1,1,58,72,4.715278,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x)^(1/2),x)","\frac{2\,\sqrt{a+b\,x}\,\left(3\,e\,{\left(a+b\,x\right)}^2+15\,b^2\,c+15\,a^2\,e-10\,a\,e\,\left(a+b\,x\right)+5\,b\,d\,\left(a+b\,x\right)-15\,a\,b\,d\right)}{15\,b^3}","Not used",1,"(2*(a + b*x)^(1/2)*(3*e*(a + b*x)^2 + 15*b^2*c + 15*a^2*e - 10*a*e*(a + b*x) + 5*b*d*(a + b*x) - 15*a*b*d))/(15*b^3)","B"
2,1,149,161,4.762039,"\text{Not used}","int((c + d*x + e*x^2)^2/(a + b*x)^(1/2),x)","\frac{2\,e^2\,{\left(a+b\,x\right)}^{9/2}}{9\,b^5}+\frac{{\left(a+b\,x\right)}^{5/2}\,\left(12\,a^2\,e^2-12\,a\,b\,d\,e+2\,b^2\,d^2+4\,c\,b^2\,e\right)}{5\,b^5}+\frac{2\,\sqrt{a+b\,x}\,{\left(e\,a^2-d\,a\,b+c\,b^2\right)}^2}{b^5}-\frac{\left(8\,a\,e^2-4\,b\,d\,e\right)\,{\left(a+b\,x\right)}^{7/2}}{7\,b^5}-\frac{4\,\left(2\,a\,e-b\,d\right)\,{\left(a+b\,x\right)}^{3/2}\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{3\,b^5}","Not used",1,"(2*e^2*(a + b*x)^(9/2))/(9*b^5) + ((a + b*x)^(5/2)*(12*a^2*e^2 + 2*b^2*d^2 + 4*b^2*c*e - 12*a*b*d*e))/(5*b^5) + (2*(a + b*x)^(1/2)*(b^2*c + a^2*e - a*b*d)^2)/b^5 - ((8*a*e^2 - 4*b*d*e)*(a + b*x)^(7/2))/(7*b^5) - (4*(2*a*e - b*d)*(a + b*x)^(3/2)*(b^2*c + a^2*e - a*b*d))/(3*b^5)","B"
3,1,299,274,0.097561,"\text{Not used}","int((c + d*x + e*x^2)^3/(a + b*x)^(1/2),x)","\frac{2\,e^3\,{\left(a+b\,x\right)}^{13/2}}{13\,b^7}-\frac{\left(12\,a\,e^3-6\,b\,d\,e^2\right)\,{\left(a+b\,x\right)}^{11/2}}{11\,b^7}+\frac{{\left(a+b\,x\right)}^{9/2}\,\left(30\,a^2\,e^3-30\,a\,b\,d\,e^2+6\,b^2\,d^2\,e+6\,c\,b^2\,e^2\right)}{9\,b^7}+\frac{2\,\sqrt{a+b\,x}\,{\left(e\,a^2-d\,a\,b+c\,b^2\right)}^3}{b^7}+\frac{{\left(a+b\,x\right)}^{5/2}\,\left(30\,a^4\,e^3-60\,a^3\,b\,d\,e^2+36\,a^2\,b^2\,c\,e^2+36\,a^2\,b^2\,d^2\,e-36\,a\,b^3\,c\,d\,e-6\,a\,b^3\,d^3+6\,b^4\,c^2\,e+6\,b^4\,c\,d^2\right)}{5\,b^7}-\frac{2\,\left(2\,a\,e-b\,d\right)\,{\left(a+b\,x\right)}^{7/2}\,\left(10\,a^2\,e^2-10\,a\,b\,d\,e+b^2\,d^2+6\,c\,b^2\,e\right)}{7\,b^7}-\frac{2\,\left(2\,a\,e-b\,d\right)\,{\left(a+b\,x\right)}^{3/2}\,{\left(e\,a^2-d\,a\,b+c\,b^2\right)}^2}{b^7}","Not used",1,"(2*e^3*(a + b*x)^(13/2))/(13*b^7) - ((12*a*e^3 - 6*b*d*e^2)*(a + b*x)^(11/2))/(11*b^7) + ((a + b*x)^(9/2)*(30*a^2*e^3 + 6*b^2*c*e^2 + 6*b^2*d^2*e - 30*a*b*d*e^2))/(9*b^7) + (2*(a + b*x)^(1/2)*(b^2*c + a^2*e - a*b*d)^3)/b^7 + ((a + b*x)^(5/2)*(30*a^4*e^3 - 6*a*b^3*d^3 + 6*b^4*c*d^2 + 6*b^4*c^2*e + 36*a^2*b^2*c*e^2 + 36*a^2*b^2*d^2*e - 60*a^3*b*d*e^2 - 36*a*b^3*c*d*e))/(5*b^7) - (2*(2*a*e - b*d)*(a + b*x)^(7/2)*(10*a^2*e^2 + b^2*d^2 + 6*b^2*c*e - 10*a*b*d*e))/(7*b^7) - (2*(2*a*e - b*d)*(a + b*x)^(3/2)*(b^2*c + a^2*e - a*b*d)^2)/b^7","B"
4,1,103,114,4.813656,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a + b*x)^(1/2),x)","\frac{{\left(a+b\,x\right)}^{3/2}\,\left(6\,f\,a^2-4\,e\,a\,b+2\,d\,b^2\right)}{3\,b^4}-\frac{\left(6\,a\,f-2\,b\,e\right)\,{\left(a+b\,x\right)}^{5/2}}{5\,b^4}+\frac{\sqrt{a+b\,x}\,\left(-2\,f\,a^3+2\,e\,a^2\,b-2\,d\,a\,b^2+2\,c\,b^3\right)}{b^4}+\frac{2\,f\,{\left(a+b\,x\right)}^{7/2}}{7\,b^4}","Not used",1,"((a + b*x)^(3/2)*(2*b^2*d + 6*a^2*f - 4*a*b*e))/(3*b^4) - ((6*a*f - 2*b*e)*(a + b*x)^(5/2))/(5*b^4) + ((a + b*x)^(1/2)*(2*b^3*c - 2*a^3*f - 2*a*b^2*d + 2*a^2*b*e))/b^4 + (2*f*(a + b*x)^(7/2))/(7*b^4)","B"
5,1,316,320,4.697766,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)^2/(a + b*x)^(1/2),x)","\frac{2\,\sqrt{a+b\,x}\,{\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}^2}{b^7}+\frac{2\,f^2\,{\left(a+b\,x\right)}^{13/2}}{13\,b^7}-\frac{{\left(a+b\,x\right)}^{7/2}\,\left(40\,a^3\,f^2-40\,a^2\,b\,e\,f+8\,a\,b^2\,e^2+16\,d\,a\,b^2\,f-4\,d\,b^3\,e-4\,c\,b^3\,f\right)}{7\,b^7}+\frac{{\left(a+b\,x\right)}^{9/2}\,\left(30\,a^2\,f^2-20\,a\,b\,e\,f+2\,b^2\,e^2+4\,d\,b^2\,f\right)}{9\,b^7}+\frac{{\left(a+b\,x\right)}^{5/2}\,\left(30\,a^4\,f^2-40\,a^3\,b\,e\,f+24\,a^2\,b^2\,d\,f+12\,a^2\,b^2\,e^2-12\,a\,b^3\,d\,e-12\,c\,a\,b^3\,f+2\,b^4\,d^2+4\,c\,b^4\,e\right)}{5\,b^7}-\frac{\left(12\,a\,f^2-4\,b\,e\,f\right)\,{\left(a+b\,x\right)}^{11/2}}{11\,b^7}+\frac{4\,{\left(a+b\,x\right)}^{3/2}\,\left(3\,f\,a^2-2\,e\,a\,b+d\,b^2\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^7}","Not used",1,"(2*(a + b*x)^(1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e)^2)/b^7 + (2*f^2*(a + b*x)^(13/2))/(13*b^7) - ((a + b*x)^(7/2)*(40*a^3*f^2 + 8*a*b^2*e^2 - 4*b^3*c*f - 4*b^3*d*e + 16*a*b^2*d*f - 40*a^2*b*e*f))/(7*b^7) + ((a + b*x)^(9/2)*(30*a^2*f^2 + 2*b^2*e^2 + 4*b^2*d*f - 20*a*b*e*f))/(9*b^7) + ((a + b*x)^(5/2)*(2*b^4*d^2 + 30*a^4*f^2 + 12*a^2*b^2*e^2 + 4*b^4*c*e - 12*a*b^3*c*f - 12*a*b^3*d*e - 40*a^3*b*e*f + 24*a^2*b^2*d*f))/(5*b^7) - ((12*a*f^2 - 4*b*e*f)*(a + b*x)^(11/2))/(11*b^7) + (4*(a + b*x)^(3/2)*(b^2*d + 3*a^2*f - 2*a*b*e)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^7)","B"
6,1,896,708,0.242033,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)^3/(a + b*x)^(1/2),x)","\frac{{\left(a+b\,x\right)}^{11/2}\,\left(252\,a^4\,f^3-336\,a^3\,b\,e\,f^2+126\,a^2\,b^2\,d\,f^2+126\,a^2\,b^2\,e^2\,f-72\,a\,b^3\,d\,e\,f-12\,a\,b^3\,e^3-36\,c\,a\,b^3\,f^2+6\,b^4\,d^2\,f+6\,b^4\,d\,e^2+12\,c\,b^4\,e\,f\right)}{11\,b^{10}}+\frac{2\,\sqrt{a+b\,x}\,{\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}^3}{b^{10}}+\frac{{\left(a+b\,x\right)}^{9/2}\,\left(-252\,a^5\,f^3+420\,a^4\,b\,e\,f^2-210\,a^3\,b^2\,d\,f^2-210\,a^3\,b^2\,e^2\,f+180\,a^2\,b^3\,d\,e\,f+30\,a^2\,b^3\,e^3+90\,c\,a^2\,b^3\,f^2-30\,a\,b^4\,d^2\,f-30\,a\,b^4\,d\,e^2-60\,c\,a\,b^4\,e\,f+6\,b^5\,d^2\,e+12\,c\,b^5\,d\,f+6\,c\,b^5\,e^2\right)}{9\,b^{10}}+\frac{2\,f^3\,{\left(a+b\,x\right)}^{19/2}}{19\,b^{10}}+\frac{{\left(a+b\,x\right)}^{13/2}\,\left(-168\,a^3\,f^3+168\,a^2\,b\,e\,f^2-42\,a\,b^2\,e^2\,f-42\,d\,a\,b^2\,f^2+2\,b^3\,e^3+12\,d\,b^3\,e\,f+6\,c\,b^3\,f^2\right)}{13\,b^{10}}-\frac{\left(18\,a\,f^3-6\,b\,e\,f^2\right)\,{\left(a+b\,x\right)}^{17/2}}{17\,b^{10}}+\frac{{\left(a+b\,x\right)}^{15/2}\,\left(72\,a^2\,f^3-48\,a\,b\,e\,f^2+6\,b^2\,e^2\,f+6\,d\,b^2\,f^2\right)}{15\,b^{10}}-\frac{{\left(a+b\,x\right)}^{5/2}\,\left(72\,a^7\,f^3-168\,a^6\,b\,e\,f^2+126\,a^5\,b^2\,d\,f^2+126\,a^5\,b^2\,e^2\,f-90\,a^4\,b^3\,c\,f^2-180\,a^4\,b^3\,d\,e\,f-30\,a^4\,b^3\,e^3+120\,a^3\,b^4\,c\,e\,f+60\,a^3\,b^4\,d^2\,f+60\,a^3\,b^4\,d\,e^2-72\,a^2\,b^5\,c\,d\,f-36\,a^2\,b^5\,c\,e^2-36\,a^2\,b^5\,d^2\,e+18\,a\,b^6\,c^2\,f+36\,a\,b^6\,c\,d\,e+6\,a\,b^6\,d^3-6\,b^7\,c^2\,e-6\,b^7\,c\,d^2\right)}{5\,b^{10}}+\frac{{\left(a+b\,x\right)}^{7/2}\,\left(168\,a^6\,f^3-336\,a^5\,b\,e\,f^2+210\,a^4\,b^2\,d\,f^2+210\,a^4\,b^2\,e^2\,f-120\,a^3\,b^3\,c\,f^2-240\,a^3\,b^3\,d\,e\,f-40\,a^3\,b^3\,e^3+120\,a^2\,b^4\,c\,e\,f+60\,a^2\,b^4\,d^2\,f+60\,a^2\,b^4\,d\,e^2-48\,a\,b^5\,c\,d\,f-24\,a\,b^5\,c\,e^2-24\,a\,b^5\,d^2\,e+6\,b^6\,c^2\,f+12\,b^6\,c\,d\,e+2\,b^6\,d^3\right)}{7\,b^{10}}+\frac{2\,{\left(a+b\,x\right)}^{3/2}\,\left(3\,f\,a^2-2\,e\,a\,b+d\,b^2\right)\,{\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}^2}{b^{10}}","Not used",1,"((a + b*x)^(11/2)*(252*a^4*f^3 - 12*a*b^3*e^3 + 6*b^4*d*e^2 + 6*b^4*d^2*f + 126*a^2*b^2*d*f^2 + 126*a^2*b^2*e^2*f + 12*b^4*c*e*f - 36*a*b^3*c*f^2 - 336*a^3*b*e*f^2 - 72*a*b^3*d*e*f))/(11*b^10) + (2*(a + b*x)^(1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e)^3)/b^10 + ((a + b*x)^(9/2)*(6*b^5*c*e^2 - 252*a^5*f^3 + 6*b^5*d^2*e + 30*a^2*b^3*e^3 + 90*a^2*b^3*c*f^2 - 210*a^3*b^2*d*f^2 - 210*a^3*b^2*e^2*f + 12*b^5*c*d*f - 30*a*b^4*d*e^2 - 30*a*b^4*d^2*f + 420*a^4*b*e*f^2 + 180*a^2*b^3*d*e*f - 60*a*b^4*c*e*f))/(9*b^10) + (2*f^3*(a + b*x)^(19/2))/(19*b^10) + ((a + b*x)^(13/2)*(2*b^3*e^3 - 168*a^3*f^3 + 6*b^3*c*f^2 + 12*b^3*d*e*f - 42*a*b^2*d*f^2 - 42*a*b^2*e^2*f + 168*a^2*b*e*f^2))/(13*b^10) - ((18*a*f^3 - 6*b*e*f^2)*(a + b*x)^(17/2))/(17*b^10) + ((a + b*x)^(15/2)*(72*a^2*f^3 + 6*b^2*d*f^2 + 6*b^2*e^2*f - 48*a*b*e*f^2))/(15*b^10) - ((a + b*x)^(5/2)*(72*a^7*f^3 + 6*a*b^6*d^3 - 6*b^7*c*d^2 - 6*b^7*c^2*e - 30*a^4*b^3*e^3 - 36*a^2*b^5*c*e^2 - 36*a^2*b^5*d^2*e + 60*a^3*b^4*d*e^2 - 90*a^4*b^3*c*f^2 + 60*a^3*b^4*d^2*f + 126*a^5*b^2*d*f^2 + 126*a^5*b^2*e^2*f + 18*a*b^6*c^2*f - 168*a^6*b*e*f^2 - 72*a^2*b^5*c*d*f + 120*a^3*b^4*c*e*f - 180*a^4*b^3*d*e*f + 36*a*b^6*c*d*e))/(5*b^10) + ((a + b*x)^(7/2)*(2*b^6*d^3 + 168*a^6*f^3 + 6*b^6*c^2*f - 40*a^3*b^3*e^3 + 60*a^2*b^4*d*e^2 - 120*a^3*b^3*c*f^2 + 60*a^2*b^4*d^2*f + 210*a^4*b^2*d*f^2 + 210*a^4*b^2*e^2*f + 12*b^6*c*d*e - 24*a*b^5*c*e^2 - 24*a*b^5*d^2*e - 336*a^5*b*e*f^2 + 120*a^2*b^4*c*e*f - 240*a^3*b^3*d*e*f - 48*a*b^5*c*d*f))/(7*b^10) + (2*(a + b*x)^(3/2)*(b^2*d + 3*a^2*f - 2*a*b*e)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e)^2)/b^10","B"
7,1,127,161,5.511124,"\text{Not used}","int((c + d*x)/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(b\,\left(c\,d+d^2\,x+{\mathrm{root}\left(27\,a^2\,b^2\,z^3+9\,a\,b\,c\,d\,z+a\,d^3-b\,c^3,z,k\right)}^2\,a\,b\,9+\mathrm{root}\left(27\,a^2\,b^2\,z^3+9\,a\,b\,c\,d\,z+a\,d^3-b\,c^3,z,k\right)\,b\,c\,x\,3\right)\right)\,\mathrm{root}\left(27\,a^2\,b^2\,z^3+9\,a\,b\,c\,d\,z+a\,d^3-b\,c^3,z,k\right)","Not used",1,"symsum(log(b*(c*d + d^2*x + 9*root(27*a^2*b^2*z^3 + 9*a*b*c*d*z + a*d^3 - b*c^3, z, k)^2*a*b + 3*root(27*a^2*b^2*z^3 + 9*a*b*c*d*z + a*d^3 - b*c^3, z, k)*b*c*x))*root(27*a^2*b^2*z^3 + 9*a*b*c*d*z + a*d^3 - b*c^3, z, k), k, 1, 3)","B"
8,1,169,189,4.872487,"\text{Not used}","int((c + d*x)/(a + b*x^3)^2,x)","\left(\sum _{k=1}^3\ln\left(\frac{b\,\left(2\,c\,d+d^2\,x+{\mathrm{root}\left(729\,a^5\,b^2\,z^3+54\,a^2\,b\,c\,d\,z-8\,b\,c^3+a\,d^3,z,k\right)}^2\,a^3\,b\,81+\mathrm{root}\left(729\,a^5\,b^2\,z^3+54\,a^2\,b\,c\,d\,z-8\,b\,c^3+a\,d^3,z,k\right)\,a\,b\,c\,x\,18\right)}{a^2\,9}\right)\,\mathrm{root}\left(729\,a^5\,b^2\,z^3+54\,a^2\,b\,c\,d\,z-8\,b\,c^3+a\,d^3,z,k\right)\right)+\frac{\frac{d\,x^2}{3\,a}+\frac{c\,x}{3\,a}}{b\,x^3+a}","Not used",1,"symsum(log((b*(2*c*d + d^2*x + 81*root(729*a^5*b^2*z^3 + 54*a^2*b*c*d*z - 8*b*c^3 + a*d^3, z, k)^2*a^3*b + 18*root(729*a^5*b^2*z^3 + 54*a^2*b*c*d*z - 8*b*c^3 + a*d^3, z, k)*a*b*c*x))/(9*a^2))*root(729*a^5*b^2*z^3 + 54*a^2*b*c*d*z - 8*b*c^3 + a*d^3, z, k), k, 1, 3) + ((d*x^2)/(3*a) + (c*x)/(3*a))/(a + b*x^3)","B"
9,1,206,215,0.268098,"\text{Not used}","int((c + d*x)/(a + b*x^3)^3,x)","\frac{\frac{7\,d\,x^2}{18\,a}+\frac{4\,c\,x}{9\,a}+\frac{5\,b\,c\,x^4}{18\,a^2}+\frac{2\,b\,d\,x^5}{9\,a^2}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\left(\sum _{k=1}^3\ln\left(\frac{b\,\left(10\,c\,d+4\,d^2\,x+{\mathrm{root}\left(19683\,a^8\,b^2\,z^3+810\,a^3\,b\,c\,d\,z-125\,b\,c^3+8\,a\,d^3,z,k\right)}^2\,a^5\,b\,729+\mathrm{root}\left(19683\,a^8\,b^2\,z^3+810\,a^3\,b\,c\,d\,z-125\,b\,c^3+8\,a\,d^3,z,k\right)\,a^2\,b\,c\,x\,135\right)}{a^4\,81}\right)\,\mathrm{root}\left(19683\,a^8\,b^2\,z^3+810\,a^3\,b\,c\,d\,z-125\,b\,c^3+8\,a\,d^3,z,k\right)\right)","Not used",1,"((7*d*x^2)/(18*a) + (4*c*x)/(9*a) + (5*b*c*x^4)/(18*a^2) + (2*b*d*x^5)/(9*a^2))/(a^2 + b^2*x^6 + 2*a*b*x^3) + symsum(log((b*(10*c*d + 4*d^2*x + 729*root(19683*a^8*b^2*z^3 + 810*a^3*b*c*d*z - 125*b*c^3 + 8*a*d^3, z, k)^2*a^5*b + 135*root(19683*a^8*b^2*z^3 + 810*a^3*b*c*d*z - 125*b*c^3 + 8*a*d^3, z, k)*a^2*b*c*x))/(81*a^4))*root(19683*a^8*b^2*z^3 + 810*a^3*b*c*d*z - 125*b*c^3 + 8*a*d^3, z, k), k, 1, 3)","B"
10,1,241,240,4.930827,"\text{Not used}","int((c + d*x)/(a + b*x^3)^4,x)","\left(\sum _{k=1}^3\ln\left(\frac{b\,\left(560\,c\,d+196\,d^2\,x+{\mathrm{root}\left(14348907\,a^{11}\,b^2\,z^3+408240\,a^4\,b\,c\,d\,z-64000\,b\,c^3+2744\,a\,d^3,z,k\right)}^2\,a^7\,b\,59049+\mathrm{root}\left(14348907\,a^{11}\,b^2\,z^3+408240\,a^4\,b\,c\,d\,z-64000\,b\,c^3+2744\,a\,d^3,z,k\right)\,a^3\,b\,c\,x\,9720\right)}{a^6\,6561}\right)\,\mathrm{root}\left(14348907\,a^{11}\,b^2\,z^3+408240\,a^4\,b\,c\,d\,z-64000\,b\,c^3+2744\,a\,d^3,z,k\right)\right)+\frac{\frac{67\,d\,x^2}{162\,a}+\frac{41\,c\,x}{81\,a}+\frac{20\,b^2\,c\,x^7}{81\,a^3}+\frac{14\,b^2\,d\,x^8}{81\,a^3}+\frac{52\,b\,c\,x^4}{81\,a^2}+\frac{77\,b\,d\,x^5}{162\,a^2}}{a^3+3\,a^2\,b\,x^3+3\,a\,b^2\,x^6+b^3\,x^9}","Not used",1,"symsum(log((b*(560*c*d + 196*d^2*x + 59049*root(14348907*a^11*b^2*z^3 + 408240*a^4*b*c*d*z - 64000*b*c^3 + 2744*a*d^3, z, k)^2*a^7*b + 9720*root(14348907*a^11*b^2*z^3 + 408240*a^4*b*c*d*z - 64000*b*c^3 + 2744*a*d^3, z, k)*a^3*b*c*x))/(6561*a^6))*root(14348907*a^11*b^2*z^3 + 408240*a^4*b*c*d*z - 64000*b*c^3 + 2744*a*d^3, z, k), k, 1, 3) + ((67*d*x^2)/(162*a) + (41*c*x)/(81*a) + (20*b^2*c*x^7)/(81*a^3) + (14*b^2*d*x^8)/(81*a^3) + (52*b*c*x^4)/(81*a^2) + (77*b*d*x^5)/(162*a^2))/(a^3 + b^3*x^9 + 3*a^2*b*x^3 + 3*a*b^2*x^6)","B"
11,1,127,161,4.847335,"\text{Not used}","int((a + b*x)/(d + e*x^3),x)","\sum _{k=1}^3\ln\left(e\,\left(a\,b+b^2\,x+{\mathrm{root}\left(27\,d^2\,e^2\,z^3+9\,a\,b\,d\,e\,z+b^3\,d-a^3\,e,z,k\right)}^2\,d\,e\,9+\mathrm{root}\left(27\,d^2\,e^2\,z^3+9\,a\,b\,d\,e\,z+b^3\,d-a^3\,e,z,k\right)\,a\,e\,x\,3\right)\right)\,\mathrm{root}\left(27\,d^2\,e^2\,z^3+9\,a\,b\,d\,e\,z+b^3\,d-a^3\,e,z,k\right)","Not used",1,"symsum(log(e*(a*b + b^2*x + 9*root(27*d^2*e^2*z^3 + 9*a*b*d*e*z + b^3*d - a^3*e, z, k)^2*d*e + 3*root(27*d^2*e^2*z^3 + 9*a*b*d*e*z + b^3*d - a^3*e, z, k)*a*e*x))*root(27*d^2*e^2*z^3 + 9*a*b*d*e*z + b^3*d - a^3*e, z, k), k, 1, 3)","B"
12,1,124,161,0.213275,"\text{Not used}","int((a + b*x)/(d - e*x^3),x)","\sum _{k=1}^3\ln\left(e\,\left(a\,b+b^2\,x-{\mathrm{root}\left(27\,d^2\,e^2\,z^3-9\,a\,b\,d\,e\,z+b^3\,d+a^3\,e,z,k\right)}^2\,d\,e\,9-\mathrm{root}\left(27\,d^2\,e^2\,z^3-9\,a\,b\,d\,e\,z+b^3\,d+a^3\,e,z,k\right)\,a\,e\,x\,3\right)\right)\,\mathrm{root}\left(27\,d^2\,e^2\,z^3-9\,a\,b\,d\,e\,z+b^3\,d+a^3\,e,z,k\right)","Not used",1,"symsum(log(e*(a*b + b^2*x - 9*root(27*d^2*e^2*z^3 - 9*a*b*d*e*z + b^3*d + a^3*e, z, k)^2*d*e - 3*root(27*d^2*e^2*z^3 - 9*a*b*d*e*z + b^3*d + a^3*e, z, k)*a*e*x))*root(27*d^2*e^2*z^3 - 9*a*b*d*e*z + b^3*d + a^3*e, z, k), k, 1, 3)","B"
13,1,16,19,4.699339,"\text{Not used}","int((x + 1)/(x^3 + 1),x)","\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}\,\left(2\,x-1\right)}{3}\right)}{3}","Not used",1,"(2*3^(1/2)*atan((3^(1/2)*(2*x - 1))/3))/3","B"
14,1,16,19,4.670467,"\text{Not used}","int((x - 1)/(x^3 - 1),x)","\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}\,\left(2\,x+1\right)}{3}\right)}{3}","Not used",1,"(2*3^(1/2)*atan((3^(1/2)*(2*x + 1))/3))/3","B"
15,1,16,22,0.062723,"\text{Not used}","int(-(x + 1)/(x^3 - 1),x)","\frac{\ln\left(x^2+x+1\right)}{3}-\frac{2\,\ln\left(x-1\right)}{3}","Not used",1,"log(x + x^2 + 1)/3 - (2*log(x - 1))/3","B"
16,1,18,22,0.111651,"\text{Not used}","int(-(x - 1)/(x^3 + 1),x)","\frac{2\,\ln\left(x+1\right)}{3}-\frac{\ln\left(x^2-x+1\right)}{3}","Not used",1,"(2*log(x + 1))/3 - log(x^2 - x + 1)/3","B"
17,1,46,41,0.140354,"\text{Not used}","int((x - 3)/(x^3 - 1),x)","-\frac{2\,\ln\left(x-1\right)}{3}-\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{3}+\frac{\sqrt{3}\,2{}\mathrm{i}}{3}\right)+\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{3}+\frac{\sqrt{3}\,2{}\mathrm{i}}{3}\right)","Not used",1,"log(x + (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*2i)/3 + 1/3) - log(x - (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*2i)/3 - 1/3) - (2*log(x - 1))/3","B"
18,1,28,29,0.053820,"\text{Not used}","int((c + d*x)/(c^3 + d^3*x^3),x)","-\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}}{3}-\frac{2\,\sqrt{3}\,d\,x}{3\,c}\right)}{3\,c\,d}","Not used",1,"-(2*3^(1/2)*atan(3^(1/2)/3 - (2*3^(1/2)*d*x)/(3*c)))/(3*c*d)","B"
19,1,28,29,0.044943,"\text{Not used}","int((c - d*x)/(c^3 - d^3*x^3),x)","\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}}{3}+\frac{2\,\sqrt{3}\,d\,x}{3\,c}\right)}{3\,c\,d}","Not used",1,"(2*3^(1/2)*atan(3^(1/2)/3 + (2*3^(1/2)*d*x)/(3*c)))/(3*c*d)","B"
20,1,49,39,4.820803,"\text{Not used}","int((B*a^(1/3)*b^(1/3) + B*b^(2/3)*x)/(a + b*x^3),x)","\frac{2\,\sqrt{3}\,B\,\sqrt{b}\,\mathrm{atanh}\left(\frac{\sqrt{3}\,\sqrt{b}}{3\,\sqrt{-b}}-\frac{2\,\sqrt{3}\,b^{5/6}\,x}{3\,a^{1/3}\,\sqrt{-b}}\right)}{3\,a^{1/3}\,\sqrt{-b}}","Not used",1,"(2*3^(1/2)*B*b^(1/2)*atanh((3^(1/2)*b^(1/2))/(3*(-b)^(1/2)) - (2*3^(1/2)*b^(5/6)*x)/(3*a^(1/3)*(-b)^(1/2))))/(3*a^(1/3)*(-b)^(1/2))","B"
21,1,49,41,0.230828,"\text{Not used}","int(-(B*(-b)^(2/3)*x - B*a^(1/3)*(-b)^(1/3))/(a + b*x^3),x)","-\frac{2\,\sqrt{3}\,B\,\sqrt{-b}\,\mathrm{atanh}\left(\frac{\sqrt{3}\,\sqrt{-b}}{3\,\sqrt{b}}-\frac{2\,\sqrt{3}\,\sqrt{b}\,x}{3\,a^{1/3}\,{\left(-b\right)}^{1/6}}\right)}{3\,a^{1/3}\,\sqrt{b}}","Not used",1,"-(2*3^(1/2)*B*(-b)^(1/2)*atanh((3^(1/2)*(-b)^(1/2))/(3*b^(1/2)) - (2*3^(1/2)*b^(1/2)*x)/(3*a^(1/3)*(-b)^(1/6))))/(3*a^(1/3)*b^(1/2))","B"
22,1,98,118,4.944320,"\text{Not used}","int((B*x + C*x^2)/(a + b*x^3) - (C*x^2)/(a + b*x^3),x)","-\frac{B\,\ln\left(b^{1/3}\,x+a^{1/3}\right)}{3\,a^{1/3}\,b^{2/3}}+\frac{\ln\left(4\,b^{1/3}\,x-2\,a^{1/3}-\sqrt{3}\,a^{1/3}\,2{}\mathrm{i}\right)\,\left(B-\sqrt{3}\,B\,1{}\mathrm{i}\right)}{6\,a^{1/3}\,b^{2/3}}+\frac{\ln\left(4\,b^{1/3}\,x-2\,a^{1/3}+\sqrt{3}\,a^{1/3}\,2{}\mathrm{i}\right)\,\left(B+\sqrt{3}\,B\,1{}\mathrm{i}\right)}{6\,a^{1/3}\,b^{2/3}}","Not used",1,"(log(4*b^(1/3)*x - 3^(1/2)*a^(1/3)*2i - 2*a^(1/3))*(B - 3^(1/2)*B*1i))/(6*a^(1/3)*b^(2/3)) - (B*log(b^(1/3)*x + a^(1/3)))/(3*a^(1/3)*b^(2/3)) + (log(3^(1/2)*a^(1/3)*2i + 4*b^(1/3)*x - 2*a^(1/3))*(B + 3^(1/2)*B*1i))/(6*a^(1/3)*b^(2/3))","B"
23,1,96,118,5.014775,"\text{Not used}","int((A + C*x^2)/(a + b*x^3) - (C*x^2)/(a + b*x^3),x)","\frac{A\,\ln\left(b^{1/3}\,x+a^{1/3}\right)}{3\,a^{2/3}\,b^{1/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x-\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(A-\sqrt{3}\,A\,1{}\mathrm{i}\right)}{6\,a^{2/3}\,b^{1/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}-\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(A+\sqrt{3}\,A\,1{}\mathrm{i}\right)}{6\,a^{2/3}\,b^{1/3}}","Not used",1,"(A*log(b^(1/3)*x + a^(1/3)))/(3*a^(2/3)*b^(1/3)) - (log(a^(1/3) - 2*b^(1/3)*x - 3^(1/2)*a^(1/3)*1i)*(A - 3^(1/2)*A*1i))/(6*a^(2/3)*b^(1/3)) - (log(2*b^(1/3)*x - 3^(1/2)*a^(1/3)*1i - a^(1/3))*(A + 3^(1/2)*A*1i))/(6*a^(2/3)*b^(1/3))","B"
24,1,127,161,4.922598,"\text{Not used}","int((A + B*x + C*x^2)/(a + b*x^3) - (C*x^2)/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(b\,\left(B^2\,x+A\,B+{\mathrm{root}\left(27\,a^2\,b^2\,z^3+9\,A\,B\,a\,b\,z+B^3\,a-A^3\,b,z,k\right)}^2\,a\,b\,9+A\,\mathrm{root}\left(27\,a^2\,b^2\,z^3+9\,A\,B\,a\,b\,z+B^3\,a-A^3\,b,z,k\right)\,b\,x\,3\right)\right)\,\mathrm{root}\left(27\,a^2\,b^2\,z^3+9\,A\,B\,a\,b\,z+B^3\,a-A^3\,b,z,k\right)","Not used",1,"symsum(log(b*(B^2*x + A*B + 9*root(27*a^2*b^2*z^3 + 9*A*B*a*b*z + B^3*a - A^3*b, z, k)^2*a*b + 3*A*root(27*a^2*b^2*z^3 + 9*A*B*a*b*z + B^3*a - A^3*b, z, k)*b*x))*root(27*a^2*b^2*z^3 + 9*A*B*a*b*z + B^3*a - A^3*b, z, k), k, 1, 3)","B"
25,1,158,134,0.188515,"\text{Not used}","int((b*x + c*x^2)/(d + e*x^3),x)","\sum _{k=1}^3\ln\left(-\mathrm{root}\left(27\,d\,e^3\,z^3-27\,c\,d\,e^2\,z^2+9\,c^2\,d\,e\,z+b^3\,e-c^3\,d,z,k\right)\,\left(6\,c\,d\,e-\mathrm{root}\left(27\,d\,e^3\,z^3-27\,c\,d\,e^2\,z^2+9\,c^2\,d\,e\,z+b^3\,e-c^3\,d,z,k\right)\,d\,e^2\,9\right)+c^2\,d+b^2\,e\,x\right)\,\mathrm{root}\left(27\,d\,e^3\,z^3-27\,c\,d\,e^2\,z^2+9\,c^2\,d\,e\,z+b^3\,e-c^3\,d,z,k\right)","Not used",1,"symsum(log(c^2*d - root(27*d*e^3*z^3 - 27*c*d*e^2*z^2 + 9*c^2*d*e*z + b^3*e - c^3*d, z, k)*(6*c*d*e - 9*root(27*d*e^3*z^3 - 27*c*d*e^2*z^2 + 9*c^2*d*e*z + b^3*e - c^3*d, z, k)*d*e^2) + b^2*e*x)*root(27*d*e^3*z^3 - 27*c*d*e^2*z^2 + 9*c^2*d*e*z + b^3*e - c^3*d, z, k), k, 1, 3)","B"
26,1,178,134,5.009189,"\text{Not used}","int((a + c*x^2)/(d - e*x^3),x)","\sum _{k=1}^3\ln\left(-\left(c+\mathrm{root}\left(27\,d^2\,e^3\,z^3+27\,c\,d^2\,e^2\,z^2+9\,c^2\,d^2\,e\,z+c^3\,d^2+a^3\,e^2,z,k\right)\,e\,3\right)\,\left(c\,d+\mathrm{root}\left(27\,d^2\,e^3\,z^3+27\,c\,d^2\,e^2\,z^2+9\,c^2\,d^2\,e\,z+c^3\,d^2+a^3\,e^2,z,k\right)\,d\,e\,3+a\,e\,x\right)\right)\,\mathrm{root}\left(27\,d^2\,e^3\,z^3+27\,c\,d^2\,e^2\,z^2+9\,c^2\,d^2\,e\,z+c^3\,d^2+a^3\,e^2,z,k\right)","Not used",1,"symsum(log(-(c + 3*root(27*d^2*e^3*z^3 + 27*c*d^2*e^2*z^2 + 9*c^2*d^2*e*z + c^3*d^2 + a^3*e^2, z, k)*e)*(c*d + 3*root(27*d^2*e^3*z^3 + 27*c*d^2*e^2*z^2 + 9*c^2*d^2*e*z + c^3*d^2 + a^3*e^2, z, k)*d*e + a*e*x))*root(27*d^2*e^3*z^3 + 27*c*d^2*e^2*z^2 + 9*c^2*d^2*e*z + c^3*d^2 + a^3*e^2, z, k), k, 1, 3)","B"
27,1,84,37,4.808905,"\text{Not used}","int((2*a^2 + b^2*x^2)/(a^3 + b^3*x^3),x)","\frac{\ln\left(a+b\,x\right)}{b}-\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{4\,\sqrt{3}\,a^3\,b^4}{4\,a^3\,b^4+4\,x\,a^2\,b^5}-\frac{4\,\sqrt{3}\,a^2\,b^5\,x}{4\,a^3\,b^4+4\,x\,a^2\,b^5}\right)}{3\,b}","Not used",1,"log(a + b*x)/b - (2*3^(1/2)*atan((4*3^(1/2)*a^3*b^4)/(4*a^3*b^4 + 4*a^2*b^5*x) - (4*3^(1/2)*a^2*b^5*x)/(4*a^3*b^4 + 4*a^2*b^5*x)))/(3*b)","B"
28,1,86,39,0.093022,"\text{Not used}","int((2*a^2 + b^2*x^2)/(a^3 - b^3*x^3),x)","\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{4\,\sqrt{3}\,a^3\,b^4}{4\,a^3\,b^4-4\,a^2\,b^5\,x}+\frac{4\,\sqrt{3}\,a^2\,b^5\,x}{4\,a^3\,b^4-4\,a^2\,b^5\,x}\right)}{3\,b}-\frac{\ln\left(a-b\,x\right)}{b}","Not used",1,"(2*3^(1/2)*atan((4*3^(1/2)*a^3*b^4)/(4*a^3*b^4 - 4*a^2*b^5*x) + (4*3^(1/2)*a^2*b^5*x)/(4*a^3*b^4 - 4*a^2*b^5*x)))/(3*b) - log(a - b*x)/b","B"
29,1,147,48,5.137280,"\text{Not used}","int((8*C + C*b^(2/3)*x^2)/(b*x^3 + 8),x)","\sum _{k=1}^3\ln\left(-\frac{\left(C-\mathrm{root}\left(27\,b^3\,z^3-27\,C\,b^{8/3}\,z^2+9\,C^2\,b^{7/3}\,z-9\,C^3\,b^2,z,k\right)\,b^{1/3}\,3\right)\,\left(-C+\mathrm{root}\left(27\,b^3\,z^3-27\,C\,b^{8/3}\,z^2+9\,C^2\,b^{7/3}\,z-9\,C^3\,b^2,z,k\right)\,b^{1/3}\,3+C\,b^{1/3}\,x\right)\,8}{b^{5/3}}\right)\,\mathrm{root}\left(27\,b^3\,z^3-27\,C\,b^{8/3}\,z^2+9\,C^2\,b^{7/3}\,z-9\,C^3\,b^2,z,k\right)","Not used",1,"symsum(log(-(8*(C - 3*root(27*b^3*z^3 - 27*C*b^(8/3)*z^2 + 9*C^2*b^(7/3)*z - 9*C^3*b^2, z, k)*b^(1/3))*(3*root(27*b^3*z^3 - 27*C*b^(8/3)*z^2 + 9*C^2*b^(7/3)*z - 9*C^3*b^2, z, k)*b^(1/3) - C + C*b^(1/3)*x))/b^(5/3))*root(27*b^3*z^3 - 27*C*b^(8/3)*z^2 + 9*C^2*b^(7/3)*z - 9*C^3*b^2, z, k), k, 1, 3)","B"
30,1,145,47,5.024422,"\text{Not used}","int((C*a^(2/3) + 2*C*x^2)/(a + 8*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{a^{2/3}\,\left(C-12\,\mathrm{root}\left(1728\,a^2\,z^3-432\,C\,a^2\,z^2+36\,C^2\,a^2\,z-9\,C^3\,a^2,z,k\right)\right)\,\left(4\,C\,x-C\,a^{1/3}+\mathrm{root}\left(1728\,a^2\,z^3-432\,C\,a^2\,z^2+36\,C^2\,a^2\,z-9\,C^3\,a^2,z,k\right)\,a^{1/3}\,12\right)}{128}\right)\,\mathrm{root}\left(1728\,a^2\,z^3-432\,C\,a^2\,z^2+36\,C^2\,a^2\,z-9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log(-(a^(2/3)*(C - 12*root(1728*a^2*z^3 - 432*C*a^2*z^2 + 36*C^2*a^2*z - 9*C^3*a^2, z, k))*(4*C*x - C*a^(1/3) + 12*root(1728*a^2*z^3 - 432*C*a^2*z^2 + 36*C^2*a^2*z - 9*C^3*a^2, z, k)*a^(1/3)))/128)*root(1728*a^2*z^3 - 432*C*a^2*z^2 + 36*C^2*a^2*z - 9*C^3*a^2, z, k), k, 1, 3)","B"
31,1,176,57,5.272163,"\text{Not used}","int((8*C + C*(-b)^(2/3)*x^2)/(b*x^3 - 8),x)","\sum _{k=1}^3\ln\left(\frac{8\,C^2}{{\left(-b\right)}^{5/3}}+\mathrm{root}\left(27\,b^3\,z^3-27\,C\,{\left(-b\right)}^{8/3}\,z^2-9\,C^2\,{\left(-b\right)}^{7/3}\,z-9\,C^3\,b^2,z,k\right)\,\left(-\frac{\mathrm{root}\left(27\,b^3\,z^3-27\,C\,{\left(-b\right)}^{8/3}\,z^2-9\,C^2\,{\left(-b\right)}^{7/3}\,z-9\,C^3\,b^2,z,k\right)\,72}{b}+\frac{48\,C}{{\left(-b\right)}^{4/3}}+\frac{24\,C\,x}{b}\right)-\frac{8\,C^2\,x}{{\left(-b\right)}^{4/3}}\right)\,\mathrm{root}\left(27\,b^3\,z^3-27\,C\,{\left(-b\right)}^{8/3}\,z^2-9\,C^2\,{\left(-b\right)}^{7/3}\,z-9\,C^3\,b^2,z,k\right)","Not used",1,"symsum(log((8*C^2)/(-b)^(5/3) + root(27*b^3*z^3 - 27*C*(-b)^(8/3)*z^2 - 9*C^2*(-b)^(7/3)*z - 9*C^3*b^2, z, k)*((48*C)/(-b)^(4/3) - (72*root(27*b^3*z^3 - 27*C*(-b)^(8/3)*z^2 - 9*C^2*(-b)^(7/3)*z - 9*C^3*b^2, z, k))/b + (24*C*x)/b) - (8*C^2*x)/(-b)^(4/3))*root(27*b^3*z^3 - 27*C*(-b)^(8/3)*z^2 - 9*C^2*(-b)^(7/3)*z - 9*C^3*b^2, z, k), k, 1, 3)","B"
32,1,142,47,0.328360,"\text{Not used}","int((2*C*x^2 + C*(-a)^(2/3))/(a - 8*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{\left(C+12\,\mathrm{root}\left(1728\,a^2\,z^3+432\,C\,a^2\,z^2+36\,C^2\,a^2\,z+9\,C^3\,a^2,z,k\right)\right)\,\left(C\,a+\mathrm{root}\left(1728\,a^2\,z^3+432\,C\,a^2\,z^2+36\,C^2\,a^2\,z+9\,C^3\,a^2,z,k\right)\,a\,12+4\,C\,{\left(-a\right)}^{2/3}\,x\right)}{128}\right)\,\mathrm{root}\left(1728\,a^2\,z^3+432\,C\,a^2\,z^2+36\,C^2\,a^2\,z+9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log(-((C + 12*root(1728*a^2*z^3 + 432*C*a^2*z^2 + 36*C^2*a^2*z + 9*C^3*a^2, z, k))*(C*a + 12*root(1728*a^2*z^3 + 432*C*a^2*z^2 + 36*C^2*a^2*z + 9*C^3*a^2, z, k)*a + 4*C*(-a)^(2/3)*x))/128)*root(1728*a^2*z^3 + 432*C*a^2*z^2 + 36*C^2*a^2*z + 9*C^3*a^2, z, k), k, 1, 3)","B"
33,1,172,50,5.098049,"\text{Not used}","int((C*x^2 + 2*C*(a/b)^(2/3))/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{\left(C-\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z-9\,C^3\,a^2,z,k\right)\,b\,3\right)\,\left(-C\,a+\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z-9\,C^3\,a^2,z,k\right)\,a\,b\,3+2\,C\,b\,x\,{\left(\frac{a}{b}\right)}^{2/3}\right)}{b^3}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z-9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log(-((C - 3*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z - 9*C^3*a^2, z, k)*b)*(3*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z - 9*C^3*a^2, z, k)*a*b - C*a + 2*C*b*x*(a/b)^(2/3)))/b^3)*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z - 9*C^3*a^2, z, k), k, 1, 3)","B"
34,1,172,53,5.401955,"\text{Not used}","int((C*x^2 + 2*C*(-a/b)^(2/3))/(a - b*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{\left(C+\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z+9\,C^3\,a^2,z,k\right)\,b\,3\right)\,\left(C\,a+\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z+9\,C^3\,a^2,z,k\right)\,a\,b\,3+2\,C\,b\,x\,{\left(-\frac{a}{b}\right)}^{2/3}\right)}{b^3}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z+9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log(-((C + 3*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z + 9*C^3*a^2, z, k)*b)*(C*a + 3*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z + 9*C^3*a^2, z, k)*a*b + 2*C*b*x*(-a/b)^(2/3)))/b^3)*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z + 9*C^3*a^2, z, k), k, 1, 3)","B"
35,1,173,54,5.269938,"\text{Not used}","int((C*x^2 + 2*C*(-a/b)^(2/3))/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{\left(C-\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z-9\,C^3\,a^2,z,k\right)\,b\,3\right)\,\left(-C\,a+\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z-9\,C^3\,a^2,z,k\right)\,a\,b\,3+2\,C\,b\,x\,{\left(-\frac{a}{b}\right)}^{2/3}\right)}{b^3}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z-9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log(-((C - 3*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z - 9*C^3*a^2, z, k)*b)*(3*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z - 9*C^3*a^2, z, k)*a*b - C*a + 2*C*b*x*(-a/b)^(2/3)))/b^3)*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z - 9*C^3*a^2, z, k), k, 1, 3)","B"
36,1,171,53,5.191238,"\text{Not used}","int((C*x^2 + 2*C*(a/b)^(2/3))/(a - b*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{\left(C+\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z+9\,C^3\,a^2,z,k\right)\,b\,3\right)\,\left(C\,a+\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z+9\,C^3\,a^2,z,k\right)\,a\,b\,3+2\,C\,b\,x\,{\left(\frac{a}{b}\right)}^{2/3}\right)}{b^3}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2+9\,C^2\,a^2\,b\,z+9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log(-((C + 3*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z + 9*C^3*a^2, z, k)*b)*(C*a + 3*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z + 9*C^3*a^2, z, k)*a*b + 2*C*b*x*(a/b)^(2/3)))/b^3)*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 + 9*C^2*a^2*b*z + 9*C^3*a^2, z, k), k, 1, 3)","B"
37,1,193,61,5.307171,"\text{Not used}","int((2*C*a^(2/3) + C*b^(2/3)*x^2)/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{a^{2/3}\,\left(C-\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^{8/3}\,z^2+9\,C^2\,a^2\,b^{7/3}\,z-9\,C^3\,a^2\,b^2,z,k\right)\,b^{1/3}\,3\right)\,\left(-C\,a^{1/3}+\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^{8/3}\,z^2+9\,C^2\,a^2\,b^{7/3}\,z-9\,C^3\,a^2\,b^2,z,k\right)\,a^{1/3}\,b^{1/3}\,3+2\,C\,b^{1/3}\,x\right)}{b^{5/3}}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^{8/3}\,z^2+9\,C^2\,a^2\,b^{7/3}\,z-9\,C^3\,a^2\,b^2,z,k\right)","Not used",1,"symsum(log(-(a^(2/3)*(C - 3*root(27*a^2*b^3*z^3 - 27*C*a^2*b^(8/3)*z^2 + 9*C^2*a^2*b^(7/3)*z - 9*C^3*a^2*b^2, z, k)*b^(1/3))*(3*root(27*a^2*b^3*z^3 - 27*C*a^2*b^(8/3)*z^2 + 9*C^2*a^2*b^(7/3)*z - 9*C^3*a^2*b^2, z, k)*a^(1/3)*b^(1/3) - C*a^(1/3) + 2*C*b^(1/3)*x))/b^(5/3))*root(27*a^2*b^3*z^3 - 27*C*a^2*b^(8/3)*z^2 + 9*C^2*a^2*b^(7/3)*z - 9*C^3*a^2*b^2, z, k), k, 1, 3)","B"
38,1,221,70,5.239175,"\text{Not used}","int(-(2*C*a^(2/3) + C*(-b)^(2/3)*x^2)/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,{\left(-b\right)}^{8/3}\,z^2-9\,C^2\,a^2\,{\left(-b\right)}^{7/3}\,z+9\,C^3\,a^2\,b^2,z,k\right)\,\left(\frac{6\,C\,a}{{\left(-b\right)}^{4/3}}+\frac{\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,{\left(-b\right)}^{8/3}\,z^2-9\,C^2\,a^2\,{\left(-b\right)}^{7/3}\,z+9\,C^3\,a^2\,b^2,z,k\right)\,a\,9}{b}-\frac{6\,C\,a^{2/3}\,x}{b}\right)-\frac{C^2\,a}{{\left(-b\right)}^{5/3}}-\frac{2\,C^2\,a^{2/3}\,x}{{\left(-b\right)}^{4/3}}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,{\left(-b\right)}^{8/3}\,z^2-9\,C^2\,a^2\,{\left(-b\right)}^{7/3}\,z+9\,C^3\,a^2\,b^2,z,k\right)","Not used",1,"symsum(log(root(27*a^2*b^3*z^3 + 27*C*a^2*(-b)^(8/3)*z^2 - 9*C^2*a^2*(-b)^(7/3)*z + 9*C^3*a^2*b^2, z, k)*((6*C*a)/(-b)^(4/3) + (9*root(27*a^2*b^3*z^3 + 27*C*a^2*(-b)^(8/3)*z^2 - 9*C^2*a^2*(-b)^(7/3)*z + 9*C^3*a^2*b^2, z, k)*a)/b - (6*C*a^(2/3)*x)/b) - (C^2*a)/(-b)^(5/3) - (2*C^2*a^(2/3)*x)/(-b)^(4/3))*root(27*a^2*b^3*z^3 + 27*C*a^2*(-b)^(8/3)*z^2 - 9*C^2*a^2*(-b)^(7/3)*z + 9*C^3*a^2*b^2, z, k), k, 1, 3)","B"
39,1,46,40,0.155405,"\text{Not used}","int((x^2 - 3)/(x^3 - 1),x)","-\frac{2\,\ln\left(x-1\right)}{3}-\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{5}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)+\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{5}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)","Not used",1,"log(x + (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/2 + 5/6) - log(x - (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/2 - 5/6) - (2*log(x - 1))/3","B"
40,1,386,70,6.232174,"\text{Not used}","int((2*C*a^(2/3) + B*a^(1/3)*b^(1/3) + C*b^(2/3)*x^2 + B*b^(2/3)*x)/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{x\,\left(2\,C^2\,a^{2/3}\,b^{2/3}-B^2\,b^{4/3}+B\,C\,a^{1/3}\,b\right)}{b^2}+\frac{a^{1/3}\,{\left(B\,b^{1/3}+C\,a^{1/3}\right)}^2}{b^{5/3}}+\frac{\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^{8/3}\,z^2+18\,B\,C\,a^{5/3}\,b^{8/3}\,z+9\,C^2\,a^2\,b^{7/3}\,z+9\,B^2\,a^{4/3}\,b^3\,z-18\,B\,C^2\,a^{5/3}\,b^{7/3}-9\,B^2\,C\,a^{4/3}\,b^{8/3}-9\,C^3\,a^2\,b^2,z,k\right)\,\left(-6\,C\,a+\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^{8/3}\,z^2+18\,B\,C\,a^{5/3}\,b^{8/3}\,z+9\,C^2\,a^2\,b^{7/3}\,z+9\,B^2\,a^{4/3}\,b^3\,z-18\,B\,C^2\,a^{5/3}\,b^{7/3}-9\,B^2\,C\,a^{4/3}\,b^{8/3}-9\,C^3\,a^2\,b^2,z,k\right)\,a\,b^{1/3}\,9+3\,B\,a^{1/3}\,b^{2/3}\,x+6\,C\,a^{2/3}\,b^{1/3}\,x\right)}{b^{4/3}}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^{8/3}\,z^2+18\,B\,C\,a^{5/3}\,b^{8/3}\,z+9\,C^2\,a^2\,b^{7/3}\,z+9\,B^2\,a^{4/3}\,b^3\,z-18\,B\,C^2\,a^{5/3}\,b^{7/3}-9\,B^2\,C\,a^{4/3}\,b^{8/3}-9\,C^3\,a^2\,b^2,z,k\right)","Not used",1,"symsum(log((a^(1/3)*(B*b^(1/3) + C*a^(1/3))^2)/b^(5/3) - (x*(2*C^2*a^(2/3)*b^(2/3) - B^2*b^(4/3) + B*C*a^(1/3)*b))/b^2 + (root(27*a^2*b^3*z^3 - 27*C*a^2*b^(8/3)*z^2 + 18*B*C*a^(5/3)*b^(8/3)*z + 9*C^2*a^2*b^(7/3)*z + 9*B^2*a^(4/3)*b^3*z - 18*B*C^2*a^(5/3)*b^(7/3) - 9*B^2*C*a^(4/3)*b^(8/3) - 9*C^3*a^2*b^2, z, k)*(9*root(27*a^2*b^3*z^3 - 27*C*a^2*b^(8/3)*z^2 + 18*B*C*a^(5/3)*b^(8/3)*z + 9*C^2*a^2*b^(7/3)*z + 9*B^2*a^(4/3)*b^3*z - 18*B*C^2*a^(5/3)*b^(7/3) - 9*B^2*C*a^(4/3)*b^(8/3) - 9*C^3*a^2*b^2, z, k)*a*b^(1/3) - 6*C*a + 3*B*a^(1/3)*b^(2/3)*x + 6*C*a^(2/3)*b^(1/3)*x))/b^(4/3))*root(27*a^2*b^3*z^3 - 27*C*a^2*b^(8/3)*z^2 + 18*B*C*a^(5/3)*b^(8/3)*z + 9*C^2*a^2*b^(7/3)*z + 9*B^2*a^(4/3)*b^3*z - 18*B*C^2*a^(5/3)*b^(7/3) - 9*B^2*C*a^(4/3)*b^(8/3) - 9*C^3*a^2*b^2, z, k), k, 1, 3)","B"
41,1,444,88,6.324108,"\text{Not used}","int(-(2*C*a^(2/3) + B*(-b)^(2/3)*x - B*a^(1/3)*(-b)^(1/3) + C*(-b)^(2/3)*x^2)/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,{\left(-b\right)}^{8/3}\,z^2+18\,B\,C\,a^{5/3}\,{\left(-b\right)}^{8/3}\,z+9\,B^2\,a^{4/3}\,b^3\,z-9\,C^2\,a^2\,{\left(-b\right)}^{7/3}\,z-18\,B\,C^2\,a^{5/3}\,{\left(-b\right)}^{7/3}+9\,B^2\,C\,a^{4/3}\,{\left(-b\right)}^{8/3}+9\,C^3\,a^2\,b^2,z,k\right)\,\left(\frac{6\,C\,a}{{\left(-b\right)}^{4/3}}-\frac{x\,\left(3\,B\,a^{1/3}\,{\left(-b\right)}^{4/3}+6\,C\,a^{2/3}\,b\right)}{b^2}+\frac{\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,{\left(-b\right)}^{8/3}\,z^2+18\,B\,C\,a^{5/3}\,{\left(-b\right)}^{8/3}\,z+9\,B^2\,a^{4/3}\,b^3\,z-9\,C^2\,a^2\,{\left(-b\right)}^{7/3}\,z-18\,B\,C^2\,a^{5/3}\,{\left(-b\right)}^{7/3}+9\,B^2\,C\,a^{4/3}\,{\left(-b\right)}^{8/3}+9\,C^3\,a^2\,b^2,z,k\right)\,a\,9}{b}\right)+\frac{B^2\,a^{1/3}\,b^2+C^2\,a\,{\left(-b\right)}^{4/3}-2\,B\,C\,a^{2/3}\,{\left(-b\right)}^{5/3}}{b^3}-\frac{x\,\left(2\,C^2\,a^{2/3}\,{\left(-b\right)}^{2/3}-B^2\,{\left(-b\right)}^{4/3}+B\,C\,a^{1/3}\,b\right)}{b^2}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,{\left(-b\right)}^{8/3}\,z^2+18\,B\,C\,a^{5/3}\,{\left(-b\right)}^{8/3}\,z+9\,B^2\,a^{4/3}\,b^3\,z-9\,C^2\,a^2\,{\left(-b\right)}^{7/3}\,z-18\,B\,C^2\,a^{5/3}\,{\left(-b\right)}^{7/3}+9\,B^2\,C\,a^{4/3}\,{\left(-b\right)}^{8/3}+9\,C^3\,a^2\,b^2,z,k\right)","Not used",1,"symsum(log(root(27*a^2*b^3*z^3 + 27*C*a^2*(-b)^(8/3)*z^2 + 18*B*C*a^(5/3)*(-b)^(8/3)*z + 9*B^2*a^(4/3)*b^3*z - 9*C^2*a^2*(-b)^(7/3)*z - 18*B*C^2*a^(5/3)*(-b)^(7/3) + 9*B^2*C*a^(4/3)*(-b)^(8/3) + 9*C^3*a^2*b^2, z, k)*((6*C*a)/(-b)^(4/3) - (x*(3*B*a^(1/3)*(-b)^(4/3) + 6*C*a^(2/3)*b))/b^2 + (9*root(27*a^2*b^3*z^3 + 27*C*a^2*(-b)^(8/3)*z^2 + 18*B*C*a^(5/3)*(-b)^(8/3)*z + 9*B^2*a^(4/3)*b^3*z - 9*C^2*a^2*(-b)^(7/3)*z - 18*B*C^2*a^(5/3)*(-b)^(7/3) + 9*B^2*C*a^(4/3)*(-b)^(8/3) + 9*C^3*a^2*b^2, z, k)*a)/b) + (B^2*a^(1/3)*b^2 + C^2*a*(-b)^(4/3) - 2*B*C*a^(2/3)*(-b)^(5/3))/b^3 - (x*(2*C^2*a^(2/3)*(-b)^(2/3) - B^2*(-b)^(4/3) + B*C*a^(1/3)*b))/b^2)*root(27*a^2*b^3*z^3 + 27*C*a^2*(-b)^(8/3)*z^2 + 18*B*C*a^(5/3)*(-b)^(8/3)*z + 9*B^2*a^(4/3)*b^3*z - 9*C^2*a^2*(-b)^(7/3)*z - 18*B*C^2*a^(5/3)*(-b)^(7/3) + 9*B^2*C*a^(4/3)*(-b)^(8/3) + 9*C^3*a^2*b^2, z, k), k, 1, 3)","B"
42,1,12,11,0.036452,"\text{Not used}","int(-(B^2 + C^2*x^2 + B*C*x)/(B^3 - C^3*x^3),x)","\frac{\ln\left(C\,x-B\right)}{C}","Not used",1,"log(C*x - B)/C","B"
43,1,15,21,4.902733,"\text{Not used}","int((C*a^(2/3) + C*b^(2/3)*x^2 - C*a^(1/3)*b^(1/3)*x)/(a + b*x^3),x)","\frac{C\,\ln\left(x+\frac{a^{1/3}}{b^{1/3}}\right)}{b^{1/3}}","Not used",1,"(C*log(x + a^(1/3)/b^(1/3)))/b^(1/3)","B"
44,1,436,71,6.076536,"\text{Not used}","int((B*x + C*x^2 + B*(a/b)^(1/3) + 2*C*(a/b)^(2/3))/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(\frac{C^2\,a+B^2\,b\,{\left(\frac{a}{b}\right)}^{1/3}+2\,B\,C\,b\,{\left(\frac{a}{b}\right)}^{2/3}}{b^3}+\frac{\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+18\,B\,C\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{2/3}+9\,B^2\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(\frac{a}{b}\right)}^{2/3}-9\,B^2\,C\,a\,b\,{\left(\frac{a}{b}\right)}^{1/3}-9\,C^3\,a^2,z,k\right)\,\left(-6\,C\,a+\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+18\,B\,C\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{2/3}+9\,B^2\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(\frac{a}{b}\right)}^{2/3}-9\,B^2\,C\,a\,b\,{\left(\frac{a}{b}\right)}^{1/3}-9\,C^3\,a^2,z,k\right)\,a\,b\,9+3\,B\,b\,x\,{\left(\frac{a}{b}\right)}^{1/3}+6\,C\,b\,x\,{\left(\frac{a}{b}\right)}^{2/3}\right)}{b^2}-\frac{x\,\left(2\,C^2\,{\left(\frac{a}{b}\right)}^{2/3}-B^2+B\,C\,{\left(\frac{a}{b}\right)}^{1/3}\right)}{b^2}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+18\,B\,C\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{2/3}+9\,B^2\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(\frac{a}{b}\right)}^{2/3}-9\,B^2\,C\,a\,b\,{\left(\frac{a}{b}\right)}^{1/3}-9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log((C^2*a + B^2*b*(a/b)^(1/3) + 2*B*C*b*(a/b)^(2/3))/b^3 + (root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 18*B*C*a*b^2*z*(a/b)^(2/3) + 9*B^2*a*b^2*z*(a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(a/b)^(2/3) - 9*B^2*C*a*b*(a/b)^(1/3) - 9*C^3*a^2, z, k)*(9*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 18*B*C*a*b^2*z*(a/b)^(2/3) + 9*B^2*a*b^2*z*(a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(a/b)^(2/3) - 9*B^2*C*a*b*(a/b)^(1/3) - 9*C^3*a^2, z, k)*a*b - 6*C*a + 3*B*b*x*(a/b)^(1/3) + 6*C*b*x*(a/b)^(2/3)))/b^2 - (x*(2*C^2*(a/b)^(2/3) - B^2 + B*C*(a/b)^(1/3)))/b^2)*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 18*B*C*a*b^2*z*(a/b)^(2/3) + 9*B^2*a*b^2*z*(a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(a/b)^(2/3) - 9*B^2*C*a*b*(a/b)^(1/3) - 9*C^3*a^2, z, k), k, 1, 3)","B"
45,1,456,76,6.479150,"\text{Not used}","int((B*x + C*x^2 + B*(-a/b)^(1/3) + 2*C*(-a/b)^(2/3))/(a - b*x^3),x)","\sum _{k=1}^3\ln\left(\frac{B^2\,b\,{\left(-\frac{a}{b}\right)}^{1/3}-C^2\,a+2\,B\,C\,b\,{\left(-\frac{a}{b}\right)}^{2/3}}{b^3}-\frac{\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2-18\,B\,C\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{2/3}-9\,B^2\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(-\frac{a}{b}\right)}^{2/3}-9\,B^2\,C\,a\,b\,{\left(-\frac{a}{b}\right)}^{1/3}+9\,C^3\,a^2,z,k\right)\,\left(6\,C\,a+\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2-18\,B\,C\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{2/3}-9\,B^2\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(-\frac{a}{b}\right)}^{2/3}-9\,B^2\,C\,a\,b\,{\left(-\frac{a}{b}\right)}^{1/3}+9\,C^3\,a^2,z,k\right)\,a\,b\,9+3\,B\,b\,x\,{\left(-\frac{a}{b}\right)}^{1/3}+6\,C\,b\,x\,{\left(-\frac{a}{b}\right)}^{2/3}\right)}{b^2}-\frac{x\,\left(2\,C^2\,{\left(-\frac{a}{b}\right)}^{2/3}-B^2+B\,C\,{\left(-\frac{a}{b}\right)}^{1/3}\right)}{b^2}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2-18\,B\,C\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{2/3}-9\,B^2\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(-\frac{a}{b}\right)}^{2/3}-9\,B^2\,C\,a\,b\,{\left(-\frac{a}{b}\right)}^{1/3}+9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log((B^2*b*(-a/b)^(1/3) - C^2*a + 2*B*C*b*(-a/b)^(2/3))/b^3 - (root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 - 18*B*C*a*b^2*z*(-a/b)^(2/3) - 9*B^2*a*b^2*z*(-a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(-a/b)^(2/3) - 9*B^2*C*a*b*(-a/b)^(1/3) + 9*C^3*a^2, z, k)*(6*C*a + 9*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 - 18*B*C*a*b^2*z*(-a/b)^(2/3) - 9*B^2*a*b^2*z*(-a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(-a/b)^(2/3) - 9*B^2*C*a*b*(-a/b)^(1/3) + 9*C^3*a^2, z, k)*a*b + 3*B*b*x*(-a/b)^(1/3) + 6*C*b*x*(-a/b)^(2/3)))/b^2 - (x*(2*C^2*(-a/b)^(2/3) - B^2 + B*C*(-a/b)^(1/3)))/b^2)*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 - 18*B*C*a*b^2*z*(-a/b)^(2/3) - 9*B^2*a*b^2*z*(-a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(-a/b)^(2/3) - 9*B^2*C*a*b*(-a/b)^(1/3) + 9*C^3*a^2, z, k), k, 1, 3)","B"
46,1,453,78,6.053266,"\text{Not used}","int((B*x + C*x^2 - B*(-a/b)^(1/3) + 2*C*(-a/b)^(2/3))/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(\frac{C^2\,a-B^2\,b\,{\left(-\frac{a}{b}\right)}^{1/3}+2\,B\,C\,b\,{\left(-\frac{a}{b}\right)}^{2/3}}{b^3}-\frac{\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+18\,B\,C\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{2/3}-9\,B^2\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(-\frac{a}{b}\right)}^{2/3}+9\,B^2\,C\,a\,b\,{\left(-\frac{a}{b}\right)}^{1/3}-9\,C^3\,a^2,z,k\right)\,\left(6\,C\,a-\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+18\,B\,C\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{2/3}-9\,B^2\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(-\frac{a}{b}\right)}^{2/3}+9\,B^2\,C\,a\,b\,{\left(-\frac{a}{b}\right)}^{1/3}-9\,C^3\,a^2,z,k\right)\,a\,b\,9+3\,B\,b\,x\,{\left(-\frac{a}{b}\right)}^{1/3}-6\,C\,b\,x\,{\left(-\frac{a}{b}\right)}^{2/3}\right)}{b^2}+\frac{x\,\left(B^2-2\,C^2\,{\left(-\frac{a}{b}\right)}^{2/3}+B\,C\,{\left(-\frac{a}{b}\right)}^{1/3}\right)}{b^2}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,C\,a^2\,b^2\,z^2+18\,B\,C\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{2/3}-9\,B^2\,a\,b^2\,z\,{\left(-\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(-\frac{a}{b}\right)}^{2/3}+9\,B^2\,C\,a\,b\,{\left(-\frac{a}{b}\right)}^{1/3}-9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log((C^2*a - B^2*b*(-a/b)^(1/3) + 2*B*C*b*(-a/b)^(2/3))/b^3 - (root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 18*B*C*a*b^2*z*(-a/b)^(2/3) - 9*B^2*a*b^2*z*(-a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(-a/b)^(2/3) + 9*B^2*C*a*b*(-a/b)^(1/3) - 9*C^3*a^2, z, k)*(6*C*a - 9*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 18*B*C*a*b^2*z*(-a/b)^(2/3) - 9*B^2*a*b^2*z*(-a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(-a/b)^(2/3) + 9*B^2*C*a*b*(-a/b)^(1/3) - 9*C^3*a^2, z, k)*a*b + 3*B*b*x*(-a/b)^(1/3) - 6*C*b*x*(-a/b)^(2/3)))/b^2 + (x*(B^2 - 2*C^2*(-a/b)^(2/3) + B*C*(-a/b)^(1/3)))/b^2)*root(27*a^2*b^3*z^3 - 27*C*a^2*b^2*z^2 + 18*B*C*a*b^2*z*(-a/b)^(2/3) - 9*B^2*a*b^2*z*(-a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(-a/b)^(2/3) + 9*B^2*C*a*b*(-a/b)^(1/3) - 9*C^3*a^2, z, k), k, 1, 3)","B"
47,1,435,75,6.357106,"\text{Not used}","int((B*x + C*x^2 - B*(a/b)^(1/3) + 2*C*(a/b)^(2/3))/(a - b*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{C^2\,a+B^2\,b\,{\left(\frac{a}{b}\right)}^{1/3}-2\,B\,C\,b\,{\left(\frac{a}{b}\right)}^{2/3}}{b^3}-\frac{\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2-18\,B\,C\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{2/3}+9\,B^2\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(\frac{a}{b}\right)}^{2/3}+9\,B^2\,C\,a\,b\,{\left(\frac{a}{b}\right)}^{1/3}+9\,C^3\,a^2,z,k\right)\,\left(6\,C\,a+\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2-18\,B\,C\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{2/3}+9\,B^2\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(\frac{a}{b}\right)}^{2/3}+9\,B^2\,C\,a\,b\,{\left(\frac{a}{b}\right)}^{1/3}+9\,C^3\,a^2,z,k\right)\,a\,b\,9-3\,B\,b\,x\,{\left(\frac{a}{b}\right)}^{1/3}+6\,C\,b\,x\,{\left(\frac{a}{b}\right)}^{2/3}\right)}{b^2}+\frac{x\,\left(B^2-2\,C^2\,{\left(\frac{a}{b}\right)}^{2/3}+B\,C\,{\left(\frac{a}{b}\right)}^{1/3}\right)}{b^2}\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3+27\,C\,a^2\,b^2\,z^2-18\,B\,C\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{2/3}+9\,B^2\,a\,b^2\,z\,{\left(\frac{a}{b}\right)}^{1/3}+9\,C^2\,a^2\,b\,z-18\,B\,C^2\,a\,b\,{\left(\frac{a}{b}\right)}^{2/3}+9\,B^2\,C\,a\,b\,{\left(\frac{a}{b}\right)}^{1/3}+9\,C^3\,a^2,z,k\right)","Not used",1,"symsum(log((x*(B^2 - 2*C^2*(a/b)^(2/3) + B*C*(a/b)^(1/3)))/b^2 - (root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 - 18*B*C*a*b^2*z*(a/b)^(2/3) + 9*B^2*a*b^2*z*(a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(a/b)^(2/3) + 9*B^2*C*a*b*(a/b)^(1/3) + 9*C^3*a^2, z, k)*(6*C*a + 9*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 - 18*B*C*a*b^2*z*(a/b)^(2/3) + 9*B^2*a*b^2*z*(a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(a/b)^(2/3) + 9*B^2*C*a*b*(a/b)^(1/3) + 9*C^3*a^2, z, k)*a*b - 3*B*b*x*(a/b)^(1/3) + 6*C*b*x*(a/b)^(2/3)))/b^2 - (C^2*a + B^2*b*(a/b)^(1/3) - 2*B*C*b*(a/b)^(2/3))/b^3)*root(27*a^2*b^3*z^3 + 27*C*a^2*b^2*z^2 - 18*B*C*a*b^2*z*(a/b)^(2/3) + 9*B^2*a*b^2*z*(a/b)^(1/3) + 9*C^2*a^2*b*z - 18*B*C^2*a*b*(a/b)^(2/3) + 9*B^2*C*a*b*(a/b)^(1/3) + 9*C^3*a^2, z, k), k, 1, 3)","B"
48,1,35,32,4.778007,"\text{Not used}","int(-(a + a*x + c*x^2)/(x^3 - 1),x)","\frac{a\,\ln\left(x^2+x+1\right)}{3}-\frac{c\,\ln\left(x-1\right)}{3}-\frac{2\,a\,\ln\left(x-1\right)}{3}-\frac{c\,\ln\left(x^2+x+1\right)}{3}","Not used",1,"(a*log(x + x^2 + 1))/3 - (c*log(x - 1))/3 - (2*a*log(x - 1))/3 - (c*log(x + x^2 + 1))/3","B"
49,1,87,55,4.947939,"\text{Not used}","int(-(a + b*x + c*x^2)/(x^3 - 1),x)","\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{a}{6}+\frac{b}{6}-\frac{c}{3}-\frac{\sqrt{3}\,a\,1{}\mathrm{i}}{6}+\frac{\sqrt{3}\,b\,1{}\mathrm{i}}{6}\right)+\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{a}{6}+\frac{b}{6}-\frac{c}{3}+\frac{\sqrt{3}\,a\,1{}\mathrm{i}}{6}-\frac{\sqrt{3}\,b\,1{}\mathrm{i}}{6}\right)-\ln\left(x-1\right)\,\left(\frac{a}{3}+\frac{b}{3}+\frac{c}{3}\right)","Not used",1,"log(x - (3^(1/2)*1i)/2 + 1/2)*(a/6 + b/6 - c/3 - (3^(1/2)*a*1i)/6 + (3^(1/2)*b*1i)/6) + log(x + (3^(1/2)*1i)/2 + 1/2)*(a/6 + b/6 - c/3 + (3^(1/2)*a*1i)/6 - (3^(1/2)*b*1i)/6) - log(x - 1)*(a/3 + b/3 + c/3)","B"
50,1,6,8,0.023112,"\text{Not used}","int(-(x + x^2 + 1)/(x^3 - 1),x)","-\ln\left(x-1\right)","Not used",1,"-log(x - 1)","B"
51,1,63,30,4.929710,"\text{Not used}","int(-(3*x^2 - x + 1)/(x^3 - 1),x)","-\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-\ln\left(x-1\right)-\frac{\sqrt{3}\,\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{3}+\frac{\sqrt{3}\,\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{3}","Not used",1,"(3^(1/2)*log(x + (3^(1/2)*1i)/2 + 1/2)*1i)/3 - log(x + (3^(1/2)*1i)/2 + 1/2) - log(x - 1) - (3^(1/2)*log(x - (3^(1/2)*1i)/2 + 1/2)*1i)/3 - log(x - (3^(1/2)*1i)/2 + 1/2)","B"
52,1,16,18,0.040737,"\text{Not used}","int(-(x + 4*x^2 + 1)/(x^3 - 1),x)","-\ln\left(x^2+x+1\right)-2\,\ln\left(x-1\right)","Not used",1,"- log(x + x^2 + 1) - 2*log(x - 1)","B"
53,1,97,113,0.060686,"\text{Not used}","int((a + b*x^3)^3*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x)","\frac{d\,a^4\,x^2}{2}+c\,a^4\,x+\frac{4\,d\,a^3\,b\,x^5}{5}+c\,a^3\,b\,x^4+\frac{3\,d\,a^2\,b^2\,x^8}{4}+\frac{6\,c\,a^2\,b^2\,x^7}{7}+\frac{4\,d\,a\,b^3\,x^{11}}{11}+\frac{2\,c\,a\,b^3\,x^{10}}{5}+\frac{d\,b^4\,x^{14}}{14}+\frac{c\,b^4\,x^{13}}{13}","Not used",1,"(a^4*d*x^2)/2 + (b^4*c*x^13)/13 + (b^4*d*x^14)/14 + a^4*c*x + (6*a^2*b^2*c*x^7)/7 + (3*a^2*b^2*d*x^8)/4 + a^3*b*c*x^4 + (2*a*b^3*c*x^10)/5 + (4*a^3*b*d*x^5)/5 + (4*a*b^3*d*x^11)/11","B"
54,1,74,88,0.035731,"\text{Not used}","int((a + b*x^3)^2*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x)","\frac{d\,a^3\,x^2}{2}+c\,a^3\,x+\frac{3\,d\,a^2\,b\,x^5}{5}+\frac{3\,c\,a^2\,b\,x^4}{4}+\frac{3\,d\,a\,b^2\,x^8}{8}+\frac{3\,c\,a\,b^2\,x^7}{7}+\frac{d\,b^3\,x^{11}}{11}+\frac{c\,b^3\,x^{10}}{10}","Not used",1,"(a^3*d*x^2)/2 + (b^3*c*x^10)/10 + (b^3*d*x^11)/11 + a^3*c*x + (3*a^2*b*c*x^4)/4 + (3*a*b^2*c*x^7)/7 + (3*a^2*b*d*x^5)/5 + (3*a*b^2*d*x^8)/8","B"
55,1,50,60,0.028167,"\text{Not used}","int((a + b*x^3)*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x)","\frac{d\,a^2\,x^2}{2}+c\,a^2\,x+\frac{2\,d\,a\,b\,x^5}{5}+\frac{c\,a\,b\,x^4}{2}+\frac{d\,b^2\,x^8}{8}+\frac{c\,b^2\,x^7}{7}","Not used",1,"(a^2*d*x^2)/2 + (b^2*c*x^7)/7 + (b^2*d*x^8)/8 + a^2*c*x + (a*b*c*x^4)/2 + (2*a*b*d*x^5)/5","B"
56,1,10,12,0.017719,"\text{Not used}","int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3),x)","\frac{d\,x^2}{2}+c\,x","Not used",1,"c*x + (d*x^2)/2","B"
57,1,127,161,5.094177,"\text{Not used}","int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^2,x)","\sum _{k=1}^3\ln\left(b\,\left(c\,d+d^2\,x+{\mathrm{root}\left(27\,a^2\,b^2\,z^3+9\,a\,b\,c\,d\,z+a\,d^3-b\,c^3,z,k\right)}^2\,a\,b\,9+\mathrm{root}\left(27\,a^2\,b^2\,z^3+9\,a\,b\,c\,d\,z+a\,d^3-b\,c^3,z,k\right)\,b\,c\,x\,3\right)\right)\,\mathrm{root}\left(27\,a^2\,b^2\,z^3+9\,a\,b\,c\,d\,z+a\,d^3-b\,c^3,z,k\right)","Not used",1,"symsum(log(b*(c*d + d^2*x + 9*root(27*a^2*b^2*z^3 + 9*a*b*c*d*z + a*d^3 - b*c^3, z, k)^2*a*b + 3*root(27*a^2*b^2*z^3 + 9*a*b*c*d*z + a*d^3 - b*c^3, z, k)*b*c*x))*root(27*a^2*b^2*z^3 + 9*a*b*c*d*z + a*d^3 - b*c^3, z, k), k, 1, 3)","B"
58,1,169,189,5.083899,"\text{Not used}","int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^3,x)","\left(\sum _{k=1}^3\ln\left(\frac{b\,\left(2\,c\,d+d^2\,x+{\mathrm{root}\left(729\,a^5\,b^2\,z^3+54\,a^2\,b\,c\,d\,z-8\,b\,c^3+a\,d^3,z,k\right)}^2\,a^3\,b\,81+\mathrm{root}\left(729\,a^5\,b^2\,z^3+54\,a^2\,b\,c\,d\,z-8\,b\,c^3+a\,d^3,z,k\right)\,a\,b\,c\,x\,18\right)}{a^2\,9}\right)\,\mathrm{root}\left(729\,a^5\,b^2\,z^3+54\,a^2\,b\,c\,d\,z-8\,b\,c^3+a\,d^3,z,k\right)\right)+\frac{\frac{d\,x^2}{3\,a}+\frac{c\,x}{3\,a}}{b\,x^3+a}","Not used",1,"symsum(log((b*(2*c*d + d^2*x + 81*root(729*a^5*b^2*z^3 + 54*a^2*b*c*d*z - 8*b*c^3 + a*d^3, z, k)^2*a^3*b + 18*root(729*a^5*b^2*z^3 + 54*a^2*b*c*d*z - 8*b*c^3 + a*d^3, z, k)*a*b*c*x))/(9*a^2))*root(729*a^5*b^2*z^3 + 54*a^2*b*c*d*z - 8*b*c^3 + a*d^3, z, k), k, 1, 3) + ((d*x^2)/(3*a) + (c*x)/(3*a))/(a + b*x^3)","B"
59,0,-1,585,0.000000,"\text{Not used}","int((a + b*x^3)^(3/2)*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x)","\int {\left(b\,x^3+a\right)}^{3/2}\,\left(b\,d\,x^4+b\,c\,x^3+a\,d\,x+a\,c\right) \,d x","Not used",1,"int((a + b*x^3)^(3/2)*(a*c + a*d*x + b*c*x^3 + b*d*x^4), x)","F"
60,0,-1,556,0.000000,"\text{Not used}","int((a + b*x^3)^(1/2)*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x)","\int \sqrt{b\,x^3+a}\,\left(b\,d\,x^4+b\,c\,x^3+a\,d\,x+a\,c\right) \,d x","Not used",1,"int((a + b*x^3)^(1/2)*(a*c + a*d*x + b*c*x^3 + b*d*x^4), x)","F"
61,0,-1,525,0.000000,"\text{Not used}","int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(1/2),x)","\int \frac{b\,d\,x^4+b\,c\,x^3+a\,d\,x+a\,c}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(1/2), x)","F"
62,0,-1,490,0.000000,"\text{Not used}","int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(3/2),x)","\int \frac{b\,d\,x^4+b\,c\,x^3+a\,d\,x+a\,c}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(3/2), x)","F"
63,0,-1,522,0.000000,"\text{Not used}","int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(5/2),x)","\int \frac{b\,d\,x^4+b\,c\,x^3+a\,d\,x+a\,c}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(5/2), x)","F"
64,0,-1,554,0.000000,"\text{Not used}","int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(7/2),x)","\int \frac{b\,d\,x^4+b\,c\,x^3+a\,d\,x+a\,c}{{\left(b\,x^3+a\right)}^{7/2}} \,d x","Not used",1,"int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(7/2), x)","F"
65,0,-1,581,0.000000,"\text{Not used}","int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(9/2),x)","\int \frac{b\,d\,x^4+b\,c\,x^3+a\,d\,x+a\,c}{{\left(b\,x^3+a\right)}^{9/2}} \,d x","Not used",1,"int((a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(9/2), x)","F"
66,0,-1,590,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(1/2),x)","\int \frac{g\,x^4+f\,x^3+e\,x^2+d\,x+c}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(1/2), x)","F"
67,0,-1,594,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(3/2),x)","\int \frac{g\,x^4+f\,x^3+e\,x^2+d\,x+c}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(3/2), x)","F"
68,0,-1,628,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(5/2),x)","\int \frac{g\,x^4+f\,x^3+e\,x^2+d\,x+c}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(5/2), x)","F"
69,0,-1,676,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(7/2),x)","\int \frac{g\,x^4+f\,x^3+e\,x^2+d\,x+c}{{\left(b\,x^3+a\right)}^{7/2}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(7/2), x)","F"
70,1,357,186,0.262078,"\text{Not used}","int((a + b*x)^2/(c + d*x^3),x)","\sum _{k=1}^3\ln\left(b^4\,c+{\mathrm{root}\left(27\,c^2\,d^3\,z^3-27\,b^2\,c^2\,d^2\,z^2+18\,a^3\,b\,c\,d^2\,z+9\,b^4\,c^2\,d\,z+2\,a^3\,b^3\,c\,d-b^6\,c^2-a^6\,d^2,z,k\right)}^2\,c\,d^2\,9+2\,a^3\,b\,d-\mathrm{root}\left(27\,c^2\,d^3\,z^3-27\,b^2\,c^2\,d^2\,z^2+18\,a^3\,b\,c\,d^2\,z+9\,b^4\,c^2\,d\,z+2\,a^3\,b^3\,c\,d-b^6\,c^2-a^6\,d^2,z,k\right)\,b^2\,c\,d\,6+\mathrm{root}\left(27\,c^2\,d^3\,z^3-27\,b^2\,c^2\,d^2\,z^2+18\,a^3\,b\,c\,d^2\,z+9\,b^4\,c^2\,d\,z+2\,a^3\,b^3\,c\,d-b^6\,c^2-a^6\,d^2,z,k\right)\,a^2\,d^2\,x\,3+3\,a^2\,b^2\,d\,x\right)\,\mathrm{root}\left(27\,c^2\,d^3\,z^3-27\,b^2\,c^2\,d^2\,z^2+18\,a^3\,b\,c\,d^2\,z+9\,b^4\,c^2\,d\,z+2\,a^3\,b^3\,c\,d-b^6\,c^2-a^6\,d^2,z,k\right)","Not used",1,"symsum(log(b^4*c + 9*root(27*c^2*d^3*z^3 - 27*b^2*c^2*d^2*z^2 + 18*a^3*b*c*d^2*z + 9*b^4*c^2*d*z + 2*a^3*b^3*c*d - b^6*c^2 - a^6*d^2, z, k)^2*c*d^2 + 2*a^3*b*d - 6*root(27*c^2*d^3*z^3 - 27*b^2*c^2*d^2*z^2 + 18*a^3*b*c*d^2*z + 9*b^4*c^2*d*z + 2*a^3*b^3*c*d - b^6*c^2 - a^6*d^2, z, k)*b^2*c*d + 3*root(27*c^2*d^3*z^3 - 27*b^2*c^2*d^2*z^2 + 18*a^3*b*c*d^2*z + 9*b^4*c^2*d*z + 2*a^3*b^3*c*d - b^6*c^2 - a^6*d^2, z, k)*a^2*d^2*x + 3*a^2*b^2*d*x)*root(27*c^2*d^3*z^3 - 27*b^2*c^2*d^2*z^2 + 18*a^3*b*c*d^2*z + 9*b^4*c^2*d*z + 2*a^3*b^3*c*d - b^6*c^2 - a^6*d^2, z, k), k, 1, 3)","B"
71,1,370,222,5.143074,"\text{Not used}","int((a + b*x)^3/(c + d*x^3),x)","\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,c^2\,d^4\,z^3-81\,a\,b^2\,c^2\,d^3\,z^2+54\,a^2\,b^4\,c^2\,d^2\,z+27\,a^5\,b\,c\,d^3\,z+3\,a^6\,b^3\,c\,d^2-3\,a^3\,b^6\,c^2\,d+b^9\,c^3-a^9\,d^3,z,k\right)\,\left(x\,\left(3\,a^3\,d^2-3\,b^3\,c\,d\right)+\mathrm{root}\left(27\,c^2\,d^4\,z^3-81\,a\,b^2\,c^2\,d^3\,z^2+54\,a^2\,b^4\,c^2\,d^2\,z+27\,a^5\,b\,c\,d^3\,z+3\,a^6\,b^3\,c\,d^2-3\,a^3\,b^6\,c^2\,d+b^9\,c^3-a^9\,d^3,z,k\right)\,c\,d^2\,9-18\,a\,b^2\,c\,d\right)+x\,\left(6\,d\,a^4\,b^2+3\,c\,a\,b^5\right)+6\,a^2\,b^4\,c+3\,a^5\,b\,d\right)\,\mathrm{root}\left(27\,c^2\,d^4\,z^3-81\,a\,b^2\,c^2\,d^3\,z^2+54\,a^2\,b^4\,c^2\,d^2\,z+27\,a^5\,b\,c\,d^3\,z+3\,a^6\,b^3\,c\,d^2-3\,a^3\,b^6\,c^2\,d+b^9\,c^3-a^9\,d^3,z,k\right)\right)+\frac{b^3\,x}{d}","Not used",1,"symsum(log(root(27*c^2*d^4*z^3 - 81*a*b^2*c^2*d^3*z^2 + 54*a^2*b^4*c^2*d^2*z + 27*a^5*b*c*d^3*z + 3*a^6*b^3*c*d^2 - 3*a^3*b^6*c^2*d + b^9*c^3 - a^9*d^3, z, k)*(x*(3*a^3*d^2 - 3*b^3*c*d) + 9*root(27*c^2*d^4*z^3 - 81*a*b^2*c^2*d^3*z^2 + 54*a^2*b^4*c^2*d^2*z + 27*a^5*b*c*d^3*z + 3*a^6*b^3*c*d^2 - 3*a^3*b^6*c^2*d + b^9*c^3 - a^9*d^3, z, k)*c*d^2 - 18*a*b^2*c*d) + x*(6*a^4*b^2*d + 3*a*b^5*c) + 6*a^2*b^4*c + 3*a^5*b*d)*root(27*c^2*d^4*z^3 - 81*a*b^2*c^2*d^3*z^2 + 54*a^2*b^4*c^2*d^2*z + 27*a^5*b*c*d^3*z + 3*a^6*b^3*c*d^2 - 3*a^3*b^6*c^2*d + b^9*c^3 - a^9*d^3, z, k), k, 1, 3) + (b^3*x)/d","B"
72,1,513,282,4.973404,"\text{Not used}","int((a + b*x)^4/(c + d*x^3),x)","\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,c^2\,d^5\,z^3-162\,a^2\,b^2\,c^2\,d^4\,z^2+171\,a^4\,b^4\,c^2\,d^3\,z+36\,a\,b^7\,c^3\,d^2\,z+36\,a^7\,b\,c\,d^4\,z-6\,a^6\,b^6\,c^2\,d^2+4\,a^9\,b^3\,c\,d^3+4\,a^3\,b^9\,c^3\,d-b^{12}\,c^4-a^{12}\,d^4,z,k\right)\,\left(\frac{x\,\left(3\,a^4\,d^3-12\,a\,b^3\,c\,d^2\right)}{d}+\mathrm{root}\left(27\,c^2\,d^5\,z^3-162\,a^2\,b^2\,c^2\,d^4\,z^2+171\,a^4\,b^4\,c^2\,d^3\,z+36\,a\,b^7\,c^3\,d^2\,z+36\,a^7\,b\,c\,d^4\,z-6\,a^6\,b^6\,c^2\,d^2+4\,a^9\,b^3\,c\,d^3+4\,a^3\,b^9\,c^3\,d-b^{12}\,c^4-a^{12}\,d^4,z,k\right)\,c\,d^2\,9-36\,a^2\,b^2\,c\,d\right)+\frac{4\,a^7\,b\,d^2+19\,a^4\,b^4\,c\,d+4\,a\,b^7\,c^2}{d}+\frac{x\,\left(10\,a^6\,b^2\,d^2+16\,a^3\,b^5\,c\,d+b^8\,c^2\right)}{d}\right)\,\mathrm{root}\left(27\,c^2\,d^5\,z^3-162\,a^2\,b^2\,c^2\,d^4\,z^2+171\,a^4\,b^4\,c^2\,d^3\,z+36\,a\,b^7\,c^3\,d^2\,z+36\,a^7\,b\,c\,d^4\,z-6\,a^6\,b^6\,c^2\,d^2+4\,a^9\,b^3\,c\,d^3+4\,a^3\,b^9\,c^3\,d-b^{12}\,c^4-a^{12}\,d^4,z,k\right)\right)+\frac{b^4\,x^2}{2\,d}+\frac{4\,a\,b^3\,x}{d}","Not used",1,"symsum(log(root(27*c^2*d^5*z^3 - 162*a^2*b^2*c^2*d^4*z^2 + 171*a^4*b^4*c^2*d^3*z + 36*a*b^7*c^3*d^2*z + 36*a^7*b*c*d^4*z - 6*a^6*b^6*c^2*d^2 + 4*a^9*b^3*c*d^3 + 4*a^3*b^9*c^3*d - b^12*c^4 - a^12*d^4, z, k)*((x*(3*a^4*d^3 - 12*a*b^3*c*d^2))/d + 9*root(27*c^2*d^5*z^3 - 162*a^2*b^2*c^2*d^4*z^2 + 171*a^4*b^4*c^2*d^3*z + 36*a*b^7*c^3*d^2*z + 36*a^7*b*c*d^4*z - 6*a^6*b^6*c^2*d^2 + 4*a^9*b^3*c*d^3 + 4*a^3*b^9*c^3*d - b^12*c^4 - a^12*d^4, z, k)*c*d^2 - 36*a^2*b^2*c*d) + (4*a*b^7*c^2 + 4*a^7*b*d^2 + 19*a^4*b^4*c*d)/d + (x*(b^8*c^2 + 10*a^6*b^2*d^2 + 16*a^3*b^5*c*d))/d)*root(27*c^2*d^5*z^3 - 162*a^2*b^2*c^2*d^4*z^2 + 171*a^4*b^4*c^2*d^3*z + 36*a*b^7*c^3*d^2*z + 36*a^7*b*c*d^4*z - 6*a^6*b^6*c^2*d^2 + 4*a^9*b^3*c*d^3 + 4*a^3*b^9*c^3*d - b^12*c^4 - a^12*d^4, z, k), k, 1, 3) + (b^4*x^2)/(2*d) + (4*a*b^3*x)/d","B"
73,1,769,272,5.133779,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x^3),x)","\left(\sum _{k=1}^3\ln\left(\frac{2\,a^3\,b\,e^2+3\,a^2\,c^2\,d\,e+b^4\,d\,e+2\,b\,c^3\,d^2}{e}+\frac{x\,\left(-2\,a^3\,c\,e^2+3\,a^2\,b^2\,e^2+2\,b^3\,c\,d\,e+c^4\,d^2\right)}{e}-\mathrm{root}\left(27\,d^2\,e^5\,z^3-54\,a\,c\,d^2\,e^4\,z^2-27\,b^2\,d^2\,e^4\,z^2+27\,a^2\,c^2\,d^2\,e^3\,z+18\,b\,c^3\,d^3\,e^2\,z+18\,a^3\,b\,d\,e^4\,z+9\,b^4\,d^2\,e^3\,z+6\,a\,b^4\,c\,d^2\,e^2-9\,a^2\,b^2\,c^2\,d^2\,e^2-6\,a^4\,b\,c\,d\,e^3-6\,a\,b\,c^4\,d^3\,e-2\,a^3\,c^3\,d^2\,e^2+2\,b^3\,c^3\,d^3\,e+2\,a^3\,b^3\,d\,e^3-b^6\,d^2\,e^2-c^6\,d^4-a^6\,e^4,z,k\right)\,e\,\left(2\,b^2\,d-\mathrm{root}\left(27\,d^2\,e^5\,z^3-54\,a\,c\,d^2\,e^4\,z^2-27\,b^2\,d^2\,e^4\,z^2+27\,a^2\,c^2\,d^2\,e^3\,z+18\,b\,c^3\,d^3\,e^2\,z+18\,a^3\,b\,d\,e^4\,z+9\,b^4\,d^2\,e^3\,z+6\,a\,b^4\,c\,d^2\,e^2-9\,a^2\,b^2\,c^2\,d^2\,e^2-6\,a^4\,b\,c\,d\,e^3-6\,a\,b\,c^4\,d^3\,e-2\,a^3\,c^3\,d^2\,e^2+2\,b^3\,c^3\,d^3\,e+2\,a^3\,b^3\,d\,e^3-b^6\,d^2\,e^2-c^6\,d^4-a^6\,e^4,z,k\right)\,d\,e\,3+4\,a\,c\,d-a^2\,e\,x+2\,b\,c\,d\,x\right)\,3\right)\,\mathrm{root}\left(27\,d^2\,e^5\,z^3-54\,a\,c\,d^2\,e^4\,z^2-27\,b^2\,d^2\,e^4\,z^2+27\,a^2\,c^2\,d^2\,e^3\,z+18\,b\,c^3\,d^3\,e^2\,z+18\,a^3\,b\,d\,e^4\,z+9\,b^4\,d^2\,e^3\,z+6\,a\,b^4\,c\,d^2\,e^2-9\,a^2\,b^2\,c^2\,d^2\,e^2-6\,a^4\,b\,c\,d\,e^3-6\,a\,b\,c^4\,d^3\,e-2\,a^3\,c^3\,d^2\,e^2+2\,b^3\,c^3\,d^3\,e+2\,a^3\,b^3\,d\,e^3-b^6\,d^2\,e^2-c^6\,d^4-a^6\,e^4,z,k\right)\right)+\frac{c^2\,x^2}{2\,e}+\frac{2\,b\,c\,x}{e}","Not used",1,"symsum(log((2*a^3*b*e^2 + 2*b*c^3*d^2 + b^4*d*e + 3*a^2*c^2*d*e)/e + (x*(c^4*d^2 - 2*a^3*c*e^2 + 3*a^2*b^2*e^2 + 2*b^3*c*d*e))/e - 3*root(27*d^2*e^5*z^3 - 54*a*c*d^2*e^4*z^2 - 27*b^2*d^2*e^4*z^2 + 27*a^2*c^2*d^2*e^3*z + 18*b*c^3*d^3*e^2*z + 18*a^3*b*d*e^4*z + 9*b^4*d^2*e^3*z + 6*a*b^4*c*d^2*e^2 - 9*a^2*b^2*c^2*d^2*e^2 - 6*a^4*b*c*d*e^3 - 6*a*b*c^4*d^3*e - 2*a^3*c^3*d^2*e^2 + 2*b^3*c^3*d^3*e + 2*a^3*b^3*d*e^3 - b^6*d^2*e^2 - c^6*d^4 - a^6*e^4, z, k)*e*(2*b^2*d - 3*root(27*d^2*e^5*z^3 - 54*a*c*d^2*e^4*z^2 - 27*b^2*d^2*e^4*z^2 + 27*a^2*c^2*d^2*e^3*z + 18*b*c^3*d^3*e^2*z + 18*a^3*b*d*e^4*z + 9*b^4*d^2*e^3*z + 6*a*b^4*c*d^2*e^2 - 9*a^2*b^2*c^2*d^2*e^2 - 6*a^4*b*c*d*e^3 - 6*a*b*c^4*d^3*e - 2*a^3*c^3*d^2*e^2 + 2*b^3*c^3*d^3*e + 2*a^3*b^3*d*e^3 - b^6*d^2*e^2 - c^6*d^4 - a^6*e^4, z, k)*d*e + 4*a*c*d - a^2*e*x + 2*b*c*d*x))*root(27*d^2*e^5*z^3 - 54*a*c*d^2*e^4*z^2 - 27*b^2*d^2*e^4*z^2 + 27*a^2*c^2*d^2*e^3*z + 18*b*c^3*d^3*e^2*z + 18*a^3*b*d*e^4*z + 9*b^4*d^2*e^3*z + 6*a*b^4*c*d^2*e^2 - 9*a^2*b^2*c^2*d^2*e^2 - 6*a^4*b*c*d*e^3 - 6*a*b*c^4*d^3*e - 2*a^3*c^3*d^2*e^2 + 2*b^3*c^3*d^3*e + 2*a^3*b^3*d*e^3 - b^6*d^2*e^2 - c^6*d^4 - a^6*e^4, z, k), k, 1, 3) + (c^2*x^2)/(2*e) + (2*b*c*x)/e","B"
74,1,1700,416,4.913144,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x^3),x)","x\,\left(\frac{b^3+6\,a\,c\,b}{e}-\frac{c^3\,d}{e^2}\right)+\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,d^2\,e^7\,z^3+81\,b\,c^2\,d^3\,e^5\,z^2-81\,a^2\,c\,d^2\,e^6\,z^2-81\,a\,b^2\,d^2\,e^6\,z^2-27\,a^3\,b^2\,c\,d^2\,e^5\,z+27\,a^2\,b\,c^3\,d^3\,e^4\,z+27\,a\,b^3\,c^2\,d^3\,e^4\,z+54\,b^2\,c^4\,d^4\,e^3\,z+54\,a^4\,c^2\,d^2\,e^5\,z+54\,a^2\,b^4\,d^2\,e^5\,z+27\,b^5\,c\,d^3\,e^4\,z-27\,a\,c^5\,d^4\,e^3\,z+27\,a^5\,b\,d\,e^6\,z+18\,a^4\,b^4\,c\,d^2\,e^4-18\,a^4\,b\,c^4\,d^3\,e^3+18\,a\,b^4\,c^4\,d^4\,e^2-9\,a\,b^7\,c\,d^3\,e^3-27\,a^5\,b^2\,c^2\,d^2\,e^4+27\,a^2\,b^5\,c^2\,d^3\,e^3-27\,a^2\,b^2\,c^5\,d^4\,e^2-21\,a^3\,b^3\,c^3\,d^3\,e^3-9\,a^7\,b\,c\,d\,e^5-9\,a\,b\,c^7\,d^5\,e-3\,b^6\,c^3\,d^4\,e^2-3\,a^6\,c^3\,d^2\,e^4-3\,a^3\,c^6\,d^4\,e^2-3\,a^3\,b^6\,d^2\,e^4+3\,b^3\,c^6\,d^5\,e+3\,a^6\,b^3\,d\,e^5+b^9\,d^3\,e^3-c^9\,d^6-a^9\,e^6,z,k\right)\,\left(-\frac{3\,\left(6\,a^2\,c\,d\,e^3+6\,a\,b^2\,d\,e^3-6\,b\,c^2\,d^2\,e^2\right)}{e^2}+\frac{3\,x\,\left(a^3\,e^4-6\,a\,b\,c\,d\,e^3-b^3\,d\,e^3+c^3\,d^2\,e^2\right)}{e^2}+\mathrm{root}\left(27\,d^2\,e^7\,z^3+81\,b\,c^2\,d^3\,e^5\,z^2-81\,a^2\,c\,d^2\,e^6\,z^2-81\,a\,b^2\,d^2\,e^6\,z^2-27\,a^3\,b^2\,c\,d^2\,e^5\,z+27\,a^2\,b\,c^3\,d^3\,e^4\,z+27\,a\,b^3\,c^2\,d^3\,e^4\,z+54\,b^2\,c^4\,d^4\,e^3\,z+54\,a^4\,c^2\,d^2\,e^5\,z+54\,a^2\,b^4\,d^2\,e^5\,z+27\,b^5\,c\,d^3\,e^4\,z-27\,a\,c^5\,d^4\,e^3\,z+27\,a^5\,b\,d\,e^6\,z+18\,a^4\,b^4\,c\,d^2\,e^4-18\,a^4\,b\,c^4\,d^3\,e^3+18\,a\,b^4\,c^4\,d^4\,e^2-9\,a\,b^7\,c\,d^3\,e^3-27\,a^5\,b^2\,c^2\,d^2\,e^4+27\,a^2\,b^5\,c^2\,d^3\,e^3-27\,a^2\,b^2\,c^5\,d^4\,e^2-21\,a^3\,b^3\,c^3\,d^3\,e^3-9\,a^7\,b\,c\,d\,e^5-9\,a\,b\,c^7\,d^5\,e-3\,b^6\,c^3\,d^4\,e^2-3\,a^6\,c^3\,d^2\,e^4-3\,a^3\,c^6\,d^4\,e^2-3\,a^3\,b^6\,d^2\,e^4+3\,b^3\,c^6\,d^5\,e+3\,a^6\,b^3\,d\,e^5+b^9\,d^3\,e^3-c^9\,d^6-a^9\,e^6,z,k\right)\,d\,e^2\,9\right)+\frac{3\,\left(a^5\,b\,e^3+2\,a^4\,c^2\,d\,e^2-a^3\,b^2\,c\,d\,e^2+2\,a^2\,b^4\,d\,e^2+a^2\,b\,c^3\,d^2\,e+a\,b^3\,c^2\,d^2\,e-a\,c^5\,d^3+b^5\,c\,d^2\,e+2\,b^2\,c^4\,d^3\right)}{e^2}+\frac{3\,x\,\left(-a^5\,c\,e^3+2\,a^4\,b^2\,e^3+a^3\,b\,c^2\,d\,e^2+a^2\,b^3\,c\,d\,e^2+2\,a^2\,c^4\,d^2\,e+a\,b^5\,d\,e^2-a\,b^2\,c^3\,d^2\,e+2\,b^4\,c^2\,d^2\,e+b\,c^5\,d^3\right)}{e^2}\right)\,\mathrm{root}\left(27\,d^2\,e^7\,z^3+81\,b\,c^2\,d^3\,e^5\,z^2-81\,a^2\,c\,d^2\,e^6\,z^2-81\,a\,b^2\,d^2\,e^6\,z^2-27\,a^3\,b^2\,c\,d^2\,e^5\,z+27\,a^2\,b\,c^3\,d^3\,e^4\,z+27\,a\,b^3\,c^2\,d^3\,e^4\,z+54\,b^2\,c^4\,d^4\,e^3\,z+54\,a^4\,c^2\,d^2\,e^5\,z+54\,a^2\,b^4\,d^2\,e^5\,z+27\,b^5\,c\,d^3\,e^4\,z-27\,a\,c^5\,d^4\,e^3\,z+27\,a^5\,b\,d\,e^6\,z+18\,a^4\,b^4\,c\,d^2\,e^4-18\,a^4\,b\,c^4\,d^3\,e^3+18\,a\,b^4\,c^4\,d^4\,e^2-9\,a\,b^7\,c\,d^3\,e^3-27\,a^5\,b^2\,c^2\,d^2\,e^4+27\,a^2\,b^5\,c^2\,d^3\,e^3-27\,a^2\,b^2\,c^5\,d^4\,e^2-21\,a^3\,b^3\,c^3\,d^3\,e^3-9\,a^7\,b\,c\,d\,e^5-9\,a\,b\,c^7\,d^5\,e-3\,b^6\,c^3\,d^4\,e^2-3\,a^6\,c^3\,d^2\,e^4-3\,a^3\,c^6\,d^4\,e^2-3\,a^3\,b^6\,d^2\,e^4+3\,b^3\,c^6\,d^5\,e+3\,a^6\,b^3\,d\,e^5+b^9\,d^3\,e^3-c^9\,d^6-a^9\,e^6,z,k\right)\right)+\frac{c^3\,x^4}{4\,e}+\frac{b\,c^2\,x^3}{e}+\frac{3\,c\,x^2\,\left(b^2+a\,c\right)}{2\,e}","Not used",1,"x*((b^3 + 6*a*b*c)/e - (c^3*d)/e^2) + symsum(log(root(27*d^2*e^7*z^3 + 81*b*c^2*d^3*e^5*z^2 - 81*a^2*c*d^2*e^6*z^2 - 81*a*b^2*d^2*e^6*z^2 - 27*a^3*b^2*c*d^2*e^5*z + 27*a^2*b*c^3*d^3*e^4*z + 27*a*b^3*c^2*d^3*e^4*z + 54*b^2*c^4*d^4*e^3*z + 54*a^4*c^2*d^2*e^5*z + 54*a^2*b^4*d^2*e^5*z + 27*b^5*c*d^3*e^4*z - 27*a*c^5*d^4*e^3*z + 27*a^5*b*d*e^6*z + 18*a^4*b^4*c*d^2*e^4 - 18*a^4*b*c^4*d^3*e^3 + 18*a*b^4*c^4*d^4*e^2 - 9*a*b^7*c*d^3*e^3 - 27*a^5*b^2*c^2*d^2*e^4 + 27*a^2*b^5*c^2*d^3*e^3 - 27*a^2*b^2*c^5*d^4*e^2 - 21*a^3*b^3*c^3*d^3*e^3 - 9*a^7*b*c*d*e^5 - 9*a*b*c^7*d^5*e - 3*b^6*c^3*d^4*e^2 - 3*a^6*c^3*d^2*e^4 - 3*a^3*c^6*d^4*e^2 - 3*a^3*b^6*d^2*e^4 + 3*b^3*c^6*d^5*e + 3*a^6*b^3*d*e^5 + b^9*d^3*e^3 - c^9*d^6 - a^9*e^6, z, k)*((3*x*(a^3*e^4 - b^3*d*e^3 + c^3*d^2*e^2 - 6*a*b*c*d*e^3))/e^2 - (3*(6*a*b^2*d*e^3 - 6*b*c^2*d^2*e^2 + 6*a^2*c*d*e^3))/e^2 + 9*root(27*d^2*e^7*z^3 + 81*b*c^2*d^3*e^5*z^2 - 81*a^2*c*d^2*e^6*z^2 - 81*a*b^2*d^2*e^6*z^2 - 27*a^3*b^2*c*d^2*e^5*z + 27*a^2*b*c^3*d^3*e^4*z + 27*a*b^3*c^2*d^3*e^4*z + 54*b^2*c^4*d^4*e^3*z + 54*a^4*c^2*d^2*e^5*z + 54*a^2*b^4*d^2*e^5*z + 27*b^5*c*d^3*e^4*z - 27*a*c^5*d^4*e^3*z + 27*a^5*b*d*e^6*z + 18*a^4*b^4*c*d^2*e^4 - 18*a^4*b*c^4*d^3*e^3 + 18*a*b^4*c^4*d^4*e^2 - 9*a*b^7*c*d^3*e^3 - 27*a^5*b^2*c^2*d^2*e^4 + 27*a^2*b^5*c^2*d^3*e^3 - 27*a^2*b^2*c^5*d^4*e^2 - 21*a^3*b^3*c^3*d^3*e^3 - 9*a^7*b*c*d*e^5 - 9*a*b*c^7*d^5*e - 3*b^6*c^3*d^4*e^2 - 3*a^6*c^3*d^2*e^4 - 3*a^3*c^6*d^4*e^2 - 3*a^3*b^6*d^2*e^4 + 3*b^3*c^6*d^5*e + 3*a^6*b^3*d*e^5 + b^9*d^3*e^3 - c^9*d^6 - a^9*e^6, z, k)*d*e^2) + (3*(a^5*b*e^3 - a*c^5*d^3 + 2*b^2*c^4*d^3 + 2*a^2*b^4*d*e^2 + 2*a^4*c^2*d*e^2 + b^5*c*d^2*e + a*b^3*c^2*d^2*e + a^2*b*c^3*d^2*e - a^3*b^2*c*d*e^2))/e^2 + (3*x*(b*c^5*d^3 - a^5*c*e^3 + 2*a^4*b^2*e^3 + 2*a^2*c^4*d^2*e + 2*b^4*c^2*d^2*e + a*b^5*d*e^2 - a*b^2*c^3*d^2*e + a^2*b^3*c*d*e^2 + a^3*b*c^2*d*e^2))/e^2)*root(27*d^2*e^7*z^3 + 81*b*c^2*d^3*e^5*z^2 - 81*a^2*c*d^2*e^6*z^2 - 81*a*b^2*d^2*e^6*z^2 - 27*a^3*b^2*c*d^2*e^5*z + 27*a^2*b*c^3*d^3*e^4*z + 27*a*b^3*c^2*d^3*e^4*z + 54*b^2*c^4*d^4*e^3*z + 54*a^4*c^2*d^2*e^5*z + 54*a^2*b^4*d^2*e^5*z + 27*b^5*c*d^3*e^4*z - 27*a*c^5*d^4*e^3*z + 27*a^5*b*d*e^6*z + 18*a^4*b^4*c*d^2*e^4 - 18*a^4*b*c^4*d^3*e^3 + 18*a*b^4*c^4*d^4*e^2 - 9*a*b^7*c*d^3*e^3 - 27*a^5*b^2*c^2*d^2*e^4 + 27*a^2*b^5*c^2*d^3*e^3 - 27*a^2*b^2*c^5*d^4*e^2 - 21*a^3*b^3*c^3*d^3*e^3 - 9*a^7*b*c*d*e^5 - 9*a*b*c^7*d^5*e - 3*b^6*c^3*d^4*e^2 - 3*a^6*c^3*d^2*e^4 - 3*a^3*c^6*d^4*e^2 - 3*a^3*b^6*d^2*e^4 + 3*b^3*c^6*d^5*e + 3*a^6*b^3*d*e^5 + b^9*d^3*e^3 - c^9*d^6 - a^9*e^6, z, k), k, 1, 3) + (c^3*x^4)/(4*e) + (b*c^2*x^3)/e + (3*c*x^2*(a*c + b^2))/(2*e)","B"
75,1,2971,645,5.046937,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x^3),x)","x^2\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{2\,e}-\frac{2\,b\,c^3\,d}{e^2}\right)-x^3\,\left(\frac{c^4\,d}{3\,e^2}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{3\,e}\right)+\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,d^2\,e^9\,z^3+324\,a\,b\,c^2\,d^3\,e^7\,z^2+108\,b^3\,c\,d^3\,e^7\,z^2-108\,a^3\,c\,d^2\,e^8\,z^2-162\,a^2\,b^2\,d^2\,e^8\,z^2-27\,c^4\,d^4\,e^6\,z^2-72\,a\,b\,c^6\,d^5\,e^4\,z+216\,a^2\,b^2\,c^4\,d^4\,e^5\,z+144\,a^3\,b^3\,c^2\,d^3\,e^6\,z-108\,a^5\,b^2\,c\,d^2\,e^7\,z+108\,a^2\,b^5\,c\,d^3\,e^6\,z-36\,a^4\,b\,c^3\,d^3\,e^6\,z+36\,a\,b^4\,c^3\,d^4\,e^5\,z+144\,b^3\,c^5\,d^5\,e^4\,z+90\,b^6\,c^2\,d^4\,e^5\,z-144\,a^3\,c^5\,d^4\,e^5\,z+90\,a^6\,c^2\,d^2\,e^7\,z+171\,a^4\,b^4\,d^2\,e^7\,z+36\,a\,b^7\,d^3\,e^6\,z+36\,a^7\,b\,d\,e^8\,z+9\,c^8\,d^6\,e^3\,z+36\,a^7\,b^4\,c\,d^2\,e^6-36\,a^7\,b\,c^4\,d^3\,e^5-36\,a^4\,b^7\,c\,d^3\,e^5-36\,a^4\,b\,c^7\,d^5\,e^3-36\,a\,b^7\,c^4\,d^5\,e^3+36\,a\,b^4\,c^7\,d^6\,e^2+12\,a\,b^{10}\,c\,d^4\,e^4+108\,a^5\,b^5\,c^2\,d^3\,e^5-108\,a^5\,b^2\,c^5\,d^4\,e^4+108\,a^2\,b^5\,c^5\,d^5\,e^3-96\,a^6\,b^3\,c^3\,d^3\,e^5+96\,a^3\,b^6\,c^3\,d^4\,e^4-96\,a^3\,b^3\,c^6\,d^5\,e^3-54\,a^8\,b^2\,c^2\,d^2\,e^6-54\,a^2\,b^8\,c^2\,d^4\,e^4-54\,a^2\,b^2\,c^8\,d^6\,e^2-9\,a^4\,b^4\,c^4\,d^4\,e^4-12\,a^{10}\,b\,c\,d\,e^7-12\,a\,b\,c^{10}\,d^7\,e-6\,b^6\,c^6\,d^6\,e^2+4\,b^9\,c^3\,d^5\,e^3-6\,a^6\,c^6\,d^4\,e^4-4\,a^9\,c^3\,d^2\,e^6-4\,a^3\,c^9\,d^6\,e^2-6\,a^6\,b^6\,d^2\,e^6+4\,a^3\,b^9\,d^3\,e^5+4\,b^3\,c^9\,d^7\,e+4\,a^9\,b^3\,d\,e^7-b^{12}\,d^4\,e^4-c^{12}\,d^8-a^{12}\,e^8,z,k\right)\,\left(-\frac{24\,a^3\,c\,d\,e^5+36\,a^2\,b^2\,d\,e^5-72\,a\,b\,c^2\,d^2\,e^4-24\,b^3\,c\,d^2\,e^4+6\,c^4\,d^3\,e^3}{e^4}+\frac{x\,\left(3\,a^4\,e^5-36\,a^2\,b\,c\,d\,e^4-12\,a\,b^3\,d\,e^4+12\,a\,c^3\,d^2\,e^3+18\,b^2\,c^2\,d^2\,e^3\right)}{e^3}+\mathrm{root}\left(27\,d^2\,e^9\,z^3+324\,a\,b\,c^2\,d^3\,e^7\,z^2+108\,b^3\,c\,d^3\,e^7\,z^2-108\,a^3\,c\,d^2\,e^8\,z^2-162\,a^2\,b^2\,d^2\,e^8\,z^2-27\,c^4\,d^4\,e^6\,z^2-72\,a\,b\,c^6\,d^5\,e^4\,z+216\,a^2\,b^2\,c^4\,d^4\,e^5\,z+144\,a^3\,b^3\,c^2\,d^3\,e^6\,z-108\,a^5\,b^2\,c\,d^2\,e^7\,z+108\,a^2\,b^5\,c\,d^3\,e^6\,z-36\,a^4\,b\,c^3\,d^3\,e^6\,z+36\,a\,b^4\,c^3\,d^4\,e^5\,z+144\,b^3\,c^5\,d^5\,e^4\,z+90\,b^6\,c^2\,d^4\,e^5\,z-144\,a^3\,c^5\,d^4\,e^5\,z+90\,a^6\,c^2\,d^2\,e^7\,z+171\,a^4\,b^4\,d^2\,e^7\,z+36\,a\,b^7\,d^3\,e^6\,z+36\,a^7\,b\,d\,e^8\,z+9\,c^8\,d^6\,e^3\,z+36\,a^7\,b^4\,c\,d^2\,e^6-36\,a^7\,b\,c^4\,d^3\,e^5-36\,a^4\,b^7\,c\,d^3\,e^5-36\,a^4\,b\,c^7\,d^5\,e^3-36\,a\,b^7\,c^4\,d^5\,e^3+36\,a\,b^4\,c^7\,d^6\,e^2+12\,a\,b^{10}\,c\,d^4\,e^4+108\,a^5\,b^5\,c^2\,d^3\,e^5-108\,a^5\,b^2\,c^5\,d^4\,e^4+108\,a^2\,b^5\,c^5\,d^5\,e^3-96\,a^6\,b^3\,c^3\,d^3\,e^5+96\,a^3\,b^6\,c^3\,d^4\,e^4-96\,a^3\,b^3\,c^6\,d^5\,e^3-54\,a^8\,b^2\,c^2\,d^2\,e^6-54\,a^2\,b^8\,c^2\,d^4\,e^4-54\,a^2\,b^2\,c^8\,d^6\,e^2-9\,a^4\,b^4\,c^4\,d^4\,e^4-12\,a^{10}\,b\,c\,d\,e^7-12\,a\,b\,c^{10}\,d^7\,e-6\,b^6\,c^6\,d^6\,e^2+4\,b^9\,c^3\,d^5\,e^3-6\,a^6\,c^6\,d^4\,e^4-4\,a^9\,c^3\,d^2\,e^6-4\,a^3\,c^9\,d^6\,e^2-6\,a^6\,b^6\,d^2\,e^6+4\,a^3\,b^9\,d^3\,e^5+4\,b^3\,c^9\,d^7\,e+4\,a^9\,b^3\,d\,e^7-b^{12}\,d^4\,e^4-c^{12}\,d^8-a^{12}\,e^8,z,k\right)\,d\,e^2\,9\right)+\frac{4\,a^7\,b\,e^5+10\,a^6\,c^2\,d\,e^4-12\,a^5\,b^2\,c\,d\,e^4+19\,a^4\,b^4\,d\,e^4-4\,a^4\,b\,c^3\,d^2\,e^3+16\,a^3\,b^3\,c^2\,d^2\,e^3-16\,a^3\,c^5\,d^3\,e^2+12\,a^2\,b^5\,c\,d^2\,e^3+24\,a^2\,b^2\,c^4\,d^3\,e^2+4\,a\,b^7\,d^2\,e^3+4\,a\,b^4\,c^3\,d^3\,e^2-8\,a\,b\,c^6\,d^4\,e+10\,b^6\,c^2\,d^3\,e^2+16\,b^3\,c^5\,d^4\,e+c^8\,d^5}{e^4}+\frac{x\,\left(-4\,a^7\,c\,e^4+10\,a^6\,b^2\,e^4+12\,a^5\,b\,c^2\,d\,e^3-4\,a^4\,b^3\,c\,d\,e^3+19\,a^4\,c^4\,d^2\,e^2+16\,a^3\,b^5\,d\,e^3-16\,a^3\,b^2\,c^3\,d^2\,e^2+24\,a^2\,b^4\,c^2\,d^2\,e^2+12\,a^2\,b\,c^5\,d^3\,e+8\,a\,b^6\,c\,d^2\,e^2-4\,a\,b^3\,c^4\,d^3\,e-4\,a\,c^7\,d^4+b^8\,d^2\,e^2+16\,b^5\,c^3\,d^3\,e+10\,b^2\,c^6\,d^4\right)}{e^3}\right)\,\mathrm{root}\left(27\,d^2\,e^9\,z^3+324\,a\,b\,c^2\,d^3\,e^7\,z^2+108\,b^3\,c\,d^3\,e^7\,z^2-108\,a^3\,c\,d^2\,e^8\,z^2-162\,a^2\,b^2\,d^2\,e^8\,z^2-27\,c^4\,d^4\,e^6\,z^2-72\,a\,b\,c^6\,d^5\,e^4\,z+216\,a^2\,b^2\,c^4\,d^4\,e^5\,z+144\,a^3\,b^3\,c^2\,d^3\,e^6\,z-108\,a^5\,b^2\,c\,d^2\,e^7\,z+108\,a^2\,b^5\,c\,d^3\,e^6\,z-36\,a^4\,b\,c^3\,d^3\,e^6\,z+36\,a\,b^4\,c^3\,d^4\,e^5\,z+144\,b^3\,c^5\,d^5\,e^4\,z+90\,b^6\,c^2\,d^4\,e^5\,z-144\,a^3\,c^5\,d^4\,e^5\,z+90\,a^6\,c^2\,d^2\,e^7\,z+171\,a^4\,b^4\,d^2\,e^7\,z+36\,a\,b^7\,d^3\,e^6\,z+36\,a^7\,b\,d\,e^8\,z+9\,c^8\,d^6\,e^3\,z+36\,a^7\,b^4\,c\,d^2\,e^6-36\,a^7\,b\,c^4\,d^3\,e^5-36\,a^4\,b^7\,c\,d^3\,e^5-36\,a^4\,b\,c^7\,d^5\,e^3-36\,a\,b^7\,c^4\,d^5\,e^3+36\,a\,b^4\,c^7\,d^6\,e^2+12\,a\,b^{10}\,c\,d^4\,e^4+108\,a^5\,b^5\,c^2\,d^3\,e^5-108\,a^5\,b^2\,c^5\,d^4\,e^4+108\,a^2\,b^5\,c^5\,d^5\,e^3-96\,a^6\,b^3\,c^3\,d^3\,e^5+96\,a^3\,b^6\,c^3\,d^4\,e^4-96\,a^3\,b^3\,c^6\,d^5\,e^3-54\,a^8\,b^2\,c^2\,d^2\,e^6-54\,a^2\,b^8\,c^2\,d^4\,e^4-54\,a^2\,b^2\,c^8\,d^6\,e^2-9\,a^4\,b^4\,c^4\,d^4\,e^4-12\,a^{10}\,b\,c\,d\,e^7-12\,a\,b\,c^{10}\,d^7\,e-6\,b^6\,c^6\,d^6\,e^2+4\,b^9\,c^3\,d^5\,e^3-6\,a^6\,c^6\,d^4\,e^4-4\,a^9\,c^3\,d^2\,e^6-4\,a^3\,c^9\,d^6\,e^2-6\,a^6\,b^6\,d^2\,e^6+4\,a^3\,b^9\,d^3\,e^5+4\,b^3\,c^9\,d^7\,e+4\,a^9\,b^3\,d\,e^7-b^{12}\,d^4\,e^4-c^{12}\,d^8-a^{12}\,e^8,z,k\right)\right)-x\,\left(\frac{d\,\left(6\,b^2\,c^2+4\,a\,c^3\right)}{e^2}-\frac{4\,a\,b\,\left(b^2+3\,a\,c\right)}{e}\right)+\frac{c^4\,x^6}{6\,e}+\frac{x^4\,\left(6\,b^2\,c^2+4\,a\,c^3\right)}{4\,e}+\frac{4\,b\,c^3\,x^5}{5\,e}","Not used",1,"x^2*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/(2*e) - (2*b*c^3*d)/e^2) - x^3*((c^4*d)/(3*e^2) - (4*b*c*(3*a*c + b^2))/(3*e)) + symsum(log(root(27*d^2*e^9*z^3 + 324*a*b*c^2*d^3*e^7*z^2 + 108*b^3*c*d^3*e^7*z^2 - 108*a^3*c*d^2*e^8*z^2 - 162*a^2*b^2*d^2*e^8*z^2 - 27*c^4*d^4*e^6*z^2 - 72*a*b*c^6*d^5*e^4*z + 216*a^2*b^2*c^4*d^4*e^5*z + 144*a^3*b^3*c^2*d^3*e^6*z - 108*a^5*b^2*c*d^2*e^7*z + 108*a^2*b^5*c*d^3*e^6*z - 36*a^4*b*c^3*d^3*e^6*z + 36*a*b^4*c^3*d^4*e^5*z + 144*b^3*c^5*d^5*e^4*z + 90*b^6*c^2*d^4*e^5*z - 144*a^3*c^5*d^4*e^5*z + 90*a^6*c^2*d^2*e^7*z + 171*a^4*b^4*d^2*e^7*z + 36*a*b^7*d^3*e^6*z + 36*a^7*b*d*e^8*z + 9*c^8*d^6*e^3*z + 36*a^7*b^4*c*d^2*e^6 - 36*a^7*b*c^4*d^3*e^5 - 36*a^4*b^7*c*d^3*e^5 - 36*a^4*b*c^7*d^5*e^3 - 36*a*b^7*c^4*d^5*e^3 + 36*a*b^4*c^7*d^6*e^2 + 12*a*b^10*c*d^4*e^4 + 108*a^5*b^5*c^2*d^3*e^5 - 108*a^5*b^2*c^5*d^4*e^4 + 108*a^2*b^5*c^5*d^5*e^3 - 96*a^6*b^3*c^3*d^3*e^5 + 96*a^3*b^6*c^3*d^4*e^4 - 96*a^3*b^3*c^6*d^5*e^3 - 54*a^8*b^2*c^2*d^2*e^6 - 54*a^2*b^8*c^2*d^4*e^4 - 54*a^2*b^2*c^8*d^6*e^2 - 9*a^4*b^4*c^4*d^4*e^4 - 12*a^10*b*c*d*e^7 - 12*a*b*c^10*d^7*e - 6*b^6*c^6*d^6*e^2 + 4*b^9*c^3*d^5*e^3 - 6*a^6*c^6*d^4*e^4 - 4*a^9*c^3*d^2*e^6 - 4*a^3*c^9*d^6*e^2 - 6*a^6*b^6*d^2*e^6 + 4*a^3*b^9*d^3*e^5 + 4*b^3*c^9*d^7*e + 4*a^9*b^3*d*e^7 - b^12*d^4*e^4 - c^12*d^8 - a^12*e^8, z, k)*((x*(3*a^4*e^5 + 12*a*c^3*d^2*e^3 + 18*b^2*c^2*d^2*e^3 - 12*a*b^3*d*e^4 - 36*a^2*b*c*d*e^4))/e^3 - (6*c^4*d^3*e^3 + 36*a^2*b^2*d*e^5 - 24*b^3*c*d^2*e^4 + 24*a^3*c*d*e^5 - 72*a*b*c^2*d^2*e^4)/e^4 + 9*root(27*d^2*e^9*z^3 + 324*a*b*c^2*d^3*e^7*z^2 + 108*b^3*c*d^3*e^7*z^2 - 108*a^3*c*d^2*e^8*z^2 - 162*a^2*b^2*d^2*e^8*z^2 - 27*c^4*d^4*e^6*z^2 - 72*a*b*c^6*d^5*e^4*z + 216*a^2*b^2*c^4*d^4*e^5*z + 144*a^3*b^3*c^2*d^3*e^6*z - 108*a^5*b^2*c*d^2*e^7*z + 108*a^2*b^5*c*d^3*e^6*z - 36*a^4*b*c^3*d^3*e^6*z + 36*a*b^4*c^3*d^4*e^5*z + 144*b^3*c^5*d^5*e^4*z + 90*b^6*c^2*d^4*e^5*z - 144*a^3*c^5*d^4*e^5*z + 90*a^6*c^2*d^2*e^7*z + 171*a^4*b^4*d^2*e^7*z + 36*a*b^7*d^3*e^6*z + 36*a^7*b*d*e^8*z + 9*c^8*d^6*e^3*z + 36*a^7*b^4*c*d^2*e^6 - 36*a^7*b*c^4*d^3*e^5 - 36*a^4*b^7*c*d^3*e^5 - 36*a^4*b*c^7*d^5*e^3 - 36*a*b^7*c^4*d^5*e^3 + 36*a*b^4*c^7*d^6*e^2 + 12*a*b^10*c*d^4*e^4 + 108*a^5*b^5*c^2*d^3*e^5 - 108*a^5*b^2*c^5*d^4*e^4 + 108*a^2*b^5*c^5*d^5*e^3 - 96*a^6*b^3*c^3*d^3*e^5 + 96*a^3*b^6*c^3*d^4*e^4 - 96*a^3*b^3*c^6*d^5*e^3 - 54*a^8*b^2*c^2*d^2*e^6 - 54*a^2*b^8*c^2*d^4*e^4 - 54*a^2*b^2*c^8*d^6*e^2 - 9*a^4*b^4*c^4*d^4*e^4 - 12*a^10*b*c*d*e^7 - 12*a*b*c^10*d^7*e - 6*b^6*c^6*d^6*e^2 + 4*b^9*c^3*d^5*e^3 - 6*a^6*c^6*d^4*e^4 - 4*a^9*c^3*d^2*e^6 - 4*a^3*c^9*d^6*e^2 - 6*a^6*b^6*d^2*e^6 + 4*a^3*b^9*d^3*e^5 + 4*b^3*c^9*d^7*e + 4*a^9*b^3*d*e^7 - b^12*d^4*e^4 - c^12*d^8 - a^12*e^8, z, k)*d*e^2) + (c^8*d^5 + 4*a^7*b*e^5 + 4*a*b^7*d^2*e^3 + 19*a^4*b^4*d*e^4 + 10*a^6*c^2*d*e^4 + 16*b^3*c^5*d^4*e - 16*a^3*c^5*d^3*e^2 + 10*b^6*c^2*d^3*e^2 - 8*a*b*c^6*d^4*e + 24*a^2*b^2*c^4*d^3*e^2 + 16*a^3*b^3*c^2*d^2*e^3 - 12*a^5*b^2*c*d*e^4 + 4*a*b^4*c^3*d^3*e^2 + 12*a^2*b^5*c*d^2*e^3 - 4*a^4*b*c^3*d^2*e^3)/e^4 + (x*(10*a^6*b^2*e^4 - 4*a^7*c*e^4 - 4*a*c^7*d^4 + 10*b^2*c^6*d^4 + b^8*d^2*e^2 + 16*a^3*b^5*d*e^3 + 16*b^5*c^3*d^3*e + 19*a^4*c^4*d^2*e^2 + 24*a^2*b^4*c^2*d^2*e^2 - 16*a^3*b^2*c^3*d^2*e^2 - 4*a*b^3*c^4*d^3*e + 8*a*b^6*c*d^2*e^2 + 12*a^2*b*c^5*d^3*e - 4*a^4*b^3*c*d*e^3 + 12*a^5*b*c^2*d*e^3))/e^3)*root(27*d^2*e^9*z^3 + 324*a*b*c^2*d^3*e^7*z^2 + 108*b^3*c*d^3*e^7*z^2 - 108*a^3*c*d^2*e^8*z^2 - 162*a^2*b^2*d^2*e^8*z^2 - 27*c^4*d^4*e^6*z^2 - 72*a*b*c^6*d^5*e^4*z + 216*a^2*b^2*c^4*d^4*e^5*z + 144*a^3*b^3*c^2*d^3*e^6*z - 108*a^5*b^2*c*d^2*e^7*z + 108*a^2*b^5*c*d^3*e^6*z - 36*a^4*b*c^3*d^3*e^6*z + 36*a*b^4*c^3*d^4*e^5*z + 144*b^3*c^5*d^5*e^4*z + 90*b^6*c^2*d^4*e^5*z - 144*a^3*c^5*d^4*e^5*z + 90*a^6*c^2*d^2*e^7*z + 171*a^4*b^4*d^2*e^7*z + 36*a*b^7*d^3*e^6*z + 36*a^7*b*d*e^8*z + 9*c^8*d^6*e^3*z + 36*a^7*b^4*c*d^2*e^6 - 36*a^7*b*c^4*d^3*e^5 - 36*a^4*b^7*c*d^3*e^5 - 36*a^4*b*c^7*d^5*e^3 - 36*a*b^7*c^4*d^5*e^3 + 36*a*b^4*c^7*d^6*e^2 + 12*a*b^10*c*d^4*e^4 + 108*a^5*b^5*c^2*d^3*e^5 - 108*a^5*b^2*c^5*d^4*e^4 + 108*a^2*b^5*c^5*d^5*e^3 - 96*a^6*b^3*c^3*d^3*e^5 + 96*a^3*b^6*c^3*d^4*e^4 - 96*a^3*b^3*c^6*d^5*e^3 - 54*a^8*b^2*c^2*d^2*e^6 - 54*a^2*b^8*c^2*d^4*e^4 - 54*a^2*b^2*c^8*d^6*e^2 - 9*a^4*b^4*c^4*d^4*e^4 - 12*a^10*b*c*d*e^7 - 12*a*b*c^10*d^7*e - 6*b^6*c^6*d^6*e^2 + 4*b^9*c^3*d^5*e^3 - 6*a^6*c^6*d^4*e^4 - 4*a^9*c^3*d^2*e^6 - 4*a^3*c^9*d^6*e^2 - 6*a^6*b^6*d^2*e^6 + 4*a^3*b^9*d^3*e^5 + 4*b^3*c^9*d^7*e + 4*a^9*b^3*d*e^7 - b^12*d^4*e^4 - c^12*d^8 - a^12*e^8, z, k), k, 1, 3) - x*((d*(4*a*c^3 + 6*b^2*c^2))/e^2 - (4*a*b*(3*a*c + b^2))/e) + (c^4*x^6)/(6*e) + (x^4*(4*a*c^3 + 6*b^2*c^2))/(4*e) + (4*b*c^3*x^5)/(5*e)","B"
76,1,49,43,0.098348,"\text{Not used}","int((2*x^2 + x^4)/(x^3 + 1),x)","\ln\left(x+1\right)+\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)+\frac{x^2}{2}","Not used",1,"log(x + 1) + log(x - (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 + 1/2) - log(x + (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 - 1/2) + x^2/2","B"
77,1,51,46,0.093012,"\text{Not used}","int(-(2*x^2 + x^4)/(x^3 - 1),x)","-\ln\left(x-1\right)+\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\frac{x^2}{2}","Not used",1,"log(x - (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/6 - 1/2) - log(x - 1) - log(x + (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/6 + 1/2) - x^2/2","B"
78,1,49,44,4.697379,"\text{Not used}","int((4*x^3 - x + 1)/(x^3 + 1),x)","4\,x-\frac{2\,\ln\left(x+1\right)}{3}+\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{3}+\frac{\sqrt{3}\,2{}\mathrm{i}}{3}\right)-\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{3}+\frac{\sqrt{3}\,2{}\mathrm{i}}{3}\right)","Not used",1,"4*x - (2*log(x + 1))/3 + log(x - (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*2i)/3 + 1/3) - log(x + (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*2i)/3 - 1/3)","B"
79,1,312,230,0.152059,"\text{Not used}","int((x + 3^(1/2) + 1)/(x^3 + 1)^(1/2),x)","\sqrt{3}\,x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ -x^3\right)-\frac{6\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{6\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"3^(1/2)*x*hypergeom([1/3, 1/2], 4/3, -x^3) - (6*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) + (6*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
80,1,342,257,5.137719,"\text{Not used}","int((3^(1/2) - x + 1)/(1 - x^3)^(1/2),x)","\sqrt{3}\,x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ x^3\right)+\frac{6\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{6\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"3^(1/2)*x*hypergeom([1/3, 1/2], 4/3, x^3) + (6*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) - (6*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
81,1,326,144,4.874675,"\text{Not used}","int((3^(1/2) - x + 1)/(x^3 - 1)^(1/2),x)","\frac{\sqrt{3}\,x\,\sqrt{1-x^3}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ x^3\right)}{\sqrt{x^3-1}}+\frac{6\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{6\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(3^(1/2)*x*(1 - x^3)^(1/2)*hypergeom([1/3, 1/2], 4/3, x^3))/(x^3 - 1)^(1/2) + (6*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) - (6*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)","B"
82,1,360,135,4.908742,"\text{Not used}","int((x + 3^(1/2) + 1)/(- x^3 - 1)^(1/2),x)","\frac{\sqrt{3}\,x\,\sqrt{x^3+1}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ -x^3\right)}{\sqrt{-x^3-1}}-\frac{6\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{6\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(3^(1/2)*x*(x^3 + 1)^(1/2)*hypergeom([1/3, 1/2], 4/3, -x^3))/(- x^3 - 1)^(1/2) - (6*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) + (6*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
83,0,-1,468,0.000000,"\text{Not used}","int((b^(1/3)*x + a^(1/3)*(3^(1/2) + 1))/(a + b*x^3)^(1/2),x)","\int \frac{b^{1/3}\,x+a^{1/3}\,\left(\sqrt{3}+1\right)}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((b^(1/3)*x + a^(1/3)*(3^(1/2) + 1))/(a + b*x^3)^(1/2), x)","F"
84,0,-1,481,0.000000,"\text{Not used}","int(-(b^(1/3)*x - a^(1/3)*(3^(1/2) + 1))/(a - b*x^3)^(1/2),x)","-\int \frac{b^{1/3}\,x-a^{1/3}\,\left(\sqrt{3}+1\right)}{\sqrt{a-b\,x^3}} \,d x","Not used",1,"-int((b^(1/3)*x - a^(1/3)*(3^(1/2) + 1))/(a - b*x^3)^(1/2), x)","F"
85,0,-1,271,0.000000,"\text{Not used}","int(-(b^(1/3)*x - a^(1/3)*(3^(1/2) + 1))/(b*x^3 - a)^(1/2),x)","-\int \frac{b^{1/3}\,x-a^{1/3}\,\left(\sqrt{3}+1\right)}{\sqrt{b\,x^3-a}} \,d x","Not used",1,"-int((b^(1/3)*x - a^(1/3)*(3^(1/2) + 1))/(b*x^3 - a)^(1/2), x)","F"
86,0,-1,266,0.000000,"\text{Not used}","int((b^(1/3)*x + a^(1/3)*(3^(1/2) + 1))/(- a - b*x^3)^(1/2),x)","\int \frac{b^{1/3}\,x+a^{1/3}\,\left(\sqrt{3}+1\right)}{\sqrt{-b\,x^3-a}} \,d x","Not used",1,"int((b^(1/3)*x + a^(1/3)*(3^(1/2) + 1))/(- a - b*x^3)^(1/2), x)","F"
87,0,-1,520,0.000000,"\text{Not used}","int((3^(1/2) + x*(b/a)^(1/3) + 1)/(a + b*x^3)^(1/2),x)","\int \frac{\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}+1}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((3^(1/2) + x*(b/a)^(1/3) + 1)/(a + b*x^3)^(1/2), x)","F"
88,0,-1,533,0.000000,"\text{Not used}","int((3^(1/2) - x*(b/a)^(1/3) + 1)/(a - b*x^3)^(1/2),x)","\int \frac{\sqrt{3}-x\,{\left(\frac{b}{a}\right)}^{1/3}+1}{\sqrt{a-b\,x^3}} \,d x","Not used",1,"int((3^(1/2) - x*(b/a)^(1/3) + 1)/(a - b*x^3)^(1/2), x)","F"
89,0,-1,256,0.000000,"\text{Not used}","int((3^(1/2) - x*(b/a)^(1/3) + 1)/(b*x^3 - a)^(1/2),x)","\int \frac{\sqrt{3}-x\,{\left(\frac{b}{a}\right)}^{1/3}+1}{\sqrt{b\,x^3-a}} \,d x","Not used",1,"int((3^(1/2) - x*(b/a)^(1/3) + 1)/(b*x^3 - a)^(1/2), x)","F"
90,0,-1,251,0.000000,"\text{Not used}","int((3^(1/2) + x*(b/a)^(1/3) + 1)/(- a - b*x^3)^(1/2),x)","\int \frac{\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}+1}{\sqrt{-b\,x^3-a}} \,d x","Not used",1,"int((3^(1/2) + x*(b/a)^(1/3) + 1)/(- a - b*x^3)^(1/2), x)","F"
91,1,313,127,0.126308,"\text{Not used}","int((x - 3^(1/2) + 1)/(x^3 + 1)^(1/2),x)","-\sqrt{3}\,x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ -x^3\right)-\frac{6\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{6\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(6*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) - (6*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) - 3^(1/2)*x*hypergeom([1/3, 1/2], 4/3, -x^3)","B"
92,1,343,142,4.738188,"\text{Not used}","int(-(x + 3^(1/2) - 1)/(1 - x^3)^(1/2),x)","-\sqrt{3}\,x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ x^3\right)+\frac{6\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{6\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(6*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) - 3^(1/2)*x*hypergeom([1/3, 1/2], 4/3, x^3) - (6*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
93,1,327,264,4.749934,"\text{Not used}","int(-(x + 3^(1/2) - 1)/(x^3 - 1)^(1/2),x)","-\frac{\sqrt{3}\,x\,\sqrt{1-x^3}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ x^3\right)}{\sqrt{x^3-1}}+\frac{6\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{6\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(6*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) - (3^(1/2)*x*(1 - x^3)^(1/2)*hypergeom([1/3, 1/2], 4/3, x^3))/(x^3 - 1)^(1/2) - (6*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)","B"
94,1,361,247,4.823722,"\text{Not used}","int((x - 3^(1/2) + 1)/(- x^3 - 1)^(1/2),x)","-\frac{\sqrt{3}\,x\,\sqrt{x^3+1}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ -x^3\right)}{\sqrt{-x^3-1}}-\frac{6\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{6\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(6*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) - (6*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) - (3^(1/2)*x*(x^3 + 1)^(1/2)*hypergeom([1/3, 1/2], 4/3, -x^3))/(- x^3 - 1)^(1/2)","B"
95,1,312,126,4.819633,"\text{Not used}","int(-(x - 3^(1/2) + 1)/(x^3 + 1)^(1/2),x)","\sqrt{3}\,x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ -x^3\right)+\frac{6\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{6\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"3^(1/2)*x*hypergeom([1/3, 1/2], 4/3, -x^3) + (6*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) - (6*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
96,1,342,143,0.051972,"\text{Not used}","int((x + 3^(1/2) - 1)/(1 - x^3)^(1/2),x)","\sqrt{3}\,x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ x^3\right)-\frac{6\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{6\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"3^(1/2)*x*hypergeom([1/3, 1/2], 4/3, x^3) - (6*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) + (6*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
97,1,326,263,0.060629,"\text{Not used}","int((x + 3^(1/2) - 1)/(x^3 - 1)^(1/2),x)","\frac{\sqrt{3}\,x\,\sqrt{1-x^3}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ x^3\right)}{\sqrt{x^3-1}}-\frac{6\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{6\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(3^(1/2)*x*(1 - x^3)^(1/2)*hypergeom([1/3, 1/2], 4/3, x^3))/(x^3 - 1)^(1/2) - (6*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) + (6*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)","B"
98,1,360,248,4.899994,"\text{Not used}","int(-(x - 3^(1/2) + 1)/(- x^3 - 1)^(1/2),x)","\frac{\sqrt{3}\,x\,\sqrt{x^3+1}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ -x^3\right)}{\sqrt{-x^3-1}}+\frac{6\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{6\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(3^(1/2)*x*(x^3 + 1)^(1/2)*hypergeom([1/3, 1/2], 4/3, -x^3))/(- x^3 - 1)^(1/2) + (6*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticE(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) - (6*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
99,0,-1,256,0.000000,"\text{Not used}","int((b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))/(a + b*x^3)^(1/2),x)","\int \frac{b^{1/3}\,x-a^{1/3}\,\left(\sqrt{3}-1\right)}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))/(a + b*x^3)^(1/2), x)","F"
100,0,-1,263,0.000000,"\text{Not used}","int(-(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))/(a - b*x^3)^(1/2),x)","\int -\frac{b^{1/3}\,x+a^{1/3}\,\left(\sqrt{3}-1\right)}{\sqrt{a-b\,x^3}} \,d x","Not used",1,"int(-(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))/(a - b*x^3)^(1/2), x)","F"
101,0,-1,497,0.000000,"\text{Not used}","int(-(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))/(b*x^3 - a)^(1/2),x)","\int -\frac{b^{1/3}\,x+a^{1/3}\,\left(\sqrt{3}-1\right)}{\sqrt{b\,x^3-a}} \,d x","Not used",1,"int(-(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))/(b*x^3 - a)^(1/2), x)","F"
102,0,-1,488,0.000000,"\text{Not used}","int((b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))/(- a - b*x^3)^(1/2),x)","\int \frac{b^{1/3}\,x-a^{1/3}\,\left(\sqrt{3}-1\right)}{\sqrt{-b\,x^3-a}} \,d x","Not used",1,"int((b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))/(- a - b*x^3)^(1/2), x)","F"
103,0,-1,241,0.000000,"\text{Not used}","int((x*(b/a)^(1/3) - 3^(1/2) + 1)/(a + b*x^3)^(1/2),x)","\int \frac{x\,{\left(\frac{b}{a}\right)}^{1/3}-\sqrt{3}+1}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((x*(b/a)^(1/3) - 3^(1/2) + 1)/(a + b*x^3)^(1/2), x)","F"
104,0,-1,248,0.000000,"\text{Not used}","int(-(3^(1/2) + x*(b/a)^(1/3) - 1)/(a - b*x^3)^(1/2),x)","\int -\frac{\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}-1}{\sqrt{a-b\,x^3}} \,d x","Not used",1,"int(-(3^(1/2) + x*(b/a)^(1/3) - 1)/(a - b*x^3)^(1/2), x)","F"
105,0,-1,549,0.000000,"\text{Not used}","int(-(3^(1/2) + x*(b/a)^(1/3) - 1)/(b*x^3 - a)^(1/2),x)","\int -\frac{\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}-1}{\sqrt{b\,x^3-a}} \,d x","Not used",1,"int(-(3^(1/2) + x*(b/a)^(1/3) - 1)/(b*x^3 - a)^(1/2), x)","F"
106,0,-1,540,0.000000,"\text{Not used}","int((x*(b/a)^(1/3) - 3^(1/2) + 1)/(- a - b*x^3)^(1/2),x)","\int \frac{x\,{\left(\frac{b}{a}\right)}^{1/3}-\sqrt{3}+1}{\sqrt{-b\,x^3-a}} \,d x","Not used",1,"int((x*(b/a)^(1/3) - 3^(1/2) + 1)/(- a - b*x^3)^(1/2), x)","F"
107,0,-1,490,0.000000,"\text{Not used}","int((c + d*x)/(a + b*x^3)^(1/2),x)","\int \frac{c+d\,x}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((c + d*x)/(a + b*x^3)^(1/2), x)","F"
108,0,-1,503,0.000000,"\text{Not used}","int((c + d*x)/(a - b*x^3)^(1/2),x)","\int \frac{c+d\,x}{\sqrt{a-b\,x^3}} \,d x","Not used",1,"int((c + d*x)/(a - b*x^3)^(1/2), x)","F"
109,0,-1,515,0.000000,"\text{Not used}","int((c + d*x)/(b*x^3 - a)^(1/2),x)","\int \frac{c+d\,x}{\sqrt{b\,x^3-a}} \,d x","Not used",1,"int((c + d*x)/(b*x^3 - a)^(1/2), x)","F"
110,0,-1,508,0.000000,"\text{Not used}","int((c + d*x)/(- a - b*x^3)^(1/2),x)","\int \frac{c+d\,x}{\sqrt{-b\,x^3-a}} \,d x","Not used",1,"int((c + d*x)/(- a - b*x^3)^(1/2), x)","F"
111,1,373,246,4.769853,"\text{Not used}","int((c + d*x)/(x^3 + 1)^(1/2),x)","-\frac{2\,d\,\left(\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-\left(-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{2\,c\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*c*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) - (2*d*(((3^(1/2)*1i)/2 - 1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ((3^(1/2)*1i)/2 - 3/2)*ellipticE(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
112,1,406,271,5.069610,"\text{Not used}","int((c + d*x)/(1 - x^3)^(1/2),x)","-\frac{2\,c\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,d\,\left(\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-\left(-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"- (2*c*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) - (2*d*(((3^(1/2)*1i)/2 - 1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ((3^(1/2)*1i)/2 - 3/2)*ellipticE(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
113,1,374,275,0.120193,"\text{Not used}","int((c + d*x)/(x^3 - 1)^(1/2),x)","-\frac{2\,c\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,d\,\left(\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-\left(-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"- (2*c*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) - (2*d*(((3^(1/2)*1i)/2 - 1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ((3^(1/2)*1i)/2 - 3/2)*ellipticE(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)","B"
114,1,405,261,4.820653,"\text{Not used}","int((c + d*x)/(- x^3 - 1)^(1/2),x)","\frac{2\,c\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,d\,\left(\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-\left(-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*c*((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) - (2*d*(((3^(1/2)*1i)/2 - 1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ((3^(1/2)*1i)/2 - 3/2)*ellipticE(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
115,1,182,87,5.012086,"\text{Not used}","int((c + d*x)/(a - b*x^4),x)","\left\{\begin{array}{cl} \frac{2\,c+3\,d\,x}{6\,b\,x^3} & \text{\ if\ \ }a=0\\ \frac{\mathrm{atan}\left(\frac{\sqrt{2}\,{\left(-b\right)}^{1/4}\,x}{a^{1/4}}-1\right)\,\left(2\,a^{1/4}\,d+\sqrt{2}\,{\left(-b\right)}^{1/4}\,c\right)}{4\,a^{3/4}\,\sqrt{-b}}-\frac{\mathrm{atan}\left(\frac{\sqrt{2}\,{\left(-b\right)}^{1/4}\,x}{a^{1/4}}+1\right)\,\left(4\,a^{1/4}\,d-2\,\sqrt{2}\,{\left(-b\right)}^{1/4}\,c\right)}{8\,a^{3/4}\,\sqrt{-b}}+\frac{\sqrt{2}\,c\,\ln\left(\frac{\sqrt{-b}\,x^2+\sqrt{a}+\sqrt{2}\,a^{1/4}\,{\left(-b\right)}^{1/4}\,x}{\sqrt{-b}\,x^2+\sqrt{a}-\sqrt{2}\,a^{1/4}\,{\left(-b\right)}^{1/4}\,x}\right)}{8\,a^{3/4}\,{\left(-b\right)}^{1/4}} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, (2*c + 3*d*x)/(6*b*x^3), a ~= 0, (atan((2^(1/2)*(-b)^(1/4)*x)/a^(1/4) - 1)*(2*a^(1/4)*d + 2^(1/2)*(-b)^(1/4)*c))/(4*a^(3/4)*(-b)^(1/2)) - (atan((2^(1/2)*(-b)^(1/4)*x)/a^(1/4) + 1)*(4*a^(1/4)*d - 2*2^(1/2)*(-b)^(1/4)*c))/(8*a^(3/4)*(-b)^(1/2)) + (2^(1/2)*c*log(((-b)^(1/2)*x^2 + a^(1/2) + 2^(1/2)*a^(1/4)*(-b)^(1/4)*x)/((-b)^(1/2)*x^2 + a^(1/2) - 2^(1/2)*a^(1/4)*(-b)^(1/4)*x)))/(8*a^(3/4)*(-b)^(1/4)))","B"
116,1,160,219,4.798365,"\text{Not used}","int((c + d*x)/(a + b*x^4),x)","\left\{\begin{array}{cl} -\frac{2\,c+3\,d\,x}{6\,b\,x^3} & \text{\ if\ \ }a=0\\ \frac{\mathrm{atan}\left(\frac{\sqrt{2}\,b^{1/4}\,x}{a^{1/4}}-1\right)\,\left(2\,a^{1/4}\,d+\sqrt{2}\,b^{1/4}\,c\right)}{4\,a^{3/4}\,\sqrt{b}}-\frac{\mathrm{atan}\left(\frac{\sqrt{2}\,b^{1/4}\,x}{a^{1/4}}+1\right)\,\left(4\,a^{1/4}\,d-2\,\sqrt{2}\,b^{1/4}\,c\right)}{8\,a^{3/4}\,\sqrt{b}}+\frac{\sqrt{2}\,c\,\ln\left(\frac{\sqrt{a}+\sqrt{b}\,x^2+\sqrt{2}\,a^{1/4}\,b^{1/4}\,x}{\sqrt{a}+\sqrt{b}\,x^2-\sqrt{2}\,a^{1/4}\,b^{1/4}\,x}\right)}{8\,a^{3/4}\,b^{1/4}} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, -(2*c + 3*d*x)/(6*b*x^3), a ~= 0, (atan((2^(1/2)*b^(1/4)*x)/a^(1/4) - 1)*(2*a^(1/4)*d + 2^(1/2)*b^(1/4)*c))/(4*a^(3/4)*b^(1/2)) - (atan((2^(1/2)*b^(1/4)*x)/a^(1/4) + 1)*(4*a^(1/4)*d - 2*2^(1/2)*b^(1/4)*c))/(8*a^(3/4)*b^(1/2)) + (2^(1/2)*c*log((a^(1/2) + b^(1/2)*x^2 + 2^(1/2)*a^(1/4)*b^(1/4)*x)/(a^(1/2) + b^(1/2)*x^2 - 2^(1/2)*a^(1/4)*b^(1/4)*x)))/(8*a^(3/4)*b^(1/4)))","B"
117,1,283,110,4.918991,"\text{Not used}","int((c + d*x)/(a - b*x^4)^2,x)","\left(\sum _{k=1}^4\ln\left(-\frac{b^2\,\left(3\,c\,d^2+2\,d^3\,x+{\mathrm{root}\left(65536\,a^7\,b^2\,z^4-2048\,a^4\,b\,d^2\,z^2+1152\,a^2\,b\,c^2\,d\,z-81\,b\,c^4+16\,a\,d^4,z,k\right)}^2\,a^3\,b\,c\,192-{\mathrm{root}\left(65536\,a^7\,b^2\,z^4-2048\,a^4\,b\,d^2\,z^2+1152\,a^2\,b\,c^2\,d\,z-81\,b\,c^4+16\,a\,d^4,z,k\right)}^2\,a^3\,b\,d\,x\,128+\mathrm{root}\left(65536\,a^7\,b^2\,z^4-2048\,a^4\,b\,d^2\,z^2+1152\,a^2\,b\,c^2\,d\,z-81\,b\,c^4+16\,a\,d^4,z,k\right)\,a\,b\,c^2\,x\,36\right)}{a^3\,16}\right)\,\mathrm{root}\left(65536\,a^7\,b^2\,z^4-2048\,a^4\,b\,d^2\,z^2+1152\,a^2\,b\,c^2\,d\,z-81\,b\,c^4+16\,a\,d^4,z,k\right)\right)+\frac{\frac{d\,x^2}{4\,a}+\frac{c\,x}{4\,a}}{a-b\,x^4}","Not used",1,"symsum(log(-(b^2*(3*c*d^2 + 2*d^3*x + 192*root(65536*a^7*b^2*z^4 - 2048*a^4*b*d^2*z^2 + 1152*a^2*b*c^2*d*z - 81*b*c^4 + 16*a*d^4, z, k)^2*a^3*b*c - 128*root(65536*a^7*b^2*z^4 - 2048*a^4*b*d^2*z^2 + 1152*a^2*b*c^2*d*z - 81*b*c^4 + 16*a*d^4, z, k)^2*a^3*b*d*x + 36*root(65536*a^7*b^2*z^4 - 2048*a^4*b*d^2*z^2 + 1152*a^2*b*c^2*d*z - 81*b*c^4 + 16*a*d^4, z, k)*a*b*c^2*x))/(16*a^3))*root(65536*a^7*b^2*z^4 - 2048*a^4*b*d^2*z^2 + 1152*a^2*b*c^2*d*z - 81*b*c^4 + 16*a*d^4, z, k), k, 1, 4) + ((d*x^2)/(4*a) + (c*x)/(4*a))/(a - b*x^4)","B"
118,1,282,241,4.944393,"\text{Not used}","int((c + d*x)/(a + b*x^4)^2,x)","\left(\sum _{k=1}^4\ln\left(\frac{b^2\,\left(3\,c\,d^2+2\,d^3\,x-{\mathrm{root}\left(65536\,a^7\,b^2\,z^4+2048\,a^4\,b\,d^2\,z^2-1152\,a^2\,b\,c^2\,d\,z+81\,b\,c^4+16\,a\,d^4,z,k\right)}^2\,a^3\,b\,c\,192+{\mathrm{root}\left(65536\,a^7\,b^2\,z^4+2048\,a^4\,b\,d^2\,z^2-1152\,a^2\,b\,c^2\,d\,z+81\,b\,c^4+16\,a\,d^4,z,k\right)}^2\,a^3\,b\,d\,x\,128-\mathrm{root}\left(65536\,a^7\,b^2\,z^4+2048\,a^4\,b\,d^2\,z^2-1152\,a^2\,b\,c^2\,d\,z+81\,b\,c^4+16\,a\,d^4,z,k\right)\,a\,b\,c^2\,x\,36\right)}{a^3\,16}\right)\,\mathrm{root}\left(65536\,a^7\,b^2\,z^4+2048\,a^4\,b\,d^2\,z^2-1152\,a^2\,b\,c^2\,d\,z+81\,b\,c^4+16\,a\,d^4,z,k\right)\right)+\frac{\frac{d\,x^2}{4\,a}+\frac{c\,x}{4\,a}}{b\,x^4+a}","Not used",1,"symsum(log((b^2*(3*c*d^2 + 2*d^3*x - 192*root(65536*a^7*b^2*z^4 + 2048*a^4*b*d^2*z^2 - 1152*a^2*b*c^2*d*z + 81*b*c^4 + 16*a*d^4, z, k)^2*a^3*b*c + 128*root(65536*a^7*b^2*z^4 + 2048*a^4*b*d^2*z^2 - 1152*a^2*b*c^2*d*z + 81*b*c^4 + 16*a*d^4, z, k)^2*a^3*b*d*x - 36*root(65536*a^7*b^2*z^4 + 2048*a^4*b*d^2*z^2 - 1152*a^2*b*c^2*d*z + 81*b*c^4 + 16*a*d^4, z, k)*a*b*c^2*x))/(16*a^3))*root(65536*a^7*b^2*z^4 + 2048*a^4*b*d^2*z^2 - 1152*a^2*b*c^2*d*z + 81*b*c^4 + 16*a*d^4, z, k), k, 1, 4) + ((d*x^2)/(4*a) + (c*x)/(4*a))/(a + b*x^4)","B"
119,1,315,136,4.979021,"\text{Not used}","int((c + d*x)/(a - b*x^4)^3,x)","\frac{\frac{5\,d\,x^2}{16\,a}+\frac{11\,c\,x}{32\,a}-\frac{7\,b\,c\,x^5}{32\,a^2}-\frac{3\,b\,d\,x^6}{16\,a^2}}{a^2-2\,a\,b\,x^4+b^2\,x^8}+\left(\sum _{k=1}^4\ln\left(-\frac{b^2\,\left(63\,c\,d^2+36\,d^3\,x+{\mathrm{root}\left(268435456\,a^{11}\,b^2\,z^4-4718592\,a^6\,b\,d^2\,z^2+2709504\,a^3\,b\,c^2\,d\,z-194481\,b\,c^4+20736\,a\,d^4,z,k\right)}^2\,a^5\,b\,c\,7168+\mathrm{root}\left(268435456\,a^{11}\,b^2\,z^4-4718592\,a^6\,b\,d^2\,z^2+2709504\,a^3\,b\,c^2\,d\,z-194481\,b\,c^4+20736\,a\,d^4,z,k\right)\,a^2\,b\,c^2\,x\,1176-{\mathrm{root}\left(268435456\,a^{11}\,b^2\,z^4-4718592\,a^6\,b\,d^2\,z^2+2709504\,a^3\,b\,c^2\,d\,z-194481\,b\,c^4+20736\,a\,d^4,z,k\right)}^2\,a^5\,b\,d\,x\,4096\right)\,3}{a^6\,2048}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^2\,z^4-4718592\,a^6\,b\,d^2\,z^2+2709504\,a^3\,b\,c^2\,d\,z-194481\,b\,c^4+20736\,a\,d^4,z,k\right)\right)","Not used",1,"((5*d*x^2)/(16*a) + (11*c*x)/(32*a) - (7*b*c*x^5)/(32*a^2) - (3*b*d*x^6)/(16*a^2))/(a^2 + b^2*x^8 - 2*a*b*x^4) + symsum(log(-(3*b^2*(63*c*d^2 + 36*d^3*x + 7168*root(268435456*a^11*b^2*z^4 - 4718592*a^6*b*d^2*z^2 + 2709504*a^3*b*c^2*d*z - 194481*b*c^4 + 20736*a*d^4, z, k)^2*a^5*b*c + 1176*root(268435456*a^11*b^2*z^4 - 4718592*a^6*b*d^2*z^2 + 2709504*a^3*b*c^2*d*z - 194481*b*c^4 + 20736*a*d^4, z, k)*a^2*b*c^2*x - 4096*root(268435456*a^11*b^2*z^4 - 4718592*a^6*b*d^2*z^2 + 2709504*a^3*b*c^2*d*z - 194481*b*c^4 + 20736*a*d^4, z, k)^2*a^5*b*d*x))/(2048*a^6))*root(268435456*a^11*b^2*z^4 - 4718592*a^6*b*d^2*z^2 + 2709504*a^3*b*c^2*d*z - 194481*b*c^4 + 20736*a*d^4, z, k), k, 1, 4)","B"
120,1,315,266,4.988805,"\text{Not used}","int((c + d*x)/(a + b*x^4)^3,x)","\frac{\frac{5\,d\,x^2}{16\,a}+\frac{11\,c\,x}{32\,a}+\frac{7\,b\,c\,x^5}{32\,a^2}+\frac{3\,b\,d\,x^6}{16\,a^2}}{a^2+2\,a\,b\,x^4+b^2\,x^8}+\left(\sum _{k=1}^4\ln\left(\frac{b^2\,\left(63\,c\,d^2+36\,d^3\,x-{\mathrm{root}\left(268435456\,a^{11}\,b^2\,z^4+4718592\,a^6\,b\,d^2\,z^2-2709504\,a^3\,b\,c^2\,d\,z+194481\,b\,c^4+20736\,a\,d^4,z,k\right)}^2\,a^5\,b\,c\,7168-\mathrm{root}\left(268435456\,a^{11}\,b^2\,z^4+4718592\,a^6\,b\,d^2\,z^2-2709504\,a^3\,b\,c^2\,d\,z+194481\,b\,c^4+20736\,a\,d^4,z,k\right)\,a^2\,b\,c^2\,x\,1176+{\mathrm{root}\left(268435456\,a^{11}\,b^2\,z^4+4718592\,a^6\,b\,d^2\,z^2-2709504\,a^3\,b\,c^2\,d\,z+194481\,b\,c^4+20736\,a\,d^4,z,k\right)}^2\,a^5\,b\,d\,x\,4096\right)\,3}{a^6\,2048}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^2\,z^4+4718592\,a^6\,b\,d^2\,z^2-2709504\,a^3\,b\,c^2\,d\,z+194481\,b\,c^4+20736\,a\,d^4,z,k\right)\right)","Not used",1,"((5*d*x^2)/(16*a) + (11*c*x)/(32*a) + (7*b*c*x^5)/(32*a^2) + (3*b*d*x^6)/(16*a^2))/(a^2 + b^2*x^8 + 2*a*b*x^4) + symsum(log((3*b^2*(63*c*d^2 + 36*d^3*x - 7168*root(268435456*a^11*b^2*z^4 + 4718592*a^6*b*d^2*z^2 - 2709504*a^3*b*c^2*d*z + 194481*b*c^4 + 20736*a*d^4, z, k)^2*a^5*b*c - 1176*root(268435456*a^11*b^2*z^4 + 4718592*a^6*b*d^2*z^2 - 2709504*a^3*b*c^2*d*z + 194481*b*c^4 + 20736*a*d^4, z, k)*a^2*b*c^2*x + 4096*root(268435456*a^11*b^2*z^4 + 4718592*a^6*b*d^2*z^2 - 2709504*a^3*b*c^2*d*z + 194481*b*c^4 + 20736*a*d^4, z, k)^2*a^5*b*d*x))/(2048*a^6))*root(268435456*a^11*b^2*z^4 + 4718592*a^6*b*d^2*z^2 - 2709504*a^3*b*c^2*d*z + 194481*b*c^4 + 20736*a*d^4, z, k), k, 1, 4)","B"
121,1,351,162,4.974972,"\text{Not used}","int((c + d*x)/(a - b*x^4)^4,x)","\left(\sum _{k=1}^4\ln\left(-\frac{b^2\,\left(1925\,c\,d^2+1000\,d^3\,x+{\mathrm{root}\left(68719476736\,a^{15}\,b^2\,z^4-838860800\,a^8\,b\,d^2\,z^2+485703680\,a^4\,b\,c^2\,d\,z-35153041\,b\,c^4+2560000\,a\,d^4,z,k\right)}^2\,a^7\,b\,c\,315392+\mathrm{root}\left(68719476736\,a^{15}\,b^2\,z^4-838860800\,a^8\,b\,d^2\,z^2+485703680\,a^4\,b\,c^2\,d\,z-35153041\,b\,c^4+2560000\,a\,d^4,z,k\right)\,a^3\,b\,c^2\,x\,47432-{\mathrm{root}\left(68719476736\,a^{15}\,b^2\,z^4-838860800\,a^8\,b\,d^2\,z^2+485703680\,a^4\,b\,c^2\,d\,z-35153041\,b\,c^4+2560000\,a\,d^4,z,k\right)}^2\,a^7\,b\,d\,x\,163840\right)}{a^9\,32768}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^2\,z^4-838860800\,a^8\,b\,d^2\,z^2+485703680\,a^4\,b\,c^2\,d\,z-35153041\,b\,c^4+2560000\,a\,d^4,z,k\right)\right)+\frac{\frac{11\,d\,x^2}{32\,a}+\frac{51\,c\,x}{128\,a}+\frac{77\,b^2\,c\,x^9}{384\,a^3}+\frac{5\,b^2\,d\,x^{10}}{32\,a^3}-\frac{33\,b\,c\,x^5}{64\,a^2}-\frac{5\,b\,d\,x^6}{12\,a^2}}{a^3-3\,a^2\,b\,x^4+3\,a\,b^2\,x^8-b^3\,x^{12}}","Not used",1,"symsum(log(-(b^2*(1925*c*d^2 + 1000*d^3*x + 315392*root(68719476736*a^15*b^2*z^4 - 838860800*a^8*b*d^2*z^2 + 485703680*a^4*b*c^2*d*z - 35153041*b*c^4 + 2560000*a*d^4, z, k)^2*a^7*b*c + 47432*root(68719476736*a^15*b^2*z^4 - 838860800*a^8*b*d^2*z^2 + 485703680*a^4*b*c^2*d*z - 35153041*b*c^4 + 2560000*a*d^4, z, k)*a^3*b*c^2*x - 163840*root(68719476736*a^15*b^2*z^4 - 838860800*a^8*b*d^2*z^2 + 485703680*a^4*b*c^2*d*z - 35153041*b*c^4 + 2560000*a*d^4, z, k)^2*a^7*b*d*x))/(32768*a^9))*root(68719476736*a^15*b^2*z^4 - 838860800*a^8*b*d^2*z^2 + 485703680*a^4*b*c^2*d*z - 35153041*b*c^4 + 2560000*a*d^4, z, k), k, 1, 4) + ((11*d*x^2)/(32*a) + (51*c*x)/(128*a) + (77*b^2*c*x^9)/(384*a^3) + (5*b^2*d*x^10)/(32*a^3) - (33*b*c*x^5)/(64*a^2) - (5*b*d*x^6)/(12*a^2))/(a^3 - b^3*x^12 - 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
122,1,350,291,0.309032,"\text{Not used}","int((c + d*x)/(a + b*x^4)^4,x)","\left(\sum _{k=1}^4\ln\left(\frac{b^2\,\left(1925\,c\,d^2+1000\,d^3\,x-{\mathrm{root}\left(68719476736\,a^{15}\,b^2\,z^4+838860800\,a^8\,b\,d^2\,z^2-485703680\,a^4\,b\,c^2\,d\,z+35153041\,b\,c^4+2560000\,a\,d^4,z,k\right)}^2\,a^7\,b\,c\,315392-\mathrm{root}\left(68719476736\,a^{15}\,b^2\,z^4+838860800\,a^8\,b\,d^2\,z^2-485703680\,a^4\,b\,c^2\,d\,z+35153041\,b\,c^4+2560000\,a\,d^4,z,k\right)\,a^3\,b\,c^2\,x\,47432+{\mathrm{root}\left(68719476736\,a^{15}\,b^2\,z^4+838860800\,a^8\,b\,d^2\,z^2-485703680\,a^4\,b\,c^2\,d\,z+35153041\,b\,c^4+2560000\,a\,d^4,z,k\right)}^2\,a^7\,b\,d\,x\,163840\right)}{a^9\,32768}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^2\,z^4+838860800\,a^8\,b\,d^2\,z^2-485703680\,a^4\,b\,c^2\,d\,z+35153041\,b\,c^4+2560000\,a\,d^4,z,k\right)\right)+\frac{\frac{11\,d\,x^2}{32\,a}+\frac{51\,c\,x}{128\,a}+\frac{77\,b^2\,c\,x^9}{384\,a^3}+\frac{5\,b^2\,d\,x^{10}}{32\,a^3}+\frac{33\,b\,c\,x^5}{64\,a^2}+\frac{5\,b\,d\,x^6}{12\,a^2}}{a^3+3\,a^2\,b\,x^4+3\,a\,b^2\,x^8+b^3\,x^{12}}","Not used",1,"symsum(log((b^2*(1925*c*d^2 + 1000*d^3*x - 315392*root(68719476736*a^15*b^2*z^4 + 838860800*a^8*b*d^2*z^2 - 485703680*a^4*b*c^2*d*z + 35153041*b*c^4 + 2560000*a*d^4, z, k)^2*a^7*b*c - 47432*root(68719476736*a^15*b^2*z^4 + 838860800*a^8*b*d^2*z^2 - 485703680*a^4*b*c^2*d*z + 35153041*b*c^4 + 2560000*a*d^4, z, k)*a^3*b*c^2*x + 163840*root(68719476736*a^15*b^2*z^4 + 838860800*a^8*b*d^2*z^2 - 485703680*a^4*b*c^2*d*z + 35153041*b*c^4 + 2560000*a*d^4, z, k)^2*a^7*b*d*x))/(32768*a^9))*root(68719476736*a^15*b^2*z^4 + 838860800*a^8*b*d^2*z^2 - 485703680*a^4*b*c^2*d*z + 35153041*b*c^4 + 2560000*a*d^4, z, k), k, 1, 4) + ((11*d*x^2)/(32*a) + (51*c*x)/(128*a) + (77*b^2*c*x^9)/(384*a^3) + (5*b^2*d*x^10)/(32*a^3) + (33*b*c*x^5)/(64*a^2) + (5*b*d*x^6)/(12*a^2))/(a^3 + b^3*x^12 + 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
123,1,100,24,4.917599,"\text{Not used}","int(-(c + d*x)/(x^4 - 1),x)","-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left({\left(-1\right)}^{3/4}\,\sqrt{2}\,x+1\right)\,\left(\sqrt{2}\,c+2\,{\left(-1\right)}^{1/4}\,d\right)}{4}-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left({\left(-1\right)}^{3/4}\,\sqrt{2}\,x-1\right)\,\left(2\,\sqrt{2}\,c-4\,{\left(-1\right)}^{1/4}\,d\right)}{8}+\frac{{\left(-1\right)}^{1/4}\,\sqrt{2}\,c\,\ln\left(\frac{x^2+{\left(-1\right)}^{1/4}\,\sqrt{2}\,x+1{}\mathrm{i}}{x^2-{\left(-1\right)}^{1/4}\,\sqrt{2}\,x+1{}\mathrm{i}}\right)}{8}","Not used",1,"((-1)^(1/4)*2^(1/2)*c*log((x^2 + (-1)^(1/4)*2^(1/2)*x + 1i)/(x^2 - (-1)^(1/4)*2^(1/2)*x + 1i)))/8 - ((-1)^(1/4)*atan((-1)^(3/4)*2^(1/2)*x - 1)*(2*2^(1/2)*c - 4*(-1)^(1/4)*d))/8 - ((-1)^(1/4)*atan((-1)^(3/4)*2^(1/2)*x + 1)*(2^(1/2)*c + 2*(-1)^(1/4)*d))/4","B"
124,1,71,98,0.092027,"\text{Not used}","int((c + d*x)/(x^4 + 1),x)","\mathrm{atan}\left(\sqrt{2}\,x-1\right)\,\left(\frac{d}{2}+\frac{\sqrt{2}\,c}{4}\right)-\mathrm{atan}\left(\sqrt{2}\,x+1\right)\,\left(\frac{d}{2}-\frac{\sqrt{2}\,c}{4}\right)+\frac{\sqrt{2}\,c\,\ln\left(\frac{x^2+\sqrt{2}\,x+1}{x^2-\sqrt{2}\,x+1}\right)}{8}","Not used",1,"atan(2^(1/2)*x - 1)*(d/2 + (2^(1/2)*c)/4) - atan(2^(1/2)*x + 1)*(d/2 - (2^(1/2)*c)/4) + (2^(1/2)*c*log((2^(1/2)*x + x^2 + 1)/(x^2 - 2^(1/2)*x + 1)))/8","B"
125,1,725,116,5.142857,"\text{Not used}","int((c + d*x + e*x^2)/(a - b*x^4),x)","\sum _{k=1}^4\ln\left(-b^2\,c\,d^2+b^2\,c^2\,e-b^2\,d^3\,x-a\,b\,e^3-{\mathrm{root}\left(256\,a^3\,b^3\,z^4-64\,a^2\,b^2\,c\,e\,z^2-32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z+16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4-a^2\,e^4-b^2\,c^4,z,k\right)}^2\,a\,b^3\,c\,16-\mathrm{root}\left(256\,a^3\,b^3\,z^4-64\,a^2\,b^2\,c\,e\,z^2-32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z+16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4-a^2\,e^4-b^2\,c^4,z,k\right)\,b^3\,c^2\,x\,4+{\mathrm{root}\left(256\,a^3\,b^3\,z^4-64\,a^2\,b^2\,c\,e\,z^2-32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z+16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4-a^2\,e^4-b^2\,c^4,z,k\right)}^2\,a\,b^3\,d\,x\,16-\mathrm{root}\left(256\,a^3\,b^3\,z^4-64\,a^2\,b^2\,c\,e\,z^2-32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z+16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4-a^2\,e^4-b^2\,c^4,z,k\right)\,a\,b^2\,e^2\,x\,4+\mathrm{root}\left(256\,a^3\,b^3\,z^4-64\,a^2\,b^2\,c\,e\,z^2-32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z+16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4-a^2\,e^4-b^2\,c^4,z,k\right)\,a\,b^2\,d\,e\,8+2\,b^2\,c\,d\,e\,x\right)\,\mathrm{root}\left(256\,a^3\,b^3\,z^4-64\,a^2\,b^2\,c\,e\,z^2-32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z+16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4-a^2\,e^4-b^2\,c^4,z,k\right)","Not used",1,"symsum(log(b^2*c^2*e - b^2*c*d^2 - b^2*d^3*x - a*b*e^3 - 16*root(256*a^3*b^3*z^4 - 64*a^2*b^2*c*e*z^2 - 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z + 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 - a^2*e^4 - b^2*c^4, z, k)^2*a*b^3*c - 4*root(256*a^3*b^3*z^4 - 64*a^2*b^2*c*e*z^2 - 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z + 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 - a^2*e^4 - b^2*c^4, z, k)*b^3*c^2*x + 16*root(256*a^3*b^3*z^4 - 64*a^2*b^2*c*e*z^2 - 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z + 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 - a^2*e^4 - b^2*c^4, z, k)^2*a*b^3*d*x - 4*root(256*a^3*b^3*z^4 - 64*a^2*b^2*c*e*z^2 - 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z + 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 - a^2*e^4 - b^2*c^4, z, k)*a*b^2*e^2*x + 8*root(256*a^3*b^3*z^4 - 64*a^2*b^2*c*e*z^2 - 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z + 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 - a^2*e^4 - b^2*c^4, z, k)*a*b^2*d*e + 2*b^2*c*d*e*x)*root(256*a^3*b^3*z^4 - 64*a^2*b^2*c*e*z^2 - 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z + 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 - a^2*e^4 - b^2*c^4, z, k), k, 1, 4)","B"
126,1,712,277,5.085742,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^4),x)","\sum _{k=1}^4\ln\left(b^2\,c\,d^2-b^2\,c^2\,e+b^2\,d^3\,x-a\,b\,e^3-{\mathrm{root}\left(256\,a^3\,b^3\,z^4+64\,a^2\,b^2\,c\,e\,z^2+32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z-16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4+a^2\,e^4+b^2\,c^4,z,k\right)}^2\,a\,b^3\,c\,16-\mathrm{root}\left(256\,a^3\,b^3\,z^4+64\,a^2\,b^2\,c\,e\,z^2+32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z-16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4+a^2\,e^4+b^2\,c^4,z,k\right)\,b^3\,c^2\,x\,4+{\mathrm{root}\left(256\,a^3\,b^3\,z^4+64\,a^2\,b^2\,c\,e\,z^2+32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z-16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4+a^2\,e^4+b^2\,c^4,z,k\right)}^2\,a\,b^3\,d\,x\,16+\mathrm{root}\left(256\,a^3\,b^3\,z^4+64\,a^2\,b^2\,c\,e\,z^2+32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z-16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4+a^2\,e^4+b^2\,c^4,z,k\right)\,a\,b^2\,e^2\,x\,4-\mathrm{root}\left(256\,a^3\,b^3\,z^4+64\,a^2\,b^2\,c\,e\,z^2+32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z-16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4+a^2\,e^4+b^2\,c^4,z,k\right)\,a\,b^2\,d\,e\,8-2\,b^2\,c\,d\,e\,x\right)\,\mathrm{root}\left(256\,a^3\,b^3\,z^4+64\,a^2\,b^2\,c\,e\,z^2+32\,a^2\,b^2\,d^2\,z^2+16\,a^2\,b\,d\,e^2\,z-16\,a\,b^2\,c^2\,d\,z-4\,a\,b\,c\,d^2\,e+2\,a\,b\,c^2\,e^2+a\,b\,d^4+a^2\,e^4+b^2\,c^4,z,k\right)","Not used",1,"symsum(log(b^2*c*d^2 - b^2*c^2*e + b^2*d^3*x - a*b*e^3 - 16*root(256*a^3*b^3*z^4 + 64*a^2*b^2*c*e*z^2 + 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z - 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 + a^2*e^4 + b^2*c^4, z, k)^2*a*b^3*c - 4*root(256*a^3*b^3*z^4 + 64*a^2*b^2*c*e*z^2 + 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z - 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 + a^2*e^4 + b^2*c^4, z, k)*b^3*c^2*x + 16*root(256*a^3*b^3*z^4 + 64*a^2*b^2*c*e*z^2 + 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z - 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 + a^2*e^4 + b^2*c^4, z, k)^2*a*b^3*d*x + 4*root(256*a^3*b^3*z^4 + 64*a^2*b^2*c*e*z^2 + 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z - 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 + a^2*e^4 + b^2*c^4, z, k)*a*b^2*e^2*x - 8*root(256*a^3*b^3*z^4 + 64*a^2*b^2*c*e*z^2 + 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z - 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 + a^2*e^4 + b^2*c^4, z, k)*a*b^2*d*e - 2*b^2*c*d*e*x)*root(256*a^3*b^3*z^4 + 64*a^2*b^2*c*e*z^2 + 32*a^2*b^2*d^2*z^2 + 16*a^2*b*d*e^2*z - 16*a*b^2*c^2*d*z - 4*a*b*c*d^2*e + 2*a*b*c^2*e^2 + a*b*d^4 + a^2*e^4 + b^2*c^4, z, k), k, 1, 4)","B"
