(-4342 + 11154*x - 9275*x^2 + 6850*x^3))/(6 + 7*x + 16*x^2 + x^3 + 10*x^4) - 5322018*Sqrt[23]*ArcTan[(-1 + 4*x)/Sqrt[23]] + 13376294*Sqrt[31]*ArcTan[(3 + 10*x)/Sqrt[31]] + 9659011*Log[3 - x + 2*x^2] - 9659011*Log[2 + 3*x + 5*x^2])/5413113112","A",1
50,1,136,148,0.0759762,"\int \frac{1}{\left(3-x+2 x^2\right)^2 \left(2+3 x+5 x^2\right)^3} \, dx","Integrate[1/((3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^3),x]","\frac{90 x-11}{244904 \left(2 x^2-x+3\right)}+\frac{164380 x+67573}{10232728 \left(5 x^2+3 x+2\right)}+\frac{345 x-98}{30008 \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{4 x-1}{\sqrt{23}}\right)}{5387888 \sqrt{23}}+\frac{4464079 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{225120016 \sqrt{31}}","\frac{13-6 x}{506 \left(2 x^2-x+3\right) \left(5 x^2+3 x+2\right)^2}+\frac{3996965 x+1765599}{235352744 \left(5 x^2+3 x+2\right)}+\frac{5765 x-9446}{690184 \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,"(-11 + 90*x)/(244904*(3 - x + 2*x^2)) + (-98 + 345*x)/(30008*(2 + 3*x + 5*x^2)^2) + (67573 + 164380*x)/(10232728*(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",1
51,1,98,98,0.0379655,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\left(3-x+2 x^2\right)^3} \, dx","Integrate[(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{4 x-1}{\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",1
52,1,84,84,0.037134,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\left(3-x+2 x^2\right)^3} \, dx","Integrate[(2 + 3*x + 5*x^2)^3/(3 - x + 2*x^2)^3,x]","-\frac{121 (12828 x-21193)}{33856 \left(2 x^2-x+3\right)}+\frac{1331 (45 x-17)}{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{4 x-1}{\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",1
53,1,51,64,0.0292463,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\left(3-x+2 x^2\right)^3} \, dx","Integrate[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2)^3,x]","\frac{4330 \tan ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{529 \sqrt{23}}-\frac{11 \left(1660 x^3+4045 x^2+938 x+4909\right)}{4232 \left(-2 x^2+x-3\right)^2}","\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,"(-11*(4909 + 938*x + 4045*x^2 + 1660*x^3))/(4232*(-3 + x - 2*x^2)^2) + (4330*ArcTan[(-1 + 4*x)/Sqrt[23]])/(529*Sqrt[23])","A",1
54,1,51,64,0.0282038,"\int \frac{2+3 x+5 x^2}{\left(3-x+2 x^2\right)^3} \, dx","Integrate[(2 + 3*x + 5*x^2)/(3 - x + 2*x^2)^3,x]","\frac{\frac{46 \left(524 x^3-393 x^2+472 x-829\right)}{\left(-2 x^2+x-3\right)^2}+1048 \sqrt{23} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{48668}","-\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,"((46*(-829 + 472*x - 393*x^2 + 524*x^3))/(-3 + x - 2*x^2)^2 + 1048*Sqrt[23]*ArcTan[(-1 + 4*x)/Sqrt[23]])/48668","A",1
55,1,99,115,0.1606855,"\int \frac{1}{\left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)} \, dx","Integrate[1/((3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)),x]","\frac{713 \left(-62951 \log \left(2 x^2-x+3\right)+62951 \log \left(5 x^2+3 x+2\right)-\frac{44 \left(1492 x^3-7996 x^2+7381 x-14164\right)}{\left(-2 x^2+x-3\right)^2}\right)+3310986 \sqrt{23} \tan ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)+6010498 \sqrt{31} \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{8032361392}","\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,"(3310986*Sqrt[23]*ArcTan[(-1 + 4*x)/Sqrt[23]] + 6010498*Sqrt[31]*ArcTan[(3 + 10*x)/Sqrt[31]] + 713*((-44*(-14164 + 7381*x - 7996*x^2 + 1492*x^3))/(-3 + x - 2*x^2)^2 - 62951*Log[3 - x + 2*x^2] + 62951*Log[2 + 3*x + 5*x^2]))/8032361392","A",1
56,1,136,160,0.1243405,"\int \frac{1}{\left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^2} \, dx","Integrate[1/((3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)^2),x]","\frac{-2923 x-1782}{1408198 \left(2 x^2-x+3\right)}+\frac{1235 x-1474}{330088 \left(5 x^2+3 x+2\right)}+\frac{-14 x-31}{22264 \left(2 x^2-x+3\right)^2}+\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{4 x-1}{\sqrt{23}}\right)}{123921424 \sqrt{23}}+\frac{246757 \tan ^{-1}\left(\frac{10 x+3}{\sqrt{31}}\right)}{7261936 \sqrt{31}}","\frac{-252815 x-2328909}{174616552 \left(5 x^2+3 x+2\right)}+\frac{9665-1446 x}{512072 \left(2 x^2-x+3\right) \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,"(-31 - 14*x)/(22264*(3 - x + 2*x^2)^2) + (-1782 - 2923*x)/(1408198*(3 - x + 2*x^2)) + (-1474 + 1235*x)/(330088*(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",1
57,1,151,181,0.0952062,"\int \frac{1}{\left(3-x+2 x^2\right)^3 \left(2+3 x+5 x^2\right)^3} \, dx","Integrate[1/((3 - x + 2*x^2)^3*(2 + 3*x + 5*x^2)^3),x]","\frac{405 \log \left(2 x^2-x+3\right)}{1288408}-\frac{405 \log \left(5 x^2+3 x+2\right)}{1288408}+\frac{6850 x^3-9275 x^2+11154 x-4342}{345092 \left(10 x^4+x^3+16 x^2+7 x+6\right)^2}+\frac{5 \left(42842610 x^3-5711469 x^2+51156233 x+14085977\right)}{14886061058 \left(10 x^4+x^3+16 x^2+7 x+6\right)}+\frac{880575 \tan ^{-1}\left(\frac{4 x-1}{\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,"(-4342 + 11154*x - 9275*x^2 + 6850*x^3)/(345092*(6 + 7*x + 16*x^2 + x^3 + 10*x^4)^2) + (5*(14085977 + 51156233*x - 5711469*x^2 + 42842610*x^3))/(14886061058*(6 + 7*x + 16*x^2 + x^3 + 10*x^4)) + (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",1
58,1,85,208,0.2963604,"\int \sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^4 \, dx","Integrate[Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^4,x]","\frac{4 \sqrt{2 x^2-x+3} \left(1321205760000 x^9+3486515200000 x^8+6327795712000 x^7+7725962035200 x^6+7612808028160 x^5+5354741991424 x^4+2211683657856 x^3-174418077792 x^2+537752185764 x+3801512106459\right)-2604371039235 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{84557168640}","-\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{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{8267844569 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{134217728 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(3801512106459 + 537752185764*x - 174418077792*x^2 + 2211683657856*x^3 + 5354741991424*x^4 + 7612808028160*x^5 + 7725962035200*x^6 + 6327795712000*x^7 + 3486515200000*x^8 + 1321205760000*x^9) - 2604371039235*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/84557168640","A",1
59,1,75,166,0.1714447,"\int \sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^3 \, dx","Integrate[Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^3,x]","\frac{4 \sqrt{2 x^2-x+3} \left(3440640000 x^7+6955008000 x^6+10958233600 x^5+11212171264 x^4+9872163456 x^3+4583812128 x^2-1621307916 x-3957369321\right)-16340124255 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{880803840}","\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{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{155620231 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4194304 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(-3957369321 - 1621307916*x + 4583812128*x^2 + 9872163456*x^3 + 11212171264*x^4 + 10958233600*x^5 + 6955008000*x^6 + 3440640000*x^7) - 16340124255*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/880803840","A",1
60,1,65,124,0.1045797,"\int \sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^2 \, dx","Integrate[Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^2,x]","\frac{4 \sqrt{2 x^2-x+3} \left(204800 x^5+284672 x^4+408960 x^3+365536 x^2+328204 x-64023\right)+853599 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{196608}","\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{25}{12} \left(2 x^2-x+3\right)^{3/2} x^3+\frac{284533 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{32768 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(-64023 + 328204*x + 365536*x^2 + 408960*x^3 + 284672*x^4 + 204800*x^5) + 853599*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/196608","A",1
61,1,55,82,0.051842,"\int \sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right) \, dx","Integrate[Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2),x]","\frac{4 \sqrt{2 x^2-x+3} \left(1920 x^3+1376 x^2+2684 x+3261\right)-5589 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{6144}","\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,"(4*Sqrt[3 - x + 2*x^2]*(3261 + 2684*x + 1376*x^2 + 1920*x^3) - 5589*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/6144","A",1
62,1,185,174,0.4569926,"\int \frac{\sqrt{3-x+2 x^2}}{2+3 x+5 x^2} \, dx","Integrate[Sqrt[3 - x + 2*x^2]/(2 + 3*x + 5*x^2),x]","-\frac{1}{5} \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)-\frac{1}{5} i \sqrt{\frac{11}{62}} \left(\sqrt{13+i \sqrt{31}} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x-22 x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)-\sqrt{13-i \sqrt{31}} \tanh ^{-1}\left(\frac{4 i \sqrt{31} x-22 x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)\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,"-1/5*(Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]]) - (I/5)*Sqrt[11/62]*(Sqrt[13 + I*Sqrt[31]]*ArcTanh[(63 + I*Sqrt[31] - 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - Sqrt[13 - I*Sqrt[31]]*ArcTanh[(63 - I*Sqrt[31] - 22*x + (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])","C",1
63,1,214,188,1.0356506,"\int \frac{\sqrt{3-x+2 x^2}}{\left(2+3 x+5 x^2\right)^2} \, dx","Integrate[Sqrt[3 - x + 2*x^2]/(2 + 3*x + 5*x^2)^2,x]","\frac{\frac{27280 \sqrt{2 x^2-x+3} (10 x+3)}{5 x^2+3 x+2}+i \sqrt{286-22 i \sqrt{31}} \left(973 \sqrt{31}+1271 i\right) \tanh ^{-1}\left(\frac{4 i \sqrt{31} x-22 x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)-i \sqrt{286+22 i \sqrt{31}} \left(973 \sqrt{31}-1271 i\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{845680}","\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,"((27280*(3 + 10*x)*Sqrt[3 - x + 2*x^2])/(2 + 3*x + 5*x^2) + I*Sqrt[286 - (22*I)*Sqrt[31]]*(1271*I + 973*Sqrt[31])*ArcTanh[(63 - I*Sqrt[31] - 22*x + (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - I*Sqrt[286 + (22*I)*Sqrt[31]]*(-1271*I + 973*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/845680","C",1
64,1,299,223,2.0752926,"\int \frac{\sqrt{3-x+2 x^2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Integrate[Sqrt[3 - x + 2*x^2]/(2 + 3*x + 5*x^2)^3,x]","\frac{5 \left(\frac{i \sqrt{286+22 i \sqrt{31}} \left(258253 \sqrt{31}+1004586 i\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{\left(\sqrt{31}-13 i\right)^2}+\frac{2000 \left(1364 \left(\sqrt{31}+13 i\right) \sqrt{2 x^2-x+3} \left(68325 x^3+58315 x^2+51362 x+11020\right)-5 \sqrt{286-22 i \sqrt{31}} \left(174475 \sqrt{31}-202151 i\right) \left(5 x^2+3 x+2\right)^2 \tanh ^{-1}\left(\frac{\left(-22+4 i \sqrt{31}\right) x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)\right)}{\left(\sqrt{31}-13 i\right) \left(\sqrt{31}+13 i\right)^2 \left(-10 i x+\sqrt{31}-3 i\right)^2 \left(10 i x+\sqrt{31}+3 i\right)^2}\right)}{14418844}","\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,"(5*((I*Sqrt[286 + (22*I)*Sqrt[31]]*(1004586*I + 258253*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(-13*I + Sqrt[31])^2 + (2000*(1364*(13*I + Sqrt[31])*Sqrt[3 - x + 2*x^2]*(11020 + 51362*x + 58315*x^2 + 68325*x^3) - 5*Sqrt[286 - (22*I)*Sqrt[31]]*(-202151*I + 174475*Sqrt[31])*(2 + 3*x + 5*x^2)^2*ArcTanh[(63 - I*Sqrt[31] + (-22 + (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])]))/((-13*I + Sqrt[31])*(13*I + Sqrt[31])^2*(-3*I + Sqrt[31] - (10*I)*x)^2*(3*I + Sqrt[31] + (10*I)*x)^2)))/14418844","C",1
65,1,95,231,0.3665419,"\int \left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^4 \, dx","Integrate[(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^4,x]","\frac{4 \sqrt{2 x^2-x+3} \left(70464307200000 x^{11}+144451829760000 x^{10}+349379651174400 x^9+534038708224000 x^8+745133229998080 x^7+765087080448000 x^6+675479464714240 x^5+451581382260736 x^4+239021184223104 x^3+65151998063712 x^2+12971175524316 x+74032009514181\right)-191024672914845 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2705829396480}","-\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{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{606427533063 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4294967296 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(74032009514181 + 12971175524316*x + 65151998063712*x^2 + 239021184223104*x^3 + 451581382260736*x^4 + 675479464714240*x^5 + 765087080448000*x^6 + 745133229998080*x^7 + 534038708224000*x^8 + 349379651174400*x^9 + 144451829760000*x^10 + 70464307200000*x^11) - 191024672914845*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/2705829396480","A",1
66,1,85,189,0.2306545,"\int \left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^3 \, dx","Integrate[(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^3,x]","\frac{4 \sqrt{2 x^2-x+3} \left(88080384000 x^9+124780544000 x^8+328328806400 x^7+430820229120 x^6+571298324480 x^5+487891884032 x^4+389257196928 x^3+199615064544 x^2+53985432012 x-72152399943\right)-111278019825 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{14092861440}","\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{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{1059790665 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{67108864 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(-72152399943 + 53985432012*x + 199615064544*x^2 + 389257196928*x^3 + 487891884032*x^4 + 571298324480*x^5 + 430820229120*x^6 + 328328806400*x^7 + 124780544000*x^8 + 88080384000*x^9) - 111278019825*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/14092861440","A",1
67,1,75,147,0.1414295,"\int \left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^2 \, dx","Integrate[(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^2,x]","\frac{4 \sqrt{2 x^2-x+3} \left(688128000 x^7+525926400 x^6+2025840640 x^5+2061273088 x^4+2728413312 x^3+1799647136 x^2+1619403428 x+439831323\right)+1349354685 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{440401920}","\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{25}{16} \left(2 x^2-x+3\right)^{5/2} x^3+\frac{12850997 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2097152 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(439831323 + 1619403428*x + 1799647136*x^2 + 2728413312*x^3 + 2061273088*x^4 + 2025840640*x^5 + 525926400*x^6 + 688128000*x^7) + 1349354685*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/440401920","A",1
