1,1,223,0,11.049744," ","integrate((e*x**2+d*x+c)/(b*x+a)**(1/2),x)","\begin{cases} \frac{- \frac{2 a c}{\sqrt{a + b x}} - \frac{2 a d \left(- \frac{a}{\sqrt{a + b x}} - \sqrt{a + b x}\right)}{b} - \frac{2 a e \left(\frac{a^{2}}{\sqrt{a + b x}} + 2 a \sqrt{a + b x} - \frac{\left(a + b x\right)^{\frac{3}{2}}}{3}\right)}{b^{2}} - 2 c \left(- \frac{a}{\sqrt{a + b x}} - \sqrt{a + b x}\right) - \frac{2 d \left(\frac{a^{2}}{\sqrt{a + b x}} + 2 a \sqrt{a + b x} - \frac{\left(a + b x\right)^{\frac{3}{2}}}{3}\right)}{b} - \frac{2 e \left(- \frac{a^{3}}{\sqrt{a + b x}} - 3 a^{2} \sqrt{a + b x} + a \left(a + b x\right)^{\frac{3}{2}} - \frac{\left(a + b x\right)^{\frac{5}{2}}}{5}\right)}{b^{2}}}{b} & \text{for}\: b \neq 0 \\\frac{c x + \frac{d x^{2}}{2} + \frac{e x^{3}}{3}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*c/sqrt(a + b*x) - 2*a*d*(-a/sqrt(a + b*x) - sqrt(a + b*x))/b - 2*a*e*(a**2/sqrt(a + b*x) + 2*a*sqrt(a + b*x) - (a + b*x)**(3/2)/3)/b**2 - 2*c*(-a/sqrt(a + b*x) - sqrt(a + b*x)) - 2*d*(a**2/sqrt(a + b*x) + 2*a*sqrt(a + b*x) - (a + b*x)**(3/2)/3)/b - 2*e*(-a**3/sqrt(a + b*x) - 3*a**2*sqrt(a + b*x) + a*(a + b*x)**(3/2) - (a + b*x)**(5/2)/5)/b**2)/b, Ne(b, 0)), ((c*x + d*x**2/2 + e*x**3/3)/sqrt(a), True))","A",0
2,1,644,0,85.150342," ","integrate((e*x**2+d*x+c)**2/(b*x+a)**(1/2),x)","\begin{cases} \frac{- \frac{2 a c^{2}}{\sqrt{a + b x}} - \frac{4 a c d \left(- \frac{a}{\sqrt{a + b x}} - \sqrt{a + b x}\right)}{b} - \frac{4 a c e \left(\frac{a^{2}}{\sqrt{a + b x}} + 2 a \sqrt{a + b x} - \frac{\left(a + b x\right)^{\frac{3}{2}}}{3}\right)}{b^{2}} - \frac{2 a d^{2} \left(\frac{a^{2}}{\sqrt{a + b x}} + 2 a \sqrt{a + b x} - \frac{\left(a + b x\right)^{\frac{3}{2}}}{3}\right)}{b^{2}} - \frac{4 a d e \left(- \frac{a^{3}}{\sqrt{a + b x}} - 3 a^{2} \sqrt{a + b x} + a \left(a + b x\right)^{\frac{3}{2}} - \frac{\left(a + b x\right)^{\frac{5}{2}}}{5}\right)}{b^{3}} - \frac{2 a e^{2} \left(\frac{a^{4}}{\sqrt{a + b x}} + 4 a^{3} \sqrt{a + b x} - 2 a^{2} \left(a + b x\right)^{\frac{3}{2}} + \frac{4 a \left(a + b x\right)^{\frac{5}{2}}}{5} - \frac{\left(a + b x\right)^{\frac{7}{2}}}{7}\right)}{b^{4}} - 2 c^{2} \left(- \frac{a}{\sqrt{a + b x}} - \sqrt{a + b x}\right) - \frac{4 c d \left(\frac{a^{2}}{\sqrt{a + b x}} + 2 a \sqrt{a + b x} - \frac{\left(a + b x\right)^{\frac{3}{2}}}{3}\right)}{b} - \frac{4 c e \left(- \frac{a^{3}}{\sqrt{a + b x}} - 3 a^{2} \sqrt{a + b x} + a \left(a + b x\right)^{\frac{3}{2}} - \frac{\left(a + b x\right)^{\frac{5}{2}}}{5}\right)}{b^{2}} - \frac{2 d^{2} \left(- \frac{a^{3}}{\sqrt{a + b x}} - 3 a^{2} \sqrt{a + b x} + a \left(a + b x\right)^{\frac{3}{2}} - \frac{\left(a + b x\right)^{\frac{5}{2}}}{5}\right)}{b^{2}} - \frac{4 d e \left(\frac{a^{4}}{\sqrt{a + b x}} + 4 a^{3} \sqrt{a + b x} - 2 a^{2} \left(a + b x\right)^{\frac{3}{2}} + \frac{4 a \left(a + b x\right)^{\frac{5}{2}}}{5} - \frac{\left(a + b x\right)^{\frac{7}{2}}}{7}\right)}{b^{3}} - \frac{2 e^{2} \left(- \frac{a^{5}}{\sqrt{a + b x}} - 5 a^{4} \sqrt{a + b x} + \frac{10 a^{3} \left(a + b x\right)^{\frac{3}{2}}}{3} - 2 a^{2} \left(a + b x\right)^{\frac{5}{2}} + \frac{5 a \left(a + b x\right)^{\frac{7}{2}}}{7} - \frac{\left(a + b x\right)^{\frac{9}{2}}}{9}\right)}{b^{4}}}{b} & \text{for}\: b \neq 0 \\\frac{c^{2} x + c d x^{2} + \frac{d e x^{4}}{2} + \frac{e^{2} x^{5}}{5} + \frac{x^{3} \left(2 c e + d^{2}\right)}{3}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*c**2/sqrt(a + b*x) - 4*a*c*d*(-a/sqrt(a + b*x) - sqrt(a + b*x))/b - 4*a*c*e*(a**2/sqrt(a + b*x) + 2*a*sqrt(a + b*x) - (a + b*x)**(3/2)/3)/b**2 - 2*a*d**2*(a**2/sqrt(a + b*x) + 2*a*sqrt(a + b*x) - (a + b*x)**(3/2)/3)/b**2 - 4*a*d*e*(-a**3/sqrt(a + b*x) - 3*a**2*sqrt(a + b*x) + a*(a + b*x)**(3/2) - (a + b*x)**(5/2)/5)/b**3 - 2*a*e**2*(a**4/sqrt(a + b*x) + 4*a**3*sqrt(a + b*x) - 2*a**2*(a + b*x)**(3/2) + 4*a*(a + b*x)**(5/2)/5 - (a + b*x)**(7/2)/7)/b**4 - 2*c**2*(-a/sqrt(a + b*x) - sqrt(a + b*x)) - 4*c*d*(a**2/sqrt(a + b*x) + 2*a*sqrt(a + b*x) - (a + b*x)**(3/2)/3)/b - 4*c*e*(-a**3/sqrt(a + b*x) - 3*a**2*sqrt(a + b*x) + a*(a + b*x)**(3/2) - (a + b*x)**(5/2)/5)/b**2 - 2*d**2*(-a**3/sqrt(a + b*x) - 3*a**2*sqrt(a + b*x) + a*(a + b*x)**(3/2) - (a + b*x)**(5/2)/5)/b**2 - 4*d*e*(a**4/sqrt(a + b*x) + 4*a**3*sqrt(a + b*x) - 2*a**2*(a + b*x)**(3/2) + 4*a*(a + b*x)**(5/2)/5 - (a + b*x)**(7/2)/7)/b**3 - 2*e**2*(-a**5/sqrt(a + b*x) - 5*a**4*sqrt(a + b*x) + 10*a**3*(a + b*x)**(3/2)/3 - 2*a**2*(a + b*x)**(5/2) + 5*a*(a + b*x)**(7/2)/7 - (a + b*x)**(9/2)/9)/b**4)/b, Ne(b, 0)), ((c**2*x + c*d*x**2 + d*e*x**4/2 + e**2*x**5/5 + x**3*(2*c*e + d**2)/3)/sqrt(a), True))","A",0
3,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)**3/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
4,1,354,0,45.833802," ","integrate((f*x**3+e*x**2+d*x+c)/(b*x+a)**(1/2),x)","\begin{cases} \frac{- \frac{2 a c}{\sqrt{a + b x}} - \frac{2 a d \left(- \frac{a}{\sqrt{a + b x}} - \sqrt{a + b x}\right)}{b} - \frac{2 a e \left(\frac{a^{2}}{\sqrt{a + b x}} + 2 a \sqrt{a + b x} - \frac{\left(a + b x\right)^{\frac{3}{2}}}{3}\right)}{b^{2}} - \frac{2 a f \left(- \frac{a^{3}}{\sqrt{a + b x}} - 3 a^{2} \sqrt{a + b x} + a \left(a + b x\right)^{\frac{3}{2}} - \frac{\left(a + b x\right)^{\frac{5}{2}}}{5}\right)}{b^{3}} - 2 c \left(- \frac{a}{\sqrt{a + b x}} - \sqrt{a + b x}\right) - \frac{2 d \left(\frac{a^{2}}{\sqrt{a + b x}} + 2 a \sqrt{a + b x} - \frac{\left(a + b x\right)^{\frac{3}{2}}}{3}\right)}{b} - \frac{2 e \left(- \frac{a^{3}}{\sqrt{a + b x}} - 3 a^{2} \sqrt{a + b x} + a \left(a + b x\right)^{\frac{3}{2}} - \frac{\left(a + b x\right)^{\frac{5}{2}}}{5}\right)}{b^{2}} - \frac{2 f \left(\frac{a^{4}}{\sqrt{a + b x}} + 4 a^{3} \sqrt{a + b x} - 2 a^{2} \left(a + b x\right)^{\frac{3}{2}} + \frac{4 a \left(a + b x\right)^{\frac{5}{2}}}{5} - \frac{\left(a + b x\right)^{\frac{7}{2}}}{7}\right)}{b^{3}}}{b} & \text{for}\: b \neq 0 \\\frac{c x + \frac{d x^{2}}{2} + \frac{e x^{3}}{3} + \frac{f x^{4}}{4}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*c/sqrt(a + b*x) - 2*a*d*(-a/sqrt(a + b*x) - sqrt(a + b*x))/b - 2*a*e*(a**2/sqrt(a + b*x) + 2*a*sqrt(a + b*x) - (a + b*x)**(3/2)/3)/b**2 - 2*a*f*(-a**3/sqrt(a + b*x) - 3*a**2*sqrt(a + b*x) + a*(a + b*x)**(3/2) - (a + b*x)**(5/2)/5)/b**3 - 2*c*(-a/sqrt(a + b*x) - sqrt(a + b*x)) - 2*d*(a**2/sqrt(a + b*x) + 2*a*sqrt(a + b*x) - (a + b*x)**(3/2)/3)/b - 2*e*(-a**3/sqrt(a + b*x) - 3*a**2*sqrt(a + b*x) + a*(a + b*x)**(3/2) - (a + b*x)**(5/2)/5)/b**2 - 2*f*(a**4/sqrt(a + b*x) + 4*a**3*sqrt(a + b*x) - 2*a**2*(a + b*x)**(3/2) + 4*a*(a + b*x)**(5/2)/5 - (a + b*x)**(7/2)/7)/b**3)/b, Ne(b, 0)), ((c*x + d*x**2/2 + e*x**3/3 + f*x**4/4)/sqrt(a), True))","A",0
5,-1,0,0,0.000000," ","integrate((f*x**3+e*x**2+d*x+c)**2/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
6,-1,0,0,0.000000," ","integrate((f*x**3+e*x**2+d*x+c)**3/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,1,76,0,1.186561," ","integrate((d*x+c)/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a^{2} b^{2} + 9 t a b c d + a d^{3} - b c^{3}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a^{2} b d + 3 t a b c^{2} + 2 a c d^{2}}{a d^{3} + b c^{3}} \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*a**2*b**2 + 9*_t*a*b*c*d + a*d**3 - b*c**3, Lambda(_t, _t*log(x + (9*_t**2*a**2*b*d + 3*_t*a*b*c**2 + 2*a*c*d**2)/(a*d**3 + b*c**3))))","A",0
8,1,105,0,2.145722," ","integrate((d*x+c)/(b*x**3+a)**2,x)","\operatorname{RootSum} {\left(729 t^{3} a^{5} b^{2} + 54 t a^{2} b c d + a d^{3} - 8 b c^{3}, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a^{4} b d + 36 t a^{2} b c^{2} + 4 a c d^{2}}{a d^{3} + 8 b c^{3}} \right)} \right)\right)} + \frac{c x + d x^{2}}{3 a^{2} + 3 a b x^{3}}"," ",0,"RootSum(729*_t**3*a**5*b**2 + 54*_t*a**2*b*c*d + a*d**3 - 8*b*c**3, Lambda(_t, _t*log(x + (81*_t**2*a**4*b*d + 36*_t*a**2*b*c**2 + 4*a*c*d**2)/(a*d**3 + 8*b*c**3)))) + (c*x + d*x**2)/(3*a**2 + 3*a*b*x**3)","A",0
9,1,146,0,2.470145," ","integrate((d*x+c)/(b*x**3+a)**3,x)","\operatorname{RootSum} {\left(19683 t^{3} a^{8} b^{2} + 810 t a^{3} b c d + 8 a d^{3} - 125 b c^{3}, \left( t \mapsto t \log{\left(x + \frac{1458 t^{2} a^{6} b d + 675 t a^{3} b c^{2} + 40 a c d^{2}}{8 a d^{3} + 125 b c^{3}} \right)} \right)\right)} + \frac{8 a c x + 7 a d x^{2} + 5 b c x^{4} + 4 b d x^{5}}{18 a^{4} + 36 a^{3} b x^{3} + 18 a^{2} b^{2} x^{6}}"," ",0,"RootSum(19683*_t**3*a**8*b**2 + 810*_t*a**3*b*c*d + 8*a*d**3 - 125*b*c**3, Lambda(_t, _t*log(x + (1458*_t**2*a**6*b*d + 675*_t*a**3*b*c**2 + 40*a*c*d**2)/(8*a*d**3 + 125*b*c**3)))) + (8*a*c*x + 7*a*d*x**2 + 5*b*c*x**4 + 4*b*d*x**5)/(18*a**4 + 36*a**3*b*x**3 + 18*a**2*b**2*x**6)","A",0
10,1,185,0,3.637530," ","integrate((d*x+c)/(b*x**3+a)**4,x)","\operatorname{RootSum} {\left(14348907 t^{3} a^{11} b^{2} + 408240 t a^{4} b c d + 2744 a d^{3} - 64000 b c^{3}, \left( t \mapsto t \log{\left(x + \frac{413343 t^{2} a^{8} b d + 194400 t a^{4} b c^{2} + 7840 a c d^{2}}{1372 a d^{3} + 32000 b c^{3}} \right)} \right)\right)} + \frac{82 a^{2} c x + 67 a^{2} d x^{2} + 104 a b c x^{4} + 77 a b d x^{5} + 40 b^{2} c x^{7} + 28 b^{2} d x^{8}}{162 a^{6} + 486 a^{5} b x^{3} + 486 a^{4} b^{2} x^{6} + 162 a^{3} b^{3} x^{9}}"," ",0,"RootSum(14348907*_t**3*a**11*b**2 + 408240*_t*a**4*b*c*d + 2744*a*d**3 - 64000*b*c**3, Lambda(_t, _t*log(x + (413343*_t**2*a**8*b*d + 194400*_t*a**4*b*c**2 + 7840*a*c*d**2)/(1372*a*d**3 + 32000*b*c**3)))) + (82*a**2*c*x + 67*a**2*d*x**2 + 104*a*b*c*x**4 + 77*a*b*d*x**5 + 40*b**2*c*x**7 + 28*b**2*d*x**8)/(162*a**6 + 486*a**5*b*x**3 + 486*a**4*b**2*x**6 + 162*a**3*b**3*x**9)","A",0
11,1,76,0,1.432812," ","integrate((b*x+a)/(e*x**3+d),x)","\operatorname{RootSum} {\left(27 t^{3} d^{2} e^{2} + 9 t a b d e - a^{3} e + b^{3} d, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} b d^{2} e + 3 t a^{2} d e + 2 a b^{2} d}{a^{3} e + b^{3} d} \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*d**2*e**2 + 9*_t*a*b*d*e - a**3*e + b**3*d, Lambda(_t, _t*log(x + (9*_t**2*b*d**2*e + 3*_t*a**2*d*e + 2*a*b**2*d)/(a**3*e + b**3*d))))","A",0
12,1,78,0,1.491932," ","integrate((b*x+a)/(-e*x**3+d),x)","- \operatorname{RootSum} {\left(27 t^{3} d^{2} e^{2} - 9 t a b d e - a^{3} e - b^{3} d, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} b d^{2} e - 3 t a^{2} d e - 2 a b^{2} d}{a^{3} e - b^{3} d} \right)} \right)\right)}"," ",0,"-RootSum(27*_t**3*d**2*e**2 - 9*_t*a*b*d*e - a**3*e - b**3*d, Lambda(_t, _t*log(x + (9*_t**2*b*d**2*e - 3*_t*a**2*d*e - 2*a*b**2*d)/(a**3*e - b**3*d))))","A",0
13,1,26,0,0.370000," ","integrate((1+x)/(x**3+1),x)","\frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"2*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
14,1,26,0,0.216728," ","integrate((1-x)/(-x**3+1),x)","\frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"2*sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3","A",0
15,1,17,0,0.252695," ","integrate((1+x)/(-x**3+1),x)","- \frac{2 \log{\left(x - 1 \right)}}{3} + \frac{\log{\left(x^{2} + x + 1 \right)}}{3}"," ",0,"-2*log(x - 1)/3 + log(x**2 + x + 1)/3","A",0
16,1,17,0,0.225428," ","integrate((1-x)/(x**3+1),x)","\frac{2 \log{\left(x + 1 \right)}}{3} - \frac{\log{\left(x^{2} - x + 1 \right)}}{3}"," ",0,"2*log(x + 1)/3 - log(x**2 - x + 1)/3","A",0
17,1,44,0,0.467983," ","integrate((3-x)/(-x**3+1),x)","- \frac{2 \log{\left(x - 1 \right)}}{3} + \frac{\log{\left(x^{2} + x + 1 \right)}}{3} + \frac{4 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-2*log(x - 1)/3 + log(x**2 + x + 1)/3 + 4*sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3","A",0
18,1,54,0,0.397482," ","integrate((d*x+c)/(d**3*x**3+c**3),x)","\frac{- \frac{\sqrt{3} i \log{\left(x + \frac{- c - \sqrt{3} i c}{2 d} \right)}}{3} + \frac{\sqrt{3} i \log{\left(x + \frac{- c + \sqrt{3} i c}{2 d} \right)}}{3}}{c d}"," ",0,"(-sqrt(3)*I*log(x + (-c - sqrt(3)*I*c)/(2*d))/3 + sqrt(3)*I*log(x + (-c + sqrt(3)*I*c)/(2*d))/3)/(c*d)","C",0
19,1,53,0,0.465259," ","integrate((-d*x+c)/(-d**3*x**3+c**3),x)","\frac{- \frac{\sqrt{3} i \log{\left(x + \frac{c - \sqrt{3} i c}{2 d} \right)}}{3} + \frac{\sqrt{3} i \log{\left(x + \frac{c + \sqrt{3} i c}{2 d} \right)}}{3}}{c d}"," ",0,"(-sqrt(3)*I*log(x + (c - sqrt(3)*I*c)/(2*d))/3 + sqrt(3)*I*log(x + (c + sqrt(3)*I*c)/(2*d))/3)/(c*d)","C",0
20,1,88,0,0.588399," ","integrate((a**(1/3)*b**(1/3)*B+b**(2/3)*B*x)/(b*x**3+a),x)","\frac{B \left(- \frac{\sqrt{3} i \log{\left(x + \frac{- B \sqrt[3]{a} - \sqrt{3} i B \sqrt[3]{a}}{2 B \sqrt[3]{b}} \right)}}{3} + \frac{\sqrt{3} i \log{\left(x + \frac{- B \sqrt[3]{a} + \sqrt{3} i B \sqrt[3]{a}}{2 B \sqrt[3]{b}} \right)}}{3}\right)}{\sqrt[3]{a}}"," ",0,"B*(-sqrt(3)*I*log(x + (-B*a**(1/3) - sqrt(3)*I*B*a**(1/3))/(2*B*b**(1/3)))/3 + sqrt(3)*I*log(x + (-B*a**(1/3) + sqrt(3)*I*B*a**(1/3))/(2*B*b**(1/3)))/3)/a**(1/3)","C",0
21,1,105,0,0.854008," ","integrate((a**(1/3)*(-b)**(1/3)*B-(-b)**(2/3)*B*x)/(b*x**3+a),x)","- \frac{B \left(- \frac{\sqrt{3} i \log{\left(- \frac{\sqrt[3]{a} \left(- b\right)^{\frac{2}{3}}}{2 b} - \frac{\sqrt{3} i \sqrt[3]{a} \left(- b\right)^{\frac{2}{3}}}{2 b} + x \right)}}{3} + \frac{\sqrt{3} i \log{\left(- \frac{\sqrt[3]{a} \left(- b\right)^{\frac{2}{3}}}{2 b} + \frac{\sqrt{3} i \sqrt[3]{a} \left(- b\right)^{\frac{2}{3}}}{2 b} + x \right)}}{3}\right)}{\sqrt[3]{a}}"," ",0,"-B*(-sqrt(3)*I*log(-a**(1/3)*(-b)**(2/3)/(2*b) - sqrt(3)*I*a**(1/3)*(-b)**(2/3)/(2*b) + x)/3 + sqrt(3)*I*log(-a**(1/3)*(-b)**(2/3)/(2*b) + sqrt(3)*I*a**(1/3)*(-b)**(2/3)/(2*b) + x)/3)/a**(1/3)","C",0
22,1,26,0,0.477397," ","integrate(-C*x**2/(b*x**3+a)+(C*x**2+B*x)/(b*x**3+a),x)","B \operatorname{RootSum} {\left(27 t^{3} a b^{2} + 1, \left( t \mapsto t \log{\left(9 t^{2} a b + x \right)} \right)\right)}"," ",0,"B*RootSum(27*_t**3*a*b**2 + 1, Lambda(_t, _t*log(9*_t**2*a*b + x)))","A",0
23,1,22,0,0.213601," ","integrate(-C*x**2/(b*x**3+a)+(C*x**2+A)/(b*x**3+a),x)","A \operatorname{RootSum} {\left(27 t^{3} a^{2} b - 1, \left( t \mapsto t \log{\left(3 t a + x \right)} \right)\right)}"," ",0,"A*RootSum(27*_t**3*a**2*b - 1, Lambda(_t, _t*log(3*_t*a + x)))","A",0
24,1,76,0,1.281831," ","integrate(-C*x**2/(b*x**3+a)+(C*x**2+B*x+A)/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a^{2} b^{2} + 9 t A B a b - A^{3} b + B^{3} a, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} B a^{2} b + 3 t A^{2} a b + 2 A B^{2} a}{A^{3} b + B^{3} a} \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*a**2*b**2 + 9*_t*A*B*a*b - A**3*b + B**3*a, Lambda(_t, _t*log(x + (9*_t**2*B*a**2*b + 3*_t*A**2*a*b + 2*A*B**2*a)/(A**3*b + B**3*a))))","A",0
25,1,75,0,0.713073," ","integrate((c*x**2+b*x)/(e*x**3+d),x)","\operatorname{RootSum} {\left(27 t^{3} d e^{3} - 27 t^{2} c d e^{2} + 9 t c^{2} d e + b^{3} e - c^{3} d, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} d e^{2} - 6 t c d e + c^{2} d}{b^{2} e} \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*d*e**3 - 27*_t**2*c*d*e**2 + 9*_t*c**2*d*e + b**3*e - c**3*d, Lambda(_t, _t*log(x + (9*_t**2*d*e**2 - 6*_t*c*d*e + c**2*d)/(b**2*e))))","A",0
26,1,70,0,0.589931," ","integrate((c*x**2+a)/(-e*x**3+d),x)","- \operatorname{RootSum} {\left(27 t^{3} d^{2} e^{3} - 27 t^{2} c d^{2} e^{2} + 9 t c^{2} d^{2} e - a^{3} e^{2} - c^{3} d^{2}, \left( t \mapsto t \log{\left(x + \frac{- 3 t d e + c d}{a e} \right)} \right)\right)}"," ",0,"-RootSum(27*_t**3*d**2*e**3 - 27*_t**2*c*d**2*e**2 + 9*_t*c**2*d**2*e - a**3*e**2 - c**3*d**2, Lambda(_t, _t*log(x + (-3*_t*d*e + c*d)/(a*e))))","A",0
27,1,60,0,0.499814," ","integrate((b**2*x**2+2*a**2)/(b**3*x**3+a**3),x)","\frac{- \frac{\sqrt{3} i \log{\left(x + \frac{- a - \sqrt{3} i a}{2 b} \right)}}{3} + \frac{\sqrt{3} i \log{\left(x + \frac{- a + \sqrt{3} i a}{2 b} \right)}}{3} + \log{\left(\frac{a}{b} + x \right)}}{b}"," ",0,"(-sqrt(3)*I*log(x + (-a - sqrt(3)*I*a)/(2*b))/3 + sqrt(3)*I*log(x + (-a + sqrt(3)*I*a)/(2*b))/3 + log(a/b + x))/b","C",0
28,1,60,0,0.697317," ","integrate((b**2*x**2+2*a**2)/(-b**3*x**3+a**3),x)","- \frac{\frac{\sqrt{3} i \log{\left(x + \frac{a - \sqrt{3} i a}{2 b} \right)}}{3} - \frac{\sqrt{3} i \log{\left(x + \frac{a + \sqrt{3} i a}{2 b} \right)}}{3} + \log{\left(- \frac{a}{b} + x \right)}}{b}"," ",0,"-(sqrt(3)*I*log(x + (a - sqrt(3)*I*a)/(2*b))/3 - sqrt(3)*I*log(x + (a + sqrt(3)*I*a)/(2*b))/3 + log(-a/b + x))/b","C",0
29,1,58,0,0.625168," ","integrate((8*C+b**(2/3)*C*x**2)/(b*x**3+8),x)","\operatorname{RootSum} {\left(3 t^{3} b^{\frac{5}{3}} - 3 t^{2} C b^{\frac{4}{3}} + t C^{2} b - C^{3} b^{\frac{2}{3}}, \left( t \mapsto t \log{\left(x + \frac{3 t \sqrt[3]{b} - C}{C \sqrt[3]{b}} \right)} \right)\right)}"," ",0,"RootSum(3*_t**3*b**(5/3) - 3*_t**2*C*b**(4/3) + _t*C**2*b - C**3*b**(2/3), Lambda(_t, _t*log(x + (3*_t*b**(1/3) - C)/(C*b**(1/3)))))","A",0
30,1,85,0,0.744828," ","integrate((a**(2/3)*C+2*C*x**2)/(8*x**3+a),x)","C \left(\frac{\log{\left(\frac{\sqrt[3]{a}}{2} + x \right)}}{4} - \frac{\sqrt{3} i \log{\left(x + \frac{- C \sqrt[3]{a} - \sqrt{3} i C \sqrt[3]{a}}{4 C} \right)}}{12} + \frac{\sqrt{3} i \log{\left(x + \frac{- C \sqrt[3]{a} + \sqrt{3} i C \sqrt[3]{a}}{4 C} \right)}}{12}\right)"," ",0,"C*(log(a**(1/3)/2 + x)/4 - sqrt(3)*I*log(x + (-C*a**(1/3) - sqrt(3)*I*C*a**(1/3))/(4*C))/12 + sqrt(3)*I*log(x + (-C*a**(1/3) + sqrt(3)*I*C*a**(1/3))/(4*C))/12)","C",0
31,1,58,0,0.986750," ","integrate((8*C+(-b)**(2/3)*C*x**2)/(b*x**3-8),x)","\operatorname{RootSum} {\left(3 t^{3} b^{2} - 3 t^{2} C b \left(- b\right)^{\frac{2}{3}} + t C^{2} \left(- b\right)^{\frac{4}{3}} - C^{3} b, \left( t \mapsto t \log{\left(- \frac{3 t}{C} + x + \frac{\left(- b\right)^{\frac{2}{3}}}{b} \right)} \right)\right)}"," ",0,"RootSum(3*_t**3*b**2 - 3*_t**2*C*b*(-b)**(2/3) + _t*C**2*(-b)**(4/3) - C**3*b, Lambda(_t, _t*log(-3*_t/C + x + (-b)**(2/3)/b)))","A",0
32,1,95,0,0.933543," ","integrate(((-a)**(2/3)*C+2*C*x**2)/(-8*x**3+a),x)","- C \left(\frac{\log{\left(- \frac{a}{2 \left(- a\right)^{\frac{2}{3}}} + x \right)}}{4} + \frac{\sqrt{3} i \log{\left(\frac{a}{4 \left(- a\right)^{\frac{2}{3}}} - \frac{\sqrt{3} i a}{4 \left(- a\right)^{\frac{2}{3}}} + x \right)}}{12} - \frac{\sqrt{3} i \log{\left(\frac{a}{4 \left(- a\right)^{\frac{2}{3}}} + \frac{\sqrt{3} i a}{4 \left(- a\right)^{\frac{2}{3}}} + x \right)}}{12}\right)"," ",0,"-C*(log(-a/(2*(-a)**(2/3)) + x)/4 + sqrt(3)*I*log(a/(4*(-a)**(2/3)) - sqrt(3)*I*a/(4*(-a)**(2/3)) + x)/12 - sqrt(3)*I*log(a/(4*(-a)**(2/3)) + sqrt(3)*I*a/(4*(-a)**(2/3)) + x)/12)","C",0
33,1,100,0,0.738211," ","integrate((2*(a/b)**(2/3)*C+C*x**2)/(b*x**3+a),x)","\frac{C \left(\log{\left(\frac{a}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)} - \frac{\sqrt{3} i \log{\left(- \frac{a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt{3} i a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3} + \frac{\sqrt{3} i \log{\left(- \frac{a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt{3} i a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3}\right)}{b}"," ",0,"C*(log(a/(b*(a/b)**(2/3)) + x) - sqrt(3)*I*log(-a/(2*b*(a/b)**(2/3)) - sqrt(3)*I*a/(2*b*(a/b)**(2/3)) + x)/3 + sqrt(3)*I*log(-a/(2*b*(a/b)**(2/3)) + sqrt(3)*I*a/(2*b*(a/b)**(2/3)) + x)/3)/b","C",0
34,1,110,0,0.843092," ","integrate((2*(-a/b)**(2/3)*C+C*x**2)/(-b*x**3+a),x)","- \frac{C \left(\log{\left(- \frac{a}{b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)} + \frac{\sqrt{3} i \log{\left(\frac{a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt{3} i a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3} - \frac{\sqrt{3} i \log{\left(\frac{a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt{3} i a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3}\right)}{b}"," ",0,"-C*(log(-a/(b*(-a/b)**(2/3)) + x) + sqrt(3)*I*log(a/(2*b*(-a/b)**(2/3)) - sqrt(3)*I*a/(2*b*(-a/b)**(2/3)) + x)/3 - sqrt(3)*I*log(a/(2*b*(-a/b)**(2/3)) + sqrt(3)*I*a/(2*b*(-a/b)**(2/3)) + x)/3)/b","C",0
35,1,109,0,0.770762," ","integrate((2*(-a/b)**(2/3)*C+C*x**2)/(b*x**3+a),x)","\frac{C \left(\log{\left(\frac{a}{b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)} - \frac{\sqrt{3} i \log{\left(- \frac{a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt{3} i a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3} + \frac{\sqrt{3} i \log{\left(- \frac{a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt{3} i a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3}\right)}{b}"," ",0,"C*(log(a/(b*(-a/b)**(2/3)) + x) - sqrt(3)*I*log(-a/(2*b*(-a/b)**(2/3)) - sqrt(3)*I*a/(2*b*(-a/b)**(2/3)) + x)/3 + sqrt(3)*I*log(-a/(2*b*(-a/b)**(2/3)) + sqrt(3)*I*a/(2*b*(-a/b)**(2/3)) + x)/3)/b","C",0
36,1,102,0,0.790894," ","integrate((2*(a/b)**(2/3)*C+C*x**2)/(-b*x**3+a),x)","- \frac{C \left(\log{\left(- \frac{a}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)} + \frac{\sqrt{3} i \log{\left(\frac{a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt{3} i a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3} - \frac{\sqrt{3} i \log{\left(\frac{a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt{3} i a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3}\right)}{b}"," ",0,"-C*(log(-a/(b*(a/b)**(2/3)) + x) + sqrt(3)*I*log(a/(2*b*(a/b)**(2/3)) - sqrt(3)*I*a/(2*b*(a/b)**(2/3)) + x)/3 - sqrt(3)*I*log(a/(2*b*(a/b)**(2/3)) + sqrt(3)*I*a/(2*b*(a/b)**(2/3)) + x)/3)/b","C",0
37,1,70,0,0.732446," ","integrate((2*a**(2/3)*C+b**(2/3)*C*x**2)/(b*x**3+a),x)","\operatorname{RootSum} {\left(3 t^{3} b^{\frac{5}{3}} - 3 t^{2} C b^{\frac{4}{3}} + t C^{2} b - C^{3} b^{\frac{2}{3}}, \left( t \mapsto t \log{\left(x + \frac{3 t \sqrt[3]{a} \sqrt[3]{b} - C \sqrt[3]{a}}{2 C \sqrt[3]{b}} \right)} \right)\right)}"," ",0,"RootSum(3*_t**3*b**(5/3) - 3*_t**2*C*b**(4/3) + _t*C**2*b - C**3*b**(2/3), Lambda(_t, _t*log(x + (3*_t*a**(1/3)*b**(1/3) - C*a**(1/3))/(2*C*b**(1/3)))))","A",0
38,1,73,0,1.241021," ","integrate((-2*a**(2/3)*C-(-b)**(2/3)*C*x**2)/(b*x**3+a),x)","- \operatorname{RootSum} {\left(3 t^{3} b^{2} - 3 t^{2} C b \left(- b\right)^{\frac{2}{3}} + t C^{2} \left(- b\right)^{\frac{4}{3}} - C^{3} b, \left( t \mapsto t \log{\left(\frac{3 t \sqrt[3]{a}}{2 C} - \frac{\sqrt[3]{a} \left(- b\right)^{\frac{2}{3}}}{2 b} + x \right)} \right)\right)}"," ",0,"-RootSum(3*_t**3*b**2 - 3*_t**2*C*b*(-b)**(2/3) + _t*C**2*(-b)**(4/3) - C**3*b, Lambda(_t, _t*log(3*_t*a**(1/3)/(2*C) - a**(1/3)*(-b)**(2/3)/(2*b) + x)))","A",0
39,1,42,0,0.293836," ","integrate((x**2-3)/(x**3-1),x)","- \frac{2 \log{\left(x - 1 \right)}}{3} + \frac{5 \log{\left(x^{2} + x + 1 \right)}}{6} + \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}"," ",0,"-2*log(x - 1)/3 + 5*log(x**2 + x + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)","A",0
40,-1,0,0,0.000000," ","integrate((a**(1/3)*b**(1/3)*B+2*a**(2/3)*C+b**(2/3)*B*x+b**(2/3)*C*x**2)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate((a**(1/3)*(-b)**(1/3)*B-2*a**(2/3)*C-(-b)**(2/3)*B*x-(-b)**(2/3)*C*x**2)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,1,7,0,0.244364," ","integrate((C**2*x**2+B*C*x+B**2)/(C**3*x**3-B**3),x)","\frac{\log{\left(- B + C x \right)}}{C}"," ",0,"log(-B + C*x)/C","A",0
43,1,20,0,0.262817," ","integrate((a**(2/3)*C-a**(1/3)*b**(1/3)*C*x+b**(2/3)*C*x**2)/(b*x**3+a),x)","\frac{C \log{\left(\sqrt[3]{a} b^{\frac{2}{3}} + b x \right)}}{\sqrt[3]{b}}"," ",0,"C*log(a**(1/3)*b**(2/3) + b*x)/b**(1/3)","A",0
44,-1,0,0,0.000000," ","integrate(((a/b)**(1/3)*B+2*(a/b)**(2/3)*C+B*x+C*x**2)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,-1,0,0,0.000000," ","integrate(((-a/b)**(1/3)*B+2*(-a/b)**(2/3)*C+B*x+C*x**2)/(-b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,-1,0,0,0.000000," ","integrate((-(-a/b)**(1/3)*B+2*(-a/b)**(2/3)*C+B*x+C*x**2)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,-1,0,0,0.000000," ","integrate((-(a/b)**(1/3)*B+2*(a/b)**(2/3)*C+B*x+C*x**2)/(-b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,1,24,0,0.868632," ","integrate((c*x**2+a*x+a)/(-x**3+1),x)","\frac{\left(a - c\right) \log{\left(x^{2} + x + 1 \right)}}{3} - \frac{\left(2 a + c\right) \log{\left(x - 1 \right)}}{3}"," ",0,"(a - c)*log(x**2 + x + 1)/3 - (2*a + c)*log(x - 1)/3","A",0
49,1,323,0,1.885405," ","integrate((c*x**2+b*x+a)/(-x**3+1),x)","- \frac{\left(a + b + c\right) \log{\left(x + \frac{a^{2} c - a^{2} \left(a + b + c\right) - 2 a b^{2} + b c^{2} - 2 b c \left(a + b + c\right) + b \left(a + b + c\right)^{2}}{a^{3} - b^{3}} \right)}}{3} - \left(- \frac{a}{6} - \frac{b}{6} + \frac{c}{3} - \frac{\sqrt{3} i \left(a - b\right)}{6}\right) \log{\left(x + \frac{a^{2} c - 3 a^{2} \left(- \frac{a}{6} - \frac{b}{6} + \frac{c}{3} - \frac{\sqrt{3} i \left(a - b\right)}{6}\right) - 2 a b^{2} + b c^{2} - 6 b c \left(- \frac{a}{6} - \frac{b}{6} + \frac{c}{3} - \frac{\sqrt{3} i \left(a - b\right)}{6}\right) + 9 b \left(- \frac{a}{6} - \frac{b}{6} + \frac{c}{3} - \frac{\sqrt{3} i \left(a - b\right)}{6}\right)^{2}}{a^{3} - b^{3}} \right)} - \left(- \frac{a}{6} - \frac{b}{6} + \frac{c}{3} + \frac{\sqrt{3} i \left(a - b\right)}{6}\right) \log{\left(x + \frac{a^{2} c - 3 a^{2} \left(- \frac{a}{6} - \frac{b}{6} + \frac{c}{3} + \frac{\sqrt{3} i \left(a - b\right)}{6}\right) - 2 a b^{2} + b c^{2} - 6 b c \left(- \frac{a}{6} - \frac{b}{6} + \frac{c}{3} + \frac{\sqrt{3} i \left(a - b\right)}{6}\right) + 9 b \left(- \frac{a}{6} - \frac{b}{6} + \frac{c}{3} + \frac{\sqrt{3} i \left(a - b\right)}{6}\right)^{2}}{a^{3} - b^{3}} \right)}"," ",0,"-(a + b + c)*log(x + (a**2*c - a**2*(a + b + c) - 2*a*b**2 + b*c**2 - 2*b*c*(a + b + c) + b*(a + b + c)**2)/(a**3 - b**3))/3 - (-a/6 - b/6 + c/3 - sqrt(3)*I*(a - b)/6)*log(x + (a**2*c - 3*a**2*(-a/6 - b/6 + c/3 - sqrt(3)*I*(a - b)/6) - 2*a*b**2 + b*c**2 - 6*b*c*(-a/6 - b/6 + c/3 - sqrt(3)*I*(a - b)/6) + 9*b*(-a/6 - b/6 + c/3 - sqrt(3)*I*(a - b)/6)**2)/(a**3 - b**3)) - (-a/6 - b/6 + c/3 + sqrt(3)*I*(a - b)/6)*log(x + (a**2*c - 3*a**2*(-a/6 - b/6 + c/3 + sqrt(3)*I*(a - b)/6) - 2*a*b**2 + b*c**2 - 6*b*c*(-a/6 - b/6 + c/3 + sqrt(3)*I*(a - b)/6) + 9*b*(-a/6 - b/6 + c/3 + sqrt(3)*I*(a - b)/6)**2)/(a**3 - b**3))","C",0
50,1,5,0,0.133537," ","integrate((x**2+x+1)/(-x**3+1),x)","- \log{\left(x - 1 \right)}"," ",0,"-log(x - 1)","A",0
51,1,5,0,0.335646," ","integrate((3*x**2-x+1)/(-x**3+1),x)","- \log{\left(x - 1 \right)}"," ",0,"-log(x - 1)","A",0
52,1,15,0,0.161390," ","integrate((4*x**2+x+1)/(-x**3+1),x)","- 2 \log{\left(x - 1 \right)} - \log{\left(x^{2} + x + 1 \right)}"," ",0,"-2*log(x - 1) - log(x**2 + x + 1)","A",0
53,1,117,0,0.730898," ","integrate((b*x**3+a)**3*(b*d*x**4+b*c*x**3+a*d*x+a*c),x)","a^{4} c x + \frac{a^{4} d x^{2}}{2} + a^{3} b c x^{4} + \frac{4 a^{3} b d x^{5}}{5} + \frac{6 a^{2} b^{2} c x^{7}}{7} + \frac{3 a^{2} b^{2} d x^{8}}{4} + \frac{2 a b^{3} c x^{10}}{5} + \frac{4 a b^{3} d x^{11}}{11} + \frac{b^{4} c x^{13}}{13} + \frac{b^{4} d x^{14}}{14}"," ",0,"a**4*c*x + a**4*d*x**2/2 + a**3*b*c*x**4 + 4*a**3*b*d*x**5/5 + 6*a**2*b**2*c*x**7/7 + 3*a**2*b**2*d*x**8/4 + 2*a*b**3*c*x**10/5 + 4*a*b**3*d*x**11/11 + b**4*c*x**13/13 + b**4*d*x**14/14","A",0
54,1,90,0,0.155085," ","integrate((b*x**3+a)**2*(b*d*x**4+b*c*x**3+a*d*x+a*c),x)","a^{3} c x + \frac{a^{3} d x^{2}}{2} + \frac{3 a^{2} b c x^{4}}{4} + \frac{3 a^{2} b d x^{5}}{5} + \frac{3 a b^{2} c x^{7}}{7} + \frac{3 a b^{2} d x^{8}}{8} + \frac{b^{3} c x^{10}}{10} + \frac{b^{3} d x^{11}}{11}"," ",0,"a**3*c*x + a**3*d*x**2/2 + 3*a**2*b*c*x**4/4 + 3*a**2*b*d*x**5/5 + 3*a*b**2*c*x**7/7 + 3*a*b**2*d*x**8/8 + b**3*c*x**10/10 + b**3*d*x**11/11","A",0
55,1,58,0,0.096637," ","integrate((b*x**3+a)*(b*d*x**4+b*c*x**3+a*d*x+a*c),x)","a^{2} c x + \frac{a^{2} d x^{2}}{2} + \frac{a b c x^{4}}{2} + \frac{2 a b d x^{5}}{5} + \frac{b^{2} c x^{7}}{7} + \frac{b^{2} d x^{8}}{8}"," ",0,"a**2*c*x + a**2*d*x**2/2 + a*b*c*x**4/2 + 2*a*b*d*x**5/5 + b**2*c*x**7/7 + b**2*d*x**8/8","A",0
56,1,8,0,0.127341," ","integrate((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a),x)","c x + \frac{d x^{2}}{2}"," ",0,"c*x + d*x**2/2","A",0
57,1,76,0,1.337765," ","integrate((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a)**2,x)","\operatorname{RootSum} {\left(27 t^{3} a^{2} b^{2} + 9 t a b c d + a d^{3} - b c^{3}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a^{2} b d + 3 t a b c^{2} + 2 a c d^{2}}{a d^{3} + b c^{3}} \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*a**2*b**2 + 9*_t*a*b*c*d + a*d**3 - b*c**3, Lambda(_t, _t*log(x + (9*_t**2*a**2*b*d + 3*_t*a*b*c**2 + 2*a*c*d**2)/(a*d**3 + b*c**3))))","A",0
58,1,105,0,1.851400," ","integrate((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a)**3,x)","\operatorname{RootSum} {\left(729 t^{3} a^{5} b^{2} + 54 t a^{2} b c d + a d^{3} - 8 b c^{3}, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a^{4} b d + 36 t a^{2} b c^{2} + 4 a c d^{2}}{a d^{3} + 8 b c^{3}} \right)} \right)\right)} + \frac{c x + d x^{2}}{3 a^{2} + 3 a b x^{3}}"," ",0,"RootSum(729*_t**3*a**5*b**2 + 54*_t*a**2*b*c*d + a*d**3 - 8*b*c**3, Lambda(_t, _t*log(x + (81*_t**2*a**4*b*d + 36*_t*a**2*b*c**2 + 4*a*c*d**2)/(a*d**3 + 8*b*c**3)))) + (c*x + d*x**2)/(3*a**2 + 3*a*b*x**3)","A",0
59,1,265,0,11.796185," ","integrate((b*x**3+a)**(3/2)*(b*d*x**4+b*c*x**3+a*d*x+a*c),x)","\frac{a^{\frac{5}{2}} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{5}{2}} d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{2 a^{\frac{3}{2}} b c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{2 a^{\frac{3}{2}} b d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{\sqrt{a} b^{2} c x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt{a} b^{2} d x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)}"," ",0,"a**(5/2)*c*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(5/2)*d*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + 2*a**(3/2)*b*c*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + 2*a**(3/2)*b*d*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + sqrt(a)*b**2*c*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + sqrt(a)*b**2*d*x**8*gamma(8/3)*hyper((-1/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(11/3))","A",0
60,1,170,0,7.357559," ","integrate((b*x**3+a)**(1/2)*(b*d*x**4+b*c*x**3+a*d*x+a*c),x)","\frac{a^{\frac{3}{2}} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{3}{2}} d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt{a} b c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} b d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}"," ",0,"a**(3/2)*c*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(3/2)*d*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + sqrt(a)*b*c*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*b*d*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3))","A",0
61,1,163,0,8.148526," ","integrate((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{a} d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{b c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{7}{3}\right)} + \frac{b d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{8}{3}\right)}"," ",0,"sqrt(a)*c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + sqrt(a)*d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + b*c*x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(7/3)) + b*d*x**5*gamma(5/3)*hyper((1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(8/3))","A",0
62,1,78,0,8.053844," ","integrate((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a)**(3/2),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3))","A",0
63,1,163,0,20.907936," ","integrate((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a)**(5/2),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{5}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{5}{2} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{5}{3}\right)} + \frac{b c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{5}{2} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{2}} \Gamma\left(\frac{7}{3}\right)} + \frac{b d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{3}, \frac{5}{2} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{2}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 5/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((2/3, 5/2), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(5/3)) + b*c*x**4*gamma(4/3)*hyper((4/3, 5/2), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(5/2)*gamma(7/3)) + b*d*x**5*gamma(5/3)*hyper((5/3, 5/2), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(5/2)*gamma(8/3))","A",0
64,1,163,0,68.681042," ","integrate((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a)**(7/2),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{7}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{2}} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{7}{2} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{2}} \Gamma\left(\frac{5}{3}\right)} + \frac{b c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{7}{2} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{7}{2}} \Gamma\left(\frac{7}{3}\right)} + \frac{b d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{3}, \frac{7}{2} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{7}{2}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 7/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(5/2)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((2/3, 7/2), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(5/2)*gamma(5/3)) + b*c*x**4*gamma(4/3)*hyper((4/3, 7/2), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(7/2)*gamma(7/3)) + b*d*x**5*gamma(5/3)*hyper((5/3, 7/2), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(7/2)*gamma(8/3))","A",0
65,-1,0,0,0.000000," ","integrate((b*d*x**4+b*c*x**3+a*d*x+a*c)/(b*x**3+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,1,187,0,8.043077," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**3+a)**(1/2),x)","e \left(\begin{cases} \frac{x^{3}}{3 \sqrt{a}} & \text{for}\: b = 0 \\\frac{2 \sqrt{a + b x^{3}}}{3 b} & \text{otherwise} \end{cases}\right) + \frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} + \frac{f x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{7}{3}\right)} + \frac{g x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{8}{3}\right)}"," ",0,"e*Piecewise((x**3/(3*sqrt(a)), Eq(b, 0)), (2*sqrt(a + b*x**3)/(3*b), True)) + c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) + f*x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(7/3)) + g*x**5*gamma(5/3)*hyper((1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(8/3))","A",0
67,1,189,0,32.600248," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**3+a)**(3/2),x)","e \left(\begin{cases} - \frac{2}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{3}{2} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{5}{3}\right)} + \frac{f x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{3}{2} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{7}{3}\right)} + \frac{g x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"e*Piecewise((-2/(3*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**3/(3*a**(3/2)), True)) + c*x*gamma(1/3)*hyper((1/3, 3/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((2/3, 3/2), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(5/3)) + f*x**4*gamma(4/3)*hyper((4/3, 3/2), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(7/3)) + g*x**5*gamma(5/3)*hyper((3/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(8/3))","A",0
68,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**3+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**3+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,1,156,0,1.383663," ","integrate((b*x+a)**2/(d*x**3+c),x)","\operatorname{RootSum} {\left(27 t^{3} c^{2} d^{3} - 27 t^{2} b^{2} c^{2} d^{2} + t \left(18 a^{3} b c d^{2} + 9 b^{4} c^{2} d\right) - a^{6} d^{2} + 2 a^{3} b^{3} c d - b^{6} c^{2}, \left( t \mapsto t \log{\left(x + \frac{18 t^{2} b c^{2} d^{2} + 3 t a^{3} c d^{2} - 12 t b^{3} c^{2} d + 7 a^{3} b^{2} c d + 2 b^{5} c^{2}}{a^{5} d^{2} + 8 a^{2} b^{3} c d} \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*c**2*d**3 - 27*_t**2*b**2*c**2*d**2 + _t*(18*a**3*b*c*d**2 + 9*b**4*c**2*d) - a**6*d**2 + 2*a**3*b**3*c*d - b**6*c**2, Lambda(_t, _t*log(x + (18*_t**2*b*c**2*d**2 + 3*_t*a**3*c*d**2 - 12*_t*b**3*c**2*d + 7*a**3*b**2*c*d + 2*b**5*c**2)/(a**5*d**2 + 8*a**2*b**3*c*d))))","A",0
71,1,245,0,5.713628," ","integrate((b*x+a)**3/(d*x**3+c),x)","\frac{b^{3} x}{d} + \operatorname{RootSum} {\left(27 t^{3} c^{2} d^{4} - 81 t^{2} a b^{2} c^{2} d^{3} + t \left(27 a^{5} b c d^{3} + 54 a^{2} b^{4} c^{2} d^{2}\right) - a^{9} d^{3} + 3 a^{6} b^{3} c d^{2} - 3 a^{3} b^{6} c^{2} d + b^{9} c^{3}, \left( t \mapsto t \log{\left(x + \frac{27 t^{2} a^{2} b c^{2} d^{3} + 3 t a^{6} c d^{3} - 60 t a^{3} b^{3} c^{2} d^{2} + 3 t b^{6} c^{3} d + 15 a^{7} b^{2} c d^{2} + 15 a^{4} b^{5} c^{2} d - 3 a b^{8} c^{3}}{a^{9} d^{3} + 24 a^{6} b^{3} c d^{2} + 3 a^{3} b^{6} c^{2} d - b^{9} c^{3}} \right)} \right)\right)}"," ",0,"b**3*x/d + RootSum(27*_t**3*c**2*d**4 - 81*_t**2*a*b**2*c**2*d**3 + _t*(27*a**5*b*c*d**3 + 54*a**2*b**4*c**2*d**2) - a**9*d**3 + 3*a**6*b**3*c*d**2 - 3*a**3*b**6*c**2*d + b**9*c**3, Lambda(_t, _t*log(x + (27*_t**2*a**2*b*c**2*d**3 + 3*_t*a**6*c*d**3 - 60*_t*a**3*b**3*c**2*d**2 + 3*_t*b**6*c**3*d + 15*a**7*b**2*c*d**2 + 15*a**4*b**5*c**2*d - 3*a*b**8*c**3)/(a**9*d**3 + 24*a**6*b**3*c*d**2 + 3*a**3*b**6*c**2*d - b**9*c**3))))","A",0
72,1,325,0,60.245072," ","integrate((b*x+a)**4/(d*x**3+c),x)","\frac{4 a b^{3} x}{d} + \frac{b^{4} x^{2}}{2 d} + \operatorname{RootSum} {\left(27 t^{3} c^{2} d^{5} - 162 t^{2} a^{2} b^{2} c^{2} d^{4} + t \left(36 a^{7} b c d^{4} + 171 a^{4} b^{4} c^{2} d^{3} + 36 a b^{7} c^{3} d^{2}\right) - a^{12} d^{4} + 4 a^{9} b^{3} c d^{3} - 6 a^{6} b^{6} c^{2} d^{2} + 4 a^{3} b^{9} c^{3} d - b^{12} c^{4}, \left( t \mapsto t \log{\left(x + \frac{36 t^{2} a^{3} b c^{2} d^{4} - 9 t^{2} b^{4} c^{3} d^{3} + 3 t a^{8} c d^{4} - 168 t a^{5} b^{3} c^{2} d^{3} + 84 t a^{2} b^{6} c^{3} d^{2} + 26 a^{10} b^{2} c d^{3} + 48 a^{7} b^{5} c^{2} d^{2} - 66 a^{4} b^{8} c^{3} d - 8 a b^{11} c^{4}}{a^{12} d^{4} + 52 a^{9} b^{3} c d^{3} - 52 a^{3} b^{9} c^{3} d - b^{12} c^{4}} \right)} \right)\right)}"," ",0,"4*a*b**3*x/d + b**4*x**2/(2*d) + RootSum(27*_t**3*c**2*d**5 - 162*_t**2*a**2*b**2*c**2*d**4 + _t*(36*a**7*b*c*d**4 + 171*a**4*b**4*c**2*d**3 + 36*a*b**7*c**3*d**2) - a**12*d**4 + 4*a**9*b**3*c*d**3 - 6*a**6*b**6*c**2*d**2 + 4*a**3*b**9*c**3*d - b**12*c**4, Lambda(_t, _t*log(x + (36*_t**2*a**3*b*c**2*d**4 - 9*_t**2*b**4*c**3*d**3 + 3*_t*a**8*c*d**4 - 168*_t*a**5*b**3*c**2*d**3 + 84*_t*a**2*b**6*c**3*d**2 + 26*a**10*b**2*c*d**3 + 48*a**7*b**5*c**2*d**2 - 66*a**4*b**8*c**3*d - 8*a*b**11*c**4)/(a**12*d**4 + 52*a**9*b**3*c*d**3 - 52*a**3*b**9*c**3*d - b**12*c**4))))","A",0