127,1,477,146,4.982019,"\text{Not used}","int((c + d*x + e*x^2)/(a - b*x^4)^2,x)","\frac{\frac{d\,x^2}{4\,a}+\frac{e\,x^3}{4\,a}+\frac{c\,x}{4\,a}}{a-b\,x^4}+\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^3\,z^4-3072\,a^4\,b^2\,c\,e\,z^2-2048\,a^4\,b^2\,d^2\,z^2+1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4-81\,b^2\,c^4-a^2\,e^4,z,k\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^3\,z^4-3072\,a^4\,b^2\,c\,e\,z^2-2048\,a^4\,b^2\,d^2\,z^2+1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4-81\,b^2\,c^4-a^2\,e^4,z,k\right)\,\left(12\,b^3\,c-8\,b^3\,d\,x\right)+\frac{x\,\left(4\,a^2\,b^2\,e^2+36\,a\,b^3\,c^2\right)}{16\,a^3}-\frac{b^2\,d\,e}{a}\right)-\frac{-9\,b^2\,c^2\,e+12\,b^2\,c\,d^2+a\,b\,e^3}{64\,a^3}-\frac{x\,\left(2\,b^2\,d^3-3\,b^2\,c\,d\,e\right)}{16\,a^3}\right)\,\mathrm{root}\left(65536\,a^7\,b^3\,z^4-3072\,a^4\,b^2\,c\,e\,z^2-2048\,a^4\,b^2\,d^2\,z^2+1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4-81\,b^2\,c^4-a^2\,e^4,z,k\right)\right)","Not used",1,"((d*x^2)/(4*a) + (e*x^3)/(4*a) + (c*x)/(4*a))/(a - b*x^4) + symsum(log(- root(65536*a^7*b^3*z^4 - 3072*a^4*b^2*c*e*z^2 - 2048*a^4*b^2*d^2*z^2 + 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 - 81*b^2*c^4 - a^2*e^4, z, k)*(root(65536*a^7*b^3*z^4 - 3072*a^4*b^2*c*e*z^2 - 2048*a^4*b^2*d^2*z^2 + 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 - 81*b^2*c^4 - a^2*e^4, z, k)*(12*b^3*c - 8*b^3*d*x) + (x*(36*a*b^3*c^2 + 4*a^2*b^2*e^2))/(16*a^3) - (b^2*d*e)/a) - (12*b^2*c*d^2 - 9*b^2*c^2*e + a*b*e^3)/(64*a^3) - (x*(2*b^2*d^3 - 3*b^2*c*d*e))/(16*a^3))*root(65536*a^7*b^3*z^4 - 3072*a^4*b^2*c*e*z^2 - 2048*a^4*b^2*d^2*z^2 + 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 - 81*b^2*c^4 - a^2*e^4, z, k), k, 1, 4)","B"
128,1,472,308,0.333291,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^4)^2,x)","\frac{\frac{d\,x^2}{4\,a}+\frac{e\,x^3}{4\,a}+\frac{c\,x}{4\,a}}{b\,x^4+a}+\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^3\,z^4+3072\,a^4\,b^2\,c\,e\,z^2+2048\,a^4\,b^2\,d^2\,z^2-1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4+81\,b^2\,c^4+a^2\,e^4,z,k\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^3\,z^4+3072\,a^4\,b^2\,c\,e\,z^2+2048\,a^4\,b^2\,d^2\,z^2-1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4+81\,b^2\,c^4+a^2\,e^4,z,k\right)\,\left(12\,b^3\,c-8\,b^3\,d\,x\right)+\frac{x\,\left(36\,a\,b^3\,c^2-4\,a^2\,b^2\,e^2\right)}{16\,a^3}+\frac{b^2\,d\,e}{a}\right)-\frac{9\,b^2\,c^2\,e-12\,b^2\,c\,d^2+a\,b\,e^3}{64\,a^3}+\frac{x\,\left(2\,b^2\,d^3-3\,b^2\,c\,d\,e\right)}{16\,a^3}\right)\,\mathrm{root}\left(65536\,a^7\,b^3\,z^4+3072\,a^4\,b^2\,c\,e\,z^2+2048\,a^4\,b^2\,d^2\,z^2-1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4+81\,b^2\,c^4+a^2\,e^4,z,k\right)\right)","Not used",1,"((d*x^2)/(4*a) + (e*x^3)/(4*a) + (c*x)/(4*a))/(a + b*x^4) + symsum(log((x*(2*b^2*d^3 - 3*b^2*c*d*e))/(16*a^3) - (9*b^2*c^2*e - 12*b^2*c*d^2 + a*b*e^3)/(64*a^3) - root(65536*a^7*b^3*z^4 + 3072*a^4*b^2*c*e*z^2 + 2048*a^4*b^2*d^2*z^2 - 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 + 81*b^2*c^4 + a^2*e^4, z, k)*(root(65536*a^7*b^3*z^4 + 3072*a^4*b^2*c*e*z^2 + 2048*a^4*b^2*d^2*z^2 - 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 + 81*b^2*c^4 + a^2*e^4, z, k)*(12*b^3*c - 8*b^3*d*x) + (x*(36*a*b^3*c^2 - 4*a^2*b^2*e^2))/(16*a^3) + (b^2*d*e)/a))*root(65536*a^7*b^3*z^4 + 3072*a^4*b^2*c*e*z^2 + 2048*a^4*b^2*d^2*z^2 - 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 + 81*b^2*c^4 + a^2*e^4, z, k), k, 1, 4)","B"
129,1,826,179,5.110530,"\text{Not used}","int((c + d*x + e*x^2)/(a - b*x^4)^3,x)","\frac{\frac{5\,d\,x^2}{16\,a}+\frac{9\,e\,x^3}{32\,a}+\frac{11\,c\,x}{32\,a}-\frac{7\,b\,c\,x^5}{32\,a^2}-\frac{3\,b\,d\,x^6}{16\,a^2}-\frac{5\,b\,e\,x^7}{32\,a^2}}{a^2-2\,a\,b\,x^4+b^2\,x^8}+\left(\sum _{k=1}^4\ln\left(-\frac{b\,\left(125\,a\,e^3+3024\,b\,c\,d^2-2205\,b\,c^2\,e+1728\,b\,d^3\,x+{\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)}^2\,a^5\,b^2\,c\,344064+\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)\,a^3\,b\,e^2\,x\,3200-2520\,b\,c\,d\,e\,x+\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)\,a^2\,b^2\,c^2\,x\,56448-{\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)}^2\,a^5\,b^2\,d\,x\,196608-\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)\,a^3\,b\,d\,e\,15360\right)}{a^6\,32768}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)\right)","Not used",1,"((5*d*x^2)/(16*a) + (9*e*x^3)/(32*a) + (11*c*x)/(32*a) - (7*b*c*x^5)/(32*a^2) - (3*b*d*x^6)/(16*a^2) - (5*b*e*x^7)/(32*a^2))/(a^2 + b^2*x^8 - 2*a*b*x^4) + symsum(log(-(b*(125*a*e^3 + 3024*b*c*d^2 - 2205*b*c^2*e + 1728*b*d^3*x + 344064*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)^2*a^5*b^2*c + 3200*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)*a^3*b*e^2*x - 2520*b*c*d*e*x + 56448*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)*a^2*b^2*c^2*x - 196608*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)^2*a^5*b^2*d*x - 15360*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)*a^3*b*d*e))/(32768*a^6))*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k), k, 1, 4)","B"
130,1,826,341,5.047316,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^4)^3,x)","\frac{\frac{5\,d\,x^2}{16\,a}+\frac{9\,e\,x^3}{32\,a}+\frac{11\,c\,x}{32\,a}+\frac{7\,b\,c\,x^5}{32\,a^2}+\frac{3\,b\,d\,x^6}{16\,a^2}+\frac{5\,b\,e\,x^7}{32\,a^2}}{a^2+2\,a\,b\,x^4+b^2\,x^8}+\left(\sum _{k=1}^4\ln\left(-\frac{b\,\left(125\,a\,e^3-3024\,b\,c\,d^2+2205\,b\,c^2\,e-1728\,b\,d^3\,x+{\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)}^2\,a^5\,b^2\,c\,344064-\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)\,a^3\,b\,e^2\,x\,3200+2520\,b\,c\,d\,e\,x+\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)\,a^2\,b^2\,c^2\,x\,56448-{\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)}^2\,a^5\,b^2\,d\,x\,196608+\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)\,a^3\,b\,d\,e\,15360\right)}{a^6\,32768}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)\right)","Not used",1,"((5*d*x^2)/(16*a) + (9*e*x^3)/(32*a) + (11*c*x)/(32*a) + (7*b*c*x^5)/(32*a^2) + (3*b*d*x^6)/(16*a^2) + (5*b*e*x^7)/(32*a^2))/(a^2 + b^2*x^8 + 2*a*b*x^4) + symsum(log(-(b*(125*a*e^3 - 3024*b*c*d^2 + 2205*b*c^2*e - 1728*b*d^3*x + 344064*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)^2*a^5*b^2*c - 3200*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)*a^3*b*e^2*x + 2520*b*c*d*e*x + 56448*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)*a^2*b^2*c^2*x - 196608*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)^2*a^5*b^2*d*x + 15360*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)*a^3*b*d*e))/(32768*a^6))*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k), k, 1, 4)","B"
131,1,874,211,5.220349,"\text{Not used}","int((c + d*x + e*x^2)/(a - b*x^4)^4,x)","\frac{\frac{11\,d\,x^2}{32\,a}+\frac{113\,e\,x^3}{384\,a}+\frac{51\,c\,x}{128\,a}+\frac{77\,b^2\,c\,x^9}{384\,a^3}+\frac{5\,b^2\,d\,x^{10}}{32\,a^3}+\frac{15\,b^2\,e\,x^{11}}{128\,a^3}-\frac{33\,b\,c\,x^5}{64\,a^2}-\frac{5\,b\,d\,x^6}{12\,a^2}-\frac{21\,b\,e\,x^7}{64\,a^2}}{a^3-3\,a^2\,b\,x^4+3\,a\,b^2\,x^8-b^3\,x^{12}}+\left(\sum _{k=1}^4\ln\left(-\frac{b\,\left(3375\,a\,e^3+123200\,b\,c\,d^2-88935\,b\,c^2\,e+64000\,b\,d^3\,x+{\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)}^2\,a^7\,b^2\,c\,20185088+\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)\,a^4\,b\,e^2\,x\,115200-92400\,b\,c\,d\,e\,x+\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)\,a^3\,b^2\,c^2\,x\,3035648-{\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)}^2\,a^7\,b^2\,d\,x\,10485760-\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)\,a^4\,b\,d\,e\,614400\right)}{a^9\,2097152}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)\right)","Not used",1,"((11*d*x^2)/(32*a) + (113*e*x^3)/(384*a) + (51*c*x)/(128*a) + (77*b^2*c*x^9)/(384*a^3) + (5*b^2*d*x^10)/(32*a^3) + (15*b^2*e*x^11)/(128*a^3) - (33*b*c*x^5)/(64*a^2) - (5*b*d*x^6)/(12*a^2) - (21*b*e*x^7)/(64*a^2))/(a^3 - b^3*x^12 - 3*a^2*b*x^4 + 3*a*b^2*x^8) + symsum(log(-(b*(3375*a*e^3 + 123200*b*c*d^2 - 88935*b*c^2*e + 64000*b*d^3*x + 20185088*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)^2*a^7*b^2*c + 115200*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)*a^4*b*e^2*x - 92400*b*c*d*e*x + 3035648*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)*a^3*b^2*c^2*x - 10485760*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)^2*a^7*b^2*d*x - 614400*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)*a^4*b*d*e))/(2097152*a^9))*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k), k, 1, 4)","B"
132,1,873,372,5.137181,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^4)^4,x)","\frac{\frac{11\,d\,x^2}{32\,a}+\frac{113\,e\,x^3}{384\,a}+\frac{51\,c\,x}{128\,a}+\frac{77\,b^2\,c\,x^9}{384\,a^3}+\frac{5\,b^2\,d\,x^{10}}{32\,a^3}+\frac{15\,b^2\,e\,x^{11}}{128\,a^3}+\frac{33\,b\,c\,x^5}{64\,a^2}+\frac{5\,b\,d\,x^6}{12\,a^2}+\frac{21\,b\,e\,x^7}{64\,a^2}}{a^3+3\,a^2\,b\,x^4+3\,a\,b^2\,x^8+b^3\,x^{12}}+\left(\sum _{k=1}^4\ln\left(-\frac{b\,\left(3375\,a\,e^3-123200\,b\,c\,d^2+88935\,b\,c^2\,e-64000\,b\,d^3\,x+{\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)}^2\,a^7\,b^2\,c\,20185088-\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)\,a^4\,b\,e^2\,x\,115200+92400\,b\,c\,d\,e\,x+\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)\,a^3\,b^2\,c^2\,x\,3035648-{\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)}^2\,a^7\,b^2\,d\,x\,10485760+\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)\,a^4\,b\,d\,e\,614400\right)}{a^9\,2097152}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)\right)","Not used",1,"((11*d*x^2)/(32*a) + (113*e*x^3)/(384*a) + (51*c*x)/(128*a) + (77*b^2*c*x^9)/(384*a^3) + (5*b^2*d*x^10)/(32*a^3) + (15*b^2*e*x^11)/(128*a^3) + (33*b*c*x^5)/(64*a^2) + (5*b*d*x^6)/(12*a^2) + (21*b*e*x^7)/(64*a^2))/(a^3 + b^3*x^12 + 3*a^2*b*x^4 + 3*a*b^2*x^8) + symsum(log(-(b*(3375*a*e^3 - 123200*b*c*d^2 + 88935*b*c^2*e - 64000*b*d^3*x + 20185088*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)^2*a^7*b^2*c - 115200*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)*a^4*b*e^2*x + 92400*b*c*d*e*x + 3035648*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)*a^3*b^2*c^2*x - 10485760*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)^2*a^7*b^2*d*x + 614400*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)*a^4*b*d*e))/(2097152*a^9))*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k), k, 1, 4)","B"
133,1,25,28,4.673714,"\text{Not used}","int(a*(e + f*x^4)^2,x)","\frac{a\,x\,\left(45\,e^2+18\,e\,f\,x^4+5\,f^2\,x^8\right)}{45}","Not used",1,"(a*x*(45*e^2 + 5*f^2*x^8 + 18*e*f*x^4))/45","B"
134,1,27,33,0.034270,"\text{Not used}","int(b*x*(e + f*x^4)^2,x)","\frac{b\,x^2\,\left(15\,e^2+10\,e\,f\,x^4+3\,f^2\,x^8\right)}{30}","Not used",1,"(b*x^2*(15*e^2 + 3*f^2*x^8 + 10*e*f*x^4))/30","B"
135,1,50,60,0.024700,"\text{Not used}","int((e + f*x^4)^2*(a + b*x),x)","\frac{b\,e^2\,x^2}{2}+a\,e^2\,x+\frac{b\,e\,f\,x^6}{3}+\frac{2\,a\,e\,f\,x^5}{5}+\frac{b\,f^2\,x^{10}}{10}+\frac{a\,f^2\,x^9}{9}","Not used",1,"(b*e^2*x^2)/2 + (a*f^2*x^9)/9 + (b*f^2*x^10)/10 + a*e^2*x + (2*a*e*f*x^5)/5 + (b*e*f*x^6)/3","B"
136,1,27,33,0.038572,"\text{Not used}","int(c*x^2*(e + f*x^4)^2,x)","\frac{c\,x^3\,\left(77\,e^2+66\,e\,f\,x^4+21\,f^2\,x^8\right)}{231}","Not used",1,"(c*x^3*(77*e^2 + 21*f^2*x^8 + 66*e*f*x^4))/231","B"
137,1,50,60,0.025313,"\text{Not used}","int((a + c*x^2)*(e + f*x^4)^2,x)","\frac{c\,e^2\,x^3}{3}+a\,e^2\,x+\frac{2\,c\,e\,f\,x^7}{7}+\frac{2\,a\,e\,f\,x^5}{5}+\frac{c\,f^2\,x^{11}}{11}+\frac{a\,f^2\,x^9}{9}","Not used",1,"(a*f^2*x^9)/9 + (c*e^2*x^3)/3 + (c*f^2*x^11)/11 + a*e^2*x + (2*a*e*f*x^5)/5 + (2*c*e*f*x^7)/7","B"
138,1,53,65,0.026718,"\text{Not used}","int((b*x + c*x^2)*(e + f*x^4)^2,x)","\frac{c\,e^2\,x^3}{3}+\frac{b\,e^2\,x^2}{2}+\frac{2\,c\,e\,f\,x^7}{7}+\frac{b\,e\,f\,x^6}{3}+\frac{c\,f^2\,x^{11}}{11}+\frac{b\,f^2\,x^{10}}{10}","Not used",1,"(b*e^2*x^2)/2 + (c*e^2*x^3)/3 + (b*f^2*x^10)/10 + (c*f^2*x^11)/11 + (b*e*f*x^6)/3 + (2*c*e*f*x^7)/7","B"
139,1,76,92,0.038427,"\text{Not used}","int((e + f*x^4)^2*(a + b*x + c*x^2),x)","\frac{c\,e^2\,x^3}{3}+\frac{b\,e^2\,x^2}{2}+a\,e^2\,x+\frac{2\,c\,e\,f\,x^7}{7}+\frac{b\,e\,f\,x^6}{3}+\frac{2\,a\,e\,f\,x^5}{5}+\frac{c\,f^2\,x^{11}}{11}+\frac{b\,f^2\,x^{10}}{10}+\frac{a\,f^2\,x^9}{9}","Not used",1,"(b*e^2*x^2)/2 + (a*f^2*x^9)/9 + (c*e^2*x^3)/3 + (b*f^2*x^10)/10 + (c*f^2*x^11)/11 + a*e^2*x + (2*a*e*f*x^5)/5 + (b*e*f*x^6)/3 + (2*c*e*f*x^7)/7","B"
140,1,26,17,0.033007,"\text{Not used}","int(d*x^3*(e + f*x^4)^2,x)","\frac{d\,x^4\,\left(3\,e^2+3\,e\,f\,x^4+f^2\,x^8\right)}{12}","Not used",1,"(d*x^4*(3*e^2 + f^2*x^8 + 3*e*f*x^4))/12","B"
141,1,50,45,0.024376,"\text{Not used}","int((a + d*x^3)*(e + f*x^4)^2,x)","\frac{d\,e^2\,x^4}{4}+a\,e^2\,x+\frac{d\,e\,f\,x^8}{4}+\frac{2\,a\,e\,f\,x^5}{5}+\frac{d\,f^2\,x^{12}}{12}+\frac{a\,f^2\,x^9}{9}","Not used",1,"(a*f^2*x^9)/9 + (d*e^2*x^4)/4 + (d*f^2*x^12)/12 + a*e^2*x + (2*a*e*f*x^5)/5 + (d*e*f*x^8)/4","B"
142,1,53,50,0.027382,"\text{Not used}","int((b*x + d*x^3)*(e + f*x^4)^2,x)","\frac{d\,e^2\,x^4}{4}+\frac{b\,e^2\,x^2}{2}+\frac{d\,e\,f\,x^8}{4}+\frac{b\,e\,f\,x^6}{3}+\frac{d\,f^2\,x^{12}}{12}+\frac{b\,f^2\,x^{10}}{10}","Not used",1,"(b*e^2*x^2)/2 + (b*f^2*x^10)/10 + (d*e^2*x^4)/4 + (d*f^2*x^12)/12 + (b*e*f*x^6)/3 + (d*e*f*x^8)/4","B"
143,1,76,77,0.037867,"\text{Not used}","int((e + f*x^4)^2*(a + b*x + d*x^3),x)","\frac{d\,e^2\,x^4}{4}+\frac{b\,e^2\,x^2}{2}+a\,e^2\,x+\frac{d\,e\,f\,x^8}{4}+\frac{b\,e\,f\,x^6}{3}+\frac{2\,a\,e\,f\,x^5}{5}+\frac{d\,f^2\,x^{12}}{12}+\frac{b\,f^2\,x^{10}}{10}+\frac{a\,f^2\,x^9}{9}","Not used",1,"(b*e^2*x^2)/2 + (a*f^2*x^9)/9 + (b*f^2*x^10)/10 + (d*e^2*x^4)/4 + (d*f^2*x^12)/12 + a*e^2*x + (2*a*e*f*x^5)/5 + (b*e*f*x^6)/3 + (d*e*f*x^8)/4","B"
144,1,53,50,0.027053,"\text{Not used}","int((e + f*x^4)^2*(c*x^2 + d*x^3),x)","\frac{d\,e^2\,x^4}{4}+\frac{c\,e^2\,x^3}{3}+\frac{d\,e\,f\,x^8}{4}+\frac{2\,c\,e\,f\,x^7}{7}+\frac{d\,f^2\,x^{12}}{12}+\frac{c\,f^2\,x^{11}}{11}","Not used",1,"(c*e^2*x^3)/3 + (d*e^2*x^4)/4 + (c*f^2*x^11)/11 + (d*f^2*x^12)/12 + (2*c*e*f*x^7)/7 + (d*e*f*x^8)/4","B"
145,1,76,77,0.037882,"\text{Not used}","int((e + f*x^4)^2*(a + c*x^2 + d*x^3),x)","\frac{d\,e^2\,x^4}{4}+\frac{c\,e^2\,x^3}{3}+a\,e^2\,x+\frac{d\,e\,f\,x^8}{4}+\frac{2\,c\,e\,f\,x^7}{7}+\frac{2\,a\,e\,f\,x^5}{5}+\frac{d\,f^2\,x^{12}}{12}+\frac{c\,f^2\,x^{11}}{11}+\frac{a\,f^2\,x^9}{9}","Not used",1,"(a*f^2*x^9)/9 + (c*e^2*x^3)/3 + (d*e^2*x^4)/4 + (c*f^2*x^11)/11 + (d*f^2*x^12)/12 + a*e^2*x + (2*a*e*f*x^5)/5 + (2*c*e*f*x^7)/7 + (d*e*f*x^8)/4","B"
146,1,79,82,0.040584,"\text{Not used}","int((e + f*x^4)^2*(b*x + c*x^2 + d*x^3),x)","\frac{d\,e^2\,x^4}{4}+\frac{c\,e^2\,x^3}{3}+\frac{b\,e^2\,x^2}{2}+\frac{d\,e\,f\,x^8}{4}+\frac{2\,c\,e\,f\,x^7}{7}+\frac{b\,e\,f\,x^6}{3}+\frac{d\,f^2\,x^{12}}{12}+\frac{c\,f^2\,x^{11}}{11}+\frac{b\,f^2\,x^{10}}{10}","Not used",1,"(b*e^2*x^2)/2 + (c*e^2*x^3)/3 + (b*f^2*x^10)/10 + (d*e^2*x^4)/4 + (c*f^2*x^11)/11 + (d*f^2*x^12)/12 + (b*e*f*x^6)/3 + (2*c*e*f*x^7)/7 + (d*e*f*x^8)/4","B"
147,1,102,109,4.677162,"\text{Not used}","int((a + b*x^4)^2*(c + d*x + e*x^2 + f*x^3),x)","\frac{f\,a^2\,x^4}{4}+\frac{e\,a^2\,x^3}{3}+\frac{d\,a^2\,x^2}{2}+c\,a^2\,x+\frac{f\,a\,b\,x^8}{4}+\frac{2\,e\,a\,b\,x^7}{7}+\frac{d\,a\,b\,x^6}{3}+\frac{2\,c\,a\,b\,x^5}{5}+\frac{f\,b^2\,x^{12}}{12}+\frac{e\,b^2\,x^{11}}{11}+\frac{d\,b^2\,x^{10}}{10}+\frac{c\,b^2\,x^9}{9}","Not used",1,"(a^2*d*x^2)/2 + (b^2*c*x^9)/9 + (a^2*e*x^3)/3 + (b^2*d*x^10)/10 + (a^2*f*x^4)/4 + (b^2*e*x^11)/11 + (b^2*f*x^12)/12 + a^2*c*x + (2*a*b*c*x^5)/5 + (a*b*d*x^6)/3 + (2*a*b*e*x^7)/7 + (a*b*f*x^8)/4","B"
148,1,150,151,4.863441,"\text{Not used}","int((a + b*x^4)^3*(c + d*x + e*x^2 + f*x^3),x)","\frac{f\,a^3\,x^4}{4}+\frac{e\,a^3\,x^3}{3}+\frac{d\,a^3\,x^2}{2}+c\,a^3\,x+\frac{3\,f\,a^2\,b\,x^8}{8}+\frac{3\,e\,a^2\,b\,x^7}{7}+\frac{d\,a^2\,b\,x^6}{2}+\frac{3\,c\,a^2\,b\,x^5}{5}+\frac{f\,a\,b^2\,x^{12}}{4}+\frac{3\,e\,a\,b^2\,x^{11}}{11}+\frac{3\,d\,a\,b^2\,x^{10}}{10}+\frac{c\,a\,b^2\,x^9}{3}+\frac{f\,b^3\,x^{16}}{16}+\frac{e\,b^3\,x^{15}}{15}+\frac{d\,b^3\,x^{14}}{14}+\frac{c\,b^3\,x^{13}}{13}","Not used",1,"(a^3*d*x^2)/2 + (b^3*c*x^13)/13 + (a^3*e*x^3)/3 + (b^3*d*x^14)/14 + (a^3*f*x^4)/4 + (b^3*e*x^15)/15 + (b^3*f*x^16)/16 + a^3*c*x + (3*a^2*b*c*x^5)/5 + (a*b^2*c*x^9)/3 + (a^2*b*d*x^6)/2 + (3*a*b^2*d*x^10)/10 + (3*a^2*b*e*x^7)/7 + (3*a*b^2*e*x^11)/11 + (3*a^2*b*f*x^8)/8 + (a*b^2*f*x^12)/4","B"
149,1,483,155,0.414533,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a - b*x^4)^2,x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^3\,z^4-3072\,a^4\,b^2\,c\,e\,z^2-2048\,a^4\,b^2\,d^2\,z^2+1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4-81\,b^2\,c^4-a^2\,e^4,z,k\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^3\,z^4-3072\,a^4\,b^2\,c\,e\,z^2-2048\,a^4\,b^2\,d^2\,z^2+1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4-81\,b^2\,c^4-a^2\,e^4,z,k\right)\,\left(12\,b^3\,c-8\,b^3\,d\,x\right)+\frac{x\,\left(4\,a^2\,b^2\,e^2+36\,a\,b^3\,c^2\right)}{16\,a^3}-\frac{b^2\,d\,e}{a}\right)-\frac{-9\,b^2\,c^2\,e+12\,b^2\,c\,d^2+a\,b\,e^3}{64\,a^3}-\frac{x\,\left(2\,b^2\,d^3-3\,b^2\,c\,d\,e\right)}{16\,a^3}\right)\,\mathrm{root}\left(65536\,a^7\,b^3\,z^4-3072\,a^4\,b^2\,c\,e\,z^2-2048\,a^4\,b^2\,d^2\,z^2+1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4-81\,b^2\,c^4-a^2\,e^4,z,k\right)\right)+\frac{\frac{f}{4\,b}+\frac{d\,x^2}{4\,a}+\frac{e\,x^3}{4\,a}+\frac{c\,x}{4\,a}}{a-b\,x^4}","Not used",1,"symsum(log(- root(65536*a^7*b^3*z^4 - 3072*a^4*b^2*c*e*z^2 - 2048*a^4*b^2*d^2*z^2 + 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 - 81*b^2*c^4 - a^2*e^4, z, k)*(root(65536*a^7*b^3*z^4 - 3072*a^4*b^2*c*e*z^2 - 2048*a^4*b^2*d^2*z^2 + 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 - 81*b^2*c^4 - a^2*e^4, z, k)*(12*b^3*c - 8*b^3*d*x) + (x*(36*a*b^3*c^2 + 4*a^2*b^2*e^2))/(16*a^3) - (b^2*d*e)/a) - (12*b^2*c*d^2 - 9*b^2*c^2*e + a*b*e^3)/(64*a^3) - (x*(2*b^2*d^3 - 3*b^2*c*d*e))/(16*a^3))*root(65536*a^7*b^3*z^4 - 3072*a^4*b^2*c*e*z^2 - 2048*a^4*b^2*d^2*z^2 + 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 - 81*b^2*c^4 - a^2*e^4, z, k), k, 1, 4) + (f/(4*b) + (d*x^2)/(4*a) + (e*x^3)/(4*a) + (c*x)/(4*a))/(a - b*x^4)","B"
150,1,832,188,5.184838,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a - b*x^4)^3,x)","\left(\sum _{k=1}^4\ln\left(-\frac{b\,\left(125\,a\,e^3+3024\,b\,c\,d^2-2205\,b\,c^2\,e+1728\,b\,d^3\,x+{\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)}^2\,a^5\,b^2\,c\,344064+\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)\,a^3\,b\,e^2\,x\,3200-2520\,b\,c\,d\,e\,x+\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)\,a^2\,b^2\,c^2\,x\,56448-{\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)}^2\,a^5\,b^2\,d\,x\,196608-\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)\,a^3\,b\,d\,e\,15360\right)}{a^6\,32768}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4-6881280\,a^6\,b^2\,c\,e\,z^2-4718592\,a^6\,b^2\,d^2\,z^2+2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4-625\,a^2\,e^4-194481\,b^2\,c^4,z,k\right)\right)+\frac{\frac{f}{8\,b}+\frac{5\,d\,x^2}{16\,a}+\frac{9\,e\,x^3}{32\,a}+\frac{11\,c\,x}{32\,a}-\frac{7\,b\,c\,x^5}{32\,a^2}-\frac{3\,b\,d\,x^6}{16\,a^2}-\frac{5\,b\,e\,x^7}{32\,a^2}}{a^2-2\,a\,b\,x^4+b^2\,x^8}","Not used",1,"symsum(log(-(b*(125*a*e^3 + 3024*b*c*d^2 - 2205*b*c^2*e + 1728*b*d^3*x + 344064*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)^2*a^5*b^2*c + 3200*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)*a^3*b*e^2*x - 2520*b*c*d*e*x + 56448*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)*a^2*b^2*c^2*x - 196608*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)^2*a^5*b^2*d*x - 15360*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k)*a^3*b*d*e))/(32768*a^6))*root(268435456*a^11*b^3*z^4 - 6881280*a^6*b^2*c*e*z^2 - 4718592*a^6*b^2*d^2*z^2 + 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 - 625*a^2*e^4 - 194481*b^2*c^4, z, k), k, 1, 4) + (f/(8*b) + (5*d*x^2)/(16*a) + (9*e*x^3)/(32*a) + (11*c*x)/(32*a) - (7*b*c*x^5)/(32*a^2) - (3*b*d*x^6)/(16*a^2) - (5*b*e*x^7)/(32*a^2))/(a^2 + b^2*x^8 - 2*a*b*x^4)","B"
151,1,880,220,5.245871,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a - b*x^4)^4,x)","\left(\sum _{k=1}^4\ln\left(-\frac{b\,\left(3375\,a\,e^3+123200\,b\,c\,d^2-88935\,b\,c^2\,e+64000\,b\,d^3\,x+{\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)}^2\,a^7\,b^2\,c\,20185088+\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)\,a^4\,b\,e^2\,x\,115200-92400\,b\,c\,d\,e\,x+\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)\,a^3\,b^2\,c^2\,x\,3035648-{\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)}^2\,a^7\,b^2\,d\,x\,10485760-\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)\,a^4\,b\,d\,e\,614400\right)}{a^9\,2097152}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4-1211105280\,a^8\,b^2\,c\,e\,z^2-838860800\,a^8\,b^2\,d^2\,z^2+485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4-35153041\,b^2\,c^4-50625\,a^2\,e^4,z,k\right)\right)+\frac{\frac{f}{12\,b}+\frac{11\,d\,x^2}{32\,a}+\frac{113\,e\,x^3}{384\,a}+\frac{51\,c\,x}{128\,a}+\frac{77\,b^2\,c\,x^9}{384\,a^3}+\frac{5\,b^2\,d\,x^{10}}{32\,a^3}+\frac{15\,b^2\,e\,x^{11}}{128\,a^3}-\frac{33\,b\,c\,x^5}{64\,a^2}-\frac{5\,b\,d\,x^6}{12\,a^2}-\frac{21\,b\,e\,x^7}{64\,a^2}}{a^3-3\,a^2\,b\,x^4+3\,a\,b^2\,x^8-b^3\,x^{12}}","Not used",1,"symsum(log(-(b*(3375*a*e^3 + 123200*b*c*d^2 - 88935*b*c^2*e + 64000*b*d^3*x + 20185088*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)^2*a^7*b^2*c + 115200*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)*a^4*b*e^2*x - 92400*b*c*d*e*x + 3035648*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)*a^3*b^2*c^2*x - 10485760*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)^2*a^7*b^2*d*x - 614400*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k)*a^4*b*d*e))/(2097152*a^9))*root(68719476736*a^15*b^3*z^4 - 1211105280*a^8*b^2*c*e*z^2 - 838860800*a^8*b^2*d^2*z^2 + 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 - 35153041*b^2*c^4 - 50625*a^2*e^4, z, k), k, 1, 4) + (f/(12*b) + (11*d*x^2)/(32*a) + (113*e*x^3)/(384*a) + (51*c*x)/(128*a) + (77*b^2*c*x^9)/(384*a^3) + (5*b^2*d*x^10)/(32*a^3) + (15*b^2*e*x^11)/(128*a^3) - (33*b*c*x^5)/(64*a^2) - (5*b*d*x^6)/(12*a^2) - (21*b*e*x^7)/(64*a^2))/(a^3 - b^3*x^12 - 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
152,1,36,101,0.124707,"\text{Not used}","int(a/(3*x^4 + 2),x)","-\frac{{\left(-1\right)}^{1/4}\,{6144}^{3/4}\,a\,\left(\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,{6144}^{1/4}\,x}{8}\right)\,1{}\mathrm{i}+\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,{6144}^{1/4}\,x}{8}\right)\,1{}\mathrm{i}\right)}{3072}","Not used",1,"-((-1)^(1/4)*6144^(3/4)*a*(atan(((-1)^(1/4)*6144^(1/4)*x)/8)*1i + atanh(((-1)^(1/4)*6144^(1/4)*x)/8)*1i))/3072","B"
153,1,15,22,4.773564,"\text{Not used}","int((b*x)/(3*x^4 + 2),x)","\frac{\sqrt{6}\,b\,\mathrm{atan}\left(\frac{\sqrt{6}\,x^2}{2}\right)}{12}","Not used",1,"(6^(1/2)*b*atan((6^(1/2)*x^2)/2))/12","B"
154,1,119,123,0.200496,"\text{Not used}","int((a + b*x)/(3*x^4 + 2),x)","\frac{2^{3/4}\,3^{3/4}\,a\,\ln\left(x^2+\frac{6^{3/4}\,x}{3}+\frac{\sqrt{6}}{3}\right)}{48}-\frac{2^{3/4}\,3^{3/4}\,a\,\ln\left(x^2-\frac{6^{3/4}\,x}{3}+\frac{\sqrt{6}}{3}\right)}{48}+\frac{2^{3/4}\,3^{3/4}\,a\,\mathrm{atan}\left(6^{1/4}\,x-1\right)}{24}+\frac{2^{3/4}\,3^{3/4}\,a\,\mathrm{atan}\left(6^{1/4}\,x+1\right)}{24}+\frac{\sqrt{2}\,\sqrt{3}\,b\,\mathrm{atan}\left(6^{1/4}\,x-1\right)}{12}-\frac{\sqrt{2}\,\sqrt{3}\,b\,\mathrm{atan}\left(6^{1/4}\,x+1\right)}{12}","Not used",1,"(2^(3/4)*3^(3/4)*a*log((6^(3/4)*x)/3 + 6^(1/2)/3 + x^2))/48 - (2^(3/4)*3^(3/4)*a*log(6^(1/2)/3 - (6^(3/4)*x)/3 + x^2))/48 + (2^(3/4)*3^(3/4)*a*atan(6^(1/4)*x - 1))/24 + (2^(3/4)*3^(3/4)*a*atan(6^(1/4)*x + 1))/24 + (2^(1/2)*3^(1/2)*b*atan(6^(1/4)*x - 1))/12 - (2^(1/2)*3^(1/2)*b*atan(6^(1/4)*x + 1))/12","B"
155,1,32,101,4.974139,"\text{Not used}","int((c*x^2)/(3*x^4 + 2),x)","\frac{{\left(-1\right)}^{1/4}\,{24}^{1/4}\,c\,\left(\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,{24}^{1/4}\,x}{2}\right)-\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,{24}^{1/4}\,x}{2}\right)\right)}{12}","Not used",1,"((-1)^(1/4)*24^(1/4)*c*(atan(((-1)^(1/4)*24^(1/4)*x)/2) - atanh(((-1)^(1/4)*24^(1/4)*x)/2)))/12","B"
156,1,315,141,5.110260,"\text{Not used}","int((a + c*x^2)/(3*x^4 + 2),x)","-2\,\mathrm{atanh}\left(\frac{216\,a^2\,x\,\sqrt{-\frac{1{}\mathrm{i}\,\sqrt{6}\,a^2}{192}-\frac{a\,c}{48}+\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{288}}}{9{}\mathrm{i}\,\sqrt{6}\,a^3+18\,a^2\,c-6{}\mathrm{i}\,\sqrt{6}\,a\,c^2-12\,c^3}-\frac{144\,c^2\,x\,\sqrt{-\frac{1{}\mathrm{i}\,\sqrt{6}\,a^2}{192}-\frac{a\,c}{48}+\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{288}}}{9{}\mathrm{i}\,\sqrt{6}\,a^3+18\,a^2\,c-6{}\mathrm{i}\,\sqrt{6}\,a\,c^2-12\,c^3}\right)\,\sqrt{-\frac{1{}\mathrm{i}\,\sqrt{6}\,a^2}{192}-\frac{a\,c}{48}+\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{288}}+2\,\mathrm{atanh}\left(\frac{216\,a^2\,x\,\sqrt{\frac{1{}\mathrm{i}\,\sqrt{6}\,a^2}{192}-\frac{a\,c}{48}-\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{288}}}{9{}\mathrm{i}\,\sqrt{6}\,a^3-18\,a^2\,c-6{}\mathrm{i}\,\sqrt{6}\,a\,c^2+12\,c^3}-\frac{144\,c^2\,x\,\sqrt{\frac{1{}\mathrm{i}\,\sqrt{6}\,a^2}{192}-\frac{a\,c}{48}-\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{288}}}{9{}\mathrm{i}\,\sqrt{6}\,a^3-18\,a^2\,c-6{}\mathrm{i}\,\sqrt{6}\,a\,c^2+12\,c^3}\right)\,\sqrt{\frac{1{}\mathrm{i}\,\sqrt{6}\,a^2}{192}-\frac{a\,c}{48}-\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{288}}","Not used",1,"2*atanh((216*a^2*x*((6^(1/2)*a^2*1i)/192 - (a*c)/48 - (6^(1/2)*c^2*1i)/288)^(1/2))/(6^(1/2)*a^3*9i - 18*a^2*c + 12*c^3 - 6^(1/2)*a*c^2*6i) - (144*c^2*x*((6^(1/2)*a^2*1i)/192 - (a*c)/48 - (6^(1/2)*c^2*1i)/288)^(1/2))/(6^(1/2)*a^3*9i - 18*a^2*c + 12*c^3 - 6^(1/2)*a*c^2*6i))*((6^(1/2)*a^2*1i)/192 - (a*c)/48 - (6^(1/2)*c^2*1i)/288)^(1/2) - 2*atanh((216*a^2*x*((6^(1/2)*c^2*1i)/288 - (6^(1/2)*a^2*1i)/192 - (a*c)/48)^(1/2))/(6^(1/2)*a^3*9i + 18*a^2*c - 12*c^3 - 6^(1/2)*a*c^2*6i) - (144*c^2*x*((6^(1/2)*c^2*1i)/288 - (6^(1/2)*a^2*1i)/192 - (a*c)/48)^(1/2))/(6^(1/2)*a^3*9i + 18*a^2*c - 12*c^3 - 6^(1/2)*a*c^2*6i))*((6^(1/2)*c^2*1i)/288 - (6^(1/2)*a^2*1i)/192 - (a*c)/48)^(1/2)","B"
157,1,162,123,0.217489,"\text{Not used}","int((b*x + c*x^2)/(3*x^4 + 2),x)","\sum _{k=1}^4\ln\left(9\,b^3\,x-6\,c^3-\mathrm{root}\left(z^4+\frac{b^2\,z^2}{48}+\frac{b\,c^2\,z}{288}+\frac{c^4}{13824}+\frac{b^4}{9216},z,k\right)\,b\,c\,144+{\mathrm{root}\left(z^4+\frac{b^2\,z^2}{48}+\frac{b\,c^2\,z}{288}+\frac{c^4}{13824}+\frac{b^4}{9216},z,k\right)}^2\,b\,x\,864+\mathrm{root}\left(z^4+\frac{b^2\,z^2}{48}+\frac{b\,c^2\,z}{288}+\frac{c^4}{13824}+\frac{b^4}{9216},z,k\right)\,c^2\,x\,72\right)\,\mathrm{root}\left(z^4+\frac{b^2\,z^2}{48}+\frac{b\,c^2\,z}{288}+\frac{c^4}{13824}+\frac{b^4}{9216},z,k\right)","Not used",1,"symsum(log(9*b^3*x - 6*c^3 - 144*root(z^4 + (b^2*z^2)/48 + (b*c^2*z)/288 + c^4/13824 + b^4/9216, z, k)*b*c + 864*root(z^4 + (b^2*z^2)/48 + (b*c^2*z)/288 + c^4/13824 + b^4/9216, z, k)^2*b*x + 72*root(z^4 + (b^2*z^2)/48 + (b*c^2*z)/288 + c^4/13824 + b^4/9216, z, k)*c^2*x)*root(z^4 + (b^2*z^2)/48 + (b*c^2*z)/288 + c^4/13824 + b^4/9216, z, k), k, 1, 4)","B"
158,1,270,163,5.519050,"\text{Not used}","int((a + b*x + c*x^2)/(3*x^4 + 2),x)","\sum _{k=1}^4\ln\left(9\,a\,b^2-9\,a^2\,c-\mathrm{root}\left(z^4+\frac{z^2\,\left(2304\,a\,c+1152\,b^2\right)}{55296}-\frac{z\,\left(288\,a^2\,b-192\,b\,c^2\right)}{55296}-\frac{a\,b^2\,c}{2304}+\frac{a^2\,c^2}{4608}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)\,\left(\mathrm{root}\left(z^4+\frac{z^2\,\left(2304\,a\,c+1152\,b^2\right)}{55296}-\frac{z\,\left(288\,a^2\,b-192\,b\,c^2\right)}{55296}-\frac{a\,b^2\,c}{2304}+\frac{a^2\,c^2}{4608}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)\,\left(864\,a-864\,b\,x\right)+144\,b\,c+x\,\left(108\,a^2-72\,c^2\right)\right)-6\,c^3+x\,\left(9\,b^3-18\,a\,b\,c\right)\right)\,\mathrm{root}\left(z^4+\frac{z^2\,\left(2304\,a\,c+1152\,b^2\right)}{55296}-\frac{z\,\left(288\,a^2\,b-192\,b\,c^2\right)}{55296}-\frac{a\,b^2\,c}{2304}+\frac{a^2\,c^2}{4608}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)","Not used",1,"symsum(log(9*a*b^2 - 9*a^2*c - root(z^4 + (z^2*(2304*a*c + 1152*b^2))/55296 - (z*(288*a^2*b - 192*b*c^2))/55296 - (a*b^2*c)/2304 + (a^2*c^2)/4608 + c^4/13824 + b^4/9216 + a^4/6144, z, k)*(root(z^4 + (z^2*(2304*a*c + 1152*b^2))/55296 - (z*(288*a^2*b - 192*b*c^2))/55296 - (a*b^2*c)/2304 + (a^2*c^2)/4608 + c^4/13824 + b^4/9216 + a^4/6144, z, k)*(864*a - 864*b*x) + 144*b*c + x*(108*a^2 - 72*c^2)) - 6*c^3 + x*(9*b^3 - 18*a*b*c))*root(z^4 + (z^2*(2304*a*c + 1152*b^2))/55296 - (z*(288*a^2*b - 192*b*c^2))/55296 - (a*b^2*c)/2304 + (a^2*c^2)/4608 + c^4/13824 + b^4/9216 + a^4/6144, z, k), k, 1, 4)","B"
159,1,9,13,0.030187,"\text{Not used}","int((d*x^3)/(3*x^4 + 2),x)","\frac{d\,\ln\left(x^4+\frac{2}{3}\right)}{12}","Not used",1,"(d*log(x^4 + 2/3))/12","B"
160,1,117,114,0.283497,"\text{Not used}","int((a + d*x^3)/(3*x^4 + 2),x)","\ln\left(x-\frac{{\left(-1\right)}^{1/4}\,2^{1/4}\,3^{3/4}}{3}\right)\,\left(\frac{d}{12}-\frac{6^{1/4}\,\sqrt{\frac{3}{4}{}\mathrm{i}}\,a}{12}\right)+\ln\left(x+\frac{{\left(-1\right)}^{1/4}\,2^{1/4}\,3^{3/4}}{3}\right)\,\left(\frac{d}{12}+\frac{6^{1/4}\,\sqrt{\frac{3}{4}{}\mathrm{i}}\,a}{12}\right)+\ln\left(x-\frac{{\left(-1\right)}^{3/4}\,2^{1/4}\,3^{3/4}}{3}\right)\,\left(\frac{d}{12}+\frac{6^{1/4}\,\sqrt{-\frac{3}{4}{}\mathrm{i}}\,a}{12}\right)+\ln\left(x+\frac{{\left(-1\right)}^{3/4}\,2^{1/4}\,3^{3/4}}{3}\right)\,\left(\frac{d}{12}-\frac{6^{1/4}\,\sqrt{-\frac{3}{4}{}\mathrm{i}}\,a}{12}\right)","Not used",1,"log(x - ((-1)^(1/4)*2^(1/4)*3^(3/4))/3)*(d/12 - (6^(1/4)*(3i/4)^(1/2)*a)/12) + log(x + ((-1)^(1/4)*2^(1/4)*3^(3/4))/3)*(d/12 + (6^(1/4)*(3i/4)^(1/2)*a)/12) + log(x - ((-1)^(3/4)*2^(1/4)*3^(3/4))/3)*(d/12 + (6^(1/4)*(-3i/4)^(1/2)*a)/12) + log(x + ((-1)^(3/4)*2^(1/4)*3^(3/4))/3)*(d/12 - (6^(1/4)*(-3i/4)^(1/2)*a)/12)","B"
161,1,25,36,0.055526,"\text{Not used}","int((b*x + d*x^3)/(3*x^4 + 2),x)","\frac{d\,\ln\left(x^4+\frac{2}{3}\right)}{12}+\frac{\sqrt{6}\,b\,\mathrm{atan}\left(\frac{\sqrt{6}\,x^2}{2}\right)}{12}","Not used",1,"(d*log(x^4 + 2/3))/12 + (6^(1/2)*b*atan((6^(1/2)*x^2)/2))/12","B"
162,1,307,136,5.496420,"\text{Not used}","int((a + b*x + d*x^3)/(3*x^4 + 2),x)","\sum _{k=1}^4\ln\left(x\,\left(9\,a^2\,d+9\,b^3+6\,b\,d^2\right)+9\,a\,b^2-6\,a\,d^2-\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{z^2\,\left(3456\,b^2+6912\,d^2\right)}{165888}-\frac{z\,\left(864\,a^2\,b+576\,b^2\,d+384\,d^3\right)}{165888}+\frac{a^2\,b\,d}{2304}+\frac{b^2\,d^2}{6912}+\frac{d^4}{20736}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)\,\left(\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{z^2\,\left(3456\,b^2+6912\,d^2\right)}{165888}-\frac{z\,\left(864\,a^2\,b+576\,b^2\,d+384\,d^3\right)}{165888}+\frac{a^2\,b\,d}{2304}+\frac{b^2\,d^2}{6912}+\frac{d^4}{20736}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)\,\left(864\,a-864\,b\,x\right)-144\,a\,d+x\,\left(108\,a^2+144\,b\,d\right)\right)\right)\,\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{z^2\,\left(3456\,b^2+6912\,d^2\right)}{165888}-\frac{z\,\left(864\,a^2\,b+576\,b^2\,d+384\,d^3\right)}{165888}+\frac{a^2\,b\,d}{2304}+\frac{b^2\,d^2}{6912}+\frac{d^4}{20736}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)","Not used",1,"symsum(log(x*(9*a^2*d + 6*b*d^2 + 9*b^3) + 9*a*b^2 - 6*a*d^2 - root(z^4 - (d*z^3)/3 + (z^2*(3456*b^2 + 6912*d^2))/165888 - (z*(864*a^2*b + 576*b^2*d + 384*d^3))/165888 + (a^2*b*d)/2304 + (b^2*d^2)/6912 + d^4/20736 + b^4/9216 + a^4/6144, z, k)*(root(z^4 - (d*z^3)/3 + (z^2*(3456*b^2 + 6912*d^2))/165888 - (z*(864*a^2*b + 576*b^2*d + 384*d^3))/165888 + (a^2*b*d)/2304 + (b^2*d^2)/6912 + d^4/20736 + b^4/9216 + a^4/6144, z, k)*(864*a - 864*b*x) - 144*a*d + x*(144*b*d + 108*a^2)))*root(z^4 - (d*z^3)/3 + (z^2*(3456*b^2 + 6912*d^2))/165888 - (z*(864*a^2*b + 576*b^2*d + 384*d^3))/165888 + (a^2*b*d)/2304 + (b^2*d^2)/6912 + d^4/20736 + b^4/9216 + a^4/6144, z, k), k, 1, 4)","B"
163,1,117,114,0.373768,"\text{Not used}","int((c*x^2 + d*x^3)/(3*x^4 + 2),x)","\ln\left(x-\frac{{\left(-1\right)}^{1/4}\,2^{1/4}\,3^{3/4}}{3}\right)\,\left(\frac{d}{12}+\frac{6^{1/4}\,\sqrt{-\frac{1}{2}{}\mathrm{i}}\,c}{12}\right)+\ln\left(x+\frac{{\left(-1\right)}^{1/4}\,2^{1/4}\,3^{3/4}}{3}\right)\,\left(\frac{d}{12}-\frac{6^{1/4}\,\sqrt{-\frac{1}{2}{}\mathrm{i}}\,c}{12}\right)+\ln\left(x-\frac{{\left(-1\right)}^{3/4}\,2^{1/4}\,3^{3/4}}{3}\right)\,\left(\frac{d}{12}-\frac{6^{1/4}\,\sqrt{\frac{1}{2}{}\mathrm{i}}\,c}{12}\right)+\ln\left(x+\frac{{\left(-1\right)}^{3/4}\,2^{1/4}\,3^{3/4}}{3}\right)\,\left(\frac{d}{12}+\frac{6^{1/4}\,\sqrt{\frac{1}{2}{}\mathrm{i}}\,c}{12}\right)","Not used",1,"log(x - ((-1)^(1/4)*2^(1/4)*3^(3/4))/3)*(d/12 + (6^(1/4)*(-1i/2)^(1/2)*c)/12) + log(x + ((-1)^(1/4)*2^(1/4)*3^(3/4))/3)*(d/12 - (6^(1/4)*(-1i/2)^(1/2)*c)/12) + log(x - ((-1)^(3/4)*2^(1/4)*3^(3/4))/3)*(d/12 - (6^(1/4)*(1i/2)^(1/2)*c)/12) + log(x + ((-1)^(3/4)*2^(1/4)*3^(3/4))/3)*(d/12 + (6^(1/4)*(1i/2)^(1/2)*c)/12)","B"
164,1,286,154,5.809908,"\text{Not used}","int((a + c*x^2 + d*x^3)/(3*x^4 + 2),x)","\ln\left(-2\,c+\sqrt{6}\,a\,1{}\mathrm{i}+x\,\sqrt{3{}\mathrm{i}\,\sqrt{6}\,a^2-12\,a\,c-2{}\mathrm{i}\,\sqrt{6}\,c^2}\right)\,\left(\frac{d}{12}+\frac{\sqrt{\frac{3{}\mathrm{i}\,\sqrt{6}\,a^2}{4}-3\,a\,c-\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{2}}}{12}\right)+\ln\left(2\,c-\sqrt{6}\,a\,1{}\mathrm{i}+x\,\sqrt{3{}\mathrm{i}\,\sqrt{6}\,a^2-12\,a\,c-2{}\mathrm{i}\,\sqrt{6}\,c^2}\right)\,\left(\frac{d}{12}-\frac{\sqrt{\frac{3{}\mathrm{i}\,\sqrt{6}\,a^2}{4}-3\,a\,c-\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{2}}}{12}\right)+\ln\left(2\,c+\sqrt{6}\,a\,1{}\mathrm{i}+x\,\sqrt{-3{}\mathrm{i}\,\sqrt{6}\,a^2-12\,a\,c+2{}\mathrm{i}\,\sqrt{6}\,c^2}\right)\,\left(\frac{d}{12}-\frac{\sqrt{-\frac{3{}\mathrm{i}\,\sqrt{6}\,a^2}{4}-3\,a\,c+\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{2}}}{12}\right)+\ln\left(2\,c+\sqrt{6}\,a\,1{}\mathrm{i}-x\,\sqrt{-3{}\mathrm{i}\,\sqrt{6}\,a^2-12\,a\,c+2{}\mathrm{i}\,\sqrt{6}\,c^2}\right)\,\left(\frac{d}{12}+\frac{\sqrt{-\frac{3{}\mathrm{i}\,\sqrt{6}\,a^2}{4}-3\,a\,c+\frac{1{}\mathrm{i}\,\sqrt{6}\,c^2}{2}}}{12}\right)","Not used",1,"log(6^(1/2)*a*1i - 2*c + x*(6^(1/2)*a^2*3i - 12*a*c - 6^(1/2)*c^2*2i)^(1/2))*(d/12 + ((6^(1/2)*a^2*3i)/4 - 3*a*c - (6^(1/2)*c^2*1i)/2)^(1/2)/12) + log(2*c - 6^(1/2)*a*1i + x*(6^(1/2)*a^2*3i - 12*a*c - 6^(1/2)*c^2*2i)^(1/2))*(d/12 - ((6^(1/2)*a^2*3i)/4 - 3*a*c - (6^(1/2)*c^2*1i)/2)^(1/2)/12) + log(2*c + 6^(1/2)*a*1i + x*(6^(1/2)*c^2*2i - 6^(1/2)*a^2*3i - 12*a*c)^(1/2))*(d/12 - ((6^(1/2)*c^2*1i)/2 - (6^(1/2)*a^2*3i)/4 - 3*a*c)^(1/2)/12) + log(2*c + 6^(1/2)*a*1i - x*(6^(1/2)*c^2*2i - 6^(1/2)*a^2*3i - 12*a*c)^(1/2))*(d/12 + ((6^(1/2)*c^2*1i)/2 - (6^(1/2)*a^2*3i)/4 - 3*a*c)^(1/2)/12)","B"
165,1,300,136,5.387829,"\text{Not used}","int((b*x + c*x^2 + d*x^3)/(3*x^4 + 2),x)","\sum _{k=1}^4\ln\left(-\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{z^2\,\left(1728\,b^2+3456\,d^2\right)}{82944}-\frac{z\,\left(-288\,b\,c^2+288\,b^2\,d+192\,d^3\right)}{82944}-\frac{b\,c^2\,d}{3456}+\frac{b^2\,d^2}{6912}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216},z,k\right)\,\left(144\,b\,c+x\,\left(144\,b\,d-72\,c^2\right)-\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{z^2\,\left(1728\,b^2+3456\,d^2\right)}{82944}-\frac{z\,\left(-288\,b\,c^2+288\,b^2\,d+192\,d^3\right)}{82944}-\frac{b\,c^2\,d}{3456}+\frac{b^2\,d^2}{6912}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216},z,k\right)\,b\,x\,864\right)+x\,\left(9\,b^3+6\,b\,d^2-6\,c^2\,d\right)-6\,c^3+12\,b\,c\,d\right)\,\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{z^2\,\left(1728\,b^2+3456\,d^2\right)}{82944}-\frac{z\,\left(-288\,b\,c^2+288\,b^2\,d+192\,d^3\right)}{82944}-\frac{b\,c^2\,d}{3456}+\frac{b^2\,d^2}{6912}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216},z,k\right)","Not used",1,"symsum(log(x*(6*b*d^2 - 6*c^2*d + 9*b^3) - root(z^4 - (d*z^3)/3 + (z^2*(1728*b^2 + 3456*d^2))/82944 - (z*(- 288*b*c^2 + 288*b^2*d + 192*d^3))/82944 - (b*c^2*d)/3456 + (b^2*d^2)/6912 + d^4/20736 + c^4/13824 + b^4/9216, z, k)*(144*b*c + x*(144*b*d - 72*c^2) - 864*root(z^4 - (d*z^3)/3 + (z^2*(1728*b^2 + 3456*d^2))/82944 - (z*(- 288*b*c^2 + 288*b^2*d + 192*d^3))/82944 - (b*c^2*d)/3456 + (b^2*d^2)/6912 + d^4/20736 + c^4/13824 + b^4/9216, z, k)*b*x) - 6*c^3 + 12*b*c*d)*root(z^4 - (d*z^3)/3 + (z^2*(1728*b^2 + 3456*d^2))/82944 - (z*(- 288*b*c^2 + 288*b^2*d + 192*d^3))/82944 - (b*c^2*d)/3456 + (b^2*d^2)/6912 + d^4/20736 + c^4/13824 + b^4/9216, z, k), k, 1, 4)","B"
166,1,1168,176,5.635943,"\text{Not used}","int((a + b*x + c*x^2 + d*x^3)/(3*x^4 + 2),x)","\sum _{k=1}^4\ln\left(-{\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{a\,c\,z^2}{24}+\frac{d^2\,z^2}{24}+\frac{b^2\,z^2}{48}-\frac{a\,c\,d\,z}{144}-\frac{b^2\,d\,z}{288}+\frac{b\,c^2\,z}{288}-\frac{a^2\,b\,z}{192}-\frac{d^3\,z}{432}-\frac{b\,c^2\,d}{3456}+\frac{a\,c\,d^2}{3456}+\frac{a^2\,b\,d}{2304}-\frac{a\,b^2\,c}{2304}+\frac{b^2\,d^2}{6912}+\frac{a^2\,c^2}{4608}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)}^2\,a\,864+9\,a\,b^2-9\,a^2\,c-6\,a\,d^2+9\,b^3\,x-6\,c^3+\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{a\,c\,z^2}{24}+\frac{d^2\,z^2}{24}+\frac{b^2\,z^2}{48}-\frac{a\,c\,d\,z}{144}-\frac{b^2\,d\,z}{288}+\frac{b\,c^2\,z}{288}-\frac{a^2\,b\,z}{192}-\frac{d^3\,z}{432}-\frac{b\,c^2\,d}{3456}+\frac{a\,c\,d^2}{3456}+\frac{a^2\,b\,d}{2304}-\frac{a\,b^2\,c}{2304}+\frac{b^2\,d^2}{6912}+\frac{a^2\,c^2}{4608}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)\,a\,d\,144-\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{a\,c\,z^2}{24}+\frac{d^2\,z^2}{24}+\frac{b^2\,z^2}{48}-\frac{a\,c\,d\,z}{144}-\frac{b^2\,d\,z}{288}+\frac{b\,c^2\,z}{288}-\frac{a^2\,b\,z}{192}-\frac{d^3\,z}{432}-\frac{b\,c^2\,d}{3456}+\frac{a\,c\,d^2}{3456}+\frac{a^2\,b\,d}{2304}-\frac{a\,b^2\,c}{2304}+\frac{b^2\,d^2}{6912}+\frac{a^2\,c^2}{4608}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)\,b\,c\,144+12\,b\,c\,d-\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{a\,c\,z^2}{24}+\frac{d^2\,z^2}{24}+\frac{b^2\,z^2}{48}-\frac{a\,c\,d\,z}{144}-\frac{b^2\,d\,z}{288}+\frac{b\,c^2\,z}{288}-\frac{a^2\,b\,z}{192}-\frac{d^3\,z}{432}-\frac{b\,c^2\,d}{3456}+\frac{a\,c\,d^2}{3456}+\frac{a^2\,b\,d}{2304}-\frac{a\,b^2\,c}{2304}+\frac{b^2\,d^2}{6912}+\frac{a^2\,c^2}{4608}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)\,a^2\,x\,108+{\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{a\,c\,z^2}{24}+\frac{d^2\,z^2}{24}+\frac{b^2\,z^2}{48}-\frac{a\,c\,d\,z}{144}-\frac{b^2\,d\,z}{288}+\frac{b\,c^2\,z}{288}-\frac{a^2\,b\,z}{192}-\frac{d^3\,z}{432}-\frac{b\,c^2\,d}{3456}+\frac{a\,c\,d^2}{3456}+\frac{a^2\,b\,d}{2304}-\frac{a\,b^2\,c}{2304}+\frac{b^2\,d^2}{6912}+\frac{a^2\,c^2}{4608}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)}^2\,b\,x\,864+\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{a\,c\,z^2}{24}+\frac{d^2\,z^2}{24}+\frac{b^2\,z^2}{48}-\frac{a\,c\,d\,z}{144}-\frac{b^2\,d\,z}{288}+\frac{b\,c^2\,z}{288}-\frac{a^2\,b\,z}{192}-\frac{d^3\,z}{432}-\frac{b\,c^2\,d}{3456}+\frac{a\,c\,d^2}{3456}+\frac{a^2\,b\,d}{2304}-\frac{a\,b^2\,c}{2304}+\frac{b^2\,d^2}{6912}+\frac{a^2\,c^2}{4608}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)\,c^2\,x\,72+9\,a^2\,d\,x+6\,b\,d^2\,x-6\,c^2\,d\,x-\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{a\,c\,z^2}{24}+\frac{d^2\,z^2}{24}+\frac{b^2\,z^2}{48}-\frac{a\,c\,d\,z}{144}-\frac{b^2\,d\,z}{288}+\frac{b\,c^2\,z}{288}-\frac{a^2\,b\,z}{192}-\frac{d^3\,z}{432}-\frac{b\,c^2\,d}{3456}+\frac{a\,c\,d^2}{3456}+\frac{a^2\,b\,d}{2304}-\frac{a\,b^2\,c}{2304}+\frac{b^2\,d^2}{6912}+\frac{a^2\,c^2}{4608}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)\,b\,d\,x\,144-18\,a\,b\,c\,x\right)\,\mathrm{root}\left(z^4-\frac{d\,z^3}{3}+\frac{a\,c\,z^2}{24}+\frac{d^2\,z^2}{24}+\frac{b^2\,z^2}{48}-\frac{a\,c\,d\,z}{144}-\frac{b^2\,d\,z}{288}+\frac{b\,c^2\,z}{288}-\frac{a^2\,b\,z}{192}-\frac{d^3\,z}{432}-\frac{b\,c^2\,d}{3456}+\frac{a\,c\,d^2}{3456}+\frac{a^2\,b\,d}{2304}-\frac{a\,b^2\,c}{2304}+\frac{b^2\,d^2}{6912}+\frac{a^2\,c^2}{4608}+\frac{d^4}{20736}+\frac{c^4}{13824}+\frac{b^4}{9216}+\frac{a^4}{6144},z,k\right)","Not used",1,"symsum(log(9*a*b^2 - 864*root(z^4 - (d*z^3)/3 + (a*c*z^2)/24 + (d^2*z^2)/24 + (b^2*z^2)/48 - (a*c*d*z)/144 - (b^2*d*z)/288 + (b*c^2*z)/288 - (a^2*b*z)/192 - (d^3*z)/432 - (b*c^2*d)/3456 + (a*c*d^2)/3456 + (a^2*b*d)/2304 - (a*b^2*c)/2304 + (b^2*d^2)/6912 + (a^2*c^2)/4608 + d^4/20736 + c^4/13824 + b^4/9216 + a^4/6144, z, k)^2*a - 9*a^2*c - 6*a*d^2 + 9*b^3*x - 6*c^3 + 144*root(z^4 - (d*z^3)/3 + (a*c*z^2)/24 + (d^2*z^2)/24 + (b^2*z^2)/48 - (a*c*d*z)/144 - (b^2*d*z)/288 + (b*c^2*z)/288 - (a^2*b*z)/192 - (d^3*z)/432 - (b*c^2*d)/3456 + (a*c*d^2)/3456 + (a^2*b*d)/2304 - (a*b^2*c)/2304 + (b^2*d^2)/6912 + (a^2*c^2)/4608 + d^4/20736 + c^4/13824 + b^4/9216 + a^4/6144, z, k)*a*d - 144*root(z^4 - (d*z^3)/3 + (a*c*z^2)/24 + (d^2*z^2)/24 + (b^2*z^2)/48 - (a*c*d*z)/144 - (b^2*d*z)/288 + (b*c^2*z)/288 - (a^2*b*z)/192 - (d^3*z)/432 - (b*c^2*d)/3456 + (a*c*d^2)/3456 + (a^2*b*d)/2304 - (a*b^2*c)/2304 + (b^2*d^2)/6912 + (a^2*c^2)/4608 + d^4/20736 + c^4/13824 + b^4/9216 + a^4/6144, z, k)*b*c + 12*b*c*d - 108*root(z^4 - (d*z^3)/3 + (a*c*z^2)/24 + (d^2*z^2)/24 + (b^2*z^2)/48 - (a*c*d*z)/144 - (b^2*d*z)/288 + (b*c^2*z)/288 - (a^2*b*z)/192 - (d^3*z)/432 - (b*c^2*d)/3456 + (a*c*d^2)/3456 + (a^2*b*d)/2304 - (a*b^2*c)/2304 + (b^2*d^2)/6912 + (a^2*c^2)/4608 + d^4/20736 + c^4/13824 + b^4/9216 + a^4/6144, z, k)*a^2*x + 864*root(z^4 - (d*z^3)/3 + (a*c*z^2)/24 + (d^2*z^2)/24 + (b^2*z^2)/48 - (a*c*d*z)/144 - (b^2*d*z)/288 + (b*c^2*z)/288 - (a^2*b*z)/192 - (d^3*z)/432 - (b*c^2*d)/3456 + (a*c*d^2)/3456 + (a^2*b*d)/2304 - (a*b^2*c)/2304 + (b^2*d^2)/6912 + (a^2*c^2)/4608 + d^4/20736 + c^4/13824 + b^4/9216 + a^4/6144, z, k)^2*b*x + 72*root(z^4 - (d*z^3)/3 + (a*c*z^2)/24 + (d^2*z^2)/24 + (b^2*z^2)/48 - (a*c*d*z)/144 - (b^2*d*z)/288 + (b*c^2*z)/288 - (a^2*b*z)/192 - (d^3*z)/432 - (b*c^2*d)/3456 + (a*c*d^2)/3456 + (a^2*b*d)/2304 - (a*b^2*c)/2304 + (b^2*d^2)/6912 + (a^2*c^2)/4608 + d^4/20736 + c^4/13824 + b^4/9216 + a^4/6144, z, k)*c^2*x + 9*a^2*d*x + 6*b*d^2*x - 6*c^2*d*x - 144*root(z^4 - (d*z^3)/3 + (a*c*z^2)/24 + (d^2*z^2)/24 + (b^2*z^2)/48 - (a*c*d*z)/144 - (b^2*d*z)/288 + (b*c^2*z)/288 - (a^2*b*z)/192 - (d^3*z)/432 - (b*c^2*d)/3456 + (a*c*d^2)/3456 + (a^2*b*d)/2304 - (a*b^2*c)/2304 + (b^2*d^2)/6912 + (a^2*c^2)/4608 + d^4/20736 + c^4/13824 + b^4/9216 + a^4/6144, z, k)*b*d*x - 18*a*b*c*x)*root(z^4 - (d*z^3)/3 + (a*c*z^2)/24 + (d^2*z^2)/24 + (b^2*z^2)/48 - (a*c*d*z)/144 - (b^2*d*z)/288 + (b*c^2*z)/288 - (a^2*b*z)/192 - (d^3*z)/432 - (b*c^2*d)/3456 + (a*c*d^2)/3456 + (a^2*b*d)/2304 - (a*b^2*c)/2304 + (b^2*d^2)/6912 + (a^2*c^2)/4608 + d^4/20736 + c^4/13824 + b^4/9216 + a^4/6144, z, k), k, 1, 4)","B"
167,1,6,8,0.022644,"\text{Not used}","int(-(x + x^2 + x^3 + 1)/(x^4 - 1),x)","-\ln\left(x-1\right)","Not used",1,"-log(x - 1)","B"
168,1,156,53,0.401855,"\text{Not used}","int((x + x^2 + x^3 + 1)/(x^4 + 1),x)","\ln\left(\left(16\,x-16\right)\,\left(\frac{\sqrt{-2\,\sqrt{2}-3}}{4}+\frac{1}{4}\right)-8\,x\right)\,\left(\frac{\sqrt{-2\,\sqrt{2}-3}}{4}+\frac{1}{4}\right)-\ln\left(8\,x+\left(16\,x-16\right)\,\left(\frac{\sqrt{-2\,\sqrt{2}-3}}{4}-\frac{1}{4}\right)\right)\,\left(\frac{\sqrt{-2\,\sqrt{2}-3}}{4}-\frac{1}{4}\right)-\ln\left(8\,x+\left(16\,x-16\right)\,\left(\frac{\sqrt{2\,\sqrt{2}-3}}{4}-\frac{1}{4}\right)\right)\,\left(\frac{\sqrt{2\,\sqrt{2}-3}}{4}-\frac{1}{4}\right)+\ln\left(8\,x-\left(16\,x-16\right)\,\left(\frac{\sqrt{2\,\sqrt{2}-3}}{4}+\frac{1}{4}\right)\right)\,\left(\frac{\sqrt{2\,\sqrt{2}-3}}{4}+\frac{1}{4}\right)","Not used",1,"log((16*x - 16)*((- 2*2^(1/2) - 3)^(1/2)/4 + 1/4) - 8*x)*((- 2*2^(1/2) - 3)^(1/2)/4 + 1/4) - log(8*x + (16*x - 16)*((- 2*2^(1/2) - 3)^(1/2)/4 - 1/4))*((- 2*2^(1/2) - 3)^(1/2)/4 - 1/4) - log(8*x + (16*x - 16)*((2*2^(1/2) - 3)^(1/2)/4 - 1/4))*((2*2^(1/2) - 3)^(1/2)/4 - 1/4) + log(8*x - (16*x - 16)*((2*2^(1/2) - 3)^(1/2)/4 + 1/4))*((2*2^(1/2) - 3)^(1/2)/4 + 1/4)","B"
169,1,312,124,5.033588,"\text{Not used}","int((x + x^2 + x^3 + 1)/(a - b*x^4),x)","\sum _{k=1}^4\ln\left(-\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,z^3+96\,a^3\,b^2\,z^2-96\,a^2\,b^3\,z^2+16\,a^3\,b\,z+16\,a\,b^3\,z-32\,a^2\,b^2\,z-3\,a^2\,b+3\,a\,b^2-b^3+a^3,z,k\right)\,\left(\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,z^3+96\,a^3\,b^2\,z^2-96\,a^2\,b^3\,z^2+16\,a^3\,b\,z+16\,a\,b^3\,z-32\,a^2\,b^2\,z-3\,a^2\,b+3\,a\,b^2-b^3+a^3,z,k\right)\,\left(16\,a\,b^3-16\,a\,b^3\,x\right)-x\,\left(4\,a\,b^2-4\,b^3\right)\right)\right)\,\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,z^3+96\,a^3\,b^2\,z^2-96\,a^2\,b^3\,z^2+16\,a^3\,b\,z+16\,a\,b^3\,z-32\,a^2\,b^2\,z-3\,a^2\,b+3\,a\,b^2-b^3+a^3,z,k\right)","Not used",1,"symsum(log(-root(256*a^3*b^4*z^4 + 256*a^3*b^3*z^3 + 96*a^3*b^2*z^2 - 96*a^2*b^3*z^2 + 16*a^3*b*z + 16*a*b^3*z - 32*a^2*b^2*z - 3*a^2*b + 3*a*b^2 - b^3 + a^3, z, k)*(root(256*a^3*b^4*z^4 + 256*a^3*b^3*z^3 + 96*a^3*b^2*z^2 - 96*a^2*b^3*z^2 + 16*a^3*b*z + 16*a*b^3*z - 32*a^2*b^2*z - 3*a^2*b + 3*a*b^2 - b^3 + a^3, z, k)*(16*a*b^3 - 16*a*b^3*x) - x*(4*a*b^2 - 4*b^3)))*root(256*a^3*b^4*z^4 + 256*a^3*b^3*z^3 + 96*a^3*b^2*z^2 - 96*a^2*b^3*z^2 + 16*a^3*b*z + 16*a*b^3*z - 32*a^2*b^2*z - 3*a^2*b + 3*a*b^2 - b^3 + a^3, z, k), k, 1, 4)","B"
170,1,305,277,5.041319,"\text{Not used}","int((x + x^2 + x^3 + 1)/(a + b*x^4),x)","\sum _{k=1}^4\ln\left(-\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,z^3+96\,a^3\,b^2\,z^2+96\,a^2\,b^3\,z^2-16\,a^3\,b\,z-16\,a\,b^3\,z-32\,a^2\,b^2\,z+3\,a^2\,b+3\,a\,b^2+b^3+a^3,z,k\right)\,\left(\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,z^3+96\,a^3\,b^2\,z^2+96\,a^2\,b^3\,z^2-16\,a^3\,b\,z-16\,a\,b^3\,z-32\,a^2\,b^2\,z+3\,a^2\,b+3\,a\,b^2+b^3+a^3,z,k\right)\,\left(16\,a\,b^3-16\,a\,b^3\,x\right)+x\,\left(4\,b^3+4\,a\,b^2\right)\right)\right)\,\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,z^3+96\,a^3\,b^2\,z^2+96\,a^2\,b^3\,z^2-16\,a^3\,b\,z-16\,a\,b^3\,z-32\,a^2\,b^2\,z+3\,a^2\,b+3\,a\,b^2+b^3+a^3,z,k\right)","Not used",1,"symsum(log(-root(256*a^3*b^4*z^4 - 256*a^3*b^3*z^3 + 96*a^3*b^2*z^2 + 96*a^2*b^3*z^2 - 16*a^3*b*z - 16*a*b^3*z - 32*a^2*b^2*z + 3*a^2*b + 3*a*b^2 + b^3 + a^3, z, k)*(root(256*a^3*b^4*z^4 - 256*a^3*b^3*z^3 + 96*a^3*b^2*z^2 + 96*a^2*b^3*z^2 - 16*a^3*b*z - 16*a*b^3*z - 32*a^2*b^2*z + 3*a^2*b + 3*a*b^2 + b^3 + a^3, z, k)*(16*a*b^3 - 16*a*b^3*x) + x*(4*a*b^2 + 4*b^3)))*root(256*a^3*b^4*z^4 - 256*a^3*b^3*z^3 + 96*a^3*b^2*z^2 + 96*a^2*b^3*z^2 - 16*a^3*b*z - 16*a*b^3*z - 32*a^2*b^2*z + 3*a^2*b + 3*a*b^2 + b^3 + a^3, z, k), k, 1, 4)","B"
171,1,5082,148,5.506633,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4),x)","\left(\sum _{k=1}^4\ln\left(-b^2\,c\,d^2+b^2\,c^2\,e+a^2\,e\,g^2-a^2\,f^2\,g-b^2\,d^3\,x-a\,b\,e^3-a\,b\,c\,f^2-a\,b\,d^2\,g-{\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)}^2\,a\,b^3\,c\,16-\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)\,b^3\,c^2\,x\,4-b^2\,c^2\,f\,x-a^2\,f\,g^2\,x-{\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)}^2\,a^2\,b^2\,g\,16+{\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)}^2\,a\,b^3\,d\,x\,16-\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)\,a\,b^2\,e^2\,x\,4-\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)\,a^2\,b\,g^2\,x\,4+2\,a\,b\,c\,e\,g+2\,a\,b\,d\,e\,f-\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)\,a\,b^2\,c\,f\,8+\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)\,a\,b^2\,d\,e\,8-\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)\,a^2\,b\,f\,g\,8+a\,b\,d\,f^2\,x-a\,b\,e^2\,f\,x+2\,b^2\,c\,d\,e\,x-\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)\,a\,b^2\,c\,g\,x\,8+\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)\,a\,b^2\,d\,f\,x\,8-2\,a\,b\,c\,f\,g\,x+2\,a\,b\,d\,e\,g\,x\right)\,\mathrm{root}\left(256\,a^3\,b^5\,z^4+256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2-64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2-32\,a^2\,b^4\,d^2\,z^2-32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z+16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z+16\,a\,b^4\,c^2\,d\,z+16\,a^3\,b^2\,f^3\,z+8\,a^2\,b^2\,c\,d\,f\,g-4\,a^2\,b^2\,d^2\,e\,g+4\,a^2\,b^2\,d\,e^2\,f+4\,a^2\,b^2\,c\,e^2\,g-4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g-6\,a^2\,b^2\,c^2\,g^2-2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^3\,b\,f^4+a\,b^3\,d^4-a^2\,b^2\,e^4-a^4\,g^4-b^4\,c^4,z,k\right)\right)-\frac{g\,x}{b}","Not used",1,"symsum(log(b^2*c^2*e - b^2*c*d^2 + a^2*e*g^2 - a^2*f^2*g - b^2*d^3*x - a*b*e^3 - a*b*c*f^2 - a*b*d^2*g - 16*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)^2*a*b^3*c - 4*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)*b^3*c^2*x - b^2*c^2*f*x - a^2*f*g^2*x - 16*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)^2*a^2*b^2*g + 16*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)^2*a*b^3*d*x - 4*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)*a*b^2*e^2*x - 4*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)*a^2*b*g^2*x + 2*a*b*c*e*g + 2*a*b*d*e*f - 8*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)*a*b^2*c*f + 8*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)*a*b^2*d*e - 8*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)*a^2*b*f*g + a*b*d*f^2*x - a*b*e^2*f*x + 2*b^2*c*d*e*x - 8*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)*a*b^2*c*g*x + 8*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k)*a*b^2*d*f*x - 2*a*b*c*f*g*x + 2*a*b*d*e*g*x)*root(256*a^3*b^5*z^4 + 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 - 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 - 32*a^2*b^4*d^2*z^2 - 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z + 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z + 16*a*b^4*c^2*d*z + 16*a^3*b^2*f^3*z + 8*a^2*b^2*c*d*f*g - 4*a^2*b^2*d^2*e*g + 4*a^2*b^2*d*e^2*f + 4*a^2*b^2*c*e^2*g - 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g - 6*a^2*b^2*c^2*g^2 - 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^3*b*f^4 + a*b^3*d^4 - a^2*b^2*e^4 - a^4*g^4 - b^4*c^4, z, k), k, 1, 4) - (g*x)/b","B"
172,1,1393,172,5.559684,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^2,x)","\left(\sum _{k=1}^4\ln\left(-\frac{-a^2\,e\,g^2+6\,a\,b\,c\,e\,g-4\,a\,b\,d^2\,g+a\,b\,e^3-9\,b^2\,c^2\,e+12\,b^2\,c\,d^2}{64\,a^3}-\frac{\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2-3072\,a^4\,b^4\,c\,e\,z^2-2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z+128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z+1152\,a^2\,b^4\,c^2\,d\,z+16\,a^2\,b^2\,d^2\,e\,g-12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3-54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4-81\,b^4\,c^4-a^2\,b^2\,e^4-a^4\,g^4,z,k\right)\,b\,\left(9\,b^2\,c^2\,x+a^2\,g^2\,x-\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2-3072\,a^4\,b^4\,c\,e\,z^2-2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z+128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z+1152\,a^2\,b^4\,c^2\,d\,z+16\,a^2\,b^2\,d^2\,e\,g-12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3-54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4-81\,b^4\,c^4-a^2\,b^2\,e^4-a^4\,g^4,z,k\right)\,a^3\,b\,g\,16+a\,b\,e^2\,x+\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2-3072\,a^4\,b^4\,c\,e\,z^2-2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z+128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z+1152\,a^2\,b^4\,c^2\,d\,z+16\,a^2\,b^2\,d^2\,e\,g-12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3-54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4-81\,b^4\,c^4-a^2\,b^2\,e^4-a^4\,g^4,z,k\right)\,a^2\,b^2\,c\,48-4\,a\,b\,d\,e-\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2-3072\,a^4\,b^4\,c\,e\,z^2-2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z+128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z+1152\,a^2\,b^4\,c^2\,d\,z+16\,a^2\,b^2\,d^2\,e\,g-12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3-54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4-81\,b^4\,c^4-a^2\,b^2\,e^4-a^4\,g^4,z,k\right)\,a^2\,b^2\,d\,x\,32-6\,a\,b\,c\,g\,x\right)}{a^2\,4}-\frac{b\,d\,x\,\left(2\,b\,d^2-3\,b\,c\,e+a\,e\,g\right)}{16\,a^3}\right)\,\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2-3072\,a^4\,b^4\,c\,e\,z^2-2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z+128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z+1152\,a^2\,b^4\,c^2\,d\,z+16\,a^2\,b^2\,d^2\,e\,g-12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3-54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4-81\,b^4\,c^4-a^2\,b^2\,e^4-a^4\,g^4,z,k\right)\right)+\frac{\frac{f}{4\,b}+\frac{d\,x^2}{4\,a}+\frac{e\,x^3}{4\,a}+\frac{x\,\left(b\,c+a\,g\right)}{4\,a\,b}}{a-b\,x^4}","Not used",1,"symsum(log(- (12*b^2*c*d^2 - 9*b^2*c^2*e - a^2*e*g^2 + a*b*e^3 - 4*a*b*d^2*g + 6*a*b*c*e*g)/(64*a^3) - (root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 - 3072*a^4*b^4*c*e*z^2 - 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z + 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z + 1152*a^2*b^4*c^2*d*z + 16*a^2*b^2*d^2*e*g - 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 - 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 - 81*b^4*c^4 - a^2*b^2*e^4 - a^4*g^4, z, k)*b*(9*b^2*c^2*x + a^2*g^2*x - 16*root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 - 3072*a^4*b^4*c*e*z^2 - 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z + 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z + 1152*a^2*b^4*c^2*d*z + 16*a^2*b^2*d^2*e*g - 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 - 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 - 81*b^4*c^4 - a^2*b^2*e^4 - a^4*g^4, z, k)*a^3*b*g + a*b*e^2*x + 48*root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 - 3072*a^4*b^4*c*e*z^2 - 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z + 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z + 1152*a^2*b^4*c^2*d*z + 16*a^2*b^2*d^2*e*g - 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 - 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 - 81*b^4*c^4 - a^2*b^2*e^4 - a^4*g^4, z, k)*a^2*b^2*c - 4*a*b*d*e - 32*root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 - 3072*a^4*b^4*c*e*z^2 - 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z + 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z + 1152*a^2*b^4*c^2*d*z + 16*a^2*b^2*d^2*e*g - 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 - 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 - 81*b^4*c^4 - a^2*b^2*e^4 - a^4*g^4, z, k)*a^2*b^2*d*x - 6*a*b*c*g*x))/(4*a^2) - (b*d*x*(2*b*d^2 - 3*b*c*e + a*e*g))/(16*a^3))*root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 - 3072*a^4*b^4*c*e*z^2 - 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z + 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z + 1152*a^2*b^4*c^2*d*z + 16*a^2*b^2*d^2*e*g - 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 - 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 - 81*b^4*c^4 - a^2*b^2*e^4 - a^4*g^4, z, k), k, 1, 4) + (f/(4*b) + (d*x^2)/(4*a) + (e*x^3)/(4*a) + (x*(b*c + a*g))/(4*a*b))/(a - b*x^4)","B"
173,1,1002,221,5.436322,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^3,x)","\frac{\frac{f}{8\,b}+\frac{5\,d\,x^2}{16\,a}+\frac{9\,e\,x^3}{32\,a}-\frac{x^5\,\left(7\,b\,c-a\,g\right)}{32\,a^2}+\frac{x\,\left(11\,b\,c+3\,a\,g\right)}{32\,a\,b}-\frac{3\,b\,d\,x^6}{16\,a^2}-\frac{5\,b\,e\,x^7}{32\,a^2}}{a^2-2\,a\,b\,x^4+b^2\,x^8}+\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(268435456\,a^{11}\,b^5\,z^4+983040\,a^7\,b^3\,e\,g\,z^2-6881280\,a^6\,b^4\,c\,e\,z^2-4718592\,a^6\,b^4\,d^2\,z^2-774144\,a^4\,b^3\,c\,d\,g\,z+55296\,a^5\,b^2\,d\,g^2\,z+153600\,a^4\,b^3\,d\,e^2\,z+2709504\,a^3\,b^4\,c^2\,d\,z+8640\,a^2\,b^2\,d^2\,e\,g-6300\,a^2\,b^2\,c\,e^2\,g-60480\,a\,b^3\,c\,d^2\,e+111132\,a\,b^3\,c^3\,g+2268\,a^3\,b\,c\,g^3-23814\,a^2\,b^2\,c^2\,g^2+450\,a^3\,b\,e^2\,g^2+22050\,a\,b^3\,c^2\,e^2-625\,a^2\,b^2\,e^4+20736\,a\,b^3\,d^4-81\,a^4\,g^4-194481\,b^4\,c^4,z,k\right)\,\left(\mathrm{root}\left(268435456\,a^{11}\,b^5\,z^4+983040\,a^7\,b^3\,e\,g\,z^2-6881280\,a^6\,b^4\,c\,e\,z^2-4718592\,a^6\,b^4\,d^2\,z^2-774144\,a^4\,b^3\,c\,d\,g\,z+55296\,a^5\,b^2\,d\,g^2\,z+153600\,a^4\,b^3\,d\,e^2\,z+2709504\,a^3\,b^4\,c^2\,d\,z+8640\,a^2\,b^2\,d^2\,e\,g-6300\,a^2\,b^2\,c\,e^2\,g-60480\,a\,b^3\,c\,d^2\,e+111132\,a\,b^3\,c^3\,g+2268\,a^3\,b\,c\,g^3-23814\,a^2\,b^2\,c^2\,g^2+450\,a^3\,b\,e^2\,g^2+22050\,a\,b^3\,c^2\,e^2-625\,a^2\,b^2\,e^4+20736\,a\,b^3\,d^4-81\,a^4\,g^4-194481\,b^4\,c^4,z,k\right)\,\left(\frac{344064\,a^5\,b^3\,c-49152\,a^6\,b^2\,g}{32768\,a^6}-\frac{6\,b^3\,d\,x}{a}\right)+\frac{x\,\left(144\,a^4\,b\,g^2-2016\,a^3\,b^2\,c\,g+400\,a^3\,b^2\,e^2+7056\,a^2\,b^3\,c^2\right)}{4096\,a^6}-\frac{15\,b^2\,d\,e}{32\,a^3}\right)-\frac{-45\,a^2\,e\,g^2+630\,a\,b\,c\,e\,g-432\,a\,b\,d^2\,g+125\,a\,b\,e^3-2205\,b^2\,c^2\,e+3024\,b^2\,c\,d^2}{32768\,a^6}-\frac{x\,\left(216\,b^2\,d^3-315\,c\,e\,b^2\,d+45\,a\,e\,g\,b\,d\right)}{4096\,a^6}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^5\,z^4+983040\,a^7\,b^3\,e\,g\,z^2-6881280\,a^6\,b^4\,c\,e\,z^2-4718592\,a^6\,b^4\,d^2\,z^2-774144\,a^4\,b^3\,c\,d\,g\,z+55296\,a^5\,b^2\,d\,g^2\,z+153600\,a^4\,b^3\,d\,e^2\,z+2709504\,a^3\,b^4\,c^2\,d\,z+8640\,a^2\,b^2\,d^2\,e\,g-6300\,a^2\,b^2\,c\,e^2\,g-60480\,a\,b^3\,c\,d^2\,e+111132\,a\,b^3\,c^3\,g+2268\,a^3\,b\,c\,g^3-23814\,a^2\,b^2\,c^2\,g^2+450\,a^3\,b\,e^2\,g^2+22050\,a\,b^3\,c^2\,e^2-625\,a^2\,b^2\,e^4+20736\,a\,b^3\,d^4-81\,a^4\,g^4-194481\,b^4\,c^4,z,k\right)\right)","Not used",1,"(f/(8*b) + (5*d*x^2)/(16*a) + (9*e*x^3)/(32*a) - (x^5*(7*b*c - a*g))/(32*a^2) + (x*(11*b*c + 3*a*g))/(32*a*b) - (3*b*d*x^6)/(16*a^2) - (5*b*e*x^7)/(32*a^2))/(a^2 + b^2*x^8 - 2*a*b*x^4) + symsum(log(- root(268435456*a^11*b^5*z^4 + 983040*a^7*b^3*e*g*z^2 - 6881280*a^6*b^4*c*e*z^2 - 4718592*a^6*b^4*d^2*z^2 - 774144*a^4*b^3*c*d*g*z + 55296*a^5*b^2*d*g^2*z + 153600*a^4*b^3*d*e^2*z + 2709504*a^3*b^4*c^2*d*z + 8640*a^2*b^2*d^2*e*g - 6300*a^2*b^2*c*e^2*g - 60480*a*b^3*c*d^2*e + 111132*a*b^3*c^3*g + 2268*a^3*b*c*g^3 - 23814*a^2*b^2*c^2*g^2 + 450*a^3*b*e^2*g^2 + 22050*a*b^3*c^2*e^2 - 625*a^2*b^2*e^4 + 20736*a*b^3*d^4 - 81*a^4*g^4 - 194481*b^4*c^4, z, k)*(root(268435456*a^11*b^5*z^4 + 983040*a^7*b^3*e*g*z^2 - 6881280*a^6*b^4*c*e*z^2 - 4718592*a^6*b^4*d^2*z^2 - 774144*a^4*b^3*c*d*g*z + 55296*a^5*b^2*d*g^2*z + 153600*a^4*b^3*d*e^2*z + 2709504*a^3*b^4*c^2*d*z + 8640*a^2*b^2*d^2*e*g - 6300*a^2*b^2*c*e^2*g - 60480*a*b^3*c*d^2*e + 111132*a*b^3*c^3*g + 2268*a^3*b*c*g^3 - 23814*a^2*b^2*c^2*g^2 + 450*a^3*b*e^2*g^2 + 22050*a*b^3*c^2*e^2 - 625*a^2*b^2*e^4 + 20736*a*b^3*d^4 - 81*a^4*g^4 - 194481*b^4*c^4, z, k)*((344064*a^5*b^3*c - 49152*a^6*b^2*g)/(32768*a^6) - (6*b^3*d*x)/a) + (x*(144*a^4*b*g^2 + 7056*a^2*b^3*c^2 + 400*a^3*b^2*e^2 - 2016*a^3*b^2*c*g))/(4096*a^6) - (15*b^2*d*e)/(32*a^3)) - (3024*b^2*c*d^2 - 2205*b^2*c^2*e - 45*a^2*e*g^2 + 125*a*b*e^3 - 432*a*b*d^2*g + 630*a*b*c*e*g)/(32768*a^6) - (x*(216*b^2*d^3 - 315*b^2*c*d*e + 45*a*b*d*e*g))/(4096*a^6))*root(268435456*a^11*b^5*z^4 + 983040*a^7*b^3*e*g*z^2 - 6881280*a^6*b^4*c*e*z^2 - 4718592*a^6*b^4*d^2*z^2 - 774144*a^4*b^3*c*d*g*z + 55296*a^5*b^2*d*g^2*z + 153600*a^4*b^3*d*e^2*z + 2709504*a^3*b^4*c^2*d*z + 8640*a^2*b^2*d^2*e*g - 6300*a^2*b^2*c*e^2*g - 60480*a*b^3*c*d^2*e + 111132*a*b^3*c^3*g + 2268*a^3*b*c*g^3 - 23814*a^2*b^2*c^2*g^2 + 450*a^3*b*e^2*g^2 + 22050*a*b^3*c^2*e^2 - 625*a^2*b^2*e^4 + 20736*a*b^3*d^4 - 81*a^4*g^4 - 194481*b^4*c^4, z, k), k, 1, 4)","B"
174,1,1056,266,5.662002,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^4,x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(68719476736\,a^{15}\,b^5\,z^4-1211105280\,a^8\,b^4\,c\,e\,z^2+110100480\,a^9\,b^3\,e\,g\,z^2-838860800\,a^8\,b^4\,d^2\,z^2-88309760\,a^5\,b^3\,c\,d\,g\,z+485703680\,a^4\,b^4\,c^2\,d\,z+4014080\,a^6\,b^2\,d\,g^2\,z+18432000\,a^5\,b^3\,d\,e^2\,z+672000\,a^2\,b^2\,d^2\,e\,g-485100\,a^2\,b^2\,c\,e^2\,g-7392000\,a\,b^3\,c\,d^2\,e+12782924\,a\,b^3\,c^3\,g+105644\,a^3\,b\,c\,g^3-1743126\,a^2\,b^2\,c^2\,g^2+22050\,a^3\,b\,e^2\,g^2+2668050\,a\,b^3\,c^2\,e^2-50625\,a^2\,b^2\,e^4+2560000\,a\,b^3\,d^4-2401\,a^4\,g^4-35153041\,b^4\,c^4,z,k\right)\,\left(\mathrm{root}\left(68719476736\,a^{15}\,b^5\,z^4-1211105280\,a^8\,b^4\,c\,e\,z^2+110100480\,a^9\,b^3\,e\,g\,z^2-838860800\,a^8\,b^4\,d^2\,z^2-88309760\,a^5\,b^3\,c\,d\,g\,z+485703680\,a^4\,b^4\,c^2\,d\,z+4014080\,a^6\,b^2\,d\,g^2\,z+18432000\,a^5\,b^3\,d\,e^2\,z+672000\,a^2\,b^2\,d^2\,e\,g-485100\,a^2\,b^2\,c\,e^2\,g-7392000\,a\,b^3\,c\,d^2\,e+12782924\,a\,b^3\,c^3\,g+105644\,a^3\,b\,c\,g^3-1743126\,a^2\,b^2\,c^2\,g^2+22050\,a^3\,b\,e^2\,g^2+2668050\,a\,b^3\,c^2\,e^2-50625\,a^2\,b^2\,e^4+2560000\,a\,b^3\,d^4-2401\,a^4\,g^4-35153041\,b^4\,c^4,z,k\right)\,\left(\frac{20185088\,a^7\,b^3\,c-1835008\,a^8\,b^2\,g}{2097152\,a^9}-\frac{5\,b^3\,d\,x}{a^2}\right)+\frac{x\,\left(1568\,a^5\,b\,g^2-34496\,a^4\,b^2\,c\,g+7200\,a^4\,b^2\,e^2+189728\,a^3\,b^3\,c^2\right)}{131072\,a^9}-\frac{75\,b^2\,d\,e}{256\,a^5}\right)-\frac{-735\,a^2\,e\,g^2+16170\,a\,b\,c\,e\,g-11200\,a\,b\,d^2\,g+3375\,a\,b\,e^3-88935\,b^2\,c^2\,e+123200\,b^2\,c\,d^2}{2097152\,a^9}-\frac{x\,\left(4000\,b^2\,d^3-5775\,c\,e\,b^2\,d+525\,a\,e\,g\,b\,d\right)}{131072\,a^9}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^5\,z^4-1211105280\,a^8\,b^4\,c\,e\,z^2+110100480\,a^9\,b^3\,e\,g\,z^2-838860800\,a^8\,b^4\,d^2\,z^2-88309760\,a^5\,b^3\,c\,d\,g\,z+485703680\,a^4\,b^4\,c^2\,d\,z+4014080\,a^6\,b^2\,d\,g^2\,z+18432000\,a^5\,b^3\,d\,e^2\,z+672000\,a^2\,b^2\,d^2\,e\,g-485100\,a^2\,b^2\,c\,e^2\,g-7392000\,a\,b^3\,c\,d^2\,e+12782924\,a\,b^3\,c^3\,g+105644\,a^3\,b\,c\,g^3-1743126\,a^2\,b^2\,c^2\,g^2+22050\,a^3\,b\,e^2\,g^2+2668050\,a\,b^3\,c^2\,e^2-50625\,a^2\,b^2\,e^4+2560000\,a\,b^3\,d^4-2401\,a^4\,g^4-35153041\,b^4\,c^4,z,k\right)\right)+\frac{\frac{f}{12\,b}+\frac{11\,d\,x^2}{32\,a}+\frac{113\,e\,x^3}{384\,a}-\frac{3\,x^5\,\left(11\,b\,c-a\,g\right)}{64\,a^2}+\frac{7\,b\,x^9\,\left(11\,b\,c-a\,g\right)}{384\,a^3}+\frac{x\,\left(51\,b\,c+7\,a\,g\right)}{128\,a\,b}+\frac{5\,b^2\,d\,x^{10}}{32\,a^3}+\frac{15\,b^2\,e\,x^{11}}{128\,a^3}-\frac{5\,b\,d\,x^6}{12\,a^2}-\frac{21\,b\,e\,x^7}{64\,a^2}}{a^3-3\,a^2\,b\,x^4+3\,a\,b^2\,x^8-b^3\,x^{12}}","Not used",1,"symsum(log(- root(68719476736*a^15*b^5*z^4 - 1211105280*a^8*b^4*c*e*z^2 + 110100480*a^9*b^3*e*g*z^2 - 838860800*a^8*b^4*d^2*z^2 - 88309760*a^5*b^3*c*d*g*z + 485703680*a^4*b^4*c^2*d*z + 4014080*a^6*b^2*d*g^2*z + 18432000*a^5*b^3*d*e^2*z + 672000*a^2*b^2*d^2*e*g - 485100*a^2*b^2*c*e^2*g - 7392000*a*b^3*c*d^2*e + 12782924*a*b^3*c^3*g + 105644*a^3*b*c*g^3 - 1743126*a^2*b^2*c^2*g^2 + 22050*a^3*b*e^2*g^2 + 2668050*a*b^3*c^2*e^2 - 50625*a^2*b^2*e^4 + 2560000*a*b^3*d^4 - 2401*a^4*g^4 - 35153041*b^4*c^4, z, k)*(root(68719476736*a^15*b^5*z^4 - 1211105280*a^8*b^4*c*e*z^2 + 110100480*a^9*b^3*e*g*z^2 - 838860800*a^8*b^4*d^2*z^2 - 88309760*a^5*b^3*c*d*g*z + 485703680*a^4*b^4*c^2*d*z + 4014080*a^6*b^2*d*g^2*z + 18432000*a^5*b^3*d*e^2*z + 672000*a^2*b^2*d^2*e*g - 485100*a^2*b^2*c*e^2*g - 7392000*a*b^3*c*d^2*e + 12782924*a*b^3*c^3*g + 105644*a^3*b*c*g^3 - 1743126*a^2*b^2*c^2*g^2 + 22050*a^3*b*e^2*g^2 + 2668050*a*b^3*c^2*e^2 - 50625*a^2*b^2*e^4 + 2560000*a*b^3*d^4 - 2401*a^4*g^4 - 35153041*b^4*c^4, z, k)*((20185088*a^7*b^3*c - 1835008*a^8*b^2*g)/(2097152*a^9) - (5*b^3*d*x)/a^2) + (x*(1568*a^5*b*g^2 + 189728*a^3*b^3*c^2 + 7200*a^4*b^2*e^2 - 34496*a^4*b^2*c*g))/(131072*a^9) - (75*b^2*d*e)/(256*a^5)) - (123200*b^2*c*d^2 - 88935*b^2*c^2*e - 735*a^2*e*g^2 + 3375*a*b*e^3 - 11200*a*b*d^2*g + 16170*a*b*c*e*g)/(2097152*a^9) - (x*(4000*b^2*d^3 - 5775*b^2*c*d*e + 525*a*b*d*e*g))/(131072*a^9))*root(68719476736*a^15*b^5*z^4 - 1211105280*a^8*b^4*c*e*z^2 + 110100480*a^9*b^3*e*g*z^2 - 838860800*a^8*b^4*d^2*z^2 - 88309760*a^5*b^3*c*d*g*z + 485703680*a^4*b^4*c^2*d*z + 4014080*a^6*b^2*d*g^2*z + 18432000*a^5*b^3*d*e^2*z + 672000*a^2*b^2*d^2*e*g - 485100*a^2*b^2*c*e^2*g - 7392000*a*b^3*c*d^2*e + 12782924*a*b^3*c^3*g + 105644*a^3*b*c*g^3 - 1743126*a^2*b^2*c^2*g^2 + 22050*a^3*b*e^2*g^2 + 2668050*a*b^3*c^2*e^2 - 50625*a^2*b^2*e^4 + 2560000*a*b^3*d^4 - 2401*a^4*g^4 - 35153041*b^4*c^4, z, k), k, 1, 4) + (f/(12*b) + (11*d*x^2)/(32*a) + (113*e*x^3)/(384*a) - (3*x^5*(11*b*c - a*g))/(64*a^2) + (7*b*x^9*(11*b*c - a*g))/(384*a^3) + (x*(51*b*c + 7*a*g))/(128*a*b) + (5*b^2*d*x^10)/(32*a^3) + (15*b^2*e*x^11)/(128*a^3) - (5*b*d*x^6)/(12*a^2) - (21*b*e*x^7)/(64*a^2))/(a^3 - b^3*x^12 - 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
175,1,5042,319,5.588404,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4),x)","\left(\sum _{k=1}^4\ln\left(b^2\,c\,d^2-b^2\,c^2\,e-a^2\,e\,g^2+a^2\,f^2\,g+b^2\,d^3\,x-a\,b\,e^3-a\,b\,c\,f^2-a\,b\,d^2\,g-{\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)}^2\,a\,b^3\,c\,16-\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)\,b^3\,c^2\,x\,4+b^2\,c^2\,f\,x+a^2\,f\,g^2\,x+{\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)}^2\,a^2\,b^2\,g\,16+{\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)}^2\,a\,b^3\,d\,x\,16+\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)\,a\,b^2\,e^2\,x\,4-\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)\,a^2\,b\,g^2\,x\,4+2\,a\,b\,c\,e\,g+2\,a\,b\,d\,e\,f+\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)\,a\,b^2\,c\,f\,8-\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)\,a\,b^2\,d\,e\,8-\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)\,a^2\,b\,f\,g\,8+a\,b\,d\,f^2\,x-a\,b\,e^2\,f\,x-2\,b^2\,c\,d\,e\,x+\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)\,a\,b^2\,c\,g\,x\,8-\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)\,a\,b^2\,d\,f\,x\,8-2\,a\,b\,c\,f\,g\,x+2\,a\,b\,d\,e\,g\,x\right)\,\mathrm{root}\left(256\,a^3\,b^5\,z^4-256\,a^3\,b^4\,f\,z^3-64\,a^3\,b^3\,e\,g\,z^2+64\,a^2\,b^4\,c\,e\,z^2+96\,a^3\,b^3\,f^2\,z^2+32\,a^2\,b^4\,d^2\,z^2+32\,a^3\,b^2\,e\,f\,g\,z-32\,a^2\,b^3\,c\,e\,f\,z+32\,a^2\,b^3\,c\,d\,g\,z-16\,a^3\,b^2\,d\,g^2\,z-16\,a^2\,b^3\,d^2\,f\,z+16\,a^2\,b^3\,d\,e^2\,z-16\,a\,b^4\,c^2\,d\,z-16\,a^3\,b^2\,f^3\,z-8\,a^2\,b^2\,c\,d\,f\,g+4\,a^2\,b^2\,d^2\,e\,g-4\,a^2\,b^2\,d\,e^2\,f-4\,a^2\,b^2\,c\,e^2\,g+4\,a^2\,b^2\,c\,e\,f^2-4\,a^3\,b\,e\,f^2\,g+4\,a^3\,b\,d\,f\,g^2+4\,a\,b^3\,c^2\,d\,f-4\,a\,b^3\,c\,d^2\,e-4\,a^3\,b\,c\,g^3-4\,a\,b^3\,c^3\,g+6\,a^2\,b^2\,c^2\,g^2+2\,a^2\,b^2\,d^2\,f^2+2\,a^3\,b\,e^2\,g^2+2\,a\,b^3\,c^2\,e^2+a^2\,b^2\,e^4+a^3\,b\,f^4+a\,b^3\,d^4+a^4\,g^4+b^4\,c^4,z,k\right)\right)+\frac{g\,x}{b}","Not used",1,"symsum(log(b^2*c*d^2 - b^2*c^2*e - a^2*e*g^2 + a^2*f^2*g + b^2*d^3*x - a*b*e^3 - a*b*c*f^2 - a*b*d^2*g - 16*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)^2*a*b^3*c - 4*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)*b^3*c^2*x + b^2*c^2*f*x + a^2*f*g^2*x + 16*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)^2*a^2*b^2*g + 16*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)^2*a*b^3*d*x + 4*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)*a*b^2*e^2*x - 4*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)*a^2*b*g^2*x + 2*a*b*c*e*g + 2*a*b*d*e*f + 8*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)*a*b^2*c*f - 8*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)*a*b^2*d*e - 8*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)*a^2*b*f*g + a*b*d*f^2*x - a*b*e^2*f*x - 2*b^2*c*d*e*x + 8*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)*a*b^2*c*g*x - 8*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k)*a*b^2*d*f*x - 2*a*b*c*f*g*x + 2*a*b*d*e*g*x)*root(256*a^3*b^5*z^4 - 256*a^3*b^4*f*z^3 - 64*a^3*b^3*e*g*z^2 + 64*a^2*b^4*c*e*z^2 + 96*a^3*b^3*f^2*z^2 + 32*a^2*b^4*d^2*z^2 + 32*a^3*b^2*e*f*g*z - 32*a^2*b^3*c*e*f*z + 32*a^2*b^3*c*d*g*z - 16*a^3*b^2*d*g^2*z - 16*a^2*b^3*d^2*f*z + 16*a^2*b^3*d*e^2*z - 16*a*b^4*c^2*d*z - 16*a^3*b^2*f^3*z - 8*a^2*b^2*c*d*f*g + 4*a^2*b^2*d^2*e*g - 4*a^2*b^2*d*e^2*f - 4*a^2*b^2*c*e^2*g + 4*a^2*b^2*c*e*f^2 - 4*a^3*b*e*f^2*g + 4*a^3*b*d*f*g^2 + 4*a*b^3*c^2*d*f - 4*a*b^3*c*d^2*e - 4*a^3*b*c*g^3 - 4*a*b^3*c^3*g + 6*a^2*b^2*c^2*g^2 + 2*a^2*b^2*d^2*f^2 + 2*a^3*b*e^2*g^2 + 2*a*b^3*c^2*e^2 + a^2*b^2*e^4 + a^3*b*f^4 + a*b^3*d^4 + a^4*g^4 + b^4*c^4, z, k), k, 1, 4) + (g*x)/b","B"
176,1,1383,341,5.591625,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^2,x)","\left(\sum _{k=1}^4\ln\left(-\frac{a^2\,e\,g^2+6\,a\,b\,c\,e\,g-4\,a\,b\,d^2\,g+a\,b\,e^3+9\,b^2\,c^2\,e-12\,b^2\,c\,d^2}{64\,a^3}-\frac{\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2+3072\,a^4\,b^4\,c\,e\,z^2+2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z-128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z-1152\,a^2\,b^4\,c^2\,d\,z-16\,a^2\,b^2\,d^2\,e\,g+12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3+54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4+81\,b^4\,c^4+a^2\,b^2\,e^4+a^4\,g^4,z,k\right)\,b\,\left(9\,b^2\,c^2\,x+a^2\,g^2\,x+\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2+3072\,a^4\,b^4\,c\,e\,z^2+2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z-128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z-1152\,a^2\,b^4\,c^2\,d\,z-16\,a^2\,b^2\,d^2\,e\,g+12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3+54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4+81\,b^4\,c^4+a^2\,b^2\,e^4+a^4\,g^4,z,k\right)\,a^3\,b\,g\,16-a\,b\,e^2\,x+\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2+3072\,a^4\,b^4\,c\,e\,z^2+2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z-128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z-1152\,a^2\,b^4\,c^2\,d\,z-16\,a^2\,b^2\,d^2\,e\,g+12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3+54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4+81\,b^4\,c^4+a^2\,b^2\,e^4+a^4\,g^4,z,k\right)\,a^2\,b^2\,c\,48+4\,a\,b\,d\,e-\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2+3072\,a^4\,b^4\,c\,e\,z^2+2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z-128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z-1152\,a^2\,b^4\,c^2\,d\,z-16\,a^2\,b^2\,d^2\,e\,g+12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3+54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4+81\,b^4\,c^4+a^2\,b^2\,e^4+a^4\,g^4,z,k\right)\,a^2\,b^2\,d\,x\,32+6\,a\,b\,c\,g\,x\right)}{a^2\,4}-\frac{b\,d\,x\,\left(-2\,b\,d^2+3\,b\,c\,e+a\,e\,g\right)}{16\,a^3}\right)\,\mathrm{root}\left(65536\,a^7\,b^5\,z^4+1024\,a^5\,b^3\,e\,g\,z^2+3072\,a^4\,b^4\,c\,e\,z^2+2048\,a^4\,b^4\,d^2\,z^2-768\,a^3\,b^3\,c\,d\,g\,z-128\,a^4\,b^2\,d\,g^2\,z+128\,a^3\,b^3\,d\,e^2\,z-1152\,a^2\,b^4\,c^2\,d\,z-16\,a^2\,b^2\,d^2\,e\,g+12\,a^2\,b^2\,c\,e^2\,g-48\,a\,b^3\,c\,d^2\,e+108\,a\,b^3\,c^3\,g+12\,a^3\,b\,c\,g^3+54\,a^2\,b^2\,c^2\,g^2+2\,a^3\,b\,e^2\,g^2+18\,a\,b^3\,c^2\,e^2+16\,a\,b^3\,d^4+81\,b^4\,c^4+a^2\,b^2\,e^4+a^4\,g^4,z,k\right)\right)+\frac{\frac{d\,x^2}{4\,a}-\frac{f}{4\,b}+\frac{e\,x^3}{4\,a}+\frac{x\,\left(b\,c-a\,g\right)}{4\,a\,b}}{b\,x^4+a}","Not used",1,"symsum(log(- (9*b^2*c^2*e - 12*b^2*c*d^2 + a^2*e*g^2 + a*b*e^3 - 4*a*b*d^2*g + 6*a*b*c*e*g)/(64*a^3) - (root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 + 3072*a^4*b^4*c*e*z^2 + 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z - 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z - 1152*a^2*b^4*c^2*d*z - 16*a^2*b^2*d^2*e*g + 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 + 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 + 81*b^4*c^4 + a^2*b^2*e^4 + a^4*g^4, z, k)*b*(9*b^2*c^2*x + a^2*g^2*x + 16*root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 + 3072*a^4*b^4*c*e*z^2 + 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z - 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z - 1152*a^2*b^4*c^2*d*z - 16*a^2*b^2*d^2*e*g + 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 + 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 + 81*b^4*c^4 + a^2*b^2*e^4 + a^4*g^4, z, k)*a^3*b*g - a*b*e^2*x + 48*root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 + 3072*a^4*b^4*c*e*z^2 + 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z - 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z - 1152*a^2*b^4*c^2*d*z - 16*a^2*b^2*d^2*e*g + 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 + 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 + 81*b^4*c^4 + a^2*b^2*e^4 + a^4*g^4, z, k)*a^2*b^2*c + 4*a*b*d*e - 32*root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 + 3072*a^4*b^4*c*e*z^2 + 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z - 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z - 1152*a^2*b^4*c^2*d*z - 16*a^2*b^2*d^2*e*g + 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 + 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 + 81*b^4*c^4 + a^2*b^2*e^4 + a^4*g^4, z, k)*a^2*b^2*d*x + 6*a*b*c*g*x))/(4*a^2) - (b*d*x*(3*b*c*e - 2*b*d^2 + a*e*g))/(16*a^3))*root(65536*a^7*b^5*z^4 + 1024*a^5*b^3*e*g*z^2 + 3072*a^4*b^4*c*e*z^2 + 2048*a^4*b^4*d^2*z^2 - 768*a^3*b^3*c*d*g*z - 128*a^4*b^2*d*g^2*z + 128*a^3*b^3*d*e^2*z - 1152*a^2*b^4*c^2*d*z - 16*a^2*b^2*d^2*e*g + 12*a^2*b^2*c*e^2*g - 48*a*b^3*c*d^2*e + 108*a*b^3*c^3*g + 12*a^3*b*c*g^3 + 54*a^2*b^2*c^2*g^2 + 2*a^3*b*e^2*g^2 + 18*a*b^3*c^2*e^2 + 16*a*b^3*d^4 + 81*b^4*c^4 + a^2*b^2*e^4 + a^4*g^4, z, k), k, 1, 4) + ((d*x^2)/(4*a) - f/(4*b) + (e*x^3)/(4*a) + (x*(b*c - a*g))/(4*a*b))/(a + b*x^4)","B"
177,1,1001,394,0.705415,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^3,x)","\frac{\frac{5\,d\,x^2}{16\,a}-\frac{f}{8\,b}+\frac{9\,e\,x^3}{32\,a}+\frac{x^5\,\left(7\,b\,c+a\,g\right)}{32\,a^2}+\frac{x\,\left(11\,b\,c-3\,a\,g\right)}{32\,a\,b}+\frac{3\,b\,d\,x^6}{16\,a^2}+\frac{5\,b\,e\,x^7}{32\,a^2}}{a^2+2\,a\,b\,x^4+b^2\,x^8}+\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(268435456\,a^{11}\,b^5\,z^4+983040\,a^7\,b^3\,e\,g\,z^2+6881280\,a^6\,b^4\,c\,e\,z^2+4718592\,a^6\,b^4\,d^2\,z^2-774144\,a^4\,b^3\,c\,d\,g\,z-55296\,a^5\,b^2\,d\,g^2\,z+153600\,a^4\,b^3\,d\,e^2\,z-2709504\,a^3\,b^4\,c^2\,d\,z-8640\,a^2\,b^2\,d^2\,e\,g+6300\,a^2\,b^2\,c\,e^2\,g-60480\,a\,b^3\,c\,d^2\,e+111132\,a\,b^3\,c^3\,g+2268\,a^3\,b\,c\,g^3+23814\,a^2\,b^2\,c^2\,g^2+450\,a^3\,b\,e^2\,g^2+22050\,a\,b^3\,c^2\,e^2+625\,a^2\,b^2\,e^4+20736\,a\,b^3\,d^4+81\,a^4\,g^4+194481\,b^4\,c^4,z,k\right)\,\left(\mathrm{root}\left(268435456\,a^{11}\,b^5\,z^4+983040\,a^7\,b^3\,e\,g\,z^2+6881280\,a^6\,b^4\,c\,e\,z^2+4718592\,a^6\,b^4\,d^2\,z^2-774144\,a^4\,b^3\,c\,d\,g\,z-55296\,a^5\,b^2\,d\,g^2\,z+153600\,a^4\,b^3\,d\,e^2\,z-2709504\,a^3\,b^4\,c^2\,d\,z-8640\,a^2\,b^2\,d^2\,e\,g+6300\,a^2\,b^2\,c\,e^2\,g-60480\,a\,b^3\,c\,d^2\,e+111132\,a\,b^3\,c^3\,g+2268\,a^3\,b\,c\,g^3+23814\,a^2\,b^2\,c^2\,g^2+450\,a^3\,b\,e^2\,g^2+22050\,a\,b^3\,c^2\,e^2+625\,a^2\,b^2\,e^4+20736\,a\,b^3\,d^4+81\,a^4\,g^4+194481\,b^4\,c^4,z,k\right)\,\left(\frac{49152\,g\,a^6\,b^2+344064\,c\,a^5\,b^3}{32768\,a^6}-\frac{6\,b^3\,d\,x}{a}\right)+\frac{x\,\left(144\,a^4\,b\,g^2+2016\,a^3\,b^2\,c\,g-400\,a^3\,b^2\,e^2+7056\,a^2\,b^3\,c^2\right)}{4096\,a^6}+\frac{15\,b^2\,d\,e}{32\,a^3}\right)-\frac{45\,a^2\,e\,g^2+630\,a\,b\,c\,e\,g-432\,a\,b\,d^2\,g+125\,a\,b\,e^3+2205\,b^2\,c^2\,e-3024\,b^2\,c\,d^2}{32768\,a^6}-\frac{x\,\left(-216\,b^2\,d^3+315\,c\,e\,b^2\,d+45\,a\,e\,g\,b\,d\right)}{4096\,a^6}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^5\,z^4+983040\,a^7\,b^3\,e\,g\,z^2+6881280\,a^6\,b^4\,c\,e\,z^2+4718592\,a^6\,b^4\,d^2\,z^2-774144\,a^4\,b^3\,c\,d\,g\,z-55296\,a^5\,b^2\,d\,g^2\,z+153600\,a^4\,b^3\,d\,e^2\,z-2709504\,a^3\,b^4\,c^2\,d\,z-8640\,a^2\,b^2\,d^2\,e\,g+6300\,a^2\,b^2\,c\,e^2\,g-60480\,a\,b^3\,c\,d^2\,e+111132\,a\,b^3\,c^3\,g+2268\,a^3\,b\,c\,g^3+23814\,a^2\,b^2\,c^2\,g^2+450\,a^3\,b\,e^2\,g^2+22050\,a\,b^3\,c^2\,e^2+625\,a^2\,b^2\,e^4+20736\,a\,b^3\,d^4+81\,a^4\,g^4+194481\,b^4\,c^4,z,k\right)\right)","Not used",1,"((5*d*x^2)/(16*a) - f/(8*b) + (9*e*x^3)/(32*a) + (x^5*(7*b*c + a*g))/(32*a^2) + (x*(11*b*c - 3*a*g))/(32*a*b) + (3*b*d*x^6)/(16*a^2) + (5*b*e*x^7)/(32*a^2))/(a^2 + b^2*x^8 + 2*a*b*x^4) + symsum(log(- root(268435456*a^11*b^5*z^4 + 983040*a^7*b^3*e*g*z^2 + 6881280*a^6*b^4*c*e*z^2 + 4718592*a^6*b^4*d^2*z^2 - 774144*a^4*b^3*c*d*g*z - 55296*a^5*b^2*d*g^2*z + 153600*a^4*b^3*d*e^2*z - 2709504*a^3*b^4*c^2*d*z - 8640*a^2*b^2*d^2*e*g + 6300*a^2*b^2*c*e^2*g - 60480*a*b^3*c*d^2*e + 111132*a*b^3*c^3*g + 2268*a^3*b*c*g^3 + 23814*a^2*b^2*c^2*g^2 + 450*a^3*b*e^2*g^2 + 22050*a*b^3*c^2*e^2 + 625*a^2*b^2*e^4 + 20736*a*b^3*d^4 + 81*a^4*g^4 + 194481*b^4*c^4, z, k)*(root(268435456*a^11*b^5*z^4 + 983040*a^7*b^3*e*g*z^2 + 6881280*a^6*b^4*c*e*z^2 + 4718592*a^6*b^4*d^2*z^2 - 774144*a^4*b^3*c*d*g*z - 55296*a^5*b^2*d*g^2*z + 153600*a^4*b^3*d*e^2*z - 2709504*a^3*b^4*c^2*d*z - 8640*a^2*b^2*d^2*e*g + 6300*a^2*b^2*c*e^2*g - 60480*a*b^3*c*d^2*e + 111132*a*b^3*c^3*g + 2268*a^3*b*c*g^3 + 23814*a^2*b^2*c^2*g^2 + 450*a^3*b*e^2*g^2 + 22050*a*b^3*c^2*e^2 + 625*a^2*b^2*e^4 + 20736*a*b^3*d^4 + 81*a^4*g^4 + 194481*b^4*c^4, z, k)*((344064*a^5*b^3*c + 49152*a^6*b^2*g)/(32768*a^6) - (6*b^3*d*x)/a) + (x*(144*a^4*b*g^2 + 7056*a^2*b^3*c^2 - 400*a^3*b^2*e^2 + 2016*a^3*b^2*c*g))/(4096*a^6) + (15*b^2*d*e)/(32*a^3)) - (2205*b^2*c^2*e - 3024*b^2*c*d^2 + 45*a^2*e*g^2 + 125*a*b*e^3 - 432*a*b*d^2*g + 630*a*b*c*e*g)/(32768*a^6) - (x*(315*b^2*c*d*e - 216*b^2*d^3 + 45*a*b*d*e*g))/(4096*a^6))*root(268435456*a^11*b^5*z^4 + 983040*a^7*b^3*e*g*z^2 + 6881280*a^6*b^4*c*e*z^2 + 4718592*a^6*b^4*d^2*z^2 - 774144*a^4*b^3*c*d*g*z - 55296*a^5*b^2*d*g^2*z + 153600*a^4*b^3*d*e^2*z - 2709504*a^3*b^4*c^2*d*z - 8640*a^2*b^2*d^2*e*g + 6300*a^2*b^2*c*e^2*g - 60480*a*b^3*c*d^2*e + 111132*a*b^3*c^3*g + 2268*a^3*b*c*g^3 + 23814*a^2*b^2*c^2*g^2 + 450*a^3*b*e^2*g^2 + 22050*a*b^3*c^2*e^2 + 625*a^2*b^2*e^4 + 20736*a*b^3*d^4 + 81*a^4*g^4 + 194481*b^4*c^4, z, k), k, 1, 4)","B"
178,1,1053,437,5.561542,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^4,x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(68719476736\,a^{15}\,b^5\,z^4+1211105280\,a^8\,b^4\,c\,e\,z^2+110100480\,a^9\,b^3\,e\,g\,z^2+838860800\,a^8\,b^4\,d^2\,z^2-88309760\,a^5\,b^3\,c\,d\,g\,z-485703680\,a^4\,b^4\,c^2\,d\,z-4014080\,a^6\,b^2\,d\,g^2\,z+18432000\,a^5\,b^3\,d\,e^2\,z-672000\,a^2\,b^2\,d^2\,e\,g+485100\,a^2\,b^2\,c\,e^2\,g-7392000\,a\,b^3\,c\,d^2\,e+12782924\,a\,b^3\,c^3\,g+105644\,a^3\,b\,c\,g^3+1743126\,a^2\,b^2\,c^2\,g^2+22050\,a^3\,b\,e^2\,g^2+2668050\,a\,b^3\,c^2\,e^2+50625\,a^2\,b^2\,e^4+2560000\,a\,b^3\,d^4+2401\,a^4\,g^4+35153041\,b^4\,c^4,z,k\right)\,\left(\mathrm{root}\left(68719476736\,a^{15}\,b^5\,z^4+1211105280\,a^8\,b^4\,c\,e\,z^2+110100480\,a^9\,b^3\,e\,g\,z^2+838860800\,a^8\,b^4\,d^2\,z^2-88309760\,a^5\,b^3\,c\,d\,g\,z-485703680\,a^4\,b^4\,c^2\,d\,z-4014080\,a^6\,b^2\,d\,g^2\,z+18432000\,a^5\,b^3\,d\,e^2\,z-672000\,a^2\,b^2\,d^2\,e\,g+485100\,a^2\,b^2\,c\,e^2\,g-7392000\,a\,b^3\,c\,d^2\,e+12782924\,a\,b^3\,c^3\,g+105644\,a^3\,b\,c\,g^3+1743126\,a^2\,b^2\,c^2\,g^2+22050\,a^3\,b\,e^2\,g^2+2668050\,a\,b^3\,c^2\,e^2+50625\,a^2\,b^2\,e^4+2560000\,a\,b^3\,d^4+2401\,a^4\,g^4+35153041\,b^4\,c^4,z,k\right)\,\left(\frac{1835008\,g\,a^8\,b^2+20185088\,c\,a^7\,b^3}{2097152\,a^9}-\frac{5\,b^3\,d\,x}{a^2}\right)+\frac{x\,\left(1568\,a^5\,b\,g^2+34496\,a^4\,b^2\,c\,g-7200\,a^4\,b^2\,e^2+189728\,a^3\,b^3\,c^2\right)}{131072\,a^9}+\frac{75\,b^2\,d\,e}{256\,a^5}\right)-\frac{735\,a^2\,e\,g^2+16170\,a\,b\,c\,e\,g-11200\,a\,b\,d^2\,g+3375\,a\,b\,e^3+88935\,b^2\,c^2\,e-123200\,b^2\,c\,d^2}{2097152\,a^9}-\frac{x\,\left(-4000\,b^2\,d^3+5775\,c\,e\,b^2\,d+525\,a\,e\,g\,b\,d\right)}{131072\,a^9}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^5\,z^4+1211105280\,a^8\,b^4\,c\,e\,z^2+110100480\,a^9\,b^3\,e\,g\,z^2+838860800\,a^8\,b^4\,d^2\,z^2-88309760\,a^5\,b^3\,c\,d\,g\,z-485703680\,a^4\,b^4\,c^2\,d\,z-4014080\,a^6\,b^2\,d\,g^2\,z+18432000\,a^5\,b^3\,d\,e^2\,z-672000\,a^2\,b^2\,d^2\,e\,g+485100\,a^2\,b^2\,c\,e^2\,g-7392000\,a\,b^3\,c\,d^2\,e+12782924\,a\,b^3\,c^3\,g+105644\,a^3\,b\,c\,g^3+1743126\,a^2\,b^2\,c^2\,g^2+22050\,a^3\,b\,e^2\,g^2+2668050\,a\,b^3\,c^2\,e^2+50625\,a^2\,b^2\,e^4+2560000\,a\,b^3\,d^4+2401\,a^4\,g^4+35153041\,b^4\,c^4,z,k\right)\right)+\frac{\frac{11\,d\,x^2}{32\,a}-\frac{f}{12\,b}+\frac{113\,e\,x^3}{384\,a}+\frac{3\,x^5\,\left(11\,b\,c+a\,g\right)}{64\,a^2}+\frac{7\,b\,x^9\,\left(11\,b\,c+a\,g\right)}{384\,a^3}+\frac{x\,\left(51\,b\,c-7\,a\,g\right)}{128\,a\,b}+\frac{5\,b^2\,d\,x^{10}}{32\,a^3}+\frac{15\,b^2\,e\,x^{11}}{128\,a^3}+\frac{5\,b\,d\,x^6}{12\,a^2}+\frac{21\,b\,e\,x^7}{64\,a^2}}{a^3+3\,a^2\,b\,x^4+3\,a\,b^2\,x^8+b^3\,x^{12}}","Not used",1,"symsum(log(- root(68719476736*a^15*b^5*z^4 + 1211105280*a^8*b^4*c*e*z^2 + 110100480*a^9*b^3*e*g*z^2 + 838860800*a^8*b^4*d^2*z^2 - 88309760*a^5*b^3*c*d*g*z - 485703680*a^4*b^4*c^2*d*z - 4014080*a^6*b^2*d*g^2*z + 18432000*a^5*b^3*d*e^2*z - 672000*a^2*b^2*d^2*e*g + 485100*a^2*b^2*c*e^2*g - 7392000*a*b^3*c*d^2*e + 12782924*a*b^3*c^3*g + 105644*a^3*b*c*g^3 + 1743126*a^2*b^2*c^2*g^2 + 22050*a^3*b*e^2*g^2 + 2668050*a*b^3*c^2*e^2 + 50625*a^2*b^2*e^4 + 2560000*a*b^3*d^4 + 2401*a^4*g^4 + 35153041*b^4*c^4, z, k)*(root(68719476736*a^15*b^5*z^4 + 1211105280*a^8*b^4*c*e*z^2 + 110100480*a^9*b^3*e*g*z^2 + 838860800*a^8*b^4*d^2*z^2 - 88309760*a^5*b^3*c*d*g*z - 485703680*a^4*b^4*c^2*d*z - 4014080*a^6*b^2*d*g^2*z + 18432000*a^5*b^3*d*e^2*z - 672000*a^2*b^2*d^2*e*g + 485100*a^2*b^2*c*e^2*g - 7392000*a*b^3*c*d^2*e + 12782924*a*b^3*c^3*g + 105644*a^3*b*c*g^3 + 1743126*a^2*b^2*c^2*g^2 + 22050*a^3*b*e^2*g^2 + 2668050*a*b^3*c^2*e^2 + 50625*a^2*b^2*e^4 + 2560000*a*b^3*d^4 + 2401*a^4*g^4 + 35153041*b^4*c^4, z, k)*((20185088*a^7*b^3*c + 1835008*a^8*b^2*g)/(2097152*a^9) - (5*b^3*d*x)/a^2) + (x*(1568*a^5*b*g^2 + 189728*a^3*b^3*c^2 - 7200*a^4*b^2*e^2 + 34496*a^4*b^2*c*g))/(131072*a^9) + (75*b^2*d*e)/(256*a^5)) - (88935*b^2*c^2*e - 123200*b^2*c*d^2 + 735*a^2*e*g^2 + 3375*a*b*e^3 - 11200*a*b*d^2*g + 16170*a*b*c*e*g)/(2097152*a^9) - (x*(5775*b^2*c*d*e - 4000*b^2*d^3 + 525*a*b*d*e*g))/(131072*a^9))*root(68719476736*a^15*b^5*z^4 + 1211105280*a^8*b^4*c*e*z^2 + 110100480*a^9*b^3*e*g*z^2 + 838860800*a^8*b^4*d^2*z^2 - 88309760*a^5*b^3*c*d*g*z - 485703680*a^4*b^4*c^2*d*z - 4014080*a^6*b^2*d*g^2*z + 18432000*a^5*b^3*d*e^2*z - 672000*a^2*b^2*d^2*e*g + 485100*a^2*b^2*c*e^2*g - 7392000*a*b^3*c*d^2*e + 12782924*a*b^3*c^3*g + 105644*a^3*b*c*g^3 + 1743126*a^2*b^2*c^2*g^2 + 22050*a^3*b*e^2*g^2 + 2668050*a*b^3*c^2*e^2 + 50625*a^2*b^2*e^4 + 2560000*a*b^3*d^4 + 2401*a^4*g^4 + 35153041*b^4*c^4, z, k), k, 1, 4) + ((11*d*x^2)/(32*a) - f/(12*b) + (113*e*x^3)/(384*a) + (3*x^5*(11*b*c + a*g))/(64*a^2) + (7*b*x^9*(11*b*c + a*g))/(384*a^3) + (x*(51*b*c - 7*a*g))/(128*a*b) + (5*b^2*d*x^10)/(32*a^3) + (15*b^2*e*x^11)/(128*a^3) + (5*b*d*x^6)/(12*a^2) + (21*b*e*x^7)/(64*a^2))/(a^3 + b^3*x^12 + 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
179,1,15,11,0.031292,"\text{Not used}","int(-(x^4 - 1)^3/(x + x^2 + x^3 + 1)^3,x)","-\frac{x^4}{4}+x^3-\frac{3\,x^2}{2}+x","Not used",1,"x - (3*x^2)/2 + x^3 - x^4/4","B"
180,1,11,11,0.023566,"\text{Not used}","int((x^4 - 1)^2/(x + x^2 + x^3 + 1)^2,x)","\frac{x\,\left(x^2-3\,x+3\right)}{3}","Not used",1,"(x*(x^2 - 3*x + 3))/3","B"
181,1,6,9,0.018579,"\text{Not used}","int(-(x^4 - 1)/(x + x^2 + x^3 + 1),x)","-\frac{x\,\left(x-2\right)}{2}","Not used",1,"-(x*(x - 2))/2","B"
182,1,6,8,0.002000,"\text{Not used}","int(-(x + x^2 + x^3 + 1)/(x^4 - 1),x)","-\ln\left(x-1\right)","Not used",1,"-log(x - 1)","B"
183,1,7,7,0.030811,"\text{Not used}","int((x + x^2 + x^3 + 1)^2/(x^4 - 1)^2,x)","-\frac{1}{x-1}","Not used",1,"-1/(x - 1)","B"
184,1,7,11,4.837012,"\text{Not used}","int(-(x + x^2 + x^3 + 1)^3/(x^4 - 1)^3,x)","\frac{1}{2\,{\left(x-1\right)}^2}","Not used",1,"1/(2*(x - 1)^2)","B"
185,1,7,11,4.805936,"\text{Not used}","int((x + x^2 + x^3 + 1)^4/(x^4 - 1)^4,x)","-\frac{1}{3\,{\left(x-1\right)}^3}","Not used",1,"-1/(3*(x - 1)^3)","B"
186,1,2478,165,5.544061,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4),x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(256\,a^3\,b^6\,z^4+256\,a^3\,b^5\,f\,z^3-64\,a^3\,b^4\,e\,g\,z^2-64\,a^3\,b^4\,d\,h\,z^2-64\,a^2\,b^5\,c\,e\,z^2-32\,a^4\,b^3\,h^2\,z^2+96\,a^3\,b^4\,f^2\,z^2-32\,a^2\,b^5\,d^2\,z^2-32\,a^3\,b^3\,e\,f\,g\,z-32\,a^3\,b^3\,d\,f\,h\,z+32\,a^3\,b^3\,c\,g\,h\,z-32\,a^2\,b^4\,c\,e\,f\,z+32\,a^2\,b^4\,c\,d\,g\,z+16\,a^4\,b^2\,g^2\,h\,z-16\,a^4\,b^2\,f\,h^2\,z+16\,a^3\,b^3\,e^2\,h\,z+16\,a^3\,b^3\,d\,g^2\,z+16\,a^2\,b^4\,c^2\,h\,z-16\,a^2\,b^4\,d^2\,f\,z+16\,a^2\,b^4\,d\,e^2\,z+16\,a\,b^5\,c^2\,d\,z+16\,a^3\,b^3\,f^3\,z-8\,a^3\,b^2\,d\,e\,g\,h+8\,a^3\,b^2\,c\,f\,g\,h+8\,a^2\,b^3\,c\,d\,f\,g-8\,a^2\,b^3\,c\,d\,e\,h+4\,a^3\,b^2\,e^2\,f\,h-4\,a^3\,b^2\,e\,f^2\,g-4\,a^3\,b^2\,d\,f^2\,h+4\,a^3\,b^2\,d\,f\,g^2+4\,a^2\,b^3\,c^2\,f\,h-4\,a^3\,b^2\,c\,e\,h^2-4\,a^2\,b^3\,d^2\,e\,g+4\,a^2\,b^3\,d\,e^2\,f+4\,a^2\,b^3\,c\,e^2\,g-4\,a^2\,b^3\,c\,e\,f^2+4\,a^4\,b\,f\,g^2\,h-4\,a^4\,b\,e\,g\,h^2+4\,a\,b^4\,c^2\,d\,f-4\,a\,b^4\,c\,d^2\,e+4\,a^4\,b\,d\,h^3-4\,a\,b^4\,c^3\,g+6\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2-6\,a^2\,b^3\,c^2\,g^2-2\,a^2\,b^3\,d^2\,f^2-2\,a^4\,b\,f^2\,h^2+4\,a^2\,b^3\,d^3\,h-4\,a^3\,b^2\,c\,g^3+2\,a\,b^4\,c^2\,e^2+a^3\,b^2\,f^4+a\,b^4\,d^4+a^5\,h^4-a^2\,b^3\,e^4-a^4\,b\,g^4-b^5\,c^4,z,k\right)\,\left(\frac{8\,a\,b^3\,c\,f-8\,a\,b^3\,d\,e-8\,a^2\,b^2\,e\,h+8\,a^2\,b^2\,f\,g}{b}+\mathrm{root}\left(256\,a^3\,b^6\,z^4+256\,a^3\,b^5\,f\,z^3-64\,a^3\,b^4\,e\,g\,z^2-64\,a^3\,b^4\,d\,h\,z^2-64\,a^2\,b^5\,c\,e\,z^2-32\,a^4\,b^3\,h^2\,z^2+96\,a^3\,b^4\,f^2\,z^2-32\,a^2\,b^5\,d^2\,z^2-32\,a^3\,b^3\,e\,f\,g\,z-32\,a^3\,b^3\,d\,f\,h\,z+32\,a^3\,b^3\,c\,g\,h\,z-32\,a^2\,b^4\,c\,e\,f\,z+32\,a^2\,b^4\,c\,d\,g\,z+16\,a^4\,b^2\,g^2\,h\,z-16\,a^4\,b^2\,f\,h^2\,z+16\,a^3\,b^3\,e^2\,h\,z+16\,a^3\,b^3\,d\,g^2\,z+16\,a^2\,b^4\,c^2\,h\,z-16\,a^2\,b^4\,d^2\,f\,z+16\,a^2\,b^4\,d\,e^2\,z+16\,a\,b^5\,c^2\,d\,z+16\,a^3\,b^3\,f^3\,z-8\,a^3\,b^2\,d\,e\,g\,h+8\,a^3\,b^2\,c\,f\,g\,h+8\,a^2\,b^3\,c\,d\,f\,g-8\,a^2\,b^3\,c\,d\,e\,h+4\,a^3\,b^2\,e^2\,f\,h-4\,a^3\,b^2\,e\,f^2\,g-4\,a^3\,b^2\,d\,f^2\,h+4\,a^3\,b^2\,d\,f\,g^2+4\,a^2\,b^3\,c^2\,f\,h-4\,a^3\,b^2\,c\,e\,h^2-4\,a^2\,b^3\,d^2\,e\,g+4\,a^2\,b^3\,d\,e^2\,f+4\,a^2\,b^3\,c\,e^2\,g-4\,a^2\,b^3\,c\,e\,f^2+4\,a^4\,b\,f\,g^2\,h-4\,a^4\,b\,e\,g\,h^2+4\,a\,b^4\,c^2\,d\,f-4\,a\,b^4\,c\,d^2\,e+4\,a^4\,b\,d\,h^3-4\,a\,b^4\,c^3\,g+6\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2-6\,a^2\,b^3\,c^2\,g^2-2\,a^2\,b^3\,d^2\,f^2-2\,a^4\,b\,f^2\,h^2+4\,a^2\,b^3\,d^3\,h-4\,a^3\,b^2\,c\,g^3+2\,a\,b^4\,c^2\,e^2+a^3\,b^2\,f^4+a\,b^4\,d^4+a^5\,h^4-a^2\,b^3\,e^4-a^4\,b\,g^4-b^5\,c^4,z,k\right)\,\left(\frac{16\,g\,a^2\,b^3+16\,c\,a\,b^4}{b}-\frac{x\,\left(16\,h\,a^2\,b^3+16\,d\,a\,b^4\right)}{b}\right)+\frac{x\,\left(4\,a^2\,b^2\,g^2-8\,f\,h\,a^2\,b^2+8\,a\,b^3\,c\,g+4\,a\,b^3\,e^2-8\,d\,f\,a\,b^3+4\,b^4\,c^2\right)}{b}\right)-\frac{a^3\,g\,h^2+a^2\,b\,c\,h^2+2\,a^2\,b\,d\,g\,h-2\,a^2\,b\,e\,f\,h-a^2\,b\,e\,g^2+a^2\,b\,f^2\,g+2\,a\,b^2\,c\,d\,h-2\,a\,b^2\,c\,e\,g+a\,b^2\,c\,f^2+a\,b^2\,d^2\,g-2\,a\,b^2\,d\,e\,f+a\,b^2\,e^3-b^3\,c^2\,e+b^3\,c\,d^2}{b}-\frac{x\,\left(a^3\,h^3+3\,a^2\,b\,d\,h^2-2\,a^2\,b\,e\,g\,h-a^2\,b\,f^2\,h+a^2\,b\,f\,g^2-2\,a\,b^2\,c\,e\,h+2\,a\,b^2\,c\,f\,g+3\,a\,b^2\,d^2\,h-2\,a\,b^2\,d\,e\,g-a\,b^2\,d\,f^2+a\,b^2\,e^2\,f+b^3\,c^2\,f-2\,b^3\,c\,d\,e+b^3\,d^3\right)}{b}\right)\,\mathrm{root}\left(256\,a^3\,b^6\,z^4+256\,a^3\,b^5\,f\,z^3-64\,a^3\,b^4\,e\,g\,z^2-64\,a^3\,b^4\,d\,h\,z^2-64\,a^2\,b^5\,c\,e\,z^2-32\,a^4\,b^3\,h^2\,z^2+96\,a^3\,b^4\,f^2\,z^2-32\,a^2\,b^5\,d^2\,z^2-32\,a^3\,b^3\,e\,f\,g\,z-32\,a^3\,b^3\,d\,f\,h\,z+32\,a^3\,b^3\,c\,g\,h\,z-32\,a^2\,b^4\,c\,e\,f\,z+32\,a^2\,b^4\,c\,d\,g\,z+16\,a^4\,b^2\,g^2\,h\,z-16\,a^4\,b^2\,f\,h^2\,z+16\,a^3\,b^3\,e^2\,h\,z+16\,a^3\,b^3\,d\,g^2\,z+16\,a^2\,b^4\,c^2\,h\,z-16\,a^2\,b^4\,d^2\,f\,z+16\,a^2\,b^4\,d\,e^2\,z+16\,a\,b^5\,c^2\,d\,z+16\,a^3\,b^3\,f^3\,z-8\,a^3\,b^2\,d\,e\,g\,h+8\,a^3\,b^2\,c\,f\,g\,h+8\,a^2\,b^3\,c\,d\,f\,g-8\,a^2\,b^3\,c\,d\,e\,h+4\,a^3\,b^2\,e^2\,f\,h-4\,a^3\,b^2\,e\,f^2\,g-4\,a^3\,b^2\,d\,f^2\,h+4\,a^3\,b^2\,d\,f\,g^2+4\,a^2\,b^3\,c^2\,f\,h-4\,a^3\,b^2\,c\,e\,h^2-4\,a^2\,b^3\,d^2\,e\,g+4\,a^2\,b^3\,d\,e^2\,f+4\,a^2\,b^3\,c\,e^2\,g-4\,a^2\,b^3\,c\,e\,f^2+4\,a^4\,b\,f\,g^2\,h-4\,a^4\,b\,e\,g\,h^2+4\,a\,b^4\,c^2\,d\,f-4\,a\,b^4\,c\,d^2\,e+4\,a^4\,b\,d\,h^3-4\,a\,b^4\,c^3\,g+6\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2-6\,a^2\,b^3\,c^2\,g^2-2\,a^2\,b^3\,d^2\,f^2-2\,a^4\,b\,f^2\,h^2+4\,a^2\,b^3\,d^3\,h-4\,a^3\,b^2\,c\,g^3+2\,a\,b^4\,c^2\,e^2+a^3\,b^2\,f^4+a\,b^4\,d^4+a^5\,h^4-a^2\,b^3\,e^4-a^4\,b\,g^4-b^5\,c^4,z,k\right)\right)-\frac{h\,x^2}{2\,b}-\frac{g\,x}{b}","Not used",1,"symsum(log(- root(256*a^3*b^6*z^4 + 256*a^3*b^5*f*z^3 - 64*a^3*b^4*e*g*z^2 - 64*a^3*b^4*d*h*z^2 - 64*a^2*b^5*c*e*z^2 - 32*a^4*b^3*h^2*z^2 + 96*a^3*b^4*f^2*z^2 - 32*a^2*b^5*d^2*z^2 - 32*a^3*b^3*e*f*g*z - 32*a^3*b^3*d*f*h*z + 32*a^3*b^3*c*g*h*z - 32*a^2*b^4*c*e*f*z + 32*a^2*b^4*c*d*g*z + 16*a^4*b^2*g^2*h*z - 16*a^4*b^2*f*h^2*z + 16*a^3*b^3*e^2*h*z + 16*a^3*b^3*d*g^2*z + 16*a^2*b^4*c^2*h*z - 16*a^2*b^4*d^2*f*z + 16*a^2*b^4*d*e^2*z + 16*a*b^5*c^2*d*z + 16*a^3*b^3*f^3*z - 8*a^3*b^2*d*e*g*h + 8*a^3*b^2*c*f*g*h + 8*a^2*b^3*c*d*f*g - 8*a^2*b^3*c*d*e*h + 4*a^3*b^2*e^2*f*h - 4*a^3*b^2*e*f^2*g - 4*a^3*b^2*d*f^2*h + 4*a^3*b^2*d*f*g^2 + 4*a^2*b^3*c^2*f*h - 4*a^3*b^2*c*e*h^2 - 4*a^2*b^3*d^2*e*g + 4*a^2*b^3*d*e^2*f + 4*a^2*b^3*c*e^2*g - 4*a^2*b^3*c*e*f^2 + 4*a^4*b*f*g^2*h - 4*a^4*b*e*g*h^2 + 4*a*b^4*c^2*d*f - 4*a*b^4*c*d^2*e + 4*a^4*b*d*h^3 - 4*a*b^4*c^3*g + 6*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 - 6*a^2*b^3*c^2*g^2 - 2*a^2*b^3*d^2*f^2 - 2*a^4*b*f^2*h^2 + 4*a^2*b^3*d^3*h - 4*a^3*b^2*c*g^3 + 2*a*b^4*c^2*e^2 + a^3*b^2*f^4 + a*b^4*d^4 + a^5*h^4 - a^2*b^3*e^4 - a^4*b*g^4 - b^5*c^4, z, k)*((8*a*b^3*c*f - 8*a*b^3*d*e - 8*a^2*b^2*e*h + 8*a^2*b^2*f*g)/b + root(256*a^3*b^6*z^4 + 256*a^3*b^5*f*z^3 - 64*a^3*b^4*e*g*z^2 - 64*a^3*b^4*d*h*z^2 - 64*a^2*b^5*c*e*z^2 - 32*a^4*b^3*h^2*z^2 + 96*a^3*b^4*f^2*z^2 - 32*a^2*b^5*d^2*z^2 - 32*a^3*b^3*e*f*g*z - 32*a^3*b^3*d*f*h*z + 32*a^3*b^3*c*g*h*z - 32*a^2*b^4*c*e*f*z + 32*a^2*b^4*c*d*g*z + 16*a^4*b^2*g^2*h*z - 16*a^4*b^2*f*h^2*z + 16*a^3*b^3*e^2*h*z + 16*a^3*b^3*d*g^2*z + 16*a^2*b^4*c^2*h*z - 16*a^2*b^4*d^2*f*z + 16*a^2*b^4*d*e^2*z + 16*a*b^5*c^2*d*z + 16*a^3*b^3*f^3*z - 8*a^3*b^2*d*e*g*h + 8*a^3*b^2*c*f*g*h + 8*a^2*b^3*c*d*f*g - 8*a^2*b^3*c*d*e*h + 4*a^3*b^2*e^2*f*h - 4*a^3*b^2*e*f^2*g - 4*a^3*b^2*d*f^2*h + 4*a^3*b^2*d*f*g^2 + 4*a^2*b^3*c^2*f*h - 4*a^3*b^2*c*e*h^2 - 4*a^2*b^3*d^2*e*g + 4*a^2*b^3*d*e^2*f + 4*a^2*b^3*c*e^2*g - 4*a^2*b^3*c*e*f^2 + 4*a^4*b*f*g^2*h - 4*a^4*b*e*g*h^2 + 4*a*b^4*c^2*d*f - 4*a*b^4*c*d^2*e + 4*a^4*b*d*h^3 - 4*a*b^4*c^3*g + 6*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 - 6*a^2*b^3*c^2*g^2 - 2*a^2*b^3*d^2*f^2 - 2*a^4*b*f^2*h^2 + 4*a^2*b^3*d^3*h - 4*a^3*b^2*c*g^3 + 2*a*b^4*c^2*e^2 + a^3*b^2*f^4 + a*b^4*d^4 + a^5*h^4 - a^2*b^3*e^4 - a^4*b*g^4 - b^5*c^4, z, k)*((16*a^2*b^3*g + 16*a*b^4*c)/b - (x*(16*a^2*b^3*h + 16*a*b^4*d))/b) + (x*(4*b^4*c^2 + 4*a*b^3*e^2 + 4*a^2*b^2*g^2 + 8*a*b^3*c*g - 8*a*b^3*d*f - 8*a^2*b^2*f*h))/b) - (a*b^2*e^3 + b^3*c*d^2 - b^3*c^2*e + a^3*g*h^2 + a*b^2*c*f^2 + a*b^2*d^2*g + a^2*b*c*h^2 - a^2*b*e*g^2 + a^2*b*f^2*g + 2*a*b^2*c*d*h - 2*a*b^2*c*e*g - 2*a*b^2*d*e*f + 2*a^2*b*d*g*h - 2*a^2*b*e*f*h)/b - (x*(b^3*d^3 + a^3*h^3 + b^3*c^2*f - 2*b^3*c*d*e - a*b^2*d*f^2 + a*b^2*e^2*f + 3*a*b^2*d^2*h + 3*a^2*b*d*h^2 + a^2*b*f*g^2 - a^2*b*f^2*h - 2*a*b^2*c*e*h + 2*a*b^2*c*f*g - 2*a*b^2*d*e*g - 2*a^2*b*e*g*h))/b)*root(256*a^3*b^6*z^4 + 256*a^3*b^5*f*z^3 - 64*a^3*b^4*e*g*z^2 - 64*a^3*b^4*d*h*z^2 - 64*a^2*b^5*c*e*z^2 - 32*a^4*b^3*h^2*z^2 + 96*a^3*b^4*f^2*z^2 - 32*a^2*b^5*d^2*z^2 - 32*a^3*b^3*e*f*g*z - 32*a^3*b^3*d*f*h*z + 32*a^3*b^3*c*g*h*z - 32*a^2*b^4*c*e*f*z + 32*a^2*b^4*c*d*g*z + 16*a^4*b^2*g^2*h*z - 16*a^4*b^2*f*h^2*z + 16*a^3*b^3*e^2*h*z + 16*a^3*b^3*d*g^2*z + 16*a^2*b^4*c^2*h*z - 16*a^2*b^4*d^2*f*z + 16*a^2*b^4*d*e^2*z + 16*a*b^5*c^2*d*z + 16*a^3*b^3*f^3*z - 8*a^3*b^2*d*e*g*h + 8*a^3*b^2*c*f*g*h + 8*a^2*b^3*c*d*f*g - 8*a^2*b^3*c*d*e*h + 4*a^3*b^2*e^2*f*h - 4*a^3*b^2*e*f^2*g - 4*a^3*b^2*d*f^2*h + 4*a^3*b^2*d*f*g^2 + 4*a^2*b^3*c^2*f*h - 4*a^3*b^2*c*e*h^2 - 4*a^2*b^3*d^2*e*g + 4*a^2*b^3*d*e^2*f + 4*a^2*b^3*c*e^2*g - 4*a^2*b^3*c*e*f^2 + 4*a^4*b*f*g^2*h - 4*a^4*b*e*g*h^2 + 4*a*b^4*c^2*d*f - 4*a*b^4*c*d^2*e + 4*a^4*b*d*h^3 - 4*a*b^4*c^3*g + 6*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 - 6*a^2*b^3*c^2*g^2 - 2*a^2*b^3*d^2*f^2 - 2*a^4*b*f^2*h^2 + 4*a^2*b^3*d^3*h - 4*a^3*b^2*c*g^3 + 2*a*b^4*c^2*e^2 + a^3*b^2*f^4 + a*b^4*d^4 + a^5*h^4 - a^2*b^3*e^4 - a^4*b*g^4 - b^5*c^4, z, k), k, 1, 4) - (h*x^2)/(2*b) - (g*x)/b","B"
187,1,3810,188,5.074265,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a - b*x^4),x)","\left(\sum _{l=1}^4\ln\left(-\frac{a^4\,i^3+3\,a^3\,b\,e\,i^2-2\,a^3\,b\,f\,h\,i-a^3\,b\,g^2\,i+a^3\,b\,g\,h^2-2\,a^2\,b^2\,c\,g\,i+a^2\,b^2\,c\,h^2-2\,a^2\,b^2\,d\,f\,i+2\,a^2\,b^2\,d\,g\,h+3\,a^2\,b^2\,e^2\,i-2\,a^2\,b^2\,e\,f\,h-a^2\,b^2\,e\,g^2+a^2\,b^2\,f^2\,g-a\,b^3\,c^2\,i+2\,a\,b^3\,c\,d\,h-2\,a\,b^3\,c\,e\,g+a\,b^3\,c\,f^2+a\,b^3\,d^2\,g-2\,a\,b^3\,d\,e\,f+a\,b^3\,e^3-b^4\,c^2\,e+b^4\,c\,d^2}{b^2}-\mathrm{root}\left(256\,a^3\,b^7\,z^4+256\,a^3\,b^6\,f\,z^3-64\,a^4\,b^4\,g\,i\,z^2-64\,a^3\,b^5\,e\,g\,z^2-64\,a^3\,b^5\,d\,h\,z^2-64\,a^3\,b^5\,c\,i\,z^2-64\,a^2\,b^6\,c\,e\,z^2-32\,a^4\,b^4\,h^2\,z^2+96\,a^3\,b^5\,f^2\,z^2-32\,a^2\,b^6\,d^2\,z^2-32\,a^4\,b^3\,f\,g\,i\,z+32\,a^4\,b^3\,e\,h\,i\,z-32\,a^3\,b^4\,e\,f\,g\,z-32\,a^3\,b^4\,d\,f\,h\,z+32\,a^3\,b^4\,d\,e\,i\,z+32\,a^3\,b^4\,c\,g\,h\,z-32\,a^3\,b^4\,c\,f\,i\,z-32\,a^2\,b^5\,c\,e\,f\,z+32\,a^2\,b^5\,c\,d\,g\,z+16\,a^5\,b^2\,h\,i^2\,z+16\,a^4\,b^3\,g^2\,h\,z-16\,a^4\,b^3\,f\,h^2\,z+16\,a^4\,b^3\,d\,i^2\,z+16\,a^3\,b^4\,e^2\,h\,z+16\,a^3\,b^4\,d\,g^2\,z+16\,a^2\,b^5\,c^2\,h\,z-16\,a^2\,b^5\,d^2\,f\,z+16\,a^2\,b^5\,d\,e^2\,z+16\,a\,b^6\,c^2\,d\,z+16\,a^3\,b^4\,f^3\,z+8\,a^4\,b^2\,e\,f\,h\,i-8\,a^4\,b^2\,d\,g\,h\,i-8\,a^3\,b^3\,d\,e\,g\,h+8\,a^3\,b^3\,d\,e\,f\,i+8\,a^3\,b^3\,c\,f\,g\,h+8\,a^3\,b^3\,c\,e\,g\,i-8\,a^3\,b^3\,c\,d\,h\,i+8\,a^2\,b^4\,c\,d\,f\,g-8\,a^2\,b^4\,c\,d\,e\,h-4\,a^4\,b^2\,f^2\,g\,i+4\,a^4\,b^2\,f\,g^2\,h+4\,a^4\,b^2\,e\,g^2\,i-4\,a^4\,b^2\,e\,g\,h^2-4\,a^4\,b^2\,c\,h^2\,i-4\,a^3\,b^3\,d^2\,g\,i+4\,a^4\,b^2\,d\,f\,i^2+4\,a^4\,b^2\,c\,g\,i^2+4\,a^3\,b^3\,e^2\,f\,h-4\,a^3\,b^3\,e\,f^2\,g-4\,a^3\,b^3\,d\,f^2\,h-4\,a^3\,b^3\,c\,f^2\,i+4\,a^3\,b^3\,d\,f\,g^2+4\,a^2\,b^4\,c^2\,f\,h+4\,a^2\,b^4\,c^2\,e\,i-4\,a^3\,b^3\,c\,e\,h^2-4\,a^2\,b^4\,d^2\,e\,g-4\,a^2\,b^4\,c\,d^2\,i+4\,a^2\,b^4\,d\,e^2\,f+4\,a^2\,b^4\,c\,e^2\,g-4\,a^2\,b^4\,c\,e\,f^2-4\,a^5\,b\,g\,h^2\,i+4\,a^5\,b\,f\,h\,i^2+4\,a\,b^5\,c^2\,d\,f-4\,a\,b^5\,c\,d^2\,e-4\,a^5\,b\,e\,i^3-4\,a\,b^5\,c^3\,g-6\,a^4\,b^2\,e^2\,i^2-2\,a^4\,b^2\,f^2\,h^2+6\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2+2\,a^3\,b^3\,c^2\,i^2-6\,a^2\,b^4\,c^2\,g^2-2\,a^2\,b^4\,d^2\,f^2+2\,a^5\,b\,g^2\,i^2-4\,a^3\,b^3\,e^3\,i+4\,a^4\,b^2\,d\,h^3+4\,a^2\,b^4\,d^3\,h-4\,a^3\,b^3\,c\,g^3+2\,a\,b^5\,c^2\,e^2+a^3\,b^3\,f^4+a^5\,b\,h^4+a\,b^5\,d^4-a^4\,b^2\,g^4-a^2\,b^4\,e^4-a^6\,i^4-b^6\,c^4,z,l\right)\,\left(-\frac{8\,a\,b^4\,d\,e-8\,a\,b^4\,c\,f+8\,a^2\,b^3\,d\,i+8\,a^2\,b^3\,e\,h-8\,a^2\,b^3\,f\,g+8\,a^3\,b^2\,h\,i}{b^2}+\mathrm{root}\left(256\,a^3\,b^7\,z^4+256\,a^3\,b^6\,f\,z^3-64\,a^4\,b^4\,g\,i\,z^2-64\,a^3\,b^5\,e\,g\,z^2-64\,a^3\,b^5\,d\,h\,z^2-64\,a^3\,b^5\,c\,i\,z^2-64\,a^2\,b^6\,c\,e\,z^2-32\,a^4\,b^4\,h^2\,z^2+96\,a^3\,b^5\,f^2\,z^2-32\,a^2\,b^6\,d^2\,z^2-32\,a^4\,b^3\,f\,g\,i\,z+32\,a^4\,b^3\,e\,h\,i\,z-32\,a^3\,b^4\,e\,f\,g\,z-32\,a^3\,b^4\,d\,f\,h\,z+32\,a^3\,b^4\,d\,e\,i\,z+32\,a^3\,b^4\,c\,g\,h\,z-32\,a^3\,b^4\,c\,f\,i\,z-32\,a^2\,b^5\,c\,e\,f\,z+32\,a^2\,b^5\,c\,d\,g\,z+16\,a^5\,b^2\,h\,i^2\,z+16\,a^4\,b^3\,g^2\,h\,z-16\,a^4\,b^3\,f\,h^2\,z+16\,a^4\,b^3\,d\,i^2\,z+16\,a^3\,b^4\,e^2\,h\,z+16\,a^3\,b^4\,d\,g^2\,z+16\,a^2\,b^5\,c^2\,h\,z-16\,a^2\,b^5\,d^2\,f\,z+16\,a^2\,b^5\,d\,e^2\,z+16\,a\,b^6\,c^2\,d\,z+16\,a^3\,b^4\,f^3\,z+8\,a^4\,b^2\,e\,f\,h\,i-8\,a^4\,b^2\,d\,g\,h\,i-8\,a^3\,b^3\,d\,e\,g\,h+8\,a^3\,b^3\,d\,e\,f\,i+8\,a^3\,b^3\,c\,f\,g\,h+8\,a^3\,b^3\,c\,e\,g\,i-8\,a^3\,b^3\,c\,d\,h\,i+8\,a^2\,b^4\,c\,d\,f\,g-8\,a^2\,b^4\,c\,d\,e\,h-4\,a^4\,b^2\,f^2\,g\,i+4\,a^4\,b^2\,f\,g^2\,h+4\,a^4\,b^2\,e\,g^2\,i-4\,a^4\,b^2\,e\,g\,h^2-4\,a^4\,b^2\,c\,h^2\,i-4\,a^3\,b^3\,d^2\,g\,i+4\,a^4\,b^2\,d\,f\,i^2+4\,a^4\,b^2\,c\,g\,i^2+4\,a^3\,b^3\,e^2\,f\,h-4\,a^3\,b^3\,e\,f^2\,g-4\,a^3\,b^3\,d\,f^2\,h-4\,a^3\,b^3\,c\,f^2\,i+4\,a^3\,b^3\,d\,f\,g^2+4\,a^2\,b^4\,c^2\,f\,h+4\,a^2\,b^4\,c^2\,e\,i-4\,a^3\,b^3\,c\,e\,h^2-4\,a^2\,b^4\,d^2\,e\,g-4\,a^2\,b^4\,c\,d^2\,i+4\,a^2\,b^4\,d\,e^2\,f+4\,a^2\,b^4\,c\,e^2\,g-4\,a^2\,b^4\,c\,e\,f^2-4\,a^5\,b\,g\,h^2\,i+4\,a^5\,b\,f\,h\,i^2+4\,a\,b^5\,c^2\,d\,f-4\,a\,b^5\,c\,d^2\,e-4\,a^5\,b\,e\,i^3-4\,a\,b^5\,c^3\,g-6\,a^4\,b^2\,e^2\,i^2-2\,a^4\,b^2\,f^2\,h^2+6\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2+2\,a^3\,b^3\,c^2\,i^2-6\,a^2\,b^4\,c^2\,g^2-2\,a^2\,b^4\,d^2\,f^2+2\,a^5\,b\,g^2\,i^2-4\,a^3\,b^3\,e^3\,i+4\,a^4\,b^2\,d\,h^3+4\,a^2\,b^4\,d^3\,h-4\,a^3\,b^3\,c\,g^3+2\,a\,b^5\,c^2\,e^2+a^3\,b^3\,f^4+a^5\,b\,h^4+a\,b^5\,d^4-a^4\,b^2\,g^4-a^2\,b^4\,e^4-a^6\,i^4-b^6\,c^4,z,l\right)\,\left(\frac{16\,g\,a^2\,b^4+16\,c\,a\,b^5}{b^2}-\frac{x\,\left(16\,h\,a^2\,b^3+16\,d\,a\,b^4\right)}{b}\right)+\frac{x\,\left(4\,a^3\,b\,i^2+8\,a^2\,b^2\,e\,i+4\,a^2\,b^2\,g^2-8\,f\,h\,a^2\,b^2+8\,a\,b^3\,c\,g+4\,a\,b^3\,e^2-8\,d\,f\,a\,b^3+4\,b^4\,c^2\right)}{b}\right)-\frac{x\,\left(a^3\,f\,i^2-2\,a^3\,g\,h\,i+a^3\,h^3-2\,a^2\,b\,c\,h\,i-2\,a^2\,b\,d\,g\,i+3\,a^2\,b\,d\,h^2+2\,a^2\,b\,e\,f\,i-2\,a^2\,b\,e\,g\,h-a^2\,b\,f^2\,h+a^2\,b\,f\,g^2-2\,a\,b^2\,c\,d\,i-2\,a\,b^2\,c\,e\,h+2\,a\,b^2\,c\,f\,g+3\,a\,b^2\,d^2\,h-2\,a\,b^2\,d\,e\,g-a\,b^2\,d\,f^2+a\,b^2\,e^2\,f+b^3\,c^2\,f-2\,b^3\,c\,d\,e+b^3\,d^3\right)}{b}\right)\,\mathrm{root}\left(256\,a^3\,b^7\,z^4+256\,a^3\,b^6\,f\,z^3-64\,a^4\,b^4\,g\,i\,z^2-64\,a^3\,b^5\,e\,g\,z^2-64\,a^3\,b^5\,d\,h\,z^2-64\,a^3\,b^5\,c\,i\,z^2-64\,a^2\,b^6\,c\,e\,z^2-32\,a^4\,b^4\,h^2\,z^2+96\,a^3\,b^5\,f^2\,z^2-32\,a^2\,b^6\,d^2\,z^2-32\,a^4\,b^3\,f\,g\,i\,z+32\,a^4\,b^3\,e\,h\,i\,z-32\,a^3\,b^4\,e\,f\,g\,z-32\,a^3\,b^4\,d\,f\,h\,z+32\,a^3\,b^4\,d\,e\,i\,z+32\,a^3\,b^4\,c\,g\,h\,z-32\,a^3\,b^4\,c\,f\,i\,z-32\,a^2\,b^5\,c\,e\,f\,z+32\,a^2\,b^5\,c\,d\,g\,z+16\,a^5\,b^2\,h\,i^2\,z+16\,a^4\,b^3\,g^2\,h\,z-16\,a^4\,b^3\,f\,h^2\,z+16\,a^4\,b^3\,d\,i^2\,z+16\,a^3\,b^4\,e^2\,h\,z+16\,a^3\,b^4\,d\,g^2\,z+16\,a^2\,b^5\,c^2\,h\,z-16\,a^2\,b^5\,d^2\,f\,z+16\,a^2\,b^5\,d\,e^2\,z+16\,a\,b^6\,c^2\,d\,z+16\,a^3\,b^4\,f^3\,z+8\,a^4\,b^2\,e\,f\,h\,i-8\,a^4\,b^2\,d\,g\,h\,i-8\,a^3\,b^3\,d\,e\,g\,h+8\,a^3\,b^3\,d\,e\,f\,i+8\,a^3\,b^3\,c\,f\,g\,h+8\,a^3\,b^3\,c\,e\,g\,i-8\,a^3\,b^3\,c\,d\,h\,i+8\,a^2\,b^4\,c\,d\,f\,g-8\,a^2\,b^4\,c\,d\,e\,h-4\,a^4\,b^2\,f^2\,g\,i+4\,a^4\,b^2\,f\,g^2\,h+4\,a^4\,b^2\,e\,g^2\,i-4\,a^4\,b^2\,e\,g\,h^2-4\,a^4\,b^2\,c\,h^2\,i-4\,a^3\,b^3\,d^2\,g\,i+4\,a^4\,b^2\,d\,f\,i^2+4\,a^4\,b^2\,c\,g\,i^2+4\,a^3\,b^3\,e^2\,f\,h-4\,a^3\,b^3\,e\,f^2\,g-4\,a^3\,b^3\,d\,f^2\,h-4\,a^3\,b^3\,c\,f^2\,i+4\,a^3\,b^3\,d\,f\,g^2+4\,a^2\,b^4\,c^2\,f\,h+4\,a^2\,b^4\,c^2\,e\,i-4\,a^3\,b^3\,c\,e\,h^2-4\,a^2\,b^4\,d^2\,e\,g-4\,a^2\,b^4\,c\,d^2\,i+4\,a^2\,b^4\,d\,e^2\,f+4\,a^2\,b^4\,c\,e^2\,g-4\,a^2\,b^4\,c\,e\,f^2-4\,a^5\,b\,g\,h^2\,i+4\,a^5\,b\,f\,h\,i^2+4\,a\,b^5\,c^2\,d\,f-4\,a\,b^5\,c\,d^2\,e-4\,a^5\,b\,e\,i^3-4\,a\,b^5\,c^3\,g-6\,a^4\,b^2\,e^2\,i^2-2\,a^4\,b^2\,f^2\,h^2+6\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2+2\,a^3\,b^3\,c^2\,i^2-6\,a^2\,b^4\,c^2\,g^2-2\,a^2\,b^4\,d^2\,f^2+2\,a^5\,b\,g^2\,i^2-4\,a^3\,b^3\,e^3\,i+4\,a^4\,b^2\,d\,h^3+4\,a^2\,b^4\,d^3\,h-4\,a^3\,b^3\,c\,g^3+2\,a\,b^5\,c^2\,e^2+a^3\,b^3\,f^4+a^5\,b\,h^4+a\,b^5\,d^4-a^4\,b^2\,g^4-a^2\,b^4\,e^4-a^6\,i^4-b^6\,c^4,z,l\right)\right)-\frac{h\,x^2}{2\,b}-\frac{i\,x^3}{3\,b}-\frac{g\,x}{b}","Not used",1,"symsum(log(- (a^4*i^3 + a*b^3*e^3 + b^4*c*d^2 - b^4*c^2*e + a^2*b^2*c*h^2 - a^2*b^2*e*g^2 + a^2*b^2*f^2*g + 3*a^2*b^2*e^2*i + a*b^3*c*f^2 + a*b^3*d^2*g - a*b^3*c^2*i + 3*a^3*b*e*i^2 + a^3*b*g*h^2 - a^3*b*g^2*i - 2*a^2*b^2*c*g*i - 2*a^2*b^2*d*f*i + 2*a^2*b^2*d*g*h - 2*a^2*b^2*e*f*h + 2*a*b^3*c*d*h - 2*a*b^3*c*e*g - 2*a*b^3*d*e*f - 2*a^3*b*f*h*i)/b^2 - root(256*a^3*b^7*z^4 + 256*a^3*b^6*f*z^3 - 64*a^4*b^4*g*i*z^2 - 64*a^3*b^5*e*g*z^2 - 64*a^3*b^5*d*h*z^2 - 64*a^3*b^5*c*i*z^2 - 64*a^2*b^6*c*e*z^2 - 32*a^4*b^4*h^2*z^2 + 96*a^3*b^5*f^2*z^2 - 32*a^2*b^6*d^2*z^2 - 32*a^4*b^3*f*g*i*z + 32*a^4*b^3*e*h*i*z - 32*a^3*b^4*e*f*g*z - 32*a^3*b^4*d*f*h*z + 32*a^3*b^4*d*e*i*z + 32*a^3*b^4*c*g*h*z - 32*a^3*b^4*c*f*i*z - 32*a^2*b^5*c*e*f*z + 32*a^2*b^5*c*d*g*z + 16*a^5*b^2*h*i^2*z + 16*a^4*b^3*g^2*h*z - 16*a^4*b^3*f*h^2*z + 16*a^4*b^3*d*i^2*z + 16*a^3*b^4*e^2*h*z + 16*a^3*b^4*d*g^2*z + 16*a^2*b^5*c^2*h*z - 16*a^2*b^5*d^2*f*z + 16*a^2*b^5*d*e^2*z + 16*a*b^6*c^2*d*z + 16*a^3*b^4*f^3*z + 8*a^4*b^2*e*f*h*i - 8*a^4*b^2*d*g*h*i - 8*a^3*b^3*d*e*g*h + 8*a^3*b^3*d*e*f*i + 8*a^3*b^3*c*f*g*h + 8*a^3*b^3*c*e*g*i - 8*a^3*b^3*c*d*h*i + 8*a^2*b^4*c*d*f*g - 8*a^2*b^4*c*d*e*h - 4*a^4*b^2*f^2*g*i + 4*a^4*b^2*f*g^2*h + 4*a^4*b^2*e*g^2*i - 4*a^4*b^2*e*g*h^2 - 4*a^4*b^2*c*h^2*i - 4*a^3*b^3*d^2*g*i + 4*a^4*b^2*d*f*i^2 + 4*a^4*b^2*c*g*i^2 + 4*a^3*b^3*e^2*f*h - 4*a^3*b^3*e*f^2*g - 4*a^3*b^3*d*f^2*h - 4*a^3*b^3*c*f^2*i + 4*a^3*b^3*d*f*g^2 + 4*a^2*b^4*c^2*f*h + 4*a^2*b^4*c^2*e*i - 4*a^3*b^3*c*e*h^2 - 4*a^2*b^4*d^2*e*g - 4*a^2*b^4*c*d^2*i + 4*a^2*b^4*d*e^2*f + 4*a^2*b^4*c*e^2*g - 4*a^2*b^4*c*e*f^2 - 4*a^5*b*g*h^2*i + 4*a^5*b*f*h*i^2 + 4*a*b^5*c^2*d*f - 4*a*b^5*c*d^2*e - 4*a^5*b*e*i^3 - 4*a*b^5*c^3*g - 6*a^4*b^2*e^2*i^2 - 2*a^4*b^2*f^2*h^2 + 6*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 + 2*a^3*b^3*c^2*i^2 - 6*a^2*b^4*c^2*g^2 - 2*a^2*b^4*d^2*f^2 + 2*a^5*b*g^2*i^2 - 4*a^3*b^3*e^3*i + 4*a^4*b^2*d*h^3 + 4*a^2*b^4*d^3*h - 4*a^3*b^3*c*g^3 + 2*a*b^5*c^2*e^2 + a^3*b^3*f^4 + a^5*b*h^4 + a*b^5*d^4 - a^4*b^2*g^4 - a^2*b^4*e^4 - a^6*i^4 - b^6*c^4, z, l)*(root(256*a^3*b^7*z^4 + 256*a^3*b^6*f*z^3 - 64*a^4*b^4*g*i*z^2 - 64*a^3*b^5*e*g*z^2 - 64*a^3*b^5*d*h*z^2 - 64*a^3*b^5*c*i*z^2 - 64*a^2*b^6*c*e*z^2 - 32*a^4*b^4*h^2*z^2 + 96*a^3*b^5*f^2*z^2 - 32*a^2*b^6*d^2*z^2 - 32*a^4*b^3*f*g*i*z + 32*a^4*b^3*e*h*i*z - 32*a^3*b^4*e*f*g*z - 32*a^3*b^4*d*f*h*z + 32*a^3*b^4*d*e*i*z + 32*a^3*b^4*c*g*h*z - 32*a^3*b^4*c*f*i*z - 32*a^2*b^5*c*e*f*z + 32*a^2*b^5*c*d*g*z + 16*a^5*b^2*h*i^2*z + 16*a^4*b^3*g^2*h*z - 16*a^4*b^3*f*h^2*z + 16*a^4*b^3*d*i^2*z + 16*a^3*b^4*e^2*h*z + 16*a^3*b^4*d*g^2*z + 16*a^2*b^5*c^2*h*z - 16*a^2*b^5*d^2*f*z + 16*a^2*b^5*d*e^2*z + 16*a*b^6*c^2*d*z + 16*a^3*b^4*f^3*z + 8*a^4*b^2*e*f*h*i - 8*a^4*b^2*d*g*h*i - 8*a^3*b^3*d*e*g*h + 8*a^3*b^3*d*e*f*i + 8*a^3*b^3*c*f*g*h + 8*a^3*b^3*c*e*g*i - 8*a^3*b^3*c*d*h*i + 8*a^2*b^4*c*d*f*g - 8*a^2*b^4*c*d*e*h - 4*a^4*b^2*f^2*g*i + 4*a^4*b^2*f*g^2*h + 4*a^4*b^2*e*g^2*i - 4*a^4*b^2*e*g*h^2 - 4*a^4*b^2*c*h^2*i - 4*a^3*b^3*d^2*g*i + 4*a^4*b^2*d*f*i^2 + 4*a^4*b^2*c*g*i^2 + 4*a^3*b^3*e^2*f*h - 4*a^3*b^3*e*f^2*g - 4*a^3*b^3*d*f^2*h - 4*a^3*b^3*c*f^2*i + 4*a^3*b^3*d*f*g^2 + 4*a^2*b^4*c^2*f*h + 4*a^2*b^4*c^2*e*i - 4*a^3*b^3*c*e*h^2 - 4*a^2*b^4*d^2*e*g - 4*a^2*b^4*c*d^2*i + 4*a^2*b^4*d*e^2*f + 4*a^2*b^4*c*e^2*g - 4*a^2*b^4*c*e*f^2 - 4*a^5*b*g*h^2*i + 4*a^5*b*f*h*i^2 + 4*a*b^5*c^2*d*f - 4*a*b^5*c*d^2*e - 4*a^5*b*e*i^3 - 4*a*b^5*c^3*g - 6*a^4*b^2*e^2*i^2 - 2*a^4*b^2*f^2*h^2 + 6*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 + 2*a^3*b^3*c^2*i^2 - 6*a^2*b^4*c^2*g^2 - 2*a^2*b^4*d^2*f^2 + 2*a^5*b*g^2*i^2 - 4*a^3*b^3*e^3*i + 4*a^4*b^2*d*h^3 + 4*a^2*b^4*d^3*h - 4*a^3*b^3*c*g^3 + 2*a*b^5*c^2*e^2 + a^3*b^3*f^4 + a^5*b*h^4 + a*b^5*d^4 - a^4*b^2*g^4 - a^2*b^4*e^4 - a^6*i^4 - b^6*c^4, z, l)*((16*a^2*b^4*g + 16*a*b^5*c)/b^2 - (x*(16*a^2*b^3*h + 16*a*b^4*d))/b) - (8*a*b^4*d*e - 8*a*b^4*c*f + 8*a^2*b^3*d*i + 8*a^2*b^3*e*h - 8*a^2*b^3*f*g + 8*a^3*b^2*h*i)/b^2 + (x*(4*b^4*c^2 + 4*a*b^3*e^2 + 4*a^3*b*i^2 + 4*a^2*b^2*g^2 + 8*a*b^3*c*g - 8*a*b^3*d*f + 8*a^2*b^2*e*i - 8*a^2*b^2*f*h))/b) - (x*(b^3*d^3 + a^3*h^3 + b^3*c^2*f + a^3*f*i^2 - 2*b^3*c*d*e - 2*a^3*g*h*i - a*b^2*d*f^2 + a*b^2*e^2*f + 3*a*b^2*d^2*h + 3*a^2*b*d*h^2 + a^2*b*f*g^2 - a^2*b*f^2*h - 2*a*b^2*c*d*i - 2*a*b^2*c*e*h + 2*a*b^2*c*f*g - 2*a*b^2*d*e*g - 2*a^2*b*c*h*i - 2*a^2*b*d*g*i + 2*a^2*b*e*f*i - 2*a^2*b*e*g*h))/b)*root(256*a^3*b^7*z^4 + 256*a^3*b^6*f*z^3 - 64*a^4*b^4*g*i*z^2 - 64*a^3*b^5*e*g*z^2 - 64*a^3*b^5*d*h*z^2 - 64*a^3*b^5*c*i*z^2 - 64*a^2*b^6*c*e*z^2 - 32*a^4*b^4*h^2*z^2 + 96*a^3*b^5*f^2*z^2 - 32*a^2*b^6*d^2*z^2 - 32*a^4*b^3*f*g*i*z + 32*a^4*b^3*e*h*i*z - 32*a^3*b^4*e*f*g*z - 32*a^3*b^4*d*f*h*z + 32*a^3*b^4*d*e*i*z + 32*a^3*b^4*c*g*h*z - 32*a^3*b^4*c*f*i*z - 32*a^2*b^5*c*e*f*z + 32*a^2*b^5*c*d*g*z + 16*a^5*b^2*h*i^2*z + 16*a^4*b^3*g^2*h*z - 16*a^4*b^3*f*h^2*z + 16*a^4*b^3*d*i^2*z + 16*a^3*b^4*e^2*h*z + 16*a^3*b^4*d*g^2*z + 16*a^2*b^5*c^2*h*z - 16*a^2*b^5*d^2*f*z + 16*a^2*b^5*d*e^2*z + 16*a*b^6*c^2*d*z + 16*a^3*b^4*f^3*z + 8*a^4*b^2*e*f*h*i - 8*a^4*b^2*d*g*h*i - 8*a^3*b^3*d*e*g*h + 8*a^3*b^3*d*e*f*i + 8*a^3*b^3*c*f*g*h + 8*a^3*b^3*c*e*g*i - 8*a^3*b^3*c*d*h*i + 8*a^2*b^4*c*d*f*g - 8*a^2*b^4*c*d*e*h - 4*a^4*b^2*f^2*g*i + 4*a^4*b^2*f*g^2*h + 4*a^4*b^2*e*g^2*i - 4*a^4*b^2*e*g*h^2 - 4*a^4*b^2*c*h^2*i - 4*a^3*b^3*d^2*g*i + 4*a^4*b^2*d*f*i^2 + 4*a^4*b^2*c*g*i^2 + 4*a^3*b^3*e^2*f*h - 4*a^3*b^3*e*f^2*g - 4*a^3*b^3*d*f^2*h - 4*a^3*b^3*c*f^2*i + 4*a^3*b^3*d*f*g^2 + 4*a^2*b^4*c^2*f*h + 4*a^2*b^4*c^2*e*i - 4*a^3*b^3*c*e*h^2 - 4*a^2*b^4*d^2*e*g - 4*a^2*b^4*c*d^2*i + 4*a^2*b^4*d*e^2*f + 4*a^2*b^4*c*e^2*g - 4*a^2*b^4*c*e*f^2 - 4*a^5*b*g*h^2*i + 4*a^5*b*f*h*i^2 + 4*a*b^5*c^2*d*f - 4*a*b^5*c*d^2*e - 4*a^5*b*e*i^3 - 4*a*b^5*c^3*g - 6*a^4*b^2*e^2*i^2 - 2*a^4*b^2*f^2*h^2 + 6*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 + 2*a^3*b^3*c^2*i^2 - 6*a^2*b^4*c^2*g^2 - 2*a^2*b^4*d^2*f^2 + 2*a^5*b*g^2*i^2 - 4*a^3*b^3*e^3*i + 4*a^4*b^2*d*h^3 + 4*a^2*b^4*d^3*h - 4*a^3*b^3*c*g^3 + 2*a*b^5*c^2*e^2 + a^3*b^3*f^4 + a^5*b*h^4 + a*b^5*d^4 - a^4*b^2*g^4 - a^2*b^4*e^4 - a^6*i^4 - b^6*c^4, z, l), l, 1, 4) - (h*x^2)/(2*b) - (i*x^3)/(3*b) - (g*x)/b","B"