68,1,65,105,0.0795784,"\int \left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right) \, dx","Integrate[(3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2),x]","\frac{4 \sqrt{2 x^2-x+3} \left(204800 x^5+14336 x^4+561024 x^3+319072 x^2+565276 x+388341\right)-1420365 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{491520}","\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,"(4*Sqrt[3 - x + 2*x^2]*(388341 + 565276*x + 319072*x^2 + 561024*x^3 + 14336*x^4 + 204800*x^5) - 1420365*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/491520","A",1
69,1,310,197,0.6933966,"\int \frac{\left(3-x+2 x^2\right)^{3/2}}{2+3 x+5 x^2} \, dx","Integrate[(3 - x + 2*x^2)^(3/2)/(2 + 3*x + 5*x^2),x]","\frac{400 \sqrt{31} \sqrt{2 x^2-x+3} x-980 \sqrt{31} \sqrt{2 x^2-x+3}+44 \sqrt{286+22 i \sqrt{31}} \left(\sqrt{31}-13 i\right) \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x-22 x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+572 i \sqrt{286-22 i \sqrt{31}} \tanh ^{-1}\left(\frac{4 i \sqrt{31} x-22 x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+44 \sqrt{682 \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{4 i \sqrt{31} x-22 x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)-2203 \sqrt{62} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2000 \sqrt{31}}","-\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,"(-980*Sqrt[31]*Sqrt[3 - x + 2*x^2] + 400*Sqrt[31]*x*Sqrt[3 - x + 2*x^2] - 2203*Sqrt[62]*ArcSinh[(1 - 4*x)/Sqrt[23]] + 44*Sqrt[286 + (22*I)*Sqrt[31]]*(-13*I + Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] - 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 44*Sqrt[682*(13 - I*Sqrt[31])]*ArcTanh[(63 - I*Sqrt[31] - 22*x + (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + (572*I)*Sqrt[286 - (22*I)*Sqrt[31]]*ArcTanh[(63 - I*Sqrt[31] - 22*x + (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(2000*Sqrt[31])","C",1
70,1,530,232,2.56212,"\int \frac{\left(3-x+2 x^2\right)^{3/2}}{\left(2+3 x+5 x^2\right)^2} \, dx","Integrate[(3 - x + 2*x^2)^(3/2)/(2 + 3*x + 5*x^2)^2,x]","\frac{\frac{62000 \sqrt{2 x^2-x+3} x^2}{10 x-i \sqrt{31}+3}+\frac{62000 \sqrt{2 x^2-x+3} x^2}{10 x+i \sqrt{31}+3}-\frac{31000 \sqrt{2 x^2-x+3} x}{10 x-i \sqrt{31}+3}-\frac{31000 \sqrt{2 x^2-x+3} x}{10 x+i \sqrt{31}+3}-12400 \sqrt{2 x^2-x+3} x+\frac{93000 \sqrt{2 x^2-x+3}}{10 x-i \sqrt{31}+3}+\frac{93000 \sqrt{2 x^2-x+3}}{10 x+i \sqrt{31}+3}+9920 \sqrt{2 x^2-x+3}-\frac{\sqrt{286+22 i \sqrt{31}} \left(6477 \sqrt{31}+10199 i\right) \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x-22 x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{\sqrt{31}-13 i}+\frac{10199 i \sqrt{286-22 i \sqrt{31}} \tanh ^{-1}\left(\frac{4 i \sqrt{31} x-22 x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{\sqrt{31}+13 i}-\frac{6477 \sqrt{682 \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{4 i \sqrt{31} x-22 x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{\sqrt{31}+13 i}-7688 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{96100}","\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,"(9920*Sqrt[3 - x + 2*x^2] - 12400*x*Sqrt[3 - x + 2*x^2] + (93000*Sqrt[3 - x + 2*x^2])/(3 - I*Sqrt[31] + 10*x) - (31000*x*Sqrt[3 - x + 2*x^2])/(3 - I*Sqrt[31] + 10*x) + (62000*x^2*Sqrt[3 - x + 2*x^2])/(3 - I*Sqrt[31] + 10*x) + (93000*Sqrt[3 - x + 2*x^2])/(3 + I*Sqrt[31] + 10*x) - (31000*x*Sqrt[3 - x + 2*x^2])/(3 + I*Sqrt[31] + 10*x) + (62000*x^2*Sqrt[3 - x + 2*x^2])/(3 + I*Sqrt[31] + 10*x) - 7688*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]] - (Sqrt[286 + (22*I)*Sqrt[31]]*(10199*I + 6477*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] - 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(-13*I + Sqrt[31]) - (6477*Sqrt[682*(13 - I*Sqrt[31])]*ArcTanh[(63 - I*Sqrt[31] - 22*x + (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(13*I + Sqrt[31]) + ((10199*I)*Sqrt[286 - (22*I)*Sqrt[31]]*ArcTanh[(63 - I*Sqrt[31] - 22*x + (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(13*I + Sqrt[31]))/96100","C",1
71,1,1262,223,5.3424984,"\int \frac{\left(3-x+2 x^2\right)^{3/2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Integrate[(3 - x + 2*x^2)^(3/2)/(2 + 3*x + 5*x^2)^3,x]","\frac{\frac{744000 \left(2 x^2-x+3\right)^{3/2}}{10 x-i \sqrt{31}+3}+\frac{744000 \left(2 x^2-x+3\right)^{3/2}}{10 x+i \sqrt{31}+3}+\frac{248000 i \sqrt{31} \left(2 x^2-x+3\right)^{3/2}}{\left(10 i x+\sqrt{31}+3 i\right)^2}+\frac{248000 i \sqrt{31} \left(2 x^2-x+3\right)^{3/2}}{\left(10 x+i \sqrt{31}+3\right)^2}+3 i \sqrt{31} \left(20 \sqrt{2 x^2-x+3} \left(-20 \left(11+2 i \sqrt{31}\right) x+98 i \sqrt{31}+1199\right)+\sqrt{2} \left(13453+4406 i \sqrt{31}\right) \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)-\frac{352 \sqrt{286+22 i \sqrt{31}} \left(-69 i+13 \sqrt{31}\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{-13 i+\sqrt{31}}\right)+558 \left(20 \sqrt{2 x^2-x+3} \left(-20 x+4 i \sqrt{31}+27\right)+\sqrt{2} \left(569+88 i \sqrt{31}\right) \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)-\frac{4 \sqrt{286+22 i \sqrt{31}} \left(-81 i+37 \sqrt{31}\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{-13 i+\sqrt{31}}\right)+\frac{744 \sqrt{31} \left(220 \sqrt{2 x^2-x+3} \left(20 \left(69+13 i \sqrt{31}\right) x+497 i \sqrt{31}-439\right)+88 \sqrt{2} \left(5 \left(47-281 i \sqrt{31}\right) x-398 i \sqrt{31}+4426\right) \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)+\sqrt{286+22 i \sqrt{31}} \left(\left(-23345-8565 i \sqrt{31}\right) x-4904 i \sqrt{31}+19548\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)\right)}{11 \left(-13 i+\sqrt{31}\right)^2 \left(-10 i x+\sqrt{31}-3 i\right)}+\frac{744 \sqrt{31} \left(220 \sqrt{2 x^2-x+3} \left(20 \left(69-13 i \sqrt{31}\right) x-497 i \sqrt{31}-439\right)+88 \sqrt{2} \left(5 \left(47+281 i \sqrt{31}\right) x+398 i \sqrt{31}+4426\right) \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)+\sqrt{286-22 i \sqrt{31}} \left(5 \left(4669-1713 i \sqrt{31}\right) x-4904 i \sqrt{31}-19548\right) \tanh ^{-1}\left(\frac{\left(22-4 i \sqrt{31}\right) x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)\right)}{11 \left(13 i+\sqrt{31}\right)^2 \left(10 i x+\sqrt{31}+3 i\right)}+\frac{3 \sqrt{31} \left(20 \sqrt{2 x^2-x+3} \left(20 i \left(81 i+37 \sqrt{31}\right) x-2473 i \sqrt{31}+12549\right)+\sqrt{2} \left(38303-70731 i \sqrt{31}\right) \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)+352 i \sqrt{286-22 i \sqrt{31}} \left(69 i+13 \sqrt{31}\right) \tanh ^{-1}\left(\frac{\left(-22+4 i \sqrt{31}\right) x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)\right)}{13 i+\sqrt{31}}+558 \left(-20 \sqrt{2 x^2-x+3} \left(20 x+4 i \sqrt{31}-27\right)+\sqrt{2} \left(569-88 i \sqrt{31}\right) \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)-\frac{4 \sqrt{286-22 i \sqrt{31}} \left(81 i+37 \sqrt{31}\right) \tanh ^{-1}\left(\frac{\left(-22+4 i \sqrt{31}\right) x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{13 i+\sqrt{31}}\right)}{4766560}","\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,"(((248000*I)*Sqrt[31]*(3 - x + 2*x^2)^(3/2))/(3*I + Sqrt[31] + (10*I)*x)^2 + (744000*(3 - x + 2*x^2)^(3/2))/(3 - I*Sqrt[31] + 10*x) + ((248000*I)*Sqrt[31]*(3 - x + 2*x^2)^(3/2))/(3 + I*Sqrt[31] + 10*x)^2 + (744000*(3 - x + 2*x^2)^(3/2))/(3 + I*Sqrt[31] + 10*x) + (3*I)*Sqrt[31]*(20*(1199 + (98*I)*Sqrt[31] - 20*(11 + (2*I)*Sqrt[31])*x)*Sqrt[3 - x + 2*x^2] + Sqrt[2]*(13453 + (4406*I)*Sqrt[31])*ArcSinh[(1 - 4*x)/Sqrt[23]] - (352*Sqrt[286 + (22*I)*Sqrt[31]]*(-69*I + 13*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(-13*I + Sqrt[31])) + 558*(20*(27 + (4*I)*Sqrt[31] - 20*x)*Sqrt[3 - x + 2*x^2] + Sqrt[2]*(569 + (88*I)*Sqrt[31])*ArcSinh[(1 - 4*x)/Sqrt[23]] - (4*Sqrt[286 + (22*I)*Sqrt[31]]*(-81*I + 37*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(-13*I + Sqrt[31])) + (744*Sqrt[31]*(220*(-439 + (497*I)*Sqrt[31] + 20*(69 + (13*I)*Sqrt[31])*x)*Sqrt[3 - x + 2*x^2] + 88*Sqrt[2]*(4426 - (398*I)*Sqrt[31] + 5*(47 - (281*I)*Sqrt[31])*x)*ArcSinh[(-1 + 4*x)/Sqrt[23]] + Sqrt[286 + (22*I)*Sqrt[31]]*(19548 - (4904*I)*Sqrt[31] + (-23345 - (8565*I)*Sqrt[31])*x)*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])]))/(11*(-13*I + Sqrt[31])^2*(-3*I + Sqrt[31] - (10*I)*x)) + (744*Sqrt[31]*(220*(-439 - (497*I)*Sqrt[31] + 20*(69 - (13*I)*Sqrt[31])*x)*Sqrt[3 - x + 2*x^2] + 88*Sqrt[2]*(4426 + (398*I)*Sqrt[31] + 5*(47 + (281*I)*Sqrt[31])*x)*ArcSinh[(-1 + 4*x)/Sqrt[23]] + Sqrt[286 - (22*I)*Sqrt[31]]*(-19548 - (4904*I)*Sqrt[31] + 5*(4669 - (1713*I)*Sqrt[31])*x)*ArcTanh[(-63 + I*Sqrt[31] + (22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])]))/(11*(13*I + Sqrt[31])^2*(3*I + Sqrt[31] + (10*I)*x)) + (3*Sqrt[31]*(20*(12549 - (2473*I)*Sqrt[31] + (20*I)*(81*I + 37*Sqrt[31])*x)*Sqrt[3 - x + 2*x^2] + Sqrt[2]*(38303 - (70731*I)*Sqrt[31])*ArcSinh[(1 - 4*x)/Sqrt[23]] + (352*I)*Sqrt[286 - (22*I)*Sqrt[31]]*(69*I + 13*Sqrt[31])*ArcTanh[(63 - I*Sqrt[31] + (-22 + (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])]))/(13*I + Sqrt[31]) + 558*(-20*(-27 + (4*I)*Sqrt[31] + 20*x)*Sqrt[3 - x + 2*x^2] + Sqrt[2]*(569 - (88*I)*Sqrt[31])*ArcSinh[(1 - 4*x)/Sqrt[23]] - (4*Sqrt[286 - (22*I)*Sqrt[31]]*(81*I + 37*Sqrt[31])*ArcTanh[(63 - I*Sqrt[31] + (-22 + (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(13*I + Sqrt[31])))/4766560","C",1
72,1,105,254,0.4523184,"\int \left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^4 \, dx","Integrate[(3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^4,x]","\frac{4 \sqrt{2 x^2-x+3} \left(25125558681600000 x^{13}+37398427729920000 x^{12}+137233466130432000 x^{11}+204932411660697600 x^{10}+363646430503501824 x^9+439064558846345216 x^8+530502956133122048 x^7+485091164642279424 x^6+405468382284161024 x^5+257786732552566784 x^4+142490931553577856 x^3+50064174038215008 x^2+12071614275862524 x+10820567498568669\right)-59958384968446965 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{562812514467840}","\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{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{14641852251147 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{68719476736 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(10820567498568669 + 12071614275862524*x + 50064174038215008*x^2 + 142490931553577856*x^3 + 257786732552566784*x^4 + 405468382284161024*x^5 + 485091164642279424*x^6 + 530502956133122048*x^7 + 439064558846345216*x^8 + 363646430503501824*x^9 + 204932411660697600*x^10 + 137233466130432000*x^11 + 37398427729920000*x^12 + 25125558681600000*x^13) - 59958384968446965*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/562812514467840","A",1
73,1,95,212,0.295578,"\int \left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^3 \, dx","Integrate[(3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^3,x]","\frac{4 \sqrt{2 x^2-x+3} \left(2818572288000 x^{11}+2395786444800 x^{10}+12943588589568 x^9+14341894045696 x^8+27835561148416 x^7+28347538538496 x^6+34378613923840 x^5+26186527209472 x^4+20384824684416 x^3+10060731582048 x^2+4560943728924 x-1191399152715\right)-665895955725 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{270582939648}","\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{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{10569777075 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2147483648 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(-1191399152715 + 4560943728924*x + 10060731582048*x^2 + 20384824684416*x^3 + 26186527209472*x^4 + 34378613923840*x^5 + 28347538538496*x^6 + 27835561148416*x^7 + 14341894045696*x^8 + 12943588589568*x^9 + 2395786444800*x^10 + 2818572288000*x^11) - 665895955725*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/270582939648","A",1
74,1,85,170,0.1829691,"\int \left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^2 \, dx","Integrate[(3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^2,x]","\frac{4 \sqrt{2 x^2-x+3} \left(10569646080 x^9+2055208960 x^8+44163137536 x^7+26401898496 x^6+75389820928 x^5+57147467776 x^4+77872272000 x^3+42992644128 x^2+39533249652 x+14824182519\right)-5929039935 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4227858432}","\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{5}{4} x^3 \left(2 x^2-x+3\right)^{7/2}-\frac{94111745 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{33554432 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(14824182519 + 39533249652*x + 42992644128*x^2 + 77872272000*x^3 + 57147467776*x^4 + 75389820928*x^5 + 26401898496*x^6 + 44163137536*x^7 + 2055208960*x^8 + 10569646080*x^9) - 5929039935*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/4227858432","A",1
75,1,75,128,0.1124952,"\int \left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right) \, dx","Integrate[(3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2),x]","\frac{4 \sqrt{2 x^2-x+3} \left(27525120 x^7-13565952 x^6+118808576 x^5-1619968 x^4+172684416 x^3+67272352 x^2+148957444 x+58536675\right)-353877195 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{44040192}","\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,"(4*Sqrt[3 - x + 2*x^2]*(58536675 + 148957444*x + 67272352*x^2 + 172684416*x^3 - 1619968*x^4 + 118808576*x^5 - 13565952*x^6 + 27525120*x^7) - 353877195*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/44040192","A",1
76,1,229,222,1.0468819,"\int \frac{\left(3-x+2 x^2\right)^{5/2}}{2+3 x+5 x^2} \, dx","Integrate[(3 - x + 2*x^2)^(5/2)/(2 + 3*x + 5*x^2),x]","\frac{46464 \sqrt{286+22 i \sqrt{31}} \left(403-69 i \sqrt{31}\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)-46464 i \sqrt{286-22 i \sqrt{31}} \left(69 \sqrt{31}-403 i\right) \tanh ^{-1}\left(\frac{\left(22-4 i \sqrt{31}\right) x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+620 \sqrt{2 x^2-x+3} \left(48000 x^3-106400 x^2+412060 x-802347\right)+671106879 \sqrt{2} \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{148800000}","-\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(\left(690+247 \sqrt{2}\right) x\right)-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(\left(690-247 \sqrt{2}\right) x\right)+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,"(620*Sqrt[3 - x + 2*x^2]*(-802347 + 412060*x - 106400*x^2 + 48000*x^3) + 671106879*Sqrt[2]*ArcSinh[(-1 + 4*x)/Sqrt[23]] + 46464*Sqrt[286 + (22*I)*Sqrt[31]]*(403 - (69*I)*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - (46464*I)*Sqrt[286 - (22*I)*Sqrt[31]]*(-403*I + 69*Sqrt[31])*ArcTanh[(-63 + I*Sqrt[31] + (22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/148800000","C",1