73,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**2/(e*x**3+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(e*x**3+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**4/(e*x**3+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,1,44,0,0.250544," ","integrate((x**4+2*x**2)/(x**3+1),x)","\frac{x^{2}}{2} + \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} - x + 1 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"x**2/2 + log(x + 1) + log(x**2 - x + 1)/2 - sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
77,1,46,0,0.307587," ","integrate((x**4+2*x**2)/(-x**3+1),x)","- \frac{x^{2}}{2} - \log{\left(x - 1 \right)} - \frac{\log{\left(x^{2} + x + 1 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-x**2/2 - log(x - 1) - log(x**2 + x + 1)/2 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3","A",0
78,1,48,0,0.327321," ","integrate((4*x**3-x+1)/(x**3+1),x)","4 x - \frac{2 \log{\left(x + 1 \right)}}{3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{3} - \frac{4 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"4*x - 2*log(x + 1)/3 + log(x**2 - x + 1)/3 - 4*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
79,1,92,0,3.352022," ","integrate((1+x+3**(1/2))/(x**3+1)**(1/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) + sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
80,1,97,0,5.453685," ","integrate((1-x+3**(1/2))/(-x**3+1)**(1/2),x)","- \frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"-x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(2*I*pi))/(3*gamma(5/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3)) + sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3))","A",0
81,1,82,0,6.186580," ","integrate((1-x+3**(1/2))/(x**3-1)**(1/2),x)","\frac{i x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"I*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3)/(3*gamma(5/3)) - sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3))","A",0
82,1,99,0,3.578710," ","integrate((1+x+3**(1/2))/(-x**3-1)**(1/2),x)","- \frac{i x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"-I*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3)) - sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
83,1,122,0,10.490207," ","integrate((b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(b*x**3+a)**(1/2),x)","\frac{\sqrt[3]{b} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"b**(1/3)*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/6)*gamma(4/3)) + sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/6)*gamma(4/3))","A",0
84,1,128,0,14.662658," ","integrate((-b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(-b*x**3+a)**(1/2),x)","- \frac{\sqrt[3]{b} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-b**(1/3)*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(5/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*a**(1/6)*gamma(4/3)) + sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*a**(1/6)*gamma(4/3))","A",0
85,1,112,0,9.213866," ","integrate((-b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(b*x**3-a)**(1/2),x)","\frac{i \sqrt[3]{b} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"I*b**(1/3)*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3/a)/(3*sqrt(a)*gamma(5/3)) - sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3/a)/(3*a**(1/6)*gamma(4/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3/a)/(3*a**(1/6)*gamma(4/3))","A",0
86,1,129,0,8.679271," ","integrate((b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(-b*x**3-a)**(1/2),x)","- \frac{i \sqrt[3]{b} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-I*b**(1/3)*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) - sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/6)*gamma(4/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/6)*gamma(4/3))","A",0
87,1,124,0,5.128191," ","integrate((1+(b/a)**(1/3)*x+3**(1/2))/(b*x**3+a)**(1/2),x)","\frac{x^{2} \sqrt[3]{\frac{b}{a}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"x**2*(b/a)**(1/3)*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3))","A",0
88,1,129,0,5.968820," ","integrate((1-(b/a)**(1/3)*x+3**(1/2))/(-b*x**3+a)**(1/2),x)","- \frac{x^{2} \sqrt[3]{\frac{b}{a}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-x**2*(b/a)**(1/3)*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(5/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(4/3))","A",0
89,1,114,0,5.174408," ","integrate((1-(b/a)**(1/3)*x+3**(1/2))/(b*x**3-a)**(1/2),x)","\frac{i x^{2} \sqrt[3]{\frac{b}{a}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"I*x**2*(b/a)**(1/3)*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3/a)/(3*sqrt(a)*gamma(5/3)) - sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3/a)/(3*sqrt(a)*gamma(4/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3/a)/(3*sqrt(a)*gamma(4/3))","A",0
90,1,131,0,6.612454," ","integrate((1+(b/a)**(1/3)*x+3**(1/2))/(-b*x**3-a)**(1/2),x)","- \frac{i x^{2} \sqrt[3]{\frac{b}{a}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-I*x**2*(b/a)**(1/3)*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) - sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3))","A",0
91,1,92,0,3.515726," ","integrate((1+x-3**(1/2))/(x**3+1)**(1/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3)) - sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
92,1,97,0,4.389174," ","integrate((1-x-3**(1/2))/(-x**3+1)**(1/2),x)","- \frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"-x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(2*I*pi))/(3*gamma(5/3)) - sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3))","A",0
93,1,82,0,5.715186," ","integrate((1-x-3**(1/2))/(x**3-1)**(1/2),x)","\frac{i x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"I*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3)/(3*gamma(5/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3)) + sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3))","A",0
94,1,97,0,3.363392," ","integrate((1+x-3**(1/2))/(-x**3-1)**(1/2),x)","- \frac{i x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"-I*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) + sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
95,1,92,0,3.301408," ","integrate((-1-x+3**(1/2))/(x**3+1)**(1/2),x)","- \frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"-x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3)) - x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) + sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
96,1,97,0,4.885843," ","integrate((-1+x+3**(1/2))/(-x**3+1)**(1/2),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(2*I*pi))/(3*gamma(5/3)) - x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3)) + sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3))","A",0
97,1,82,0,3.159498," ","integrate((-1+x+3**(1/2))/(x**3-1)**(1/2),x)","- \frac{i x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"-I*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3)/(3*gamma(5/3)) - sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3)) + I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3))","A",0
98,1,97,0,5.216851," ","integrate((-1-x+3**(1/2))/(-x**3-1)**(1/2),x)","\frac{i x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"I*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3)) - sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) + I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
99,1,122,0,11.533161," ","integrate((b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b*x**3+a)**(1/2),x)","\frac{\sqrt[3]{b} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"b**(1/3)*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) - sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/6)*gamma(4/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/6)*gamma(4/3))","A",0
100,1,128,0,13.434149," ","integrate((-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b*x**3+a)**(1/2),x)","- \frac{\sqrt[3]{b} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-b**(1/3)*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(5/3)) - sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*a**(1/6)*gamma(4/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*a**(1/6)*gamma(4/3))","A",0
101,1,112,0,12.956228," ","integrate((-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b*x**3-a)**(1/2),x)","\frac{i \sqrt[3]{b} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"I*b**(1/3)*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3/a)/(3*sqrt(a)*gamma(5/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3/a)/(3*a**(1/6)*gamma(4/3)) + sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3/a)/(3*a**(1/6)*gamma(4/3))","A",0
102,1,128,0,9.878815," ","integrate((b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b*x**3-a)**(1/2),x)","- \frac{i \sqrt[3]{b} x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-I*b**(1/3)*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/6)*gamma(4/3)) + sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/6)*gamma(4/3))","A",0
103,1,124,0,6.498182," ","integrate((1+(b/a)**(1/3)*x-3**(1/2))/(b*x**3+a)**(1/2),x)","\frac{x^{2} \sqrt[3]{\frac{b}{a}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"x**2*(b/a)**(1/3)*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) - sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3))","A",0
104,1,129,0,6.190983," ","integrate((1-(b/a)**(1/3)*x-3**(1/2))/(-b*x**3+a)**(1/2),x)","- \frac{x^{2} \sqrt[3]{\frac{b}{a}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-x**2*(b/a)**(1/3)*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(5/3)) - sqrt(3)*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(4/3))","A",0
105,1,114,0,6.151279," ","integrate((1-(b/a)**(1/3)*x-3**(1/2))/(b*x**3-a)**(1/2),x)","\frac{i x^{2} \sqrt[3]{\frac{b}{a}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"I*x**2*(b/a)**(1/3)*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3/a)/(3*sqrt(a)*gamma(5/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3/a)/(3*sqrt(a)*gamma(4/3)) + sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3/a)/(3*sqrt(a)*gamma(4/3))","A",0
106,1,129,0,3.700203," ","integrate((1+(b/a)**(1/3)*x-3**(1/2))/(-b*x**3-a)**(1/2),x)","- \frac{i x^{2} \sqrt[3]{\frac{b}{a}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} - \frac{i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{3} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-I*x**2*(b/a)**(1/3)*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) - I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + sqrt(3)*I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3))","A",0
107,1,78,0,3.916215," ","integrate((d*x+c)/(b*x**3+a)**(1/2),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3))","A",0
108,1,82,0,3.294052," ","integrate((d*x+c)/(-b*x**3+a)**(1/2),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{2 i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(2*I*pi)/a)/(3*sqrt(a)*gamma(5/3))","A",0
109,1,73,0,3.709427," ","integrate((d*x+c)/(b*x**3-a)**(1/2),x)","- \frac{i c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} - \frac{i d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-I*c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3/a)/(3*sqrt(a)*gamma(4/3)) - I*d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3/a)/(3*sqrt(a)*gamma(5/3))","A",0
110,1,83,0,4.200357," ","integrate((d*x+c)/(-b*x**3-a)**(1/2),x)","- \frac{i c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} - \frac{i d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-I*c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) - I*d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3))","A",0
111,1,61,0,3.046256," ","integrate((d*x+c)/(x**3+1)**(1/2),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3))","A",0
112,1,65,0,3.540604," ","integrate((d*x+c)/(-x**3+1)**(1/2),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(2*I*pi))/(3*gamma(5/3))","A",0
113,1,56,0,2.945448," ","integrate((d*x+c)/(x**3-1)**(1/2),x)","- \frac{i c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{i d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"-I*c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3)) - I*d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3)/(3*gamma(5/3))","A",0
114,1,66,0,2.735413," ","integrate((d*x+c)/(-x**3-1)**(1/2),x)","- \frac{i c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{i d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"-I*c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) - I*d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), x**3*exp_polar(I*pi))/(3*gamma(5/3))","A",0
115,1,126,0,1.219304," ","integrate((d*x+c)/(-b*x**4+a),x)","- \operatorname{RootSum} {\left(256 t^{4} a^{3} b^{2} - 32 t^{2} a^{2} b d^{2} - 16 t a b c^{2} d + a d^{4} - b c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 128 t^{3} a^{3} b d^{2} + 16 t^{2} a^{2} b c^{2} d + 8 t a^{2} d^{4} - 4 t a b c^{4} + 5 a c^{2} d^{3}}{4 a c d^{4} + b c^{5}} \right)} \right)\right)}"," ",0,"-RootSum(256*_t**4*a**3*b**2 - 32*_t**2*a**2*b*d**2 - 16*_t*a*b*c**2*d + a*d**4 - b*c**4, Lambda(_t, _t*log(x + (-128*_t**3*a**3*b*d**2 + 16*_t**2*a**2*b*c**2*d + 8*_t*a**2*d**4 - 4*_t*a*b*c**4 + 5*a*c**2*d**3)/(4*a*c*d**4 + b*c**5))))","A",0
116,1,124,0,1.029896," ","integrate((d*x+c)/(b*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} b^{2} + 32 t^{2} a^{2} b d^{2} - 16 t a b c^{2} d + a d^{4} + b c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 128 t^{3} a^{3} b d^{2} - 16 t^{2} a^{2} b c^{2} d - 8 t a^{2} d^{4} - 4 t a b c^{4} + 5 a c^{2} d^{3}}{4 a c d^{4} - b c^{5}} \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*b**2 + 32*_t**2*a**2*b*d**2 - 16*_t*a*b*c**2*d + a*d**4 + b*c**4, Lambda(_t, _t*log(x + (-128*_t**3*a**3*b*d**2 - 16*_t**2*a**2*b*c**2*d - 8*_t*a**2*d**4 - 4*_t*a*b*c**4 + 5*a*c**2*d**3)/(4*a*c*d**4 - b*c**5))))","A",0
117,1,156,0,1.797790," ","integrate((d*x+c)/(-b*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{2} - 2048 t^{2} a^{4} b d^{2} + 1152 t a^{2} b c^{2} d + 16 a d^{4} - 81 b c^{4}, \left( t \mapsto t \log{\left(x + \frac{32768 t^{3} a^{6} b d^{2} + 4608 t^{2} a^{4} b c^{2} d - 512 t a^{3} d^{4} + 1296 t a^{2} b c^{4} + 360 a c^{2} d^{3}}{192 a c d^{4} + 243 b c^{5}} \right)} \right)\right)} + \frac{- c x - d x^{2}}{- 4 a^{2} + 4 a b x^{4}}"," ",0,"RootSum(65536*_t**4*a**7*b**2 - 2048*_t**2*a**4*b*d**2 + 1152*_t*a**2*b*c**2*d + 16*a*d**4 - 81*b*c**4, Lambda(_t, _t*log(x + (32768*_t**3*a**6*b*d**2 + 4608*_t**2*a**4*b*c**2*d - 512*_t*a**3*d**4 + 1296*_t*a**2*b*c**4 + 360*a*c**2*d**3)/(192*a*c*d**4 + 243*b*c**5)))) + (-c*x - d*x**2)/(-4*a**2 + 4*a*b*x**4)","A",0
118,1,155,0,1.510904," ","integrate((d*x+c)/(b*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{2} + 2048 t^{2} a^{4} b d^{2} - 1152 t a^{2} b c^{2} d + 16 a d^{4} + 81 b c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 32768 t^{3} a^{6} b d^{2} - 4608 t^{2} a^{4} b c^{2} d - 512 t a^{3} d^{4} - 1296 t a^{2} b c^{4} + 360 a c^{2} d^{3}}{192 a c d^{4} - 243 b c^{5}} \right)} \right)\right)} + \frac{c x + d x^{2}}{4 a^{2} + 4 a b x^{4}}"," ",0,"RootSum(65536*_t**4*a**7*b**2 + 2048*_t**2*a**4*b*d**2 - 1152*_t*a**2*b*c**2*d + 16*a*d**4 + 81*b*c**4, Lambda(_t, _t*log(x + (-32768*_t**3*a**6*b*d**2 - 4608*_t**2*a**4*b*c**2*d - 512*_t*a**3*d**4 - 1296*_t*a**2*b*c**4 + 360*a*c**2*d**3)/(192*a*c*d**4 - 243*b*c**5)))) + (c*x + d*x**2)/(4*a**2 + 4*a*b*x**4)","A",0
119,1,194,0,1.970214," ","integrate((d*x+c)/(-b*x**4+a)**3,x)","- \operatorname{RootSum} {\left(268435456 t^{4} a^{11} b^{2} - 4718592 t^{2} a^{6} b d^{2} - 2709504 t a^{3} b c^{2} d + 20736 a d^{4} - 194481 b c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 67108864 t^{3} a^{9} b d^{2} + 9633792 t^{2} a^{6} b c^{2} d + 589824 t a^{4} d^{4} - 2765952 t a^{3} b c^{4} + 423360 a c^{2} d^{3}}{193536 a c d^{4} + 453789 b c^{5}} \right)} \right)\right)} - \frac{- 11 a c x - 10 a d x^{2} + 7 b c x^{5} + 6 b d x^{6}}{32 a^{4} - 64 a^{3} b x^{4} + 32 a^{2} b^{2} x^{8}}"," ",0,"-RootSum(268435456*_t**4*a**11*b**2 - 4718592*_t**2*a**6*b*d**2 - 2709504*_t*a**3*b*c**2*d + 20736*a*d**4 - 194481*b*c**4, Lambda(_t, _t*log(x + (-67108864*_t**3*a**9*b*d**2 + 9633792*_t**2*a**6*b*c**2*d + 589824*_t*a**4*d**4 - 2765952*_t*a**3*b*c**4 + 423360*a*c**2*d**3)/(193536*a*c*d**4 + 453789*b*c**5)))) - (-11*a*c*x - 10*a*d*x**2 + 7*b*c*x**5 + 6*b*d*x**6)/(32*a**4 - 64*a**3*b*x**4 + 32*a**2*b**2*x**8)","A",0
120,1,192,0,1.988989," ","integrate((d*x+c)/(b*x**4+a)**3,x)","\operatorname{RootSum} {\left(268435456 t^{4} a^{11} b^{2} + 4718592 t^{2} a^{6} b d^{2} - 2709504 t a^{3} b c^{2} d + 20736 a d^{4} + 194481 b c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 67108864 t^{3} a^{9} b d^{2} - 9633792 t^{2} a^{6} b c^{2} d - 589824 t a^{4} d^{4} - 2765952 t a^{3} b c^{4} + 423360 a c^{2} d^{3}}{193536 a c d^{4} - 453789 b c^{5}} \right)} \right)\right)} + \frac{11 a c x + 10 a d x^{2} + 7 b c x^{5} + 6 b d x^{6}}{32 a^{4} + 64 a^{3} b x^{4} + 32 a^{2} b^{2} x^{8}}"," ",0,"RootSum(268435456*_t**4*a**11*b**2 + 4718592*_t**2*a**6*b*d**2 - 2709504*_t*a**3*b*c**2*d + 20736*a*d**4 + 194481*b*c**4, Lambda(_t, _t*log(x + (-67108864*_t**3*a**9*b*d**2 - 9633792*_t**2*a**6*b*c**2*d - 589824*_t*a**4*d**4 - 2765952*_t*a**3*b*c**4 + 423360*a*c**2*d**3)/(193536*a*c*d**4 - 453789*b*c**5)))) + (11*a*c*x + 10*a*d*x**2 + 7*b*c*x**5 + 6*b*d*x**6)/(32*a**4 + 64*a**3*b*x**4 + 32*a**2*b**2*x**8)","A",0
121,1,231,0,2.062104," ","integrate((d*x+c)/(-b*x**4+a)**4,x)","\operatorname{RootSum} {\left(68719476736 t^{4} a^{15} b^{2} - 838860800 t^{2} a^{8} b d^{2} + 485703680 t a^{4} b c^{2} d + 2560000 a d^{4} - 35153041 b c^{4}, \left( t \mapsto t \log{\left(x + \frac{429496729600 t^{3} a^{12} b d^{2} + 62170071040 t^{2} a^{8} b c^{2} d - 2621440000 t a^{5} d^{4} + 17998356992 t a^{4} b c^{4} + 1897280000 a c^{2} d^{3}}{788480000 a c d^{4} + 2706784157 b c^{5}} \right)} \right)\right)} + \frac{- 153 a^{2} c x - 132 a^{2} d x^{2} + 198 a b c x^{5} + 160 a b d x^{6} - 77 b^{2} c x^{9} - 60 b^{2} d x^{10}}{- 384 a^{6} + 1152 a^{5} b x^{4} - 1152 a^{4} b^{2} x^{8} + 384 a^{3} b^{3} x^{12}}"," ",0,"RootSum(68719476736*_t**4*a**15*b**2 - 838860800*_t**2*a**8*b*d**2 + 485703680*_t*a**4*b*c**2*d + 2560000*a*d**4 - 35153041*b*c**4, Lambda(_t, _t*log(x + (429496729600*_t**3*a**12*b*d**2 + 62170071040*_t**2*a**8*b*c**2*d - 2621440000*_t*a**5*d**4 + 17998356992*_t*a**4*b*c**4 + 1897280000*a*c**2*d**3)/(788480000*a*c*d**4 + 2706784157*b*c**5)))) + (-153*a**2*c*x - 132*a**2*d*x**2 + 198*a*b*c*x**5 + 160*a*b*d*x**6 - 77*b**2*c*x**9 - 60*b**2*d*x**10)/(-384*a**6 + 1152*a**5*b*x**4 - 1152*a**4*b**2*x**8 + 384*a**3*b**3*x**12)","A",0
122,1,231,0,1.807254," ","integrate((d*x+c)/(b*x**4+a)**4,x)","\operatorname{RootSum} {\left(68719476736 t^{4} a^{15} b^{2} + 838860800 t^{2} a^{8} b d^{2} - 485703680 t a^{4} b c^{2} d + 2560000 a d^{4} + 35153041 b c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 429496729600 t^{3} a^{12} b d^{2} - 62170071040 t^{2} a^{8} b c^{2} d - 2621440000 t a^{5} d^{4} - 17998356992 t a^{4} b c^{4} + 1897280000 a c^{2} d^{3}}{788480000 a c d^{4} - 2706784157 b c^{5}} \right)} \right)\right)} + \frac{153 a^{2} c x + 132 a^{2} d x^{2} + 198 a b c x^{5} + 160 a b d x^{6} + 77 b^{2} c x^{9} + 60 b^{2} d x^{10}}{384 a^{6} + 1152 a^{5} b x^{4} + 1152 a^{4} b^{2} x^{8} + 384 a^{3} b^{3} x^{12}}"," ",0,"RootSum(68719476736*_t**4*a**15*b**2 + 838860800*_t**2*a**8*b*d**2 - 485703680*_t*a**4*b*c**2*d + 2560000*a*d**4 + 35153041*b*c**4, Lambda(_t, _t*log(x + (-429496729600*_t**3*a**12*b*d**2 - 62170071040*_t**2*a**8*b*c**2*d - 2621440000*_t*a**5*d**4 - 17998356992*_t*a**4*b*c**4 + 1897280000*a*c**2*d**3)/(788480000*a*c*d**4 - 2706784157*b*c**5)))) + (153*a**2*c*x + 132*a**2*d*x**2 + 198*a*b*c*x**5 + 160*a*b*d*x**6 + 77*b**2*c*x**9 + 60*b**2*d*x**10)/(384*a**6 + 1152*a**5*b*x**4 + 1152*a**4*b**2*x**8 + 384*a**3*b**3*x**12)","A",0
123,1,313,0,0.922755," ","integrate((d*x+c)/(-x**4+1),x)","\frac{\left(c - d\right) \log{\left(x + \frac{c^{4} \left(c - d\right) + 5 c^{2} d^{3} + c^{2} d \left(c - d\right)^{2} - 2 d^{4} \left(c - d\right) + 2 d^{2} \left(c - d\right)^{3}}{c^{5} + 4 c d^{4}} \right)}}{4} - \frac{\left(c + d\right) \log{\left(x + \frac{- c^{4} \left(c + d\right) + 5 c^{2} d^{3} + c^{2} d \left(c + d\right)^{2} + 2 d^{4} \left(c + d\right) - 2 d^{2} \left(c + d\right)^{3}}{c^{5} + 4 c d^{4}} \right)}}{4} - \left(- \frac{i c}{4} - \frac{d}{4}\right) \log{\left(x + \frac{- 4 c^{4} \left(- \frac{i c}{4} - \frac{d}{4}\right) + 5 c^{2} d^{3} + 16 c^{2} d \left(- \frac{i c}{4} - \frac{d}{4}\right)^{2} + 8 d^{4} \left(- \frac{i c}{4} - \frac{d}{4}\right) - 128 d^{2} \left(- \frac{i c}{4} - \frac{d}{4}\right)^{3}}{c^{5} + 4 c d^{4}} \right)} - \left(\frac{i c}{4} - \frac{d}{4}\right) \log{\left(x + \frac{- 4 c^{4} \left(\frac{i c}{4} - \frac{d}{4}\right) + 5 c^{2} d^{3} + 16 c^{2} d \left(\frac{i c}{4} - \frac{d}{4}\right)^{2} + 8 d^{4} \left(\frac{i c}{4} - \frac{d}{4}\right) - 128 d^{2} \left(\frac{i c}{4} - \frac{d}{4}\right)^{3}}{c^{5} + 4 c d^{4}} \right)}"," ",0,"(c - d)*log(x + (c**4*(c - d) + 5*c**2*d**3 + c**2*d*(c - d)**2 - 2*d**4*(c - d) + 2*d**2*(c - d)**3)/(c**5 + 4*c*d**4))/4 - (c + d)*log(x + (-c**4*(c + d) + 5*c**2*d**3 + c**2*d*(c + d)**2 + 2*d**4*(c + d) - 2*d**2*(c + d)**3)/(c**5 + 4*c*d**4))/4 - (-I*c/4 - d/4)*log(x + (-4*c**4*(-I*c/4 - d/4) + 5*c**2*d**3 + 16*c**2*d*(-I*c/4 - d/4)**2 + 8*d**4*(-I*c/4 - d/4) - 128*d**2*(-I*c/4 - d/4)**3)/(c**5 + 4*c*d**4)) - (I*c/4 - d/4)*log(x + (-4*c**4*(I*c/4 - d/4) + 5*c**2*d**3 + 16*c**2*d*(I*c/4 - d/4)**2 + 8*d**4*(I*c/4 - d/4) - 128*d**2*(I*c/4 - d/4)**3)/(c**5 + 4*c*d**4))","C",0
124,1,83,0,0.705237," ","integrate((d*x+c)/(x**4+1),x)","\operatorname{RootSum} {\left(256 t^{4} + 32 t^{2} d^{2} - 16 t c^{2} d + c^{4} + d^{4}, \left( t \mapsto t \log{\left(x + \frac{128 t^{3} d^{2} + 16 t^{2} c^{2} d + 4 t c^{4} + 8 t d^{4} - 5 c^{2} d^{3}}{c^{5} - 4 c d^{4}} \right)} \right)\right)}"," ",0,"RootSum(256*_t**4 + 32*_t**2*d**2 - 16*_t*c**2*d + c**4 + d**4, Lambda(_t, _t*log(x + (128*_t**3*d**2 + 16*_t**2*c**2*d + 4*_t*c**4 + 8*_t*d**4 - 5*c**2*d**3)/(c**5 - 4*c*d**4))))","A",0
125,1,471,0,11.043532," ","integrate((e*x**2+d*x+c)/(-b*x**4+a),x)","- \operatorname{RootSum} {\left(256 t^{4} a^{3} b^{3} + t^{2} \left(- 64 a^{2} b^{2} c e - 32 a^{2} b^{2} d^{2}\right) + t \left(- 16 a^{2} b d e^{2} - 16 a b^{2} c^{2} d\right) - a^{2} e^{4} + 2 a b c^{2} e^{2} - 4 a b c d^{2} e + a b d^{4} - b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{4} b^{2} e^{3} - 64 t^{3} a^{3} b^{3} c^{2} e + 128 t^{3} a^{3} b^{3} c d^{2} + 48 t^{2} a^{3} b^{2} c d e^{2} - 32 t^{2} a^{3} b^{2} d^{3} e - 16 t^{2} a^{2} b^{3} c^{3} d + 12 t a^{3} b c e^{4} + 12 t a^{3} b d^{2} e^{3} + 16 t a^{2} b^{2} c^{3} e^{2} - 36 t a^{2} b^{2} c^{2} d^{2} e - 8 t a^{2} b^{2} c d^{4} + 4 t a b^{3} c^{5} + 3 a^{3} d e^{5} - 5 a^{2} b c d^{3} e^{2} + 2 a^{2} b d^{5} e + 5 a b^{2} c^{4} d e - 5 a b^{2} c^{3} d^{3}}{a^{3} e^{6} + a^{2} b c^{2} e^{4} - 8 a^{2} b c d^{2} e^{3} + 4 a^{2} b d^{4} e^{2} - a b^{2} c^{4} e^{2} + 8 a b^{2} c^{3} d^{2} e - 4 a b^{2} c^{2} d^{4} - b^{3} c^{6}} \right)} \right)\right)}"," ",0,"-RootSum(256*_t**4*a**3*b**3 + _t**2*(-64*a**2*b**2*c*e - 32*a**2*b**2*d**2) + _t*(-16*a**2*b*d*e**2 - 16*a*b**2*c**2*d) - a**2*e**4 + 2*a*b*c**2*e**2 - 4*a*b*c*d**2*e + a*b*d**4 - b**2*c**4, Lambda(_t, _t*log(x + (-64*_t**3*a**4*b**2*e**3 - 64*_t**3*a**3*b**3*c**2*e + 128*_t**3*a**3*b**3*c*d**2 + 48*_t**2*a**3*b**2*c*d*e**2 - 32*_t**2*a**3*b**2*d**3*e - 16*_t**2*a**2*b**3*c**3*d + 12*_t*a**3*b*c*e**4 + 12*_t*a**3*b*d**2*e**3 + 16*_t*a**2*b**2*c**3*e**2 - 36*_t*a**2*b**2*c**2*d**2*e - 8*_t*a**2*b**2*c*d**4 + 4*_t*a*b**3*c**5 + 3*a**3*d*e**5 - 5*a**2*b*c*d**3*e**2 + 2*a**2*b*d**5*e + 5*a*b**2*c**4*d*e - 5*a*b**2*c**3*d**3)/(a**3*e**6 + a**2*b*c**2*e**4 - 8*a**2*b*c*d**2*e**3 + 4*a**2*b*d**4*e**2 - a*b**2*c**4*e**2 + 8*a*b**2*c**3*d**2*e - 4*a*b**2*c**2*d**4 - b**3*c**6))))","B",0
126,1,466,0,10.540295," ","integrate((e*x**2+d*x+c)/(b*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} b^{3} + t^{2} \left(64 a^{2} b^{2} c e + 32 a^{2} b^{2} d^{2}\right) + t \left(16 a^{2} b d e^{2} - 16 a b^{2} c^{2} d\right) + a^{2} e^{4} + 2 a b c^{2} e^{2} - 4 a b c d^{2} e + a b d^{4} + b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a^{4} b^{2} e^{3} - 64 t^{3} a^{3} b^{3} c^{2} e + 128 t^{3} a^{3} b^{3} c d^{2} + 48 t^{2} a^{3} b^{2} c d e^{2} - 32 t^{2} a^{3} b^{2} d^{3} e + 16 t^{2} a^{2} b^{3} c^{3} d + 12 t a^{3} b c e^{4} + 12 t a^{3} b d^{2} e^{3} - 16 t a^{2} b^{2} c^{3} e^{2} + 36 t a^{2} b^{2} c^{2} d^{2} e + 8 t a^{2} b^{2} c d^{4} + 4 t a b^{3} c^{5} + 3 a^{3} d e^{5} + 5 a^{2} b c d^{3} e^{2} - 2 a^{2} b d^{5} e + 5 a b^{2} c^{4} d e - 5 a b^{2} c^{3} d^{3}}{a^{3} e^{6} - a^{2} b c^{2} e^{4} + 8 a^{2} b c d^{2} e^{3} - 4 a^{2} b d^{4} e^{2} - a b^{2} c^{4} e^{2} + 8 a b^{2} c^{3} d^{2} e - 4 a b^{2} c^{2} d^{4} + b^{3} c^{6}} \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*b**3 + _t**2*(64*a**2*b**2*c*e + 32*a**2*b**2*d**2) + _t*(16*a**2*b*d*e**2 - 16*a*b**2*c**2*d) + a**2*e**4 + 2*a*b*c**2*e**2 - 4*a*b*c*d**2*e + a*b*d**4 + b**2*c**4, Lambda(_t, _t*log(x + (64*_t**3*a**4*b**2*e**3 - 64*_t**3*a**3*b**3*c**2*e + 128*_t**3*a**3*b**3*c*d**2 + 48*_t**2*a**3*b**2*c*d*e**2 - 32*_t**2*a**3*b**2*d**3*e + 16*_t**2*a**2*b**3*c**3*d + 12*_t*a**3*b*c*e**4 + 12*_t*a**3*b*d**2*e**3 - 16*_t*a**2*b**2*c**3*e**2 + 36*_t*a**2*b**2*c**2*d**2*e + 8*_t*a**2*b**2*c*d**4 + 4*_t*a*b**3*c**5 + 3*a**3*d*e**5 + 5*a**2*b*c*d**3*e**2 - 2*a**2*b*d**5*e + 5*a*b**2*c**4*d*e - 5*a*b**2*c**3*d**3)/(a**3*e**6 - a**2*b*c**2*e**4 + 8*a**2*b*c*d**2*e**3 - 4*a**2*b*d**4*e**2 - a*b**2*c**4*e**2 + 8*a*b**2*c**3*d**2*e - 4*a*b**2*c**2*d**4 + b**3*c**6))))","A",0
127,1,508,0,13.739730," ","integrate((e*x**2+d*x+c)/(-b*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{3} + t^{2} \left(- 3072 a^{4} b^{2} c e - 2048 a^{4} b^{2} d^{2}\right) + t \left(128 a^{3} b d e^{2} + 1152 a^{2} b^{2} c^{2} d\right) - a^{2} e^{4} + 18 a b c^{2} e^{2} - 48 a b c d^{2} e + 16 a b d^{4} - 81 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{4096 t^{3} a^{7} b^{2} e^{3} + 36864 t^{3} a^{6} b^{3} c^{2} e - 98304 t^{3} a^{6} b^{3} c d^{2} + 4608 t^{2} a^{5} b^{2} c d e^{2} - 4096 t^{2} a^{5} b^{2} d^{3} e - 13824 t^{2} a^{4} b^{3} c^{3} d - 144 t a^{4} b c e^{4} - 192 t a^{4} b d^{2} e^{3} - 1728 t a^{3} b^{2} c^{3} e^{2} + 5184 t a^{3} b^{2} c^{2} d^{2} e + 1536 t a^{3} b^{2} c d^{4} - 3888 t a^{2} b^{3} c^{5} + 6 a^{3} d e^{5} - 120 a^{2} b c d^{3} e^{2} + 64 a^{2} b d^{5} e + 810 a b^{2} c^{4} d e - 1080 a b^{2} c^{3} d^{3}}{a^{3} e^{6} + 9 a^{2} b c^{2} e^{4} - 96 a^{2} b c d^{2} e^{3} + 64 a^{2} b d^{4} e^{2} - 81 a b^{2} c^{4} e^{2} + 864 a b^{2} c^{3} d^{2} e - 576 a b^{2} c^{2} d^{4} - 729 b^{3} c^{6}} \right)} \right)\right)} + \frac{- c x - d x^{2} - e x^{3}}{- 4 a^{2} + 4 a b x^{4}}"," ",0,"RootSum(65536*_t**4*a**7*b**3 + _t**2*(-3072*a**4*b**2*c*e - 2048*a**4*b**2*d**2) + _t*(128*a**3*b*d*e**2 + 1152*a**2*b**2*c**2*d) - a**2*e**4 + 18*a*b*c**2*e**2 - 48*a*b*c*d**2*e + 16*a*b*d**4 - 81*b**2*c**4, Lambda(_t, _t*log(x + (4096*_t**3*a**7*b**2*e**3 + 36864*_t**3*a**6*b**3*c**2*e - 98304*_t**3*a**6*b**3*c*d**2 + 4608*_t**2*a**5*b**2*c*d*e**2 - 4096*_t**2*a**5*b**2*d**3*e - 13824*_t**2*a**4*b**3*c**3*d - 144*_t*a**4*b*c*e**4 - 192*_t*a**4*b*d**2*e**3 - 1728*_t*a**3*b**2*c**3*e**2 + 5184*_t*a**3*b**2*c**2*d**2*e + 1536*_t*a**3*b**2*c*d**4 - 3888*_t*a**2*b**3*c**5 + 6*a**3*d*e**5 - 120*a**2*b*c*d**3*e**2 + 64*a**2*b*d**5*e + 810*a*b**2*c**4*d*e - 1080*a*b**2*c**3*d**3)/(a**3*e**6 + 9*a**2*b*c**2*e**4 - 96*a**2*b*c*d**2*e**3 + 64*a**2*b*d**4*e**2 - 81*a*b**2*c**4*e**2 + 864*a*b**2*c**3*d**2*e - 576*a*b**2*c**2*d**4 - 729*b**3*c**6)))) + (-c*x - d*x**2 - e*x**3)/(-4*a**2 + 4*a*b*x**4)","B",0
128,1,505,0,11.547626," ","integrate((e*x**2+d*x+c)/(b*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{3} + t^{2} \left(3072 a^{4} b^{2} c e + 2048 a^{4} b^{2} d^{2}\right) + t \left(128 a^{3} b d e^{2} - 1152 a^{2} b^{2} c^{2} d\right) + a^{2} e^{4} + 18 a b c^{2} e^{2} - 48 a b c d^{2} e + 16 a b d^{4} + 81 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{4096 t^{3} a^{7} b^{2} e^{3} - 36864 t^{3} a^{6} b^{3} c^{2} e + 98304 t^{3} a^{6} b^{3} c d^{2} + 4608 t^{2} a^{5} b^{2} c d e^{2} - 4096 t^{2} a^{5} b^{2} d^{3} e + 13824 t^{2} a^{4} b^{3} c^{3} d + 144 t a^{4} b c e^{4} + 192 t a^{4} b d^{2} e^{3} - 1728 t a^{3} b^{2} c^{3} e^{2} + 5184 t a^{3} b^{2} c^{2} d^{2} e + 1536 t a^{3} b^{2} c d^{4} + 3888 t a^{2} b^{3} c^{5} + 6 a^{3} d e^{5} + 120 a^{2} b c d^{3} e^{2} - 64 a^{2} b d^{5} e + 810 a b^{2} c^{4} d e - 1080 a b^{2} c^{3} d^{3}}{a^{3} e^{6} - 9 a^{2} b c^{2} e^{4} + 96 a^{2} b c d^{2} e^{3} - 64 a^{2} b d^{4} e^{2} - 81 a b^{2} c^{4} e^{2} + 864 a b^{2} c^{3} d^{2} e - 576 a b^{2} c^{2} d^{4} + 729 b^{3} c^{6}} \right)} \right)\right)} + \frac{c x + d x^{2} + e x^{3}}{4 a^{2} + 4 a b x^{4}}"," ",0,"RootSum(65536*_t**4*a**7*b**3 + _t**2*(3072*a**4*b**2*c*e + 2048*a**4*b**2*d**2) + _t*(128*a**3*b*d*e**2 - 1152*a**2*b**2*c**2*d) + a**2*e**4 + 18*a*b*c**2*e**2 - 48*a*b*c*d**2*e + 16*a*b*d**4 + 81*b**2*c**4, Lambda(_t, _t*log(x + (4096*_t**3*a**7*b**2*e**3 - 36864*_t**3*a**6*b**3*c**2*e + 98304*_t**3*a**6*b**3*c*d**2 + 4608*_t**2*a**5*b**2*c*d*e**2 - 4096*_t**2*a**5*b**2*d**3*e + 13824*_t**2*a**4*b**3*c**3*d + 144*_t*a**4*b*c*e**4 + 192*_t*a**4*b*d**2*e**3 - 1728*_t*a**3*b**2*c**3*e**2 + 5184*_t*a**3*b**2*c**2*d**2*e + 1536*_t*a**3*b**2*c*d**4 + 3888*_t*a**2*b**3*c**5 + 6*a**3*d*e**5 + 120*a**2*b*c*d**3*e**2 - 64*a**2*b*d**5*e + 810*a*b**2*c**4*d*e - 1080*a*b**2*c**3*d**3)/(a**3*e**6 - 9*a**2*b*c**2*e**4 + 96*a**2*b*c*d**2*e**3 - 64*a**2*b*d**4*e**2 - 81*a*b**2*c**4*e**2 + 864*a*b**2*c**3*d**2*e - 576*a*b**2*c**2*d**4 + 729*b**3*c**6)))) + (c*x + d*x**2 + e*x**3)/(4*a**2 + 4*a*b*x**4)","A",0
129,1,563,0,45.341017," ","integrate((e*x**2+d*x+c)/(-b*x**4+a)**3,x)","- \operatorname{RootSum} {\left(268435456 t^{4} a^{11} b^{3} + t^{2} \left(- 6881280 a^{6} b^{2} c e - 4718592 a^{6} b^{2} d^{2}\right) + t \left(- 153600 a^{4} b d e^{2} - 2709504 a^{3} b^{2} c^{2} d\right) - 625 a^{2} e^{4} + 22050 a b c^{2} e^{2} - 60480 a b c d^{2} e + 20736 a b d^{4} - 194481 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 262144000 t^{3} a^{10} b^{2} e^{3} - 4624220160 t^{3} a^{9} b^{3} c^{2} e + 12683575296 t^{3} a^{9} b^{3} c d^{2} + 309657600 t^{2} a^{7} b^{2} c d e^{2} - 283115520 t^{2} a^{7} b^{2} d^{3} e - 1820786688 t^{2} a^{6} b^{3} c^{3} d + 5040000 t a^{5} b c e^{4} + 6912000 t a^{5} b d^{2} e^{3} + 118540800 t a^{4} b^{2} c^{3} e^{2} - 365783040 t a^{4} b^{2} c^{2} d^{2} e - 111476736 t a^{4} b^{2} c d^{4} + 522764928 t a^{3} b^{3} c^{5} + 112500 a^{3} d e^{5} - 4536000 a^{2} b c d^{3} e^{2} + 2488320 a^{2} b d^{5} e + 58344300 a b^{2} c^{4} d e - 80015040 a b^{2} c^{3} d^{3}}{15625 a^{3} e^{6} + 275625 a^{2} b c^{2} e^{4} - 3024000 a^{2} b c d^{2} e^{3} + 2073600 a^{2} b d^{4} e^{2} - 4862025 a b^{2} c^{4} e^{2} + 53343360 a b^{2} c^{3} d^{2} e - 36578304 a b^{2} c^{2} d^{4} - 85766121 b^{3} c^{6}} \right)} \right)\right)} - \frac{- 11 a c x - 10 a d x^{2} - 9 a e x^{3} + 7 b c x^{5} + 6 b d x^{6} + 5 b e x^{7}}{32 a^{4} - 64 a^{3} b x^{4} + 32 a^{2} b^{2} x^{8}}"," ",0,"-RootSum(268435456*_t**4*a**11*b**3 + _t**2*(-6881280*a**6*b**2*c*e - 4718592*a**6*b**2*d**2) + _t*(-153600*a**4*b*d*e**2 - 2709504*a**3*b**2*c**2*d) - 625*a**2*e**4 + 22050*a*b*c**2*e**2 - 60480*a*b*c*d**2*e + 20736*a*b*d**4 - 194481*b**2*c**4, Lambda(_t, _t*log(x + (-262144000*_t**3*a**10*b**2*e**3 - 4624220160*_t**3*a**9*b**3*c**2*e + 12683575296*_t**3*a**9*b**3*c*d**2 + 309657600*_t**2*a**7*b**2*c*d*e**2 - 283115520*_t**2*a**7*b**2*d**3*e - 1820786688*_t**2*a**6*b**3*c**3*d + 5040000*_t*a**5*b*c*e**4 + 6912000*_t*a**5*b*d**2*e**3 + 118540800*_t*a**4*b**2*c**3*e**2 - 365783040*_t*a**4*b**2*c**2*d**2*e - 111476736*_t*a**4*b**2*c*d**4 + 522764928*_t*a**3*b**3*c**5 + 112500*a**3*d*e**5 - 4536000*a**2*b*c*d**3*e**2 + 2488320*a**2*b*d**5*e + 58344300*a*b**2*c**4*d*e - 80015040*a*b**2*c**3*d**3)/(15625*a**3*e**6 + 275625*a**2*b*c**2*e**4 - 3024000*a**2*b*c*d**2*e**3 + 2073600*a**2*b*d**4*e**2 - 4862025*a*b**2*c**4*e**2 + 53343360*a*b**2*c**3*d**2*e - 36578304*a*b**2*c**2*d**4 - 85766121*b**3*c**6)))) - (-11*a*c*x - 10*a*d*x**2 - 9*a*e*x**3 + 7*b*c*x**5 + 6*b*d*x**6 + 5*b*e*x**7)/(32*a**4 - 64*a**3*b*x**4 + 32*a**2*b**2*x**8)","B",0
130,1,558,0,40.859834," ","integrate((e*x**2+d*x+c)/(b*x**4+a)**3,x)","\operatorname{RootSum} {\left(268435456 t^{4} a^{11} b^{3} + t^{2} \left(6881280 a^{6} b^{2} c e + 4718592 a^{6} b^{2} d^{2}\right) + t \left(153600 a^{4} b d e^{2} - 2709504 a^{3} b^{2} c^{2} d\right) + 625 a^{2} e^{4} + 22050 a b c^{2} e^{2} - 60480 a b c d^{2} e + 20736 a b d^{4} + 194481 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{262144000 t^{3} a^{10} b^{2} e^{3} - 4624220160 t^{3} a^{9} b^{3} c^{2} e + 12683575296 t^{3} a^{9} b^{3} c d^{2} + 309657600 t^{2} a^{7} b^{2} c d e^{2} - 283115520 t^{2} a^{7} b^{2} d^{3} e + 1820786688 t^{2} a^{6} b^{3} c^{3} d + 5040000 t a^{5} b c e^{4} + 6912000 t a^{5} b d^{2} e^{3} - 118540800 t a^{4} b^{2} c^{3} e^{2} + 365783040 t a^{4} b^{2} c^{2} d^{2} e + 111476736 t a^{4} b^{2} c d^{4} + 522764928 t a^{3} b^{3} c^{5} + 112500 a^{3} d e^{5} + 4536000 a^{2} b c d^{3} e^{2} - 2488320 a^{2} b d^{5} e + 58344300 a b^{2} c^{4} d e - 80015040 a b^{2} c^{3} d^{3}}{15625 a^{3} e^{6} - 275625 a^{2} b c^{2} e^{4} + 3024000 a^{2} b c d^{2} e^{3} - 2073600 a^{2} b d^{4} e^{2} - 4862025 a b^{2} c^{4} e^{2} + 53343360 a b^{2} c^{3} d^{2} e - 36578304 a b^{2} c^{2} d^{4} + 85766121 b^{3} c^{6}} \right)} \right)\right)} + \frac{11 a c x + 10 a d x^{2} + 9 a e x^{3} + 7 b c x^{5} + 6 b d x^{6} + 5 b e x^{7}}{32 a^{4} + 64 a^{3} b x^{4} + 32 a^{2} b^{2} x^{8}}"," ",0,"RootSum(268435456*_t**4*a**11*b**3 + _t**2*(6881280*a**6*b**2*c*e + 4718592*a**6*b**2*d**2) + _t*(153600*a**4*b*d*e**2 - 2709504*a**3*b**2*c**2*d) + 625*a**2*e**4 + 22050*a*b*c**2*e**2 - 60480*a*b*c*d**2*e + 20736*a*b*d**4 + 194481*b**2*c**4, Lambda(_t, _t*log(x + (262144000*_t**3*a**10*b**2*e**3 - 4624220160*_t**3*a**9*b**3*c**2*e + 12683575296*_t**3*a**9*b**3*c*d**2 + 309657600*_t**2*a**7*b**2*c*d*e**2 - 283115520*_t**2*a**7*b**2*d**3*e + 1820786688*_t**2*a**6*b**3*c**3*d + 5040000*_t*a**5*b*c*e**4 + 6912000*_t*a**5*b*d**2*e**3 - 118540800*_t*a**4*b**2*c**3*e**2 + 365783040*_t*a**4*b**2*c**2*d**2*e + 111476736*_t*a**4*b**2*c*d**4 + 522764928*_t*a**3*b**3*c**5 + 112500*a**3*d*e**5 + 4536000*a**2*b*c*d**3*e**2 - 2488320*a**2*b*d**5*e + 58344300*a*b**2*c**4*d*e - 80015040*a*b**2*c**3*d**3)/(15625*a**3*e**6 - 275625*a**2*b*c**2*e**4 + 3024000*a**2*b*c*d**2*e**3 - 2073600*a**2*b*d**4*e**2 - 4862025*a*b**2*c**4*e**2 + 53343360*a*b**2*c**3*d**2*e - 36578304*a*b**2*c**2*d**4 + 85766121*b**3*c**6)))) + (11*a*c*x + 10*a*d*x**2 + 9*a*e*x**3 + 7*b*c*x**5 + 6*b*d*x**6 + 5*b*e*x**7)/(32*a**4 + 64*a**3*b*x**4 + 32*a**2*b**2*x**8)","A",0
131,1,612,0,59.743887," ","integrate((e*x**2+d*x+c)/(-b*x**4+a)**4,x)","\operatorname{RootSum} {\left(68719476736 t^{4} a^{15} b^{3} + t^{2} \left(- 1211105280 a^{8} b^{2} c e - 838860800 a^{8} b^{2} d^{2}\right) + t \left(18432000 a^{5} b d e^{2} + 485703680 a^{4} b^{2} c^{2} d\right) - 50625 a^{2} e^{4} + 2668050 a b c^{2} e^{2} - 7392000 a b c d^{2} e + 2560000 a b d^{4} - 35153041 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{452984832000 t^{3} a^{13} b^{2} e^{3} + 11936653639680 t^{3} a^{12} b^{3} c^{2} e - 33071248179200 t^{3} a^{12} b^{3} c d^{2} + 544997376000 t^{2} a^{9} b^{2} c d e^{2} - 503316480000 t^{2} a^{9} b^{2} d^{3} e - 4787095470080 t^{2} a^{8} b^{3} c^{3} d - 5987520000 t a^{6} b c e^{4} - 8294400000 t a^{6} b d^{2} e^{3} - 210370406400 t a^{5} b^{2} c^{3} e^{2} + 655699968000 t a^{5} b^{2} c^{2} d^{2} e + 201850880000 t a^{5} b^{2} c d^{4} - 1385873488384 t a^{4} b^{3} c^{5} + 91125000 a^{3} d e^{5} - 5544000000 a^{2} b c d^{3} e^{2} + 3072000000 a^{2} b d^{5} e + 105459123000 a b^{2} c^{4} d e - 146090560000 a b^{2} c^{3} d^{3}}{11390625 a^{3} e^{6} + 300155625 a^{2} b c^{2} e^{4} - 3326400000 a^{2} b c d^{2} e^{3} + 2304000000 a^{2} b d^{4} e^{2} - 7909434225 a b^{2} c^{4} e^{2} + 87654336000 a b^{2} c^{3} d^{2} e - 60712960000 a b^{2} c^{2} d^{4} - 208422380089 b^{3} c^{6}} \right)} \right)\right)} + \frac{- 153 a^{2} c x - 132 a^{2} d x^{2} - 113 a^{2} e x^{3} + 198 a b c x^{5} + 160 a b d x^{6} + 126 a b e x^{7} - 77 b^{2} c x^{9} - 60 b^{2} d x^{10} - 45 b^{2} e x^{11}}{- 384 a^{6} + 1152 a^{5} b x^{4} - 1152 a^{4} b^{2} x^{8} + 384 a^{3} b^{3} x^{12}}"," ",0,"RootSum(68719476736*_t**4*a**15*b**3 + _t**2*(-1211105280*a**8*b**2*c*e - 838860800*a**8*b**2*d**2) + _t*(18432000*a**5*b*d*e**2 + 485703680*a**4*b**2*c**2*d) - 50625*a**2*e**4 + 2668050*a*b*c**2*e**2 - 7392000*a*b*c*d**2*e + 2560000*a*b*d**4 - 35153041*b**2*c**4, Lambda(_t, _t*log(x + (452984832000*_t**3*a**13*b**2*e**3 + 11936653639680*_t**3*a**12*b**3*c**2*e - 33071248179200*_t**3*a**12*b**3*c*d**2 + 544997376000*_t**2*a**9*b**2*c*d*e**2 - 503316480000*_t**2*a**9*b**2*d**3*e - 4787095470080*_t**2*a**8*b**3*c**3*d - 5987520000*_t*a**6*b*c*e**4 - 8294400000*_t*a**6*b*d**2*e**3 - 210370406400*_t*a**5*b**2*c**3*e**2 + 655699968000*_t*a**5*b**2*c**2*d**2*e + 201850880000*_t*a**5*b**2*c*d**4 - 1385873488384*_t*a**4*b**3*c**5 + 91125000*a**3*d*e**5 - 5544000000*a**2*b*c*d**3*e**2 + 3072000000*a**2*b*d**5*e + 105459123000*a*b**2*c**4*d*e - 146090560000*a*b**2*c**3*d**3)/(11390625*a**3*e**6 + 300155625*a**2*b*c**2*e**4 - 3326400000*a**2*b*c*d**2*e**3 + 2304000000*a**2*b*d**4*e**2 - 7909434225*a*b**2*c**4*e**2 + 87654336000*a*b**2*c**3*d**2*e - 60712960000*a*b**2*c**2*d**4 - 208422380089*b**3*c**6)))) + (-153*a**2*c*x - 132*a**2*d*x**2 - 113*a**2*e*x**3 + 198*a*b*c*x**5 + 160*a*b*d*x**6 + 126*a*b*e*x**7 - 77*b**2*c*x**9 - 60*b**2*d*x**10 - 45*b**2*e*x**11)/(-384*a**6 + 1152*a**5*b*x**4 - 1152*a**4*b**2*x**8 + 384*a**3*b**3*x**12)","B",0