188,1,5673,205,5.161011,"\text{Not used}","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)","\left(\sum 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3\,b^4\,c\,d\,h\,i+8\,a^3\,b^4\,c\,d\,g\,j+8\,a^2\,b^5\,c\,d\,f\,g-8\,a^2\,b^5\,c\,d\,e\,h+4\,a^5\,b^2\,g^2\,h\,j-4\,a^5\,b^2\,g\,h^2\,i-4\,a^5\,b^2\,f\,h^2\,j+4\,a^5\,b^2\,f\,h\,i^2+4\,a^5\,b^2\,d\,i^2\,j+4\,a^4\,b^3\,e^2\,h\,j-4\,a^5\,b^2\,e\,g\,j^2-4\,a^5\,b^2\,d\,h\,j^2-4\,a^5\,b^2\,c\,i\,j^2-4\,a^4\,b^3\,f^2\,g\,i+4\,a^4\,b^3\,f\,g^2\,h+4\,a^4\,b^3\,e\,g^2\,i+4\,a^4\,b^3\,d\,g^2\,j+4\,a^3\,b^4\,c^2\,h\,j-4\,a^4\,b^3\,e\,g\,h^2-4\,a^4\,b^3\,c\,h^2\,i-4\,a^3\,b^4\,d^2\,g\,i-4\,a^3\,b^4\,d^2\,f\,j+4\,a^4\,b^3\,d\,f\,i^2+4\,a^4\,b^3\,c\,g\,i^2+4\,a^3\,b^4\,e^2\,f\,h+4\,a^3\,b^4\,d\,e^2\,j-4\,a^4\,b^3\,c\,e\,j^2-4\,a^3\,b^4\,e\,f^2\,g-4\,a^3\,b^4\,d\,f^2\,h-4\,a^3\,b^4\,c\,f^2\,i+4\,a^3\,b^4\,d\,f\,g^2+4\,a^2\,b^5\,c^2\,f\,h+4\,a^2\,b^5\,c^2\,e\,i+4\,a^2\,b^5\,c^2\,d\,j-4\,a^3\,b^4\,c\,e\,h^2-4\,a^2\,b^5\,d^2\,e\,g-4\,a^2\,b^5\,c\,d^2\,i+4\,a^2\,b^5\,d\,e^2\,f+4\,a^2\,b^5\,c\,e^2\,g-4\,a^2\,b^5\,c\,e\,f^2+4\,a^6\,b\,h\,i^2\,j-4\,a^6\,b\,g\,i\,j^2+4\,a\,b^6\,c^2\,d\,f-4\,a\,b^6\,c\,d^2\,e+4\,a^6\,b\,f\,j^3-4\,a\,b^6\,c^3\,g+6\,a^5\,b^2\,f^2\,j^2+2\,a^5\,b^2\,g^2\,i^2-6\,a^4\,b^3\,e^2\,i^2-2\,a^4\,b^3\,f^2\,h^2-2\,a^4\,b^3\,d^2\,j^2+6\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2+2\,a^3\,b^4\,c^2\,i^2-6\,a^2\,b^5\,c^2\,g^2-2\,a^2\,b^5\,d^2\,f^2-2\,a^6\,b\,h^2\,j^2+4\,a^4\,b^3\,f^3\,j-4\,a^5\,b^2\,e\,i^3-4\,a^3\,b^4\,e^3\,i+4\,a^4\,b^3\,d\,h^3+4\,a^2\,b^5\,d^3\,h-4\,a^3\,b^4\,c\,g^3+2\,a\,b^6\,c^2\,e^2+a^5\,b^2\,h^4+a^3\,b^4\,f^4+a\,b^6\,d^4+a^7\,j^4-a^4\,b^3\,g^4-a^2\,b^5\,e^4-a^6\,b\,i^4-b^7\,c^4,z,m\right)\,\left(\frac{16\,g\,a^2\,b^4+16\,c\,a\,b^5}{b^2}-\frac{x\,\left(16\,h\,a^2\,b^4+16\,d\,a\,b^5\right)}{b^2}\right)+\frac{x\,\left(4\,b^5\,c^2+4\,a\,b^4\,e^2+4\,a^2\,b^3\,g^2+4\,a^3\,b^2\,i^2+8\,a\,b^4\,c\,g-8\,a\,b^4\,d\,f-8\,a^2\,b^3\,d\,j+8\,a^2\,b^3\,e\,i-8\,a^2\,b^3\,f\,h-8\,a^3\,b^2\,h\,j\right)}{b^2}\right)-\frac{x\,\left(-a^4\,h\,j^2+a^4\,i^2\,j-a^3\,b\,d\,j^2+2\,a^3\,b\,e\,i\,j-2\,a^3\,b\,f\,h\,j+a^3\,b\,f\,i^2+a^3\,b\,g^2\,j-2\,a^3\,b\,g\,h\,i+a^3\,b\,h^3+2\,a^2\,b^2\,c\,g\,j-2\,a^2\,b^2\,c\,h\,i-2\,a^2\,b^2\,d\,f\,j-2\,a^2\,b^2\,d\,g\,i+3\,a^2\,b^2\,d\,h^2+a^2\,b^2\,e^2\,j+2\,a^2\,b^2\,e\,f\,i-2\,a^2\,b^2\,e\,g\,h-a^2\,b^2\,f^2\,h+a^2\,b^2\,f\,g^2+a\,b^3\,c^2\,j-2\,a\,b^3\,c\,d\,i-2\,a\,b^3\,c\,e\,h+2\,a\,b^3\,c\,f\,g+3\,a\,b^3\,d^2\,h-2\,a\,b^3\,d\,e\,g-a\,b^3\,d\,f^2+a\,b^3\,e^2\,f+b^4\,c^2\,f-2\,b^4\,c\,d\,e+b^4\,d^3\right)}{b^2}\right)\,\mathrm{root}\left(256\,a^3\,b^8\,z^4+256\,a^4\,b^6\,j\,z^3+256\,a^3\,b^7\,f\,z^3+192\,a^4\,b^5\,f\,j\,z^2-64\,a^4\,b^5\,g\,i\,z^2-64\,a^3\,b^6\,e\,g\,z^2-64\,a^3\,b^6\,d\,h\,z^2-64\,a^3\,b^6\,c\,i\,z^2-64\,a^2\,b^7\,c\,e\,z^2+96\,a^5\,b^4\,j^2\,z^2-32\,a^4\,b^5\,h^2\,z^2+96\,a^3\,b^6\,f^2\,z^2-32\,a^2\,b^7\,d^2\,z^2-32\,a^5\,b^3\,g\,i\,j\,z-32\,a^4\,b^4\,f\,g\,i\,z+32\,a^4\,b^4\,e\,h\,i\,z-32\,a^4\,b^4\,e\,g\,j\,z-32\,a^4\,b^4\,d\,h\,j\,z-32\,a^4\,b^4\,c\,i\,j\,z-32\,a^3\,b^5\,e\,f\,g\,z-32\,a^3\,b^5\,d\,f\,h\,z+32\,a^3\,b^5\,d\,e\,i\,z+32\,a^3\,b^5\,c\,g\,h\,z-32\,a^3\,b^5\,c\,f\,i\,z-32\,a^3\,b^5\,c\,e\,j\,z-32\,a^2\,b^6\,c\,e\,f\,z+32\,a^2\,b^6\,c\,d\,g\,z-16\,a^5\,b^3\,h^2\,j\,z+16\,a^5\,b^3\,h\,i^2\,z+48\,a^5\,b^3\,f\,j^2\,z+48\,a^4\,b^4\,f^2\,j\,z+16\,a^4\,b^4\,g^2\,h\,z-16\,a^4\,b^4\,f\,h^2\,z-16\,a^3\,b^5\,d^2\,j\,z+16\,a^4\,b^4\,d\,i^2\,z+16\,a^3\,b^5\,e^2\,h\,z+16\,a^3\,b^5\,d\,g^2\,z+16\,a^2\,b^6\,c^2\,h\,z-16\,a^2\,b^6\,d^2\,f\,z+16\,a^2\,b^6\,d\,e^2\,z+16\,a\,b^7\,c^2\,d\,z+16\,a^6\,b^2\,j^3\,z+16\,a^3\,b^5\,f^3\,z-8\,a^5\,b^2\,f\,g\,i\,j+8\,a^5\,b^2\,e\,h\,i\,j+8\,a^4\,b^3\,e\,f\,h\,i-8\,a^4\,b^3\,e\,f\,g\,j-8\,a^4\,b^3\,d\,g\,h\,i-8\,a^4\,b^3\,d\,f\,h\,j+8\,a^4\,b^3\,d\,e\,i\,j+8\,a^4\,b^3\,c\,g\,h\,j-8\,a^4\,b^3\,c\,f\,i\,j-8\,a^3\,b^4\,d\,e\,g\,h+8\,a^3\,b^4\,d\,e\,f\,i+8\,a^3\,b^4\,c\,f\,g\,h+8\,a^3\,b^4\,c\,e\,g\,i-8\,a^3\,b^4\,c\,e\,f\,j-8\,a^3\,b^4\,c\,d\,h\,i+8\,a^3\,b^4\,c\,d\,g\,j+8\,a^2\,b^5\,c\,d\,f\,g-8\,a^2\,b^5\,c\,d\,e\,h+4\,a^5\,b^2\,g^2\,h\,j-4\,a^5\,b^2\,g\,h^2\,i-4\,a^5\,b^2\,f\,h^2\,j+4\,a^5\,b^2\,f\,h\,i^2+4\,a^5\,b^2\,d\,i^2\,j+4\,a^4\,b^3\,e^2\,h\,j-4\,a^5\,b^2\,e\,g\,j^2-4\,a^5\,b^2\,d\,h\,j^2-4\,a^5\,b^2\,c\,i\,j^2-4\,a^4\,b^3\,f^2\,g\,i+4\,a^4\,b^3\,f\,g^2\,h+4\,a^4\,b^3\,e\,g^2\,i+4\,a^4\,b^3\,d\,g^2\,j+4\,a^3\,b^4\,c^2\,h\,j-4\,a^4\,b^3\,e\,g\,h^2-4\,a^4\,b^3\,c\,h^2\,i-4\,a^3\,b^4\,d^2\,g\,i-4\,a^3\,b^4\,d^2\,f\,j+4\,a^4\,b^3\,d\,f\,i^2+4\,a^4\,b^3\,c\,g\,i^2+4\,a^3\,b^4\,e^2\,f\,h+4\,a^3\,b^4\,d\,e^2\,j-4\,a^4\,b^3\,c\,e\,j^2-4\,a^3\,b^4\,e\,f^2\,g-4\,a^3\,b^4\,d\,f^2\,h-4\,a^3\,b^4\,c\,f^2\,i+4\,a^3\,b^4\,d\,f\,g^2+4\,a^2\,b^5\,c^2\,f\,h+4\,a^2\,b^5\,c^2\,e\,i+4\,a^2\,b^5\,c^2\,d\,j-4\,a^3\,b^4\,c\,e\,h^2-4\,a^2\,b^5\,d^2\,e\,g-4\,a^2\,b^5\,c\,d^2\,i+4\,a^2\,b^5\,d\,e^2\,f+4\,a^2\,b^5\,c\,e^2\,g-4\,a^2\,b^5\,c\,e\,f^2+4\,a^6\,b\,h\,i^2\,j-4\,a^6\,b\,g\,i\,j^2+4\,a\,b^6\,c^2\,d\,f-4\,a\,b^6\,c\,d^2\,e+4\,a^6\,b\,f\,j^3-4\,a\,b^6\,c^3\,g+6\,a^5\,b^2\,f^2\,j^2+2\,a^5\,b^2\,g^2\,i^2-6\,a^4\,b^3\,e^2\,i^2-2\,a^4\,b^3\,f^2\,h^2-2\,a^4\,b^3\,d^2\,j^2+6\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2+2\,a^3\,b^4\,c^2\,i^2-6\,a^2\,b^5\,c^2\,g^2-2\,a^2\,b^5\,d^2\,f^2-2\,a^6\,b\,h^2\,j^2+4\,a^4\,b^3\,f^3\,j-4\,a^5\,b^2\,e\,i^3-4\,a^3\,b^4\,e^3\,i+4\,a^4\,b^3\,d\,h^3+4\,a^2\,b^5\,d^3\,h-4\,a^3\,b^4\,c\,g^3+2\,a\,b^6\,c^2\,e^2+a^5\,b^2\,h^4+a^3\,b^4\,f^4+a\,b^6\,d^4+a^7\,j^4-a^4\,b^3\,g^4-a^2\,b^5\,e^4-a^6\,b\,i^4-b^7\,c^4,z,m\right)\right)-\frac{h\,x^2}{2\,b}-\frac{i\,x^3}{3\,b}-\frac{j\,x^4}{4\,b}-\frac{g\,x}{b}","Not used",1,"symsum(log(- (a^4*i^3 + a*b^3*e^3 + b^4*c*d^2 - b^4*c^2*e + a^4*g*j^2 + a^2*b^2*c*h^2 - a^2*b^2*e*g^2 + a^2*b^2*f^2*g + 3*a^2*b^2*e^2*i - 2*a^4*h*i*j + a*b^3*c*f^2 + a*b^3*d^2*g - a*b^3*c^2*i + a^3*b*c*j^2 + 3*a^3*b*e*i^2 + a^3*b*g*h^2 - a^3*b*g^2*i + 2*a^2*b^2*c*f*j - 2*a^2*b^2*c*g*i - 2*a^2*b^2*d*e*j - 2*a^2*b^2*d*f*i + 2*a^2*b^2*d*g*h - 2*a^2*b^2*e*f*h + 2*a*b^3*c*d*h - 2*a*b^3*c*e*g - 2*a*b^3*d*e*f - 2*a^3*b*d*i*j - 2*a^3*b*e*h*j + 2*a^3*b*f*g*j - 2*a^3*b*f*h*i)/b^2 - root(256*a^3*b^8*z^4 + 256*a^4*b^6*j*z^3 + 256*a^3*b^7*f*z^3 + 192*a^4*b^5*f*j*z^2 - 64*a^4*b^5*g*i*z^2 - 64*a^3*b^6*e*g*z^2 - 64*a^3*b^6*d*h*z^2 - 64*a^3*b^6*c*i*z^2 - 64*a^2*b^7*c*e*z^2 + 96*a^5*b^4*j^2*z^2 - 32*a^4*b^5*h^2*z^2 + 96*a^3*b^6*f^2*z^2 - 32*a^2*b^7*d^2*z^2 - 32*a^5*b^3*g*i*j*z - 32*a^4*b^4*f*g*i*z + 32*a^4*b^4*e*h*i*z - 32*a^4*b^4*e*g*j*z - 32*a^4*b^4*d*h*j*z - 32*a^4*b^4*c*i*j*z - 32*a^3*b^5*e*f*g*z - 32*a^3*b^5*d*f*h*z + 32*a^3*b^5*d*e*i*z + 32*a^3*b^5*c*g*h*z - 32*a^3*b^5*c*f*i*z - 32*a^3*b^5*c*e*j*z - 32*a^2*b^6*c*e*f*z + 32*a^2*b^6*c*d*g*z - 16*a^5*b^3*h^2*j*z + 16*a^5*b^3*h*i^2*z + 48*a^5*b^3*f*j^2*z + 48*a^4*b^4*f^2*j*z + 16*a^4*b^4*g^2*h*z - 16*a^4*b^4*f*h^2*z - 16*a^3*b^5*d^2*j*z + 16*a^4*b^4*d*i^2*z + 16*a^3*b^5*e^2*h*z + 16*a^3*b^5*d*g^2*z + 16*a^2*b^6*c^2*h*z - 16*a^2*b^6*d^2*f*z + 16*a^2*b^6*d*e^2*z + 16*a*b^7*c^2*d*z + 16*a^6*b^2*j^3*z + 16*a^3*b^5*f^3*z - 8*a^5*b^2*f*g*i*j + 8*a^5*b^2*e*h*i*j + 8*a^4*b^3*e*f*h*i - 8*a^4*b^3*e*f*g*j - 8*a^4*b^3*d*g*h*i - 8*a^4*b^3*d*f*h*j + 8*a^4*b^3*d*e*i*j + 8*a^4*b^3*c*g*h*j - 8*a^4*b^3*c*f*i*j - 8*a^3*b^4*d*e*g*h + 8*a^3*b^4*d*e*f*i + 8*a^3*b^4*c*f*g*h + 8*a^3*b^4*c*e*g*i - 8*a^3*b^4*c*e*f*j - 8*a^3*b^4*c*d*h*i + 8*a^3*b^4*c*d*g*j + 8*a^2*b^5*c*d*f*g - 8*a^2*b^5*c*d*e*h + 4*a^5*b^2*g^2*h*j - 4*a^5*b^2*g*h^2*i - 4*a^5*b^2*f*h^2*j + 4*a^5*b^2*f*h*i^2 + 4*a^5*b^2*d*i^2*j + 4*a^4*b^3*e^2*h*j - 4*a^5*b^2*e*g*j^2 - 4*a^5*b^2*d*h*j^2 - 4*a^5*b^2*c*i*j^2 - 4*a^4*b^3*f^2*g*i + 4*a^4*b^3*f*g^2*h + 4*a^4*b^3*e*g^2*i + 4*a^4*b^3*d*g^2*j + 4*a^3*b^4*c^2*h*j - 4*a^4*b^3*e*g*h^2 - 4*a^4*b^3*c*h^2*i - 4*a^3*b^4*d^2*g*i - 4*a^3*b^4*d^2*f*j + 4*a^4*b^3*d*f*i^2 + 4*a^4*b^3*c*g*i^2 + 4*a^3*b^4*e^2*f*h + 4*a^3*b^4*d*e^2*j - 4*a^4*b^3*c*e*j^2 - 4*a^3*b^4*e*f^2*g - 4*a^3*b^4*d*f^2*h - 4*a^3*b^4*c*f^2*i + 4*a^3*b^4*d*f*g^2 + 4*a^2*b^5*c^2*f*h + 4*a^2*b^5*c^2*e*i + 4*a^2*b^5*c^2*d*j - 4*a^3*b^4*c*e*h^2 - 4*a^2*b^5*d^2*e*g - 4*a^2*b^5*c*d^2*i + 4*a^2*b^5*d*e^2*f + 4*a^2*b^5*c*e^2*g - 4*a^2*b^5*c*e*f^2 + 4*a^6*b*h*i^2*j - 4*a^6*b*g*i*j^2 + 4*a*b^6*c^2*d*f - 4*a*b^6*c*d^2*e + 4*a^6*b*f*j^3 - 4*a*b^6*c^3*g + 6*a^5*b^2*f^2*j^2 + 2*a^5*b^2*g^2*i^2 - 6*a^4*b^3*e^2*i^2 - 2*a^4*b^3*f^2*h^2 - 2*a^4*b^3*d^2*j^2 + 6*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 + 2*a^3*b^4*c^2*i^2 - 6*a^2*b^5*c^2*g^2 - 2*a^2*b^5*d^2*f^2 - 2*a^6*b*h^2*j^2 + 4*a^4*b^3*f^3*j - 4*a^5*b^2*e*i^3 - 4*a^3*b^4*e^3*i + 4*a^4*b^3*d*h^3 + 4*a^2*b^5*d^3*h - 4*a^3*b^4*c*g^3 + 2*a*b^6*c^2*e^2 + a^5*b^2*h^4 + a^3*b^4*f^4 + a*b^6*d^4 + a^7*j^4 - a^4*b^3*g^4 - a^2*b^5*e^4 - a^6*b*i^4 - b^7*c^4, z, m)*((8*a*b^4*c*f - 8*a*b^4*d*e + 8*a^2*b^3*c*j - 8*a^2*b^3*d*i - 8*a^2*b^3*e*h + 8*a^2*b^3*f*g + 8*a^3*b^2*g*j - 8*a^3*b^2*h*i)/b^2 + root(256*a^3*b^8*z^4 + 256*a^4*b^6*j*z^3 + 256*a^3*b^7*f*z^3 + 192*a^4*b^5*f*j*z^2 - 64*a^4*b^5*g*i*z^2 - 64*a^3*b^6*e*g*z^2 - 64*a^3*b^6*d*h*z^2 - 64*a^3*b^6*c*i*z^2 - 64*a^2*b^7*c*e*z^2 + 96*a^5*b^4*j^2*z^2 - 32*a^4*b^5*h^2*z^2 + 96*a^3*b^6*f^2*z^2 - 32*a^2*b^7*d^2*z^2 - 32*a^5*b^3*g*i*j*z - 32*a^4*b^4*f*g*i*z + 32*a^4*b^4*e*h*i*z - 32*a^4*b^4*e*g*j*z - 32*a^4*b^4*d*h*j*z - 32*a^4*b^4*c*i*j*z - 32*a^3*b^5*e*f*g*z - 32*a^3*b^5*d*f*h*z + 32*a^3*b^5*d*e*i*z + 32*a^3*b^5*c*g*h*z - 32*a^3*b^5*c*f*i*z - 32*a^3*b^5*c*e*j*z - 32*a^2*b^6*c*e*f*z + 32*a^2*b^6*c*d*g*z - 16*a^5*b^3*h^2*j*z + 16*a^5*b^3*h*i^2*z + 48*a^5*b^3*f*j^2*z + 48*a^4*b^4*f^2*j*z + 16*a^4*b^4*g^2*h*z - 16*a^4*b^4*f*h^2*z - 16*a^3*b^5*d^2*j*z + 16*a^4*b^4*d*i^2*z + 16*a^3*b^5*e^2*h*z + 16*a^3*b^5*d*g^2*z + 16*a^2*b^6*c^2*h*z - 16*a^2*b^6*d^2*f*z + 16*a^2*b^6*d*e^2*z + 16*a*b^7*c^2*d*z + 16*a^6*b^2*j^3*z + 16*a^3*b^5*f^3*z - 8*a^5*b^2*f*g*i*j + 8*a^5*b^2*e*h*i*j + 8*a^4*b^3*e*f*h*i - 8*a^4*b^3*e*f*g*j - 8*a^4*b^3*d*g*h*i - 8*a^4*b^3*d*f*h*j + 8*a^4*b^3*d*e*i*j + 8*a^4*b^3*c*g*h*j - 8*a^4*b^3*c*f*i*j - 8*a^3*b^4*d*e*g*h + 8*a^3*b^4*d*e*f*i + 8*a^3*b^4*c*f*g*h + 8*a^3*b^4*c*e*g*i - 8*a^3*b^4*c*e*f*j - 8*a^3*b^4*c*d*h*i + 8*a^3*b^4*c*d*g*j + 8*a^2*b^5*c*d*f*g - 8*a^2*b^5*c*d*e*h + 4*a^5*b^2*g^2*h*j - 4*a^5*b^2*g*h^2*i - 4*a^5*b^2*f*h^2*j + 4*a^5*b^2*f*h*i^2 + 4*a^5*b^2*d*i^2*j + 4*a^4*b^3*e^2*h*j - 4*a^5*b^2*e*g*j^2 - 4*a^5*b^2*d*h*j^2 - 4*a^5*b^2*c*i*j^2 - 4*a^4*b^3*f^2*g*i + 4*a^4*b^3*f*g^2*h + 4*a^4*b^3*e*g^2*i + 4*a^4*b^3*d*g^2*j + 4*a^3*b^4*c^2*h*j - 4*a^4*b^3*e*g*h^2 - 4*a^4*b^3*c*h^2*i - 4*a^3*b^4*d^2*g*i - 4*a^3*b^4*d^2*f*j + 4*a^4*b^3*d*f*i^2 + 4*a^4*b^3*c*g*i^2 + 4*a^3*b^4*e^2*f*h + 4*a^3*b^4*d*e^2*j - 4*a^4*b^3*c*e*j^2 - 4*a^3*b^4*e*f^2*g - 4*a^3*b^4*d*f^2*h - 4*a^3*b^4*c*f^2*i + 4*a^3*b^4*d*f*g^2 + 4*a^2*b^5*c^2*f*h + 4*a^2*b^5*c^2*e*i + 4*a^2*b^5*c^2*d*j - 4*a^3*b^4*c*e*h^2 - 4*a^2*b^5*d^2*e*g - 4*a^2*b^5*c*d^2*i + 4*a^2*b^5*d*e^2*f + 4*a^2*b^5*c*e^2*g - 4*a^2*b^5*c*e*f^2 + 4*a^6*b*h*i^2*j - 4*a^6*b*g*i*j^2 + 4*a*b^6*c^2*d*f - 4*a*b^6*c*d^2*e + 4*a^6*b*f*j^3 - 4*a*b^6*c^3*g + 6*a^5*b^2*f^2*j^2 + 2*a^5*b^2*g^2*i^2 - 6*a^4*b^3*e^2*i^2 - 2*a^4*b^3*f^2*h^2 - 2*a^4*b^3*d^2*j^2 + 6*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 + 2*a^3*b^4*c^2*i^2 - 6*a^2*b^5*c^2*g^2 - 2*a^2*b^5*d^2*f^2 - 2*a^6*b*h^2*j^2 + 4*a^4*b^3*f^3*j - 4*a^5*b^2*e*i^3 - 4*a^3*b^4*e^3*i + 4*a^4*b^3*d*h^3 + 4*a^2*b^5*d^3*h - 4*a^3*b^4*c*g^3 + 2*a*b^6*c^2*e^2 + a^5*b^2*h^4 + a^3*b^4*f^4 + a*b^6*d^4 + a^7*j^4 - a^4*b^3*g^4 - a^2*b^5*e^4 - a^6*b*i^4 - b^7*c^4, z, m)*((16*a^2*b^4*g + 16*a*b^5*c)/b^2 - (x*(16*a^2*b^4*h + 16*a*b^5*d))/b^2) + (x*(4*b^5*c^2 + 4*a*b^4*e^2 + 4*a^2*b^3*g^2 + 4*a^3*b^2*i^2 + 8*a*b^4*c*g - 8*a*b^4*d*f - 8*a^2*b^3*d*j + 8*a^2*b^3*e*i - 8*a^2*b^3*f*h - 8*a^3*b^2*h*j))/b^2) - (x*(b^4*d^3 + a^3*b*h^3 + b^4*c^2*f - a^4*h*j^2 + a^4*i^2*j + 3*a^2*b^2*d*h^2 + a^2*b^2*f*g^2 - a^2*b^2*f^2*h + a^2*b^2*e^2*j - 2*b^4*c*d*e - a*b^3*d*f^2 + a*b^3*e^2*f + 3*a*b^3*d^2*h + a*b^3*c^2*j - a^3*b*d*j^2 + a^3*b*f*i^2 + a^3*b*g^2*j + 2*a^2*b^2*c*g*j - 2*a^2*b^2*c*h*i - 2*a^2*b^2*d*f*j - 2*a^2*b^2*d*g*i + 2*a^2*b^2*e*f*i - 2*a^2*b^2*e*g*h - 2*a*b^3*c*d*i - 2*a*b^3*c*e*h + 2*a*b^3*c*f*g - 2*a*b^3*d*e*g + 2*a^3*b*e*i*j - 2*a^3*b*f*h*j - 2*a^3*b*g*h*i))/b^2)*root(256*a^3*b^8*z^4 + 256*a^4*b^6*j*z^3 + 256*a^3*b^7*f*z^3 + 192*a^4*b^5*f*j*z^2 - 64*a^4*b^5*g*i*z^2 - 64*a^3*b^6*e*g*z^2 - 64*a^3*b^6*d*h*z^2 - 64*a^3*b^6*c*i*z^2 - 64*a^2*b^7*c*e*z^2 + 96*a^5*b^4*j^2*z^2 - 32*a^4*b^5*h^2*z^2 + 96*a^3*b^6*f^2*z^2 - 32*a^2*b^7*d^2*z^2 - 32*a^5*b^3*g*i*j*z - 32*a^4*b^4*f*g*i*z + 32*a^4*b^4*e*h*i*z - 32*a^4*b^4*e*g*j*z - 32*a^4*b^4*d*h*j*z - 32*a^4*b^4*c*i*j*z - 32*a^3*b^5*e*f*g*z - 32*a^3*b^5*d*f*h*z + 32*a^3*b^5*d*e*i*z + 32*a^3*b^5*c*g*h*z - 32*a^3*b^5*c*f*i*z - 32*a^3*b^5*c*e*j*z - 32*a^2*b^6*c*e*f*z + 32*a^2*b^6*c*d*g*z - 16*a^5*b^3*h^2*j*z + 16*a^5*b^3*h*i^2*z + 48*a^5*b^3*f*j^2*z + 48*a^4*b^4*f^2*j*z + 16*a^4*b^4*g^2*h*z - 16*a^4*b^4*f*h^2*z - 16*a^3*b^5*d^2*j*z + 16*a^4*b^4*d*i^2*z + 16*a^3*b^5*e^2*h*z + 16*a^3*b^5*d*g^2*z + 16*a^2*b^6*c^2*h*z - 16*a^2*b^6*d^2*f*z + 16*a^2*b^6*d*e^2*z + 16*a*b^7*c^2*d*z + 16*a^6*b^2*j^3*z + 16*a^3*b^5*f^3*z - 8*a^5*b^2*f*g*i*j + 8*a^5*b^2*e*h*i*j + 8*a^4*b^3*e*f*h*i - 8*a^4*b^3*e*f*g*j - 8*a^4*b^3*d*g*h*i - 8*a^4*b^3*d*f*h*j + 8*a^4*b^3*d*e*i*j + 8*a^4*b^3*c*g*h*j - 8*a^4*b^3*c*f*i*j - 8*a^3*b^4*d*e*g*h + 8*a^3*b^4*d*e*f*i + 8*a^3*b^4*c*f*g*h + 8*a^3*b^4*c*e*g*i - 8*a^3*b^4*c*e*f*j - 8*a^3*b^4*c*d*h*i + 8*a^3*b^4*c*d*g*j + 8*a^2*b^5*c*d*f*g - 8*a^2*b^5*c*d*e*h + 4*a^5*b^2*g^2*h*j - 4*a^5*b^2*g*h^2*i - 4*a^5*b^2*f*h^2*j + 4*a^5*b^2*f*h*i^2 + 4*a^5*b^2*d*i^2*j + 4*a^4*b^3*e^2*h*j - 4*a^5*b^2*e*g*j^2 - 4*a^5*b^2*d*h*j^2 - 4*a^5*b^2*c*i*j^2 - 4*a^4*b^3*f^2*g*i + 4*a^4*b^3*f*g^2*h + 4*a^4*b^3*e*g^2*i + 4*a^4*b^3*d*g^2*j + 4*a^3*b^4*c^2*h*j - 4*a^4*b^3*e*g*h^2 - 4*a^4*b^3*c*h^2*i - 4*a^3*b^4*d^2*g*i - 4*a^3*b^4*d^2*f*j + 4*a^4*b^3*d*f*i^2 + 4*a^4*b^3*c*g*i^2 + 4*a^3*b^4*e^2*f*h + 4*a^3*b^4*d*e^2*j - 4*a^4*b^3*c*e*j^2 - 4*a^3*b^4*e*f^2*g - 4*a^3*b^4*d*f^2*h - 4*a^3*b^4*c*f^2*i + 4*a^3*b^4*d*f*g^2 + 4*a^2*b^5*c^2*f*h + 4*a^2*b^5*c^2*e*i + 4*a^2*b^5*c^2*d*j - 4*a^3*b^4*c*e*h^2 - 4*a^2*b^5*d^2*e*g - 4*a^2*b^5*c*d^2*i + 4*a^2*b^5*d*e^2*f + 4*a^2*b^5*c*e^2*g - 4*a^2*b^5*c*e*f^2 + 4*a^6*b*h*i^2*j - 4*a^6*b*g*i*j^2 + 4*a*b^6*c^2*d*f - 4*a*b^6*c*d^2*e + 4*a^6*b*f*j^3 - 4*a*b^6*c^3*g + 6*a^5*b^2*f^2*j^2 + 2*a^5*b^2*g^2*i^2 - 6*a^4*b^3*e^2*i^2 - 2*a^4*b^3*f^2*h^2 - 2*a^4*b^3*d^2*j^2 + 6*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 + 2*a^3*b^4*c^2*i^2 - 6*a^2*b^5*c^2*g^2 - 2*a^2*b^5*d^2*f^2 - 2*a^6*b*h^2*j^2 + 4*a^4*b^3*f^3*j - 4*a^5*b^2*e*i^3 - 4*a^3*b^4*e^3*i + 4*a^4*b^3*d*h^3 + 4*a^2*b^5*d^3*h - 4*a^3*b^4*c*g^3 + 2*a*b^6*c^2*e^2 + a^5*b^2*h^4 + a^3*b^4*f^4 + a*b^6*d^4 + a^7*j^4 - a^4*b^3*g^4 - a^2*b^5*e^4 - a^6*b*i^4 - b^7*c^4, z, m), m, 1, 4) - (h*x^2)/(2*b) - (i*x^3)/(3*b) - (j*x^4)/(4*b) - (g*x)/b","B"
189,1,2469,337,5.541880,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4),x)","\left(\sum _{k=1}^4\ln\left(\mathrm{root}\left(256\,a^3\,b^6\,z^4-256\,a^3\,b^5\,f\,z^3-64\,a^3\,b^4\,e\,g\,z^2-64\,a^3\,b^4\,d\,h\,z^2+64\,a^2\,b^5\,c\,e\,z^2+32\,a^4\,b^3\,h^2\,z^2+96\,a^3\,b^4\,f^2\,z^2+32\,a^2\,b^5\,d^2\,z^2+32\,a^3\,b^3\,e\,f\,g\,z+32\,a^3\,b^3\,d\,f\,h\,z-32\,a^3\,b^3\,c\,g\,h\,z-32\,a^2\,b^4\,c\,e\,f\,z+32\,a^2\,b^4\,c\,d\,g\,z+16\,a^4\,b^2\,g^2\,h\,z-16\,a^4\,b^2\,f\,h^2\,z-16\,a^3\,b^3\,e^2\,h\,z-16\,a^3\,b^3\,d\,g^2\,z+16\,a^2\,b^4\,c^2\,h\,z-16\,a^2\,b^4\,d^2\,f\,z+16\,a^2\,b^4\,d\,e^2\,z-16\,a\,b^5\,c^2\,d\,z-16\,a^3\,b^3\,f^3\,z-8\,a^3\,b^2\,d\,e\,g\,h+8\,a^3\,b^2\,c\,f\,g\,h-8\,a^2\,b^3\,c\,d\,f\,g+8\,a^2\,b^3\,c\,d\,e\,h+4\,a^3\,b^2\,e^2\,f\,h-4\,a^3\,b^2\,e\,f^2\,g-4\,a^3\,b^2\,d\,f^2\,h+4\,a^3\,b^2\,d\,f\,g^2-4\,a^2\,b^3\,c^2\,f\,h-4\,a^3\,b^2\,c\,e\,h^2+4\,a^2\,b^3\,d^2\,e\,g-4\,a^2\,b^3\,d\,e^2\,f-4\,a^2\,b^3\,c\,e^2\,g+4\,a^2\,b^3\,c\,e\,f^2-4\,a^4\,b\,f\,g^2\,h+4\,a^4\,b\,e\,g\,h^2+4\,a\,b^4\,c^2\,d\,f-4\,a\,b^4\,c\,d^2\,e-4\,a^4\,b\,d\,h^3-4\,a\,b^4\,c^3\,g+6\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2+6\,a^2\,b^3\,c^2\,g^2+2\,a^2\,b^3\,d^2\,f^2+2\,a^4\,b\,f^2\,h^2-4\,a^2\,b^3\,d^3\,h-4\,a^3\,b^2\,c\,g^3+2\,a\,b^4\,c^2\,e^2+a^3\,b^2\,f^4+a^2\,b^3\,e^4+a^4\,b\,g^4+a\,b^4\,d^4+a^5\,h^4+b^5\,c^4,z,k\right)\,\left(\frac{8\,a\,b^3\,c\,f-8\,a\,b^3\,d\,e+8\,a^2\,b^2\,e\,h-8\,a^2\,b^2\,f\,g}{b}+\mathrm{root}\left(256\,a^3\,b^6\,z^4-256\,a^3\,b^5\,f\,z^3-64\,a^3\,b^4\,e\,g\,z^2-64\,a^3\,b^4\,d\,h\,z^2+64\,a^2\,b^5\,c\,e\,z^2+32\,a^4\,b^3\,h^2\,z^2+96\,a^3\,b^4\,f^2\,z^2+32\,a^2\,b^5\,d^2\,z^2+32\,a^3\,b^3\,e\,f\,g\,z+32\,a^3\,b^3\,d\,f\,h\,z-32\,a^3\,b^3\,c\,g\,h\,z-32\,a^2\,b^4\,c\,e\,f\,z+32\,a^2\,b^4\,c\,d\,g\,z+16\,a^4\,b^2\,g^2\,h\,z-16\,a^4\,b^2\,f\,h^2\,z-16\,a^3\,b^3\,e^2\,h\,z-16\,a^3\,b^3\,d\,g^2\,z+16\,a^2\,b^4\,c^2\,h\,z-16\,a^2\,b^4\,d^2\,f\,z+16\,a^2\,b^4\,d\,e^2\,z-16\,a\,b^5\,c^2\,d\,z-16\,a^3\,b^3\,f^3\,z-8\,a^3\,b^2\,d\,e\,g\,h+8\,a^3\,b^2\,c\,f\,g\,h-8\,a^2\,b^3\,c\,d\,f\,g+8\,a^2\,b^3\,c\,d\,e\,h+4\,a^3\,b^2\,e^2\,f\,h-4\,a^3\,b^2\,e\,f^2\,g-4\,a^3\,b^2\,d\,f^2\,h+4\,a^3\,b^2\,d\,f\,g^2-4\,a^2\,b^3\,c^2\,f\,h-4\,a^3\,b^2\,c\,e\,h^2+4\,a^2\,b^3\,d^2\,e\,g-4\,a^2\,b^3\,d\,e^2\,f-4\,a^2\,b^3\,c\,e^2\,g+4\,a^2\,b^3\,c\,e\,f^2-4\,a^4\,b\,f\,g^2\,h+4\,a^4\,b\,e\,g\,h^2+4\,a\,b^4\,c^2\,d\,f-4\,a\,b^4\,c\,d^2\,e-4\,a^4\,b\,d\,h^3-4\,a\,b^4\,c^3\,g+6\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2+6\,a^2\,b^3\,c^2\,g^2+2\,a^2\,b^3\,d^2\,f^2+2\,a^4\,b\,f^2\,h^2-4\,a^2\,b^3\,d^3\,h-4\,a^3\,b^2\,c\,g^3+2\,a\,b^4\,c^2\,e^2+a^3\,b^2\,f^4+a^2\,b^3\,e^4+a^4\,b\,g^4+a\,b^4\,d^4+a^5\,h^4+b^5\,c^4,z,k\right)\,\left(\frac{16\,a^2\,b^3\,g-16\,a\,b^4\,c}{b}-\frac{x\,\left(16\,a^2\,b^3\,h-16\,a\,b^4\,d\right)}{b}\right)-\frac{x\,\left(4\,a^2\,b^2\,g^2-8\,f\,h\,a^2\,b^2-8\,a\,b^3\,c\,g-4\,a\,b^3\,e^2+8\,d\,f\,a\,b^3+4\,b^4\,c^2\right)}{b}\right)-\frac{a^3\,g\,h^2-a^2\,b\,c\,h^2-2\,a^2\,b\,d\,g\,h+2\,a^2\,b\,e\,f\,h+a^2\,b\,e\,g^2-a^2\,b\,f^2\,g+2\,a\,b^2\,c\,d\,h-2\,a\,b^2\,c\,e\,g+a\,b^2\,c\,f^2+a\,b^2\,d^2\,g-2\,a\,b^2\,d\,e\,f+a\,b^2\,e^3+b^3\,c^2\,e-b^3\,c\,d^2}{b}+\frac{x\,\left(-a^3\,h^3+3\,a^2\,b\,d\,h^2-2\,a^2\,b\,e\,g\,h-a^2\,b\,f^2\,h+a^2\,b\,f\,g^2+2\,a\,b^2\,c\,e\,h-2\,a\,b^2\,c\,f\,g-3\,a\,b^2\,d^2\,h+2\,a\,b^2\,d\,e\,g+a\,b^2\,d\,f^2-a\,b^2\,e^2\,f+b^3\,c^2\,f-2\,b^3\,c\,d\,e+b^3\,d^3\right)}{b}\right)\,\mathrm{root}\left(256\,a^3\,b^6\,z^4-256\,a^3\,b^5\,f\,z^3-64\,a^3\,b^4\,e\,g\,z^2-64\,a^3\,b^4\,d\,h\,z^2+64\,a^2\,b^5\,c\,e\,z^2+32\,a^4\,b^3\,h^2\,z^2+96\,a^3\,b^4\,f^2\,z^2+32\,a^2\,b^5\,d^2\,z^2+32\,a^3\,b^3\,e\,f\,g\,z+32\,a^3\,b^3\,d\,f\,h\,z-32\,a^3\,b^3\,c\,g\,h\,z-32\,a^2\,b^4\,c\,e\,f\,z+32\,a^2\,b^4\,c\,d\,g\,z+16\,a^4\,b^2\,g^2\,h\,z-16\,a^4\,b^2\,f\,h^2\,z-16\,a^3\,b^3\,e^2\,h\,z-16\,a^3\,b^3\,d\,g^2\,z+16\,a^2\,b^4\,c^2\,h\,z-16\,a^2\,b^4\,d^2\,f\,z+16\,a^2\,b^4\,d\,e^2\,z-16\,a\,b^5\,c^2\,d\,z-16\,a^3\,b^3\,f^3\,z-8\,a^3\,b^2\,d\,e\,g\,h+8\,a^3\,b^2\,c\,f\,g\,h-8\,a^2\,b^3\,c\,d\,f\,g+8\,a^2\,b^3\,c\,d\,e\,h+4\,a^3\,b^2\,e^2\,f\,h-4\,a^3\,b^2\,e\,f^2\,g-4\,a^3\,b^2\,d\,f^2\,h+4\,a^3\,b^2\,d\,f\,g^2-4\,a^2\,b^3\,c^2\,f\,h-4\,a^3\,b^2\,c\,e\,h^2+4\,a^2\,b^3\,d^2\,e\,g-4\,a^2\,b^3\,d\,e^2\,f-4\,a^2\,b^3\,c\,e^2\,g+4\,a^2\,b^3\,c\,e\,f^2-4\,a^4\,b\,f\,g^2\,h+4\,a^4\,b\,e\,g\,h^2+4\,a\,b^4\,c^2\,d\,f-4\,a\,b^4\,c\,d^2\,e-4\,a^4\,b\,d\,h^3-4\,a\,b^4\,c^3\,g+6\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2+6\,a^2\,b^3\,c^2\,g^2+2\,a^2\,b^3\,d^2\,f^2+2\,a^4\,b\,f^2\,h^2-4\,a^2\,b^3\,d^3\,h-4\,a^3\,b^2\,c\,g^3+2\,a\,b^4\,c^2\,e^2+a^3\,b^2\,f^4+a^2\,b^3\,e^4+a^4\,b\,g^4+a\,b^4\,d^4+a^5\,h^4+b^5\,c^4,z,k\right)\right)+\frac{h\,x^2}{2\,b}+\frac{g\,x}{b}","Not used",1,"symsum(log(root(256*a^3*b^6*z^4 - 256*a^3*b^5*f*z^3 - 64*a^3*b^4*e*g*z^2 - 64*a^3*b^4*d*h*z^2 + 64*a^2*b^5*c*e*z^2 + 32*a^4*b^3*h^2*z^2 + 96*a^3*b^4*f^2*z^2 + 32*a^2*b^5*d^2*z^2 + 32*a^3*b^3*e*f*g*z + 32*a^3*b^3*d*f*h*z - 32*a^3*b^3*c*g*h*z - 32*a^2*b^4*c*e*f*z + 32*a^2*b^4*c*d*g*z + 16*a^4*b^2*g^2*h*z - 16*a^4*b^2*f*h^2*z - 16*a^3*b^3*e^2*h*z - 16*a^3*b^3*d*g^2*z + 16*a^2*b^4*c^2*h*z - 16*a^2*b^4*d^2*f*z + 16*a^2*b^4*d*e^2*z - 16*a*b^5*c^2*d*z - 16*a^3*b^3*f^3*z - 8*a^3*b^2*d*e*g*h + 8*a^3*b^2*c*f*g*h - 8*a^2*b^3*c*d*f*g + 8*a^2*b^3*c*d*e*h + 4*a^3*b^2*e^2*f*h - 4*a^3*b^2*e*f^2*g - 4*a^3*b^2*d*f^2*h + 4*a^3*b^2*d*f*g^2 - 4*a^2*b^3*c^2*f*h - 4*a^3*b^2*c*e*h^2 + 4*a^2*b^3*d^2*e*g - 4*a^2*b^3*d*e^2*f - 4*a^2*b^3*c*e^2*g + 4*a^2*b^3*c*e*f^2 - 4*a^4*b*f*g^2*h + 4*a^4*b*e*g*h^2 + 4*a*b^4*c^2*d*f - 4*a*b^4*c*d^2*e - 4*a^4*b*d*h^3 - 4*a*b^4*c^3*g + 6*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 + 6*a^2*b^3*c^2*g^2 + 2*a^2*b^3*d^2*f^2 + 2*a^4*b*f^2*h^2 - 4*a^2*b^3*d^3*h - 4*a^3*b^2*c*g^3 + 2*a*b^4*c^2*e^2 + a^3*b^2*f^4 + a^2*b^3*e^4 + a^4*b*g^4 + a*b^4*d^4 + a^5*h^4 + b^5*c^4, z, k)*((8*a*b^3*c*f - 8*a*b^3*d*e + 8*a^2*b^2*e*h - 8*a^2*b^2*f*g)/b + root(256*a^3*b^6*z^4 - 256*a^3*b^5*f*z^3 - 64*a^3*b^4*e*g*z^2 - 64*a^3*b^4*d*h*z^2 + 64*a^2*b^5*c*e*z^2 + 32*a^4*b^3*h^2*z^2 + 96*a^3*b^4*f^2*z^2 + 32*a^2*b^5*d^2*z^2 + 32*a^3*b^3*e*f*g*z + 32*a^3*b^3*d*f*h*z - 32*a^3*b^3*c*g*h*z - 32*a^2*b^4*c*e*f*z + 32*a^2*b^4*c*d*g*z + 16*a^4*b^2*g^2*h*z - 16*a^4*b^2*f*h^2*z - 16*a^3*b^3*e^2*h*z - 16*a^3*b^3*d*g^2*z + 16*a^2*b^4*c^2*h*z - 16*a^2*b^4*d^2*f*z + 16*a^2*b^4*d*e^2*z - 16*a*b^5*c^2*d*z - 16*a^3*b^3*f^3*z - 8*a^3*b^2*d*e*g*h + 8*a^3*b^2*c*f*g*h - 8*a^2*b^3*c*d*f*g + 8*a^2*b^3*c*d*e*h + 4*a^3*b^2*e^2*f*h - 4*a^3*b^2*e*f^2*g - 4*a^3*b^2*d*f^2*h + 4*a^3*b^2*d*f*g^2 - 4*a^2*b^3*c^2*f*h - 4*a^3*b^2*c*e*h^2 + 4*a^2*b^3*d^2*e*g - 4*a^2*b^3*d*e^2*f - 4*a^2*b^3*c*e^2*g + 4*a^2*b^3*c*e*f^2 - 4*a^4*b*f*g^2*h + 4*a^4*b*e*g*h^2 + 4*a*b^4*c^2*d*f - 4*a*b^4*c*d^2*e - 4*a^4*b*d*h^3 - 4*a*b^4*c^3*g + 6*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 + 6*a^2*b^3*c^2*g^2 + 2*a^2*b^3*d^2*f^2 + 2*a^4*b*f^2*h^2 - 4*a^2*b^3*d^3*h - 4*a^3*b^2*c*g^3 + 2*a*b^4*c^2*e^2 + a^3*b^2*f^4 + a^2*b^3*e^4 + a^4*b*g^4 + a*b^4*d^4 + a^5*h^4 + b^5*c^4, z, k)*((16*a^2*b^3*g - 16*a*b^4*c)/b - (x*(16*a^2*b^3*h - 16*a*b^4*d))/b) - (x*(4*b^4*c^2 - 4*a*b^3*e^2 + 4*a^2*b^2*g^2 - 8*a*b^3*c*g + 8*a*b^3*d*f - 8*a^2*b^2*f*h))/b) - (a*b^2*e^3 - b^3*c*d^2 + b^3*c^2*e + a^3*g*h^2 + a*b^2*c*f^2 + a*b^2*d^2*g - a^2*b*c*h^2 + a^2*b*e*g^2 - a^2*b*f^2*g + 2*a*b^2*c*d*h - 2*a*b^2*c*e*g - 2*a*b^2*d*e*f - 2*a^2*b*d*g*h + 2*a^2*b*e*f*h)/b + (x*(b^3*d^3 - a^3*h^3 + b^3*c^2*f - 2*b^3*c*d*e + a*b^2*d*f^2 - a*b^2*e^2*f - 3*a*b^2*d^2*h + 3*a^2*b*d*h^2 + a^2*b*f*g^2 - a^2*b*f^2*h + 2*a*b^2*c*e*h - 2*a*b^2*c*f*g + 2*a*b^2*d*e*g - 2*a^2*b*e*g*h))/b)*root(256*a^3*b^6*z^4 - 256*a^3*b^5*f*z^3 - 64*a^3*b^4*e*g*z^2 - 64*a^3*b^4*d*h*z^2 + 64*a^2*b^5*c*e*z^2 + 32*a^4*b^3*h^2*z^2 + 96*a^3*b^4*f^2*z^2 + 32*a^2*b^5*d^2*z^2 + 32*a^3*b^3*e*f*g*z + 32*a^3*b^3*d*f*h*z - 32*a^3*b^3*c*g*h*z - 32*a^2*b^4*c*e*f*z + 32*a^2*b^4*c*d*g*z + 16*a^4*b^2*g^2*h*z - 16*a^4*b^2*f*h^2*z - 16*a^3*b^3*e^2*h*z - 16*a^3*b^3*d*g^2*z + 16*a^2*b^4*c^2*h*z - 16*a^2*b^4*d^2*f*z + 16*a^2*b^4*d*e^2*z - 16*a*b^5*c^2*d*z - 16*a^3*b^3*f^3*z - 8*a^3*b^2*d*e*g*h + 8*a^3*b^2*c*f*g*h - 8*a^2*b^3*c*d*f*g + 8*a^2*b^3*c*d*e*h + 4*a^3*b^2*e^2*f*h - 4*a^3*b^2*e*f^2*g - 4*a^3*b^2*d*f^2*h + 4*a^3*b^2*d*f*g^2 - 4*a^2*b^3*c^2*f*h - 4*a^3*b^2*c*e*h^2 + 4*a^2*b^3*d^2*e*g - 4*a^2*b^3*d*e^2*f - 4*a^2*b^3*c*e^2*g + 4*a^2*b^3*c*e*f^2 - 4*a^4*b*f*g^2*h + 4*a^4*b*e*g*h^2 + 4*a*b^4*c^2*d*f - 4*a*b^4*c*d^2*e - 4*a^4*b*d*h^3 - 4*a*b^4*c^3*g + 6*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 + 6*a^2*b^3*c^2*g^2 + 2*a^2*b^3*d^2*f^2 + 2*a^4*b*f^2*h^2 - 4*a^2*b^3*d^3*h - 4*a^3*b^2*c*g^3 + 2*a*b^4*c^2*e^2 + a^3*b^2*f^4 + a^2*b^3*e^4 + a^4*b*g^4 + a*b^4*d^4 + a^5*h^4 + b^5*c^4, z, k), k, 1, 4) + (h*x^2)/(2*b) + (g*x)/b","B"
190,1,3798,384,5.053809,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4),x)","\left(\sum _{l=1}^4\ln\left(\frac{a^4\,i^3-3\,a^3\,b\,e\,i^2+2\,a^3\,b\,f\,h\,i+a^3\,b\,g^2\,i-a^3\,b\,g\,h^2-2\,a^2\,b^2\,c\,g\,i+a^2\,b^2\,c\,h^2-2\,a^2\,b^2\,d\,f\,i+2\,a^2\,b^2\,d\,g\,h+3\,a^2\,b^2\,e^2\,i-2\,a^2\,b^2\,e\,f\,h-a^2\,b^2\,e\,g^2+a^2\,b^2\,f^2\,g+a\,b^3\,c^2\,i-2\,a\,b^3\,c\,d\,h+2\,a\,b^3\,c\,e\,g-a\,b^3\,c\,f^2-a\,b^3\,d^2\,g+2\,a\,b^3\,d\,e\,f-a\,b^3\,e^3-b^4\,c^2\,e+b^4\,c\,d^2}{b^2}+\mathrm{root}\left(256\,a^3\,b^7\,z^4-256\,a^3\,b^6\,f\,z^3+64\,a^4\,b^4\,g\,i\,z^2-64\,a^3\,b^5\,e\,g\,z^2-64\,a^3\,b^5\,d\,h\,z^2-64\,a^3\,b^5\,c\,i\,z^2+64\,a^2\,b^6\,c\,e\,z^2+32\,a^4\,b^4\,h^2\,z^2+96\,a^3\,b^5\,f^2\,z^2+32\,a^2\,b^6\,d^2\,z^2-32\,a^4\,b^3\,f\,g\,i\,z+32\,a^4\,b^3\,e\,h\,i\,z+32\,a^3\,b^4\,e\,f\,g\,z+32\,a^3\,b^4\,d\,f\,h\,z-32\,a^3\,b^4\,d\,e\,i\,z-32\,a^3\,b^4\,c\,g\,h\,z+32\,a^3\,b^4\,c\,f\,i\,z-32\,a^2\,b^5\,c\,e\,f\,z+32\,a^2\,b^5\,c\,d\,g\,z-16\,a^5\,b^2\,h\,i^2\,z+16\,a^4\,b^3\,g^2\,h\,z-16\,a^4\,b^3\,f\,h^2\,z+16\,a^4\,b^3\,d\,i^2\,z-16\,a^3\,b^4\,e^2\,h\,z-16\,a^3\,b^4\,d\,g^2\,z+16\,a^2\,b^5\,c^2\,h\,z-16\,a^2\,b^5\,d^2\,f\,z+16\,a^2\,b^5\,d\,e^2\,z-16\,a\,b^6\,c^2\,d\,z-16\,a^3\,b^4\,f^3\,z-8\,a^4\,b^2\,e\,f\,h\,i+8\,a^4\,b^2\,d\,g\,h\,i-8\,a^3\,b^3\,d\,e\,g\,h+8\,a^3\,b^3\,d\,e\,f\,i+8\,a^3\,b^3\,c\,f\,g\,h+8\,a^3\,b^3\,c\,e\,g\,i-8\,a^3\,b^3\,c\,d\,h\,i-8\,a^2\,b^4\,c\,d\,f\,g+8\,a^2\,b^4\,c\,d\,e\,h+4\,a^4\,b^2\,f^2\,g\,i-4\,a^4\,b^2\,f\,g^2\,h-4\,a^4\,b^2\,e\,g^2\,i+4\,a^4\,b^2\,e\,g\,h^2+4\,a^4\,b^2\,c\,h^2\,i-4\,a^3\,b^3\,d^2\,g\,i-4\,a^4\,b^2\,d\,f\,i^2-4\,a^4\,b^2\,c\,g\,i^2+4\,a^3\,b^3\,e^2\,f\,h-4\,a^3\,b^3\,e\,f^2\,g-4\,a^3\,b^3\,d\,f^2\,h-4\,a^3\,b^3\,c\,f^2\,i+4\,a^3\,b^3\,d\,f\,g^2-4\,a^2\,b^4\,c^2\,f\,h-4\,a^2\,b^4\,c^2\,e\,i-4\,a^3\,b^3\,c\,e\,h^2+4\,a^2\,b^4\,d^2\,e\,g+4\,a^2\,b^4\,c\,d^2\,i-4\,a^2\,b^4\,d\,e^2\,f-4\,a^2\,b^4\,c\,e^2\,g+4\,a^2\,b^4\,c\,e\,f^2-4\,a^5\,b\,g\,h^2\,i+4\,a^5\,b\,f\,h\,i^2+4\,a\,b^5\,c^2\,d\,f-4\,a\,b^5\,c\,d^2\,e-4\,a^5\,b\,e\,i^3-4\,a\,b^5\,c^3\,g+6\,a^4\,b^2\,e^2\,i^2+2\,a^4\,b^2\,f^2\,h^2+6\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2+2\,a^3\,b^3\,c^2\,i^2+6\,a^2\,b^4\,c^2\,g^2+2\,a^2\,b^4\,d^2\,f^2+2\,a^5\,b\,g^2\,i^2-4\,a^3\,b^3\,e^3\,i-4\,a^4\,b^2\,d\,h^3-4\,a^2\,b^4\,d^3\,h-4\,a^3\,b^3\,c\,g^3+2\,a\,b^5\,c^2\,e^2+a^4\,b^2\,g^4+a^3\,b^3\,f^4+a^2\,b^4\,e^4+a^5\,b\,h^4+a\,b^5\,d^4+a^6\,i^4+b^6\,c^4,z,l\right)\,\left(\frac{8\,a\,b^4\,c\,f-8\,a\,b^4\,d\,e+8\,a^2\,b^3\,d\,i+8\,a^2\,b^3\,e\,h-8\,a^2\,b^3\,f\,g-8\,a^3\,b^2\,h\,i}{b^2}+\mathrm{root}\left(256\,a^3\,b^7\,z^4-256\,a^3\,b^6\,f\,z^3+64\,a^4\,b^4\,g\,i\,z^2-64\,a^3\,b^5\,e\,g\,z^2-64\,a^3\,b^5\,d\,h\,z^2-64\,a^3\,b^5\,c\,i\,z^2+64\,a^2\,b^6\,c\,e\,z^2+32\,a^4\,b^4\,h^2\,z^2+96\,a^3\,b^5\,f^2\,z^2+32\,a^2\,b^6\,d^2\,z^2-32\,a^4\,b^3\,f\,g\,i\,z+32\,a^4\,b^3\,e\,h\,i\,z+32\,a^3\,b^4\,e\,f\,g\,z+32\,a^3\,b^4\,d\,f\,h\,z-32\,a^3\,b^4\,d\,e\,i\,z-32\,a^3\,b^4\,c\,g\,h\,z+32\,a^3\,b^4\,c\,f\,i\,z-32\,a^2\,b^5\,c\,e\,f\,z+32\,a^2\,b^5\,c\,d\,g\,z-16\,a^5\,b^2\,h\,i^2\,z+16\,a^4\,b^3\,g^2\,h\,z-16\,a^4\,b^3\,f\,h^2\,z+16\,a^4\,b^3\,d\,i^2\,z-16\,a^3\,b^4\,e^2\,h\,z-16\,a^3\,b^4\,d\,g^2\,z+16\,a^2\,b^5\,c^2\,h\,z-16\,a^2\,b^5\,d^2\,f\,z+16\,a^2\,b^5\,d\,e^2\,z-16\,a\,b^6\,c^2\,d\,z-16\,a^3\,b^4\,f^3\,z-8\,a^4\,b^2\,e\,f\,h\,i+8\,a^4\,b^2\,d\,g\,h\,i-8\,a^3\,b^3\,d\,e\,g\,h+8\,a^3\,b^3\,d\,e\,f\,i+8\,a^3\,b^3\,c\,f\,g\,h+8\,a^3\,b^3\,c\,e\,g\,i-8\,a^3\,b^3\,c\,d\,h\,i-8\,a^2\,b^4\,c\,d\,f\,g+8\,a^2\,b^4\,c\,d\,e\,h+4\,a^4\,b^2\,f^2\,g\,i-4\,a^4\,b^2\,f\,g^2\,h-4\,a^4\,b^2\,e\,g^2\,i+4\,a^4\,b^2\,e\,g\,h^2+4\,a^4\,b^2\,c\,h^2\,i-4\,a^3\,b^3\,d^2\,g\,i-4\,a^4\,b^2\,d\,f\,i^2-4\,a^4\,b^2\,c\,g\,i^2+4\,a^3\,b^3\,e^2\,f\,h-4\,a^3\,b^3\,e\,f^2\,g-4\,a^3\,b^3\,d\,f^2\,h-4\,a^3\,b^3\,c\,f^2\,i+4\,a^3\,b^3\,d\,f\,g^2-4\,a^2\,b^4\,c^2\,f\,h-4\,a^2\,b^4\,c^2\,e\,i-4\,a^3\,b^3\,c\,e\,h^2+4\,a^2\,b^4\,d^2\,e\,g+4\,a^2\,b^4\,c\,d^2\,i-4\,a^2\,b^4\,d\,e^2\,f-4\,a^2\,b^4\,c\,e^2\,g+4\,a^2\,b^4\,c\,e\,f^2-4\,a^5\,b\,g\,h^2\,i+4\,a^5\,b\,f\,h\,i^2+4\,a\,b^5\,c^2\,d\,f-4\,a\,b^5\,c\,d^2\,e-4\,a^5\,b\,e\,i^3-4\,a\,b^5\,c^3\,g+6\,a^4\,b^2\,e^2\,i^2+2\,a^4\,b^2\,f^2\,h^2+6\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2+2\,a^3\,b^3\,c^2\,i^2+6\,a^2\,b^4\,c^2\,g^2+2\,a^2\,b^4\,d^2\,f^2+2\,a^5\,b\,g^2\,i^2-4\,a^3\,b^3\,e^3\,i-4\,a^4\,b^2\,d\,h^3-4\,a^2\,b^4\,d^3\,h-4\,a^3\,b^3\,c\,g^3+2\,a\,b^5\,c^2\,e^2+a^4\,b^2\,g^4+a^3\,b^3\,f^4+a^2\,b^4\,e^4+a^5\,b\,h^4+a\,b^5\,d^4+a^6\,i^4+b^6\,c^4,z,l\right)\,\left(\frac{16\,a^2\,b^4\,g-16\,a\,b^5\,c}{b^2}-\frac{x\,\left(16\,a^2\,b^3\,h-16\,a\,b^4\,d\right)}{b}\right)-\frac{x\,\left(-4\,a^3\,b\,i^2+8\,a^2\,b^2\,e\,i+4\,a^2\,b^2\,g^2-8\,f\,h\,a^2\,b^2-8\,a\,b^3\,c\,g-4\,a\,b^3\,e^2+8\,d\,f\,a\,b^3+4\,b^4\,c^2\right)}{b}\right)+\frac{x\,\left(-a^3\,f\,i^2+2\,a^3\,g\,h\,i-a^3\,h^3-2\,a^2\,b\,c\,h\,i-2\,a^2\,b\,d\,g\,i+3\,a^2\,b\,d\,h^2+2\,a^2\,b\,e\,f\,i-2\,a^2\,b\,e\,g\,h-a^2\,b\,f^2\,h+a^2\,b\,f\,g^2+2\,a\,b^2\,c\,d\,i+2\,a\,b^2\,c\,e\,h-2\,a\,b^2\,c\,f\,g-3\,a\,b^2\,d^2\,h+2\,a\,b^2\,d\,e\,g+a\,b^2\,d\,f^2-a\,b^2\,e^2\,f+b^3\,c^2\,f-2\,b^3\,c\,d\,e+b^3\,d^3\right)}{b}\right)\,\mathrm{root}\left(256\,a^3\,b^7\,z^4-256\,a^3\,b^6\,f\,z^3+64\,a^4\,b^4\,g\,i\,z^2-64\,a^3\,b^5\,e\,g\,z^2-64\,a^3\,b^5\,d\,h\,z^2-64\,a^3\,b^5\,c\,i\,z^2+64\,a^2\,b^6\,c\,e\,z^2+32\,a^4\,b^4\,h^2\,z^2+96\,a^3\,b^5\,f^2\,z^2+32\,a^2\,b^6\,d^2\,z^2-32\,a^4\,b^3\,f\,g\,i\,z+32\,a^4\,b^3\,e\,h\,i\,z+32\,a^3\,b^4\,e\,f\,g\,z+32\,a^3\,b^4\,d\,f\,h\,z-32\,a^3\,b^4\,d\,e\,i\,z-32\,a^3\,b^4\,c\,g\,h\,z+32\,a^3\,b^4\,c\,f\,i\,z-32\,a^2\,b^5\,c\,e\,f\,z+32\,a^2\,b^5\,c\,d\,g\,z-16\,a^5\,b^2\,h\,i^2\,z+16\,a^4\,b^3\,g^2\,h\,z-16\,a^4\,b^3\,f\,h^2\,z+16\,a^4\,b^3\,d\,i^2\,z-16\,a^3\,b^4\,e^2\,h\,z-16\,a^3\,b^4\,d\,g^2\,z+16\,a^2\,b^5\,c^2\,h\,z-16\,a^2\,b^5\,d^2\,f\,z+16\,a^2\,b^5\,d\,e^2\,z-16\,a\,b^6\,c^2\,d\,z-16\,a^3\,b^4\,f^3\,z-8\,a^4\,b^2\,e\,f\,h\,i+8\,a^4\,b^2\,d\,g\,h\,i-8\,a^3\,b^3\,d\,e\,g\,h+8\,a^3\,b^3\,d\,e\,f\,i+8\,a^3\,b^3\,c\,f\,g\,h+8\,a^3\,b^3\,c\,e\,g\,i-8\,a^3\,b^3\,c\,d\,h\,i-8\,a^2\,b^4\,c\,d\,f\,g+8\,a^2\,b^4\,c\,d\,e\,h+4\,a^4\,b^2\,f^2\,g\,i-4\,a^4\,b^2\,f\,g^2\,h-4\,a^4\,b^2\,e\,g^2\,i+4\,a^4\,b^2\,e\,g\,h^2+4\,a^4\,b^2\,c\,h^2\,i-4\,a^3\,b^3\,d^2\,g\,i-4\,a^4\,b^2\,d\,f\,i^2-4\,a^4\,b^2\,c\,g\,i^2+4\,a^3\,b^3\,e^2\,f\,h-4\,a^3\,b^3\,e\,f^2\,g-4\,a^3\,b^3\,d\,f^2\,h-4\,a^3\,b^3\,c\,f^2\,i+4\,a^3\,b^3\,d\,f\,g^2-4\,a^2\,b^4\,c^2\,f\,h-4\,a^2\,b^4\,c^2\,e\,i-4\,a^3\,b^3\,c\,e\,h^2+4\,a^2\,b^4\,d^2\,e\,g+4\,a^2\,b^4\,c\,d^2\,i-4\,a^2\,b^4\,d\,e^2\,f-4\,a^2\,b^4\,c\,e^2\,g+4\,a^2\,b^4\,c\,e\,f^2-4\,a^5\,b\,g\,h^2\,i+4\,a^5\,b\,f\,h\,i^2+4\,a\,b^5\,c^2\,d\,f-4\,a\,b^5\,c\,d^2\,e-4\,a^5\,b\,e\,i^3-4\,a\,b^5\,c^3\,g+6\,a^4\,b^2\,e^2\,i^2+2\,a^4\,b^2\,f^2\,h^2+6\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2+2\,a^3\,b^3\,c^2\,i^2+6\,a^2\,b^4\,c^2\,g^2+2\,a^2\,b^4\,d^2\,f^2+2\,a^5\,b\,g^2\,i^2-4\,a^3\,b^3\,e^3\,i-4\,a^4\,b^2\,d\,h^3-4\,a^2\,b^4\,d^3\,h-4\,a^3\,b^3\,c\,g^3+2\,a\,b^5\,c^2\,e^2+a^4\,b^2\,g^4+a^3\,b^3\,f^4+a^2\,b^4\,e^4+a^5\,b\,h^4+a\,b^5\,d^4+a^6\,i^4+b^6\,c^4,z,l\right)\right)+\frac{h\,x^2}{2\,b}+\frac{i\,x^3}{3\,b}+\frac{g\,x}{b}","Not used",1,"symsum(log((a^4*i^3 - a*b^3*e^3 + b^4*c*d^2 - b^4*c^2*e + a^2*b^2*c*h^2 - a^2*b^2*e*g^2 + a^2*b^2*f^2*g + 3*a^2*b^2*e^2*i - a*b^3*c*f^2 - a*b^3*d^2*g + a*b^3*c^2*i - 3*a^3*b*e*i^2 - a^3*b*g*h^2 + a^3*b*g^2*i - 2*a^2*b^2*c*g*i - 2*a^2*b^2*d*f*i + 2*a^2*b^2*d*g*h - 2*a^2*b^2*e*f*h - 2*a*b^3*c*d*h + 2*a*b^3*c*e*g + 2*a*b^3*d*e*f + 2*a^3*b*f*h*i)/b^2 + root(256*a^3*b^7*z^4 - 256*a^3*b^6*f*z^3 + 64*a^4*b^4*g*i*z^2 - 64*a^3*b^5*e*g*z^2 - 64*a^3*b^5*d*h*z^2 - 64*a^3*b^5*c*i*z^2 + 64*a^2*b^6*c*e*z^2 + 32*a^4*b^4*h^2*z^2 + 96*a^3*b^5*f^2*z^2 + 32*a^2*b^6*d^2*z^2 - 32*a^4*b^3*f*g*i*z + 32*a^4*b^3*e*h*i*z + 32*a^3*b^4*e*f*g*z + 32*a^3*b^4*d*f*h*z - 32*a^3*b^4*d*e*i*z - 32*a^3*b^4*c*g*h*z + 32*a^3*b^4*c*f*i*z - 32*a^2*b^5*c*e*f*z + 32*a^2*b^5*c*d*g*z - 16*a^5*b^2*h*i^2*z + 16*a^4*b^3*g^2*h*z - 16*a^4*b^3*f*h^2*z + 16*a^4*b^3*d*i^2*z - 16*a^3*b^4*e^2*h*z - 16*a^3*b^4*d*g^2*z + 16*a^2*b^5*c^2*h*z - 16*a^2*b^5*d^2*f*z + 16*a^2*b^5*d*e^2*z - 16*a*b^6*c^2*d*z - 16*a^3*b^4*f^3*z - 8*a^4*b^2*e*f*h*i + 8*a^4*b^2*d*g*h*i - 8*a^3*b^3*d*e*g*h + 8*a^3*b^3*d*e*f*i + 8*a^3*b^3*c*f*g*h + 8*a^3*b^3*c*e*g*i - 8*a^3*b^3*c*d*h*i - 8*a^2*b^4*c*d*f*g + 8*a^2*b^4*c*d*e*h + 4*a^4*b^2*f^2*g*i - 4*a^4*b^2*f*g^2*h - 4*a^4*b^2*e*g^2*i + 4*a^4*b^2*e*g*h^2 + 4*a^4*b^2*c*h^2*i - 4*a^3*b^3*d^2*g*i - 4*a^4*b^2*d*f*i^2 - 4*a^4*b^2*c*g*i^2 + 4*a^3*b^3*e^2*f*h - 4*a^3*b^3*e*f^2*g - 4*a^3*b^3*d*f^2*h - 4*a^3*b^3*c*f^2*i + 4*a^3*b^3*d*f*g^2 - 4*a^2*b^4*c^2*f*h - 4*a^2*b^4*c^2*e*i - 4*a^3*b^3*c*e*h^2 + 4*a^2*b^4*d^2*e*g + 4*a^2*b^4*c*d^2*i - 4*a^2*b^4*d*e^2*f - 4*a^2*b^4*c*e^2*g + 4*a^2*b^4*c*e*f^2 - 4*a^5*b*g*h^2*i + 4*a^5*b*f*h*i^2 + 4*a*b^5*c^2*d*f - 4*a*b^5*c*d^2*e - 4*a^5*b*e*i^3 - 4*a*b^5*c^3*g + 6*a^4*b^2*e^2*i^2 + 2*a^4*b^2*f^2*h^2 + 6*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 + 2*a^3*b^3*c^2*i^2 + 6*a^2*b^4*c^2*g^2 + 2*a^2*b^4*d^2*f^2 + 2*a^5*b*g^2*i^2 - 4*a^3*b^3*e^3*i - 4*a^4*b^2*d*h^3 - 4*a^2*b^4*d^3*h - 4*a^3*b^3*c*g^3 + 2*a*b^5*c^2*e^2 + a^4*b^2*g^4 + a^3*b^3*f^4 + a^2*b^4*e^4 + a^5*b*h^4 + a*b^5*d^4 + a^6*i^4 + b^6*c^4, z, l)*((8*a*b^4*c*f - 8*a*b^4*d*e + 8*a^2*b^3*d*i + 8*a^2*b^3*e*h - 8*a^2*b^3*f*g - 8*a^3*b^2*h*i)/b^2 + root(256*a^3*b^7*z^4 - 256*a^3*b^6*f*z^3 + 64*a^4*b^4*g*i*z^2 - 64*a^3*b^5*e*g*z^2 - 64*a^3*b^5*d*h*z^2 - 64*a^3*b^5*c*i*z^2 + 64*a^2*b^6*c*e*z^2 + 32*a^4*b^4*h^2*z^2 + 96*a^3*b^5*f^2*z^2 + 32*a^2*b^6*d^2*z^2 - 32*a^4*b^3*f*g*i*z + 32*a^4*b^3*e*h*i*z + 32*a^3*b^4*e*f*g*z + 32*a^3*b^4*d*f*h*z - 32*a^3*b^4*d*e*i*z - 32*a^3*b^4*c*g*h*z + 32*a^3*b^4*c*f*i*z - 32*a^2*b^5*c*e*f*z + 32*a^2*b^5*c*d*g*z - 16*a^5*b^2*h*i^2*z + 16*a^4*b^3*g^2*h*z - 16*a^4*b^3*f*h^2*z + 16*a^4*b^3*d*i^2*z - 16*a^3*b^4*e^2*h*z - 16*a^3*b^4*d*g^2*z + 16*a^2*b^5*c^2*h*z - 16*a^2*b^5*d^2*f*z + 16*a^2*b^5*d*e^2*z - 16*a*b^6*c^2*d*z - 16*a^3*b^4*f^3*z - 8*a^4*b^2*e*f*h*i + 8*a^4*b^2*d*g*h*i - 8*a^3*b^3*d*e*g*h + 8*a^3*b^3*d*e*f*i + 8*a^3*b^3*c*f*g*h + 8*a^3*b^3*c*e*g*i - 8*a^3*b^3*c*d*h*i - 8*a^2*b^4*c*d*f*g + 8*a^2*b^4*c*d*e*h + 4*a^4*b^2*f^2*g*i - 4*a^4*b^2*f*g^2*h - 4*a^4*b^2*e*g^2*i + 4*a^4*b^2*e*g*h^2 + 4*a^4*b^2*c*h^2*i - 4*a^3*b^3*d^2*g*i - 4*a^4*b^2*d*f*i^2 - 4*a^4*b^2*c*g*i^2 + 4*a^3*b^3*e^2*f*h - 4*a^3*b^3*e*f^2*g - 4*a^3*b^3*d*f^2*h - 4*a^3*b^3*c*f^2*i + 4*a^3*b^3*d*f*g^2 - 4*a^2*b^4*c^2*f*h - 4*a^2*b^4*c^2*e*i - 4*a^3*b^3*c*e*h^2 + 4*a^2*b^4*d^2*e*g + 4*a^2*b^4*c*d^2*i - 4*a^2*b^4*d*e^2*f - 4*a^2*b^4*c*e^2*g + 4*a^2*b^4*c*e*f^2 - 4*a^5*b*g*h^2*i + 4*a^5*b*f*h*i^2 + 4*a*b^5*c^2*d*f - 4*a*b^5*c*d^2*e - 4*a^5*b*e*i^3 - 4*a*b^5*c^3*g + 6*a^4*b^2*e^2*i^2 + 2*a^4*b^2*f^2*h^2 + 6*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 + 2*a^3*b^3*c^2*i^2 + 6*a^2*b^4*c^2*g^2 + 2*a^2*b^4*d^2*f^2 + 2*a^5*b*g^2*i^2 - 4*a^3*b^3*e^3*i - 4*a^4*b^2*d*h^3 - 4*a^2*b^4*d^3*h - 4*a^3*b^3*c*g^3 + 2*a*b^5*c^2*e^2 + a^4*b^2*g^4 + a^3*b^3*f^4 + a^2*b^4*e^4 + a^5*b*h^4 + a*b^5*d^4 + a^6*i^4 + b^6*c^4, z, l)*((16*a^2*b^4*g - 16*a*b^5*c)/b^2 - (x*(16*a^2*b^3*h - 16*a*b^4*d))/b) - (x*(4*b^4*c^2 - 4*a*b^3*e^2 - 4*a^3*b*i^2 + 4*a^2*b^2*g^2 - 8*a*b^3*c*g + 8*a*b^3*d*f + 8*a^2*b^2*e*i - 8*a^2*b^2*f*h))/b) + (x*(b^3*d^3 - a^3*h^3 + b^3*c^2*f - a^3*f*i^2 - 2*b^3*c*d*e + 2*a^3*g*h*i + a*b^2*d*f^2 - a*b^2*e^2*f - 3*a*b^2*d^2*h + 3*a^2*b*d*h^2 + a^2*b*f*g^2 - a^2*b*f^2*h + 2*a*b^2*c*d*i + 2*a*b^2*c*e*h - 2*a*b^2*c*f*g + 2*a*b^2*d*e*g - 2*a^2*b*c*h*i - 2*a^2*b*d*g*i + 2*a^2*b*e*f*i - 2*a^2*b*e*g*h))/b)*root(256*a^3*b^7*z^4 - 256*a^3*b^6*f*z^3 + 64*a^4*b^4*g*i*z^2 - 64*a^3*b^5*e*g*z^2 - 64*a^3*b^5*d*h*z^2 - 64*a^3*b^5*c*i*z^2 + 64*a^2*b^6*c*e*z^2 + 32*a^4*b^4*h^2*z^2 + 96*a^3*b^5*f^2*z^2 + 32*a^2*b^6*d^2*z^2 - 32*a^4*b^3*f*g*i*z + 32*a^4*b^3*e*h*i*z + 32*a^3*b^4*e*f*g*z + 32*a^3*b^4*d*f*h*z - 32*a^3*b^4*d*e*i*z - 32*a^3*b^4*c*g*h*z + 32*a^3*b^4*c*f*i*z - 32*a^2*b^5*c*e*f*z + 32*a^2*b^5*c*d*g*z - 16*a^5*b^2*h*i^2*z + 16*a^4*b^3*g^2*h*z - 16*a^4*b^3*f*h^2*z + 16*a^4*b^3*d*i^2*z - 16*a^3*b^4*e^2*h*z - 16*a^3*b^4*d*g^2*z + 16*a^2*b^5*c^2*h*z - 16*a^2*b^5*d^2*f*z + 16*a^2*b^5*d*e^2*z - 16*a*b^6*c^2*d*z - 16*a^3*b^4*f^3*z - 8*a^4*b^2*e*f*h*i + 8*a^4*b^2*d*g*h*i - 8*a^3*b^3*d*e*g*h + 8*a^3*b^3*d*e*f*i + 8*a^3*b^3*c*f*g*h + 8*a^3*b^3*c*e*g*i - 8*a^3*b^3*c*d*h*i - 8*a^2*b^4*c*d*f*g + 8*a^2*b^4*c*d*e*h + 4*a^4*b^2*f^2*g*i - 4*a^4*b^2*f*g^2*h - 4*a^4*b^2*e*g^2*i + 4*a^4*b^2*e*g*h^2 + 4*a^4*b^2*c*h^2*i - 4*a^3*b^3*d^2*g*i - 4*a^4*b^2*d*f*i^2 - 4*a^4*b^2*c*g*i^2 + 4*a^3*b^3*e^2*f*h - 4*a^3*b^3*e*f^2*g - 4*a^3*b^3*d*f^2*h - 4*a^3*b^3*c*f^2*i + 4*a^3*b^3*d*f*g^2 - 4*a^2*b^4*c^2*f*h - 4*a^2*b^4*c^2*e*i - 4*a^3*b^3*c*e*h^2 + 4*a^2*b^4*d^2*e*g + 4*a^2*b^4*c*d^2*i - 4*a^2*b^4*d*e^2*f - 4*a^2*b^4*c*e^2*g + 4*a^2*b^4*c*e*f^2 - 4*a^5*b*g*h^2*i + 4*a^5*b*f*h*i^2 + 4*a*b^5*c^2*d*f - 4*a*b^5*c*d^2*e - 4*a^5*b*e*i^3 - 4*a*b^5*c^3*g + 6*a^4*b^2*e^2*i^2 + 2*a^4*b^2*f^2*h^2 + 6*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 + 2*a^3*b^3*c^2*i^2 + 6*a^2*b^4*c^2*g^2 + 2*a^2*b^4*d^2*f^2 + 2*a^5*b*g^2*i^2 - 4*a^3*b^3*e^3*i - 4*a^4*b^2*d*h^3 - 4*a^2*b^4*d^3*h - 4*a^3*b^3*c*g^3 + 2*a*b^5*c^2*e^2 + a^4*b^2*g^4 + a^3*b^3*f^4 + a^2*b^4*e^4 + a^5*b*h^4 + a*b^5*d^4 + a^6*i^4 + b^6*c^4, z, l), l, 1, 4) + (h*x^2)/(2*b) + (i*x^3)/(3*b) + (g*x)/b","B"
191,1,5664,402,5.203325,"\text{Not used}","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)","\left(\sum _{m=1}^4\ln\left(\frac{a^4\,g\,j^2-2\,a^4\,h\,i\,j+a^4\,i^3-a^3\,b\,c\,j^2+2\,a^3\,b\,d\,i\,j+2\,a^3\,b\,e\,h\,j-3\,a^3\,b\,e\,i^2-2\,a^3\,b\,f\,g\,j+2\,a^3\,b\,f\,h\,i+a^3\,b\,g^2\,i-a^3\,b\,g\,h^2+2\,a^2\,b^2\,c\,f\,j-2\,a^2\,b^2\,c\,g\,i+a^2\,b^2\,c\,h^2-2\,a^2\,b^2\,d\,e\,j-2\,a^2\,b^2\,d\,f\,i+2\,a^2\,b^2\,d\,g\,h+3\,a^2\,b^2\,e^2\,i-2\,a^2\,b^2\,e\,f\,h-a^2\,b^2\,e\,g^2+a^2\,b^2\,f^2\,g+a\,b^3\,c^2\,i-2\,a\,b^3\,c\,d\,h+2\,a\,b^3\,c\,e\,g-a\,b^3\,c\,f^2-a\,b^3\,d^2\,g+2\,a\,b^3\,d\,e\,f-a\,b^3\,e^3-b^4\,c^2\,e+b^4\,c\,d^2}{b^2}+\mathrm{root}\left(256\,a^3\,b^8\,z^4+256\,a^4\,b^6\,j\,z^3-256\,a^3\,b^7\,f\,z^3-192\,a^4\,b^5\,f\,j\,z^2+64\,a^4\,b^5\,g\,i\,z^2-64\,a^3\,b^6\,e\,g\,z^2-64\,a^3\,b^6\,d\,h\,z^2-64\,a^3\,b^6\,c\,i\,z^2+64\,a^2\,b^7\,c\,e\,z^2+96\,a^5\,b^4\,j^2\,z^2+32\,a^4\,b^5\,h^2\,z^2+96\,a^3\,b^6\,f^2\,z^2+32\,a^2\,b^7\,d^2\,z^2+32\,a^5\,b^3\,g\,i\,j\,z-32\,a^4\,b^4\,f\,g\,i\,z+32\,a^4\,b^4\,e\,h\,i\,z-32\,a^4\,b^4\,e\,g\,j\,z-32\,a^4\,b^4\,d\,h\,j\,z-32\,a^4\,b^4\,c\,i\,j\,z+32\,a^3\,b^5\,e\,f\,g\,z+32\,a^3\,b^5\,d\,f\,h\,z-32\,a^3\,b^5\,d\,e\,i\,z-32\,a^3\,b^5\,c\,g\,h\,z+32\,a^3\,b^5\,c\,f\,i\,z+32\,a^3\,b^5\,c\,e\,j\,z-32\,a^2\,b^6\,c\,e\,f\,z+32\,a^2\,b^6\,c\,d\,g\,z+16\,a^5\,b^3\,h^2\,j\,z-16\,a^5\,b^3\,h\,i^2\,z-48\,a^5\,b^3\,f\,j^2\,z+48\,a^4\,b^4\,f^2\,j\,z+16\,a^4\,b^4\,g^2\,h\,z-16\,a^4\,b^4\,f\,h^2\,z+16\,a^3\,b^5\,d^2\,j\,z+16\,a^4\,b^4\,d\,i^2\,z-16\,a^3\,b^5\,e^2\,h\,z-16\,a^3\,b^5\,d\,g^2\,z+16\,a^2\,b^6\,c^2\,h\,z-16\,a^2\,b^6\,d^2\,f\,z+16\,a^2\,b^6\,d\,e^2\,z-16\,a\,b^7\,c^2\,d\,z+16\,a^6\,b^2\,j^3\,z-16\,a^3\,b^5\,f^3\,z-8\,a^5\,b^2\,f\,g\,i\,j+8\,a^5\,b^2\,e\,h\,i\,j-8\,a^4\,b^3\,e\,f\,h\,i+8\,a^4\,b^3\,e\,f\,g\,j+8\,a^4\,b^3\,d\,g\,h\,i+8\,a^4\,b^3\,d\,f\,h\,j-8\,a^4\,b^3\,d\,e\,i\,j-8\,a^4\,b^3\,c\,g\,h\,j+8\,a^4\,b^3\,c\,f\,i\,j-8\,a^3\,b^4\,d\,e\,g\,h+8\,a^3\,b^4\,d\,e\,f\,i+8\,a^3\,b^4\,c\,f\,g\,h+8\,a^3\,b^4\,c\,e\,g\,i-8\,a^3\,b^4\,c\,e\,f\,j-8\,a^3\,b^4\,c\,d\,h\,i+8\,a^3\,b^4\,c\,d\,g\,j-8\,a^2\,b^5\,c\,d\,f\,g+8\,a^2\,b^5\,c\,d\,e\,h+4\,a^5\,b^2\,g^2\,h\,j-4\,a^5\,b^2\,g\,h^2\,i-4\,a^5\,b^2\,f\,h^2\,j+4\,a^5\,b^2\,f\,h\,i^2+4\,a^5\,b^2\,d\,i^2\,j-4\,a^4\,b^3\,e^2\,h\,j-4\,a^5\,b^2\,e\,g\,j^2-4\,a^5\,b^2\,d\,h\,j^2-4\,a^5\,b^2\,c\,i\,j^2+4\,a^4\,b^3\,f^2\,g\,i-4\,a^4\,b^3\,f\,g^2\,h-4\,a^4\,b^3\,e\,g^2\,i-4\,a^4\,b^3\,d\,g^2\,j+4\,a^3\,b^4\,c^2\,h\,j+4\,a^4\,b^3\,e\,g\,h^2+4\,a^4\,b^3\,c\,h^2\,i-4\,a^3\,b^4\,d^2\,g\,i-4\,a^3\,b^4\,d^2\,f\,j-4\,a^4\,b^3\,d\,f\,i^2-4\,a^4\,b^3\,c\,g\,i^2+4\,a^3\,b^4\,e^2\,f\,h+4\,a^3\,b^4\,d\,e^2\,j+4\,a^4\,b^3\,c\,e\,j^2-4\,a^3\,b^4\,e\,f^2\,g-4\,a^3\,b^4\,d\,f^2\,h-4\,a^3\,b^4\,c\,f^2\,i+4\,a^3\,b^4\,d\,f\,g^2-4\,a^2\,b^5\,c^2\,f\,h-4\,a^2\,b^5\,c^2\,e\,i-4\,a^2\,b^5\,c^2\,d\,j-4\,a^3\,b^4\,c\,e\,h^2+4\,a^2\,b^5\,d^2\,e\,g+4\,a^2\,b^5\,c\,d^2\,i-4\,a^2\,b^5\,d\,e^2\,f-4\,a^2\,b^5\,c\,e^2\,g+4\,a^2\,b^5\,c\,e\,f^2-4\,a^6\,b\,h\,i^2\,j+4\,a^6\,b\,g\,i\,j^2+4\,a\,b^6\,c^2\,d\,f-4\,a\,b^6\,c\,d^2\,e-4\,a^6\,b\,f\,j^3-4\,a\,b^6\,c^3\,g+6\,a^5\,b^2\,f^2\,j^2+2\,a^5\,b^2\,g^2\,i^2+6\,a^4\,b^3\,e^2\,i^2+2\,a^4\,b^3\,f^2\,h^2+2\,a^4\,b^3\,d^2\,j^2+6\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2+2\,a^3\,b^4\,c^2\,i^2+6\,a^2\,b^5\,c^2\,g^2+2\,a^2\,b^5\,d^2\,f^2+2\,a^6\,b\,h^2\,j^2-4\,a^4\,b^3\,f^3\,j-4\,a^5\,b^2\,e\,i^3-4\,a^3\,b^4\,e^3\,i-4\,a^4\,b^3\,d\,h^3-4\,a^2\,b^5\,d^3\,h-4\,a^3\,b^4\,c\,g^3+2\,a\,b^6\,c^2\,e^2+a^5\,b^2\,h^4+a^4\,b^3\,g^4+a^3\,b^4\,f^4+a^2\,b^5\,e^4+a^6\,b\,i^4+a\,b^6\,d^4+a^7\,j^4+b^7\,c^4,z,m\right)\,\left(\frac{8\,a\,b^4\,c\,f-8\,a\,b^4\,d\,e-8\,a^2\,b^3\,c\,j+8\,a^2\,b^3\,d\,i+8\,a^2\,b^3\,e\,h-8\,a^2\,b^3\,f\,g+8\,a^3\,b^2\,g\,j-8\,a^3\,b^2\,h\,i}{b^2}+\mathrm{root}\left(256\,a^3\,b^8\,z^4+256\,a^4\,b^6\,j\,z^3-256\,a^3\,b^7\,f\,z^3-192\,a^4\,b^5\,f\,j\,z^2+64\,a^4\,b^5\,g\,i\,z^2-64\,a^3\,b^6\,e\,g\,z^2-64\,a^3\,b^6\,d\,h\,z^2-64\,a^3\,b^6\,c\,i\,z^2+64\,a^2\,b^7\,c\,e\,z^2+96\,a^5\,b^4\,j^2\,z^2+32\,a^4\,b^5\,h^2\,z^2+96\,a^3\,b^6\,f^2\,z^2+32\,a^2\,b^7\,d^2\,z^2+32\,a^5\,b^3\,g\,i\,j\,z-32\,a^4\,b^4\,f\,g\,i\,z+32\,a^4\,b^4\,e\,h\,i\,z-32\,a^4\,b^4\,e\,g\,j\,z-32\,a^4\,b^4\,d\,h\,j\,z-32\,a^4\,b^4\,c\,i\,j\,z+32\,a^3\,b^5\,e\,f\,g\,z+32\,a^3\,b^5\,d\,f\,h\,z-32\,a^3\,b^5\,d\,e\,i\,z-32\,a^3\,b^5\,c\,g\,h\,z+32\,a^3\,b^5\,c\,f\,i\,z+32\,a^3\,b^5\,c\,e\,j\,z-32\,a^2\,b^6\,c\,e\,f\,z+32\,a^2\,b^6\,c\,d\,g\,z+16\,a^5\,b^3\,h^2\,j\,z-16\,a^5\,b^3\,h\,i^2\,z-48\,a^5\,b^3\,f\,j^2\,z+48\,a^4\,b^4\,f^2\,j\,z+16\,a^4\,b^4\,g^2\,h\,z-16\,a^4\,b^4\,f\,h^2\,z+16\,a^3\,b^5\,d^2\,j\,z+16\,a^4\,b^4\,d\,i^2\,z-16\,a^3\,b^5\,e^2\,h\,z-16\,a^3\,b^5\,d\,g^2\,z+16\,a^2\,b^6\,c^2\,h\,z-16\,a^2\,b^6\,d^2\,f\,z+16\,a^2\,b^6\,d\,e^2\,z-16\,a\,b^7\,c^2\,d\,z+16\,a^6\,b^2\,j^3\,z-16\,a^3\,b^5\,f^3\,z-8\,a^5\,b^2\,f\,g\,i\,j+8\,a^5\,b^2\,e\,h\,i\,j-8\,a^4\,b^3\,e\,f\,h\,i+8\,a^4\,b^3\,e\,f\,g\,j+8\,a^4\,b^3\,d\,g\,h\,i+8\,a^4\,b^3\,d\,f\,h\,j-8\,a^4\,b^3\,d\,e\,i\,j-8\,a^4\,b^3\,c\,g\,h\,j+8\,a^4\,b^3\,c\,f\,i\,j-8\,a^3\,b^4\,d\,e\,g\,h+8\,a^3\,b^4\,d\,e\,f\,i+8\,a^3\,b^4\,c\,f\,g\,h+8\,a^3\,b^4\,c\,e\,g\,i-8\,a^3\,b^4\,c\,e\,f\,j-8\,a^3\,b^4\,c\,d\,h\,i+8\,a^3\,b^4\,c\,d\,g\,j-8\,a^2\,b^5\,c\,d\,f\,g+8\,a^2\,b^5\,c\,d\,e\,h+4\,a^5\,b^2\,g^2\,h\,j-4\,a^5\,b^2\,g\,h^2\,i-4\,a^5\,b^2\,f\,h^2\,j+4\,a^5\,b^2\,f\,h\,i^2+4\,a^5\,b^2\,d\,i^2\,j-4\,a^4\,b^3\,e^2\,h\,j-4\,a^5\,b^2\,e\,g\,j^2-4\,a^5\,b^2\,d\,h\,j^2-4\,a^5\,b^2\,c\,i\,j^2+4\,a^4\,b^3\,f^2\,g\,i-4\,a^4\,b^3\,f\,g^2\,h-4\,a^4\,b^3\,e\,g^2\,i-4\,a^4\,b^3\,d\,g^2\,j+4\,a^3\,b^4\,c^2\,h\,j+4\,a^4\,b^3\,e\,g\,h^2+4\,a^4\,b^3\,c\,h^2\,i-4\,a^3\,b^4\,d^2\,g\,i-4\,a^3\,b^4\,d^2\,f\,j-4\,a^4\,b^3\,d\,f\,i^2-4\,a^4\,b^3\,c\,g\,i^2+4\,a^3\,b^4\,e^2\,f\,h+4\,a^3\,b^4\,d\,e^2\,j+4\,a^4\,b^3\,c\,e\,j^2-4\,a^3\,b^4\,e\,f^2\,g-4\,a^3\,b^4\,d\,f^2\,h-4\,a^3\,b^4\,c\,f^2\,i+4\,a^3\,b^4\,d\,f\,g^2-4\,a^2\,b^5\,c^2\,f\,h-4\,a^2\,b^5\,c^2\,e\,i-4\,a^2\,b^5\,c^2\,d\,j-4\,a^3\,b^4\,c\,e\,h^2+4\,a^2\,b^5\,d^2\,e\,g+4\,a^2\,b^5\,c\,d^2\,i-4\,a^2\,b^5\,d\,e^2\,f-4\,a^2\,b^5\,c\,e^2\,g+4\,a^2\,b^5\,c\,e\,f^2-4\,a^6\,b\,h\,i^2\,j+4\,a^6\,b\,g\,i\,j^2+4\,a\,b^6\,c^2\,d\,f-4\,a\,b^6\,c\,d^2\,e-4\,a^6\,b\,f\,j^3-4\,a\,b^6\,c^3\,g+6\,a^5\,b^2\,f^2\,j^2+2\,a^5\,b^2\,g^2\,i^2+6\,a^4\,b^3\,e^2\,i^2+2\,a^4\,b^3\,f^2\,h^2+2\,a^4\,b^3\,d^2\,j^2+6\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2+2\,a^3\,b^4\,c^2\,i^2+6\,a^2\,b^5\,c^2\,g^2+2\,a^2\,b^5\,d^2\,f^2+2\,a^6\,b\,h^2\,j^2-4\,a^4\,b^3\,f^3\,j-4\,a^5\,b^2\,e\,i^3-4\,a^3\,b^4\,e^3\,i-4\,a^4\,b^3\,d\,h^3-4\,a^2\,b^5\,d^3\,h-4\,a^3\,b^4\,c\,g^3+2\,a\,b^6\,c^2\,e^2+a^5\,b^2\,h^4+a^4\,b^3\,g^4+a^3\,b^4\,f^4+a^2\,b^5\,e^4+a^6\,b\,i^4+a\,b^6\,d^4+a^7\,j^4+b^7\,c^4,z,m\right)\,\left(\frac{16\,a^2\,b^4\,g-16\,a\,b^5\,c}{b^2}-\frac{x\,\left(16\,a^2\,b^4\,h-16\,a\,b^5\,d\right)}{b^2}\right)-\frac{x\,\left(4\,b^5\,c^2-4\,a\,b^4\,e^2+4\,a^2\,b^3\,g^2-4\,a^3\,b^2\,i^2-8\,a\,b^4\,c\,g+8\,a\,b^4\,d\,f-8\,a^2\,b^3\,d\,j+8\,a^2\,b^3\,e\,i-8\,a^2\,b^3\,f\,h+8\,a^3\,b^2\,h\,j\right)}{b^2}\right)+\frac{x\,\left(-a^4\,h\,j^2+a^4\,i^2\,j+a^3\,b\,d\,j^2-2\,a^3\,b\,e\,i\,j+2\,a^3\,b\,f\,h\,j-a^3\,b\,f\,i^2-a^3\,b\,g^2\,j+2\,a^3\,b\,g\,h\,i-a^3\,b\,h^3+2\,a^2\,b^2\,c\,g\,j-2\,a^2\,b^2\,c\,h\,i-2\,a^2\,b^2\,d\,f\,j-2\,a^2\,b^2\,d\,g\,i+3\,a^2\,b^2\,d\,h^2+a^2\,b^2\,e^2\,j+2\,a^2\,b^2\,e\,f\,i-2\,a^2\,b^2\,e\,g\,h-a^2\,b^2\,f^2\,h+a^2\,b^2\,f\,g^2-a\,b^3\,c^2\,j+2\,a\,b^3\,c\,d\,i+2\,a\,b^3\,c\,e\,h-2\,a\,b^3\,c\,f\,g-3\,a\,b^3\,d^2\,h+2\,a\,b^3\,d\,e\,g+a\,b^3\,d\,f^2-a\,b^3\,e^2\,f+b^4\,c^2\,f-2\,b^4\,c\,d\,e+b^4\,d^3\right)}{b^2}\right)\,\mathrm{root}\left(256\,a^3\,b^8\,z^4+256\,a^4\,b^6\,j\,z^3-256\,a^3\,b^7\,f\,z^3-192\,a^4\,b^5\,f\,j\,z^2+64\,a^4\,b^5\,g\,i\,z^2-64\,a^3\,b^6\,e\,g\,z^2-64\,a^3\,b^6\,d\,h\,z^2-64\,a^3\,b^6\,c\,i\,z^2+64\,a^2\,b^7\,c\,e\,z^2+96\,a^5\,b^4\,j^2\,z^2+32\,a^4\,b^5\,h^2\,z^2+96\,a^3\,b^6\,f^2\,z^2+32\,a^2\,b^7\,d^2\,z^2+32\,a^5\,b^3\,g\,i\,j\,z-32\,a^4\,b^4\,f\,g\,i\,z+32\,a^4\,b^4\,e\,h\,i\,z-32\,a^4\,b^4\,e\,g\,j\,z-32\,a^4\,b^4\,d\,h\,j\,z-32\,a^4\,b^4\,c\,i\,j\,z+32\,a^3\,b^5\,e\,f\,g\,z+32\,a^3\,b^5\,d\,f\,h\,z-32\,a^3\,b^5\,d\,e\,i\,z-32\,a^3\,b^5\,c\,g\,h\,z+32\,a^3\,b^5\,c\,f\,i\,z+32\,a^3\,b^5\,c\,e\,j\,z-32\,a^2\,b^6\,c\,e\,f\,z+32\,a^2\,b^6\,c\,d\,g\,z+16\,a^5\,b^3\,h^2\,j\,z-16\,a^5\,b^3\,h\,i^2\,z-48\,a^5\,b^3\,f\,j^2\,z+48\,a^4\,b^4\,f^2\,j\,z+16\,a^4\,b^4\,g^2\,h\,z-16\,a^4\,b^4\,f\,h^2\,z+16\,a^3\,b^5\,d^2\,j\,z+16\,a^4\,b^4\,d\,i^2\,z-16\,a^3\,b^5\,e^2\,h\,z-16\,a^3\,b^5\,d\,g^2\,z+16\,a^2\,b^6\,c^2\,h\,z-16\,a^2\,b^6\,d^2\,f\,z+16\,a^2\,b^6\,d\,e^2\,z-16\,a\,b^7\,c^2\,d\,z+16\,a^6\,b^2\,j^3\,z-16\,a^3\,b^5\,f^3\,z-8\,a^5\,b^2\,f\,g\,i\,j+8\,a^5\,b^2\,e\,h\,i\,j-8\,a^4\,b^3\,e\,f\,h\,i+8\,a^4\,b^3\,e\,f\,g\,j+8\,a^4\,b^3\,d\,g\,h\,i+8\,a^4\,b^3\,d\,f\,h\,j-8\,a^4\,b^3\,d\,e\,i\,j-8\,a^4\,b^3\,c\,g\,h\,j+8\,a^4\,b^3\,c\,f\,i\,j-8\,a^3\,b^4\,d\,e\,g\,h+8\,a^3\,b^4\,d\,e\,f\,i+8\,a^3\,b^4\,c\,f\,g\,h+8\,a^3\,b^4\,c\,e\,g\,i-8\,a^3\,b^4\,c\,e\,f\,j-8\,a^3\,b^4\,c\,d\,h\,i+8\,a^3\,b^4\,c\,d\,g\,j-8\,a^2\,b^5\,c\,d\,f\,g+8\,a^2\,b^5\,c\,d\,e\,h+4\,a^5\,b^2\,g^2\,h\,j-4\,a^5\,b^2\,g\,h^2\,i-4\,a^5\,b^2\,f\,h^2\,j+4\,a^5\,b^2\,f\,h\,i^2+4\,a^5\,b^2\,d\,i^2\,j-4\,a^4\,b^3\,e^2\,h\,j-4\,a^5\,b^2\,e\,g\,j^2-4\,a^5\,b^2\,d\,h\,j^2-4\,a^5\,b^2\,c\,i\,j^2+4\,a^4\,b^3\,f^2\,g\,i-4\,a^4\,b^3\,f\,g^2\,h-4\,a^4\,b^3\,e\,g^2\,i-4\,a^4\,b^3\,d\,g^2\,j+4\,a^3\,b^4\,c^2\,h\,j+4\,a^4\,b^3\,e\,g\,h^2+4\,a^4\,b^3\,c\,h^2\,i-4\,a^3\,b^4\,d^2\,g\,i-4\,a^3\,b^4\,d^2\,f\,j-4\,a^4\,b^3\,d\,f\,i^2-4\,a^4\,b^3\,c\,g\,i^2+4\,a^3\,b^4\,e^2\,f\,h+4\,a^3\,b^4\,d\,e^2\,j+4\,a^4\,b^3\,c\,e\,j^2-4\,a^3\,b^4\,e\,f^2\,g-4\,a^3\,b^4\,d\,f^2\,h-4\,a^3\,b^4\,c\,f^2\,i+4\,a^3\,b^4\,d\,f\,g^2-4\,a^2\,b^5\,c^2\,f\,h-4\,a^2\,b^5\,c^2\,e\,i-4\,a^2\,b^5\,c^2\,d\,j-4\,a^3\,b^4\,c\,e\,h^2+4\,a^2\,b^5\,d^2\,e\,g+4\,a^2\,b^5\,c\,d^2\,i-4\,a^2\,b^5\,d\,e^2\,f-4\,a^2\,b^5\,c\,e^2\,g+4\,a^2\,b^5\,c\,e\,f^2-4\,a^6\,b\,h\,i^2\,j+4\,a^6\,b\,g\,i\,j^2+4\,a\,b^6\,c^2\,d\,f-4\,a\,b^6\,c\,d^2\,e-4\,a^6\,b\,f\,j^3-4\,a\,b^6\,c^3\,g+6\,a^5\,b^2\,f^2\,j^2+2\,a^5\,b^2\,g^2\,i^2+6\,a^4\,b^3\,e^2\,i^2+2\,a^4\,b^3\,f^2\,h^2+2\,a^4\,b^3\,d^2\,j^2+6\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2+2\,a^3\,b^4\,c^2\,i^2+6\,a^2\,b^5\,c^2\,g^2+2\,a^2\,b^5\,d^2\,f^2+2\,a^6\,b\,h^2\,j^2-4\,a^4\,b^3\,f^3\,j-4\,a^5\,b^2\,e\,i^3-4\,a^3\,b^4\,e^3\,i-4\,a^4\,b^3\,d\,h^3-4\,a^2\,b^5\,d^3\,h-4\,a^3\,b^4\,c\,g^3+2\,a\,b^6\,c^2\,e^2+a^5\,b^2\,h^4+a^4\,b^3\,g^4+a^3\,b^4\,f^4+a^2\,b^5\,e^4+a^6\,b\,i^4+a\,b^6\,d^4+a^7\,j^4+b^7\,c^4,z,m\right)\right)+\frac{h\,x^2}{2\,b}+\frac{i\,x^3}{3\,b}+\frac{j\,x^4}{4\,b}+\frac{g\,x}{b}","Not used",1,"symsum(log((a^4*i^3 - a*b^3*e^3 + b^4*c*d^2 - b^4*c^2*e + a^4*g*j^2 + a^2*b^2*c*h^2 - a^2*b^2*e*g^2 + a^2*b^2*f^2*g + 3*a^2*b^2*e^2*i - 2*a^4*h*i*j - a*b^3*c*f^2 - a*b^3*d^2*g + a*b^3*c^2*i - a^3*b*c*j^2 - 3*a^3*b*e*i^2 - a^3*b*g*h^2 + a^3*b*g^2*i + 2*a^2*b^2*c*f*j - 2*a^2*b^2*c*g*i - 2*a^2*b^2*d*e*j - 2*a^2*b^2*d*f*i + 2*a^2*b^2*d*g*h - 2*a^2*b^2*e*f*h - 2*a*b^3*c*d*h + 2*a*b^3*c*e*g + 2*a*b^3*d*e*f + 2*a^3*b*d*i*j + 2*a^3*b*e*h*j - 2*a^3*b*f*g*j + 2*a^3*b*f*h*i)/b^2 + root(256*a^3*b^8*z^4 + 256*a^4*b^6*j*z^3 - 256*a^3*b^7*f*z^3 - 192*a^4*b^5*f*j*z^2 + 64*a^4*b^5*g*i*z^2 - 64*a^3*b^6*e*g*z^2 - 64*a^3*b^6*d*h*z^2 - 64*a^3*b^6*c*i*z^2 + 64*a^2*b^7*c*e*z^2 + 96*a^5*b^4*j^2*z^2 + 32*a^4*b^5*h^2*z^2 + 96*a^3*b^6*f^2*z^2 + 32*a^2*b^7*d^2*z^2 + 32*a^5*b^3*g*i*j*z - 32*a^4*b^4*f*g*i*z + 32*a^4*b^4*e*h*i*z - 32*a^4*b^4*e*g*j*z - 32*a^4*b^4*d*h*j*z - 32*a^4*b^4*c*i*j*z + 32*a^3*b^5*e*f*g*z + 32*a^3*b^5*d*f*h*z - 32*a^3*b^5*d*e*i*z - 32*a^3*b^5*c*g*h*z + 32*a^3*b^5*c*f*i*z + 32*a^3*b^5*c*e*j*z - 32*a^2*b^6*c*e*f*z + 32*a^2*b^6*c*d*g*z + 16*a^5*b^3*h^2*j*z - 16*a^5*b^3*h*i^2*z - 48*a^5*b^3*f*j^2*z + 48*a^4*b^4*f^2*j*z + 16*a^4*b^4*g^2*h*z - 16*a^4*b^4*f*h^2*z + 16*a^3*b^5*d^2*j*z + 16*a^4*b^4*d*i^2*z - 16*a^3*b^5*e^2*h*z - 16*a^3*b^5*d*g^2*z + 16*a^2*b^6*c^2*h*z - 16*a^2*b^6*d^2*f*z + 16*a^2*b^6*d*e^2*z - 16*a*b^7*c^2*d*z + 16*a^6*b^2*j^3*z - 16*a^3*b^5*f^3*z - 8*a^5*b^2*f*g*i*j + 8*a^5*b^2*e*h*i*j - 8*a^4*b^3*e*f*h*i + 8*a^4*b^3*e*f*g*j + 8*a^4*b^3*d*g*h*i + 8*a^4*b^3*d*f*h*j - 8*a^4*b^3*d*e*i*j - 8*a^4*b^3*c*g*h*j + 8*a^4*b^3*c*f*i*j - 8*a^3*b^4*d*e*g*h + 8*a^3*b^4*d*e*f*i + 8*a^3*b^4*c*f*g*h + 8*a^3*b^4*c*e*g*i - 8*a^3*b^4*c*e*f*j - 8*a^3*b^4*c*d*h*i + 8*a^3*b^4*c*d*g*j - 8*a^2*b^5*c*d*f*g + 8*a^2*b^5*c*d*e*h + 4*a^5*b^2*g^2*h*j - 4*a^5*b^2*g*h^2*i - 4*a^5*b^2*f*h^2*j + 4*a^5*b^2*f*h*i^2 + 4*a^5*b^2*d*i^2*j - 4*a^4*b^3*e^2*h*j - 4*a^5*b^2*e*g*j^2 - 4*a^5*b^2*d*h*j^2 - 4*a^5*b^2*c*i*j^2 + 4*a^4*b^3*f^2*g*i - 4*a^4*b^3*f*g^2*h - 4*a^4*b^3*e*g^2*i - 4*a^4*b^3*d*g^2*j + 4*a^3*b^4*c^2*h*j + 4*a^4*b^3*e*g*h^2 + 4*a^4*b^3*c*h^2*i - 4*a^3*b^4*d^2*g*i - 4*a^3*b^4*d^2*f*j - 4*a^4*b^3*d*f*i^2 - 4*a^4*b^3*c*g*i^2 + 4*a^3*b^4*e^2*f*h + 4*a^3*b^4*d*e^2*j + 4*a^4*b^3*c*e*j^2 - 4*a^3*b^4*e*f^2*g - 4*a^3*b^4*d*f^2*h - 4*a^3*b^4*c*f^2*i + 4*a^3*b^4*d*f*g^2 - 4*a^2*b^5*c^2*f*h - 4*a^2*b^5*c^2*e*i - 4*a^2*b^5*c^2*d*j - 4*a^3*b^4*c*e*h^2 + 4*a^2*b^5*d^2*e*g + 4*a^2*b^5*c*d^2*i - 4*a^2*b^5*d*e^2*f - 4*a^2*b^5*c*e^2*g + 4*a^2*b^5*c*e*f^2 - 4*a^6*b*h*i^2*j + 4*a^6*b*g*i*j^2 + 4*a*b^6*c^2*d*f - 4*a*b^6*c*d^2*e - 4*a^6*b*f*j^3 - 4*a*b^6*c^3*g + 6*a^5*b^2*f^2*j^2 + 2*a^5*b^2*g^2*i^2 + 6*a^4*b^3*e^2*i^2 + 2*a^4*b^3*f^2*h^2 + 2*a^4*b^3*d^2*j^2 + 6*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 + 2*a^3*b^4*c^2*i^2 + 6*a^2*b^5*c^2*g^2 + 2*a^2*b^5*d^2*f^2 + 2*a^6*b*h^2*j^2 - 4*a^4*b^3*f^3*j - 4*a^5*b^2*e*i^3 - 4*a^3*b^4*e^3*i - 4*a^4*b^3*d*h^3 - 4*a^2*b^5*d^3*h - 4*a^3*b^4*c*g^3 + 2*a*b^6*c^2*e^2 + a^5*b^2*h^4 + a^4*b^3*g^4 + a^3*b^4*f^4 + a^2*b^5*e^4 + a^6*b*i^4 + a*b^6*d^4 + a^7*j^4 + b^7*c^4, z, m)*((8*a*b^4*c*f - 8*a*b^4*d*e - 8*a^2*b^3*c*j + 8*a^2*b^3*d*i + 8*a^2*b^3*e*h - 8*a^2*b^3*f*g + 8*a^3*b^2*g*j - 8*a^3*b^2*h*i)/b^2 + root(256*a^3*b^8*z^4 + 256*a^4*b^6*j*z^3 - 256*a^3*b^7*f*z^3 - 192*a^4*b^5*f*j*z^2 + 64*a^4*b^5*g*i*z^2 - 64*a^3*b^6*e*g*z^2 - 64*a^3*b^6*d*h*z^2 - 64*a^3*b^6*c*i*z^2 + 64*a^2*b^7*c*e*z^2 + 96*a^5*b^4*j^2*z^2 + 32*a^4*b^5*h^2*z^2 + 96*a^3*b^6*f^2*z^2 + 32*a^2*b^7*d^2*z^2 + 32*a^5*b^3*g*i*j*z - 32*a^4*b^4*f*g*i*z + 32*a^4*b^4*e*h*i*z - 32*a^4*b^4*e*g*j*z - 32*a^4*b^4*d*h*j*z - 32*a^4*b^4*c*i*j*z + 32*a^3*b^5*e*f*g*z + 32*a^3*b^5*d*f*h*z - 32*a^3*b^5*d*e*i*z - 32*a^3*b^5*c*g*h*z + 32*a^3*b^5*c*f*i*z + 32*a^3*b^5*c*e*j*z - 32*a^2*b^6*c*e*f*z + 32*a^2*b^6*c*d*g*z + 16*a^5*b^3*h^2*j*z - 16*a^5*b^3*h*i^2*z - 48*a^5*b^3*f*j^2*z + 48*a^4*b^4*f^2*j*z + 16*a^4*b^4*g^2*h*z - 16*a^4*b^4*f*h^2*z + 16*a^3*b^5*d^2*j*z + 16*a^4*b^4*d*i^2*z - 16*a^3*b^5*e^2*h*z - 16*a^3*b^5*d*g^2*z + 16*a^2*b^6*c^2*h*z - 16*a^2*b^6*d^2*f*z + 16*a^2*b^6*d*e^2*z - 16*a*b^7*c^2*d*z + 16*a^6*b^2*j^3*z - 16*a^3*b^5*f^3*z - 8*a^5*b^2*f*g*i*j + 8*a^5*b^2*e*h*i*j - 8*a^4*b^3*e*f*h*i + 8*a^4*b^3*e*f*g*j + 8*a^4*b^3*d*g*h*i + 8*a^4*b^3*d*f*h*j - 8*a^4*b^3*d*e*i*j - 8*a^4*b^3*c*g*h*j + 8*a^4*b^3*c*f*i*j - 8*a^3*b^4*d*e*g*h + 8*a^3*b^4*d*e*f*i + 8*a^3*b^4*c*f*g*h + 8*a^3*b^4*c*e*g*i - 8*a^3*b^4*c*e*f*j - 8*a^3*b^4*c*d*h*i + 8*a^3*b^4*c*d*g*j - 8*a^2*b^5*c*d*f*g + 8*a^2*b^5*c*d*e*h + 4*a^5*b^2*g^2*h*j - 4*a^5*b^2*g*h^2*i - 4*a^5*b^2*f*h^2*j + 4*a^5*b^2*f*h*i^2 + 4*a^5*b^2*d*i^2*j - 4*a^4*b^3*e^2*h*j - 4*a^5*b^2*e*g*j^2 - 4*a^5*b^2*d*h*j^2 - 4*a^5*b^2*c*i*j^2 + 4*a^4*b^3*f^2*g*i - 4*a^4*b^3*f*g^2*h - 4*a^4*b^3*e*g^2*i - 4*a^4*b^3*d*g^2*j + 4*a^3*b^4*c^2*h*j + 4*a^4*b^3*e*g*h^2 + 4*a^4*b^3*c*h^2*i - 4*a^3*b^4*d^2*g*i - 4*a^3*b^4*d^2*f*j - 4*a^4*b^3*d*f*i^2 - 4*a^4*b^3*c*g*i^2 + 4*a^3*b^4*e^2*f*h + 4*a^3*b^4*d*e^2*j + 4*a^4*b^3*c*e*j^2 - 4*a^3*b^4*e*f^2*g - 4*a^3*b^4*d*f^2*h - 4*a^3*b^4*c*f^2*i + 4*a^3*b^4*d*f*g^2 - 4*a^2*b^5*c^2*f*h - 4*a^2*b^5*c^2*e*i - 4*a^2*b^5*c^2*d*j - 4*a^3*b^4*c*e*h^2 + 4*a^2*b^5*d^2*e*g + 4*a^2*b^5*c*d^2*i - 4*a^2*b^5*d*e^2*f - 4*a^2*b^5*c*e^2*g + 4*a^2*b^5*c*e*f^2 - 4*a^6*b*h*i^2*j + 4*a^6*b*g*i*j^2 + 4*a*b^6*c^2*d*f - 4*a*b^6*c*d^2*e - 4*a^6*b*f*j^3 - 4*a*b^6*c^3*g + 6*a^5*b^2*f^2*j^2 + 2*a^5*b^2*g^2*i^2 + 6*a^4*b^3*e^2*i^2 + 2*a^4*b^3*f^2*h^2 + 2*a^4*b^3*d^2*j^2 + 6*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 + 2*a^3*b^4*c^2*i^2 + 6*a^2*b^5*c^2*g^2 + 2*a^2*b^5*d^2*f^2 + 2*a^6*b*h^2*j^2 - 4*a^4*b^3*f^3*j - 4*a^5*b^2*e*i^3 - 4*a^3*b^4*e^3*i - 4*a^4*b^3*d*h^3 - 4*a^2*b^5*d^3*h - 4*a^3*b^4*c*g^3 + 2*a*b^6*c^2*e^2 + a^5*b^2*h^4 + a^4*b^3*g^4 + a^3*b^4*f^4 + a^2*b^5*e^4 + a^6*b*i^4 + a*b^6*d^4 + a^7*j^4 + b^7*c^4, z, m)*((16*a^2*b^4*g - 16*a*b^5*c)/b^2 - (x*(16*a^2*b^4*h - 16*a*b^5*d))/b^2) - (x*(4*b^5*c^2 - 4*a*b^4*e^2 + 4*a^2*b^3*g^2 - 4*a^3*b^2*i^2 - 8*a*b^4*c*g + 8*a*b^4*d*f - 8*a^2*b^3*d*j + 8*a^2*b^3*e*i - 8*a^2*b^3*f*h + 8*a^3*b^2*h*j))/b^2) + (x*(b^4*d^3 - a^3*b*h^3 + b^4*c^2*f - a^4*h*j^2 + a^4*i^2*j + 3*a^2*b^2*d*h^2 + a^2*b^2*f*g^2 - a^2*b^2*f^2*h + a^2*b^2*e^2*j - 2*b^4*c*d*e + a*b^3*d*f^2 - a*b^3*e^2*f - 3*a*b^3*d^2*h - a*b^3*c^2*j + a^3*b*d*j^2 - a^3*b*f*i^2 - a^3*b*g^2*j + 2*a^2*b^2*c*g*j - 2*a^2*b^2*c*h*i - 2*a^2*b^2*d*f*j - 2*a^2*b^2*d*g*i + 2*a^2*b^2*e*f*i - 2*a^2*b^2*e*g*h + 2*a*b^3*c*d*i + 2*a*b^3*c*e*h - 2*a*b^3*c*f*g + 2*a*b^3*d*e*g - 2*a^3*b*e*i*j + 2*a^3*b*f*h*j + 2*a^3*b*g*h*i))/b^2)*root(256*a^3*b^8*z^4 + 256*a^4*b^6*j*z^3 - 256*a^3*b^7*f*z^3 - 192*a^4*b^5*f*j*z^2 + 64*a^4*b^5*g*i*z^2 - 64*a^3*b^6*e*g*z^2 - 64*a^3*b^6*d*h*z^2 - 64*a^3*b^6*c*i*z^2 + 64*a^2*b^7*c*e*z^2 + 96*a^5*b^4*j^2*z^2 + 32*a^4*b^5*h^2*z^2 + 96*a^3*b^6*f^2*z^2 + 32*a^2*b^7*d^2*z^2 + 32*a^5*b^3*g*i*j*z - 32*a^4*b^4*f*g*i*z + 32*a^4*b^4*e*h*i*z - 32*a^4*b^4*e*g*j*z - 32*a^4*b^4*d*h*j*z - 32*a^4*b^4*c*i*j*z + 32*a^3*b^5*e*f*g*z + 32*a^3*b^5*d*f*h*z - 32*a^3*b^5*d*e*i*z - 32*a^3*b^5*c*g*h*z + 32*a^3*b^5*c*f*i*z + 32*a^3*b^5*c*e*j*z - 32*a^2*b^6*c*e*f*z + 32*a^2*b^6*c*d*g*z + 16*a^5*b^3*h^2*j*z - 16*a^5*b^3*h*i^2*z - 48*a^5*b^3*f*j^2*z + 48*a^4*b^4*f^2*j*z + 16*a^4*b^4*g^2*h*z - 16*a^4*b^4*f*h^2*z + 16*a^3*b^5*d^2*j*z + 16*a^4*b^4*d*i^2*z - 16*a^3*b^5*e^2*h*z - 16*a^3*b^5*d*g^2*z + 16*a^2*b^6*c^2*h*z - 16*a^2*b^6*d^2*f*z + 16*a^2*b^6*d*e^2*z - 16*a*b^7*c^2*d*z + 16*a^6*b^2*j^3*z - 16*a^3*b^5*f^3*z - 8*a^5*b^2*f*g*i*j + 8*a^5*b^2*e*h*i*j - 8*a^4*b^3*e*f*h*i + 8*a^4*b^3*e*f*g*j + 8*a^4*b^3*d*g*h*i + 8*a^4*b^3*d*f*h*j - 8*a^4*b^3*d*e*i*j - 8*a^4*b^3*c*g*h*j + 8*a^4*b^3*c*f*i*j - 8*a^3*b^4*d*e*g*h + 8*a^3*b^4*d*e*f*i + 8*a^3*b^4*c*f*g*h + 8*a^3*b^4*c*e*g*i - 8*a^3*b^4*c*e*f*j - 8*a^3*b^4*c*d*h*i + 8*a^3*b^4*c*d*g*j - 8*a^2*b^5*c*d*f*g + 8*a^2*b^5*c*d*e*h + 4*a^5*b^2*g^2*h*j - 4*a^5*b^2*g*h^2*i - 4*a^5*b^2*f*h^2*j + 4*a^5*b^2*f*h*i^2 + 4*a^5*b^2*d*i^2*j - 4*a^4*b^3*e^2*h*j - 4*a^5*b^2*e*g*j^2 - 4*a^5*b^2*d*h*j^2 - 4*a^5*b^2*c*i*j^2 + 4*a^4*b^3*f^2*g*i - 4*a^4*b^3*f*g^2*h - 4*a^4*b^3*e*g^2*i - 4*a^4*b^3*d*g^2*j + 4*a^3*b^4*c^2*h*j + 4*a^4*b^3*e*g*h^2 + 4*a^4*b^3*c*h^2*i - 4*a^3*b^4*d^2*g*i - 4*a^3*b^4*d^2*f*j - 4*a^4*b^3*d*f*i^2 - 4*a^4*b^3*c*g*i^2 + 4*a^3*b^4*e^2*f*h + 4*a^3*b^4*d*e^2*j + 4*a^4*b^3*c*e*j^2 - 4*a^3*b^4*e*f^2*g - 4*a^3*b^4*d*f^2*h - 4*a^3*b^4*c*f^2*i + 4*a^3*b^4*d*f*g^2 - 4*a^2*b^5*c^2*f*h - 4*a^2*b^5*c^2*e*i - 4*a^2*b^5*c^2*d*j - 4*a^3*b^4*c*e*h^2 + 4*a^2*b^5*d^2*e*g + 4*a^2*b^5*c*d^2*i - 4*a^2*b^5*d*e^2*f - 4*a^2*b^5*c*e^2*g + 4*a^2*b^5*c*e*f^2 - 4*a^6*b*h*i^2*j + 4*a^6*b*g*i*j^2 + 4*a*b^6*c^2*d*f - 4*a*b^6*c*d^2*e - 4*a^6*b*f*j^3 - 4*a*b^6*c^3*g + 6*a^5*b^2*f^2*j^2 + 2*a^5*b^2*g^2*i^2 + 6*a^4*b^3*e^2*i^2 + 2*a^4*b^3*f^2*h^2 + 2*a^4*b^3*d^2*j^2 + 6*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 + 2*a^3*b^4*c^2*i^2 + 6*a^2*b^5*c^2*g^2 + 2*a^2*b^5*d^2*f^2 + 2*a^6*b*h^2*j^2 - 4*a^4*b^3*f^3*j - 4*a^5*b^2*e*i^3 - 4*a^3*b^4*e^3*i - 4*a^4*b^3*d*h^3 - 4*a^2*b^5*d^3*h - 4*a^3*b^4*c*g^3 + 2*a*b^6*c^2*e^2 + a^5*b^2*h^4 + a^4*b^3*g^4 + a^3*b^4*f^4 + a^2*b^5*e^4 + a^6*b*i^4 + a*b^6*d^4 + a^7*j^4 + b^7*c^4, z, m), m, 1, 4) + (h*x^2)/(2*b) + (i*x^3)/(3*b) + (j*x^4)/(4*b) + (g*x)/b","B"
192,1,1626,184,5.614561,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4)^2,x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^6\,z^4+4096\,a^5\,b^4\,d\,h\,z^2+1024\,a^5\,b^4\,e\,g\,z^2-3072\,a^4\,b^5\,c\,e\,z^2-2048\,a^6\,b^3\,h^2\,z^2-2048\,a^4\,b^5\,d^2\,z^2+768\,a^4\,b^3\,c\,g\,h\,z-768\,a^3\,b^4\,c\,d\,g\,z-128\,a^5\,b^2\,g^2\,h\,z-128\,a^4\,b^3\,e^2\,h\,z-1152\,a^3\,b^4\,c^2\,h\,z+128\,a^4\,b^3\,d\,g^2\,z+128\,a^3\,b^4\,d\,e^2\,z+1152\,a^2\,b^5\,c^2\,d\,z-32\,a^3\,b^2\,d\,e\,g\,h+96\,a^2\,b^3\,c\,d\,e\,h-48\,a^3\,b^2\,c\,e\,h^2+16\,a^2\,b^3\,d^2\,e\,g-12\,a^2\,b^3\,c\,e^2\,g+16\,a^4\,b\,e\,g\,h^2-48\,a\,b^4\,c\,d^2\,e-64\,a^4\,b\,d\,h^3+108\,a\,b^4\,c^3\,g+96\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2-54\,a^2\,b^3\,c^2\,g^2-64\,a^2\,b^3\,d^3\,h+12\,a^3\,b^2\,c\,g^3+18\,a\,b^4\,c^2\,e^2+16\,a\,b^4\,d^4+16\,a^5\,h^4-81\,b^5\,c^4-a^2\,b^3\,e^4-a^4\,b\,g^4,z,k\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^6\,z^4+4096\,a^5\,b^4\,d\,h\,z^2+1024\,a^5\,b^4\,e\,g\,z^2-3072\,a^4\,b^5\,c\,e\,z^2-2048\,a^6\,b^3\,h^2\,z^2-2048\,a^4\,b^5\,d^2\,z^2+768\,a^4\,b^3\,c\,g\,h\,z-768\,a^3\,b^4\,c\,d\,g\,z-128\,a^5\,b^2\,g^2\,h\,z-128\,a^4\,b^3\,e^2\,h\,z-1152\,a^3\,b^4\,c^2\,h\,z+128\,a^4\,b^3\,d\,g^2\,z+128\,a^3\,b^4\,d\,e^2\,z+1152\,a^2\,b^5\,c^2\,d\,z-32\,a^3\,b^2\,d\,e\,g\,h+96\,a^2\,b^3\,c\,d\,e\,h-48\,a^3\,b^2\,c\,e\,h^2+16\,a^2\,b^3\,d^2\,e\,g-12\,a^2\,b^3\,c\,e^2\,g+16\,a^4\,b\,e\,g\,h^2-48\,a\,b^4\,c\,d^2\,e-64\,a^4\,b\,d\,h^3+108\,a\,b^4\,c^3\,g+96\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2-54\,a^2\,b^3\,c^2\,g^2-64\,a^2\,b^3\,d^3\,h+12\,a^3\,b^2\,c\,g^3+18\,a\,b^4\,c^2\,e^2+16\,a\,b^4\,d^4+16\,a^5\,h^4-81\,b^5\,c^4-a^2\,b^3\,e^4-a^4\,b\,g^4,z,k\right)\,\left(\frac{768\,a^3\,b^4\,c-256\,a^4\,b^3\,g}{64\,a^3\,b}-\frac{x\,\left(128\,a^3\,b^4\,d-128\,a^4\,b^3\,h\right)}{16\,a^3\,b}\right)-\frac{64\,a^2\,b^3\,d\,e-64\,a^3\,b^2\,e\,h}{64\,a^3\,b}+\frac{x\,\left(4\,a^3\,b^2\,g^2-24\,a^2\,b^3\,c\,g+4\,a^2\,b^3\,e^2+36\,a\,b^4\,c^2\right)}{16\,a^3\,b}\right)-\frac{-4\,a^3\,g\,h^2+12\,a^2\,b\,c\,h^2+8\,a^2\,b\,d\,g\,h-a^2\,b\,e\,g^2-24\,a\,b^2\,c\,d\,h+6\,a\,b^2\,c\,e\,g-4\,a\,b^2\,d^2\,g+a\,b^2\,e^3-9\,b^3\,c^2\,e+12\,b^3\,c\,d^2}{64\,a^3\,b}-\frac{x\,\left(-2\,a^3\,h^3+6\,a^2\,b\,d\,h^2-e\,g\,a^2\,b\,h-6\,a\,b^2\,d^2\,h+e\,g\,a\,b^2\,d+3\,c\,e\,a\,b^2\,h+2\,b^3\,d^3-3\,c\,e\,b^3\,d\right)}{16\,a^3\,b}\right)\,\mathrm{root}\left(65536\,a^7\,b^6\,z^4+4096\,a^5\,b^4\,d\,h\,z^2+1024\,a^5\,b^4\,e\,g\,z^2-3072\,a^4\,b^5\,c\,e\,z^2-2048\,a^6\,b^3\,h^2\,z^2-2048\,a^4\,b^5\,d^2\,z^2+768\,a^4\,b^3\,c\,g\,h\,z-768\,a^3\,b^4\,c\,d\,g\,z-128\,a^5\,b^2\,g^2\,h\,z-128\,a^4\,b^3\,e^2\,h\,z-1152\,a^3\,b^4\,c^2\,h\,z+128\,a^4\,b^3\,d\,g^2\,z+128\,a^3\,b^4\,d\,e^2\,z+1152\,a^2\,b^5\,c^2\,d\,z-32\,a^3\,b^2\,d\,e\,g\,h+96\,a^2\,b^3\,c\,d\,e\,h-48\,a^3\,b^2\,c\,e\,h^2+16\,a^2\,b^3\,d^2\,e\,g-12\,a^2\,b^3\,c\,e^2\,g+16\,a^4\,b\,e\,g\,h^2-48\,a\,b^4\,c\,d^2\,e-64\,a^4\,b\,d\,h^3+108\,a\,b^4\,c^3\,g+96\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2-54\,a^2\,b^3\,c^2\,g^2-64\,a^2\,b^3\,d^3\,h+12\,a^3\,b^2\,c\,g^3+18\,a\,b^4\,c^2\,e^2+16\,a\,b^4\,d^4+16\,a^5\,h^4-81\,b^5\,c^4-a^2\,b^3\,e^4-a^4\,b\,g^4,z,k\right)\right)+\frac{\frac{f}{4\,b}+\frac{e\,x^3}{4\,a}+\frac{x\,\left(b\,c+a\,g\right)}{4\,a\,b}+\frac{x^2\,\left(b\,d+a\,h\right)}{4\,a\,b}}{a-b\,x^4}","Not used",1,"symsum(log(- root(65536*a^7*b^6*z^4 + 4096*a^5*b^4*d*h*z^2 + 1024*a^5*b^4*e*g*z^2 - 3072*a^4*b^5*c*e*z^2 - 2048*a^6*b^3*h^2*z^2 - 2048*a^4*b^5*d^2*z^2 + 768*a^4*b^3*c*g*h*z - 768*a^3*b^4*c*d*g*z - 128*a^5*b^2*g^2*h*z - 128*a^4*b^3*e^2*h*z - 1152*a^3*b^4*c^2*h*z + 128*a^4*b^3*d*g^2*z + 128*a^3*b^4*d*e^2*z + 1152*a^2*b^5*c^2*d*z - 32*a^3*b^2*d*e*g*h + 96*a^2*b^3*c*d*e*h - 48*a^3*b^2*c*e*h^2 + 16*a^2*b^3*d^2*e*g - 12*a^2*b^3*c*e^2*g + 16*a^4*b*e*g*h^2 - 48*a*b^4*c*d^2*e - 64*a^4*b*d*h^3 + 108*a*b^4*c^3*g + 96*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 - 54*a^2*b^3*c^2*g^2 - 64*a^2*b^3*d^3*h + 12*a^3*b^2*c*g^3 + 18*a*b^4*c^2*e^2 + 16*a*b^4*d^4 + 16*a^5*h^4 - 81*b^5*c^4 - a^2*b^3*e^4 - a^4*b*g^4, z, k)*(root(65536*a^7*b^6*z^4 + 4096*a^5*b^4*d*h*z^2 + 1024*a^5*b^4*e*g*z^2 - 3072*a^4*b^5*c*e*z^2 - 2048*a^6*b^3*h^2*z^2 - 2048*a^4*b^5*d^2*z^2 + 768*a^4*b^3*c*g*h*z - 768*a^3*b^4*c*d*g*z - 128*a^5*b^2*g^2*h*z - 128*a^4*b^3*e^2*h*z - 1152*a^3*b^4*c^2*h*z + 128*a^4*b^3*d*g^2*z + 128*a^3*b^4*d*e^2*z + 1152*a^2*b^5*c^2*d*z - 32*a^3*b^2*d*e*g*h + 96*a^2*b^3*c*d*e*h - 48*a^3*b^2*c*e*h^2 + 16*a^2*b^3*d^2*e*g - 12*a^2*b^3*c*e^2*g + 16*a^4*b*e*g*h^2 - 48*a*b^4*c*d^2*e - 64*a^4*b*d*h^3 + 108*a*b^4*c^3*g + 96*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 - 54*a^2*b^3*c^2*g^2 - 64*a^2*b^3*d^3*h + 12*a^3*b^2*c*g^3 + 18*a*b^4*c^2*e^2 + 16*a*b^4*d^4 + 16*a^5*h^4 - 81*b^5*c^4 - a^2*b^3*e^4 - a^4*b*g^4, z, k)*((768*a^3*b^4*c - 256*a^4*b^3*g)/(64*a^3*b) - (x*(128*a^3*b^4*d - 128*a^4*b^3*h))/(16*a^3*b)) - (64*a^2*b^3*d*e - 64*a^3*b^2*e*h)/(64*a^3*b) + (x*(36*a*b^4*c^2 + 4*a^2*b^3*e^2 + 4*a^3*b^2*g^2 - 24*a^2*b^3*c*g))/(16*a^3*b)) - (a*b^2*e^3 + 12*b^3*c*d^2 - 9*b^3*c^2*e - 4*a^3*g*h^2 - 4*a*b^2*d^2*g + 12*a^2*b*c*h^2 - a^2*b*e*g^2 - 24*a*b^2*c*d*h + 6*a*b^2*c*e*g + 8*a^2*b*d*g*h)/(64*a^3*b) - (x*(2*b^3*d^3 - 2*a^3*h^3 - 3*b^3*c*d*e - 6*a*b^2*d^2*h + 6*a^2*b*d*h^2 + 3*a*b^2*c*e*h + a*b^2*d*e*g - a^2*b*e*g*h))/(16*a^3*b))*root(65536*a^7*b^6*z^4 + 4096*a^5*b^4*d*h*z^2 + 1024*a^5*b^4*e*g*z^2 - 3072*a^4*b^5*c*e*z^2 - 2048*a^6*b^3*h^2*z^2 - 2048*a^4*b^5*d^2*z^2 + 768*a^4*b^3*c*g*h*z - 768*a^3*b^4*c*d*g*z - 128*a^5*b^2*g^2*h*z - 128*a^4*b^3*e^2*h*z - 1152*a^3*b^4*c^2*h*z + 128*a^4*b^3*d*g^2*z + 128*a^3*b^4*d*e^2*z + 1152*a^2*b^5*c^2*d*z - 32*a^3*b^2*d*e*g*h + 96*a^2*b^3*c*d*e*h - 48*a^3*b^2*c*e*h^2 + 16*a^2*b^3*d^2*e*g - 12*a^2*b^3*c*e^2*g + 16*a^4*b*e*g*h^2 - 48*a*b^4*c*d^2*e - 64*a^4*b*d*h^3 + 108*a*b^4*c^3*g + 96*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 - 54*a^2*b^3*c^2*g^2 - 64*a^2*b^3*d^3*h + 12*a^3*b^2*c*g^3 + 18*a*b^4*c^2*e^2 + 16*a*b^4*d^4 + 16*a^5*h^4 - 81*b^5*c^4 - a^2*b^3*e^4 - a^4*b*g^4, z, k), k, 1, 4) + (f/(4*b) + (e*x^3)/(4*a) + (x*(b*c + a*g))/(4*a*b) + (x^2*(b*d + a*h))/(4*a*b))/(a - b*x^4)","B"
193,1,2611,203,5.670989,"\text{Not used}","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)","\left(\sum _{l=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^7\,z^4-3072\,a^6\,b^4\,g\,i\,z^2+9216\,a^5\,b^5\,c\,i\,z^2+4096\,a^5\,b^5\,d\,h\,z^2+1024\,a^5\,b^5\,e\,g\,z^2-3072\,a^4\,b^6\,c\,e\,z^2-2048\,a^6\,b^4\,h^2\,z^2-2048\,a^4\,b^6\,d^2\,z^2+768\,a^5\,b^3\,e\,h\,i\,z-768\,a^4\,b^4\,d\,e\,i\,z+768\,a^4\,b^4\,c\,g\,h\,z-768\,a^3\,b^5\,c\,d\,g\,z-1152\,a^6\,b^2\,h\,i^2\,z-128\,a^5\,b^3\,g^2\,h\,z+1152\,a^5\,b^3\,d\,i^2\,z-128\,a^4\,b^4\,e^2\,h\,z-1152\,a^3\,b^5\,c^2\,h\,z+128\,a^4\,b^4\,d\,g^2\,z+128\,a^3\,b^5\,d\,e^2\,z+1152\,a^2\,b^6\,c^2\,d\,z+96\,a^4\,b^2\,d\,g\,h\,i-288\,a^3\,b^3\,c\,d\,h\,i+72\,a^3\,b^3\,c\,e\,g\,i-32\,a^3\,b^3\,d\,e\,g\,h+96\,a^2\,b^4\,c\,d\,e\,h-12\,a^4\,b^2\,e\,g^2\,i+144\,a^4\,b^2\,c\,h^2\,i-48\,a^3\,b^3\,d^2\,g\,i+16\,a^4\,b^2\,e\,g\,h^2-108\,a^4\,b^2\,c\,g\,i^2-108\,a^2\,b^4\,c^2\,e\,i+144\,a^2\,b^4\,c\,d^2\,i-48\,a^3\,b^3\,c\,e\,h^2+16\,a^2\,b^4\,d^2\,e\,g-12\,a^2\,b^4\,c\,e^2\,g-48\,a^5\,b\,g\,h^2\,i-48\,a\,b^5\,c\,d^2\,e+108\,a^5\,b\,e\,i^3+108\,a\,b^5\,c^3\,g-54\,a^4\,b^2\,e^2\,i^2+162\,a^3\,b^3\,c^2\,i^2+96\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2-54\,a^2\,b^4\,c^2\,g^2+18\,a^5\,b\,g^2\,i^2+12\,a^3\,b^3\,e^3\,i-64\,a^4\,b^2\,d\,h^3-64\,a^2\,b^4\,d^3\,h+12\,a^3\,b^3\,c\,g^3+18\,a\,b^5\,c^2\,e^2+16\,a^5\,b\,h^4+16\,a\,b^5\,d^4-81\,a^6\,i^4-81\,b^6\,c^4-a^4\,b^2\,g^4-a^2\,b^4\,e^4,z,l\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^7\,z^4-3072\,a^6\,b^4\,g\,i\,z^2+9216\,a^5\,b^5\,c\,i\,z^2+4096\,a^5\,b^5\,d\,h\,z^2+1024\,a^5\,b^5\,e\,g\,z^2-3072\,a^4\,b^6\,c\,e\,z^2-2048\,a^6\,b^4\,h^2\,z^2-2048\,a^4\,b^6\,d^2\,z^2+768\,a^5\,b^3\,e\,h\,i\,z-768\,a^4\,b^4\,d\,e\,i\,z+768\,a^4\,b^4\,c\,g\,h\,z-768\,a^3\,b^5\,c\,d\,g\,z-1152\,a^6\,b^2\,h\,i^2\,z-128\,a^5\,b^3\,g^2\,h\,z+1152\,a^5\,b^3\,d\,i^2\,z-128\,a^4\,b^4\,e^2\,h\,z-1152\,a^3\,b^5\,c^2\,h\,z+128\,a^4\,b^4\,d\,g^2\,z+128\,a^3\,b^5\,d\,e^2\,z+1152\,a^2\,b^6\,c^2\,d\,z+96\,a^4\,b^2\,d\,g\,h\,i-288\,a^3\,b^3\,c\,d\,h\,i+72\,a^3\,b^3\,c\,e\,g\,i-32\,a^3\,b^3\,d\,e\,g\,h+96\,a^2\,b^4\,c\,d\,e\,h-12\,a^4\,b^2\,e\,g^2\,i+144\,a^4\,b^2\,c\,h^2\,i-48\,a^3\,b^3\,d^2\,g\,i+16\,a^4\,b^2\,e\,g\,h^2-108\,a^4\,b^2\,c\,g\,i^2-108\,a^2\,b^4\,c^2\,e\,i+144\,a^2\,b^4\,c\,d^2\,i-48\,a^3\,b^3\,c\,e\,h^2+16\,a^2\,b^4\,d^2\,e\,g-12\,a^2\,b^4\,c\,e^2\,g-48\,a^5\,b\,g\,h^2\,i-48\,a\,b^5\,c\,d^2\,e+108\,a^5\,b\,e\,i^3+108\,a\,b^5\,c^3\,g-54\,a^4\,b^2\,e^2\,i^2+162\,a^3\,b^3\,c^2\,i^2+96\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2-54\,a^2\,b^4\,c^2\,g^2+18\,a^5\,b\,g^2\,i^2+12\,a^3\,b^3\,e^3\,i-64\,a^4\,b^2\,d\,h^3-64\,a^2\,b^4\,d^3\,h+12\,a^3\,b^3\,c\,g^3+18\,a\,b^5\,c^2\,e^2+16\,a^5\,b\,h^4+16\,a\,b^5\,d^4-81\,a^6\,i^4-81\,b^6\,c^4-a^4\,b^2\,g^4-a^2\,b^4\,e^4,z,l\right)\,\left(\frac{768\,a^3\,b^5\,c-256\,a^4\,b^4\,g}{64\,a^3\,b^2}-\frac{x\,\left(128\,a^3\,b^4\,d-128\,a^4\,b^3\,h\right)}{16\,a^3\,b}\right)-\frac{64\,a^2\,b^4\,d\,e-192\,a^3\,b^3\,d\,i-64\,a^3\,b^3\,e\,h+192\,a^4\,b^2\,h\,i}{64\,a^3\,b^2}+\frac{x\,\left(36\,a^4\,b\,i^2-24\,a^3\,b^2\,e\,i+4\,a^3\,b^2\,g^2-24\,a^2\,b^3\,c\,g+4\,a^2\,b^3\,e^2+36\,a\,b^4\,c^2\right)}{16\,a^3\,b}\right)+\frac{27\,a^4\,i^3-27\,a^3\,b\,e\,i^2-3\,a^3\,b\,g^2\,i+4\,a^3\,b\,g\,h^2+18\,a^2\,b^2\,c\,g\,i-12\,a^2\,b^2\,c\,h^2-8\,a^2\,b^2\,d\,g\,h+9\,a^2\,b^2\,e^2\,i+a^2\,b^2\,e\,g^2-27\,a\,b^3\,c^2\,i+24\,a\,b^3\,c\,d\,h-6\,a\,b^3\,c\,e\,g+4\,a\,b^3\,d^2\,g-a\,b^3\,e^3+9\,b^4\,c^2\,e-12\,b^4\,c\,d^2}{64\,a^3\,b^2}-\frac{x\,\left(2\,b^3\,d^3-2\,a^3\,h^3-3\,b^3\,c\,d\,e+3\,a^3\,g\,h\,i-6\,a\,b^2\,d^2\,h+6\,a^2\,b\,d\,h^2+9\,a\,b^2\,c\,d\,i+3\,a\,b^2\,c\,e\,h+a\,b^2\,d\,e\,g-9\,a^2\,b\,c\,h\,i-3\,a^2\,b\,d\,g\,i-a^2\,b\,e\,g\,h\right)}{16\,a^3\,b}\right)\,\mathrm{root}\left(65536\,a^7\,b^7\,z^4-3072\,a^6\,b^4\,g\,i\,z^2+9216\,a^5\,b^5\,c\,i\,z^2+4096\,a^5\,b^5\,d\,h\,z^2+1024\,a^5\,b^5\,e\,g\,z^2-3072\,a^4\,b^6\,c\,e\,z^2-2048\,a^6\,b^4\,h^2\,z^2-2048\,a^4\,b^6\,d^2\,z^2+768\,a^5\,b^3\,e\,h\,i\,z-768\,a^4\,b^4\,d\,e\,i\,z+768\,a^4\,b^4\,c\,g\,h\,z-768\,a^3\,b^5\,c\,d\,g\,z-1152\,a^6\,b^2\,h\,i^2\,z-128\,a^5\,b^3\,g^2\,h\,z+1152\,a^5\,b^3\,d\,i^2\,z-128\,a^4\,b^4\,e^2\,h\,z-1152\,a^3\,b^5\,c^2\,h\,z+128\,a^4\,b^4\,d\,g^2\,z+128\,a^3\,b^5\,d\,e^2\,z+1152\,a^2\,b^6\,c^2\,d\,z+96\,a^4\,b^2\,d\,g\,h\,i-288\,a^3\,b^3\,c\,d\,h\,i+72\,a^3\,b^3\,c\,e\,g\,i-32\,a^3\,b^3\,d\,e\,g\,h+96\,a^2\,b^4\,c\,d\,e\,h-12\,a^4\,b^2\,e\,g^2\,i+144\,a^4\,b^2\,c\,h^2\,i-48\,a^3\,b^3\,d^2\,g\,i+16\,a^4\,b^2\,e\,g\,h^2-108\,a^4\,b^2\,c\,g\,i^2-108\,a^2\,b^4\,c^2\,e\,i+144\,a^2\,b^4\,c\,d^2\,i-48\,a^3\,b^3\,c\,e\,h^2+16\,a^2\,b^4\,d^2\,e\,g-12\,a^2\,b^4\,c\,e^2\,g-48\,a^5\,b\,g\,h^2\,i-48\,a\,b^5\,c\,d^2\,e+108\,a^5\,b\,e\,i^3+108\,a\,b^5\,c^3\,g-54\,a^4\,b^2\,e^2\,i^2+162\,a^3\,b^3\,c^2\,i^2+96\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2-54\,a^2\,b^4\,c^2\,g^2+18\,a^5\,b\,g^2\,i^2+12\,a^3\,b^3\,e^3\,i-64\,a^4\,b^2\,d\,h^3-64\,a^2\,b^4\,d^3\,h+12\,a^3\,b^3\,c\,g^3+18\,a\,b^5\,c^2\,e^2+16\,a^5\,b\,h^4+16\,a\,b^5\,d^4-81\,a^6\,i^4-81\,b^6\,c^4-a^4\,b^2\,g^4-a^2\,b^4\,e^4,z,l\right)\right)+\frac{\frac{f}{4\,b}+\frac{x\,\left(b\,c+a\,g\right)}{4\,a\,b}+\frac{x^2\,\left(b\,d+a\,h\right)}{4\,a\,b}+\frac{x^3\,\left(b\,e+a\,i\right)}{4\,a\,b}}{a-b\,x^4}","Not used",1,"symsum(log((27*a^4*i^3 - a*b^3*e^3 - 12*b^4*c*d^2 + 9*b^4*c^2*e - 12*a^2*b^2*c*h^2 + a^2*b^2*e*g^2 + 9*a^2*b^2*e^2*i + 4*a*b^3*d^2*g - 27*a*b^3*c^2*i - 27*a^3*b*e*i^2 + 4*a^3*b*g*h^2 - 3*a^3*b*g^2*i + 18*a^2*b^2*c*g*i - 8*a^2*b^2*d*g*h + 24*a*b^3*c*d*h - 6*a*b^3*c*e*g)/(64*a^3*b^2) - root(65536*a^7*b^7*z^4 - 3072*a^6*b^4*g*i*z^2 + 9216*a^5*b^5*c*i*z^2 + 4096*a^5*b^5*d*h*z^2 + 1024*a^5*b^5*e*g*z^2 - 3072*a^4*b^6*c*e*z^2 - 2048*a^6*b^4*h^2*z^2 - 2048*a^4*b^6*d^2*z^2 + 768*a^5*b^3*e*h*i*z - 768*a^4*b^4*d*e*i*z + 768*a^4*b^4*c*g*h*z - 768*a^3*b^5*c*d*g*z - 1152*a^6*b^2*h*i^2*z - 128*a^5*b^3*g^2*h*z + 1152*a^5*b^3*d*i^2*z - 128*a^4*b^4*e^2*h*z - 1152*a^3*b^5*c^2*h*z + 128*a^4*b^4*d*g^2*z + 128*a^3*b^5*d*e^2*z + 1152*a^2*b^6*c^2*d*z + 96*a^4*b^2*d*g*h*i - 288*a^3*b^3*c*d*h*i + 72*a^3*b^3*c*e*g*i - 32*a^3*b^3*d*e*g*h + 96*a^2*b^4*c*d*e*h - 12*a^4*b^2*e*g^2*i + 144*a^4*b^2*c*h^2*i - 48*a^3*b^3*d^2*g*i + 16*a^4*b^2*e*g*h^2 - 108*a^4*b^2*c*g*i^2 - 108*a^2*b^4*c^2*e*i + 144*a^2*b^4*c*d^2*i - 48*a^3*b^3*c*e*h^2 + 16*a^2*b^4*d^2*e*g - 12*a^2*b^4*c*e^2*g - 48*a^5*b*g*h^2*i - 48*a*b^5*c*d^2*e + 108*a^5*b*e*i^3 + 108*a*b^5*c^3*g - 54*a^4*b^2*e^2*i^2 + 162*a^3*b^3*c^2*i^2 + 96*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 - 54*a^2*b^4*c^2*g^2 + 18*a^5*b*g^2*i^2 + 12*a^3*b^3*e^3*i - 64*a^4*b^2*d*h^3 - 64*a^2*b^4*d^3*h + 12*a^3*b^3*c*g^3 + 18*a*b^5*c^2*e^2 + 16*a^5*b*h^4 + 16*a*b^5*d^4 - 81*a^6*i^4 - 81*b^6*c^4 - a^4*b^2*g^4 - a^2*b^4*e^4, z, l)*(root(65536*a^7*b^7*z^4 - 3072*a^6*b^4*g*i*z^2 + 9216*a^5*b^5*c*i*z^2 + 4096*a^5*b^5*d*h*z^2 + 1024*a^5*b^5*e*g*z^2 - 3072*a^4*b^6*c*e*z^2 - 2048*a^6*b^4*h^2*z^2 - 2048*a^4*b^6*d^2*z^2 + 768*a^5*b^3*e*h*i*z - 768*a^4*b^4*d*e*i*z + 768*a^4*b^4*c*g*h*z - 768*a^3*b^5*c*d*g*z - 1152*a^6*b^2*h*i^2*z - 128*a^5*b^3*g^2*h*z + 1152*a^5*b^3*d*i^2*z - 128*a^4*b^4*e^2*h*z - 1152*a^3*b^5*c^2*h*z + 128*a^4*b^4*d*g^2*z + 128*a^3*b^5*d*e^2*z + 1152*a^2*b^6*c^2*d*z + 96*a^4*b^2*d*g*h*i - 288*a^3*b^3*c*d*h*i + 72*a^3*b^3*c*e*g*i - 32*a^3*b^3*d*e*g*h + 96*a^2*b^4*c*d*e*h - 12*a^4*b^2*e*g^2*i + 144*a^4*b^2*c*h^2*i - 48*a^3*b^3*d^2*g*i + 16*a^4*b^2*e*g*h^2 - 108*a^4*b^2*c*g*i^2 - 108*a^2*b^4*c^2*e*i + 144*a^2*b^4*c*d^2*i - 48*a^3*b^3*c*e*h^2 + 16*a^2*b^4*d^2*e*g - 12*a^2*b^4*c*e^2*g - 48*a^5*b*g*h^2*i - 48*a*b^5*c*d^2*e + 108*a^5*b*e*i^3 + 108*a*b^5*c^3*g - 54*a^4*b^2*e^2*i^2 + 162*a^3*b^3*c^2*i^2 + 96*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 - 54*a^2*b^4*c^2*g^2 + 18*a^5*b*g^2*i^2 + 12*a^3*b^3*e^3*i - 64*a^4*b^2*d*h^3 - 64*a^2*b^4*d^3*h + 12*a^3*b^3*c*g^3 + 18*a*b^5*c^2*e^2 + 16*a^5*b*h^4 + 16*a*b^5*d^4 - 81*a^6*i^4 - 81*b^6*c^4 - a^4*b^2*g^4 - a^2*b^4*e^4, z, l)*((768*a^3*b^5*c - 256*a^4*b^4*g)/(64*a^3*b^2) - (x*(128*a^3*b^4*d - 128*a^4*b^3*h))/(16*a^3*b)) - (64*a^2*b^4*d*e - 192*a^3*b^3*d*i - 64*a^3*b^3*e*h + 192*a^4*b^2*h*i)/(64*a^3*b^2) + (x*(36*a*b^4*c^2 + 36*a^4*b*i^2 + 4*a^2*b^3*e^2 + 4*a^3*b^2*g^2 - 24*a^2*b^3*c*g - 24*a^3*b^2*e*i))/(16*a^3*b)) - (x*(2*b^3*d^3 - 2*a^3*h^3 - 3*b^3*c*d*e + 3*a^3*g*h*i - 6*a*b^2*d^2*h + 6*a^2*b*d*h^2 + 9*a*b^2*c*d*i + 3*a*b^2*c*e*h + a*b^2*d*e*g - 9*a^2*b*c*h*i - 3*a^2*b*d*g*i - a^2*b*e*g*h))/(16*a^3*b))*root(65536*a^7*b^7*z^4 - 3072*a^6*b^4*g*i*z^2 + 9216*a^5*b^5*c*i*z^2 + 4096*a^5*b^5*d*h*z^2 + 1024*a^5*b^5*e*g*z^2 - 3072*a^4*b^6*c*e*z^2 - 2048*a^6*b^4*h^2*z^2 - 2048*a^4*b^6*d^2*z^2 + 768*a^5*b^3*e*h*i*z - 768*a^4*b^4*d*e*i*z + 768*a^4*b^4*c*g*h*z - 768*a^3*b^5*c*d*g*z - 1152*a^6*b^2*h*i^2*z - 128*a^5*b^3*g^2*h*z + 1152*a^5*b^3*d*i^2*z - 128*a^4*b^4*e^2*h*z - 1152*a^3*b^5*c^2*h*z + 128*a^4*b^4*d*g^2*z + 128*a^3*b^5*d*e^2*z + 1152*a^2*b^6*c^2*d*z + 96*a^4*b^2*d*g*h*i - 288*a^3*b^3*c*d*h*i + 72*a^3*b^3*c*e*g*i - 32*a^3*b^3*d*e*g*h + 96*a^2*b^4*c*d*e*h - 12*a^4*b^2*e*g^2*i + 144*a^4*b^2*c*h^2*i - 48*a^3*b^3*d^2*g*i + 16*a^4*b^2*e*g*h^2 - 108*a^4*b^2*c*g*i^2 - 108*a^2*b^4*c^2*e*i + 144*a^2*b^4*c*d^2*i - 48*a^3*b^3*c*e*h^2 + 16*a^2*b^4*d^2*e*g - 12*a^2*b^4*c*e^2*g - 48*a^5*b*g*h^2*i - 48*a*b^5*c*d^2*e + 108*a^5*b*e*i^3 + 108*a*b^5*c^3*g - 54*a^4*b^2*e^2*i^2 + 162*a^3*b^3*c^2*i^2 + 96*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 - 54*a^2*b^4*c^2*g^2 + 18*a^5*b*g^2*i^2 + 12*a^3*b^3*e^3*i - 64*a^4*b^2*d*h^3 - 64*a^2*b^4*d^3*h + 12*a^3*b^3*c*g^3 + 18*a*b^5*c^2*e^2 + 16*a^5*b*h^4 + 16*a*b^5*d^4 - 81*a^6*i^4 - 81*b^6*c^4 - a^4*b^2*g^4 - a^2*b^4*e^4, z, l), l, 1, 4) + (f/(4*b) + (x*(b*c + a*g))/(4*a*b) + (x^2*(b*d + a*h))/(4*a*b) + (x^3*(b*e + a*i))/(4*a*b))/(a - b*x^4)","B"
194,1,3943,225,5.909483,"\text{Not used}","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{\frac{b\,f+a\,j}{4\,b^2}+\frac{x\,\left(b\,c+a\,g\right)}{4\,a\,b}+\frac{x^2\,\left(b\,d+a\,h\right)}{4\,a\,b}+\frac{x^3\,\left(b\,e+a\,i\right)}{4\,a\,b}}{a-b\,x^4}+\left(\sum _{m=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^8\,z^4-65536\,a^7\,b^6\,j\,z^3-3072\,a^6\,b^5\,g\,i\,z^2+9216\,a^5\,b^6\,c\,i\,z^2+4096\,a^5\,b^6\,d\,h\,z^2+1024\,a^5\,b^6\,e\,g\,z^2-3072\,a^4\,b^7\,c\,e\,z^2+24576\,a^7\,b^4\,j^2\,z^2-2048\,a^6\,b^5\,h^2\,z^2-2048\,a^4\,b^7\,d^2\,z^2+1536\,a^6\,b^3\,g\,i\,j\,z-4608\,a^5\,b^4\,c\,i\,j\,z-2048\,a^5\,b^4\,d\,h\,j\,z+768\,a^5\,b^4\,e\,h\,i\,z-512\,a^5\,b^4\,e\,g\,j\,z+1536\,a^4\,b^5\,c\,e\,j\,z-768\,a^4\,b^5\,d\,e\,i\,z+768\,a^4\,b^5\,c\,g\,h\,z-768\,a^3\,b^6\,c\,d\,g\,z+1024\,a^6\,b^3\,h^2\,j\,z-1152\,a^6\,b^3\,h\,i^2\,z-128\,a^5\,b^4\,g^2\,h\,z+1024\,a^4\,b^5\,d^2\,j\,z+1152\,a^5\,b^4\,d\,i^2\,z-128\,a^4\,b^5\,e^2\,h\,z-1152\,a^3\,b^6\,c^2\,h\,z+128\,a^4\,b^5\,d\,g^2\,z+128\,a^3\,b^6\,d\,e^2\,z+1152\,a^2\,b^7\,c^2\,d\,z-4096\,a^7\,b^2\,j^3\,z-192\,a^5\,b^2\,e\,h\,i\,j+192\,a^4\,b^3\,d\,e\,i\,j-192\,a^4\,b^3\,c\,g\,h\,j+96\,a^4\,b^3\,d\,g\,h\,i-288\,a^3\,b^4\,c\,d\,h\,i+192\,a^3\,b^4\,c\,d\,g\,j+72\,a^3\,b^4\,c\,e\,g\,i-32\,a^3\,b^4\,d\,e\,g\,h+96\,a^2\,b^5\,c\,d\,e\,h+32\,a^5\,b^2\,g^2\,h\,j-48\,a^5\,b^2\,g\,h^2\,i-288\,a^5\,b^2\,d\,i^2\,j+32\,a^4\,b^3\,e^2\,h\,j+576\,a^5\,b^2\,c\,i\,j^2+256\,a^5\,b^2\,d\,h\,j^2+64\,a^5\,b^2\,e\,g\,j^2+288\,a^3\,b^4\,c^2\,h\,j-32\,a^4\,b^3\,d\,g^2\,j-12\,a^4\,b^3\,e\,g^2\,i+144\,a^4\,b^3\,c\,h^2\,i-48\,a^3\,b^4\,d^2\,g\,i+16\,a^4\,b^3\,e\,g\,h^2-108\,a^4\,b^3\,c\,g\,i^2-32\,a^3\,b^4\,d\,e^2\,j-192\,a^4\,b^3\,c\,e\,j^2-288\,a^2\,b^5\,c^2\,d\,j-108\,a^2\,b^5\,c^2\,e\,i+144\,a^2\,b^5\,c\,d^2\,i-48\,a^3\,b^4\,c\,e\,h^2+16\,a^2\,b^5\,d^2\,e\,g-12\,a^2\,b^5\,c\,e^2\,g+288\,a^6\,b\,h\,i^2\,j-192\,a^6\,b\,g\,i\,j^2-48\,a\,b^6\,c\,d^2\,e+108\,a\,b^6\,c^3\,g+18\,a^5\,b^2\,g^2\,i^2-128\,a^4\,b^3\,d^2\,j^2-54\,a^4\,b^3\,e^2\,i^2+162\,a^3\,b^4\,c^2\,i^2+96\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2-54\,a^2\,b^5\,c^2\,g^2-128\,a^6\,b\,h^2\,j^2+108\,a^5\,b^2\,e\,i^3+12\,a^3\,b^4\,e^3\,i-64\,a^4\,b^3\,d\,h^3-64\,a^2\,b^5\,d^3\,h+12\,a^3\,b^4\,c\,g^3+18\,a\,b^6\,c^2\,e^2+16\,a^5\,b^2\,h^4-81\,a^6\,b\,i^4+16\,a\,b^6\,d^4+256\,a^7\,j^4-81\,b^7\,c^4-a^4\,b^3\,g^4-a^2\,b^5\,e^4,z,m\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^8\,z^4-65536\,a^7\,b^6\,j\,z^3-3072\,a^6\,b^5\,g\,i\,z^2+9216\,a^5\,b^6\,c\,i\,z^2+4096\,a^5\,b^6\,d\,h\,z^2+1024\,a^5\,b^6\,e\,g\,z^2-3072\,a^4\,b^7\,c\,e\,z^2+24576\,a^7\,b^4\,j^2\,z^2-2048\,a^6\,b^5\,h^2\,z^2-2048\,a^4\,b^7\,d^2\,z^2+1536\,a^6\,b^3\,g\,i\,j\,z-4608\,a^5\,b^4\,c\,i\,j\,z-2048\,a^5\,b^4\,d\,h\,j\,z+768\,a^5\,b^4\,e\,h\,i\,z-512\,a^5\,b^4\,e\,g\,j\,z+1536\,a^4\,b^5\,c\,e\,j\,z-768\,a^4\,b^5\,d\,e\,i\,z+768\,a^4\,b^5\,c\,g\,h\,z-768\,a^3\,b^6\,c\,d\,g\,z+1024\,a^6\,b^3\,h^2\,j\,z-1152\,a^6\,b^3\,h\,i^2\,z-128\,a^5\,b^4\,g^2\,h\,z+1024\,a^4\,b^5\,d^2\,j\,z+1152\,a^5\,b^4\,d\,i^2\,z-128\,a^4\,b^5\,e^2\,h\,z-1152\,a^3\,b^6\,c^2\,h\,z+128\,a^4\,b^5\,d\,g^2\,z+128\,a^3\,b^6\,d\,e^2\,z+1152\,a^2\,b^7\,c^2\,d\,z-4096\,a^7\,b^2\,j^3\,z-192\,a^5\,b^2\,e\,h\,i\,j+192\,a^4\,b^3\,d\,e\,i\,j-192\,a^4\,b^3\,c\,g\,h\,j+96\,a^4\,b^3\,d\,g\,h\,i-288\,a^3\,b^4\,c\,d\,h\,i+192\,a^3\,b^4\,c\,d\,g\,j+72\,a^3\,b^4\,c\,e\,g\,i-32\,a^3\,b^4\,d\,e\,g\,h+96\,a^2\,b^5\,c\,d\,e\,h+32\,a^5\,b^2\,g^2\,h\,j-48\,a^5\,b^2\,g\,h^2\,i-288\,a^5\,b^2\,d\,i^2\,j+32\,a^4\,b^3\,e^2\,h\,j+576\,a^5\,b^2\,c\,i\,j^2+256\,a^5\,b^2\,d\,h\,j^2+64\,a^5\,b^2\,e\,g\,j^2+288\,a^3\,b^4\,c^2\,h\,j-32\,a^4\,b^3\,d\,g^2\,j-12\,a^4\,b^3\,e\,g^2\,i+144\,a^4\,b^3\,c\,h^2\,i-48\,a^3\,b^4\,d^2\,g\,i+16\,a^4\,b^3\,e\,g\,h^2-108\,a^4\,b^3\,c\,g\,i^2-32\,a^3\,b^4\,d\,e^2\,j-192\,a^4\,b^3\,c\,e\,j^2-288\,a^2\,b^5\,c^2\,d\,j-108\,a^2\,b^5\,c^2\,e\,i+144\,a^2\,b^5\,c\,d^2\,i-48\,a^3\,b^4\,c\,e\,h^2+16\,a^2\,b^5\,d^2\,e\,g-12\,a^2\,b^5\,c\,e^2\,g+288\,a^6\,b\,h\,i^2\,j-192\,a^6\,b\,g\,i\,j^2-48\,a\,b^6\,c\,d^2\,e+108\,a\,b^6\,c^3\,g+18\,a^5\,b^2\,g^2\,i^2-128\,a^4\,b^3\,d^2\,j^2-54\,a^4\,b^3\,e^2\,i^2+162\,a^3\,b^4\,c^2\,i^2+96\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2-54\,a^2\,b^5\,c^2\,g^2-128\,a^6\,b\,h^2\,j^2+108\,a^5\,b^2\,e\,i^3+12\,a^3\,b^4\,e^3\,i-64\,a^4\,b^3\,d\,h^3-64\,a^2\,b^5\,d^3\,h+12\,a^3\,b^4\,c\,g^3+18\,a\,b^6\,c^2\,e^2+16\,a^5\,b^2\,h^4-81\,a^6\,b\,i^4+16\,a\,b^6\,d^4+256\,a^7\,j^4-81\,b^7\,c^4-a^4\,b^3\,g^4-a^2\,b^5\,e^4,z,m\right)\,\left(\frac{768\,a^3\,b^5\,c-256\,a^4\,b^4\,g}{64\,a^3\,b^2}-\frac{x\,\left(128\,a^3\,b^5\,d-128\,a^4\,b^4\,h\right)}{16\,a^3\,b^2}\right)-\frac{64\,a^2\,b^4\,d\,e+384\,a^3\,b^3\,c\,j-192\,a^3\,b^3\,d\,i-64\,a^3\,b^3\,e\,h-128\,a^4\,b^2\,g\,j+192\,a^4\,b^2\,h\,i}{64\,a^3\,b^2}+\frac{x\,\left(36\,a^4\,b^2\,i^2-64\,h\,j\,a^4\,b^2-24\,a^3\,b^3\,e\,i+4\,a^3\,b^3\,g^2+64\,d\,j\,a^3\,b^3-24\,a^2\,b^4\,c\,g+4\,a^2\,b^4\,e^2+36\,a\,b^5\,c^2\right)}{16\,a^3\,b^2}\right)+\frac{16\,a^4\,g\,j^2-48\,a^4\,h\,i\,j+27\,a^4\,i^3-48\,a^3\,b\,c\,j^2+48\,a^3\,b\,d\,i\,j+16\,a^3\,b\,e\,h\,j-27\,a^3\,b\,e\,i^2-3\,a^3\,b\,g^2\,i+4\,a^3\,b\,g\,h^2+18\,a^2\,b^2\,c\,g\,i-12\,a^2\,b^2\,c\,h^2-16\,a^2\,b^2\,d\,e\,j-8\,a^2\,b^2\,d\,g\,h+9\,a^2\,b^2\,e^2\,i+a^2\,b^2\,e\,g^2-27\,a\,b^3\,c^2\,i+24\,a\,b^3\,c\,d\,h-6\,a\,b^3\,c\,e\,g+4\,a\,b^3\,d^2\,g-a\,b^3\,e^3+9\,b^4\,c^2\,e-12\,b^4\,c\,d^2}{64\,a^3\,b^2}+\frac{x\,\left(-8\,a^4\,h\,j^2+9\,a^4\,i^2\,j+8\,a^3\,b\,d\,j^2-6\,a^3\,b\,e\,i\,j+a^3\,b\,g^2\,j-3\,a^3\,b\,g\,h\,i+2\,a^3\,b\,h^3-6\,a^2\,b^2\,c\,g\,j+9\,a^2\,b^2\,c\,h\,i+3\,a^2\,b^2\,d\,g\,i-6\,a^2\,b^2\,d\,h^2+a^2\,b^2\,e^2\,j+a^2\,b^2\,e\,g\,h+9\,a\,b^3\,c^2\,j-9\,a\,b^3\,c\,d\,i-3\,a\,b^3\,c\,e\,h+6\,a\,b^3\,d^2\,h-a\,b^3\,d\,e\,g+3\,b^4\,c\,d\,e-2\,b^4\,d^3\right)}{16\,a^3\,b^2}\right)\,\mathrm{root}\left(65536\,a^7\,b^8\,z^4-65536\,a^7\,b^6\,j\,z^3-3072\,a^6\,b^5\,g\,i\,z^2+9216\,a^5\,b^6\,c\,i\,z^2+4096\,a^5\,b^6\,d\,h\,z^2+1024\,a^5\,b^6\,e\,g\,z^2-3072\,a^4\,b^7\,c\,e\,z^2+24576\,a^7\,b^4\,j^2\,z^2-2048\,a^6\,b^5\,h^2\,z^2-2048\,a^4\,b^7\,d^2\,z^2+1536\,a^6\,b^3\,g\,i\,j\,z-4608\,a^5\,b^4\,c\,i\,j\,z-2048\,a^5\,b^4\,d\,h\,j\,z+768\,a^5\,b^4\,e\,h\,i\,z-512\,a^5\,b^4\,e\,g\,j\,z+1536\,a^4\,b^5\,c\,e\,j\,z-768\,a^4\,b^5\,d\,e\,i\,z+768\,a^4\,b^5\,c\,g\,h\,z-768\,a^3\,b^6\,c\,d\,g\,z+1024\,a^6\,b^3\,h^2\,j\,z-1152\,a^6\,b^3\,h\,i^2\,z-128\,a^5\,b^4\,g^2\,h\,z+1024\,a^4\,b^5\,d^2\,j\,z+1152\,a^5\,b^4\,d\,i^2\,z-128\,a^4\,b^5\,e^2\,h\,z-1152\,a^3\,b^6\,c^2\,h\,z+128\,a^4\,b^5\,d\,g^2\,z+128\,a^3\,b^6\,d\,e^2\,z+1152\,a^2\,b^7\,c^2\,d\,z-4096\,a^7\,b^2\,j^3\,z-192\,a^5\,b^2\,e\,h\,i\,j+192\,a^4\,b^3\,d\,e\,i\,j-192\,a^4\,b^3\,c\,g\,h\,j+96\,a^4\,b^3\,d\,g\,h\,i-288\,a^3\,b^4\,c\,d\,h\,i+192\,a^3\,b^4\,c\,d\,g\,j+72\,a^3\,b^4\,c\,e\,g\,i-32\,a^3\,b^4\,d\,e\,g\,h+96\,a^2\,b^5\,c\,d\,e\,h+32\,a^5\,b^2\,g^2\,h\,j-48\,a^5\,b^2\,g\,h^2\,i-288\,a^5\,b^2\,d\,i^2\,j+32\,a^4\,b^3\,e^2\,h\,j+576\,a^5\,b^2\,c\,i\,j^2+256\,a^5\,b^2\,d\,h\,j^2+64\,a^5\,b^2\,e\,g\,j^2+288\,a^3\,b^4\,c^2\,h\,j-32\,a^4\,b^3\,d\,g^2\,j-12\,a^4\,b^3\,e\,g^2\,i+144\,a^4\,b^3\,c\,h^2\,i-48\,a^3\,b^4\,d^2\,g\,i+16\,a^4\,b^3\,e\,g\,h^2-108\,a^4\,b^3\,c\,g\,i^2-32\,a^3\,b^4\,d\,e^2\,j-192\,a^4\,b^3\,c\,e\,j^2-288\,a^2\,b^5\,c^2\,d\,j-108\,a^2\,b^5\,c^2\,e\,i+144\,a^2\,b^5\,c\,d^2\,i-48\,a^3\,b^4\,c\,e\,h^2+16\,a^2\,b^5\,d^2\,e\,g-12\,a^2\,b^5\,c\,e^2\,g+288\,a^6\,b\,h\,i^2\,j-192\,a^6\,b\,g\,i\,j^2-48\,a\,b^6\,c\,d^2\,e+108\,a\,b^6\,c^3\,g+18\,a^5\,b^2\,g^2\,i^2-128\,a^4\,b^3\,d^2\,j^2-54\,a^4\,b^3\,e^2\,i^2+162\,a^3\,b^4\,c^2\,i^2+96\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2-54\,a^2\,b^5\,c^2\,g^2-128\,a^6\,b\,h^2\,j^2+108\,a^5\,b^2\,e\,i^3+12\,a^3\,b^4\,e^3\,i-64\,a^4\,b^3\,d\,h^3-64\,a^2\,b^5\,d^3\,h+12\,a^3\,b^4\,c\,g^3+18\,a\,b^6\,c^2\,e^2+16\,a^5\,b^2\,h^4-81\,a^6\,b\,i^4+16\,a\,b^6\,d^4+256\,a^7\,j^4-81\,b^7\,c^4-a^4\,b^3\,g^4-a^2\,b^5\,e^4,z,m\right)\right)","Not used",1,"((b*f + a*j)/(4*b^2) + (x*(b*c + a*g))/(4*a*b) + (x^2*(b*d + a*h))/(4*a*b) + (x^3*(b*e + a*i))/(4*a*b))/(a - b*x^4) + symsum(log((27*a^4*i^3 - a*b^3*e^3 - 12*b^4*c*d^2 + 9*b^4*c^2*e + 16*a^4*g*j^2 - 12*a^2*b^2*c*h^2 + a^2*b^2*e*g^2 + 9*a^2*b^2*e^2*i - 48*a^4*h*i*j + 4*a*b^3*d^2*g - 27*a*b^3*c^2*i - 48*a^3*b*c*j^2 - 27*a^3*b*e*i^2 + 4*a^3*b*g*h^2 - 3*a^3*b*g^2*i + 18*a^2*b^2*c*g*i - 16*a^2*b^2*d*e*j - 8*a^2*b^2*d*g*h + 24*a*b^3*c*d*h - 6*a*b^3*c*e*g + 48*a^3*b*d*i*j + 16*a^3*b*e*h*j)/(64*a^3*b^2) - root(65536*a^7*b^8*z^4 - 65536*a^7*b^6*j*z^3 - 3072*a^6*b^5*g*i*z^2 + 9216*a^5*b^6*c*i*z^2 + 4096*a^5*b^6*d*h*z^2 + 1024*a^5*b^6*e*g*z^2 - 3072*a^4*b^7*c*e*z^2 + 24576*a^7*b^4*j^2*z^2 - 2048*a^6*b^5*h^2*z^2 - 2048*a^4*b^7*d^2*z^2 + 1536*a^6*b^3*g*i*j*z - 4608*a^5*b^4*c*i*j*z - 2048*a^5*b^4*d*h*j*z + 768*a^5*b^4*e*h*i*z - 512*a^5*b^4*e*g*j*z + 1536*a^4*b^5*c*e*j*z - 768*a^4*b^5*d*e*i*z + 768*a^4*b^5*c*g*h*z - 768*a^3*b^6*c*d*g*z + 1024*a^6*b^3*h^2*j*z - 1152*a^6*b^3*h*i^2*z - 128*a^5*b^4*g^2*h*z + 1024*a^4*b^5*d^2*j*z + 1152*a^5*b^4*d*i^2*z - 128*a^4*b^5*e^2*h*z - 1152*a^3*b^6*c^2*h*z + 128*a^4*b^5*d*g^2*z + 128*a^3*b^6*d*e^2*z + 1152*a^2*b^7*c^2*d*z - 4096*a^7*b^2*j^3*z - 192*a^5*b^2*e*h*i*j + 192*a^4*b^3*d*e*i*j - 192*a^4*b^3*c*g*h*j + 96*a^4*b^3*d*g*h*i - 288*a^3*b^4*c*d*h*i + 192*a^3*b^4*c*d*g*j + 72*a^3*b^4*c*e*g*i - 32*a^3*b^4*d*e*g*h + 96*a^2*b^5*c*d*e*h + 32*a^5*b^2*g^2*h*j - 48*a^5*b^2*g*h^2*i - 288*a^5*b^2*d*i^2*j + 32*a^4*b^3*e^2*h*j + 576*a^5*b^2*c*i*j^2 + 256*a^5*b^2*d*h*j^2 + 64*a^5*b^2*e*g*j^2 + 288*a^3*b^4*c^2*h*j - 32*a^4*b^3*d*g^2*j - 12*a^4*b^3*e*g^2*i + 144*a^4*b^3*c*h^2*i - 48*a^3*b^4*d^2*g*i + 16*a^4*b^3*e*g*h^2 - 108*a^4*b^3*c*g*i^2 - 32*a^3*b^4*d*e^2*j - 192*a^4*b^3*c*e*j^2 - 288*a^2*b^5*c^2*d*j - 108*a^2*b^5*c^2*e*i + 144*a^2*b^5*c*d^2*i - 48*a^3*b^4*c*e*h^2 + 16*a^2*b^5*d^2*e*g - 12*a^2*b^5*c*e^2*g + 288*a^6*b*h*i^2*j - 192*a^6*b*g*i*j^2 - 48*a*b^6*c*d^2*e + 108*a*b^6*c^3*g + 18*a^5*b^2*g^2*i^2 - 128*a^4*b^3*d^2*j^2 - 54*a^4*b^3*e^2*i^2 + 162*a^3*b^4*c^2*i^2 + 96*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 - 54*a^2*b^5*c^2*g^2 - 128*a^6*b*h^2*j^2 + 108*a^5*b^2*e*i^3 + 12*a^3*b^4*e^3*i - 64*a^4*b^3*d*h^3 - 64*a^2*b^5*d^3*h + 12*a^3*b^4*c*g^3 + 18*a*b^6*c^2*e^2 + 16*a^5*b^2*h^4 - 81*a^6*b*i^4 + 16*a*b^6*d^4 + 256*a^7*j^4 - 81*b^7*c^4 - a^4*b^3*g^4 - a^2*b^5*e^4, z, m)*(root(65536*a^7*b^8*z^4 - 65536*a^7*b^6*j*z^3 - 3072*a^6*b^5*g*i*z^2 + 9216*a^5*b^6*c*i*z^2 + 4096*a^5*b^6*d*h*z^2 + 1024*a^5*b^6*e*g*z^2 - 3072*a^4*b^7*c*e*z^2 + 24576*a^7*b^4*j^2*z^2 - 2048*a^6*b^5*h^2*z^2 - 2048*a^4*b^7*d^2*z^2 + 1536*a^6*b^3*g*i*j*z - 4608*a^5*b^4*c*i*j*z - 2048*a^5*b^4*d*h*j*z + 768*a^5*b^4*e*h*i*z - 512*a^5*b^4*e*g*j*z + 1536*a^4*b^5*c*e*j*z - 768*a^4*b^5*d*e*i*z + 768*a^4*b^5*c*g*h*z - 768*a^3*b^6*c*d*g*z + 1024*a^6*b^3*h^2*j*z - 1152*a^6*b^3*h*i^2*z - 128*a^5*b^4*g^2*h*z + 1024*a^4*b^5*d^2*j*z + 1152*a^5*b^4*d*i^2*z - 128*a^4*b^5*e^2*h*z - 1152*a^3*b^6*c^2*h*z + 128*a^4*b^5*d*g^2*z + 128*a^3*b^6*d*e^2*z + 1152*a^2*b^7*c^2*d*z - 4096*a^7*b^2*j^3*z - 192*a^5*b^2*e*h*i*j + 192*a^4*b^3*d*e*i*j - 192*a^4*b^3*c*g*h*j + 96*a^4*b^3*d*g*h*i - 288*a^3*b^4*c*d*h*i + 192*a^3*b^4*c*d*g*j + 72*a^3*b^4*c*e*g*i - 32*a^3*b^4*d*e*g*h + 96*a^2*b^5*c*d*e*h + 32*a^5*b^2*g^2*h*j - 48*a^5*b^2*g*h^2*i - 288*a^5*b^2*d*i^2*j + 32*a^4*b^3*e^2*h*j + 576*a^5*b^2*c*i*j^2 + 256*a^5*b^2*d*h*j^2 + 64*a^5*b^2*e*g*j^2 + 288*a^3*b^4*c^2*h*j - 32*a^4*b^3*d*g^2*j - 12*a^4*b^3*e*g^2*i + 144*a^4*b^3*c*h^2*i - 48*a^3*b^4*d^2*g*i + 16*a^4*b^3*e*g*h^2 - 108*a^4*b^3*c*g*i^2 - 32*a^3*b^4*d*e^2*j - 192*a^4*b^3*c*e*j^2 - 288*a^2*b^5*c^2*d*j - 108*a^2*b^5*c^2*e*i + 144*a^2*b^5*c*d^2*i - 48*a^3*b^4*c*e*h^2 + 16*a^2*b^5*d^2*e*g - 12*a^2*b^5*c*e^2*g + 288*a^6*b*h*i^2*j - 192*a^6*b*g*i*j^2 - 48*a*b^6*c*d^2*e + 108*a*b^6*c^3*g + 18*a^5*b^2*g^2*i^2 - 128*a^4*b^3*d^2*j^2 - 54*a^4*b^3*e^2*i^2 + 162*a^3*b^4*c^2*i^2 + 96*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 - 54*a^2*b^5*c^2*g^2 - 128*a^6*b*h^2*j^2 + 108*a^5*b^2*e*i^3 + 12*a^3*b^4*e^3*i - 64*a^4*b^3*d*h^3 - 64*a^2*b^5*d^3*h + 12*a^3*b^4*c*g^3 + 18*a*b^6*c^2*e^2 + 16*a^5*b^2*h^4 - 81*a^6*b*i^4 + 16*a*b^6*d^4 + 256*a^7*j^4 - 81*b^7*c^4 - a^4*b^3*g^4 - a^2*b^5*e^4, z, m)*((768*a^3*b^5*c - 256*a^4*b^4*g)/(64*a^3*b^2) - (x*(128*a^3*b^5*d - 128*a^4*b^4*h))/(16*a^3*b^2)) - (64*a^2*b^4*d*e + 384*a^3*b^3*c*j - 192*a^3*b^3*d*i - 64*a^3*b^3*e*h - 128*a^4*b^2*g*j + 192*a^4*b^2*h*i)/(64*a^3*b^2) + (x*(36*a*b^5*c^2 + 4*a^2*b^4*e^2 + 4*a^3*b^3*g^2 + 36*a^4*b^2*i^2 - 24*a^2*b^4*c*g + 64*a^3*b^3*d*j - 24*a^3*b^3*e*i - 64*a^4*b^2*h*j))/(16*a^3*b^2)) + (x*(2*a^3*b*h^3 - 2*b^4*d^3 - 8*a^4*h*j^2 + 9*a^4*i^2*j - 6*a^2*b^2*d*h^2 + a^2*b^2*e^2*j + 3*b^4*c*d*e + 6*a*b^3*d^2*h + 9*a*b^3*c^2*j + 8*a^3*b*d*j^2 + a^3*b*g^2*j - 6*a^2*b^2*c*g*j + 9*a^2*b^2*c*h*i + 3*a^2*b^2*d*g*i + a^2*b^2*e*g*h - 9*a*b^3*c*d*i - 3*a*b^3*c*e*h - a*b^3*d*e*g - 6*a^3*b*e*i*j - 3*a^3*b*g*h*i))/(16*a^3*b^2))*root(65536*a^7*b^8*z^4 - 65536*a^7*b^6*j*z^3 - 3072*a^6*b^5*g*i*z^2 + 9216*a^5*b^6*c*i*z^2 + 4096*a^5*b^6*d*h*z^2 + 1024*a^5*b^6*e*g*z^2 - 3072*a^4*b^7*c*e*z^2 + 24576*a^7*b^4*j^2*z^2 - 2048*a^6*b^5*h^2*z^2 - 2048*a^4*b^7*d^2*z^2 + 1536*a^6*b^3*g*i*j*z - 4608*a^5*b^4*c*i*j*z - 2048*a^5*b^4*d*h*j*z + 768*a^5*b^4*e*h*i*z - 512*a^5*b^4*e*g*j*z + 1536*a^4*b^5*c*e*j*z - 768*a^4*b^5*d*e*i*z + 768*a^4*b^5*c*g*h*z - 768*a^3*b^6*c*d*g*z + 1024*a^6*b^3*h^2*j*z - 1152*a^6*b^3*h*i^2*z - 128*a^5*b^4*g^2*h*z + 1024*a^4*b^5*d^2*j*z + 1152*a^5*b^4*d*i^2*z - 128*a^4*b^5*e^2*h*z - 1152*a^3*b^6*c^2*h*z + 128*a^4*b^5*d*g^2*z + 128*a^3*b^6*d*e^2*z + 1152*a^2*b^7*c^2*d*z - 4096*a^7*b^2*j^3*z - 192*a^5*b^2*e*h*i*j + 192*a^4*b^3*d*e*i*j - 192*a^4*b^3*c*g*h*j + 96*a^4*b^3*d*g*h*i - 288*a^3*b^4*c*d*h*i + 192*a^3*b^4*c*d*g*j + 72*a^3*b^4*c*e*g*i - 32*a^3*b^4*d*e*g*h + 96*a^2*b^5*c*d*e*h + 32*a^5*b^2*g^2*h*j - 48*a^5*b^2*g*h^2*i - 288*a^5*b^2*d*i^2*j + 32*a^4*b^3*e^2*h*j + 576*a^5*b^2*c*i*j^2 + 256*a^5*b^2*d*h*j^2 + 64*a^5*b^2*e*g*j^2 + 288*a^3*b^4*c^2*h*j - 32*a^4*b^3*d*g^2*j - 12*a^4*b^3*e*g^2*i + 144*a^4*b^3*c*h^2*i - 48*a^3*b^4*d^2*g*i + 16*a^4*b^3*e*g*h^2 - 108*a^4*b^3*c*g*i^2 - 32*a^3*b^4*d*e^2*j - 192*a^4*b^3*c*e*j^2 - 288*a^2*b^5*c^2*d*j - 108*a^2*b^5*c^2*e*i + 144*a^2*b^5*c*d^2*i - 48*a^3*b^4*c*e*h^2 + 16*a^2*b^5*d^2*e*g - 12*a^2*b^5*c*e^2*g + 288*a^6*b*h*i^2*j - 192*a^6*b*g*i*j^2 - 48*a*b^6*c*d^2*e + 108*a*b^6*c^3*g + 18*a^5*b^2*g^2*i^2 - 128*a^4*b^3*d^2*j^2 - 54*a^4*b^3*e^2*i^2 + 162*a^3*b^4*c^2*i^2 + 96*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 - 54*a^2*b^5*c^2*g^2 - 128*a^6*b*h^2*j^2 + 108*a^5*b^2*e*i^3 + 12*a^3*b^4*e^3*i - 64*a^4*b^3*d*h^3 - 64*a^2*b^5*d^3*h + 12*a^3*b^4*c*g^3 + 18*a*b^6*c^2*e^2 + 16*a^5*b^2*h^4 - 81*a^6*b*i^4 + 16*a*b^6*d^4 + 256*a^7*j^4 - 81*b^7*c^4 - a^4*b^3*g^4 - a^2*b^5*e^4, z, m), m, 1, 4)","B"
195,1,1623,353,5.578070,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4)^2,x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^6\,z^4+4096\,a^5\,b^4\,d\,h\,z^2+1024\,a^5\,b^4\,e\,g\,z^2+3072\,a^4\,b^5\,c\,e\,z^2+2048\,a^6\,b^3\,h^2\,z^2+2048\,a^4\,b^5\,d^2\,z^2-768\,a^4\,b^3\,c\,g\,h\,z-768\,a^3\,b^4\,c\,d\,g\,z-128\,a^5\,b^2\,g^2\,h\,z+128\,a^4\,b^3\,e^2\,h\,z-1152\,a^3\,b^4\,c^2\,h\,z-128\,a^4\,b^3\,d\,g^2\,z+128\,a^3\,b^4\,d\,e^2\,z-1152\,a^2\,b^5\,c^2\,d\,z-32\,a^3\,b^2\,d\,e\,g\,h-96\,a^2\,b^3\,c\,d\,e\,h-48\,a^3\,b^2\,c\,e\,h^2-16\,a^2\,b^3\,d^2\,e\,g+12\,a^2\,b^3\,c\,e^2\,g-16\,a^4\,b\,e\,g\,h^2-48\,a\,b^4\,c\,d^2\,e+64\,a^4\,b\,d\,h^3+108\,a\,b^4\,c^3\,g+96\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2+54\,a^2\,b^3\,c^2\,g^2+64\,a^2\,b^3\,d^3\,h+12\,a^3\,b^2\,c\,g^3+18\,a\,b^4\,c^2\,e^2+16\,a\,b^4\,d^4+16\,a^5\,h^4+81\,b^5\,c^4+a^2\,b^3\,e^4+a^4\,b\,g^4,z,k\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^6\,z^4+4096\,a^5\,b^4\,d\,h\,z^2+1024\,a^5\,b^4\,e\,g\,z^2+3072\,a^4\,b^5\,c\,e\,z^2+2048\,a^6\,b^3\,h^2\,z^2+2048\,a^4\,b^5\,d^2\,z^2-768\,a^4\,b^3\,c\,g\,h\,z-768\,a^3\,b^4\,c\,d\,g\,z-128\,a^5\,b^2\,g^2\,h\,z+128\,a^4\,b^3\,e^2\,h\,z-1152\,a^3\,b^4\,c^2\,h\,z-128\,a^4\,b^3\,d\,g^2\,z+128\,a^3\,b^4\,d\,e^2\,z-1152\,a^2\,b^5\,c^2\,d\,z-32\,a^3\,b^2\,d\,e\,g\,h-96\,a^2\,b^3\,c\,d\,e\,h-48\,a^3\,b^2\,c\,e\,h^2-16\,a^2\,b^3\,d^2\,e\,g+12\,a^2\,b^3\,c\,e^2\,g-16\,a^4\,b\,e\,g\,h^2-48\,a\,b^4\,c\,d^2\,e+64\,a^4\,b\,d\,h^3+108\,a\,b^4\,c^3\,g+96\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2+54\,a^2\,b^3\,c^2\,g^2+64\,a^2\,b^3\,d^3\,h+12\,a^3\,b^2\,c\,g^3+18\,a\,b^4\,c^2\,e^2+16\,a\,b^4\,d^4+16\,a^5\,h^4+81\,b^5\,c^4+a^2\,b^3\,e^4+a^4\,b\,g^4,z,k\right)\,\left(\frac{256\,g\,a^4\,b^3+768\,c\,a^3\,b^4}{64\,a^3\,b}-\frac{x\,\left(128\,h\,a^4\,b^3+128\,d\,a^3\,b^4\right)}{16\,a^3\,b}\right)+\frac{64\,e\,h\,a^3\,b^2+64\,d\,e\,a^2\,b^3}{64\,a^3\,b}+\frac{x\,\left(4\,a^3\,b^2\,g^2+24\,a^2\,b^3\,c\,g-4\,a^2\,b^3\,e^2+36\,a\,b^4\,c^2\right)}{16\,a^3\,b}\right)+\frac{4\,a^3\,g\,h^2+12\,a^2\,b\,c\,h^2+8\,a^2\,b\,d\,g\,h-a^2\,b\,e\,g^2+24\,a\,b^2\,c\,d\,h-6\,a\,b^2\,c\,e\,g+4\,a\,b^2\,d^2\,g-a\,b^2\,e^3-9\,b^3\,c^2\,e+12\,b^3\,c\,d^2}{64\,a^3\,b}+\frac{x\,\left(2\,a^3\,h^3+6\,a^2\,b\,d\,h^2-e\,g\,a^2\,b\,h+6\,a\,b^2\,d^2\,h-e\,g\,a\,b^2\,d-3\,c\,e\,a\,b^2\,h+2\,b^3\,d^3-3\,c\,e\,b^3\,d\right)}{16\,a^3\,b}\right)\,\mathrm{root}\left(65536\,a^7\,b^6\,z^4+4096\,a^5\,b^4\,d\,h\,z^2+1024\,a^5\,b^4\,e\,g\,z^2+3072\,a^4\,b^5\,c\,e\,z^2+2048\,a^6\,b^3\,h^2\,z^2+2048\,a^4\,b^5\,d^2\,z^2-768\,a^4\,b^3\,c\,g\,h\,z-768\,a^3\,b^4\,c\,d\,g\,z-128\,a^5\,b^2\,g^2\,h\,z+128\,a^4\,b^3\,e^2\,h\,z-1152\,a^3\,b^4\,c^2\,h\,z-128\,a^4\,b^3\,d\,g^2\,z+128\,a^3\,b^4\,d\,e^2\,z-1152\,a^2\,b^5\,c^2\,d\,z-32\,a^3\,b^2\,d\,e\,g\,h-96\,a^2\,b^3\,c\,d\,e\,h-48\,a^3\,b^2\,c\,e\,h^2-16\,a^2\,b^3\,d^2\,e\,g+12\,a^2\,b^3\,c\,e^2\,g-16\,a^4\,b\,e\,g\,h^2-48\,a\,b^4\,c\,d^2\,e+64\,a^4\,b\,d\,h^3+108\,a\,b^4\,c^3\,g+96\,a^3\,b^2\,d^2\,h^2+2\,a^3\,b^2\,e^2\,g^2+54\,a^2\,b^3\,c^2\,g^2+64\,a^2\,b^3\,d^3\,h+12\,a^3\,b^2\,c\,g^3+18\,a\,b^4\,c^2\,e^2+16\,a\,b^4\,d^4+16\,a^5\,h^4+81\,b^5\,c^4+a^2\,b^3\,e^4+a^4\,b\,g^4,z,k\right)\right)+\frac{\frac{e\,x^3}{4\,a}-\frac{f}{4\,b}+\frac{x\,\left(b\,c-a\,g\right)}{4\,a\,b}+\frac{x^2\,\left(b\,d-a\,h\right)}{4\,a\,b}}{b\,x^4+a}","Not used",1,"symsum(log((12*b^3*c*d^2 - a*b^2*e^3 - 9*b^3*c^2*e + 4*a^3*g*h^2 + 4*a*b^2*d^2*g + 12*a^2*b*c*h^2 - a^2*b*e*g^2 + 24*a*b^2*c*d*h - 6*a*b^2*c*e*g + 8*a^2*b*d*g*h)/(64*a^3*b) - root(65536*a^7*b^6*z^4 + 4096*a^5*b^4*d*h*z^2 + 1024*a^5*b^4*e*g*z^2 + 3072*a^4*b^5*c*e*z^2 + 2048*a^6*b^3*h^2*z^2 + 2048*a^4*b^5*d^2*z^2 - 768*a^4*b^3*c*g*h*z - 768*a^3*b^4*c*d*g*z - 128*a^5*b^2*g^2*h*z + 128*a^4*b^3*e^2*h*z - 1152*a^3*b^4*c^2*h*z - 128*a^4*b^3*d*g^2*z + 128*a^3*b^4*d*e^2*z - 1152*a^2*b^5*c^2*d*z - 32*a^3*b^2*d*e*g*h - 96*a^2*b^3*c*d*e*h - 48*a^3*b^2*c*e*h^2 - 16*a^2*b^3*d^2*e*g + 12*a^2*b^3*c*e^2*g - 16*a^4*b*e*g*h^2 - 48*a*b^4*c*d^2*e + 64*a^4*b*d*h^3 + 108*a*b^4*c^3*g + 96*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 + 54*a^2*b^3*c^2*g^2 + 64*a^2*b^3*d^3*h + 12*a^3*b^2*c*g^3 + 18*a*b^4*c^2*e^2 + 16*a*b^4*d^4 + 16*a^5*h^4 + 81*b^5*c^4 + a^2*b^3*e^4 + a^4*b*g^4, z, k)*(root(65536*a^7*b^6*z^4 + 4096*a^5*b^4*d*h*z^2 + 1024*a^5*b^4*e*g*z^2 + 3072*a^4*b^5*c*e*z^2 + 2048*a^6*b^3*h^2*z^2 + 2048*a^4*b^5*d^2*z^2 - 768*a^4*b^3*c*g*h*z - 768*a^3*b^4*c*d*g*z - 128*a^5*b^2*g^2*h*z + 128*a^4*b^3*e^2*h*z - 1152*a^3*b^4*c^2*h*z - 128*a^4*b^3*d*g^2*z + 128*a^3*b^4*d*e^2*z - 1152*a^2*b^5*c^2*d*z - 32*a^3*b^2*d*e*g*h - 96*a^2*b^3*c*d*e*h - 48*a^3*b^2*c*e*h^2 - 16*a^2*b^3*d^2*e*g + 12*a^2*b^3*c*e^2*g - 16*a^4*b*e*g*h^2 - 48*a*b^4*c*d^2*e + 64*a^4*b*d*h^3 + 108*a*b^4*c^3*g + 96*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 + 54*a^2*b^3*c^2*g^2 + 64*a^2*b^3*d^3*h + 12*a^3*b^2*c*g^3 + 18*a*b^4*c^2*e^2 + 16*a*b^4*d^4 + 16*a^5*h^4 + 81*b^5*c^4 + a^2*b^3*e^4 + a^4*b*g^4, z, k)*((768*a^3*b^4*c + 256*a^4*b^3*g)/(64*a^3*b) - (x*(128*a^3*b^4*d + 128*a^4*b^3*h))/(16*a^3*b)) + (64*a^2*b^3*d*e + 64*a^3*b^2*e*h)/(64*a^3*b) + (x*(36*a*b^4*c^2 - 4*a^2*b^3*e^2 + 4*a^3*b^2*g^2 + 24*a^2*b^3*c*g))/(16*a^3*b)) + (x*(2*b^3*d^3 + 2*a^3*h^3 - 3*b^3*c*d*e + 6*a*b^2*d^2*h + 6*a^2*b*d*h^2 - 3*a*b^2*c*e*h - a*b^2*d*e*g - a^2*b*e*g*h))/(16*a^3*b))*root(65536*a^7*b^6*z^4 + 4096*a^5*b^4*d*h*z^2 + 1024*a^5*b^4*e*g*z^2 + 3072*a^4*b^5*c*e*z^2 + 2048*a^6*b^3*h^2*z^2 + 2048*a^4*b^5*d^2*z^2 - 768*a^4*b^3*c*g*h*z - 768*a^3*b^4*c*d*g*z - 128*a^5*b^2*g^2*h*z + 128*a^4*b^3*e^2*h*z - 1152*a^3*b^4*c^2*h*z - 128*a^4*b^3*d*g^2*z + 128*a^3*b^4*d*e^2*z - 1152*a^2*b^5*c^2*d*z - 32*a^3*b^2*d*e*g*h - 96*a^2*b^3*c*d*e*h - 48*a^3*b^2*c*e*h^2 - 16*a^2*b^3*d^2*e*g + 12*a^2*b^3*c*e^2*g - 16*a^4*b*e*g*h^2 - 48*a*b^4*c*d^2*e + 64*a^4*b*d*h^3 + 108*a*b^4*c^3*g + 96*a^3*b^2*d^2*h^2 + 2*a^3*b^2*e^2*g^2 + 54*a^2*b^3*c^2*g^2 + 64*a^2*b^3*d^3*h + 12*a^3*b^2*c*g^3 + 18*a*b^4*c^2*e^2 + 16*a*b^4*d^4 + 16*a^5*h^4 + 81*b^5*c^4 + a^2*b^3*e^4 + a^4*b*g^4, z, k), k, 1, 4) + ((e*x^3)/(4*a) - f/(4*b) + (x*(b*c - a*g))/(4*a*b) + (x^2*(b*d - a*h))/(4*a*b))/(a + b*x^4)","B"
196,1,2605,395,5.702438,"\text{Not used}","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)","\left(\sum _{l=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^7\,z^4+3072\,a^6\,b^4\,g\,i\,z^2+9216\,a^5\,b^5\,c\,i\,z^2+4096\,a^5\,b^5\,d\,h\,z^2+1024\,a^5\,b^5\,e\,g\,z^2+3072\,a^4\,b^6\,c\,e\,z^2+2048\,a^6\,b^4\,h^2\,z^2+2048\,a^4\,b^6\,d^2\,z^2+768\,a^5\,b^3\,e\,h\,i\,z+768\,a^4\,b^4\,d\,e\,i\,z-768\,a^4\,b^4\,c\,g\,h\,z-768\,a^3\,b^5\,c\,d\,g\,z+1152\,a^6\,b^2\,h\,i^2\,z-128\,a^5\,b^3\,g^2\,h\,z+1152\,a^5\,b^3\,d\,i^2\,z+128\,a^4\,b^4\,e^2\,h\,z-1152\,a^3\,b^5\,c^2\,h\,z-128\,a^4\,b^4\,d\,g^2\,z+128\,a^3\,b^5\,d\,e^2\,z-1152\,a^2\,b^6\,c^2\,d\,z-96\,a^4\,b^2\,d\,g\,h\,i-288\,a^3\,b^3\,c\,d\,h\,i+72\,a^3\,b^3\,c\,e\,g\,i-32\,a^3\,b^3\,d\,e\,g\,h-96\,a^2\,b^4\,c\,d\,e\,h+12\,a^4\,b^2\,e\,g^2\,i-144\,a^4\,b^2\,c\,h^2\,i-48\,a^3\,b^3\,d^2\,g\,i-16\,a^4\,b^2\,e\,g\,h^2+108\,a^4\,b^2\,c\,g\,i^2+108\,a^2\,b^4\,c^2\,e\,i-144\,a^2\,b^4\,c\,d^2\,i-48\,a^3\,b^3\,c\,e\,h^2-16\,a^2\,b^4\,d^2\,e\,g+12\,a^2\,b^4\,c\,e^2\,g-48\,a^5\,b\,g\,h^2\,i-48\,a\,b^5\,c\,d^2\,e+108\,a^5\,b\,e\,i^3+108\,a\,b^5\,c^3\,g+54\,a^4\,b^2\,e^2\,i^2+162\,a^3\,b^3\,c^2\,i^2+96\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2+54\,a^2\,b^4\,c^2\,g^2+18\,a^5\,b\,g^2\,i^2+12\,a^3\,b^3\,e^3\,i+64\,a^4\,b^2\,d\,h^3+64\,a^2\,b^4\,d^3\,h+12\,a^3\,b^3\,c\,g^3+18\,a\,b^5\,c^2\,e^2+16\,a^5\,b\,h^4+16\,a\,b^5\,d^4+81\,a^6\,i^4+81\,b^6\,c^4+a^4\,b^2\,g^4+a^2\,b^4\,e^4,z,l\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^7\,z^4+3072\,a^6\,b^4\,g\,i\,z^2+9216\,a^5\,b^5\,c\,i\,z^2+4096\,a^5\,b^5\,d\,h\,z^2+1024\,a^5\,b^5\,e\,g\,z^2+3072\,a^4\,b^6\,c\,e\,z^2+2048\,a^6\,b^4\,h^2\,z^2+2048\,a^4\,b^6\,d^2\,z^2+768\,a^5\,b^3\,e\,h\,i\,z+768\,a^4\,b^4\,d\,e\,i\,z-768\,a^4\,b^4\,c\,g\,h\,z-768\,a^3\,b^5\,c\,d\,g\,z+1152\,a^6\,b^2\,h\,i^2\,z-128\,a^5\,b^3\,g^2\,h\,z+1152\,a^5\,b^3\,d\,i^2\,z+128\,a^4\,b^4\,e^2\,h\,z-1152\,a^3\,b^5\,c^2\,h\,z-128\,a^4\,b^4\,d\,g^2\,z+128\,a^3\,b^5\,d\,e^2\,z-1152\,a^2\,b^6\,c^2\,d\,z-96\,a^4\,b^2\,d\,g\,h\,i-288\,a^3\,b^3\,c\,d\,h\,i+72\,a^3\,b^3\,c\,e\,g\,i-32\,a^3\,b^3\,d\,e\,g\,h-96\,a^2\,b^4\,c\,d\,e\,h+12\,a^4\,b^2\,e\,g^2\,i-144\,a^4\,b^2\,c\,h^2\,i-48\,a^3\,b^3\,d^2\,g\,i-16\,a^4\,b^2\,e\,g\,h^2+108\,a^4\,b^2\,c\,g\,i^2+108\,a^2\,b^4\,c^2\,e\,i-144\,a^2\,b^4\,c\,d^2\,i-48\,a^3\,b^3\,c\,e\,h^2-16\,a^2\,b^4\,d^2\,e\,g+12\,a^2\,b^4\,c\,e^2\,g-48\,a^5\,b\,g\,h^2\,i-48\,a\,b^5\,c\,d^2\,e+108\,a^5\,b\,e\,i^3+108\,a\,b^5\,c^3\,g+54\,a^4\,b^2\,e^2\,i^2+162\,a^3\,b^3\,c^2\,i^2+96\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2+54\,a^2\,b^4\,c^2\,g^2+18\,a^5\,b\,g^2\,i^2+12\,a^3\,b^3\,e^3\,i+64\,a^4\,b^2\,d\,h^3+64\,a^2\,b^4\,d^3\,h+12\,a^3\,b^3\,c\,g^3+18\,a\,b^5\,c^2\,e^2+16\,a^5\,b\,h^4+16\,a\,b^5\,d^4+81\,a^6\,i^4+81\,b^6\,c^4+a^4\,b^2\,g^4+a^2\,b^4\,e^4,z,l\right)\,\left(\frac{256\,g\,a^4\,b^4+768\,c\,a^3\,b^5}{64\,a^3\,b^2}-\frac{x\,\left(128\,h\,a^4\,b^3+128\,d\,a^3\,b^4\right)}{16\,a^3\,b}\right)+\frac{64\,a^2\,b^4\,d\,e+192\,a^3\,b^3\,d\,i+64\,a^3\,b^3\,e\,h+192\,a^4\,b^2\,h\,i}{64\,a^3\,b^2}+\frac{x\,\left(-36\,a^4\,b\,i^2-24\,a^3\,b^2\,e\,i+4\,a^3\,b^2\,g^2+24\,a^2\,b^3\,c\,g-4\,a^2\,b^3\,e^2+36\,a\,b^4\,c^2\right)}{16\,a^3\,b}\right)-\frac{27\,a^4\,i^3+27\,a^3\,b\,e\,i^2+3\,a^3\,b\,g^2\,i-4\,a^3\,b\,g\,h^2+18\,a^2\,b^2\,c\,g\,i-12\,a^2\,b^2\,c\,h^2-8\,a^2\,b^2\,d\,g\,h+9\,a^2\,b^2\,e^2\,i+a^2\,b^2\,e\,g^2+27\,a\,b^3\,c^2\,i-24\,a\,b^3\,c\,d\,h+6\,a\,b^3\,c\,e\,g-4\,a\,b^3\,d^2\,g+a\,b^3\,e^3+9\,b^4\,c^2\,e-12\,b^4\,c\,d^2}{64\,a^3\,b^2}-\frac{x\,\left(3\,b^3\,c\,d\,e-2\,a^3\,h^3-2\,b^3\,d^3+3\,a^3\,g\,h\,i-6\,a\,b^2\,d^2\,h-6\,a^2\,b\,d\,h^2+9\,a\,b^2\,c\,d\,i+3\,a\,b^2\,c\,e\,h+a\,b^2\,d\,e\,g+9\,a^2\,b\,c\,h\,i+3\,a^2\,b\,d\,g\,i+a^2\,b\,e\,g\,h\right)}{16\,a^3\,b}\right)\,\mathrm{root}\left(65536\,a^7\,b^7\,z^4+3072\,a^6\,b^4\,g\,i\,z^2+9216\,a^5\,b^5\,c\,i\,z^2+4096\,a^5\,b^5\,d\,h\,z^2+1024\,a^5\,b^5\,e\,g\,z^2+3072\,a^4\,b^6\,c\,e\,z^2+2048\,a^6\,b^4\,h^2\,z^2+2048\,a^4\,b^6\,d^2\,z^2+768\,a^5\,b^3\,e\,h\,i\,z+768\,a^4\,b^4\,d\,e\,i\,z-768\,a^4\,b^4\,c\,g\,h\,z-768\,a^3\,b^5\,c\,d\,g\,z+1152\,a^6\,b^2\,h\,i^2\,z-128\,a^5\,b^3\,g^2\,h\,z+1152\,a^5\,b^3\,d\,i^2\,z+128\,a^4\,b^4\,e^2\,h\,z-1152\,a^3\,b^5\,c^2\,h\,z-128\,a^4\,b^4\,d\,g^2\,z+128\,a^3\,b^5\,d\,e^2\,z-1152\,a^2\,b^6\,c^2\,d\,z-96\,a^4\,b^2\,d\,g\,h\,i-288\,a^3\,b^3\,c\,d\,h\,i+72\,a^3\,b^3\,c\,e\,g\,i-32\,a^3\,b^3\,d\,e\,g\,h-96\,a^2\,b^4\,c\,d\,e\,h+12\,a^4\,b^2\,e\,g^2\,i-144\,a^4\,b^2\,c\,h^2\,i-48\,a^3\,b^3\,d^2\,g\,i-16\,a^4\,b^2\,e\,g\,h^2+108\,a^4\,b^2\,c\,g\,i^2+108\,a^2\,b^4\,c^2\,e\,i-144\,a^2\,b^4\,c\,d^2\,i-48\,a^3\,b^3\,c\,e\,h^2-16\,a^2\,b^4\,d^2\,e\,g+12\,a^2\,b^4\,c\,e^2\,g-48\,a^5\,b\,g\,h^2\,i-48\,a\,b^5\,c\,d^2\,e+108\,a^5\,b\,e\,i^3+108\,a\,b^5\,c^3\,g+54\,a^4\,b^2\,e^2\,i^2+162\,a^3\,b^3\,c^2\,i^2+96\,a^3\,b^3\,d^2\,h^2+2\,a^3\,b^3\,e^2\,g^2+54\,a^2\,b^4\,c^2\,g^2+18\,a^5\,b\,g^2\,i^2+12\,a^3\,b^3\,e^3\,i+64\,a^4\,b^2\,d\,h^3+64\,a^2\,b^4\,d^3\,h+12\,a^3\,b^3\,c\,g^3+18\,a\,b^5\,c^2\,e^2+16\,a^5\,b\,h^4+16\,a\,b^5\,d^4+81\,a^6\,i^4+81\,b^6\,c^4+a^4\,b^2\,g^4+a^2\,b^4\,e^4,z,l\right)\right)+\frac{\frac{x\,\left(b\,c-a\,g\right)}{4\,a\,b}-\frac{f}{4\,b}+\frac{x^2\,\left(b\,d-a\,h\right)}{4\,a\,b}+\frac{x^3\,\left(b\,e-a\,i\right)}{4\,a\,b}}{b\,x^4+a}","Not used",1,"symsum(log(- root(65536*a^7*b^7*z^4 + 3072*a^6*b^4*g*i*z^2 + 9216*a^5*b^5*c*i*z^2 + 4096*a^5*b^5*d*h*z^2 + 1024*a^5*b^5*e*g*z^2 + 3072*a^4*b^6*c*e*z^2 + 2048*a^6*b^4*h^2*z^2 + 2048*a^4*b^6*d^2*z^2 + 768*a^5*b^3*e*h*i*z + 768*a^4*b^4*d*e*i*z - 768*a^4*b^4*c*g*h*z - 768*a^3*b^5*c*d*g*z + 1152*a^6*b^2*h*i^2*z - 128*a^5*b^3*g^2*h*z + 1152*a^5*b^3*d*i^2*z + 128*a^4*b^4*e^2*h*z - 1152*a^3*b^5*c^2*h*z - 128*a^4*b^4*d*g^2*z + 128*a^3*b^5*d*e^2*z - 1152*a^2*b^6*c^2*d*z - 96*a^4*b^2*d*g*h*i - 288*a^3*b^3*c*d*h*i + 72*a^3*b^3*c*e*g*i - 32*a^3*b^3*d*e*g*h - 96*a^2*b^4*c*d*e*h + 12*a^4*b^2*e*g^2*i - 144*a^4*b^2*c*h^2*i - 48*a^3*b^3*d^2*g*i - 16*a^4*b^2*e*g*h^2 + 108*a^4*b^2*c*g*i^2 + 108*a^2*b^4*c^2*e*i - 144*a^2*b^4*c*d^2*i - 48*a^3*b^3*c*e*h^2 - 16*a^2*b^4*d^2*e*g + 12*a^2*b^4*c*e^2*g - 48*a^5*b*g*h^2*i - 48*a*b^5*c*d^2*e + 108*a^5*b*e*i^3 + 108*a*b^5*c^3*g + 54*a^4*b^2*e^2*i^2 + 162*a^3*b^3*c^2*i^2 + 96*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 + 54*a^2*b^4*c^2*g^2 + 18*a^5*b*g^2*i^2 + 12*a^3*b^3*e^3*i + 64*a^4*b^2*d*h^3 + 64*a^2*b^4*d^3*h + 12*a^3*b^3*c*g^3 + 18*a*b^5*c^2*e^2 + 16*a^5*b*h^4 + 16*a*b^5*d^4 + 81*a^6*i^4 + 81*b^6*c^4 + a^4*b^2*g^4 + a^2*b^4*e^4, z, l)*(root(65536*a^7*b^7*z^4 + 3072*a^6*b^4*g*i*z^2 + 9216*a^5*b^5*c*i*z^2 + 4096*a^5*b^5*d*h*z^2 + 1024*a^5*b^5*e*g*z^2 + 3072*a^4*b^6*c*e*z^2 + 2048*a^6*b^4*h^2*z^2 + 2048*a^4*b^6*d^2*z^2 + 768*a^5*b^3*e*h*i*z + 768*a^4*b^4*d*e*i*z - 768*a^4*b^4*c*g*h*z - 768*a^3*b^5*c*d*g*z + 1152*a^6*b^2*h*i^2*z - 128*a^5*b^3*g^2*h*z + 1152*a^5*b^3*d*i^2*z + 128*a^4*b^4*e^2*h*z - 1152*a^3*b^5*c^2*h*z - 128*a^4*b^4*d*g^2*z + 128*a^3*b^5*d*e^2*z - 1152*a^2*b^6*c^2*d*z - 96*a^4*b^2*d*g*h*i - 288*a^3*b^3*c*d*h*i + 72*a^3*b^3*c*e*g*i - 32*a^3*b^3*d*e*g*h - 96*a^2*b^4*c*d*e*h + 12*a^4*b^2*e*g^2*i - 144*a^4*b^2*c*h^2*i - 48*a^3*b^3*d^2*g*i - 16*a^4*b^2*e*g*h^2 + 108*a^4*b^2*c*g*i^2 + 108*a^2*b^4*c^2*e*i - 144*a^2*b^4*c*d^2*i - 48*a^3*b^3*c*e*h^2 - 16*a^2*b^4*d^2*e*g + 12*a^2*b^4*c*e^2*g - 48*a^5*b*g*h^2*i - 48*a*b^5*c*d^2*e + 108*a^5*b*e*i^3 + 108*a*b^5*c^3*g + 54*a^4*b^2*e^2*i^2 + 162*a^3*b^3*c^2*i^2 + 96*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 + 54*a^2*b^4*c^2*g^2 + 18*a^5*b*g^2*i^2 + 12*a^3*b^3*e^3*i + 64*a^4*b^2*d*h^3 + 64*a^2*b^4*d^3*h + 12*a^3*b^3*c*g^3 + 18*a*b^5*c^2*e^2 + 16*a^5*b*h^4 + 16*a*b^5*d^4 + 81*a^6*i^4 + 81*b^6*c^4 + a^4*b^2*g^4 + a^2*b^4*e^4, z, l)*((768*a^3*b^5*c + 256*a^4*b^4*g)/(64*a^3*b^2) - (x*(128*a^3*b^4*d + 128*a^4*b^3*h))/(16*a^3*b)) + (64*a^2*b^4*d*e + 192*a^3*b^3*d*i + 64*a^3*b^3*e*h + 192*a^4*b^2*h*i)/(64*a^3*b^2) + (x*(36*a*b^4*c^2 - 36*a^4*b*i^2 - 4*a^2*b^3*e^2 + 4*a^3*b^2*g^2 + 24*a^2*b^3*c*g - 24*a^3*b^2*e*i))/(16*a^3*b)) - (27*a^4*i^3 + a*b^3*e^3 - 12*b^4*c*d^2 + 9*b^4*c^2*e - 12*a^2*b^2*c*h^2 + a^2*b^2*e*g^2 + 9*a^2*b^2*e^2*i - 4*a*b^3*d^2*g + 27*a*b^3*c^2*i + 27*a^3*b*e*i^2 - 4*a^3*b*g*h^2 + 3*a^3*b*g^2*i + 18*a^2*b^2*c*g*i - 8*a^2*b^2*d*g*h - 24*a*b^3*c*d*h + 6*a*b^3*c*e*g)/(64*a^3*b^2) - (x*(3*b^3*c*d*e - 2*a^3*h^3 - 2*b^3*d^3 + 3*a^3*g*h*i - 6*a*b^2*d^2*h - 6*a^2*b*d*h^2 + 9*a*b^2*c*d*i + 3*a*b^2*c*e*h + a*b^2*d*e*g + 9*a^2*b*c*h*i + 3*a^2*b*d*g*i + a^2*b*e*g*h))/(16*a^3*b))*root(65536*a^7*b^7*z^4 + 3072*a^6*b^4*g*i*z^2 + 9216*a^5*b^5*c*i*z^2 + 4096*a^5*b^5*d*h*z^2 + 1024*a^5*b^5*e*g*z^2 + 3072*a^4*b^6*c*e*z^2 + 2048*a^6*b^4*h^2*z^2 + 2048*a^4*b^6*d^2*z^2 + 768*a^5*b^3*e*h*i*z + 768*a^4*b^4*d*e*i*z - 768*a^4*b^4*c*g*h*z - 768*a^3*b^5*c*d*g*z + 1152*a^6*b^2*h*i^2*z - 128*a^5*b^3*g^2*h*z + 1152*a^5*b^3*d*i^2*z + 128*a^4*b^4*e^2*h*z - 1152*a^3*b^5*c^2*h*z - 128*a^4*b^4*d*g^2*z + 128*a^3*b^5*d*e^2*z - 1152*a^2*b^6*c^2*d*z - 96*a^4*b^2*d*g*h*i - 288*a^3*b^3*c*d*h*i + 72*a^3*b^3*c*e*g*i - 32*a^3*b^3*d*e*g*h - 96*a^2*b^4*c*d*e*h + 12*a^4*b^2*e*g^2*i - 144*a^4*b^2*c*h^2*i - 48*a^3*b^3*d^2*g*i - 16*a^4*b^2*e*g*h^2 + 108*a^4*b^2*c*g*i^2 + 108*a^2*b^4*c^2*e*i - 144*a^2*b^4*c*d^2*i - 48*a^3*b^3*c*e*h^2 - 16*a^2*b^4*d^2*e*g + 12*a^2*b^4*c*e^2*g - 48*a^5*b*g*h^2*i - 48*a*b^5*c*d^2*e + 108*a^5*b*e*i^3 + 108*a*b^5*c^3*g + 54*a^4*b^2*e^2*i^2 + 162*a^3*b^3*c^2*i^2 + 96*a^3*b^3*d^2*h^2 + 2*a^3*b^3*e^2*g^2 + 54*a^2*b^4*c^2*g^2 + 18*a^5*b*g^2*i^2 + 12*a^3*b^3*e^3*i + 64*a^4*b^2*d*h^3 + 64*a^2*b^4*d^3*h + 12*a^3*b^3*c*g^3 + 18*a*b^5*c^2*e^2 + 16*a^5*b*h^4 + 16*a*b^5*d^4 + 81*a^6*i^4 + 81*b^6*c^4 + a^4*b^2*g^4 + a^2*b^4*e^4, z, l), l, 1, 4) + ((x*(b*c - a*g))/(4*a*b) - f/(4*b) + (x^2*(b*d - a*h))/(4*a*b) + (x^3*(b*e - a*i))/(4*a*b))/(a + b*x^4)","B"