77,1,685,255,1.6546968,"\int \frac{\left(3-x+2 x^2\right)^{5/2}}{\left(2+3 x+5 x^2\right)^2} \, dx","Integrate[(3 - x + 2*x^2)^(5/2)/(2 + 3*x + 5*x^2)^2,x]","-\frac{7784100 \sqrt{2 x^2-x+3} x^2-5759180 \sqrt{2 x^2-x+3} x-5577520 \sqrt{2 x^2-x+3}-4611839 \sqrt{2} \left(5 x^2+3 x+2\right) \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)+284735 \sqrt{286-22 i \sqrt{31}} x^2 \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+482405 i \sqrt{682 \left(13-i \sqrt{31}\right)} x^2 \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+170841 \sqrt{286-22 i \sqrt{31}} x \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+289443 i \sqrt{682 \left(13-i \sqrt{31}\right)} x \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+11 i \sqrt{286+22 i \sqrt{31}} \left(8771 \sqrt{31}+5177 i\right) \left(5 x^2+3 x+2\right) \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x-22 x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+113894 \sqrt{286-22 i \sqrt{31}} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+192962 i \sqrt{682 \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)-1922000 \sqrt{2 x^2-x+3} x^3}{4805000 \left(5 x^2+3 x+2\right)}","\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,"-1/4805000*(-5577520*Sqrt[3 - x + 2*x^2] - 5759180*x*Sqrt[3 - x + 2*x^2] + 7784100*x^2*Sqrt[3 - x + 2*x^2] - 1922000*x^3*Sqrt[3 - x + 2*x^2] - 4611839*Sqrt[2]*(2 + 3*x + 5*x^2)*ArcSinh[(-1 + 4*x)/Sqrt[23]] + (11*I)*Sqrt[286 + (22*I)*Sqrt[31]]*(5177*I + 8771*Sqrt[31])*(2 + 3*x + 5*x^2)*ArcTanh[(63 + I*Sqrt[31] - 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + (192962*I)*Sqrt[682*(13 - I*Sqrt[31])]*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 113894*Sqrt[286 - (22*I)*Sqrt[31]]*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + (289443*I)*Sqrt[682*(13 - I*Sqrt[31])]*x*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 170841*Sqrt[286 - (22*I)*Sqrt[31]]*x*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + (482405*I)*Sqrt[682*(13 - I*Sqrt[31])]*x^2*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 284735*Sqrt[286 - (22*I)*Sqrt[31]]*x^2*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(2 + 3*x + 5*x^2)","C",1
78,1,1009,281,1.9962362,"\int \frac{\left(3-x+2 x^2\right)^{5/2}}{\left(2+3 x+5 x^2\right)^3} \, dx","Integrate[(3 - x + 2*x^2)^(5/2)/(2 + 3*x + 5*x^2)^3,x]","\frac{12599950 \sqrt{286-22 i \sqrt{31}} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right) x^4-12290525 i \sqrt{682 \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right) x^4+15119940 \sqrt{286-22 i \sqrt{31}} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right) x^3-14748630 i \sqrt{682 \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right) x^3+662597100 \sqrt{2 x^2-x+3} x^3+14615942 \sqrt{286-22 i \sqrt{31}} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right) x^2-14257009 i \sqrt{682 \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right) x^2+640207040 \sqrt{2 x^2-x+3} x^2+6047976 \sqrt{286-22 i \sqrt{31}} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right) x-5899452 i \sqrt{682 \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right) x+474815220 \sqrt{2 x^2-x+3} x+1906624 \sqrt{2} \left(5 x^2+3 x+2\right)^2 \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)-i \sqrt{286+22 i \sqrt{31}} \left(-503998 i+491621 \sqrt{31}\right) \left(5 x^2+3 x+2\right)^2 \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x-22 x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+2015992 \sqrt{286-22 i \sqrt{31}} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)-1966484 i \sqrt{682 \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{-4 i \sqrt{31} x+22 x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+153804640 \sqrt{2 x^2-x+3}}{59582000 \left(5 x^2+3 x+2\right)^2}","\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,"(153804640*Sqrt[3 - x + 2*x^2] + 474815220*x*Sqrt[3 - x + 2*x^2] + 640207040*x^2*Sqrt[3 - x + 2*x^2] + 662597100*x^3*Sqrt[3 - x + 2*x^2] + 1906624*Sqrt[2]*(2 + 3*x + 5*x^2)^2*ArcSinh[(-1 + 4*x)/Sqrt[23]] - I*Sqrt[286 + (22*I)*Sqrt[31]]*(-503998*I + 491621*Sqrt[31])*(2 + 3*x + 5*x^2)^2*ArcTanh[(63 + I*Sqrt[31] - 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - (1966484*I)*Sqrt[682*(13 - I*Sqrt[31])]*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 2015992*Sqrt[286 - (22*I)*Sqrt[31]]*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - (5899452*I)*Sqrt[682*(13 - I*Sqrt[31])]*x*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 6047976*Sqrt[286 - (22*I)*Sqrt[31]]*x*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - (14257009*I)*Sqrt[682*(13 - I*Sqrt[31])]*x^2*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 14615942*Sqrt[286 - (22*I)*Sqrt[31]]*x^2*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - (14748630*I)*Sqrt[682*(13 - I*Sqrt[31])]*x^3*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 15119940*Sqrt[286 - (22*I)*Sqrt[31]]*x^3*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - (12290525*I)*Sqrt[682*(13 - I*Sqrt[31])]*x^4*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 12599950*Sqrt[286 - (22*I)*Sqrt[31]]*x^4*ArcTanh[(-63 + I*Sqrt[31] + 22*x - (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(59582000*(2 + 3*x + 5*x^2)^2)","C",1
79,1,75,185,0.2413833,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\sqrt{3-x+2 x^2}} \, dx","Integrate[(2 + 3*x + 5*x^2)^4/Sqrt[3 - x + 2*x^2],x]","\frac{4 \sqrt{2 x^2-x+3} \left(3440640000 x^7+11280384000 x^6+17338163200 x^5+9842108416 x^4-7584175488 x^3-10367779296 x^2+18864088884 x+49479262983\right)+60886698033 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{352321536}","-\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{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{2899366573 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8388608 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(49479262983 + 18864088884*x - 10367779296*x^2 - 7584175488*x^3 + 9842108416*x^4 + 17338163200*x^5 + 11280384000*x^6 + 3440640000*x^7) + 60886698033*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/352321536","A",1
80,1,65,143,0.1338057,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\sqrt{3-x+2 x^2}} \, dx","Integrate[(2 + 3*x + 5*x^2)^3/Sqrt[3 - x + 2*x^2],x]","\frac{4 \sqrt{2 x^2-x+3} \left(1024000 x^5+2775040 x^4+3143040 x^3-325152 x^2-4473396 x-610119\right)-27803121 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{393216}","-\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{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{9267707 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{65536 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(-610119 - 4473396*x - 325152*x^2 + 3143040*x^3 + 2775040*x^4 + 1024000*x^5) - 27803121*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/393216","A",1
81,1,55,101,0.0753788,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\sqrt{3-x+2 x^2}} \, dx","Integrate[(2 + 3*x + 5*x^2)^2/Sqrt[3 - x + 2*x^2],x]","\frac{4 \sqrt{2 x^2-x+3} \left(9600 x^3+20960 x^2+13772 x-34119\right)+92175 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{12288}","\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{25}{8} \sqrt{2 x^2-x+3} x^3+\frac{30725 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{2048 \sqrt{2}}",1,"(4*Sqrt[3 - x + 2*x^2]*(-34119 + 13772*x + 20960*x^2 + 9600*x^3) + 92175*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/12288","A",1
82,1,45,59,0.0387761,"\int \frac{2+3 x+5 x^2}{\sqrt{3-x+2 x^2}} \, dx","Integrate[(2 + 3*x + 5*x^2)/Sqrt[3 - x + 2*x^2],x]","\frac{1}{64} \left(4 \sqrt{2 x^2-x+3} (20 x+39)+17 \sqrt{2} \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)\right)","\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,"(4*(39 + 20*x)*Sqrt[3 - x + 2*x^2] + 17*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]])/64","A",1
83,1,176,148,0.3002383,"\int \frac{1}{\sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)} \, dx","Integrate[1/(Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)),x]","-\frac{\sqrt{13+i \sqrt{31}} \left(\sqrt{31}+13 i\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+\sqrt{13-i \sqrt{31}} \left(\sqrt{31}-13 i\right) \tanh ^{-1}\left(\frac{\left(-22+4 i \sqrt{31}\right) x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{20 \sqrt{682}}","\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,"-1/20*(Sqrt[13 + I*Sqrt[31]]*(13*I + Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + Sqrt[13 - I*Sqrt[31]]*(-13*I + Sqrt[31])*ArcTanh[(63 - I*Sqrt[31] + (-22 + (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/Sqrt[682]","C",1
84,1,287,188,0.9963807,"\int \frac{1}{\sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^2} \, dx","Integrate[1/(Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^2),x]","\frac{25 \left(\frac{i \sqrt{286+22 i \sqrt{31}} \left(224 \sqrt{31}+1023 i\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{\left(\sqrt{31}-13 i\right)^2}+\frac{10 i \left(1364 \left(\sqrt{31}+13 i\right) (65 x+4) \sqrt{2 x^2-x+3}-5 \sqrt{286-22 i \sqrt{31}} \left(787 \sqrt{31}-1271 i\right) \left(5 x^2+3 x+2\right) \tanh ^{-1}\left(\frac{\left(-22+4 i \sqrt{31}\right) x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)\right)}{\left(\sqrt{31}+13 i\right)^2 \left(10 i x+\sqrt{31}+3 i\right) \left(5 \left(\sqrt{31}-13 i\right) x+8 \sqrt{31}-4 i\right)}\right)}{116281}","\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,"(25*((I*Sqrt[286 + (22*I)*Sqrt[31]]*(1023*I + 224*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(-13*I + Sqrt[31])^2 + ((10*I)*(1364*(13*I + Sqrt[31])*(4 + 65*x)*Sqrt[3 - x + 2*x^2] - 5*Sqrt[286 - (22*I)*Sqrt[31]]*(-1271*I + 787*Sqrt[31])*(2 + 3*x + 5*x^2)*ArcTanh[(63 - I*Sqrt[31] + (-22 + (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])]))/((13*I + Sqrt[31])^2*(3*I + Sqrt[31] + (10*I)*x)*(-4*I + 8*Sqrt[31] + 5*(-13*I + Sqrt[31])*x))))/116281","C",1
85,1,1277,223,6.2302019,"\int \frac{1}{\sqrt{3-x+2 x^2} \left(2+3 x+5 x^2\right)^3} \, dx","Integrate[1/(Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^3),x]","-\frac{750 \sqrt{\frac{2}{341} \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{-2 \left(11-2 i \sqrt{31}\right) x-i \sqrt{31}+63}{2 \sqrt{22 \left(13-i \sqrt{31}\right)} \sqrt{2 x^2-x+3}}\right)}{961 \left(13 i+\sqrt{31}\right)}-\frac{375 \sqrt{\frac{2}{11} \left(13-i \sqrt{31}\right)} \left(11-2 i \sqrt{31}\right) \tanh ^{-1}\left(\frac{-2 \left(11-2 i \sqrt{31}\right) x-i \sqrt{31}+63}{2 \sqrt{22 \left(13-i \sqrt{31}\right)} \sqrt{2 x^2-x+3}}\right)}{10571 \left(13 i+\sqrt{31}\right)^2}-\frac{375 \sqrt{\frac{2}{11} \left(13+i \sqrt{31}\right)} \left(11+2 i \sqrt{31}\right) \tanh ^{-1}\left(\frac{-2 \left(11+2 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{22 \left(13+i \sqrt{31}\right)} \sqrt{2 x^2-x+3}}\right)}{10571 \left(13 i-\sqrt{31}\right)^2}+\frac{750 \sqrt{\frac{2}{341} \left(13+i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{-2 \left(11+2 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{22 \left(13+i \sqrt{31}\right)} \sqrt{2 x^2-x+3}}\right)}{961 \left(13 i-\sqrt{31}\right)}+\frac{500 i \left(\frac{2 \sqrt{22 \left(13-i \sqrt{31}\right)} \left(20 \left(-3+i \sqrt{31}\right)+10 \left(27-4 i \sqrt{31}\right)-2 \left(600+2 \left(-3+i \sqrt{31}\right) \left(27-4 i \sqrt{31}\right)\right)\right) \tanh ^{-1}\left(\frac{-\left(\left(-10+4 \left(-3+i \sqrt{31}\right)\right) x\right)+i \sqrt{31}-63}{2 \sqrt{22 \left(13-i \sqrt{31}\right)} \sqrt{2 x^2-x+3}}\right)}{\left(300-10 \left(-3+i \sqrt{31}\right)+2 \left(-3+i \sqrt{31}\right)^2\right) \left(1200-40 \left(-3+i \sqrt{31}\right)+8 \left(-3+i \sqrt{31}\right)^2\right)}+\frac{\left(-20 \left(-3+i \sqrt{31}\right)+10 \left(27-4 i \sqrt{31}\right)\right) \sqrt{2 x^2-x+3}}{\left(300-10 \left(-3+i \sqrt{31}\right)+2 \left(-3+i \sqrt{31}\right)^2\right) \left(-10 x+i \sqrt{31}-3\right)}\right)}{31 \sqrt{31} \left(300-10 \left(-3+i \sqrt{31}\right)+2 \left(-3+i \sqrt{31}\right)^2\right)}+\frac{500 i \left(\frac{2 \sqrt{22 \left(13+i \sqrt{31}\right)} \left(-20 \left(3+i \sqrt{31}\right)-10 \left(-27-4 i \sqrt{31}\right)-2 \left(600+2 \left(3+i \sqrt{31}\right) \left(-27-4 i \sqrt{31}\right)\right)\right) \tanh ^{-1}\left(\frac{-\left(\left(10+4 \left(3+i \sqrt{31}\right)\right) x\right)+i \sqrt{31}+63}{2 \sqrt{22 \left(13+i \sqrt{31}\right)} \sqrt{2 x^2-x+3}}\right)}{\left(300+10 \left(3+i \sqrt{31}\right)+2 \left(3+i \sqrt{31}\right)^2\right) \left(1200+40 \left(3+i \sqrt{31}\right)+8 \left(3+i \sqrt{31}\right)^2\right)}+\frac{\left(20 \left(3+i \sqrt{31}\right)-10 \left(-27-4 i \sqrt{31}\right)\right) \sqrt{2 x^2-x+3}}{\left(300+10 \left(3+i \sqrt{31}\right)+2 \left(3+i \sqrt{31}\right)^2\right) \left(10 x+i \sqrt{31}+3\right)}\right)}{31 \sqrt{31} \left(300+10 \left(3+i \sqrt{31}\right)+2 \left(3+i \sqrt{31}\right)^2\right)}+\frac{7500 \sqrt{2 x^2-x+3}}{10571 \left(13-i \sqrt{31}\right) \left(10 x-i \sqrt{31}+3\right)}+\frac{7500 \sqrt{2 x^2-x+3}}{10571 \left(13+i \sqrt{31}\right) \left(10 x+i \sqrt{31}+3\right)}+\frac{2500 \sqrt{2 x^2-x+3}}{341 \sqrt{31} \left(13 i+\sqrt{31}\right) \left(10 x-i \sqrt{31}+3\right)^2}-\frac{2500 \sqrt{2 x^2-x+3}}{341 \sqrt{31} \left(13 i-\sqrt{31}\right) \left(10 x+i \sqrt{31}+3\right)^2}","\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,"(2500*Sqrt[3 - x + 2*x^2])/(341*Sqrt[31]*(13*I + Sqrt[31])*(3 - I*Sqrt[31] + 10*x)^2) + (7500*Sqrt[3 - x + 2*x^2])/(10571*(13 - I*Sqrt[31])*(3 - I*Sqrt[31] + 10*x)) - (2500*Sqrt[3 - x + 2*x^2])/(341*Sqrt[31]*(13*I - Sqrt[31])*(3 + I*Sqrt[31] + 10*x)^2) + (7500*Sqrt[3 - x + 2*x^2])/(10571*(13 + I*Sqrt[31])*(3 + I*Sqrt[31] + 10*x)) - (375*Sqrt[(2*(13 - I*Sqrt[31]))/11]*(11 - (2*I)*Sqrt[31])*ArcTanh[(63 - I*Sqrt[31] - 2*(11 - (2*I)*Sqrt[31])*x)/(2*Sqrt[22*(13 - I*Sqrt[31])]*Sqrt[3 - x + 2*x^2])])/(10571*(13*I + Sqrt[31])^2) - (750*Sqrt[(2*(13 - I*Sqrt[31]))/341]*ArcTanh[(63 - I*Sqrt[31] - 2*(11 - (2*I)*Sqrt[31])*x)/(2*Sqrt[22*(13 - I*Sqrt[31])]*Sqrt[3 - x + 2*x^2])])/(961*(13*I + Sqrt[31])) + (750*Sqrt[(2*(13 + I*Sqrt[31]))/341]*ArcTanh[(63 + I*Sqrt[31] - 2*(11 + (2*I)*Sqrt[31])*x)/(2*Sqrt[22*(13 + I*Sqrt[31])]*Sqrt[3 - x + 2*x^2])])/(961*(13*I - Sqrt[31])) - (375*Sqrt[(2*(13 + I*Sqrt[31]))/11]*(11 + (2*I)*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] - 2*(11 + (2*I)*Sqrt[31])*x)/(2*Sqrt[22*(13 + I*Sqrt[31])]*Sqrt[3 - x + 2*x^2])])/(10571*(13*I - Sqrt[31])^2) + (((500*I)/31)*(((-20*(-3 + I*Sqrt[31]) + 10*(27 - (4*I)*Sqrt[31]))*Sqrt[3 - x + 2*x^2])/((300 - 10*(-3 + I*Sqrt[31]) + 2*(-3 + I*Sqrt[31])^2)*(-3 + I*Sqrt[31] - 10*x)) + (2*Sqrt[22*(13 - I*Sqrt[31])]*(20*(-3 + I*Sqrt[31]) + 10*(27 - (4*I)*Sqrt[31]) - 2*(600 + 2*(-3 + I*Sqrt[31])*(27 - (4*I)*Sqrt[31])))*ArcTanh[(-63 + I*Sqrt[31] - (-10 + 4*(-3 + I*Sqrt[31]))*x)/(2*Sqrt[22*(13 - I*Sqrt[31])]*Sqrt[3 - x + 2*x^2])])/((300 - 10*(-3 + I*Sqrt[31]) + 2*(-3 + I*Sqrt[31])^2)*(1200 - 40*(-3 + I*Sqrt[31]) + 8*(-3 + I*Sqrt[31])^2))))/(Sqrt[31]*(300 - 10*(-3 + I*Sqrt[31]) + 2*(-3 + I*Sqrt[31])^2)) + (((500*I)/31)*(((20*(3 + I*Sqrt[31]) - 10*(-27 - (4*I)*Sqrt[31]))*Sqrt[3 - x + 2*x^2])/((300 + 10*(3 + I*Sqrt[31]) + 2*(3 + I*Sqrt[31])^2)*(3 + I*Sqrt[31] + 10*x)) + (2*Sqrt[22*(13 + I*Sqrt[31])]*(-20*(3 + I*Sqrt[31]) - 10*(-27 - (4*I)*Sqrt[31]) - 2*(600 + 2*(3 + I*Sqrt[31])*(-27 - (4*I)*Sqrt[31])))*ArcTanh[(63 + I*Sqrt[31] - (10 + 4*(3 + I*Sqrt[31]))*x)/(2*Sqrt[22*(13 + I*Sqrt[31])]*Sqrt[3 - x + 2*x^2])])/((300 + 10*(3 + I*Sqrt[31]) + 2*(3 + I*Sqrt[31])^2)*(1200 + 40*(3 + I*Sqrt[31]) + 8*(3 + I*Sqrt[31])^2))))/(Sqrt[31]*(300 + 10*(3 + I*Sqrt[31]) + 2*(3 + I*Sqrt[31])^2))","C",1