132,1,610,0,63.469677," ","integrate((e*x**2+d*x+c)/(b*x**4+a)**4,x)","\operatorname{RootSum} {\left(68719476736 t^{4} a^{15} b^{3} + t^{2} \left(1211105280 a^{8} b^{2} c e + 838860800 a^{8} b^{2} d^{2}\right) + t \left(18432000 a^{5} b d e^{2} - 485703680 a^{4} b^{2} c^{2} d\right) + 50625 a^{2} e^{4} + 2668050 a b c^{2} e^{2} - 7392000 a b c d^{2} e + 2560000 a b d^{4} + 35153041 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{452984832000 t^{3} a^{13} b^{2} e^{3} - 11936653639680 t^{3} a^{12} b^{3} c^{2} e + 33071248179200 t^{3} a^{12} b^{3} c d^{2} + 544997376000 t^{2} a^{9} b^{2} c d e^{2} - 503316480000 t^{2} a^{9} b^{2} d^{3} e + 4787095470080 t^{2} a^{8} b^{3} c^{3} d + 5987520000 t a^{6} b c e^{4} + 8294400000 t a^{6} b d^{2} e^{3} - 210370406400 t a^{5} b^{2} c^{3} e^{2} + 655699968000 t a^{5} b^{2} c^{2} d^{2} e + 201850880000 t a^{5} b^{2} c d^{4} + 1385873488384 t a^{4} b^{3} c^{5} + 91125000 a^{3} d e^{5} + 5544000000 a^{2} b c d^{3} e^{2} - 3072000000 a^{2} b d^{5} e + 105459123000 a b^{2} c^{4} d e - 146090560000 a b^{2} c^{3} d^{3}}{11390625 a^{3} e^{6} - 300155625 a^{2} b c^{2} e^{4} + 3326400000 a^{2} b c d^{2} e^{3} - 2304000000 a^{2} b d^{4} e^{2} - 7909434225 a b^{2} c^{4} e^{2} + 87654336000 a b^{2} c^{3} d^{2} e - 60712960000 a b^{2} c^{2} d^{4} + 208422380089 b^{3} c^{6}} \right)} \right)\right)} + \frac{153 a^{2} c x + 132 a^{2} d x^{2} + 113 a^{2} e x^{3} + 198 a b c x^{5} + 160 a b d x^{6} + 126 a b e x^{7} + 77 b^{2} c x^{9} + 60 b^{2} d x^{10} + 45 b^{2} e x^{11}}{384 a^{6} + 1152 a^{5} b x^{4} + 1152 a^{4} b^{2} x^{8} + 384 a^{3} b^{3} x^{12}}"," ",0,"RootSum(68719476736*_t**4*a**15*b**3 + _t**2*(1211105280*a**8*b**2*c*e + 838860800*a**8*b**2*d**2) + _t*(18432000*a**5*b*d*e**2 - 485703680*a**4*b**2*c**2*d) + 50625*a**2*e**4 + 2668050*a*b*c**2*e**2 - 7392000*a*b*c*d**2*e + 2560000*a*b*d**4 + 35153041*b**2*c**4, Lambda(_t, _t*log(x + (452984832000*_t**3*a**13*b**2*e**3 - 11936653639680*_t**3*a**12*b**3*c**2*e + 33071248179200*_t**3*a**12*b**3*c*d**2 + 544997376000*_t**2*a**9*b**2*c*d*e**2 - 503316480000*_t**2*a**9*b**2*d**3*e + 4787095470080*_t**2*a**8*b**3*c**3*d + 5987520000*_t*a**6*b*c*e**4 + 8294400000*_t*a**6*b*d**2*e**3 - 210370406400*_t*a**5*b**2*c**3*e**2 + 655699968000*_t*a**5*b**2*c**2*d**2*e + 201850880000*_t*a**5*b**2*c*d**4 + 1385873488384*_t*a**4*b**3*c**5 + 91125000*a**3*d*e**5 + 5544000000*a**2*b*c*d**3*e**2 - 3072000000*a**2*b*d**5*e + 105459123000*a*b**2*c**4*d*e - 146090560000*a*b**2*c**3*d**3)/(11390625*a**3*e**6 - 300155625*a**2*b*c**2*e**4 + 3326400000*a**2*b*c*d**2*e**3 - 2304000000*a**2*b*d**4*e**2 - 7909434225*a*b**2*c**4*e**2 + 87654336000*a*b**2*c**3*d**2*e - 60712960000*a*b**2*c**2*d**4 + 208422380089*b**3*c**6)))) + (153*a**2*c*x + 132*a**2*d*x**2 + 113*a**2*e*x**3 + 198*a*b*c*x**5 + 160*a*b*d*x**6 + 126*a*b*e*x**7 + 77*b**2*c*x**9 + 60*b**2*d*x**10 + 45*b**2*e*x**11)/(384*a**6 + 1152*a**5*b*x**4 + 1152*a**4*b**2*x**8 + 384*a**3*b**3*x**12)","A",0
133,1,27,0,0.118824," ","integrate(a*(f*x**4+e)**2,x)","a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9}"," ",0,"a*e**2*x + 2*a*e*f*x**5/5 + a*f**2*x**9/9","A",0
134,1,29,0,0.073320," ","integrate(b*x*(f*x**4+e)**2,x)","\frac{b e^{2} x^{2}}{2} + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10}"," ",0,"b*e**2*x**2/2 + b*e*f*x**6/3 + b*f**2*x**10/10","A",0
135,1,58,0,0.109814," ","integrate((b*x+a)*(f*x**4+e)**2,x)","a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + \frac{b e^{2} x^{2}}{2} + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10}"," ",0,"a*e**2*x + 2*a*e*f*x**5/5 + a*f**2*x**9/9 + b*e**2*x**2/2 + b*e*f*x**6/3 + b*f**2*x**10/10","A",0
136,1,31,0,0.131998," ","integrate(c*x**2*(f*x**4+e)**2,x)","\frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11}"," ",0,"c*e**2*x**3/3 + 2*c*e*f*x**7/7 + c*f**2*x**11/11","A",0
137,1,60,0,0.082803," ","integrate((c*x**2+a)*(f*x**4+e)**2,x)","a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + \frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11}"," ",0,"a*e**2*x + 2*a*e*f*x**5/5 + a*f**2*x**9/9 + c*e**2*x**3/3 + 2*c*e*f*x**7/7 + c*f**2*x**11/11","A",0
138,1,61,0,0.135064," ","integrate((c*x**2+b*x)*(f*x**4+e)**2,x)","\frac{b e^{2} x^{2}}{2} + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10} + \frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11}"," ",0,"b*e**2*x**2/2 + b*e*f*x**6/3 + b*f**2*x**10/10 + c*e**2*x**3/3 + 2*c*e*f*x**7/7 + c*f**2*x**11/11","A",0
139,1,90,0,0.163258," ","integrate((c*x**2+b*x+a)*(f*x**4+e)**2,x)","a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + \frac{b e^{2} x^{2}}{2} + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10} + \frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11}"," ",0,"a*e**2*x + 2*a*e*f*x**5/5 + a*f**2*x**9/9 + b*e**2*x**2/2 + b*e*f*x**6/3 + b*f**2*x**10/10 + c*e**2*x**3/3 + 2*c*e*f*x**7/7 + c*f**2*x**11/11","A",0
140,1,29,0,0.244164," ","integrate(d*x**3*(f*x**4+e)**2,x)","\frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12}"," ",0,"d*e**2*x**4/4 + d*e*f*x**8/4 + d*f**2*x**12/12","B",0
141,1,58,0,0.077674," ","integrate((d*x**3+a)*(f*x**4+e)**2,x)","a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + \frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12}"," ",0,"a*e**2*x + 2*a*e*f*x**5/5 + a*f**2*x**9/9 + d*e**2*x**4/4 + d*e*f*x**8/4 + d*f**2*x**12/12","A",0
142,1,60,0,0.115930," ","integrate((d*x**3+b*x)*(f*x**4+e)**2,x)","\frac{b e^{2} x^{2}}{2} + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10} + \frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12}"," ",0,"b*e**2*x**2/2 + b*e*f*x**6/3 + b*f**2*x**10/10 + d*e**2*x**4/4 + d*e*f*x**8/4 + d*f**2*x**12/12","A",0
143,1,88,0,0.084539," ","integrate((d*x**3+b*x+a)*(f*x**4+e)**2,x)","a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + \frac{b e^{2} x^{2}}{2} + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10} + \frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12}"," ",0,"a*e**2*x + 2*a*e*f*x**5/5 + a*f**2*x**9/9 + b*e**2*x**2/2 + b*e*f*x**6/3 + b*f**2*x**10/10 + d*e**2*x**4/4 + d*e*f*x**8/4 + d*f**2*x**12/12","A",0
144,1,61,0,0.084933," ","integrate((d*x**3+c*x**2)*(f*x**4+e)**2,x)","\frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11} + \frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12}"," ",0,"c*e**2*x**3/3 + 2*c*e*f*x**7/7 + c*f**2*x**11/11 + d*e**2*x**4/4 + d*e*f*x**8/4 + d*f**2*x**12/12","A",0
145,1,90,0,0.146147," ","integrate((d*x**3+c*x**2+a)*(f*x**4+e)**2,x)","a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + \frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11} + \frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12}"," ",0,"a*e**2*x + 2*a*e*f*x**5/5 + a*f**2*x**9/9 + c*e**2*x**3/3 + 2*c*e*f*x**7/7 + c*f**2*x**11/11 + d*e**2*x**4/4 + d*e*f*x**8/4 + d*f**2*x**12/12","A",0
146,1,92,0,0.111516," ","integrate((d*x**3+c*x**2+b*x)*(f*x**4+e)**2,x)","\frac{b e^{2} x^{2}}{2} + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10} + \frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11} + \frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12}"," ",0,"b*e**2*x**2/2 + b*e*f*x**6/3 + b*f**2*x**10/10 + c*e**2*x**3/3 + 2*c*e*f*x**7/7 + c*f**2*x**11/11 + d*e**2*x**4/4 + d*e*f*x**8/4 + d*f**2*x**12/12","A",0
147,1,121,0,0.088927," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**2,x)","a^{2} c x + \frac{a^{2} d x^{2}}{2} + \frac{a^{2} e x^{3}}{3} + \frac{a^{2} f x^{4}}{4} + \frac{2 a b c x^{5}}{5} + \frac{a b d x^{6}}{3} + \frac{2 a b e x^{7}}{7} + \frac{a b f x^{8}}{4} + \frac{b^{2} c x^{9}}{9} + \frac{b^{2} d x^{10}}{10} + \frac{b^{2} e x^{11}}{11} + \frac{b^{2} f x^{12}}{12}"," ",0,"a**2*c*x + a**2*d*x**2/2 + a**2*e*x**3/3 + a**2*f*x**4/4 + 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**2*c*x**9/9 + b**2*d*x**10/10 + b**2*e*x**11/11 + b**2*f*x**12/12","A",0
148,1,180,0,0.132923," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**3,x)","a^{3} c x + \frac{a^{3} d x^{2}}{2} + \frac{a^{3} e x^{3}}{3} + \frac{a^{3} f x^{4}}{4} + \frac{3 a^{2} b c x^{5}}{5} + \frac{a^{2} b d x^{6}}{2} + \frac{3 a^{2} b e x^{7}}{7} + \frac{3 a^{2} b f x^{8}}{8} + \frac{a b^{2} c x^{9}}{3} + \frac{3 a b^{2} d x^{10}}{10} + \frac{3 a b^{2} e x^{11}}{11} + \frac{a b^{2} f x^{12}}{4} + \frac{b^{3} c x^{13}}{13} + \frac{b^{3} d x^{14}}{14} + \frac{b^{3} e x^{15}}{15} + \frac{b^{3} f x^{16}}{16}"," ",0,"a**3*c*x + a**3*d*x**2/2 + a**3*e*x**3/3 + a**3*f*x**4/4 + 3*a**2*b*c*x**5/5 + a**2*b*d*x**6/2 + 3*a**2*b*e*x**7/7 + 3*a**2*b*f*x**8/8 + a*b**2*c*x**9/3 + 3*a*b**2*d*x**10/10 + 3*a*b**2*e*x**11/11 + a*b**2*f*x**12/4 + b**3*c*x**13/13 + b**3*d*x**14/14 + b**3*e*x**15/15 + b**3*f*x**16/16","A",0
149,1,520,0,24.168904," ","integrate((f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{3} + t^{2} \left(- 3072 a^{4} b^{2} c e - 2048 a^{4} b^{2} d^{2}\right) + t \left(128 a^{3} b d e^{2} + 1152 a^{2} b^{2} c^{2} d\right) - a^{2} e^{4} + 18 a b c^{2} e^{2} - 48 a b c d^{2} e + 16 a b d^{4} - 81 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{4096 t^{3} a^{7} b^{2} e^{3} + 36864 t^{3} a^{6} b^{3} c^{2} e - 98304 t^{3} a^{6} b^{3} c d^{2} + 4608 t^{2} a^{5} b^{2} c d e^{2} - 4096 t^{2} a^{5} b^{2} d^{3} e - 13824 t^{2} a^{4} b^{3} c^{3} d - 144 t a^{4} b c e^{4} - 192 t a^{4} b d^{2} e^{3} - 1728 t a^{3} b^{2} c^{3} e^{2} + 5184 t a^{3} b^{2} c^{2} d^{2} e + 1536 t a^{3} b^{2} c d^{4} - 3888 t a^{2} b^{3} c^{5} + 6 a^{3} d e^{5} - 120 a^{2} b c d^{3} e^{2} + 64 a^{2} b d^{5} e + 810 a b^{2} c^{4} d e - 1080 a b^{2} c^{3} d^{3}}{a^{3} e^{6} + 9 a^{2} b c^{2} e^{4} - 96 a^{2} b c d^{2} e^{3} + 64 a^{2} b d^{4} e^{2} - 81 a b^{2} c^{4} e^{2} + 864 a b^{2} c^{3} d^{2} e - 576 a b^{2} c^{2} d^{4} - 729 b^{3} c^{6}} \right)} \right)\right)} + \frac{- a f - b c x - b d x^{2} - b e x^{3}}{- 4 a^{2} b + 4 a b^{2} x^{4}}"," ",0,"RootSum(65536*_t**4*a**7*b**3 + _t**2*(-3072*a**4*b**2*c*e - 2048*a**4*b**2*d**2) + _t*(128*a**3*b*d*e**2 + 1152*a**2*b**2*c**2*d) - a**2*e**4 + 18*a*b*c**2*e**2 - 48*a*b*c*d**2*e + 16*a*b*d**4 - 81*b**2*c**4, Lambda(_t, _t*log(x + (4096*_t**3*a**7*b**2*e**3 + 36864*_t**3*a**6*b**3*c**2*e - 98304*_t**3*a**6*b**3*c*d**2 + 4608*_t**2*a**5*b**2*c*d*e**2 - 4096*_t**2*a**5*b**2*d**3*e - 13824*_t**2*a**4*b**3*c**3*d - 144*_t*a**4*b*c*e**4 - 192*_t*a**4*b*d**2*e**3 - 1728*_t*a**3*b**2*c**3*e**2 + 5184*_t*a**3*b**2*c**2*d**2*e + 1536*_t*a**3*b**2*c*d**4 - 3888*_t*a**2*b**3*c**5 + 6*a**3*d*e**5 - 120*a**2*b*c*d**3*e**2 + 64*a**2*b*d**5*e + 810*a*b**2*c**4*d*e - 1080*a*b**2*c**3*d**3)/(a**3*e**6 + 9*a**2*b*c**2*e**4 - 96*a**2*b*c*d**2*e**3 + 64*a**2*b*d**4*e**2 - 81*a*b**2*c**4*e**2 + 864*a*b**2*c**3*d**2*e - 576*a*b**2*c**2*d**4 - 729*b**3*c**6)))) + (-a*f - b*c*x - b*d*x**2 - b*e*x**3)/(-4*a**2*b + 4*a*b**2*x**4)","B",0
150,1,583,0,116.916471," ","integrate((f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**3,x)","- \operatorname{RootSum} {\left(268435456 t^{4} a^{11} b^{3} + t^{2} \left(- 6881280 a^{6} b^{2} c e - 4718592 a^{6} b^{2} d^{2}\right) + t \left(- 153600 a^{4} b d e^{2} - 2709504 a^{3} b^{2} c^{2} d\right) - 625 a^{2} e^{4} + 22050 a b c^{2} e^{2} - 60480 a b c d^{2} e + 20736 a b d^{4} - 194481 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 262144000 t^{3} a^{10} b^{2} e^{3} - 4624220160 t^{3} a^{9} b^{3} c^{2} e + 12683575296 t^{3} a^{9} b^{3} c d^{2} + 309657600 t^{2} a^{7} b^{2} c d e^{2} - 283115520 t^{2} a^{7} b^{2} d^{3} e - 1820786688 t^{2} a^{6} b^{3} c^{3} d + 5040000 t a^{5} b c e^{4} + 6912000 t a^{5} b d^{2} e^{3} + 118540800 t a^{4} b^{2} c^{3} e^{2} - 365783040 t a^{4} b^{2} c^{2} d^{2} e - 111476736 t a^{4} b^{2} c d^{4} + 522764928 t a^{3} b^{3} c^{5} + 112500 a^{3} d e^{5} - 4536000 a^{2} b c d^{3} e^{2} + 2488320 a^{2} b d^{5} e + 58344300 a b^{2} c^{4} d e - 80015040 a b^{2} c^{3} d^{3}}{15625 a^{3} e^{6} + 275625 a^{2} b c^{2} e^{4} - 3024000 a^{2} b c d^{2} e^{3} + 2073600 a^{2} b d^{4} e^{2} - 4862025 a b^{2} c^{4} e^{2} + 53343360 a b^{2} c^{3} d^{2} e - 36578304 a b^{2} c^{2} d^{4} - 85766121 b^{3} c^{6}} \right)} \right)\right)} - \frac{- 4 a^{2} f - 11 a b c x - 10 a b d x^{2} - 9 a b e x^{3} + 7 b^{2} c x^{5} + 6 b^{2} d x^{6} + 5 b^{2} e x^{7}}{32 a^{4} b - 64 a^{3} b^{2} x^{4} + 32 a^{2} b^{3} x^{8}}"," ",0,"-RootSum(268435456*_t**4*a**11*b**3 + _t**2*(-6881280*a**6*b**2*c*e - 4718592*a**6*b**2*d**2) + _t*(-153600*a**4*b*d*e**2 - 2709504*a**3*b**2*c**2*d) - 625*a**2*e**4 + 22050*a*b*c**2*e**2 - 60480*a*b*c*d**2*e + 20736*a*b*d**4 - 194481*b**2*c**4, Lambda(_t, _t*log(x + (-262144000*_t**3*a**10*b**2*e**3 - 4624220160*_t**3*a**9*b**3*c**2*e + 12683575296*_t**3*a**9*b**3*c*d**2 + 309657600*_t**2*a**7*b**2*c*d*e**2 - 283115520*_t**2*a**7*b**2*d**3*e - 1820786688*_t**2*a**6*b**3*c**3*d + 5040000*_t*a**5*b*c*e**4 + 6912000*_t*a**5*b*d**2*e**3 + 118540800*_t*a**4*b**2*c**3*e**2 - 365783040*_t*a**4*b**2*c**2*d**2*e - 111476736*_t*a**4*b**2*c*d**4 + 522764928*_t*a**3*b**3*c**5 + 112500*a**3*d*e**5 - 4536000*a**2*b*c*d**3*e**2 + 2488320*a**2*b*d**5*e + 58344300*a*b**2*c**4*d*e - 80015040*a*b**2*c**3*d**3)/(15625*a**3*e**6 + 275625*a**2*b*c**2*e**4 - 3024000*a**2*b*c*d**2*e**3 + 2073600*a**2*b*d**4*e**2 - 4862025*a*b**2*c**4*e**2 + 53343360*a*b**2*c**3*d**2*e - 36578304*a*b**2*c**2*d**4 - 85766121*b**3*c**6)))) - (-4*a**2*f - 11*a*b*c*x - 10*a*b*d*x**2 - 9*a*b*e*x**3 + 7*b**2*c*x**5 + 6*b**2*d*x**6 + 5*b**2*e*x**7)/(32*a**4*b - 64*a**3*b**2*x**4 + 32*a**2*b**3*x**8)","B",0
151,-1,0,0,0.000000," ","integrate((f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,1,88,0,0.441343," ","integrate(a/(3*x**4+2),x)","a \left(- \frac{6^{\frac{3}{4}} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{48} + \frac{6^{\frac{3}{4}} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{48} + \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{24} + \frac{6^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{24}\right)"," ",0,"a*(-6**(3/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/48 + 6**(3/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/48 + 6**(3/4)*atan(6**(1/4)*x - 1)/24 + 6**(3/4)*atan(6**(1/4)*x + 1)/24)","A",0
153,1,19,0,0.134378," ","integrate(b*x/(3*x**4+2),x)","\frac{\sqrt{6} b \operatorname{atan}{\left(\frac{\sqrt{6} x^{2}}{2} \right)}}{12}"," ",0,"sqrt(6)*b*atan(sqrt(6)*x**2/2)/12","A",0
154,1,88,0,0.716885," ","integrate((b*x+a)/(3*x**4+2),x)","\operatorname{RootSum} {\left(18432 t^{4} + 384 t^{2} b^{2} - 96 t a^{2} b + 3 a^{4} + 2 b^{4}, \left( t \mapsto t \log{\left(x + \frac{3072 t^{3} b^{2} + 192 t^{2} a^{2} b + 24 t a^{4} + 32 t b^{4} - 10 a^{2} b^{3}}{3 a^{5} - 8 a b^{4}} \right)} \right)\right)}"," ",0,"RootSum(18432*_t**4 + 384*_t**2*b**2 - 96*_t*a**2*b + 3*a**4 + 2*b**4, Lambda(_t, _t*log(x + (3072*_t**3*b**2 + 192*_t**2*a**2*b + 24*_t*a**4 + 32*_t*b**4 - 10*a**2*b**3)/(3*a**5 - 8*a*b**4))))","A",0
155,1,88,0,0.430309," ","integrate(c*x**2/(3*x**4+2),x)","c \left(\frac{\sqrt[4]{6} \log{\left(x^{2} - \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{24} - \frac{\sqrt[4]{6} \log{\left(x^{2} + \frac{6^{\frac{3}{4}} x}{3} + \frac{\sqrt{6}}{3} \right)}}{24} + \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x - 1 \right)}}{12} + \frac{\sqrt[4]{6} \operatorname{atan}{\left(\sqrt[4]{6} x + 1 \right)}}{12}\right)"," ",0,"c*(6**(1/4)*log(x**2 - 6**(3/4)*x/3 + sqrt(6)/3)/24 - 6**(1/4)*log(x**2 + 6**(3/4)*x/3 + sqrt(6)/3)/24 + 6**(1/4)*atan(6**(1/4)*x - 1)/12 + 6**(1/4)*atan(6**(1/4)*x + 1)/12)","A",0
156,1,68,0,0.572835," ","integrate((c*x**2+a)/(3*x**4+2),x)","\operatorname{RootSum} {\left(55296 t^{4} + 2304 t^{2} a c + 9 a^{4} + 12 a^{2} c^{2} + 4 c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 4608 t^{3} c + 72 t a^{3} - 144 t a c^{2}}{9 a^{4} - 4 c^{4}} \right)} \right)\right)}"," ",0,"RootSum(55296*_t**4 + 2304*_t**2*a*c + 9*a**4 + 12*a**2*c**2 + 4*c**4, Lambda(_t, _t*log(x + (-4608*_t**3*c + 72*_t*a**3 - 144*_t*a*c**2)/(9*a**4 - 4*c**4))))","A",0
157,1,85,0,0.770337," ","integrate((c*x**2+b*x)/(3*x**4+2),x)","\operatorname{RootSum} {\left(27648 t^{4} + 576 t^{2} b^{2} + 96 t b c^{2} + 3 b^{4} + 2 c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 1152 t^{3} c^{2} + 288 t^{2} b^{3} - 36 t b^{2} c^{2} + 3 b^{5} - 3 b c^{4}}{6 b^{4} c - c^{5}} \right)} \right)\right)}"," ",0,"RootSum(27648*_t**4 + 576*_t**2*b**2 + 96*_t*b*c**2 + 3*b**4 + 2*c**4, Lambda(_t, _t*log(x + (-1152*_t**3*c**2 + 288*_t**2*b**3 - 36*_t*b**2*c**2 + 3*b**5 - 3*b*c**4)/(6*b**4*c - c**5))))","A",0
158,1,292,0,5.070420," ","integrate((c*x**2+b*x+a)/(3*x**4+2),x)","\operatorname{RootSum} {\left(55296 t^{4} + t^{2} \left(2304 a c + 1152 b^{2}\right) + t \left(- 288 a^{2} b + 192 b c^{2}\right) + 9 a^{4} + 12 a^{2} c^{2} - 24 a b^{2} c + 6 b^{4} + 4 c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 13824 t^{3} a^{2} c + 27648 t^{3} a b^{2} + 9216 t^{3} c^{3} + 1728 t^{2} a^{3} b + 3456 t^{2} a b c^{2} - 2304 t^{2} b^{3} c + 216 t a^{5} - 576 t a^{3} c^{2} + 1296 t a^{2} b^{2} c + 288 t a b^{4} + 288 t a c^{4} + 288 t b^{2} c^{3} + 90 a^{4} b c - 90 a^{3} b^{3} + 60 a b^{3} c^{2} - 24 b^{5} c + 24 b c^{5}}{27 a^{6} - 18 a^{4} c^{2} + 144 a^{3} b^{2} c - 72 a^{2} b^{4} - 12 a^{2} c^{4} + 96 a b^{2} c^{3} - 48 b^{4} c^{2} + 8 c^{6}} \right)} \right)\right)}"," ",0,"RootSum(55296*_t**4 + _t**2*(2304*a*c + 1152*b**2) + _t*(-288*a**2*b + 192*b*c**2) + 9*a**4 + 12*a**2*c**2 - 24*a*b**2*c + 6*b**4 + 4*c**4, Lambda(_t, _t*log(x + (-13824*_t**3*a**2*c + 27648*_t**3*a*b**2 + 9216*_t**3*c**3 + 1728*_t**2*a**3*b + 3456*_t**2*a*b*c**2 - 2304*_t**2*b**3*c + 216*_t*a**5 - 576*_t*a**3*c**2 + 1296*_t*a**2*b**2*c + 288*_t*a*b**4 + 288*_t*a*c**4 + 288*_t*b**2*c**3 + 90*a**4*b*c - 90*a**3*b**3 + 60*a*b**3*c**2 - 24*b**5*c + 24*b*c**5)/(27*a**6 - 18*a**4*c**2 + 144*a**3*b**2*c - 72*a**2*b**4 - 12*a**2*c**4 + 96*a*b**2*c**3 - 48*b**4*c**2 + 8*c**6))))","B",0
159,1,10,0,0.094359," ","integrate(d*x**3/(3*x**4+2),x)","\frac{d \log{\left(3 x^{4} + 2 \right)}}{12}"," ",0,"d*log(3*x**4 + 2)/12","A",0
160,1,51,0,0.417142," ","integrate((d*x**3+a)/(3*x**4+2),x)","\operatorname{RootSum} {\left(165888 t^{4} - 55296 t^{3} d + 6912 t^{2} d^{2} - 384 t d^{3} + 27 a^{4} + 8 d^{4}, \left( t \mapsto t \log{\left(x + \frac{24 t - 2 d}{3 a} \right)} \right)\right)}"," ",0,"RootSum(165888*_t**4 - 55296*_t**3*d + 6912*_t**2*d**2 - 384*_t*d**3 + 27*a**4 + 8*d**4, Lambda(_t, _t*log(x + (24*_t - 2*d)/(3*a))))","A",0
161,1,53,0,0.410795," ","integrate((d*x**3+b*x)/(3*x**4+2),x)","\left(- \frac{\sqrt{6} i b}{24} + \frac{d}{12}\right) \log{\left(x^{2} - \frac{\sqrt{6} i}{3} \right)} + \left(\frac{\sqrt{6} i b}{24} + \frac{d}{12}\right) \log{\left(x^{2} + \frac{\sqrt{6} i}{3} \right)}"," ",0,"(-sqrt(6)*I*b/24 + d/12)*log(x**2 - sqrt(6)*I/3) + (sqrt(6)*I*b/24 + d/12)*log(x**2 + sqrt(6)*I/3)","C",0
162,1,199,0,1.683720," ","integrate((d*x**3+b*x+a)/(3*x**4+2),x)","\operatorname{RootSum} {\left(165888 t^{4} - 55296 t^{3} d + t^{2} \left(3456 b^{2} + 6912 d^{2}\right) + t \left(- 864 a^{2} b - 576 b^{2} d - 384 d^{3}\right) + 27 a^{4} + 72 a^{2} b d + 18 b^{4} + 24 b^{2} d^{2} + 8 d^{4}, \left( t \mapsto t \log{\left(x + \frac{27648 t^{3} b^{2} + 1728 t^{2} a^{2} b - 6912 t^{2} b^{2} d + 216 t a^{4} - 288 t a^{2} b d + 288 t b^{4} + 576 t b^{2} d^{2} - 18 a^{4} d - 90 a^{2} b^{3} + 12 a^{2} b d^{2} - 24 b^{4} d - 16 b^{2} d^{3}}{27 a^{5} - 72 a b^{4}} \right)} \right)\right)}"," ",0,"RootSum(165888*_t**4 - 55296*_t**3*d + _t**2*(3456*b**2 + 6912*d**2) + _t*(-864*a**2*b - 576*b**2*d - 384*d**3) + 27*a**4 + 72*a**2*b*d + 18*b**4 + 24*b**2*d**2 + 8*d**4, Lambda(_t, _t*log(x + (27648*_t**3*b**2 + 1728*_t**2*a**2*b - 6912*_t**2*b**2*d + 216*_t*a**4 - 288*_t*a**2*b*d + 288*_t*b**4 + 576*_t*b**2*d**2 - 18*a**4*d - 90*a**2*b**3 + 12*a**2*b*d**2 - 24*b**4*d - 16*b**2*d**3)/(27*a**5 - 72*a*b**4))))","A",0
163,1,70,0,0.421917," ","integrate((d*x**3+c*x**2)/(3*x**4+2),x)","\operatorname{RootSum} {\left(41472 t^{4} - 13824 t^{3} d + 1728 t^{2} d^{2} - 96 t d^{3} + 3 c^{4} + 2 d^{4}, \left( t \mapsto t \log{\left(x + \frac{3456 t^{3} - 864 t^{2} d + 72 t d^{2} - 2 d^{3}}{3 c^{3}} \right)} \right)\right)}"," ",0,"RootSum(41472*_t**4 - 13824*_t**3*d + 1728*_t**2*d**2 - 96*_t*d**3 + 3*c**4 + 2*d**4, Lambda(_t, _t*log(x + (3456*_t**3 - 864*_t**2*d + 72*_t*d**2 - 2*d**3)/(3*c**3))))","A",0
164,1,148,0,1.379261," ","integrate((d*x**3+c*x**2+a)/(3*x**4+2),x)","\operatorname{RootSum} {\left(165888 t^{4} - 55296 t^{3} d + t^{2} \left(6912 a c + 6912 d^{2}\right) + t \left(- 1152 a c d - 384 d^{3}\right) + 27 a^{4} + 36 a^{2} c^{2} + 48 a c d^{2} + 12 c^{4} + 8 d^{4}, \left( t \mapsto t \log{\left(x + \frac{- 13824 t^{3} c + 3456 t^{2} c d + 216 t a^{3} - 432 t a c^{2} - 288 t c d^{2} - 18 a^{3} d + 36 a c^{2} d + 8 c d^{3}}{27 a^{4} - 12 c^{4}} \right)} \right)\right)}"," ",0,"RootSum(165888*_t**4 - 55296*_t**3*d + _t**2*(6912*a*c + 6912*d**2) + _t*(-1152*a*c*d - 384*d**3) + 27*a**4 + 36*a**2*c**2 + 48*a*c*d**2 + 12*c**4 + 8*d**4, Lambda(_t, _t*log(x + (-13824*_t**3*c + 3456*_t**2*c*d + 216*_t*a**3 - 432*_t*a*c**2 - 288*_t*c*d**2 - 18*a**3*d + 36*a*c**2*d + 8*c*d**3)/(27*a**4 - 12*c**4))))","A",0
165,1,189,0,1.990583," ","integrate((d*x**3+c*x**2+b*x)/(3*x**4+2),x)","\operatorname{RootSum} {\left(82944 t^{4} - 27648 t^{3} d + t^{2} \left(1728 b^{2} + 3456 d^{2}\right) + t \left(- 288 b^{2} d + 288 b c^{2} - 192 d^{3}\right) + 9 b^{4} + 12 b^{2} d^{2} - 24 b c^{2} d + 6 c^{4} + 4 d^{4}, \left( t \mapsto t \log{\left(x + \frac{- 3456 t^{3} c^{2} + 864 t^{2} b^{3} + 864 t^{2} c^{2} d - 144 t b^{3} d - 108 t b^{2} c^{2} - 72 t c^{2} d^{2} + 9 b^{5} + 6 b^{3} d^{2} + 9 b^{2} c^{2} d - 9 b c^{4} + 2 c^{2} d^{3}}{18 b^{4} c - 3 c^{5}} \right)} \right)\right)}"," ",0,"RootSum(82944*_t**4 - 27648*_t**3*d + _t**2*(1728*b**2 + 3456*d**2) + _t*(-288*b**2*d + 288*b*c**2 - 192*d**3) + 9*b**4 + 12*b**2*d**2 - 24*b*c**2*d + 6*c**4 + 4*d**4, Lambda(_t, _t*log(x + (-3456*_t**3*c**2 + 864*_t**2*b**3 + 864*_t**2*c**2*d - 144*_t*b**3*d - 108*_t*b**2*c**2 - 72*_t*c**2*d**2 + 9*b**5 + 6*b**3*d**2 + 9*b**2*c**2*d - 9*b*c**4 + 2*c**2*d**3)/(18*b**4*c - 3*c**5))))","A",0
166,1,580,0,13.068488," ","integrate((d*x**3+c*x**2+b*x+a)/(3*x**4+2),x)","\operatorname{RootSum} {\left(165888 t^{4} - 55296 t^{3} d + t^{2} \left(6912 a c + 3456 b^{2} + 6912 d^{2}\right) + t \left(- 864 a^{2} b - 1152 a c d - 576 b^{2} d + 576 b c^{2} - 384 d^{3}\right) + 27 a^{4} + 72 a^{2} b d + 36 a^{2} c^{2} - 72 a b^{2} c + 48 a c d^{2} + 18 b^{4} + 24 b^{2} d^{2} - 48 b c^{2} d + 12 c^{4} + 8 d^{4}, \left( t \mapsto t \log{\left(x + \frac{- 41472 t^{3} a^{2} c + 82944 t^{3} a b^{2} + 27648 t^{3} c^{3} + 5184 t^{2} a^{3} b + 10368 t^{2} a^{2} c d - 20736 t^{2} a b^{2} d + 10368 t^{2} a b c^{2} - 6912 t^{2} b^{3} c - 6912 t^{2} c^{3} d + 648 t a^{5} - 864 t a^{3} b d - 1728 t a^{3} c^{2} + 3888 t a^{2} b^{2} c - 864 t a^{2} c d^{2} + 864 t a b^{4} + 1728 t a b^{2} d^{2} - 1728 t a b c^{2} d + 864 t a c^{4} + 1152 t b^{3} c d + 864 t b^{2} c^{3} + 576 t c^{3} d^{2} - 54 a^{5} d + 270 a^{4} b c - 270 a^{3} b^{3} + 36 a^{3} b d^{2} + 144 a^{3} c^{2} d - 324 a^{2} b^{2} c d + 24 a^{2} c d^{3} - 72 a b^{4} d + 180 a b^{3} c^{2} - 48 a b^{2} d^{3} + 72 a b c^{2} d^{2} - 72 a c^{4} d - 72 b^{5} c - 48 b^{3} c d^{2} - 72 b^{2} c^{3} d + 72 b c^{5} - 16 c^{3} d^{3}}{81 a^{6} - 54 a^{4} c^{2} + 432 a^{3} b^{2} c - 216 a^{2} b^{4} - 36 a^{2} c^{4} + 288 a b^{2} c^{3} - 144 b^{4} c^{2} + 24 c^{6}} \right)} \right)\right)}"," ",0,"RootSum(165888*_t**4 - 55296*_t**3*d + _t**2*(6912*a*c + 3456*b**2 + 6912*d**2) + _t*(-864*a**2*b - 1152*a*c*d - 576*b**2*d + 576*b*c**2 - 384*d**3) + 27*a**4 + 72*a**2*b*d + 36*a**2*c**2 - 72*a*b**2*c + 48*a*c*d**2 + 18*b**4 + 24*b**2*d**2 - 48*b*c**2*d + 12*c**4 + 8*d**4, Lambda(_t, _t*log(x + (-41472*_t**3*a**2*c + 82944*_t**3*a*b**2 + 27648*_t**3*c**3 + 5184*_t**2*a**3*b + 10368*_t**2*a**2*c*d - 20736*_t**2*a*b**2*d + 10368*_t**2*a*b*c**2 - 6912*_t**2*b**3*c - 6912*_t**2*c**3*d + 648*_t*a**5 - 864*_t*a**3*b*d - 1728*_t*a**3*c**2 + 3888*_t*a**2*b**2*c - 864*_t*a**2*c*d**2 + 864*_t*a*b**4 + 1728*_t*a*b**2*d**2 - 1728*_t*a*b*c**2*d + 864*_t*a*c**4 + 1152*_t*b**3*c*d + 864*_t*b**2*c**3 + 576*_t*c**3*d**2 - 54*a**5*d + 270*a**4*b*c - 270*a**3*b**3 + 36*a**3*b*d**2 + 144*a**3*c**2*d - 324*a**2*b**2*c*d + 24*a**2*c*d**3 - 72*a*b**4*d + 180*a*b**3*c**2 - 48*a*b**2*d**3 + 72*a*b*c**2*d**2 - 72*a*c**4*d - 72*b**5*c - 48*b**3*c*d**2 - 72*b**2*c**3*d + 72*b*c**5 - 16*c**3*d**3)/(81*a**6 - 54*a**4*c**2 + 432*a**3*b**2*c - 216*a**2*b**4 - 36*a**2*c**4 + 288*a*b**2*c**3 - 144*b**4*c**2 + 24*c**6))))","B",0
167,1,5,0,0.073116," ","integrate((x**3+x**2+x+1)/(-x**4+1),x)","- \log{\left(x - 1 \right)}"," ",0,"-log(x - 1)","A",0
168,1,73,0,0.426679," ","integrate((x**3+x**2+x+1)/(x**4+1),x)","\frac{\log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{4} + \frac{\log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{4} + 2 \left(\frac{1}{4} + \frac{\sqrt{2}}{4}\right) \operatorname{atan}{\left(\sqrt{2} x - 1 \right)} + 2 \left(- \frac{1}{4} + \frac{\sqrt{2}}{4}\right) \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}"," ",0,"log(x**2 - sqrt(2)*x + 1)/4 + log(x**2 + sqrt(2)*x + 1)/4 + 2*(1/4 + sqrt(2)/4)*atan(sqrt(2)*x - 1) + 2*(-1/4 + sqrt(2)/4)*atan(sqrt(2)*x + 1)","A",0
169,1,187,0,2.277697," ","integrate((x**3+x**2+x+1)/(-b*x**4+a),x)","- \operatorname{RootSum} {\left(256 t^{4} a^{3} b^{4} - 256 t^{3} a^{3} b^{3} + t^{2} \left(96 a^{3} b^{2} - 96 a^{2} b^{3}\right) + t \left(- 16 a^{3} b + 32 a^{2} b^{2} - 16 a b^{3}\right) + a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{3} b^{3} + 48 t^{2} a^{3} b^{2} + 16 t^{2} a^{2} b^{3} - 12 t a^{3} b + 16 t a^{2} b^{2} - 4 t a b^{3} + a^{3} - 2 a^{2} b + a b^{2}}{a^{2} b - 2 a b^{2} + b^{3}} \right)} \right)\right)}"," ",0,"-RootSum(256*_t**4*a**3*b**4 - 256*_t**3*a**3*b**3 + _t**2*(96*a**3*b**2 - 96*a**2*b**3) + _t*(-16*a**3*b + 32*a**2*b**2 - 16*a*b**3) + a**3 - 3*a**2*b + 3*a*b**2 - b**3, Lambda(_t, _t*log(x + (-64*_t**3*a**3*b**3 + 48*_t**2*a**3*b**2 + 16*_t**2*a**2*b**3 - 12*_t*a**3*b + 16*_t*a**2*b**2 - 4*_t*a*b**3 + a**3 - 2*a**2*b + a*b**2)/(a**2*b - 2*a*b**2 + b**3))))","A",0
170,1,187,0,2.267826," ","integrate((x**3+x**2+x+1)/(b*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} b^{4} - 256 t^{3} a^{3} b^{3} + t^{2} \left(96 a^{3} b^{2} + 96 a^{2} b^{3}\right) + t \left(- 16 a^{3} b - 32 a^{2} b^{2} - 16 a b^{3}\right) + a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a^{3} b^{3} - 48 t^{2} a^{3} b^{2} + 16 t^{2} a^{2} b^{3} + 12 t a^{3} b + 16 t a^{2} b^{2} + 4 t a b^{3} - a^{3} - 2 a^{2} b - a b^{2}}{a^{2} b + 2 a b^{2} + b^{3}} \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*b**4 - 256*_t**3*a**3*b**3 + _t**2*(96*a**3*b**2 + 96*a**2*b**3) + _t*(-16*a**3*b - 32*a**2*b**2 - 16*a*b**3) + a**3 + 3*a**2*b + 3*a*b**2 + b**3, Lambda(_t, _t*log(x + (64*_t**3*a**3*b**3 - 48*_t**2*a**3*b**2 + 16*_t**2*a**2*b**3 + 12*_t*a**3*b + 16*_t*a**2*b**2 + 4*_t*a*b**3 - a**3 - 2*a**2*b - a*b**2)/(a**2*b + 2*a*b**2 + b**3))))","A",0
171,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,1,15,0,0.092668," ","integrate((-x**4+1)**3/(x**3+x**2+x+1)**3,x)","- \frac{x^{4}}{4} + x^{3} - \frac{3 x^{2}}{2} + x"," ",0,"-x**4/4 + x**3 - 3*x**2/2 + x","B",0
180,1,8,0,0.081595," ","integrate((-x**4+1)**2/(x**3+x**2+x+1)**2,x)","\frac{x^{3}}{3} - x^{2} + x"," ",0,"x**3/3 - x**2 + x","A",0
181,1,5,0,0.069599," ","integrate((-x**4+1)/(x**3+x**2+x+1),x)","- \frac{x^{2}}{2} + x"," ",0,"-x**2/2 + x","A",0
182,1,5,0,0.072957," ","integrate((x**3+x**2+x+1)/(-x**4+1),x)","- \log{\left(x - 1 \right)}"," ",0,"-log(x - 1)","A",0
183,1,5,0,0.106795," ","integrate((x**3+x**2+x+1)**2/(-x**4+1)**2,x)","- \frac{1}{x - 1}"," ",0,"-1/(x - 1)","A",0
184,1,10,0,0.209735," ","integrate((x**3+x**2+x+1)**3/(-x**4+1)**3,x)","\frac{1}{2 x^{2} - 4 x + 2}"," ",0,"1/(2*x**2 - 4*x + 2)","A",0
185,1,17,0,0.149793," ","integrate((x**3+x**2+x+1)**4/(-x**4+1)**4,x)","- \frac{1}{3 x^{3} - 9 x^{2} + 9 x - 3}"," ",0,"-1/(3*x**3 - 9*x**2 + 9*x - 3)","B",0
186,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate((j*x**7+i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate((i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate((j*x**7+i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate((i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate((j*x**7+i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate((i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate((j*x**7+i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate((i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate((j*x**7+i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate((i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate((j*x**7+i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate((i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate((j*x**7+i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(-b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate((i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate((j*x**7+i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,1,61,0,2.981276," ","integrate((d*x+c)/(b*x**4+a)**(1/2),x)","\frac{d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"d*asinh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)) + c*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4))","C",0
211,1,95,0,2.958042," ","integrate((d*x+c)/(-b*x**4+a)**(1/2),x)","d \left(\begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} & \text{for}\: \left|{\frac{b x^{4}}{a}}\right| > 1 \\\frac{\operatorname{asin}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} & \text{otherwise} \end{cases}\right) + \frac{c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"d*Piecewise((-I*acosh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)), Abs(b*x**4/a) > 1), (asin(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)), True)) + c*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(5/4))","A",0
212,1,90,0,2.892208," ","integrate((d*x+c)/(b*x**4-a)**(1/2),x)","d \left(\begin{cases} \frac{\operatorname{acosh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} & \text{for}\: \left|{\frac{b x^{4}}{a}}\right| > 1 \\- \frac{i \operatorname{asin}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} & \text{otherwise} \end{cases}\right) - \frac{i c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"d*Piecewise((acosh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)), Abs(b*x**4/a) > 1), (-I*asin(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)), True)) - I*c*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4/a)/(4*sqrt(a)*gamma(5/4))","A",0
213,1,66,0,3.244705," ","integrate((d*x+c)/(-b*x**4-a)**(1/2),x)","- \frac{i d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} - \frac{i c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"-I*d*asinh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)) - I*c*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4))","C",0
214,1,102,0,3.383005," ","integrate((e*x**2+d*x+c)/(b*x**4+a)**(1/2),x)","\frac{d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} + \frac{e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"d*asinh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)) + c*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) + e*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4))","C",0
215,1,80,0,9.597617," ","integrate((-b*g*x**4+a*g)/(b*x**4+a)**(3/2),x)","\frac{g x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} - \frac{b g x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"g*x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) - b*g*x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(9/4))","C",0
216,1,104,0,12.387272," ","integrate((-b*g*x**4+a*g+e*x)/(b*x**4+a)**(3/2),x)","\frac{g x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} - \frac{b g x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{e x^{2}}{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"g*x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) - b*g*x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(9/4)) + e*x**2/(2*a**(3/2)*sqrt(1 + b*x**4/a))","C",0
217,1,109,0,17.799361," ","integrate((-b*g*x**4+f*x**3+a*g)/(b*x**4+a)**(3/2),x)","f \left(\begin{cases} - \frac{1}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{g x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} - \frac{b g x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"f*Piecewise((-1/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**4/(4*a**(3/2)), True)) + g*x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) - b*g*x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(9/4))","A",0
218,1,133,0,21.514562," ","integrate((-b*g*x**4+f*x**3+a*g+e*x)/(b*x**4+a)**(3/2),x)","f \left(\begin{cases} - \frac{1}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{g x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} - \frac{b g x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{e x^{2}}{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"f*Piecewise((-1/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**4/(4*a**(3/2)), True)) + g*x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) - b*g*x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(9/4)) + e*x**2/(2*a**(3/2)*sqrt(1 + b*x**4/a))","A",0
219,1,58,0,5.208020," ","integrate((x**4-1)/(x**4+1)**(3/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} - \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), x**4*exp_polar(I*pi))/(4*gamma(9/4)) - x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
220,1,260,0,7.363567," ","integrate((i*x**6+h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(1/2),x)","\frac{\sqrt{a} h x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4 b} - \frac{a h \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} + f \left(\begin{cases} \frac{x^{4}}{4 \sqrt{a}} & \text{for}\: b = 0 \\\frac{\sqrt{a + b x^{4}}}{2 b} & \text{otherwise} \end{cases}\right) + \frac{d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} + \frac{e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)} + \frac{g x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)} + \frac{i x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"sqrt(a)*h*x**2*sqrt(1 + b*x**4/a)/(4*b) - a*h*asinh(sqrt(b)*x**2/sqrt(a))/(4*b**(3/2)) + f*Piecewise((x**4/(4*sqrt(a)), Eq(b, 0)), (sqrt(a + b*x**4)/(2*b), True)) + d*asinh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)) + c*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) + e*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4)) + g*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(9/4)) + i*x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(11/4))","A",0
221,1,1287,0,1.202496," ","integrate((1+x)/(x**5+1),x)","\frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{21 \sqrt{5}}{11} + \frac{4 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22}\right) - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{10} - \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{48}{11} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{4 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{21 \sqrt{5}}{11}\right) - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{10} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{96}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{8 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{42 \sqrt{5}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{96}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{42 \sqrt{5}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{8 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}"," ",0,"sqrt(5)*log(x**2 + x*(-48/11 - 21*sqrt(5)/11 + 4*sqrt(10)*sqrt(sqrt(5) + 3)/11 + 45*sqrt(2)*sqrt(sqrt(5) + 3)/22) - 1381*sqrt(10)*sqrt(sqrt(5) + 3)/484 - 3045*sqrt(2)*sqrt(sqrt(5) + 3)/484 + 2213*sqrt(5)/242 + 5217/242)/10 - sqrt(5)*log(x**2 + x*(-48/11 - 45*sqrt(2)*sqrt(3 - sqrt(5))/22 + 4*sqrt(10)*sqrt(3 - sqrt(5))/11 + 21*sqrt(5)/11) - 2213*sqrt(5)/242 - 1381*sqrt(10)*sqrt(3 - sqrt(5))/484 + 3045*sqrt(2)*sqrt(3 - sqrt(5))/484 + 5217/242)/10 + 2*sqrt(-sqrt(10)*sqrt(3 - sqrt(5))/50 + 3/20)*atan(44*x/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15)) - 96/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15)) - 45*sqrt(2)*sqrt(3 - sqrt(5))/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15)) + 8*sqrt(10)*sqrt(3 - sqrt(5))/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15)) + 42*sqrt(5)/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15))) + 2*sqrt(-sqrt(10)*sqrt(sqrt(5) + 3)/50 + 3/20)*atan(44*x/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)) - 96/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)) - 42*sqrt(5)/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)) + 8*sqrt(10)*sqrt(sqrt(5) + 3)/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)) + 45*sqrt(2)*sqrt(sqrt(5) + 3)/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)))","B",0