197,1,3939,417,5.843780,"\text{Not used}","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{\frac{x\,\left(b\,c-a\,g\right)}{4\,a\,b}-\frac{b\,f-a\,j}{4\,b^2}+\frac{x^2\,\left(b\,d-a\,h\right)}{4\,a\,b}+\frac{x^3\,\left(b\,e-a\,i\right)}{4\,a\,b}}{b\,x^4+a}+\left(\sum _{m=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^8\,z^4-65536\,a^7\,b^6\,j\,z^3+3072\,a^6\,b^5\,g\,i\,z^2+9216\,a^5\,b^6\,c\,i\,z^2+4096\,a^5\,b^6\,d\,h\,z^2+1024\,a^5\,b^6\,e\,g\,z^2+3072\,a^4\,b^7\,c\,e\,z^2+24576\,a^7\,b^4\,j^2\,z^2+2048\,a^6\,b^5\,h^2\,z^2+2048\,a^4\,b^7\,d^2\,z^2-1536\,a^6\,b^3\,g\,i\,j\,z-4608\,a^5\,b^4\,c\,i\,j\,z-2048\,a^5\,b^4\,d\,h\,j\,z+768\,a^5\,b^4\,e\,h\,i\,z-512\,a^5\,b^4\,e\,g\,j\,z-1536\,a^4\,b^5\,c\,e\,j\,z+768\,a^4\,b^5\,d\,e\,i\,z-768\,a^4\,b^5\,c\,g\,h\,z-768\,a^3\,b^6\,c\,d\,g\,z-1024\,a^6\,b^3\,h^2\,j\,z+1152\,a^6\,b^3\,h\,i^2\,z-128\,a^5\,b^4\,g^2\,h\,z-1024\,a^4\,b^5\,d^2\,j\,z+1152\,a^5\,b^4\,d\,i^2\,z+128\,a^4\,b^5\,e^2\,h\,z-1152\,a^3\,b^6\,c^2\,h\,z-128\,a^4\,b^5\,d\,g^2\,z+128\,a^3\,b^6\,d\,e^2\,z-1152\,a^2\,b^7\,c^2\,d\,z-4096\,a^7\,b^2\,j^3\,z-192\,a^5\,b^2\,e\,h\,i\,j-192\,a^4\,b^3\,d\,e\,i\,j+192\,a^4\,b^3\,c\,g\,h\,j-96\,a^4\,b^3\,d\,g\,h\,i-288\,a^3\,b^4\,c\,d\,h\,i+192\,a^3\,b^4\,c\,d\,g\,j+72\,a^3\,b^4\,c\,e\,g\,i-32\,a^3\,b^4\,d\,e\,g\,h-96\,a^2\,b^5\,c\,d\,e\,h+32\,a^5\,b^2\,g^2\,h\,j-48\,a^5\,b^2\,g\,h^2\,i-288\,a^5\,b^2\,d\,i^2\,j-32\,a^4\,b^3\,e^2\,h\,j+576\,a^5\,b^2\,c\,i\,j^2+256\,a^5\,b^2\,d\,h\,j^2+64\,a^5\,b^2\,e\,g\,j^2+288\,a^3\,b^4\,c^2\,h\,j+32\,a^4\,b^3\,d\,g^2\,j+12\,a^4\,b^3\,e\,g^2\,i-144\,a^4\,b^3\,c\,h^2\,i-48\,a^3\,b^4\,d^2\,g\,i-16\,a^4\,b^3\,e\,g\,h^2+108\,a^4\,b^3\,c\,g\,i^2-32\,a^3\,b^4\,d\,e^2\,j+192\,a^4\,b^3\,c\,e\,j^2+288\,a^2\,b^5\,c^2\,d\,j+108\,a^2\,b^5\,c^2\,e\,i-144\,a^2\,b^5\,c\,d^2\,i-48\,a^3\,b^4\,c\,e\,h^2-16\,a^2\,b^5\,d^2\,e\,g+12\,a^2\,b^5\,c\,e^2\,g-288\,a^6\,b\,h\,i^2\,j+192\,a^6\,b\,g\,i\,j^2-48\,a\,b^6\,c\,d^2\,e+108\,a\,b^6\,c^3\,g+18\,a^5\,b^2\,g^2\,i^2+128\,a^4\,b^3\,d^2\,j^2+54\,a^4\,b^3\,e^2\,i^2+162\,a^3\,b^4\,c^2\,i^2+96\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2+54\,a^2\,b^5\,c^2\,g^2+128\,a^6\,b\,h^2\,j^2+108\,a^5\,b^2\,e\,i^3+12\,a^3\,b^4\,e^3\,i+64\,a^4\,b^3\,d\,h^3+64\,a^2\,b^5\,d^3\,h+12\,a^3\,b^4\,c\,g^3+18\,a\,b^6\,c^2\,e^2+16\,a^5\,b^2\,h^4+81\,a^6\,b\,i^4+16\,a\,b^6\,d^4+256\,a^7\,j^4+81\,b^7\,c^4+a^4\,b^3\,g^4+a^2\,b^5\,e^4,z,m\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^8\,z^4-65536\,a^7\,b^6\,j\,z^3+3072\,a^6\,b^5\,g\,i\,z^2+9216\,a^5\,b^6\,c\,i\,z^2+4096\,a^5\,b^6\,d\,h\,z^2+1024\,a^5\,b^6\,e\,g\,z^2+3072\,a^4\,b^7\,c\,e\,z^2+24576\,a^7\,b^4\,j^2\,z^2+2048\,a^6\,b^5\,h^2\,z^2+2048\,a^4\,b^7\,d^2\,z^2-1536\,a^6\,b^3\,g\,i\,j\,z-4608\,a^5\,b^4\,c\,i\,j\,z-2048\,a^5\,b^4\,d\,h\,j\,z+768\,a^5\,b^4\,e\,h\,i\,z-512\,a^5\,b^4\,e\,g\,j\,z-1536\,a^4\,b^5\,c\,e\,j\,z+768\,a^4\,b^5\,d\,e\,i\,z-768\,a^4\,b^5\,c\,g\,h\,z-768\,a^3\,b^6\,c\,d\,g\,z-1024\,a^6\,b^3\,h^2\,j\,z+1152\,a^6\,b^3\,h\,i^2\,z-128\,a^5\,b^4\,g^2\,h\,z-1024\,a^4\,b^5\,d^2\,j\,z+1152\,a^5\,b^4\,d\,i^2\,z+128\,a^4\,b^5\,e^2\,h\,z-1152\,a^3\,b^6\,c^2\,h\,z-128\,a^4\,b^5\,d\,g^2\,z+128\,a^3\,b^6\,d\,e^2\,z-1152\,a^2\,b^7\,c^2\,d\,z-4096\,a^7\,b^2\,j^3\,z-192\,a^5\,b^2\,e\,h\,i\,j-192\,a^4\,b^3\,d\,e\,i\,j+192\,a^4\,b^3\,c\,g\,h\,j-96\,a^4\,b^3\,d\,g\,h\,i-288\,a^3\,b^4\,c\,d\,h\,i+192\,a^3\,b^4\,c\,d\,g\,j+72\,a^3\,b^4\,c\,e\,g\,i-32\,a^3\,b^4\,d\,e\,g\,h-96\,a^2\,b^5\,c\,d\,e\,h+32\,a^5\,b^2\,g^2\,h\,j-48\,a^5\,b^2\,g\,h^2\,i-288\,a^5\,b^2\,d\,i^2\,j-32\,a^4\,b^3\,e^2\,h\,j+576\,a^5\,b^2\,c\,i\,j^2+256\,a^5\,b^2\,d\,h\,j^2+64\,a^5\,b^2\,e\,g\,j^2+288\,a^3\,b^4\,c^2\,h\,j+32\,a^4\,b^3\,d\,g^2\,j+12\,a^4\,b^3\,e\,g^2\,i-144\,a^4\,b^3\,c\,h^2\,i-48\,a^3\,b^4\,d^2\,g\,i-16\,a^4\,b^3\,e\,g\,h^2+108\,a^4\,b^3\,c\,g\,i^2-32\,a^3\,b^4\,d\,e^2\,j+192\,a^4\,b^3\,c\,e\,j^2+288\,a^2\,b^5\,c^2\,d\,j+108\,a^2\,b^5\,c^2\,e\,i-144\,a^2\,b^5\,c\,d^2\,i-48\,a^3\,b^4\,c\,e\,h^2-16\,a^2\,b^5\,d^2\,e\,g+12\,a^2\,b^5\,c\,e^2\,g-288\,a^6\,b\,h\,i^2\,j+192\,a^6\,b\,g\,i\,j^2-48\,a\,b^6\,c\,d^2\,e+108\,a\,b^6\,c^3\,g+18\,a^5\,b^2\,g^2\,i^2+128\,a^4\,b^3\,d^2\,j^2+54\,a^4\,b^3\,e^2\,i^2+162\,a^3\,b^4\,c^2\,i^2+96\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2+54\,a^2\,b^5\,c^2\,g^2+128\,a^6\,b\,h^2\,j^2+108\,a^5\,b^2\,e\,i^3+12\,a^3\,b^4\,e^3\,i+64\,a^4\,b^3\,d\,h^3+64\,a^2\,b^5\,d^3\,h+12\,a^3\,b^4\,c\,g^3+18\,a\,b^6\,c^2\,e^2+16\,a^5\,b^2\,h^4+81\,a^6\,b\,i^4+16\,a\,b^6\,d^4+256\,a^7\,j^4+81\,b^7\,c^4+a^4\,b^3\,g^4+a^2\,b^5\,e^4,z,m\right)\,\left(\frac{256\,g\,a^4\,b^4+768\,c\,a^3\,b^5}{64\,a^3\,b^2}-\frac{x\,\left(128\,h\,a^4\,b^4+128\,d\,a^3\,b^5\right)}{16\,a^3\,b^2}\right)+\frac{64\,a^2\,b^4\,d\,e-384\,a^3\,b^3\,c\,j+192\,a^3\,b^3\,d\,i+64\,a^3\,b^3\,e\,h-128\,a^4\,b^2\,g\,j+192\,a^4\,b^2\,h\,i}{64\,a^3\,b^2}+\frac{x\,\left(-36\,a^4\,b^2\,i^2+64\,h\,j\,a^4\,b^2-24\,a^3\,b^3\,e\,i+4\,a^3\,b^3\,g^2+64\,d\,j\,a^3\,b^3+24\,a^2\,b^4\,c\,g-4\,a^2\,b^4\,e^2+36\,a\,b^5\,c^2\right)}{16\,a^3\,b^2}\right)-\frac{16\,a^4\,g\,j^2-48\,a^4\,h\,i\,j+27\,a^4\,i^3+48\,a^3\,b\,c\,j^2-48\,a^3\,b\,d\,i\,j-16\,a^3\,b\,e\,h\,j+27\,a^3\,b\,e\,i^2+3\,a^3\,b\,g^2\,i-4\,a^3\,b\,g\,h^2+18\,a^2\,b^2\,c\,g\,i-12\,a^2\,b^2\,c\,h^2-16\,a^2\,b^2\,d\,e\,j-8\,a^2\,b^2\,d\,g\,h+9\,a^2\,b^2\,e^2\,i+a^2\,b^2\,e\,g^2+27\,a\,b^3\,c^2\,i-24\,a\,b^3\,c\,d\,h+6\,a\,b^3\,c\,e\,g-4\,a\,b^3\,d^2\,g+a\,b^3\,e^3+9\,b^4\,c^2\,e-12\,b^4\,c\,d^2}{64\,a^3\,b^2}-\frac{x\,\left(-8\,a^4\,h\,j^2+9\,a^4\,i^2\,j-8\,a^3\,b\,d\,j^2+6\,a^3\,b\,e\,i\,j-a^3\,b\,g^2\,j+3\,a^3\,b\,g\,h\,i-2\,a^3\,b\,h^3-6\,a^2\,b^2\,c\,g\,j+9\,a^2\,b^2\,c\,h\,i+3\,a^2\,b^2\,d\,g\,i-6\,a^2\,b^2\,d\,h^2+a^2\,b^2\,e^2\,j+a^2\,b^2\,e\,g\,h-9\,a\,b^3\,c^2\,j+9\,a\,b^3\,c\,d\,i+3\,a\,b^3\,c\,e\,h-6\,a\,b^3\,d^2\,h+a\,b^3\,d\,e\,g+3\,b^4\,c\,d\,e-2\,b^4\,d^3\right)}{16\,a^3\,b^2}\right)\,\mathrm{root}\left(65536\,a^7\,b^8\,z^4-65536\,a^7\,b^6\,j\,z^3+3072\,a^6\,b^5\,g\,i\,z^2+9216\,a^5\,b^6\,c\,i\,z^2+4096\,a^5\,b^6\,d\,h\,z^2+1024\,a^5\,b^6\,e\,g\,z^2+3072\,a^4\,b^7\,c\,e\,z^2+24576\,a^7\,b^4\,j^2\,z^2+2048\,a^6\,b^5\,h^2\,z^2+2048\,a^4\,b^7\,d^2\,z^2-1536\,a^6\,b^3\,g\,i\,j\,z-4608\,a^5\,b^4\,c\,i\,j\,z-2048\,a^5\,b^4\,d\,h\,j\,z+768\,a^5\,b^4\,e\,h\,i\,z-512\,a^5\,b^4\,e\,g\,j\,z-1536\,a^4\,b^5\,c\,e\,j\,z+768\,a^4\,b^5\,d\,e\,i\,z-768\,a^4\,b^5\,c\,g\,h\,z-768\,a^3\,b^6\,c\,d\,g\,z-1024\,a^6\,b^3\,h^2\,j\,z+1152\,a^6\,b^3\,h\,i^2\,z-128\,a^5\,b^4\,g^2\,h\,z-1024\,a^4\,b^5\,d^2\,j\,z+1152\,a^5\,b^4\,d\,i^2\,z+128\,a^4\,b^5\,e^2\,h\,z-1152\,a^3\,b^6\,c^2\,h\,z-128\,a^4\,b^5\,d\,g^2\,z+128\,a^3\,b^6\,d\,e^2\,z-1152\,a^2\,b^7\,c^2\,d\,z-4096\,a^7\,b^2\,j^3\,z-192\,a^5\,b^2\,e\,h\,i\,j-192\,a^4\,b^3\,d\,e\,i\,j+192\,a^4\,b^3\,c\,g\,h\,j-96\,a^4\,b^3\,d\,g\,h\,i-288\,a^3\,b^4\,c\,d\,h\,i+192\,a^3\,b^4\,c\,d\,g\,j+72\,a^3\,b^4\,c\,e\,g\,i-32\,a^3\,b^4\,d\,e\,g\,h-96\,a^2\,b^5\,c\,d\,e\,h+32\,a^5\,b^2\,g^2\,h\,j-48\,a^5\,b^2\,g\,h^2\,i-288\,a^5\,b^2\,d\,i^2\,j-32\,a^4\,b^3\,e^2\,h\,j+576\,a^5\,b^2\,c\,i\,j^2+256\,a^5\,b^2\,d\,h\,j^2+64\,a^5\,b^2\,e\,g\,j^2+288\,a^3\,b^4\,c^2\,h\,j+32\,a^4\,b^3\,d\,g^2\,j+12\,a^4\,b^3\,e\,g^2\,i-144\,a^4\,b^3\,c\,h^2\,i-48\,a^3\,b^4\,d^2\,g\,i-16\,a^4\,b^3\,e\,g\,h^2+108\,a^4\,b^3\,c\,g\,i^2-32\,a^3\,b^4\,d\,e^2\,j+192\,a^4\,b^3\,c\,e\,j^2+288\,a^2\,b^5\,c^2\,d\,j+108\,a^2\,b^5\,c^2\,e\,i-144\,a^2\,b^5\,c\,d^2\,i-48\,a^3\,b^4\,c\,e\,h^2-16\,a^2\,b^5\,d^2\,e\,g+12\,a^2\,b^5\,c\,e^2\,g-288\,a^6\,b\,h\,i^2\,j+192\,a^6\,b\,g\,i\,j^2-48\,a\,b^6\,c\,d^2\,e+108\,a\,b^6\,c^3\,g+18\,a^5\,b^2\,g^2\,i^2+128\,a^4\,b^3\,d^2\,j^2+54\,a^4\,b^3\,e^2\,i^2+162\,a^3\,b^4\,c^2\,i^2+96\,a^3\,b^4\,d^2\,h^2+2\,a^3\,b^4\,e^2\,g^2+54\,a^2\,b^5\,c^2\,g^2+128\,a^6\,b\,h^2\,j^2+108\,a^5\,b^2\,e\,i^3+12\,a^3\,b^4\,e^3\,i+64\,a^4\,b^3\,d\,h^3+64\,a^2\,b^5\,d^3\,h+12\,a^3\,b^4\,c\,g^3+18\,a\,b^6\,c^2\,e^2+16\,a^5\,b^2\,h^4+81\,a^6\,b\,i^4+16\,a\,b^6\,d^4+256\,a^7\,j^4+81\,b^7\,c^4+a^4\,b^3\,g^4+a^2\,b^5\,e^4,z,m\right)\right)","Not used",1,"((x*(b*c - a*g))/(4*a*b) - (b*f - a*j)/(4*b^2) + (x^2*(b*d - a*h))/(4*a*b) + (x^3*(b*e - a*i))/(4*a*b))/(a + b*x^4) + symsum(log(- root(65536*a^7*b^8*z^4 - 65536*a^7*b^6*j*z^3 + 3072*a^6*b^5*g*i*z^2 + 9216*a^5*b^6*c*i*z^2 + 4096*a^5*b^6*d*h*z^2 + 1024*a^5*b^6*e*g*z^2 + 3072*a^4*b^7*c*e*z^2 + 24576*a^7*b^4*j^2*z^2 + 2048*a^6*b^5*h^2*z^2 + 2048*a^4*b^7*d^2*z^2 - 1536*a^6*b^3*g*i*j*z - 4608*a^5*b^4*c*i*j*z - 2048*a^5*b^4*d*h*j*z + 768*a^5*b^4*e*h*i*z - 512*a^5*b^4*e*g*j*z - 1536*a^4*b^5*c*e*j*z + 768*a^4*b^5*d*e*i*z - 768*a^4*b^5*c*g*h*z - 768*a^3*b^6*c*d*g*z - 1024*a^6*b^3*h^2*j*z + 1152*a^6*b^3*h*i^2*z - 128*a^5*b^4*g^2*h*z - 1024*a^4*b^5*d^2*j*z + 1152*a^5*b^4*d*i^2*z + 128*a^4*b^5*e^2*h*z - 1152*a^3*b^6*c^2*h*z - 128*a^4*b^5*d*g^2*z + 128*a^3*b^6*d*e^2*z - 1152*a^2*b^7*c^2*d*z - 4096*a^7*b^2*j^3*z - 192*a^5*b^2*e*h*i*j - 192*a^4*b^3*d*e*i*j + 192*a^4*b^3*c*g*h*j - 96*a^4*b^3*d*g*h*i - 288*a^3*b^4*c*d*h*i + 192*a^3*b^4*c*d*g*j + 72*a^3*b^4*c*e*g*i - 32*a^3*b^4*d*e*g*h - 96*a^2*b^5*c*d*e*h + 32*a^5*b^2*g^2*h*j - 48*a^5*b^2*g*h^2*i - 288*a^5*b^2*d*i^2*j - 32*a^4*b^3*e^2*h*j + 576*a^5*b^2*c*i*j^2 + 256*a^5*b^2*d*h*j^2 + 64*a^5*b^2*e*g*j^2 + 288*a^3*b^4*c^2*h*j + 32*a^4*b^3*d*g^2*j + 12*a^4*b^3*e*g^2*i - 144*a^4*b^3*c*h^2*i - 48*a^3*b^4*d^2*g*i - 16*a^4*b^3*e*g*h^2 + 108*a^4*b^3*c*g*i^2 - 32*a^3*b^4*d*e^2*j + 192*a^4*b^3*c*e*j^2 + 288*a^2*b^5*c^2*d*j + 108*a^2*b^5*c^2*e*i - 144*a^2*b^5*c*d^2*i - 48*a^3*b^4*c*e*h^2 - 16*a^2*b^5*d^2*e*g + 12*a^2*b^5*c*e^2*g - 288*a^6*b*h*i^2*j + 192*a^6*b*g*i*j^2 - 48*a*b^6*c*d^2*e + 108*a*b^6*c^3*g + 18*a^5*b^2*g^2*i^2 + 128*a^4*b^3*d^2*j^2 + 54*a^4*b^3*e^2*i^2 + 162*a^3*b^4*c^2*i^2 + 96*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 + 54*a^2*b^5*c^2*g^2 + 128*a^6*b*h^2*j^2 + 108*a^5*b^2*e*i^3 + 12*a^3*b^4*e^3*i + 64*a^4*b^3*d*h^3 + 64*a^2*b^5*d^3*h + 12*a^3*b^4*c*g^3 + 18*a*b^6*c^2*e^2 + 16*a^5*b^2*h^4 + 81*a^6*b*i^4 + 16*a*b^6*d^4 + 256*a^7*j^4 + 81*b^7*c^4 + a^4*b^3*g^4 + a^2*b^5*e^4, z, m)*(root(65536*a^7*b^8*z^4 - 65536*a^7*b^6*j*z^3 + 3072*a^6*b^5*g*i*z^2 + 9216*a^5*b^6*c*i*z^2 + 4096*a^5*b^6*d*h*z^2 + 1024*a^5*b^6*e*g*z^2 + 3072*a^4*b^7*c*e*z^2 + 24576*a^7*b^4*j^2*z^2 + 2048*a^6*b^5*h^2*z^2 + 2048*a^4*b^7*d^2*z^2 - 1536*a^6*b^3*g*i*j*z - 4608*a^5*b^4*c*i*j*z - 2048*a^5*b^4*d*h*j*z + 768*a^5*b^4*e*h*i*z - 512*a^5*b^4*e*g*j*z - 1536*a^4*b^5*c*e*j*z + 768*a^4*b^5*d*e*i*z - 768*a^4*b^5*c*g*h*z - 768*a^3*b^6*c*d*g*z - 1024*a^6*b^3*h^2*j*z + 1152*a^6*b^3*h*i^2*z - 128*a^5*b^4*g^2*h*z - 1024*a^4*b^5*d^2*j*z + 1152*a^5*b^4*d*i^2*z + 128*a^4*b^5*e^2*h*z - 1152*a^3*b^6*c^2*h*z - 128*a^4*b^5*d*g^2*z + 128*a^3*b^6*d*e^2*z - 1152*a^2*b^7*c^2*d*z - 4096*a^7*b^2*j^3*z - 192*a^5*b^2*e*h*i*j - 192*a^4*b^3*d*e*i*j + 192*a^4*b^3*c*g*h*j - 96*a^4*b^3*d*g*h*i - 288*a^3*b^4*c*d*h*i + 192*a^3*b^4*c*d*g*j + 72*a^3*b^4*c*e*g*i - 32*a^3*b^4*d*e*g*h - 96*a^2*b^5*c*d*e*h + 32*a^5*b^2*g^2*h*j - 48*a^5*b^2*g*h^2*i - 288*a^5*b^2*d*i^2*j - 32*a^4*b^3*e^2*h*j + 576*a^5*b^2*c*i*j^2 + 256*a^5*b^2*d*h*j^2 + 64*a^5*b^2*e*g*j^2 + 288*a^3*b^4*c^2*h*j + 32*a^4*b^3*d*g^2*j + 12*a^4*b^3*e*g^2*i - 144*a^4*b^3*c*h^2*i - 48*a^3*b^4*d^2*g*i - 16*a^4*b^3*e*g*h^2 + 108*a^4*b^3*c*g*i^2 - 32*a^3*b^4*d*e^2*j + 192*a^4*b^3*c*e*j^2 + 288*a^2*b^5*c^2*d*j + 108*a^2*b^5*c^2*e*i - 144*a^2*b^5*c*d^2*i - 48*a^3*b^4*c*e*h^2 - 16*a^2*b^5*d^2*e*g + 12*a^2*b^5*c*e^2*g - 288*a^6*b*h*i^2*j + 192*a^6*b*g*i*j^2 - 48*a*b^6*c*d^2*e + 108*a*b^6*c^3*g + 18*a^5*b^2*g^2*i^2 + 128*a^4*b^3*d^2*j^2 + 54*a^4*b^3*e^2*i^2 + 162*a^3*b^4*c^2*i^2 + 96*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 + 54*a^2*b^5*c^2*g^2 + 128*a^6*b*h^2*j^2 + 108*a^5*b^2*e*i^3 + 12*a^3*b^4*e^3*i + 64*a^4*b^3*d*h^3 + 64*a^2*b^5*d^3*h + 12*a^3*b^4*c*g^3 + 18*a*b^6*c^2*e^2 + 16*a^5*b^2*h^4 + 81*a^6*b*i^4 + 16*a*b^6*d^4 + 256*a^7*j^4 + 81*b^7*c^4 + a^4*b^3*g^4 + a^2*b^5*e^4, z, m)*((768*a^3*b^5*c + 256*a^4*b^4*g)/(64*a^3*b^2) - (x*(128*a^3*b^5*d + 128*a^4*b^4*h))/(16*a^3*b^2)) + (64*a^2*b^4*d*e - 384*a^3*b^3*c*j + 192*a^3*b^3*d*i + 64*a^3*b^3*e*h - 128*a^4*b^2*g*j + 192*a^4*b^2*h*i)/(64*a^3*b^2) + (x*(36*a*b^5*c^2 - 4*a^2*b^4*e^2 + 4*a^3*b^3*g^2 - 36*a^4*b^2*i^2 + 24*a^2*b^4*c*g + 64*a^3*b^3*d*j - 24*a^3*b^3*e*i + 64*a^4*b^2*h*j))/(16*a^3*b^2)) - (27*a^4*i^3 + a*b^3*e^3 - 12*b^4*c*d^2 + 9*b^4*c^2*e + 16*a^4*g*j^2 - 12*a^2*b^2*c*h^2 + a^2*b^2*e*g^2 + 9*a^2*b^2*e^2*i - 48*a^4*h*i*j - 4*a*b^3*d^2*g + 27*a*b^3*c^2*i + 48*a^3*b*c*j^2 + 27*a^3*b*e*i^2 - 4*a^3*b*g*h^2 + 3*a^3*b*g^2*i + 18*a^2*b^2*c*g*i - 16*a^2*b^2*d*e*j - 8*a^2*b^2*d*g*h - 24*a*b^3*c*d*h + 6*a*b^3*c*e*g - 48*a^3*b*d*i*j - 16*a^3*b*e*h*j)/(64*a^3*b^2) - (x*(9*a^4*i^2*j - 2*a^3*b*h^3 - 8*a^4*h*j^2 - 2*b^4*d^3 - 6*a^2*b^2*d*h^2 + a^2*b^2*e^2*j + 3*b^4*c*d*e - 6*a*b^3*d^2*h - 9*a*b^3*c^2*j - 8*a^3*b*d*j^2 - a^3*b*g^2*j - 6*a^2*b^2*c*g*j + 9*a^2*b^2*c*h*i + 3*a^2*b^2*d*g*i + a^2*b^2*e*g*h + 9*a*b^3*c*d*i + 3*a*b^3*c*e*h + a*b^3*d*e*g + 6*a^3*b*e*i*j + 3*a^3*b*g*h*i))/(16*a^3*b^2))*root(65536*a^7*b^8*z^4 - 65536*a^7*b^6*j*z^3 + 3072*a^6*b^5*g*i*z^2 + 9216*a^5*b^6*c*i*z^2 + 4096*a^5*b^6*d*h*z^2 + 1024*a^5*b^6*e*g*z^2 + 3072*a^4*b^7*c*e*z^2 + 24576*a^7*b^4*j^2*z^2 + 2048*a^6*b^5*h^2*z^2 + 2048*a^4*b^7*d^2*z^2 - 1536*a^6*b^3*g*i*j*z - 4608*a^5*b^4*c*i*j*z - 2048*a^5*b^4*d*h*j*z + 768*a^5*b^4*e*h*i*z - 512*a^5*b^4*e*g*j*z - 1536*a^4*b^5*c*e*j*z + 768*a^4*b^5*d*e*i*z - 768*a^4*b^5*c*g*h*z - 768*a^3*b^6*c*d*g*z - 1024*a^6*b^3*h^2*j*z + 1152*a^6*b^3*h*i^2*z - 128*a^5*b^4*g^2*h*z - 1024*a^4*b^5*d^2*j*z + 1152*a^5*b^4*d*i^2*z + 128*a^4*b^5*e^2*h*z - 1152*a^3*b^6*c^2*h*z - 128*a^4*b^5*d*g^2*z + 128*a^3*b^6*d*e^2*z - 1152*a^2*b^7*c^2*d*z - 4096*a^7*b^2*j^3*z - 192*a^5*b^2*e*h*i*j - 192*a^4*b^3*d*e*i*j + 192*a^4*b^3*c*g*h*j - 96*a^4*b^3*d*g*h*i - 288*a^3*b^4*c*d*h*i + 192*a^3*b^4*c*d*g*j + 72*a^3*b^4*c*e*g*i - 32*a^3*b^4*d*e*g*h - 96*a^2*b^5*c*d*e*h + 32*a^5*b^2*g^2*h*j - 48*a^5*b^2*g*h^2*i - 288*a^5*b^2*d*i^2*j - 32*a^4*b^3*e^2*h*j + 576*a^5*b^2*c*i*j^2 + 256*a^5*b^2*d*h*j^2 + 64*a^5*b^2*e*g*j^2 + 288*a^3*b^4*c^2*h*j + 32*a^4*b^3*d*g^2*j + 12*a^4*b^3*e*g^2*i - 144*a^4*b^3*c*h^2*i - 48*a^3*b^4*d^2*g*i - 16*a^4*b^3*e*g*h^2 + 108*a^4*b^3*c*g*i^2 - 32*a^3*b^4*d*e^2*j + 192*a^4*b^3*c*e*j^2 + 288*a^2*b^5*c^2*d*j + 108*a^2*b^5*c^2*e*i - 144*a^2*b^5*c*d^2*i - 48*a^3*b^4*c*e*h^2 - 16*a^2*b^5*d^2*e*g + 12*a^2*b^5*c*e^2*g - 288*a^6*b*h*i^2*j + 192*a^6*b*g*i*j^2 - 48*a*b^6*c*d^2*e + 108*a*b^6*c^3*g + 18*a^5*b^2*g^2*i^2 + 128*a^4*b^3*d^2*j^2 + 54*a^4*b^3*e^2*i^2 + 162*a^3*b^4*c^2*i^2 + 96*a^3*b^4*d^2*h^2 + 2*a^3*b^4*e^2*g^2 + 54*a^2*b^5*c^2*g^2 + 128*a^6*b*h^2*j^2 + 108*a^5*b^2*e*i^3 + 12*a^3*b^4*e^3*i + 64*a^4*b^3*d*h^3 + 64*a^2*b^5*d^3*h + 12*a^3*b^4*c*g^3 + 18*a*b^6*c^2*e^2 + 16*a^5*b^2*h^4 + 81*a^6*b*i^4 + 16*a*b^6*d^4 + 256*a^7*j^4 + 81*b^7*c^4 + a^4*b^3*g^4 + a^2*b^5*e^4, z, m), m, 1, 4)","B"
198,1,1687,241,5.732434,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4)^3,x)","\frac{\frac{f}{8\,b}+\frac{9\,e\,x^3}{32\,a}-\frac{x^5\,\left(7\,b\,c-a\,g\right)}{32\,a^2}-\frac{x^6\,\left(3\,b\,d-a\,h\right)}{16\,a^2}+\frac{x\,\left(11\,b\,c+3\,a\,g\right)}{32\,a\,b}+\frac{x^2\,\left(5\,b\,d+a\,h\right)}{16\,a\,b}-\frac{5\,b\,e\,x^7}{32\,a^2}}{a^2-2\,a\,b\,x^4+b^2\,x^8}+\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(268435456\,a^{11}\,b^6\,z^4+3145728\,a^7\,b^4\,d\,h\,z^2+983040\,a^7\,b^4\,e\,g\,z^2-6881280\,a^6\,b^5\,c\,e\,z^2-524288\,a^8\,b^3\,h^2\,z^2-4718592\,a^6\,b^5\,d^2\,z^2+258048\,a^5\,b^3\,c\,g\,h\,z-774144\,a^4\,b^4\,c\,d\,g\,z-18432\,a^6\,b^2\,g^2\,h\,z-51200\,a^5\,b^3\,e^2\,h\,z-903168\,a^4\,b^4\,c^2\,h\,z+55296\,a^5\,b^3\,d\,g^2\,z+153600\,a^4\,b^4\,d\,e^2\,z+2709504\,a^3\,b^5\,c^2\,d\,z-5760\,a^3\,b^2\,d\,e\,g\,h+40320\,a^2\,b^3\,c\,d\,e\,h+8640\,a^2\,b^3\,d^2\,e\,g-6720\,a^3\,b^2\,c\,e\,h^2-6300\,a^2\,b^3\,c\,e^2\,g+960\,a^4\,b\,e\,g\,h^2-60480\,a\,b^4\,c\,d^2\,e-3072\,a^4\,b\,d\,h^3+111132\,a\,b^4\,c^3\,g+13824\,a^3\,b^2\,d^2\,h^2+450\,a^3\,b^2\,e^2\,g^2-23814\,a^2\,b^3\,c^2\,g^2-27648\,a^2\,b^3\,d^3\,h+2268\,a^3\,b^2\,c\,g^3+22050\,a\,b^4\,c^2\,e^2-625\,a^2\,b^3\,e^4-81\,a^4\,b\,g^4+20736\,a\,b^4\,d^4+256\,a^5\,h^4-194481\,b^5\,c^4,z,k\right)\,\left(\mathrm{root}\left(268435456\,a^{11}\,b^6\,z^4+3145728\,a^7\,b^4\,d\,h\,z^2+983040\,a^7\,b^4\,e\,g\,z^2-6881280\,a^6\,b^5\,c\,e\,z^2-524288\,a^8\,b^3\,h^2\,z^2-4718592\,a^6\,b^5\,d^2\,z^2+258048\,a^5\,b^3\,c\,g\,h\,z-774144\,a^4\,b^4\,c\,d\,g\,z-18432\,a^6\,b^2\,g^2\,h\,z-51200\,a^5\,b^3\,e^2\,h\,z-903168\,a^4\,b^4\,c^2\,h\,z+55296\,a^5\,b^3\,d\,g^2\,z+153600\,a^4\,b^4\,d\,e^2\,z+2709504\,a^3\,b^5\,c^2\,d\,z-5760\,a^3\,b^2\,d\,e\,g\,h+40320\,a^2\,b^3\,c\,d\,e\,h+8640\,a^2\,b^3\,d^2\,e\,g-6720\,a^3\,b^2\,c\,e\,h^2-6300\,a^2\,b^3\,c\,e^2\,g+960\,a^4\,b\,e\,g\,h^2-60480\,a\,b^4\,c\,d^2\,e-3072\,a^4\,b\,d\,h^3+111132\,a\,b^4\,c^3\,g+13824\,a^3\,b^2\,d^2\,h^2+450\,a^3\,b^2\,e^2\,g^2-23814\,a^2\,b^3\,c^2\,g^2-27648\,a^2\,b^3\,d^3\,h+2268\,a^3\,b^2\,c\,g^3+22050\,a\,b^4\,c^2\,e^2-625\,a^2\,b^3\,e^4-81\,a^4\,b\,g^4+20736\,a\,b^4\,d^4+256\,a^5\,h^4-194481\,b^5\,c^4,z,k\right)\,\left(\frac{344064\,a^5\,b^4\,c-49152\,a^6\,b^3\,g}{32768\,a^6\,b}-\frac{x\,\left(24576\,a^5\,b^4\,d-8192\,a^6\,b^3\,h\right)}{4096\,a^6\,b}\right)-\frac{15360\,a^3\,b^3\,d\,e-5120\,a^4\,b^2\,e\,h}{32768\,a^6\,b}+\frac{x\,\left(144\,a^4\,b^2\,g^2-2016\,a^3\,b^3\,c\,g+400\,a^3\,b^3\,e^2+7056\,a^2\,b^4\,c^2\right)}{4096\,a^6\,b}\right)-\frac{-48\,a^3\,g\,h^2+336\,a^2\,b\,c\,h^2+288\,a^2\,b\,d\,g\,h-45\,a^2\,b\,e\,g^2-2016\,a\,b^2\,c\,d\,h+630\,a\,b^2\,c\,e\,g-432\,a\,b^2\,d^2\,g+125\,a\,b^2\,e^3-2205\,b^3\,c^2\,e+3024\,b^3\,c\,d^2}{32768\,a^6\,b}-\frac{x\,\left(-8\,a^3\,h^3+72\,a^2\,b\,d\,h^2-15\,e\,g\,a^2\,b\,h-216\,a\,b^2\,d^2\,h+45\,e\,g\,a\,b^2\,d+105\,c\,e\,a\,b^2\,h+216\,b^3\,d^3-315\,c\,e\,b^3\,d\right)}{4096\,a^6\,b}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^6\,z^4+3145728\,a^7\,b^4\,d\,h\,z^2+983040\,a^7\,b^4\,e\,g\,z^2-6881280\,a^6\,b^5\,c\,e\,z^2-524288\,a^8\,b^3\,h^2\,z^2-4718592\,a^6\,b^5\,d^2\,z^2+258048\,a^5\,b^3\,c\,g\,h\,z-774144\,a^4\,b^4\,c\,d\,g\,z-18432\,a^6\,b^2\,g^2\,h\,z-51200\,a^5\,b^3\,e^2\,h\,z-903168\,a^4\,b^4\,c^2\,h\,z+55296\,a^5\,b^3\,d\,g^2\,z+153600\,a^4\,b^4\,d\,e^2\,z+2709504\,a^3\,b^5\,c^2\,d\,z-5760\,a^3\,b^2\,d\,e\,g\,h+40320\,a^2\,b^3\,c\,d\,e\,h+8640\,a^2\,b^3\,d^2\,e\,g-6720\,a^3\,b^2\,c\,e\,h^2-6300\,a^2\,b^3\,c\,e^2\,g+960\,a^4\,b\,e\,g\,h^2-60480\,a\,b^4\,c\,d^2\,e-3072\,a^4\,b\,d\,h^3+111132\,a\,b^4\,c^3\,g+13824\,a^3\,b^2\,d^2\,h^2+450\,a^3\,b^2\,e^2\,g^2-23814\,a^2\,b^3\,c^2\,g^2-27648\,a^2\,b^3\,d^3\,h+2268\,a^3\,b^2\,c\,g^3+22050\,a\,b^4\,c^2\,e^2-625\,a^2\,b^3\,e^4-81\,a^4\,b\,g^4+20736\,a\,b^4\,d^4+256\,a^5\,h^4-194481\,b^5\,c^4,z,k\right)\right)","Not used",1,"(f/(8*b) + (9*e*x^3)/(32*a) - (x^5*(7*b*c - a*g))/(32*a^2) - (x^6*(3*b*d - a*h))/(16*a^2) + (x*(11*b*c + 3*a*g))/(32*a*b) + (x^2*(5*b*d + a*h))/(16*a*b) - (5*b*e*x^7)/(32*a^2))/(a^2 + b^2*x^8 - 2*a*b*x^4) + symsum(log(- root(268435456*a^11*b^6*z^4 + 3145728*a^7*b^4*d*h*z^2 + 983040*a^7*b^4*e*g*z^2 - 6881280*a^6*b^5*c*e*z^2 - 524288*a^8*b^3*h^2*z^2 - 4718592*a^6*b^5*d^2*z^2 + 258048*a^5*b^3*c*g*h*z - 774144*a^4*b^4*c*d*g*z - 18432*a^6*b^2*g^2*h*z - 51200*a^5*b^3*e^2*h*z - 903168*a^4*b^4*c^2*h*z + 55296*a^5*b^3*d*g^2*z + 153600*a^4*b^4*d*e^2*z + 2709504*a^3*b^5*c^2*d*z - 5760*a^3*b^2*d*e*g*h + 40320*a^2*b^3*c*d*e*h + 8640*a^2*b^3*d^2*e*g - 6720*a^3*b^2*c*e*h^2 - 6300*a^2*b^3*c*e^2*g + 960*a^4*b*e*g*h^2 - 60480*a*b^4*c*d^2*e - 3072*a^4*b*d*h^3 + 111132*a*b^4*c^3*g + 13824*a^3*b^2*d^2*h^2 + 450*a^3*b^2*e^2*g^2 - 23814*a^2*b^3*c^2*g^2 - 27648*a^2*b^3*d^3*h + 2268*a^3*b^2*c*g^3 + 22050*a*b^4*c^2*e^2 - 625*a^2*b^3*e^4 - 81*a^4*b*g^4 + 20736*a*b^4*d^4 + 256*a^5*h^4 - 194481*b^5*c^4, z, k)*(root(268435456*a^11*b^6*z^4 + 3145728*a^7*b^4*d*h*z^2 + 983040*a^7*b^4*e*g*z^2 - 6881280*a^6*b^5*c*e*z^2 - 524288*a^8*b^3*h^2*z^2 - 4718592*a^6*b^5*d^2*z^2 + 258048*a^5*b^3*c*g*h*z - 774144*a^4*b^4*c*d*g*z - 18432*a^6*b^2*g^2*h*z - 51200*a^5*b^3*e^2*h*z - 903168*a^4*b^4*c^2*h*z + 55296*a^5*b^3*d*g^2*z + 153600*a^4*b^4*d*e^2*z + 2709504*a^3*b^5*c^2*d*z - 5760*a^3*b^2*d*e*g*h + 40320*a^2*b^3*c*d*e*h + 8640*a^2*b^3*d^2*e*g - 6720*a^3*b^2*c*e*h^2 - 6300*a^2*b^3*c*e^2*g + 960*a^4*b*e*g*h^2 - 60480*a*b^4*c*d^2*e - 3072*a^4*b*d*h^3 + 111132*a*b^4*c^3*g + 13824*a^3*b^2*d^2*h^2 + 450*a^3*b^2*e^2*g^2 - 23814*a^2*b^3*c^2*g^2 - 27648*a^2*b^3*d^3*h + 2268*a^3*b^2*c*g^3 + 22050*a*b^4*c^2*e^2 - 625*a^2*b^3*e^4 - 81*a^4*b*g^4 + 20736*a*b^4*d^4 + 256*a^5*h^4 - 194481*b^5*c^4, z, k)*((344064*a^5*b^4*c - 49152*a^6*b^3*g)/(32768*a^6*b) - (x*(24576*a^5*b^4*d - 8192*a^6*b^3*h))/(4096*a^6*b)) - (15360*a^3*b^3*d*e - 5120*a^4*b^2*e*h)/(32768*a^6*b) + (x*(7056*a^2*b^4*c^2 + 400*a^3*b^3*e^2 + 144*a^4*b^2*g^2 - 2016*a^3*b^3*c*g))/(4096*a^6*b)) - (125*a*b^2*e^3 + 3024*b^3*c*d^2 - 2205*b^3*c^2*e - 48*a^3*g*h^2 - 432*a*b^2*d^2*g + 336*a^2*b*c*h^2 - 45*a^2*b*e*g^2 - 2016*a*b^2*c*d*h + 630*a*b^2*c*e*g + 288*a^2*b*d*g*h)/(32768*a^6*b) - (x*(216*b^3*d^3 - 8*a^3*h^3 - 315*b^3*c*d*e - 216*a*b^2*d^2*h + 72*a^2*b*d*h^2 + 105*a*b^2*c*e*h + 45*a*b^2*d*e*g - 15*a^2*b*e*g*h))/(4096*a^6*b))*root(268435456*a^11*b^6*z^4 + 3145728*a^7*b^4*d*h*z^2 + 983040*a^7*b^4*e*g*z^2 - 6881280*a^6*b^5*c*e*z^2 - 524288*a^8*b^3*h^2*z^2 - 4718592*a^6*b^5*d^2*z^2 + 258048*a^5*b^3*c*g*h*z - 774144*a^4*b^4*c*d*g*z - 18432*a^6*b^2*g^2*h*z - 51200*a^5*b^3*e^2*h*z - 903168*a^4*b^4*c^2*h*z + 55296*a^5*b^3*d*g^2*z + 153600*a^4*b^4*d*e^2*z + 2709504*a^3*b^5*c^2*d*z - 5760*a^3*b^2*d*e*g*h + 40320*a^2*b^3*c*d*e*h + 8640*a^2*b^3*d^2*e*g - 6720*a^3*b^2*c*e*h^2 - 6300*a^2*b^3*c*e^2*g + 960*a^4*b*e*g*h^2 - 60480*a*b^4*c*d^2*e - 3072*a^4*b*d*h^3 + 111132*a*b^4*c^3*g + 13824*a^3*b^2*d^2*h^2 + 450*a^3*b^2*e^2*g^2 - 23814*a^2*b^3*c^2*g^2 - 27648*a^2*b^3*d^3*h + 2268*a^3*b^2*c*g^3 + 22050*a*b^4*c^2*e^2 - 625*a^2*b^3*e^4 - 81*a^4*b*g^4 + 20736*a*b^4*d^4 + 256*a^5*h^4 - 194481*b^5*c^4, z, k), k, 1, 4)","B"
199,1,2680,268,5.800517,"\text{Not used}","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)","\left(\sum _{l=1}^4\ln\left(-\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4-589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2-6881280\,a^6\,b^6\,c\,e\,z^2-524288\,a^8\,b^4\,h^2\,z^2-4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z+258048\,a^5\,b^4\,c\,g\,h\,z-184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z-18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z-51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z+55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z+2709504\,a^3\,b^6\,c^2\,d\,z+3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h+40320\,a^2\,b^4\,c\,d\,e\,h-540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i+4032\,a^4\,b^2\,c\,h^2\,i+960\,a^4\,b^2\,e\,g\,h^2-2268\,a^4\,b^2\,c\,g\,i^2-26460\,a^2\,b^4\,c^2\,e\,i+36288\,a^2\,b^4\,c\,d^2\,i+8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2-6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g-1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2-23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i-27648\,a^2\,b^4\,d^3\,h-3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2-81\,a^4\,b^2\,g^4-625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4-81\,a^6\,i^4-194481\,b^6\,c^4,z,l\right)\,\left(\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4-589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2-6881280\,a^6\,b^6\,c\,e\,z^2-524288\,a^8\,b^4\,h^2\,z^2-4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z+258048\,a^5\,b^4\,c\,g\,h\,z-184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z-18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z-51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z+55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z+2709504\,a^3\,b^6\,c^2\,d\,z+3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h+40320\,a^2\,b^4\,c\,d\,e\,h-540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i+4032\,a^4\,b^2\,c\,h^2\,i+960\,a^4\,b^2\,e\,g\,h^2-2268\,a^4\,b^2\,c\,g\,i^2-26460\,a^2\,b^4\,c^2\,e\,i+36288\,a^2\,b^4\,c\,d^2\,i+8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2-6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g-1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2-23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i-27648\,a^2\,b^4\,d^3\,h-3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2-81\,a^4\,b^2\,g^4-625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4-81\,a^6\,i^4-194481\,b^6\,c^4,z,l\right)\,\left(\frac{344064\,a^5\,b^5\,c-49152\,a^6\,b^4\,g}{32768\,a^6\,b^2}-\frac{x\,\left(24576\,a^5\,b^4\,d-8192\,a^6\,b^3\,h\right)}{4096\,a^6\,b}\right)-\frac{15360\,a^3\,b^4\,d\,e-9216\,a^4\,b^3\,d\,i-5120\,a^4\,b^3\,e\,h+3072\,a^5\,b^2\,h\,i}{32768\,a^6\,b^2}+\frac{x\,\left(144\,a^5\,b\,i^2-480\,a^4\,b^2\,e\,i+144\,a^4\,b^2\,g^2-2016\,a^3\,b^3\,c\,g+400\,a^3\,b^3\,e^2+7056\,a^2\,b^4\,c^2\right)}{4096\,a^6\,b}\right)+\frac{27\,a^4\,i^3-135\,a^3\,b\,e\,i^2-27\,a^3\,b\,g^2\,i+48\,a^3\,b\,g\,h^2+378\,a^2\,b^2\,c\,g\,i-336\,a^2\,b^2\,c\,h^2-288\,a^2\,b^2\,d\,g\,h+225\,a^2\,b^2\,e^2\,i+45\,a^2\,b^2\,e\,g^2-1323\,a\,b^3\,c^2\,i+2016\,a\,b^3\,c\,d\,h-630\,a\,b^3\,c\,e\,g+432\,a\,b^3\,d^2\,g-125\,a\,b^3\,e^3+2205\,b^4\,c^2\,e-3024\,b^4\,c\,d^2}{32768\,a^6\,b^2}-\frac{x\,\left(216\,b^3\,d^3-8\,a^3\,h^3-315\,b^3\,c\,d\,e+9\,a^3\,g\,h\,i-216\,a\,b^2\,d^2\,h+72\,a^2\,b\,d\,h^2+189\,a\,b^2\,c\,d\,i+105\,a\,b^2\,c\,e\,h+45\,a\,b^2\,d\,e\,g-63\,a^2\,b\,c\,h\,i-27\,a^2\,b\,d\,g\,i-15\,a^2\,b\,e\,g\,h\right)}{4096\,a^6\,b}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4-589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2-6881280\,a^6\,b^6\,c\,e\,z^2-524288\,a^8\,b^4\,h^2\,z^2-4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z+258048\,a^5\,b^4\,c\,g\,h\,z-184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z-18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z-51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z+55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z+2709504\,a^3\,b^6\,c^2\,d\,z+3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h+40320\,a^2\,b^4\,c\,d\,e\,h-540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i+4032\,a^4\,b^2\,c\,h^2\,i+960\,a^4\,b^2\,e\,g\,h^2-2268\,a^4\,b^2\,c\,g\,i^2-26460\,a^2\,b^4\,c^2\,e\,i+36288\,a^2\,b^4\,c\,d^2\,i+8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2-6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g-1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2-23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i-27648\,a^2\,b^4\,d^3\,h-3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2-81\,a^4\,b^2\,g^4-625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4-81\,a^6\,i^4-194481\,b^6\,c^4,z,l\right)\right)+\frac{\frac{f}{8\,b}-\frac{x^5\,\left(7\,b\,c-a\,g\right)}{32\,a^2}-\frac{x^6\,\left(3\,b\,d-a\,h\right)}{16\,a^2}-\frac{x^7\,\left(5\,b\,e-3\,a\,i\right)}{32\,a^2}+\frac{x\,\left(11\,b\,c+3\,a\,g\right)}{32\,a\,b}+\frac{x^2\,\left(5\,b\,d+a\,h\right)}{16\,a\,b}+\frac{x^3\,\left(9\,b\,e+a\,i\right)}{32\,a\,b}}{a^2-2\,a\,b\,x^4+b^2\,x^8}","Not used",1,"symsum(log((27*a^4*i^3 - 125*a*b^3*e^3 - 3024*b^4*c*d^2 + 2205*b^4*c^2*e - 336*a^2*b^2*c*h^2 + 45*a^2*b^2*e*g^2 + 225*a^2*b^2*e^2*i + 432*a*b^3*d^2*g - 1323*a*b^3*c^2*i - 135*a^3*b*e*i^2 + 48*a^3*b*g*h^2 - 27*a^3*b*g^2*i + 378*a^2*b^2*c*g*i - 288*a^2*b^2*d*g*h + 2016*a*b^3*c*d*h - 630*a*b^3*c*e*g)/(32768*a^6*b^2) - root(268435456*a^11*b^7*z^4 - 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 - 6881280*a^6*b^6*c*e*z^2 - 524288*a^8*b^4*h^2*z^2 - 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z + 258048*a^5*b^4*c*g*h*z - 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z - 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z - 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z + 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z + 2709504*a^3*b^6*c^2*d*z + 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h + 40320*a^2*b^4*c*d*e*h - 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i + 4032*a^4*b^2*c*h^2*i + 960*a^4*b^2*e*g*h^2 - 2268*a^4*b^2*c*g*i^2 - 26460*a^2*b^4*c^2*e*i + 36288*a^2*b^4*c*d^2*i + 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 - 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g - 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 - 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i - 27648*a^2*b^4*d^3*h - 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 - 81*a^4*b^2*g^4 - 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 - 81*a^6*i^4 - 194481*b^6*c^4, z, l)*(root(268435456*a^11*b^7*z^4 - 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 - 6881280*a^6*b^6*c*e*z^2 - 524288*a^8*b^4*h^2*z^2 - 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z + 258048*a^5*b^4*c*g*h*z - 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z - 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z - 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z + 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z + 2709504*a^3*b^6*c^2*d*z + 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h + 40320*a^2*b^4*c*d*e*h - 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i + 4032*a^4*b^2*c*h^2*i + 960*a^4*b^2*e*g*h^2 - 2268*a^4*b^2*c*g*i^2 - 26460*a^2*b^4*c^2*e*i + 36288*a^2*b^4*c*d^2*i + 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 - 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g - 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 - 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i - 27648*a^2*b^4*d^3*h - 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 - 81*a^4*b^2*g^4 - 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 - 81*a^6*i^4 - 194481*b^6*c^4, z, l)*((344064*a^5*b^5*c - 49152*a^6*b^4*g)/(32768*a^6*b^2) - (x*(24576*a^5*b^4*d - 8192*a^6*b^3*h))/(4096*a^6*b)) - (15360*a^3*b^4*d*e - 9216*a^4*b^3*d*i - 5120*a^4*b^3*e*h + 3072*a^5*b^2*h*i)/(32768*a^6*b^2) + (x*(144*a^5*b*i^2 + 7056*a^2*b^4*c^2 + 400*a^3*b^3*e^2 + 144*a^4*b^2*g^2 - 2016*a^3*b^3*c*g - 480*a^4*b^2*e*i))/(4096*a^6*b)) - (x*(216*b^3*d^3 - 8*a^3*h^3 - 315*b^3*c*d*e + 9*a^3*g*h*i - 216*a*b^2*d^2*h + 72*a^2*b*d*h^2 + 189*a*b^2*c*d*i + 105*a*b^2*c*e*h + 45*a*b^2*d*e*g - 63*a^2*b*c*h*i - 27*a^2*b*d*g*i - 15*a^2*b*e*g*h))/(4096*a^6*b))*root(268435456*a^11*b^7*z^4 - 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 - 6881280*a^6*b^6*c*e*z^2 - 524288*a^8*b^4*h^2*z^2 - 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z + 258048*a^5*b^4*c*g*h*z - 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z - 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z - 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z + 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z + 2709504*a^3*b^6*c^2*d*z + 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h + 40320*a^2*b^4*c*d*e*h - 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i + 4032*a^4*b^2*c*h^2*i + 960*a^4*b^2*e*g*h^2 - 2268*a^4*b^2*c*g*i^2 - 26460*a^2*b^4*c^2*e*i + 36288*a^2*b^4*c*d^2*i + 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 - 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g - 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 - 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i - 27648*a^2*b^4*d^3*h - 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 - 81*a^4*b^2*g^4 - 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 - 81*a^6*i^4 - 194481*b^6*c^4, z, l), l, 1, 4) + (f/(8*b) - (x^5*(7*b*c - a*g))/(32*a^2) - (x^6*(3*b*d - a*h))/(16*a^2) - (x^7*(5*b*e - 3*a*i))/(32*a^2) + (x*(11*b*c + 3*a*g))/(32*a*b) + (x^2*(5*b*d + a*h))/(16*a*b) + (x^3*(9*b*e + a*i))/(32*a*b))/(a^2 + b^2*x^8 - 2*a*b*x^4)","B"
200,1,2696,285,5.909694,"\text{Not used}","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)","\left(\sum _{m=1}^4\ln\left(-\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4-589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2-6881280\,a^6\,b^6\,c\,e\,z^2-524288\,a^8\,b^4\,h^2\,z^2-4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z+258048\,a^5\,b^4\,c\,g\,h\,z-184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z-18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z-51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z+55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z+2709504\,a^3\,b^6\,c^2\,d\,z+3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h+40320\,a^2\,b^4\,c\,d\,e\,h-540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i+4032\,a^4\,b^2\,c\,h^2\,i+960\,a^4\,b^2\,e\,g\,h^2-2268\,a^4\,b^2\,c\,g\,i^2-26460\,a^2\,b^4\,c^2\,e\,i+36288\,a^2\,b^4\,c\,d^2\,i+8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2-6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g-1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2-23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i-27648\,a^2\,b^4\,d^3\,h-3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2-81\,a^4\,b^2\,g^4-625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4-81\,a^6\,i^4-194481\,b^6\,c^4,z,m\right)\,\left(\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4-589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2-6881280\,a^6\,b^6\,c\,e\,z^2-524288\,a^8\,b^4\,h^2\,z^2-4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z+258048\,a^5\,b^4\,c\,g\,h\,z-184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z-18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z-51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z+55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z+2709504\,a^3\,b^6\,c^2\,d\,z+3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h+40320\,a^2\,b^4\,c\,d\,e\,h-540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i+4032\,a^4\,b^2\,c\,h^2\,i+960\,a^4\,b^2\,e\,g\,h^2-2268\,a^4\,b^2\,c\,g\,i^2-26460\,a^2\,b^4\,c^2\,e\,i+36288\,a^2\,b^4\,c\,d^2\,i+8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2-6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g-1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2-23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i-27648\,a^2\,b^4\,d^3\,h-3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2-81\,a^4\,b^2\,g^4-625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4-81\,a^6\,i^4-194481\,b^6\,c^4,z,m\right)\,\left(\frac{344064\,a^5\,b^5\,c-49152\,a^6\,b^4\,g}{32768\,a^6\,b^2}-\frac{x\,\left(24576\,a^5\,b^4\,d-8192\,a^6\,b^3\,h\right)}{4096\,a^6\,b}\right)-\frac{15360\,a^3\,b^4\,d\,e-9216\,a^4\,b^3\,d\,i-5120\,a^4\,b^3\,e\,h+3072\,a^5\,b^2\,h\,i}{32768\,a^6\,b^2}+\frac{x\,\left(144\,a^5\,b\,i^2-480\,a^4\,b^2\,e\,i+144\,a^4\,b^2\,g^2-2016\,a^3\,b^3\,c\,g+400\,a^3\,b^3\,e^2+7056\,a^2\,b^4\,c^2\right)}{4096\,a^6\,b}\right)+\frac{27\,a^4\,i^3-135\,a^3\,b\,e\,i^2-27\,a^3\,b\,g^2\,i+48\,a^3\,b\,g\,h^2+378\,a^2\,b^2\,c\,g\,i-336\,a^2\,b^2\,c\,h^2-288\,a^2\,b^2\,d\,g\,h+225\,a^2\,b^2\,e^2\,i+45\,a^2\,b^2\,e\,g^2-1323\,a\,b^3\,c^2\,i+2016\,a\,b^3\,c\,d\,h-630\,a\,b^3\,c\,e\,g+432\,a\,b^3\,d^2\,g-125\,a\,b^3\,e^3+2205\,b^4\,c^2\,e-3024\,b^4\,c\,d^2}{32768\,a^6\,b^2}-\frac{x\,\left(216\,b^3\,d^3-8\,a^3\,h^3-315\,b^3\,c\,d\,e+9\,a^3\,g\,h\,i-216\,a\,b^2\,d^2\,h+72\,a^2\,b\,d\,h^2+189\,a\,b^2\,c\,d\,i+105\,a\,b^2\,c\,e\,h+45\,a\,b^2\,d\,e\,g-63\,a^2\,b\,c\,h\,i-27\,a^2\,b\,d\,g\,i-15\,a^2\,b\,e\,g\,h\right)}{4096\,a^6\,b}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4-589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2-6881280\,a^6\,b^6\,c\,e\,z^2-524288\,a^8\,b^4\,h^2\,z^2-4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z+258048\,a^5\,b^4\,c\,g\,h\,z-184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z-18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z-51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z+55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z+2709504\,a^3\,b^6\,c^2\,d\,z+3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h+40320\,a^2\,b^4\,c\,d\,e\,h-540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i+4032\,a^4\,b^2\,c\,h^2\,i+960\,a^4\,b^2\,e\,g\,h^2-2268\,a^4\,b^2\,c\,g\,i^2-26460\,a^2\,b^4\,c^2\,e\,i+36288\,a^2\,b^4\,c\,d^2\,i+8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2-6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g-1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2-23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i-27648\,a^2\,b^4\,d^3\,h-3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2-81\,a^4\,b^2\,g^4-625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4-81\,a^6\,i^4-194481\,b^6\,c^4,z,m\right)\right)+\frac{\frac{b\,f-a\,j}{8\,b^2}+\frac{j\,x^4}{4\,b}-\frac{x^5\,\left(7\,b\,c-a\,g\right)}{32\,a^2}-\frac{x^6\,\left(3\,b\,d-a\,h\right)}{16\,a^2}-\frac{x^7\,\left(5\,b\,e-3\,a\,i\right)}{32\,a^2}+\frac{x\,\left(11\,b\,c+3\,a\,g\right)}{32\,a\,b}+\frac{x^2\,\left(5\,b\,d+a\,h\right)}{16\,a\,b}+\frac{x^3\,\left(9\,b\,e+a\,i\right)}{32\,a\,b}}{a^2-2\,a\,b\,x^4+b^2\,x^8}","Not used",1,"symsum(log((27*a^4*i^3 - 125*a*b^3*e^3 - 3024*b^4*c*d^2 + 2205*b^4*c^2*e - 336*a^2*b^2*c*h^2 + 45*a^2*b^2*e*g^2 + 225*a^2*b^2*e^2*i + 432*a*b^3*d^2*g - 1323*a*b^3*c^2*i - 135*a^3*b*e*i^2 + 48*a^3*b*g*h^2 - 27*a^3*b*g^2*i + 378*a^2*b^2*c*g*i - 288*a^2*b^2*d*g*h + 2016*a*b^3*c*d*h - 630*a*b^3*c*e*g)/(32768*a^6*b^2) - root(268435456*a^11*b^7*z^4 - 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 - 6881280*a^6*b^6*c*e*z^2 - 524288*a^8*b^4*h^2*z^2 - 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z + 258048*a^5*b^4*c*g*h*z - 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z - 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z - 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z + 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z + 2709504*a^3*b^6*c^2*d*z + 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h + 40320*a^2*b^4*c*d*e*h - 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i + 4032*a^4*b^2*c*h^2*i + 960*a^4*b^2*e*g*h^2 - 2268*a^4*b^2*c*g*i^2 - 26460*a^2*b^4*c^2*e*i + 36288*a^2*b^4*c*d^2*i + 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 - 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g - 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 - 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i - 27648*a^2*b^4*d^3*h - 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 - 81*a^4*b^2*g^4 - 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 - 81*a^6*i^4 - 194481*b^6*c^4, z, m)*(root(268435456*a^11*b^7*z^4 - 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 - 6881280*a^6*b^6*c*e*z^2 - 524288*a^8*b^4*h^2*z^2 - 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z + 258048*a^5*b^4*c*g*h*z - 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z - 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z - 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z + 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z + 2709504*a^3*b^6*c^2*d*z + 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h + 40320*a^2*b^4*c*d*e*h - 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i + 4032*a^4*b^2*c*h^2*i + 960*a^4*b^2*e*g*h^2 - 2268*a^4*b^2*c*g*i^2 - 26460*a^2*b^4*c^2*e*i + 36288*a^2*b^4*c*d^2*i + 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 - 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g - 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 - 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i - 27648*a^2*b^4*d^3*h - 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 - 81*a^4*b^2*g^4 - 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 - 81*a^6*i^4 - 194481*b^6*c^4, z, m)*((344064*a^5*b^5*c - 49152*a^6*b^4*g)/(32768*a^6*b^2) - (x*(24576*a^5*b^4*d - 8192*a^6*b^3*h))/(4096*a^6*b)) - (15360*a^3*b^4*d*e - 9216*a^4*b^3*d*i - 5120*a^4*b^3*e*h + 3072*a^5*b^2*h*i)/(32768*a^6*b^2) + (x*(144*a^5*b*i^2 + 7056*a^2*b^4*c^2 + 400*a^3*b^3*e^2 + 144*a^4*b^2*g^2 - 2016*a^3*b^3*c*g - 480*a^4*b^2*e*i))/(4096*a^6*b)) - (x*(216*b^3*d^3 - 8*a^3*h^3 - 315*b^3*c*d*e + 9*a^3*g*h*i - 216*a*b^2*d^2*h + 72*a^2*b*d*h^2 + 189*a*b^2*c*d*i + 105*a*b^2*c*e*h + 45*a*b^2*d*e*g - 63*a^2*b*c*h*i - 27*a^2*b*d*g*i - 15*a^2*b*e*g*h))/(4096*a^6*b))*root(268435456*a^11*b^7*z^4 - 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 - 6881280*a^6*b^6*c*e*z^2 - 524288*a^8*b^4*h^2*z^2 - 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z + 258048*a^5*b^4*c*g*h*z - 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z - 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z - 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z + 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z + 2709504*a^3*b^6*c^2*d*z + 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h + 40320*a^2*b^4*c*d*e*h - 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i + 4032*a^4*b^2*c*h^2*i + 960*a^4*b^2*e*g*h^2 - 2268*a^4*b^2*c*g*i^2 - 26460*a^2*b^4*c^2*e*i + 36288*a^2*b^4*c*d^2*i + 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 - 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g - 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 - 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i - 27648*a^2*b^4*d^3*h - 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 - 81*a^4*b^2*g^4 - 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 - 81*a^6*i^4 - 194481*b^6*c^4, z, m), m, 1, 4) + ((b*f - a*j)/(8*b^2) + (j*x^4)/(4*b) - (x^5*(7*b*c - a*g))/(32*a^2) - (x^6*(3*b*d - a*h))/(16*a^2) - (x^7*(5*b*e - 3*a*i))/(32*a^2) + (x*(11*b*c + 3*a*g))/(32*a*b) + (x^2*(5*b*d + a*h))/(16*a*b) + (x^3*(9*b*e + a*i))/(32*a*b))/(a^2 + b^2*x^8 - 2*a*b*x^4)","B"
201,1,1686,413,5.691119,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4)^3,x)","\frac{\frac{9\,e\,x^3}{32\,a}-\frac{f}{8\,b}+\frac{x^5\,\left(7\,b\,c+a\,g\right)}{32\,a^2}+\frac{x^6\,\left(3\,b\,d+a\,h\right)}{16\,a^2}+\frac{x\,\left(11\,b\,c-3\,a\,g\right)}{32\,a\,b}+\frac{x^2\,\left(5\,b\,d-a\,h\right)}{16\,a\,b}+\frac{5\,b\,e\,x^7}{32\,a^2}}{a^2+2\,a\,b\,x^4+b^2\,x^8}+\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(268435456\,a^{11}\,b^6\,z^4+3145728\,a^7\,b^4\,d\,h\,z^2+983040\,a^7\,b^4\,e\,g\,z^2+6881280\,a^6\,b^5\,c\,e\,z^2+524288\,a^8\,b^3\,h^2\,z^2+4718592\,a^6\,b^5\,d^2\,z^2-258048\,a^5\,b^3\,c\,g\,h\,z-774144\,a^4\,b^4\,c\,d\,g\,z-18432\,a^6\,b^2\,g^2\,h\,z+51200\,a^5\,b^3\,e^2\,h\,z-903168\,a^4\,b^4\,c^2\,h\,z-55296\,a^5\,b^3\,d\,g^2\,z+153600\,a^4\,b^4\,d\,e^2\,z-2709504\,a^3\,b^5\,c^2\,d\,z-5760\,a^3\,b^2\,d\,e\,g\,h-40320\,a^2\,b^3\,c\,d\,e\,h-8640\,a^2\,b^3\,d^2\,e\,g-6720\,a^3\,b^2\,c\,e\,h^2+6300\,a^2\,b^3\,c\,e^2\,g-960\,a^4\,b\,e\,g\,h^2-60480\,a\,b^4\,c\,d^2\,e+3072\,a^4\,b\,d\,h^3+111132\,a\,b^4\,c^3\,g+13824\,a^3\,b^2\,d^2\,h^2+450\,a^3\,b^2\,e^2\,g^2+23814\,a^2\,b^3\,c^2\,g^2+27648\,a^2\,b^3\,d^3\,h+2268\,a^3\,b^2\,c\,g^3+22050\,a\,b^4\,c^2\,e^2+625\,a^2\,b^3\,e^4+81\,a^4\,b\,g^4+20736\,a\,b^4\,d^4+256\,a^5\,h^4+194481\,b^5\,c^4,z,k\right)\,\left(\mathrm{root}\left(268435456\,a^{11}\,b^6\,z^4+3145728\,a^7\,b^4\,d\,h\,z^2+983040\,a^7\,b^4\,e\,g\,z^2+6881280\,a^6\,b^5\,c\,e\,z^2+524288\,a^8\,b^3\,h^2\,z^2+4718592\,a^6\,b^5\,d^2\,z^2-258048\,a^5\,b^3\,c\,g\,h\,z-774144\,a^4\,b^4\,c\,d\,g\,z-18432\,a^6\,b^2\,g^2\,h\,z+51200\,a^5\,b^3\,e^2\,h\,z-903168\,a^4\,b^4\,c^2\,h\,z-55296\,a^5\,b^3\,d\,g^2\,z+153600\,a^4\,b^4\,d\,e^2\,z-2709504\,a^3\,b^5\,c^2\,d\,z-5760\,a^3\,b^2\,d\,e\,g\,h-40320\,a^2\,b^3\,c\,d\,e\,h-8640\,a^2\,b^3\,d^2\,e\,g-6720\,a^3\,b^2\,c\,e\,h^2+6300\,a^2\,b^3\,c\,e^2\,g-960\,a^4\,b\,e\,g\,h^2-60480\,a\,b^4\,c\,d^2\,e+3072\,a^4\,b\,d\,h^3+111132\,a\,b^4\,c^3\,g+13824\,a^3\,b^2\,d^2\,h^2+450\,a^3\,b^2\,e^2\,g^2+23814\,a^2\,b^3\,c^2\,g^2+27648\,a^2\,b^3\,d^3\,h+2268\,a^3\,b^2\,c\,g^3+22050\,a\,b^4\,c^2\,e^2+625\,a^2\,b^3\,e^4+81\,a^4\,b\,g^4+20736\,a\,b^4\,d^4+256\,a^5\,h^4+194481\,b^5\,c^4,z,k\right)\,\left(\frac{49152\,g\,a^6\,b^3+344064\,c\,a^5\,b^4}{32768\,a^6\,b}-\frac{x\,\left(8192\,h\,a^6\,b^3+24576\,d\,a^5\,b^4\right)}{4096\,a^6\,b}\right)+\frac{5120\,e\,h\,a^4\,b^2+15360\,d\,e\,a^3\,b^3}{32768\,a^6\,b}+\frac{x\,\left(144\,a^4\,b^2\,g^2+2016\,a^3\,b^3\,c\,g-400\,a^3\,b^3\,e^2+7056\,a^2\,b^4\,c^2\right)}{4096\,a^6\,b}\right)+\frac{48\,a^3\,g\,h^2+336\,a^2\,b\,c\,h^2+288\,a^2\,b\,d\,g\,h-45\,a^2\,b\,e\,g^2+2016\,a\,b^2\,c\,d\,h-630\,a\,b^2\,c\,e\,g+432\,a\,b^2\,d^2\,g-125\,a\,b^2\,e^3-2205\,b^3\,c^2\,e+3024\,b^3\,c\,d^2}{32768\,a^6\,b}+\frac{x\,\left(8\,a^3\,h^3+72\,a^2\,b\,d\,h^2-15\,e\,g\,a^2\,b\,h+216\,a\,b^2\,d^2\,h-45\,e\,g\,a\,b^2\,d-105\,c\,e\,a\,b^2\,h+216\,b^3\,d^3-315\,c\,e\,b^3\,d\right)}{4096\,a^6\,b}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^6\,z^4+3145728\,a^7\,b^4\,d\,h\,z^2+983040\,a^7\,b^4\,e\,g\,z^2+6881280\,a^6\,b^5\,c\,e\,z^2+524288\,a^8\,b^3\,h^2\,z^2+4718592\,a^6\,b^5\,d^2\,z^2-258048\,a^5\,b^3\,c\,g\,h\,z-774144\,a^4\,b^4\,c\,d\,g\,z-18432\,a^6\,b^2\,g^2\,h\,z+51200\,a^5\,b^3\,e^2\,h\,z-903168\,a^4\,b^4\,c^2\,h\,z-55296\,a^5\,b^3\,d\,g^2\,z+153600\,a^4\,b^4\,d\,e^2\,z-2709504\,a^3\,b^5\,c^2\,d\,z-5760\,a^3\,b^2\,d\,e\,g\,h-40320\,a^2\,b^3\,c\,d\,e\,h-8640\,a^2\,b^3\,d^2\,e\,g-6720\,a^3\,b^2\,c\,e\,h^2+6300\,a^2\,b^3\,c\,e^2\,g-960\,a^4\,b\,e\,g\,h^2-60480\,a\,b^4\,c\,d^2\,e+3072\,a^4\,b\,d\,h^3+111132\,a\,b^4\,c^3\,g+13824\,a^3\,b^2\,d^2\,h^2+450\,a^3\,b^2\,e^2\,g^2+23814\,a^2\,b^3\,c^2\,g^2+27648\,a^2\,b^3\,d^3\,h+2268\,a^3\,b^2\,c\,g^3+22050\,a\,b^4\,c^2\,e^2+625\,a^2\,b^3\,e^4+81\,a^4\,b\,g^4+20736\,a\,b^4\,d^4+256\,a^5\,h^4+194481\,b^5\,c^4,z,k\right)\right)","Not used",1,"((9*e*x^3)/(32*a) - f/(8*b) + (x^5*(7*b*c + a*g))/(32*a^2) + (x^6*(3*b*d + a*h))/(16*a^2) + (x*(11*b*c - 3*a*g))/(32*a*b) + (x^2*(5*b*d - a*h))/(16*a*b) + (5*b*e*x^7)/(32*a^2))/(a^2 + b^2*x^8 + 2*a*b*x^4) + symsum(log((3024*b^3*c*d^2 - 125*a*b^2*e^3 - 2205*b^3*c^2*e + 48*a^3*g*h^2 + 432*a*b^2*d^2*g + 336*a^2*b*c*h^2 - 45*a^2*b*e*g^2 + 2016*a*b^2*c*d*h - 630*a*b^2*c*e*g + 288*a^2*b*d*g*h)/(32768*a^6*b) - root(268435456*a^11*b^6*z^4 + 3145728*a^7*b^4*d*h*z^2 + 983040*a^7*b^4*e*g*z^2 + 6881280*a^6*b^5*c*e*z^2 + 524288*a^8*b^3*h^2*z^2 + 4718592*a^6*b^5*d^2*z^2 - 258048*a^5*b^3*c*g*h*z - 774144*a^4*b^4*c*d*g*z - 18432*a^6*b^2*g^2*h*z + 51200*a^5*b^3*e^2*h*z - 903168*a^4*b^4*c^2*h*z - 55296*a^5*b^3*d*g^2*z + 153600*a^4*b^4*d*e^2*z - 2709504*a^3*b^5*c^2*d*z - 5760*a^3*b^2*d*e*g*h - 40320*a^2*b^3*c*d*e*h - 8640*a^2*b^3*d^2*e*g - 6720*a^3*b^2*c*e*h^2 + 6300*a^2*b^3*c*e^2*g - 960*a^4*b*e*g*h^2 - 60480*a*b^4*c*d^2*e + 3072*a^4*b*d*h^3 + 111132*a*b^4*c^3*g + 13824*a^3*b^2*d^2*h^2 + 450*a^3*b^2*e^2*g^2 + 23814*a^2*b^3*c^2*g^2 + 27648*a^2*b^3*d^3*h + 2268*a^3*b^2*c*g^3 + 22050*a*b^4*c^2*e^2 + 625*a^2*b^3*e^4 + 81*a^4*b*g^4 + 20736*a*b^4*d^4 + 256*a^5*h^4 + 194481*b^5*c^4, z, k)*(root(268435456*a^11*b^6*z^4 + 3145728*a^7*b^4*d*h*z^2 + 983040*a^7*b^4*e*g*z^2 + 6881280*a^6*b^5*c*e*z^2 + 524288*a^8*b^3*h^2*z^2 + 4718592*a^6*b^5*d^2*z^2 - 258048*a^5*b^3*c*g*h*z - 774144*a^4*b^4*c*d*g*z - 18432*a^6*b^2*g^2*h*z + 51200*a^5*b^3*e^2*h*z - 903168*a^4*b^4*c^2*h*z - 55296*a^5*b^3*d*g^2*z + 153600*a^4*b^4*d*e^2*z - 2709504*a^3*b^5*c^2*d*z - 5760*a^3*b^2*d*e*g*h - 40320*a^2*b^3*c*d*e*h - 8640*a^2*b^3*d^2*e*g - 6720*a^3*b^2*c*e*h^2 + 6300*a^2*b^3*c*e^2*g - 960*a^4*b*e*g*h^2 - 60480*a*b^4*c*d^2*e + 3072*a^4*b*d*h^3 + 111132*a*b^4*c^3*g + 13824*a^3*b^2*d^2*h^2 + 450*a^3*b^2*e^2*g^2 + 23814*a^2*b^3*c^2*g^2 + 27648*a^2*b^3*d^3*h + 2268*a^3*b^2*c*g^3 + 22050*a*b^4*c^2*e^2 + 625*a^2*b^3*e^4 + 81*a^4*b*g^4 + 20736*a*b^4*d^4 + 256*a^5*h^4 + 194481*b^5*c^4, z, k)*((344064*a^5*b^4*c + 49152*a^6*b^3*g)/(32768*a^6*b) - (x*(24576*a^5*b^4*d + 8192*a^6*b^3*h))/(4096*a^6*b)) + (15360*a^3*b^3*d*e + 5120*a^4*b^2*e*h)/(32768*a^6*b) + (x*(7056*a^2*b^4*c^2 - 400*a^3*b^3*e^2 + 144*a^4*b^2*g^2 + 2016*a^3*b^3*c*g))/(4096*a^6*b)) + (x*(216*b^3*d^3 + 8*a^3*h^3 - 315*b^3*c*d*e + 216*a*b^2*d^2*h + 72*a^2*b*d*h^2 - 105*a*b^2*c*e*h - 45*a*b^2*d*e*g - 15*a^2*b*e*g*h))/(4096*a^6*b))*root(268435456*a^11*b^6*z^4 + 3145728*a^7*b^4*d*h*z^2 + 983040*a^7*b^4*e*g*z^2 + 6881280*a^6*b^5*c*e*z^2 + 524288*a^8*b^3*h^2*z^2 + 4718592*a^6*b^5*d^2*z^2 - 258048*a^5*b^3*c*g*h*z - 774144*a^4*b^4*c*d*g*z - 18432*a^6*b^2*g^2*h*z + 51200*a^5*b^3*e^2*h*z - 903168*a^4*b^4*c^2*h*z - 55296*a^5*b^3*d*g^2*z + 153600*a^4*b^4*d*e^2*z - 2709504*a^3*b^5*c^2*d*z - 5760*a^3*b^2*d*e*g*h - 40320*a^2*b^3*c*d*e*h - 8640*a^2*b^3*d^2*e*g - 6720*a^3*b^2*c*e*h^2 + 6300*a^2*b^3*c*e^2*g - 960*a^4*b*e*g*h^2 - 60480*a*b^4*c*d^2*e + 3072*a^4*b*d*h^3 + 111132*a*b^4*c^3*g + 13824*a^3*b^2*d^2*h^2 + 450*a^3*b^2*e^2*g^2 + 23814*a^2*b^3*c^2*g^2 + 27648*a^2*b^3*d^3*h + 2268*a^3*b^2*c*g^3 + 22050*a*b^4*c^2*e^2 + 625*a^2*b^3*e^4 + 81*a^4*b*g^4 + 20736*a*b^4*d^4 + 256*a^5*h^4 + 194481*b^5*c^4, z, k), k, 1, 4)","B"
202,1,2680,463,5.749008,"\text{Not used}","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)","\left(\sum _{l=1}^4\ln\left(-\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4+589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2+6881280\,a^6\,b^6\,c\,e\,z^2+524288\,a^8\,b^4\,h^2\,z^2+4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z-258048\,a^5\,b^4\,c\,g\,h\,z+184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z+18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z+51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z-55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z-2709504\,a^3\,b^6\,c^2\,d\,z-3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h-40320\,a^2\,b^4\,c\,d\,e\,h+540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i-4032\,a^4\,b^2\,c\,h^2\,i-960\,a^4\,b^2\,e\,g\,h^2+2268\,a^4\,b^2\,c\,g\,i^2+26460\,a^2\,b^4\,c^2\,e\,i-36288\,a^2\,b^4\,c\,d^2\,i-8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2+6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g+1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2+23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i+27648\,a^2\,b^4\,d^3\,h+3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2+81\,a^4\,b^2\,g^4+625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4+81\,a^6\,i^4+194481\,b^6\,c^4,z,l\right)\,\left(\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4+589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2+6881280\,a^6\,b^6\,c\,e\,z^2+524288\,a^8\,b^4\,h^2\,z^2+4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z-258048\,a^5\,b^4\,c\,g\,h\,z+184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z+18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z+51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z-55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z-2709504\,a^3\,b^6\,c^2\,d\,z-3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h-40320\,a^2\,b^4\,c\,d\,e\,h+540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i-4032\,a^4\,b^2\,c\,h^2\,i-960\,a^4\,b^2\,e\,g\,h^2+2268\,a^4\,b^2\,c\,g\,i^2+26460\,a^2\,b^4\,c^2\,e\,i-36288\,a^2\,b^4\,c\,d^2\,i-8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2+6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g+1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2+23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i+27648\,a^2\,b^4\,d^3\,h+3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2+81\,a^4\,b^2\,g^4+625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4+81\,a^6\,i^4+194481\,b^6\,c^4,z,l\right)\,\left(\frac{49152\,g\,a^6\,b^4+344064\,c\,a^5\,b^5}{32768\,a^6\,b^2}-\frac{x\,\left(8192\,h\,a^6\,b^3+24576\,d\,a^5\,b^4\right)}{4096\,a^6\,b}\right)+\frac{15360\,a^3\,b^4\,d\,e+9216\,a^4\,b^3\,d\,i+5120\,a^4\,b^3\,e\,h+3072\,a^5\,b^2\,h\,i}{32768\,a^6\,b^2}-\frac{x\,\left(144\,a^5\,b\,i^2+480\,a^4\,b^2\,e\,i-144\,a^4\,b^2\,g^2-2016\,a^3\,b^3\,c\,g+400\,a^3\,b^3\,e^2-7056\,a^2\,b^4\,c^2\right)}{4096\,a^6\,b}\right)-\frac{27\,a^4\,i^3+135\,a^3\,b\,e\,i^2+27\,a^3\,b\,g^2\,i-48\,a^3\,b\,g\,h^2+378\,a^2\,b^2\,c\,g\,i-336\,a^2\,b^2\,c\,h^2-288\,a^2\,b^2\,d\,g\,h+225\,a^2\,b^2\,e^2\,i+45\,a^2\,b^2\,e\,g^2+1323\,a\,b^3\,c^2\,i-2016\,a\,b^3\,c\,d\,h+630\,a\,b^3\,c\,e\,g-432\,a\,b^3\,d^2\,g+125\,a\,b^3\,e^3+2205\,b^4\,c^2\,e-3024\,b^4\,c\,d^2}{32768\,a^6\,b^2}-\frac{x\,\left(315\,b^3\,c\,d\,e-8\,a^3\,h^3-216\,b^3\,d^3+9\,a^3\,g\,h\,i-216\,a\,b^2\,d^2\,h-72\,a^2\,b\,d\,h^2+189\,a\,b^2\,c\,d\,i+105\,a\,b^2\,c\,e\,h+45\,a\,b^2\,d\,e\,g+63\,a^2\,b\,c\,h\,i+27\,a^2\,b\,d\,g\,i+15\,a^2\,b\,e\,g\,h\right)}{4096\,a^6\,b}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4+589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2+6881280\,a^6\,b^6\,c\,e\,z^2+524288\,a^8\,b^4\,h^2\,z^2+4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z-258048\,a^5\,b^4\,c\,g\,h\,z+184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z+18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z+51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z-55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z-2709504\,a^3\,b^6\,c^2\,d\,z-3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h-40320\,a^2\,b^4\,c\,d\,e\,h+540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i-4032\,a^4\,b^2\,c\,h^2\,i-960\,a^4\,b^2\,e\,g\,h^2+2268\,a^4\,b^2\,c\,g\,i^2+26460\,a^2\,b^4\,c^2\,e\,i-36288\,a^2\,b^4\,c\,d^2\,i-8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2+6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g+1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2+23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i+27648\,a^2\,b^4\,d^3\,h+3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2+81\,a^4\,b^2\,g^4+625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4+81\,a^6\,i^4+194481\,b^6\,c^4,z,l\right)\right)+\frac{\frac{x^5\,\left(7\,b\,c+a\,g\right)}{32\,a^2}-\frac{f}{8\,b}+\frac{x^6\,\left(3\,b\,d+a\,h\right)}{16\,a^2}+\frac{x^7\,\left(5\,b\,e+3\,a\,i\right)}{32\,a^2}+\frac{x\,\left(11\,b\,c-3\,a\,g\right)}{32\,a\,b}+\frac{x^2\,\left(5\,b\,d-a\,h\right)}{16\,a\,b}+\frac{x^3\,\left(9\,b\,e-a\,i\right)}{32\,a\,b}}{a^2+2\,a\,b\,x^4+b^2\,x^8}","Not used",1,"symsum(log(- root(268435456*a^11*b^7*z^4 + 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 + 6881280*a^6*b^6*c*e*z^2 + 524288*a^8*b^4*h^2*z^2 + 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z - 258048*a^5*b^4*c*g*h*z + 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z + 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z + 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z - 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z - 2709504*a^3*b^6*c^2*d*z - 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h - 40320*a^2*b^4*c*d*e*h + 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i - 4032*a^4*b^2*c*h^2*i - 960*a^4*b^2*e*g*h^2 + 2268*a^4*b^2*c*g*i^2 + 26460*a^2*b^4*c^2*e*i - 36288*a^2*b^4*c*d^2*i - 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 + 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g + 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 + 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i + 27648*a^2*b^4*d^3*h + 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 + 81*a^4*b^2*g^4 + 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 + 81*a^6*i^4 + 194481*b^6*c^4, z, l)*(root(268435456*a^11*b^7*z^4 + 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 + 6881280*a^6*b^6*c*e*z^2 + 524288*a^8*b^4*h^2*z^2 + 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z - 258048*a^5*b^4*c*g*h*z + 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z + 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z + 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z - 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z - 2709504*a^3*b^6*c^2*d*z - 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h - 40320*a^2*b^4*c*d*e*h + 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i - 4032*a^4*b^2*c*h^2*i - 960*a^4*b^2*e*g*h^2 + 2268*a^4*b^2*c*g*i^2 + 26460*a^2*b^4*c^2*e*i - 36288*a^2*b^4*c*d^2*i - 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 + 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g + 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 + 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i + 27648*a^2*b^4*d^3*h + 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 + 81*a^4*b^2*g^4 + 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 + 81*a^6*i^4 + 194481*b^6*c^4, z, l)*((344064*a^5*b^5*c + 49152*a^6*b^4*g)/(32768*a^6*b^2) - (x*(24576*a^5*b^4*d + 8192*a^6*b^3*h))/(4096*a^6*b)) + (15360*a^3*b^4*d*e + 9216*a^4*b^3*d*i + 5120*a^4*b^3*e*h + 3072*a^5*b^2*h*i)/(32768*a^6*b^2) - (x*(144*a^5*b*i^2 - 7056*a^2*b^4*c^2 + 400*a^3*b^3*e^2 - 144*a^4*b^2*g^2 - 2016*a^3*b^3*c*g + 480*a^4*b^2*e*i))/(4096*a^6*b)) - (27*a^4*i^3 + 125*a*b^3*e^3 - 3024*b^4*c*d^2 + 2205*b^4*c^2*e - 336*a^2*b^2*c*h^2 + 45*a^2*b^2*e*g^2 + 225*a^2*b^2*e^2*i - 432*a*b^3*d^2*g + 1323*a*b^3*c^2*i + 135*a^3*b*e*i^2 - 48*a^3*b*g*h^2 + 27*a^3*b*g^2*i + 378*a^2*b^2*c*g*i - 288*a^2*b^2*d*g*h - 2016*a*b^3*c*d*h + 630*a*b^3*c*e*g)/(32768*a^6*b^2) - (x*(315*b^3*c*d*e - 8*a^3*h^3 - 216*b^3*d^3 + 9*a^3*g*h*i - 216*a*b^2*d^2*h - 72*a^2*b*d*h^2 + 189*a*b^2*c*d*i + 105*a*b^2*c*e*h + 45*a*b^2*d*e*g + 63*a^2*b*c*h*i + 27*a^2*b*d*g*i + 15*a^2*b*e*g*h))/(4096*a^6*b))*root(268435456*a^11*b^7*z^4 + 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 + 6881280*a^6*b^6*c*e*z^2 + 524288*a^8*b^4*h^2*z^2 + 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z - 258048*a^5*b^4*c*g*h*z + 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z + 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z + 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z - 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z - 2709504*a^3*b^6*c^2*d*z - 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h - 40320*a^2*b^4*c*d*e*h + 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i - 4032*a^4*b^2*c*h^2*i - 960*a^4*b^2*e*g*h^2 + 2268*a^4*b^2*c*g*i^2 + 26460*a^2*b^4*c^2*e*i - 36288*a^2*b^4*c*d^2*i - 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 + 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g + 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 + 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i + 27648*a^2*b^4*d^3*h + 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 + 81*a^4*b^2*g^4 + 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 + 81*a^6*i^4 + 194481*b^6*c^4, z, l), l, 1, 4) + ((x^5*(7*b*c + a*g))/(32*a^2) - f/(8*b) + (x^6*(3*b*d + a*h))/(16*a^2) + (x^7*(5*b*e + 3*a*i))/(32*a^2) + (x*(11*b*c - 3*a*g))/(32*a*b) + (x^2*(5*b*d - a*h))/(16*a*b) + (x^3*(9*b*e - a*i))/(32*a*b))/(a^2 + b^2*x^8 + 2*a*b*x^4)","B"
203,1,2695,480,5.787780,"\text{Not used}","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)","\left(\sum _{m=1}^4\ln\left(-\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4+589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2+6881280\,a^6\,b^6\,c\,e\,z^2+524288\,a^8\,b^4\,h^2\,z^2+4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z-258048\,a^5\,b^4\,c\,g\,h\,z+184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z+18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z+51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z-55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z-2709504\,a^3\,b^6\,c^2\,d\,z-3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h-40320\,a^2\,b^4\,c\,d\,e\,h+540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i-4032\,a^4\,b^2\,c\,h^2\,i-960\,a^4\,b^2\,e\,g\,h^2+2268\,a^4\,b^2\,c\,g\,i^2+26460\,a^2\,b^4\,c^2\,e\,i-36288\,a^2\,b^4\,c\,d^2\,i-8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2+6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g+1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2+23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i+27648\,a^2\,b^4\,d^3\,h+3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2+81\,a^4\,b^2\,g^4+625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4+81\,a^6\,i^4+194481\,b^6\,c^4,z,m\right)\,\left(\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4+589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2+6881280\,a^6\,b^6\,c\,e\,z^2+524288\,a^8\,b^4\,h^2\,z^2+4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z-258048\,a^5\,b^4\,c\,g\,h\,z+184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z+18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z+51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z-55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z-2709504\,a^3\,b^6\,c^2\,d\,z-3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h-40320\,a^2\,b^4\,c\,d\,e\,h+540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i-4032\,a^4\,b^2\,c\,h^2\,i-960\,a^4\,b^2\,e\,g\,h^2+2268\,a^4\,b^2\,c\,g\,i^2+26460\,a^2\,b^4\,c^2\,e\,i-36288\,a^2\,b^4\,c\,d^2\,i-8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2+6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g+1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2+23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i+27648\,a^2\,b^4\,d^3\,h+3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2+81\,a^4\,b^2\,g^4+625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4+81\,a^6\,i^4+194481\,b^6\,c^4,z,m\right)\,\left(\frac{49152\,g\,a^6\,b^4+344064\,c\,a^5\,b^5}{32768\,a^6\,b^2}-\frac{x\,\left(8192\,h\,a^6\,b^3+24576\,d\,a^5\,b^4\right)}{4096\,a^6\,b}\right)+\frac{15360\,a^3\,b^4\,d\,e+9216\,a^4\,b^3\,d\,i+5120\,a^4\,b^3\,e\,h+3072\,a^5\,b^2\,h\,i}{32768\,a^6\,b^2}-\frac{x\,\left(144\,a^5\,b\,i^2+480\,a^4\,b^2\,e\,i-144\,a^4\,b^2\,g^2-2016\,a^3\,b^3\,c\,g+400\,a^3\,b^3\,e^2-7056\,a^2\,b^4\,c^2\right)}{4096\,a^6\,b}\right)-\frac{27\,a^4\,i^3+135\,a^3\,b\,e\,i^2+27\,a^3\,b\,g^2\,i-48\,a^3\,b\,g\,h^2+378\,a^2\,b^2\,c\,g\,i-336\,a^2\,b^2\,c\,h^2-288\,a^2\,b^2\,d\,g\,h+225\,a^2\,b^2\,e^2\,i+45\,a^2\,b^2\,e\,g^2+1323\,a\,b^3\,c^2\,i-2016\,a\,b^3\,c\,d\,h+630\,a\,b^3\,c\,e\,g-432\,a\,b^3\,d^2\,g+125\,a\,b^3\,e^3+2205\,b^4\,c^2\,e-3024\,b^4\,c\,d^2}{32768\,a^6\,b^2}-\frac{x\,\left(315\,b^3\,c\,d\,e-8\,a^3\,h^3-216\,b^3\,d^3+9\,a^3\,g\,h\,i-216\,a\,b^2\,d^2\,h-72\,a^2\,b\,d\,h^2+189\,a\,b^2\,c\,d\,i+105\,a\,b^2\,c\,e\,h+45\,a\,b^2\,d\,e\,g+63\,a^2\,b\,c\,h\,i+27\,a^2\,b\,d\,g\,i+15\,a^2\,b\,e\,g\,h\right)}{4096\,a^6\,b}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^7\,z^4+589824\,a^8\,b^4\,g\,i\,z^2+4128768\,a^7\,b^5\,c\,i\,z^2+3145728\,a^7\,b^5\,d\,h\,z^2+983040\,a^7\,b^5\,e\,g\,z^2+6881280\,a^6\,b^6\,c\,e\,z^2+524288\,a^8\,b^4\,h^2\,z^2+4718592\,a^6\,b^6\,d^2\,z^2+61440\,a^6\,b^3\,e\,h\,i\,z-258048\,a^5\,b^4\,c\,g\,h\,z+184320\,a^5\,b^4\,d\,e\,i\,z-774144\,a^4\,b^5\,c\,d\,g\,z+18432\,a^7\,b^2\,h\,i^2\,z-18432\,a^6\,b^3\,g^2\,h\,z+55296\,a^6\,b^3\,d\,i^2\,z+51200\,a^5\,b^4\,e^2\,h\,z-903168\,a^4\,b^5\,c^2\,h\,z-55296\,a^5\,b^4\,d\,g^2\,z+153600\,a^4\,b^5\,d\,e^2\,z-2709504\,a^3\,b^6\,c^2\,d\,z-3456\,a^4\,b^2\,d\,g\,h\,i-24192\,a^3\,b^3\,c\,d\,h\,i+7560\,a^3\,b^3\,c\,e\,g\,i-5760\,a^3\,b^3\,d\,e\,g\,h-40320\,a^2\,b^4\,c\,d\,e\,h+540\,a^4\,b^2\,e\,g^2\,i-5184\,a^3\,b^3\,d^2\,g\,i-4032\,a^4\,b^2\,c\,h^2\,i-960\,a^4\,b^2\,e\,g\,h^2+2268\,a^4\,b^2\,c\,g\,i^2+26460\,a^2\,b^4\,c^2\,e\,i-36288\,a^2\,b^4\,c\,d^2\,i-8640\,a^2\,b^4\,d^2\,e\,g-6720\,a^3\,b^3\,c\,e\,h^2+6300\,a^2\,b^4\,c\,e^2\,g-576\,a^5\,b\,g\,h^2\,i-60480\,a\,b^5\,c\,d^2\,e+540\,a^5\,b\,e\,i^3+111132\,a\,b^5\,c^3\,g+1350\,a^4\,b^2\,e^2\,i^2+13824\,a^3\,b^3\,d^2\,h^2+7938\,a^3\,b^3\,c^2\,i^2+450\,a^3\,b^3\,e^2\,g^2+23814\,a^2\,b^4\,c^2\,g^2+162\,a^5\,b\,g^2\,i^2+1500\,a^3\,b^3\,e^3\,i+27648\,a^2\,b^4\,d^3\,h+3072\,a^4\,b^2\,d\,h^3+2268\,a^3\,b^3\,c\,g^3+22050\,a\,b^5\,c^2\,e^2+81\,a^4\,b^2\,g^4+625\,a^2\,b^4\,e^4+256\,a^5\,b\,h^4+20736\,a\,b^5\,d^4+81\,a^6\,i^4+194481\,b^6\,c^4,z,m\right)\right)+\frac{\frac{x^5\,\left(7\,b\,c+a\,g\right)}{32\,a^2}-\frac{j\,x^4}{4\,b}-\frac{b\,f+a\,j}{8\,b^2}+\frac{x^6\,\left(3\,b\,d+a\,h\right)}{16\,a^2}+\frac{x^7\,\left(5\,b\,e+3\,a\,i\right)}{32\,a^2}+\frac{x\,\left(11\,b\,c-3\,a\,g\right)}{32\,a\,b}+\frac{x^2\,\left(5\,b\,d-a\,h\right)}{16\,a\,b}+\frac{x^3\,\left(9\,b\,e-a\,i\right)}{32\,a\,b}}{a^2+2\,a\,b\,x^4+b^2\,x^8}","Not used",1,"symsum(log(- root(268435456*a^11*b^7*z^4 + 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 + 6881280*a^6*b^6*c*e*z^2 + 524288*a^8*b^4*h^2*z^2 + 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z - 258048*a^5*b^4*c*g*h*z + 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z + 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z + 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z - 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z - 2709504*a^3*b^6*c^2*d*z - 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h - 40320*a^2*b^4*c*d*e*h + 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i - 4032*a^4*b^2*c*h^2*i - 960*a^4*b^2*e*g*h^2 + 2268*a^4*b^2*c*g*i^2 + 26460*a^2*b^4*c^2*e*i - 36288*a^2*b^4*c*d^2*i - 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 + 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g + 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 + 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i + 27648*a^2*b^4*d^3*h + 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 + 81*a^4*b^2*g^4 + 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 + 81*a^6*i^4 + 194481*b^6*c^4, z, m)*(root(268435456*a^11*b^7*z^4 + 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 + 6881280*a^6*b^6*c*e*z^2 + 524288*a^8*b^4*h^2*z^2 + 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z - 258048*a^5*b^4*c*g*h*z + 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z + 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z + 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z - 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z - 2709504*a^3*b^6*c^2*d*z - 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h - 40320*a^2*b^4*c*d*e*h + 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i - 4032*a^4*b^2*c*h^2*i - 960*a^4*b^2*e*g*h^2 + 2268*a^4*b^2*c*g*i^2 + 26460*a^2*b^4*c^2*e*i - 36288*a^2*b^4*c*d^2*i - 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 + 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g + 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 + 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i + 27648*a^2*b^4*d^3*h + 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 + 81*a^4*b^2*g^4 + 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 + 81*a^6*i^4 + 194481*b^6*c^4, z, m)*((344064*a^5*b^5*c + 49152*a^6*b^4*g)/(32768*a^6*b^2) - (x*(24576*a^5*b^4*d + 8192*a^6*b^3*h))/(4096*a^6*b)) + (15360*a^3*b^4*d*e + 9216*a^4*b^3*d*i + 5120*a^4*b^3*e*h + 3072*a^5*b^2*h*i)/(32768*a^6*b^2) - (x*(144*a^5*b*i^2 - 7056*a^2*b^4*c^2 + 400*a^3*b^3*e^2 - 144*a^4*b^2*g^2 - 2016*a^3*b^3*c*g + 480*a^4*b^2*e*i))/(4096*a^6*b)) - (27*a^4*i^3 + 125*a*b^3*e^3 - 3024*b^4*c*d^2 + 2205*b^4*c^2*e - 336*a^2*b^2*c*h^2 + 45*a^2*b^2*e*g^2 + 225*a^2*b^2*e^2*i - 432*a*b^3*d^2*g + 1323*a*b^3*c^2*i + 135*a^3*b*e*i^2 - 48*a^3*b*g*h^2 + 27*a^3*b*g^2*i + 378*a^2*b^2*c*g*i - 288*a^2*b^2*d*g*h - 2016*a*b^3*c*d*h + 630*a*b^3*c*e*g)/(32768*a^6*b^2) - (x*(315*b^3*c*d*e - 8*a^3*h^3 - 216*b^3*d^3 + 9*a^3*g*h*i - 216*a*b^2*d^2*h - 72*a^2*b*d*h^2 + 189*a*b^2*c*d*i + 105*a*b^2*c*e*h + 45*a*b^2*d*e*g + 63*a^2*b*c*h*i + 27*a^2*b*d*g*i + 15*a^2*b*e*g*h))/(4096*a^6*b))*root(268435456*a^11*b^7*z^4 + 589824*a^8*b^4*g*i*z^2 + 4128768*a^7*b^5*c*i*z^2 + 3145728*a^7*b^5*d*h*z^2 + 983040*a^7*b^5*e*g*z^2 + 6881280*a^6*b^6*c*e*z^2 + 524288*a^8*b^4*h^2*z^2 + 4718592*a^6*b^6*d^2*z^2 + 61440*a^6*b^3*e*h*i*z - 258048*a^5*b^4*c*g*h*z + 184320*a^5*b^4*d*e*i*z - 774144*a^4*b^5*c*d*g*z + 18432*a^7*b^2*h*i^2*z - 18432*a^6*b^3*g^2*h*z + 55296*a^6*b^3*d*i^2*z + 51200*a^5*b^4*e^2*h*z - 903168*a^4*b^5*c^2*h*z - 55296*a^5*b^4*d*g^2*z + 153600*a^4*b^5*d*e^2*z - 2709504*a^3*b^6*c^2*d*z - 3456*a^4*b^2*d*g*h*i - 24192*a^3*b^3*c*d*h*i + 7560*a^3*b^3*c*e*g*i - 5760*a^3*b^3*d*e*g*h - 40320*a^2*b^4*c*d*e*h + 540*a^4*b^2*e*g^2*i - 5184*a^3*b^3*d^2*g*i - 4032*a^4*b^2*c*h^2*i - 960*a^4*b^2*e*g*h^2 + 2268*a^4*b^2*c*g*i^2 + 26460*a^2*b^4*c^2*e*i - 36288*a^2*b^4*c*d^2*i - 8640*a^2*b^4*d^2*e*g - 6720*a^3*b^3*c*e*h^2 + 6300*a^2*b^4*c*e^2*g - 576*a^5*b*g*h^2*i - 60480*a*b^5*c*d^2*e + 540*a^5*b*e*i^3 + 111132*a*b^5*c^3*g + 1350*a^4*b^2*e^2*i^2 + 13824*a^3*b^3*d^2*h^2 + 7938*a^3*b^3*c^2*i^2 + 450*a^3*b^3*e^2*g^2 + 23814*a^2*b^4*c^2*g^2 + 162*a^5*b*g^2*i^2 + 1500*a^3*b^3*e^3*i + 27648*a^2*b^4*d^3*h + 3072*a^4*b^2*d*h^3 + 2268*a^3*b^3*c*g^3 + 22050*a*b^5*c^2*e^2 + 81*a^4*b^2*g^4 + 625*a^2*b^4*e^4 + 256*a^5*b*h^4 + 20736*a*b^5*d^4 + 81*a^6*i^4 + 194481*b^6*c^4, z, m), m, 1, 4) + ((x^5*(7*b*c + a*g))/(32*a^2) - (j*x^4)/(4*b) - (b*f + a*j)/(8*b^2) + (x^6*(3*b*d + a*h))/(16*a^2) + (x^7*(5*b*e + 3*a*i))/(32*a^2) + (x*(11*b*c - 3*a*g))/(32*a*b) + (x^2*(5*b*d - a*h))/(16*a*b) + (x^3*(9*b*e - a*i))/(32*a*b))/(a^2 + b^2*x^8 + 2*a*b*x^4)","B"
204,1,1747,293,5.993670,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4)^4,x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(68719476736\,a^{15}\,b^6\,z^4-1211105280\,a^8\,b^5\,c\,e\,z^2+335544320\,a^9\,b^4\,d\,h\,z^2+110100480\,a^9\,b^4\,e\,g\,z^2-838860800\,a^8\,b^5\,d^2\,z^2-33554432\,a^{10}\,b^3\,h^2\,z^2-88309760\,a^5\,b^4\,c\,d\,g\,z+17661952\,a^6\,b^3\,c\,g\,h\,z+485703680\,a^4\,b^5\,c^2\,d\,z-97140736\,a^5\,b^4\,c^2\,h\,z-802816\,a^7\,b^2\,g^2\,h\,z-3686400\,a^6\,b^3\,e^2\,h\,z+4014080\,a^6\,b^3\,d\,g^2\,z+18432000\,a^5\,b^4\,d\,e^2\,z-268800\,a^3\,b^2\,d\,e\,g\,h+2956800\,a^2\,b^3\,c\,d\,e\,h+672000\,a^2\,b^3\,d^2\,e\,g-295680\,a^3\,b^2\,c\,e\,h^2-485100\,a^2\,b^3\,c\,e^2\,g+26880\,a^4\,b\,e\,g\,h^2-7392000\,a\,b^4\,c\,d^2\,e-81920\,a^4\,b\,d\,h^3+12782924\,a\,b^4\,c^3\,g+614400\,a^3\,b^2\,d^2\,h^2+22050\,a^3\,b^2\,e^2\,g^2-1743126\,a^2\,b^3\,c^2\,g^2-2048000\,a^2\,b^3\,d^3\,h+105644\,a^3\,b^2\,c\,g^3+2668050\,a\,b^4\,c^2\,e^2-50625\,a^2\,b^3\,e^4-2401\,a^4\,b\,g^4+2560000\,a\,b^4\,d^4+4096\,a^5\,h^4-35153041\,b^5\,c^4,z,k\right)\,\left(\mathrm{root}\left(68719476736\,a^{15}\,b^6\,z^4-1211105280\,a^8\,b^5\,c\,e\,z^2+335544320\,a^9\,b^4\,d\,h\,z^2+110100480\,a^9\,b^4\,e\,g\,z^2-838860800\,a^8\,b^5\,d^2\,z^2-33554432\,a^{10}\,b^3\,h^2\,z^2-88309760\,a^5\,b^4\,c\,d\,g\,z+17661952\,a^6\,b^3\,c\,g\,h\,z+485703680\,a^4\,b^5\,c^2\,d\,z-97140736\,a^5\,b^4\,c^2\,h\,z-802816\,a^7\,b^2\,g^2\,h\,z-3686400\,a^6\,b^3\,e^2\,h\,z+4014080\,a^6\,b^3\,d\,g^2\,z+18432000\,a^5\,b^4\,d\,e^2\,z-268800\,a^3\,b^2\,d\,e\,g\,h+2956800\,a^2\,b^3\,c\,d\,e\,h+672000\,a^2\,b^3\,d^2\,e\,g-295680\,a^3\,b^2\,c\,e\,h^2-485100\,a^2\,b^3\,c\,e^2\,g+26880\,a^4\,b\,e\,g\,h^2-7392000\,a\,b^4\,c\,d^2\,e-81920\,a^4\,b\,d\,h^3+12782924\,a\,b^4\,c^3\,g+614400\,a^3\,b^2\,d^2\,h^2+22050\,a^3\,b^2\,e^2\,g^2-1743126\,a^2\,b^3\,c^2\,g^2-2048000\,a^2\,b^3\,d^3\,h+105644\,a^3\,b^2\,c\,g^3+2668050\,a\,b^4\,c^2\,e^2-50625\,a^2\,b^3\,e^4-2401\,a^4\,b\,g^4+2560000\,a\,b^4\,d^4+4096\,a^5\,h^4-35153041\,b^5\,c^4,z,k\right)\,\left(\frac{20185088\,a^7\,b^4\,c-1835008\,a^8\,b^3\,g}{2097152\,a^9\,b}-\frac{x\,\left(655360\,a^7\,b^4\,d-131072\,a^8\,b^3\,h\right)}{131072\,a^9\,b}\right)-\frac{614400\,a^4\,b^3\,d\,e-122880\,a^5\,b^2\,e\,h}{2097152\,a^9\,b}+\frac{x\,\left(1568\,a^5\,b^2\,g^2-34496\,a^4\,b^3\,c\,g+7200\,a^4\,b^3\,e^2+189728\,a^3\,b^4\,c^2\right)}{131072\,a^9\,b}\right)-\frac{-448\,a^3\,g\,h^2+4928\,a^2\,b\,c\,h^2+4480\,a^2\,b\,d\,g\,h-735\,a^2\,b\,e\,g^2-49280\,a\,b^2\,c\,d\,h+16170\,a\,b^2\,c\,e\,g-11200\,a\,b^2\,d^2\,g+3375\,a\,b^2\,e^3-88935\,b^3\,c^2\,e+123200\,b^3\,c\,d^2}{2097152\,a^9\,b}-\frac{x\,\left(-32\,a^3\,h^3+480\,a^2\,b\,d\,h^2-105\,e\,g\,a^2\,b\,h-2400\,a\,b^2\,d^2\,h+525\,e\,g\,a\,b^2\,d+1155\,c\,e\,a\,b^2\,h+4000\,b^3\,d^3-5775\,c\,e\,b^3\,d\right)}{131072\,a^9\,b}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^6\,z^4-1211105280\,a^8\,b^5\,c\,e\,z^2+335544320\,a^9\,b^4\,d\,h\,z^2+110100480\,a^9\,b^4\,e\,g\,z^2-838860800\,a^8\,b^5\,d^2\,z^2-33554432\,a^{10}\,b^3\,h^2\,z^2-88309760\,a^5\,b^4\,c\,d\,g\,z+17661952\,a^6\,b^3\,c\,g\,h\,z+485703680\,a^4\,b^5\,c^2\,d\,z-97140736\,a^5\,b^4\,c^2\,h\,z-802816\,a^7\,b^2\,g^2\,h\,z-3686400\,a^6\,b^3\,e^2\,h\,z+4014080\,a^6\,b^3\,d\,g^2\,z+18432000\,a^5\,b^4\,d\,e^2\,z-268800\,a^3\,b^2\,d\,e\,g\,h+2956800\,a^2\,b^3\,c\,d\,e\,h+672000\,a^2\,b^3\,d^2\,e\,g-295680\,a^3\,b^2\,c\,e\,h^2-485100\,a^2\,b^3\,c\,e^2\,g+26880\,a^4\,b\,e\,g\,h^2-7392000\,a\,b^4\,c\,d^2\,e-81920\,a^4\,b\,d\,h^3+12782924\,a\,b^4\,c^3\,g+614400\,a^3\,b^2\,d^2\,h^2+22050\,a^3\,b^2\,e^2\,g^2-1743126\,a^2\,b^3\,c^2\,g^2-2048000\,a^2\,b^3\,d^3\,h+105644\,a^3\,b^2\,c\,g^3+2668050\,a\,b^4\,c^2\,e^2-50625\,a^2\,b^3\,e^4-2401\,a^4\,b\,g^4+2560000\,a\,b^4\,d^4+4096\,a^5\,h^4-35153041\,b^5\,c^4,z,k\right)\right)+\frac{\frac{f}{12\,b}+\frac{113\,e\,x^3}{384\,a}-\frac{3\,x^5\,\left(11\,b\,c-a\,g\right)}{64\,a^2}-\frac{x^6\,\left(5\,b\,d-a\,h\right)}{12\,a^2}+\frac{7\,b\,x^9\,\left(11\,b\,c-a\,g\right)}{384\,a^3}+\frac{x\,\left(51\,b\,c+7\,a\,g\right)}{128\,a\,b}+\frac{b\,x^{10}\,\left(5\,b\,d-a\,h\right)}{32\,a^3}+\frac{15\,b^2\,e\,x^{11}}{128\,a^3}+\frac{x^2\,\left(11\,b\,d+a\,h\right)}{32\,a\,b}-\frac{21\,b\,e\,x^7}{64\,a^2}}{a^3-3\,a^2\,b\,x^4+3\,a\,b^2\,x^8-b^3\,x^{12}}","Not used",1,"symsum(log(- root(68719476736*a^15*b^6*z^4 - 1211105280*a^8*b^5*c*e*z^2 + 335544320*a^9*b^4*d*h*z^2 + 110100480*a^9*b^4*e*g*z^2 - 838860800*a^8*b^5*d^2*z^2 - 33554432*a^10*b^3*h^2*z^2 - 88309760*a^5*b^4*c*d*g*z + 17661952*a^6*b^3*c*g*h*z + 485703680*a^4*b^5*c^2*d*z - 97140736*a^5*b^4*c^2*h*z - 802816*a^7*b^2*g^2*h*z - 3686400*a^6*b^3*e^2*h*z + 4014080*a^6*b^3*d*g^2*z + 18432000*a^5*b^4*d*e^2*z - 268800*a^3*b^2*d*e*g*h + 2956800*a^2*b^3*c*d*e*h + 672000*a^2*b^3*d^2*e*g - 295680*a^3*b^2*c*e*h^2 - 485100*a^2*b^3*c*e^2*g + 26880*a^4*b*e*g*h^2 - 7392000*a*b^4*c*d^2*e - 81920*a^4*b*d*h^3 + 12782924*a*b^4*c^3*g + 614400*a^3*b^2*d^2*h^2 + 22050*a^3*b^2*e^2*g^2 - 1743126*a^2*b^3*c^2*g^2 - 2048000*a^2*b^3*d^3*h + 105644*a^3*b^2*c*g^3 + 2668050*a*b^4*c^2*e^2 - 50625*a^2*b^3*e^4 - 2401*a^4*b*g^4 + 2560000*a*b^4*d^4 + 4096*a^5*h^4 - 35153041*b^5*c^4, z, k)*(root(68719476736*a^15*b^6*z^4 - 1211105280*a^8*b^5*c*e*z^2 + 335544320*a^9*b^4*d*h*z^2 + 110100480*a^9*b^4*e*g*z^2 - 838860800*a^8*b^5*d^2*z^2 - 33554432*a^10*b^3*h^2*z^2 - 88309760*a^5*b^4*c*d*g*z + 17661952*a^6*b^3*c*g*h*z + 485703680*a^4*b^5*c^2*d*z - 97140736*a^5*b^4*c^2*h*z - 802816*a^7*b^2*g^2*h*z - 3686400*a^6*b^3*e^2*h*z + 4014080*a^6*b^3*d*g^2*z + 18432000*a^5*b^4*d*e^2*z - 268800*a^3*b^2*d*e*g*h + 2956800*a^2*b^3*c*d*e*h + 672000*a^2*b^3*d^2*e*g - 295680*a^3*b^2*c*e*h^2 - 485100*a^2*b^3*c*e^2*g + 26880*a^4*b*e*g*h^2 - 7392000*a*b^4*c*d^2*e - 81920*a^4*b*d*h^3 + 12782924*a*b^4*c^3*g + 614400*a^3*b^2*d^2*h^2 + 22050*a^3*b^2*e^2*g^2 - 1743126*a^2*b^3*c^2*g^2 - 2048000*a^2*b^3*d^3*h + 105644*a^3*b^2*c*g^3 + 2668050*a*b^4*c^2*e^2 - 50625*a^2*b^3*e^4 - 2401*a^4*b*g^4 + 2560000*a*b^4*d^4 + 4096*a^5*h^4 - 35153041*b^5*c^4, z, k)*((20185088*a^7*b^4*c - 1835008*a^8*b^3*g)/(2097152*a^9*b) - (x*(655360*a^7*b^4*d - 131072*a^8*b^3*h))/(131072*a^9*b)) - (614400*a^4*b^3*d*e - 122880*a^5*b^2*e*h)/(2097152*a^9*b) + (x*(189728*a^3*b^4*c^2 + 7200*a^4*b^3*e^2 + 1568*a^5*b^2*g^2 - 34496*a^4*b^3*c*g))/(131072*a^9*b)) - (3375*a*b^2*e^3 + 123200*b^3*c*d^2 - 88935*b^3*c^2*e - 448*a^3*g*h^2 - 11200*a*b^2*d^2*g + 4928*a^2*b*c*h^2 - 735*a^2*b*e*g^2 - 49280*a*b^2*c*d*h + 16170*a*b^2*c*e*g + 4480*a^2*b*d*g*h)/(2097152*a^9*b) - (x*(4000*b^3*d^3 - 32*a^3*h^3 - 5775*b^3*c*d*e - 2400*a*b^2*d^2*h + 480*a^2*b*d*h^2 + 1155*a*b^2*c*e*h + 525*a*b^2*d*e*g - 105*a^2*b*e*g*h))/(131072*a^9*b))*root(68719476736*a^15*b^6*z^4 - 1211105280*a^8*b^5*c*e*z^2 + 335544320*a^9*b^4*d*h*z^2 + 110100480*a^9*b^4*e*g*z^2 - 838860800*a^8*b^5*d^2*z^2 - 33554432*a^10*b^3*h^2*z^2 - 88309760*a^5*b^4*c*d*g*z + 17661952*a^6*b^3*c*g*h*z + 485703680*a^4*b^5*c^2*d*z - 97140736*a^5*b^4*c^2*h*z - 802816*a^7*b^2*g^2*h*z - 3686400*a^6*b^3*e^2*h*z + 4014080*a^6*b^3*d*g^2*z + 18432000*a^5*b^4*d*e^2*z - 268800*a^3*b^2*d*e*g*h + 2956800*a^2*b^3*c*d*e*h + 672000*a^2*b^3*d^2*e*g - 295680*a^3*b^2*c*e*h^2 - 485100*a^2*b^3*c*e^2*g + 26880*a^4*b*e*g*h^2 - 7392000*a*b^4*c*d^2*e - 81920*a^4*b*d*h^3 + 12782924*a*b^4*c^3*g + 614400*a^3*b^2*d^2*h^2 + 22050*a^3*b^2*e^2*g^2 - 1743126*a^2*b^3*c^2*g^2 - 2048000*a^2*b^3*d^3*h + 105644*a^3*b^2*c*g^3 + 2668050*a*b^4*c^2*e^2 - 50625*a^2*b^3*e^4 - 2401*a^4*b*g^4 + 2560000*a*b^4*d^4 + 4096*a^5*h^4 - 35153041*b^5*c^4, z, k), k, 1, 4) + (f/(12*b) + (113*e*x^3)/(384*a) - (3*x^5*(11*b*c - a*g))/(64*a^2) - (x^6*(5*b*d - a*h))/(12*a^2) + (7*b*x^9*(11*b*c - a*g))/(384*a^3) + (x*(51*b*c + 7*a*g))/(128*a*b) + (b*x^10*(5*b*d - a*h))/(32*a^3) + (15*b^2*e*x^11)/(128*a^3) + (x^2*(11*b*d + a*h))/(32*a*b) - (21*b*e*x^7)/(64*a^2))/(a^3 - b^3*x^12 - 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
205,1,2747,331,6.139789,"\text{Not used}","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{\frac{f}{12\,b}-\frac{3\,x^5\,\left(11\,b\,c-a\,g\right)}{64\,a^2}-\frac{x^6\,\left(5\,b\,d-a\,h\right)}{12\,a^2}-\frac{7\,x^7\,\left(3\,b\,e-a\,i\right)}{64\,a^2}+\frac{7\,b\,x^9\,\left(11\,b\,c-a\,g\right)}{384\,a^3}+\frac{x\,\left(51\,b\,c+7\,a\,g\right)}{128\,a\,b}+\frac{b\,x^{10}\,\left(5\,b\,d-a\,h\right)}{32\,a^3}+\frac{5\,b\,x^{11}\,\left(3\,b\,e-a\,i\right)}{128\,a^3}+\frac{x^2\,\left(11\,b\,d+a\,h\right)}{32\,a\,b}+\frac{x^3\,\left(113\,b\,e+5\,a\,i\right)}{384\,a\,b}}{a^3-3\,a^2\,b\,x^4+3\,a\,b^2\,x^8-b^3\,x^{12}}+\left(\sum _{l=1}^4\ln\left(-\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4-1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2-36700160\,a^{10}\,b^4\,g\,i\,z^2-838860800\,a^8\,b^6\,d^2\,z^2-33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z+17661952\,a^6\,b^4\,c\,g\,h\,z-12288000\,a^6\,b^4\,d\,e\,i\,z+485703680\,a^4\,b^6\,c^2\,d\,z-409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z-3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z+4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z+89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h+2956800\,a^2\,b^4\,c\,d\,e\,h-14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i+98560\,a^4\,b^2\,c\,h^2\,i+26880\,a^4\,b^2\,e\,g\,h^2-53900\,a^4\,b^2\,c\,g\,i^2-1778700\,a^2\,b^4\,c^2\,e\,i+2464000\,a^2\,b^4\,c\,d^2\,i+672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2-485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g-33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2-1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i-2048000\,a^2\,b^4\,d^3\,h-81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2-2401\,a^4\,b^2\,g^4-50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4-625\,a^6\,i^4-35153041\,b^6\,c^4,z,l\right)\,\left(\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4-1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2-36700160\,a^{10}\,b^4\,g\,i\,z^2-838860800\,a^8\,b^6\,d^2\,z^2-33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z+17661952\,a^6\,b^4\,c\,g\,h\,z-12288000\,a^6\,b^4\,d\,e\,i\,z+485703680\,a^4\,b^6\,c^2\,d\,z-409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z-3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z+4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z+89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h+2956800\,a^2\,b^4\,c\,d\,e\,h-14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i+98560\,a^4\,b^2\,c\,h^2\,i+26880\,a^4\,b^2\,e\,g\,h^2-53900\,a^4\,b^2\,c\,g\,i^2-1778700\,a^2\,b^4\,c^2\,e\,i+2464000\,a^2\,b^4\,c\,d^2\,i+672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2-485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g-33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2-1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i-2048000\,a^2\,b^4\,d^3\,h-81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2-2401\,a^4\,b^2\,g^4-50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4-625\,a^6\,i^4-35153041\,b^6\,c^4,z,l\right)\,\left(\frac{20185088\,a^7\,b^5\,c-1835008\,a^8\,b^4\,g}{2097152\,a^9\,b^2}-\frac{x\,\left(655360\,a^7\,b^4\,d-131072\,a^8\,b^3\,h\right)}{131072\,a^9\,b}\right)-\frac{614400\,a^4\,b^4\,d\,e-204800\,a^5\,b^3\,d\,i-122880\,a^5\,b^3\,e\,h+40960\,a^6\,b^2\,h\,i}{2097152\,a^9\,b^2}+\frac{x\,\left(800\,a^6\,b\,i^2-4800\,a^5\,b^2\,e\,i+1568\,a^5\,b^2\,g^2-34496\,a^4\,b^3\,c\,g+7200\,a^4\,b^3\,e^2+189728\,a^3\,b^4\,c^2\right)}{131072\,a^9\,b}\right)+\frac{125\,a^4\,i^3-1125\,a^3\,b\,e\,i^2-245\,a^3\,b\,g^2\,i+448\,a^3\,b\,g\,h^2+5390\,a^2\,b^2\,c\,g\,i-4928\,a^2\,b^2\,c\,h^2-4480\,a^2\,b^2\,d\,g\,h+3375\,a^2\,b^2\,e^2\,i+735\,a^2\,b^2\,e\,g^2-29645\,a\,b^3\,c^2\,i+49280\,a\,b^3\,c\,d\,h-16170\,a\,b^3\,c\,e\,g+11200\,a\,b^3\,d^2\,g-3375\,a\,b^3\,e^3+88935\,b^4\,c^2\,e-123200\,b^4\,c\,d^2}{2097152\,a^9\,b^2}-\frac{x\,\left(4000\,b^3\,d^3-32\,a^3\,h^3-5775\,b^3\,c\,d\,e+35\,a^3\,g\,h\,i-2400\,a\,b^2\,d^2\,h+480\,a^2\,b\,d\,h^2+1925\,a\,b^2\,c\,d\,i+1155\,a\,b^2\,c\,e\,h+525\,a\,b^2\,d\,e\,g-385\,a^2\,b\,c\,h\,i-175\,a^2\,b\,d\,g\,i-105\,a^2\,b\,e\,g\,h\right)}{131072\,a^9\,b}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4-1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2-36700160\,a^{10}\,b^4\,g\,i\,z^2-838860800\,a^8\,b^6\,d^2\,z^2-33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z+17661952\,a^6\,b^4\,c\,g\,h\,z-12288000\,a^6\,b^4\,d\,e\,i\,z+485703680\,a^4\,b^6\,c^2\,d\,z-409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z-3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z+4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z+89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h+2956800\,a^2\,b^4\,c\,d\,e\,h-14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i+98560\,a^4\,b^2\,c\,h^2\,i+26880\,a^4\,b^2\,e\,g\,h^2-53900\,a^4\,b^2\,c\,g\,i^2-1778700\,a^2\,b^4\,c^2\,e\,i+2464000\,a^2\,b^4\,c\,d^2\,i+672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2-485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g-33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2-1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i-2048000\,a^2\,b^4\,d^3\,h-81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2-2401\,a^4\,b^2\,g^4-50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4-625\,a^6\,i^4-35153041\,b^6\,c^4,z,l\right)\right)","Not used",1,"(f/(12*b) - (3*x^5*(11*b*c - a*g))/(64*a^2) - (x^6*(5*b*d - a*h))/(12*a^2) - (7*x^7*(3*b*e - a*i))/(64*a^2) + (7*b*x^9*(11*b*c - a*g))/(384*a^3) + (x*(51*b*c + 7*a*g))/(128*a*b) + (b*x^10*(5*b*d - a*h))/(32*a^3) + (5*b*x^11*(3*b*e - a*i))/(128*a^3) + (x^2*(11*b*d + a*h))/(32*a*b) + (x^3*(113*b*e + 5*a*i))/(384*a*b))/(a^3 - b^3*x^12 - 3*a^2*b*x^4 + 3*a*b^2*x^8) + symsum(log((125*a^4*i^3 - 3375*a*b^3*e^3 - 123200*b^4*c*d^2 + 88935*b^4*c^2*e - 4928*a^2*b^2*c*h^2 + 735*a^2*b^2*e*g^2 + 3375*a^2*b^2*e^2*i + 11200*a*b^3*d^2*g - 29645*a*b^3*c^2*i - 1125*a^3*b*e*i^2 + 448*a^3*b*g*h^2 - 245*a^3*b*g^2*i + 5390*a^2*b^2*c*g*i - 4480*a^2*b^2*d*g*h + 49280*a*b^3*c*d*h - 16170*a*b^3*c*e*g)/(2097152*a^9*b^2) - root(68719476736*a^15*b^7*z^4 - 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 - 36700160*a^10*b^4*g*i*z^2 - 838860800*a^8*b^6*d^2*z^2 - 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z + 17661952*a^6*b^4*c*g*h*z - 12288000*a^6*b^4*d*e*i*z + 485703680*a^4*b^6*c^2*d*z - 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z - 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z + 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z + 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h + 2956800*a^2*b^4*c*d*e*h - 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i + 98560*a^4*b^2*c*h^2*i + 26880*a^4*b^2*e*g*h^2 - 53900*a^4*b^2*c*g*i^2 - 1778700*a^2*b^4*c^2*e*i + 2464000*a^2*b^4*c*d^2*i + 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 - 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g - 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 - 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i - 2048000*a^2*b^4*d^3*h - 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 - 2401*a^4*b^2*g^4 - 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 - 625*a^6*i^4 - 35153041*b^6*c^4, z, l)*(root(68719476736*a^15*b^7*z^4 - 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 - 36700160*a^10*b^4*g*i*z^2 - 838860800*a^8*b^6*d^2*z^2 - 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z + 17661952*a^6*b^4*c*g*h*z - 12288000*a^6*b^4*d*e*i*z + 485703680*a^4*b^6*c^2*d*z - 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z - 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z + 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z + 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h + 2956800*a^2*b^4*c*d*e*h - 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i + 98560*a^4*b^2*c*h^2*i + 26880*a^4*b^2*e*g*h^2 - 53900*a^4*b^2*c*g*i^2 - 1778700*a^2*b^4*c^2*e*i + 2464000*a^2*b^4*c*d^2*i + 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 - 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g - 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 - 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i - 2048000*a^2*b^4*d^3*h - 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 - 2401*a^4*b^2*g^4 - 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 - 625*a^6*i^4 - 35153041*b^6*c^4, z, l)*((20185088*a^7*b^5*c - 1835008*a^8*b^4*g)/(2097152*a^9*b^2) - (x*(655360*a^7*b^4*d - 131072*a^8*b^3*h))/(131072*a^9*b)) - (614400*a^4*b^4*d*e - 204800*a^5*b^3*d*i - 122880*a^5*b^3*e*h + 40960*a^6*b^2*h*i)/(2097152*a^9*b^2) + (x*(800*a^6*b*i^2 + 189728*a^3*b^4*c^2 + 7200*a^4*b^3*e^2 + 1568*a^5*b^2*g^2 - 34496*a^4*b^3*c*g - 4800*a^5*b^2*e*i))/(131072*a^9*b)) - (x*(4000*b^3*d^3 - 32*a^3*h^3 - 5775*b^3*c*d*e + 35*a^3*g*h*i - 2400*a*b^2*d^2*h + 480*a^2*b*d*h^2 + 1925*a*b^2*c*d*i + 1155*a*b^2*c*e*h + 525*a*b^2*d*e*g - 385*a^2*b*c*h*i - 175*a^2*b*d*g*i - 105*a^2*b*e*g*h))/(131072*a^9*b))*root(68719476736*a^15*b^7*z^4 - 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 - 36700160*a^10*b^4*g*i*z^2 - 838860800*a^8*b^6*d^2*z^2 - 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z + 17661952*a^6*b^4*c*g*h*z - 12288000*a^6*b^4*d*e*i*z + 485703680*a^4*b^6*c^2*d*z - 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z - 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z + 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z + 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h + 2956800*a^2*b^4*c*d*e*h - 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i + 98560*a^4*b^2*c*h^2*i + 26880*a^4*b^2*e*g*h^2 - 53900*a^4*b^2*c*g*i^2 - 1778700*a^2*b^4*c^2*e*i + 2464000*a^2*b^4*c*d^2*i + 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 - 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g - 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 - 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i - 2048000*a^2*b^4*d^3*h - 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 - 2401*a^4*b^2*g^4 - 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 - 625*a^6*i^4 - 35153041*b^6*c^4, z, l), l, 1, 4)","B"
206,1,2764,349,6.396363,"\text{Not used}","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)","\left(\sum _{m=1}^4\ln\left(-\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4-1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2-36700160\,a^{10}\,b^4\,g\,i\,z^2-838860800\,a^8\,b^6\,d^2\,z^2-33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z+17661952\,a^6\,b^4\,c\,g\,h\,z-12288000\,a^6\,b^4\,d\,e\,i\,z+485703680\,a^4\,b^6\,c^2\,d\,z-409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z-3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z+4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z+89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h+2956800\,a^2\,b^4\,c\,d\,e\,h-14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i+98560\,a^4\,b^2\,c\,h^2\,i+26880\,a^4\,b^2\,e\,g\,h^2-53900\,a^4\,b^2\,c\,g\,i^2-1778700\,a^2\,b^4\,c^2\,e\,i+2464000\,a^2\,b^4\,c\,d^2\,i+672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2-485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g-33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2-1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i-2048000\,a^2\,b^4\,d^3\,h-81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2-2401\,a^4\,b^2\,g^4-50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4-625\,a^6\,i^4-35153041\,b^6\,c^4,z,m\right)\,\left(\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4-1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2-36700160\,a^{10}\,b^4\,g\,i\,z^2-838860800\,a^8\,b^6\,d^2\,z^2-33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z+17661952\,a^6\,b^4\,c\,g\,h\,z-12288000\,a^6\,b^4\,d\,e\,i\,z+485703680\,a^4\,b^6\,c^2\,d\,z-409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z-3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z+4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z+89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h+2956800\,a^2\,b^4\,c\,d\,e\,h-14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i+98560\,a^4\,b^2\,c\,h^2\,i+26880\,a^4\,b^2\,e\,g\,h^2-53900\,a^4\,b^2\,c\,g\,i^2-1778700\,a^2\,b^4\,c^2\,e\,i+2464000\,a^2\,b^4\,c\,d^2\,i+672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2-485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g-33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2-1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i-2048000\,a^2\,b^4\,d^3\,h-81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2-2401\,a^4\,b^2\,g^4-50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4-625\,a^6\,i^4-35153041\,b^6\,c^4,z,m\right)\,\left(\frac{20185088\,a^7\,b^5\,c-1835008\,a^8\,b^4\,g}{2097152\,a^9\,b^2}-\frac{x\,\left(655360\,a^7\,b^4\,d-131072\,a^8\,b^3\,h\right)}{131072\,a^9\,b}\right)-\frac{614400\,a^4\,b^4\,d\,e-204800\,a^5\,b^3\,d\,i-122880\,a^5\,b^3\,e\,h+40960\,a^6\,b^2\,h\,i}{2097152\,a^9\,b^2}+\frac{x\,\left(800\,a^6\,b\,i^2-4800\,a^5\,b^2\,e\,i+1568\,a^5\,b^2\,g^2-34496\,a^4\,b^3\,c\,g+7200\,a^4\,b^3\,e^2+189728\,a^3\,b^4\,c^2\right)}{131072\,a^9\,b}\right)+\frac{125\,a^4\,i^3-1125\,a^3\,b\,e\,i^2-245\,a^3\,b\,g^2\,i+448\,a^3\,b\,g\,h^2+5390\,a^2\,b^2\,c\,g\,i-4928\,a^2\,b^2\,c\,h^2-4480\,a^2\,b^2\,d\,g\,h+3375\,a^2\,b^2\,e^2\,i+735\,a^2\,b^2\,e\,g^2-29645\,a\,b^3\,c^2\,i+49280\,a\,b^3\,c\,d\,h-16170\,a\,b^3\,c\,e\,g+11200\,a\,b^3\,d^2\,g-3375\,a\,b^3\,e^3+88935\,b^4\,c^2\,e-123200\,b^4\,c\,d^2}{2097152\,a^9\,b^2}-\frac{x\,\left(4000\,b^3\,d^3-32\,a^3\,h^3-5775\,b^3\,c\,d\,e+35\,a^3\,g\,h\,i-2400\,a\,b^2\,d^2\,h+480\,a^2\,b\,d\,h^2+1925\,a\,b^2\,c\,d\,i+1155\,a\,b^2\,c\,e\,h+525\,a\,b^2\,d\,e\,g-385\,a^2\,b\,c\,h\,i-175\,a^2\,b\,d\,g\,i-105\,a^2\,b\,e\,g\,h\right)}{131072\,a^9\,b}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4-1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2-36700160\,a^{10}\,b^4\,g\,i\,z^2-838860800\,a^8\,b^6\,d^2\,z^2-33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z+17661952\,a^6\,b^4\,c\,g\,h\,z-12288000\,a^6\,b^4\,d\,e\,i\,z+485703680\,a^4\,b^6\,c^2\,d\,z-409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z-3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z+4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z+89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h+2956800\,a^2\,b^4\,c\,d\,e\,h-14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i+98560\,a^4\,b^2\,c\,h^2\,i+26880\,a^4\,b^2\,e\,g\,h^2-53900\,a^4\,b^2\,c\,g\,i^2-1778700\,a^2\,b^4\,c^2\,e\,i+2464000\,a^2\,b^4\,c\,d^2\,i+672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2-485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g-33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2-1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i-2048000\,a^2\,b^4\,d^3\,h-81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2-2401\,a^4\,b^2\,g^4-50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4-625\,a^6\,i^4-35153041\,b^6\,c^4,z,m\right)\right)+\frac{\frac{2\,b\,f-a\,j}{24\,b^2}+\frac{j\,x^4}{8\,b}-\frac{3\,x^5\,\left(11\,b\,c-a\,g\right)}{64\,a^2}-\frac{x^6\,\left(5\,b\,d-a\,h\right)}{12\,a^2}-\frac{7\,x^7\,\left(3\,b\,e-a\,i\right)}{64\,a^2}+\frac{7\,b\,x^9\,\left(11\,b\,c-a\,g\right)}{384\,a^3}+\frac{x\,\left(51\,b\,c+7\,a\,g\right)}{128\,a\,b}+\frac{b\,x^{10}\,\left(5\,b\,d-a\,h\right)}{32\,a^3}+\frac{5\,b\,x^{11}\,\left(3\,b\,e-a\,i\right)}{128\,a^3}+\frac{x^2\,\left(11\,b\,d+a\,h\right)}{32\,a\,b}+\frac{x^3\,\left(113\,b\,e+5\,a\,i\right)}{384\,a\,b}}{a^3-3\,a^2\,b\,x^4+3\,a\,b^2\,x^8-b^3\,x^{12}}","Not used",1,"symsum(log((125*a^4*i^3 - 3375*a*b^3*e^3 - 123200*b^4*c*d^2 + 88935*b^4*c^2*e - 4928*a^2*b^2*c*h^2 + 735*a^2*b^2*e*g^2 + 3375*a^2*b^2*e^2*i + 11200*a*b^3*d^2*g - 29645*a*b^3*c^2*i - 1125*a^3*b*e*i^2 + 448*a^3*b*g*h^2 - 245*a^3*b*g^2*i + 5390*a^2*b^2*c*g*i - 4480*a^2*b^2*d*g*h + 49280*a*b^3*c*d*h - 16170*a*b^3*c*e*g)/(2097152*a^9*b^2) - root(68719476736*a^15*b^7*z^4 - 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 - 36700160*a^10*b^4*g*i*z^2 - 838860800*a^8*b^6*d^2*z^2 - 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z + 17661952*a^6*b^4*c*g*h*z - 12288000*a^6*b^4*d*e*i*z + 485703680*a^4*b^6*c^2*d*z - 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z - 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z + 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z + 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h + 2956800*a^2*b^4*c*d*e*h - 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i + 98560*a^4*b^2*c*h^2*i + 26880*a^4*b^2*e*g*h^2 - 53900*a^4*b^2*c*g*i^2 - 1778700*a^2*b^4*c^2*e*i + 2464000*a^2*b^4*c*d^2*i + 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 - 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g - 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 - 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i - 2048000*a^2*b^4*d^3*h - 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 - 2401*a^4*b^2*g^4 - 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 - 625*a^6*i^4 - 35153041*b^6*c^4, z, m)*(root(68719476736*a^15*b^7*z^4 - 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 - 36700160*a^10*b^4*g*i*z^2 - 838860800*a^8*b^6*d^2*z^2 - 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z + 17661952*a^6*b^4*c*g*h*z - 12288000*a^6*b^4*d*e*i*z + 485703680*a^4*b^6*c^2*d*z - 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z - 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z + 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z + 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h + 2956800*a^2*b^4*c*d*e*h - 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i + 98560*a^4*b^2*c*h^2*i + 26880*a^4*b^2*e*g*h^2 - 53900*a^4*b^2*c*g*i^2 - 1778700*a^2*b^4*c^2*e*i + 2464000*a^2*b^4*c*d^2*i + 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 - 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g - 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 - 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i - 2048000*a^2*b^4*d^3*h - 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 - 2401*a^4*b^2*g^4 - 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 - 625*a^6*i^4 - 35153041*b^6*c^4, z, m)*((20185088*a^7*b^5*c - 1835008*a^8*b^4*g)/(2097152*a^9*b^2) - (x*(655360*a^7*b^4*d - 131072*a^8*b^3*h))/(131072*a^9*b)) - (614400*a^4*b^4*d*e - 204800*a^5*b^3*d*i - 122880*a^5*b^3*e*h + 40960*a^6*b^2*h*i)/(2097152*a^9*b^2) + (x*(800*a^6*b*i^2 + 189728*a^3*b^4*c^2 + 7200*a^4*b^3*e^2 + 1568*a^5*b^2*g^2 - 34496*a^4*b^3*c*g - 4800*a^5*b^2*e*i))/(131072*a^9*b)) - (x*(4000*b^3*d^3 - 32*a^3*h^3 - 5775*b^3*c*d*e + 35*a^3*g*h*i - 2400*a*b^2*d^2*h + 480*a^2*b*d*h^2 + 1925*a*b^2*c*d*i + 1155*a*b^2*c*e*h + 525*a*b^2*d*e*g - 385*a^2*b*c*h*i - 175*a^2*b*d*g*i - 105*a^2*b*e*g*h))/(131072*a^9*b))*root(68719476736*a^15*b^7*z^4 - 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 - 36700160*a^10*b^4*g*i*z^2 - 838860800*a^8*b^6*d^2*z^2 - 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z + 17661952*a^6*b^4*c*g*h*z - 12288000*a^6*b^4*d*e*i*z + 485703680*a^4*b^6*c^2*d*z - 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z - 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z + 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z + 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h + 2956800*a^2*b^4*c*d*e*h - 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i + 98560*a^4*b^2*c*h^2*i + 26880*a^4*b^2*e*g*h^2 - 53900*a^4*b^2*c*g*i^2 - 1778700*a^2*b^4*c^2*e*i + 2464000*a^2*b^4*c*d^2*i + 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 - 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g - 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 - 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i - 2048000*a^2*b^4*d^3*h - 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 - 2401*a^4*b^2*g^4 - 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 - 625*a^6*i^4 - 35153041*b^6*c^4, z, m), m, 1, 4) + ((2*b*f - a*j)/(24*b^2) + (j*x^4)/(8*b) - (3*x^5*(11*b*c - a*g))/(64*a^2) - (x^6*(5*b*d - a*h))/(12*a^2) - (7*x^7*(3*b*e - a*i))/(64*a^2) + (7*b*x^9*(11*b*c - a*g))/(384*a^3) + (x*(51*b*c + 7*a*g))/(128*a*b) + (b*x^10*(5*b*d - a*h))/(32*a^3) + (5*b*x^11*(3*b*e - a*i))/(128*a^3) + (x^2*(11*b*d + a*h))/(32*a*b) + (x^3*(113*b*e + 5*a*i))/(384*a*b))/(a^3 - b^3*x^12 - 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
207,1,1743,462,6.075031,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4)^4,x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(68719476736\,a^{15}\,b^6\,z^4+1211105280\,a^8\,b^5\,c\,e\,z^2+335544320\,a^9\,b^4\,d\,h\,z^2+110100480\,a^9\,b^4\,e\,g\,z^2+838860800\,a^8\,b^5\,d^2\,z^2+33554432\,a^{10}\,b^3\,h^2\,z^2-88309760\,a^5\,b^4\,c\,d\,g\,z-17661952\,a^6\,b^3\,c\,g\,h\,z-485703680\,a^4\,b^5\,c^2\,d\,z-97140736\,a^5\,b^4\,c^2\,h\,z-802816\,a^7\,b^2\,g^2\,h\,z+3686400\,a^6\,b^3\,e^2\,h\,z-4014080\,a^6\,b^3\,d\,g^2\,z+18432000\,a^5\,b^4\,d\,e^2\,z-268800\,a^3\,b^2\,d\,e\,g\,h-2956800\,a^2\,b^3\,c\,d\,e\,h-672000\,a^2\,b^3\,d^2\,e\,g-295680\,a^3\,b^2\,c\,e\,h^2+485100\,a^2\,b^3\,c\,e^2\,g-26880\,a^4\,b\,e\,g\,h^2-7392000\,a\,b^4\,c\,d^2\,e+81920\,a^4\,b\,d\,h^3+12782924\,a\,b^4\,c^3\,g+614400\,a^3\,b^2\,d^2\,h^2+22050\,a^3\,b^2\,e^2\,g^2+1743126\,a^2\,b^3\,c^2\,g^2+2048000\,a^2\,b^3\,d^3\,h+105644\,a^3\,b^2\,c\,g^3+2668050\,a\,b^4\,c^2\,e^2+50625\,a^2\,b^3\,e^4+2401\,a^4\,b\,g^4+2560000\,a\,b^4\,d^4+4096\,a^5\,h^4+35153041\,b^5\,c^4,z,k\right)\,\left(\mathrm{root}\left(68719476736\,a^{15}\,b^6\,z^4+1211105280\,a^8\,b^5\,c\,e\,z^2+335544320\,a^9\,b^4\,d\,h\,z^2+110100480\,a^9\,b^4\,e\,g\,z^2+838860800\,a^8\,b^5\,d^2\,z^2+33554432\,a^{10}\,b^3\,h^2\,z^2-88309760\,a^5\,b^4\,c\,d\,g\,z-17661952\,a^6\,b^3\,c\,g\,h\,z-485703680\,a^4\,b^5\,c^2\,d\,z-97140736\,a^5\,b^4\,c^2\,h\,z-802816\,a^7\,b^2\,g^2\,h\,z+3686400\,a^6\,b^3\,e^2\,h\,z-4014080\,a^6\,b^3\,d\,g^2\,z+18432000\,a^5\,b^4\,d\,e^2\,z-268800\,a^3\,b^2\,d\,e\,g\,h-2956800\,a^2\,b^3\,c\,d\,e\,h-672000\,a^2\,b^3\,d^2\,e\,g-295680\,a^3\,b^2\,c\,e\,h^2+485100\,a^2\,b^3\,c\,e^2\,g-26880\,a^4\,b\,e\,g\,h^2-7392000\,a\,b^4\,c\,d^2\,e+81920\,a^4\,b\,d\,h^3+12782924\,a\,b^4\,c^3\,g+614400\,a^3\,b^2\,d^2\,h^2+22050\,a^3\,b^2\,e^2\,g^2+1743126\,a^2\,b^3\,c^2\,g^2+2048000\,a^2\,b^3\,d^3\,h+105644\,a^3\,b^2\,c\,g^3+2668050\,a\,b^4\,c^2\,e^2+50625\,a^2\,b^3\,e^4+2401\,a^4\,b\,g^4+2560000\,a\,b^4\,d^4+4096\,a^5\,h^4+35153041\,b^5\,c^4,z,k\right)\,\left(\frac{1835008\,g\,a^8\,b^3+20185088\,c\,a^7\,b^4}{2097152\,a^9\,b}-\frac{x\,\left(131072\,h\,a^8\,b^3+655360\,d\,a^7\,b^4\right)}{131072\,a^9\,b}\right)+\frac{122880\,e\,h\,a^5\,b^2+614400\,d\,e\,a^4\,b^3}{2097152\,a^9\,b}+\frac{x\,\left(1568\,a^5\,b^2\,g^2+34496\,a^4\,b^3\,c\,g-7200\,a^4\,b^3\,e^2+189728\,a^3\,b^4\,c^2\right)}{131072\,a^9\,b}\right)+\frac{448\,a^3\,g\,h^2+4928\,a^2\,b\,c\,h^2+4480\,a^2\,b\,d\,g\,h-735\,a^2\,b\,e\,g^2+49280\,a\,b^2\,c\,d\,h-16170\,a\,b^2\,c\,e\,g+11200\,a\,b^2\,d^2\,g-3375\,a\,b^2\,e^3-88935\,b^3\,c^2\,e+123200\,b^3\,c\,d^2}{2097152\,a^9\,b}+\frac{x\,\left(32\,a^3\,h^3+480\,a^2\,b\,d\,h^2-105\,e\,g\,a^2\,b\,h+2400\,a\,b^2\,d^2\,h-525\,e\,g\,a\,b^2\,d-1155\,c\,e\,a\,b^2\,h+4000\,b^3\,d^3-5775\,c\,e\,b^3\,d\right)}{131072\,a^9\,b}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^6\,z^4+1211105280\,a^8\,b^5\,c\,e\,z^2+335544320\,a^9\,b^4\,d\,h\,z^2+110100480\,a^9\,b^4\,e\,g\,z^2+838860800\,a^8\,b^5\,d^2\,z^2+33554432\,a^{10}\,b^3\,h^2\,z^2-88309760\,a^5\,b^4\,c\,d\,g\,z-17661952\,a^6\,b^3\,c\,g\,h\,z-485703680\,a^4\,b^5\,c^2\,d\,z-97140736\,a^5\,b^4\,c^2\,h\,z-802816\,a^7\,b^2\,g^2\,h\,z+3686400\,a^6\,b^3\,e^2\,h\,z-4014080\,a^6\,b^3\,d\,g^2\,z+18432000\,a^5\,b^4\,d\,e^2\,z-268800\,a^3\,b^2\,d\,e\,g\,h-2956800\,a^2\,b^3\,c\,d\,e\,h-672000\,a^2\,b^3\,d^2\,e\,g-295680\,a^3\,b^2\,c\,e\,h^2+485100\,a^2\,b^3\,c\,e^2\,g-26880\,a^4\,b\,e\,g\,h^2-7392000\,a\,b^4\,c\,d^2\,e+81920\,a^4\,b\,d\,h^3+12782924\,a\,b^4\,c^3\,g+614400\,a^3\,b^2\,d^2\,h^2+22050\,a^3\,b^2\,e^2\,g^2+1743126\,a^2\,b^3\,c^2\,g^2+2048000\,a^2\,b^3\,d^3\,h+105644\,a^3\,b^2\,c\,g^3+2668050\,a\,b^4\,c^2\,e^2+50625\,a^2\,b^3\,e^4+2401\,a^4\,b\,g^4+2560000\,a\,b^4\,d^4+4096\,a^5\,h^4+35153041\,b^5\,c^4,z,k\right)\right)+\frac{\frac{113\,e\,x^3}{384\,a}-\frac{f}{12\,b}+\frac{3\,x^5\,\left(11\,b\,c+a\,g\right)}{64\,a^2}+\frac{x^6\,\left(5\,b\,d+a\,h\right)}{12\,a^2}+\frac{7\,b\,x^9\,\left(11\,b\,c+a\,g\right)}{384\,a^3}+\frac{x\,\left(51\,b\,c-7\,a\,g\right)}{128\,a\,b}+\frac{b\,x^{10}\,\left(5\,b\,d+a\,h\right)}{32\,a^3}+\frac{15\,b^2\,e\,x^{11}}{128\,a^3}+\frac{x^2\,\left(11\,b\,d-a\,h\right)}{32\,a\,b}+\frac{21\,b\,e\,x^7}{64\,a^2}}{a^3+3\,a^2\,b\,x^4+3\,a\,b^2\,x^8+b^3\,x^{12}}","Not used",1,"symsum(log((123200*b^3*c*d^2 - 3375*a*b^2*e^3 - 88935*b^3*c^2*e + 448*a^3*g*h^2 + 11200*a*b^2*d^2*g + 4928*a^2*b*c*h^2 - 735*a^2*b*e*g^2 + 49280*a*b^2*c*d*h - 16170*a*b^2*c*e*g + 4480*a^2*b*d*g*h)/(2097152*a^9*b) - root(68719476736*a^15*b^6*z^4 + 1211105280*a^8*b^5*c*e*z^2 + 335544320*a^9*b^4*d*h*z^2 + 110100480*a^9*b^4*e*g*z^2 + 838860800*a^8*b^5*d^2*z^2 + 33554432*a^10*b^3*h^2*z^2 - 88309760*a^5*b^4*c*d*g*z - 17661952*a^6*b^3*c*g*h*z - 485703680*a^4*b^5*c^2*d*z - 97140736*a^5*b^4*c^2*h*z - 802816*a^7*b^2*g^2*h*z + 3686400*a^6*b^3*e^2*h*z - 4014080*a^6*b^3*d*g^2*z + 18432000*a^5*b^4*d*e^2*z - 268800*a^3*b^2*d*e*g*h - 2956800*a^2*b^3*c*d*e*h - 672000*a^2*b^3*d^2*e*g - 295680*a^3*b^2*c*e*h^2 + 485100*a^2*b^3*c*e^2*g - 26880*a^4*b*e*g*h^2 - 7392000*a*b^4*c*d^2*e + 81920*a^4*b*d*h^3 + 12782924*a*b^4*c^3*g + 614400*a^3*b^2*d^2*h^2 + 22050*a^3*b^2*e^2*g^2 + 1743126*a^2*b^3*c^2*g^2 + 2048000*a^2*b^3*d^3*h + 105644*a^3*b^2*c*g^3 + 2668050*a*b^4*c^2*e^2 + 50625*a^2*b^3*e^4 + 2401*a^4*b*g^4 + 2560000*a*b^4*d^4 + 4096*a^5*h^4 + 35153041*b^5*c^4, z, k)*(root(68719476736*a^15*b^6*z^4 + 1211105280*a^8*b^5*c*e*z^2 + 335544320*a^9*b^4*d*h*z^2 + 110100480*a^9*b^4*e*g*z^2 + 838860800*a^8*b^5*d^2*z^2 + 33554432*a^10*b^3*h^2*z^2 - 88309760*a^5*b^4*c*d*g*z - 17661952*a^6*b^3*c*g*h*z - 485703680*a^4*b^5*c^2*d*z - 97140736*a^5*b^4*c^2*h*z - 802816*a^7*b^2*g^2*h*z + 3686400*a^6*b^3*e^2*h*z - 4014080*a^6*b^3*d*g^2*z + 18432000*a^5*b^4*d*e^2*z - 268800*a^3*b^2*d*e*g*h - 2956800*a^2*b^3*c*d*e*h - 672000*a^2*b^3*d^2*e*g - 295680*a^3*b^2*c*e*h^2 + 485100*a^2*b^3*c*e^2*g - 26880*a^4*b*e*g*h^2 - 7392000*a*b^4*c*d^2*e + 81920*a^4*b*d*h^3 + 12782924*a*b^4*c^3*g + 614400*a^3*b^2*d^2*h^2 + 22050*a^3*b^2*e^2*g^2 + 1743126*a^2*b^3*c^2*g^2 + 2048000*a^2*b^3*d^3*h + 105644*a^3*b^2*c*g^3 + 2668050*a*b^4*c^2*e^2 + 50625*a^2*b^3*e^4 + 2401*a^4*b*g^4 + 2560000*a*b^4*d^4 + 4096*a^5*h^4 + 35153041*b^5*c^4, z, k)*((20185088*a^7*b^4*c + 1835008*a^8*b^3*g)/(2097152*a^9*b) - (x*(655360*a^7*b^4*d + 131072*a^8*b^3*h))/(131072*a^9*b)) + (614400*a^4*b^3*d*e + 122880*a^5*b^2*e*h)/(2097152*a^9*b) + (x*(189728*a^3*b^4*c^2 - 7200*a^4*b^3*e^2 + 1568*a^5*b^2*g^2 + 34496*a^4*b^3*c*g))/(131072*a^9*b)) + (x*(4000*b^3*d^3 + 32*a^3*h^3 - 5775*b^3*c*d*e + 2400*a*b^2*d^2*h + 480*a^2*b*d*h^2 - 1155*a*b^2*c*e*h - 525*a*b^2*d*e*g - 105*a^2*b*e*g*h))/(131072*a^9*b))*root(68719476736*a^15*b^6*z^4 + 1211105280*a^8*b^5*c*e*z^2 + 335544320*a^9*b^4*d*h*z^2 + 110100480*a^9*b^4*e*g*z^2 + 838860800*a^8*b^5*d^2*z^2 + 33554432*a^10*b^3*h^2*z^2 - 88309760*a^5*b^4*c*d*g*z - 17661952*a^6*b^3*c*g*h*z - 485703680*a^4*b^5*c^2*d*z - 97140736*a^5*b^4*c^2*h*z - 802816*a^7*b^2*g^2*h*z + 3686400*a^6*b^3*e^2*h*z - 4014080*a^6*b^3*d*g^2*z + 18432000*a^5*b^4*d*e^2*z - 268800*a^3*b^2*d*e*g*h - 2956800*a^2*b^3*c*d*e*h - 672000*a^2*b^3*d^2*e*g - 295680*a^3*b^2*c*e*h^2 + 485100*a^2*b^3*c*e^2*g - 26880*a^4*b*e*g*h^2 - 7392000*a*b^4*c*d^2*e + 81920*a^4*b*d*h^3 + 12782924*a*b^4*c^3*g + 614400*a^3*b^2*d^2*h^2 + 22050*a^3*b^2*e^2*g^2 + 1743126*a^2*b^3*c^2*g^2 + 2048000*a^2*b^3*d^3*h + 105644*a^3*b^2*c*g^3 + 2668050*a*b^4*c^2*e^2 + 50625*a^2*b^3*e^4 + 2401*a^4*b*g^4 + 2560000*a*b^4*d^4 + 4096*a^5*h^4 + 35153041*b^5*c^4, z, k), k, 1, 4) + ((113*e*x^3)/(384*a) - f/(12*b) + (3*x^5*(11*b*c + a*g))/(64*a^2) + (x^6*(5*b*d + a*h))/(12*a^2) + (7*b*x^9*(11*b*c + a*g))/(384*a^3) + (x*(51*b*c - 7*a*g))/(128*a*b) + (b*x^10*(5*b*d + a*h))/(32*a^3) + (15*b^2*e*x^11)/(128*a^3) + (x^2*(11*b*d - a*h))/(32*a*b) + (21*b*e*x^7)/(64*a^2))/(a^3 + b^3*x^12 + 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
208,1,2741,516,6.084171,"\text{Not used}","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{\frac{3\,x^5\,\left(11\,b\,c+a\,g\right)}{64\,a^2}-\frac{f}{12\,b}+\frac{x^6\,\left(5\,b\,d+a\,h\right)}{12\,a^2}+\frac{7\,x^7\,\left(3\,b\,e+a\,i\right)}{64\,a^2}+\frac{7\,b\,x^9\,\left(11\,b\,c+a\,g\right)}{384\,a^3}+\frac{x\,\left(51\,b\,c-7\,a\,g\right)}{128\,a\,b}+\frac{b\,x^{10}\,\left(5\,b\,d+a\,h\right)}{32\,a^3}+\frac{5\,b\,x^{11}\,\left(3\,b\,e+a\,i\right)}{128\,a^3}+\frac{x^2\,\left(11\,b\,d-a\,h\right)}{32\,a\,b}+\frac{x^3\,\left(113\,b\,e-5\,a\,i\right)}{384\,a\,b}}{a^3+3\,a^2\,b\,x^4+3\,a\,b^2\,x^8+b^3\,x^{12}}+\left(\sum _{l=1}^4\ln\left(-\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4+1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2+36700160\,a^{10}\,b^4\,g\,i\,z^2+838860800\,a^8\,b^6\,d^2\,z^2+33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z-17661952\,a^6\,b^4\,c\,g\,h\,z+12288000\,a^6\,b^4\,d\,e\,i\,z-485703680\,a^4\,b^6\,c^2\,d\,z+409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z+3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z-4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z-89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h-2956800\,a^2\,b^4\,c\,d\,e\,h+14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i-98560\,a^4\,b^2\,c\,h^2\,i-26880\,a^4\,b^2\,e\,g\,h^2+53900\,a^4\,b^2\,c\,g\,i^2+1778700\,a^2\,b^4\,c^2\,e\,i-2464000\,a^2\,b^4\,c\,d^2\,i-672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2+485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g+33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2+1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i+2048000\,a^2\,b^4\,d^3\,h+81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2+2401\,a^4\,b^2\,g^4+50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4+625\,a^6\,i^4+35153041\,b^6\,c^4,z,l\right)\,\left(\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4+1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2+36700160\,a^{10}\,b^4\,g\,i\,z^2+838860800\,a^8\,b^6\,d^2\,z^2+33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z-17661952\,a^6\,b^4\,c\,g\,h\,z+12288000\,a^6\,b^4\,d\,e\,i\,z-485703680\,a^4\,b^6\,c^2\,d\,z+409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z+3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z-4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z-89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h-2956800\,a^2\,b^4\,c\,d\,e\,h+14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i-98560\,a^4\,b^2\,c\,h^2\,i-26880\,a^4\,b^2\,e\,g\,h^2+53900\,a^4\,b^2\,c\,g\,i^2+1778700\,a^2\,b^4\,c^2\,e\,i-2464000\,a^2\,b^4\,c\,d^2\,i-672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2+485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g+33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2+1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i+2048000\,a^2\,b^4\,d^3\,h+81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2+2401\,a^4\,b^2\,g^4+50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4+625\,a^6\,i^4+35153041\,b^6\,c^4,z,l\right)\,\left(\frac{1835008\,g\,a^8\,b^4+20185088\,c\,a^7\,b^5}{2097152\,a^9\,b^2}-\frac{x\,\left(131072\,h\,a^8\,b^3+655360\,d\,a^7\,b^4\right)}{131072\,a^9\,b}\right)+\frac{614400\,a^4\,b^4\,d\,e+204800\,a^5\,b^3\,d\,i+122880\,a^5\,b^3\,e\,h+40960\,a^6\,b^2\,h\,i}{2097152\,a^9\,b^2}-\frac{x\,\left(800\,a^6\,b\,i^2+4800\,a^5\,b^2\,e\,i-1568\,a^5\,b^2\,g^2-34496\,a^4\,b^3\,c\,g+7200\,a^4\,b^3\,e^2-189728\,a^3\,b^4\,c^2\right)}{131072\,a^9\,b}\right)-\frac{125\,a^4\,i^3+1125\,a^3\,b\,e\,i^2+245\,a^3\,b\,g^2\,i-448\,a^3\,b\,g\,h^2+5390\,a^2\,b^2\,c\,g\,i-4928\,a^2\,b^2\,c\,h^2-4480\,a^2\,b^2\,d\,g\,h+3375\,a^2\,b^2\,e^2\,i+735\,a^2\,b^2\,e\,g^2+29645\,a\,b^3\,c^2\,i-49280\,a\,b^3\,c\,d\,h+16170\,a\,b^3\,c\,e\,g-11200\,a\,b^3\,d^2\,g+3375\,a\,b^3\,e^3+88935\,b^4\,c^2\,e-123200\,b^4\,c\,d^2}{2097152\,a^9\,b^2}-\frac{x\,\left(5775\,b^3\,c\,d\,e-32\,a^3\,h^3-4000\,b^3\,d^3+35\,a^3\,g\,h\,i-2400\,a\,b^2\,d^2\,h-480\,a^2\,b\,d\,h^2+1925\,a\,b^2\,c\,d\,i+1155\,a\,b^2\,c\,e\,h+525\,a\,b^2\,d\,e\,g+385\,a^2\,b\,c\,h\,i+175\,a^2\,b\,d\,g\,i+105\,a^2\,b\,e\,g\,h\right)}{131072\,a^9\,b}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4+1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2+36700160\,a^{10}\,b^4\,g\,i\,z^2+838860800\,a^8\,b^6\,d^2\,z^2+33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z-17661952\,a^6\,b^4\,c\,g\,h\,z+12288000\,a^6\,b^4\,d\,e\,i\,z-485703680\,a^4\,b^6\,c^2\,d\,z+409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z+3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z-4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z-89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h-2956800\,a^2\,b^4\,c\,d\,e\,h+14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i-98560\,a^4\,b^2\,c\,h^2\,i-26880\,a^4\,b^2\,e\,g\,h^2+53900\,a^4\,b^2\,c\,g\,i^2+1778700\,a^2\,b^4\,c^2\,e\,i-2464000\,a^2\,b^4\,c\,d^2\,i-672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2+485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g+33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2+1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i+2048000\,a^2\,b^4\,d^3\,h+81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2+2401\,a^4\,b^2\,g^4+50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4+625\,a^6\,i^4+35153041\,b^6\,c^4,z,l\right)\right)","Not used",1,"((3*x^5*(11*b*c + a*g))/(64*a^2) - f/(12*b) + (x^6*(5*b*d + a*h))/(12*a^2) + (7*x^7*(3*b*e + a*i))/(64*a^2) + (7*b*x^9*(11*b*c + a*g))/(384*a^3) + (x*(51*b*c - 7*a*g))/(128*a*b) + (b*x^10*(5*b*d + a*h))/(32*a^3) + (5*b*x^11*(3*b*e + a*i))/(128*a^3) + (x^2*(11*b*d - a*h))/(32*a*b) + (x^3*(113*b*e - 5*a*i))/(384*a*b))/(a^3 + b^3*x^12 + 3*a^2*b*x^4 + 3*a*b^2*x^8) + symsum(log(- root(68719476736*a^15*b^7*z^4 + 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 + 36700160*a^10*b^4*g*i*z^2 + 838860800*a^8*b^6*d^2*z^2 + 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z - 17661952*a^6*b^4*c*g*h*z + 12288000*a^6*b^4*d*e*i*z - 485703680*a^4*b^6*c^2*d*z + 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z + 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z - 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z - 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h - 2956800*a^2*b^4*c*d*e*h + 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i - 98560*a^4*b^2*c*h^2*i - 26880*a^4*b^2*e*g*h^2 + 53900*a^4*b^2*c*g*i^2 + 1778700*a^2*b^4*c^2*e*i - 2464000*a^2*b^4*c*d^2*i - 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 + 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g + 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 + 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i + 2048000*a^2*b^4*d^3*h + 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 + 2401*a^4*b^2*g^4 + 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 + 625*a^6*i^4 + 35153041*b^6*c^4, z, l)*(root(68719476736*a^15*b^7*z^4 + 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 + 36700160*a^10*b^4*g*i*z^2 + 838860800*a^8*b^6*d^2*z^2 + 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z - 17661952*a^6*b^4*c*g*h*z + 12288000*a^6*b^4*d*e*i*z - 485703680*a^4*b^6*c^2*d*z + 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z + 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z - 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z - 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h - 2956800*a^2*b^4*c*d*e*h + 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i - 98560*a^4*b^2*c*h^2*i - 26880*a^4*b^2*e*g*h^2 + 53900*a^4*b^2*c*g*i^2 + 1778700*a^2*b^4*c^2*e*i - 2464000*a^2*b^4*c*d^2*i - 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 + 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g + 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 + 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i + 2048000*a^2*b^4*d^3*h + 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 + 2401*a^4*b^2*g^4 + 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 + 625*a^6*i^4 + 35153041*b^6*c^4, z, l)*((20185088*a^7*b^5*c + 1835008*a^8*b^4*g)/(2097152*a^9*b^2) - (x*(655360*a^7*b^4*d + 131072*a^8*b^3*h))/(131072*a^9*b)) + (614400*a^4*b^4*d*e + 204800*a^5*b^3*d*i + 122880*a^5*b^3*e*h + 40960*a^6*b^2*h*i)/(2097152*a^9*b^2) - (x*(800*a^6*b*i^2 - 189728*a^3*b^4*c^2 + 7200*a^4*b^3*e^2 - 1568*a^5*b^2*g^2 - 34496*a^4*b^3*c*g + 4800*a^5*b^2*e*i))/(131072*a^9*b)) - (125*a^4*i^3 + 3375*a*b^3*e^3 - 123200*b^4*c*d^2 + 88935*b^4*c^2*e - 4928*a^2*b^2*c*h^2 + 735*a^2*b^2*e*g^2 + 3375*a^2*b^2*e^2*i - 11200*a*b^3*d^2*g + 29645*a*b^3*c^2*i + 1125*a^3*b*e*i^2 - 448*a^3*b*g*h^2 + 245*a^3*b*g^2*i + 5390*a^2*b^2*c*g*i - 4480*a^2*b^2*d*g*h - 49280*a*b^3*c*d*h + 16170*a*b^3*c*e*g)/(2097152*a^9*b^2) - (x*(5775*b^3*c*d*e - 32*a^3*h^3 - 4000*b^3*d^3 + 35*a^3*g*h*i - 2400*a*b^2*d^2*h - 480*a^2*b*d*h^2 + 1925*a*b^2*c*d*i + 1155*a*b^2*c*e*h + 525*a*b^2*d*e*g + 385*a^2*b*c*h*i + 175*a^2*b*d*g*i + 105*a^2*b*e*g*h))/(131072*a^9*b))*root(68719476736*a^15*b^7*z^4 + 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 + 36700160*a^10*b^4*g*i*z^2 + 838860800*a^8*b^6*d^2*z^2 + 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z - 17661952*a^6*b^4*c*g*h*z + 12288000*a^6*b^4*d*e*i*z - 485703680*a^4*b^6*c^2*d*z + 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z + 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z - 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z - 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h - 2956800*a^2*b^4*c*d*e*h + 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i - 98560*a^4*b^2*c*h^2*i - 26880*a^4*b^2*e*g*h^2 + 53900*a^4*b^2*c*g*i^2 + 1778700*a^2*b^4*c^2*e*i - 2464000*a^2*b^4*c*d^2*i - 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 + 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g + 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 + 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i + 2048000*a^2*b^4*d^3*h + 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 + 2401*a^4*b^2*g^4 + 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 + 625*a^6*i^4 + 35153041*b^6*c^4, z, l), l, 1, 4)","B"