86,1,95,166,0.3731836,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Integrate[(2 + 3*x + 5*x^2)^4/(3 - x + 2*x^2)^(3/2),x]","\sqrt{2 x^2-x+3} \left(\frac{625 x^5}{24}+\frac{10075 x^4}{96}+\frac{79425 x^3}{512}-\frac{111315 x^2}{2048}-\frac{14641 (79 x+101)}{1472 \left(2 x^2-x+3\right)}-\frac{8992487 x}{16384}-\frac{31009685}{65536}\right)+\frac{310445587 \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{131072 \sqrt{2}}","-\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{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{310445587 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{131072 \sqrt{2}}",1,"Sqrt[3 - x + 2*x^2]*(-31009685/65536 - (8992487*x)/16384 - (111315*x^2)/2048 + (79425*x^3)/512 + (10075*x^4)/96 + (625*x^5)/24 - (14641*(101 + 79*x))/(1472*(3 - x + 2*x^2))) + (310445587*ArcSinh[(-1 + 4*x)/Sqrt[23]])/(131072*Sqrt[2])","A",1
87,1,65,124,0.2324986,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Integrate[(2 + 3*x + 5*x^2)^3/(3 - x + 2*x^2)^(3/2),x]","\frac{\frac{4 \left(736000 x^5+2318400 x^4+2624760 x^3-5754186 x^2+16138403 x-15423965\right)}{\sqrt{2 x^2-x+3}}-26884263 \sqrt{2} \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{188416}","\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{125}{16} \sqrt{2 x^2-x+3} x^3+\frac{1168881 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{4096 \sqrt{2}}",1,"((4*(-15423965 + 16138403*x - 5754186*x^2 + 2624760*x^3 + 2318400*x^4 + 736000*x^5))/Sqrt[3 - x + 2*x^2] - 26884263*Sqrt[2]*ArcSinh[(-1 + 4*x)/Sqrt[23]])/188416","A",1
88,1,55,82,0.1431815,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Integrate[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2)^(3/2),x]","\frac{4600 x^3+16790 x^2-9421 x+47027}{736 \sqrt{2 x^2-x+3}}+\frac{223 \sinh ^{-1}\left(\frac{4 x-1}{\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,"(47027 - 9421*x + 16790*x^2 + 4600*x^3)/(736*Sqrt[3 - x + 2*x^2]) + (223*ArcSinh[(-1 + 4*x)/Sqrt[23]])/(64*Sqrt[2])","A",1
89,1,45,45,0.0757725,"\int \frac{2+3 x+5 x^2}{\left(3-x+2 x^2\right)^{3/2}} \, dx","Integrate[(2 + 3*x + 5*x^2)/(3 - x + 2*x^2)^(3/2),x]","\frac{5 \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{2 \sqrt{2}}-\frac{11 (3 x+5)}{23 \sqrt{2 x^2-x+3}}","-\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",1
90,1,202,176,1.2868496,"\int \frac{1}{\left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)} \, dx","Integrate[1/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)),x]","\frac{-\frac{27280 (6 x-13)}{\sqrt{2 x^2-x+3}}-23 \sqrt{682 \left(13+i \sqrt{31}\right)} \left(13 \sqrt{31}+69 i\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)-23 \sqrt{682 \left(13-i \sqrt{31}\right)} \left(13 \sqrt{31}-69 i\right) \tanh ^{-1}\left(\frac{\left(-22+4 i \sqrt{31}\right) x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{6901840}","\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,"((-27280*(-13 + 6*x))/Sqrt[3 - x + 2*x^2] - 23*Sqrt[682*(13 + I*Sqrt[31])]*(69*I + 13*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - 23*Sqrt[682*(13 - I*Sqrt[31])]*(-69*I + 13*Sqrt[31])*ArcTanh[(63 - I*Sqrt[31] + (-22 + (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/6901840","C",1
91,1,740,211,1.5251599,"\int \frac{1}{\left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^2} \, dx","Integrate[1/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^2),x]","\frac{100 \left(\frac{682 \left(\left(22-4 i \sqrt{31}\right) x+i \sqrt{31}+52\right)}{\left(\sqrt{31}+13 i\right) \left(10 i x+\sqrt{31}+3 i\right) \sqrt{2 x^2-x+3}}+\frac{682 \left(\left(22+4 i \sqrt{31}\right) x-i \sqrt{31}+52\right)}{\left(\sqrt{31}-13 i\right) \left(-10 i x+\sqrt{31}-3 i\right) \sqrt{2 x^2-x+3}}+\frac{22 \left(2 \left(11 \sqrt{31}-62 i\right) x+52 \sqrt{31}+31 i\right)}{\left(\sqrt{31}+13 i\right) \sqrt{2 x^2-x+3}}+\frac{22 \left(2 \left(11 \sqrt{31}+62 i\right) x+52 \sqrt{31}-31 i\right)}{\left(\sqrt{31}-13 i\right) \sqrt{2 x^2-x+3}}+\frac{575 i \sqrt{682 \left(13+i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{\left(\sqrt{31}-13 i\right)^2}+\frac{155 \left(44 \left(16353+581 i \sqrt{31}\right) \sqrt{2 x^2-x+3}+345 \sqrt{286+22 i \sqrt{31}} \left(10 \left(11+2 i \sqrt{31}\right) x+17 i \sqrt{31}-29\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)\right)}{22 \left(\sqrt{31}-13 i\right)^3 \left(-10 i x+\sqrt{31}-3 i\right)}+\frac{155 \left(44 \left(16353-581 i \sqrt{31}\right) \sqrt{2 x^2-x+3}+345 \sqrt{286-22 i \sqrt{31}} \left(\left(-110+20 i \sqrt{31}\right) x+17 i \sqrt{31}+29\right) \tanh ^{-1}\left(\frac{\left(22-4 i \sqrt{31}\right) x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)\right)}{22 \left(\sqrt{31}+13 i\right)^3 \left(10 i x+\sqrt{31}+3 i\right)}-\frac{575 i \sqrt{682 \left(13-i \sqrt{31}\right)} \tanh ^{-1}\left(\frac{\left(-22+4 i \sqrt{31}\right) x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{\left(\sqrt{31}+13 i\right)^2}\right)}{2674463}","-\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,"(100*((682*(52 + I*Sqrt[31] + (22 - (4*I)*Sqrt[31])*x))/((13*I + Sqrt[31])*(3*I + Sqrt[31] + (10*I)*x)*Sqrt[3 - x + 2*x^2]) + (682*(52 - I*Sqrt[31] + (22 + (4*I)*Sqrt[31])*x))/((-13*I + Sqrt[31])*(-3*I + Sqrt[31] - (10*I)*x)*Sqrt[3 - x + 2*x^2]) + (22*(31*I + 52*Sqrt[31] + 2*(-62*I + 11*Sqrt[31])*x))/((13*I + Sqrt[31])*Sqrt[3 - x + 2*x^2]) + (22*(-31*I + 52*Sqrt[31] + 2*(62*I + 11*Sqrt[31])*x))/((-13*I + Sqrt[31])*Sqrt[3 - x + 2*x^2]) + ((575*I)*Sqrt[682*(13 + I*Sqrt[31])]*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(-13*I + Sqrt[31])^2 + (155*(44*(16353 + (581*I)*Sqrt[31])*Sqrt[3 - x + 2*x^2] + 345*Sqrt[286 + (22*I)*Sqrt[31]]*(-29 + (17*I)*Sqrt[31] + 10*(11 + (2*I)*Sqrt[31])*x)*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])]))/(22*(-13*I + Sqrt[31])^3*(-3*I + Sqrt[31] - (10*I)*x)) + (155*(44*(16353 - (581*I)*Sqrt[31])*Sqrt[3 - x + 2*x^2] + 345*Sqrt[286 - (22*I)*Sqrt[31]]*(29 + (17*I)*Sqrt[31] + (-110 + (20*I)*Sqrt[31])*x)*ArcTanh[(-63 + I*Sqrt[31] + (22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])]))/(22*(13*I + Sqrt[31])^3*(3*I + Sqrt[31] + (10*I)*x)) - ((575*I)*Sqrt[682*(13 - I*Sqrt[31])]*ArcTanh[(63 - I*Sqrt[31] + (-22 + (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/(13*I + Sqrt[31])^2))/2674463","C",1
92,1,231,246,2.2061735,"\int \frac{1}{\left(3-x+2 x^2\right)^{3/2} \left(2+3 x+5 x^2\right)^3} \, dx","Integrate[1/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^3),x]","\frac{69 \sqrt{286-22 i \sqrt{31}} \left(13785797 \sqrt{31}+14026539 i\right) \tan ^{-1}\left(\frac{-2 \left(2 \sqrt{31}+11 i\right) x+\sqrt{31}+63 i}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)-69 i \sqrt{286+22 i \sqrt{31}} \left(13785797 \sqrt{31}-14026539 i\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+\frac{27280 \left(162716650 x^5+86411405 x^4+277167774 x^3+175833195 x^2+161806828 x+22374044\right)}{\sqrt{2 x^2-x+3} \left(5 x^2+3 x+2\right)^2}}{25681691425280}","-\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,"((27280*(22374044 + 161806828*x + 175833195*x^2 + 277167774*x^3 + 86411405*x^4 + 162716650*x^5))/(Sqrt[3 - x + 2*x^2]*(2 + 3*x + 5*x^2)^2) + 69*Sqrt[286 - (22*I)*Sqrt[31]]*(14026539*I + 13785797*Sqrt[31])*ArcTan[(63*I + Sqrt[31] - 2*(11*I + 2*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - (69*I)*Sqrt[286 + (22*I)*Sqrt[31]]*(-14026539*I + 13785797*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/25681691425280","C",1
93,1,75,147,0.5133199,"\int \frac{\left(2+3 x+5 x^2\right)^4}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Integrate[(2 + 3*x + 5*x^2)^4/(3 - x + 2*x^2)^(5/2),x]","\frac{507840000 x^7+2090608000 x^6+3504730800 x^5-5076781260 x^4+39848900984 x^3-36481630395 x^2+49883864262 x-18974698519}{6500352 \left(2 x^2-x+3\right)^{3/2}}-\frac{16955197 \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{8192 \sqrt{2}}","\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{625}{32} \sqrt{2 x^2-x+3} x^3+\frac{16955197 \sinh ^{-1}\left(\frac{1-4 x}{\sqrt{23}}\right)}{8192 \sqrt{2}}",1,"(-18974698519 + 49883864262*x - 36481630395*x^2 + 39848900984*x^3 - 5076781260*x^4 + 3504730800*x^5 + 2090608000*x^6 + 507840000*x^7)/(6500352*(3 - x + 2*x^2)^(3/2)) - (16955197*ArcSinh[(-1 + 4*x)/Sqrt[23]])/(8192*Sqrt[2])","A",1
94,1,65,105,0.3378651,"\int \frac{\left(2+3 x+5 x^2\right)^3}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Integrate[(2 + 3*x + 5*x^2)^3/(3 - x + 2*x^2)^(5/2),x]","\frac{3174000 x^5+16980900 x^4-29423976 x^3+101546529 x^2-62463282 x+89784565}{101568 \left(2 x^2-x+3\right)^{3/2}}+\frac{7495 \sinh ^{-1}\left(\frac{4 x-1}{\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,"(89784565 - 62463282*x + 101546529*x^2 - 29423976*x^3 + 16980900*x^4 + 3174000*x^5)/(101568*(3 - x + 2*x^2)^(3/2)) + (7495*ArcSinh[(-1 + 4*x)/Sqrt[23]])/(128*Sqrt[2])","A",1
95,1,55,68,0.2364005,"\int \frac{\left(2+3 x+5 x^2\right)^2}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Integrate[(2 + 3*x + 5*x^2)^2/(3 - x + 2*x^2)^(5/2),x]","\frac{25 \sinh ^{-1}\left(\frac{4 x-1}{\sqrt{23}}\right)}{4 \sqrt{2}}-\frac{11 \left(2336 x^3+6183 x^2+714 x+8623\right)}{3174 \left(2 x^2-x+3\right)^{3/2}}","\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,"(-11*(8623 + 714*x + 6183*x^2 + 2336*x^3))/(3174*(3 - x + 2*x^2)^(3/2)) + (25*ArcSinh[(-1 + 4*x)/Sqrt[23]])/(4*Sqrt[2])","A",1
96,1,33,47,0.1027677,"\int \frac{2+3 x+5 x^2}{\left(3-x+2 x^2\right)^{5/2}} \, dx","Integrate[(2 + 3*x + 5*x^2)/(3 - x + 2*x^2)^(5/2),x]","\frac{2 \left(852 x^3-639 x^2+1005 x-952\right)}{1587 \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,"(2*(-952 + 1005*x - 639*x^2 + 852*x^3))/(1587*(3 - x + 2*x^2)^(3/2))","A",1
97,1,218,199,0.8675251,"\int \frac{1}{\left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)} \, dx","Integrate[1/((3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)),x]","-\frac{\sqrt{\frac{1}{682} \left(13+i \sqrt{31}\right)} \left(119 \sqrt{31}+247 i\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{9680}+\frac{\sqrt{\frac{1}{682} \left(13-i \sqrt{31}\right)} \left(119 \sqrt{31}-247 i\right) \tanh ^{-1}\left(\frac{\left(22-4 i \sqrt{31}\right) x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)}{9680}+\frac{-3948 x^3+23592 x^2-19767 x+39005}{384054 \left(2 x^2-x+3\right)^{3/2}}","\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,"(39005 - 19767*x + 23592*x^2 - 3948*x^3)/(384054*(3 - x + 2*x^2)^(3/2)) - (Sqrt[(13 + I*Sqrt[31])/682]*(247*I + 119*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/9680 + (Sqrt[(13 - I*Sqrt[31])/682]*(-247*I + 119*Sqrt[31])*ArcTanh[(-63 + I*Sqrt[31] + (22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/9680","C",1
98,1,296,234,1.1529712,"\int \frac{1}{\left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^2} \, dx","Integrate[1/((3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^2),x]","-\frac{198375 i \sqrt{286+22 i \sqrt{31}} \left(687 \sqrt{31}+31 i\right) \sqrt{2 x^2-x+3} \left(10 x^4+x^3+16 x^2+7 x+6\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+198375 \sqrt{286-22 i \sqrt{31}} \left(31+687 i \sqrt{31}\right) \sqrt{2 x^2-x+3} \left(10 x^4+x^3+16 x^2+7 x+6\right) \tanh ^{-1}\left(\frac{\left(22-4 i \sqrt{31}\right) x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+5456 \left(13525420 x^5+32686812 x^4+2879479 x^3+84671384 x^2-5712309 x+31010342\right)}{2858123723136 \left(2 x^2-x+3\right)^{3/2} \left(5 x^2+3 x+2\right)}","-\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,"-1/2858123723136*(5456*(31010342 - 5712309*x + 84671384*x^2 + 2879479*x^3 + 32686812*x^4 + 13525420*x^5) + (198375*I)*Sqrt[286 + (22*I)*Sqrt[31]]*(31*I + 687*Sqrt[31])*Sqrt[3 - x + 2*x^2]*(6 + 7*x + 16*x^2 + x^3 + 10*x^4)*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] + 198375*Sqrt[286 - (22*I)*Sqrt[31]]*(31 + (687*I)*Sqrt[31])*Sqrt[3 - x + 2*x^2]*(6 + 7*x + 16*x^2 + x^3 + 10*x^4)*ArcTanh[(-63 + I*Sqrt[31] + (22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2))","C",1
99,1,242,269,1.958211,"\int \frac{1}{\left(3-x+2 x^2\right)^{5/2} \left(2+3 x+5 x^2\right)^3} \, dx","Integrate[1/((3 - x + 2*x^2)^(5/2)*(2 + 3*x + 5*x^2)^3),x]","\frac{11109 \sqrt{286+22 i \sqrt{31}} \left(4541903-6290431 i \sqrt{31}\right) \tanh ^{-1}\left(\frac{\left(-22-4 i \sqrt{31}\right) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)-11109 i \sqrt{286-22 i \sqrt{31}} \left(6290431 \sqrt{31}-4541903 i\right) \tanh ^{-1}\left(\frac{\left(22-4 i \sqrt{31}\right) x+i \sqrt{31}-63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right)+\frac{5456 \left(225699113100 x^7-12234606480 x^6+592923725931 x^5+174241614961 x^4+519223213785 x^3+178650961091 x^2+218659985088 x+9739335532\right)}{\left(2 x^2-x+3\right)^{3/2} \left(5 x^2+3 x+2\right)^2}}{7796961516715008}","-\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,"((5456*(9739335532 + 218659985088*x + 178650961091*x^2 + 519223213785*x^3 + 174241614961*x^4 + 592923725931*x^5 - 12234606480*x^6 + 225699113100*x^7))/((3 - x + 2*x^2)^(3/2)*(2 + 3*x + 5*x^2)^2) + 11109*Sqrt[286 + (22*I)*Sqrt[31]]*(4541903 - (6290431*I)*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] - (11109*I)*Sqrt[286 - (22*I)*Sqrt[31]]*(-4541903*I + 6290431*Sqrt[31])*ArcTanh[(-63 + I*Sqrt[31] + (22 - (4*I)*Sqrt[31])*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/7796961516715008","C",1
