1,1,72,0,0.0330131,"\int \frac{c+d x+e x^2}{\sqrt{a+b x}} \, dx","Int[(c + d*x + e*x^2)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(a^2 e-a b d+b^2 c\right)}{b^3}+\frac{2 (a+b x)^{3/2} (b d-2 a e)}{3 b^3}+\frac{2 e (a+b x)^{5/2}}{5 b^3}","\frac{2 \sqrt{a+b x} \left(a^2 e-a b d+b^2 c\right)}{b^3}+\frac{2 (a+b x)^{3/2} (b d-2 a e)}{3 b^3}+\frac{2 e (a+b x)^{5/2}}{5 b^3}",1,"(2*(b^2*c - a*b*d + a^2*e)*Sqrt[a + b*x])/b^3 + (2*(b*d - 2*a*e)*(a + b*x)^(3/2))/(3*b^3) + (2*e*(a + b*x)^(5/2))/(5*b^3)","A",2,1,20,0.05000,1,"{698}"
2,1,161,0,0.1054971,"\int \frac{\left(c+d x+e x^2\right)^2}{\sqrt{a+b x}} \, dx","Int[(c + d*x + e*x^2)^2/Sqrt[a + b*x],x]","-\frac{2 (a+b x)^{5/2} \left(-6 a^2 e^2+6 a b d e+b^2 \left(-\left(2 c e+d^2\right)\right)\right)}{5 b^5}+\frac{4 (a+b x)^{3/2} (b d-2 a e) \left(a^2 e-a b d+b^2 c\right)}{3 b^5}+\frac{2 \sqrt{a+b x} \left(a^2 e-a b d+b^2 c\right)^2}{b^5}+\frac{4 e (a+b x)^{7/2} (b d-2 a e)}{7 b^5}+\frac{2 e^2 (a+b x)^{9/2}}{9 b^5}","-\frac{2 (a+b x)^{5/2} \left(-6 a^2 e^2+6 a b d e+b^2 \left(-\left(2 c e+d^2\right)\right)\right)}{5 b^5}+\frac{4 (a+b x)^{3/2} (b d-2 a e) \left(a^2 e-a b d+b^2 c\right)}{3 b^5}+\frac{2 \sqrt{a+b x} \left(a^2 e-a b d+b^2 c\right)^2}{b^5}+\frac{4 e (a+b x)^{7/2} (b d-2 a e)}{7 b^5}+\frac{2 e^2 (a+b x)^{9/2}}{9 b^5}",1,"(2*(b^2*c - a*b*d + a^2*e)^2*Sqrt[a + b*x])/b^5 + (4*(b*d - 2*a*e)*(b^2*c - a*b*d + a^2*e)*(a + b*x)^(3/2))/(3*b^5) - (2*(6*a*b*d*e - 6*a^2*e^2 - b^2*(d^2 + 2*c*e))*(a + b*x)^(5/2))/(5*b^5) + (4*e*(b*d - 2*a*e)*(a + b*x)^(7/2))/(7*b^5) + (2*e^2*(a + b*x)^(9/2))/(9*b^5)","A",2,1,22,0.04545,1,"{698}"
3,1,274,0,0.1938349,"\int \frac{\left(c+d x+e x^2\right)^3}{\sqrt{a+b x}} \, dx","Int[(c + d*x + e*x^2)^3/Sqrt[a + b*x],x]","-\frac{2 e (a+b x)^{9/2} \left(-5 a^2 e^2+5 a b d e+b^2 \left(-\left(c e+d^2\right)\right)\right)}{3 b^7}-\frac{2 (a+b x)^{7/2} (b d-2 a e) \left(-10 a^2 e^2+10 a b d e+b^2 \left(-\left(6 c e+d^2\right)\right)\right)}{7 b^7}-\frac{6 (a+b x)^{5/2} \left(a^2 e-a b d+b^2 c\right) \left(-5 a^2 e^2+5 a b d e+b^2 \left(-\left(c e+d^2\right)\right)\right)}{5 b^7}+\frac{2 (a+b x)^{3/2} (b d-2 a e) \left(a^2 e-a b d+b^2 c\right)^2}{b^7}+\frac{2 \sqrt{a+b x} \left(a^2 e-a b d+b^2 c\right)^3}{b^7}+\frac{6 e^2 (a+b x)^{11/2} (b d-2 a e)}{11 b^7}+\frac{2 e^3 (a+b x)^{13/2}}{13 b^7}","-\frac{2 e (a+b x)^{9/2} \left(-5 a^2 e^2+5 a b d e+b^2 \left(-\left(c e+d^2\right)\right)\right)}{3 b^7}-\frac{2 (a+b x)^{7/2} (b d-2 a e) \left(-10 a^2 e^2+10 a b d e+b^2 \left(-\left(6 c e+d^2\right)\right)\right)}{7 b^7}-\frac{6 (a+b x)^{5/2} \left(a^2 e-a b d+b^2 c\right) \left(-5 a^2 e^2+5 a b d e+b^2 \left(-\left(c e+d^2\right)\right)\right)}{5 b^7}+\frac{2 (a+b x)^{3/2} (b d-2 a e) \left(a^2 e-a b d+b^2 c\right)^2}{b^7}+\frac{2 \sqrt{a+b x} \left(a^2 e-a b d+b^2 c\right)^3}{b^7}+\frac{6 e^2 (a+b x)^{11/2} (b d-2 a e)}{11 b^7}+\frac{2 e^3 (a+b x)^{13/2}}{13 b^7}",1,"(2*(b^2*c - a*b*d + a^2*e)^3*Sqrt[a + b*x])/b^7 + (2*(b*d - 2*a*e)*(b^2*c - a*b*d + a^2*e)^2*(a + b*x)^(3/2))/b^7 - (6*(b^2*c - a*b*d + a^2*e)*(5*a*b*d*e - 5*a^2*e^2 - b^2*(d^2 + c*e))*(a + b*x)^(5/2))/(5*b^7) - (2*(b*d - 2*a*e)*(10*a*b*d*e - 10*a^2*e^2 - b^2*(d^2 + 6*c*e))*(a + b*x)^(7/2))/(7*b^7) - (2*e*(5*a*b*d*e - 5*a^2*e^2 - b^2*(d^2 + c*e))*(a + b*x)^(9/2))/(3*b^7) + (6*e^2*(b*d - 2*a*e)*(a + b*x)^(11/2))/(11*b^7) + (2*e^3*(a + b*x)^(13/2))/(13*b^7)","A",2,1,22,0.04545,1,"{698}"
4,1,114,0,0.0707695,"\int \frac{c+d x+e x^2+f x^3}{\sqrt{a+b x}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/Sqrt[a + b*x],x]","\frac{2 \sqrt{a+b x} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}+\frac{2 (a+b x)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{2 (a+b x)^{5/2} (b e-3 a f)}{5 b^4}+\frac{2 f (a+b x)^{7/2}}{7 b^4}","\frac{2 \sqrt{a+b x} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}+\frac{2 (a+b x)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{2 (a+b x)^{5/2} (b e-3 a f)}{5 b^4}+\frac{2 f (a+b x)^{7/2}}{7 b^4}",1,"(2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Sqrt[a + b*x])/b^4 + (2*(b^2*d - 2*a*b*e + 3*a^2*f)*(a + b*x)^(3/2))/(3*b^4) + (2*(b*e - 3*a*f)*(a + b*x)^(5/2))/(5*b^4) + (2*f*(a + b*x)^(7/2))/(7*b^4)","A",2,1,25,0.04000,1,"{1850}"
5,1,320,0,0.2436527,"\int \frac{\left(c+d x+e x^2+f x^3\right)^2}{\sqrt{a+b x}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)^2/Sqrt[a + b*x],x]","\frac{2 (a+b x)^{5/2} \left(6 a^2 b^2 \left(2 d f+e^2\right)-20 a^3 b e f+15 a^4 f^2-6 a b^3 (c f+d e)+b^4 \left(2 c e+d^2\right)\right)}{5 b^7}+\frac{4 (a+b x)^{7/2} \left(10 a^2 b e f-10 a^3 f^2-2 a b^2 \left(2 d f+e^2\right)+b^3 (c f+d e)\right)}{7 b^7}+\frac{4 (a+b x)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^7}+\frac{2 \sqrt{a+b x} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)^2}{b^7}-\frac{2 (a+b x)^{9/2} \left(-15 a^2 f^2+10 a b e f+b^2 \left(-\left(2 d f+e^2\right)\right)\right)}{9 b^7}+\frac{4 f (a+b x)^{11/2} (b e-3 a f)}{11 b^7}+\frac{2 f^2 (a+b x)^{13/2}}{13 b^7}","\frac{2 (a+b x)^{5/2} \left(6 a^2 b^2 \left(2 d f+e^2\right)-20 a^3 b e f+15 a^4 f^2-6 a b^3 (c f+d e)+b^4 \left(2 c e+d^2\right)\right)}{5 b^7}+\frac{4 (a+b x)^{7/2} \left(10 a^2 b e f-10 a^3 f^2-2 a b^2 \left(2 d f+e^2\right)+b^3 (c f+d e)\right)}{7 b^7}+\frac{4 (a+b x)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^7}+\frac{2 \sqrt{a+b x} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)^2}{b^7}-\frac{2 (a+b x)^{9/2} \left(-15 a^2 f^2+10 a b e f+b^2 \left(-\left(2 d f+e^2\right)\right)\right)}{9 b^7}+\frac{4 f (a+b x)^{11/2} (b e-3 a f)}{11 b^7}+\frac{2 f^2 (a+b x)^{13/2}}{13 b^7}",1,"(2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)^2*Sqrt[a + b*x])/b^7 + (4*(b^2*d - 2*a*b*e + 3*a^2*f)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*(a + b*x)^(3/2))/(3*b^7) + (2*(b^4*(d^2 + 2*c*e) - 20*a^3*b*e*f + 15*a^4*f^2 - 6*a*b^3*(d*e + c*f) + 6*a^2*b^2*(e^2 + 2*d*f))*(a + b*x)^(5/2))/(5*b^7) + (4*(10*a^2*b*e*f - 10*a^3*f^2 + b^3*(d*e + c*f) - 2*a*b^2*(e^2 + 2*d*f))*(a + b*x)^(7/2))/(7*b^7) - (2*(10*a*b*e*f - 15*a^2*f^2 - b^2*(e^2 + 2*d*f))*(a + b*x)^(9/2))/(9*b^7) + (4*f*(b*e - 3*a*f)*(a + b*x)^(11/2))/(11*b^7) + (2*f^2*(a + b*x)^(13/2))/(13*b^7)","A",2,1,27,0.03704,1,"{1850}"
6,1,708,0,0.6251859,"\int \frac{\left(c+d x+e x^2+f x^3\right)^3}{\sqrt{a+b x}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)^3/Sqrt[a + b*x],x]","-\frac{2 (a+b x)^{7/2} \left(-30 a^2 b^4 \left(2 c e f+d^2 f+d e^2\right)+20 a^3 b^3 \left(3 c f^2+6 d e f+e^3\right)-105 a^4 b^2 f \left(d f+e^2\right)+168 a^5 b e f^2-84 a^6 f^3+12 a b^5 \left(2 c d f+c e^2+d^2 e\right)-b^6 \left(3 c^2 f+6 c d e+d^3\right)\right)}{7 b^{10}}-\frac{6 (a+b x)^{11/2} \left(-21 a^2 b^2 f \left(d f+e^2\right)+56 a^3 b e f^2-42 a^4 f^3+2 a b^3 \left(3 c f^2+6 d e f+e^3\right)-b^4 \left(2 c e f+d^2 f+d e^2\right)\right)}{11 b^{10}}+\frac{2 (a+b x)^{9/2} \left(5 a^2 b^3 \left(3 c f^2+6 d e f+e^3\right)-35 a^3 b^2 f \left(d f+e^2\right)+70 a^4 b e f^2-42 a^5 f^3-5 a b^4 \left(2 c e f+d^2 f+d e^2\right)+b^5 \left(2 c d f+c e^2+d^2 e\right)\right)}{3 b^{10}}+\frac{6 (a+b x)^{5/2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right) \left(a^2 b^2 \left(9 d f+5 e^2\right)-16 a^3 b e f+12 a^4 f^2-a b^3 (3 c f+5 d e)+b^4 \left(c e+d^2\right)\right)}{5 b^{10}}+\frac{2 (a+b x)^{13/2} \left(84 a^2 b e f^2-84 a^3 f^3-21 a b^2 f \left(d f+e^2\right)+b^3 \left(3 c f^2+6 d e f+e^3\right)\right)}{13 b^{10}}+\frac{2 (a+b x)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)^2}{b^{10}}+\frac{2 \sqrt{a+b x} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)^3}{b^{10}}-\frac{2 f (a+b x)^{15/2} \left(-12 a^2 f^2+8 a b e f+b^2 \left(-\left(d f+e^2\right)\right)\right)}{5 b^{10}}+\frac{6 f^2 (a+b x)^{17/2} (b e-3 a f)}{17 b^{10}}+\frac{2 f^3 (a+b x)^{19/2}}{19 b^{10}}","-\frac{2 (a+b x)^{7/2} \left(-30 a^2 b^4 \left(2 c e f+d^2 f+d e^2\right)+20 a^3 b^3 \left(3 c f^2+6 d e f+e^3\right)-105 a^4 b^2 f \left(d f+e^2\right)+168 a^5 b e f^2-84 a^6 f^3+12 a b^5 \left(2 c d f+c e^2+d^2 e\right)-b^6 \left(3 c^2 f+6 c d e+d^3\right)\right)}{7 b^{10}}-\frac{6 (a+b x)^{11/2} \left(-21 a^2 b^2 f \left(d f+e^2\right)+56 a^3 b e f^2-42 a^4 f^3+2 a b^3 \left(3 c f^2+6 d e f+e^3\right)-b^4 \left(2 c e f+d^2 f+d e^2\right)\right)}{11 b^{10}}+\frac{2 (a+b x)^{9/2} \left(5 a^2 b^3 \left(3 c f^2+6 d e f+e^3\right)-35 a^3 b^2 f \left(d f+e^2\right)+70 a^4 b e f^2-42 a^5 f^3-5 a b^4 \left(2 c e f+d^2 f+d e^2\right)+b^5 \left(2 c d f+c e^2+d^2 e\right)\right)}{3 b^{10}}+\frac{6 (a+b x)^{5/2} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right) \left(a^2 b^2 \left(9 d f+5 e^2\right)-16 a^3 b e f+12 a^4 f^2-a b^3 (3 c f+5 d e)+b^4 \left(c e+d^2\right)\right)}{5 b^{10}}+\frac{2 (a+b x)^{13/2} \left(84 a^2 b e f^2-84 a^3 f^3-21 a b^2 f \left(d f+e^2\right)+b^3 \left(3 c f^2+6 d e f+e^3\right)\right)}{13 b^{10}}+\frac{2 (a+b x)^{3/2} \left(3 a^2 f-2 a b e+b^2 d\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)^2}{b^{10}}+\frac{2 \sqrt{a+b x} \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)^3}{b^{10}}-\frac{2 f (a+b x)^{15/2} \left(-12 a^2 f^2+8 a b e f+b^2 \left(-\left(d f+e^2\right)\right)\right)}{5 b^{10}}+\frac{6 f^2 (a+b x)^{17/2} (b e-3 a f)}{17 b^{10}}+\frac{2 f^3 (a+b x)^{19/2}}{19 b^{10}}",1,"(2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)^3*Sqrt[a + b*x])/b^10 + (2*(b^2*d - 2*a*b*e + 3*a^2*f)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)^2*(a + b*x)^(3/2))/b^10 + (6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*(b^4*(d^2 + c*e) - 16*a^3*b*e*f + 12*a^4*f^2 - a*b^3*(5*d*e + 3*c*f) + a^2*b^2*(5*e^2 + 9*d*f))*(a + b*x)^(5/2))/(5*b^10) - (2*(168*a^5*b*e*f^2 - 84*a^6*f^3 - b^6*(d^3 + 6*c*d*e + 3*c^2*f) - 105*a^4*b^2*f*(e^2 + d*f) + 12*a*b^5*(d^2*e + c*e^2 + 2*c*d*f) - 30*a^2*b^4*(d*e^2 + d^2*f + 2*c*e*f) + 20*a^3*b^3*(e^3 + 6*d*e*f + 3*c*f^2))*(a + b*x)^(7/2))/(7*b^10) + (2*(70*a^4*b*e*f^2 - 42*a^5*f^3 - 35*a^3*b^2*f*(e^2 + d*f) + b^5*(d^2*e + c*e^2 + 2*c*d*f) - 5*a*b^4*(d*e^2 + d^2*f + 2*c*e*f) + 5*a^2*b^3*(e^3 + 6*d*e*f + 3*c*f^2))*(a + b*x)^(9/2))/(3*b^10) - (6*(56*a^3*b*e*f^2 - 42*a^4*f^3 - 21*a^2*b^2*f*(e^2 + d*f) - b^4*(d*e^2 + d^2*f + 2*c*e*f) + 2*a*b^3*(e^3 + 6*d*e*f + 3*c*f^2))*(a + b*x)^(11/2))/(11*b^10) + (2*(84*a^2*b*e*f^2 - 84*a^3*f^3 - 21*a*b^2*f*(e^2 + d*f) + b^3*(e^3 + 6*d*e*f + 3*c*f^2))*(a + b*x)^(13/2))/(13*b^10) - (2*f*(8*a*b*e*f - 12*a^2*f^2 - b^2*(e^2 + d*f))*(a + b*x)^(15/2))/(5*b^10) + (6*f^2*(b*e - 3*a*f)*(a + b*x)^(17/2))/(17*b^10) + (2*f^3*(a + b*x)^(19/2))/(19*b^10)","A",2,1,27,0.03704,1,"{1850}"
7,1,161,0,0.1111378,"\int \frac{c+d x}{a+b x^3} \, dx","Int[(c + d*x)/(a + b*x^3),x]","-\frac{\left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}","-\frac{\left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}",1,"-(((b^(1/3)*c + a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(2/3))) + ((b^(1/3)*c - a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(2/3)) - ((c - (a^(1/3)*d)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(1/3))","A",6,6,15,0.4000,1,"{1860, 31, 634, 617, 204, 628}"
8,1,189,0,0.1393977,"\int \frac{c+d x}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x)/(a + b*x^3)^2,x]","-\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{2/3}}+\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+2 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{2/3}}+\frac{x (c+d x)}{3 a \left(a+b x^3\right)}","-\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{2/3}}+\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+2 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{2/3}}+\frac{x (c+d x)}{3 a \left(a+b x^3\right)}",1,"(x*(c + d*x))/(3*a*(a + b*x^3)) - ((2*b^(1/3)*c + a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(2/3)) + ((2*b^(1/3)*c - a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(2/3)) - ((2*b^(1/3)*c - a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(2/3))","A",7,7,15,0.4667,1,"{1855, 1860, 31, 634, 617, 204, 628}"
9,1,215,0,0.1870461,"\int \frac{c+d x}{\left(a+b x^3\right)^3} \, dx","Int[(c + d*x)/(a + b*x^3)^3,x]","-\frac{\left(5 \sqrt[3]{b} c-2 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} b^{2/3}}+\frac{\left(5 \sqrt[3]{b} c-2 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} b^{2/3}}-\frac{\left(2 \sqrt[3]{a} d+5 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} b^{2/3}}+\frac{x (5 c+4 d x)}{18 a^2 \left(a+b x^3\right)}+\frac{x (c+d x)}{6 a \left(a+b x^3\right)^2}","-\frac{\left(5 \sqrt[3]{b} c-2 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} b^{2/3}}+\frac{\left(5 \sqrt[3]{b} c-2 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} b^{2/3}}-\frac{\left(2 \sqrt[3]{a} d+5 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} b^{2/3}}+\frac{x (5 c+4 d x)}{18 a^2 \left(a+b x^3\right)}+\frac{x (c+d x)}{6 a \left(a+b x^3\right)^2}",1,"(x*(c + d*x))/(6*a*(a + b*x^3)^2) + (x*(5*c + 4*d*x))/(18*a^2*(a + b*x^3)) - ((5*b^(1/3)*c + 2*a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(2/3)) + ((5*b^(1/3)*c - 2*a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(8/3)*b^(2/3)) - ((5*b^(1/3)*c - 2*a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(8/3)*b^(2/3))","A",8,7,15,0.4667,1,"{1855, 1860, 31, 634, 617, 204, 628}"
10,1,240,0,0.2231053,"\int \frac{c+d x}{\left(a+b x^3\right)^4} \, dx","Int[(c + d*x)/(a + b*x^3)^4,x]","-\frac{\left(20 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{11/3} b^{2/3}}+\frac{2 \left(20 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{11/3} b^{2/3}}-\frac{2 \left(7 \sqrt[3]{a} d+20 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{11/3} b^{2/3}}+\frac{2 x (10 c+7 d x)}{81 a^3 \left(a+b x^3\right)}+\frac{x (8 c+7 d x)}{54 a^2 \left(a+b x^3\right)^2}+\frac{x (c+d x)}{9 a \left(a+b x^3\right)^3}","-\frac{\left(20 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{11/3} b^{2/3}}+\frac{2 \left(20 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{11/3} b^{2/3}}-\frac{2 \left(7 \sqrt[3]{a} d+20 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{11/3} b^{2/3}}+\frac{2 x (10 c+7 d x)}{81 a^3 \left(a+b x^3\right)}+\frac{x (8 c+7 d x)}{54 a^2 \left(a+b x^3\right)^2}+\frac{x (c+d x)}{9 a \left(a+b x^3\right)^3}",1,"(x*(c + d*x))/(9*a*(a + b*x^3)^3) + (x*(8*c + 7*d*x))/(54*a^2*(a + b*x^3)^2) + (2*x*(10*c + 7*d*x))/(81*a^3*(a + b*x^3)) - (2*(20*b^(1/3)*c + 7*a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(81*Sqrt[3]*a^(11/3)*b^(2/3)) + (2*(20*b^(1/3)*c - 7*a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(243*a^(11/3)*b^(2/3)) - ((20*b^(1/3)*c - 7*a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(243*a^(11/3)*b^(2/3))","A",9,7,15,0.4667,1,"{1855, 1860, 31, 634, 617, 204, 628}"
11,1,161,0,0.1214662,"\int \frac{a+b x}{d+e x^3} \, dx","Int[(a + b*x)/(d + e*x^3),x]","-\frac{\left(a-\frac{b \sqrt[3]{d}}{\sqrt[3]{e}}\right) \log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right)}{6 d^{2/3} \sqrt[3]{e}}-\frac{\left(b \sqrt[3]{d}-a \sqrt[3]{e}\right) \log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{3 d^{2/3} e^{2/3}}-\frac{\left(a \sqrt[3]{e}+b \sqrt[3]{d}\right) \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} d^{2/3} e^{2/3}}","-\frac{\left(a-\frac{b \sqrt[3]{d}}{\sqrt[3]{e}}\right) \log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right)}{6 d^{2/3} \sqrt[3]{e}}-\frac{\left(b \sqrt[3]{d}-a \sqrt[3]{e}\right) \log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{3 d^{2/3} e^{2/3}}-\frac{\left(a \sqrt[3]{e}+b \sqrt[3]{d}\right) \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} d^{2/3} e^{2/3}}",1,"-(((b*d^(1/3) + a*e^(1/3))*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(Sqrt[3]*d^(2/3)*e^(2/3))) - ((b*d^(1/3) - a*e^(1/3))*Log[d^(1/3) + e^(1/3)*x])/(3*d^(2/3)*e^(2/3)) - ((a - (b*d^(1/3))/e^(1/3))*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(6*d^(2/3)*e^(1/3))","A",6,6,15,0.4000,1,"{1860, 31, 634, 617, 204, 628}"
12,1,161,0,0.1003568,"\int \frac{a+b x}{d-e x^3} \, dx","Int[(a + b*x)/(d - e*x^3),x]","\frac{\left(a \sqrt[3]{e}+b \sqrt[3]{d}\right) \log \left(d^{2/3}+\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right)}{6 d^{2/3} e^{2/3}}-\frac{\left(a \sqrt[3]{e}+b \sqrt[3]{d}\right) \log \left(\sqrt[3]{d}-\sqrt[3]{e} x\right)}{3 d^{2/3} e^{2/3}}-\frac{\left(b \sqrt[3]{d}-a \sqrt[3]{e}\right) \tan ^{-1}\left(\frac{\sqrt[3]{d}+2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} d^{2/3} e^{2/3}}","\frac{\left(a \sqrt[3]{e}+b \sqrt[3]{d}\right) \log \left(d^{2/3}+\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right)}{6 d^{2/3} e^{2/3}}-\frac{\left(a \sqrt[3]{e}+b \sqrt[3]{d}\right) \log \left(\sqrt[3]{d}-\sqrt[3]{e} x\right)}{3 d^{2/3} e^{2/3}}-\frac{\left(b \sqrt[3]{d}-a \sqrt[3]{e}\right) \tan ^{-1}\left(\frac{\sqrt[3]{d}+2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} d^{2/3} e^{2/3}}",1,"-(((b*d^(1/3) - a*e^(1/3))*ArcTan[(d^(1/3) + 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(Sqrt[3]*d^(2/3)*e^(2/3))) - ((b*d^(1/3) + a*e^(1/3))*Log[d^(1/3) - e^(1/3)*x])/(3*d^(2/3)*e^(2/3)) + ((b*d^(1/3) + a*e^(1/3))*Log[d^(2/3) + d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(6*d^(2/3)*e^(2/3))","A",6,6,16,0.3750,1,"{1861, 31, 634, 617, 204, 628}"
13,1,19,0,0.0152534,"\int \frac{1+x}{1+x^3} \, dx","Int[(1 + x)/(1 + x^3),x]","-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(-2*ArcTan[(1 - 2*x)/Sqrt[3]])/Sqrt[3]","A",3,3,11,0.2727,1,"{1586, 618, 204}"
14,1,19,0,0.0133185,"\int \frac{1-x}{1-x^3} \, dx","Int[(1 - x)/(1 - x^3),x]","\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(2*ArcTan[(1 + 2*x)/Sqrt[3]])/Sqrt[3]","A",3,3,15,0.2000,1,"{1586, 618, 204}"
15,1,22,0,0.0121661,"\int \frac{1+x}{1-x^3} \, dx","Int[(1 + x)/(1 - x^3),x]","\frac{1}{3} \log \left(x^2+x+1\right)-\frac{2}{3} \log (1-x)","\frac{1}{3} \log \left(x^2+x+1\right)-\frac{2}{3} \log (1-x)",1,"(-2*Log[1 - x])/3 + Log[1 + x + x^2]/3","A",3,3,13,0.2308,1,"{1861, 31, 628}"
16,1,22,0,0.0126704,"\int \frac{1-x}{1+x^3} \, dx","Int[(1 - x)/(1 + x^3),x]","\frac{2}{3} \log (x+1)-\frac{1}{3} \log \left(x^2-x+1\right)","\frac{2}{3} \log (x+1)-\frac{1}{3} \log \left(x^2-x+1\right)",1,"(2*Log[1 + x])/3 - Log[1 - x + x^2]/3","A",3,3,13,0.2308,1,"{1860, 31, 628}"
17,1,41,0,0.0272263,"\int \frac{3-x}{1-x^3} \, dx","Int[(3 - x)/(1 - x^3),x]","\frac{1}{3} \log \left(x^2+x+1\right)-\frac{2}{3} \log (1-x)+\frac{4 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{3} \log \left(x^2+x+1\right)-\frac{2}{3} \log (1-x)+\frac{4 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(4*ArcTan[(1 + 2*x)/Sqrt[3]])/Sqrt[3] - (2*Log[1 - x])/3 + Log[1 + x + x^2]/3","A",6,6,15,0.4000,1,"{1861, 31, 634, 618, 204, 628}"
18,1,29,0,0.0216336,"\int \frac{c+d x}{c^3+d^3 x^3} \, dx","Int[(c + d*x)/(c^3 + d^3*x^3),x]","-\frac{2 \tan ^{-1}\left(\frac{c-2 d x}{\sqrt{3} c}\right)}{\sqrt{3} c d}","-\frac{2 \tan ^{-1}\left(\frac{c-2 d x}{\sqrt{3} c}\right)}{\sqrt{3} c d}",1,"(-2*ArcTan[(c - 2*d*x)/(Sqrt[3]*c)])/(Sqrt[3]*c*d)","A",3,3,19,0.1579,1,"{1586, 617, 204}"
19,1,29,0,0.0203174,"\int \frac{c-d x}{c^3-d^3 x^3} \, dx","Int[(c - d*x)/(c^3 - d^3*x^3),x]","\frac{2 \tan ^{-1}\left(\frac{c+2 d x}{\sqrt{3} c}\right)}{\sqrt{3} c d}","\frac{2 \tan ^{-1}\left(\frac{c+2 d x}{\sqrt{3} c}\right)}{\sqrt{3} c d}",1,"(2*ArcTan[(c + 2*d*x)/(Sqrt[3]*c)])/(Sqrt[3]*c*d)","A",3,3,21,0.1429,1,"{1586, 617, 204}"
20,1,39,0,0.0266326,"\int \frac{\sqrt[3]{a} \sqrt[3]{b} B+b^{2/3} B x}{a+b x^3} \, dx","Int[(a^(1/3)*b^(1/3)*B + b^(2/3)*B*x)/(a + b*x^3),x]","-\frac{2 B \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}","-\frac{2 B \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}",1,"(-2*B*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3))","A",3,3,31,0.09677,1,"{1586, 617, 204}"
21,1,41,0,0.0431953,"\int \frac{\sqrt[3]{a} \sqrt[3]{-b} B-(-b)^{2/3} B x}{a+b x^3} \, dx","Int[(a^(1/3)*(-b)^(1/3)*B - (-b)^(2/3)*B*x)/(a + b*x^3),x]","\frac{2 B \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{-b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}","\frac{2 B \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{-b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}",1,"(2*B*ArcTan[(a^(1/3) + 2*(-b)^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3))","A",3,3,36,0.08333,1,"{1586, 617, 204}"
22,1,118,0,0.1263675,"\int \left(-\frac{C x^2}{a+b x^3}+\frac{B x+C x^2}{a+b x^3}\right) \, dx","Int[-((C*x^2)/(a + b*x^3)) + (B*x + C*x^2)/(a + b*x^3),x]","\frac{B \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{B \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{B \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}","\frac{B \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{B \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{B \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}",1,"-((B*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b^(2/3))) - (B*Log[a^(1/3) + b^(1/3)*x])/(3*a^(1/3)*b^(2/3)) + (B*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(1/3)*b^(2/3))","A",12,10,35,0.2857,1,"{260, 1593, 1871, 12, 292, 31, 634, 617, 204, 628}"
23,1,118,0,0.1062678,"\int \left(-\frac{C x^2}{a+b x^3}+\frac{A+C x^2}{a+b x^3}\right) \, dx","Int[-((C*x^2)/(a + b*x^3)) + (A + C*x^2)/(a + b*x^3),x]","-\frac{A \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{A \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{A \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}","-\frac{A \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{A \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{A \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}",1,"-((A*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(1/3))) + (A*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(1/3)) - (A*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(1/3))","A",11,9,33,0.2727,1,"{260, 1871, 12, 200, 31, 634, 617, 204, 628}"
24,1,161,0,0.1662974,"\int \left(-\frac{C x^2}{a+b x^3}+\frac{A+B x+C x^2}{a+b x^3}\right) \, dx","Int[-((C*x^2)/(a + b*x^3)) + (A + B*x + C*x^2)/(a + b*x^3),x]","-\frac{\left(A-\frac{\sqrt[3]{a} B}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(A \sqrt[3]{b}-\sqrt[3]{a} B\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} B+A \sqrt[3]{b}\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}","-\frac{\left(A-\frac{\sqrt[3]{a} B}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(A \sqrt[3]{b}-\sqrt[3]{a} B\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} B+A \sqrt[3]{b}\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}",1,"-(((A*b^(1/3) + a^(1/3)*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(2/3))) + ((A*b^(1/3) - a^(1/3)*B)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(2/3)) - ((A - (a^(1/3)*B)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(1/3))","A",10,8,36,0.2222,1,"{260, 1871, 1860, 31, 634, 617, 204, 628}"
25,1,134,0,0.1131445,"\int \frac{b x+c x^2}{d+e x^3} \, dx","Int[(b*x + c*x^2)/(d + e*x^3),x]","\frac{b \log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right)}{6 \sqrt[3]{d} e^{2/3}}-\frac{b \log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{3 \sqrt[3]{d} e^{2/3}}-\frac{b \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} \sqrt[3]{d} e^{2/3}}+\frac{c \log \left(d+e x^3\right)}{3 e}","\frac{b \log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right)}{6 \sqrt[3]{d} e^{2/3}}-\frac{b \log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{3 \sqrt[3]{d} e^{2/3}}-\frac{b \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} \sqrt[3]{d} e^{2/3}}+\frac{c \log \left(d+e x^3\right)}{3 e}",1,"-((b*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(Sqrt[3]*d^(1/3)*e^(2/3))) - (b*Log[d^(1/3) + e^(1/3)*x])/(3*d^(1/3)*e^(2/3)) + (b*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(6*d^(1/3)*e^(2/3)) + (c*Log[d + e*x^3])/(3*e)","A",10,10,19,0.5263,1,"{1593, 1871, 12, 292, 31, 634, 617, 204, 628, 260}"
26,1,134,0,0.0891273,"\int \frac{a+c x^2}{d-e x^3} \, dx","Int[(a + c*x^2)/(d - e*x^3),x]","\frac{a \log \left(d^{2/3}+\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right)}{6 d^{2/3} \sqrt[3]{e}}-\frac{a \log \left(\sqrt[3]{d}-\sqrt[3]{e} x\right)}{3 d^{2/3} \sqrt[3]{e}}+\frac{a \tan ^{-1}\left(\frac{\sqrt[3]{d}+2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} d^{2/3} \sqrt[3]{e}}-\frac{c \log \left(d-e x^3\right)}{3 e}","\frac{a \log \left(d^{2/3}+\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right)}{6 d^{2/3} \sqrt[3]{e}}-\frac{a \log \left(\sqrt[3]{d}-\sqrt[3]{e} x\right)}{3 d^{2/3} \sqrt[3]{e}}+\frac{a \tan ^{-1}\left(\frac{\sqrt[3]{d}+2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt{3} d^{2/3} \sqrt[3]{e}}-\frac{c \log \left(d-e x^3\right)}{3 e}",1,"(a*ArcTan[(d^(1/3) + 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(Sqrt[3]*d^(2/3)*e^(1/3)) - (a*Log[d^(1/3) - e^(1/3)*x])/(3*d^(2/3)*e^(1/3)) + (a*Log[d^(2/3) + d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(6*d^(2/3)*e^(1/3)) - (c*Log[d - e*x^3])/(3*e)","A",9,9,18,0.5000,1,"{1871, 12, 200, 31, 634, 617, 204, 628, 260}"
27,1,37,0,0.0576785,"\int \frac{2 a^2+b^2 x^2}{a^3+b^3 x^3} \, dx","Int[(2*a^2 + b^2*x^2)/(a^3 + b^3*x^3),x]","\frac{\log (a+b x)}{b}-\frac{2 \tan ^{-1}\left(\frac{a-2 b x}{\sqrt{3} a}\right)}{\sqrt{3} b}","\frac{\log (a+b x)}{b}-\frac{2 \tan ^{-1}\left(\frac{a-2 b x}{\sqrt{3} a}\right)}{\sqrt{3} b}",1,"(-2*ArcTan[(a - 2*b*x)/(Sqrt[3]*a)])/(Sqrt[3]*b) + Log[a + b*x]/b","A",4,4,27,0.1481,1,"{1868, 31, 617, 204}"
28,1,39,0,0.0421376,"\int \frac{2 a^2+b^2 x^2}{a^3-b^3 x^3} \, dx","Int[(2*a^2 + b^2*x^2)/(a^3 - b^3*x^3),x]","\frac{2 \tan ^{-1}\left(\frac{a+2 b x}{\sqrt{3} a}\right)}{\sqrt{3} b}-\frac{\log (a-b x)}{b}","\frac{2 \tan ^{-1}\left(\frac{a+2 b x}{\sqrt{3} a}\right)}{\sqrt{3} b}-\frac{\log (a-b x)}{b}",1,"(2*ArcTan[(a + 2*b*x)/(Sqrt[3]*a)])/(Sqrt[3]*b) - Log[a - b*x]/b","A",4,4,28,0.1429,1,"{1868, 31, 617, 204}"
29,1,48,0,0.0369016,"\int \frac{8 C+b^{2/3} C x^2}{8+b x^3} \, dx","Int[(8*C + b^(2/3)*C*x^2)/(8 + b*x^3),x]","\frac{C \log \left(\sqrt[3]{b} x+2\right)}{\sqrt[3]{b}}-\frac{2 C \tan ^{-1}\left(\frac{1-\sqrt[3]{b} x}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}","\frac{C \log \left(\sqrt[3]{b} x+2\right)}{\sqrt[3]{b}}-\frac{2 C \tan ^{-1}\left(\frac{1-\sqrt[3]{b} x}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"(-2*C*ArcTan[(1 - b^(1/3)*x)/Sqrt[3]])/(Sqrt[3]*b^(1/3)) + (C*Log[2 + b^(1/3)*x])/b^(1/3)","A",4,4,24,0.1667,1,"{1863, 31, 617, 204}"
30,1,47,0,0.0343279,"\int \frac{a^{2/3} C+2 C x^2}{a+8 x^3} \, dx","Int[(a^(2/3)*C + 2*C*x^2)/(a + 8*x^3),x]","\frac{1}{4} C \log \left(\sqrt[3]{a}+2 x\right)-\frac{C \tan ^{-1}\left(\frac{\sqrt[3]{a}-4 x}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3}}","\frac{1}{4} C \log \left(\sqrt[3]{a}+2 x\right)-\frac{C \tan ^{-1}\left(\frac{\sqrt[3]{a}-4 x}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3}}",1,"-(C*ArcTan[(a^(1/3) - 4*x)/(Sqrt[3]*a^(1/3))])/(2*Sqrt[3]) + (C*Log[a^(1/3) + 2*x])/4","A",4,4,24,0.1667,1,"{1863, 31, 617, 204}"
31,1,57,0,0.0689679,"\int \frac{8 C+(-b)^{2/3} C x^2}{-8+b x^3} \, dx","Int[(8*C + (-b)^(2/3)*C*x^2)/(-8 + b*x^3),x]","\frac{2 C \tan ^{-1}\left(\frac{1-\sqrt[3]{-b} x}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{-b}}-\frac{C \log \left(\sqrt[3]{-b} x+2\right)}{\sqrt[3]{-b}}","\frac{2 C \tan ^{-1}\left(\frac{1-\sqrt[3]{-b} x}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{-b}}-\frac{C \log \left(\sqrt[3]{-b} x+2\right)}{\sqrt[3]{-b}}",1,"(2*C*ArcTan[(1 - (-b)^(1/3)*x)/Sqrt[3]])/(Sqrt[3]*(-b)^(1/3)) - (C*Log[2 + (-b)^(1/3)*x])/(-b)^(1/3)","A",4,4,26,0.1538,1,"{1864, 31, 617, 204}"
32,1,47,0,0.061084,"\int \frac{(-a)^{2/3} C+2 C x^2}{a-8 x^3} \, dx","Int[((-a)^(2/3)*C + 2*C*x^2)/(a - 8*x^3),x]","\frac{C \tan ^{-1}\left(\frac{1-\frac{4 x}{\sqrt[3]{-a}}}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{4} C \log \left(\sqrt[3]{-a}+2 x\right)","\frac{C \tan ^{-1}\left(\frac{1-\frac{4 x}{\sqrt[3]{-a}}}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{4} C \log \left(\sqrt[3]{-a}+2 x\right)",1,"(C*ArcTan[(1 - (4*x)/(-a)^(1/3))/Sqrt[3]])/(2*Sqrt[3]) - (C*Log[(-a)^(1/3) + 2*x])/4","A",4,4,26,0.1538,1,"{1864, 31, 617, 204}"
33,1,50,0,0.0765061,"\int \frac{2 \left(\frac{a}{b}\right)^{2/3} C+C x^2}{a+b x^3} \, dx","Int[(2*(a/b)^(2/3)*C + C*x^2)/(a + b*x^3),x]","\frac{C \log \left(\sqrt[3]{\frac{a}{b}}+x\right)}{b}-\frac{2 C \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b}","\frac{C \log \left(\sqrt[3]{\frac{a}{b}}+x\right)}{b}-\frac{2 C \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b}",1,"(-2*C*ArcTan[(1 - (2*x)/(a/b)^(1/3))/Sqrt[3]])/(Sqrt[3]*b) + (C*Log[(a/b)^(1/3) + x])/b","A",4,4,28,0.1429,1,"{1867, 31, 617, 204}"
34,1,53,0,0.0808304,"\int \frac{2 \left(-\frac{a}{b}\right)^{2/3} C+C x^2}{a-b x^3} \, dx","Int[(2*(-(a/b))^(2/3)*C + C*x^2)/(a - b*x^3),x]","\frac{2 C \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b}-\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}+x\right)}{b}","\frac{2 C \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b}-\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}+x\right)}{b}",1,"(2*C*ArcTan[(1 - (2*x)/(-(a/b))^(1/3))/Sqrt[3]])/(Sqrt[3]*b) - (C*Log[(-(a/b))^(1/3) + x])/b","A",4,4,30,0.1333,1,"{1867, 31, 617, 204}"
35,1,54,0,0.0598418,"\int \frac{2 \left(-\frac{a}{b}\right)^{2/3} C+C x^2}{a+b x^3} \, dx","Int[(2*(-(a/b))^(2/3)*C + C*x^2)/(a + b*x^3),x]","\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}-x\right)}{b}-\frac{2 C \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b}","\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}-x\right)}{b}-\frac{2 C \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b}",1,"(-2*C*ArcTan[(1 + (2*x)/(-(a/b))^(1/3))/Sqrt[3]])/(Sqrt[3]*b) + (C*Log[(-(a/b))^(1/3) - x])/b","A",4,4,29,0.1379,1,"{1869, 31, 617, 204}"
36,1,53,0,0.0582328,"\int \frac{2 \left(\frac{a}{b}\right)^{2/3} C+C x^2}{a-b x^3} \, dx","Int[(2*(a/b)^(2/3)*C + C*x^2)/(a - b*x^3),x]","\frac{2 C \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b}-\frac{C \log \left(\sqrt[3]{\frac{a}{b}}-x\right)}{b}","\frac{2 C \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b}-\frac{C \log \left(\sqrt[3]{\frac{a}{b}}-x\right)}{b}",1,"(2*C*ArcTan[(1 + (2*x)/(a/b)^(1/3))/Sqrt[3]])/(Sqrt[3]*b) - (C*Log[(a/b)^(1/3) - x])/b","A",4,4,29,0.1379,1,"{1869, 31, 617, 204}"
37,1,61,0,0.0412275,"\int \frac{2 a^{2/3} C+b^{2/3} C x^2}{a+b x^3} \, dx","Int[(2*a^(2/3)*C + b^(2/3)*C*x^2)/(a + b*x^3),x]","\frac{C \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{2 C \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{b}}","\frac{C \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{2 C \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"(-2*C*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(1/3)) + (C*Log[a^(1/3) + b^(1/3)*x])/b^(1/3)","A",4,4,29,0.1379,1,"{1863, 31, 617, 204}"
38,1,70,0,0.0718664,"\int \frac{-2 a^{2/3} C-(-b)^{2/3} C x^2}{a+b x^3} \, dx","Int[(-2*a^(2/3)*C - (-b)^(2/3)*C*x^2)/(a + b*x^3),x]","\frac{C \log \left(\sqrt[3]{a}-\sqrt[3]{-b} x\right)}{\sqrt[3]{-b}}-\frac{2 C \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{-b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{-b}}","\frac{C \log \left(\sqrt[3]{a}-\sqrt[3]{-b} x\right)}{\sqrt[3]{-b}}-\frac{2 C \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{-b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{-b}}",1,"(-2*C*ArcTan[(a^(1/3) + 2*(-b)^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*(-b)^(1/3)) + (C*Log[a^(1/3) - (-b)^(1/3)*x])/(-b)^(1/3)","A",4,4,32,0.1250,1,"{1866, 31, 617, 204}"
39,1,40,0,0.0301783,"\int \frac{-3+x^2}{-1+x^3} \, dx","Int[(-3 + x^2)/(-1 + x^3),x]","\frac{5}{6} \log \left(x^2+x+1\right)-\frac{2}{3} \log (1-x)+\sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","\frac{5}{6} \log \left(x^2+x+1\right)-\frac{2}{3} \log (1-x)+\sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - (2*Log[1 - x])/3 + (5*Log[1 + x + x^2])/6","A",6,6,13,0.4615,1,"{1875, 31, 634, 618, 204, 628}"
40,1,70,0,0.0665512,"\int \frac{\sqrt[3]{a} \sqrt[3]{b} B+2 a^{2/3} C+b^{2/3} B x+b^{2/3} C x^2}{a+b x^3} \, dx","Int[(a^(1/3)*b^(1/3)*B + 2*a^(2/3)*C + b^(2/3)*B*x + b^(2/3)*C*x^2)/(a + b*x^3),x]","\frac{C \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{2 \left(\frac{B}{\sqrt[3]{a}}+\frac{C}{\sqrt[3]{b}}\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}","\frac{C \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{2 \left(\frac{B}{\sqrt[3]{a}}+\frac{C}{\sqrt[3]{b}}\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}",1,"(-2*(B/a^(1/3) + C/b^(1/3))*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/Sqrt[3] + (C*Log[a^(1/3) + b^(1/3)*x])/b^(1/3)","A",4,4,49,0.08163,1,"{1863, 31, 617, 204}"
41,1,88,0,0.1123427,"\int \frac{\sqrt[3]{a} \sqrt[3]{-b} B-2 a^{2/3} C-(-b)^{2/3} B x-(-b)^{2/3} C x^2}{a+b x^3} \, dx","Int[(a^(1/3)*(-b)^(1/3)*B - 2*a^(2/3)*C - (-b)^(2/3)*B*x - (-b)^(2/3)*C*x^2)/(a + b*x^3),x]","\frac{2 \left(\sqrt[3]{a} (-b)^{2/3} C+b B\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{-b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b}+\frac{C \log \left(\sqrt[3]{a}-\sqrt[3]{-b} x\right)}{\sqrt[3]{-b}}","\frac{2 \left(\sqrt[3]{a} (-b)^{2/3} C+b B\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{-b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b}+\frac{C \log \left(\sqrt[3]{a}-\sqrt[3]{-b} x\right)}{\sqrt[3]{-b}}",1,"(2*(b*B + a^(1/3)*(-b)^(2/3)*C)*ArcTan[(a^(1/3) + 2*(-b)^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b) + (C*Log[a^(1/3) - (-b)^(1/3)*x])/(-b)^(1/3)","A",4,4,57,0.07018,1,"{1866, 31, 617, 204}"
42,1,11,0,0.0105686,"\int \frac{B^2+B C x+C^2 x^2}{-B^3+C^3 x^3} \, dx","Int[(B^2 + B*C*x + C^2*x^2)/(-B^3 + C^3*x^3),x]","\frac{\log (B-C x)}{C}","\frac{\log (B-C x)}{C}",1,"Log[B - C*x]/C","A",2,2,31,0.06452,1,"{1586, 31}"
43,1,21,0,0.0145199,"\int \frac{a^{2/3} C-\sqrt[3]{a} \sqrt[3]{b} C x+b^{2/3} C x^2}{a+b x^3} \, dx","Int[(a^(2/3)*C - a^(1/3)*b^(1/3)*C*x + b^(2/3)*C*x^2)/(a + b*x^3),x]","\frac{C \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}","\frac{C \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}",1,"(C*Log[a^(1/3) + b^(1/3)*x])/b^(1/3)","A",2,2,42,0.04762,1,"{1586, 31}"
44,1,71,0,0.0941567,"\int \frac{\sqrt[3]{\frac{a}{b}} B+2 \left(\frac{a}{b}\right)^{2/3} C+B x+C x^2}{a+b x^3} \, dx","Int[((a/b)^(1/3)*B + 2*(a/b)^(2/3)*C + B*x + C*x^2)/(a + b*x^3),x]","\frac{C \log \left(\sqrt[3]{\frac{a}{b}}+x\right)}{b}-\frac{2 \left(\frac{a}{b}\right)^{2/3} \left(C \sqrt[3]{\frac{a}{b}}+B\right) \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} a}","\frac{C \log \left(\sqrt[3]{\frac{a}{b}}+x\right)}{b}-\frac{2 \left(\frac{a}{b}\right)^{2/3} \left(C \sqrt[3]{\frac{a}{b}}+B\right) \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} a}",1,"(-2*(a/b)^(2/3)*(B + (a/b)^(1/3)*C)*ArcTan[(1 - (2*x)/(a/b)^(1/3))/Sqrt[3]])/(Sqrt[3]*a) + (C*Log[(a/b)^(1/3) + x])/b","A",4,4,42,0.09524,1,"{1867, 31, 617, 204}"
45,1,76,0,0.1021254,"\int \frac{\sqrt[3]{-\frac{a}{b}} B+2 \left(-\frac{a}{b}\right)^{2/3} C+B x+C x^2}{a-b x^3} \, dx","Int[((-(a/b))^(1/3)*B + 2*(-(a/b))^(2/3)*C + B*x + C*x^2)/(a - b*x^3),x]","\frac{2 \left(C \sqrt[3]{-\frac{a}{b}}+B\right) \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b \sqrt[3]{-\frac{a}{b}}}-\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}+x\right)}{b}","\frac{2 \left(C \sqrt[3]{-\frac{a}{b}}+B\right) \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b \sqrt[3]{-\frac{a}{b}}}-\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}+x\right)}{b}",1,"(2*(B + (-(a/b))^(1/3)*C)*ArcTan[(1 - (2*x)/(-(a/b))^(1/3))/Sqrt[3]])/(Sqrt[3]*(-(a/b))^(1/3)*b) - (C*Log[(-(a/b))^(1/3) + x])/b","A",4,4,45,0.08889,1,"{1867, 31, 617, 204}"
46,1,78,0,0.1076227,"\int \frac{-\sqrt[3]{-\frac{a}{b}} B+2 \left(-\frac{a}{b}\right)^{2/3} C+B x+C x^2}{a+b x^3} \, dx","Int[(-((-(a/b))^(1/3)*B) + 2*(-(a/b))^(2/3)*C + B*x + C*x^2)/(a + b*x^3),x]","\frac{2 \left(B-C \sqrt[3]{-\frac{a}{b}}\right) \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b \sqrt[3]{-\frac{a}{b}}}+\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}-x\right)}{b}","\frac{2 \left(B-C \sqrt[3]{-\frac{a}{b}}\right) \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b \sqrt[3]{-\frac{a}{b}}}+\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}-x\right)}{b}",1,"(2*(B - (-(a/b))^(1/3)*C)*ArcTan[(1 + (2*x)/(-(a/b))^(1/3))/Sqrt[3]])/(Sqrt[3]*(-(a/b))^(1/3)*b) + (C*Log[(-(a/b))^(1/3) - x])/b","A",4,4,45,0.08889,1,"{1869, 31, 617, 204}"
47,1,75,0,0.1046939,"\int \frac{-\sqrt[3]{\frac{a}{b}} B+2 \left(\frac{a}{b}\right)^{2/3} C+B x+C x^2}{a-b x^3} \, dx","Int[(-((a/b)^(1/3)*B) + 2*(a/b)^(2/3)*C + B*x + C*x^2)/(a - b*x^3),x]","-\frac{2 \left(\frac{a}{b}\right)^{2/3} \left(B-C \sqrt[3]{\frac{a}{b}}\right) \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} a}-\frac{C \log \left(\sqrt[3]{\frac{a}{b}}-x\right)}{b}","-\frac{2 \left(\frac{a}{b}\right)^{2/3} \left(B-C \sqrt[3]{\frac{a}{b}}\right) \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} a}-\frac{C \log \left(\sqrt[3]{\frac{a}{b}}-x\right)}{b}",1,"(-2*(a/b)^(2/3)*(B - (a/b)^(1/3)*C)*ArcTan[(1 + (2*x)/(a/b)^(1/3))/Sqrt[3]])/(Sqrt[3]*a) - (C*Log[(a/b)^(1/3) - x])/b","A",4,4,44,0.09091,1,"{1869, 31, 617, 204}"
48,1,32,0,0.0337987,"\int \frac{a+a x+c x^2}{1-x^3} \, dx","Int[(a + a*x + c*x^2)/(1 - x^3),x]","\frac{1}{3} (a-c) \log \left(x^2+x+1\right)-\frac{1}{3} (2 a+c) \log (1-x)","\frac{1}{3} (a-c) \log \left(x^2+x+1\right)-\frac{1}{3} (2 a+c) \log (1-x)",1,"-((2*a + c)*Log[1 - x])/3 + ((a - c)*Log[1 + x + x^2])/3","A",3,3,20,0.1500,1,"{1875, 31, 628}"
49,1,55,0,0.0567216,"\int \frac{a+b x+c x^2}{1-x^3} \, dx","Int[(a + b*x + c*x^2)/(1 - x^3),x]","\frac{1}{6} \log \left(x^2+x+1\right) (a+b-2 c)-\frac{1}{3} \log (1-x) (a+b+c)+\frac{(a-b) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{6} \log \left(x^2+x+1\right) (a+b-2 c)-\frac{1}{3} \log (1-x) (a+b+c)+\frac{(a-b) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"((a - b)*ArcTan[(1 + 2*x)/Sqrt[3]])/Sqrt[3] - ((a + b + c)*Log[1 - x])/3 + ((a + b - 2*c)*Log[1 + x + x^2])/6","A",6,6,20,0.3000,1,"{1875, 31, 634, 618, 204, 628}"
50,1,8,0,0.0060494,"\int \frac{1+x+x^2}{1-x^3} \, dx","Int[(1 + x + x^2)/(1 - x^3),x]","-\log (1-x)","-\log (1-x)",1,"-Log[1 - x]","A",2,2,16,0.1250,1,"{1586, 31}"
51,1,30,0,0.0302431,"\int \frac{1-x+3 x^2}{1-x^3} \, dx","Int[(1 - x + 3*x^2)/(1 - x^3),x]","\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}-\log \left(1-x^3\right)","\frac{2 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}-\log \left(1-x^3\right)",1,"(2*ArcTan[(1 + 2*x)/Sqrt[3]])/Sqrt[3] - Log[1 - x^3]","A",5,5,20,0.2500,1,"{1871, 1586, 618, 204, 260}"
52,1,18,0,0.0188959,"\int \frac{1+x+4 x^2}{1-x^3} \, dx","Int[(1 + x + 4*x^2)/(1 - x^3),x]","-\log \left(x^2+x+1\right)-2 \log (1-x)","-\log \left(x^2+x+1\right)-2 \log (1-x)",1,"-2*Log[1 - x] - Log[1 + x + x^2]","A",3,3,18,0.1667,1,"{1875, 31, 628}"
53,1,113,0,0.0986718,"\int \left(a+b x^3\right)^3 \left(a c+a d x+b c x^3+b d x^4\right) \, dx","Int[(a + b*x^3)^3*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x]","\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+a^4 c x+\frac{1}{2} a^4 d x^2+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14}","\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+a^4 c x+\frac{1}{2} a^4 d x^2+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14}",1,"a^4*c*x + (a^4*d*x^2)/2 + a^3*b*c*x^4 + (4*a^3*b*d*x^5)/5 + (6*a^2*b^2*c*x^7)/7 + (3*a^2*b^2*d*x^8)/4 + (2*a*b^3*c*x^10)/5 + (4*a*b^3*d*x^11)/11 + (b^4*c*x^13)/13 + (b^4*d*x^14)/14","A",2,1,30,0.03333,1,"{1850}"
54,1,88,0,0.0602554,"\int \left(a+b x^3\right)^2 \left(a c+a d x+b c x^3+b d x^4\right) \, dx","Int[(a + b*x^3)^2*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x]","\frac{3}{4} a^2 b c x^4+\frac{3}{5} a^2 b d x^5+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{3}{7} a b^2 c x^7+\frac{3}{8} a b^2 d x^8+\frac{1}{10} b^3 c x^{10}+\frac{1}{11} b^3 d x^{11}","\frac{3}{4} a^2 b c x^4+\frac{3}{5} a^2 b d x^5+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{3}{7} a b^2 c x^7+\frac{3}{8} a b^2 d x^8+\frac{1}{10} b^3 c x^{10}+\frac{1}{11} b^3 d x^{11}",1,"a^3*c*x + (a^3*d*x^2)/2 + (3*a^2*b*c*x^4)/4 + (3*a^2*b*d*x^5)/5 + (3*a*b^2*c*x^7)/7 + (3*a*b^2*d*x^8)/8 + (b^3*c*x^10)/10 + (b^3*d*x^11)/11","A",2,1,30,0.03333,1,"{1850}"
55,1,60,0,0.0380882,"\int \left(a+b x^3\right) \left(a c+a d x+b c x^3+b d x^4\right) \, dx","Int[(a + b*x^3)*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x]","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{2} a b c x^4+\frac{2}{5} a b d x^5+\frac{1}{7} b^2 c x^7+\frac{1}{8} b^2 d x^8","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{2} a b c x^4+\frac{2}{5} a b d x^5+\frac{1}{7} b^2 c x^7+\frac{1}{8} b^2 d x^8",1,"a^2*c*x + (a^2*d*x^2)/2 + (a*b*c*x^4)/2 + (2*a*b*d*x^5)/5 + (b^2*c*x^7)/7 + (b^2*d*x^8)/8","A",2,1,28,0.03571,1,"{1850}"
56,1,12,0,0.0138278,"\int \frac{a c+a d x+b c x^3+b d x^4}{a+b x^3} \, dx","Int[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3),x]","c x+\frac{d x^2}{2}","c x+\frac{d x^2}{2}",1,"c*x + (d*x^2)/2","A",2,1,30,0.03333,1,"{1586}"
57,1,161,0,0.0979056,"\int \frac{a c+a d x+b c x^3+b d x^4}{\left(a+b x^3\right)^2} \, dx","Int[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^2,x]","-\frac{\left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}","-\frac{\left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}",1,"-(((b^(1/3)*c + a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(2/3))) + ((b^(1/3)*c - a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(2/3)) - ((c - (a^(1/3)*d)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(1/3))","A",7,7,30,0.2333,1,"{1586, 1860, 31, 634, 617, 204, 628}"
58,1,189,0,0.1268843,"\int \frac{a c+a d x+b c x^3+b d x^4}{\left(a+b x^3\right)^3} \, dx","Int[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^3,x]","-\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{2/3}}+\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+2 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{2/3}}+\frac{x (c+d x)}{3 a \left(a+b x^3\right)}","-\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{2/3}}+\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+2 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{2/3}}+\frac{x (c+d x)}{3 a \left(a+b x^3\right)}",1,"(x*(c + d*x))/(3*a*(a + b*x^3)) - ((2*b^(1/3)*c + a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(2/3)) + ((2*b^(1/3)*c - a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(2/3)) - ((2*b^(1/3)*c - a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(2/3))","A",8,8,30,0.2667,1,"{1586, 1855, 1860, 31, 634, 617, 204, 628}"
59,1,585,0,0.4638319,"\int \left(a+b x^3\right)^{3/2} \left(a c+a d x+b c x^3+b d x^4\right) \, dx","Int[(a + b*x^3)^(3/2)*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x]","\frac{54\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(1729 \sqrt[3]{b} c-935 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{323323 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{810 a^3 d \sqrt{a+b x^3}}{1729 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{405 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 \sqrt{a+b x^3} \left(1729 c x+935 d x^2\right)}{323323}+\frac{30 a \left(a+b x^3\right)^{3/2} \left(247 c x+187 d x^2\right)}{46189}+\frac{2}{323} \left(a+b x^3\right)^{5/2} \left(19 c x+17 d x^2\right)","\frac{54\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(1729 \sqrt[3]{b} c-935 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{323323 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{810 a^3 d \sqrt{a+b x^3}}{1729 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{405 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 \sqrt{a+b x^3} \left(1729 c x+935 d x^2\right)}{323323}+\frac{30 a \left(a+b x^3\right)^{3/2} \left(247 c x+187 d x^2\right)}{46189}+\frac{2}{323} \left(a+b x^3\right)^{5/2} \left(19 c x+17 d x^2\right)",1,"(810*a^3*d*Sqrt[a + b*x^3])/(1729*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (54*a^2*(1729*c*x + 935*d*x^2)*Sqrt[a + b*x^3])/323323 + (30*a*(247*c*x + 187*d*x^2)*(a + b*x^3)^(3/2))/46189 + (2*(19*c*x + 17*d*x^2)*(a + b*x^3)^(5/2))/323 - (405*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(10/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (54*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^3*(1729*b^(1/3)*c - 935*(1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(323323*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,5,32,0.1562,1,"{1852, 1853, 1878, 218, 1877}"
60,1,556,0,0.3273153,"\int \sqrt{a+b x^3} \left(a c+a d x+b c x^3+b d x^4\right) \, dx","Int[Sqrt[a + b*x^3]*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x]","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(91 \sqrt[3]{b} c-55 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5005 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 d \sqrt{a+b x^3}}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{18 a \sqrt{a+b x^3} \left(91 c x+55 d x^2\right)}{5005}+\frac{2}{143} \left(a+b x^3\right)^{3/2} \left(13 c x+11 d x^2\right)","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(91 \sqrt[3]{b} c-55 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5005 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 d \sqrt{a+b x^3}}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{18 a \sqrt{a+b x^3} \left(91 c x+55 d x^2\right)}{5005}+\frac{2}{143} \left(a+b x^3\right)^{3/2} \left(13 c x+11 d x^2\right)",1,"(54*a^2*d*Sqrt[a + b*x^3])/(91*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (18*a*(91*c*x + 55*d*x^2)*Sqrt[a + b*x^3])/5005 + (2*(13*c*x + 11*d*x^2)*(a + b*x^3)^(3/2))/143 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (18*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(91*b^(1/3)*c - 55*(1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(5005*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,32,0.1562,1,"{1852, 1853, 1878, 218, 1877}"
61,1,525,0,0.2387712,"\int \frac{a c+a d x+b c x^3+b d x^4}{\sqrt{a+b x^3}} \, dx","Int[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/Sqrt[a + b*x^3],x]","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(7 \sqrt[3]{b} c-5 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{35 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a d \sqrt{a+b x^3}}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2}{35} \sqrt{a+b x^3} \left(7 c x+5 d x^2\right)","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(7 \sqrt[3]{b} c-5 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{35 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a d \sqrt{a+b x^3}}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2}{35} \sqrt{a+b x^3} \left(7 c x+5 d x^2\right)",1,"(6*a*d*Sqrt[a + b*x^3])/(7*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*(7*c*x + 5*d*x^2)*Sqrt[a + b*x^3])/35 - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*(7*b^(1/3)*c - 5*(1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(35*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,32,0.1562,1,"{1586, 1853, 1878, 218, 1877}"
62,1,490,0,0.1579612,"\int \frac{a c+a d x+b c x^3+b d x^4}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(3/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-\left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 d \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-\left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 d \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(2*d*Sqrt[a + b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*c - (1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,32,0.1250,1,"{1586, 1878, 218, 1877}"
63,1,522,0,0.2485942,"\int \frac{a c+a d x+b c x^3+b d x^4}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(5/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 d \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x (c+d x)}{3 a \sqrt{a+b x^3}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 d \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x (c+d x)}{3 a \sqrt{a+b x^3}}",1,"(2*x*(c + d*x))/(3*a*Sqrt[a + b*x^3]) - (2*d*Sqrt[a + b*x^3])/(3*a*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (Sqrt[2 - Sqrt[3]]*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(2/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*c + (1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,32,0.1562,1,"{1586, 1855, 1878, 218, 1877}"
64,1,554,0,0.3168354,"\int \frac{a c+a d x+b c x^3+b d x^4}{\left(a+b x^3\right)^{7/2}} \, dx","Int[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(7/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(5 \left(1-\sqrt{3}\right) \sqrt[3]{a} d+7 \sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^2 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{10 d \sqrt{a+b x^3}}{27 a^2 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{5 \sqrt{2-\sqrt{3}} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} a^{5/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x (7 c+5 d x)}{27 a^2 \sqrt{a+b x^3}}+\frac{2 x (c+d x)}{9 a \left(a+b x^3\right)^{3/2}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(5 \left(1-\sqrt{3}\right) \sqrt[3]{a} d+7 \sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^2 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{10 d \sqrt{a+b x^3}}{27 a^2 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{5 \sqrt{2-\sqrt{3}} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} a^{5/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x (7 c+5 d x)}{27 a^2 \sqrt{a+b x^3}}+\frac{2 x (c+d x)}{9 a \left(a+b x^3\right)^{3/2}}",1,"(2*x*(c + d*x))/(9*a*(a + b*x^3)^(3/2)) + (2*x*(7*c + 5*d*x))/(27*a^2*Sqrt[a + b*x^3]) - (10*d*Sqrt[a + b*x^3])/(27*a^2*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (5*Sqrt[2 - Sqrt[3]]*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*a^(5/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(7*b^(1/3)*c + 5*(1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*a^2*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,32,0.1562,1,"{1586, 1855, 1878, 218, 1877}"
65,1,581,0,0.4096808,"\int \frac{a c+a d x+b c x^3+b d x^4}{\left(a+b x^3\right)^{9/2}} \, dx","Int[(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(9/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(55 \left(1-\sqrt{3}\right) \sqrt[3]{a} d+91 \sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{405 \sqrt[4]{3} a^3 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{22 d \sqrt{a+b x^3}}{81 a^3 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{11 \sqrt{2-\sqrt{3}} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27\ 3^{3/4} a^{8/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x (91 c+55 d x)}{405 a^3 \sqrt{a+b x^3}}+\frac{2 x (13 c+11 d x)}{135 a^2 \left(a+b x^3\right)^{3/2}}+\frac{2 x (c+d x)}{15 a \left(a+b x^3\right)^{5/2}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(55 \left(1-\sqrt{3}\right) \sqrt[3]{a} d+91 \sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{405 \sqrt[4]{3} a^3 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{22 d \sqrt{a+b x^3}}{81 a^3 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{11 \sqrt{2-\sqrt{3}} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27\ 3^{3/4} a^{8/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x (91 c+55 d x)}{405 a^3 \sqrt{a+b x^3}}+\frac{2 x (13 c+11 d x)}{135 a^2 \left(a+b x^3\right)^{3/2}}+\frac{2 x (c+d x)}{15 a \left(a+b x^3\right)^{5/2}}",1,"(2*x*(c + d*x))/(15*a*(a + b*x^3)^(5/2)) + (2*x*(13*c + 11*d*x))/(135*a^2*(a + b*x^3)^(3/2)) + (2*x*(91*c + 55*d*x))/(405*a^3*Sqrt[a + b*x^3]) - (22*d*Sqrt[a + b*x^3])/(81*a^3*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (11*Sqrt[2 - Sqrt[3]]*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(3/4)*a^(8/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(91*b^(1/3)*c + 55*(1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(405*3^(1/4)*a^3*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,5,32,0.1562,1,"{1586, 1855, 1878, 218, 1877}"
66,1,590,0,0.5555986,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\sqrt{a+b x^3}} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (5 b c-2 a f)-5 \left(1-\sqrt{3}\right) \sqrt[3]{a} (7 b d-4 a g)\right)}{35 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 b d-4 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3} (7 b d-4 a g)}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 e \sqrt{a+b x^3}}{3 b}+\frac{2 f x \sqrt{a+b x^3}}{5 b}+\frac{2 g x^2 \sqrt{a+b x^3}}{7 b}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (5 b c-2 a f)-5 \left(1-\sqrt{3}\right) \sqrt[3]{a} (7 b d-4 a g)\right)}{35 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 b d-4 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3} (7 b d-4 a g)}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 e \sqrt{a+b x^3}}{3 b}+\frac{2 f x \sqrt{a+b x^3}}{5 b}+\frac{2 g x^2 \sqrt{a+b x^3}}{7 b}",1,"(2*e*Sqrt[a + b*x^3])/(3*b) + (2*f*x*Sqrt[a + b*x^3])/(5*b) + (2*g*x^2*Sqrt[a + b*x^3])/(7*b) + (2*(7*b*d - 4*a*g)*Sqrt[a + b*x^3])/(7*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(7*b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(7*b^(1/3)*(5*b*c - 2*a*f) - 5*(1 - Sqrt[3])*a^(1/3)*(7*b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(35*3^(1/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,6,32,0.1875,1,"{1888, 1886, 261, 1878, 218, 1877}"
67,1,594,0,0.432719,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(3/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(\sqrt[3]{b} (2 a f+b c)+\left(1-\sqrt{3}\right) \sqrt[3]{a} (b d-4 a g)\right)}{3 \sqrt[4]{3} a b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (b d-4 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (b d-4 a g)}{3 a b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x \left(x (b d-a g)-a f+b c+b e x^2\right)}{3 a b \sqrt{a+b x^3}}-\frac{2 e \sqrt{a+b x^3}}{3 a b}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(\sqrt[3]{b} (2 a f+b c)+\left(1-\sqrt{3}\right) \sqrt[3]{a} (b d-4 a g)\right)}{3 \sqrt[4]{3} a b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (b d-4 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (b d-4 a g)}{3 a b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x \left(x (b d-a g)-a f+b c+b e x^2\right)}{3 a b \sqrt{a+b x^3}}-\frac{2 e \sqrt{a+b x^3}}{3 a b}",1,"(2*x*(b*c - a*f + (b*d - a*g)*x + b*e*x^2))/(3*a*b*Sqrt[a + b*x^3]) - (2*e*Sqrt[a + b*x^3])/(3*a*b) - (2*(b*d - 4*a*g)*Sqrt[a + b*x^3])/(3*a*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (Sqrt[2 - Sqrt[3]]*(b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(2/3)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*(b*c + 2*a*f) + (1 - Sqrt[3])*a^(1/3)*(b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,32,0.1875,1,"{1858, 1886, 261, 1878, 218, 1877}"
68,1,628,0,0.5003767,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(5/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(\sqrt[3]{b} (2 a f+7 b c)+\left(1-\sqrt{3}\right) \sqrt[3]{a} (4 a g+5 b d)\right)}{27 \sqrt[4]{3} a^2 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (4 a g+5 b d)}{27 a^2 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a g+5 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 (3 a e-x (x (4 a g+5 b d)+2 a f+7 b c))}{27 a^2 b \sqrt{a+b x^3}}+\frac{2 x \left(x (b d-a g)-a f+b c+b e x^2\right)}{9 a b \left(a+b x^3\right)^{3/2}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(\sqrt[3]{b} (2 a f+7 b c)+\left(1-\sqrt{3}\right) \sqrt[3]{a} (4 a g+5 b d)\right)}{27 \sqrt[4]{3} a^2 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (4 a g+5 b d)}{27 a^2 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a g+5 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 (3 a e-x (x (4 a g+5 b d)+2 a f+7 b c))}{27 a^2 b \sqrt{a+b x^3}}+\frac{2 x \left(x (b d-a g)-a f+b c+b e x^2\right)}{9 a b \left(a+b x^3\right)^{3/2}}",1,"(2*x*(b*c - a*f + (b*d - a*g)*x + b*e*x^2))/(9*a*b*(a + b*x^3)^(3/2)) - (2*(5*b*d + 4*a*g)*Sqrt[a + b*x^3])/(27*a^2*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*(3*a*e - x*(7*b*c + 2*a*f + (5*b*d + 4*a*g)*x)))/(27*a^2*b*Sqrt[a + b*x^3]) + (Sqrt[2 - Sqrt[3]]*(5*b*d + 4*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*a^(5/3)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*(7*b*c + 2*a*f) + (1 - Sqrt[3])*a^(1/3)*(5*b*d + 4*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*a^2*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,32,0.1562,1,"{1858, 1854, 1878, 218, 1877}"
69,1,676,0,0.6749682,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\left(a+b x^3\right)^{7/2}} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(7/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (2 a f+13 b c)+5 \left(1-\sqrt{3}\right) \sqrt[3]{a} (4 a g+11 b d)\right)}{405 \sqrt[4]{3} a^3 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (4 a g+11 b d)}{81 a^3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a g+11 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27\ 3^{3/4} a^{8/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 (9 a e-x (x (4 a g+11 b d)+2 a f+13 b c))}{135 a^2 b \left(a+b x^3\right)^{3/2}}+\frac{2 x (7 (2 a f+13 b c)+5 x (4 a g+11 b d))}{405 a^3 b \sqrt{a+b x^3}}+\frac{2 x \left(x (b d-a g)-a f+b c+b e x^2\right)}{15 a b \left(a+b x^3\right)^{5/2}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (2 a f+13 b c)+5 \left(1-\sqrt{3}\right) \sqrt[3]{a} (4 a g+11 b d)\right)}{405 \sqrt[4]{3} a^3 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (4 a g+11 b d)}{81 a^3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a g+11 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27\ 3^{3/4} a^{8/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 (9 a e-x (x (4 a g+11 b d)+2 a f+13 b c))}{135 a^2 b \left(a+b x^3\right)^{3/2}}+\frac{2 x (7 (2 a f+13 b c)+5 x (4 a g+11 b d))}{405 a^3 b \sqrt{a+b x^3}}+\frac{2 x \left(x (b d-a g)-a f+b c+b e x^2\right)}{15 a b \left(a+b x^3\right)^{5/2}}",1,"(2*x*(b*c - a*f + (b*d - a*g)*x + b*e*x^2))/(15*a*b*(a + b*x^3)^(5/2)) + (2*x*(7*(13*b*c + 2*a*f) + 5*(11*b*d + 4*a*g)*x))/(405*a^3*b*Sqrt[a + b*x^3]) - (2*(11*b*d + 4*a*g)*Sqrt[a + b*x^3])/(81*a^3*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*(9*a*e - x*(13*b*c + 2*a*f + (11*b*d + 4*a*g)*x)))/(135*a^2*b*(a + b*x^3)^(3/2)) + (Sqrt[2 - Sqrt[3]]*(11*b*d + 4*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(3/4)*a^(8/3)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(7*b^(1/3)*(13*b*c + 2*a*f) + 5*(1 - Sqrt[3])*a^(1/3)*(11*b*d + 4*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(405*3^(1/4)*a^3*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,32,0.1875,1,"{1858, 1854, 1855, 1878, 218, 1877}"
70,1,186,0,0.1776349,"\int \frac{(a+b x)^2}{c+d x^3} \, dx","Int[(a + b*x)^2/(c + d*x^3),x]","\frac{a \left(2 b \sqrt[3]{c}-a \sqrt[3]{d}\right) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{2/3}}-\frac{a \left(2 b \sqrt[3]{c}-a \sqrt[3]{d}\right) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{2/3}}-\frac{a \left(a \sqrt[3]{d}+2 b \sqrt[3]{c}\right) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{2/3}}+\frac{b^2 \log \left(c+d x^3\right)}{3 d}","\frac{a \left(2 b \sqrt[3]{c}-a \sqrt[3]{d}\right) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{2/3}}-\frac{a \left(2 b \sqrt[3]{c}-a \sqrt[3]{d}\right) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{2/3}}-\frac{a \left(a \sqrt[3]{d}+2 b \sqrt[3]{c}\right) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{2/3}}+\frac{b^2 \log \left(c+d x^3\right)}{3 d}",1,"-((a*(2*b*c^(1/3) + a*d^(1/3))*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*d^(2/3))) - (a*(2*b*c^(1/3) - a*d^(1/3))*Log[c^(1/3) + d^(1/3)*x])/(3*c^(2/3)*d^(2/3)) + (a*(2*b*c^(1/3) - a*d^(1/3))*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(2/3)*d^(2/3)) + (b^2*Log[c + d*x^3])/(3*d)","A",8,8,17,0.4706,1,"{1871, 1860, 31, 634, 617, 204, 628, 260}"
71,1,222,0,0.3185662,"\int \frac{(a+b x)^3}{c+d x^3} \, dx","Int[(a + b*x)^3/(c + d*x^3),x]","\frac{\left(3 a^2 b \sqrt[3]{c} d^{2/3}+a^3 (-d)+b^3 c\right) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{4/3}}-\frac{\left(3 a^2 b \sqrt[3]{c} d^{2/3}+a^3 (-d)+b^3 c\right) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{4/3}}+\frac{\left(-3 a^2 b \sqrt[3]{c} d^{2/3}+a^3 (-d)+b^3 c\right) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{4/3}}+\frac{a b^2 \log \left(c+d x^3\right)}{d}+\frac{b^3 x}{d}","\frac{\left(3 a^2 b \sqrt[3]{c} d^{2/3}+a^3 (-d)+b^3 c\right) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{4/3}}-\frac{\left(3 a^2 b \sqrt[3]{c} d^{2/3}+a^3 (-d)+b^3 c\right) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{4/3}}+\frac{\left(-3 a^2 b \sqrt[3]{c} d^{2/3}+a^3 (-d)+b^3 c\right) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{4/3}}+\frac{a b^2 \log \left(c+d x^3\right)}{d}+\frac{b^3 x}{d}",1,"(b^3*x)/d + ((b^3*c - 3*a^2*b*c^(1/3)*d^(2/3) - a^3*d)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*d^(4/3)) - ((b^3*c + 3*a^2*b*c^(1/3)*d^(2/3) - a^3*d)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(2/3)*d^(4/3)) + ((b^3*c + 3*a^2*b*c^(1/3)*d^(2/3) - a^3*d)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(2/3)*d^(4/3)) + (a*b^2*Log[c + d*x^3])/d","A",10,9,17,0.5294,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
72,1,280,0,0.4432014,"\int \frac{(a+b x)^4}{c+d x^3} \, dx","Int[(a + b*x)^4/(c + d*x^3),x]","\frac{\left(-\frac{b \sqrt[3]{c} \left(b^3 c-4 a^3 d\right)}{\sqrt[3]{d}}+a^4 (-d)+4 a b^3 c\right) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{4/3}}+\frac{\left(b \sqrt[3]{c} \left(b^3 c-4 a^3 d\right)-\sqrt[3]{d} \left(4 a b^3 c-a^4 d\right)\right) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{5/3}}+\frac{\left(-4 a^3 b \sqrt[3]{c} d+a^4 \left(-d^{4/3}\right)+4 a b^3 c \sqrt[3]{d}+b^4 c^{4/3}\right) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{5/3}}+\frac{2 a^2 b^2 \log \left(c+d x^3\right)}{d}+\frac{4 a b^3 x}{d}+\frac{b^4 x^2}{2 d}","-\frac{\left(b \sqrt[3]{c} \left(b^3 c-4 a^3 d\right)-\sqrt[3]{d} \left(4 a b^3 c-a^4 d\right)\right) \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} d^{5/3}}+\frac{\left(b \sqrt[3]{c} \left(b^3 c-4 a^3 d\right)-\sqrt[3]{d} \left(4 a b^3 c-a^4 d\right)\right) \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} d^{5/3}}+\frac{\left(-4 a^3 b \sqrt[3]{c} d+a^4 \left(-d^{4/3}\right)+4 a b^3 c \sqrt[3]{d}+b^4 c^{4/3}\right) \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} d^{5/3}}+\frac{2 a^2 b^2 \log \left(c+d x^3\right)}{d}+\frac{4 a b^3 x}{d}+\frac{b^4 x^2}{2 d}",1,"(4*a*b^3*x)/d + (b^4*x^2)/(2*d) + ((b^4*c^(4/3) + 4*a*b^3*c*d^(1/3) - 4*a^3*b*c^(1/3)*d - a^4*d^(4/3))*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*d^(5/3)) + ((b*c^(1/3)*(b^3*c - 4*a^3*d) - d^(1/3)*(4*a*b^3*c - a^4*d))*Log[c^(1/3) + d^(1/3)*x])/(3*c^(2/3)*d^(5/3)) + ((4*a*b^3*c - a^4*d - (b*c^(1/3)*(b^3*c - 4*a^3*d))/d^(1/3))*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(2/3)*d^(4/3)) + (2*a^2*b^2*Log[c + d*x^3])/d","A",10,9,17,0.5294,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
73,1,270,0,0.490332,"\int \frac{\left(a+b x+c x^2\right)^2}{d+e x^3} \, dx","Int[(a + b*x + c*x^2)^2/(d + e*x^3),x]","\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(a^2 (-e)-\frac{\sqrt[3]{d} \left(c^2 d-2 a b e\right)}{\sqrt[3]{e}}+2 b c d\right)}{6 d^{2/3} e^{4/3}}-\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(\sqrt[3]{e} \left(2 b c d-a^2 e\right)-\sqrt[3]{d} \left(c^2 d-2 a b e\right)\right)}{3 d^{2/3} e^{5/3}}+\frac{\left(2 a c+b^2\right) \log \left(d+e x^3\right)}{3 e}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(-a e \left(a \sqrt[3]{e}+2 b \sqrt[3]{d}\right)+2 b c d \sqrt[3]{e}+c^2 d^{4/3}\right)}{\sqrt{3} d^{2/3} e^{5/3}}+\frac{2 b c x}{e}+\frac{c^2 x^2}{2 e}","\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(\sqrt[3]{e} \left(2 b c d-a^2 e\right)-\sqrt[3]{d} \left(c^2 d-2 a b e\right)\right)}{6 d^{2/3} e^{5/3}}-\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(\sqrt[3]{e} \left(2 b c d-a^2 e\right)-\sqrt[3]{d} \left(c^2 d-2 a b e\right)\right)}{3 d^{2/3} e^{5/3}}+\frac{\left(2 a c+b^2\right) \log \left(d+e x^3\right)}{3 e}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(-a e \left(a \sqrt[3]{e}+2 b \sqrt[3]{d}\right)+2 b c d \sqrt[3]{e}+c^2 d^{4/3}\right)}{\sqrt{3} d^{2/3} e^{5/3}}+\frac{2 b c x}{e}+\frac{c^2 x^2}{2 e}",1,"(2*b*c*x)/e + (c^2*x^2)/(2*e) + ((c^2*d^(4/3) + 2*b*c*d*e^(1/3) - a*(2*b*d^(1/3) + a*e^(1/3))*e)*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(Sqrt[3]*d^(2/3)*e^(5/3)) - ((e^(1/3)*(2*b*c*d - a^2*e) - d^(1/3)*(c^2*d - 2*a*b*e))*Log[d^(1/3) + e^(1/3)*x])/(3*d^(2/3)*e^(5/3)) + ((2*b*c*d - a^2*e - (d^(1/3)*(c^2*d - 2*a*b*e))/e^(1/3))*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(6*d^(2/3)*e^(4/3)) + ((b^2 + 2*a*c)*Log[d + e*x^3])/(3*e)","A",10,9,22,0.4091,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
74,1,416,0,0.7002897,"\int \frac{\left(a+b x+c x^2\right)^3}{d+e x^3} \, dx","Int[(a + b*x + c*x^2)^3/(d + e*x^3),x]","-\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(3 \sqrt[3]{d} e^{2/3} \left(a^2 (-b) e+a c^2 d+b^2 c d\right)-e \left(b^3 d-a^3 e\right)-6 a b c d e+c^3 d^2\right)}{6 d^{2/3} e^{7/3}}+\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(3 \sqrt[3]{d} e^{2/3} \left(a^2 (-b) e+a c^2 d+b^2 c d\right)-e \left(b^3 d-a^3 e\right)-6 a b c d e+c^3 d^2\right)}{3 d^{2/3} e^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(3 a^2 b \sqrt[3]{d} e^{5/3}+a^3 e^2-6 a b c d e-3 a c^2 d^{4/3} e^{2/3}-3 b^2 c d^{4/3} e^{2/3}-b^3 d e+c^3 d^2\right)}{\sqrt{3} d^{2/3} e^{7/3}}-\frac{\log \left(d+e x^3\right) \left(a^2 (-c) e-a b^2 e+b c^2 d\right)}{e^2}-\frac{x \left(-6 a b c e+b^3 (-e)+c^3 d\right)}{e^2}+\frac{3 c x^2 \left(a c+b^2\right)}{2 e}+\frac{b c^2 x^3}{e}+\frac{c^3 x^4}{4 e}","-\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(3 \sqrt[3]{d} e^{2/3} \left(a^2 (-b) e+a c^2 d+b^2 c d\right)-e \left(b^3 d-a^3 e\right)-6 a b c d e+c^3 d^2\right)}{6 d^{2/3} e^{7/3}}+\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(3 \sqrt[3]{d} e^{2/3} \left(a^2 (-b) e+a c^2 d+b^2 c d\right)-e \left(b^3 d-a^3 e\right)-6 a b c d e+c^3 d^2\right)}{3 d^{2/3} e^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(3 a^2 b \sqrt[3]{d} e^{5/3}+a^3 e^2-6 a b c d e-3 a c^2 d^{4/3} e^{2/3}-3 b^2 c d^{4/3} e^{2/3}-b^3 d e+c^3 d^2\right)}{\sqrt{3} d^{2/3} e^{7/3}}-\frac{\log \left(d+e x^3\right) \left(a^2 (-c) e-a b^2 e+b c^2 d\right)}{e^2}-\frac{x \left(-6 a b c e+b^3 (-e)+c^3 d\right)}{e^2}+\frac{3 c x^2 \left(a c+b^2\right)}{2 e}+\frac{b c^2 x^3}{e}+\frac{c^3 x^4}{4 e}",1,"-(((c^3*d - b^3*e - 6*a*b*c*e)*x)/e^2) + (3*c*(b^2 + a*c)*x^2)/(2*e) + (b*c^2*x^3)/e + (c^3*x^4)/(4*e) - ((c^3*d^2 - 3*b^2*c*d^(4/3)*e^(2/3) - 3*a*c^2*d^(4/3)*e^(2/3) - b^3*d*e - 6*a*b*c*d*e + 3*a^2*b*d^(1/3)*e^(5/3) + a^3*e^2)*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(Sqrt[3]*d^(2/3)*e^(7/3)) + ((c^3*d^2 - 6*a*b*c*d*e - e*(b^3*d - a^3*e) + 3*d^(1/3)*e^(2/3)*(b^2*c*d + a*c^2*d - a^2*b*e))*Log[d^(1/3) + e^(1/3)*x])/(3*d^(2/3)*e^(7/3)) - ((c^3*d^2 - 6*a*b*c*d*e - e*(b^3*d - a^3*e) + 3*d^(1/3)*e^(2/3)*(b^2*c*d + a*c^2*d - a^2*b*e))*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(6*d^(2/3)*e^(7/3)) - ((b*c^2*d - a*b^2*e - a^2*c*e)*Log[d + e*x^3])/e^2","A",10,9,22,0.4091,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
75,1,643,0,1.0966399,"\int \frac{\left(a+b x+c x^2\right)^4}{d+e x^3} \, dx","Int[(a + b*x + c*x^2)^4/(d + e*x^3),x]","-\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(\frac{\sqrt[3]{d} \left(-4 b \left(a^3 e^2+c^3 d^2\right)+6 a^2 c^2 d e+12 a b^2 c d e+b^4 d e\right)}{\sqrt[3]{e}}-12 a^2 b c d e+a^4 e^2-4 a b^3 d e+4 a c^3 d^2+6 b^2 c^2 d^2\right)}{6 d^{2/3} e^{7/3}}+\frac{\log \left(d+e x^3\right) \left(-4 c e \left(b^3 d-a^3 e\right)+6 a^2 b^2 e^2-12 a b c^2 d e+c^4 d^2\right)}{3 e^3}+\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(\sqrt[3]{e} \left(-12 a^2 b c d e+a^4 e^2-4 a b^3 d e+4 a c^3 d^2+6 b^2 c^2 d^2\right)+\sqrt[3]{d} \left(-4 b \left(a^3 e^2+c^3 d^2\right)+6 a^2 c^2 d e+12 a b^2 c d e+b^4 d e\right)\right)}{3 d^{2/3} e^{8/3}}-\frac{\left(a \sqrt[3]{e}+b \sqrt[3]{d}\right) \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(-e \left(-3 a^2 b \sqrt[3]{d} e^{2/3}+a^3 (-e)+3 a b^2 d^{2/3} \sqrt[3]{e}+b^3 d\right)+6 c^2 \left(b d^{5/3} \sqrt[3]{e}-a d^{4/3} e^{2/3}\right)-12 a b c d e+4 c^3 d^2\right)}{\sqrt{3} d^{2/3} e^{8/3}}-\frac{x^2 \left(-6 a^2 c^2 e-12 a b^2 c e+b^4 (-e)+4 b c^3 d\right)}{2 e^2}-\frac{2 x \left(-6 a^2 b c e-2 a b^3 e+2 a c^3 d+3 b^2 c^2 d\right)}{e^2}-\frac{c x^3 \left(-12 a b c e-4 b^3 e+c^3 d\right)}{3 e^2}+\frac{c^2 x^4 \left(2 a c+3 b^2\right)}{2 e}+\frac{4 b c^3 x^5}{5 e}+\frac{c^4 x^6}{6 e}","-\frac{\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} x+e^{2/3} x^2\right) \left(\sqrt[3]{e} \left(-12 a^2 b c d e+a^4 e^2-4 a b^3 d e+4 a c^3 d^2+6 b^2 c^2 d^2\right)+\sqrt[3]{d} \left(-4 b \left(a^3 e^2+c^3 d^2\right)+6 a^2 c^2 d e+12 a b^2 c d e+b^4 d e\right)\right)}{6 d^{2/3} e^{8/3}}+\frac{\log \left(d+e x^3\right) \left(-4 c e \left(b^3 d-a^3 e\right)+6 a^2 b^2 e^2-12 a b c^2 d e+c^4 d^2\right)}{3 e^3}+\frac{\log \left(\sqrt[3]{d}+\sqrt[3]{e} x\right) \left(\sqrt[3]{e} \left(-12 a^2 b c d e+a^4 e^2-4 a b^3 d e+4 a c^3 d^2+6 b^2 c^2 d^2\right)+\sqrt[3]{d} \left(-4 b \left(a^3 e^2+c^3 d^2\right)+6 a^2 c^2 d e+12 a b^2 c d e+b^4 d e\right)\right)}{3 d^{2/3} e^{8/3}}-\frac{\left(a \sqrt[3]{e}+b \sqrt[3]{d}\right) \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) \left(-e \left(-3 a^2 b \sqrt[3]{d} e^{2/3}+a^3 (-e)+3 a b^2 d^{2/3} \sqrt[3]{e}+b^3 d\right)+6 c^2 \left(b d^{5/3} \sqrt[3]{e}-a d^{4/3} e^{2/3}\right)-12 a b c d e+4 c^3 d^2\right)}{\sqrt{3} d^{2/3} e^{8/3}}-\frac{x^2 \left(-6 a^2 c^2 e-12 a b^2 c e+b^4 (-e)+4 b c^3 d\right)}{2 e^2}-\frac{2 x \left(-6 a^2 b c e-2 a b^3 e+2 a c^3 d+3 b^2 c^2 d\right)}{e^2}-\frac{c x^3 \left(-12 a b c e-4 b^3 e+c^3 d\right)}{3 e^2}+\frac{c^2 x^4 \left(2 a c+3 b^2\right)}{2 e}+\frac{4 b c^3 x^5}{5 e}+\frac{c^4 x^6}{6 e}",1,"(-2*(3*b^2*c^2*d + 2*a*c^3*d - 2*a*b^3*e - 6*a^2*b*c*e)*x)/e^2 - ((4*b*c^3*d - b^4*e - 12*a*b^2*c*e - 6*a^2*c^2*e)*x^2)/(2*e^2) - (c*(c^3*d - 4*b^3*e - 12*a*b*c*e)*x^3)/(3*e^2) + (c^2*(3*b^2 + 2*a*c)*x^4)/(2*e) + (4*b*c^3*x^5)/(5*e) + (c^4*x^6)/(6*e) - ((b*d^(1/3) + a*e^(1/3))*(4*c^3*d^2 + 6*c^2*(b*d^(5/3)*e^(1/3) - a*d^(4/3)*e^(2/3)) - 12*a*b*c*d*e - e*(b^3*d + 3*a*b^2*d^(2/3)*e^(1/3) - 3*a^2*b*d^(1/3)*e^(2/3) - a^3*e))*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(Sqrt[3]*d^(2/3)*e^(8/3)) + ((e^(1/3)*(6*b^2*c^2*d^2 + 4*a*c^3*d^2 - 4*a*b^3*d*e - 12*a^2*b*c*d*e + a^4*e^2) + d^(1/3)*(b^4*d*e + 12*a*b^2*c*d*e + 6*a^2*c^2*d*e - 4*b*(c^3*d^2 + a^3*e^2)))*Log[d^(1/3) + e^(1/3)*x])/(3*d^(2/3)*e^(8/3)) - ((6*b^2*c^2*d^2 + 4*a*c^3*d^2 - 4*a*b^3*d*e - 12*a^2*b*c*d*e + a^4*e^2 + (d^(1/3)*(b^4*d*e + 12*a*b^2*c*d*e + 6*a^2*c^2*d*e - 4*b*(c^3*d^2 + a^3*e^2)))/e^(1/3))*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(6*d^(2/3)*e^(7/3)) + ((c^4*d^2 - 12*a*b*c^2*d*e + 6*a^2*b^2*e^2 - 4*c*e*(b^3*d - a^3*e))*Log[d + e*x^3])/(3*e^3)","A",10,9,22,0.4091,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
76,1,43,0,0.078164,"\int \frac{2 x^2+x^4}{1+x^3} \, dx","Int[(2*x^2 + x^4)/(1 + x^3),x]","\frac{x^2}{2}+\frac{1}{2} \log \left(x^2-x+1\right)+\log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{x^2}{2}+\frac{1}{2} \log \left(x^2-x+1\right)+\log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"x^2/2 + ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3] + Log[1 + x] + Log[1 - x + x^2]/2","A",9,8,17,0.4706,1,"{1593, 1887, 1874, 31, 634, 618, 204, 628}"
77,1,46,0,0.0838093,"\int \frac{2 x^2+x^4}{1-x^3} \, dx","Int[(2*x^2 + x^4)/(1 - x^3),x]","-\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+x+1\right)-\log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{x^2}{2}-\frac{1}{2} \log \left(x^2+x+1\right)-\log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-x^2/2 - ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3] - Log[1 - x] - Log[1 + x + x^2]/2","A",9,8,19,0.4211,1,"{1593, 1887, 1875, 31, 634, 618, 204, 628}"
78,1,44,0,0.0426502,"\int \frac{1-x+4 x^3}{1+x^3} \, dx","Int[(1 - x + 4*x^3)/(1 + x^3),x]","\frac{1}{3} \log \left(x^2-x+1\right)+4 x-\frac{2}{3} \log (x+1)+\frac{4 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{3} \log \left(x^2-x+1\right)+4 x-\frac{2}{3} \log (x+1)+\frac{4 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"4*x + (4*ArcTan[(1 - 2*x)/Sqrt[3]])/Sqrt[3] - (2*Log[1 + x])/3 + Log[1 - x + x^2]/3","A",8,7,18,0.3889,1,"{1887, 1860, 31, 634, 618, 204, 628}"
79,1,230,0,0.0595062,"\int \frac{1+\sqrt{3}+x}{\sqrt{1+x^3}} \, dx","Int[(1 + Sqrt[3] + x)/Sqrt[1 + x^3],x]","\frac{2 \sqrt{x^3+1}}{x+\sqrt{3}+1}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2 \sqrt{x^3+1}}{x+\sqrt{3}+1}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*Sqrt[1 + x^3])/(1 + Sqrt[3] + x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",3,3,18,0.1667,1,"{1878, 218, 1877}"
80,1,257,0,0.0669402,"\int \frac{1+\sqrt{3}-x}{\sqrt{1-x^3}} \, dx","Int[(1 + Sqrt[3] - x)/Sqrt[1 - x^3],x]","-\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(-2*Sqrt[1 - x^3])/(1 + Sqrt[3] - x) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) - (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",3,3,22,0.1364,1,"{1878, 218, 1877}"
81,1,144,0,0.0270309,"\int \frac{1+\sqrt{3}-x}{\sqrt{-1+x^3}} \, dx","Int[(1 + Sqrt[3] - x)/Sqrt[-1 + x^3],x]","\frac{2 \sqrt{x^3-1}}{-x-\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{2 \sqrt{x^3-1}}{-x-\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(2*Sqrt[-1 + x^3])/(1 - Sqrt[3] - x) - (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",1,1,20,0.05000,1,"{1879}"
82,1,135,0,0.0327293,"\int \frac{1+\sqrt{3}+x}{\sqrt{-1-x^3}} \, dx","Int[(1 + Sqrt[3] + x)/Sqrt[-1 - x^3],x]","\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{2 \sqrt{-x^3-1}}{x-\sqrt{3}+1}","\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{2 \sqrt{-x^3-1}}{x-\sqrt{3}+1}",1,"(-2*Sqrt[-1 - x^3])/(1 - Sqrt[3] + x) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",1,1,20,0.05000,1,"{1879}"
83,1,468,0,0.1207207,"\int \frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt{a+b x^3}} \, dx","Int[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/Sqrt[a + b*x^3],x]","\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{\sqrt[3]{b} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{\sqrt[3]{b} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(2*Sqrt[a + b*x^3])/(b^(1/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,33,0.09091,1,"{1878, 218, 1877}"
84,1,481,0,0.1389494,"\int \frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\sqrt{a-b x^3}} \, dx","Int[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/Sqrt[a - b*x^3],x]","-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \sqrt{a-b x^3}}{\sqrt[3]{b} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}","-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \sqrt{a-b x^3}}{\sqrt[3]{b} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}",1,"(-2*Sqrt[a - b*x^3])/(b^(1/3)*((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3]) - (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",3,3,35,0.08571,1,"{1878, 218, 1877}"
85,1,271,0,0.0657175,"\int \frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\sqrt{-a+b x^3}} \, dx","Int[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/Sqrt[-a + b*x^3],x]","\frac{2 \sqrt{b x^3-a}}{\sqrt[3]{b} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}","\frac{2 \sqrt{b x^3-a}}{\sqrt[3]{b} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}",1,"(2*Sqrt[-a + b*x^3])/(b^(1/3)*((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(1/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",1,1,36,0.02778,1,"{1879}"
86,1,266,0,0.0618671,"\int \frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt{-a-b x^3}} \, dx","Int[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/Sqrt[-a - b*x^3],x]","\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \sqrt{-a-b x^3}}{\sqrt[3]{b} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \sqrt{-a-b x^3}}{\sqrt[3]{b} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(-2*Sqrt[-a - b*x^3])/(b^(1/3)*((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(1/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",1,1,36,0.02778,1,"{1879}"
87,1,520,0,0.213352,"\int \frac{1+\sqrt{3}+\sqrt[3]{\frac{b}{a}} x}{\sqrt{a+b x^3}} \, dx","Int[(1 + Sqrt[3] + (b/a)^(1/3)*x)/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{b}-\left(1-\sqrt{3}\right) \sqrt[3]{a} \sqrt[3]{\frac{b}{a}}\right) \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{\frac{b}{a}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt[3]{\frac{b}{a}} \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{2 \sqrt{2+\sqrt{3}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{b}-\left(1-\sqrt{3}\right) \sqrt[3]{a} \sqrt[3]{\frac{b}{a}}\right) \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{\frac{b}{a}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt[3]{\frac{b}{a}} \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(2*(b/a)^(1/3)*Sqrt[a + b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(b/a)^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*((1 + Sqrt[3])*b^(1/3) - (1 - Sqrt[3])*a^(1/3)*(b/a)^(1/3))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,30,0.1000,1,"{1878, 218, 1877}"
88,1,533,0,0.1723005,"\int \frac{1+\sqrt{3}-\sqrt[3]{\frac{b}{a}} x}{\sqrt{a-b x^3}} \, dx","Int[(1 + Sqrt[3] - (b/a)^(1/3)*x)/Sqrt[a - b*x^3],x]","-\frac{2 \sqrt{2+\sqrt{3}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{b}-\left(1-\sqrt{3}\right) \sqrt[3]{a} \sqrt[3]{\frac{b}{a}}\right) \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{\frac{b}{a}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \sqrt[3]{\frac{b}{a}} \sqrt{a-b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}","-\frac{2 \sqrt{2+\sqrt{3}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{b}-\left(1-\sqrt{3}\right) \sqrt[3]{a} \sqrt[3]{\frac{b}{a}}\right) \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{\frac{b}{a}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \sqrt[3]{\frac{b}{a}} \sqrt{a-b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}",1,"(-2*(b/a)^(1/3)*Sqrt[a - b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(b/a)^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3]) - (2*Sqrt[2 + Sqrt[3]]*((1 + Sqrt[3])*b^(1/3) - (1 - Sqrt[3])*a^(1/3)*(b/a)^(1/3))*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",3,3,32,0.09375,1,"{1878, 218, 1877}"
89,1,256,0,0.0831561,"\int \frac{1+\sqrt{3}-\sqrt[3]{\frac{b}{a}} x}{\sqrt{-a+b x^3}} \, dx","Int[(1 + Sqrt[3] - (b/a)^(1/3)*x)/Sqrt[-a + b*x^3],x]","\frac{2 \left(\frac{b}{a}\right)^{2/3} \sqrt{b x^3-a}}{b \left(x \left(-\sqrt[3]{\frac{b}{a}}\right)-\sqrt{3}+1\right)}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-x \sqrt[3]{\frac{b}{a}}\right) \sqrt{\frac{x^2 \left(\frac{b}{a}\right)^{2/3}+x \sqrt[3]{\frac{b}{a}}+1}{\left(x \left(-\sqrt[3]{\frac{b}{a}}\right)-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b}{a}} x+\sqrt{3}+1}{-\sqrt[3]{\frac{b}{a}} x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{\frac{b}{a}} \sqrt{-\frac{1-x \sqrt[3]{\frac{b}{a}}}{\left(x \left(-\sqrt[3]{\frac{b}{a}}\right)-\sqrt{3}+1\right)^2}} \sqrt{b x^3-a}}","\frac{2 \left(\frac{b}{a}\right)^{2/3} \sqrt{b x^3-a}}{b \left(x \left(-\sqrt[3]{\frac{b}{a}}\right)-\sqrt{3}+1\right)}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-x \sqrt[3]{\frac{b}{a}}\right) \sqrt{\frac{x^2 \left(\frac{b}{a}\right)^{2/3}+x \sqrt[3]{\frac{b}{a}}+1}{\left(x \left(-\sqrt[3]{\frac{b}{a}}\right)-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b}{a}} x+\sqrt{3}+1}{-\sqrt[3]{\frac{b}{a}} x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{\frac{b}{a}} \sqrt{-\frac{1-x \sqrt[3]{\frac{b}{a}}}{\left(x \left(-\sqrt[3]{\frac{b}{a}}\right)-\sqrt{3}+1\right)^2}} \sqrt{b x^3-a}}",1,"(2*(b/a)^(2/3)*Sqrt[-a + b*x^3])/(b*(1 - Sqrt[3] - (b/a)^(1/3)*x)) - (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (b/a)^(1/3)*x)*Sqrt[(1 + (b/a)^(1/3)*x + (b/a)^(2/3)*x^2)/(1 - Sqrt[3] - (b/a)^(1/3)*x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (b/a)^(1/3)*x)/(1 - Sqrt[3] - (b/a)^(1/3)*x)], -7 + 4*Sqrt[3]])/((b/a)^(1/3)*Sqrt[-((1 - (b/a)^(1/3)*x)/(1 - Sqrt[3] - (b/a)^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",1,1,33,0.03030,1,"{1879}"
90,1,251,0,0.0644166,"\int \frac{1+\sqrt{3}+\sqrt[3]{\frac{b}{a}} x}{\sqrt{-a-b x^3}} \, dx","Int[(1 + Sqrt[3] + (b/a)^(1/3)*x)/Sqrt[-a - b*x^3],x]","\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(x \sqrt[3]{\frac{b}{a}}+1\right) \sqrt{\frac{x^2 \left(\frac{b}{a}\right)^{2/3}-x \sqrt[3]{\frac{b}{a}}+1}{\left(x \sqrt[3]{\frac{b}{a}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{\frac{b}{a}} x+\sqrt{3}+1}{\sqrt[3]{\frac{b}{a}} x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{\frac{b}{a}} \sqrt{-\frac{x \sqrt[3]{\frac{b}{a}}+1}{\left(x \sqrt[3]{\frac{b}{a}}-\sqrt{3}+1\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \left(\frac{b}{a}\right)^{2/3} \sqrt{-a-b x^3}}{b \left(x \sqrt[3]{\frac{b}{a}}-\sqrt{3}+1\right)}","\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(x \sqrt[3]{\frac{b}{a}}+1\right) \sqrt{\frac{x^2 \left(\frac{b}{a}\right)^{2/3}-x \sqrt[3]{\frac{b}{a}}+1}{\left(x \sqrt[3]{\frac{b}{a}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{\frac{b}{a}} x+\sqrt{3}+1}{\sqrt[3]{\frac{b}{a}} x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{\frac{b}{a}} \sqrt{-\frac{x \sqrt[3]{\frac{b}{a}}+1}{\left(x \sqrt[3]{\frac{b}{a}}-\sqrt{3}+1\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \left(\frac{b}{a}\right)^{2/3} \sqrt{-a-b x^3}}{b \left(x \sqrt[3]{\frac{b}{a}}-\sqrt{3}+1\right)}",1,"(-2*(b/a)^(2/3)*Sqrt[-a - b*x^3])/(b*(1 - Sqrt[3] + (b/a)^(1/3)*x)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + (b/a)^(1/3)*x)*Sqrt[(1 - (b/a)^(1/3)*x + (b/a)^(2/3)*x^2)/(1 - Sqrt[3] + (b/a)^(1/3)*x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + (b/a)^(1/3)*x)/(1 - Sqrt[3] + (b/a)^(1/3)*x)], -7 + 4*Sqrt[3]])/((b/a)^(1/3)*Sqrt[-((1 + (b/a)^(1/3)*x)/(1 - Sqrt[3] + (b/a)^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",1,1,33,0.03030,1,"{1879}"
91,1,127,0,0.0190498,"\int \frac{1-\sqrt{3}+x}{\sqrt{1+x^3}} \, dx","Int[(1 - Sqrt[3] + x)/Sqrt[1 + x^3],x]","\frac{2 \sqrt{x^3+1}}{x+\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2 \sqrt{x^3+1}}{x+\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*Sqrt[1 + x^3])/(1 + Sqrt[3] + x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",1,1,20,0.05000,1,"{1877}"
92,1,142,0,0.0252626,"\int \frac{1-\sqrt{3}-x}{\sqrt{1-x^3}} \, dx","Int[(1 - Sqrt[3] - x)/Sqrt[1 - x^3],x]","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}",1,"(-2*Sqrt[1 - x^3])/(1 + Sqrt[3] - x) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",1,1,24,0.04167,1,"{1877}"
93,1,264,0,0.0540904,"\int \frac{1-\sqrt{3}-x}{\sqrt{-1+x^3}} \, dx","Int[(1 - Sqrt[3] - x)/Sqrt[-1 + x^3],x]","\frac{2 \sqrt{x^3-1}}{-x-\sqrt{3}+1}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{2 \sqrt{x^3-1}}{-x-\sqrt{3}+1}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(2*Sqrt[-1 + x^3])/(1 - Sqrt[3] - x) - (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",3,3,22,0.1364,1,"{1880, 219, 1879}"
94,1,247,0,0.0543306,"\int \frac{1-\sqrt{3}+x}{\sqrt{-1-x^3}} \, dx","Int[(1 - Sqrt[3] + x)/Sqrt[-1 - x^3],x]","-\frac{2 \sqrt{-x^3-1}}{x-\sqrt{3}+1}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","-\frac{2 \sqrt{-x^3-1}}{x-\sqrt{3}+1}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(-2*Sqrt[-1 - x^3])/(1 - Sqrt[3] + x) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) - (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",3,3,22,0.1364,1,"{1880, 219, 1879}"
95,1,126,0,0.0246693,"\int \frac{-1+\sqrt{3}-x}{\sqrt{1+x^3}} \, dx","Int[(-1 + Sqrt[3] - x)/Sqrt[1 + x^3],x]","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2 \sqrt{x^3+1}}{x+\sqrt{3}+1}","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2 \sqrt{x^3+1}}{x+\sqrt{3}+1}",1,"(-2*Sqrt[1 + x^3])/(1 + Sqrt[3] + x) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",1,1,20,0.05000,1,"{1877}"
96,1,143,0,0.024946,"\int \frac{-1+\sqrt{3}+x}{\sqrt{1-x^3}} \, dx","Int[(-1 + Sqrt[3] + x)/Sqrt[1 - x^3],x]","\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(2*Sqrt[1 - x^3])/(1 + Sqrt[3] - x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",1,1,20,0.05000,1,"{1877}"
97,1,263,0,0.0502606,"\int \frac{-1+\sqrt{3}+x}{\sqrt{-1+x^3}} \, dx","Int[(-1 + Sqrt[3] + x)/Sqrt[-1 + x^3],x]","-\frac{2 \sqrt{x^3-1}}{-x-\sqrt{3}+1}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-\frac{2 \sqrt{x^3-1}}{-x-\sqrt{3}+1}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(-2*Sqrt[-1 + x^3])/(1 - Sqrt[3] - x) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",3,3,18,0.1667,1,"{1880, 219, 1879}"
98,1,248,0,0.0519657,"\int \frac{-1+\sqrt{3}-x}{\sqrt{-1-x^3}} \, dx","Int[(-1 + Sqrt[3] - x)/Sqrt[-1 - x^3],x]","\frac{2 \sqrt{-x^3-1}}{x-\sqrt{3}+1}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{2 \sqrt{-x^3-1}}{x-\sqrt{3}+1}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(2*Sqrt[-1 - x^3])/(1 - Sqrt[3] + x) - (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",3,3,22,0.1364,1,"{1880, 219, 1879}"
99,1,256,0,0.0447983,"\int \frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt{a+b x^3}} \, dx","Int[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{a+b x^3}}{\sqrt[3]{b} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}","\frac{2 \sqrt{a+b x^3}}{\sqrt[3]{b} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}",1,"(2*Sqrt[a + b*x^3])/(b^(1/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",1,1,35,0.02857,1,"{1877}"
100,1,263,0,0.0417543,"\int \frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\sqrt{a-b x^3}} \, dx","Int[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/Sqrt[a - b*x^3],x]","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \sqrt{a-b x^3}}{\sqrt[3]{b} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \sqrt{a-b x^3}}{\sqrt[3]{b} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}",1,"(-2*Sqrt[a - b*x^3])/(b^(1/3)*((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",1,1,37,0.02703,1,"{1877}"
101,1,497,0,0.1328153,"\int \frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\sqrt{-a+b x^3}} \, dx","Int[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/Sqrt[-a + b*x^3],x]","\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{2 \sqrt{b x^3-a}}{\sqrt[3]{b} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}","\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{2 \sqrt{b x^3-a}}{\sqrt[3]{b} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}",1,"(2*Sqrt[-a + b*x^3])/(b^(1/3)*((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(1/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3]) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(1/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",3,3,38,0.07895,1,"{1880, 219, 1879}"
102,1,488,0,0.114932,"\int \frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt{-a-b x^3}} \, dx","Int[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/Sqrt[-a - b*x^3],x]","-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \sqrt{-a-b x^3}}{\sqrt[3]{b} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \sqrt{-a-b x^3}}{\sqrt[3]{b} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(-2*Sqrt[-a - b*x^3])/(b^(1/3)*((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(1/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3]) - (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(1/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",3,3,38,0.07895,1,"{1880, 219, 1879}"
103,1,241,0,0.0692954,"\int \frac{1-\sqrt{3}+\sqrt[3]{\frac{b}{a}} x}{\sqrt{a+b x^3}} \, dx","Int[(1 - Sqrt[3] + (b/a)^(1/3)*x)/Sqrt[a + b*x^3],x]","\frac{2 \left(\frac{b}{a}\right)^{2/3} \sqrt{a+b x^3}}{b \left(x \sqrt[3]{\frac{b}{a}}+\sqrt{3}+1\right)}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(x \sqrt[3]{\frac{b}{a}}+1\right) \sqrt{\frac{x^2 \left(\frac{b}{a}\right)^{2/3}-x \sqrt[3]{\frac{b}{a}}+1}{\left(x \sqrt[3]{\frac{b}{a}}+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{\frac{b}{a}} x-\sqrt{3}+1}{\sqrt[3]{\frac{b}{a}} x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{\frac{b}{a}} \sqrt{\frac{x \sqrt[3]{\frac{b}{a}}+1}{\left(x \sqrt[3]{\frac{b}{a}}+\sqrt{3}+1\right)^2}} \sqrt{a+b x^3}}","\frac{2 \left(\frac{b}{a}\right)^{2/3} \sqrt{a+b x^3}}{b \left(x \sqrt[3]{\frac{b}{a}}+\sqrt{3}+1\right)}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(x \sqrt[3]{\frac{b}{a}}+1\right) \sqrt{\frac{x^2 \left(\frac{b}{a}\right)^{2/3}-x \sqrt[3]{\frac{b}{a}}+1}{\left(x \sqrt[3]{\frac{b}{a}}+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{\frac{b}{a}} x-\sqrt{3}+1}{\sqrt[3]{\frac{b}{a}} x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{\frac{b}{a}} \sqrt{\frac{x \sqrt[3]{\frac{b}{a}}+1}{\left(x \sqrt[3]{\frac{b}{a}}+\sqrt{3}+1\right)^2}} \sqrt{a+b x^3}}",1,"(2*(b/a)^(2/3)*Sqrt[a + b*x^3])/(b*(1 + Sqrt[3] + (b/a)^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + (b/a)^(1/3)*x)*Sqrt[(1 - (b/a)^(1/3)*x + (b/a)^(2/3)*x^2)/(1 + Sqrt[3] + (b/a)^(1/3)*x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + (b/a)^(1/3)*x)/(1 + Sqrt[3] + (b/a)^(1/3)*x)], -7 - 4*Sqrt[3]])/((b/a)^(1/3)*Sqrt[(1 + (b/a)^(1/3)*x)/(1 + Sqrt[3] + (b/a)^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",1,1,32,0.03125,1,"{1877}"
104,1,248,0,0.060878,"\int \frac{1-\sqrt{3}-\sqrt[3]{\frac{b}{a}} x}{\sqrt{a-b x^3}} \, dx","Int[(1 - Sqrt[3] - (b/a)^(1/3)*x)/Sqrt[a - b*x^3],x]","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(1-x \sqrt[3]{\frac{b}{a}}\right) \sqrt{\frac{x^2 \left(\frac{b}{a}\right)^{2/3}+x \sqrt[3]{\frac{b}{a}}+1}{\left(x \left(-\sqrt[3]{\frac{b}{a}}\right)+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b}{a}} x-\sqrt{3}+1}{-\sqrt[3]{\frac{b}{a}} x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{\frac{b}{a}} \sqrt{\frac{1-x \sqrt[3]{\frac{b}{a}}}{\left(x \left(-\sqrt[3]{\frac{b}{a}}\right)+\sqrt{3}+1\right)^2}} \sqrt{a-b x^3}}-\frac{2 \left(\frac{b}{a}\right)^{2/3} \sqrt{a-b x^3}}{b \left(x \left(-\sqrt[3]{\frac{b}{a}}\right)+\sqrt{3}+1\right)}","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(1-x \sqrt[3]{\frac{b}{a}}\right) \sqrt{\frac{x^2 \left(\frac{b}{a}\right)^{2/3}+x \sqrt[3]{\frac{b}{a}}+1}{\left(x \left(-\sqrt[3]{\frac{b}{a}}\right)+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b}{a}} x-\sqrt{3}+1}{-\sqrt[3]{\frac{b}{a}} x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[3]{\frac{b}{a}} \sqrt{\frac{1-x \sqrt[3]{\frac{b}{a}}}{\left(x \left(-\sqrt[3]{\frac{b}{a}}\right)+\sqrt{3}+1\right)^2}} \sqrt{a-b x^3}}-\frac{2 \left(\frac{b}{a}\right)^{2/3} \sqrt{a-b x^3}}{b \left(x \left(-\sqrt[3]{\frac{b}{a}}\right)+\sqrt{3}+1\right)}",1,"(-2*(b/a)^(2/3)*Sqrt[a - b*x^3])/(b*(1 + Sqrt[3] - (b/a)^(1/3)*x)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - (b/a)^(1/3)*x)*Sqrt[(1 + (b/a)^(1/3)*x + (b/a)^(2/3)*x^2)/(1 + Sqrt[3] - (b/a)^(1/3)*x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - (b/a)^(1/3)*x)/(1 + Sqrt[3] - (b/a)^(1/3)*x)], -7 - 4*Sqrt[3]])/((b/a)^(1/3)*Sqrt[(1 - (b/a)^(1/3)*x)/(1 + Sqrt[3] - (b/a)^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",1,1,34,0.02941,1,"{1877}"