209,1,2757,534,6.480292,"\text{Not used}","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)","\left(\sum _{m=1}^4\ln\left(-\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4+1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2+36700160\,a^{10}\,b^4\,g\,i\,z^2+838860800\,a^8\,b^6\,d^2\,z^2+33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z-17661952\,a^6\,b^4\,c\,g\,h\,z+12288000\,a^6\,b^4\,d\,e\,i\,z-485703680\,a^4\,b^6\,c^2\,d\,z+409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z+3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z-4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z-89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h-2956800\,a^2\,b^4\,c\,d\,e\,h+14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i-98560\,a^4\,b^2\,c\,h^2\,i-26880\,a^4\,b^2\,e\,g\,h^2+53900\,a^4\,b^2\,c\,g\,i^2+1778700\,a^2\,b^4\,c^2\,e\,i-2464000\,a^2\,b^4\,c\,d^2\,i-672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2+485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g+33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2+1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i+2048000\,a^2\,b^4\,d^3\,h+81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2+2401\,a^4\,b^2\,g^4+50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4+625\,a^6\,i^4+35153041\,b^6\,c^4,z,m\right)\,\left(\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4+1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2+36700160\,a^{10}\,b^4\,g\,i\,z^2+838860800\,a^8\,b^6\,d^2\,z^2+33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z-17661952\,a^6\,b^4\,c\,g\,h\,z+12288000\,a^6\,b^4\,d\,e\,i\,z-485703680\,a^4\,b^6\,c^2\,d\,z+409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z+3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z-4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z-89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h-2956800\,a^2\,b^4\,c\,d\,e\,h+14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i-98560\,a^4\,b^2\,c\,h^2\,i-26880\,a^4\,b^2\,e\,g\,h^2+53900\,a^4\,b^2\,c\,g\,i^2+1778700\,a^2\,b^4\,c^2\,e\,i-2464000\,a^2\,b^4\,c\,d^2\,i-672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2+485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g+33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2+1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i+2048000\,a^2\,b^4\,d^3\,h+81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2+2401\,a^4\,b^2\,g^4+50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4+625\,a^6\,i^4+35153041\,b^6\,c^4,z,m\right)\,\left(\frac{1835008\,g\,a^8\,b^4+20185088\,c\,a^7\,b^5}{2097152\,a^9\,b^2}-\frac{x\,\left(131072\,h\,a^8\,b^3+655360\,d\,a^7\,b^4\right)}{131072\,a^9\,b}\right)+\frac{614400\,a^4\,b^4\,d\,e+204800\,a^5\,b^3\,d\,i+122880\,a^5\,b^3\,e\,h+40960\,a^6\,b^2\,h\,i}{2097152\,a^9\,b^2}-\frac{x\,\left(800\,a^6\,b\,i^2+4800\,a^5\,b^2\,e\,i-1568\,a^5\,b^2\,g^2-34496\,a^4\,b^3\,c\,g+7200\,a^4\,b^3\,e^2-189728\,a^3\,b^4\,c^2\right)}{131072\,a^9\,b}\right)-\frac{125\,a^4\,i^3+1125\,a^3\,b\,e\,i^2+245\,a^3\,b\,g^2\,i-448\,a^3\,b\,g\,h^2+5390\,a^2\,b^2\,c\,g\,i-4928\,a^2\,b^2\,c\,h^2-4480\,a^2\,b^2\,d\,g\,h+3375\,a^2\,b^2\,e^2\,i+735\,a^2\,b^2\,e\,g^2+29645\,a\,b^3\,c^2\,i-49280\,a\,b^3\,c\,d\,h+16170\,a\,b^3\,c\,e\,g-11200\,a\,b^3\,d^2\,g+3375\,a\,b^3\,e^3+88935\,b^4\,c^2\,e-123200\,b^4\,c\,d^2}{2097152\,a^9\,b^2}-\frac{x\,\left(5775\,b^3\,c\,d\,e-32\,a^3\,h^3-4000\,b^3\,d^3+35\,a^3\,g\,h\,i-2400\,a\,b^2\,d^2\,h-480\,a^2\,b\,d\,h^2+1925\,a\,b^2\,c\,d\,i+1155\,a\,b^2\,c\,e\,h+525\,a\,b^2\,d\,e\,g+385\,a^2\,b\,c\,h\,i+175\,a^2\,b\,d\,g\,i+105\,a^2\,b\,e\,g\,h\right)}{131072\,a^9\,b}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^7\,z^4+1211105280\,a^8\,b^6\,c\,e\,z^2+403701760\,a^9\,b^5\,c\,i\,z^2+335544320\,a^9\,b^5\,d\,h\,z^2+110100480\,a^9\,b^5\,e\,g\,z^2+36700160\,a^{10}\,b^4\,g\,i\,z^2+838860800\,a^8\,b^6\,d^2\,z^2+33554432\,a^{10}\,b^4\,h^2\,z^2+2457600\,a^7\,b^3\,e\,h\,i\,z-88309760\,a^5\,b^5\,c\,d\,g\,z-17661952\,a^6\,b^4\,c\,g\,h\,z+12288000\,a^6\,b^4\,d\,e\,i\,z-485703680\,a^4\,b^6\,c^2\,d\,z+409600\,a^8\,b^2\,h\,i^2\,z-97140736\,a^5\,b^5\,c^2\,h\,z-802816\,a^7\,b^3\,g^2\,h\,z+3686400\,a^6\,b^4\,e^2\,h\,z+2048000\,a^7\,b^3\,d\,i^2\,z-4014080\,a^6\,b^4\,d\,g^2\,z+18432000\,a^5\,b^5\,d\,e^2\,z-89600\,a^4\,b^2\,d\,g\,h\,i-985600\,a^3\,b^3\,c\,d\,h\,i+323400\,a^3\,b^3\,c\,e\,g\,i-268800\,a^3\,b^3\,d\,e\,g\,h-2956800\,a^2\,b^4\,c\,d\,e\,h+14700\,a^4\,b^2\,e\,g^2\,i-224000\,a^3\,b^3\,d^2\,g\,i-98560\,a^4\,b^2\,c\,h^2\,i-26880\,a^4\,b^2\,e\,g\,h^2+53900\,a^4\,b^2\,c\,g\,i^2+1778700\,a^2\,b^4\,c^2\,e\,i-2464000\,a^2\,b^4\,c\,d^2\,i-672000\,a^2\,b^4\,d^2\,e\,g-295680\,a^3\,b^3\,c\,e\,h^2+485100\,a^2\,b^4\,c\,e^2\,g-8960\,a^5\,b\,g\,h^2\,i-7392000\,a\,b^5\,c\,d^2\,e+7500\,a^5\,b\,e\,i^3+12782924\,a\,b^5\,c^3\,g+33750\,a^4\,b^2\,e^2\,i^2+614400\,a^3\,b^3\,d^2\,h^2+296450\,a^3\,b^3\,c^2\,i^2+22050\,a^3\,b^3\,e^2\,g^2+1743126\,a^2\,b^4\,c^2\,g^2+2450\,a^5\,b\,g^2\,i^2+67500\,a^3\,b^3\,e^3\,i+2048000\,a^2\,b^4\,d^3\,h+81920\,a^4\,b^2\,d\,h^3+105644\,a^3\,b^3\,c\,g^3+2668050\,a\,b^5\,c^2\,e^2+2401\,a^4\,b^2\,g^4+50625\,a^2\,b^4\,e^4+4096\,a^5\,b\,h^4+2560000\,a\,b^5\,d^4+625\,a^6\,i^4+35153041\,b^6\,c^4,z,m\right)\right)+\frac{\frac{3\,x^5\,\left(11\,b\,c+a\,g\right)}{64\,a^2}-\frac{j\,x^4}{8\,b}-\frac{2\,b\,f+a\,j}{24\,b^2}+\frac{x^6\,\left(5\,b\,d+a\,h\right)}{12\,a^2}+\frac{7\,x^7\,\left(3\,b\,e+a\,i\right)}{64\,a^2}+\frac{7\,b\,x^9\,\left(11\,b\,c+a\,g\right)}{384\,a^3}+\frac{x\,\left(51\,b\,c-7\,a\,g\right)}{128\,a\,b}+\frac{b\,x^{10}\,\left(5\,b\,d+a\,h\right)}{32\,a^3}+\frac{5\,b\,x^{11}\,\left(3\,b\,e+a\,i\right)}{128\,a^3}+\frac{x^2\,\left(11\,b\,d-a\,h\right)}{32\,a\,b}+\frac{x^3\,\left(113\,b\,e-5\,a\,i\right)}{384\,a\,b}}{a^3+3\,a^2\,b\,x^4+3\,a\,b^2\,x^8+b^3\,x^{12}}","Not used",1,"symsum(log(- root(68719476736*a^15*b^7*z^4 + 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 + 36700160*a^10*b^4*g*i*z^2 + 838860800*a^8*b^6*d^2*z^2 + 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z - 17661952*a^6*b^4*c*g*h*z + 12288000*a^6*b^4*d*e*i*z - 485703680*a^4*b^6*c^2*d*z + 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z + 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z - 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z - 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h - 2956800*a^2*b^4*c*d*e*h + 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i - 98560*a^4*b^2*c*h^2*i - 26880*a^4*b^2*e*g*h^2 + 53900*a^4*b^2*c*g*i^2 + 1778700*a^2*b^4*c^2*e*i - 2464000*a^2*b^4*c*d^2*i - 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 + 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g + 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 + 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i + 2048000*a^2*b^4*d^3*h + 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 + 2401*a^4*b^2*g^4 + 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 + 625*a^6*i^4 + 35153041*b^6*c^4, z, m)*(root(68719476736*a^15*b^7*z^4 + 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 + 36700160*a^10*b^4*g*i*z^2 + 838860800*a^8*b^6*d^2*z^2 + 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z - 17661952*a^6*b^4*c*g*h*z + 12288000*a^6*b^4*d*e*i*z - 485703680*a^4*b^6*c^2*d*z + 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z + 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z - 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z - 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h - 2956800*a^2*b^4*c*d*e*h + 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i - 98560*a^4*b^2*c*h^2*i - 26880*a^4*b^2*e*g*h^2 + 53900*a^4*b^2*c*g*i^2 + 1778700*a^2*b^4*c^2*e*i - 2464000*a^2*b^4*c*d^2*i - 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 + 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g + 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 + 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i + 2048000*a^2*b^4*d^3*h + 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 + 2401*a^4*b^2*g^4 + 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 + 625*a^6*i^4 + 35153041*b^6*c^4, z, m)*((20185088*a^7*b^5*c + 1835008*a^8*b^4*g)/(2097152*a^9*b^2) - (x*(655360*a^7*b^4*d + 131072*a^8*b^3*h))/(131072*a^9*b)) + (614400*a^4*b^4*d*e + 204800*a^5*b^3*d*i + 122880*a^5*b^3*e*h + 40960*a^6*b^2*h*i)/(2097152*a^9*b^2) - (x*(800*a^6*b*i^2 - 189728*a^3*b^4*c^2 + 7200*a^4*b^3*e^2 - 1568*a^5*b^2*g^2 - 34496*a^4*b^3*c*g + 4800*a^5*b^2*e*i))/(131072*a^9*b)) - (125*a^4*i^3 + 3375*a*b^3*e^3 - 123200*b^4*c*d^2 + 88935*b^4*c^2*e - 4928*a^2*b^2*c*h^2 + 735*a^2*b^2*e*g^2 + 3375*a^2*b^2*e^2*i - 11200*a*b^3*d^2*g + 29645*a*b^3*c^2*i + 1125*a^3*b*e*i^2 - 448*a^3*b*g*h^2 + 245*a^3*b*g^2*i + 5390*a^2*b^2*c*g*i - 4480*a^2*b^2*d*g*h - 49280*a*b^3*c*d*h + 16170*a*b^3*c*e*g)/(2097152*a^9*b^2) - (x*(5775*b^3*c*d*e - 32*a^3*h^3 - 4000*b^3*d^3 + 35*a^3*g*h*i - 2400*a*b^2*d^2*h - 480*a^2*b*d*h^2 + 1925*a*b^2*c*d*i + 1155*a*b^2*c*e*h + 525*a*b^2*d*e*g + 385*a^2*b*c*h*i + 175*a^2*b*d*g*i + 105*a^2*b*e*g*h))/(131072*a^9*b))*root(68719476736*a^15*b^7*z^4 + 1211105280*a^8*b^6*c*e*z^2 + 403701760*a^9*b^5*c*i*z^2 + 335544320*a^9*b^5*d*h*z^2 + 110100480*a^9*b^5*e*g*z^2 + 36700160*a^10*b^4*g*i*z^2 + 838860800*a^8*b^6*d^2*z^2 + 33554432*a^10*b^4*h^2*z^2 + 2457600*a^7*b^3*e*h*i*z - 88309760*a^5*b^5*c*d*g*z - 17661952*a^6*b^4*c*g*h*z + 12288000*a^6*b^4*d*e*i*z - 485703680*a^4*b^6*c^2*d*z + 409600*a^8*b^2*h*i^2*z - 97140736*a^5*b^5*c^2*h*z - 802816*a^7*b^3*g^2*h*z + 3686400*a^6*b^4*e^2*h*z + 2048000*a^7*b^3*d*i^2*z - 4014080*a^6*b^4*d*g^2*z + 18432000*a^5*b^5*d*e^2*z - 89600*a^4*b^2*d*g*h*i - 985600*a^3*b^3*c*d*h*i + 323400*a^3*b^3*c*e*g*i - 268800*a^3*b^3*d*e*g*h - 2956800*a^2*b^4*c*d*e*h + 14700*a^4*b^2*e*g^2*i - 224000*a^3*b^3*d^2*g*i - 98560*a^4*b^2*c*h^2*i - 26880*a^4*b^2*e*g*h^2 + 53900*a^4*b^2*c*g*i^2 + 1778700*a^2*b^4*c^2*e*i - 2464000*a^2*b^4*c*d^2*i - 672000*a^2*b^4*d^2*e*g - 295680*a^3*b^3*c*e*h^2 + 485100*a^2*b^4*c*e^2*g - 8960*a^5*b*g*h^2*i - 7392000*a*b^5*c*d^2*e + 7500*a^5*b*e*i^3 + 12782924*a*b^5*c^3*g + 33750*a^4*b^2*e^2*i^2 + 614400*a^3*b^3*d^2*h^2 + 296450*a^3*b^3*c^2*i^2 + 22050*a^3*b^3*e^2*g^2 + 1743126*a^2*b^4*c^2*g^2 + 2450*a^5*b*g^2*i^2 + 67500*a^3*b^3*e^3*i + 2048000*a^2*b^4*d^3*h + 81920*a^4*b^2*d*h^3 + 105644*a^3*b^3*c*g^3 + 2668050*a*b^5*c^2*e^2 + 2401*a^4*b^2*g^4 + 50625*a^2*b^4*e^4 + 4096*a^5*b*h^4 + 2560000*a*b^5*d^4 + 625*a^6*i^4 + 35153041*b^6*c^4, z, m), m, 1, 4) + ((3*x^5*(11*b*c + a*g))/(64*a^2) - (j*x^4)/(8*b) - (2*b*f + a*j)/(24*b^2) + (x^6*(5*b*d + a*h))/(12*a^2) + (7*x^7*(3*b*e + a*i))/(64*a^2) + (7*b*x^9*(11*b*c + a*g))/(384*a^3) + (x*(51*b*c - 7*a*g))/(128*a*b) + (b*x^10*(5*b*d + a*h))/(32*a^3) + (5*b*x^11*(3*b*e + a*i))/(128*a^3) + (x^2*(11*b*d - a*h))/(32*a*b) + (x^3*(113*b*e - 5*a*i))/(384*a*b))/(a^3 + b^3*x^12 + 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
210,0,-1,121,0.000000,"\text{Not used}","int((c + d*x)/(a + b*x^4)^(1/2),x)","\int \frac{c+d\,x}{\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((c + d*x)/(a + b*x^4)^(1/2), x)","F"
211,0,-1,87,0.000000,"\text{Not used}","int((c + d*x)/(a - b*x^4)^(1/2),x)","\int \frac{c+d\,x}{\sqrt{a-b\,x^4}} \,d x","Not used",1,"int((c + d*x)/(a - b*x^4)^(1/2), x)","F"
212,0,-1,89,0.000000,"\text{Not used}","int((c + d*x)/(b*x^4 - a)^(1/2),x)","\int \frac{c+d\,x}{\sqrt{b\,x^4-a}} \,d x","Not used",1,"int((c + d*x)/(b*x^4 - a)^(1/2), x)","F"
213,0,-1,127,0.000000,"\text{Not used}","int((c + d*x)/(- a - b*x^4)^(1/2),x)","\int \frac{c+d\,x}{\sqrt{-b\,x^4-a}} \,d x","Not used",1,"int((c + d*x)/(- a - b*x^4)^(1/2), x)","F"
214,0,-1,257,0.000000,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^4)^(1/2),x)","\int \frac{e\,x^2+d\,x+c}{\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((c + d*x + e*x^2)/(a + b*x^4)^(1/2), x)","F"
215,1,12,14,5.036266,"\text{Not used}","int((a*g - b*g*x^4)/(a + b*x^4)^(3/2),x)","\frac{g\,x}{\sqrt{b\,x^4+a}}","Not used",1,"(g*x)/(a + b*x^4)^(1/2)","B"
216,1,23,29,4.905468,"\text{Not used}","int((a*g + e*x - b*g*x^4)/(a + b*x^4)^(3/2),x)","\frac{g\,x+\frac{e\,x^2}{2\,a}}{\sqrt{b\,x^4+a}}","Not used",1,"(g*x + (e*x^2)/(2*a))/(a + b*x^4)^(1/2)","B"
217,1,20,25,4.901201,"\text{Not used}","int((a*g + f*x^3 - b*g*x^4)/(a + b*x^4)^(3/2),x)","\frac{g\,x-\frac{f}{2\,b}}{\sqrt{b\,x^4+a}}","Not used",1,"(g*x - f/(2*b))/(a + b*x^4)^(1/2)","B"
218,1,29,38,4.836285,"\text{Not used}","int((a*g + e*x + f*x^3 - b*g*x^4)/(a + b*x^4)^(3/2),x)","\frac{g\,x-\frac{f}{2\,b}+\frac{e\,x^2}{2\,a}}{\sqrt{b\,x^4+a}}","Not used",1,"(g*x - f/(2*b) + (e*x^2)/(2*a))/(a + b*x^4)^(1/2)","B"
219,1,10,12,4.847094,"\text{Not used}","int((x^4 - 1)/(x^4 + 1)^(3/2),x)","-\frac{x}{\sqrt{x^4+1}}","Not used",1,"-x/(x^4 + 1)^(1/2)","B"
220,0,-1,385,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4)^(1/2),x)","\int \frac{i\,x^6+h\,x^5+g\,x^4+f\,x^3+e\,x^2+d\,x+c}{\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4)^(1/2), x)","F"
221,1,64,109,4.917518,"\text{Not used}","int((x + 1)/(x^5 + 1),x)","\sum _{k=1}^4\ln\left(\mathrm{root}\left(z^4-\frac{z}{25}+\frac{1}{125},z,k\right)\,\left(-4\,x+\mathrm{root}\left(z^4-\frac{z}{25}+\frac{1}{125},z,k\right)\,\left(25\,\mathrm{root}\left(z^4-\frac{z}{25}+\frac{1}{125},z,k\right)+15\,x-15\right)+1\right)\right)\,\mathrm{root}\left(z^4-\frac{z}{25}+\frac{1}{125},z,k\right)","Not used",1,"symsum(log(root(z^4 - z/25 + 1/125, z, k)*(root(z^4 - z/25 + 1/125, z, k)*(25*root(z^4 - z/25 + 1/125, z, k) + 15*x - 15) - 4*x + 1))*root(z^4 - z/25 + 1/125, z, k), k, 1, 4)","B"
222,1,65,109,4.981363,"\text{Not used}","int((x - 1)/(x^5 - 1),x)","\sum _{k=1}^4\ln\left(-\mathrm{root}\left(z^4+\frac{z}{25}+\frac{1}{125},z,k\right)\,\left(4\,x+\mathrm{root}\left(z^4+\frac{z}{25}+\frac{1}{125},z,k\right)\,\left(25\,\mathrm{root}\left(z^4+\frac{z}{25}+\frac{1}{125},z,k\right)+15\,x+15\right)+1\right)\right)\,\mathrm{root}\left(z^4+\frac{z}{25}+\frac{1}{125},z,k\right)","Not used",1,"symsum(log(-root(z^4 + z/25 + 1/125, z, k)*(4*x + root(z^4 + z/25 + 1/125, z, k)*(25*root(z^4 + z/25 + 1/125, z, k) + 15*x + 15) + 1))*root(z^4 + z/25 + 1/125, z, k), k, 1, 4)","B"
223,1,237,208,4.920075,"\text{Not used}","int((x^11*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^{15}\,\left(\frac{e}{15\,b}-\frac{a\,f}{15\,b^2}\right)+x^{12}\,\left(\frac{d}{12\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{12\,b}\right)+x^9\,\left(\frac{c}{9\,b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{9\,b}\right)+\frac{\ln\left(b\,x^3+a\right)\,\left(f\,a^6-e\,a^5\,b+d\,a^4\,b^2-c\,a^3\,b^3\right)}{3\,b^7}+\frac{f\,x^{18}}{18\,b}+\frac{a^2\,x^3\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{3\,b^2}-\frac{a\,x^6\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{6\,b}","Not used",1,"x^15*(e/(15*b) - (a*f)/(15*b^2)) + x^12*(d/(12*b) - (a*(e/b - (a*f)/b^2))/(12*b)) + x^9*(c/(9*b) - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/(9*b)) + (log(a + b*x^3)*(a^6*f - a^3*b^3*c + a^4*b^2*d - a^5*b*e))/(3*b^7) + (f*x^18)/(18*b) + (a^2*x^3*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/(3*b^2) - (a*x^6*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/(6*b)","B"
224,1,189,170,4.959431,"\text{Not used}","int((x^8*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^{12}\,\left(\frac{e}{12\,b}-\frac{a\,f}{12\,b^2}\right)+x^9\,\left(\frac{d}{9\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{9\,b}\right)+x^6\,\left(\frac{c}{6\,b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{6\,b}\right)-\frac{\ln\left(b\,x^3+a\right)\,\left(f\,a^5-e\,a^4\,b+d\,a^3\,b^2-c\,a^2\,b^3\right)}{3\,b^6}+\frac{f\,x^{15}}{15\,b}-\frac{a\,x^3\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{3\,b}","Not used",1,"x^12*(e/(12*b) - (a*f)/(12*b^2)) + x^9*(d/(9*b) - (a*(e/b - (a*f)/b^2))/(9*b)) + x^6*(c/(6*b) - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/(6*b)) - (log(a + b*x^3)*(a^5*f - a^2*b^3*c + a^3*b^2*d - a^4*b*e))/(3*b^6) + (f*x^15)/(15*b) - (a*x^3*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/(3*b)","B"
225,1,141,132,4.927451,"\text{Not used}","int((x^5*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^9\,\left(\frac{e}{9\,b}-\frac{a\,f}{9\,b^2}\right)+x^6\,\left(\frac{d}{6\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{6\,b}\right)+x^3\,\left(\frac{c}{3\,b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{3\,b}\right)+\frac{f\,x^{12}}{12\,b}+\frac{\ln\left(b\,x^3+a\right)\,\left(f\,a^4-e\,a^3\,b+d\,a^2\,b^2-c\,a\,b^3\right)}{3\,b^5}","Not used",1,"x^9*(e/(9*b) - (a*f)/(9*b^2)) + x^6*(d/(6*b) - (a*(e/b - (a*f)/b^2))/(6*b)) + x^3*(c/(3*b) - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/(3*b)) + (f*x^12)/(12*b) + (log(a + b*x^3)*(a^4*f + a^2*b^2*d - a*b^3*c - a^3*b*e))/(3*b^5)","B"
226,1,96,96,4.827347,"\text{Not used}","int((x^2*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^6\,\left(\frac{e}{6\,b}-\frac{a\,f}{6\,b^2}\right)+x^3\,\left(\frac{d}{3\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{3\,b}\right)+\frac{\ln\left(b\,x^3+a\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^4}+\frac{f\,x^9}{9\,b}","Not used",1,"x^6*(e/(6*b) - (a*f)/(6*b^2)) + x^3*(d/(3*b) - (a*(e/b - (a*f)/b^2))/(3*b)) + (log(a + b*x^3)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^4) + (f*x^9)/(9*b)","B"
227,1,76,80,4.925094,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x*(a + b*x^3)),x)","x^3\,\left(\frac{e}{3\,b}-\frac{a\,f}{3\,b^2}\right)+\frac{f\,x^6}{6\,b}+\frac{c\,\ln\left(x\right)}{a}-\frac{\ln\left(b\,x^3+a\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a\,b^3}","Not used",1,"x^3*(e/(3*b) - (a*f)/(3*b^2)) + (f*x^6)/(6*b) + (c*log(x))/a - (log(a + b*x^3)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a*b^3)","B"
228,1,74,81,4.973018,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^4*(a + b*x^3)),x)","\frac{f\,x^3}{3\,b}-\frac{c}{3\,a\,x^3}+\frac{\ln\left(x\right)\,\left(a\,d-b\,c\right)}{a^2}+\frac{\ln\left(b\,x^3+a\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^2\,b^2}","Not used",1,"(f*x^3)/(3*b) - c/(3*a*x^3) + (log(x)*(a*d - b*c))/a^2 + (log(a + b*x^3)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^2*b^2)","B"
229,1,92,95,4.992796,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^7*(a + b*x^3)),x)","\frac{\ln\left(x\right)\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{a^3}-\frac{\frac{c}{6\,a}+\frac{x^3\,\left(a\,d-b\,c\right)}{3\,a^2}}{x^6}-\frac{\ln\left(b\,x^3+a\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^3\,b}","Not used",1,"(log(x)*(b^2*c + a^2*e - a*b*d))/a^3 - (c/(6*a) + (x^3*(a*d - b*c))/(3*a^2))/x^6 - (log(a + b*x^3)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^3*b)","B"
230,1,123,128,5.024907,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^10*(a + b*x^3)),x)","\frac{\ln\left(b\,x^3+a\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^4}-\frac{\frac{c}{9\,a}+\frac{x^3\,\left(a\,d-b\,c\right)}{6\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{3\,a^3}}{x^9}-\frac{\ln\left(x\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^4}","Not used",1,"(log(a + b*x^3)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^4) - (c/(9*a) + (x^3*(a*d - b*c))/(6*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/(3*a^3))/x^9 - (log(x)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^4","B"
231,1,161,164,5.073166,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^13*(a + b*x^3)),x)","\frac{\ln\left(x\right)\,\left(-f\,a^3\,b+e\,a^2\,b^2-d\,a\,b^3+c\,b^4\right)}{a^5}-\frac{\ln\left(b\,x^3+a\right)\,\left(-f\,a^3\,b+e\,a^2\,b^2-d\,a\,b^3+c\,b^4\right)}{3\,a^5}-\frac{\frac{c}{12\,a}-\frac{x^9\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^4}+\frac{x^3\,\left(a\,d-b\,c\right)}{9\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{6\,a^3}}{x^{12}}","Not used",1,"(log(x)*(b^4*c + a^2*b^2*e - a*b^3*d - a^3*b*f))/a^5 - (log(a + b*x^3)*(b^4*c + a^2*b^2*e - a*b^3*d - a^3*b*f))/(3*a^5) - (c/(12*a) - (x^9*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^4) + (x^3*(a*d - b*c))/(9*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/(6*a^3))/x^12","B"
232,1,200,205,0.257414,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^16*(a + b*x^3)),x)","\frac{\ln\left(b\,x^3+a\right)\,\left(-f\,a^3\,b^2+e\,a^2\,b^3-d\,a\,b^4+c\,b^5\right)}{3\,a^6}-\frac{\frac{c}{15\,a}-\frac{x^9\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{6\,a^4}+\frac{x^3\,\left(a\,d-b\,c\right)}{12\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{9\,a^3}+\frac{b\,x^{12}\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^5}}{x^{15}}-\frac{\ln\left(x\right)\,\left(-f\,a^3\,b^2+e\,a^2\,b^3-d\,a\,b^4+c\,b^5\right)}{a^6}","Not used",1,"(log(a + b*x^3)*(b^5*c + a^2*b^3*e - a^3*b^2*f - a*b^4*d))/(3*a^6) - (c/(15*a) - (x^9*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(6*a^4) + (x^3*(a*d - b*c))/(12*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/(9*a^3) + (b*x^12*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^5))/x^15 - (log(x)*(b^5*c + a^2*b^3*e - a^3*b^2*f - a*b^4*d))/a^6","B"
233,1,358,348,0.310893,"\text{Not used}","int((x^9*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^{13}\,\left(\frac{e}{13\,b}-\frac{a\,f}{13\,b^2}\right)+x^{10}\,\left(\frac{d}{10\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{10\,b}\right)+x^7\,\left(\frac{c}{7\,b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{7\,b}\right)+\frac{f\,x^{16}}{16\,b}-\frac{a^{7/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{19/3}}+\frac{a^2\,x\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{b^2}-\frac{a\,x^4\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{4\,b}-\frac{a^{7/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{19/3}}+\frac{a^{7/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{19/3}}","Not used",1,"x^13*(e/(13*b) - (a*f)/(13*b^2)) + x^10*(d/(10*b) - (a*(e/b - (a*f)/b^2))/(10*b)) + x^7*(c/(7*b) - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/(7*b)) + (f*x^16)/(16*b) - (a^(7/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(19/3)) + (a^2*x*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/b^2 - (a*x^4*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/(4*b) - (a^(7/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(19/3)) + (a^(7/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(19/3))","B"
234,1,313,316,5.162405,"\text{Not used}","int((x^7*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^{11}\,\left(\frac{e}{11\,b}-\frac{a\,f}{11\,b^2}\right)+x^8\,\left(\frac{d}{8\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{8\,b}\right)+x^5\,\left(\frac{c}{5\,b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{5\,b}\right)+\frac{f\,x^{14}}{14\,b}-\frac{a^{5/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{17/3}}-\frac{a\,x^2\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{2\,b}+\frac{a^{5/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{17/3}}-\frac{a^{5/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{17/3}}","Not used",1,"x^11*(e/(11*b) - (a*f)/(11*b^2)) + x^8*(d/(8*b) - (a*(e/b - (a*f)/b^2))/(8*b)) + x^5*(c/(5*b) - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/(5*b)) + (f*x^14)/(14*b) - (a^(5/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(17/3)) - (a*x^2*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/(2*b) + (a^(5/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(17/3)) - (a^(5/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(17/3))","B"
235,1,311,312,5.186552,"\text{Not used}","int((x^6*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^{10}\,\left(\frac{e}{10\,b}-\frac{a\,f}{10\,b^2}\right)+x^7\,\left(\frac{d}{7\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{7\,b}\right)+x^4\,\left(\frac{c}{4\,b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{4\,b}\right)+\frac{f\,x^{13}}{13\,b}+\frac{a^{4/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{16/3}}-\frac{a\,x\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{b}+\frac{a^{4/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{16/3}}-\frac{a^{4/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{16/3}}","Not used",1,"x^10*(e/(10*b) - (a*f)/(10*b^2)) + x^7*(d/(7*b) - (a*(e/b - (a*f)/b^2))/(7*b)) + x^4*(c/(4*b) - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/(4*b)) + (f*x^13)/(13*b) + (a^(4/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(16/3)) - (a*x*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/b + (a^(4/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(16/3)) - (a^(4/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(16/3))","B"
236,1,267,279,5.146722,"\text{Not used}","int((x^4*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^8\,\left(\frac{e}{8\,b}-\frac{a\,f}{8\,b^2}\right)+x^5\,\left(\frac{d}{5\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{5\,b}\right)+x^2\,\left(\frac{c}{2\,b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{2\,b}\right)+\frac{f\,x^{11}}{11\,b}+\frac{a^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{14/3}}-\frac{a^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{14/3}}+\frac{a^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{14/3}}","Not used",1,"x^8*(e/(8*b) - (a*f)/(8*b^2)) + x^5*(d/(5*b) - (a*(e/b - (a*f)/b^2))/(5*b)) + x^2*(c/(2*b) - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/(2*b)) + (f*x^11)/(11*b) + (a^(2/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(14/3)) - (a^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(14/3)) + (a^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(14/3))","B"
237,1,264,274,5.101079,"\text{Not used}","int((x^3*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^7\,\left(\frac{e}{7\,b}-\frac{a\,f}{7\,b^2}\right)+x^4\,\left(\frac{d}{4\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{4\,b}\right)+x\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)+\frac{f\,x^{10}}{10\,b}-\frac{a^{1/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{13/3}}-\frac{a^{1/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{13/3}}+\frac{a^{1/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,b^{13/3}}","Not used",1,"x^7*(e/(7*b) - (a*f)/(7*b^2)) + x^4*(d/(4*b) - (a*(e/b - (a*f)/b^2))/(4*b)) + x*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b) + (f*x^10)/(10*b) - (a^(1/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(13/3)) - (a^(1/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(13/3)) + (a^(1/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*b^(13/3))","B"
238,1,225,245,5.135130,"\text{Not used}","int((x*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3),x)","x^5\,\left(\frac{e}{5\,b}-\frac{a\,f}{5\,b^2}\right)+x^2\,\left(\frac{d}{2\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{2\,b}\right)+\frac{f\,x^8}{8\,b}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{1/3}\,b^{11/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{1/3}\,b^{11/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{1/3}\,b^{11/3}}","Not used",1,"x^5*(e/(5*b) - (a*f)/(5*b^2)) + x^2*(d/(2*b) - (a*(e/b - (a*f)/b^2))/(2*b)) + (f*x^8)/(8*b) - (log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(1/3)*b^(11/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(1/3)*b^(11/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(1/3)*b^(11/3))","B"
239,1,222,240,5.173908,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3),x)","x^4\,\left(\frac{e}{4\,b}-\frac{a\,f}{4\,b^2}\right)+x\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)+\frac{f\,x^7}{7\,b}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{2/3}\,b^{10/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{2/3}\,b^{10/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{2/3}\,b^{10/3}}","Not used",1,"x^4*(e/(4*b) - (a*f)/(4*b^2)) + x*(d/b - (a*(e/b - (a*f)/b^2))/b) + (f*x^7)/(7*b) + (log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(2/3)*b^(10/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(2/3)*b^(10/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(2/3)*b^(10/3))","B"
240,1,204,227,5.372312,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^2*(a + b*x^3)),x)","x^2\,\left(\frac{e}{2\,b}-\frac{a\,f}{2\,b^2}\right)-\frac{c}{a\,x}+\frac{f\,x^5}{5\,b}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{4/3}\,b^{8/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{4/3}\,b^{8/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{4/3}\,b^{8/3}}","Not used",1,"x^2*(e/(2*b) - (a*f)/(2*b^2)) - c/(a*x) + (f*x^5)/(5*b) + (log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(4/3)*b^(8/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(4/3)*b^(8/3)) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(4/3)*b^(8/3))","B"
241,1,201,224,0.283934,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^3*(a + b*x^3)),x)","x\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)-\frac{c}{2\,a\,x^2}+\frac{f\,x^4}{4\,b}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{5/3}\,b^{7/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{5/3}\,b^{7/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{5/3}\,b^{7/3}}","Not used",1,"x*(e/b - (a*f)/b^2) - c/(2*a*x^2) + (f*x^4)/(4*b) - (log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(5/3)*b^(7/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(5/3)*b^(7/3)) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(5/3)*b^(7/3))","B"
242,1,209,227,5.163617,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^5*(a + b*x^3)),x)","\frac{f\,x^2}{2\,b}-\frac{\frac{b\,c}{4\,a}+\frac{b\,x^3\,\left(a\,d-b\,c\right)}{a^2}}{b\,x^4}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{7/3}\,b^{5/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{7/3}\,b^{5/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{7/3}\,b^{5/3}}","Not used",1,"(f*x^2)/(2*b) - ((b*c)/(4*a) + (b*x^3*(a*d - b*c))/a^2)/(b*x^4) - (log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(7/3)*b^(5/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(7/3)*b^(5/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(7/3)*b^(5/3))","B"
243,1,207,225,5.090959,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^6*(a + b*x^3)),x)","\frac{f\,x}{b}-\frac{\frac{b\,c}{5\,a}+\frac{b\,x^3\,\left(a\,d-b\,c\right)}{2\,a^2}}{b\,x^5}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{8/3}\,b^{4/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{8/3}\,b^{4/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{8/3}\,b^{4/3}}","Not used",1,"(f*x)/b - ((b*c)/(5*a) + (b*x^3*(a*d - b*c))/(2*a^2))/(b*x^5) + (log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(8/3)*b^(4/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(8/3)*b^(4/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(8/3)*b^(4/3))","B"
244,1,219,242,5.199980,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^8*(a + b*x^3)),x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{10/3}\,b^{2/3}}-\frac{\frac{c}{7\,a}+\frac{x^3\,\left(a\,d-b\,c\right)}{4\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{a^3}}{x^7}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{10/3}\,b^{2/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{10/3}\,b^{2/3}}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(10/3)*b^(2/3)) - (c/(7*a) + (x^3*(a*d - b*c))/(4*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/a^3)/x^7 - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(10/3)*b^(2/3)) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(10/3)*b^(2/3))","B"
245,1,220,244,5.125869,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^9*(a + b*x^3)),x)","-\frac{\frac{c}{8\,a}+\frac{x^3\,\left(a\,d-b\,c\right)}{5\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{2\,a^3}}{x^8}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{11/3}\,b^{1/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{11/3}\,b^{1/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{11/3}\,b^{1/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(11/3)*b^(1/3)) - (log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(11/3)*b^(1/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(11/3)*b^(1/3)) - (c/(8*a) + (x^3*(a*d - b*c))/(5*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/(2*a^3))/x^8","B"
246,1,253,277,5.328984,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^11*(a + b*x^3)),x)","-\frac{\frac{c}{10\,a}-\frac{x^9\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^4}+\frac{x^3\,\left(a\,d-b\,c\right)}{7\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{4\,a^3}}{x^{10}}-\frac{b^{1/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{13/3}}+\frac{b^{1/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{13/3}}-\frac{b^{1/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{13/3}}","Not used",1,"(b^(1/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(13/3)) - (b^(1/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(13/3)) - (c/(10*a) - (x^9*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^4 + (x^3*(a*d - b*c))/(7*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/(4*a^3))/x^10 - (b^(1/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(13/3))","B"
247,1,253,280,5.152649,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^12*(a + b*x^3)),x)","\frac{b^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{14/3}}-\frac{\frac{c}{11\,a}-\frac{x^9\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{2\,a^4}+\frac{x^3\,\left(a\,d-b\,c\right)}{8\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{5\,a^3}}{x^{11}}+\frac{b^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{14/3}}-\frac{b^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{14/3}}","Not used",1,"(b^(2/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(14/3)) - (c/(11*a) - (x^9*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(2*a^4) + (x^3*(a*d - b*c))/(8*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/(5*a^3))/x^11 + (b^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(14/3)) - (b^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(14/3))","B"
248,1,286,313,5.228100,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^14*(a + b*x^3)),x)","\frac{b^{4/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{16/3}}-\frac{\frac{c}{13\,a}-\frac{x^9\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{4\,a^4}+\frac{x^3\,\left(a\,d-b\,c\right)}{10\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{7\,a^3}+\frac{b\,x^{12}\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^5}}{x^{13}}-\frac{b^{4/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{16/3}}+\frac{b^{4/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{16/3}}","Not used",1,"(b^(4/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(16/3)) - (c/(13*a) - (x^9*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(4*a^4) + (x^3*(a*d - b*c))/(10*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/(7*a^3) + (b*x^12*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^5)/x^13 - (b^(4/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(16/3)) + (b^(4/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(16/3))","B"
249,1,287,315,5.170738,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^15*(a + b*x^3)),x)","-\frac{\frac{c}{14\,a}-\frac{x^9\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{5\,a^4}+\frac{x^3\,\left(a\,d-b\,c\right)}{11\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{8\,a^3}+\frac{b\,x^{12}\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{2\,a^5}}{x^{14}}-\frac{b^{5/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{17/3}}-\frac{b^{5/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{17/3}}+\frac{b^{5/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{17/3}}","Not used",1,"(b^(5/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(17/3)) - (b^(5/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(17/3)) - (b^(5/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(17/3)) - (c/(14*a) - (x^9*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(5*a^4) + (x^3*(a*d - b*c))/(11*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/(8*a^3) + (b*x^12*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(2*a^5))/x^14","B"
250,1,323,351,5.163719,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^17*(a + b*x^3)),x)","-\frac{\frac{c}{16\,a}-\frac{x^9\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{7\,a^4}+\frac{x^3\,\left(a\,d-b\,c\right)}{13\,a^2}+\frac{x^6\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{10\,a^3}+\frac{b\,x^{12}\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{4\,a^5}-\frac{b^2\,x^{15}\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^6}}{x^{16}}-\frac{b^{7/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{19/3}}+\frac{b^{7/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{19/3}}-\frac{b^{7/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^{19/3}}","Not used",1,"(b^(7/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(19/3)) - (b^(7/3)*log(b^(1/3)*x + a^(1/3))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(19/3)) - (c/(16*a) - (x^9*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(7*a^4) + (x^3*(a*d - b*c))/(13*a^2) + (x^6*(b^2*c + a^2*e - a*b*d))/(10*a^3) + (b*x^12*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(4*a^5) - (b^2*x^15*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^6)/x^16 - (b^(7/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^(19/3))","B"
251,1,356,220,4.987825,"\text{Not used}","int((x^11*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^{12}\,\left(\frac{e}{12\,b^2}-\frac{a\,f}{6\,b^3}\right)-x^3\,\left(\frac{2\,a\,\left(\frac{c}{b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b^2}+\frac{2\,a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{b}\right)}{3\,b}-\frac{a^2\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{3\,b^2}\right)-x^9\,\left(\frac{a^2\,f}{9\,b^4}-\frac{d}{9\,b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{9\,b}\right)+x^6\,\left(\frac{c}{6\,b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{6\,b^2}+\frac{a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{3\,b}\right)-\frac{\ln\left(b\,x^3+a\right)\,\left(6\,f\,a^5-5\,e\,a^4\,b+4\,d\,a^3\,b^2-3\,c\,a^2\,b^3\right)}{3\,b^7}+\frac{f\,x^{15}}{15\,b^2}-\frac{f\,a^6-e\,a^5\,b+d\,a^4\,b^2-c\,a^3\,b^3}{3\,b\,\left(b^7\,x^3+a\,b^6\right)}","Not used",1,"x^12*(e/(12*b^2) - (a*f)/(6*b^3)) - x^3*((2*a*(c/b^2 - (a^2*(e/b^2 - (2*a*f)/b^3))/b^2 + (2*a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/b))/(3*b) - (a^2*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/(3*b^2)) - x^9*((a^2*f)/(9*b^4) - d/(9*b^2) + (2*a*(e/b^2 - (2*a*f)/b^3))/(9*b)) + x^6*(c/(6*b^2) - (a^2*(e/b^2 - (2*a*f)/b^3))/(6*b^2) + (a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/(3*b)) - (log(a + b*x^3)*(6*a^5*f - 3*a^2*b^3*c + 4*a^3*b^2*d - 5*a^4*b*e))/(3*b^7) + (f*x^15)/(15*b^2) - (a^6*f - a^3*b^3*c + a^4*b^2*d - a^5*b*e)/(3*b*(a*b^6 + b^7*x^3))","B"
252,1,233,180,4.995156,"\text{Not used}","int((x^8*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^9\,\left(\frac{e}{9\,b^2}-\frac{2\,a\,f}{9\,b^3}\right)-x^6\,\left(\frac{a^2\,f}{6\,b^4}-\frac{d}{6\,b^2}+\frac{a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{3\,b}\right)+x^3\,\left(\frac{c}{3\,b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{3\,b^2}+\frac{2\,a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{3\,b}\right)+\frac{f\,x^{12}}{12\,b^2}+\frac{f\,a^5-e\,a^4\,b+d\,a^3\,b^2-c\,a^2\,b^3}{3\,b\,\left(b^6\,x^3+a\,b^5\right)}+\frac{\ln\left(b\,x^3+a\right)\,\left(5\,f\,a^4-4\,e\,a^3\,b+3\,d\,a^2\,b^2-2\,c\,a\,b^3\right)}{3\,b^6}","Not used",1,"x^9*(e/(9*b^2) - (2*a*f)/(9*b^3)) - x^6*((a^2*f)/(6*b^4) - d/(6*b^2) + (a*(e/b^2 - (2*a*f)/b^3))/(3*b)) + x^3*(c/(3*b^2) - (a^2*(e/b^2 - (2*a*f)/b^3))/(3*b^2) + (2*a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/(3*b)) + (f*x^12)/(12*b^2) + (a^5*f - a^2*b^3*c + a^3*b^2*d - a^4*b*e)/(3*b*(a*b^5 + b^6*x^3)) + (log(a + b*x^3)*(5*a^4*f + 3*a^2*b^2*d - 2*a*b^3*c - 4*a^3*b*e))/(3*b^6)","B"
253,1,155,140,4.929798,"\text{Not used}","int((x^5*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^6\,\left(\frac{e}{6\,b^2}-\frac{a\,f}{3\,b^3}\right)-x^3\,\left(\frac{a^2\,f}{3\,b^4}-\frac{d}{3\,b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{3\,b}\right)+\frac{\ln\left(b\,x^3+a\right)\,\left(-4\,f\,a^3+3\,e\,a^2\,b-2\,d\,a\,b^2+c\,b^3\right)}{3\,b^5}-\frac{f\,a^4-e\,a^3\,b+d\,a^2\,b^2-c\,a\,b^3}{3\,b\,\left(b^5\,x^3+a\,b^4\right)}+\frac{f\,x^9}{9\,b^2}","Not used",1,"x^6*(e/(6*b^2) - (a*f)/(3*b^3)) - x^3*((a^2*f)/(3*b^4) - d/(3*b^2) + (2*a*(e/b^2 - (2*a*f)/b^3))/(3*b)) + (log(a + b*x^3)*(b^3*c - 4*a^3*f - 2*a*b^2*d + 3*a^2*b*e))/(3*b^5) - (a^4*f + a^2*b^2*d - a*b^3*c - a^3*b*e)/(3*b*(a*b^4 + b^5*x^3)) + (f*x^9)/(9*b^2)","B"
254,1,103,103,0.085072,"\text{Not used}","int((x^2*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^3\,\left(\frac{e}{3\,b^2}-\frac{2\,a\,f}{3\,b^3}\right)+\frac{f\,x^6}{6\,b^2}-\frac{-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3}{3\,b\,\left(b^4\,x^3+a\,b^3\right)}+\frac{\ln\left(b\,x^3+a\right)\,\left(3\,f\,a^2-2\,e\,a\,b+d\,b^2\right)}{3\,b^4}","Not used",1,"x^3*(e/(3*b^2) - (2*a*f)/(3*b^3)) + (f*x^6)/(6*b^2) - (b^3*c - a^3*f - a*b^2*d + a^2*b*e)/(3*b*(a*b^3 + b^4*x^3)) + (log(a + b*x^3)*(b^2*d + 3*a^2*f - 2*a*b*e))/(3*b^4)","B"
255,1,100,100,5.032905,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x*(a + b*x^3)^2),x)","\frac{f\,x^3}{3\,b^2}+\frac{c\,\ln\left(x\right)}{a^2}+\frac{-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3}{3\,a\,b\,\left(b^3\,x^3+a\,b^2\right)}-\frac{\ln\left(b\,x^3+a\right)\,\left(2\,f\,a^3-e\,a^2\,b+c\,b^3\right)}{3\,a^2\,b^3}","Not used",1,"(f*x^3)/(3*b^2) + (c*log(x))/a^2 + (b^3*c - a^3*f - a*b^2*d + a^2*b*e)/(3*a*b*(a*b^2 + b^3*x^3)) - (log(a + b*x^3)*(b^3*c + 2*a^3*f - a^2*b*e))/(3*a^2*b^3)","B"
256,1,109,109,5.046207,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^4*(a + b*x^3)^2),x)","\frac{\ln\left(x\right)\,\left(a\,d-2\,b\,c\right)}{a^3}-\frac{\frac{c}{3\,a}+\frac{x^3\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+2\,c\,b^3\right)}{3\,a^2\,b^2}}{b\,x^6+a\,x^3}+\frac{\ln\left(b\,x^3+a\right)\,\left(f\,a^3-d\,a\,b^2+2\,c\,b^3\right)}{3\,a^3\,b^2}","Not used",1,"(log(x)*(a*d - 2*b*c))/a^3 - (c/(3*a) + (x^3*(2*b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^2*b^2))/(a*x^3 + b*x^6) + (log(a + b*x^3)*(2*b^3*c + a^3*f - a*b^2*d))/(3*a^3*b^2)","B"
257,1,130,130,5.014041,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^7*(a + b*x^3)^2),x)","\frac{\ln\left(x\right)\,\left(e\,a^2-2\,d\,a\,b+3\,c\,b^2\right)}{a^4}-\frac{\ln\left(b\,x^3+a\right)\,\left(e\,a^2-2\,d\,a\,b+3\,c\,b^2\right)}{3\,a^4}-\frac{\frac{c}{6\,a}+\frac{x^3\,\left(2\,a\,d-3\,b\,c\right)}{6\,a^2}-\frac{x^6\,\left(-f\,a^3+e\,a^2\,b-2\,d\,a\,b^2+3\,c\,b^3\right)}{3\,a^3\,b}}{b\,x^9+a\,x^6}","Not used",1,"(log(x)*(3*b^2*c + a^2*e - 2*a*b*d))/a^4 - (log(a + b*x^3)*(3*b^2*c + a^2*e - 2*a*b*d))/(3*a^4) - (c/(6*a) + (x^3*(2*a*d - 3*b*c))/(6*a^2) - (x^6*(3*b^3*c - a^3*f - 2*a*b^2*d + a^2*b*e))/(3*a^3*b))/(a*x^6 + b*x^9)","B"
258,1,175,175,5.084254,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^10*(a + b*x^3)^2),x)","\frac{\ln\left(b\,x^3+a\right)\,\left(-f\,a^3+2\,e\,a^2\,b-3\,d\,a\,b^2+4\,c\,b^3\right)}{3\,a^5}-\frac{\frac{c}{9\,a}+\frac{x^9\,\left(-f\,a^3+2\,e\,a^2\,b-3\,d\,a\,b^2+4\,c\,b^3\right)}{3\,a^4}+\frac{x^3\,\left(3\,a\,d-4\,b\,c\right)}{18\,a^2}+\frac{x^6\,\left(2\,e\,a^2-3\,d\,a\,b+4\,c\,b^2\right)}{6\,a^3}}{b\,x^{12}+a\,x^9}-\frac{\ln\left(x\right)\,\left(-f\,a^3+2\,e\,a^2\,b-3\,d\,a\,b^2+4\,c\,b^3\right)}{a^5}","Not used",1,"(log(a + b*x^3)*(4*b^3*c - a^3*f - 3*a*b^2*d + 2*a^2*b*e))/(3*a^5) - (c/(9*a) + (x^9*(4*b^3*c - a^3*f - 3*a*b^2*d + 2*a^2*b*e))/(3*a^4) + (x^3*(3*a*d - 4*b*c))/(18*a^2) + (x^6*(4*b^2*c + 2*a^2*e - 3*a*b*d))/(6*a^3))/(a*x^9 + b*x^12) - (log(x)*(4*b^3*c - a^3*f - 3*a*b^2*d + 2*a^2*b*e))/a^5","B"
259,1,216,214,5.086722,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^13*(a + b*x^3)^2),x)","\frac{\ln\left(x\right)\,\left(-2\,f\,a^3\,b+3\,e\,a^2\,b^2-4\,d\,a\,b^3+5\,c\,b^4\right)}{a^6}-\frac{\ln\left(b\,x^3+a\right)\,\left(-2\,f\,a^3\,b+3\,e\,a^2\,b^2-4\,d\,a\,b^3+5\,c\,b^4\right)}{3\,a^6}-\frac{\frac{c}{12\,a}-\frac{x^9\,\left(-2\,f\,a^3+3\,e\,a^2\,b-4\,d\,a\,b^2+5\,c\,b^3\right)}{6\,a^4}+\frac{x^3\,\left(4\,a\,d-5\,b\,c\right)}{36\,a^2}+\frac{x^6\,\left(3\,e\,a^2-4\,d\,a\,b+5\,c\,b^2\right)}{18\,a^3}-\frac{b\,x^{12}\,\left(-2\,f\,a^3+3\,e\,a^2\,b-4\,d\,a\,b^2+5\,c\,b^3\right)}{3\,a^5}}{b\,x^{15}+a\,x^{12}}","Not used",1,"(log(x)*(5*b^4*c + 3*a^2*b^2*e - 4*a*b^3*d - 2*a^3*b*f))/a^6 - (log(a + b*x^3)*(5*b^4*c + 3*a^2*b^2*e - 4*a*b^3*d - 2*a^3*b*f))/(3*a^6) - (c/(12*a) - (x^9*(5*b^3*c - 2*a^3*f - 4*a*b^2*d + 3*a^2*b*e))/(6*a^4) + (x^3*(4*a*d - 5*b*c))/(36*a^2) + (x^6*(5*b^2*c + 3*a^2*e - 4*a*b*d))/(18*a^3) - (b*x^12*(5*b^3*c - 2*a^3*f - 4*a*b^2*d + 3*a^2*b*e))/(3*a^5))/(a*x^12 + b*x^15)","B"
260,1,481,369,0.346563,"\text{Not used}","int((x^9*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^{10}\,\left(\frac{e}{10\,b^2}-\frac{a\,f}{5\,b^3}\right)-x\,\left(\frac{2\,a\,\left(\frac{c}{b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b^2}+\frac{2\,a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{b}\right)}{b}-\frac{a^2\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{b^2}\right)-x^7\,\left(\frac{a^2\,f}{7\,b^4}-\frac{d}{7\,b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{7\,b}\right)+x^4\,\left(\frac{c}{4\,b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{4\,b^2}+\frac{a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{2\,b}\right)+\frac{f\,x^{13}}{13\,b^2}+\frac{x\,\left(\frac{f\,a^5}{3}-\frac{e\,a^4\,b}{3}+\frac{d\,a^3\,b^2}{3}-\frac{c\,a^2\,b^3}{3}\right)}{b^7\,x^3+a\,b^6}+\frac{a^{4/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-16\,f\,a^3+13\,e\,a^2\,b-10\,d\,a\,b^2+7\,c\,b^3\right)}{9\,b^{19/3}}+\frac{a^{4/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-16\,f\,a^3+13\,e\,a^2\,b-10\,d\,a\,b^2+7\,c\,b^3\right)}{9\,b^{19/3}}-\frac{a^{4/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-16\,f\,a^3+13\,e\,a^2\,b-10\,d\,a\,b^2+7\,c\,b^3\right)}{9\,b^{19/3}}","Not used",1,"x^10*(e/(10*b^2) - (a*f)/(5*b^3)) - x*((2*a*(c/b^2 - (a^2*(e/b^2 - (2*a*f)/b^3))/b^2 + (2*a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/b))/b - (a^2*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/b^2) - x^7*((a^2*f)/(7*b^4) - d/(7*b^2) + (2*a*(e/b^2 - (2*a*f)/b^3))/(7*b)) + x^4*(c/(4*b^2) - (a^2*(e/b^2 - (2*a*f)/b^3))/(4*b^2) + (a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/(2*b)) + (f*x^13)/(13*b^2) + (x*((a^5*f)/3 - (a^2*b^3*c)/3 + (a^3*b^2*d)/3 - (a^4*b*e)/3))/(a*b^6 + b^7*x^3) + (a^(4/3)*log(b^(1/3)*x + a^(1/3))*(7*b^3*c - 16*a^3*f - 10*a*b^2*d + 13*a^2*b*e))/(9*b^(19/3)) + (a^(4/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(7*b^3*c - 16*a^3*f - 10*a*b^2*d + 13*a^2*b*e))/(9*b^(19/3)) - (a^(4/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(7*b^3*c - 16*a^3*f - 10*a*b^2*d + 13*a^2*b*e))/(9*b^(19/3))","B"
261,1,362,335,5.277927,"\text{Not used}","int((x^7*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^8\,\left(\frac{e}{8\,b^2}-\frac{a\,f}{4\,b^3}\right)-x^5\,\left(\frac{a^2\,f}{5\,b^4}-\frac{d}{5\,b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{5\,b}\right)+x^2\,\left(\frac{c}{2\,b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{2\,b^2}+\frac{a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{b}\right)+\frac{f\,x^{11}}{11\,b^2}-\frac{x^2\,\left(\frac{f\,a^4}{3}-\frac{e\,a^3\,b}{3}+\frac{d\,a^2\,b^2}{3}-\frac{c\,a\,b^3}{3}\right)}{b^6\,x^3+a\,b^5}+\frac{a^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-14\,f\,a^3+11\,e\,a^2\,b-8\,d\,a\,b^2+5\,c\,b^3\right)}{9\,b^{17/3}}-\frac{a^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-14\,f\,a^3+11\,e\,a^2\,b-8\,d\,a\,b^2+5\,c\,b^3\right)}{9\,b^{17/3}}+\frac{a^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-14\,f\,a^3+11\,e\,a^2\,b-8\,d\,a\,b^2+5\,c\,b^3\right)}{9\,b^{17/3}}","Not used",1,"x^8*(e/(8*b^2) - (a*f)/(4*b^3)) - x^5*((a^2*f)/(5*b^4) - d/(5*b^2) + (2*a*(e/b^2 - (2*a*f)/b^3))/(5*b)) + x^2*(c/(2*b^2) - (a^2*(e/b^2 - (2*a*f)/b^3))/(2*b^2) + (a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/b) + (f*x^11)/(11*b^2) - (x^2*((a^4*f)/3 + (a^2*b^2*d)/3 - (a*b^3*c)/3 - (a^3*b*e)/3))/(a*b^5 + b^6*x^3) + (a^(2/3)*log(b^(1/3)*x + a^(1/3))*(5*b^3*c - 14*a^3*f - 8*a*b^2*d + 11*a^2*b*e))/(9*b^(17/3)) - (a^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*b^3*c - 14*a^3*f - 8*a*b^2*d + 11*a^2*b*e))/(9*b^(17/3)) + (a^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*b^3*c - 14*a^3*f - 8*a*b^2*d + 11*a^2*b*e))/(9*b^(17/3))","B"
262,1,358,328,5.201214,"\text{Not used}","int((x^6*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^7\,\left(\frac{e}{7\,b^2}-\frac{2\,a\,f}{7\,b^3}\right)+x\,\left(\frac{c}{b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b^2}+\frac{2\,a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{b}\right)-x^4\,\left(\frac{a^2\,f}{4\,b^4}-\frac{d}{4\,b^2}+\frac{a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{2\,b}\right)-\frac{x\,\left(\frac{f\,a^4}{3}-\frac{e\,a^3\,b}{3}+\frac{d\,a^2\,b^2}{3}-\frac{c\,a\,b^3}{3}\right)}{b^6\,x^3+a\,b^5}+\frac{f\,x^{10}}{10\,b^2}-\frac{a^{1/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-13\,f\,a^3+10\,e\,a^2\,b-7\,d\,a\,b^2+4\,c\,b^3\right)}{9\,b^{16/3}}-\frac{a^{1/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-13\,f\,a^3+10\,e\,a^2\,b-7\,d\,a\,b^2+4\,c\,b^3\right)}{9\,b^{16/3}}+\frac{a^{1/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-13\,f\,a^3+10\,e\,a^2\,b-7\,d\,a\,b^2+4\,c\,b^3\right)}{9\,b^{16/3}}","Not used",1,"x^7*(e/(7*b^2) - (2*a*f)/(7*b^3)) + x*(c/b^2 - (a^2*(e/b^2 - (2*a*f)/b^3))/b^2 + (2*a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/b) - x^4*((a^2*f)/(4*b^4) - d/(4*b^2) + (a*(e/b^2 - (2*a*f)/b^3))/(2*b)) - (x*((a^4*f)/3 + (a^2*b^2*d)/3 - (a*b^3*c)/3 - (a^3*b*e)/3))/(a*b^5 + b^6*x^3) + (f*x^10)/(10*b^2) - (a^(1/3)*log(b^(1/3)*x + a^(1/3))*(4*b^3*c - 13*a^3*f - 7*a*b^2*d + 10*a^2*b*e))/(9*b^(16/3)) - (a^(1/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(4*b^3*c - 13*a^3*f - 7*a*b^2*d + 10*a^2*b*e))/(9*b^(16/3)) + (a^(1/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(4*b^3*c - 13*a^3*f - 7*a*b^2*d + 10*a^2*b*e))/(9*b^(16/3))","B"
263,1,287,298,5.222385,"\text{Not used}","int((x^4*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^5\,\left(\frac{e}{5\,b^2}-\frac{2\,a\,f}{5\,b^3}\right)-x^2\,\left(\frac{a^2\,f}{2\,b^4}-\frac{d}{2\,b^2}+\frac{a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)+\frac{f\,x^8}{8\,b^2}-\frac{x^2\,\left(-\frac{f\,a^3}{3}+\frac{e\,a^2\,b}{3}-\frac{d\,a\,b^2}{3}+\frac{c\,b^3}{3}\right)}{b^5\,x^3+a\,b^4}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-11\,f\,a^3+8\,e\,a^2\,b-5\,d\,a\,b^2+2\,c\,b^3\right)}{9\,a^{1/3}\,b^{14/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-11\,f\,a^3+8\,e\,a^2\,b-5\,d\,a\,b^2+2\,c\,b^3\right)}{9\,a^{1/3}\,b^{14/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-11\,f\,a^3+8\,e\,a^2\,b-5\,d\,a\,b^2+2\,c\,b^3\right)}{9\,a^{1/3}\,b^{14/3}}","Not used",1,"x^5*(e/(5*b^2) - (2*a*f)/(5*b^3)) - x^2*((a^2*f)/(2*b^4) - d/(2*b^2) + (a*(e/b^2 - (2*a*f)/b^3))/b) + (f*x^8)/(8*b^2) - (x^2*((b^3*c)/3 - (a^3*f)/3 - (a*b^2*d)/3 + (a^2*b*e)/3))/(a*b^4 + b^5*x^3) - (log(b^(1/3)*x + a^(1/3))*(2*b^3*c - 11*a^3*f - 5*a*b^2*d + 8*a^2*b*e))/(9*a^(1/3)*b^(14/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(2*b^3*c - 11*a^3*f - 5*a*b^2*d + 8*a^2*b*e))/(9*a^(1/3)*b^(14/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(2*b^3*c - 11*a^3*f - 5*a*b^2*d + 8*a^2*b*e))/(9*a^(1/3)*b^(14/3))","B"
264,1,280,288,0.311067,"\text{Not used}","int((x^3*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^4\,\left(\frac{e}{4\,b^2}-\frac{a\,f}{2\,b^3}\right)-x\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)-\frac{x\,\left(-\frac{f\,a^3}{3}+\frac{e\,a^2\,b}{3}-\frac{d\,a\,b^2}{3}+\frac{c\,b^3}{3}\right)}{b^5\,x^3+a\,b^4}+\frac{f\,x^7}{7\,b^2}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-10\,f\,a^3+7\,e\,a^2\,b-4\,d\,a\,b^2+c\,b^3\right)}{9\,a^{2/3}\,b^{13/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-10\,f\,a^3+7\,e\,a^2\,b-4\,d\,a\,b^2+c\,b^3\right)}{9\,a^{2/3}\,b^{13/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-10\,f\,a^3+7\,e\,a^2\,b-4\,d\,a\,b^2+c\,b^3\right)}{9\,a^{2/3}\,b^{13/3}}","Not used",1,"x^4*(e/(4*b^2) - (a*f)/(2*b^3)) - x*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b) - (x*((b^3*c)/3 - (a^3*f)/3 - (a*b^2*d)/3 + (a^2*b*e)/3))/(a*b^4 + b^5*x^3) + (f*x^7)/(7*b^2) + (log(b^(1/3)*x + a^(1/3))*(b^3*c - 10*a^3*f - 4*a*b^2*d + 7*a^2*b*e))/(9*a^(2/3)*b^(13/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c - 10*a^3*f - 4*a*b^2*d + 7*a^2*b*e))/(9*a^(2/3)*b^(13/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c - 10*a^3*f - 4*a*b^2*d + 7*a^2*b*e))/(9*a^(2/3)*b^(13/3))","B"
265,1,246,271,5.231705,"\text{Not used}","int((x*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^2,x)","x^2\,\left(\frac{e}{2\,b^2}-\frac{a\,f}{b^3}\right)+\frac{f\,x^5}{5\,b^2}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(8\,f\,a^3-5\,e\,a^2\,b+2\,d\,a\,b^2+c\,b^3\right)}{9\,a^{4/3}\,b^{11/3}}+\frac{x^2\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a\,\left(b^4\,x^3+a\,b^3\right)}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(8\,f\,a^3-5\,e\,a^2\,b+2\,d\,a\,b^2+c\,b^3\right)}{9\,a^{4/3}\,b^{11/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(8\,f\,a^3-5\,e\,a^2\,b+2\,d\,a\,b^2+c\,b^3\right)}{9\,a^{4/3}\,b^{11/3}}","Not used",1,"x^2*(e/(2*b^2) - (a*f)/b^3) + (f*x^5)/(5*b^2) - (log(b^(1/3)*x + a^(1/3))*(b^3*c + 8*a^3*f + 2*a*b^2*d - 5*a^2*b*e))/(9*a^(4/3)*b^(11/3)) + (x^2*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a*(a*b^3 + b^4*x^3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c + 8*a^3*f + 2*a*b^2*d - 5*a^2*b*e))/(9*a^(4/3)*b^(11/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c + 8*a^3*f + 2*a*b^2*d - 5*a^2*b*e))/(9*a^(4/3)*b^(11/3))","B"
266,1,241,264,5.177328,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2,x)","x\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)+\frac{f\,x^4}{4\,b^2}+\frac{x\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a\,\left(b^4\,x^3+a\,b^3\right)}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(7\,f\,a^3-4\,e\,a^2\,b+d\,a\,b^2+2\,c\,b^3\right)}{9\,a^{5/3}\,b^{10/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,f\,a^3-4\,e\,a^2\,b+d\,a\,b^2+2\,c\,b^3\right)}{9\,a^{5/3}\,b^{10/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,f\,a^3-4\,e\,a^2\,b+d\,a\,b^2+2\,c\,b^3\right)}{9\,a^{5/3}\,b^{10/3}}","Not used",1,"x*(e/b^2 - (2*a*f)/b^3) + (f*x^4)/(4*b^2) + (x*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a*(a*b^3 + b^4*x^3)) + (log(b^(1/3)*x + a^(1/3))*(2*b^3*c + 7*a^3*f + a*b^2*d - 4*a^2*b*e))/(9*a^(5/3)*b^(10/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(2*b^3*c + 7*a^3*f + a*b^2*d - 4*a^2*b*e))/(9*a^(5/3)*b^(10/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(2*b^3*c + 7*a^3*f + a*b^2*d - 4*a^2*b*e))/(9*a^(5/3)*b^(10/3))","B"
267,1,244,265,5.390460,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^2*(a + b*x^3)^2),x)","\frac{f\,x^2}{2\,b^2}-\frac{\frac{x^3\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+4\,c\,b^3\right)}{3\,a^2}+\frac{b^2\,c}{a}}{b^3\,x^4+a\,b^2\,x}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(5\,f\,a^3-2\,e\,a^2\,b-d\,a\,b^2+4\,c\,b^3\right)}{9\,a^{7/3}\,b^{8/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,f\,a^3-2\,e\,a^2\,b-d\,a\,b^2+4\,c\,b^3\right)}{9\,a^{7/3}\,b^{8/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,f\,a^3-2\,e\,a^2\,b-d\,a\,b^2+4\,c\,b^3\right)}{9\,a^{7/3}\,b^{8/3}}","Not used",1,"(f*x^2)/(2*b^2) - ((x^3*(4*b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^2) + (b^2*c)/a)/(b^3*x^4 + a*b^2*x) + (log(b^(1/3)*x + a^(1/3))*(4*b^3*c + 5*a^3*f - a*b^2*d - 2*a^2*b*e))/(9*a^(7/3)*b^(8/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(4*b^3*c + 5*a^3*f - a*b^2*d - 2*a^2*b*e))/(9*a^(7/3)*b^(8/3)) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(4*b^3*c + 5*a^3*f - a*b^2*d - 2*a^2*b*e))/(9*a^(7/3)*b^(8/3))","B"
268,1,245,260,5.222358,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^3*(a + b*x^3)^2),x)","\frac{f\,x}{b^2}-\frac{\frac{x^3\,\left(-2\,f\,a^3+2\,e\,a^2\,b-2\,d\,a\,b^2+5\,c\,b^3\right)}{6\,a^2}+\frac{b^2\,c}{2\,a}}{b^3\,x^5+a\,b^2\,x^2}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(4\,f\,a^3-e\,a^2\,b-2\,d\,a\,b^2+5\,c\,b^3\right)}{9\,a^{8/3}\,b^{7/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(4\,f\,a^3-e\,a^2\,b-2\,d\,a\,b^2+5\,c\,b^3\right)}{9\,a^{8/3}\,b^{7/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(4\,f\,a^3-e\,a^2\,b-2\,d\,a\,b^2+5\,c\,b^3\right)}{9\,a^{8/3}\,b^{7/3}}","Not used",1,"(f*x)/b^2 - ((x^3*(5*b^3*c - 2*a^3*f - 2*a*b^2*d + 2*a^2*b*e))/(6*a^2) + (b^2*c)/(2*a))/(b^3*x^5 + a*b^2*x^2) - (log(b^(1/3)*x + a^(1/3))*(5*b^3*c + 4*a^3*f - 2*a*b^2*d - a^2*b*e))/(9*a^(8/3)*b^(7/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*b^3*c + 4*a^3*f - 2*a*b^2*d - a^2*b*e))/(9*a^(8/3)*b^(7/3)) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*b^3*c + 4*a^3*f - 2*a*b^2*d - a^2*b*e))/(9*a^(8/3)*b^(7/3))","B"
269,1,247,269,5.177218,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^5*(a + b*x^3)^2),x)","-\frac{\frac{c}{4\,a}+\frac{x^3\,\left(4\,a\,d-7\,b\,c\right)}{4\,a^2}-\frac{x^6\,\left(-f\,a^3+e\,a^2\,b-4\,d\,a\,b^2+7\,c\,b^3\right)}{3\,a^3\,b}}{b\,x^7+a\,x^4}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(2\,f\,a^3+e\,a^2\,b-4\,d\,a\,b^2+7\,c\,b^3\right)}{9\,a^{10/3}\,b^{5/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,f\,a^3+e\,a^2\,b-4\,d\,a\,b^2+7\,c\,b^3\right)}{9\,a^{10/3}\,b^{5/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,f\,a^3+e\,a^2\,b-4\,d\,a\,b^2+7\,c\,b^3\right)}{9\,a^{10/3}\,b^{5/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(7*b^3*c + 2*a^3*f - 4*a*b^2*d + a^2*b*e))/(9*a^(10/3)*b^(5/3)) - (log(b^(1/3)*x + a^(1/3))*(7*b^3*c + 2*a^3*f - 4*a*b^2*d + a^2*b*e))/(9*a^(10/3)*b^(5/3)) - (c/(4*a) + (x^3*(4*a*d - 7*b*c))/(4*a^2) - (x^6*(7*b^3*c - a^3*f - 4*a*b^2*d + a^2*b*e))/(3*a^3*b))/(a*x^4 + b*x^7) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(7*b^3*c + 2*a^3*f - 4*a*b^2*d + a^2*b*e))/(9*a^(10/3)*b^(5/3))","B"
270,1,248,270,5.127096,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^6*(a + b*x^3)^2),x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(f\,a^3+2\,e\,a^2\,b-5\,d\,a\,b^2+8\,c\,b^3\right)}{9\,a^{11/3}\,b^{4/3}}-\frac{\frac{c}{5\,a}+\frac{x^3\,\left(5\,a\,d-8\,b\,c\right)}{10\,a^2}-\frac{x^6\,\left(-2\,f\,a^3+2\,e\,a^2\,b-5\,d\,a\,b^2+8\,c\,b^3\right)}{6\,a^3\,b}}{b\,x^8+a\,x^5}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(f\,a^3+2\,e\,a^2\,b-5\,d\,a\,b^2+8\,c\,b^3\right)}{9\,a^{11/3}\,b^{4/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(f\,a^3+2\,e\,a^2\,b-5\,d\,a\,b^2+8\,c\,b^3\right)}{9\,a^{11/3}\,b^{4/3}}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(8*b^3*c + a^3*f - 5*a*b^2*d + 2*a^2*b*e))/(9*a^(11/3)*b^(4/3)) - (c/(5*a) + (x^3*(5*a*d - 8*b*c))/(10*a^2) - (x^6*(8*b^3*c - 2*a^3*f - 5*a*b^2*d + 2*a^2*b*e))/(6*a^3*b))/(a*x^5 + b*x^8) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(8*b^3*c + a^3*f - 5*a*b^2*d + 2*a^2*b*e))/(9*a^(11/3)*b^(4/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(8*b^3*c + a^3*f - 5*a*b^2*d + 2*a^2*b*e))/(9*a^(11/3)*b^(4/3))","B"
271,1,274,297,5.183726,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^8*(a + b*x^3)^2),x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-f\,a^3+4\,e\,a^2\,b-7\,d\,a\,b^2+10\,c\,b^3\right)}{9\,a^{13/3}\,b^{2/3}}-\frac{\frac{c}{7\,a}+\frac{x^9\,\left(-f\,a^3+4\,e\,a^2\,b-7\,d\,a\,b^2+10\,c\,b^3\right)}{3\,a^4}+\frac{x^3\,\left(7\,a\,d-10\,b\,c\right)}{28\,a^2}+\frac{x^6\,\left(4\,e\,a^2-7\,d\,a\,b+10\,c\,b^2\right)}{4\,a^3}}{b\,x^{10}+a\,x^7}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+4\,e\,a^2\,b-7\,d\,a\,b^2+10\,c\,b^3\right)}{9\,a^{13/3}\,b^{2/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-f\,a^3+4\,e\,a^2\,b-7\,d\,a\,b^2+10\,c\,b^3\right)}{9\,a^{13/3}\,b^{2/3}}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(10*b^3*c - a^3*f - 7*a*b^2*d + 4*a^2*b*e))/(9*a^(13/3)*b^(2/3)) - (c/(7*a) + (x^9*(10*b^3*c - a^3*f - 7*a*b^2*d + 4*a^2*b*e))/(3*a^4) + (x^3*(7*a*d - 10*b*c))/(28*a^2) + (x^6*(10*b^2*c + 4*a^2*e - 7*a*b*d))/(4*a^3))/(a*x^7 + b*x^10) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(10*b^3*c - a^3*f - 7*a*b^2*d + 4*a^2*b*e))/(9*a^(13/3)*b^(2/3)) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(10*b^3*c - a^3*f - 7*a*b^2*d + 4*a^2*b*e))/(9*a^(13/3)*b^(2/3))","B"
272,1,274,297,5.199707,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^9*(a + b*x^3)^2),x)","-\frac{\frac{c}{8\,a}+\frac{x^9\,\left(-2\,f\,a^3+5\,e\,a^2\,b-8\,d\,a\,b^2+11\,c\,b^3\right)}{6\,a^4}+\frac{x^3\,\left(8\,a\,d-11\,b\,c\right)}{40\,a^2}+\frac{x^6\,\left(5\,e\,a^2-8\,d\,a\,b+11\,c\,b^2\right)}{10\,a^3}}{b\,x^{11}+a\,x^8}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-2\,f\,a^3+5\,e\,a^2\,b-8\,d\,a\,b^2+11\,c\,b^3\right)}{9\,a^{14/3}\,b^{1/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-2\,f\,a^3+5\,e\,a^2\,b-8\,d\,a\,b^2+11\,c\,b^3\right)}{9\,a^{14/3}\,b^{1/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-2\,f\,a^3+5\,e\,a^2\,b-8\,d\,a\,b^2+11\,c\,b^3\right)}{9\,a^{14/3}\,b^{1/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(11*b^3*c - 2*a^3*f - 8*a*b^2*d + 5*a^2*b*e))/(9*a^(14/3)*b^(1/3)) - (log(b^(1/3)*x + a^(1/3))*(11*b^3*c - 2*a^3*f - 8*a*b^2*d + 5*a^2*b*e))/(9*a^(14/3)*b^(1/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(11*b^3*c - 2*a^3*f - 8*a*b^2*d + 5*a^2*b*e))/(9*a^(14/3)*b^(1/3)) - (c/(8*a) + (x^9*(11*b^3*c - 2*a^3*f - 8*a*b^2*d + 5*a^2*b*e))/(6*a^4) + (x^3*(8*a*d - 11*b*c))/(40*a^2) + (x^6*(11*b^2*c + 5*a^2*e - 8*a*b*d))/(10*a^3))/(a*x^8 + b*x^11)","B"
273,1,310,334,5.406029,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^11*(a + b*x^3)^2),x)","-\frac{\frac{c}{10\,a}-\frac{x^9\,\left(-4\,f\,a^3+7\,e\,a^2\,b-10\,d\,a\,b^2+13\,c\,b^3\right)}{4\,a^4}+\frac{x^3\,\left(10\,a\,d-13\,b\,c\right)}{70\,a^2}+\frac{x^6\,\left(7\,e\,a^2-10\,d\,a\,b+13\,c\,b^2\right)}{28\,a^3}-\frac{b\,x^{12}\,\left(-4\,f\,a^3+7\,e\,a^2\,b-10\,d\,a\,b^2+13\,c\,b^3\right)}{3\,a^5}}{b\,x^{13}+a\,x^{10}}-\frac{b^{1/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-4\,f\,a^3+7\,e\,a^2\,b-10\,d\,a\,b^2+13\,c\,b^3\right)}{9\,a^{16/3}}+\frac{b^{1/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-4\,f\,a^3+7\,e\,a^2\,b-10\,d\,a\,b^2+13\,c\,b^3\right)}{9\,a^{16/3}}-\frac{b^{1/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-4\,f\,a^3+7\,e\,a^2\,b-10\,d\,a\,b^2+13\,c\,b^3\right)}{9\,a^{16/3}}","Not used",1,"(b^(1/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(13*b^3*c - 4*a^3*f - 10*a*b^2*d + 7*a^2*b*e))/(9*a^(16/3)) - (b^(1/3)*log(b^(1/3)*x + a^(1/3))*(13*b^3*c - 4*a^3*f - 10*a*b^2*d + 7*a^2*b*e))/(9*a^(16/3)) - (c/(10*a) - (x^9*(13*b^3*c - 4*a^3*f - 10*a*b^2*d + 7*a^2*b*e))/(4*a^4) + (x^3*(10*a*d - 13*b*c))/(70*a^2) + (x^6*(13*b^2*c + 7*a^2*e - 10*a*b*d))/(28*a^3) - (b*x^12*(13*b^3*c - 4*a^3*f - 10*a*b^2*d + 7*a^2*b*e))/(3*a^5))/(a*x^10 + b*x^13) - (b^(1/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(13*b^3*c - 4*a^3*f - 10*a*b^2*d + 7*a^2*b*e))/(9*a^(16/3))","B"
274,1,310,335,5.121265,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^12*(a + b*x^3)^2),x)","\frac{b^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-5\,f\,a^3+8\,e\,a^2\,b-11\,d\,a\,b^2+14\,c\,b^3\right)}{9\,a^{17/3}}-\frac{\frac{c}{11\,a}-\frac{x^9\,\left(-5\,f\,a^3+8\,e\,a^2\,b-11\,d\,a\,b^2+14\,c\,b^3\right)}{10\,a^4}+\frac{x^3\,\left(11\,a\,d-14\,b\,c\right)}{88\,a^2}+\frac{x^6\,\left(8\,e\,a^2-11\,d\,a\,b+14\,c\,b^2\right)}{40\,a^3}-\frac{b\,x^{12}\,\left(-5\,f\,a^3+8\,e\,a^2\,b-11\,d\,a\,b^2+14\,c\,b^3\right)}{6\,a^5}}{b\,x^{14}+a\,x^{11}}+\frac{b^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-5\,f\,a^3+8\,e\,a^2\,b-11\,d\,a\,b^2+14\,c\,b^3\right)}{9\,a^{17/3}}-\frac{b^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-5\,f\,a^3+8\,e\,a^2\,b-11\,d\,a\,b^2+14\,c\,b^3\right)}{9\,a^{17/3}}","Not used",1,"(b^(2/3)*log(b^(1/3)*x + a^(1/3))*(14*b^3*c - 5*a^3*f - 11*a*b^2*d + 8*a^2*b*e))/(9*a^(17/3)) - (c/(11*a) - (x^9*(14*b^3*c - 5*a^3*f - 11*a*b^2*d + 8*a^2*b*e))/(10*a^4) + (x^3*(11*a*d - 14*b*c))/(88*a^2) + (x^6*(14*b^2*c + 8*a^2*e - 11*a*b*d))/(40*a^3) - (b*x^12*(14*b^3*c - 5*a^3*f - 11*a*b^2*d + 8*a^2*b*e))/(6*a^5))/(a*x^11 + b*x^14) + (b^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(14*b^3*c - 5*a^3*f - 11*a*b^2*d + 8*a^2*b*e))/(9*a^(17/3)) - (b^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(14*b^3*c - 5*a^3*f - 11*a*b^2*d + 8*a^2*b*e))/(9*a^(17/3))","B"
275,1,348,375,5.117856,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^14*(a + b*x^3)^2),x)","\frac{b^{4/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-7\,f\,a^3+10\,e\,a^2\,b-13\,d\,a\,b^2+16\,c\,b^3\right)}{9\,a^{19/3}}-\frac{\frac{c}{13\,a}-\frac{x^9\,\left(-7\,f\,a^3+10\,e\,a^2\,b-13\,d\,a\,b^2+16\,c\,b^3\right)}{28\,a^4}+\frac{x^3\,\left(13\,a\,d-16\,b\,c\right)}{130\,a^2}+\frac{x^6\,\left(10\,e\,a^2-13\,d\,a\,b+16\,c\,b^2\right)}{70\,a^3}+\frac{b\,x^{12}\,\left(-7\,f\,a^3+10\,e\,a^2\,b-13\,d\,a\,b^2+16\,c\,b^3\right)}{4\,a^5}+\frac{b^2\,x^{15}\,\left(-7\,f\,a^3+10\,e\,a^2\,b-13\,d\,a\,b^2+16\,c\,b^3\right)}{3\,a^6}}{b\,x^{16}+a\,x^{13}}-\frac{b^{4/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-7\,f\,a^3+10\,e\,a^2\,b-13\,d\,a\,b^2+16\,c\,b^3\right)}{9\,a^{19/3}}+\frac{b^{4/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-7\,f\,a^3+10\,e\,a^2\,b-13\,d\,a\,b^2+16\,c\,b^3\right)}{9\,a^{19/3}}","Not used",1,"(b^(4/3)*log(b^(1/3)*x + a^(1/3))*(16*b^3*c - 7*a^3*f - 13*a*b^2*d + 10*a^2*b*e))/(9*a^(19/3)) - (c/(13*a) - (x^9*(16*b^3*c - 7*a^3*f - 13*a*b^2*d + 10*a^2*b*e))/(28*a^4) + (x^3*(13*a*d - 16*b*c))/(130*a^2) + (x^6*(16*b^2*c + 10*a^2*e - 13*a*b*d))/(70*a^3) + (b*x^12*(16*b^3*c - 7*a^3*f - 13*a*b^2*d + 10*a^2*b*e))/(4*a^5) + (b^2*x^15*(16*b^3*c - 7*a^3*f - 13*a*b^2*d + 10*a^2*b*e))/(3*a^6))/(a*x^13 + b*x^16) - (b^(4/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(16*b^3*c - 7*a^3*f - 13*a*b^2*d + 10*a^2*b*e))/(9*a^(19/3)) + (b^(4/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(16*b^3*c - 7*a^3*f - 13*a*b^2*d + 10*a^2*b*e))/(9*a^(19/3))","B"
276,1,449,266,4.957762,"\text{Not used}","int((x^14*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^{12}\,\left(\frac{e}{12\,b^3}-\frac{a\,f}{4\,b^4}\right)+x^6\,\left(\frac{c}{6\,b^3}-\frac{a^3\,f}{6\,b^6}-\frac{a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{2\,b^2}+\frac{a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{2\,b}\right)-x^9\,\left(\frac{a^2\,f}{3\,b^5}-\frac{d}{9\,b^3}+\frac{a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{3\,b}\right)-\frac{\frac{13\,f\,a^7-11\,e\,a^6\,b+9\,d\,a^5\,b^2-7\,c\,a^4\,b^3}{6\,b}+x^3\,\left(\frac{7\,f\,a^6}{3}-2\,e\,a^5\,b+\frac{5\,d\,a^4\,b^2}{3}-\frac{4\,c\,a^3\,b^3}{3}\right)}{a^2\,b^7+2\,a\,b^8\,x^3+b^9\,x^6}-x^3\,\left(\frac{a\,\left(\frac{c}{b^3}-\frac{a^3\,f}{b^6}-\frac{3\,a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b^2}+\frac{3\,a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b}\right)}{b}-\frac{a^2\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b^2}+\frac{a^3\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{3\,b^3}\right)-\frac{\ln\left(b\,x^3+a\right)\,\left(21\,f\,a^5-15\,e\,a^4\,b+10\,d\,a^3\,b^2-6\,c\,a^2\,b^3\right)}{3\,b^8}+\frac{f\,x^{15}}{15\,b^3}","Not used",1,"x^12*(e/(12*b^3) - (a*f)/(4*b^4)) + x^6*(c/(6*b^3) - (a^3*f)/(6*b^6) - (a^2*(e/b^3 - (3*a*f)/b^4))/(2*b^2) + (a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/(2*b)) - x^9*((a^2*f)/(3*b^5) - d/(9*b^3) + (a*(e/b^3 - (3*a*f)/b^4))/(3*b)) - ((13*a^7*f - 7*a^4*b^3*c + 9*a^5*b^2*d - 11*a^6*b*e)/(6*b) + x^3*((7*a^6*f)/3 - (4*a^3*b^3*c)/3 + (5*a^4*b^2*d)/3 - 2*a^5*b*e))/(a^2*b^7 + b^9*x^6 + 2*a*b^8*x^3) - x^3*((a*(c/b^3 - (a^3*f)/b^6 - (3*a^2*(e/b^3 - (3*a*f)/b^4))/b^2 + (3*a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b))/b - (a^2*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b^2 + (a^3*(e/b^3 - (3*a*f)/b^4))/(3*b^3)) - (log(a + b*x^3)*(21*a^5*f - 6*a^2*b^3*c + 10*a^3*b^2*d - 15*a^4*b*e))/(3*b^8) + (f*x^15)/(15*b^3)","B"
277,1,293,226,4.968889,"\text{Not used}","int((x^11*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^9\,\left(\frac{e}{9\,b^3}-\frac{a\,f}{3\,b^4}\right)+x^3\,\left(\frac{c}{3\,b^3}-\frac{a^3\,f}{3\,b^6}-\frac{a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b^2}+\frac{a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b}\right)-x^6\,\left(\frac{a^2\,f}{2\,b^5}-\frac{d}{6\,b^3}+\frac{a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{2\,b}\right)+\frac{\frac{11\,f\,a^6-9\,e\,a^5\,b+7\,d\,a^4\,b^2-5\,c\,a^3\,b^3}{6\,b}+x^3\,\left(2\,f\,a^5-\frac{5\,e\,a^4\,b}{3}+\frac{4\,d\,a^3\,b^2}{3}-c\,a^2\,b^3\right)}{a^2\,b^6+2\,a\,b^7\,x^3+b^8\,x^6}+\frac{f\,x^{12}}{12\,b^3}+\frac{\ln\left(b\,x^3+a\right)\,\left(15\,f\,a^4-10\,e\,a^3\,b+6\,d\,a^2\,b^2-3\,c\,a\,b^3\right)}{3\,b^7}","Not used",1,"x^9*(e/(9*b^3) - (a*f)/(3*b^4)) + x^3*(c/(3*b^3) - (a^3*f)/(3*b^6) - (a^2*(e/b^3 - (3*a*f)/b^4))/b^2 + (a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b) - x^6*((a^2*f)/(2*b^5) - d/(6*b^3) + (a*(e/b^3 - (3*a*f)/b^4))/(2*b)) + ((11*a^6*f - 5*a^3*b^3*c + 7*a^4*b^2*d - 9*a^5*b*e)/(6*b) + x^3*(2*a^5*f - a^2*b^3*c + (4*a^3*b^2*d)/3 - (5*a^4*b*e)/3))/(a^2*b^6 + b^8*x^6 + 2*a*b^7*x^3) + (f*x^12)/(12*b^3) + (log(a + b*x^3)*(15*a^4*f + 6*a^2*b^2*d - 3*a*b^3*c - 10*a^3*b*e))/(3*b^7)","B"
278,1,204,186,4.923824,"\text{Not used}","int((x^8*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^6\,\left(\frac{e}{6\,b^3}-\frac{a\,f}{2\,b^4}\right)-\frac{x^3\,\left(\frac{5\,f\,a^4}{3}-\frac{4\,e\,a^3\,b}{3}+d\,a^2\,b^2-\frac{2\,c\,a\,b^3}{3}\right)+\frac{9\,f\,a^5-7\,e\,a^4\,b+5\,d\,a^3\,b^2-3\,c\,a^2\,b^3}{6\,b}}{a^2\,b^5+2\,a\,b^6\,x^3+b^7\,x^6}-x^3\,\left(\frac{a^2\,f}{b^5}-\frac{d}{3\,b^3}+\frac{a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)+\frac{\ln\left(b\,x^3+a\right)\,\left(-10\,f\,a^3+6\,e\,a^2\,b-3\,d\,a\,b^2+c\,b^3\right)}{3\,b^6}+\frac{f\,x^9}{9\,b^3}","Not used",1,"x^6*(e/(6*b^3) - (a*f)/(2*b^4)) - (x^3*((5*a^4*f)/3 + a^2*b^2*d - (2*a*b^3*c)/3 - (4*a^3*b*e)/3) + (9*a^5*f - 3*a^2*b^3*c + 5*a^3*b^2*d - 7*a^4*b*e)/(6*b))/(a^2*b^5 + b^7*x^6 + 2*a*b^6*x^3) - x^3*((a^2*f)/b^5 - d/(3*b^3) + (a*(e/b^3 - (3*a*f)/b^4))/b) + (log(a + b*x^3)*(b^3*c - 10*a^3*f - 3*a*b^2*d + 6*a^2*b*e))/(3*b^6) + (f*x^9)/(9*b^3)","B"
279,1,152,146,0.104710,"\text{Not used}","int((x^5*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^3\,\left(\frac{e}{3\,b^3}-\frac{a\,f}{b^4}\right)+\frac{\frac{7\,f\,a^4-5\,e\,a^3\,b+3\,d\,a^2\,b^2-c\,a\,b^3}{6\,b}-x^3\,\left(-\frac{4\,f\,a^3}{3}+e\,a^2\,b-\frac{2\,d\,a\,b^2}{3}+\frac{c\,b^3}{3}\right)}{a^2\,b^4+2\,a\,b^5\,x^3+b^6\,x^6}+\frac{f\,x^6}{6\,b^3}+\frac{\ln\left(b\,x^3+a\right)\,\left(6\,f\,a^2-3\,e\,a\,b+d\,b^2\right)}{3\,b^5}","Not used",1,"x^3*(e/(3*b^3) - (a*f)/b^4) + ((7*a^4*f + 3*a^2*b^2*d - a*b^3*c - 5*a^3*b*e)/(6*b) - x^3*((b^3*c)/3 - (4*a^3*f)/3 - (2*a*b^2*d)/3 + a^2*b*e))/(a^2*b^4 + b^6*x^6 + 2*a*b^5*x^3) + (f*x^6)/(6*b^3) + (log(a + b*x^3)*(b^2*d + 6*a^2*f - 3*a*b*e))/(3*b^5)","B"
280,1,112,109,4.938623,"\text{Not used}","int((x^2*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","\frac{f\,x^3}{3\,b^3}-\frac{x^3\,\left(f\,a^2-\frac{2\,e\,a\,b}{3}+\frac{d\,b^2}{3}\right)+\frac{5\,f\,a^3-3\,e\,a^2\,b+d\,a\,b^2+c\,b^3}{6\,b}}{a^2\,b^3+2\,a\,b^4\,x^3+b^5\,x^6}-\frac{\ln\left(b\,x^3+a\right)\,\left(3\,a\,f-b\,e\right)}{3\,b^4}","Not used",1,"(f*x^3)/(3*b^3) - (x^3*((b^2*d)/3 + a^2*f - (2*a*b*e)/3) + (b^3*c + 5*a^3*f + a*b^2*d - 3*a^2*b*e)/(6*b))/(a^2*b^3 + b^5*x^6 + 2*a*b^4*x^3) - (log(a + b*x^3)*(3*a*f - b*e))/(3*b^4)","B"
281,1,123,114,0.175030,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x*(a + b*x^3)^3),x)","\frac{\frac{3\,f\,a^3-e\,a^2\,b-d\,a\,b^2+3\,c\,b^3}{6\,a\,b^3}+\frac{x^3\,\left(2\,f\,a^3-e\,a^2\,b+c\,b^3\right)}{3\,a^2\,b^2}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\frac{c\,\ln\left(x\right)}{a^3}-\frac{\ln\left(b\,x^3+a\right)\,\left(b^3\,c-a^3\,f\right)}{3\,a^3\,b^3}","Not used",1,"((3*b^3*c + 3*a^3*f - a*b^2*d - a^2*b*e)/(6*a*b^3) + (x^3*(b^3*c + 2*a^3*f - a^2*b*e))/(3*a^2*b^2))/(a^2 + b^2*x^6 + 2*a*b*x^3) + (c*log(x))/a^3 - (log(a + b*x^3)*(b^3*c - a^3*f))/(3*a^3*b^3)","B"
282,1,135,134,5.068219,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^4*(a + b*x^3)^3),x)","\frac{\ln\left(x\right)\,\left(a\,d-3\,b\,c\right)}{a^4}-\frac{\ln\left(b\,x^3+a\right)\,\left(a\,d-3\,b\,c\right)}{3\,a^4}-\frac{\frac{c}{3\,a}+\frac{x^6\,\left(f\,a^3-d\,a\,b^2+3\,c\,b^3\right)}{3\,a^3\,b}+\frac{x^3\,\left(f\,a^3+e\,a^2\,b-3\,d\,a\,b^2+9\,c\,b^3\right)}{6\,a^2\,b^2}}{a^2\,x^3+2\,a\,b\,x^6+b^2\,x^9}","Not used",1,"(log(x)*(a*d - 3*b*c))/a^4 - (log(a + b*x^3)*(a*d - 3*b*c))/(3*a^4) - (c/(3*a) + (x^6*(3*b^3*c + a^3*f - a*b^2*d))/(3*a^3*b) + (x^3*(9*b^3*c + a^3*f - 3*a*b^2*d + a^2*b*e))/(6*a^2*b^2))/(a^2*x^3 + b^2*x^9 + 2*a*b*x^6)","B"
283,1,167,163,5.099246,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^7*(a + b*x^3)^3),x)","\frac{\ln\left(x\right)\,\left(e\,a^2-3\,d\,a\,b+6\,c\,b^2\right)}{a^5}-\frac{\ln\left(b\,x^3+a\right)\,\left(e\,a^2-3\,d\,a\,b+6\,c\,b^2\right)}{3\,a^5}-\frac{\frac{c}{6\,a}+\frac{x^3\,\left(a\,d-2\,b\,c\right)}{3\,a^2}-\frac{b\,x^9\,\left(e\,a^2-3\,d\,a\,b+6\,c\,b^2\right)}{3\,a^4}-\frac{x^6\,\left(-f\,a^3+3\,e\,a^2\,b-9\,d\,a\,b^2+18\,c\,b^3\right)}{6\,a^3\,b}}{a^2\,x^6+2\,a\,b\,x^9+b^2\,x^{12}}","Not used",1,"(log(x)*(6*b^2*c + a^2*e - 3*a*b*d))/a^5 - (log(a + b*x^3)*(6*b^2*c + a^2*e - 3*a*b*d))/(3*a^5) - (c/(6*a) + (x^3*(a*d - 2*b*c))/(3*a^2) - (b*x^9*(6*b^2*c + a^2*e - 3*a*b*d))/(3*a^4) - (x^6*(18*b^3*c - a^3*f - 9*a*b^2*d + 3*a^2*b*e))/(6*a^3*b))/(a^2*x^6 + b^2*x^12 + 2*a*b*x^9)","B"
284,1,222,218,5.170520,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^10*(a + b*x^3)^3),x)","\frac{\ln\left(b\,x^3+a\right)\,\left(-f\,a^3+3\,e\,a^2\,b-6\,d\,a\,b^2+10\,c\,b^3\right)}{3\,a^6}-\frac{\frac{c}{9\,a}+\frac{x^9\,\left(-f\,a^3+3\,e\,a^2\,b-6\,d\,a\,b^2+10\,c\,b^3\right)}{2\,a^4}+\frac{x^3\,\left(3\,a\,d-5\,b\,c\right)}{18\,a^2}+\frac{x^6\,\left(3\,e\,a^2-6\,d\,a\,b+10\,c\,b^2\right)}{9\,a^3}+\frac{b\,x^{12}\,\left(-f\,a^3+3\,e\,a^2\,b-6\,d\,a\,b^2+10\,c\,b^3\right)}{3\,a^5}}{a^2\,x^9+2\,a\,b\,x^{12}+b^2\,x^{15}}-\frac{\ln\left(x\right)\,\left(-f\,a^3+3\,e\,a^2\,b-6\,d\,a\,b^2+10\,c\,b^3\right)}{a^6}","Not used",1,"(log(a + b*x^3)*(10*b^3*c - a^3*f - 6*a*b^2*d + 3*a^2*b*e))/(3*a^6) - (c/(9*a) + (x^9*(10*b^3*c - a^3*f - 6*a*b^2*d + 3*a^2*b*e))/(2*a^4) + (x^3*(3*a*d - 5*b*c))/(18*a^2) + (x^6*(10*b^2*c + 3*a^2*e - 6*a*b*d))/(9*a^3) + (b*x^12*(10*b^3*c - a^3*f - 6*a*b^2*d + 3*a^2*b*e))/(3*a^5))/(a^2*x^9 + b^2*x^15 + 2*a*b*x^12) - (log(x)*(10*b^3*c - a^3*f - 6*a*b^2*d + 3*a^2*b*e))/a^6","B"
285,1,265,258,0.307337,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^13*(a + b*x^3)^3),x)","\frac{\ln\left(x\right)\,\left(-3\,f\,a^3\,b+6\,e\,a^2\,b^2-10\,d\,a\,b^3+15\,c\,b^4\right)}{a^7}-\frac{\ln\left(b\,x^3+a\right)\,\left(-3\,f\,a^3\,b+6\,e\,a^2\,b^2-10\,d\,a\,b^3+15\,c\,b^4\right)}{3\,a^7}-\frac{\frac{c}{12\,a}-\frac{x^9\,\left(-3\,f\,a^3+6\,e\,a^2\,b-10\,d\,a\,b^2+15\,c\,b^3\right)}{9\,a^4}+\frac{x^3\,\left(2\,a\,d-3\,b\,c\right)}{18\,a^2}+\frac{x^6\,\left(6\,e\,a^2-10\,d\,a\,b+15\,c\,b^2\right)}{36\,a^3}-\frac{b\,x^{12}\,\left(-3\,f\,a^3+6\,e\,a^2\,b-10\,d\,a\,b^2+15\,c\,b^3\right)}{2\,a^5}-\frac{b^2\,x^{15}\,\left(-3\,f\,a^3+6\,e\,a^2\,b-10\,d\,a\,b^2+15\,c\,b^3\right)}{3\,a^6}}{a^2\,x^{12}+2\,a\,b\,x^{15}+b^2\,x^{18}}","Not used",1,"(log(x)*(15*b^4*c + 6*a^2*b^2*e - 10*a*b^3*d - 3*a^3*b*f))/a^7 - (log(a + b*x^3)*(15*b^4*c + 6*a^2*b^2*e - 10*a*b^3*d - 3*a^3*b*f))/(3*a^7) - (c/(12*a) - (x^9*(15*b^3*c - 3*a^3*f - 10*a*b^2*d + 6*a^2*b*e))/(9*a^4) + (x^3*(2*a*d - 3*b*c))/(18*a^2) + (x^6*(15*b^2*c + 6*a^2*e - 10*a*b*d))/(36*a^3) - (b*x^12*(15*b^3*c - 3*a^3*f - 10*a*b^2*d + 6*a^2*b*e))/(2*a^5) - (b^2*x^15*(15*b^3*c - 3*a^3*f - 10*a*b^2*d + 6*a^2*b*e))/(3*a^6))/(a^2*x^12 + b^2*x^18 + 2*a*b*x^15)","B"
286,1,575,416,5.240909,"\text{Not used}","int((x^12*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^{10}\,\left(\frac{e}{10\,b^3}-\frac{3\,a\,f}{10\,b^4}\right)+x^4\,\left(\frac{c}{4\,b^3}-\frac{a^3\,f}{4\,b^6}-\frac{3\,a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{4\,b^2}+\frac{3\,a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{4\,b}\right)+\frac{x\,\left(\frac{17\,f\,a^6}{9}-\frac{14\,e\,a^5\,b}{9}+\frac{11\,d\,a^4\,b^2}{9}-\frac{8\,c\,a^3\,b^3}{9}\right)-x^4\,\left(-\frac{37\,f\,a^5\,b}{18}+\frac{31\,e\,a^4\,b^2}{18}-\frac{25\,d\,a^3\,b^3}{18}+\frac{19\,c\,a^2\,b^4}{18}\right)}{a^2\,b^7+2\,a\,b^8\,x^3+b^9\,x^6}-x\,\left(\frac{3\,a\,\left(\frac{c}{b^3}-\frac{a^3\,f}{b^6}-\frac{3\,a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b^2}+\frac{3\,a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b}\right)}{b}-\frac{3\,a^2\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b^2}+\frac{a^3\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b^3}\right)-x^7\,\left(\frac{3\,a^2\,f}{7\,b^5}-\frac{d}{7\,b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{7\,b}\right)+\frac{f\,x^{13}}{13\,b^3}+\frac{a^{4/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-152\,f\,a^3+104\,e\,a^2\,b-65\,d\,a\,b^2+35\,c\,b^3\right)}{27\,b^{22/3}}+\frac{a^{4/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-152\,f\,a^3+104\,e\,a^2\,b-65\,d\,a\,b^2+35\,c\,b^3\right)}{27\,b^{22/3}}-\frac{a^{4/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-152\,f\,a^3+104\,e\,a^2\,b-65\,d\,a\,b^2+35\,c\,b^3\right)}{27\,b^{22/3}}","Not used",1,"x^10*(e/(10*b^3) - (3*a*f)/(10*b^4)) + x^4*(c/(4*b^3) - (a^3*f)/(4*b^6) - (3*a^2*(e/b^3 - (3*a*f)/b^4))/(4*b^2) + (3*a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/(4*b)) + (x*((17*a^6*f)/9 - (8*a^3*b^3*c)/9 + (11*a^4*b^2*d)/9 - (14*a^5*b*e)/9) - x^4*((19*a^2*b^4*c)/18 - (25*a^3*b^3*d)/18 + (31*a^4*b^2*e)/18 - (37*a^5*b*f)/18))/(a^2*b^7 + b^9*x^6 + 2*a*b^8*x^3) - x*((3*a*(c/b^3 - (a^3*f)/b^6 - (3*a^2*(e/b^3 - (3*a*f)/b^4))/b^2 + (3*a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b))/b - (3*a^2*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b^2 + (a^3*(e/b^3 - (3*a*f)/b^4))/b^3) - x^7*((3*a^2*f)/(7*b^5) - d/(7*b^3) + (3*a*(e/b^3 - (3*a*f)/b^4))/(7*b)) + (f*x^13)/(13*b^3) + (a^(4/3)*log(b^(1/3)*x + a^(1/3))*(35*b^3*c - 152*a^3*f - 65*a*b^2*d + 104*a^2*b*e))/(27*b^(22/3)) + (a^(4/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(35*b^3*c - 152*a^3*f - 65*a*b^2*d + 104*a^2*b*e))/(27*b^(22/3)) - (a^(4/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(35*b^3*c - 152*a^3*f - 65*a*b^2*d + 104*a^2*b*e))/(27*b^(22/3))","B"
287,1,425,384,5.339147,"\text{Not used}","int((x^10*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^8\,\left(\frac{e}{8\,b^3}-\frac{3\,a\,f}{8\,b^4}\right)+x^2\,\left(\frac{c}{2\,b^3}-\frac{a^3\,f}{2\,b^6}-\frac{3\,a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{2\,b^2}+\frac{3\,a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{2\,b}\right)-\frac{\left(\frac{16\,f\,a^4\,b}{9}-\frac{13\,e\,a^3\,b^2}{9}+\frac{10\,d\,a^2\,b^3}{9}-\frac{7\,c\,a\,b^4}{9}\right)\,x^5+\left(\frac{29\,f\,a^5}{18}-\frac{23\,e\,a^4\,b}{18}+\frac{17\,d\,a^3\,b^2}{18}-\frac{11\,c\,a^2\,b^3}{18}\right)\,x^2}{a^2\,b^6+2\,a\,b^7\,x^3+b^8\,x^6}-x^5\,\left(\frac{3\,a^2\,f}{5\,b^5}-\frac{d}{5\,b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{5\,b}\right)+\frac{f\,x^{11}}{11\,b^3}+\frac{a^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-119\,f\,a^3+77\,e\,a^2\,b-44\,d\,a\,b^2+20\,c\,b^3\right)}{27\,b^{20/3}}-\frac{a^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-119\,f\,a^3+77\,e\,a^2\,b-44\,d\,a\,b^2+20\,c\,b^3\right)}{27\,b^{20/3}}+\frac{a^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-119\,f\,a^3+77\,e\,a^2\,b-44\,d\,a\,b^2+20\,c\,b^3\right)}{27\,b^{20/3}}","Not used",1,"x^8*(e/(8*b^3) - (3*a*f)/(8*b^4)) + x^2*(c/(2*b^3) - (a^3*f)/(2*b^6) - (3*a^2*(e/b^3 - (3*a*f)/b^4))/(2*b^2) + (3*a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/(2*b)) - (x^2*((29*a^5*f)/18 - (11*a^2*b^3*c)/18 + (17*a^3*b^2*d)/18 - (23*a^4*b*e)/18) + x^5*((10*a^2*b^3*d)/9 - (13*a^3*b^2*e)/9 - (7*a*b^4*c)/9 + (16*a^4*b*f)/9))/(a^2*b^6 + b^8*x^6 + 2*a*b^7*x^3) - x^5*((3*a^2*f)/(5*b^5) - d/(5*b^3) + (3*a*(e/b^3 - (3*a*f)/b^4))/(5*b)) + (f*x^11)/(11*b^3) + (a^(2/3)*log(b^(1/3)*x + a^(1/3))*(20*b^3*c - 119*a^3*f - 44*a*b^2*d + 77*a^2*b*e))/(27*b^(20/3)) - (a^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(20*b^3*c - 119*a^3*f - 44*a*b^2*d + 77*a^2*b*e))/(27*b^(20/3)) + (a^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(20*b^3*c - 119*a^3*f - 44*a*b^2*d + 77*a^2*b*e))/(27*b^(20/3))","B"
288,1,420,375,5.351444,"\text{Not used}","int((x^9*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^7\,\left(\frac{e}{7\,b^3}-\frac{3\,a\,f}{7\,b^4}\right)+x\,\left(\frac{c}{b^3}-\frac{a^3\,f}{b^6}-\frac{3\,a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b^2}+\frac{3\,a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b}\right)-x^4\,\left(\frac{3\,a^2\,f}{4\,b^5}-\frac{d}{4\,b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{4\,b}\right)-\frac{\left(\frac{31\,f\,a^4\,b}{18}-\frac{25\,e\,a^3\,b^2}{18}+\frac{19\,d\,a^2\,b^3}{18}-\frac{13\,c\,a\,b^4}{18}\right)\,x^4+\left(\frac{14\,f\,a^5}{9}-\frac{11\,e\,a^4\,b}{9}+\frac{8\,d\,a^3\,b^2}{9}-\frac{5\,c\,a^2\,b^3}{9}\right)\,x}{a^2\,b^6+2\,a\,b^7\,x^3+b^8\,x^6}+\frac{f\,x^{10}}{10\,b^3}-\frac{a^{1/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-104\,f\,a^3+65\,e\,a^2\,b-35\,d\,a\,b^2+14\,c\,b^3\right)}{27\,b^{19/3}}-\frac{a^{1/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-104\,f\,a^3+65\,e\,a^2\,b-35\,d\,a\,b^2+14\,c\,b^3\right)}{27\,b^{19/3}}+\frac{a^{1/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-104\,f\,a^3+65\,e\,a^2\,b-35\,d\,a\,b^2+14\,c\,b^3\right)}{27\,b^{19/3}}","Not used",1,"x^7*(e/(7*b^3) - (3*a*f)/(7*b^4)) + x*(c/b^3 - (a^3*f)/b^6 - (3*a^2*(e/b^3 - (3*a*f)/b^4))/b^2 + (3*a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b) - x^4*((3*a^2*f)/(4*b^5) - d/(4*b^3) + (3*a*(e/b^3 - (3*a*f)/b^4))/(4*b)) - (x*((14*a^5*f)/9 - (5*a^2*b^3*c)/9 + (8*a^3*b^2*d)/9 - (11*a^4*b*e)/9) + x^4*((19*a^2*b^3*d)/18 - (25*a^3*b^2*e)/18 - (13*a*b^4*c)/18 + (31*a^4*b*f)/18))/(a^2*b^6 + b^8*x^6 + 2*a*b^7*x^3) + (f*x^10)/(10*b^3) - (a^(1/3)*log(b^(1/3)*x + a^(1/3))*(14*b^3*c - 104*a^3*f - 35*a*b^2*d + 65*a^2*b*e))/(27*b^(19/3)) - (a^(1/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(14*b^3*c - 104*a^3*f - 35*a*b^2*d + 65*a^2*b*e))/(27*b^(19/3)) + (a^(1/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(14*b^3*c - 104*a^3*f - 35*a*b^2*d + 65*a^2*b*e))/(27*b^(19/3))","B"
289,1,338,345,5.529928,"\text{Not used}","int((x^7*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^5\,\left(\frac{e}{5\,b^3}-\frac{3\,a\,f}{5\,b^4}\right)+\frac{x^2\,\left(\frac{23\,f\,a^4}{18}-\frac{17\,e\,a^3\,b}{18}+\frac{11\,d\,a^2\,b^2}{18}-\frac{5\,c\,a\,b^3}{18}\right)-x^5\,\left(-\frac{13\,f\,a^3\,b}{9}+\frac{10\,e\,a^2\,b^2}{9}-\frac{7\,d\,a\,b^3}{9}+\frac{4\,c\,b^4}{9}\right)}{a^2\,b^5+2\,a\,b^6\,x^3+b^7\,x^6}-x^2\,\left(\frac{3\,a^2\,f}{2\,b^5}-\frac{d}{2\,b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{2\,b}\right)+\frac{f\,x^8}{8\,b^3}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-77\,f\,a^3+44\,e\,a^2\,b-20\,d\,a\,b^2+5\,c\,b^3\right)}{27\,a^{1/3}\,b^{17/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-77\,f\,a^3+44\,e\,a^2\,b-20\,d\,a\,b^2+5\,c\,b^3\right)}{27\,a^{1/3}\,b^{17/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-77\,f\,a^3+44\,e\,a^2\,b-20\,d\,a\,b^2+5\,c\,b^3\right)}{27\,a^{1/3}\,b^{17/3}}","Not used",1,"x^5*(e/(5*b^3) - (3*a*f)/(5*b^4)) + (x^2*((23*a^4*f)/18 + (11*a^2*b^2*d)/18 - (5*a*b^3*c)/18 - (17*a^3*b*e)/18) - x^5*((4*b^4*c)/9 + (10*a^2*b^2*e)/9 - (7*a*b^3*d)/9 - (13*a^3*b*f)/9))/(a^2*b^5 + b^7*x^6 + 2*a*b^6*x^3) - x^2*((3*a^2*f)/(2*b^5) - d/(2*b^3) + (3*a*(e/b^3 - (3*a*f)/b^4))/(2*b)) + (f*x^8)/(8*b^3) - (log(b^(1/3)*x + a^(1/3))*(5*b^3*c - 77*a^3*f - 20*a*b^2*d + 44*a^2*b*e))/(27*a^(1/3)*b^(17/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*b^3*c - 77*a^3*f - 20*a*b^2*d + 44*a^2*b*e))/(27*a^(1/3)*b^(17/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*b^3*c - 77*a^3*f - 20*a*b^2*d + 44*a^2*b*e))/(27*a^(1/3)*b^(17/3))","B"
290,1,335,336,5.301690,"\text{Not used}","int((x^6*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^4\,\left(\frac{e}{4\,b^3}-\frac{3\,a\,f}{4\,b^4}\right)-x\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)-\frac{x^4\,\left(-\frac{25\,f\,a^3\,b}{18}+\frac{19\,e\,a^2\,b^2}{18}-\frac{13\,d\,a\,b^3}{18}+\frac{7\,c\,b^4}{18}\right)-x\,\left(\frac{11\,f\,a^4}{9}-\frac{8\,e\,a^3\,b}{9}+\frac{5\,d\,a^2\,b^2}{9}-\frac{2\,c\,a\,b^3}{9}\right)}{a^2\,b^5+2\,a\,b^6\,x^3+b^7\,x^6}+\frac{f\,x^7}{7\,b^3}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-65\,f\,a^3+35\,e\,a^2\,b-14\,d\,a\,b^2+2\,c\,b^3\right)}{27\,a^{2/3}\,b^{16/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-65\,f\,a^3+35\,e\,a^2\,b-14\,d\,a\,b^2+2\,c\,b^3\right)}{27\,a^{2/3}\,b^{16/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-65\,f\,a^3+35\,e\,a^2\,b-14\,d\,a\,b^2+2\,c\,b^3\right)}{27\,a^{2/3}\,b^{16/3}}","Not used",1,"x^4*(e/(4*b^3) - (3*a*f)/(4*b^4)) - x*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b) - (x^4*((7*b^4*c)/18 + (19*a^2*b^2*e)/18 - (13*a*b^3*d)/18 - (25*a^3*b*f)/18) - x*((11*a^4*f)/9 + (5*a^2*b^2*d)/9 - (2*a*b^3*c)/9 - (8*a^3*b*e)/9))/(a^2*b^5 + b^7*x^6 + 2*a*b^6*x^3) + (f*x^7)/(7*b^3) + (log(b^(1/3)*x + a^(1/3))*(2*b^3*c - 65*a^3*f - 14*a*b^2*d + 35*a^2*b*e))/(27*a^(2/3)*b^(16/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(2*b^3*c - 65*a^3*f - 14*a*b^2*d + 35*a^2*b*e))/(27*a^(2/3)*b^(16/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(2*b^3*c - 65*a^3*f - 14*a*b^2*d + 35*a^2*b*e))/(27*a^(2/3)*b^(16/3))","B"
291,1,295,316,5.270964,"\text{Not used}","int((x^4*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x^2\,\left(\frac{e}{2\,b^3}-\frac{3\,a\,f}{2\,b^4}\right)-\frac{x^2\,\left(\frac{17\,f\,a^3}{18}-\frac{11\,e\,a^2\,b}{18}+\frac{5\,d\,a\,b^2}{18}+\frac{c\,b^3}{18}\right)-\frac{x^5\,\left(-10\,f\,a^3\,b+7\,e\,a^2\,b^2-4\,d\,a\,b^3+c\,b^4\right)}{9\,a}}{a^2\,b^4+2\,a\,b^5\,x^3+b^6\,x^6}+\frac{f\,x^5}{5\,b^3}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(44\,f\,a^3-20\,e\,a^2\,b+5\,d\,a\,b^2+c\,b^3\right)}{27\,a^{4/3}\,b^{14/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(44\,f\,a^3-20\,e\,a^2\,b+5\,d\,a\,b^2+c\,b^3\right)}{27\,a^{4/3}\,b^{14/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(44\,f\,a^3-20\,e\,a^2\,b+5\,d\,a\,b^2+c\,b^3\right)}{27\,a^{4/3}\,b^{14/3}}","Not used",1,"x^2*(e/(2*b^3) - (3*a*f)/(2*b^4)) - (x^2*((b^3*c)/18 + (17*a^3*f)/18 + (5*a*b^2*d)/18 - (11*a^2*b*e)/18) - (x^5*(b^4*c + 7*a^2*b^2*e - 4*a*b^3*d - 10*a^3*b*f))/(9*a))/(a^2*b^4 + b^6*x^6 + 2*a*b^5*x^3) + (f*x^5)/(5*b^3) - (log(b^(1/3)*x + a^(1/3))*(b^3*c + 44*a^3*f + 5*a*b^2*d - 20*a^2*b*e))/(27*a^(4/3)*b^(14/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c + 44*a^3*f + 5*a*b^2*d - 20*a^2*b*e))/(27*a^(4/3)*b^(14/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c + 44*a^3*f + 5*a*b^2*d - 20*a^2*b*e))/(27*a^(4/3)*b^(14/3))","B"
292,1,290,307,5.143338,"\text{Not used}","int((x^3*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","x\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)-\frac{x\,\left(\frac{8\,f\,a^3}{9}-\frac{5\,e\,a^2\,b}{9}+\frac{2\,d\,a\,b^2}{9}+\frac{c\,b^3}{9}\right)-\frac{x^4\,\left(-19\,f\,a^3\,b+13\,e\,a^2\,b^2-7\,d\,a\,b^3+c\,b^4\right)}{18\,a}}{a^2\,b^4+2\,a\,b^5\,x^3+b^6\,x^6}+\frac{f\,x^4}{4\,b^3}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(35\,f\,a^3-14\,e\,a^2\,b+2\,d\,a\,b^2+c\,b^3\right)}{27\,a^{5/3}\,b^{13/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(35\,f\,a^3-14\,e\,a^2\,b+2\,d\,a\,b^2+c\,b^3\right)}{27\,a^{5/3}\,b^{13/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(35\,f\,a^3-14\,e\,a^2\,b+2\,d\,a\,b^2+c\,b^3\right)}{27\,a^{5/3}\,b^{13/3}}","Not used",1,"x*(e/b^3 - (3*a*f)/b^4) - (x*((b^3*c)/9 + (8*a^3*f)/9 + (2*a*b^2*d)/9 - (5*a^2*b*e)/9) - (x^4*(b^4*c + 13*a^2*b^2*e - 7*a*b^3*d - 19*a^3*b*f))/(18*a))/(a^2*b^4 + b^6*x^6 + 2*a*b^5*x^3) + (f*x^4)/(4*b^3) + (log(b^(1/3)*x + a^(1/3))*(b^3*c + 35*a^3*f + 2*a*b^2*d - 14*a^2*b*e))/(27*a^(5/3)*b^(13/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(b^3*c + 35*a^3*f + 2*a*b^2*d - 14*a^2*b*e))/(27*a^(5/3)*b^(13/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(b^3*c + 35*a^3*f + 2*a*b^2*d - 14*a^2*b*e))/(27*a^(5/3)*b^(13/3))","B"
293,1,280,301,5.268063,"\text{Not used}","int((x*(c + d*x^3 + e*x^6 + f*x^9))/(a + b*x^3)^3,x)","\frac{\frac{x^2\,\left(11\,f\,a^3-5\,e\,a^2\,b-d\,a\,b^2+7\,c\,b^3\right)}{18\,a}+\frac{x^5\,\left(7\,f\,a^3\,b-4\,e\,a^2\,b^2+d\,a\,b^3+2\,c\,b^4\right)}{9\,a^2}}{a^2\,b^3+2\,a\,b^4\,x^3+b^5\,x^6}+\frac{f\,x^2}{2\,b^3}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-20\,f\,a^3+5\,e\,a^2\,b+d\,a\,b^2+2\,c\,b^3\right)}{27\,a^{7/3}\,b^{11/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-20\,f\,a^3+5\,e\,a^2\,b+d\,a\,b^2+2\,c\,b^3\right)}{27\,a^{7/3}\,b^{11/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-20\,f\,a^3+5\,e\,a^2\,b+d\,a\,b^2+2\,c\,b^3\right)}{27\,a^{7/3}\,b^{11/3}}","Not used",1,"((x^2*(7*b^3*c + 11*a^3*f - a*b^2*d - 5*a^2*b*e))/(18*a) + (x^5*(2*b^4*c - 4*a^2*b^2*e + a*b^3*d + 7*a^3*b*f))/(9*a^2))/(a^2*b^3 + b^5*x^6 + 2*a*b^4*x^3) + (f*x^2)/(2*b^3) - (log(b^(1/3)*x + a^(1/3))*(2*b^3*c - 20*a^3*f + a*b^2*d + 5*a^2*b*e))/(27*a^(7/3)*b^(11/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(2*b^3*c - 20*a^3*f + a*b^2*d + 5*a^2*b*e))/(27*a^(7/3)*b^(11/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(2*b^3*c - 20*a^3*f + a*b^2*d + 5*a^2*b*e))/(27*a^(7/3)*b^(11/3))","B"
294,1,275,292,5.195801,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3,x)","\frac{\frac{x\,\left(5\,f\,a^3-2\,e\,a^2\,b-d\,a\,b^2+4\,c\,b^3\right)}{9\,a}+\frac{x^4\,\left(13\,f\,a^3\,b-7\,e\,a^2\,b^2+d\,a\,b^3+5\,c\,b^4\right)}{18\,a^2}}{a^2\,b^3+2\,a\,b^4\,x^3+b^5\,x^6}+\frac{f\,x}{b^3}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-14\,f\,a^3+2\,e\,a^2\,b+d\,a\,b^2+5\,c\,b^3\right)}{27\,a^{8/3}\,b^{10/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-14\,f\,a^3+2\,e\,a^2\,b+d\,a\,b^2+5\,c\,b^3\right)}{27\,a^{8/3}\,b^{10/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-14\,f\,a^3+2\,e\,a^2\,b+d\,a\,b^2+5\,c\,b^3\right)}{27\,a^{8/3}\,b^{10/3}}","Not used",1,"((x*(4*b^3*c + 5*a^3*f - a*b^2*d - 2*a^2*b*e))/(9*a) + (x^4*(5*b^4*c - 7*a^2*b^2*e + a*b^3*d + 13*a^3*b*f))/(18*a^2))/(a^2*b^3 + b^5*x^6 + 2*a*b^4*x^3) + (f*x)/b^3 + (log(b^(1/3)*x + a^(1/3))*(5*b^3*c - 14*a^3*f + a*b^2*d + 2*a^2*b*e))/(27*a^(8/3)*b^(10/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*b^3*c - 14*a^3*f + a*b^2*d + 2*a^2*b*e))/(27*a^(8/3)*b^(10/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*b^3*c - 14*a^3*f + a*b^2*d + 2*a^2*b*e))/(27*a^(8/3)*b^(10/3))","B"
295,1,276,303,5.198092,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^2*(a + b*x^3)^3),x)","-\frac{\frac{c}{a}+\frac{x^6\,\left(4\,f\,a^3-e\,a^2\,b-2\,d\,a\,b^2+14\,c\,b^3\right)}{9\,a^3\,b}+\frac{x^3\,\left(5\,f\,a^3+e\,a^2\,b-7\,d\,a\,b^2+49\,c\,b^3\right)}{18\,a^2\,b^2}}{a^2\,x+2\,a\,b\,x^4+b^2\,x^7}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(5\,f\,a^3+e\,a^2\,b+2\,d\,a\,b^2-14\,c\,b^3\right)}{27\,a^{10/3}\,b^{8/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,f\,a^3+e\,a^2\,b+2\,d\,a\,b^2-14\,c\,b^3\right)}{27\,a^{10/3}\,b^{8/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,f\,a^3+e\,a^2\,b+2\,d\,a\,b^2-14\,c\,b^3\right)}{27\,a^{10/3}\,b^{8/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*a^3*f - 14*b^3*c + 2*a*b^2*d + a^2*b*e))/(27*a^(10/3)*b^(8/3)) - (log(b^(1/3)*x + a^(1/3))*(5*a^3*f - 14*b^3*c + 2*a*b^2*d + a^2*b*e))/(27*a^(10/3)*b^(8/3)) - (c/a + (x^6*(14*b^3*c + 4*a^3*f - 2*a*b^2*d - a^2*b*e))/(9*a^3*b) + (x^3*(49*b^3*c + 5*a^3*f - 7*a*b^2*d + a^2*b*e))/(18*a^2*b^2))/(a^2*x + b^2*x^7 + 2*a*b*x^4) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*a^3*f - 14*b^3*c + 2*a*b^2*d + a^2*b*e))/(27*a^(10/3)*b^(8/3))","B"
296,1,279,301,5.163589,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^3*(a + b*x^3)^3),x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(2\,f\,a^3+e\,a^2\,b+5\,d\,a\,b^2-20\,c\,b^3\right)}{27\,a^{11/3}\,b^{7/3}}-\frac{\frac{c}{2\,a}+\frac{x^3\,\left(2\,f\,a^3+e\,a^2\,b-4\,d\,a\,b^2+16\,c\,b^3\right)}{9\,a^2\,b^2}+\frac{x^6\,\left(7\,f\,a^3-e\,a^2\,b-5\,d\,a\,b^2+20\,c\,b^3\right)}{18\,a^3\,b}}{a^2\,x^2+2\,a\,b\,x^5+b^2\,x^8}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,f\,a^3+e\,a^2\,b+5\,d\,a\,b^2-20\,c\,b^3\right)}{27\,a^{11/3}\,b^{7/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,f\,a^3+e\,a^2\,b+5\,d\,a\,b^2-20\,c\,b^3\right)}{27\,a^{11/3}\,b^{7/3}}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(2*a^3*f - 20*b^3*c + 5*a*b^2*d + a^2*b*e))/(27*a^(11/3)*b^(7/3)) - (c/(2*a) + (x^3*(16*b^3*c + 2*a^3*f - 4*a*b^2*d + a^2*b*e))/(9*a^2*b^2) + (x^6*(20*b^3*c + 7*a^3*f - 5*a*b^2*d - a^2*b*e))/(18*a^3*b))/(a^2*x^2 + b^2*x^8 + 2*a*b*x^5) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(2*a^3*f - 20*b^3*c + 5*a*b^2*d + a^2*b*e))/(27*a^(11/3)*b^(7/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(2*a^3*f - 20*b^3*c + 5*a*b^2*d + a^2*b*e))/(27*a^(11/3)*b^(7/3))","B"
297,1,293,317,5.232146,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^5*(a + b*x^3)^3),x)","-\frac{\frac{c}{4\,a}-\frac{x^9\,\left(f\,a^3+2\,e\,a^2\,b-14\,d\,a\,b^2+35\,c\,b^3\right)}{9\,a^4}+\frac{x^3\,\left(2\,a\,d-5\,b\,c\right)}{2\,a^2}-\frac{x^6\,\left(-2\,f\,a^3+14\,e\,a^2\,b-98\,d\,a\,b^2+245\,c\,b^3\right)}{36\,a^3\,b}}{a^2\,x^4+2\,a\,b\,x^7+b^2\,x^{10}}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(f\,a^3+2\,e\,a^2\,b-14\,d\,a\,b^2+35\,c\,b^3\right)}{27\,a^{13/3}\,b^{5/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(f\,a^3+2\,e\,a^2\,b-14\,d\,a\,b^2+35\,c\,b^3\right)}{27\,a^{13/3}\,b^{5/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(f\,a^3+2\,e\,a^2\,b-14\,d\,a\,b^2+35\,c\,b^3\right)}{27\,a^{13/3}\,b^{5/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(35*b^3*c + a^3*f - 14*a*b^2*d + 2*a^2*b*e))/(27*a^(13/3)*b^(5/3)) - (log(b^(1/3)*x + a^(1/3))*(35*b^3*c + a^3*f - 14*a*b^2*d + 2*a^2*b*e))/(27*a^(13/3)*b^(5/3)) - (c/(4*a) - (x^9*(35*b^3*c + a^3*f - 14*a*b^2*d + 2*a^2*b*e))/(9*a^4) + (x^3*(2*a*d - 5*b*c))/(2*a^2) - (x^6*(245*b^3*c - 2*a^3*f - 98*a*b^2*d + 14*a^2*b*e))/(36*a^3*b))/(a^2*x^4 + b^2*x^10 + 2*a*b*x^7) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(35*b^3*c + a^3*f - 14*a*b^2*d + 2*a^2*b*e))/(27*a^(13/3)*b^(5/3))","B"
298,1,293,316,5.195692,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^6*(a + b*x^3)^3),x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(f\,a^3+5\,e\,a^2\,b-20\,d\,a\,b^2+44\,c\,b^3\right)}{27\,a^{14/3}\,b^{4/3}}-\frac{\frac{c}{5\,a}-\frac{x^9\,\left(f\,a^3+5\,e\,a^2\,b-20\,d\,a\,b^2+44\,c\,b^3\right)}{18\,a^4}+\frac{x^3\,\left(5\,a\,d-11\,b\,c\right)}{10\,a^2}-\frac{x^6\,\left(-5\,f\,a^3+20\,e\,a^2\,b-80\,d\,a\,b^2+176\,c\,b^3\right)}{45\,a^3\,b}}{a^2\,x^5+2\,a\,b\,x^8+b^2\,x^{11}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(f\,a^3+5\,e\,a^2\,b-20\,d\,a\,b^2+44\,c\,b^3\right)}{27\,a^{14/3}\,b^{4/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(f\,a^3+5\,e\,a^2\,b-20\,d\,a\,b^2+44\,c\,b^3\right)}{27\,a^{14/3}\,b^{4/3}}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(44*b^3*c + a^3*f - 20*a*b^2*d + 5*a^2*b*e))/(27*a^(14/3)*b^(4/3)) - (c/(5*a) - (x^9*(44*b^3*c + a^3*f - 20*a*b^2*d + 5*a^2*b*e))/(18*a^4) + (x^3*(5*a*d - 11*b*c))/(10*a^2) - (x^6*(176*b^3*c - 5*a^3*f - 80*a*b^2*d + 20*a^2*b*e))/(45*a^3*b))/(a^2*x^5 + b^2*x^11 + 2*a*b*x^8) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(44*b^3*c + a^3*f - 20*a*b^2*d + 5*a^2*b*e))/(27*a^(14/3)*b^(4/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(44*b^3*c + a^3*f - 20*a*b^2*d + 5*a^2*b*e))/(27*a^(14/3)*b^(4/3))","B"
299,1,321,343,5.262429,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^8*(a + b*x^3)^3),x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-2\,f\,a^3+14\,e\,a^2\,b-35\,d\,a\,b^2+65\,c\,b^3\right)}{27\,a^{16/3}\,b^{2/3}}-\frac{\frac{c}{7\,a}+\frac{7\,x^9\,\left(-2\,f\,a^3+14\,e\,a^2\,b-35\,d\,a\,b^2+65\,c\,b^3\right)}{36\,a^4}+\frac{x^3\,\left(7\,a\,d-13\,b\,c\right)}{28\,a^2}+\frac{x^6\,\left(14\,e\,a^2-35\,d\,a\,b+65\,c\,b^2\right)}{14\,a^3}+\frac{b\,x^{12}\,\left(-2\,f\,a^3+14\,e\,a^2\,b-35\,d\,a\,b^2+65\,c\,b^3\right)}{9\,a^5}}{a^2\,x^7+2\,a\,b\,x^{10}+b^2\,x^{13}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-2\,f\,a^3+14\,e\,a^2\,b-35\,d\,a\,b^2+65\,c\,b^3\right)}{27\,a^{16/3}\,b^{2/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-2\,f\,a^3+14\,e\,a^2\,b-35\,d\,a\,b^2+65\,c\,b^3\right)}{27\,a^{16/3}\,b^{2/3}}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(65*b^3*c - 2*a^3*f - 35*a*b^2*d + 14*a^2*b*e))/(27*a^(16/3)*b^(2/3)) - (c/(7*a) + (7*x^9*(65*b^3*c - 2*a^3*f - 35*a*b^2*d + 14*a^2*b*e))/(36*a^4) + (x^3*(7*a*d - 13*b*c))/(28*a^2) + (x^6*(65*b^2*c + 14*a^2*e - 35*a*b*d))/(14*a^3) + (b*x^12*(65*b^3*c - 2*a^3*f - 35*a*b^2*d + 14*a^2*b*e))/(9*a^5))/(a^2*x^7 + b^2*x^13 + 2*a*b*x^10) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(65*b^3*c - 2*a^3*f - 35*a*b^2*d + 14*a^2*b*e))/(27*a^(16/3)*b^(2/3)) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(65*b^3*c - 2*a^3*f - 35*a*b^2*d + 14*a^2*b*e))/(27*a^(16/3)*b^(2/3))","B"
300,1,321,341,5.217209,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^9*(a + b*x^3)^3),x)","-\frac{\frac{c}{8\,a}+\frac{4\,x^9\,\left(-5\,f\,a^3+20\,e\,a^2\,b-44\,d\,a\,b^2+77\,c\,b^3\right)}{45\,a^4}+\frac{x^3\,\left(4\,a\,d-7\,b\,c\right)}{20\,a^2}+\frac{x^6\,\left(20\,e\,a^2-44\,d\,a\,b+77\,c\,b^2\right)}{40\,a^3}+\frac{b\,x^{12}\,\left(-5\,f\,a^3+20\,e\,a^2\,b-44\,d\,a\,b^2+77\,c\,b^3\right)}{18\,a^5}}{a^2\,x^8+2\,a\,b\,x^{11}+b^2\,x^{14}}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-5\,f\,a^3+20\,e\,a^2\,b-44\,d\,a\,b^2+77\,c\,b^3\right)}{27\,a^{17/3}\,b^{1/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-5\,f\,a^3+20\,e\,a^2\,b-44\,d\,a\,b^2+77\,c\,b^3\right)}{27\,a^{17/3}\,b^{1/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-5\,f\,a^3+20\,e\,a^2\,b-44\,d\,a\,b^2+77\,c\,b^3\right)}{27\,a^{17/3}\,b^{1/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(77*b^3*c - 5*a^3*f - 44*a*b^2*d + 20*a^2*b*e))/(27*a^(17/3)*b^(1/3)) - (log(b^(1/3)*x + a^(1/3))*(77*b^3*c - 5*a^3*f - 44*a*b^2*d + 20*a^2*b*e))/(27*a^(17/3)*b^(1/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(77*b^3*c - 5*a^3*f - 44*a*b^2*d + 20*a^2*b*e))/(27*a^(17/3)*b^(1/3)) - (c/(8*a) + (4*x^9*(77*b^3*c - 5*a^3*f - 44*a*b^2*d + 20*a^2*b*e))/(45*a^4) + (x^3*(4*a*d - 7*b*c))/(20*a^2) + (x^6*(77*b^2*c + 20*a^2*e - 44*a*b*d))/(40*a^3) + (b*x^12*(77*b^3*c - 5*a^3*f - 44*a*b^2*d + 20*a^2*b*e))/(18*a^5))/(a^2*x^8 + b^2*x^14 + 2*a*b*x^11)","B"
301,1,359,381,5.278965,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^11*(a + b*x^3)^3),x)","-\frac{\frac{c}{10\,a}-\frac{x^9\,\left(-14\,f\,a^3+35\,e\,a^2\,b-65\,d\,a\,b^2+104\,c\,b^3\right)}{14\,a^4}+\frac{x^3\,\left(5\,a\,d-8\,b\,c\right)}{35\,a^2}+\frac{x^6\,\left(35\,e\,a^2-65\,d\,a\,b+104\,c\,b^2\right)}{140\,a^3}-\frac{7\,b\,x^{12}\,\left(-14\,f\,a^3+35\,e\,a^2\,b-65\,d\,a\,b^2+104\,c\,b^3\right)}{36\,a^5}-\frac{b^2\,x^{15}\,\left(-14\,f\,a^3+35\,e\,a^2\,b-65\,d\,a\,b^2+104\,c\,b^3\right)}{9\,a^6}}{a^2\,x^{10}+2\,a\,b\,x^{13}+b^2\,x^{16}}-\frac{b^{1/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-14\,f\,a^3+35\,e\,a^2\,b-65\,d\,a\,b^2+104\,c\,b^3\right)}{27\,a^{19/3}}+\frac{b^{1/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-14\,f\,a^3+35\,e\,a^2\,b-65\,d\,a\,b^2+104\,c\,b^3\right)}{27\,a^{19/3}}-\frac{b^{1/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-14\,f\,a^3+35\,e\,a^2\,b-65\,d\,a\,b^2+104\,c\,b^3\right)}{27\,a^{19/3}}","Not used",1,"(b^(1/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(104*b^3*c - 14*a^3*f - 65*a*b^2*d + 35*a^2*b*e))/(27*a^(19/3)) - (b^(1/3)*log(b^(1/3)*x + a^(1/3))*(104*b^3*c - 14*a^3*f - 65*a*b^2*d + 35*a^2*b*e))/(27*a^(19/3)) - (c/(10*a) - (x^9*(104*b^3*c - 14*a^3*f - 65*a*b^2*d + 35*a^2*b*e))/(14*a^4) + (x^3*(5*a*d - 8*b*c))/(35*a^2) + (x^6*(104*b^2*c + 35*a^2*e - 65*a*b*d))/(140*a^3) - (7*b*x^12*(104*b^3*c - 14*a^3*f - 65*a*b^2*d + 35*a^2*b*e))/(36*a^5) - (b^2*x^15*(104*b^3*c - 14*a^3*f - 65*a*b^2*d + 35*a^2*b*e))/(9*a^6))/(a^2*x^10 + b^2*x^16 + 2*a*b*x^13) - (b^(1/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(104*b^3*c - 14*a^3*f - 65*a*b^2*d + 35*a^2*b*e))/(27*a^(19/3))","B"
302,1,359,380,5.175653,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^12*(a + b*x^3)^3),x)","\frac{b^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-20\,f\,a^3+44\,e\,a^2\,b-77\,d\,a\,b^2+119\,c\,b^3\right)}{27\,a^{20/3}}-\frac{\frac{c}{11\,a}-\frac{x^9\,\left(-20\,f\,a^3+44\,e\,a^2\,b-77\,d\,a\,b^2+119\,c\,b^3\right)}{40\,a^4}+\frac{x^3\,\left(11\,a\,d-17\,b\,c\right)}{88\,a^2}+\frac{x^6\,\left(44\,e\,a^2-77\,d\,a\,b+119\,c\,b^2\right)}{220\,a^3}-\frac{4\,b\,x^{12}\,\left(-20\,f\,a^3+44\,e\,a^2\,b-77\,d\,a\,b^2+119\,c\,b^3\right)}{45\,a^5}-\frac{b^2\,x^{15}\,\left(-20\,f\,a^3+44\,e\,a^2\,b-77\,d\,a\,b^2+119\,c\,b^3\right)}{18\,a^6}}{a^2\,x^{11}+2\,a\,b\,x^{14}+b^2\,x^{17}}+\frac{b^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-20\,f\,a^3+44\,e\,a^2\,b-77\,d\,a\,b^2+119\,c\,b^3\right)}{27\,a^{20/3}}-\frac{b^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-20\,f\,a^3+44\,e\,a^2\,b-77\,d\,a\,b^2+119\,c\,b^3\right)}{27\,a^{20/3}}","Not used",1,"(b^(2/3)*log(b^(1/3)*x + a^(1/3))*(119*b^3*c - 20*a^3*f - 77*a*b^2*d + 44*a^2*b*e))/(27*a^(20/3)) - (c/(11*a) - (x^9*(119*b^3*c - 20*a^3*f - 77*a*b^2*d + 44*a^2*b*e))/(40*a^4) + (x^3*(11*a*d - 17*b*c))/(88*a^2) + (x^6*(119*b^2*c + 44*a^2*e - 77*a*b*d))/(220*a^3) - (4*b*x^12*(119*b^3*c - 20*a^3*f - 77*a*b^2*d + 44*a^2*b*e))/(45*a^5) - (b^2*x^15*(119*b^3*c - 20*a^3*f - 77*a*b^2*d + 44*a^2*b*e))/(18*a^6))/(a^2*x^11 + b^2*x^17 + 2*a*b*x^14) + (b^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(119*b^3*c - 20*a^3*f - 77*a*b^2*d + 44*a^2*b*e))/(27*a^(20/3)) - (b^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(119*b^3*c - 20*a^3*f - 77*a*b^2*d + 44*a^2*b*e))/(27*a^(20/3))","B"
303,1,397,424,5.303982,"\text{Not used}","int((c + d*x^3 + e*x^6 + f*x^9)/(x^14*(a + b*x^3)^3),x)","\frac{b^{4/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(-35\,f\,a^3+65\,e\,a^2\,b-104\,d\,a\,b^2+152\,c\,b^3\right)}{27\,a^{22/3}}-\frac{\frac{c}{13\,a}-\frac{x^9\,\left(-35\,f\,a^3+65\,e\,a^2\,b-104\,d\,a\,b^2+152\,c\,b^3\right)}{140\,a^4}+\frac{x^3\,\left(13\,a\,d-19\,b\,c\right)}{130\,a^2}+\frac{x^6\,\left(65\,e\,a^2-104\,d\,a\,b+152\,c\,b^2\right)}{455\,a^3}+\frac{b\,x^{12}\,\left(-35\,f\,a^3+65\,e\,a^2\,b-104\,d\,a\,b^2+152\,c\,b^3\right)}{14\,a^5}+\frac{7\,b^2\,x^{15}\,\left(-35\,f\,a^3+65\,e\,a^2\,b-104\,d\,a\,b^2+152\,c\,b^3\right)}{36\,a^6}+\frac{b^3\,x^{18}\,\left(-35\,f\,a^3+65\,e\,a^2\,b-104\,d\,a\,b^2+152\,c\,b^3\right)}{9\,a^7}}{a^2\,x^{13}+2\,a\,b\,x^{16}+b^2\,x^{19}}-\frac{b^{4/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-35\,f\,a^3+65\,e\,a^2\,b-104\,d\,a\,b^2+152\,c\,b^3\right)}{27\,a^{22/3}}+\frac{b^{4/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-35\,f\,a^3+65\,e\,a^2\,b-104\,d\,a\,b^2+152\,c\,b^3\right)}{27\,a^{22/3}}","Not used",1,"(b^(4/3)*log(b^(1/3)*x + a^(1/3))*(152*b^3*c - 35*a^3*f - 104*a*b^2*d + 65*a^2*b*e))/(27*a^(22/3)) - (c/(13*a) - (x^9*(152*b^3*c - 35*a^3*f - 104*a*b^2*d + 65*a^2*b*e))/(140*a^4) + (x^3*(13*a*d - 19*b*c))/(130*a^2) + (x^6*(152*b^2*c + 65*a^2*e - 104*a*b*d))/(455*a^3) + (b*x^12*(152*b^3*c - 35*a^3*f - 104*a*b^2*d + 65*a^2*b*e))/(14*a^5) + (7*b^2*x^15*(152*b^3*c - 35*a^3*f - 104*a*b^2*d + 65*a^2*b*e))/(36*a^6) + (b^3*x^18*(152*b^3*c - 35*a^3*f - 104*a*b^2*d + 65*a^2*b*e))/(9*a^7))/(a^2*x^13 + b^2*x^19 + 2*a*b*x^16) - (b^(4/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(152*b^3*c - 35*a^3*f - 104*a*b^2*d + 65*a^2*b*e))/(27*a^(22/3)) + (b^(4/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(152*b^3*c - 35*a^3*f - 104*a*b^2*d + 65*a^2*b*e))/(27*a^(22/3))","B"
304,1,56,54,0.098558,"\text{Not used}","int(-(x^4*(x - 1))/(x^3 + 1),x)","\frac{2\,\ln\left(x+1\right)}{3}+\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)+\frac{x^2}{2}-\frac{x^3}{3}","Not used",1,"(2*log(x + 1))/3 + log(x - (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 + 1/6) - log(x + (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 - 1/6) + x^2/2 - x^3/3","B"
305,1,24,30,0.031936,"\text{Not used}","int(-(x^3*(x - 1))/(x^3 + 1),x)","x-\frac{2\,\ln\left(x+1\right)}{3}+\frac{\ln\left(x^2-x+1\right)}{3}-\frac{x^2}{2}","Not used",1,"x - (2*log(x + 1))/3 + log(x^2 - x + 1)/3 - x^2/2","B"
306,1,49,44,4.961158,"\text{Not used}","int(-(x^2*(x - 1))/(x^3 + 1),x)","\frac{2\,\ln\left(x+1\right)}{3}-x-\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)+\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)","Not used",1,"(2*log(x + 1))/3 - x - log(x - (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 - 1/6) + log(x + (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 + 1/6)","B"