100,1,657,436,0.9346765,"\int \sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)^2 \, dx","Integrate[Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2)^2,x]","\frac{-f^2 \left(-15 \left(16 a^2 c^2-56 a b^2 c+21 b^4\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)+16 c^{3/2} \left(-196 a b c+120 a c^2 x+105 b^3-126 b^2 c x\right) (a+x (b+c x))^{3/2}+2304 b c^{7/2} x^2 (a+x (b+c x))^{3/2}\right)+8 c e f \left(-16 c^{3/2} \left(32 a c-35 b^2+42 b c x\right) (a+x (b+c x))^{3/2}-15 b \left(7 b^2-12 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)-1920 c^4 d^2 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-1920 b c^3 d e \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)-40 c^2 \left(2 d f+e^2\right) \left(80 b c^{3/2} (a+x (b+c x))^{3/2}-3 \left(5 b^2-4 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)+3840 c^{9/2} d^2 (b+2 c x) \sqrt{a+x (b+c x)}+3840 c^{9/2} x \left(2 d f+e^2\right) (a+x (b+c x))^{3/2}+10240 c^{9/2} d e (a+x (b+c x))^{3/2}+6144 c^{9/2} e f x^2 (a+x (b+c x))^{3/2}+2560 c^{9/2} f^2 x^3 (a+x (b+c x))^{3/2}}{15360 c^{11/2}}","-\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{(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(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{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{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,"(3840*c^(9/2)*d^2*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + 10240*c^(9/2)*d*e*(a + x*(b + c*x))^(3/2) + 3840*c^(9/2)*(e^2 + 2*d*f)*x*(a + x*(b + c*x))^(3/2) + 6144*c^(9/2)*e*f*x^2*(a + x*(b + c*x))^(3/2) + 2560*c^(9/2)*f^2*x^3*(a + x*(b + c*x))^(3/2) - 1920*c^4*(b^2 - 4*a*c)*d^2*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])] - 1920*b*c^3*d*e*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]) + 8*c*e*f*(-16*c^(3/2)*(-35*b^2 + 32*a*c + 42*b*c*x)*(a + x*(b + c*x))^(3/2) - 15*b*(7*b^2 - 12*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])) - 40*c^2*(e^2 + 2*d*f)*(80*b*c^(3/2)*(a + x*(b + c*x))^(3/2) - 3*(5*b^2 - 4*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])) - f^2*(2304*b*c^(7/2)*x^2*(a + x*(b + c*x))^(3/2) + 16*c^(3/2)*(105*b^3 - 196*a*b*c - 126*b^2*c*x + 120*a*c^2*x)*(a + x*(b + c*x))^(3/2) - 15*(21*b^4 - 56*a*b^2*c + 16*a^2*c^2)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])))/(15360*c^(11/2))","A",1
101,1,173,175,0.2729664,"\int \sqrt{a+b x+c x^2} \left(d+e x+f x^2\right) \, dx","Integrate[Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2),x]","\frac{2 \sqrt{c} \sqrt{a+x (b+c x)} \left(4 b c \left(2 c \left(6 d+2 e x+f x^2\right)-13 a f\right)+8 c^2 \left(a (8 e+3 f x)+2 c x \left(6 d+4 e x+3 f x^2\right)\right)+15 b^3 f-2 b^2 c (12 e+5 f x)\right)-3 \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right) \left(-4 c (a f+2 b e)+5 b^2 f+16 c^2 d\right)}{384 c^{7/2}}","-\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{(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(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,"(2*Sqrt[c]*Sqrt[a + x*(b + c*x)]*(15*b^3*f - 2*b^2*c*(12*e + 5*f*x) + 4*b*c*(-13*a*f + 2*c*(6*d + 2*e*x + f*x^2)) + 8*c^2*(a*(8*e + 3*f*x) + 2*c*x*(6*d + 4*e*x + 3*f*x^2))) - 3*(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 + x*(b + c*x)])])/(384*c^(7/2))","A",1
102,1,417,431,1.2194385,"\int \frac{\sqrt{a+b x+c x^2}}{d+e x+f x^2} \, dx","Integrate[Sqrt[a + b*x + c*x^2]/(d + e*x + f*x^2),x]","\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-b \left(\sqrt{e^2-4 d f}+e-2 f x\right)-2 c x \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+x (b+c x)} \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)}}\right)-\sqrt{f \left(2 a f+b \sqrt{e^2-4 d f}+b (-e)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)} \tanh ^{-1}\left(\frac{4 a f+b \left(\sqrt{e^2-4 d f}-e+2 f x\right)+2 c x \left(\sqrt{e^2-4 d f}-e\right)}{2 \sqrt{2} \sqrt{a+x (b+c x)} \sqrt{f \left(2 a f+b \sqrt{e^2-4 d f}+b (-e)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)}}\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+x (b+c x)}}\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 + x*(b + c*x)])])/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 - 2*c*(e + Sqrt[e^2 - 4*d*f])*x - b*(e + Sqrt[e^2 - 4*d*f] - 2*f*x))/(2*Sqrt[2]*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]))]*Sqrt[a + x*(b + c*x)])] - Sqrt[f*(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f]) + c*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f])]*ArcTanh[(4*a*f + 2*c*(-e + Sqrt[e^2 - 4*d*f])*x + b*(-e + Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*Sqrt[2]*Sqrt[f*(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f]) + c*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f])]*Sqrt[a + x*(b + c*x)])])/(Sqrt[2]*f*Sqrt[e^2 - 4*d*f])","A",1
103,1,555,488,5.0926185,"\int \frac{\sqrt{a+b x+c x^2}}{\left(d+e x+f x^2\right)^2} \, dx","Integrate[Sqrt[a + b*x + c*x^2]/(d + e*x + f*x^2)^2,x]","\frac{4 f (e+2 f x) \sqrt{a+x (b+c x)}}{\left(e^2-4 d f\right) \left(\sqrt{e^2-4 d f}-e-2 f x\right) \left(\sqrt{e^2-4 d f}+e+2 f x\right)}+\frac{\left(c e \left(\sqrt{e^2-4 d f}-e\right)-f \left(4 a f+b \left(\sqrt{e^2-4 d f}-2 e\right)\right)\right) \tanh ^{-1}\left(\frac{-4 a f+b \left(-\sqrt{e^2-4 d f}+e-2 f x\right)+2 c x \left(e-\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{a+x (b+c x)} \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)}}\right)}{\sqrt{2} \left(e^2-4 d f\right)^{3/2} \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{\left(f \left(4 a f-b \left(\sqrt{e^2-4 d f}+2 e\right)\right)+c e \left(\sqrt{e^2-4 d f}+e\right)\right) \tanh ^{-1}\left(\frac{4 a f-b \left(\sqrt{e^2-4 d f}+e-2 f x\right)-2 c x \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+x (b+c x)} \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)}}\right)}{\sqrt{2} \left(e^2-4 d f\right)^{3/2} \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{\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,"(4*f*(e + 2*f*x)*Sqrt[a + x*(b + c*x)])/((e^2 - 4*d*f)*(-e + Sqrt[e^2 - 4*d*f] - 2*f*x)*(e + Sqrt[e^2 - 4*d*f] + 2*f*x)) + ((c*e*(-e + Sqrt[e^2 - 4*d*f]) - f*(4*a*f + b*(-2*e + Sqrt[e^2 - 4*d*f])))*ArcTanh[(-4*a*f + 2*c*(e - Sqrt[e^2 - 4*d*f])*x + b*(e - Sqrt[e^2 - 4*d*f] - 2*f*x))/(2*Sqrt[2]*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]))]*Sqrt[a + x*(b + c*x)])])/(Sqrt[2]*(e^2 - 4*d*f)^(3/2)*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]))]) - ((c*e*(e + Sqrt[e^2 - 4*d*f]) + f*(4*a*f - b*(2*e + Sqrt[e^2 - 4*d*f])))*ArcTanh[(4*a*f - 2*c*(e + Sqrt[e^2 - 4*d*f])*x - b*(e + Sqrt[e^2 - 4*d*f] - 2*f*x))/(2*Sqrt[2]*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]))]*Sqrt[a + x*(b + c*x)])])/(Sqrt[2]*(e^2 - 4*d*f)^(3/2)*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",1
104,1,829,564,1.7622306,"\int \left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)^2 \, dx","Integrate[(a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2)^2,x]","\frac{430080 f^2 (a+x (b+c x))^{5/2} x^3+983040 e f (a+x (b+c x))^{5/2} x^2+573440 \left(e^2+2 d f\right) (a+x (b+c x))^{5/2} x+1376256 d e (a+x (b+c x))^{5/2}+430080 d^2 (b+2 c x) (a+x (b+c x))^{3/2}+\frac{80640 \left(b^2-4 a c\right) d^2 \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{c^{3/2}}-\frac{26880 b d e \left(16 c^{3/2} (b+2 c x) (a+x (b+c x))^{3/2}-3 \left(b^2-4 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)}{c^{5/2}}+\frac{96 e f \left(-256 c^{5/2} \left(-21 b^2+30 c x b+16 a c\right) (a+x (b+c x))^{5/2}-35 b \left(3 b^2-4 a c\right) \left(16 c^{3/2} (b+2 c x) (a+x (b+c x))^{3/2}-3 \left(b^2-4 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{c^{9/2}}-\frac{224 \left(e^2+2 d f\right) \left(1792 b c^{5/2} (a+x (b+c x))^{5/2}-5 \left(7 b^2-4 a c\right) \left(16 c^{3/2} (b+2 c x) (a+x (b+c x))^{3/2}-3 \left(b^2-4 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{c^{7/2}}-\frac{3 f^2 \left(112640 b x^2 (a+x (b+c x))^{5/2} c^{9/2}+256 \left(231 b^3-330 c x b^2-372 a c b+280 a c^2 x\right) (a+x (b+c x))^{5/2} c^{5/2}-35 \left(33 b^4-72 a c b^2+16 a^2 c^2\right) \left(16 c^{3/2} (b+2 c x) (a+x (b+c x))^{3/2}-3 \left(b^2-4 a c\right) \left(2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}-\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)\right)\right)\right)}{c^{11/2}}}{3440640 c}","\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{\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{(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(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{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{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,"(430080*d^2*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) + 1376256*d*e*(a + x*(b + c*x))^(5/2) + 573440*(e^2 + 2*d*f)*x*(a + x*(b + c*x))^(5/2) + 983040*e*f*x^2*(a + x*(b + c*x))^(5/2) + 430080*f^2*x^3*(a + x*(b + c*x))^(5/2) + (80640*(b^2 - 4*a*c)*d^2*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/c^(3/2) - (26880*b*d*e*(16*c^(3/2)*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])))/c^(5/2) + (96*e*f*(-256*c^(5/2)*(-21*b^2 + 16*a*c + 30*b*c*x)*(a + x*(b + c*x))^(5/2) - 35*b*(3*b^2 - 4*a*c)*(16*c^(3/2)*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))))/c^(9/2) - (224*(e^2 + 2*d*f)*(1792*b*c^(5/2)*(a + x*(b + c*x))^(5/2) - 5*(7*b^2 - 4*a*c)*(16*c^(3/2)*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))))/c^(7/2) - (3*f^2*(112640*b*c^(9/2)*x^2*(a + x*(b + c*x))^(5/2) + 256*c^(5/2)*(231*b^3 - 372*a*b*c - 330*b^2*c*x + 280*a*c^2*x)*(a + x*(b + c*x))^(5/2) - 35*(33*b^4 - 72*a*b^2*c + 16*a^2*c^2)*(16*c^(3/2)*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) - 3*(b^2 - 4*a*c)*(2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))))/c^(11/2))/(3440640*c)","A",1
105,1,392,236,0.6057878,"\int \left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right) \, dx","Integrate[(a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2),x]","\frac{\frac{360 d \left(b^2-4 a c\right) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{c^{3/2}}-60 b e \left(\frac{3 \left(b^2-4 a c\right) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{c^{5/2}}+\frac{16 (b+2 c x) (a+x (b+c x))^{3/2}}{c}\right)+\frac{f \left(5 \left(7 b^2-4 a c\right) \left(\frac{3 \left(b^2-4 a c\right) \left(\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)-2 \sqrt{c} (b+2 c x) \sqrt{a+x (b+c x)}\right)}{c^{5/2}}+\frac{16 (b+2 c x) (a+x (b+c x))^{3/2}}{c}\right)-1792 b (a+x (b+c x))^{5/2}\right)}{c}+1920 d (b+2 c x) (a+x (b+c x))^{3/2}+3072 e (a+x (b+c x))^{5/2}+2560 f x (a+x (b+c x))^{5/2}}{15360 c}","\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(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{(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(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,"(1920*d*(b + 2*c*x)*(a + x*(b + c*x))^(3/2) + 3072*e*(a + x*(b + c*x))^(5/2) + 2560*f*x*(a + x*(b + c*x))^(5/2) + (360*(b^2 - 4*a*c)*d*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/c^(3/2) - 60*b*e*((16*(b + 2*c*x)*(a + x*(b + c*x))^(3/2))/c + (3*(b^2 - 4*a*c)*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/c^(5/2)) + (f*(-1792*b*(a + x*(b + c*x))^(5/2) + 5*(7*b^2 - 4*a*c)*((16*(b + 2*c*x)*(a + x*(b + c*x))^(3/2))/c + (3*(b^2 - 4*a*c)*(-2*Sqrt[c]*(b + 2*c*x)*Sqrt[a + x*(b + c*x)] + (b^2 - 4*a*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])]))/c^(5/2))))/c)/(15360*c)","A",1
106,1,1232,679,4.5761525,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{d+e x+f x^2} \, dx","Integrate[(a + b*x + c*x^2)^(3/2)/(d + e*x + f*x^2),x]","\frac{\sqrt{a+x (b+c x)} \left(-4 \left(e+\sqrt{e^2-4 d f}\right)^2 c^2+4 f \left(e+\sqrt{e^2-4 d f}\right) x c^2-16 a f^2 c+10 b f \left(e+\sqrt{e^2-4 d f}\right) c-4 b f^2 x c-2 b^2 f^2\right)+2 \sqrt{a+x (b+c x)} \left(-2 \left(-2 e^2+f x e+2 \sqrt{e^2-4 d f} e+4 d f-f \sqrt{e^2-4 d f} x\right) c^2+f \left(8 a f+b \left(-5 e+2 f x+5 \sqrt{e^2-4 d f}\right)\right) c+b^2 f^2\right)-\frac{\left(b f+c \left(\sqrt{e^2-4 d f}-e\right)\right) \left(4 \left(-e^2+\sqrt{e^2-4 d f} e+2 d f\right) c^2-4 f \left(3 a f+b \left(\sqrt{e^2-4 d f}-e\right)\right) c+b^2 f^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{\sqrt{c} f}+\frac{\left(c \left(e+\sqrt{e^2-4 d f}\right)-b f\right) \left(4 \left(e^2+\sqrt{e^2-4 d f} e-2 d f\right) c^2-4 f \left(b \left(e+\sqrt{e^2-4 d f}\right)-3 a f\right) c-b^2 f^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right)}{\sqrt{c} f}+\frac{8 \sqrt{2} c \left(\left(e^4+\sqrt{e^2-4 d f} e^3-4 d f e^2-2 d f \sqrt{e^2-4 d f} e+2 d^2 f^2\right) c^2+2 f \left(a f \left(e^2+\sqrt{e^2-4 d f} e-2 d f\right)-b \left(e^3+\sqrt{e^2-4 d f} e^2-3 d f e-d f \sqrt{e^2-4 d f}\right)\right) c+f^2 \left(\left(e^2+\sqrt{e^2-4 d f} e-2 d f\right) b^2-2 a f \left(e+\sqrt{e^2-4 d f}\right) b+2 a^2 f^2\right)\right) \tanh ^{-1}\left(\frac{4 a f-2 c \left(e+\sqrt{e^2-4 d f}\right) x-b \left(e-2 f x+\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{c \left(e^2+\sqrt{e^2-4 d f} e-2 d f\right)+f \left(2 a f-b \left(e+\sqrt{e^2-4 d f}\right)\right)} \sqrt{a+x (b+c x)}}\right)}{f \sqrt{c \left(e^2+\sqrt{e^2-4 d f} e-2 d f\right)+f \left(2 a f-b \left(e+\sqrt{e^2-4 d f}\right)\right)}}+\frac{8 \sqrt{2} c \left(\left(-e^4+\sqrt{e^2-4 d f} e^3+4 d f e^2-2 d f \sqrt{e^2-4 d f} e-2 d^2 f^2\right) c^2+2 f \left(a f \left(-e^2+\sqrt{e^2-4 d f} e+2 d f\right)+b \left(e^3-\sqrt{e^2-4 d f} e^2-3 d f e+d f \sqrt{e^2-4 d f}\right)\right) c+f^2 \left(\left(-e^2+\sqrt{e^2-4 d f} e+2 d f\right) b^2+2 a f \left(e-\sqrt{e^2-4 d f}\right) b-2 a^2 f^2\right)\right) \tanh ^{-1}\left(\frac{4 a f+2 c \left(\sqrt{e^2-4 d f}-e\right) x+b \left(-e+2 f x+\sqrt{e^2-4 d f}\right)}{2 \sqrt{2} \sqrt{c \left(e^2-\sqrt{e^2-4 d f} e-2 d f\right)+f \left(2 a f+b \left(\sqrt{e^2-4 d f}-e\right)\right)} \sqrt{a+x (b+c x)}}\right)}{f \sqrt{c \left(e^2-\sqrt{e^2-4 d f} e-2 d f\right)+f \left(2 a f+b \left(\sqrt{e^2-4 d f}-e\right)\right)}}}{16 c f^2 \sqrt{e^2-4 d f}}","\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,"((-2*b^2*f^2 - 16*a*c*f^2 + 10*b*c*f*(e + Sqrt[e^2 - 4*d*f]) - 4*c^2*(e + Sqrt[e^2 - 4*d*f])^2 - 4*b*c*f^2*x + 4*c^2*f*(e + Sqrt[e^2 - 4*d*f])*x)*Sqrt[a + x*(b + c*x)] + 2*Sqrt[a + x*(b + c*x)]*(b^2*f^2 - 2*c^2*(-2*e^2 + 4*d*f + 2*e*Sqrt[e^2 - 4*d*f] + e*f*x - f*Sqrt[e^2 - 4*d*f]*x) + c*f*(8*a*f + b*(-5*e + 5*Sqrt[e^2 - 4*d*f] + 2*f*x))) - ((b*f + c*(-e + Sqrt[e^2 - 4*d*f]))*(b^2*f^2 + 4*c^2*(-e^2 + 2*d*f + e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(3*a*f + b*(-e + Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(Sqrt[c]*f) + ((-(b*f) + c*(e + Sqrt[e^2 - 4*d*f]))*(-(b^2*f^2) + 4*c^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(-3*a*f + b*(e + Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(Sqrt[c]*f) + (8*Sqrt[2]*c*(c^2*(e^4 - 4*d*e^2*f + 2*d^2*f^2 + e^3*Sqrt[e^2 - 4*d*f] - 2*d*e*f*Sqrt[e^2 - 4*d*f]) + f^2*(2*a^2*f^2 - 2*a*b*f*(e + Sqrt[e^2 - 4*d*f]) + b^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f])) + 2*c*f*(a*f*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) - b*(e^3 - 3*d*e*f + e^2*Sqrt[e^2 - 4*d*f] - d*f*Sqrt[e^2 - 4*d*f])))*ArcTanh[(4*a*f - 2*c*(e + Sqrt[e^2 - 4*d*f])*x - b*(e + Sqrt[e^2 - 4*d*f] - 2*f*x))/(2*Sqrt[2]*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]))]*Sqrt[a + x*(b + c*x)])])/(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]))]) + (8*Sqrt[2]*c*(c^2*(-e^4 + 4*d*e^2*f - 2*d^2*f^2 + e^3*Sqrt[e^2 - 4*d*f] - 2*d*e*f*Sqrt[e^2 - 4*d*f]) + f^2*(-2*a^2*f^2 + 2*a*b*f*(e - Sqrt[e^2 - 4*d*f]) + b^2*(-e^2 + 2*d*f + e*Sqrt[e^2 - 4*d*f])) + 2*c*f*(a*f*(-e^2 + 2*d*f + e*Sqrt[e^2 - 4*d*f]) + b*(e^3 - 3*d*e*f - e^2*Sqrt[e^2 - 4*d*f] + d*f*Sqrt[e^2 - 4*d*f])))*ArcTanh[(4*a*f + 2*c*(-e + Sqrt[e^2 - 4*d*f])*x + b*(-e + Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*Sqrt[2]*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]))]*Sqrt[a + x*(b + c*x)])])/(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]))]))/(16*c*f^2*Sqrt[e^2 - 4*d*f])","A",0