105,1,549,0,0.2176968,"\int \frac{1-\sqrt{3}-\sqrt[3]{\frac{b}{a}} x}{\sqrt{-a+b x^3}} \, dx","Int[(1 - Sqrt[3] - (b/a)^(1/3)*x)/Sqrt[-a + b*x^3],x]","-\frac{2 \sqrt{2-\sqrt{3}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{b}-\left(1+\sqrt{3}\right) \sqrt[3]{a} \sqrt[3]{\frac{b}{a}}\right) \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \sqrt[3]{\frac{b}{a}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{2 \sqrt[3]{\frac{b}{a}} \sqrt{b x^3-a}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}","-\frac{2 \sqrt{2-\sqrt{3}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{b}-\left(1+\sqrt{3}\right) \sqrt[3]{a} \sqrt[3]{\frac{b}{a}}\right) \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \sqrt[3]{\frac{b}{a}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{2 \sqrt[3]{\frac{b}{a}} \sqrt{b x^3-a}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}",1,"(2*(b/a)^(1/3)*Sqrt[-a + b*x^3])/(b^(2/3)*((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(b/a)^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3]) - (2*Sqrt[2 - Sqrt[3]]*((1 - Sqrt[3])*b^(1/3) - (1 + Sqrt[3])*a^(1/3)*(b/a)^(1/3))*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",3,3,35,0.08571,1,"{1880, 219, 1879}"
106,1,540,0,0.1628199,"\int \frac{1-\sqrt{3}+\sqrt[3]{\frac{b}{a}} x}{\sqrt{-a-b x^3}} \, dx","Int[(1 - Sqrt[3] + (b/a)^(1/3)*x)/Sqrt[-a - b*x^3],x]","\frac{2 \sqrt{2-\sqrt{3}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{b}-\left(1+\sqrt{3}\right) \sqrt[3]{a} \sqrt[3]{\frac{b}{a}}\right) \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \sqrt[3]{\frac{b}{a}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \sqrt[3]{\frac{b}{a}} \sqrt{-a-b x^3}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{2 \sqrt{2-\sqrt{3}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{b}-\left(1+\sqrt{3}\right) \sqrt[3]{a} \sqrt[3]{\frac{b}{a}}\right) \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \sqrt[3]{\frac{b}{a}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \sqrt[3]{\frac{b}{a}} \sqrt{-a-b x^3}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(-2*(b/a)^(1/3)*Sqrt[-a - b*x^3])/(b^(2/3)*((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(b/a)^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3]) + (2*Sqrt[2 - Sqrt[3]]*((1 - Sqrt[3])*b^(1/3) - (1 + Sqrt[3])*a^(1/3)*(b/a)^(1/3))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",3,3,35,0.08571,1,"{1880, 219, 1879}"
107,1,490,0,0.1477411,"\int \frac{c+d x}{\sqrt{a+b x^3}} \, dx","Int[(c + d*x)/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-\left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 d \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-\left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 d \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(2*d*Sqrt[a + b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*c - (1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,17,0.1765,1,"{1878, 218, 1877}"
108,1,503,0,0.1485059,"\int \frac{c+d x}{\sqrt{a-b x^3}} \, dx","Int[(c + d*x)/Sqrt[a - b*x^3],x]","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{2 d \sqrt{a-b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{2 d \sqrt{a-b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}",1,"(2*d*Sqrt[a - b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*d*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3]) - (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*c + (1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",3,3,18,0.1667,1,"{1878, 218, 1877}"
109,1,515,0,0.1634776,"\int \frac{c+d x}{\sqrt{-a+b x^3}} \, dx","Int[(c + d*x)/Sqrt[-a + b*x^3],x]","-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 d \sqrt{b x^3-a}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}","-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 d \sqrt{b x^3-a}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}",1,"(-2*d*Sqrt[-a + b*x^3])/(b^(2/3)*((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*d*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3]) - (2*Sqrt[2 - Sqrt[3]]*(b^(1/3)*c + (1 + Sqrt[3])*a^(1/3)*d)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",3,3,19,0.1579,1,"{1880, 219, 1879}"
110,1,508,0,0.1536262,"\int \frac{c+d x}{\sqrt{-a-b x^3}} \, dx","Int[(c + d*x)/Sqrt[-a - b*x^3],x]","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-\left(1+\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 d \sqrt{-a-b x^3}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-\left(1+\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 d \sqrt{-a-b x^3}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(-2*d*Sqrt[-a - b*x^3])/(b^(2/3)*((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3]) + (2*Sqrt[2 - Sqrt[3]]*(b^(1/3)*c - (1 + Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",3,3,20,0.1500,1,"{1880, 219, 1879}"
111,1,246,0,0.0810052,"\int \frac{c+d x}{\sqrt{1+x^3}} \, dx","Int[(c + d*x)/Sqrt[1 + x^3],x]","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(c-\left(1-\sqrt{3}\right) d\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{2 d \sqrt{x^3+1}}{x+\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(c-\left(1-\sqrt{3}\right) d\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{2 d \sqrt{x^3+1}}{x+\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*d*Sqrt[1 + x^3])/(1 + Sqrt[3] + x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*d*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (2*Sqrt[2 + Sqrt[3]]*(c - (1 - Sqrt[3])*d)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",3,3,15,0.2000,1,"{1878, 218, 1877}"
112,1,271,0,0.0873074,"\int \frac{c+d x}{\sqrt{1-x^3}} \, dx","Int[(c + d*x)/Sqrt[1 - x^3],x]","-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(c-\sqrt{3} d+d\right) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{2 d \sqrt{1-x^3}}{-x+\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(c-\sqrt{3} d+d\right) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{2 d \sqrt{1-x^3}}{-x+\sqrt{3}+1}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(2*d*Sqrt[1 - x^3])/(1 + Sqrt[3] - x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*d*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) - (2*Sqrt[2 + Sqrt[3]]*(c + d - Sqrt[3]*d)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",3,3,17,0.1765,1,"{1878, 218, 1877}"
113,1,275,0,0.0873031,"\int \frac{c+d x}{\sqrt{-1+x^3}} \, dx","Int[(c + d*x)/Sqrt[-1 + x^3],x]","-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(c+\sqrt{3} d+d\right) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 d \sqrt{x^3-1}}{-x-\sqrt{3}+1}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} d (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(c+\sqrt{3} d+d\right) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 d \sqrt{x^3-1}}{-x-\sqrt{3}+1}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} d (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(-2*d*Sqrt[-1 + x^3])/(1 - Sqrt[3] - x) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*d*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (2*Sqrt[2 - Sqrt[3]]*(c + d + Sqrt[3]*d)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",3,3,15,0.2000,1,"{1880, 219, 1879}"
114,1,261,0,0.0777453,"\int \frac{c+d x}{\sqrt{-1-x^3}} \, dx","Int[(c + d*x)/Sqrt[-1 - x^3],x]","\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(c-\left(1+\sqrt{3}\right) d\right) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{2 d \sqrt{-x^3-1}}{x-\sqrt{3}+1}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} d (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(c-\left(1+\sqrt{3}\right) d\right) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{2 d \sqrt{-x^3-1}}{x-\sqrt{3}+1}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} d (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(-2*d*Sqrt[-1 - x^3])/(1 - Sqrt[3] + x) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*d*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) + (2*Sqrt[2 - Sqrt[3]]*(c - (1 + Sqrt[3])*d)*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",3,3,17,0.1765,1,"{1880, 219, 1879}"
115,1,87,0,0.0654591,"\int \frac{c+d x}{a-b x^4} \, dx","Int[(c + d*x)/(a - b*x^4),x]","\frac{c \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} \sqrt[4]{b}}+\frac{c \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} \sqrt[4]{b}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}","\frac{c \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} \sqrt[4]{b}}+\frac{c \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} \sqrt[4]{b}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"(c*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(1/4)) + (c*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(1/4)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b])","A",7,5,16,0.3125,1,"{1876, 212, 208, 205, 275}"
116,1,219,0,0.1706931,"\int \frac{c+d x}{a+b x^4} \, dx","Int[(c + d*x)/(a + b*x^4),x]","-\frac{c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}","-\frac{c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"(d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b]) - (c*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(1/4)) + (c*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(1/4)) - (c*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(1/4)) + (c*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(1/4))","A",13,9,15,0.6000,1,"{1876, 211, 1165, 628, 1162, 617, 204, 275, 205}"
117,1,110,0,0.0816042,"\int \frac{c+d x}{\left(a-b x^4\right)^2} \, dx","Int[(c + d*x)/(a - b*x^4)^2,x]","\frac{3 c \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} \sqrt[4]{b}}+\frac{3 c \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} \sqrt[4]{b}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x (c+d x)}{4 a \left(a-b x^4\right)}","\frac{3 c \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} \sqrt[4]{b}}+\frac{3 c \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} \sqrt[4]{b}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x (c+d x)}{4 a \left(a-b x^4\right)}",1,"(x*(c + d*x))/(4*a*(a - b*x^4)) + (3*c*ArcTan[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(1/4)) + (3*c*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(1/4)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[b])","A",8,6,16,0.3750,1,"{1855, 1876, 212, 208, 205, 275}"
118,1,241,0,0.2015994,"\int \frac{c+d x}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x)/(a + b*x^4)^2,x]","-\frac{3 c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{3 c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{3 c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{3 c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x (c+d x)}{4 a \left(a+b x^4\right)}","-\frac{3 c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{3 c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{3 c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{3 c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x (c+d x)}{4 a \left(a+b x^4\right)}",1,"(x*(c + d*x))/(4*a*(a + b*x^4)) + (d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[b]) - (3*c*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(1/4)) + (3*c*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(1/4)) - (3*c*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(1/4)) + (3*c*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(1/4))","A",14,10,15,0.6667,1,"{1855, 1876, 211, 1165, 628, 1162, 617, 204, 275, 205}"
119,1,136,0,0.1100734,"\int \frac{c+d x}{\left(a-b x^4\right)^3} \, dx","Int[(c + d*x)/(a - b*x^4)^3,x]","\frac{x (7 c+6 d x)}{32 a^2 \left(a-b x^4\right)}+\frac{21 c \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} \sqrt[4]{b}}+\frac{21 c \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} \sqrt[4]{b}}+\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x (c+d x)}{8 a \left(a-b x^4\right)^2}","\frac{x (7 c+6 d x)}{32 a^2 \left(a-b x^4\right)}+\frac{21 c \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} \sqrt[4]{b}}+\frac{21 c \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} \sqrt[4]{b}}+\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x (c+d x)}{8 a \left(a-b x^4\right)^2}",1,"(x*(c + d*x))/(8*a*(a - b*x^4)^2) + (x*(7*c + 6*d*x))/(32*a^2*(a - b*x^4)) + (21*c*ArcTan[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(1/4)) + (21*c*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(1/4)) + (3*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[b])","A",9,6,16,0.3750,1,"{1855, 1876, 212, 208, 205, 275}"
120,1,266,0,0.2304976,"\int \frac{c+d x}{\left(a+b x^4\right)^3} \, dx","Int[(c + d*x)/(a + b*x^4)^3,x]","\frac{x (7 c+6 d x)}{32 a^2 \left(a+b x^4\right)}-\frac{21 c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{21 c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{b}}-\frac{21 c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{21 c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x (c+d x)}{8 a \left(a+b x^4\right)^2}","\frac{x (7 c+6 d x)}{32 a^2 \left(a+b x^4\right)}-\frac{21 c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{21 c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{b}}-\frac{21 c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{21 c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x (c+d x)}{8 a \left(a+b x^4\right)^2}",1,"(x*(c + d*x))/(8*a*(a + b*x^4)^2) + (x*(7*c + 6*d*x))/(32*a^2*(a + b*x^4)) + (3*d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[b]) - (21*c*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(1/4)) + (21*c*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(1/4)) - (21*c*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(1/4)) + (21*c*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(1/4))","A",15,10,15,0.6667,1,"{1855, 1876, 211, 1165, 628, 1162, 617, 204, 275, 205}"
121,1,162,0,0.1304892,"\int \frac{c+d x}{\left(a-b x^4\right)^4} \, dx","Int[(c + d*x)/(a - b*x^4)^4,x]","\frac{x (77 c+60 d x)}{384 a^3 \left(a-b x^4\right)}+\frac{x (11 c+10 d x)}{96 a^2 \left(a-b x^4\right)^2}+\frac{77 c \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} \sqrt[4]{b}}+\frac{77 c \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} \sqrt[4]{b}}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x (c+d x)}{12 a \left(a-b x^4\right)^3}","\frac{x (77 c+60 d x)}{384 a^3 \left(a-b x^4\right)}+\frac{x (11 c+10 d x)}{96 a^2 \left(a-b x^4\right)^2}+\frac{77 c \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} \sqrt[4]{b}}+\frac{77 c \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} \sqrt[4]{b}}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x (c+d x)}{12 a \left(a-b x^4\right)^3}",1,"(x*(c + d*x))/(12*a*(a - b*x^4)^3) + (x*(11*c + 10*d*x))/(96*a^2*(a - b*x^4)^2) + (x*(77*c + 60*d*x))/(384*a^3*(a - b*x^4)) + (77*c*ArcTan[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(1/4)) + (77*c*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(1/4)) + (5*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*Sqrt[b])","A",10,6,16,0.3750,1,"{1855, 1876, 212, 208, 205, 275}"
122,1,291,0,0.2675767,"\int \frac{c+d x}{\left(a+b x^4\right)^4} \, dx","Int[(c + d*x)/(a + b*x^4)^4,x]","\frac{x (77 c+60 d x)}{384 a^3 \left(a+b x^4\right)}+\frac{x (11 c+10 d x)}{96 a^2 \left(a+b x^4\right)^2}-\frac{77 c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{77 c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{77 c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{77 c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{256 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x (c+d x)}{12 a \left(a+b x^4\right)^3}","\frac{x (77 c+60 d x)}{384 a^3 \left(a+b x^4\right)}+\frac{x (11 c+10 d x)}{96 a^2 \left(a+b x^4\right)^2}-\frac{77 c \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{77 c \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{77 c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{77 c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{256 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x (c+d x)}{12 a \left(a+b x^4\right)^3}",1,"(x*(c + d*x))/(12*a*(a + b*x^4)^3) + (x*(11*c + 10*d*x))/(96*a^2*(a + b*x^4)^2) + (x*(77*c + 60*d*x))/(384*a^3*(a + b*x^4)) + (5*d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*Sqrt[b]) - (77*c*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(1/4)) + (77*c*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(1/4)) - (77*c*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(1/4)) + (77*c*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(1/4))","A",16,10,15,0.6667,1,"{1855, 1876, 211, 1165, 628, 1162, 617, 204, 275, 205}"
123,1,24,0,0.0180047,"\int \frac{c+d x}{1-x^4} \, dx","Int[(c + d*x)/(1 - x^4),x]","\frac{1}{2} c \tan ^{-1}(x)+\frac{1}{2} c \tanh ^{-1}(x)+\frac{1}{2} d \tanh ^{-1}\left(x^2\right)","\frac{1}{2} c \tan ^{-1}(x)+\frac{1}{2} c \tanh ^{-1}(x)+\frac{1}{2} d \tanh ^{-1}\left(x^2\right)",1,"(c*ArcTan[x])/2 + (c*ArcTanh[x])/2 + (d*ArcTanh[x^2])/2","A",7,5,15,0.3333,1,"{1876, 212, 206, 203, 275}"
124,1,98,0,0.0672962,"\int \frac{c+d x}{1+x^4} \, dx","Int[(c + d*x)/(1 + x^4),x]","-\frac{c \log \left(x^2-\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{c \log \left(x^2+\sqrt{2} x+1\right)}{4 \sqrt{2}}-\frac{c \tan ^{-1}\left(1-\sqrt{2} x\right)}{2 \sqrt{2}}+\frac{c \tan ^{-1}\left(\sqrt{2} x+1\right)}{2 \sqrt{2}}+\frac{1}{2} d \tan ^{-1}\left(x^2\right)","-\frac{c \log \left(x^2-\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{c \log \left(x^2+\sqrt{2} x+1\right)}{4 \sqrt{2}}-\frac{c \tan ^{-1}\left(1-\sqrt{2} x\right)}{2 \sqrt{2}}+\frac{c \tan ^{-1}\left(\sqrt{2} x+1\right)}{2 \sqrt{2}}+\frac{1}{2} d \tan ^{-1}\left(x^2\right)",1,"(d*ArcTan[x^2])/2 - (c*ArcTan[1 - Sqrt[2]*x])/(2*Sqrt[2]) + (c*ArcTan[1 + Sqrt[2]*x])/(2*Sqrt[2]) - (c*Log[1 - Sqrt[2]*x + x^2])/(4*Sqrt[2]) + (c*Log[1 + Sqrt[2]*x + x^2])/(4*Sqrt[2])","A",13,9,13,0.6923,1,"{1876, 211, 1165, 628, 1162, 617, 204, 275, 203}"
125,1,116,0,0.0954763,"\int \frac{c+d x+e x^2}{a-b x^4} \, dx","Int[(c + d*x + e*x^2)/(a - b*x^4),x]","\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}","\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"((Sqrt[b]*c - Sqrt[a]*e)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c + Sqrt[a]*e)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b])","A",7,5,21,0.2381,1,"{1876, 275, 208, 1167, 205}"
126,1,277,0,0.1966241,"\int \frac{c+d x+e x^2}{a+b x^4} \, dx","Int[(c + d*x + e*x^2)/(a + b*x^4),x]","-\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}","-\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"(d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b]) - ((Sqrt[b]*c + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) - ((Sqrt[b]*c - Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c - Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4))","A",13,9,20,0.4500,1,"{1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
127,1,146,0,0.1275154,"\int \frac{c+d x+e x^2}{\left(a-b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2)/(a - b*x^4)^2,x]","\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} b^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} b^{3/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{4 a \left(a-b x^4\right)}","\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} b^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} b^{3/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{4 a \left(a-b x^4\right)}",1,"(x*(c + d*x + e*x^2))/(4*a*(a - b*x^4)) + ((3*Sqrt[b]*c - Sqrt[a]*e)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(3/4)) + ((3*Sqrt[b]*c + Sqrt[a]*e)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(3/4)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[b])","A",8,6,21,0.2857,1,"{1855, 1876, 275, 208, 1167, 205}"
128,1,308,0,0.2546368,"\int \frac{c+d x+e x^2}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2)/(a + b*x^4)^2,x]","-\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{3/4}}+\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{3/4}}-\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{3/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{4 a \left(a+b x^4\right)}","-\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{3/4}}+\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{3/4}}-\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{3/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{4 a \left(a+b x^4\right)}",1,"(x*(c + d*x + e*x^2))/(4*a*(a + b*x^4)) + (d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[b]) - ((3*Sqrt[b]*c + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(3/4)) + ((3*Sqrt[b]*c + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(3/4)) - ((3*Sqrt[b]*c - Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(3/4)) + ((3*Sqrt[b]*c - Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(3/4))","A",14,10,20,0.5000,1,"{1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
129,1,179,0,0.1670088,"\int \frac{c+d x+e x^2}{\left(a-b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2)/(a - b*x^4)^3,x]","\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} b^{3/4}}+\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} b^{3/4}}+\frac{x \left(7 c+6 d x+5 e x^2\right)}{32 a^2 \left(a-b x^4\right)}+\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{8 a \left(a-b x^4\right)^2}","\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} b^{3/4}}+\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} b^{3/4}}+\frac{x \left(7 c+6 d x+5 e x^2\right)}{32 a^2 \left(a-b x^4\right)}+\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{8 a \left(a-b x^4\right)^2}",1,"(x*(c + d*x + e*x^2))/(8*a*(a - b*x^4)^2) + (x*(7*c + 6*d*x + 5*e*x^2))/(32*a^2*(a - b*x^4)) + ((21*Sqrt[b]*c - 5*Sqrt[a]*e)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(3/4)) + ((21*Sqrt[b]*c + 5*Sqrt[a]*e)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(3/4)) + (3*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[b])","A",9,6,21,0.2857,1,"{1855, 1876, 275, 208, 1167, 205}"
130,1,341,0,0.3107192,"\int \frac{c+d x+e x^2}{\left(a+b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2)/(a + b*x^4)^3,x]","-\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} b^{3/4}}+\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} b^{3/4}}-\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} b^{3/4}}+\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} b^{3/4}}+\frac{x \left(7 c+6 d x+5 e x^2\right)}{32 a^2 \left(a+b x^4\right)}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{8 a \left(a+b x^4\right)^2}","-\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} b^{3/4}}+\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} b^{3/4}}-\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} b^{3/4}}+\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} b^{3/4}}+\frac{x \left(7 c+6 d x+5 e x^2\right)}{32 a^2 \left(a+b x^4\right)}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{8 a \left(a+b x^4\right)^2}",1,"(x*(c + d*x + e*x^2))/(8*a*(a + b*x^4)^2) + (x*(7*c + 6*d*x + 5*e*x^2))/(32*a^2*(a + b*x^4)) + (3*d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[b]) - ((21*Sqrt[b]*c + 5*Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(3/4)) + ((21*Sqrt[b]*c + 5*Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(3/4)) - ((21*Sqrt[b]*c - 5*Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(3/4)) + ((21*Sqrt[b]*c - 5*Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(3/4))","A",15,10,20,0.5000,1,"{1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
131,1,211,0,0.2113125,"\int \frac{c+d x+e x^2}{\left(a-b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2)/(a - b*x^4)^4,x]","\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} b^{3/4}}+\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} b^{3/4}}+\frac{x \left(77 c+60 d x+45 e x^2\right)}{384 a^3 \left(a-b x^4\right)}+\frac{x \left(11 c+10 d x+9 e x^2\right)}{96 a^2 \left(a-b x^4\right)^2}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{12 a \left(a-b x^4\right)^3}","\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} b^{3/4}}+\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} b^{3/4}}+\frac{x \left(77 c+60 d x+45 e x^2\right)}{384 a^3 \left(a-b x^4\right)}+\frac{x \left(11 c+10 d x+9 e x^2\right)}{96 a^2 \left(a-b x^4\right)^2}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{12 a \left(a-b x^4\right)^3}",1,"(x*(c + d*x + e*x^2))/(12*a*(a - b*x^4)^3) + (x*(11*c + 10*d*x + 9*e*x^2))/(96*a^2*(a - b*x^4)^2) + (x*(77*c + 60*d*x + 45*e*x^2))/(384*a^3*(a - b*x^4)) + ((77*Sqrt[b]*c - 15*Sqrt[a]*e)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(3/4)) + ((77*Sqrt[b]*c + 15*Sqrt[a]*e)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(3/4)) + (5*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*Sqrt[b])","A",10,6,21,0.2857,1,"{1855, 1876, 275, 208, 1167, 205}"
132,1,372,0,0.3794634,"\int \frac{c+d x+e x^2}{\left(a+b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2)/(a + b*x^4)^4,x]","-\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} b^{3/4}}+\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} b^{3/4}}-\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 \sqrt{2} a^{15/4} b^{3/4}}+\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{256 \sqrt{2} a^{15/4} b^{3/4}}+\frac{x \left(77 c+60 d x+45 e x^2\right)}{384 a^3 \left(a+b x^4\right)}+\frac{x \left(11 c+10 d x+9 e x^2\right)}{96 a^2 \left(a+b x^4\right)^2}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{12 a \left(a+b x^4\right)^3}","-\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} b^{3/4}}+\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} b^{3/4}}-\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 \sqrt{2} a^{15/4} b^{3/4}}+\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{256 \sqrt{2} a^{15/4} b^{3/4}}+\frac{x \left(77 c+60 d x+45 e x^2\right)}{384 a^3 \left(a+b x^4\right)}+\frac{x \left(11 c+10 d x+9 e x^2\right)}{96 a^2 \left(a+b x^4\right)^2}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x \left(c+d x+e x^2\right)}{12 a \left(a+b x^4\right)^3}",1,"(x*(c + d*x + e*x^2))/(12*a*(a + b*x^4)^3) + (x*(11*c + 10*d*x + 9*e*x^2))/(96*a^2*(a + b*x^4)^2) + (x*(77*c + 60*d*x + 45*e*x^2))/(384*a^3*(a + b*x^4)) + (5*d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*Sqrt[b]) - ((77*Sqrt[b]*c + 15*Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(3/4)) + ((77*Sqrt[b]*c + 15*Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(3/4)) - ((77*Sqrt[b]*c - 15*Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(3/4)) + ((77*Sqrt[b]*c - 15*Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(3/4))","A",16,10,20,0.5000,1,"{1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
133,1,28,0,0.0113591,"\int a \left(e+f x^4\right)^2 \, dx","Int[a*(e + f*x^4)^2,x]","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9",1,"a*e^2*x + (2*a*e*f*x^5)/5 + (a*f^2*x^9)/9","A",3,2,11,0.1818,1,"{12, 194}"
134,1,33,0,0.0143123,"\int b x \left(e+f x^4\right)^2 \, dx","Int[b*x*(e + f*x^4)^2,x]","\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}","\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}",1,"(b*e^2*x^2)/2 + (b*e*f*x^6)/3 + (b*f^2*x^10)/10","A",3,2,12,0.1667,1,"{12, 270}"
135,1,60,0,0.0624218,"\int (a+b x) \left(e+f x^4\right)^2 \, dx","Int[(a + b*x)*(e + f*x^4)^2,x]","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}",1,"a*e^2*x + (b*e^2*x^2)/2 + (2*a*e*f*x^5)/5 + (b*e*f*x^6)/3 + (a*f^2*x^9)/9 + (b*f^2*x^10)/10","A",2,1,15,0.06667,1,"{1850}"
136,1,33,0,0.0132649,"\int c x^2 \left(e+f x^4\right)^2 \, dx","Int[c*x^2*(e + f*x^4)^2,x]","\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}","\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}",1,"(c*e^2*x^3)/3 + (2*c*e*f*x^7)/7 + (c*f^2*x^11)/11","A",3,2,14,0.1429,1,"{12, 270}"
137,1,60,0,0.0266964,"\int \left(a+c x^2\right) \left(e+f x^4\right)^2 \, dx","Int[(a + c*x^2)*(e + f*x^4)^2,x]","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}",1,"a*e^2*x + (c*e^2*x^3)/3 + (2*a*e*f*x^5)/5 + (2*c*e*f*x^7)/7 + (a*f^2*x^9)/9 + (c*f^2*x^11)/11","A",2,1,17,0.05882,1,"{1154}"
138,1,65,0,0.0975165,"\int \left(b x+c x^2\right) \left(e+f x^4\right)^2 \, dx","Int[(b*x + c*x^2)*(e + f*x^4)^2,x]","\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}","\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}",1,"(b*e^2*x^2)/2 + (c*e^2*x^3)/3 + (b*e*f*x^6)/3 + (2*c*e*f*x^7)/7 + (b*f^2*x^10)/10 + (c*f^2*x^11)/11","A",3,2,19,0.1053,1,"{1593, 1620}"
139,1,92,0,0.0531848,"\int \left(a+b x+c x^2\right) \left(e+f x^4\right)^2 \, dx","Int[(a + b*x + c*x^2)*(e + f*x^4)^2,x]","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}",1,"a*e^2*x + (b*e^2*x^2)/2 + (c*e^2*x^3)/3 + (2*a*e*f*x^5)/5 + (b*e*f*x^6)/3 + (2*c*e*f*x^7)/7 + (a*f^2*x^9)/9 + (b*f^2*x^10)/10 + (c*f^2*x^11)/11","A",2,1,20,0.05000,1,"{1657}"
140,1,17,0,0.0050034,"\int d x^3 \left(e+f x^4\right)^2 \, dx","Int[d*x^3*(e + f*x^4)^2,x]","\frac{d \left(e+f x^4\right)^3}{12 f}","\frac{d \left(e+f x^4\right)^3}{12 f}",1,"(d*(e + f*x^4)^3)/(12*f)","A",2,2,14,0.1429,1,"{12, 261}"
141,1,45,0,0.0190194,"\int \left(a+d x^3\right) \left(e+f x^4\right)^2 \, dx","Int[(a + d*x^3)*(e + f*x^4)^2,x]","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{d \left(e+f x^4\right)^3}{12 f}","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{d \left(e+f x^4\right)^3}{12 f}",1,"a*e^2*x + (2*a*e*f*x^5)/5 + (a*f^2*x^9)/9 + (d*(e + f*x^4)^3)/(12*f)","A",4,3,17,0.1765,1,"{1582, 12, 194}"
142,1,50,0,0.0198986,"\int \left(b x+d x^3\right) \left(e+f x^4\right)^2 \, dx","Int[(b*x + d*x^3)*(e + f*x^4)^2,x]","\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{d \left(e+f x^4\right)^3}{12 f}","\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{d \left(e+f x^4\right)^3}{12 f}",1,"(b*e^2*x^2)/2 + (b*e*f*x^6)/3 + (b*f^2*x^10)/10 + (d*(e + f*x^4)^3)/(12*f)","A",4,3,19,0.1579,1,"{1582, 12, 270}"
143,1,77,0,0.0511904,"\int \left(a+b x+d x^3\right) \left(e+f x^4\right)^2 \, dx","Int[(a + b*x + d*x^3)*(e + f*x^4)^2,x]","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{d \left(e+f x^4\right)^3}{12 f}","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{d \left(e+f x^4\right)^3}{12 f}",1,"a*e^2*x + (b*e^2*x^2)/2 + (2*a*e*f*x^5)/5 + (b*e*f*x^6)/3 + (a*f^2*x^9)/9 + (b*f^2*x^10)/10 + (d*(e + f*x^4)^3)/(12*f)","A",3,2,20,0.1000,1,"{1582, 1850}"
144,1,50,0,0.0234746,"\int \left(c x^2+d x^3\right) \left(e+f x^4\right)^2 \, dx","Int[(c*x^2 + d*x^3)*(e + f*x^4)^2,x]","\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}+\frac{d \left(e+f x^4\right)^3}{12 f}","\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}+\frac{d \left(e+f x^4\right)^3}{12 f}",1,"(c*e^2*x^3)/3 + (2*c*e*f*x^7)/7 + (c*f^2*x^11)/11 + (d*(e + f*x^4)^3)/(12*f)","A",4,3,21,0.1429,1,"{1582, 12, 270}"
145,1,77,0,0.04152,"\int \left(a+c x^2+d x^3\right) \left(e+f x^4\right)^2 \, dx","Int[(a + c*x^2 + d*x^3)*(e + f*x^4)^2,x]","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}+\frac{d \left(e+f x^4\right)^3}{12 f}","a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}+\frac{d \left(e+f x^4\right)^3}{12 f}",1,"a*e^2*x + (c*e^2*x^3)/3 + (2*a*e*f*x^5)/5 + (2*c*e*f*x^7)/7 + (a*f^2*x^9)/9 + (c*f^2*x^11)/11 + (d*(e + f*x^4)^3)/(12*f)","A",3,2,22,0.09091,1,"{1582, 1154}"
146,1,82,0,0.0835611,"\int \left(b x+c x^2+d x^3\right) \left(e+f x^4\right)^2 \, dx","Int[(b*x + c*x^2 + d*x^3)*(e + f*x^4)^2,x]","\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}+\frac{d \left(e+f x^4\right)^3}{12 f}","\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10}+\frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11}+\frac{d \left(e+f x^4\right)^3}{12 f}",1,"(b*e^2*x^2)/2 + (c*e^2*x^3)/3 + (b*e*f*x^6)/3 + (2*c*e*f*x^7)/7 + (b*f^2*x^10)/10 + (c*f^2*x^11)/11 + (d*(e + f*x^4)^3)/(12*f)","A",4,3,24,0.1250,1,"{1582, 1593, 1620}"
147,1,109,0,0.0804812,"\int \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^2 \, dx","Int[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^2,x]","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{3} a^2 e x^3+\frac{2}{5} a b c x^5+\frac{1}{3} a b d x^6+\frac{2}{7} a b e x^7+\frac{f \left(a+b x^4\right)^3}{12 b}+\frac{1}{9} b^2 c x^9+\frac{1}{10} b^2 d x^{10}+\frac{1}{11} b^2 e x^{11}","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{3} a^2 e x^3+\frac{2}{5} a b c x^5+\frac{1}{3} a b d x^6+\frac{2}{7} a b e x^7+\frac{f \left(a+b x^4\right)^3}{12 b}+\frac{1}{9} b^2 c x^9+\frac{1}{10} b^2 d x^{10}+\frac{1}{11} b^2 e x^{11}",1,"a^2*c*x + (a^2*d*x^2)/2 + (a^2*e*x^3)/3 + (2*a*b*c*x^5)/5 + (a*b*d*x^6)/3 + (2*a*b*e*x^7)/7 + (b^2*c*x^9)/9 + (b^2*d*x^10)/10 + (b^2*e*x^11)/11 + (f*(a + b*x^4)^3)/(12*b)","A",3,2,25,0.08000,1,"{1582, 1657}"
148,1,151,0,0.1058366,"\int \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^3 \, dx","Int[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^3,x]","\frac{3}{5} a^2 b c x^5+\frac{1}{2} a^2 b d x^6+\frac{3}{7} a^2 b e x^7+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{1}{3} a^3 e x^3+\frac{1}{3} a b^2 c x^9+\frac{3}{10} a b^2 d x^{10}+\frac{3}{11} a b^2 e x^{11}+\frac{f \left(a+b x^4\right)^4}{16 b}+\frac{1}{13} b^3 c x^{13}+\frac{1}{14} b^3 d x^{14}+\frac{1}{15} b^3 e x^{15}","\frac{3}{5} a^2 b c x^5+\frac{1}{2} a^2 b d x^6+\frac{3}{7} a^2 b e x^7+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{1}{3} a^3 e x^3+\frac{1}{3} a b^2 c x^9+\frac{3}{10} a b^2 d x^{10}+\frac{3}{11} a b^2 e x^{11}+\frac{f \left(a+b x^4\right)^4}{16 b}+\frac{1}{13} b^3 c x^{13}+\frac{1}{14} b^3 d x^{14}+\frac{1}{15} b^3 e x^{15}",1,"a^3*c*x + (a^3*d*x^2)/2 + (a^3*e*x^3)/3 + (3*a^2*b*c*x^5)/5 + (a^2*b*d*x^6)/2 + (3*a^2*b*e*x^7)/7 + (a*b^2*c*x^9)/3 + (3*a*b^2*d*x^10)/10 + (3*a*b^2*e*x^11)/11 + (b^3*c*x^13)/13 + (b^3*d*x^14)/14 + (b^3*e*x^15)/15 + (f*(a + b*x^4)^4)/(16*b)","A",3,2,25,0.08000,1,"{1582, 1657}"
149,1,155,0,0.1183349,"\int \frac{c+d x+e x^2+f x^3}{\left(a-b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(a - b*x^4)^2,x]","\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} b^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} b^{3/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{a f+b x \left(c+d x+e x^2\right)}{4 a b \left(a-b x^4\right)}","\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} b^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 a^{7/4} b^{3/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{a f+b x \left(c+d x+e x^2\right)}{4 a b \left(a-b x^4\right)}",1,"(a*f + b*x*(c + d*x + e*x^2))/(4*a*b*(a - b*x^4)) + ((3*Sqrt[b]*c - Sqrt[a]*e)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(3/4)) + ((3*Sqrt[b]*c + Sqrt[a]*e)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(3/4)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[b])","A",8,6,26,0.2308,1,"{1854, 1876, 275, 208, 1167, 205}"
150,1,188,0,0.1546008,"\int \frac{c+d x+e x^2+f x^3}{\left(a-b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(a - b*x^4)^3,x]","\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} b^{3/4}}+\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} b^{3/4}}+\frac{x \left(7 c+6 d x+5 e x^2\right)}{32 a^2 \left(a-b x^4\right)}+\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{a f+b x \left(c+d x+e x^2\right)}{8 a b \left(a-b x^4\right)^2}","\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} b^{3/4}}+\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 a^{11/4} b^{3/4}}+\frac{x \left(7 c+6 d x+5 e x^2\right)}{32 a^2 \left(a-b x^4\right)}+\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{a f+b x \left(c+d x+e x^2\right)}{8 a b \left(a-b x^4\right)^2}",1,"(x*(7*c + 6*d*x + 5*e*x^2))/(32*a^2*(a - b*x^4)) + (a*f + b*x*(c + d*x + e*x^2))/(8*a*b*(a - b*x^4)^2) + ((21*Sqrt[b]*c - 5*Sqrt[a]*e)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(3/4)) + ((21*Sqrt[b]*c + 5*Sqrt[a]*e)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(3/4)) + (3*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[b])","A",9,7,26,0.2692,1,"{1854, 1855, 1876, 275, 208, 1167, 205}"
151,1,220,0,0.1887267,"\int \frac{c+d x+e x^2+f x^3}{\left(a-b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(a - b*x^4)^4,x]","\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} b^{3/4}}+\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} b^{3/4}}+\frac{x \left(11 c+10 d x+9 e x^2\right)}{96 a^2 \left(a-b x^4\right)^2}+\frac{x \left(77 c+60 d x+45 e x^2\right)}{384 a^3 \left(a-b x^4\right)}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{a f+b x \left(c+d x+e x^2\right)}{12 a b \left(a-b x^4\right)^3}","\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} b^{3/4}}+\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 a^{15/4} b^{3/4}}+\frac{x \left(11 c+10 d x+9 e x^2\right)}{96 a^2 \left(a-b x^4\right)^2}+\frac{x \left(77 c+60 d x+45 e x^2\right)}{384 a^3 \left(a-b x^4\right)}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{a f+b x \left(c+d x+e x^2\right)}{12 a b \left(a-b x^4\right)^3}",1,"(x*(11*c + 10*d*x + 9*e*x^2))/(96*a^2*(a - b*x^4)^2) + (x*(77*c + 60*d*x + 45*e*x^2))/(384*a^3*(a - b*x^4)) + (a*f + b*x*(c + d*x + e*x^2))/(12*a*b*(a - b*x^4)^3) + ((77*Sqrt[b]*c - 15*Sqrt[a]*e)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(3/4)) + ((77*Sqrt[b]*c + 15*Sqrt[a]*e)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(3/4)) + (5*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*Sqrt[b])","A",10,7,26,0.2692,1,"{1854, 1855, 1876, 275, 208, 1167, 205}"
152,1,101,0,0.0960809,"\int \frac{a}{2+3 x^4} \, dx","Int[a/(2 + 3*x^4),x]","-\frac{a \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{a \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{a \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{a \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}","-\frac{a \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{a \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{a \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{a \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}",1,"-(a*ArcTan[1 - 6^(1/4)*x])/(4*6^(1/4)) + (a*ArcTan[1 + 6^(1/4)*x])/(4*6^(1/4)) - (a*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(8*6^(1/4)) + (a*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(8*6^(1/4))","A",10,7,11,0.6364,1,"{12, 211, 1165, 628, 1162, 617, 204}"
153,1,22,0,0.0130876,"\int \frac{b x}{2+3 x^4} \, dx","Int[(b*x)/(2 + 3*x^4),x]","\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}","\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}",1,"(b*ArcTan[Sqrt[3/2]*x^2])/(2*Sqrt[6])","A",3,3,12,0.2500,1,"{12, 275, 203}"
154,1,123,0,0.1029323,"\int \frac{a+b x}{2+3 x^4} \, dx","Int[(a + b*x)/(2 + 3*x^4),x]","-\frac{a \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{a \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{a \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{a \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}+\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}","-\frac{a \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{a \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{a \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{a \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}+\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}",1,"(b*ArcTan[Sqrt[3/2]*x^2])/(2*Sqrt[6]) - (a*ArcTan[1 - 6^(1/4)*x])/(4*6^(1/4)) + (a*ArcTan[1 + 6^(1/4)*x])/(4*6^(1/4)) - (a*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(8*6^(1/4)) + (a*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(8*6^(1/4))","A",13,9,15,0.6000,1,"{1876, 211, 1165, 628, 1162, 617, 204, 275, 203}"
155,1,101,0,0.0765918,"\int \frac{c x^2}{2+3 x^4} \, dx","Int[(c*x^2)/(2 + 3*x^4),x]","\frac{c \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{c \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}","\frac{c \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{c \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}",1,"-(c*ArcTan[1 - 6^(1/4)*x])/(2*6^(3/4)) + (c*ArcTan[1 + 6^(1/4)*x])/(2*6^(3/4)) + (c*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(4*6^(3/4)) - (c*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(4*6^(3/4))","A",10,7,14,0.5000,1,"{12, 297, 1162, 617, 204, 1165, 628}"
156,1,141,0,0.0977998,"\int \frac{a+c x^2}{2+3 x^4} \, dx","Int[(a + c*x^2)/(2 + 3*x^4),x]","-\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}+\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}-\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 6^{3/4}}+\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 6^{3/4}}","-\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}+\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}-\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 6^{3/4}}+\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 6^{3/4}}",1,"-((Sqrt[6]*a + 2*c)*ArcTan[1 - 6^(1/4)*x])/(4*6^(3/4)) + ((Sqrt[6]*a + 2*c)*ArcTan[1 + 6^(1/4)*x])/(4*6^(3/4)) - ((Sqrt[6]*a - 2*c)*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(8*6^(3/4)) + ((Sqrt[6]*a - 2*c)*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(8*6^(3/4))","A",9,6,17,0.3529,1,"{1168, 1162, 617, 204, 1165, 628}"
157,1,123,0,0.1176722,"\int \frac{b x+c x^2}{2+3 x^4} \, dx","Int[(b*x + c*x^2)/(2 + 3*x^4),x]","\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{c \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{c \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}","\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{c \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{c \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}",1,"(b*ArcTan[Sqrt[3/2]*x^2])/(2*Sqrt[6]) - (c*ArcTan[1 - 6^(1/4)*x])/(2*6^(3/4)) + (c*ArcTan[1 + 6^(1/4)*x])/(2*6^(3/4)) + (c*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(4*6^(3/4)) - (c*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(4*6^(3/4))","A",14,10,19,0.5263,1,"{1593, 1831, 275, 203, 297, 1162, 617, 204, 1165, 628}"
158,1,163,0,0.1236795,"\int \frac{a+b x+c x^2}{2+3 x^4} \, dx","Int[(a + b*x + c*x^2)/(2 + 3*x^4),x]","-\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}+\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}-\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 6^{3/4}}+\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 6^{3/4}}+\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}","-\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}+\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}-\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 6^{3/4}}+\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 6^{3/4}}+\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}",1,"(b*ArcTan[Sqrt[3/2]*x^2])/(2*Sqrt[6]) - ((Sqrt[6]*a + 2*c)*ArcTan[1 - 6^(1/4)*x])/(4*6^(3/4)) + ((Sqrt[6]*a + 2*c)*ArcTan[1 + 6^(1/4)*x])/(4*6^(3/4)) - ((Sqrt[6]*a - 2*c)*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(8*6^(3/4)) + ((Sqrt[6]*a - 2*c)*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(8*6^(3/4))","A",13,9,20,0.4500,1,"{1876, 275, 203, 1168, 1162, 617, 204, 1165, 628}"
159,1,13,0,0.0037983,"\int \frac{d x^3}{2+3 x^4} \, dx","Int[(d*x^3)/(2 + 3*x^4),x]","\frac{1}{12} d \log \left(3 x^4+2\right)","\frac{1}{12} d \log \left(3 x^4+2\right)",1,"(d*Log[2 + 3*x^4])/12","A",2,2,14,0.1429,1,"{12, 260}"
160,1,114,0,0.0991563,"\int \frac{a+d x^3}{2+3 x^4} \, dx","Int[(a + d*x^3)/(2 + 3*x^4),x]","-\frac{a \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{a \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{a \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{a \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}+\frac{1}{12} d \log \left(3 x^4+2\right)","-\frac{a \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{a \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{a \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{a \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}+\frac{1}{12} d \log \left(3 x^4+2\right)",1,"-(a*ArcTan[1 - 6^(1/4)*x])/(4*6^(1/4)) + (a*ArcTan[1 + 6^(1/4)*x])/(4*6^(1/4)) - (a*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(8*6^(1/4)) + (a*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(8*6^(1/4)) + (d*Log[2 + 3*x^4])/12","A",12,8,17,0.4706,1,"{1876, 211, 1165, 628, 1162, 617, 204, 260}"
161,1,36,0,0.0314551,"\int \frac{b x+d x^3}{2+3 x^4} \, dx","Int[(b*x + d*x^3)/(2 + 3*x^4),x]","\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{1}{12} d \log \left(3 x^4+2\right)","\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{1}{12} d \log \left(3 x^4+2\right)",1,"(b*ArcTan[Sqrt[3/2]*x^2])/(2*Sqrt[6]) + (d*Log[2 + 3*x^4])/12","A",5,5,19,0.2632,1,"{1593, 1248, 635, 203, 260}"
162,1,136,0,0.1177207,"\int \frac{a+b x+d x^3}{2+3 x^4} \, dx","Int[(a + b*x + d*x^3)/(2 + 3*x^4),x]","-\frac{a \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{a \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{a \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{a \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}+\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{1}{12} d \log \left(3 x^4+2\right)","-\frac{a \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{a \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{a \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{a \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}+\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{1}{12} d \log \left(3 x^4+2\right)",1,"(b*ArcTan[Sqrt[3/2]*x^2])/(2*Sqrt[6]) - (a*ArcTan[1 - 6^(1/4)*x])/(4*6^(1/4)) + (a*ArcTan[1 + 6^(1/4)*x])/(4*6^(1/4)) - (a*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(8*6^(1/4)) + (a*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(8*6^(1/4)) + (d*Log[2 + 3*x^4])/12","A",15,11,20,0.5500,1,"{1876, 211, 1165, 628, 1162, 617, 204, 1248, 635, 203, 260}"
163,1,114,0,0.1209055,"\int \frac{c x^2+d x^3}{2+3 x^4} \, dx","Int[(c*x^2 + d*x^3)/(2 + 3*x^4),x]","\frac{c \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{c \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}+\frac{1}{12} d \log \left(3 x^4+2\right)","\frac{c \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{c \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}+\frac{1}{12} d \log \left(3 x^4+2\right)",1,"-(c*ArcTan[1 - 6^(1/4)*x])/(2*6^(3/4)) + (c*ArcTan[1 + 6^(1/4)*x])/(2*6^(3/4)) + (c*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(4*6^(3/4)) - (c*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(4*6^(3/4)) + (d*Log[2 + 3*x^4])/12","A",13,9,21,0.4286,1,"{1593, 1831, 297, 1162, 617, 204, 1165, 628, 260}"
164,1,154,0,0.1170185,"\int \frac{a+c x^2+d x^3}{2+3 x^4} \, dx","Int[(a + c*x^2 + d*x^3)/(2 + 3*x^4),x]","-\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}+\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}-\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 6^{3/4}}+\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 6^{3/4}}+\frac{1}{12} d \log \left(3 x^4+2\right)","-\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}+\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}-\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 6^{3/4}}+\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 6^{3/4}}+\frac{1}{12} d \log \left(3 x^4+2\right)",1,"-((Sqrt[6]*a + 2*c)*ArcTan[1 - 6^(1/4)*x])/(4*6^(3/4)) + ((Sqrt[6]*a + 2*c)*ArcTan[1 + 6^(1/4)*x])/(4*6^(3/4)) - ((Sqrt[6]*a - 2*c)*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(8*6^(3/4)) + ((Sqrt[6]*a - 2*c)*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(8*6^(3/4)) + (d*Log[2 + 3*x^4])/12","A",12,8,22,0.3636,1,"{1876, 260, 1168, 1162, 617, 204, 1165, 628}"
165,1,136,0,0.1397482,"\int \frac{b x+c x^2+d x^3}{2+3 x^4} \, dx","Int[(b*x + c*x^2 + d*x^3)/(2 + 3*x^4),x]","\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{c \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{c \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}+\frac{1}{12} d \log \left(3 x^4+2\right)","\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{c \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{c \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{c \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}+\frac{1}{12} d \log \left(3 x^4+2\right)",1,"(b*ArcTan[Sqrt[3/2]*x^2])/(2*Sqrt[6]) - (c*ArcTan[1 - 6^(1/4)*x])/(2*6^(3/4)) + (c*ArcTan[1 + 6^(1/4)*x])/(2*6^(3/4)) + (c*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(4*6^(3/4)) - (c*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(4*6^(3/4)) + (d*Log[2 + 3*x^4])/12","A",16,12,24,0.5000,1,"{1594, 1831, 297, 1162, 617, 204, 1165, 628, 1248, 635, 203, 260}"
166,1,176,0,0.1437385,"\int \frac{a+b x+c x^2+d x^3}{2+3 x^4} \, dx","Int[(a + b*x + c*x^2 + d*x^3)/(2 + 3*x^4),x]","-\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}+\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}-\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 6^{3/4}}+\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 6^{3/4}}+\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{1}{12} d \log \left(3 x^4+2\right)","-\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}+\frac{\left(\sqrt{6} a-2 c\right) \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 6^{3/4}}-\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 6^{3/4}}+\frac{\left(\sqrt{6} a+2 c\right) \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 6^{3/4}}+\frac{b \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}+\frac{1}{12} d \log \left(3 x^4+2\right)",1,"(b*ArcTan[Sqrt[3/2]*x^2])/(2*Sqrt[6]) - ((Sqrt[6]*a + 2*c)*ArcTan[1 - 6^(1/4)*x])/(4*6^(3/4)) + ((Sqrt[6]*a + 2*c)*ArcTan[1 + 6^(1/4)*x])/(4*6^(3/4)) - ((Sqrt[6]*a - 2*c)*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(8*6^(3/4)) + ((Sqrt[6]*a - 2*c)*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(8*6^(3/4)) + (d*Log[2 + 3*x^4])/12","A",15,11,25,0.4400,1,"{1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 203, 260}"
167,1,8,0,0.0076716,"\int \frac{1+x+x^2+x^3}{1-x^4} \, dx","Int[(1 + x + x^2 + x^3)/(1 - x^4),x]","-\log (1-x)","-\log (1-x)",1,"-Log[1 - x]","A",2,2,19,0.1053,1,"{1586, 31}"
168,1,53,0,0.0418564,"\int \frac{1+x+x^2+x^3}{1+x^4} \, dx","Int[(1 + x + x^2 + x^3)/(1 + x^4),x]","\frac{1}{4} \log \left(x^4+1\right)+\frac{1}{2} \tan ^{-1}\left(x^2\right)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{\sqrt{2}}","\frac{1}{4} \log \left(x^4+1\right)+\frac{1}{2} \tan ^{-1}\left(x^2\right)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{\sqrt{2}}",1,"ArcTan[x^2]/2 - ArcTan[1 - Sqrt[2]*x]/Sqrt[2] + ArcTan[1 + Sqrt[2]*x]/Sqrt[2] + Log[1 + x^4]/4","A",11,8,17,0.4706,1,"{1876, 1162, 617, 204, 1248, 635, 203, 260}"
169,1,124,0,0.0870212,"\int \frac{1+x+x^2+x^3}{a-b x^4} \, dx","Int[(1 + x + x^2 + x^3)/(a - b*x^4),x]","-\frac{\left(\sqrt{a}-\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a}+\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}-\frac{\log \left(a-b x^4\right)}{4 b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}","-\frac{\left(\sqrt{a}-\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a}+\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}-\frac{\log \left(a-b x^4\right)}{4 b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"-((Sqrt[a] - Sqrt[b])*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4)) + ((Sqrt[a] + Sqrt[b])*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4)) + ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]]/(2*Sqrt[a]*Sqrt[b]) - Log[a - b*x^4]/(4*b)","A",9,7,20,0.3500,1,"{1876, 1167, 205, 208, 1248, 635, 260}"
170,1,277,0,0.195501,"\int \frac{1+x+x^2+x^3}{a+b x^4} \, dx","Int[(1 + x + x^2 + x^3)/(a + b*x^4),x]","\frac{\left(\sqrt{a}-\sqrt{b}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a}-\sqrt{b}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a}+\sqrt{b}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a}+\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\log \left(a+b x^4\right)}{4 b}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}","\frac{\left(\sqrt{a}-\sqrt{b}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a}-\sqrt{b}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a}+\sqrt{b}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a}+\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\log \left(a+b x^4\right)}{4 b}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/(2*Sqrt[a]*Sqrt[b]) - ((Sqrt[a] + Sqrt[b])*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[a] + Sqrt[b])*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[a] - Sqrt[b])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)) - ((Sqrt[a] - Sqrt[b])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)) + Log[a + b*x^4]/(4*b)","A",15,11,19,0.5789,1,"{1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 205, 260}"
171,1,148,0,0.2030527,"\int \frac{c+d x+e x^2+f x^3+g x^4}{a-b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\sqrt{a} \sqrt{b} e+a g+b c\right)}{2 a^{3/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e+a g+b c\right)}{2 a^{3/4} b^{5/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}-\frac{f \log \left(a-b x^4\right)}{4 b}-\frac{g x}{b}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\sqrt{a} \sqrt{b} e+a g+b c\right)}{2 a^{3/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e+a g+b c\right)}{2 a^{3/4} b^{5/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}-\frac{f \log \left(a-b x^4\right)}{4 b}-\frac{g x}{b}",1,"-((g*x)/b) + ((b*c - Sqrt[a]*Sqrt[b]*e + a*g)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(5/4)) + ((b*c + Sqrt[a]*Sqrt[b]*e + a*g)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(5/4)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b]) - (f*Log[a - b*x^4])/(4*b)","A",11,8,31,0.2581,1,"{1885, 1248, 635, 208, 260, 1887, 1167, 205}"
172,1,172,0,0.164898,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\left(a-b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\sqrt{a} \sqrt{b} e-a g+3 b c\right)}{8 a^{7/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e-a g+3 b c\right)}{8 a^{7/4} b^{5/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x \left(a g+b c+b d x+b e x^2+b f x^3\right)}{4 a b \left(a-b x^4\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\sqrt{a} \sqrt{b} e-a g+3 b c\right)}{8 a^{7/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e-a g+3 b c\right)}{8 a^{7/4} b^{5/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x \left(a g+b c+b d x+b e x^2+b f x^3\right)}{4 a b \left(a-b x^4\right)}",1,"(x*(b*c + a*g + b*d*x + b*e*x^2 + b*f*x^3))/(4*a*b*(a - b*x^4)) + ((3*b*c - Sqrt[a]*Sqrt[b]*e - a*g)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(5/4)) + ((3*b*c + Sqrt[a]*Sqrt[b]*e - a*g)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(5/4)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[b])","A",8,6,31,0.1935,1,"{1858, 1876, 275, 208, 1167, 205}"
173,1,221,0,0.2632975,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\left(a-b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^3,x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-5 \sqrt{a} \sqrt{b} e-3 a g+21 b c\right)}{64 a^{11/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(5 \sqrt{a} \sqrt{b} e-3 a g+21 b c\right)}{64 a^{11/4} b^{5/4}}+\frac{x \left(-a g+7 b c+6 b d x+5 b e x^2\right)+4 a f}{32 a^2 b \left(a-b x^4\right)}+\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x \left(a g+b c+b d x+b e x^2+b f x^3\right)}{8 a b \left(a-b x^4\right)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-5 \sqrt{a} \sqrt{b} e-3 a g+21 b c\right)}{64 a^{11/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(5 \sqrt{a} \sqrt{b} e-3 a g+21 b c\right)}{64 a^{11/4} b^{5/4}}+\frac{x \left(-a g+7 b c+6 b d x+5 b e x^2\right)+4 a f}{32 a^2 b \left(a-b x^4\right)}+\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x \left(a g+b c+b d x+b e x^2+b f x^3\right)}{8 a b \left(a-b x^4\right)^2}",1,"(x*(b*c + a*g + b*d*x + b*e*x^2 + b*f*x^3))/(8*a*b*(a - b*x^4)^2) + (4*a*f + x*(7*b*c - a*g + 6*b*d*x + 5*b*e*x^2))/(32*a^2*b*(a - b*x^4)) + ((21*b*c - 5*Sqrt[a]*Sqrt[b]*e - 3*a*g)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(5/4)) + ((21*b*c + 5*Sqrt[a]*Sqrt[b]*e - 3*a*g)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(5/4)) + (3*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[b])","A",9,7,31,0.2258,1,"{1858, 1854, 1876, 275, 208, 1167, 205}"
174,1,266,0,0.320272,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\left(a-b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^4,x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-15 \sqrt{a} \sqrt{b} e-7 a g+77 b c\right)}{256 a^{15/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(15 \sqrt{a} \sqrt{b} e-7 a g+77 b c\right)}{256 a^{15/4} b^{5/4}}+\frac{x \left(-a g+11 b c+10 b d x+9 b e x^2\right)+8 a f}{96 a^2 b \left(a-b x^4\right)^2}+\frac{x \left(7 (11 b c-a g)+60 b d x+45 b e x^2\right)}{384 a^3 b \left(a-b x^4\right)}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x \left(a g+b c+b d x+b e x^2+b f x^3\right)}{12 a b \left(a-b x^4\right)^3}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-15 \sqrt{a} \sqrt{b} e-7 a g+77 b c\right)}{256 a^{15/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(15 \sqrt{a} \sqrt{b} e-7 a g+77 b c\right)}{256 a^{15/4} b^{5/4}}+\frac{x \left(-a g+11 b c+10 b d x+9 b e x^2\right)+8 a f}{96 a^2 b \left(a-b x^4\right)^2}+\frac{x \left(7 (11 b c-a g)+60 b d x+45 b e x^2\right)}{384 a^3 b \left(a-b x^4\right)}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x \left(a g+b c+b d x+b e x^2+b f x^3\right)}{12 a b \left(a-b x^4\right)^3}",1,"(x*(b*c + a*g + b*d*x + b*e*x^2 + b*f*x^3))/(12*a*b*(a - b*x^4)^3) + (x*(7*(11*b*c - a*g) + 60*b*d*x + 45*b*e*x^2))/(384*a^3*b*(a - b*x^4)) + (8*a*f + x*(11*b*c - a*g + 10*b*d*x + 9*b*e*x^2))/(96*a^2*b*(a - b*x^4)^2) + ((77*b*c - 15*Sqrt[a]*Sqrt[b]*e - 7*a*g)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(5/4)) + ((77*b*c + 15*Sqrt[a]*Sqrt[b]*e - 7*a*g)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(5/4)) + (5*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*Sqrt[b])","A",10,8,31,0.2581,1,"{1858, 1854, 1855, 1876, 275, 208, 1167, 205}"
175,1,319,0,0.3505046,"\int \frac{c+d x+e x^2+f x^3+g x^4}{a+b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e-a g+b c\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e-a g+b c\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e-a g+b c\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{a} \sqrt{b} e-a g+b c\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}+\frac{f \log \left(a+b x^4\right)}{4 b}+\frac{g x}{b}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e-a g+b c\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e-a g+b c\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e-a g+b c\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{a} \sqrt{b} e-a g+b c\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}+\frac{f \log \left(a+b x^4\right)}{4 b}+\frac{g x}{b}",1,"(g*x)/b + (d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b]) - ((b*c + Sqrt[a]*Sqrt[b]*e - a*g)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(5/4)) + ((b*c + Sqrt[a]*Sqrt[b]*e - a*g)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(5/4)) - ((b*c - Sqrt[a]*Sqrt[b]*e - a*g)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(5/4)) + ((b*c - Sqrt[a]*Sqrt[b]*e - a*g)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(5/4)) + (f*Log[a + b*x^4])/(4*b)","A",17,12,30,0.4000,1,"{1885, 1248, 635, 205, 260, 1887, 1168, 1162, 617, 204, 1165, 628}"
176,1,341,0,0.3050062,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^2,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x \left(-a g+b c+b d x+b e x^2+b f x^3\right)}{4 a b \left(a+b x^4\right)}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}+\frac{x \left(-a g+b c+b d x+b e x^2+b f x^3\right)}{4 a b \left(a+b x^4\right)}",1,"(x*(b*c - a*g + b*d*x + b*e*x^2 + b*f*x^3))/(4*a*b*(a + b*x^4)) + (d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[b]) - ((3*b*c + Sqrt[a]*Sqrt[b]*e + a*g)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(5/4)) + ((3*b*c + Sqrt[a]*Sqrt[b]*e + a*g)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(5/4)) - ((3*b*c - Sqrt[a]*Sqrt[b]*e + a*g)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(5/4)) + ((3*b*c - Sqrt[a]*Sqrt[b]*e + a*g)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(5/4))","A",14,10,30,0.3333,1,"{1858, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
177,1,394,0,0.4385788,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\left(a+b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^3,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}-\frac{4 a f-x \left(a g+7 b c+6 b d x+5 b e x^2\right)}{32 a^2 b \left(a+b x^4\right)}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x \left(-a g+b c+b d x+b e x^2+b f x^3\right)}{8 a b \left(a+b x^4\right)^2}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}-\frac{4 a f-x \left(a g+7 b c+6 b d x+5 b e x^2\right)}{32 a^2 b \left(a+b x^4\right)}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}+\frac{x \left(-a g+b c+b d x+b e x^2+b f x^3\right)}{8 a b \left(a+b x^4\right)^2}",1,"(x*(b*c - a*g + b*d*x + b*e*x^2 + b*f*x^3))/(8*a*b*(a + b*x^4)^2) - (4*a*f - x*(7*b*c + a*g + 6*b*d*x + 5*b*e*x^2))/(32*a^2*b*(a + b*x^4)) + (3*d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[b]) - ((21*b*c + 5*Sqrt[a]*Sqrt[b]*e + 3*a*g)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(5/4)) + ((21*b*c + 5*Sqrt[a]*Sqrt[b]*e + 3*a*g)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(5/4)) - ((21*b*c - 5*Sqrt[a]*Sqrt[b]*e + 3*a*g)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(5/4)) + ((21*b*c - 5*Sqrt[a]*Sqrt[b]*e + 3*a*g)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(5/4))","A",15,11,30,0.3667,1,"{1858, 1854, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
178,1,437,0,0.5313774,"\int \frac{c+d x+e x^2+f x^3+g x^4}{\left(a+b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^4,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{512 \sqrt{2} a^{15/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{512 \sqrt{2} a^{15/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{256 \sqrt{2} a^{15/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{256 \sqrt{2} a^{15/4} b^{5/4}}-\frac{8 a f-x \left(a g+11 b c+10 b d x+9 b e x^2\right)}{96 a^2 b \left(a+b x^4\right)^2}+\frac{x \left(7 (a g+11 b c)+60 b d x+45 b e x^2\right)}{384 a^3 b \left(a+b x^4\right)}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x \left(-a g+b c+b d x+b e x^2+b f x^3\right)}{12 a b \left(a+b x^4\right)^3}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{512 \sqrt{2} a^{15/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{512 \sqrt{2} a^{15/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{256 \sqrt{2} a^{15/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{256 \sqrt{2} a^{15/4} b^{5/4}}-\frac{8 a f-x \left(a g+11 b c+10 b d x+9 b e x^2\right)}{96 a^2 b \left(a+b x^4\right)^2}+\frac{x \left(7 (a g+11 b c)+60 b d x+45 b e x^2\right)}{384 a^3 b \left(a+b x^4\right)}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}+\frac{x \left(-a g+b c+b d x+b e x^2+b f x^3\right)}{12 a b \left(a+b x^4\right)^3}",1,"(x*(b*c - a*g + b*d*x + b*e*x^2 + b*f*x^3))/(12*a*b*(a + b*x^4)^3) + (x*(7*(11*b*c + a*g) + 60*b*d*x + 45*b*e*x^2))/(384*a^3*b*(a + b*x^4)) - (8*a*f - x*(11*b*c + a*g + 10*b*d*x + 9*b*e*x^2))/(96*a^2*b*(a + b*x^4)^2) + (5*d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*Sqrt[b]) - ((77*b*c + 15*Sqrt[a]*Sqrt[b]*e + 7*a*g)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(5/4)) + ((77*b*c + 15*Sqrt[a]*Sqrt[b]*e + 7*a*g)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(5/4)) - ((77*b*c - 15*Sqrt[a]*Sqrt[b]*e + 7*a*g)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(5/4)) + ((77*b*c - 15*Sqrt[a]*Sqrt[b]*e + 7*a*g)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(5/4))","A",16,12,30,0.4000,1,"{1858, 1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
179,1,11,0,0.0125012,"\int \frac{\left(1-x^4\right)^3}{\left(1+x+x^2+x^3\right)^3} \, dx","Int[(1 - x^4)^3/(1 + x + x^2 + x^3)^3,x]","-\frac{1}{4} (1-x)^4","-\frac{1}{4} (1-x)^4",1,"-(1 - x)^4/4","A",2,2,21,0.09524,1,"{1586, 32}"
180,1,11,0,0.0122637,"\int \frac{\left(1-x^4\right)^2}{\left(1+x+x^2+x^3\right)^2} \, dx","Int[(1 - x^4)^2/(1 + x + x^2 + x^3)^2,x]","-\frac{1}{3} (1-x)^3","-\frac{1}{3} (1-x)^3",1,"-(1 - x)^3/3","A",2,2,21,0.09524,1,"{1586, 32}"
181,1,9,0,0.0086773,"\int \frac{1-x^4}{1+x+x^2+x^3} \, dx","Int[(1 - x^4)/(1 + x + x^2 + x^3),x]","x-\frac{x^2}{2}","x-\frac{x^2}{2}",1,"x - x^2/2","A",2,1,19,0.05263,1,"{1586}"
182,1,8,0,0.0074175,"\int \frac{1+x+x^2+x^3}{1-x^4} \, dx","Int[(1 + x + x^2 + x^3)/(1 - x^4),x]","-\log (1-x)","-\log (1-x)",1,"-Log[1 - x]","A",2,2,19,0.1053,1,"{1586, 31}"
183,1,7,0,0.015811,"\int \frac{\left(1+x+x^2+x^3\right)^2}{\left(1-x^4\right)^2} \, dx","Int[(1 + x + x^2 + x^3)^2/(1 - x^4)^2,x]","\frac{1}{1-x}","\frac{1}{1-x}",1,"(1 - x)^(-1)","A",2,2,21,0.09524,1,"{1586, 32}"
184,1,11,0,0.0181356,"\int \frac{\left(1+x+x^2+x^3\right)^3}{\left(1-x^4\right)^3} \, dx","Int[(1 + x + x^2 + x^3)^3/(1 - x^4)^3,x]","\frac{1}{2 (1-x)^2}","\frac{1}{2 (1-x)^2}",1,"1/(2*(1 - x)^2)","A",2,2,21,0.09524,1,"{1586, 32}"
185,1,11,0,0.0193226,"\int \frac{\left(1+x+x^2+x^3\right)^4}{\left(1-x^4\right)^4} \, dx","Int[(1 + x + x^2 + x^3)^4/(1 - x^4)^4,x]","\frac{1}{3 (1-x)^3}","\frac{1}{3 (1-x)^3}",1,"1/(3*(1 - x)^3)","A",2,2,21,0.09524,1,"{1586, 32}"
186,1,165,0,0.2606277,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{a-b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\sqrt{a} \sqrt{b} e+a g+b c\right)}{2 a^{3/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e+a g+b c\right)}{2 a^{3/4} b^{5/4}}+\frac{(a h+b d) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{f \log \left(a-b x^4\right)}{4 b}-\frac{g x}{b}-\frac{h x^2}{2 b}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\sqrt{a} \sqrt{b} e+a g+b c\right)}{2 a^{3/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e+a g+b c\right)}{2 a^{3/4} b^{5/4}}+\frac{(a h+b d) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{f \log \left(a-b x^4\right)}{4 b}-\frac{g x}{b}-\frac{h x^2}{2 b}",1,"-((g*x)/b) - (h*x^2)/(2*b) + ((b*c - Sqrt[a]*Sqrt[b]*e + a*g)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(5/4)) + ((b*c + Sqrt[a]*Sqrt[b]*e + a*g)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(5/4)) + ((b*d + a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*b^(3/2)) - (f*Log[a - b*x^4])/(4*b)","A",13,9,36,0.2500,1,"{1885, 1887, 1167, 205, 208, 1819, 1810, 635, 260}"
187,1,188,0,0.3265832,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6}{a-b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a - b*x^4),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{\sqrt{b} (a g+b c)}{\sqrt{a}}+a i+b e\right)}{2 \sqrt[4]{a} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{\sqrt{b} (a g+b c)}{\sqrt{a}}+a i+b e\right)}{2 \sqrt[4]{a} b^{7/4}}+\frac{(a h+b d) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{f \log \left(a-b x^4\right)}{4 b}-\frac{g x}{b}-\frac{h x^2}{2 b}-\frac{i x^3}{3 b}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{\sqrt{b} (a g+b c)}{\sqrt{a}}+a i+b e\right)}{2 \sqrt[4]{a} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{\sqrt{b} (a g+b c)}{\sqrt{a}}+a i+b e\right)}{2 \sqrt[4]{a} b^{7/4}}+\frac{(a h+b d) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{f \log \left(a-b x^4\right)}{4 b}-\frac{g x}{b}-\frac{h x^2}{2 b}-\frac{i x^3}{3 b}",1,"-((g*x)/b) - (h*x^2)/(2*b) - (i*x^3)/(3*b) - ((b*e - (Sqrt[b]*(b*c + a*g))/Sqrt[a] + a*i)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(1/4)*b^(7/4)) + ((b*e + (Sqrt[b]*(b*c + a*g))/Sqrt[a] + a*i)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(1/4)*b^(7/4)) + ((b*d + a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*b^(3/2)) - (f*Log[a - b*x^4])/(4*b)","A",13,9,41,0.2195,1,"{1885, 1819, 1810, 635, 208, 260, 1887, 1167, 205}"
188,1,205,0,0.3134439,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6+j x^7}{a-b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a - b*x^4),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{\sqrt{b} (a g+b c)}{\sqrt{a}}+a i+b e\right)}{2 \sqrt[4]{a} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{\sqrt{b} (a g+b c)}{\sqrt{a}}+a i+b e\right)}{2 \sqrt[4]{a} b^{7/4}}+\frac{(a h+b d) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{(a j+b f) \log \left(a-b x^4\right)}{4 b^2}-\frac{g x}{b}-\frac{h x^2}{2 b}-\frac{i x^3}{3 b}-\frac{j x^4}{4 b}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{\sqrt{b} (a g+b c)}{\sqrt{a}}+a i+b e\right)}{2 \sqrt[4]{a} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{\sqrt{b} (a g+b c)}{\sqrt{a}}+a i+b e\right)}{2 \sqrt[4]{a} b^{7/4}}+\frac{(a h+b d) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{(a j+b f) \log \left(a-b x^4\right)}{4 b^2}-\frac{g x}{b}-\frac{h x^2}{2 b}-\frac{i x^3}{3 b}-\frac{j x^4}{4 b}",1,"-((g*x)/b) - (h*x^2)/(2*b) - (i*x^3)/(3*b) - (j*x^4)/(4*b) - ((b*e - (Sqrt[b]*(b*c + a*g))/Sqrt[a] + a*i)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(1/4)*b^(7/4)) + ((b*e + (Sqrt[b]*(b*c + a*g))/Sqrt[a] + a*i)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(1/4)*b^(7/4)) + ((b*d + a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*b^(3/2)) - ((b*f + a*j)*Log[a - b*x^4])/(4*b^2)","A",13,9,46,0.1957,1,"{1885, 1887, 1167, 205, 208, 1819, 1810, 635, 260}"
189,1,337,0,0.3993563,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{a+b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e-a g+b c\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e-a g+b c\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e-a g+b c\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{a} \sqrt{b} e-a g+b c\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{(b d-a h) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}+\frac{f \log \left(a+b x^4\right)}{4 b}+\frac{g x}{b}+\frac{h x^2}{2 b}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e-a g+b c\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e-a g+b c\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e-a g+b c\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{a} \sqrt{b} e-a g+b c\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{(b d-a h) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}+\frac{f \log \left(a+b x^4\right)}{4 b}+\frac{g x}{b}+\frac{h x^2}{2 b}",1,"(g*x)/b + (h*x^2)/(2*b) + ((b*d - a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*b^(3/2)) - ((b*c + Sqrt[a]*Sqrt[b]*e - a*g)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(5/4)) + ((b*c + Sqrt[a]*Sqrt[b]*e - a*g)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(5/4)) - ((b*c - Sqrt[a]*Sqrt[b]*e - a*g)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(5/4)) + ((b*c - Sqrt[a]*Sqrt[b]*e - a*g)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(5/4)) + (f*Log[a + b*x^4])/(4*b)","A",19,13,35,0.3714,1,"{1885, 1887, 1168, 1162, 617, 204, 1165, 628, 1819, 1810, 635, 205, 260}"
190,1,384,0,0.5651766,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6}{a+b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (b c-a g)-\sqrt{a} (b e-a i)\right)}{4 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (b c-a g)-\sqrt{a} (b e-a i)\right)}{4 \sqrt{2} a^{3/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{b} (b c-a g)+\sqrt{a} (b e-a i)\right)}{2 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{b} (b c-a g)+\sqrt{a} (b e-a i)\right)}{2 \sqrt{2} a^{3/4} b^{7/4}}+\frac{(b d-a h) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}+\frac{f \log \left(a+b x^4\right)}{4 b}+\frac{g x}{b}+\frac{h x^2}{2 b}+\frac{i x^3}{3 b}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (b c-a g)-\sqrt{a} (b e-a i)\right)}{4 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (b c-a g)-\sqrt{a} (b e-a i)\right)}{4 \sqrt{2} a^{3/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{b} (b c-a g)+\sqrt{a} (b e-a i)\right)}{2 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{b} (b c-a g)+\sqrt{a} (b e-a i)\right)}{2 \sqrt{2} a^{3/4} b^{7/4}}+\frac{(b d-a h) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}+\frac{f \log \left(a+b x^4\right)}{4 b}+\frac{g x}{b}+\frac{h x^2}{2 b}+\frac{i x^3}{3 b}",1,"(g*x)/b + (h*x^2)/(2*b) + (i*x^3)/(3*b) + ((b*d - a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*b^(3/2)) - ((Sqrt[b]*(b*c - a*g) + Sqrt[a]*(b*e - a*i))*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(7/4)) + ((Sqrt[b]*(b*c - a*g) + Sqrt[a]*(b*e - a*i))*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(7/4)) - ((Sqrt[b]*(b*c - a*g) - Sqrt[a]*(b*e - a*i))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(7/4)) + ((Sqrt[b]*(b*c - a*g) - Sqrt[a]*(b*e - a*i))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(7/4)) + (f*Log[a + b*x^4])/(4*b)","A",19,13,40,0.3250,1,"{1885, 1819, 1810, 635, 205, 260, 1887, 1168, 1162, 617, 204, 1165, 628}"
191,1,402,0,0.5669192,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6+j x^7}{a+b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a + b*x^4),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (b c-a g)-\sqrt{a} (b e-a i)\right)}{4 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (b c-a g)-\sqrt{a} (b e-a i)\right)}{4 \sqrt{2} a^{3/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{b} (b c-a g)+\sqrt{a} (b e-a i)\right)}{2 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{b} (b c-a g)+\sqrt{a} (b e-a i)\right)}{2 \sqrt{2} a^{3/4} b^{7/4}}+\frac{(b d-a h) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}+\frac{(b f-a j) \log \left(a+b x^4\right)}{4 b^2}+\frac{g x}{b}+\frac{h x^2}{2 b}+\frac{i x^3}{3 b}+\frac{j x^4}{4 b}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (b c-a g)-\sqrt{a} (b e-a i)\right)}{4 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (b c-a g)-\sqrt{a} (b e-a i)\right)}{4 \sqrt{2} a^{3/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{b} (b c-a g)+\sqrt{a} (b e-a i)\right)}{2 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{b} (b c-a g)+\sqrt{a} (b e-a i)\right)}{2 \sqrt{2} a^{3/4} b^{7/4}}+\frac{(b d-a h) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}+\frac{(b f-a j) \log \left(a+b x^4\right)}{4 b^2}+\frac{g x}{b}+\frac{h x^2}{2 b}+\frac{i x^3}{3 b}+\frac{j x^4}{4 b}",1,"(g*x)/b + (h*x^2)/(2*b) + (i*x^3)/(3*b) + (j*x^4)/(4*b) + ((b*d - a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*b^(3/2)) - ((Sqrt[b]*(b*c - a*g) + Sqrt[a]*(b*e - a*i))*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(7/4)) + ((Sqrt[b]*(b*c - a*g) + Sqrt[a]*(b*e - a*i))*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(7/4)) - ((Sqrt[b]*(b*c - a*g) - Sqrt[a]*(b*e - a*i))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(7/4)) + ((Sqrt[b]*(b*c - a*g) - Sqrt[a]*(b*e - a*i))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(7/4)) + ((b*f - a*j)*Log[a + b*x^4])/(4*b^2)","A",19,13,45,0.2889,1,"{1885, 1887, 1168, 1162, 617, 204, 1165, 628, 1819, 1810, 635, 205, 260}"
192,1,184,0,0.2038574,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{\left(a-b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\sqrt{a} \sqrt{b} e-a g+3 b c\right)}{8 a^{7/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e-a g+3 b c\right)}{8 a^{7/4} b^{5/4}}+\frac{(b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{x \left(x (a h+b d)+a g+b c+b e x^2+b f x^3\right)}{4 a b \left(a-b x^4\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\sqrt{a} \sqrt{b} e-a g+3 b c\right)}{8 a^{7/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e-a g+3 b c\right)}{8 a^{7/4} b^{5/4}}+\frac{(b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{x \left(x (a h+b d)+a g+b c+b e x^2+b f x^3\right)}{4 a b \left(a-b x^4\right)}",1,"(x*(b*c + a*g + (b*d + a*h)*x + b*e*x^2 + b*f*x^3))/(4*a*b*(a - b*x^4)) + ((3*b*c - Sqrt[a]*Sqrt[b]*e - a*g)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(5/4)) + ((3*b*c + Sqrt[a]*Sqrt[b]*e - a*g)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(8*a^(7/4)*b^(5/4)) + ((b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*b^(3/2))","A",8,6,36,0.1667,1,"{1858, 1876, 275, 208, 1167, 205}"
193,1,203,0,0.2742802,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6}{\left(a-b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a - b*x^4)^2,x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{\sqrt{b} (3 b c-a g)}{\sqrt{a}}-3 a i+b e\right)}{8 a^{5/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{\sqrt{b} (3 b c-a g)}{\sqrt{a}}-3 a i+b e\right)}{8 a^{5/4} b^{7/4}}+\frac{(b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+a g+b c+b f x^3\right)}{4 a b \left(a-b x^4\right)}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{\sqrt{b} (3 b c-a g)}{\sqrt{a}}-3 a i+b e\right)}{8 a^{5/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{\sqrt{b} (3 b c-a g)}{\sqrt{a}}-3 a i+b e\right)}{8 a^{5/4} b^{7/4}}+\frac{(b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+a g+b c+b f x^3\right)}{4 a b \left(a-b x^4\right)}",1,"(x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + b*f*x^3))/(4*a*b*(a - b*x^4)) - ((b*e - (Sqrt[b]*(3*b*c - a*g))/Sqrt[a] - 3*a*i)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(8*a^(5/4)*b^(7/4)) + ((b*e + (Sqrt[b]*(3*b*c - a*g))/Sqrt[a] - 3*a*i)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(8*a^(5/4)*b^(7/4)) + ((b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*b^(3/2))","A",8,6,41,0.1463,1,"{1858, 1876, 275, 208, 1167, 205}"
194,1,225,0,0.310455,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6+j x^7}{\left(a-b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a - b*x^4)^2,x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{\sqrt{b} (3 b c-a g)}{\sqrt{a}}-3 a i+b e\right)}{8 a^{5/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{\sqrt{b} (3 b c-a g)}{\sqrt{a}}-3 a i+b e\right)}{8 a^{5/4} b^{7/4}}+\frac{(b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{j \log \left(a-b x^4\right)}{4 b^2}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+x^3 (a j+b f)+a g+b c\right)}{4 a b \left(a-b x^4\right)}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{\sqrt{b} (3 b c-a g)}{\sqrt{a}}-3 a i+b e\right)}{8 a^{5/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{\sqrt{b} (3 b c-a g)}{\sqrt{a}}-3 a i+b e\right)}{8 a^{5/4} b^{7/4}}+\frac{(b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{j \log \left(a-b x^4\right)}{4 b^2}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+x^3 (a j+b f)+a g+b c\right)}{4 a b \left(a-b x^4\right)}",1,"(x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + (b*f + a*j)*x^3))/(4*a*b*(a - b*x^4)) - ((b*e - (Sqrt[b]*(3*b*c - a*g))/Sqrt[a] - 3*a*i)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(8*a^(5/4)*b^(7/4)) + ((b*e + (Sqrt[b]*(3*b*c - a*g))/Sqrt[a] - 3*a*i)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(8*a^(5/4)*b^(7/4)) + ((b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*b^(3/2)) + (j*Log[a - b*x^4])/(4*b^2)","A",10,8,46,0.1739,1,"{1858, 1876, 1167, 205, 208, 1248, 635, 260}"
195,1,353,0,0.3404093,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4)^2,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a h+b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{x \left(x (b d-a h)-a g+b c+b e x^2+b f x^3\right)}{4 a b \left(a+b x^4\right)}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{16 \sqrt{2} a^{7/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{a} \sqrt{b} e+a g+3 b c\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a h+b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{x \left(x (b d-a h)-a g+b c+b e x^2+b f x^3\right)}{4 a b \left(a+b x^4\right)}",1,"(x*(b*c - a*g + (b*d - a*h)*x + b*e*x^2 + b*f*x^3))/(4*a*b*(a + b*x^4)) + ((b*d + a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*b^(3/2)) - ((3*b*c + Sqrt[a]*Sqrt[b]*e + a*g)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(5/4)) + ((3*b*c + Sqrt[a]*Sqrt[b]*e + a*g)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(5/4)) - ((3*b*c - Sqrt[a]*Sqrt[b]*e + a*g)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(5/4)) + ((3*b*c - Sqrt[a]*Sqrt[b]*e + a*g)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(5/4))","A",14,10,35,0.2857,1,"{1858, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
196,1,395,0,0.4923867,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4)^2,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (a g+3 b c)-\sqrt{a} (3 a i+b e)\right)}{16 \sqrt{2} a^{7/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (a g+3 b c)-\sqrt{a} (3 a i+b e)\right)}{16 \sqrt{2} a^{7/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{b} (a g+3 b c)+\sqrt{a} (3 a i+b e)\right)}{8 \sqrt{2} a^{7/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{b} (a g+3 b c)+\sqrt{a} (3 a i+b e)\right)}{8 \sqrt{2} a^{7/4} b^{7/4}}+\frac{(a h+b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)-a g+b c+b f x^3\right)}{4 a b \left(a+b x^4\right)}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (a g+3 b c)-\sqrt{a} (3 a i+b e)\right)}{16 \sqrt{2} a^{7/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (a g+3 b c)-\sqrt{a} (3 a i+b e)\right)}{16 \sqrt{2} a^{7/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{b} (a g+3 b c)+\sqrt{a} (3 a i+b e)\right)}{8 \sqrt{2} a^{7/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{b} (a g+3 b c)+\sqrt{a} (3 a i+b e)\right)}{8 \sqrt{2} a^{7/4} b^{7/4}}+\frac{(a h+b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)-a g+b c+b f x^3\right)}{4 a b \left(a+b x^4\right)}",1,"(x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + b*f*x^3))/(4*a*b*(a + b*x^4)) + ((b*d + a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*b^(3/2)) - ((Sqrt[b]*(3*b*c + a*g) + Sqrt[a]*(b*e + 3*a*i))*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(7/4)) + ((Sqrt[b]*(3*b*c + a*g) + Sqrt[a]*(b*e + 3*a*i))*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(7/4)) - ((Sqrt[b]*(3*b*c + a*g) - Sqrt[a]*(b*e + 3*a*i))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(7/4)) + ((Sqrt[b]*(3*b*c + a*g) - Sqrt[a]*(b*e + 3*a*i))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(7/4))","A",14,10,40,0.2500,1,"{1858, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
197,1,417,0,0.5360196,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6+j x^7}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a + b*x^4)^2,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (a g+3 b c)-\sqrt{a} (3 a i+b e)\right)}{16 \sqrt{2} a^{7/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (a g+3 b c)-\sqrt{a} (3 a i+b e)\right)}{16 \sqrt{2} a^{7/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{b} (a g+3 b c)+\sqrt{a} (3 a i+b e)\right)}{8 \sqrt{2} a^{7/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{b} (a g+3 b c)+\sqrt{a} (3 a i+b e)\right)}{8 \sqrt{2} a^{7/4} b^{7/4}}+\frac{(a h+b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{j \log \left(a+b x^4\right)}{4 b^2}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)+x^3 (b f-a j)-a g+b c\right)}{4 a b \left(a+b x^4\right)}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (a g+3 b c)-\sqrt{a} (3 a i+b e)\right)}{16 \sqrt{2} a^{7/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(\sqrt{b} (a g+3 b c)-\sqrt{a} (3 a i+b e)\right)}{16 \sqrt{2} a^{7/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\sqrt{b} (a g+3 b c)+\sqrt{a} (3 a i+b e)\right)}{8 \sqrt{2} a^{7/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(\sqrt{b} (a g+3 b c)+\sqrt{a} (3 a i+b e)\right)}{8 \sqrt{2} a^{7/4} b^{7/4}}+\frac{(a h+b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} b^{3/2}}+\frac{j \log \left(a+b x^4\right)}{4 b^2}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)+x^3 (b f-a j)-a g+b c\right)}{4 a b \left(a+b x^4\right)}",1,"(x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + (b*f - a*j)*x^3))/(4*a*b*(a + b*x^4)) + ((b*d + a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*b^(3/2)) - ((Sqrt[b]*(3*b*c + a*g) + Sqrt[a]*(b*e + 3*a*i))*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(7/4)) + ((Sqrt[b]*(3*b*c + a*g) + Sqrt[a]*(b*e + 3*a*i))*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(7/4)) - ((Sqrt[b]*(3*b*c + a*g) - Sqrt[a]*(b*e + 3*a*i))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(7/4)) + ((Sqrt[b]*(3*b*c + a*g) - Sqrt[a]*(b*e + 3*a*i))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(7/4)) + (j*Log[a + b*x^4])/(4*b^2)","A",16,12,45,0.2667,1,"{1858, 1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 205, 260}"
198,1,241,0,0.3389171,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{\left(a-b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4)^3,x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-5 \sqrt{a} \sqrt{b} e-3 a g+21 b c\right)}{64 a^{11/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(5 \sqrt{a} \sqrt{b} e-3 a g+21 b c\right)}{64 a^{11/4} b^{5/4}}+\frac{(3 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x \left(2 x (3 b d-a h)-a g+7 b c+5 b e x^2\right)+4 a f}{32 a^2 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+a g+b c+b e x^2+b f x^3\right)}{8 a b \left(a-b x^4\right)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-5 \sqrt{a} \sqrt{b} e-3 a g+21 b c\right)}{64 a^{11/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(5 \sqrt{a} \sqrt{b} e-3 a g+21 b c\right)}{64 a^{11/4} b^{5/4}}+\frac{(3 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x \left(2 x (3 b d-a h)-a g+7 b c+5 b e x^2\right)+4 a f}{32 a^2 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+a g+b c+b e x^2+b f x^3\right)}{8 a b \left(a-b x^4\right)^2}",1,"(x*(b*c + a*g + (b*d + a*h)*x + b*e*x^2 + b*f*x^3))/(8*a*b*(a - b*x^4)^2) + (4*a*f + x*(7*b*c - a*g + 2*(3*b*d - a*h)*x + 5*b*e*x^2))/(32*a^2*b*(a - b*x^4)) + ((21*b*c - 5*Sqrt[a]*Sqrt[b]*e - 3*a*g)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(5/4)) + ((21*b*c + 5*Sqrt[a]*Sqrt[b]*e - 3*a*g)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(64*a^(11/4)*b^(5/4)) + ((3*b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*b^(3/2))","A",9,7,36,0.1944,1,"{1858, 1854, 1876, 275, 208, 1167, 205}"
199,1,268,0,0.4346776,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6}{\left(a-b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a - b*x^4)^3,x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{3 \sqrt{b} (7 b c-a g)}{\sqrt{a}}-3 a i+5 b e\right)}{64 a^{9/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{3 \sqrt{b} (7 b c-a g)}{\sqrt{a}}-3 a i+5 b e\right)}{64 a^{9/4} b^{7/4}}+\frac{(3 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x \left(2 x (3 b d-a h)+x^2 (5 b e-3 a i)-a g+7 b c\right)+4 a f}{32 a^2 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+a g+b c+b f x^3\right)}{8 a b \left(a-b x^4\right)^2}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{3 \sqrt{b} (7 b c-a g)}{\sqrt{a}}-3 a i+5 b e\right)}{64 a^{9/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{3 \sqrt{b} (7 b c-a g)}{\sqrt{a}}-3 a i+5 b e\right)}{64 a^{9/4} b^{7/4}}+\frac{(3 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x \left(2 x (3 b d-a h)+x^2 (5 b e-3 a i)-a g+7 b c\right)+4 a f}{32 a^2 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+a g+b c+b f x^3\right)}{8 a b \left(a-b x^4\right)^2}",1,"(x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + b*f*x^3))/(8*a*b*(a - b*x^4)^2) + (4*a*f + x*(7*b*c - a*g + 2*(3*b*d - a*h)*x + (5*b*e - 3*a*i)*x^2))/(32*a^2*b*(a - b*x^4)) - ((5*b*e - (3*Sqrt[b]*(7*b*c - a*g))/Sqrt[a] - 3*a*i)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(64*a^(9/4)*b^(7/4)) + ((5*b*e + (3*Sqrt[b]*(7*b*c - a*g))/Sqrt[a] - 3*a*i)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(64*a^(9/4)*b^(7/4)) + ((3*b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*b^(3/2))","A",9,7,41,0.1707,1,"{1858, 1854, 1876, 275, 208, 1167, 205}"
200,1,285,0,0.3914484,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6+j x^7}{\left(a-b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a - b*x^4)^3,x]","\frac{x \left(b (7 b c-a g)+2 b x (3 b d-a h)+b x^2 (5 b e-3 a i)\right)+4 a (b f-a j)}{32 a^2 b^2 \left(a-b x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{3 \sqrt{b} (7 b c-a g)}{\sqrt{a}}-3 a i+5 b e\right)}{64 a^{9/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{3 \sqrt{b} (7 b c-a g)}{\sqrt{a}}-3 a i+5 b e\right)}{64 a^{9/4} b^{7/4}}+\frac{(3 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+x^3 (a j+b f)+a g+b c\right)}{8 a b \left(a-b x^4\right)^2}","\frac{x \left(b (7 b c-a g)+2 b x (3 b d-a h)+b x^2 (5 b e-3 a i)\right)+4 a (b f-a j)}{32 a^2 b^2 \left(a-b x^4\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-\frac{3 \sqrt{b} (7 b c-a g)}{\sqrt{a}}-3 a i+5 b e\right)}{64 a^{9/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{3 \sqrt{b} (7 b c-a g)}{\sqrt{a}}-3 a i+5 b e\right)}{64 a^{9/4} b^{7/4}}+\frac{(3 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+x^3 (a j+b f)+a g+b c\right)}{8 a b \left(a-b x^4\right)^2}",1,"(x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + (b*f + a*j)*x^3))/(8*a*b*(a - b*x^4)^2) + (4*a*(b*f - a*j) + x*(b*(7*b*c - a*g) + 2*b*(3*b*d - a*h)*x + b*(5*b*e - 3*a*i)*x^2))/(32*a^2*b^2*(a - b*x^4)) - ((5*b*e - (3*Sqrt[b]*(7*b*c - a*g))/Sqrt[a] - 3*a*i)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(64*a^(9/4)*b^(7/4)) + ((5*b*e + (3*Sqrt[b]*(7*b*c - a*g))/Sqrt[a] - 3*a*i)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(64*a^(9/4)*b^(7/4)) + ((3*b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*b^(3/2))","A",9,7,46,0.1522,1,"{1858, 1854, 1876, 275, 208, 1167, 205}"