222,1,1287,0,1.283624," ","integrate((1-x)/(-x**5+1),x)","\frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{21 \sqrt{5}}{11} - \frac{4 \sqrt{10} \sqrt{3 - \sqrt{5}}}{11} + \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{22} + \frac{48}{11}\right) - \frac{2213 \sqrt{5}}{242} - \frac{1381 \sqrt{10} \sqrt{3 - \sqrt{5}}}{484} + \frac{3045 \sqrt{2} \sqrt{3 - \sqrt{5}}}{484} + \frac{5217}{242} \right)}}{10} - \frac{\sqrt{5} \log{\left(x^{2} + x \left(- \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{22} - \frac{4 \sqrt{10} \sqrt{\sqrt{5} + 3}}{11} + \frac{21 \sqrt{5}}{11} + \frac{48}{11}\right) - \frac{1381 \sqrt{10} \sqrt{\sqrt{5} + 3}}{484} - \frac{3045 \sqrt{2} \sqrt{\sqrt{5} + 3}}{484} + \frac{2213 \sqrt{5}}{242} + \frac{5217}{242} \right)}}{10} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{3 - \sqrt{5}}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{42 \sqrt{5}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} - \frac{8 \sqrt{10} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{45 \sqrt{2} \sqrt{3 - \sqrt{5}}}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} + \frac{96}{- 8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 3 \sqrt{10} \sqrt{3 - \sqrt{5}} \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{3 - \sqrt{5}} + 15}} \right)} + 2 \sqrt{- \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{50} + \frac{3}{20}} \operatorname{atan}{\left(\frac{44 x}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{45 \sqrt{2} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} - \frac{8 \sqrt{10} \sqrt{\sqrt{5} + 3}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{42 \sqrt{5}}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} + \frac{96}{8 \sqrt{5} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 18 \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15} + 3 \sqrt{10} \sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{10} \sqrt{\sqrt{5} + 3} + 15}} \right)}"," ",0,"sqrt(5)*log(x**2 + x*(-21*sqrt(5)/11 - 4*sqrt(10)*sqrt(3 - sqrt(5))/11 + 45*sqrt(2)*sqrt(3 - sqrt(5))/22 + 48/11) - 2213*sqrt(5)/242 - 1381*sqrt(10)*sqrt(3 - sqrt(5))/484 + 3045*sqrt(2)*sqrt(3 - sqrt(5))/484 + 5217/242)/10 - sqrt(5)*log(x**2 + x*(-45*sqrt(2)*sqrt(sqrt(5) + 3)/22 - 4*sqrt(10)*sqrt(sqrt(5) + 3)/11 + 21*sqrt(5)/11 + 48/11) - 1381*sqrt(10)*sqrt(sqrt(5) + 3)/484 - 3045*sqrt(2)*sqrt(sqrt(5) + 3)/484 + 2213*sqrt(5)/242 + 5217/242)/10 + 2*sqrt(-sqrt(10)*sqrt(3 - sqrt(5))/50 + 3/20)*atan(44*x/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15)) - 42*sqrt(5)/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15)) - 8*sqrt(10)*sqrt(3 - sqrt(5))/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15)) + 45*sqrt(2)*sqrt(3 - sqrt(5))/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15)) + 96/(-8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 3*sqrt(10)*sqrt(3 - sqrt(5))*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(3 - sqrt(5)) + 15))) + 2*sqrt(-sqrt(10)*sqrt(sqrt(5) + 3)/50 + 3/20)*atan(44*x/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)) - 45*sqrt(2)*sqrt(sqrt(5) + 3)/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)) - 8*sqrt(10)*sqrt(sqrt(5) + 3)/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)) + 42*sqrt(5)/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)) + 96/(8*sqrt(5)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 18*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15) + 3*sqrt(10)*sqrt(sqrt(5) + 3)*sqrt(-2*sqrt(10)*sqrt(sqrt(5) + 3) + 15)))","B",0
223,1,216,0,1.317549," ","integrate(x**11*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","\frac{a^{3} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(a + b x^{3} \right)}}{3 b^{7}} + x^{15} \left(- \frac{a f}{15 b^{2}} + \frac{e}{15 b}\right) + x^{12} \left(\frac{a^{2} f}{12 b^{3}} - \frac{a e}{12 b^{2}} + \frac{d}{12 b}\right) + x^{9} \left(- \frac{a^{3} f}{9 b^{4}} + \frac{a^{2} e}{9 b^{3}} - \frac{a d}{9 b^{2}} + \frac{c}{9 b}\right) + x^{6} \left(\frac{a^{4} f}{6 b^{5}} - \frac{a^{3} e}{6 b^{4}} + \frac{a^{2} d}{6 b^{3}} - \frac{a c}{6 b^{2}}\right) + x^{3} \left(- \frac{a^{5} f}{3 b^{6}} + \frac{a^{4} e}{3 b^{5}} - \frac{a^{3} d}{3 b^{4}} + \frac{a^{2} c}{3 b^{3}}\right) + \frac{f x^{18}}{18 b}"," ",0,"a**3*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a + b*x**3)/(3*b**7) + x**15*(-a*f/(15*b**2) + e/(15*b)) + x**12*(a**2*f/(12*b**3) - a*e/(12*b**2) + d/(12*b)) + x**9*(-a**3*f/(9*b**4) + a**2*e/(9*b**3) - a*d/(9*b**2) + c/(9*b)) + x**6*(a**4*f/(6*b**5) - a**3*e/(6*b**4) + a**2*d/(6*b**3) - a*c/(6*b**2)) + x**3*(-a**5*f/(3*b**6) + a**4*e/(3*b**5) - a**3*d/(3*b**4) + a**2*c/(3*b**3)) + f*x**18/(18*b)","A",0
224,1,172,0,1.345186," ","integrate(x**8*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","- \frac{a^{2} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(a + b x^{3} \right)}}{3 b^{6}} + x^{12} \left(- \frac{a f}{12 b^{2}} + \frac{e}{12 b}\right) + x^{9} \left(\frac{a^{2} f}{9 b^{3}} - \frac{a e}{9 b^{2}} + \frac{d}{9 b}\right) + x^{6} \left(- \frac{a^{3} f}{6 b^{4}} + \frac{a^{2} e}{6 b^{3}} - \frac{a d}{6 b^{2}} + \frac{c}{6 b}\right) + x^{3} \left(\frac{a^{4} f}{3 b^{5}} - \frac{a^{3} e}{3 b^{4}} + \frac{a^{2} d}{3 b^{3}} - \frac{a c}{3 b^{2}}\right) + \frac{f x^{15}}{15 b}"," ",0,"-a**2*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a + b*x**3)/(3*b**6) + x**12*(-a*f/(12*b**2) + e/(12*b)) + x**9*(a**2*f/(9*b**3) - a*e/(9*b**2) + d/(9*b)) + x**6*(-a**3*f/(6*b**4) + a**2*e/(6*b**3) - a*d/(6*b**2) + c/(6*b)) + x**3*(a**4*f/(3*b**5) - a**3*e/(3*b**4) + a**2*d/(3*b**3) - a*c/(3*b**2)) + f*x**15/(15*b)","A",0
225,1,128,0,1.045361," ","integrate(x**5*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","\frac{a \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(a + b x^{3} \right)}}{3 b^{5}} + x^{9} \left(- \frac{a f}{9 b^{2}} + \frac{e}{9 b}\right) + x^{6} \left(\frac{a^{2} f}{6 b^{3}} - \frac{a e}{6 b^{2}} + \frac{d}{6 b}\right) + x^{3} \left(- \frac{a^{3} f}{3 b^{4}} + \frac{a^{2} e}{3 b^{3}} - \frac{a d}{3 b^{2}} + \frac{c}{3 b}\right) + \frac{f x^{12}}{12 b}"," ",0,"a*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a + b*x**3)/(3*b**5) + x**9*(-a*f/(9*b**2) + e/(9*b)) + x**6*(a**2*f/(6*b**3) - a*e/(6*b**2) + d/(6*b)) + x**3*(-a**3*f/(3*b**4) + a**2*e/(3*b**3) - a*d/(3*b**2) + c/(3*b)) + f*x**12/(12*b)","A",0
226,1,88,0,1.126290," ","integrate(x**2*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","x^{6} \left(- \frac{a f}{6 b^{2}} + \frac{e}{6 b}\right) + x^{3} \left(\frac{a^{2} f}{3 b^{3}} - \frac{a e}{3 b^{2}} + \frac{d}{3 b}\right) + \frac{f x^{9}}{9 b} - \frac{\left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(a + b x^{3} \right)}}{3 b^{4}}"," ",0,"x**6*(-a*f/(6*b**2) + e/(6*b)) + x**3*(a**2*f/(3*b**3) - a*e/(3*b**2) + d/(3*b)) + f*x**9/(9*b) - (a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a + b*x**3)/(3*b**4)","A",0
227,1,70,0,5.262202," ","integrate((f*x**9+e*x**6+d*x**3+c)/x/(b*x**3+a),x)","x^{3} \left(- \frac{a f}{3 b^{2}} + \frac{e}{3 b}\right) + \frac{f x^{6}}{6 b} + \frac{c \log{\left(x \right)}}{a} + \frac{\left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(\frac{a}{b} + x^{3} \right)}}{3 a b^{3}}"," ",0,"x**3*(-a*f/(3*b**2) + e/(3*b)) + f*x**6/(6*b) + c*log(x)/a + (a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a/b + x**3)/(3*a*b**3)","A",0
228,1,70,0,14.560708," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**4/(b*x**3+a),x)","\frac{f x^{3}}{3 b} - \frac{c}{3 a x^{3}} + \frac{\left(a d - b c\right) \log{\left(x \right)}}{a^{2}} - \frac{\left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(\frac{a}{b} + x^{3} \right)}}{3 a^{2} b^{2}}"," ",0,"f*x**3/(3*b) - c/(3*a*x**3) + (a*d - b*c)*log(x)/a**2 - (a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a/b + x**3)/(3*a**2*b**2)","A",0
229,1,85,0,74.001012," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**7/(b*x**3+a),x)","\frac{- a c + x^{3} \left(- 2 a d + 2 b c\right)}{6 a^{2} x^{6}} + \frac{\left(a^{2} e - a b d + b^{2} c\right) \log{\left(x \right)}}{a^{3}} + \frac{\left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(\frac{a}{b} + x^{3} \right)}}{3 a^{3} b}"," ",0,"(-a*c + x**3*(-2*a*d + 2*b*c))/(6*a**2*x**6) + (a**2*e - a*b*d + b**2*c)*log(x)/a**3 + (a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a/b + x**3)/(3*a**3*b)","A",0
230,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**10/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**13/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**16/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,1,469,0,4.350368," ","integrate(x**9*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","x^{13} \left(- \frac{a f}{13 b^{2}} + \frac{e}{13 b}\right) + x^{10} \left(\frac{a^{2} f}{10 b^{3}} - \frac{a e}{10 b^{2}} + \frac{d}{10 b}\right) + x^{7} \left(- \frac{a^{3} f}{7 b^{4}} + \frac{a^{2} e}{7 b^{3}} - \frac{a d}{7 b^{2}} + \frac{c}{7 b}\right) + x^{4} \left(\frac{a^{4} f}{4 b^{5}} - \frac{a^{3} e}{4 b^{4}} + \frac{a^{2} d}{4 b^{3}} - \frac{a c}{4 b^{2}}\right) + x \left(- \frac{a^{5} f}{b^{6}} + \frac{a^{4} e}{b^{5}} - \frac{a^{3} d}{b^{4}} + \frac{a^{2} c}{b^{3}}\right) + \operatorname{RootSum} {\left(27 t^{3} b^{19} - a^{16} f^{3} + 3 a^{15} b e f^{2} - 3 a^{14} b^{2} d f^{2} - 3 a^{14} b^{2} e^{2} f + 3 a^{13} b^{3} c f^{2} + 6 a^{13} b^{3} d e f + a^{13} b^{3} e^{3} - 6 a^{12} b^{4} c e f - 3 a^{12} b^{4} d^{2} f - 3 a^{12} b^{4} d e^{2} + 6 a^{11} b^{5} c d f + 3 a^{11} b^{5} c e^{2} + 3 a^{11} b^{5} d^{2} e - 3 a^{10} b^{6} c^{2} f - 6 a^{10} b^{6} c d e - a^{10} b^{6} d^{3} + 3 a^{9} b^{7} c^{2} e + 3 a^{9} b^{7} c d^{2} - 3 a^{8} b^{8} c^{2} d + a^{7} b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{3 t b^{6}}{a^{5} f - a^{4} b e + a^{3} b^{2} d - a^{2} b^{3} c} + x \right)} \right)\right)} + \frac{f x^{16}}{16 b}"," ",0,"x**13*(-a*f/(13*b**2) + e/(13*b)) + x**10*(a**2*f/(10*b**3) - a*e/(10*b**2) + d/(10*b)) + x**7*(-a**3*f/(7*b**4) + a**2*e/(7*b**3) - a*d/(7*b**2) + c/(7*b)) + x**4*(a**4*f/(4*b**5) - a**3*e/(4*b**4) + a**2*d/(4*b**3) - a*c/(4*b**2)) + x*(-a**5*f/b**6 + a**4*e/b**5 - a**3*d/b**4 + a**2*c/b**3) + RootSum(27*_t**3*b**19 - a**16*f**3 + 3*a**15*b*e*f**2 - 3*a**14*b**2*d*f**2 - 3*a**14*b**2*e**2*f + 3*a**13*b**3*c*f**2 + 6*a**13*b**3*d*e*f + a**13*b**3*e**3 - 6*a**12*b**4*c*e*f - 3*a**12*b**4*d**2*f - 3*a**12*b**4*d*e**2 + 6*a**11*b**5*c*d*f + 3*a**11*b**5*c*e**2 + 3*a**11*b**5*d**2*e - 3*a**10*b**6*c**2*f - 6*a**10*b**6*c*d*e - a**10*b**6*d**3 + 3*a**9*b**7*c**2*e + 3*a**9*b**7*c*d**2 - 3*a**8*b**8*c**2*d + a**7*b**9*c**3, Lambda(_t, _t*log(3*_t*b**6/(a**5*f - a**4*b*e + a**3*b**2*d - a**2*b**3*c) + x))) + f*x**16/(16*b)","A",0
234,1,513,0,4.056658," ","integrate(x**7*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","x^{11} \left(- \frac{a f}{11 b^{2}} + \frac{e}{11 b}\right) + x^{8} \left(\frac{a^{2} f}{8 b^{3}} - \frac{a e}{8 b^{2}} + \frac{d}{8 b}\right) + x^{5} \left(- \frac{a^{3} f}{5 b^{4}} + \frac{a^{2} e}{5 b^{3}} - \frac{a d}{5 b^{2}} + \frac{c}{5 b}\right) + x^{2} \left(\frac{a^{4} f}{2 b^{5}} - \frac{a^{3} e}{2 b^{4}} + \frac{a^{2} d}{2 b^{3}} - \frac{a c}{2 b^{2}}\right) + \operatorname{RootSum} {\left(27 t^{3} b^{17} - a^{14} f^{3} + 3 a^{13} b e f^{2} - 3 a^{12} b^{2} d f^{2} - 3 a^{12} b^{2} e^{2} f + 3 a^{11} b^{3} c f^{2} + 6 a^{11} b^{3} d e f + a^{11} b^{3} e^{3} - 6 a^{10} b^{4} c e f - 3 a^{10} b^{4} d^{2} f - 3 a^{10} b^{4} d e^{2} + 6 a^{9} b^{5} c d f + 3 a^{9} b^{5} c e^{2} + 3 a^{9} b^{5} d^{2} e - 3 a^{8} b^{6} c^{2} f - 6 a^{8} b^{6} c d e - a^{8} b^{6} d^{3} + 3 a^{7} b^{7} c^{2} e + 3 a^{7} b^{7} c d^{2} - 3 a^{6} b^{8} c^{2} d + a^{5} b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t^{2} b^{11}}{a^{9} f^{2} - 2 a^{8} b e f + 2 a^{7} b^{2} d f + a^{7} b^{2} e^{2} - 2 a^{6} b^{3} c f - 2 a^{6} b^{3} d e + 2 a^{5} b^{4} c e + a^{5} b^{4} d^{2} - 2 a^{4} b^{5} c d + a^{3} b^{6} c^{2}} + x \right)} \right)\right)} + \frac{f x^{14}}{14 b}"," ",0,"x**11*(-a*f/(11*b**2) + e/(11*b)) + x**8*(a**2*f/(8*b**3) - a*e/(8*b**2) + d/(8*b)) + x**5*(-a**3*f/(5*b**4) + a**2*e/(5*b**3) - a*d/(5*b**2) + c/(5*b)) + x**2*(a**4*f/(2*b**5) - a**3*e/(2*b**4) + a**2*d/(2*b**3) - a*c/(2*b**2)) + RootSum(27*_t**3*b**17 - a**14*f**3 + 3*a**13*b*e*f**2 - 3*a**12*b**2*d*f**2 - 3*a**12*b**2*e**2*f + 3*a**11*b**3*c*f**2 + 6*a**11*b**3*d*e*f + a**11*b**3*e**3 - 6*a**10*b**4*c*e*f - 3*a**10*b**4*d**2*f - 3*a**10*b**4*d*e**2 + 6*a**9*b**5*c*d*f + 3*a**9*b**5*c*e**2 + 3*a**9*b**5*d**2*e - 3*a**8*b**6*c**2*f - 6*a**8*b**6*c*d*e - a**8*b**6*d**3 + 3*a**7*b**7*c**2*e + 3*a**7*b**7*c*d**2 - 3*a**6*b**8*c**2*d + a**5*b**9*c**3, Lambda(_t, _t*log(9*_t**2*b**11/(a**9*f**2 - 2*a**8*b*e*f + 2*a**7*b**2*d*f + a**7*b**2*e**2 - 2*a**6*b**3*c*f - 2*a**6*b**3*d*e + 2*a**5*b**4*c*e + a**5*b**4*d**2 - 2*a**4*b**5*c*d + a**3*b**6*c**2) + x))) + f*x**14/(14*b)","A",0
235,1,423,0,3.243458," ","integrate(x**6*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","x^{10} \left(- \frac{a f}{10 b^{2}} + \frac{e}{10 b}\right) + x^{7} \left(\frac{a^{2} f}{7 b^{3}} - \frac{a e}{7 b^{2}} + \frac{d}{7 b}\right) + x^{4} \left(- \frac{a^{3} f}{4 b^{4}} + \frac{a^{2} e}{4 b^{3}} - \frac{a d}{4 b^{2}} + \frac{c}{4 b}\right) + x \left(\frac{a^{4} f}{b^{5}} - \frac{a^{3} e}{b^{4}} + \frac{a^{2} d}{b^{3}} - \frac{a c}{b^{2}}\right) + \operatorname{RootSum} {\left(27 t^{3} b^{16} + a^{13} f^{3} - 3 a^{12} b e f^{2} + 3 a^{11} b^{2} d f^{2} + 3 a^{11} b^{2} e^{2} f - 3 a^{10} b^{3} c f^{2} - 6 a^{10} b^{3} d e f - a^{10} b^{3} e^{3} + 6 a^{9} b^{4} c e f + 3 a^{9} b^{4} d^{2} f + 3 a^{9} b^{4} d e^{2} - 6 a^{8} b^{5} c d f - 3 a^{8} b^{5} c e^{2} - 3 a^{8} b^{5} d^{2} e + 3 a^{7} b^{6} c^{2} f + 6 a^{7} b^{6} c d e + a^{7} b^{6} d^{3} - 3 a^{6} b^{7} c^{2} e - 3 a^{6} b^{7} c d^{2} + 3 a^{5} b^{8} c^{2} d - a^{4} b^{9} c^{3}, \left( t \mapsto t \log{\left(- \frac{3 t b^{5}}{a^{4} f - a^{3} b e + a^{2} b^{2} d - a b^{3} c} + x \right)} \right)\right)} + \frac{f x^{13}}{13 b}"," ",0,"x**10*(-a*f/(10*b**2) + e/(10*b)) + x**7*(a**2*f/(7*b**3) - a*e/(7*b**2) + d/(7*b)) + x**4*(-a**3*f/(4*b**4) + a**2*e/(4*b**3) - a*d/(4*b**2) + c/(4*b)) + x*(a**4*f/b**5 - a**3*e/b**4 + a**2*d/b**3 - a*c/b**2) + RootSum(27*_t**3*b**16 + a**13*f**3 - 3*a**12*b*e*f**2 + 3*a**11*b**2*d*f**2 + 3*a**11*b**2*e**2*f - 3*a**10*b**3*c*f**2 - 6*a**10*b**3*d*e*f - a**10*b**3*e**3 + 6*a**9*b**4*c*e*f + 3*a**9*b**4*d**2*f + 3*a**9*b**4*d*e**2 - 6*a**8*b**5*c*d*f - 3*a**8*b**5*c*e**2 - 3*a**8*b**5*d**2*e + 3*a**7*b**6*c**2*f + 6*a**7*b**6*c*d*e + a**7*b**6*d**3 - 3*a**6*b**7*c**2*e - 3*a**6*b**7*c*d**2 + 3*a**5*b**8*c**2*d - a**4*b**9*c**3, Lambda(_t, _t*log(-3*_t*b**5/(a**4*f - a**3*b*e + a**2*b**2*d - a*b**3*c) + x))) + f*x**13/(13*b)","A",0
236,1,469,0,2.480809," ","integrate(x**4*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","x^{8} \left(- \frac{a f}{8 b^{2}} + \frac{e}{8 b}\right) + x^{5} \left(\frac{a^{2} f}{5 b^{3}} - \frac{a e}{5 b^{2}} + \frac{d}{5 b}\right) + x^{2} \left(- \frac{a^{3} f}{2 b^{4}} + \frac{a^{2} e}{2 b^{3}} - \frac{a d}{2 b^{2}} + \frac{c}{2 b}\right) + \operatorname{RootSum} {\left(27 t^{3} b^{14} + a^{11} f^{3} - 3 a^{10} b e f^{2} + 3 a^{9} b^{2} d f^{2} + 3 a^{9} b^{2} e^{2} f - 3 a^{8} b^{3} c f^{2} - 6 a^{8} b^{3} d e f - a^{8} b^{3} e^{3} + 6 a^{7} b^{4} c e f + 3 a^{7} b^{4} d^{2} f + 3 a^{7} b^{4} d e^{2} - 6 a^{6} b^{5} c d f - 3 a^{6} b^{5} c e^{2} - 3 a^{6} b^{5} d^{2} e + 3 a^{5} b^{6} c^{2} f + 6 a^{5} b^{6} c d e + a^{5} b^{6} d^{3} - 3 a^{4} b^{7} c^{2} e - 3 a^{4} b^{7} c d^{2} + 3 a^{3} b^{8} c^{2} d - a^{2} b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t^{2} b^{9}}{a^{7} f^{2} - 2 a^{6} b e f + 2 a^{5} b^{2} d f + a^{5} b^{2} e^{2} - 2 a^{4} b^{3} c f - 2 a^{4} b^{3} d e + 2 a^{3} b^{4} c e + a^{3} b^{4} d^{2} - 2 a^{2} b^{5} c d + a b^{6} c^{2}} + x \right)} \right)\right)} + \frac{f x^{11}}{11 b}"," ",0,"x**8*(-a*f/(8*b**2) + e/(8*b)) + x**5*(a**2*f/(5*b**3) - a*e/(5*b**2) + d/(5*b)) + x**2*(-a**3*f/(2*b**4) + a**2*e/(2*b**3) - a*d/(2*b**2) + c/(2*b)) + RootSum(27*_t**3*b**14 + a**11*f**3 - 3*a**10*b*e*f**2 + 3*a**9*b**2*d*f**2 + 3*a**9*b**2*e**2*f - 3*a**8*b**3*c*f**2 - 6*a**8*b**3*d*e*f - a**8*b**3*e**3 + 6*a**7*b**4*c*e*f + 3*a**7*b**4*d**2*f + 3*a**7*b**4*d*e**2 - 6*a**6*b**5*c*d*f - 3*a**6*b**5*c*e**2 - 3*a**6*b**5*d**2*e + 3*a**5*b**6*c**2*f + 6*a**5*b**6*c*d*e + a**5*b**6*d**3 - 3*a**4*b**7*c**2*e - 3*a**4*b**7*c*d**2 + 3*a**3*b**8*c**2*d - a**2*b**9*c**3, Lambda(_t, _t*log(9*_t**2*b**9/(a**7*f**2 - 2*a**6*b*e*f + 2*a**5*b**2*d*f + a**5*b**2*e**2 - 2*a**4*b**3*c*f - 2*a**4*b**3*d*e + 2*a**3*b**4*c*e + a**3*b**4*d**2 - 2*a**2*b**5*c*d + a*b**6*c**2) + x))) + f*x**11/(11*b)","A",0
237,1,376,0,2.511374," ","integrate(x**3*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","x^{7} \left(- \frac{a f}{7 b^{2}} + \frac{e}{7 b}\right) + x^{4} \left(\frac{a^{2} f}{4 b^{3}} - \frac{a e}{4 b^{2}} + \frac{d}{4 b}\right) + x \left(- \frac{a^{3} f}{b^{4}} + \frac{a^{2} e}{b^{3}} - \frac{a d}{b^{2}} + \frac{c}{b}\right) + \operatorname{RootSum} {\left(27 t^{3} b^{13} - a^{10} f^{3} + 3 a^{9} b e f^{2} - 3 a^{8} b^{2} d f^{2} - 3 a^{8} b^{2} e^{2} f + 3 a^{7} b^{3} c f^{2} + 6 a^{7} b^{3} d e f + a^{7} b^{3} e^{3} - 6 a^{6} b^{4} c e f - 3 a^{6} b^{4} d^{2} f - 3 a^{6} b^{4} d e^{2} + 6 a^{5} b^{5} c d f + 3 a^{5} b^{5} c e^{2} + 3 a^{5} b^{5} d^{2} e - 3 a^{4} b^{6} c^{2} f - 6 a^{4} b^{6} c d e - a^{4} b^{6} d^{3} + 3 a^{3} b^{7} c^{2} e + 3 a^{3} b^{7} c d^{2} - 3 a^{2} b^{8} c^{2} d + a b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{3 t b^{4}}{a^{3} f - a^{2} b e + a b^{2} d - b^{3} c} + x \right)} \right)\right)} + \frac{f x^{10}}{10 b}"," ",0,"x**7*(-a*f/(7*b**2) + e/(7*b)) + x**4*(a**2*f/(4*b**3) - a*e/(4*b**2) + d/(4*b)) + x*(-a**3*f/b**4 + a**2*e/b**3 - a*d/b**2 + c/b) + RootSum(27*_t**3*b**13 - a**10*f**3 + 3*a**9*b*e*f**2 - 3*a**8*b**2*d*f**2 - 3*a**8*b**2*e**2*f + 3*a**7*b**3*c*f**2 + 6*a**7*b**3*d*e*f + a**7*b**3*e**3 - 6*a**6*b**4*c*e*f - 3*a**6*b**4*d**2*f - 3*a**6*b**4*d*e**2 + 6*a**5*b**5*c*d*f + 3*a**5*b**5*c*e**2 + 3*a**5*b**5*d**2*e - 3*a**4*b**6*c**2*f - 6*a**4*b**6*c*d*e - a**4*b**6*d**3 + 3*a**3*b**7*c**2*e + 3*a**3*b**7*c*d**2 - 3*a**2*b**8*c**2*d + a*b**9*c**3, Lambda(_t, _t*log(3*_t*b**4/(a**3*f - a**2*b*e + a*b**2*d - b**3*c) + x))) + f*x**10/(10*b)","A",0
238,1,427,0,2.380120," ","integrate(x*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","x^{5} \left(- \frac{a f}{5 b^{2}} + \frac{e}{5 b}\right) + x^{2} \left(\frac{a^{2} f}{2 b^{3}} - \frac{a e}{2 b^{2}} + \frac{d}{2 b}\right) + \operatorname{RootSum} {\left(27 t^{3} a b^{11} - a^{9} f^{3} + 3 a^{8} b e f^{2} - 3 a^{7} b^{2} d f^{2} - 3 a^{7} b^{2} e^{2} f + 3 a^{6} b^{3} c f^{2} + 6 a^{6} b^{3} d e f + a^{6} b^{3} e^{3} - 6 a^{5} b^{4} c e f - 3 a^{5} b^{4} d^{2} f - 3 a^{5} b^{4} d e^{2} + 6 a^{4} b^{5} c d f + 3 a^{4} b^{5} c e^{2} + 3 a^{4} b^{5} d^{2} e - 3 a^{3} b^{6} c^{2} f - 6 a^{3} b^{6} c d e - a^{3} b^{6} d^{3} + 3 a^{2} b^{7} c^{2} e + 3 a^{2} b^{7} c d^{2} - 3 a b^{8} c^{2} d + b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t^{2} a b^{7}}{a^{6} f^{2} - 2 a^{5} b e f + 2 a^{4} b^{2} d f + a^{4} b^{2} e^{2} - 2 a^{3} b^{3} c f - 2 a^{3} b^{3} d e + 2 a^{2} b^{4} c e + a^{2} b^{4} d^{2} - 2 a b^{5} c d + b^{6} c^{2}} + x \right)} \right)\right)} + \frac{f x^{8}}{8 b}"," ",0,"x**5*(-a*f/(5*b**2) + e/(5*b)) + x**2*(a**2*f/(2*b**3) - a*e/(2*b**2) + d/(2*b)) + RootSum(27*_t**3*a*b**11 - a**9*f**3 + 3*a**8*b*e*f**2 - 3*a**7*b**2*d*f**2 - 3*a**7*b**2*e**2*f + 3*a**6*b**3*c*f**2 + 6*a**6*b**3*d*e*f + a**6*b**3*e**3 - 6*a**5*b**4*c*e*f - 3*a**5*b**4*d**2*f - 3*a**5*b**4*d*e**2 + 6*a**4*b**5*c*d*f + 3*a**4*b**5*c*e**2 + 3*a**4*b**5*d**2*e - 3*a**3*b**6*c**2*f - 6*a**3*b**6*c*d*e - a**3*b**6*d**3 + 3*a**2*b**7*c**2*e + 3*a**2*b**7*c*d**2 - 3*a*b**8*c**2*d + b**9*c**3, Lambda(_t, _t*log(9*_t**2*a*b**7/(a**6*f**2 - 2*a**5*b*e*f + 2*a**4*b**2*d*f + a**4*b**2*e**2 - 2*a**3*b**3*c*f - 2*a**3*b**3*d*e + 2*a**2*b**4*c*e + a**2*b**4*d**2 - 2*a*b**5*c*d + b**6*c**2) + x))) + f*x**8/(8*b)","A",0
239,1,342,0,3.413578," ","integrate((f*x**9+e*x**6+d*x**3+c)/(b*x**3+a),x)","x^{4} \left(- \frac{a f}{4 b^{2}} + \frac{e}{4 b}\right) + x \left(\frac{a^{2} f}{b^{3}} - \frac{a e}{b^{2}} + \frac{d}{b}\right) + \operatorname{RootSum} {\left(27 t^{3} a^{2} b^{10} + a^{9} f^{3} - 3 a^{8} b e f^{2} + 3 a^{7} b^{2} d f^{2} + 3 a^{7} b^{2} e^{2} f - 3 a^{6} b^{3} c f^{2} - 6 a^{6} b^{3} d e f - a^{6} b^{3} e^{3} + 6 a^{5} b^{4} c e f + 3 a^{5} b^{4} d^{2} f + 3 a^{5} b^{4} d e^{2} - 6 a^{4} b^{5} c d f - 3 a^{4} b^{5} c e^{2} - 3 a^{4} b^{5} d^{2} e + 3 a^{3} b^{6} c^{2} f + 6 a^{3} b^{6} c d e + a^{3} b^{6} d^{3} - 3 a^{2} b^{7} c^{2} e - 3 a^{2} b^{7} c d^{2} + 3 a b^{8} c^{2} d - b^{9} c^{3}, \left( t \mapsto t \log{\left(- \frac{3 t a b^{3}}{a^{3} f - a^{2} b e + a b^{2} d - b^{3} c} + x \right)} \right)\right)} + \frac{f x^{7}}{7 b}"," ",0,"x**4*(-a*f/(4*b**2) + e/(4*b)) + x*(a**2*f/b**3 - a*e/b**2 + d/b) + RootSum(27*_t**3*a**2*b**10 + a**9*f**3 - 3*a**8*b*e*f**2 + 3*a**7*b**2*d*f**2 + 3*a**7*b**2*e**2*f - 3*a**6*b**3*c*f**2 - 6*a**6*b**3*d*e*f - a**6*b**3*e**3 + 6*a**5*b**4*c*e*f + 3*a**5*b**4*d**2*f + 3*a**5*b**4*d*e**2 - 6*a**4*b**5*c*d*f - 3*a**4*b**5*c*e**2 - 3*a**4*b**5*d**2*e + 3*a**3*b**6*c**2*f + 6*a**3*b**6*c*d*e + a**3*b**6*d**3 - 3*a**2*b**7*c**2*e - 3*a**2*b**7*c*d**2 + 3*a*b**8*c**2*d - b**9*c**3, Lambda(_t, _t*log(-3*_t*a*b**3/(a**3*f - a**2*b*e + a*b**2*d - b**3*c) + x))) + f*x**7/(7*b)","A",0
240,1,408,0,4.724073," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**2/(b*x**3+a),x)","x^{2} \left(- \frac{a f}{2 b^{2}} + \frac{e}{2 b}\right) + \operatorname{RootSum} {\left(27 t^{3} a^{4} b^{8} + a^{9} f^{3} - 3 a^{8} b e f^{2} + 3 a^{7} b^{2} d f^{2} + 3 a^{7} b^{2} e^{2} f - 3 a^{6} b^{3} c f^{2} - 6 a^{6} b^{3} d e f - a^{6} b^{3} e^{3} + 6 a^{5} b^{4} c e f + 3 a^{5} b^{4} d^{2} f + 3 a^{5} b^{4} d e^{2} - 6 a^{4} b^{5} c d f - 3 a^{4} b^{5} c e^{2} - 3 a^{4} b^{5} d^{2} e + 3 a^{3} b^{6} c^{2} f + 6 a^{3} b^{6} c d e + a^{3} b^{6} d^{3} - 3 a^{2} b^{7} c^{2} e - 3 a^{2} b^{7} c d^{2} + 3 a b^{8} c^{2} d - b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t^{2} a^{3} b^{5}}{a^{6} f^{2} - 2 a^{5} b e f + 2 a^{4} b^{2} d f + a^{4} b^{2} e^{2} - 2 a^{3} b^{3} c f - 2 a^{3} b^{3} d e + 2 a^{2} b^{4} c e + a^{2} b^{4} d^{2} - 2 a b^{5} c d + b^{6} c^{2}} + x \right)} \right)\right)} + \frac{f x^{5}}{5 b} - \frac{c}{a x}"," ",0,"x**2*(-a*f/(2*b**2) + e/(2*b)) + RootSum(27*_t**3*a**4*b**8 + a**9*f**3 - 3*a**8*b*e*f**2 + 3*a**7*b**2*d*f**2 + 3*a**7*b**2*e**2*f - 3*a**6*b**3*c*f**2 - 6*a**6*b**3*d*e*f - a**6*b**3*e**3 + 6*a**5*b**4*c*e*f + 3*a**5*b**4*d**2*f + 3*a**5*b**4*d*e**2 - 6*a**4*b**5*c*d*f - 3*a**4*b**5*c*e**2 - 3*a**4*b**5*d**2*e + 3*a**3*b**6*c**2*f + 6*a**3*b**6*c*d*e + a**3*b**6*d**3 - 3*a**2*b**7*c**2*e - 3*a**2*b**7*c*d**2 + 3*a*b**8*c**2*d - b**9*c**3, Lambda(_t, _t*log(9*_t**2*a**3*b**5/(a**6*f**2 - 2*a**5*b*e*f + 2*a**4*b**2*d*f + a**4*b**2*e**2 - 2*a**3*b**3*c*f - 2*a**3*b**3*d*e + 2*a**2*b**4*c*e + a**2*b**4*d**2 - 2*a*b**5*c*d + b**6*c**2) + x))) + f*x**5/(5*b) - c/(a*x)","A",0
241,1,326,0,4.364496," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**3/(b*x**3+a),x)","x \left(- \frac{a f}{b^{2}} + \frac{e}{b}\right) + \operatorname{RootSum} {\left(27 t^{3} a^{5} b^{7} - a^{9} f^{3} + 3 a^{8} b e f^{2} - 3 a^{7} b^{2} d f^{2} - 3 a^{7} b^{2} e^{2} f + 3 a^{6} b^{3} c f^{2} + 6 a^{6} b^{3} d e f + a^{6} b^{3} e^{3} - 6 a^{5} b^{4} c e f - 3 a^{5} b^{4} d^{2} f - 3 a^{5} b^{4} d e^{2} + 6 a^{4} b^{5} c d f + 3 a^{4} b^{5} c e^{2} + 3 a^{4} b^{5} d^{2} e - 3 a^{3} b^{6} c^{2} f - 6 a^{3} b^{6} c d e - a^{3} b^{6} d^{3} + 3 a^{2} b^{7} c^{2} e + 3 a^{2} b^{7} c d^{2} - 3 a b^{8} c^{2} d + b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{3 t a^{2} b^{2}}{a^{3} f - a^{2} b e + a b^{2} d - b^{3} c} + x \right)} \right)\right)} + \frac{f x^{4}}{4 b} - \frac{c}{2 a x^{2}}"," ",0,"x*(-a*f/b**2 + e/b) + RootSum(27*_t**3*a**5*b**7 - a**9*f**3 + 3*a**8*b*e*f**2 - 3*a**7*b**2*d*f**2 - 3*a**7*b**2*e**2*f + 3*a**6*b**3*c*f**2 + 6*a**6*b**3*d*e*f + a**6*b**3*e**3 - 6*a**5*b**4*c*e*f - 3*a**5*b**4*d**2*f - 3*a**5*b**4*d*e**2 + 6*a**4*b**5*c*d*f + 3*a**4*b**5*c*e**2 + 3*a**4*b**5*d**2*e - 3*a**3*b**6*c**2*f - 6*a**3*b**6*c*d*e - a**3*b**6*d**3 + 3*a**2*b**7*c**2*e + 3*a**2*b**7*c*d**2 - 3*a*b**8*c**2*d + b**9*c**3, Lambda(_t, _t*log(3*_t*a**2*b**2/(a**3*f - a**2*b*e + a*b**2*d - b**3*c) + x))) + f*x**4/(4*b) - c/(2*a*x**2)","A",0
242,1,411,0,11.527034," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**5/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a^{7} b^{5} - a^{9} f^{3} + 3 a^{8} b e f^{2} - 3 a^{7} b^{2} d f^{2} - 3 a^{7} b^{2} e^{2} f + 3 a^{6} b^{3} c f^{2} + 6 a^{6} b^{3} d e f + a^{6} b^{3} e^{3} - 6 a^{5} b^{4} c e f - 3 a^{5} b^{4} d^{2} f - 3 a^{5} b^{4} d e^{2} + 6 a^{4} b^{5} c d f + 3 a^{4} b^{5} c e^{2} + 3 a^{4} b^{5} d^{2} e - 3 a^{3} b^{6} c^{2} f - 6 a^{3} b^{6} c d e - a^{3} b^{6} d^{3} + 3 a^{2} b^{7} c^{2} e + 3 a^{2} b^{7} c d^{2} - 3 a b^{8} c^{2} d + b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t^{2} a^{5} b^{3}}{a^{6} f^{2} - 2 a^{5} b e f + 2 a^{4} b^{2} d f + a^{4} b^{2} e^{2} - 2 a^{3} b^{3} c f - 2 a^{3} b^{3} d e + 2 a^{2} b^{4} c e + a^{2} b^{4} d^{2} - 2 a b^{5} c d + b^{6} c^{2}} + x \right)} \right)\right)} + \frac{f x^{2}}{2 b} + \frac{- a c + x^{3} \left(- 4 a d + 4 b c\right)}{4 a^{2} x^{4}}"," ",0,"RootSum(27*_t**3*a**7*b**5 - a**9*f**3 + 3*a**8*b*e*f**2 - 3*a**7*b**2*d*f**2 - 3*a**7*b**2*e**2*f + 3*a**6*b**3*c*f**2 + 6*a**6*b**3*d*e*f + a**6*b**3*e**3 - 6*a**5*b**4*c*e*f - 3*a**5*b**4*d**2*f - 3*a**5*b**4*d*e**2 + 6*a**4*b**5*c*d*f + 3*a**4*b**5*c*e**2 + 3*a**4*b**5*d**2*e - 3*a**3*b**6*c**2*f - 6*a**3*b**6*c*d*e - a**3*b**6*d**3 + 3*a**2*b**7*c**2*e + 3*a**2*b**7*c*d**2 - 3*a*b**8*c**2*d + b**9*c**3, Lambda(_t, _t*log(9*_t**2*a**5*b**3/(a**6*f**2 - 2*a**5*b*e*f + 2*a**4*b**2*d*f + a**4*b**2*e**2 - 2*a**3*b**3*c*f - 2*a**3*b**3*d*e + 2*a**2*b**4*c*e + a**2*b**4*d**2 - 2*a*b**5*c*d + b**6*c**2) + x))) + f*x**2/(2*b) + (-a*c + x**3*(-4*a*d + 4*b*c))/(4*a**2*x**4)","A",0
243,1,328,0,19.682686," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**6/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a^{8} b^{4} + a^{9} f^{3} - 3 a^{8} b e f^{2} + 3 a^{7} b^{2} d f^{2} + 3 a^{7} b^{2} e^{2} f - 3 a^{6} b^{3} c f^{2} - 6 a^{6} b^{3} d e f - a^{6} b^{3} e^{3} + 6 a^{5} b^{4} c e f + 3 a^{5} b^{4} d^{2} f + 3 a^{5} b^{4} d e^{2} - 6 a^{4} b^{5} c d f - 3 a^{4} b^{5} c e^{2} - 3 a^{4} b^{5} d^{2} e + 3 a^{3} b^{6} c^{2} f + 6 a^{3} b^{6} c d e + a^{3} b^{6} d^{3} - 3 a^{2} b^{7} c^{2} e - 3 a^{2} b^{7} c d^{2} + 3 a b^{8} c^{2} d - b^{9} c^{3}, \left( t \mapsto t \log{\left(- \frac{3 t a^{3} b}{a^{3} f - a^{2} b e + a b^{2} d - b^{3} c} + x \right)} \right)\right)} + \frac{f x}{b} + \frac{- 2 a c + x^{3} \left(- 5 a d + 5 b c\right)}{10 a^{2} x^{5}}"," ",0,"RootSum(27*_t**3*a**8*b**4 + a**9*f**3 - 3*a**8*b*e*f**2 + 3*a**7*b**2*d*f**2 + 3*a**7*b**2*e**2*f - 3*a**6*b**3*c*f**2 - 6*a**6*b**3*d*e*f - a**6*b**3*e**3 + 6*a**5*b**4*c*e*f + 3*a**5*b**4*d**2*f + 3*a**5*b**4*d*e**2 - 6*a**4*b**5*c*d*f - 3*a**4*b**5*c*e**2 - 3*a**4*b**5*d**2*e + 3*a**3*b**6*c**2*f + 6*a**3*b**6*c*d*e + a**3*b**6*d**3 - 3*a**2*b**7*c**2*e - 3*a**2*b**7*c*d**2 + 3*a*b**8*c**2*d - b**9*c**3, Lambda(_t, _t*log(-3*_t*a**3*b/(a**3*f - a**2*b*e + a*b**2*d - b**3*c) + x))) + f*x/b + (-2*a*c + x**3*(-5*a*d + 5*b*c))/(10*a**2*x**5)","A",0
244,1,432,0,46.610037," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**8/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a^{10} b^{2} + a^{9} f^{3} - 3 a^{8} b e f^{2} + 3 a^{7} b^{2} d f^{2} + 3 a^{7} b^{2} e^{2} f - 3 a^{6} b^{3} c f^{2} - 6 a^{6} b^{3} d e f - a^{6} b^{3} e^{3} + 6 a^{5} b^{4} c e f + 3 a^{5} b^{4} d^{2} f + 3 a^{5} b^{4} d e^{2} - 6 a^{4} b^{5} c d f - 3 a^{4} b^{5} c e^{2} - 3 a^{4} b^{5} d^{2} e + 3 a^{3} b^{6} c^{2} f + 6 a^{3} b^{6} c d e + a^{3} b^{6} d^{3} - 3 a^{2} b^{7} c^{2} e - 3 a^{2} b^{7} c d^{2} + 3 a b^{8} c^{2} d - b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t^{2} a^{7} b}{a^{6} f^{2} - 2 a^{5} b e f + 2 a^{4} b^{2} d f + a^{4} b^{2} e^{2} - 2 a^{3} b^{3} c f - 2 a^{3} b^{3} d e + 2 a^{2} b^{4} c e + a^{2} b^{4} d^{2} - 2 a b^{5} c d + b^{6} c^{2}} + x \right)} \right)\right)} + \frac{- 4 a^{2} c + x^{6} \left(- 28 a^{2} e + 28 a b d - 28 b^{2} c\right) + x^{3} \left(- 7 a^{2} d + 7 a b c\right)}{28 a^{3} x^{7}}"," ",0,"RootSum(27*_t**3*a**10*b**2 + a**9*f**3 - 3*a**8*b*e*f**2 + 3*a**7*b**2*d*f**2 + 3*a**7*b**2*e**2*f - 3*a**6*b**3*c*f**2 - 6*a**6*b**3*d*e*f - a**6*b**3*e**3 + 6*a**5*b**4*c*e*f + 3*a**5*b**4*d**2*f + 3*a**5*b**4*d*e**2 - 6*a**4*b**5*c*d*f - 3*a**4*b**5*c*e**2 - 3*a**4*b**5*d**2*e + 3*a**3*b**6*c**2*f + 6*a**3*b**6*c*d*e + a**3*b**6*d**3 - 3*a**2*b**7*c**2*e - 3*a**2*b**7*c*d**2 + 3*a*b**8*c**2*d - b**9*c**3, Lambda(_t, _t*log(9*_t**2*a**7*b/(a**6*f**2 - 2*a**5*b*e*f + 2*a**4*b**2*d*f + a**4*b**2*e**2 - 2*a**3*b**3*c*f - 2*a**3*b**3*d*e + 2*a**2*b**4*c*e + a**2*b**4*d**2 - 2*a*b**5*c*d + b**6*c**2) + x))) + (-4*a**2*c + x**6*(-28*a**2*e + 28*a*b*d - 28*b**2*c) + x**3*(-7*a**2*d + 7*a*b*c))/(28*a**3*x**7)","A",0
245,1,348,0,88.516005," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**9/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a^{11} b - a^{9} f^{3} + 3 a^{8} b e f^{2} - 3 a^{7} b^{2} d f^{2} - 3 a^{7} b^{2} e^{2} f + 3 a^{6} b^{3} c f^{2} + 6 a^{6} b^{3} d e f + a^{6} b^{3} e^{3} - 6 a^{5} b^{4} c e f - 3 a^{5} b^{4} d^{2} f - 3 a^{5} b^{4} d e^{2} + 6 a^{4} b^{5} c d f + 3 a^{4} b^{5} c e^{2} + 3 a^{4} b^{5} d^{2} e - 3 a^{3} b^{6} c^{2} f - 6 a^{3} b^{6} c d e - a^{3} b^{6} d^{3} + 3 a^{2} b^{7} c^{2} e + 3 a^{2} b^{7} c d^{2} - 3 a b^{8} c^{2} d + b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{3 t a^{4}}{a^{3} f - a^{2} b e + a b^{2} d - b^{3} c} + x \right)} \right)\right)} + \frac{- 5 a^{2} c + x^{6} \left(- 20 a^{2} e + 20 a b d - 20 b^{2} c\right) + x^{3} \left(- 8 a^{2} d + 8 a b c\right)}{40 a^{3} x^{8}}"," ",0,"RootSum(27*_t**3*a**11*b - a**9*f**3 + 3*a**8*b*e*f**2 - 3*a**7*b**2*d*f**2 - 3*a**7*b**2*e**2*f + 3*a**6*b**3*c*f**2 + 6*a**6*b**3*d*e*f + a**6*b**3*e**3 - 6*a**5*b**4*c*e*f - 3*a**5*b**4*d**2*f - 3*a**5*b**4*d*e**2 + 6*a**4*b**5*c*d*f + 3*a**4*b**5*c*e**2 + 3*a**4*b**5*d**2*e - 3*a**3*b**6*c**2*f - 6*a**3*b**6*c*d*e - a**3*b**6*d**3 + 3*a**2*b**7*c**2*e + 3*a**2*b**7*c*d**2 - 3*a*b**8*c**2*d + b**9*c**3, Lambda(_t, _t*log(3*_t*a**4/(a**3*f - a**2*b*e + a*b**2*d - b**3*c) + x))) + (-5*a**2*c + x**6*(-20*a**2*e + 20*a*b*d - 20*b**2*c) + x**3*(-8*a**2*d + 8*a*b*c))/(40*a**3*x**8)","A",0
246,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**11/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**12/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**14/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**15/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**17/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,1,236,0,14.416196," ","integrate(x**11*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","- \frac{a^{2} \left(6 a^{3} f - 5 a^{2} b e + 4 a b^{2} d - 3 b^{3} c\right) \log{\left(a + b x^{3} \right)}}{3 b^{7}} + x^{12} \left(- \frac{a f}{6 b^{3}} + \frac{e}{12 b^{2}}\right) + x^{9} \left(\frac{a^{2} f}{3 b^{4}} - \frac{2 a e}{9 b^{3}} + \frac{d}{9 b^{2}}\right) + x^{6} \left(- \frac{2 a^{3} f}{3 b^{5}} + \frac{a^{2} e}{2 b^{4}} - \frac{a d}{3 b^{3}} + \frac{c}{6 b^{2}}\right) + x^{3} \left(\frac{5 a^{4} f}{3 b^{6}} - \frac{4 a^{3} e}{3 b^{5}} + \frac{a^{2} d}{b^{4}} - \frac{2 a c}{3 b^{3}}\right) + \frac{- a^{6} f + a^{5} b e - a^{4} b^{2} d + a^{3} b^{3} c}{3 a b^{7} + 3 b^{8} x^{3}} + \frac{f x^{15}}{15 b^{2}}"," ",0,"-a**2*(6*a**3*f - 5*a**2*b*e + 4*a*b**2*d - 3*b**3*c)*log(a + b*x**3)/(3*b**7) + x**12*(-a*f/(6*b**3) + e/(12*b**2)) + x**9*(a**2*f/(3*b**4) - 2*a*e/(9*b**3) + d/(9*b**2)) + x**6*(-2*a**3*f/(3*b**5) + a**2*e/(2*b**4) - a*d/(3*b**3) + c/(6*b**2)) + x**3*(5*a**4*f/(3*b**6) - 4*a**3*e/(3*b**5) + a**2*d/b**4 - 2*a*c/(3*b**3)) + (-a**6*f + a**5*b*e - a**4*b**2*d + a**3*b**3*c)/(3*a*b**7 + 3*b**8*x**3) + f*x**15/(15*b**2)","A",0
252,1,189,0,12.380956," ","integrate(x**8*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","\frac{a \left(5 a^{3} f - 4 a^{2} b e + 3 a b^{2} d - 2 b^{3} c\right) \log{\left(a + b x^{3} \right)}}{3 b^{6}} + x^{9} \left(- \frac{2 a f}{9 b^{3}} + \frac{e}{9 b^{2}}\right) + x^{6} \left(\frac{a^{2} f}{2 b^{4}} - \frac{a e}{3 b^{3}} + \frac{d}{6 b^{2}}\right) + x^{3} \left(- \frac{4 a^{3} f}{3 b^{5}} + \frac{a^{2} e}{b^{4}} - \frac{2 a d}{3 b^{3}} + \frac{c}{3 b^{2}}\right) + \frac{a^{5} f - a^{4} b e + a^{3} b^{2} d - a^{2} b^{3} c}{3 a b^{6} + 3 b^{7} x^{3}} + \frac{f x^{12}}{12 b^{2}}"," ",0,"a*(5*a**3*f - 4*a**2*b*e + 3*a*b**2*d - 2*b**3*c)*log(a + b*x**3)/(3*b**6) + x**9*(-2*a*f/(9*b**3) + e/(9*b**2)) + x**6*(a**2*f/(2*b**4) - a*e/(3*b**3) + d/(6*b**2)) + x**3*(-4*a**3*f/(3*b**5) + a**2*e/b**4 - 2*a*d/(3*b**3) + c/(3*b**2)) + (a**5*f - a**4*b*e + a**3*b**2*d - a**2*b**3*c)/(3*a*b**6 + 3*b**7*x**3) + f*x**12/(12*b**2)","A",0
253,1,141,0,12.811928," ","integrate(x**5*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","x^{6} \left(- \frac{a f}{3 b^{3}} + \frac{e}{6 b^{2}}\right) + x^{3} \left(\frac{a^{2} f}{b^{4}} - \frac{2 a e}{3 b^{3}} + \frac{d}{3 b^{2}}\right) + \frac{- a^{4} f + a^{3} b e - a^{2} b^{2} d + a b^{3} c}{3 a b^{5} + 3 b^{6} x^{3}} + \frac{f x^{9}}{9 b^{2}} - \frac{\left(4 a^{3} f - 3 a^{2} b e + 2 a b^{2} d - b^{3} c\right) \log{\left(a + b x^{3} \right)}}{3 b^{5}}"," ",0,"x**6*(-a*f/(3*b**3) + e/(6*b**2)) + x**3*(a**2*f/b**4 - 2*a*e/(3*b**3) + d/(3*b**2)) + (-a**4*f + a**3*b*e - a**2*b**2*d + a*b**3*c)/(3*a*b**5 + 3*b**6*x**3) + f*x**9/(9*b**2) - (4*a**3*f - 3*a**2*b*e + 2*a*b**2*d - b**3*c)*log(a + b*x**3)/(3*b**5)","A",0
254,1,100,0,11.613522," ","integrate(x**2*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","x^{3} \left(- \frac{2 a f}{3 b^{3}} + \frac{e}{3 b^{2}}\right) + \frac{a^{3} f - a^{2} b e + a b^{2} d - b^{3} c}{3 a b^{4} + 3 b^{5} x^{3}} + \frac{f x^{6}}{6 b^{2}} + \frac{\left(3 a^{2} f - 2 a b e + b^{2} d\right) \log{\left(a + b x^{3} \right)}}{3 b^{4}}"," ",0,"x**3*(-2*a*f/(3*b**3) + e/(3*b**2)) + (a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(3*a*b**4 + 3*b**5*x**3) + f*x**6/(6*b**2) + (3*a**2*f - 2*a*b*e + b**2*d)*log(a + b*x**3)/(3*b**4)","A",0
255,1,95,0,41.960306," ","integrate((f*x**9+e*x**6+d*x**3+c)/x/(b*x**3+a)**2,x)","\frac{- a^{3} f + a^{2} b e - a b^{2} d + b^{3} c}{3 a^{2} b^{3} + 3 a b^{4} x^{3}} + \frac{f x^{3}}{3 b^{2}} + \frac{c \log{\left(x \right)}}{a^{2}} - \frac{\left(2 a^{3} f - a^{2} b e + b^{3} c\right) \log{\left(\frac{a}{b} + x^{3} \right)}}{3 a^{2} b^{3}}"," ",0,"(-a**3*f + a**2*b*e - a*b**2*d + b**3*c)/(3*a**2*b**3 + 3*a*b**4*x**3) + f*x**3/(3*b**2) + c*log(x)/a**2 - (2*a**3*f - a**2*b*e + b**3*c)*log(a/b + x**3)/(3*a**2*b**3)","A",0
256,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**4/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**7/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**10/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**13/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,1,500,0,15.902925," ","integrate(x**9*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","x^{10} \left(- \frac{a f}{5 b^{3}} + \frac{e}{10 b^{2}}\right) + x^{7} \left(\frac{3 a^{2} f}{7 b^{4}} - \frac{2 a e}{7 b^{3}} + \frac{d}{7 b^{2}}\right) + x^{4} \left(- \frac{a^{3} f}{b^{5}} + \frac{3 a^{2} e}{4 b^{4}} - \frac{a d}{2 b^{3}} + \frac{c}{4 b^{2}}\right) + x \left(\frac{5 a^{4} f}{b^{6}} - \frac{4 a^{3} e}{b^{5}} + \frac{3 a^{2} d}{b^{4}} - \frac{2 a c}{b^{3}}\right) + \frac{x \left(a^{5} f - a^{4} b e + a^{3} b^{2} d - a^{2} b^{3} c\right)}{3 a b^{6} + 3 b^{7} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} b^{19} + 4096 a^{13} f^{3} - 9984 a^{12} b e f^{2} + 7680 a^{11} b^{2} d f^{2} + 8112 a^{11} b^{2} e^{2} f - 5376 a^{10} b^{3} c f^{2} - 12480 a^{10} b^{3} d e f - 2197 a^{10} b^{3} e^{3} + 8736 a^{9} b^{4} c e f + 4800 a^{9} b^{4} d^{2} f + 5070 a^{9} b^{4} d e^{2} - 6720 a^{8} b^{5} c d f - 3549 a^{8} b^{5} c e^{2} - 3900 a^{8} b^{5} d^{2} e + 2352 a^{7} b^{6} c^{2} f + 5460 a^{7} b^{6} c d e + 1000 a^{7} b^{6} d^{3} - 1911 a^{6} b^{7} c^{2} e - 2100 a^{6} b^{7} c d^{2} + 1470 a^{5} b^{8} c^{2} d - 343 a^{4} b^{9} c^{3}, \left( t \mapsto t \log{\left(- \frac{9 t b^{6}}{16 a^{4} f - 13 a^{3} b e + 10 a^{2} b^{2} d - 7 a b^{3} c} + x \right)} \right)\right)} + \frac{f x^{13}}{13 b^{2}}"," ",0,"x**10*(-a*f/(5*b**3) + e/(10*b**2)) + x**7*(3*a**2*f/(7*b**4) - 2*a*e/(7*b**3) + d/(7*b**2)) + x**4*(-a**3*f/b**5 + 3*a**2*e/(4*b**4) - a*d/(2*b**3) + c/(4*b**2)) + x*(5*a**4*f/b**6 - 4*a**3*e/b**5 + 3*a**2*d/b**4 - 2*a*c/b**3) + x*(a**5*f - a**4*b*e + a**3*b**2*d - a**2*b**3*c)/(3*a*b**6 + 3*b**7*x**3) + RootSum(729*_t**3*b**19 + 4096*a**13*f**3 - 9984*a**12*b*e*f**2 + 7680*a**11*b**2*d*f**2 + 8112*a**11*b**2*e**2*f - 5376*a**10*b**3*c*f**2 - 12480*a**10*b**3*d*e*f - 2197*a**10*b**3*e**3 + 8736*a**9*b**4*c*e*f + 4800*a**9*b**4*d**2*f + 5070*a**9*b**4*d*e**2 - 6720*a**8*b**5*c*d*f - 3549*a**8*b**5*c*e**2 - 3900*a**8*b**5*d**2*e + 2352*a**7*b**6*c**2*f + 5460*a**7*b**6*c*d*e + 1000*a**7*b**6*d**3 - 1911*a**6*b**7*c**2*e - 2100*a**6*b**7*c*d**2 + 1470*a**5*b**8*c**2*d - 343*a**4*b**9*c**3, Lambda(_t, _t*log(-9*_t*b**6/(16*a**4*f - 13*a**3*b*e + 10*a**2*b**2*d - 7*a*b**3*c) + x))) + f*x**13/(13*b**2)","A",0