107,1,2843,704,6.8312387,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{\left(d+e x+f x^2\right)^2} \, dx","Integrate[(a + b*x + c*x^2)^(3/2)/(d + e*x + f*x^2)^2,x]","\text{Result too large to show}","-\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,"(-2*f*(a + x*(b + c*x))^(3/2))/((e^2 - 4*d*f)*(e - Sqrt[e^2 - 4*d*f] + 2*f*x)) - (2*f*(a + x*(b + c*x))^(3/2))/((e^2 - 4*d*f)*(e + Sqrt[e^2 - 4*d*f] + 2*f*x)) - (3*f*(a + x*(b + c*x))^(3/2)*(((-4*b*c*f - 2*c*(b*f + 2*c*(-e + Sqrt[e^2 - 4*d*f])) - 4*c^2*f*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((2*Sqrt[c]*(b^2*f^2 + 4*c^2*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) + 4*c*f*(a*f - b*(e - Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/f + (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - c*e*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*(4*c*f*(8*a*b*f^2 - 3*b^2*f*(e - Sqrt[e^2 - 4*d*f]) - 4*a*c*f*(e - Sqrt[e^2 - 4*d*f]) + 4*b*c*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f])) + 4*c*(-e + Sqrt[e^2 - 4*d*f])*(b^2*f^2 + 4*c^2*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) + 4*c*f*(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 + 2*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*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 + 8*b*f*(-e + Sqrt[e^2 - 4*d*f]) + 4*c*(-e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2)))/((e^2 - 4*d*f)*(a + b*x + c*x^2)^(3/2)) + (f*(a + x*(b + c*x))^(3/2)*(((-4*c*f*(4*a*f - b*(e - Sqrt[e^2 - 4*d*f])) - 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*(b*f + 2*c*(-e + Sqrt[e^2 - 4*d*f])) - 4*c*f*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((-2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*(b^2*f^2 - 4*c^2*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(3*a*f - b*(e - Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c]*f) + (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - c*e*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*(-4*(-e + Sqrt[e^2 - 4*d*f])*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*(b^2*f^2 - 4*c^2*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(3*a*f - b*(e - Sqrt[e^2 - 4*d*f]))) + 4*f*(2*c*f*(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]))^2 - (e - Sqrt[e^2 - 4*d*f])*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*(b^2*f + 4*a*c*f - 2*b*c*(e - Sqrt[e^2 - 4*d*f]))))*ArcTanh[(-4*a*f - b*(-e + Sqrt[e^2 - 4*d*f]) - (2*b*f + 2*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*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 + 8*b*f*(-e + Sqrt[e^2 - 4*d*f]) + 4*c*(-e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2)))/((e^2 - 4*d*f)^(3/2)*(a + b*x + c*x^2)^(3/2)) - (f*(a + x*(b + c*x))^(3/2)*(((4*c*f*(-4*a*f + b*(e + Sqrt[e^2 - 4*d*f])) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*(-(b*f) + 2*c*(e + Sqrt[e^2 - 4*d*f])) - 4*c*f*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((-2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*(b^2*f^2 - 4*c^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(3*a*f - b*(e + Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c]*f) - (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + c*e*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*(4*(e + Sqrt[e^2 - 4*d*f])*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*(b^2*f^2 - 4*c^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(3*a*f - b*(e + Sqrt[e^2 - 4*d*f]))) + 4*f*(2*c*f*(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]))^2 - (e + Sqrt[e^2 - 4*d*f])*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*(b^2*f + 4*a*c*f - 2*b*c*(e + Sqrt[e^2 - 4*d*f]))))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) - (-2*b*f + 2*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*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 - 8*b*f*(e + Sqrt[e^2 - 4*d*f]) + 4*c*(e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2)))/((e^2 - 4*d*f)^(3/2)*(a + b*x + c*x^2)^(3/2)) + (3*f*(a + x*(b + c*x))^(3/2)*(((4*b*c*f - 2*c*(-(b*f) + 2*c*(e + Sqrt[e^2 - 4*d*f])) + 4*c^2*f*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((-2*Sqrt[c]*(b^2*f^2 + 4*c^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) + 4*c*f*(a*f - b*(e + Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/f - (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + c*e*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*(4*c*(e + Sqrt[e^2 - 4*d*f])*(b^2*f^2 + 4*c^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) + 4*c*f*(a*f - b*(e + Sqrt[e^2 - 4*d*f]))) + 4*c*f*(3*b^2*f*(e + Sqrt[e^2 - 4*d*f]) + 4*a*c*f*(e + Sqrt[e^2 - 4*d*f]) - 4*b*(2*a*f^2 + c*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]))))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) - (-2*b*f + 2*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*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 - 8*b*f*(e + Sqrt[e^2 - 4*d*f]) + 4*c*(e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2)))/((e^2 - 4*d*f)*(a + b*x + c*x^2)^(3/2))","B",0
108,1,4727,671,7.2286417,"\int \frac{\left(a+b x+c x^2\right)^{3/2}}{\left(d+e x+f x^2\right)^3} \, dx","Integrate[(a + b*x + c*x^2)^(3/2)/(d + e*x + f*x^2)^3,x]","\text{Result too large to show}","-\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)-\left(b^2 \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)-\left(b^2 \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,"(-2*f^2*(a + x*(b + c*x))^(3/2))/((e^2 - 4*d*f)^(3/2)*(e - Sqrt[e^2 - 4*d*f] + 2*f*x)^2) + (6*f^2*(a + x*(b + c*x))^(3/2))/((e^2 - 4*d*f)^2*(e - Sqrt[e^2 - 4*d*f] + 2*f*x)) + (2*f^2*(a + x*(b + c*x))^(3/2))/((e^2 - 4*d*f)^(3/2)*(e + Sqrt[e^2 - 4*d*f] + 2*f*x)^2) + (6*f^2*(a + x*(b + c*x))^(3/2))/((e^2 - 4*d*f)^2*(e + Sqrt[e^2 - 4*d*f] + 2*f*x)) + (9*f^2*(a + x*(b + c*x))^(3/2)*(((-4*b*c*f - 2*c*(b*f + 2*c*(-e + Sqrt[e^2 - 4*d*f])) - 4*c^2*f*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((2*Sqrt[c]*(b^2*f^2 + 4*c^2*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) + 4*c*f*(a*f - b*(e - Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/f + (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - c*e*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*(4*c*f*(8*a*b*f^2 - 3*b^2*f*(e - Sqrt[e^2 - 4*d*f]) - 4*a*c*f*(e - Sqrt[e^2 - 4*d*f]) + 4*b*c*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f])) + 4*c*(-e + Sqrt[e^2 - 4*d*f])*(b^2*f^2 + 4*c^2*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) + 4*c*f*(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 + 2*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*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 + 8*b*f*(-e + Sqrt[e^2 - 4*d*f]) + 4*c*(-e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2)))/((e^2 - 4*d*f)^2*(a + b*x + c*x^2)^(3/2)) - (3*f^2*(a + x*(b + c*x))^(3/2)*(((-4*c*f*(4*a*f - b*(e - Sqrt[e^2 - 4*d*f])) - 2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*(b*f + 2*c*(-e + Sqrt[e^2 - 4*d*f])) - 4*c*f*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((-2*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*(b^2*f^2 - 4*c^2*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(3*a*f - b*(e - Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c]*f) + (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - c*e*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*(-4*(-e + Sqrt[e^2 - 4*d*f])*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*(b^2*f^2 - 4*c^2*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(3*a*f - b*(e - Sqrt[e^2 - 4*d*f]))) + 4*f*(2*c*f*(4*a*f - b*(e - Sqrt[e^2 - 4*d*f]))^2 - (e - Sqrt[e^2 - 4*d*f])*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*(b^2*f + 4*a*c*f - 2*b*c*(e - Sqrt[e^2 - 4*d*f]))))*ArcTanh[(-4*a*f - b*(-e + Sqrt[e^2 - 4*d*f]) - (2*b*f + 2*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*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 + 8*b*f*(-e + Sqrt[e^2 - 4*d*f]) + 4*c*(-e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2)))/((e^2 - 4*d*f)^(5/2)*(a + b*x + c*x^2)^(3/2)) + (3*f^2*(a + x*(b + c*x))^(3/2)*(((-2*b*f - 2*c*(-e + Sqrt[e^2 - 4*d*f]))*(a + b*x + c*x^2)^(3/2))/((-4*a*f^2 - 2*b*f*(-e + Sqrt[e^2 - 4*d*f]) - c*(-e + Sqrt[e^2 - 4*d*f])^2)*(-e + Sqrt[e^2 - 4*d*f] - 2*f*x)) + (((-4*c*f*(b^2*f + 4*a*c*f - 2*b*c*(e - Sqrt[e^2 - 4*d*f])) - 4*c*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*(b*f + 2*c*(-e + Sqrt[e^2 - 4*d*f])) - 8*c^2*f*(b*f - c*(e - Sqrt[e^2 - 4*d*f]))*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((16*c^(3/2)*(b*f - c*(e - Sqrt[e^2 - 4*d*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[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/f + (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - c*e*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*(32*c^2*(-e + Sqrt[e^2 - 4*d*f])*(b*f - c*(e - Sqrt[e^2 - 4*d*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]))) + 16*c*f*(b^2*f + 4*a*c*f - 2*b*c*(e - Sqrt[e^2 - 4*d*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 + 2*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*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 + 8*b*f*(-e + Sqrt[e^2 - 4*d*f]) + 4*c*(-e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2))/(-4*a*f^2 - 2*b*f*(-e + Sqrt[e^2 - 4*d*f]) - c*(-e + Sqrt[e^2 - 4*d*f])^2)))/((e^2 - 4*d*f)^(3/2)*(a + b*x + c*x^2)^(3/2)) + (3*f^2*(a + x*(b + c*x))^(3/2)*(((4*c*f*(-4*a*f + b*(e + Sqrt[e^2 - 4*d*f])) + 2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*(-(b*f) + 2*c*(e + Sqrt[e^2 - 4*d*f])) - 4*c*f*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((-2*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*(b^2*f^2 - 4*c^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(3*a*f - b*(e + Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c]*f) - (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + c*e*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*(4*(e + Sqrt[e^2 - 4*d*f])*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*(b^2*f^2 - 4*c^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) - 4*c*f*(3*a*f - b*(e + Sqrt[e^2 - 4*d*f]))) + 4*f*(2*c*f*(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]))^2 - (e + Sqrt[e^2 - 4*d*f])*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*(b^2*f + 4*a*c*f - 2*b*c*(e + Sqrt[e^2 - 4*d*f]))))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) - (-2*b*f + 2*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*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 - 8*b*f*(e + Sqrt[e^2 - 4*d*f]) + 4*c*(e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2)))/((e^2 - 4*d*f)^(5/2)*(a + b*x + c*x^2)^(3/2)) - (9*f^2*(a + x*(b + c*x))^(3/2)*(((4*b*c*f - 2*c*(-(b*f) + 2*c*(e + Sqrt[e^2 - 4*d*f])) + 4*c^2*f*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((-2*Sqrt[c]*(b^2*f^2 + 4*c^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) + 4*c*f*(a*f - b*(e + Sqrt[e^2 - 4*d*f])))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/f - (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + c*e*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*(4*c*(e + Sqrt[e^2 - 4*d*f])*(b^2*f^2 + 4*c^2*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]) + 4*c*f*(a*f - b*(e + Sqrt[e^2 - 4*d*f]))) + 4*c*f*(3*b^2*f*(e + Sqrt[e^2 - 4*d*f]) + 4*a*c*f*(e + Sqrt[e^2 - 4*d*f]) - 4*b*(2*a*f^2 + c*(e^2 - 2*d*f + e*Sqrt[e^2 - 4*d*f]))))*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) - (-2*b*f + 2*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*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 - 8*b*f*(e + Sqrt[e^2 - 4*d*f]) + 4*c*(e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2)))/((e^2 - 4*d*f)^2*(a + b*x + c*x^2)^(3/2)) - (3*f^2*(a + x*(b + c*x))^(3/2)*(((2*b*f - 2*c*(e + Sqrt[e^2 - 4*d*f]))*(a + b*x + c*x^2)^(3/2))/((-4*a*f^2 + 2*b*f*(e + Sqrt[e^2 - 4*d*f]) - c*(e + Sqrt[e^2 - 4*d*f])^2)*(e + Sqrt[e^2 - 4*d*f] + 2*f*x)) + (((4*c*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*(-(b*f) + 2*c*(e + Sqrt[e^2 - 4*d*f])) + 4*c*f*(-(b^2*f) - 4*a*c*f + 2*b*c*(e + Sqrt[e^2 - 4*d*f])) - 8*c^2*f*(b*f - c*(e + Sqrt[e^2 - 4*d*f]))*x)*Sqrt[a + b*x + c*x^2])/(8*c*f^2) - ((16*c^(3/2)*(b*f - c*(e + Sqrt[e^2 - 4*d*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[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/f - (2*Sqrt[2]*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + c*e*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*(-32*c^2*(e + Sqrt[e^2 - 4*d*f])*(b*f - c*(e + Sqrt[e^2 - 4*d*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]))) + 16*c*f*(b^2*f + 4*a*c*f - 2*b*c*(e + Sqrt[e^2 - 4*d*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 + 2*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*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/(f*(16*a*f^2 - 8*b*f*(e + Sqrt[e^2 - 4*d*f]) + 4*c*(e + Sqrt[e^2 - 4*d*f])^2)))/(16*c*f^2))/(-4*a*f^2 + 2*b*f*(e + Sqrt[e^2 - 4*d*f]) - c*(e + Sqrt[e^2 - 4*d*f])^2)))/((e^2 - 4*d*f)^(3/2)*(a + b*x + c*x^2)^(3/2))","B",0