201,1,413,0,0.4864203,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{\left(a+b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4)^3,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}+\frac{(a h+3 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}-\frac{4 a f-x \left(2 x (a h+3 b d)+a g+7 b c+5 b e x^2\right)}{32 a^2 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)-a g+b c+b e x^2+b f x^3\right)}{8 a b \left(a+b x^4\right)^2}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(5 \sqrt{a} \sqrt{b} e+3 a g+21 b c\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}+\frac{(a h+3 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}-\frac{4 a f-x \left(2 x (a h+3 b d)+a g+7 b c+5 b e x^2\right)}{32 a^2 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)-a g+b c+b e x^2+b f x^3\right)}{8 a b \left(a+b x^4\right)^2}",1,"(x*(b*c - a*g + (b*d - a*h)*x + b*e*x^2 + b*f*x^3))/(8*a*b*(a + b*x^4)^2) - (4*a*f - x*(7*b*c + a*g + 2*(3*b*d + a*h)*x + 5*b*e*x^2))/(32*a^2*b*(a + b*x^4)) + ((3*b*d + a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*b^(3/2)) - ((21*b*c + 5*Sqrt[a]*Sqrt[b]*e + 3*a*g)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(5/4)) + ((21*b*c + 5*Sqrt[a]*Sqrt[b]*e + 3*a*g)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(5/4)) - ((21*b*c - 5*Sqrt[a]*Sqrt[b]*e + 3*a*g)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(5/4)) + ((21*b*c - 5*Sqrt[a]*Sqrt[b]*e + 3*a*g)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(5/4))","A",15,11,35,0.3143,1,"{1858, 1854, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
202,1,463,0,0.6857778,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6}{\left(a+b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4)^3,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(3 \sqrt{b} (a g+7 b c)-\sqrt{a} (3 a i+5 b e)\right)}{128 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(3 \sqrt{b} (a g+7 b c)-\sqrt{a} (3 a i+5 b e)\right)}{128 \sqrt{2} a^{11/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(3 \sqrt{b} (a g+7 b c)+\sqrt{a} (3 a i+5 b e)\right)}{64 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(3 \sqrt{b} (a g+7 b c)+\sqrt{a} (3 a i+5 b e)\right)}{64 \sqrt{2} a^{11/4} b^{7/4}}+\frac{(a h+3 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}-\frac{4 a f-x \left(2 x (a h+3 b d)+x^2 (3 a i+5 b e)+a g+7 b c\right)}{32 a^2 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)-a g+b c+b f x^3\right)}{8 a b \left(a+b x^4\right)^2}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(3 \sqrt{b} (a g+7 b c)-\sqrt{a} (3 a i+5 b e)\right)}{128 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(3 \sqrt{b} (a g+7 b c)-\sqrt{a} (3 a i+5 b e)\right)}{128 \sqrt{2} a^{11/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(3 \sqrt{b} (a g+7 b c)+\sqrt{a} (3 a i+5 b e)\right)}{64 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(3 \sqrt{b} (a g+7 b c)+\sqrt{a} (3 a i+5 b e)\right)}{64 \sqrt{2} a^{11/4} b^{7/4}}+\frac{(a h+3 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}-\frac{4 a f-x \left(2 x (a h+3 b d)+x^2 (3 a i+5 b e)+a g+7 b c\right)}{32 a^2 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)-a g+b c+b f x^3\right)}{8 a b \left(a+b x^4\right)^2}",1,"(x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + b*f*x^3))/(8*a*b*(a + b*x^4)^2) - (4*a*f - x*(7*b*c + a*g + 2*(3*b*d + a*h)*x + (5*b*e + 3*a*i)*x^2))/(32*a^2*b*(a + b*x^4)) + ((3*b*d + a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*b^(3/2)) - ((3*Sqrt[b]*(7*b*c + a*g) + Sqrt[a]*(5*b*e + 3*a*i))*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(7/4)) + ((3*Sqrt[b]*(7*b*c + a*g) + Sqrt[a]*(5*b*e + 3*a*i))*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(7/4)) - ((3*Sqrt[b]*(7*b*c + a*g) - Sqrt[a]*(5*b*e + 3*a*i))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(7/4)) + ((3*Sqrt[b]*(7*b*c + a*g) - Sqrt[a]*(5*b*e + 3*a*i))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(7/4))","A",15,11,40,0.2750,1,"{1858, 1854, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
203,1,480,0,0.6657608,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6+j x^7}{\left(a+b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a + b*x^4)^3,x]","-\frac{4 a (a j+b f)-x \left(b (a g+7 b c)+2 b x (a h+3 b d)+b x^2 (3 a i+5 b e)\right)}{32 a^2 b^2 \left(a+b x^4\right)}-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(3 \sqrt{b} (a g+7 b c)-\sqrt{a} (3 a i+5 b e)\right)}{128 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(3 \sqrt{b} (a g+7 b c)-\sqrt{a} (3 a i+5 b e)\right)}{128 \sqrt{2} a^{11/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(3 \sqrt{b} (a g+7 b c)+\sqrt{a} (3 a i+5 b e)\right)}{64 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(3 \sqrt{b} (a g+7 b c)+\sqrt{a} (3 a i+5 b e)\right)}{64 \sqrt{2} a^{11/4} b^{7/4}}+\frac{(a h+3 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)+x^3 (b f-a j)-a g+b c\right)}{8 a b \left(a+b x^4\right)^2}","-\frac{4 a (a j+b f)-x \left(b (a g+7 b c)+2 b x (a h+3 b d)+b x^2 (3 a i+5 b e)\right)}{32 a^2 b^2 \left(a+b x^4\right)}-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(3 \sqrt{b} (a g+7 b c)-\sqrt{a} (3 a i+5 b e)\right)}{128 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(3 \sqrt{b} (a g+7 b c)-\sqrt{a} (3 a i+5 b e)\right)}{128 \sqrt{2} a^{11/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(3 \sqrt{b} (a g+7 b c)+\sqrt{a} (3 a i+5 b e)\right)}{64 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(3 \sqrt{b} (a g+7 b c)+\sqrt{a} (3 a i+5 b e)\right)}{64 \sqrt{2} a^{11/4} b^{7/4}}+\frac{(a h+3 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)+x^3 (b f-a j)-a g+b c\right)}{8 a b \left(a+b x^4\right)^2}",1,"(x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + (b*f - a*j)*x^3))/(8*a*b*(a + b*x^4)^2) - (4*a*(b*f + a*j) - x*(b*(7*b*c + a*g) + 2*b*(3*b*d + a*h)*x + b*(5*b*e + 3*a*i)*x^2))/(32*a^2*b^2*(a + b*x^4)) + ((3*b*d + a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*b^(3/2)) - ((3*Sqrt[b]*(7*b*c + a*g) + Sqrt[a]*(5*b*e + 3*a*i))*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(7/4)) + ((3*Sqrt[b]*(7*b*c + a*g) + Sqrt[a]*(5*b*e + 3*a*i))*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(7/4)) - ((3*Sqrt[b]*(7*b*c + a*g) - Sqrt[a]*(5*b*e + 3*a*i))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(7/4)) + ((3*Sqrt[b]*(7*b*c + a*g) - Sqrt[a]*(5*b*e + 3*a*i))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(7/4))","A",15,11,45,0.2444,1,"{1858, 1854, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
204,1,293,0,0.4305523,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{\left(a-b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4)^4,x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-15 \sqrt{a} \sqrt{b} e-7 a g+77 b c\right)}{256 a^{15/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(15 \sqrt{a} \sqrt{b} e-7 a g+77 b c\right)}{256 a^{15/4} b^{5/4}}+\frac{(5 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}+\frac{x \left(2 x (5 b d-a h)-a g+11 b c+9 b e x^2\right)+8 a f}{96 a^2 b \left(a-b x^4\right)^2}+\frac{x \left(7 (11 b c-a g)+12 x (5 b d-a h)+45 b e x^2\right)}{384 a^3 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+a g+b c+b e x^2+b f x^3\right)}{12 a b \left(a-b x^4\right)^3}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(-15 \sqrt{a} \sqrt{b} e-7 a g+77 b c\right)}{256 a^{15/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(15 \sqrt{a} \sqrt{b} e-7 a g+77 b c\right)}{256 a^{15/4} b^{5/4}}+\frac{(5 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}+\frac{x \left(2 x (5 b d-a h)-a g+11 b c+9 b e x^2\right)+8 a f}{96 a^2 b \left(a-b x^4\right)^2}+\frac{x \left(7 (11 b c-a g)+12 x (5 b d-a h)+45 b e x^2\right)}{384 a^3 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+a g+b c+b e x^2+b f x^3\right)}{12 a b \left(a-b x^4\right)^3}",1,"(x*(b*c + a*g + (b*d + a*h)*x + b*e*x^2 + b*f*x^3))/(12*a*b*(a - b*x^4)^3) + (x*(7*(11*b*c - a*g) + 12*(5*b*d - a*h)*x + 45*b*e*x^2))/(384*a^3*b*(a - b*x^4)) + (8*a*f + x*(11*b*c - a*g + 2*(5*b*d - a*h)*x + 9*b*e*x^2))/(96*a^2*b*(a - b*x^4)^2) + ((77*b*c - 15*Sqrt[a]*Sqrt[b]*e - 7*a*g)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(5/4)) + ((77*b*c + 15*Sqrt[a]*Sqrt[b]*e - 7*a*g)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(256*a^(15/4)*b^(5/4)) + ((5*b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*b^(3/2))","A",10,8,36,0.2222,1,"{1858, 1854, 1855, 1876, 275, 208, 1167, 205}"
205,1,331,0,0.5671833,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6}{\left(a-b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a - b*x^4)^4,x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{7 \sqrt{b} (11 b c-a g)}{\sqrt{a}}-5 (3 b e-a i)\right)}{256 a^{13/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{7 \sqrt{b} (11 b c-a g)}{\sqrt{a}}-5 a i+15 b e\right)}{256 a^{13/4} b^{7/4}}+\frac{(5 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}+\frac{x \left(2 x (5 b d-a h)+3 x^2 (3 b e-a i)-a g+11 b c\right)+8 a f}{96 a^2 b \left(a-b x^4\right)^2}+\frac{x \left(7 (11 b c-a g)+12 x (5 b d-a h)+15 x^2 (3 b e-a i)\right)}{384 a^3 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+a g+b c+b f x^3\right)}{12 a b \left(a-b x^4\right)^3}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{7 \sqrt{b} (11 b c-a g)}{\sqrt{a}}-5 (3 b e-a i)\right)}{256 a^{13/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{7 \sqrt{b} (11 b c-a g)}{\sqrt{a}}-5 a i+15 b e\right)}{256 a^{13/4} b^{7/4}}+\frac{(5 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}+\frac{x \left(2 x (5 b d-a h)+3 x^2 (3 b e-a i)-a g+11 b c\right)+8 a f}{96 a^2 b \left(a-b x^4\right)^2}+\frac{x \left(7 (11 b c-a g)+12 x (5 b d-a h)+15 x^2 (3 b e-a i)\right)}{384 a^3 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+a g+b c+b f x^3\right)}{12 a b \left(a-b x^4\right)^3}",1,"(x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + b*f*x^3))/(12*a*b*(a - b*x^4)^3) + (x*(7*(11*b*c - a*g) + 12*(5*b*d - a*h)*x + 15*(3*b*e - a*i)*x^2))/(384*a^3*b*(a - b*x^4)) + (8*a*f + x*(11*b*c - a*g + 2*(5*b*d - a*h)*x + 3*(3*b*e - a*i)*x^2))/(96*a^2*b*(a - b*x^4)^2) + (((7*Sqrt[b]*(11*b*c - a*g))/Sqrt[a] - 5*(3*b*e - a*i))*ArcTan[(b^(1/4)*x)/a^(1/4)])/(256*a^(13/4)*b^(7/4)) + ((15*b*e + (7*Sqrt[b]*(11*b*c - a*g))/Sqrt[a] - 5*a*i)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(256*a^(13/4)*b^(7/4)) + ((5*b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*b^(3/2))","A",10,8,41,0.1951,1,"{1858, 1854, 1855, 1876, 275, 208, 1167, 205}"
206,1,349,0,0.5238315,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6+j x^7}{\left(a-b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a - b*x^4)^4,x]","\frac{x \left(b (11 b c-a g)+2 b x (5 b d-a h)+3 b x^2 (3 b e-a i)\right)+4 a (2 b f-a j)}{96 a^2 b^2 \left(a-b x^4\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{7 \sqrt{b} (11 b c-a g)}{\sqrt{a}}-5 (3 b e-a i)\right)}{256 a^{13/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{7 \sqrt{b} (11 b c-a g)}{\sqrt{a}}-5 a i+15 b e\right)}{256 a^{13/4} b^{7/4}}+\frac{(5 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}+\frac{x \left(7 (11 b c-a g)+12 x (5 b d-a h)+15 x^2 (3 b e-a i)\right)}{384 a^3 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+x^3 (a j+b f)+a g+b c\right)}{12 a b \left(a-b x^4\right)^3}","\frac{x \left(b (11 b c-a g)+2 b x (5 b d-a h)+3 b x^2 (3 b e-a i)\right)+4 a (2 b f-a j)}{96 a^2 b^2 \left(a-b x^4\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{7 \sqrt{b} (11 b c-a g)}{\sqrt{a}}-5 (3 b e-a i)\right)}{256 a^{13/4} b^{7/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(\frac{7 \sqrt{b} (11 b c-a g)}{\sqrt{a}}-5 a i+15 b e\right)}{256 a^{13/4} b^{7/4}}+\frac{(5 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}+\frac{x \left(7 (11 b c-a g)+12 x (5 b d-a h)+15 x^2 (3 b e-a i)\right)}{384 a^3 b \left(a-b x^4\right)}+\frac{x \left(x (a h+b d)+x^2 (a i+b e)+x^3 (a j+b f)+a g+b c\right)}{12 a b \left(a-b x^4\right)^3}",1,"(x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + (b*f + a*j)*x^3))/(12*a*b*(a - b*x^4)^3) + (x*(7*(11*b*c - a*g) + 12*(5*b*d - a*h)*x + 15*(3*b*e - a*i)*x^2))/(384*a^3*b*(a - b*x^4)) + (4*a*(2*b*f - a*j) + x*(b*(11*b*c - a*g) + 2*b*(5*b*d - a*h)*x + 3*b*(3*b*e - a*i)*x^2))/(96*a^2*b^2*(a - b*x^4)^2) + (((7*Sqrt[b]*(11*b*c - a*g))/Sqrt[a] - 5*(3*b*e - a*i))*ArcTan[(b^(1/4)*x)/a^(1/4)])/(256*a^(13/4)*b^(7/4)) + ((15*b*e + (7*Sqrt[b]*(11*b*c - a*g))/Sqrt[a] - 5*a*i)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(256*a^(13/4)*b^(7/4)) + ((5*b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*b^(3/2))","A",10,8,46,0.1739,1,"{1858, 1854, 1855, 1876, 275, 208, 1167, 205}"
207,1,462,0,0.6186922,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{\left(a+b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4)^4,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{512 \sqrt{2} a^{15/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{512 \sqrt{2} a^{15/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{256 \sqrt{2} a^{15/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{256 \sqrt{2} a^{15/4} b^{5/4}}+\frac{(a h+5 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}-\frac{8 a f-x \left(2 x (a h+5 b d)+a g+11 b c+9 b e x^2\right)}{96 a^2 b \left(a+b x^4\right)^2}+\frac{x \left(7 (a g+11 b c)+12 x (a h+5 b d)+45 b e x^2\right)}{384 a^3 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)-a g+b c+b e x^2+b f x^3\right)}{12 a b \left(a+b x^4\right)^3}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{512 \sqrt{2} a^{15/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(-15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{512 \sqrt{2} a^{15/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{256 \sqrt{2} a^{15/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(15 \sqrt{a} \sqrt{b} e+7 a g+77 b c\right)}{256 \sqrt{2} a^{15/4} b^{5/4}}+\frac{(a h+5 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}-\frac{8 a f-x \left(2 x (a h+5 b d)+a g+11 b c+9 b e x^2\right)}{96 a^2 b \left(a+b x^4\right)^2}+\frac{x \left(7 (a g+11 b c)+12 x (a h+5 b d)+45 b e x^2\right)}{384 a^3 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)-a g+b c+b e x^2+b f x^3\right)}{12 a b \left(a+b x^4\right)^3}",1,"(x*(b*c - a*g + (b*d - a*h)*x + b*e*x^2 + b*f*x^3))/(12*a*b*(a + b*x^4)^3) + (x*(7*(11*b*c + a*g) + 12*(5*b*d + a*h)*x + 45*b*e*x^2))/(384*a^3*b*(a + b*x^4)) - (8*a*f - x*(11*b*c + a*g + 2*(5*b*d + a*h)*x + 9*b*e*x^2))/(96*a^2*b*(a + b*x^4)^2) + ((5*b*d + a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*b^(3/2)) - ((77*b*c + 15*Sqrt[a]*Sqrt[b]*e + 7*a*g)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(5/4)) + ((77*b*c + 15*Sqrt[a]*Sqrt[b]*e + 7*a*g)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(5/4)) - ((77*b*c - 15*Sqrt[a]*Sqrt[b]*e + 7*a*g)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(5/4)) + ((77*b*c - 15*Sqrt[a]*Sqrt[b]*e + 7*a*g)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(5/4))","A",16,12,35,0.3429,1,"{1858, 1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
208,1,516,0,0.8500281,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6}{\left(a+b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4)^4,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(7 \sqrt{b} (a g+11 b c)-5 \sqrt{a} (a i+3 b e)\right)}{512 \sqrt{2} a^{15/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(7 \sqrt{b} (a g+11 b c)-5 \sqrt{a} (a i+3 b e)\right)}{512 \sqrt{2} a^{15/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(7 \sqrt{b} (a g+11 b c)+5 \sqrt{a} (a i+3 b e)\right)}{256 \sqrt{2} a^{15/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(7 \sqrt{b} (a g+11 b c)+5 \sqrt{a} (a i+3 b e)\right)}{256 \sqrt{2} a^{15/4} b^{7/4}}+\frac{(a h+5 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}-\frac{8 a f-x \left(2 x (a h+5 b d)+3 x^2 (a i+3 b e)+a g+11 b c\right)}{96 a^2 b \left(a+b x^4\right)^2}+\frac{x \left(7 (a g+11 b c)+12 x (a h+5 b d)+15 x^2 (a i+3 b e)\right)}{384 a^3 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)-a g+b c+b f x^3\right)}{12 a b \left(a+b x^4\right)^3}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(7 \sqrt{b} (a g+11 b c)-5 \sqrt{a} (a i+3 b e)\right)}{512 \sqrt{2} a^{15/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(7 \sqrt{b} (a g+11 b c)-5 \sqrt{a} (a i+3 b e)\right)}{512 \sqrt{2} a^{15/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(7 \sqrt{b} (a g+11 b c)+5 \sqrt{a} (a i+3 b e)\right)}{256 \sqrt{2} a^{15/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(7 \sqrt{b} (a g+11 b c)+5 \sqrt{a} (a i+3 b e)\right)}{256 \sqrt{2} a^{15/4} b^{7/4}}+\frac{(a h+5 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}-\frac{8 a f-x \left(2 x (a h+5 b d)+3 x^2 (a i+3 b e)+a g+11 b c\right)}{96 a^2 b \left(a+b x^4\right)^2}+\frac{x \left(7 (a g+11 b c)+12 x (a h+5 b d)+15 x^2 (a i+3 b e)\right)}{384 a^3 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)-a g+b c+b f x^3\right)}{12 a b \left(a+b x^4\right)^3}",1,"(x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + b*f*x^3))/(12*a*b*(a + b*x^4)^3) + (x*(7*(11*b*c + a*g) + 12*(5*b*d + a*h)*x + 15*(3*b*e + a*i)*x^2))/(384*a^3*b*(a + b*x^4)) - (8*a*f - x*(11*b*c + a*g + 2*(5*b*d + a*h)*x + 3*(3*b*e + a*i)*x^2))/(96*a^2*b*(a + b*x^4)^2) + ((5*b*d + a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*b^(3/2)) - ((7*Sqrt[b]*(11*b*c + a*g) + 5*Sqrt[a]*(3*b*e + a*i))*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(7/4)) + ((7*Sqrt[b]*(11*b*c + a*g) + 5*Sqrt[a]*(3*b*e + a*i))*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(7/4)) - ((7*Sqrt[b]*(11*b*c + a*g) - 5*Sqrt[a]*(3*b*e + a*i))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(7/4)) + ((7*Sqrt[b]*(11*b*c + a*g) - 5*Sqrt[a]*(3*b*e + a*i))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(7/4))","A",16,12,40,0.3000,1,"{1858, 1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
209,1,534,0,0.8241889,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6+j x^7}{\left(a+b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a + b*x^4)^4,x]","-\frac{4 a (a j+2 b f)-x \left(b (a g+11 b c)+2 b x (a h+5 b d)+3 b x^2 (a i+3 b e)\right)}{96 a^2 b^2 \left(a+b x^4\right)^2}-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(7 \sqrt{b} (a g+11 b c)-5 \sqrt{a} (a i+3 b e)\right)}{512 \sqrt{2} a^{15/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(7 \sqrt{b} (a g+11 b c)-5 \sqrt{a} (a i+3 b e)\right)}{512 \sqrt{2} a^{15/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(7 \sqrt{b} (a g+11 b c)+5 \sqrt{a} (a i+3 b e)\right)}{256 \sqrt{2} a^{15/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(7 \sqrt{b} (a g+11 b c)+5 \sqrt{a} (a i+3 b e)\right)}{256 \sqrt{2} a^{15/4} b^{7/4}}+\frac{(a h+5 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}+\frac{x \left(7 (a g+11 b c)+12 x (a h+5 b d)+15 x^2 (a i+3 b e)\right)}{384 a^3 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)+x^3 (b f-a j)-a g+b c\right)}{12 a b \left(a+b x^4\right)^3}","-\frac{4 a (a j+2 b f)-x \left(b (a g+11 b c)+2 b x (a h+5 b d)+3 b x^2 (a i+3 b e)\right)}{96 a^2 b^2 \left(a+b x^4\right)^2}-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(7 \sqrt{b} (a g+11 b c)-5 \sqrt{a} (a i+3 b e)\right)}{512 \sqrt{2} a^{15/4} b^{7/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right) \left(7 \sqrt{b} (a g+11 b c)-5 \sqrt{a} (a i+3 b e)\right)}{512 \sqrt{2} a^{15/4} b^{7/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right) \left(7 \sqrt{b} (a g+11 b c)+5 \sqrt{a} (a i+3 b e)\right)}{256 \sqrt{2} a^{15/4} b^{7/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right) \left(7 \sqrt{b} (a g+11 b c)+5 \sqrt{a} (a i+3 b e)\right)}{256 \sqrt{2} a^{15/4} b^{7/4}}+\frac{(a h+5 b d) \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} b^{3/2}}+\frac{x \left(7 (a g+11 b c)+12 x (a h+5 b d)+15 x^2 (a i+3 b e)\right)}{384 a^3 b \left(a+b x^4\right)}+\frac{x \left(x (b d-a h)+x^2 (b e-a i)+x^3 (b f-a j)-a g+b c\right)}{12 a b \left(a+b x^4\right)^3}",1,"(x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + (b*f - a*j)*x^3))/(12*a*b*(a + b*x^4)^3) + (x*(7*(11*b*c + a*g) + 12*(5*b*d + a*h)*x + 15*(3*b*e + a*i)*x^2))/(384*a^3*b*(a + b*x^4)) - (4*a*(2*b*f + a*j) - x*(b*(11*b*c + a*g) + 2*b*(5*b*d + a*h)*x + 3*b*(3*b*e + a*i)*x^2))/(96*a^2*b^2*(a + b*x^4)^2) + ((5*b*d + a*h)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*b^(3/2)) - ((7*Sqrt[b]*(11*b*c + a*g) + 5*Sqrt[a]*(3*b*e + a*i))*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(7/4)) + ((7*Sqrt[b]*(11*b*c + a*g) + 5*Sqrt[a]*(3*b*e + a*i))*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(7/4)) - ((7*Sqrt[b]*(11*b*c + a*g) - 5*Sqrt[a]*(3*b*e + a*i))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(7/4)) + ((7*Sqrt[b]*(11*b*c + a*g) - 5*Sqrt[a]*(3*b*e + a*i))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(7/4))","A",16,12,45,0.2667,1,"{1858, 1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
210,1,121,0,0.0678343,"\int \frac{c+d x}{\sqrt{a+b x^4}} \, dx","Int[(c + d*x)/Sqrt[a + b*x^4],x]","\frac{c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}","\frac{c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}",1,"(d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*Sqrt[b]) + (c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*Sqrt[a + b*x^4])","A",6,5,17,0.2941,1,"{1885, 220, 275, 217, 206}"
211,1,87,0,0.0621967,"\int \frac{c+d x}{\sqrt{a-b x^4}} \, dx","Int[(c + d*x)/Sqrt[a - b*x^4],x]","\frac{\sqrt[4]{a} c \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{b} \sqrt{a-b x^4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}\right)}{2 \sqrt{b}}","\frac{\sqrt[4]{a} c \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{b} \sqrt{a-b x^4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}\right)}{2 \sqrt{b}}",1,"(d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a - b*x^4]])/(2*Sqrt[b]) + (a^(1/4)*c*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(b^(1/4)*Sqrt[a - b*x^4])","A",7,6,18,0.3333,1,"{1885, 224, 221, 275, 217, 203}"
212,1,89,0,0.0599722,"\int \frac{c+d x}{\sqrt{-a+b x^4}} \, dx","Int[(c + d*x)/Sqrt[-a + b*x^4],x]","\frac{\sqrt[4]{a} c \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{b} \sqrt{b x^4-a}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{b x^4-a}}\right)}{2 \sqrt{b}}","\frac{\sqrt[4]{a} c \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{b} \sqrt{b x^4-a}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{b x^4-a}}\right)}{2 \sqrt{b}}",1,"(d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[-a + b*x^4]])/(2*Sqrt[b]) + (a^(1/4)*c*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(b^(1/4)*Sqrt[-a + b*x^4])","A",7,6,19,0.3158,1,"{1885, 224, 221, 275, 217, 206}"
213,1,127,0,0.0721643,"\int \frac{c+d x}{\sqrt{-a-b x^4}} \, dx","Int[(c + d*x)/Sqrt[-a - b*x^4],x]","\frac{c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{-a-b x^4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{-a-b x^4}}\right)}{2 \sqrt{b}}","\frac{c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{-a-b x^4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{-a-b x^4}}\right)}{2 \sqrt{b}}",1,"(d*ArcTan[(Sqrt[b]*x^2)/Sqrt[-a - b*x^4]])/(2*Sqrt[b]) + (c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*Sqrt[-a - b*x^4])","A",6,5,20,0.2500,1,"{1885, 220, 275, 217, 203}"
214,1,257,0,0.1244203,"\int \frac{c+d x+e x^2}{\sqrt{a+b x^4}} \, dx","Int[(c + d*x + e*x^2)/Sqrt[a + b*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\frac{\sqrt{b} c}{\sqrt{a}}+e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}+\frac{e x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\frac{\sqrt{b} c}{\sqrt{a}}+e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}+\frac{e x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"(e*x*Sqrt[a + b*x^4])/(Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*Sqrt[b]) - (a^(1/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(b^(3/4)*Sqrt[a + b*x^4]) + (a^(1/4)*((Sqrt[b]*c)/Sqrt[a] + e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*b^(3/4)*Sqrt[a + b*x^4])","A",8,7,22,0.3182,1,"{1885, 275, 217, 206, 1198, 220, 1196}"
215,1,14,0,0.0055367,"\int \frac{a g-b g x^4}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(a*g - b*g*x^4)/(a + b*x^4)^(3/2),x]","\frac{g x}{\sqrt{a+b x^4}}","\frac{g x}{\sqrt{a+b x^4}}",1,"(g*x)/Sqrt[a + b*x^4]","A",1,1,23,0.04348,1,"{383}"
216,1,29,0,0.0230818,"\int \frac{a g+e x-b g x^4}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(a*g + e*x - b*g*x^4)/(a + b*x^4)^(3/2),x]","\frac{2 a g x+e x^2}{2 a \sqrt{a+b x^4}}","\frac{2 a g x+e x^2}{2 a \sqrt{a+b x^4}}",1,"(2*a*g*x + e*x^2)/(2*a*Sqrt[a + b*x^4])","A",1,1,26,0.03846,1,"{1856}"
217,1,25,0,0.0282155,"\int \frac{a g+f x^3-b g x^4}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(a*g + f*x^3 - b*g*x^4)/(a + b*x^4)^(3/2),x]","-\frac{f-2 b g x}{2 b \sqrt{a+b x^4}}","-\frac{f-2 b g x}{2 b \sqrt{a+b x^4}}",1,"-(f - 2*b*g*x)/(2*b*Sqrt[a + b*x^4])","A",1,1,28,0.03571,1,"{1856}"
218,1,38,0,0.0298362,"\int \frac{a g+e x+f x^3-b g x^4}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(a*g + e*x + f*x^3 - b*g*x^4)/(a + b*x^4)^(3/2),x]","-\frac{-2 a b g x+a f-b e x^2}{2 a b \sqrt{a+b x^4}}","-\frac{-2 a b g x+a f-b e x^2}{2 a b \sqrt{a+b x^4}}",1,"-(a*f - 2*a*b*g*x - b*e*x^2)/(2*a*b*Sqrt[a + b*x^4])","A",1,1,31,0.03226,1,"{1856}"
219,1,12,0,0.0031383,"\int \frac{-1+x^4}{\left(1+x^4\right)^{3/2}} \, dx","Int[(-1 + x^4)/(1 + x^4)^(3/2),x]","-\frac{x}{\sqrt{x^4+1}}","-\frac{x}{\sqrt{x^4+1}}",1,"-(x/Sqrt[1 + x^4])","A",1,1,15,0.06667,1,"{383}"
220,1,385,0,0.4237483,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5+i x^6}{\sqrt{a+b x^4}} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/Sqrt[a + b*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) \left(\frac{5 \sqrt{b} (3 b c-a g)}{\sqrt{a}}-9 a i+15 b e\right)}{30 b^{7/4} \sqrt{a+b x^4}}+\frac{(2 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}+\frac{x \sqrt{a+b x^4} (5 b e-3 a i)}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} (5 b e-3 a i) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^4}}+\frac{f \sqrt{a+b x^4}}{2 b}+\frac{g x \sqrt{a+b x^4}}{3 b}+\frac{h x^2 \sqrt{a+b x^4}}{4 b}+\frac{i x^3 \sqrt{a+b x^4}}{5 b}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) \left(\frac{5 \sqrt{b} (3 b c-a g)}{\sqrt{a}}-9 a i+15 b e\right)}{30 b^{7/4} \sqrt{a+b x^4}}+\frac{(2 b d-a h) \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}+\frac{x \sqrt{a+b x^4} (5 b e-3 a i)}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} (5 b e-3 a i) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^4}}+\frac{f \sqrt{a+b x^4}}{2 b}+\frac{g x \sqrt{a+b x^4}}{3 b}+\frac{h x^2 \sqrt{a+b x^4}}{4 b}+\frac{i x^3 \sqrt{a+b x^4}}{5 b}",1,"(f*Sqrt[a + b*x^4])/(2*b) + (g*x*Sqrt[a + b*x^4])/(3*b) + (h*x^2*Sqrt[a + b*x^4])/(4*b) + (i*x^3*Sqrt[a + b*x^4])/(5*b) + ((5*b*e - 3*a*i)*x*Sqrt[a + b*x^4])/(5*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + ((2*b*d - a*h)*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*b^(3/2)) - (a^(1/4)*(5*b*e - 3*a*i)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[a + b*x^4]) + (a^(1/4)*(15*b*e + (5*Sqrt[b]*(3*b*c - a*g))/Sqrt[a] - 9*a*i)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(30*b^(7/4)*Sqrt[a + b*x^4])","A",12,10,42,0.2381,1,"{1885, 1819, 1815, 641, 217, 206, 1888, 1198, 220, 1196}"
221,1,109,0,0.0641871,"\int \frac{1+x}{1+x^5} \, dx","Int[(1 + x)/(1 + x^5),x]","-\frac{1}{5} \sqrt[5]{-1} \left(1+\sqrt[5]{-1}\right) \log \left(\sqrt[5]{-1}-x\right)+\frac{1}{5} (-1)^{4/5} \left(1-(-1)^{4/5}\right) \log \left(-x-(-1)^{4/5}\right)+\frac{1}{5} (-1)^{2/5} \left(1-(-1)^{2/5}\right) \log \left(x+(-1)^{2/5}\right)-\frac{1}{5} (-1)^{3/5} \left(1+(-1)^{3/5}\right) \log \left(x-(-1)^{3/5}\right)","-\frac{1}{5} \sqrt[5]{-1} \left(1+\sqrt[5]{-1}\right) \log \left(\sqrt[5]{-1}-x\right)+\frac{1}{5} (-1)^{4/5} \left(1-(-1)^{4/5}\right) \log \left(-x-(-1)^{4/5}\right)+\frac{1}{5} (-1)^{2/5} \left(1-(-1)^{2/5}\right) \log \left(x+(-1)^{2/5}\right)-\frac{1}{5} (-1)^{3/5} \left(1+(-1)^{3/5}\right) \log \left(x-(-1)^{3/5}\right)",1,"-((-1)^(1/5)*(1 + (-1)^(1/5))*Log[(-1)^(1/5) - x])/5 + ((-1)^(4/5)*(1 - (-1)^(4/5))*Log[-(-1)^(4/5) - x])/5 + ((-1)^(2/5)*(1 - (-1)^(2/5))*Log[(-1)^(2/5) + x])/5 - ((-1)^(3/5)*(1 + (-1)^(3/5))*Log[-(-1)^(3/5) + x])/5","A",3,2,11,0.1818,1,"{1586, 2068}"
222,1,109,0,0.0407916,"\int \frac{1-x}{1-x^5} \, dx","Int[(1 - x)/(1 - x^5),x]","-\frac{1}{5} (-1)^{2/5} \left(1-(-1)^{2/5}\right) \log \left((-1)^{2/5}-x\right)+\frac{1}{5} (-1)^{3/5} \left(1+(-1)^{3/5}\right) \log \left(-x-(-1)^{3/5}\right)+\frac{1}{5} \sqrt[5]{-1} \left(1+\sqrt[5]{-1}\right) \log \left(x+\sqrt[5]{-1}\right)-\frac{1}{5} (-1)^{4/5} \left(1-(-1)^{4/5}\right) \log \left(x-(-1)^{4/5}\right)","-\frac{1}{5} (-1)^{2/5} \left(1-(-1)^{2/5}\right) \log \left((-1)^{2/5}-x\right)+\frac{1}{5} (-1)^{3/5} \left(1+(-1)^{3/5}\right) \log \left(-x-(-1)^{3/5}\right)+\frac{1}{5} \sqrt[5]{-1} \left(1+\sqrt[5]{-1}\right) \log \left(x+\sqrt[5]{-1}\right)-\frac{1}{5} (-1)^{4/5} \left(1-(-1)^{4/5}\right) \log \left(x-(-1)^{4/5}\right)",1,"-((-1)^(2/5)*(1 - (-1)^(2/5))*Log[(-1)^(2/5) - x])/5 + ((-1)^(3/5)*(1 + (-1)^(3/5))*Log[-(-1)^(3/5) - x])/5 + ((-1)^(1/5)*(1 + (-1)^(1/5))*Log[(-1)^(1/5) + x])/5 - ((-1)^(4/5)*(1 - (-1)^(4/5))*Log[-(-1)^(4/5) + x])/5","A",3,2,15,0.1333,1,"{1586, 2068}"
223,1,208,0,0.3156862,"\int \frac{x^{11} \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x^11*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{x^9 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{9 b^4}-\frac{a x^6 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^5}+\frac{a^2 x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^6}-\frac{a^3 \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^7}+\frac{x^{12} \left(a^2 f-a b e+b^2 d\right)}{12 b^3}+\frac{x^{15} (b e-a f)}{15 b^2}+\frac{f x^{18}}{18 b}","\frac{x^9 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{9 b^4}-\frac{a x^6 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^5}+\frac{a^2 x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^6}-\frac{a^3 \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^7}+\frac{x^{12} \left(a^2 f-a b e+b^2 d\right)}{12 b^3}+\frac{x^{15} (b e-a f)}{15 b^2}+\frac{f x^{18}}{18 b}",1,"(a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(3*b^6) - (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^6)/(6*b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^9)/(9*b^4) + ((b^2*d - a*b*e + a^2*f)*x^12)/(12*b^3) + ((b*e - a*f)*x^15)/(15*b^2) + (f*x^18)/(18*b) - (a^3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*b^7)","A",3,2,30,0.06667,1,"{1821, 1620}"
224,1,170,0,0.2423317,"\int \frac{x^8 \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x^8*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{x^6 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^4}-\frac{a x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5}+\frac{a^2 \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^6}+\frac{x^9 \left(a^2 f-a b e+b^2 d\right)}{9 b^3}+\frac{x^{12} (b e-a f)}{12 b^2}+\frac{f x^{15}}{15 b}","\frac{x^6 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^4}-\frac{a x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5}+\frac{a^2 \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^6}+\frac{x^9 \left(a^2 f-a b e+b^2 d\right)}{9 b^3}+\frac{x^{12} (b e-a f)}{12 b^2}+\frac{f x^{15}}{15 b}",1,"-(a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(3*b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^6)/(6*b^4) + ((b^2*d - a*b*e + a^2*f)*x^9)/(9*b^3) + ((b*e - a*f)*x^12)/(12*b^2) + (f*x^15)/(15*b) + (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*b^6)","A",3,2,30,0.06667,1,"{1821, 1620}"
225,1,132,0,0.1833187,"\int \frac{x^5 \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x^5*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4}-\frac{a \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5}+\frac{x^6 \left(a^2 f-a b e+b^2 d\right)}{6 b^3}+\frac{x^9 (b e-a f)}{9 b^2}+\frac{f x^{12}}{12 b}","\frac{x^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4}-\frac{a \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5}+\frac{x^6 \left(a^2 f-a b e+b^2 d\right)}{6 b^3}+\frac{x^9 (b e-a f)}{9 b^2}+\frac{f x^{12}}{12 b}",1,"((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(3*b^4) + ((b^2*d - a*b*e + a^2*f)*x^6)/(6*b^3) + ((b*e - a*f)*x^9)/(9*b^2) + (f*x^12)/(12*b) - (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*b^5)","A",3,2,30,0.06667,1,"{1821, 1620}"
226,1,96,0,0.1399117,"\int \frac{x^2 \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x^2*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4}+\frac{x^3 \left(a^2 f-a b e+b^2 d\right)}{3 b^3}+\frac{x^6 (b e-a f)}{6 b^2}+\frac{f x^9}{9 b}","\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4}+\frac{x^3 \left(a^2 f-a b e+b^2 d\right)}{3 b^3}+\frac{x^6 (b e-a f)}{6 b^2}+\frac{f x^9}{9 b}",1,"((b^2*d - a*b*e + a^2*f)*x^3)/(3*b^3) + ((b*e - a*f)*x^6)/(6*b^2) + (f*x^9)/(9*b) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*b^4)","A",3,2,30,0.06667,1,"{1819, 1850}"
227,1,80,0,0.1201134,"\int \frac{c+d x^3+e x^6+f x^9}{x \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x*(a + b*x^3)),x]","-\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a b^3}+\frac{x^3 (b e-a f)}{3 b^2}+\frac{c \log (x)}{a}+\frac{f x^6}{6 b}","-\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a b^3}+\frac{x^3 (b e-a f)}{3 b^2}+\frac{c \log (x)}{a}+\frac{f x^6}{6 b}",1,"((b*e - a*f)*x^3)/(3*b^2) + (f*x^6)/(6*b) + (c*Log[x])/a - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*a*b^3)","A",3,2,30,0.06667,1,"{1821, 1620}"
228,1,81,0,0.1161363,"\int \frac{c+d x^3+e x^6+f x^9}{x^4 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^4*(a + b*x^3)),x]","\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^2 b^2}-\frac{\log (x) (b c-a d)}{a^2}-\frac{c}{3 a x^3}+\frac{f x^3}{3 b}","\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^2 b^2}-\frac{\log (x) (b c-a d)}{a^2}-\frac{c}{3 a x^3}+\frac{f x^3}{3 b}",1,"-c/(3*a*x^3) + (f*x^3)/(3*b) - ((b*c - a*d)*Log[x])/a^2 + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*a^2*b^2)","A",3,2,30,0.06667,1,"{1821, 1620}"
229,1,95,0,0.1289755,"\int \frac{c+d x^3+e x^6+f x^9}{x^7 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^7*(a + b*x^3)),x]","-\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^3 b}+\frac{\log (x) \left(a^2 e-a b d+b^2 c\right)}{a^3}+\frac{b c-a d}{3 a^2 x^3}-\frac{c}{6 a x^6}","-\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^3 b}+\frac{\log (x) \left(a^2 e-a b d+b^2 c\right)}{a^3}+\frac{b c-a d}{3 a^2 x^3}-\frac{c}{6 a x^6}",1,"-c/(6*a*x^6) + (b*c - a*d)/(3*a^2*x^3) + ((b^2*c - a*b*d + a^2*e)*Log[x])/a^3 - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*a^3*b)","A",3,2,30,0.06667,1,"{1821, 1620}"
230,1,128,0,0.1616492,"\int \frac{c+d x^3+e x^6+f x^9}{x^{10} \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^10*(a + b*x^3)),x]","\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^4}-\frac{\log (x) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^4}-\frac{a^2 e-a b d+b^2 c}{3 a^3 x^3}+\frac{b c-a d}{6 a^2 x^6}-\frac{c}{9 a x^9}","\frac{\log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^4}-\frac{\log (x) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^4}-\frac{a^2 e-a b d+b^2 c}{3 a^3 x^3}+\frac{b c-a d}{6 a^2 x^6}-\frac{c}{9 a x^9}",1,"-c/(9*a*x^9) + (b*c - a*d)/(6*a^2*x^6) - (b^2*c - a*b*d + a^2*e)/(3*a^3*x^3) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[x])/a^4 + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*a^4)","A",3,2,30,0.06667,1,"{1821, 1620}"
231,1,164,0,0.1814388,"\int \frac{c+d x^3+e x^6+f x^9}{x^{13} \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^13*(a + b*x^3)),x]","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^4 x^3}-\frac{b \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5}+\frac{b \log (x) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^5}-\frac{a^2 e-a b d+b^2 c}{6 a^3 x^6}+\frac{b c-a d}{9 a^2 x^9}-\frac{c}{12 a x^{12}}","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^4 x^3}-\frac{b \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5}+\frac{b \log (x) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^5}-\frac{a^2 e-a b d+b^2 c}{6 a^3 x^6}+\frac{b c-a d}{9 a^2 x^9}-\frac{c}{12 a x^{12}}",1,"-c/(12*a*x^12) + (b*c - a*d)/(9*a^2*x^9) - (b^2*c - a*b*d + a^2*e)/(6*a^3*x^6) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a^4*x^3) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[x])/a^5 - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*a^5)","A",3,2,30,0.06667,1,"{1821, 1620}"
232,1,205,0,0.2088723,"\int \frac{c+d x^3+e x^6+f x^9}{x^{16} \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^16*(a + b*x^3)),x]","-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 x^3}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a^4 x^6}+\frac{b^2 \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^6}-\frac{b^2 \log (x) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^6}-\frac{a^2 e-a b d+b^2 c}{9 a^3 x^9}+\frac{b c-a d}{12 a^2 x^{12}}-\frac{c}{15 a x^{15}}","-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 x^3}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a^4 x^6}+\frac{b^2 \log \left(a+b x^3\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^6}-\frac{b^2 \log (x) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^6}-\frac{a^2 e-a b d+b^2 c}{9 a^3 x^9}+\frac{b c-a d}{12 a^2 x^{12}}-\frac{c}{15 a x^{15}}",1,"-c/(15*a*x^15) + (b*c - a*d)/(12*a^2*x^12) - (b^2*c - a*b*d + a^2*e)/(9*a^3*x^9) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a^4*x^6) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*a^5*x^3) - (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[x])/a^6 + (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*a^6)","A",3,2,30,0.06667,1,"{1821, 1620}"
233,1,348,0,0.3329086,"\int \frac{x^9 \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x^9*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{x^7 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{7 b^4}-\frac{a x^4 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 b^5}+\frac{a^{7/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{19/3}}+\frac{a^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^6}-\frac{a^{7/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{19/3}}+\frac{a^{7/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{19/3}}+\frac{x^{10} \left(a^2 f-a b e+b^2 d\right)}{10 b^3}+\frac{x^{13} (b e-a f)}{13 b^2}+\frac{f x^{16}}{16 b}","\frac{x^7 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{7 b^4}-\frac{a x^4 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 b^5}+\frac{a^{7/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{19/3}}+\frac{a^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^6}-\frac{a^{7/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{19/3}}+\frac{a^{7/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{19/3}}+\frac{x^{10} \left(a^2 f-a b e+b^2 d\right)}{10 b^3}+\frac{x^{13} (b e-a f)}{13 b^2}+\frac{f x^{16}}{16 b}",1,"(a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^6 - (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^4)/(4*b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^7)/(7*b^4) + ((b^2*d - a*b*e + a^2*f)*x^10)/(10*b^3) + ((b*e - a*f)*x^13)/(13*b^2) + (f*x^16)/(16*b) + (a^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(19/3)) - (a^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(19/3)) + (a^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(19/3))","A",9,8,30,0.2667,1,"{1836, 1488, 200, 31, 634, 617, 204, 628}"
234,1,316,0,0.3060784,"\int \frac{x^7 \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x^7*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{x^5 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{5 b^4}-\frac{a x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 b^5}+\frac{a^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{17/3}}-\frac{a^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{17/3}}-\frac{a^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{17/3}}+\frac{x^8 \left(a^2 f-a b e+b^2 d\right)}{8 b^3}+\frac{x^{11} (b e-a f)}{11 b^2}+\frac{f x^{14}}{14 b}","\frac{x^5 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{5 b^4}-\frac{a x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 b^5}+\frac{a^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{17/3}}-\frac{a^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{17/3}}-\frac{a^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{17/3}}+\frac{x^8 \left(a^2 f-a b e+b^2 d\right)}{8 b^3}+\frac{x^{11} (b e-a f)}{11 b^2}+\frac{f x^{14}}{14 b}",1,"-(a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(2*b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^5)/(5*b^4) + ((b^2*d - a*b*e + a^2*f)*x^8)/(8*b^3) + ((b*e - a*f)*x^11)/(11*b^2) + (f*x^14)/(14*b) - (a^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(17/3)) - (a^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(17/3)) + (a^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(17/3))","A",9,8,30,0.2667,1,"{1836, 1488, 292, 31, 634, 617, 204, 628}"
235,1,312,0,0.297768,"\int \frac{x^6 \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x^6*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{x^4 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 b^4}-\frac{a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{16/3}}-\frac{a x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^5}+\frac{a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{16/3}}-\frac{a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{16/3}}+\frac{x^7 \left(a^2 f-a b e+b^2 d\right)}{7 b^3}+\frac{x^{10} (b e-a f)}{10 b^2}+\frac{f x^{13}}{13 b}","\frac{x^4 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 b^4}-\frac{a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{16/3}}-\frac{a x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^5}+\frac{a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{16/3}}-\frac{a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{16/3}}+\frac{x^7 \left(a^2 f-a b e+b^2 d\right)}{7 b^3}+\frac{x^{10} (b e-a f)}{10 b^2}+\frac{f x^{13}}{13 b}",1,"-((a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^4)/(4*b^4) + ((b^2*d - a*b*e + a^2*f)*x^7)/(7*b^3) + ((b*e - a*f)*x^10)/(10*b^2) + (f*x^13)/(13*b) - (a^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(16/3)) + (a^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(16/3)) - (a^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(16/3))","A",9,8,30,0.2667,1,"{1836, 1488, 200, 31, 634, 617, 204, 628}"
236,1,279,0,0.2733382,"\int \frac{x^4 \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x^4*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 b^4}-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{14/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{14/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{14/3}}+\frac{x^5 \left(a^2 f-a b e+b^2 d\right)}{5 b^3}+\frac{x^8 (b e-a f)}{8 b^2}+\frac{f x^{11}}{11 b}","\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 b^4}-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{14/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{14/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{14/3}}+\frac{x^5 \left(a^2 f-a b e+b^2 d\right)}{5 b^3}+\frac{x^8 (b e-a f)}{8 b^2}+\frac{f x^{11}}{11 b}",1,"((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(2*b^4) + ((b^2*d - a*b*e + a^2*f)*x^5)/(5*b^3) + ((b*e - a*f)*x^8)/(8*b^2) + (f*x^11)/(11*b) + (a^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(14/3)) + (a^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(14/3)) - (a^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(14/3))","A",9,8,30,0.2667,1,"{1836, 1488, 292, 31, 634, 617, 204, 628}"
237,1,274,0,0.2672203,"\int \frac{x^3 \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x^3*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{13/3}}+\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{13/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{13/3}}+\frac{x^4 \left(a^2 f-a b e+b^2 d\right)}{4 b^3}+\frac{x^7 (b e-a f)}{7 b^2}+\frac{f x^{10}}{10 b}","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^{13/3}}+\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{b^4}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^{13/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} b^{13/3}}+\frac{x^4 \left(a^2 f-a b e+b^2 d\right)}{4 b^3}+\frac{x^7 (b e-a f)}{7 b^2}+\frac{f x^{10}}{10 b}",1,"((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^4 + ((b^2*d - a*b*e + a^2*f)*x^4)/(4*b^3) + ((b*e - a*f)*x^7)/(7*b^2) + (f*x^10)/(10*b) + (a^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(13/3)) - (a^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(13/3)) + (a^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(13/3))","A",9,8,30,0.2667,1,"{1836, 1488, 200, 31, 634, 617, 204, 628}"
238,1,245,0,0.2155671,"\int \frac{x \left(c+d x^3+e x^6+f x^9\right)}{a+b x^3} \, dx","Int[(x*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 \sqrt[3]{a} b^{11/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 \sqrt[3]{a} b^{11/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} \sqrt[3]{a} b^{11/3}}+\frac{x^2 \left(a^2 f-a b e+b^2 d\right)}{2 b^3}+\frac{x^5 (b e-a f)}{5 b^2}+\frac{f x^8}{8 b}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 \sqrt[3]{a} b^{11/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 \sqrt[3]{a} b^{11/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} \sqrt[3]{a} b^{11/3}}+\frac{x^2 \left(a^2 f-a b e+b^2 d\right)}{2 b^3}+\frac{x^5 (b e-a f)}{5 b^2}+\frac{f x^8}{8 b}",1,"((b^2*d - a*b*e + a^2*f)*x^2)/(2*b^3) + ((b*e - a*f)*x^5)/(5*b^2) + (f*x^8)/(8*b) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b^(11/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(1/3)*b^(11/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(1/3)*b^(11/3))","A",9,8,28,0.2857,1,"{1836, 1488, 292, 31, 634, 617, 204, 628}"
239,1,240,0,0.1526893,"\int \frac{c+d x^3+e x^6+f x^9}{a+b x^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{2/3} b^{10/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{2/3} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{2/3} b^{10/3}}+\frac{x \left(a^2 f-a b e+b^2 d\right)}{b^3}+\frac{x^4 (b e-a f)}{4 b^2}+\frac{f x^7}{7 b}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{2/3} b^{10/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{2/3} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{2/3} b^{10/3}}+\frac{x \left(a^2 f-a b e+b^2 d\right)}{b^3}+\frac{x^4 (b e-a f)}{4 b^2}+\frac{f x^7}{7 b}",1,"((b^2*d - a*b*e + a^2*f)*x)/b^3 + ((b*e - a*f)*x^4)/(4*b^2) + (f*x^7)/(7*b) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(10/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(10/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(10/3))","A",8,7,27,0.2593,1,"{1887, 200, 31, 634, 617, 204, 628}"
240,1,227,0,0.1926119,"\int \frac{c+d x^3+e x^6+f x^9}{x^2 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^2*(a + b*x^3)),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{4/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{4/3} b^{8/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{4/3} b^{8/3}}+\frac{x^2 (b e-a f)}{2 b^2}-\frac{c}{a x}+\frac{f x^5}{5 b}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{4/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{4/3} b^{8/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{4/3} b^{8/3}}+\frac{x^2 (b e-a f)}{2 b^2}-\frac{c}{a x}+\frac{f x^5}{5 b}",1,"-(c/(a*x)) + ((b*e - a*f)*x^2)/(2*b^2) + (f*x^5)/(5*b) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*b^(8/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(4/3)*b^(8/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(4/3)*b^(8/3))","A",8,7,30,0.2333,1,"{1834, 292, 31, 634, 617, 204, 628}"
241,1,224,0,0.1698222,"\int \frac{c+d x^3+e x^6+f x^9}{x^3 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^3*(a + b*x^3)),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{5/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{5/3} b^{7/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{5/3} b^{7/3}}+\frac{x (b e-a f)}{b^2}-\frac{c}{2 a x^2}+\frac{f x^4}{4 b}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{5/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{5/3} b^{7/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{5/3} b^{7/3}}+\frac{x (b e-a f)}{b^2}-\frac{c}{2 a x^2}+\frac{f x^4}{4 b}",1,"-c/(2*a*x^2) + ((b*e - a*f)*x)/b^2 + (f*x^4)/(4*b) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*b^(7/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(5/3)*b^(7/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3)*b^(7/3))","A",8,7,30,0.2333,1,"{1834, 200, 31, 634, 617, 204, 628}"
242,1,227,0,0.1857033,"\int \frac{c+d x^3+e x^6+f x^9}{x^5 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^5*(a + b*x^3)),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{7/3} b^{5/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{7/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{7/3} b^{5/3}}+\frac{b c-a d}{a^2 x}-\frac{c}{4 a x^4}+\frac{f x^2}{2 b}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{7/3} b^{5/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{7/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{7/3} b^{5/3}}+\frac{b c-a d}{a^2 x}-\frac{c}{4 a x^4}+\frac{f x^2}{2 b}",1,"-c/(4*a*x^4) + (b*c - a*d)/(a^2*x) + (f*x^2)/(2*b) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)*b^(5/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(7/3)*b^(5/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(7/3)*b^(5/3))","A",8,7,30,0.2333,1,"{1834, 292, 31, 634, 617, 204, 628}"
243,1,225,0,0.1697741,"\int \frac{c+d x^3+e x^6+f x^9}{x^6 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^6*(a + b*x^3)),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{8/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{8/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{8/3} b^{4/3}}+\frac{b c-a d}{2 a^2 x^2}-\frac{c}{5 a x^5}+\frac{f x}{b}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{8/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{8/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{8/3} b^{4/3}}+\frac{b c-a d}{2 a^2 x^2}-\frac{c}{5 a x^5}+\frac{f x}{b}",1,"-c/(5*a*x^5) + (b*c - a*d)/(2*a^2*x^2) + (f*x)/b - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(8/3)*b^(4/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(8/3)*b^(4/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(8/3)*b^(4/3))","A",8,7,30,0.2333,1,"{1834, 200, 31, 634, 617, 204, 628}"
244,1,242,0,0.1879635,"\int \frac{c+d x^3+e x^6+f x^9}{x^8 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^8*(a + b*x^3)),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{10/3} b^{2/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{10/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{10/3} b^{2/3}}-\frac{a^2 e-a b d+b^2 c}{a^3 x}+\frac{b c-a d}{4 a^2 x^4}-\frac{c}{7 a x^7}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{10/3} b^{2/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{10/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{10/3} b^{2/3}}-\frac{a^2 e-a b d+b^2 c}{a^3 x}+\frac{b c-a d}{4 a^2 x^4}-\frac{c}{7 a x^7}",1,"-c/(7*a*x^7) + (b*c - a*d)/(4*a^2*x^4) - (b^2*c - a*b*d + a^2*e)/(a^3*x) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(10/3)*b^(2/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(10/3)*b^(2/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(10/3)*b^(2/3))","A",8,7,30,0.2333,1,"{1834, 292, 31, 634, 617, 204, 628}"
245,1,244,0,0.1740325,"\int \frac{c+d x^3+e x^6+f x^9}{x^9 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^9*(a + b*x^3)),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{11/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{11/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{11/3} \sqrt[3]{b}}-\frac{a^2 e-a b d+b^2 c}{2 a^3 x^2}+\frac{b c-a d}{5 a^2 x^5}-\frac{c}{8 a x^8}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{11/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{11/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{11/3} \sqrt[3]{b}}-\frac{a^2 e-a b d+b^2 c}{2 a^3 x^2}+\frac{b c-a d}{5 a^2 x^5}-\frac{c}{8 a x^8}",1,"-c/(8*a*x^8) + (b*c - a*d)/(5*a^2*x^5) - (b^2*c - a*b*d + a^2*e)/(2*a^3*x^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(11/3)*b^(1/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(11/3)*b^(1/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(11/3)*b^(1/3))","A",8,7,30,0.2333,1,"{1834, 200, 31, 634, 617, 204, 628}"
246,1,277,0,0.2224777,"\int \frac{c+d x^3+e x^6+f x^9}{x^{11} \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^11*(a + b*x^3)),x]","\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{13/3}}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{a^4 x}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{13/3}}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{13/3}}-\frac{a^2 e-a b d+b^2 c}{4 a^3 x^4}+\frac{b c-a d}{7 a^2 x^7}-\frac{c}{10 a x^{10}}","\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{13/3}}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{a^4 x}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{13/3}}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{13/3}}-\frac{a^2 e-a b d+b^2 c}{4 a^3 x^4}+\frac{b c-a d}{7 a^2 x^7}-\frac{c}{10 a x^{10}}",1,"-c/(10*a*x^10) + (b*c - a*d)/(7*a^2*x^7) - (b^2*c - a*b*d + a^2*e)/(4*a^3*x^4) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(a^4*x) - (b^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(13/3)) - (b^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(13/3)) + (b^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(13/3))","A",8,7,30,0.2333,1,"{1834, 292, 31, 634, 617, 204, 628}"
247,1,280,0,0.1993539,"\int \frac{c+d x^3+e x^6+f x^9}{x^{12} \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^12*(a + b*x^3)),x]","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{2 a^4 x^2}-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{14/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{14/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{14/3}}-\frac{a^2 e-a b d+b^2 c}{5 a^3 x^5}+\frac{b c-a d}{8 a^2 x^8}-\frac{c}{11 a x^{11}}","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{2 a^4 x^2}-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{14/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{14/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{14/3}}-\frac{a^2 e-a b d+b^2 c}{5 a^3 x^5}+\frac{b c-a d}{8 a^2 x^8}-\frac{c}{11 a x^{11}}",1,"-c/(11*a*x^11) + (b*c - a*d)/(8*a^2*x^8) - (b^2*c - a*b*d + a^2*e)/(5*a^3*x^5) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(2*a^4*x^2) - (b^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(14/3)) + (b^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(14/3)) - (b^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(14/3))","A",8,7,30,0.2333,1,"{1834, 200, 31, 634, 617, 204, 628}"
248,1,313,0,0.2382356,"\int \frac{c+d x^3+e x^6+f x^9}{x^{14} \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^14*(a + b*x^3)),x]","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{4 a^4 x^4}-\frac{b^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{16/3}}-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^5 x}+\frac{b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{16/3}}+\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{16/3}}-\frac{a^2 e-a b d+b^2 c}{7 a^3 x^7}+\frac{b c-a d}{10 a^2 x^{10}}-\frac{c}{13 a x^{13}}","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{4 a^4 x^4}-\frac{b^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{16/3}}-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^5 x}+\frac{b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{16/3}}+\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{16/3}}-\frac{a^2 e-a b d+b^2 c}{7 a^3 x^7}+\frac{b c-a d}{10 a^2 x^{10}}-\frac{c}{13 a x^{13}}",1,"-c/(13*a*x^13) + (b*c - a*d)/(10*a^2*x^10) - (b^2*c - a*b*d + a^2*e)/(7*a^3*x^7) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(4*a^4*x^4) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(a^5*x) + (b^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(16/3)) + (b^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(16/3)) - (b^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(16/3))","A",8,7,30,0.2333,1,"{1834, 292, 31, 634, 617, 204, 628}"
249,1,315,0,0.2289946,"\int \frac{c+d x^3+e x^6+f x^9}{x^{15} \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^15*(a + b*x^3)),x]","-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 a^5 x^2}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{5 a^4 x^5}+\frac{b^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{17/3}}-\frac{b^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{17/3}}+\frac{b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{17/3}}-\frac{a^2 e-a b d+b^2 c}{8 a^3 x^8}+\frac{b c-a d}{11 a^2 x^{11}}-\frac{c}{14 a x^{14}}","-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{2 a^5 x^2}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{5 a^4 x^5}+\frac{b^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{17/3}}-\frac{b^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{17/3}}+\frac{b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{17/3}}-\frac{a^2 e-a b d+b^2 c}{8 a^3 x^8}+\frac{b c-a d}{11 a^2 x^{11}}-\frac{c}{14 a x^{14}}",1,"-c/(14*a*x^14) + (b*c - a*d)/(11*a^2*x^11) - (b^2*c - a*b*d + a^2*e)/(8*a^3*x^8) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(5*a^4*x^5) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(2*a^5*x^2) + (b^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(17/3)) - (b^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(17/3)) + (b^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(17/3))","A",8,7,30,0.2333,1,"{1834, 200, 31, 634, 617, 204, 628}"
250,1,351,0,0.2578107,"\int \frac{c+d x^3+e x^6+f x^9}{x^{17} \left(a+b x^3\right)} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^17*(a + b*x^3)),x]","-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 a^5 x^4}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{7 a^4 x^7}+\frac{b^{7/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{19/3}}+\frac{b^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^6 x}-\frac{b^{7/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{19/3}}-\frac{b^{7/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{19/3}}-\frac{a^2 e-a b d+b^2 c}{10 a^3 x^{10}}+\frac{b c-a d}{13 a^2 x^{13}}-\frac{c}{16 a x^{16}}","-\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{4 a^5 x^4}+\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{7 a^4 x^7}+\frac{b^{7/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^{19/3}}+\frac{b^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{a^6 x}-\frac{b^{7/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^{19/3}}-\frac{b^{7/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{\sqrt{3} a^{19/3}}-\frac{a^2 e-a b d+b^2 c}{10 a^3 x^{10}}+\frac{b c-a d}{13 a^2 x^{13}}-\frac{c}{16 a x^{16}}",1,"-c/(16*a*x^16) + (b*c - a*d)/(13*a^2*x^13) - (b^2*c - a*b*d + a^2*e)/(10*a^3*x^10) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(7*a^4*x^7) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(4*a^5*x^4) + (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(a^6*x) - (b^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(19/3)) - (b^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(19/3)) + (b^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(19/3))","A",8,7,30,0.2333,1,"{1834, 292, 31, 634, 617, 204, 628}"
251,1,220,0,0.3411784,"\int \frac{x^{11} \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^11*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","\frac{x^6 \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{6 b^5}-\frac{a x^3 \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6}+\frac{a^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^7 \left(a+b x^3\right)}+\frac{a^2 \log \left(a+b x^3\right) \left(5 a^2 b e-6 a^3 f-4 a b^2 d+3 b^3 c\right)}{3 b^7}+\frac{x^9 \left(3 a^2 f-2 a b e+b^2 d\right)}{9 b^4}+\frac{x^{12} (b e-2 a f)}{12 b^3}+\frac{f x^{15}}{15 b^2}","\frac{x^6 \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{6 b^5}-\frac{a x^3 \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6}+\frac{a^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^7 \left(a+b x^3\right)}+\frac{a^2 \log \left(a+b x^3\right) \left(5 a^2 b e-6 a^3 f-4 a b^2 d+3 b^3 c\right)}{3 b^7}+\frac{x^9 \left(3 a^2 f-2 a b e+b^2 d\right)}{9 b^4}+\frac{x^{12} (b e-2 a f)}{12 b^3}+\frac{f x^{15}}{15 b^2}",1,"-(a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f)*x^3)/(3*b^6) + ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^6)/(6*b^5) + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^9)/(9*b^4) + ((b*e - 2*a*f)*x^12)/(12*b^3) + (f*x^15)/(15*b^2) + (a^3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*b^7*(a + b*x^3)) + (a^2*(3*b^3*c - 4*a*b^2*d + 5*a^2*b*e - 6*a^3*f)*Log[a + b*x^3])/(3*b^7)","A",3,2,30,0.06667,1,"{1821, 1620}"
252,1,180,0,0.2647704,"\int \frac{x^8 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^8*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","\frac{x^3 \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{3 b^5}-\frac{a^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^6 \left(a+b x^3\right)}-\frac{a \log \left(a+b x^3\right) \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6}+\frac{x^6 \left(3 a^2 f-2 a b e+b^2 d\right)}{6 b^4}+\frac{x^9 (b e-2 a f)}{9 b^3}+\frac{f x^{12}}{12 b^2}","\frac{x^3 \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{3 b^5}-\frac{a^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^6 \left(a+b x^3\right)}-\frac{a \log \left(a+b x^3\right) \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6}+\frac{x^6 \left(3 a^2 f-2 a b e+b^2 d\right)}{6 b^4}+\frac{x^9 (b e-2 a f)}{9 b^3}+\frac{f x^{12}}{12 b^2}",1,"((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^3)/(3*b^5) + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^6)/(6*b^4) + ((b*e - 2*a*f)*x^9)/(9*b^3) + (f*x^12)/(12*b^2) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*b^6*(a + b*x^3)) - (a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f)*Log[a + b*x^3])/(3*b^6)","A",3,2,30,0.06667,1,"{1821, 1620}"
253,1,140,0,0.1994167,"\int \frac{x^5 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^5*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","\frac{a \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right) \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{3 b^5}+\frac{x^3 \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{x^6 (b e-2 a f)}{6 b^3}+\frac{f x^9}{9 b^2}","\frac{a \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right) \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{3 b^5}+\frac{x^3 \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{x^6 (b e-2 a f)}{6 b^3}+\frac{f x^9}{9 b^2}",1,"((b^2*d - 2*a*b*e + 3*a^2*f)*x^3)/(3*b^4) + ((b*e - 2*a*f)*x^6)/(6*b^3) + (f*x^9)/(9*b^2) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*b^5*(a + b*x^3)) + ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*Log[a + b*x^3])/(3*b^5)","A",3,2,30,0.06667,1,"{1821, 1620}"
254,1,103,0,0.1451196,"\int \frac{x^2 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^2*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 b^4 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right) \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{x^3 (b e-2 a f)}{3 b^3}+\frac{f x^6}{6 b^2}","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 b^4 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right) \left(3 a^2 f-2 a b e+b^2 d\right)}{3 b^4}+\frac{x^3 (b e-2 a f)}{3 b^3}+\frac{f x^6}{6 b^2}",1,"((b*e - 2*a*f)*x^3)/(3*b^3) + (f*x^6)/(6*b^2) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*b^4*(a + b*x^3)) + ((b^2*d - 2*a*b*e + 3*a^2*f)*Log[a + b*x^3])/(3*b^4)","A",3,2,30,0.06667,1,"{1819, 1850}"
255,1,100,0,0.1253022,"\int \frac{c+d x^3+e x^6+f x^9}{x \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x*(a + b*x^3)^2),x]","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a b^3 \left(a+b x^3\right)}-\frac{\log \left(a+b x^3\right) \left(-a^2 b e+2 a^3 f+b^3 c\right)}{3 a^2 b^3}+\frac{c \log (x)}{a^2}+\frac{f x^3}{3 b^2}","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a b^3 \left(a+b x^3\right)}-\frac{\log \left(a+b x^3\right) \left(-a^2 b e+2 a^3 f+b^3 c\right)}{3 a^2 b^3}+\frac{c \log (x)}{a^2}+\frac{f x^3}{3 b^2}",1,"(f*x^3)/(3*b^2) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a*b^3*(a + b*x^3)) + (c*Log[x])/a^2 - ((b^3*c - a^2*b*e + 2*a^3*f)*Log[a + b*x^3])/(3*a^2*b^3)","A",3,2,30,0.06667,1,"{1821, 1620}"
256,1,109,0,0.1421597,"\int \frac{c+d x^3+e x^6+f x^9}{x^4 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^4*(a + b*x^3)^2),x]","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^2 b^2 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right) \left(a^3 f-a b^2 d+2 b^3 c\right)}{3 a^3 b^2}-\frac{\log (x) (2 b c-a d)}{a^3}-\frac{c}{3 a^2 x^3}","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^2 b^2 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right) \left(a^3 f-a b^2 d+2 b^3 c\right)}{3 a^3 b^2}-\frac{\log (x) (2 b c-a d)}{a^3}-\frac{c}{3 a^2 x^3}",1,"-c/(3*a^2*x^3) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a^2*b^2*(a + b*x^3)) - ((2*b*c - a*d)*Log[x])/a^3 + ((2*b^3*c - a*b^2*d + a^3*f)*Log[a + b*x^3])/(3*a^3*b^2)","A",3,2,30,0.06667,1,"{1821, 1620}"
257,1,130,0,0.1538378,"\int \frac{c+d x^3+e x^6+f x^9}{x^7 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^7*(a + b*x^3)^2),x]","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^3 b \left(a+b x^3\right)}-\frac{\log \left(a+b x^3\right) \left(a^2 e-2 a b d+3 b^2 c\right)}{3 a^4}+\frac{\log (x) \left(a^2 e-2 a b d+3 b^2 c\right)}{a^4}+\frac{2 b c-a d}{3 a^3 x^3}-\frac{c}{6 a^2 x^6}","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^3 b \left(a+b x^3\right)}-\frac{\log \left(a+b x^3\right) \left(a^2 e-2 a b d+3 b^2 c\right)}{3 a^4}+\frac{\log (x) \left(a^2 e-2 a b d+3 b^2 c\right)}{a^4}+\frac{2 b c-a d}{3 a^3 x^3}-\frac{c}{6 a^2 x^6}",1,"-c/(6*a^2*x^6) + (2*b*c - a*d)/(3*a^3*x^3) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a^3*b*(a + b*x^3)) + ((3*b^2*c - 2*a*b*d + a^2*e)*Log[x])/a^4 - ((3*b^2*c - 2*a*b*d + a^2*e)*Log[a + b*x^3])/(3*a^4)","A",3,2,30,0.06667,1,"{1821, 1620}"
258,1,175,0,0.2025406,"\int \frac{c+d x^3+e x^6+f x^9}{x^{10} \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^10*(a + b*x^3)^2),x]","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^4 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right) \left(2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c\right)}{3 a^5}-\frac{\log (x) \left(2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c\right)}{a^5}-\frac{a^2 e-2 a b d+3 b^2 c}{3 a^4 x^3}+\frac{2 b c-a d}{6 a^3 x^6}-\frac{c}{9 a^2 x^9}","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{3 a^4 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right) \left(2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c\right)}{3 a^5}-\frac{\log (x) \left(2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c\right)}{a^5}-\frac{a^2 e-2 a b d+3 b^2 c}{3 a^4 x^3}+\frac{2 b c-a d}{6 a^3 x^6}-\frac{c}{9 a^2 x^9}",1,"-c/(9*a^2*x^9) + (2*b*c - a*d)/(6*a^3*x^6) - (3*b^2*c - 2*a*b*d + a^2*e)/(3*a^4*x^3) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a^4*(a + b*x^3)) - ((4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)*Log[x])/a^5 + ((4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*a^5)","A",3,2,30,0.06667,1,"{1821, 1620}"
259,1,214,0,0.2339973,"\int \frac{c+d x^3+e x^6+f x^9}{x^{13} \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^13*(a + b*x^3)^2),x]","\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 \left(a+b x^3\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{3 a^5 x^3}-\frac{b \log \left(a+b x^3\right) \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{3 a^6}+\frac{b \log (x) \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{a^6}-\frac{a^2 e-2 a b d+3 b^2 c}{6 a^4 x^6}+\frac{2 b c-a d}{9 a^3 x^9}-\frac{c}{12 a^2 x^{12}}","\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 \left(a+b x^3\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{3 a^5 x^3}-\frac{b \log \left(a+b x^3\right) \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{3 a^6}+\frac{b \log (x) \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{a^6}-\frac{a^2 e-2 a b d+3 b^2 c}{6 a^4 x^6}+\frac{2 b c-a d}{9 a^3 x^9}-\frac{c}{12 a^2 x^{12}}",1,"-c/(12*a^2*x^12) + (2*b*c - a*d)/(9*a^3*x^9) - (3*b^2*c - 2*a*b*d + a^2*e)/(6*a^4*x^6) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(3*a^5*x^3) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*a^5*(a + b*x^3)) + (b*(5*b^3*c - 4*a*b^2*d + 3*a^2*b*e - 2*a^3*f)*Log[x])/a^6 - (b*(5*b^3*c - 4*a*b^2*d + 3*a^2*b*e - 2*a^3*f)*Log[a + b*x^3])/(3*a^6)","A",3,2,30,0.06667,1,"{1821, 1620}"
260,1,369,0,0.4670514,"\int \frac{x^9 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^9*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","\frac{x^4 \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{4 b^5}-\frac{a^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^6 \left(a+b x^3\right)}-\frac{a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right)}{18 b^{19/3}}-\frac{a x \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{b^6}+\frac{a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right)}{9 b^{19/3}}-\frac{a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right)}{3 \sqrt{3} b^{19/3}}+\frac{x^7 \left(3 a^2 f-2 a b e+b^2 d\right)}{7 b^4}+\frac{x^{10} (b e-2 a f)}{10 b^3}+\frac{f x^{13}}{13 b^2}","\frac{x^4 \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{4 b^5}-\frac{a^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^6 \left(a+b x^3\right)}-\frac{a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right)}{18 b^{19/3}}-\frac{a x \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{b^6}+\frac{a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right)}{9 b^{19/3}}-\frac{a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right)}{3 \sqrt{3} b^{19/3}}+\frac{x^7 \left(3 a^2 f-2 a b e+b^2 d\right)}{7 b^4}+\frac{x^{10} (b e-2 a f)}{10 b^3}+\frac{f x^{13}}{13 b^2}",1,"-((a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f)*x)/b^6) + ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^4)/(4*b^5) + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^7)/(7*b^4) + ((b*e - 2*a*f)*x^10)/(10*b^3) + (f*x^13)/(13*b^2) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*b^6*(a + b*x^3)) - (a^(4/3)*(7*b^3*c - 10*a*b^2*d + 13*a^2*b*e - 16*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*b^(19/3)) + (a^(4/3)*(7*b^3*c - 10*a*b^2*d + 13*a^2*b*e - 16*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*b^(19/3)) - (a^(4/3)*(7*b^3*c - 10*a*b^2*d + 13*a^2*b*e - 16*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*b^(19/3))","A",9,8,30,0.2667,1,"{1828, 1887, 200, 31, 634, 617, 204, 628}"
261,1,335,0,0.7050222,"\int \frac{x^7 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^7*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","\frac{x^2 \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{2 b^5}+\frac{a x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5 \left(a+b x^3\right)}-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(11 a^2 b e-14 a^3 f-8 a b^2 d+5 b^3 c\right)}{18 b^{17/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(11 a^2 b e-14 a^3 f-8 a b^2 d+5 b^3 c\right)}{9 b^{17/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(11 a^2 b e-14 a^3 f-8 a b^2 d+5 b^3 c\right)}{3 \sqrt{3} b^{17/3}}+\frac{x^5 \left(3 a^2 f-2 a b e+b^2 d\right)}{5 b^4}+\frac{x^8 (b e-2 a f)}{8 b^3}+\frac{f x^{11}}{11 b^2}","\frac{x^2 \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{2 b^5}+\frac{a x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5 \left(a+b x^3\right)}-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(11 a^2 b e-14 a^3 f-8 a b^2 d+5 b^3 c\right)}{18 b^{17/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(11 a^2 b e-14 a^3 f-8 a b^2 d+5 b^3 c\right)}{9 b^{17/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(11 a^2 b e-14 a^3 f-8 a b^2 d+5 b^3 c\right)}{3 \sqrt{3} b^{17/3}}+\frac{x^5 \left(3 a^2 f-2 a b e+b^2 d\right)}{5 b^4}+\frac{x^8 (b e-2 a f)}{8 b^3}+\frac{f x^{11}}{11 b^2}",1,"((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^2)/(2*b^5) + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^5)/(5*b^4) + ((b*e - 2*a*f)*x^8)/(8*b^3) + (f*x^11)/(11*b^2) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*b^5*(a + b*x^3)) + (a^(2/3)*(5*b^3*c - 8*a*b^2*d + 11*a^2*b*e - 14*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*b^(17/3)) + (a^(2/3)*(5*b^3*c - 8*a*b^2*d + 11*a^2*b*e - 14*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*b^(17/3)) - (a^(2/3)*(5*b^3*c - 8*a*b^2*d + 11*a^2*b*e - 14*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*b^(17/3))","A",12,10,30,0.3333,1,"{1828, 1851, 1836, 1488, 292, 31, 634, 617, 204, 628}"
262,1,328,0,0.3688646,"\int \frac{x^6 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^6*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","\frac{a x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5 \left(a+b x^3\right)}+\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(10 a^2 b e-13 a^3 f-7 a b^2 d+4 b^3 c\right)}{18 b^{16/3}}+\frac{x \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{b^5}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(10 a^2 b e-13 a^3 f-7 a b^2 d+4 b^3 c\right)}{9 b^{16/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(10 a^2 b e-13 a^3 f-7 a b^2 d+4 b^3 c\right)}{3 \sqrt{3} b^{16/3}}+\frac{x^4 \left(3 a^2 f-2 a b e+b^2 d\right)}{4 b^4}+\frac{x^7 (b e-2 a f)}{7 b^3}+\frac{f x^{10}}{10 b^2}","\frac{a x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^5 \left(a+b x^3\right)}+\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(10 a^2 b e-13 a^3 f-7 a b^2 d+4 b^3 c\right)}{18 b^{16/3}}+\frac{x \left(3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c\right)}{b^5}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(10 a^2 b e-13 a^3 f-7 a b^2 d+4 b^3 c\right)}{9 b^{16/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(10 a^2 b e-13 a^3 f-7 a b^2 d+4 b^3 c\right)}{3 \sqrt{3} b^{16/3}}+\frac{x^4 \left(3 a^2 f-2 a b e+b^2 d\right)}{4 b^4}+\frac{x^7 (b e-2 a f)}{7 b^3}+\frac{f x^{10}}{10 b^2}",1,"((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x)/b^5 + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^4)/(4*b^4) + ((b*e - 2*a*f)*x^7)/(7*b^3) + (f*x^10)/(10*b^2) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*b^5*(a + b*x^3)) + (a^(1/3)*(4*b^3*c - 7*a*b^2*d + 10*a^2*b*e - 13*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*b^(16/3)) - (a^(1/3)*(4*b^3*c - 7*a*b^2*d + 10*a^2*b*e - 13*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*b^(16/3)) + (a^(1/3)*(4*b^3*c - 7*a*b^2*d + 10*a^2*b*e - 13*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*b^(16/3))","A",9,8,30,0.2667,1,"{1828, 1887, 200, 31, 634, 617, 204, 628}"
263,1,298,0,0.4626765,"\int \frac{x^4 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^4*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(8 a^2 b e-11 a^3 f-5 a b^2 d+2 b^3 c\right)}{18 \sqrt[3]{a} b^{14/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(8 a^2 b e-11 a^3 f-5 a b^2 d+2 b^3 c\right)}{9 \sqrt[3]{a} b^{14/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(8 a^2 b e-11 a^3 f-5 a b^2 d+2 b^3 c\right)}{3 \sqrt{3} \sqrt[3]{a} b^{14/3}}+\frac{x^2 \left(3 a^2 f-2 a b e+b^2 d\right)}{2 b^4}+\frac{x^5 (b e-2 a f)}{5 b^3}+\frac{f x^8}{8 b^2}","-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(8 a^2 b e-11 a^3 f-5 a b^2 d+2 b^3 c\right)}{18 \sqrt[3]{a} b^{14/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(8 a^2 b e-11 a^3 f-5 a b^2 d+2 b^3 c\right)}{9 \sqrt[3]{a} b^{14/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(8 a^2 b e-11 a^3 f-5 a b^2 d+2 b^3 c\right)}{3 \sqrt{3} \sqrt[3]{a} b^{14/3}}+\frac{x^2 \left(3 a^2 f-2 a b e+b^2 d\right)}{2 b^4}+\frac{x^5 (b e-2 a f)}{5 b^3}+\frac{f x^8}{8 b^2}",1,"((b^2*d - 2*a*b*e + 3*a^2*f)*x^2)/(2*b^4) + ((b*e - 2*a*f)*x^5)/(5*b^3) + (f*x^8)/(8*b^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*b^4*(a + b*x^3)) - ((2*b^3*c - 5*a*b^2*d + 8*a^2*b*e - 11*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(1/3)*b^(14/3)) - ((2*b^3*c - 5*a*b^2*d + 8*a^2*b*e - 11*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(1/3)*b^(14/3)) + ((2*b^3*c - 5*a*b^2*d + 8*a^2*b*e - 11*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(1/3)*b^(14/3))","A",11,10,30,0.3333,1,"{1828, 1851, 1836, 1488, 292, 31, 634, 617, 204, 628}"
264,1,288,0,0.3256103,"\int \frac{x^3 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^3*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(7 a^2 b e-10 a^3 f-4 a b^2 d+b^3 c\right)}{18 a^{2/3} b^{13/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(7 a^2 b e-10 a^3 f-4 a b^2 d+b^3 c\right)}{9 a^{2/3} b^{13/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(7 a^2 b e-10 a^3 f-4 a b^2 d+b^3 c\right)}{3 \sqrt{3} a^{2/3} b^{13/3}}+\frac{x \left(3 a^2 f-2 a b e+b^2 d\right)}{b^4}+\frac{x^4 (b e-2 a f)}{4 b^3}+\frac{f x^7}{7 b^2}","-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 b^4 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(7 a^2 b e-10 a^3 f-4 a b^2 d+b^3 c\right)}{18 a^{2/3} b^{13/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(7 a^2 b e-10 a^3 f-4 a b^2 d+b^3 c\right)}{9 a^{2/3} b^{13/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(7 a^2 b e-10 a^3 f-4 a b^2 d+b^3 c\right)}{3 \sqrt{3} a^{2/3} b^{13/3}}+\frac{x \left(3 a^2 f-2 a b e+b^2 d\right)}{b^4}+\frac{x^4 (b e-2 a f)}{4 b^3}+\frac{f x^7}{7 b^2}",1,"((b^2*d - 2*a*b*e + 3*a^2*f)*x)/b^4 + ((b*e - 2*a*f)*x^4)/(4*b^3) + (f*x^7)/(7*b^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*b^4*(a + b*x^3)) - ((b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)*b^(13/3)) + ((b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(2/3)*b^(13/3)) - ((b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(2/3)*b^(13/3))","A",9,8,30,0.2667,1,"{1828, 1887, 200, 31, 634, 617, 204, 628}"
265,1,271,0,0.2893885,"\int \frac{x \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x]","\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a b^3 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-5 a^2 b e+8 a^3 f+2 a b^2 d+b^3 c\right)}{18 a^{4/3} b^{11/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-5 a^2 b e+8 a^3 f+2 a b^2 d+b^3 c\right)}{9 a^{4/3} b^{11/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-5 a^2 b e+8 a^3 f+2 a b^2 d+b^3 c\right)}{3 \sqrt{3} a^{4/3} b^{11/3}}+\frac{x^2 (b e-2 a f)}{2 b^3}+\frac{f x^5}{5 b^2}","\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a b^3 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-5 a^2 b e+8 a^3 f+2 a b^2 d+b^3 c\right)}{18 a^{4/3} b^{11/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-5 a^2 b e+8 a^3 f+2 a b^2 d+b^3 c\right)}{9 a^{4/3} b^{11/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-5 a^2 b e+8 a^3 f+2 a b^2 d+b^3 c\right)}{3 \sqrt{3} a^{4/3} b^{11/3}}+\frac{x^2 (b e-2 a f)}{2 b^3}+\frac{f x^5}{5 b^2}",1,"((b*e - 2*a*f)*x^2)/(2*b^3) + (f*x^5)/(5*b^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a*b^3*(a + b*x^3)) - ((b^3*c + 2*a*b^2*d - 5*a^2*b*e + 8*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)*b^(11/3)) - ((b^3*c + 2*a*b^2*d - 5*a^2*b*e + 8*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(4/3)*b^(11/3)) + ((b^3*c + 2*a*b^2*d - 5*a^2*b*e + 8*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(4/3)*b^(11/3))","A",10,9,28,0.3214,1,"{1828, 1594, 1488, 292, 31, 634, 617, 204, 628}"
266,1,264,0,0.2641585,"\int \frac{c+d x^3+e x^6+f x^9}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2,x]","\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a b^3 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-4 a^2 b e+7 a^3 f+a b^2 d+2 b^3 c\right)}{18 a^{5/3} b^{10/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-4 a^2 b e+7 a^3 f+a b^2 d+2 b^3 c\right)}{9 a^{5/3} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-4 a^2 b e+7 a^3 f+a b^2 d+2 b^3 c\right)}{3 \sqrt{3} a^{5/3} b^{10/3}}+\frac{x (b e-2 a f)}{b^3}+\frac{f x^4}{4 b^2}","\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a b^3 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-4 a^2 b e+7 a^3 f+a b^2 d+2 b^3 c\right)}{18 a^{5/3} b^{10/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-4 a^2 b e+7 a^3 f+a b^2 d+2 b^3 c\right)}{9 a^{5/3} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-4 a^2 b e+7 a^3 f+a b^2 d+2 b^3 c\right)}{3 \sqrt{3} a^{5/3} b^{10/3}}+\frac{x (b e-2 a f)}{b^3}+\frac{f x^4}{4 b^2}",1,"((b*e - 2*a*f)*x)/b^3 + (f*x^4)/(4*b^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a*b^3*(a + b*x^3)) - ((2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(10/3)) + ((2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(10/3)) - ((2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(10/3))","A",9,9,27,0.3333,1,"{1858, 1411, 388, 200, 31, 634, 617, 204, 628}"
267,1,265,0,0.2534829,"\int \frac{c+d x^3+e x^6+f x^9}{x^2 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^2*(a + b*x^3)^2),x]","-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^2 b^2 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-2 a^2 b e+5 a^3 f-a b^2 d+4 b^3 c\right)}{18 a^{7/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-2 a^2 b e+5 a^3 f-a b^2 d+4 b^3 c\right)}{9 a^{7/3} b^{8/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-2 a^2 b e+5 a^3 f-a b^2 d+4 b^3 c\right)}{3 \sqrt{3} a^{7/3} b^{8/3}}-\frac{c}{a^2 x}+\frac{f x^2}{2 b^2}","-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^2 b^2 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-2 a^2 b e+5 a^3 f-a b^2 d+4 b^3 c\right)}{18 a^{7/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-2 a^2 b e+5 a^3 f-a b^2 d+4 b^3 c\right)}{9 a^{7/3} b^{8/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-2 a^2 b e+5 a^3 f-a b^2 d+4 b^3 c\right)}{3 \sqrt{3} a^{7/3} b^{8/3}}-\frac{c}{a^2 x}+\frac{f x^2}{2 b^2}",1,"-(c/(a^2*x)) + (f*x^2)/(2*b^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^2*b^2*(a + b*x^3)) + ((4*b^3*c - a*b^2*d - 2*a^2*b*e + 5*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)*b^(8/3)) + ((4*b^3*c - a*b^2*d - 2*a^2*b*e + 5*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(7/3)*b^(8/3)) - ((4*b^3*c - a*b^2*d - 2*a^2*b*e + 5*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(7/3)*b^(8/3))","A",9,8,30,0.2667,1,"{1829, 1488, 292, 31, 634, 617, 204, 628}"
268,1,260,0,0.2462168,"\int \frac{c+d x^3+e x^6+f x^9}{x^3 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^3*(a + b*x^3)^2),x]","-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^2 b^2 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-a^2 b e+4 a^3 f-2 a b^2 d+5 b^3 c\right)}{18 a^{8/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-a^2 b e+4 a^3 f-2 a b^2 d+5 b^3 c\right)}{9 a^{8/3} b^{7/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^2 b e+4 a^3 f-2 a b^2 d+5 b^3 c\right)}{3 \sqrt{3} a^{8/3} b^{7/3}}-\frac{c}{2 a^2 x^2}+\frac{f x}{b^2}","-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^2 b^2 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-a^2 b e+4 a^3 f-2 a b^2 d+5 b^3 c\right)}{18 a^{8/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-a^2 b e+4 a^3 f-2 a b^2 d+5 b^3 c\right)}{9 a^{8/3} b^{7/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^2 b e+4 a^3 f-2 a b^2 d+5 b^3 c\right)}{3 \sqrt{3} a^{8/3} b^{7/3}}-\frac{c}{2 a^2 x^2}+\frac{f x}{b^2}",1,"-c/(2*a^2*x^2) + (f*x)/b^2 - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a^2*b^2*(a + b*x^3)) + ((5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)*b^(7/3)) - ((5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(8/3)*b^(7/3)) + ((5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(8/3)*b^(7/3))","A",9,8,30,0.2667,1,"{1829, 1488, 200, 31, 634, 617, 204, 628}"
269,1,269,0,0.2880552,"\int \frac{c+d x^3+e x^6+f x^9}{x^5 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^5*(a + b*x^3)^2),x]","\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^3 b \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+2 a^3 f-4 a b^2 d+7 b^3 c\right)}{18 a^{10/3} b^{5/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+2 a^3 f-4 a b^2 d+7 b^3 c\right)}{9 a^{10/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+2 a^3 f-4 a b^2 d+7 b^3 c\right)}{3 \sqrt{3} a^{10/3} b^{5/3}}+\frac{2 b c-a d}{a^3 x}-\frac{c}{4 a^2 x^4}","\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^3 b \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^2 b e+2 a^3 f-4 a b^2 d+7 b^3 c\right)}{18 a^{10/3} b^{5/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^2 b e+2 a^3 f-4 a b^2 d+7 b^3 c\right)}{9 a^{10/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^2 b e+2 a^3 f-4 a b^2 d+7 b^3 c\right)}{3 \sqrt{3} a^{10/3} b^{5/3}}+\frac{2 b c-a d}{a^3 x}-\frac{c}{4 a^2 x^4}",1,"-c/(4*a^2*x^4) + (2*b*c - a*d)/(a^3*x) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^3*b*(a + b*x^3)) - ((7*b^3*c - 4*a*b^2*d + a^2*b*e + 2*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(10/3)*b^(5/3)) - ((7*b^3*c - 4*a*b^2*d + a^2*b*e + 2*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(10/3)*b^(5/3)) + ((7*b^3*c - 4*a*b^2*d + a^2*b*e + 2*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(10/3)*b^(5/3))","A",9,8,30,0.2667,1,"{1829, 1488, 292, 31, 634, 617, 204, 628}"
270,1,270,0,0.2724296,"\int \frac{c+d x^3+e x^6+f x^9}{x^6 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^6*(a + b*x^3)^2),x]","\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^3 b \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(2 a^2 b e+a^3 f-5 a b^2 d+8 b^3 c\right)}{18 a^{11/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(2 a^2 b e+a^3 f-5 a b^2 d+8 b^3 c\right)}{9 a^{11/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^2 b e+a^3 f-5 a b^2 d+8 b^3 c\right)}{3 \sqrt{3} a^{11/3} b^{4/3}}+\frac{2 b c-a d}{2 a^3 x^2}-\frac{c}{5 a^2 x^5}","\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^3 b \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(2 a^2 b e+a^3 f-5 a b^2 d+8 b^3 c\right)}{18 a^{11/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(2 a^2 b e+a^3 f-5 a b^2 d+8 b^3 c\right)}{9 a^{11/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^2 b e+a^3 f-5 a b^2 d+8 b^3 c\right)}{3 \sqrt{3} a^{11/3} b^{4/3}}+\frac{2 b c-a d}{2 a^3 x^2}-\frac{c}{5 a^2 x^5}",1,"-c/(5*a^2*x^5) + (2*b*c - a*d)/(2*a^3*x^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a^3*b*(a + b*x^3)) - ((8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(11/3)*b^(4/3)) + ((8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(11/3)*b^(4/3)) - ((8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(11/3)*b^(4/3))","A",9,8,30,0.2667,1,"{1829, 1488, 200, 31, 634, 617, 204, 628}"
271,1,297,0,0.3835724,"\int \frac{c+d x^3+e x^6+f x^9}{x^8 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^8*(a + b*x^3)^2),x]","-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^4 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(4 a^2 b e+a^3 (-f)-7 a b^2 d+10 b^3 c\right)}{18 a^{13/3} b^{2/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(4 a^2 b e+a^3 (-f)-7 a b^2 d+10 b^3 c\right)}{9 a^{13/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(4 a^2 b e+a^3 (-f)-7 a b^2 d+10 b^3 c\right)}{3 \sqrt{3} a^{13/3} b^{2/3}}-\frac{a^2 e-2 a b d+3 b^2 c}{a^4 x}+\frac{2 b c-a d}{4 a^3 x^4}-\frac{c}{7 a^2 x^7}","-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^4 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(4 a^2 b e+a^3 (-f)-7 a b^2 d+10 b^3 c\right)}{18 a^{13/3} b^{2/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(4 a^2 b e+a^3 (-f)-7 a b^2 d+10 b^3 c\right)}{9 a^{13/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(4 a^2 b e+a^3 (-f)-7 a b^2 d+10 b^3 c\right)}{3 \sqrt{3} a^{13/3} b^{2/3}}-\frac{a^2 e-2 a b d+3 b^2 c}{a^4 x}+\frac{2 b c-a d}{4 a^3 x^4}-\frac{c}{7 a^2 x^7}",1,"-c/(7*a^2*x^7) + (2*b*c - a*d)/(4*a^3*x^4) - (3*b^2*c - 2*a*b*d + a^2*e)/(a^4*x) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^4*(a + b*x^3)) + ((10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(13/3)*b^(2/3)) + ((10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(13/3)*b^(2/3)) - ((10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(13/3)*b^(2/3))","A",9,8,30,0.2667,1,"{1829, 1834, 292, 31, 634, 617, 204, 628}"
272,1,297,0,0.3699522,"\int \frac{c+d x^3+e x^6+f x^9}{x^9 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^9*(a + b*x^3)^2),x]","-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^4 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(5 a^2 b e-2 a^3 f-8 a b^2 d+11 b^3 c\right)}{18 a^{14/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 a^2 b e-2 a^3 f-8 a b^2 d+11 b^3 c\right)}{9 a^{14/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^2 b e-2 a^3 f-8 a b^2 d+11 b^3 c\right)}{3 \sqrt{3} a^{14/3} \sqrt[3]{b}}-\frac{a^2 e-2 a b d+3 b^2 c}{2 a^4 x^2}+\frac{2 b c-a d}{5 a^3 x^5}-\frac{c}{8 a^2 x^8}","-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^4 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(5 a^2 b e-2 a^3 f-8 a b^2 d+11 b^3 c\right)}{18 a^{14/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 a^2 b e-2 a^3 f-8 a b^2 d+11 b^3 c\right)}{9 a^{14/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^2 b e-2 a^3 f-8 a b^2 d+11 b^3 c\right)}{3 \sqrt{3} a^{14/3} \sqrt[3]{b}}-\frac{a^2 e-2 a b d+3 b^2 c}{2 a^4 x^2}+\frac{2 b c-a d}{5 a^3 x^5}-\frac{c}{8 a^2 x^8}",1,"-c/(8*a^2*x^8) + (2*b*c - a*d)/(5*a^3*x^5) - (3*b^2*c - 2*a*b*d + a^2*e)/(2*a^4*x^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a^4*(a + b*x^3)) + ((11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(14/3)*b^(1/3)) - ((11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(14/3)*b^(1/3)) + ((11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(14/3)*b^(1/3))","A",9,8,30,0.2667,1,"{1829, 1834, 200, 31, 634, 617, 204, 628}"