261,1,539,0,58.232200," ","integrate(x**7*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","x^{8} \left(- \frac{a f}{4 b^{3}} + \frac{e}{8 b^{2}}\right) + x^{5} \left(\frac{3 a^{2} f}{5 b^{4}} - \frac{2 a e}{5 b^{3}} + \frac{d}{5 b^{2}}\right) + x^{2} \left(- \frac{2 a^{3} f}{b^{5}} + \frac{3 a^{2} e}{2 b^{4}} - \frac{a d}{b^{3}} + \frac{c}{2 b^{2}}\right) + \frac{x^{2} \left(- a^{4} f + a^{3} b e - a^{2} b^{2} d + a b^{3} c\right)}{3 a b^{5} + 3 b^{6} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} b^{17} + 2744 a^{11} f^{3} - 6468 a^{10} b e f^{2} + 4704 a^{9} b^{2} d f^{2} + 5082 a^{9} b^{2} e^{2} f - 2940 a^{8} b^{3} c f^{2} - 7392 a^{8} b^{3} d e f - 1331 a^{8} b^{3} e^{3} + 4620 a^{7} b^{4} c e f + 2688 a^{7} b^{4} d^{2} f + 2904 a^{7} b^{4} d e^{2} - 3360 a^{6} b^{5} c d f - 1815 a^{6} b^{5} c e^{2} - 2112 a^{6} b^{5} d^{2} e + 1050 a^{5} b^{6} c^{2} f + 2640 a^{5} b^{6} c d e + 512 a^{5} b^{6} d^{3} - 825 a^{4} b^{7} c^{2} e - 960 a^{4} b^{7} c d^{2} + 600 a^{3} b^{8} c^{2} d - 125 a^{2} b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{81 t^{2} b^{11}}{196 a^{7} f^{2} - 308 a^{6} b e f + 224 a^{5} b^{2} d f + 121 a^{5} b^{2} e^{2} - 140 a^{4} b^{3} c f - 176 a^{4} b^{3} d e + 110 a^{3} b^{4} c e + 64 a^{3} b^{4} d^{2} - 80 a^{2} b^{5} c d + 25 a b^{6} c^{2}} + x \right)} \right)\right)} + \frac{f x^{11}}{11 b^{2}}"," ",0,"x**8*(-a*f/(4*b**3) + e/(8*b**2)) + x**5*(3*a**2*f/(5*b**4) - 2*a*e/(5*b**3) + d/(5*b**2)) + x**2*(-2*a**3*f/b**5 + 3*a**2*e/(2*b**4) - a*d/b**3 + c/(2*b**2)) + x**2*(-a**4*f + a**3*b*e - a**2*b**2*d + a*b**3*c)/(3*a*b**5 + 3*b**6*x**3) + RootSum(729*_t**3*b**17 + 2744*a**11*f**3 - 6468*a**10*b*e*f**2 + 4704*a**9*b**2*d*f**2 + 5082*a**9*b**2*e**2*f - 2940*a**8*b**3*c*f**2 - 7392*a**8*b**3*d*e*f - 1331*a**8*b**3*e**3 + 4620*a**7*b**4*c*e*f + 2688*a**7*b**4*d**2*f + 2904*a**7*b**4*d*e**2 - 3360*a**6*b**5*c*d*f - 1815*a**6*b**5*c*e**2 - 2112*a**6*b**5*d**2*e + 1050*a**5*b**6*c**2*f + 2640*a**5*b**6*c*d*e + 512*a**5*b**6*d**3 - 825*a**4*b**7*c**2*e - 960*a**4*b**7*c*d**2 + 600*a**3*b**8*c**2*d - 125*a**2*b**9*c**3, Lambda(_t, _t*log(81*_t**2*b**11/(196*a**7*f**2 - 308*a**6*b*e*f + 224*a**5*b**2*d*f + 121*a**5*b**2*e**2 - 140*a**4*b**3*c*f - 176*a**4*b**3*d*e + 110*a**3*b**4*c*e + 64*a**3*b**4*d**2 - 80*a**2*b**5*c*d + 25*a*b**6*c**2) + x))) + f*x**11/(11*b**2)","A",0
262,1,449,0,14.983188," ","integrate(x**6*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","x^{7} \left(- \frac{2 a f}{7 b^{3}} + \frac{e}{7 b^{2}}\right) + x^{4} \left(\frac{3 a^{2} f}{4 b^{4}} - \frac{a e}{2 b^{3}} + \frac{d}{4 b^{2}}\right) + x \left(- \frac{4 a^{3} f}{b^{5}} + \frac{3 a^{2} e}{b^{4}} - \frac{2 a d}{b^{3}} + \frac{c}{b^{2}}\right) + \frac{x \left(- a^{4} f + a^{3} b e - a^{2} b^{2} d + a b^{3} c\right)}{3 a b^{5} + 3 b^{6} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} b^{16} - 2197 a^{10} f^{3} + 5070 a^{9} b e f^{2} - 3549 a^{8} b^{2} d f^{2} - 3900 a^{8} b^{2} e^{2} f + 2028 a^{7} b^{3} c f^{2} + 5460 a^{7} b^{3} d e f + 1000 a^{7} b^{3} e^{3} - 3120 a^{6} b^{4} c e f - 1911 a^{6} b^{4} d^{2} f - 2100 a^{6} b^{4} d e^{2} + 2184 a^{5} b^{5} c d f + 1200 a^{5} b^{5} c e^{2} + 1470 a^{5} b^{5} d^{2} e - 624 a^{4} b^{6} c^{2} f - 1680 a^{4} b^{6} c d e - 343 a^{4} b^{6} d^{3} + 480 a^{3} b^{7} c^{2} e + 588 a^{3} b^{7} c d^{2} - 336 a^{2} b^{8} c^{2} d + 64 a b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t b^{5}}{13 a^{3} f - 10 a^{2} b e + 7 a b^{2} d - 4 b^{3} c} + x \right)} \right)\right)} + \frac{f x^{10}}{10 b^{2}}"," ",0,"x**7*(-2*a*f/(7*b**3) + e/(7*b**2)) + x**4*(3*a**2*f/(4*b**4) - a*e/(2*b**3) + d/(4*b**2)) + x*(-4*a**3*f/b**5 + 3*a**2*e/b**4 - 2*a*d/b**3 + c/b**2) + x*(-a**4*f + a**3*b*e - a**2*b**2*d + a*b**3*c)/(3*a*b**5 + 3*b**6*x**3) + RootSum(729*_t**3*b**16 - 2197*a**10*f**3 + 5070*a**9*b*e*f**2 - 3549*a**8*b**2*d*f**2 - 3900*a**8*b**2*e**2*f + 2028*a**7*b**3*c*f**2 + 5460*a**7*b**3*d*e*f + 1000*a**7*b**3*e**3 - 3120*a**6*b**4*c*e*f - 1911*a**6*b**4*d**2*f - 2100*a**6*b**4*d*e**2 + 2184*a**5*b**5*c*d*f + 1200*a**5*b**5*c*e**2 + 1470*a**5*b**5*d**2*e - 624*a**4*b**6*c**2*f - 1680*a**4*b**6*c*d*e - 343*a**4*b**6*d**3 + 480*a**3*b**7*c**2*e + 588*a**3*b**7*c*d**2 - 336*a**2*b**8*c**2*d + 64*a*b**9*c**3, Lambda(_t, _t*log(9*_t*b**5/(13*a**3*f - 10*a**2*b*e + 7*a*b**2*d - 4*b**3*c) + x))) + f*x**10/(10*b**2)","A",0
263,1,490,0,51.285074," ","integrate(x**4*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","x^{5} \left(- \frac{2 a f}{5 b^{3}} + \frac{e}{5 b^{2}}\right) + x^{2} \left(\frac{3 a^{2} f}{2 b^{4}} - \frac{a e}{b^{3}} + \frac{d}{2 b^{2}}\right) + \frac{x^{2} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{3 a b^{4} + 3 b^{5} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a b^{14} - 1331 a^{9} f^{3} + 2904 a^{8} b e f^{2} - 1815 a^{7} b^{2} d f^{2} - 2112 a^{7} b^{2} e^{2} f + 726 a^{6} b^{3} c f^{2} + 2640 a^{6} b^{3} d e f + 512 a^{6} b^{3} e^{3} - 1056 a^{5} b^{4} c e f - 825 a^{5} b^{4} d^{2} f - 960 a^{5} b^{4} d e^{2} + 660 a^{4} b^{5} c d f + 384 a^{4} b^{5} c e^{2} + 600 a^{4} b^{5} d^{2} e - 132 a^{3} b^{6} c^{2} f - 480 a^{3} b^{6} c d e - 125 a^{3} b^{6} d^{3} + 96 a^{2} b^{7} c^{2} e + 150 a^{2} b^{7} c d^{2} - 60 a b^{8} c^{2} d + 8 b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{81 t^{2} a b^{9}}{121 a^{6} f^{2} - 176 a^{5} b e f + 110 a^{4} b^{2} d f + 64 a^{4} b^{2} e^{2} - 44 a^{3} b^{3} c f - 80 a^{3} b^{3} d e + 32 a^{2} b^{4} c e + 25 a^{2} b^{4} d^{2} - 20 a b^{5} c d + 4 b^{6} c^{2}} + x \right)} \right)\right)} + \frac{f x^{8}}{8 b^{2}}"," ",0,"x**5*(-2*a*f/(5*b**3) + e/(5*b**2)) + x**2*(3*a**2*f/(2*b**4) - a*e/b**3 + d/(2*b**2)) + x**2*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(3*a*b**4 + 3*b**5*x**3) + RootSum(729*_t**3*a*b**14 - 1331*a**9*f**3 + 2904*a**8*b*e*f**2 - 1815*a**7*b**2*d*f**2 - 2112*a**7*b**2*e**2*f + 726*a**6*b**3*c*f**2 + 2640*a**6*b**3*d*e*f + 512*a**6*b**3*e**3 - 1056*a**5*b**4*c*e*f - 825*a**5*b**4*d**2*f - 960*a**5*b**4*d*e**2 + 660*a**4*b**5*c*d*f + 384*a**4*b**5*c*e**2 + 600*a**4*b**5*d**2*e - 132*a**3*b**6*c**2*f - 480*a**3*b**6*c*d*e - 125*a**3*b**6*d**3 + 96*a**2*b**7*c**2*e + 150*a**2*b**7*c*d**2 - 60*a*b**8*c**2*d + 8*b**9*c**3, Lambda(_t, _t*log(81*_t**2*a*b**9/(121*a**6*f**2 - 176*a**5*b*e*f + 110*a**4*b**2*d*f + 64*a**4*b**2*e**2 - 44*a**3*b**3*c*f - 80*a**3*b**3*d*e + 32*a**2*b**4*c*e + 25*a**2*b**4*d**2 - 20*a*b**5*c*d + 4*b**6*c**2) + x))) + f*x**8/(8*b**2)","A",0
264,1,401,0,12.901388," ","integrate(x**3*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","x^{4} \left(- \frac{a f}{2 b^{3}} + \frac{e}{4 b^{2}}\right) + x \left(\frac{3 a^{2} f}{b^{4}} - \frac{2 a e}{b^{3}} + \frac{d}{b^{2}}\right) + \frac{x \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{3 a b^{4} + 3 b^{5} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{2} b^{13} + 1000 a^{9} f^{3} - 2100 a^{8} b e f^{2} + 1200 a^{7} b^{2} d f^{2} + 1470 a^{7} b^{2} e^{2} f - 300 a^{6} b^{3} c f^{2} - 1680 a^{6} b^{3} d e f - 343 a^{6} b^{3} e^{3} + 420 a^{5} b^{4} c e f + 480 a^{5} b^{4} d^{2} f + 588 a^{5} b^{4} d e^{2} - 240 a^{4} b^{5} c d f - 147 a^{4} b^{5} c e^{2} - 336 a^{4} b^{5} d^{2} e + 30 a^{3} b^{6} c^{2} f + 168 a^{3} b^{6} c d e + 64 a^{3} b^{6} d^{3} - 21 a^{2} b^{7} c^{2} e - 48 a^{2} b^{7} c d^{2} + 12 a b^{8} c^{2} d - b^{9} c^{3}, \left( t \mapsto t \log{\left(- \frac{9 t a b^{4}}{10 a^{3} f - 7 a^{2} b e + 4 a b^{2} d - b^{3} c} + x \right)} \right)\right)} + \frac{f x^{7}}{7 b^{2}}"," ",0,"x**4*(-a*f/(2*b**3) + e/(4*b**2)) + x*(3*a**2*f/b**4 - 2*a*e/b**3 + d/b**2) + x*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(3*a*b**4 + 3*b**5*x**3) + RootSum(729*_t**3*a**2*b**13 + 1000*a**9*f**3 - 2100*a**8*b*e*f**2 + 1200*a**7*b**2*d*f**2 + 1470*a**7*b**2*e**2*f - 300*a**6*b**3*c*f**2 - 1680*a**6*b**3*d*e*f - 343*a**6*b**3*e**3 + 420*a**5*b**4*c*e*f + 480*a**5*b**4*d**2*f + 588*a**5*b**4*d*e**2 - 240*a**4*b**5*c*d*f - 147*a**4*b**5*c*e**2 - 336*a**4*b**5*d**2*e + 30*a**3*b**6*c**2*f + 168*a**3*b**6*c*d*e + 64*a**3*b**6*d**3 - 21*a**2*b**7*c**2*e - 48*a**2*b**7*c*d**2 + 12*a*b**8*c**2*d - b**9*c**3, Lambda(_t, _t*log(-9*_t*a*b**4/(10*a**3*f - 7*a**2*b*e + 4*a*b**2*d - b**3*c) + x))) + f*x**7/(7*b**2)","A",0
265,1,461,0,22.482498," ","integrate(x*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","x^{2} \left(- \frac{a f}{b^{3}} + \frac{e}{2 b^{2}}\right) + \frac{x^{2} \left(- a^{3} f + a^{2} b e - a b^{2} d + b^{3} c\right)}{3 a^{2} b^{3} + 3 a b^{4} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{4} b^{11} + 512 a^{9} f^{3} - 960 a^{8} b e f^{2} + 384 a^{7} b^{2} d f^{2} + 600 a^{7} b^{2} e^{2} f + 192 a^{6} b^{3} c f^{2} - 480 a^{6} b^{3} d e f - 125 a^{6} b^{3} e^{3} - 240 a^{5} b^{4} c e f + 96 a^{5} b^{4} d^{2} f + 150 a^{5} b^{4} d e^{2} + 96 a^{4} b^{5} c d f + 75 a^{4} b^{5} c e^{2} - 60 a^{4} b^{5} d^{2} e + 24 a^{3} b^{6} c^{2} f - 60 a^{3} b^{6} c d e + 8 a^{3} b^{6} d^{3} - 15 a^{2} b^{7} c^{2} e + 12 a^{2} b^{7} c d^{2} + 6 a b^{8} c^{2} d + b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{81 t^{2} a^{3} b^{7}}{64 a^{6} f^{2} - 80 a^{5} b e f + 32 a^{4} b^{2} d f + 25 a^{4} b^{2} e^{2} + 16 a^{3} b^{3} c f - 20 a^{3} b^{3} d e - 10 a^{2} b^{4} c e + 4 a^{2} b^{4} d^{2} + 4 a b^{5} c d + b^{6} c^{2}} + x \right)} \right)\right)} + \frac{f x^{5}}{5 b^{2}}"," ",0,"x**2*(-a*f/b**3 + e/(2*b**2)) + x**2*(-a**3*f + a**2*b*e - a*b**2*d + b**3*c)/(3*a**2*b**3 + 3*a*b**4*x**3) + RootSum(729*_t**3*a**4*b**11 + 512*a**9*f**3 - 960*a**8*b*e*f**2 + 384*a**7*b**2*d*f**2 + 600*a**7*b**2*e**2*f + 192*a**6*b**3*c*f**2 - 480*a**6*b**3*d*e*f - 125*a**6*b**3*e**3 - 240*a**5*b**4*c*e*f + 96*a**5*b**4*d**2*f + 150*a**5*b**4*d*e**2 + 96*a**4*b**5*c*d*f + 75*a**4*b**5*c*e**2 - 60*a**4*b**5*d**2*e + 24*a**3*b**6*c**2*f - 60*a**3*b**6*c*d*e + 8*a**3*b**6*d**3 - 15*a**2*b**7*c**2*e + 12*a**2*b**7*c*d**2 + 6*a*b**8*c**2*d + b**9*c**3, Lambda(_t, _t*log(81*_t**2*a**3*b**7/(64*a**6*f**2 - 80*a**5*b*e*f + 32*a**4*b**2*d*f + 25*a**4*b**2*e**2 + 16*a**3*b**3*c*f - 20*a**3*b**3*d*e - 10*a**2*b**4*c*e + 4*a**2*b**4*d**2 + 4*a*b**5*c*d + b**6*c**2) + x))) + f*x**5/(5*b**2)","A",0
266,1,377,0,7.022535," ","integrate((f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**2,x)","x \left(- \frac{2 a f}{b^{3}} + \frac{e}{b^{2}}\right) + \frac{x \left(- a^{3} f + a^{2} b e - a b^{2} d + b^{3} c\right)}{3 a^{2} b^{3} + 3 a b^{4} x^{3}} + \operatorname{RootSum} {\left(729 t^{3} a^{5} b^{10} - 343 a^{9} f^{3} + 588 a^{8} b e f^{2} - 147 a^{7} b^{2} d f^{2} - 336 a^{7} b^{2} e^{2} f - 294 a^{6} b^{3} c f^{2} + 168 a^{6} b^{3} d e f + 64 a^{6} b^{3} e^{3} + 336 a^{5} b^{4} c e f - 21 a^{5} b^{4} d^{2} f - 48 a^{5} b^{4} d e^{2} - 84 a^{4} b^{5} c d f - 96 a^{4} b^{5} c e^{2} + 12 a^{4} b^{5} d^{2} e - 84 a^{3} b^{6} c^{2} f + 48 a^{3} b^{6} c d e - a^{3} b^{6} d^{3} + 48 a^{2} b^{7} c^{2} e - 6 a^{2} b^{7} c d^{2} - 12 a b^{8} c^{2} d - 8 b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{9 t a^{2} b^{3}}{7 a^{3} f - 4 a^{2} b e + a b^{2} d + 2 b^{3} c} + x \right)} \right)\right)} + \frac{f x^{4}}{4 b^{2}}"," ",0,"x*(-2*a*f/b**3 + e/b**2) + x*(-a**3*f + a**2*b*e - a*b**2*d + b**3*c)/(3*a**2*b**3 + 3*a*b**4*x**3) + RootSum(729*_t**3*a**5*b**10 - 343*a**9*f**3 + 588*a**8*b*e*f**2 - 147*a**7*b**2*d*f**2 - 336*a**7*b**2*e**2*f - 294*a**6*b**3*c*f**2 + 168*a**6*b**3*d*e*f + 64*a**6*b**3*e**3 + 336*a**5*b**4*c*e*f - 21*a**5*b**4*d**2*f - 48*a**5*b**4*d*e**2 - 84*a**4*b**5*c*d*f - 96*a**4*b**5*c*e**2 + 12*a**4*b**5*d**2*e - 84*a**3*b**6*c**2*f + 48*a**3*b**6*c*d*e - a**3*b**6*d**3 + 48*a**2*b**7*c**2*e - 6*a**2*b**7*c*d**2 - 12*a*b**8*c**2*d - 8*b**9*c**3, Lambda(_t, _t*log(9*_t*a**2*b**3/(7*a**3*f - 4*a**2*b*e + a*b**2*d + 2*b**3*c) + x))) + f*x**4/(4*b**2)","A",0
267,1,457,0,32.215849," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**2/(b*x**3+a)**2,x)","\frac{- 3 a b^{2} c + x^{3} \left(a^{3} f - a^{2} b e + a b^{2} d - 4 b^{3} c\right)}{3 a^{3} b^{2} x + 3 a^{2} b^{3} x^{4}} + \operatorname{RootSum} {\left(729 t^{3} a^{7} b^{8} - 125 a^{9} f^{3} + 150 a^{8} b e f^{2} + 75 a^{7} b^{2} d f^{2} - 60 a^{7} b^{2} e^{2} f - 300 a^{6} b^{3} c f^{2} - 60 a^{6} b^{3} d e f + 8 a^{6} b^{3} e^{3} + 240 a^{5} b^{4} c e f - 15 a^{5} b^{4} d^{2} f + 12 a^{5} b^{4} d e^{2} + 120 a^{4} b^{5} c d f - 48 a^{4} b^{5} c e^{2} + 6 a^{4} b^{5} d^{2} e - 240 a^{3} b^{6} c^{2} f - 48 a^{3} b^{6} c d e + a^{3} b^{6} d^{3} + 96 a^{2} b^{7} c^{2} e - 12 a^{2} b^{7} c d^{2} + 48 a b^{8} c^{2} d - 64 b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{81 t^{2} a^{5} b^{5}}{25 a^{6} f^{2} - 20 a^{5} b e f - 10 a^{4} b^{2} d f + 4 a^{4} b^{2} e^{2} + 40 a^{3} b^{3} c f + 4 a^{3} b^{3} d e - 16 a^{2} b^{4} c e + a^{2} b^{4} d^{2} - 8 a b^{5} c d + 16 b^{6} c^{2}} + x \right)} \right)\right)} + \frac{f x^{2}}{2 b^{2}}"," ",0,"(-3*a*b**2*c + x**3*(a**3*f - a**2*b*e + a*b**2*d - 4*b**3*c))/(3*a**3*b**2*x + 3*a**2*b**3*x**4) + RootSum(729*_t**3*a**7*b**8 - 125*a**9*f**3 + 150*a**8*b*e*f**2 + 75*a**7*b**2*d*f**2 - 60*a**7*b**2*e**2*f - 300*a**6*b**3*c*f**2 - 60*a**6*b**3*d*e*f + 8*a**6*b**3*e**3 + 240*a**5*b**4*c*e*f - 15*a**5*b**4*d**2*f + 12*a**5*b**4*d*e**2 + 120*a**4*b**5*c*d*f - 48*a**4*b**5*c*e**2 + 6*a**4*b**5*d**2*e - 240*a**3*b**6*c**2*f - 48*a**3*b**6*c*d*e + a**3*b**6*d**3 + 96*a**2*b**7*c**2*e - 12*a**2*b**7*c*d**2 + 48*a*b**8*c**2*d - 64*b**9*c**3, Lambda(_t, _t*log(81*_t**2*a**5*b**5/(25*a**6*f**2 - 20*a**5*b*e*f - 10*a**4*b**2*d*f + 4*a**4*b**2*e**2 + 40*a**3*b**3*c*f + 4*a**3*b**3*d*e - 16*a**2*b**4*c*e + a**2*b**4*d**2 - 8*a*b**5*c*d + 16*b**6*c**2) + x))) + f*x**2/(2*b**2)","A",0
268,1,381,0,77.381479," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**3/(b*x**3+a)**2,x)","\frac{- 3 a b^{2} c + x^{3} \left(2 a^{3} f - 2 a^{2} b e + 2 a b^{2} d - 5 b^{3} c\right)}{6 a^{3} b^{2} x^{2} + 6 a^{2} b^{3} x^{5}} + \operatorname{RootSum} {\left(729 t^{3} a^{8} b^{7} + 64 a^{9} f^{3} - 48 a^{8} b e f^{2} - 96 a^{7} b^{2} d f^{2} + 12 a^{7} b^{2} e^{2} f + 240 a^{6} b^{3} c f^{2} + 48 a^{6} b^{3} d e f - a^{6} b^{3} e^{3} - 120 a^{5} b^{4} c e f + 48 a^{5} b^{4} d^{2} f - 6 a^{5} b^{4} d e^{2} - 240 a^{4} b^{5} c d f + 15 a^{4} b^{5} c e^{2} - 12 a^{4} b^{5} d^{2} e + 300 a^{3} b^{6} c^{2} f + 60 a^{3} b^{6} c d e - 8 a^{3} b^{6} d^{3} - 75 a^{2} b^{7} c^{2} e + 60 a^{2} b^{7} c d^{2} - 150 a b^{8} c^{2} d + 125 b^{9} c^{3}, \left( t \mapsto t \log{\left(- \frac{9 t a^{3} b^{2}}{4 a^{3} f - a^{2} b e - 2 a b^{2} d + 5 b^{3} c} + x \right)} \right)\right)} + \frac{f x}{b^{2}}"," ",0,"(-3*a*b**2*c + x**3*(2*a**3*f - 2*a**2*b*e + 2*a*b**2*d - 5*b**3*c))/(6*a**3*b**2*x**2 + 6*a**2*b**3*x**5) + RootSum(729*_t**3*a**8*b**7 + 64*a**9*f**3 - 48*a**8*b*e*f**2 - 96*a**7*b**2*d*f**2 + 12*a**7*b**2*e**2*f + 240*a**6*b**3*c*f**2 + 48*a**6*b**3*d*e*f - a**6*b**3*e**3 - 120*a**5*b**4*c*e*f + 48*a**5*b**4*d**2*f - 6*a**5*b**4*d*e**2 - 240*a**4*b**5*c*d*f + 15*a**4*b**5*c*e**2 - 12*a**4*b**5*d**2*e + 300*a**3*b**6*c**2*f + 60*a**3*b**6*c*d*e - 8*a**3*b**6*d**3 - 75*a**2*b**7*c**2*e + 60*a**2*b**7*c*d**2 - 150*a*b**8*c**2*d + 125*b**9*c**3, Lambda(_t, _t*log(-9*_t*a**3*b**2/(4*a**3*f - a**2*b*e - 2*a*b**2*d + 5*b**3*c) + x))) + f*x/b**2","A",0
269,1,473,0,177.026348," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**5/(b*x**3+a)**2,x)","\operatorname{RootSum} {\left(729 t^{3} a^{10} b^{5} + 8 a^{9} f^{3} + 12 a^{8} b e f^{2} - 48 a^{7} b^{2} d f^{2} + 6 a^{7} b^{2} e^{2} f + 84 a^{6} b^{3} c f^{2} - 48 a^{6} b^{3} d e f + a^{6} b^{3} e^{3} + 84 a^{5} b^{4} c e f + 96 a^{5} b^{4} d^{2} f - 12 a^{5} b^{4} d e^{2} - 336 a^{4} b^{5} c d f + 21 a^{4} b^{5} c e^{2} + 48 a^{4} b^{5} d^{2} e + 294 a^{3} b^{6} c^{2} f - 168 a^{3} b^{6} c d e - 64 a^{3} b^{6} d^{3} + 147 a^{2} b^{7} c^{2} e + 336 a^{2} b^{7} c d^{2} - 588 a b^{8} c^{2} d + 343 b^{9} c^{3}, \left( t \mapsto t \log{\left(\frac{81 t^{2} a^{7} b^{3}}{4 a^{6} f^{2} + 4 a^{5} b e f - 16 a^{4} b^{2} d f + a^{4} b^{2} e^{2} + 28 a^{3} b^{3} c f - 8 a^{3} b^{3} d e + 14 a^{2} b^{4} c e + 16 a^{2} b^{4} d^{2} - 56 a b^{5} c d + 49 b^{6} c^{2}} + x \right)} \right)\right)} + \frac{- 3 a^{2} b c + x^{6} \left(- 4 a^{3} f + 4 a^{2} b e - 16 a b^{2} d + 28 b^{3} c\right) + x^{3} \left(- 12 a^{2} b d + 21 a b^{2} c\right)}{12 a^{4} b x^{4} + 12 a^{3} b^{2} x^{7}}"," ",0,"RootSum(729*_t**3*a**10*b**5 + 8*a**9*f**3 + 12*a**8*b*e*f**2 - 48*a**7*b**2*d*f**2 + 6*a**7*b**2*e**2*f + 84*a**6*b**3*c*f**2 - 48*a**6*b**3*d*e*f + a**6*b**3*e**3 + 84*a**5*b**4*c*e*f + 96*a**5*b**4*d**2*f - 12*a**5*b**4*d*e**2 - 336*a**4*b**5*c*d*f + 21*a**4*b**5*c*e**2 + 48*a**4*b**5*d**2*e + 294*a**3*b**6*c**2*f - 168*a**3*b**6*c*d*e - 64*a**3*b**6*d**3 + 147*a**2*b**7*c**2*e + 336*a**2*b**7*c*d**2 - 588*a*b**8*c**2*d + 343*b**9*c**3, Lambda(_t, _t*log(81*_t**2*a**7*b**3/(4*a**6*f**2 + 4*a**5*b*e*f - 16*a**4*b**2*d*f + a**4*b**2*e**2 + 28*a**3*b**3*c*f - 8*a**3*b**3*d*e + 14*a**2*b**4*c*e + 16*a**2*b**4*d**2 - 56*a*b**5*c*d + 49*b**6*c**2) + x))) + (-3*a**2*b*c + x**6*(-4*a**3*f + 4*a**2*b*e - 16*a*b**2*d + 28*b**3*c) + x**3*(-12*a**2*b*d + 21*a*b**2*c))/(12*a**4*b*x**4 + 12*a**3*b**2*x**7)","A",0
270,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**6/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**8/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**9/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**11/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**12/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**14/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,-1,0,0,0.000000," ","integrate(x**14*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,-1,0,0,0.000000," ","integrate(x**11*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,-1,0,0,0.000000," ","integrate(x**8*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,-1,0,0,0.000000," ","integrate(x**5*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,-1,0,0,0.000000," ","integrate(x**2*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**4/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**7/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**10/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**13/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate(x**12*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate(x**10*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate(x**9*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate(x**7*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,-1,0,0,0.000000," ","integrate(x**6*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate(x**4*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate(x**3*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate(x*(f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**2/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**3/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**5/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**6/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**8/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**9/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**11/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**12/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate((f*x**9+e*x**6+d*x**3+c)/x**14/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,1,53,0,0.179706," ","integrate((1-x)*x**4/(x**3+1),x)","- \frac{x^{3}}{3} + \frac{x^{2}}{2} + \frac{2 \log{\left(x + 1 \right)}}{3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-x**3/3 + x**2/2 + 2*log(x + 1)/3 + log(x**2 - x + 1)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
305,1,24,0,0.116625," ","integrate((1-x)*x**3/(x**3+1),x)","- \frac{x^{2}}{2} + x - \frac{2 \log{\left(x + 1 \right)}}{3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{3}"," ",0,"-x**2/2 + x - 2*log(x + 1)/3 + log(x**2 - x + 1)/3","A",0
306,1,44,0,0.230017," ","integrate((1-x)*x**2/(x**3+1),x)","- x + \frac{2 \log{\left(x + 1 \right)}}{3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-x + 2*log(x + 1)/3 + log(x**2 - x + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
307,1,42,0,0.270348," ","integrate((1-x)*x/(x**3+1),x)","- \frac{2 \log{\left(x + 1 \right)}}{3} - \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-2*log(x + 1)/3 - log(x**2 - x + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
308,1,46,0,0.208236," ","integrate((1-x)/x/(x**3+1),x)","\log{\left(x \right)} - \frac{2 \log{\left(x + 1 \right)}}{3} - \frac{\log{\left(x^{2} - x + 1 \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"log(x) - 2*log(x + 1)/3 - log(x**2 - x + 1)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
309,1,49,0,0.223209," ","integrate((1-x)/x**2/(x**3+1),x)","- \log{\left(x \right)} + \frac{2 \log{\left(x + 1 \right)}}{3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3} - \frac{1}{x}"," ",0,"-log(x) + 2*log(x + 1)/3 + log(x**2 - x + 1)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3 - 1/x","A",0
310,1,27,0,0.128484," ","integrate((1-x)/x**3/(x**3+1),x)","- \frac{2 \log{\left(x + 1 \right)}}{3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{3} - \frac{1 - 2 x}{2 x^{2}}"," ",0,"-2*log(x + 1)/3 + log(x**2 - x + 1)/3 - (1 - 2*x)/(2*x**2)","A",0
311,1,42,0,0.184138," ","integrate(x*(1+2*x)/(x**3+1),x)","\frac{\log{\left(x + 1 \right)}}{3} + \frac{5 \log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"log(x + 1)/3 + 5*log(x**2 - x + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
312,1,41,0,0.159252," ","integrate(x*(1+2*x)/(-x**3+1),x)","- \log{\left(x - 1 \right)} - \frac{\log{\left(x^{2} + x + 1 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-log(x - 1) - log(x**2 + x + 1)/2 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3","A",0
313,1,49,0,0.075316," ","integrate(x**2*(e*x**2+d*x+c)*(b*x**3+a),x)","\frac{a c x^{3}}{3} + \frac{a d x^{4}}{4} + \frac{a e x^{5}}{5} + \frac{b c x^{6}}{6} + \frac{b d x^{7}}{7} + \frac{b e x^{8}}{8}"," ",0,"a*c*x**3/3 + a*d*x**4/4 + a*e*x**5/5 + b*c*x**6/6 + b*d*x**7/7 + b*e*x**8/8","A",0
314,1,49,0,0.074366," ","integrate(x*(e*x**2+d*x+c)*(b*x**3+a),x)","\frac{a c x^{2}}{2} + \frac{a d x^{3}}{3} + \frac{a e x^{4}}{4} + \frac{b c x^{5}}{5} + \frac{b d x^{6}}{6} + \frac{b e x^{7}}{7}"," ",0,"a*c*x**2/2 + a*d*x**3/3 + a*e*x**4/4 + b*c*x**5/5 + b*d*x**6/6 + b*e*x**7/7","A",0
315,1,46,0,0.074380," ","integrate((e*x**2+d*x+c)*(b*x**3+a),x)","a c x + \frac{a d x^{2}}{2} + \frac{a e x^{3}}{3} + \frac{b c x^{4}}{4} + \frac{b d x^{5}}{5} + \frac{b e x^{6}}{6}"," ",0,"a*c*x + a*d*x**2/2 + a*e*x**3/3 + b*c*x**4/4 + b*d*x**5/5 + b*e*x**6/6","A",0
316,1,44,0,0.139184," ","integrate((e*x**2+d*x+c)*(b*x**3+a)/x,x)","a c \log{\left(x \right)} + a d x + \frac{a e x^{2}}{2} + \frac{b c x^{3}}{3} + \frac{b d x^{4}}{4} + \frac{b e x^{5}}{5}"," ",0,"a*c*log(x) + a*d*x + a*e*x**2/2 + b*c*x**3/3 + b*d*x**4/4 + b*e*x**5/5","A",0
317,1,41,0,0.164192," ","integrate((e*x**2+d*x+c)*(b*x**3+a)/x**2,x)","- \frac{a c}{x} + a d \log{\left(x \right)} + a e x + \frac{b c x^{2}}{2} + \frac{b d x^{3}}{3} + \frac{b e x^{4}}{4}"," ",0,"-a*c/x + a*d*log(x) + a*e*x + b*c*x**2/2 + b*d*x**3/3 + b*e*x**4/4","A",0
318,1,44,0,0.247232," ","integrate((e*x**2+d*x+c)*(b*x**3+a)/x**3,x)","a e \log{\left(x \right)} + b c x + \frac{b d x^{2}}{2} + \frac{b e x^{3}}{3} + \frac{- a c - 2 a d x}{2 x^{2}}"," ",0,"a*e*log(x) + b*c*x + b*d*x**2/2 + b*e*x**3/3 + (-a*c - 2*a*d*x)/(2*x**2)","A",0
319,1,92,0,0.088881," ","integrate(x**2*(e*x**2+d*x+c)*(b*x**3+a)**2,x)","\frac{a^{2} c x^{3}}{3} + \frac{a^{2} d x^{4}}{4} + \frac{a^{2} e x^{5}}{5} + \frac{a b c x^{6}}{3} + \frac{2 a b d x^{7}}{7} + \frac{a b e x^{8}}{4} + \frac{b^{2} c x^{9}}{9} + \frac{b^{2} d x^{10}}{10} + \frac{b^{2} e x^{11}}{11}"," ",0,"a**2*c*x**3/3 + a**2*d*x**4/4 + a**2*e*x**5/5 + a*b*c*x**6/3 + 2*a*b*d*x**7/7 + a*b*e*x**8/4 + b**2*c*x**9/9 + b**2*d*x**10/10 + b**2*e*x**11/11","A",0
320,1,94,0,0.085831," ","integrate(x*(e*x**2+d*x+c)*(b*x**3+a)**2,x)","\frac{a^{2} c x^{2}}{2} + \frac{a^{2} d x^{3}}{3} + \frac{a^{2} e x^{4}}{4} + \frac{2 a b c x^{5}}{5} + \frac{a b d x^{6}}{3} + \frac{2 a b e x^{7}}{7} + \frac{b^{2} c x^{8}}{8} + \frac{b^{2} d x^{9}}{9} + \frac{b^{2} e x^{10}}{10}"," ",0,"a**2*c*x**2/2 + a**2*d*x**3/3 + a**2*e*x**4/4 + 2*a*b*c*x**5/5 + a*b*d*x**6/3 + 2*a*b*e*x**7/7 + b**2*c*x**8/8 + b**2*d*x**9/9 + b**2*e*x**10/10","A",0
321,1,88,0,0.087347," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**2,x)","a^{2} c x + \frac{a^{2} d x^{2}}{2} + \frac{a^{2} e x^{3}}{3} + \frac{a b c x^{4}}{2} + \frac{2 a b d x^{5}}{5} + \frac{a b e x^{6}}{3} + \frac{b^{2} c x^{7}}{7} + \frac{b^{2} d x^{8}}{8} + \frac{b^{2} e x^{9}}{9}"," ",0,"a**2*c*x + a**2*d*x**2/2 + a**2*e*x**3/3 + a*b*c*x**4/2 + 2*a*b*d*x**5/5 + a*b*e*x**6/3 + b**2*c*x**7/7 + b**2*d*x**8/8 + b**2*e*x**9/9","A",0
322,1,88,0,0.189776," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**2/x,x)","a^{2} c \log{\left(x \right)} + a^{2} d x + \frac{a^{2} e x^{2}}{2} + \frac{2 a b c x^{3}}{3} + \frac{a b d x^{4}}{2} + \frac{2 a b e x^{5}}{5} + \frac{b^{2} c x^{6}}{6} + \frac{b^{2} d x^{7}}{7} + \frac{b^{2} e x^{8}}{8}"," ",0,"a**2*c*log(x) + a**2*d*x + a**2*e*x**2/2 + 2*a*b*c*x**3/3 + a*b*d*x**4/2 + 2*a*b*e*x**5/5 + b**2*c*x**6/6 + b**2*d*x**7/7 + b**2*e*x**8/8","A",0
323,1,82,0,0.247510," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**2/x**2,x)","- \frac{a^{2} c}{x} + a^{2} d \log{\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} + \frac{b^{2} c x^{5}}{5} + \frac{b^{2} d x^{6}}{6} + \frac{b^{2} e x^{7}}{7}"," ",0,"-a**2*c/x + 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**2*c*x**5/5 + b**2*d*x**6/6 + b**2*e*x**7/7","A",0
324,1,87,0,0.308373," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**2/x**3,x)","a^{2} e \log{\left(x \right)} + 2 a b c x + a b d x^{2} + \frac{2 a b e x^{3}}{3} + \frac{b^{2} c x^{4}}{4} + \frac{b^{2} d x^{5}}{5} + \frac{b^{2} e x^{6}}{6} + \frac{- a^{2} c - 2 a^{2} d x}{2 x^{2}}"," ",0,"a**2*e*log(x) + 2*a*b*c*x + a*b*d*x**2 + 2*a*b*e*x**3/3 + b**2*c*x**4/4 + b**2*d*x**5/5 + b**2*e*x**6/6 + (-a**2*c - 2*a**2*d*x)/(2*x**2)","A",0
325,1,138,0,0.090599," ","integrate(x**2*(e*x**2+d*x+c)*(b*x**3+a)**3,x)","\frac{a^{3} c x^{3}}{3} + \frac{a^{3} d x^{4}}{4} + \frac{a^{3} e x^{5}}{5} + \frac{a^{2} b c x^{6}}{2} + \frac{3 a^{2} b d x^{7}}{7} + \frac{3 a^{2} b e x^{8}}{8} + \frac{a b^{2} c x^{9}}{3} + \frac{3 a b^{2} d x^{10}}{10} + \frac{3 a b^{2} e x^{11}}{11} + \frac{b^{3} c x^{12}}{12} + \frac{b^{3} d x^{13}}{13} + \frac{b^{3} e x^{14}}{14}"," ",0,"a**3*c*x**3/3 + a**3*d*x**4/4 + a**3*e*x**5/5 + a**2*b*c*x**6/2 + 3*a**2*b*d*x**7/7 + 3*a**2*b*e*x**8/8 + a*b**2*c*x**9/3 + 3*a*b**2*d*x**10/10 + 3*a*b**2*e*x**11/11 + b**3*c*x**12/12 + b**3*d*x**13/13 + b**3*e*x**14/14","A",0
326,1,138,0,0.088983," ","integrate(x*(e*x**2+d*x+c)*(b*x**3+a)**3,x)","\frac{a^{3} c x^{2}}{2} + \frac{a^{3} d x^{3}}{3} + \frac{a^{3} e x^{4}}{4} + \frac{3 a^{2} b c x^{5}}{5} + \frac{a^{2} b d x^{6}}{2} + \frac{3 a^{2} b e x^{7}}{7} + \frac{3 a b^{2} c x^{8}}{8} + \frac{a b^{2} d x^{9}}{3} + \frac{3 a b^{2} e x^{10}}{10} + \frac{b^{3} c x^{11}}{11} + \frac{b^{3} d x^{12}}{12} + \frac{b^{3} e x^{13}}{13}"," ",0,"a**3*c*x**2/2 + a**3*d*x**3/3 + a**3*e*x**4/4 + 3*a**2*b*c*x**5/5 + a**2*b*d*x**6/2 + 3*a**2*b*e*x**7/7 + 3*a*b**2*c*x**8/8 + a*b**2*d*x**9/3 + 3*a*b**2*e*x**10/10 + b**3*c*x**11/11 + b**3*d*x**12/12 + b**3*e*x**13/13","A",0
327,1,134,0,0.138643," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**3,x)","a^{3} c x + \frac{a^{3} d x^{2}}{2} + \frac{a^{3} e x^{3}}{3} + \frac{3 a^{2} b c x^{4}}{4} + \frac{3 a^{2} b d x^{5}}{5} + \frac{a^{2} b e x^{6}}{2} + \frac{3 a b^{2} c x^{7}}{7} + \frac{3 a b^{2} d x^{8}}{8} + \frac{a b^{2} e x^{9}}{3} + \frac{b^{3} c x^{10}}{10} + \frac{b^{3} d x^{11}}{11} + \frac{b^{3} e x^{12}}{12}"," ",0,"a**3*c*x + a**3*d*x**2/2 + a**3*e*x**3/3 + 3*a**2*b*c*x**4/4 + 3*a**2*b*d*x**5/5 + a**2*b*e*x**6/2 + 3*a*b**2*c*x**7/7 + 3*a*b**2*d*x**8/8 + a*b**2*e*x**9/3 + b**3*c*x**10/10 + b**3*d*x**11/11 + b**3*e*x**12/12","A",0
328,1,131,0,0.294388," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**3/x,x)","a^{3} c \log{\left(x \right)} + a^{3} d x + \frac{a^{3} e x^{2}}{2} + a^{2} b c x^{3} + \frac{3 a^{2} b d x^{4}}{4} + \frac{3 a^{2} b e x^{5}}{5} + \frac{a b^{2} c x^{6}}{2} + \frac{3 a b^{2} d x^{7}}{7} + \frac{3 a b^{2} e x^{8}}{8} + \frac{b^{3} c x^{9}}{9} + \frac{b^{3} d x^{10}}{10} + \frac{b^{3} e x^{11}}{11}"," ",0,"a**3*c*log(x) + a**3*d*x + a**3*e*x**2/2 + a**2*b*c*x**3 + 3*a**2*b*d*x**4/4 + 3*a**2*b*e*x**5/5 + a*b**2*c*x**6/2 + 3*a*b**2*d*x**7/7 + 3*a*b**2*e*x**8/8 + b**3*c*x**9/9 + b**3*d*x**10/10 + b**3*e*x**11/11","A",0
329,1,128,0,0.289227," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**3/x**2,x)","- \frac{a^{3} c}{x} + a^{3} d \log{\left(x \right)} + a^{3} e x + \frac{3 a^{2} b c x^{2}}{2} + a^{2} b d x^{3} + \frac{3 a^{2} b e x^{4}}{4} + \frac{3 a b^{2} c x^{5}}{5} + \frac{a b^{2} d x^{6}}{2} + \frac{3 a b^{2} e x^{7}}{7} + \frac{b^{3} c x^{8}}{8} + \frac{b^{3} d x^{9}}{9} + \frac{b^{3} e x^{10}}{10}"," ",0,"-a**3*c/x + a**3*d*log(x) + a**3*e*x + 3*a**2*b*c*x**2/2 + a**2*b*d*x**3 + 3*a**2*b*e*x**4/4 + 3*a*b**2*c*x**5/5 + a*b**2*d*x**6/2 + 3*a*b**2*e*x**7/7 + b**3*c*x**8/8 + b**3*d*x**9/9 + b**3*e*x**10/10","A",0
330,1,131,0,0.361732," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**3/x**3,x)","a^{3} e \log{\left(x \right)} + 3 a^{2} b c x + \frac{3 a^{2} b d x^{2}}{2} + a^{2} b e x^{3} + \frac{3 a b^{2} c x^{4}}{4} + \frac{3 a b^{2} d x^{5}}{5} + \frac{a b^{2} e x^{6}}{2} + \frac{b^{3} c x^{7}}{7} + \frac{b^{3} d x^{8}}{8} + \frac{b^{3} e x^{9}}{9} + \frac{- a^{3} c - 2 a^{3} d x}{2 x^{2}}"," ",0,"a**3*e*log(x) + 3*a**2*b*c*x + 3*a**2*b*d*x**2/2 + a**2*b*e*x**3 + 3*a*b**2*c*x**4/4 + 3*a*b**2*d*x**5/5 + a*b**2*e*x**6/2 + b**3*c*x**7/7 + b**3*d*x**8/8 + b**3*e*x**9/9 + (-a**3*c - 2*a**3*d*x)/(2*x**2)","A",0
331,1,184,0,0.107497," ","integrate(x**2*(e*x**2+d*x+c)*(b*x**3+a)**4,x)","\frac{a^{4} c x^{3}}{3} + \frac{a^{4} d x^{4}}{4} + \frac{a^{4} e x^{5}}{5} + \frac{2 a^{3} b c x^{6}}{3} + \frac{4 a^{3} b d x^{7}}{7} + \frac{a^{3} b e x^{8}}{2} + \frac{2 a^{2} b^{2} c x^{9}}{3} + \frac{3 a^{2} b^{2} d x^{10}}{5} + \frac{6 a^{2} b^{2} e x^{11}}{11} + \frac{a b^{3} c x^{12}}{3} + \frac{4 a b^{3} d x^{13}}{13} + \frac{2 a b^{3} e x^{14}}{7} + \frac{b^{4} c x^{15}}{15} + \frac{b^{4} d x^{16}}{16} + \frac{b^{4} e x^{17}}{17}"," ",0,"a**4*c*x**3/3 + a**4*d*x**4/4 + a**4*e*x**5/5 + 2*a**3*b*c*x**6/3 + 4*a**3*b*d*x**7/7 + a**3*b*e*x**8/2 + 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*b**3*c*x**12/3 + 4*a*b**3*d*x**13/13 + 2*a*b**3*e*x**14/7 + b**4*c*x**15/15 + b**4*d*x**16/16 + b**4*e*x**17/17","A",0
332,1,185,0,0.113367," ","integrate(x*(e*x**2+d*x+c)*(b*x**3+a)**4,x)","\frac{a^{4} c x^{2}}{2} + \frac{a^{4} d x^{3}}{3} + \frac{a^{4} e x^{4}}{4} + \frac{4 a^{3} b c x^{5}}{5} + \frac{2 a^{3} b d x^{6}}{3} + \frac{4 a^{3} b e x^{7}}{7} + \frac{3 a^{2} b^{2} c x^{8}}{4} + \frac{2 a^{2} b^{2} d x^{9}}{3} + \frac{3 a^{2} b^{2} e x^{10}}{5} + \frac{4 a b^{3} c x^{11}}{11} + \frac{a b^{3} d x^{12}}{3} + \frac{4 a b^{3} e x^{13}}{13} + \frac{b^{4} c x^{14}}{14} + \frac{b^{4} d x^{15}}{15} + \frac{b^{4} e x^{16}}{16}"," ",0,"a**4*c*x**2/2 + a**4*d*x**3/3 + a**4*e*x**4/4 + 4*a**3*b*c*x**5/5 + 2*a**3*b*d*x**6/3 + 4*a**3*b*e*x**7/7 + 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*b**3*c*x**11/11 + a*b**3*d*x**12/3 + 4*a*b**3*e*x**13/13 + b**4*c*x**14/14 + b**4*d*x**15/15 + b**4*e*x**16/16","A",0
333,1,178,0,0.101710," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**4,x)","a^{4} c x + \frac{a^{4} d x^{2}}{2} + \frac{a^{4} e x^{3}}{3} + a^{3} b c x^{4} + \frac{4 a^{3} b d x^{5}}{5} + \frac{2 a^{3} b e x^{6}}{3} + \frac{6 a^{2} b^{2} c x^{7}}{7} + \frac{3 a^{2} b^{2} d x^{8}}{4} + \frac{2 a^{2} b^{2} e x^{9}}{3} + \frac{2 a b^{3} c x^{10}}{5} + \frac{4 a b^{3} d x^{11}}{11} + \frac{a b^{3} e x^{12}}{3} + \frac{b^{4} c x^{13}}{13} + \frac{b^{4} d x^{14}}{14} + \frac{b^{4} e x^{15}}{15}"," ",0,"a**4*c*x + a**4*d*x**2/2 + a**4*e*x**3/3 + a**3*b*c*x**4 + 4*a**3*b*d*x**5/5 + 2*a**3*b*e*x**6/3 + 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 + 2*a*b**3*c*x**10/5 + 4*a*b**3*d*x**11/11 + a*b**3*e*x**12/3 + b**4*c*x**13/13 + b**4*d*x**14/14 + b**4*e*x**15/15","A",0
334,1,175,0,0.336443," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**4/x,x)","a^{4} c \log{\left(x \right)} + a^{4} d x + \frac{a^{4} e x^{2}}{2} + \frac{4 a^{3} b c x^{3}}{3} + a^{3} b d x^{4} + \frac{4 a^{3} b e x^{5}}{5} + 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 b^{3} c x^{9}}{9} + \frac{2 a b^{3} d x^{10}}{5} + \frac{4 a b^{3} e x^{11}}{11} + \frac{b^{4} c x^{12}}{12} + \frac{b^{4} d x^{13}}{13} + \frac{b^{4} e x^{14}}{14}"," ",0,"a**4*c*log(x) + a**4*d*x + a**4*e*x**2/2 + 4*a**3*b*c*x**3/3 + a**3*b*d*x**4 + 4*a**3*b*e*x**5/5 + a**2*b**2*c*x**6 + 6*a**2*b**2*d*x**7/7 + 3*a**2*b**2*e*x**8/4 + 4*a*b**3*c*x**9/9 + 2*a*b**3*d*x**10/5 + 4*a*b**3*e*x**11/11 + b**4*c*x**12/12 + b**4*d*x**13/13 + b**4*e*x**14/14","A",0
335,1,168,0,0.379243," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**4/x**2,x)","- \frac{a^{4} c}{x} + a^{4} d \log{\left(x \right)} + a^{4} e x + 2 a^{3} b c x^{2} + \frac{4 a^{3} b d x^{3}}{3} + a^{3} b e x^{4} + \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} + \frac{a b^{3} c x^{8}}{2} + \frac{4 a b^{3} d x^{9}}{9} + \frac{2 a b^{3} e x^{10}}{5} + \frac{b^{4} c x^{11}}{11} + \frac{b^{4} d x^{12}}{12} + \frac{b^{4} e x^{13}}{13}"," ",0,"-a**4*c/x + a**4*d*log(x) + a**4*e*x + 2*a**3*b*c*x**2 + 4*a**3*b*d*x**3/3 + a**3*b*e*x**4 + 6*a**2*b**2*c*x**5/5 + a**2*b**2*d*x**6 + 6*a**2*b**2*e*x**7/7 + a*b**3*c*x**8/2 + 4*a*b**3*d*x**9/9 + 2*a*b**3*e*x**10/5 + b**4*c*x**11/11 + b**4*d*x**12/12 + b**4*e*x**13/13","A",0
336,1,175,0,0.443131," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**4/x**3,x)","a^{4} e \log{\left(x \right)} + 4 a^{3} b c x + 2 a^{3} b d x^{2} + \frac{4 a^{3} b e x^{3}}{3} + \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} + \frac{4 a b^{3} c x^{7}}{7} + \frac{a b^{3} d x^{8}}{2} + \frac{4 a b^{3} e x^{9}}{9} + \frac{b^{4} c x^{10}}{10} + \frac{b^{4} d x^{11}}{11} + \frac{b^{4} e x^{12}}{12} + \frac{- a^{4} c - 2 a^{4} d x}{2 x^{2}}"," ",0,"a**4*e*log(x) + 4*a**3*b*c*x + 2*a**3*b*d*x**2 + 4*a**3*b*e*x**3/3 + 3*a**2*b**2*c*x**4/2 + 6*a**2*b**2*d*x**5/5 + a**2*b**2*e*x**6 + 4*a*b**3*c*x**7/7 + a*b**3*d*x**8/2 + 4*a*b**3*e*x**9/9 + b**4*c*x**10/10 + b**4*d*x**11/11 + b**4*e*x**12/12 + (-a**4*c - 2*a**4*d*x)/(2*x**2)","A",0
337,1,178,0,1.639350," ","integrate(x**3*(e*x**2+d*x+c)/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} b^{6} + 27 t^{2} a b^{4} e + t \left(9 a^{2} b^{2} e^{2} + 9 a b^{3} c d\right) + a^{3} e^{3} + 3 a^{2} b c d e - a^{2} b d^{3} + a b^{2} c^{3}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} b^{4} d + 6 t a b^{2} d e - 3 t b^{3} c^{2} + a^{2} d e^{2} - a b c^{2} e + 2 a b c d^{2}}{a b d^{3} + b^{2} c^{3}} \right)} \right)\right)} + \frac{c x}{b} + \frac{d x^{2}}{2 b} + \frac{e x^{3}}{3 b}"," ",0,"RootSum(27*_t**3*b**6 + 27*_t**2*a*b**4*e + _t*(9*a**2*b**2*e**2 + 9*a*b**3*c*d) + a**3*e**3 + 3*a**2*b*c*d*e - a**2*b*d**3 + a*b**2*c**3, Lambda(_t, _t*log(x + (9*_t**2*b**4*d + 6*_t*a*b**2*d*e - 3*_t*b**3*c**2 + a**2*d*e**2 - a*b*c**2*e + 2*a*b*c*d**2)/(a*b*d**3 + b**2*c**3)))) + c*x/b + d*x**2/(2*b) + e*x**3/(3*b)","A",0
338,1,150,0,1.490075," ","integrate(x**2*(e*x**2+d*x+c)/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} b^{5} - 27 t^{2} b^{4} c + t \left(9 a b^{2} d e + 9 b^{3} c^{2}\right) - a^{2} e^{3} - 3 a b c d e + a b d^{3} - b^{2} c^{3}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} b^{3} e - 6 t b^{2} c e - 3 t b^{2} d^{2} + 2 a d e^{2} + b c^{2} e + b c d^{2}}{a e^{3} + b d^{3}} \right)} \right)\right)} + \frac{d x}{b} + \frac{e x^{2}}{2 b}"," ",0,"RootSum(27*_t**3*b**5 - 27*_t**2*b**4*c + _t*(9*a*b**2*d*e + 9*b**3*c**2) - a**2*e**3 - 3*a*b*c*d*e + a*b*d**3 - b**2*c**3, Lambda(_t, _t*log(x + (9*_t**2*b**3*e - 6*_t*b**2*c*e - 3*_t*b**2*d**2 + 2*a*d*e**2 + b*c**2*e + b*c*d**2)/(a*e**3 + b*d**3)))) + d*x/b + e*x**2/(2*b)","A",0
339,1,160,0,1.432129," ","integrate(x*(e*x**2+d*x+c)/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a b^{4} - 27 t^{2} a b^{3} d + t \left(- 9 a b^{2} c e + 9 a b^{2} d^{2}\right) + a^{2} e^{3} + 3 a b c d e - a b d^{3} + b^{2} c^{3}, \left( t \mapsto t \log{\left(x + \frac{- 9 t^{2} a b^{3} c - 3 t a^{2} b e^{2} + 6 t a b^{2} c d + a^{2} d e^{2} + 2 a b c^{2} e - a b c d^{2}}{a^{2} e^{3} - b^{2} c^{3}} \right)} \right)\right)} + \frac{e x}{b}"," ",0,"RootSum(27*_t**3*a*b**4 - 27*_t**2*a*b**3*d + _t*(-9*a*b**2*c*e + 9*a*b**2*d**2) + a**2*e**3 + 3*a*b*c*d*e - a*b*d**3 + b**2*c**3, Lambda(_t, _t*log(x + (-9*_t**2*a*b**3*c - 3*_t*a**2*b*e**2 + 6*_t*a*b**2*c*d + a**2*d*e**2 + 2*a*b*c**2*e - a*b*c*d**2)/(a**2*e**3 - b**2*c**3)))) + e*x/b","A",0
340,1,160,0,1.423265," ","integrate((e*x**2+d*x+c)/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a^{2} b^{3} - 27 t^{2} a^{2} b^{2} e + t \left(9 a^{2} b e^{2} + 9 a b^{2} c d\right) - a^{2} e^{3} - 3 a b c d e + a b d^{3} - b^{2} c^{3}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a^{2} b^{2} d - 6 t a^{2} b d e + 3 t a b^{2} c^{2} + a^{2} d e^{2} - a b c^{2} e + 2 a b c d^{2}}{a b d^{3} + b^{2} c^{3}} \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*a**2*b**3 - 27*_t**2*a**2*b**2*e + _t*(9*a**2*b*e**2 + 9*a*b**2*c*d) - a**2*e**3 - 3*a*b*c*d*e + a*b*d**3 - b**2*c**3, Lambda(_t, _t*log(x + (9*_t**2*a**2*b**2*d - 6*_t*a**2*b*d*e + 3*_t*a*b**2*c**2 + a**2*d*e**2 - a*b*c**2*e + 2*a*b*c*d**2)/(a*b*d**3 + b**2*c**3))))","A",0
341,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**2/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**3/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,1,110,0,2.332605," ","integrate(x**2*(e*x**2+d*x+c)/(b*x**3+a)**2,x)","\operatorname{RootSum} {\left(729 t^{3} a^{2} b^{5} + 54 t a b^{2} d e + 8 a e^{3} - b d^{3}, \left( t \mapsto t \log{\left(x + \frac{162 t^{2} a^{2} b^{3} e + 9 t a b^{2} d^{2} + 8 a d e^{2}}{8 a e^{3} + b d^{3}} \right)} \right)\right)} + \frac{- c - d x - e x^{2}}{3 a b + 3 b^{2} x^{3}}"," ",0,"RootSum(729*_t**3*a**2*b**5 + 54*_t*a*b**2*d*e + 8*a*e**3 - b*d**3, Lambda(_t, _t*log(x + (162*_t**2*a**2*b**3*e + 9*_t*a*b**2*d**2 + 8*a*d*e**2)/(8*a*e**3 + b*d**3)))) + (-c - d*x - e*x**2)/(3*a*b + 3*b**2*x**3)","A",0