307,1,63,41,0.080266,"\text{Not used}","int(-(x*(x - 1))/(x^3 + 1),x)","-\frac{\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{6}-\frac{\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{6}-\frac{2\,\ln\left(x+1\right)}{3}-\frac{\sqrt{3}\,\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{6}+\frac{\sqrt{3}\,\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{6}","Not used",1,"(3^(1/2)*log(x + (3^(1/2)*1i)/2 - 1/2)*1i)/6 - log(x + (3^(1/2)*1i)/2 - 1/2)/6 - (2*log(x + 1))/3 - (3^(1/2)*log(x - (3^(1/2)*1i)/2 - 1/2)*1i)/6 - log(x - (3^(1/2)*1i)/2 - 1/2)/6","B"
308,1,48,42,4.960420,"\text{Not used}","int(-(x - 1)/(x*(x^3 + 1)),x)","\ln\left(x\right)-\frac{2\,\ln\left(x+1\right)}{3}+\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)","Not used",1,"log(x) - (2*log(x + 1))/3 + log(x - (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 - 1/6) - log(x + (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 + 1/6)","B"
309,1,55,49,0.079673,"\text{Not used}","int(-(x - 1)/(x^2*(x^3 + 1)),x)","\frac{2\,\ln\left(x+1\right)}{3}-\ln\left(x\right)+\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\frac{1}{x}","Not used",1,"(2*log(x + 1))/3 - log(x) + log(x - (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 + 1/6) - log(x + (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 - 1/6) - 1/x","B"
310,1,25,32,0.069405,"\text{Not used}","int(-(x - 1)/(x^3*(x^3 + 1)),x)","\frac{\ln\left(x^2-x+1\right)}{3}-\frac{2\,\ln\left(x+1\right)}{3}+\frac{x-\frac{1}{2}}{x^2}","Not used",1,"log(x^2 - x + 1)/3 - (2*log(x + 1))/3 + (x - 1/2)/x^2","B"
311,1,63,41,4.955782,"\text{Not used}","int((x*(2*x + 1))/(x^3 + 1),x)","\frac{5\,\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{6}+\frac{5\,\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{6}+\frac{\ln\left(x+1\right)}{3}-\frac{\sqrt{3}\,\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{6}+\frac{\sqrt{3}\,\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{6}","Not used",1,"(5*log(x - (3^(1/2)*1i)/2 - 1/2))/6 + (5*log(x + (3^(1/2)*1i)/2 - 1/2))/6 + log(x + 1)/3 - (3^(1/2)*log(x - (3^(1/2)*1i)/2 - 1/2)*1i)/6 + (3^(1/2)*log(x + (3^(1/2)*1i)/2 - 1/2)*1i)/6","B"
312,1,63,39,0.088967,"\text{Not used}","int(-(x*(2*x + 1))/(x^3 - 1),x)","-\frac{\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2}-\frac{\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2}-\ln\left(x-1\right)+\frac{\sqrt{3}\,\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{6}-\frac{\sqrt{3}\,\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{6}","Not used",1,"(3^(1/2)*log(x - (3^(1/2)*1i)/2 + 1/2)*1i)/6 - log(x + (3^(1/2)*1i)/2 + 1/2)/2 - log(x - 1) - log(x - (3^(1/2)*1i)/2 + 1/2)/2 - (3^(1/2)*log(x + (3^(1/2)*1i)/2 + 1/2)*1i)/6","B"
313,1,43,55,0.027835,"\text{Not used}","int(x^2*(a + b*x^3)*(c + d*x + e*x^2),x)","\frac{b\,e\,x^8}{8}+\frac{b\,d\,x^7}{7}+\frac{b\,c\,x^6}{6}+\frac{a\,e\,x^5}{5}+\frac{a\,d\,x^4}{4}+\frac{a\,c\,x^3}{3}","Not used",1,"(a*c*x^3)/3 + (a*d*x^4)/4 + (b*c*x^6)/6 + (a*e*x^5)/5 + (b*d*x^7)/7 + (b*e*x^8)/8","B"
314,1,43,55,0.025496,"\text{Not used}","int(x*(a + b*x^3)*(c + d*x + e*x^2),x)","\frac{b\,e\,x^7}{7}+\frac{b\,d\,x^6}{6}+\frac{b\,c\,x^5}{5}+\frac{a\,e\,x^4}{4}+\frac{a\,d\,x^3}{3}+\frac{a\,c\,x^2}{2}","Not used",1,"(a*c*x^2)/2 + (a*d*x^3)/3 + (b*c*x^5)/5 + (a*e*x^4)/4 + (b*d*x^6)/6 + (b*e*x^7)/7","B"
315,1,40,50,0.023663,"\text{Not used}","int((a + b*x^3)*(c + d*x + e*x^2),x)","\frac{b\,e\,x^6}{6}+\frac{b\,d\,x^5}{5}+\frac{b\,c\,x^4}{4}+\frac{a\,e\,x^3}{3}+\frac{a\,d\,x^2}{2}+a\,c\,x","Not used",1,"a*c*x + (a*d*x^2)/2 + (b*c*x^4)/4 + (a*e*x^3)/3 + (b*d*x^5)/5 + (b*e*x^6)/6","B"
316,1,38,46,0.028522,"\text{Not used}","int(((a + b*x^3)*(c + d*x + e*x^2))/x,x)","a\,c\,\ln\left(x\right)+a\,d\,x+\frac{b\,c\,x^3}{3}+\frac{a\,e\,x^2}{2}+\frac{b\,d\,x^4}{4}+\frac{b\,e\,x^5}{5}","Not used",1,"a*c*log(x) + a*d*x + (b*c*x^3)/3 + (a*e*x^2)/2 + (b*d*x^4)/4 + (b*e*x^5)/5","B"
317,1,38,44,0.029580,"\text{Not used}","int(((a + b*x^3)*(c + d*x + e*x^2))/x^2,x)","a\,d\,\ln\left(x\right)+a\,e\,x-\frac{a\,c}{x}+\frac{b\,c\,x^2}{2}+\frac{b\,d\,x^3}{3}+\frac{b\,e\,x^4}{4}","Not used",1,"a*d*log(x) + a*e*x - (a*c)/x + (b*c*x^2)/2 + (b*d*x^3)/3 + (b*e*x^4)/4","B"
318,1,38,44,0.027917,"\text{Not used}","int(((a + b*x^3)*(c + d*x + e*x^2))/x^3,x)","a\,e\,\ln\left(x\right)-\frac{\frac{a\,c}{2}+a\,d\,x}{x^2}+b\,c\,x+\frac{b\,d\,x^2}{2}+\frac{b\,e\,x^3}{3}","Not used",1,"a*e*log(x) - ((a*c)/2 + a*d*x)/x^2 + b*c*x + (b*d*x^2)/2 + (b*e*x^3)/3","B"
319,1,79,82,0.039762,"\text{Not used}","int(x^2*(a + b*x^3)^2*(c + d*x + e*x^2),x)","\frac{e\,a^2\,x^5}{5}+\frac{d\,a^2\,x^4}{4}+\frac{c\,a^2\,x^3}{3}+\frac{e\,a\,b\,x^8}{4}+\frac{2\,d\,a\,b\,x^7}{7}+\frac{c\,a\,b\,x^6}{3}+\frac{e\,b^2\,x^{11}}{11}+\frac{d\,b^2\,x^{10}}{10}+\frac{c\,b^2\,x^9}{9}","Not used",1,"(a^2*c*x^3)/3 + (a^2*d*x^4)/4 + (b^2*c*x^9)/9 + (a^2*e*x^5)/5 + (b^2*d*x^10)/10 + (b^2*e*x^11)/11 + (a*b*c*x^6)/3 + (2*a*b*d*x^7)/7 + (a*b*e*x^8)/4","B"
320,1,79,82,0.038258,"\text{Not used}","int(x*(a + b*x^3)^2*(c + d*x + e*x^2),x)","\frac{e\,a^2\,x^4}{4}+\frac{d\,a^2\,x^3}{3}+\frac{c\,a^2\,x^2}{2}+\frac{2\,e\,a\,b\,x^7}{7}+\frac{d\,a\,b\,x^6}{3}+\frac{2\,c\,a\,b\,x^5}{5}+\frac{e\,b^2\,x^{10}}{10}+\frac{d\,b^2\,x^9}{9}+\frac{c\,b^2\,x^8}{8}","Not used",1,"(a^2*c*x^2)/2 + (a^2*d*x^3)/3 + (b^2*c*x^8)/8 + (a^2*e*x^4)/4 + (b^2*d*x^9)/9 + (b^2*e*x^10)/10 + (2*a*b*c*x^5)/5 + (a*b*d*x^6)/3 + (2*a*b*e*x^7)/7","B"
321,1,76,77,0.038331,"\text{Not used}","int((a + b*x^3)^2*(c + d*x + e*x^2),x)","\frac{e\,a^2\,x^3}{3}+\frac{d\,a^2\,x^2}{2}+c\,a^2\,x+\frac{e\,a\,b\,x^6}{3}+\frac{2\,d\,a\,b\,x^5}{5}+\frac{c\,a\,b\,x^4}{2}+\frac{e\,b^2\,x^9}{9}+\frac{d\,b^2\,x^8}{8}+\frac{c\,b^2\,x^7}{7}","Not used",1,"(a^2*d*x^2)/2 + (b^2*c*x^7)/7 + (a^2*e*x^3)/3 + (b^2*d*x^8)/8 + (b^2*e*x^9)/9 + a^2*c*x + (a*b*c*x^4)/2 + (2*a*b*d*x^5)/5 + (a*b*e*x^6)/3","B"
322,1,74,88,0.041750,"\text{Not used}","int(((a + b*x^3)^2*(c + d*x + e*x^2))/x,x)","\frac{b^2\,c\,x^6}{6}+\frac{a^2\,e\,x^2}{2}+\frac{b^2\,d\,x^7}{7}+\frac{b^2\,e\,x^8}{8}+a^2\,c\,\ln\left(x\right)+a^2\,d\,x+\frac{2\,a\,b\,c\,x^3}{3}+\frac{a\,b\,d\,x^4}{2}+\frac{2\,a\,b\,e\,x^5}{5}","Not used",1,"(b^2*c*x^6)/6 + (a^2*e*x^2)/2 + (b^2*d*x^7)/7 + (b^2*e*x^8)/8 + a^2*c*log(x) + a^2*d*x + (2*a*b*c*x^3)/3 + (a*b*d*x^4)/2 + (2*a*b*e*x^5)/5","B"
323,1,73,83,0.042425,"\text{Not used}","int(((a + b*x^3)^2*(c + d*x + e*x^2))/x^2,x)","\frac{b^2\,c\,x^5}{5}-\frac{a^2\,c}{x}+\frac{b^2\,d\,x^6}{6}+\frac{b^2\,e\,x^7}{7}+a^2\,d\,\ln\left(x\right)+a^2\,e\,x+a\,b\,c\,x^2+\frac{2\,a\,b\,d\,x^3}{3}+\frac{a\,b\,e\,x^4}{2}","Not used",1,"(b^2*c*x^5)/5 - (a^2*c)/x + (b^2*d*x^6)/6 + (b^2*e*x^7)/7 + a^2*d*log(x) + a^2*e*x + a*b*c*x^2 + (2*a*b*d*x^3)/3 + (a*b*e*x^4)/2","B"
324,1,74,84,0.037760,"\text{Not used}","int(((a + b*x^3)^2*(c + d*x + e*x^2))/x^3,x)","\frac{b^2\,c\,x^4}{4}-\frac{\frac{a^2\,c}{2}+a^2\,d\,x}{x^2}+\frac{b^2\,d\,x^5}{5}+\frac{b^2\,e\,x^6}{6}+a^2\,e\,\ln\left(x\right)+a\,b\,d\,x^2+\frac{2\,a\,b\,e\,x^3}{3}+2\,a\,b\,c\,x","Not used",1,"(b^2*c*x^4)/4 - ((a^2*c)/2 + a^2*d*x)/x^2 + (b^2*d*x^5)/5 + (b^2*e*x^6)/6 + a^2*e*log(x) + a*b*d*x^2 + (2*a*b*e*x^3)/3 + 2*a*b*c*x","B"
325,1,115,110,0.077527,"\text{Not used}","int(x^2*(a + b*x^3)^3*(c + d*x + e*x^2),x)","\frac{e\,a^3\,x^5}{5}+\frac{d\,a^3\,x^4}{4}+\frac{c\,a^3\,x^3}{3}+\frac{3\,e\,a^2\,b\,x^8}{8}+\frac{3\,d\,a^2\,b\,x^7}{7}+\frac{c\,a^2\,b\,x^6}{2}+\frac{3\,e\,a\,b^2\,x^{11}}{11}+\frac{3\,d\,a\,b^2\,x^{10}}{10}+\frac{c\,a\,b^2\,x^9}{3}+\frac{e\,b^3\,x^{14}}{14}+\frac{d\,b^3\,x^{13}}{13}+\frac{c\,b^3\,x^{12}}{12}","Not used",1,"(a^3*c*x^3)/3 + (a^3*d*x^4)/4 + (b^3*c*x^12)/12 + (a^3*e*x^5)/5 + (b^3*d*x^13)/13 + (b^3*e*x^14)/14 + (a^2*b*c*x^6)/2 + (a*b^2*c*x^9)/3 + (3*a^2*b*d*x^7)/7 + (3*a*b^2*d*x^10)/10 + (3*a^2*b*e*x^8)/8 + (3*a*b^2*e*x^11)/11","B"
326,1,115,110,0.073929,"\text{Not used}","int(x*(a + b*x^3)^3*(c + d*x + e*x^2),x)","\frac{e\,a^3\,x^4}{4}+\frac{d\,a^3\,x^3}{3}+\frac{c\,a^3\,x^2}{2}+\frac{3\,e\,a^2\,b\,x^7}{7}+\frac{d\,a^2\,b\,x^6}{2}+\frac{3\,c\,a^2\,b\,x^5}{5}+\frac{3\,e\,a\,b^2\,x^{10}}{10}+\frac{d\,a\,b^2\,x^9}{3}+\frac{3\,c\,a\,b^2\,x^8}{8}+\frac{e\,b^3\,x^{13}}{13}+\frac{d\,b^3\,x^{12}}{12}+\frac{c\,b^3\,x^{11}}{11}","Not used",1,"(a^3*c*x^2)/2 + (a^3*d*x^3)/3 + (b^3*c*x^11)/11 + (a^3*e*x^4)/4 + (b^3*d*x^12)/12 + (b^3*e*x^13)/13 + (3*a^2*b*c*x^5)/5 + (3*a*b^2*c*x^8)/8 + (a^2*b*d*x^6)/2 + (a*b^2*d*x^9)/3 + (3*a^2*b*e*x^7)/7 + (3*a*b^2*e*x^10)/10","B"
327,1,112,105,0.073445,"\text{Not used}","int((a + b*x^3)^3*(c + d*x + e*x^2),x)","\frac{e\,a^3\,x^3}{3}+\frac{d\,a^3\,x^2}{2}+c\,a^3\,x+\frac{e\,a^2\,b\,x^6}{2}+\frac{3\,d\,a^2\,b\,x^5}{5}+\frac{3\,c\,a^2\,b\,x^4}{4}+\frac{e\,a\,b^2\,x^9}{3}+\frac{3\,d\,a\,b^2\,x^8}{8}+\frac{3\,c\,a\,b^2\,x^7}{7}+\frac{e\,b^3\,x^{12}}{12}+\frac{d\,b^3\,x^{11}}{11}+\frac{c\,b^3\,x^{10}}{10}","Not used",1,"(a^3*d*x^2)/2 + (b^3*c*x^10)/10 + (a^3*e*x^3)/3 + (b^3*d*x^11)/11 + (b^3*e*x^12)/12 + a^3*c*x + (3*a^2*b*c*x^4)/4 + (3*a*b^2*c*x^7)/7 + (3*a^2*b*d*x^5)/5 + (3*a*b^2*d*x^8)/8 + (a^2*b*e*x^6)/2 + (a*b^2*e*x^9)/3","B"
328,1,109,127,0.078877,"\text{Not used}","int(((a + b*x^3)^3*(c + d*x + e*x^2))/x,x)","\frac{b^3\,c\,x^9}{9}+\frac{a^3\,e\,x^2}{2}+\frac{b^3\,d\,x^{10}}{10}+\frac{b^3\,e\,x^{11}}{11}+a^3\,c\,\ln\left(x\right)+a^3\,d\,x+a^2\,b\,c\,x^3+\frac{a\,b^2\,c\,x^6}{2}+\frac{3\,a^2\,b\,d\,x^4}{4}+\frac{3\,a\,b^2\,d\,x^7}{7}+\frac{3\,a^2\,b\,e\,x^5}{5}+\frac{3\,a\,b^2\,e\,x^8}{8}","Not used",1,"(b^3*c*x^9)/9 + (a^3*e*x^2)/2 + (b^3*d*x^10)/10 + (b^3*e*x^11)/11 + a^3*c*log(x) + a^3*d*x + a^2*b*c*x^3 + (a*b^2*c*x^6)/2 + (3*a^2*b*d*x^4)/4 + (3*a*b^2*d*x^7)/7 + (3*a^2*b*e*x^5)/5 + (3*a*b^2*e*x^8)/8","B"
329,1,109,125,0.081071,"\text{Not used}","int(((a + b*x^3)^3*(c + d*x + e*x^2))/x^2,x)","\frac{b^3\,c\,x^8}{8}-\frac{a^3\,c}{x}+\frac{b^3\,d\,x^9}{9}+\frac{b^3\,e\,x^{10}}{10}+a^3\,d\,\ln\left(x\right)+a^3\,e\,x+\frac{3\,a^2\,b\,c\,x^2}{2}+\frac{3\,a\,b^2\,c\,x^5}{5}+a^2\,b\,d\,x^3+\frac{a\,b^2\,d\,x^6}{2}+\frac{3\,a^2\,b\,e\,x^4}{4}+\frac{3\,a\,b^2\,e\,x^7}{7}","Not used",1,"(b^3*c*x^8)/8 - (a^3*c)/x + (b^3*d*x^9)/9 + (b^3*e*x^10)/10 + a^3*d*log(x) + a^3*e*x + (3*a^2*b*c*x^2)/2 + (3*a*b^2*c*x^5)/5 + a^2*b*d*x^3 + (a*b^2*d*x^6)/2 + (3*a^2*b*e*x^4)/4 + (3*a*b^2*e*x^7)/7","B"
330,1,110,126,4.895685,"\text{Not used}","int(((a + b*x^3)^3*(c + d*x + e*x^2))/x^3,x)","\frac{b^3\,c\,x^7}{7}-\frac{\frac{a^3\,c}{2}+a^3\,d\,x}{x^2}+\frac{b^3\,d\,x^8}{8}+\frac{b^3\,e\,x^9}{9}+a^3\,e\,\ln\left(x\right)+3\,a^2\,b\,c\,x+\frac{3\,a\,b^2\,c\,x^4}{4}+\frac{3\,a^2\,b\,d\,x^2}{2}+\frac{3\,a\,b^2\,d\,x^5}{5}+a^2\,b\,e\,x^3+\frac{a\,b^2\,e\,x^6}{2}","Not used",1,"(b^3*c*x^7)/7 - ((a^3*c)/2 + a^3*d*x)/x^2 + (b^3*d*x^8)/8 + (b^3*e*x^9)/9 + a^3*e*log(x) + 3*a^2*b*c*x + (3*a*b^2*c*x^4)/4 + (3*a^2*b*d*x^2)/2 + (3*a*b^2*d*x^5)/5 + a^2*b*e*x^3 + (a*b^2*e*x^6)/2","B"
331,1,151,138,5.073251,"\text{Not used}","int(x^2*(a + b*x^3)^4*(c + d*x + e*x^2),x)","\frac{e\,a^4\,x^5}{5}+\frac{d\,a^4\,x^4}{4}+\frac{c\,a^4\,x^3}{3}+\frac{e\,a^3\,b\,x^8}{2}+\frac{4\,d\,a^3\,b\,x^7}{7}+\frac{2\,c\,a^3\,b\,x^6}{3}+\frac{6\,e\,a^2\,b^2\,x^{11}}{11}+\frac{3\,d\,a^2\,b^2\,x^{10}}{5}+\frac{2\,c\,a^2\,b^2\,x^9}{3}+\frac{2\,e\,a\,b^3\,x^{14}}{7}+\frac{4\,d\,a\,b^3\,x^{13}}{13}+\frac{c\,a\,b^3\,x^{12}}{3}+\frac{e\,b^4\,x^{17}}{17}+\frac{d\,b^4\,x^{16}}{16}+\frac{c\,b^4\,x^{15}}{15}","Not used",1,"(a^4*c*x^3)/3 + (a^4*d*x^4)/4 + (b^4*c*x^15)/15 + (a^4*e*x^5)/5 + (b^4*d*x^16)/16 + (b^4*e*x^17)/17 + (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 + (2*a^3*b*c*x^6)/3 + (a*b^3*c*x^12)/3 + (4*a^3*b*d*x^7)/7 + (4*a*b^3*d*x^13)/13 + (a^3*b*e*x^8)/2 + (2*a*b^3*e*x^14)/7","B"
332,1,151,138,0.131218,"\text{Not used}","int(x*(a + b*x^3)^4*(c + d*x + e*x^2),x)","\frac{e\,a^4\,x^4}{4}+\frac{d\,a^4\,x^3}{3}+\frac{c\,a^4\,x^2}{2}+\frac{4\,e\,a^3\,b\,x^7}{7}+\frac{2\,d\,a^3\,b\,x^6}{3}+\frac{4\,c\,a^3\,b\,x^5}{5}+\frac{3\,e\,a^2\,b^2\,x^{10}}{5}+\frac{2\,d\,a^2\,b^2\,x^9}{3}+\frac{3\,c\,a^2\,b^2\,x^8}{4}+\frac{4\,e\,a\,b^3\,x^{13}}{13}+\frac{d\,a\,b^3\,x^{12}}{3}+\frac{4\,c\,a\,b^3\,x^{11}}{11}+\frac{e\,b^4\,x^{16}}{16}+\frac{d\,b^4\,x^{15}}{15}+\frac{c\,b^4\,x^{14}}{14}","Not used",1,"(a^4*c*x^2)/2 + (a^4*d*x^3)/3 + (b^4*c*x^14)/14 + (a^4*e*x^4)/4 + (b^4*d*x^15)/15 + (b^4*e*x^16)/16 + (3*a^2*b^2*c*x^8)/4 + (2*a^2*b^2*d*x^9)/3 + (3*a^2*b^2*e*x^10)/5 + (4*a^3*b*c*x^5)/5 + (4*a*b^3*c*x^11)/11 + (2*a^3*b*d*x^6)/3 + (a*b^3*d*x^12)/3 + (4*a^3*b*e*x^7)/7 + (4*a*b^3*e*x^13)/13","B"
333,1,147,130,0.152385,"\text{Not used}","int((a + b*x^3)^4*(c + d*x + e*x^2),x)","\frac{e\,a^4\,x^3}{3}+\frac{d\,a^4\,x^2}{2}+c\,a^4\,x+\frac{2\,e\,a^3\,b\,x^6}{3}+\frac{4\,d\,a^3\,b\,x^5}{5}+c\,a^3\,b\,x^4+\frac{2\,e\,a^2\,b^2\,x^9}{3}+\frac{3\,d\,a^2\,b^2\,x^8}{4}+\frac{6\,c\,a^2\,b^2\,x^7}{7}+\frac{e\,a\,b^3\,x^{12}}{3}+\frac{4\,d\,a\,b^3\,x^{11}}{11}+\frac{2\,c\,a\,b^3\,x^{10}}{5}+\frac{e\,b^4\,x^{15}}{15}+\frac{d\,b^4\,x^{14}}{14}+\frac{c\,b^4\,x^{13}}{13}","Not used",1,"(a^4*d*x^2)/2 + (b^4*c*x^13)/13 + (a^4*e*x^3)/3 + (b^4*d*x^14)/14 + (b^4*e*x^15)/15 + a^4*c*x + (6*a^2*b^2*c*x^7)/7 + (3*a^2*b^2*d*x^8)/4 + (2*a^2*b^2*e*x^9)/3 + a^3*b*c*x^4 + (2*a*b^3*c*x^10)/5 + (4*a^3*b*d*x^5)/5 + (4*a*b^3*d*x^11)/11 + (2*a^3*b*e*x^6)/3 + (a*b^3*e*x^12)/3","B"
334,1,144,166,0.141444,"\text{Not used}","int(((a + b*x^3)^4*(c + d*x + e*x^2))/x,x)","\frac{b^4\,c\,x^{12}}{12}+\frac{a^4\,e\,x^2}{2}+\frac{b^4\,d\,x^{13}}{13}+\frac{b^4\,e\,x^{14}}{14}+a^4\,c\,\ln\left(x\right)+a^4\,d\,x+a^2\,b^2\,c\,x^6+\frac{6\,a^2\,b^2\,d\,x^7}{7}+\frac{3\,a^2\,b^2\,e\,x^8}{4}+\frac{4\,a^3\,b\,c\,x^3}{3}+\frac{4\,a\,b^3\,c\,x^9}{9}+a^3\,b\,d\,x^4+\frac{2\,a\,b^3\,d\,x^{10}}{5}+\frac{4\,a^3\,b\,e\,x^5}{5}+\frac{4\,a\,b^3\,e\,x^{11}}{11}","Not used",1,"(b^4*c*x^12)/12 + (a^4*e*x^2)/2 + (b^4*d*x^13)/13 + (b^4*e*x^14)/14 + a^4*c*log(x) + a^4*d*x + 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^3*b*c*x^3)/3 + (4*a*b^3*c*x^9)/9 + a^3*b*d*x^4 + (2*a*b^3*d*x^10)/5 + (4*a^3*b*e*x^5)/5 + (4*a*b^3*e*x^11)/11","B"
335,1,144,162,4.994087,"\text{Not used}","int(((a + b*x^3)^4*(c + d*x + e*x^2))/x^2,x)","\frac{b^4\,c\,x^{11}}{11}-\frac{a^4\,c}{x}+\frac{b^4\,d\,x^{12}}{12}+\frac{b^4\,e\,x^{13}}{13}+a^4\,d\,\ln\left(x\right)+a^4\,e\,x+\frac{6\,a^2\,b^2\,c\,x^5}{5}+a^2\,b^2\,d\,x^6+\frac{6\,a^2\,b^2\,e\,x^7}{7}+2\,a^3\,b\,c\,x^2+\frac{a\,b^3\,c\,x^8}{2}+\frac{4\,a^3\,b\,d\,x^3}{3}+\frac{4\,a\,b^3\,d\,x^9}{9}+a^3\,b\,e\,x^4+\frac{2\,a\,b^3\,e\,x^{10}}{5}","Not used",1,"(b^4*c*x^11)/11 - (a^4*c)/x + (b^4*d*x^12)/12 + (b^4*e*x^13)/13 + a^4*d*log(x) + a^4*e*x + (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 + 2*a^3*b*c*x^2 + (a*b^3*c*x^8)/2 + (4*a^3*b*d*x^3)/3 + (4*a*b^3*d*x^9)/9 + a^3*b*e*x^4 + (2*a*b^3*e*x^10)/5","B"
336,1,146,166,4.992564,"\text{Not used}","int(((a + b*x^3)^4*(c + d*x + e*x^2))/x^3,x)","\frac{b^4\,c\,x^{10}}{10}-\frac{\frac{a^4\,c}{2}+a^4\,d\,x}{x^2}+\frac{b^4\,d\,x^{11}}{11}+\frac{b^4\,e\,x^{12}}{12}+a^4\,e\,\ln\left(x\right)+\frac{3\,a^2\,b^2\,c\,x^4}{2}+\frac{6\,a^2\,b^2\,d\,x^5}{5}+a^2\,b^2\,e\,x^6+4\,a^3\,b\,c\,x+\frac{4\,a\,b^3\,c\,x^7}{7}+2\,a^3\,b\,d\,x^2+\frac{a\,b^3\,d\,x^8}{2}+\frac{4\,a^3\,b\,e\,x^3}{3}+\frac{4\,a\,b^3\,e\,x^9}{9}","Not used",1,"(b^4*c*x^10)/10 - ((a^4*c)/2 + a^4*d*x)/x^2 + (b^4*d*x^11)/11 + (b^4*e*x^12)/12 + a^4*e*log(x) + (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^3*b*c*x + (4*a*b^3*c*x^7)/7 + 2*a^3*b*d*x^2 + (a*b^3*d*x^8)/2 + (4*a^3*b*e*x^3)/3 + (4*a*b^3*e*x^9)/9","B"
337,1,319,205,5.066801,"\text{Not used}","int((x^3*(c + d*x + e*x^2))/(a + b*x^3),x)","\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,b^6\,z^3+27\,a\,b^4\,e\,z^2+9\,a\,b^3\,c\,d\,z+9\,a^2\,b^2\,e^2\,z+3\,a^2\,b\,c\,d\,e+a\,b^2\,c^3+a^3\,e^3-a^2\,b\,d^3,z,k\right)\,\left(6\,a^2\,e+\mathrm{root}\left(27\,b^6\,z^3+27\,a\,b^4\,e\,z^2+9\,a\,b^3\,c\,d\,z+9\,a^2\,b^2\,e^2\,z+3\,a^2\,b\,c\,d\,e+a\,b^2\,c^3+a^3\,e^3-a^2\,b\,d^3,z,k\right)\,a\,b^2\,9-3\,a\,b\,c\,x\right)+\frac{a^3\,e^2+b\,c\,d\,a^2}{b^2}+\frac{x\,\left(a^2\,d^2-a^2\,c\,e\right)}{b}\right)\,\mathrm{root}\left(27\,b^6\,z^3+27\,a\,b^4\,e\,z^2+9\,a\,b^3\,c\,d\,z+9\,a^2\,b^2\,e^2\,z+3\,a^2\,b\,c\,d\,e+a\,b^2\,c^3+a^3\,e^3-a^2\,b\,d^3,z,k\right)\right)+\frac{d\,x^2}{2\,b}+\frac{e\,x^3}{3\,b}+\frac{c\,x}{b}","Not used",1,"symsum(log(root(27*b^6*z^3 + 27*a*b^4*e*z^2 + 9*a*b^3*c*d*z + 9*a^2*b^2*e^2*z + 3*a^2*b*c*d*e + a*b^2*c^3 + a^3*e^3 - a^2*b*d^3, z, k)*(6*a^2*e + 9*root(27*b^6*z^3 + 27*a*b^4*e*z^2 + 9*a*b^3*c*d*z + 9*a^2*b^2*e^2*z + 3*a^2*b*c*d*e + a*b^2*c^3 + a^3*e^3 - a^2*b*d^3, z, k)*a*b^2 - 3*a*b*c*x) + (a^3*e^2 + a^2*b*c*d)/b^2 + (x*(a^2*d^2 - a^2*c*e))/b)*root(27*b^6*z^3 + 27*a*b^4*e*z^2 + 9*a*b^3*c*d*z + 9*a^2*b^2*e^2*z + 3*a^2*b*c*d*e + a*b^2*c^3 + a^3*e^3 - a^2*b*d^3, z, k), k, 1, 3) + (d*x^2)/(2*b) + (e*x^3)/(3*b) + (c*x)/b","B"
338,1,340,193,5.132897,"\text{Not used}","int((x^2*(c + d*x + e*x^2))/(a + b*x^3),x)","\left(\sum _{k=1}^3\ln\left(\frac{a\,\left(b\,c^2+{\mathrm{root}\left(27\,b^5\,z^3-27\,b^4\,c\,z^2+9\,a\,b^2\,d\,e\,z+9\,b^3\,c^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)}^2\,b^3\,9+a\,d\,e-\mathrm{root}\left(27\,b^5\,z^3-27\,b^4\,c\,z^2+9\,a\,b^2\,d\,e\,z+9\,b^3\,c^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\,b^2\,c\,6+a\,e^2\,x+b\,c\,d\,x-\mathrm{root}\left(27\,b^5\,z^3-27\,b^4\,c\,z^2+9\,a\,b^2\,d\,e\,z+9\,b^3\,c^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\,b^2\,d\,x\,3\right)}{b}\right)\,\mathrm{root}\left(27\,b^5\,z^3-27\,b^4\,c\,z^2+9\,a\,b^2\,d\,e\,z+9\,b^3\,c^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\right)+\frac{e\,x^2}{2\,b}+\frac{d\,x}{b}","Not used",1,"symsum(log((a*(b*c^2 + 9*root(27*b^5*z^3 - 27*b^4*c*z^2 + 9*a*b^2*d*e*z + 9*b^3*c^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)^2*b^3 + a*d*e - 6*root(27*b^5*z^3 - 27*b^4*c*z^2 + 9*a*b^2*d*e*z + 9*b^3*c^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)*b^2*c + a*e^2*x + b*c*d*x - 3*root(27*b^5*z^3 - 27*b^4*c*z^2 + 9*a*b^2*d*e*z + 9*b^3*c^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)*b^2*d*x))/b)*root(27*b^5*z^3 - 27*b^4*c*z^2 + 9*a*b^2*d*e*z + 9*b^3*c^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k), k, 1, 3) + (e*x^2)/(2*b) + (d*x)/b","B"
339,1,266,183,5.162263,"\text{Not used}","int((x*(c + d*x + e*x^2))/(a + b*x^3),x)","\left(\sum _{k=1}^3\ln\left(x\,\left(b\,c^2+a\,d\,e\right)-\mathrm{root}\left(27\,a\,b^4\,z^3-27\,a\,b^3\,d\,z^2-9\,a\,b^2\,c\,e\,z+9\,a\,b^2\,d^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,\left(6\,a\,b\,d-\mathrm{root}\left(27\,a\,b^4\,z^3-27\,a\,b^3\,d\,z^2-9\,a\,b^2\,c\,e\,z+9\,a\,b^2\,d^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,a\,b^2\,9+3\,a\,b\,e\,x\right)+a\,d^2-a\,c\,e\right)\,\mathrm{root}\left(27\,a\,b^4\,z^3-27\,a\,b^3\,d\,z^2-9\,a\,b^2\,c\,e\,z+9\,a\,b^2\,d^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\right)+\frac{e\,x}{b}","Not used",1,"symsum(log(x*(b*c^2 + a*d*e) - root(27*a*b^4*z^3 - 27*a*b^3*d*z^2 - 9*a*b^2*c*e*z + 9*a*b^2*d^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*(6*a*b*d - 9*root(27*a*b^4*z^3 - 27*a*b^3*d*z^2 - 9*a*b^2*c*e*z + 9*a*b^2*d^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*a*b^2 + 3*a*b*e*x) + a*d^2 - a*c*e)*root(27*a*b^4*z^3 - 27*a*b^3*d*z^2 - 9*a*b^2*c*e*z + 9*a*b^2*d^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k), k, 1, 3) + (e*x)/b","B"
340,1,274,177,0.257272,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(x\,\left(b\,d^2-b\,c\,e\right)+\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,a^2\,b^2\,e\,z^2+9\,a\,b^2\,c\,d\,z+9\,a^2\,b\,e^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\,\left(-6\,a\,b\,e+\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,a^2\,b^2\,e\,z^2+9\,a\,b^2\,c\,d\,z+9\,a^2\,b\,e^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\,a\,b^2\,9+3\,b^2\,c\,x\right)+a\,e^2+b\,c\,d\right)\,\mathrm{root}\left(27\,a^2\,b^3\,z^3-27\,a^2\,b^2\,e\,z^2+9\,a\,b^2\,c\,d\,z+9\,a^2\,b\,e^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)","Not used",1,"symsum(log(x*(b*d^2 - b*c*e) + root(27*a^2*b^3*z^3 - 27*a^2*b^2*e*z^2 + 9*a*b^2*c*d*z + 9*a^2*b*e^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)*(9*root(27*a^2*b^3*z^3 - 27*a^2*b^2*e*z^2 + 9*a*b^2*c*d*z + 9*a^2*b*e^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)*a*b^2 - 6*a*b*e + 3*b^2*c*x) + a*e^2 + b*c*d)*root(27*a^2*b^3*z^3 - 27*a^2*b^2*e*z^2 + 9*a*b^2*c*d*z + 9*a^2*b*e^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k), k, 1, 3)","B"
341,1,716,184,5.247092,"\text{Not used}","int((c + d*x + e*x^2)/(x*(a + b*x^3)),x)","\left(\sum _{k=1}^3\ln\left(b^2\,c\,d^2-b^2\,c^2\,e+b^2\,d^3\,x-{\mathrm{root}\left(27\,a^3\,b^2\,z^3+27\,a^2\,b^2\,c\,z^2+9\,a^2\,b\,d\,e\,z+9\,a\,b^2\,c^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)}^3\,a^2\,b^3\,x\,36-a\,b\,e^3\,x-\mathrm{root}\left(27\,a^3\,b^2\,z^3+27\,a^2\,b^2\,c\,z^2+9\,a^2\,b\,d\,e\,z+9\,a\,b^2\,c^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,a\,b^2\,d^2-\mathrm{root}\left(27\,a^3\,b^2\,z^3+27\,a^2\,b^2\,c\,z^2+9\,a^2\,b\,d\,e\,z+9\,a\,b^2\,c^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,b^3\,c^2\,x\,4+{\mathrm{root}\left(27\,a^3\,b^2\,z^3+27\,a^2\,b^2\,c\,z^2+9\,a^2\,b\,d\,e\,z+9\,a\,b^2\,c^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)}^2\,a^2\,b^2\,e\,3-{\mathrm{root}\left(27\,a^3\,b^2\,z^3+27\,a^2\,b^2\,c\,z^2+9\,a^2\,b\,d\,e\,z+9\,a\,b^2\,c^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)}^2\,a\,b^3\,c\,x\,24-\mathrm{root}\left(27\,a^3\,b^2\,z^3+27\,a^2\,b^2\,c\,z^2+9\,a^2\,b\,d\,e\,z+9\,a\,b^2\,c^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,a\,b^2\,c\,e\,2-2\,b^2\,c\,d\,e\,x-\mathrm{root}\left(27\,a^3\,b^2\,z^3+27\,a^2\,b^2\,c\,z^2+9\,a^2\,b\,d\,e\,z+9\,a\,b^2\,c^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,a\,b^2\,d\,e\,x\,10\right)\,\mathrm{root}\left(27\,a^3\,b^2\,z^3+27\,a^2\,b^2\,c\,z^2+9\,a^2\,b\,d\,e\,z+9\,a\,b^2\,c^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\right)+\frac{c\,\ln\left(x\right)}{a}","Not used",1,"symsum(log(b^2*c*d^2 - b^2*c^2*e + b^2*d^3*x - 36*root(27*a^3*b^2*z^3 + 27*a^2*b^2*c*z^2 + 9*a^2*b*d*e*z + 9*a*b^2*c^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)^3*a^2*b^3*x - a*b*e^3*x - root(27*a^3*b^2*z^3 + 27*a^2*b^2*c*z^2 + 9*a^2*b*d*e*z + 9*a*b^2*c^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*a*b^2*d^2 - 4*root(27*a^3*b^2*z^3 + 27*a^2*b^2*c*z^2 + 9*a^2*b*d*e*z + 9*a*b^2*c^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*b^3*c^2*x + 3*root(27*a^3*b^2*z^3 + 27*a^2*b^2*c*z^2 + 9*a^2*b*d*e*z + 9*a*b^2*c^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)^2*a^2*b^2*e - 24*root(27*a^3*b^2*z^3 + 27*a^2*b^2*c*z^2 + 9*a^2*b*d*e*z + 9*a*b^2*c^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)^2*a*b^3*c*x - 2*root(27*a^3*b^2*z^3 + 27*a^2*b^2*c*z^2 + 9*a^2*b*d*e*z + 9*a*b^2*c^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*a*b^2*c*e - 2*b^2*c*d*e*x - 10*root(27*a^3*b^2*z^3 + 27*a^2*b^2*c*z^2 + 9*a^2*b*d*e*z + 9*a*b^2*c^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*a*b^2*d*e*x)*root(27*a^3*b^2*z^3 + 27*a^2*b^2*c*z^2 + 9*a^2*b*d*e*z + 9*a*b^2*c^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k), k, 1, 3) + (c*log(x))/a","B"
342,1,723,192,5.055523,"\text{Not used}","int((c + d*x + e*x^2)/(x^2*(a + b*x^3)),x)","\left(\sum _{k=1}^3\ln\left(\frac{b^4\,c^3\,x+a^2\,b^2\,d\,e^2-{\mathrm{root}\left(27\,a^4\,b\,z^3+27\,a^3\,b\,d\,z^2-9\,a^2\,b\,c\,e\,z+9\,a^2\,b\,d^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)}^3\,a^4\,b^3\,x\,36+a^2\,b^2\,e^3\,x+a\,b^3\,c\,d^2-{\mathrm{root}\left(27\,a^4\,b\,z^3+27\,a^3\,b\,d\,z^2-9\,a^2\,b\,c\,e\,z+9\,a^2\,b\,d^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)}^2\,a^3\,b^3\,c\,3-\mathrm{root}\left(27\,a^4\,b\,z^3+27\,a^3\,b\,d\,z^2-9\,a^2\,b\,c\,e\,z+9\,a^2\,b\,d^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\,a^3\,b^2\,e^2-\mathrm{root}\left(27\,a^4\,b\,z^3+27\,a^3\,b\,d\,z^2-9\,a^2\,b\,c\,e\,z+9\,a^2\,b\,d^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\,a^2\,b^3\,d^2\,x\,4-{\mathrm{root}\left(27\,a^4\,b\,z^3+27\,a^3\,b\,d\,z^2-9\,a^2\,b\,c\,e\,z+9\,a^2\,b\,d^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)}^2\,a^3\,b^3\,d\,x\,24+\mathrm{root}\left(27\,a^4\,b\,z^3+27\,a^3\,b\,d\,z^2-9\,a^2\,b\,c\,e\,z+9\,a^2\,b\,d^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\,a^2\,b^3\,c\,d\,2+2\,a\,b^3\,c\,d\,e\,x+\mathrm{root}\left(27\,a^4\,b\,z^3+27\,a^3\,b\,d\,z^2-9\,a^2\,b\,c\,e\,z+9\,a^2\,b\,d^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\,a^2\,b^3\,c\,e\,x\,10}{a^2}\right)\,\mathrm{root}\left(27\,a^4\,b\,z^3+27\,a^3\,b\,d\,z^2-9\,a^2\,b\,c\,e\,z+9\,a^2\,b\,d^2\,z-3\,a\,b\,c\,d\,e+a\,b\,d^3-a^2\,e^3-b^2\,c^3,z,k\right)\right)-\frac{c}{a\,x}+\frac{d\,\ln\left(x\right)}{a}","Not used",1,"symsum(log((b^4*c^3*x + a^2*b^2*d*e^2 - 36*root(27*a^4*b*z^3 + 27*a^3*b*d*z^2 - 9*a^2*b*c*e*z + 9*a^2*b*d^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)^3*a^4*b^3*x + a^2*b^2*e^3*x + a*b^3*c*d^2 - 3*root(27*a^4*b*z^3 + 27*a^3*b*d*z^2 - 9*a^2*b*c*e*z + 9*a^2*b*d^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)^2*a^3*b^3*c - root(27*a^4*b*z^3 + 27*a^3*b*d*z^2 - 9*a^2*b*c*e*z + 9*a^2*b*d^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)*a^3*b^2*e^2 - 4*root(27*a^4*b*z^3 + 27*a^3*b*d*z^2 - 9*a^2*b*c*e*z + 9*a^2*b*d^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)*a^2*b^3*d^2*x - 24*root(27*a^4*b*z^3 + 27*a^3*b*d*z^2 - 9*a^2*b*c*e*z + 9*a^2*b*d^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)^2*a^3*b^3*d*x + 2*root(27*a^4*b*z^3 + 27*a^3*b*d*z^2 - 9*a^2*b*c*e*z + 9*a^2*b*d^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)*a^2*b^3*c*d + 2*a*b^3*c*d*e*x + 10*root(27*a^4*b*z^3 + 27*a^3*b*d*z^2 - 9*a^2*b*c*e*z + 9*a^2*b*d^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k)*a^2*b^3*c*e*x)/a^2)*root(27*a^4*b*z^3 + 27*a^3*b*d*z^2 - 9*a^2*b*c*e*z + 9*a^2*b*d^2*z - 3*a*b*c*d*e + a*b*d^3 - a^2*e^3 - b^2*c^3, z, k), k, 1, 3) - c/(a*x) + (d*log(x))/a","B"
343,1,701,203,0.131191,"\text{Not used}","int((c + d*x + e*x^2)/(x^3*(a + b*x^3)),x)","\left(\sum _{k=1}^3\ln\left(-\frac{b^5\,c^3\,x-a^2\,b^3\,d\,e^2+{\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,e\,z^2+9\,a^2\,b\,c\,d\,z+9\,a^3\,e^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)}^3\,a^5\,b^3\,x\,36-a\,b^4\,c^2\,e-a\,b^4\,d^3\,x+\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,e\,z^2+9\,a^2\,b\,c\,d\,z+9\,a^3\,e^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,a^2\,b^4\,c^2+{\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,e\,z^2+9\,a^2\,b\,c\,d\,z+9\,a^3\,e^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)}^2\,a^4\,b^3\,d\,3+\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,e\,z^2+9\,a^2\,b\,c\,d\,z+9\,a^3\,e^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,a^3\,b^3\,e^2\,x\,4+{\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,e\,z^2+9\,a^2\,b\,c\,d\,z+9\,a^3\,e^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)}^2\,a^4\,b^3\,e\,x\,24-\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,e\,z^2+9\,a^2\,b\,c\,d\,z+9\,a^3\,e^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,a^3\,b^3\,d\,e\,2+2\,a\,b^4\,c\,d\,e\,x+\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,e\,z^2+9\,a^2\,b\,c\,d\,z+9\,a^3\,e^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\,a^2\,b^4\,c\,d\,x\,10}{a^3}\right)\,\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,e\,z^2+9\,a^2\,b\,c\,d\,z+9\,a^3\,e^2\,z+3\,a\,b\,c\,d\,e-a\,b\,d^3+a^2\,e^3+b^2\,c^3,z,k\right)\right)-\frac{c}{2\,a\,x^2}-\frac{d}{a\,x}+\frac{e\,\ln\left(x\right)}{a}","Not used",1,"symsum(log(-(b^5*c^3*x - a^2*b^3*d*e^2 + 36*root(27*a^5*z^3 + 27*a^4*e*z^2 + 9*a^2*b*c*d*z + 9*a^3*e^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)^3*a^5*b^3*x - a*b^4*c^2*e - a*b^4*d^3*x + root(27*a^5*z^3 + 27*a^4*e*z^2 + 9*a^2*b*c*d*z + 9*a^3*e^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*a^2*b^4*c^2 + 3*root(27*a^5*z^3 + 27*a^4*e*z^2 + 9*a^2*b*c*d*z + 9*a^3*e^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)^2*a^4*b^3*d + 4*root(27*a^5*z^3 + 27*a^4*e*z^2 + 9*a^2*b*c*d*z + 9*a^3*e^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*a^3*b^3*e^2*x + 24*root(27*a^5*z^3 + 27*a^4*e*z^2 + 9*a^2*b*c*d*z + 9*a^3*e^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)^2*a^4*b^3*e*x - 2*root(27*a^5*z^3 + 27*a^4*e*z^2 + 9*a^2*b*c*d*z + 9*a^3*e^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*a^3*b^3*d*e + 2*a*b^4*c*d*e*x + 10*root(27*a^5*z^3 + 27*a^4*e*z^2 + 9*a^2*b*c*d*z + 9*a^3*e^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k)*a^2*b^4*c*d*x)/a^3)*root(27*a^5*z^3 + 27*a^4*e*z^2 + 9*a^2*b*c*d*z + 9*a^3*e^2*z + 3*a*b*c*d*e - a*b*d^3 + a^2*e^3 + b^2*c^3, z, k), k, 1, 3) - c/(2*a*x^2) - d/(a*x) + (e*log(x))/a","B"
344,1,180,190,0.220102,"\text{Not used}","int((x^2*(c + d*x + e*x^2))/(a + b*x^3)^2,x)","\left(\sum _{k=1}^3\ln\left(\frac{2\,d\,e+4\,e^2\,x+{\mathrm{root}\left(729\,a^2\,b^5\,z^3+54\,a\,b^2\,d\,e\,z+8\,a\,e^3-b\,d^3,z,k\right)}^2\,a\,b^3\,81+\mathrm{root}\left(729\,a^2\,b^5\,z^3+54\,a\,b^2\,d\,e\,z+8\,a\,e^3-b\,d^3,z,k\right)\,b^2\,d\,x\,9}{b\,9}\right)\,\mathrm{root}\left(729\,a^2\,b^5\,z^3+54\,a\,b^2\,d\,e\,z+8\,a\,e^3-b\,d^3,z,k\right)\right)-\frac{\frac{c}{3\,b}+\frac{e\,x^2}{3\,b}+\frac{d\,x}{3\,b}}{b\,x^3+a}","Not used",1,"symsum(log((2*d*e + 4*e^2*x + 81*root(729*a^2*b^5*z^3 + 54*a*b^2*d*e*z + 8*a*e^3 - b*d^3, z, k)^2*a*b^3 + 9*root(729*a^2*b^5*z^3 + 54*a*b^2*d*e*z + 8*a*e^3 - b*d^3, z, k)*b^2*d*x)/(9*b))*root(729*a^2*b^5*z^3 + 54*a*b^2*d*e*z + 8*a*e^3 - b*d^3, z, k), k, 1, 3) - (c/(3*b) + (e*x^2)/(3*b) + (d*x)/(3*b))/(a + b*x^3)","B"
345,1,194,200,5.166539,"\text{Not used}","int((x*(c + d*x + e*x^2))/(a + b*x^3)^2,x)","\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(729\,a^4\,b^4\,z^3+27\,a^2\,b^2\,c\,e\,z+b^2\,c^3-a^2\,e^3,z,k\right)\,\left(b\,e\,x+\mathrm{root}\left(729\,a^4\,b^4\,z^3+27\,a^2\,b^2\,c\,e\,z+b^2\,c^3-a^2\,e^3,z,k\right)\,a\,b^2\,9\right)+\frac{c\,e}{9\,a}+\frac{b\,c^2\,x}{9\,a^2}\right)\,\mathrm{root}\left(729\,a^4\,b^4\,z^3+27\,a^2\,b^2\,c\,e\,z+b^2\,c^3-a^2\,e^3,z,k\right)\right)-\frac{\frac{d}{3\,b}-\frac{c\,x^2}{3\,a}+\frac{e\,x}{3\,b}}{b\,x^3+a}","Not used",1,"symsum(log(root(729*a^4*b^4*z^3 + 27*a^2*b^2*c*e*z + b^2*c^3 - a^2*e^3, z, k)*(b*e*x + 9*root(729*a^4*b^4*z^3 + 27*a^2*b^2*c*e*z + b^2*c^3 - a^2*e^3, z, k)*a*b^2) + (c*e)/(9*a) + (b*c^2*x)/(9*a^2))*root(729*a^4*b^4*z^3 + 27*a^2*b^2*c*e*z + b^2*c^3 - a^2*e^3, z, k), k, 1, 3) - (d/(3*b) - (c*x^2)/(3*a) + (e*x)/(3*b))/(a + b*x^3)","B"
346,1,175,199,0.251074,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^3)^2,x)","\left(\sum _{k=1}^3\ln\left(\frac{b\,\left(2\,c\,d+d^2\,x+{\mathrm{root}\left(729\,a^5\,b^2\,z^3+54\,a^2\,b\,c\,d\,z-8\,b\,c^3+a\,d^3,z,k\right)}^2\,a^3\,b\,81+\mathrm{root}\left(729\,a^5\,b^2\,z^3+54\,a^2\,b\,c\,d\,z-8\,b\,c^3+a\,d^3,z,k\right)\,a\,b\,c\,x\,18\right)}{a^2\,9}\right)\,\mathrm{root}\left(729\,a^5\,b^2\,z^3+54\,a^2\,b\,c\,d\,z-8\,b\,c^3+a\,d^3,z,k\right)\right)+\frac{\frac{d\,x^2}{3\,a}-\frac{e}{3\,b}+\frac{c\,x}{3\,a}}{b\,x^3+a}","Not used",1,"symsum(log((b*(2*c*d + d^2*x + 81*root(729*a^5*b^2*z^3 + 54*a^2*b*c*d*z - 8*b*c^3 + a*d^3, z, k)^2*a^3*b + 18*root(729*a^5*b^2*z^3 + 54*a^2*b*c*d*z - 8*b*c^3 + a*d^3, z, k)*a*b*c*x))/(9*a^2))*root(729*a^5*b^2*z^3 + 54*a^2*b*c*d*z - 8*b*c^3 + a*d^3, z, k), k, 1, 3) + ((d*x^2)/(3*a) - e/(3*b) + (c*x)/(3*a))/(a + b*x^3)","B"
347,1,490,222,0.379977,"\text{Not used}","int((c + d*x + e*x^2)/(x*(a + b*x^3)^2),x)","\frac{\frac{c}{3\,a}+\frac{e\,x^2}{3\,a}+\frac{d\,x}{3\,a}}{b\,x^3+a}+\left(\sum _{k=1}^3\ln\left(\frac{4\,b^2\,c\,d^2-3\,b^2\,c^2\,e}{9\,a^3}-\mathrm{root}\left(729\,a^6\,b^2\,z^3+729\,a^4\,b^2\,c\,z^2+54\,a^3\,b\,d\,e\,z+243\,a^2\,b^2\,c^2\,z+18\,a\,b\,c\,d\,e-8\,a\,b\,d^3+27\,b^2\,c^3+a^2\,e^3,z,k\right)\,\left(\mathrm{root}\left(729\,a^6\,b^2\,z^3+729\,a^4\,b^2\,c\,z^2+54\,a^3\,b\,d\,e\,z+243\,a^2\,b^2\,c^2\,z+18\,a\,b\,c\,d\,e-8\,a\,b\,d^3+27\,b^2\,c^3+a^2\,e^3,z,k\right)\,\left(-a\,b^2\,e+24\,b^3\,c\,x+\mathrm{root}\left(729\,a^6\,b^2\,z^3+729\,a^4\,b^2\,c\,z^2+54\,a^3\,b\,d\,e\,z+243\,a^2\,b^2\,c^2\,z+18\,a\,b\,c\,d\,e-8\,a\,b\,d^3+27\,b^2\,c^3+a^2\,e^3,z,k\right)\,a^2\,b^3\,x\,36\right)+\frac{4\,a^2\,b^2\,d^2+6\,c\,e\,a^2\,b^2}{9\,a^3}+\frac{x\,\left(60\,d\,e\,a^2\,b^2+108\,a\,b^3\,c^2\right)}{27\,a^3}\right)-\frac{x\,\left(-8\,b^2\,d^3+12\,c\,b^2\,d\,e+a\,b\,e^3\right)}{27\,a^3}\right)\,\mathrm{root}\left(729\,a^6\,b^2\,z^3+729\,a^4\,b^2\,c\,z^2+54\,a^3\,b\,d\,e\,z+243\,a^2\,b^2\,c^2\,z+18\,a\,b\,c\,d\,e-8\,a\,b\,d^3+27\,b^2\,c^3+a^2\,e^3,z,k\right)\right)+\frac{c\,\ln\left(x\right)}{a^2}","Not used",1,"(c/(3*a) + (e*x^2)/(3*a) + (d*x)/(3*a))/(a + b*x^3) + symsum(log((4*b^2*c*d^2 - 3*b^2*c^2*e)/(9*a^3) - root(729*a^6*b^2*z^3 + 729*a^4*b^2*c*z^2 + 54*a^3*b*d*e*z + 243*a^2*b^2*c^2*z + 18*a*b*c*d*e - 8*a*b*d^3 + 27*b^2*c^3 + a^2*e^3, z, k)*(root(729*a^6*b^2*z^3 + 729*a^4*b^2*c*z^2 + 54*a^3*b*d*e*z + 243*a^2*b^2*c^2*z + 18*a*b*c*d*e - 8*a*b*d^3 + 27*b^2*c^3 + a^2*e^3, z, k)*(24*b^3*c*x - a*b^2*e + 36*root(729*a^6*b^2*z^3 + 729*a^4*b^2*c*z^2 + 54*a^3*b*d*e*z + 243*a^2*b^2*c^2*z + 18*a*b*c*d*e - 8*a*b*d^3 + 27*b^2*c^3 + a^2*e^3, z, k)*a^2*b^3*x) + (4*a^2*b^2*d^2 + 6*a^2*b^2*c*e)/(9*a^3) + (x*(108*a*b^3*c^2 + 60*a^2*b^2*d*e))/(27*a^3)) - (x*(a*b*e^3 - 8*b^2*d^3 + 12*b^2*c*d*e))/(27*a^3))*root(729*a^6*b^2*z^3 + 729*a^4*b^2*c*z^2 + 54*a^3*b*d*e*z + 243*a^2*b^2*c^2*z + 18*a*b*c*d*e - 8*a*b*d^3 + 27*b^2*c^3 + a^2*e^3, z, k), k, 1, 3) + (c*log(x))/a^2","B"
348,1,488,231,5.468447,"\text{Not used}","int((c + d*x + e*x^2)/(x^2*(a + b*x^3)^2),x)","\left(\sum _{k=1}^3\ln\left(-\mathrm{root}\left(729\,a^7\,b\,z^3+729\,a^5\,b\,d\,z^2-216\,a^3\,b\,c\,e\,z+243\,a^3\,b\,d^2\,z-72\,a\,b\,c\,d\,e+27\,a\,b\,d^3-8\,a^2\,e^3-64\,b^2\,c^3,z,k\right)\,\left(\mathrm{root}\left(729\,a^7\,b\,z^3+729\,a^5\,b\,d\,z^2-216\,a^3\,b\,c\,e\,z+243\,a^3\,b\,d^2\,z-72\,a\,b\,c\,d\,e+27\,a\,b\,d^3-8\,a^2\,e^3-64\,b^2\,c^3,z,k\right)\,\left(4\,b^3\,c+24\,b^3\,d\,x+\mathrm{root}\left(729\,a^7\,b\,z^3+729\,a^5\,b\,d\,z^2-216\,a^3\,b\,c\,e\,z+243\,a^3\,b\,d^2\,z-72\,a\,b\,c\,d\,e+27\,a\,b\,d^3-8\,a^2\,e^3-64\,b^2\,c^3,z,k\right)\,a^2\,b^3\,x\,36\right)+\frac{4\,\left(a^3\,b^2\,e^2-6\,a^2\,b^3\,c\,d\right)}{9\,a^4}+\frac{4\,x\,\left(27\,a^3\,b^3\,d^2-60\,a^3\,b^3\,c\,e\right)}{27\,a^5}\right)+\frac{4\,\left(3\,c\,b^3\,d^2+a\,b^2\,d\,e^2\right)}{9\,a^4}+\frac{4\,x\,\left(2\,a^2\,b^2\,e^3+12\,d\,a\,b^3\,c\,e+16\,b^4\,c^3\right)}{27\,a^5}\right)\,\mathrm{root}\left(729\,a^7\,b\,z^3+729\,a^5\,b\,d\,z^2-216\,a^3\,b\,c\,e\,z+243\,a^3\,b\,d^2\,z-72\,a\,b\,c\,d\,e+27\,a\,b\,d^3-8\,a^2\,e^3-64\,b^2\,c^3,z,k\right)\right)-\frac{\frac{c}{a}-\frac{e\,x^2}{3\,a}-\frac{d\,x}{3\,a}+\frac{4\,b\,c\,x^3}{3\,a^2}}{b\,x^4+a\,x}+\frac{d\,\ln\left(x\right)}{a^2}","Not used",1,"symsum(log((4*(3*b^3*c*d^2 + a*b^2*d*e^2))/(9*a^4) - root(729*a^7*b*z^3 + 729*a^5*b*d*z^2 - 216*a^3*b*c*e*z + 243*a^3*b*d^2*z - 72*a*b*c*d*e + 27*a*b*d^3 - 8*a^2*e^3 - 64*b^2*c^3, z, k)*(root(729*a^7*b*z^3 + 729*a^5*b*d*z^2 - 216*a^3*b*c*e*z + 243*a^3*b*d^2*z - 72*a*b*c*d*e + 27*a*b*d^3 - 8*a^2*e^3 - 64*b^2*c^3, z, k)*(4*b^3*c + 24*b^3*d*x + 36*root(729*a^7*b*z^3 + 729*a^5*b*d*z^2 - 216*a^3*b*c*e*z + 243*a^3*b*d^2*z - 72*a*b*c*d*e + 27*a*b*d^3 - 8*a^2*e^3 - 64*b^2*c^3, z, k)*a^2*b^3*x) + (4*(a^3*b^2*e^2 - 6*a^2*b^3*c*d))/(9*a^4) + (4*x*(27*a^3*b^3*d^2 - 60*a^3*b^3*c*e))/(27*a^5)) + (4*x*(16*b^4*c^3 + 2*a^2*b^2*e^3 + 12*a*b^3*c*d*e))/(27*a^5))*root(729*a^7*b*z^3 + 729*a^5*b*d*z^2 - 216*a^3*b*c*e*z + 243*a^3*b*d^2*z - 72*a*b*c*d*e + 27*a*b*d^3 - 8*a^2*e^3 - 64*b^2*c^3, z, k), k, 1, 3) - (c/a - (e*x^2)/(3*a) - (d*x)/(3*a) + (4*b*c*x^3)/(3*a^2))/(a*x + b*x^4) + (d*log(x))/a^2","B"
349,1,733,242,5.393679,"\text{Not used}","int((c + d*x + e*x^2)/(x^3*(a + b*x^3)^2),x)","\left(\sum _{k=1}^3\ln\left(-\frac{b^3\,\left({\mathrm{root}\left(729\,a^8\,z^3+729\,a^6\,e\,z^2+540\,a^3\,b\,c\,d\,z+243\,a^4\,e^2\,z+180\,a\,b\,c\,d\,e-64\,a\,b\,d^3+27\,a^2\,e^3+125\,b^2\,c^3,z,k\right)}^2\,a^6\,d\,108-36\,a^2\,d\,e^2+{\mathrm{root}\left(729\,a^8\,z^3+729\,a^6\,e\,z^2+540\,a^3\,b\,c\,d\,z+243\,a^4\,e^2\,z+180\,a\,b\,c\,d\,e-64\,a\,b\,d^3+27\,a^2\,e^3+125\,b^2\,c^3,z,k\right)}^3\,a^8\,x\,972+125\,b^2\,c^3\,x-\mathrm{root}\left(729\,a^8\,z^3+729\,a^6\,e\,z^2+540\,a^3\,b\,c\,d\,z+243\,a^4\,e^2\,z+180\,a\,b\,c\,d\,e-64\,a\,b\,d^3+27\,a^2\,e^3+125\,b^2\,c^3,z,k\right)\,a^4\,d\,e\,72-75\,a\,b\,c^2\,e-64\,a\,b\,d^3\,x+\mathrm{root}\left(729\,a^8\,z^3+729\,a^6\,e\,z^2+540\,a^3\,b\,c\,d\,z+243\,a^4\,e^2\,z+180\,a\,b\,c\,d\,e-64\,a\,b\,d^3+27\,a^2\,e^3+125\,b^2\,c^3,z,k\right)\,a^3\,b\,c^2\,75+\mathrm{root}\left(729\,a^8\,z^3+729\,a^6\,e\,z^2+540\,a^3\,b\,c\,d\,z+243\,a^4\,e^2\,z+180\,a\,b\,c\,d\,e-64\,a\,b\,d^3+27\,a^2\,e^3+125\,b^2\,c^3,z,k\right)\,a^4\,e^2\,x\,108+{\mathrm{root}\left(729\,a^8\,z^3+729\,a^6\,e\,z^2+540\,a^3\,b\,c\,d\,z+243\,a^4\,e^2\,z+180\,a\,b\,c\,d\,e-64\,a\,b\,d^3+27\,a^2\,e^3+125\,b^2\,c^3,z,k\right)}^2\,a^6\,e\,x\,648+\mathrm{root}\left(729\,a^8\,z^3+729\,a^6\,e\,z^2+540\,a^3\,b\,c\,d\,z+243\,a^4\,e^2\,z+180\,a\,b\,c\,d\,e-64\,a\,b\,d^3+27\,a^2\,e^3+125\,b^2\,c^3,z,k\right)\,a^3\,b\,c\,d\,x\,600+120\,a\,b\,c\,d\,e\,x\right)}{a^6\,27}\right)\,\mathrm{root}\left(729\,a^8\,z^3+729\,a^6\,e\,z^2+540\,a^3\,b\,c\,d\,z+243\,a^4\,e^2\,z+180\,a\,b\,c\,d\,e-64\,a\,b\,d^3+27\,a^2\,e^3+125\,b^2\,c^3,z,k\right)\right)-\frac{\frac{c}{2\,a}-\frac{e\,x^2}{3\,a}+\frac{d\,x}{a}+\frac{5\,b\,c\,x^3}{6\,a^2}+\frac{4\,b\,d\,x^4}{3\,a^2}}{b\,x^5+a\,x^2}+\frac{e\,\ln\left(x\right)}{a^2}","Not used",1,"symsum(log(-(b^3*(108*root(729*a^8*z^3 + 729*a^6*e*z^2 + 540*a^3*b*c*d*z + 243*a^4*e^2*z + 180*a*b*c*d*e - 64*a*b*d^3 + 27*a^2*e^3 + 125*b^2*c^3, z, k)^2*a^6*d - 36*a^2*d*e^2 + 972*root(729*a^8*z^3 + 729*a^6*e*z^2 + 540*a^3*b*c*d*z + 243*a^4*e^2*z + 180*a*b*c*d*e - 64*a*b*d^3 + 27*a^2*e^3 + 125*b^2*c^3, z, k)^3*a^8*x + 125*b^2*c^3*x - 72*root(729*a^8*z^3 + 729*a^6*e*z^2 + 540*a^3*b*c*d*z + 243*a^4*e^2*z + 180*a*b*c*d*e - 64*a*b*d^3 + 27*a^2*e^3 + 125*b^2*c^3, z, k)*a^4*d*e - 75*a*b*c^2*e - 64*a*b*d^3*x + 75*root(729*a^8*z^3 + 729*a^6*e*z^2 + 540*a^3*b*c*d*z + 243*a^4*e^2*z + 180*a*b*c*d*e - 64*a*b*d^3 + 27*a^2*e^3 + 125*b^2*c^3, z, k)*a^3*b*c^2 + 108*root(729*a^8*z^3 + 729*a^6*e*z^2 + 540*a^3*b*c*d*z + 243*a^4*e^2*z + 180*a*b*c*d*e - 64*a*b*d^3 + 27*a^2*e^3 + 125*b^2*c^3, z, k)*a^4*e^2*x + 648*root(729*a^8*z^3 + 729*a^6*e*z^2 + 540*a^3*b*c*d*z + 243*a^4*e^2*z + 180*a*b*c*d*e - 64*a*b*d^3 + 27*a^2*e^3 + 125*b^2*c^3, z, k)^2*a^6*e*x + 600*root(729*a^8*z^3 + 729*a^6*e*z^2 + 540*a^3*b*c*d*z + 243*a^4*e^2*z + 180*a*b*c*d*e - 64*a*b*d^3 + 27*a^2*e^3 + 125*b^2*c^3, z, k)*a^3*b*c*d*x + 120*a*b*c*d*e*x))/(27*a^6))*root(729*a^8*z^3 + 729*a^6*e*z^2 + 540*a^3*b*c*d*z + 243*a^4*e^2*z + 180*a*b*c*d*e - 64*a*b*d^3 + 27*a^2*e^3 + 125*b^2*c^3, z, k), k, 1, 3) - (c/(2*a) - (e*x^2)/(3*a) + (d*x)/a + (5*b*c*x^3)/(6*a^2) + (4*b*d*x^4)/(3*a^2))/(a*x^2 + b*x^5) + (e*log(x))/a^2","B"
350,1,537,262,5.483683,"\text{Not used}","int((c + d*x + e*x^2)/(x^4*(a + b*x^3)^2),x)","\left(\sum _{k=1}^3\ln\left(-\frac{50\,b^5\,c\,d^2-48\,b^5\,c^2\,e}{9\,a^6}-\mathrm{root}\left(729\,a^9\,z^3-1458\,a^6\,b\,c\,z^2+540\,a^4\,b\,d\,e\,z+972\,a^3\,b^2\,c^2\,z-360\,a\,b^2\,c\,d\,e-64\,a^2\,b\,e^3+125\,a\,b^2\,d^3-216\,b^3\,c^3,z,k\right)\,\left(\frac{25\,a^3\,b^4\,d^2+48\,c\,e\,a^3\,b^4}{9\,a^6}+\mathrm{root}\left(729\,a^9\,z^3-1458\,a^6\,b\,c\,z^2+540\,a^4\,b\,d\,e\,z+972\,a^3\,b^2\,c^2\,z-360\,a\,b^2\,c\,d\,e-64\,a^2\,b\,e^3+125\,a\,b^2\,d^3-216\,b^3\,c^3,z,k\right)\,\left(4\,b^3\,e+\mathrm{root}\left(729\,a^9\,z^3-1458\,a^6\,b\,c\,z^2+540\,a^4\,b\,d\,e\,z+972\,a^3\,b^2\,c^2\,z-360\,a\,b^2\,c\,d\,e-64\,a^2\,b\,e^3+125\,a\,b^2\,d^3-216\,b^3\,c^3,z,k\right)\,a^2\,b^3\,x\,36-\frac{48\,b^4\,c\,x}{a}\right)+\frac{x\,\left(600\,d\,e\,a^3\,b^4+432\,a^2\,b^5\,c^2\right)}{27\,a^6}\right)+\frac{x\,\left(-125\,b^5\,d^3+240\,c\,b^5\,d\,e+64\,a\,b^4\,e^3\right)}{27\,a^6}\right)\,\mathrm{root}\left(729\,a^9\,z^3-1458\,a^6\,b\,c\,z^2+540\,a^4\,b\,d\,e\,z+972\,a^3\,b^2\,c^2\,z-360\,a\,b^2\,c\,d\,e-64\,a^2\,b\,e^3+125\,a\,b^2\,d^3-216\,b^3\,c^3,z,k\right)\right)-\frac{\frac{c}{3\,a}+\frac{e\,x^2}{a}+\frac{d\,x}{2\,a}+\frac{2\,b\,c\,x^3}{3\,a^2}+\frac{5\,b\,d\,x^4}{6\,a^2}+\frac{4\,b\,e\,x^5}{3\,a^2}}{b\,x^6+a\,x^3}-\frac{2\,b\,c\,\ln\left(x\right)}{a^3}","Not used",1,"symsum(log((x*(64*a*b^4*e^3 - 125*b^5*d^3 + 240*b^5*c*d*e))/(27*a^6) - root(729*a^9*z^3 - 1458*a^6*b*c*z^2 + 540*a^4*b*d*e*z + 972*a^3*b^2*c^2*z - 360*a*b^2*c*d*e - 64*a^2*b*e^3 + 125*a*b^2*d^3 - 216*b^3*c^3, z, k)*((25*a^3*b^4*d^2 + 48*a^3*b^4*c*e)/(9*a^6) + root(729*a^9*z^3 - 1458*a^6*b*c*z^2 + 540*a^4*b*d*e*z + 972*a^3*b^2*c^2*z - 360*a*b^2*c*d*e - 64*a^2*b*e^3 + 125*a*b^2*d^3 - 216*b^3*c^3, z, k)*(4*b^3*e + 36*root(729*a^9*z^3 - 1458*a^6*b*c*z^2 + 540*a^4*b*d*e*z + 972*a^3*b^2*c^2*z - 360*a*b^2*c*d*e - 64*a^2*b*e^3 + 125*a*b^2*d^3 - 216*b^3*c^3, z, k)*a^2*b^3*x - (48*b^4*c*x)/a) + (x*(432*a^2*b^5*c^2 + 600*a^3*b^4*d*e))/(27*a^6)) - (50*b^5*c*d^2 - 48*b^5*c^2*e)/(9*a^6))*root(729*a^9*z^3 - 1458*a^6*b*c*z^2 + 540*a^4*b*d*e*z + 972*a^3*b^2*c^2*z - 360*a*b^2*c*d*e - 64*a^2*b*e^3 + 125*a*b^2*d^3 - 216*b^3*c^3, z, k), k, 1, 3) - (c/(3*a) + (e*x^2)/a + (d*x)/(2*a) + (2*b*c*x^3)/(3*a^2) + (5*b*d*x^4)/(6*a^2) + (4*b*e*x^5)/(3*a^2))/(a*x^3 + b*x^6) - (2*b*c*log(x))/a^3","B"
351,1,216,215,0.231665,"\text{Not used}","int((x^2*(c + d*x + e*x^2))/(a + b*x^3)^3,x)","\left(\sum _{k=1}^3\ln\left(\frac{d\,e+e^2\,x+{\mathrm{root}\left(19683\,a^5\,b^5\,z^3+81\,a^2\,b^2\,d\,e\,z+a\,e^3-b\,d^3,z,k\right)}^2\,a^3\,b^3\,729+\mathrm{root}\left(19683\,a^5\,b^5\,z^3+81\,a^2\,b^2\,d\,e\,z+a\,e^3-b\,d^3,z,k\right)\,a\,b^2\,d\,x\,27}{a^2\,b\,81}\right)\,\mathrm{root}\left(19683\,a^5\,b^5\,z^3+81\,a^2\,b^2\,d\,e\,z+a\,e^3-b\,d^3,z,k\right)\right)-\frac{\frac{c}{6\,b}-\frac{d\,x^4}{18\,a}-\frac{e\,x^5}{9\,a}+\frac{e\,x^2}{18\,b}+\frac{d\,x}{9\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}","Not used",1,"symsum(log((d*e + e^2*x + 729*root(19683*a^5*b^5*z^3 + 81*a^2*b^2*d*e*z + a*e^3 - b*d^3, z, k)^2*a^3*b^3 + 27*root(19683*a^5*b^5*z^3 + 81*a^2*b^2*d*e*z + a*e^3 - b*d^3, z, k)*a*b^2*d*x)/(81*a^2*b))*root(19683*a^5*b^5*z^3 + 81*a^2*b^2*d*e*z + a*e^3 - b*d^3, z, k), k, 1, 3) - (c/(6*b) - (d*x^4)/(18*a) - (e*x^5)/(9*a) + (e*x^2)/(18*b) + (d*x)/(9*b))/(a^2 + b^2*x^6 + 2*a*b*x^3)","B"
352,1,232,239,0.225279,"\text{Not used}","int((x*(c + d*x + e*x^2))/(a + b*x^3)^3,x)","\frac{\frac{7\,c\,x^2}{18\,a}-\frac{d}{6\,b}+\frac{e\,x^4}{18\,a}-\frac{e\,x}{9\,b}+\frac{2\,b\,c\,x^5}{9\,a^2}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\left(\sum _{k=1}^3\ln\left(\frac{2\,a\,c\,e+{\mathrm{root}\left(19683\,a^7\,b^4\,z^3+162\,a^3\,b^2\,c\,e\,z+8\,b^2\,c^3-a^2\,e^3,z,k\right)}^2\,a^5\,b^2\,729+4\,b\,c^2\,x+\mathrm{root}\left(19683\,a^7\,b^4\,z^3+162\,a^3\,b^2\,c\,e\,z+8\,b^2\,c^3-a^2\,e^3,z,k\right)\,a^3\,b\,e\,x\,27}{a^4\,81}\right)\,\mathrm{root}\left(19683\,a^7\,b^4\,z^3+162\,a^3\,b^2\,c\,e\,z+8\,b^2\,c^3-a^2\,e^3,z,k\right)\right)","Not used",1,"((7*c*x^2)/(18*a) - d/(6*b) + (e*x^4)/(18*a) - (e*x)/(9*b) + (2*b*c*x^5)/(9*a^2))/(a^2 + b^2*x^6 + 2*a*b*x^3) + symsum(log((2*a*c*e + 729*root(19683*a^7*b^4*z^3 + 162*a^3*b^2*c*e*z + 8*b^2*c^3 - a^2*e^3, z, k)^2*a^5*b^2 + 4*b*c^2*x + 27*root(19683*a^7*b^4*z^3 + 162*a^3*b^2*c*e*z + 8*b^2*c^3 - a^2*e^3, z, k)*a^3*b*e*x)/(81*a^4))*root(19683*a^7*b^4*z^3 + 162*a^3*b^2*c*e*z + 8*b^2*c^3 - a^2*e^3, z, k), k, 1, 3)","B"
353,1,212,225,0.262365,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^3)^3,x)","\frac{\frac{7\,d\,x^2}{18\,a}-\frac{e}{6\,b}+\frac{4\,c\,x}{9\,a}+\frac{5\,b\,c\,x^4}{18\,a^2}+\frac{2\,b\,d\,x^5}{9\,a^2}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\left(\sum _{k=1}^3\ln\left(\frac{b\,\left(10\,c\,d+4\,d^2\,x+{\mathrm{root}\left(19683\,a^8\,b^2\,z^3+810\,a^3\,b\,c\,d\,z-125\,b\,c^3+8\,a\,d^3,z,k\right)}^2\,a^5\,b\,729+\mathrm{root}\left(19683\,a^8\,b^2\,z^3+810\,a^3\,b\,c\,d\,z-125\,b\,c^3+8\,a\,d^3,z,k\right)\,a^2\,b\,c\,x\,135\right)}{a^4\,81}\right)\,\mathrm{root}\left(19683\,a^8\,b^2\,z^3+810\,a^3\,b\,c\,d\,z-125\,b\,c^3+8\,a\,d^3,z,k\right)\right)","Not used",1,"((7*d*x^2)/(18*a) - e/(6*b) + (4*c*x)/(9*a) + (5*b*c*x^4)/(18*a^2) + (2*b*d*x^5)/(9*a^2))/(a^2 + b^2*x^6 + 2*a*b*x^3) + symsum(log((b*(10*c*d + 4*d^2*x + 729*root(19683*a^8*b^2*z^3 + 810*a^3*b*c*d*z - 125*b*c^3 + 8*a*d^3, z, k)^2*a^5*b + 135*root(19683*a^8*b^2*z^3 + 810*a^3*b*c*d*z - 125*b*c^3 + 8*a*d^3, z, k)*a^2*b*c*x))/(81*a^4))*root(19683*a^8*b^2*z^3 + 810*a^3*b*c*d*z - 125*b*c^3 + 8*a*d^3, z, k), k, 1, 3)","B"
354,1,540,257,5.440321,"\text{Not used}","int((c + d*x + e*x^2)/(x*(a + b*x^3)^3),x)","\frac{\frac{c}{2\,a}+\frac{7\,e\,x^2}{18\,a}+\frac{4\,d\,x}{9\,a}+\frac{b\,c\,x^3}{3\,a^2}+\frac{5\,b\,d\,x^4}{18\,a^2}+\frac{2\,b\,e\,x^5}{9\,a^2}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\left(\sum _{k=1}^3\ln\left(\frac{25\,b^2\,c\,d^2-18\,b^2\,c^2\,e}{81\,a^6}-\mathrm{root}\left(19683\,a^9\,b^2\,z^3+19683\,a^6\,b^2\,c\,z^2+810\,a^4\,b\,d\,e\,z+6561\,a^3\,b^2\,c^2\,z+270\,a\,b\,c\,d\,e-125\,a\,b\,d^3+8\,a^2\,e^3+729\,b^2\,c^3,z,k\right)\,\left(\frac{25\,a^3\,b^2\,d^2+36\,c\,e\,a^3\,b^2}{81\,a^6}+\mathrm{root}\left(19683\,a^9\,b^2\,z^3+19683\,a^6\,b^2\,c\,z^2+810\,a^4\,b\,d\,e\,z+6561\,a^3\,b^2\,c^2\,z+270\,a\,b\,c\,d\,e-125\,a\,b\,d^3+8\,a^2\,e^3+729\,b^2\,c^3,z,k\right)\,\left(-\frac{2\,b^2\,e}{3}+\mathrm{root}\left(19683\,a^9\,b^2\,z^3+19683\,a^6\,b^2\,c\,z^2+810\,a^4\,b\,d\,e\,z+6561\,a^3\,b^2\,c^2\,z+270\,a\,b\,c\,d\,e-125\,a\,b\,d^3+8\,a^2\,e^3+729\,b^2\,c^3,z,k\right)\,a^2\,b^3\,x\,36+\frac{24\,b^3\,c\,x}{a}\right)+\frac{x\,\left(900\,d\,e\,a^3\,b^2+2916\,a^2\,b^3\,c^2\right)}{729\,a^6}\right)-\frac{x\,\left(-125\,b^2\,d^3+180\,c\,b^2\,d\,e+8\,a\,b\,e^3\right)}{729\,a^6}\right)\,\mathrm{root}\left(19683\,a^9\,b^2\,z^3+19683\,a^6\,b^2\,c\,z^2+810\,a^4\,b\,d\,e\,z+6561\,a^3\,b^2\,c^2\,z+270\,a\,b\,c\,d\,e-125\,a\,b\,d^3+8\,a^2\,e^3+729\,b^2\,c^3,z,k\right)\right)+\frac{c\,\ln\left(x\right)}{a^3}","Not used",1,"(c/(2*a) + (7*e*x^2)/(18*a) + (4*d*x)/(9*a) + (b*c*x^3)/(3*a^2) + (5*b*d*x^4)/(18*a^2) + (2*b*e*x^5)/(9*a^2))/(a^2 + b^2*x^6 + 2*a*b*x^3) + symsum(log((25*b^2*c*d^2 - 18*b^2*c^2*e)/(81*a^6) - root(19683*a^9*b^2*z^3 + 19683*a^6*b^2*c*z^2 + 810*a^4*b*d*e*z + 6561*a^3*b^2*c^2*z + 270*a*b*c*d*e - 125*a*b*d^3 + 8*a^2*e^3 + 729*b^2*c^3, z, k)*((25*a^3*b^2*d^2 + 36*a^3*b^2*c*e)/(81*a^6) + root(19683*a^9*b^2*z^3 + 19683*a^6*b^2*c*z^2 + 810*a^4*b*d*e*z + 6561*a^3*b^2*c^2*z + 270*a*b*c*d*e - 125*a*b*d^3 + 8*a^2*e^3 + 729*b^2*c^3, z, k)*(36*root(19683*a^9*b^2*z^3 + 19683*a^6*b^2*c*z^2 + 810*a^4*b*d*e*z + 6561*a^3*b^2*c^2*z + 270*a*b*c*d*e - 125*a*b*d^3 + 8*a^2*e^3 + 729*b^2*c^3, z, k)*a^2*b^3*x - (2*b^2*e)/3 + (24*b^3*c*x)/a) + (x*(2916*a^2*b^3*c^2 + 900*a^3*b^2*d*e))/(729*a^6)) - (x*(8*a*b*e^3 - 125*b^2*d^3 + 180*b^2*c*d*e))/(729*a^6))*root(19683*a^9*b^2*z^3 + 19683*a^6*b^2*c*z^2 + 810*a^4*b*d*e*z + 6561*a^3*b^2*c^2*z + 270*a*b*c*d*e - 125*a*b*d^3 + 8*a^2*e^3 + 729*b^2*c^3, z, k), k, 1, 3) + (c*log(x))/a^3","B"
355,1,793,267,5.460416,"\text{Not used}","int((c + d*x + e*x^2)/(x^2*(a + b*x^3)^3),x)","\frac{\frac{4\,e\,x^2}{9\,a}-\frac{c}{a}+\frac{d\,x}{2\,a}-\frac{14\,b^2\,c\,x^6}{9\,a^3}-\frac{49\,b\,c\,x^3}{18\,a^2}+\frac{b\,d\,x^4}{3\,a^2}+\frac{5\,b\,e\,x^5}{18\,a^2}}{a^2\,x+2\,a\,b\,x^4+b^2\,x^7}+\left(\sum _{k=1}^3\ln\left(\frac{b^2\,\left(-\mathrm{root}\left(19683\,a^{10}\,b\,z^3+19683\,a^7\,b\,d\,z^2-5670\,a^4\,b\,c\,e\,z+6561\,a^4\,b\,d^2\,z-1890\,a\,b\,c\,d\,e+729\,a\,b\,d^3-125\,a^2\,e^3-2744\,b^2\,c^3,z,k\right)\,a^5\,e^2\,225+225\,a^2\,d\,e^2+2744\,b^2\,c^3\,x+125\,a^2\,e^3\,x+1134\,a\,b\,c\,d^2-{\mathrm{root}\left(19683\,a^{10}\,b\,z^3+19683\,a^7\,b\,d\,z^2-5670\,a^4\,b\,c\,e\,z+6561\,a^4\,b\,d^2\,z-1890\,a\,b\,c\,d\,e+729\,a\,b\,d^3-125\,a^2\,e^3-2744\,b^2\,c^3,z,k\right)}^2\,a^7\,b\,c\,3402-{\mathrm{root}\left(19683\,a^{10}\,b\,z^3+19683\,a^7\,b\,d\,z^2-5670\,a^4\,b\,c\,e\,z+6561\,a^4\,b\,d^2\,z-1890\,a\,b\,c\,d\,e+729\,a\,b\,d^3-125\,a^2\,e^3-2744\,b^2\,c^3,z,k\right)}^3\,a^{10}\,b\,x\,26244-\mathrm{root}\left(19683\,a^{10}\,b\,z^3+19683\,a^7\,b\,d\,z^2-5670\,a^4\,b\,c\,e\,z+6561\,a^4\,b\,d^2\,z-1890\,a\,b\,c\,d\,e+729\,a\,b\,d^3-125\,a^2\,e^3-2744\,b^2\,c^3,z,k\right)\,a^4\,b\,d^2\,x\,2916-{\mathrm{root}\left(19683\,a^{10}\,b\,z^3+19683\,a^7\,b\,d\,z^2-5670\,a^4\,b\,c\,e\,z+6561\,a^4\,b\,d^2\,z-1890\,a\,b\,c\,d\,e+729\,a\,b\,d^3-125\,a^2\,e^3-2744\,b^2\,c^3,z,k\right)}^2\,a^7\,b\,d\,x\,17496+\mathrm{root}\left(19683\,a^{10}\,b\,z^3+19683\,a^7\,b\,d\,z^2-5670\,a^4\,b\,c\,e\,z+6561\,a^4\,b\,d^2\,z-1890\,a\,b\,c\,d\,e+729\,a\,b\,d^3-125\,a^2\,e^3-2744\,b^2\,c^3,z,k\right)\,a^4\,b\,c\,d\,2268+\mathrm{root}\left(19683\,a^{10}\,b\,z^3+19683\,a^7\,b\,d\,z^2-5670\,a^4\,b\,c\,e\,z+6561\,a^4\,b\,d^2\,z-1890\,a\,b\,c\,d\,e+729\,a\,b\,d^3-125\,a^2\,e^3-2744\,b^2\,c^3,z,k\right)\,a^4\,b\,c\,e\,x\,6300+1260\,a\,b\,c\,d\,e\,x\right)}{a^8\,729}\right)\,\mathrm{root}\left(19683\,a^{10}\,b\,z^3+19683\,a^7\,b\,d\,z^2-5670\,a^4\,b\,c\,e\,z+6561\,a^4\,b\,d^2\,z-1890\,a\,b\,c\,d\,e+729\,a\,b\,d^3-125\,a^2\,e^3-2744\,b^2\,c^3,z,k\right)\right)+\frac{d\,\ln\left(x\right)}{a^3}","Not used",1,"((4*e*x^2)/(9*a) - c/a + (d*x)/(2*a) - (14*b^2*c*x^6)/(9*a^3) - (49*b*c*x^3)/(18*a^2) + (b*d*x^4)/(3*a^2) + (5*b*e*x^5)/(18*a^2))/(a^2*x + b^2*x^7 + 2*a*b*x^4) + symsum(log((b^2*(225*a^2*d*e^2 - 225*root(19683*a^10*b*z^3 + 19683*a^7*b*d*z^2 - 5670*a^4*b*c*e*z + 6561*a^4*b*d^2*z - 1890*a*b*c*d*e + 729*a*b*d^3 - 125*a^2*e^3 - 2744*b^2*c^3, z, k)*a^5*e^2 + 2744*b^2*c^3*x + 125*a^2*e^3*x + 1134*a*b*c*d^2 - 3402*root(19683*a^10*b*z^3 + 19683*a^7*b*d*z^2 - 5670*a^4*b*c*e*z + 6561*a^4*b*d^2*z - 1890*a*b*c*d*e + 729*a*b*d^3 - 125*a^2*e^3 - 2744*b^2*c^3, z, k)^2*a^7*b*c - 26244*root(19683*a^10*b*z^3 + 19683*a^7*b*d*z^2 - 5670*a^4*b*c*e*z + 6561*a^4*b*d^2*z - 1890*a*b*c*d*e + 729*a*b*d^3 - 125*a^2*e^3 - 2744*b^2*c^3, z, k)^3*a^10*b*x - 2916*root(19683*a^10*b*z^3 + 19683*a^7*b*d*z^2 - 5670*a^4*b*c*e*z + 6561*a^4*b*d^2*z - 1890*a*b*c*d*e + 729*a*b*d^3 - 125*a^2*e^3 - 2744*b^2*c^3, z, k)*a^4*b*d^2*x - 17496*root(19683*a^10*b*z^3 + 19683*a^7*b*d*z^2 - 5670*a^4*b*c*e*z + 6561*a^4*b*d^2*z - 1890*a*b*c*d*e + 729*a*b*d^3 - 125*a^2*e^3 - 2744*b^2*c^3, z, k)^2*a^7*b*d*x + 2268*root(19683*a^10*b*z^3 + 19683*a^7*b*d*z^2 - 5670*a^4*b*c*e*z + 6561*a^4*b*d^2*z - 1890*a*b*c*d*e + 729*a*b*d^3 - 125*a^2*e^3 - 2744*b^2*c^3, z, k)*a^4*b*c*d + 6300*root(19683*a^10*b*z^3 + 19683*a^7*b*d*z^2 - 5670*a^4*b*c*e*z + 6561*a^4*b*d^2*z - 1890*a*b*c*d*e + 729*a*b*d^3 - 125*a^2*e^3 - 2744*b^2*c^3, z, k)*a^4*b*c*e*x + 1260*a*b*c*d*e*x))/(729*a^8))*root(19683*a^10*b*z^3 + 19683*a^7*b*d*z^2 - 5670*a^4*b*c*e*z + 6561*a^4*b*d^2*z - 1890*a*b*c*d*e + 729*a*b*d^3 - 125*a^2*e^3 - 2744*b^2*c^3, z, k), k, 1, 3) + (d*log(x))/a^3","B"
356,1,778,276,5.358090,"\text{Not used}","int((c + d*x + e*x^2)/(x^3*(a + b*x^3)^3),x)","\left(\sum _{k=1}^3\ln\left(-\frac{b^3\,\left({\mathrm{root}\left(19683\,a^{11}\,z^3+19683\,a^8\,e\,z^2+22680\,a^4\,b\,c\,d\,z+6561\,a^5\,e^2\,z+7560\,a\,b\,c\,d\,e-2744\,a\,b\,d^3+729\,a^2\,e^3+8000\,b^2\,c^3,z,k\right)}^2\,a^8\,d\,1701-567\,a^2\,d\,e^2+{\mathrm{root}\left(19683\,a^{11}\,z^3+19683\,a^8\,e\,z^2+22680\,a^4\,b\,c\,d\,z+6561\,a^5\,e^2\,z+7560\,a\,b\,c\,d\,e-2744\,a\,b\,d^3+729\,a^2\,e^3+8000\,b^2\,c^3,z,k\right)}^3\,a^{11}\,x\,13122+4000\,b^2\,c^3\,x-\mathrm{root}\left(19683\,a^{11}\,z^3+19683\,a^8\,e\,z^2+22680\,a^4\,b\,c\,d\,z+6561\,a^5\,e^2\,z+7560\,a\,b\,c\,d\,e-2744\,a\,b\,d^3+729\,a^2\,e^3+8000\,b^2\,c^3,z,k\right)\,a^5\,d\,e\,1134-1800\,a\,b\,c^2\,e-1372\,a\,b\,d^3\,x+\mathrm{root}\left(19683\,a^{11}\,z^3+19683\,a^8\,e\,z^2+22680\,a^4\,b\,c\,d\,z+6561\,a^5\,e^2\,z+7560\,a\,b\,c\,d\,e-2744\,a\,b\,d^3+729\,a^2\,e^3+8000\,b^2\,c^3,z,k\right)\,a^4\,b\,c^2\,1800+\mathrm{root}\left(19683\,a^{11}\,z^3+19683\,a^8\,e\,z^2+22680\,a^4\,b\,c\,d\,z+6561\,a^5\,e^2\,z+7560\,a\,b\,c\,d\,e-2744\,a\,b\,d^3+729\,a^2\,e^3+8000\,b^2\,c^3,z,k\right)\,a^5\,e^2\,x\,1458+{\mathrm{root}\left(19683\,a^{11}\,z^3+19683\,a^8\,e\,z^2+22680\,a^4\,b\,c\,d\,z+6561\,a^5\,e^2\,z+7560\,a\,b\,c\,d\,e-2744\,a\,b\,d^3+729\,a^2\,e^3+8000\,b^2\,c^3,z,k\right)}^2\,a^8\,e\,x\,8748+\mathrm{root}\left(19683\,a^{11}\,z^3+19683\,a^8\,e\,z^2+22680\,a^4\,b\,c\,d\,z+6561\,a^5\,e^2\,z+7560\,a\,b\,c\,d\,e-2744\,a\,b\,d^3+729\,a^2\,e^3+8000\,b^2\,c^3,z,k\right)\,a^4\,b\,c\,d\,x\,12600+2520\,a\,b\,c\,d\,e\,x\right)\,2}{a^9\,729}\right)\,\mathrm{root}\left(19683\,a^{11}\,z^3+19683\,a^8\,e\,z^2+22680\,a^4\,b\,c\,d\,z+6561\,a^5\,e^2\,z+7560\,a\,b\,c\,d\,e-2744\,a\,b\,d^3+729\,a^2\,e^3+8000\,b^2\,c^3,z,k\right)\right)-\frac{\frac{c}{2\,a}-\frac{e\,x^2}{2\,a}+\frac{d\,x}{a}+\frac{10\,b^2\,c\,x^6}{9\,a^3}+\frac{14\,b^2\,d\,x^7}{9\,a^3}+\frac{16\,b\,c\,x^3}{9\,a^2}+\frac{49\,b\,d\,x^4}{18\,a^2}-\frac{b\,e\,x^5}{3\,a^2}}{a^2\,x^2+2\,a\,b\,x^5+b^2\,x^8}+\frac{e\,\ln\left(x\right)}{a^3}","Not used",1,"symsum(log(-(2*b^3*(1701*root(19683*a^11*z^3 + 19683*a^8*e*z^2 + 22680*a^4*b*c*d*z + 6561*a^5*e^2*z + 7560*a*b*c*d*e - 2744*a*b*d^3 + 729*a^2*e^3 + 8000*b^2*c^3, z, k)^2*a^8*d - 567*a^2*d*e^2 + 13122*root(19683*a^11*z^3 + 19683*a^8*e*z^2 + 22680*a^4*b*c*d*z + 6561*a^5*e^2*z + 7560*a*b*c*d*e - 2744*a*b*d^3 + 729*a^2*e^3 + 8000*b^2*c^3, z, k)^3*a^11*x + 4000*b^2*c^3*x - 1134*root(19683*a^11*z^3 + 19683*a^8*e*z^2 + 22680*a^4*b*c*d*z + 6561*a^5*e^2*z + 7560*a*b*c*d*e - 2744*a*b*d^3 + 729*a^2*e^3 + 8000*b^2*c^3, z, k)*a^5*d*e - 1800*a*b*c^2*e - 1372*a*b*d^3*x + 1800*root(19683*a^11*z^3 + 19683*a^8*e*z^2 + 22680*a^4*b*c*d*z + 6561*a^5*e^2*z + 7560*a*b*c*d*e - 2744*a*b*d^3 + 729*a^2*e^3 + 8000*b^2*c^3, z, k)*a^4*b*c^2 + 1458*root(19683*a^11*z^3 + 19683*a^8*e*z^2 + 22680*a^4*b*c*d*z + 6561*a^5*e^2*z + 7560*a*b*c*d*e - 2744*a*b*d^3 + 729*a^2*e^3 + 8000*b^2*c^3, z, k)*a^5*e^2*x + 8748*root(19683*a^11*z^3 + 19683*a^8*e*z^2 + 22680*a^4*b*c*d*z + 6561*a^5*e^2*z + 7560*a*b*c*d*e - 2744*a*b*d^3 + 729*a^2*e^3 + 8000*b^2*c^3, z, k)^2*a^8*e*x + 12600*root(19683*a^11*z^3 + 19683*a^8*e*z^2 + 22680*a^4*b*c*d*z + 6561*a^5*e^2*z + 7560*a*b*c*d*e - 2744*a*b*d^3 + 729*a^2*e^3 + 8000*b^2*c^3, z, k)*a^4*b*c*d*x + 2520*a*b*c*d*e*x))/(729*a^9))*root(19683*a^11*z^3 + 19683*a^8*e*z^2 + 22680*a^4*b*c*d*z + 6561*a^5*e^2*z + 7560*a*b*c*d*e - 2744*a*b*d^3 + 729*a^2*e^3 + 8000*b^2*c^3, z, k), k, 1, 3) - (c/(2*a) - (e*x^2)/(2*a) + (d*x)/a + (10*b^2*c*x^6)/(9*a^3) + (14*b^2*d*x^7)/(9*a^3) + (16*b*c*x^3)/(9*a^2) + (49*b*d*x^4)/(18*a^2) - (b*e*x^5)/(3*a^2))/(a^2*x^2 + b^2*x^8 + 2*a*b*x^5) + (e*log(x))/a^3","B"
357,1,870,298,0.464982,"\text{Not used}","int((c + d*x + e*x^2)/(x^4*(a + b*x^3)^3),x)","\left(\sum _{k=1}^3\ln\left(-\frac{b^3\,\left({\mathrm{root}\left(19683\,a^{12}\,z^3-59049\,a^8\,b\,c\,z^2+22680\,a^5\,b\,d\,e\,z+59049\,a^4\,b^2\,c^2\,z-22680\,a\,b^2\,c\,d\,e-2744\,a^2\,b\,e^3+8000\,a\,b^2\,d^3-19683\,b^3\,c^3,z,k\right)}^2\,a^8\,e\,1701+5400\,b^2\,c\,d^2-5103\,b^2\,c^2\,e+{\mathrm{root}\left(19683\,a^{12}\,z^3-59049\,a^8\,b\,c\,z^2+22680\,a^5\,b\,d\,e\,z+59049\,a^4\,b^2\,c^2\,z-22680\,a\,b^2\,c\,d\,e-2744\,a^2\,b\,e^3+8000\,a\,b^2\,d^3-19683\,b^3\,c^3,z,k\right)}^3\,a^{11}\,x\,13122+4000\,b^2\,d^3\,x-1372\,a\,b\,e^3\,x+\mathrm{root}\left(19683\,a^{12}\,z^3-59049\,a^8\,b\,c\,z^2+22680\,a^5\,b\,d\,e\,z+59049\,a^4\,b^2\,c^2\,z-22680\,a\,b^2\,c\,d\,e-2744\,a^2\,b\,e^3+8000\,a\,b^2\,d^3-19683\,b^3\,c^3,z,k\right)\,a^4\,b\,d^2\,1800-{\mathrm{root}\left(19683\,a^{12}\,z^3-59049\,a^8\,b\,c\,z^2+22680\,a^5\,b\,d\,e\,z+59049\,a^4\,b^2\,c^2\,z-22680\,a\,b^2\,c\,d\,e-2744\,a^2\,b\,e^3+8000\,a\,b^2\,d^3-19683\,b^3\,c^3,z,k\right)}^2\,a^7\,b\,c\,x\,26244+\mathrm{root}\left(19683\,a^{12}\,z^3-59049\,a^8\,b\,c\,z^2+22680\,a^5\,b\,d\,e\,z+59049\,a^4\,b^2\,c^2\,z-22680\,a\,b^2\,c\,d\,e-2744\,a^2\,b\,e^3+8000\,a\,b^2\,d^3-19683\,b^3\,c^3,z,k\right)\,a^3\,b^2\,c^2\,x\,13122+\mathrm{root}\left(19683\,a^{12}\,z^3-59049\,a^8\,b\,c\,z^2+22680\,a^5\,b\,d\,e\,z+59049\,a^4\,b^2\,c^2\,z-22680\,a\,b^2\,c\,d\,e-2744\,a^2\,b\,e^3+8000\,a\,b^2\,d^3-19683\,b^3\,c^3,z,k\right)\,a^4\,b\,c\,e\,3402-7560\,b^2\,c\,d\,e\,x+\mathrm{root}\left(19683\,a^{12}\,z^3-59049\,a^8\,b\,c\,z^2+22680\,a^5\,b\,d\,e\,z+59049\,a^4\,b^2\,c^2\,z-22680\,a\,b^2\,c\,d\,e-2744\,a^2\,b\,e^3+8000\,a\,b^2\,d^3-19683\,b^3\,c^3,z,k\right)\,a^4\,b\,d\,e\,x\,12600\right)\,2}{a^9\,729}\right)\,\mathrm{root}\left(19683\,a^{12}\,z^3-59049\,a^8\,b\,c\,z^2+22680\,a^5\,b\,d\,e\,z+59049\,a^4\,b^2\,c^2\,z-22680\,a\,b^2\,c\,d\,e-2744\,a^2\,b\,e^3+8000\,a\,b^2\,d^3-19683\,b^3\,c^3,z,k\right)\right)-\frac{\frac{c}{3\,a}+\frac{e\,x^2}{a}+\frac{d\,x}{2\,a}+\frac{b^2\,c\,x^6}{a^3}+\frac{10\,b^2\,d\,x^7}{9\,a^3}+\frac{14\,b^2\,e\,x^8}{9\,a^3}+\frac{3\,b\,c\,x^3}{2\,a^2}+\frac{16\,b\,d\,x^4}{9\,a^2}+\frac{49\,b\,e\,x^5}{18\,a^2}}{a^2\,x^3+2\,a\,b\,x^6+b^2\,x^9}-\frac{3\,b\,c\,\ln\left(x\right)}{a^4}","Not used",1,"symsum(log(-(2*b^3*(1701*root(19683*a^12*z^3 - 59049*a^8*b*c*z^2 + 22680*a^5*b*d*e*z + 59049*a^4*b^2*c^2*z - 22680*a*b^2*c*d*e - 2744*a^2*b*e^3 + 8000*a*b^2*d^3 - 19683*b^3*c^3, z, k)^2*a^8*e + 5400*b^2*c*d^2 - 5103*b^2*c^2*e + 13122*root(19683*a^12*z^3 - 59049*a^8*b*c*z^2 + 22680*a^5*b*d*e*z + 59049*a^4*b^2*c^2*z - 22680*a*b^2*c*d*e - 2744*a^2*b*e^3 + 8000*a*b^2*d^3 - 19683*b^3*c^3, z, k)^3*a^11*x + 4000*b^2*d^3*x - 1372*a*b*e^3*x + 1800*root(19683*a^12*z^3 - 59049*a^8*b*c*z^2 + 22680*a^5*b*d*e*z + 59049*a^4*b^2*c^2*z - 22680*a*b^2*c*d*e - 2744*a^2*b*e^3 + 8000*a*b^2*d^3 - 19683*b^3*c^3, z, k)*a^4*b*d^2 - 26244*root(19683*a^12*z^3 - 59049*a^8*b*c*z^2 + 22680*a^5*b*d*e*z + 59049*a^4*b^2*c^2*z - 22680*a*b^2*c*d*e - 2744*a^2*b*e^3 + 8000*a*b^2*d^3 - 19683*b^3*c^3, z, k)^2*a^7*b*c*x + 13122*root(19683*a^12*z^3 - 59049*a^8*b*c*z^2 + 22680*a^5*b*d*e*z + 59049*a^4*b^2*c^2*z - 22680*a*b^2*c*d*e - 2744*a^2*b*e^3 + 8000*a*b^2*d^3 - 19683*b^3*c^3, z, k)*a^3*b^2*c^2*x + 3402*root(19683*a^12*z^3 - 59049*a^8*b*c*z^2 + 22680*a^5*b*d*e*z + 59049*a^4*b^2*c^2*z - 22680*a*b^2*c*d*e - 2744*a^2*b*e^3 + 8000*a*b^2*d^3 - 19683*b^3*c^3, z, k)*a^4*b*c*e - 7560*b^2*c*d*e*x + 12600*root(19683*a^12*z^3 - 59049*a^8*b*c*z^2 + 22680*a^5*b*d*e*z + 59049*a^4*b^2*c^2*z - 22680*a*b^2*c*d*e - 2744*a^2*b*e^3 + 8000*a*b^2*d^3 - 19683*b^3*c^3, z, k)*a^4*b*d*e*x))/(729*a^9))*root(19683*a^12*z^3 - 59049*a^8*b*c*z^2 + 22680*a^5*b*d*e*z + 59049*a^4*b^2*c^2*z - 22680*a*b^2*c*d*e - 2744*a^2*b*e^3 + 8000*a*b^2*d^3 - 19683*b^3*c^3, z, k), k, 1, 3) - (c/(3*a) + (e*x^2)/a + (d*x)/(2*a) + (b^2*c*x^6)/a^3 + (10*b^2*d*x^7)/(9*a^3) + (14*b^2*e*x^8)/(9*a^3) + (3*b*c*x^3)/(2*a^2) + (16*b*d*x^4)/(9*a^2) + (49*b*e*x^5)/(18*a^2))/(a^2*x^3 + b^2*x^9 + 2*a*b*x^6) - (3*b*c*log(x))/a^4","B"
358,1,253,248,0.266664,"\text{Not used}","int((x^2*(c + d*x + e*x^2))/(a + b*x^3)^4,x)","\left(\sum _{k=1}^3\ln\left(\frac{20\,d\,e+16\,e^2\,x+{\mathrm{root}\left(14348907\,a^8\,b^5\,z^3+14580\,a^3\,b^2\,d\,e\,z-125\,b\,d^3+64\,a\,e^3,z,k\right)}^2\,a^5\,b^3\,59049+\mathrm{root}\left(14348907\,a^8\,b^5\,z^3+14580\,a^3\,b^2\,d\,e\,z-125\,b\,d^3+64\,a\,e^3,z,k\right)\,a^2\,b^2\,d\,x\,1215}{a^4\,b\,6561}\right)\,\mathrm{root}\left(14348907\,a^8\,b^5\,z^3+14580\,a^3\,b^2\,d\,e\,z-125\,b\,d^3+64\,a\,e^3,z,k\right)\right)+\frac{\frac{13\,d\,x^4}{162\,a}-\frac{c}{9\,b}+\frac{11\,e\,x^5}{81\,a}-\frac{2\,e\,x^2}{81\,b}-\frac{5\,d\,x}{81\,b}+\frac{5\,b\,d\,x^7}{162\,a^2}+\frac{4\,b\,e\,x^8}{81\,a^2}}{a^3+3\,a^2\,b\,x^3+3\,a\,b^2\,x^6+b^3\,x^9}","Not used",1,"symsum(log((20*d*e + 16*e^2*x + 59049*root(14348907*a^8*b^5*z^3 + 14580*a^3*b^2*d*e*z - 125*b*d^3 + 64*a*e^3, z, k)^2*a^5*b^3 + 1215*root(14348907*a^8*b^5*z^3 + 14580*a^3*b^2*d*e*z - 125*b*d^3 + 64*a*e^3, z, k)*a^2*b^2*d*x)/(6561*a^4*b))*root(14348907*a^8*b^5*z^3 + 14580*a^3*b^2*d*e*z - 125*b*d^3 + 64*a*e^3, z, k), k, 1, 3) + ((13*d*x^4)/(162*a) - c/(9*b) + (11*e*x^5)/(81*a) - (2*e*x^2)/(81*b) - (5*d*x)/(81*b) + (5*b*d*x^7)/(162*a^2) + (4*b*e*x^8)/(81*a^2))/(a^3 + b^3*x^9 + 3*a^2*b*x^3 + 3*a*b^2*x^6)","B"
359,1,265,270,0.239065,"\text{Not used}","int((x*(c + d*x + e*x^2))/(a + b*x^3)^4,x)","\frac{\frac{67\,c\,x^2}{162\,a}-\frac{d}{9\,b}+\frac{13\,e\,x^4}{162\,a}-\frac{5\,e\,x}{81\,b}+\frac{14\,b^2\,c\,x^8}{81\,a^3}+\frac{77\,b\,c\,x^5}{162\,a^2}+\frac{5\,b\,e\,x^7}{162\,a^2}}{a^3+3\,a^2\,b\,x^3+3\,a\,b^2\,x^6+b^3\,x^9}+\left(\sum _{k=1}^3\ln\left(\frac{70\,a\,c\,e+{\mathrm{root}\left(14348907\,a^{10}\,b^4\,z^3+51030\,a^4\,b^2\,c\,e\,z-125\,a^2\,e^3+2744\,b^2\,c^3,z,k\right)}^2\,a^7\,b^2\,59049+196\,b\,c^2\,x+\mathrm{root}\left(14348907\,a^{10}\,b^4\,z^3+51030\,a^4\,b^2\,c\,e\,z-125\,a^2\,e^3+2744\,b^2\,c^3,z,k\right)\,a^4\,b\,e\,x\,1215}{a^6\,6561}\right)\,\mathrm{root}\left(14348907\,a^{10}\,b^4\,z^3+51030\,a^4\,b^2\,c\,e\,z-125\,a^2\,e^3+2744\,b^2\,c^3,z,k\right)\right)","Not used",1,"((67*c*x^2)/(162*a) - d/(9*b) + (13*e*x^4)/(162*a) - (5*e*x)/(81*b) + (14*b^2*c*x^8)/(81*a^3) + (77*b*c*x^5)/(162*a^2) + (5*b*e*x^7)/(162*a^2))/(a^3 + b^3*x^9 + 3*a^2*b*x^3 + 3*a*b^2*x^6) + symsum(log((70*a*c*e + 59049*root(14348907*a^10*b^4*z^3 + 51030*a^4*b^2*c*e*z - 125*a^2*e^3 + 2744*b^2*c^3, z, k)^2*a^7*b^2 + 196*b*c^2*x + 1215*root(14348907*a^10*b^4*z^3 + 51030*a^4*b^2*c*e*z - 125*a^2*e^3 + 2744*b^2*c^3, z, k)*a^4*b*e*x)/(6561*a^6))*root(14348907*a^10*b^4*z^3 + 51030*a^4*b^2*c*e*z - 125*a^2*e^3 + 2744*b^2*c^3, z, k), k, 1, 3)","B"
360,1,247,250,0.278624,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^3)^4,x)","\frac{\frac{67\,d\,x^2}{162\,a}-\frac{e}{9\,b}+\frac{41\,c\,x}{81\,a}+\frac{20\,b^2\,c\,x^7}{81\,a^3}+\frac{14\,b^2\,d\,x^8}{81\,a^3}+\frac{52\,b\,c\,x^4}{81\,a^2}+\frac{77\,b\,d\,x^5}{162\,a^2}}{a^3+3\,a^2\,b\,x^3+3\,a\,b^2\,x^6+b^3\,x^9}+\left(\sum _{k=1}^3\ln\left(\frac{b\,\left(560\,c\,d+196\,d^2\,x+{\mathrm{root}\left(14348907\,a^{11}\,b^2\,z^3+408240\,a^4\,b\,c\,d\,z-64000\,b\,c^3+2744\,a\,d^3,z,k\right)}^2\,a^7\,b\,59049+\mathrm{root}\left(14348907\,a^{11}\,b^2\,z^3+408240\,a^4\,b\,c\,d\,z-64000\,b\,c^3+2744\,a\,d^3,z,k\right)\,a^3\,b\,c\,x\,9720\right)}{a^6\,6561}\right)\,\mathrm{root}\left(14348907\,a^{11}\,b^2\,z^3+408240\,a^4\,b\,c\,d\,z-64000\,b\,c^3+2744\,a\,d^3,z,k\right)\right)","Not used",1,"((67*d*x^2)/(162*a) - e/(9*b) + (41*c*x)/(81*a) + (20*b^2*c*x^7)/(81*a^3) + (14*b^2*d*x^8)/(81*a^3) + (52*b*c*x^4)/(81*a^2) + (77*b*d*x^5)/(162*a^2))/(a^3 + b^3*x^9 + 3*a^2*b*x^3 + 3*a*b^2*x^6) + symsum(log((b*(560*c*d + 196*d^2*x + 59049*root(14348907*a^11*b^2*z^3 + 408240*a^4*b*c*d*z - 64000*b*c^3 + 2744*a*d^3, z, k)^2*a^7*b + 9720*root(14348907*a^11*b^2*z^3 + 408240*a^4*b*c*d*z - 64000*b*c^3 + 2744*a*d^3, z, k)*a^3*b*c*x))/(6561*a^6))*root(14348907*a^11*b^2*z^3 + 408240*a^4*b*c*d*z - 64000*b*c^3 + 2744*a*d^3, z, k), k, 1, 3)","B"
361,1,871,291,5.401981,"\text{Not used}","int((c + d*x + e*x^2)/(x*(a + b*x^3)^4),x)","\frac{\frac{11\,c}{18\,a}+\frac{67\,e\,x^2}{162\,a}+\frac{41\,d\,x}{81\,a}+\frac{b^2\,c\,x^6}{3\,a^3}+\frac{20\,b^2\,d\,x^7}{81\,a^3}+\frac{14\,b^2\,e\,x^8}{81\,a^3}+\frac{5\,b\,c\,x^3}{6\,a^2}+\frac{52\,b\,d\,x^4}{81\,a^2}+\frac{77\,b\,e\,x^5}{162\,a^2}}{a^3+3\,a^2\,b\,x^3+3\,a\,b^2\,x^6+b^3\,x^9}+\left(\sum _{k=1}^3\ln\left(-\frac{b\,\left(-64800\,b\,c\,d^2+45927\,b\,c^2\,e+1372\,a\,e^3\,x-32000\,b\,d^3\,x+{\mathrm{root}\left(14348907\,a^{12}\,b^2\,z^3+14348907\,a^8\,b^2\,c\,z^2+408240\,a^5\,b\,d\,e\,z+4782969\,a^4\,b^2\,c^2\,z+136080\,a\,b\,c\,d\,e-64000\,a\,b\,d^3+2744\,a^2\,e^3+531441\,b^2\,c^3,z,k\right)}^3\,a^{11}\,b^2\,x\,9565938+\mathrm{root}\left(14348907\,a^{12}\,b^2\,z^3+14348907\,a^8\,b^2\,c\,z^2+408240\,a^5\,b\,d\,e\,z+4782969\,a^4\,b^2\,c^2\,z+136080\,a\,b\,c\,d\,e-64000\,a\,b\,d^3+2744\,a^2\,e^3+531441\,b^2\,c^3,z,k\right)\,a^4\,b\,d^2\,64800-{\mathrm{root}\left(14348907\,a^{12}\,b^2\,z^3+14348907\,a^8\,b^2\,c\,z^2+408240\,a^5\,b\,d\,e\,z+4782969\,a^4\,b^2\,c^2\,z+136080\,a\,b\,c\,d\,e-64000\,a\,b\,d^3+2744\,a^2\,e^3+531441\,b^2\,c^3,z,k\right)}^2\,a^8\,b\,e\,137781+45360\,b\,c\,d\,e\,x+\mathrm{root}\left(14348907\,a^{12}\,b^2\,z^3+14348907\,a^8\,b^2\,c\,z^2+408240\,a^5\,b\,d\,e\,z+4782969\,a^4\,b^2\,c^2\,z+136080\,a\,b\,c\,d\,e-64000\,a\,b\,d^3+2744\,a^2\,e^3+531441\,b^2\,c^3,z,k\right)\,a^3\,b^2\,c^2\,x\,1062882+{\mathrm{root}\left(14348907\,a^{12}\,b^2\,z^3+14348907\,a^8\,b^2\,c\,z^2+408240\,a^5\,b\,d\,e\,z+4782969\,a^4\,b^2\,c^2\,z+136080\,a\,b\,c\,d\,e-64000\,a\,b\,d^3+2744\,a^2\,e^3+531441\,b^2\,c^3,z,k\right)}^2\,a^7\,b^2\,c\,x\,6377292+\mathrm{root}\left(14348907\,a^{12}\,b^2\,z^3+14348907\,a^8\,b^2\,c\,z^2+408240\,a^5\,b\,d\,e\,z+4782969\,a^4\,b^2\,c^2\,z+136080\,a\,b\,c\,d\,e-64000\,a\,b\,d^3+2744\,a^2\,e^3+531441\,b^2\,c^3,z,k\right)\,a^4\,b\,c\,e\,91854+\mathrm{root}\left(14348907\,a^{12}\,b^2\,z^3+14348907\,a^8\,b^2\,c\,z^2+408240\,a^5\,b\,d\,e\,z+4782969\,a^4\,b^2\,c^2\,z+136080\,a\,b\,c\,d\,e-64000\,a\,b\,d^3+2744\,a^2\,e^3+531441\,b^2\,c^3,z,k\right)\,a^4\,b\,d\,e\,x\,226800\right)\,2}{a^9\,531441}\right)\,\mathrm{root}\left(14348907\,a^{12}\,b^2\,z^3+14348907\,a^8\,b^2\,c\,z^2+408240\,a^5\,b\,d\,e\,z+4782969\,a^4\,b^2\,c^2\,z+136080\,a\,b\,c\,d\,e-64000\,a\,b\,d^3+2744\,a^2\,e^3+531441\,b^2\,c^3,z,k\right)\right)+\frac{c\,\ln\left(x\right)}{a^4}","Not used",1,"((11*c)/(18*a) + (67*e*x^2)/(162*a) + (41*d*x)/(81*a) + (b^2*c*x^6)/(3*a^3) + (20*b^2*d*x^7)/(81*a^3) + (14*b^2*e*x^8)/(81*a^3) + (5*b*c*x^3)/(6*a^2) + (52*b*d*x^4)/(81*a^2) + (77*b*e*x^5)/(162*a^2))/(a^3 + b^3*x^9 + 3*a^2*b*x^3 + 3*a*b^2*x^6) + symsum(log(-(2*b*(45927*b*c^2*e - 64800*b*c*d^2 + 1372*a*e^3*x - 32000*b*d^3*x + 9565938*root(14348907*a^12*b^2*z^3 + 14348907*a^8*b^2*c*z^2 + 408240*a^5*b*d*e*z + 4782969*a^4*b^2*c^2*z + 136080*a*b*c*d*e - 64000*a*b*d^3 + 2744*a^2*e^3 + 531441*b^2*c^3, z, k)^3*a^11*b^2*x + 64800*root(14348907*a^12*b^2*z^3 + 14348907*a^8*b^2*c*z^2 + 408240*a^5*b*d*e*z + 4782969*a^4*b^2*c^2*z + 136080*a*b*c*d*e - 64000*a*b*d^3 + 2744*a^2*e^3 + 531441*b^2*c^3, z, k)*a^4*b*d^2 - 137781*root(14348907*a^12*b^2*z^3 + 14348907*a^8*b^2*c*z^2 + 408240*a^5*b*d*e*z + 4782969*a^4*b^2*c^2*z + 136080*a*b*c*d*e - 64000*a*b*d^3 + 2744*a^2*e^3 + 531441*b^2*c^3, z, k)^2*a^8*b*e + 45360*b*c*d*e*x + 1062882*root(14348907*a^12*b^2*z^3 + 14348907*a^8*b^2*c*z^2 + 408240*a^5*b*d*e*z + 4782969*a^4*b^2*c^2*z + 136080*a*b*c*d*e - 64000*a*b*d^3 + 2744*a^2*e^3 + 531441*b^2*c^3, z, k)*a^3*b^2*c^2*x + 6377292*root(14348907*a^12*b^2*z^3 + 14348907*a^8*b^2*c*z^2 + 408240*a^5*b*d*e*z + 4782969*a^4*b^2*c^2*z + 136080*a*b*c*d*e - 64000*a*b*d^3 + 2744*a^2*e^3 + 531441*b^2*c^3, z, k)^2*a^7*b^2*c*x + 91854*root(14348907*a^12*b^2*z^3 + 14348907*a^8*b^2*c*z^2 + 408240*a^5*b*d*e*z + 4782969*a^4*b^2*c^2*z + 136080*a*b*c*d*e - 64000*a*b*d^3 + 2744*a^2*e^3 + 531441*b^2*c^3, z, k)*a^4*b*c*e + 226800*root(14348907*a^12*b^2*z^3 + 14348907*a^8*b^2*c*z^2 + 408240*a^5*b*d*e*z + 4782969*a^4*b^2*c^2*z + 136080*a*b*c*d*e - 64000*a*b*d^3 + 2744*a^2*e^3 + 531441*b^2*c^3, z, k)*a^4*b*d*e*x))/(531441*a^9))*root(14348907*a^12*b^2*z^3 + 14348907*a^8*b^2*c*z^2 + 408240*a^5*b*d*e*z + 4782969*a^4*b^2*c^2*z + 136080*a*b*c*d*e - 64000*a*b*d^3 + 2744*a^2*e^3 + 531441*b^2*c^3, z, k), k, 1, 3) + (c*log(x))/a^4","B"
362,1,840,301,5.434365,"\text{Not used}","int((c + d*x + e*x^2)/(x^2*(a + b*x^3)^4),x)","\frac{\frac{41\,e\,x^2}{81\,a}-\frac{c}{a}+\frac{11\,d\,x}{18\,a}-\frac{385\,b^2\,c\,x^6}{81\,a^3}-\frac{140\,b^3\,c\,x^9}{81\,a^4}+\frac{b^2\,d\,x^7}{3\,a^3}+\frac{20\,b^2\,e\,x^8}{81\,a^3}-\frac{335\,b\,c\,x^3}{81\,a^2}+\frac{5\,b\,d\,x^4}{6\,a^2}+\frac{52\,b\,e\,x^5}{81\,a^2}}{a^3\,x+3\,a^2\,b\,x^4+3\,a\,b^2\,x^7+b^3\,x^{10}}+\left(\sum _{k=1}^3\ln\left(\frac{b^2\,\left(-\mathrm{root}\left(14348907\,a^{13}\,b\,z^3+14348907\,a^9\,b\,d\,z^2-4082400\,a^5\,b\,c\,e\,z+4782969\,a^5\,b\,d^2\,z-1360800\,a\,b\,c\,d\,e+531441\,a\,b\,d^3-64000\,a^2\,e^3-2744000\,b^2\,c^3,z,k\right)\,a^6\,e^2\,32400+32400\,a^2\,d\,e^2+686000\,b^2\,c^3\,x+16000\,a^2\,e^3\,x+229635\,a\,b\,c\,d^2-{\mathrm{root}\left(14348907\,a^{13}\,b\,z^3+14348907\,a^9\,b\,d\,z^2-4082400\,a^5\,b\,c\,e\,z+4782969\,a^5\,b\,d^2\,z-1360800\,a\,b\,c\,d\,e+531441\,a\,b\,d^3-64000\,a^2\,e^3-2744000\,b^2\,c^3,z,k\right)}^2\,a^9\,b\,c\,688905-{\mathrm{root}\left(14348907\,a^{13}\,b\,z^3+14348907\,a^9\,b\,d\,z^2-4082400\,a^5\,b\,c\,e\,z+4782969\,a^5\,b\,d^2\,z-1360800\,a\,b\,c\,d\,e+531441\,a\,b\,d^3-64000\,a^2\,e^3-2744000\,b^2\,c^3,z,k\right)}^3\,a^{13}\,b\,x\,4782969-\mathrm{root}\left(14348907\,a^{13}\,b\,z^3+14348907\,a^9\,b\,d\,z^2-4082400\,a^5\,b\,c\,e\,z+4782969\,a^5\,b\,d^2\,z-1360800\,a\,b\,c\,d\,e+531441\,a\,b\,d^3-64000\,a^2\,e^3-2744000\,b^2\,c^3,z,k\right)\,a^5\,b\,d^2\,x\,531441-{\mathrm{root}\left(14348907\,a^{13}\,b\,z^3+14348907\,a^9\,b\,d\,z^2-4082400\,a^5\,b\,c\,e\,z+4782969\,a^5\,b\,d^2\,z-1360800\,a\,b\,c\,d\,e+531441\,a\,b\,d^3-64000\,a^2\,e^3-2744000\,b^2\,c^3,z,k\right)}^2\,a^9\,b\,d\,x\,3188646+\mathrm{root}\left(14348907\,a^{13}\,b\,z^3+14348907\,a^9\,b\,d\,z^2-4082400\,a^5\,b\,c\,e\,z+4782969\,a^5\,b\,d^2\,z-1360800\,a\,b\,c\,d\,e+531441\,a\,b\,d^3-64000\,a^2\,e^3-2744000\,b^2\,c^3,z,k\right)\,a^5\,b\,c\,d\,459270+\mathrm{root}\left(14348907\,a^{13}\,b\,z^3+14348907\,a^9\,b\,d\,z^2-4082400\,a^5\,b\,c\,e\,z+4782969\,a^5\,b\,d^2\,z-1360800\,a\,b\,c\,d\,e+531441\,a\,b\,d^3-64000\,a^2\,e^3-2744000\,b^2\,c^3,z,k\right)\,a^5\,b\,c\,e\,x\,1134000+226800\,a\,b\,c\,d\,e\,x\right)\,4}{a^{11}\,531441}\right)\,\mathrm{root}\left(14348907\,a^{13}\,b\,z^3+14348907\,a^9\,b\,d\,z^2-4082400\,a^5\,b\,c\,e\,z+4782969\,a^5\,b\,d^2\,z-1360800\,a\,b\,c\,d\,e+531441\,a\,b\,d^3-64000\,a^2\,e^3-2744000\,b^2\,c^3,z,k\right)\right)+\frac{d\,\ln\left(x\right)}{a^4}","Not used",1,"((41*e*x^2)/(81*a) - c/a + (11*d*x)/(18*a) - (385*b^2*c*x^6)/(81*a^3) - (140*b^3*c*x^9)/(81*a^4) + (b^2*d*x^7)/(3*a^3) + (20*b^2*e*x^8)/(81*a^3) - (335*b*c*x^3)/(81*a^2) + (5*b*d*x^4)/(6*a^2) + (52*b*e*x^5)/(81*a^2))/(a^3*x + b^3*x^10 + 3*a^2*b*x^4 + 3*a*b^2*x^7) + symsum(log((4*b^2*(32400*a^2*d*e^2 - 32400*root(14348907*a^13*b*z^3 + 14348907*a^9*b*d*z^2 - 4082400*a^5*b*c*e*z + 4782969*a^5*b*d^2*z - 1360800*a*b*c*d*e + 531441*a*b*d^3 - 64000*a^2*e^3 - 2744000*b^2*c^3, z, k)*a^6*e^2 + 686000*b^2*c^3*x + 16000*a^2*e^3*x + 229635*a*b*c*d^2 - 688905*root(14348907*a^13*b*z^3 + 14348907*a^9*b*d*z^2 - 4082400*a^5*b*c*e*z + 4782969*a^5*b*d^2*z - 1360800*a*b*c*d*e + 531441*a*b*d^3 - 64000*a^2*e^3 - 2744000*b^2*c^3, z, k)^2*a^9*b*c - 4782969*root(14348907*a^13*b*z^3 + 14348907*a^9*b*d*z^2 - 4082400*a^5*b*c*e*z + 4782969*a^5*b*d^2*z - 1360800*a*b*c*d*e + 531441*a*b*d^3 - 64000*a^2*e^3 - 2744000*b^2*c^3, z, k)^3*a^13*b*x - 531441*root(14348907*a^13*b*z^3 + 14348907*a^9*b*d*z^2 - 4082400*a^5*b*c*e*z + 4782969*a^5*b*d^2*z - 1360800*a*b*c*d*e + 531441*a*b*d^3 - 64000*a^2*e^3 - 2744000*b^2*c^3, z, k)*a^5*b*d^2*x - 3188646*root(14348907*a^13*b*z^3 + 14348907*a^9*b*d*z^2 - 4082400*a^5*b*c*e*z + 4782969*a^5*b*d^2*z - 1360800*a*b*c*d*e + 531441*a*b*d^3 - 64000*a^2*e^3 - 2744000*b^2*c^3, z, k)^2*a^9*b*d*x + 459270*root(14348907*a^13*b*z^3 + 14348907*a^9*b*d*z^2 - 4082400*a^5*b*c*e*z + 4782969*a^5*b*d^2*z - 1360800*a*b*c*d*e + 531441*a*b*d^3 - 64000*a^2*e^3 - 2744000*b^2*c^3, z, k)*a^5*b*c*d + 1134000*root(14348907*a^13*b*z^3 + 14348907*a^9*b*d*z^2 - 4082400*a^5*b*c*e*z + 4782969*a^5*b*d^2*z - 1360800*a*b*c*d*e + 531441*a*b*d^3 - 64000*a^2*e^3 - 2744000*b^2*c^3, z, k)*a^5*b*c*e*x + 226800*a*b*c*d*e*x))/(531441*a^11))*root(14348907*a^13*b*z^3 + 14348907*a^9*b*d*z^2 - 4082400*a^5*b*c*e*z + 4782969*a^5*b*d^2*z - 1360800*a*b*c*d*e + 531441*a*b*d^3 - 64000*a^2*e^3 - 2744000*b^2*c^3, z, k), k, 1, 3) + (d*log(x))/a^4","B"
363,1,825,310,5.375380,"\text{Not used}","int((c + d*x + e*x^2)/(x^3*(a + b*x^3)^4),x)","\left(\sum _{k=1}^3\ln\left(-\frac{b^3\,\left({\mathrm{root}\left(14348907\,a^{14}\,z^3+14348907\,a^{10}\,e\,z^2+22453200\,a^5\,b\,c\,d\,z+4782969\,a^6\,e^2\,z+7484400\,a\,b\,c\,d\,e-2744000\,a\,b\,d^3+531441\,a^2\,e^3+10648000\,b^2\,c^3,z,k\right)}^2\,a^{10}\,d\,688905-229635\,a^2\,d\,e^2+{\mathrm{root}\left(14348907\,a^{14}\,z^3+14348907\,a^{10}\,e\,z^2+22453200\,a^5\,b\,c\,d\,z+4782969\,a^6\,e^2\,z+7484400\,a\,b\,c\,d\,e-2744000\,a\,b\,d^3+531441\,a^2\,e^3+10648000\,b^2\,c^3,z,k\right)}^3\,a^{14}\,x\,4782969+2662000\,b^2\,c^3\,x-\mathrm{root}\left(14348907\,a^{14}\,z^3+14348907\,a^{10}\,e\,z^2+22453200\,a^5\,b\,c\,d\,z+4782969\,a^6\,e^2\,z+7484400\,a\,b\,c\,d\,e-2744000\,a\,b\,d^3+531441\,a^2\,e^3+10648000\,b^2\,c^3,z,k\right)\,a^6\,d\,e\,459270-980100\,a\,b\,c^2\,e-686000\,a\,b\,d^3\,x+\mathrm{root}\left(14348907\,a^{14}\,z^3+14348907\,a^{10}\,e\,z^2+22453200\,a^5\,b\,c\,d\,z+4782969\,a^6\,e^2\,z+7484400\,a\,b\,c\,d\,e-2744000\,a\,b\,d^3+531441\,a^2\,e^3+10648000\,b^2\,c^3,z,k\right)\,a^5\,b\,c^2\,980100+\mathrm{root}\left(14348907\,a^{14}\,z^3+14348907\,a^{10}\,e\,z^2+22453200\,a^5\,b\,c\,d\,z+4782969\,a^6\,e^2\,z+7484400\,a\,b\,c\,d\,e-2744000\,a\,b\,d^3+531441\,a^2\,e^3+10648000\,b^2\,c^3,z,k\right)\,a^6\,e^2\,x\,531441+{\mathrm{root}\left(14348907\,a^{14}\,z^3+14348907\,a^{10}\,e\,z^2+22453200\,a^5\,b\,c\,d\,z+4782969\,a^6\,e^2\,z+7484400\,a\,b\,c\,d\,e-2744000\,a\,b\,d^3+531441\,a^2\,e^3+10648000\,b^2\,c^3,z,k\right)}^2\,a^{10}\,e\,x\,3188646+\mathrm{root}\left(14348907\,a^{14}\,z^3+14348907\,a^{10}\,e\,z^2+22453200\,a^5\,b\,c\,d\,z+4782969\,a^6\,e^2\,z+7484400\,a\,b\,c\,d\,e-2744000\,a\,b\,d^3+531441\,a^2\,e^3+10648000\,b^2\,c^3,z,k\right)\,a^5\,b\,c\,d\,x\,6237000+1247400\,a\,b\,c\,d\,e\,x\right)\,4}{a^{12}\,531441}\right)\,\mathrm{root}\left(14348907\,a^{14}\,z^3+14348907\,a^{10}\,e\,z^2+22453200\,a^5\,b\,c\,d\,z+4782969\,a^6\,e^2\,z+7484400\,a\,b\,c\,d\,e-2744000\,a\,b\,d^3+531441\,a^2\,e^3+10648000\,b^2\,c^3,z,k\right)\right)-\frac{\frac{c}{2\,a}-\frac{11\,e\,x^2}{18\,a}+\frac{d\,x}{a}+\frac{286\,b^2\,c\,x^6}{81\,a^3}+\frac{110\,b^3\,c\,x^9}{81\,a^4}+\frac{385\,b^2\,d\,x^7}{81\,a^3}+\frac{140\,b^3\,d\,x^{10}}{81\,a^4}-\frac{b^2\,e\,x^8}{3\,a^3}+\frac{451\,b\,c\,x^3}{162\,a^2}+\frac{335\,b\,d\,x^4}{81\,a^2}-\frac{5\,b\,e\,x^5}{6\,a^2}}{a^3\,x^2+3\,a^2\,b\,x^5+3\,a\,b^2\,x^8+b^3\,x^{11}}+\frac{e\,\ln\left(x\right)}{a^4}","Not used",1,"symsum(log(-(4*b^3*(688905*root(14348907*a^14*z^3 + 14348907*a^10*e*z^2 + 22453200*a^5*b*c*d*z + 4782969*a^6*e^2*z + 7484400*a*b*c*d*e - 2744000*a*b*d^3 + 531441*a^2*e^3 + 10648000*b^2*c^3, z, k)^2*a^10*d - 229635*a^2*d*e^2 + 4782969*root(14348907*a^14*z^3 + 14348907*a^10*e*z^2 + 22453200*a^5*b*c*d*z + 4782969*a^6*e^2*z + 7484400*a*b*c*d*e - 2744000*a*b*d^3 + 531441*a^2*e^3 + 10648000*b^2*c^3, z, k)^3*a^14*x + 2662000*b^2*c^3*x - 459270*root(14348907*a^14*z^3 + 14348907*a^10*e*z^2 + 22453200*a^5*b*c*d*z + 4782969*a^6*e^2*z + 7484400*a*b*c*d*e - 2744000*a*b*d^3 + 531441*a^2*e^3 + 10648000*b^2*c^3, z, k)*a^6*d*e - 980100*a*b*c^2*e - 686000*a*b*d^3*x + 980100*root(14348907*a^14*z^3 + 14348907*a^10*e*z^2 + 22453200*a^5*b*c*d*z + 4782969*a^6*e^2*z + 7484400*a*b*c*d*e - 2744000*a*b*d^3 + 531441*a^2*e^3 + 10648000*b^2*c^3, z, k)*a^5*b*c^2 + 531441*root(14348907*a^14*z^3 + 14348907*a^10*e*z^2 + 22453200*a^5*b*c*d*z + 4782969*a^6*e^2*z + 7484400*a*b*c*d*e - 2744000*a*b*d^3 + 531441*a^2*e^3 + 10648000*b^2*c^3, z, k)*a^6*e^2*x + 3188646*root(14348907*a^14*z^3 + 14348907*a^10*e*z^2 + 22453200*a^5*b*c*d*z + 4782969*a^6*e^2*z + 7484400*a*b*c*d*e - 2744000*a*b*d^3 + 531441*a^2*e^3 + 10648000*b^2*c^3, z, k)^2*a^10*e*x + 6237000*root(14348907*a^14*z^3 + 14348907*a^10*e*z^2 + 22453200*a^5*b*c*d*z + 4782969*a^6*e^2*z + 7484400*a*b*c*d*e - 2744000*a*b*d^3 + 531441*a^2*e^3 + 10648000*b^2*c^3, z, k)*a^5*b*c*d*x + 1247400*a*b*c*d*e*x))/(531441*a^12))*root(14348907*a^14*z^3 + 14348907*a^10*e*z^2 + 22453200*a^5*b*c*d*z + 4782969*a^6*e^2*z + 7484400*a*b*c*d*e - 2744000*a*b*d^3 + 531441*a^2*e^3 + 10648000*b^2*c^3, z, k), k, 1, 3) - (c/(2*a) - (11*e*x^2)/(18*a) + (d*x)/a + (286*b^2*c*x^6)/(81*a^3) + (110*b^3*c*x^9)/(81*a^4) + (385*b^2*d*x^7)/(81*a^3) + (140*b^3*d*x^10)/(81*a^4) - (b^2*e*x^8)/(3*a^3) + (451*b*c*x^3)/(162*a^2) + (335*b*d*x^4)/(81*a^2) - (5*b*e*x^5)/(6*a^2))/(a^3*x^2 + b^3*x^11 + 3*a^2*b*x^5 + 3*a*b^2*x^8) + (e*log(x))/a^4","B"
364,1,918,340,0.524608,"\text{Not used}","int((c + d*x + e*x^2)/(x^4*(a + b*x^3)^4),x)","\left(\sum _{k=1}^3\ln\left(-\frac{b^3\,\left({\mathrm{root}\left(14348907\,a^{15}\,z^3-57395628\,a^{10}\,b\,c\,z^2+22453200\,a^6\,b\,d\,e\,z+76527504\,a^5\,b^2\,c^2\,z-29937600\,a\,b^2\,c\,d\,e-2744000\,a^2\,b\,e^3+10648000\,a\,b^2\,d^3-34012224\,b^3\,c^3,z,k\right)}^2\,a^{10}\,e\,688905+3920400\,b^2\,c\,d^2-3674160\,b^2\,c^2\,e+{\mathrm{root}\left(14348907\,a^{15}\,z^3-57395628\,a^{10}\,b\,c\,z^2+22453200\,a^6\,b\,d\,e\,z+76527504\,a^5\,b^2\,c^2\,z-29937600\,a\,b^2\,c\,d\,e-2744000\,a^2\,b\,e^3+10648000\,a\,b^2\,d^3-34012224\,b^3\,c^3,z,k\right)}^3\,a^{14}\,x\,4782969+2662000\,b^2\,d^3\,x-686000\,a\,b\,e^3\,x+\mathrm{root}\left(14348907\,a^{15}\,z^3-57395628\,a^{10}\,b\,c\,z^2+22453200\,a^6\,b\,d\,e\,z+76527504\,a^5\,b^2\,c^2\,z-29937600\,a\,b^2\,c\,d\,e-2744000\,a^2\,b\,e^3+10648000\,a\,b^2\,d^3-34012224\,b^3\,c^3,z,k\right)\,a^5\,b\,d^2\,980100-{\mathrm{root}\left(14348907\,a^{15}\,z^3-57395628\,a^{10}\,b\,c\,z^2+22453200\,a^6\,b\,d\,e\,z+76527504\,a^5\,b^2\,c^2\,z-29937600\,a\,b^2\,c\,d\,e-2744000\,a^2\,b\,e^3+10648000\,a\,b^2\,d^3-34012224\,b^3\,c^3,z,k\right)}^2\,a^9\,b\,c\,x\,12754584+\mathrm{root}\left(14348907\,a^{15}\,z^3-57395628\,a^{10}\,b\,c\,z^2+22453200\,a^6\,b\,d\,e\,z+76527504\,a^5\,b^2\,c^2\,z-29937600\,a\,b^2\,c\,d\,e-2744000\,a^2\,b\,e^3+10648000\,a\,b^2\,d^3-34012224\,b^3\,c^3,z,k\right)\,a^4\,b^2\,c^2\,x\,8503056+\mathrm{root}\left(14348907\,a^{15}\,z^3-57395628\,a^{10}\,b\,c\,z^2+22453200\,a^6\,b\,d\,e\,z+76527504\,a^5\,b^2\,c^2\,z-29937600\,a\,b^2\,c\,d\,e-2744000\,a^2\,b\,e^3+10648000\,a\,b^2\,d^3-34012224\,b^3\,c^3,z,k\right)\,a^5\,b\,c\,e\,1837080-4989600\,b^2\,c\,d\,e\,x+\mathrm{root}\left(14348907\,a^{15}\,z^3-57395628\,a^{10}\,b\,c\,z^2+22453200\,a^6\,b\,d\,e\,z+76527504\,a^5\,b^2\,c^2\,z-29937600\,a\,b^2\,c\,d\,e-2744000\,a^2\,b\,e^3+10648000\,a\,b^2\,d^3-34012224\,b^3\,c^3,z,k\right)\,a^5\,b\,d\,e\,x\,6237000\right)\,4}{a^{12}\,531441}\right)\,\mathrm{root}\left(14348907\,a^{15}\,z^3-57395628\,a^{10}\,b\,c\,z^2+22453200\,a^6\,b\,d\,e\,z+76527504\,a^5\,b^2\,c^2\,z-29937600\,a\,b^2\,c\,d\,e-2744000\,a^2\,b\,e^3+10648000\,a\,b^2\,d^3-34012224\,b^3\,c^3,z,k\right)\right)-\frac{\frac{c}{3\,a}+\frac{e\,x^2}{a}+\frac{d\,x}{2\,a}+\frac{10\,b^2\,c\,x^6}{3\,a^3}+\frac{4\,b^3\,c\,x^9}{3\,a^4}+\frac{286\,b^2\,d\,x^7}{81\,a^3}+\frac{110\,b^3\,d\,x^{10}}{81\,a^4}+\frac{385\,b^2\,e\,x^8}{81\,a^3}+\frac{140\,b^3\,e\,x^{11}}{81\,a^4}+\frac{22\,b\,c\,x^3}{9\,a^2}+\frac{451\,b\,d\,x^4}{162\,a^2}+\frac{335\,b\,e\,x^5}{81\,a^2}}{a^3\,x^3+3\,a^2\,b\,x^6+3\,a\,b^2\,x^9+b^3\,x^{12}}-\frac{4\,b\,c\,\ln\left(x\right)}{a^5}","Not used",1,"symsum(log(-(4*b^3*(688905*root(14348907*a^15*z^3 - 57395628*a^10*b*c*z^2 + 22453200*a^6*b*d*e*z + 76527504*a^5*b^2*c^2*z - 29937600*a*b^2*c*d*e - 2744000*a^2*b*e^3 + 10648000*a*b^2*d^3 - 34012224*b^3*c^3, z, k)^2*a^10*e + 3920400*b^2*c*d^2 - 3674160*b^2*c^2*e + 4782969*root(14348907*a^15*z^3 - 57395628*a^10*b*c*z^2 + 22453200*a^6*b*d*e*z + 76527504*a^5*b^2*c^2*z - 29937600*a*b^2*c*d*e - 2744000*a^2*b*e^3 + 10648000*a*b^2*d^3 - 34012224*b^3*c^3, z, k)^3*a^14*x + 2662000*b^2*d^3*x - 686000*a*b*e^3*x + 980100*root(14348907*a^15*z^3 - 57395628*a^10*b*c*z^2 + 22453200*a^6*b*d*e*z + 76527504*a^5*b^2*c^2*z - 29937600*a*b^2*c*d*e - 2744000*a^2*b*e^3 + 10648000*a*b^2*d^3 - 34012224*b^3*c^3, z, k)*a^5*b*d^2 - 12754584*root(14348907*a^15*z^3 - 57395628*a^10*b*c*z^2 + 22453200*a^6*b*d*e*z + 76527504*a^5*b^2*c^2*z - 29937600*a*b^2*c*d*e - 2744000*a^2*b*e^3 + 10648000*a*b^2*d^3 - 34012224*b^3*c^3, z, k)^2*a^9*b*c*x + 8503056*root(14348907*a^15*z^3 - 57395628*a^10*b*c*z^2 + 22453200*a^6*b*d*e*z + 76527504*a^5*b^2*c^2*z - 29937600*a*b^2*c*d*e - 2744000*a^2*b*e^3 + 10648000*a*b^2*d^3 - 34012224*b^3*c^3, z, k)*a^4*b^2*c^2*x + 1837080*root(14348907*a^15*z^3 - 57395628*a^10*b*c*z^2 + 22453200*a^6*b*d*e*z + 76527504*a^5*b^2*c^2*z - 29937600*a*b^2*c*d*e - 2744000*a^2*b*e^3 + 10648000*a*b^2*d^3 - 34012224*b^3*c^3, z, k)*a^5*b*c*e - 4989600*b^2*c*d*e*x + 6237000*root(14348907*a^15*z^3 - 57395628*a^10*b*c*z^2 + 22453200*a^6*b*d*e*z + 76527504*a^5*b^2*c^2*z - 29937600*a*b^2*c*d*e - 2744000*a^2*b*e^3 + 10648000*a*b^2*d^3 - 34012224*b^3*c^3, z, k)*a^5*b*d*e*x))/(531441*a^12))*root(14348907*a^15*z^3 - 57395628*a^10*b*c*z^2 + 22453200*a^6*b*d*e*z + 76527504*a^5*b^2*c^2*z - 29937600*a*b^2*c*d*e - 2744000*a^2*b*e^3 + 10648000*a*b^2*d^3 - 34012224*b^3*c^3, z, k), k, 1, 3) - (c/(3*a) + (e*x^2)/a + (d*x)/(2*a) + (10*b^2*c*x^6)/(3*a^3) + (4*b^3*c*x^9)/(3*a^4) + (286*b^2*d*x^7)/(81*a^3) + (110*b^3*d*x^10)/(81*a^4) + (385*b^2*e*x^8)/(81*a^3) + (140*b^3*e*x^11)/(81*a^4) + (22*b*c*x^3)/(9*a^2) + (451*b*d*x^4)/(162*a^2) + (335*b*e*x^5)/(81*a^2))/(a^3*x^3 + b^3*x^12 + 3*a^2*b*x^6 + 3*a*b^2*x^9) - (4*b*c*log(x))/a^5","B"
365,1,26,29,4.969896,"\text{Not used}","int((2*a*x - x^2)/(a^3 + x^3),x)","-\ln\left(a+x\right)-\frac{2\,\sqrt{3}\,\mathrm{atan}\left(-\frac{\sqrt{3}\,a}{a-2\,x}\right)}{3}","Not used",1,"- log(a + x) - (2*3^(1/2)*atan(-(3^(1/2)*a)/(a - 2*x)))/3","B"
366,1,26,29,0.027262,"\text{Not used}","int((x*(2*a - x))/(a^3 + x^3),x)","-\ln\left(a+x\right)-\frac{2\,\sqrt{3}\,\mathrm{atan}\left(-\frac{\sqrt{3}\,a}{a-2\,x}\right)}{3}","Not used",1,"- log(a + x) - (2*3^(1/2)*atan(-(3^(1/2)*a)/(a - 2*x)))/3","B"
367,1,27,31,4.946104,"\text{Not used}","int((2*a*x + x^2)/(a^3 - x^3),x)","\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}\,a}{a+2\,x}\right)}{3}-\ln\left(x-a\right)","Not used",1,"(2*3^(1/2)*atan((3^(1/2)*a)/(a + 2*x)))/3 - log(x - a)","B"
368,1,27,31,0.030420,"\text{Not used}","int((x*(2*a + x))/(a^3 - x^3),x)","\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}\,a}{a+2\,x}\right)}{3}-\ln\left(x-a\right)","Not used",1,"(2*3^(1/2)*atan((3^(1/2)*a)/(a + 2*x)))/3 - log(x - a)","B"
369,1,154,50,5.222983,"\text{Not used}","int((x*(C*x - 2*C*(a/b)^(1/3)))/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(\frac{C^2\,a+{\mathrm{root}\left(27\,a\,b^3\,z^3-27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z-9\,C^3\,a,z,k\right)}^2\,a\,b^2\,9-C\,\mathrm{root}\left(27\,a\,b^3\,z^3-27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z-9\,C^3\,a,z,k\right)\,a\,b\,6+4\,C^2\,b\,x\,{\left(\frac{a}{b}\right)}^{2/3}}{b^3}\right)\,\mathrm{root}\left(27\,a\,b^3\,z^3-27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z-9\,C^3\,a,z,k\right)","Not used",1,"symsum(log((C^2*a + 9*root(27*a*b^3*z^3 - 27*C*a*b^2*z^2 + 9*C^2*a*b*z - 9*C^3*a, z, k)^2*a*b^2 - 6*C*root(27*a*b^3*z^3 - 27*C*a*b^2*z^2 + 9*C^2*a*b*z - 9*C^3*a, z, k)*a*b + 4*C^2*b*x*(a/b)^(2/3))/b^3)*root(27*a*b^3*z^3 - 27*C*a*b^2*z^2 + 9*C^2*a*b*z - 9*C^3*a, z, k), k, 1, 3)","B"
370,1,156,53,5.250011,"\text{Not used}","int((x*(C*x - 2*C*(-a/b)^(1/3)))/(a - b*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{C^2\,a+{\mathrm{root}\left(27\,a\,b^3\,z^3+27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z+9\,C^3\,a,z,k\right)}^2\,a\,b^2\,9+C\,\mathrm{root}\left(27\,a\,b^3\,z^3+27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z+9\,C^3\,a,z,k\right)\,a\,b\,6-4\,C^2\,b\,x\,{\left(-\frac{a}{b}\right)}^{2/3}}{b^3}\right)\,\mathrm{root}\left(27\,a\,b^3\,z^3+27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z+9\,C^3\,a,z,k\right)","Not used",1,"symsum(log(-(C^2*a + 9*root(27*a*b^3*z^3 + 27*C*a*b^2*z^2 + 9*C^2*a*b*z + 9*C^3*a, z, k)^2*a*b^2 + 6*C*root(27*a*b^3*z^3 + 27*C*a*b^2*z^2 + 9*C^2*a*b*z + 9*C^3*a, z, k)*a*b - 4*C^2*b*x*(-a/b)^(2/3))/b^3)*root(27*a*b^3*z^3 + 27*C*a*b^2*z^2 + 9*C^2*a*b*z + 9*C^3*a, z, k), k, 1, 3)","B"
371,1,155,54,5.223935,"\text{Not used}","int((x*(C*x + 2*C*(-a/b)^(1/3)))/(a + b*x^3),x)","\sum _{k=1}^3\ln\left(\frac{C^2\,a+{\mathrm{root}\left(27\,a\,b^3\,z^3-27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z-9\,C^3\,a,z,k\right)}^2\,a\,b^2\,9-C\,\mathrm{root}\left(27\,a\,b^3\,z^3-27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z-9\,C^3\,a,z,k\right)\,a\,b\,6+4\,C^2\,b\,x\,{\left(-\frac{a}{b}\right)}^{2/3}}{b^3}\right)\,\mathrm{root}\left(27\,a\,b^3\,z^3-27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z-9\,C^3\,a,z,k\right)","Not used",1,"symsum(log((C^2*a + 9*root(27*a*b^3*z^3 - 27*C*a*b^2*z^2 + 9*C^2*a*b*z - 9*C^3*a, z, k)^2*a*b^2 - 6*C*root(27*a*b^3*z^3 - 27*C*a*b^2*z^2 + 9*C^2*a*b*z - 9*C^3*a, z, k)*a*b + 4*C^2*b*x*(-a/b)^(2/3))/b^3)*root(27*a*b^3*z^3 - 27*C*a*b^2*z^2 + 9*C^2*a*b*z - 9*C^3*a, z, k), k, 1, 3)","B"
372,1,155,53,5.234036,"\text{Not used}","int((x*(C*x + 2*C*(a/b)^(1/3)))/(a - b*x^3),x)","\sum _{k=1}^3\ln\left(-\frac{C^2\,a+{\mathrm{root}\left(27\,a\,b^3\,z^3+27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z+9\,C^3\,a,z,k\right)}^2\,a\,b^2\,9+C\,\mathrm{root}\left(27\,a\,b^3\,z^3+27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z+9\,C^3\,a,z,k\right)\,a\,b\,6-4\,C^2\,b\,x\,{\left(\frac{a}{b}\right)}^{2/3}}{b^3}\right)\,\mathrm{root}\left(27\,a\,b^3\,z^3+27\,C\,a\,b^2\,z^2+9\,C^2\,a\,b\,z+9\,C^3\,a,z,k\right)","Not used",1,"symsum(log(-(C^2*a + 9*root(27*a*b^3*z^3 + 27*C*a*b^2*z^2 + 9*C^2*a*b*z + 9*C^3*a, z, k)^2*a*b^2 + 6*C*root(27*a*b^3*z^3 + 27*C*a*b^2*z^2 + 9*C^2*a*b*z + 9*C^3*a, z, k)*a*b - 4*C^2*b*x*(a/b)^(2/3))/b^3)*root(27*a*b^3*z^3 + 27*C*a*b^2*z^2 + 9*C^2*a*b*z + 9*C^3*a, z, k), k, 1, 3)","B"
373,1,82,97,0.051426,"\text{Not used}","int(x^4*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","\frac{b\,h\,x^{13}}{13}+\frac{b\,g\,x^{12}}{12}+\frac{b\,f\,x^{11}}{11}+\left(\frac{b\,e}{10}+\frac{a\,h}{10}\right)\,x^{10}+\left(\frac{b\,d}{9}+\frac{a\,g}{9}\right)\,x^9+\left(\frac{b\,c}{8}+\frac{a\,f}{8}\right)\,x^8+\frac{a\,e\,x^7}{7}+\frac{a\,d\,x^6}{6}+\frac{a\,c\,x^5}{5}","Not used",1,"x^8*((b*c)/8 + (a*f)/8) + x^9*((b*d)/9 + (a*g)/9) + x^10*((b*e)/10 + (a*h)/10) + (b*h*x^13)/13 + (a*c*x^5)/5 + (a*d*x^6)/6 + (a*e*x^7)/7 + (b*f*x^11)/11 + (b*g*x^12)/12","B"
374,1,82,97,0.042156,"\text{Not used}","int(x^3*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","\frac{b\,h\,x^{12}}{12}+\frac{b\,g\,x^{11}}{11}+\frac{b\,f\,x^{10}}{10}+\left(\frac{b\,e}{9}+\frac{a\,h}{9}\right)\,x^9+\left(\frac{b\,d}{8}+\frac{a\,g}{8}\right)\,x^8+\left(\frac{b\,c}{7}+\frac{a\,f}{7}\right)\,x^7+\frac{a\,e\,x^6}{6}+\frac{a\,d\,x^5}{5}+\frac{a\,c\,x^4}{4}","Not used",1,"x^7*((b*c)/7 + (a*f)/7) + x^8*((b*d)/8 + (a*g)/8) + x^9*((b*e)/9 + (a*h)/9) + (b*h*x^12)/12 + (a*c*x^4)/4 + (a*d*x^5)/5 + (a*e*x^6)/6 + (b*f*x^10)/10 + (b*g*x^11)/11","B"
375,1,82,97,0.044205,"\text{Not used}","int(x^2*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","\frac{b\,h\,x^{11}}{11}+\frac{b\,g\,x^{10}}{10}+\frac{b\,f\,x^9}{9}+\left(\frac{b\,e}{8}+\frac{a\,h}{8}\right)\,x^8+\left(\frac{b\,d}{7}+\frac{a\,g}{7}\right)\,x^7+\left(\frac{b\,c}{6}+\frac{a\,f}{6}\right)\,x^6+\frac{a\,e\,x^5}{5}+\frac{a\,d\,x^4}{4}+\frac{a\,c\,x^3}{3}","Not used",1,"x^6*((b*c)/6 + (a*f)/6) + x^7*((b*d)/7 + (a*g)/7) + x^8*((b*e)/8 + (a*h)/8) + (b*h*x^11)/11 + (a*c*x^3)/3 + (a*d*x^4)/4 + (a*e*x^5)/5 + (b*f*x^9)/9 + (b*g*x^10)/10","B"
376,1,82,97,0.042925,"\text{Not used}","int(x*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","\frac{b\,h\,x^{10}}{10}+\frac{b\,g\,x^9}{9}+\frac{b\,f\,x^8}{8}+\left(\frac{b\,e}{7}+\frac{a\,h}{7}\right)\,x^7+\left(\frac{b\,d}{6}+\frac{a\,g}{6}\right)\,x^6+\left(\frac{b\,c}{5}+\frac{a\,f}{5}\right)\,x^5+\frac{a\,e\,x^4}{4}+\frac{a\,d\,x^3}{3}+\frac{a\,c\,x^2}{2}","Not used",1,"x^5*((b*c)/5 + (a*f)/5) + x^6*((b*d)/6 + (a*g)/6) + x^7*((b*e)/7 + (a*h)/7) + (b*h*x^10)/10 + (a*c*x^2)/2 + (a*d*x^3)/3 + (a*e*x^4)/4 + (b*f*x^8)/8 + (b*g*x^9)/9","B"
377,1,79,92,0.040768,"\text{Not used}","int((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","\frac{b\,h\,x^9}{9}+\frac{b\,g\,x^8}{8}+\frac{b\,f\,x^7}{7}+\left(\frac{b\,e}{6}+\frac{a\,h}{6}\right)\,x^6+\left(\frac{b\,d}{5}+\frac{a\,g}{5}\right)\,x^5+\left(\frac{b\,c}{4}+\frac{a\,f}{4}\right)\,x^4+\frac{a\,e\,x^3}{3}+\frac{a\,d\,x^2}{2}+a\,c\,x","Not used",1,"x^4*((b*c)/4 + (a*f)/4) + x^5*((b*d)/5 + (a*g)/5) + x^6*((b*e)/6 + (a*h)/6) + (b*h*x^9)/9 + a*c*x + (a*d*x^2)/2 + (a*e*x^3)/3 + (b*f*x^7)/7 + (b*g*x^8)/8","B"
378,1,77,88,0.046787,"\text{Not used}","int(((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x,x)","x^3\,\left(\frac{b\,c}{3}+\frac{a\,f}{3}\right)+x^4\,\left(\frac{b\,d}{4}+\frac{a\,g}{4}\right)+x^5\,\left(\frac{b\,e}{5}+\frac{a\,h}{5}\right)+\frac{b\,h\,x^8}{8}+a\,c\,\ln\left(x\right)+a\,d\,x+\frac{a\,e\,x^2}{2}+\frac{b\,f\,x^6}{6}+\frac{b\,g\,x^7}{7}","Not used",1,"x^3*((b*c)/3 + (a*f)/3) + x^4*((b*d)/4 + (a*g)/4) + x^5*((b*e)/5 + (a*h)/5) + (b*h*x^8)/8 + a*c*log(x) + a*d*x + (a*e*x^2)/2 + (b*f*x^6)/6 + (b*g*x^7)/7","B"
379,1,77,86,0.047760,"\text{Not used}","int(((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^2,x)","x^2\,\left(\frac{b\,c}{2}+\frac{a\,f}{2}\right)+x^3\,\left(\frac{b\,d}{3}+\frac{a\,g}{3}\right)+x^4\,\left(\frac{b\,e}{4}+\frac{a\,h}{4}\right)+\frac{b\,h\,x^7}{7}+a\,d\,\ln\left(x\right)+a\,e\,x-\frac{a\,c}{x}+\frac{b\,f\,x^5}{5}+\frac{b\,g\,x^6}{6}","Not used",1,"x^2*((b*c)/2 + (a*f)/2) + x^3*((b*d)/3 + (a*g)/3) + x^4*((b*e)/4 + (a*h)/4) + (b*h*x^7)/7 + a*d*log(x) + a*e*x - (a*c)/x + (b*f*x^5)/5 + (b*g*x^6)/6","B"
380,1,76,86,0.043464,"\text{Not used}","int(((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^3,x)","x\,\left(b\,c+a\,f\right)-\frac{\frac{a\,c}{2}+a\,d\,x}{x^2}+x^2\,\left(\frac{b\,d}{2}+\frac{a\,g}{2}\right)+x^3\,\left(\frac{b\,e}{3}+\frac{a\,h}{3}\right)+\frac{b\,h\,x^6}{6}+a\,e\,\ln\left(x\right)+\frac{b\,f\,x^4}{4}+\frac{b\,g\,x^5}{5}","Not used",1,"x*(b*c + a*f) - ((a*c)/2 + a*d*x)/x^2 + x^2*((b*d)/2 + (a*g)/2) + x^3*((b*e)/3 + (a*h)/3) + (b*h*x^6)/6 + a*e*log(x) + (b*f*x^4)/4 + (b*g*x^5)/5","B"
381,1,75,86,0.041345,"\text{Not used}","int(((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^4,x)","x\,\left(b\,d+a\,g\right)-\frac{a\,e\,x^2+\frac{a\,d\,x}{2}+\frac{a\,c}{3}}{x^3}+x^2\,\left(\frac{b\,e}{2}+\frac{a\,h}{2}\right)+\ln\left(x\right)\,\left(b\,c+a\,f\right)+\frac{b\,h\,x^5}{5}+\frac{b\,f\,x^3}{3}+\frac{b\,g\,x^4}{4}","Not used",1,"x*(b*d + a*g) - ((a*c)/3 + (a*d*x)/2 + a*e*x^2)/x^3 + x^2*((b*e)/2 + (a*h)/2) + log(x)*(b*c + a*f) + (b*h*x^5)/5 + (b*f*x^3)/3 + (b*g*x^4)/4","B"
382,1,74,86,4.976281,"\text{Not used}","int(((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5,x)","x\,\left(b\,e+a\,h\right)-\frac{\left(b\,c+a\,f\right)\,x^3+\frac{a\,e\,x^2}{2}+\frac{a\,d\,x}{3}+\frac{a\,c}{4}}{x^4}+\ln\left(x\right)\,\left(b\,d+a\,g\right)+\frac{b\,h\,x^4}{4}+\frac{b\,f\,x^2}{2}+\frac{b\,g\,x^3}{3}","Not used",1,"x*(b*e + a*h) - ((a*c)/4 + x^3*(b*c + a*f) + (a*d*x)/3 + (a*e*x^2)/2)/x^4 + log(x)*(b*d + a*g) + (b*h*x^4)/4 + (b*f*x^2)/2 + (b*g*x^3)/3","B"
383,1,151,163,0.101613,"\text{Not used}","int(x^4*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^8\,\left(\frac{f\,a^2}{8}+\frac{b\,c\,a}{4}\right)+x^{11}\,\left(\frac{c\,b^2}{11}+\frac{2\,a\,f\,b}{11}\right)+x^9\,\left(\frac{g\,a^2}{9}+\frac{2\,b\,d\,a}{9}\right)+x^{12}\,\left(\frac{d\,b^2}{12}+\frac{a\,g\,b}{6}\right)+x^{10}\,\left(\frac{h\,a^2}{10}+\frac{b\,e\,a}{5}\right)+x^{13}\,\left(\frac{e\,b^2}{13}+\frac{2\,a\,h\,b}{13}\right)+\frac{a^2\,c\,x^5}{5}+\frac{a^2\,d\,x^6}{6}+\frac{a^2\,e\,x^7}{7}+\frac{b^2\,f\,x^{14}}{14}+\frac{b^2\,g\,x^{15}}{15}+\frac{b^2\,h\,x^{16}}{16}","Not used",1,"x^8*((a^2*f)/8 + (a*b*c)/4) + x^11*((b^2*c)/11 + (2*a*b*f)/11) + x^9*((a^2*g)/9 + (2*a*b*d)/9) + x^12*((b^2*d)/12 + (a*b*g)/6) + x^10*((a^2*h)/10 + (a*b*e)/5) + x^13*((b^2*e)/13 + (2*a*b*h)/13) + (a^2*c*x^5)/5 + (a^2*d*x^6)/6 + (a^2*e*x^7)/7 + (b^2*f*x^14)/14 + (b^2*g*x^15)/15 + (b^2*h*x^16)/16","B"
384,1,151,163,0.088009,"\text{Not used}","int(x^3*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^7\,\left(\frac{f\,a^2}{7}+\frac{2\,b\,c\,a}{7}\right)+x^{10}\,\left(\frac{c\,b^2}{10}+\frac{a\,f\,b}{5}\right)+x^8\,\left(\frac{g\,a^2}{8}+\frac{b\,d\,a}{4}\right)+x^{11}\,\left(\frac{d\,b^2}{11}+\frac{2\,a\,g\,b}{11}\right)+x^9\,\left(\frac{h\,a^2}{9}+\frac{2\,b\,e\,a}{9}\right)+x^{12}\,\left(\frac{e\,b^2}{12}+\frac{a\,h\,b}{6}\right)+\frac{a^2\,c\,x^4}{4}+\frac{a^2\,d\,x^5}{5}+\frac{a^2\,e\,x^6}{6}+\frac{b^2\,f\,x^{13}}{13}+\frac{b^2\,g\,x^{14}}{14}+\frac{b^2\,h\,x^{15}}{15}","Not used",1,"x^7*((a^2*f)/7 + (2*a*b*c)/7) + x^10*((b^2*c)/10 + (a*b*f)/5) + x^8*((a^2*g)/8 + (a*b*d)/4) + x^11*((b^2*d)/11 + (2*a*b*g)/11) + x^9*((a^2*h)/9 + (2*a*b*e)/9) + x^12*((b^2*e)/12 + (a*b*h)/6) + (a^2*c*x^4)/4 + (a^2*d*x^5)/5 + (a^2*e*x^6)/6 + (b^2*f*x^13)/13 + (b^2*g*x^14)/14 + (b^2*h*x^15)/15","B"
385,1,151,158,0.091327,"\text{Not used}","int(x^2*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^6\,\left(\frac{f\,a^2}{6}+\frac{b\,c\,a}{3}\right)+x^9\,\left(\frac{c\,b^2}{9}+\frac{2\,a\,f\,b}{9}\right)+x^7\,\left(\frac{g\,a^2}{7}+\frac{2\,b\,d\,a}{7}\right)+x^{10}\,\left(\frac{d\,b^2}{10}+\frac{a\,g\,b}{5}\right)+x^8\,\left(\frac{h\,a^2}{8}+\frac{b\,e\,a}{4}\right)+x^{11}\,\left(\frac{e\,b^2}{11}+\frac{2\,a\,h\,b}{11}\right)+\frac{a^2\,c\,x^3}{3}+\frac{a^2\,d\,x^4}{4}+\frac{a^2\,e\,x^5}{5}+\frac{b^2\,f\,x^{12}}{12}+\frac{b^2\,g\,x^{13}}{13}+\frac{b^2\,h\,x^{14}}{14}","Not used",1,"x^6*((a^2*f)/6 + (a*b*c)/3) + x^9*((b^2*c)/9 + (2*a*b*f)/9) + x^7*((a^2*g)/7 + (2*a*b*d)/7) + x^10*((b^2*d)/10 + (a*b*g)/5) + x^8*((a^2*h)/8 + (a*b*e)/4) + x^11*((b^2*e)/11 + (2*a*b*h)/11) + (a^2*c*x^3)/3 + (a^2*d*x^4)/4 + (a^2*e*x^5)/5 + (b^2*f*x^12)/12 + (b^2*g*x^13)/13 + (b^2*h*x^14)/14","B"
386,1,151,158,0.090936,"\text{Not used}","int(x*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^5\,\left(\frac{f\,a^2}{5}+\frac{2\,b\,c\,a}{5}\right)+x^8\,\left(\frac{c\,b^2}{8}+\frac{a\,f\,b}{4}\right)+x^6\,\left(\frac{g\,a^2}{6}+\frac{b\,d\,a}{3}\right)+x^9\,\left(\frac{d\,b^2}{9}+\frac{2\,a\,g\,b}{9}\right)+x^7\,\left(\frac{h\,a^2}{7}+\frac{2\,b\,e\,a}{7}\right)+x^{10}\,\left(\frac{e\,b^2}{10}+\frac{a\,h\,b}{5}\right)+\frac{a^2\,c\,x^2}{2}+\frac{a^2\,d\,x^3}{3}+\frac{a^2\,e\,x^4}{4}+\frac{b^2\,f\,x^{11}}{11}+\frac{b^2\,g\,x^{12}}{12}+\frac{b^2\,h\,x^{13}}{13}","Not used",1,"x^5*((a^2*f)/5 + (2*a*b*c)/5) + x^8*((b^2*c)/8 + (a*b*f)/4) + x^6*((a^2*g)/6 + (a*b*d)/3) + x^9*((b^2*d)/9 + (2*a*b*g)/9) + x^7*((a^2*h)/7 + (2*a*b*e)/7) + x^10*((b^2*e)/10 + (a*b*h)/5) + (a^2*c*x^2)/2 + (a^2*d*x^3)/3 + (a^2*e*x^4)/4 + (b^2*f*x^11)/11 + (b^2*g*x^12)/12 + (b^2*h*x^13)/13","B"
387,1,148,153,0.091595,"\text{Not used}","int((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^4\,\left(\frac{f\,a^2}{4}+\frac{b\,c\,a}{2}\right)+x^7\,\left(\frac{c\,b^2}{7}+\frac{2\,a\,f\,b}{7}\right)+x^5\,\left(\frac{g\,a^2}{5}+\frac{2\,b\,d\,a}{5}\right)+x^8\,\left(\frac{d\,b^2}{8}+\frac{a\,g\,b}{4}\right)+x^6\,\left(\frac{h\,a^2}{6}+\frac{b\,e\,a}{3}\right)+x^9\,\left(\frac{e\,b^2}{9}+\frac{2\,a\,h\,b}{9}\right)+\frac{a^2\,d\,x^2}{2}+\frac{a^2\,e\,x^3}{3}+\frac{b^2\,f\,x^{10}}{10}+\frac{b^2\,g\,x^{11}}{11}+\frac{b^2\,h\,x^{12}}{12}+a^2\,c\,x","Not used",1,"x^4*((a^2*f)/4 + (a*b*c)/2) + x^7*((b^2*c)/7 + (2*a*b*f)/7) + x^5*((a^2*g)/5 + (2*a*b*d)/5) + x^8*((b^2*d)/8 + (a*b*g)/4) + x^6*((a^2*h)/6 + (a*b*e)/3) + x^9*((b^2*e)/9 + (2*a*b*h)/9) + (a^2*d*x^2)/2 + (a^2*e*x^3)/3 + (b^2*f*x^10)/10 + (b^2*g*x^11)/11 + (b^2*h*x^12)/12 + a^2*c*x","B"
388,1,146,149,0.095942,"\text{Not used}","int(((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x,x)","x^3\,\left(\frac{f\,a^2}{3}+\frac{2\,b\,c\,a}{3}\right)+x^6\,\left(\frac{c\,b^2}{6}+\frac{a\,f\,b}{3}\right)+x^4\,\left(\frac{g\,a^2}{4}+\frac{b\,d\,a}{2}\right)+x^7\,\left(\frac{d\,b^2}{7}+\frac{2\,a\,g\,b}{7}\right)+x^5\,\left(\frac{h\,a^2}{5}+\frac{2\,b\,e\,a}{5}\right)+x^8\,\left(\frac{e\,b^2}{8}+\frac{a\,h\,b}{4}\right)+\frac{a^2\,e\,x^2}{2}+\frac{b^2\,f\,x^9}{9}+\frac{b^2\,g\,x^{10}}{10}+\frac{b^2\,h\,x^{11}}{11}+a^2\,c\,\ln\left(x\right)+a^2\,d\,x","Not used",1,"x^3*((a^2*f)/3 + (2*a*b*c)/3) + x^6*((b^2*c)/6 + (a*b*f)/3) + x^4*((a^2*g)/4 + (a*b*d)/2) + x^7*((b^2*d)/7 + (2*a*b*g)/7) + x^5*((a^2*h)/5 + (2*a*b*e)/5) + x^8*((b^2*e)/8 + (a*b*h)/4) + (a^2*e*x^2)/2 + (b^2*f*x^9)/9 + (b^2*g*x^10)/10 + (b^2*h*x^11)/11 + a^2*c*log(x) + a^2*d*x","B"
389,1,145,147,0.098008,"\text{Not used}","int(((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^2,x)","x^2\,\left(\frac{f\,a^2}{2}+b\,c\,a\right)+x^5\,\left(\frac{c\,b^2}{5}+\frac{2\,a\,f\,b}{5}\right)+x^3\,\left(\frac{g\,a^2}{3}+\frac{2\,b\,d\,a}{3}\right)+x^6\,\left(\frac{d\,b^2}{6}+\frac{a\,g\,b}{3}\right)+x^4\,\left(\frac{h\,a^2}{4}+\frac{b\,e\,a}{2}\right)+x^7\,\left(\frac{e\,b^2}{7}+\frac{2\,a\,h\,b}{7}\right)-\frac{a^2\,c}{x}+\frac{b^2\,f\,x^8}{8}+\frac{b^2\,g\,x^9}{9}+\frac{b^2\,h\,x^{10}}{10}+a^2\,d\,\ln\left(x\right)+a^2\,e\,x","Not used",1,"x^2*((a^2*f)/2 + a*b*c) + x^5*((b^2*c)/5 + (2*a*b*f)/5) + x^3*((a^2*g)/3 + (2*a*b*d)/3) + x^6*((b^2*d)/6 + (a*b*g)/3) + x^4*((a^2*h)/4 + (a*b*e)/2) + x^7*((b^2*e)/7 + (2*a*b*h)/7) - (a^2*c)/x + (b^2*f*x^8)/8 + (b^2*g*x^9)/9 + (b^2*h*x^10)/10 + a^2*d*log(x) + a^2*e*x","B"
390,1,145,147,5.008485,"\text{Not used}","int(((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^3,x)","x\,\left(f\,a^2+2\,b\,c\,a\right)-\frac{\frac{a^2\,c}{2}+a^2\,d\,x}{x^2}+x^4\,\left(\frac{c\,b^2}{4}+\frac{a\,f\,b}{2}\right)+x^2\,\left(\frac{g\,a^2}{2}+b\,d\,a\right)+x^5\,\left(\frac{d\,b^2}{5}+\frac{2\,a\,g\,b}{5}\right)+x^3\,\left(\frac{h\,a^2}{3}+\frac{2\,b\,e\,a}{3}\right)+x^6\,\left(\frac{e\,b^2}{6}+\frac{a\,h\,b}{3}\right)+\frac{b^2\,f\,x^7}{7}+\frac{b^2\,g\,x^8}{8}+\frac{b^2\,h\,x^9}{9}+a^2\,e\,\ln\left(x\right)","Not used",1,"x*(a^2*f + 2*a*b*c) - ((a^2*c)/2 + a^2*d*x)/x^2 + x^4*((b^2*c)/4 + (a*b*f)/2) + x^2*((a^2*g)/2 + a*b*d) + x^5*((b^2*d)/5 + (2*a*b*g)/5) + x^3*((a^2*h)/3 + (2*a*b*e)/3) + x^6*((b^2*e)/6 + (a*b*h)/3) + (b^2*f*x^7)/7 + (b^2*g*x^8)/8 + (b^2*h*x^9)/9 + a^2*e*log(x)","B"
391,1,145,152,0.075824,"\text{Not used}","int(((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^4,x)","x\,\left(g\,a^2+2\,b\,d\,a\right)-\frac{e\,a^2\,x^2+\frac{d\,a^2\,x}{2}+\frac{c\,a^2}{3}}{x^3}+x^3\,\left(\frac{c\,b^2}{3}+\frac{2\,a\,f\,b}{3}\right)+x^4\,\left(\frac{d\,b^2}{4}+\frac{a\,g\,b}{2}\right)+x^2\,\left(\frac{h\,a^2}{2}+b\,e\,a\right)+x^5\,\left(\frac{e\,b^2}{5}+\frac{2\,a\,h\,b}{5}\right)+\ln\left(x\right)\,\left(f\,a^2+2\,b\,c\,a\right)+\frac{b^2\,f\,x^6}{6}+\frac{b^2\,g\,x^7}{7}+\frac{b^2\,h\,x^8}{8}","Not used",1,"x*(a^2*g + 2*a*b*d) - ((a^2*c)/3 + a^2*e*x^2 + (a^2*d*x)/2)/x^3 + x^3*((b^2*c)/3 + (2*a*b*f)/3) + x^4*((b^2*d)/4 + (a*b*g)/2) + x^2*((a^2*h)/2 + a*b*e) + x^5*((b^2*e)/5 + (2*a*b*h)/5) + log(x)*(a^2*f + 2*a*b*c) + (b^2*f*x^6)/6 + (b^2*g*x^7)/7 + (b^2*h*x^8)/8","B"
392,1,145,152,0.065714,"\text{Not used}","int(((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5,x)","x\,\left(h\,a^2+2\,b\,e\,a\right)-\frac{\frac{a^2\,c}{4}+x^3\,\left(f\,a^2+2\,b\,c\,a\right)+\frac{a^2\,e\,x^2}{2}+\frac{a^2\,d\,x}{3}}{x^4}+x^2\,\left(\frac{c\,b^2}{2}+a\,f\,b\right)+x^3\,\left(\frac{d\,b^2}{3}+\frac{2\,a\,g\,b}{3}\right)+x^4\,\left(\frac{e\,b^2}{4}+\frac{a\,h\,b}{2}\right)+\ln\left(x\right)\,\left(g\,a^2+2\,b\,d\,a\right)+\frac{b^2\,f\,x^5}{5}+\frac{b^2\,g\,x^6}{6}+\frac{b^2\,h\,x^7}{7}","Not used",1,"x*(a^2*h + 2*a*b*e) - ((a^2*c)/4 + x^3*(a^2*f + 2*a*b*c) + (a^2*e*x^2)/2 + (a^2*d*x)/3)/x^4 + x^2*((b^2*c)/2 + a*b*f) + x^3*((b^2*d)/3 + (2*a*b*g)/3) + x^4*((b^2*e)/4 + (a*b*h)/2) + log(x)*(a^2*g + 2*a*b*d) + (b^2*f*x^5)/5 + (b^2*g*x^6)/6 + (b^2*h*x^7)/7","B"
393,1,205,223,0.173716,"\text{Not used}","int(x^4*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^8\,\left(\frac{f\,a^3}{8}+\frac{3\,b\,c\,a^2}{8}\right)+x^{14}\,\left(\frac{c\,b^3}{14}+\frac{3\,a\,f\,b^2}{14}\right)+x^9\,\left(\frac{g\,a^3}{9}+\frac{b\,d\,a^2}{3}\right)+x^{15}\,\left(\frac{d\,b^3}{15}+\frac{a\,g\,b^2}{5}\right)+x^{10}\,\left(\frac{h\,a^3}{10}+\frac{3\,b\,e\,a^2}{10}\right)+x^{16}\,\left(\frac{e\,b^3}{16}+\frac{3\,a\,h\,b^2}{16}\right)+\frac{a^3\,c\,x^5}{5}+\frac{a^3\,d\,x^6}{6}+\frac{a^3\,e\,x^7}{7}+\frac{b^3\,f\,x^{17}}{17}+\frac{b^3\,g\,x^{18}}{18}+\frac{b^3\,h\,x^{19}}{19}+\frac{3\,a\,b\,x^{11}\,\left(b\,c+a\,f\right)}{11}+\frac{a\,b\,x^{12}\,\left(b\,d+a\,g\right)}{4}+\frac{3\,a\,b\,x^{13}\,\left(b\,e+a\,h\right)}{13}","Not used",1,"x^8*((a^3*f)/8 + (3*a^2*b*c)/8) + x^14*((b^3*c)/14 + (3*a*b^2*f)/14) + x^9*((a^3*g)/9 + (a^2*b*d)/3) + x^15*((b^3*d)/15 + (a*b^2*g)/5) + x^10*((a^3*h)/10 + (3*a^2*b*e)/10) + x^16*((b^3*e)/16 + (3*a*b^2*h)/16) + (a^3*c*x^5)/5 + (a^3*d*x^6)/6 + (a^3*e*x^7)/7 + (b^3*f*x^17)/17 + (b^3*g*x^18)/18 + (b^3*h*x^19)/19 + (3*a*b*x^11*(b*c + a*f))/11 + (a*b*x^12*(b*d + a*g))/4 + (3*a*b*x^13*(b*e + a*h))/13","B"
394,1,205,223,5.164834,"\text{Not used}","int(x^3*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^7\,\left(\frac{f\,a^3}{7}+\frac{3\,b\,c\,a^2}{7}\right)+x^{13}\,\left(\frac{c\,b^3}{13}+\frac{3\,a\,f\,b^2}{13}\right)+x^8\,\left(\frac{g\,a^3}{8}+\frac{3\,b\,d\,a^2}{8}\right)+x^{14}\,\left(\frac{d\,b^3}{14}+\frac{3\,a\,g\,b^2}{14}\right)+x^9\,\left(\frac{h\,a^3}{9}+\frac{b\,e\,a^2}{3}\right)+x^{15}\,\left(\frac{e\,b^3}{15}+\frac{a\,h\,b^2}{5}\right)+\frac{a^3\,c\,x^4}{4}+\frac{a^3\,d\,x^5}{5}+\frac{a^3\,e\,x^6}{6}+\frac{b^3\,f\,x^{16}}{16}+\frac{b^3\,g\,x^{17}}{17}+\frac{b^3\,h\,x^{18}}{18}+\frac{3\,a\,b\,x^{10}\,\left(b\,c+a\,f\right)}{10}+\frac{3\,a\,b\,x^{11}\,\left(b\,d+a\,g\right)}{11}+\frac{a\,b\,x^{12}\,\left(b\,e+a\,h\right)}{4}","Not used",1,"x^7*((a^3*f)/7 + (3*a^2*b*c)/7) + x^13*((b^3*c)/13 + (3*a*b^2*f)/13) + x^8*((a^3*g)/8 + (3*a^2*b*d)/8) + x^14*((b^3*d)/14 + (3*a*b^2*g)/14) + x^9*((a^3*h)/9 + (a^2*b*e)/3) + x^15*((b^3*e)/15 + (a*b^2*h)/5) + (a^3*c*x^4)/4 + (a^3*d*x^5)/5 + (a^3*e*x^6)/6 + (b^3*f*x^16)/16 + (b^3*g*x^17)/17 + (b^3*h*x^18)/18 + (3*a*b*x^10*(b*c + a*f))/10 + (3*a*b*x^11*(b*d + a*g))/11 + (a*b*x^12*(b*e + a*h))/4","B"
395,1,205,212,0.161736,"\text{Not used}","int(x^2*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^6\,\left(\frac{f\,a^3}{6}+\frac{b\,c\,a^2}{2}\right)+x^{12}\,\left(\frac{c\,b^3}{12}+\frac{a\,f\,b^2}{4}\right)+x^7\,\left(\frac{g\,a^3}{7}+\frac{3\,b\,d\,a^2}{7}\right)+x^{13}\,\left(\frac{d\,b^3}{13}+\frac{3\,a\,g\,b^2}{13}\right)+x^8\,\left(\frac{h\,a^3}{8}+\frac{3\,b\,e\,a^2}{8}\right)+x^{14}\,\left(\frac{e\,b^3}{14}+\frac{3\,a\,h\,b^2}{14}\right)+\frac{a^3\,c\,x^3}{3}+\frac{a^3\,d\,x^4}{4}+\frac{a^3\,e\,x^5}{5}+\frac{b^3\,f\,x^{15}}{15}+\frac{b^3\,g\,x^{16}}{16}+\frac{b^3\,h\,x^{17}}{17}+\frac{a\,b\,x^9\,\left(b\,c+a\,f\right)}{3}+\frac{3\,a\,b\,x^{10}\,\left(b\,d+a\,g\right)}{10}+\frac{3\,a\,b\,x^{11}\,\left(b\,e+a\,h\right)}{11}","Not used",1,"x^6*((a^3*f)/6 + (a^2*b*c)/2) + x^12*((b^3*c)/12 + (a*b^2*f)/4) + x^7*((a^3*g)/7 + (3*a^2*b*d)/7) + x^13*((b^3*d)/13 + (3*a*b^2*g)/13) + x^8*((a^3*h)/8 + (3*a^2*b*e)/8) + x^14*((b^3*e)/14 + (3*a*b^2*h)/14) + (a^3*c*x^3)/3 + (a^3*d*x^4)/4 + (a^3*e*x^5)/5 + (b^3*f*x^15)/15 + (b^3*g*x^16)/16 + (b^3*h*x^17)/17 + (a*b*x^9*(b*c + a*f))/3 + (3*a*b*x^10*(b*d + a*g))/10 + (3*a*b*x^11*(b*e + a*h))/11","B"
396,1,205,212,0.157041,"\text{Not used}","int(x*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^5\,\left(\frac{f\,a^3}{5}+\frac{3\,b\,c\,a^2}{5}\right)+x^{11}\,\left(\frac{c\,b^3}{11}+\frac{3\,a\,f\,b^2}{11}\right)+x^6\,\left(\frac{g\,a^3}{6}+\frac{b\,d\,a^2}{2}\right)+x^{12}\,\left(\frac{d\,b^3}{12}+\frac{a\,g\,b^2}{4}\right)+x^7\,\left(\frac{h\,a^3}{7}+\frac{3\,b\,e\,a^2}{7}\right)+x^{13}\,\left(\frac{e\,b^3}{13}+\frac{3\,a\,h\,b^2}{13}\right)+\frac{a^3\,c\,x^2}{2}+\frac{a^3\,d\,x^3}{3}+\frac{a^3\,e\,x^4}{4}+\frac{b^3\,f\,x^{14}}{14}+\frac{b^3\,g\,x^{15}}{15}+\frac{b^3\,h\,x^{16}}{16}+\frac{3\,a\,b\,x^8\,\left(b\,c+a\,f\right)}{8}+\frac{a\,b\,x^9\,\left(b\,d+a\,g\right)}{3}+\frac{3\,a\,b\,x^{10}\,\left(b\,e+a\,h\right)}{10}","Not used",1,"x^5*((a^3*f)/5 + (3*a^2*b*c)/5) + x^11*((b^3*c)/11 + (3*a*b^2*f)/11) + x^6*((a^3*g)/6 + (a^2*b*d)/2) + x^12*((b^3*d)/12 + (a*b^2*g)/4) + x^7*((a^3*h)/7 + (3*a^2*b*e)/7) + x^13*((b^3*e)/13 + (3*a*b^2*h)/13) + (a^3*c*x^2)/2 + (a^3*d*x^3)/3 + (a^3*e*x^4)/4 + (b^3*f*x^14)/14 + (b^3*g*x^15)/15 + (b^3*h*x^16)/16 + (3*a*b*x^8*(b*c + a*f))/8 + (a*b*x^9*(b*d + a*g))/3 + (3*a*b*x^10*(b*e + a*h))/10","B"
397,1,202,207,0.156796,"\text{Not used}","int((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5),x)","x^4\,\left(\frac{f\,a^3}{4}+\frac{3\,b\,c\,a^2}{4}\right)+x^{10}\,\left(\frac{c\,b^3}{10}+\frac{3\,a\,f\,b^2}{10}\right)+x^5\,\left(\frac{g\,a^3}{5}+\frac{3\,b\,d\,a^2}{5}\right)+x^{11}\,\left(\frac{d\,b^3}{11}+\frac{3\,a\,g\,b^2}{11}\right)+x^6\,\left(\frac{h\,a^3}{6}+\frac{b\,e\,a^2}{2}\right)+x^{12}\,\left(\frac{e\,b^3}{12}+\frac{a\,h\,b^2}{4}\right)+\frac{a^3\,d\,x^2}{2}+\frac{a^3\,e\,x^3}{3}+\frac{b^3\,f\,x^{13}}{13}+\frac{b^3\,g\,x^{14}}{14}+\frac{b^3\,h\,x^{15}}{15}+a^3\,c\,x+\frac{3\,a\,b\,x^7\,\left(b\,c+a\,f\right)}{7}+\frac{3\,a\,b\,x^8\,\left(b\,d+a\,g\right)}{8}+\frac{a\,b\,x^9\,\left(b\,e+a\,h\right)}{3}","Not used",1,"x^4*((a^3*f)/4 + (3*a^2*b*c)/4) + x^10*((b^3*c)/10 + (3*a*b^2*f)/10) + x^5*((a^3*g)/5 + (3*a^2*b*d)/5) + x^11*((b^3*d)/11 + (3*a*b^2*g)/11) + x^6*((a^3*h)/6 + (a^2*b*e)/2) + x^12*((b^3*e)/12 + (a*b^2*h)/4) + (a^3*d*x^2)/2 + (a^3*e*x^3)/3 + (b^3*f*x^13)/13 + (b^3*g*x^14)/14 + (b^3*h*x^15)/15 + a^3*c*x + (3*a*b*x^7*(b*c + a*f))/7 + (3*a*b*x^8*(b*d + a*g))/8 + (a*b*x^9*(b*e + a*h))/3","B"
398,1,199,200,5.113341,"\text{Not used}","int(((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x,x)","x^3\,\left(\frac{f\,a^3}{3}+b\,c\,a^2\right)+x^9\,\left(\frac{c\,b^3}{9}+\frac{a\,f\,b^2}{3}\right)+x^4\,\left(\frac{g\,a^3}{4}+\frac{3\,b\,d\,a^2}{4}\right)+x^{10}\,\left(\frac{d\,b^3}{10}+\frac{3\,a\,g\,b^2}{10}\right)+x^5\,\left(\frac{h\,a^3}{5}+\frac{3\,b\,e\,a^2}{5}\right)+x^{11}\,\left(\frac{e\,b^3}{11}+\frac{3\,a\,h\,b^2}{11}\right)+\frac{a^3\,e\,x^2}{2}+\frac{b^3\,f\,x^{12}}{12}+\frac{b^3\,g\,x^{13}}{13}+\frac{b^3\,h\,x^{14}}{14}+a^3\,c\,\ln\left(x\right)+a^3\,d\,x+\frac{a\,b\,x^6\,\left(b\,c+a\,f\right)}{2}+\frac{3\,a\,b\,x^7\,\left(b\,d+a\,g\right)}{7}+\frac{3\,a\,b\,x^8\,\left(b\,e+a\,h\right)}{8}","Not used",1,"x^3*((a^3*f)/3 + a^2*b*c) + x^9*((b^3*c)/9 + (a*b^2*f)/3) + x^4*((a^3*g)/4 + (3*a^2*b*d)/4) + x^10*((b^3*d)/10 + (3*a*b^2*g)/10) + x^5*((a^3*h)/5 + (3*a^2*b*e)/5) + x^11*((b^3*e)/11 + (3*a*b^2*h)/11) + (a^3*e*x^2)/2 + (b^3*f*x^12)/12 + (b^3*g*x^13)/13 + (b^3*h*x^14)/14 + a^3*c*log(x) + a^3*d*x + (a*b*x^6*(b*c + a*f))/2 + (3*a*b*x^7*(b*d + a*g))/7 + (3*a*b*x^8*(b*e + a*h))/8","B"
399,1,199,198,5.045095,"\text{Not used}","int(((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^2,x)","x^2\,\left(\frac{f\,a^3}{2}+\frac{3\,b\,c\,a^2}{2}\right)+x^8\,\left(\frac{c\,b^3}{8}+\frac{3\,a\,f\,b^2}{8}\right)+x^3\,\left(\frac{g\,a^3}{3}+b\,d\,a^2\right)+x^9\,\left(\frac{d\,b^3}{9}+\frac{a\,g\,b^2}{3}\right)+x^4\,\left(\frac{h\,a^3}{4}+\frac{3\,b\,e\,a^2}{4}\right)+x^{10}\,\left(\frac{e\,b^3}{10}+\frac{3\,a\,h\,b^2}{10}\right)-\frac{a^3\,c}{x}+\frac{b^3\,f\,x^{11}}{11}+\frac{b^3\,g\,x^{12}}{12}+\frac{b^3\,h\,x^{13}}{13}+a^3\,d\,\ln\left(x\right)+a^3\,e\,x+\frac{3\,a\,b\,x^5\,\left(b\,c+a\,f\right)}{5}+\frac{a\,b\,x^6\,\left(b\,d+a\,g\right)}{2}+\frac{3\,a\,b\,x^7\,\left(b\,e+a\,h\right)}{7}","Not used",1,"x^2*((a^3*f)/2 + (3*a^2*b*c)/2) + x^8*((b^3*c)/8 + (3*a*b^2*f)/8) + x^3*((a^3*g)/3 + a^2*b*d) + x^9*((b^3*d)/9 + (a*b^2*g)/3) + x^4*((a^3*h)/4 + (3*a^2*b*e)/4) + x^10*((b^3*e)/10 + (3*a*b^2*h)/10) - (a^3*c)/x + (b^3*f*x^11)/11 + (b^3*g*x^12)/12 + (b^3*h*x^13)/13 + a^3*d*log(x) + a^3*e*x + (3*a*b*x^5*(b*c + a*f))/5 + (a*b*x^6*(b*d + a*g))/2 + (3*a*b*x^7*(b*e + a*h))/7","B"
400,1,199,198,0.137433,"\text{Not used}","int(((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^3,x)","x^7\,\left(\frac{c\,b^3}{7}+\frac{3\,a\,f\,b^2}{7}\right)+x^2\,\left(\frac{g\,a^3}{2}+\frac{3\,b\,d\,a^2}{2}\right)+x^8\,\left(\frac{d\,b^3}{8}+\frac{3\,a\,g\,b^2}{8}\right)+x^3\,\left(\frac{h\,a^3}{3}+b\,e\,a^2\right)+x^9\,\left(\frac{e\,b^3}{9}+\frac{a\,h\,b^2}{3}\right)-\frac{\frac{a^3\,c}{2}+a^3\,d\,x}{x^2}+x\,\left(f\,a^3+3\,b\,c\,a^2\right)+\frac{b^3\,f\,x^{10}}{10}+\frac{b^3\,g\,x^{11}}{11}+\frac{b^3\,h\,x^{12}}{12}+a^3\,e\,\ln\left(x\right)+\frac{3\,a\,b\,x^4\,\left(b\,c+a\,f\right)}{4}+\frac{3\,a\,b\,x^5\,\left(b\,d+a\,g\right)}{5}+\frac{a\,b\,x^6\,\left(b\,e+a\,h\right)}{2}","Not used",1,"x^7*((b^3*c)/7 + (3*a*b^2*f)/7) + x^2*((a^3*g)/2 + (3*a^2*b*d)/2) + x^8*((b^3*d)/8 + (3*a*b^2*g)/8) + x^3*((a^3*h)/3 + a^2*b*e) + x^9*((b^3*e)/9 + (a*b^2*h)/3) - ((a^3*c)/2 + a^3*d*x)/x^2 + x*(a^3*f + 3*a^2*b*c) + (b^3*f*x^10)/10 + (b^3*g*x^11)/11 + (b^3*h*x^12)/12 + a^3*e*log(x) + (3*a*b*x^4*(b*c + a*f))/4 + (3*a*b*x^5*(b*d + a*g))/5 + (a*b*x^6*(b*e + a*h))/2","B"