273,1,334,0,0.4567391,"\int \frac{c+d x^3+e x^6+f x^9}{x^{11} \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^11*(a + b*x^3)^2),x]","\frac{b x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 \left(a+b x^3\right)}+\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(7 a^2 b e-4 a^3 f-10 a b^2 d+13 b^3 c\right)}{18 a^{16/3}}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{a^5 x}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(7 a^2 b e-4 a^3 f-10 a b^2 d+13 b^3 c\right)}{9 a^{16/3}}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(7 a^2 b e-4 a^3 f-10 a b^2 d+13 b^3 c\right)}{3 \sqrt{3} a^{16/3}}-\frac{a^2 e-2 a b d+3 b^2 c}{4 a^4 x^4}+\frac{2 b c-a d}{7 a^3 x^7}-\frac{c}{10 a^2 x^{10}}","\frac{b x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 \left(a+b x^3\right)}+\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(7 a^2 b e-4 a^3 f-10 a b^2 d+13 b^3 c\right)}{18 a^{16/3}}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{a^5 x}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(7 a^2 b e-4 a^3 f-10 a b^2 d+13 b^3 c\right)}{9 a^{16/3}}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(7 a^2 b e-4 a^3 f-10 a b^2 d+13 b^3 c\right)}{3 \sqrt{3} a^{16/3}}-\frac{a^2 e-2 a b d+3 b^2 c}{4 a^4 x^4}+\frac{2 b c-a d}{7 a^3 x^7}-\frac{c}{10 a^2 x^{10}}",1,"-c/(10*a^2*x^10) + (2*b*c - a*d)/(7*a^3*x^7) - (3*b^2*c - 2*a*b*d + a^2*e)/(4*a^4*x^4) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(a^5*x) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^5*(a + b*x^3)) - (b^(1/3)*(13*b^3*c - 10*a*b^2*d + 7*a^2*b*e - 4*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(16/3)) - (b^(1/3)*(13*b^3*c - 10*a*b^2*d + 7*a^2*b*e - 4*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(16/3)) + (b^(1/3)*(13*b^3*c - 10*a*b^2*d + 7*a^2*b*e - 4*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(16/3))","A",9,8,30,0.2667,1,"{1829, 1834, 292, 31, 634, 617, 204, 628}"
274,1,335,0,0.4341954,"\int \frac{c+d x^3+e x^6+f x^9}{x^{12} \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^12*(a + b*x^3)^2),x]","\frac{b x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 \left(a+b x^3\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{2 a^5 x^2}-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(8 a^2 b e-5 a^3 f-11 a b^2 d+14 b^3 c\right)}{18 a^{17/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(8 a^2 b e-5 a^3 f-11 a b^2 d+14 b^3 c\right)}{9 a^{17/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(8 a^2 b e-5 a^3 f-11 a b^2 d+14 b^3 c\right)}{3 \sqrt{3} a^{17/3}}-\frac{a^2 e-2 a b d+3 b^2 c}{5 a^4 x^5}+\frac{2 b c-a d}{8 a^3 x^8}-\frac{c}{11 a^2 x^{11}}","\frac{b x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^5 \left(a+b x^3\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{2 a^5 x^2}-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(8 a^2 b e-5 a^3 f-11 a b^2 d+14 b^3 c\right)}{18 a^{17/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(8 a^2 b e-5 a^3 f-11 a b^2 d+14 b^3 c\right)}{9 a^{17/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(8 a^2 b e-5 a^3 f-11 a b^2 d+14 b^3 c\right)}{3 \sqrt{3} a^{17/3}}-\frac{a^2 e-2 a b d+3 b^2 c}{5 a^4 x^5}+\frac{2 b c-a d}{8 a^3 x^8}-\frac{c}{11 a^2 x^{11}}",1,"-c/(11*a^2*x^11) + (2*b*c - a*d)/(8*a^3*x^8) - (3*b^2*c - 2*a*b*d + a^2*e)/(5*a^4*x^5) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(2*a^5*x^2) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a^5*(a + b*x^3)) - (b^(2/3)*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(17/3)) + (b^(2/3)*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(17/3)) - (b^(2/3)*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(17/3))","A",9,8,30,0.2667,1,"{1829, 1834, 200, 31, 634, 617, 204, 628}"
275,1,375,0,0.5335455,"\int \frac{c+d x^3+e x^6+f x^9}{x^{14} \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^14*(a + b*x^3)^2),x]","-\frac{b^2 x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^6 \left(a+b x^3\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{4 a^5 x^4}-\frac{b^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(10 a^2 b e-7 a^3 f-13 a b^2 d+16 b^3 c\right)}{18 a^{19/3}}-\frac{b \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{a^6 x}+\frac{b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(10 a^2 b e-7 a^3 f-13 a b^2 d+16 b^3 c\right)}{9 a^{19/3}}+\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(10 a^2 b e-7 a^3 f-13 a b^2 d+16 b^3 c\right)}{3 \sqrt{3} a^{19/3}}-\frac{a^2 e-2 a b d+3 b^2 c}{7 a^4 x^7}+\frac{2 b c-a d}{10 a^3 x^{10}}-\frac{c}{13 a^2 x^{13}}","-\frac{b^2 x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{3 a^6 \left(a+b x^3\right)}+\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{4 a^5 x^4}-\frac{b^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(10 a^2 b e-7 a^3 f-13 a b^2 d+16 b^3 c\right)}{18 a^{19/3}}-\frac{b \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{a^6 x}+\frac{b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(10 a^2 b e-7 a^3 f-13 a b^2 d+16 b^3 c\right)}{9 a^{19/3}}+\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(10 a^2 b e-7 a^3 f-13 a b^2 d+16 b^3 c\right)}{3 \sqrt{3} a^{19/3}}-\frac{a^2 e-2 a b d+3 b^2 c}{7 a^4 x^7}+\frac{2 b c-a d}{10 a^3 x^{10}}-\frac{c}{13 a^2 x^{13}}",1,"-c/(13*a^2*x^13) + (2*b*c - a*d)/(10*a^3*x^10) - (3*b^2*c - 2*a*b*d + a^2*e)/(7*a^4*x^7) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(4*a^5*x^4) - (b*(5*b^3*c - 4*a*b^2*d + 3*a^2*b*e - 2*a^3*f))/(a^6*x) - (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^6*(a + b*x^3)) + (b^(4/3)*(16*b^3*c - 13*a*b^2*d + 10*a^2*b*e - 7*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(19/3)) + (b^(4/3)*(16*b^3*c - 13*a*b^2*d + 10*a^2*b*e - 7*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(19/3)) - (b^(4/3)*(16*b^3*c - 13*a*b^2*d + 10*a^2*b*e - 7*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(19/3))","A",9,8,30,0.2667,1,"{1829, 1834, 292, 31, 634, 617, 204, 628}"
276,1,266,0,0.4360414,"\int \frac{x^{14} \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^14*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","\frac{x^6 \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{6 b^6}-\frac{a x^3 \left(10 a^2 b e-15 a^3 f-6 a b^2 d+3 b^3 c\right)}{3 b^7}+\frac{a^3 \left(6 a^2 b e-7 a^3 f-5 a b^2 d+4 b^3 c\right)}{3 b^8 \left(a+b x^3\right)}-\frac{a^4 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^8 \left(a+b x^3\right)^2}+\frac{a^2 \log \left(a+b x^3\right) \left(15 a^2 b e-21 a^3 f-10 a b^2 d+6 b^3 c\right)}{3 b^8}+\frac{x^9 \left(6 a^2 f-3 a b e+b^2 d\right)}{9 b^5}+\frac{x^{12} (b e-3 a f)}{12 b^4}+\frac{f x^{15}}{15 b^3}","\frac{x^6 \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{6 b^6}-\frac{a x^3 \left(10 a^2 b e-15 a^3 f-6 a b^2 d+3 b^3 c\right)}{3 b^7}+\frac{a^3 \left(6 a^2 b e-7 a^3 f-5 a b^2 d+4 b^3 c\right)}{3 b^8 \left(a+b x^3\right)}-\frac{a^4 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^8 \left(a+b x^3\right)^2}+\frac{a^2 \log \left(a+b x^3\right) \left(15 a^2 b e-21 a^3 f-10 a b^2 d+6 b^3 c\right)}{3 b^8}+\frac{x^9 \left(6 a^2 f-3 a b e+b^2 d\right)}{9 b^5}+\frac{x^{12} (b e-3 a f)}{12 b^4}+\frac{f x^{15}}{15 b^3}",1,"-(a*(3*b^3*c - 6*a*b^2*d + 10*a^2*b*e - 15*a^3*f)*x^3)/(3*b^7) + ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^6)/(6*b^6) + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^9)/(9*b^5) + ((b*e - 3*a*f)*x^12)/(12*b^4) + (f*x^15)/(15*b^3) - (a^4*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*b^8*(a + b*x^3)^2) + (a^3*(4*b^3*c - 5*a*b^2*d + 6*a^2*b*e - 7*a^3*f))/(3*b^8*(a + b*x^3)) + (a^2*(6*b^3*c - 10*a*b^2*d + 15*a^2*b*e - 21*a^3*f)*Log[a + b*x^3])/(3*b^8)","A",3,2,30,0.06667,1,"{1821, 1620}"
277,1,226,0,0.3306785,"\int \frac{x^{11} \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^11*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","\frac{x^3 \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{3 b^6}-\frac{a^2 \left(5 a^2 b e-6 a^3 f-4 a b^2 d+3 b^3 c\right)}{3 b^7 \left(a+b x^3\right)}+\frac{a^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^7 \left(a+b x^3\right)^2}-\frac{a \log \left(a+b x^3\right) \left(10 a^2 b e-15 a^3 f-6 a b^2 d+3 b^3 c\right)}{3 b^7}+\frac{x^6 \left(6 a^2 f-3 a b e+b^2 d\right)}{6 b^5}+\frac{x^9 (b e-3 a f)}{9 b^4}+\frac{f x^{12}}{12 b^3}","\frac{x^3 \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{3 b^6}-\frac{a^2 \left(5 a^2 b e-6 a^3 f-4 a b^2 d+3 b^3 c\right)}{3 b^7 \left(a+b x^3\right)}+\frac{a^3 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^7 \left(a+b x^3\right)^2}-\frac{a \log \left(a+b x^3\right) \left(10 a^2 b e-15 a^3 f-6 a b^2 d+3 b^3 c\right)}{3 b^7}+\frac{x^6 \left(6 a^2 f-3 a b e+b^2 d\right)}{6 b^5}+\frac{x^9 (b e-3 a f)}{9 b^4}+\frac{f x^{12}}{12 b^3}",1,"((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^3)/(3*b^6) + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^6)/(6*b^5) + ((b*e - 3*a*f)*x^9)/(9*b^4) + (f*x^12)/(12*b^3) + (a^3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*b^7*(a + b*x^3)^2) - (a^2*(3*b^3*c - 4*a*b^2*d + 5*a^2*b*e - 6*a^3*f))/(3*b^7*(a + b*x^3)) - (a*(3*b^3*c - 6*a*b^2*d + 10*a^2*b*e - 15*a^3*f)*Log[a + b*x^3])/(3*b^7)","A",3,2,30,0.06667,1,"{1821, 1620}"
278,1,186,0,0.2689364,"\int \frac{x^8 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^8*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","\frac{a \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6 \left(a+b x^3\right)}-\frac{a^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^6 \left(a+b x^3\right)^2}+\frac{\log \left(a+b x^3\right) \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{3 b^6}+\frac{x^3 \left(6 a^2 f-3 a b e+b^2 d\right)}{3 b^5}+\frac{x^6 (b e-3 a f)}{6 b^4}+\frac{f x^9}{9 b^3}","\frac{a \left(4 a^2 b e-5 a^3 f-3 a b^2 d+2 b^3 c\right)}{3 b^6 \left(a+b x^3\right)}-\frac{a^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^6 \left(a+b x^3\right)^2}+\frac{\log \left(a+b x^3\right) \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{3 b^6}+\frac{x^3 \left(6 a^2 f-3 a b e+b^2 d\right)}{3 b^5}+\frac{x^6 (b e-3 a f)}{6 b^4}+\frac{f x^9}{9 b^3}",1,"((b^2*d - 3*a*b*e + 6*a^2*f)*x^3)/(3*b^5) + ((b*e - 3*a*f)*x^6)/(6*b^4) + (f*x^9)/(9*b^3) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*b^6*(a + b*x^3)^2) + (a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f))/(3*b^6*(a + b*x^3)) + ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*Log[a + b*x^3])/(3*b^6)","A",3,2,30,0.06667,1,"{1821, 1620}"
279,1,146,0,0.2009946,"\int \frac{x^5 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^5*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","-\frac{3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c}{3 b^5 \left(a+b x^3\right)}+\frac{a \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^5 \left(a+b x^3\right)^2}+\frac{\log \left(a+b x^3\right) \left(6 a^2 f-3 a b e+b^2 d\right)}{3 b^5}+\frac{x^3 (b e-3 a f)}{3 b^4}+\frac{f x^6}{6 b^3}","-\frac{3 a^2 b e-4 a^3 f-2 a b^2 d+b^3 c}{3 b^5 \left(a+b x^3\right)}+\frac{a \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^5 \left(a+b x^3\right)^2}+\frac{\log \left(a+b x^3\right) \left(6 a^2 f-3 a b e+b^2 d\right)}{3 b^5}+\frac{x^3 (b e-3 a f)}{3 b^4}+\frac{f x^6}{6 b^3}",1,"((b*e - 3*a*f)*x^3)/(3*b^4) + (f*x^6)/(6*b^3) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*b^5*(a + b*x^3)^2) - (b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)/(3*b^5*(a + b*x^3)) + ((b^2*d - 3*a*b*e + 6*a^2*f)*Log[a + b*x^3])/(3*b^5)","A",3,2,30,0.06667,1,"{1821, 1620}"
280,1,109,0,0.1515458,"\int \frac{x^2 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^2*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 b^4 \left(a+b x^3\right)^2}-\frac{3 a^2 f-2 a b e+b^2 d}{3 b^4 \left(a+b x^3\right)}+\frac{(b e-3 a f) \log \left(a+b x^3\right)}{3 b^4}+\frac{f x^3}{3 b^3}","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 b^4 \left(a+b x^3\right)^2}-\frac{3 a^2 f-2 a b e+b^2 d}{3 b^4 \left(a+b x^3\right)}+\frac{(b e-3 a f) \log \left(a+b x^3\right)}{3 b^4}+\frac{f x^3}{3 b^3}",1,"(f*x^3)/(3*b^3) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*b^4*(a + b*x^3)^2) - (b^2*d - 2*a*b*e + 3*a^2*f)/(3*b^4*(a + b*x^3)) + ((b*e - 3*a*f)*Log[a + b*x^3])/(3*b^4)","A",3,2,30,0.06667,1,"{1819, 1850}"
281,1,114,0,0.1547703,"\int \frac{c+d x^3+e x^6+f x^9}{x \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x*(a + b*x^3)^3),x]","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a b^3 \left(a+b x^3\right)^2}+\frac{-a^2 b e+2 a^3 f+b^3 c}{3 a^2 b^3 \left(a+b x^3\right)}-\frac{1}{3} \left(\frac{c}{a^3}-\frac{f}{b^3}\right) \log \left(a+b x^3\right)+\frac{c \log (x)}{a^3}","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a b^3 \left(a+b x^3\right)^2}+\frac{-a^2 b e+2 a^3 f+b^3 c}{3 a^2 b^3 \left(a+b x^3\right)}-\frac{1}{3} \left(\frac{c}{a^3}-\frac{f}{b^3}\right) \log \left(a+b x^3\right)+\frac{c \log (x)}{a^3}",1,"(b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a*b^3*(a + b*x^3)^2) + (b^3*c - a^2*b*e + 2*a^3*f)/(3*a^2*b^3*(a + b*x^3)) + (c*Log[x])/a^3 - ((c/a^3 - f/b^3)*Log[a + b*x^3])/3","A",3,2,30,0.06667,1,"{1821, 1620}"
282,1,134,0,0.1712512,"\int \frac{c+d x^3+e x^6+f x^9}{x^4 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^4*(a + b*x^3)^3),x]","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a^2 b^2 \left(a+b x^3\right)^2}-\frac{a^3 f-a b^2 d+2 b^3 c}{3 a^3 b^2 \left(a+b x^3\right)}+\frac{(3 b c-a d) \log \left(a+b x^3\right)}{3 a^4}-\frac{\log (x) (3 b c-a d)}{a^4}-\frac{c}{3 a^3 x^3}","-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a^2 b^2 \left(a+b x^3\right)^2}-\frac{a^3 f-a b^2 d+2 b^3 c}{3 a^3 b^2 \left(a+b x^3\right)}+\frac{(3 b c-a d) \log \left(a+b x^3\right)}{3 a^4}-\frac{\log (x) (3 b c-a d)}{a^4}-\frac{c}{3 a^3 x^3}",1,"-c/(3*a^3*x^3) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a^2*b^2*(a + b*x^3)^2) - (2*b^3*c - a*b^2*d + a^3*f)/(3*a^3*b^2*(a + b*x^3)) - ((3*b*c - a*d)*Log[x])/a^4 + ((3*b*c - a*d)*Log[a + b*x^3])/(3*a^4)","A",3,2,30,0.06667,1,"{1821, 1620}"
283,1,163,0,0.1995321,"\int \frac{c+d x^3+e x^6+f x^9}{x^7 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^7*(a + b*x^3)^3),x]","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a^3 b \left(a+b x^3\right)^2}+\frac{a^2 e-2 a b d+3 b^2 c}{3 a^4 \left(a+b x^3\right)}-\frac{\log \left(a+b x^3\right) \left(a^2 e-3 a b d+6 b^2 c\right)}{3 a^5}+\frac{\log (x) \left(a^2 e-3 a b d+6 b^2 c\right)}{a^5}+\frac{3 b c-a d}{3 a^4 x^3}-\frac{c}{6 a^3 x^6}","\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a^3 b \left(a+b x^3\right)^2}+\frac{a^2 e-2 a b d+3 b^2 c}{3 a^4 \left(a+b x^3\right)}-\frac{\log \left(a+b x^3\right) \left(a^2 e-3 a b d+6 b^2 c\right)}{3 a^5}+\frac{\log (x) \left(a^2 e-3 a b d+6 b^2 c\right)}{a^5}+\frac{3 b c-a d}{3 a^4 x^3}-\frac{c}{6 a^3 x^6}",1,"-c/(6*a^3*x^6) + (3*b*c - a*d)/(3*a^4*x^3) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a^3*b*(a + b*x^3)^2) + (3*b^2*c - 2*a*b*d + a^2*e)/(3*a^4*(a + b*x^3)) + ((6*b^2*c - 3*a*b*d + a^2*e)*Log[x])/a^5 - ((6*b^2*c - 3*a*b*d + a^2*e)*Log[a + b*x^3])/(3*a^5)","A",3,2,30,0.06667,1,"{1821, 1620}"
284,1,218,0,0.2637109,"\int \frac{c+d x^3+e x^6+f x^9}{x^{10} \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^10*(a + b*x^3)^3),x]","-\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{3 a^5 \left(a+b x^3\right)}-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a^4 \left(a+b x^3\right)^2}+\frac{\log \left(a+b x^3\right) \left(3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c\right)}{3 a^6}-\frac{\log (x) \left(3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c\right)}{a^6}-\frac{a^2 e-3 a b d+6 b^2 c}{3 a^5 x^3}+\frac{3 b c-a d}{6 a^4 x^6}-\frac{c}{9 a^3 x^9}","-\frac{2 a^2 b e+a^3 (-f)-3 a b^2 d+4 b^3 c}{3 a^5 \left(a+b x^3\right)}-\frac{a^2 b e+a^3 (-f)-a b^2 d+b^3 c}{6 a^4 \left(a+b x^3\right)^2}+\frac{\log \left(a+b x^3\right) \left(3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c\right)}{3 a^6}-\frac{\log (x) \left(3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c\right)}{a^6}-\frac{a^2 e-3 a b d+6 b^2 c}{3 a^5 x^3}+\frac{3 b c-a d}{6 a^4 x^6}-\frac{c}{9 a^3 x^9}",1,"-c/(9*a^3*x^9) + (3*b*c - a*d)/(6*a^4*x^6) - (6*b^2*c - 3*a*b*d + a^2*e)/(3*a^5*x^3) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a^4*(a + b*x^3)^2) - (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(3*a^5*(a + b*x^3)) - ((10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)*Log[x])/a^6 + ((10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)*Log[a + b*x^3])/(3*a^6)","A",3,2,30,0.06667,1,"{1821, 1620}"
285,1,258,0,0.3044932,"\int \frac{c+d x^3+e x^6+f x^9}{x^{13} \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^13*(a + b*x^3)^3),x]","\frac{b \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{3 a^6 \left(a+b x^3\right)}+\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^5 \left(a+b x^3\right)^2}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{3 a^6 x^3}-\frac{b \log \left(a+b x^3\right) \left(6 a^2 b e-3 a^3 f-10 a b^2 d+15 b^3 c\right)}{3 a^7}+\frac{b \log (x) \left(6 a^2 b e-3 a^3 f-10 a b^2 d+15 b^3 c\right)}{a^7}-\frac{a^2 e-3 a b d+6 b^2 c}{6 a^5 x^6}+\frac{3 b c-a d}{9 a^4 x^9}-\frac{c}{12 a^3 x^{12}}","\frac{b \left(3 a^2 b e-2 a^3 f-4 a b^2 d+5 b^3 c\right)}{3 a^6 \left(a+b x^3\right)}+\frac{b \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^5 \left(a+b x^3\right)^2}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{3 a^6 x^3}-\frac{b \log \left(a+b x^3\right) \left(6 a^2 b e-3 a^3 f-10 a b^2 d+15 b^3 c\right)}{3 a^7}+\frac{b \log (x) \left(6 a^2 b e-3 a^3 f-10 a b^2 d+15 b^3 c\right)}{a^7}-\frac{a^2 e-3 a b d+6 b^2 c}{6 a^5 x^6}+\frac{3 b c-a d}{9 a^4 x^9}-\frac{c}{12 a^3 x^{12}}",1,"-c/(12*a^3*x^12) + (3*b*c - a*d)/(9*a^4*x^9) - (6*b^2*c - 3*a*b*d + a^2*e)/(6*a^5*x^6) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(3*a^6*x^3) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*a^5*(a + b*x^3)^2) + (b*(5*b^3*c - 4*a*b^2*d + 3*a^2*b*e - 2*a^3*f))/(3*a^6*(a + b*x^3)) + (b*(15*b^3*c - 10*a*b^2*d + 6*a^2*b*e - 3*a^3*f)*Log[x])/a^7 - (b*(15*b^3*c - 10*a*b^2*d + 6*a^2*b*e - 3*a^3*f)*Log[a + b*x^3])/(3*a^7)","A",3,2,30,0.06667,1,"{1821, 1620}"
286,1,416,0,0.7421615,"\int \frac{x^{12} \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^12*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","\frac{x^4 \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{4 b^6}-\frac{a^2 x \left(31 a^2 b e-37 a^3 f-25 a b^2 d+19 b^3 c\right)}{18 b^7 \left(a+b x^3\right)}+\frac{a^3 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^7 \left(a+b x^3\right)^2}-\frac{a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(104 a^2 b e-152 a^3 f-65 a b^2 d+35 b^3 c\right)}{54 b^{22/3}}-\frac{a x \left(10 a^2 b e-15 a^3 f-6 a b^2 d+3 b^3 c\right)}{b^7}+\frac{a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(104 a^2 b e-152 a^3 f-65 a b^2 d+35 b^3 c\right)}{27 b^{22/3}}-\frac{a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(104 a^2 b e-152 a^3 f-65 a b^2 d+35 b^3 c\right)}{9 \sqrt{3} b^{22/3}}+\frac{x^7 \left(6 a^2 f-3 a b e+b^2 d\right)}{7 b^5}+\frac{x^{10} (b e-3 a f)}{10 b^4}+\frac{f x^{13}}{13 b^3}","\frac{x^4 \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{4 b^6}-\frac{a^2 x \left(31 a^2 b e-37 a^3 f-25 a b^2 d+19 b^3 c\right)}{18 b^7 \left(a+b x^3\right)}+\frac{a^3 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^7 \left(a+b x^3\right)^2}-\frac{a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(104 a^2 b e-152 a^3 f-65 a b^2 d+35 b^3 c\right)}{54 b^{22/3}}-\frac{a x \left(10 a^2 b e-15 a^3 f-6 a b^2 d+3 b^3 c\right)}{b^7}+\frac{a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(104 a^2 b e-152 a^3 f-65 a b^2 d+35 b^3 c\right)}{27 b^{22/3}}-\frac{a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(104 a^2 b e-152 a^3 f-65 a b^2 d+35 b^3 c\right)}{9 \sqrt{3} b^{22/3}}+\frac{x^7 \left(6 a^2 f-3 a b e+b^2 d\right)}{7 b^5}+\frac{x^{10} (b e-3 a f)}{10 b^4}+\frac{f x^{13}}{13 b^3}",1,"-((a*(3*b^3*c - 6*a*b^2*d + 10*a^2*b*e - 15*a^3*f)*x)/b^7) + ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^4)/(4*b^6) + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^7)/(7*b^5) + ((b*e - 3*a*f)*x^10)/(10*b^4) + (f*x^13)/(13*b^3) + (a^3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*b^7*(a + b*x^3)^2) - (a^2*(19*b^3*c - 25*a*b^2*d + 31*a^2*b*e - 37*a^3*f)*x)/(18*b^7*(a + b*x^3)) - (a^(4/3)*(35*b^3*c - 65*a*b^2*d + 104*a^2*b*e - 152*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*b^(22/3)) + (a^(4/3)*(35*b^3*c - 65*a*b^2*d + 104*a^2*b*e - 152*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*b^(22/3)) - (a^(4/3)*(35*b^3*c - 65*a*b^2*d + 104*a^2*b*e - 152*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*b^(22/3))","A",10,9,30,0.3000,1,"{1828, 1858, 1887, 200, 31, 634, 617, 204, 628}"
287,1,384,0,1.0504559,"\int \frac{x^{10} \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^10*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","\frac{x^2 \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{2 b^6}+\frac{a x^2 \left(13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right)}{9 b^6 \left(a+b x^3\right)}-\frac{a^2 x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^6 \left(a+b x^3\right)^2}-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right)}{54 b^{20/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right)}{27 b^{20/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right)}{9 \sqrt{3} b^{20/3}}+\frac{x^5 \left(6 a^2 f-3 a b e+b^2 d\right)}{5 b^5}+\frac{x^8 (b e-3 a f)}{8 b^4}+\frac{f x^{11}}{11 b^3}","\frac{x^2 \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{2 b^6}+\frac{a x^2 \left(13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right)}{9 b^6 \left(a+b x^3\right)}-\frac{a^2 x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^6 \left(a+b x^3\right)^2}-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right)}{54 b^{20/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right)}{27 b^{20/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right)}{9 \sqrt{3} b^{20/3}}+\frac{x^5 \left(6 a^2 f-3 a b e+b^2 d\right)}{5 b^5}+\frac{x^8 (b e-3 a f)}{8 b^4}+\frac{f x^{11}}{11 b^3}",1,"((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^2)/(2*b^6) + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^5)/(5*b^5) + ((b*e - 3*a*f)*x^8)/(8*b^4) + (f*x^11)/(11*b^3) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*b^6*(a + b*x^3)^2) + (a*(7*b^3*c - 10*a*b^2*d + 13*a^2*b*e - 16*a^3*f)*x^2)/(9*b^6*(a + b*x^3)) + (a^(2/3)*(20*b^3*c - 44*a*b^2*d + 77*a^2*b*e - 119*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*b^(20/3)) + (a^(2/3)*(20*b^3*c - 44*a*b^2*d + 77*a^2*b*e - 119*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*b^(20/3)) - (a^(2/3)*(20*b^3*c - 44*a*b^2*d + 77*a^2*b*e - 119*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*b^(20/3))","A",14,10,30,0.3333,1,"{1828, 1851, 1836, 1488, 292, 31, 634, 617, 204, 628}"
288,1,375,0,0.606352,"\int \frac{x^9 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^9*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","\frac{a x \left(25 a^2 b e-31 a^3 f-19 a b^2 d+13 b^3 c\right)}{18 b^6 \left(a+b x^3\right)}-\frac{a^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^6 \left(a+b x^3\right)^2}+\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(65 a^2 b e-104 a^3 f-35 a b^2 d+14 b^3 c\right)}{54 b^{19/3}}+\frac{x \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{b^6}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(65 a^2 b e-104 a^3 f-35 a b^2 d+14 b^3 c\right)}{27 b^{19/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(65 a^2 b e-104 a^3 f-35 a b^2 d+14 b^3 c\right)}{9 \sqrt{3} b^{19/3}}+\frac{x^4 \left(6 a^2 f-3 a b e+b^2 d\right)}{4 b^5}+\frac{x^7 (b e-3 a f)}{7 b^4}+\frac{f x^{10}}{10 b^3}","\frac{a x \left(25 a^2 b e-31 a^3 f-19 a b^2 d+13 b^3 c\right)}{18 b^6 \left(a+b x^3\right)}-\frac{a^2 x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^6 \left(a+b x^3\right)^2}+\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(65 a^2 b e-104 a^3 f-35 a b^2 d+14 b^3 c\right)}{54 b^{19/3}}+\frac{x \left(6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right)}{b^6}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(65 a^2 b e-104 a^3 f-35 a b^2 d+14 b^3 c\right)}{27 b^{19/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(65 a^2 b e-104 a^3 f-35 a b^2 d+14 b^3 c\right)}{9 \sqrt{3} b^{19/3}}+\frac{x^4 \left(6 a^2 f-3 a b e+b^2 d\right)}{4 b^5}+\frac{x^7 (b e-3 a f)}{7 b^4}+\frac{f x^{10}}{10 b^3}",1,"((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x)/b^6 + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^4)/(4*b^5) + ((b*e - 3*a*f)*x^7)/(7*b^4) + (f*x^10)/(10*b^3) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*b^6*(a + b*x^3)^2) + (a*(13*b^3*c - 19*a*b^2*d + 25*a^2*b*e - 31*a^3*f)*x)/(18*b^6*(a + b*x^3)) + (a^(1/3)*(14*b^3*c - 35*a*b^2*d + 65*a^2*b*e - 104*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*b^(19/3)) - (a^(1/3)*(14*b^3*c - 35*a*b^2*d + 65*a^2*b*e - 104*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*b^(19/3)) + (a^(1/3)*(14*b^3*c - 35*a*b^2*d + 65*a^2*b*e - 104*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*b^(19/3))","A",10,9,30,0.3000,1,"{1828, 1858, 1887, 200, 31, 634, 617, 204, 628}"
289,1,345,0,0.7632215,"\int \frac{x^7 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^7*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","-\frac{x^2 \left(10 a^2 b e-13 a^3 f-7 a b^2 d+4 b^3 c\right)}{9 b^5 \left(a+b x^3\right)}+\frac{a x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^5 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(44 a^2 b e-77 a^3 f-20 a b^2 d+5 b^3 c\right)}{54 \sqrt[3]{a} b^{17/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(44 a^2 b e-77 a^3 f-20 a b^2 d+5 b^3 c\right)}{27 \sqrt[3]{a} b^{17/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(44 a^2 b e-77 a^3 f-20 a b^2 d+5 b^3 c\right)}{9 \sqrt{3} \sqrt[3]{a} b^{17/3}}+\frac{x^2 \left(6 a^2 f-3 a b e+b^2 d\right)}{2 b^5}+\frac{x^5 (b e-3 a f)}{5 b^4}+\frac{f x^8}{8 b^3}","-\frac{x^2 \left(10 a^2 b e-13 a^3 f-7 a b^2 d+4 b^3 c\right)}{9 b^5 \left(a+b x^3\right)}+\frac{a x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^5 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(44 a^2 b e-77 a^3 f-20 a b^2 d+5 b^3 c\right)}{54 \sqrt[3]{a} b^{17/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(44 a^2 b e-77 a^3 f-20 a b^2 d+5 b^3 c\right)}{27 \sqrt[3]{a} b^{17/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(44 a^2 b e-77 a^3 f-20 a b^2 d+5 b^3 c\right)}{9 \sqrt{3} \sqrt[3]{a} b^{17/3}}+\frac{x^2 \left(6 a^2 f-3 a b e+b^2 d\right)}{2 b^5}+\frac{x^5 (b e-3 a f)}{5 b^4}+\frac{f x^8}{8 b^3}",1,"((b^2*d - 3*a*b*e + 6*a^2*f)*x^2)/(2*b^5) + ((b*e - 3*a*f)*x^5)/(5*b^4) + (f*x^8)/(8*b^3) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*b^5*(a + b*x^3)^2) - ((4*b^3*c - 7*a*b^2*d + 10*a^2*b*e - 13*a^3*f)*x^2)/(9*b^5*(a + b*x^3)) - ((5*b^3*c - 20*a*b^2*d + 44*a^2*b*e - 77*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(1/3)*b^(17/3)) - ((5*b^3*c - 20*a*b^2*d + 44*a^2*b*e - 77*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(1/3)*b^(17/3)) + ((5*b^3*c - 20*a*b^2*d + 44*a^2*b*e - 77*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(1/3)*b^(17/3))","A",13,10,30,0.3333,1,"{1828, 1851, 1836, 1488, 292, 31, 634, 617, 204, 628}"
290,1,336,0,0.5087357,"\int \frac{x^6 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^6*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","-\frac{x \left(19 a^2 b e-25 a^3 f-13 a b^2 d+7 b^3 c\right)}{18 b^5 \left(a+b x^3\right)}+\frac{a x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^5 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(35 a^2 b e-65 a^3 f-14 a b^2 d+2 b^3 c\right)}{54 a^{2/3} b^{16/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(35 a^2 b e-65 a^3 f-14 a b^2 d+2 b^3 c\right)}{27 a^{2/3} b^{16/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(35 a^2 b e-65 a^3 f-14 a b^2 d+2 b^3 c\right)}{9 \sqrt{3} a^{2/3} b^{16/3}}+\frac{x \left(6 a^2 f-3 a b e+b^2 d\right)}{b^5}+\frac{x^4 (b e-3 a f)}{4 b^4}+\frac{f x^7}{7 b^3}","-\frac{x \left(19 a^2 b e-25 a^3 f-13 a b^2 d+7 b^3 c\right)}{18 b^5 \left(a+b x^3\right)}+\frac{a x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^5 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(35 a^2 b e-65 a^3 f-14 a b^2 d+2 b^3 c\right)}{54 a^{2/3} b^{16/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(35 a^2 b e-65 a^3 f-14 a b^2 d+2 b^3 c\right)}{27 a^{2/3} b^{16/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(35 a^2 b e-65 a^3 f-14 a b^2 d+2 b^3 c\right)}{9 \sqrt{3} a^{2/3} b^{16/3}}+\frac{x \left(6 a^2 f-3 a b e+b^2 d\right)}{b^5}+\frac{x^4 (b e-3 a f)}{4 b^4}+\frac{f x^7}{7 b^3}",1,"((b^2*d - 3*a*b*e + 6*a^2*f)*x)/b^5 + ((b*e - 3*a*f)*x^4)/(4*b^4) + (f*x^7)/(7*b^3) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*b^5*(a + b*x^3)^2) - ((7*b^3*c - 13*a*b^2*d + 19*a^2*b*e - 25*a^3*f)*x)/(18*b^5*(a + b*x^3)) - ((2*b^3*c - 14*a*b^2*d + 35*a^2*b*e - 65*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(2/3)*b^(16/3)) + ((2*b^3*c - 14*a*b^2*d + 35*a^2*b*e - 65*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(2/3)*b^(16/3)) - ((2*b^3*c - 14*a*b^2*d + 35*a^2*b*e - 65*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(2/3)*b^(16/3))","A",10,9,30,0.3000,1,"{1828, 1858, 1887, 200, 31, 634, 617, 204, 628}"
291,1,316,0,0.5046461,"\int \frac{x^4 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^4*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","\frac{x^2 \left(7 a^2 b e-10 a^3 f-4 a b^2 d+b^3 c\right)}{9 a b^4 \left(a+b x^3\right)}-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^4 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-20 a^2 b e+44 a^3 f+5 a b^2 d+b^3 c\right)}{54 a^{4/3} b^{14/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-20 a^2 b e+44 a^3 f+5 a b^2 d+b^3 c\right)}{27 a^{4/3} b^{14/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-20 a^2 b e+44 a^3 f+5 a b^2 d+b^3 c\right)}{9 \sqrt{3} a^{4/3} b^{14/3}}+\frac{x^2 (b e-3 a f)}{2 b^4}+\frac{f x^5}{5 b^3}","\frac{x^2 \left(7 a^2 b e-10 a^3 f-4 a b^2 d+b^3 c\right)}{9 a b^4 \left(a+b x^3\right)}-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^4 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-20 a^2 b e+44 a^3 f+5 a b^2 d+b^3 c\right)}{54 a^{4/3} b^{14/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-20 a^2 b e+44 a^3 f+5 a b^2 d+b^3 c\right)}{27 a^{4/3} b^{14/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-20 a^2 b e+44 a^3 f+5 a b^2 d+b^3 c\right)}{9 \sqrt{3} a^{4/3} b^{14/3}}+\frac{x^2 (b e-3 a f)}{2 b^4}+\frac{f x^5}{5 b^3}",1,"((b*e - 3*a*f)*x^2)/(2*b^4) + (f*x^5)/(5*b^3) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*b^4*(a + b*x^3)^2) + ((b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*x^2)/(9*a*b^4*(a + b*x^3)) - ((b^3*c + 5*a*b^2*d - 20*a^2*b*e + 44*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(4/3)*b^(14/3)) - ((b^3*c + 5*a*b^2*d - 20*a^2*b*e + 44*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(4/3)*b^(14/3)) + ((b^3*c + 5*a*b^2*d - 20*a^2*b*e + 44*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(4/3)*b^(14/3))","A",12,10,30,0.3333,1,"{1828, 1851, 1594, 1488, 292, 31, 634, 617, 204, 628}"
292,1,307,0,0.4117023,"\int \frac{x^3 \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^3*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","\frac{x \left(13 a^2 b e-19 a^3 f-7 a b^2 d+b^3 c\right)}{18 a b^4 \left(a+b x^3\right)}-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^4 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-14 a^2 b e+35 a^3 f+2 a b^2 d+b^3 c\right)}{54 a^{5/3} b^{13/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-14 a^2 b e+35 a^3 f+2 a b^2 d+b^3 c\right)}{27 a^{5/3} b^{13/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-14 a^2 b e+35 a^3 f+2 a b^2 d+b^3 c\right)}{9 \sqrt{3} a^{5/3} b^{13/3}}+\frac{x (b e-3 a f)}{b^4}+\frac{f x^4}{4 b^3}","\frac{x \left(13 a^2 b e-19 a^3 f-7 a b^2 d+b^3 c\right)}{18 a b^4 \left(a+b x^3\right)}-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 b^4 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-14 a^2 b e+35 a^3 f+2 a b^2 d+b^3 c\right)}{54 a^{5/3} b^{13/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-14 a^2 b e+35 a^3 f+2 a b^2 d+b^3 c\right)}{27 a^{5/3} b^{13/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-14 a^2 b e+35 a^3 f+2 a b^2 d+b^3 c\right)}{9 \sqrt{3} a^{5/3} b^{13/3}}+\frac{x (b e-3 a f)}{b^4}+\frac{f x^4}{4 b^3}",1,"((b*e - 3*a*f)*x)/b^4 + (f*x^4)/(4*b^3) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*b^4*(a + b*x^3)^2) + ((b^3*c - 7*a*b^2*d + 13*a^2*b*e - 19*a^3*f)*x)/(18*a*b^4*(a + b*x^3)) - ((b^3*c + 2*a*b^2*d - 14*a^2*b*e + 35*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(5/3)*b^(13/3)) + ((b^3*c + 2*a*b^2*d - 14*a^2*b*e + 35*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(5/3)*b^(13/3)) - ((b^3*c + 2*a*b^2*d - 14*a^2*b*e + 35*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(5/3)*b^(13/3))","A",10,10,30,0.3333,1,"{1828, 1858, 1411, 388, 200, 31, 634, 617, 204, 628}"
293,1,301,0,0.3680461,"\int \frac{x \left(c+d x^3+e x^6+f x^9\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x]","\frac{x^2 \left(-4 a^2 b e+7 a^3 f+a b^2 d+2 b^3 c\right)}{9 a^2 b^3 \left(a+b x^3\right)}+\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a b^3 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(5 a^2 b e-20 a^3 f+a b^2 d+2 b^3 c\right)}{54 a^{7/3} b^{11/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 a^2 b e-20 a^3 f+a b^2 d+2 b^3 c\right)}{27 a^{7/3} b^{11/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^2 b e-20 a^3 f+a b^2 d+2 b^3 c\right)}{9 \sqrt{3} a^{7/3} b^{11/3}}+\frac{f x^2}{2 b^3}","\frac{x^2 \left(-4 a^2 b e+7 a^3 f+a b^2 d+2 b^3 c\right)}{9 a^2 b^3 \left(a+b x^3\right)}+\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a b^3 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(5 a^2 b e-20 a^3 f+a b^2 d+2 b^3 c\right)}{54 a^{7/3} b^{11/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 a^2 b e-20 a^3 f+a b^2 d+2 b^3 c\right)}{27 a^{7/3} b^{11/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^2 b e-20 a^3 f+a b^2 d+2 b^3 c\right)}{9 \sqrt{3} a^{7/3} b^{11/3}}+\frac{f x^2}{2 b^3}",1,"(f*x^2)/(2*b^3) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a*b^3*(a + b*x^3)^2) + ((2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*x^2)/(9*a^2*b^3*(a + b*x^3)) - ((2*b^3*c + a*b^2*d + 5*a^2*b*e - 20*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(7/3)*b^(11/3)) - ((2*b^3*c + a*b^2*d + 5*a^2*b*e - 20*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(7/3)*b^(11/3)) + ((2*b^3*c + a*b^2*d + 5*a^2*b*e - 20*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(7/3)*b^(11/3))","A",10,10,28,0.3571,1,"{1828, 1594, 1482, 459, 292, 31, 634, 617, 204, 628}"
294,1,292,0,0.3071925,"\int \frac{c+d x^3+e x^6+f x^9}{\left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3,x]","\frac{x \left(-7 a^2 b e+13 a^3 f+a b^2 d+5 b^3 c\right)}{18 a^2 b^3 \left(a+b x^3\right)}+\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a b^3 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(2 a^2 b e-14 a^3 f+a b^2 d+5 b^3 c\right)}{54 a^{8/3} b^{10/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(2 a^2 b e-14 a^3 f+a b^2 d+5 b^3 c\right)}{27 a^{8/3} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^2 b e-14 a^3 f+a b^2 d+5 b^3 c\right)}{9 \sqrt{3} a^{8/3} b^{10/3}}+\frac{f x}{b^3}","\frac{x \left(-7 a^2 b e+13 a^3 f+a b^2 d+5 b^3 c\right)}{18 a^2 b^3 \left(a+b x^3\right)}+\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a b^3 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(2 a^2 b e-14 a^3 f+a b^2 d+5 b^3 c\right)}{54 a^{8/3} b^{10/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(2 a^2 b e-14 a^3 f+a b^2 d+5 b^3 c\right)}{27 a^{8/3} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^2 b e-14 a^3 f+a b^2 d+5 b^3 c\right)}{9 \sqrt{3} a^{8/3} b^{10/3}}+\frac{f x}{b^3}",1,"(f*x)/b^3 + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a*b^3*(a + b*x^3)^2) + ((5*b^3*c + a*b^2*d - 7*a^2*b*e + 13*a^3*f)*x)/(18*a^2*b^3*(a + b*x^3)) - ((5*b^3*c + a*b^2*d + 2*a^2*b*e - 14*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(10/3)) + ((5*b^3*c + a*b^2*d + 2*a^2*b*e - 14*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(8/3)*b^(10/3)) - ((5*b^3*c + a*b^2*d + 2*a^2*b*e - 14*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(8/3)*b^(10/3))","A",9,9,27,0.3333,1,"{1858, 1409, 388, 200, 31, 634, 617, 204, 628}"
295,1,303,0,0.3390391,"\int \frac{c+d x^3+e x^6+f x^9}{x^2 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^2*(a + b*x^3)^3),x]","-\frac{x^2 \left(-a^2 b e+4 a^3 f-2 a b^2 d+5 b^3 c\right)}{9 a^3 b^2 \left(a+b x^3\right)}-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^2 b^2 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-a^2 b e-5 a^3 f-2 a b^2 d+14 b^3 c\right)}{54 a^{10/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-a^2 b e-5 a^3 f-2 a b^2 d+14 b^3 c\right)}{27 a^{10/3} b^{8/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^2 b e-5 a^3 f-2 a b^2 d+14 b^3 c\right)}{9 \sqrt{3} a^{10/3} b^{8/3}}-\frac{c}{a^3 x}","-\frac{x^2 \left(-a^2 b e+4 a^3 f-2 a b^2 d+5 b^3 c\right)}{9 a^3 b^2 \left(a+b x^3\right)}-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^2 b^2 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-a^2 b e-5 a^3 f-2 a b^2 d+14 b^3 c\right)}{54 a^{10/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-a^2 b e-5 a^3 f-2 a b^2 d+14 b^3 c\right)}{27 a^{10/3} b^{8/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^2 b e-5 a^3 f-2 a b^2 d+14 b^3 c\right)}{9 \sqrt{3} a^{10/3} b^{8/3}}-\frac{c}{a^3 x}",1,"-(c/(a^3*x)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^2*b^2*(a + b*x^3)^2) - ((5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*x^2)/(9*a^3*b^2*(a + b*x^3)) + ((14*b^3*c - 2*a*b^2*d - a^2*b*e - 5*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(10/3)*b^(8/3)) + ((14*b^3*c - 2*a*b^2*d - a^2*b*e - 5*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(10/3)*b^(8/3)) - ((14*b^3*c - 2*a*b^2*d - a^2*b*e - 5*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(10/3)*b^(8/3))","A",9,9,30,0.3000,1,"{1829, 1484, 453, 292, 31, 634, 617, 204, 628}"
296,1,301,0,0.3291539,"\int \frac{c+d x^3+e x^6+f x^9}{x^3 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^3*(a + b*x^3)^3),x]","-\frac{x \left(-a^2 b e+7 a^3 f-5 a b^2 d+11 b^3 c\right)}{18 a^3 b^2 \left(a+b x^3\right)}-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^2 b^2 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-a^2 b e-2 a^3 f-5 a b^2 d+20 b^3 c\right)}{54 a^{11/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-a^2 b e-2 a^3 f-5 a b^2 d+20 b^3 c\right)}{27 a^{11/3} b^{7/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^2 b e-2 a^3 f-5 a b^2 d+20 b^3 c\right)}{9 \sqrt{3} a^{11/3} b^{7/3}}-\frac{c}{2 a^3 x^2}","-\frac{x \left(-a^2 b e+7 a^3 f-5 a b^2 d+11 b^3 c\right)}{18 a^3 b^2 \left(a+b x^3\right)}-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^2 b^2 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-a^2 b e-2 a^3 f-5 a b^2 d+20 b^3 c\right)}{54 a^{11/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(-a^2 b e-2 a^3 f-5 a b^2 d+20 b^3 c\right)}{27 a^{11/3} b^{7/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^2 b e-2 a^3 f-5 a b^2 d+20 b^3 c\right)}{9 \sqrt{3} a^{11/3} b^{7/3}}-\frac{c}{2 a^3 x^2}",1,"-c/(2*a^3*x^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a^2*b^2*(a + b*x^3)^2) - ((11*b^3*c - 5*a*b^2*d - a^2*b*e + 7*a^3*f)*x)/(18*a^3*b^2*(a + b*x^3)) + ((20*b^3*c - 5*a*b^2*d - a^2*b*e - 2*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(11/3)*b^(7/3)) - ((20*b^3*c - 5*a*b^2*d - a^2*b*e - 2*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(11/3)*b^(7/3)) + ((20*b^3*c - 5*a*b^2*d - a^2*b*e - 2*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(11/3)*b^(7/3))","A",9,9,30,0.3000,1,"{1829, 1484, 453, 200, 31, 634, 617, 204, 628}"
297,1,317,0,0.3695234,"\int \frac{c+d x^3+e x^6+f x^9}{x^5 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^5*(a + b*x^3)^3),x]","\frac{x^2 \left(2 a^2 b e+a^3 f-5 a b^2 d+8 b^3 c\right)}{9 a^4 b \left(a+b x^3\right)}+\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^3 b \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(2 a^2 b e+a^3 f-14 a b^2 d+35 b^3 c\right)}{54 a^{13/3} b^{5/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(2 a^2 b e+a^3 f-14 a b^2 d+35 b^3 c\right)}{27 a^{13/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^2 b e+a^3 f-14 a b^2 d+35 b^3 c\right)}{9 \sqrt{3} a^{13/3} b^{5/3}}+\frac{3 b c-a d}{a^4 x}-\frac{c}{4 a^3 x^4}","\frac{x^2 \left(2 a^2 b e+a^3 f-5 a b^2 d+8 b^3 c\right)}{9 a^4 b \left(a+b x^3\right)}+\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^3 b \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(2 a^2 b e+a^3 f-14 a b^2 d+35 b^3 c\right)}{54 a^{13/3} b^{5/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(2 a^2 b e+a^3 f-14 a b^2 d+35 b^3 c\right)}{27 a^{13/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^2 b e+a^3 f-14 a b^2 d+35 b^3 c\right)}{9 \sqrt{3} a^{13/3} b^{5/3}}+\frac{3 b c-a d}{a^4 x}-\frac{c}{4 a^3 x^4}",1,"-c/(4*a^3*x^4) + (3*b*c - a*d)/(a^4*x) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^3*b*(a + b*x^3)^2) + ((8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*x^2)/(9*a^4*b*(a + b*x^3)) - ((35*b^3*c - 14*a*b^2*d + 2*a^2*b*e + a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(13/3)*b^(5/3)) - ((35*b^3*c - 14*a*b^2*d + 2*a^2*b*e + a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(13/3)*b^(5/3)) + ((35*b^3*c - 14*a*b^2*d + 2*a^2*b*e + a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(13/3)*b^(5/3))","A",10,9,30,0.3000,1,"{1829, 1484, 1488, 292, 31, 634, 617, 204, 628}"
298,1,316,0,0.3680284,"\int \frac{c+d x^3+e x^6+f x^9}{x^6 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^6*(a + b*x^3)^3),x]","\frac{x \left(5 a^2 b e+a^3 f-11 a b^2 d+17 b^3 c\right)}{18 a^4 b \left(a+b x^3\right)}+\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^3 b \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(5 a^2 b e+a^3 f-20 a b^2 d+44 b^3 c\right)}{54 a^{14/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 a^2 b e+a^3 f-20 a b^2 d+44 b^3 c\right)}{27 a^{14/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^2 b e+a^3 f-20 a b^2 d+44 b^3 c\right)}{9 \sqrt{3} a^{14/3} b^{4/3}}+\frac{3 b c-a d}{2 a^4 x^2}-\frac{c}{5 a^3 x^5}","\frac{x \left(5 a^2 b e+a^3 f-11 a b^2 d+17 b^3 c\right)}{18 a^4 b \left(a+b x^3\right)}+\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^3 b \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(5 a^2 b e+a^3 f-20 a b^2 d+44 b^3 c\right)}{54 a^{14/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 a^2 b e+a^3 f-20 a b^2 d+44 b^3 c\right)}{27 a^{14/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^2 b e+a^3 f-20 a b^2 d+44 b^3 c\right)}{9 \sqrt{3} a^{14/3} b^{4/3}}+\frac{3 b c-a d}{2 a^4 x^2}-\frac{c}{5 a^3 x^5}",1,"-c/(5*a^3*x^5) + (3*b*c - a*d)/(2*a^4*x^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a^3*b*(a + b*x^3)^2) + ((17*b^3*c - 11*a*b^2*d + 5*a^2*b*e + a^3*f)*x)/(18*a^4*b*(a + b*x^3)) - ((44*b^3*c - 20*a*b^2*d + 5*a^2*b*e + a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(14/3)*b^(4/3)) + ((44*b^3*c - 20*a*b^2*d + 5*a^2*b*e + a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(14/3)*b^(4/3)) - ((44*b^3*c - 20*a*b^2*d + 5*a^2*b*e + a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(14/3)*b^(4/3))","A",10,9,30,0.3000,1,"{1829, 1484, 1488, 200, 31, 634, 617, 204, 628}"
299,1,343,0,0.5693095,"\int \frac{c+d x^3+e x^6+f x^9}{x^8 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^8*(a + b*x^3)^3),x]","-\frac{x^2 \left(5 a^2 b e-2 a^3 f-8 a b^2 d+11 b^3 c\right)}{9 a^5 \left(a+b x^3\right)}-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^4 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(14 a^2 b e-2 a^3 f-35 a b^2 d+65 b^3 c\right)}{54 a^{16/3} b^{2/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(14 a^2 b e-2 a^3 f-35 a b^2 d+65 b^3 c\right)}{27 a^{16/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(14 a^2 b e-2 a^3 f-35 a b^2 d+65 b^3 c\right)}{9 \sqrt{3} a^{16/3} b^{2/3}}-\frac{a^2 e-3 a b d+6 b^2 c}{a^5 x}+\frac{3 b c-a d}{4 a^4 x^4}-\frac{c}{7 a^3 x^7}","-\frac{x^2 \left(5 a^2 b e-2 a^3 f-8 a b^2 d+11 b^3 c\right)}{9 a^5 \left(a+b x^3\right)}-\frac{x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^4 \left(a+b x^3\right)^2}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(14 a^2 b e-2 a^3 f-35 a b^2 d+65 b^3 c\right)}{54 a^{16/3} b^{2/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(14 a^2 b e-2 a^3 f-35 a b^2 d+65 b^3 c\right)}{27 a^{16/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(14 a^2 b e-2 a^3 f-35 a b^2 d+65 b^3 c\right)}{9 \sqrt{3} a^{16/3} b^{2/3}}-\frac{a^2 e-3 a b d+6 b^2 c}{a^5 x}+\frac{3 b c-a d}{4 a^4 x^4}-\frac{c}{7 a^3 x^7}",1,"-c/(7*a^3*x^7) + (3*b*c - a*d)/(4*a^4*x^4) - (6*b^2*c - 3*a*b*d + a^2*e)/(a^5*x) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^4*(a + b*x^3)^2) - ((11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*x^2)/(9*a^5*(a + b*x^3)) + ((65*b^3*c - 35*a*b^2*d + 14*a^2*b*e - 2*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(16/3)*b^(2/3)) + ((65*b^3*c - 35*a*b^2*d + 14*a^2*b*e - 2*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(16/3)*b^(2/3)) - ((65*b^3*c - 35*a*b^2*d + 14*a^2*b*e - 2*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(16/3)*b^(2/3))","A",10,8,30,0.2667,1,"{1829, 1834, 292, 31, 634, 617, 204, 628}"
300,1,341,0,0.5467599,"\int \frac{c+d x^3+e x^6+f x^9}{x^9 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^9*(a + b*x^3)^3),x]","-\frac{x \left(11 a^2 b e-5 a^3 f-17 a b^2 d+23 b^3 c\right)}{18 a^5 \left(a+b x^3\right)}-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^4 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(20 a^2 b e-5 a^3 f-44 a b^2 d+77 b^3 c\right)}{54 a^{17/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(20 a^2 b e-5 a^3 f-44 a b^2 d+77 b^3 c\right)}{27 a^{17/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(20 a^2 b e-5 a^3 f-44 a b^2 d+77 b^3 c\right)}{9 \sqrt{3} a^{17/3} \sqrt[3]{b}}-\frac{a^2 e-3 a b d+6 b^2 c}{2 a^5 x^2}+\frac{3 b c-a d}{5 a^4 x^5}-\frac{c}{8 a^3 x^8}","-\frac{x \left(11 a^2 b e-5 a^3 f-17 a b^2 d+23 b^3 c\right)}{18 a^5 \left(a+b x^3\right)}-\frac{x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^4 \left(a+b x^3\right)^2}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(20 a^2 b e-5 a^3 f-44 a b^2 d+77 b^3 c\right)}{54 a^{17/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(20 a^2 b e-5 a^3 f-44 a b^2 d+77 b^3 c\right)}{27 a^{17/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(20 a^2 b e-5 a^3 f-44 a b^2 d+77 b^3 c\right)}{9 \sqrt{3} a^{17/3} \sqrt[3]{b}}-\frac{a^2 e-3 a b d+6 b^2 c}{2 a^5 x^2}+\frac{3 b c-a d}{5 a^4 x^5}-\frac{c}{8 a^3 x^8}",1,"-c/(8*a^3*x^8) + (3*b*c - a*d)/(5*a^4*x^5) - (6*b^2*c - 3*a*b*d + a^2*e)/(2*a^5*x^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a^4*(a + b*x^3)^2) - ((23*b^3*c - 17*a*b^2*d + 11*a^2*b*e - 5*a^3*f)*x)/(18*a^5*(a + b*x^3)) + ((77*b^3*c - 44*a*b^2*d + 20*a^2*b*e - 5*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(17/3)*b^(1/3)) - ((77*b^3*c - 44*a*b^2*d + 20*a^2*b*e - 5*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(17/3)*b^(1/3)) + ((77*b^3*c - 44*a*b^2*d + 20*a^2*b*e - 5*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(17/3)*b^(1/3))","A",10,8,30,0.2667,1,"{1829, 1834, 200, 31, 634, 617, 204, 628}"
301,1,381,0,0.7135721,"\int \frac{c+d x^3+e x^6+f x^9}{x^{11} \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^11*(a + b*x^3)^3),x]","\frac{b x^2 \left(8 a^2 b e-5 a^3 f-11 a b^2 d+14 b^3 c\right)}{9 a^6 \left(a+b x^3\right)}+\frac{b x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^5 \left(a+b x^3\right)^2}+\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(35 a^2 b e-14 a^3 f-65 a b^2 d+104 b^3 c\right)}{54 a^{19/3}}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{a^6 x}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(35 a^2 b e-14 a^3 f-65 a b^2 d+104 b^3 c\right)}{27 a^{19/3}}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(35 a^2 b e-14 a^3 f-65 a b^2 d+104 b^3 c\right)}{9 \sqrt{3} a^{19/3}}-\frac{a^2 e-3 a b d+6 b^2 c}{4 a^5 x^4}+\frac{3 b c-a d}{7 a^4 x^7}-\frac{c}{10 a^3 x^{10}}","\frac{b x^2 \left(8 a^2 b e-5 a^3 f-11 a b^2 d+14 b^3 c\right)}{9 a^6 \left(a+b x^3\right)}+\frac{b x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^5 \left(a+b x^3\right)^2}+\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(35 a^2 b e-14 a^3 f-65 a b^2 d+104 b^3 c\right)}{54 a^{19/3}}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{a^6 x}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(35 a^2 b e-14 a^3 f-65 a b^2 d+104 b^3 c\right)}{27 a^{19/3}}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(35 a^2 b e-14 a^3 f-65 a b^2 d+104 b^3 c\right)}{9 \sqrt{3} a^{19/3}}-\frac{a^2 e-3 a b d+6 b^2 c}{4 a^5 x^4}+\frac{3 b c-a d}{7 a^4 x^7}-\frac{c}{10 a^3 x^{10}}",1,"-c/(10*a^3*x^10) + (3*b*c - a*d)/(7*a^4*x^7) - (6*b^2*c - 3*a*b*d + a^2*e)/(4*a^5*x^4) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(a^6*x) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^5*(a + b*x^3)^2) + (b*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*x^2)/(9*a^6*(a + b*x^3)) - (b^(1/3)*(104*b^3*c - 65*a*b^2*d + 35*a^2*b*e - 14*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(19/3)) - (b^(1/3)*(104*b^3*c - 65*a*b^2*d + 35*a^2*b*e - 14*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(19/3)) + (b^(1/3)*(104*b^3*c - 65*a*b^2*d + 35*a^2*b*e - 14*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(19/3))","A",10,8,30,0.2667,1,"{1829, 1834, 292, 31, 634, 617, 204, 628}"
302,1,380,0,0.6689658,"\int \frac{c+d x^3+e x^6+f x^9}{x^{12} \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^12*(a + b*x^3)^3),x]","\frac{b x \left(17 a^2 b e-11 a^3 f-23 a b^2 d+29 b^3 c\right)}{18 a^6 \left(a+b x^3\right)}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{2 a^6 x^2}+\frac{b x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^5 \left(a+b x^3\right)^2}-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(44 a^2 b e-20 a^3 f-77 a b^2 d+119 b^3 c\right)}{54 a^{20/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(44 a^2 b e-20 a^3 f-77 a b^2 d+119 b^3 c\right)}{27 a^{20/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(44 a^2 b e-20 a^3 f-77 a b^2 d+119 b^3 c\right)}{9 \sqrt{3} a^{20/3}}-\frac{a^2 e-3 a b d+6 b^2 c}{5 a^5 x^5}+\frac{3 b c-a d}{8 a^4 x^8}-\frac{c}{11 a^3 x^{11}}","\frac{b x \left(17 a^2 b e-11 a^3 f-23 a b^2 d+29 b^3 c\right)}{18 a^6 \left(a+b x^3\right)}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{2 a^6 x^2}+\frac{b x \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^5 \left(a+b x^3\right)^2}-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(44 a^2 b e-20 a^3 f-77 a b^2 d+119 b^3 c\right)}{54 a^{20/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(44 a^2 b e-20 a^3 f-77 a b^2 d+119 b^3 c\right)}{27 a^{20/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(44 a^2 b e-20 a^3 f-77 a b^2 d+119 b^3 c\right)}{9 \sqrt{3} a^{20/3}}-\frac{a^2 e-3 a b d+6 b^2 c}{5 a^5 x^5}+\frac{3 b c-a d}{8 a^4 x^8}-\frac{c}{11 a^3 x^{11}}",1,"-c/(11*a^3*x^11) + (3*b*c - a*d)/(8*a^4*x^8) - (6*b^2*c - 3*a*b*d + a^2*e)/(5*a^5*x^5) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(2*a^6*x^2) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a^5*(a + b*x^3)^2) + (b*(29*b^3*c - 23*a*b^2*d + 17*a^2*b*e - 11*a^3*f)*x)/(18*a^6*(a + b*x^3)) - (b^(2/3)*(119*b^3*c - 77*a*b^2*d + 44*a^2*b*e - 20*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(20/3)) + (b^(2/3)*(119*b^3*c - 77*a*b^2*d + 44*a^2*b*e - 20*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(20/3)) - (b^(2/3)*(119*b^3*c - 77*a*b^2*d + 44*a^2*b*e - 20*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(20/3))","A",10,8,30,0.2667,1,"{1829, 1834, 200, 31, 634, 617, 204, 628}"
303,1,424,0,0.8531375,"\int \frac{c+d x^3+e x^6+f x^9}{x^{14} \left(a+b x^3\right)^3} \, dx","Int[(c + d*x^3 + e*x^6 + f*x^9)/(x^14*(a + b*x^3)^3),x]","-\frac{b^2 x^2 \left(11 a^2 b e-8 a^3 f-14 a b^2 d+17 b^3 c\right)}{9 a^7 \left(a+b x^3\right)}-\frac{b^2 x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^6 \left(a+b x^3\right)^2}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{4 a^6 x^4}-\frac{b^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(65 a^2 b e-35 a^3 f-104 a b^2 d+152 b^3 c\right)}{54 a^{22/3}}-\frac{b \left(6 a^2 b e-3 a^3 f-10 a b^2 d+15 b^3 c\right)}{a^7 x}+\frac{b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(65 a^2 b e-35 a^3 f-104 a b^2 d+152 b^3 c\right)}{27 a^{22/3}}+\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(65 a^2 b e-35 a^3 f-104 a b^2 d+152 b^3 c\right)}{9 \sqrt{3} a^{22/3}}-\frac{a^2 e-3 a b d+6 b^2 c}{7 a^5 x^7}+\frac{3 b c-a d}{10 a^4 x^{10}}-\frac{c}{13 a^3 x^{13}}","-\frac{b^2 x^2 \left(11 a^2 b e-8 a^3 f-14 a b^2 d+17 b^3 c\right)}{9 a^7 \left(a+b x^3\right)}-\frac{b^2 x^2 \left(a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right)}{6 a^6 \left(a+b x^3\right)^2}+\frac{3 a^2 b e+a^3 (-f)-6 a b^2 d+10 b^3 c}{4 a^6 x^4}-\frac{b^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(65 a^2 b e-35 a^3 f-104 a b^2 d+152 b^3 c\right)}{54 a^{22/3}}-\frac{b \left(6 a^2 b e-3 a^3 f-10 a b^2 d+15 b^3 c\right)}{a^7 x}+\frac{b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(65 a^2 b e-35 a^3 f-104 a b^2 d+152 b^3 c\right)}{27 a^{22/3}}+\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(65 a^2 b e-35 a^3 f-104 a b^2 d+152 b^3 c\right)}{9 \sqrt{3} a^{22/3}}-\frac{a^2 e-3 a b d+6 b^2 c}{7 a^5 x^7}+\frac{3 b c-a d}{10 a^4 x^{10}}-\frac{c}{13 a^3 x^{13}}",1,"-c/(13*a^3*x^13) + (3*b*c - a*d)/(10*a^4*x^10) - (6*b^2*c - 3*a*b*d + a^2*e)/(7*a^5*x^7) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(4*a^6*x^4) - (b*(15*b^3*c - 10*a*b^2*d + 6*a^2*b*e - 3*a^3*f))/(a^7*x) - (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^6*(a + b*x^3)^2) - (b^2*(17*b^3*c - 14*a*b^2*d + 11*a^2*b*e - 8*a^3*f)*x^2)/(9*a^7*(a + b*x^3)) + (b^(4/3)*(152*b^3*c - 104*a*b^2*d + 65*a^2*b*e - 35*a^3*f)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(22/3)) + (b^(4/3)*(152*b^3*c - 104*a*b^2*d + 65*a^2*b*e - 35*a^3*f)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(22/3)) - (b^(4/3)*(152*b^3*c - 104*a*b^2*d + 65*a^2*b*e - 35*a^3*f)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(22/3))","A",10,8,30,0.2667,1,"{1829, 1834, 292, 31, 634, 617, 204, 628}"
304,1,54,0,0.0719371,"\int \frac{(1-x) x^4}{1+x^3} \, dx","Int[((1 - x)*x^4)/(1 + x^3),x]","-\frac{x^3}{3}+\frac{x^2}{2}+\frac{1}{6} \log \left(x^2-x+1\right)+\frac{2}{3} \log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{x^3}{3}+\frac{x^2}{2}+\frac{1}{6} \log \left(x^2-x+1\right)+\frac{2}{3} \log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"x^2/2 - x^3/3 + ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3] + (2*Log[1 + x])/3 + Log[1 - x + x^2]/6","A",8,7,16,0.4375,1,"{1887, 1874, 31, 634, 618, 204, 628}"
305,1,30,0,0.0400098,"\int \frac{(1-x) x^3}{1+x^3} \, dx","Int[((1 - x)*x^3)/(1 + x^3),x]","-\frac{x^2}{2}+\frac{1}{3} \log \left(x^2-x+1\right)+x-\frac{2}{3} \log (x+1)","-\frac{x^2}{2}+\frac{1}{3} \log \left(x^2-x+1\right)+x-\frac{2}{3} \log (x+1)",1,"x - x^2/2 - (2*Log[1 + x])/3 + Log[1 - x + x^2]/3","A",5,4,16,0.2500,1,"{1887, 1860, 31, 628}"
306,1,44,0,0.0598778,"\int \frac{(1-x) x^2}{1+x^3} \, dx","Int[((1 - x)*x^2)/(1 + x^3),x]","\frac{1}{6} \log \left(x^2-x+1\right)-x+\frac{2}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{6} \log \left(x^2-x+1\right)-x+\frac{2}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-x - ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3] + (2*Log[1 + x])/3 + Log[1 - x + x^2]/6","A",8,7,16,0.4375,1,"{1887, 1874, 31, 634, 618, 204, 628}"
307,1,41,0,0.0418063,"\int \frac{(1-x) x}{1+x^3} \, dx","Int[((1 - x)*x)/(1 + x^3),x]","-\frac{1}{6} \log \left(x^2-x+1\right)-\frac{2}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{6} \log \left(x^2-x+1\right)-\frac{2}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3]) - (2*Log[1 + x])/3 - Log[1 - x + x^2]/6","A",6,6,14,0.4286,1,"{1874, 31, 634, 618, 204, 628}"
308,1,42,0,0.0493821,"\int \frac{1-x}{x \left(1+x^3\right)} \, dx","Int[(1 - x)/(x*(1 + x^3)),x]","-\frac{1}{6} \log \left(x^2-x+1\right)+\log (x)-\frac{2}{3} \log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{6} \log \left(x^2-x+1\right)+\log (x)-\frac{2}{3} \log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3] + Log[x] - (2*Log[1 + x])/3 - Log[1 - x + x^2]/6","A",6,5,16,0.3125,1,"{1834, 634, 618, 204, 628}"
309,1,49,0,0.049683,"\int \frac{1-x}{x^2 \left(1+x^3\right)} \, dx","Int[(1 - x)/(x^2*(1 + x^3)),x]","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{x}-\log (x)+\frac{2}{3} \log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{x}-\log (x)+\frac{2}{3} \log (x+1)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-x^(-1) + ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3] - Log[x] + (2*Log[1 + x])/3 + Log[1 - x + x^2]/6","A",6,5,16,0.3125,1,"{1834, 634, 618, 204, 628}"
310,1,32,0,0.0326286,"\int \frac{1-x}{x^3 \left(1+x^3\right)} \, dx","Int[(1 - x)/(x^3*(1 + x^3)),x]","-\frac{1}{2 x^2}+\frac{1}{3} \log \left(x^2-x+1\right)+\frac{1}{x}-\frac{2}{3} \log (x+1)","-\frac{1}{2 x^2}+\frac{1}{3} \log \left(x^2-x+1\right)+\frac{1}{x}-\frac{2}{3} \log (x+1)",1,"-1/(2*x^2) + x^(-1) - (2*Log[1 + x])/3 + Log[1 - x + x^2]/3","A",3,2,16,0.1250,1,"{1834, 628}"
311,1,41,0,0.0410974,"\int \frac{x (1+2 x)}{1+x^3} \, dx","Int[(x*(1 + 2*x))/(1 + x^3),x]","\frac{5}{6} \log \left(x^2-x+1\right)+\frac{1}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{5}{6} \log \left(x^2-x+1\right)+\frac{1}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3]) + Log[1 + x]/3 + (5*Log[1 - x + x^2])/6","A",6,6,14,0.4286,1,"{1874, 31, 634, 618, 204, 628}"
312,1,39,0,0.0395694,"\int \frac{x (1+2 x)}{1-x^3} \, dx","Int[(x*(1 + 2*x))/(1 - x^3),x]","-\frac{1}{2} \log \left(x^2+x+1\right)-\log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{2} \log \left(x^2+x+1\right)-\log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) - Log[1 - x] - Log[1 + x + x^2]/2","A",6,6,16,0.3750,1,"{1875, 31, 634, 618, 204, 628}"
313,1,55,0,0.0554037,"\int x^2 \left(c+d x+e x^2\right) \left(a+b x^3\right) \, dx","Int[x^2*(c + d*x + e*x^2)*(a + b*x^3),x]","\frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{6} b c x^6+\frac{1}{7} b d x^7+\frac{1}{8} b e x^8","\frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{6} b c x^6+\frac{1}{7} b d x^7+\frac{1}{8} b e x^8",1,"(a*c*x^3)/3 + (a*d*x^4)/4 + (a*e*x^5)/5 + (b*c*x^6)/6 + (b*d*x^7)/7 + (b*e*x^8)/8","A",2,1,21,0.04762,1,"{1628}"
314,1,55,0,0.0376349,"\int x \left(c+d x+e x^2\right) \left(a+b x^3\right) \, dx","Int[x*(c + d*x + e*x^2)*(a + b*x^3),x]","\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7","\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7",1,"(a*c*x^2)/2 + (a*d*x^3)/3 + (a*e*x^4)/4 + (b*c*x^5)/5 + (b*d*x^6)/6 + (b*e*x^7)/7","A",2,1,19,0.05263,1,"{1628}"
315,1,50,0,0.0245263,"\int \left(c+d x+e x^2\right) \left(a+b x^3\right) \, dx","Int[(c + d*x + e*x^2)*(a + b*x^3),x]","a c x+\frac{1}{2} a d x^2+\frac{1}{3} a e x^3+\frac{1}{4} b c x^4+\frac{1}{5} b d x^5+\frac{1}{6} b e x^6","a c x+\frac{1}{2} a d x^2+\frac{1}{3} a e x^3+\frac{1}{4} b c x^4+\frac{1}{5} b d x^5+\frac{1}{6} b e x^6",1,"a*c*x + (a*d*x^2)/2 + (a*e*x^3)/3 + (b*c*x^4)/4 + (b*d*x^5)/5 + (b*e*x^6)/6","A",2,1,18,0.05556,1,"{1657}"
316,1,46,0,0.0245177,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)}{x} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3))/x,x]","a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{3} b c x^3+\frac{1}{4} b d x^4+\frac{1}{5} b e x^5","a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{3} b c x^3+\frac{1}{4} b d x^4+\frac{1}{5} b e x^5",1,"a*d*x + (a*e*x^2)/2 + (b*c*x^3)/3 + (b*d*x^4)/4 + (b*e*x^5)/5 + a*c*Log[x]","A",2,1,21,0.04762,1,"{1628}"
317,1,44,0,0.0350813,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)}{x^2} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3))/x^2,x]","-\frac{a c}{x}+a d \log (x)+a e x+\frac{1}{2} b c x^2+\frac{1}{3} b d x^3+\frac{1}{4} b e x^4","-\frac{a c}{x}+a d \log (x)+a e x+\frac{1}{2} b c x^2+\frac{1}{3} b d x^3+\frac{1}{4} b e x^4",1,"-((a*c)/x) + a*e*x + (b*c*x^2)/2 + (b*d*x^3)/3 + (b*e*x^4)/4 + a*d*Log[x]","A",2,1,21,0.04762,1,"{1628}"
318,1,44,0,0.0341978,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)}{x^3} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3))/x^3,x]","-\frac{a c}{2 x^2}-\frac{a d}{x}+a e \log (x)+b c x+\frac{1}{2} b d x^2+\frac{1}{3} b e x^3","-\frac{a c}{2 x^2}-\frac{a d}{x}+a e \log (x)+b c x+\frac{1}{2} b d x^2+\frac{1}{3} b e x^3",1,"-(a*c)/(2*x^2) - (a*d)/x + b*c*x + (b*d*x^2)/2 + (b*e*x^3)/3 + a*e*Log[x]","A",2,1,21,0.04762,1,"{1628}"
319,1,82,0,0.0589412,"\int x^2 \left(c+d x+e x^2\right) \left(a+b x^3\right)^2 \, dx","Int[x^2*(c + d*x + e*x^2)*(a + b*x^3)^2,x]","\frac{1}{4} a^2 d x^4+\frac{1}{5} a^2 e x^5+\frac{c \left(a+b x^3\right)^3}{9 b}+\frac{2}{7} a b d x^7+\frac{1}{4} a b e x^8+\frac{1}{10} b^2 d x^{10}+\frac{1}{11} b^2 e x^{11}","\frac{1}{4} a^2 d x^4+\frac{1}{5} a^2 e x^5+\frac{c \left(a+b x^3\right)^3}{9 b}+\frac{2}{7} a b d x^7+\frac{1}{4} a b e x^8+\frac{1}{10} b^2 d x^{10}+\frac{1}{11} b^2 e x^{11}",1,"(a^2*d*x^4)/4 + (a^2*e*x^5)/5 + (2*a*b*d*x^7)/7 + (a*b*e*x^8)/4 + (b^2*d*x^10)/10 + (b^2*e*x^11)/11 + (c*(a + b*x^3)^3)/(9*b)","A",3,2,23,0.08696,1,"{1582, 1850}"
320,1,82,0,0.0510239,"\int x \left(c+d x+e x^2\right) \left(a+b x^3\right)^2 \, dx","Int[x*(c + d*x + e*x^2)*(a + b*x^3)^2,x]","\frac{1}{2} a^2 c x^2+\frac{1}{4} a^2 e x^4+\frac{2}{5} a b c x^5+\frac{d \left(a+b x^3\right)^3}{9 b}+\frac{2}{7} a b e x^7+\frac{1}{8} b^2 c x^8+\frac{1}{10} b^2 e x^{10}","\frac{1}{2} a^2 c x^2+\frac{1}{4} a^2 e x^4+\frac{2}{5} a b c x^5+\frac{d \left(a+b x^3\right)^3}{9 b}+\frac{2}{7} a b e x^7+\frac{1}{8} b^2 c x^8+\frac{1}{10} b^2 e x^{10}",1,"(a^2*c*x^2)/2 + (a^2*e*x^4)/4 + (2*a*b*c*x^5)/5 + (2*a*b*e*x^7)/7 + (b^2*c*x^8)/8 + (b^2*e*x^10)/10 + (d*(a + b*x^3)^3)/(9*b)","A",3,2,21,0.09524,1,"{1582, 1850}"
321,1,77,0,0.0610721,"\int \left(c+d x+e x^2\right) \left(a+b x^3\right)^2 \, dx","Int[(c + d*x + e*x^2)*(a + b*x^3)^2,x]","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{2} a b c x^4+\frac{2}{5} a b d x^5+\frac{e \left(a+b x^3\right)^3}{9 b}+\frac{1}{7} b^2 c x^7+\frac{1}{8} b^2 d x^8","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{2} a b c x^4+\frac{2}{5} a b d x^5+\frac{e \left(a+b x^3\right)^3}{9 b}+\frac{1}{7} b^2 c x^7+\frac{1}{8} b^2 d x^8",1,"a^2*c*x + (a^2*d*x^2)/2 + (a*b*c*x^4)/2 + (2*a*b*d*x^5)/5 + (b^2*c*x^7)/7 + (b^2*d*x^8)/8 + (e*(a + b*x^3)^3)/(9*b)","A",3,2,20,0.1000,1,"{1582, 1850}"
322,1,88,0,0.0518618,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)^2}{x} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3)^2)/x,x]","a^2 c \log (x)+a^2 d x+\frac{1}{2} a^2 e x^2+\frac{2}{3} a b c x^3+\frac{1}{2} a b d x^4+\frac{2}{5} a b e x^5+\frac{1}{6} b^2 c x^6+\frac{1}{7} b^2 d x^7+\frac{1}{8} b^2 e x^8","a^2 c \log (x)+a^2 d x+\frac{1}{2} a^2 e x^2+\frac{2}{3} a b c x^3+\frac{1}{2} a b d x^4+\frac{2}{5} a b e x^5+\frac{1}{6} b^2 c x^6+\frac{1}{7} b^2 d x^7+\frac{1}{8} b^2 e x^8",1,"a^2*d*x + (a^2*e*x^2)/2 + (2*a*b*c*x^3)/3 + (a*b*d*x^4)/2 + (2*a*b*e*x^5)/5 + (b^2*c*x^6)/6 + (b^2*d*x^7)/7 + (b^2*e*x^8)/8 + a^2*c*Log[x]","A",2,1,23,0.04348,1,"{1628}"
323,1,83,0,0.0629493,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)^2}{x^2} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3)^2)/x^2,x]","-\frac{a^2 c}{x}+a^2 d \log (x)+a^2 e x+a b c x^2+\frac{2}{3} a b d x^3+\frac{1}{2} a b e x^4+\frac{1}{5} b^2 c x^5+\frac{1}{6} b^2 d x^6+\frac{1}{7} b^2 e x^7","-\frac{a^2 c}{x}+a^2 d \log (x)+a^2 e x+a b c x^2+\frac{2}{3} a b d x^3+\frac{1}{2} a b e x^4+\frac{1}{5} b^2 c x^5+\frac{1}{6} b^2 d x^6+\frac{1}{7} b^2 e x^7",1,"-((a^2*c)/x) + a^2*e*x + a*b*c*x^2 + (2*a*b*d*x^3)/3 + (a*b*e*x^4)/2 + (b^2*c*x^5)/5 + (b^2*d*x^6)/6 + (b^2*e*x^7)/7 + a^2*d*Log[x]","A",2,1,23,0.04348,1,"{1628}"
324,1,84,0,0.0641961,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)^2}{x^3} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3)^2)/x^3,x]","-\frac{a^2 c}{2 x^2}-\frac{a^2 d}{x}+a^2 e \log (x)+2 a b c x+a b d x^2+\frac{2}{3} a b e x^3+\frac{1}{4} b^2 c x^4+\frac{1}{5} b^2 d x^5+\frac{1}{6} b^2 e x^6","-\frac{a^2 c}{2 x^2}-\frac{a^2 d}{x}+a^2 e \log (x)+2 a b c x+a b d x^2+\frac{2}{3} a b e x^3+\frac{1}{4} b^2 c x^4+\frac{1}{5} b^2 d x^5+\frac{1}{6} b^2 e x^6",1,"-(a^2*c)/(2*x^2) - (a^2*d)/x + 2*a*b*c*x + a*b*d*x^2 + (2*a*b*e*x^3)/3 + (b^2*c*x^4)/4 + (b^2*d*x^5)/5 + (b^2*e*x^6)/6 + a^2*e*Log[x]","A",2,1,23,0.04348,1,"{1628}"
325,1,110,0,0.0787603,"\int x^2 \left(c+d x+e x^2\right) \left(a+b x^3\right)^3 \, dx","Int[x^2*(c + d*x + e*x^2)*(a + b*x^3)^3,x]","\frac{3}{7} a^2 b d x^7+\frac{3}{8} a^2 b e x^8+\frac{1}{4} a^3 d x^4+\frac{1}{5} a^3 e x^5+\frac{3}{10} a b^2 d x^{10}+\frac{3}{11} a b^2 e x^{11}+\frac{c \left(a+b x^3\right)^4}{12 b}+\frac{1}{13} b^3 d x^{13}+\frac{1}{14} b^3 e x^{14}","\frac{3}{7} a^2 b d x^7+\frac{3}{8} a^2 b e x^8+\frac{1}{4} a^3 d x^4+\frac{1}{5} a^3 e x^5+\frac{3}{10} a b^2 d x^{10}+\frac{3}{11} a b^2 e x^{11}+\frac{c \left(a+b x^3\right)^4}{12 b}+\frac{1}{13} b^3 d x^{13}+\frac{1}{14} b^3 e x^{14}",1,"(a^3*d*x^4)/4 + (a^3*e*x^5)/5 + (3*a^2*b*d*x^7)/7 + (3*a^2*b*e*x^8)/8 + (3*a*b^2*d*x^10)/10 + (3*a*b^2*e*x^11)/11 + (b^3*d*x^13)/13 + (b^3*e*x^14)/14 + (c*(a + b*x^3)^4)/(12*b)","A",3,2,23,0.08696,1,"{1582, 1850}"
326,1,110,0,0.0693723,"\int x \left(c+d x+e x^2\right) \left(a+b x^3\right)^3 \, dx","Int[x*(c + d*x + e*x^2)*(a + b*x^3)^3,x]","\frac{3}{5} a^2 b c x^5+\frac{3}{7} a^2 b e x^7+\frac{1}{2} a^3 c x^2+\frac{1}{4} a^3 e x^4+\frac{3}{8} a b^2 c x^8+\frac{3}{10} a b^2 e x^{10}+\frac{d \left(a+b x^3\right)^4}{12 b}+\frac{1}{11} b^3 c x^{11}+\frac{1}{13} b^3 e x^{13}","\frac{3}{5} a^2 b c x^5+\frac{3}{7} a^2 b e x^7+\frac{1}{2} a^3 c x^2+\frac{1}{4} a^3 e x^4+\frac{3}{8} a b^2 c x^8+\frac{3}{10} a b^2 e x^{10}+\frac{d \left(a+b x^3\right)^4}{12 b}+\frac{1}{11} b^3 c x^{11}+\frac{1}{13} b^3 e x^{13}",1,"(a^3*c*x^2)/2 + (a^3*e*x^4)/4 + (3*a^2*b*c*x^5)/5 + (3*a^2*b*e*x^7)/7 + (3*a*b^2*c*x^8)/8 + (3*a*b^2*e*x^10)/10 + (b^3*c*x^11)/11 + (b^3*e*x^13)/13 + (d*(a + b*x^3)^4)/(12*b)","A",3,2,21,0.09524,1,"{1582, 1850}"
327,1,105,0,0.0969183,"\int \left(c+d x+e x^2\right) \left(a+b x^3\right)^3 \, dx","Int[(c + d*x + e*x^2)*(a + b*x^3)^3,x]","\frac{3}{4} a^2 b c x^4+\frac{3}{5} a^2 b d x^5+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{3}{7} a b^2 c x^7+\frac{3}{8} a b^2 d x^8+\frac{e \left(a+b x^3\right)^4}{12 b}+\frac{1}{10} b^3 c x^{10}+\frac{1}{11} b^3 d x^{11}","\frac{3}{4} a^2 b c x^4+\frac{3}{5} a^2 b d x^5+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{3}{7} a b^2 c x^7+\frac{3}{8} a b^2 d x^8+\frac{e \left(a+b x^3\right)^4}{12 b}+\frac{1}{10} b^3 c x^{10}+\frac{1}{11} b^3 d x^{11}",1,"a^3*c*x + (a^3*d*x^2)/2 + (3*a^2*b*c*x^4)/4 + (3*a^2*b*d*x^5)/5 + (3*a*b^2*c*x^7)/7 + (3*a*b^2*d*x^8)/8 + (b^3*c*x^10)/10 + (b^3*d*x^11)/11 + (e*(a + b*x^3)^4)/(12*b)","A",3,2,20,0.1000,1,"{1582, 1850}"
328,1,127,0,0.0736885,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)^3}{x} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3)^3)/x,x]","a^2 b c x^3+\frac{3}{4} a^2 b d x^4+\frac{3}{5} a^2 b e x^5+a^3 c \log (x)+a^3 d x+\frac{1}{2} a^3 e x^2+\frac{1}{2} a b^2 c x^6+\frac{3}{7} a b^2 d x^7+\frac{3}{8} a b^2 e x^8+\frac{1}{9} b^3 c x^9+\frac{1}{10} b^3 d x^{10}+\frac{1}{11} b^3 e x^{11}","a^2 b c x^3+\frac{3}{4} a^2 b d x^4+\frac{3}{5} a^2 b e x^5+a^3 c \log (x)+a^3 d x+\frac{1}{2} a^3 e x^2+\frac{1}{2} a b^2 c x^6+\frac{3}{7} a b^2 d x^7+\frac{3}{8} a b^2 e x^8+\frac{1}{9} b^3 c x^9+\frac{1}{10} b^3 d x^{10}+\frac{1}{11} b^3 e x^{11}",1,"a^3*d*x + (a^3*e*x^2)/2 + a^2*b*c*x^3 + (3*a^2*b*d*x^4)/4 + (3*a^2*b*e*x^5)/5 + (a*b^2*c*x^6)/2 + (3*a*b^2*d*x^7)/7 + (3*a*b^2*e*x^8)/8 + (b^3*c*x^9)/9 + (b^3*d*x^10)/10 + (b^3*e*x^11)/11 + a^3*c*Log[x]","A",2,1,23,0.04348,1,"{1628}"
329,1,125,0,0.0922203,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)^3}{x^2} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3)^3)/x^2,x]","\frac{3}{2} a^2 b c x^2+a^2 b d x^3+\frac{3}{4} a^2 b e x^4-\frac{a^3 c}{x}+a^3 d \log (x)+a^3 e x+\frac{3}{5} a b^2 c x^5+\frac{1}{2} a b^2 d x^6+\frac{3}{7} a b^2 e x^7+\frac{1}{8} b^3 c x^8+\frac{1}{9} b^3 d x^9+\frac{1}{10} b^3 e x^{10}","\frac{3}{2} a^2 b c x^2+a^2 b d x^3+\frac{3}{4} a^2 b e x^4-\frac{a^3 c}{x}+a^3 d \log (x)+a^3 e x+\frac{3}{5} a b^2 c x^5+\frac{1}{2} a b^2 d x^6+\frac{3}{7} a b^2 e x^7+\frac{1}{8} b^3 c x^8+\frac{1}{9} b^3 d x^9+\frac{1}{10} b^3 e x^{10}",1,"-((a^3*c)/x) + a^3*e*x + (3*a^2*b*c*x^2)/2 + a^2*b*d*x^3 + (3*a^2*b*e*x^4)/4 + (3*a*b^2*c*x^5)/5 + (a*b^2*d*x^6)/2 + (3*a*b^2*e*x^7)/7 + (b^3*c*x^8)/8 + (b^3*d*x^9)/9 + (b^3*e*x^10)/10 + a^3*d*Log[x]","A",2,1,23,0.04348,1,"{1628}"
330,1,126,0,0.0864589,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)^3}{x^3} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3)^3)/x^3,x]","3 a^2 b c x+\frac{3}{2} a^2 b d x^2+a^2 b e x^3-\frac{a^3 c}{2 x^2}-\frac{a^3 d}{x}+a^3 e \log (x)+\frac{3}{4} a b^2 c x^4+\frac{3}{5} a b^2 d x^5+\frac{1}{2} a b^2 e x^6+\frac{1}{7} b^3 c x^7+\frac{1}{8} b^3 d x^8+\frac{1}{9} b^3 e x^9","3 a^2 b c x+\frac{3}{2} a^2 b d x^2+a^2 b e x^3-\frac{a^3 c}{2 x^2}-\frac{a^3 d}{x}+a^3 e \log (x)+\frac{3}{4} a b^2 c x^4+\frac{3}{5} a b^2 d x^5+\frac{1}{2} a b^2 e x^6+\frac{1}{7} b^3 c x^7+\frac{1}{8} b^3 d x^8+\frac{1}{9} b^3 e x^9",1,"-(a^3*c)/(2*x^2) - (a^3*d)/x + 3*a^2*b*c*x + (3*a^2*b*d*x^2)/2 + a^2*b*e*x^3 + (3*a*b^2*c*x^4)/4 + (3*a*b^2*d*x^5)/5 + (a*b^2*e*x^6)/2 + (b^3*c*x^7)/7 + (b^3*d*x^8)/8 + (b^3*e*x^9)/9 + a^3*e*Log[x]","A",2,1,23,0.04348,1,"{1628}"
331,1,138,0,0.0985253,"\int x^2 \left(c+d x+e x^2\right) \left(a+b x^3\right)^4 \, dx","Int[x^2*(c + d*x + e*x^2)*(a + b*x^3)^4,x]","\frac{3}{5} a^2 b^2 d x^{10}+\frac{6}{11} a^2 b^2 e x^{11}+\frac{4}{7} a^3 b d x^7+\frac{1}{2} a^3 b e x^8+\frac{1}{4} a^4 d x^4+\frac{1}{5} a^4 e x^5+\frac{4}{13} a b^3 d x^{13}+\frac{2}{7} a b^3 e x^{14}+\frac{c \left(a+b x^3\right)^5}{15 b}+\frac{1}{16} b^4 d x^{16}+\frac{1}{17} b^4 e x^{17}","\frac{3}{5} a^2 b^2 d x^{10}+\frac{6}{11} a^2 b^2 e x^{11}+\frac{4}{7} a^3 b d x^7+\frac{1}{2} a^3 b e x^8+\frac{1}{4} a^4 d x^4+\frac{1}{5} a^4 e x^5+\frac{4}{13} a b^3 d x^{13}+\frac{2}{7} a b^3 e x^{14}+\frac{c \left(a+b x^3\right)^5}{15 b}+\frac{1}{16} b^4 d x^{16}+\frac{1}{17} b^4 e x^{17}",1,"(a^4*d*x^4)/4 + (a^4*e*x^5)/5 + (4*a^3*b*d*x^7)/7 + (a^3*b*e*x^8)/2 + (3*a^2*b^2*d*x^10)/5 + (6*a^2*b^2*e*x^11)/11 + (4*a*b^3*d*x^13)/13 + (2*a*b^3*e*x^14)/7 + (b^4*d*x^16)/16 + (b^4*e*x^17)/17 + (c*(a + b*x^3)^5)/(15*b)","A",3,2,23,0.08696,1,"{1582, 1850}"
332,1,138,0,0.0934948,"\int x \left(c+d x+e x^2\right) \left(a+b x^3\right)^4 \, dx","Int[x*(c + d*x + e*x^2)*(a + b*x^3)^4,x]","\frac{3}{4} a^2 b^2 c x^8+\frac{3}{5} a^2 b^2 e x^{10}+\frac{4}{5} a^3 b c x^5+\frac{4}{7} a^3 b e x^7+\frac{1}{2} a^4 c x^2+\frac{1}{4} a^4 e x^4+\frac{4}{11} a b^3 c x^{11}+\frac{4}{13} a b^3 e x^{13}+\frac{d \left(a+b x^3\right)^5}{15 b}+\frac{1}{14} b^4 c x^{14}+\frac{1}{16} b^4 e x^{16}","\frac{3}{4} a^2 b^2 c x^8+\frac{3}{5} a^2 b^2 e x^{10}+\frac{4}{5} a^3 b c x^5+\frac{4}{7} a^3 b e x^7+\frac{1}{2} a^4 c x^2+\frac{1}{4} a^4 e x^4+\frac{4}{11} a b^3 c x^{11}+\frac{4}{13} a b^3 e x^{13}+\frac{d \left(a+b x^3\right)^5}{15 b}+\frac{1}{14} b^4 c x^{14}+\frac{1}{16} b^4 e x^{16}",1,"(a^4*c*x^2)/2 + (a^4*e*x^4)/4 + (4*a^3*b*c*x^5)/5 + (4*a^3*b*e*x^7)/7 + (3*a^2*b^2*c*x^8)/4 + (3*a^2*b^2*e*x^10)/5 + (4*a*b^3*c*x^11)/11 + (4*a*b^3*e*x^13)/13 + (b^4*c*x^14)/14 + (b^4*e*x^16)/16 + (d*(a + b*x^3)^5)/(15*b)","A",3,2,21,0.09524,1,"{1582, 1850}"
333,1,130,0,0.1449085,"\int \left(c+d x+e x^2\right) \left(a+b x^3\right)^4 \, dx","Int[(c + d*x + e*x^2)*(a + b*x^3)^4,x]","\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+a^4 c x+\frac{1}{2} a^4 d x^2+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{e \left(a+b x^3\right)^5}{15 b}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14}","\frac{6}{7} a^2 b^2 c x^7+\frac{3}{4} a^2 b^2 d x^8+a^3 b c x^4+\frac{4}{5} a^3 b d x^5+a^4 c x+\frac{1}{2} a^4 d x^2+\frac{2}{5} a b^3 c x^{10}+\frac{4}{11} a b^3 d x^{11}+\frac{e \left(a+b x^3\right)^5}{15 b}+\frac{1}{13} b^4 c x^{13}+\frac{1}{14} b^4 d x^{14}",1,"a^4*c*x + (a^4*d*x^2)/2 + a^3*b*c*x^4 + (4*a^3*b*d*x^5)/5 + (6*a^2*b^2*c*x^7)/7 + (3*a^2*b^2*d*x^8)/4 + (2*a*b^3*c*x^10)/5 + (4*a*b^3*d*x^11)/11 + (b^4*c*x^13)/13 + (b^4*d*x^14)/14 + (e*(a + b*x^3)^5)/(15*b)","A",3,2,20,0.1000,1,"{1582, 1850}"
334,1,166,0,0.1085342,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)^4}{x} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3)^4)/x,x]","a^2 b^2 c x^6+\frac{6}{7} a^2 b^2 d x^7+\frac{3}{4} a^2 b^2 e x^8+\frac{4}{3} a^3 b c x^3+a^3 b d x^4+\frac{4}{5} a^3 b e x^5+a^4 c \log (x)+a^4 d x+\frac{1}{2} a^4 e x^2+\frac{4}{9} a b^3 c x^9+\frac{2}{5} a b^3 d x^{10}+\frac{4}{11} a b^3 e x^{11}+\frac{1}{12} b^4 c x^{12}+\frac{1}{13} b^4 d x^{13}+\frac{1}{14} b^4 e x^{14}","a^2 b^2 c x^6+\frac{6}{7} a^2 b^2 d x^7+\frac{3}{4} a^2 b^2 e x^8+\frac{4}{3} a^3 b c x^3+a^3 b d x^4+\frac{4}{5} a^3 b e x^5+a^4 c \log (x)+a^4 d x+\frac{1}{2} a^4 e x^2+\frac{4}{9} a b^3 c x^9+\frac{2}{5} a b^3 d x^{10}+\frac{4}{11} a b^3 e x^{11}+\frac{1}{12} b^4 c x^{12}+\frac{1}{13} b^4 d x^{13}+\frac{1}{14} b^4 e x^{14}",1,"a^4*d*x + (a^4*e*x^2)/2 + (4*a^3*b*c*x^3)/3 + a^3*b*d*x^4 + (4*a^3*b*e*x^5)/5 + a^2*b^2*c*x^6 + (6*a^2*b^2*d*x^7)/7 + (3*a^2*b^2*e*x^8)/4 + (4*a*b^3*c*x^9)/9 + (2*a*b^3*d*x^10)/5 + (4*a*b^3*e*x^11)/11 + (b^4*c*x^12)/12 + (b^4*d*x^13)/13 + (b^4*e*x^14)/14 + a^4*c*Log[x]","A",2,1,23,0.04348,1,"{1628}"
335,1,162,0,0.1333203,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)^4}{x^2} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3)^4)/x^2,x]","\frac{6}{5} a^2 b^2 c x^5+a^2 b^2 d x^6+\frac{6}{7} a^2 b^2 e x^7+2 a^3 b c x^2+\frac{4}{3} a^3 b d x^3+a^3 b e x^4-\frac{a^4 c}{x}+a^4 d \log (x)+a^4 e x+\frac{1}{2} a b^3 c x^8+\frac{4}{9} a b^3 d x^9+\frac{2}{5} a b^3 e x^{10}+\frac{1}{11} b^4 c x^{11}+\frac{1}{12} b^4 d x^{12}+\frac{1}{13} b^4 e x^{13}","\frac{6}{5} a^2 b^2 c x^5+a^2 b^2 d x^6+\frac{6}{7} a^2 b^2 e x^7+2 a^3 b c x^2+\frac{4}{3} a^3 b d x^3+a^3 b e x^4-\frac{a^4 c}{x}+a^4 d \log (x)+a^4 e x+\frac{1}{2} a b^3 c x^8+\frac{4}{9} a b^3 d x^9+\frac{2}{5} a b^3 e x^{10}+\frac{1}{11} b^4 c x^{11}+\frac{1}{12} b^4 d x^{12}+\frac{1}{13} b^4 e x^{13}",1,"-((a^4*c)/x) + a^4*e*x + 2*a^3*b*c*x^2 + (4*a^3*b*d*x^3)/3 + a^3*b*e*x^4 + (6*a^2*b^2*c*x^5)/5 + a^2*b^2*d*x^6 + (6*a^2*b^2*e*x^7)/7 + (a*b^3*c*x^8)/2 + (4*a*b^3*d*x^9)/9 + (2*a*b^3*e*x^10)/5 + (b^4*c*x^11)/11 + (b^4*d*x^12)/12 + (b^4*e*x^13)/13 + a^4*d*Log[x]","A",2,1,23,0.04348,1,"{1628}"
336,1,166,0,0.1247751,"\int \frac{\left(c+d x+e x^2\right) \left(a+b x^3\right)^4}{x^3} \, dx","Int[((c + d*x + e*x^2)*(a + b*x^3)^4)/x^3,x]","\frac{3}{2} a^2 b^2 c x^4+\frac{6}{5} a^2 b^2 d x^5+a^2 b^2 e x^6+4 a^3 b c x+2 a^3 b d x^2+\frac{4}{3} a^3 b e x^3-\frac{a^4 c}{2 x^2}-\frac{a^4 d}{x}+a^4 e \log (x)+\frac{4}{7} a b^3 c x^7+\frac{1}{2} a b^3 d x^8+\frac{4}{9} a b^3 e x^9+\frac{1}{10} b^4 c x^{10}+\frac{1}{11} b^4 d x^{11}+\frac{1}{12} b^4 e x^{12}","\frac{3}{2} a^2 b^2 c x^4+\frac{6}{5} a^2 b^2 d x^5+a^2 b^2 e x^6+4 a^3 b c x+2 a^3 b d x^2+\frac{4}{3} a^3 b e x^3-\frac{a^4 c}{2 x^2}-\frac{a^4 d}{x}+a^4 e \log (x)+\frac{4}{7} a b^3 c x^7+\frac{1}{2} a b^3 d x^8+\frac{4}{9} a b^3 e x^9+\frac{1}{10} b^4 c x^{10}+\frac{1}{11} b^4 d x^{11}+\frac{1}{12} b^4 e x^{12}",1,"-(a^4*c)/(2*x^2) - (a^4*d)/x + 4*a^3*b*c*x + 2*a^3*b*d*x^2 + (4*a^3*b*e*x^3)/3 + (3*a^2*b^2*c*x^4)/2 + (6*a^2*b^2*d*x^5)/5 + a^2*b^2*e*x^6 + (4*a*b^3*c*x^7)/7 + (a*b^3*d*x^8)/2 + (4*a*b^3*e*x^9)/9 + (b^4*c*x^10)/10 + (b^4*d*x^11)/11 + (b^4*e*x^12)/12 + a^4*e*Log[x]","A",2,1,23,0.04348,1,"{1628}"
337,1,205,0,0.2614643,"\int \frac{x^3 \left(c+d x+e x^2\right)}{a+b x^3} \, dx","Int[(x^3*(c + d*x + e*x^2))/(a + b*x^3),x]","\frac{\sqrt[3]{a} \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3}}-\frac{\sqrt[3]{a} \left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3}}+\frac{\sqrt[3]{a} \left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}-\frac{a e \log \left(a+b x^3\right)}{3 b^2}+\frac{c x}{b}+\frac{d x^2}{2 b}+\frac{e x^3}{3 b}","\frac{\sqrt[3]{a} \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3}}-\frac{\sqrt[3]{a} \left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3}}+\frac{\sqrt[3]{a} \left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}-\frac{a e \log \left(a+b x^3\right)}{3 b^2}+\frac{c x}{b}+\frac{d x^2}{2 b}+\frac{e x^3}{3 b}",1,"(c*x)/b + (d*x^2)/(2*b) + (e*x^3)/(3*b) + (a^(1/3)*(b^(1/3)*c + a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(5/3)) - (a^(1/3)*(b^(1/3)*c - a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(5/3)) + (a^(1/3)*(c - (a^(1/3)*d)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(4/3)) - (a*e*Log[a + b*x^3])/(3*b^2)","A",10,9,23,0.3913,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
338,1,193,0,0.2478586,"\int \frac{x^2 \left(c+d x+e x^2\right)}{a+b x^3} \, dx","Int[(x^2*(c + d*x + e*x^2))/(a + b*x^3),x]","\frac{\sqrt[3]{a} \left(d-\frac{\sqrt[3]{a} e}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3}}-\frac{\sqrt[3]{a} \left(\sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3}}+\frac{\sqrt[3]{a} \left(\sqrt[3]{a} e+\sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}+\frac{c \log \left(a+b x^3\right)}{3 b}+\frac{d x}{b}+\frac{e x^2}{2 b}","\frac{\sqrt[3]{a} \left(d-\frac{\sqrt[3]{a} e}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3}}-\frac{\sqrt[3]{a} \left(\sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3}}+\frac{\sqrt[3]{a} \left(\sqrt[3]{a} e+\sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}+\frac{c \log \left(a+b x^3\right)}{3 b}+\frac{d x}{b}+\frac{e x^2}{2 b}",1,"(d*x)/b + (e*x^2)/(2*b) + (a^(1/3)*(b^(1/3)*d + a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(5/3)) - (a^(1/3)*(b^(1/3)*d - a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(5/3)) + (a^(1/3)*(d - (a^(1/3)*e)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(4/3)) + (c*Log[a + b*x^3])/(3*b)","A",10,9,23,0.3913,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
339,1,183,0,0.2255882,"\int \frac{x \left(c+d x+e x^2\right)}{a+b x^3} \, dx","Int[(x*(c + d*x + e*x^2))/(a + b*x^3),x]","\frac{\left(a^{2/3} e+b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{4/3}}-\frac{\left(a^{2/3} e+b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{4/3}}-\frac{\left(b^{2/3} c-a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{4/3}}+\frac{d \log \left(a+b x^3\right)}{3 b}+\frac{e x}{b}","\frac{\left(a^{2/3} e+b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{4/3}}-\frac{\left(a^{2/3} e+b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{4/3}}-\frac{\left(b^{2/3} c-a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{4/3}}+\frac{d \log \left(a+b x^3\right)}{3 b}+\frac{e x}{b}",1,"(e*x)/b - ((b^(2/3)*c - a^(2/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b^(4/3)) - ((b^(2/3)*c + a^(2/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(1/3)*b^(4/3)) + ((b^(2/3)*c + a^(2/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(1/3)*b^(4/3)) + (d*Log[a + b*x^3])/(3*b)","A",10,9,21,0.4286,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
340,1,177,0,0.1324351,"\int \frac{c+d x+e x^2}{a+b x^3} \, dx","Int[(c + d*x + e*x^2)/(a + b*x^3),x]","-\frac{\left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}+\frac{e \log \left(a+b x^3\right)}{3 b}","-\frac{\left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}+\frac{e \log \left(a+b x^3\right)}{3 b}",1,"-(((b^(1/3)*c + a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(2/3))) + ((b^(1/3)*c - a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(2/3)) - ((c - (a^(1/3)*d)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(1/3)) + (e*Log[a + b*x^3])/(3*b)","A",8,8,20,0.4000,1,"{1871, 1860, 31, 634, 617, 204, 628, 260}"
341,1,184,0,0.2064113,"\int \frac{c+d x+e x^2}{x \left(a+b x^3\right)} \, dx","Int[(c + d*x + e*x^2)/(x*(a + b*x^3)),x]","-\frac{\left(d-\frac{\sqrt[3]{a} e}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(\sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} e+\sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}-\frac{c \log \left(a+b x^3\right)}{3 a}+\frac{c \log (x)}{a}","-\frac{\left(d-\frac{\sqrt[3]{a} e}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\left(\sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} e+\sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{2/3}}-\frac{c \log \left(a+b x^3\right)}{3 a}+\frac{c \log (x)}{a}",1,"-(((b^(1/3)*d + a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(2/3))) + (c*Log[x])/a + ((b^(1/3)*d - a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(2/3)) - ((d - (a^(1/3)*e)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(1/3)) - (c*Log[a + b*x^3])/(3*a)","A",10,9,23,0.3913,1,"{1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
342,1,192,0,0.2137567,"\int \frac{c+d x+e x^2}{x^2 \left(a+b x^3\right)} \, dx","Int[(c + d*x + e*x^2)/(x^2*(a + b*x^3)),x]","-\frac{\left(a^{2/3} e+b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3} \sqrt[3]{b}}+\frac{\left(a^{2/3} e+b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3} \sqrt[3]{b}}+\frac{\left(b^{2/3} c-a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} \sqrt[3]{b}}-\frac{d \log \left(a+b x^3\right)}{3 a}-\frac{c}{a x}+\frac{d \log (x)}{a}","-\frac{\left(a^{2/3} e+b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3} \sqrt[3]{b}}+\frac{\left(a^{2/3} e+b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3} \sqrt[3]{b}}+\frac{\left(b^{2/3} c-a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} \sqrt[3]{b}}-\frac{d \log \left(a+b x^3\right)}{3 a}-\frac{c}{a x}+\frac{d \log (x)}{a}",1,"-(c/(a*x)) + ((b^(2/3)*c - a^(2/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*b^(1/3)) + (d*Log[x])/a + ((b^(2/3)*c + a^(2/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(4/3)*b^(1/3)) - ((b^(2/3)*c + a^(2/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(4/3)*b^(1/3)) - (d*Log[a + b*x^3])/(3*a)","A",10,9,23,0.3913,1,"{1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
343,1,203,0,0.1936865,"\int \frac{c+d x+e x^2}{x^3 \left(a+b x^3\right)} \, dx","Int[(c + d*x + e*x^2)/(x^3*(a + b*x^3)),x]","\frac{b^{2/3} \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3}}-\frac{\sqrt[3]{b} \left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3}}+\frac{\sqrt[3]{b} \left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{e \log \left(a+b x^3\right)}{3 a}-\frac{c}{2 a x^2}-\frac{d}{a x}+\frac{e \log (x)}{a}","\frac{b^{2/3} \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3}}-\frac{\sqrt[3]{b} \left(\sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3}}+\frac{\sqrt[3]{b} \left(\sqrt[3]{a} d+\sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{e \log \left(a+b x^3\right)}{3 a}-\frac{c}{2 a x^2}-\frac{d}{a x}+\frac{e \log (x)}{a}",1,"-c/(2*a*x^2) - d/(a*x) + (b^(1/3)*(b^(1/3)*c + a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)) + (e*Log[x])/a - (b^(1/3)*(b^(1/3)*c - a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(5/3)) + (b^(2/3)*(c - (a^(1/3)*d)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3)) - (e*Log[a + b*x^3])/(3*a)","A",10,9,23,0.3913,1,"{1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
344,1,190,0,0.1661598,"\int \frac{x^2 \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^2*(c + d*x + e*x^2))/(a + b*x^3)^2,x]","-\frac{\left(d-\frac{2 \sqrt[3]{a} e}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{2/3} b^{4/3}}+\frac{\left(\sqrt[3]{b} d-2 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{2/3} b^{5/3}}-\frac{\left(2 \sqrt[3]{a} e+\sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{5/3}}-\frac{c+d x+e x^2}{3 b \left(a+b x^3\right)}","-\frac{\left(d-\frac{2 \sqrt[3]{a} e}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{2/3} b^{4/3}}+\frac{\left(\sqrt[3]{b} d-2 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{2/3} b^{5/3}}-\frac{\left(2 \sqrt[3]{a} e+\sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{5/3}}-\frac{c+d x+e x^2}{3 b \left(a+b x^3\right)}",1,"-(c + d*x + e*x^2)/(3*b*(a + b*x^3)) - ((b^(1/3)*d + 2*a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)*b^(5/3)) + ((b^(1/3)*d - 2*a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(2/3)*b^(5/3)) - ((d - (2*a^(1/3)*e)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(2/3)*b^(4/3))","A",7,7,23,0.3043,1,"{1823, 1860, 31, 634, 617, 204, 628}"
345,1,200,0,0.1526902,"\int \frac{x \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x*(c + d*x + e*x^2))/(a + b*x^3)^2,x]","\frac{\left(b^{2/3} c-a^{2/3} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{4/3} b^{4/3}}-\frac{\left(b^{2/3} c-a^{2/3} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{4/3} b^{4/3}}-\frac{\left(a^{2/3} e+b^{2/3} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{4/3}}-\frac{x \left(a e-b c x-b d x^2\right)}{3 a b \left(a+b x^3\right)}","\frac{\left(b^{2/3} c-a^{2/3} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{4/3} b^{4/3}}-\frac{\left(b^{2/3} c-a^{2/3} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{4/3} b^{4/3}}-\frac{\left(a^{2/3} e+b^{2/3} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{4/3}}-\frac{x \left(a e-b c x-b d x^2\right)}{3 a b \left(a+b x^3\right)}",1,"-(x*(a*e - b*c*x - b*d*x^2))/(3*a*b*(a + b*x^3)) - ((b^(2/3)*c + a^(2/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)*b^(4/3)) - ((b^(2/3)*c - a^(2/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(4/3)*b^(4/3)) + ((b^(2/3)*c - a^(2/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(4/3)*b^(4/3))","A",7,7,21,0.3333,1,"{1828, 1860, 31, 634, 617, 204, 628}"
346,1,199,0,0.1322736,"\int \frac{c+d x+e x^2}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2)/(a + b*x^3)^2,x]","-\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{2/3}}+\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+2 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{2/3}}-\frac{a e-b x (c+d x)}{3 a b \left(a+b x^3\right)}","-\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{2/3}}+\frac{\left(2 \sqrt[3]{b} c-\sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} d+2 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{2/3}}-\frac{a e-b x (c+d x)}{3 a b \left(a+b x^3\right)}",1,"-(a*e - b*x*(c + d*x))/(3*a*b*(a + b*x^3)) - ((2*b^(1/3)*c + a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(2/3)) + ((2*b^(1/3)*c - a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(2/3)) - ((2*b^(1/3)*c - a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(2/3))","A",7,7,20,0.3500,1,"{1854, 1860, 31, 634, 617, 204, 628}"
347,1,222,0,0.3126883,"\int \frac{c+d x+e x^2}{x \left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2)/(x*(a + b*x^3)^2),x]","-\frac{\left(2 \sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{2/3}}+\frac{\left(2 \sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} e+2 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{2/3}}+\frac{x \left(a d+a e x-b c x^2\right)}{3 a^2 \left(a+b x^3\right)}-\frac{c \log \left(a+b x^3\right)}{3 a^2}+\frac{c \log (x)}{a^2}","-\frac{\left(2 \sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{2/3}}+\frac{\left(2 \sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{2/3}}-\frac{\left(\sqrt[3]{a} e+2 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{2/3}}+\frac{x \left(a d+a e x-b c x^2\right)}{3 a^2 \left(a+b x^3\right)}-\frac{c \log \left(a+b x^3\right)}{3 a^2}+\frac{c \log (x)}{a^2}",1,"(x*(a*d + a*e*x - b*c*x^2))/(3*a^2*(a + b*x^3)) - ((2*b^(1/3)*d + a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(2/3)) + (c*Log[x])/a^2 + ((2*b^(1/3)*d - a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(2/3)) - ((2*b^(1/3)*d - a^(1/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(2/3)) - (c*Log[a + b*x^3])/(3*a^2)","A",11,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
348,1,231,0,0.3431256,"\int \frac{c+d x+e x^2}{x^2 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2)/(x^2*(a + b*x^3)^2),x]","-\frac{\left(a^{2/3} e+2 b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{7/3} \sqrt[3]{b}}+\frac{2 \left(a^{2/3} e+2 b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{7/3} \sqrt[3]{b}}+\frac{2 \left(2 b^{2/3} c-a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} \sqrt[3]{b}}+\frac{x \left(a e-b c x-b d x^2\right)}{3 a^2 \left(a+b x^3\right)}-\frac{d \log \left(a+b x^3\right)}{3 a^2}-\frac{c}{a^2 x}+\frac{d \log (x)}{a^2}","-\frac{\left(a^{2/3} e+2 b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{7/3} \sqrt[3]{b}}+\frac{2 \left(a^{2/3} e+2 b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{7/3} \sqrt[3]{b}}+\frac{2 \left(2 b^{2/3} c-a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} \sqrt[3]{b}}+\frac{x \left(a e-b c x-b d x^2\right)}{3 a^2 \left(a+b x^3\right)}-\frac{d \log \left(a+b x^3\right)}{3 a^2}-\frac{c}{a^2 x}+\frac{d \log (x)}{a^2}",1,"-(c/(a^2*x)) + (x*(a*e - b*c*x - b*d*x^2))/(3*a^2*(a + b*x^3)) + (2*(2*b^(2/3)*c - a^(2/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)*b^(1/3)) + (d*Log[x])/a^2 + (2*(2*b^(2/3)*c + a^(2/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(7/3)*b^(1/3)) - ((2*b^(2/3)*c + a^(2/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(9*a^(7/3)*b^(1/3)) - (d*Log[a + b*x^3])/(3*a^2)","A",11,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
349,1,242,0,0.3453954,"\int \frac{c+d x+e x^2}{x^3 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2)/(x^3*(a + b*x^3)^2),x]","\frac{\sqrt[3]{b} \left(5 \sqrt[3]{b} c-4 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{8/3}}-\frac{x \left(b c+b d x+b e x^2\right)}{3 a^2 \left(a+b x^3\right)}-\frac{\sqrt[3]{b} \left(5 \sqrt[3]{b} c-4 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{8/3}}+\frac{\sqrt[3]{b} \left(4 \sqrt[3]{a} d+5 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3}}-\frac{e \log \left(a+b x^3\right)}{3 a^2}-\frac{c}{2 a^2 x^2}-\frac{d}{a^2 x}+\frac{e \log (x)}{a^2}","\frac{\sqrt[3]{b} \left(5 \sqrt[3]{b} c-4 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{8/3}}-\frac{x \left(b c+b d x+b e x^2\right)}{3 a^2 \left(a+b x^3\right)}-\frac{\sqrt[3]{b} \left(5 \sqrt[3]{b} c-4 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{8/3}}+\frac{\sqrt[3]{b} \left(4 \sqrt[3]{a} d+5 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3}}-\frac{e \log \left(a+b x^3\right)}{3 a^2}-\frac{c}{2 a^2 x^2}-\frac{d}{a^2 x}+\frac{e \log (x)}{a^2}",1,"-c/(2*a^2*x^2) - d/(a^2*x) - (x*(b*c + b*d*x + b*e*x^2))/(3*a^2*(a + b*x^3)) + (b^(1/3)*(5*b^(1/3)*c + 4*a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)) + (e*Log[x])/a^2 - (b^(1/3)*(5*b^(1/3)*c - 4*a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(8/3)) + (b^(1/3)*(5*b^(1/3)*c - 4*a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(8/3)) - (e*Log[a + b*x^3])/(3*a^2)","A",11,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