345,1,124,0,1.853024," ","integrate(x*(e*x**2+d*x+c)/(b*x**3+a)**2,x)","\operatorname{RootSum} {\left(729 t^{3} a^{4} b^{4} + 27 t a^{2} b^{2} c e - a^{2} e^{3} + b^{2} c^{3}, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a^{3} b^{3} c + 9 t a^{3} b e^{2} + 2 a b c^{2} e}{a^{2} e^{3} + b^{2} c^{3}} \right)} \right)\right)} + \frac{- a d - a e x + b c x^{2}}{3 a^{2} b + 3 a b^{2} x^{3}}"," ",0,"RootSum(729*_t**3*a**4*b**4 + 27*_t*a**2*b**2*c*e - a**2*e**3 + b**2*c**3, Lambda(_t, _t*log(x + (81*_t**2*a**3*b**3*c + 9*_t*a**3*b*e**2 + 2*a*b*c**2*e)/(a**2*e**3 + b**2*c**3)))) + (-a*d - a*e*x + b*c*x**2)/(3*a**2*b + 3*a*b**2*x**3)","A",0
346,1,116,0,1.384945," ","integrate((e*x**2+d*x+c)/(b*x**3+a)**2,x)","\operatorname{RootSum} {\left(729 t^{3} a^{5} b^{2} + 54 t a^{2} b c d + a d^{3} - 8 b c^{3}, \left( t \mapsto t \log{\left(x + \frac{81 t^{2} a^{4} b d + 36 t a^{2} b c^{2} + 4 a c d^{2}}{a d^{3} + 8 b c^{3}} \right)} \right)\right)} + \frac{- a e + b c x + b d x^{2}}{3 a^{2} b + 3 a b^{2} x^{3}}"," ",0,"RootSum(729*_t**3*a**5*b**2 + 54*_t*a**2*b*c*d + a*d**3 - 8*b*c**3, Lambda(_t, _t*log(x + (81*_t**2*a**4*b*d + 36*_t*a**2*b*c**2 + 4*a*c*d**2)/(a*d**3 + 8*b*c**3)))) + (-a*e + b*c*x + b*d*x**2)/(3*a**2*b + 3*a*b**2*x**3)","A",0
347,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**2/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**3/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**4/(b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,1,148,0,6.261017," ","integrate(x**2*(e*x**2+d*x+c)/(b*x**3+a)**3,x)","\operatorname{RootSum} {\left(19683 t^{3} a^{5} b^{5} + 81 t a^{2} b^{2} d e + a e^{3} - b d^{3}, \left( t \mapsto t \log{\left(x + \frac{729 t^{2} a^{4} b^{3} e + 27 t a^{2} b^{2} d^{2} + 2 a d e^{2}}{a e^{3} + b d^{3}} \right)} \right)\right)} + \frac{- 3 a c - 2 a d x - a e x^{2} + b d x^{4} + 2 b e x^{5}}{18 a^{3} b + 36 a^{2} b^{2} x^{3} + 18 a b^{3} x^{6}}"," ",0,"RootSum(19683*_t**3*a**5*b**5 + 81*_t*a**2*b**2*d*e + a*e**3 - b*d**3, Lambda(_t, _t*log(x + (729*_t**2*a**4*b**3*e + 27*_t*a**2*b**2*d**2 + 2*a*d*e**2)/(a*e**3 + b*d**3)))) + (-3*a*c - 2*a*d*x - a*e*x**2 + b*d*x**4 + 2*b*e*x**5)/(18*a**3*b + 36*a**2*b**2*x**3 + 18*a*b**3*x**6)","A",0
352,1,170,0,3.991387," ","integrate(x*(e*x**2+d*x+c)/(b*x**3+a)**3,x)","\operatorname{RootSum} {\left(19683 t^{3} a^{7} b^{4} + 162 t a^{3} b^{2} c e - a^{2} e^{3} + 8 b^{2} c^{3}, \left( t \mapsto t \log{\left(x + \frac{1458 t^{2} a^{5} b^{3} c + 27 t a^{4} b e^{2} + 8 a b c^{2} e}{a^{2} e^{3} + 8 b^{2} c^{3}} \right)} \right)\right)} + \frac{- 3 a^{2} d - 2 a^{2} e x + 7 a b c x^{2} + a b e x^{4} + 4 b^{2} c x^{5}}{18 a^{4} b + 36 a^{3} b^{2} x^{3} + 18 a^{2} b^{3} x^{6}}"," ",0,"RootSum(19683*_t**3*a**7*b**4 + 162*_t*a**3*b**2*c*e - a**2*e**3 + 8*b**2*c**3, Lambda(_t, _t*log(x + (1458*_t**2*a**5*b**3*c + 27*_t*a**4*b*e**2 + 8*a*b*c**2*e)/(a**2*e**3 + 8*b**2*c**3)))) + (-3*a**2*d - 2*a**2*e*x + 7*a*b*c*x**2 + a*b*e*x**4 + 4*b**2*c*x**5)/(18*a**4*b + 36*a**3*b**2*x**3 + 18*a**2*b**3*x**6)","A",0
353,1,163,0,2.276690," ","integrate((e*x**2+d*x+c)/(b*x**3+a)**3,x)","\operatorname{RootSum} {\left(19683 t^{3} a^{8} b^{2} + 810 t a^{3} b c d + 8 a d^{3} - 125 b c^{3}, \left( t \mapsto t \log{\left(x + \frac{1458 t^{2} a^{6} b d + 675 t a^{3} b c^{2} + 40 a c d^{2}}{8 a d^{3} + 125 b c^{3}} \right)} \right)\right)} + \frac{- 3 a^{2} e + 8 a b c x + 7 a b d x^{2} + 5 b^{2} c x^{4} + 4 b^{2} d x^{5}}{18 a^{4} b + 36 a^{3} b^{2} x^{3} + 18 a^{2} b^{3} x^{6}}"," ",0,"RootSum(19683*_t**3*a**8*b**2 + 810*_t*a**3*b*c*d + 8*a*d**3 - 125*b*c**3, Lambda(_t, _t*log(x + (1458*_t**2*a**6*b*d + 675*_t*a**3*b*c**2 + 40*a*c*d**2)/(8*a*d**3 + 125*b*c**3)))) + (-3*a**2*e + 8*a*b*c*x + 7*a*b*d*x**2 + 5*b**2*c*x**4 + 4*b**2*d*x**5)/(18*a**4*b + 36*a**3*b**2*x**3 + 18*a**2*b**3*x**6)","A",0
354,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**2/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**3/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**4/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,1,201,0,17.943409," ","integrate(x**2*(e*x**2+d*x+c)/(b*x**3+a)**4,x)","\operatorname{RootSum} {\left(14348907 t^{3} a^{8} b^{5} + 14580 t a^{3} b^{2} d e + 64 a e^{3} - 125 b d^{3}, \left( t \mapsto t \log{\left(x + \frac{236196 t^{2} a^{6} b^{3} e + 6075 t a^{3} b^{2} d^{2} + 160 a d e^{2}}{64 a e^{3} + 125 b d^{3}} \right)} \right)\right)} + \frac{- 18 a^{2} c - 10 a^{2} d x - 4 a^{2} e x^{2} + 13 a b d x^{4} + 22 a b e x^{5} + 5 b^{2} d x^{7} + 8 b^{2} e x^{8}}{162 a^{5} b + 486 a^{4} b^{2} x^{3} + 486 a^{3} b^{3} x^{6} + 162 a^{2} b^{4} x^{9}}"," ",0,"RootSum(14348907*_t**3*a**8*b**5 + 14580*_t*a**3*b**2*d*e + 64*a*e**3 - 125*b*d**3, Lambda(_t, _t*log(x + (236196*_t**2*a**6*b**3*e + 6075*_t*a**3*b**2*d**2 + 160*a*d*e**2)/(64*a*e**3 + 125*b*d**3)))) + (-18*a**2*c - 10*a**2*d*x - 4*a**2*e*x**2 + 13*a*b*d*x**4 + 22*a*b*e*x**5 + 5*b**2*d*x**7 + 8*b**2*e*x**8)/(162*a**5*b + 486*a**4*b**2*x**3 + 486*a**3*b**3*x**6 + 162*a**2*b**4*x**9)","A",0
359,1,214,0,8.787203," ","integrate(x*(e*x**2+d*x+c)/(b*x**3+a)**4,x)","\operatorname{RootSum} {\left(14348907 t^{3} a^{10} b^{4} + 51030 t a^{4} b^{2} c e - 125 a^{2} e^{3} + 2744 b^{2} c^{3}, \left( t \mapsto t \log{\left(x + \frac{826686 t^{2} a^{7} b^{3} c + 6075 t a^{5} b e^{2} + 1960 a b c^{2} e}{125 a^{2} e^{3} + 2744 b^{2} c^{3}} \right)} \right)\right)} + \frac{- 18 a^{3} d - 10 a^{3} e x + 67 a^{2} b c x^{2} + 13 a^{2} b e x^{4} + 77 a b^{2} c x^{5} + 5 a b^{2} e x^{7} + 28 b^{3} c x^{8}}{162 a^{6} b + 486 a^{5} b^{2} x^{3} + 486 a^{4} b^{3} x^{6} + 162 a^{3} b^{4} x^{9}}"," ",0,"RootSum(14348907*_t**3*a**10*b**4 + 51030*_t*a**4*b**2*c*e - 125*a**2*e**3 + 2744*b**2*c**3, Lambda(_t, _t*log(x + (826686*_t**2*a**7*b**3*c + 6075*_t*a**5*b*e**2 + 1960*a*b*c**2*e)/(125*a**2*e**3 + 2744*b**2*c**3)))) + (-18*a**3*d - 10*a**3*e*x + 67*a**2*b*c*x**2 + 13*a**2*b*e*x**4 + 77*a*b**2*c*x**5 + 5*a*b**2*e*x**7 + 28*b**3*c*x**8)/(162*a**6*b + 486*a**5*b**2*x**3 + 486*a**4*b**3*x**6 + 162*a**3*b**4*x**9)","A",0
360,1,202,0,4.469524," ","integrate((e*x**2+d*x+c)/(b*x**3+a)**4,x)","\operatorname{RootSum} {\left(14348907 t^{3} a^{11} b^{2} + 408240 t a^{4} b c d + 2744 a d^{3} - 64000 b c^{3}, \left( t \mapsto t \log{\left(x + \frac{413343 t^{2} a^{8} b d + 194400 t a^{4} b c^{2} + 7840 a c d^{2}}{1372 a d^{3} + 32000 b c^{3}} \right)} \right)\right)} + \frac{- 18 a^{3} e + 82 a^{2} b c x + 67 a^{2} b d x^{2} + 104 a b^{2} c x^{4} + 77 a b^{2} d x^{5} + 40 b^{3} c x^{7} + 28 b^{3} d x^{8}}{162 a^{6} b + 486 a^{5} b^{2} x^{3} + 486 a^{4} b^{3} x^{6} + 162 a^{3} b^{4} x^{9}}"," ",0,"RootSum(14348907*_t**3*a**11*b**2 + 408240*_t*a**4*b*c*d + 2744*a*d**3 - 64000*b*c**3, Lambda(_t, _t*log(x + (413343*_t**2*a**8*b*d + 194400*_t*a**4*b*c**2 + 7840*a*c*d**2)/(1372*a*d**3 + 32000*b*c**3)))) + (-18*a**3*e + 82*a**2*b*c*x + 67*a**2*b*d*x**2 + 104*a*b**2*c*x**4 + 77*a*b**2*d*x**5 + 40*b**3*c*x**7 + 28*b**3*d*x**8)/(162*a**6*b + 486*a**5*b**2*x**3 + 486*a**4*b**3*x**6 + 162*a**3*b**4*x**9)","A",0
361,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x/(b*x**3+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**2/(b*x**3+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**3/(b*x**3+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-1,0,0,0.000000," ","integrate((e*x**2+d*x+c)/x**4/(b*x**3+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,1,54,0,0.178960," ","integrate((2*a*x-x**2)/(a**3+x**3),x)","- \log{\left(a + x \right)} - \frac{\sqrt{3} i \log{\left(- \frac{a}{2} - \frac{\sqrt{3} i a}{2} + x \right)}}{3} + \frac{\sqrt{3} i \log{\left(- \frac{a}{2} + \frac{\sqrt{3} i a}{2} + x \right)}}{3}"," ",0,"-log(a + x) - sqrt(3)*I*log(-a/2 - sqrt(3)*I*a/2 + x)/3 + sqrt(3)*I*log(-a/2 + sqrt(3)*I*a/2 + x)/3","C",0
366,1,54,0,0.168245," ","integrate((2*a-x)*x/(a**3+x**3),x)","- \log{\left(a + x \right)} - \frac{\sqrt{3} i \log{\left(- \frac{a}{2} - \frac{\sqrt{3} i a}{2} + x \right)}}{3} + \frac{\sqrt{3} i \log{\left(- \frac{a}{2} + \frac{\sqrt{3} i a}{2} + x \right)}}{3}"," ",0,"-log(a + x) - sqrt(3)*I*log(-a/2 - sqrt(3)*I*a/2 + x)/3 + sqrt(3)*I*log(-a/2 + sqrt(3)*I*a/2 + x)/3","C",0
367,1,54,0,0.172558," ","integrate((2*a*x+x**2)/(a**3-x**3),x)","- \log{\left(- a + x \right)} + \frac{\sqrt{3} i \log{\left(\frac{a}{2} - \frac{\sqrt{3} i a}{2} + x \right)}}{3} - \frac{\sqrt{3} i \log{\left(\frac{a}{2} + \frac{\sqrt{3} i a}{2} + x \right)}}{3}"," ",0,"-log(-a + x) + sqrt(3)*I*log(a/2 - sqrt(3)*I*a/2 + x)/3 - sqrt(3)*I*log(a/2 + sqrt(3)*I*a/2 + x)/3","C",0
368,1,54,0,0.168924," ","integrate(x*(2*a+x)/(a**3-x**3),x)","- \log{\left(- a + x \right)} + \frac{\sqrt{3} i \log{\left(\frac{a}{2} - \frac{\sqrt{3} i a}{2} + x \right)}}{3} - \frac{\sqrt{3} i \log{\left(\frac{a}{2} + \frac{\sqrt{3} i a}{2} + x \right)}}{3}"," ",0,"-log(-a + x) + sqrt(3)*I*log(a/2 - sqrt(3)*I*a/2 + x)/3 - sqrt(3)*I*log(a/2 + sqrt(3)*I*a/2 + x)/3","C",0
369,1,100,0,0.322234," ","integrate(x*(-2*(a/b)**(1/3)*C+C*x)/(b*x**3+a),x)","\frac{C \left(\log{\left(\frac{a}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)} + \frac{\sqrt{3} i \log{\left(- \frac{a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt{3} i a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3} - \frac{\sqrt{3} i \log{\left(- \frac{a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt{3} i a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3}\right)}{b}"," ",0,"C*(log(a/(b*(a/b)**(2/3)) + x) + sqrt(3)*I*log(-a/(2*b*(a/b)**(2/3)) - sqrt(3)*I*a/(2*b*(a/b)**(2/3)) + x)/3 - sqrt(3)*I*log(-a/(2*b*(a/b)**(2/3)) + sqrt(3)*I*a/(2*b*(a/b)**(2/3)) + x)/3)/b","C",0
370,1,110,0,0.348815," ","integrate(x*(-2*(-a/b)**(1/3)*C+C*x)/(-b*x**3+a),x)","- \frac{C \left(\log{\left(- \frac{a}{b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)} - \frac{\sqrt{3} i \log{\left(\frac{a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt{3} i a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3} + \frac{\sqrt{3} i \log{\left(\frac{a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt{3} i a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3}\right)}{b}"," ",0,"-C*(log(-a/(b*(-a/b)**(2/3)) + x) - sqrt(3)*I*log(a/(2*b*(-a/b)**(2/3)) - sqrt(3)*I*a/(2*b*(-a/b)**(2/3)) + x)/3 + sqrt(3)*I*log(a/(2*b*(-a/b)**(2/3)) + sqrt(3)*I*a/(2*b*(-a/b)**(2/3)) + x)/3)/b","C",0
371,1,109,0,0.318832," ","integrate(x*(2*(-a/b)**(1/3)*C+C*x)/(b*x**3+a),x)","\frac{C \left(\log{\left(\frac{a}{b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)} + \frac{\sqrt{3} i \log{\left(- \frac{a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt{3} i a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3} - \frac{\sqrt{3} i \log{\left(- \frac{a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt{3} i a}{2 b \left(- \frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3}\right)}{b}"," ",0,"C*(log(a/(b*(-a/b)**(2/3)) + x) + sqrt(3)*I*log(-a/(2*b*(-a/b)**(2/3)) - sqrt(3)*I*a/(2*b*(-a/b)**(2/3)) + x)/3 - sqrt(3)*I*log(-a/(2*b*(-a/b)**(2/3)) + sqrt(3)*I*a/(2*b*(-a/b)**(2/3)) + x)/3)/b","C",0
372,1,102,0,0.371965," ","integrate(x*(2*(a/b)**(1/3)*C+C*x)/(-b*x**3+a),x)","- \frac{C \left(\log{\left(- \frac{a}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)} - \frac{\sqrt{3} i \log{\left(\frac{a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt{3} i a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3} + \frac{\sqrt{3} i \log{\left(\frac{a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt{3} i a}{2 b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + x \right)}}{3}\right)}{b}"," ",0,"-C*(log(-a/(b*(a/b)**(2/3)) + x) - sqrt(3)*I*log(a/(2*b*(a/b)**(2/3)) - sqrt(3)*I*a/(2*b*(a/b)**(2/3)) + x)/3 + sqrt(3)*I*log(a/(2*b*(a/b)**(2/3)) + sqrt(3)*I*a/(2*b*(a/b)**(2/3)) + x)/3)/b","C",0
373,1,90,0,0.085546," ","integrate(x**4*(b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\frac{a c x^{5}}{5} + \frac{a d x^{6}}{6} + \frac{a e x^{7}}{7} + \frac{b f x^{11}}{11} + \frac{b g x^{12}}{12} + \frac{b h x^{13}}{13} + x^{10} \left(\frac{a h}{10} + \frac{b e}{10}\right) + x^{9} \left(\frac{a g}{9} + \frac{b d}{9}\right) + x^{8} \left(\frac{a f}{8} + \frac{b c}{8}\right)"," ",0,"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*h*x**13/13 + x**10*(a*h/10 + b*e/10) + x**9*(a*g/9 + b*d/9) + x**8*(a*f/8 + b*c/8)","A",0
374,1,90,0,0.086554," ","integrate(x**3*(b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\frac{a c x^{4}}{4} + \frac{a d x^{5}}{5} + \frac{a e x^{6}}{6} + \frac{b f x^{10}}{10} + \frac{b g x^{11}}{11} + \frac{b h x^{12}}{12} + x^{9} \left(\frac{a h}{9} + \frac{b e}{9}\right) + x^{8} \left(\frac{a g}{8} + \frac{b d}{8}\right) + x^{7} \left(\frac{a f}{7} + \frac{b c}{7}\right)"," ",0,"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*h*x**12/12 + x**9*(a*h/9 + b*e/9) + x**8*(a*g/8 + b*d/8) + x**7*(a*f/7 + b*c/7)","A",0
375,1,90,0,0.084728," ","integrate(x**2*(b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\frac{a c x^{3}}{3} + \frac{a d x^{4}}{4} + \frac{a e x^{5}}{5} + \frac{b f x^{9}}{9} + \frac{b g x^{10}}{10} + \frac{b h x^{11}}{11} + x^{8} \left(\frac{a h}{8} + \frac{b e}{8}\right) + x^{7} \left(\frac{a g}{7} + \frac{b d}{7}\right) + x^{6} \left(\frac{a f}{6} + \frac{b c}{6}\right)"," ",0,"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*h*x**11/11 + x**8*(a*h/8 + b*e/8) + x**7*(a*g/7 + b*d/7) + x**6*(a*f/6 + b*c/6)","A",0
376,1,90,0,0.084284," ","integrate(x*(b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\frac{a c x^{2}}{2} + \frac{a d x^{3}}{3} + \frac{a e x^{4}}{4} + \frac{b f x^{8}}{8} + \frac{b g x^{9}}{9} + \frac{b h x^{10}}{10} + x^{7} \left(\frac{a h}{7} + \frac{b e}{7}\right) + x^{6} \left(\frac{a g}{6} + \frac{b d}{6}\right) + x^{5} \left(\frac{a f}{5} + \frac{b c}{5}\right)"," ",0,"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*h*x**10/10 + x**7*(a*h/7 + b*e/7) + x**6*(a*g/6 + b*d/6) + x**5*(a*f/5 + b*c/5)","A",0
377,1,87,0,0.083961," ","integrate((b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","a c x + \frac{a d x^{2}}{2} + \frac{a e x^{3}}{3} + \frac{b f x^{7}}{7} + \frac{b g x^{8}}{8} + \frac{b h x^{9}}{9} + x^{6} \left(\frac{a h}{6} + \frac{b e}{6}\right) + x^{5} \left(\frac{a g}{5} + \frac{b d}{5}\right) + x^{4} \left(\frac{a f}{4} + \frac{b c}{4}\right)"," ",0,"a*c*x + a*d*x**2/2 + a*e*x**3/3 + b*f*x**7/7 + b*g*x**8/8 + b*h*x**9/9 + x**6*(a*h/6 + b*e/6) + x**5*(a*g/5 + b*d/5) + x**4*(a*f/4 + b*c/4)","A",0
378,1,85,0,0.222460," ","integrate((b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x,x)","a c \log{\left(x \right)} + a d x + \frac{a e x^{2}}{2} + \frac{b f x^{6}}{6} + \frac{b g x^{7}}{7} + \frac{b h x^{8}}{8} + x^{5} \left(\frac{a h}{5} + \frac{b e}{5}\right) + x^{4} \left(\frac{a g}{4} + \frac{b d}{4}\right) + x^{3} \left(\frac{a f}{3} + \frac{b c}{3}\right)"," ",0,"a*c*log(x) + a*d*x + a*e*x**2/2 + b*f*x**6/6 + b*g*x**7/7 + b*h*x**8/8 + x**5*(a*h/5 + b*e/5) + x**4*(a*g/4 + b*d/4) + x**3*(a*f/3 + b*c/3)","A",0
379,1,82,0,0.234842," ","integrate((b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**2,x)","- \frac{a c}{x} + a d \log{\left(x \right)} + a e x + \frac{b f x^{5}}{5} + \frac{b g x^{6}}{6} + \frac{b h x^{7}}{7} + x^{4} \left(\frac{a h}{4} + \frac{b e}{4}\right) + x^{3} \left(\frac{a g}{3} + \frac{b d}{3}\right) + x^{2} \left(\frac{a f}{2} + \frac{b c}{2}\right)"," ",0,"-a*c/x + a*d*log(x) + a*e*x + b*f*x**5/5 + b*g*x**6/6 + b*h*x**7/7 + x**4*(a*h/4 + b*e/4) + x**3*(a*g/3 + b*d/3) + x**2*(a*f/2 + b*c/2)","A",0
380,1,83,0,0.305775," ","integrate((b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**3,x)","a e \log{\left(x \right)} + \frac{b f x^{4}}{4} + \frac{b g x^{5}}{5} + \frac{b h x^{6}}{6} + x^{3} \left(\frac{a h}{3} + \frac{b e}{3}\right) + x^{2} \left(\frac{a g}{2} + \frac{b d}{2}\right) + x \left(a f + b c\right) + \frac{- a c - 2 a d x}{2 x^{2}}"," ",0,"a*e*log(x) + b*f*x**4/4 + b*g*x**5/5 + b*h*x**6/6 + x**3*(a*h/3 + b*e/3) + x**2*(a*g/2 + b*d/2) + x*(a*f + b*c) + (-a*c - 2*a*d*x)/(2*x**2)","A",0
381,1,83,0,0.669122," ","integrate((b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**4,x)","\frac{b f x^{3}}{3} + \frac{b g x^{4}}{4} + \frac{b h x^{5}}{5} + x^{2} \left(\frac{a h}{2} + \frac{b e}{2}\right) + x \left(a g + b d\right) + \left(a f + b c\right) \log{\left(x \right)} + \frac{- 2 a c - 3 a d x - 6 a e x^{2}}{6 x^{3}}"," ",0,"b*f*x**3/3 + b*g*x**4/4 + b*h*x**5/5 + x**2*(a*h/2 + b*e/2) + x*(a*g + b*d) + (a*f + b*c)*log(x) + (-2*a*c - 3*a*d*x - 6*a*e*x**2)/(6*x**3)","A",0
382,1,83,0,2.569449," ","integrate((b*x**3+a)*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**5,x)","\frac{b f x^{2}}{2} + \frac{b g x^{3}}{3} + \frac{b h x^{4}}{4} + x \left(a h + b e\right) + \left(a g + b d\right) \log{\left(x \right)} + \frac{- 3 a c - 4 a d x - 6 a e x^{2} + x^{3} \left(- 12 a f - 12 b c\right)}{12 x^{4}}"," ",0,"b*f*x**2/2 + b*g*x**3/3 + b*h*x**4/4 + x*(a*h + b*e) + (a*g + b*d)*log(x) + (-3*a*c - 4*a*d*x - 6*a*e*x**2 + x**3*(-12*a*f - 12*b*c))/(12*x**4)","A",0
383,1,167,0,0.101387," ","integrate(x**4*(b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\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} + x^{13} \left(\frac{2 a b h}{13} + \frac{b^{2} e}{13}\right) + x^{12} \left(\frac{a b g}{6} + \frac{b^{2} d}{12}\right) + x^{11} \left(\frac{2 a b f}{11} + \frac{b^{2} c}{11}\right) + x^{10} \left(\frac{a^{2} h}{10} + \frac{a b e}{5}\right) + x^{9} \left(\frac{a^{2} g}{9} + \frac{2 a b d}{9}\right) + x^{8} \left(\frac{a^{2} f}{8} + \frac{a b c}{4}\right)"," ",0,"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 + x**13*(2*a*b*h/13 + b**2*e/13) + x**12*(a*b*g/6 + b**2*d/12) + x**11*(2*a*b*f/11 + b**2*c/11) + x**10*(a**2*h/10 + a*b*e/5) + x**9*(a**2*g/9 + 2*a*b*d/9) + x**8*(a**2*f/8 + a*b*c/4)","A",0
384,1,167,0,0.105201," ","integrate(x**3*(b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\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} + x^{12} \left(\frac{a b h}{6} + \frac{b^{2} e}{12}\right) + x^{11} \left(\frac{2 a b g}{11} + \frac{b^{2} d}{11}\right) + x^{10} \left(\frac{a b f}{5} + \frac{b^{2} c}{10}\right) + x^{9} \left(\frac{a^{2} h}{9} + \frac{2 a b e}{9}\right) + x^{8} \left(\frac{a^{2} g}{8} + \frac{a b d}{4}\right) + x^{7} \left(\frac{a^{2} f}{7} + \frac{2 a b c}{7}\right)"," ",0,"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 + x**12*(a*b*h/6 + b**2*e/12) + x**11*(2*a*b*g/11 + b**2*d/11) + x**10*(a*b*f/5 + b**2*c/10) + x**9*(a**2*h/9 + 2*a*b*e/9) + x**8*(a**2*g/8 + a*b*d/4) + x**7*(a**2*f/7 + 2*a*b*c/7)","A",0
385,1,167,0,0.103932," ","integrate(x**2*(b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\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} + x^{11} \left(\frac{2 a b h}{11} + \frac{b^{2} e}{11}\right) + x^{10} \left(\frac{a b g}{5} + \frac{b^{2} d}{10}\right) + x^{9} \left(\frac{2 a b f}{9} + \frac{b^{2} c}{9}\right) + x^{8} \left(\frac{a^{2} h}{8} + \frac{a b e}{4}\right) + x^{7} \left(\frac{a^{2} g}{7} + \frac{2 a b d}{7}\right) + x^{6} \left(\frac{a^{2} f}{6} + \frac{a b c}{3}\right)"," ",0,"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 + x**11*(2*a*b*h/11 + b**2*e/11) + x**10*(a*b*g/5 + b**2*d/10) + x**9*(2*a*b*f/9 + b**2*c/9) + x**8*(a**2*h/8 + a*b*e/4) + x**7*(a**2*g/7 + 2*a*b*d/7) + x**6*(a**2*f/6 + a*b*c/3)","A",0
386,1,167,0,0.104276," ","integrate(x*(b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\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} + x^{10} \left(\frac{a b h}{5} + \frac{b^{2} e}{10}\right) + x^{9} \left(\frac{2 a b g}{9} + \frac{b^{2} d}{9}\right) + x^{8} \left(\frac{a b f}{4} + \frac{b^{2} c}{8}\right) + x^{7} \left(\frac{a^{2} h}{7} + \frac{2 a b e}{7}\right) + x^{6} \left(\frac{a^{2} g}{6} + \frac{a b d}{3}\right) + x^{5} \left(\frac{a^{2} f}{5} + \frac{2 a b c}{5}\right)"," ",0,"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 + x**10*(a*b*h/5 + b**2*e/10) + x**9*(2*a*b*g/9 + b**2*d/9) + x**8*(a*b*f/4 + b**2*c/8) + x**7*(a**2*h/7 + 2*a*b*e/7) + x**6*(a**2*g/6 + a*b*d/3) + x**5*(a**2*f/5 + 2*a*b*c/5)","A",0
387,1,163,0,0.102890," ","integrate((b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","a^{2} c x + \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} + x^{9} \left(\frac{2 a b h}{9} + \frac{b^{2} e}{9}\right) + x^{8} \left(\frac{a b g}{4} + \frac{b^{2} d}{8}\right) + x^{7} \left(\frac{2 a b f}{7} + \frac{b^{2} c}{7}\right) + x^{6} \left(\frac{a^{2} h}{6} + \frac{a b e}{3}\right) + x^{5} \left(\frac{a^{2} g}{5} + \frac{2 a b d}{5}\right) + x^{4} \left(\frac{a^{2} f}{4} + \frac{a b c}{2}\right)"," ",0,"a**2*c*x + 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 + x**9*(2*a*b*h/9 + b**2*e/9) + x**8*(a*b*g/4 + b**2*d/8) + x**7*(2*a*b*f/7 + b**2*c/7) + x**6*(a**2*h/6 + a*b*e/3) + x**5*(a**2*g/5 + 2*a*b*d/5) + x**4*(a**2*f/4 + a*b*c/2)","A",0
388,1,162,0,0.340719," ","integrate((b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x,x)","a^{2} c \log{\left(x \right)} + a^{2} d x + \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} + x^{8} \left(\frac{a b h}{4} + \frac{b^{2} e}{8}\right) + x^{7} \left(\frac{2 a b g}{7} + \frac{b^{2} d}{7}\right) + x^{6} \left(\frac{a b f}{3} + \frac{b^{2} c}{6}\right) + x^{5} \left(\frac{a^{2} h}{5} + \frac{2 a b e}{5}\right) + x^{4} \left(\frac{a^{2} g}{4} + \frac{a b d}{2}\right) + x^{3} \left(\frac{a^{2} f}{3} + \frac{2 a b c}{3}\right)"," ",0,"a**2*c*log(x) + a**2*d*x + a**2*e*x**2/2 + b**2*f*x**9/9 + b**2*g*x**10/10 + b**2*h*x**11/11 + x**8*(a*b*h/4 + b**2*e/8) + x**7*(2*a*b*g/7 + b**2*d/7) + x**6*(a*b*f/3 + b**2*c/6) + x**5*(a**2*h/5 + 2*a*b*e/5) + x**4*(a**2*g/4 + a*b*d/2) + x**3*(a**2*f/3 + 2*a*b*c/3)","A",0
389,1,156,0,0.360260," ","integrate((b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**2,x)","- \frac{a^{2} c}{x} + a^{2} d \log{\left(x \right)} + a^{2} e x + \frac{b^{2} f x^{8}}{8} + \frac{b^{2} g x^{9}}{9} + \frac{b^{2} h x^{10}}{10} + x^{7} \left(\frac{2 a b h}{7} + \frac{b^{2} e}{7}\right) + x^{6} \left(\frac{a b g}{3} + \frac{b^{2} d}{6}\right) + x^{5} \left(\frac{2 a b f}{5} + \frac{b^{2} c}{5}\right) + x^{4} \left(\frac{a^{2} h}{4} + \frac{a b e}{2}\right) + x^{3} \left(\frac{a^{2} g}{3} + \frac{2 a b d}{3}\right) + x^{2} \left(\frac{a^{2} f}{2} + a b c\right)"," ",0,"-a**2*c/x + a**2*d*log(x) + a**2*e*x + b**2*f*x**8/8 + b**2*g*x**9/9 + b**2*h*x**10/10 + x**7*(2*a*b*h/7 + b**2*e/7) + x**6*(a*b*g/3 + b**2*d/6) + x**5*(2*a*b*f/5 + b**2*c/5) + x**4*(a**2*h/4 + a*b*e/2) + x**3*(a**2*g/3 + 2*a*b*d/3) + x**2*(a**2*f/2 + a*b*c)","A",0
390,1,158,0,0.446109," ","integrate((b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**3,x)","a^{2} e \log{\left(x \right)} + \frac{b^{2} f x^{7}}{7} + \frac{b^{2} g x^{8}}{8} + \frac{b^{2} h x^{9}}{9} + x^{6} \left(\frac{a b h}{3} + \frac{b^{2} e}{6}\right) + x^{5} \left(\frac{2 a b g}{5} + \frac{b^{2} d}{5}\right) + x^{4} \left(\frac{a b f}{2} + \frac{b^{2} c}{4}\right) + x^{3} \left(\frac{a^{2} h}{3} + \frac{2 a b e}{3}\right) + x^{2} \left(\frac{a^{2} g}{2} + a b d\right) + x \left(a^{2} f + 2 a b c\right) + \frac{- a^{2} c - 2 a^{2} d x}{2 x^{2}}"," ",0,"a**2*e*log(x) + b**2*f*x**7/7 + b**2*g*x**8/8 + b**2*h*x**9/9 + x**6*(a*b*h/3 + b**2*e/6) + x**5*(2*a*b*g/5 + b**2*d/5) + x**4*(a*b*f/2 + b**2*c/4) + x**3*(a**2*h/3 + 2*a*b*e/3) + x**2*(a**2*g/2 + a*b*d) + x*(a**2*f + 2*a*b*c) + (-a**2*c - 2*a**2*d*x)/(2*x**2)","A",0
391,1,158,0,0.880066," ","integrate((b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**4,x)","a \left(a f + 2 b c\right) \log{\left(x \right)} + \frac{b^{2} f x^{6}}{6} + \frac{b^{2} g x^{7}}{7} + \frac{b^{2} h x^{8}}{8} + x^{5} \left(\frac{2 a b h}{5} + \frac{b^{2} e}{5}\right) + x^{4} \left(\frac{a b g}{2} + \frac{b^{2} d}{4}\right) + x^{3} \left(\frac{2 a b f}{3} + \frac{b^{2} c}{3}\right) + x^{2} \left(\frac{a^{2} h}{2} + a b e\right) + x \left(a^{2} g + 2 a b d\right) + \frac{- 2 a^{2} c - 3 a^{2} d x - 6 a^{2} e x^{2}}{6 x^{3}}"," ",0,"a*(a*f + 2*b*c)*log(x) + b**2*f*x**6/6 + b**2*g*x**7/7 + b**2*h*x**8/8 + x**5*(2*a*b*h/5 + b**2*e/5) + x**4*(a*b*g/2 + b**2*d/4) + x**3*(2*a*b*f/3 + b**2*c/3) + x**2*(a**2*h/2 + a*b*e) + x*(a**2*g + 2*a*b*d) + (-2*a**2*c - 3*a**2*d*x - 6*a**2*e*x**2)/(6*x**3)","A",0
392,1,156,0,3.234587," ","integrate((b*x**3+a)**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**5,x)","a \left(a g + 2 b d\right) \log{\left(x \right)} + \frac{b^{2} f x^{5}}{5} + \frac{b^{2} g x^{6}}{6} + \frac{b^{2} h x^{7}}{7} + x^{4} \left(\frac{a b h}{2} + \frac{b^{2} e}{4}\right) + x^{3} \left(\frac{2 a b g}{3} + \frac{b^{2} d}{3}\right) + x^{2} \left(a b f + \frac{b^{2} c}{2}\right) + x \left(a^{2} h + 2 a b e\right) + \frac{- 3 a^{2} c - 4 a^{2} d x - 6 a^{2} e x^{2} + x^{3} \left(- 12 a^{2} f - 24 a b c\right)}{12 x^{4}}"," ",0,"a*(a*g + 2*b*d)*log(x) + b**2*f*x**5/5 + b**2*g*x**6/6 + b**2*h*x**7/7 + x**4*(a*b*h/2 + b**2*e/4) + x**3*(2*a*b*g/3 + b**2*d/3) + x**2*(a*b*f + b**2*c/2) + x*(a**2*h + 2*a*b*e) + (-3*a**2*c - 4*a**2*d*x - 6*a**2*e*x**2 + x**3*(-12*a**2*f - 24*a*b*c))/(12*x**4)","A",0
393,1,246,0,0.123527," ","integrate(x**4*(b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\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} + x^{16} \left(\frac{3 a b^{2} h}{16} + \frac{b^{3} e}{16}\right) + x^{15} \left(\frac{a b^{2} g}{5} + \frac{b^{3} d}{15}\right) + x^{14} \left(\frac{3 a b^{2} f}{14} + \frac{b^{3} c}{14}\right) + x^{13} \left(\frac{3 a^{2} b h}{13} + \frac{3 a b^{2} e}{13}\right) + x^{12} \left(\frac{a^{2} b g}{4} + \frac{a b^{2} d}{4}\right) + x^{11} \left(\frac{3 a^{2} b f}{11} + \frac{3 a b^{2} c}{11}\right) + x^{10} \left(\frac{a^{3} h}{10} + \frac{3 a^{2} b e}{10}\right) + x^{9} \left(\frac{a^{3} g}{9} + \frac{a^{2} b d}{3}\right) + x^{8} \left(\frac{a^{3} f}{8} + \frac{3 a^{2} b c}{8}\right)"," ",0,"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 + x**16*(3*a*b**2*h/16 + b**3*e/16) + x**15*(a*b**2*g/5 + b**3*d/15) + x**14*(3*a*b**2*f/14 + b**3*c/14) + x**13*(3*a**2*b*h/13 + 3*a*b**2*e/13) + x**12*(a**2*b*g/4 + a*b**2*d/4) + x**11*(3*a**2*b*f/11 + 3*a*b**2*c/11) + x**10*(a**3*h/10 + 3*a**2*b*e/10) + x**9*(a**3*g/9 + a**2*b*d/3) + x**8*(a**3*f/8 + 3*a**2*b*c/8)","A",0
394,1,246,0,0.118412," ","integrate(x**3*(b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\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} + x^{15} \left(\frac{a b^{2} h}{5} + \frac{b^{3} e}{15}\right) + x^{14} \left(\frac{3 a b^{2} g}{14} + \frac{b^{3} d}{14}\right) + x^{13} \left(\frac{3 a b^{2} f}{13} + \frac{b^{3} c}{13}\right) + x^{12} \left(\frac{a^{2} b h}{4} + \frac{a b^{2} e}{4}\right) + x^{11} \left(\frac{3 a^{2} b g}{11} + \frac{3 a b^{2} d}{11}\right) + x^{10} \left(\frac{3 a^{2} b f}{10} + \frac{3 a b^{2} c}{10}\right) + x^{9} \left(\frac{a^{3} h}{9} + \frac{a^{2} b e}{3}\right) + x^{8} \left(\frac{a^{3} g}{8} + \frac{3 a^{2} b d}{8}\right) + x^{7} \left(\frac{a^{3} f}{7} + \frac{3 a^{2} b c}{7}\right)"," ",0,"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 + x**15*(a*b**2*h/5 + b**3*e/15) + x**14*(3*a*b**2*g/14 + b**3*d/14) + x**13*(3*a*b**2*f/13 + b**3*c/13) + x**12*(a**2*b*h/4 + a*b**2*e/4) + x**11*(3*a**2*b*g/11 + 3*a*b**2*d/11) + x**10*(3*a**2*b*f/10 + 3*a*b**2*c/10) + x**9*(a**3*h/9 + a**2*b*e/3) + x**8*(a**3*g/8 + 3*a**2*b*d/8) + x**7*(a**3*f/7 + 3*a**2*b*c/7)","A",0
395,1,246,0,0.124735," ","integrate(x**2*(b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\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} + x^{14} \left(\frac{3 a b^{2} h}{14} + \frac{b^{3} e}{14}\right) + x^{13} \left(\frac{3 a b^{2} g}{13} + \frac{b^{3} d}{13}\right) + x^{12} \left(\frac{a b^{2} f}{4} + \frac{b^{3} c}{12}\right) + x^{11} \left(\frac{3 a^{2} b h}{11} + \frac{3 a b^{2} e}{11}\right) + x^{10} \left(\frac{3 a^{2} b g}{10} + \frac{3 a b^{2} d}{10}\right) + x^{9} \left(\frac{a^{2} b f}{3} + \frac{a b^{2} c}{3}\right) + x^{8} \left(\frac{a^{3} h}{8} + \frac{3 a^{2} b e}{8}\right) + x^{7} \left(\frac{a^{3} g}{7} + \frac{3 a^{2} b d}{7}\right) + x^{6} \left(\frac{a^{3} f}{6} + \frac{a^{2} b c}{2}\right)"," ",0,"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 + x**14*(3*a*b**2*h/14 + b**3*e/14) + x**13*(3*a*b**2*g/13 + b**3*d/13) + x**12*(a*b**2*f/4 + b**3*c/12) + x**11*(3*a**2*b*h/11 + 3*a*b**2*e/11) + x**10*(3*a**2*b*g/10 + 3*a*b**2*d/10) + x**9*(a**2*b*f/3 + a*b**2*c/3) + x**8*(a**3*h/8 + 3*a**2*b*e/8) + x**7*(a**3*g/7 + 3*a**2*b*d/7) + x**6*(a**3*f/6 + a**2*b*c/2)","A",0
396,1,246,0,0.113595," ","integrate(x*(b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","\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} + x^{13} \left(\frac{3 a b^{2} h}{13} + \frac{b^{3} e}{13}\right) + x^{12} \left(\frac{a b^{2} g}{4} + \frac{b^{3} d}{12}\right) + x^{11} \left(\frac{3 a b^{2} f}{11} + \frac{b^{3} c}{11}\right) + x^{10} \left(\frac{3 a^{2} b h}{10} + \frac{3 a b^{2} e}{10}\right) + x^{9} \left(\frac{a^{2} b g}{3} + \frac{a b^{2} d}{3}\right) + x^{8} \left(\frac{3 a^{2} b f}{8} + \frac{3 a b^{2} c}{8}\right) + x^{7} \left(\frac{a^{3} h}{7} + \frac{3 a^{2} b e}{7}\right) + x^{6} \left(\frac{a^{3} g}{6} + \frac{a^{2} b d}{2}\right) + x^{5} \left(\frac{a^{3} f}{5} + \frac{3 a^{2} b c}{5}\right)"," ",0,"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 + x**13*(3*a*b**2*h/13 + b**3*e/13) + x**12*(a*b**2*g/4 + b**3*d/12) + x**11*(3*a*b**2*f/11 + b**3*c/11) + x**10*(3*a**2*b*h/10 + 3*a*b**2*e/10) + x**9*(a**2*b*g/3 + a*b**2*d/3) + x**8*(3*a**2*b*f/8 + 3*a*b**2*c/8) + x**7*(a**3*h/7 + 3*a**2*b*e/7) + x**6*(a**3*g/6 + a**2*b*d/2) + x**5*(a**3*f/5 + 3*a**2*b*c/5)","A",0
397,1,243,0,0.121351," ","integrate((b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c),x)","a^{3} c x + \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} + x^{12} \left(\frac{a b^{2} h}{4} + \frac{b^{3} e}{12}\right) + x^{11} \left(\frac{3 a b^{2} g}{11} + \frac{b^{3} d}{11}\right) + x^{10} \left(\frac{3 a b^{2} f}{10} + \frac{b^{3} c}{10}\right) + x^{9} \left(\frac{a^{2} b h}{3} + \frac{a b^{2} e}{3}\right) + x^{8} \left(\frac{3 a^{2} b g}{8} + \frac{3 a b^{2} d}{8}\right) + x^{7} \left(\frac{3 a^{2} b f}{7} + \frac{3 a b^{2} c}{7}\right) + x^{6} \left(\frac{a^{3} h}{6} + \frac{a^{2} b e}{2}\right) + x^{5} \left(\frac{a^{3} g}{5} + \frac{3 a^{2} b d}{5}\right) + x^{4} \left(\frac{a^{3} f}{4} + \frac{3 a^{2} b c}{4}\right)"," ",0,"a**3*c*x + 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 + x**12*(a*b**2*h/4 + b**3*e/12) + x**11*(3*a*b**2*g/11 + b**3*d/11) + x**10*(3*a*b**2*f/10 + b**3*c/10) + x**9*(a**2*b*h/3 + a*b**2*e/3) + x**8*(3*a**2*b*g/8 + 3*a*b**2*d/8) + x**7*(3*a**2*b*f/7 + 3*a*b**2*c/7) + x**6*(a**3*h/6 + a**2*b*e/2) + x**5*(a**3*g/5 + 3*a**2*b*d/5) + x**4*(a**3*f/4 + 3*a**2*b*c/4)","A",0
398,1,240,0,0.540556," ","integrate((b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x,x)","a^{3} c \log{\left(x \right)} + a^{3} d x + \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} + x^{11} \left(\frac{3 a b^{2} h}{11} + \frac{b^{3} e}{11}\right) + x^{10} \left(\frac{3 a b^{2} g}{10} + \frac{b^{3} d}{10}\right) + x^{9} \left(\frac{a b^{2} f}{3} + \frac{b^{3} c}{9}\right) + x^{8} \left(\frac{3 a^{2} b h}{8} + \frac{3 a b^{2} e}{8}\right) + x^{7} \left(\frac{3 a^{2} b g}{7} + \frac{3 a b^{2} d}{7}\right) + x^{6} \left(\frac{a^{2} b f}{2} + \frac{a b^{2} c}{2}\right) + x^{5} \left(\frac{a^{3} h}{5} + \frac{3 a^{2} b e}{5}\right) + x^{4} \left(\frac{a^{3} g}{4} + \frac{3 a^{2} b d}{4}\right) + x^{3} \left(\frac{a^{3} f}{3} + a^{2} b c\right)"," ",0,"a**3*c*log(x) + a**3*d*x + a**3*e*x**2/2 + b**3*f*x**12/12 + b**3*g*x**13/13 + b**3*h*x**14/14 + x**11*(3*a*b**2*h/11 + b**3*e/11) + x**10*(3*a*b**2*g/10 + b**3*d/10) + x**9*(a*b**2*f/3 + b**3*c/9) + x**8*(3*a**2*b*h/8 + 3*a*b**2*e/8) + x**7*(3*a**2*b*g/7 + 3*a*b**2*d/7) + x**6*(a**2*b*f/2 + a*b**2*c/2) + x**5*(a**3*h/5 + 3*a**2*b*e/5) + x**4*(a**3*g/4 + 3*a**2*b*d/4) + x**3*(a**3*f/3 + a**2*b*c)","A",0
399,1,236,0,0.511089," ","integrate((b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**2,x)","- \frac{a^{3} c}{x} + a^{3} d \log{\left(x \right)} + a^{3} e x + \frac{b^{3} f x^{11}}{11} + \frac{b^{3} g x^{12}}{12} + \frac{b^{3} h x^{13}}{13} + x^{10} \left(\frac{3 a b^{2} h}{10} + \frac{b^{3} e}{10}\right) + x^{9} \left(\frac{a b^{2} g}{3} + \frac{b^{3} d}{9}\right) + x^{8} \left(\frac{3 a b^{2} f}{8} + \frac{b^{3} c}{8}\right) + x^{7} \left(\frac{3 a^{2} b h}{7} + \frac{3 a b^{2} e}{7}\right) + x^{6} \left(\frac{a^{2} b g}{2} + \frac{a b^{2} d}{2}\right) + x^{5} \left(\frac{3 a^{2} b f}{5} + \frac{3 a b^{2} c}{5}\right) + x^{4} \left(\frac{a^{3} h}{4} + \frac{3 a^{2} b e}{4}\right) + x^{3} \left(\frac{a^{3} g}{3} + a^{2} b d\right) + x^{2} \left(\frac{a^{3} f}{2} + \frac{3 a^{2} b c}{2}\right)"," ",0,"-a**3*c/x + a**3*d*log(x) + a**3*e*x + b**3*f*x**11/11 + b**3*g*x**12/12 + b**3*h*x**13/13 + x**10*(3*a*b**2*h/10 + b**3*e/10) + x**9*(a*b**2*g/3 + b**3*d/9) + x**8*(3*a*b**2*f/8 + b**3*c/8) + x**7*(3*a**2*b*h/7 + 3*a*b**2*e/7) + x**6*(a**2*b*g/2 + a*b**2*d/2) + x**5*(3*a**2*b*f/5 + 3*a*b**2*c/5) + x**4*(a**3*h/4 + 3*a**2*b*e/4) + x**3*(a**3*g/3 + a**2*b*d) + x**2*(a**3*f/2 + 3*a**2*b*c/2)","A",0
400,1,238,0,0.592737," ","integrate((b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**3,x)","a^{3} e \log{\left(x \right)} + \frac{b^{3} f x^{10}}{10} + \frac{b^{3} g x^{11}}{11} + \frac{b^{3} h x^{12}}{12} + x^{9} \left(\frac{a b^{2} h}{3} + \frac{b^{3} e}{9}\right) + x^{8} \left(\frac{3 a b^{2} g}{8} + \frac{b^{3} d}{8}\right) + x^{7} \left(\frac{3 a b^{2} f}{7} + \frac{b^{3} c}{7}\right) + x^{6} \left(\frac{a^{2} b h}{2} + \frac{a b^{2} e}{2}\right) + x^{5} \left(\frac{3 a^{2} b g}{5} + \frac{3 a b^{2} d}{5}\right) + x^{4} \left(\frac{3 a^{2} b f}{4} + \frac{3 a b^{2} c}{4}\right) + x^{3} \left(\frac{a^{3} h}{3} + a^{2} b e\right) + x^{2} \left(\frac{a^{3} g}{2} + \frac{3 a^{2} b d}{2}\right) + x \left(a^{3} f + 3 a^{2} b c\right) + \frac{- a^{3} c - 2 a^{3} d x}{2 x^{2}}"," ",0,"a**3*e*log(x) + b**3*f*x**10/10 + b**3*g*x**11/11 + b**3*h*x**12/12 + x**9*(a*b**2*h/3 + b**3*e/9) + x**8*(3*a*b**2*g/8 + b**3*d/8) + x**7*(3*a*b**2*f/7 + b**3*c/7) + x**6*(a**2*b*h/2 + a*b**2*e/2) + x**5*(3*a**2*b*g/5 + 3*a*b**2*d/5) + x**4*(3*a**2*b*f/4 + 3*a*b**2*c/4) + x**3*(a**3*h/3 + a**2*b*e) + x**2*(a**3*g/2 + 3*a**2*b*d/2) + x*(a**3*f + 3*a**2*b*c) + (-a**3*c - 2*a**3*d*x)/(2*x**2)","A",0
401,1,236,0,1.042748," ","integrate((b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**4,x)","a^{2} \left(a f + 3 b c\right) \log{\left(x \right)} + \frac{b^{3} f x^{9}}{9} + \frac{b^{3} g x^{10}}{10} + \frac{b^{3} h x^{11}}{11} + x^{8} \left(\frac{3 a b^{2} h}{8} + \frac{b^{3} e}{8}\right) + x^{7} \left(\frac{3 a b^{2} g}{7} + \frac{b^{3} d}{7}\right) + x^{6} \left(\frac{a b^{2} f}{2} + \frac{b^{3} c}{6}\right) + x^{5} \left(\frac{3 a^{2} b h}{5} + \frac{3 a b^{2} e}{5}\right) + x^{4} \left(\frac{3 a^{2} b g}{4} + \frac{3 a b^{2} d}{4}\right) + x^{3} \left(a^{2} b f + a b^{2} c\right) + x^{2} \left(\frac{a^{3} h}{2} + \frac{3 a^{2} b e}{2}\right) + x \left(a^{3} g + 3 a^{2} b d\right) + \frac{- 2 a^{3} c - 3 a^{3} d x - 6 a^{3} e x^{2}}{6 x^{3}}"," ",0,"a**2*(a*f + 3*b*c)*log(x) + b**3*f*x**9/9 + b**3*g*x**10/10 + b**3*h*x**11/11 + x**8*(3*a*b**2*h/8 + b**3*e/8) + x**7*(3*a*b**2*g/7 + b**3*d/7) + x**6*(a*b**2*f/2 + b**3*c/6) + x**5*(3*a**2*b*h/5 + 3*a*b**2*e/5) + x**4*(3*a**2*b*g/4 + 3*a*b**2*d/4) + x**3*(a**2*b*f + a*b**2*c) + x**2*(a**3*h/2 + 3*a**2*b*e/2) + x*(a**3*g + 3*a**2*b*d) + (-2*a**3*c - 3*a**3*d*x - 6*a**3*e*x**2)/(6*x**3)","A",0
402,1,235,0,3.137179," ","integrate((b*x**3+a)**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**5,x)","a^{2} \left(a g + 3 b d\right) \log{\left(x \right)} + \frac{b^{3} f x^{8}}{8} + \frac{b^{3} g x^{9}}{9} + \frac{b^{3} h x^{10}}{10} + x^{7} \left(\frac{3 a b^{2} h}{7} + \frac{b^{3} e}{7}\right) + x^{6} \left(\frac{a b^{2} g}{2} + \frac{b^{3} d}{6}\right) + x^{5} \left(\frac{3 a b^{2} f}{5} + \frac{b^{3} c}{5}\right) + x^{4} \left(\frac{3 a^{2} b h}{4} + \frac{3 a b^{2} e}{4}\right) + x^{3} \left(a^{2} b g + a b^{2} d\right) + x^{2} \left(\frac{3 a^{2} b f}{2} + \frac{3 a b^{2} c}{2}\right) + x \left(a^{3} h + 3 a^{2} b e\right) + \frac{- 3 a^{3} c - 4 a^{3} d x - 6 a^{3} e x^{2} + x^{3} \left(- 12 a^{3} f - 36 a^{2} b c\right)}{12 x^{4}}"," ",0,"a**2*(a*g + 3*b*d)*log(x) + b**3*f*x**8/8 + b**3*g*x**9/9 + b**3*h*x**10/10 + x**7*(3*a*b**2*h/7 + b**3*e/7) + x**6*(a*b**2*g/2 + b**3*d/6) + x**5*(3*a*b**2*f/5 + b**3*c/5) + x**4*(3*a**2*b*h/4 + 3*a*b**2*e/4) + x**3*(a**2*b*g + a*b**2*d) + x**2*(3*a**2*b*f/2 + 3*a*b**2*c/2) + x*(a**3*h + 3*a**2*b*e) + (-3*a**3*c - 4*a**3*d*x - 6*a**3*e*x**2 + x**3*(-12*a**3*f - 36*a**2*b*c))/(12*x**4)","A",0