401,1,199,209,0.122056,"\text{Not used}","int(((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^4,x)","x^6\,\left(\frac{c\,b^3}{6}+\frac{a\,f\,b^2}{2}\right)+x^7\,\left(\frac{d\,b^3}{7}+\frac{3\,a\,g\,b^2}{7}\right)+x^2\,\left(\frac{h\,a^3}{2}+\frac{3\,b\,e\,a^2}{2}\right)+x^8\,\left(\frac{e\,b^3}{8}+\frac{3\,a\,h\,b^2}{8}\right)+\ln\left(x\right)\,\left(f\,a^3+3\,b\,c\,a^2\right)-\frac{e\,a^3\,x^2+\frac{d\,a^3\,x}{2}+\frac{c\,a^3}{3}}{x^3}+x\,\left(g\,a^3+3\,b\,d\,a^2\right)+\frac{b^3\,f\,x^9}{9}+\frac{b^3\,g\,x^{10}}{10}+\frac{b^3\,h\,x^{11}}{11}+a\,b\,x^3\,\left(b\,c+a\,f\right)+\frac{3\,a\,b\,x^4\,\left(b\,d+a\,g\right)}{4}+\frac{3\,a\,b\,x^5\,\left(b\,e+a\,h\right)}{5}","Not used",1,"x^6*((b^3*c)/6 + (a*b^2*f)/2) + x^7*((b^3*d)/7 + (3*a*b^2*g)/7) + x^2*((a^3*h)/2 + (3*a^2*b*e)/2) + x^8*((b^3*e)/8 + (3*a*b^2*h)/8) + log(x)*(a^3*f + 3*a^2*b*c) - ((a^3*c)/3 + a^3*e*x^2 + (a^3*d*x)/2)/x^3 + x*(a^3*g + 3*a^2*b*d) + (b^3*f*x^9)/9 + (b^3*g*x^10)/10 + (b^3*h*x^11)/11 + a*b*x^3*(b*c + a*f) + (3*a*b*x^4*(b*d + a*g))/4 + (3*a*b*x^5*(b*e + a*h))/5","B"
402,1,199,209,5.027187,"\text{Not used}","int(((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5,x)","x^5\,\left(\frac{c\,b^3}{5}+\frac{3\,a\,f\,b^2}{5}\right)+x^6\,\left(\frac{d\,b^3}{6}+\frac{a\,g\,b^2}{2}\right)+x^7\,\left(\frac{e\,b^3}{7}+\frac{3\,a\,h\,b^2}{7}\right)+\ln\left(x\right)\,\left(g\,a^3+3\,b\,d\,a^2\right)-\frac{x^3\,\left(f\,a^3+3\,b\,c\,a^2\right)+\frac{a^3\,c}{4}+\frac{a^3\,e\,x^2}{2}+\frac{a^3\,d\,x}{3}}{x^4}+x\,\left(h\,a^3+3\,b\,e\,a^2\right)+\frac{b^3\,f\,x^8}{8}+\frac{b^3\,g\,x^9}{9}+\frac{b^3\,h\,x^{10}}{10}+\frac{3\,a\,b\,x^2\,\left(b\,c+a\,f\right)}{2}+a\,b\,x^3\,\left(b\,d+a\,g\right)+\frac{3\,a\,b\,x^4\,\left(b\,e+a\,h\right)}{4}","Not used",1,"x^5*((b^3*c)/5 + (3*a*b^2*f)/5) + x^6*((b^3*d)/6 + (a*b^2*g)/2) + x^7*((b^3*e)/7 + (3*a*b^2*h)/7) + log(x)*(a^3*g + 3*a^2*b*d) - (x^3*(a^3*f + 3*a^2*b*c) + (a^3*c)/4 + (a^3*e*x^2)/2 + (a^3*d*x)/3)/x^4 + x*(a^3*h + 3*a^2*b*e) + (b^3*f*x^8)/8 + (b^3*g*x^9)/9 + (b^3*h*x^10)/10 + (3*a*b*x^2*(b*c + a*f))/2 + a*b*x^3*(b*d + a*g) + (3*a*b*x^4*(b*e + a*h))/4","B"
403,1,1271,331,5.086184,"\text{Not used}","int((x^4*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3),x)","x^2\,\left(\frac{c}{2\,b}-\frac{a\,f}{2\,b^2}\right)+x^3\,\left(\frac{d}{3\,b}-\frac{a\,g}{3\,b^2}\right)+x^4\,\left(\frac{e}{4\,b}-\frac{a\,h}{4\,b^2}\right)+\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,b^{10}\,z^3+27\,a\,b^8\,d\,z^2-27\,a^2\,b^7\,g\,z^2-9\,a^4\,b^4\,f\,h\,z-18\,a^3\,b^5\,d\,g\,z+9\,a^3\,b^5\,e\,f\,z+9\,a^3\,b^5\,c\,h\,z-9\,a^2\,b^6\,c\,e\,z+9\,a^4\,b^4\,g^2\,z+9\,a^2\,b^6\,d^2\,z+3\,a^6\,b\,f\,g\,h-3\,a^5\,b^2\,e\,f\,g-3\,a^5\,b^2\,d\,f\,h-3\,a^5\,b^2\,c\,g\,h+3\,a^4\,b^3\,d\,e\,f+3\,a^4\,b^3\,c\,e\,g+3\,a^4\,b^3\,c\,d\,h-3\,a^3\,b^4\,c\,d\,e-3\,a^6\,b\,e\,h^2+3\,a^5\,b^2\,e^2\,h+3\,a^5\,b^2\,d\,g^2-3\,a^4\,b^3\,d^2\,g-3\,a^4\,b^3\,c\,f^2+3\,a^3\,b^4\,c^2\,f+a^5\,b^2\,f^3+a^3\,b^4\,d^3+a^7\,h^3-a^4\,b^3\,e^3-a^2\,b^5\,c^3-a^6\,b\,g^3,z,k\right)\,\left(\frac{6\,a^2\,b^4\,d-6\,a^3\,b^3\,g}{b^4}+\frac{x\,\left(3\,a^2\,b^4\,e-3\,a^3\,b^3\,h\right)}{b^4}+\mathrm{root}\left(27\,b^{10}\,z^3+27\,a\,b^8\,d\,z^2-27\,a^2\,b^7\,g\,z^2-9\,a^4\,b^4\,f\,h\,z-18\,a^3\,b^5\,d\,g\,z+9\,a^3\,b^5\,e\,f\,z+9\,a^3\,b^5\,c\,h\,z-9\,a^2\,b^6\,c\,e\,z+9\,a^4\,b^4\,g^2\,z+9\,a^2\,b^6\,d^2\,z+3\,a^6\,b\,f\,g\,h-3\,a^5\,b^2\,e\,f\,g-3\,a^5\,b^2\,d\,f\,h-3\,a^5\,b^2\,c\,g\,h+3\,a^4\,b^3\,d\,e\,f+3\,a^4\,b^3\,c\,e\,g+3\,a^4\,b^3\,c\,d\,h-3\,a^3\,b^4\,c\,d\,e-3\,a^6\,b\,e\,h^2+3\,a^5\,b^2\,e^2\,h+3\,a^5\,b^2\,d\,g^2-3\,a^4\,b^3\,d^2\,g-3\,a^4\,b^3\,c\,f^2+3\,a^3\,b^4\,c^2\,f+a^5\,b^2\,f^3+a^3\,b^4\,d^3+a^7\,h^3-a^4\,b^3\,e^3-a^2\,b^5\,c^3-a^6\,b\,g^3,z,k\right)\,a\,b^2\,9\right)+\frac{a^5\,g^2+a^3\,b^2\,d^2-a^5\,f\,h+a^4\,b\,c\,h-2\,a^4\,b\,d\,g+a^4\,b\,e\,f-a^3\,b^2\,c\,e}{b^4}+\frac{x\,\left(a^4\,b\,f^2+a^2\,b^3\,c^2+a^5\,g\,h-a^4\,b\,d\,h-a^4\,b\,e\,g-2\,a^3\,b^2\,c\,f+a^3\,b^2\,d\,e\right)}{b^4}\right)\,\mathrm{root}\left(27\,b^{10}\,z^3+27\,a\,b^8\,d\,z^2-27\,a^2\,b^7\,g\,z^2-9\,a^4\,b^4\,f\,h\,z-18\,a^3\,b^5\,d\,g\,z+9\,a^3\,b^5\,e\,f\,z+9\,a^3\,b^5\,c\,h\,z-9\,a^2\,b^6\,c\,e\,z+9\,a^4\,b^4\,g^2\,z+9\,a^2\,b^6\,d^2\,z+3\,a^6\,b\,f\,g\,h-3\,a^5\,b^2\,e\,f\,g-3\,a^5\,b^2\,d\,f\,h-3\,a^5\,b^2\,c\,g\,h+3\,a^4\,b^3\,d\,e\,f+3\,a^4\,b^3\,c\,e\,g+3\,a^4\,b^3\,c\,d\,h-3\,a^3\,b^4\,c\,d\,e-3\,a^6\,b\,e\,h^2+3\,a^5\,b^2\,e^2\,h+3\,a^5\,b^2\,d\,g^2-3\,a^4\,b^3\,d^2\,g-3\,a^4\,b^3\,c\,f^2+3\,a^3\,b^4\,c^2\,f+a^5\,b^2\,f^3+a^3\,b^4\,d^3+a^7\,h^3-a^4\,b^3\,e^3-a^2\,b^5\,c^3-a^6\,b\,g^3,z,k\right)\right)+\frac{f\,x^5}{5\,b}+\frac{g\,x^6}{6\,b}+\frac{h\,x^7}{7\,b}-\frac{a\,x\,\left(\frac{e}{b}-\frac{a\,h}{b^2}\right)}{b}","Not used",1,"x^2*(c/(2*b) - (a*f)/(2*b^2)) + x^3*(d/(3*b) - (a*g)/(3*b^2)) + x^4*(e/(4*b) - (a*h)/(4*b^2)) + symsum(log(root(27*b^10*z^3 + 27*a*b^8*d*z^2 - 27*a^2*b^7*g*z^2 - 9*a^4*b^4*f*h*z - 18*a^3*b^5*d*g*z + 9*a^3*b^5*e*f*z + 9*a^3*b^5*c*h*z - 9*a^2*b^6*c*e*z + 9*a^4*b^4*g^2*z + 9*a^2*b^6*d^2*z + 3*a^6*b*f*g*h - 3*a^5*b^2*e*f*g - 3*a^5*b^2*d*f*h - 3*a^5*b^2*c*g*h + 3*a^4*b^3*d*e*f + 3*a^4*b^3*c*e*g + 3*a^4*b^3*c*d*h - 3*a^3*b^4*c*d*e - 3*a^6*b*e*h^2 + 3*a^5*b^2*e^2*h + 3*a^5*b^2*d*g^2 - 3*a^4*b^3*d^2*g - 3*a^4*b^3*c*f^2 + 3*a^3*b^4*c^2*f + a^5*b^2*f^3 + a^3*b^4*d^3 + a^7*h^3 - a^4*b^3*e^3 - a^2*b^5*c^3 - a^6*b*g^3, z, k)*((6*a^2*b^4*d - 6*a^3*b^3*g)/b^4 + (x*(3*a^2*b^4*e - 3*a^3*b^3*h))/b^4 + 9*root(27*b^10*z^3 + 27*a*b^8*d*z^2 - 27*a^2*b^7*g*z^2 - 9*a^4*b^4*f*h*z - 18*a^3*b^5*d*g*z + 9*a^3*b^5*e*f*z + 9*a^3*b^5*c*h*z - 9*a^2*b^6*c*e*z + 9*a^4*b^4*g^2*z + 9*a^2*b^6*d^2*z + 3*a^6*b*f*g*h - 3*a^5*b^2*e*f*g - 3*a^5*b^2*d*f*h - 3*a^5*b^2*c*g*h + 3*a^4*b^3*d*e*f + 3*a^4*b^3*c*e*g + 3*a^4*b^3*c*d*h - 3*a^3*b^4*c*d*e - 3*a^6*b*e*h^2 + 3*a^5*b^2*e^2*h + 3*a^5*b^2*d*g^2 - 3*a^4*b^3*d^2*g - 3*a^4*b^3*c*f^2 + 3*a^3*b^4*c^2*f + a^5*b^2*f^3 + a^3*b^4*d^3 + a^7*h^3 - a^4*b^3*e^3 - a^2*b^5*c^3 - a^6*b*g^3, z, k)*a*b^2) + (a^5*g^2 + a^3*b^2*d^2 - a^5*f*h + a^4*b*c*h - 2*a^4*b*d*g + a^4*b*e*f - a^3*b^2*c*e)/b^4 + (x*(a^4*b*f^2 + a^2*b^3*c^2 + a^5*g*h - a^4*b*d*h - a^4*b*e*g - 2*a^3*b^2*c*f + a^3*b^2*d*e))/b^4)*root(27*b^10*z^3 + 27*a*b^8*d*z^2 - 27*a^2*b^7*g*z^2 - 9*a^4*b^4*f*h*z - 18*a^3*b^5*d*g*z + 9*a^3*b^5*e*f*z + 9*a^3*b^5*c*h*z - 9*a^2*b^6*c*e*z + 9*a^4*b^4*g^2*z + 9*a^2*b^6*d^2*z + 3*a^6*b*f*g*h - 3*a^5*b^2*e*f*g - 3*a^5*b^2*d*f*h - 3*a^5*b^2*c*g*h + 3*a^4*b^3*d*e*f + 3*a^4*b^3*c*e*g + 3*a^4*b^3*c*d*h - 3*a^3*b^4*c*d*e - 3*a^6*b*e*h^2 + 3*a^5*b^2*e^2*h + 3*a^5*b^2*d*g^2 - 3*a^4*b^3*d^2*g - 3*a^4*b^3*c*f^2 + 3*a^3*b^4*c^2*f + a^5*b^2*f^3 + a^3*b^4*d^3 + a^7*h^3 - a^4*b^3*e^3 - a^2*b^5*c^3 - a^6*b*g^3, z, k), k, 1, 3) + (f*x^5)/(5*b) + (g*x^6)/(6*b) + (h*x^7)/(7*b) - (a*x*(e/b - (a*h)/b^2))/b","B"
404,1,1236,313,4.991673,"\text{Not used}","int((x^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3),x)","x^2\,\left(\frac{d}{2\,b}-\frac{a\,g}{2\,b^2}\right)+x^3\,\left(\frac{e}{3\,b}-\frac{a\,h}{3\,b^2}\right)+\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,b^9\,z^3+27\,a\,b^7\,e\,z^2-27\,a^2\,b^6\,h\,z^2+9\,a\,b^6\,c\,d\,z-18\,a^3\,b^4\,e\,h\,z+9\,a^3\,b^4\,f\,g\,z-9\,a^2\,b^5\,d\,f\,z-9\,a^2\,b^5\,c\,g\,z+9\,a^4\,b^3\,h^2\,z+9\,a^2\,b^5\,e^2\,z-3\,a^5\,b\,f\,g\,h+3\,a^4\,b^2\,e\,f\,g+3\,a^4\,b^2\,d\,f\,h+3\,a^4\,b^2\,c\,g\,h-3\,a^3\,b^3\,d\,e\,f-3\,a^3\,b^3\,c\,e\,g-3\,a^3\,b^3\,c\,d\,h+3\,a^2\,b^4\,c\,d\,e+3\,a^5\,b\,e\,h^2-3\,a^4\,b^2\,e^2\,h-3\,a^4\,b^2\,d\,g^2+3\,a^3\,b^3\,d^2\,g+3\,a^3\,b^3\,c\,f^2-3\,a^2\,b^4\,c^2\,f+a^3\,b^3\,e^3+a^5\,b\,g^3+a\,b^5\,c^3-a^4\,b^2\,f^3-a^2\,b^4\,d^3-a^6\,h^3,z,k\right)\,\left(\frac{6\,a^2\,b^4\,e-6\,a^3\,b^3\,h}{b^4}+\frac{x\,\left(3\,a^2\,b^3\,f-3\,a\,b^4\,c\right)}{b^3}+\mathrm{root}\left(27\,b^9\,z^3+27\,a\,b^7\,e\,z^2-27\,a^2\,b^6\,h\,z^2+9\,a\,b^6\,c\,d\,z-18\,a^3\,b^4\,e\,h\,z+9\,a^3\,b^4\,f\,g\,z-9\,a^2\,b^5\,d\,f\,z-9\,a^2\,b^5\,c\,g\,z+9\,a^4\,b^3\,h^2\,z+9\,a^2\,b^5\,e^2\,z-3\,a^5\,b\,f\,g\,h+3\,a^4\,b^2\,e\,f\,g+3\,a^4\,b^2\,d\,f\,h+3\,a^4\,b^2\,c\,g\,h-3\,a^3\,b^3\,d\,e\,f-3\,a^3\,b^3\,c\,e\,g-3\,a^3\,b^3\,c\,d\,h+3\,a^2\,b^4\,c\,d\,e+3\,a^5\,b\,e\,h^2-3\,a^4\,b^2\,e^2\,h-3\,a^4\,b^2\,d\,g^2+3\,a^3\,b^3\,d^2\,g+3\,a^3\,b^3\,c\,f^2-3\,a^2\,b^4\,c^2\,f+a^3\,b^3\,e^3+a^5\,b\,g^3+a\,b^5\,c^3-a^4\,b^2\,f^3-a^2\,b^4\,d^3-a^6\,h^3,z,k\right)\,a\,b^2\,9\right)+\frac{a^5\,h^2+a^3\,b^2\,e^2-2\,a^4\,b\,e\,h+a^4\,b\,f\,g+a^2\,b^3\,c\,d-a^3\,b^2\,c\,g-a^3\,b^2\,d\,f}{b^4}+\frac{x\,\left(a^4\,g^2+a^2\,b^2\,d^2-a^4\,f\,h+a^3\,b\,c\,h-2\,a^3\,b\,d\,g+a^3\,b\,e\,f-a^2\,b^2\,c\,e\right)}{b^3}\right)\,\mathrm{root}\left(27\,b^9\,z^3+27\,a\,b^7\,e\,z^2-27\,a^2\,b^6\,h\,z^2+9\,a\,b^6\,c\,d\,z-18\,a^3\,b^4\,e\,h\,z+9\,a^3\,b^4\,f\,g\,z-9\,a^2\,b^5\,d\,f\,z-9\,a^2\,b^5\,c\,g\,z+9\,a^4\,b^3\,h^2\,z+9\,a^2\,b^5\,e^2\,z-3\,a^5\,b\,f\,g\,h+3\,a^4\,b^2\,e\,f\,g+3\,a^4\,b^2\,d\,f\,h+3\,a^4\,b^2\,c\,g\,h-3\,a^3\,b^3\,d\,e\,f-3\,a^3\,b^3\,c\,e\,g-3\,a^3\,b^3\,c\,d\,h+3\,a^2\,b^4\,c\,d\,e+3\,a^5\,b\,e\,h^2-3\,a^4\,b^2\,e^2\,h-3\,a^4\,b^2\,d\,g^2+3\,a^3\,b^3\,d^2\,g+3\,a^3\,b^3\,c\,f^2-3\,a^2\,b^4\,c^2\,f+a^3\,b^3\,e^3+a^5\,b\,g^3+a\,b^5\,c^3-a^4\,b^2\,f^3-a^2\,b^4\,d^3-a^6\,h^3,z,k\right)\right)+x\,\left(\frac{c}{b}-\frac{a\,f}{b^2}\right)+\frac{f\,x^4}{4\,b}+\frac{g\,x^5}{5\,b}+\frac{h\,x^6}{6\,b}","Not used",1,"x^2*(d/(2*b) - (a*g)/(2*b^2)) + x^3*(e/(3*b) - (a*h)/(3*b^2)) + symsum(log(root(27*b^9*z^3 + 27*a*b^7*e*z^2 - 27*a^2*b^6*h*z^2 + 9*a*b^6*c*d*z - 18*a^3*b^4*e*h*z + 9*a^3*b^4*f*g*z - 9*a^2*b^5*d*f*z - 9*a^2*b^5*c*g*z + 9*a^4*b^3*h^2*z + 9*a^2*b^5*e^2*z - 3*a^5*b*f*g*h + 3*a^4*b^2*e*f*g + 3*a^4*b^2*d*f*h + 3*a^4*b^2*c*g*h - 3*a^3*b^3*d*e*f - 3*a^3*b^3*c*e*g - 3*a^3*b^3*c*d*h + 3*a^2*b^4*c*d*e + 3*a^5*b*e*h^2 - 3*a^4*b^2*e^2*h - 3*a^4*b^2*d*g^2 + 3*a^3*b^3*d^2*g + 3*a^3*b^3*c*f^2 - 3*a^2*b^4*c^2*f + a^3*b^3*e^3 + a^5*b*g^3 + a*b^5*c^3 - a^4*b^2*f^3 - a^2*b^4*d^3 - a^6*h^3, z, k)*((6*a^2*b^4*e - 6*a^3*b^3*h)/b^4 + (x*(3*a^2*b^3*f - 3*a*b^4*c))/b^3 + 9*root(27*b^9*z^3 + 27*a*b^7*e*z^2 - 27*a^2*b^6*h*z^2 + 9*a*b^6*c*d*z - 18*a^3*b^4*e*h*z + 9*a^3*b^4*f*g*z - 9*a^2*b^5*d*f*z - 9*a^2*b^5*c*g*z + 9*a^4*b^3*h^2*z + 9*a^2*b^5*e^2*z - 3*a^5*b*f*g*h + 3*a^4*b^2*e*f*g + 3*a^4*b^2*d*f*h + 3*a^4*b^2*c*g*h - 3*a^3*b^3*d*e*f - 3*a^3*b^3*c*e*g - 3*a^3*b^3*c*d*h + 3*a^2*b^4*c*d*e + 3*a^5*b*e*h^2 - 3*a^4*b^2*e^2*h - 3*a^4*b^2*d*g^2 + 3*a^3*b^3*d^2*g + 3*a^3*b^3*c*f^2 - 3*a^2*b^4*c^2*f + a^3*b^3*e^3 + a^5*b*g^3 + a*b^5*c^3 - a^4*b^2*f^3 - a^2*b^4*d^3 - a^6*h^3, z, k)*a*b^2) + (a^5*h^2 + a^3*b^2*e^2 - 2*a^4*b*e*h + a^4*b*f*g + a^2*b^3*c*d - a^3*b^2*c*g - a^3*b^2*d*f)/b^4 + (x*(a^4*g^2 + a^2*b^2*d^2 - a^4*f*h + a^3*b*c*h - 2*a^3*b*d*g + a^3*b*e*f - a^2*b^2*c*e))/b^3)*root(27*b^9*z^3 + 27*a*b^7*e*z^2 - 27*a^2*b^6*h*z^2 + 9*a*b^6*c*d*z - 18*a^3*b^4*e*h*z + 9*a^3*b^4*f*g*z - 9*a^2*b^5*d*f*z - 9*a^2*b^5*c*g*z + 9*a^4*b^3*h^2*z + 9*a^2*b^5*e^2*z - 3*a^5*b*f*g*h + 3*a^4*b^2*e*f*g + 3*a^4*b^2*d*f*h + 3*a^4*b^2*c*g*h - 3*a^3*b^3*d*e*f - 3*a^3*b^3*c*e*g - 3*a^3*b^3*c*d*h + 3*a^2*b^4*c*d*e + 3*a^5*b*e*h^2 - 3*a^4*b^2*e^2*h - 3*a^4*b^2*d*g^2 + 3*a^3*b^3*d^2*g + 3*a^3*b^3*c*f^2 - 3*a^2*b^4*c^2*f + a^3*b^3*e^3 + a^5*b*g^3 + a*b^5*c^3 - a^4*b^2*f^3 - a^2*b^4*d^3 - a^6*h^3, z, k), k, 1, 3) + x*(c/b - (a*f)/b^2) + (f*x^4)/(4*b) + (g*x^5)/(5*b) + (h*x^6)/(6*b)","B"
405,1,1170,294,5.022862,"\text{Not used}","int((x^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3),x)","x^2\,\left(\frac{e}{2\,b}-\frac{a\,h}{2\,b^2}\right)+\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,b^8\,z^3+27\,a\,b^6\,f\,z^2-27\,b^7\,c\,z^2-18\,a\,b^5\,c\,f\,z+9\,a\,b^5\,d\,e\,z+9\,a^3\,b^3\,g\,h\,z-9\,a^2\,b^4\,e\,g\,z-9\,a^2\,b^4\,d\,h\,z+9\,a^2\,b^4\,f^2\,z+9\,b^6\,c^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3,z,k\right)\,\left(\frac{6\,a^2\,b^3\,f-6\,a\,b^4\,c}{b^3}+\frac{x\,\left(3\,a^2\,b^3\,g-3\,a\,b^4\,d\right)}{b^3}+\mathrm{root}\left(27\,b^8\,z^3+27\,a\,b^6\,f\,z^2-27\,b^7\,c\,z^2-18\,a\,b^5\,c\,f\,z+9\,a\,b^5\,d\,e\,z+9\,a^3\,b^3\,g\,h\,z-9\,a^2\,b^4\,e\,g\,z-9\,a^2\,b^4\,d\,h\,z+9\,a^2\,b^4\,f^2\,z+9\,b^6\,c^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3,z,k\right)\,a\,b^2\,9\right)+\frac{a\,b^3\,c^2+a^3\,b\,f^2+a^4\,g\,h-a^3\,b\,d\,h-a^3\,b\,e\,g-2\,a^2\,b^2\,c\,f+a^2\,b^2\,d\,e}{b^3}+\frac{x\,\left(a^4\,h^2+a^2\,b^2\,e^2+a\,b^3\,c\,d-2\,a^3\,b\,e\,h+a^3\,b\,f\,g-a^2\,b^2\,c\,g-a^2\,b^2\,d\,f\right)}{b^3}\right)\,\mathrm{root}\left(27\,b^8\,z^3+27\,a\,b^6\,f\,z^2-27\,b^7\,c\,z^2-18\,a\,b^5\,c\,f\,z+9\,a\,b^5\,d\,e\,z+9\,a^3\,b^3\,g\,h\,z-9\,a^2\,b^4\,e\,g\,z-9\,a^2\,b^4\,d\,h\,z+9\,a^2\,b^4\,f^2\,z+9\,b^6\,c^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3,z,k\right)\right)+x\,\left(\frac{d}{b}-\frac{a\,g}{b^2}\right)+\frac{f\,x^3}{3\,b}+\frac{g\,x^4}{4\,b}+\frac{h\,x^5}{5\,b}","Not used",1,"x^2*(e/(2*b) - (a*h)/(2*b^2)) + symsum(log(root(27*b^8*z^3 + 27*a*b^6*f*z^2 - 27*b^7*c*z^2 - 18*a*b^5*c*f*z + 9*a*b^5*d*e*z + 9*a^3*b^3*g*h*z - 9*a^2*b^4*e*g*z - 9*a^2*b^4*d*h*z + 9*a^2*b^4*f^2*z + 9*b^6*c^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3, z, k)*((6*a^2*b^3*f - 6*a*b^4*c)/b^3 + (x*(3*a^2*b^3*g - 3*a*b^4*d))/b^3 + 9*root(27*b^8*z^3 + 27*a*b^6*f*z^2 - 27*b^7*c*z^2 - 18*a*b^5*c*f*z + 9*a*b^5*d*e*z + 9*a^3*b^3*g*h*z - 9*a^2*b^4*e*g*z - 9*a^2*b^4*d*h*z + 9*a^2*b^4*f^2*z + 9*b^6*c^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3, z, k)*a*b^2) + (a*b^3*c^2 + a^3*b*f^2 + a^4*g*h - a^3*b*d*h - a^3*b*e*g - 2*a^2*b^2*c*f + a^2*b^2*d*e)/b^3 + (x*(a^4*h^2 + a^2*b^2*e^2 + a*b^3*c*d - 2*a^3*b*e*h + a^3*b*f*g - a^2*b^2*c*g - a^2*b^2*d*f))/b^3)*root(27*b^8*z^3 + 27*a*b^6*f*z^2 - 27*b^7*c*z^2 - 18*a*b^5*c*f*z + 9*a*b^5*d*e*z + 9*a^3*b^3*g*h*z - 9*a^2*b^4*e*g*z - 9*a^2*b^4*d*h*z + 9*a^2*b^4*f^2*z + 9*b^6*c^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3, z, k), k, 1, 3) + x*(d/b - (a*g)/b^2) + (f*x^3)/(3*b) + (g*x^4)/(4*b) + (h*x^5)/(5*b)","B"
406,1,1161,275,4.988948,"\text{Not used}","int((x*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3),x)","\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(27\,a\,b^7\,z^3-27\,a\,b^6\,d\,z^2+27\,a^2\,b^5\,g\,z^2-9\,a\,b^5\,c\,e\,z-9\,a^3\,b^3\,f\,h\,z-18\,a^2\,b^4\,d\,g\,z+9\,a^2\,b^4\,e\,f\,z+9\,a^2\,b^4\,c\,h\,z+9\,a\,b^5\,d^2\,z+9\,a^3\,b^3\,g^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3,z,k\right)\,\left(\frac{6\,a^2\,b^2\,g-6\,a\,b^3\,d}{b^2}+\frac{x\,\left(3\,a^2\,b^2\,h-3\,a\,b^3\,e\right)}{b^2}+\mathrm{root}\left(27\,a\,b^7\,z^3-27\,a\,b^6\,d\,z^2+27\,a^2\,b^5\,g\,z^2-9\,a\,b^5\,c\,e\,z-9\,a^3\,b^3\,f\,h\,z-18\,a^2\,b^4\,d\,g\,z+9\,a^2\,b^4\,e\,f\,z+9\,a^2\,b^4\,c\,h\,z+9\,a\,b^5\,d^2\,z+9\,a^3\,b^3\,g^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3,z,k\right)\,a\,b^2\,9\right)+\frac{a^3\,g^2+a\,b^2\,d^2-a^3\,f\,h-a\,b^2\,c\,e+a^2\,b\,c\,h-2\,a^2\,b\,d\,g+a^2\,b\,e\,f}{b^2}+\frac{x\,\left(b^3\,c^2+a^2\,b\,f^2+a^3\,g\,h-2\,a\,b^2\,c\,f+a\,b^2\,d\,e-a^2\,b\,d\,h-a^2\,b\,e\,g\right)}{b^2}\right)\,\mathrm{root}\left(27\,a\,b^7\,z^3-27\,a\,b^6\,d\,z^2+27\,a^2\,b^5\,g\,z^2-9\,a\,b^5\,c\,e\,z-9\,a^3\,b^3\,f\,h\,z-18\,a^2\,b^4\,d\,g\,z+9\,a^2\,b^4\,e\,f\,z+9\,a^2\,b^4\,c\,h\,z+9\,a\,b^5\,d^2\,z+9\,a^3\,b^3\,g^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3,z,k\right)\right)+x\,\left(\frac{e}{b}-\frac{a\,h}{b^2}\right)+\frac{f\,x^2}{2\,b}+\frac{g\,x^3}{3\,b}+\frac{h\,x^4}{4\,b}","Not used",1,"symsum(log(root(27*a*b^7*z^3 - 27*a*b^6*d*z^2 + 27*a^2*b^5*g*z^2 - 9*a*b^5*c*e*z - 9*a^3*b^3*f*h*z - 18*a^2*b^4*d*g*z + 9*a^2*b^4*e*f*z + 9*a^2*b^4*c*h*z + 9*a*b^5*d^2*z + 9*a^3*b^3*g^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3, z, k)*((6*a^2*b^2*g - 6*a*b^3*d)/b^2 + (x*(3*a^2*b^2*h - 3*a*b^3*e))/b^2 + 9*root(27*a*b^7*z^3 - 27*a*b^6*d*z^2 + 27*a^2*b^5*g*z^2 - 9*a*b^5*c*e*z - 9*a^3*b^3*f*h*z - 18*a^2*b^4*d*g*z + 9*a^2*b^4*e*f*z + 9*a^2*b^4*c*h*z + 9*a*b^5*d^2*z + 9*a^3*b^3*g^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3, z, k)*a*b^2) + (a^3*g^2 + a*b^2*d^2 - a^3*f*h - a*b^2*c*e + a^2*b*c*h - 2*a^2*b*d*g + a^2*b*e*f)/b^2 + (x*(b^3*c^2 + a^2*b*f^2 + a^3*g*h - 2*a*b^2*c*f + a*b^2*d*e - a^2*b*d*h - a^2*b*e*g))/b^2)*root(27*a*b^7*z^3 - 27*a*b^6*d*z^2 + 27*a^2*b^5*g*z^2 - 9*a*b^5*c*e*z - 9*a^3*b^3*f*h*z - 18*a^2*b^4*d*g*z + 9*a^2*b^4*e*f*z + 9*a^2*b^4*c*h*z + 9*a*b^5*d^2*z + 9*a^3*b^3*g^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3, z, k), k, 1, 3) + x*(e/b - (a*h)/b^2) + (f*x^2)/(2*b) + (g*x^3)/(3*b) + (h*x^4)/(4*b)","B"
407,1,1150,259,5.033430,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3),x)","\left(\sum _{k=1}^3\ln\left(\frac{a^3\,h^2+a\,b^2\,e^2+b^3\,c\,d-a\,b^2\,c\,g-a\,b^2\,d\,f-2\,a^2\,b\,e\,h+a^2\,b\,f\,g}{b^2}+\mathrm{root}\left(27\,a^2\,b^6\,z^3+27\,a^3\,b^4\,h\,z^2-27\,a^2\,b^5\,e\,z^2+9\,a\,b^5\,c\,d\,z-18\,a^3\,b^3\,e\,h\,z+9\,a^3\,b^3\,f\,g\,z-9\,a^2\,b^4\,d\,f\,z-9\,a^2\,b^4\,c\,g\,z+9\,a^4\,b^2\,h^2\,z+9\,a^2\,b^4\,e^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3,z,k\right)\,\left(\frac{6\,a^2\,b^2\,h-6\,a\,b^3\,e}{b^2}+\frac{x\,\left(3\,b^3\,c-3\,a\,b^2\,f\right)}{b}+\mathrm{root}\left(27\,a^2\,b^6\,z^3+27\,a^3\,b^4\,h\,z^2-27\,a^2\,b^5\,e\,z^2+9\,a\,b^5\,c\,d\,z-18\,a^3\,b^3\,e\,h\,z+9\,a^3\,b^3\,f\,g\,z-9\,a^2\,b^4\,d\,f\,z-9\,a^2\,b^4\,c\,g\,z+9\,a^4\,b^2\,h^2\,z+9\,a^2\,b^4\,e^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3,z,k\right)\,a\,b^2\,9\right)+\frac{x\,\left(b^2\,d^2+a^2\,g^2-b^2\,c\,e-a^2\,f\,h+a\,b\,c\,h-2\,a\,b\,d\,g+a\,b\,e\,f\right)}{b}\right)\,\mathrm{root}\left(27\,a^2\,b^6\,z^3+27\,a^3\,b^4\,h\,z^2-27\,a^2\,b^5\,e\,z^2+9\,a\,b^5\,c\,d\,z-18\,a^3\,b^3\,e\,h\,z+9\,a^3\,b^3\,f\,g\,z-9\,a^2\,b^4\,d\,f\,z-9\,a^2\,b^4\,c\,g\,z+9\,a^4\,b^2\,h^2\,z+9\,a^2\,b^4\,e^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3,z,k\right)\right)+\frac{g\,x^2}{2\,b}+\frac{h\,x^3}{3\,b}+\frac{f\,x}{b}","Not used",1,"symsum(log((a^3*h^2 + a*b^2*e^2 + b^3*c*d - a*b^2*c*g - a*b^2*d*f - 2*a^2*b*e*h + a^2*b*f*g)/b^2 + root(27*a^2*b^6*z^3 + 27*a^3*b^4*h*z^2 - 27*a^2*b^5*e*z^2 + 9*a*b^5*c*d*z - 18*a^3*b^3*e*h*z + 9*a^3*b^3*f*g*z - 9*a^2*b^4*d*f*z - 9*a^2*b^4*c*g*z + 9*a^4*b^2*h^2*z + 9*a^2*b^4*e^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3, z, k)*((6*a^2*b^2*h - 6*a*b^3*e)/b^2 + (x*(3*b^3*c - 3*a*b^2*f))/b + 9*root(27*a^2*b^6*z^3 + 27*a^3*b^4*h*z^2 - 27*a^2*b^5*e*z^2 + 9*a*b^5*c*d*z - 18*a^3*b^3*e*h*z + 9*a^3*b^3*f*g*z - 9*a^2*b^4*d*f*z - 9*a^2*b^4*c*g*z + 9*a^4*b^2*h^2*z + 9*a^2*b^4*e^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3, z, k)*a*b^2) + (x*(b^2*d^2 + a^2*g^2 - b^2*c*e - a^2*f*h + a*b*c*h - 2*a*b*d*g + a*b*e*f))/b)*root(27*a^2*b^6*z^3 + 27*a^3*b^4*h*z^2 - 27*a^2*b^5*e*z^2 + 9*a*b^5*c*d*z - 18*a^3*b^3*e*h*z + 9*a^3*b^3*f*g*z - 9*a^2*b^4*d*f*z - 9*a^2*b^4*c*g*z + 9*a^4*b^2*h^2*z + 9*a^2*b^4*e^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3, z, k), k, 1, 3) + (g*x^2)/(2*b) + (h*x^3)/(3*b) + (f*x)/b","B"
408,1,1731,258,5.097089,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x*(a + b*x^3)),x)","\left(\sum _{k=1}^3\ln\left(b^2\,c\,d^2-\mathrm{root}\left(27\,a^3\,b^5\,z^3-27\,a^3\,b^4\,f\,z^2+27\,a^2\,b^5\,c\,z^2+9\,a^4\,b^2\,g\,h\,z-9\,a^3\,b^3\,e\,g\,z-9\,a^3\,b^3\,d\,h\,z-18\,a^2\,b^4\,c\,f\,z+9\,a^2\,b^4\,d\,e\,z+9\,a\,b^5\,c^2\,z+9\,a^3\,b^3\,f^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3,z,k\right)\,\left(a^3\,g^2-\mathrm{root}\left(27\,a^3\,b^5\,z^3-27\,a^3\,b^4\,f\,z^2+27\,a^2\,b^5\,c\,z^2+9\,a^4\,b^2\,g\,h\,z-9\,a^3\,b^3\,e\,g\,z-9\,a^3\,b^3\,d\,h\,z-18\,a^2\,b^4\,c\,f\,z+9\,a^2\,b^4\,d\,e\,z+9\,a\,b^5\,c^2\,z+9\,a^3\,b^3\,f^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3,z,k\right)\,\left(\frac{x\,\left(33\,a^2\,b^4\,f-24\,a\,b^5\,c\right)}{b^2}+3\,a^2\,b^2\,e-3\,a^3\,b\,h-\mathrm{root}\left(27\,a^3\,b^5\,z^3-27\,a^3\,b^4\,f\,z^2+27\,a^2\,b^5\,c\,z^2+9\,a^4\,b^2\,g\,h\,z-9\,a^3\,b^3\,e\,g\,z-9\,a^3\,b^3\,d\,h\,z-18\,a^2\,b^4\,c\,f\,z+9\,a^2\,b^4\,d\,e\,z+9\,a\,b^5\,c^2\,z+9\,a^3\,b^3\,f^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3,z,k\right)\,a^2\,b^3\,x\,36\right)+\frac{x\,\left(4\,b^5\,c^2+10\,a^2\,b^3\,f^2-14\,a\,b^4\,c\,f+10\,a\,b^4\,d\,e-10\,a^2\,b^3\,d\,h-10\,a^2\,b^3\,e\,g+10\,a^3\,b^2\,g\,h\right)}{b^2}+a\,b^2\,d^2-a^3\,f\,h+2\,a\,b^2\,c\,e-2\,a^2\,b\,c\,h-2\,a^2\,b\,d\,g+a^2\,b\,e\,f\right)-b^2\,c^2\,e+a^2\,c\,g^2+\frac{x\,\left(a^4\,h^3-3\,a^3\,b\,e\,h^2+3\,a^3\,b\,f\,g\,h-a^3\,b\,g^3-2\,a^2\,b^2\,c\,g\,h-3\,a^2\,b^2\,d\,f\,h+3\,a^2\,b^2\,d\,g^2+3\,a^2\,b^2\,e^2\,h-3\,a^2\,b^2\,e\,f\,g+a^2\,b^2\,f^3+2\,a\,b^3\,c\,d\,h+2\,a\,b^3\,c\,e\,g-2\,a\,b^3\,c\,f^2-3\,a\,b^3\,d^2\,g+3\,a\,b^3\,d\,e\,f-a\,b^3\,e^3+b^4\,c^2\,f-2\,b^4\,c\,d\,e+b^4\,d^3\right)}{b^2}+a\,b\,c^2\,h-a^2\,c\,f\,h-2\,a\,b\,c\,d\,g+a\,b\,c\,e\,f\right)\,\mathrm{root}\left(27\,a^3\,b^5\,z^3-27\,a^3\,b^4\,f\,z^2+27\,a^2\,b^5\,c\,z^2+9\,a^4\,b^2\,g\,h\,z-9\,a^3\,b^3\,e\,g\,z-9\,a^3\,b^3\,d\,h\,z-18\,a^2\,b^4\,c\,f\,z+9\,a^2\,b^4\,d\,e\,z+9\,a\,b^5\,c^2\,z+9\,a^3\,b^3\,f^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3,z,k\right)\right)+\frac{h\,x^2}{2\,b}+\frac{c\,\ln\left(x\right)}{a}+\frac{g\,x}{b}","Not used",1,"symsum(log(b^2*c*d^2 - root(27*a^3*b^5*z^3 - 27*a^3*b^4*f*z^2 + 27*a^2*b^5*c*z^2 + 9*a^4*b^2*g*h*z - 9*a^3*b^3*e*g*z - 9*a^3*b^3*d*h*z - 18*a^2*b^4*c*f*z + 9*a^2*b^4*d*e*z + 9*a*b^5*c^2*z + 9*a^3*b^3*f^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3, z, k)*(a^3*g^2 - root(27*a^3*b^5*z^3 - 27*a^3*b^4*f*z^2 + 27*a^2*b^5*c*z^2 + 9*a^4*b^2*g*h*z - 9*a^3*b^3*e*g*z - 9*a^3*b^3*d*h*z - 18*a^2*b^4*c*f*z + 9*a^2*b^4*d*e*z + 9*a*b^5*c^2*z + 9*a^3*b^3*f^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3, z, k)*((x*(33*a^2*b^4*f - 24*a*b^5*c))/b^2 + 3*a^2*b^2*e - 3*a^3*b*h - 36*root(27*a^3*b^5*z^3 - 27*a^3*b^4*f*z^2 + 27*a^2*b^5*c*z^2 + 9*a^4*b^2*g*h*z - 9*a^3*b^3*e*g*z - 9*a^3*b^3*d*h*z - 18*a^2*b^4*c*f*z + 9*a^2*b^4*d*e*z + 9*a*b^5*c^2*z + 9*a^3*b^3*f^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3, z, k)*a^2*b^3*x) + (x*(4*b^5*c^2 + 10*a^2*b^3*f^2 - 14*a*b^4*c*f + 10*a*b^4*d*e - 10*a^2*b^3*d*h - 10*a^2*b^3*e*g + 10*a^3*b^2*g*h))/b^2 + a*b^2*d^2 - a^3*f*h + 2*a*b^2*c*e - 2*a^2*b*c*h - 2*a^2*b*d*g + a^2*b*e*f) - b^2*c^2*e + a^2*c*g^2 + (x*(b^4*d^3 + a^4*h^3 - a*b^3*e^3 - a^3*b*g^3 + b^4*c^2*f + a^2*b^2*f^3 + 3*a^2*b^2*d*g^2 + 3*a^2*b^2*e^2*h - 2*b^4*c*d*e - 2*a*b^3*c*f^2 - 3*a*b^3*d^2*g - 3*a^3*b*e*h^2 - 2*a^2*b^2*c*g*h - 3*a^2*b^2*d*f*h - 3*a^2*b^2*e*f*g + 2*a*b^3*c*d*h + 2*a*b^3*c*e*g + 3*a*b^3*d*e*f + 3*a^3*b*f*g*h))/b^2 + a*b*c^2*h - a^2*c*f*h - 2*a*b*c*d*g + a*b*c*e*f)*root(27*a^3*b^5*z^3 - 27*a^3*b^4*f*z^2 + 27*a^2*b^5*c*z^2 + 9*a^4*b^2*g*h*z - 9*a^3*b^3*e*g*z - 9*a^3*b^3*d*h*z - 18*a^2*b^4*c*f*z + 9*a^2*b^4*d*e*z + 9*a*b^5*c^2*z + 9*a^3*b^3*f^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3, z, k), k, 1, 3) + (h*x^2)/(2*b) + (c*log(x))/a + (g*x)/b","B"
409,1,1802,253,5.087011,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^2*(a + b*x^3)),x)","\left(\sum _{k=1}^3\ln\left(\frac{a^3\,d\,h^2-2\,a^2\,b\,d\,e\,h+f\,g\,a^2\,b\,d-f\,a\,b^2\,d^2+a\,b^2\,d\,e^2-c\,g\,a\,b^2\,d+c\,b^3\,d^2}{a}-\mathrm{root}\left(27\,a^4\,b^4\,z^3-27\,a^4\,b^3\,g\,z^2+27\,a^3\,b^4\,d\,z^2-9\,a^4\,b^2\,f\,h\,z-18\,a^3\,b^3\,d\,g\,z+9\,a^3\,b^3\,e\,f\,z+9\,a^3\,b^3\,c\,h\,z-9\,a^2\,b^4\,c\,e\,z+9\,a^4\,b^2\,g^2\,z+9\,a^2\,b^4\,d^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3,z,k\right)\,\left(\mathrm{root}\left(27\,a^4\,b^4\,z^3-27\,a^4\,b^3\,g\,z^2+27\,a^3\,b^4\,d\,z^2-9\,a^4\,b^2\,f\,h\,z-18\,a^3\,b^3\,d\,g\,z+9\,a^3\,b^3\,e\,f\,z+9\,a^3\,b^3\,c\,h\,z-9\,a^2\,b^4\,c\,e\,z+9\,a^4\,b^2\,g^2\,z+9\,a^2\,b^4\,d^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3,z,k\right)\,\left(\frac{3\,a^2\,b^3\,c-3\,a^3\,b^2\,f}{a}+\frac{x\,\left(24\,a^3\,b^4\,d-33\,a^4\,b^3\,g\right)}{a^2\,b}+\mathrm{root}\left(27\,a^4\,b^4\,z^3-27\,a^4\,b^3\,g\,z^2+27\,a^3\,b^4\,d\,z^2-9\,a^4\,b^2\,f\,h\,z-18\,a^3\,b^3\,d\,g\,z+9\,a^3\,b^3\,e\,f\,z+9\,a^3\,b^3\,c\,h\,z-9\,a^2\,b^4\,c\,e\,z+9\,a^4\,b^2\,g^2\,z+9\,a^2\,b^4\,d^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3,z,k\right)\,a^2\,b^3\,x\,36\right)+\frac{a^4\,h^2+a^2\,b^2\,e^2-2\,a\,b^3\,c\,d-2\,a^3\,b\,e\,h+a^3\,b\,f\,g-a^2\,b^2\,c\,g+2\,a^2\,b^2\,d\,f}{a}+\frac{x\,\left(4\,a^2\,b^4\,d^2+10\,a^4\,b^2\,g^2-10\,a^2\,b^4\,c\,e+10\,a^3\,b^3\,c\,h-14\,a^3\,b^3\,d\,g+10\,a^3\,b^3\,e\,f-10\,a^4\,b^2\,f\,h\right)}{a^2\,b}\right)+\frac{x\,\left(-a^5\,h^3+3\,a^4\,b\,e\,h^2-3\,a^4\,b\,f\,g\,h+a^4\,b\,g^3+3\,a^3\,b^2\,c\,g\,h+2\,a^3\,b^2\,d\,f\,h-2\,a^3\,b^2\,d\,g^2-3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,e\,f\,g-a^3\,b^2\,f^3-2\,a^2\,b^3\,c\,d\,h-3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,f^2+a^2\,b^3\,d^2\,g-2\,a^2\,b^3\,d\,e\,f+a^2\,b^3\,e^3-3\,a\,b^4\,c^2\,f+2\,a\,b^4\,c\,d\,e+b^5\,c^3\right)}{a^2\,b}\right)\,\mathrm{root}\left(27\,a^4\,b^4\,z^3-27\,a^4\,b^3\,g\,z^2+27\,a^3\,b^4\,d\,z^2-9\,a^4\,b^2\,f\,h\,z-18\,a^3\,b^3\,d\,g\,z+9\,a^3\,b^3\,e\,f\,z+9\,a^3\,b^3\,c\,h\,z-9\,a^2\,b^4\,c\,e\,z+9\,a^4\,b^2\,g^2\,z+9\,a^2\,b^4\,d^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3,z,k\right)\right)+\frac{h\,x}{b}-\frac{c}{a\,x}+\frac{d\,\ln\left(x\right)}{a}","Not used",1,"symsum(log((b^3*c*d^2 + a^3*d*h^2 + a*b^2*d*e^2 - a*b^2*d^2*f - a*b^2*c*d*g - 2*a^2*b*d*e*h + a^2*b*d*f*g)/a - root(27*a^4*b^4*z^3 - 27*a^4*b^3*g*z^2 + 27*a^3*b^4*d*z^2 - 9*a^4*b^2*f*h*z - 18*a^3*b^3*d*g*z + 9*a^3*b^3*e*f*z + 9*a^3*b^3*c*h*z - 9*a^2*b^4*c*e*z + 9*a^4*b^2*g^2*z + 9*a^2*b^4*d^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3, z, k)*(root(27*a^4*b^4*z^3 - 27*a^4*b^3*g*z^2 + 27*a^3*b^4*d*z^2 - 9*a^4*b^2*f*h*z - 18*a^3*b^3*d*g*z + 9*a^3*b^3*e*f*z + 9*a^3*b^3*c*h*z - 9*a^2*b^4*c*e*z + 9*a^4*b^2*g^2*z + 9*a^2*b^4*d^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3, z, k)*((3*a^2*b^3*c - 3*a^3*b^2*f)/a + (x*(24*a^3*b^4*d - 33*a^4*b^3*g))/(a^2*b) + 36*root(27*a^4*b^4*z^3 - 27*a^4*b^3*g*z^2 + 27*a^3*b^4*d*z^2 - 9*a^4*b^2*f*h*z - 18*a^3*b^3*d*g*z + 9*a^3*b^3*e*f*z + 9*a^3*b^3*c*h*z - 9*a^2*b^4*c*e*z + 9*a^4*b^2*g^2*z + 9*a^2*b^4*d^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3, z, k)*a^2*b^3*x) + (a^4*h^2 + a^2*b^2*e^2 - 2*a*b^3*c*d - 2*a^3*b*e*h + a^3*b*f*g - a^2*b^2*c*g + 2*a^2*b^2*d*f)/a + (x*(4*a^2*b^4*d^2 + 10*a^4*b^2*g^2 - 10*a^2*b^4*c*e + 10*a^3*b^3*c*h - 14*a^3*b^3*d*g + 10*a^3*b^3*e*f - 10*a^4*b^2*f*h))/(a^2*b)) + (x*(b^5*c^3 - a^5*h^3 + a^4*b*g^3 + a^2*b^3*e^3 - a^3*b^2*f^3 + 3*a^2*b^3*c*f^2 + a^2*b^3*d^2*g - 2*a^3*b^2*d*g^2 - 3*a^3*b^2*e^2*h - 3*a*b^4*c^2*f + 3*a^4*b*e*h^2 - 2*a^2*b^3*c*d*h - 3*a^2*b^3*c*e*g - 2*a^2*b^3*d*e*f + 3*a^3*b^2*c*g*h + 2*a^3*b^2*d*f*h + 3*a^3*b^2*e*f*g + 2*a*b^4*c*d*e - 3*a^4*b*f*g*h))/(a^2*b))*root(27*a^4*b^4*z^3 - 27*a^4*b^3*g*z^2 + 27*a^3*b^4*d*z^2 - 9*a^4*b^2*f*h*z - 18*a^3*b^3*d*g*z + 9*a^3*b^3*e*f*z + 9*a^3*b^3*c*h*z - 9*a^2*b^4*c*e*z + 9*a^4*b^2*g^2*z + 9*a^2*b^4*d^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3, z, k), k, 1, 3) + (h*x)/b - c/(a*x) + (d*log(x))/a","B"
410,1,6948,260,5.204868,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^3*(a + b*x^3)),x)","\left(\sum _{k=1}^3\ln\left(-\frac{b^5\,c^3\,x-a^5\,h^3\,x-a^2\,b^3\,d\,e^2+{\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)}^3\,a^5\,b^3\,x\,36-a^3\,b^2\,e\,f^2+a^3\,b^2\,e^2\,g-a^3\,b^2\,f^3\,x-a\,b^4\,c^2\,e-a\,b^4\,d^3\,x+a^4\,b\,g^3\,x+\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)\,a^2\,b^4\,c^2+{\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)}^2\,a^4\,b^3\,d\,3+\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)\,a^4\,b^2\,f^2-{\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)}^2\,a^5\,b^2\,g\,3+2\,a^2\,b^3\,c\,e\,f+a^3\,b^2\,d\,e\,h+\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)\,a^5\,b\,h^2\,x\,10-3\,a\,b^4\,c^2\,f\,x+2\,a^4\,b\,e\,h^2\,x+\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)\,a^3\,b^3\,e^2\,x\,4+{\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3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,g^3+b^5\,c^3,z,k\right)\,a^3\,b^3\,c\,g\,x\,10-\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)\,a^3\,b^3\,d\,f\,x\,10-\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)\,a^4\,b^2\,e\,h\,x\,14+\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)\,a^4\,b^2\,f\,g\,x\,10-3\,a^2\,b^3\,c\,d\,h\,x-2\,a^2\,b^3\,c\,e\,g\,x-2\,a^2\,b^3\,d\,e\,f\,x+3\,a^3\,b^2\,c\,g\,h\,x+3\,a^3\,b^2\,d\,f\,h\,x+2\,a^3\,b^2\,e\,f\,g\,x}{a^3}\right)\,\mathrm{root}\left(27\,a^5\,b^3\,z^3-27\,a^5\,b^2\,h\,z^2+27\,a^4\,b^3\,e\,z^2-18\,a^4\,b^2\,e\,h\,z+9\,a^4\,b^2\,f\,g\,z-9\,a^3\,b^3\,d\,f\,z-9\,a^3\,b^3\,c\,g\,z+9\,a^2\,b^4\,c\,d\,z+9\,a^5\,b\,h^2\,z+9\,a^3\,b^3\,e^2\,z-3\,a^4\,b\,f\,g\,h+3\,a\,b^4\,c\,d\,e+3\,a^3\,b^2\,e\,f\,g+3\,a^3\,b^2\,d\,f\,h+3\,a^3\,b^2\,c\,g\,h-3\,a^2\,b^3\,d\,e\,f-3\,a^2\,b^3\,c\,e\,g-3\,a^2\,b^3\,c\,d\,h+3\,a^4\,b\,e\,h^2-3\,a\,b^4\,c^2\,f-3\,a^3\,b^2\,e^2\,h-3\,a^3\,b^2\,d\,g^2+3\,a^2\,b^3\,d^2\,g+3\,a^2\,b^3\,c\,f^2-a^3\,b^2\,f^3-a\,b^4\,d^3-a^5\,h^3+a^2\,b^3\,e^3+a^4\,b\,g^3+b^5\,c^3,z,k\right)\right)-\frac{c}{2\,a\,x^2}-\frac{d}{a\,x}+\frac{e\,\ln\left(x\right)}{a}","Not used",1,"symsum(log(-(b^5*c^3*x - a^5*h^3*x - a^2*b^3*d*e^2 + 36*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)^3*a^5*b^3*x - a^3*b^2*e*f^2 + a^3*b^2*e^2*g - a^3*b^2*f^3*x - a*b^4*c^2*e - a*b^4*d^3*x + a^4*b*g^3*x + root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^2*b^4*c^2 + 3*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)^2*a^4*b^3*d + root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^4*b^2*f^2 - 3*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)^2*a^5*b^2*g + 2*a^2*b^3*c*e*f + a^3*b^2*d*e*h + 10*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^5*b*h^2*x - 3*a*b^4*c^2*f*x + 2*a^4*b*e*h^2*x + 4*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^3*b^3*e^2*x + 24*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)^2*a^4*b^3*e*x - 33*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)^2*a^5*b^2*h*x + 3*a^2*b^3*c*f^2*x + 3*a^2*b^3*d^2*g*x - 3*a^3*b^2*d*g^2*x - a^3*b^2*e^2*h*x + root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^5*b*g*h - a^4*b*e*g*h - 2*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^3*b^3*c*f - 2*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^3*b^3*d*e - root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^4*b^2*d*h + 2*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^4*b^2*e*g + 2*a*b^4*c*d*e*x - 3*a^4*b*f*g*h*x + 10*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^2*b^4*c*d*x - 10*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^3*b^3*c*g*x - 10*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^3*b^3*d*f*x - 14*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^4*b^2*e*h*x + 10*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k)*a^4*b^2*f*g*x - 3*a^2*b^3*c*d*h*x - 2*a^2*b^3*c*e*g*x - 2*a^2*b^3*d*e*f*x + 3*a^3*b^2*c*g*h*x + 3*a^3*b^2*d*f*h*x + 2*a^3*b^2*e*f*g*x)/a^3)*root(27*a^5*b^3*z^3 - 27*a^5*b^2*h*z^2 + 27*a^4*b^3*e*z^2 - 18*a^4*b^2*e*h*z + 9*a^4*b^2*f*g*z - 9*a^3*b^3*d*f*z - 9*a^3*b^3*c*g*z + 9*a^2*b^4*c*d*z + 9*a^5*b*h^2*z + 9*a^3*b^3*e^2*z - 3*a^4*b*f*g*h + 3*a*b^4*c*d*e + 3*a^3*b^2*e*f*g + 3*a^3*b^2*d*f*h + 3*a^3*b^2*c*g*h - 3*a^2*b^3*d*e*f - 3*a^2*b^3*c*e*g - 3*a^2*b^3*c*d*h + 3*a^4*b*e*h^2 - 3*a*b^4*c^2*f - 3*a^3*b^2*e^2*h - 3*a^3*b^2*d*g^2 + 3*a^2*b^3*d^2*g + 3*a^2*b^3*c*f^2 - a^3*b^2*f^3 - a*b^4*d^3 - a^5*h^3 + a^2*b^3*e^3 + a^4*b*g^3 + b^5*c^3, z, k), k, 1, 3) - c/(2*a*x^2) - d/(a*x) + (e*log(x))/a","B"
411,1,1842,276,5.870296,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^4*(a + b*x^3)),x)","\left(\sum _{k=1}^3\ln\left(-\frac{h\,a^3\,b^2\,f^2-a^3\,b^2\,f\,g^2-2\,h\,a^2\,b^3\,c\,f+a^2\,b^3\,c\,g^2+2\,a^2\,b^3\,d\,f\,g-e\,a^2\,b^3\,f^2+h\,a\,b^4\,c^2-2\,a\,b^4\,c\,d\,g+2\,e\,a\,b^4\,c\,f-a\,b^4\,d^2\,f-e\,b^5\,c^2+b^5\,c\,d^2}{a^3}-\mathrm{root}\left(27\,a^6\,b^2\,z^3+27\,a^5\,b^2\,f\,z^2-27\,a^4\,b^3\,c\,z^2+9\,a^5\,b\,g\,h\,z-9\,a^4\,b^2\,e\,g\,z-9\,a^4\,b^2\,d\,h\,z-18\,a^3\,b^3\,c\,f\,z+9\,a^3\,b^3\,d\,e\,z+9\,a^4\,b^2\,f^2\,z+9\,a^2\,b^4\,c^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3,z,k\right)\,\left(\frac{a^2\,b^4\,d^2+a^4\,b^2\,g^2+2\,a^2\,b^4\,c\,e-2\,a^3\,b^3\,c\,h-2\,a^3\,b^3\,d\,g-2\,a^3\,b^3\,e\,f+2\,a^4\,b^2\,f\,h}{a^3}+\mathrm{root}\left(27\,a^6\,b^2\,z^3+27\,a^5\,b^2\,f\,z^2-27\,a^4\,b^3\,c\,z^2+9\,a^5\,b\,g\,h\,z-9\,a^4\,b^2\,e\,g\,z-9\,a^4\,b^2\,d\,h\,z-18\,a^3\,b^3\,c\,f\,z+9\,a^3\,b^3\,d\,e\,z+9\,a^4\,b^2\,f^2\,z+9\,a^2\,b^4\,c^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3,z,k\right)\,\left(\frac{3\,a^4\,b^3\,e-3\,a^5\,b^2\,h}{a^3}-\frac{x\,\left(24\,a^3\,b^4\,c-24\,a^4\,b^3\,f\right)}{a^3}+\mathrm{root}\left(27\,a^6\,b^2\,z^3+27\,a^5\,b^2\,f\,z^2-27\,a^4\,b^3\,c\,z^2+9\,a^5\,b\,g\,h\,z-9\,a^4\,b^2\,e\,g\,z-9\,a^4\,b^2\,d\,h\,z-18\,a^3\,b^3\,c\,f\,z+9\,a^3\,b^3\,d\,e\,z+9\,a^4\,b^2\,f^2\,z+9\,a^2\,b^4\,c^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3,z,k\right)\,a^2\,b^3\,x\,36\right)+\frac{x\,\left(4\,a\,b^5\,c^2+4\,a^3\,b^3\,f^2-8\,a^2\,b^4\,c\,f+10\,a^2\,b^4\,d\,e-10\,a^3\,b^3\,d\,h-10\,a^3\,b^3\,e\,g+10\,a^4\,b^2\,g\,h\right)}{a^3}\right)-\frac{x\,\left(a^4\,b\,h^3-3\,a^3\,b^2\,e\,h^2-a^3\,b^2\,g^3+2\,f\,a^3\,b^2\,g\,h+3\,a^2\,b^3\,d\,g^2-2\,f\,a^2\,b^3\,d\,h+3\,a^2\,b^3\,e^2\,h-2\,f\,a^2\,b^3\,e\,g-2\,c\,a^2\,b^3\,g\,h-3\,a\,b^4\,d^2\,g+2\,f\,a\,b^4\,d\,e+2\,c\,a\,b^4\,d\,h-a\,b^4\,e^3+2\,c\,a\,b^4\,e\,g+b^5\,d^3-2\,c\,b^5\,d\,e\right)}{a^3}\right)\,\mathrm{root}\left(27\,a^6\,b^2\,z^3+27\,a^5\,b^2\,f\,z^2-27\,a^4\,b^3\,c\,z^2+9\,a^5\,b\,g\,h\,z-9\,a^4\,b^2\,e\,g\,z-9\,a^4\,b^2\,d\,h\,z-18\,a^3\,b^3\,c\,f\,z+9\,a^3\,b^3\,d\,e\,z+9\,a^4\,b^2\,f^2\,z+9\,a^2\,b^4\,c^2\,z+3\,a^4\,b\,f\,g\,h-3\,a\,b^4\,c\,d\,e-3\,a^3\,b^2\,e\,f\,g-3\,a^3\,b^2\,d\,f\,h-3\,a^3\,b^2\,c\,g\,h+3\,a^2\,b^3\,d\,e\,f+3\,a^2\,b^3\,c\,e\,g+3\,a^2\,b^3\,c\,d\,h-3\,a^4\,b\,e\,h^2+3\,a\,b^4\,c^2\,f+3\,a^3\,b^2\,e^2\,h+3\,a^3\,b^2\,d\,g^2-3\,a^2\,b^3\,d^2\,g-3\,a^2\,b^3\,c\,f^2-a^2\,b^3\,e^3-a^4\,b\,g^3-b^5\,c^3+a^3\,b^2\,f^3+a\,b^4\,d^3+a^5\,h^3,z,k\right)\right)-\frac{\frac{c}{3\,a}+\frac{e\,x^2}{a}+\frac{d\,x}{2\,a}}{x^3}-\frac{\ln\left(x\right)\,\left(b\,c-a\,f\right)}{a^2}","Not used",1,"symsum(log(- (b^5*c*d^2 - b^5*c^2*e + a^2*b^3*c*g^2 - a^2*b^3*e*f^2 - a^3*b^2*f*g^2 + a^3*b^2*f^2*h - a*b^4*d^2*f + a*b^4*c^2*h - 2*a^2*b^3*c*f*h + 2*a^2*b^3*d*f*g - 2*a*b^4*c*d*g + 2*a*b^4*c*e*f)/a^3 - root(27*a^6*b^2*z^3 + 27*a^5*b^2*f*z^2 - 27*a^4*b^3*c*z^2 + 9*a^5*b*g*h*z - 9*a^4*b^2*e*g*z - 9*a^4*b^2*d*h*z - 18*a^3*b^3*c*f*z + 9*a^3*b^3*d*e*z + 9*a^4*b^2*f^2*z + 9*a^2*b^4*c^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3, z, k)*((a^2*b^4*d^2 + a^4*b^2*g^2 + 2*a^2*b^4*c*e - 2*a^3*b^3*c*h - 2*a^3*b^3*d*g - 2*a^3*b^3*e*f + 2*a^4*b^2*f*h)/a^3 + root(27*a^6*b^2*z^3 + 27*a^5*b^2*f*z^2 - 27*a^4*b^3*c*z^2 + 9*a^5*b*g*h*z - 9*a^4*b^2*e*g*z - 9*a^4*b^2*d*h*z - 18*a^3*b^3*c*f*z + 9*a^3*b^3*d*e*z + 9*a^4*b^2*f^2*z + 9*a^2*b^4*c^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3, z, k)*((3*a^4*b^3*e - 3*a^5*b^2*h)/a^3 - (x*(24*a^3*b^4*c - 24*a^4*b^3*f))/a^3 + 36*root(27*a^6*b^2*z^3 + 27*a^5*b^2*f*z^2 - 27*a^4*b^3*c*z^2 + 9*a^5*b*g*h*z - 9*a^4*b^2*e*g*z - 9*a^4*b^2*d*h*z - 18*a^3*b^3*c*f*z + 9*a^3*b^3*d*e*z + 9*a^4*b^2*f^2*z + 9*a^2*b^4*c^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3, z, k)*a^2*b^3*x) + (x*(4*a*b^5*c^2 + 4*a^3*b^3*f^2 - 8*a^2*b^4*c*f + 10*a^2*b^4*d*e - 10*a^3*b^3*d*h - 10*a^3*b^3*e*g + 10*a^4*b^2*g*h))/a^3) - (x*(b^5*d^3 - a*b^4*e^3 + a^4*b*h^3 - a^3*b^2*g^3 + 3*a^2*b^3*d*g^2 + 3*a^2*b^3*e^2*h - 3*a^3*b^2*e*h^2 - 2*b^5*c*d*e - 3*a*b^4*d^2*g - 2*a^2*b^3*c*g*h - 2*a^2*b^3*d*f*h - 2*a^2*b^3*e*f*g + 2*a^3*b^2*f*g*h + 2*a*b^4*c*d*h + 2*a*b^4*c*e*g + 2*a*b^4*d*e*f))/a^3)*root(27*a^6*b^2*z^3 + 27*a^5*b^2*f*z^2 - 27*a^4*b^3*c*z^2 + 9*a^5*b*g*h*z - 9*a^4*b^2*e*g*z - 9*a^4*b^2*d*h*z - 18*a^3*b^3*c*f*z + 9*a^3*b^3*d*e*z + 9*a^4*b^2*f^2*z + 9*a^2*b^4*c^2*z + 3*a^4*b*f*g*h - 3*a*b^4*c*d*e - 3*a^3*b^2*e*f*g - 3*a^3*b^2*d*f*h - 3*a^3*b^2*c*g*h + 3*a^2*b^3*d*e*f + 3*a^2*b^3*c*e*g + 3*a^2*b^3*c*d*h - 3*a^4*b*e*h^2 + 3*a*b^4*c^2*f + 3*a^3*b^2*e^2*h + 3*a^3*b^2*d*g^2 - 3*a^2*b^3*d^2*g - 3*a^2*b^3*c*f^2 - a^2*b^3*e^3 - a^4*b*g^3 - b^5*c^3 + a^3*b^2*f^3 + a*b^4*d^3 + a^5*h^3, z, k), k, 1, 3) - (c/(3*a) + (e*x^2)/a + (d*x)/(2*a))/x^3 - (log(x)*(b*c - a*f))/a^2","B"
412,1,1241,337,5.108594,"\text{Not used}","int((x^4*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^2,x)","\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(729\,a\,b^{10}\,z^3-729\,a\,b^8\,d\,z^2+1458\,a^2\,b^7\,g\,z^2-216\,a\,b^6\,c\,e\,z-945\,a^3\,b^4\,f\,h\,z-972\,a^2\,b^5\,d\,g\,z+540\,a^2\,b^5\,e\,f\,z+378\,a^2\,b^5\,c\,h\,z+243\,a\,b^6\,d^2\,z+972\,a^3\,b^4\,g^2\,z-630\,a^4\,b\,f\,g\,h+72\,a\,b^4\,c\,d\,e+360\,a^3\,b^2\,e\,f\,g+315\,a^3\,b^2\,d\,f\,h+252\,a^3\,b^2\,c\,g\,h-180\,a^2\,b^3\,d\,e\,f-144\,a^2\,b^3\,c\,e\,g-126\,a^2\,b^3\,c\,d\,h+588\,a^4\,b\,e\,h^2-60\,a\,b^4\,c^2\,f-336\,a^3\,b^2\,e^2\,h-324\,a^3\,b^2\,d\,g^2+162\,a^2\,b^3\,d^2\,g+150\,a^2\,b^3\,c\,f^2-125\,a^3\,b^2\,f^3+64\,a^2\,b^3\,e^3+216\,a^4\,b\,g^3-27\,a\,b^4\,d^3-343\,a^5\,h^3+8\,b^5\,c^3,z,k\right)\,\left(\frac{108\,a^2\,b^3\,g-54\,a\,b^4\,d}{9\,b^4}+\frac{x\,\left(63\,a^2\,b^3\,h-36\,a\,b^4\,e\right)}{9\,b^4}+\mathrm{root}\left(729\,a\,b^{10}\,z^3-729\,a\,b^8\,d\,z^2+1458\,a^2\,b^7\,g\,z^2-216\,a\,b^6\,c\,e\,z-945\,a^3\,b^4\,f\,h\,z-972\,a^2\,b^5\,d\,g\,z+540\,a^2\,b^5\,e\,f\,z+378\,a^2\,b^5\,c\,h\,z+243\,a\,b^6\,d^2\,z+972\,a^3\,b^4\,g^2\,z-630\,a^4\,b\,f\,g\,h+72\,a\,b^4\,c\,d\,e+360\,a^3\,b^2\,e\,f\,g+315\,a^3\,b^2\,d\,f\,h+252\,a^3\,b^2\,c\,g\,h-180\,a^2\,b^3\,d\,e\,f-144\,a^2\,b^3\,c\,e\,g-126\,a^2\,b^3\,c\,d\,h+588\,a^4\,b\,e\,h^2-60\,a\,b^4\,c^2\,f-336\,a^3\,b^2\,e^2\,h-324\,a^3\,b^2\,d\,g^2+162\,a^2\,b^3\,d^2\,g+150\,a^2\,b^3\,c\,f^2-125\,a^3\,b^2\,f^3+64\,a^2\,b^3\,e^3+216\,a^4\,b\,g^3-27\,a\,b^4\,d^3-343\,a^5\,h^3+8\,b^5\,c^3,z,k\right)\,a\,b^2\,9\right)+\frac{36\,a^3\,g^2+9\,a\,b^2\,d^2-35\,a^3\,f\,h-8\,a\,b^2\,c\,e+14\,a^2\,b\,c\,h-36\,a^2\,b\,d\,g+20\,a^2\,b\,e\,f}{9\,b^4}+\frac{x\,\left(4\,b^3\,c^2+25\,a^2\,b\,f^2+42\,a^3\,g\,h-20\,a\,b^2\,c\,f+12\,a\,b^2\,d\,e-21\,a^2\,b\,d\,h-24\,a^2\,b\,e\,g\right)}{9\,b^4}\right)\,\mathrm{root}\left(729\,a\,b^{10}\,z^3-729\,a\,b^8\,d\,z^2+1458\,a^2\,b^7\,g\,z^2-216\,a\,b^6\,c\,e\,z-945\,a^3\,b^4\,f\,h\,z-972\,a^2\,b^5\,d\,g\,z+540\,a^2\,b^5\,e\,f\,z+378\,a^2\,b^5\,c\,h\,z+243\,a\,b^6\,d^2\,z+972\,a^3\,b^4\,g^2\,z-630\,a^4\,b\,f\,g\,h+72\,a\,b^4\,c\,d\,e+360\,a^3\,b^2\,e\,f\,g+315\,a^3\,b^2\,d\,f\,h+252\,a^3\,b^2\,c\,g\,h-180\,a^2\,b^3\,d\,e\,f-144\,a^2\,b^3\,c\,e\,g-126\,a^2\,b^3\,c\,d\,h+588\,a^4\,b\,e\,h^2-60\,a\,b^4\,c^2\,f-336\,a^3\,b^2\,e^2\,h-324\,a^3\,b^2\,d\,g^2+162\,a^2\,b^3\,d^2\,g+150\,a^2\,b^3\,c\,f^2-125\,a^3\,b^2\,f^3+64\,a^2\,b^3\,e^3+216\,a^4\,b\,g^3-27\,a\,b^4\,d^3-343\,a^5\,h^3+8\,b^5\,c^3,z,k\right)\right)+x\,\left(\frac{e}{b^2}-\frac{2\,a\,h}{b^3}\right)-\frac{x\,\left(\frac{a^2\,h}{3}-\frac{a\,b\,e}{3}\right)+\frac{a^2\,g}{3}+x^2\,\left(\frac{b^2\,c}{3}-\frac{a\,b\,f}{3}\right)-\frac{a\,b\,d}{3}}{b^4\,x^3+a\,b^3}+\frac{f\,x^2}{2\,b^2}+\frac{g\,x^3}{3\,b^2}+\frac{h\,x^4}{4\,b^2}","Not used",1,"symsum(log(root(729*a*b^10*z^3 - 729*a*b^8*d*z^2 + 1458*a^2*b^7*g*z^2 - 216*a*b^6*c*e*z - 945*a^3*b^4*f*h*z - 972*a^2*b^5*d*g*z + 540*a^2*b^5*e*f*z + 378*a^2*b^5*c*h*z + 243*a*b^6*d^2*z + 972*a^3*b^4*g^2*z - 630*a^4*b*f*g*h + 72*a*b^4*c*d*e + 360*a^3*b^2*e*f*g + 315*a^3*b^2*d*f*h + 252*a^3*b^2*c*g*h - 180*a^2*b^3*d*e*f - 144*a^2*b^3*c*e*g - 126*a^2*b^3*c*d*h + 588*a^4*b*e*h^2 - 60*a*b^4*c^2*f - 336*a^3*b^2*e^2*h - 324*a^3*b^2*d*g^2 + 162*a^2*b^3*d^2*g + 150*a^2*b^3*c*f^2 - 125*a^3*b^2*f^3 + 64*a^2*b^3*e^3 + 216*a^4*b*g^3 - 27*a*b^4*d^3 - 343*a^5*h^3 + 8*b^5*c^3, z, k)*((108*a^2*b^3*g - 54*a*b^4*d)/(9*b^4) + (x*(63*a^2*b^3*h - 36*a*b^4*e))/(9*b^4) + 9*root(729*a*b^10*z^3 - 729*a*b^8*d*z^2 + 1458*a^2*b^7*g*z^2 - 216*a*b^6*c*e*z - 945*a^3*b^4*f*h*z - 972*a^2*b^5*d*g*z + 540*a^2*b^5*e*f*z + 378*a^2*b^5*c*h*z + 243*a*b^6*d^2*z + 972*a^3*b^4*g^2*z - 630*a^4*b*f*g*h + 72*a*b^4*c*d*e + 360*a^3*b^2*e*f*g + 315*a^3*b^2*d*f*h + 252*a^3*b^2*c*g*h - 180*a^2*b^3*d*e*f - 144*a^2*b^3*c*e*g - 126*a^2*b^3*c*d*h + 588*a^4*b*e*h^2 - 60*a*b^4*c^2*f - 336*a^3*b^2*e^2*h - 324*a^3*b^2*d*g^2 + 162*a^2*b^3*d^2*g + 150*a^2*b^3*c*f^2 - 125*a^3*b^2*f^3 + 64*a^2*b^3*e^3 + 216*a^4*b*g^3 - 27*a*b^4*d^3 - 343*a^5*h^3 + 8*b^5*c^3, z, k)*a*b^2) + (36*a^3*g^2 + 9*a*b^2*d^2 - 35*a^3*f*h - 8*a*b^2*c*e + 14*a^2*b*c*h - 36*a^2*b*d*g + 20*a^2*b*e*f)/(9*b^4) + (x*(4*b^3*c^2 + 25*a^2*b*f^2 + 42*a^3*g*h - 20*a*b^2*c*f + 12*a*b^2*d*e - 21*a^2*b*d*h - 24*a^2*b*e*g))/(9*b^4))*root(729*a*b^10*z^3 - 729*a*b^8*d*z^2 + 1458*a^2*b^7*g*z^2 - 216*a*b^6*c*e*z - 945*a^3*b^4*f*h*z - 972*a^2*b^5*d*g*z + 540*a^2*b^5*e*f*z + 378*a^2*b^5*c*h*z + 243*a*b^6*d^2*z + 972*a^3*b^4*g^2*z - 630*a^4*b*f*g*h + 72*a*b^4*c*d*e + 360*a^3*b^2*e*f*g + 315*a^3*b^2*d*f*h + 252*a^3*b^2*c*g*h - 180*a^2*b^3*d*e*f - 144*a^2*b^3*c*e*g - 126*a^2*b^3*c*d*h + 588*a^4*b*e*h^2 - 60*a*b^4*c^2*f - 336*a^3*b^2*e^2*h - 324*a^3*b^2*d*g^2 + 162*a^2*b^3*d^2*g + 150*a^2*b^3*c*f^2 - 125*a^3*b^2*f^3 + 64*a^2*b^3*e^3 + 216*a^4*b*g^3 - 27*a*b^4*d^3 - 343*a^5*h^3 + 8*b^5*c^3, z, k), k, 1, 3) + x*(e/b^2 - (2*a*h)/b^3) - (x*((a^2*h)/3 - (a*b*e)/3) + (a^2*g)/3 + x^2*((b^2*c)/3 - (a*b*f)/3) - (a*b*d)/3)/(a*b^3 + b^4*x^3) + (f*x^2)/(2*b^2) + (g*x^3)/(3*b^2) + (h*x^4)/(4*b^2)","B"
413,1,1229,311,0.151834,"\text{Not used}","int((x^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^2,x)","\left(\sum _{k=1}^3\ln\left(\frac{36\,a^3\,h^2+9\,a\,b^2\,e^2+2\,b^3\,c\,d-5\,a\,b^2\,c\,g-8\,a\,b^2\,d\,f-36\,a^2\,b\,e\,h+20\,a^2\,b\,f\,g}{9\,b^4}+\mathrm{root}\left(729\,a^2\,b^9\,z^3+1458\,a^3\,b^6\,h\,z^2-729\,a^2\,b^7\,e\,z^2+54\,a\,b^6\,c\,d\,z-972\,a^3\,b^4\,e\,h\,z+540\,a^3\,b^4\,f\,g\,z-216\,a^2\,b^5\,d\,f\,z-135\,a^2\,b^5\,c\,g\,z+972\,a^4\,b^3\,h^2\,z+243\,a^2\,b^5\,e^2\,z+360\,a^4\,b\,f\,g\,h-18\,a\,b^4\,c\,d\,e-180\,a^3\,b^2\,e\,f\,g-144\,a^3\,b^2\,d\,f\,h-90\,a^3\,b^2\,c\,g\,h+72\,a^2\,b^3\,d\,e\,f+45\,a^2\,b^3\,c\,e\,g+36\,a^2\,b^3\,c\,d\,h-324\,a^4\,b\,e\,h^2+12\,a\,b^4\,c^2\,f+162\,a^3\,b^2\,e^2\,h+150\,a^3\,b^2\,d\,g^2-60\,a^2\,b^3\,d^2\,g-48\,a^2\,b^3\,c\,f^2+64\,a^3\,b^2\,f^3-27\,a^2\,b^3\,e^3-125\,a^4\,b\,g^3+8\,a\,b^4\,d^3+216\,a^5\,h^3-b^5\,c^3,z,k\right)\,\left(\frac{108\,a^2\,b^3\,h-54\,a\,b^4\,e}{9\,b^4}+\frac{x\,\left(9\,b^4\,c-36\,a\,b^3\,f\right)}{9\,b^3}+\mathrm{root}\left(729\,a^2\,b^9\,z^3+1458\,a^3\,b^6\,h\,z^2-729\,a^2\,b^7\,e\,z^2+54\,a\,b^6\,c\,d\,z-972\,a^3\,b^4\,e\,h\,z+540\,a^3\,b^4\,f\,g\,z-216\,a^2\,b^5\,d\,f\,z-135\,a^2\,b^5\,c\,g\,z+972\,a^4\,b^3\,h^2\,z+243\,a^2\,b^5\,e^2\,z+360\,a^4\,b\,f\,g\,h-18\,a\,b^4\,c\,d\,e-180\,a^3\,b^2\,e\,f\,g-144\,a^3\,b^2\,d\,f\,h-90\,a^3\,b^2\,c\,g\,h+72\,a^2\,b^3\,d\,e\,f+45\,a^2\,b^3\,c\,e\,g+36\,a^2\,b^3\,c\,d\,h-324\,a^4\,b\,e\,h^2+12\,a\,b^4\,c^2\,f+162\,a^3\,b^2\,e^2\,h+150\,a^3\,b^2\,d\,g^2-60\,a^2\,b^3\,d^2\,g-48\,a^2\,b^3\,c\,f^2+64\,a^3\,b^2\,f^3-27\,a^2\,b^3\,e^3-125\,a^4\,b\,g^3+8\,a\,b^4\,d^3+216\,a^5\,h^3-b^5\,c^3,z,k\right)\,a\,b^2\,9\right)+\frac{x\,\left(4\,b^2\,d^2+25\,a^2\,g^2-3\,b^2\,c\,e-24\,a^2\,f\,h+6\,a\,b\,c\,h-20\,a\,b\,d\,g+12\,a\,b\,e\,f\right)}{9\,b^3}\right)\,\mathrm{root}\left(729\,a^2\,b^9\,z^3+1458\,a^3\,b^6\,h\,z^2-729\,a^2\,b^7\,e\,z^2+54\,a\,b^6\,c\,d\,z-972\,a^3\,b^4\,e\,h\,z+540\,a^3\,b^4\,f\,g\,z-216\,a^2\,b^5\,d\,f\,z-135\,a^2\,b^5\,c\,g\,z+972\,a^4\,b^3\,h^2\,z+243\,a^2\,b^5\,e^2\,z+360\,a^4\,b\,f\,g\,h-18\,a\,b^4\,c\,d\,e-180\,a^3\,b^2\,e\,f\,g-144\,a^3\,b^2\,d\,f\,h-90\,a^3\,b^2\,c\,g\,h+72\,a^2\,b^3\,d\,e\,f+45\,a^2\,b^3\,c\,e\,g+36\,a^2\,b^3\,c\,d\,h-324\,a^4\,b\,e\,h^2+12\,a\,b^4\,c^2\,f+162\,a^3\,b^2\,e^2\,h+150\,a^3\,b^2\,d\,g^2-60\,a^2\,b^3\,d^2\,g-48\,a^2\,b^3\,c\,f^2+64\,a^3\,b^2\,f^3-27\,a^2\,b^3\,e^3-125\,a^4\,b\,g^3+8\,a\,b^4\,d^3+216\,a^5\,h^3-b^5\,c^3,z,k\right)\right)-\frac{x\,\left(\frac{b\,c}{3}-\frac{a\,f}{3}\right)+\frac{a^2\,h-a\,b\,e}{3\,b}+x^2\,\left(\frac{b\,d}{3}-\frac{a\,g}{3}\right)}{b^3\,x^3+a\,b^2}+\frac{g\,x^2}{2\,b^2}+\frac{h\,x^3}{3\,b^2}+\frac{f\,x}{b^2}","Not used",1,"symsum(log((36*a^3*h^2 + 9*a*b^2*e^2 + 2*b^3*c*d - 5*a*b^2*c*g - 8*a*b^2*d*f - 36*a^2*b*e*h + 20*a^2*b*f*g)/(9*b^4) + root(729*a^2*b^9*z^3 + 1458*a^3*b^6*h*z^2 - 729*a^2*b^7*e*z^2 + 54*a*b^6*c*d*z - 972*a^3*b^4*e*h*z + 540*a^3*b^4*f*g*z - 216*a^2*b^5*d*f*z - 135*a^2*b^5*c*g*z + 972*a^4*b^3*h^2*z + 243*a^2*b^5*e^2*z + 360*a^4*b*f*g*h - 18*a*b^4*c*d*e - 180*a^3*b^2*e*f*g - 144*a^3*b^2*d*f*h - 90*a^3*b^2*c*g*h + 72*a^2*b^3*d*e*f + 45*a^2*b^3*c*e*g + 36*a^2*b^3*c*d*h - 324*a^4*b*e*h^2 + 12*a*b^4*c^2*f + 162*a^3*b^2*e^2*h + 150*a^3*b^2*d*g^2 - 60*a^2*b^3*d^2*g - 48*a^2*b^3*c*f^2 + 64*a^3*b^2*f^3 - 27*a^2*b^3*e^3 - 125*a^4*b*g^3 + 8*a*b^4*d^3 + 216*a^5*h^3 - b^5*c^3, z, k)*((108*a^2*b^3*h - 54*a*b^4*e)/(9*b^4) + (x*(9*b^4*c - 36*a*b^3*f))/(9*b^3) + 9*root(729*a^2*b^9*z^3 + 1458*a^3*b^6*h*z^2 - 729*a^2*b^7*e*z^2 + 54*a*b^6*c*d*z - 972*a^3*b^4*e*h*z + 540*a^3*b^4*f*g*z - 216*a^2*b^5*d*f*z - 135*a^2*b^5*c*g*z + 972*a^4*b^3*h^2*z + 243*a^2*b^5*e^2*z + 360*a^4*b*f*g*h - 18*a*b^4*c*d*e - 180*a^3*b^2*e*f*g - 144*a^3*b^2*d*f*h - 90*a^3*b^2*c*g*h + 72*a^2*b^3*d*e*f + 45*a^2*b^3*c*e*g + 36*a^2*b^3*c*d*h - 324*a^4*b*e*h^2 + 12*a*b^4*c^2*f + 162*a^3*b^2*e^2*h + 150*a^3*b^2*d*g^2 - 60*a^2*b^3*d^2*g - 48*a^2*b^3*c*f^2 + 64*a^3*b^2*f^3 - 27*a^2*b^3*e^3 - 125*a^4*b*g^3 + 8*a*b^4*d^3 + 216*a^5*h^3 - b^5*c^3, z, k)*a*b^2) + (x*(4*b^2*d^2 + 25*a^2*g^2 - 3*b^2*c*e - 24*a^2*f*h + 6*a*b*c*h - 20*a*b*d*g + 12*a*b*e*f))/(9*b^3))*root(729*a^2*b^9*z^3 + 1458*a^3*b^6*h*z^2 - 729*a^2*b^7*e*z^2 + 54*a*b^6*c*d*z - 972*a^3*b^4*e*h*z + 540*a^3*b^4*f*g*z - 216*a^2*b^5*d*f*z - 135*a^2*b^5*c*g*z + 972*a^4*b^3*h^2*z + 243*a^2*b^5*e^2*z + 360*a^4*b*f*g*h - 18*a*b^4*c*d*e - 180*a^3*b^2*e*f*g - 144*a^3*b^2*d*f*h - 90*a^3*b^2*c*g*h + 72*a^2*b^3*d*e*f + 45*a^2*b^3*c*e*g + 36*a^2*b^3*c*d*h - 324*a^4*b*e*h^2 + 12*a*b^4*c^2*f + 162*a^3*b^2*e^2*h + 150*a^3*b^2*d*g^2 - 60*a^2*b^3*d^2*g - 48*a^2*b^3*c*f^2 + 64*a^3*b^2*f^3 - 27*a^2*b^3*e^3 - 125*a^4*b*g^3 + 8*a*b^4*d^3 + 216*a^5*h^3 - b^5*c^3, z, k), k, 1, 3) - (x*((b*c)/3 - (a*f)/3) + (a^2*h - a*b*e)/(3*b) + x^2*((b*d)/3 - (a*g)/3))/(a*b^2 + b^3*x^3) + (g*x^2)/(2*b^2) + (h*x^3)/(3*b^2) + (f*x)/b^2","B"
414,1,816,290,0.137240,"\text{Not used}","int((x^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^2,x)","\left(\sum _{k=1}^3\ln\left(\frac{9\,a\,b\,f^2+2\,b^2\,d\,e+20\,a^2\,g\,h-5\,a\,b\,d\,h-8\,a\,b\,e\,g}{9\,b^3}+\mathrm{root}\left(729\,a^2\,b^8\,z^3-729\,a^2\,b^6\,f\,z^2+54\,a\,b^5\,d\,e\,z+540\,a^3\,b^3\,g\,h\,z-216\,a^2\,b^4\,e\,g\,z-135\,a^2\,b^4\,d\,h\,z+243\,a^2\,b^4\,f^2\,z-180\,a^3\,b\,f\,g\,h-18\,a\,b^3\,d\,e\,f+72\,a^2\,b^2\,e\,f\,g+45\,a^2\,b^2\,d\,f\,h+150\,a^3\,b\,e\,h^2+12\,a\,b^3\,d^2\,g-60\,a^2\,b^2\,e^2\,h-48\,a^2\,b^2\,d\,g^2-27\,a^2\,b^2\,f^3+64\,a^3\,b\,g^3+8\,a\,b^3\,e^3-125\,a^4\,h^3-b^4\,d^3,z,k\right)\,\left(-6\,a\,f+\frac{x\,\left(9\,b^4\,d-36\,a\,b^3\,g\right)}{9\,b^3}+\mathrm{root}\left(729\,a^2\,b^8\,z^3-729\,a^2\,b^6\,f\,z^2+54\,a\,b^5\,d\,e\,z+540\,a^3\,b^3\,g\,h\,z-216\,a^2\,b^4\,e\,g\,z-135\,a^2\,b^4\,d\,h\,z+243\,a^2\,b^4\,f^2\,z-180\,a^3\,b\,f\,g\,h-18\,a\,b^3\,d\,e\,f+72\,a^2\,b^2\,e\,f\,g+45\,a^2\,b^2\,d\,f\,h+150\,a^3\,b\,e\,h^2+12\,a\,b^3\,d^2\,g-60\,a^2\,b^2\,e^2\,h-48\,a^2\,b^2\,d\,g^2-27\,a^2\,b^2\,f^3+64\,a^3\,b\,g^3+8\,a\,b^3\,e^3-125\,a^4\,h^3-b^4\,d^3,z,k\right)\,a\,b^2\,9\right)+\frac{x\,\left(25\,a^2\,h^2-20\,a\,b\,e\,h+12\,f\,g\,a\,b+4\,b^2\,e^2-3\,d\,f\,b^2\right)}{9\,b^3}\right)\,\mathrm{root}\left(729\,a^2\,b^8\,z^3-729\,a^2\,b^6\,f\,z^2+54\,a\,b^5\,d\,e\,z+540\,a^3\,b^3\,g\,h\,z-216\,a^2\,b^4\,e\,g\,z-135\,a^2\,b^4\,d\,h\,z+243\,a^2\,b^4\,f^2\,z-180\,a^3\,b\,f\,g\,h-18\,a\,b^3\,d\,e\,f+72\,a^2\,b^2\,e\,f\,g+45\,a^2\,b^2\,d\,f\,h+150\,a^3\,b\,e\,h^2+12\,a\,b^3\,d^2\,g-60\,a^2\,b^2\,e^2\,h-48\,a^2\,b^2\,d\,g^2-27\,a^2\,b^2\,f^3+64\,a^3\,b\,g^3+8\,a\,b^3\,e^3-125\,a^4\,h^3-b^4\,d^3,z,k\right)\right)-\frac{\left(\frac{b\,e}{3}-\frac{a\,h}{3}\right)\,x^2+\left(\frac{b\,d}{3}-\frac{a\,g}{3}\right)\,x+\frac{b\,c}{3}-\frac{a\,f}{3}}{b^3\,x^3+a\,b^2}+\frac{h\,x^2}{2\,b^2}+\frac{g\,x}{b^2}","Not used",1,"symsum(log((9*a*b*f^2 + 2*b^2*d*e + 20*a^2*g*h - 5*a*b*d*h - 8*a*b*e*g)/(9*b^3) + root(729*a^2*b^8*z^3 - 729*a^2*b^6*f*z^2 + 54*a*b^5*d*e*z + 540*a^3*b^3*g*h*z - 216*a^2*b^4*e*g*z - 135*a^2*b^4*d*h*z + 243*a^2*b^4*f^2*z - 180*a^3*b*f*g*h - 18*a*b^3*d*e*f + 72*a^2*b^2*e*f*g + 45*a^2*b^2*d*f*h + 150*a^3*b*e*h^2 + 12*a*b^3*d^2*g - 60*a^2*b^2*e^2*h - 48*a^2*b^2*d*g^2 - 27*a^2*b^2*f^3 + 64*a^3*b*g^3 + 8*a*b^3*e^3 - 125*a^4*h^3 - b^4*d^3, z, k)*((x*(9*b^4*d - 36*a*b^3*g))/(9*b^3) - 6*a*f + 9*root(729*a^2*b^8*z^3 - 729*a^2*b^6*f*z^2 + 54*a*b^5*d*e*z + 540*a^3*b^3*g*h*z - 216*a^2*b^4*e*g*z - 135*a^2*b^4*d*h*z + 243*a^2*b^4*f^2*z - 180*a^3*b*f*g*h - 18*a*b^3*d*e*f + 72*a^2*b^2*e*f*g + 45*a^2*b^2*d*f*h + 150*a^3*b*e*h^2 + 12*a*b^3*d^2*g - 60*a^2*b^2*e^2*h - 48*a^2*b^2*d*g^2 - 27*a^2*b^2*f^3 + 64*a^3*b*g^3 + 8*a*b^3*e^3 - 125*a^4*h^3 - b^4*d^3, z, k)*a*b^2) + (x*(4*b^2*e^2 + 25*a^2*h^2 - 3*b^2*d*f - 20*a*b*e*h + 12*a*b*f*g))/(9*b^3))*root(729*a^2*b^8*z^3 - 729*a^2*b^6*f*z^2 + 54*a*b^5*d*e*z + 540*a^3*b^3*g*h*z - 216*a^2*b^4*e*g*z - 135*a^2*b^4*d*h*z + 243*a^2*b^4*f^2*z - 180*a^3*b*f*g*h - 18*a*b^3*d*e*f + 72*a^2*b^2*e*f*g + 45*a^2*b^2*d*f*h + 150*a^3*b*e*h^2 + 12*a*b^3*d^2*g - 60*a^2*b^2*e^2*h - 48*a^2*b^2*d*g^2 - 27*a^2*b^2*f^3 + 64*a^3*b*g^3 + 8*a*b^3*e^3 - 125*a^4*h^3 - b^4*d^3, z, k), k, 1, 3) - ((b*c)/3 - (a*f)/3 + x*((b*d)/3 - (a*g)/3) + x^2*((b*e)/3 - (a*h)/3))/(a*b^2 + b^3*x^3) + (h*x^2)/(2*b^2) + (g*x)/b^2","B"
415,1,827,289,5.389846,"\text{Not used}","int((x*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^2,x)","\left(\sum _{k=1}^3\ln\left(\frac{9\,a^2\,g^2+b^2\,c\,e-8\,a^2\,f\,h-4\,a\,b\,c\,h+2\,a\,b\,e\,f}{9\,a\,b^2}-\mathrm{root}\left(729\,a^4\,b^7\,z^3-729\,a^4\,b^5\,g\,z^2-216\,a^4\,b^3\,f\,h\,z-108\,a^3\,b^4\,c\,h\,z+54\,a^3\,b^4\,e\,f\,z+27\,a^2\,b^5\,c\,e\,z+243\,a^4\,b^3\,g^2\,z+72\,a^4\,b\,f\,g\,h+36\,a^3\,b^2\,c\,g\,h-18\,a^3\,b^2\,e\,f\,g-9\,a^2\,b^3\,c\,e\,g-48\,a^4\,b\,e\,h^2+6\,a\,b^4\,c^2\,f+12\,a^3\,b^2\,e^2\,h+12\,a^2\,b^3\,c\,f^2+8\,a^3\,b^2\,f^3-27\,a^4\,b\,g^3+64\,a^5\,h^3+b^5\,c^3-a^2\,b^3\,e^3,z,k\right)\,\left(6\,a\,g-b\,e\,x+4\,a\,h\,x-\mathrm{root}\left(729\,a^4\,b^7\,z^3-729\,a^4\,b^5\,g\,z^2-216\,a^4\,b^3\,f\,h\,z-108\,a^3\,b^4\,c\,h\,z+54\,a^3\,b^4\,e\,f\,z+27\,a^2\,b^5\,c\,e\,z+243\,a^4\,b^3\,g^2\,z+72\,a^4\,b\,f\,g\,h+36\,a^3\,b^2\,c\,g\,h-18\,a^3\,b^2\,e\,f\,g-9\,a^2\,b^3\,c\,e\,g-48\,a^4\,b\,e\,h^2+6\,a\,b^4\,c^2\,f+12\,a^3\,b^2\,e^2\,h+12\,a^2\,b^3\,c\,f^2+8\,a^3\,b^2\,f^3-27\,a^4\,b\,g^3+64\,a^5\,h^3+b^5\,c^3-a^2\,b^3\,e^3,z,k\right)\,a\,b^2\,9\right)+\frac{x\,\left(12\,g\,h\,a^3+4\,a^2\,b\,f^2-3\,e\,g\,a^2\,b+4\,a\,b^2\,c\,f+b^3\,c^2\right)}{9\,a^2\,b^2}\right)\,\mathrm{root}\left(729\,a^4\,b^7\,z^3-729\,a^4\,b^5\,g\,z^2-216\,a^4\,b^3\,f\,h\,z-108\,a^3\,b^4\,c\,h\,z+54\,a^3\,b^4\,e\,f\,z+27\,a^2\,b^5\,c\,e\,z+243\,a^4\,b^3\,g^2\,z+72\,a^4\,b\,f\,g\,h+36\,a^3\,b^2\,c\,g\,h-18\,a^3\,b^2\,e\,f\,g-9\,a^2\,b^3\,c\,e\,g-48\,a^4\,b\,e\,h^2+6\,a\,b^4\,c^2\,f+12\,a^3\,b^2\,e^2\,h+12\,a^2\,b^3\,c\,f^2+8\,a^3\,b^2\,f^3-27\,a^4\,b\,g^3+64\,a^5\,h^3+b^5\,c^3-a^2\,b^3\,e^3,z,k\right)\right)-\frac{\frac{b\,d}{3}-\frac{a\,g}{3}+x\,\left(\frac{b\,e}{3}-\frac{a\,h}{3}\right)-\frac{b\,x^2\,\left(b\,c-a\,f\right)}{3\,a}}{b^3\,x^3+a\,b^2}+\frac{h\,x}{b^2}","Not used",1,"symsum(log((9*a^2*g^2 + b^2*c*e - 8*a^2*f*h - 4*a*b*c*h + 2*a*b*e*f)/(9*a*b^2) - root(729*a^4*b^7*z^3 - 729*a^4*b^5*g*z^2 - 216*a^4*b^3*f*h*z - 108*a^3*b^4*c*h*z + 54*a^3*b^4*e*f*z + 27*a^2*b^5*c*e*z + 243*a^4*b^3*g^2*z + 72*a^4*b*f*g*h + 36*a^3*b^2*c*g*h - 18*a^3*b^2*e*f*g - 9*a^2*b^3*c*e*g - 48*a^4*b*e*h^2 + 6*a*b^4*c^2*f + 12*a^3*b^2*e^2*h + 12*a^2*b^3*c*f^2 + 8*a^3*b^2*f^3 - 27*a^4*b*g^3 + 64*a^5*h^3 + b^5*c^3 - a^2*b^3*e^3, z, k)*(6*a*g - b*e*x + 4*a*h*x - 9*root(729*a^4*b^7*z^3 - 729*a^4*b^5*g*z^2 - 216*a^4*b^3*f*h*z - 108*a^3*b^4*c*h*z + 54*a^3*b^4*e*f*z + 27*a^2*b^5*c*e*z + 243*a^4*b^3*g^2*z + 72*a^4*b*f*g*h + 36*a^3*b^2*c*g*h - 18*a^3*b^2*e*f*g - 9*a^2*b^3*c*e*g - 48*a^4*b*e*h^2 + 6*a*b^4*c^2*f + 12*a^3*b^2*e^2*h + 12*a^2*b^3*c*f^2 + 8*a^3*b^2*f^3 - 27*a^4*b*g^3 + 64*a^5*h^3 + b^5*c^3 - a^2*b^3*e^3, z, k)*a*b^2) + (x*(b^3*c^2 + 4*a^2*b*f^2 + 12*a^3*g*h + 4*a*b^2*c*f - 3*a^2*b*e*g))/(9*a^2*b^2))*root(729*a^4*b^7*z^3 - 729*a^4*b^5*g*z^2 - 216*a^4*b^3*f*h*z - 108*a^3*b^4*c*h*z + 54*a^3*b^4*e*f*z + 27*a^2*b^5*c*e*z + 243*a^4*b^3*g^2*z + 72*a^4*b*f*g*h + 36*a^3*b^2*c*g*h - 18*a^3*b^2*e*f*g - 9*a^2*b^3*c*e*g - 48*a^4*b*e*h^2 + 6*a*b^4*c^2*f + 12*a^3*b^2*e^2*h + 12*a^2*b^3*c*f^2 + 8*a^3*b^2*f^3 - 27*a^4*b*g^3 + 64*a^5*h^3 + b^5*c^3 - a^2*b^3*e^3, z, k), k, 1, 3) - ((b*d)/3 - (a*g)/3 + x*((b*e)/3 - (a*h)/3) - (b*x^2*(b*c - a*f))/(3*a))/(a*b^2 + b^3*x^3) + (h*x)/b^2","B"
416,1,835,276,5.540432,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^2,x)","\left(\sum _{k=1}^3\ln\left(\frac{\mathrm{root}\left(729\,a^5\,b^6\,z^3-729\,a^5\,b^4\,h\,z^2+54\,a^4\,b^3\,f\,g\,z+108\,a^3\,b^4\,c\,g\,z+27\,a^3\,b^4\,d\,f\,z+54\,a^2\,b^5\,c\,d\,z+243\,a^5\,b^2\,h^2\,z-18\,a^4\,b\,f\,g\,h-36\,a^3\,b^2\,c\,g\,h-9\,a^3\,b^2\,d\,f\,h-18\,a^2\,b^3\,c\,d\,h-12\,a\,b^4\,c^2\,f+12\,a^3\,b^2\,d\,g^2+6\,a^2\,b^3\,d^2\,g-6\,a^2\,b^3\,c\,f^2+8\,a^4\,b\,g^3+a\,b^4\,d^3-27\,a^5\,h^3-8\,b^5\,c^3-a^3\,b^2\,f^3,z,k\right)\,\left(-6\,a^2\,h+\mathrm{root}\left(729\,a^5\,b^6\,z^3-729\,a^5\,b^4\,h\,z^2+54\,a^4\,b^3\,f\,g\,z+108\,a^3\,b^4\,c\,g\,z+27\,a^3\,b^4\,d\,f\,z+54\,a^2\,b^5\,c\,d\,z+243\,a^5\,b^2\,h^2\,z-18\,a^4\,b\,f\,g\,h-36\,a^3\,b^2\,c\,g\,h-9\,a^3\,b^2\,d\,f\,h-18\,a^2\,b^3\,c\,d\,h-12\,a\,b^4\,c^2\,f+12\,a^3\,b^2\,d\,g^2+6\,a^2\,b^3\,d^2\,g-6\,a^2\,b^3\,c\,f^2+8\,a^4\,b\,g^3+a\,b^4\,d^3-27\,a^5\,h^3-8\,b^5\,c^3-a^3\,b^2\,f^3,z,k\right)\,a^2\,b^2\,9+2\,b^2\,c\,x+a\,b\,f\,x\right)}{a}+\frac{9\,a^3\,h^2+2\,b^3\,c\,d+4\,a\,b^2\,c\,g+a\,b^2\,d\,f+2\,a^2\,b\,f\,g}{9\,a^2\,b^2}+\frac{x\,\left(4\,a^2\,g^2-3\,f\,h\,a^2+4\,a\,b\,d\,g-6\,c\,h\,a\,b+b^2\,d^2\right)}{9\,a^2\,b}\right)\,\mathrm{root}\left(729\,a^5\,b^6\,z^3-729\,a^5\,b^4\,h\,z^2+54\,a^4\,b^3\,f\,g\,z+108\,a^3\,b^4\,c\,g\,z+27\,a^3\,b^4\,d\,f\,z+54\,a^2\,b^5\,c\,d\,z+243\,a^5\,b^2\,h^2\,z-18\,a^4\,b\,f\,g\,h-36\,a^3\,b^2\,c\,g\,h-9\,a^3\,b^2\,d\,f\,h-18\,a^2\,b^3\,c\,d\,h-12\,a\,b^4\,c^2\,f+12\,a^3\,b^2\,d\,g^2+6\,a^2\,b^3\,d^2\,g-6\,a^2\,b^3\,c\,f^2+8\,a^4\,b\,g^3+a\,b^4\,d^3-27\,a^5\,h^3-8\,b^5\,c^3-a^3\,b^2\,f^3,z,k\right)\right)+\frac{\frac{x\,\left(b\,c-a\,f\right)}{3\,a\,b}-\frac{b\,e-a\,h}{3\,b^2}+\frac{x^2\,\left(b\,d-a\,g\right)}{3\,a\,b}}{b\,x^3+a}","Not used",1,"symsum(log((root(729*a^5*b^6*z^3 - 729*a^5*b^4*h*z^2 + 54*a^4*b^3*f*g*z + 108*a^3*b^4*c*g*z + 27*a^3*b^4*d*f*z + 54*a^2*b^5*c*d*z + 243*a^5*b^2*h^2*z - 18*a^4*b*f*g*h - 36*a^3*b^2*c*g*h - 9*a^3*b^2*d*f*h - 18*a^2*b^3*c*d*h - 12*a*b^4*c^2*f + 12*a^3*b^2*d*g^2 + 6*a^2*b^3*d^2*g - 6*a^2*b^3*c*f^2 + 8*a^4*b*g^3 + a*b^4*d^3 - 27*a^5*h^3 - 8*b^5*c^3 - a^3*b^2*f^3, z, k)*(9*root(729*a^5*b^6*z^3 - 729*a^5*b^4*h*z^2 + 54*a^4*b^3*f*g*z + 108*a^3*b^4*c*g*z + 27*a^3*b^4*d*f*z + 54*a^2*b^5*c*d*z + 243*a^5*b^2*h^2*z - 18*a^4*b*f*g*h - 36*a^3*b^2*c*g*h - 9*a^3*b^2*d*f*h - 18*a^2*b^3*c*d*h - 12*a*b^4*c^2*f + 12*a^3*b^2*d*g^2 + 6*a^2*b^3*d^2*g - 6*a^2*b^3*c*f^2 + 8*a^4*b*g^3 + a*b^4*d^3 - 27*a^5*h^3 - 8*b^5*c^3 - a^3*b^2*f^3, z, k)*a^2*b^2 - 6*a^2*h + 2*b^2*c*x + a*b*f*x))/a + (9*a^3*h^2 + 2*b^3*c*d + 4*a*b^2*c*g + a*b^2*d*f + 2*a^2*b*f*g)/(9*a^2*b^2) + (x*(b^2*d^2 + 4*a^2*g^2 - 3*a^2*f*h - 6*a*b*c*h + 4*a*b*d*g))/(9*a^2*b))*root(729*a^5*b^6*z^3 - 729*a^5*b^4*h*z^2 + 54*a^4*b^3*f*g*z + 108*a^3*b^4*c*g*z + 27*a^3*b^4*d*f*z + 54*a^2*b^5*c*d*z + 243*a^5*b^2*h^2*z - 18*a^4*b*f*g*h - 36*a^3*b^2*c*g*h - 9*a^3*b^2*d*f*h - 18*a^2*b^3*c*d*h - 12*a*b^4*c^2*f + 12*a^3*b^2*d*g^2 + 6*a^2*b^3*d^2*g - 6*a^2*b^3*c*f^2 + 8*a^4*b*g^3 + a*b^4*d^3 - 27*a^5*h^3 - 8*b^5*c^3 - a^3*b^2*f^3, z, k), k, 1, 3) + ((x*(b*c - a*f))/(3*a*b) - (b*e - a*h)/(3*b^2) + (x^2*(b*d - a*g))/(3*a*b))/(a + b*x^3)","B"
417,1,1660,289,5.601122,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x*(a + b*x^3)^2),x)","\frac{\frac{b\,c-a\,f}{3\,a\,b}+\frac{x\,\left(b\,d-a\,g\right)}{3\,a\,b}+\frac{x^2\,\left(b\,e-a\,h\right)}{3\,a\,b}}{b\,x^3+a}+\left(\sum _{k=1}^3\ln\left(\frac{c\,\left(a^2\,g^2+4\,a\,b\,d\,g-6\,c\,h\,a\,b+4\,b^2\,d^2-3\,c\,e\,b^2\right)}{9\,a^3}-\frac{\mathrm{root}\left(729\,a^6\,b^5\,z^3+729\,a^4\,b^5\,c\,z^2+54\,a^5\,b^2\,g\,h\,z+108\,a^4\,b^3\,d\,h\,z+27\,a^4\,b^3\,e\,g\,z+54\,a^3\,b^4\,d\,e\,z+243\,a^2\,b^5\,c^2\,z+18\,a\,b^4\,c\,d\,e+18\,a^3\,b^2\,c\,g\,h+36\,a^2\,b^3\,c\,d\,h+9\,a^2\,b^3\,c\,e\,g+12\,a^4\,b\,e\,h^2+6\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,d^2\,g-6\,a^3\,b^2\,d\,g^2-a^4\,b\,g^3-8\,a\,b^4\,d^3+8\,a^5\,h^3+27\,b^5\,c^3+a^2\,b^3\,e^3,z,k\right)\,\left(a^3\,g^2+4\,a\,b^2\,d^2+36\,b^3\,c^2\,x+{\mathrm{root}\left(729\,a^6\,b^5\,z^3+729\,a^4\,b^5\,c\,z^2+54\,a^5\,b^2\,g\,h\,z+108\,a^4\,b^3\,d\,h\,z+27\,a^4\,b^3\,e\,g\,z+54\,a^3\,b^4\,d\,e\,z+243\,a^2\,b^5\,c^2\,z+18\,a\,b^4\,c\,d\,e+18\,a^3\,b^2\,c\,g\,h+36\,a^2\,b^3\,c\,d\,h+9\,a^2\,b^3\,c\,e\,g+12\,a^4\,b\,e\,h^2+6\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,d^2\,g-6\,a^3\,b^2\,d\,g^2-a^4\,b\,g^3-8\,a\,b^4\,d^3+8\,a^5\,h^3+27\,b^5\,c^3+a^2\,b^3\,e^3,z,k\right)}^2\,a^4\,b^3\,x\,324-\mathrm{root}\left(729\,a^6\,b^5\,z^3+729\,a^4\,b^5\,c\,z^2+54\,a^5\,b^2\,g\,h\,z+108\,a^4\,b^3\,d\,h\,z+27\,a^4\,b^3\,e\,g\,z+54\,a^3\,b^4\,d\,e\,z+243\,a^2\,b^5\,c^2\,z+18\,a\,b^4\,c\,d\,e+18\,a^3\,b^2\,c\,g\,h+36\,a^2\,b^3\,c\,d\,h+9\,a^2\,b^3\,c\,e\,g+12\,a^4\,b\,e\,h^2+6\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,d^2\,g-6\,a^3\,b^2\,d\,g^2-a^4\,b\,g^3-8\,a\,b^4\,d^3+8\,a^5\,h^3+27\,b^5\,c^3+a^2\,b^3\,e^3,z,k\right)\,a^4\,b\,h\,18+6\,a\,b^2\,c\,e+12\,a^2\,b\,c\,h+4\,a^2\,b\,d\,g+20\,a^3\,g\,h\,x-\mathrm{root}\left(729\,a^6\,b^5\,z^3+729\,a^4\,b^5\,c\,z^2+54\,a^5\,b^2\,g\,h\,z+108\,a^4\,b^3\,d\,h\,z+27\,a^4\,b^3\,e\,g\,z+54\,a^3\,b^4\,d\,e\,z+243\,a^2\,b^5\,c^2\,z+18\,a\,b^4\,c\,d\,e+18\,a^3\,b^2\,c\,g\,h+36\,a^2\,b^3\,c\,d\,h+9\,a^2\,b^3\,c\,e\,g+12\,a^4\,b\,e\,h^2+6\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,d^2\,g-6\,a^3\,b^2\,d\,g^2-a^4\,b\,g^3-8\,a\,b^4\,d^3+8\,a^5\,h^3+27\,b^5\,c^3+a^2\,b^3\,e^3,z,k\right)\,a^3\,b^2\,e\,9+\mathrm{root}\left(729\,a^6\,b^5\,z^3+729\,a^4\,b^5\,c\,z^2+54\,a^5\,b^2\,g\,h\,z+108\,a^4\,b^3\,d\,h\,z+27\,a^4\,b^3\,e\,g\,z+54\,a^3\,b^4\,d\,e\,z+243\,a^2\,b^5\,c^2\,z+18\,a\,b^4\,c\,d\,e+18\,a^3\,b^2\,c\,g\,h+36\,a^2\,b^3\,c\,d\,h+9\,a^2\,b^3\,c\,e\,g+12\,a^4\,b\,e\,h^2+6\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,d^2\,g-6\,a^3\,b^2\,d\,g^2-a^4\,b\,g^3-8\,a\,b^4\,d^3+8\,a^5\,h^3+27\,b^5\,c^3+a^2\,b^3\,e^3,z,k\right)\,a^2\,b^3\,c\,x\,216+20\,a\,b^2\,d\,e\,x+40\,a^2\,b\,d\,h\,x+10\,a^2\,b\,e\,g\,x\right)}{a^2\,9}-\frac{x\,\left(8\,a^4\,h^3+12\,a^3\,b\,e\,h^2-a^3\,b\,g^3-6\,a^2\,b^2\,d\,g^2+6\,a^2\,b^2\,e^2\,h+12\,c\,a^2\,b^2\,g\,h-12\,a\,b^3\,d^2\,g+24\,c\,a\,b^3\,d\,h+a\,b^3\,e^3+6\,c\,a\,b^3\,e\,g-8\,b^4\,d^3+12\,c\,b^4\,d\,e\right)}{27\,a^3\,b^2}\right)\,\mathrm{root}\left(729\,a^6\,b^5\,z^3+729\,a^4\,b^5\,c\,z^2+54\,a^5\,b^2\,g\,h\,z+108\,a^4\,b^3\,d\,h\,z+27\,a^4\,b^3\,e\,g\,z+54\,a^3\,b^4\,d\,e\,z+243\,a^2\,b^5\,c^2\,z+18\,a\,b^4\,c\,d\,e+18\,a^3\,b^2\,c\,g\,h+36\,a^2\,b^3\,c\,d\,h+9\,a^2\,b^3\,c\,e\,g+12\,a^4\,b\,e\,h^2+6\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,d^2\,g-6\,a^3\,b^2\,d\,g^2-a^4\,b\,g^3-8\,a\,b^4\,d^3+8\,a^5\,h^3+27\,b^5\,c^3+a^2\,b^3\,e^3,z,k\right)\right)+\frac{c\,\ln\left(x\right)}{a^2}","Not used",1,"((b*c - a*f)/(3*a*b) + (x*(b*d - a*g))/(3*a*b) + (x^2*(b*e - a*h))/(3*a*b))/(a + b*x^3) + symsum(log((c*(4*b^2*d^2 + a^2*g^2 - 3*b^2*c*e - 6*a*b*c*h + 4*a*b*d*g))/(9*a^3) - (root(729*a^6*b^5*z^3 + 729*a^4*b^5*c*z^2 + 54*a^5*b^2*g*h*z + 108*a^4*b^3*d*h*z + 27*a^4*b^3*e*g*z + 54*a^3*b^4*d*e*z + 243*a^2*b^5*c^2*z + 18*a*b^4*c*d*e + 18*a^3*b^2*c*g*h + 36*a^2*b^3*c*d*h + 9*a^2*b^3*c*e*g + 12*a^4*b*e*h^2 + 6*a^3*b^2*e^2*h - 12*a^2*b^3*d^2*g - 6*a^3*b^2*d*g^2 - a^4*b*g^3 - 8*a*b^4*d^3 + 8*a^5*h^3 + 27*b^5*c^3 + a^2*b^3*e^3, z, k)*(a^3*g^2 + 4*a*b^2*d^2 + 36*b^3*c^2*x + 324*root(729*a^6*b^5*z^3 + 729*a^4*b^5*c*z^2 + 54*a^5*b^2*g*h*z + 108*a^4*b^3*d*h*z + 27*a^4*b^3*e*g*z + 54*a^3*b^4*d*e*z + 243*a^2*b^5*c^2*z + 18*a*b^4*c*d*e + 18*a^3*b^2*c*g*h + 36*a^2*b^3*c*d*h + 9*a^2*b^3*c*e*g + 12*a^4*b*e*h^2 + 6*a^3*b^2*e^2*h - 12*a^2*b^3*d^2*g - 6*a^3*b^2*d*g^2 - a^4*b*g^3 - 8*a*b^4*d^3 + 8*a^5*h^3 + 27*b^5*c^3 + a^2*b^3*e^3, z, k)^2*a^4*b^3*x - 18*root(729*a^6*b^5*z^3 + 729*a^4*b^5*c*z^2 + 54*a^5*b^2*g*h*z + 108*a^4*b^3*d*h*z + 27*a^4*b^3*e*g*z + 54*a^3*b^4*d*e*z + 243*a^2*b^5*c^2*z + 18*a*b^4*c*d*e + 18*a^3*b^2*c*g*h + 36*a^2*b^3*c*d*h + 9*a^2*b^3*c*e*g + 12*a^4*b*e*h^2 + 6*a^3*b^2*e^2*h - 12*a^2*b^3*d^2*g - 6*a^3*b^2*d*g^2 - a^4*b*g^3 - 8*a*b^4*d^3 + 8*a^5*h^3 + 27*b^5*c^3 + a^2*b^3*e^3, z, k)*a^4*b*h + 6*a*b^2*c*e + 12*a^2*b*c*h + 4*a^2*b*d*g + 20*a^3*g*h*x - 9*root(729*a^6*b^5*z^3 + 729*a^4*b^5*c*z^2 + 54*a^5*b^2*g*h*z + 108*a^4*b^3*d*h*z + 27*a^4*b^3*e*g*z + 54*a^3*b^4*d*e*z + 243*a^2*b^5*c^2*z + 18*a*b^4*c*d*e + 18*a^3*b^2*c*g*h + 36*a^2*b^3*c*d*h + 9*a^2*b^3*c*e*g + 12*a^4*b*e*h^2 + 6*a^3*b^2*e^2*h - 12*a^2*b^3*d^2*g - 6*a^3*b^2*d*g^2 - a^4*b*g^3 - 8*a*b^4*d^3 + 8*a^5*h^3 + 27*b^5*c^3 + a^2*b^3*e^3, z, k)*a^3*b^2*e + 216*root(729*a^6*b^5*z^3 + 729*a^4*b^5*c*z^2 + 54*a^5*b^2*g*h*z + 108*a^4*b^3*d*h*z + 27*a^4*b^3*e*g*z + 54*a^3*b^4*d*e*z + 243*a^2*b^5*c^2*z + 18*a*b^4*c*d*e + 18*a^3*b^2*c*g*h + 36*a^2*b^3*c*d*h + 9*a^2*b^3*c*e*g + 12*a^4*b*e*h^2 + 6*a^3*b^2*e^2*h - 12*a^2*b^3*d^2*g - 6*a^3*b^2*d*g^2 - a^4*b*g^3 - 8*a*b^4*d^3 + 8*a^5*h^3 + 27*b^5*c^3 + a^2*b^3*e^3, z, k)*a^2*b^3*c*x + 20*a*b^2*d*e*x + 40*a^2*b*d*h*x + 10*a^2*b*e*g*x))/(9*a^2) - (x*(8*a^4*h^3 - 8*b^4*d^3 + a*b^3*e^3 - a^3*b*g^3 - 6*a^2*b^2*d*g^2 + 6*a^2*b^2*e^2*h + 12*b^4*c*d*e - 12*a*b^3*d^2*g + 12*a^3*b*e*h^2 + 12*a^2*b^2*c*g*h + 24*a*b^3*c*d*h + 6*a*b^3*c*e*g))/(27*a^3*b^2))*root(729*a^6*b^5*z^3 + 729*a^4*b^5*c*z^2 + 54*a^5*b^2*g*h*z + 108*a^4*b^3*d*h*z + 27*a^4*b^3*e*g*z + 54*a^3*b^4*d*e*z + 243*a^2*b^5*c^2*z + 18*a*b^4*c*d*e + 18*a^3*b^2*c*g*h + 36*a^2*b^3*c*d*h + 9*a^2*b^3*c*e*g + 12*a^4*b*e*h^2 + 6*a^3*b^2*e^2*h - 12*a^2*b^3*d^2*g - 6*a^3*b^2*d*g^2 - a^4*b*g^3 - 8*a*b^4*d^3 + 8*a^5*h^3 + 27*b^5*c^3 + a^2*b^3*e^3, z, k), k, 1, 3) + (c*log(x))/a^2","B"
418,1,1684,301,5.768416,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^2*(a + b*x^3)^2),x)","\left(\sum _{k=1}^3\ln\left(\frac{d\,\left(a^3\,h^2+4\,a^2\,b\,e\,h+4\,a\,b^2\,e^2-3\,d\,f\,a\,b^2+12\,c\,d\,b^3\right)}{9\,a^4}-\frac{\mathrm{root}\left(729\,a^7\,b^4\,z^3+729\,a^5\,b^4\,d\,z^2+27\,a^5\,b^2\,f\,h\,z-108\,a^4\,b^3\,c\,h\,z+54\,a^4\,b^3\,e\,f\,z-216\,a^3\,b^4\,c\,e\,z+243\,a^3\,b^4\,d^2\,z-72\,a\,b^4\,c\,d\,e+9\,a^3\,b^2\,d\,f\,h-36\,a^2\,b^3\,c\,d\,h+18\,a^2\,b^3\,d\,e\,f-6\,a^4\,b\,e\,h^2+48\,a\,b^4\,c^2\,f-12\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,c\,f^2-8\,a^2\,b^3\,e^3+27\,a\,b^4\,d^3-a^5\,h^3-64\,b^5\,c^3+a^3\,b^2\,f^3,z,k\right)\,\left(a^3\,h^2+4\,a\,b^2\,e^2+36\,b^3\,d^2\,x-24\,b^3\,c\,d+{\mathrm{root}\left(729\,a^7\,b^4\,z^3+729\,a^5\,b^4\,d\,z^2+27\,a^5\,b^2\,f\,h\,z-108\,a^4\,b^3\,c\,h\,z+54\,a^4\,b^3\,e\,f\,z-216\,a^3\,b^4\,c\,e\,z+243\,a^3\,b^4\,d^2\,z-72\,a\,b^4\,c\,d\,e+9\,a^3\,b^2\,d\,f\,h-36\,a^2\,b^3\,c\,d\,h+18\,a^2\,b^3\,d\,e\,f-6\,a^4\,b\,e\,h^2+48\,a\,b^4\,c^2\,f-12\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,c\,f^2-8\,a^2\,b^3\,e^3+27\,a\,b^4\,d^3-a^5\,h^3-64\,b^5\,c^3+a^3\,b^2\,f^3,z,k\right)}^2\,a^4\,b^3\,x\,324+6\,a\,b^2\,d\,f+4\,a^2\,b\,e\,h-80\,b^3\,c\,e\,x+\mathrm{root}\left(729\,a^7\,b^4\,z^3+729\,a^5\,b^4\,d\,z^2+27\,a^5\,b^2\,f\,h\,z-108\,a^4\,b^3\,c\,h\,z+54\,a^4\,b^3\,e\,f\,z-216\,a^3\,b^4\,c\,e\,z+243\,a^3\,b^4\,d^2\,z-72\,a\,b^4\,c\,d\,e+9\,a^3\,b^2\,d\,f\,h-36\,a^2\,b^3\,c\,d\,h+18\,a^2\,b^3\,d\,e\,f-6\,a^4\,b\,e\,h^2+48\,a\,b^4\,c^2\,f-12\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,c\,f^2-8\,a^2\,b^3\,e^3+27\,a\,b^4\,d^3-a^5\,h^3-64\,b^5\,c^3+a^3\,b^2\,f^3,z,k\right)\,a^2\,b^3\,c\,36-\mathrm{root}\left(729\,a^7\,b^4\,z^3+729\,a^5\,b^4\,d\,z^2+27\,a^5\,b^2\,f\,h\,z-108\,a^4\,b^3\,c\,h\,z+54\,a^4\,b^3\,e\,f\,z-216\,a^3\,b^4\,c\,e\,z+243\,a^3\,b^4\,d^2\,z-72\,a\,b^4\,c\,d\,e+9\,a^3\,b^2\,d\,f\,h-36\,a^2\,b^3\,c\,d\,h+18\,a^2\,b^3\,d\,e\,f-6\,a^4\,b\,e\,h^2+48\,a\,b^4\,c^2\,f-12\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,c\,f^2-8\,a^2\,b^3\,e^3+27\,a\,b^4\,d^3-a^5\,h^3-64\,b^5\,c^3+a^3\,b^2\,f^3,z,k\right)\,a^3\,b^2\,f\,9+\mathrm{root}\left(729\,a^7\,b^4\,z^3+729\,a^5\,b^4\,d\,z^2+27\,a^5\,b^2\,f\,h\,z-108\,a^4\,b^3\,c\,h\,z+54\,a^4\,b^3\,e\,f\,z-216\,a^3\,b^4\,c\,e\,z+243\,a^3\,b^4\,d^2\,z-72\,a\,b^4\,c\,d\,e+9\,a^3\,b^2\,d\,f\,h-36\,a^2\,b^3\,c\,d\,h+18\,a^2\,b^3\,d\,e\,f-6\,a^4\,b\,e\,h^2+48\,a\,b^4\,c^2\,f-12\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,c\,f^2-8\,a^2\,b^3\,e^3+27\,a\,b^4\,d^3-a^5\,h^3-64\,b^5\,c^3+a^3\,b^2\,f^3,z,k\right)\,a^2\,b^3\,d\,x\,216-40\,a\,b^2\,c\,h\,x+20\,a\,b^2\,e\,f\,x+10\,a^2\,b\,f\,h\,x\right)}{a^2\,9}+\frac{x\,\left(a^5\,h^3+6\,a^4\,b\,e\,h^2+12\,a^3\,b^2\,e^2\,h-a^3\,b^2\,f^3-6\,d\,a^3\,b^2\,f\,h+12\,a^2\,b^3\,c\,f^2+24\,d\,a^2\,b^3\,c\,h+8\,a^2\,b^3\,e^3-12\,d\,a^2\,b^3\,e\,f-48\,a\,b^4\,c^2\,f+48\,d\,a\,b^4\,c\,e+64\,b^5\,c^3\right)}{27\,a^5\,b}\right)\,\mathrm{root}\left(729\,a^7\,b^4\,z^3+729\,a^5\,b^4\,d\,z^2+27\,a^5\,b^2\,f\,h\,z-108\,a^4\,b^3\,c\,h\,z+54\,a^4\,b^3\,e\,f\,z-216\,a^3\,b^4\,c\,e\,z+243\,a^3\,b^4\,d^2\,z-72\,a\,b^4\,c\,d\,e+9\,a^3\,b^2\,d\,f\,h-36\,a^2\,b^3\,c\,d\,h+18\,a^2\,b^3\,d\,e\,f-6\,a^4\,b\,e\,h^2+48\,a\,b^4\,c^2\,f-12\,a^3\,b^2\,e^2\,h-12\,a^2\,b^3\,c\,f^2-8\,a^2\,b^3\,e^3+27\,a\,b^4\,d^3-a^5\,h^3-64\,b^5\,c^3+a^3\,b^2\,f^3,z,k\right)\right)-\frac{\frac{c}{a}+\frac{x^3\,\left(4\,b\,c-a\,f\right)}{3\,a^2}-\frac{x\,\left(b\,d-a\,g\right)}{3\,a\,b}-\frac{x^2\,\left(b\,e-a\,h\right)}{3\,a\,b}}{b\,x^4+a\,x}+\frac{d\,\ln\left(x\right)}{a^2}","Not used",1,"symsum(log((d*(a^3*h^2 + 4*a*b^2*e^2 + 12*b^3*c*d - 3*a*b^2*d*f + 4*a^2*b*e*h))/(9*a^4) - (root(729*a^7*b^4*z^3 + 729*a^5*b^4*d*z^2 + 27*a^5*b^2*f*h*z - 108*a^4*b^3*c*h*z + 54*a^4*b^3*e*f*z - 216*a^3*b^4*c*e*z + 243*a^3*b^4*d^2*z - 72*a*b^4*c*d*e + 9*a^3*b^2*d*f*h - 36*a^2*b^3*c*d*h + 18*a^2*b^3*d*e*f - 6*a^4*b*e*h^2 + 48*a*b^4*c^2*f - 12*a^3*b^2*e^2*h - 12*a^2*b^3*c*f^2 - 8*a^2*b^3*e^3 + 27*a*b^4*d^3 - a^5*h^3 - 64*b^5*c^3 + a^3*b^2*f^3, z, k)*(a^3*h^2 + 4*a*b^2*e^2 + 36*b^3*d^2*x - 24*b^3*c*d + 324*root(729*a^7*b^4*z^3 + 729*a^5*b^4*d*z^2 + 27*a^5*b^2*f*h*z - 108*a^4*b^3*c*h*z + 54*a^4*b^3*e*f*z - 216*a^3*b^4*c*e*z + 243*a^3*b^4*d^2*z - 72*a*b^4*c*d*e + 9*a^3*b^2*d*f*h - 36*a^2*b^3*c*d*h + 18*a^2*b^3*d*e*f - 6*a^4*b*e*h^2 + 48*a*b^4*c^2*f - 12*a^3*b^2*e^2*h - 12*a^2*b^3*c*f^2 - 8*a^2*b^3*e^3 + 27*a*b^4*d^3 - a^5*h^3 - 64*b^5*c^3 + a^3*b^2*f^3, z, k)^2*a^4*b^3*x + 6*a*b^2*d*f + 4*a^2*b*e*h - 80*b^3*c*e*x + 36*root(729*a^7*b^4*z^3 + 729*a^5*b^4*d*z^2 + 27*a^5*b^2*f*h*z - 108*a^4*b^3*c*h*z + 54*a^4*b^3*e*f*z - 216*a^3*b^4*c*e*z + 243*a^3*b^4*d^2*z - 72*a*b^4*c*d*e + 9*a^3*b^2*d*f*h - 36*a^2*b^3*c*d*h + 18*a^2*b^3*d*e*f - 6*a^4*b*e*h^2 + 48*a*b^4*c^2*f - 12*a^3*b^2*e^2*h - 12*a^2*b^3*c*f^2 - 8*a^2*b^3*e^3 + 27*a*b^4*d^3 - a^5*h^3 - 64*b^5*c^3 + a^3*b^2*f^3, z, k)*a^2*b^3*c - 9*root(729*a^7*b^4*z^3 + 729*a^5*b^4*d*z^2 + 27*a^5*b^2*f*h*z - 108*a^4*b^3*c*h*z + 54*a^4*b^3*e*f*z - 216*a^3*b^4*c*e*z + 243*a^3*b^4*d^2*z - 72*a*b^4*c*d*e + 9*a^3*b^2*d*f*h - 36*a^2*b^3*c*d*h + 18*a^2*b^3*d*e*f - 6*a^4*b*e*h^2 + 48*a*b^4*c^2*f - 12*a^3*b^2*e^2*h - 12*a^2*b^3*c*f^2 - 8*a^2*b^3*e^3 + 27*a*b^4*d^3 - a^5*h^3 - 64*b^5*c^3 + a^3*b^2*f^3, z, k)*a^3*b^2*f + 216*root(729*a^7*b^4*z^3 + 729*a^5*b^4*d*z^2 + 27*a^5*b^2*f*h*z - 108*a^4*b^3*c*h*z + 54*a^4*b^3*e*f*z - 216*a^3*b^4*c*e*z + 243*a^3*b^4*d^2*z - 72*a*b^4*c*d*e + 9*a^3*b^2*d*f*h - 36*a^2*b^3*c*d*h + 18*a^2*b^3*d*e*f - 6*a^4*b*e*h^2 + 48*a*b^4*c^2*f - 12*a^3*b^2*e^2*h - 12*a^2*b^3*c*f^2 - 8*a^2*b^3*e^3 + 27*a*b^4*d^3 - a^5*h^3 - 64*b^5*c^3 + a^3*b^2*f^3, z, k)*a^2*b^3*d*x - 40*a*b^2*c*h*x + 20*a*b^2*e*f*x + 10*a^2*b*f*h*x))/(9*a^2) + (x*(64*b^5*c^3 + a^5*h^3 + 8*a^2*b^3*e^3 - a^3*b^2*f^3 + 12*a^2*b^3*c*f^2 + 12*a^3*b^2*e^2*h - 48*a*b^4*c^2*f + 6*a^4*b*e*h^2 + 24*a^2*b^3*c*d*h - 12*a^2*b^3*d*e*f - 6*a^3*b^2*d*f*h + 48*a*b^4*c*d*e))/(27*a^5*b))*root(729*a^7*b^4*z^3 + 729*a^5*b^4*d*z^2 + 27*a^5*b^2*f*h*z - 108*a^4*b^3*c*h*z + 54*a^4*b^3*e*f*z - 216*a^3*b^4*c*e*z + 243*a^3*b^4*d^2*z - 72*a*b^4*c*d*e + 9*a^3*b^2*d*f*h - 36*a^2*b^3*c*d*h + 18*a^2*b^3*d*e*f - 6*a^4*b*e*h^2 + 48*a*b^4*c^2*f - 12*a^3*b^2*e^2*h - 12*a^2*b^3*c*f^2 - 8*a^2*b^3*e^3 + 27*a*b^4*d^3 - a^5*h^3 - 64*b^5*c^3 + a^3*b^2*f^3, z, k), k, 1, 3) - (c/a + (x^3*(4*b*c - a*f))/(3*a^2) - (x*(b*d - a*g))/(3*a*b) - (x^2*(b*e - a*h))/(3*a*b))/(a*x + b*x^4) + (d*log(x))/a^2","B"
419,1,1632,306,5.711701,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^3*(a + b*x^3)^2),x)","\left(\sum _{k=1}^3\ln\left(\frac{b^2\,e\,\left(4\,a^2\,f^2-3\,e\,g\,a^2-20\,a\,b\,c\,f+12\,d\,e\,a\,b+25\,b^2\,c^2\right)}{9\,a^5}-\frac{\mathrm{root}\left(729\,a^8\,b^2\,z^3+729\,a^6\,b^2\,e\,z^2+54\,a^5\,b\,f\,g\,z-216\,a^4\,b^2\,d\,f\,z-135\,a^4\,b^2\,c\,g\,z+540\,a^3\,b^3\,c\,d\,z+243\,a^4\,b^2\,e^2\,z+18\,a^3\,b\,e\,f\,g+180\,a\,b^3\,c\,d\,e-72\,a^2\,b^2\,d\,e\,f-45\,a^2\,b^2\,c\,e\,g-12\,a^3\,b\,d\,g^2-150\,a\,b^3\,c^2\,f+48\,a^2\,b^2\,d^2\,g+60\,a^2\,b^2\,c\,f^2+27\,a^2\,b^2\,e^3-8\,a^3\,b\,f^3-64\,a\,b^3\,d^3+125\,b^4\,c^3+a^4\,g^3,z,k\right)\,b^2\,\left(25\,b^2\,c^2+4\,a^2\,f^2-\mathrm{root}\left(729\,a^8\,b^2\,z^3+729\,a^6\,b^2\,e\,z^2+54\,a^5\,b\,f\,g\,z-216\,a^4\,b^2\,d\,f\,z-135\,a^4\,b^2\,c\,g\,z+540\,a^3\,b^3\,c\,d\,z+243\,a^4\,b^2\,e^2\,z+18\,a^3\,b\,e\,f\,g+180\,a\,b^3\,c\,d\,e-72\,a^2\,b^2\,d\,e\,f-45\,a^2\,b^2\,c\,e\,g-12\,a^3\,b\,d\,g^2-150\,a\,b^3\,c^2\,f+48\,a^2\,b^2\,d^2\,g+60\,a^2\,b^2\,c\,f^2+27\,a^2\,b^2\,e^3-8\,a^3\,b\,f^3-64\,a\,b^3\,d^3+125\,b^4\,c^3+a^4\,g^3,z,k\right)\,a^4\,g\,9+6\,a^2\,e\,g+\mathrm{root}\left(729\,a^8\,b^2\,z^3+729\,a^6\,b^2\,e\,z^2+54\,a^5\,b\,f\,g\,z-216\,a^4\,b^2\,d\,f\,z-135\,a^4\,b^2\,c\,g\,z+540\,a^3\,b^3\,c\,d\,z+243\,a^4\,b^2\,e^2\,z+18\,a^3\,b\,e\,f\,g+180\,a\,b^3\,c\,d\,e-72\,a^2\,b^2\,d\,e\,f-45\,a^2\,b^2\,c\,e\,g-12\,a^3\,b\,d\,g^2-150\,a\,b^3\,c^2\,f+48\,a^2\,b^2\,d^2\,g+60\,a^2\,b^2\,c\,f^2+27\,a^2\,b^2\,e^3-8\,a^3\,b\,f^3-64\,a\,b^3\,d^3+125\,b^4\,c^3+a^4\,g^3,z,k\right)\,a^3\,b\,d\,36+36\,a\,b\,e^2\,x+200\,b^2\,c\,d\,x+20\,a^2\,f\,g\,x+{\mathrm{root}\left(729\,a^8\,b^2\,z^3+729\,a^6\,b^2\,e\,z^2+54\,a^5\,b\,f\,g\,z-216\,a^4\,b^2\,d\,f\,z-135\,a^4\,b^2\,c\,g\,z+540\,a^3\,b^3\,c\,d\,z+243\,a^4\,b^2\,e^2\,z+18\,a^3\,b\,e\,f\,g+180\,a\,b^3\,c\,d\,e-72\,a^2\,b^2\,d\,e\,f-45\,a^2\,b^2\,c\,e\,g-12\,a^3\,b\,d\,g^2-150\,a\,b^3\,c^2\,f+48\,a^2\,b^2\,d^2\,g+60\,a^2\,b^2\,c\,f^2+27\,a^2\,b^2\,e^3-8\,a^3\,b\,f^3-64\,a\,b^3\,d^3+125\,b^4\,c^3+a^4\,g^3,z,k\right)}^2\,a^5\,b\,x\,324-20\,a\,b\,c\,f-24\,a\,b\,d\,e-50\,a\,b\,c\,g\,x-80\,a\,b\,d\,f\,x+\mathrm{root}\left(729\,a^8\,b^2\,z^3+729\,a^6\,b^2\,e\,z^2+54\,a^5\,b\,f\,g\,z-216\,a^4\,b^2\,d\,f\,z-135\,a^4\,b^2\,c\,g\,z+540\,a^3\,b^3\,c\,d\,z+243\,a^4\,b^2\,e^2\,z+18\,a^3\,b\,e\,f\,g+180\,a\,b^3\,c\,d\,e-72\,a^2\,b^2\,d\,e\,f-45\,a^2\,b^2\,c\,e\,g-12\,a^3\,b\,d\,g^2-150\,a\,b^3\,c^2\,f+48\,a^2\,b^2\,d^2\,g+60\,a^2\,b^2\,c\,f^2+27\,a^2\,b^2\,e^3-8\,a^3\,b\,f^3-64\,a\,b^3\,d^3+125\,b^4\,c^3+a^4\,g^3,z,k\right)\,a^3\,b\,e\,x\,216\right)}{a^3\,9}-\frac{b\,x\,\left(a^4\,g^3-12\,a^3\,b\,d\,g^2-8\,a^3\,b\,f^3+12\,e\,a^3\,b\,f\,g+60\,a^2\,b^2\,c\,f^2-30\,e\,a^2\,b^2\,c\,g+48\,a^2\,b^2\,d^2\,g-48\,e\,a^2\,b^2\,d\,f-150\,a\,b^3\,c^2\,f+120\,e\,a\,b^3\,c\,d-64\,a\,b^3\,d^3+125\,b^4\,c^3\right)}{27\,a^6}\right)\,\mathrm{root}\left(729\,a^8\,b^2\,z^3+729\,a^6\,b^2\,e\,z^2+54\,a^5\,b\,f\,g\,z-216\,a^4\,b^2\,d\,f\,z-135\,a^4\,b^2\,c\,g\,z+540\,a^3\,b^3\,c\,d\,z+243\,a^4\,b^2\,e^2\,z+18\,a^3\,b\,e\,f\,g+180\,a\,b^3\,c\,d\,e-72\,a^2\,b^2\,d\,e\,f-45\,a^2\,b^2\,c\,e\,g-12\,a^3\,b\,d\,g^2-150\,a\,b^3\,c^2\,f+48\,a^2\,b^2\,d^2\,g+60\,a^2\,b^2\,c\,f^2+27\,a^2\,b^2\,e^3-8\,a^3\,b\,f^3-64\,a\,b^3\,d^3+125\,b^4\,c^3+a^4\,g^3,z,k\right)\right)-\frac{\frac{c}{2\,a}+\frac{x^3\,\left(5\,b\,c-2\,a\,f\right)}{6\,a^2}+\frac{x^4\,\left(4\,b\,d-a\,g\right)}{3\,a^2}+\frac{d\,x}{a}-\frac{x^2\,\left(b\,e-a\,h\right)}{3\,a\,b}}{b\,x^5+a\,x^2}+\frac{e\,\ln\left(x\right)}{a^2}","Not used",1,"symsum(log((b^2*e*(25*b^2*c^2 + 4*a^2*f^2 - 3*a^2*e*g - 20*a*b*c*f + 12*a*b*d*e))/(9*a^5) - (root(729*a^8*b^2*z^3 + 729*a^6*b^2*e*z^2 + 54*a^5*b*f*g*z - 216*a^4*b^2*d*f*z - 135*a^4*b^2*c*g*z + 540*a^3*b^3*c*d*z + 243*a^4*b^2*e^2*z + 18*a^3*b*e*f*g + 180*a*b^3*c*d*e - 72*a^2*b^2*d*e*f - 45*a^2*b^2*c*e*g - 12*a^3*b*d*g^2 - 150*a*b^3*c^2*f + 48*a^2*b^2*d^2*g + 60*a^2*b^2*c*f^2 + 27*a^2*b^2*e^3 - 8*a^3*b*f^3 - 64*a*b^3*d^3 + 125*b^4*c^3 + a^4*g^3, z, k)*b^2*(25*b^2*c^2 + 4*a^2*f^2 - 9*root(729*a^8*b^2*z^3 + 729*a^6*b^2*e*z^2 + 54*a^5*b*f*g*z - 216*a^4*b^2*d*f*z - 135*a^4*b^2*c*g*z + 540*a^3*b^3*c*d*z + 243*a^4*b^2*e^2*z + 18*a^3*b*e*f*g + 180*a*b^3*c*d*e - 72*a^2*b^2*d*e*f - 45*a^2*b^2*c*e*g - 12*a^3*b*d*g^2 - 150*a*b^3*c^2*f + 48*a^2*b^2*d^2*g + 60*a^2*b^2*c*f^2 + 27*a^2*b^2*e^3 - 8*a^3*b*f^3 - 64*a*b^3*d^3 + 125*b^4*c^3 + a^4*g^3, z, k)*a^4*g + 6*a^2*e*g + 36*root(729*a^8*b^2*z^3 + 729*a^6*b^2*e*z^2 + 54*a^5*b*f*g*z - 216*a^4*b^2*d*f*z - 135*a^4*b^2*c*g*z + 540*a^3*b^3*c*d*z + 243*a^4*b^2*e^2*z + 18*a^3*b*e*f*g + 180*a*b^3*c*d*e - 72*a^2*b^2*d*e*f - 45*a^2*b^2*c*e*g - 12*a^3*b*d*g^2 - 150*a*b^3*c^2*f + 48*a^2*b^2*d^2*g + 60*a^2*b^2*c*f^2 + 27*a^2*b^2*e^3 - 8*a^3*b*f^3 - 64*a*b^3*d^3 + 125*b^4*c^3 + a^4*g^3, z, k)*a^3*b*d + 36*a*b*e^2*x + 200*b^2*c*d*x + 20*a^2*f*g*x + 324*root(729*a^8*b^2*z^3 + 729*a^6*b^2*e*z^2 + 54*a^5*b*f*g*z - 216*a^4*b^2*d*f*z - 135*a^4*b^2*c*g*z + 540*a^3*b^3*c*d*z + 243*a^4*b^2*e^2*z + 18*a^3*b*e*f*g + 180*a*b^3*c*d*e - 72*a^2*b^2*d*e*f - 45*a^2*b^2*c*e*g - 12*a^3*b*d*g^2 - 150*a*b^3*c^2*f + 48*a^2*b^2*d^2*g + 60*a^2*b^2*c*f^2 + 27*a^2*b^2*e^3 - 8*a^3*b*f^3 - 64*a*b^3*d^3 + 125*b^4*c^3 + a^4*g^3, z, k)^2*a^5*b*x - 20*a*b*c*f - 24*a*b*d*e - 50*a*b*c*g*x - 80*a*b*d*f*x + 216*root(729*a^8*b^2*z^3 + 729*a^6*b^2*e*z^2 + 54*a^5*b*f*g*z - 216*a^4*b^2*d*f*z - 135*a^4*b^2*c*g*z + 540*a^3*b^3*c*d*z + 243*a^4*b^2*e^2*z + 18*a^3*b*e*f*g + 180*a*b^3*c*d*e - 72*a^2*b^2*d*e*f - 45*a^2*b^2*c*e*g - 12*a^3*b*d*g^2 - 150*a*b^3*c^2*f + 48*a^2*b^2*d^2*g + 60*a^2*b^2*c*f^2 + 27*a^2*b^2*e^3 - 8*a^3*b*f^3 - 64*a*b^3*d^3 + 125*b^4*c^3 + a^4*g^3, z, k)*a^3*b*e*x))/(9*a^3) - (b*x*(125*b^4*c^3 + a^4*g^3 - 64*a*b^3*d^3 - 8*a^3*b*f^3 + 60*a^2*b^2*c*f^2 + 48*a^2*b^2*d^2*g - 150*a*b^3*c^2*f - 12*a^3*b*d*g^2 - 30*a^2*b^2*c*e*g - 48*a^2*b^2*d*e*f + 120*a*b^3*c*d*e + 12*a^3*b*e*f*g))/(27*a^6))*root(729*a^8*b^2*z^3 + 729*a^6*b^2*e*z^2 + 54*a^5*b*f*g*z - 216*a^4*b^2*d*f*z - 135*a^4*b^2*c*g*z + 540*a^3*b^3*c*d*z + 243*a^4*b^2*e^2*z + 18*a^3*b*e*f*g + 180*a*b^3*c*d*e - 72*a^2*b^2*d*e*f - 45*a^2*b^2*c*e*g - 12*a^3*b*d*g^2 - 150*a*b^3*c^2*f + 48*a^2*b^2*d^2*g + 60*a^2*b^2*c*f^2 + 27*a^2*b^2*e^3 - 8*a^3*b*f^3 - 64*a*b^3*d^3 + 125*b^4*c^3 + a^4*g^3, z, k), k, 1, 3) - (c/(2*a) + (x^3*(5*b*c - 2*a*f))/(6*a^2) + (x^4*(4*b*d - a*g))/(3*a^2) + (d*x)/a - (x^2*(b*e - a*h))/(3*a*b))/(a*x^2 + b*x^5) + (e*log(x))/a^2","B"
420,1,1924,338,5.957865,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^4*(a + b*x^3)^2),x)","\left(\sum _{k=1}^3\ln\left(-\frac{3\,h\,a^3\,b^2\,f^2-4\,a^3\,b^2\,f\,g^2-12\,h\,a^2\,b^3\,c\,f+8\,a^2\,b^3\,c\,g^2+20\,a^2\,b^3\,d\,f\,g-12\,e\,a^2\,b^3\,f^2+12\,h\,a\,b^4\,c^2-40\,a\,b^4\,c\,d\,g+48\,e\,a\,b^4\,c\,f-25\,a\,b^4\,d^2\,f-48\,e\,b^5\,c^2+50\,b^5\,c\,d^2}{9\,a^6}-\mathrm{root}\left(729\,a^9\,b^2\,z^3+729\,a^7\,b^2\,f\,z^2-1458\,a^6\,b^3\,c\,z^2+54\,a^6\,b\,g\,h\,z-216\,a^5\,b^2\,e\,g\,z-135\,a^5\,b^2\,d\,h\,z-972\,a^4\,b^3\,c\,f\,z+540\,a^4\,b^3\,d\,e\,z+243\,a^5\,b^2\,f^2\,z+972\,a^3\,b^4\,c^2\,z+18\,a^4\,b\,f\,g\,h-360\,a\,b^4\,c\,d\,e-72\,a^3\,b^2\,e\,f\,g-45\,a^3\,b^2\,d\,f\,h-36\,a^3\,b^2\,c\,g\,h+180\,a^2\,b^3\,d\,e\,f+144\,a^2\,b^3\,c\,e\,g+90\,a^2\,b^3\,c\,d\,h-12\,a^4\,b\,e\,h^2+324\,a\,b^4\,c^2\,f+48\,a^3\,b^2\,e^2\,h-150\,a^2\,b^3\,d^2\,g+60\,a^3\,b^2\,d\,g^2-162\,a^2\,b^3\,c\,f^2+27\,a^3\,b^2\,f^3-64\,a^2\,b^3\,e^3-8\,a^4\,b\,g^3+125\,a\,b^4\,d^3-216\,b^5\,c^3+a^5\,h^3,z,k\right)\,\left(\frac{25\,a^3\,b^4\,d^2+4\,a^5\,b^2\,g^2+48\,a^3\,b^4\,c\,e-12\,a^4\,b^3\,c\,h-20\,a^4\,b^3\,d\,g-24\,a^4\,b^3\,e\,f+6\,a^5\,b^2\,f\,h}{9\,a^6}+\mathrm{root}\left(729\,a^9\,b^2\,z^3+729\,a^7\,b^2\,f\,z^2-1458\,a^6\,b^3\,c\,z^2+54\,a^6\,b\,g\,h\,z-216\,a^5\,b^2\,e\,g\,z-135\,a^5\,b^2\,d\,h\,z-972\,a^4\,b^3\,c\,f\,z+540\,a^4\,b^3\,d\,e\,z+243\,a^5\,b^2\,f^2\,z+972\,a^3\,b^4\,c^2\,z+18\,a^4\,b\,f\,g\,h-360\,a\,b^4\,c\,d\,e-72\,a^3\,b^2\,e\,f\,g-45\,a^3\,b^2\,d\,f\,h-36\,a^3\,b^2\,c\,g\,h+180\,a^2\,b^3\,d\,e\,f+144\,a^2\,b^3\,c\,e\,g+90\,a^2\,b^3\,c\,d\,h-12\,a^4\,b\,e\,h^2+324\,a\,b^4\,c^2\,f+48\,a^3\,b^2\,e^2\,h-150\,a^2\,b^3\,d^2\,g+60\,a^3\,b^2\,d\,g^2-162\,a^2\,b^3\,c\,f^2+27\,a^3\,b^2\,f^3-64\,a^2\,b^3\,e^3-8\,a^4\,b\,g^3+125\,a\,b^4\,d^3-216\,b^5\,c^3+a^5\,h^3,z,k\right)\,\left(\frac{36\,a^6\,b^3\,e-9\,a^7\,b^2\,h}{9\,a^6}-\frac{x\,\left(1296\,a^5\,b^4\,c-648\,a^6\,b^3\,f\right)}{27\,a^6}+\mathrm{root}\left(729\,a^9\,b^2\,z^3+729\,a^7\,b^2\,f\,z^2-1458\,a^6\,b^3\,c\,z^2+54\,a^6\,b\,g\,h\,z-216\,a^5\,b^2\,e\,g\,z-135\,a^5\,b^2\,d\,h\,z-972\,a^4\,b^3\,c\,f\,z+540\,a^4\,b^3\,d\,e\,z+243\,a^5\,b^2\,f^2\,z+972\,a^3\,b^4\,c^2\,z+18\,a^4\,b\,f\,g\,h-360\,a\,b^4\,c\,d\,e-72\,a^3\,b^2\,e\,f\,g-45\,a^3\,b^2\,d\,f\,h-36\,a^3\,b^2\,c\,g\,h+180\,a^2\,b^3\,d\,e\,f+144\,a^2\,b^3\,c\,e\,g+90\,a^2\,b^3\,c\,d\,h-12\,a^4\,b\,e\,h^2+324\,a\,b^4\,c^2\,f+48\,a^3\,b^2\,e^2\,h-150\,a^2\,b^3\,d^2\,g+60\,a^3\,b^2\,d\,g^2-162\,a^2\,b^3\,c\,f^2+27\,a^3\,b^2\,f^3-64\,a^2\,b^3\,e^3-8\,a^4\,b\,g^3+125\,a\,b^4\,d^3-216\,b^5\,c^3+a^5\,h^3,z,k\right)\,a^2\,b^3\,x\,36\right)+\frac{x\,\left(432\,a^2\,b^5\,c^2+108\,a^4\,b^3\,f^2-432\,a^3\,b^4\,c\,f+600\,a^3\,b^4\,d\,e-150\,a^4\,b^3\,d\,h-240\,a^4\,b^3\,e\,g+60\,a^5\,b^2\,g\,h\right)}{27\,a^6}\right)-\frac{x\,\left(a^4\,b\,h^3-12\,a^3\,b^2\,e\,h^2-8\,a^3\,b^2\,g^3+12\,f\,a^3\,b^2\,g\,h+60\,a^2\,b^3\,d\,g^2-30\,f\,a^2\,b^3\,d\,h+48\,a^2\,b^3\,e^2\,h-48\,f\,a^2\,b^3\,e\,g-24\,c\,a^2\,b^3\,g\,h-150\,a\,b^4\,d^2\,g+120\,f\,a\,b^4\,d\,e+60\,c\,a\,b^4\,d\,h-64\,a\,b^4\,e^3+96\,c\,a\,b^4\,e\,g+125\,b^5\,d^3-240\,c\,b^5\,d\,e\right)}{27\,a^6}\right)\,\mathrm{root}\left(729\,a^9\,b^2\,z^3+729\,a^7\,b^2\,f\,z^2-1458\,a^6\,b^3\,c\,z^2+54\,a^6\,b\,g\,h\,z-216\,a^5\,b^2\,e\,g\,z-135\,a^5\,b^2\,d\,h\,z-972\,a^4\,b^3\,c\,f\,z+540\,a^4\,b^3\,d\,e\,z+243\,a^5\,b^2\,f^2\,z+972\,a^3\,b^4\,c^2\,z+18\,a^4\,b\,f\,g\,h-360\,a\,b^4\,c\,d\,e-72\,a^3\,b^2\,e\,f\,g-45\,a^3\,b^2\,d\,f\,h-36\,a^3\,b^2\,c\,g\,h+180\,a^2\,b^3\,d\,e\,f+144\,a^2\,b^3\,c\,e\,g+90\,a^2\,b^3\,c\,d\,h-12\,a^4\,b\,e\,h^2+324\,a\,b^4\,c^2\,f+48\,a^3\,b^2\,e^2\,h-150\,a^2\,b^3\,d^2\,g+60\,a^3\,b^2\,d\,g^2-162\,a^2\,b^3\,c\,f^2+27\,a^3\,b^2\,f^3-64\,a^2\,b^3\,e^3-8\,a^4\,b\,g^3+125\,a\,b^4\,d^3-216\,b^5\,c^3+a^5\,h^3,z,k\right)\right)-\frac{\frac{c}{3\,a}+\frac{e\,x^2}{a}+\frac{x^3\,\left(2\,b\,c-a\,f\right)}{3\,a^2}+\frac{x^4\,\left(5\,b\,d-2\,a\,g\right)}{6\,a^2}+\frac{x^5\,\left(4\,b\,e-a\,h\right)}{3\,a^2}+\frac{d\,x}{2\,a}}{b\,x^6+a\,x^3}-\frac{\ln\left(x\right)\,\left(2\,b\,c-a\,f\right)}{a^3}","Not used",1,"symsum(log(- (50*b^5*c*d^2 - 48*b^5*c^2*e + 8*a^2*b^3*c*g^2 - 12*a^2*b^3*e*f^2 - 4*a^3*b^2*f*g^2 + 3*a^3*b^2*f^2*h - 25*a*b^4*d^2*f + 12*a*b^4*c^2*h - 12*a^2*b^3*c*f*h + 20*a^2*b^3*d*f*g - 40*a*b^4*c*d*g + 48*a*b^4*c*e*f)/(9*a^6) - root(729*a^9*b^2*z^3 + 729*a^7*b^2*f*z^2 - 1458*a^6*b^3*c*z^2 + 54*a^6*b*g*h*z - 216*a^5*b^2*e*g*z - 135*a^5*b^2*d*h*z - 972*a^4*b^3*c*f*z + 540*a^4*b^3*d*e*z + 243*a^5*b^2*f^2*z + 972*a^3*b^4*c^2*z + 18*a^4*b*f*g*h - 360*a*b^4*c*d*e - 72*a^3*b^2*e*f*g - 45*a^3*b^2*d*f*h - 36*a^3*b^2*c*g*h + 180*a^2*b^3*d*e*f + 144*a^2*b^3*c*e*g + 90*a^2*b^3*c*d*h - 12*a^4*b*e*h^2 + 324*a*b^4*c^2*f + 48*a^3*b^2*e^2*h - 150*a^2*b^3*d^2*g + 60*a^3*b^2*d*g^2 - 162*a^2*b^3*c*f^2 + 27*a^3*b^2*f^3 - 64*a^2*b^3*e^3 - 8*a^4*b*g^3 + 125*a*b^4*d^3 - 216*b^5*c^3 + a^5*h^3, z, k)*((25*a^3*b^4*d^2 + 4*a^5*b^2*g^2 + 48*a^3*b^4*c*e - 12*a^4*b^3*c*h - 20*a^4*b^3*d*g - 24*a^4*b^3*e*f + 6*a^5*b^2*f*h)/(9*a^6) + root(729*a^9*b^2*z^3 + 729*a^7*b^2*f*z^2 - 1458*a^6*b^3*c*z^2 + 54*a^6*b*g*h*z - 216*a^5*b^2*e*g*z - 135*a^5*b^2*d*h*z - 972*a^4*b^3*c*f*z + 540*a^4*b^3*d*e*z + 243*a^5*b^2*f^2*z + 972*a^3*b^4*c^2*z + 18*a^4*b*f*g*h - 360*a*b^4*c*d*e - 72*a^3*b^2*e*f*g - 45*a^3*b^2*d*f*h - 36*a^3*b^2*c*g*h + 180*a^2*b^3*d*e*f + 144*a^2*b^3*c*e*g + 90*a^2*b^3*c*d*h - 12*a^4*b*e*h^2 + 324*a*b^4*c^2*f + 48*a^3*b^2*e^2*h - 150*a^2*b^3*d^2*g + 60*a^3*b^2*d*g^2 - 162*a^2*b^3*c*f^2 + 27*a^3*b^2*f^3 - 64*a^2*b^3*e^3 - 8*a^4*b*g^3 + 125*a*b^4*d^3 - 216*b^5*c^3 + a^5*h^3, z, k)*((36*a^6*b^3*e - 9*a^7*b^2*h)/(9*a^6) - (x*(1296*a^5*b^4*c - 648*a^6*b^3*f))/(27*a^6) + 36*root(729*a^9*b^2*z^3 + 729*a^7*b^2*f*z^2 - 1458*a^6*b^3*c*z^2 + 54*a^6*b*g*h*z - 216*a^5*b^2*e*g*z - 135*a^5*b^2*d*h*z - 972*a^4*b^3*c*f*z + 540*a^4*b^3*d*e*z + 243*a^5*b^2*f^2*z + 972*a^3*b^4*c^2*z + 18*a^4*b*f*g*h - 360*a*b^4*c*d*e - 72*a^3*b^2*e*f*g - 45*a^3*b^2*d*f*h - 36*a^3*b^2*c*g*h + 180*a^2*b^3*d*e*f + 144*a^2*b^3*c*e*g + 90*a^2*b^3*c*d*h - 12*a^4*b*e*h^2 + 324*a*b^4*c^2*f + 48*a^3*b^2*e^2*h - 150*a^2*b^3*d^2*g + 60*a^3*b^2*d*g^2 - 162*a^2*b^3*c*f^2 + 27*a^3*b^2*f^3 - 64*a^2*b^3*e^3 - 8*a^4*b*g^3 + 125*a*b^4*d^3 - 216*b^5*c^3 + a^5*h^3, z, k)*a^2*b^3*x) + (x*(432*a^2*b^5*c^2 + 108*a^4*b^3*f^2 - 432*a^3*b^4*c*f + 600*a^3*b^4*d*e - 150*a^4*b^3*d*h - 240*a^4*b^3*e*g + 60*a^5*b^2*g*h))/(27*a^6)) - (x*(125*b^5*d^3 - 64*a*b^4*e^3 + a^4*b*h^3 - 8*a^3*b^2*g^3 + 60*a^2*b^3*d*g^2 + 48*a^2*b^3*e^2*h - 12*a^3*b^2*e*h^2 - 240*b^5*c*d*e - 150*a*b^4*d^2*g - 24*a^2*b^3*c*g*h - 30*a^2*b^3*d*f*h - 48*a^2*b^3*e*f*g + 12*a^3*b^2*f*g*h + 60*a*b^4*c*d*h + 96*a*b^4*c*e*g + 120*a*b^4*d*e*f))/(27*a^6))*root(729*a^9*b^2*z^3 + 729*a^7*b^2*f*z^2 - 1458*a^6*b^3*c*z^2 + 54*a^6*b*g*h*z - 216*a^5*b^2*e*g*z - 135*a^5*b^2*d*h*z - 972*a^4*b^3*c*f*z + 540*a^4*b^3*d*e*z + 243*a^5*b^2*f^2*z + 972*a^3*b^4*c^2*z + 18*a^4*b*f*g*h - 360*a*b^4*c*d*e - 72*a^3*b^2*e*f*g - 45*a^3*b^2*d*f*h - 36*a^3*b^2*c*g*h + 180*a^2*b^3*d*e*f + 144*a^2*b^3*c*e*g + 90*a^2*b^3*c*d*h - 12*a^4*b*e*h^2 + 324*a*b^4*c^2*f + 48*a^3*b^2*e^2*h - 150*a^2*b^3*d^2*g + 60*a^3*b^2*d*g^2 - 162*a^2*b^3*c*f^2 + 27*a^3*b^2*f^3 - 64*a^2*b^3*e^3 - 8*a^4*b*g^3 + 125*a*b^4*d^3 - 216*b^5*c^3 + a^5*h^3, z, k), k, 1, 3) - (c/(3*a) + (e*x^2)/a + (x^3*(2*b*c - a*f))/(3*a^2) + (x^4*(5*b*d - 2*a*g))/(6*a^2) + (x^5*(4*b*e - a*h))/(3*a^2) + (d*x)/(2*a))/(a*x^3 + b*x^6) - (log(x)*(2*b*c - a*f))/a^3","B"
421,1,916,345,0.578835,"\text{Not used}","int((x^4*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^3,x)","\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(19683\,a^4\,b^{10}\,z^3-19683\,a^4\,b^7\,g\,z^2-5670\,a^4\,b^4\,f\,h\,z-1134\,a^3\,b^5\,c\,h\,z+810\,a^3\,b^5\,e\,f\,z+162\,a^2\,b^6\,c\,e\,z+6561\,a^4\,b^4\,g^2\,z+1890\,a^4\,b\,f\,g\,h+378\,a^3\,b^2\,c\,g\,h-270\,a^3\,b^2\,e\,f\,g-54\,a^2\,b^3\,c\,e\,g-1176\,a^4\,b\,e\,h^2+15\,a\,b^4\,c^2\,f+168\,a^3\,b^2\,e^2\,h+75\,a^2\,b^3\,c\,f^2+125\,a^3\,b^2\,f^3-8\,a^2\,b^3\,e^3-729\,a^4\,b\,g^3+2744\,a^5\,h^3+b^5\,c^3,z,k\right)\,\left(\mathrm{root}\left(19683\,a^4\,b^{10}\,z^3-19683\,a^4\,b^7\,g\,z^2-5670\,a^4\,b^4\,f\,h\,z-1134\,a^3\,b^5\,c\,h\,z+810\,a^3\,b^5\,e\,f\,z+162\,a^2\,b^6\,c\,e\,z+6561\,a^4\,b^4\,g^2\,z+1890\,a^4\,b\,f\,g\,h+378\,a^3\,b^2\,c\,g\,h-270\,a^3\,b^2\,e\,f\,g-54\,a^2\,b^3\,c\,e\,g-1176\,a^4\,b\,e\,h^2+15\,a\,b^4\,c^2\,f+168\,a^3\,b^2\,e^2\,h+75\,a^2\,b^3\,c\,f^2+125\,a^3\,b^2\,f^3-8\,a^2\,b^3\,e^3-729\,a^4\,b\,g^3+2744\,a^5\,h^3+b^5\,c^3,z,k\right)\,a\,b^2\,9-\frac{6\,a\,g}{b}+\frac{x\,\left(54\,a^2\,b^4\,e-378\,a^3\,b^3\,h\right)}{81\,a^2\,b^4}\right)+\frac{81\,a^2\,g^2+2\,b^2\,c\,e-70\,a^2\,f\,h-14\,a\,b\,c\,h+10\,a\,b\,e\,f}{81\,a\,b^4}+\frac{x\,\left(126\,g\,h\,a^3+25\,a^2\,b\,f^2-18\,e\,g\,a^2\,b+10\,a\,b^2\,c\,f+b^3\,c^2\right)}{81\,a^2\,b^4}\right)\,\mathrm{root}\left(19683\,a^4\,b^{10}\,z^3-19683\,a^4\,b^7\,g\,z^2-5670\,a^4\,b^4\,f\,h\,z-1134\,a^3\,b^5\,c\,h\,z+810\,a^3\,b^5\,e\,f\,z+162\,a^2\,b^6\,c\,e\,z+6561\,a^4\,b^4\,g^2\,z+1890\,a^4\,b\,f\,g\,h+378\,a^3\,b^2\,c\,g\,h-270\,a^3\,b^2\,e\,f\,g-54\,a^2\,b^3\,c\,e\,g-1176\,a^4\,b\,e\,h^2+15\,a\,b^4\,c^2\,f+168\,a^3\,b^2\,e^2\,h+75\,a^2\,b^3\,c\,f^2+125\,a^3\,b^2\,f^3-8\,a^2\,b^3\,e^3-729\,a^4\,b\,g^3+2744\,a^5\,h^3+b^5\,c^3,z,k\right)\right)-\frac{x^2\,\left(\frac{c\,b^2}{18}+\frac{5\,a\,f\,b}{18}\right)-\frac{a^2\,g}{2}-x\,\left(\frac{5\,a^2\,h}{9}-\frac{2\,a\,b\,e}{9}\right)+x^3\,\left(\frac{b^2\,d}{3}-\frac{2\,a\,b\,g}{3}\right)+\frac{b\,x^4\,\left(7\,b\,e-13\,a\,h\right)}{18}+\frac{a\,b\,d}{6}-\frac{b\,x^5\,\left(b^2\,c-4\,a\,b\,f\right)}{9\,a}}{a^2\,b^3+2\,a\,b^4\,x^3+b^5\,x^6}+\frac{h\,x}{b^3}","Not used",1,"symsum(log(root(19683*a^4*b^10*z^3 - 19683*a^4*b^7*g*z^2 - 5670*a^4*b^4*f*h*z - 1134*a^3*b^5*c*h*z + 810*a^3*b^5*e*f*z + 162*a^2*b^6*c*e*z + 6561*a^4*b^4*g^2*z + 1890*a^4*b*f*g*h + 378*a^3*b^2*c*g*h - 270*a^3*b^2*e*f*g - 54*a^2*b^3*c*e*g - 1176*a^4*b*e*h^2 + 15*a*b^4*c^2*f + 168*a^3*b^2*e^2*h + 75*a^2*b^3*c*f^2 + 125*a^3*b^2*f^3 - 8*a^2*b^3*e^3 - 729*a^4*b*g^3 + 2744*a^5*h^3 + b^5*c^3, z, k)*(9*root(19683*a^4*b^10*z^3 - 19683*a^4*b^7*g*z^2 - 5670*a^4*b^4*f*h*z - 1134*a^3*b^5*c*h*z + 810*a^3*b^5*e*f*z + 162*a^2*b^6*c*e*z + 6561*a^4*b^4*g^2*z + 1890*a^4*b*f*g*h + 378*a^3*b^2*c*g*h - 270*a^3*b^2*e*f*g - 54*a^2*b^3*c*e*g - 1176*a^4*b*e*h^2 + 15*a*b^4*c^2*f + 168*a^3*b^2*e^2*h + 75*a^2*b^3*c*f^2 + 125*a^3*b^2*f^3 - 8*a^2*b^3*e^3 - 729*a^4*b*g^3 + 2744*a^5*h^3 + b^5*c^3, z, k)*a*b^2 - (6*a*g)/b + (x*(54*a^2*b^4*e - 378*a^3*b^3*h))/(81*a^2*b^4)) + (81*a^2*g^2 + 2*b^2*c*e - 70*a^2*f*h - 14*a*b*c*h + 10*a*b*e*f)/(81*a*b^4) + (x*(b^3*c^2 + 25*a^2*b*f^2 + 126*a^3*g*h + 10*a*b^2*c*f - 18*a^2*b*e*g))/(81*a^2*b^4))*root(19683*a^4*b^10*z^3 - 19683*a^4*b^7*g*z^2 - 5670*a^4*b^4*f*h*z - 1134*a^3*b^5*c*h*z + 810*a^3*b^5*e*f*z + 162*a^2*b^6*c*e*z + 6561*a^4*b^4*g^2*z + 1890*a^4*b*f*g*h + 378*a^3*b^2*c*g*h - 270*a^3*b^2*e*f*g - 54*a^2*b^3*c*e*g - 1176*a^4*b*e*h^2 + 15*a*b^4*c^2*f + 168*a^3*b^2*e^2*h + 75*a^2*b^3*c*f^2 + 125*a^3*b^2*f^3 - 8*a^2*b^3*e^3 - 729*a^4*b*g^3 + 2744*a^5*h^3 + b^5*c^3, z, k), k, 1, 3) - (x^2*((b^2*c)/18 + (5*a*b*f)/18) - (a^2*g)/2 - x*((5*a^2*h)/9 - (2*a*b*e)/9) + x^3*((b^2*d)/3 - (2*a*b*g)/3) + (b*x^4*(7*b*e - 13*a*h))/18 + (a*b*d)/6 - (b*x^5*(b^2*c - 4*a*b*f))/(9*a))/(a^2*b^3 + b^5*x^6 + 2*a*b^4*x^3) + (h*x)/b^3","B"
422,1,908,325,5.658665,"\text{Not used}","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{\frac{3\,a^2\,h-a\,b\,e}{6\,b^3}-\frac{x\,\left(b\,c+2\,a\,f\right)}{9\,b^2}-\frac{x^2\,\left(b\,d+5\,a\,g\right)}{18\,b^2}-\frac{x^3\,\left(b\,e-2\,a\,h\right)}{3\,b^2}+\frac{x^4\,\left(b\,c-7\,a\,f\right)}{18\,a\,b}+\frac{x^5\,\left(b\,d-4\,a\,g\right)}{9\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(19683\,a^5\,b^9\,z^3-19683\,a^5\,b^6\,h\,z^2+810\,a^4\,b^4\,f\,g\,z+405\,a^3\,b^5\,c\,g\,z+162\,a^3\,b^5\,d\,f\,z+81\,a^2\,b^6\,c\,d\,z+6561\,a^5\,b^3\,h^2\,z-270\,a^4\,b\,f\,g\,h-135\,a^3\,b^2\,c\,g\,h-54\,a^3\,b^2\,d\,f\,h-27\,a^2\,b^3\,c\,d\,h-6\,a\,b^4\,c^2\,f+75\,a^3\,b^2\,d\,g^2+15\,a^2\,b^3\,d^2\,g-12\,a^2\,b^3\,c\,f^2-8\,a^3\,b^2\,f^3+125\,a^4\,b\,g^3+a\,b^4\,d^3-729\,a^5\,h^3-b^5\,c^3,z,k\right)\,\left(\mathrm{root}\left(19683\,a^5\,b^9\,z^3-19683\,a^5\,b^6\,h\,z^2+810\,a^4\,b^4\,f\,g\,z+405\,a^3\,b^5\,c\,g\,z+162\,a^3\,b^5\,d\,f\,z+81\,a^2\,b^6\,c\,d\,z+6561\,a^5\,b^3\,h^2\,z-270\,a^4\,b\,f\,g\,h-135\,a^3\,b^2\,c\,g\,h-54\,a^3\,b^2\,d\,f\,h-27\,a^2\,b^3\,c\,d\,h-6\,a\,b^4\,c^2\,f+75\,a^3\,b^2\,d\,g^2+15\,a^2\,b^3\,d^2\,g-12\,a^2\,b^3\,c\,f^2-8\,a^3\,b^2\,f^3+125\,a^4\,b\,g^3+a\,b^4\,d^3-729\,a^5\,h^3-b^5\,c^3,z,k\right)\,a\,b^2\,9-\frac{6\,a\,h}{b}+\frac{x\,\left(54\,f\,a^2\,b^3+27\,c\,a\,b^4\right)}{81\,a^2\,b^3}\right)+\frac{81\,a^3\,h^2+b^3\,c\,d+5\,a\,b^2\,c\,g+2\,a\,b^2\,d\,f+10\,a^2\,b\,f\,g}{81\,a^2\,b^4}+\frac{x\,\left(25\,a^2\,g^2-18\,f\,h\,a^2+10\,a\,b\,d\,g-9\,c\,h\,a\,b+b^2\,d^2\right)}{81\,a^2\,b^3}\right)\,\mathrm{root}\left(19683\,a^5\,b^9\,z^3-19683\,a^5\,b^6\,h\,z^2+810\,a^4\,b^4\,f\,g\,z+405\,a^3\,b^5\,c\,g\,z+162\,a^3\,b^5\,d\,f\,z+81\,a^2\,b^6\,c\,d\,z+6561\,a^5\,b^3\,h^2\,z-270\,a^4\,b\,f\,g\,h-135\,a^3\,b^2\,c\,g\,h-54\,a^3\,b^2\,d\,f\,h-27\,a^2\,b^3\,c\,d\,h-6\,a\,b^4\,c^2\,f+75\,a^3\,b^2\,d\,g^2+15\,a^2\,b^3\,d^2\,g-12\,a^2\,b^3\,c\,f^2-8\,a^3\,b^2\,f^3+125\,a^4\,b\,g^3+a\,b^4\,d^3-729\,a^5\,h^3-b^5\,c^3,z,k\right)\right)","Not used",1,"((3*a^2*h - a*b*e)/(6*b^3) - (x*(b*c + 2*a*f))/(9*b^2) - (x^2*(b*d + 5*a*g))/(18*b^2) - (x^3*(b*e - 2*a*h))/(3*b^2) + (x^4*(b*c - 7*a*f))/(18*a*b) + (x^5*(b*d - 4*a*g))/(9*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3) + symsum(log(root(19683*a^5*b^9*z^3 - 19683*a^5*b^6*h*z^2 + 810*a^4*b^4*f*g*z + 405*a^3*b^5*c*g*z + 162*a^3*b^5*d*f*z + 81*a^2*b^6*c*d*z + 6561*a^5*b^3*h^2*z - 270*a^4*b*f*g*h - 135*a^3*b^2*c*g*h - 54*a^3*b^2*d*f*h - 27*a^2*b^3*c*d*h - 6*a*b^4*c^2*f + 75*a^3*b^2*d*g^2 + 15*a^2*b^3*d^2*g - 12*a^2*b^3*c*f^2 - 8*a^3*b^2*f^3 + 125*a^4*b*g^3 + a*b^4*d^3 - 729*a^5*h^3 - b^5*c^3, z, k)*(9*root(19683*a^5*b^9*z^3 - 19683*a^5*b^6*h*z^2 + 810*a^4*b^4*f*g*z + 405*a^3*b^5*c*g*z + 162*a^3*b^5*d*f*z + 81*a^2*b^6*c*d*z + 6561*a^5*b^3*h^2*z - 270*a^4*b*f*g*h - 135*a^3*b^2*c*g*h - 54*a^3*b^2*d*f*h - 27*a^2*b^3*c*d*h - 6*a*b^4*c^2*f + 75*a^3*b^2*d*g^2 + 15*a^2*b^3*d^2*g - 12*a^2*b^3*c*f^2 - 8*a^3*b^2*f^3 + 125*a^4*b*g^3 + a*b^4*d^3 - 729*a^5*h^3 - b^5*c^3, z, k)*a*b^2 - (6*a*h)/b + (x*(54*a^2*b^3*f + 27*a*b^4*c))/(81*a^2*b^3)) + (81*a^3*h^2 + b^3*c*d + 5*a*b^2*c*g + 2*a*b^2*d*f + 10*a^2*b*f*g)/(81*a^2*b^4) + (x*(b^2*d^2 + 25*a^2*g^2 - 18*a^2*f*h - 9*a*b*c*h + 10*a*b*d*g))/(81*a^2*b^3))*root(19683*a^5*b^9*z^3 - 19683*a^5*b^6*h*z^2 + 810*a^4*b^4*f*g*z + 405*a^3*b^5*c*g*z + 162*a^3*b^5*d*f*z + 81*a^2*b^6*c*d*z + 6561*a^5*b^3*h^2*z - 270*a^4*b*f*g*h - 135*a^3*b^2*c*g*h - 54*a^3*b^2*d*f*h - 27*a^2*b^3*c*d*h - 6*a*b^4*c^2*f + 75*a^3*b^2*d*g^2 + 15*a^2*b^3*d^2*g - 12*a^2*b^3*c*f^2 - 8*a^3*b^2*f^3 + 125*a^4*b*g^3 + a*b^4*d^3 - 729*a^5*h^3 - b^5*c^3, z, k), k, 1, 3)","B"
423,1,627,297,5.689556,"\text{Not used}","int((x^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^3,x)","\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(19683\,a^5\,b^8\,z^3+810\,a^4\,b^3\,g\,h\,z+405\,a^3\,b^4\,d\,h\,z+162\,a^3\,b^4\,e\,g\,z+81\,a^2\,b^5\,d\,e\,z+75\,a^3\,b\,e\,h^2-6\,a\,b^3\,d^2\,g+15\,a^2\,b^2\,e^2\,h-12\,a^2\,b^2\,d\,g^2-8\,a^3\,b\,g^3+a\,b^3\,e^3+125\,a^4\,h^3-b^4\,d^3,z,k\right)\,\left(\mathrm{root}\left(19683\,a^5\,b^8\,z^3+810\,a^4\,b^3\,g\,h\,z+405\,a^3\,b^4\,d\,h\,z+162\,a^3\,b^4\,e\,g\,z+81\,a^2\,b^5\,d\,e\,z+75\,a^3\,b\,e\,h^2-6\,a\,b^3\,d^2\,g+15\,a^2\,b^2\,e^2\,h-12\,a^2\,b^2\,d\,g^2-8\,a^3\,b\,g^3+a\,b^3\,e^3+125\,a^4\,h^3-b^4\,d^3,z,k\right)\,a\,b^2\,9+\frac{x\,\left(54\,g\,a^2\,b^3+27\,d\,a\,b^4\right)}{81\,a^2\,b^3}\right)+\frac{b^2\,d\,e+10\,a^2\,g\,h+5\,a\,b\,d\,h+2\,a\,b\,e\,g}{81\,a^2\,b^3}+\frac{x\,\left(25\,a^2\,h^2+10\,a\,b\,e\,h+b^2\,e^2\right)}{81\,a^2\,b^3}\right)\,\mathrm{root}\left(19683\,a^5\,b^8\,z^3+810\,a^4\,b^3\,g\,h\,z+405\,a^3\,b^4\,d\,h\,z+162\,a^3\,b^4\,e\,g\,z+81\,a^2\,b^5\,d\,e\,z+75\,a^3\,b\,e\,h^2-6\,a\,b^3\,d^2\,g+15\,a^2\,b^2\,e^2\,h-12\,a^2\,b^2\,d\,g^2-8\,a^3\,b\,g^3+a\,b^3\,e^3+125\,a^4\,h^3-b^4\,d^3,z,k\right)\right)-\frac{\frac{b\,c+a\,f}{6\,b^2}+\frac{x\,\left(b\,d+2\,a\,g\right)}{9\,b^2}+\frac{f\,x^3}{3\,b}+\frac{x^2\,\left(b\,e+5\,a\,h\right)}{18\,b^2}-\frac{x^4\,\left(b\,d-7\,a\,g\right)}{18\,a\,b}-\frac{x^5\,\left(b\,e-4\,a\,h\right)}{9\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}","Not used",1,"symsum(log(root(19683*a^5*b^8*z^3 + 810*a^4*b^3*g*h*z + 405*a^3*b^4*d*h*z + 162*a^3*b^4*e*g*z + 81*a^2*b^5*d*e*z + 75*a^3*b*e*h^2 - 6*a*b^3*d^2*g + 15*a^2*b^2*e^2*h - 12*a^2*b^2*d*g^2 - 8*a^3*b*g^3 + a*b^3*e^3 + 125*a^4*h^3 - b^4*d^3, z, k)*(9*root(19683*a^5*b^8*z^3 + 810*a^4*b^3*g*h*z + 405*a^3*b^4*d*h*z + 162*a^3*b^4*e*g*z + 81*a^2*b^5*d*e*z + 75*a^3*b*e*h^2 - 6*a*b^3*d^2*g + 15*a^2*b^2*e^2*h - 12*a^2*b^2*d*g^2 - 8*a^3*b*g^3 + a*b^3*e^3 + 125*a^4*h^3 - b^4*d^3, z, k)*a*b^2 + (x*(54*a^2*b^3*g + 27*a*b^4*d))/(81*a^2*b^3)) + (b^2*d*e + 10*a^2*g*h + 5*a*b*d*h + 2*a*b*e*g)/(81*a^2*b^3) + (x*(b^2*e^2 + 25*a^2*h^2 + 10*a*b*e*h))/(81*a^2*b^3))*root(19683*a^5*b^8*z^3 + 810*a^4*b^3*g*h*z + 405*a^3*b^4*d*h*z + 162*a^3*b^4*e*g*z + 81*a^2*b^5*d*e*z + 75*a^3*b*e*h^2 - 6*a*b^3*d^2*g + 15*a^2*b^2*e^2*h - 12*a^2*b^2*d*g^2 - 8*a^3*b*g^3 + a*b^3*e^3 + 125*a^4*h^3 - b^4*d^3, z, k), k, 1, 3) - ((b*c + a*f)/(6*b^2) + (x*(b*d + 2*a*g))/(9*b^2) + (f*x^3)/(3*b) + (x^2*(b*e + 5*a*h))/(18*b^2) - (x^4*(b*d - 7*a*g))/(18*a*b) - (x^5*(b*e - 4*a*h))/(9*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3)","B"
424,1,640,323,5.364552,"\text{Not used}","int((x*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/(a + b*x^3)^3,x)","\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(19683\,a^7\,b^7\,z^3+162\,a^5\,b^3\,f\,h\,z+324\,a^4\,b^4\,c\,h\,z+81\,a^4\,b^4\,e\,f\,z+162\,a^3\,b^5\,c\,e\,z-12\,a^4\,b\,e\,h^2+12\,a\,b^4\,c^2\,f-6\,a^3\,b^2\,e^2\,h+6\,a^2\,b^3\,c\,f^2+a^3\,b^2\,f^3-8\,a^5\,h^3+8\,b^5\,c^3-a^2\,b^3\,e^3,z,k\right)\,\left(\mathrm{root}\left(19683\,a^7\,b^7\,z^3+162\,a^5\,b^3\,f\,h\,z+324\,a^4\,b^4\,c\,h\,z+81\,a^4\,b^4\,e\,f\,z+162\,a^3\,b^5\,c\,e\,z-12\,a^4\,b\,e\,h^2+12\,a\,b^4\,c^2\,f-6\,a^3\,b^2\,e^2\,h+6\,a^2\,b^3\,c\,f^2+a^3\,b^2\,f^3-8\,a^5\,h^3+8\,b^5\,c^3-a^2\,b^3\,e^3,z,k\right)\,a\,b^2\,9+\frac{x\,\left(54\,h\,a^4\,b+27\,e\,a^3\,b^2\right)}{81\,a^4\,b}\right)+\frac{2\,b^2\,c\,e+2\,a^2\,f\,h+4\,a\,b\,c\,h+a\,b\,e\,f}{81\,a^3\,b^2}+\frac{x\,\left(a^2\,f^2+4\,a\,b\,c\,f+4\,b^2\,c^2\right)}{81\,a^4\,b}\right)\,\mathrm{root}\left(19683\,a^7\,b^7\,z^3+162\,a^5\,b^3\,f\,h\,z+324\,a^4\,b^4\,c\,h\,z+81\,a^4\,b^4\,e\,f\,z+162\,a^3\,b^5\,c\,e\,z-12\,a^4\,b\,e\,h^2+12\,a\,b^4\,c^2\,f-6\,a^3\,b^2\,e^2\,h+6\,a^2\,b^3\,c\,f^2+a^3\,b^2\,f^3-8\,a^5\,h^3+8\,b^5\,c^3-a^2\,b^3\,e^3,z,k\right)\right)-\frac{\frac{b\,d+a\,g}{6\,b^2}+\frac{x\,\left(b\,e+2\,a\,h\right)}{9\,b^2}+\frac{g\,x^3}{3\,b}-\frac{x^5\,\left(2\,b\,c+a\,f\right)}{9\,a^2}-\frac{x^2\,\left(7\,b\,c-a\,f\right)}{18\,a\,b}-\frac{x^4\,\left(b\,e-7\,a\,h\right)}{18\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}","Not used",1,"symsum(log(root(19683*a^7*b^7*z^3 + 162*a^5*b^3*f*h*z + 324*a^4*b^4*c*h*z + 81*a^4*b^4*e*f*z + 162*a^3*b^5*c*e*z - 12*a^4*b*e*h^2 + 12*a*b^4*c^2*f - 6*a^3*b^2*e^2*h + 6*a^2*b^3*c*f^2 + a^3*b^2*f^3 - 8*a^5*h^3 + 8*b^5*c^3 - a^2*b^3*e^3, z, k)*(9*root(19683*a^7*b^7*z^3 + 162*a^5*b^3*f*h*z + 324*a^4*b^4*c*h*z + 81*a^4*b^4*e*f*z + 162*a^3*b^5*c*e*z - 12*a^4*b*e*h^2 + 12*a*b^4*c^2*f - 6*a^3*b^2*e^2*h + 6*a^2*b^3*c*f^2 + a^3*b^2*f^3 - 8*a^5*h^3 + 8*b^5*c^3 - a^2*b^3*e^3, z, k)*a*b^2 + (x*(27*a^3*b^2*e + 54*a^4*b*h))/(81*a^4*b)) + (2*b^2*c*e + 2*a^2*f*h + 4*a*b*c*h + a*b*e*f)/(81*a^3*b^2) + (x*(4*b^2*c^2 + a^2*f^2 + 4*a*b*c*f))/(81*a^4*b))*root(19683*a^7*b^7*z^3 + 162*a^5*b^3*f*h*z + 324*a^4*b^4*c*h*z + 81*a^4*b^4*e*f*z + 162*a^3*b^5*c*e*z - 12*a^4*b*e*h^2 + 12*a*b^4*c^2*f - 6*a^3*b^2*e^2*h + 6*a^2*b^3*c*f^2 + a^3*b^2*f^3 - 8*a^5*h^3 + 8*b^5*c^3 - a^2*b^3*e^3, z, k), k, 1, 3) - ((b*d + a*g)/(6*b^2) + (x*(b*e + 2*a*h))/(9*b^2) + (g*x^3)/(3*b) - (x^5*(2*b*c + a*f))/(9*a^2) - (x^2*(7*b*c - a*f))/(18*a*b) - (x^4*(b*e - 7*a*h))/(18*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3)","B"
425,1,630,313,0.432215,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^3,x)","\frac{\frac{x^4\,\left(5\,b\,c+a\,f\right)}{18\,a^2}-\frac{h\,x^3}{3\,b}-\frac{b\,e+a\,h}{6\,b^2}+\frac{x^5\,\left(2\,b\,d+a\,g\right)}{9\,a^2}+\frac{x\,\left(4\,b\,c-a\,f\right)}{9\,a\,b}+\frac{x^2\,\left(7\,b\,d-a\,g\right)}{18\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\left(\sum _{k=1}^3\ln\left(\mathrm{root}\left(19683\,a^8\,b^5\,z^3+81\,a^5\,b^2\,f\,g\,z+405\,a^4\,b^3\,c\,g\,z+162\,a^4\,b^3\,d\,f\,z+810\,a^3\,b^4\,c\,d\,z+6\,a^3\,b\,d\,g^2-75\,a\,b^3\,c^2\,f+12\,a^2\,b^2\,d^2\,g-15\,a^2\,b^2\,c\,f^2+8\,a\,b^3\,d^3+a^4\,g^3-125\,b^4\,c^3-a^3\,b\,f^3,z,k\right)\,\left(\mathrm{root}\left(19683\,a^8\,b^5\,z^3+81\,a^5\,b^2\,f\,g\,z+405\,a^4\,b^3\,c\,g\,z+162\,a^4\,b^3\,d\,f\,z+810\,a^3\,b^4\,c\,d\,z+6\,a^3\,b\,d\,g^2-75\,a\,b^3\,c^2\,f+12\,a^2\,b^2\,d^2\,g-15\,a^2\,b^2\,c\,f^2+8\,a\,b^3\,d^3+a^4\,g^3-125\,b^4\,c^3-a^3\,b\,f^3,z,k\right)\,a\,b^2\,9+\frac{x\,\left(27\,f\,a^3\,b^2+135\,c\,a^2\,b^3\right)}{81\,a^4\,b}\right)+\frac{10\,b^2\,c\,d+a^2\,f\,g+5\,a\,b\,c\,g+2\,a\,b\,d\,f}{81\,a^4\,b}+\frac{x\,\left(a^2\,g^2+4\,a\,b\,d\,g+4\,b^2\,d^2\right)}{81\,a^4\,b}\right)\,\mathrm{root}\left(19683\,a^8\,b^5\,z^3+81\,a^5\,b^2\,f\,g\,z+405\,a^4\,b^3\,c\,g\,z+162\,a^4\,b^3\,d\,f\,z+810\,a^3\,b^4\,c\,d\,z+6\,a^3\,b\,d\,g^2-75\,a\,b^3\,c^2\,f+12\,a^2\,b^2\,d^2\,g-15\,a^2\,b^2\,c\,f^2+8\,a\,b^3\,d^3+a^4\,g^3-125\,b^4\,c^3-a^3\,b\,f^3,z,k\right)\right)","Not used",1,"((x^4*(5*b*c + a*f))/(18*a^2) - (h*x^3)/(3*b) - (b*e + a*h)/(6*b^2) + (x^5*(2*b*d + a*g))/(9*a^2) + (x*(4*b*c - a*f))/(9*a*b) + (x^2*(7*b*d - a*g))/(18*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3) + symsum(log(root(19683*a^8*b^5*z^3 + 81*a^5*b^2*f*g*z + 405*a^4*b^3*c*g*z + 162*a^4*b^3*d*f*z + 810*a^3*b^4*c*d*z + 6*a^3*b*d*g^2 - 75*a*b^3*c^2*f + 12*a^2*b^2*d^2*g - 15*a^2*b^2*c*f^2 + 8*a*b^3*d^3 + a^4*g^3 - 125*b^4*c^3 - a^3*b*f^3, z, k)*(9*root(19683*a^8*b^5*z^3 + 81*a^5*b^2*f*g*z + 405*a^4*b^3*c*g*z + 162*a^4*b^3*d*f*z + 810*a^3*b^4*c*d*z + 6*a^3*b*d*g^2 - 75*a*b^3*c^2*f + 12*a^2*b^2*d^2*g - 15*a^2*b^2*c*f^2 + 8*a*b^3*d^3 + a^4*g^3 - 125*b^4*c^3 - a^3*b*f^3, z, k)*a*b^2 + (x*(135*a^2*b^3*c + 27*a^3*b^2*f))/(81*a^4*b)) + (10*b^2*c*d + a^2*f*g + 5*a*b*c*g + 2*a*b*d*f)/(81*a^4*b) + (x*(4*b^2*d^2 + a^2*g^2 + 4*a*b*d*g))/(81*a^4*b))*root(19683*a^8*b^5*z^3 + 81*a^5*b^2*f*g*z + 405*a^4*b^3*c*g*z + 162*a^4*b^3*d*f*z + 810*a^3*b^4*c*d*z + 6*a^3*b*d*g^2 - 75*a*b^3*c^2*f + 12*a^2*b^2*d^2*g - 15*a^2*b^2*c*f^2 + 8*a*b^3*d^3 + a^4*g^3 - 125*b^4*c^3 - a^3*b*f^3, z, k), k, 1, 3)","B"
426,1,1716,347,5.704898,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x*(a + b*x^3)^3),x)","\frac{\frac{3\,b\,c-a\,f}{6\,a\,b}+\frac{x^4\,\left(5\,b\,d+a\,g\right)}{18\,a^2}+\frac{x^5\,\left(2\,b\,e+a\,h\right)}{9\,a^2}+\frac{x\,\left(4\,b\,d-a\,g\right)}{9\,a\,b}+\frac{x^2\,\left(7\,b\,e-a\,h\right)}{18\,a\,b}+\frac{b\,c\,x^3}{3\,a^2}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\left(\sum _{k=1}^3\ln\left(\frac{c\,\left(a^2\,g^2+10\,a\,b\,d\,g-9\,c\,h\,a\,b+25\,b^2\,d^2-18\,c\,e\,b^2\right)}{81\,a^6}-\frac{\mathrm{root}\left(19683\,a^9\,b^5\,z^3+19683\,a^6\,b^5\,c\,z^2+81\,a^6\,b^2\,g\,h\,z+405\,a^5\,b^3\,d\,h\,z+162\,a^5\,b^3\,e\,g\,z+810\,a^4\,b^4\,d\,e\,z+6561\,a^3\,b^5\,c^2\,z+270\,a\,b^4\,c\,d\,e+27\,a^3\,b^2\,c\,g\,h+135\,a^2\,b^3\,c\,d\,h+54\,a^2\,b^3\,c\,e\,g+6\,a^4\,b\,e\,h^2+12\,a^3\,b^2\,e^2\,h-75\,a^2\,b^3\,d^2\,g-15\,a^3\,b^2\,d\,g^2+8\,a^2\,b^3\,e^3-a^4\,b\,g^3-125\,a\,b^4\,d^3+729\,b^5\,c^3+a^5\,h^3,z,k\right)\,\left(a^3\,g^2+25\,a\,b^2\,d^2+324\,b^3\,c^2\,x+{\mathrm{root}\left(19683\,a^9\,b^5\,z^3+19683\,a^6\,b^5\,c\,z^2+81\,a^6\,b^2\,g\,h\,z+405\,a^5\,b^3\,d\,h\,z+162\,a^5\,b^3\,e\,g\,z+810\,a^4\,b^4\,d\,e\,z+6561\,a^3\,b^5\,c^2\,z+270\,a\,b^4\,c\,d\,e+27\,a^3\,b^2\,c\,g\,h+135\,a^2\,b^3\,c\,d\,h+54\,a^2\,b^3\,c\,e\,g+6\,a^4\,b\,e\,h^2+12\,a^3\,b^2\,e^2\,h-75\,a^2\,b^3\,d^2\,g-15\,a^3\,b^2\,d\,g^2+8\,a^2\,b^3\,e^3-a^4\,b\,g^3-125\,a\,b^4\,d^3+729\,b^5\,c^3+a^5\,h^3,z,k\right)}^2\,a^6\,b^3\,x\,2916-\mathrm{root}\left(19683\,a^9\,b^5\,z^3+19683\,a^6\,b^5\,c\,z^2+81\,a^6\,b^2\,g\,h\,z+405\,a^5\,b^3\,d\,h\,z+162\,a^5\,b^3\,e\,g\,z+810\,a^4\,b^4\,d\,e\,z+6561\,a^3\,b^5\,c^2\,z+270\,a\,b^4\,c\,d\,e+27\,a^3\,b^2\,c\,g\,h+135\,a^2\,b^3\,c\,d\,h+54\,a^2\,b^3\,c\,e\,g+6\,a^4\,b\,e\,h^2+12\,a^3\,b^2\,e^2\,h-75\,a^2\,b^3\,d^2\,g-15\,a^3\,b^2\,d\,g^2+8\,a^2\,b^3\,e^3-a^4\,b\,g^3-125\,a\,b^4\,d^3+729\,b^5\,c^3+a^5\,h^3,z,k\right)\,a^5\,b\,h\,27+36\,a\,b^2\,c\,e+18\,a^2\,b\,c\,h+10\,a^2\,b\,d\,g+10\,a^3\,g\,h\,x-\mathrm{root}\left(19683\,a^9\,b^5\,z^3+19683\,a^6\,b^5\,c\,z^2+81\,a^6\,b^2\,g\,h\,z+405\,a^5\,b^3\,d\,h\,z+162\,a^5\,b^3\,e\,g\,z+810\,a^4\,b^4\,d\,e\,z+6561\,a^3\,b^5\,c^2\,z+270\,a\,b^4\,c\,d\,e+27\,a^3\,b^2\,c\,g\,h+135\,a^2\,b^3\,c\,d\,h+54\,a^2\,b^3\,c\,e\,g+6\,a^4\,b\,e\,h^2+12\,a^3\,b^2\,e^2\,h-75\,a^2\,b^3\,d^2\,g-15\,a^3\,b^2\,d\,g^2+8\,a^2\,b^3\,e^3-a^4\,b\,g^3-125\,a\,b^4\,d^3+729\,b^5\,c^3+a^5\,h^3,z,k\right)\,a^4\,b^2\,e\,54+\mathrm{root}\left(19683\,a^9\,b^5\,z^3+19683\,a^6\,b^5\,c\,z^2+81\,a^6\,b^2\,g\,h\,z+405\,a^5\,b^3\,d\,h\,z+162\,a^5\,b^3\,e\,g\,z+810\,a^4\,b^4\,d\,e\,z+6561\,a^3\,b^5\,c^2\,z+270\,a\,b^4\,c\,d\,e+27\,a^3\,b^2\,c\,g\,h+135\,a^2\,b^3\,c\,d\,h+54\,a^2\,b^3\,c\,e\,g+6\,a^4\,b\,e\,h^2+12\,a^3\,b^2\,e^2\,h-75\,a^2\,b^3\,d^2\,g-15\,a^3\,b^2\,d\,g^2+8\,a^2\,b^3\,e^3-a^4\,b\,g^3-125\,a\,b^4\,d^3+729\,b^5\,c^3+a^5\,h^3,z,k\right)\,a^3\,b^3\,c\,x\,1944+100\,a\,b^2\,d\,e\,x+50\,a^2\,b\,d\,h\,x+20\,a^2\,b\,e\,g\,x\right)}{a^4\,81}-\frac{x\,\left(a^4\,h^3+6\,a^3\,b\,e\,h^2-a^3\,b\,g^3-15\,a^2\,b^2\,d\,g^2+12\,a^2\,b^2\,e^2\,h+18\,c\,a^2\,b^2\,g\,h-75\,a\,b^3\,d^2\,g+90\,c\,a\,b^3\,d\,h+8\,a\,b^3\,e^3+36\,c\,a\,b^3\,e\,g-125\,b^4\,d^3+180\,c\,b^4\,d\,e\right)}{729\,a^6\,b^2}\right)\,\mathrm{root}\left(19683\,a^9\,b^5\,z^3+19683\,a^6\,b^5\,c\,z^2+81\,a^6\,b^2\,g\,h\,z+405\,a^5\,b^3\,d\,h\,z+162\,a^5\,b^3\,e\,g\,z+810\,a^4\,b^4\,d\,e\,z+6561\,a^3\,b^5\,c^2\,z+270\,a\,b^4\,c\,d\,e+27\,a^3\,b^2\,c\,g\,h+135\,a^2\,b^3\,c\,d\,h+54\,a^2\,b^3\,c\,e\,g+6\,a^4\,b\,e\,h^2+12\,a^3\,b^2\,e^2\,h-75\,a^2\,b^3\,d^2\,g-15\,a^3\,b^2\,d\,g^2+8\,a^2\,b^3\,e^3-a^4\,b\,g^3-125\,a\,b^4\,d^3+729\,b^5\,c^3+a^5\,h^3,z,k\right)\right)+\frac{c\,\ln\left(x\right)}{a^3}","Not used",1,"((3*b*c - a*f)/(6*a*b) + (x^4*(5*b*d + a*g))/(18*a^2) + (x^5*(2*b*e + a*h))/(9*a^2) + (x*(4*b*d - a*g))/(9*a*b) + (x^2*(7*b*e - a*h))/(18*a*b) + (b*c*x^3)/(3*a^2))/(a^2 + b^2*x^6 + 2*a*b*x^3) + symsum(log((c*(25*b^2*d^2 + a^2*g^2 - 18*b^2*c*e - 9*a*b*c*h + 10*a*b*d*g))/(81*a^6) - (root(19683*a^9*b^5*z^3 + 19683*a^6*b^5*c*z^2 + 81*a^6*b^2*g*h*z + 405*a^5*b^3*d*h*z + 162*a^5*b^3*e*g*z + 810*a^4*b^4*d*e*z + 6561*a^3*b^5*c^2*z + 270*a*b^4*c*d*e + 27*a^3*b^2*c*g*h + 135*a^2*b^3*c*d*h + 54*a^2*b^3*c*e*g + 6*a^4*b*e*h^2 + 12*a^3*b^2*e^2*h - 75*a^2*b^3*d^2*g - 15*a^3*b^2*d*g^2 + 8*a^2*b^3*e^3 - a^4*b*g^3 - 125*a*b^4*d^3 + 729*b^5*c^3 + a^5*h^3, z, k)*(a^3*g^2 + 25*a*b^2*d^2 + 324*b^3*c^2*x + 2916*root(19683*a^9*b^5*z^3 + 19683*a^6*b^5*c*z^2 + 81*a^6*b^2*g*h*z + 405*a^5*b^3*d*h*z + 162*a^5*b^3*e*g*z + 810*a^4*b^4*d*e*z + 6561*a^3*b^5*c^2*z + 270*a*b^4*c*d*e + 27*a^3*b^2*c*g*h + 135*a^2*b^3*c*d*h + 54*a^2*b^3*c*e*g + 6*a^4*b*e*h^2 + 12*a^3*b^2*e^2*h - 75*a^2*b^3*d^2*g - 15*a^3*b^2*d*g^2 + 8*a^2*b^3*e^3 - a^4*b*g^3 - 125*a*b^4*d^3 + 729*b^5*c^3 + a^5*h^3, z, k)^2*a^6*b^3*x - 27*root(19683*a^9*b^5*z^3 + 19683*a^6*b^5*c*z^2 + 81*a^6*b^2*g*h*z + 405*a^5*b^3*d*h*z + 162*a^5*b^3*e*g*z + 810*a^4*b^4*d*e*z + 6561*a^3*b^5*c^2*z + 270*a*b^4*c*d*e + 27*a^3*b^2*c*g*h + 135*a^2*b^3*c*d*h + 54*a^2*b^3*c*e*g + 6*a^4*b*e*h^2 + 12*a^3*b^2*e^2*h - 75*a^2*b^3*d^2*g - 15*a^3*b^2*d*g^2 + 8*a^2*b^3*e^3 - a^4*b*g^3 - 125*a*b^4*d^3 + 729*b^5*c^3 + a^5*h^3, z, k)*a^5*b*h + 36*a*b^2*c*e + 18*a^2*b*c*h + 10*a^2*b*d*g + 10*a^3*g*h*x - 54*root(19683*a^9*b^5*z^3 + 19683*a^6*b^5*c*z^2 + 81*a^6*b^2*g*h*z + 405*a^5*b^3*d*h*z + 162*a^5*b^3*e*g*z + 810*a^4*b^4*d*e*z + 6561*a^3*b^5*c^2*z + 270*a*b^4*c*d*e + 27*a^3*b^2*c*g*h + 135*a^2*b^3*c*d*h + 54*a^2*b^3*c*e*g + 6*a^4*b*e*h^2 + 12*a^3*b^2*e^2*h - 75*a^2*b^3*d^2*g - 15*a^3*b^2*d*g^2 + 8*a^2*b^3*e^3 - a^4*b*g^3 - 125*a*b^4*d^3 + 729*b^5*c^3 + a^5*h^3, z, k)*a^4*b^2*e + 1944*root(19683*a^9*b^5*z^3 + 19683*a^6*b^5*c*z^2 + 81*a^6*b^2*g*h*z + 405*a^5*b^3*d*h*z + 162*a^5*b^3*e*g*z + 810*a^4*b^4*d*e*z + 6561*a^3*b^5*c^2*z + 270*a*b^4*c*d*e + 27*a^3*b^2*c*g*h + 135*a^2*b^3*c*d*h + 54*a^2*b^3*c*e*g + 6*a^4*b*e*h^2 + 12*a^3*b^2*e^2*h - 75*a^2*b^3*d^2*g - 15*a^3*b^2*d*g^2 + 8*a^2*b^3*e^3 - a^4*b*g^3 - 125*a*b^4*d^3 + 729*b^5*c^3 + a^5*h^3, z, k)*a^3*b^3*c*x + 100*a*b^2*d*e*x + 50*a^2*b*d*h*x + 20*a^2*b*e*g*x))/(81*a^4) - (x*(a^4*h^3 - 125*b^4*d^3 + 8*a*b^3*e^3 - a^3*b*g^3 - 15*a^2*b^2*d*g^2 + 12*a^2*b^2*e^2*h + 180*b^4*c*d*e - 75*a*b^3*d^2*g + 6*a^3*b*e*h^2 + 18*a^2*b^2*c*g*h + 90*a*b^3*c*d*h + 36*a*b^3*c*e*g))/(729*a^6*b^2))*root(19683*a^9*b^5*z^3 + 19683*a^6*b^5*c*z^2 + 81*a^6*b^2*g*h*z + 405*a^5*b^3*d*h*z + 162*a^5*b^3*e*g*z + 810*a^4*b^4*d*e*z + 6561*a^3*b^5*c^2*z + 270*a*b^4*c*d*e + 27*a^3*b^2*c*g*h + 135*a^2*b^3*c*d*h + 54*a^2*b^3*c*e*g + 6*a^4*b*e*h^2 + 12*a^3*b^2*e^2*h - 75*a^2*b^3*d^2*g - 15*a^3*b^2*d*g^2 + 8*a^2*b^3*e^3 - a^4*b*g^3 - 125*a*b^4*d^3 + 729*b^5*c^3 + a^5*h^3, z, k), k, 1, 3) + (c*log(x))/a^3","B"