350,1,262,0,0.4035723,"\int \frac{c+d x+e x^2}{x^4 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2)/(x^4*(a + b*x^3)^2),x]","-\frac{x \left(-\frac{b^2 c x^2}{a}+b d+b e x\right)}{3 a^2 \left(a+b x^3\right)}+\frac{\sqrt[3]{b} \left(5 \sqrt[3]{b} d-4 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{8/3}}+\frac{2 b c \log \left(a+b x^3\right)}{3 a^3}-\frac{2 b c \log (x)}{a^3}-\frac{\sqrt[3]{b} \left(5 \sqrt[3]{b} d-4 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{8/3}}+\frac{\sqrt[3]{b} \left(4 \sqrt[3]{a} e+5 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3}}-\frac{c}{3 a^2 x^3}-\frac{d}{2 a^2 x^2}-\frac{e}{a^2 x}","-\frac{x \left(-\frac{b^2 c x^2}{a}+b d+b e x\right)}{3 a^2 \left(a+b x^3\right)}+\frac{\sqrt[3]{b} \left(5 \sqrt[3]{b} d-4 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{8/3}}+\frac{2 b c \log \left(a+b x^3\right)}{3 a^3}-\frac{2 b c \log (x)}{a^3}-\frac{\sqrt[3]{b} \left(5 \sqrt[3]{b} d-4 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{8/3}}+\frac{\sqrt[3]{b} \left(4 \sqrt[3]{a} e+5 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3}}-\frac{c}{3 a^2 x^3}-\frac{d}{2 a^2 x^2}-\frac{e}{a^2 x}",1,"-c/(3*a^2*x^3) - d/(2*a^2*x^2) - e/(a^2*x) - (x*(b*d + b*e*x - (b^2*c*x^2)/a))/(3*a^2*(a + b*x^3)) + (b^(1/3)*(5*b^(1/3)*d + 4*a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)) - (2*b*c*Log[x])/a^3 - (b^(1/3)*(5*b^(1/3)*d - 4*a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(8/3)) + (b^(1/3)*(5*b^(1/3)*d - 4*a^(1/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(8/3)) + (2*b*c*Log[a + b*x^3])/(3*a^3)","A",11,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
351,1,215,0,0.1968848,"\int \frac{x^2 \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^2*(c + d*x + e*x^2))/(a + b*x^3)^3,x]","-\frac{\left(d-\frac{\sqrt[3]{a} e}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{5/3} b^{4/3}}+\frac{\left(\sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{5/3} b^{5/3}}-\frac{\left(\sqrt[3]{a} e+\sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{5/3}}-\frac{c+d x+e x^2}{6 b \left(a+b x^3\right)^2}+\frac{x (d+2 e x)}{18 a b \left(a+b x^3\right)}","-\frac{\left(d-\frac{\sqrt[3]{a} e}{\sqrt[3]{b}}\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{5/3} b^{4/3}}+\frac{\left(\sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{5/3} b^{5/3}}-\frac{\left(\sqrt[3]{a} e+\sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{5/3}}-\frac{c+d x+e x^2}{6 b \left(a+b x^3\right)^2}+\frac{x (d+2 e x)}{18 a b \left(a+b x^3\right)}",1,"-(c + d*x + e*x^2)/(6*b*(a + b*x^3)^2) + (x*(d + 2*e*x))/(18*a*b*(a + b*x^3)) - ((b^(1/3)*d + a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(5/3)*b^(5/3)) + ((b^(1/3)*d - a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(5/3)*b^(5/3)) - ((d - (a^(1/3)*e)/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(5/3)*b^(4/3))","A",8,8,23,0.3478,1,"{1823, 1855, 1860, 31, 634, 617, 204, 628}"
352,1,239,0,0.2040252,"\int \frac{x \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x*(c + d*x + e*x^2))/(a + b*x^3)^3,x]","\frac{\left(2 b^{2/3} c-a^{2/3} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{7/3} b^{4/3}}-\frac{\left(2 b^{2/3} c-a^{2/3} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{7/3} b^{4/3}}-\frac{\left(a^{2/3} e+2 b^{2/3} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{4/3}}-\frac{3 a d-x (a e+4 b c x)}{18 a^2 b \left(a+b x^3\right)}-\frac{x \left(a e-b c x-b d x^2\right)}{6 a b \left(a+b x^3\right)^2}","\frac{\left(2 b^{2/3} c-a^{2/3} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{7/3} b^{4/3}}-\frac{\left(2 b^{2/3} c-a^{2/3} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{7/3} b^{4/3}}-\frac{\left(a^{2/3} e+2 b^{2/3} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{4/3}}-\frac{3 a d-x (a e+4 b c x)}{18 a^2 b \left(a+b x^3\right)}-\frac{x \left(a e-b c x-b d x^2\right)}{6 a b \left(a+b x^3\right)^2}",1,"-(x*(a*e - b*c*x - b*d*x^2))/(6*a*b*(a + b*x^3)^2) - (3*a*d - x*(a*e + 4*b*c*x))/(18*a^2*b*(a + b*x^3)) - ((2*b^(2/3)*c + a^(2/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(7/3)*b^(4/3)) - ((2*b^(2/3)*c - a^(2/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(7/3)*b^(4/3)) + ((2*b^(2/3)*c - a^(2/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(7/3)*b^(4/3))","A",8,8,21,0.3810,1,"{1828, 1854, 1860, 31, 634, 617, 204, 628}"
353,1,225,0,0.1884954,"\int \frac{c+d x+e x^2}{\left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2)/(a + b*x^3)^3,x]","-\frac{\left(5 \sqrt[3]{b} c-2 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} b^{2/3}}+\frac{\left(5 \sqrt[3]{b} c-2 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} b^{2/3}}-\frac{\left(2 \sqrt[3]{a} d+5 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} b^{2/3}}+\frac{x (5 c+4 d x)}{18 a^2 \left(a+b x^3\right)}-\frac{a e-b x (c+d x)}{6 a b \left(a+b x^3\right)^2}","-\frac{\left(5 \sqrt[3]{b} c-2 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} b^{2/3}}+\frac{\left(5 \sqrt[3]{b} c-2 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} b^{2/3}}-\frac{\left(2 \sqrt[3]{a} d+5 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} b^{2/3}}+\frac{x (5 c+4 d x)}{18 a^2 \left(a+b x^3\right)}-\frac{a e-b x (c+d x)}{6 a b \left(a+b x^3\right)^2}",1,"(x*(5*c + 4*d*x))/(18*a^2*(a + b*x^3)) - (a*e - b*x*(c + d*x))/(6*a*b*(a + b*x^3)^2) - ((5*b^(1/3)*c + 2*a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(2/3)) + ((5*b^(1/3)*c - 2*a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(8/3)*b^(2/3)) - ((5*b^(1/3)*c - 2*a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(8/3)*b^(2/3))","A",8,8,20,0.4000,1,"{1854, 1855, 1860, 31, 634, 617, 204, 628}"
354,1,257,0,0.4138201,"\int \frac{c+d x+e x^2}{x \left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2)/(x*(a + b*x^3)^3),x]","-\frac{\left(5 \sqrt[3]{b} d-2 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} b^{2/3}}+\frac{\left(5 \sqrt[3]{b} d-2 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} b^{2/3}}-\frac{\left(2 \sqrt[3]{a} e+5 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} b^{2/3}}+\frac{x \left(5 a d+4 a e x-9 b c x^2\right)}{18 a^3 \left(a+b x^3\right)}+\frac{x \left(a d+a e x-b c x^2\right)}{6 a^2 \left(a+b x^3\right)^2}-\frac{c \log \left(a+b x^3\right)}{3 a^3}+\frac{c \log (x)}{a^3}","-\frac{\left(5 \sqrt[3]{b} d-2 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} b^{2/3}}+\frac{\left(5 \sqrt[3]{b} d-2 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} b^{2/3}}-\frac{\left(2 \sqrt[3]{a} e+5 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} b^{2/3}}+\frac{x \left(5 a d+4 a e x-9 b c x^2\right)}{18 a^3 \left(a+b x^3\right)}+\frac{x \left(a d+a e x-b c x^2\right)}{6 a^2 \left(a+b x^3\right)^2}-\frac{c \log \left(a+b x^3\right)}{3 a^3}+\frac{c \log (x)}{a^3}",1,"(x*(a*d + a*e*x - b*c*x^2))/(6*a^2*(a + b*x^3)^2) + (x*(5*a*d + 4*a*e*x - 9*b*c*x^2))/(18*a^3*(a + b*x^3)) - ((5*b^(1/3)*d + 2*a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(2/3)) + (c*Log[x])/a^3 + ((5*b^(1/3)*d - 2*a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(8/3)*b^(2/3)) - ((5*b^(1/3)*d - 2*a^(1/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(8/3)*b^(2/3)) - (c*Log[a + b*x^3])/(3*a^3)","A",12,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
355,1,267,0,0.4617987,"\int \frac{c+d x+e x^2}{x^2 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2)/(x^2*(a + b*x^3)^3),x]","-\frac{\left(5 a^{2/3} e+14 b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{10/3} \sqrt[3]{b}}+\frac{\left(5 a^{2/3} e+14 b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{10/3} \sqrt[3]{b}}+\frac{\left(14 b^{2/3} c-5 a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} \sqrt[3]{b}}+\frac{x \left(5 a e-10 b c x-9 b d x^2\right)}{18 a^3 \left(a+b x^3\right)}+\frac{x \left(a e-b c x-b d x^2\right)}{6 a^2 \left(a+b x^3\right)^2}-\frac{d \log \left(a+b x^3\right)}{3 a^3}-\frac{c}{a^3 x}+\frac{d \log (x)}{a^3}","-\frac{\left(5 a^{2/3} e+14 b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{10/3} \sqrt[3]{b}}+\frac{\left(5 a^{2/3} e+14 b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{10/3} \sqrt[3]{b}}+\frac{\left(14 b^{2/3} c-5 a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} \sqrt[3]{b}}+\frac{x \left(5 a e-10 b c x-9 b d x^2\right)}{18 a^3 \left(a+b x^3\right)}+\frac{x \left(a e-b c x-b d x^2\right)}{6 a^2 \left(a+b x^3\right)^2}-\frac{d \log \left(a+b x^3\right)}{3 a^3}-\frac{c}{a^3 x}+\frac{d \log (x)}{a^3}",1,"-(c/(a^3*x)) + (x*(a*e - b*c*x - b*d*x^2))/(6*a^2*(a + b*x^3)^2) + (x*(5*a*e - 10*b*c*x - 9*b*d*x^2))/(18*a^3*(a + b*x^3)) + ((14*b^(2/3)*c - 5*a^(2/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(10/3)*b^(1/3)) + (d*Log[x])/a^3 + ((14*b^(2/3)*c + 5*a^(2/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(10/3)*b^(1/3)) - ((14*b^(2/3)*c + 5*a^(2/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(10/3)*b^(1/3)) - (d*Log[a + b*x^3])/(3*a^3)","A",12,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
356,1,276,0,0.4999149,"\int \frac{c+d x+e x^2}{x^3 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2)/(x^3*(a + b*x^3)^3),x]","\frac{\sqrt[3]{b} \left(10 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{11/3}}-\frac{x \left(11 b c+10 b d x+9 b e x^2\right)}{18 a^3 \left(a+b x^3\right)}-\frac{x \left(b c+b d x+b e x^2\right)}{6 a^2 \left(a+b x^3\right)^2}-\frac{2 \sqrt[3]{b} \left(10 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{11/3}}+\frac{2 \sqrt[3]{b} \left(7 \sqrt[3]{a} d+10 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3}}-\frac{e \log \left(a+b x^3\right)}{3 a^3}-\frac{c}{2 a^3 x^2}-\frac{d}{a^3 x}+\frac{e \log (x)}{a^3}","\frac{\sqrt[3]{b} \left(10 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{11/3}}-\frac{x \left(11 b c+10 b d x+9 b e x^2\right)}{18 a^3 \left(a+b x^3\right)}-\frac{x \left(b c+b d x+b e x^2\right)}{6 a^2 \left(a+b x^3\right)^2}-\frac{2 \sqrt[3]{b} \left(10 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{11/3}}+\frac{2 \sqrt[3]{b} \left(7 \sqrt[3]{a} d+10 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3}}-\frac{e \log \left(a+b x^3\right)}{3 a^3}-\frac{c}{2 a^3 x^2}-\frac{d}{a^3 x}+\frac{e \log (x)}{a^3}",1,"-c/(2*a^3*x^2) - d/(a^3*x) - (x*(b*c + b*d*x + b*e*x^2))/(6*a^2*(a + b*x^3)^2) - (x*(11*b*c + 10*b*d*x + 9*b*e*x^2))/(18*a^3*(a + b*x^3)) + (2*b^(1/3)*(10*b^(1/3)*c + 7*a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(11/3)) + (e*Log[x])/a^3 - (2*b^(1/3)*(10*b^(1/3)*c - 7*a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(11/3)) + (b^(1/3)*(10*b^(1/3)*c - 7*a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(27*a^(11/3)) - (e*Log[a + b*x^3])/(3*a^3)","A",12,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
357,1,298,0,0.5894556,"\int \frac{c+d x+e x^2}{x^4 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2)/(x^4*(a + b*x^3)^3),x]","-\frac{x \left(-\frac{15 b^2 c x^2}{a}+11 b d+10 b e x\right)}{18 a^3 \left(a+b x^3\right)}-\frac{x \left(-\frac{b^2 c x^2}{a}+b d+b e x\right)}{6 a^2 \left(a+b x^3\right)^2}+\frac{\sqrt[3]{b} \left(10 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{11/3}}+\frac{b c \log \left(a+b x^3\right)}{a^4}-\frac{3 b c \log (x)}{a^4}-\frac{2 \sqrt[3]{b} \left(10 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{11/3}}+\frac{2 \sqrt[3]{b} \left(7 \sqrt[3]{a} e+10 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3}}-\frac{c}{3 a^3 x^3}-\frac{d}{2 a^3 x^2}-\frac{e}{a^3 x}","-\frac{x \left(-\frac{15 b^2 c x^2}{a}+11 b d+10 b e x\right)}{18 a^3 \left(a+b x^3\right)}-\frac{x \left(-\frac{b^2 c x^2}{a}+b d+b e x\right)}{6 a^2 \left(a+b x^3\right)^2}+\frac{\sqrt[3]{b} \left(10 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{11/3}}+\frac{b c \log \left(a+b x^3\right)}{a^4}-\frac{3 b c \log (x)}{a^4}-\frac{2 \sqrt[3]{b} \left(10 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{11/3}}+\frac{2 \sqrt[3]{b} \left(7 \sqrt[3]{a} e+10 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3}}-\frac{c}{3 a^3 x^3}-\frac{d}{2 a^3 x^2}-\frac{e}{a^3 x}",1,"-c/(3*a^3*x^3) - d/(2*a^3*x^2) - e/(a^3*x) - (x*(b*d + b*e*x - (b^2*c*x^2)/a))/(6*a^2*(a + b*x^3)^2) - (x*(11*b*d + 10*b*e*x - (15*b^2*c*x^2)/a))/(18*a^3*(a + b*x^3)) + (2*b^(1/3)*(10*b^(1/3)*d + 7*a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(11/3)) - (3*b*c*Log[x])/a^4 - (2*b^(1/3)*(10*b^(1/3)*d - 7*a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(11/3)) + (b^(1/3)*(10*b^(1/3)*d - 7*a^(1/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(27*a^(11/3)) + (b*c*Log[a + b*x^3])/a^4","A",12,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
358,1,248,0,0.2423144,"\int \frac{x^2 \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^4} \, dx","Int[(x^2*(c + d*x + e*x^2))/(a + b*x^3)^4,x]","-\frac{\left(5 \sqrt[3]{b} d-4 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{486 a^{8/3} b^{5/3}}+\frac{\left(5 \sqrt[3]{b} d-4 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{8/3} b^{5/3}}-\frac{\left(4 \sqrt[3]{a} e+5 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{8/3} b^{5/3}}+\frac{x (5 d+8 e x)}{162 a^2 b \left(a+b x^3\right)}-\frac{c+d x+e x^2}{9 b \left(a+b x^3\right)^3}+\frac{x (d+2 e x)}{54 a b \left(a+b x^3\right)^2}","-\frac{\left(5 \sqrt[3]{b} d-4 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{486 a^{8/3} b^{5/3}}+\frac{\left(5 \sqrt[3]{b} d-4 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{8/3} b^{5/3}}-\frac{\left(4 \sqrt[3]{a} e+5 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{8/3} b^{5/3}}+\frac{x (5 d+8 e x)}{162 a^2 b \left(a+b x^3\right)}-\frac{c+d x+e x^2}{9 b \left(a+b x^3\right)^3}+\frac{x (d+2 e x)}{54 a b \left(a+b x^3\right)^2}",1,"-(c + d*x + e*x^2)/(9*b*(a + b*x^3)^3) + (x*(d + 2*e*x))/(54*a*b*(a + b*x^3)^2) + (x*(5*d + 8*e*x))/(162*a^2*b*(a + b*x^3)) - ((5*b^(1/3)*d + 4*a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(81*Sqrt[3]*a^(8/3)*b^(5/3)) + ((5*b^(1/3)*d - 4*a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(243*a^(8/3)*b^(5/3)) - ((5*b^(1/3)*d - 4*a^(1/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(486*a^(8/3)*b^(5/3))","A",9,8,23,0.3478,1,"{1823, 1855, 1860, 31, 634, 617, 204, 628}"
359,1,270,0,0.2535497,"\int \frac{x \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^4} \, dx","Int[(x*(c + d*x + e*x^2))/(a + b*x^3)^4,x]","\frac{\left(14 b^{2/3} c-5 a^{2/3} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{486 a^{10/3} b^{4/3}}-\frac{\left(14 b^{2/3} c-5 a^{2/3} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{10/3} b^{4/3}}-\frac{\left(5 a^{2/3} e+14 b^{2/3} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{10/3} b^{4/3}}-\frac{6 a d-x (a e+7 b c x)}{54 a^2 b \left(a+b x^3\right)^2}+\frac{x (5 a e+28 b c x)}{162 a^3 b \left(a+b x^3\right)}-\frac{x \left(a e-b c x-b d x^2\right)}{9 a b \left(a+b x^3\right)^3}","\frac{\left(14 b^{2/3} c-5 a^{2/3} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{486 a^{10/3} b^{4/3}}-\frac{\left(14 b^{2/3} c-5 a^{2/3} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{10/3} b^{4/3}}-\frac{\left(5 a^{2/3} e+14 b^{2/3} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{10/3} b^{4/3}}-\frac{6 a d-x (a e+7 b c x)}{54 a^2 b \left(a+b x^3\right)^2}+\frac{x (5 a e+28 b c x)}{162 a^3 b \left(a+b x^3\right)}-\frac{x \left(a e-b c x-b d x^2\right)}{9 a b \left(a+b x^3\right)^3}",1,"-(x*(a*e - b*c*x - b*d*x^2))/(9*a*b*(a + b*x^3)^3) + (x*(5*a*e + 28*b*c*x))/(162*a^3*b*(a + b*x^3)) - (6*a*d - x*(a*e + 7*b*c*x))/(54*a^2*b*(a + b*x^3)^2) - ((14*b^(2/3)*c + 5*a^(2/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(81*Sqrt[3]*a^(10/3)*b^(4/3)) - ((14*b^(2/3)*c - 5*a^(2/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(243*a^(10/3)*b^(4/3)) + ((14*b^(2/3)*c - 5*a^(2/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(486*a^(10/3)*b^(4/3))","A",9,9,21,0.4286,1,"{1828, 1854, 1855, 1860, 31, 634, 617, 204, 628}"
360,1,250,0,0.2222368,"\int \frac{c+d x+e x^2}{\left(a+b x^3\right)^4} \, dx","Int[(c + d*x + e*x^2)/(a + b*x^3)^4,x]","-\frac{\left(20 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{11/3} b^{2/3}}+\frac{2 \left(20 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{11/3} b^{2/3}}-\frac{2 \left(7 \sqrt[3]{a} d+20 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{11/3} b^{2/3}}+\frac{x (8 c+7 d x)}{54 a^2 \left(a+b x^3\right)^2}+\frac{2 x (10 c+7 d x)}{81 a^3 \left(a+b x^3\right)}-\frac{a e-b x (c+d x)}{9 a b \left(a+b x^3\right)^3}","-\frac{\left(20 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{11/3} b^{2/3}}+\frac{2 \left(20 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{11/3} b^{2/3}}-\frac{2 \left(7 \sqrt[3]{a} d+20 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{11/3} b^{2/3}}+\frac{x (8 c+7 d x)}{54 a^2 \left(a+b x^3\right)^2}+\frac{2 x (10 c+7 d x)}{81 a^3 \left(a+b x^3\right)}-\frac{a e-b x (c+d x)}{9 a b \left(a+b x^3\right)^3}",1,"(x*(8*c + 7*d*x))/(54*a^2*(a + b*x^3)^2) + (2*x*(10*c + 7*d*x))/(81*a^3*(a + b*x^3)) - (a*e - b*x*(c + d*x))/(9*a*b*(a + b*x^3)^3) - (2*(20*b^(1/3)*c + 7*a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(81*Sqrt[3]*a^(11/3)*b^(2/3)) + (2*(20*b^(1/3)*c - 7*a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(243*a^(11/3)*b^(2/3)) - ((20*b^(1/3)*c - 7*a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(243*a^(11/3)*b^(2/3))","A",9,8,20,0.4000,1,"{1854, 1855, 1860, 31, 634, 617, 204, 628}"
361,1,291,0,0.5168819,"\int \frac{c+d x+e x^2}{x \left(a+b x^3\right)^4} \, dx","Int[(c + d*x + e*x^2)/(x*(a + b*x^3)^4),x]","-\frac{\left(20 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{11/3} b^{2/3}}+\frac{2 \left(20 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{11/3} b^{2/3}}-\frac{2 \left(7 \sqrt[3]{a} e+20 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{11/3} b^{2/3}}+\frac{x \left(40 a d+28 a e x-99 b c x^2\right)}{162 a^4 \left(a+b x^3\right)}+\frac{x \left(8 a d+7 a e x-15 b c x^2\right)}{54 a^3 \left(a+b x^3\right)^2}+\frac{x \left(a d+a e x-b c x^2\right)}{9 a^2 \left(a+b x^3\right)^3}-\frac{c \log \left(a+b x^3\right)}{3 a^4}+\frac{c \log (x)}{a^4}","-\frac{\left(20 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{11/3} b^{2/3}}+\frac{2 \left(20 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{11/3} b^{2/3}}-\frac{2 \left(7 \sqrt[3]{a} e+20 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{11/3} b^{2/3}}+\frac{x \left(40 a d+28 a e x-99 b c x^2\right)}{162 a^4 \left(a+b x^3\right)}+\frac{x \left(8 a d+7 a e x-15 b c x^2\right)}{54 a^3 \left(a+b x^3\right)^2}+\frac{x \left(a d+a e x-b c x^2\right)}{9 a^2 \left(a+b x^3\right)^3}-\frac{c \log \left(a+b x^3\right)}{3 a^4}+\frac{c \log (x)}{a^4}",1,"(x*(a*d + a*e*x - b*c*x^2))/(9*a^2*(a + b*x^3)^3) + (x*(8*a*d + 7*a*e*x - 15*b*c*x^2))/(54*a^3*(a + b*x^3)^2) + (x*(40*a*d + 28*a*e*x - 99*b*c*x^2))/(162*a^4*(a + b*x^3)) - (2*(20*b^(1/3)*d + 7*a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(81*Sqrt[3]*a^(11/3)*b^(2/3)) + (c*Log[x])/a^4 + (2*(20*b^(1/3)*d - 7*a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(243*a^(11/3)*b^(2/3)) - ((20*b^(1/3)*d - 7*a^(1/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(243*a^(11/3)*b^(2/3)) - (c*Log[a + b*x^3])/(3*a^4)","A",13,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
362,1,301,0,0.6011745,"\int \frac{c+d x+e x^2}{x^2 \left(a+b x^3\right)^4} \, dx","Int[(c + d*x + e*x^2)/(x^2*(a + b*x^3)^4),x]","-\frac{10 \left(2 a^{2/3} e+7 b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{13/3} \sqrt[3]{b}}+\frac{20 \left(2 a^{2/3} e+7 b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{13/3} \sqrt[3]{b}}+\frac{20 \left(7 b^{2/3} c-2 a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{13/3} \sqrt[3]{b}}+\frac{x \left(40 a e-118 b c x-99 b d x^2\right)}{162 a^4 \left(a+b x^3\right)}+\frac{x \left(8 a e-16 b c x-15 b d x^2\right)}{54 a^3 \left(a+b x^3\right)^2}+\frac{x \left(a e-b c x-b d x^2\right)}{9 a^2 \left(a+b x^3\right)^3}-\frac{d \log \left(a+b x^3\right)}{3 a^4}-\frac{c}{a^4 x}+\frac{d \log (x)}{a^4}","-\frac{10 \left(2 a^{2/3} e+7 b^{2/3} c\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{13/3} \sqrt[3]{b}}+\frac{20 \left(2 a^{2/3} e+7 b^{2/3} c\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{13/3} \sqrt[3]{b}}+\frac{20 \left(7 b^{2/3} c-2 a^{2/3} e\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{13/3} \sqrt[3]{b}}+\frac{x \left(40 a e-118 b c x-99 b d x^2\right)}{162 a^4 \left(a+b x^3\right)}+\frac{x \left(8 a e-16 b c x-15 b d x^2\right)}{54 a^3 \left(a+b x^3\right)^2}+\frac{x \left(a e-b c x-b d x^2\right)}{9 a^2 \left(a+b x^3\right)^3}-\frac{d \log \left(a+b x^3\right)}{3 a^4}-\frac{c}{a^4 x}+\frac{d \log (x)}{a^4}",1,"-(c/(a^4*x)) + (x*(a*e - b*c*x - b*d*x^2))/(9*a^2*(a + b*x^3)^3) + (x*(8*a*e - 16*b*c*x - 15*b*d*x^2))/(54*a^3*(a + b*x^3)^2) + (x*(40*a*e - 118*b*c*x - 99*b*d*x^2))/(162*a^4*(a + b*x^3)) + (20*(7*b^(2/3)*c - 2*a^(2/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(81*Sqrt[3]*a^(13/3)*b^(1/3)) + (d*Log[x])/a^4 + (20*(7*b^(2/3)*c + 2*a^(2/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(243*a^(13/3)*b^(1/3)) - (10*(7*b^(2/3)*c + 2*a^(2/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(243*a^(13/3)*b^(1/3)) - (d*Log[a + b*x^3])/(3*a^4)","A",13,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
363,1,310,0,0.6562204,"\int \frac{c+d x+e x^2}{x^3 \left(a+b x^3\right)^4} \, dx","Int[(c + d*x + e*x^2)/(x^3*(a + b*x^3)^4),x]","\frac{10 \sqrt[3]{b} \left(11 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{14/3}}-\frac{x \left(139 b c+118 b d x+99 b e x^2\right)}{162 a^4 \left(a+b x^3\right)}-\frac{x \left(17 b c+16 b d x+15 b e x^2\right)}{54 a^3 \left(a+b x^3\right)^2}-\frac{x \left(b c+b d x+b e x^2\right)}{9 a^2 \left(a+b x^3\right)^3}-\frac{20 \sqrt[3]{b} \left(11 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{14/3}}+\frac{20 \sqrt[3]{b} \left(7 \sqrt[3]{a} d+11 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{14/3}}-\frac{e \log \left(a+b x^3\right)}{3 a^4}-\frac{c}{2 a^4 x^2}-\frac{d}{a^4 x}+\frac{e \log (x)}{a^4}","\frac{10 \sqrt[3]{b} \left(11 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{14/3}}-\frac{x \left(139 b c+118 b d x+99 b e x^2\right)}{162 a^4 \left(a+b x^3\right)}-\frac{x \left(17 b c+16 b d x+15 b e x^2\right)}{54 a^3 \left(a+b x^3\right)^2}-\frac{x \left(b c+b d x+b e x^2\right)}{9 a^2 \left(a+b x^3\right)^3}-\frac{20 \sqrt[3]{b} \left(11 \sqrt[3]{b} c-7 \sqrt[3]{a} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{14/3}}+\frac{20 \sqrt[3]{b} \left(7 \sqrt[3]{a} d+11 \sqrt[3]{b} c\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{14/3}}-\frac{e \log \left(a+b x^3\right)}{3 a^4}-\frac{c}{2 a^4 x^2}-\frac{d}{a^4 x}+\frac{e \log (x)}{a^4}",1,"-c/(2*a^4*x^2) - d/(a^4*x) - (x*(b*c + b*d*x + b*e*x^2))/(9*a^2*(a + b*x^3)^3) - (x*(17*b*c + 16*b*d*x + 15*b*e*x^2))/(54*a^3*(a + b*x^3)^2) - (x*(139*b*c + 118*b*d*x + 99*b*e*x^2))/(162*a^4*(a + b*x^3)) + (20*b^(1/3)*(11*b^(1/3)*c + 7*a^(1/3)*d)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(81*Sqrt[3]*a^(14/3)) + (e*Log[x])/a^4 - (20*b^(1/3)*(11*b^(1/3)*c - 7*a^(1/3)*d)*Log[a^(1/3) + b^(1/3)*x])/(243*a^(14/3)) + (10*b^(1/3)*(11*b^(1/3)*c - 7*a^(1/3)*d)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(243*a^(14/3)) - (e*Log[a + b*x^3])/(3*a^4)","A",13,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
364,1,340,0,0.7726997,"\int \frac{c+d x+e x^2}{x^4 \left(a+b x^3\right)^4} \, dx","Int[(c + d*x + e*x^2)/(x^4*(a + b*x^3)^4),x]","-\frac{x \left(-\frac{234 b^2 c x^2}{a}+139 b d+118 b e x\right)}{162 a^4 \left(a+b x^3\right)}-\frac{x \left(-\frac{24 b^2 c x^2}{a}+17 b d+16 b e x\right)}{54 a^3 \left(a+b x^3\right)^2}-\frac{x \left(-\frac{b^2 c x^2}{a}+b d+b e x\right)}{9 a^2 \left(a+b x^3\right)^3}+\frac{10 \sqrt[3]{b} \left(11 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{14/3}}+\frac{4 b c \log \left(a+b x^3\right)}{3 a^5}-\frac{4 b c \log (x)}{a^5}-\frac{20 \sqrt[3]{b} \left(11 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{14/3}}+\frac{20 \sqrt[3]{b} \left(7 \sqrt[3]{a} e+11 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{14/3}}-\frac{c}{3 a^4 x^3}-\frac{d}{2 a^4 x^2}-\frac{e}{a^4 x}","-\frac{x \left(-\frac{234 b^2 c x^2}{a}+139 b d+118 b e x\right)}{162 a^4 \left(a+b x^3\right)}-\frac{x \left(-\frac{24 b^2 c x^2}{a}+17 b d+16 b e x\right)}{54 a^3 \left(a+b x^3\right)^2}-\frac{x \left(-\frac{b^2 c x^2}{a}+b d+b e x\right)}{9 a^2 \left(a+b x^3\right)^3}+\frac{10 \sqrt[3]{b} \left(11 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{243 a^{14/3}}+\frac{4 b c \log \left(a+b x^3\right)}{3 a^5}-\frac{4 b c \log (x)}{a^5}-\frac{20 \sqrt[3]{b} \left(11 \sqrt[3]{b} d-7 \sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{243 a^{14/3}}+\frac{20 \sqrt[3]{b} \left(7 \sqrt[3]{a} e+11 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{81 \sqrt{3} a^{14/3}}-\frac{c}{3 a^4 x^3}-\frac{d}{2 a^4 x^2}-\frac{e}{a^4 x}",1,"-c/(3*a^4*x^3) - d/(2*a^4*x^2) - e/(a^4*x) - (x*(b*d + b*e*x - (b^2*c*x^2)/a))/(9*a^2*(a + b*x^3)^3) - (x*(17*b*d + 16*b*e*x - (24*b^2*c*x^2)/a))/(54*a^3*(a + b*x^3)^2) - (x*(139*b*d + 118*b*e*x - (234*b^2*c*x^2)/a))/(162*a^4*(a + b*x^3)) + (20*b^(1/3)*(11*b^(1/3)*d + 7*a^(1/3)*e)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(81*Sqrt[3]*a^(14/3)) - (4*b*c*Log[x])/a^5 - (20*b^(1/3)*(11*b^(1/3)*d - 7*a^(1/3)*e)*Log[a^(1/3) + b^(1/3)*x])/(243*a^(14/3)) + (10*b^(1/3)*(11*b^(1/3)*d - 7*a^(1/3)*e)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(243*a^(14/3)) + (4*b*c*Log[a + b*x^3])/(3*a^5)","A",13,10,23,0.4348,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
365,1,29,0,0.0578282,"\int \frac{2 a x-x^2}{a^3+x^3} \, dx","Int[(2*a*x - x^2)/(a^3 + x^3),x]","-\log (a+x)-\frac{2 \tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3}}","-\log (a+x)-\frac{2 \tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3}}",1,"(-2*ArcTan[(a - 2*x)/(Sqrt[3]*a)])/Sqrt[3] - Log[a + x]","A",5,5,20,0.2500,1,"{1593, 1868, 31, 617, 204}"
366,1,29,0,0.0347537,"\int \frac{(2 a-x) x}{a^3+x^3} \, dx","Int[((2*a - x)*x)/(a^3 + x^3),x]","-\log (a+x)-\frac{2 \tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3}}","-\log (a+x)-\frac{2 \tan ^{-1}\left(\frac{a-2 x}{\sqrt{3} a}\right)}{\sqrt{3}}",1,"(-2*ArcTan[(a - 2*x)/(Sqrt[3]*a)])/Sqrt[3] - Log[a + x]","A",4,4,18,0.2222,1,"{1868, 31, 617, 204}"
367,1,31,0,0.0564489,"\int \frac{2 a x+x^2}{a^3-x^3} \, dx","Int[(2*a*x + x^2)/(a^3 - x^3),x]","-\log (a-x)-\frac{2 \tan ^{-1}\left(\frac{a+2 x}{\sqrt{3} a}\right)}{\sqrt{3}}","-\log (a-x)-\frac{2 \tan ^{-1}\left(\frac{a+2 x}{\sqrt{3} a}\right)}{\sqrt{3}}",1,"(-2*ArcTan[(a + 2*x)/(Sqrt[3]*a)])/Sqrt[3] - Log[a - x]","A",5,5,20,0.2500,1,"{1593, 1868, 31, 617, 204}"
368,1,31,0,0.0367465,"\int \frac{x (2 a+x)}{a^3-x^3} \, dx","Int[(x*(2*a + x))/(a^3 - x^3),x]","-\log (a-x)-\frac{2 \tan ^{-1}\left(\frac{a+2 x}{\sqrt{3} a}\right)}{\sqrt{3}}","-\log (a-x)-\frac{2 \tan ^{-1}\left(\frac{a+2 x}{\sqrt{3} a}\right)}{\sqrt{3}}",1,"(-2*ArcTan[(a + 2*x)/(Sqrt[3]*a)])/Sqrt[3] - Log[a - x]","A",4,4,18,0.2222,1,"{1868, 31, 617, 204}"
369,1,50,0,0.086742,"\int \frac{x \left(-2 \sqrt[3]{\frac{a}{b}} C+C x\right)}{a+b x^3} \, dx","Int[(x*(-2*(a/b)^(1/3)*C + C*x))/(a + b*x^3),x]","\frac{C \log \left(\sqrt[3]{\frac{a}{b}}+x\right)}{b}+\frac{2 C \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b}","\frac{C \log \left(\sqrt[3]{\frac{a}{b}}+x\right)}{b}+\frac{2 C \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b}",1,"(2*C*ArcTan[(1 - (2*x)/(a/b)^(1/3))/Sqrt[3]])/(Sqrt[3]*b) + (C*Log[(a/b)^(1/3) + x])/b","A",4,4,27,0.1481,1,"{1867, 31, 617, 204}"
370,1,53,0,0.0931049,"\int \frac{x \left(-2 \sqrt[3]{-\frac{a}{b}} C+C x\right)}{a-b x^3} \, dx","Int[(x*(-2*(-(a/b))^(1/3)*C + C*x))/(a - b*x^3),x]","-\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}+x\right)}{b}-\frac{2 C \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b}","-\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}+x\right)}{b}-\frac{2 C \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}}{\sqrt{3}}\right)}{\sqrt{3} b}",1,"(-2*C*ArcTan[(1 - (2*x)/(-(a/b))^(1/3))/Sqrt[3]])/(Sqrt[3]*b) - (C*Log[(-(a/b))^(1/3) + x])/b","A",4,4,29,0.1379,1,"{1867, 31, 617, 204}"
371,1,54,0,0.0772552,"\int \frac{x \left(2 \sqrt[3]{-\frac{a}{b}} C+C x\right)}{a+b x^3} \, dx","Int[(x*(2*(-(a/b))^(1/3)*C + C*x))/(a + b*x^3),x]","\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}-x\right)}{b}+\frac{2 C \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b}","\frac{C \log \left(\sqrt[3]{-\frac{a}{b}}-x\right)}{b}+\frac{2 C \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{-\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b}",1,"(2*C*ArcTan[(1 + (2*x)/(-(a/b))^(1/3))/Sqrt[3]])/(Sqrt[3]*b) + (C*Log[(-(a/b))^(1/3) - x])/b","A",4,4,28,0.1429,1,"{1869, 31, 617, 204}"
372,1,53,0,0.0755327,"\int \frac{x \left(2 \sqrt[3]{\frac{a}{b}} C+C x\right)}{a-b x^3} \, dx","Int[(x*(2*(a/b)^(1/3)*C + C*x))/(a - b*x^3),x]","-\frac{C \log \left(\sqrt[3]{\frac{a}{b}}-x\right)}{b}-\frac{2 C \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b}","-\frac{C \log \left(\sqrt[3]{\frac{a}{b}}-x\right)}{b}-\frac{2 C \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{\frac{a}{b}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b}",1,"(-2*C*ArcTan[(1 + (2*x)/(a/b)^(1/3))/Sqrt[3]])/(Sqrt[3]*b) - (C*Log[(a/b)^(1/3) - x])/b","A",4,4,28,0.1429,1,"{1869, 31, 617, 204}"
373,1,97,0,0.1213687,"\int x^4 \left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x^4*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{8} x^8 (a f+b c)+\frac{1}{9} x^9 (a g+b d)+\frac{1}{10} x^{10} (a h+b e)+\frac{1}{5} a c x^5+\frac{1}{6} a d x^6+\frac{1}{7} a e x^7+\frac{1}{11} b f x^{11}+\frac{1}{12} b g x^{12}+\frac{1}{13} b h x^{13}","\frac{1}{8} x^8 (a f+b c)+\frac{1}{9} x^9 (a g+b d)+\frac{1}{10} x^{10} (a h+b e)+\frac{1}{5} a c x^5+\frac{1}{6} a d x^6+\frac{1}{7} a e x^7+\frac{1}{11} b f x^{11}+\frac{1}{12} b g x^{12}+\frac{1}{13} b h x^{13}",1,"(a*c*x^5)/5 + (a*d*x^6)/6 + (a*e*x^7)/7 + ((b*c + a*f)*x^8)/8 + ((b*d + a*g)*x^9)/9 + ((b*e + a*h)*x^10)/10 + (b*f*x^11)/11 + (b*g*x^12)/12 + (b*h*x^13)/13","A",2,1,36,0.02778,1,"{1820}"
374,1,97,0,0.100829,"\int x^3 \left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x^3*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{7} x^7 (a f+b c)+\frac{1}{8} x^8 (a g+b d)+\frac{1}{9} x^9 (a h+b e)+\frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{10} b f x^{10}+\frac{1}{11} b g x^{11}+\frac{1}{12} b h x^{12}","\frac{1}{7} x^7 (a f+b c)+\frac{1}{8} x^8 (a g+b d)+\frac{1}{9} x^9 (a h+b e)+\frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{10} b f x^{10}+\frac{1}{11} b g x^{11}+\frac{1}{12} b h x^{12}",1,"(a*c*x^4)/4 + (a*d*x^5)/5 + (a*e*x^6)/6 + ((b*c + a*f)*x^7)/7 + ((b*d + a*g)*x^8)/8 + ((b*e + a*h)*x^9)/9 + (b*f*x^10)/10 + (b*g*x^11)/11 + (b*h*x^12)/12","A",2,1,36,0.02778,1,"{1820}"
375,1,97,0,0.0914639,"\int x^2 \left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x^2*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{6} x^6 (a f+b c)+\frac{1}{7} x^7 (a g+b d)+\frac{1}{8} x^8 (a h+b e)+\frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{9} b f x^9+\frac{1}{10} b g x^{10}+\frac{1}{11} b h x^{11}","\frac{1}{6} x^6 (a f+b c)+\frac{1}{7} x^7 (a g+b d)+\frac{1}{8} x^8 (a h+b e)+\frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{9} b f x^9+\frac{1}{10} b g x^{10}+\frac{1}{11} b h x^{11}",1,"(a*c*x^3)/3 + (a*d*x^4)/4 + (a*e*x^5)/5 + ((b*c + a*f)*x^6)/6 + ((b*d + a*g)*x^7)/7 + ((b*e + a*h)*x^8)/8 + (b*f*x^9)/9 + (b*g*x^10)/10 + (b*h*x^11)/11","A",2,1,36,0.02778,1,"{1820}"
376,1,97,0,0.0802172,"\int x \left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{5} x^5 (a f+b c)+\frac{1}{6} x^6 (a g+b d)+\frac{1}{7} x^7 (a h+b e)+\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{8} b f x^8+\frac{1}{9} b g x^9+\frac{1}{10} b h x^{10}","\frac{1}{5} x^5 (a f+b c)+\frac{1}{6} x^6 (a g+b d)+\frac{1}{7} x^7 (a h+b e)+\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{8} b f x^8+\frac{1}{9} b g x^9+\frac{1}{10} b h x^{10}",1,"(a*c*x^2)/2 + (a*d*x^3)/3 + (a*e*x^4)/4 + ((b*c + a*f)*x^5)/5 + ((b*d + a*g)*x^6)/6 + ((b*e + a*h)*x^7)/7 + (b*f*x^8)/8 + (b*g*x^9)/9 + (b*h*x^10)/10","A",2,1,34,0.02941,1,"{1820}"
377,1,92,0,0.0734568,"\int \left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{4} x^4 (a f+b c)+\frac{1}{5} x^5 (a g+b d)+\frac{1}{6} x^6 (a h+b e)+a c x+\frac{1}{2} a d x^2+\frac{1}{3} a e x^3+\frac{1}{7} b f x^7+\frac{1}{8} b g x^8+\frac{1}{9} b h x^9","\frac{1}{4} x^4 (a f+b c)+\frac{1}{5} x^5 (a g+b d)+\frac{1}{6} x^6 (a h+b e)+a c x+\frac{1}{2} a d x^2+\frac{1}{3} a e x^3+\frac{1}{7} b f x^7+\frac{1}{8} b g x^8+\frac{1}{9} b h x^9",1,"a*c*x + (a*d*x^2)/2 + (a*e*x^3)/3 + ((b*c + a*f)*x^4)/4 + ((b*d + a*g)*x^5)/5 + ((b*e + a*h)*x^6)/6 + (b*f*x^7)/7 + (b*g*x^8)/8 + (b*h*x^9)/9","A",2,1,33,0.03030,1,"{1850}"
378,1,88,0,0.0578865,"\int \frac{\left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x} \, dx","Int[((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x,x]","\frac{1}{3} x^3 (a f+b c)+\frac{1}{4} x^4 (a g+b d)+\frac{1}{5} x^5 (a h+b e)+a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{6} b f x^6+\frac{1}{7} b g x^7+\frac{1}{8} b h x^8","\frac{1}{3} x^3 (a f+b c)+\frac{1}{4} x^4 (a g+b d)+\frac{1}{5} x^5 (a h+b e)+a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{6} b f x^6+\frac{1}{7} b g x^7+\frac{1}{8} b h x^8",1,"a*d*x + (a*e*x^2)/2 + ((b*c + a*f)*x^3)/3 + ((b*d + a*g)*x^4)/4 + ((b*e + a*h)*x^5)/5 + (b*f*x^6)/6 + (b*g*x^7)/7 + (b*h*x^8)/8 + a*c*Log[x]","A",2,1,36,0.02778,1,"{1820}"
379,1,86,0,0.0662083,"\int \frac{\left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^2} \, dx","Int[((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^2,x]","\frac{1}{2} x^2 (a f+b c)+\frac{1}{3} x^3 (a g+b d)+\frac{1}{4} x^4 (a h+b e)-\frac{a c}{x}+a d \log (x)+a e x+\frac{1}{5} b f x^5+\frac{1}{6} b g x^6+\frac{1}{7} b h x^7","\frac{1}{2} x^2 (a f+b c)+\frac{1}{3} x^3 (a g+b d)+\frac{1}{4} x^4 (a h+b e)-\frac{a c}{x}+a d \log (x)+a e x+\frac{1}{5} b f x^5+\frac{1}{6} b g x^6+\frac{1}{7} b h x^7",1,"-((a*c)/x) + a*e*x + ((b*c + a*f)*x^2)/2 + ((b*d + a*g)*x^3)/3 + ((b*e + a*h)*x^4)/4 + (b*f*x^5)/5 + (b*g*x^6)/6 + (b*h*x^7)/7 + a*d*Log[x]","A",2,1,36,0.02778,1,"{1820}"
380,1,86,0,0.0724331,"\int \frac{\left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^3} \, dx","Int[((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^3,x]","x (a f+b c)+\frac{1}{2} x^2 (a g+b d)+\frac{1}{3} x^3 (a h+b e)-\frac{a c}{2 x^2}-\frac{a d}{x}+a e \log (x)+\frac{1}{4} b f x^4+\frac{1}{5} b g x^5+\frac{1}{6} b h x^6","x (a f+b c)+\frac{1}{2} x^2 (a g+b d)+\frac{1}{3} x^3 (a h+b e)-\frac{a c}{2 x^2}-\frac{a d}{x}+a e \log (x)+\frac{1}{4} b f x^4+\frac{1}{5} b g x^5+\frac{1}{6} b h x^6",1,"-(a*c)/(2*x^2) - (a*d)/x + (b*c + a*f)*x + ((b*d + a*g)*x^2)/2 + ((b*e + a*h)*x^3)/3 + (b*f*x^4)/4 + (b*g*x^5)/5 + (b*h*x^6)/6 + a*e*Log[x]","A",2,1,36,0.02778,1,"{1820}"
381,1,86,0,0.070949,"\int \frac{\left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^4} \, dx","Int[((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^4,x]","\log (x) (a f+b c)+x (a g+b d)+\frac{1}{2} x^2 (a h+b e)-\frac{a c}{3 x^3}-\frac{a d}{2 x^2}-\frac{a e}{x}+\frac{1}{3} b f x^3+\frac{1}{4} b g x^4+\frac{1}{5} b h x^5","\log (x) (a f+b c)+x (a g+b d)+\frac{1}{2} x^2 (a h+b e)-\frac{a c}{3 x^3}-\frac{a d}{2 x^2}-\frac{a e}{x}+\frac{1}{3} b f x^3+\frac{1}{4} b g x^4+\frac{1}{5} b h x^5",1,"-(a*c)/(3*x^3) - (a*d)/(2*x^2) - (a*e)/x + (b*d + a*g)*x + ((b*e + a*h)*x^2)/2 + (b*f*x^3)/3 + (b*g*x^4)/4 + (b*h*x^5)/5 + (b*c + a*f)*Log[x]","A",2,1,36,0.02778,1,"{1820}"
382,1,86,0,0.0729936,"\int \frac{\left(a+b x^3\right) \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^5} \, dx","Int[((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5,x]","-\frac{a f+b c}{x}+\log (x) (a g+b d)+x (a h+b e)-\frac{a c}{4 x^4}-\frac{a d}{3 x^3}-\frac{a e}{2 x^2}+\frac{1}{2} b f x^2+\frac{1}{3} b g x^3+\frac{1}{4} b h x^4","-\frac{a f+b c}{x}+\log (x) (a g+b d)+x (a h+b e)-\frac{a c}{4 x^4}-\frac{a d}{3 x^3}-\frac{a e}{2 x^2}+\frac{1}{2} b f x^2+\frac{1}{3} b g x^3+\frac{1}{4} b h x^4",1,"-(a*c)/(4*x^4) - (a*d)/(3*x^3) - (a*e)/(2*x^2) - (b*c + a*f)/x + (b*e + a*h)*x + (b*f*x^2)/2 + (b*g*x^3)/3 + (b*h*x^4)/4 + (b*d + a*g)*Log[x]","A",2,1,36,0.02778,1,"{1820}"
383,1,163,0,0.2101107,"\int x^4 \left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x^4*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{5} a^2 c x^5+\frac{1}{6} a^2 d x^6+\frac{1}{7} a^2 e x^7+\frac{1}{11} b x^{11} (2 a f+b c)+\frac{1}{8} a x^8 (a f+2 b c)+\frac{1}{12} b x^{12} (2 a g+b d)+\frac{1}{9} a x^9 (a g+2 b d)+\frac{1}{13} b x^{13} (2 a h+b e)+\frac{1}{10} a x^{10} (a h+2 b e)+\frac{1}{14} b^2 f x^{14}+\frac{1}{15} b^2 g x^{15}+\frac{1}{16} b^2 h x^{16}","\frac{1}{5} a^2 c x^5+\frac{1}{6} a^2 d x^6+\frac{1}{7} a^2 e x^7+\frac{1}{11} b x^{11} (2 a f+b c)+\frac{1}{8} a x^8 (a f+2 b c)+\frac{1}{12} b x^{12} (2 a g+b d)+\frac{1}{9} a x^9 (a g+2 b d)+\frac{1}{13} b x^{13} (2 a h+b e)+\frac{1}{10} a x^{10} (a h+2 b e)+\frac{1}{14} b^2 f x^{14}+\frac{1}{15} b^2 g x^{15}+\frac{1}{16} b^2 h x^{16}",1,"(a^2*c*x^5)/5 + (a^2*d*x^6)/6 + (a^2*e*x^7)/7 + (a*(2*b*c + a*f)*x^8)/8 + (a*(2*b*d + a*g)*x^9)/9 + (a*(2*b*e + a*h)*x^10)/10 + (b*(b*c + 2*a*f)*x^11)/11 + (b*(b*d + 2*a*g)*x^12)/12 + (b*(b*e + 2*a*h)*x^13)/13 + (b^2*f*x^14)/14 + (b^2*g*x^15)/15 + (b^2*h*x^16)/16","A",2,1,38,0.02632,1,"{1820}"
384,1,163,0,0.15901,"\int x^3 \left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x^3*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{4} a^2 c x^4+\frac{1}{5} a^2 d x^5+\frac{1}{6} a^2 e x^6+\frac{1}{10} b x^{10} (2 a f+b c)+\frac{1}{7} a x^7 (a f+2 b c)+\frac{1}{11} b x^{11} (2 a g+b d)+\frac{1}{8} a x^8 (a g+2 b d)+\frac{1}{12} b x^{12} (2 a h+b e)+\frac{1}{9} a x^9 (a h+2 b e)+\frac{1}{13} b^2 f x^{13}+\frac{1}{14} b^2 g x^{14}+\frac{1}{15} b^2 h x^{15}","\frac{1}{4} a^2 c x^4+\frac{1}{5} a^2 d x^5+\frac{1}{6} a^2 e x^6+\frac{1}{10} b x^{10} (2 a f+b c)+\frac{1}{7} a x^7 (a f+2 b c)+\frac{1}{11} b x^{11} (2 a g+b d)+\frac{1}{8} a x^8 (a g+2 b d)+\frac{1}{12} b x^{12} (2 a h+b e)+\frac{1}{9} a x^9 (a h+2 b e)+\frac{1}{13} b^2 f x^{13}+\frac{1}{14} b^2 g x^{14}+\frac{1}{15} b^2 h x^{15}",1,"(a^2*c*x^4)/4 + (a^2*d*x^5)/5 + (a^2*e*x^6)/6 + (a*(2*b*c + a*f)*x^7)/7 + (a*(2*b*d + a*g)*x^8)/8 + (a*(2*b*e + a*h)*x^9)/9 + (b*(b*c + 2*a*f)*x^10)/10 + (b*(b*d + 2*a*g)*x^11)/11 + (b*(b*e + 2*a*h)*x^12)/12 + (b^2*f*x^13)/13 + (b^2*g*x^14)/14 + (b^2*h*x^15)/15","A",2,1,38,0.02632,1,"{1820}"
385,1,158,0,0.1257774,"\int x^2 \left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x^2*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{4} a^2 d x^4+\frac{1}{5} a^2 e x^5+\frac{1}{6} a^2 f x^6+\frac{c \left(a+b x^3\right)^3}{9 b}+\frac{1}{10} b x^{10} (2 a g+b d)+\frac{1}{7} a x^7 (a g+2 b d)+\frac{1}{11} b x^{11} (2 a h+b e)+\frac{1}{8} a x^8 (a h+2 b e)+\frac{2}{9} a b f x^9+\frac{1}{12} b^2 f x^{12}+\frac{1}{13} b^2 g x^{13}+\frac{1}{14} b^2 h x^{14}","\frac{1}{4} a^2 d x^4+\frac{1}{5} a^2 e x^5+\frac{1}{6} a^2 f x^6+\frac{c \left(a+b x^3\right)^3}{9 b}+\frac{1}{10} b x^{10} (2 a g+b d)+\frac{1}{7} a x^7 (a g+2 b d)+\frac{1}{11} b x^{11} (2 a h+b e)+\frac{1}{8} a x^8 (a h+2 b e)+\frac{2}{9} a b f x^9+\frac{1}{12} b^2 f x^{12}+\frac{1}{13} b^2 g x^{13}+\frac{1}{14} b^2 h x^{14}",1,"(a^2*d*x^4)/4 + (a^2*e*x^5)/5 + (a^2*f*x^6)/6 + (a*(2*b*d + a*g)*x^7)/7 + (a*(2*b*e + a*h)*x^8)/8 + (2*a*b*f*x^9)/9 + (b*(b*d + 2*a*g)*x^10)/10 + (b*(b*e + 2*a*h)*x^11)/11 + (b^2*f*x^12)/12 + (b^2*g*x^13)/13 + (b^2*h*x^14)/14 + (c*(a + b*x^3)^3)/(9*b)","A",3,2,38,0.05263,1,"{1582, 1850}"
386,1,158,0,0.1290483,"\int x \left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{2} a^2 c x^2+\frac{1}{4} a^2 e x^4+\frac{1}{6} a^2 g x^6+\frac{1}{8} b x^8 (2 a f+b c)+\frac{1}{5} a x^5 (a f+2 b c)+\frac{d \left(a+b x^3\right)^3}{9 b}+\frac{1}{10} b x^{10} (2 a h+b e)+\frac{1}{7} a x^7 (a h+2 b e)+\frac{2}{9} a b g x^9+\frac{1}{11} b^2 f x^{11}+\frac{1}{12} b^2 g x^{12}+\frac{1}{13} b^2 h x^{13}","\frac{1}{2} a^2 c x^2+\frac{1}{4} a^2 e x^4+\frac{1}{6} a^2 g x^6+\frac{1}{8} b x^8 (2 a f+b c)+\frac{1}{5} a x^5 (a f+2 b c)+\frac{d \left(a+b x^3\right)^3}{9 b}+\frac{1}{10} b x^{10} (2 a h+b e)+\frac{1}{7} a x^7 (a h+2 b e)+\frac{2}{9} a b g x^9+\frac{1}{11} b^2 f x^{11}+\frac{1}{12} b^2 g x^{12}+\frac{1}{13} b^2 h x^{13}",1,"(a^2*c*x^2)/2 + (a^2*e*x^4)/4 + (a*(2*b*c + a*f)*x^5)/5 + (a^2*g*x^6)/6 + (a*(2*b*e + a*h)*x^7)/7 + (b*(b*c + 2*a*f)*x^8)/8 + (2*a*b*g*x^9)/9 + (b*(b*e + 2*a*h)*x^10)/10 + (b^2*f*x^11)/11 + (b^2*g*x^12)/12 + (b^2*h*x^13)/13 + (d*(a + b*x^3)^3)/(9*b)","A",3,2,36,0.05556,1,"{1582, 1850}"
387,1,153,0,0.1265795,"\int \left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{6} a^2 h x^6+\frac{1}{7} b x^7 (2 a f+b c)+\frac{1}{4} a x^4 (a f+2 b c)+\frac{1}{8} b x^8 (2 a g+b d)+\frac{1}{5} a x^5 (a g+2 b d)+\frac{e \left(a+b x^3\right)^3}{9 b}+\frac{2}{9} a b h x^9+\frac{1}{10} b^2 f x^{10}+\frac{1}{11} b^2 g x^{11}+\frac{1}{12} b^2 h x^{12}","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{6} a^2 h x^6+\frac{1}{7} b x^7 (2 a f+b c)+\frac{1}{4} a x^4 (a f+2 b c)+\frac{1}{8} b x^8 (2 a g+b d)+\frac{1}{5} a x^5 (a g+2 b d)+\frac{e \left(a+b x^3\right)^3}{9 b}+\frac{2}{9} a b h x^9+\frac{1}{10} b^2 f x^{10}+\frac{1}{11} b^2 g x^{11}+\frac{1}{12} b^2 h x^{12}",1,"a^2*c*x + (a^2*d*x^2)/2 + (a*(2*b*c + a*f)*x^4)/4 + (a*(2*b*d + a*g)*x^5)/5 + (a^2*h*x^6)/6 + (b*(b*c + 2*a*f)*x^7)/7 + (b*(b*d + 2*a*g)*x^8)/8 + (2*a*b*h*x^9)/9 + (b^2*f*x^10)/10 + (b^2*g*x^11)/11 + (b^2*h*x^12)/12 + (e*(a + b*x^3)^3)/(9*b)","A",3,2,35,0.05714,1,"{1582, 1850}"
388,1,149,0,0.1057029,"\int \frac{\left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x} \, dx","Int[((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x,x]","a^2 c \log (x)+a^2 d x+\frac{1}{2} a^2 e x^2+\frac{2}{3} a b c x^3+\frac{1}{7} b x^7 (2 a g+b d)+\frac{1}{4} a x^4 (a g+2 b d)+\frac{1}{8} b x^8 (2 a h+b e)+\frac{1}{5} a x^5 (a h+2 b e)+\frac{f \left(a+b x^3\right)^3}{9 b}+\frac{1}{6} b^2 c x^6+\frac{1}{10} b^2 g x^{10}+\frac{1}{11} b^2 h x^{11}","a^2 c \log (x)+a^2 d x+\frac{1}{2} a^2 e x^2+\frac{2}{3} a b c x^3+\frac{1}{7} b x^7 (2 a g+b d)+\frac{1}{4} a x^4 (a g+2 b d)+\frac{1}{8} b x^8 (2 a h+b e)+\frac{1}{5} a x^5 (a h+2 b e)+\frac{f \left(a+b x^3\right)^3}{9 b}+\frac{1}{6} b^2 c x^6+\frac{1}{10} b^2 g x^{10}+\frac{1}{11} b^2 h x^{11}",1,"a^2*d*x + (a^2*e*x^2)/2 + (2*a*b*c*x^3)/3 + (a*(2*b*d + a*g)*x^4)/4 + (a*(2*b*e + a*h)*x^5)/5 + (b^2*c*x^6)/6 + (b*(b*d + 2*a*g)*x^7)/7 + (b*(b*e + 2*a*h)*x^8)/8 + (b^2*g*x^10)/10 + (b^2*h*x^11)/11 + (f*(a + b*x^3)^3)/(9*b) + a^2*c*Log[x]","A",3,2,38,0.05263,1,"{1583, 1820}"
389,1,147,0,0.1275436,"\int \frac{\left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^2} \, dx","Int[((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^2,x]","-\frac{a^2 c}{x}+a^2 d \log (x)+a^2 e x+\frac{1}{5} b x^5 (2 a f+b c)+\frac{1}{2} a x^2 (a f+2 b c)+\frac{2}{3} a b d x^3+\frac{1}{7} b x^7 (2 a h+b e)+\frac{1}{4} a x^4 (a h+2 b e)+\frac{g \left(a+b x^3\right)^3}{9 b}+\frac{1}{6} b^2 d x^6+\frac{1}{8} b^2 f x^8+\frac{1}{10} b^2 h x^{10}","-\frac{a^2 c}{x}+a^2 d \log (x)+a^2 e x+\frac{1}{5} b x^5 (2 a f+b c)+\frac{1}{2} a x^2 (a f+2 b c)+\frac{2}{3} a b d x^3+\frac{1}{7} b x^7 (2 a h+b e)+\frac{1}{4} a x^4 (a h+2 b e)+\frac{g \left(a+b x^3\right)^3}{9 b}+\frac{1}{6} b^2 d x^6+\frac{1}{8} b^2 f x^8+\frac{1}{10} b^2 h x^{10}",1,"-((a^2*c)/x) + a^2*e*x + (a*(2*b*c + a*f)*x^2)/2 + (2*a*b*d*x^3)/3 + (a*(2*b*e + a*h)*x^4)/4 + (b*(b*c + 2*a*f)*x^5)/5 + (b^2*d*x^6)/6 + (b*(b*e + 2*a*h)*x^7)/7 + (b^2*f*x^8)/8 + (b^2*h*x^10)/10 + (g*(a + b*x^3)^3)/(9*b) + a^2*d*Log[x]","A",3,2,38,0.05263,1,"{1583, 1820}"
390,1,147,0,0.1283724,"\int \frac{\left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^3} \, dx","Int[((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^3,x]","-\frac{a^2 c}{2 x^2}-\frac{a^2 d}{x}+a^2 e \log (x)+\frac{1}{4} b x^4 (2 a f+b c)+a x (a f+2 b c)+\frac{1}{5} b x^5 (2 a g+b d)+\frac{1}{2} a x^2 (a g+2 b d)+\frac{2}{3} a b e x^3+\frac{h \left(a+b x^3\right)^3}{9 b}+\frac{1}{6} b^2 e x^6+\frac{1}{7} b^2 f x^7+\frac{1}{8} b^2 g x^8","-\frac{a^2 c}{2 x^2}-\frac{a^2 d}{x}+a^2 e \log (x)+\frac{1}{4} b x^4 (2 a f+b c)+a x (a f+2 b c)+\frac{1}{5} b x^5 (2 a g+b d)+\frac{1}{2} a x^2 (a g+2 b d)+\frac{2}{3} a b e x^3+\frac{h \left(a+b x^3\right)^3}{9 b}+\frac{1}{6} b^2 e x^6+\frac{1}{7} b^2 f x^7+\frac{1}{8} b^2 g x^8",1,"-(a^2*c)/(2*x^2) - (a^2*d)/x + a*(2*b*c + a*f)*x + (a*(2*b*d + a*g)*x^2)/2 + (2*a*b*e*x^3)/3 + (b*(b*c + 2*a*f)*x^4)/4 + (b*(b*d + 2*a*g)*x^5)/5 + (b^2*e*x^6)/6 + (b^2*f*x^7)/7 + (b^2*g*x^8)/8 + (h*(a + b*x^3)^3)/(9*b) + a^2*e*Log[x]","A",3,2,38,0.05263,1,"{1583, 1820}"
391,1,152,0,0.1179998,"\int \frac{\left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^4} \, dx","Int[((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^4,x]","-\frac{a^2 c}{3 x^3}-\frac{a^2 d}{2 x^2}-\frac{a^2 e}{x}+\frac{1}{3} b x^3 (2 a f+b c)+a \log (x) (a f+2 b c)+\frac{1}{4} b x^4 (2 a g+b d)+a x (a g+2 b d)+\frac{1}{5} b x^5 (2 a h+b e)+\frac{1}{2} a x^2 (a h+2 b e)+\frac{1}{6} b^2 f x^6+\frac{1}{7} b^2 g x^7+\frac{1}{8} b^2 h x^8","-\frac{a^2 c}{3 x^3}-\frac{a^2 d}{2 x^2}-\frac{a^2 e}{x}+\frac{1}{3} b x^3 (2 a f+b c)+a \log (x) (a f+2 b c)+\frac{1}{4} b x^4 (2 a g+b d)+a x (a g+2 b d)+\frac{1}{5} b x^5 (2 a h+b e)+\frac{1}{2} a x^2 (a h+2 b e)+\frac{1}{6} b^2 f x^6+\frac{1}{7} b^2 g x^7+\frac{1}{8} b^2 h x^8",1,"-(a^2*c)/(3*x^3) - (a^2*d)/(2*x^2) - (a^2*e)/x + a*(2*b*d + a*g)*x + (a*(2*b*e + a*h)*x^2)/2 + (b*(b*c + 2*a*f)*x^3)/3 + (b*(b*d + 2*a*g)*x^4)/4 + (b*(b*e + 2*a*h)*x^5)/5 + (b^2*f*x^6)/6 + (b^2*g*x^7)/7 + (b^2*h*x^8)/8 + a*(2*b*c + a*f)*Log[x]","A",2,1,38,0.02632,1,"{1820}"
392,1,152,0,0.1172739,"\int \frac{\left(a+b x^3\right)^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^5} \, dx","Int[((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5,x]","-\frac{a^2 c}{4 x^4}-\frac{a^2 d}{3 x^3}-\frac{a^2 e}{2 x^2}+\frac{1}{2} b x^2 (2 a f+b c)-\frac{a (a f+2 b c)}{x}+\frac{1}{3} b x^3 (2 a g+b d)+a \log (x) (a g+2 b d)+\frac{1}{4} b x^4 (2 a h+b e)+a x (a h+2 b e)+\frac{1}{5} b^2 f x^5+\frac{1}{6} b^2 g x^6+\frac{1}{7} b^2 h x^7","-\frac{a^2 c}{4 x^4}-\frac{a^2 d}{3 x^3}-\frac{a^2 e}{2 x^2}+\frac{1}{2} b x^2 (2 a f+b c)-\frac{a (a f+2 b c)}{x}+\frac{1}{3} b x^3 (2 a g+b d)+a \log (x) (a g+2 b d)+\frac{1}{4} b x^4 (2 a h+b e)+a x (a h+2 b e)+\frac{1}{5} b^2 f x^5+\frac{1}{6} b^2 g x^6+\frac{1}{7} b^2 h x^7",1,"-(a^2*c)/(4*x^4) - (a^2*d)/(3*x^3) - (a^2*e)/(2*x^2) - (a*(2*b*c + a*f))/x + a*(2*b*e + a*h)*x + (b*(b*c + 2*a*f)*x^2)/2 + (b*(b*d + 2*a*g)*x^3)/3 + (b*(b*e + 2*a*h)*x^4)/4 + (b^2*f*x^5)/5 + (b^2*g*x^6)/6 + (b^2*h*x^7)/7 + a*(2*b*d + a*g)*Log[x]","A",2,1,38,0.02632,1,"{1820}"
393,1,223,0,0.2926116,"\int x^4 \left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x^4*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{8} a^2 x^8 (a f+3 b c)+\frac{1}{9} a^2 x^9 (a g+3 b d)+\frac{1}{10} a^2 x^{10} (a h+3 b e)+\frac{1}{5} a^3 c x^5+\frac{1}{6} a^3 d x^6+\frac{1}{7} a^3 e x^7+\frac{1}{14} b^2 x^{14} (3 a f+b c)+\frac{1}{15} b^2 x^{15} (3 a g+b d)+\frac{1}{16} b^2 x^{16} (3 a h+b e)+\frac{3}{11} a b x^{11} (a f+b c)+\frac{1}{4} a b x^{12} (a g+b d)+\frac{3}{13} a b x^{13} (a h+b e)+\frac{1}{17} b^3 f x^{17}+\frac{1}{18} b^3 g x^{18}+\frac{1}{19} b^3 h x^{19}","\frac{1}{8} a^2 x^8 (a f+3 b c)+\frac{1}{9} a^2 x^9 (a g+3 b d)+\frac{1}{10} a^2 x^{10} (a h+3 b e)+\frac{1}{5} a^3 c x^5+\frac{1}{6} a^3 d x^6+\frac{1}{7} a^3 e x^7+\frac{1}{14} b^2 x^{14} (3 a f+b c)+\frac{1}{15} b^2 x^{15} (3 a g+b d)+\frac{1}{16} b^2 x^{16} (3 a h+b e)+\frac{3}{11} a b x^{11} (a f+b c)+\frac{1}{4} a b x^{12} (a g+b d)+\frac{3}{13} a b x^{13} (a h+b e)+\frac{1}{17} b^3 f x^{17}+\frac{1}{18} b^3 g x^{18}+\frac{1}{19} b^3 h x^{19}",1,"(a^3*c*x^5)/5 + (a^3*d*x^6)/6 + (a^3*e*x^7)/7 + (a^2*(3*b*c + a*f)*x^8)/8 + (a^2*(3*b*d + a*g)*x^9)/9 + (a^2*(3*b*e + a*h)*x^10)/10 + (3*a*b*(b*c + a*f)*x^11)/11 + (a*b*(b*d + a*g)*x^12)/4 + (3*a*b*(b*e + a*h)*x^13)/13 + (b^2*(b*c + 3*a*f)*x^14)/14 + (b^2*(b*d + 3*a*g)*x^15)/15 + (b^2*(b*e + 3*a*h)*x^16)/16 + (b^3*f*x^17)/17 + (b^3*g*x^18)/18 + (b^3*h*x^19)/19","A",2,1,38,0.02632,1,"{1820}"
394,1,223,0,0.2275743,"\int x^3 \left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x^3*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{7} a^2 x^7 (a f+3 b c)+\frac{1}{8} a^2 x^8 (a g+3 b d)+\frac{1}{9} a^2 x^9 (a h+3 b e)+\frac{1}{4} a^3 c x^4+\frac{1}{5} a^3 d x^5+\frac{1}{6} a^3 e x^6+\frac{1}{13} b^2 x^{13} (3 a f+b c)+\frac{1}{14} b^2 x^{14} (3 a g+b d)+\frac{1}{15} b^2 x^{15} (3 a h+b e)+\frac{3}{10} a b x^{10} (a f+b c)+\frac{3}{11} a b x^{11} (a g+b d)+\frac{1}{4} a b x^{12} (a h+b e)+\frac{1}{16} b^3 f x^{16}+\frac{1}{17} b^3 g x^{17}+\frac{1}{18} b^3 h x^{18}","\frac{1}{7} a^2 x^7 (a f+3 b c)+\frac{1}{8} a^2 x^8 (a g+3 b d)+\frac{1}{9} a^2 x^9 (a h+3 b e)+\frac{1}{4} a^3 c x^4+\frac{1}{5} a^3 d x^5+\frac{1}{6} a^3 e x^6+\frac{1}{13} b^2 x^{13} (3 a f+b c)+\frac{1}{14} b^2 x^{14} (3 a g+b d)+\frac{1}{15} b^2 x^{15} (3 a h+b e)+\frac{3}{10} a b x^{10} (a f+b c)+\frac{3}{11} a b x^{11} (a g+b d)+\frac{1}{4} a b x^{12} (a h+b e)+\frac{1}{16} b^3 f x^{16}+\frac{1}{17} b^3 g x^{17}+\frac{1}{18} b^3 h x^{18}",1,"(a^3*c*x^4)/4 + (a^3*d*x^5)/5 + (a^3*e*x^6)/6 + (a^2*(3*b*c + a*f)*x^7)/7 + (a^2*(3*b*d + a*g)*x^8)/8 + (a^2*(3*b*e + a*h)*x^9)/9 + (3*a*b*(b*c + a*f)*x^10)/10 + (3*a*b*(b*d + a*g)*x^11)/11 + (a*b*(b*e + a*h)*x^12)/4 + (b^2*(b*c + 3*a*f)*x^13)/13 + (b^2*(b*d + 3*a*g)*x^14)/14 + (b^2*(b*e + 3*a*h)*x^15)/15 + (b^3*f*x^16)/16 + (b^3*g*x^17)/17 + (b^3*h*x^18)/18","A",2,1,38,0.02632,1,"{1820}"
395,1,212,0,0.1792451,"\int x^2 \left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x^2*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{7} a^2 x^7 (a g+3 b d)+\frac{1}{8} a^2 x^8 (a h+3 b e)+\frac{1}{3} a^2 b f x^9+\frac{1}{4} a^3 d x^4+\frac{1}{5} a^3 e x^5+\frac{1}{6} a^3 f x^6+\frac{1}{13} b^2 x^{13} (3 a g+b d)+\frac{1}{14} b^2 x^{14} (3 a h+b e)+\frac{1}{4} a b^2 f x^{12}+\frac{c \left(a+b x^3\right)^4}{12 b}+\frac{3}{10} a b x^{10} (a g+b d)+\frac{3}{11} a b x^{11} (a h+b e)+\frac{1}{15} b^3 f x^{15}+\frac{1}{16} b^3 g x^{16}+\frac{1}{17} b^3 h x^{17}","\frac{1}{7} a^2 x^7 (a g+3 b d)+\frac{1}{8} a^2 x^8 (a h+3 b e)+\frac{1}{3} a^2 b f x^9+\frac{1}{4} a^3 d x^4+\frac{1}{5} a^3 e x^5+\frac{1}{6} a^3 f x^6+\frac{1}{13} b^2 x^{13} (3 a g+b d)+\frac{1}{14} b^2 x^{14} (3 a h+b e)+\frac{1}{4} a b^2 f x^{12}+\frac{c \left(a+b x^3\right)^4}{12 b}+\frac{3}{10} a b x^{10} (a g+b d)+\frac{3}{11} a b x^{11} (a h+b e)+\frac{1}{15} b^3 f x^{15}+\frac{1}{16} b^3 g x^{16}+\frac{1}{17} b^3 h x^{17}",1,"(a^3*d*x^4)/4 + (a^3*e*x^5)/5 + (a^3*f*x^6)/6 + (a^2*(3*b*d + a*g)*x^7)/7 + (a^2*(3*b*e + a*h)*x^8)/8 + (a^2*b*f*x^9)/3 + (3*a*b*(b*d + a*g)*x^10)/10 + (3*a*b*(b*e + a*h)*x^11)/11 + (a*b^2*f*x^12)/4 + (b^2*(b*d + 3*a*g)*x^13)/13 + (b^2*(b*e + 3*a*h)*x^14)/14 + (b^3*f*x^15)/15 + (b^3*g*x^16)/16 + (b^3*h*x^17)/17 + (c*(a + b*x^3)^4)/(12*b)","A",3,2,38,0.05263,1,"{1582, 1850}"
396,1,212,0,0.1770175,"\int x \left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[x*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{5} a^2 x^5 (a f+3 b c)+\frac{1}{7} a^2 x^7 (a h+3 b e)+\frac{1}{3} a^2 b g x^9+\frac{1}{2} a^3 c x^2+\frac{1}{4} a^3 e x^4+\frac{1}{6} a^3 g x^6+\frac{1}{11} b^2 x^{11} (3 a f+b c)+\frac{1}{13} b^2 x^{13} (3 a h+b e)+\frac{1}{4} a b^2 g x^{12}+\frac{3}{8} a b x^8 (a f+b c)+\frac{d \left(a+b x^3\right)^4}{12 b}+\frac{3}{10} a b x^{10} (a h+b e)+\frac{1}{14} b^3 f x^{14}+\frac{1}{15} b^3 g x^{15}+\frac{1}{16} b^3 h x^{16}","\frac{1}{5} a^2 x^5 (a f+3 b c)+\frac{1}{7} a^2 x^7 (a h+3 b e)+\frac{1}{3} a^2 b g x^9+\frac{1}{2} a^3 c x^2+\frac{1}{4} a^3 e x^4+\frac{1}{6} a^3 g x^6+\frac{1}{11} b^2 x^{11} (3 a f+b c)+\frac{1}{13} b^2 x^{13} (3 a h+b e)+\frac{1}{4} a b^2 g x^{12}+\frac{3}{8} a b x^8 (a f+b c)+\frac{d \left(a+b x^3\right)^4}{12 b}+\frac{3}{10} a b x^{10} (a h+b e)+\frac{1}{14} b^3 f x^{14}+\frac{1}{15} b^3 g x^{15}+\frac{1}{16} b^3 h x^{16}",1,"(a^3*c*x^2)/2 + (a^3*e*x^4)/4 + (a^2*(3*b*c + a*f)*x^5)/5 + (a^3*g*x^6)/6 + (a^2*(3*b*e + a*h)*x^7)/7 + (3*a*b*(b*c + a*f)*x^8)/8 + (a^2*b*g*x^9)/3 + (3*a*b*(b*e + a*h)*x^10)/10 + (b^2*(b*c + 3*a*f)*x^11)/11 + (a*b^2*g*x^12)/4 + (b^2*(b*e + 3*a*h)*x^13)/13 + (b^3*f*x^14)/14 + (b^3*g*x^15)/15 + (b^3*h*x^16)/16 + (d*(a + b*x^3)^4)/(12*b)","A",3,2,36,0.05556,1,"{1582, 1850}"
397,1,207,0,0.1773187,"\int \left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right) \, dx","Int[(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x]","\frac{1}{4} a^2 x^4 (a f+3 b c)+\frac{1}{5} a^2 x^5 (a g+3 b d)+\frac{1}{3} a^2 b h x^9+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{1}{6} a^3 h x^6+\frac{1}{10} b^2 x^{10} (3 a f+b c)+\frac{1}{11} b^2 x^{11} (3 a g+b d)+\frac{1}{4} a b^2 h x^{12}+\frac{3}{7} a b x^7 (a f+b c)+\frac{3}{8} a b x^8 (a g+b d)+\frac{e \left(a+b x^3\right)^4}{12 b}+\frac{1}{13} b^3 f x^{13}+\frac{1}{14} b^3 g x^{14}+\frac{1}{15} b^3 h x^{15}","\frac{1}{4} a^2 x^4 (a f+3 b c)+\frac{1}{5} a^2 x^5 (a g+3 b d)+\frac{1}{3} a^2 b h x^9+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{1}{6} a^3 h x^6+\frac{1}{10} b^2 x^{10} (3 a f+b c)+\frac{1}{11} b^2 x^{11} (3 a g+b d)+\frac{1}{4} a b^2 h x^{12}+\frac{3}{7} a b x^7 (a f+b c)+\frac{3}{8} a b x^8 (a g+b d)+\frac{e \left(a+b x^3\right)^4}{12 b}+\frac{1}{13} b^3 f x^{13}+\frac{1}{14} b^3 g x^{14}+\frac{1}{15} b^3 h x^{15}",1,"a^3*c*x + (a^3*d*x^2)/2 + (a^2*(3*b*c + a*f)*x^4)/4 + (a^2*(3*b*d + a*g)*x^5)/5 + (a^3*h*x^6)/6 + (3*a*b*(b*c + a*f)*x^7)/7 + (3*a*b*(b*d + a*g)*x^8)/8 + (a^2*b*h*x^9)/3 + (b^2*(b*c + 3*a*f)*x^10)/10 + (b^2*(b*d + 3*a*g)*x^11)/11 + (a*b^2*h*x^12)/4 + (b^3*f*x^13)/13 + (b^3*g*x^14)/14 + (b^3*h*x^15)/15 + (e*(a + b*x^3)^4)/(12*b)","A",3,2,35,0.05714,1,"{1582, 1850}"
398,1,200,0,0.1456085,"\int \frac{\left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x} \, dx","Int[((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x,x]","a^2 b c x^3+\frac{1}{4} a^2 x^4 (a g+3 b d)+\frac{1}{5} a^2 x^5 (a h+3 b e)+a^3 c \log (x)+a^3 d x+\frac{1}{2} a^3 e x^2+\frac{1}{2} a b^2 c x^6+\frac{1}{10} b^2 x^{10} (3 a g+b d)+\frac{1}{11} b^2 x^{11} (3 a h+b e)+\frac{3}{7} a b x^7 (a g+b d)+\frac{3}{8} a b x^8 (a h+b e)+\frac{f \left(a+b x^3\right)^4}{12 b}+\frac{1}{9} b^3 c x^9+\frac{1}{13} b^3 g x^{13}+\frac{1}{14} b^3 h x^{14}","a^2 b c x^3+\frac{1}{4} a^2 x^4 (a g+3 b d)+\frac{1}{5} a^2 x^5 (a h+3 b e)+a^3 c \log (x)+a^3 d x+\frac{1}{2} a^3 e x^2+\frac{1}{2} a b^2 c x^6+\frac{1}{10} b^2 x^{10} (3 a g+b d)+\frac{1}{11} b^2 x^{11} (3 a h+b e)+\frac{3}{7} a b x^7 (a g+b d)+\frac{3}{8} a b x^8 (a h+b e)+\frac{f \left(a+b x^3\right)^4}{12 b}+\frac{1}{9} b^3 c x^9+\frac{1}{13} b^3 g x^{13}+\frac{1}{14} b^3 h x^{14}",1,"a^3*d*x + (a^3*e*x^2)/2 + a^2*b*c*x^3 + (a^2*(3*b*d + a*g)*x^4)/4 + (a^2*(3*b*e + a*h)*x^5)/5 + (a*b^2*c*x^6)/2 + (3*a*b*(b*d + a*g)*x^7)/7 + (3*a*b*(b*e + a*h)*x^8)/8 + (b^3*c*x^9)/9 + (b^2*(b*d + 3*a*g)*x^10)/10 + (b^2*(b*e + 3*a*h)*x^11)/11 + (b^3*g*x^13)/13 + (b^3*h*x^14)/14 + (f*(a + b*x^3)^4)/(12*b) + a^3*c*Log[x]","A",3,2,38,0.05263,1,"{1583, 1820}"
399,1,198,0,0.1821057,"\int \frac{\left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^2} \, dx","Int[((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^2,x]","\frac{1}{2} a^2 x^2 (a f+3 b c)+a^2 b d x^3+\frac{1}{4} a^2 x^4 (a h+3 b e)-\frac{a^3 c}{x}+a^3 d \log (x)+a^3 e x+\frac{1}{8} b^2 x^8 (3 a f+b c)+\frac{1}{2} a b^2 d x^6+\frac{1}{10} b^2 x^{10} (3 a h+b e)+\frac{3}{5} a b x^5 (a f+b c)+\frac{3}{7} a b x^7 (a h+b e)+\frac{g \left(a+b x^3\right)^4}{12 b}+\frac{1}{9} b^3 d x^9+\frac{1}{11} b^3 f x^{11}+\frac{1}{13} b^3 h x^{13}","\frac{1}{2} a^2 x^2 (a f+3 b c)+a^2 b d x^3+\frac{1}{4} a^2 x^4 (a h+3 b e)-\frac{a^3 c}{x}+a^3 d \log (x)+a^3 e x+\frac{1}{8} b^2 x^8 (3 a f+b c)+\frac{1}{2} a b^2 d x^6+\frac{1}{10} b^2 x^{10} (3 a h+b e)+\frac{3}{5} a b x^5 (a f+b c)+\frac{3}{7} a b x^7 (a h+b e)+\frac{g \left(a+b x^3\right)^4}{12 b}+\frac{1}{9} b^3 d x^9+\frac{1}{11} b^3 f x^{11}+\frac{1}{13} b^3 h x^{13}",1,"-((a^3*c)/x) + a^3*e*x + (a^2*(3*b*c + a*f)*x^2)/2 + a^2*b*d*x^3 + (a^2*(3*b*e + a*h)*x^4)/4 + (3*a*b*(b*c + a*f)*x^5)/5 + (a*b^2*d*x^6)/2 + (3*a*b*(b*e + a*h)*x^7)/7 + (b^2*(b*c + 3*a*f)*x^8)/8 + (b^3*d*x^9)/9 + (b^2*(b*e + 3*a*h)*x^10)/10 + (b^3*f*x^11)/11 + (b^3*h*x^13)/13 + (g*(a + b*x^3)^4)/(12*b) + a^3*d*Log[x]","A",3,2,38,0.05263,1,"{1583, 1820}"
400,1,198,0,0.1967742,"\int \frac{\left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^3} \, dx","Int[((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^3,x]","a^2 x (a f+3 b c)+\frac{1}{2} a^2 x^2 (a g+3 b d)+a^2 b e x^3-\frac{a^3 c}{2 x^2}-\frac{a^3 d}{x}+a^3 e \log (x)+\frac{1}{7} b^2 x^7 (3 a f+b c)+\frac{1}{8} b^2 x^8 (3 a g+b d)+\frac{1}{2} a b^2 e x^6+\frac{3}{4} a b x^4 (a f+b c)+\frac{3}{5} a b x^5 (a g+b d)+\frac{h \left(a+b x^3\right)^4}{12 b}+\frac{1}{9} b^3 e x^9+\frac{1}{10} b^3 f x^{10}+\frac{1}{11} b^3 g x^{11}","a^2 x (a f+3 b c)+\frac{1}{2} a^2 x^2 (a g+3 b d)+a^2 b e x^3-\frac{a^3 c}{2 x^2}-\frac{a^3 d}{x}+a^3 e \log (x)+\frac{1}{7} b^2 x^7 (3 a f+b c)+\frac{1}{8} b^2 x^8 (3 a g+b d)+\frac{1}{2} a b^2 e x^6+\frac{3}{4} a b x^4 (a f+b c)+\frac{3}{5} a b x^5 (a g+b d)+\frac{h \left(a+b x^3\right)^4}{12 b}+\frac{1}{9} b^3 e x^9+\frac{1}{10} b^3 f x^{10}+\frac{1}{11} b^3 g x^{11}",1,"-(a^3*c)/(2*x^2) - (a^3*d)/x + a^2*(3*b*c + a*f)*x + (a^2*(3*b*d + a*g)*x^2)/2 + a^2*b*e*x^3 + (3*a*b*(b*c + a*f)*x^4)/4 + (3*a*b*(b*d + a*g)*x^5)/5 + (a*b^2*e*x^6)/2 + (b^2*(b*c + 3*a*f)*x^7)/7 + (b^2*(b*d + 3*a*g)*x^8)/8 + (b^3*e*x^9)/9 + (b^3*f*x^10)/10 + (b^3*g*x^11)/11 + (h*(a + b*x^3)^4)/(12*b) + a^3*e*Log[x]","A",3,2,38,0.05263,1,"{1583, 1820}"
401,1,209,0,0.1795483,"\int \frac{\left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^4} \, dx","Int[((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^4,x]","a^2 \log (x) (a f+3 b c)+a^2 x (a g+3 b d)+\frac{1}{2} a^2 x^2 (a h+3 b e)-\frac{a^3 c}{3 x^3}-\frac{a^3 d}{2 x^2}-\frac{a^3 e}{x}+\frac{1}{6} b^2 x^6 (3 a f+b c)+\frac{1}{7} b^2 x^7 (3 a g+b d)+\frac{1}{8} b^2 x^8 (3 a h+b e)+a b x^3 (a f+b c)+\frac{3}{4} a b x^4 (a g+b d)+\frac{3}{5} a b x^5 (a h+b e)+\frac{1}{9} b^3 f x^9+\frac{1}{10} b^3 g x^{10}+\frac{1}{11} b^3 h x^{11}","a^2 \log (x) (a f+3 b c)+a^2 x (a g+3 b d)+\frac{1}{2} a^2 x^2 (a h+3 b e)-\frac{a^3 c}{3 x^3}-\frac{a^3 d}{2 x^2}-\frac{a^3 e}{x}+\frac{1}{6} b^2 x^6 (3 a f+b c)+\frac{1}{7} b^2 x^7 (3 a g+b d)+\frac{1}{8} b^2 x^8 (3 a h+b e)+a b x^3 (a f+b c)+\frac{3}{4} a b x^4 (a g+b d)+\frac{3}{5} a b x^5 (a h+b e)+\frac{1}{9} b^3 f x^9+\frac{1}{10} b^3 g x^{10}+\frac{1}{11} b^3 h x^{11}",1,"-(a^3*c)/(3*x^3) - (a^3*d)/(2*x^2) - (a^3*e)/x + a^2*(3*b*d + a*g)*x + (a^2*(3*b*e + a*h)*x^2)/2 + a*b*(b*c + a*f)*x^3 + (3*a*b*(b*d + a*g)*x^4)/4 + (3*a*b*(b*e + a*h)*x^5)/5 + (b^2*(b*c + 3*a*f)*x^6)/6 + (b^2*(b*d + 3*a*g)*x^7)/7 + (b^2*(b*e + 3*a*h)*x^8)/8 + (b^3*f*x^9)/9 + (b^3*g*x^10)/10 + (b^3*h*x^11)/11 + a^2*(3*b*c + a*f)*Log[x]","A",2,1,38,0.02632,1,"{1820}"
402,1,209,0,0.1767417,"\int \frac{\left(a+b x^3\right)^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{x^5} \, dx","Int[((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5,x]","-\frac{a^2 (a f+3 b c)}{x}+a^2 \log (x) (a g+3 b d)+a^2 x (a h+3 b e)-\frac{a^3 c}{4 x^4}-\frac{a^3 d}{3 x^3}-\frac{a^3 e}{2 x^2}+\frac{1}{5} b^2 x^5 (3 a f+b c)+\frac{1}{6} b^2 x^6 (3 a g+b d)+\frac{1}{7} b^2 x^7 (3 a h+b e)+\frac{3}{2} a b x^2 (a f+b c)+a b x^3 (a g+b d)+\frac{3}{4} a b x^4 (a h+b e)+\frac{1}{8} b^3 f x^8+\frac{1}{9} b^3 g x^9+\frac{1}{10} b^3 h x^{10}","-\frac{a^2 (a f+3 b c)}{x}+a^2 \log (x) (a g+3 b d)+a^2 x (a h+3 b e)-\frac{a^3 c}{4 x^4}-\frac{a^3 d}{3 x^3}-\frac{a^3 e}{2 x^2}+\frac{1}{5} b^2 x^5 (3 a f+b c)+\frac{1}{6} b^2 x^6 (3 a g+b d)+\frac{1}{7} b^2 x^7 (3 a h+b e)+\frac{3}{2} a b x^2 (a f+b c)+a b x^3 (a g+b d)+\frac{3}{4} a b x^4 (a h+b e)+\frac{1}{8} b^3 f x^8+\frac{1}{9} b^3 g x^9+\frac{1}{10} b^3 h x^{10}",1,"-(a^3*c)/(4*x^4) - (a^3*d)/(3*x^3) - (a^3*e)/(2*x^2) - (a^2*(3*b*c + a*f))/x + a^2*(3*b*e + a*h)*x + (3*a*b*(b*c + a*f)*x^2)/2 + a*b*(b*d + a*g)*x^3 + (3*a*b*(b*e + a*h)*x^4)/4 + (b^2*(b*c + 3*a*f)*x^5)/5 + (b^2*(b*d + 3*a*g)*x^6)/6 + (b^2*(b*e + 3*a*h)*x^7)/7 + (b^3*f*x^8)/8 + (b^3*g*x^9)/9 + (b^3*h*x^10)/10 + a^2*(3*b*d + a*g)*Log[x]","A",2,1,38,0.02632,1,"{1820}"
403,1,331,0,1.0696689,"\int \frac{x^4 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{a+b x^3} \, dx","Int[(x^4*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3),x]","-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{6 b^{10/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{3 b^{10/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^{2/3} b e+a^{5/3} h-a b^{2/3} f+b^{5/3} c\right)}{\sqrt{3} b^{10/3}}+\frac{x^2 (b c-a f)}{2 b^2}+\frac{x^3 (b d-a g)}{3 b^2}-\frac{a (b d-a g) \log \left(a+b x^3\right)}{3 b^3}+\frac{x^4 (b e-a h)}{4 b^2}-\frac{a x (b e-a h)}{b^3}+\frac{f x^5}{5 b}+\frac{g x^6}{6 b}+\frac{h x^7}{7 b}","-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{6 b^{10/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{3 b^{10/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^{2/3} b e+a^{5/3} h-a b^{2/3} f+b^{5/3} c\right)}{\sqrt{3} b^{10/3}}+\frac{x^2 (b c-a f)}{2 b^2}+\frac{x^3 (b d-a g)}{3 b^2}-\frac{a (b d-a g) \log \left(a+b x^3\right)}{3 b^3}+\frac{x^4 (b e-a h)}{4 b^2}-\frac{a x (b e-a h)}{b^3}+\frac{f x^5}{5 b}+\frac{g x^6}{6 b}+\frac{h x^7}{7 b}",1,"-((a*(b*e - a*h)*x)/b^3) + ((b*c - a*f)*x^2)/(2*b^2) + ((b*d - a*g)*x^3)/(3*b^2) + ((b*e - a*h)*x^4)/(4*b^2) + (f*x^5)/(5*b) + (g*x^6)/(6*b) + (h*x^7)/(7*b) + (a^(2/3)*(b^(5/3)*c - a^(2/3)*b*e - a*b^(2/3)*f + a^(5/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(10/3)) + (a^(2/3)*(b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*Log[a^(1/3) + b^(1/3)*x])/(3*b^(10/3)) - (a^(2/3)*(b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(10/3)) - (a*(b*d - a*g)*Log[a + b*x^3])/(3*b^3)","A",13,10,38,0.2632,1,"{1836, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
404,1,313,0,0.9882445,"\int \frac{x^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{a+b x^3} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3),x]","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{6 b^{8/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-g)+\sqrt[3]{a} b d-a \sqrt[3]{b} f+b^{4/3} c\right)}{\sqrt{3} b^{8/3}}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{3 b^{8/3}}+\frac{x (b c-a f)}{b^2}+\frac{x^2 (b d-a g)}{2 b^2}+\frac{x^3 (b e-a h)}{3 b^2}-\frac{a (b e-a h) \log \left(a+b x^3\right)}{3 b^3}+\frac{f x^4}{4 b}+\frac{g x^5}{5 b}+\frac{h x^6}{6 b}","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{6 b^{8/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-g)+\sqrt[3]{a} b d-a \sqrt[3]{b} f+b^{4/3} c\right)}{\sqrt{3} b^{8/3}}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{3 b^{8/3}}+\frac{x (b c-a f)}{b^2}+\frac{x^2 (b d-a g)}{2 b^2}+\frac{x^3 (b e-a h)}{3 b^2}-\frac{a (b e-a h) \log \left(a+b x^3\right)}{3 b^3}+\frac{f x^4}{4 b}+\frac{g x^5}{5 b}+\frac{h x^6}{6 b}",1,"((b*c - a*f)*x)/b^2 + ((b*d - a*g)*x^2)/(2*b^2) + ((b*e - a*h)*x^3)/(3*b^2) + (f*x^4)/(4*b) + (g*x^5)/(5*b) + (h*x^6)/(6*b) + (a^(1/3)*(b^(4/3)*c + a^(1/3)*b*d - a*b^(1/3)*f - a^(4/3)*g)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(8/3)) - (a^(1/3)*(b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*Log[a^(1/3) + b^(1/3)*x])/(3*b^(8/3)) + (a^(1/3)*(b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(8/3)) - (a*(b*e - a*h)*Log[a + b*x^3])/(3*b^3)","A",13,10,38,0.2632,1,"{1836, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
405,1,294,0,0.9762625,"\int \frac{x^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{a+b x^3} \, dx","Int[(x^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3),x]","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{6 b^{8/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-h)+\sqrt[3]{a} b e-a \sqrt[3]{b} g+b^{4/3} d\right)}{\sqrt{3} b^{8/3}}+\frac{(b c-a f) \log \left(a+b x^3\right)}{3 b^2}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{3 b^{8/3}}+\frac{x (b d-a g)}{b^2}+\frac{x^2 (b e-a h)}{2 b^2}+\frac{f x^3}{3 b}+\frac{g x^4}{4 b}+\frac{h x^5}{5 b}","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{6 b^{8/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-h)+\sqrt[3]{a} b e-a \sqrt[3]{b} g+b^{4/3} d\right)}{\sqrt{3} b^{8/3}}+\frac{(b c-a f) \log \left(a+b x^3\right)}{3 b^2}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{3 b^{8/3}}+\frac{x (b d-a g)}{b^2}+\frac{x^2 (b e-a h)}{2 b^2}+\frac{f x^3}{3 b}+\frac{g x^4}{4 b}+\frac{h x^5}{5 b}",1,"((b*d - a*g)*x)/b^2 + ((b*e - a*h)*x^2)/(2*b^2) + (f*x^3)/(3*b) + (g*x^4)/(4*b) + (h*x^5)/(5*b) + (a^(1/3)*(b^(4/3)*d + a^(1/3)*b*e - a*b^(1/3)*g - a^(4/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(8/3)) - (a^(1/3)*(b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*Log[a^(1/3) + b^(1/3)*x])/(3*b^(8/3)) + (a^(1/3)*(b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(8/3)) + ((b*c - a*f)*Log[a + b*x^3])/(3*b^2)","A",13,10,38,0.2632,1,"{1836, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
406,1,275,0,0.9214778,"\int \frac{x \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{a+b x^3} \, dx","Int[(x*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{6 \sqrt[3]{a} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{3 \sqrt[3]{a} b^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^{2/3} b e+a^{5/3} h-a b^{2/3} f+b^{5/3} c\right)}{\sqrt{3} \sqrt[3]{a} b^{7/3}}+\frac{(b d-a g) \log \left(a+b x^3\right)}{3 b^2}+\frac{x (b e-a h)}{b^2}+\frac{f x^2}{2 b}+\frac{g x^3}{3 b}+\frac{h x^4}{4 b}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{6 \sqrt[3]{a} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{3 \sqrt[3]{a} b^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^{2/3} b e+a^{5/3} h-a b^{2/3} f+b^{5/3} c\right)}{\sqrt{3} \sqrt[3]{a} b^{7/3}}+\frac{(b d-a g) \log \left(a+b x^3\right)}{3 b^2}+\frac{x (b e-a h)}{b^2}+\frac{f x^2}{2 b}+\frac{g x^3}{3 b}+\frac{h x^4}{4 b}",1,"((b*e - a*h)*x)/b^2 + (f*x^2)/(2*b) + (g*x^3)/(3*b) + (h*x^4)/(4*b) - ((b^(5/3)*c - a^(2/3)*b*e - a*b^(2/3)*f + a^(5/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b^(7/3)) - ((b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*Log[a^(1/3) + b^(1/3)*x])/(3*a^(1/3)*b^(7/3)) + ((b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(1/3)*b^(7/3)) + ((b*d - a*g)*Log[a + b*x^3])/(3*b^2)","A",13,10,36,0.2778,1,"{1836, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
407,1,257,0,0.3733965,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{a+b x^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{\sqrt[3]{a} (b d-a g)}{\sqrt[3]{b}}-a f+b c\right)}{6 a^{2/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{3 a^{2/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-g)+\sqrt[3]{a} b d-a \sqrt[3]{b} f+b^{4/3} c\right)}{\sqrt{3} a^{2/3} b^{5/3}}+\frac{(b e-a h) \log \left(a+b x^3\right)}{3 b^2}+\frac{f x}{b}+\frac{g x^2}{2 b}+\frac{h x^3}{3 b}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{6 a^{2/3} b^{5/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{3 a^{2/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-g)+\sqrt[3]{a} b d-a \sqrt[3]{b} f+b^{4/3} c\right)}{\sqrt{3} a^{2/3} b^{5/3}}+\frac{(b e-a h) \log \left(a+b x^3\right)}{3 b^2}+\frac{f x}{b}+\frac{g x^2}{2 b}+\frac{h x^3}{3 b}",1,"(f*x)/b + (g*x^2)/(2*b) + (h*x^3)/(3*b) - ((b^(4/3)*c + a^(1/3)*b*d - a*b^(1/3)*f - a^(4/3)*g)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(5/3)) + ((b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(5/3)) - ((b*c - a*f - (a^(1/3)*(b*d - a*g))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(4/3)) + ((b*e - a*h)*Log[a + b*x^3])/(3*b^2)","A",10,9,35,0.2571,1,"{1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
408,1,256,0,0.4706112,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x \left(a+b x^3\right)} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x*(a + b*x^3)),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{\sqrt[3]{a} (b e-a h)}{\sqrt[3]{b}}-a g+b d\right)}{6 a^{2/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{3 a^{2/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-h)+\sqrt[3]{a} b e-a \sqrt[3]{b} g+b^{4/3} d\right)}{\sqrt{3} a^{2/3} b^{5/3}}-\frac{(b c-a f) \log \left(a+b x^3\right)}{3 a b}+\frac{c \log (x)}{a}+\frac{g x}{b}+\frac{h x^2}{2 b}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{6 a^{2/3} b^{5/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{3 a^{2/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-h)+\sqrt[3]{a} b e-a \sqrt[3]{b} g+b^{4/3} d\right)}{\sqrt{3} a^{2/3} b^{5/3}}-\frac{(b c-a f) \log \left(a+b x^3\right)}{3 a b}+\frac{c \log (x)}{a}+\frac{g x}{b}+\frac{h x^2}{2 b}",1,"(g*x)/b + (h*x^2)/(2*b) - ((b^(4/3)*d + a^(1/3)*b*e - a*b^(1/3)*g - a^(4/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(5/3)) + (c*Log[x])/a + ((b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(5/3)) - ((b*d - a*g - (a^(1/3)*(b*e - a*h))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(4/3)) - ((b*c - a*f)*Log[a + b*x^3])/(3*a*b)","A",10,9,38,0.2368,1,"{1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
409,1,253,0,0.4539536,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x^2 \left(a+b x^3\right)} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^2*(a + b*x^3)),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{6 a^{4/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{3 a^{4/3} b^{4/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^{2/3} b e+a^{5/3} h-a b^{2/3} f+b^{5/3} c\right)}{\sqrt{3} a^{4/3} b^{4/3}}-\frac{(b d-a g) \log \left(a+b x^3\right)}{3 a b}-\frac{c}{a x}+\frac{d \log (x)}{a}+\frac{h x}{b}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{6 a^{4/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (b e-a h)+b^{2/3} (b c-a f)\right)}{3 a^{4/3} b^{4/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-a^{2/3} b e+a^{5/3} h-a b^{2/3} f+b^{5/3} c\right)}{\sqrt{3} a^{4/3} b^{4/3}}-\frac{(b d-a g) \log \left(a+b x^3\right)}{3 a b}-\frac{c}{a x}+\frac{d \log (x)}{a}+\frac{h x}{b}",1,"-(c/(a*x)) + (h*x)/b + ((b^(5/3)*c - a^(2/3)*b*e - a*b^(2/3)*f + a^(5/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*b^(4/3)) + (d*Log[x])/a + ((b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*Log[a^(1/3) + b^(1/3)*x])/(3*a^(4/3)*b^(4/3)) - ((b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(4/3)*b^(4/3)) - ((b*d - a*g)*Log[a + b*x^3])/(3*a*b)","A",10,9,38,0.2368,1,"{1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
410,1,258,0,0.3800247,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x^3 \left(a+b x^3\right)} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^3*(a + b*x^3)),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{\sqrt[3]{a} (b d-a g)}{\sqrt[3]{b}}-a f+b c\right)}{6 a^{5/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{3 a^{5/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-g)+\sqrt[3]{a} b d-a \sqrt[3]{b} f+b^{4/3} c\right)}{\sqrt{3} a^{5/3} b^{2/3}}-\frac{(b e-a h) \log \left(a+b x^3\right)}{3 a b}-\frac{c}{2 a x^2}-\frac{d}{a x}+\frac{e \log (x)}{a}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{6 a^{5/3} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b c-a f)-\sqrt[3]{a} (b d-a g)\right)}{3 a^{5/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-g)+\sqrt[3]{a} b d-a \sqrt[3]{b} f+b^{4/3} c\right)}{\sqrt{3} a^{5/3} b^{2/3}}-\frac{(b e-a h) \log \left(a+b x^3\right)}{3 a b}-\frac{c}{2 a x^2}-\frac{d}{a x}+\frac{e \log (x)}{a}",1,"-c/(2*a*x^2) - d/(a*x) + ((b^(4/3)*c + a^(1/3)*b*d - a*b^(1/3)*f - a^(4/3)*g)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*b^(2/3)) + (e*Log[x])/a - ((b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*Log[a^(1/3) + b^(1/3)*x])/(3*a^(5/3)*b^(2/3)) + ((b*c - a*f - (a^(1/3)*(b*d - a*g))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3)*b^(1/3)) - ((b*e - a*h)*Log[a + b*x^3])/(3*a*b)","A",10,9,38,0.2368,1,"{1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
411,1,274,0,0.435676,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x^4 \left(a+b x^3\right)} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^4*(a + b*x^3)),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{\sqrt[3]{a} (b e-a h)}{\sqrt[3]{b}}-a g+b d\right)}{6 a^{5/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{3 a^{5/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-h)+\sqrt[3]{a} b e-a \sqrt[3]{b} g+b^{4/3} d\right)}{\sqrt{3} a^{5/3} b^{2/3}}+\frac{(b c-a f) \log \left(a+b x^3\right)}{3 a^2}-\frac{\log (x) (b c-a f)}{a^2}-\frac{c}{3 a x^3}-\frac{d}{2 a x^2}-\frac{e}{a x}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{6 a^{5/3} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b d-a g)-\sqrt[3]{a} (b e-a h)\right)}{3 a^{5/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-h)+\sqrt[3]{a} b e-a \sqrt[3]{b} g+b^{4/3} d\right)}{\sqrt{3} a^{5/3} b^{2/3}}+\frac{(b c-a f) \log \left(a+b x^3\right)}{3 a^2}-\frac{\log (x) (b c-a f)}{a^2}-\frac{c}{3 a x^3}-\frac{d}{2 a x^2}-\frac{e}{a x}",1,"-c/(3*a*x^3) - d/(2*a*x^2) - e/(a*x) + ((b^(4/3)*d + a^(1/3)*b*e - a*b^(1/3)*g - a^(4/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*b^(2/3)) - ((b*c - a*f)*Log[x])/a^2 - ((b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*Log[a^(1/3) + b^(1/3)*x])/(3*a^(5/3)*b^(2/3)) + ((b*d - a*g - (a^(1/3)*(b*e - a*h))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3)*b^(1/3)) + ((b*c - a*f)*Log[a + b*x^3])/(3*a^2)","A",10,9,38,0.2368,1,"{1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
412,1,337,0,0.7170881,"\int \frac{x^4 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^4*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^2,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (4 b e-7 a h)+b^{2/3} (2 b c-5 a f)\right)}{18 \sqrt[3]{a} b^{10/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (4 b e-7 a h)+b^{2/3} (2 b c-5 a f)\right)}{9 \sqrt[3]{a} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-4 a^{2/3} b e+7 a^{5/3} h-5 a b^{2/3} f+2 b^{5/3} c\right)}{3 \sqrt{3} \sqrt[3]{a} b^{10/3}}+\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{3 b^3 \left(a+b x^3\right)}+\frac{(b d-2 a g) \log \left(a+b x^3\right)}{3 b^3}+\frac{x (b e-2 a h)}{b^3}+\frac{f x^2}{2 b^2}+\frac{g x^3}{3 b^2}+\frac{h x^4}{4 b^2}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (4 b e-7 a h)+b^{2/3} (2 b c-5 a f)\right)}{18 \sqrt[3]{a} b^{10/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (4 b e-7 a h)+b^{2/3} (2 b c-5 a f)\right)}{9 \sqrt[3]{a} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-4 a^{2/3} b e+7 a^{5/3} h-5 a b^{2/3} f+2 b^{5/3} c\right)}{3 \sqrt{3} \sqrt[3]{a} b^{10/3}}+\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{3 b^3 \left(a+b x^3\right)}+\frac{(b d-2 a g) \log \left(a+b x^3\right)}{3 b^3}+\frac{x (b e-2 a h)}{b^3}+\frac{f x^2}{2 b^2}+\frac{g x^3}{3 b^2}+\frac{h x^4}{4 b^2}",1,"((b*e - 2*a*h)*x)/b^3 + (f*x^2)/(2*b^2) + (g*x^3)/(3*b^2) + (h*x^4)/(4*b^2) + (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(3*b^3*(a + b*x^3)) - ((2*b^(5/3)*c - 4*a^(2/3)*b*e - 5*a*b^(2/3)*f + 7*a^(5/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(1/3)*b^(10/3)) - ((b^(2/3)*(2*b*c - 5*a*f) + a^(2/3)*(4*b*e - 7*a*h))*Log[a^(1/3) + b^(1/3)*x])/(9*a^(1/3)*b^(10/3)) + ((b^(2/3)*(2*b*c - 5*a*f) + a^(2/3)*(4*b*e - 7*a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(1/3)*b^(10/3)) + ((b*d - 2*a*g)*Log[a + b*x^3])/(3*b^3)","A",11,10,38,0.2632,1,"{1828, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
413,1,311,0,0.6396386,"\int \frac{x^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^2,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b c-4 a f)-\sqrt[3]{a} (2 b d-5 a g)\right)}{18 a^{2/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b c-4 a f)-\sqrt[3]{a} (2 b d-5 a g)\right)}{9 a^{2/3} b^{8/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-5 a^{4/3} g+2 \sqrt[3]{a} b d-4 a \sqrt[3]{b} f+b^{4/3} c\right)}{3 \sqrt{3} a^{2/3} b^{8/3}}-\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{3 b^2 \left(a+b x^3\right)}+\frac{(b e-2 a h) \log \left(a+b x^3\right)}{3 b^3}+\frac{f x}{b^2}+\frac{g x^2}{2 b^2}+\frac{h x^3}{3 b^2}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b c-4 a f)-\sqrt[3]{a} (2 b d-5 a g)\right)}{18 a^{2/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b c-4 a f)-\sqrt[3]{a} (2 b d-5 a g)\right)}{9 a^{2/3} b^{8/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-5 a^{4/3} g+2 \sqrt[3]{a} b d-4 a \sqrt[3]{b} f+b^{4/3} c\right)}{3 \sqrt{3} a^{2/3} b^{8/3}}-\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{3 b^2 \left(a+b x^3\right)}+\frac{(b e-2 a h) \log \left(a+b x^3\right)}{3 b^3}+\frac{f x}{b^2}+\frac{g x^2}{2 b^2}+\frac{h x^3}{3 b^2}",1,"(f*x)/b^2 + (g*x^2)/(2*b^2) + (h*x^3)/(3*b^2) - (x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(3*b^2*(a + b*x^3)) - ((b^(4/3)*c + 2*a^(1/3)*b*d - 4*a*b^(1/3)*f - 5*a^(4/3)*g)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)*b^(8/3)) + ((b^(1/3)*(b*c - 4*a*f) - a^(1/3)*(2*b*d - 5*a*g))*Log[a^(1/3) + b^(1/3)*x])/(9*a^(2/3)*b^(8/3)) - ((b^(1/3)*(b*c - 4*a*f) - a^(1/3)*(2*b*d - 5*a*g))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(2/3)*b^(8/3)) + ((b*e - 2*a*h)*Log[a + b*x^3])/(3*b^3)","A",11,10,38,0.2632,1,"{1828, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
414,1,288,0,0.4979354,"\int \frac{x^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^2,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{\sqrt[3]{a} (2 b e-5 a h)}{\sqrt[3]{b}}-4 a g+b d\right)}{18 a^{2/3} b^{7/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b d-4 a g)-\sqrt[3]{a} (2 b e-5 a h)\right)}{9 a^{2/3} b^{8/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-5 a^{4/3} h+2 \sqrt[3]{a} b e-4 a \sqrt[3]{b} g+b^{4/3} d\right)}{3 \sqrt{3} a^{2/3} b^{8/3}}+\frac{f \log \left(a+b x^3\right)}{3 b^2}-\frac{c+d x+e x^2+f x^3+g x^4+h x^5}{3 b \left(a+b x^3\right)}+\frac{4 g x}{3 b^2}+\frac{5 h x^2}{6 b^2}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (b d-4 a g)-\sqrt[3]{a} (2 b e-5 a h)\right)}{18 a^{2/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (b d-4 a g)-\sqrt[3]{a} (2 b e-5 a h)\right)}{9 a^{2/3} b^{8/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-5 a^{4/3} h+2 \sqrt[3]{a} b e-4 a \sqrt[3]{b} g+b^{4/3} d\right)}{3 \sqrt{3} a^{2/3} b^{8/3}}+\frac{f \log \left(a+b x^3\right)}{3 b^2}-\frac{c+d x+e x^2+f x^3+g x^4+h x^5}{3 b \left(a+b x^3\right)}+\frac{4 g x}{3 b^2}+\frac{5 h x^2}{6 b^2}",1,"(4*g*x)/(3*b^2) + (5*h*x^2)/(6*b^2) - (c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(3*b*(a + b*x^3)) - ((b^(4/3)*d + 2*a^(1/3)*b*e - 4*a*b^(1/3)*g - 5*a^(4/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)*b^(8/3)) + ((b^(1/3)*(b*d - 4*a*g) - a^(1/3)*(2*b*e - 5*a*h))*Log[a^(1/3) + b^(1/3)*x])/(9*a^(2/3)*b^(8/3)) - ((b*d - 4*a*g - (a^(1/3)*(2*b*e - 5*a*h))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(2/3)*b^(7/3)) + (f*Log[a + b*x^3])/(3*b^2)","A",11,10,38,0.2632,1,"{1823, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
415,1,289,0,0.505355,"\int \frac{x \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^2,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(b^{2/3} (2 a f+b c)-a^{2/3} (b e-4 a h)\right)}{18 a^{4/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(b^{2/3} (2 a f+b c)-a^{2/3} (b e-4 a h)\right)}{9 a^{4/3} b^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{2/3} b e-4 a^{5/3} h+2 a b^{2/3} f+b^{5/3} c\right)}{3 \sqrt{3} a^{4/3} b^{7/3}}-\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{3 a b^2 \left(a+b x^3\right)}+\frac{g \log \left(a+b x^3\right)}{3 b^2}+\frac{h x}{b^2}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(b^{2/3} (2 a f+b c)-a^{2/3} (b e-4 a h)\right)}{18 a^{4/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(b^{2/3} (2 a f+b c)-a^{2/3} (b e-4 a h)\right)}{9 a^{4/3} b^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{2/3} b e-4 a^{5/3} h+2 a b^{2/3} f+b^{5/3} c\right)}{3 \sqrt{3} a^{4/3} b^{7/3}}-\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{3 a b^2 \left(a+b x^3\right)}+\frac{g \log \left(a+b x^3\right)}{3 b^2}+\frac{h x}{b^2}",1,"(h*x)/b^2 - (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(3*a*b^2*(a + b*x^3)) - ((b^(5/3)*c + a^(2/3)*b*e + 2*a*b^(2/3)*f - 4*a^(5/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)*b^(7/3)) - ((b^(2/3)*(b*c + 2*a*f) - a^(2/3)*(b*e - 4*a*h))*Log[a^(1/3) + b^(1/3)*x])/(9*a^(4/3)*b^(7/3)) + ((b^(2/3)*(b*c + 2*a*f) - a^(2/3)*(b*e - 4*a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(4/3)*b^(7/3)) + (g*Log[a + b*x^3])/(3*b^2)","A",11,10,36,0.2778,1,"{1828, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
416,1,276,0,0.369973,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^2,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (a f+2 b c)-\sqrt[3]{a} (2 a g+b d)\right)}{18 a^{5/3} b^{5/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (a f+2 b c)-\sqrt[3]{a} (2 a g+b d)\right)}{9 a^{5/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^{4/3} g+\sqrt[3]{a} b d+a \sqrt[3]{b} f+2 b^{4/3} c\right)}{3 \sqrt{3} a^{5/3} b^{5/3}}+\frac{h \log \left(a+b x^3\right)}{3 b^2}+\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{3 a b \left(a+b x^3\right)}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (a f+2 b c)-\sqrt[3]{a} (2 a g+b d)\right)}{18 a^{5/3} b^{5/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (a f+2 b c)-\sqrt[3]{a} (2 a g+b d)\right)}{9 a^{5/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^{4/3} g+\sqrt[3]{a} b d+a \sqrt[3]{b} f+2 b^{4/3} c\right)}{3 \sqrt{3} a^{5/3} b^{5/3}}+\frac{h \log \left(a+b x^3\right)}{3 b^2}+\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{3 a b \left(a+b x^3\right)}",1,"(x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(3*a*b*(a + b*x^3)) - ((2*b^(4/3)*c + a^(1/3)*b*d + a*b^(1/3)*f + 2*a^(4/3)*g)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(5/3)) + ((b^(1/3)*(2*b*c + a*f) - a^(1/3)*(b*d + 2*a*g))*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(5/3)) - ((b^(1/3)*(2*b*c + a*f) - a^(1/3)*(b*d + 2*a*g))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(5/3)) + (h*Log[a + b*x^3])/(3*b^2)","A",9,9,35,0.2571,1,"{1858, 1871, 1860, 31, 634, 617, 204, 628, 260}"
417,1,287,0,0.5594149,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x \left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x*(a + b*x^3)^2),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{\sqrt[3]{a} (2 a h+b e)}{\sqrt[3]{b}}+a g+2 b d\right)}{18 a^{5/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (a g+2 b d)-\sqrt[3]{a} (2 a h+b e)\right)}{9 a^{5/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^{4/3} h+\sqrt[3]{a} b e+a \sqrt[3]{b} g+2 b^{4/3} d\right)}{3 \sqrt{3} a^{5/3} b^{5/3}}+\frac{x \left(-b x^2 (b c-a f)+a (b d-a g)+a x (b e-a h)\right)}{3 a^2 b \left(a+b x^3\right)}-\frac{c \log \left(a+b x^3\right)}{3 a^2}+\frac{c \log (x)}{a^2}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (a g+2 b d)-\sqrt[3]{a} (2 a h+b e)\right)}{18 a^{5/3} b^{5/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (a g+2 b d)-\sqrt[3]{a} (2 a h+b e)\right)}{9 a^{5/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^{4/3} h+\sqrt[3]{a} b e+a \sqrt[3]{b} g+2 b^{4/3} d\right)}{3 \sqrt{3} a^{5/3} b^{5/3}}+\frac{x \left(-b x^2 (b c-a f)+a (b d-a g)+a x (b e-a h)\right)}{3 a^2 b \left(a+b x^3\right)}-\frac{c \log \left(a+b x^3\right)}{3 a^2}+\frac{c \log (x)}{a^2}",1,"(x*(a*(b*d - a*g) + a*(b*e - a*h)*x - b*(b*c - a*f)*x^2))/(3*a^2*b*(a + b*x^3)) - ((2*b^(4/3)*d + a^(1/3)*b*e + a*b^(1/3)*g + 2*a^(4/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(5/3)) + (c*Log[x])/a^2 + ((b^(1/3)*(2*b*d + a*g) - a^(1/3)*(b*e + 2*a*h))*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(5/3)) - ((2*b*d + a*g - (a^(1/3)*(b*e + 2*a*h))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(4/3)) - (c*Log[a + b*x^3])/(3*a^2)","A",11,10,38,0.2632,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
418,1,301,0,0.5934314,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x^2 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^2*(a + b*x^3)^2),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (a h+2 b e)+b^{2/3} (4 b c-a f)\right)}{18 a^{7/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (a h+2 b e)+b^{2/3} (4 b c-a f)\right)}{9 a^{7/3} b^{4/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-2 a^{2/3} b e+a^{5/3} (-h)-a b^{2/3} f+4 b^{5/3} c\right)}{3 \sqrt{3} a^{7/3} b^{4/3}}+\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{3 a^2 b \left(a+b x^3\right)}-\frac{d \log \left(a+b x^3\right)}{3 a^2}-\frac{c}{a^2 x}+\frac{d \log (x)}{a^2}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (a h+2 b e)+b^{2/3} (4 b c-a f)\right)}{18 a^{7/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (a h+2 b e)+b^{2/3} (4 b c-a f)\right)}{9 a^{7/3} b^{4/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-2 a^{2/3} b e+a^{5/3} (-h)-a b^{2/3} f+4 b^{5/3} c\right)}{3 \sqrt{3} a^{7/3} b^{4/3}}+\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{3 a^2 b \left(a+b x^3\right)}-\frac{d \log \left(a+b x^3\right)}{3 a^2}-\frac{c}{a^2 x}+\frac{d \log (x)}{a^2}",1,"-(c/(a^2*x)) + (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(3*a^2*b*(a + b*x^3)) + ((4*b^(5/3)*c - 2*a^(2/3)*b*e - a*b^(2/3)*f - a^(5/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)*b^(4/3)) + (d*Log[x])/a^2 + ((b^(2/3)*(4*b*c - a*f) + a^(2/3)*(2*b*e + a*h))*Log[a^(1/3) + b^(1/3)*x])/(9*a^(7/3)*b^(4/3)) - ((b^(2/3)*(4*b*c - a*f) + a^(2/3)*(2*b*e + a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(7/3)*b^(4/3)) - (d*Log[a + b*x^3])/(3*a^2)","A",11,10,38,0.2632,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
419,1,304,0,0.5768669,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x^3 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^3*(a + b*x^3)^2),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{\sqrt[3]{a} (4 b d-a g)}{\sqrt[3]{b}}-2 a f+5 b c\right)}{18 a^{8/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (5 b c-2 a f)-\sqrt[3]{a} (4 b d-a g)\right)}{9 a^{8/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-g)+4 \sqrt[3]{a} b d-2 a \sqrt[3]{b} f+5 b^{4/3} c\right)}{3 \sqrt{3} a^{8/3} b^{2/3}}-\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{3 a^2 \left(a+b x^3\right)}-\frac{e \log \left(a+b x^3\right)}{3 a^2}-\frac{c}{2 a^2 x^2}-\frac{d}{a^2 x}+\frac{e \log (x)}{a^2}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (5 b c-2 a f)-\sqrt[3]{a} (4 b d-a g)\right)}{18 a^{8/3} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (5 b c-2 a f)-\sqrt[3]{a} (4 b d-a g)\right)}{9 a^{8/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-g)+4 \sqrt[3]{a} b d-2 a \sqrt[3]{b} f+5 b^{4/3} c\right)}{3 \sqrt{3} a^{8/3} b^{2/3}}-\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{3 a^2 \left(a+b x^3\right)}-\frac{e \log \left(a+b x^3\right)}{3 a^2}-\frac{c}{2 a^2 x^2}-\frac{d}{a^2 x}+\frac{e \log (x)}{a^2}",1,"-c/(2*a^2*x^2) - d/(a^2*x) - (x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(3*a^2*(a + b*x^3)) + ((5*b^(4/3)*c + 4*a^(1/3)*b*d - 2*a*b^(1/3)*f - a^(4/3)*g)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)*b^(2/3)) + (e*Log[x])/a^2 - ((b^(1/3)*(5*b*c - 2*a*f) - a^(1/3)*(4*b*d - a*g))*Log[a^(1/3) + b^(1/3)*x])/(9*a^(8/3)*b^(2/3)) + ((5*b*c - 2*a*f - (a^(1/3)*(4*b*d - a*g))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(8/3)*b^(1/3)) - (e*Log[a + b*x^3])/(3*a^2)","A",11,10,38,0.2632,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
420,1,336,0,0.7273172,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x^4 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^4*(a + b*x^3)^2),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{\sqrt[3]{a} (4 b e-a h)}{\sqrt[3]{b}}-2 a g+5 b d\right)}{18 a^{8/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (5 b d-2 a g)-\sqrt[3]{a} (4 b e-a h)\right)}{9 a^{8/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-h)+4 \sqrt[3]{a} b e-2 a \sqrt[3]{b} g+5 b^{4/3} d\right)}{3 \sqrt{3} a^{8/3} b^{2/3}}-\frac{x \left(-b x^2 \left(\frac{b c}{a}-f\right)+x (b e-a h)-a g+b d\right)}{3 a^2 \left(a+b x^3\right)}+\frac{(2 b c-a f) \log \left(a+b x^3\right)}{3 a^3}-\frac{\log (x) (2 b c-a f)}{a^3}-\frac{c}{3 a^2 x^3}-\frac{d}{2 a^2 x^2}-\frac{e}{a^2 x}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (5 b d-2 a g)-\sqrt[3]{a} (4 b e-a h)\right)}{18 a^{8/3} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (5 b d-2 a g)-\sqrt[3]{a} (4 b e-a h)\right)}{9 a^{8/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} (-h)+4 \sqrt[3]{a} b e-2 a \sqrt[3]{b} g+5 b^{4/3} d\right)}{3 \sqrt{3} a^{8/3} b^{2/3}}-\frac{x \left(-b x^2 \left(\frac{b c}{a}-f\right)+x (b e-a h)-a g+b d\right)}{3 a^2 \left(a+b x^3\right)}+\frac{(2 b c-a f) \log \left(a+b x^3\right)}{3 a^3}-\frac{\log (x) (2 b c-a f)}{a^3}-\frac{c}{3 a^2 x^3}-\frac{d}{2 a^2 x^2}-\frac{e}{a^2 x}",1,"-c/(3*a^2*x^3) - d/(2*a^2*x^2) - e/(a^2*x) - (x*(b*d - a*g + (b*e - a*h)*x - b*((b*c)/a - f)*x^2))/(3*a^2*(a + b*x^3)) + ((5*b^(4/3)*d + 4*a^(1/3)*b*e - 2*a*b^(1/3)*g - a^(4/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)*b^(2/3)) - ((2*b*c - a*f)*Log[x])/a^3 - ((b^(1/3)*(5*b*d - 2*a*g) - a^(1/3)*(4*b*e - a*h))*Log[a^(1/3) + b^(1/3)*x])/(9*a^(8/3)*b^(2/3)) + ((5*b*d - 2*a*g - (a^(1/3)*(4*b*e - a*h))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(8/3)*b^(1/3)) + ((2*b*c - a*f)*Log[a + b*x^3])/(3*a^3)","A",11,10,38,0.2632,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