109,1,615,717,1.345724,"\int \frac{\left(d+e x+f x^2\right)^3}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(d + e*x + f*x^2)^3/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+x (b+c x)} \left(48 c^3 \left(2 a^2 f^2 (128 e+25 f x)+2 a b f \left(f \left(275 d+39 f x^2\right)+275 e^2+161 e f x\right)+b^2 \left(6 e f \left(100 d+21 f x^2\right)+f^2 x \left(175 d+33 f x^2\right)+100 e^3+175 e^2 f x\right)\right)-168 b c^2 f \left(66 a^2 f^2+42 a b f (5 e+f x)+b^2 \left(75 d f+75 e^2+45 e f x+11 f^2 x^2\right)\right)+210 b^3 c f^2 (68 a f+54 b e+11 b f x)-64 c^4 \left(a \left(96 e f \left(5 d+f x^2\right)+5 f^2 x \left(27 d+5 f x^2\right)+80 e^3+135 e^2 f x\right)+b \left(270 d^2 f+15 d \left(18 e^2+20 e f x+7 f^2 x^2\right)+x \left(50 e^3+105 e^2 f x+81 e f^2 x^2+22 f^3 x^3\right)\right)\right)-3465 b^5 f^3+128 c^5 \left(90 d^2 (2 e+f x)+15 d x \left(6 e^2+8 e f x+3 f^2 x^2\right)+x^2 \left(20 e^3+45 e^2 f x+36 e f^2 x^2+10 f^3 x^3\right)\right)\right)}{7680 c^6}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+x (b+c x)}}\right) \left(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)+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(a^3 f^3+9 a^2 b e f^2+9 a b^2 f \left(d f+e^2\right)+b^3 \left(6 d e f+e^3\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{\sqrt{a+b x+c x^2} \left(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)-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)+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(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)+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(a^3 f^3+9 a^2 b e f^2+9 a b^2 f \left(d f+e^2\right)+b^3 \left(6 d e f+e^3\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^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 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{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,"(Sqrt[a + x*(b + c*x)]*(-3465*b^5*f^3 + 210*b^3*c*f^2*(54*b*e + 68*a*f + 11*b*f*x) - 168*b*c^2*f*(66*a^2*f^2 + 42*a*b*f*(5*e + f*x) + b^2*(75*e^2 + 75*d*f + 45*e*f*x + 11*f^2*x^2)) + 128*c^5*(90*d^2*(2*e + f*x) + 15*d*x*(6*e^2 + 8*e*f*x + 3*f^2*x^2) + x^2*(20*e^3 + 45*e^2*f*x + 36*e*f^2*x^2 + 10*f^3*x^3)) + 48*c^3*(2*a^2*f^2*(128*e + 25*f*x) + b^2*(100*e^3 + 175*e^2*f*x + 6*e*f*(100*d + 21*f*x^2) + f^2*x*(175*d + 33*f*x^2)) + 2*a*b*f*(275*e^2 + 161*e*f*x + f*(275*d + 39*f*x^2))) - 64*c^4*(a*(80*e^3 + 135*e^2*f*x + 96*e*f*(5*d + f*x^2) + 5*f^2*x*(27*d + 5*f*x^2)) + b*(270*d^2*f + 15*d*(18*e^2 + 20*e*f*x + 7*f^2*x^2) + x*(50*e^3 + 105*e^2*f*x + 81*e*f^2*x^2 + 22*f^3*x^3)))))/(7680*c^6) + ((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 + x*(b + c*x)])])/(1024*c^(13/2))","A",1
110,1,251,316,0.502761,"\int \frac{\left(d+e x+f x^2\right)^2}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(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+x (b+c x)}}\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{\sqrt{a+x (b+c x)} \left(-8 c^2 \left(a f (32 e+9 f x)+b \left(36 d f+18 e^2+20 e f x+7 f^2 x^2\right)\right)+10 b c f (22 a f+24 b e+7 b f x)-105 b^3 f^2+16 c^3 \left(12 d (2 e+f x)+x \left(6 e^2+8 e f x+3 f^2 x^2\right)\right)\right)}{192 c^4}","\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{\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{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{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,"(Sqrt[a + x*(b + c*x)]*(-105*b^3*f^2 + 10*b*c*f*(24*b*e + 22*a*f + 7*b*f*x) + 16*c^3*(12*d*(2*e + f*x) + x*(6*e^2 + 8*e*f*x + 3*f^2*x^2)) - 8*c^2*(a*f*(32*e + 9*f*x) + b*(18*e^2 + 36*d*f + 20*e*f*x + 7*f^2*x^2))))/(192*c^4) + ((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 + x*(b + c*x)])])/(128*c^(9/2))","A",1
111,1,96,116,0.1464255,"\int \frac{d+e x+f x^2}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(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+x (b+c x)}}\right) \left(-4 c (a f+b e)+3 b^2 f+8 c^2 d\right)}{8 c^{5/2}}+\frac{\sqrt{a+x (b+c x)} (-3 b f+4 c e+2 c f x)}{4 c^2}","\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 + 2*c*f*x)*Sqrt[a + x*(b + c*x)])/(4*c^2) + ((8*c^2*d + 3*b^2*f - 4*c*(b*e + a*f))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + x*(b + c*x)])])/(8*c^(5/2))","A",1
112,1,376,374,1.4541926,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)} \, dx","Integrate[1/(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2)),x]","\frac{\sqrt{2} f \left(\frac{\tanh ^{-1}\left(\frac{4 a f-b \left(\sqrt{e^2-4 d f}+e-2 f x\right)-2 c x \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+x (b+c x)} \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)}}\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{\tanh ^{-1}\left(\frac{4 a f+b \left(\sqrt{e^2-4 d f}-e+2 f x\right)+2 c x \left(\sqrt{e^2-4 d f}-e\right)}{2 \sqrt{2} \sqrt{a+x (b+c x)} \sqrt{f \left(2 a f+b \sqrt{e^2-4 d f}+b (-e)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)}}\right)}{\sqrt{f \left(2 a f+b \sqrt{e^2-4 d f}+b (-e)\right)+c \left(-e \sqrt{e^2-4 d f}-2 d f+e^2\right)}}\right)}{\sqrt{e^2-4 d f}}","\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 - 2*c*(e + Sqrt[e^2 - 4*d*f])*x - b*(e + Sqrt[e^2 - 4*d*f] - 2*f*x))/(2*Sqrt[2]*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]))]*Sqrt[a + x*(b + c*x)])]/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 + 2*c*(-e + Sqrt[e^2 - 4*d*f])*x + b*(-e + Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*Sqrt[2]*Sqrt[f*(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f]) + c*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f])]*Sqrt[a + x*(b + c*x)])]/Sqrt[f*(-(b*e) + 2*a*f + b*Sqrt[e^2 - 4*d*f]) + c*(e^2 - 2*d*f - e*Sqrt[e^2 - 4*d*f])]))/Sqrt[e^2 - 4*d*f]","A",1
113,1,1377,789,6.6892023,"\int \frac{1}{\sqrt{a+b x+c x^2} \left(d+e x+f x^2\right)^2} \, dx","Integrate[1/(Sqrt[a + b*x + c*x^2]*(d + e*x + f*x^2)^2),x]","-\frac{8 \left(c x^2+b x+a\right) f^3}{\left(e^2-4 d f\right) \left(4 a f^2-2 b \left(e-\sqrt{e^2-4 d f}\right) f+c \left(e-\sqrt{e^2-4 d f}\right)^2\right) \left(e+2 f x-\sqrt{e^2-4 d f}\right) \sqrt{a+x (b+c x)}}-\frac{8 \left(c x^2+b x+a\right) f^3}{\left(e^2-4 d f\right) \left(4 a f^2-2 b \left(e+\sqrt{e^2-4 d f}\right) f+c \left(e+\sqrt{e^2-4 d f}\right)^2\right) \left(e+2 f x+\sqrt{e^2-4 d f}\right) \sqrt{a+x (b+c x)}}+\frac{2 \sqrt{2} \sqrt{c x^2+b x+a} \tanh ^{-1}\left(\frac{4 a f-b \left(e-\sqrt{e^2-4 d f}\right)+2 \left(b f-c \left(e-\sqrt{e^2-4 d f}\right)\right) x}{2 \sqrt{2} \sqrt{c \left(e^2-\sqrt{e^2-4 d f} e-2 d f\right)+f \left(2 a f-b \left(e-\sqrt{e^2-4 d f}\right)\right)} \sqrt{c x^2+b x+a}}\right) f^2}{\left(e^2-4 d f\right)^{3/2} \sqrt{c \left(e^2-\sqrt{e^2-4 d f} e-2 d f\right)+f \left(2 a f-b \left(e-\sqrt{e^2-4 d f}\right)\right)} \sqrt{a+x (b+c x)}}-\frac{8 \sqrt{2} \sqrt{c e^2-b f e-c \sqrt{e^2-4 d f} e+2 a f^2-2 c d f+b f \sqrt{e^2-4 d f}} \left(2 b f+2 c \left(\sqrt{e^2-4 d f}-e\right)\right) \sqrt{c x^2+b x+a} \tanh ^{-1}\left(\frac{-4 a f-b \left(\sqrt{e^2-4 d f}-e\right)-\left(2 b f+2 c \left(\sqrt{e^2-4 d f}-e\right)\right) x}{2 \sqrt{2} \sqrt{c e^2-b f e-c \sqrt{e^2-4 d f} e+2 a f^2-2 c d f+b f \sqrt{e^2-4 d f}} \sqrt{c x^2+b x+a}}\right) f^2}{\left(e^2-4 d f\right) \left(4 a f^2+2 b \left(\sqrt{e^2-4 d f}-e\right) f+c \left(\sqrt{e^2-4 d f}-e\right)^2\right) \left(16 a f^2+8 b \left(\sqrt{e^2-4 d f}-e\right) f+4 c \left(\sqrt{e^2-4 d f}-e\right)^2\right) \sqrt{a+x (b+c x)}}-\frac{2 \sqrt{2} \sqrt{c x^2+b x+a} \tanh ^{-1}\left(\frac{4 a f-b \left(e+\sqrt{e^2-4 d f}\right)+2 \left(b f-c \left(e+\sqrt{e^2-4 d f}\right)\right) x}{2 \sqrt{2} \sqrt{c \left(e^2+\sqrt{e^2-4 d f} e-2 d f\right)+f \left(2 a f-b \left(e+\sqrt{e^2-4 d f}\right)\right)} \sqrt{c x^2+b x+a}}\right) f^2}{\left(e^2-4 d f\right)^{3/2} \sqrt{c \left(e^2+\sqrt{e^2-4 d f} e-2 d f\right)+f \left(2 a f-b \left(e+\sqrt{e^2-4 d f}\right)\right)} \sqrt{a+x (b+c x)}}-\frac{8 \sqrt{2} \sqrt{c e^2-b f e+c \sqrt{e^2-4 d f} e+2 a f^2-2 c d f-b f \sqrt{e^2-4 d f}} \left(2 c \left(e+\sqrt{e^2-4 d f}\right)-2 b f\right) \sqrt{c x^2+b x+a} \tanh ^{-1}\left(\frac{4 a f-b \left(e+\sqrt{e^2-4 d f}\right)-\left(2 c \left(e+\sqrt{e^2-4 d f}\right)-2 b f\right) x}{2 \sqrt{2} \sqrt{c e^2-b f e+c \sqrt{e^2-4 d f} e+2 a f^2-2 c d f-b f \sqrt{e^2-4 d f}} \sqrt{c x^2+b x+a}}\right) f^2}{\left(e^2-4 d f\right) \left(4 a f^2-2 b \left(e+\sqrt{e^2-4 d f}\right) f+c \left(e+\sqrt{e^2-4 d f}\right)^2\right) \left(16 a f^2-8 b \left(e+\sqrt{e^2-4 d f}\right) f+4 c \left(e+\sqrt{e^2-4 d f}\right)^2\right) \sqrt{a+x (b+c 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(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,"(-8*f^3*(a + b*x + c*x^2))/((e^2 - 4*d*f)*(4*a*f^2 - 2*b*f*(e - Sqrt[e^2 - 4*d*f]) + c*(e - Sqrt[e^2 - 4*d*f])^2)*(e - Sqrt[e^2 - 4*d*f] + 2*f*x)*Sqrt[a + x*(b + c*x)]) - (8*f^3*(a + b*x + c*x^2))/((e^2 - 4*d*f)*(4*a*f^2 - 2*b*f*(e + Sqrt[e^2 - 4*d*f]) + c*(e + Sqrt[e^2 - 4*d*f])^2)*(e + Sqrt[e^2 - 4*d*f] + 2*f*x)*Sqrt[a + x*(b + c*x)]) + (2*Sqrt[2]*f^2*Sqrt[a + b*x + c*x^2]*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*d*f - e*Sqrt[e^2 - 4*d*f]) + f*(2*a*f - b*(e - Sqrt[e^2 - 4*d*f]))]*Sqrt[a + b*x + c*x^2])])/((e^2 - 4*d*f)^(3/2)*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]))]*Sqrt[a + x*(b + c*x)]) - (8*Sqrt[2]*f^2*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 - c*e*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*(2*b*f + 2*c*(-e + Sqrt[e^2 - 4*d*f]))*Sqrt[a + b*x + c*x^2]*ArcTanh[(-4*a*f - b*(-e + Sqrt[e^2 - 4*d*f]) - (2*b*f + 2*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*Sqrt[e^2 - 4*d*f] + b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/((e^2 - 4*d*f)*(4*a*f^2 + 2*b*f*(-e + Sqrt[e^2 - 4*d*f]) + c*(-e + Sqrt[e^2 - 4*d*f])^2)*(16*a*f^2 + 8*b*f*(-e + Sqrt[e^2 - 4*d*f]) + 4*c*(-e + Sqrt[e^2 - 4*d*f])^2)*Sqrt[a + x*(b + c*x)]) - (2*Sqrt[2]*f^2*Sqrt[a + b*x + c*x^2]*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*d*f + e*Sqrt[e^2 - 4*d*f]) + f*(2*a*f - b*(e + Sqrt[e^2 - 4*d*f]))]*Sqrt[a + b*x + c*x^2])])/((e^2 - 4*d*f)^(3/2)*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]))]*Sqrt[a + x*(b + c*x)]) - (8*Sqrt[2]*f^2*Sqrt[c*e^2 - 2*c*d*f - b*e*f + 2*a*f^2 + c*e*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*(-2*b*f + 2*c*(e + Sqrt[e^2 - 4*d*f]))*Sqrt[a + b*x + c*x^2]*ArcTanh[(4*a*f - b*(e + Sqrt[e^2 - 4*d*f]) - (-2*b*f + 2*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*Sqrt[e^2 - 4*d*f] - b*f*Sqrt[e^2 - 4*d*f]]*Sqrt[a + b*x + c*x^2])])/((e^2 - 4*d*f)*(4*a*f^2 - 2*b*f*(e + Sqrt[e^2 - 4*d*f]) + c*(e + Sqrt[e^2 - 4*d*f])^2)*(16*a*f^2 - 8*b*f*(e + Sqrt[e^2 - 4*d*f]) + 4*c*(e + Sqrt[e^2 - 4*d*f])^2)*Sqrt[a + x*(b + c*x)])","A",0
114,1,745,649,1.664357,"\int \frac{\left(d+e x+f x^2\right)^3}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(d + e*x + f*x^2)^3/(a + b*x + c*x^2)^(3/2),x]","\frac{3 \log \left(2 \sqrt{c} \sqrt{a+x (b+c x)}+b+2 c x\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{-8 b^3 c \left(210 a^2 f^3+a c f \left(f \left(77 f x^2-90 d\right)-90 e^2-530 e f x\right)-c^2 x \left(2 e f \left(7 f x^2-72 d\right)+3 f^2 x \left(10 d+f x^2\right)-24 e^3+30 e^2 f x\right)\right)-16 b^2 c^2 \left(-a^2 f^2 (230 e+169 f x)+a c \left(2 e f \left(36 d-43 f x^2\right)+f^2 x \left(186 d-13 f x^2\right)+12 e^3+186 e^2 f x\right)+c^2 x \left(-24 d^2 f+6 d \left(-4 e^2+4 e f x+f^2 x^2\right)+x \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right)\right)\right)+16 b c^2 \left(113 a^3 f^3+a^2 c f \left(f \left(49 f x^2-156 d\right)-156 e^2-244 e f x\right)+2 a c^2 \left(12 d^2 f+6 d \left(2 e^2+20 e f x-5 f^2 x^2\right)-x \left(-20 e^3+30 e^2 f x+14 e f^2 x^2+3 f^3 x^3\right)\right)+8 c^3 d^2 (d-3 e x)\right)+32 c^3 \left(a^3 \left(-f^2\right) (64 e+15 f x)+a^2 c \left(-32 e f \left(f x^2-3 d\right)+f^2 x \left(36 d-5 f x^2\right)+16 e^3+36 e^2 f x\right)+2 a c^2 \left(-12 d^2 (e+f x)+6 d x \left(-2 e^2+4 e f x+f^2 x^2\right)+x^2 \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right)\right)+8 c^3 d^3 x\right)+105 b^5 f^2 (3 a f+c x (f x-8 e))-2 b^4 c f \left(105 a f (4 e+9 f x)+c x \left(-360 d f-360 e^2+140 e f x+21 f^2 x^2\right)\right)+315 b^6 f^3 x}{64 c^5 \left(4 a c-b^2\right) \sqrt{a+x (b+c x)}}","\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{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^4 f^2-2 b^3 c e f+b^2 c^2 d f+b^2 c^2 e^2-b c^3 d e+c^4 d^2\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)-b c^2 \left(5 a^3 f^3-9 a^2 c f \left(d f+e^2\right)+3 a c^2 d \left(d f+e^2\right)+c^3 d^3\right)-a b^5 f^3+3 a b^4 c e f^2+a b^3 c f \left(5 a f^2-3 c \left(d f+e^2\right)\right)-a b^2 c^2 e \left(12 a f^2-c \left(6 d f+e^2\right)\right)\right)}{c^5 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\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 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{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,"(315*b^6*f^3*x + 105*b^5*f^2*(3*a*f + c*x*(-8*e + f*x)) - 2*b^4*c*f*(105*a*f*(4*e + 9*f*x) + c*x*(-360*e^2 - 360*d*f + 140*e*f*x + 21*f^2*x^2)) - 8*b^3*c*(210*a^2*f^3 - c^2*x*(-24*e^3 + 30*e^2*f*x + 3*f^2*x*(10*d + f*x^2) + 2*e*f*(-72*d + 7*f*x^2)) + a*c*f*(-90*e^2 - 530*e*f*x + f*(-90*d + 77*f*x^2))) - 16*b^2*c^2*(-(a^2*f^2*(230*e + 169*f*x)) + a*c*(12*e^3 + 186*e^2*f*x + 2*e*f*(36*d - 43*f*x^2) + f^2*x*(186*d - 13*f*x^2)) + c^2*x*(-24*d^2*f + 6*d*(-4*e^2 + 4*e*f*x + f^2*x^2) + x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3))) + 32*c^3*(8*c^3*d^3*x - a^3*f^2*(64*e + 15*f*x) + a^2*c*(16*e^3 + 36*e^2*f*x + f^2*x*(36*d - 5*f*x^2) - 32*e*f*(-3*d + f*x^2)) + 2*a*c^2*(-12*d^2*(e + f*x) + 6*d*x*(-2*e^2 + 4*e*f*x + f^2*x^2) + x^2*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3))) + 16*b*c^2*(113*a^3*f^3 + 8*c^3*d^2*(d - 3*e*x) + a^2*c*f*(-156*e^2 - 244*e*f*x + f*(-156*d + 49*f*x^2)) + 2*a*c^2*(12*d^2*f + 6*d*(2*e^2 + 20*e*f*x - 5*f^2*x^2) - x*(-20*e^3 + 30*e^2*f*x + 14*e*f^2*x^2 + 3*f^3*x^3))))/(64*c^5*(-b^2 + 4*a*c)*Sqrt[a + x*(b + c*x)]) + (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)))*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/(128*c^(11/2))","A",1
115,1,288,309,0.7332153,"\int \frac{\left(d+e x+f x^2\right)^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(d + e*x + f*x^2)^2/(a + b*x + c*x^2)^(3/2),x]","\frac{4 b c \left(-13 a^2 f^2+a c \left(4 d f+2 e^2+20 e f x-5 f^2 x^2\right)+2 c^2 d (d-2 e x)\right)+8 c^2 \left(a^2 f (8 e+3 f x)+a c \left(x \left(-2 e^2+4 e f x+f^2 x^2\right)-4 d (e+f x)\right)+2 c^2 d^2 x\right)+b^3 f (15 a f+c x (5 f x-24 e))-2 b^2 c \left(a f (12 e+31 f x)+c x \left(-8 d f-4 e^2+4 e f x+f^2 x^2\right)\right)+15 b^4 f^2 x}{4 c^3 \left(4 a c-b^2\right) \sqrt{a+x (b+c x)}}+\frac{\log \left(2 \sqrt{c} \sqrt{a+x (b+c x)}+b+2 c x\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{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)-a b^3 f^2+2 a b^2 c e f+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,"(15*b^4*f^2*x + b^3*f*(15*a*f + c*x*(-24*e + 5*f*x)) + 4*b*c*(-13*a^2*f^2 + 2*c^2*d*(d - 2*e*x) + a*c*(2*e^2 + 4*d*f + 20*e*f*x - 5*f^2*x^2)) - 2*b^2*c*(a*f*(12*e + 31*f*x) + c*x*(-4*e^2 - 8*d*f + 4*e*f*x + f^2*x^2)) + 8*c^2*(2*c^2*d^2*x + a^2*f*(8*e + 3*f*x) + a*c*(-4*d*(e + f*x) + x*(-2*e^2 + 4*e*f*x + f^2*x^2))))/(4*c^3*(-b^2 + 4*a*c)*Sqrt[a + x*(b + c*x)]) + ((15*b^2*f^2 - 12*c*f*(2*b*e + a*f) + 8*c^2*(e^2 + 2*d*f))*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/(8*c^(7/2))","A",1