427,1,1747,362,5.747486,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^2*(a + b*x^3)^3),x)","\left(\sum _{k=1}^3\ln\left(\frac{d\,\left(a^3\,h^2+10\,a^2\,b\,e\,h+25\,a\,b^2\,e^2-18\,d\,f\,a\,b^2+126\,c\,d\,b^3\right)}{81\,a^7}-\frac{\mathrm{root}\left(19683\,a^{10}\,b^4\,z^3+19683\,a^7\,b^4\,d\,z^2+162\,a^6\,b^2\,f\,h\,z-1134\,a^5\,b^3\,c\,h\,z+810\,a^5\,b^3\,e\,f\,z-5670\,a^4\,b^4\,c\,e\,z+6561\,a^4\,b^4\,d^2\,z-1890\,a\,b^4\,c\,d\,e+54\,a^3\,b^2\,d\,f\,h-378\,a^2\,b^3\,c\,d\,h+270\,a^2\,b^3\,d\,e\,f-15\,a^4\,b\,e\,h^2+1176\,a\,b^4\,c^2\,f-75\,a^3\,b^2\,e^2\,h-168\,a^2\,b^3\,c\,f^2+8\,a^3\,b^2\,f^3-125\,a^2\,b^3\,e^3+729\,a\,b^4\,d^3-a^5\,h^3-2744\,b^5\,c^3,z,k\right)\,\left(a^3\,h^2+25\,a\,b^2\,e^2+324\,b^3\,d^2\,x-252\,b^3\,c\,d+{\mathrm{root}\left(19683\,a^{10}\,b^4\,z^3+19683\,a^7\,b^4\,d\,z^2+162\,a^6\,b^2\,f\,h\,z-1134\,a^5\,b^3\,c\,h\,z+810\,a^5\,b^3\,e\,f\,z-5670\,a^4\,b^4\,c\,e\,z+6561\,a^4\,b^4\,d^2\,z-1890\,a\,b^4\,c\,d\,e+54\,a^3\,b^2\,d\,f\,h-378\,a^2\,b^3\,c\,d\,h+270\,a^2\,b^3\,d\,e\,f-15\,a^4\,b\,e\,h^2+1176\,a\,b^4\,c^2\,f-75\,a^3\,b^2\,e^2\,h-168\,a^2\,b^3\,c\,f^2+8\,a^3\,b^2\,f^3-125\,a^2\,b^3\,e^3+729\,a\,b^4\,d^3-a^5\,h^3-2744\,b^5\,c^3,z,k\right)}^2\,a^6\,b^3\,x\,2916+36\,a\,b^2\,d\,f+10\,a^2\,b\,e\,h-700\,b^3\,c\,e\,x+\mathrm{root}\left(19683\,a^{10}\,b^4\,z^3+19683\,a^7\,b^4\,d\,z^2+162\,a^6\,b^2\,f\,h\,z-1134\,a^5\,b^3\,c\,h\,z+810\,a^5\,b^3\,e\,f\,z-5670\,a^4\,b^4\,c\,e\,z+6561\,a^4\,b^4\,d^2\,z-1890\,a\,b^4\,c\,d\,e+54\,a^3\,b^2\,d\,f\,h-378\,a^2\,b^3\,c\,d\,h+270\,a^2\,b^3\,d\,e\,f-15\,a^4\,b\,e\,h^2+1176\,a\,b^4\,c^2\,f-75\,a^3\,b^2\,e^2\,h-168\,a^2\,b^3\,c\,f^2+8\,a^3\,b^2\,f^3-125\,a^2\,b^3\,e^3+729\,a\,b^4\,d^3-a^5\,h^3-2744\,b^5\,c^3,z,k\right)\,a^3\,b^3\,c\,378-\mathrm{root}\left(19683\,a^{10}\,b^4\,z^3+19683\,a^7\,b^4\,d\,z^2+162\,a^6\,b^2\,f\,h\,z-1134\,a^5\,b^3\,c\,h\,z+810\,a^5\,b^3\,e\,f\,z-5670\,a^4\,b^4\,c\,e\,z+6561\,a^4\,b^4\,d^2\,z-1890\,a\,b^4\,c\,d\,e+54\,a^3\,b^2\,d\,f\,h-378\,a^2\,b^3\,c\,d\,h+270\,a^2\,b^3\,d\,e\,f-15\,a^4\,b\,e\,h^2+1176\,a\,b^4\,c^2\,f-75\,a^3\,b^2\,e^2\,h-168\,a^2\,b^3\,c\,f^2+8\,a^3\,b^2\,f^3-125\,a^2\,b^3\,e^3+729\,a\,b^4\,d^3-a^5\,h^3-2744\,b^5\,c^3,z,k\right)\,a^4\,b^2\,f\,54+\mathrm{root}\left(19683\,a^{10}\,b^4\,z^3+19683\,a^7\,b^4\,d\,z^2+162\,a^6\,b^2\,f\,h\,z-1134\,a^5\,b^3\,c\,h\,z+810\,a^5\,b^3\,e\,f\,z-5670\,a^4\,b^4\,c\,e\,z+6561\,a^4\,b^4\,d^2\,z-1890\,a\,b^4\,c\,d\,e+54\,a^3\,b^2\,d\,f\,h-378\,a^2\,b^3\,c\,d\,h+270\,a^2\,b^3\,d\,e\,f-15\,a^4\,b\,e\,h^2+1176\,a\,b^4\,c^2\,f-75\,a^3\,b^2\,e^2\,h-168\,a^2\,b^3\,c\,f^2+8\,a^3\,b^2\,f^3-125\,a^2\,b^3\,e^3+729\,a\,b^4\,d^3-a^5\,h^3-2744\,b^5\,c^3,z,k\right)\,a^3\,b^3\,d\,x\,1944-140\,a\,b^2\,c\,h\,x+100\,a\,b^2\,e\,f\,x+20\,a^2\,b\,f\,h\,x\right)}{a^4\,81}+\frac{x\,\left(a^5\,h^3+15\,a^4\,b\,e\,h^2+75\,a^3\,b^2\,e^2\,h-8\,a^3\,b^2\,f^3-36\,d\,a^3\,b^2\,f\,h+168\,a^2\,b^3\,c\,f^2+252\,d\,a^2\,b^3\,c\,h+125\,a^2\,b^3\,e^3-180\,d\,a^2\,b^3\,e\,f-1176\,a\,b^4\,c^2\,f+1260\,d\,a\,b^4\,c\,e+2744\,b^5\,c^3\right)}{729\,a^8\,b}\right)\,\mathrm{root}\left(19683\,a^{10}\,b^4\,z^3+19683\,a^7\,b^4\,d\,z^2+162\,a^6\,b^2\,f\,h\,z-1134\,a^5\,b^3\,c\,h\,z+810\,a^5\,b^3\,e\,f\,z-5670\,a^4\,b^4\,c\,e\,z+6561\,a^4\,b^4\,d^2\,z-1890\,a\,b^4\,c\,d\,e+54\,a^3\,b^2\,d\,f\,h-378\,a^2\,b^3\,c\,d\,h+270\,a^2\,b^3\,d\,e\,f-15\,a^4\,b\,e\,h^2+1176\,a\,b^4\,c^2\,f-75\,a^3\,b^2\,e^2\,h-168\,a^2\,b^3\,c\,f^2+8\,a^3\,b^2\,f^3-125\,a^2\,b^3\,e^3+729\,a\,b^4\,d^3-a^5\,h^3-2744\,b^5\,c^3,z,k\right)\right)+\frac{\frac{x^5\,\left(5\,b\,e+a\,h\right)}{18\,a^2}-\frac{7\,x^3\,\left(7\,b\,c-a\,f\right)}{18\,a^2}-\frac{c}{a}-\frac{2\,b\,x^6\,\left(7\,b\,c-a\,f\right)}{9\,a^3}+\frac{x\,\left(3\,b\,d-a\,g\right)}{6\,a\,b}+\frac{x^2\,\left(4\,b\,e-a\,h\right)}{9\,a\,b}+\frac{b\,d\,x^4}{3\,a^2}}{a^2\,x+2\,a\,b\,x^4+b^2\,x^7}+\frac{d\,\ln\left(x\right)}{a^3}","Not used",1,"symsum(log((d*(a^3*h^2 + 25*a*b^2*e^2 + 126*b^3*c*d - 18*a*b^2*d*f + 10*a^2*b*e*h))/(81*a^7) - (root(19683*a^10*b^4*z^3 + 19683*a^7*b^4*d*z^2 + 162*a^6*b^2*f*h*z - 1134*a^5*b^3*c*h*z + 810*a^5*b^3*e*f*z - 5670*a^4*b^4*c*e*z + 6561*a^4*b^4*d^2*z - 1890*a*b^4*c*d*e + 54*a^3*b^2*d*f*h - 378*a^2*b^3*c*d*h + 270*a^2*b^3*d*e*f - 15*a^4*b*e*h^2 + 1176*a*b^4*c^2*f - 75*a^3*b^2*e^2*h - 168*a^2*b^3*c*f^2 + 8*a^3*b^2*f^3 - 125*a^2*b^3*e^3 + 729*a*b^4*d^3 - a^5*h^3 - 2744*b^5*c^3, z, k)*(a^3*h^2 + 25*a*b^2*e^2 + 324*b^3*d^2*x - 252*b^3*c*d + 2916*root(19683*a^10*b^4*z^3 + 19683*a^7*b^4*d*z^2 + 162*a^6*b^2*f*h*z - 1134*a^5*b^3*c*h*z + 810*a^5*b^3*e*f*z - 5670*a^4*b^4*c*e*z + 6561*a^4*b^4*d^2*z - 1890*a*b^4*c*d*e + 54*a^3*b^2*d*f*h - 378*a^2*b^3*c*d*h + 270*a^2*b^3*d*e*f - 15*a^4*b*e*h^2 + 1176*a*b^4*c^2*f - 75*a^3*b^2*e^2*h - 168*a^2*b^3*c*f^2 + 8*a^3*b^2*f^3 - 125*a^2*b^3*e^3 + 729*a*b^4*d^3 - a^5*h^3 - 2744*b^5*c^3, z, k)^2*a^6*b^3*x + 36*a*b^2*d*f + 10*a^2*b*e*h - 700*b^3*c*e*x + 378*root(19683*a^10*b^4*z^3 + 19683*a^7*b^4*d*z^2 + 162*a^6*b^2*f*h*z - 1134*a^5*b^3*c*h*z + 810*a^5*b^3*e*f*z - 5670*a^4*b^4*c*e*z + 6561*a^4*b^4*d^2*z - 1890*a*b^4*c*d*e + 54*a^3*b^2*d*f*h - 378*a^2*b^3*c*d*h + 270*a^2*b^3*d*e*f - 15*a^4*b*e*h^2 + 1176*a*b^4*c^2*f - 75*a^3*b^2*e^2*h - 168*a^2*b^3*c*f^2 + 8*a^3*b^2*f^3 - 125*a^2*b^3*e^3 + 729*a*b^4*d^3 - a^5*h^3 - 2744*b^5*c^3, z, k)*a^3*b^3*c - 54*root(19683*a^10*b^4*z^3 + 19683*a^7*b^4*d*z^2 + 162*a^6*b^2*f*h*z - 1134*a^5*b^3*c*h*z + 810*a^5*b^3*e*f*z - 5670*a^4*b^4*c*e*z + 6561*a^4*b^4*d^2*z - 1890*a*b^4*c*d*e + 54*a^3*b^2*d*f*h - 378*a^2*b^3*c*d*h + 270*a^2*b^3*d*e*f - 15*a^4*b*e*h^2 + 1176*a*b^4*c^2*f - 75*a^3*b^2*e^2*h - 168*a^2*b^3*c*f^2 + 8*a^3*b^2*f^3 - 125*a^2*b^3*e^3 + 729*a*b^4*d^3 - a^5*h^3 - 2744*b^5*c^3, z, k)*a^4*b^2*f + 1944*root(19683*a^10*b^4*z^3 + 19683*a^7*b^4*d*z^2 + 162*a^6*b^2*f*h*z - 1134*a^5*b^3*c*h*z + 810*a^5*b^3*e*f*z - 5670*a^4*b^4*c*e*z + 6561*a^4*b^4*d^2*z - 1890*a*b^4*c*d*e + 54*a^3*b^2*d*f*h - 378*a^2*b^3*c*d*h + 270*a^2*b^3*d*e*f - 15*a^4*b*e*h^2 + 1176*a*b^4*c^2*f - 75*a^3*b^2*e^2*h - 168*a^2*b^3*c*f^2 + 8*a^3*b^2*f^3 - 125*a^2*b^3*e^3 + 729*a*b^4*d^3 - a^5*h^3 - 2744*b^5*c^3, z, k)*a^3*b^3*d*x - 140*a*b^2*c*h*x + 100*a*b^2*e*f*x + 20*a^2*b*f*h*x))/(81*a^4) + (x*(2744*b^5*c^3 + a^5*h^3 + 125*a^2*b^3*e^3 - 8*a^3*b^2*f^3 + 168*a^2*b^3*c*f^2 + 75*a^3*b^2*e^2*h - 1176*a*b^4*c^2*f + 15*a^4*b*e*h^2 + 252*a^2*b^3*c*d*h - 180*a^2*b^3*d*e*f - 36*a^3*b^2*d*f*h + 1260*a*b^4*c*d*e))/(729*a^8*b))*root(19683*a^10*b^4*z^3 + 19683*a^7*b^4*d*z^2 + 162*a^6*b^2*f*h*z - 1134*a^5*b^3*c*h*z + 810*a^5*b^3*e*f*z - 5670*a^4*b^4*c*e*z + 6561*a^4*b^4*d^2*z - 1890*a*b^4*c*d*e + 54*a^3*b^2*d*f*h - 378*a^2*b^3*c*d*h + 270*a^2*b^3*d*e*f - 15*a^4*b*e*h^2 + 1176*a*b^4*c^2*f - 75*a^3*b^2*e^2*h - 168*a^2*b^3*c*f^2 + 8*a^3*b^2*f^3 - 125*a^2*b^3*e^3 + 729*a*b^4*d^3 - a^5*h^3 - 2744*b^5*c^3, z, k), k, 1, 3) + ((x^5*(5*b*e + a*h))/(18*a^2) - (7*x^3*(7*b*c - a*f))/(18*a^2) - c/a - (2*b*x^6*(7*b*c - a*f))/(9*a^3) + (x*(3*b*d - a*g))/(6*a*b) + (x^2*(4*b*e - a*h))/(9*a*b) + (b*d*x^4)/(3*a^2))/(a^2*x + b^2*x^7 + 2*a*b*x^4) + (d*log(x))/a^3","B"
428,1,1697,360,5.659009,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^3*(a + b*x^3)^3),x)","\left(\sum _{k=1}^3\ln\left(\frac{b^2\,e\,\left(25\,a^2\,f^2-18\,e\,g\,a^2-200\,a\,b\,c\,f+126\,d\,e\,a\,b+400\,b^2\,c^2\right)}{81\,a^8}-\frac{\mathrm{root}\left(19683\,a^{11}\,b^2\,z^3+19683\,a^8\,b^2\,e\,z^2+810\,a^6\,b\,f\,g\,z-5670\,a^5\,b^2\,d\,f\,z-3240\,a^5\,b^2\,c\,g\,z+22680\,a^4\,b^3\,c\,d\,z+6561\,a^5\,b^2\,e^2\,z+270\,a^3\,b\,e\,f\,g+7560\,a\,b^3\,c\,d\,e-1890\,a^2\,b^2\,d\,e\,f-1080\,a^2\,b^2\,c\,e\,g-168\,a^3\,b\,d\,g^2-6000\,a\,b^3\,c^2\,f+1176\,a^2\,b^2\,d^2\,g+1500\,a^2\,b^2\,c\,f^2+729\,a^2\,b^2\,e^3-125\,a^3\,b\,f^3-2744\,a\,b^3\,d^3+8\,a^4\,g^3+8000\,b^4\,c^3,z,k\right)\,b^2\,\left(400\,b^2\,c^2+25\,a^2\,f^2-\mathrm{root}\left(19683\,a^{11}\,b^2\,z^3+19683\,a^8\,b^2\,e\,z^2+810\,a^6\,b\,f\,g\,z-5670\,a^5\,b^2\,d\,f\,z-3240\,a^5\,b^2\,c\,g\,z+22680\,a^4\,b^3\,c\,d\,z+6561\,a^5\,b^2\,e^2\,z+270\,a^3\,b\,e\,f\,g+7560\,a\,b^3\,c\,d\,e-1890\,a^2\,b^2\,d\,e\,f-1080\,a^2\,b^2\,c\,e\,g-168\,a^3\,b\,d\,g^2-6000\,a\,b^3\,c^2\,f+1176\,a^2\,b^2\,d^2\,g+1500\,a^2\,b^2\,c\,f^2+729\,a^2\,b^2\,e^3-125\,a^3\,b\,f^3-2744\,a\,b^3\,d^3+8\,a^4\,g^3+8000\,b^4\,c^3,z,k\right)\,a^5\,g\,54+36\,a^2\,e\,g+\mathrm{root}\left(19683\,a^{11}\,b^2\,z^3+19683\,a^8\,b^2\,e\,z^2+810\,a^6\,b\,f\,g\,z-5670\,a^5\,b^2\,d\,f\,z-3240\,a^5\,b^2\,c\,g\,z+22680\,a^4\,b^3\,c\,d\,z+6561\,a^5\,b^2\,e^2\,z+270\,a^3\,b\,e\,f\,g+7560\,a\,b^3\,c\,d\,e-1890\,a^2\,b^2\,d\,e\,f-1080\,a^2\,b^2\,c\,e\,g-168\,a^3\,b\,d\,g^2-6000\,a\,b^3\,c^2\,f+1176\,a^2\,b^2\,d^2\,g+1500\,a^2\,b^2\,c\,f^2+729\,a^2\,b^2\,e^3-125\,a^3\,b\,f^3-2744\,a\,b^3\,d^3+8\,a^4\,g^3+8000\,b^4\,c^3,z,k\right)\,a^4\,b\,d\,378+324\,a\,b\,e^2\,x+2800\,b^2\,c\,d\,x+100\,a^2\,f\,g\,x+{\mathrm{root}\left(19683\,a^{11}\,b^2\,z^3+19683\,a^8\,b^2\,e\,z^2+810\,a^6\,b\,f\,g\,z-5670\,a^5\,b^2\,d\,f\,z-3240\,a^5\,b^2\,c\,g\,z+22680\,a^4\,b^3\,c\,d\,z+6561\,a^5\,b^2\,e^2\,z+270\,a^3\,b\,e\,f\,g+7560\,a\,b^3\,c\,d\,e-1890\,a^2\,b^2\,d\,e\,f-1080\,a^2\,b^2\,c\,e\,g-168\,a^3\,b\,d\,g^2-6000\,a\,b^3\,c^2\,f+1176\,a^2\,b^2\,d^2\,g+1500\,a^2\,b^2\,c\,f^2+729\,a^2\,b^2\,e^3-125\,a^3\,b\,f^3-2744\,a\,b^3\,d^3+8\,a^4\,g^3+8000\,b^4\,c^3,z,k\right)}^2\,a^7\,b\,x\,2916-200\,a\,b\,c\,f-252\,a\,b\,d\,e-400\,a\,b\,c\,g\,x-700\,a\,b\,d\,f\,x+\mathrm{root}\left(19683\,a^{11}\,b^2\,z^3+19683\,a^8\,b^2\,e\,z^2+810\,a^6\,b\,f\,g\,z-5670\,a^5\,b^2\,d\,f\,z-3240\,a^5\,b^2\,c\,g\,z+22680\,a^4\,b^3\,c\,d\,z+6561\,a^5\,b^2\,e^2\,z+270\,a^3\,b\,e\,f\,g+7560\,a\,b^3\,c\,d\,e-1890\,a^2\,b^2\,d\,e\,f-1080\,a^2\,b^2\,c\,e\,g-168\,a^3\,b\,d\,g^2-6000\,a\,b^3\,c^2\,f+1176\,a^2\,b^2\,d^2\,g+1500\,a^2\,b^2\,c\,f^2+729\,a^2\,b^2\,e^3-125\,a^3\,b\,f^3-2744\,a\,b^3\,d^3+8\,a^4\,g^3+8000\,b^4\,c^3,z,k\right)\,a^4\,b\,e\,x\,1944\right)}{a^5\,81}-\frac{b\,x\,\left(8\,a^4\,g^3-168\,a^3\,b\,d\,g^2-125\,a^3\,b\,f^3+180\,e\,a^3\,b\,f\,g+1500\,a^2\,b^2\,c\,f^2-720\,e\,a^2\,b^2\,c\,g+1176\,a^2\,b^2\,d^2\,g-1260\,e\,a^2\,b^2\,d\,f-6000\,a\,b^3\,c^2\,f+5040\,e\,a\,b^3\,c\,d-2744\,a\,b^3\,d^3+8000\,b^4\,c^3\right)}{729\,a^9}\right)\,\mathrm{root}\left(19683\,a^{11}\,b^2\,z^3+19683\,a^8\,b^2\,e\,z^2+810\,a^6\,b\,f\,g\,z-5670\,a^5\,b^2\,d\,f\,z-3240\,a^5\,b^2\,c\,g\,z+22680\,a^4\,b^3\,c\,d\,z+6561\,a^5\,b^2\,e^2\,z+270\,a^3\,b\,e\,f\,g+7560\,a\,b^3\,c\,d\,e-1890\,a^2\,b^2\,d\,e\,f-1080\,a^2\,b^2\,c\,e\,g-168\,a^3\,b\,d\,g^2-6000\,a\,b^3\,c^2\,f+1176\,a^2\,b^2\,d^2\,g+1500\,a^2\,b^2\,c\,f^2+729\,a^2\,b^2\,e^3-125\,a^3\,b\,f^3-2744\,a\,b^3\,d^3+8\,a^4\,g^3+8000\,b^4\,c^3,z,k\right)\right)-\frac{\frac{c}{2\,a}+\frac{4\,x^3\,\left(4\,b\,c-a\,f\right)}{9\,a^2}+\frac{7\,x^4\,\left(7\,b\,d-a\,g\right)}{18\,a^2}+\frac{d\,x}{a}+\frac{5\,b\,x^6\,\left(4\,b\,c-a\,f\right)}{18\,a^3}+\frac{2\,b\,x^7\,\left(7\,b\,d-a\,g\right)}{9\,a^3}-\frac{x^2\,\left(3\,b\,e-a\,h\right)}{6\,a\,b}-\frac{b\,e\,x^5}{3\,a^2}}{a^2\,x^2+2\,a\,b\,x^5+b^2\,x^8}+\frac{e\,\ln\left(x\right)}{a^3}","Not used",1,"symsum(log((b^2*e*(400*b^2*c^2 + 25*a^2*f^2 - 18*a^2*e*g - 200*a*b*c*f + 126*a*b*d*e))/(81*a^8) - (root(19683*a^11*b^2*z^3 + 19683*a^8*b^2*e*z^2 + 810*a^6*b*f*g*z - 5670*a^5*b^2*d*f*z - 3240*a^5*b^2*c*g*z + 22680*a^4*b^3*c*d*z + 6561*a^5*b^2*e^2*z + 270*a^3*b*e*f*g + 7560*a*b^3*c*d*e - 1890*a^2*b^2*d*e*f - 1080*a^2*b^2*c*e*g - 168*a^3*b*d*g^2 - 6000*a*b^3*c^2*f + 1176*a^2*b^2*d^2*g + 1500*a^2*b^2*c*f^2 + 729*a^2*b^2*e^3 - 125*a^3*b*f^3 - 2744*a*b^3*d^3 + 8*a^4*g^3 + 8000*b^4*c^3, z, k)*b^2*(400*b^2*c^2 + 25*a^2*f^2 - 54*root(19683*a^11*b^2*z^3 + 19683*a^8*b^2*e*z^2 + 810*a^6*b*f*g*z - 5670*a^5*b^2*d*f*z - 3240*a^5*b^2*c*g*z + 22680*a^4*b^3*c*d*z + 6561*a^5*b^2*e^2*z + 270*a^3*b*e*f*g + 7560*a*b^3*c*d*e - 1890*a^2*b^2*d*e*f - 1080*a^2*b^2*c*e*g - 168*a^3*b*d*g^2 - 6000*a*b^3*c^2*f + 1176*a^2*b^2*d^2*g + 1500*a^2*b^2*c*f^2 + 729*a^2*b^2*e^3 - 125*a^3*b*f^3 - 2744*a*b^3*d^3 + 8*a^4*g^3 + 8000*b^4*c^3, z, k)*a^5*g + 36*a^2*e*g + 378*root(19683*a^11*b^2*z^3 + 19683*a^8*b^2*e*z^2 + 810*a^6*b*f*g*z - 5670*a^5*b^2*d*f*z - 3240*a^5*b^2*c*g*z + 22680*a^4*b^3*c*d*z + 6561*a^5*b^2*e^2*z + 270*a^3*b*e*f*g + 7560*a*b^3*c*d*e - 1890*a^2*b^2*d*e*f - 1080*a^2*b^2*c*e*g - 168*a^3*b*d*g^2 - 6000*a*b^3*c^2*f + 1176*a^2*b^2*d^2*g + 1500*a^2*b^2*c*f^2 + 729*a^2*b^2*e^3 - 125*a^3*b*f^3 - 2744*a*b^3*d^3 + 8*a^4*g^3 + 8000*b^4*c^3, z, k)*a^4*b*d + 324*a*b*e^2*x + 2800*b^2*c*d*x + 100*a^2*f*g*x + 2916*root(19683*a^11*b^2*z^3 + 19683*a^8*b^2*e*z^2 + 810*a^6*b*f*g*z - 5670*a^5*b^2*d*f*z - 3240*a^5*b^2*c*g*z + 22680*a^4*b^3*c*d*z + 6561*a^5*b^2*e^2*z + 270*a^3*b*e*f*g + 7560*a*b^3*c*d*e - 1890*a^2*b^2*d*e*f - 1080*a^2*b^2*c*e*g - 168*a^3*b*d*g^2 - 6000*a*b^3*c^2*f + 1176*a^2*b^2*d^2*g + 1500*a^2*b^2*c*f^2 + 729*a^2*b^2*e^3 - 125*a^3*b*f^3 - 2744*a*b^3*d^3 + 8*a^4*g^3 + 8000*b^4*c^3, z, k)^2*a^7*b*x - 200*a*b*c*f - 252*a*b*d*e - 400*a*b*c*g*x - 700*a*b*d*f*x + 1944*root(19683*a^11*b^2*z^3 + 19683*a^8*b^2*e*z^2 + 810*a^6*b*f*g*z - 5670*a^5*b^2*d*f*z - 3240*a^5*b^2*c*g*z + 22680*a^4*b^3*c*d*z + 6561*a^5*b^2*e^2*z + 270*a^3*b*e*f*g + 7560*a*b^3*c*d*e - 1890*a^2*b^2*d*e*f - 1080*a^2*b^2*c*e*g - 168*a^3*b*d*g^2 - 6000*a*b^3*c^2*f + 1176*a^2*b^2*d^2*g + 1500*a^2*b^2*c*f^2 + 729*a^2*b^2*e^3 - 125*a^3*b*f^3 - 2744*a*b^3*d^3 + 8*a^4*g^3 + 8000*b^4*c^3, z, k)*a^4*b*e*x))/(81*a^5) - (b*x*(8000*b^4*c^3 + 8*a^4*g^3 - 2744*a*b^3*d^3 - 125*a^3*b*f^3 + 1500*a^2*b^2*c*f^2 + 1176*a^2*b^2*d^2*g - 6000*a*b^3*c^2*f - 168*a^3*b*d*g^2 - 720*a^2*b^2*c*e*g - 1260*a^2*b^2*d*e*f + 5040*a*b^3*c*d*e + 180*a^3*b*e*f*g))/(729*a^9))*root(19683*a^11*b^2*z^3 + 19683*a^8*b^2*e*z^2 + 810*a^6*b*f*g*z - 5670*a^5*b^2*d*f*z - 3240*a^5*b^2*c*g*z + 22680*a^4*b^3*c*d*z + 6561*a^5*b^2*e^2*z + 270*a^3*b*e*f*g + 7560*a*b^3*c*d*e - 1890*a^2*b^2*d*e*f - 1080*a^2*b^2*c*e*g - 168*a^3*b*d*g^2 - 6000*a*b^3*c^2*f + 1176*a^2*b^2*d^2*g + 1500*a^2*b^2*c*f^2 + 729*a^2*b^2*e^3 - 125*a^3*b*f^3 - 2744*a*b^3*d^3 + 8*a^4*g^3 + 8000*b^4*c^3, z, k), k, 1, 3) - (c/(2*a) + (4*x^3*(4*b*c - a*f))/(9*a^2) + (7*x^4*(7*b*d - a*g))/(18*a^2) + (d*x)/a + (5*b*x^6*(4*b*c - a*f))/(18*a^3) + (2*b*x^7*(7*b*d - a*g))/(9*a^3) - (x^2*(3*b*e - a*h))/(6*a*b) - (b*e*x^5)/(3*a^2))/(a^2*x^2 + b^2*x^8 + 2*a*b*x^5) + (e*log(x))/a^3","B"
429,1,1994,395,6.321489,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^4*(a + b*x^3)^3),x)","\left(\sum _{k=1}^3\ln\left(-\frac{18\,h\,a^3\,b^2\,f^2-25\,a^3\,b^2\,f\,g^2-108\,h\,a^2\,b^3\,c\,f+75\,a^2\,b^3\,c\,g^2+200\,a^2\,b^3\,d\,f\,g-126\,e\,a^2\,b^3\,f^2+162\,h\,a\,b^4\,c^2-600\,a\,b^4\,c\,d\,g+756\,e\,a\,b^4\,c\,f-400\,a\,b^4\,d^2\,f-1134\,e\,b^5\,c^2+1200\,b^5\,c\,d^2}{81\,a^9}-\mathrm{root}\left(19683\,a^{12}\,b^2\,z^3+19683\,a^9\,b^2\,f\,z^2-59049\,a^8\,b^3\,c\,z^2+810\,a^7\,b\,g\,h\,z-5670\,a^6\,b^2\,e\,g\,z-3240\,a^6\,b^2\,d\,h\,z-39366\,a^5\,b^3\,c\,f\,z+22680\,a^5\,b^3\,d\,e\,z+6561\,a^6\,b^2\,f^2\,z+59049\,a^4\,b^4\,c^2\,z+270\,a^4\,b\,f\,g\,h-22680\,a\,b^4\,c\,d\,e-1890\,a^3\,b^2\,e\,f\,g-1080\,a^3\,b^2\,d\,f\,h-810\,a^3\,b^2\,c\,g\,h+7560\,a^2\,b^3\,d\,e\,f+5670\,a^2\,b^3\,c\,e\,g+3240\,a^2\,b^3\,c\,d\,h-168\,a^4\,b\,e\,h^2+19683\,a\,b^4\,c^2\,f+1176\,a^3\,b^2\,e^2\,h-6000\,a^2\,b^3\,d^2\,g+1500\,a^3\,b^2\,d\,g^2-6561\,a^2\,b^3\,c\,f^2+729\,a^3\,b^2\,f^3-2744\,a^2\,b^3\,e^3-125\,a^4\,b\,g^3+8000\,a\,b^4\,d^3+8\,a^5\,h^3-19683\,b^5\,c^3,z,k\right)\,\left(\frac{400\,a^4\,b^4\,d^2+25\,a^6\,b^2\,g^2+756\,a^4\,b^4\,c\,e-108\,a^5\,b^3\,c\,h-200\,a^5\,b^3\,d\,g-252\,a^5\,b^3\,e\,f+36\,a^6\,b^2\,f\,h}{81\,a^9}+\mathrm{root}\left(19683\,a^{12}\,b^2\,z^3+19683\,a^9\,b^2\,f\,z^2-59049\,a^8\,b^3\,c\,z^2+810\,a^7\,b\,g\,h\,z-5670\,a^6\,b^2\,e\,g\,z-3240\,a^6\,b^2\,d\,h\,z-39366\,a^5\,b^3\,c\,f\,z+22680\,a^5\,b^3\,d\,e\,z+6561\,a^6\,b^2\,f^2\,z+59049\,a^4\,b^4\,c^2\,z+270\,a^4\,b\,f\,g\,h-22680\,a\,b^4\,c\,d\,e-1890\,a^3\,b^2\,e\,f\,g-1080\,a^3\,b^2\,d\,f\,h-810\,a^3\,b^2\,c\,g\,h+7560\,a^2\,b^3\,d\,e\,f+5670\,a^2\,b^3\,c\,e\,g+3240\,a^2\,b^3\,c\,d\,h-168\,a^4\,b\,e\,h^2+19683\,a\,b^4\,c^2\,f+1176\,a^3\,b^2\,e^2\,h-6000\,a^2\,b^3\,d^2\,g+1500\,a^3\,b^2\,d\,g^2-6561\,a^2\,b^3\,c\,f^2+729\,a^3\,b^2\,f^3-2744\,a^2\,b^3\,e^3-125\,a^4\,b\,g^3+8000\,a\,b^4\,d^3+8\,a^5\,h^3-19683\,b^5\,c^3,z,k\right)\,\left(\frac{378\,a^8\,b^3\,e-54\,a^9\,b^2\,h}{81\,a^9}-\frac{x\,\left(52488\,a^7\,b^4\,c-17496\,a^8\,b^3\,f\right)}{729\,a^9}+\mathrm{root}\left(19683\,a^{12}\,b^2\,z^3+19683\,a^9\,b^2\,f\,z^2-59049\,a^8\,b^3\,c\,z^2+810\,a^7\,b\,g\,h\,z-5670\,a^6\,b^2\,e\,g\,z-3240\,a^6\,b^2\,d\,h\,z-39366\,a^5\,b^3\,c\,f\,z+22680\,a^5\,b^3\,d\,e\,z+6561\,a^6\,b^2\,f^2\,z+59049\,a^4\,b^4\,c^2\,z+270\,a^4\,b\,f\,g\,h-22680\,a\,b^4\,c\,d\,e-1890\,a^3\,b^2\,e\,f\,g-1080\,a^3\,b^2\,d\,f\,h-810\,a^3\,b^2\,c\,g\,h+7560\,a^2\,b^3\,d\,e\,f+5670\,a^2\,b^3\,c\,e\,g+3240\,a^2\,b^3\,c\,d\,h-168\,a^4\,b\,e\,h^2+19683\,a\,b^4\,c^2\,f+1176\,a^3\,b^2\,e^2\,h-6000\,a^2\,b^3\,d^2\,g+1500\,a^3\,b^2\,d\,g^2-6561\,a^2\,b^3\,c\,f^2+729\,a^3\,b^2\,f^3-2744\,a^2\,b^3\,e^3-125\,a^4\,b\,g^3+8000\,a\,b^4\,d^3+8\,a^5\,h^3-19683\,b^5\,c^3,z,k\right)\,a^2\,b^3\,x\,36\right)+\frac{x\,\left(26244\,a^3\,b^5\,c^2+2916\,a^5\,b^3\,f^2-17496\,a^4\,b^4\,c\,f+25200\,a^4\,b^4\,d\,e-3600\,a^5\,b^3\,d\,h-6300\,a^5\,b^3\,e\,g+900\,a^6\,b^2\,g\,h\right)}{729\,a^9}\right)-\frac{x\,\left(8\,a^4\,b\,h^3-168\,a^3\,b^2\,e\,h^2-125\,a^3\,b^2\,g^3+180\,f\,a^3\,b^2\,g\,h+1500\,a^2\,b^3\,d\,g^2-720\,f\,a^2\,b^3\,d\,h+1176\,a^2\,b^3\,e^2\,h-1260\,f\,a^2\,b^3\,e\,g-540\,c\,a^2\,b^3\,g\,h-6000\,a\,b^4\,d^2\,g+5040\,f\,a\,b^4\,d\,e+2160\,c\,a\,b^4\,d\,h-2744\,a\,b^4\,e^3+3780\,c\,a\,b^4\,e\,g+8000\,b^5\,d^3-15120\,c\,b^5\,d\,e\right)}{729\,a^9}\right)\,\mathrm{root}\left(19683\,a^{12}\,b^2\,z^3+19683\,a^9\,b^2\,f\,z^2-59049\,a^8\,b^3\,c\,z^2+810\,a^7\,b\,g\,h\,z-5670\,a^6\,b^2\,e\,g\,z-3240\,a^6\,b^2\,d\,h\,z-39366\,a^5\,b^3\,c\,f\,z+22680\,a^5\,b^3\,d\,e\,z+6561\,a^6\,b^2\,f^2\,z+59049\,a^4\,b^4\,c^2\,z+270\,a^4\,b\,f\,g\,h-22680\,a\,b^4\,c\,d\,e-1890\,a^3\,b^2\,e\,f\,g-1080\,a^3\,b^2\,d\,f\,h-810\,a^3\,b^2\,c\,g\,h+7560\,a^2\,b^3\,d\,e\,f+5670\,a^2\,b^3\,c\,e\,g+3240\,a^2\,b^3\,c\,d\,h-168\,a^4\,b\,e\,h^2+19683\,a\,b^4\,c^2\,f+1176\,a^3\,b^2\,e^2\,h-6000\,a^2\,b^3\,d^2\,g+1500\,a^3\,b^2\,d\,g^2-6561\,a^2\,b^3\,c\,f^2+729\,a^3\,b^2\,f^3-2744\,a^2\,b^3\,e^3-125\,a^4\,b\,g^3+8000\,a\,b^4\,d^3+8\,a^5\,h^3-19683\,b^5\,c^3,z,k\right)\right)-\frac{\frac{c}{3\,a}+\frac{e\,x^2}{a}+\frac{x^3\,\left(3\,b\,c-a\,f\right)}{2\,a^2}+\frac{4\,x^4\,\left(4\,b\,d-a\,g\right)}{9\,a^2}+\frac{7\,x^5\,\left(7\,b\,e-a\,h\right)}{18\,a^2}+\frac{d\,x}{2\,a}+\frac{b\,x^6\,\left(3\,b\,c-a\,f\right)}{3\,a^3}+\frac{5\,b\,x^7\,\left(4\,b\,d-a\,g\right)}{18\,a^3}+\frac{2\,b\,x^8\,\left(7\,b\,e-a\,h\right)}{9\,a^3}}{a^2\,x^3+2\,a\,b\,x^6+b^2\,x^9}-\frac{\ln\left(x\right)\,\left(3\,b\,c-a\,f\right)}{a^4}","Not used",1,"symsum(log(- (1200*b^5*c*d^2 - 1134*b^5*c^2*e + 75*a^2*b^3*c*g^2 - 126*a^2*b^3*e*f^2 - 25*a^3*b^2*f*g^2 + 18*a^3*b^2*f^2*h - 400*a*b^4*d^2*f + 162*a*b^4*c^2*h - 108*a^2*b^3*c*f*h + 200*a^2*b^3*d*f*g - 600*a*b^4*c*d*g + 756*a*b^4*c*e*f)/(81*a^9) - root(19683*a^12*b^2*z^3 + 19683*a^9*b^2*f*z^2 - 59049*a^8*b^3*c*z^2 + 810*a^7*b*g*h*z - 5670*a^6*b^2*e*g*z - 3240*a^6*b^2*d*h*z - 39366*a^5*b^3*c*f*z + 22680*a^5*b^3*d*e*z + 6561*a^6*b^2*f^2*z + 59049*a^4*b^4*c^2*z + 270*a^4*b*f*g*h - 22680*a*b^4*c*d*e - 1890*a^3*b^2*e*f*g - 1080*a^3*b^2*d*f*h - 810*a^3*b^2*c*g*h + 7560*a^2*b^3*d*e*f + 5670*a^2*b^3*c*e*g + 3240*a^2*b^3*c*d*h - 168*a^4*b*e*h^2 + 19683*a*b^4*c^2*f + 1176*a^3*b^2*e^2*h - 6000*a^2*b^3*d^2*g + 1500*a^3*b^2*d*g^2 - 6561*a^2*b^3*c*f^2 + 729*a^3*b^2*f^3 - 2744*a^2*b^3*e^3 - 125*a^4*b*g^3 + 8000*a*b^4*d^3 + 8*a^5*h^3 - 19683*b^5*c^3, z, k)*((400*a^4*b^4*d^2 + 25*a^6*b^2*g^2 + 756*a^4*b^4*c*e - 108*a^5*b^3*c*h - 200*a^5*b^3*d*g - 252*a^5*b^3*e*f + 36*a^6*b^2*f*h)/(81*a^9) + root(19683*a^12*b^2*z^3 + 19683*a^9*b^2*f*z^2 - 59049*a^8*b^3*c*z^2 + 810*a^7*b*g*h*z - 5670*a^6*b^2*e*g*z - 3240*a^6*b^2*d*h*z - 39366*a^5*b^3*c*f*z + 22680*a^5*b^3*d*e*z + 6561*a^6*b^2*f^2*z + 59049*a^4*b^4*c^2*z + 270*a^4*b*f*g*h - 22680*a*b^4*c*d*e - 1890*a^3*b^2*e*f*g - 1080*a^3*b^2*d*f*h - 810*a^3*b^2*c*g*h + 7560*a^2*b^3*d*e*f + 5670*a^2*b^3*c*e*g + 3240*a^2*b^3*c*d*h - 168*a^4*b*e*h^2 + 19683*a*b^4*c^2*f + 1176*a^3*b^2*e^2*h - 6000*a^2*b^3*d^2*g + 1500*a^3*b^2*d*g^2 - 6561*a^2*b^3*c*f^2 + 729*a^3*b^2*f^3 - 2744*a^2*b^3*e^3 - 125*a^4*b*g^3 + 8000*a*b^4*d^3 + 8*a^5*h^3 - 19683*b^5*c^3, z, k)*((378*a^8*b^3*e - 54*a^9*b^2*h)/(81*a^9) - (x*(52488*a^7*b^4*c - 17496*a^8*b^3*f))/(729*a^9) + 36*root(19683*a^12*b^2*z^3 + 19683*a^9*b^2*f*z^2 - 59049*a^8*b^3*c*z^2 + 810*a^7*b*g*h*z - 5670*a^6*b^2*e*g*z - 3240*a^6*b^2*d*h*z - 39366*a^5*b^3*c*f*z + 22680*a^5*b^3*d*e*z + 6561*a^6*b^2*f^2*z + 59049*a^4*b^4*c^2*z + 270*a^4*b*f*g*h - 22680*a*b^4*c*d*e - 1890*a^3*b^2*e*f*g - 1080*a^3*b^2*d*f*h - 810*a^3*b^2*c*g*h + 7560*a^2*b^3*d*e*f + 5670*a^2*b^3*c*e*g + 3240*a^2*b^3*c*d*h - 168*a^4*b*e*h^2 + 19683*a*b^4*c^2*f + 1176*a^3*b^2*e^2*h - 6000*a^2*b^3*d^2*g + 1500*a^3*b^2*d*g^2 - 6561*a^2*b^3*c*f^2 + 729*a^3*b^2*f^3 - 2744*a^2*b^3*e^3 - 125*a^4*b*g^3 + 8000*a*b^4*d^3 + 8*a^5*h^3 - 19683*b^5*c^3, z, k)*a^2*b^3*x) + (x*(26244*a^3*b^5*c^2 + 2916*a^5*b^3*f^2 - 17496*a^4*b^4*c*f + 25200*a^4*b^4*d*e - 3600*a^5*b^3*d*h - 6300*a^5*b^3*e*g + 900*a^6*b^2*g*h))/(729*a^9)) - (x*(8000*b^5*d^3 - 2744*a*b^4*e^3 + 8*a^4*b*h^3 - 125*a^3*b^2*g^3 + 1500*a^2*b^3*d*g^2 + 1176*a^2*b^3*e^2*h - 168*a^3*b^2*e*h^2 - 15120*b^5*c*d*e - 6000*a*b^4*d^2*g - 540*a^2*b^3*c*g*h - 720*a^2*b^3*d*f*h - 1260*a^2*b^3*e*f*g + 180*a^3*b^2*f*g*h + 2160*a*b^4*c*d*h + 3780*a*b^4*c*e*g + 5040*a*b^4*d*e*f))/(729*a^9))*root(19683*a^12*b^2*z^3 + 19683*a^9*b^2*f*z^2 - 59049*a^8*b^3*c*z^2 + 810*a^7*b*g*h*z - 5670*a^6*b^2*e*g*z - 3240*a^6*b^2*d*h*z - 39366*a^5*b^3*c*f*z + 22680*a^5*b^3*d*e*z + 6561*a^6*b^2*f^2*z + 59049*a^4*b^4*c^2*z + 270*a^4*b*f*g*h - 22680*a*b^4*c*d*e - 1890*a^3*b^2*e*f*g - 1080*a^3*b^2*d*f*h - 810*a^3*b^2*c*g*h + 7560*a^2*b^3*d*e*f + 5670*a^2*b^3*c*e*g + 3240*a^2*b^3*c*d*h - 168*a^4*b*e*h^2 + 19683*a*b^4*c^2*f + 1176*a^3*b^2*e^2*h - 6000*a^2*b^3*d^2*g + 1500*a^3*b^2*d*g^2 - 6561*a^2*b^3*c*f^2 + 729*a^3*b^2*f^3 - 2744*a^2*b^3*e^3 - 125*a^4*b*g^3 + 8000*a*b^4*d^3 + 8*a^5*h^3 - 19683*b^5*c^3, z, k), k, 1, 3) - (c/(3*a) + (e*x^2)/a + (x^3*(3*b*c - a*f))/(2*a^2) + (4*x^4*(4*b*d - a*g))/(9*a^2) + (7*x^5*(7*b*e - a*h))/(18*a^2) + (d*x)/(2*a) + (b*x^6*(3*b*c - a*f))/(3*a^3) + (5*b*x^7*(4*b*d - a*g))/(18*a^3) + (2*b*x^8*(7*b*e - a*h))/(9*a^3))/(a^2*x^3 + b^2*x^9 + 2*a*b*x^6) - (log(x)*(3*b*c - a*f))/a^4","B"
430,0,-1,583,0.000000,"\text{Not used}","int((x^3*(c + d*x + e*x^2))/(a + b*x^3)^(1/2),x)","\int \frac{x^3\,\left(e\,x^2+d\,x+c\right)}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((x^3*(c + d*x + e*x^2))/(a + b*x^3)^(1/2), x)","F"
431,0,-1,560,0.000000,"\text{Not used}","int((x^2*(c + d*x + e*x^2))/(a + b*x^3)^(1/2),x)","\int \frac{x^2\,\left(e\,x^2+d\,x+c\right)}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((x^2*(c + d*x + e*x^2))/(a + b*x^3)^(1/2), x)","F"
432,0,-1,537,0.000000,"\text{Not used}","int((x*(c + d*x + e*x^2))/(a + b*x^3)^(1/2),x)","\int \frac{x\,\left(e\,x^2+d\,x+c\right)}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((x*(c + d*x + e*x^2))/(a + b*x^3)^(1/2), x)","F"
433,0,-1,509,0.000000,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^3)^(1/2),x)","\int \frac{e\,x^2+d\,x+c}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((c + d*x + e*x^2)/(a + b*x^3)^(1/2), x)","F"
434,0,-1,518,0.000000,"\text{Not used}","int((c + d*x + e*x^2)/(x*(a + b*x^3)^(1/2)),x)","\int \frac{e\,x^2+d\,x+c}{x\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((c + d*x + e*x^2)/(x*(a + b*x^3)^(1/2)), x)","F"
435,1,121,547,5.956877,"\text{Not used}","int((c + d*x + e*x^2)/(x^2*(a + b*x^3)^(1/2)),x)","\frac{d\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)}{3\,\sqrt{a}}-\frac{2\,c\,\sqrt{\frac{a}{b\,x^3}+1}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{5}{6};\ \frac{11}{6};\ -\frac{a}{b\,x^3}\right)}{5\,x\,\sqrt{b\,x^3+a}}+\frac{e\,x\,\sqrt{\frac{b\,x^3}{a}+1}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{4}{3};\ -\frac{b\,x^3}{a}\right)}{\sqrt{b\,x^3+a}}","Not used",1,"(d*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6))/(3*a^(1/2)) - (2*c*(a/(b*x^3) + 1)^(1/2)*hypergeom([1/2, 5/6], 11/6, -a/(b*x^3)))/(5*x*(a + b*x^3)^(1/2)) + (e*x*((b*x^3)/a + 1)^(1/2)*hypergeom([1/3, 1/2], 4/3, -(b*x^3)/a))/(a + b*x^3)^(1/2)","B"
436,0,-1,569,0.000000,"\text{Not used}","int((c + d*x + e*x^2)/(x^3*(a + b*x^3)^(1/2)),x)","\int \frac{e\,x^2+d\,x+c}{x^3\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((c + d*x + e*x^2)/(x^3*(a + b*x^3)^(1/2)), x)","F"
437,0,-1,594,0.000000,"\text{Not used}","int((x^5*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x)","\int \frac{x^5\,\left(e\,x^2+d\,x+c\right)}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((x^5*(c + d*x + e*x^2))/(a + b*x^3)^(3/2), x)","F"
438,0,-1,574,0.000000,"\text{Not used}","int((x^4*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x)","\int \frac{x^4\,\left(e\,x^2+d\,x+c\right)}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((x^4*(c + d*x + e*x^2))/(a + b*x^3)^(3/2), x)","F"
439,0,-1,542,0.000000,"\text{Not used}","int((x^3*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x)","\int \frac{x^3\,\left(e\,x^2+d\,x+c\right)}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((x^3*(c + d*x + e*x^2))/(a + b*x^3)^(3/2), x)","F"
440,0,-1,522,0.000000,"\text{Not used}","int((x^2*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x)","\int \frac{x^2\,\left(e\,x^2+d\,x+c\right)}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((x^2*(c + d*x + e*x^2))/(a + b*x^3)^(3/2), x)","F"
441,0,-1,561,0.000000,"\text{Not used}","int((x*(c + d*x + e*x^2))/(a + b*x^3)^(3/2),x)","\int \frac{x\,\left(e\,x^2+d\,x+c\right)}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((x*(c + d*x + e*x^2))/(a + b*x^3)^(3/2), x)","F"
442,0,-1,532,0.000000,"\text{Not used}","int((c + d*x + e*x^2)/(a + b*x^3)^(3/2),x)","\int \frac{e\,x^2+d\,x+c}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x + e*x^2)/(a + b*x^3)^(3/2), x)","F"
443,0,-1,579,0.000000,"\text{Not used}","int((c + d*x + e*x^2)/(x*(a + b*x^3)^(3/2)),x)","\int \frac{e\,x^2+d\,x+c}{x\,{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x + e*x^2)/(x*(a + b*x^3)^(3/2)), x)","F"
444,1,136,607,5.803563,"\text{Not used}","int((c + d*x + e*x^2)/(x^2*(a + b*x^3)^(3/2)),x)","\frac{2\,d}{3\,a\,\sqrt{b\,x^3+a}}+\frac{d\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)}{3\,a^{3/2}}-\frac{2\,c\,{\left(\frac{a}{b\,x^3}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{3}{2},\frac{11}{6};\ \frac{17}{6};\ -\frac{a}{b\,x^3}\right)}{11\,x\,{\left(b\,x^3+a\right)}^{3/2}}+\frac{e\,x\,{\left(\frac{b\,x^3}{a}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{3}{2};\ \frac{4}{3};\ -\frac{b\,x^3}{a}\right)}{{\left(b\,x^3+a\right)}^{3/2}}","Not used",1,"(2*d)/(3*a*(a + b*x^3)^(1/2)) + (d*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6))/(3*a^(3/2)) - (2*c*(a/(b*x^3) + 1)^(3/2)*hypergeom([3/2, 11/6], 17/6, -a/(b*x^3)))/(11*x*(a + b*x^3)^(3/2)) + (e*x*((b*x^3)/a + 1)^(3/2)*hypergeom([1/3, 3/2], 4/3, -(b*x^3)/a))/(a + b*x^3)^(3/2)","B"
445,0,-1,733,0.000000,"\text{Not used}","int(x^3*(a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x)","\int x^3\,\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^3*(a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4), x)","F"
446,0,-1,681,0.000000,"\text{Not used}","int(x^2*(a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x)","\int x^2\,\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^2*(a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4), x)","F"
447,0,-1,667,0.000000,"\text{Not used}","int(x*(a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x)","\int x\,\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x*(a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4), x)","F"
448,0,-1,639,0.000000,"\text{Not used}","int((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x)","\int \sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4), x)","F"
449,0,-1,620,0.000000,"\text{Not used}","int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x,x)","\int \frac{\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x} \,d x","Not used",1,"int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x, x)","F"
450,0,-1,638,0.000000,"\text{Not used}","int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^2,x)","\int \frac{\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^2} \,d x","Not used",1,"int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^2, x)","F"
451,0,-1,640,0.000000,"\text{Not used}","int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^3,x)","\int \frac{\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^3} \,d x","Not used",1,"int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^3, x)","F"
452,0,-1,637,0.000000,"\text{Not used}","int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^4,x)","\int \frac{\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^4} \,d x","Not used",1,"int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^4, x)","F"
453,0,-1,694,0.000000,"\text{Not used}","int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^5,x)","\int \frac{\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^5} \,d x","Not used",1,"int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^5, x)","F"
454,0,-1,652,0.000000,"\text{Not used}","int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^6,x)","\int \frac{\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^6} \,d x","Not used",1,"int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^6, x)","F"
455,0,-1,659,0.000000,"\text{Not used}","int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^7,x)","\int \frac{\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^7} \,d x","Not used",1,"int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^7, x)","F"
456,0,-1,711,0.000000,"\text{Not used}","int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^8,x)","\int \frac{\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^8} \,d x","Not used",1,"int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^8, x)","F"
457,0,-1,743,0.000000,"\text{Not used}","int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^9,x)","\int \frac{\sqrt{b\,x^3+a}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^9} \,d x","Not used",1,"int(((a + b*x^3)^(1/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^9, x)","F"
458,0,-1,791,0.000000,"\text{Not used}","int(x^3*(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x)","\int x^3\,{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^3*(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4), x)","F"
459,0,-1,742,0.000000,"\text{Not used}","int(x^2*(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x)","\int x^2\,{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^2*(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4), x)","F"
460,0,-1,723,0.000000,"\text{Not used}","int(x*(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x)","\int x\,{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x*(a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4), x)","F"
461,0,-1,694,0.000000,"\text{Not used}","int((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4),x)","\int {\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4), x)","F"
462,0,-1,676,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x, x)","F"
463,0,-1,692,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^2,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^2} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^2, x)","F"
464,0,-1,694,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^3,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^3} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^3, x)","F"
465,0,-1,692,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^4,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^4} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^4, x)","F"
466,0,-1,741,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^5,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^5} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^5, x)","F"
467,0,-1,689,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^6,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^6} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^6, x)","F"
468,0,-1,692,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^7,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^7} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^7, x)","F"
469,0,-1,746,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^8,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^8} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^8, x)","F"
470,0,-1,705,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^9,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^9} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^9, x)","F"
471,0,-1,714,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^10,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^{10}} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^10, x)","F"
472,0,-1,764,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^11,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^{11}} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^11, x)","F"
473,0,-1,796,0.000000,"\text{Not used}","int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^12,x)","\int \frac{{\left(b\,x^3+a\right)}^{3/2}\,\left(g\,x^4+f\,x^3+e\,x^2+d\,x+c\right)}{x^{12}} \,d x","Not used",1,"int(((a + b*x^3)^(3/2)*(c + d*x + e*x^2 + f*x^3 + g*x^4))/x^12, x)","F"
474,0,-1,102,0.000000,"\text{Not used}","int((a + b*x^3)^p*(c + d*x + e*x^2),x)","\int {\left(b\,x^3+a\right)}^p\,\left(e\,x^2+d\,x+c\right) \,d x","Not used",1,"int((a + b*x^3)^p*(c + d*x + e*x^2), x)","F"
475,0,-1,107,0.000000,"\text{Not used}","int(x*(a + b*x^3)^p*(c + d*x + e*x^2),x)","\int x\,{\left(b\,x^3+a\right)}^p\,\left(e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x*(a + b*x^3)^p*(c + d*x + e*x^2), x)","F"
476,0,-1,107,0.000000,"\text{Not used}","int(x^2*(a + b*x^3)^p*(c + d*x + e*x^2),x)","\int x^2\,{\left(b\,x^3+a\right)}^p\,\left(e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^2*(a + b*x^3)^p*(c + d*x + e*x^2), x)","F"
477,1,54,68,0.035350,"\text{Not used}","int((a + b*x^4)*(c + d*x + e*x^2 + f*x^3),x)","\frac{b\,f\,x^8}{8}+\frac{b\,e\,x^7}{7}+\frac{b\,d\,x^6}{6}+\frac{b\,c\,x^5}{5}+\frac{a\,f\,x^4}{4}+\frac{a\,e\,x^3}{3}+\frac{a\,d\,x^2}{2}+a\,c\,x","Not used",1,"a*c*x + (a*d*x^2)/2 + (b*c*x^5)/5 + (a*e*x^3)/3 + (b*d*x^6)/6 + (a*f*x^4)/4 + (b*e*x^7)/7 + (b*f*x^8)/8","B"
478,1,57,73,0.031015,"\text{Not used}","int(x^3*(a + b*x^4)*(c + d*x + e*x^2 + f*x^3),x)","\frac{b\,f\,x^{11}}{11}+\frac{b\,e\,x^{10}}{10}+\frac{b\,d\,x^9}{9}+\frac{b\,c\,x^8}{8}+\frac{a\,f\,x^7}{7}+\frac{a\,e\,x^6}{6}+\frac{a\,d\,x^5}{5}+\frac{a\,c\,x^4}{4}","Not used",1,"(a*c*x^4)/4 + (a*d*x^5)/5 + (b*c*x^8)/8 + (a*e*x^6)/6 + (b*d*x^9)/9 + (a*f*x^7)/7 + (b*e*x^10)/10 + (b*f*x^11)/11","B"
479,1,102,109,0.080103,"\text{Not used}","int((a + b*x^4)^2*(c + d*x + e*x^2 + f*x^3),x)","\frac{f\,a^2\,x^4}{4}+\frac{e\,a^2\,x^3}{3}+\frac{d\,a^2\,x^2}{2}+c\,a^2\,x+\frac{f\,a\,b\,x^8}{4}+\frac{2\,e\,a\,b\,x^7}{7}+\frac{d\,a\,b\,x^6}{3}+\frac{2\,c\,a\,b\,x^5}{5}+\frac{f\,b^2\,x^{12}}{12}+\frac{e\,b^2\,x^{11}}{11}+\frac{d\,b^2\,x^{10}}{10}+\frac{c\,b^2\,x^9}{9}","Not used",1,"(a^2*d*x^2)/2 + (b^2*c*x^9)/9 + (a^2*e*x^3)/3 + (b^2*d*x^10)/10 + (a^2*f*x^4)/4 + (b^2*e*x^11)/11 + (b^2*f*x^12)/12 + a^2*c*x + (2*a*b*c*x^5)/5 + (a*b*d*x^6)/3 + (2*a*b*e*x^7)/7 + (a*b*f*x^8)/4","B"
480,1,105,114,0.072473,"\text{Not used}","int(x^3*(a + b*x^4)^2*(c + d*x + e*x^2 + f*x^3),x)","\frac{f\,a^2\,x^7}{7}+\frac{e\,a^2\,x^6}{6}+\frac{d\,a^2\,x^5}{5}+\frac{c\,a^2\,x^4}{4}+\frac{2\,f\,a\,b\,x^{11}}{11}+\frac{e\,a\,b\,x^{10}}{5}+\frac{2\,d\,a\,b\,x^9}{9}+\frac{c\,a\,b\,x^8}{4}+\frac{f\,b^2\,x^{15}}{15}+\frac{e\,b^2\,x^{14}}{14}+\frac{d\,b^2\,x^{13}}{13}+\frac{c\,b^2\,x^{12}}{12}","Not used",1,"(a^2*c*x^4)/4 + (a^2*d*x^5)/5 + (b^2*c*x^12)/12 + (a^2*e*x^6)/6 + (b^2*d*x^13)/13 + (a^2*f*x^7)/7 + (b^2*e*x^14)/14 + (b^2*f*x^15)/15 + (a*b*c*x^8)/4 + (2*a*b*d*x^9)/9 + (a*b*e*x^10)/5 + (2*a*b*f*x^11)/11","B"
481,1,150,151,0.163981,"\text{Not used}","int((a + b*x^4)^3*(c + d*x + e*x^2 + f*x^3),x)","\frac{f\,a^3\,x^4}{4}+\frac{e\,a^3\,x^3}{3}+\frac{d\,a^3\,x^2}{2}+c\,a^3\,x+\frac{3\,f\,a^2\,b\,x^8}{8}+\frac{3\,e\,a^2\,b\,x^7}{7}+\frac{d\,a^2\,b\,x^6}{2}+\frac{3\,c\,a^2\,b\,x^5}{5}+\frac{f\,a\,b^2\,x^{12}}{4}+\frac{3\,e\,a\,b^2\,x^{11}}{11}+\frac{3\,d\,a\,b^2\,x^{10}}{10}+\frac{c\,a\,b^2\,x^9}{3}+\frac{f\,b^3\,x^{16}}{16}+\frac{e\,b^3\,x^{15}}{15}+\frac{d\,b^3\,x^{14}}{14}+\frac{c\,b^3\,x^{13}}{13}","Not used",1,"(a^3*d*x^2)/2 + (b^3*c*x^13)/13 + (a^3*e*x^3)/3 + (b^3*d*x^14)/14 + (a^3*f*x^4)/4 + (b^3*e*x^15)/15 + (b^3*f*x^16)/16 + a^3*c*x + (3*a^2*b*c*x^5)/5 + (a*b^2*c*x^9)/3 + (a^2*b*d*x^6)/2 + (3*a*b^2*d*x^10)/10 + (3*a^2*b*e*x^7)/7 + (3*a*b^2*e*x^11)/11 + (3*a^2*b*f*x^8)/8 + (a*b^2*f*x^12)/4","B"
482,1,153,156,0.160995,"\text{Not used}","int(x^3*(a + b*x^4)^3*(c + d*x + e*x^2 + f*x^3),x)","\frac{f\,a^3\,x^7}{7}+\frac{e\,a^3\,x^6}{6}+\frac{d\,a^3\,x^5}{5}+\frac{c\,a^3\,x^4}{4}+\frac{3\,f\,a^2\,b\,x^{11}}{11}+\frac{3\,e\,a^2\,b\,x^{10}}{10}+\frac{d\,a^2\,b\,x^9}{3}+\frac{3\,c\,a^2\,b\,x^8}{8}+\frac{f\,a\,b^2\,x^{15}}{5}+\frac{3\,e\,a\,b^2\,x^{14}}{14}+\frac{3\,d\,a\,b^2\,x^{13}}{13}+\frac{c\,a\,b^2\,x^{12}}{4}+\frac{f\,b^3\,x^{19}}{19}+\frac{e\,b^3\,x^{18}}{18}+\frac{d\,b^3\,x^{17}}{17}+\frac{c\,b^3\,x^{16}}{16}","Not used",1,"(a^3*c*x^4)/4 + (a^3*d*x^5)/5 + (b^3*c*x^16)/16 + (a^3*e*x^6)/6 + (b^3*d*x^17)/17 + (a^3*f*x^7)/7 + (b^3*e*x^18)/18 + (b^3*f*x^19)/19 + (3*a^2*b*c*x^8)/8 + (a*b^2*c*x^12)/4 + (a^2*b*d*x^9)/3 + (3*a*b^2*d*x^13)/13 + (3*a^2*b*e*x^10)/10 + (3*a*b^2*e*x^14)/14 + (3*a^2*b*f*x^11)/11 + (a*b^2*f*x^15)/5","B"
483,1,198,193,5.080181,"\text{Not used}","int((a + b*x^4)^4*(c + d*x + e*x^2 + f*x^3),x)","\frac{f\,a^4\,x^4}{4}+\frac{e\,a^4\,x^3}{3}+\frac{d\,a^4\,x^2}{2}+c\,a^4\,x+\frac{f\,a^3\,b\,x^8}{2}+\frac{4\,e\,a^3\,b\,x^7}{7}+\frac{2\,d\,a^3\,b\,x^6}{3}+\frac{4\,c\,a^3\,b\,x^5}{5}+\frac{f\,a^2\,b^2\,x^{12}}{2}+\frac{6\,e\,a^2\,b^2\,x^{11}}{11}+\frac{3\,d\,a^2\,b^2\,x^{10}}{5}+\frac{2\,c\,a^2\,b^2\,x^9}{3}+\frac{f\,a\,b^3\,x^{16}}{4}+\frac{4\,e\,a\,b^3\,x^{15}}{15}+\frac{2\,d\,a\,b^3\,x^{14}}{7}+\frac{4\,c\,a\,b^3\,x^{13}}{13}+\frac{f\,b^4\,x^{20}}{20}+\frac{e\,b^4\,x^{19}}{19}+\frac{d\,b^4\,x^{18}}{18}+\frac{c\,b^4\,x^{17}}{17}","Not used",1,"(a^4*d*x^2)/2 + (b^4*c*x^17)/17 + (a^4*e*x^3)/3 + (b^4*d*x^18)/18 + (a^4*f*x^4)/4 + (b^4*e*x^19)/19 + (b^4*f*x^20)/20 + a^4*c*x + (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 + (a^2*b^2*f*x^12)/2 + (4*a^3*b*c*x^5)/5 + (4*a*b^3*c*x^13)/13 + (2*a^3*b*d*x^6)/3 + (2*a*b^3*d*x^14)/7 + (4*a^3*b*e*x^7)/7 + (4*a*b^3*e*x^15)/15 + (a^3*b*f*x^8)/2 + (a*b^3*f*x^16)/4","B"
484,1,201,198,0.359074,"\text{Not used}","int(x^3*(a + b*x^4)^4*(c + d*x + e*x^2 + f*x^3),x)","\frac{f\,a^4\,x^7}{7}+\frac{e\,a^4\,x^6}{6}+\frac{d\,a^4\,x^5}{5}+\frac{c\,a^4\,x^4}{4}+\frac{4\,f\,a^3\,b\,x^{11}}{11}+\frac{2\,e\,a^3\,b\,x^{10}}{5}+\frac{4\,d\,a^3\,b\,x^9}{9}+\frac{c\,a^3\,b\,x^8}{2}+\frac{2\,f\,a^2\,b^2\,x^{15}}{5}+\frac{3\,e\,a^2\,b^2\,x^{14}}{7}+\frac{6\,d\,a^2\,b^2\,x^{13}}{13}+\frac{c\,a^2\,b^2\,x^{12}}{2}+\frac{4\,f\,a\,b^3\,x^{19}}{19}+\frac{2\,e\,a\,b^3\,x^{18}}{9}+\frac{4\,d\,a\,b^3\,x^{17}}{17}+\frac{c\,a\,b^3\,x^{16}}{4}+\frac{f\,b^4\,x^{23}}{23}+\frac{e\,b^4\,x^{22}}{22}+\frac{d\,b^4\,x^{21}}{21}+\frac{c\,b^4\,x^{20}}{20}","Not used",1,"(a^4*c*x^4)/4 + (a^4*d*x^5)/5 + (b^4*c*x^20)/20 + (a^4*e*x^6)/6 + (b^4*d*x^21)/21 + (a^4*f*x^7)/7 + (b^4*e*x^22)/22 + (b^4*f*x^23)/23 + (a^2*b^2*c*x^12)/2 + (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 + (a^3*b*c*x^8)/2 + (a*b^3*c*x^16)/4 + (4*a^3*b*d*x^9)/9 + (4*a*b^3*d*x^17)/17 + (2*a^3*b*e*x^10)/5 + (2*a*b^3*e*x^18)/9 + (4*a^3*b*f*x^11)/11 + (4*a*b^3*f*x^19)/19","B"
485,1,1970,133,5.657679,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a - b*x^4),x)","\sum _{k=1}^4\ln\left(-b^2\,c\,d^2+b^2\,c^2\,e-b^2\,d^3\,x-a\,b\,e^3-a\,b\,c\,f^2-{\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,f\,z^3-64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2-32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z+16\,a\,b^3\,c^2\,d\,z+16\,a^3\,b\,f^3\,z+4\,a^2\,b\,d\,e^2\,f-4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e-2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a\,b^2\,d^4+a^3\,f^4-a^2\,b\,e^4-b^3\,c^4,z,k\right)}^2\,a\,b^3\,c\,16-\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,f\,z^3-64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2-32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z+16\,a\,b^3\,c^2\,d\,z+16\,a^3\,b\,f^3\,z+4\,a^2\,b\,d\,e^2\,f-4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e-2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a\,b^2\,d^4+a^3\,f^4-a^2\,b\,e^4-b^3\,c^4,z,k\right)\,b^3\,c^2\,x\,4-b^2\,c^2\,f\,x+{\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,f\,z^3-64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2-32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z+16\,a\,b^3\,c^2\,d\,z+16\,a^3\,b\,f^3\,z+4\,a^2\,b\,d\,e^2\,f-4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e-2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a\,b^2\,d^4+a^3\,f^4-a^2\,b\,e^4-b^3\,c^4,z,k\right)}^2\,a\,b^3\,d\,x\,16-\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,f\,z^3-64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2-32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z+16\,a\,b^3\,c^2\,d\,z+16\,a^3\,b\,f^3\,z+4\,a^2\,b\,d\,e^2\,f-4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e-2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a\,b^2\,d^4+a^3\,f^4-a^2\,b\,e^4-b^3\,c^4,z,k\right)\,a\,b^2\,e^2\,x\,4+2\,a\,b\,d\,e\,f-\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,f\,z^3-64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2-32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z+16\,a\,b^3\,c^2\,d\,z+16\,a^3\,b\,f^3\,z+4\,a^2\,b\,d\,e^2\,f-4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e-2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a\,b^2\,d^4+a^3\,f^4-a^2\,b\,e^4-b^3\,c^4,z,k\right)\,a\,b^2\,c\,f\,8+\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,f\,z^3-64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2-32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z+16\,a\,b^3\,c^2\,d\,z+16\,a^3\,b\,f^3\,z+4\,a^2\,b\,d\,e^2\,f-4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e-2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a\,b^2\,d^4+a^3\,f^4-a^2\,b\,e^4-b^3\,c^4,z,k\right)\,a\,b^2\,d\,e\,8+a\,b\,d\,f^2\,x-a\,b\,e^2\,f\,x+2\,b^2\,c\,d\,e\,x+\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,f\,z^3-64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2-32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z+16\,a\,b^3\,c^2\,d\,z+16\,a^3\,b\,f^3\,z+4\,a^2\,b\,d\,e^2\,f-4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e-2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a\,b^2\,d^4+a^3\,f^4-a^2\,b\,e^4-b^3\,c^4,z,k\right)\,a\,b^2\,d\,f\,x\,8\right)\,\mathrm{root}\left(256\,a^3\,b^4\,z^4+256\,a^3\,b^3\,f\,z^3-64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2-32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z+16\,a\,b^3\,c^2\,d\,z+16\,a^3\,b\,f^3\,z+4\,a^2\,b\,d\,e^2\,f-4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e-2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a\,b^2\,d^4+a^3\,f^4-a^2\,b\,e^4-b^3\,c^4,z,k\right)","Not used",1,"symsum(log(b^2*c^2*e - b^2*c*d^2 - b^2*d^3*x - a*b*e^3 - a*b*c*f^2 - 16*root(256*a^3*b^4*z^4 + 256*a^3*b^3*f*z^3 - 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 - 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z + 16*a*b^3*c^2*d*z + 16*a^3*b*f^3*z + 4*a^2*b*d*e^2*f - 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e - 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a*b^2*d^4 + a^3*f^4 - a^2*b*e^4 - b^3*c^4, z, k)^2*a*b^3*c - 4*root(256*a^3*b^4*z^4 + 256*a^3*b^3*f*z^3 - 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 - 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z + 16*a*b^3*c^2*d*z + 16*a^3*b*f^3*z + 4*a^2*b*d*e^2*f - 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e - 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a*b^2*d^4 + a^3*f^4 - a^2*b*e^4 - b^3*c^4, z, k)*b^3*c^2*x - b^2*c^2*f*x + 16*root(256*a^3*b^4*z^4 + 256*a^3*b^3*f*z^3 - 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 - 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z + 16*a*b^3*c^2*d*z + 16*a^3*b*f^3*z + 4*a^2*b*d*e^2*f - 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e - 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a*b^2*d^4 + a^3*f^4 - a^2*b*e^4 - b^3*c^4, z, k)^2*a*b^3*d*x - 4*root(256*a^3*b^4*z^4 + 256*a^3*b^3*f*z^3 - 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 - 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z + 16*a*b^3*c^2*d*z + 16*a^3*b*f^3*z + 4*a^2*b*d*e^2*f - 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e - 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a*b^2*d^4 + a^3*f^4 - a^2*b*e^4 - b^3*c^4, z, k)*a*b^2*e^2*x + 2*a*b*d*e*f - 8*root(256*a^3*b^4*z^4 + 256*a^3*b^3*f*z^3 - 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 - 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z + 16*a*b^3*c^2*d*z + 16*a^3*b*f^3*z + 4*a^2*b*d*e^2*f - 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e - 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a*b^2*d^4 + a^3*f^4 - a^2*b*e^4 - b^3*c^4, z, k)*a*b^2*c*f + 8*root(256*a^3*b^4*z^4 + 256*a^3*b^3*f*z^3 - 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 - 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z + 16*a*b^3*c^2*d*z + 16*a^3*b*f^3*z + 4*a^2*b*d*e^2*f - 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e - 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a*b^2*d^4 + a^3*f^4 - a^2*b*e^4 - b^3*c^4, z, k)*a*b^2*d*e + a*b*d*f^2*x - a*b*e^2*f*x + 2*b^2*c*d*e*x + 8*root(256*a^3*b^4*z^4 + 256*a^3*b^3*f*z^3 - 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 - 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z + 16*a*b^3*c^2*d*z + 16*a^3*b*f^3*z + 4*a^2*b*d*e^2*f - 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e - 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a*b^2*d^4 + a^3*f^4 - a^2*b*e^4 - b^3*c^4, z, k)*a*b^2*d*f*x)*root(256*a^3*b^4*z^4 + 256*a^3*b^3*f*z^3 - 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 - 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z + 16*a*b^3*c^2*d*z + 16*a^3*b*f^3*z + 4*a^2*b*d*e^2*f - 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e - 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a*b^2*d^4 + a^3*f^4 - a^2*b*e^4 - b^3*c^4, z, k), k, 1, 4)","B"
486,1,846,162,4.846255,"\text{Not used}","int((x^3*(c + d*x + e*x^2 + f*x^3))/(a - b*x^4),x)","\left(\sum _{k=1}^4\ln\left(-\frac{a^4\,f^3-2\,a^3\,b\,c\,e\,f-a^3\,b\,d^2\,f+a^3\,b\,d\,e^2+a^2\,b^2\,c^2\,d}{b^2}-\mathrm{root}\left(256\,b^7\,z^4+256\,b^6\,c\,z^3-64\,a\,b^4\,d\,f\,z^2-32\,a\,b^4\,e^2\,z^2+96\,b^5\,c^2\,z^2-32\,a\,b^3\,c\,d\,f\,z+16\,a^2\,b^2\,e\,f^2\,z+16\,a\,b^3\,d^2\,e\,z-16\,a\,b^3\,c\,e^2\,z+16\,b^4\,c^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2-4\,a\,b^2\,c^2\,d\,f+4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2-2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+b^3\,c^4-a\,b^2\,d^4-a^3\,f^4,z,k\right)\,\left(\mathrm{root}\left(256\,b^7\,z^4+256\,b^6\,c\,z^3-64\,a\,b^4\,d\,f\,z^2-32\,a\,b^4\,e^2\,z^2+96\,b^5\,c^2\,z^2-32\,a\,b^3\,c\,d\,f\,z+16\,a^2\,b^2\,e\,f^2\,z+16\,a\,b^3\,d^2\,e\,z-16\,a\,b^3\,c\,e^2\,z+16\,b^4\,c^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2-4\,a\,b^2\,c^2\,d\,f+4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2-2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+b^3\,c^4-a\,b^2\,d^4-a^3\,f^4,z,k\right)\,\left(16\,a^2\,b^2\,d-16\,a^2\,b^2\,e\,x\right)+\frac{8\,a^2\,b^3\,c\,d-8\,a^3\,b^2\,e\,f}{b^2}+\frac{x\,\left(4\,a^3\,b\,f^2+4\,a^2\,b^2\,d^2-8\,c\,e\,a^2\,b^2\right)}{b}\right)-\frac{x\,\left(a^3\,c\,f^2-2\,a^3\,d\,e\,f+a^3\,e^3-b\,a^2\,c^2\,e+b\,a^2\,c\,d^2\right)}{b}\right)\,\mathrm{root}\left(256\,b^7\,z^4+256\,b^6\,c\,z^3-64\,a\,b^4\,d\,f\,z^2-32\,a\,b^4\,e^2\,z^2+96\,b^5\,c^2\,z^2-32\,a\,b^3\,c\,d\,f\,z+16\,a^2\,b^2\,e\,f^2\,z+16\,a\,b^3\,d^2\,e\,z-16\,a\,b^3\,c\,e^2\,z+16\,b^4\,c^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2-4\,a\,b^2\,c^2\,d\,f+4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2-2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+b^3\,c^4-a\,b^2\,d^4-a^3\,f^4,z,k\right)\right)-\frac{e\,x^2}{2\,b}-\frac{f\,x^3}{3\,b}-\frac{d\,x}{b}","Not used",1,"symsum(log(- (a^4*f^3 + a^2*b^2*c^2*d + a^3*b*d*e^2 - a^3*b*d^2*f - 2*a^3*b*c*e*f)/b^2 - root(256*b^7*z^4 + 256*b^6*c*z^3 - 64*a*b^4*d*f*z^2 - 32*a*b^4*e^2*z^2 + 96*b^5*c^2*z^2 - 32*a*b^3*c*d*f*z + 16*a^2*b^2*e*f^2*z + 16*a*b^3*d^2*e*z - 16*a*b^3*c*e^2*z + 16*b^4*c^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 - 4*a*b^2*c^2*d*f + 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 - 2*a*b^2*c^2*e^2 + a^2*b*e^4 + b^3*c^4 - a*b^2*d^4 - a^3*f^4, z, k)*(root(256*b^7*z^4 + 256*b^6*c*z^3 - 64*a*b^4*d*f*z^2 - 32*a*b^4*e^2*z^2 + 96*b^5*c^2*z^2 - 32*a*b^3*c*d*f*z + 16*a^2*b^2*e*f^2*z + 16*a*b^3*d^2*e*z - 16*a*b^3*c*e^2*z + 16*b^4*c^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 - 4*a*b^2*c^2*d*f + 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 - 2*a*b^2*c^2*e^2 + a^2*b*e^4 + b^3*c^4 - a*b^2*d^4 - a^3*f^4, z, k)*(16*a^2*b^2*d - 16*a^2*b^2*e*x) + (8*a^2*b^3*c*d - 8*a^3*b^2*e*f)/b^2 + (x*(4*a^3*b*f^2 + 4*a^2*b^2*d^2 - 8*a^2*b^2*c*e))/b) - (x*(a^3*e^3 + a^3*c*f^2 - 2*a^3*d*e*f + a^2*b*c*d^2 - a^2*b*c^2*e))/b)*root(256*b^7*z^4 + 256*b^6*c*z^3 - 64*a*b^4*d*f*z^2 - 32*a*b^4*e^2*z^2 + 96*b^5*c^2*z^2 - 32*a*b^3*c*d*f*z + 16*a^2*b^2*e*f^2*z + 16*a*b^3*d^2*e*z - 16*a*b^3*c*e^2*z + 16*b^4*c^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 - 4*a*b^2*c^2*d*f + 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 - 2*a*b^2*c^2*e^2 + a^2*b*e^4 + b^3*c^4 - a*b^2*d^4 - a^3*f^4, z, k), k, 1, 4) - (e*x^2)/(2*b) - (f*x^3)/(3*b) - (d*x)/b","B"
487,1,1952,293,0.926695,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a + b*x^4),x)","\sum _{k=1}^4\ln\left(b^2\,c\,d^2-b^2\,c^2\,e+b^2\,d^3\,x-a\,b\,e^3-a\,b\,c\,f^2-{\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,f\,z^3+64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2+32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z-16\,a\,b^3\,c^2\,d\,z-16\,a^3\,b\,f^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)}^2\,a\,b^3\,c\,16-\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,f\,z^3+64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2+32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z-16\,a\,b^3\,c^2\,d\,z-16\,a^3\,b\,f^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)\,b^3\,c^2\,x\,4+b^2\,c^2\,f\,x+{\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,f\,z^3+64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2+32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z-16\,a\,b^3\,c^2\,d\,z-16\,a^3\,b\,f^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)}^2\,a\,b^3\,d\,x\,16+\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,f\,z^3+64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2+32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z-16\,a\,b^3\,c^2\,d\,z-16\,a^3\,b\,f^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)\,a\,b^2\,e^2\,x\,4+2\,a\,b\,d\,e\,f+\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,f\,z^3+64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2+32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z-16\,a\,b^3\,c^2\,d\,z-16\,a^3\,b\,f^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)\,a\,b^2\,c\,f\,8-\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,f\,z^3+64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2+32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z-16\,a\,b^3\,c^2\,d\,z-16\,a^3\,b\,f^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)\,a\,b^2\,d\,e\,8+a\,b\,d\,f^2\,x-a\,b\,e^2\,f\,x-2\,b^2\,c\,d\,e\,x-\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,f\,z^3+64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2+32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z-16\,a\,b^3\,c^2\,d\,z-16\,a^3\,b\,f^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)\,a\,b^2\,d\,f\,x\,8\right)\,\mathrm{root}\left(256\,a^3\,b^4\,z^4-256\,a^3\,b^3\,f\,z^3+64\,a^2\,b^3\,c\,e\,z^2+96\,a^3\,b^2\,f^2\,z^2+32\,a^2\,b^3\,d^2\,z^2-32\,a^2\,b^2\,c\,e\,f\,z-16\,a^2\,b^2\,d^2\,f\,z+16\,a^2\,b^2\,d\,e^2\,z-16\,a\,b^3\,c^2\,d\,z-16\,a^3\,b\,f^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)","Not used",1,"symsum(log(b^2*c*d^2 - b^2*c^2*e + b^2*d^3*x - a*b*e^3 - a*b*c*f^2 - 16*root(256*a^3*b^4*z^4 - 256*a^3*b^3*f*z^3 + 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 + 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z - 16*a*b^3*c^2*d*z - 16*a^3*b*f^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k)^2*a*b^3*c - 4*root(256*a^3*b^4*z^4 - 256*a^3*b^3*f*z^3 + 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 + 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z - 16*a*b^3*c^2*d*z - 16*a^3*b*f^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k)*b^3*c^2*x + b^2*c^2*f*x + 16*root(256*a^3*b^4*z^4 - 256*a^3*b^3*f*z^3 + 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 + 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z - 16*a*b^3*c^2*d*z - 16*a^3*b*f^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k)^2*a*b^3*d*x + 4*root(256*a^3*b^4*z^4 - 256*a^3*b^3*f*z^3 + 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 + 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z - 16*a*b^3*c^2*d*z - 16*a^3*b*f^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k)*a*b^2*e^2*x + 2*a*b*d*e*f + 8*root(256*a^3*b^4*z^4 - 256*a^3*b^3*f*z^3 + 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 + 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z - 16*a*b^3*c^2*d*z - 16*a^3*b*f^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k)*a*b^2*c*f - 8*root(256*a^3*b^4*z^4 - 256*a^3*b^3*f*z^3 + 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 + 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z - 16*a*b^3*c^2*d*z - 16*a^3*b*f^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k)*a*b^2*d*e + a*b*d*f^2*x - a*b*e^2*f*x - 2*b^2*c*d*e*x - 8*root(256*a^3*b^4*z^4 - 256*a^3*b^3*f*z^3 + 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 + 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z - 16*a*b^3*c^2*d*z - 16*a^3*b*f^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k)*a*b^2*d*f*x)*root(256*a^3*b^4*z^4 - 256*a^3*b^3*f*z^3 + 64*a^2*b^3*c*e*z^2 + 96*a^3*b^2*f^2*z^2 + 32*a^2*b^3*d^2*z^2 - 32*a^2*b^2*c*e*f*z - 16*a^2*b^2*d^2*f*z + 16*a^2*b^2*d*e^2*z - 16*a*b^3*c^2*d*z - 16*a^3*b*f^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k), k, 1, 4)","B"
488,1,838,321,4.854245,"\text{Not used}","int((x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4),x)","\left(\sum _{k=1}^4\ln\left(\frac{a^4\,f^3+2\,a^3\,b\,c\,e\,f+a^3\,b\,d^2\,f-a^3\,b\,d\,e^2+a^2\,b^2\,c^2\,d}{b^2}+\mathrm{root}\left(256\,b^7\,z^4-256\,b^6\,c\,z^3+64\,a\,b^4\,d\,f\,z^2+32\,a\,b^4\,e^2\,z^2+96\,b^5\,c^2\,z^2-32\,a\,b^3\,c\,d\,f\,z-16\,a^2\,b^2\,e\,f^2\,z+16\,a\,b^3\,d^2\,e\,z-16\,a\,b^3\,c\,e^2\,z-16\,b^4\,c^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)\,\left(\mathrm{root}\left(256\,b^7\,z^4-256\,b^6\,c\,z^3+64\,a\,b^4\,d\,f\,z^2+32\,a\,b^4\,e^2\,z^2+96\,b^5\,c^2\,z^2-32\,a\,b^3\,c\,d\,f\,z-16\,a^2\,b^2\,e\,f^2\,z+16\,a\,b^3\,d^2\,e\,z-16\,a\,b^3\,c\,e^2\,z-16\,b^4\,c^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)\,\left(16\,a^2\,b^2\,d-16\,a^2\,b^2\,e\,x\right)-\frac{8\,e\,f\,a^3\,b^2+8\,c\,d\,a^2\,b^3}{b^2}+\frac{x\,\left(4\,a^3\,b\,f^2-4\,a^2\,b^2\,d^2+8\,c\,e\,a^2\,b^2\right)}{b}\right)-\frac{x\,\left(a^3\,c\,f^2-2\,a^3\,d\,e\,f+a^3\,e^3+b\,a^2\,c^2\,e-b\,a^2\,c\,d^2\right)}{b}\right)\,\mathrm{root}\left(256\,b^7\,z^4-256\,b^6\,c\,z^3+64\,a\,b^4\,d\,f\,z^2+32\,a\,b^4\,e^2\,z^2+96\,b^5\,c^2\,z^2-32\,a\,b^3\,c\,d\,f\,z-16\,a^2\,b^2\,e\,f^2\,z+16\,a\,b^3\,d^2\,e\,z-16\,a\,b^3\,c\,e^2\,z-16\,b^4\,c^3\,z-4\,a^2\,b\,d\,e^2\,f+4\,a^2\,b\,c\,e\,f^2+4\,a\,b^2\,c^2\,d\,f-4\,a\,b^2\,c\,d^2\,e+2\,a^2\,b\,d^2\,f^2+2\,a\,b^2\,c^2\,e^2+a^2\,b\,e^4+a\,b^2\,d^4+a^3\,f^4+b^3\,c^4,z,k\right)\right)+\frac{e\,x^2}{2\,b}+\frac{f\,x^3}{3\,b}+\frac{d\,x}{b}","Not used",1,"symsum(log((a^4*f^3 + a^2*b^2*c^2*d - a^3*b*d*e^2 + a^3*b*d^2*f + 2*a^3*b*c*e*f)/b^2 + root(256*b^7*z^4 - 256*b^6*c*z^3 + 64*a*b^4*d*f*z^2 + 32*a*b^4*e^2*z^2 + 96*b^5*c^2*z^2 - 32*a*b^3*c*d*f*z - 16*a^2*b^2*e*f^2*z + 16*a*b^3*d^2*e*z - 16*a*b^3*c*e^2*z - 16*b^4*c^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k)*(root(256*b^7*z^4 - 256*b^6*c*z^3 + 64*a*b^4*d*f*z^2 + 32*a*b^4*e^2*z^2 + 96*b^5*c^2*z^2 - 32*a*b^3*c*d*f*z - 16*a^2*b^2*e*f^2*z + 16*a*b^3*d^2*e*z - 16*a*b^3*c*e^2*z - 16*b^4*c^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k)*(16*a^2*b^2*d - 16*a^2*b^2*e*x) - (8*a^2*b^3*c*d + 8*a^3*b^2*e*f)/b^2 + (x*(4*a^3*b*f^2 - 4*a^2*b^2*d^2 + 8*a^2*b^2*c*e))/b) - (x*(a^3*e^3 + a^3*c*f^2 - 2*a^3*d*e*f - a^2*b*c*d^2 + a^2*b*c^2*e))/b)*root(256*b^7*z^4 - 256*b^6*c*z^3 + 64*a*b^4*d*f*z^2 + 32*a*b^4*e^2*z^2 + 96*b^5*c^2*z^2 - 32*a*b^3*c*d*f*z - 16*a^2*b^2*e*f^2*z + 16*a*b^3*d^2*e*z - 16*a*b^3*c*e^2*z - 16*b^4*c^3*z - 4*a^2*b*d*e^2*f + 4*a^2*b*c*e*f^2 + 4*a*b^2*c^2*d*f - 4*a*b^2*c*d^2*e + 2*a^2*b*d^2*f^2 + 2*a*b^2*c^2*e^2 + a^2*b*e^4 + a*b^2*d^4 + a^3*f^4 + b^3*c^4, z, k), k, 1, 4) + (e*x^2)/(2*b) + (f*x^3)/(3*b) + (d*x)/b","B"
489,1,478,318,0.359702,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^2,x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(65536\,a^7\,b^3\,z^4+3072\,a^4\,b^2\,c\,e\,z^2+2048\,a^4\,b^2\,d^2\,z^2-1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4+81\,b^2\,c^4+a^2\,e^4,z,k\right)\,\left(\mathrm{root}\left(65536\,a^7\,b^3\,z^4+3072\,a^4\,b^2\,c\,e\,z^2+2048\,a^4\,b^2\,d^2\,z^2-1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4+81\,b^2\,c^4+a^2\,e^4,z,k\right)\,\left(12\,b^3\,c-8\,b^3\,d\,x\right)+\frac{x\,\left(36\,a\,b^3\,c^2-4\,a^2\,b^2\,e^2\right)}{16\,a^3}+\frac{b^2\,d\,e}{a}\right)-\frac{9\,b^2\,c^2\,e-12\,b^2\,c\,d^2+a\,b\,e^3}{64\,a^3}+\frac{x\,\left(2\,b^2\,d^3-3\,b^2\,c\,d\,e\right)}{16\,a^3}\right)\,\mathrm{root}\left(65536\,a^7\,b^3\,z^4+3072\,a^4\,b^2\,c\,e\,z^2+2048\,a^4\,b^2\,d^2\,z^2-1152\,a^2\,b^2\,c^2\,d\,z+128\,a^3\,b\,d\,e^2\,z-48\,a\,b\,c\,d^2\,e+18\,a\,b\,c^2\,e^2+16\,a\,b\,d^4+81\,b^2\,c^4+a^2\,e^4,z,k\right)\right)+\frac{\frac{d\,x^2}{4\,a}-\frac{f}{4\,b}+\frac{e\,x^3}{4\,a}+\frac{c\,x}{4\,a}}{b\,x^4+a}","Not used",1,"symsum(log((x*(2*b^2*d^3 - 3*b^2*c*d*e))/(16*a^3) - (9*b^2*c^2*e - 12*b^2*c*d^2 + a*b*e^3)/(64*a^3) - root(65536*a^7*b^3*z^4 + 3072*a^4*b^2*c*e*z^2 + 2048*a^4*b^2*d^2*z^2 - 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 + 81*b^2*c^4 + a^2*e^4, z, k)*(root(65536*a^7*b^3*z^4 + 3072*a^4*b^2*c*e*z^2 + 2048*a^4*b^2*d^2*z^2 - 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 + 81*b^2*c^4 + a^2*e^4, z, k)*(12*b^3*c - 8*b^3*d*x) + (x*(36*a*b^3*c^2 - 4*a^2*b^2*e^2))/(16*a^3) + (b^2*d*e)/a))*root(65536*a^7*b^3*z^4 + 3072*a^4*b^2*c*e*z^2 + 2048*a^4*b^2*d^2*z^2 - 1152*a^2*b^2*c^2*d*z + 128*a^3*b*d*e^2*z - 48*a*b*c*d^2*e + 18*a*b*c^2*e^2 + 16*a*b*d^4 + 81*b^2*c^4 + a^2*e^4, z, k), k, 1, 4) + ((d*x^2)/(4*a) - f/(4*b) + (e*x^3)/(4*a) + (c*x)/(4*a))/(a + b*x^4)","B"
490,1,559,310,5.096851,"\text{Not used}","int((x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^2,x)","\left(\sum _{k=1}^4\ln\left(\frac{x\,\left(2\,e^3-3\,d\,e\,f\right)}{16\,b}-\frac{3\,b\,d^2\,f-4\,b\,d\,e^2+27\,a\,f^3}{64\,b^2}-\mathrm{root}\left(65536\,a^3\,b^7\,z^4+3072\,a^2\,b^4\,d\,f\,z^2+2048\,a^2\,b^4\,e^2\,z^2+1152\,a^2\,b^2\,e\,f^2\,z-128\,a\,b^3\,d^2\,e\,z-48\,a\,b\,d\,e^2\,f+18\,a\,b\,d^2\,f^2+16\,a\,b\,e^4+81\,a^2\,f^4+b^2\,d^4,z,k\right)\,\left(3\,a\,e\,f+\frac{b\,d^2\,x}{4}-\frac{9\,a\,f^2\,x}{4}+\mathrm{root}\left(65536\,a^3\,b^7\,z^4+3072\,a^2\,b^4\,d\,f\,z^2+2048\,a^2\,b^4\,e^2\,z^2+1152\,a^2\,b^2\,e\,f^2\,z-128\,a\,b^3\,d^2\,e\,z-48\,a\,b\,d\,e^2\,f+18\,a\,b\,d^2\,f^2+16\,a\,b\,e^4+81\,a^2\,f^4+b^2\,d^4,z,k\right)\,a\,b^2\,d\,4-\mathrm{root}\left(65536\,a^3\,b^7\,z^4+3072\,a^2\,b^4\,d\,f\,z^2+2048\,a^2\,b^4\,e^2\,z^2+1152\,a^2\,b^2\,e\,f^2\,z-128\,a\,b^3\,d^2\,e\,z-48\,a\,b\,d\,e^2\,f+18\,a\,b\,d^2\,f^2+16\,a\,b\,e^4+81\,a^2\,f^4+b^2\,d^4,z,k\right)\,a\,b^2\,e\,x\,8\right)\right)\,\mathrm{root}\left(65536\,a^3\,b^7\,z^4+3072\,a^2\,b^4\,d\,f\,z^2+2048\,a^2\,b^4\,e^2\,z^2+1152\,a^2\,b^2\,e\,f^2\,z-128\,a\,b^3\,d^2\,e\,z-48\,a\,b\,d\,e^2\,f+18\,a\,b\,d^2\,f^2+16\,a\,b\,e^4+81\,a^2\,f^4+b^2\,d^4,z,k\right)\right)-\frac{\frac{c}{4\,b}+\frac{e\,x^2}{4\,b}+\frac{f\,x^3}{4\,b}+\frac{d\,x}{4\,b}}{b\,x^4+a}","Not used",1,"symsum(log((x*(2*e^3 - 3*d*e*f))/(16*b) - (27*a*f^3 - 4*b*d*e^2 + 3*b*d^2*f)/(64*b^2) - root(65536*a^3*b^7*z^4 + 3072*a^2*b^4*d*f*z^2 + 2048*a^2*b^4*e^2*z^2 + 1152*a^2*b^2*e*f^2*z - 128*a*b^3*d^2*e*z - 48*a*b*d*e^2*f + 18*a*b*d^2*f^2 + 16*a*b*e^4 + 81*a^2*f^4 + b^2*d^4, z, k)*(3*a*e*f + (b*d^2*x)/4 - (9*a*f^2*x)/4 + 4*root(65536*a^3*b^7*z^4 + 3072*a^2*b^4*d*f*z^2 + 2048*a^2*b^4*e^2*z^2 + 1152*a^2*b^2*e*f^2*z - 128*a*b^3*d^2*e*z - 48*a*b*d*e^2*f + 18*a*b*d^2*f^2 + 16*a*b*e^4 + 81*a^2*f^4 + b^2*d^4, z, k)*a*b^2*d - 8*root(65536*a^3*b^7*z^4 + 3072*a^2*b^4*d*f*z^2 + 2048*a^2*b^4*e^2*z^2 + 1152*a^2*b^2*e*f^2*z - 128*a*b^3*d^2*e*z - 48*a*b*d*e^2*f + 18*a*b*d^2*f^2 + 16*a*b*e^4 + 81*a^2*f^4 + b^2*d^4, z, k)*a*b^2*e*x))*root(65536*a^3*b^7*z^4 + 3072*a^2*b^4*d*f*z^2 + 2048*a^2*b^4*e^2*z^2 + 1152*a^2*b^2*e*f^2*z - 128*a*b^3*d^2*e*z - 48*a*b*d*e^2*f + 18*a*b*d^2*f^2 + 16*a*b*e^4 + 81*a^2*f^4 + b^2*d^4, z, k), k, 1, 4) - (c/(4*b) + (e*x^2)/(4*b) + (f*x^3)/(4*b) + (d*x)/(4*b))/(a + b*x^4)","B"
491,1,832,351,5.199136,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^3,x)","\left(\sum _{k=1}^4\ln\left(-\frac{b\,\left(125\,a\,e^3-3024\,b\,c\,d^2+2205\,b\,c^2\,e-1728\,b\,d^3\,x+{\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)}^2\,a^5\,b^2\,c\,344064-\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)\,a^3\,b\,e^2\,x\,3200+2520\,b\,c\,d\,e\,x+\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)\,a^2\,b^2\,c^2\,x\,56448-{\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)}^2\,a^5\,b^2\,d\,x\,196608+\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)\,a^3\,b\,d\,e\,15360\right)}{a^6\,32768}\right)\,\mathrm{root}\left(268435456\,a^{11}\,b^3\,z^4+6881280\,a^6\,b^2\,c\,e\,z^2+4718592\,a^6\,b^2\,d^2\,z^2-2709504\,a^3\,b^2\,c^2\,d\,z+153600\,a^4\,b\,d\,e^2\,z-60480\,a\,b\,c\,d^2\,e+22050\,a\,b\,c^2\,e^2+20736\,a\,b\,d^4+625\,a^2\,e^4+194481\,b^2\,c^4,z,k\right)\right)+\frac{\frac{5\,d\,x^2}{16\,a}-\frac{f}{8\,b}+\frac{9\,e\,x^3}{32\,a}+\frac{11\,c\,x}{32\,a}+\frac{7\,b\,c\,x^5}{32\,a^2}+\frac{3\,b\,d\,x^6}{16\,a^2}+\frac{5\,b\,e\,x^7}{32\,a^2}}{a^2+2\,a\,b\,x^4+b^2\,x^8}","Not used",1,"symsum(log(-(b*(125*a*e^3 - 3024*b*c*d^2 + 2205*b*c^2*e - 1728*b*d^3*x + 344064*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)^2*a^5*b^2*c - 3200*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)*a^3*b*e^2*x + 2520*b*c*d*e*x + 56448*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)*a^2*b^2*c^2*x - 196608*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)^2*a^5*b^2*d*x + 15360*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k)*a^3*b*d*e))/(32768*a^6))*root(268435456*a^11*b^3*z^4 + 6881280*a^6*b^2*c*e*z^2 + 4718592*a^6*b^2*d^2*z^2 - 2709504*a^3*b^2*c^2*d*z + 153600*a^4*b*d*e^2*z - 60480*a*b*c*d^2*e + 22050*a*b*c^2*e^2 + 20736*a*b*d^4 + 625*a^2*e^4 + 194481*b^2*c^4, z, k), k, 1, 4) + ((5*d*x^2)/(16*a) - f/(8*b) + (9*e*x^3)/(32*a) + (11*c*x)/(32*a) + (7*b*c*x^5)/(32*a^2) + (3*b*d*x^6)/(16*a^2) + (5*b*e*x^7)/(32*a^2))/(a^2 + b^2*x^8 + 2*a*b*x^4)","B"
492,1,521,340,0.396409,"\text{Not used}","int((x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^3,x)","\left(\sum _{k=1}^4\ln\left(-\mathrm{root}\left(268435456\,a^7\,b^7\,z^4+589824\,a^4\,b^4\,d\,f\,z^2+524288\,a^4\,b^4\,e^2\,z^2+18432\,a^3\,b^2\,e\,f^2\,z-18432\,a^2\,b^3\,d^2\,e\,z-576\,a\,b\,d\,e^2\,f+162\,a\,b\,d^2\,f^2+256\,a\,b\,e^4+81\,a^2\,f^4+81\,b^2\,d^4,z,k\right)\,\left(\mathrm{root}\left(268435456\,a^7\,b^7\,z^4+589824\,a^4\,b^4\,d\,f\,z^2+524288\,a^4\,b^4\,e^2\,z^2+18432\,a^3\,b^2\,e\,f^2\,z-18432\,a^2\,b^3\,d^2\,e\,z-576\,a\,b\,d\,e^2\,f+162\,a\,b\,d^2\,f^2+256\,a\,b\,e^4+81\,a^2\,f^4+81\,b^2\,d^4,z,k\right)\,\left(\frac{3\,b^2\,d}{2}-2\,b^2\,e\,x\right)+\frac{3\,e\,f}{32\,a}+\frac{x\,\left(144\,a\,b^2\,d^2-144\,a^2\,b\,f^2\right)}{4096\,a^3\,b}\right)-\frac{3\,\left(9\,b\,d^2\,f-16\,b\,d\,e^2+9\,a\,f^3\right)}{32768\,a^3\,b^2}+\frac{x\,\left(8\,e^3-9\,d\,e\,f\right)}{4096\,a^3\,b}\right)\,\mathrm{root}\left(268435456\,a^7\,b^7\,z^4+589824\,a^4\,b^4\,d\,f\,z^2+524288\,a^4\,b^4\,e^2\,z^2+18432\,a^3\,b^2\,e\,f^2\,z-18432\,a^2\,b^3\,d^2\,e\,z-576\,a\,b\,d\,e^2\,f+162\,a\,b\,d^2\,f^2+256\,a\,b\,e^4+81\,a^2\,f^4+81\,b^2\,d^4,z,k\right)\right)-\frac{\frac{c}{8\,b}-\frac{d\,x^5}{32\,a}-\frac{e\,x^6}{16\,a}+\frac{e\,x^2}{16\,b}-\frac{3\,f\,x^7}{32\,a}+\frac{f\,x^3}{32\,b}+\frac{3\,d\,x}{32\,b}}{a^2+2\,a\,b\,x^4+b^2\,x^8}","Not used",1,"symsum(log((x*(8*e^3 - 9*d*e*f))/(4096*a^3*b) - (3*(9*a*f^3 - 16*b*d*e^2 + 9*b*d^2*f))/(32768*a^3*b^2) - root(268435456*a^7*b^7*z^4 + 589824*a^4*b^4*d*f*z^2 + 524288*a^4*b^4*e^2*z^2 + 18432*a^3*b^2*e*f^2*z - 18432*a^2*b^3*d^2*e*z - 576*a*b*d*e^2*f + 162*a*b*d^2*f^2 + 256*a*b*e^4 + 81*a^2*f^4 + 81*b^2*d^4, z, k)*(root(268435456*a^7*b^7*z^4 + 589824*a^4*b^4*d*f*z^2 + 524288*a^4*b^4*e^2*z^2 + 18432*a^3*b^2*e*f^2*z - 18432*a^2*b^3*d^2*e*z - 576*a*b*d*e^2*f + 162*a*b*d^2*f^2 + 256*a*b*e^4 + 81*a^2*f^4 + 81*b^2*d^4, z, k)*((3*b^2*d)/2 - 2*b^2*e*x) + (3*e*f)/(32*a) + (x*(144*a*b^2*d^2 - 144*a^2*b*f^2))/(4096*a^3*b)))*root(268435456*a^7*b^7*z^4 + 589824*a^4*b^4*d*f*z^2 + 524288*a^4*b^4*e^2*z^2 + 18432*a^3*b^2*e*f^2*z - 18432*a^2*b^3*d^2*e*z - 576*a*b*d*e^2*f + 162*a*b*d^2*f^2 + 256*a*b*e^4 + 81*a^2*f^4 + 81*b^2*d^4, z, k), k, 1, 4) - (c/(8*b) - (d*x^5)/(32*a) - (e*x^6)/(16*a) + (e*x^2)/(16*b) - (3*f*x^7)/(32*a) + (f*x^3)/(32*b) + (3*d*x)/(32*b))/(a^2 + b^2*x^8 + 2*a*b*x^4)","B"
493,1,879,382,5.254841,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^4,x)","\left(\sum _{k=1}^4\ln\left(-\frac{b\,\left(3375\,a\,e^3-123200\,b\,c\,d^2+88935\,b\,c^2\,e-64000\,b\,d^3\,x+{\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)}^2\,a^7\,b^2\,c\,20185088-\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)\,a^4\,b\,e^2\,x\,115200+92400\,b\,c\,d\,e\,x+\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)\,a^3\,b^2\,c^2\,x\,3035648-{\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)}^2\,a^7\,b^2\,d\,x\,10485760+\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)\,a^4\,b\,d\,e\,614400\right)}{a^9\,2097152}\right)\,\mathrm{root}\left(68719476736\,a^{15}\,b^3\,z^4+1211105280\,a^8\,b^2\,c\,e\,z^2+838860800\,a^8\,b^2\,d^2\,z^2-485703680\,a^4\,b^2\,c^2\,d\,z+18432000\,a^5\,b\,d\,e^2\,z-7392000\,a\,b\,c\,d^2\,e+2668050\,a\,b\,c^2\,e^2+2560000\,a\,b\,d^4+35153041\,b^2\,c^4+50625\,a^2\,e^4,z,k\right)\right)+\frac{\frac{11\,d\,x^2}{32\,a}-\frac{f}{12\,b}+\frac{113\,e\,x^3}{384\,a}+\frac{51\,c\,x}{128\,a}+\frac{77\,b^2\,c\,x^9}{384\,a^3}+\frac{5\,b^2\,d\,x^{10}}{32\,a^3}+\frac{15\,b^2\,e\,x^{11}}{128\,a^3}+\frac{33\,b\,c\,x^5}{64\,a^2}+\frac{5\,b\,d\,x^6}{12\,a^2}+\frac{21\,b\,e\,x^7}{64\,a^2}}{a^3+3\,a^2\,b\,x^4+3\,a\,b^2\,x^8+b^3\,x^{12}}","Not used",1,"symsum(log(-(b*(3375*a*e^3 - 123200*b*c*d^2 + 88935*b*c^2*e - 64000*b*d^3*x + 20185088*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)^2*a^7*b^2*c - 115200*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)*a^4*b*e^2*x + 92400*b*c*d*e*x + 3035648*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)*a^3*b^2*c^2*x - 10485760*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)^2*a^7*b^2*d*x + 614400*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k)*a^4*b*d*e))/(2097152*a^9))*root(68719476736*a^15*b^3*z^4 + 1211105280*a^8*b^2*c*e*z^2 + 838860800*a^8*b^2*d^2*z^2 - 485703680*a^4*b^2*c^2*d*z + 18432000*a^5*b*d*e^2*z - 7392000*a*b*c*d^2*e + 2668050*a*b*c^2*e^2 + 2560000*a*b*d^4 + 35153041*b^2*c^4 + 50625*a^2*e^4, z, k), k, 1, 4) + ((11*d*x^2)/(32*a) - f/(12*b) + (113*e*x^3)/(384*a) + (51*c*x)/(128*a) + (77*b^2*c*x^9)/(384*a^3) + (5*b^2*d*x^10)/(32*a^3) + (15*b^2*e*x^11)/(128*a^3) + (33*b*c*x^5)/(64*a^2) + (5*b*d*x^6)/(12*a^2) + (21*b*e*x^7)/(64*a^2))/(a^3 + b^3*x^12 + 3*a^2*b*x^4 + 3*a*b^2*x^8)","B"
494,1,888,380,0.482152,"\text{Not used}","int((x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^4,x)","\frac{\frac{3\,d\,x^5}{64\,a}-\frac{c}{12\,b}+\frac{e\,x^6}{12\,a}-\frac{e\,x^2}{32\,b}+\frac{7\,f\,x^7}{64\,a}-\frac{5\,f\,x^3}{384\,b}-\frac{7\,d\,x}{128\,b}+\frac{7\,b\,d\,x^9}{384\,a^2}+\frac{b\,e\,x^{10}}{32\,a^2}+\frac{5\,b\,f\,x^{11}}{128\,a^2}}{a^3+3\,a^2\,b\,x^4+3\,a\,b^2\,x^8+b^3\,x^{12}}+\left(\sum _{k=1}^4\ln\left(-\frac{125\,a\,f^3-448\,b\,d\,e^2+245\,b\,d^2\,f-512\,b\,e^3\,x+{\mathrm{root}\left(68719476736\,a^{11}\,b^7\,z^4+36700160\,a^6\,b^4\,d\,f\,z^2+33554432\,a^6\,b^4\,e^2\,z^2+409600\,a^4\,b^2\,e\,f^2\,z-802816\,a^3\,b^3\,d^2\,e\,z-8960\,a\,b\,d\,e^2\,f+2450\,a\,b\,d^2\,f^2+4096\,a\,b\,e^4+625\,a^2\,f^4+2401\,b^2\,d^4,z,k\right)}^2\,a^5\,b^4\,d\,1835008+560\,b\,d\,e\,f\,x+\mathrm{root}\left(68719476736\,a^{11}\,b^7\,z^4+36700160\,a^6\,b^4\,d\,f\,z^2+33554432\,a^6\,b^4\,e^2\,z^2+409600\,a^4\,b^2\,e\,f^2\,z-802816\,a^3\,b^3\,d^2\,e\,z-8960\,a\,b\,d\,e^2\,f+2450\,a\,b\,d^2\,f^2+4096\,a\,b\,e^4+625\,a^2\,f^4+2401\,b^2\,d^4,z,k\right)\,a^2\,b^3\,d^2\,x\,25088-{\mathrm{root}\left(68719476736\,a^{11}\,b^7\,z^4+36700160\,a^6\,b^4\,d\,f\,z^2+33554432\,a^6\,b^4\,e^2\,z^2+409600\,a^4\,b^2\,e\,f^2\,z-802816\,a^3\,b^3\,d^2\,e\,z-8960\,a\,b\,d\,e^2\,f+2450\,a\,b\,d^2\,f^2+4096\,a\,b\,e^4+625\,a^2\,f^4+2401\,b^2\,d^4,z,k\right)}^2\,a^5\,b^4\,e\,x\,2097152-\mathrm{root}\left(68719476736\,a^{11}\,b^7\,z^4+36700160\,a^6\,b^4\,d\,f\,z^2+33554432\,a^6\,b^4\,e^2\,z^2+409600\,a^4\,b^2\,e\,f^2\,z-802816\,a^3\,b^3\,d^2\,e\,z-8960\,a\,b\,d\,e^2\,f+2450\,a\,b\,d^2\,f^2+4096\,a\,b\,e^4+625\,a^2\,f^4+2401\,b^2\,d^4,z,k\right)\,a^3\,b^2\,f^2\,x\,12800+\mathrm{root}\left(68719476736\,a^{11}\,b^7\,z^4+36700160\,a^6\,b^4\,d\,f\,z^2+33554432\,a^6\,b^4\,e^2\,z^2+409600\,a^4\,b^2\,e\,f^2\,z-802816\,a^3\,b^3\,d^2\,e\,z-8960\,a\,b\,d\,e^2\,f+2450\,a\,b\,d^2\,f^2+4096\,a\,b\,e^4+625\,a^2\,f^4+2401\,b^2\,d^4,z,k\right)\,a^3\,b^2\,e\,f\,40960}{a^6\,b^2\,2097152}\right)\,\mathrm{root}\left(68719476736\,a^{11}\,b^7\,z^4+36700160\,a^6\,b^4\,d\,f\,z^2+33554432\,a^6\,b^4\,e^2\,z^2+409600\,a^4\,b^2\,e\,f^2\,z-802816\,a^3\,b^3\,d^2\,e\,z-8960\,a\,b\,d\,e^2\,f+2450\,a\,b\,d^2\,f^2+4096\,a\,b\,e^4+625\,a^2\,f^4+2401\,b^2\,d^4,z,k\right)\right)","Not used",1,"((3*d*x^5)/(64*a) - c/(12*b) + (e*x^6)/(12*a) - (e*x^2)/(32*b) + (7*f*x^7)/(64*a) - (5*f*x^3)/(384*b) - (7*d*x)/(128*b) + (7*b*d*x^9)/(384*a^2) + (b*e*x^10)/(32*a^2) + (5*b*f*x^11)/(128*a^2))/(a^3 + b^3*x^12 + 3*a^2*b*x^4 + 3*a*b^2*x^8) + symsum(log(-(125*a*f^3 - 448*b*d*e^2 + 245*b*d^2*f - 512*b*e^3*x + 1835008*root(68719476736*a^11*b^7*z^4 + 36700160*a^6*b^4*d*f*z^2 + 33554432*a^6*b^4*e^2*z^2 + 409600*a^4*b^2*e*f^2*z - 802816*a^3*b^3*d^2*e*z - 8960*a*b*d*e^2*f + 2450*a*b*d^2*f^2 + 4096*a*b*e^4 + 625*a^2*f^4 + 2401*b^2*d^4, z, k)^2*a^5*b^4*d + 560*b*d*e*f*x + 25088*root(68719476736*a^11*b^7*z^4 + 36700160*a^6*b^4*d*f*z^2 + 33554432*a^6*b^4*e^2*z^2 + 409600*a^4*b^2*e*f^2*z - 802816*a^3*b^3*d^2*e*z - 8960*a*b*d*e^2*f + 2450*a*b*d^2*f^2 + 4096*a*b*e^4 + 625*a^2*f^4 + 2401*b^2*d^4, z, k)*a^2*b^3*d^2*x - 2097152*root(68719476736*a^11*b^7*z^4 + 36700160*a^6*b^4*d*f*z^2 + 33554432*a^6*b^4*e^2*z^2 + 409600*a^4*b^2*e*f^2*z - 802816*a^3*b^3*d^2*e*z - 8960*a*b*d*e^2*f + 2450*a*b*d^2*f^2 + 4096*a*b*e^4 + 625*a^2*f^4 + 2401*b^2*d^4, z, k)^2*a^5*b^4*e*x - 12800*root(68719476736*a^11*b^7*z^4 + 36700160*a^6*b^4*d*f*z^2 + 33554432*a^6*b^4*e^2*z^2 + 409600*a^4*b^2*e*f^2*z - 802816*a^3*b^3*d^2*e*z - 8960*a*b*d*e^2*f + 2450*a*b*d^2*f^2 + 4096*a*b*e^4 + 625*a^2*f^4 + 2401*b^2*d^4, z, k)*a^3*b^2*f^2*x + 40960*root(68719476736*a^11*b^7*z^4 + 36700160*a^6*b^4*d*f*z^2 + 33554432*a^6*b^4*e^2*z^2 + 409600*a^4*b^2*e*f^2*z - 802816*a^3*b^3*d^2*e*z - 8960*a*b*d*e^2*f + 2450*a*b*d^2*f^2 + 4096*a*b*e^4 + 625*a^2*f^4 + 2401*b^2*d^4, z, k)*a^3*b^2*e*f)/(2097152*a^6*b^2))*root(68719476736*a^11*b^7*z^4 + 36700160*a^6*b^4*d*f*z^2 + 33554432*a^6*b^4*e^2*z^2 + 409600*a^4*b^2*e*f^2*z - 802816*a^3*b^3*d^2*e*z - 8960*a*b*d*e^2*f + 2450*a*b*d^2*f^2 + 4096*a*b*e^4 + 625*a^2*f^4 + 2401*b^2*d^4, z, k), k, 1, 4)","B"
495,0,-1,418,0.000000,"\text{Not used}","int(x^4*(a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3),x)","\int x^4\,\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^4*(a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
496,0,-1,394,0.000000,"\text{Not used}","int(x^3*(a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3),x)","\int x^3\,\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^3*(a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
497,0,-1,369,0.000000,"\text{Not used}","int(x^2*(a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3),x)","\int x^2\,\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^2*(a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
498,0,-1,354,0.000000,"\text{Not used}","int(x*(a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3),x)","\int x\,\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x*(a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
499,0,-1,331,0.000000,"\text{Not used}","int((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3),x)","\int \sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
500,0,-1,345,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x, x)","F"
501,0,-1,341,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^2,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^2} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^2, x)","F"
502,0,-1,342,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^3,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^3} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^3, x)","F"
503,0,-1,357,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^4,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^4} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^4, x)","F"
504,0,-1,329,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^5,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^5} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^5, x)","F"
505,0,-1,360,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^6,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^6} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^6, x)","F"
506,0,-1,352,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^7,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^7} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^7, x)","F"
507,0,-1,375,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^8,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^8} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^8, x)","F"
508,0,-1,400,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^9,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^9} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^9, x)","F"
509,0,-1,425,0.000000,"\text{Not used}","int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^10,x)","\int \frac{\sqrt{b\,x^4+a}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^{10}} \,d x","Not used",1,"int(((a + b*x^4)^(1/2)*(c + d*x + e*x^2 + f*x^3))/x^10, x)","F"
510,0,-1,476,0.000000,"\text{Not used}","int(x^4*(a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3),x)","\int x^4\,{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^4*(a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
511,0,-1,452,0.000000,"\text{Not used}","int(x^3*(a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3),x)","\int x^3\,{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^3*(a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
512,0,-1,427,0.000000,"\text{Not used}","int(x^2*(a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3),x)","\int x^2\,{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^2*(a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
513,0,-1,409,0.000000,"\text{Not used}","int(x*(a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3),x)","\int x\,{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x*(a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
514,0,-1,382,0.000000,"\text{Not used}","int((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3),x)","\int {\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3), x)","F"
515,0,-1,403,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x, x)","F"
516,0,-1,404,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^2,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^2} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^2, x)","F"
517,0,-1,406,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^3,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^3} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^3, x)","F"
518,0,-1,408,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^4,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^4} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^4, x)","F"
519,0,-1,386,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^5,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^5} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^5, x)","F"
520,0,-1,387,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^6,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^6} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^6, x)","F"
521,0,-1,392,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^7,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^7} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^7, x)","F"
522,0,-1,412,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^8,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^8} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^8, x)","F"
523,0,-1,377,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^9,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^9} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^9, x)","F"
524,0,-1,405,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^10,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^{10}} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^10, x)","F"
525,0,-1,399,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^11,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^{11}} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^11, x)","F"
526,0,-1,424,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^12,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^{12}} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^12, x)","F"
527,0,-1,449,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^13,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^{13}} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^13, x)","F"
528,0,-1,474,0.000000,"\text{Not used}","int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^14,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{x^{14}} \,d x","Not used",1,"int(((a + b*x^4)^(3/2)*(c + d*x + e*x^2 + f*x^3))/x^14, x)","F"
529,0,-1,361,0.000000,"\text{Not used}","int((x^4*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(1/2),x)","\int \frac{x^4\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((x^4*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(1/2), x)","F"
530,0,-1,336,0.000000,"\text{Not used}","int((x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(1/2),x)","\int \frac{x^3\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(1/2), x)","F"
531,0,-1,308,0.000000,"\text{Not used}","int((x^2*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(1/2),x)","\int \frac{x^2\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((x^2*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(1/2), x)","F"
532,0,-1,299,0.000000,"\text{Not used}","int((x*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(1/2),x)","\int \frac{x\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((x*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(1/2), x)","F"
533,0,-1,276,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^(1/2),x)","\int \frac{f\,x^3+e\,x^2+d\,x+c}{\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^(1/2), x)","F"
534,0,-1,285,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x*(a + b*x^4)^(1/2)),x)","\int \frac{f\,x^3+e\,x^2+d\,x+c}{x\,\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3)/(x*(a + b*x^4)^(1/2)), x)","F"
535,0,-1,309,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x^2*(a + b*x^4)^(1/2)),x)","\int \frac{f\,x^3+e\,x^2+d\,x+c}{x^2\,\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3)/(x^2*(a + b*x^4)^(1/2)), x)","F"
536,1,118,300,5.848833,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x^3*(a + b*x^4)^(1/2)),x)","\frac{f\,x\,\sqrt{\frac{b\,x^4}{a}+1}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{4},\frac{1}{2};\ \frac{5}{4};\ -\frac{b\,x^4}{a}\right)}{\sqrt{b\,x^4+a}}-\frac{c\,\sqrt{b\,x^4+a}}{2\,a\,x^2}-\frac{d\,\sqrt{\frac{a}{b\,x^4}+1}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{3}{4};\ \frac{7}{4};\ -\frac{a}{b\,x^4}\right)}{3\,x\,\sqrt{b\,x^4+a}}-\frac{e\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^4+a}}{\sqrt{a}}\right)}{2\,\sqrt{a}}","Not used",1,"(f*x*((b*x^4)/a + 1)^(1/2)*hypergeom([1/4, 1/2], 5/4, -(b*x^4)/a))/(a + b*x^4)^(1/2) - (c*(a + b*x^4)^(1/2))/(2*a*x^2) - (d*(a/(b*x^4) + 1)^(1/2)*hypergeom([1/2, 3/4], 7/4, -a/(b*x^4)))/(3*x*(a + b*x^4)^(1/2)) - (e*atanh((a + b*x^4)^(1/2)/a^(1/2)))/(2*a^(1/2))","B"
537,0,-1,323,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x^4*(a + b*x^4)^(1/2)),x)","\int \frac{f\,x^3+e\,x^2+d\,x+c}{x^4\,\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3)/(x^4*(a + b*x^4)^(1/2)), x)","F"
538,0,-1,346,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x^5*(a + b*x^4)^(1/2)),x)","\int \frac{f\,x^3+e\,x^2+d\,x+c}{x^5\,\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3)/(x^5*(a + b*x^4)^(1/2)), x)","F"
539,0,-1,377,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x^6*(a + b*x^4)^(1/2)),x)","\int \frac{f\,x^3+e\,x^2+d\,x+c}{x^6\,\sqrt{b\,x^4+a}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3)/(x^6*(a + b*x^4)^(1/2)), x)","F"
540,0,-1,365,0.000000,"\text{Not used}","int((x^6*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x)","\int \frac{x^6\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{{\left(b\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((x^6*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x)","F"
541,0,-1,343,0.000000,"\text{Not used}","int((x^5*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x)","\int \frac{x^5\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{{\left(b\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((x^5*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x)","F"
542,0,-1,314,0.000000,"\text{Not used}","int((x^4*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x)","\int \frac{x^4\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{{\left(b\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((x^4*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x)","F"
543,0,-1,302,0.000000,"\text{Not used}","int((x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x)","\int \frac{x^3\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{{\left(b\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x)","F"
544,0,-1,333,0.000000,"\text{Not used}","int((x^2*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x)","\int \frac{x^2\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{{\left(b\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((x^2*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x)","F"
545,0,-1,303,0.000000,"\text{Not used}","int((x*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2),x)","\int \frac{x\,\left(f\,x^3+e\,x^2+d\,x+c\right)}{{\left(b\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((x*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x)","F"
546,0,-1,275,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^(3/2),x)","\int \frac{f\,x^3+e\,x^2+d\,x+c}{{\left(b\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^(3/2), x)","F"
547,0,-1,323,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x*(a + b*x^4)^(3/2)),x)","\int \frac{f\,x^3+e\,x^2+d\,x+c}{x\,{\left(b\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3)/(x*(a + b*x^4)^(3/2)), x)","F"
548,1,133,344,5.944676,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x^2*(a + b*x^4)^(3/2)),x)","\frac{d}{2\,a\,\sqrt{b\,x^4+a}}-\frac{d\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^4+a}}{\sqrt{a}}\right)}{2\,a^{3/2}}+\frac{f\,x^2}{2\,a\,\sqrt{b\,x^4+a}}-\frac{c\,{\left(\frac{a}{b\,x^4}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{3}{2},\frac{7}{4};\ \frac{11}{4};\ -\frac{a}{b\,x^4}\right)}{7\,x\,{\left(b\,x^4+a\right)}^{3/2}}+\frac{e\,x\,{\left(\frac{b\,x^4}{a}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{4},\frac{3}{2};\ \frac{5}{4};\ -\frac{b\,x^4}{a}\right)}{{\left(b\,x^4+a\right)}^{3/2}}","Not used",1,"d/(2*a*(a + b*x^4)^(1/2)) - (d*atanh((a + b*x^4)^(1/2)/a^(1/2)))/(2*a^(3/2)) + (f*x^2)/(2*a*(a + b*x^4)^(1/2)) - (c*(a/(b*x^4) + 1)^(3/2)*hypergeom([3/2, 7/4], 11/4, -a/(b*x^4)))/(7*x*(a + b*x^4)^(3/2)) + (e*x*((b*x^4)/a + 1)^(3/2)*hypergeom([1/4, 3/2], 5/4, -(b*x^4)/a))/(a + b*x^4)^(3/2)","B"
549,1,147,367,6.075967,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x^3*(a + b*x^4)^(3/2)),x)","\frac{e}{2\,a\,\sqrt{b\,x^4+a}}-\frac{e\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^4+a}}{\sqrt{a}}\right)}{2\,a^{3/2}}-\frac{2\,c\,\left(b\,x^4+a\right)-a\,c}{2\,a^2\,x^2\,\sqrt{b\,x^4+a}}-\frac{d\,{\left(\frac{a}{b\,x^4}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{3}{2},\frac{7}{4};\ \frac{11}{4};\ -\frac{a}{b\,x^4}\right)}{7\,x\,{\left(b\,x^4+a\right)}^{3/2}}+\frac{f\,x\,{\left(\frac{b\,x^4}{a}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{4},\frac{3}{2};\ \frac{5}{4};\ -\frac{b\,x^4}{a}\right)}{{\left(b\,x^4+a\right)}^{3/2}}","Not used",1,"e/(2*a*(a + b*x^4)^(1/2)) - (e*atanh((a + b*x^4)^(1/2)/a^(1/2)))/(2*a^(3/2)) - (2*c*(a + b*x^4) - a*c)/(2*a^2*x^2*(a + b*x^4)^(1/2)) - (d*(a/(b*x^4) + 1)^(3/2)*hypergeom([3/2, 7/4], 11/4, -a/(b*x^4)))/(7*x*(a + b*x^4)^(3/2)) + (f*x*((b*x^4)/a + 1)^(3/2)*hypergeom([1/4, 3/2], 5/4, -(b*x^4)/a))/(a + b*x^4)^(3/2)","B"
550,0,-1,387,0.000000,"\text{Not used}","int((c + d*x + e*x^2 + f*x^3)/(x^4*(a + b*x^4)^(3/2)),x)","\int \frac{f\,x^3+e\,x^2+d\,x+c}{x^4\,{\left(b\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x + e*x^2 + f*x^3)/(x^4*(a + b*x^4)^(3/2)), x)","F"
551,0,-1,269,0.000000,"\text{Not used}","int((g*x)^m*(a + b*x^4)^p*(c + d*x + e*x^2 + f*x^3),x)","\int {\left(g\,x\right)}^m\,{\left(b\,x^4+a\right)}^p\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int((g*x)^m*(a + b*x^4)^p*(c + d*x + e*x^2 + f*x^3), x)","F"
552,0,-1,143,0.000000,"\text{Not used}","int((a + b*x^4)^p*(c + d*x + e*x^2 + f*x^3),x)","\int {\left(b\,x^4+a\right)}^p\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int((a + b*x^4)^p*(c + d*x + e*x^2 + f*x^3), x)","F"
553,0,-1,175,0.000000,"\text{Not used}","int(x^3*(a + b*x^4)^p*(c + d*x + e*x^2 + f*x^3),x)","\int x^3\,{\left(b\,x^4+a\right)}^p\,\left(f\,x^3+e\,x^2+d\,x+c\right) \,d x","Not used",1,"int(x^3*(a + b*x^4)^p*(c + d*x + e*x^2 + f*x^3), x)","F"
554,1,6,8,0.023203,"\text{Not used}","int(-(x + x^2 + x^3 + x^4 + 1)/(x^5 - 1),x)","-\ln\left(x-1\right)","Not used",1,"-log(x - 1)","B"
555,1,6,10,0.055827,"\text{Not used}","int((162*x - 108*x^2 + 72*x^3 - 48*x^4 + 32*x^5 - 243)/(64*x^6 - 729),x)","\frac{\ln\left(x+\frac{3}{2}\right)}{2}","Not used",1,"log(x + 3/2)/2","B"
556,1,6,10,4.992082,"\text{Not used}","int(-(162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5 + 243)/(64*x^6 - 729),x)","-\frac{\ln\left(x-\frac{3}{2}\right)}{2}","Not used",1,"-log(x - 3/2)/2","B"
557,1,6,10,0.097034,"\text{Not used}","int(-(36*x^2 + 16*x^4 + 81)/(64*x^6 - 729),x)","\frac{\mathrm{atanh}\left(\frac{2\,x}{3}\right)}{6}","Not used",1,"atanh((2*x)/3)/6","B"
558,1,16,24,0.030293,"\text{Not used}","int(-(54*x - 24*x^3 - 16*x^4 + 81)/(64*x^6 - 729),x)","\frac{\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}\,\left(4\,x-3\right)}{9}\right)}{9}","Not used",1,"(3^(1/2)*atan((3^(1/2)*(4*x - 3))/9))/9","B"
559,1,49,50,0.131105,"\text{Not used}","int((2*x - 3)/(64*x^6 - 729),x)","\frac{\ln\left(x+\frac{3}{2}\right)}{486}-\frac{\ln\left(x^2-\frac{3\,x}{2}+\frac{9}{4}\right)}{972}-\frac{\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}}{1327104\,\left(\frac{x}{884736}+\frac{1}{884736}\right)}-\frac{\sqrt{3}\,x}{7962624\,\left(\frac{x}{884736}+\frac{1}{884736}\right)}\right)}{486}","Not used",1,"log(x + 3/2)/486 - log(x^2 - (3*x)/2 + 9/4)/972 - (3^(1/2)*atan(3^(1/2)/(1327104*(x/884736 + 1/884736)) - (3^(1/2)*x)/(7962624*(x/884736 + 1/884736))))/486","B"
560,1,48,50,4.987413,"\text{Not used}","int(-(2*x + 3)/(64*x^6 - 729),x)","\frac{\ln\left(x^2+\frac{3\,x}{2}+\frac{9}{4}\right)}{972}-\frac{\ln\left(x-\frac{3}{2}\right)}{486}-\frac{\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}}{1327104\,\left(\frac{x}{884736}-\frac{1}{884736}\right)}+\frac{\sqrt{3}\,x}{7962624\,\left(\frac{x}{884736}-\frac{1}{884736}\right)}\right)}{486}","Not used",1,"log((3*x)/2 + x^2 + 9/4)/972 - log(x - 3/2)/486 - (3^(1/2)*atan(3^(1/2)/(1327104*(x/884736 - 1/884736)) + (3^(1/2)*x)/(7962624*(x/884736 - 1/884736))))/486","B"
561,1,52,60,5.009592,"\text{Not used}","int(-(4*x^2 - 6*x + 9)/(64*x^6 - 729),x)","\frac{\ln\left(x+\frac{3}{2}\right)}{108}-\frac{\ln\left(x-\frac{3}{2}\right)}{324}-\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{324}+\frac{\sqrt{3}\,1{}\mathrm{i}}{324}\right)+\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{324}+\frac{\sqrt{3}\,1{}\mathrm{i}}{324}\right)","Not used",1,"log(x + 3/2)/108 - log(x - 3/2)/324 - log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/324 + 1/324) + log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/324 - 1/324)","B"
562,1,52,60,4.975057,"\text{Not used}","int(-(6*x + 4*x^2 + 9)/(64*x^6 - 729),x)","\frac{\ln\left(x+\frac{3}{2}\right)}{324}-\frac{\ln\left(x-\frac{3}{2}\right)}{108}-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{324}+\frac{\sqrt{3}\,1{}\mathrm{i}}{324}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{324}+\frac{\sqrt{3}\,1{}\mathrm{i}}{324}\right)","Not used",1,"log(x + 3/2)/324 - log(x - 3/2)/108 - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/324 - 1/324) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/324 + 1/324)","B"
563,1,46,50,0.085927,"\text{Not used}","int((8*x^3 - 27)/(64*x^6 - 729),x)","\frac{\ln\left(x+\frac{3}{2}\right)}{54}-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)","Not used",1,"log(x + 3/2)/54 - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/108 + 1/108) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/108 - 1/108)","B"
564,1,46,50,0.099695,"\text{Not used}","int(-(36*x + 24*x^2 + 8*x^3 + 27)/(64*x^6 - 729),x)","-\frac{\ln\left(x-\frac{3}{2}\right)}{18}-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)","Not used",1,"log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/108 + 1/36) - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/108 - 1/36) - log(x - 3/2)/18","B"
565,1,100,110,5.097666,"\text{Not used}","int(-(162*x - 108*x^2 + 72*x^3 - 48*x^4 + 32*x^5 - 243)/(64*x^6 - 729)^2,x)","\frac{5\,\ln\left(x+\frac{3}{2}\right)}{17496}-\frac{\ln\left(x-\frac{3}{2}\right)}{17496}-\frac{1}{5832\,\left(x+\frac{3}{2}\right)}-\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{17496}+\frac{\sqrt{3}\,1{}\mathrm{i}}{17496}\right)+\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{17496}+\frac{\sqrt{3}\,1{}\mathrm{i}}{17496}\right)-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{17496}+\frac{\sqrt{3}\,1{}\mathrm{i}}{52488}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{17496}+\frac{\sqrt{3}\,1{}\mathrm{i}}{52488}\right)","Not used",1,"(5*log(x + 3/2))/17496 - log(x - 3/2)/17496 - 1/(5832*(x + 3/2)) - log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/17496 + 1/17496) + log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/17496 - 1/17496) - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/52488 + 1/17496) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/52488 - 1/17496)","B"
566,1,100,110,0.188891,"\text{Not used}","int((162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5 + 243)/(64*x^6 - 729)^2,x)","\frac{\ln\left(x+\frac{3}{2}\right)}{17496}-\frac{5\,\ln\left(x-\frac{3}{2}\right)}{17496}-\frac{1}{5832\,\left(x-\frac{3}{2}\right)}-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{17496}+\frac{\sqrt{3}\,1{}\mathrm{i}}{17496}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{17496}+\frac{\sqrt{3}\,1{}\mathrm{i}}{17496}\right)-\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{17496}+\frac{\sqrt{3}\,1{}\mathrm{i}}{52488}\right)+\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{17496}+\frac{\sqrt{3}\,1{}\mathrm{i}}{52488}\right)","Not used",1,"log(x + 3/2)/17496 - (5*log(x - 3/2))/17496 - 1/(5832*(x - 3/2)) - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/17496 - 1/17496) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/17496 + 1/17496) - log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/52488 - 1/17496) + log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/52488 + 1/17496)","B"
567,1,52,81,4.923490,"\text{Not used}","int((36*x^2 + 16*x^4 + 81)/(64*x^6 - 729)^2,x)","\frac{\mathrm{atanh}\left(\frac{2\,x}{3}\right)}{8748}+\frac{\sqrt{3}\,\left(2\,\mathrm{atan}\left(\frac{8\,\sqrt{3}\,x^3}{81}+\frac{4\,\sqrt{3}\,x}{9}\right)+2\,\mathrm{atan}\left(\frac{2\,\sqrt{3}\,x}{9}\right)\right)}{78732}-\frac{x}{17496\,\left(x^2-\frac{9}{4}\right)}","Not used",1,"atanh((2*x)/3)/8748 + (3^(1/2)*(2*atan((4*3^(1/2)*x)/9 + (8*3^(1/2)*x^3)/81) + 2*atan((2*3^(1/2)*x)/9)))/78732 - x/(17496*(x^2 - 9/4))","B"
568,1,77,92,0.123409,"\text{Not used}","int((54*x - 24*x^3 - 16*x^4 + 81)/(64*x^6 - 729)^2,x)","\frac{\ln\left(x+\frac{3}{2}\right)}{78732}-\frac{\ln\left(x-\frac{3}{2}\right)}{26244}+\frac{\ln\left(x^2+\frac{3\,x}{2}+\frac{9}{4}\right)}{52488}+\frac{x}{17496\,\left(x^2-\frac{3\,x}{2}+\frac{9}{4}\right)}-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{157464}+\frac{\sqrt{3}\,1{}\mathrm{i}}{26244}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{157464}+\frac{\sqrt{3}\,1{}\mathrm{i}}{26244}\right)","Not used",1,"log(x + 3/2)/78732 - log(x - 3/2)/26244 + log((3*x)/2 + x^2 + 9/4)/52488 + x/(17496*(x^2 - (3*x)/2 + 9/4)) - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/26244 + 1/157464) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/26244 - 1/157464)","B"
569,1,120,148,0.190101,"\text{Not used}","int(-(2*x - 3)/(64*x^6 - 729)^2,x)","\frac{\ln\left(x+\frac{3}{2}\right)}{472392}-\frac{\ln\left(x-\frac{3}{2}\right)}{4251528}-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{944784}+\frac{\sqrt{3}\,1{}\mathrm{i}}{8503056}\right)-\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{8503056}+\frac{\sqrt{3}\,1{}\mathrm{i}}{944784}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{944784}+\frac{\sqrt{3}\,1{}\mathrm{i}}{8503056}\right)+\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{8503056}+\frac{\sqrt{3}\,1{}\mathrm{i}}{944784}\right)+\frac{x}{139968\,\left(x^5+\frac{3\,x^4}{2}+\frac{9\,x^3}{4}+\frac{27\,x^2}{8}+\frac{81\,x}{16}+\frac{243}{32}\right)}","Not used",1,"log(x + 3/2)/472392 - log(x - 3/2)/4251528 - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/8503056 + 1/944784) - log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/944784 - 1/8503056) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/8503056 - 1/944784) + log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/944784 + 1/8503056) + x/(139968*((81*x)/16 + (27*x^2)/8 + (9*x^3)/4 + (3*x^4)/2 + x^5 + 243/32))","B"
570,1,121,146,5.088673,"\text{Not used}","int((2*x + 3)/(64*x^6 - 729)^2,x)","\frac{\ln\left(x+\frac{3}{2}\right)}{4251528}-\frac{\ln\left(x-\frac{3}{2}\right)}{472392}-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{8503056}+\frac{\sqrt{3}\,1{}\mathrm{i}}{944784}\right)-\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{944784}+\frac{\sqrt{3}\,1{}\mathrm{i}}{8503056}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{8503056}+\frac{\sqrt{3}\,1{}\mathrm{i}}{944784}\right)+\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{944784}+\frac{\sqrt{3}\,1{}\mathrm{i}}{8503056}\right)-\frac{x}{139968\,\left(x^5-\frac{3\,x^4}{2}+\frac{9\,x^3}{4}-\frac{27\,x^2}{8}+\frac{81\,x}{16}-\frac{243}{32}\right)}","Not used",1,"log(x + 3/2)/4251528 - log(x - 3/2)/472392 - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/944784 + 1/8503056) - log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/8503056 - 1/944784) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/944784 - 1/8503056) + log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/8503056 + 1/944784) - x/(139968*((81*x)/16 - (27*x^2)/8 + (9*x^3)/4 - (3*x^4)/2 + x^5 - 243/32))","B"
571,1,110,142,5.079843,"\text{Not used}","int((4*x^2 - 6*x + 9)/(64*x^6 - 729)^2,x)","\frac{\ln\left(x+\frac{3}{2}\right)}{118098}-\frac{\ln\left(x-\frac{3}{2}\right)}{354294}-\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{5}{2834352}+\frac{\sqrt{3}\,1{}\mathrm{i}}{314928}\right)+\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{5}{2834352}+\frac{\sqrt{3}\,1{}\mathrm{i}}{314928}\right)-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{944784}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2834352}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{944784}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2834352}\right)+\frac{x}{69984\,\left(-x^4-\frac{3\,x^3}{2}+\frac{27\,x}{8}+\frac{81}{16}\right)}","Not used",1,"log(x + 3/2)/118098 - log(x - 3/2)/354294 - log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/314928 + 5/2834352) + log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/314928 - 5/2834352) - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/2834352 + 1/944784) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/2834352 - 1/944784) + x/(69984*((27*x)/8 - (3*x^3)/2 - x^4 + 81/16))","B"
572,1,111,142,0.189111,"\text{Not used}","int((6*x + 4*x^2 + 9)/(64*x^6 - 729)^2,x)","\frac{\ln\left(x+\frac{3}{2}\right)}{354294}-\frac{\ln\left(x-\frac{3}{2}\right)}{118098}-\frac{x}{69984\,\left(x^4-\frac{3\,x^3}{2}+\frac{27\,x}{8}-\frac{81}{16}\right)}-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{5}{2834352}+\frac{\sqrt{3}\,1{}\mathrm{i}}{314928}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{5}{2834352}+\frac{\sqrt{3}\,1{}\mathrm{i}}{314928}\right)-\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{944784}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2834352}\right)+\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{944784}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2834352}\right)","Not used",1,"log(x + 3/2)/354294 - log(x - 3/2)/118098 - x/(69984*((27*x)/8 - (3*x^3)/2 + x^4 - 81/16)) - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/314928 - 5/2834352) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*1i)/314928 + 5/2834352) - log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/2834352 - 1/944784) + log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/2834352 + 1/944784)","B"
573,1,102,113,0.171824,"\text{Not used}","int(-(8*x^3 - 27)/(64*x^6 - 729)^2,x)","\frac{7\,\ln\left(x+\frac{3}{2}\right)}{472392}-\frac{\ln\left(x-\frac{3}{2}\right)}{157464}+\frac{x}{34992\,\left(x^3+\frac{27}{8}\right)}-\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{314928}+\frac{\sqrt{3}\,1{}\mathrm{i}}{314928}\right)+\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{314928}+\frac{\sqrt{3}\,1{}\mathrm{i}}{314928}\right)-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{7}{944784}+\frac{\sqrt{3}\,7{}\mathrm{i}}{944784}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{7}{944784}+\frac{\sqrt{3}\,7{}\mathrm{i}}{944784}\right)","Not used",1,"(7*log(x + 3/2))/472392 - log(x - 3/2)/157464 + x/(34992*(x^3 + 27/8)) - log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/314928 - 1/314928) + log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/314928 + 1/314928) - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*7i)/944784 + 7/944784) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*7i)/944784 - 7/944784)","B"
574,1,111,131,0.189792,"\text{Not used}","int((36*x + 24*x^2 + 8*x^3 + 27)/(64*x^6 - 729)^2,x)","\frac{\ln\left(x+\frac{3}{2}\right)}{472392}-\frac{7\,\ln\left(x-\frac{3}{2}\right)}{157464}-\frac{x}{34992\,\left(x^3-3\,x^2+\frac{9\,x}{2}-\frac{27}{8}\right)}+\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{314928}+\frac{\sqrt{3}\,1{}\mathrm{i}}{944784}\right)-\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{314928}+\frac{\sqrt{3}\,1{}\mathrm{i}}{944784}\right)-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{17}{944784}+\frac{\sqrt{3}\,11{}\mathrm{i}}{944784}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{17}{944784}+\frac{\sqrt{3}\,11{}\mathrm{i}}{944784}\right)","Not used",1,"log(x + 3/2)/472392 - (7*log(x - 3/2))/157464 - x/(34992*((9*x)/2 - 3*x^2 + x^3 - 27/8)) + log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/944784 + 1/314928) - log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/944784 - 1/314928) - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*11i)/944784 - 17/944784) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*11i)/944784 + 17/944784)","B"
575,1,91,99,5.095972,"\text{Not used}","int((x*(2*x^3 - 27))/(64*x^6 - 729),x)","-\frac{\ln\left(x-\frac{3}{2}\right)}{96}-\frac{5\,\ln\left(x+\frac{3}{2}\right)}{288}+\ln\left(x+\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{1}{192}+\frac{\sqrt{3}\,1{}\mathrm{i}}{192}\right)-\ln\left(x+\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{1}{192}+\frac{\sqrt{3}\,1{}\mathrm{i}}{192}\right)-\ln\left(x-\frac{3}{4}-\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(-\frac{5}{576}+\frac{\sqrt{3}\,5{}\mathrm{i}}{576}\right)+\ln\left(x-\frac{3}{4}+\frac{\sqrt{3}\,3{}\mathrm{i}}{4}\right)\,\left(\frac{5}{576}+\frac{\sqrt{3}\,5{}\mathrm{i}}{576}\right)","Not used",1,"log(x - (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/192 + 1/192) - (5*log(x + 3/2))/288 - log(x - 3/2)/96 - log(x + (3^(1/2)*3i)/4 + 3/4)*((3^(1/2)*1i)/192 - 1/192) - log(x - (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*5i)/576 - 5/576) + log(x + (3^(1/2)*3i)/4 - 3/4)*((3^(1/2)*5i)/576 + 5/576)","B"
576,0,-1,162,0.000000,"\text{Not used}","int(((c*x)^m*(d + e*x^n + f*x^(2*n) + g*x^(3*n)))/(a + b*x^n),x)","\int \frac{{\left(c\,x\right)}^m\,\left(d+e\,x^n+f\,x^{2\,n}+g\,x^{3\,n}\right)}{a+b\,x^n} \,d x","Not used",1,"int(((c*x)^m*(d + e*x^n + f*x^(2*n) + g*x^(3*n)))/(a + b*x^n), x)","F"
577,1,115,84,5.134906,"\text{Not used}","int((c + d*x^(n - 1))*(a + b*x^n)^3,x)","a^3\,c\,x+\frac{a^3\,d\,x^n}{n}+\frac{b^3\,d\,x^{4\,n}}{4\,n}+\frac{b^3\,c\,x\,x^{3\,n}}{3\,n+1}+\frac{3\,a^2\,b\,d\,x^{2\,n}}{2\,n}+\frac{a\,b^2\,d\,x^{3\,n}}{n}+\frac{3\,a\,b^2\,c\,x\,x^{2\,n}}{2\,n+1}+\frac{3\,a^2\,b\,c\,x\,x^n}{n+1}","Not used",1,"a^3*c*x + (a^3*d*x^n)/n + (b^3*d*x^(4*n))/(4*n) + (b^3*c*x*x^(3*n))/(3*n + 1) + (3*a^2*b*d*x^(2*n))/(2*n) + (a*b^2*d*x^(3*n))/n + (3*a*b^2*c*x*x^(2*n))/(2*n + 1) + (3*a^2*b*c*x*x^n)/(n + 1)","B"
578,1,76,61,5.058152,"\text{Not used}","int((c + d*x^(n - 1))*(a + b*x^n)^2,x)","a^2\,c\,x+\frac{a^2\,d\,x^n}{n}+\frac{b^2\,d\,x^{3\,n}}{3\,n}+\frac{b^2\,c\,x\,x^{2\,n}}{2\,n+1}+\frac{a\,b\,d\,x^{2\,n}}{n}+\frac{2\,a\,b\,c\,x\,x^n}{n+1}","Not used",1,"a^2*c*x + (a^2*d*x^n)/n + (b^2*d*x^(3*n))/(3*n) + (b^2*c*x*x^(2*n))/(2*n + 1) + (a*b*d*x^(2*n))/n + (2*a*b*c*x*x^n)/(n + 1)","B"
579,1,38,41,5.055746,"\text{Not used}","int((c + d*x^(n - 1))*(a + b*x^n),x)","a\,c\,x+\frac{a\,d\,x^n}{n}+\frac{b\,d\,x^{2\,n}}{2\,n}+\frac{b\,c\,x\,x^n}{n+1}","Not used",1,"a*c*x + (a*d*x^n)/n + (b*d*x^(2*n))/(2*n) + (b*c*x*x^n)/(n + 1)","B"
580,1,12,12,5.010872,"\text{Not used}","int(c + d*x^(n - 1),x)","c\,x+\frac{d\,x^n}{n}","Not used",1,"c*x + (d*x^n)/n","B"
581,1,43,42,5.325826,"\text{Not used}","int((c + d*x^(n - 1))/(a + b*x^n),x)","\frac{c\,x\,{{}}_2{\mathrm{F}}_1\left(1,\frac{1}{n};\ \frac{1}{n}+1;\ -\frac{b\,x^n}{a}\right)}{a}+\frac{d\,\ln\left(a+b\,x^n\right)}{b\,n}","Not used",1,"(c*x*hypergeom([1, 1/n], 1/n + 1, -(b*x^n)/a))/a + (d*log(a + b*x^n))/(b*n)","B"
582,1,49,44,5.348624,"\text{Not used}","int((c + d*x^(n - 1))/(a + b*x^n)^2,x)","\frac{c\,x\,{{}}_2{\mathrm{F}}_1\left(2,\frac{1}{n};\ \frac{1}{n}+1;\ -\frac{b\,x^n}{a}\right)}{a^2}-\frac{a\,d}{b\,\left(a^2\,n+a\,b\,n\,x^n\right)}","Not used",1,"(c*x*hypergeom([2, 1/n], 1/n + 1, -(b*x^n)/a))/a^2 - (a*d)/(b*(a^2*n + a*b*n*x^n))","B"
583,1,59,46,5.413564,"\text{Not used}","int((c + d*x^(n - 1))/(a + b*x^n)^3,x)","\frac{c\,x\,{{}}_2{\mathrm{F}}_1\left(3,\frac{1}{n};\ \frac{1}{n}+1;\ -\frac{b\,x^n}{a}\right)}{a^3}-\frac{d}{2\,b\,\left(a^2\,n+b^2\,n\,x^{2\,n}+2\,a\,b\,n\,x^n\right)}","Not used",1,"(c*x*hypergeom([3, 1/n], 1/n + 1, -(b*x^n)/a))/a^3 - d/(2*b*(a^2*n + b^2*n*x^(2*n) + 2*a*b*n*x^n))","B"
584,0,-1,305,0.000000,"\text{Not used}","int(((c*x)^m*(d + e*x^n + f*x^(2*n) + g*x^(3*n)))/(a + b*x^n)^(1/2),x)","\int \frac{{\left(c\,x\right)}^m\,\left(d+e\,x^n+f\,x^{2\,n}+g\,x^{3\,n}\right)}{\sqrt{a+b\,x^n}} \,d x","Not used",1,"int(((c*x)^m*(d + e*x^n + f*x^(2*n) + g*x^(3*n)))/(a + b*x^n)^(1/2), x)","F"
585,0,-1,45,0.000000,"\text{Not used}","int((b*f*x^(n/2 - 1) - a*h*x^(n/4 - 1) + b*h*x^((5*n)/4 - 1) + b*g*x^(n - 1))/(a + b*x^n)^(3/2),x)","\int \frac{b\,f\,x^{\frac{n}{2}-1}-a\,h\,x^{\frac{n}{4}-1}+b\,h\,x^{\frac{5\,n}{4}-1}+b\,g\,x^{n-1}}{{\left(a+b\,x^n\right)}^{3/2}} \,d x","Not used",1,"int((b*f*x^(n/2 - 1) - a*h*x^(n/4 - 1) + b*h*x^((5*n)/4 - 1) + b*g*x^(n - 1))/(a + b*x^n)^(3/2), x)","F"
586,0,-1,273,0.000000,"\text{Not used}","int((c*x)^m*(a + b*x^n)^p*(d + e*x + f*x^2 + g*x^3),x)","\int {\left(c\,x\right)}^m\,{\left(a+b\,x^n\right)}^p\,\left(g\,x^3+f\,x^2+e\,x+d\right) \,d x","Not used",1,"int((c*x)^m*(a + b*x^n)^p*(d + e*x + f*x^2 + g*x^3), x)","F"
587,0,-1,297,0.000000,"\text{Not used}","int((c*x)^m*(a + b*x^n)^p*(d + e*x^n + f*x^(2*n) + g*x^(3*n)),x)","\int {\left(c\,x\right)}^m\,{\left(a+b\,x^n\right)}^p\,\left(d+e\,x^n+f\,x^{2\,n}+g\,x^{3\,n}\right) \,d x","Not used",1,"int((c*x)^m*(a + b*x^n)^p*(d + e*x^n + f*x^(2*n) + g*x^(3*n)), x)","F"
588,0,-1,162,0.000000,"\text{Not used}","int((c + e*x^n + d*x^(n/2) + f*x^((3*n)/2))/(a + b*x^n)^2,x)","\int \frac{c+e\,x^n+d\,x^{n/2}+f\,x^{\frac{3\,n}{2}}}{{\left(a+b\,x^n\right)}^2} \,d x","Not used",1,"int((c + e*x^n + d*x^(n/2) + f*x^((3*n)/2))/(a + b*x^n)^2, x)","F"
589,1,20,24,5.587427,"\text{Not used}","int((a*c + 2*x^2*(a*d + b*c) + 3*b*d*x^4)/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","x\,\sqrt{b\,x^2+a}\,\sqrt{d\,x^2+c}","Not used",1,"x*(a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)","B"
590,0,-1,103,0.000000,"\text{Not used}","int(-(x^3 + 1)/((x^4 - 1)*(x^4 + 1)^(1/4)),x)","\int -\frac{x^3+1}{\left(x^4-1\right)\,{\left(x^4+1\right)}^{1/4}} \,d x","Not used",1,"int(-(x^3 + 1)/((x^4 - 1)*(x^4 + 1)^(1/4)), x)","F"
591,1,95,28,5.197066,"\text{Not used}","int((a*c - b*d*x^(2*n))/((a + b*x^n)^((n + 1)/n)*(c + d*x^n)^((n + 1)/n)),x)","\frac{\frac{a\,c\,x}{{\left(a+b\,x^n\right)}^{\frac{n+1}{n}}}+\frac{x\,x^n\,\left(a\,d+b\,c\right)}{{\left(a+b\,x^n\right)}^{\frac{n+1}{n}}}+\frac{b\,d\,x\,x^{2\,n}}{{\left(a+b\,x^n\right)}^{\frac{n+1}{n}}}}{{\left(c+d\,x^n\right)}^{\frac{n+1}{n}}}","Not used",1,"((a*c*x)/(a + b*x^n)^((n + 1)/n) + (x*x^n*(a*d + b*c))/(a + b*x^n)^((n + 1)/n) + (b*d*x*x^(2*n))/(a + b*x^n)^((n + 1)/n))/(c + d*x^n)^((n + 1)/n)","B"
592,1,124,45,5.367379,"\text{Not used}","int(((a*c - b*d*x^(2*n))*(a + b*x^n)^p*(c + d*x^n)^p)/(h*x)^(n + n*p + 1),x)","-{\left(c+d\,x^n\right)}^p\,\left(\frac{a\,c\,x\,{\left(a+b\,x^n\right)}^p}{n\,{\left(h\,x\right)}^{n+n\,p+1}\,\left(p+1\right)}+\frac{x\,x^n\,\left(a\,d+b\,c\right)\,{\left(a+b\,x^n\right)}^p}{n\,{\left(h\,x\right)}^{n+n\,p+1}\,\left(p+1\right)}+\frac{b\,d\,x\,x^{2\,n}\,{\left(a+b\,x^n\right)}^p}{n\,{\left(h\,x\right)}^{n+n\,p+1}\,\left(p+1\right)}\right)","Not used",1,"-(c + d*x^n)^p*((a*c*x*(a + b*x^n)^p)/(n*(h*x)^(n + n*p + 1)*(p + 1)) + (x*x^n*(a*d + b*c)*(a + b*x^n)^p)/(n*(h*x)^(n + n*p + 1)*(p + 1)) + (b*d*x*x^(2*n)*(a + b*x^n)^p)/(n*(h*x)^(n + n*p + 1)*(p + 1)))","B"
593,1,76,31,5.298471,"\text{Not used}","int((a + b*x^n)^p*(c + d*x^n)^p*(e + (e*x^n*(a*d + b*c)*(n + n*p + 1))/(a*c) + (b*d*e*x^(2*n)*(2*n + 2*n*p + 1))/(a*c)),x)","{\left(c+d\,x^n\right)}^p\,\left(e\,x\,{\left(a+b\,x^n\right)}^p+\frac{e\,x\,x^n\,\left(a\,d+b\,c\right)\,{\left(a+b\,x^n\right)}^p}{a\,c}+\frac{b\,d\,e\,x\,x^{2\,n}\,{\left(a+b\,x^n\right)}^p}{a\,c}\right)","Not used",1,"(c + d*x^n)^p*(e*x*(a + b*x^n)^p + (e*x*x^n*(a*d + b*c)*(a + b*x^n)^p)/(a*c) + (b*d*e*x*x^(2*n)*(a + b*x^n)^p)/(a*c))","B"
594,1,106,45,5.639932,"\text{Not used}","int((h*x)^m*(a + b*x^n)^p*(c + d*x^n)^p*(e + (e*x^n*(a*d + b*c)*(m + n + n*p + 1))/(a*c*(m + 1)) + (b*d*e*x^(2*n)*(m + 2*n + 2*n*p + 1))/(a*c*(m + 1))),x)","{\left(c+d\,x^n\right)}^p\,\left(\frac{e\,x\,{\left(h\,x\right)}^m\,{\left(a+b\,x^n\right)}^p}{m+1}+\frac{e\,x\,x^n\,{\left(h\,x\right)}^m\,\left(a\,d+b\,c\right)\,{\left(a+b\,x^n\right)}^p}{a\,c\,\left(m+1\right)}+\frac{b\,d\,e\,x\,x^{2\,n}\,{\left(h\,x\right)}^m\,{\left(a+b\,x^n\right)}^p}{a\,c\,\left(m+1\right)}\right)","Not used",1,"(c + d*x^n)^p*((e*x*(h*x)^m*(a + b*x^n)^p)/(m + 1) + (e*x*x^n*(h*x)^m*(a*d + b*c)*(a + b*x^n)^p)/(a*c*(m + 1)) + (b*d*e*x*x^(2*n)*(h*x)^m*(a + b*x^n)^p)/(a*c*(m + 1)))","B"