421,1,345,0,0.8912653,"\int \frac{x^4 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^4*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^3,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(b^{2/3} (5 a f+b c)-2 a^{2/3} (b e-7 a h)\right)}{54 a^{4/3} b^{10/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(b^{2/3} (5 a f+b c)-2 a^{2/3} (b e-7 a h)\right)}{27 a^{4/3} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^{2/3} b e-14 a^{5/3} h+5 a b^{2/3} f+b^{5/3} c\right)}{9 \sqrt{3} a^{4/3} b^{10/3}}-\frac{x \left(-2 b x (b c-4 a f)-3 b x^2 (b d-3 a g)+a (7 b e-13 a h)\right)}{18 a b^3 \left(a+b x^3\right)}+\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{6 b^3 \left(a+b x^3\right)^2}+\frac{g \log \left(a+b x^3\right)}{3 b^3}+\frac{h x}{b^3}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(b^{2/3} (5 a f+b c)-2 a^{2/3} (b e-7 a h)\right)}{54 a^{4/3} b^{10/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(b^{2/3} (5 a f+b c)-2 a^{2/3} (b e-7 a h)\right)}{27 a^{4/3} b^{10/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(2 a^{2/3} b e-14 a^{5/3} h+5 a b^{2/3} f+b^{5/3} c\right)}{9 \sqrt{3} a^{4/3} b^{10/3}}-\frac{x \left(-2 b x (b c-4 a f)-3 b x^2 (b d-3 a g)+a (7 b e-13 a h)\right)}{18 a b^3 \left(a+b x^3\right)}+\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{6 b^3 \left(a+b x^3\right)^2}+\frac{g \log \left(a+b x^3\right)}{3 b^3}+\frac{h x}{b^3}",1,"(h*x)/b^3 + (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(6*b^3*(a + b*x^3)^2) - (x*(a*(7*b*e - 13*a*h) - 2*b*(b*c - 4*a*f)*x - 3*b*(b*d - 3*a*g)*x^2))/(18*a*b^3*(a + b*x^3)) - ((b^(5/3)*c + 2*a^(2/3)*b*e + 5*a*b^(2/3)*f - 14*a^(5/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(4/3)*b^(10/3)) - ((b^(2/3)*(b*c + 5*a*f) - 2*a^(2/3)*(b*e - 7*a*h))*Log[a^(1/3) + b^(1/3)*x])/(27*a^(4/3)*b^(10/3)) + ((b^(2/3)*(b*c + 5*a*f) - 2*a^(2/3)*(b*e - 7*a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(4/3)*b^(10/3)) + (g*Log[a + b*x^3])/(3*b^3)","A",12,11,38,0.2895,1,"{1828, 1858, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
422,1,325,0,0.6424449,"\int \frac{x^3 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^3,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (2 a f+b c)-\sqrt[3]{a} (5 a g+b d)\right)}{54 a^{5/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (2 a f+b c)-\sqrt[3]{a} (5 a g+b d)\right)}{27 a^{5/3} b^{8/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^{4/3} g+\sqrt[3]{a} b d+2 a \sqrt[3]{b} f+b^{4/3} c\right)}{9 \sqrt{3} a^{5/3} b^{8/3}}+\frac{x \left(2 x (b d-4 a g)+3 x^2 (b e-3 a h)-7 a f+b c\right)}{18 a b^2 \left(a+b x^3\right)}-\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{6 b^2 \left(a+b x^3\right)^2}+\frac{h \log \left(a+b x^3\right)}{3 b^3}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (2 a f+b c)-\sqrt[3]{a} (5 a g+b d)\right)}{54 a^{5/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (2 a f+b c)-\sqrt[3]{a} (5 a g+b d)\right)}{27 a^{5/3} b^{8/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^{4/3} g+\sqrt[3]{a} b d+2 a \sqrt[3]{b} f+b^{4/3} c\right)}{9 \sqrt{3} a^{5/3} b^{8/3}}+\frac{x \left(2 x (b d-4 a g)+3 x^2 (b e-3 a h)-7 a f+b c\right)}{18 a b^2 \left(a+b x^3\right)}-\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{6 b^2 \left(a+b x^3\right)^2}+\frac{h \log \left(a+b x^3\right)}{3 b^3}",1,"-(x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(6*b^2*(a + b*x^3)^2) + (x*(b*c - 7*a*f + 2*(b*d - 4*a*g)*x + 3*(b*e - 3*a*h)*x^2))/(18*a*b^2*(a + b*x^3)) - ((b^(4/3)*c + a^(1/3)*b*d + 2*a*b^(1/3)*f + 5*a^(4/3)*g)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(5/3)*b^(8/3)) + ((b^(1/3)*(b*c + 2*a*f) - a^(1/3)*(b*d + 5*a*g))*Log[a^(1/3) + b^(1/3)*x])/(27*a^(5/3)*b^(8/3)) - ((b^(1/3)*(b*c + 2*a*f) - a^(1/3)*(b*d + 5*a*g))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(5/3)*b^(8/3)) + (h*Log[a + b*x^3])/(3*b^3)","A",10,10,38,0.2632,1,"{1828, 1858, 1871, 1860, 31, 634, 617, 204, 628, 260}"
423,1,297,0,0.4301076,"\int \frac{x^2 \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^3,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (2 a g+b d)-\sqrt[3]{a} (5 a h+b e)\right)}{54 a^{5/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (2 a g+b d)-\sqrt[3]{a} (5 a h+b e)\right)}{27 a^{5/3} b^{8/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^{4/3} h+\sqrt[3]{a} b e+2 a \sqrt[3]{b} g+b^{4/3} d\right)}{9 \sqrt{3} a^{5/3} b^{8/3}}+\frac{x \left(x (2 b e-5 a h)-4 a g+b d+3 b f x^2\right)}{18 a b^2 \left(a+b x^3\right)}-\frac{c+d x+e x^2+f x^3+g x^4+h x^5}{6 b \left(a+b x^3\right)^2}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (2 a g+b d)-\sqrt[3]{a} (5 a h+b e)\right)}{54 a^{5/3} b^{8/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (2 a g+b d)-\sqrt[3]{a} (5 a h+b e)\right)}{27 a^{5/3} b^{8/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(5 a^{4/3} h+\sqrt[3]{a} b e+2 a \sqrt[3]{b} g+b^{4/3} d\right)}{9 \sqrt{3} a^{5/3} b^{8/3}}+\frac{x \left(x (2 b e-5 a h)-4 a g+b d+3 b f x^2\right)}{18 a b^2 \left(a+b x^3\right)}-\frac{c+d x+e x^2+f x^3+g x^4+h x^5}{6 b \left(a+b x^3\right)^2}",1,"(x*(b*d - 4*a*g + (2*b*e - 5*a*h)*x + 3*b*f*x^2))/(18*a*b^2*(a + b*x^3)) - (c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(6*b*(a + b*x^3)^2) - ((b^(4/3)*d + a^(1/3)*b*e + 2*a*b^(1/3)*g + 5*a^(4/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(5/3)*b^(8/3)) + ((b^(1/3)*(b*d + 2*a*g) - a^(1/3)*(b*e + 5*a*h))*Log[a^(1/3) + b^(1/3)*x])/(27*a^(5/3)*b^(8/3)) - ((b^(1/3)*(b*d + 2*a*g) - a^(1/3)*(b*e + 5*a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(5/3)*b^(8/3))","A",8,8,38,0.2105,1,"{1823, 1858, 1860, 31, 634, 617, 204, 628}"
424,1,323,0,0.4818276,"\int \frac{x \left(c+d x+e x^2+f x^3+g x^4+h x^5\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^3,x]","\frac{x \left(2 b x (a f+2 b c)+3 b x^2 (a g+b d)+a (b e-7 a h)\right)}{18 a^2 b^2 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(b^{2/3} (a f+2 b c)-a^{2/3} (2 a h+b e)\right)}{54 a^{7/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(b^{2/3} (a f+2 b c)-a^{2/3} (2 a h+b e)\right)}{27 a^{7/3} b^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{2/3} b e+2 a^{5/3} h+a b^{2/3} f+2 b^{5/3} c\right)}{9 \sqrt{3} a^{7/3} b^{7/3}}-\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{6 a b^2 \left(a+b x^3\right)^2}","\frac{x \left(2 b x (a f+2 b c)+3 b x^2 (a g+b d)+a (b e-7 a h)\right)}{18 a^2 b^2 \left(a+b x^3\right)}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(b^{2/3} (a f+2 b c)-a^{2/3} (2 a h+b e)\right)}{54 a^{7/3} b^{7/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(b^{2/3} (a f+2 b c)-a^{2/3} (2 a h+b e)\right)}{27 a^{7/3} b^{7/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{2/3} b e+2 a^{5/3} h+a b^{2/3} f+2 b^{5/3} c\right)}{9 \sqrt{3} a^{7/3} b^{7/3}}-\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{6 a b^2 \left(a+b x^3\right)^2}",1,"-(x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(6*a*b^2*(a + b*x^3)^2) + (x*(a*(b*e - 7*a*h) + 2*b*(2*b*c + a*f)*x + 3*b*(b*d + a*g)*x^2))/(18*a^2*b^2*(a + b*x^3)) - ((2*b^(5/3)*c + a^(2/3)*b*e + a*b^(2/3)*f + 2*a^(5/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(7/3)*b^(7/3)) - ((b^(2/3)*(2*b*c + a*f) - a^(2/3)*(b*e + 2*a*h))*Log[a^(1/3) + b^(1/3)*x])/(27*a^(7/3)*b^(7/3)) + ((b^(2/3)*(2*b*c + a*f) - a^(2/3)*(b*e + 2*a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(7/3)*b^(7/3))","A",8,8,36,0.2222,1,"{1828, 1858, 1860, 31, 634, 617, 204, 628}"
425,1,313,0,0.4293862,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{\left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^3,x]","-\frac{3 a (a h+b e)-b x (2 x (a g+2 b d)+a f+5 b c)}{18 a^2 b^2 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (a f+5 b c)-\sqrt[3]{a} (a g+2 b d)\right)}{54 a^{8/3} b^{5/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (a f+5 b c)-\sqrt[3]{a} (a g+2 b d)\right)}{27 a^{8/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} g+2 \sqrt[3]{a} b d+a \sqrt[3]{b} f+5 b^{4/3} c\right)}{9 \sqrt{3} a^{8/3} b^{5/3}}+\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{6 a b \left(a+b x^3\right)^2}","-\frac{3 a (a h+b e)-b x (2 x (a g+2 b d)+a f+5 b c)}{18 a^2 b^2 \left(a+b x^3\right)}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (a f+5 b c)-\sqrt[3]{a} (a g+2 b d)\right)}{54 a^{8/3} b^{5/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (a f+5 b c)-\sqrt[3]{a} (a g+2 b d)\right)}{27 a^{8/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} g+2 \sqrt[3]{a} b d+a \sqrt[3]{b} f+5 b^{4/3} c\right)}{9 \sqrt{3} a^{8/3} b^{5/3}}+\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{6 a b \left(a+b x^3\right)^2}",1,"(x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(6*a*b*(a + b*x^3)^2) - (3*a*(b*e + a*h) - b*x*(5*b*c + a*f + 2*(2*b*d + a*g)*x))/(18*a^2*b^2*(a + b*x^3)) - ((5*b^(4/3)*c + 2*a^(1/3)*b*d + a*b^(1/3)*f + a^(4/3)*g)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(5/3)) + ((b^(1/3)*(5*b*c + a*f) - a^(1/3)*(2*b*d + a*g))*Log[a^(1/3) + b^(1/3)*x])/(27*a^(8/3)*b^(5/3)) - ((b^(1/3)*(5*b*c + a*f) - a^(1/3)*(2*b*d + a*g))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(8/3)*b^(5/3))","A",8,8,35,0.2286,1,"{1858, 1854, 1860, 31, 634, 617, 204, 628}"
426,1,345,0,0.7230694,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x \left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x*(a + b*x^3)^3),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{\sqrt[3]{a} (a h+2 b e)}{\sqrt[3]{b}}+a g+5 b d\right)}{54 a^{8/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (a g+5 b d)-\sqrt[3]{a} (a h+2 b e)\right)}{27 a^{8/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} h+2 \sqrt[3]{a} b e+a \sqrt[3]{b} g+5 b^{4/3} d\right)}{9 \sqrt{3} a^{8/3} b^{5/3}}+\frac{x \left(-b x^2 (b c-a f)+a (b d-a g)+a x (b e-a h)\right)}{6 a^2 b \left(a+b x^3\right)^2}+\frac{x \left(-3 b x^2 (3 b c-a f)+a (a g+5 b d)+2 a x (a h+2 b e)\right)}{18 a^3 b \left(a+b x^3\right)}-\frac{c \log \left(a+b x^3\right)}{3 a^3}+\frac{c \log (x)}{a^3}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(\sqrt[3]{b} (a g+5 b d)-\sqrt[3]{a} (a h+2 b e)\right)}{54 a^{8/3} b^{5/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\sqrt[3]{b} (a g+5 b d)-\sqrt[3]{a} (a h+2 b e)\right)}{27 a^{8/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(a^{4/3} h+2 \sqrt[3]{a} b e+a \sqrt[3]{b} g+5 b^{4/3} d\right)}{9 \sqrt{3} a^{8/3} b^{5/3}}+\frac{x \left(-b x^2 (b c-a f)+a (b d-a g)+a x (b e-a h)\right)}{6 a^2 b \left(a+b x^3\right)^2}+\frac{x \left(-3 b x^2 (3 b c-a f)+a (a g+5 b d)+2 a x (a h+2 b e)\right)}{18 a^3 b \left(a+b x^3\right)}-\frac{c \log \left(a+b x^3\right)}{3 a^3}+\frac{c \log (x)}{a^3}",1,"(x*(a*(b*d - a*g) + a*(b*e - a*h)*x - b*(b*c - a*f)*x^2))/(6*a^2*b*(a + b*x^3)^2) + (x*(a*(5*b*d + a*g) + 2*a*(2*b*e + a*h)*x - 3*b*(3*b*c - a*f)*x^2))/(18*a^3*b*(a + b*x^3)) - ((5*b^(4/3)*d + 2*a^(1/3)*b*e + a*b^(1/3)*g + a^(4/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(5/3)) + (c*Log[x])/a^3 + ((b^(1/3)*(5*b*d + a*g) - a^(1/3)*(2*b*e + a*h))*Log[a^(1/3) + b^(1/3)*x])/(27*a^(8/3)*b^(5/3)) - ((5*b*d + a*g - (a^(1/3)*(2*b*e + a*h))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(8/3)*b^(4/3)) - (c*Log[a + b*x^3])/(3*a^3)","A",12,10,38,0.2632,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
427,1,362,0,0.8299613,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x^2 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^2*(a + b*x^3)^3),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (a h+5 b e)+2 b^{2/3} (7 b c-a f)\right)}{54 a^{10/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (a h+5 b e)+2 b^{2/3} (7 b c-a f)\right)}{27 a^{10/3} b^{4/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-5 a^{2/3} b e+a^{5/3} (-h)-2 a b^{2/3} f+14 b^{5/3} c\right)}{9 \sqrt{3} a^{10/3} b^{4/3}}+\frac{x \left(-2 b x (5 b c-2 a f)-3 b x^2 (3 b d-a g)+a (a h+5 b e)\right)}{18 a^3 b \left(a+b x^3\right)}+\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{6 a^2 b \left(a+b x^3\right)^2}-\frac{d \log \left(a+b x^3\right)}{3 a^3}-\frac{c}{a^3 x}+\frac{d \log (x)}{a^3}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(a^{2/3} (a h+5 b e)+2 b^{2/3} (7 b c-a f)\right)}{54 a^{10/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a^{2/3} (a h+5 b e)+2 b^{2/3} (7 b c-a f)\right)}{27 a^{10/3} b^{4/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-5 a^{2/3} b e+a^{5/3} (-h)-2 a b^{2/3} f+14 b^{5/3} c\right)}{9 \sqrt{3} a^{10/3} b^{4/3}}+\frac{x \left(-2 b x (5 b c-2 a f)-3 b x^2 (3 b d-a g)+a (a h+5 b e)\right)}{18 a^3 b \left(a+b x^3\right)}+\frac{x \left(-b x (b c-a f)-b x^2 (b d-a g)+a (b e-a h)\right)}{6 a^2 b \left(a+b x^3\right)^2}-\frac{d \log \left(a+b x^3\right)}{3 a^3}-\frac{c}{a^3 x}+\frac{d \log (x)}{a^3}",1,"-(c/(a^3*x)) + (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(6*a^2*b*(a + b*x^3)^2) + (x*(a*(5*b*e + a*h) - 2*b*(5*b*c - 2*a*f)*x - 3*b*(3*b*d - a*g)*x^2))/(18*a^3*b*(a + b*x^3)) + ((14*b^(5/3)*c - 5*a^(2/3)*b*e - 2*a*b^(2/3)*f - a^(5/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(10/3)*b^(4/3)) + (d*Log[x])/a^3 + ((2*b^(2/3)*(7*b*c - a*f) + a^(2/3)*(5*b*e + a*h))*Log[a^(1/3) + b^(1/3)*x])/(27*a^(10/3)*b^(4/3)) - ((2*b^(2/3)*(7*b*c - a*f) + a^(2/3)*(5*b*e + a*h))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(10/3)*b^(4/3)) - (d*Log[a + b*x^3])/(3*a^3)","A",12,10,38,0.2632,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
428,1,357,0,0.8138741,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x^3 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^3*(a + b*x^3)^3),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{2 \sqrt[3]{a} (7 b d-a g)}{\sqrt[3]{b}}-5 a f+20 b c\right)}{54 a^{11/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 \sqrt[3]{b} (4 b c-a f)-2 \sqrt[3]{a} (7 b d-a g)\right)}{27 a^{11/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-2 a^{4/3} g+14 \sqrt[3]{a} b d-5 a \sqrt[3]{b} f+20 b^{4/3} c\right)}{9 \sqrt{3} a^{11/3} b^{2/3}}-\frac{x \left(2 x (5 b d-2 a g)+3 x^2 (3 b e-a h)-5 a f+11 b c\right)}{18 a^3 \left(a+b x^3\right)}-\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{6 a^2 \left(a+b x^3\right)^2}-\frac{e \log \left(a+b x^3\right)}{3 a^3}-\frac{c}{2 a^3 x^2}-\frac{d}{a^3 x}+\frac{e \log (x)}{a^3}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(5 \sqrt[3]{b} (4 b c-a f)-2 \sqrt[3]{a} (7 b d-a g)\right)}{54 a^{11/3} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 \sqrt[3]{b} (4 b c-a f)-2 \sqrt[3]{a} (7 b d-a g)\right)}{27 a^{11/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-2 a^{4/3} g+14 \sqrt[3]{a} b d-5 a \sqrt[3]{b} f+20 b^{4/3} c\right)}{9 \sqrt{3} a^{11/3} b^{2/3}}-\frac{x \left(2 x (5 b d-2 a g)+3 x^2 (3 b e-a h)-5 a f+11 b c\right)}{18 a^3 \left(a+b x^3\right)}-\frac{x \left(x (b d-a g)+x^2 (b e-a h)-a f+b c\right)}{6 a^2 \left(a+b x^3\right)^2}-\frac{e \log \left(a+b x^3\right)}{3 a^3}-\frac{c}{2 a^3 x^2}-\frac{d}{a^3 x}+\frac{e \log (x)}{a^3}",1,"-c/(2*a^3*x^2) - d/(a^3*x) - (x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(6*a^2*(a + b*x^3)^2) - (x*(11*b*c - 5*a*f + 2*(5*b*d - 2*a*g)*x + 3*(3*b*e - a*h)*x^2))/(18*a^3*(a + b*x^3)) + ((20*b^(4/3)*c + 14*a^(1/3)*b*d - 5*a*b^(1/3)*f - 2*a^(4/3)*g)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(11/3)*b^(2/3)) + (e*Log[x])/a^3 - ((5*b^(1/3)*(4*b*c - a*f) - 2*a^(1/3)*(7*b*d - a*g))*Log[a^(1/3) + b^(1/3)*x])/(27*a^(11/3)*b^(2/3)) + ((20*b*c - 5*a*f - (2*a^(1/3)*(7*b*d - a*g))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(11/3)*b^(1/3)) - (e*Log[a + b*x^3])/(3*a^3)","A",12,10,38,0.2632,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
429,1,392,0,1.0061605,"\int \frac{c+d x+e x^2+f x^3+g x^4+h x^5}{x^4 \left(a+b x^3\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^4*(a + b*x^3)^3),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(-\frac{2 \sqrt[3]{a} (7 b e-a h)}{\sqrt[3]{b}}-5 a g+20 b d\right)}{54 a^{11/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 \sqrt[3]{b} (4 b d-a g)-2 \sqrt[3]{a} (7 b e-a h)\right)}{27 a^{11/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-2 a^{4/3} h+14 \sqrt[3]{a} b e-5 a \sqrt[3]{b} g+20 b^{4/3} d\right)}{9 \sqrt{3} a^{11/3} b^{2/3}}-\frac{x \left(-3 b x^2 \left(\frac{5 b c}{a}-3 f\right)+2 x (5 b e-2 a h)-5 a g+11 b d\right)}{18 a^3 \left(a+b x^3\right)}-\frac{x \left(-b x^2 \left(\frac{b c}{a}-f\right)+x (b e-a h)-a g+b d\right)}{6 a^2 \left(a+b x^3\right)^2}+\frac{(3 b c-a f) \log \left(a+b x^3\right)}{3 a^4}-\frac{\log (x) (3 b c-a f)}{a^4}-\frac{c}{3 a^3 x^3}-\frac{d}{2 a^3 x^2}-\frac{e}{a^3 x}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right) \left(5 \sqrt[3]{b} (4 b d-a g)-2 \sqrt[3]{a} (7 b e-a h)\right)}{54 a^{11/3} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \left(5 \sqrt[3]{b} (4 b d-a g)-2 \sqrt[3]{a} (7 b e-a h)\right)}{27 a^{11/3} b^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right) \left(-2 a^{4/3} h+14 \sqrt[3]{a} b e-5 a \sqrt[3]{b} g+20 b^{4/3} d\right)}{9 \sqrt{3} a^{11/3} b^{2/3}}-\frac{x \left(-3 b x^2 \left(\frac{5 b c}{a}-3 f\right)+2 x (5 b e-2 a h)-5 a g+11 b d\right)}{18 a^3 \left(a+b x^3\right)}-\frac{x \left(-b x^2 \left(\frac{b c}{a}-f\right)+x (b e-a h)-a g+b d\right)}{6 a^2 \left(a+b x^3\right)^2}+\frac{(3 b c-a f) \log \left(a+b x^3\right)}{3 a^4}-\frac{\log (x) (3 b c-a f)}{a^4}-\frac{c}{3 a^3 x^3}-\frac{d}{2 a^3 x^2}-\frac{e}{a^3 x}",1,"-c/(3*a^3*x^3) - d/(2*a^3*x^2) - e/(a^3*x) - (x*(b*d - a*g + (b*e - a*h)*x - b*((b*c)/a - f)*x^2))/(6*a^2*(a + b*x^3)^2) - (x*(11*b*d - 5*a*g + 2*(5*b*e - 2*a*h)*x - 3*b*((5*b*c)/a - 3*f)*x^2))/(18*a^3*(a + b*x^3)) + ((20*b^(4/3)*d + 14*a^(1/3)*b*e - 5*a*b^(1/3)*g - 2*a^(4/3)*h)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(11/3)*b^(2/3)) - ((3*b*c - a*f)*Log[x])/a^4 - ((5*b^(1/3)*(4*b*d - a*g) - 2*a^(1/3)*(7*b*e - a*h))*Log[a^(1/3) + b^(1/3)*x])/(27*a^(11/3)*b^(2/3)) + ((20*b*d - 5*a*g - (2*a^(1/3)*(7*b*e - a*h))/b^(1/3))*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(11/3)*b^(1/3)) + ((3*b*c - a*f)*Log[a + b*x^3])/(3*a^4)","A",12,10,38,0.2632,1,"{1829, 1834, 1871, 1860, 31, 634, 617, 204, 628, 260}"
430,1,583,0,0.7331018,"\int \frac{x^3 \left(c+d x+e x^2\right)}{\sqrt{a+b x^3}} \, dx","Int[(x^3*(c + d*x + e*x^2))/Sqrt[a + b*x^3],x]","-\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(7 \sqrt[3]{b} c-10 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{35 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 a d \sqrt{a+b x^3}}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{4 a e \sqrt{a+b x^3}}{9 b^2}+\frac{2 c x \sqrt{a+b x^3}}{5 b}+\frac{2 d x^2 \sqrt{a+b x^3}}{7 b}+\frac{2 e x^3 \sqrt{a+b x^3}}{9 b}","-\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(7 \sqrt[3]{b} c-10 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{35 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 a d \sqrt{a+b x^3}}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{4 a e \sqrt{a+b x^3}}{9 b^2}+\frac{2 c x \sqrt{a+b x^3}}{5 b}+\frac{2 d x^2 \sqrt{a+b x^3}}{7 b}+\frac{2 e x^3 \sqrt{a+b x^3}}{9 b}",1,"(-4*a*e*Sqrt[a + b*x^3])/(9*b^2) + (2*c*x*Sqrt[a + b*x^3])/(5*b) + (2*d*x^2*Sqrt[a + b*x^3])/(7*b) + (2*e*x^3*Sqrt[a + b*x^3])/(9*b) - (8*a*d*Sqrt[a + b*x^3])/(7*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (4*Sqrt[2 + Sqrt[3]]*a*(7*b^(1/3)*c - 10*(1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(35*3^(1/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",10,7,25,0.2800,1,"{1888, 1594, 1886, 261, 1878, 218, 1877}"
431,1,560,0,0.4843517,"\int \frac{x^2 \left(c+d x+e x^2\right)}{\sqrt{a+b x^3}} \, dx","Int[(x^2*(c + d*x + e*x^2))/Sqrt[a + b*x^3],x]","-\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(7 \sqrt[3]{b} d-10 \left(1-\sqrt{3}\right) \sqrt[3]{a} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{35 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 a e \sqrt{a+b x^3}}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 c \sqrt{a+b x^3}}{3 b}+\frac{2 d x \sqrt{a+b x^3}}{5 b}+\frac{2 e x^2 \sqrt{a+b x^3}}{7 b}","-\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(7 \sqrt[3]{b} d-10 \left(1-\sqrt{3}\right) \sqrt[3]{a} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{35 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 a e \sqrt{a+b x^3}}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 c \sqrt{a+b x^3}}{3 b}+\frac{2 d x \sqrt{a+b x^3}}{5 b}+\frac{2 e x^2 \sqrt{a+b x^3}}{7 b}",1,"(2*c*Sqrt[a + b*x^3])/(3*b) + (2*d*x*Sqrt[a + b*x^3])/(5*b) + (2*e*x^2*Sqrt[a + b*x^3])/(7*b) - (8*a*e*Sqrt[a + b*x^3])/(7*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (4*Sqrt[2 + Sqrt[3]]*a*(7*b^(1/3)*d - 10*(1 - Sqrt[3])*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(35*3^(1/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",8,7,25,0.2800,1,"{1888, 1594, 1886, 261, 1878, 218, 1877}"
432,1,537,0,0.3225312,"\int \frac{x \left(c+d x+e x^2\right)}{\sqrt{a+b x^3}} \, dx","Int[(x*(c + d*x + e*x^2))/Sqrt[a + b*x^3],x]","-\frac{2 \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(2 a^{2/3} e+5 \left(1-\sqrt{3}\right) b^{2/3} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 c \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 d \sqrt{a+b x^3}}{3 b}+\frac{2 e x \sqrt{a+b x^3}}{5 b}","-\frac{2 \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(2 a^{2/3} e+5 \left(1-\sqrt{3}\right) b^{2/3} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 c \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 d \sqrt{a+b x^3}}{3 b}+\frac{2 e x \sqrt{a+b x^3}}{5 b}",1,"(2*d*Sqrt[a + b*x^3])/(3*b) + (2*e*x*Sqrt[a + b*x^3])/(5*b) + (2*c*Sqrt[a + b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*c*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (2*Sqrt[2 + Sqrt[3]]*a^(1/3)*(5*(1 - Sqrt[3])*b^(2/3)*c + 2*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,23,0.2609,1,"{1888, 1886, 261, 1878, 218, 1877}"
433,1,509,0,0.1730247,"\int \frac{c+d x+e x^2}{\sqrt{a+b x^3}} \, dx","Int[(c + d*x + e*x^2)/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-\left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 d \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 e \sqrt{a+b x^3}}{3 b}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-\left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 d \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 e \sqrt{a+b x^3}}{3 b}",1,"(2*e*Sqrt[a + b*x^3])/(3*b) + (2*d*Sqrt[a + b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*c - (1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,22,0.2273,1,"{1886, 261, 1878, 218, 1877}"
434,1,518,0,0.2048736,"\int \frac{c+d x+e x^2}{x \sqrt{a+b x^3}} \, dx","Int[(c + d*x + e*x^2)/(x*Sqrt[a + b*x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} d-\left(1-\sqrt{3}\right) \sqrt[3]{a} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 e \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} d-\left(1-\sqrt{3}\right) \sqrt[3]{a} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 e \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"(2*e*Sqrt[a + b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*c*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a]) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*d - (1 - Sqrt[3])*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,7,25,0.2800,1,"{1832, 266, 63, 208, 1878, 218, 1877}"
435,1,547,0,0.3426278,"\int \frac{c+d x+e x^2}{x^2 \sqrt{a+b x^3}} \, dx","Int[(c + d*x + e*x^2)/(x^2*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) b^{2/3} c-2 a^{2/3} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{c \sqrt{a+b x^3}}{a x}+\frac{\sqrt[3]{b} c \sqrt{a+b x^3}}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) b^{2/3} c-2 a^{2/3} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{c \sqrt{a+b x^3}}{a x}+\frac{\sqrt[3]{b} c \sqrt{a+b x^3}}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"-((c*Sqrt[a + b*x^3])/(a*x)) + (b^(1/3)*c*Sqrt[a + b*x^3])/(a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*d*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a]) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*c*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (Sqrt[2 + Sqrt[3]]*((1 - Sqrt[3])*b^(2/3)*c - 2*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*a^(2/3)*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",8,8,25,0.3200,1,"{1835, 1832, 266, 63, 208, 1878, 218, 1877}"
436,1,569,0,0.4635362,"\int \frac{c+d x+e x^2}{x^3 \sqrt{a+b x^3}} \, dx","Int[(c + d*x + e*x^2)/(x^3*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{2+\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(2 \left(1-\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{c \sqrt{a+b x^3}}{2 a x^2}-\frac{d \sqrt{a+b x^3}}{a x}+\frac{\sqrt[3]{b} d \sqrt{a+b x^3}}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}","-\frac{\sqrt{2+\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(2 \left(1-\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{c \sqrt{a+b x^3}}{2 a x^2}-\frac{d \sqrt{a+b x^3}}{a x}+\frac{\sqrt[3]{b} d \sqrt{a+b x^3}}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"-(c*Sqrt[a + b*x^3])/(2*a*x^2) - (d*Sqrt[a + b*x^3])/(a*x) + (b^(1/3)*d*Sqrt[a + b*x^3])/(a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*e*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a]) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (Sqrt[2 + Sqrt[3]]*b^(1/3)*(b^(1/3)*c + 2*(1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",9,8,25,0.3200,1,"{1835, 1832, 266, 63, 208, 1878, 218, 1877}"
437,1,594,0,0.6408672,"\int \frac{x^5 \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^5*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x]","-\frac{16 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(14 \sqrt[3]{b} d-25 \left(1-\sqrt{3}\right) \sqrt[3]{a} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{105 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{40 \sqrt{2-\sqrt{3}} a^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a d+a e x-b c x^2\right)}{3 b^2 \sqrt{a+b x^3}}+\frac{4 c \sqrt{a+b x^3}}{3 b^2}+\frac{2 d x \sqrt{a+b x^3}}{5 b^2}+\frac{2 e x^2 \sqrt{a+b x^3}}{7 b^2}-\frac{80 a e \sqrt{a+b x^3}}{21 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","-\frac{16 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(14 \sqrt[3]{b} d-25 \left(1-\sqrt{3}\right) \sqrt[3]{a} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{105 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{40 \sqrt{2-\sqrt{3}} a^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a d+a e x-b c x^2\right)}{3 b^2 \sqrt{a+b x^3}}+\frac{4 c \sqrt{a+b x^3}}{3 b^2}+\frac{2 d x \sqrt{a+b x^3}}{5 b^2}+\frac{2 e x^2 \sqrt{a+b x^3}}{7 b^2}-\frac{80 a e \sqrt{a+b x^3}}{21 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(2*x*(a*d + a*e*x - b*c*x^2))/(3*b^2*Sqrt[a + b*x^3]) + (4*c*Sqrt[a + b*x^3])/(3*b^2) + (2*d*x*Sqrt[a + b*x^3])/(5*b^2) + (2*e*x^2*Sqrt[a + b*x^3])/(7*b^2) - (80*a*e*Sqrt[a + b*x^3])/(21*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (40*Sqrt[2 - Sqrt[3]]*a^(4/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(3/4)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (16*Sqrt[2 + Sqrt[3]]*a*(14*b^(1/3)*d - 25*(1 - Sqrt[3])*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(105*3^(1/4)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",8,7,25,0.2800,1,"{1828, 1888, 1886, 261, 1878, 218, 1877}"
438,1,574,0,0.4691098,"\int \frac{x^4 \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^4*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x]","-\frac{8 \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(4 a^{2/3} e+5 \left(1-\sqrt{3}\right) b^{2/3} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a e-b c x-b d x^2\right)}{3 b^2 \sqrt{a+b x^3}}+\frac{8 c \sqrt{a+b x^3}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{4 d \sqrt{a+b x^3}}{3 b^2}+\frac{2 e x \sqrt{a+b x^3}}{5 b^2}","-\frac{8 \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(4 a^{2/3} e+5 \left(1-\sqrt{3}\right) b^{2/3} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a e-b c x-b d x^2\right)}{3 b^2 \sqrt{a+b x^3}}+\frac{8 c \sqrt{a+b x^3}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{4 d \sqrt{a+b x^3}}{3 b^2}+\frac{2 e x \sqrt{a+b x^3}}{5 b^2}",1,"(2*x*(a*e - b*c*x - b*d*x^2))/(3*b^2*Sqrt[a + b*x^3]) + (4*d*Sqrt[a + b*x^3])/(3*b^2) + (2*e*x*Sqrt[a + b*x^3])/(5*b^2) + (8*c*Sqrt[a + b*x^3])/(3*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (4*Sqrt[2 - Sqrt[3]]*a^(1/3)*c*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (8*Sqrt[2 + Sqrt[3]]*a^(1/3)*(5*(1 - Sqrt[3])*b^(2/3)*c + 4*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(15*3^(1/4)*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,7,25,0.2800,1,"{1828, 1888, 1886, 261, 1878, 218, 1877}"
439,1,542,0,0.3272416,"\int \frac{x^3 \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^3*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x]","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-2 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{8 d \sqrt{a+b x^3}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{4 e \sqrt{a+b x^3}}{3 b^2}-\frac{2 x \left(c+d x+e x^2\right)}{3 b \sqrt{a+b x^3}}","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} c-2 \left(1-\sqrt{3}\right) \sqrt[3]{a} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{8 d \sqrt{a+b x^3}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{4 e \sqrt{a+b x^3}}{3 b^2}-\frac{2 x \left(c+d x+e x^2\right)}{3 b \sqrt{a+b x^3}}",1,"(-2*x*(c + d*x + e*x^2))/(3*b*Sqrt[a + b*x^3]) + (4*e*Sqrt[a + b*x^3])/(3*b^2) + (8*d*Sqrt[a + b*x^3])/(3*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (4*Sqrt[2 - Sqrt[3]]*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (4*Sqrt[2 + Sqrt[3]]*(b^(1/3)*c - 2*(1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,25,0.2400,1,"{1828, 1886, 261, 1878, 218, 1877}"
440,1,522,0,0.2616401,"\int \frac{x^2 \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^2*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x]","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} d-2 \left(1-\sqrt{3}\right) \sqrt[3]{a} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{8 e \sqrt{a+b x^3}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 \left(c+d x+e x^2\right)}{3 b \sqrt{a+b x^3}}","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} d-2 \left(1-\sqrt{3}\right) \sqrt[3]{a} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{8 e \sqrt{a+b x^3}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 \left(c+d x+e x^2\right)}{3 b \sqrt{a+b x^3}}",1,"(-2*(c + d*x + e*x^2))/(3*b*Sqrt[a + b*x^3]) + (8*e*Sqrt[a + b*x^3])/(3*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (4*Sqrt[2 - Sqrt[3]]*a^(1/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (4*Sqrt[2 + Sqrt[3]]*(b^(1/3)*d - 2*(1 - Sqrt[3])*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,25,0.1600,1,"{1823, 1878, 218, 1877}"
441,1,561,0,0.3213366,"\int \frac{x \left(c+d x+e x^2\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(2 a^{2/3} e+b^{2/3} \left(c-\sqrt{3} c\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{2/3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 c \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 x \left(a e-b c x-b d x^2\right)}{3 a b \sqrt{a+b x^3}}-\frac{2 d \sqrt{a+b x^3}}{3 a b}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(2 a^{2/3} e+b^{2/3} \left(c-\sqrt{3} c\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{2/3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 c \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 x \left(a e-b c x-b d x^2\right)}{3 a b \sqrt{a+b x^3}}-\frac{2 d \sqrt{a+b x^3}}{3 a b}",1,"(-2*x*(a*e - b*c*x - b*d*x^2))/(3*a*b*Sqrt[a + b*x^3]) - (2*d*Sqrt[a + b*x^3])/(3*a*b) - (2*c*Sqrt[a + b*x^3])/(3*a*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (Sqrt[2 - Sqrt[3]]*c*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(2/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(2/3)*(c - Sqrt[3]*c) + 2*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(2/3)*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,23,0.2609,1,"{1828, 1886, 261, 1878, 218, 1877}"
442,1,532,0,0.2459601,"\int \frac{c+d x+e x^2}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(c + d*x + e*x^2)/(a + b*x^3)^(3/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 d \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 (a e-b x (c+d x))}{3 a b \sqrt{a+b x^3}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a} d+\sqrt[3]{b} c\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} d \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 d \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 (a e-b x (c+d x))}{3 a b \sqrt{a+b x^3}}",1,"(-2*d*Sqrt[a + b*x^3])/(3*a*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*(a*e - b*x*(c + d*x)))/(3*a*b*Sqrt[a + b*x^3]) + (Sqrt[2 - Sqrt[3]]*d*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(2/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*c + (1 - Sqrt[3])*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,22,0.1818,1,"{1854, 1878, 218, 1877}"
443,1,579,0,0.3999416,"\int \frac{c+d x+e x^2}{x \left(a+b x^3\right)^{3/2}} \, dx","Int[(c + d*x + e*x^2)/(x*(a + b*x^3)^(3/2)),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a} e+\sqrt[3]{b} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a d+a e x-b c x^2\right)}{3 a^2 \sqrt{a+b x^3}}+\frac{2 c \sqrt{a+b x^3}}{3 a^2}-\frac{2 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{2 e \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a} e+\sqrt[3]{b} d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a d+a e x-b c x^2\right)}{3 a^2 \sqrt{a+b x^3}}+\frac{2 c \sqrt{a+b x^3}}{3 a^2}-\frac{2 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{2 e \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(2*x*(a*d + a*e*x - b*c*x^2))/(3*a^2*Sqrt[a + b*x^3]) + (2*c*Sqrt[a + b*x^3])/(3*a^2) - (2*e*Sqrt[a + b*x^3])/(3*a*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*c*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(3/2)) + (Sqrt[2 - Sqrt[3]]*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(2/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*d + (1 - Sqrt[3])*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",10,10,25,0.4000,1,"{1829, 1832, 266, 63, 208, 1886, 261, 1878, 218, 1877}"
444,1,607,0,0.5598124,"\int \frac{c+d x+e x^2}{x^2 \left(a+b x^3\right)^{3/2}} \, dx","Int[(c + d*x + e*x^2)/(x^2*(a + b*x^3)^(3/2)),x]","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(5 \left(1-\sqrt{3}\right) b^{2/3} c-2 a^{2/3} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{5/3} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt{2-\sqrt{3}} \sqrt[3]{b} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a e-b c x-b d x^2\right)}{3 a^2 \sqrt{a+b x^3}}-\frac{c \sqrt{a+b x^3}}{a^2 x}+\frac{5 \sqrt[3]{b} c \sqrt{a+b x^3}}{3 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 d \sqrt{a+b x^3}}{3 a^2}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(5 \left(1-\sqrt{3}\right) b^{2/3} c-2 a^{2/3} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{5/3} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt{2-\sqrt{3}} \sqrt[3]{b} c \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a e-b c x-b d x^2\right)}{3 a^2 \sqrt{a+b x^3}}-\frac{c \sqrt{a+b x^3}}{a^2 x}+\frac{5 \sqrt[3]{b} c \sqrt{a+b x^3}}{3 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 d \sqrt{a+b x^3}}{3 a^2}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}",1,"(2*x*(a*e - b*c*x - b*d*x^2))/(3*a^2*Sqrt[a + b*x^3]) + (2*d*Sqrt[a + b*x^3])/(3*a^2) - (c*Sqrt[a + b*x^3])/(a^2*x) + (5*b^(1/3)*c*Sqrt[a + b*x^3])/(3*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*d*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(3/2)) - (5*Sqrt[2 - Sqrt[3]]*b^(1/3)*c*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (Sqrt[2 + Sqrt[3]]*(5*(1 - Sqrt[3])*b^(2/3)*c - 2*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(5/3)*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",11,11,25,0.4400,1,"{1829, 1835, 1832, 266, 63, 208, 1886, 261, 1878, 218, 1877}"
445,1,733,0,1.9096555,"\int x^3 \sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right) \, dx","Int[x^3*Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4),x]","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(1729 \sqrt[3]{b} (17 b c-8 a f)-1870 \left(1-\sqrt{3}\right) \sqrt[3]{a} (19 b d-10 a g)\right)}{1616615 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{24 a^2 \sqrt{a+b x^3} (19 b d-10 a g)}{1729 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 b d-10 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 a^2 e \sqrt{a+b x^3}}{45 b^2}+\frac{6 a x \sqrt{a+b x^3} (17 b c-8 a f)}{935 b^2}+\frac{6 a x^2 \sqrt{a+b x^3} (19 b d-10 a g)}{1729 b^2}+\frac{2 x^3 \sqrt{a+b x^3} \left(62985 c x+53295 d x^2+46189 e x^3+40755 f x^4+36465 g x^5\right)}{692835}+\frac{2 a e x^3 \sqrt{a+b x^3}}{45 b}+\frac{6 a f x^4 \sqrt{a+b x^3}}{187 b}+\frac{6 a g x^5 \sqrt{a+b x^3}}{247 b}","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(1729 \sqrt[3]{b} (17 b c-8 a f)-1870 \left(1-\sqrt{3}\right) \sqrt[3]{a} (19 b d-10 a g)\right)}{1616615 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{24 a^2 \sqrt{a+b x^3} (19 b d-10 a g)}{1729 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 b d-10 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 a^2 e \sqrt{a+b x^3}}{45 b^2}+\frac{6 a x \sqrt{a+b x^3} (17 b c-8 a f)}{935 b^2}+\frac{6 a x^2 \sqrt{a+b x^3} (19 b d-10 a g)}{1729 b^2}+\frac{2 x^3 \sqrt{a+b x^3} \left(62985 c x+53295 d x^2+46189 e x^3+40755 f x^4+36465 g x^5\right)}{692835}+\frac{2 a e x^3 \sqrt{a+b x^3}}{45 b}+\frac{6 a f x^4 \sqrt{a+b x^3}}{187 b}+\frac{6 a g x^5 \sqrt{a+b x^3}}{247 b}",1,"(-4*a^2*e*Sqrt[a + b*x^3])/(45*b^2) + (6*a*(17*b*c - 8*a*f)*x*Sqrt[a + b*x^3])/(935*b^2) + (6*a*(19*b*d - 10*a*g)*x^2*Sqrt[a + b*x^3])/(1729*b^2) + (2*a*e*x^3*Sqrt[a + b*x^3])/(45*b) + (6*a*f*x^4*Sqrt[a + b*x^3])/(187*b) + (6*a*g*x^5*Sqrt[a + b*x^3])/(247*b) - (24*a^2*(19*b*d - 10*a*g)*Sqrt[a + b*x^3])/(1729*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*x^3*Sqrt[a + b*x^3]*(62985*c*x + 53295*d*x^2 + 46189*e*x^3 + 40755*f*x^4 + 36465*g*x^5))/692835 + (12*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(19*b*d - 10*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (4*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(1729*b^(1/3)*(17*b*c - 8*a*f) - 1870*(1 - Sqrt[3])*a^(1/3)*(19*b*d - 10*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1616615*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",13,9,35,0.2571,1,"{1826, 1836, 1888, 1594, 1886, 261, 1878, 218, 1877}"
446,1,681,0,1.4215212,"\int x^2 \sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right) \, dx","Int[x^2*Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4),x]","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-1870 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-728 a g+1547 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{85085 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{24 a^2 e \sqrt{a+b x^3}}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 a \sqrt{a+b x^3} (5 b c-2 a f)}{45 b^2}+\frac{6 a x \sqrt{a+b x^3} (17 b d-8 a g)}{935 b^2}+\frac{2 x^2 \sqrt{a+b x^3} \left(12155 c x+9945 d x^2+8415 e x^3+7293 f x^4+6435 g x^5\right)}{109395}+\frac{6 a e x^2 \sqrt{a+b x^3}}{91 b}+\frac{2 a f x^3 \sqrt{a+b x^3}}{45 b}+\frac{6 a g x^4 \sqrt{a+b x^3}}{187 b}","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-1870 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-728 a g+1547 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{85085 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{24 a^2 e \sqrt{a+b x^3}}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 a \sqrt{a+b x^3} (5 b c-2 a f)}{45 b^2}+\frac{6 a x \sqrt{a+b x^3} (17 b d-8 a g)}{935 b^2}+\frac{2 x^2 \sqrt{a+b x^3} \left(12155 c x+9945 d x^2+8415 e x^3+7293 f x^4+6435 g x^5\right)}{109395}+\frac{6 a e x^2 \sqrt{a+b x^3}}{91 b}+\frac{2 a f x^3 \sqrt{a+b x^3}}{45 b}+\frac{6 a g x^4 \sqrt{a+b x^3}}{187 b}",1,"(2*a*(5*b*c - 2*a*f)*Sqrt[a + b*x^3])/(45*b^2) + (6*a*(17*b*d - 8*a*g)*x*Sqrt[a + b*x^3])/(935*b^2) + (6*a*e*x^2*Sqrt[a + b*x^3])/(91*b) + (2*a*f*x^3*Sqrt[a + b*x^3])/(45*b) + (6*a*g*x^4*Sqrt[a + b*x^3])/(187*b) - (24*a^2*e*Sqrt[a + b*x^3])/(91*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*x^2*Sqrt[a + b*x^3]*(12155*c*x + 9945*d*x^2 + 8415*e*x^3 + 7293*f*x^4 + 6435*g*x^5))/109395 + (12*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (4*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(1547*b*d - 1870*(1 - Sqrt[3])*a^(1/3)*b^(2/3)*e - 728*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(85085*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",11,9,35,0.2571,1,"{1826, 1836, 1888, 1594, 1886, 261, 1878, 218, 1877}"
447,1,667,0,1.0473054,"\int x \sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right) \, dx","Int[x*Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4),x]","-\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(182 a^{2/3} \sqrt[3]{b} e+55 \left(1-\sqrt{3}\right) (13 b c-4 a f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5005 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 b c-4 a f) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a \sqrt{a+b x^3} (13 b c-4 a f)}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 a \sqrt{a+b x^3} (5 b d-2 a g)}{45 b^2}+\frac{2 x \sqrt{a+b x^3} \left(6435 c x+5005 d x^2+4095 e x^3+3465 f x^4+3003 g x^5\right)}{45045}+\frac{6 a e x \sqrt{a+b x^3}}{55 b}+\frac{6 a f x^2 \sqrt{a+b x^3}}{91 b}+\frac{2 a g x^3 \sqrt{a+b x^3}}{45 b}","-\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(182 a^{2/3} \sqrt[3]{b} e+55 \left(1-\sqrt{3}\right) (13 b c-4 a f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5005 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 b c-4 a f) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a \sqrt{a+b x^3} (13 b c-4 a f)}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 a \sqrt{a+b x^3} (5 b d-2 a g)}{45 b^2}+\frac{2 x \sqrt{a+b x^3} \left(6435 c x+5005 d x^2+4095 e x^3+3465 f x^4+3003 g x^5\right)}{45045}+\frac{6 a e x \sqrt{a+b x^3}}{55 b}+\frac{6 a f x^2 \sqrt{a+b x^3}}{91 b}+\frac{2 a g x^3 \sqrt{a+b x^3}}{45 b}",1,"(2*a*(5*b*d - 2*a*g)*Sqrt[a + b*x^3])/(45*b^2) + (6*a*e*x*Sqrt[a + b*x^3])/(55*b) + (6*a*f*x^2*Sqrt[a + b*x^3])/(91*b) + (2*a*g*x^3*Sqrt[a + b*x^3])/(45*b) + (6*a*(13*b*c - 4*a*f)*Sqrt[a + b*x^3])/(91*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*x*Sqrt[a + b*x^3]*(6435*c*x + 5005*d*x^2 + 4095*e*x^3 + 3465*f*x^4 + 3003*g*x^5))/45045 - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(13*b*c - 4*a*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^(4/3)*(182*a^(2/3)*b^(1/3)*e + 55*(1 - Sqrt[3])*(13*b*c - 4*a*f))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(5005*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",9,8,33,0.2424,1,"{1826, 1836, 1888, 1886, 261, 1878, 218, 1877}"
448,1,639,0,0.719342,"\int \sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right) \, dx","Int[Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4),x]","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(91 \sqrt[3]{b} (11 b c-2 a f)-55 \left(1-\sqrt{3}\right) \sqrt[3]{a} (13 b d-4 a g)\right)}{5005 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 b d-4 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a \sqrt{a+b x^3} (13 b d-4 a g)}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 \sqrt{a+b x^3} \left(9009 c x+6435 d x^2+5005 e x^3+4095 f x^4+3465 g x^5\right)}{45045}+\frac{2 a e \sqrt{a+b x^3}}{9 b}+\frac{6 a f x \sqrt{a+b x^3}}{55 b}+\frac{6 a g x^2 \sqrt{a+b x^3}}{91 b}","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(91 \sqrt[3]{b} (11 b c-2 a f)-55 \left(1-\sqrt{3}\right) \sqrt[3]{a} (13 b d-4 a g)\right)}{5005 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 b d-4 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a \sqrt{a+b x^3} (13 b d-4 a g)}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 \sqrt{a+b x^3} \left(9009 c x+6435 d x^2+5005 e x^3+4095 f x^4+3465 g x^5\right)}{45045}+\frac{2 a e \sqrt{a+b x^3}}{9 b}+\frac{6 a f x \sqrt{a+b x^3}}{55 b}+\frac{6 a g x^2 \sqrt{a+b x^3}}{91 b}",1,"(2*a*e*Sqrt[a + b*x^3])/(9*b) + (6*a*f*x*Sqrt[a + b*x^3])/(55*b) + (6*a*g*x^2*Sqrt[a + b*x^3])/(91*b) + (6*a*(13*b*d - 4*a*g)*Sqrt[a + b*x^3])/(91*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*Sqrt[a + b*x^3]*(9009*c*x + 6435*d*x^2 + 5005*e*x^3 + 4095*f*x^4 + 3465*g*x^5))/45045 - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(13*b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*(91*b^(1/3)*(11*b*c - 2*a*f) - 55*(1 - Sqrt[3])*a^(1/3)*(13*b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(5005*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",8,7,32,0.2188,1,"{1853, 1888, 1886, 261, 1878, 218, 1877}"
449,1,620,0,0.5471088,"\int \frac{\sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right)}{x} \, dx","Int[(Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x,x]","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-55 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-14 a g+77 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{385 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a e \sqrt{a+b x^3}}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 \sqrt{a+b x^3} \left(1155 c x+693 d x^2+495 e x^3+385 f x^4+315 g x^5\right)}{3465 x}-\frac{2}{3} \sqrt{a} c \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 a f \sqrt{a+b x^3}}{9 b}+\frac{6 a g x \sqrt{a+b x^3}}{55 b}","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-55 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-14 a g+77 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{385 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a e \sqrt{a+b x^3}}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 \sqrt{a+b x^3} \left(1155 c x+693 d x^2+495 e x^3+385 f x^4+315 g x^5\right)}{3465 x}-\frac{2}{3} \sqrt{a} c \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 a f \sqrt{a+b x^3}}{9 b}+\frac{6 a g x \sqrt{a+b x^3}}{55 b}",1,"(2*a*f*Sqrt[a + b*x^3])/(9*b) + (6*a*g*x*Sqrt[a + b*x^3])/(55*b) + (6*a*e*Sqrt[a + b*x^3])/(7*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*Sqrt[a + b*x^3]*(1155*c*x + 693*d*x^2 + 495*e*x^3 + 385*f*x^4 + 315*g*x^5))/(3465*x) - (2*Sqrt[a]*c*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3 - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*(77*b*d - 55*(1 - Sqrt[3])*a^(1/3)*b^(2/3)*e - 14*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(385*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",11,11,35,0.3143,1,"{1826, 1832, 266, 63, 208, 1888, 1886, 261, 1878, 218, 1877}"
450,1,638,0,0.6496729,"\int \frac{\sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^2} \, dx","Int[(Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^2,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(14 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (2 a f+7 b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{35 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a f+7 b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \sqrt{a+b x^3} (2 a f+7 b c)}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 \sqrt{a+b x^3} \left(315 c x+105 d x^2+63 e x^3+45 f x^4+35 g x^5\right)}{315 x^2}-\frac{3 c \sqrt{a+b x^3}}{x}-\frac{2}{3} \sqrt{a} d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 a g \sqrt{a+b x^3}}{9 b}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(14 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (2 a f+7 b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{35 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a f+7 b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \sqrt{a+b x^3} (2 a f+7 b c)}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 \sqrt{a+b x^3} \left(315 c x+105 d x^2+63 e x^3+45 f x^4+35 g x^5\right)}{315 x^2}-\frac{3 c \sqrt{a+b x^3}}{x}-\frac{2}{3} \sqrt{a} d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 a g \sqrt{a+b x^3}}{9 b}",1,"(2*a*g*Sqrt[a + b*x^3])/(9*b) - (3*c*Sqrt[a + b*x^3])/x + (3*(7*b*c + 2*a*f)*Sqrt[a + b*x^3])/(7*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*Sqrt[a + b*x^3]*(315*c*x + 105*d*x^2 + 63*e*x^3 + 45*f*x^4 + 35*g*x^5))/(315*x^2) - (2*Sqrt[a]*d*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3 - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(7*b*c + 2*a*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(14*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(14*a^(2/3)*b^(1/3)*e - 5*(1 - Sqrt[3])*(7*b*c + 2*a*f))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(35*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",11,11,35,0.3143,1,"{1826, 1835, 1832, 266, 63, 208, 1886, 261, 1878, 218, 1877}"
451,1,640,0,0.7647139,"\int \frac{\sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^3} \, dx","Int[(Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^3,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (4 a f+5 b c)-10 \left(1-\sqrt{3}\right) \sqrt[3]{a} (2 a g+7 b d)\right)}{70 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a g+7 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \sqrt{a+b x^3} (2 a g+7 b d)}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 \sqrt{a+b x^3} \left(105 c x-105 d x^2-35 e x^3-21 f x^4-15 g x^5\right)}{105 x^3}+\frac{3 c \sqrt{a+b x^3}}{2 x^2}-\frac{3 d \sqrt{a+b x^3}}{x}-\frac{2}{3} \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (4 a f+5 b c)-10 \left(1-\sqrt{3}\right) \sqrt[3]{a} (2 a g+7 b d)\right)}{70 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a g+7 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \sqrt{a+b x^3} (2 a g+7 b d)}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 \sqrt{a+b x^3} \left(105 c x-105 d x^2-35 e x^3-21 f x^4-15 g x^5\right)}{105 x^3}+\frac{3 c \sqrt{a+b x^3}}{2 x^2}-\frac{3 d \sqrt{a+b x^3}}{x}-\frac{2}{3} \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)",1,"(3*c*Sqrt[a + b*x^3])/(2*x^2) - (3*d*Sqrt[a + b*x^3])/x + (3*(7*b*d + 2*a*g)*Sqrt[a + b*x^3])/(7*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*Sqrt[a + b*x^3]*(105*c*x - 105*d*x^2 - 35*e*x^3 - 21*f*x^4 - 15*g*x^5))/(105*x^3) - (2*Sqrt[a]*e*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3 - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(7*b*d + 2*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(14*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*(7*b^(1/3)*(5*b*c + 4*a*f) - 10*(1 - Sqrt[3])*a^(1/3)*(7*b*d + 2*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(70*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",10,9,35,0.2571,1,"{1826, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
452,1,637,0,0.8443938,"\int \frac{\sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^4} \, dx","Int[(Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^4,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-10 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e+4 a g+5 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{10 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} \left(5 c x+15 d x^2-15 e x^3-5 f x^4-3 g x^5\right)}{15 x^4}-\frac{(2 a f+b c) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}+\frac{c \sqrt{a+b x^3}}{3 x^3}+\frac{3 d \sqrt{a+b x^3}}{2 x^2}-\frac{3 e \sqrt{a+b x^3}}{x}+\frac{3 \sqrt[3]{b} e \sqrt{a+b x^3}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-10 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e+4 a g+5 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{10 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} \left(5 c x+15 d x^2-15 e x^3-5 f x^4-3 g x^5\right)}{15 x^4}-\frac{(2 a f+b c) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}+\frac{c \sqrt{a+b x^3}}{3 x^3}+\frac{3 d \sqrt{a+b x^3}}{2 x^2}-\frac{3 e \sqrt{a+b x^3}}{x}+\frac{3 \sqrt[3]{b} e \sqrt{a+b x^3}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}",1,"(c*Sqrt[a + b*x^3])/(3*x^3) + (3*d*Sqrt[a + b*x^3])/(2*x^2) - (3*e*Sqrt[a + b*x^3])/x + (3*b^(1/3)*e*Sqrt[a + b*x^3])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x) - (2*Sqrt[a + b*x^3]*(5*c*x + 15*d*x^2 - 15*e*x^3 - 5*f*x^4 - 3*g*x^5))/(15*x^4) - ((b*c + 2*a*f)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a]) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(1/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*(5*b*d - 10*(1 - Sqrt[3])*a^(1/3)*b^(2/3)*e + 4*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(10*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",11,9,35,0.2571,1,"{1826, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
453,1,694,0,1.0842498,"\int \frac{\sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^5} \, dx","Int[(Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^5,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(4 a^{2/3} \sqrt[3]{b} e-\left(1-\sqrt{3}\right) (8 a f+b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a f+b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} \left(3 c x+5 d x^2+15 e x^3-15 f x^4-5 g x^5\right)}{15 x^5}-\frac{3 \sqrt{a+b x^3} (8 a f+b c)}{8 a x}+\frac{3 \sqrt[3]{b} \sqrt{a+b x^3} (8 a f+b c)}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{3 c \sqrt{a+b x^3}}{20 x^4}-\frac{(2 a g+b d) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}+\frac{d \sqrt{a+b x^3}}{3 x^3}+\frac{3 e \sqrt{a+b x^3}}{2 x^2}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(4 a^{2/3} \sqrt[3]{b} e-\left(1-\sqrt{3}\right) (8 a f+b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a f+b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} \left(3 c x+5 d x^2+15 e x^3-15 f x^4-5 g x^5\right)}{15 x^5}-\frac{3 \sqrt{a+b x^3} (8 a f+b c)}{8 a x}+\frac{3 \sqrt[3]{b} \sqrt{a+b x^3} (8 a f+b c)}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{3 c \sqrt{a+b x^3}}{20 x^4}-\frac{(2 a g+b d) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}+\frac{d \sqrt{a+b x^3}}{3 x^3}+\frac{3 e \sqrt{a+b x^3}}{2 x^2}",1,"(3*c*Sqrt[a + b*x^3])/(20*x^4) + (d*Sqrt[a + b*x^3])/(3*x^3) + (3*e*Sqrt[a + b*x^3])/(2*x^2) - (3*(b*c + 8*a*f)*Sqrt[a + b*x^3])/(8*a*x) + (3*b^(1/3)*(b*c + 8*a*f)*Sqrt[a + b*x^3])/(8*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*Sqrt[a + b*x^3]*(3*c*x + 5*d*x^2 + 15*e*x^3 - 15*f*x^4 - 5*g*x^5))/(15*x^5) - ((b*d + 2*a*g)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a]) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*(b*c + 8*a*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(1/3)*(4*a^(2/3)*b^(1/3)*e - (1 - Sqrt[3])*(b*c + 8*a*f))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(8*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",12,9,35,0.2571,1,"{1826, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
454,1,652,0,0.7870918,"\int \frac{\sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^6} \, dx","Int[(Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^6,x]","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(2 \sqrt[3]{b} (b c-10 a f)+5 \left(1-\sqrt{3}\right) \sqrt[3]{a} (8 a g+b d)\right)}{40 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a g+b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{1}{60} \sqrt{a+b x^3} \left(\frac{12 c}{x^5}+\frac{15 d}{x^4}+\frac{20 e}{x^3}+\frac{30 f}{x^2}+\frac{60 g}{x}\right)-\frac{3 b c \sqrt{a+b x^3}}{20 a x^2}+\frac{3 \sqrt[3]{b} \sqrt{a+b x^3} (8 a g+b d)}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3 b d \sqrt{a+b x^3}}{8 a x}-\frac{b e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(2 \sqrt[3]{b} (b c-10 a f)+5 \left(1-\sqrt{3}\right) \sqrt[3]{a} (8 a g+b d)\right)}{40 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a g+b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{1}{60} \sqrt{a+b x^3} \left(\frac{12 c}{x^5}+\frac{15 d}{x^4}+\frac{20 e}{x^3}+\frac{30 f}{x^2}+\frac{60 g}{x}\right)-\frac{3 b c \sqrt{a+b x^3}}{20 a x^2}+\frac{3 \sqrt[3]{b} \sqrt{a+b x^3} (8 a g+b d)}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3 b d \sqrt{a+b x^3}}{8 a x}-\frac{b e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"-(((12*c)/x^5 + (15*d)/x^4 + (20*e)/x^3 + (30*f)/x^2 + (60*g)/x)*Sqrt[a + b*x^3])/60 - (3*b*c*Sqrt[a + b*x^3])/(20*a*x^2) - (3*b*d*Sqrt[a + b*x^3])/(8*a*x) + (3*b^(1/3)*(b*d + 8*a*g)*Sqrt[a + b*x^3])/(8*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (b*e*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a]) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*(b*d + 8*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(1/3)*(2*b^(1/3)*(b*c - 10*a*f) + 5*(1 - Sqrt[3])*a^(1/3)*(b*d + 8*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(40*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",10,10,35,0.2857,1,"{14, 1825, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
455,1,659,0,0.979823,"\int \frac{\sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^7} \, dx","Int[(Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^7,x]","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(5 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-20 a g+2 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{40 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{b (b c-4 a f) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}+\frac{3 b^{4/3} e \sqrt{a+b x^3}}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{1}{60} \sqrt{a+b x^3} \left(\frac{10 c}{x^6}+\frac{12 d}{x^5}+\frac{15 e}{x^4}+\frac{20 f}{x^3}+\frac{30 g}{x^2}\right)-\frac{b c \sqrt{a+b x^3}}{12 a x^3}-\frac{3 b d \sqrt{a+b x^3}}{20 a x^2}-\frac{3 b e \sqrt{a+b x^3}}{8 a x}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(5 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-20 a g+2 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{40 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{b (b c-4 a f) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}+\frac{3 b^{4/3} e \sqrt{a+b x^3}}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{1}{60} \sqrt{a+b x^3} \left(\frac{10 c}{x^6}+\frac{12 d}{x^5}+\frac{15 e}{x^4}+\frac{20 f}{x^3}+\frac{30 g}{x^2}\right)-\frac{b c \sqrt{a+b x^3}}{12 a x^3}-\frac{3 b d \sqrt{a+b x^3}}{20 a x^2}-\frac{3 b e \sqrt{a+b x^3}}{8 a x}",1,"-(((10*c)/x^6 + (12*d)/x^5 + (15*e)/x^4 + (20*f)/x^3 + (30*g)/x^2)*Sqrt[a + b*x^3])/60 - (b*c*Sqrt[a + b*x^3])/(12*a*x^3) - (3*b*d*Sqrt[a + b*x^3])/(20*a*x^2) - (3*b*e*Sqrt[a + b*x^3])/(8*a*x) + (3*b^(4/3)*e*Sqrt[a + b*x^3])/(8*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (b*(b*c - 4*a*f)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(12*a^(3/2)) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(2/3)*(2*b*d + 5*(1 - Sqrt[3])*a^(1/3)*b^(2/3)*e - 20*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(40*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",11,10,35,0.2857,1,"{14, 1825, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
456,1,711,0,1.1230236,"\int \frac{\sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^8} \, dx","Int[(Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^8,x]","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(28 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (5 b c-14 a f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{560 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 b^{4/3} \sqrt{a+b x^3} (5 b c-14 a f)}{112 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 b c-14 a f) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b \sqrt{a+b x^3} (5 b c-14 a f)}{112 a^2 x}+\frac{b (b d-4 a g) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}-\frac{1}{420} \sqrt{a+b x^3} \left(\frac{60 c}{x^7}+\frac{70 d}{x^6}+\frac{84 e}{x^5}+\frac{105 f}{x^4}+\frac{140 g}{x^3}\right)-\frac{3 b c \sqrt{a+b x^3}}{56 a x^4}-\frac{b d \sqrt{a+b x^3}}{12 a x^3}-\frac{3 b e \sqrt{a+b x^3}}{20 a x^2}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(28 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (5 b c-14 a f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{560 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 b^{4/3} \sqrt{a+b x^3} (5 b c-14 a f)}{112 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 b c-14 a f) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b \sqrt{a+b x^3} (5 b c-14 a f)}{112 a^2 x}+\frac{b (b d-4 a g) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}-\frac{1}{420} \sqrt{a+b x^3} \left(\frac{60 c}{x^7}+\frac{70 d}{x^6}+\frac{84 e}{x^5}+\frac{105 f}{x^4}+\frac{140 g}{x^3}\right)-\frac{3 b c \sqrt{a+b x^3}}{56 a x^4}-\frac{b d \sqrt{a+b x^3}}{12 a x^3}-\frac{3 b e \sqrt{a+b x^3}}{20 a x^2}",1,"-(((60*c)/x^7 + (70*d)/x^6 + (84*e)/x^5 + (105*f)/x^4 + (140*g)/x^3)*Sqrt[a + b*x^3])/420 - (3*b*c*Sqrt[a + b*x^3])/(56*a*x^4) - (b*d*Sqrt[a + b*x^3])/(12*a*x^3) - (3*b*e*Sqrt[a + b*x^3])/(20*a*x^2) + (3*b*(5*b*c - 14*a*f)*Sqrt[a + b*x^3])/(112*a^2*x) - (3*b^(4/3)*(5*b*c - 14*a*f)*Sqrt[a + b*x^3])/(112*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (b*(b*d - 4*a*g)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(12*a^(3/2)) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(5*b*c - 14*a*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(4/3)*(28*a^(2/3)*b^(1/3)*e - 5*(1 - Sqrt[3])*(5*b*c - 14*a*f))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(560*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",12,10,35,0.2857,1,"{14, 1825, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
457,1,743,0,1.331354,"\int \frac{\sqrt{a+b x^3} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^9} \, dx","Int[(Sqrt[a + b*x^3]*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^9,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (7 b c-16 a f)+20 \left(1-\sqrt{3}\right) \sqrt[3]{a} (5 b d-14 a g)\right)}{2240 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 b^{4/3} \sqrt{a+b x^3} (5 b d-14 a g)}{112 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 b d-14 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{b^2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}+\frac{3 b \sqrt{a+b x^3} (7 b c-16 a f)}{320 a^2 x^2}+\frac{3 b \sqrt{a+b x^3} (5 b d-14 a g)}{112 a^2 x}-\frac{1}{840} \sqrt{a+b x^3} \left(\frac{105 c}{x^8}+\frac{120 d}{x^7}+\frac{140 e}{x^6}+\frac{168 f}{x^5}+\frac{210 g}{x^4}\right)-\frac{3 b c \sqrt{a+b x^3}}{80 a x^5}-\frac{3 b d \sqrt{a+b x^3}}{56 a x^4}-\frac{b e \sqrt{a+b x^3}}{12 a x^3}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (7 b c-16 a f)+20 \left(1-\sqrt{3}\right) \sqrt[3]{a} (5 b d-14 a g)\right)}{2240 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 b^{4/3} \sqrt{a+b x^3} (5 b d-14 a g)}{112 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 b d-14 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{b^2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}+\frac{3 b \sqrt{a+b x^3} (7 b c-16 a f)}{320 a^2 x^2}+\frac{3 b \sqrt{a+b x^3} (5 b d-14 a g)}{112 a^2 x}-\frac{1}{840} \sqrt{a+b x^3} \left(\frac{105 c}{x^8}+\frac{120 d}{x^7}+\frac{140 e}{x^6}+\frac{168 f}{x^5}+\frac{210 g}{x^4}\right)-\frac{3 b c \sqrt{a+b x^3}}{80 a x^5}-\frac{3 b d \sqrt{a+b x^3}}{56 a x^4}-\frac{b e \sqrt{a+b x^3}}{12 a x^3}",1,"-(((105*c)/x^8 + (120*d)/x^7 + (140*e)/x^6 + (168*f)/x^5 + (210*g)/x^4)*Sqrt[a + b*x^3])/840 - (3*b*c*Sqrt[a + b*x^3])/(80*a*x^5) - (3*b*d*Sqrt[a + b*x^3])/(56*a*x^4) - (b*e*Sqrt[a + b*x^3])/(12*a*x^3) + (3*b*(7*b*c - 16*a*f)*Sqrt[a + b*x^3])/(320*a^2*x^2) + (3*b*(5*b*d - 14*a*g)*Sqrt[a + b*x^3])/(112*a^2*x) - (3*b^(4/3)*(5*b*d - 14*a*g)*Sqrt[a + b*x^3])/(112*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (b^2*e*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(12*a^(3/2)) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(5*b*d - 14*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(4/3)*(7*b^(1/3)*(7*b*c - 16*a*f) + 20*(1 - Sqrt[3])*a^(1/3)*(5*b*d - 14*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2240*a^2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",13,10,35,0.2857,1,"{14, 1825, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
458,1,791,0,2.111225,"\int x^3 \left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right) \, dx","Int[x^3*(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x]","-\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(1729 \sqrt[3]{b} (23 b c-8 a f)-8602 \left(1-\sqrt{3}\right) \sqrt[3]{a} (5 b d-2 a g)\right)}{37182145 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x \sqrt{a+b x^3} (23 b c-8 a f)}{21505 b^2}+\frac{54 a^2 x^2 \sqrt{a+b x^3} (5 b d-2 a g)}{8645 b^2}-\frac{216 a^3 \sqrt{a+b x^3} (5 b d-2 a g)}{8645 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{108 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 b d-2 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 a^3 e \sqrt{a+b x^3}}{105 b^2}+\frac{2 a^2 e x^3 \sqrt{a+b x^3}}{105 b}+\frac{54 a^2 f x^4 \sqrt{a+b x^3}}{4301 b}+\frac{54 a^2 g x^5 \sqrt{a+b x^3}}{6175 b}+\frac{2 x^3 \left(a+b x^3\right)^{3/2} \left(229425 c x+205275 d x^2+185725 e x^3+169575 f x^4+156009 g x^5\right)}{3900225}+\frac{2 a x^3 \sqrt{a+b x^3} \left(8947575 c x+6774075 d x^2+5311735 e x^3+4279275 f x^4+3522519 g x^5\right)}{185910725}","-\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(1729 \sqrt[3]{b} (23 b c-8 a f)-8602 \left(1-\sqrt{3}\right) \sqrt[3]{a} (5 b d-2 a g)\right)}{37182145 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x \sqrt{a+b x^3} (23 b c-8 a f)}{21505 b^2}+\frac{54 a^2 x^2 \sqrt{a+b x^3} (5 b d-2 a g)}{8645 b^2}-\frac{216 a^3 \sqrt{a+b x^3} (5 b d-2 a g)}{8645 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{108 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 b d-2 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 a^3 e \sqrt{a+b x^3}}{105 b^2}+\frac{2 a^2 e x^3 \sqrt{a+b x^3}}{105 b}+\frac{54 a^2 f x^4 \sqrt{a+b x^3}}{4301 b}+\frac{54 a^2 g x^5 \sqrt{a+b x^3}}{6175 b}+\frac{2 x^3 \left(a+b x^3\right)^{3/2} \left(229425 c x+205275 d x^2+185725 e x^3+169575 f x^4+156009 g x^5\right)}{3900225}+\frac{2 a x^3 \sqrt{a+b x^3} \left(8947575 c x+6774075 d x^2+5311735 e x^3+4279275 f x^4+3522519 g x^5\right)}{185910725}",1,"(-4*a^3*e*Sqrt[a + b*x^3])/(105*b^2) + (54*a^2*(23*b*c - 8*a*f)*x*Sqrt[a + b*x^3])/(21505*b^2) + (54*a^2*(5*b*d - 2*a*g)*x^2*Sqrt[a + b*x^3])/(8645*b^2) + (2*a^2*e*x^3*Sqrt[a + b*x^3])/(105*b) + (54*a^2*f*x^4*Sqrt[a + b*x^3])/(4301*b) + (54*a^2*g*x^5*Sqrt[a + b*x^3])/(6175*b) - (216*a^3*(5*b*d - 2*a*g)*Sqrt[a + b*x^3])/(8645*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*x^3*(a + b*x^3)^(3/2)*(229425*c*x + 205275*d*x^2 + 185725*e*x^3 + 169575*f*x^4 + 156009*g*x^5))/3900225 + (2*a*x^3*Sqrt[a + b*x^3]*(8947575*c*x + 6774075*d*x^2 + 5311735*e*x^3 + 4279275*f*x^4 + 3522519*g*x^5))/185910725 + (108*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(10/3)*(5*b*d - 2*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(8645*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (36*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^3*(1729*b^(1/3)*(23*b*c - 8*a*f) - 8602*(1 - Sqrt[3])*a^(1/3)*(5*b*d - 2*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(37182145*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",14,9,35,0.2571,1,"{1826, 1836, 1888, 1594, 1886, 261, 1878, 218, 1877}"
459,1,742,0,1.5522219,"\int x^2 \left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right) \, dx","Int[x^2*(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x]","\frac{2 a^2 \sqrt{a+b x^3} (7 b c-2 a f)}{105 b^2}+\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(43010 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-1729 (23 b d-8 a g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{37182145 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x \sqrt{a+b x^3} (23 b d-8 a g)}{21505 b^2}-\frac{216 a^3 e \sqrt{a+b x^3}}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{108 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 e x^2 \sqrt{a+b x^3}}{1729 b}+\frac{2 a^2 f x^3 \sqrt{a+b x^3}}{105 b}+\frac{54 a^2 g x^4 \sqrt{a+b x^3}}{4301 b}+\frac{2 x^2 \left(a+b x^3\right)^{3/2} \left(52003 c x+45885 d x^2+41055 e x^3+37145 f x^4+33915 g x^5\right)}{780045}+\frac{2 a x^2 \sqrt{a+b x^3} \left(7436429 c x+5368545 d x^2+4064445 e x^3+3187041 f x^4+2567565 g x^5\right)}{111546435}","\frac{2 a^2 \sqrt{a+b x^3} (7 b c-2 a f)}{105 b^2}+\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(43010 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-1729 (23 b d-8 a g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{37182145 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x \sqrt{a+b x^3} (23 b d-8 a g)}{21505 b^2}-\frac{216 a^3 e \sqrt{a+b x^3}}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{108 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 e x^2 \sqrt{a+b x^3}}{1729 b}+\frac{2 a^2 f x^3 \sqrt{a+b x^3}}{105 b}+\frac{54 a^2 g x^4 \sqrt{a+b x^3}}{4301 b}+\frac{2 x^2 \left(a+b x^3\right)^{3/2} \left(52003 c x+45885 d x^2+41055 e x^3+37145 f x^4+33915 g x^5\right)}{780045}+\frac{2 a x^2 \sqrt{a+b x^3} \left(7436429 c x+5368545 d x^2+4064445 e x^3+3187041 f x^4+2567565 g x^5\right)}{111546435}",1,"(2*a^2*(7*b*c - 2*a*f)*Sqrt[a + b*x^3])/(105*b^2) + (54*a^2*(23*b*d - 8*a*g)*x*Sqrt[a + b*x^3])/(21505*b^2) + (54*a^2*e*x^2*Sqrt[a + b*x^3])/(1729*b) + (2*a^2*f*x^3*Sqrt[a + b*x^3])/(105*b) + (54*a^2*g*x^4*Sqrt[a + b*x^3])/(4301*b) - (216*a^3*e*Sqrt[a + b*x^3])/(1729*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*x^2*(a + b*x^3)^(3/2)*(52003*c*x + 45885*d*x^2 + 41055*e*x^3 + 37145*f*x^4 + 33915*g*x^5))/780045 + (2*a*x^2*Sqrt[a + b*x^3]*(7436429*c*x + 5368545*d*x^2 + 4064445*e*x^3 + 3187041*f*x^4 + 2567565*g*x^5))/111546435 + (108*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(10/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (36*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^3*(43010*(1 - Sqrt[3])*a^(1/3)*b^(2/3)*e - 1729*(23*b*d - 8*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(37182145*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",12,9,35,0.2571,1,"{1826, 1836, 1888, 1594, 1886, 261, 1878, 218, 1877}"
460,1,723,0,1.2386536,"\int x \left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right) \, dx","Int[x*(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x]","-\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(3458 a^{2/3} \sqrt[3]{b} e+935 \left(1-\sqrt{3}\right) (19 b c-4 a f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1616615 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 \sqrt{a+b x^3} (19 b c-4 a f)}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 b c-4 a f) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 a^2 \sqrt{a+b x^3} (7 b d-2 a g)}{105 b^2}+\frac{54 a^2 e x \sqrt{a+b x^3}}{935 b}+\frac{54 a^2 f x^2 \sqrt{a+b x^3}}{1729 b}+\frac{2 a^2 g x^3 \sqrt{a+b x^3}}{105 b}+\frac{2 x \left(a+b x^3\right)^{3/2} \left(33915 c x+29393 d x^2+25935 e x^3+23205 f x^4+20995 g x^5\right)}{440895}+\frac{2 a x \sqrt{a+b x^3} \left(479655 c x+323323 d x^2+233415 e x^3+176715 f x^4+138567 g x^5\right)}{4849845}","-\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(3458 a^{2/3} \sqrt[3]{b} e+935 \left(1-\sqrt{3}\right) (19 b c-4 a f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1616615 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 \sqrt{a+b x^3} (19 b c-4 a f)}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 b c-4 a f) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 a^2 \sqrt{a+b x^3} (7 b d-2 a g)}{105 b^2}+\frac{54 a^2 e x \sqrt{a+b x^3}}{935 b}+\frac{54 a^2 f x^2 \sqrt{a+b x^3}}{1729 b}+\frac{2 a^2 g x^3 \sqrt{a+b x^3}}{105 b}+\frac{2 x \left(a+b x^3\right)^{3/2} \left(33915 c x+29393 d x^2+25935 e x^3+23205 f x^4+20995 g x^5\right)}{440895}+\frac{2 a x \sqrt{a+b x^3} \left(479655 c x+323323 d x^2+233415 e x^3+176715 f x^4+138567 g x^5\right)}{4849845}",1,"(2*a^2*(7*b*d - 2*a*g)*Sqrt[a + b*x^3])/(105*b^2) + (54*a^2*e*x*Sqrt[a + b*x^3])/(935*b) + (54*a^2*f*x^2*Sqrt[a + b*x^3])/(1729*b) + (2*a^2*g*x^3*Sqrt[a + b*x^3])/(105*b) + (54*a^2*(19*b*c - 4*a*f)*Sqrt[a + b*x^3])/(1729*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*x*(a + b*x^3)^(3/2)*(33915*c*x + 29393*d*x^2 + 25935*e*x^3 + 23205*f*x^4 + 20995*g*x^5))/440895 + (2*a*x*Sqrt[a + b*x^3]*(479655*c*x + 323323*d*x^2 + 233415*e*x^3 + 176715*f*x^4 + 138567*g*x^5))/4849845 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(19*b*c - 4*a*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (18*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^(7/3)*(3458*a^(2/3)*b^(1/3)*e + 935*(1 - Sqrt[3])*(19*b*c - 4*a*f))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1616615*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",10,8,33,0.2424,1,"{1826, 1836, 1888, 1886, 261, 1878, 218, 1877}"
461,1,694,0,0.899239,"\int \left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right) \, dx","Int[(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x]","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(1729 \sqrt[3]{b} (17 b c-2 a f)-935 \left(1-\sqrt{3}\right) \sqrt[3]{a} (19 b d-4 a g)\right)}{1616615 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 \sqrt{a+b x^3} (19 b d-4 a g)}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 b d-4 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 a^2 e \sqrt{a+b x^3}}{15 b}+\frac{54 a^2 f x \sqrt{a+b x^3}}{935 b}+\frac{54 a^2 g x^2 \sqrt{a+b x^3}}{1729 b}+\frac{2 a \sqrt{a+b x^3} \left(793611 c x+479655 d x^2+323323 e x^3+233415 f x^4+176715 g x^5\right)}{4849845}+\frac{2 \left(a+b x^3\right)^{3/2} \left(62985 c x+53295 d x^2+46189 e x^3+40755 f x^4+36465 g x^5\right)}{692835}","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(1729 \sqrt[3]{b} (17 b c-2 a f)-935 \left(1-\sqrt{3}\right) \sqrt[3]{a} (19 b d-4 a g)\right)}{1616615 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 \sqrt{a+b x^3} (19 b d-4 a g)}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 b d-4 a g) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 a^2 e \sqrt{a+b x^3}}{15 b}+\frac{54 a^2 f x \sqrt{a+b x^3}}{935 b}+\frac{54 a^2 g x^2 \sqrt{a+b x^3}}{1729 b}+\frac{2 a \sqrt{a+b x^3} \left(793611 c x+479655 d x^2+323323 e x^3+233415 f x^4+176715 g x^5\right)}{4849845}+\frac{2 \left(a+b x^3\right)^{3/2} \left(62985 c x+53295 d x^2+46189 e x^3+40755 f x^4+36465 g x^5\right)}{692835}",1,"(2*a^2*e*Sqrt[a + b*x^3])/(15*b) + (54*a^2*f*x*Sqrt[a + b*x^3])/(935*b) + (54*a^2*g*x^2*Sqrt[a + b*x^3])/(1729*b) + (54*a^2*(19*b*d - 4*a*g)*Sqrt[a + b*x^3])/(1729*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*(a + b*x^3)^(3/2)*(62985*c*x + 53295*d*x^2 + 46189*e*x^3 + 40755*f*x^4 + 36465*g*x^5))/692835 + (2*a*Sqrt[a + b*x^3]*(793611*c*x + 479655*d*x^2 + 323323*e*x^3 + 233415*f*x^4 + 176715*g*x^5))/4849845 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(19*b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (18*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(1729*b^(1/3)*(17*b*c - 2*a*f) - 935*(1 - Sqrt[3])*a^(1/3)*(19*b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1616615*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",9,7,32,0.2188,1,"{1853, 1888, 1886, 261, 1878, 218, 1877}"
462,1,676,0,0.7070642,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x,x]","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-935 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-182 a g+1547 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{85085 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 e \sqrt{a+b x^3}}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2}{3} a^{3/2} c \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 a^2 f \sqrt{a+b x^3}}{15 b}+\frac{54 a^2 g x \sqrt{a+b x^3}}{935 b}+\frac{2 a \sqrt{a+b x^3} \left(85085 c x+41769 d x^2+25245 e x^3+17017 f x^4+12285 g x^5\right)}{255255 x}+\frac{2 \left(a+b x^3\right)^{3/2} \left(12155 c x+9945 d x^2+8415 e x^3+7293 f x^4+6435 g x^5\right)}{109395 x}","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-935 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-182 a g+1547 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{85085 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 e \sqrt{a+b x^3}}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2}{3} a^{3/2} c \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 a^2 f \sqrt{a+b x^3}}{15 b}+\frac{54 a^2 g x \sqrt{a+b x^3}}{935 b}+\frac{2 a \sqrt{a+b x^3} \left(85085 c x+41769 d x^2+25245 e x^3+17017 f x^4+12285 g x^5\right)}{255255 x}+\frac{2 \left(a+b x^3\right)^{3/2} \left(12155 c x+9945 d x^2+8415 e x^3+7293 f x^4+6435 g x^5\right)}{109395 x}",1,"(2*a^2*f*Sqrt[a + b*x^3])/(15*b) + (54*a^2*g*x*Sqrt[a + b*x^3])/(935*b) + (54*a^2*e*Sqrt[a + b*x^3])/(91*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*(a + b*x^3)^(3/2)*(12155*c*x + 9945*d*x^2 + 8415*e*x^3 + 7293*f*x^4 + 6435*g*x^5))/(109395*x) + (2*a*Sqrt[a + b*x^3]*(85085*c*x + 41769*d*x^2 + 25245*e*x^3 + 17017*f*x^4 + 12285*g*x^5))/(255255*x) - (2*a^(3/2)*c*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (18*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(1547*b*d - 935*(1 - Sqrt[3])*a^(1/3)*b^(2/3)*e - 182*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(85085*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",12,11,35,0.3143,1,"{1826, 1832, 266, 63, 208, 1888, 1886, 261, 1878, 218, 1877}"
463,1,692,0,0.7905456,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^2} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^2,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(182 a^{2/3} \sqrt[3]{b} e-55 \left(1-\sqrt{3}\right) (2 a f+13 b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5005 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a f+13 b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{182 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2}{3} a^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 a^2 g \sqrt{a+b x^3}}{15 b}+\frac{27 a \sqrt{a+b x^3} (2 a f+13 b c)}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 a \sqrt{a+b x^3} \left(19305 c x+5005 d x^2+2457 e x^3+1485 f x^4+1001 g x^5\right)}{15015 x^2}+\frac{2 \left(a+b x^3\right)^{3/2} \left(6435 c x+5005 d x^2+4095 e x^3+3465 f x^4+3003 g x^5\right)}{45045 x^2}-\frac{27 a c \sqrt{a+b x^3}}{7 x}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(182 a^{2/3} \sqrt[3]{b} e-55 \left(1-\sqrt{3}\right) (2 a f+13 b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5005 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a f+13 b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{182 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2}{3} a^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 a^2 g \sqrt{a+b x^3}}{15 b}+\frac{27 a \sqrt{a+b x^3} (2 a f+13 b c)}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 a \sqrt{a+b x^3} \left(19305 c x+5005 d x^2+2457 e x^3+1485 f x^4+1001 g x^5\right)}{15015 x^2}+\frac{2 \left(a+b x^3\right)^{3/2} \left(6435 c x+5005 d x^2+4095 e x^3+3465 f x^4+3003 g x^5\right)}{45045 x^2}-\frac{27 a c \sqrt{a+b x^3}}{7 x}",1,"(2*a^2*g*Sqrt[a + b*x^3])/(15*b) - (27*a*c*Sqrt[a + b*x^3])/(7*x) + (27*a*(13*b*c + 2*a*f)*Sqrt[a + b*x^3])/(91*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*a*Sqrt[a + b*x^3]*(19305*c*x + 5005*d*x^2 + 2457*e*x^3 + 1485*f*x^4 + 1001*g*x^5))/(15015*x^2) + (2*(a + b*x^3)^(3/2)*(6435*c*x + 5005*d*x^2 + 4095*e*x^3 + 3465*f*x^4 + 3003*g*x^5))/(45045*x^2) - (2*a^(3/2)*d*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(13*b*c + 2*a*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(182*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^(4/3)*(182*a^(2/3)*b^(1/3)*e - 55*(1 - Sqrt[3])*(13*b*c + 2*a*f))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(5005*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",12,11,35,0.3143,1,"{1826, 1835, 1832, 266, 63, 208, 1886, 261, 1878, 218, 1877}"
464,1,694,0,0.8875168,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^3} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^3,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(91 \sqrt[3]{b} (4 a f+11 b c)-110 \left(1-\sqrt{3}\right) \sqrt[3]{a} (2 a g+13 b d)\right)}{10010 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a g+13 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{182 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2}{3} a^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{27 a \sqrt{a+b x^3} (2 a g+13 b d)}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 a \sqrt{a+b x^3} \left(27027 c x-19305 d x^2-5005 e x^3-2457 f x^4-1485 g x^5\right)}{15015 x^3}+\frac{2 \left(a+b x^3\right)^{3/2} \left(9009 c x+6435 d x^2+5005 e x^3+4095 f x^4+3465 g x^5\right)}{45045 x^3}+\frac{27 a c \sqrt{a+b x^3}}{10 x^2}-\frac{27 a d \sqrt{a+b x^3}}{7 x}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(91 \sqrt[3]{b} (4 a f+11 b c)-110 \left(1-\sqrt{3}\right) \sqrt[3]{a} (2 a g+13 b d)\right)}{10010 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a g+13 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{182 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2}{3} a^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{27 a \sqrt{a+b x^3} (2 a g+13 b d)}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 a \sqrt{a+b x^3} \left(27027 c x-19305 d x^2-5005 e x^3-2457 f x^4-1485 g x^5\right)}{15015 x^3}+\frac{2 \left(a+b x^3\right)^{3/2} \left(9009 c x+6435 d x^2+5005 e x^3+4095 f x^4+3465 g x^5\right)}{45045 x^3}+\frac{27 a c \sqrt{a+b x^3}}{10 x^2}-\frac{27 a d \sqrt{a+b x^3}}{7 x}",1,"(27*a*c*Sqrt[a + b*x^3])/(10*x^2) - (27*a*d*Sqrt[a + b*x^3])/(7*x) + (27*a*(13*b*d + 2*a*g)*Sqrt[a + b*x^3])/(91*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*a*Sqrt[a + b*x^3]*(27027*c*x - 19305*d*x^2 - 5005*e*x^3 - 2457*f*x^4 - 1485*g*x^5))/(15015*x^3) + (2*(a + b*x^3)^(3/2)*(9009*c*x + 6435*d*x^2 + 5005*e*x^3 + 4095*f*x^4 + 3465*g*x^5))/(45045*x^3) - (2*a^(3/2)*e*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(13*b*d + 2*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(182*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*(91*b^(1/3)*(11*b*c + 4*a*f) - 110*(1 - Sqrt[3])*a^(1/3)*(13*b*d + 2*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(10010*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",11,9,35,0.2571,1,"{1826, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
465,1,692,0,0.9565846,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^4} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^4,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-110 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e+28 a g+77 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{770 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \sqrt[3]{b} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \left(a+b x^3\right)^{3/2} \left(1155 c x+693 d x^2+495 e x^3+385 f x^4+315 g x^5\right)}{3465 x^4}-\frac{2 a \sqrt{a+b x^3} \left(1155 c x+2079 d x^2-1485 e x^3-385 f x^4-189 g x^5\right)}{1155 x^4}-\frac{1}{3} \sqrt{a} (2 a f+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{a c \sqrt{a+b x^3}}{x^3}+\frac{27 a d \sqrt{a+b x^3}}{10 x^2}-\frac{27 a e \sqrt{a+b x^3}}{7 x}+\frac{27 a \sqrt[3]{b} e \sqrt{a+b x^3}}{7 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-110 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e+28 a g+77 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{770 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \sqrt[3]{b} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \left(a+b x^3\right)^{3/2} \left(1155 c x+693 d x^2+495 e x^3+385 f x^4+315 g x^5\right)}{3465 x^4}-\frac{2 a \sqrt{a+b x^3} \left(1155 c x+2079 d x^2-1485 e x^3-385 f x^4-189 g x^5\right)}{1155 x^4}-\frac{1}{3} \sqrt{a} (2 a f+3 b c) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{a c \sqrt{a+b x^3}}{x^3}+\frac{27 a d \sqrt{a+b x^3}}{10 x^2}-\frac{27 a e \sqrt{a+b x^3}}{7 x}+\frac{27 a \sqrt[3]{b} e \sqrt{a+b x^3}}{7 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(a*c*Sqrt[a + b*x^3])/x^3 + (27*a*d*Sqrt[a + b*x^3])/(10*x^2) - (27*a*e*Sqrt[a + b*x^3])/(7*x) + (27*a*b^(1/3)*e*Sqrt[a + b*x^3])/(7*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*a*Sqrt[a + b*x^3]*(1155*c*x + 2079*d*x^2 - 1485*e*x^3 - 385*f*x^4 - 189*g*x^5))/(1155*x^4) + (2*(a + b*x^3)^(3/2)*(1155*c*x + 693*d*x^2 + 495*e*x^3 + 385*f*x^4 + 315*g*x^5))/(3465*x^4) - (Sqrt[a]*(3*b*c + 2*a*f)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*b^(1/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(14*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*(77*b*d - 110*(1 - Sqrt[3])*a^(1/3)*b^(2/3)*e + 28*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(770*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",12,9,35,0.2571,1,"{1826, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
466,1,741,0,1.240174,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^5} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^5,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(28 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (8 a f+7 b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{280 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a f+7 b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{112 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \left(a+b x^3\right)^{3/2} \left(315 c x+105 d x^2+63 e x^3+45 f x^4+35 g x^5\right)}{315 x^5}-\frac{2 a \sqrt{a+b x^3} \left(189 c x+105 d x^2+189 e x^3-135 f x^4-35 g x^5\right)}{105 x^5}-\frac{27 \sqrt{a+b x^3} (8 a f+7 b c)}{56 x}+\frac{27 \sqrt[3]{b} \sqrt{a+b x^3} (8 a f+7 b c)}{56 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{27 a c \sqrt{a+b x^3}}{20 x^4}-\frac{1}{3} \sqrt{a} (2 a g+3 b d) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{a d \sqrt{a+b x^3}}{x^3}+\frac{27 a e \sqrt{a+b x^3}}{10 x^2}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(28 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (8 a f+7 b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{280 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a f+7 b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{112 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \left(a+b x^3\right)^{3/2} \left(315 c x+105 d x^2+63 e x^3+45 f x^4+35 g x^5\right)}{315 x^5}-\frac{2 a \sqrt{a+b x^3} \left(189 c x+105 d x^2+189 e x^3-135 f x^4-35 g x^5\right)}{105 x^5}-\frac{27 \sqrt{a+b x^3} (8 a f+7 b c)}{56 x}+\frac{27 \sqrt[3]{b} \sqrt{a+b x^3} (8 a f+7 b c)}{56 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{27 a c \sqrt{a+b x^3}}{20 x^4}-\frac{1}{3} \sqrt{a} (2 a g+3 b d) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{a d \sqrt{a+b x^3}}{x^3}+\frac{27 a e \sqrt{a+b x^3}}{10 x^2}",1,"(27*a*c*Sqrt[a + b*x^3])/(20*x^4) + (a*d*Sqrt[a + b*x^3])/x^3 + (27*a*e*Sqrt[a + b*x^3])/(10*x^2) - (27*(7*b*c + 8*a*f)*Sqrt[a + b*x^3])/(56*x) + (27*b^(1/3)*(7*b*c + 8*a*f)*Sqrt[a + b*x^3])/(56*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (2*a*Sqrt[a + b*x^3]*(189*c*x + 105*d*x^2 + 189*e*x^3 - 135*f*x^4 - 35*g*x^5))/(105*x^5) + (2*(a + b*x^3)^(3/2)*(315*c*x + 105*d*x^2 + 63*e*x^3 + 45*f*x^4 + 35*g*x^5))/(315*x^5) - (Sqrt[a]*(3*b*d + 2*a*g)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(1/3)*(7*b*c + 8*a*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(112*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*b^(1/3)*(28*a^(2/3)*b^(1/3)*e - 5*(1 - Sqrt[3])*(7*b*c + 8*a*f))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(280*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",13,9,35,0.2571,1,"{1826, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
467,1,689,0,0.9209221,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^6} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^6,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(14 \sqrt[3]{b} (2 a f+b c)-5 \left(1-\sqrt{3}\right) \sqrt[3]{a} (8 a g+7 b d)\right)}{280 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a g+7 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{112 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{1}{60} \left(a+b x^3\right)^{3/2} \left(\frac{12 c}{x^5}+\frac{15 d}{x^4}+\frac{20 e}{x^3}+\frac{30 f}{x^2}+\frac{60 g}{x}\right)-\frac{b \sqrt{a+b x^3} \left(252 c x-315 d x^2-140 e x^3-126 f x^4-180 g x^5\right)}{140 x^3}+\frac{27 b c \sqrt{a+b x^3}}{20 x^2}+\frac{27 \sqrt[3]{b} \sqrt{a+b x^3} (8 a g+7 b d)}{56 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 b d \sqrt{a+b x^3}}{8 x}-\sqrt{a} b e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(14 \sqrt[3]{b} (2 a f+b c)-5 \left(1-\sqrt{3}\right) \sqrt[3]{a} (8 a g+7 b d)\right)}{280 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a g+7 b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{112 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{1}{60} \left(a+b x^3\right)^{3/2} \left(\frac{12 c}{x^5}+\frac{15 d}{x^4}+\frac{20 e}{x^3}+\frac{30 f}{x^2}+\frac{60 g}{x}\right)-\frac{b \sqrt{a+b x^3} \left(252 c x-315 d x^2-140 e x^3-126 f x^4-180 g x^5\right)}{140 x^3}+\frac{27 b c \sqrt{a+b x^3}}{20 x^2}+\frac{27 \sqrt[3]{b} \sqrt{a+b x^3} (8 a g+7 b d)}{56 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 b d \sqrt{a+b x^3}}{8 x}-\sqrt{a} b e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)",1,"(27*b*c*Sqrt[a + b*x^3])/(20*x^2) - (27*b*d*Sqrt[a + b*x^3])/(8*x) + (27*b^(1/3)*(7*b*d + 8*a*g)*Sqrt[a + b*x^3])/(56*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (((12*c)/x^5 + (15*d)/x^4 + (20*e)/x^3 + (30*f)/x^2 + (60*g)/x)*(a + b*x^3)^(3/2))/60 - (b*Sqrt[a + b*x^3]*(252*c*x - 315*d*x^2 - 140*e*x^3 - 126*f*x^4 - 180*g*x^5))/(140*x^3) - Sqrt[a]*b*e*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]] - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(1/3)*(7*b*d + 8*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(112*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(1/3)*(14*b^(1/3)*(b*c + 2*a*f) - 5*(1 - Sqrt[3])*a^(1/3)*(7*b*d + 8*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(280*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",11,11,35,0.3143,1,"{14, 1825, 1826, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