403,1,881,0,60.517449," ","integrate(x**4*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**3+a),x)","x^{4} \left(- \frac{a h}{4 b^{2}} + \frac{e}{4 b}\right) + x^{3} \left(- \frac{a g}{3 b^{2}} + \frac{d}{3 b}\right) + x^{2} \left(- \frac{a f}{2 b^{2}} + \frac{c}{2 b}\right) + x \left(\frac{a^{2} h}{b^{3}} - \frac{a e}{b^{2}}\right) + \operatorname{RootSum} {\left(27 t^{3} b^{10} + t^{2} \left(- 27 a^{2} b^{7} g + 27 a b^{8} d\right) + t \left(- 9 a^{4} b^{4} f h + 9 a^{4} b^{4} g^{2} + 9 a^{3} b^{5} c h - 18 a^{3} b^{5} d g + 9 a^{3} b^{5} e f - 9 a^{2} b^{6} c e + 9 a^{2} b^{6} d^{2}\right) + a^{7} h^{3} - 3 a^{6} b e h^{2} + 3 a^{6} b f g h - a^{6} b g^{3} - 3 a^{5} b^{2} c g h - 3 a^{5} b^{2} d f h + 3 a^{5} b^{2} d g^{2} + 3 a^{5} b^{2} e^{2} h - 3 a^{5} b^{2} e f g + a^{5} b^{2} f^{3} + 3 a^{4} b^{3} c d h + 3 a^{4} b^{3} c e g - 3 a^{4} b^{3} c f^{2} - 3 a^{4} b^{3} d^{2} g + 3 a^{4} b^{3} d e f - a^{4} b^{3} e^{3} + 3 a^{3} b^{4} c^{2} f - 3 a^{3} b^{4} c d e + a^{3} b^{4} d^{3} - a^{2} b^{5} c^{3}, \left( t \mapsto t \log{\left(x + \frac{- 9 t^{2} a b^{7} f + 9 t^{2} b^{8} c - 3 t a^{4} b^{3} h^{2} + 6 t a^{3} b^{4} e h + 6 t a^{3} b^{4} f g - 6 t a^{2} b^{5} c g - 6 t a^{2} b^{5} d f - 3 t a^{2} b^{5} e^{2} + 6 t a b^{6} c d + a^{6} g h^{2} - a^{5} b d h^{2} - 2 a^{5} b e g h + 2 a^{5} b f^{2} h - a^{5} b f g^{2} - 4 a^{4} b^{2} c f h + a^{4} b^{2} c g^{2} + 2 a^{4} b^{2} d e h + 2 a^{4} b^{2} d f g + a^{4} b^{2} e^{2} g - 2 a^{4} b^{2} e f^{2} + 2 a^{3} b^{3} c^{2} h - 2 a^{3} b^{3} c d g + 4 a^{3} b^{3} c e f - a^{3} b^{3} d^{2} f - a^{3} b^{3} d e^{2} - 2 a^{2} b^{4} c^{2} e + a^{2} b^{4} c d^{2}}{a^{6} h^{3} - 3 a^{5} b e h^{2} + 3 a^{4} b^{2} e^{2} h - a^{4} b^{2} f^{3} + 3 a^{3} b^{3} c f^{2} - a^{3} b^{3} e^{3} - 3 a^{2} b^{4} c^{2} f + a b^{5} c^{3}} \right)} \right)\right)} + \frac{f x^{5}}{5 b} + \frac{g x^{6}}{6 b} + \frac{h x^{7}}{7 b}"," ",0,"x**4*(-a*h/(4*b**2) + e/(4*b)) + x**3*(-a*g/(3*b**2) + d/(3*b)) + x**2*(-a*f/(2*b**2) + c/(2*b)) + x*(a**2*h/b**3 - a*e/b**2) + RootSum(27*_t**3*b**10 + _t**2*(-27*a**2*b**7*g + 27*a*b**8*d) + _t*(-9*a**4*b**4*f*h + 9*a**4*b**4*g**2 + 9*a**3*b**5*c*h - 18*a**3*b**5*d*g + 9*a**3*b**5*e*f - 9*a**2*b**6*c*e + 9*a**2*b**6*d**2) + a**7*h**3 - 3*a**6*b*e*h**2 + 3*a**6*b*f*g*h - a**6*b*g**3 - 3*a**5*b**2*c*g*h - 3*a**5*b**2*d*f*h + 3*a**5*b**2*d*g**2 + 3*a**5*b**2*e**2*h - 3*a**5*b**2*e*f*g + a**5*b**2*f**3 + 3*a**4*b**3*c*d*h + 3*a**4*b**3*c*e*g - 3*a**4*b**3*c*f**2 - 3*a**4*b**3*d**2*g + 3*a**4*b**3*d*e*f - a**4*b**3*e**3 + 3*a**3*b**4*c**2*f - 3*a**3*b**4*c*d*e + a**3*b**4*d**3 - a**2*b**5*c**3, Lambda(_t, _t*log(x + (-9*_t**2*a*b**7*f + 9*_t**2*b**8*c - 3*_t*a**4*b**3*h**2 + 6*_t*a**3*b**4*e*h + 6*_t*a**3*b**4*f*g - 6*_t*a**2*b**5*c*g - 6*_t*a**2*b**5*d*f - 3*_t*a**2*b**5*e**2 + 6*_t*a*b**6*c*d + a**6*g*h**2 - a**5*b*d*h**2 - 2*a**5*b*e*g*h + 2*a**5*b*f**2*h - a**5*b*f*g**2 - 4*a**4*b**2*c*f*h + a**4*b**2*c*g**2 + 2*a**4*b**2*d*e*h + 2*a**4*b**2*d*f*g + a**4*b**2*e**2*g - 2*a**4*b**2*e*f**2 + 2*a**3*b**3*c**2*h - 2*a**3*b**3*c*d*g + 4*a**3*b**3*c*e*f - a**3*b**3*d**2*f - a**3*b**3*d*e**2 - 2*a**2*b**4*c**2*e + a**2*b**4*c*d**2)/(a**6*h**3 - 3*a**5*b*e*h**2 + 3*a**4*b**2*e**2*h - a**4*b**2*f**3 + 3*a**3*b**3*c*f**2 - a**3*b**3*e**3 - 3*a**2*b**4*c**2*f + a*b**5*c**3)))) + f*x**5/(5*b) + g*x**6/(6*b) + h*x**7/(7*b)","B",0
404,1,845,0,73.527133," ","integrate(x**3*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**3+a),x)","x^{3} \left(- \frac{a h}{3 b^{2}} + \frac{e}{3 b}\right) + x^{2} \left(- \frac{a g}{2 b^{2}} + \frac{d}{2 b}\right) + x \left(- \frac{a f}{b^{2}} + \frac{c}{b}\right) + \operatorname{RootSum} {\left(27 t^{3} b^{9} + t^{2} \left(- 27 a^{2} b^{6} h + 27 a b^{7} e\right) + t \left(9 a^{4} b^{3} h^{2} - 18 a^{3} b^{4} e h + 9 a^{3} b^{4} f g - 9 a^{2} b^{5} c g - 9 a^{2} b^{5} d f + 9 a^{2} b^{5} e^{2} + 9 a b^{6} c d\right) - a^{6} h^{3} + 3 a^{5} b e h^{2} - 3 a^{5} b f g h + a^{5} b g^{3} + 3 a^{4} b^{2} c g h + 3 a^{4} b^{2} d f h - 3 a^{4} b^{2} d g^{2} - 3 a^{4} b^{2} e^{2} h + 3 a^{4} b^{2} e f g - a^{4} b^{2} f^{3} - 3 a^{3} b^{3} c d h - 3 a^{3} b^{3} c e g + 3 a^{3} b^{3} c f^{2} + 3 a^{3} b^{3} d^{2} g - 3 a^{3} b^{3} d e f + a^{3} b^{3} e^{3} - 3 a^{2} b^{4} c^{2} f + 3 a^{2} b^{4} c d e - a^{2} b^{4} d^{3} + a b^{5} c^{3}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a b^{6} g - 9 t^{2} b^{7} d - 6 t a^{3} b^{3} g h + 6 t a^{2} b^{4} d h + 6 t a^{2} b^{4} e g + 3 t a^{2} b^{4} f^{2} - 6 t a b^{5} c f - 6 t a b^{5} d e + 3 t b^{6} c^{2} + a^{5} g h^{2} - a^{4} b d h^{2} - 2 a^{4} b e g h - a^{4} b f^{2} h + 2 a^{4} b f g^{2} + 2 a^{3} b^{2} c f h - 2 a^{3} b^{2} c g^{2} + 2 a^{3} b^{2} d e h - 4 a^{3} b^{2} d f g + a^{3} b^{2} e^{2} g + a^{3} b^{2} e f^{2} - a^{2} b^{3} c^{2} h + 4 a^{2} b^{3} c d g - 2 a^{2} b^{3} c e f + 2 a^{2} b^{3} d^{2} f - a^{2} b^{3} d e^{2} + a b^{4} c^{2} e - 2 a b^{4} c d^{2}}{a^{4} b g^{3} - 3 a^{3} b^{2} d g^{2} + a^{3} b^{2} f^{3} - 3 a^{2} b^{3} c f^{2} + 3 a^{2} b^{3} d^{2} g + 3 a b^{4} c^{2} f - a b^{4} d^{3} - b^{5} c^{3}} \right)} \right)\right)} + \frac{f x^{4}}{4 b} + \frac{g x^{5}}{5 b} + \frac{h x^{6}}{6 b}"," ",0,"x**3*(-a*h/(3*b**2) + e/(3*b)) + x**2*(-a*g/(2*b**2) + d/(2*b)) + x*(-a*f/b**2 + c/b) + RootSum(27*_t**3*b**9 + _t**2*(-27*a**2*b**6*h + 27*a*b**7*e) + _t*(9*a**4*b**3*h**2 - 18*a**3*b**4*e*h + 9*a**3*b**4*f*g - 9*a**2*b**5*c*g - 9*a**2*b**5*d*f + 9*a**2*b**5*e**2 + 9*a*b**6*c*d) - a**6*h**3 + 3*a**5*b*e*h**2 - 3*a**5*b*f*g*h + a**5*b*g**3 + 3*a**4*b**2*c*g*h + 3*a**4*b**2*d*f*h - 3*a**4*b**2*d*g**2 - 3*a**4*b**2*e**2*h + 3*a**4*b**2*e*f*g - a**4*b**2*f**3 - 3*a**3*b**3*c*d*h - 3*a**3*b**3*c*e*g + 3*a**3*b**3*c*f**2 + 3*a**3*b**3*d**2*g - 3*a**3*b**3*d*e*f + a**3*b**3*e**3 - 3*a**2*b**4*c**2*f + 3*a**2*b**4*c*d*e - a**2*b**4*d**3 + a*b**5*c**3, Lambda(_t, _t*log(x + (9*_t**2*a*b**6*g - 9*_t**2*b**7*d - 6*_t*a**3*b**3*g*h + 6*_t*a**2*b**4*d*h + 6*_t*a**2*b**4*e*g + 3*_t*a**2*b**4*f**2 - 6*_t*a*b**5*c*f - 6*_t*a*b**5*d*e + 3*_t*b**6*c**2 + a**5*g*h**2 - a**4*b*d*h**2 - 2*a**4*b*e*g*h - a**4*b*f**2*h + 2*a**4*b*f*g**2 + 2*a**3*b**2*c*f*h - 2*a**3*b**2*c*g**2 + 2*a**3*b**2*d*e*h - 4*a**3*b**2*d*f*g + a**3*b**2*e**2*g + a**3*b**2*e*f**2 - a**2*b**3*c**2*h + 4*a**2*b**3*c*d*g - 2*a**2*b**3*c*e*f + 2*a**2*b**3*d**2*f - a**2*b**3*d*e**2 + a*b**4*c**2*e - 2*a*b**4*c*d**2)/(a**4*b*g**3 - 3*a**3*b**2*d*g**2 + a**3*b**2*f**3 - 3*a**2*b**3*c*f**2 + 3*a**2*b**3*d**2*g + 3*a*b**4*c**2*f - a*b**4*d**3 - b**5*c**3)))) + f*x**4/(4*b) + g*x**5/(5*b) + h*x**6/(6*b)","B",0
405,1,790,0,88.695571," ","integrate(x**2*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**3+a),x)","x^{2} \left(- \frac{a h}{2 b^{2}} + \frac{e}{2 b}\right) + x \left(- \frac{a g}{b^{2}} + \frac{d}{b}\right) + \operatorname{RootSum} {\left(27 t^{3} b^{8} + t^{2} \left(27 a b^{6} f - 27 b^{7} c\right) + t \left(9 a^{3} b^{3} g h - 9 a^{2} b^{4} d h - 9 a^{2} b^{4} e g + 9 a^{2} b^{4} f^{2} - 18 a b^{5} c f + 9 a b^{5} d e + 9 b^{6} c^{2}\right) + 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 - 3 a^{3} b^{2} d f h + 3 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} + 3 a^{2} b^{3} c d h + 3 a^{2} b^{3} c e g - 3 a^{2} b^{3} c f^{2} - 3 a^{2} b^{3} d^{2} g + 3 a^{2} b^{3} d e f - a^{2} b^{3} e^{3} + 3 a b^{4} c^{2} f - 3 a b^{4} c d e + a b^{4} d^{3} - b^{5} c^{3}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a b^{5} h - 9 t^{2} b^{6} e + 6 t a^{2} b^{3} f h + 3 t a^{2} b^{3} g^{2} - 6 t a b^{4} c h - 6 t a b^{4} d g - 6 t a b^{4} e f + 6 t b^{5} c e + 3 t b^{5} d^{2} + 2 a^{4} g h^{2} - 2 a^{3} b d h^{2} - 4 a^{3} b e g h + a^{3} b f^{2} h + a^{3} b f g^{2} - 2 a^{2} b^{2} c f h - a^{2} b^{2} c g^{2} + 4 a^{2} b^{2} d e h - 2 a^{2} b^{2} d f g + 2 a^{2} b^{2} e^{2} g - a^{2} b^{2} e f^{2} + a b^{3} c^{2} h + 2 a b^{3} c d g + 2 a b^{3} c e f + a b^{3} d^{2} f - 2 a b^{3} d e^{2} - b^{4} c^{2} e - b^{4} c d^{2}}{a^{4} h^{3} - 3 a^{3} b e h^{2} + a^{3} b g^{3} - 3 a^{2} b^{2} d g^{2} + 3 a^{2} b^{2} e^{2} h + 3 a b^{3} d^{2} g - a b^{3} e^{3} - b^{4} d^{3}} \right)} \right)\right)} + \frac{f x^{3}}{3 b} + \frac{g x^{4}}{4 b} + \frac{h x^{5}}{5 b}"," ",0,"x**2*(-a*h/(2*b**2) + e/(2*b)) + x*(-a*g/b**2 + d/b) + RootSum(27*_t**3*b**8 + _t**2*(27*a*b**6*f - 27*b**7*c) + _t*(9*a**3*b**3*g*h - 9*a**2*b**4*d*h - 9*a**2*b**4*e*g + 9*a**2*b**4*f**2 - 18*a*b**5*c*f + 9*a*b**5*d*e + 9*b**6*c**2) + 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 - 3*a**3*b**2*d*f*h + 3*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 + 3*a**2*b**3*c*d*h + 3*a**2*b**3*c*e*g - 3*a**2*b**3*c*f**2 - 3*a**2*b**3*d**2*g + 3*a**2*b**3*d*e*f - a**2*b**3*e**3 + 3*a*b**4*c**2*f - 3*a*b**4*c*d*e + a*b**4*d**3 - b**5*c**3, Lambda(_t, _t*log(x + (9*_t**2*a*b**5*h - 9*_t**2*b**6*e + 6*_t*a**2*b**3*f*h + 3*_t*a**2*b**3*g**2 - 6*_t*a*b**4*c*h - 6*_t*a*b**4*d*g - 6*_t*a*b**4*e*f + 6*_t*b**5*c*e + 3*_t*b**5*d**2 + 2*a**4*g*h**2 - 2*a**3*b*d*h**2 - 4*a**3*b*e*g*h + a**3*b*f**2*h + a**3*b*f*g**2 - 2*a**2*b**2*c*f*h - a**2*b**2*c*g**2 + 4*a**2*b**2*d*e*h - 2*a**2*b**2*d*f*g + 2*a**2*b**2*e**2*g - a**2*b**2*e*f**2 + a*b**3*c**2*h + 2*a*b**3*c*d*g + 2*a*b**3*c*e*f + a*b**3*d**2*f - 2*a*b**3*d*e**2 - b**4*c**2*e - b**4*c*d**2)/(a**4*h**3 - 3*a**3*b*e*h**2 + a**3*b*g**3 - 3*a**2*b**2*d*g**2 + 3*a**2*b**2*e**2*h + 3*a*b**3*d**2*g - a*b**3*e**3 - b**4*d**3)))) + f*x**3/(3*b) + g*x**4/(4*b) + h*x**5/(5*b)","B",0
406,1,811,0,63.000659," ","integrate(x*(h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**3+a),x)","x \left(- \frac{a h}{b^{2}} + \frac{e}{b}\right) + \operatorname{RootSum} {\left(27 t^{3} a b^{7} + t^{2} \left(27 a^{2} b^{5} g - 27 a b^{6} d\right) + t \left(- 9 a^{3} b^{3} f h + 9 a^{3} b^{3} g^{2} + 9 a^{2} b^{4} c h - 18 a^{2} b^{4} d g + 9 a^{2} b^{4} e f - 9 a b^{5} c e + 9 a b^{5} d^{2}\right) - 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 + 3 a^{3} b^{2} d f h - 3 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} - 3 a^{2} b^{3} c d h - 3 a^{2} b^{3} c e g + 3 a^{2} b^{3} c f^{2} + 3 a^{2} b^{3} d^{2} g - 3 a^{2} b^{3} d e f + a^{2} b^{3} e^{3} - 3 a b^{4} c^{2} f + 3 a b^{4} c d e - a b^{4} d^{3} + b^{5} c^{3}, \left( t \mapsto t \log{\left(x + \frac{- 9 t^{2} a^{2} b^{5} f + 9 t^{2} a b^{6} c + 3 t a^{4} b^{2} h^{2} - 6 t a^{3} b^{3} e h - 6 t a^{3} b^{3} f g + 6 t a^{2} b^{4} c g + 6 t a^{2} b^{4} d f + 3 t a^{2} b^{4} e^{2} - 6 t a b^{5} c d + a^{5} g h^{2} - a^{4} b d h^{2} - 2 a^{4} b e g h + 2 a^{4} b f^{2} h - a^{4} b f g^{2} - 4 a^{3} b^{2} c f h + a^{3} b^{2} c g^{2} + 2 a^{3} b^{2} d e h + 2 a^{3} b^{2} d f g + a^{3} b^{2} e^{2} g - 2 a^{3} b^{2} e f^{2} + 2 a^{2} b^{3} c^{2} h - 2 a^{2} b^{3} c d g + 4 a^{2} b^{3} c e f - a^{2} b^{3} d^{2} f - a^{2} b^{3} d e^{2} - 2 a b^{4} c^{2} e + a b^{4} c d^{2}}{a^{5} h^{3} - 3 a^{4} b e h^{2} + 3 a^{3} b^{2} e^{2} h - a^{3} b^{2} f^{3} + 3 a^{2} b^{3} c f^{2} - a^{2} b^{3} e^{3} - 3 a b^{4} c^{2} f + b^{5} c^{3}} \right)} \right)\right)} + \frac{f x^{2}}{2 b} + \frac{g x^{3}}{3 b} + \frac{h x^{4}}{4 b}"," ",0,"x*(-a*h/b**2 + e/b) + RootSum(27*_t**3*a*b**7 + _t**2*(27*a**2*b**5*g - 27*a*b**6*d) + _t*(-9*a**3*b**3*f*h + 9*a**3*b**3*g**2 + 9*a**2*b**4*c*h - 18*a**2*b**4*d*g + 9*a**2*b**4*e*f - 9*a*b**5*c*e + 9*a*b**5*d**2) - 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 + 3*a**3*b**2*d*f*h - 3*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 - 3*a**2*b**3*c*d*h - 3*a**2*b**3*c*e*g + 3*a**2*b**3*c*f**2 + 3*a**2*b**3*d**2*g - 3*a**2*b**3*d*e*f + a**2*b**3*e**3 - 3*a*b**4*c**2*f + 3*a*b**4*c*d*e - a*b**4*d**3 + b**5*c**3, Lambda(_t, _t*log(x + (-9*_t**2*a**2*b**5*f + 9*_t**2*a*b**6*c + 3*_t*a**4*b**2*h**2 - 6*_t*a**3*b**3*e*h - 6*_t*a**3*b**3*f*g + 6*_t*a**2*b**4*c*g + 6*_t*a**2*b**4*d*f + 3*_t*a**2*b**4*e**2 - 6*_t*a*b**5*c*d + a**5*g*h**2 - a**4*b*d*h**2 - 2*a**4*b*e*g*h + 2*a**4*b*f**2*h - a**4*b*f*g**2 - 4*a**3*b**2*c*f*h + a**3*b**2*c*g**2 + 2*a**3*b**2*d*e*h + 2*a**3*b**2*d*f*g + a**3*b**2*e**2*g - 2*a**3*b**2*e*f**2 + 2*a**2*b**3*c**2*h - 2*a**2*b**3*c*d*g + 4*a**2*b**3*c*e*f - a**2*b**3*d**2*f - a**2*b**3*d*e**2 - 2*a*b**4*c**2*e + a*b**4*c*d**2)/(a**5*h**3 - 3*a**4*b*e*h**2 + 3*a**3*b**2*e**2*h - a**3*b**2*f**3 + 3*a**2*b**3*c*f**2 - a**2*b**3*e**3 - 3*a*b**4*c**2*f + b**5*c**3)))) + f*x**2/(2*b) + g*x**3/(3*b) + h*x**4/(4*b)","B",0
407,1,804,0,59.387511," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/(b*x**3+a),x)","\operatorname{RootSum} {\left(27 t^{3} a^{2} b^{6} + t^{2} \left(27 a^{3} b^{4} h - 27 a^{2} b^{5} e\right) + t \left(9 a^{4} b^{2} h^{2} - 18 a^{3} b^{3} e h + 9 a^{3} b^{3} f g - 9 a^{2} b^{4} c g - 9 a^{2} b^{4} d f + 9 a^{2} b^{4} e^{2} + 9 a b^{5} c d\right) + 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 - 3 a^{3} b^{2} d f h + 3 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} + 3 a^{2} b^{3} c d h + 3 a^{2} b^{3} c e g - 3 a^{2} b^{3} c f^{2} - 3 a^{2} b^{3} d^{2} g + 3 a^{2} b^{3} d e f - a^{2} b^{3} e^{3} + 3 a b^{4} c^{2} f - 3 a b^{4} c d e + a b^{4} d^{3} - b^{5} c^{3}, \left( t \mapsto t \log{\left(x + \frac{9 t^{2} a^{3} b^{4} g - 9 t^{2} a^{2} b^{5} d + 6 t a^{4} b^{2} g h - 6 t a^{3} b^{3} d h - 6 t a^{3} b^{3} e g - 3 t a^{3} b^{3} f^{2} + 6 t a^{2} b^{4} c f + 6 t a^{2} b^{4} d e - 3 t a b^{5} c^{2} + a^{5} g h^{2} - a^{4} b d h^{2} - 2 a^{4} b e g h - a^{4} b f^{2} h + 2 a^{4} b f g^{2} + 2 a^{3} b^{2} c f h - 2 a^{3} b^{2} c g^{2} + 2 a^{3} b^{2} d e h - 4 a^{3} b^{2} d f g + a^{3} b^{2} e^{2} g + a^{3} b^{2} e f^{2} - a^{2} b^{3} c^{2} h + 4 a^{2} b^{3} c d g - 2 a^{2} b^{3} c e f + 2 a^{2} b^{3} d^{2} f - a^{2} b^{3} d e^{2} + a b^{4} c^{2} e - 2 a b^{4} c d^{2}}{a^{4} b g^{3} - 3 a^{3} b^{2} d g^{2} + a^{3} b^{2} f^{3} - 3 a^{2} b^{3} c f^{2} + 3 a^{2} b^{3} d^{2} g + 3 a b^{4} c^{2} f - a b^{4} d^{3} - b^{5} c^{3}} \right)} \right)\right)} + \frac{f x}{b} + \frac{g x^{2}}{2 b} + \frac{h x^{3}}{3 b}"," ",0,"RootSum(27*_t**3*a**2*b**6 + _t**2*(27*a**3*b**4*h - 27*a**2*b**5*e) + _t*(9*a**4*b**2*h**2 - 18*a**3*b**3*e*h + 9*a**3*b**3*f*g - 9*a**2*b**4*c*g - 9*a**2*b**4*d*f + 9*a**2*b**4*e**2 + 9*a*b**5*c*d) + 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 - 3*a**3*b**2*d*f*h + 3*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 + 3*a**2*b**3*c*d*h + 3*a**2*b**3*c*e*g - 3*a**2*b**3*c*f**2 - 3*a**2*b**3*d**2*g + 3*a**2*b**3*d*e*f - a**2*b**3*e**3 + 3*a*b**4*c**2*f - 3*a*b**4*c*d*e + a*b**4*d**3 - b**5*c**3, Lambda(_t, _t*log(x + (9*_t**2*a**3*b**4*g - 9*_t**2*a**2*b**5*d + 6*_t*a**4*b**2*g*h - 6*_t*a**3*b**3*d*h - 6*_t*a**3*b**3*e*g - 3*_t*a**3*b**3*f**2 + 6*_t*a**2*b**4*c*f + 6*_t*a**2*b**4*d*e - 3*_t*a*b**5*c**2 + a**5*g*h**2 - a**4*b*d*h**2 - 2*a**4*b*e*g*h - a**4*b*f**2*h + 2*a**4*b*f*g**2 + 2*a**3*b**2*c*f*h - 2*a**3*b**2*c*g**2 + 2*a**3*b**2*d*e*h - 4*a**3*b**2*d*f*g + a**3*b**2*e**2*g + a**3*b**2*e*f**2 - a**2*b**3*c**2*h + 4*a**2*b**3*c*d*g - 2*a**2*b**3*c*e*f + 2*a**2*b**3*d**2*f - a**2*b**3*d*e**2 + a*b**4*c**2*e - 2*a*b**4*c*d**2)/(a**4*b*g**3 - 3*a**3*b**2*d*g**2 + a**3*b**2*f**3 - 3*a**2*b**3*c*f**2 + 3*a**2*b**3*d**2*g + 3*a*b**4*c**2*f - a*b**4*d**3 - b**5*c**3)))) + f*x/b + g*x**2/(2*b) + h*x**3/(3*b)","B",0
408,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**2/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**3/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
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427,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**2/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**3/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate((h*x**5+g*x**4+f*x**3+e*x**2+d*x+c)/x**4/(b*x**3+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,1,129,0,3.916728," ","integrate(x**3*(e*x**2+d*x+c)/(b*x**3+a)**(1/2),x)","e \left(\begin{cases} - \frac{4 a \sqrt{a + b x^{3}}}{9 b^{2}} + \frac{2 x^{3} \sqrt{a + b x^{3}}}{9 b} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 \sqrt{a}} & \text{otherwise} \end{cases}\right) + \frac{c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{7}{3}\right)} + \frac{d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{8}{3}\right)}"," ",0,"e*Piecewise((-4*a*sqrt(a + b*x**3)/(9*b**2) + 2*x**3*sqrt(a + b*x**3)/(9*b), Ne(b, 0)), (x**6/(6*sqrt(a)), True)) + c*x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(7/3)) + d*x**5*gamma(5/3)*hyper((1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(8/3))","A",0
431,1,107,0,3.665365," ","integrate(x**2*(e*x**2+d*x+c)/(b*x**3+a)**(1/2),x)","c \left(\begin{cases} \frac{x^{3}}{3 \sqrt{a}} & \text{for}\: b = 0 \\\frac{2 \sqrt{a + b x^{3}}}{3 b} & \text{otherwise} \end{cases}\right) + \frac{d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{7}{3}\right)} + \frac{e x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{8}{3}\right)}"," ",0,"c*Piecewise((x**3/(3*sqrt(a)), Eq(b, 0)), (2*sqrt(a + b*x**3)/(3*b), True)) + d*x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(7/3)) + e*x**5*gamma(5/3)*hyper((1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(8/3))","A",0
432,1,107,0,3.515512," ","integrate(x*(e*x**2+d*x+c)/(b*x**3+a)**(1/2),x)","d \left(\begin{cases} \frac{x^{3}}{3 \sqrt{a}} & \text{for}\: b = 0 \\\frac{2 \sqrt{a + b x^{3}}}{3 b} & \text{otherwise} \end{cases}\right) + \frac{c x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)} + \frac{e x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{7}{3}\right)}"," ",0,"d*Piecewise((x**3/(3*sqrt(a)), Eq(b, 0)), (2*sqrt(a + b*x**3)/(3*b), True)) + c*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3)) + e*x**4*gamma(4/3)*hyper((1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(7/3))","A",0
433,1,105,0,2.530360," ","integrate((e*x**2+d*x+c)/(b*x**3+a)**(1/2),x)","e \left(\begin{cases} \frac{x^{3}}{3 \sqrt{a}} & \text{for}\: b = 0 \\\frac{2 \sqrt{a + b x^{3}}}{3 b} & \text{otherwise} \end{cases}\right) + \frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"e*Piecewise((x**3/(3*sqrt(a)), Eq(b, 0)), (2*sqrt(a + b*x**3)/(3*b), True)) + c*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3))","A",0
434,1,105,0,4.103407," ","integrate((e*x**2+d*x+c)/x/(b*x**3+a)**(1/2),x)","- \frac{2 c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}} + \frac{d x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)} + \frac{e x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-2*c*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a)) + d*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3)) + e*x**2*gamma(2/3)*hyper((1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(5/3))","A",0
435,1,107,0,3.243829," ","integrate((e*x**2+d*x+c)/x**2/(b*x**3+a)**(1/2),x)","\frac{c \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} x \Gamma\left(\frac{2}{3}\right)} - \frac{2 d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}} + \frac{e x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{4}{3}\right)}"," ",0,"c*gamma(-1/3)*hyper((-1/3, 1/2), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*x*gamma(2/3)) - 2*d*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a)) + e*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*gamma(4/3))","A",0
436,1,112,0,3.434234," ","integrate((e*x**2+d*x+c)/x**3/(b*x**3+a)**(1/2),x)","\frac{c \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{d \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} x \Gamma\left(\frac{2}{3}\right)} - \frac{2 e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}}"," ",0,"c*gamma(-2/3)*hyper((-2/3, 1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*x**2*gamma(1/3)) + d*gamma(-1/3)*hyper((-1/3, 1/2), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*sqrt(a)*x*gamma(2/3)) - 2*e*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a))","A",0
437,1,129,0,20.585901," ","integrate(x**5*(e*x**2+d*x+c)/(b*x**3+a)**(3/2),x)","c \left(\begin{cases} \frac{4 a}{3 b^{2} \sqrt{a + b x^{3}}} + \frac{2 x^{3}}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{d x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{10}{3}\right)} + \frac{e x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{11}{3}\right)}"," ",0,"c*Piecewise((4*a/(3*b**2*sqrt(a + b*x**3)) + 2*x**3/(3*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**6/(6*a**(3/2)), True)) + d*x**7*gamma(7/3)*hyper((3/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(10/3)) + e*x**8*gamma(8/3)*hyper((3/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(11/3))","A",0
438,1,129,0,15.272224," ","integrate(x**4*(e*x**2+d*x+c)/(b*x**3+a)**(3/2),x)","d \left(\begin{cases} \frac{4 a}{3 b^{2} \sqrt{a + b x^{3}}} + \frac{2 x^{3}}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{c x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{8}{3}\right)} + \frac{e x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"d*Piecewise((4*a/(3*b**2*sqrt(a + b*x**3)) + 2*x**3/(3*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**6/(6*a**(3/2)), True)) + c*x**5*gamma(5/3)*hyper((3/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(8/3)) + e*x**7*gamma(7/3)*hyper((3/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(10/3))","A",0
439,1,129,0,12.497178," ","integrate(x**3*(e*x**2+d*x+c)/(b*x**3+a)**(3/2),x)","e \left(\begin{cases} \frac{4 a}{3 b^{2} \sqrt{a + b x^{3}}} + \frac{2 x^{3}}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{3}{2} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{7}{3}\right)} + \frac{d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"e*Piecewise((4*a/(3*b**2*sqrt(a + b*x**3)) + 2*x**3/(3*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**6/(6*a**(3/2)), True)) + c*x**4*gamma(4/3)*hyper((4/3, 3/2), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(7/3)) + d*x**5*gamma(5/3)*hyper((3/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(8/3))","A",0
440,1,109,0,11.431532," ","integrate(x**2*(e*x**2+d*x+c)/(b*x**3+a)**(3/2),x)","c \left(\begin{cases} - \frac{2}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{3}{2} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{7}{3}\right)} + \frac{e x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"c*Piecewise((-2/(3*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**3/(3*a**(3/2)), True)) + d*x**4*gamma(4/3)*hyper((4/3, 3/2), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(7/3)) + e*x**5*gamma(5/3)*hyper((3/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(8/3))","A",0
441,1,109,0,11.084772," ","integrate(x*(e*x**2+d*x+c)/(b*x**3+a)**(3/2),x)","d \left(\begin{cases} - \frac{2}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{c x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{3}{2} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{5}{3}\right)} + \frac{e x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{3}{2} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"d*Piecewise((-2/(3*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**3/(3*a**(3/2)), True)) + c*x**2*gamma(2/3)*hyper((2/3, 3/2), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(5/3)) + e*x**4*gamma(4/3)*hyper((4/3, 3/2), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(7/3))","A",0
442,1,107,0,10.859342," ","integrate((e*x**2+d*x+c)/(b*x**3+a)**(3/2),x)","e \left(\begin{cases} - \frac{2}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{4}{3}\right)} + \frac{d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{3}{2} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"e*Piecewise((-2/(3*b*sqrt(a + b*x**3)), Ne(b, 0)), (x**3/(3*a**(3/2)), True)) + c*x*gamma(1/3)*hyper((1/3, 3/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((2/3, 3/2), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(5/3))","A",0
443,1,265,0,16.572582," ","integrate((e*x**2+d*x+c)/x/(b*x**3+a)**(3/2),x)","c \left(\frac{2 a^{3} \sqrt{1 + \frac{b x^{3}}{a}}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} + \frac{a^{3} \log{\left(\frac{b x^{3}}{a} \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{3}}{a}} + 1 \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} + \frac{a^{2} b x^{3} \log{\left(\frac{b x^{3}}{a} \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} - \frac{2 a^{2} b x^{3} \log{\left(\sqrt{1 + \frac{b x^{3}}{a}} + 1 \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}}\right) + \frac{d x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{4}{3}\right)} + \frac{e x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{3}{2} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"c*(2*a**3*sqrt(1 + b*x**3/a)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) + a**3*log(b*x**3/a)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) - 2*a**3*log(sqrt(1 + b*x**3/a) + 1)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) + a**2*b*x**3*log(b*x**3/a)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) - 2*a**2*b*x**3*log(sqrt(1 + b*x**3/a) + 1)/(3*a**(9/2) + 3*a**(7/2)*b*x**3)) + d*x*gamma(1/3)*hyper((1/3, 3/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(4/3)) + e*x**2*gamma(2/3)*hyper((2/3, 3/2), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(5/3))","A",0
444,1,267,0,18.304098," ","integrate((e*x**2+d*x+c)/x**2/(b*x**3+a)**(3/2),x)","d \left(\frac{2 a^{3} \sqrt{1 + \frac{b x^{3}}{a}}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} + \frac{a^{3} \log{\left(\frac{b x^{3}}{a} \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{3}}{a}} + 1 \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} + \frac{a^{2} b x^{3} \log{\left(\frac{b x^{3}}{a} \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}} - \frac{2 a^{2} b x^{3} \log{\left(\sqrt{1 + \frac{b x^{3}}{a}} + 1 \right)}}{3 a^{\frac{9}{2}} + 3 a^{\frac{7}{2}} b x^{3}}\right) + \frac{c \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{3}{2} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} x \Gamma\left(\frac{2}{3}\right)} + \frac{e x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{2}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"d*(2*a**3*sqrt(1 + b*x**3/a)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) + a**3*log(b*x**3/a)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) - 2*a**3*log(sqrt(1 + b*x**3/a) + 1)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) + a**2*b*x**3*log(b*x**3/a)/(3*a**(9/2) + 3*a**(7/2)*b*x**3) - 2*a**2*b*x**3*log(sqrt(1 + b*x**3/a) + 1)/(3*a**(9/2) + 3*a**(7/2)*b*x**3)) + c*gamma(-1/3)*hyper((-1/3, 3/2), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*x*gamma(2/3)) + e*x*gamma(1/3)*hyper((1/3, 3/2), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(3/2)*gamma(4/3))","A",0
445,1,238,0,5.835001," ","integrate(x**3*(g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{\sqrt{a} f x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt{a} g x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)} + e \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*c*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*d*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + sqrt(a)*f*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + sqrt(a)*g*x**8*gamma(8/3)*hyper((-1/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(11/3)) + e*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
446,1,223,0,5.688890," ","integrate(x**2*(g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} e x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{\sqrt{a} g x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + c \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right) + f \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*d*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*e*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + sqrt(a)*g*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + c*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True)) + f*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
447,1,223,0,5.386528," ","integrate(x*(g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} c x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt{a} e x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} f x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + d \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right) + g \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*c*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + sqrt(a)*e*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*f*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + d*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True)) + g*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
448,1,194,0,5.124813," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2),x)","\frac{\sqrt{a} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{a} d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt{a} f x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} g x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + e \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*c*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + sqrt(a)*d*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + sqrt(a)*f*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*g*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + e*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True))","A",0
449,1,235,0,10.854038," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2)/x,x)","- \frac{2 \sqrt{a} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{\sqrt{a} d x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{a} e x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt{a} g x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{2 a c}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 \sqrt{b} c x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} + f \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right)"," ",0,"-2*sqrt(a)*c*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + sqrt(a)*d*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + sqrt(a)*e*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + sqrt(a)*g*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + 2*a*c/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*sqrt(b)*c*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) + f*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True))","A",0
450,1,236,0,6.765836," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2)/x**2,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{2 \sqrt{a} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{\sqrt{a} e x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{a} f x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{2 a d}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 \sqrt{b} d x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} + g \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*c*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - 2*sqrt(a)*d*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + sqrt(a)*e*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + sqrt(a)*f*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + 2*a*d/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*sqrt(b)*d*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) + g*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True))","A",0
451,1,255,0,7.052719," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2)/x**3,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{\sqrt{a} d \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{2 \sqrt{a} e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{\sqrt{a} f x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{a} g x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{2 a e}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 \sqrt{b} e x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}}"," ",0,"sqrt(a)*c*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + sqrt(a)*d*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - 2*sqrt(a)*e*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + sqrt(a)*f*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + sqrt(a)*g*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + 2*a*e/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*sqrt(b)*e*x**(3/2)/(3*sqrt(a/(b*x**3) + 1))","A",0
452,1,265,0,8.089419," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2)/x**4,x)","\frac{\sqrt{a} d \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{\sqrt{a} e \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{2 \sqrt{a} f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{\sqrt{a} g x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{2 a f}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{\sqrt{b} c \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} + \frac{2 \sqrt{b} f x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}}"," ",0,"sqrt(a)*d*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + sqrt(a)*e*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - 2*sqrt(a)*f*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + sqrt(a)*g*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + 2*a*f/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) - sqrt(b)*c*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) + 2*sqrt(b)*f*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) - b*c*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a))","A",0
453,1,274,0,8.270499," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2)/x**5,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{\sqrt{a} e \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{\sqrt{a} f \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{2 \sqrt{a} g \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{2 a g}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{\sqrt{b} d \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} + \frac{2 \sqrt{b} g x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}}"," ",0,"sqrt(a)*c*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + sqrt(a)*e*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + sqrt(a)*f*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - 2*sqrt(a)*g*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + 2*a*g/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) - sqrt(b)*d*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) + 2*sqrt(b)*g*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) - b*d*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a))","A",0
454,1,240,0,7.541118," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2)/x**6,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{\sqrt{a} d \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{\sqrt{a} f \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{\sqrt{a} g \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{\sqrt{b} e \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} - \frac{b e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}}"," ",0,"sqrt(a)*c*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + sqrt(a)*d*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + sqrt(a)*f*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + sqrt(a)*g*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - sqrt(b)*e*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) - b*e*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a))","A",0
455,1,304,0,10.709086," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2)/x**7,x)","\frac{\sqrt{a} d \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{\sqrt{a} e \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{\sqrt{a} g \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} - \frac{a c}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{\sqrt{b} c}{4 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{\sqrt{b} f \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} - \frac{b^{\frac{3}{2}} c}{12 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}} + \frac{b^{2} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{12 a^{\frac{3}{2}}}"," ",0,"sqrt(a)*d*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + sqrt(a)*e*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + sqrt(a)*g*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) - a*c/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) - sqrt(b)*c/(4*x**(9/2)*sqrt(a/(b*x**3) + 1)) - sqrt(b)*f*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) - b**(3/2)*c/(12*a*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b*f*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a)) + b**2*c*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(12*a**(3/2))","A",0
456,1,308,0,11.601652," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2)/x**8,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{7} \Gamma\left(- \frac{4}{3}\right)} + \frac{\sqrt{a} e \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{\sqrt{a} f \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} - \frac{a d}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{\sqrt{b} d}{4 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{\sqrt{b} g \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} - \frac{b^{\frac{3}{2}} d}{12 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b g \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3 \sqrt{a}} + \frac{b^{2} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{12 a^{\frac{3}{2}}}"," ",0,"sqrt(a)*c*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**7*gamma(-4/3)) + sqrt(a)*e*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + sqrt(a)*f*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) - a*d/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) - sqrt(b)*d/(4*x**(9/2)*sqrt(a/(b*x**3) + 1)) - sqrt(b)*g*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) - b**(3/2)*d/(12*a*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b*g*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(3*sqrt(a)) + b**2*d*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(12*a**(3/2))","A",0
457,1,304,0,11.536270," ","integrate((g*x**4+f*x**3+e*x**2+d*x+c)*(b*x**3+a)**(1/2)/x**9,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, - \frac{1}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{8} \Gamma\left(- \frac{5}{3}\right)} + \frac{\sqrt{a} d \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{7} \Gamma\left(- \frac{4}{3}\right)} + \frac{\sqrt{a} f \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{\sqrt{a} g \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} - \frac{a e}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{\sqrt{b} e}{4 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{3}{2}} e}{12 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{b^{2} e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{12 a^{\frac{3}{2}}}"," ",0,"sqrt(a)*c*gamma(-8/3)*hyper((-8/3, -1/2), (-5/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**8*gamma(-5/3)) + sqrt(a)*d*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**7*gamma(-4/3)) + sqrt(a)*f*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + sqrt(a)*g*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) - a*e/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) - sqrt(b)*e/(4*x**(9/2)*sqrt(a/(b*x**3) + 1)) - b**(3/2)*e/(12*a*x**(3/2)*sqrt(a/(b*x**3) + 1)) + b**2*e*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(12*a**(3/2))","A",0