116,1,113,111,0.3114434,"\int \frac{d+e x+f x^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(d + e*x + f*x^2)/(a + b*x + c*x^2)^(3/2),x]","\frac{\frac{2 \sqrt{c} \left(a b f-2 a c (e+f x)+b^2 f x+b c (d-e x)+2 c^2 d x\right)}{\sqrt{a+x (b+c x)}}-f \left(b^2-4 a c\right) \log \left(2 \sqrt{c} \sqrt{a+x (b+c x)}+b+2 c x\right)}{c^{3/2} \left(4 a c-b^2\right)}","\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*Sqrt[c]*(a*b*f + 2*c^2*d*x + b^2*f*x + b*c*(d - e*x) - 2*a*c*(e + f*x)))/Sqrt[a + x*(b + c*x)] - (b^2 - 4*a*c)*f*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/(c^(3/2)*(-b^2 + 4*a*c))","A",1
117,1,700,666,5.3429151,"\int \frac{1}{\left(a+b x+c x^2\right)^{3/2} \left(d+e x+f x^2\right)} \, dx","Integrate[1/((a + b*x + c*x^2)^(3/2)*(d + e*x + f*x^2)),x]","\frac{2 f \left(-\frac{2 \left(-2 c \left(2 a f+c x \left(\sqrt{e^2-4 d f}+e\right)\right)+2 b^2 f-b c \left(\sqrt{e^2-4 d f}+e-2 f x\right)\right)}{\left(b^2-4 a c\right) \sqrt{a+x (b+c x)} \left(4 a f^2-2 b f \left(\sqrt{e^2-4 d f}+e\right)+c \left(\sqrt{e^2-4 d f}+e\right)^2\right)}+\frac{2 c \left(c x \left(\sqrt{e^2-4 d f}-e\right)-2 a f\right)+2 b^2 f+b c \left(\sqrt{e^2-4 d f}-e+2 f x\right)}{\left(b^2-4 a c\right) \sqrt{a+x (b+c x)} \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)}+\frac{\sqrt{2} f^2 \tanh ^{-1}\left(\frac{4 a f-b \left(\sqrt{e^2-4 d f}+e-2 f x\right)-2 c x \left(\sqrt{e^2-4 d f}+e\right)}{2 \sqrt{2} \sqrt{a+x (b+c x)} \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)}}\right)}{\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)^{3/2}}-\frac{\sqrt{2} f^2 \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+b \left(\sqrt{e^2-4 d f}-e+2 f x\right)+2 c x \left(\sqrt{e^2-4 d f}-e\right)}{2 \sqrt{2} \sqrt{a+x (b+c x)} \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)}}\right)}{\left(f \left(b \left(e-\sqrt{e^2-4 d f}\right)-2 a f\right)+c \left(e \sqrt{e^2-4 d f}+2 d f-e^2\right)\right)^2}\right)}{\sqrt{e^2-4 d f}}","\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^3 (-f)+b^2 c e\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*f*((2*b^2*f + b*c*(-e + Sqrt[e^2 - 4*d*f] + 2*f*x) + 2*c*(-2*a*f + c*(-e + Sqrt[e^2 - 4*d*f])*x))/((b^2 - 4*a*c)*(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])))*Sqrt[a + x*(b + c*x)]) - (2*(2*b^2*f - b*c*(e + Sqrt[e^2 - 4*d*f] - 2*f*x) - 2*c*(2*a*f + c*(e + Sqrt[e^2 - 4*d*f])*x)))/((b^2 - 4*a*c)*(4*a*f^2 - 2*b*f*(e + Sqrt[e^2 - 4*d*f]) + c*(e + Sqrt[e^2 - 4*d*f])^2)*Sqrt[a + x*(b + c*x)]) + (Sqrt[2]*f^2*ArcTanh[(4*a*f - 2*c*(e + Sqrt[e^2 - 4*d*f])*x - b*(e + Sqrt[e^2 - 4*d*f] - 2*f*x))/(2*Sqrt[2]*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]))]*Sqrt[a + x*(b + c*x)])])/(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])))^(3/2) - (Sqrt[2]*f^2*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 + 2*c*(-e + Sqrt[e^2 - 4*d*f])*x + b*(-e + Sqrt[e^2 - 4*d*f] + 2*f*x))/(2*Sqrt[2]*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]))]*Sqrt[a + x*(b + c*x)])])/(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])))^2))/Sqrt[e^2 - 4*d*f]","A",1
118,1,872,891,2.1908146,"\int \frac{\left(d+e x+f x^2\right)^3}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(d + e*x + f*x^2)^3/(a + b*x + c*x^2)^(5/2),x]","\frac{-105 f^3 x^2 b^7-10 f^2 x (21 a f+2 c x (7 f x-9 e)) b^6-3 f \left(35 a^2 f^2-10 a c x (12 e+23 f x) f+c^2 x^2 \left(24 e^2-80 f x e+7 f^2 x^2+24 d f\right)\right) b^5+6 c f \left(c^2 \left(-16 e^2+6 f x e+f^2 x^2-16 d f\right) x^3-6 a c \left(4 e^2+30 f x e-31 f^2 x^2+4 d f\right) x+5 a^2 f (6 e+53 f x)\right) b^4-8 c \left(\left(d^3+9 x (e-f x) d^2-3 e x^2 (3 e+2 f x) d-e^3 x^3\right) c^3-3 a f x^2 \left(18 e^2-74 f x e+f \left(7 f x^2+18 d\right)\right) c^2+3 a^2 f \left(3 e^2+105 f x e+f \left(29 f x^2+3 d\right)\right) c-95 a^3 f^3\right) b^3-48 c^2 \left(f^2 (25 e+63 f x) a^3+c f x \left(-21 e^2-12 f x e+7 f \left(7 f x^2-3 d\right)\right) a^2+c^2 \left((e-6 f x) d^2-2 x \left(3 e^2-3 f x e+7 f^2 x^2\right) d+x^2 \left(e^3-14 f x e^2+6 f^2 x^2 e+f^3 x^3\right)\right) a-c^3 d x \left(d^2+x (f x-6 e) d+e^2 x^2\right)\right) b^2-48 c^2 \left(27 f^3 a^4-2 c f \left(5 e^2+39 f x e+f \left(5 d-14 f x^2\right)\right) a^3+c^2 \left(7 f^3 x^4-64 e f^2 x^3+4 e^3 x-4 d^2 f-4 d e (e-6 f x)\right) a^2-2 c^3 \left(d^3+3 x (f x-e) d^2+3 e x^2 (e-2 f x) d-e^3 x^3\right) a-4 c^4 d^2 x^2 (d-e x)\right) b+32 c^3 \left(3 f^2 (16 e+5 f x) a^4-2 c \left(2 e^3+9 f x e^2+12 f \left(d-3 f x^2\right) e+f^2 x \left(9 d-10 f x^2\right)\right) a^3-3 c^2 \left(2 e d^2+4 f x^2 (3 e+2 f x) d+x^2 \left(2 e^3+8 f x e^2-6 f^2 x^2 e-f^3 x^3\right)\right) a^2+6 c^3 d x \left(d^2+f x^2 d+e^2 x^2\right) a+4 c^4 d^3 x^3\right)}{12 c^4 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{3/2}}+\frac{f \left(24 \left(e^2+d f\right) c^2-20 f (3 b e+a f) c+35 b^2 f^2\right) \log \left(b+2 c x+2 \sqrt{c} \sqrt{a+x (b+c x)}\right)}{8 c^{9/2}}","\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,"(-105*b^7*f^3*x^2 - 10*b^6*f^2*x*(21*a*f + 2*c*x*(-9*e + 7*f*x)) + 6*b^4*c*f*(5*a^2*f*(6*e + 53*f*x) - 6*a*c*x*(4*e^2 + 4*d*f + 30*e*f*x - 31*f^2*x^2) + c^2*x^3*(-16*e^2 - 16*d*f + 6*e*f*x + f^2*x^2)) - 3*b^5*f*(35*a^2*f^2 - 10*a*c*f*x*(12*e + 23*f*x) + c^2*x^2*(24*e^2 + 24*d*f - 80*e*f*x + 7*f^2*x^2)) - 48*b*c^2*(27*a^4*f^3 - 4*c^4*d^2*x^2*(d - e*x) + a^2*c^2*(-4*d^2*f + 4*e^3*x - 64*e*f^2*x^3 + 7*f^3*x^4 - 4*d*e*(e - 6*f*x)) - 2*a*c^3*(d^3 - e^3*x^3 + 3*d*e*x^2*(e - 2*f*x) + 3*d^2*x*(-e + f*x)) - 2*a^3*c*f*(5*e^2 + 39*e*f*x + f*(5*d - 14*f*x^2))) - 8*b^3*c*(-95*a^3*f^3 + c^3*(d^3 - e^3*x^3 + 9*d^2*x*(e - f*x) - 3*d*e*x^2*(3*e + 2*f*x)) - 3*a*c^2*f*x^2*(18*e^2 - 74*e*f*x + f*(18*d + 7*f*x^2)) + 3*a^2*c*f*(3*e^2 + 105*e*f*x + f*(3*d + 29*f*x^2))) + 32*c^3*(4*c^4*d^3*x^3 + 3*a^4*f^2*(16*e + 5*f*x) + 6*a*c^3*d*x*(d^2 + e^2*x^2 + d*f*x^2) - 2*a^3*c*(2*e^3 + 9*e^2*f*x + f^2*x*(9*d - 10*f*x^2) + 12*e*f*(d - 3*f*x^2)) - 3*a^2*c^2*(2*d^2*e + 4*d*f*x^2*(3*e + 2*f*x) + x^2*(2*e^3 + 8*e^2*f*x - 6*e*f^2*x^2 - f^3*x^3))) - 48*b^2*c^2*(a^3*f^2*(25*e + 63*f*x) - c^3*d*x*(d^2 + e^2*x^2 + d*x*(-6*e + f*x)) + a^2*c*f*x*(-21*e^2 - 12*e*f*x + 7*f*(-3*d + 7*f*x^2)) + a*c^2*(d^2*(e - 6*f*x) - 2*d*x*(3*e^2 - 3*e*f*x + 7*f^2*x^2) + x^2*(e^3 - 14*e^2*f*x + 6*e*f^2*x^2 + f^3*x^3))))/(12*c^4*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2)) + (f*(35*b^2*f^2 - 20*c*f*(3*b*e + a*f) + 24*c^2*(e^2 + d*f))*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/(8*c^(9/2))","A",1
119,1,387,444,1.2569122,"\int \frac{\left(d+e x+f x^2\right)^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(d + e*x + f*x^2)^2/(a + b*x + c*x^2)^(5/2),x]","\frac{2 \left(b^3 \left(-3 a^2 f^2+18 a c f^2 x^2+c^2 \left(-d^2+6 d x (f x-e)+e x^2 (3 e+2 f x)\right)\right)+2 b^2 c \left(21 a^2 f^2 x-2 a c \left(d (e-6 f x)+x \left(-3 e^2+3 e f x-7 f^2 x^2\right)\right)+c^2 x \left(3 d^2+2 d x (f x-6 e)+e^2 x^2\right)\right)+4 b c \left(5 a^3 f^2+2 a^2 c \left(2 d f+e^2-6 e f x\right)+3 a c^2 (d-e x) (d+x (2 f x-e))+2 c^3 d x^2 (3 d-2 e x)\right)+8 c^2 \left(a^3 (-f) (4 e+3 f x)-2 a^2 c \left(d e+f x^2 (3 e+2 f x)\right)+a c^2 x \left(3 d^2+2 d f x^2+e^2 x^2\right)+2 c^3 d^2 x^3\right)-2 b^4 f^2 x \left(3 a+2 c x^2\right)-3 b^5 f^2 x^2\right)}{3 c^2 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{3/2}}+\frac{f^2 \log \left(2 \sqrt{c} \sqrt{a+x (b+c x)}+b+2 c x\right)}{c^{5/2}}","\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)-a b^3 f^2+2 a b^2 c e f+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{2 \left(-2 c x \left(-c^2 \left(16 a^2 f^2+12 a b e f-\left(b^2 \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+b^3 c \left(10 a f^2-c \left(2 d f+e^2\right)\right)+4 b^2 c^2 e (2 c d-3 a f)+b^5 \left(-f^2\right)+2 b^4 c e f\right)}{3 c^3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^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*(-3*b^5*f^2*x^2 - 2*b^4*f^2*x*(3*a + 2*c*x^2) + 4*b*c*(5*a^3*f^2 + 2*c^3*d*x^2*(3*d - 2*e*x) + 2*a^2*c*(e^2 + 2*d*f - 6*e*f*x) + 3*a*c^2*(d - e*x)*(d + x*(-e + 2*f*x))) + b^3*(-3*a^2*f^2 + 18*a*c*f^2*x^2 + c^2*(-d^2 + 6*d*x*(-e + f*x) + e*x^2*(3*e + 2*f*x))) + 8*c^2*(2*c^3*d^2*x^3 - a^3*f*(4*e + 3*f*x) + a*c^2*x*(3*d^2 + e^2*x^2 + 2*d*f*x^2) - 2*a^2*c*(d*e + f*x^2*(3*e + 2*f*x))) + 2*b^2*c*(21*a^2*f^2*x + c^2*x*(3*d^2 + e^2*x^2 + 2*d*x*(-6*e + f*x)) - 2*a*c*(d*(e - 6*f*x) + x*(-3*e^2 + 3*e*f*x - 7*f^2*x^2)))))/(3*c^2*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2)) + (f^2*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/c^(5/2)","A",1
120,1,147,131,0.3779365,"\int \frac{d+e x+f x^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(d + e*x + f*x^2)/(a + b*x + c*x^2)^(5/2),x]","\frac{8 b \left(2 a^2 f+3 a c \left(d-e x+f x^2\right)-2 c^2 x^2 (e x-3 d)\right)+16 c \left(-a^2 e+a c x \left(3 d+f x^2\right)+2 c^2 d x^3\right)-4 b^2 \left(a (e-6 f x)-c x \left(3 d-6 e x+f x^2\right)\right)-2 b^3 (d+3 x (e-f x))}{3 \left(b^2-4 a c\right)^2 (a+x (b+c x))^{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)}{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*b^3*(d + 3*x*(e - f*x)) + 16*c*(-(a^2*e) + 2*c^2*d*x^3 + a*c*x*(3*d + f*x^2)) - 4*b^2*(a*(e - 6*f*x) - c*x*(3*d - 6*e*x + f*x^2)) + 8*b*(2*a^2*f - 2*c^2*x^2*(-3*d + e*x) + 3*a*c*(d - e*x + f*x^2)))/(3*(b^2 - 4*a*c)^2*(a + x*(b + c*x))^(3/2))","A",1
121,1,81,51,0.0407923,"\int \frac{1}{\sqrt{-7+2 x+5 x^2} \left(8+12 x+5 x^2\right)} \, dx","Integrate[1/(Sqrt[-7 + 2*x + 5*x^2]*(8 + 12*x + 5*x^2)),x]","\left(\frac{1}{10}-\frac{i}{20}\right) \tanh ^{-1}\left(\frac{\left(\frac{1}{100}+\frac{i}{50}\right) ((100-40 i) x+(164-8 i))}{\sqrt{5 x^2+2 x-7}}\right)-\left(\frac{1}{20}-\frac{i}{10}\right) \tan ^{-1}\left(\frac{\left(\frac{1}{50}+\frac{i}{100}\right) ((-100-40 i) x-(164+8 i))}{\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,"(-1/20 + I/10)*ArcTan[((1/50 + I/100)*((-164 - 8*I) - (100 + 40*I)*x))/Sqrt[-7 + 2*x + 5*x^2]] + (1/10 - I/20)*ArcTanh[((1/100 + I/50)*((164 - 8*I) + (100 - 40*I)*x))/Sqrt[-7 + 2*x + 5*x^2]]","C",1
122,1,670,1432,2.3413243,"\int \frac{1}{\sqrt{a+b x+c x^2} \sqrt{d+e x+f x^2}} \, dx","Integrate[1/(Sqrt[a + b*x + c*x^2]*Sqrt[d + e*x + f*x^2]),x]","-\frac{\left(\sqrt{b^2-4 a c}-b-2 c x\right) \left(-\sqrt{e^2-4 d f}+e+2 f x\right) \sqrt{-\frac{c \sqrt{b^2-4 a c} \left(\sqrt{e^2-4 d f}+e+2 f x\right)}{\left(\sqrt{b^2-4 a c}-b-2 c x\right) \left(f \left(\sqrt{b^2-4 a c}+b\right)-c \left(\sqrt{e^2-4 d f}+e\right)\right)}} \sqrt{-\frac{c \left(\sqrt{b^2-4 a c} \sqrt{e^2-4 d f}-e \left(\sqrt{b^2-4 a c}+2 c x\right)-2 f x \sqrt{b^2-4 a c}+4 a f+b \left(\sqrt{e^2-4 d f}-e+2 f x\right)+2 c x \sqrt{e^2-4 d f}\right)}{\left(\sqrt{b^2-4 a c}-b-2 c x\right) \left(f \left(\sqrt{b^2-4 a c}+b\right)+c \left(\sqrt{e^2-4 d f}-e\right)\right)}} F\left(\sin ^{-1}\left(\sqrt{\frac{\left(\left(\sqrt{b^2-4 a c}-b\right) f+c \left(e-\sqrt{e^2-4 d f}\right)\right) \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{\left(\left(b+\sqrt{b^2-4 a c}\right) f+c \left(\sqrt{e^2-4 d f}-e\right)\right) \left(-b-2 c x+\sqrt{b^2-4 a c}\right)}}\right)|\frac{2 c d-b e+2 a f-\sqrt{b^2-4 a c} \sqrt{e^2-4 d f}}{2 c d-b e+2 a f+\sqrt{b^2-4 a c} \sqrt{e^2-4 d f}}\right)}{\sqrt{a+x (b+c x)} \sqrt{d+x (e+f x)} \left(f \left(\sqrt{b^2-4 a c}-b\right)+c \left(e-\sqrt{e^2-4 d f}\right)\right) \sqrt{\frac{c \sqrt{b^2-4 a c} \left(\sqrt{e^2-4 d f}-e-2 f x\right)}{\left(\sqrt{b^2-4 a c}-b-2 c x\right) \left(f \left(\sqrt{b^2-4 a c}+b\right)+c \left(\sqrt{e^2-4 d f}-e\right)\right)}}}","-\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 + Sqrt[b^2 - 4*a*c] - 2*c*x)*(e - Sqrt[e^2 - 4*d*f] + 2*f*x)*Sqrt[-((c*Sqrt[b^2 - 4*a*c]*(e + Sqrt[e^2 - 4*d*f] + 2*f*x))/(((b + Sqrt[b^2 - 4*a*c])*f - c*(e + Sqrt[e^2 - 4*d*f]))*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x)))]*Sqrt[-((c*(4*a*f + Sqrt[b^2 - 4*a*c]*Sqrt[e^2 - 4*d*f] - 2*Sqrt[b^2 - 4*a*c]*f*x + 2*c*Sqrt[e^2 - 4*d*f]*x - e*(Sqrt[b^2 - 4*a*c] + 2*c*x) + b*(-e + Sqrt[e^2 - 4*d*f] + 2*f*x)))/(((b + Sqrt[b^2 - 4*a*c])*f + c*(-e + Sqrt[e^2 - 4*d*f]))*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x)))]*EllipticF[ArcSin[Sqrt[(((-b + Sqrt[b^2 - 4*a*c])*f + c*(e - Sqrt[e^2 - 4*d*f]))*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(((b + Sqrt[b^2 - 4*a*c])*f + c*(-e + Sqrt[e^2 - 4*d*f]))*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x))]], (2*c*d - b*e + 2*a*f - Sqrt[b^2 - 4*a*c]*Sqrt[e^2 - 4*d*f])/(2*c*d - b*e + 2*a*f + Sqrt[b^2 - 4*a*c]*Sqrt[e^2 - 4*d*f])])/(((-b + Sqrt[b^2 - 4*a*c])*f + c*(e - Sqrt[e^2 - 4*d*f]))*Sqrt[(c*Sqrt[b^2 - 4*a*c]*(-e + Sqrt[e^2 - 4*d*f] - 2*f*x))/(((b + Sqrt[b^2 - 4*a*c])*f + c*(-e + Sqrt[e^2 - 4*d*f]))*(-b + Sqrt[b^2 - 4*a*c] - 2*c*x))]*Sqrt[a + x*(b + c*x)]*Sqrt[d + x*(e + f*x)]))","A",0
123,1,390,652,0.6108807,"\int \frac{1}{\sqrt{3-x+2 x^2} \sqrt{2+3 x+5 x^2}} \, dx","Integrate[1/(Sqrt[3 - x + 2*x^2]*Sqrt[2 + 3*x + 5*x^2]),x]","\frac{\left(-4 x+i \sqrt{23}+1\right) \left(10 i x+\sqrt{31}+3 i\right) \sqrt{\frac{20 i x-2 \sqrt{31}+6 i}{\left(11 i+5 \sqrt{23}-2 \sqrt{31}\right) \left(4 i x+\sqrt{23}-i\right)}} \sqrt{\frac{\left(-22-10 i \sqrt{23}+4 i \sqrt{31}\right) x-\sqrt{713}-i \sqrt{31}-3 i \sqrt{23}+63}{\left(11 i+5 \sqrt{23}+2 \sqrt{31}\right) \left(4 i x+\sqrt{23}-i\right)}} F\left(\sin ^{-1}\left(\sqrt{2} \sqrt{-\frac{2 \left(11+5 i \sqrt{23}-2 i \sqrt{31}\right) x+\sqrt{713}+i \sqrt{31}+3 i \sqrt{23}-63}{\left(11 i+5 \sqrt{23}+2 \sqrt{31}\right) \left(4 i x+\sqrt{23}-i\right)}}\right)|\frac{1}{484} \left(1197+41 \sqrt{713}\right)\right)}{\left(-11 i+5 \sqrt{23}-2 \sqrt{31}\right) \sqrt{\frac{10 i x+\sqrt{31}+3 i}{\left(11 i+5 \sqrt{23}+2 \sqrt{31}\right) \left(4 i x+\sqrt{23}-i\right)}} \sqrt{2 x^2-x+3} \sqrt{5 x^2+3 x+2}}","\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,"((1 + I*Sqrt[23] - 4*x)*(3*I + Sqrt[31] + (10*I)*x)*Sqrt[(6*I - 2*Sqrt[31] + (20*I)*x)/((11*I + 5*Sqrt[23] - 2*Sqrt[31])*(-I + Sqrt[23] + (4*I)*x))]*Sqrt[(63 - (3*I)*Sqrt[23] - I*Sqrt[31] - Sqrt[713] + (-22 - (10*I)*Sqrt[23] + (4*I)*Sqrt[31])*x)/((11*I + 5*Sqrt[23] + 2*Sqrt[31])*(-I + Sqrt[23] + (4*I)*x))]*EllipticF[ArcSin[Sqrt[2]*Sqrt[-((-63 + (3*I)*Sqrt[23] + I*Sqrt[31] + Sqrt[713] + 2*(11 + (5*I)*Sqrt[23] - (2*I)*Sqrt[31])*x)/((11*I + 5*Sqrt[23] + 2*Sqrt[31])*(-I + Sqrt[23] + (4*I)*x)))]], (1197 + 41*Sqrt[713])/484])/((-11*I + 5*Sqrt[23] - 2*Sqrt[31])*Sqrt[(3*I + Sqrt[31] + (10*I)*x)/((11*I + 5*Sqrt[23] + 2*Sqrt[31])*(-I + Sqrt[23] + (4*I)*x))]*Sqrt[3 - x + 2*x^2]*Sqrt[2 + 3*x + 5*x^2])","A",0