468,1,692,0,1.0041747,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^7} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^7,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-5 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e+4 a g+2 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{40 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} b^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 b^{4/3} e \sqrt{a+b x^3}}{8 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{1}{60} \left(a+b x^3\right)^{3/2} \left(\frac{10 c}{x^6}+\frac{12 d}{x^5}+\frac{15 e}{x^4}+\frac{20 f}{x^3}+\frac{30 g}{x^2}\right)-\frac{b \sqrt{a+b x^3} \left(10 c x+36 d x^2-45 e x^3-20 f x^4-18 g x^5\right)}{20 x^4}-\frac{b (4 a f+b c) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{b c \sqrt{a+b x^3}}{4 x^3}+\frac{27 b d \sqrt{a+b x^3}}{20 x^2}-\frac{27 b e \sqrt{a+b x^3}}{8 x}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(-5 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e+4 a g+2 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{40 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} b^{4/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 b^{4/3} e \sqrt{a+b x^3}}{8 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{1}{60} \left(a+b x^3\right)^{3/2} \left(\frac{10 c}{x^6}+\frac{12 d}{x^5}+\frac{15 e}{x^4}+\frac{20 f}{x^3}+\frac{30 g}{x^2}\right)-\frac{b \sqrt{a+b x^3} \left(10 c x+36 d x^2-45 e x^3-20 f x^4-18 g x^5\right)}{20 x^4}-\frac{b (4 a f+b c) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{b c \sqrt{a+b x^3}}{4 x^3}+\frac{27 b d \sqrt{a+b x^3}}{20 x^2}-\frac{27 b e \sqrt{a+b x^3}}{8 x}",1,"(b*c*Sqrt[a + b*x^3])/(4*x^3) + (27*b*d*Sqrt[a + b*x^3])/(20*x^2) - (27*b*e*Sqrt[a + b*x^3])/(8*x) + (27*b^(4/3)*e*Sqrt[a + b*x^3])/(8*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (((10*c)/x^6 + (12*d)/x^5 + (15*e)/x^4 + (20*f)/x^3 + (30*g)/x^2)*(a + b*x^3)^(3/2))/60 - (b*Sqrt[a + b*x^3]*(10*c*x + 36*d*x^2 - 45*e*x^3 - 20*f*x^4 - 18*g*x^5))/(20*x^4) - (b*(b*c + 4*a*f)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(4*Sqrt[a]) - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(4/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(2/3)*(2*b*d - 5*(1 - Sqrt[3])*a^(1/3)*b^(2/3)*e + 4*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(40*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",12,11,35,0.3143,1,"{14, 1825, 1826, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
469,1,746,0,1.2836722,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^8} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^8,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(28 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (14 a f+b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{560 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (14 a f+b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 b^{4/3} \sqrt{a+b x^3} (14 a f+b c)}{112 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{1}{420} \left(a+b x^3\right)^{3/2} \left(\frac{60 c}{x^7}+\frac{70 d}{x^6}+\frac{84 e}{x^5}+\frac{105 f}{x^4}+\frac{140 g}{x^3}\right)-\frac{b \sqrt{a+b x^3} \left(36 c x+70 d x^2+252 e x^3-315 f x^4-140 g x^5\right)}{140 x^5}-\frac{27 b \sqrt{a+b x^3} (14 a f+b c)}{112 a x}+\frac{27 b c \sqrt{a+b x^3}}{280 x^4}-\frac{b (4 a g+b d) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{b d \sqrt{a+b x^3}}{4 x^3}+\frac{27 b e \sqrt{a+b x^3}}{20 x^2}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(28 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (14 a f+b c)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{560 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (14 a f+b c) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 b^{4/3} \sqrt{a+b x^3} (14 a f+b c)}{112 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{1}{420} \left(a+b x^3\right)^{3/2} \left(\frac{60 c}{x^7}+\frac{70 d}{x^6}+\frac{84 e}{x^5}+\frac{105 f}{x^4}+\frac{140 g}{x^3}\right)-\frac{b \sqrt{a+b x^3} \left(36 c x+70 d x^2+252 e x^3-315 f x^4-140 g x^5\right)}{140 x^5}-\frac{27 b \sqrt{a+b x^3} (14 a f+b c)}{112 a x}+\frac{27 b c \sqrt{a+b x^3}}{280 x^4}-\frac{b (4 a g+b d) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{b d \sqrt{a+b x^3}}{4 x^3}+\frac{27 b e \sqrt{a+b x^3}}{20 x^2}",1,"(27*b*c*Sqrt[a + b*x^3])/(280*x^4) + (b*d*Sqrt[a + b*x^3])/(4*x^3) + (27*b*e*Sqrt[a + b*x^3])/(20*x^2) - (27*b*(b*c + 14*a*f)*Sqrt[a + b*x^3])/(112*a*x) + (27*b^(4/3)*(b*c + 14*a*f)*Sqrt[a + b*x^3])/(112*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (((60*c)/x^7 + (70*d)/x^6 + (84*e)/x^5 + (105*f)/x^4 + (140*g)/x^3)*(a + b*x^3)^(3/2))/420 - (b*Sqrt[a + b*x^3]*(36*c*x + 70*d*x^2 + 252*e*x^3 - 315*f*x^4 - 140*g*x^5))/(140*x^5) - (b*(b*d + 4*a*g)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(4*Sqrt[a]) - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(b*c + 14*a*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(4/3)*(28*a^(2/3)*b^(1/3)*e - 5*(1 - Sqrt[3])*(b*c + 14*a*f))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(560*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",13,11,35,0.3143,1,"{14, 1825, 1826, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
470,1,705,0,1.0079201,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^9} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^9,x]","-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (b c-16 a f)+20 \left(1-\sqrt{3}\right) \sqrt[3]{a} (14 a g+b d)\right)}{2240 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (14 a g+b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 b^2 c \sqrt{a+b x^3}}{320 a x^2}+\frac{27 b^{4/3} \sqrt{a+b x^3} (14 a g+b d)}{112 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 b^2 d \sqrt{a+b x^3}}{112 a x}-\frac{b^2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{1}{560} b \sqrt{a+b x^3} \left(\frac{63 c}{x^5}+\frac{90 d}{x^4}+\frac{140 e}{x^3}+\frac{252 f}{x^2}+\frac{630 g}{x}\right)-\frac{1}{840} \left(a+b x^3\right)^{3/2} \left(\frac{105 c}{x^8}+\frac{120 d}{x^7}+\frac{140 e}{x^6}+\frac{168 f}{x^5}+\frac{210 g}{x^4}\right)","-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) \left(7 \sqrt[3]{b} (b c-16 a f)+20 \left(1-\sqrt{3}\right) \sqrt[3]{a} (14 a g+b d)\right)}{2240 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (14 a g+b d) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 b^2 c \sqrt{a+b x^3}}{320 a x^2}+\frac{27 b^{4/3} \sqrt{a+b x^3} (14 a g+b d)}{112 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 b^2 d \sqrt{a+b x^3}}{112 a x}-\frac{b^2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{1}{560} b \sqrt{a+b x^3} \left(\frac{63 c}{x^5}+\frac{90 d}{x^4}+\frac{140 e}{x^3}+\frac{252 f}{x^2}+\frac{630 g}{x}\right)-\frac{1}{840} \left(a+b x^3\right)^{3/2} \left(\frac{105 c}{x^8}+\frac{120 d}{x^7}+\frac{140 e}{x^6}+\frac{168 f}{x^5}+\frac{210 g}{x^4}\right)",1,"-(b*((63*c)/x^5 + (90*d)/x^4 + (140*e)/x^3 + (252*f)/x^2 + (630*g)/x)*Sqrt[a + b*x^3])/560 - (27*b^2*c*Sqrt[a + b*x^3])/(320*a*x^2) - (27*b^2*d*Sqrt[a + b*x^3])/(112*a*x) + (27*b^(4/3)*(b*d + 14*a*g)*Sqrt[a + b*x^3])/(112*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (((105*c)/x^8 + (120*d)/x^7 + (140*e)/x^6 + (168*f)/x^5 + (210*g)/x^4)*(a + b*x^3)^(3/2))/840 - (b^2*e*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(4*Sqrt[a]) - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(b*d + 14*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(4/3)*(7*b^(1/3)*(b*c - 16*a*f) + 20*(1 - Sqrt[3])*a^(1/3)*(b*d + 14*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2240*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",11,10,35,0.2857,1,"{14, 1825, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
471,1,714,0,1.1229913,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^{10}} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^10,x]","\frac{b^2 (b c-6 a f) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{24 a^{3/2}}-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(20 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-112 a g+7 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2240 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{b^2 c \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 d \sqrt{a+b x^3}}{320 a x^2}+\frac{27 b^{7/3} e \sqrt{a+b x^3}}{112 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 b^2 e \sqrt{a+b x^3}}{112 a x}-\frac{b \sqrt{a+b x^3} \left(\frac{140 c}{x^6}+\frac{189 d}{x^5}+\frac{270 e}{x^4}+\frac{420 f}{x^3}+\frac{756 g}{x^2}\right)}{1680}-\frac{\left(a+b x^3\right)^{3/2} \left(\frac{280 c}{x^9}+\frac{315 d}{x^8}+\frac{360 e}{x^7}+\frac{420 f}{x^6}+\frac{504 g}{x^5}\right)}{2520}","\frac{b^2 (b c-6 a f) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{24 a^{3/2}}-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(20 \left(1-\sqrt{3}\right) \sqrt[3]{a} b^{2/3} e-112 a g+7 b d\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2240 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{b^2 c \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 d \sqrt{a+b x^3}}{320 a x^2}+\frac{27 b^{7/3} e \sqrt{a+b x^3}}{112 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{27 b^2 e \sqrt{a+b x^3}}{112 a x}-\frac{b \sqrt{a+b x^3} \left(\frac{140 c}{x^6}+\frac{189 d}{x^5}+\frac{270 e}{x^4}+\frac{420 f}{x^3}+\frac{756 g}{x^2}\right)}{1680}-\frac{\left(a+b x^3\right)^{3/2} \left(\frac{280 c}{x^9}+\frac{315 d}{x^8}+\frac{360 e}{x^7}+\frac{420 f}{x^6}+\frac{504 g}{x^5}\right)}{2520}",1,"-(b*((140*c)/x^6 + (189*d)/x^5 + (270*e)/x^4 + (420*f)/x^3 + (756*g)/x^2)*Sqrt[a + b*x^3])/1680 - (b^2*c*Sqrt[a + b*x^3])/(24*a*x^3) - (27*b^2*d*Sqrt[a + b*x^3])/(320*a*x^2) - (27*b^2*e*Sqrt[a + b*x^3])/(112*a*x) + (27*b^(7/3)*e*Sqrt[a + b*x^3])/(112*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (((280*c)/x^9 + (315*d)/x^8 + (360*e)/x^7 + (420*f)/x^6 + (504*g)/x^5)*(a + b*x^3)^(3/2))/2520 + (b^2*(b*c - 6*a*f)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(24*a^(3/2)) - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(7/3)*e*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(5/3)*(7*b*d + 20*(1 - Sqrt[3])*a^(1/3)*b^(2/3)*e - 112*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2240*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",12,10,35,0.2857,1,"{14, 1825, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
472,1,764,0,1.3301371,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^{11}} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^11,x]","-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(7 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (b c-4 a f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2240 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 b^{7/3} \sqrt{a+b x^3} (b c-4 a f)}{448 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{27 b^2 \sqrt{a+b x^3} (b c-4 a f)}{448 a^2 x}+\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (b c-4 a f) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{896 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{b^2 (b d-6 a g) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{24 a^{3/2}}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}-\frac{b \sqrt{a+b x^3} \left(\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right)}{1680}-\frac{\left(a+b x^3\right)^{3/2} \left(\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right)}{2520}","-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(7 a^{2/3} \sqrt[3]{b} e-5 \left(1-\sqrt{3}\right) (b c-4 a f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2240 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 b^{7/3} \sqrt{a+b x^3} (b c-4 a f)}{448 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{27 b^2 \sqrt{a+b x^3} (b c-4 a f)}{448 a^2 x}+\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (b c-4 a f) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{896 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{b^2 (b d-6 a g) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{24 a^{3/2}}-\frac{27 b^2 c \sqrt{a+b x^3}}{1120 a x^4}-\frac{b^2 d \sqrt{a+b x^3}}{24 a x^3}-\frac{27 b^2 e \sqrt{a+b x^3}}{320 a x^2}-\frac{b \sqrt{a+b x^3} \left(\frac{108 c}{x^7}+\frac{140 d}{x^6}+\frac{189 e}{x^5}+\frac{270 f}{x^4}+\frac{420 g}{x^3}\right)}{1680}-\frac{\left(a+b x^3\right)^{3/2} \left(\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}+\frac{420 g}{x^6}\right)}{2520}",1,"-(b*((108*c)/x^7 + (140*d)/x^6 + (189*e)/x^5 + (270*f)/x^4 + (420*g)/x^3)*Sqrt[a + b*x^3])/1680 - (27*b^2*c*Sqrt[a + b*x^3])/(1120*a*x^4) - (b^2*d*Sqrt[a + b*x^3])/(24*a*x^3) - (27*b^2*e*Sqrt[a + b*x^3])/(320*a*x^2) + (27*b^2*(b*c - 4*a*f)*Sqrt[a + b*x^3])/(448*a^2*x) - (27*b^(7/3)*(b*c - 4*a*f)*Sqrt[a + b*x^3])/(448*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (((252*c)/x^10 + (280*d)/x^9 + (315*e)/x^8 + (360*f)/x^7 + (420*g)/x^6)*(a + b*x^3)^(3/2))/2520 + (b^2*(b*d - 6*a*g)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(24*a^(3/2)) + (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(7/3)*(b*c - 4*a*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(896*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(7/3)*(7*a^(2/3)*b^(1/3)*e - 5*(1 - Sqrt[3])*(b*c - 4*a*f))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2240*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",13,10,35,0.2857,1,"{14, 1825, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
473,1,796,0,1.5337514,"\int \frac{\left(a+b x^3\right)^{3/2} \left(c+d x+e x^2+f x^3+g x^4\right)}{x^{12}} \, dx","Int[((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^12,x]","\frac{e \tanh ^{-1}\left(\frac{\sqrt{b x^3+a}}{\sqrt{a}}\right) b^3}{24 a^{3/2}}+\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (b d-4 a g) \left(\sqrt[3]{b} x+\sqrt[3]{a}\right) \sqrt{\frac{b^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+a^{2/3}}{\left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) b^{7/3}}{896 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{b} x+\sqrt[3]{a}\right)}{\left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{b x^3+a}}+\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} \left(7 \sqrt[3]{b} (7 b c-22 a f)+110 \left(1-\sqrt{3}\right) \sqrt[3]{a} (b d-4 a g)\right) \left(\sqrt[3]{b} x+\sqrt[3]{a}\right) \sqrt{\frac{b^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+a^{2/3}}{\left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) b^{7/3}}{49280 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{b} x+\sqrt[3]{a}\right)}{\left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{b x^3+a}}-\frac{27 (b d-4 a g) \sqrt{b x^3+a} b^{7/3}}{448 a^2 \left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)}+\frac{27 (b d-4 a g) \sqrt{b x^3+a} b^2}{448 a^2 x}+\frac{27 (7 b c-22 a f) \sqrt{b x^3+a} b^2}{7040 a^2 x^2}-\frac{e \sqrt{b x^3+a} b^2}{24 a x^3}-\frac{27 d \sqrt{b x^3+a} b^2}{1120 a x^4}-\frac{27 c \sqrt{b x^3+a} b^2}{1760 a x^5}-\frac{\left(\frac{945 c}{x^8}+\frac{2970 g}{x^4}+\frac{2079 f}{x^5}+\frac{1540 e}{x^6}+\frac{1188 d}{x^7}\right) \sqrt{b x^3+a} b}{18480}-\frac{\left(\frac{2520 c}{x^{11}}+\frac{3960 g}{x^7}+\frac{3465 f}{x^8}+\frac{3080 e}{x^9}+\frac{2772 d}{x^{10}}\right) \left(b x^3+a\right)^{3/2}}{27720}","\frac{e \tanh ^{-1}\left(\frac{\sqrt{b x^3+a}}{\sqrt{a}}\right) b^3}{24 a^{3/2}}+\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (b d-4 a g) \left(\sqrt[3]{b} x+\sqrt[3]{a}\right) \sqrt{\frac{b^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+a^{2/3}}{\left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) b^{7/3}}{896 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{b} x+\sqrt[3]{a}\right)}{\left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{b x^3+a}}+\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} \left(7 \sqrt[3]{b} (7 b c-22 a f)+110 \left(1-\sqrt{3}\right) \sqrt[3]{a} (b d-4 a g)\right) \left(\sqrt[3]{b} x+\sqrt[3]{a}\right) \sqrt{\frac{b^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+a^{2/3}}{\left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) b^{7/3}}{49280 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{b} x+\sqrt[3]{a}\right)}{\left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{b x^3+a}}-\frac{27 (b d-4 a g) \sqrt{b x^3+a} b^{7/3}}{448 a^2 \left(\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)}+\frac{27 (b d-4 a g) \sqrt{b x^3+a} b^2}{448 a^2 x}+\frac{27 (7 b c-22 a f) \sqrt{b x^3+a} b^2}{7040 a^2 x^2}-\frac{e \sqrt{b x^3+a} b^2}{24 a x^3}-\frac{27 d \sqrt{b x^3+a} b^2}{1120 a x^4}-\frac{27 c \sqrt{b x^3+a} b^2}{1760 a x^5}-\frac{\left(\frac{945 c}{x^8}+\frac{2970 g}{x^4}+\frac{2079 f}{x^5}+\frac{1540 e}{x^6}+\frac{1188 d}{x^7}\right) \sqrt{b x^3+a} b}{18480}-\frac{\left(\frac{2520 c}{x^{11}}+\frac{3960 g}{x^7}+\frac{3465 f}{x^8}+\frac{3080 e}{x^9}+\frac{2772 d}{x^{10}}\right) \left(b x^3+a\right)^{3/2}}{27720}",1,"-(b*((945*c)/x^8 + (1188*d)/x^7 + (1540*e)/x^6 + (2079*f)/x^5 + (2970*g)/x^4)*Sqrt[a + b*x^3])/18480 - (27*b^2*c*Sqrt[a + b*x^3])/(1760*a*x^5) - (27*b^2*d*Sqrt[a + b*x^3])/(1120*a*x^4) - (b^2*e*Sqrt[a + b*x^3])/(24*a*x^3) + (27*b^2*(7*b*c - 22*a*f)*Sqrt[a + b*x^3])/(7040*a^2*x^2) + (27*b^2*(b*d - 4*a*g)*Sqrt[a + b*x^3])/(448*a^2*x) - (27*b^(7/3)*(b*d - 4*a*g)*Sqrt[a + b*x^3])/(448*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (((2520*c)/x^11 + (2772*d)/x^10 + (3080*e)/x^9 + (3465*f)/x^8 + (3960*g)/x^7)*(a + b*x^3)^(3/2))/27720 + (b^3*e*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(24*a^(3/2)) + (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(7/3)*(b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(896*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(7/3)*(7*b^(1/3)*(7*b*c - 22*a*f) + 110*(1 - Sqrt[3])*a^(1/3)*(b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(49280*a^2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",14,10,35,0.2857,1,"{14, 1825, 1835, 1832, 266, 63, 208, 1878, 218, 1877}"
474,1,120,0,0.0762832,"\int \left(c+d x+e x^2\right) \left(a+b x^3\right)^p \, dx","Int[(c + d*x + e*x^2)*(a + b*x^3)^p,x]","c x \left(a+b x^3\right)^p \left(\frac{b x^3}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{3},-p;\frac{4}{3};-\frac{b x^3}{a}\right)+\frac{1}{2} d x^2 \left(a+b x^3\right)^p \left(\frac{b x^3}{a}+1\right)^{-p} \, _2F_1\left(\frac{2}{3},-p;\frac{5}{3};-\frac{b x^3}{a}\right)+\frac{e \left(a+b x^3\right)^{p+1}}{3 b (p+1)}","\frac{c x \left(a+b x^3\right)^{p+1} \, _2F_1\left(1,p+\frac{4}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{a}+\frac{d x^2 \left(a+b x^3\right)^{p+1} \, _2F_1\left(1,p+\frac{5}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 a}+\frac{e \left(a+b x^3\right)^{p+1}}{3 b (p+1)}",1,"(e*(a + b*x^3)^(1 + p))/(3*b*(1 + p)) + (c*x*(a + b*x^3)^p*Hypergeometric2F1[1/3, -p, 4/3, -((b*x^3)/a)])/(1 + (b*x^3)/a)^p + (d*x^2*(a + b*x^3)^p*Hypergeometric2F1[2/3, -p, 5/3, -((b*x^3)/a)])/(2*(1 + (b*x^3)/a)^p)","A",8,7,20,0.3500,1,"{1886, 261, 1893, 246, 245, 365, 364}"
475,1,125,0,0.0911636,"\int x \left(c+d x+e x^2\right) \left(a+b x^3\right)^p \, dx","Int[x*(c + d*x + e*x^2)*(a + b*x^3)^p,x]","\frac{1}{2} c x^2 \left(a+b x^3\right)^p \left(\frac{b x^3}{a}+1\right)^{-p} \, _2F_1\left(\frac{2}{3},-p;\frac{5}{3};-\frac{b x^3}{a}\right)+\frac{d \left(a+b x^3\right)^{p+1}}{3 b (p+1)}+\frac{1}{4} e x^4 \left(a+b x^3\right)^p \left(\frac{b x^3}{a}+1\right)^{-p} \, _2F_1\left(\frac{4}{3},-p;\frac{7}{3};-\frac{b x^3}{a}\right)","\frac{c x^2 \left(a+b x^3\right)^{p+1} \, _2F_1\left(1,p+\frac{5}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 a}+\frac{d \left(a+b x^3\right)^{p+1}}{3 b (p+1)}+\frac{e x^4 \left(a+b x^3\right)^{p+1} \, _2F_1\left(1,p+\frac{7}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{4 a}",1,"(d*(a + b*x^3)^(1 + p))/(3*b*(1 + p)) + (c*x^2*(a + b*x^3)^p*Hypergeometric2F1[2/3, -p, 5/3, -((b*x^3)/a)])/(2*(1 + (b*x^3)/a)^p) + (e*x^4*(a + b*x^3)^p*Hypergeometric2F1[4/3, -p, 7/3, -((b*x^3)/a)])/(4*(1 + (b*x^3)/a)^p)","A",7,4,21,0.1905,1,"{1893, 365, 364, 261}"
476,1,125,0,0.1061316,"\int x^2 \left(c+d x+e x^2\right) \left(a+b x^3\right)^p \, dx","Int[x^2*(c + d*x + e*x^2)*(a + b*x^3)^p,x]","\frac{c \left(a+b x^3\right)^{p+1}}{3 b (p+1)}+\frac{1}{4} d x^4 \left(a+b x^3\right)^p \left(\frac{b x^3}{a}+1\right)^{-p} \, _2F_1\left(\frac{4}{3},-p;\frac{7}{3};-\frac{b x^3}{a}\right)+\frac{1}{5} e x^5 \left(a+b x^3\right)^p \left(\frac{b x^3}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{3},-p;\frac{8}{3};-\frac{b x^3}{a}\right)","\frac{c \left(a+b x^3\right)^{p+1}}{3 b (p+1)}+\frac{d x^4 \left(a+b x^3\right)^{p+1} \, _2F_1\left(1,p+\frac{7}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{4 a}+\frac{e x^5 \left(a+b x^3\right)^{p+1} \, _2F_1\left(1,p+\frac{8}{3};\frac{8}{3};-\frac{b x^3}{a}\right)}{5 a}",1,"(c*(a + b*x^3)^(1 + p))/(3*b*(1 + p)) + (d*x^4*(a + b*x^3)^p*Hypergeometric2F1[4/3, -p, 7/3, -((b*x^3)/a)])/(4*(1 + (b*x^3)/a)^p) + (e*x^5*(a + b*x^3)^p*Hypergeometric2F1[5/3, -p, 8/3, -((b*x^3)/a)])/(5*(1 + (b*x^3)/a)^p)","A",7,4,23,0.1739,1,"{1893, 261, 365, 364}"
477,1,68,0,0.0444891,"\int \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right) \, dx","Int[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4),x]","a c x+\frac{1}{2} a d x^2+\frac{1}{3} a e x^3+\frac{1}{4} a f x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7+\frac{1}{8} b f x^8","a c x+\frac{1}{2} a d x^2+\frac{1}{3} a e x^3+\frac{1}{4} a f x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7+\frac{1}{8} b f x^8",1,"a*c*x + (a*d*x^2)/2 + (a*e*x^3)/3 + (a*f*x^4)/4 + (b*c*x^5)/5 + (b*d*x^6)/6 + (b*e*x^7)/7 + (b*f*x^8)/8","A",2,1,23,0.04348,1,"{1850}"
478,1,73,0,0.0641713,"\int x^3 \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right) \, dx","Int[x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4),x]","\frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{7} a f x^7+\frac{1}{8} b c x^8+\frac{1}{9} b d x^9+\frac{1}{10} b e x^{10}+\frac{1}{11} b f x^{11}","\frac{1}{4} a c x^4+\frac{1}{5} a d x^5+\frac{1}{6} a e x^6+\frac{1}{7} a f x^7+\frac{1}{8} b c x^8+\frac{1}{9} b d x^9+\frac{1}{10} b e x^{10}+\frac{1}{11} b f x^{11}",1,"(a*c*x^4)/4 + (a*d*x^5)/5 + (a*e*x^6)/6 + (a*f*x^7)/7 + (b*c*x^8)/8 + (b*d*x^9)/9 + (b*e*x^10)/10 + (b*f*x^11)/11","A",2,1,26,0.03846,1,"{1820}"
479,1,109,0,0.0744559,"\int \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^2 \, dx","Int[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^2,x]","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{3} a^2 e x^3+\frac{2}{5} a b c x^5+\frac{1}{3} a b d x^6+\frac{2}{7} a b e x^7+\frac{f \left(a+b x^4\right)^3}{12 b}+\frac{1}{9} b^2 c x^9+\frac{1}{10} b^2 d x^{10}+\frac{1}{11} b^2 e x^{11}","a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{3} a^2 e x^3+\frac{2}{5} a b c x^5+\frac{1}{3} a b d x^6+\frac{2}{7} a b e x^7+\frac{f \left(a+b x^4\right)^3}{12 b}+\frac{1}{9} b^2 c x^9+\frac{1}{10} b^2 d x^{10}+\frac{1}{11} b^2 e x^{11}",1,"a^2*c*x + (a^2*d*x^2)/2 + (a^2*e*x^3)/3 + (2*a*b*c*x^5)/5 + (a*b*d*x^6)/3 + (2*a*b*e*x^7)/7 + (b^2*c*x^9)/9 + (b^2*d*x^10)/10 + (b^2*e*x^11)/11 + (f*(a + b*x^4)^3)/(12*b)","A",3,2,25,0.08000,1,"{1582, 1657}"
480,1,114,0,0.0837339,"\int x^3 \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^2 \, dx","Int[x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^2,x]","\frac{1}{5} a^2 d x^5+\frac{1}{6} a^2 e x^6+\frac{1}{7} a^2 f x^7+\frac{c \left(a+b x^4\right)^3}{12 b}+\frac{2}{9} a b d x^9+\frac{1}{5} a b e x^{10}+\frac{2}{11} a b f x^{11}+\frac{1}{13} b^2 d x^{13}+\frac{1}{14} b^2 e x^{14}+\frac{1}{15} b^2 f x^{15}","\frac{1}{5} a^2 d x^5+\frac{1}{6} a^2 e x^6+\frac{1}{7} a^2 f x^7+\frac{c \left(a+b x^4\right)^3}{12 b}+\frac{2}{9} a b d x^9+\frac{1}{5} a b e x^{10}+\frac{2}{11} a b f x^{11}+\frac{1}{13} b^2 d x^{13}+\frac{1}{14} b^2 e x^{14}+\frac{1}{15} b^2 f x^{15}",1,"(a^2*d*x^5)/5 + (a^2*e*x^6)/6 + (a^2*f*x^7)/7 + (2*a*b*d*x^9)/9 + (a*b*e*x^10)/5 + (2*a*b*f*x^11)/11 + (b^2*d*x^13)/13 + (b^2*e*x^14)/14 + (b^2*f*x^15)/15 + (c*(a + b*x^4)^3)/(12*b)","A",3,2,28,0.07143,1,"{1582, 1850}"
481,1,151,0,0.108231,"\int \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^3 \, dx","Int[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^3,x]","\frac{3}{5} a^2 b c x^5+\frac{1}{2} a^2 b d x^6+\frac{3}{7} a^2 b e x^7+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{1}{3} a^3 e x^3+\frac{1}{3} a b^2 c x^9+\frac{3}{10} a b^2 d x^{10}+\frac{3}{11} a b^2 e x^{11}+\frac{f \left(a+b x^4\right)^4}{16 b}+\frac{1}{13} b^3 c x^{13}+\frac{1}{14} b^3 d x^{14}+\frac{1}{15} b^3 e x^{15}","\frac{3}{5} a^2 b c x^5+\frac{1}{2} a^2 b d x^6+\frac{3}{7} a^2 b e x^7+a^3 c x+\frac{1}{2} a^3 d x^2+\frac{1}{3} a^3 e x^3+\frac{1}{3} a b^2 c x^9+\frac{3}{10} a b^2 d x^{10}+\frac{3}{11} a b^2 e x^{11}+\frac{f \left(a+b x^4\right)^4}{16 b}+\frac{1}{13} b^3 c x^{13}+\frac{1}{14} b^3 d x^{14}+\frac{1}{15} b^3 e x^{15}",1,"a^3*c*x + (a^3*d*x^2)/2 + (a^3*e*x^3)/3 + (3*a^2*b*c*x^5)/5 + (a^2*b*d*x^6)/2 + (3*a^2*b*e*x^7)/7 + (a*b^2*c*x^9)/3 + (3*a*b^2*d*x^10)/10 + (3*a*b^2*e*x^11)/11 + (b^3*c*x^13)/13 + (b^3*d*x^14)/14 + (b^3*e*x^15)/15 + (f*(a + b*x^4)^4)/(16*b)","A",3,2,25,0.08000,1,"{1582, 1657}"
482,1,156,0,0.112745,"\int x^3 \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^3 \, dx","Int[x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^3,x]","\frac{1}{3} a^2 b d x^9+\frac{3}{10} a^2 b e x^{10}+\frac{3}{11} a^2 b f x^{11}+\frac{1}{5} a^3 d x^5+\frac{1}{6} a^3 e x^6+\frac{1}{7} a^3 f x^7+\frac{3}{13} a b^2 d x^{13}+\frac{3}{14} a b^2 e x^{14}+\frac{1}{5} a b^2 f x^{15}+\frac{c \left(a+b x^4\right)^4}{16 b}+\frac{1}{17} b^3 d x^{17}+\frac{1}{18} b^3 e x^{18}+\frac{1}{19} b^3 f x^{19}","\frac{1}{3} a^2 b d x^9+\frac{3}{10} a^2 b e x^{10}+\frac{3}{11} a^2 b f x^{11}+\frac{1}{5} a^3 d x^5+\frac{1}{6} a^3 e x^6+\frac{1}{7} a^3 f x^7+\frac{3}{13} a b^2 d x^{13}+\frac{3}{14} a b^2 e x^{14}+\frac{1}{5} a b^2 f x^{15}+\frac{c \left(a+b x^4\right)^4}{16 b}+\frac{1}{17} b^3 d x^{17}+\frac{1}{18} b^3 e x^{18}+\frac{1}{19} b^3 f x^{19}",1,"(a^3*d*x^5)/5 + (a^3*e*x^6)/6 + (a^3*f*x^7)/7 + (a^2*b*d*x^9)/3 + (3*a^2*b*e*x^10)/10 + (3*a^2*b*f*x^11)/11 + (3*a*b^2*d*x^13)/13 + (3*a*b^2*e*x^14)/14 + (a*b^2*f*x^15)/5 + (b^3*d*x^17)/17 + (b^3*e*x^18)/18 + (b^3*f*x^19)/19 + (c*(a + b*x^4)^4)/(16*b)","A",3,2,28,0.07143,1,"{1582, 1850}"
483,1,193,0,0.1556304,"\int \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^4 \, dx","Int[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^4,x]","\frac{2}{3} a^2 b^2 c x^9+\frac{3}{5} a^2 b^2 d x^{10}+\frac{6}{11} a^2 b^2 e x^{11}+\frac{4}{5} a^3 b c x^5+\frac{2}{3} a^3 b d x^6+\frac{4}{7} a^3 b e x^7+a^4 c x+\frac{1}{2} a^4 d x^2+\frac{1}{3} a^4 e x^3+\frac{4}{13} a b^3 c x^{13}+\frac{2}{7} a b^3 d x^{14}+\frac{4}{15} a b^3 e x^{15}+\frac{f \left(a+b x^4\right)^5}{20 b}+\frac{1}{17} b^4 c x^{17}+\frac{1}{18} b^4 d x^{18}+\frac{1}{19} b^4 e x^{19}","\frac{2}{3} a^2 b^2 c x^9+\frac{3}{5} a^2 b^2 d x^{10}+\frac{6}{11} a^2 b^2 e x^{11}+\frac{4}{5} a^3 b c x^5+\frac{2}{3} a^3 b d x^6+\frac{4}{7} a^3 b e x^7+a^4 c x+\frac{1}{2} a^4 d x^2+\frac{1}{3} a^4 e x^3+\frac{4}{13} a b^3 c x^{13}+\frac{2}{7} a b^3 d x^{14}+\frac{4}{15} a b^3 e x^{15}+\frac{f \left(a+b x^4\right)^5}{20 b}+\frac{1}{17} b^4 c x^{17}+\frac{1}{18} b^4 d x^{18}+\frac{1}{19} b^4 e x^{19}",1,"a^4*c*x + (a^4*d*x^2)/2 + (a^4*e*x^3)/3 + (4*a^3*b*c*x^5)/5 + (2*a^3*b*d*x^6)/3 + (4*a^3*b*e*x^7)/7 + (2*a^2*b^2*c*x^9)/3 + (3*a^2*b^2*d*x^10)/5 + (6*a^2*b^2*e*x^11)/11 + (4*a*b^3*c*x^13)/13 + (2*a*b^3*d*x^14)/7 + (4*a*b^3*e*x^15)/15 + (b^4*c*x^17)/17 + (b^4*d*x^18)/18 + (b^4*e*x^19)/19 + (f*(a + b*x^4)^5)/(20*b)","A",3,2,25,0.08000,1,"{1582, 1657}"
484,1,198,0,0.1504323,"\int x^3 \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^4 \, dx","Int[x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^4,x]","\frac{6}{13} a^2 b^2 d x^{13}+\frac{3}{7} a^2 b^2 e x^{14}+\frac{2}{5} a^2 b^2 f x^{15}+\frac{4}{9} a^3 b d x^9+\frac{2}{5} a^3 b e x^{10}+\frac{4}{11} a^3 b f x^{11}+\frac{1}{5} a^4 d x^5+\frac{1}{6} a^4 e x^6+\frac{1}{7} a^4 f x^7+\frac{4}{17} a b^3 d x^{17}+\frac{2}{9} a b^3 e x^{18}+\frac{4}{19} a b^3 f x^{19}+\frac{c \left(a+b x^4\right)^5}{20 b}+\frac{1}{21} b^4 d x^{21}+\frac{1}{22} b^4 e x^{22}+\frac{1}{23} b^4 f x^{23}","\frac{6}{13} a^2 b^2 d x^{13}+\frac{3}{7} a^2 b^2 e x^{14}+\frac{2}{5} a^2 b^2 f x^{15}+\frac{4}{9} a^3 b d x^9+\frac{2}{5} a^3 b e x^{10}+\frac{4}{11} a^3 b f x^{11}+\frac{1}{5} a^4 d x^5+\frac{1}{6} a^4 e x^6+\frac{1}{7} a^4 f x^7+\frac{4}{17} a b^3 d x^{17}+\frac{2}{9} a b^3 e x^{18}+\frac{4}{19} a b^3 f x^{19}+\frac{c \left(a+b x^4\right)^5}{20 b}+\frac{1}{21} b^4 d x^{21}+\frac{1}{22} b^4 e x^{22}+\frac{1}{23} b^4 f x^{23}",1,"(a^4*d*x^5)/5 + (a^4*e*x^6)/6 + (a^4*f*x^7)/7 + (4*a^3*b*d*x^9)/9 + (2*a^3*b*e*x^10)/5 + (4*a^3*b*f*x^11)/11 + (6*a^2*b^2*d*x^13)/13 + (3*a^2*b^2*e*x^14)/7 + (2*a^2*b^2*f*x^15)/5 + (4*a*b^3*d*x^17)/17 + (2*a*b^3*e*x^18)/9 + (4*a*b^3*f*x^19)/19 + (b^4*d*x^21)/21 + (b^4*e*x^22)/22 + (b^4*f*x^23)/23 + (c*(a + b*x^4)^5)/(20*b)","A",3,2,28,0.07143,1,"{1582, 1850}"
485,1,133,0,0.1243846,"\int \frac{c+d x+e x^2+f x^3}{a-b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(a - b*x^4),x]","\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}-\frac{f \log \left(a-b x^4\right)}{4 b}","\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}-\frac{f \log \left(a-b x^4\right)}{4 b}",1,"((Sqrt[b]*c - Sqrt[a]*e)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c + Sqrt[a]*e)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b]) - (f*Log[a - b*x^4])/(4*b)","A",9,7,26,0.2692,1,"{1876, 1167, 205, 208, 1248, 635, 260}"
486,1,162,0,0.2029512,"\int \frac{x^3 \left(c+d x+e x^2+f x^3\right)}{a-b x^4} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3))/(a - b*x^4),x]","\frac{\sqrt[4]{a} \left(\sqrt{b} d-\sqrt{a} f\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 b^{7/4}}+\frac{\sqrt[4]{a} \left(\sqrt{a} f+\sqrt{b} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 b^{7/4}}+\frac{\sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 b^{3/2}}-\frac{c \log \left(a-b x^4\right)}{4 b}-\frac{d x}{b}-\frac{e x^2}{2 b}-\frac{f x^3}{3 b}","\frac{\sqrt[4]{a} \left(\sqrt{b} d-\sqrt{a} f\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 b^{7/4}}+\frac{\sqrt[4]{a} \left(\sqrt{a} f+\sqrt{b} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 b^{7/4}}+\frac{\sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 b^{3/2}}-\frac{c \log \left(a-b x^4\right)}{4 b}-\frac{d x}{b}-\frac{e x^2}{2 b}-\frac{f x^3}{3 b}",1,"-((d*x)/b) - (e*x^2)/(2*b) - (f*x^3)/(3*b) + (a^(1/4)*(Sqrt[b]*d - Sqrt[a]*f)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*b^(7/4)) + (a^(1/4)*(Sqrt[b]*d + Sqrt[a]*f)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*b^(7/4)) + (Sqrt[a]*e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a]])/(2*b^(3/2)) - (c*Log[a - b*x^4])/(4*b)","A",12,9,29,0.3103,1,"{1831, 1252, 774, 635, 208, 260, 1280, 1167, 205}"
487,1,293,0,0.2224208,"\int \frac{c+d x+e x^2+f x^3}{a+b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(a + b*x^4),x]","-\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}+\frac{f \log \left(a+b x^4\right)}{4 b}","-\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b}}+\frac{f \log \left(a+b x^4\right)}{4 b}",1,"(d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b]) - ((Sqrt[b]*c + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) - ((Sqrt[b]*c - Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c - Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)) + (f*Log[a + b*x^4])/(4*b)","A",15,11,25,0.4400,1,"{1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 205, 260}"
488,1,321,0,0.3338126,"\int \frac{x^3 \left(c+d x+e x^2+f x^3\right)}{a+b x^4} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4),x]","\frac{\sqrt[4]{a} \left(\sqrt{b} d-\sqrt{a} f\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{7/4}}-\frac{\sqrt[4]{a} \left(\sqrt{b} d-\sqrt{a} f\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a} \left(\sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} b^{7/4}}-\frac{\sqrt[4]{a} \left(\sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} b^{7/4}}-\frac{\sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 b^{3/2}}+\frac{c \log \left(a+b x^4\right)}{4 b}+\frac{d x}{b}+\frac{e x^2}{2 b}+\frac{f x^3}{3 b}","\frac{\sqrt[4]{a} \left(\sqrt{b} d-\sqrt{a} f\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{7/4}}-\frac{\sqrt[4]{a} \left(\sqrt{b} d-\sqrt{a} f\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a} \left(\sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} b^{7/4}}-\frac{\sqrt[4]{a} \left(\sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} b^{7/4}}-\frac{\sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 b^{3/2}}+\frac{c \log \left(a+b x^4\right)}{4 b}+\frac{d x}{b}+\frac{e x^2}{2 b}+\frac{f x^3}{3 b}",1,"(d*x)/b + (e*x^2)/(2*b) + (f*x^3)/(3*b) - (Sqrt[a]*e*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*b^(3/2)) + (a^(1/4)*(Sqrt[b]*d + Sqrt[a]*f)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*b^(7/4)) - (a^(1/4)*(Sqrt[b]*d + Sqrt[a]*f)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*b^(7/4)) + (a^(1/4)*(Sqrt[b]*d - Sqrt[a]*f)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*b^(7/4)) - (a^(1/4)*(Sqrt[b]*d - Sqrt[a]*f)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*b^(7/4)) + (c*Log[a + b*x^4])/(4*b)","A",18,13,28,0.4643,1,"{1831, 1252, 774, 635, 205, 260, 1280, 1168, 1162, 617, 204, 1165, 628}"
489,1,318,0,0.2698699,"\int \frac{c+d x+e x^2+f x^3}{\left(a+b x^4\right)^2} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^2,x]","-\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{3/4}}+\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{3/4}}-\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{3/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}-\frac{a f-b x \left(c+d x+e x^2\right)}{4 a b \left(a+b x^4\right)}","-\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{3/4}}+\frac{\left(3 \sqrt{b} c-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{7/4} b^{3/4}}-\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} b^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} b^{3/4}}+\frac{d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b}}-\frac{a f-b x \left(c+d x+e x^2\right)}{4 a b \left(a+b x^4\right)}",1,"-(a*f - b*x*(c + d*x + e*x^2))/(4*a*b*(a + b*x^4)) + (d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(4*a^(3/2)*Sqrt[b]) - ((3*Sqrt[b]*c + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(3/4)) + ((3*Sqrt[b]*c + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*b^(3/4)) - ((3*Sqrt[b]*c - Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(3/4)) + ((3*Sqrt[b]*c - Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(7/4)*b^(3/4))","A",14,10,25,0.4000,1,"{1854, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
490,1,310,0,0.2741753,"\int \frac{x^3 \left(c+d x+e x^2+f x^3\right)}{\left(a+b x^4\right)^2} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^2,x]","-\frac{\left(\sqrt{b} d-3 \sqrt{a} f\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\left(\sqrt{b} d-3 \sqrt{a} f\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{3/4} b^{7/4}}-\frac{\left(3 \sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\left(3 \sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{3/4} b^{7/4}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 \sqrt{a} b^{3/2}}-\frac{c+d x+e x^2+f x^3}{4 b \left(a+b x^4\right)}","-\frac{\left(\sqrt{b} d-3 \sqrt{a} f\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\left(\sqrt{b} d-3 \sqrt{a} f\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{16 \sqrt{2} a^{3/4} b^{7/4}}-\frac{\left(3 \sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{3/4} b^{7/4}}+\frac{\left(3 \sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{3/4} b^{7/4}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 \sqrt{a} b^{3/2}}-\frac{c+d x+e x^2+f x^3}{4 b \left(a+b x^4\right)}",1,"-(c + d*x + e*x^2 + f*x^3)/(4*b*(a + b*x^4)) + (e*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(4*Sqrt[a]*b^(3/2)) - ((Sqrt[b]*d + 3*Sqrt[a]*f)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(3/4)*b^(7/4)) + ((Sqrt[b]*d + 3*Sqrt[a]*f)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(3/4)*b^(7/4)) - ((Sqrt[b]*d - 3*Sqrt[a]*f)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(3/4)*b^(7/4)) + ((Sqrt[b]*d - 3*Sqrt[a]*f)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(16*Sqrt[2]*a^(3/4)*b^(7/4))","A",14,10,28,0.3571,1,"{1823, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
491,1,351,0,0.3177101,"\int \frac{c+d x+e x^2+f x^3}{\left(a+b x^4\right)^3} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^3,x]","-\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} b^{3/4}}+\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} b^{3/4}}-\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} b^{3/4}}+\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} b^{3/4}}+\frac{x \left(7 c+6 d x+5 e x^2\right)}{32 a^2 \left(a+b x^4\right)}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}-\frac{a f-b x \left(c+d x+e x^2\right)}{8 a b \left(a+b x^4\right)^2}","-\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} b^{3/4}}+\frac{\left(21 \sqrt{b} c-5 \sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{11/4} b^{3/4}}-\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} b^{3/4}}+\frac{\left(5 \sqrt{a} e+21 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} b^{3/4}}+\frac{x \left(7 c+6 d x+5 e x^2\right)}{32 a^2 \left(a+b x^4\right)}+\frac{3 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b}}-\frac{a f-b x \left(c+d x+e x^2\right)}{8 a b \left(a+b x^4\right)^2}",1,"(x*(7*c + 6*d*x + 5*e*x^2))/(32*a^2*(a + b*x^4)) - (a*f - b*x*(c + d*x + e*x^2))/(8*a*b*(a + b*x^4)^2) + (3*d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[b]) - ((21*Sqrt[b]*c + 5*Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(3/4)) + ((21*Sqrt[b]*c + 5*Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*b^(3/4)) - ((21*Sqrt[b]*c - 5*Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(3/4)) + ((21*Sqrt[b]*c - 5*Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(11/4)*b^(3/4))","A",15,11,25,0.4400,1,"{1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
492,1,340,0,0.3281792,"\int \frac{x^3 \left(c+d x+e x^2+f x^3\right)}{\left(a+b x^4\right)^3} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^3,x]","-\frac{3 \left(\sqrt{b} d-\sqrt{a} f\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{7/4} b^{7/4}}+\frac{3 \left(\sqrt{b} d-\sqrt{a} f\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{7/4} b^{7/4}}-\frac{3 \left(\sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{7/4} b^{7/4}}+\frac{3 \left(\sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{7/4} b^{7/4}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{3/2} b^{3/2}}-\frac{c+d x+e x^2+f x^3}{8 b \left(a+b x^4\right)^2}+\frac{x \left(d+2 e x+3 f x^2\right)}{32 a b \left(a+b x^4\right)}","-\frac{3 \left(\sqrt{b} d-\sqrt{a} f\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{7/4} b^{7/4}}+\frac{3 \left(\sqrt{b} d-\sqrt{a} f\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{128 \sqrt{2} a^{7/4} b^{7/4}}-\frac{3 \left(\sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{7/4} b^{7/4}}+\frac{3 \left(\sqrt{a} f+\sqrt{b} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{7/4} b^{7/4}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{16 a^{3/2} b^{3/2}}-\frac{c+d x+e x^2+f x^3}{8 b \left(a+b x^4\right)^2}+\frac{x \left(d+2 e x+3 f x^2\right)}{32 a b \left(a+b x^4\right)}",1,"-(c + d*x + e*x^2 + f*x^3)/(8*b*(a + b*x^4)^2) + (x*(d + 2*e*x + 3*f*x^2))/(32*a*b*(a + b*x^4)) + (e*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(16*a^(3/2)*b^(3/2)) - (3*(Sqrt[b]*d + Sqrt[a]*f)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(7/4)*b^(7/4)) + (3*(Sqrt[b]*d + Sqrt[a]*f)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(7/4)*b^(7/4)) - (3*(Sqrt[b]*d - Sqrt[a]*f)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(7/4)*b^(7/4)) + (3*(Sqrt[b]*d - Sqrt[a]*f)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(128*Sqrt[2]*a^(7/4)*b^(7/4))","A",15,11,28,0.3929,1,"{1823, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
493,1,382,0,0.4058672,"\int \frac{c+d x+e x^2+f x^3}{\left(a+b x^4\right)^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^4,x]","-\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} b^{3/4}}+\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} b^{3/4}}-\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 \sqrt{2} a^{15/4} b^{3/4}}+\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{256 \sqrt{2} a^{15/4} b^{3/4}}+\frac{x \left(11 c+10 d x+9 e x^2\right)}{96 a^2 \left(a+b x^4\right)^2}+\frac{x \left(77 c+60 d x+45 e x^2\right)}{384 a^3 \left(a+b x^4\right)}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}-\frac{a f-b x \left(c+d x+e x^2\right)}{12 a b \left(a+b x^4\right)^3}","-\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} b^{3/4}}+\frac{\left(77 \sqrt{b} c-15 \sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{15/4} b^{3/4}}-\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 \sqrt{2} a^{15/4} b^{3/4}}+\frac{\left(15 \sqrt{a} e+77 \sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{256 \sqrt{2} a^{15/4} b^{3/4}}+\frac{x \left(11 c+10 d x+9 e x^2\right)}{96 a^2 \left(a+b x^4\right)^2}+\frac{x \left(77 c+60 d x+45 e x^2\right)}{384 a^3 \left(a+b x^4\right)}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{7/2} \sqrt{b}}-\frac{a f-b x \left(c+d x+e x^2\right)}{12 a b \left(a+b x^4\right)^3}",1,"(x*(11*c + 10*d*x + 9*e*x^2))/(96*a^2*(a + b*x^4)^2) + (x*(77*c + 60*d*x + 45*e*x^2))/(384*a^3*(a + b*x^4)) - (a*f - b*x*(c + d*x + e*x^2))/(12*a*b*(a + b*x^4)^3) + (5*d*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(7/2)*Sqrt[b]) - ((77*Sqrt[b]*c + 15*Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(3/4)) + ((77*Sqrt[b]*c + 15*Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(15/4)*b^(3/4)) - ((77*Sqrt[b]*c - 15*Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(3/4)) + ((77*Sqrt[b]*c - 15*Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(15/4)*b^(3/4))","A",16,11,25,0.4400,1,"{1854, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
494,1,380,0,0.4021783,"\int \frac{x^3 \left(c+d x+e x^2+f x^3\right)}{\left(a+b x^4\right)^4} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^4,x]","-\frac{\left(7 \sqrt{b} d-5 \sqrt{a} f\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\left(7 \sqrt{b} d-5 \sqrt{a} f\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{11/4} b^{7/4}}-\frac{\left(5 \sqrt{a} f+7 \sqrt{b} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\left(5 \sqrt{a} f+7 \sqrt{b} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{256 \sqrt{2} a^{11/4} b^{7/4}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{5/2} b^{3/2}}+\frac{x \left(7 d+12 e x+15 f x^2\right)}{384 a^2 b \left(a+b x^4\right)}-\frac{c+d x+e x^2+f x^3}{12 b \left(a+b x^4\right)^3}+\frac{x \left(d+2 e x+3 f x^2\right)}{96 a b \left(a+b x^4\right)^2}","-\frac{\left(7 \sqrt{b} d-5 \sqrt{a} f\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\left(7 \sqrt{b} d-5 \sqrt{a} f\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{512 \sqrt{2} a^{11/4} b^{7/4}}-\frac{\left(5 \sqrt{a} f+7 \sqrt{b} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{256 \sqrt{2} a^{11/4} b^{7/4}}+\frac{\left(5 \sqrt{a} f+7 \sqrt{b} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{256 \sqrt{2} a^{11/4} b^{7/4}}+\frac{e \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{32 a^{5/2} b^{3/2}}+\frac{x \left(7 d+12 e x+15 f x^2\right)}{384 a^2 b \left(a+b x^4\right)}-\frac{c+d x+e x^2+f x^3}{12 b \left(a+b x^4\right)^3}+\frac{x \left(d+2 e x+3 f x^2\right)}{96 a b \left(a+b x^4\right)^2}",1,"-(c + d*x + e*x^2 + f*x^3)/(12*b*(a + b*x^4)^3) + (x*(d + 2*e*x + 3*f*x^2))/(96*a*b*(a + b*x^4)^2) + (x*(7*d + 12*e*x + 15*f*x^2))/(384*a^2*b*(a + b*x^4)) + (e*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(32*a^(5/2)*b^(3/2)) - ((7*Sqrt[b]*d + 5*Sqrt[a]*f)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(11/4)*b^(7/4)) + ((7*Sqrt[b]*d + 5*Sqrt[a]*f)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(256*Sqrt[2]*a^(11/4)*b^(7/4)) - ((7*Sqrt[b]*d - 5*Sqrt[a]*f)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(11/4)*b^(7/4)) + ((7*Sqrt[b]*d - 5*Sqrt[a]*f)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(512*Sqrt[2]*a^(11/4)*b^(7/4))","A",16,11,28,0.3929,1,"{1823, 1855, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628}"
495,1,418,0,0.3811548,"\int x^4 \left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4} \, dx","Int[x^4*(c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4],x]","-\frac{a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(7 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{7/4} \sqrt{a+b x^4}}-\frac{a^2 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 b^{3/2}}-\frac{2 a^2 e x \sqrt{a+b x^4}}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{2 a^{9/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/2} \left(8 a f-15 b d x^2\right)}{120 b^2}+\frac{1}{63} x^5 \sqrt{a+b x^4} \left(9 c+7 e x^2\right)+\frac{2 a c x \sqrt{a+b x^4}}{21 b}-\frac{a d x^2 \sqrt{a+b x^4}}{16 b}+\frac{2 a e x^3 \sqrt{a+b x^4}}{45 b}+\frac{f x^4 \left(a+b x^4\right)^{3/2}}{10 b}","-\frac{a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(7 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{7/4} \sqrt{a+b x^4}}-\frac{a^2 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 b^{3/2}}-\frac{2 a^2 e x \sqrt{a+b x^4}}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{2 a^{9/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/2} \left(8 a f-15 b d x^2\right)}{120 b^2}+\frac{1}{63} x^5 \sqrt{a+b x^4} \left(9 c+7 e x^2\right)+\frac{2 a c x \sqrt{a+b x^4}}{21 b}-\frac{a d x^2 \sqrt{a+b x^4}}{16 b}+\frac{2 a e x^3 \sqrt{a+b x^4}}{45 b}+\frac{f x^4 \left(a+b x^4\right)^{3/2}}{10 b}",1,"(2*a*c*x*Sqrt[a + b*x^4])/(21*b) - (a*d*x^2*Sqrt[a + b*x^4])/(16*b) + (2*a*e*x^3*Sqrt[a + b*x^4])/(45*b) - (2*a^2*e*x*Sqrt[a + b*x^4])/(15*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + (x^5*(9*c + 7*e*x^2)*Sqrt[a + b*x^4])/63 + (f*x^4*(a + b*x^4)^(3/2))/(10*b) - ((8*a*f - 15*b*d*x^2)*(a + b*x^4)^(3/2))/(120*b^2) - (a^2*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(16*b^(3/2)) + (2*a^(9/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*b^(7/4)*Sqrt[a + b*x^4]) - (a^(7/4)*(5*Sqrt[b]*c + 7*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*b^(7/4)*Sqrt[a + b*x^4])","A",14,12,30,0.4000,1,"{1833, 1274, 1280, 1198, 220, 1196, 1252, 833, 780, 195, 217, 206}"
496,1,394,0,0.3342509,"\int x^3 \left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4} \, dx","Int[x^3*(c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4],x]","-\frac{a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(7 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{7/4} \sqrt{a+b x^4}}-\frac{a^2 e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 b^{3/2}}-\frac{2 a^2 f x \sqrt{a+b x^4}}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{2 a^{9/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^4}}+\frac{\left(a+b x^4\right)^{3/2} \left(4 c+3 e x^2\right)}{24 b}+\frac{1}{63} x^5 \sqrt{a+b x^4} \left(9 d+7 f x^2\right)+\frac{2 a d x \sqrt{a+b x^4}}{21 b}-\frac{a e x^2 \sqrt{a+b x^4}}{16 b}+\frac{2 a f x^3 \sqrt{a+b x^4}}{45 b}","-\frac{a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(7 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{7/4} \sqrt{a+b x^4}}-\frac{a^2 e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 b^{3/2}}-\frac{2 a^2 f x \sqrt{a+b x^4}}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{2 a^{9/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^4}}+\frac{\left(a+b x^4\right)^{3/2} \left(4 c+3 e x^2\right)}{24 b}+\frac{1}{63} x^5 \sqrt{a+b x^4} \left(9 d+7 f x^2\right)+\frac{2 a d x \sqrt{a+b x^4}}{21 b}-\frac{a e x^2 \sqrt{a+b x^4}}{16 b}+\frac{2 a f x^3 \sqrt{a+b x^4}}{45 b}",1,"(2*a*d*x*Sqrt[a + b*x^4])/(21*b) - (a*e*x^2*Sqrt[a + b*x^4])/(16*b) + (2*a*f*x^3*Sqrt[a + b*x^4])/(45*b) - (2*a^2*f*x*Sqrt[a + b*x^4])/(15*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + (x^5*(9*d + 7*f*x^2)*Sqrt[a + b*x^4])/63 + ((4*c + 3*e*x^2)*(a + b*x^4)^(3/2))/(24*b) - (a^2*e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(16*b^(3/2)) + (2*a^(9/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*b^(7/4)*Sqrt[a + b*x^4]) - (a^(7/4)*(5*Sqrt[b]*d + 7*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*b^(7/4)*Sqrt[a + b*x^4])","A",13,11,30,0.3667,1,"{1833, 1252, 780, 195, 217, 206, 1274, 1280, 1198, 220, 1196}"
497,1,369,0,0.2979244,"\int x^2 \left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4} \, dx","Int[x^2*(c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4],x]","\frac{a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(21 \sqrt{b} c-5 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{5/4} \sqrt{a+b x^4}}-\frac{2 a^{5/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^4}}-\frac{a^2 f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 b^{3/2}}+\frac{1}{35} x^3 \sqrt{a+b x^4} \left(7 c+5 e x^2\right)+\frac{2 a c x \sqrt{a+b x^4}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{\left(a+b x^4\right)^{3/2} \left(4 d+3 f x^2\right)}{24 b}+\frac{2 a e x \sqrt{a+b x^4}}{21 b}-\frac{a f x^2 \sqrt{a+b x^4}}{16 b}","\frac{a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(21 \sqrt{b} c-5 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{5/4} \sqrt{a+b x^4}}-\frac{2 a^{5/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^4}}-\frac{a^2 f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 b^{3/2}}+\frac{1}{35} x^3 \sqrt{a+b x^4} \left(7 c+5 e x^2\right)+\frac{2 a c x \sqrt{a+b x^4}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{\left(a+b x^4\right)^{3/2} \left(4 d+3 f x^2\right)}{24 b}+\frac{2 a e x \sqrt{a+b x^4}}{21 b}-\frac{a f x^2 \sqrt{a+b x^4}}{16 b}",1,"(2*a*e*x*Sqrt[a + b*x^4])/(21*b) - (a*f*x^2*Sqrt[a + b*x^4])/(16*b) + (2*a*c*x*Sqrt[a + b*x^4])/(5*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (x^3*(7*c + 5*e*x^2)*Sqrt[a + b*x^4])/35 + ((4*d + 3*f*x^2)*(a + b*x^4)^(3/2))/(24*b) - (a^2*f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(16*b^(3/2)) - (2*a^(5/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[a + b*x^4]) + (a^(5/4)*(21*Sqrt[b]*c - 5*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*b^(5/4)*Sqrt[a + b*x^4])","A",12,11,30,0.3667,1,"{1833, 1274, 1280, 1198, 220, 1196, 1252, 780, 195, 217, 206}"
498,1,354,0,0.2732056,"\int x \left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4} \, dx","Int[x*(c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4],x]","\frac{a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(21 \sqrt{b} d-5 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{5/4} \sqrt{a+b x^4}}-\frac{2 a^{5/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^4}}+\frac{1}{4} c x^2 \sqrt{a+b x^4}+\frac{a c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 \sqrt{b}}+\frac{1}{35} x^3 \sqrt{a+b x^4} \left(7 d+5 f x^2\right)+\frac{2 a d x \sqrt{a+b x^4}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{e \left(a+b x^4\right)^{3/2}}{6 b}+\frac{2 a f x \sqrt{a+b x^4}}{21 b}","\frac{a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(21 \sqrt{b} d-5 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{5/4} \sqrt{a+b x^4}}-\frac{2 a^{5/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^4}}+\frac{1}{4} c x^2 \sqrt{a+b x^4}+\frac{a c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 \sqrt{b}}+\frac{1}{35} x^3 \sqrt{a+b x^4} \left(7 d+5 f x^2\right)+\frac{2 a d x \sqrt{a+b x^4}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{e \left(a+b x^4\right)^{3/2}}{6 b}+\frac{2 a f x \sqrt{a+b x^4}}{21 b}",1,"(2*a*f*x*Sqrt[a + b*x^4])/(21*b) + (c*x^2*Sqrt[a + b*x^4])/4 + (2*a*d*x*Sqrt[a + b*x^4])/(5*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (x^3*(7*d + 5*f*x^2)*Sqrt[a + b*x^4])/35 + (e*(a + b*x^4)^(3/2))/(6*b) + (a*c*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*Sqrt[b]) - (2*a^(5/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[a + b*x^4]) + (a^(5/4)*(21*Sqrt[b]*d - 5*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*b^(5/4)*Sqrt[a + b*x^4])","A",12,11,28,0.3929,1,"{1833, 1248, 641, 195, 217, 206, 1274, 1280, 1198, 220, 1196}"
499,1,331,0,0.1941886,"\int \left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4} \, dx","Int[(c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4],x]","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}-\frac{2 a^{5/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^4}}+\frac{1}{15} x \sqrt{a+b x^4} \left(5 c+3 e x^2\right)+\frac{1}{4} d x^2 \sqrt{a+b x^4}+\frac{a d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 \sqrt{b}}+\frac{2 a e x \sqrt{a+b x^4}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{f \left(a+b x^4\right)^{3/2}}{6 b}","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}-\frac{2 a^{5/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^4}}+\frac{1}{15} x \sqrt{a+b x^4} \left(5 c+3 e x^2\right)+\frac{1}{4} d x^2 \sqrt{a+b x^4}+\frac{a d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 \sqrt{b}}+\frac{2 a e x \sqrt{a+b x^4}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{f \left(a+b x^4\right)^{3/2}}{6 b}",1,"(d*x^2*Sqrt[a + b*x^4])/4 + (2*a*e*x*Sqrt[a + b*x^4])/(5*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (x*(5*c + 3*e*x^2)*Sqrt[a + b*x^4])/15 + (f*(a + b*x^4)^(3/2))/(6*b) + (a*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*Sqrt[b]) - (2*a^(5/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[a + b*x^4]) + (a^(3/4)*(5*Sqrt[b]*c + 3*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a + b*x^4])","A",11,10,27,0.3704,1,"{1885, 1177, 1198, 220, 1196, 1248, 641, 195, 217, 206}"
500,1,345,0,0.2551588,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x,x]","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}-\frac{2 a^{5/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^4}}+\frac{1}{4} \sqrt{a+b x^4} \left(2 c+e x^2\right)-\frac{1}{2} \sqrt{a} c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{1}{15} x \sqrt{a+b x^4} \left(5 d+3 f x^2\right)+\frac{a e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 \sqrt{b}}+\frac{2 a f x \sqrt{a+b x^4}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}-\frac{2 a^{5/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^4}}+\frac{1}{4} \sqrt{a+b x^4} \left(2 c+e x^2\right)-\frac{1}{2} \sqrt{a} c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{1}{15} x \sqrt{a+b x^4} \left(5 d+3 f x^2\right)+\frac{a e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 \sqrt{b}}+\frac{2 a f x \sqrt{a+b x^4}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"(2*a*f*x*Sqrt[a + b*x^4])/(5*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + ((2*c + e*x^2)*Sqrt[a + b*x^4])/4 + (x*(5*d + 3*f*x^2)*Sqrt[a + b*x^4])/15 + (a*e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*Sqrt[b]) - (Sqrt[a]*c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/2 - (2*a^(5/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[a + b*x^4]) + (a^(3/4)*(5*Sqrt[b]*d + 3*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a + b*x^4])","A",14,13,30,0.4333,1,"{1833, 1252, 815, 844, 217, 206, 266, 63, 208, 1177, 1198, 220, 1196}"
501,1,341,0,0.2631869,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x^2} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x^2,x]","-\frac{\sqrt{a+b x^4} \left(3 c-e x^2\right)}{3 x}+\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} e+3 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{2 \sqrt{b} c x \sqrt{a+b x^4}}{\sqrt{a}+\sqrt{b} x^2}-\frac{2 \sqrt[4]{a} \sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+b x^4}}+\frac{1}{4} \sqrt{a+b x^4} \left(2 d+f x^2\right)-\frac{1}{2} \sqrt{a} d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{a f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 \sqrt{b}}","-\frac{\sqrt{a+b x^4} \left(3 c-e x^2\right)}{3 x}+\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} e+3 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{2 \sqrt{b} c x \sqrt{a+b x^4}}{\sqrt{a}+\sqrt{b} x^2}-\frac{2 \sqrt[4]{a} \sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+b x^4}}+\frac{1}{4} \sqrt{a+b x^4} \left(2 d+f x^2\right)-\frac{1}{2} \sqrt{a} d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{a f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 \sqrt{b}}",1,"(2*Sqrt[b]*c*x*Sqrt[a + b*x^4])/(Sqrt[a] + Sqrt[b]*x^2) - ((3*c - e*x^2)*Sqrt[a + b*x^4])/(3*x) + ((2*d + f*x^2)*Sqrt[a + b*x^4])/4 + (a*f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*Sqrt[b]) - (Sqrt[a]*d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/2 - (2*a^(1/4)*b^(1/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/Sqrt[a + b*x^4] + (a^(1/4)*(3*Sqrt[b]*c + Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(3*b^(1/4)*Sqrt[a + b*x^4])","A",14,13,30,0.4333,1,"{1833, 1272, 1198, 220, 1196, 1252, 815, 844, 217, 206, 266, 63, 208}"
502,1,342,0,0.2624237,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x^3} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x^3,x]","-\frac{\sqrt{a+b x^4} \left(c-e x^2\right)}{2 x^2}+\frac{1}{2} \sqrt{b} c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)-\frac{\sqrt{a+b x^4} \left(3 d-f x^2\right)}{3 x}+\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} f+3 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{2 \sqrt{b} d x \sqrt{a+b x^4}}{\sqrt{a}+\sqrt{b} x^2}-\frac{2 \sqrt[4]{a} \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+b x^4}}-\frac{1}{2} \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)","-\frac{\sqrt{a+b x^4} \left(c-e x^2\right)}{2 x^2}+\frac{1}{2} \sqrt{b} c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)-\frac{\sqrt{a+b x^4} \left(3 d-f x^2\right)}{3 x}+\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} f+3 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{2 \sqrt{b} d x \sqrt{a+b x^4}}{\sqrt{a}+\sqrt{b} x^2}-\frac{2 \sqrt[4]{a} \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+b x^4}}-\frac{1}{2} \sqrt{a} e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)",1,"(2*Sqrt[b]*d*x*Sqrt[a + b*x^4])/(Sqrt[a] + Sqrt[b]*x^2) - ((c - e*x^2)*Sqrt[a + b*x^4])/(2*x^2) - ((3*d - f*x^2)*Sqrt[a + b*x^4])/(3*x) + (Sqrt[b]*c*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/2 - (Sqrt[a]*e*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/2 - (2*a^(1/4)*b^(1/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/Sqrt[a + b*x^4] + (a^(1/4)*(3*Sqrt[b]*d + Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(3*b^(1/4)*Sqrt[a + b*x^4])","A",14,13,30,0.4333,1,"{1833, 1252, 813, 844, 217, 206, 266, 63, 208, 1272, 1198, 220, 1196}"
503,1,357,0,0.2953175,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x^4} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x^4,x]","-\frac{\sqrt{a+b x^4} \left(c-3 e x^2\right)}{3 x^3}+\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} e+\sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a+b x^4}}-\frac{\sqrt{a+b x^4} \left(d-f x^2\right)}{2 x^2}+\frac{1}{2} \sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)-\frac{2 e \sqrt{a+b x^4}}{x}+\frac{2 \sqrt{b} e x \sqrt{a+b x^4}}{\sqrt{a}+\sqrt{b} x^2}-\frac{2 \sqrt[4]{a} \sqrt[4]{b} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+b x^4}}-\frac{1}{2} \sqrt{a} f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)","-\frac{\sqrt{a+b x^4} \left(c-3 e x^2\right)}{3 x^3}+\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} e+\sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a+b x^4}}-\frac{\sqrt{a+b x^4} \left(d-f x^2\right)}{2 x^2}+\frac{1}{2} \sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)-\frac{2 e \sqrt{a+b x^4}}{x}+\frac{2 \sqrt{b} e x \sqrt{a+b x^4}}{\sqrt{a}+\sqrt{b} x^2}-\frac{2 \sqrt[4]{a} \sqrt[4]{b} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+b x^4}}-\frac{1}{2} \sqrt{a} f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)",1,"(-2*e*Sqrt[a + b*x^4])/x + (2*Sqrt[b]*e*x*Sqrt[a + b*x^4])/(Sqrt[a] + Sqrt[b]*x^2) - ((c - 3*e*x^2)*Sqrt[a + b*x^4])/(3*x^3) - ((d - f*x^2)*Sqrt[a + b*x^4])/(2*x^2) + (Sqrt[b]*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/2 - (Sqrt[a]*f*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/2 - (2*a^(1/4)*b^(1/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/Sqrt[a + b*x^4] + (b^(1/4)*(Sqrt[b]*c + 3*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(3*a^(1/4)*Sqrt[a + b*x^4])","A",15,14,30,0.4667,1,"{1833, 1272, 1282, 1198, 220, 1196, 1252, 813, 844, 217, 206, 266, 63, 208}"
504,1,329,0,0.2808732,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x^5} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x^5,x]","-\frac{1}{12} \sqrt{a+b x^4} \left(\frac{3 c}{x^4}+\frac{4 d}{x^3}+\frac{6 e}{x^2}+\frac{12 f}{x}\right)-\frac{b c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} f+\sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a+b x^4}}+\frac{1}{2} \sqrt{b} e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{2 \sqrt{b} f x \sqrt{a+b x^4}}{\sqrt{a}+\sqrt{b} x^2}-\frac{2 \sqrt[4]{a} \sqrt[4]{b} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+b x^4}}","-\frac{1}{12} \sqrt{a+b x^4} \left(\frac{3 c}{x^4}+\frac{4 d}{x^3}+\frac{6 e}{x^2}+\frac{12 f}{x}\right)-\frac{b c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} f+\sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a+b x^4}}+\frac{1}{2} \sqrt{b} e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{2 \sqrt{b} f x \sqrt{a+b x^4}}{\sqrt{a}+\sqrt{b} x^2}-\frac{2 \sqrt[4]{a} \sqrt[4]{b} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+b x^4}}",1,"-(((3*c)/x^4 + (4*d)/x^3 + (6*e)/x^2 + (12*f)/x)*Sqrt[a + b*x^4])/12 + (2*Sqrt[b]*f*x*Sqrt[a + b*x^4])/(Sqrt[a] + Sqrt[b]*x^2) + (Sqrt[b]*e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/2 - (b*c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(4*Sqrt[a]) - (2*a^(1/4)*b^(1/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/Sqrt[a + b*x^4] + (b^(1/4)*(Sqrt[b]*d + 3*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(3*a^(1/4)*Sqrt[a + b*x^4])","A",13,13,30,0.4333,1,"{14, 1825, 1832, 266, 63, 208, 1885, 275, 217, 206, 1198, 220, 1196}"
505,1,360,0,0.3235372,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x^6} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x^6,x]","\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+3 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{2 b^{5/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+b x^4}}+\frac{2 b^{3/2} c x \sqrt{a+b x^4}}{5 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{1}{60} \sqrt{a+b x^4} \left(\frac{12 c}{x^5}+\frac{15 d}{x^4}+\frac{20 e}{x^3}+\frac{30 f}{x^2}\right)-\frac{2 b c \sqrt{a+b x^4}}{5 a x}-\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{1}{2} \sqrt{b} f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)","\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+3 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{2 b^{5/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+b x^4}}+\frac{2 b^{3/2} c x \sqrt{a+b x^4}}{5 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{1}{60} \sqrt{a+b x^4} \left(\frac{12 c}{x^5}+\frac{15 d}{x^4}+\frac{20 e}{x^3}+\frac{30 f}{x^2}\right)-\frac{2 b c \sqrt{a+b x^4}}{5 a x}-\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{1}{2} \sqrt{b} f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)",1,"-(((12*c)/x^5 + (15*d)/x^4 + (20*e)/x^3 + (30*f)/x^2)*Sqrt[a + b*x^4])/60 - (2*b*c*Sqrt[a + b*x^4])/(5*a*x) + (2*b^(3/2)*c*x*Sqrt[a + b*x^4])/(5*a*(Sqrt[a] + Sqrt[b]*x^2)) + (Sqrt[b]*f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/2 - (b*d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(4*Sqrt[a]) - (2*b^(5/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[a + b*x^4]) + (b^(3/4)*(3*Sqrt[b]*c + 5*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*a^(3/4)*Sqrt[a + b*x^4])","A",14,14,30,0.4667,1,"{14, 1825, 1833, 1282, 1198, 220, 1196, 1252, 844, 217, 206, 266, 63, 208}"
506,1,352,0,0.3163379,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x^7} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x^7,x]","\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} f+3 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{2 b^{5/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+b x^4}}+\frac{2 b^{3/2} d x \sqrt{a+b x^4}}{5 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{1}{60} \sqrt{a+b x^4} \left(\frac{10 c}{x^6}+\frac{12 d}{x^5}+\frac{15 e}{x^4}+\frac{20 f}{x^3}\right)-\frac{b c \sqrt{a+b x^4}}{6 a x^2}-\frac{2 b d \sqrt{a+b x^4}}{5 a x}-\frac{b e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}","\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} f+3 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{2 b^{5/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+b x^4}}+\frac{2 b^{3/2} d x \sqrt{a+b x^4}}{5 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{1}{60} \sqrt{a+b x^4} \left(\frac{10 c}{x^6}+\frac{12 d}{x^5}+\frac{15 e}{x^4}+\frac{20 f}{x^3}\right)-\frac{b c \sqrt{a+b x^4}}{6 a x^2}-\frac{2 b d \sqrt{a+b x^4}}{5 a x}-\frac{b e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}",1,"-(((10*c)/x^6 + (12*d)/x^5 + (15*e)/x^4 + (20*f)/x^3)*Sqrt[a + b*x^4])/60 - (b*c*Sqrt[a + b*x^4])/(6*a*x^2) - (2*b*d*Sqrt[a + b*x^4])/(5*a*x) + (2*b^(3/2)*d*x*Sqrt[a + b*x^4])/(5*a*(Sqrt[a] + Sqrt[b]*x^2)) - (b*e*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(4*Sqrt[a]) - (2*b^(5/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[a + b*x^4]) + (b^(3/4)*(3*Sqrt[b]*d + 5*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*a^(3/4)*Sqrt[a + b*x^4])","A",12,12,30,0.4000,1,"{14, 1825, 1833, 1252, 807, 266, 63, 208, 1282, 1198, 220, 1196}"
507,1,375,0,0.3615932,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x^8} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x^8,x]","-\frac{b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{b} c-21 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{5/4} \sqrt{a+b x^4}}-\frac{2 b^{5/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+b x^4}}+\frac{2 b^{3/2} e x \sqrt{a+b x^4}}{5 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{1}{420} \sqrt{a+b x^4} \left(\frac{60 c}{x^7}+\frac{70 d}{x^6}+\frac{84 e}{x^5}+\frac{105 f}{x^4}\right)-\frac{2 b c \sqrt{a+b x^4}}{21 a x^3}-\frac{b d \sqrt{a+b x^4}}{6 a x^2}-\frac{2 b e \sqrt{a+b x^4}}{5 a x}-\frac{b f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}","-\frac{b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{b} c-21 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{5/4} \sqrt{a+b x^4}}-\frac{2 b^{5/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+b x^4}}+\frac{2 b^{3/2} e x \sqrt{a+b x^4}}{5 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{1}{420} \sqrt{a+b x^4} \left(\frac{60 c}{x^7}+\frac{70 d}{x^6}+\frac{84 e}{x^5}+\frac{105 f}{x^4}\right)-\frac{2 b c \sqrt{a+b x^4}}{21 a x^3}-\frac{b d \sqrt{a+b x^4}}{6 a x^2}-\frac{2 b e \sqrt{a+b x^4}}{5 a x}-\frac{b f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}",1,"-(((60*c)/x^7 + (70*d)/x^6 + (84*e)/x^5 + (105*f)/x^4)*Sqrt[a + b*x^4])/420 - (2*b*c*Sqrt[a + b*x^4])/(21*a*x^3) - (b*d*Sqrt[a + b*x^4])/(6*a*x^2) - (2*b*e*Sqrt[a + b*x^4])/(5*a*x) + (2*b^(3/2)*e*x*Sqrt[a + b*x^4])/(5*a*(Sqrt[a] + Sqrt[b]*x^2)) - (b*f*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(4*Sqrt[a]) - (2*b^(5/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[a + b*x^4]) - (b^(5/4)*(5*Sqrt[b]*c - 21*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*a^(5/4)*Sqrt[a + b*x^4])","A",13,12,30,0.4000,1,"{14, 1825, 1833, 1282, 1198, 220, 1196, 1252, 807, 266, 63, 208}"
508,1,400,0,0.3862048,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x^9} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x^9,x]","\frac{b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{b} d-21 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{5/4} \sqrt{a+b x^4}}-\frac{2 b^{5/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+b x^4}}+\frac{2 b^{3/2} f x \sqrt{a+b x^4}}{5 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{1}{840} \sqrt{a+b x^4} \left(\frac{105 c}{x^8}+\frac{120 d}{x^7}+\frac{140 e}{x^6}+\frac{168 f}{x^5}\right)-\frac{b c \sqrt{a+b x^4}}{16 a x^4}-\frac{2 b d \sqrt{a+b x^4}}{21 a x^3}-\frac{b e \sqrt{a+b x^4}}{6 a x^2}-\frac{2 b f \sqrt{a+b x^4}}{5 a x}","\frac{b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{b} d-21 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{5/4} \sqrt{a+b x^4}}-\frac{2 b^{5/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+b x^4}}+\frac{2 b^{3/2} f x \sqrt{a+b x^4}}{5 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{1}{840} \sqrt{a+b x^4} \left(\frac{105 c}{x^8}+\frac{120 d}{x^7}+\frac{140 e}{x^6}+\frac{168 f}{x^5}\right)-\frac{b c \sqrt{a+b x^4}}{16 a x^4}-\frac{2 b d \sqrt{a+b x^4}}{21 a x^3}-\frac{b e \sqrt{a+b x^4}}{6 a x^2}-\frac{2 b f \sqrt{a+b x^4}}{5 a x}",1,"-(((105*c)/x^8 + (120*d)/x^7 + (140*e)/x^6 + (168*f)/x^5)*Sqrt[a + b*x^4])/840 - (b*c*Sqrt[a + b*x^4])/(16*a*x^4) - (2*b*d*Sqrt[a + b*x^4])/(21*a*x^3) - (b*e*Sqrt[a + b*x^4])/(6*a*x^2) - (2*b*f*Sqrt[a + b*x^4])/(5*a*x) + (2*b^(3/2)*f*x*Sqrt[a + b*x^4])/(5*a*(Sqrt[a] + Sqrt[b]*x^2)) + (b^2*c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(16*a^(3/2)) - (2*b^(5/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[a + b*x^4]) - (b^(5/4)*(5*Sqrt[b]*d - 21*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*a^(5/4)*Sqrt[a + b*x^4])","A",14,13,30,0.4333,1,"{14, 1825, 1833, 1252, 835, 807, 266, 63, 208, 1282, 1198, 220, 1196}"
509,1,425,0,0.4331281,"\int \frac{\left(c+d x+e x^2+f x^3\right) \sqrt{a+b x^4}}{x^{10}} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*Sqrt[a + b*x^4])/x^10,x]","-\frac{b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+7 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{7/4} \sqrt{a+b x^4}}-\frac{2 b^{5/2} c x \sqrt{a+b x^4}}{15 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{2 b^2 c \sqrt{a+b x^4}}{15 a^2 x}+\frac{2 b^{9/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{7/4} \sqrt{a+b x^4}}+\frac{b^2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{1}{504} \sqrt{a+b x^4} \left(\frac{56 c}{x^9}+\frac{63 d}{x^8}+\frac{72 e}{x^7}+\frac{84 f}{x^6}\right)-\frac{2 b c \sqrt{a+b x^4}}{45 a x^5}-\frac{b d \sqrt{a+b x^4}}{16 a x^4}-\frac{2 b e \sqrt{a+b x^4}}{21 a x^3}-\frac{b f \sqrt{a+b x^4}}{6 a x^2}","-\frac{b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+7 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{7/4} \sqrt{a+b x^4}}-\frac{2 b^{5/2} c x \sqrt{a+b x^4}}{15 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{2 b^2 c \sqrt{a+b x^4}}{15 a^2 x}+\frac{2 b^{9/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{7/4} \sqrt{a+b x^4}}+\frac{b^2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{1}{504} \sqrt{a+b x^4} \left(\frac{56 c}{x^9}+\frac{63 d}{x^8}+\frac{72 e}{x^7}+\frac{84 f}{x^6}\right)-\frac{2 b c \sqrt{a+b x^4}}{45 a x^5}-\frac{b d \sqrt{a+b x^4}}{16 a x^4}-\frac{2 b e \sqrt{a+b x^4}}{21 a x^3}-\frac{b f \sqrt{a+b x^4}}{6 a x^2}",1,"-(((56*c)/x^9 + (63*d)/x^8 + (72*e)/x^7 + (84*f)/x^6)*Sqrt[a + b*x^4])/504 - (2*b*c*Sqrt[a + b*x^4])/(45*a*x^5) - (b*d*Sqrt[a + b*x^4])/(16*a*x^4) - (2*b*e*Sqrt[a + b*x^4])/(21*a*x^3) - (b*f*Sqrt[a + b*x^4])/(6*a*x^2) + (2*b^2*c*Sqrt[a + b*x^4])/(15*a^2*x) - (2*b^(5/2)*c*x*Sqrt[a + b*x^4])/(15*a^2*(Sqrt[a] + Sqrt[b]*x^2)) + (b^2*d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(16*a^(3/2)) + (2*b^(9/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*a^(7/4)*Sqrt[a + b*x^4]) - (b^(7/4)*(7*Sqrt[b]*c + 5*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*a^(7/4)*Sqrt[a + b*x^4])","A",15,13,30,0.4333,1,"{14, 1825, 1833, 1282, 1198, 220, 1196, 1252, 835, 807, 266, 63, 208}"
510,1,476,0,0.439691,"\int x^4 \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2} \, dx","Int[x^4*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2),x]","-\frac{2 a^{11/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(77 \sqrt{a} e+65 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5005 b^{7/4} \sqrt{a+b x^4}}-\frac{a^3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{32 b^{3/2}}-\frac{4 a^3 e x \sqrt{a+b x^4}}{65 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 a^{13/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a+b x^4}}+\frac{4 a^2 c x \sqrt{a+b x^4}}{77 b}-\frac{a^2 d x^2 \sqrt{a+b x^4}}{32 b}+\frac{4 a^2 e x^3 \sqrt{a+b x^4}}{195 b}-\frac{\left(a+b x^4\right)^{5/2} \left(12 a f-35 b d x^2\right)}{420 b^2}+\frac{1}{143} x^5 \left(a+b x^4\right)^{3/2} \left(13 c+11 e x^2\right)+\frac{2 a x^5 \sqrt{a+b x^4} \left(117 c+77 e x^2\right)}{3003}-\frac{a d x^2 \left(a+b x^4\right)^{3/2}}{48 b}+\frac{f x^4 \left(a+b x^4\right)^{5/2}}{14 b}","-\frac{2 a^{11/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(77 \sqrt{a} e+65 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5005 b^{7/4} \sqrt{a+b x^4}}-\frac{a^3 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{32 b^{3/2}}-\frac{4 a^3 e x \sqrt{a+b x^4}}{65 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 a^{13/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a+b x^4}}+\frac{4 a^2 c x \sqrt{a+b x^4}}{77 b}-\frac{a^2 d x^2 \sqrt{a+b x^4}}{32 b}+\frac{4 a^2 e x^3 \sqrt{a+b x^4}}{195 b}-\frac{\left(a+b x^4\right)^{5/2} \left(12 a f-35 b d x^2\right)}{420 b^2}+\frac{1}{143} x^5 \left(a+b x^4\right)^{3/2} \left(13 c+11 e x^2\right)+\frac{2 a x^5 \sqrt{a+b x^4} \left(117 c+77 e x^2\right)}{3003}-\frac{a d x^2 \left(a+b x^4\right)^{3/2}}{48 b}+\frac{f x^4 \left(a+b x^4\right)^{5/2}}{14 b}",1,"(4*a^2*c*x*Sqrt[a + b*x^4])/(77*b) - (a^2*d*x^2*Sqrt[a + b*x^4])/(32*b) + (4*a^2*e*x^3*Sqrt[a + b*x^4])/(195*b) - (4*a^3*e*x*Sqrt[a + b*x^4])/(65*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + (2*a*x^5*(117*c + 77*e*x^2)*Sqrt[a + b*x^4])/3003 - (a*d*x^2*(a + b*x^4)^(3/2))/(48*b) + (x^5*(13*c + 11*e*x^2)*(a + b*x^4)^(3/2))/143 + (f*x^4*(a + b*x^4)^(5/2))/(14*b) - ((12*a*f - 35*b*d*x^2)*(a + b*x^4)^(5/2))/(420*b^2) - (a^3*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(32*b^(3/2)) + (4*a^(13/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(65*b^(7/4)*Sqrt[a + b*x^4]) - (2*a^(11/4)*(65*Sqrt[b]*c + 77*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5005*b^(7/4)*Sqrt[a + b*x^4])","A",16,12,30,0.4000,1,"{1833, 1274, 1280, 1198, 220, 1196, 1252, 833, 780, 195, 217, 206}"
511,1,452,0,0.4078199,"\int x^3 \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2} \, dx","Int[x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2),x]","-\frac{2 a^{11/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(77 \sqrt{a} f+65 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5005 b^{7/4} \sqrt{a+b x^4}}-\frac{a^3 e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{32 b^{3/2}}-\frac{4 a^3 f x \sqrt{a+b x^4}}{65 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 a^{13/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a+b x^4}}+\frac{4 a^2 d x \sqrt{a+b x^4}}{77 b}-\frac{a^2 e x^2 \sqrt{a+b x^4}}{32 b}+\frac{4 a^2 f x^3 \sqrt{a+b x^4}}{195 b}+\frac{\left(a+b x^4\right)^{5/2} \left(6 c+5 e x^2\right)}{60 b}+\frac{1}{143} x^5 \left(a+b x^4\right)^{3/2} \left(13 d+11 f x^2\right)+\frac{2 a x^5 \sqrt{a+b x^4} \left(117 d+77 f x^2\right)}{3003}-\frac{a e x^2 \left(a+b x^4\right)^{3/2}}{48 b}","-\frac{2 a^{11/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(77 \sqrt{a} f+65 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5005 b^{7/4} \sqrt{a+b x^4}}-\frac{a^3 e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{32 b^{3/2}}-\frac{4 a^3 f x \sqrt{a+b x^4}}{65 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 a^{13/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a+b x^4}}+\frac{4 a^2 d x \sqrt{a+b x^4}}{77 b}-\frac{a^2 e x^2 \sqrt{a+b x^4}}{32 b}+\frac{4 a^2 f x^3 \sqrt{a+b x^4}}{195 b}+\frac{\left(a+b x^4\right)^{5/2} \left(6 c+5 e x^2\right)}{60 b}+\frac{1}{143} x^5 \left(a+b x^4\right)^{3/2} \left(13 d+11 f x^2\right)+\frac{2 a x^5 \sqrt{a+b x^4} \left(117 d+77 f x^2\right)}{3003}-\frac{a e x^2 \left(a+b x^4\right)^{3/2}}{48 b}",1,"(4*a^2*d*x*Sqrt[a + b*x^4])/(77*b) - (a^2*e*x^2*Sqrt[a + b*x^4])/(32*b) + (4*a^2*f*x^3*Sqrt[a + b*x^4])/(195*b) - (4*a^3*f*x*Sqrt[a + b*x^4])/(65*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + (2*a*x^5*(117*d + 77*f*x^2)*Sqrt[a + b*x^4])/3003 - (a*e*x^2*(a + b*x^4)^(3/2))/(48*b) + (x^5*(13*d + 11*f*x^2)*(a + b*x^4)^(3/2))/143 + ((6*c + 5*e*x^2)*(a + b*x^4)^(5/2))/(60*b) - (a^3*e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(32*b^(3/2)) + (4*a^(13/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(65*b^(7/4)*Sqrt[a + b*x^4]) - (2*a^(11/4)*(65*Sqrt[b]*d + 77*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5005*b^(7/4)*Sqrt[a + b*x^4])","A",15,11,30,0.3667,1,"{1833, 1252, 780, 195, 217, 206, 1274, 1280, 1198, 220, 1196}"
512,1,427,0,0.3527194,"\int x^2 \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2} \, dx","Int[x^2*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2),x]","\frac{2 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(77 \sqrt{b} c-15 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 b^{5/4} \sqrt{a+b x^4}}-\frac{4 a^{9/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}-\frac{a^3 f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{32 b^{3/2}}+\frac{4 a^2 c x \sqrt{a+b x^4}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 a^2 e x \sqrt{a+b x^4}}{77 b}-\frac{a^2 f x^2 \sqrt{a+b x^4}}{32 b}+\frac{2 a x^3 \sqrt{a+b x^4} \left(77 c+45 e x^2\right)}{1155}+\frac{1}{99} x^3 \left(a+b x^4\right)^{3/2} \left(11 c+9 e x^2\right)+\frac{\left(a+b x^4\right)^{5/2} \left(6 d+5 f x^2\right)}{60 b}-\frac{a f x^2 \left(a+b x^4\right)^{3/2}}{48 b}","\frac{2 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(77 \sqrt{b} c-15 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 b^{5/4} \sqrt{a+b x^4}}-\frac{4 a^{9/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}-\frac{a^3 f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{32 b^{3/2}}+\frac{4 a^2 c x \sqrt{a+b x^4}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 a^2 e x \sqrt{a+b x^4}}{77 b}-\frac{a^2 f x^2 \sqrt{a+b x^4}}{32 b}+\frac{2 a x^3 \sqrt{a+b x^4} \left(77 c+45 e x^2\right)}{1155}+\frac{1}{99} x^3 \left(a+b x^4\right)^{3/2} \left(11 c+9 e x^2\right)+\frac{\left(a+b x^4\right)^{5/2} \left(6 d+5 f x^2\right)}{60 b}-\frac{a f x^2 \left(a+b x^4\right)^{3/2}}{48 b}",1,"(4*a^2*e*x*Sqrt[a + b*x^4])/(77*b) - (a^2*f*x^2*Sqrt[a + b*x^4])/(32*b) + (4*a^2*c*x*Sqrt[a + b*x^4])/(15*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (2*a*x^3*(77*c + 45*e*x^2)*Sqrt[a + b*x^4])/1155 - (a*f*x^2*(a + b*x^4)^(3/2))/(48*b) + (x^3*(11*c + 9*e*x^2)*(a + b*x^4)^(3/2))/99 + ((6*d + 5*f*x^2)*(a + b*x^4)^(5/2))/(60*b) - (a^3*f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(32*b^(3/2)) - (4*a^(9/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a + b*x^4]) + (2*a^(9/4)*(77*Sqrt[b]*c - 15*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(1155*b^(5/4)*Sqrt[a + b*x^4])","A",14,11,30,0.3667,1,"{1833, 1274, 1280, 1198, 220, 1196, 1252, 780, 195, 217, 206}"
513,1,409,0,0.3242784,"\int x \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2} \, dx","Int[x*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2),x]","\frac{2 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(77 \sqrt{b} d-15 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 b^{5/4} \sqrt{a+b x^4}}-\frac{4 a^{9/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}+\frac{3 a^2 c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 \sqrt{b}}+\frac{4 a^2 d x \sqrt{a+b x^4}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 a^2 f x \sqrt{a+b x^4}}{77 b}+\frac{1}{8} c x^2 \left(a+b x^4\right)^{3/2}+\frac{3}{16} a c x^2 \sqrt{a+b x^4}+\frac{1}{99} x^3 \left(a+b x^4\right)^{3/2} \left(11 d+9 f x^2\right)+\frac{2 a x^3 \sqrt{a+b x^4} \left(77 d+45 f x^2\right)}{1155}+\frac{e \left(a+b x^4\right)^{5/2}}{10 b}","\frac{2 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(77 \sqrt{b} d-15 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 b^{5/4} \sqrt{a+b x^4}}-\frac{4 a^{9/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}+\frac{3 a^2 c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 \sqrt{b}}+\frac{4 a^2 d x \sqrt{a+b x^4}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 a^2 f x \sqrt{a+b x^4}}{77 b}+\frac{1}{8} c x^2 \left(a+b x^4\right)^{3/2}+\frac{3}{16} a c x^2 \sqrt{a+b x^4}+\frac{1}{99} x^3 \left(a+b x^4\right)^{3/2} \left(11 d+9 f x^2\right)+\frac{2 a x^3 \sqrt{a+b x^4} \left(77 d+45 f x^2\right)}{1155}+\frac{e \left(a+b x^4\right)^{5/2}}{10 b}",1,"(4*a^2*f*x*Sqrt[a + b*x^4])/(77*b) + (3*a*c*x^2*Sqrt[a + b*x^4])/16 + (4*a^2*d*x*Sqrt[a + b*x^4])/(15*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (2*a*x^3*(77*d + 45*f*x^2)*Sqrt[a + b*x^4])/1155 + (c*x^2*(a + b*x^4)^(3/2))/8 + (x^3*(11*d + 9*f*x^2)*(a + b*x^4)^(3/2))/99 + (e*(a + b*x^4)^(5/2))/(10*b) + (3*a^2*c*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(16*Sqrt[b]) - (4*a^(9/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a + b*x^4]) + (2*a^(9/4)*(77*Sqrt[b]*d - 15*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(1155*b^(5/4)*Sqrt[a + b*x^4])","A",14,11,28,0.3929,1,"{1833, 1248, 641, 195, 217, 206, 1274, 1280, 1198, 220, 1196}"
514,1,382,0,0.2549814,"\int \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2} \, dx","Int[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2),x]","\frac{2 a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(7 \sqrt{a} e+15 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{3/4} \sqrt{a+b x^4}}-\frac{4 a^{9/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}+\frac{3 a^2 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 \sqrt{b}}+\frac{4 a^2 e x \sqrt{a+b x^4}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{1}{63} x \left(a+b x^4\right)^{3/2} \left(9 c+7 e x^2\right)+\frac{2}{105} a x \sqrt{a+b x^4} \left(15 c+7 e x^2\right)+\frac{1}{8} d x^2 \left(a+b x^4\right)^{3/2}+\frac{3}{16} a d x^2 \sqrt{a+b x^4}+\frac{f \left(a+b x^4\right)^{5/2}}{10 b}","\frac{2 a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(7 \sqrt{a} e+15 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{3/4} \sqrt{a+b x^4}}-\frac{4 a^{9/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}+\frac{3 a^2 d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 \sqrt{b}}+\frac{4 a^2 e x \sqrt{a+b x^4}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{1}{63} x \left(a+b x^4\right)^{3/2} \left(9 c+7 e x^2\right)+\frac{2}{105} a x \sqrt{a+b x^4} \left(15 c+7 e x^2\right)+\frac{1}{8} d x^2 \left(a+b x^4\right)^{3/2}+\frac{3}{16} a d x^2 \sqrt{a+b x^4}+\frac{f \left(a+b x^4\right)^{5/2}}{10 b}",1,"(3*a*d*x^2*Sqrt[a + b*x^4])/16 + (4*a^2*e*x*Sqrt[a + b*x^4])/(15*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (2*a*x*(15*c + 7*e*x^2)*Sqrt[a + b*x^4])/105 + (d*x^2*(a + b*x^4)^(3/2))/8 + (x*(9*c + 7*e*x^2)*(a + b*x^4)^(3/2))/63 + (f*(a + b*x^4)^(5/2))/(10*b) + (3*a^2*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(16*Sqrt[b]) - (4*a^(9/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a + b*x^4]) + (2*a^(7/4)*(15*Sqrt[b]*c + 7*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*b^(3/4)*Sqrt[a + b*x^4])","A",13,10,27,0.3704,1,"{1885, 1177, 1198, 220, 1196, 1248, 641, 195, 217, 206}"
515,1,403,0,0.3525203,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x,x]","\frac{2 a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(7 \sqrt{a} f+15 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{3/4} \sqrt{a+b x^4}}-\frac{4 a^{9/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}-\frac{1}{2} a^{3/2} c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{3 a^2 e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 \sqrt{b}}+\frac{4 a^2 f x \sqrt{a+b x^4}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{1}{16} a \sqrt{a+b x^4} \left(8 c+3 e x^2\right)+\frac{1}{24} \left(a+b x^4\right)^{3/2} \left(4 c+3 e x^2\right)+\frac{2}{105} a x \sqrt{a+b x^4} \left(15 d+7 f x^2\right)+\frac{1}{63} x \left(a+b x^4\right)^{3/2} \left(9 d+7 f x^2\right)","\frac{2 a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(7 \sqrt{a} f+15 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 b^{3/4} \sqrt{a+b x^4}}-\frac{4 a^{9/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^4}}-\frac{1}{2} a^{3/2} c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{3 a^2 e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 \sqrt{b}}+\frac{4 a^2 f x \sqrt{a+b x^4}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{1}{16} a \sqrt{a+b x^4} \left(8 c+3 e x^2\right)+\frac{1}{24} \left(a+b x^4\right)^{3/2} \left(4 c+3 e x^2\right)+\frac{2}{105} a x \sqrt{a+b x^4} \left(15 d+7 f x^2\right)+\frac{1}{63} x \left(a+b x^4\right)^{3/2} \left(9 d+7 f x^2\right)",1,"(4*a^2*f*x*Sqrt[a + b*x^4])/(15*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (a*(8*c + 3*e*x^2)*Sqrt[a + b*x^4])/16 + (2*a*x*(15*d + 7*f*x^2)*Sqrt[a + b*x^4])/105 + ((4*c + 3*e*x^2)*(a + b*x^4)^(3/2))/24 + (x*(9*d + 7*f*x^2)*(a + b*x^4)^(3/2))/63 + (3*a^2*e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(16*Sqrt[b]) - (a^(3/2)*c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/2 - (4*a^(9/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a + b*x^4]) + (2*a^(7/4)*(15*Sqrt[b]*d + 7*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*b^(3/4)*Sqrt[a + b*x^4])","A",16,13,30,0.4333,1,"{1833, 1252, 815, 844, 217, 206, 266, 63, 208, 1177, 1198, 220, 1196}"
516,1,404,0,0.3480515,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^2} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^2,x]","\frac{2 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+21 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{12 a^{5/4} \sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{2} a^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{3 a^2 f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 \sqrt{b}}-\frac{\left(a+b x^4\right)^{3/2} \left(7 c-e x^2\right)}{7 x}+\frac{2}{35} x \sqrt{a+b x^4} \left(5 a e+21 b c x^2\right)+\frac{12 a \sqrt{b} c x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{1}{16} a \sqrt{a+b x^4} \left(8 d+3 f x^2\right)+\frac{1}{24} \left(a+b x^4\right)^{3/2} \left(4 d+3 f x^2\right)","\frac{2 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+21 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{12 a^{5/4} \sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{2} a^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{3 a^2 f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{16 \sqrt{b}}-\frac{\left(a+b x^4\right)^{3/2} \left(7 c-e x^2\right)}{7 x}+\frac{2}{35} x \sqrt{a+b x^4} \left(5 a e+21 b c x^2\right)+\frac{12 a \sqrt{b} c x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{1}{16} a \sqrt{a+b x^4} \left(8 d+3 f x^2\right)+\frac{1}{24} \left(a+b x^4\right)^{3/2} \left(4 d+3 f x^2\right)",1,"(12*a*Sqrt[b]*c*x*Sqrt[a + b*x^4])/(5*(Sqrt[a] + Sqrt[b]*x^2)) + (2*x*(5*a*e + 21*b*c*x^2)*Sqrt[a + b*x^4])/35 + (a*(8*d + 3*f*x^2)*Sqrt[a + b*x^4])/16 - ((7*c - e*x^2)*(a + b*x^4)^(3/2))/(7*x) + ((4*d + 3*f*x^2)*(a + b*x^4)^(3/2))/24 + (3*a^2*f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(16*Sqrt[b]) - (a^(3/2)*d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/2 - (12*a^(5/4)*b^(1/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + b*x^4]) + (2*a^(5/4)*(21*Sqrt[b]*c + 5*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(35*b^(1/4)*Sqrt[a + b*x^4])","A",16,14,30,0.4667,1,"{1833, 1272, 1177, 1198, 220, 1196, 1252, 815, 844, 217, 206, 266, 63, 208}"
517,1,406,0,0.3432117,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^3} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^3,x]","\frac{2 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} f+21 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{12 a^{5/4} \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{2} a^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)-\frac{\left(a+b x^4\right)^{3/2} \left(3 c-e x^2\right)}{6 x^2}+\frac{1}{4} \sqrt{a+b x^4} \left(2 a e+3 b c x^2\right)+\frac{3}{4} a \sqrt{b} c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)-\frac{\left(a+b x^4\right)^{3/2} \left(7 d-f x^2\right)}{7 x}+\frac{2}{35} x \sqrt{a+b x^4} \left(5 a f+21 b d x^2\right)+\frac{12 a \sqrt{b} d x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{2 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} f+21 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{12 a^{5/4} \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{2} a^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)-\frac{\left(a+b x^4\right)^{3/2} \left(3 c-e x^2\right)}{6 x^2}+\frac{1}{4} \sqrt{a+b x^4} \left(2 a e+3 b c x^2\right)+\frac{3}{4} a \sqrt{b} c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)-\frac{\left(a+b x^4\right)^{3/2} \left(7 d-f x^2\right)}{7 x}+\frac{2}{35} x \sqrt{a+b x^4} \left(5 a f+21 b d x^2\right)+\frac{12 a \sqrt{b} d x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"(12*a*Sqrt[b]*d*x*Sqrt[a + b*x^4])/(5*(Sqrt[a] + Sqrt[b]*x^2)) + ((2*a*e + 3*b*c*x^2)*Sqrt[a + b*x^4])/4 + (2*x*(5*a*f + 21*b*d*x^2)*Sqrt[a + b*x^4])/35 - ((3*c - e*x^2)*(a + b*x^4)^(3/2))/(6*x^2) - ((7*d - f*x^2)*(a + b*x^4)^(3/2))/(7*x) + (3*a*Sqrt[b]*c*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/4 - (a^(3/2)*e*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/2 - (12*a^(5/4)*b^(1/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + b*x^4]) + (2*a^(5/4)*(21*Sqrt[b]*d + 5*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(35*b^(1/4)*Sqrt[a + b*x^4])","A",16,15,30,0.5000,1,"{1833, 1252, 813, 815, 844, 217, 206, 266, 63, 208, 1272, 1177, 1198, 220, 1196}"
518,1,408,0,0.3359219,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^4} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^4,x]","\frac{2 a^{3/4} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 \sqrt{a+b x^4}}-\frac{12 a^{5/4} \sqrt[4]{b} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{2} a^{3/2} f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)-\frac{\left(a+b x^4\right)^{3/2} \left(5 c-3 e x^2\right)}{15 x^3}-\frac{2 \sqrt{a+b x^4} \left(9 a e-5 b c x^2\right)}{15 x}-\frac{\left(a+b x^4\right)^{3/2} \left(3 d-f x^2\right)}{6 x^2}+\frac{1}{4} \sqrt{a+b x^4} \left(2 a f+3 b d x^2\right)+\frac{3}{4} a \sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{12 a \sqrt{b} e x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{2 a^{3/4} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 \sqrt{a+b x^4}}-\frac{12 a^{5/4} \sqrt[4]{b} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{2} a^{3/2} f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)-\frac{\left(a+b x^4\right)^{3/2} \left(5 c-3 e x^2\right)}{15 x^3}-\frac{2 \sqrt{a+b x^4} \left(9 a e-5 b c x^2\right)}{15 x}-\frac{\left(a+b x^4\right)^{3/2} \left(3 d-f x^2\right)}{6 x^2}+\frac{1}{4} \sqrt{a+b x^4} \left(2 a f+3 b d x^2\right)+\frac{3}{4} a \sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{12 a \sqrt{b} e x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"(12*a*Sqrt[b]*e*x*Sqrt[a + b*x^4])/(5*(Sqrt[a] + Sqrt[b]*x^2)) - (2*(9*a*e - 5*b*c*x^2)*Sqrt[a + b*x^4])/(15*x) + ((2*a*f + 3*b*d*x^2)*Sqrt[a + b*x^4])/4 - ((5*c - 3*e*x^2)*(a + b*x^4)^(3/2))/(15*x^3) - ((3*d - f*x^2)*(a + b*x^4)^(3/2))/(6*x^2) + (3*a*Sqrt[b]*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/4 - (a^(3/2)*f*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/2 - (12*a^(5/4)*b^(1/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + b*x^4]) + (2*a^(3/4)*b^(1/4)*(5*Sqrt[b]*c + 9*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*Sqrt[a + b*x^4])","A",16,14,30,0.4667,1,"{1833, 1272, 1198, 220, 1196, 1252, 813, 815, 844, 217, 206, 266, 63, 208}"
519,1,386,0,0.3469809,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^5} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^5,x]","\frac{2 a^{3/4} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 \sqrt{a+b x^4}}-\frac{12 a^{5/4} \sqrt[4]{b} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{12} \left(a+b x^4\right)^{3/2} \left(\frac{3 c}{x^4}+\frac{4 d}{x^3}+\frac{6 e}{x^2}+\frac{12 f}{x}\right)+\frac{3}{4} b \sqrt{a+b x^4} \left(c+e x^2\right)-\frac{3}{4} \sqrt{a} b c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{2}{15} b x \sqrt{a+b x^4} \left(5 d+9 f x^2\right)+\frac{3}{4} a \sqrt{b} e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{12 a \sqrt{b} f x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{2 a^{3/4} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 \sqrt{a+b x^4}}-\frac{12 a^{5/4} \sqrt[4]{b} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{12} \left(a+b x^4\right)^{3/2} \left(\frac{3 c}{x^4}+\frac{4 d}{x^3}+\frac{6 e}{x^2}+\frac{12 f}{x}\right)+\frac{3}{4} b \sqrt{a+b x^4} \left(c+e x^2\right)-\frac{3}{4} \sqrt{a} b c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{2}{15} b x \sqrt{a+b x^4} \left(5 d+9 f x^2\right)+\frac{3}{4} a \sqrt{b} e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{12 a \sqrt{b} f x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"(12*a*Sqrt[b]*f*x*Sqrt[a + b*x^4])/(5*(Sqrt[a] + Sqrt[b]*x^2)) + (3*b*(c + e*x^2)*Sqrt[a + b*x^4])/4 + (2*b*x*(5*d + 9*f*x^2)*Sqrt[a + b*x^4])/15 - (((3*c)/x^4 + (4*d)/x^3 + (6*e)/x^2 + (12*f)/x)*(a + b*x^4)^(3/2))/12 + (3*a*Sqrt[b]*e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/4 - (3*Sqrt[a]*b*c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/4 - (12*a^(5/4)*b^(1/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + b*x^4]) + (2*a^(3/4)*b^(1/4)*(5*Sqrt[b]*d + 9*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*Sqrt[a + b*x^4])","A",15,15,30,0.5000,1,"{14, 1825, 1833, 1252, 815, 844, 217, 206, 266, 63, 208, 1177, 1198, 220, 1196}"
520,1,387,0,0.3490021,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^6} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^6,x]","\frac{2 \sqrt[4]{a} b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+9 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 \sqrt{a+b x^4}}+\frac{12 b^{3/2} c x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{12 \sqrt[4]{a} b^{5/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{60} \left(a+b x^4\right)^{3/2} \left(\frac{12 c}{x^5}+\frac{15 d}{x^4}+\frac{20 e}{x^3}+\frac{30 f}{x^2}\right)-\frac{2 b \sqrt{a+b x^4} \left(9 c-5 e x^2\right)}{15 x}+\frac{3}{4} b \sqrt{a+b x^4} \left(d+f x^2\right)-\frac{3}{4} \sqrt{a} b d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{3}{4} a \sqrt{b} f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)","\frac{2 \sqrt[4]{a} b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+9 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 \sqrt{a+b x^4}}+\frac{12 b^{3/2} c x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{12 \sqrt[4]{a} b^{5/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{60} \left(a+b x^4\right)^{3/2} \left(\frac{12 c}{x^5}+\frac{15 d}{x^4}+\frac{20 e}{x^3}+\frac{30 f}{x^2}\right)-\frac{2 b \sqrt{a+b x^4} \left(9 c-5 e x^2\right)}{15 x}+\frac{3}{4} b \sqrt{a+b x^4} \left(d+f x^2\right)-\frac{3}{4} \sqrt{a} b d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)+\frac{3}{4} a \sqrt{b} f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)",1,"(12*b^(3/2)*c*x*Sqrt[a + b*x^4])/(5*(Sqrt[a] + Sqrt[b]*x^2)) - (2*b*(9*c - 5*e*x^2)*Sqrt[a + b*x^4])/(15*x) + (3*b*(d + f*x^2)*Sqrt[a + b*x^4])/4 - (((12*c)/x^5 + (15*d)/x^4 + (20*e)/x^3 + (30*f)/x^2)*(a + b*x^4)^(3/2))/60 + (3*a*Sqrt[b]*f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/4 - (3*Sqrt[a]*b*d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/4 - (12*a^(1/4)*b^(5/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + b*x^4]) + (2*a^(1/4)*b^(3/4)*(9*Sqrt[b]*c + 5*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*Sqrt[a + b*x^4])","A",15,15,30,0.5000,1,"{14, 1825, 1833, 1272, 1198, 220, 1196, 1252, 815, 844, 217, 206, 266, 63, 208}"
521,1,392,0,0.3421932,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^7} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^7,x]","\frac{1}{2} b^{3/2} c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{2 \sqrt[4]{a} b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} f+9 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 \sqrt{a+b x^4}}+\frac{12 b^{3/2} d x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{12 \sqrt[4]{a} b^{5/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{60} \left(a+b x^4\right)^{3/2} \left(\frac{10 c}{x^6}+\frac{12 d}{x^5}+\frac{15 e}{x^4}+\frac{20 f}{x^3}\right)-\frac{b \sqrt{a+b x^4} \left(2 c-3 e x^2\right)}{4 x^2}-\frac{2 b \sqrt{a+b x^4} \left(9 d-5 f x^2\right)}{15 x}-\frac{3}{4} \sqrt{a} b e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)","\frac{1}{2} b^{3/2} c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{2 \sqrt[4]{a} b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} f+9 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 \sqrt{a+b x^4}}+\frac{12 b^{3/2} d x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{12 \sqrt[4]{a} b^{5/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{60} \left(a+b x^4\right)^{3/2} \left(\frac{10 c}{x^6}+\frac{12 d}{x^5}+\frac{15 e}{x^4}+\frac{20 f}{x^3}\right)-\frac{b \sqrt{a+b x^4} \left(2 c-3 e x^2\right)}{4 x^2}-\frac{2 b \sqrt{a+b x^4} \left(9 d-5 f x^2\right)}{15 x}-\frac{3}{4} \sqrt{a} b e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)",1,"(12*b^(3/2)*d*x*Sqrt[a + b*x^4])/(5*(Sqrt[a] + Sqrt[b]*x^2)) - (b*(2*c - 3*e*x^2)*Sqrt[a + b*x^4])/(4*x^2) - (2*b*(9*d - 5*f*x^2)*Sqrt[a + b*x^4])/(15*x) - (((10*c)/x^6 + (12*d)/x^5 + (15*e)/x^4 + (20*f)/x^3)*(a + b*x^4)^(3/2))/60 + (b^(3/2)*c*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/2 - (3*Sqrt[a]*b*e*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/4 - (12*a^(1/4)*b^(5/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + b*x^4]) + (2*a^(1/4)*b^(3/4)*(9*Sqrt[b]*d + 5*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*Sqrt[a + b*x^4])","A",15,15,30,0.5000,1,"{14, 1825, 1833, 1252, 813, 844, 217, 206, 266, 63, 208, 1272, 1198, 220, 1196}"
522,1,412,0,0.3939378,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^8} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^8,x]","\frac{2 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(21 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{a} \sqrt{a+b x^4}}+\frac{1}{2} b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{12 b^{3/2} e x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{12 \sqrt[4]{a} b^{5/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{420} \left(a+b x^4\right)^{3/2} \left(\frac{60 c}{x^7}+\frac{70 d}{x^6}+\frac{84 e}{x^5}+\frac{105 f}{x^4}\right)-\frac{2 b \sqrt{a+b x^4} \left(5 c-21 e x^2\right)}{35 x^3}-\frac{b \sqrt{a+b x^4} \left(2 d-3 f x^2\right)}{4 x^2}-\frac{12 b e \sqrt{a+b x^4}}{5 x}-\frac{3}{4} \sqrt{a} b f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)","\frac{2 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(21 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{a} \sqrt{a+b x^4}}+\frac{1}{2} b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{12 b^{3/2} e x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{12 \sqrt[4]{a} b^{5/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{420} \left(a+b x^4\right)^{3/2} \left(\frac{60 c}{x^7}+\frac{70 d}{x^6}+\frac{84 e}{x^5}+\frac{105 f}{x^4}\right)-\frac{2 b \sqrt{a+b x^4} \left(5 c-21 e x^2\right)}{35 x^3}-\frac{b \sqrt{a+b x^4} \left(2 d-3 f x^2\right)}{4 x^2}-\frac{12 b e \sqrt{a+b x^4}}{5 x}-\frac{3}{4} \sqrt{a} b f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)",1,"(-12*b*e*Sqrt[a + b*x^4])/(5*x) + (12*b^(3/2)*e*x*Sqrt[a + b*x^4])/(5*(Sqrt[a] + Sqrt[b]*x^2)) - (2*b*(5*c - 21*e*x^2)*Sqrt[a + b*x^4])/(35*x^3) - (b*(2*d - 3*f*x^2)*Sqrt[a + b*x^4])/(4*x^2) - (((60*c)/x^7 + (70*d)/x^6 + (84*e)/x^5 + (105*f)/x^4)*(a + b*x^4)^(3/2))/420 + (b^(3/2)*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/2 - (3*Sqrt[a]*b*f*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/4 - (12*a^(1/4)*b^(5/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + b*x^4]) + (2*b^(5/4)*(5*Sqrt[b]*c + 21*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(35*a^(1/4)*Sqrt[a + b*x^4])","A",16,16,30,0.5333,1,"{14, 1825, 1833, 1272, 1282, 1198, 220, 1196, 1252, 813, 844, 217, 206, 266, 63, 208}"
523,1,377,0,0.3709436,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^9} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^9,x]","-\frac{3 b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}+\frac{2 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(21 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{a} \sqrt{a+b x^4}}+\frac{1}{2} b^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{12 b^{3/2} f x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{12 \sqrt[4]{a} b^{5/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{560} b \sqrt{a+b x^4} \left(\frac{105 c}{x^4}+\frac{160 d}{x^3}+\frac{280 e}{x^2}+\frac{672 f}{x}\right)-\frac{1}{840} \left(a+b x^4\right)^{3/2} \left(\frac{105 c}{x^8}+\frac{120 d}{x^7}+\frac{140 e}{x^6}+\frac{168 f}{x^5}\right)","-\frac{3 b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}+\frac{2 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(21 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{a} \sqrt{a+b x^4}}+\frac{1}{2} b^{3/2} e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)+\frac{12 b^{3/2} f x \sqrt{a+b x^4}}{5 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{12 \sqrt[4]{a} b^{5/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+b x^4}}-\frac{1}{560} b \sqrt{a+b x^4} \left(\frac{105 c}{x^4}+\frac{160 d}{x^3}+\frac{280 e}{x^2}+\frac{672 f}{x}\right)-\frac{1}{840} \left(a+b x^4\right)^{3/2} \left(\frac{105 c}{x^8}+\frac{120 d}{x^7}+\frac{140 e}{x^6}+\frac{168 f}{x^5}\right)",1,"-(b*((105*c)/x^4 + (160*d)/x^3 + (280*e)/x^2 + (672*f)/x)*Sqrt[a + b*x^4])/560 + (12*b^(3/2)*f*x*Sqrt[a + b*x^4])/(5*(Sqrt[a] + Sqrt[b]*x^2)) - (((105*c)/x^8 + (120*d)/x^7 + (140*e)/x^6 + (168*f)/x^5)*(a + b*x^4)^(3/2))/840 + (b^(3/2)*e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/2 - (3*b^2*c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(16*Sqrt[a]) - (12*a^(1/4)*b^(5/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + b*x^4]) + (2*b^(5/4)*(5*Sqrt[b]*d + 21*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(35*a^(1/4)*Sqrt[a + b*x^4])","A",14,13,30,0.4333,1,"{14, 1825, 1832, 266, 63, 208, 1885, 275, 217, 206, 1198, 220, 1196}"
524,1,405,0,0.4250004,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^{10}} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^10,x]","\frac{2 b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(15 \sqrt{a} e+7 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{3/4} \sqrt{a+b x^4}}-\frac{4 b^{9/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}+\frac{4 b^{5/2} c x \sqrt{a+b x^4}}{15 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{4 b^2 c \sqrt{a+b x^4}}{15 a x}-\frac{3 b^2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}+\frac{1}{2} b^{3/2} f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)-\frac{b \sqrt{a+b x^4} \left(\frac{224 c}{x^5}+\frac{315 d}{x^4}+\frac{480 e}{x^3}+\frac{840 f}{x^2}\right)}{1680}-\frac{1}{504} \left(a+b x^4\right)^{3/2} \left(\frac{56 c}{x^9}+\frac{63 d}{x^8}+\frac{72 e}{x^7}+\frac{84 f}{x^6}\right)","\frac{2 b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(15 \sqrt{a} e+7 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{3/4} \sqrt{a+b x^4}}-\frac{4 b^{9/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}+\frac{4 b^{5/2} c x \sqrt{a+b x^4}}{15 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{4 b^2 c \sqrt{a+b x^4}}{15 a x}-\frac{3 b^2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}+\frac{1}{2} b^{3/2} f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)-\frac{b \sqrt{a+b x^4} \left(\frac{224 c}{x^5}+\frac{315 d}{x^4}+\frac{480 e}{x^3}+\frac{840 f}{x^2}\right)}{1680}-\frac{1}{504} \left(a+b x^4\right)^{3/2} \left(\frac{56 c}{x^9}+\frac{63 d}{x^8}+\frac{72 e}{x^7}+\frac{84 f}{x^6}\right)",1,"-(b*((224*c)/x^5 + (315*d)/x^4 + (480*e)/x^3 + (840*f)/x^2)*Sqrt[a + b*x^4])/1680 - (4*b^2*c*Sqrt[a + b*x^4])/(15*a*x) + (4*b^(5/2)*c*x*Sqrt[a + b*x^4])/(15*a*(Sqrt[a] + Sqrt[b]*x^2)) - (((56*c)/x^9 + (63*d)/x^8 + (72*e)/x^7 + (84*f)/x^6)*(a + b*x^4)^(3/2))/504 + (b^(3/2)*f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/2 - (3*b^2*d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(16*Sqrt[a]) - (4*b^(9/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*a^(3/4)*Sqrt[a + b*x^4]) + (2*b^(7/4)*(7*Sqrt[b]*c + 15*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*a^(3/4)*Sqrt[a + b*x^4])","A",15,14,30,0.4667,1,"{14, 1825, 1833, 1282, 1198, 220, 1196, 1252, 844, 217, 206, 266, 63, 208}"
525,1,399,0,0.4201717,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^{11}} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^11,x]","\frac{2 b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(15 \sqrt{a} f+7 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{3/4} \sqrt{a+b x^4}}-\frac{4 b^{9/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{b^2 c \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^{5/2} d x \sqrt{a+b x^4}}{15 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{4 b^2 d \sqrt{a+b x^4}}{15 a x}-\frac{3 b^2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{b \sqrt{a+b x^4} \left(\frac{168 c}{x^6}+\frac{224 d}{x^5}+\frac{315 e}{x^4}+\frac{480 f}{x^3}\right)}{1680}-\frac{\left(a+b x^4\right)^{3/2} \left(\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}\right)}{2520}","\frac{2 b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(15 \sqrt{a} f+7 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{3/4} \sqrt{a+b x^4}}-\frac{4 b^{9/4} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{b^2 c \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^{5/2} d x \sqrt{a+b x^4}}{15 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{4 b^2 d \sqrt{a+b x^4}}{15 a x}-\frac{3 b^2 e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{b \sqrt{a+b x^4} \left(\frac{168 c}{x^6}+\frac{224 d}{x^5}+\frac{315 e}{x^4}+\frac{480 f}{x^3}\right)}{1680}-\frac{\left(a+b x^4\right)^{3/2} \left(\frac{252 c}{x^{10}}+\frac{280 d}{x^9}+\frac{315 e}{x^8}+\frac{360 f}{x^7}\right)}{2520}",1,"-(b*((168*c)/x^6 + (224*d)/x^5 + (315*e)/x^4 + (480*f)/x^3)*Sqrt[a + b*x^4])/1680 - (b^2*c*Sqrt[a + b*x^4])/(10*a*x^2) - (4*b^2*d*Sqrt[a + b*x^4])/(15*a*x) + (4*b^(5/2)*d*x*Sqrt[a + b*x^4])/(15*a*(Sqrt[a] + Sqrt[b]*x^2)) - (((252*c)/x^10 + (280*d)/x^9 + (315*e)/x^8 + (360*f)/x^7)*(a + b*x^4)^(3/2))/2520 - (3*b^2*e*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(16*Sqrt[a]) - (4*b^(9/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*a^(3/4)*Sqrt[a + b*x^4]) + (2*b^(7/4)*(7*Sqrt[b]*d + 15*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(105*a^(3/4)*Sqrt[a + b*x^4])","A",13,12,30,0.4000,1,"{14, 1825, 1833, 1252, 807, 266, 63, 208, 1282, 1198, 220, 1196}"
526,1,424,0,0.4617265,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^{12}} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^12,x]","-\frac{2 b^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(15 \sqrt{b} c-77 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 a^{5/4} \sqrt{a+b x^4}}-\frac{4 b^{9/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{4 b^2 c \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 d \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^{5/2} e x \sqrt{a+b x^4}}{15 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{4 b^2 e \sqrt{a+b x^4}}{15 a x}-\frac{3 b^2 f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{b \sqrt{a+b x^4} \left(\frac{1440 c}{x^7}+\frac{1848 d}{x^6}+\frac{2464 e}{x^5}+\frac{3465 f}{x^4}\right)}{18480}-\frac{\left(a+b x^4\right)^{3/2} \left(\frac{360 c}{x^{11}}+\frac{396 d}{x^{10}}+\frac{440 e}{x^9}+\frac{495 f}{x^8}\right)}{3960}","-\frac{2 b^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(15 \sqrt{b} c-77 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 a^{5/4} \sqrt{a+b x^4}}-\frac{4 b^{9/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{4 b^2 c \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 d \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^{5/2} e x \sqrt{a+b x^4}}{15 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{4 b^2 e \sqrt{a+b x^4}}{15 a x}-\frac{3 b^2 f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{b \sqrt{a+b x^4} \left(\frac{1440 c}{x^7}+\frac{1848 d}{x^6}+\frac{2464 e}{x^5}+\frac{3465 f}{x^4}\right)}{18480}-\frac{\left(a+b x^4\right)^{3/2} \left(\frac{360 c}{x^{11}}+\frac{396 d}{x^{10}}+\frac{440 e}{x^9}+\frac{495 f}{x^8}\right)}{3960}",1,"-(b*((1440*c)/x^7 + (1848*d)/x^6 + (2464*e)/x^5 + (3465*f)/x^4)*Sqrt[a + b*x^4])/18480 - (4*b^2*c*Sqrt[a + b*x^4])/(77*a*x^3) - (b^2*d*Sqrt[a + b*x^4])/(10*a*x^2) - (4*b^2*e*Sqrt[a + b*x^4])/(15*a*x) + (4*b^(5/2)*e*x*Sqrt[a + b*x^4])/(15*a*(Sqrt[a] + Sqrt[b]*x^2)) - (((360*c)/x^11 + (396*d)/x^10 + (440*e)/x^9 + (495*f)/x^8)*(a + b*x^4)^(3/2))/3960 - (3*b^2*f*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(16*Sqrt[a]) - (4*b^(9/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*a^(3/4)*Sqrt[a + b*x^4]) - (2*b^(9/4)*(15*Sqrt[b]*c - 77*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(1155*a^(5/4)*Sqrt[a + b*x^4])","A",14,12,30,0.4000,1,"{14, 1825, 1833, 1282, 1198, 220, 1196, 1252, 807, 266, 63, 208}"
527,1,449,0,0.4901318,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^{13}} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^13,x]","\frac{b^3 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{32 a^{3/2}}-\frac{2 b^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(15 \sqrt{b} d-77 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 a^{5/4} \sqrt{a+b x^4}}-\frac{4 b^{9/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{b^2 c \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 e \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^{5/2} f x \sqrt{a+b x^4}}{15 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{4 b^2 f \sqrt{a+b x^4}}{15 a x}-\frac{b \sqrt{a+b x^4} \left(\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right)}{18480}-\frac{\left(a+b x^4\right)^{3/2} \left(\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right)}{1980}","\frac{b^3 c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{32 a^{3/2}}-\frac{2 b^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(15 \sqrt{b} d-77 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 a^{5/4} \sqrt{a+b x^4}}-\frac{4 b^{9/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a+b x^4}}-\frac{b^2 c \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 d \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 e \sqrt{a+b x^4}}{10 a x^2}+\frac{4 b^{5/2} f x \sqrt{a+b x^4}}{15 a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{4 b^2 f \sqrt{a+b x^4}}{15 a x}-\frac{b \sqrt{a+b x^4} \left(\frac{1155 c}{x^8}+\frac{1440 d}{x^7}+\frac{1848 e}{x^6}+\frac{2464 f}{x^5}\right)}{18480}-\frac{\left(a+b x^4\right)^{3/2} \left(\frac{165 c}{x^{12}}+\frac{180 d}{x^{11}}+\frac{198 e}{x^{10}}+\frac{220 f}{x^9}\right)}{1980}",1,"-(b*((1155*c)/x^8 + (1440*d)/x^7 + (1848*e)/x^6 + (2464*f)/x^5)*Sqrt[a + b*x^4])/18480 - (b^2*c*Sqrt[a + b*x^4])/(32*a*x^4) - (4*b^2*d*Sqrt[a + b*x^4])/(77*a*x^3) - (b^2*e*Sqrt[a + b*x^4])/(10*a*x^2) - (4*b^2*f*Sqrt[a + b*x^4])/(15*a*x) + (4*b^(5/2)*f*x*Sqrt[a + b*x^4])/(15*a*(Sqrt[a] + Sqrt[b]*x^2)) - (((165*c)/x^12 + (180*d)/x^11 + (198*e)/x^10 + (220*f)/x^9)*(a + b*x^4)^(3/2))/1980 + (b^3*c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(32*a^(3/2)) - (4*b^(9/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*a^(3/4)*Sqrt[a + b*x^4]) - (2*b^(9/4)*(15*Sqrt[b]*d - 77*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(1155*a^(5/4)*Sqrt[a + b*x^4])","A",15,13,30,0.4333,1,"{14, 1825, 1833, 1252, 835, 807, 266, 63, 208, 1282, 1198, 220, 1196}"
528,1,474,0,0.5493608,"\int \frac{\left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^{3/2}}{x^{14}} \, dx","Int[((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^14,x]","-\frac{2 b^{11/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(65 \sqrt{a} e+77 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5005 a^{7/4} \sqrt{a+b x^4}}-\frac{4 b^{7/2} c x \sqrt{a+b x^4}}{65 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 b^3 c \sqrt{a+b x^4}}{65 a^2 x}+\frac{4 b^{13/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 a^{7/4} \sqrt{a+b x^4}}+\frac{b^3 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{32 a^{3/2}}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{b^2 d \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 e \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 f \sqrt{a+b x^4}}{10 a x^2}-\frac{b \sqrt{a+b x^4} \left(\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right)}{240240}-\frac{\left(a+b x^4\right)^{3/2} \left(\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right)}{8580}","-\frac{2 b^{11/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(65 \sqrt{a} e+77 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5005 a^{7/4} \sqrt{a+b x^4}}-\frac{4 b^{7/2} c x \sqrt{a+b x^4}}{65 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{4 b^3 c \sqrt{a+b x^4}}{65 a^2 x}+\frac{4 b^{13/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 a^{7/4} \sqrt{a+b x^4}}+\frac{b^3 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{32 a^{3/2}}-\frac{4 b^2 c \sqrt{a+b x^4}}{195 a x^5}-\frac{b^2 d \sqrt{a+b x^4}}{32 a x^4}-\frac{4 b^2 e \sqrt{a+b x^4}}{77 a x^3}-\frac{b^2 f \sqrt{a+b x^4}}{10 a x^2}-\frac{b \sqrt{a+b x^4} \left(\frac{12320 c}{x^9}+\frac{15015 d}{x^8}+\frac{18720 e}{x^7}+\frac{24024 f}{x^6}\right)}{240240}-\frac{\left(a+b x^4\right)^{3/2} \left(\frac{660 c}{x^{13}}+\frac{715 d}{x^{12}}+\frac{780 e}{x^{11}}+\frac{858 f}{x^{10}}\right)}{8580}",1,"-(b*((12320*c)/x^9 + (15015*d)/x^8 + (18720*e)/x^7 + (24024*f)/x^6)*Sqrt[a + b*x^4])/240240 - (4*b^2*c*Sqrt[a + b*x^4])/(195*a*x^5) - (b^2*d*Sqrt[a + b*x^4])/(32*a*x^4) - (4*b^2*e*Sqrt[a + b*x^4])/(77*a*x^3) - (b^2*f*Sqrt[a + b*x^4])/(10*a*x^2) + (4*b^3*c*Sqrt[a + b*x^4])/(65*a^2*x) - (4*b^(7/2)*c*x*Sqrt[a + b*x^4])/(65*a^2*(Sqrt[a] + Sqrt[b]*x^2)) - (((660*c)/x^13 + (715*d)/x^12 + (780*e)/x^11 + (858*f)/x^10)*(a + b*x^4)^(3/2))/8580 + (b^3*d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(32*a^(3/2)) + (4*b^(13/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(65*a^(7/4)*Sqrt[a + b*x^4]) - (2*b^(11/4)*(77*Sqrt[b]*c + 65*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5005*a^(7/4)*Sqrt[a + b*x^4])","A",16,13,30,0.4333,1,"{14, 1825, 1833, 1282, 1198, 220, 1196, 1252, 835, 807, 266, 63, 208}"
529,1,361,0,0.3003903,"\int \frac{x^4 \left(c+d x+e x^2+f x^3\right)}{\sqrt{a+b x^4}} \, dx","Int[(x^4*(c + d*x + e*x^2 + f*x^3))/Sqrt[a + b*x^4],x]","-\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 b^{7/4} \sqrt{a+b x^4}}+\frac{3 a^{5/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^4}}-\frac{\sqrt{a+b x^4} \left(4 a f-3 b d x^2\right)}{12 b^2}-\frac{a d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}-\frac{3 a e x \sqrt{a+b x^4}}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{c x \sqrt{a+b x^4}}{3 b}+\frac{e x^3 \sqrt{a+b x^4}}{5 b}+\frac{f x^4 \sqrt{a+b x^4}}{6 b}","-\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{a} e+5 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 b^{7/4} \sqrt{a+b x^4}}+\frac{3 a^{5/4} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^4}}-\frac{\sqrt{a+b x^4} \left(4 a f-3 b d x^2\right)}{12 b^2}-\frac{a d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}-\frac{3 a e x \sqrt{a+b x^4}}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{c x \sqrt{a+b x^4}}{3 b}+\frac{e x^3 \sqrt{a+b x^4}}{5 b}+\frac{f x^4 \sqrt{a+b x^4}}{6 b}",1,"(c*x*Sqrt[a + b*x^4])/(3*b) + (e*x^3*Sqrt[a + b*x^4])/(5*b) + (f*x^4*Sqrt[a + b*x^4])/(6*b) - (3*a*e*x*Sqrt[a + b*x^4])/(5*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) - ((4*a*f - 3*b*d*x^2)*Sqrt[a + b*x^4])/(12*b^2) - (a*d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*b^(3/2)) + (3*a^(5/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[a + b*x^4]) - (a^(3/4)*(5*Sqrt[b]*c + 9*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(30*b^(7/4)*Sqrt[a + b*x^4])","A",12,10,30,0.3333,1,"{1833, 1280, 1198, 220, 1196, 1252, 833, 780, 217, 206}"
530,1,336,0,0.2650525,"\int \frac{x^3 \left(c+d x+e x^2+f x^3\right)}{\sqrt{a+b x^4}} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3))/Sqrt[a + b*x^4],x]","-\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 b^{7/4} \sqrt{a+b x^4}}+\frac{3 a^{5/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^4}}-\frac{a e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}-\frac{3 a f x \sqrt{a+b x^4}}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{\sqrt{a+b x^4} \left(2 c+e x^2\right)}{4 b}+\frac{d x \sqrt{a+b x^4}}{3 b}+\frac{f x^3 \sqrt{a+b x^4}}{5 b}","-\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{a} f+5 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 b^{7/4} \sqrt{a+b x^4}}+\frac{3 a^{5/4} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^4}}-\frac{a e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}-\frac{3 a f x \sqrt{a+b x^4}}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{\sqrt{a+b x^4} \left(2 c+e x^2\right)}{4 b}+\frac{d x \sqrt{a+b x^4}}{3 b}+\frac{f x^3 \sqrt{a+b x^4}}{5 b}",1,"(d*x*Sqrt[a + b*x^4])/(3*b) + (f*x^3*Sqrt[a + b*x^4])/(5*b) - (3*a*f*x*Sqrt[a + b*x^4])/(5*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + ((2*c + e*x^2)*Sqrt[a + b*x^4])/(4*b) - (a*e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*b^(3/2)) + (3*a^(5/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[a + b*x^4]) - (a^(3/4)*(5*Sqrt[b]*d + 9*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(30*b^(7/4)*Sqrt[a + b*x^4])","A",11,9,30,0.3000,1,"{1833, 1252, 780, 217, 206, 1280, 1198, 220, 1196}"
531,1,308,0,0.2219977,"\int \frac{x^2 \left(c+d x+e x^2+f x^3\right)}{\sqrt{a+b x^4}} \, dx","Int[(x^2*(c + d*x + e*x^2 + f*x^3))/Sqrt[a + b*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{b} c-\sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 b^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}-\frac{a f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}+\frac{c x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{\sqrt{a+b x^4} \left(2 d+f x^2\right)}{4 b}+\frac{e x \sqrt{a+b x^4}}{3 b}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{b} c-\sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 b^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}-\frac{a f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}+\frac{c x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{\sqrt{a+b x^4} \left(2 d+f x^2\right)}{4 b}+\frac{e x \sqrt{a+b x^4}}{3 b}",1,"(e*x*Sqrt[a + b*x^4])/(3*b) + (c*x*Sqrt[a + b*x^4])/(Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + ((2*d + f*x^2)*Sqrt[a + b*x^4])/(4*b) - (a*f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*b^(3/2)) - (a^(1/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(b^(3/4)*Sqrt[a + b*x^4]) + (a^(1/4)*(3*Sqrt[b]*c - Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(6*b^(5/4)*Sqrt[a + b*x^4])","A",10,9,30,0.3000,1,"{1833, 1280, 1198, 220, 1196, 1252, 780, 217, 206}"
532,1,299,0,0.1982888,"\int \frac{x \left(c+d x+e x^2+f x^3\right)}{\sqrt{a+b x^4}} \, dx","Int[(x*(c + d*x + e*x^2 + f*x^3))/Sqrt[a + b*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{b} d-\sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 b^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}+\frac{d x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{e \sqrt{a+b x^4}}{2 b}+\frac{f x \sqrt{a+b x^4}}{3 b}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{b} d-\sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 b^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}+\frac{d x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{e \sqrt{a+b x^4}}{2 b}+\frac{f x \sqrt{a+b x^4}}{3 b}",1,"(e*Sqrt[a + b*x^4])/(2*b) + (f*x*Sqrt[a + b*x^4])/(3*b) + (d*x*Sqrt[a + b*x^4])/(Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (c*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*Sqrt[b]) - (a^(1/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(b^(3/4)*Sqrt[a + b*x^4]) + (a^(1/4)*(3*Sqrt[b]*d - Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(6*b^(5/4)*Sqrt[a + b*x^4])","A",10,9,28,0.3214,1,"{1833, 1248, 641, 217, 206, 1280, 1198, 220, 1196}"
533,1,276,0,0.1415693,"\int \frac{c+d x+e x^2+f x^3}{\sqrt{a+b x^4}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/Sqrt[a + b*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\frac{\sqrt{b} c}{\sqrt{a}}+e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}+\frac{e x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{f \sqrt{a+b x^4}}{2 b}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\frac{\sqrt{b} c}{\sqrt{a}}+e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}+\frac{e x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{f \sqrt{a+b x^4}}{2 b}",1,"(f*Sqrt[a + b*x^4])/(2*b) + (e*x*Sqrt[a + b*x^4])/(Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*Sqrt[b]) - (a^(1/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(b^(3/4)*Sqrt[a + b*x^4]) + (a^(1/4)*((Sqrt[b]*c)/Sqrt[a] + e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*b^(3/4)*Sqrt[a + b*x^4])","A",9,8,27,0.2963,1,"{1885, 1198, 220, 1196, 1248, 641, 217, 206}"
534,1,285,0,0.1799432,"\int \frac{c+d x+e x^2+f x^3}{x \sqrt{a+b x^4}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x*Sqrt[a + b*x^4]),x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\frac{\sqrt{b} d}{\sqrt{a}}+f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}+\frac{f x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\frac{\sqrt{b} d}{\sqrt{a}}+f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}+\frac{f x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"(f*x*Sqrt[a + b*x^4])/(Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*Sqrt[b]) - (c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(2*Sqrt[a]) - (a^(1/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(b^(3/4)*Sqrt[a + b*x^4]) + (a^(1/4)*((Sqrt[b]*d)/Sqrt[a] + f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*b^(3/4)*Sqrt[a + b*x^4])","A",12,11,30,0.3667,1,"{1832, 266, 63, 208, 1885, 275, 217, 206, 1198, 220, 1196}"
535,1,309,0,0.224348,"\int \frac{c+d x+e x^2+f x^3}{x^2 \sqrt{a+b x^4}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x^2*Sqrt[a + b*x^4]),x]","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} e+\sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{a x}+\frac{\sqrt{b} c x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}+\frac{f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} e+\sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{a x}+\frac{\sqrt{b} c x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}+\frac{f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}",1,"-((c*Sqrt[a + b*x^4])/(a*x)) + (Sqrt[b]*c*x*Sqrt[a + b*x^4])/(a*(Sqrt[a] + Sqrt[b]*x^2)) + (f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*Sqrt[b]) - (d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(2*Sqrt[a]) - (b^(1/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(a^(3/4)*Sqrt[a + b*x^4]) + ((Sqrt[b]*c + Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*b^(1/4)*Sqrt[a + b*x^4])","A",13,12,30,0.4000,1,"{1833, 1282, 1198, 220, 1196, 1252, 844, 217, 206, 266, 63, 208}"
536,1,300,0,0.2158681,"\int \frac{c+d x+e x^2+f x^3}{x^3 \sqrt{a+b x^4}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x^3*Sqrt[a + b*x^4]),x]","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} f+\sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{2 a x^2}-\frac{d \sqrt{a+b x^4}}{a x}+\frac{\sqrt{b} d x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} f+\sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{2 a x^2}-\frac{d \sqrt{a+b x^4}}{a x}+\frac{\sqrt{b} d x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"-(c*Sqrt[a + b*x^4])/(2*a*x^2) - (d*Sqrt[a + b*x^4])/(a*x) + (Sqrt[b]*d*x*Sqrt[a + b*x^4])/(a*(Sqrt[a] + Sqrt[b]*x^2)) - (e*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(2*Sqrt[a]) - (b^(1/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(a^(3/4)*Sqrt[a + b*x^4]) + ((Sqrt[b]*d + Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*b^(1/4)*Sqrt[a + b*x^4])","A",11,10,30,0.3333,1,"{1833, 1252, 807, 266, 63, 208, 1282, 1198, 220, 1196}"
537,1,323,0,0.2583993,"\int \frac{c+d x+e x^2+f x^3}{x^4 \sqrt{a+b x^4}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x^4*Sqrt[a + b*x^4]),x]","-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} c-3 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{3 a x^3}-\frac{d \sqrt{a+b x^4}}{2 a x^2}-\frac{e \sqrt{a+b x^4}}{a x}+\frac{\sqrt{b} e x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}","-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} c-3 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{3 a x^3}-\frac{d \sqrt{a+b x^4}}{2 a x^2}-\frac{e \sqrt{a+b x^4}}{a x}+\frac{\sqrt{b} e x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"-(c*Sqrt[a + b*x^4])/(3*a*x^3) - (d*Sqrt[a + b*x^4])/(2*a*x^2) - (e*Sqrt[a + b*x^4])/(a*x) + (Sqrt[b]*e*x*Sqrt[a + b*x^4])/(a*(Sqrt[a] + Sqrt[b]*x^2)) - (f*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(2*Sqrt[a]) - (b^(1/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(a^(3/4)*Sqrt[a + b*x^4]) - (b^(1/4)*(Sqrt[b]*c - 3*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(6*a^(5/4)*Sqrt[a + b*x^4])","A",12,10,30,0.3333,1,"{1833, 1282, 1198, 220, 1196, 1252, 807, 266, 63, 208}"
538,1,346,0,0.2813003,"\int \frac{c+d x+e x^2+f x^3}{x^5 \sqrt{a+b x^4}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x^5*Sqrt[a + b*x^4]),x]","\frac{b c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} d-3 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{4 a x^4}-\frac{d \sqrt{a+b x^4}}{3 a x^3}-\frac{e \sqrt{a+b x^4}}{2 a x^2}-\frac{f \sqrt{a+b x^4}}{a x}+\frac{\sqrt{b} f x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{b c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} d-3 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{4 a x^4}-\frac{d \sqrt{a+b x^4}}{3 a x^3}-\frac{e \sqrt{a+b x^4}}{2 a x^2}-\frac{f \sqrt{a+b x^4}}{a x}+\frac{\sqrt{b} f x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"-(c*Sqrt[a + b*x^4])/(4*a*x^4) - (d*Sqrt[a + b*x^4])/(3*a*x^3) - (e*Sqrt[a + b*x^4])/(2*a*x^2) - (f*Sqrt[a + b*x^4])/(a*x) + (Sqrt[b]*f*x*Sqrt[a + b*x^4])/(a*(Sqrt[a] + Sqrt[b]*x^2)) + (b*c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(4*a^(3/2)) - (b^(1/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(a^(3/4)*Sqrt[a + b*x^4]) - (b^(1/4)*(Sqrt[b]*d - 3*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(6*a^(5/4)*Sqrt[a + b*x^4])","A",13,11,30,0.3667,1,"{1833, 1252, 835, 807, 266, 63, 208, 1282, 1198, 220, 1196}"
539,1,377,0,0.3265459,"\int \frac{c+d x+e x^2+f x^3}{x^6 \sqrt{a+b x^4}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x^6*Sqrt[a + b*x^4]),x]","-\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+9 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 a^{7/4} \sqrt{a+b x^4}}-\frac{3 b^{3/2} c x \sqrt{a+b x^4}}{5 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{3 b^{5/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a+b x^4}}+\frac{3 b c \sqrt{a+b x^4}}{5 a^2 x}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{c \sqrt{a+b x^4}}{5 a x^5}-\frac{d \sqrt{a+b x^4}}{4 a x^4}-\frac{e \sqrt{a+b x^4}}{3 a x^3}-\frac{f \sqrt{a+b x^4}}{2 a x^2}","-\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{a} e+9 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 a^{7/4} \sqrt{a+b x^4}}-\frac{3 b^{3/2} c x \sqrt{a+b x^4}}{5 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{3 b^{5/4} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a+b x^4}}+\frac{3 b c \sqrt{a+b x^4}}{5 a^2 x}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{c \sqrt{a+b x^4}}{5 a x^5}-\frac{d \sqrt{a+b x^4}}{4 a x^4}-\frac{e \sqrt{a+b x^4}}{3 a x^3}-\frac{f \sqrt{a+b x^4}}{2 a x^2}",1,"-(c*Sqrt[a + b*x^4])/(5*a*x^5) - (d*Sqrt[a + b*x^4])/(4*a*x^4) - (e*Sqrt[a + b*x^4])/(3*a*x^3) - (f*Sqrt[a + b*x^4])/(2*a*x^2) + (3*b*c*Sqrt[a + b*x^4])/(5*a^2*x) - (3*b^(3/2)*c*x*Sqrt[a + b*x^4])/(5*a^2*(Sqrt[a] + Sqrt[b]*x^2)) + (b*d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(4*a^(3/2)) + (3*b^(5/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*a^(7/4)*Sqrt[a + b*x^4]) - (b^(3/4)*(9*Sqrt[b]*c + 5*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(30*a^(7/4)*Sqrt[a + b*x^4])","A",14,11,30,0.3667,1,"{1833, 1282, 1198, 220, 1196, 1252, 835, 807, 266, 63, 208}"
540,1,365,0,0.5228664,"\int \frac{x^6 \left(c+d x+e x^2+f x^3\right)}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(x^6*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x]","\frac{x \left(a e+a f x-b c x^2-b d x^3\right)}{2 b^2 \sqrt{a+b x^4}}+\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{b} c-5 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 b^{9/4} \sqrt{a+b x^4}}+\frac{3 c x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{a} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}+\frac{d \sqrt{a+b x^4}}{b^2}+\frac{e x \sqrt{a+b x^4}}{3 b^2}+\frac{f x^2 \sqrt{a+b x^4}}{4 b^2}-\frac{3 a f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{5/2}}","\frac{x \left(a e+a f x-b c x^2-b d x^3\right)}{2 b^2 \sqrt{a+b x^4}}+\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{b} c-5 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 b^{9/4} \sqrt{a+b x^4}}+\frac{3 c x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{a} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}+\frac{d \sqrt{a+b x^4}}{b^2}+\frac{e x \sqrt{a+b x^4}}{3 b^2}+\frac{f x^2 \sqrt{a+b x^4}}{4 b^2}-\frac{3 a f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{5/2}}",1,"(x*(a*e + a*f*x - b*c*x^2 - b*d*x^3))/(2*b^2*Sqrt[a + b*x^4]) + (d*Sqrt[a + b*x^4])/b^2 + (e*x*Sqrt[a + b*x^4])/(3*b^2) + (f*x^2*Sqrt[a + b*x^4])/(4*b^2) + (3*c*x*Sqrt[a + b*x^4])/(2*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) - (3*a*f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*b^(5/2)) - (3*a^(1/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*b^(7/4)*Sqrt[a + b*x^4]) + (a^(1/4)*(9*Sqrt[b]*c - 5*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(12*b^(9/4)*Sqrt[a + b*x^4])","A",12,11,30,0.3667,1,"{1828, 1885, 1888, 1198, 220, 1196, 1819, 1815, 641, 217, 206}"
541,1,343,0,0.3672291,"\int \frac{x^5 \left(c+d x+e x^2+f x^3\right)}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(x^5*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x]","\frac{x \left(a f-b c x-b d x^2-b e x^3\right)}{2 b^2 \sqrt{a+b x^4}}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}+\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{b} d-5 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 b^{9/4} \sqrt{a+b x^4}}+\frac{3 d x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{a} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}+\frac{e \sqrt{a+b x^4}}{b^2}+\frac{f x \sqrt{a+b x^4}}{3 b^2}","\frac{x \left(a f-b c x-b d x^2-b e x^3\right)}{2 b^2 \sqrt{a+b x^4}}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}+\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(9 \sqrt{b} d-5 \sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 b^{9/4} \sqrt{a+b x^4}}+\frac{3 d x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{a} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}+\frac{e \sqrt{a+b x^4}}{b^2}+\frac{f x \sqrt{a+b x^4}}{3 b^2}",1,"(x*(a*f - b*c*x - b*d*x^2 - b*e*x^3))/(2*b^2*Sqrt[a + b*x^4]) + (e*Sqrt[a + b*x^4])/b^2 + (f*x*Sqrt[a + b*x^4])/(3*b^2) + (3*d*x*Sqrt[a + b*x^4])/(2*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + (c*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*b^(3/2)) - (3*a^(1/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*b^(7/4)*Sqrt[a + b*x^4]) + (a^(1/4)*(9*Sqrt[b]*d - 5*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(12*b^(9/4)*Sqrt[a + b*x^4])","A",11,10,30,0.3333,1,"{1828, 1885, 1248, 641, 217, 206, 1888, 1198, 220, 1196}"
542,1,314,0,0.2678901,"\int \frac{x^4 \left(c+d x+e x^2+f x^3\right)}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(x^4*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x]","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} e+\sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} b^{7/4} \sqrt{a+b x^4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}+\frac{3 e x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{a} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}+\frac{f \sqrt{a+b x^4}}{b^2}-\frac{x \left(c+d x+e x^2+f x^3\right)}{2 b \sqrt{a+b x^4}}","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} e+\sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} b^{7/4} \sqrt{a+b x^4}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}+\frac{3 e x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{a} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}+\frac{f \sqrt{a+b x^4}}{b^2}-\frac{x \left(c+d x+e x^2+f x^3\right)}{2 b \sqrt{a+b x^4}}",1,"-(x*(c + d*x + e*x^2 + f*x^3))/(2*b*Sqrt[a + b*x^4]) + (f*Sqrt[a + b*x^4])/b^2 + (3*e*x*Sqrt[a + b*x^4])/(2*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + (d*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*b^(3/2)) - (3*a^(1/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*b^(7/4)*Sqrt[a + b*x^4]) + ((Sqrt[b]*c + 3*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*b^(7/4)*Sqrt[a + b*x^4])","A",10,9,30,0.3000,1,"{1828, 1885, 1198, 220, 1196, 1248, 641, 217, 206}"
543,1,297,0,0.1999012,"\int \frac{x^3 \left(c+d x+e x^2+f x^3\right)}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x]","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} f+\sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} b^{7/4} \sqrt{a+b x^4}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}+\frac{3 f x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{a} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}-\frac{c+d x+e x^2+f x^3}{2 b \sqrt{a+b x^4}}","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(3 \sqrt{a} f+\sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} b^{7/4} \sqrt{a+b x^4}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}+\frac{3 f x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{a} f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}-\frac{c+d x+e x^2+f x^3}{2 b \sqrt{a+b x^4}}",1,"-(c + d*x + e*x^2 + f*x^3)/(2*b*Sqrt[a + b*x^4]) + (3*f*x*Sqrt[a + b*x^4])/(2*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + (e*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*b^(3/2)) - (3*a^(1/4)*f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*b^(7/4)*Sqrt[a + b*x^4]) + ((Sqrt[b]*d + 3*Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*b^(7/4)*Sqrt[a + b*x^4])","A",9,8,30,0.2667,1,"{1823, 1885, 275, 217, 206, 1198, 220, 1196}"
544,1,333,0,0.2509409,"\int \frac{x^2 \left(c+d x+e x^2+f x^3\right)}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(x^2*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x]","-\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} c-\sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{5/4} \sqrt{a+b x^4}}+\frac{c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}+\frac{f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}-\frac{x \left(a e+a f x-b c x^2-b d x^3\right)}{2 a b \sqrt{a+b x^4}}-\frac{c x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{d \sqrt{a+b x^4}}{2 a b}","-\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} c-\sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{5/4} \sqrt{a+b x^4}}+\frac{c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}+\frac{f \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}-\frac{x \left(a e+a f x-b c x^2-b d x^3\right)}{2 a b \sqrt{a+b x^4}}-\frac{c x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{d \sqrt{a+b x^4}}{2 a b}",1,"-(x*(a*e + a*f*x - b*c*x^2 - b*d*x^3))/(2*a*b*Sqrt[a + b*x^4]) - (d*Sqrt[a + b*x^4])/(2*a*b) - (c*x*Sqrt[a + b*x^4])/(2*a*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (f*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*b^(3/2)) + (c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*b^(3/4)*Sqrt[a + b*x^4]) - ((Sqrt[b]*c - Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(3/4)*b^(5/4)*Sqrt[a + b*x^4])","A",10,9,30,0.3000,1,"{1828, 1885, 1198, 220, 1196, 1248, 641, 217, 206}"
545,1,303,0,0.1925569,"\int \frac{x \left(c+d x+e x^2+f x^3\right)}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(x*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x]","-\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} d-\sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{5/4} \sqrt{a+b x^4}}+\frac{d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}-\frac{x \left(a f-b c x-b d x^2-b e x^3\right)}{2 a b \sqrt{a+b x^4}}-\frac{d x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{e \sqrt{a+b x^4}}{2 a b}","-\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} d-\sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{5/4} \sqrt{a+b x^4}}+\frac{d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}-\frac{x \left(a f-b c x-b d x^2-b e x^3\right)}{2 a b \sqrt{a+b x^4}}-\frac{d x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{e \sqrt{a+b x^4}}{2 a b}",1,"-(x*(a*f - b*c*x - b*d*x^2 - b*e*x^3))/(2*a*b*Sqrt[a + b*x^4]) - (e*Sqrt[a + b*x^4])/(2*a*b) - (d*x*Sqrt[a + b*x^4])/(2*a*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + (d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*b^(3/4)*Sqrt[a + b*x^4]) - ((Sqrt[b]*d - Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(3/4)*b^(5/4)*Sqrt[a + b*x^4])","A",7,6,28,0.2143,1,"{1828, 1885, 261, 1198, 220, 1196}"
546,1,275,0,0.1171979,"\int \frac{c+d x+e x^2+f x^3}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^(3/2),x]","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} c-\sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} b^{3/4} \sqrt{a+b x^4}}+\frac{e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}-\frac{a f-b x \left(c+d x+e x^2\right)}{2 a b \sqrt{a+b x^4}}-\frac{e x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} c-\sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} b^{3/4} \sqrt{a+b x^4}}+\frac{e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}-\frac{a f-b x \left(c+d x+e x^2\right)}{2 a b \sqrt{a+b x^4}}-\frac{e x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"-(e*x*Sqrt[a + b*x^4])/(2*a*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) - (a*f - b*x*(c + d*x + e*x^2))/(2*a*b*Sqrt[a + b*x^4]) + (e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*b^(3/4)*Sqrt[a + b*x^4]) + ((Sqrt[b]*c - Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(5/4)*b^(3/4)*Sqrt[a + b*x^4])","A",4,4,27,0.1481,1,"{1854, 1198, 220, 1196}"
547,1,323,0,0.2919921,"\int \frac{c+d x+e x^2+f x^3}{x \left(a+b x^4\right)^{3/2}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x*(a + b*x^4)^(3/2)),x]","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} d-\sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} b^{3/4} \sqrt{a+b x^4}}+\frac{f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}+\frac{x \left(a d+a e x+a f x^2-b c x^3\right)}{2 a^2 \sqrt{a+b x^4}}+\frac{c \sqrt{a+b x^4}}{2 a^2}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{f x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{b} d-\sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} b^{3/4} \sqrt{a+b x^4}}+\frac{f \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}+\frac{x \left(a d+a e x+a f x^2-b c x^3\right)}{2 a^2 \sqrt{a+b x^4}}+\frac{c \sqrt{a+b x^4}}{2 a^2}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{f x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"(x*(a*d + a*e*x + a*f*x^2 - b*c*x^3))/(2*a^2*Sqrt[a + b*x^4]) + (c*Sqrt[a + b*x^4])/(2*a^2) - (f*x*Sqrt[a + b*x^4])/(2*a*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) - (c*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(2*a^(3/2)) + (f*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*b^(3/4)*Sqrt[a + b*x^4]) + ((Sqrt[b]*d - Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(5/4)*b^(3/4)*Sqrt[a + b*x^4])","A",11,10,30,0.3333,1,"{1829, 1832, 266, 63, 208, 1885, 261, 1198, 220, 1196}"
548,1,344,0,0.3825746,"\int \frac{c+d x+e x^2+f x^3}{x^2 \left(a+b x^4\right)^{3/2}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x^2*(a + b*x^4)^(3/2)),x]","\frac{x \left(a e+a f x-b c x^2-b d x^3\right)}{2 a^2 \sqrt{a+b x^4}}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} e+3 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{7/4} \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{a^2 x}+\frac{3 \sqrt{b} c x \sqrt{a+b x^4}}{2 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+b x^4}}+\frac{d \sqrt{a+b x^4}}{2 a^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}","\frac{x \left(a e+a f x-b c x^2-b d x^3\right)}{2 a^2 \sqrt{a+b x^4}}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} e+3 \sqrt{b} c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{7/4} \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{a^2 x}+\frac{3 \sqrt{b} c x \sqrt{a+b x^4}}{2 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{b} c \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+b x^4}}+\frac{d \sqrt{a+b x^4}}{2 a^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}",1,"(x*(a*e + a*f*x - b*c*x^2 - b*d*x^3))/(2*a^2*Sqrt[a + b*x^4]) + (d*Sqrt[a + b*x^4])/(2*a^2) - (c*Sqrt[a + b*x^4])/(a^2*x) + (3*Sqrt[b]*c*x*Sqrt[a + b*x^4])/(2*a^2*(Sqrt[a] + Sqrt[b]*x^2)) - (d*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(2*a^(3/2)) - (3*b^(1/4)*c*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(7/4)*Sqrt[a + b*x^4]) + ((3*Sqrt[b]*c + Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(7/4)*b^(1/4)*Sqrt[a + b*x^4])","A",13,12,30,0.4000,1,"{1829, 1833, 1835, 1584, 1198, 220, 1196, 21, 266, 50, 63, 208}"
549,1,367,0,0.4777776,"\int \frac{c+d x+e x^2+f x^3}{x^3 \left(a+b x^4\right)^{3/2}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x^3*(a + b*x^4)^(3/2)),x]","\frac{x \left(a f-b c x-b d x^2-b e x^3\right)}{2 a^2 \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{2 a^2 x^2}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} f+3 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{7/4} \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{d \sqrt{a+b x^4}}{a^2 x}+\frac{3 \sqrt{b} d x \sqrt{a+b x^4}}{2 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+b x^4}}+\frac{e \sqrt{a+b x^4}}{2 a^2}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}","\frac{x \left(a f-b c x-b d x^2-b e x^3\right)}{2 a^2 \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{2 a^2 x^2}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(\sqrt{a} f+3 \sqrt{b} d\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{7/4} \sqrt[4]{b} \sqrt{a+b x^4}}-\frac{d \sqrt{a+b x^4}}{a^2 x}+\frac{3 \sqrt{b} d x \sqrt{a+b x^4}}{2 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+b x^4}}+\frac{e \sqrt{a+b x^4}}{2 a^2}-\frac{e \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}",1,"(x*(a*f - b*c*x - b*d*x^2 - b*e*x^3))/(2*a^2*Sqrt[a + b*x^4]) + (e*Sqrt[a + b*x^4])/(2*a^2) - (c*Sqrt[a + b*x^4])/(2*a^2*x^2) - (d*Sqrt[a + b*x^4])/(a^2*x) + (3*Sqrt[b]*d*x*Sqrt[a + b*x^4])/(2*a^2*(Sqrt[a] + Sqrt[b]*x^2)) - (e*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(2*a^(3/2)) - (3*b^(1/4)*d*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(7/4)*Sqrt[a + b*x^4]) + ((3*Sqrt[b]*d + Sqrt[a]*f)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(7/4)*b^(1/4)*Sqrt[a + b*x^4])","A",15,12,30,0.4000,1,"{1829, 1833, 1835, 1584, 1198, 220, 1196, 21, 266, 50, 63, 208}"
550,1,387,0,0.6062592,"\int \frac{c+d x+e x^2+f x^3}{x^4 \left(a+b x^4\right)^{3/2}} \, dx","Int[(c + d*x + e*x^2 + f*x^3)/(x^4*(a + b*x^4)^(3/2)),x]","-\frac{x \left(b c+b d x+b e x^2+b f x^3\right)}{2 a^2 \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{b} c-9 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{9/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{3 a^2 x^3}-\frac{d \sqrt{a+b x^4}}{2 a^2 x^2}-\frac{e \sqrt{a+b x^4}}{a^2 x}+\frac{3 \sqrt{b} e x \sqrt{a+b x^4}}{2 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{b} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+b x^4}}+\frac{f \sqrt{a+b x^4}}{2 a^2}-\frac{f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}","-\frac{x \left(b c+b d x+b e x^2+b f x^3\right)}{2 a^2 \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} \left(5 \sqrt{b} c-9 \sqrt{a} e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{9/4} \sqrt{a+b x^4}}-\frac{c \sqrt{a+b x^4}}{3 a^2 x^3}-\frac{d \sqrt{a+b x^4}}{2 a^2 x^2}-\frac{e \sqrt{a+b x^4}}{a^2 x}+\frac{3 \sqrt{b} e x \sqrt{a+b x^4}}{2 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt[4]{b} e \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+b x^4}}+\frac{f \sqrt{a+b x^4}}{2 a^2}-\frac{f \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}",1,"-(x*(b*c + b*d*x + b*e*x^2 + b*f*x^3))/(2*a^2*Sqrt[a + b*x^4]) + (f*Sqrt[a + b*x^4])/(2*a^2) - (c*Sqrt[a + b*x^4])/(3*a^2*x^3) - (d*Sqrt[a + b*x^4])/(2*a^2*x^2) - (e*Sqrt[a + b*x^4])/(a^2*x) + (3*Sqrt[b]*e*x*Sqrt[a + b*x^4])/(2*a^2*(Sqrt[a] + Sqrt[b]*x^2)) - (f*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(2*a^(3/2)) - (3*b^(1/4)*e*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(7/4)*Sqrt[a + b*x^4]) - (b^(1/4)*(5*Sqrt[b]*c - 9*Sqrt[a]*e)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(12*a^(9/4)*Sqrt[a + b*x^4])","A",17,13,30,0.4333,1,"{1829, 1833, 1835, 1585, 1584, 1198, 220, 1196, 21, 266, 50, 63, 208}"
551,1,269,0,0.2560171,"\int (g x)^m \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^p \, dx","Int[(g*x)^m*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^p,x]","\frac{c (g x)^{m+1} \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{4},-p;\frac{m+5}{4};-\frac{b x^4}{a}\right)}{g (m+1)}+\frac{d (g x)^{m+2} \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{4},-p;\frac{m+6}{4};-\frac{b x^4}{a}\right)}{g^2 (m+2)}+\frac{e (g x)^{m+3} \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+3}{4},-p;\frac{m+7}{4};-\frac{b x^4}{a}\right)}{g^3 (m+3)}+\frac{f (g x)^{m+4} \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+4}{4},-p;\frac{m+8}{4};-\frac{b x^4}{a}\right)}{g^4 (m+4)}","\frac{c (g x)^{m+1} \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{4},-p;\frac{m+5}{4};-\frac{b x^4}{a}\right)}{g (m+1)}+\frac{d (g x)^{m+2} \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{4},-p;\frac{m+6}{4};-\frac{b x^4}{a}\right)}{g^2 (m+2)}+\frac{e (g x)^{m+3} \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+3}{4},-p;\frac{m+7}{4};-\frac{b x^4}{a}\right)}{g^3 (m+3)}+\frac{f (g x)^{m+4} \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+4}{4},-p;\frac{m+8}{4};-\frac{b x^4}{a}\right)}{g^4 (m+4)}",1,"(c*(g*x)^(1 + m)*(a + b*x^4)^p*Hypergeometric2F1[(1 + m)/4, -p, (5 + m)/4, -((b*x^4)/a)])/(g*(1 + m)*(1 + (b*x^4)/a)^p) + (d*(g*x)^(2 + m)*(a + b*x^4)^p*Hypergeometric2F1[(2 + m)/4, -p, (6 + m)/4, -((b*x^4)/a)])/(g^2*(2 + m)*(1 + (b*x^4)/a)^p) + (e*(g*x)^(3 + m)*(a + b*x^4)^p*Hypergeometric2F1[(3 + m)/4, -p, (7 + m)/4, -((b*x^4)/a)])/(g^3*(3 + m)*(1 + (b*x^4)/a)^p) + (f*(g*x)^(4 + m)*(a + b*x^4)^p*Hypergeometric2F1[(4 + m)/4, -p, (8 + m)/4, -((b*x^4)/a)])/(g^4*(4 + m)*(1 + (b*x^4)/a)^p)","A",14,4,30,0.1333,1,"{1833, 1336, 365, 364}"
552,1,170,0,0.1310251,"\int \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^p \, dx","Int[(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^p,x]","c x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^4}{a}\right)+\frac{1}{2} d x^2 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^4}{a}\right)+\frac{1}{3} e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-\frac{b x^4}{a}\right)+\frac{f \left(a+b x^4\right)^{p+1}}{4 b (p+1)}","\frac{c x \left(a+b x^4\right)^{p+1} \, _2F_1\left(1,p+\frac{5}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{a}+\frac{d x^2 \left(a+b x^4\right)^{p+1} \, _2F_1\left(1,p+\frac{3}{2};\frac{3}{2};-\frac{b x^4}{a}\right)}{2 a}+\frac{e x^3 \left(a+b x^4\right)^{p+1} \, _2F_1\left(1,p+\frac{7}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{3 a}+\frac{f \left(a+b x^4\right)^{p+1}}{4 b (p+1)}",1,"(f*(a + b*x^4)^(1 + p))/(4*b*(1 + p)) + (c*x*(a + b*x^4)^p*Hypergeometric2F1[1/4, -p, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^p + (d*x^2*(a + b*x^4)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^4)/a)])/(2*(1 + (b*x^4)/a)^p) + (e*x^3*(a + b*x^4)^p*Hypergeometric2F1[3/4, -p, 7/4, -((b*x^4)/a)])/(3*(1 + (b*x^4)/a)^p)","A",12,8,25,0.3200,1,"{1885, 1204, 246, 245, 365, 364, 1248, 641}"
553,1,175,0,0.1822502,"\int x^3 \left(c+d x+e x^2+f x^3\right) \left(a+b x^4\right)^p \, dx","Int[x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^p,x]","\frac{c \left(a+b x^4\right)^{p+1}}{4 b (p+1)}+\frac{1}{5} d x^5 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{4},-p;\frac{9}{4};-\frac{b x^4}{a}\right)+\frac{1}{6} e x^6 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^4}{a}\right)+\frac{1}{7} f x^7 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{7}{4},-p;\frac{11}{4};-\frac{b x^4}{a}\right)","\frac{c \left(a+b x^4\right)^{p+1}}{4 b (p+1)}+\frac{1}{5} d x^5 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{4},-p;\frac{9}{4};-\frac{b x^4}{a}\right)+\frac{1}{6} e x^6 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^4}{a}\right)+\frac{1}{7} f x^7 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{7}{4},-p;\frac{11}{4};-\frac{b x^4}{a}\right)",1,"(c*(a + b*x^4)^(1 + p))/(4*b*(1 + p)) + (d*x^5*(a + b*x^4)^p*Hypergeometric2F1[5/4, -p, 9/4, -((b*x^4)/a)])/(5*(1 + (b*x^4)/a)^p) + (e*x^6*(a + b*x^4)^p*Hypergeometric2F1[3/2, -p, 5/2, -((b*x^4)/a)])/(6*(1 + (b*x^4)/a)^p) + (f*x^7*(a + b*x^4)^p*Hypergeometric2F1[7/4, -p, 11/4, -((b*x^4)/a)])/(7*(1 + (b*x^4)/a)^p)","A",13,7,28,0.2500,1,"{1833, 1252, 764, 261, 365, 364, 1336}"
554,1,8,0,0.0098654,"\int \frac{1+x+x^2+x^3+x^4}{1-x^5} \, dx","Int[(1 + x + x^2 + x^3 + x^4)/(1 - x^5),x]","-\log (1-x)","-\log (1-x)",1,"-Log[1 - x]","A",2,2,22,0.09091,1,"{1586, 31}"
555,1,10,0,0.0146238,"\int \frac{243-162 x+108 x^2-72 x^3+48 x^4-32 x^5}{729-64 x^6} \, dx","Int[(243 - 162*x + 108*x^2 - 72*x^3 + 48*x^4 - 32*x^5)/(729 - 64*x^6),x]","\frac{1}{2} \log (2 x+3)","\frac{1}{2} \log (2 x+3)",1,"Log[3 + 2*x]/2","A",2,2,35,0.05714,1,"{1586, 31}"
556,1,10,0,0.0133504,"\int \frac{243+162 x+108 x^2+72 x^3+48 x^4+32 x^5}{729-64 x^6} \, dx","Int[(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6),x]","-\frac{1}{2} \log (3-2 x)","-\frac{1}{2} \log (3-2 x)",1,"-Log[3 - 2*x]/2","A",2,2,35,0.05714,1,"{1586, 31}"
557,1,10,0,0.009933,"\int \frac{81+36 x^2+16 x^4}{729-64 x^6} \, dx","Int[(81 + 36*x^2 + 16*x^4)/(729 - 64*x^6),x]","\frac{1}{6} \tanh ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{6} \tanh ^{-1}\left(\frac{2 x}{3}\right)",1,"ArcTanh[(2*x)/3]/6","A",2,2,22,0.09091,1,"{1586, 206}"
558,1,24,0,0.0237435,"\int \frac{81+54 x-24 x^3-16 x^4}{729-64 x^6} \, dx","Int[(81 + 54*x - 24*x^3 - 16*x^4)/(729 - 64*x^6),x]","-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{3 \sqrt{3}}",1,"-ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(3*Sqrt[3])","A",3,3,25,0.1200,1,"{1586, 618, 204}"
559,1,50,0,0.049007,"\int \frac{3-2 x}{729-64 x^6} \, dx","Int[(3 - 2*x)/(729 - 64*x^6),x]","-\frac{1}{972} \log \left(4 x^2-6 x+9\right)+\frac{1}{486} \log (2 x+3)+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{162 \sqrt{3}}","-\frac{1}{972} \log \left(4 x^2-6 x+9\right)+\frac{1}{486} \log (2 x+3)+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{162 \sqrt{3}}",1,"ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(162*Sqrt[3]) + Log[3 + 2*x]/486 - Log[9 - 6*x + 4*x^2]/972","A",6,5,15,0.3333,1,"{1586, 2058, 628, 618, 204}"
560,1,50,0,0.0481794,"\int \frac{3+2 x}{729-64 x^6} \, dx","Int[(3 + 2*x)/(729 - 64*x^6),x]","\frac{1}{972} \log \left(4 x^2+6 x+9\right)-\frac{1}{486} \log (3-2 x)-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{162 \sqrt{3}}","\frac{1}{972} \log \left(4 x^2+6 x+9\right)-\frac{1}{486} \log (3-2 x)-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{162 \sqrt{3}}",1,"-ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(162*Sqrt[3]) - Log[3 - 2*x]/486 + Log[9 + 6*x + 4*x^2]/972","A",6,5,15,0.3333,1,"{1586, 2058, 618, 204, 628}"
561,1,60,0,0.0512375,"\int \frac{9-6 x+4 x^2}{729-64 x^6} \, dx","Int[(9 - 6*x + 4*x^2)/(729 - 64*x^6),x]","-\frac{1}{324} \log \left(4 x^2+6 x+9\right)-\frac{1}{324} \log (3-2 x)+\frac{1}{108} \log (2 x+3)+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{54 \sqrt{3}}","-\frac{1}{324} \log \left(4 x^2+6 x+9\right)-\frac{1}{324} \log (3-2 x)+\frac{1}{108} \log (2 x+3)+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{54 \sqrt{3}}",1,"ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(54*Sqrt[3]) - Log[3 - 2*x]/324 + Log[3 + 2*x]/108 - Log[9 + 6*x + 4*x^2]/324","A",7,6,20,0.3000,1,"{1586, 2058, 634, 618, 204, 628}"
562,1,60,0,0.0485636,"\int \frac{9+6 x+4 x^2}{729-64 x^6} \, dx","Int[(9 + 6*x + 4*x^2)/(729 - 64*x^6),x]","\frac{1}{324} \log \left(4 x^2-6 x+9\right)-\frac{1}{108} \log (3-2 x)+\frac{1}{324} \log (2 x+3)-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{54 \sqrt{3}}","\frac{1}{324} \log \left(4 x^2-6 x+9\right)-\frac{1}{108} \log (3-2 x)+\frac{1}{324} \log (2 x+3)-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{54 \sqrt{3}}",1,"-ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(54*Sqrt[3]) - Log[3 - 2*x]/108 + Log[3 + 2*x]/324 + Log[9 - 6*x + 4*x^2]/324","A",7,6,20,0.3000,1,"{1586, 2058, 634, 618, 204, 628}"
563,1,50,0,0.0262205,"\int \frac{27-8 x^3}{729-64 x^6} \, dx","Int[(27 - 8*x^3)/(729 - 64*x^6),x]","-\frac{1}{108} \log \left(4 x^2-6 x+9\right)+\frac{1}{54} \log (2 x+3)-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{18 \sqrt{3}}","-\frac{1}{108} \log \left(4 x^2-6 x+9\right)+\frac{1}{54} \log (2 x+3)-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{18 \sqrt{3}}",1,"-ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(18*Sqrt[3]) + Log[3 + 2*x]/54 - Log[9 - 6*x + 4*x^2]/108","A",7,7,17,0.4118,1,"{26, 200, 31, 634, 618, 204, 628}"
564,1,50,0,0.0428354,"\int \frac{27+36 x+24 x^2+8 x^3}{729-64 x^6} \, dx","Int[(27 + 36*x + 24*x^2 + 8*x^3)/(729 - 64*x^6),x]","\frac{1}{36} \log \left(4 x^2-6 x+9\right)-\frac{1}{18} \log (3-2 x)-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{18 \sqrt{3}}","\frac{1}{36} \log \left(4 x^2-6 x+9\right)-\frac{1}{18} \log (3-2 x)-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{18 \sqrt{3}}",1,"-ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(18*Sqrt[3]) - Log[3 - 2*x]/18 + Log[9 - 6*x + 4*x^2]/36","A",7,6,25,0.2400,1,"{1586, 2058, 634, 618, 204, 628}"
565,1,110,0,0.1181367,"\int \frac{243-162 x+108 x^2-72 x^3+48 x^4-32 x^5}{\left(729-64 x^6\right)^2} \, dx","Int[(243 - 162*x + 108*x^2 - 72*x^3 + 48*x^4 - 32*x^5)/(729 - 64*x^6)^2,x]","-\frac{\log \left(4 x^2-6 x+9\right)}{17496}-\frac{\log \left(4 x^2+6 x+9\right)}{17496}-\frac{1}{2916 (2 x+3)}-\frac{\log (3-2 x)}{17496}+\frac{5 \log (2 x+3)}{17496}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{8748 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{2916 \sqrt{3}}","-\frac{\log \left(4 x^2-6 x+9\right)}{17496}-\frac{\log \left(4 x^2+6 x+9\right)}{17496}-\frac{1}{2916 (2 x+3)}-\frac{\log (3-2 x)}{17496}+\frac{5 \log (2 x+3)}{17496}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{8748 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{2916 \sqrt{3}}",1,"-1/(2916*(3 + 2*x)) - ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(8748*Sqrt[3]) + ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(2916*Sqrt[3]) - Log[3 - 2*x]/17496 + (5*Log[3 + 2*x])/17496 - Log[9 - 6*x + 4*x^2]/17496 - Log[9 + 6*x + 4*x^2]/17496","A",11,6,35,0.1714,1,"{1586, 2074, 634, 618, 204, 628}"
566,1,110,0,0.1172629,"\int \frac{243+162 x+108 x^2+72 x^3+48 x^4+32 x^5}{\left(729-64 x^6\right)^2} \, dx","Int[(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6)^2,x]","\frac{\log \left(4 x^2-6 x+9\right)}{17496}+\frac{\log \left(4 x^2+6 x+9\right)}{17496}+\frac{1}{2916 (3-2 x)}-\frac{5 \log (3-2 x)}{17496}+\frac{\log (2 x+3)}{17496}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{2916 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{8748 \sqrt{3}}","\frac{\log \left(4 x^2-6 x+9\right)}{17496}+\frac{\log \left(4 x^2+6 x+9\right)}{17496}+\frac{1}{2916 (3-2 x)}-\frac{5 \log (3-2 x)}{17496}+\frac{\log (2 x+3)}{17496}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{2916 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{8748 \sqrt{3}}",1,"1/(2916*(3 - 2*x)) - ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(2916*Sqrt[3]) + ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(8748*Sqrt[3]) - (5*Log[3 - 2*x])/17496 + Log[3 + 2*x]/17496 + Log[9 - 6*x + 4*x^2]/17496 + Log[9 + 6*x + 4*x^2]/17496","A",11,6,35,0.1714,1,"{1586, 2074, 634, 618, 204, 628}"
567,1,81,0,0.0692554,"\int \frac{81+36 x^2+16 x^4}{\left(729-64 x^6\right)^2} \, dx","Int[(81 + 36*x^2 + 16*x^4)/(729 - 64*x^6)^2,x]","\frac{1}{17496 (3-2 x)}-\frac{1}{17496 (2 x+3)}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{13122 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{13122 \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{2 x}{3}\right)}{8748}","\frac{1}{17496 (3-2 x)}-\frac{1}{17496 (2 x+3)}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{13122 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{13122 \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{2 x}{3}\right)}{8748}",1,"1/(17496*(3 - 2*x)) - 1/(17496*(3 + 2*x)) - ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(13122*Sqrt[3]) + ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(13122*Sqrt[3]) + ArcTanh[(2*x)/3]/8748","A",8,5,22,0.2273,1,"{1586, 1170, 207, 618, 204}"
568,1,92,0,0.1164529,"\int \frac{81+54 x-24 x^3-16 x^4}{\left(729-64 x^6\right)^2} \, dx","Int[(81 + 54*x - 24*x^3 - 16*x^4)/(729 - 64*x^6)^2,x]","\frac{x}{4374 \left(4 x^2-6 x+9\right)}-\frac{\log \left(4 x^2-6 x+9\right)}{157464}+\frac{\log \left(4 x^2+6 x+9\right)}{52488}-\frac{\log (3-2 x)}{26244}+\frac{\log (2 x+3)}{78732}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{4374 \sqrt{3}}","\frac{x}{4374 \left(4 x^2-6 x+9\right)}-\frac{\log \left(4 x^2-6 x+9\right)}{157464}+\frac{\log \left(4 x^2+6 x+9\right)}{52488}-\frac{\log (3-2 x)}{26244}+\frac{\log (2 x+3)}{78732}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{4374 \sqrt{3}}",1,"x/(4374*(9 - 6*x + 4*x^2)) - ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(4374*Sqrt[3]) - Log[3 - 2*x]/26244 + Log[3 + 2*x]/78732 - Log[9 - 6*x + 4*x^2]/157464 + Log[9 + 6*x + 4*x^2]/52488","A",11,7,25,0.2800,1,"{1586, 2074, 638, 618, 204, 634, 628}"
569,1,148,0,0.1715983,"\int \frac{3-2 x}{\left(729-64 x^6\right)^2} \, dx","Int[(3 - 2*x)/(729 - 64*x^6)^2,x]","\frac{3-x}{708588 \left(4 x^2-6 x+9\right)}+\frac{x}{236196 \left(4 x^2+6 x+9\right)}-\frac{\log \left(4 x^2-6 x+9\right)}{944784}+\frac{\log \left(4 x^2+6 x+9\right)}{8503056}-\frac{1}{708588 (2 x+3)}-\frac{\log (3-2 x)}{4251528}+\frac{\log (2 x+3)}{472392}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{1417176 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}","\frac{3-x}{708588 \left(4 x^2-6 x+9\right)}+\frac{x}{236196 \left(4 x^2+6 x+9\right)}-\frac{\log \left(4 x^2-6 x+9\right)}{944784}+\frac{\log \left(4 x^2+6 x+9\right)}{8503056}-\frac{1}{708588 (2 x+3)}-\frac{\log (3-2 x)}{4251528}+\frac{\log (2 x+3)}{472392}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{1417176 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}",1,"-1/(708588*(3 + 2*x)) + (3 - x)/(708588*(9 - 6*x + 4*x^2)) + x/(236196*(9 + 6*x + 4*x^2)) - ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(1417176*Sqrt[3]) + ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(157464*Sqrt[3]) - Log[3 - 2*x]/4251528 + Log[3 + 2*x]/472392 - Log[9 - 6*x + 4*x^2]/944784 + Log[9 + 6*x + 4*x^2]/8503056","A",17,7,15,0.4667,1,"{1586, 2074, 638, 618, 204, 634, 628}"
570,1,146,0,0.1725113,"\int \frac{3+2 x}{\left(729-64 x^6\right)^2} \, dx","Int[(3 + 2*x)/(729 - 64*x^6)^2,x]","\frac{x}{236196 \left(4 x^2-6 x+9\right)}-\frac{x+3}{708588 \left(4 x^2+6 x+9\right)}-\frac{\log \left(4 x^2-6 x+9\right)}{8503056}+\frac{\log \left(4 x^2+6 x+9\right)}{944784}+\frac{1}{708588 (3-2 x)}-\frac{\log (3-2 x)}{472392}+\frac{\log (2 x+3)}{4251528}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{1417176 \sqrt{3}}","\frac{x}{236196 \left(4 x^2-6 x+9\right)}-\frac{x+3}{708588 \left(4 x^2+6 x+9\right)}-\frac{\log \left(4 x^2-6 x+9\right)}{8503056}+\frac{\log \left(4 x^2+6 x+9\right)}{944784}+\frac{1}{708588 (3-2 x)}-\frac{\log (3-2 x)}{472392}+\frac{\log (2 x+3)}{4251528}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{1417176 \sqrt{3}}",1,"1/(708588*(3 - 2*x)) + x/(236196*(9 - 6*x + 4*x^2)) - (3 + x)/(708588*(9 + 6*x + 4*x^2)) - ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(157464*Sqrt[3]) + ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(1417176*Sqrt[3]) - Log[3 - 2*x]/472392 + Log[3 + 2*x]/4251528 - Log[9 - 6*x + 4*x^2]/8503056 + Log[9 + 6*x + 4*x^2]/944784","A",17,7,15,0.4667,1,"{1586, 2074, 638, 618, 204, 634, 628}"
571,1,142,0,0.1484385,"\int \frac{9-6 x+4 x^2}{\left(729-64 x^6\right)^2} \, dx","Int[(9 - 6*x + 4*x^2)/(729 - 64*x^6)^2,x]","\frac{4 x+3}{236196 \left(4 x^2+6 x+9\right)}-\frac{\log \left(4 x^2-6 x+9\right)}{944784}-\frac{5 \log \left(4 x^2+6 x+9\right)}{2834352}+\frac{1}{472392 (3-2 x)}-\frac{1}{157464 (2 x+3)}-\frac{\log (3-2 x)}{354294}+\frac{\log (2 x+3)}{118098}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{472392 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{52488 \sqrt{3}}","\frac{4 x+3}{236196 \left(4 x^2+6 x+9\right)}-\frac{\log \left(4 x^2-6 x+9\right)}{944784}-\frac{5 \log \left(4 x^2+6 x+9\right)}{2834352}+\frac{1}{472392 (3-2 x)}-\frac{1}{157464 (2 x+3)}-\frac{\log (3-2 x)}{354294}+\frac{\log (2 x+3)}{118098}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{472392 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{52488 \sqrt{3}}",1,"1/(472392*(3 - 2*x)) - 1/(157464*(3 + 2*x)) + (3 + 4*x)/(236196*(9 + 6*x + 4*x^2)) - ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(472392*Sqrt[3]) + ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(52488*Sqrt[3]) - Log[3 - 2*x]/354294 + Log[3 + 2*x]/118098 - Log[9 - 6*x + 4*x^2]/944784 - (5*Log[9 + 6*x + 4*x^2])/2834352","A",14,7,20,0.3500,1,"{1586, 2074, 634, 618, 204, 628, 614}"
572,1,142,0,0.1448149,"\int \frac{9+6 x+4 x^2}{\left(729-64 x^6\right)^2} \, dx","Int[(9 + 6*x + 4*x^2)/(729 - 64*x^6)^2,x]","-\frac{3-4 x}{236196 \left(4 x^2-6 x+9\right)}+\frac{5 \log \left(4 x^2-6 x+9\right)}{2834352}+\frac{\log \left(4 x^2+6 x+9\right)}{944784}+\frac{1}{157464 (3-2 x)}-\frac{1}{472392 (2 x+3)}-\frac{\log (3-2 x)}{118098}+\frac{\log (2 x+3)}{354294}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{52488 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{472392 \sqrt{3}}","-\frac{3-4 x}{236196 \left(4 x^2-6 x+9\right)}+\frac{5 \log \left(4 x^2-6 x+9\right)}{2834352}+\frac{\log \left(4 x^2+6 x+9\right)}{944784}+\frac{1}{157464 (3-2 x)}-\frac{1}{472392 (2 x+3)}-\frac{\log (3-2 x)}{118098}+\frac{\log (2 x+3)}{354294}-\frac{\tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{52488 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{472392 \sqrt{3}}",1,"1/(157464*(3 - 2*x)) - 1/(472392*(3 + 2*x)) - (3 - 4*x)/(236196*(9 - 6*x + 4*x^2)) - ArcTan[(3 - 4*x)/(3*Sqrt[3])]/(52488*Sqrt[3]) + ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(472392*Sqrt[3]) - Log[3 - 2*x]/118098 + Log[3 + 2*x]/354294 + (5*Log[9 - 6*x + 4*x^2])/2834352 + Log[9 + 6*x + 4*x^2]/944784","A",14,7,20,0.3500,1,"{1586, 2074, 614, 618, 204, 634, 628}"
573,1,113,0,0.0818849,"\int \frac{27-8 x^3}{\left(729-64 x^6\right)^2} \, dx","Int[(27 - 8*x^3)/(729 - 64*x^6)^2,x]","\frac{x}{4374 \left(8 x^3+27\right)}-\frac{7 \log \left(4 x^2-6 x+9\right)}{944784}+\frac{\log \left(4 x^2+6 x+9\right)}{314928}-\frac{\log (3-2 x)}{157464}+\frac{7 \log (2 x+3)}{472392}-\frac{7 \tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{52488 \sqrt{3}}","\frac{x}{4374 \left(8 x^3+27\right)}-\frac{7 \log \left(4 x^2-6 x+9\right)}{944784}+\frac{\log \left(4 x^2+6 x+9\right)}{314928}-\frac{\log (3-2 x)}{157464}+\frac{7 \log (2 x+3)}{472392}-\frac{7 \tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{52488 \sqrt{3}}",1,"x/(4374*(27 + 8*x^3)) - (7*ArcTan[(3 - 4*x)/(3*Sqrt[3])])/(157464*Sqrt[3]) + ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(52488*Sqrt[3]) - Log[3 - 2*x]/157464 + (7*Log[3 + 2*x])/472392 - (7*Log[9 - 6*x + 4*x^2])/944784 + Log[9 + 6*x + 4*x^2]/314928","A",15,9,17,0.5294,1,"{1404, 414, 522, 200, 31, 634, 618, 204, 628}"
574,1,131,0,0.1477229,"\int \frac{27+36 x+24 x^2+8 x^3}{\left(729-64 x^6\right)^2} \, dx","Int[(27 + 36*x + 24*x^2 + 8*x^3)/(729 - 64*x^6)^2,x]","-\frac{3-2 x}{26244 \left(4 x^2-6 x+9\right)}+\frac{17 \log \left(4 x^2-6 x+9\right)}{944784}+\frac{\log \left(4 x^2+6 x+9\right)}{314928}+\frac{1}{26244 (3-2 x)}-\frac{7 \log (3-2 x)}{157464}+\frac{\log (2 x+3)}{472392}-\frac{11 \tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}","-\frac{3-2 x}{26244 \left(4 x^2-6 x+9\right)}+\frac{17 \log \left(4 x^2-6 x+9\right)}{944784}+\frac{\log \left(4 x^2+6 x+9\right)}{314928}+\frac{1}{26244 (3-2 x)}-\frac{7 \log (3-2 x)}{157464}+\frac{\log (2 x+3)}{472392}-\frac{11 \tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{157464 \sqrt{3}}",1,"1/(26244*(3 - 2*x)) - (3 - 2*x)/(26244*(9 - 6*x + 4*x^2)) - (11*ArcTan[(3 - 4*x)/(3*Sqrt[3])])/(157464*Sqrt[3]) - ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(157464*Sqrt[3]) - (7*Log[3 - 2*x])/157464 + Log[3 + 2*x]/472392 + (17*Log[9 - 6*x + 4*x^2])/944784 + Log[9 + 6*x + 4*x^2]/314928","A",14,7,25,0.2800,1,"{1586, 2074, 638, 618, 204, 634, 628}"
575,1,99,0,0.0627053,"\int \frac{x \left(27-2 x^3\right)}{729-64 x^6} \, dx","Int[(x*(27 - 2*x^3))/(729 - 64*x^6),x]","\frac{5}{576} \log \left(4 x^2-6 x+9\right)+\frac{1}{192} \log \left(4 x^2+6 x+9\right)-\frac{1}{96} \log (3-2 x)-\frac{5}{288} \log (2 x+3)-\frac{5 \tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{96 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{32 \sqrt{3}}","\frac{5}{576} \log \left(4 x^2-6 x+9\right)+\frac{1}{192} \log \left(4 x^2+6 x+9\right)-\frac{1}{96} \log (3-2 x)-\frac{5}{288} \log (2 x+3)-\frac{5 \tan ^{-1}\left(\frac{3-4 x}{3 \sqrt{3}}\right)}{96 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{4 x+3}{3 \sqrt{3}}\right)}{32 \sqrt{3}}",1,"(-5*ArcTan[(3 - 4*x)/(3*Sqrt[3])])/(96*Sqrt[3]) - ArcTan[(3 + 4*x)/(3*Sqrt[3])]/(32*Sqrt[3]) - Log[3 - 2*x]/96 - (5*Log[3 + 2*x])/288 + (5*Log[9 - 6*x + 4*x^2])/576 + Log[9 + 6*x + 4*x^2]/192","A",13,7,18,0.3889,1,"{1511, 292, 31, 634, 618, 204, 628}"
576,1,162,0,0.1671037,"\int \frac{(c x)^m \left(d+e x^n+f x^{2 n}+g x^{3 n}\right)}{a+b x^n} \, dx","Int[((c*x)^m*(d + e*x^n + f*x^(2*n) + g*x^(3*n)))/(a + b*x^n),x]","\frac{(c x)^{m+1} \left(a^2 b f+a^3 (-g)-a b^2 e+b^3 d\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a b^3 c (m+1)}+\frac{(c x)^{m+1} \left(a^2 g-a b f+b^2 e\right)}{b^3 c (m+1)}+\frac{x^{n+1} (c x)^m (b f-a g)}{b^2 (m+n+1)}+\frac{g x^{2 n+1} (c x)^m}{b (m+2 n+1)}","\frac{(c x)^{m+1} \left(a^2 b f+a^3 (-g)-a b^2 e+b^3 d\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a b^3 c (m+1)}+\frac{(c x)^{m+1} \left(a^2 g-a b f+b^2 e\right)}{b^3 c (m+1)}+\frac{x^{n+1} (c x)^m (b f-a g)}{b^2 (m+n+1)}+\frac{g x^{2 n+1} (c x)^m}{b (m+2 n+1)}",1,"((b*f - a*g)*x^(1 + n)*(c*x)^m)/(b^2*(1 + m + n)) + (g*x^(1 + 2*n)*(c*x)^m)/(b*(1 + m + 2*n)) + ((b^2*e - a*b*f + a^2*g)*(c*x)^(1 + m))/(b^3*c*(1 + m)) + ((b^3*d - a*b^2*e + a^2*b*f - a^3*g)*(c*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*b^3*c*(1 + m))","A",7,4,36,0.1111,1,"{1844, 20, 30, 364}"
577,1,84,0,0.0557268,"\int \left(c+d x^{-1+n}\right) \left(a+b x^n\right)^3 \, dx","Int[(c + d*x^(-1 + n))*(a + b*x^n)^3,x]","\frac{3 a^2 b c x^{n+1}}{n+1}+a^3 c x+\frac{3 a b^2 c x^{2 n+1}}{2 n+1}+\frac{d \left(a+b x^n\right)^4}{4 b n}+\frac{b^3 c x^{3 n+1}}{3 n+1}","\frac{3 a^2 b c x^{n+1}}{n+1}+a^3 c x+\frac{3 a b^2 c x^{2 n+1}}{2 n+1}+\frac{d \left(a+b x^n\right)^4}{4 b n}+\frac{b^3 c x^{3 n+1}}{3 n+1}",1,"a^3*c*x + (3*a^2*b*c*x^(1 + n))/(1 + n) + (3*a*b^2*c*x^(1 + 2*n))/(1 + 2*n) + (b^3*c*x^(1 + 3*n))/(1 + 3*n) + (d*(a + b*x^n)^4)/(4*b*n)","A",4,3,19,0.1579,1,"{1891, 244, 261}"
578,1,61,0,0.0402319,"\int \left(c+d x^{-1+n}\right) \left(a+b x^n\right)^2 \, dx","Int[(c + d*x^(-1 + n))*(a + b*x^n)^2,x]","a^2 c x+\frac{2 a b c x^{n+1}}{n+1}+\frac{d \left(a+b x^n\right)^3}{3 b n}+\frac{b^2 c x^{2 n+1}}{2 n+1}","a^2 c x+\frac{2 a b c x^{n+1}}{n+1}+\frac{d \left(a+b x^n\right)^3}{3 b n}+\frac{b^2 c x^{2 n+1}}{2 n+1}",1,"a^2*c*x + (2*a*b*c*x^(1 + n))/(1 + n) + (b^2*c*x^(1 + 2*n))/(1 + 2*n) + (d*(a + b*x^n)^3)/(3*b*n)","A",4,3,19,0.1579,1,"{1891, 244, 261}"
579,1,41,0,0.0227337,"\int \left(c+d x^{-1+n}\right) \left(a+b x^n\right) \, dx","Int[(c + d*x^(-1 + n))*(a + b*x^n),x]","a c x+\frac{a d x^n}{n}+\frac{b c x^{n+1}}{n+1}+\frac{b d x^{2 n}}{2 n}","a c x+\frac{a d x^n}{n}+\frac{b c x^{n+1}}{n+1}+\frac{b d x^{2 n}}{2 n}",1,"a*c*x + (a*d*x^n)/n + (b*d*x^(2*n))/(2*n) + (b*c*x^(1 + n))/(1 + n)","A",4,2,17,0.1176,1,"{1891, 14}"
580,1,12,0,0.0028014,"\int \left(c+d x^{-1+n}\right) \, dx","Int[c + d*x^(-1 + n),x]","c x+\frac{d x^n}{n}","c x+\frac{d x^n}{n}",1,"c*x + (d*x^n)/n","A",1,0,9,0,1,"{}"
581,1,42,0,0.0304338,"\int \frac{c+d x^{-1+n}}{a+b x^n} \, dx","Int[(c + d*x^(-1 + n))/(a + b*x^n),x]","\frac{c x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a}+\frac{d \log \left(a+b x^n\right)}{b n}","\frac{c x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a}+\frac{d \log \left(a+b x^n\right)}{b n}",1,"(c*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/a + (d*Log[a + b*x^n])/(b*n)","A",3,3,19,0.1579,1,"{1891, 245, 260}"
582,1,44,0,0.0288111,"\int \frac{c+d x^{-1+n}}{\left(a+b x^n\right)^2} \, dx","Int[(c + d*x^(-1 + n))/(a + b*x^n)^2,x]","\frac{c x \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2}-\frac{d}{b n \left(a+b x^n\right)}","\frac{c x \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2}-\frac{d}{b n \left(a+b x^n\right)}",1,"-(d/(b*n*(a + b*x^n))) + (c*x*Hypergeometric2F1[2, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/a^2","A",3,3,19,0.1579,1,"{1891, 245, 261}"
583,1,46,0,0.0295255,"\int \frac{c+d x^{-1+n}}{\left(a+b x^n\right)^3} \, dx","Int[(c + d*x^(-1 + n))/(a + b*x^n)^3,x]","\frac{c x \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^3}-\frac{d}{2 b n \left(a+b x^n\right)^2}","\frac{c x \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^3}-\frac{d}{2 b n \left(a+b x^n\right)^2}",1,"-d/(2*b*n*(a + b*x^n)^2) + (c*x*Hypergeometric2F1[3, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/a^3","A",3,3,19,0.1579,1,"{1891, 245, 261}"
584,1,305,0,0.2318488,"\int \frac{(c x)^m \left(d+e x^n+f x^{2 n}+g x^{3 n}\right)}{\sqrt{a+b x^n}} \, dx","Int[((c*x)^m*(d + e*x^n + f*x^(2*n) + g*x^(3*n)))/Sqrt[a + b*x^n],x]","\frac{d (c x)^{m+1} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{c (m+1) \sqrt{a+b x^n}}+\frac{e x^{n+1} (c x)^m \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+n+1}{n};\frac{m+2 n+1}{n};-\frac{b x^n}{a}\right)}{(m+n+1) \sqrt{a+b x^n}}+\frac{f x^{2 n+1} (c x)^m \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+2 n+1}{n};\frac{m+3 n+1}{n};-\frac{b x^n}{a}\right)}{(m+2 n+1) \sqrt{a+b x^n}}+\frac{g x^{3 n+1} (c x)^m \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+3 n+1}{n};\frac{m+4 n+1}{n};-\frac{b x^n}{a}\right)}{(m+3 n+1) \sqrt{a+b x^n}}","\frac{d (c x)^{m+1} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{c (m+1) \sqrt{a+b x^n}}+\frac{e x^{n+1} (c x)^m \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+n+1}{n};\frac{m+2 n+1}{n};-\frac{b x^n}{a}\right)}{(m+n+1) \sqrt{a+b x^n}}+\frac{f x^{2 n+1} (c x)^m \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+2 n+1}{n};\frac{m+3 n+1}{n};-\frac{b x^n}{a}\right)}{(m+2 n+1) \sqrt{a+b x^n}}+\frac{g x^{3 n+1} (c x)^m \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+3 n+1}{n};\frac{m+4 n+1}{n};-\frac{b x^n}{a}\right)}{(m+3 n+1) \sqrt{a+b x^n}}",1,"(d*(c*x)^(1 + m)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(c*(1 + m)*Sqrt[a + b*x^n]) + (e*x^(1 + n)*(c*x)^m*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (1 + m + n)/n, (1 + m + 2*n)/n, -((b*x^n)/a)])/((1 + m + n)*Sqrt[a + b*x^n]) + (f*x^(1 + 2*n)*(c*x)^m*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (1 + m + 2*n)/n, (1 + m + 3*n)/n, -((b*x^n)/a)])/((1 + m + 2*n)*Sqrt[a + b*x^n]) + (g*x^(1 + 3*n)*(c*x)^m*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (1 + m + 3*n)/n, (1 + m + 4*n)/n, -((b*x^n)/a)])/((1 + m + 3*n)*Sqrt[a + b*x^n])","A",13,4,38,0.1053,1,"{1844, 365, 364, 20}"
585,1,45,0,0.3947288,"\int \frac{-a h x^{-1+\frac{n}{4}}+b f x^{-1+\frac{n}{2}}+b g x^{-1+n}+b h x^{-1+\frac{5 n}{4}}}{\left(a+b x^n\right)^{3/2}} \, dx","Int[(-(a*h*x^(-1 + n/4)) + b*f*x^(-1 + n/2) + b*g*x^(-1 + n) + b*h*x^(-1 + (5*n)/4))/(a + b*x^n)^(3/2),x]","-\frac{2 \left(a g+2 a h x^{n/4}-b f x^{n/2}\right)}{a n \sqrt{a+b x^n}}","-\frac{2 \left(a g+2 a h x^{n/4}-b f x^{n/2}\right)}{a n \sqrt{a+b x^n}}",1,"(-2*(a*g + 2*a*h*x^(n/4) - b*f*x^(n/2)))/(a*n*Sqrt[a + b*x^n])","A",2,2,58,0.03448,1,"{6741, 1816}"
586,1,273,0,0.18508,"\int (c x)^m \left(d+e x+f x^2+g x^3\right) \left(a+b x^n\right)^p \, dx","Int[(c*x)^m*(d + e*x + f*x^2 + g*x^3)*(a + b*x^n)^p,x]","\frac{e (c x)^{m+2} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{n},-p;\frac{m+n+2}{n};-\frac{b x^n}{a}\right)}{c^2 (m+2)}+\frac{f (c x)^{m+3} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+3}{n},-p;\frac{m+n+3}{n};-\frac{b x^n}{a}\right)}{c^3 (m+3)}+\frac{g (c x)^{m+4} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+4}{n},-p;\frac{m+n+4}{n};-\frac{b x^n}{a}\right)}{c^4 (m+4)}+\frac{d (c x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{c (m+1)}","\frac{e (c x)^{m+2} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{n},-p;\frac{m+n+2}{n};-\frac{b x^n}{a}\right)}{c^2 (m+2)}+\frac{f (c x)^{m+3} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+3}{n},-p;\frac{m+n+3}{n};-\frac{b x^n}{a}\right)}{c^3 (m+3)}+\frac{g (c x)^{m+4} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+4}{n},-p;\frac{m+n+4}{n};-\frac{b x^n}{a}\right)}{c^4 (m+4)}+\frac{d (c x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{c (m+1)}",1,"(d*(c*x)^(1 + m)*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)])/(c*(1 + m)*(1 + (b*x^n)/a)^p) + (e*(c*x)^(2 + m)*(a + b*x^n)^p*Hypergeometric2F1[(2 + m)/n, -p, (2 + m + n)/n, -((b*x^n)/a)])/(c^2*(2 + m)*(1 + (b*x^n)/a)^p) + (f*(c*x)^(3 + m)*(a + b*x^n)^p*Hypergeometric2F1[(3 + m)/n, -p, (3 + m + n)/n, -((b*x^n)/a)])/(c^3*(3 + m)*(1 + (b*x^n)/a)^p) + (g*(c*x)^(4 + m)*(a + b*x^n)^p*Hypergeometric2F1[(4 + m)/n, -p, (4 + m + n)/n, -((b*x^n)/a)])/(c^4*(4 + m)*(1 + (b*x^n)/a)^p)","A",10,3,30,0.1000,1,"{1844, 365, 364}"
587,1,297,0,0.2081854,"\int (c x)^m \left(a+b x^n\right)^p \left(d+e x^n+f x^{2 n}+g x^{3 n}\right) \, dx","Int[(c*x)^m*(a + b*x^n)^p*(d + e*x^n + f*x^(2*n) + g*x^(3*n)),x]","\frac{d (c x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{c (m+1)}+\frac{e x^{n+1} (c x)^m \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+n+1}{n},-p;\frac{m+2 n+1}{n};-\frac{b x^n}{a}\right)}{m+n+1}+\frac{f x^{2 n+1} (c x)^m \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2 n+1}{n},-p;\frac{m+3 n+1}{n};-\frac{b x^n}{a}\right)}{m+2 n+1}+\frac{g x^{3 n+1} (c x)^m \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+3 n+1}{n},-p;\frac{m+4 n+1}{n};-\frac{b x^n}{a}\right)}{m+3 n+1}","\frac{d (c x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{c (m+1)}+\frac{e x^{n+1} (c x)^m \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+n+1}{n},-p;\frac{m+2 n+1}{n};-\frac{b x^n}{a}\right)}{m+n+1}+\frac{f x^{2 n+1} (c x)^m \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2 n+1}{n},-p;\frac{m+3 n+1}{n};-\frac{b x^n}{a}\right)}{m+2 n+1}+\frac{g x^{3 n+1} (c x)^m \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+3 n+1}{n},-p;\frac{m+4 n+1}{n};-\frac{b x^n}{a}\right)}{m+3 n+1}",1,"(d*(c*x)^(1 + m)*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)])/(c*(1 + m)*(1 + (b*x^n)/a)^p) + (e*x^(1 + n)*(c*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + n)/n, -p, (1 + m + 2*n)/n, -((b*x^n)/a)])/((1 + m + n)*(1 + (b*x^n)/a)^p) + (f*x^(1 + 2*n)*(c*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + 2*n)/n, -p, (1 + m + 3*n)/n, -((b*x^n)/a)])/((1 + m + 2*n)*(1 + (b*x^n)/a)^p) + (g*x^(1 + 3*n)*(c*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m + 3*n)/n, -p, (1 + m + 4*n)/n, -((b*x^n)/a)])/((1 + m + 3*n)*(1 + (b*x^n)/a)^p)","A",13,4,36,0.1111,1,"{1844, 365, 364, 20}"
588,1,162,0,0.1241853,"\int \frac{c+d x^{n/2}+e x^n+f x^{3 n/2}}{\left(a+b x^n\right)^2} \, dx","Int[(c + d*x^(n/2) + e*x^n + f*x^((3*n)/2))/(a + b*x^n)^2,x]","\frac{x (a e-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b n}-\frac{x^{\frac{n+2}{2}} (b d (2-n)-a f (n+2)) \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{2}{n}\right);\frac{1}{2} \left(3+\frac{2}{n}\right);-\frac{b x^n}{a}\right)}{a^2 b n (n+2)}+\frac{x \left(x^{n/2} (b d-a f)-a e+b c\right)}{a b n \left(a+b x^n\right)}","\frac{x (a e-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 b n}-\frac{x^{\frac{n+2}{2}} (b d (2-n)-a f (n+2)) \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{2}{n}\right);\frac{1}{2} \left(3+\frac{2}{n}\right);-\frac{b x^n}{a}\right)}{a^2 b n (n+2)}+\frac{x \left(x^{n/2} (b d-a f)-a e+b c\right)}{a b n \left(a+b x^n\right)}",1,"(x*(b*c - a*e + (b*d - a*f)*x^(n/2)))/(a*b*n*(a + b*x^n)) - ((b*d*(2 - n) - a*f*(2 + n))*x^((2 + n)/2)*Hypergeometric2F1[1, (1 + 2/n)/2, (3 + 2/n)/2, -((b*x^n)/a)])/(a^2*b*n*(2 + n)) + ((a*e - b*c*(1 - n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*b*n)","A",4,4,35,0.1143,1,"{1892, 1418, 245, 364}"
589,1,24,0,0.0525376,"\int \frac{a c+2 (b c+a d) x^2+3 b d x^4}{\sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[(a*c + 2*(b*c + a*d)*x^2 + 3*b*d*x^4)/(Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","x \sqrt{a+b x^2} \sqrt{c+d x^2}","x \sqrt{a+b x^2} \sqrt{c+d x^2}",1,"x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2]","A",1,1,46,0.02174,1,"{1590}"
590,1,103,0,0.1025695,"\int \frac{1+x^3}{\left(1-x^4\right) \sqrt[4]{1+x^4}} \, dx","Int[(1 + x^3)/((1 - x^4)*(1 + x^4)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{x^4+1}}{\sqrt[4]{2}}\right)}{2 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{x^4+1}}{\sqrt[4]{2}}\right)}{2 \sqrt[4]{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{x^4+1}}{\sqrt[4]{2}}\right)}{2 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{x^4+1}}{\sqrt[4]{2}}\right)}{2 \sqrt[4]{2}}",1,"ArcTan[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(2*2^(1/4)) - ArcTan[(1 + x^4)^(1/4)/2^(1/4)]/(2*2^(1/4)) + ArcTanh[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(2*2^(1/4)) + ArcTanh[(1 + x^4)^(1/4)/2^(1/4)]/(2*2^(1/4))","A",10,8,24,0.3333,1,"{1899, 377, 212, 206, 203, 444, 63, 298}"
591,1,28,0,0.1011009,"\int \left(a+b x^n\right)^{\frac{-1-n}{n}} \left(c+d x^n\right)^{\frac{-1-n}{n}} \left(a c-b d x^{2 n}\right) \, dx","Int[(a + b*x^n)^((-1 - n)/n)*(c + d*x^n)^((-1 - n)/n)*(a*c - b*d*x^(2*n)),x]","x \left(a+b x^n\right)^{-1/n} \left(c+d x^n\right)^{-1/n}","x \left(a+b x^n\right)^{-1/n} \left(c+d x^n\right)^{-1/n}",1,"x/((a + b*x^n)^n^(-1)*(c + d*x^n)^n^(-1))","A",1,1,48,0.02083,1,"{1898}"
592,1,45,0,0.1568615,"\int (h x)^{-1-n-n p} \left(a+b x^n\right)^p \left(c+d x^n\right)^p \left(a c-b d x^{2 n}\right) \, dx","Int[(h*x)^(-1 - n - n*p)*(a + b*x^n)^p*(c + d*x^n)^p*(a*c - b*d*x^(2*n)),x]","-\frac{(h x)^{-n (p+1)} \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{p+1}}{h n (p+1)}","-\frac{(h x)^{-n (p+1)} \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{p+1}}{h n (p+1)}",1,"-(((a + b*x^n)^(1 + p)*(c + d*x^n)^(1 + p))/(h*n*(1 + p)*(h*x)^(n*(1 + p))))","A",1,1,45,0.02222,1,"{1849}"
593,1,31,0,0.2053181,"\int \left(a+b x^n\right)^p \left(c+d x^n\right)^p \left(e+\frac{(b c+a d) e (1+n+n p) x^n}{a c}+\frac{b d e (1+2 n+2 n p) x^{2 n}}{a c}\right) \, dx","Int[(a + b*x^n)^p*(c + d*x^n)^p*(e + ((b*c + a*d)*e*(1 + n + n*p)*x^n)/(a*c) + (b*d*e*(1 + 2*n + 2*n*p)*x^(2*n))/(a*c)),x]","\frac{e x \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{p+1}}{a c}","\frac{e x \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{p+1}}{a c}",1,"(e*x*(a + b*x^n)^(1 + p)*(c + d*x^n)^(1 + p))/(a*c)","A",1,1,69,0.01449,1,"{1897}"
594,1,45,0,0.5531127,"\int (h x)^m \left(a+b x^n\right)^p \left(c+d x^n\right)^p \left(e+\frac{(b c+a d) e (1+m+n+n p) x^n}{a c (1+m)}+\frac{b d e (1+m+2 n+2 n p) x^{2 n}}{a c (1+m)}\right) \, dx","Int[(h*x)^m*(a + b*x^n)^p*(c + d*x^n)^p*(e + ((b*c + a*d)*e*(1 + m + n + n*p)*x^n)/(a*c*(1 + m)) + (b*d*e*(1 + m + 2*n + 2*n*p)*x^(2*n))/(a*c*(1 + m))),x]","\frac{e (h x)^{m+1} \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{p+1}}{a c h (m+1)}","\frac{e (h x)^{m+1} \left(a+b x^n\right)^{p+1} \left(c+d x^n\right)^{p+1}}{a c h (m+1)}",1,"(e*(h*x)^(1 + m)*(a + b*x^n)^(1 + p)*(c + d*x^n)^(1 + p))/(a*c*h*(1 + m))","A",1,1,86,0.01163,1,"{1848}"