458,1,512,0,13.012853," ","integrate(x**3*(b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c),x)","\frac{a^{\frac{3}{2}} c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{3}{2}} d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{a^{\frac{3}{2}} f x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{a^{\frac{3}{2}} g x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)} + \frac{\sqrt{a} b c x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt{a} b d x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)} + \frac{\sqrt{a} b f x^{10} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{13}{3}\right)} + \frac{\sqrt{a} b g x^{11} \Gamma\left(\frac{11}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{3} \\ \frac{14}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{14}{3}\right)} + a e \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + b e \left(\begin{cases} \frac{16 a^{3} \sqrt{a + b x^{3}}}{315 b^{3}} - \frac{8 a^{2} x^{3} \sqrt{a + b x^{3}}}{315 b^{2}} + \frac{2 a x^{6} \sqrt{a + b x^{3}}}{105 b} + \frac{2 x^{9} \sqrt{a + b x^{3}}}{21} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{9}}{9} & \text{otherwise} \end{cases}\right)"," ",0,"a**(3/2)*c*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(3/2)*d*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + a**(3/2)*f*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + a**(3/2)*g*x**8*gamma(8/3)*hyper((-1/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(11/3)) + sqrt(a)*b*c*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + sqrt(a)*b*d*x**8*gamma(8/3)*hyper((-1/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(11/3)) + sqrt(a)*b*f*x**10*gamma(10/3)*hyper((-1/2, 10/3), (13/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(13/3)) + sqrt(a)*b*g*x**11*gamma(11/3)*hyper((-1/2, 11/3), (14/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(14/3)) + a*e*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True)) + b*e*Piecewise((16*a**3*sqrt(a + b*x**3)/(315*b**3) - 8*a**2*x**3*sqrt(a + b*x**3)/(315*b**2) + 2*a*x**6*sqrt(a + b*x**3)/(105*b) + 2*x**9*sqrt(a + b*x**3)/21, Ne(b, 0)), (sqrt(a)*x**9/9, True))","A",0
459,1,525,0,11.686065," ","integrate(x**2*(b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c),x)","\frac{a^{\frac{3}{2}} d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{3}{2}} e x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{a^{\frac{3}{2}} g x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt{a} b d x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt{a} b e x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)} + \frac{\sqrt{a} b g x^{10} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{13}{3}\right)} + a c \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right) + a f \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + b c \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + b f \left(\begin{cases} \frac{16 a^{3} \sqrt{a + b x^{3}}}{315 b^{3}} - \frac{8 a^{2} x^{3} \sqrt{a + b x^{3}}}{315 b^{2}} + \frac{2 a x^{6} \sqrt{a + b x^{3}}}{105 b} + \frac{2 x^{9} \sqrt{a + b x^{3}}}{21} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{9}}{9} & \text{otherwise} \end{cases}\right)"," ",0,"a**(3/2)*d*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(3/2)*e*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + a**(3/2)*g*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + sqrt(a)*b*d*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + sqrt(a)*b*e*x**8*gamma(8/3)*hyper((-1/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(11/3)) + sqrt(a)*b*g*x**10*gamma(10/3)*hyper((-1/2, 10/3), (13/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(13/3)) + a*c*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True)) + a*f*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True)) + b*c*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True)) + b*f*Piecewise((16*a**3*sqrt(a + b*x**3)/(315*b**3) - 8*a**2*x**3*sqrt(a + b*x**3)/(315*b**2) + 2*a*x**6*sqrt(a + b*x**3)/(105*b) + 2*x**9*sqrt(a + b*x**3)/21, Ne(b, 0)), (sqrt(a)*x**9/9, True))","A",0
460,1,525,0,10.782714," ","integrate(x*(b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c),x)","\frac{a^{\frac{3}{2}} c x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{a^{\frac{3}{2}} e x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{3}{2}} f x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{\sqrt{a} b c x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{\sqrt{a} b e x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt{a} b f x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)} + a d \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right) + a g \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + b d \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + b g \left(\begin{cases} \frac{16 a^{3} \sqrt{a + b x^{3}}}{315 b^{3}} - \frac{8 a^{2} x^{3} \sqrt{a + b x^{3}}}{315 b^{2}} + \frac{2 a x^{6} \sqrt{a + b x^{3}}}{105 b} + \frac{2 x^{9} \sqrt{a + b x^{3}}}{21} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{9}}{9} & \text{otherwise} \end{cases}\right)"," ",0,"a**(3/2)*c*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + a**(3/2)*e*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(3/2)*f*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + sqrt(a)*b*c*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + sqrt(a)*b*e*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + sqrt(a)*b*f*x**8*gamma(8/3)*hyper((-1/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(11/3)) + a*d*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True)) + a*g*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True)) + b*d*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True)) + b*g*Piecewise((16*a**3*sqrt(a + b*x**3)/(315*b**3) - 8*a**2*x**3*sqrt(a + b*x**3)/(315*b**2) + 2*a*x**6*sqrt(a + b*x**3)/(105*b) + 2*x**9*sqrt(a + b*x**3)/21, Ne(b, 0)), (sqrt(a)*x**9/9, True))","A",0
461,1,444,0,10.134169," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c),x)","\frac{a^{\frac{3}{2}} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{3}{2}} d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{a^{\frac{3}{2}} f x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{\frac{3}{2}} g x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{\sqrt{a} b c x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} b d x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{\sqrt{a} b f x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{\sqrt{a} b g x^{8} \Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{11}{3}\right)} + a e \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right) + b e \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"a**(3/2)*c*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(3/2)*d*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + a**(3/2)*f*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(3/2)*g*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + sqrt(a)*b*c*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*b*d*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + sqrt(a)*b*f*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + sqrt(a)*b*g*x**8*gamma(8/3)*hyper((-1/2, 8/3), (11/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(11/3)) + a*e*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True)) + b*e*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
462,1,473,0,23.744472," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x,x)","- \frac{2 a^{\frac{3}{2}} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{a^{\frac{3}{2}} d x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{3}{2}} e x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{a^{\frac{3}{2}} g x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} b d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} b e x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{\sqrt{a} b g x^{7} \Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{2 a^{2} c}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 a \sqrt{b} c x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} + a f \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right) + b c \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right) + b f \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"-2*a**(3/2)*c*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + a**(3/2)*d*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(3/2)*e*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + a**(3/2)*g*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*b*d*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*b*e*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + sqrt(a)*b*g*x**7*gamma(7/3)*hyper((-1/2, 7/3), (10/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(10/3)) + 2*a**2*c/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*a*sqrt(b)*c*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) + a*f*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True)) + b*c*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True)) + b*f*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
463,1,474,0,13.432141," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**2,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{2 a^{\frac{3}{2}} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{a^{\frac{3}{2}} e x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{3}{2}} f x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt{a} b c x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt{a} b e x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} b f x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{2 a^{2} d}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 a \sqrt{b} d x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} + a g \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right) + b d \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right) + b g \left(\begin{cases} - \frac{4 a^{2} \sqrt{a + b x^{3}}}{45 b^{2}} + \frac{2 a x^{3} \sqrt{a + b x^{3}}}{45 b} + \frac{2 x^{6} \sqrt{a + b x^{3}}}{15} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"a**(3/2)*c*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - 2*a**(3/2)*d*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + a**(3/2)*e*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(3/2)*f*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + sqrt(a)*b*c*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + sqrt(a)*b*e*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*b*f*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + 2*a**2*d/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*a*sqrt(b)*d*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) + a*g*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True)) + b*d*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True)) + b*g*Piecewise((-4*a**2*sqrt(a + b*x**3)/(45*b**2) + 2*a*x**3*sqrt(a + b*x**3)/(45*b) + 2*x**6*sqrt(a + b*x**3)/15, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
464,1,462,0,12.847106," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**3,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{2 a^{\frac{3}{2}} e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{a^{\frac{3}{2}} f x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{\frac{3}{2}} g x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt{a} b c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{a} b d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt{a} b f x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{\sqrt{a} b g x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{2 a^{2} e}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 a \sqrt{b} e x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} + b e \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**(3/2)*c*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + a**(3/2)*d*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - 2*a**(3/2)*e*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + a**(3/2)*f*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(3/2)*g*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + sqrt(a)*b*c*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + sqrt(a)*b*d*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + sqrt(a)*b*f*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + sqrt(a)*b*g*x**5*gamma(5/3)*hyper((-1/2, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + 2*a**2*e/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*a*sqrt(b)*e*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) + b*e*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True))","A",0
465,1,484,0,14.265972," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**4,x)","\frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{2 a^{\frac{3}{2}} f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{a^{\frac{3}{2}} g x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \sqrt{a} b c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)} + \frac{\sqrt{a} b d x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{a} b e x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt{a} b g x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{2 a^{2} f}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a \sqrt{b} c \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} + \frac{2 a \sqrt{b} c}{3 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 a \sqrt{b} f x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 b^{\frac{3}{2}} c x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} + b f \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**(3/2)*d*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + a**(3/2)*e*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - 2*a**(3/2)*f*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + a**(3/2)*g*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) - sqrt(a)*b*c*asinh(sqrt(a)/(sqrt(b)*x**(3/2))) + sqrt(a)*b*d*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + sqrt(a)*b*e*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + sqrt(a)*b*g*x**4*gamma(4/3)*hyper((-1/2, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + 2*a**2*f/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) - a*sqrt(b)*c*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) + 2*a*sqrt(b)*c/(3*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*a*sqrt(b)*f*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) + 2*b**(3/2)*c*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) + b*f*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True))","A",0
466,1,495,0,14.640868," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**5,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{2 a^{\frac{3}{2}} g \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{3} + \frac{\sqrt{a} b c \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \sqrt{a} b d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)} + \frac{\sqrt{a} b e x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{a} b f x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{2 a^{2} g}{3 \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a \sqrt{b} d \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} + \frac{2 a \sqrt{b} d}{3 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 a \sqrt{b} g x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 b^{\frac{3}{2}} d x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} + b g \left(\begin{cases} \frac{\sqrt{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 \left(a + b x^{3}\right)^{\frac{3}{2}}}{9 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**(3/2)*c*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + a**(3/2)*e*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + a**(3/2)*f*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - 2*a**(3/2)*g*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/3 + sqrt(a)*b*c*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - sqrt(a)*b*d*asinh(sqrt(a)/(sqrt(b)*x**(3/2))) + sqrt(a)*b*e*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + sqrt(a)*b*f*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + 2*a**2*g/(3*sqrt(b)*x**(3/2)*sqrt(a/(b*x**3) + 1)) - a*sqrt(b)*d*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) + 2*a*sqrt(b)*d/(3*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*a*sqrt(b)*g*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) + 2*b**(3/2)*d*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) + b*g*Piecewise((sqrt(a)*x**3/3, Eq(b, 0)), (2*(a + b*x**3)**(3/2)/(9*b), True))","A",0
467,1,476,0,14.430066," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**6,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{a^{\frac{3}{2}} g \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} + \frac{\sqrt{a} b c \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{\sqrt{a} b d \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \sqrt{a} b e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)} + \frac{\sqrt{a} b f x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt{a} b g x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} - \frac{a \sqrt{b} e \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} + \frac{2 a \sqrt{b} e}{3 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 b^{\frac{3}{2}} e x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}}"," ",0,"a**(3/2)*c*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + a**(3/2)*d*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + a**(3/2)*f*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + a**(3/2)*g*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) + sqrt(a)*b*c*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + sqrt(a)*b*d*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - sqrt(a)*b*e*asinh(sqrt(a)/(sqrt(b)*x**(3/2))) + sqrt(a)*b*f*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + sqrt(a)*b*g*x**2*gamma(2/3)*hyper((-1/2, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) - a*sqrt(b)*e*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) + 2*a*sqrt(b)*e/(3*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*b**(3/2)*e*x**(3/2)/(3*sqrt(a/(b*x**3) + 1))","A",0
468,1,524,0,17.916472," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**7,x)","\frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{a^{\frac{3}{2}} g \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{\sqrt{a} b d \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{\sqrt{a} b e \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \sqrt{a} b f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)} + \frac{\sqrt{a} b g x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} - \frac{a^{2} c}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a \sqrt{b} c}{4 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a \sqrt{b} f \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} + \frac{2 a \sqrt{b} f}{3 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{3}{2}} c \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} - \frac{b^{\frac{3}{2}} c}{12 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 b^{\frac{3}{2}} f x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{2} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{4 \sqrt{a}}"," ",0,"a**(3/2)*d*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + a**(3/2)*e*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + a**(3/2)*g*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + sqrt(a)*b*d*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + sqrt(a)*b*e*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - sqrt(a)*b*f*asinh(sqrt(a)/(sqrt(b)*x**(3/2))) + sqrt(a)*b*g*x*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) - a**2*c/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) - a*sqrt(b)*c/(4*x**(9/2)*sqrt(a/(b*x**3) + 1)) - a*sqrt(b)*f*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) + 2*a*sqrt(b)*f/(3*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b**(3/2)*c*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) - b**(3/2)*c/(12*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*b**(3/2)*f*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) - b**2*c*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(4*sqrt(a))","A",0
469,1,536,0,18.714657," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**8,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{7} \Gamma\left(- \frac{4}{3}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{\sqrt{a} b c \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{\sqrt{a} b e \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{\sqrt{a} b f \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \sqrt{a} b g \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)} - \frac{a^{2} d}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a \sqrt{b} d}{4 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a \sqrt{b} g \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} + \frac{2 a \sqrt{b} g}{3 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{3}{2}} d \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} - \frac{b^{\frac{3}{2}} d}{12 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{2 b^{\frac{3}{2}} g x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{2} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{4 \sqrt{a}}"," ",0,"a**(3/2)*c*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**7*gamma(-4/3)) + a**(3/2)*e*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + a**(3/2)*f*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + sqrt(a)*b*c*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + sqrt(a)*b*e*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + sqrt(a)*b*f*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - sqrt(a)*b*g*asinh(sqrt(a)/(sqrt(b)*x**(3/2))) - a**2*d/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) - a*sqrt(b)*d/(4*x**(9/2)*sqrt(a/(b*x**3) + 1)) - a*sqrt(b)*g*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) + 2*a*sqrt(b)*g/(3*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b**(3/2)*d*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) - b**(3/2)*d/(12*x**(3/2)*sqrt(a/(b*x**3) + 1)) + 2*b**(3/2)*g*x**(3/2)/(3*sqrt(a/(b*x**3) + 1)) - b**2*d*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(4*sqrt(a))","A",0
470,1,527,0,17.276655," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**9,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, - \frac{1}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{8} \Gamma\left(- \frac{5}{3}\right)} + \frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{7} \Gamma\left(- \frac{4}{3}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{a^{\frac{3}{2}} g \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{\sqrt{a} b c \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{\sqrt{a} b d \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{\sqrt{a} b f \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} + \frac{\sqrt{a} b g \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x \Gamma\left(\frac{2}{3}\right)} - \frac{a^{2} e}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a \sqrt{b} e}{4 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{3}{2}} e \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} - \frac{b^{\frac{3}{2}} e}{12 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{2} e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{4 \sqrt{a}}"," ",0,"a**(3/2)*c*gamma(-8/3)*hyper((-8/3, -1/2), (-5/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**8*gamma(-5/3)) + a**(3/2)*d*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**7*gamma(-4/3)) + a**(3/2)*f*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + a**(3/2)*g*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + sqrt(a)*b*c*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + sqrt(a)*b*d*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + sqrt(a)*b*f*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) + sqrt(a)*b*g*gamma(-1/3)*hyper((-1/2, -1/3), (2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x*gamma(2/3)) - a**2*e/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) - a*sqrt(b)*e/(4*x**(9/2)*sqrt(a/(b*x**3) + 1)) - b**(3/2)*e*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) - b**(3/2)*e/(12*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b**2*e*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(4*sqrt(a))","A",0
471,1,573,0,25.787656," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**10,x)","\frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, - \frac{1}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{8} \Gamma\left(- \frac{5}{3}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{7} \Gamma\left(- \frac{4}{3}\right)} + \frac{a^{\frac{3}{2}} g \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{\sqrt{a} b d \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{\sqrt{a} b e \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} + \frac{\sqrt{a} b g \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{2} \Gamma\left(\frac{1}{3}\right)} - \frac{a^{2} c}{9 \sqrt{b} x^{\frac{21}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a^{2} f}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{11 a \sqrt{b} c}{36 x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a \sqrt{b} f}{4 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{17 b^{\frac{3}{2}} c}{72 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{3}{2}} f \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} - \frac{b^{\frac{3}{2}} f}{12 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{5}{2}} c}{24 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{2} f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{4 \sqrt{a}} + \frac{b^{3} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{24 a^{\frac{3}{2}}}"," ",0,"a**(3/2)*d*gamma(-8/3)*hyper((-8/3, -1/2), (-5/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**8*gamma(-5/3)) + a**(3/2)*e*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**7*gamma(-4/3)) + a**(3/2)*g*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + sqrt(a)*b*d*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + sqrt(a)*b*e*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) + sqrt(a)*b*g*gamma(-2/3)*hyper((-2/3, -1/2), (1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**2*gamma(1/3)) - a**2*c/(9*sqrt(b)*x**(21/2)*sqrt(a/(b*x**3) + 1)) - a**2*f/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) - 11*a*sqrt(b)*c/(36*x**(15/2)*sqrt(a/(b*x**3) + 1)) - a*sqrt(b)*f/(4*x**(9/2)*sqrt(a/(b*x**3) + 1)) - 17*b**(3/2)*c/(72*x**(9/2)*sqrt(a/(b*x**3) + 1)) - b**(3/2)*f*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) - b**(3/2)*f/(12*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b**(5/2)*c/(24*a*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b**2*f*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(4*sqrt(a)) + b**3*c*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(24*a**(3/2))","A",0
472,1,576,0,26.655749," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**11,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{10}{3}, - \frac{1}{2} \\ - \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{10} \Gamma\left(- \frac{7}{3}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, - \frac{1}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{8} \Gamma\left(- \frac{5}{3}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{7} \Gamma\left(- \frac{4}{3}\right)} + \frac{\sqrt{a} b c \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{7} \Gamma\left(- \frac{4}{3}\right)} + \frac{\sqrt{a} b e \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{\sqrt{a} b f \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} - \frac{a^{2} d}{9 \sqrt{b} x^{\frac{21}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a^{2} g}{6 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{11 a \sqrt{b} d}{36 x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{a \sqrt{b} g}{4 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{17 b^{\frac{3}{2}} d}{72 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{3}{2}} g \sqrt{\frac{a}{b x^{3}} + 1}}{3 x^{\frac{3}{2}}} - \frac{b^{\frac{3}{2}} g}{12 x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{5}{2}} d}{24 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{2} g \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{4 \sqrt{a}} + \frac{b^{3} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{24 a^{\frac{3}{2}}}"," ",0,"a**(3/2)*c*gamma(-10/3)*hyper((-10/3, -1/2), (-7/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**10*gamma(-7/3)) + a**(3/2)*e*gamma(-8/3)*hyper((-8/3, -1/2), (-5/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**8*gamma(-5/3)) + a**(3/2)*f*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**7*gamma(-4/3)) + sqrt(a)*b*c*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**7*gamma(-4/3)) + sqrt(a)*b*e*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + sqrt(a)*b*f*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) - a**2*d/(9*sqrt(b)*x**(21/2)*sqrt(a/(b*x**3) + 1)) - a**2*g/(6*sqrt(b)*x**(15/2)*sqrt(a/(b*x**3) + 1)) - 11*a*sqrt(b)*d/(36*x**(15/2)*sqrt(a/(b*x**3) + 1)) - a*sqrt(b)*g/(4*x**(9/2)*sqrt(a/(b*x**3) + 1)) - 17*b**(3/2)*d/(72*x**(9/2)*sqrt(a/(b*x**3) + 1)) - b**(3/2)*g*sqrt(a/(b*x**3) + 1)/(3*x**(3/2)) - b**(3/2)*g/(12*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b**(5/2)*d/(24*a*x**(3/2)*sqrt(a/(b*x**3) + 1)) - b**2*g*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(4*sqrt(a)) + b**3*d*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(24*a**(3/2))","A",0
473,1,541,0,24.052134," ","integrate((b*x**3+a)**(3/2)*(g*x**4+f*x**3+e*x**2+d*x+c)/x**12,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{11}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{11}{3}, - \frac{1}{2} \\ - \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{11} \Gamma\left(- \frac{8}{3}\right)} + \frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{10}{3}, - \frac{1}{2} \\ - \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{10} \Gamma\left(- \frac{7}{3}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, - \frac{1}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{8} \Gamma\left(- \frac{5}{3}\right)} + \frac{a^{\frac{3}{2}} g \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{7} \Gamma\left(- \frac{4}{3}\right)} + \frac{\sqrt{a} b c \Gamma\left(- \frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{8}{3}, - \frac{1}{2} \\ - \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{8} \Gamma\left(- \frac{5}{3}\right)} + \frac{\sqrt{a} b d \Gamma\left(- \frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{3}, - \frac{1}{2} \\ - \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{7} \Gamma\left(- \frac{4}{3}\right)} + \frac{\sqrt{a} b f \Gamma\left(- \frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{3}, - \frac{1}{2} \\ - \frac{2}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{5} \Gamma\left(- \frac{2}{3}\right)} + \frac{\sqrt{a} b g \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 x^{4} \Gamma\left(- \frac{1}{3}\right)} - \frac{a^{2} e}{9 \sqrt{b} x^{\frac{21}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{11 a \sqrt{b} e}{36 x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{17 b^{\frac{3}{2}} e}{72 x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{\frac{5}{2}} e}{24 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{b^{3} e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right)}}{24 a^{\frac{3}{2}}}"," ",0,"a**(3/2)*c*gamma(-11/3)*hyper((-11/3, -1/2), (-8/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**11*gamma(-8/3)) + a**(3/2)*d*gamma(-10/3)*hyper((-10/3, -1/2), (-7/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**10*gamma(-7/3)) + a**(3/2)*f*gamma(-8/3)*hyper((-8/3, -1/2), (-5/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**8*gamma(-5/3)) + a**(3/2)*g*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**7*gamma(-4/3)) + sqrt(a)*b*c*gamma(-8/3)*hyper((-8/3, -1/2), (-5/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**8*gamma(-5/3)) + sqrt(a)*b*d*gamma(-7/3)*hyper((-7/3, -1/2), (-4/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**7*gamma(-4/3)) + sqrt(a)*b*f*gamma(-5/3)*hyper((-5/3, -1/2), (-2/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**5*gamma(-2/3)) + sqrt(a)*b*g*gamma(-4/3)*hyper((-4/3, -1/2), (-1/3,), b*x**3*exp_polar(I*pi)/a)/(3*x**4*gamma(-1/3)) - a**2*e/(9*sqrt(b)*x**(21/2)*sqrt(a/(b*x**3) + 1)) - 11*a*sqrt(b)*e/(36*x**(15/2)*sqrt(a/(b*x**3) + 1)) - 17*b**(3/2)*e/(72*x**(9/2)*sqrt(a/(b*x**3) + 1)) - b**(5/2)*e/(24*a*x**(3/2)*sqrt(a/(b*x**3) + 1)) + b**3*e*asinh(sqrt(a)/(sqrt(b)*x**(3/2)))/(24*a**(3/2))","A",0
474,1,112,0,59.325739," ","integrate((e*x**2+d*x+c)*(b*x**3+a)**p,x)","\frac{a^{p} c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, - p \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{a^{p} d x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, - p \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + e \left(\begin{cases} \frac{a^{p} x^{3}}{3} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{3}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{3} \right)} & \text{otherwise} \end{cases}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*c*x*gamma(1/3)*hyper((1/3, -p), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**p*d*x**2*gamma(2/3)*hyper((2/3, -p), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + e*Piecewise((a**p*x**3/3, Eq(b, 0)), (Piecewise(((a + b*x**3)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**3), True))/(3*b), True))","A",0
475,1,114,0,88.352768," ","integrate(x*(e*x**2+d*x+c)*(b*x**3+a)**p,x)","\frac{a^{p} c x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, - p \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{a^{p} e x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, - p \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + d \left(\begin{cases} \frac{a^{p} x^{3}}{3} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{3}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{3} \right)} & \text{otherwise} \end{cases}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*c*x**2*gamma(2/3)*hyper((2/3, -p), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + a**p*e*x**4*gamma(4/3)*hyper((4/3, -p), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + d*Piecewise((a**p*x**3/3, Eq(b, 0)), (Piecewise(((a + b*x**3)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**3), True))/(3*b), True))","A",0
476,1,114,0,124.185354," ","integrate(x**2*(e*x**2+d*x+c)*(b*x**3+a)**p,x)","\frac{a^{p} d x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, - p \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{a^{p} e x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{3}, - p \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)} + c \left(\begin{cases} \frac{a^{p} x^{3}}{3} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{3}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{3} \right)} & \text{otherwise} \end{cases}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d*x**4*gamma(4/3)*hyper((4/3, -p), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**p*e*x**5*gamma(5/3)*hyper((5/3, -p), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + c*Piecewise((a**p*x**3/3, Eq(b, 0)), (Piecewise(((a + b*x**3)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**3), True))/(3*b), True))","A",0
477,1,63,0,0.078242," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a),x)","a c x + \frac{a d x^{2}}{2} + \frac{a e x^{3}}{3} + \frac{a f x^{4}}{4} + \frac{b c x^{5}}{5} + \frac{b d x^{6}}{6} + \frac{b e x^{7}}{7} + \frac{b f x^{8}}{8}"," ",0,"a*c*x + a*d*x**2/2 + a*e*x**3/3 + a*f*x**4/4 + b*c*x**5/5 + b*d*x**6/6 + b*e*x**7/7 + b*f*x**8/8","A",0
478,1,66,0,0.073119," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)*(b*x**4+a),x)","\frac{a c x^{4}}{4} + \frac{a d x^{5}}{5} + \frac{a e x^{6}}{6} + \frac{a f x^{7}}{7} + \frac{b c x^{8}}{8} + \frac{b d x^{9}}{9} + \frac{b e x^{10}}{10} + \frac{b f x^{11}}{11}"," ",0,"a*c*x**4/4 + a*d*x**5/5 + a*e*x**6/6 + a*f*x**7/7 + b*c*x**8/8 + b*d*x**9/9 + b*e*x**10/10 + b*f*x**11/11","A",0
479,1,121,0,0.087569," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**2,x)","a^{2} c x + \frac{a^{2} d x^{2}}{2} + \frac{a^{2} e x^{3}}{3} + \frac{a^{2} f x^{4}}{4} + \frac{2 a b c x^{5}}{5} + \frac{a b d x^{6}}{3} + \frac{2 a b e x^{7}}{7} + \frac{a b f x^{8}}{4} + \frac{b^{2} c x^{9}}{9} + \frac{b^{2} d x^{10}}{10} + \frac{b^{2} e x^{11}}{11} + \frac{b^{2} f x^{12}}{12}"," ",0,"a**2*c*x + a**2*d*x**2/2 + a**2*e*x**3/3 + a**2*f*x**4/4 + 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**2*c*x**9/9 + b**2*d*x**10/10 + b**2*e*x**11/11 + b**2*f*x**12/12","A",0
480,1,124,0,0.089152," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**2,x)","\frac{a^{2} c x^{4}}{4} + \frac{a^{2} d x^{5}}{5} + \frac{a^{2} e x^{6}}{6} + \frac{a^{2} f x^{7}}{7} + \frac{a b c x^{8}}{4} + \frac{2 a b d x^{9}}{9} + \frac{a b e x^{10}}{5} + \frac{2 a b f x^{11}}{11} + \frac{b^{2} c x^{12}}{12} + \frac{b^{2} d x^{13}}{13} + \frac{b^{2} e x^{14}}{14} + \frac{b^{2} f x^{15}}{15}"," ",0,"a**2*c*x**4/4 + a**2*d*x**5/5 + a**2*e*x**6/6 + a**2*f*x**7/7 + 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**2*c*x**12/12 + b**2*d*x**13/13 + b**2*e*x**14/14 + b**2*f*x**15/15","A",0
481,1,180,0,0.096162," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**3,x)","a^{3} c x + \frac{a^{3} d x^{2}}{2} + \frac{a^{3} e x^{3}}{3} + \frac{a^{3} f x^{4}}{4} + \frac{3 a^{2} b c x^{5}}{5} + \frac{a^{2} b d x^{6}}{2} + \frac{3 a^{2} b e x^{7}}{7} + \frac{3 a^{2} b f x^{8}}{8} + \frac{a b^{2} c x^{9}}{3} + \frac{3 a b^{2} d x^{10}}{10} + \frac{3 a b^{2} e x^{11}}{11} + \frac{a b^{2} f x^{12}}{4} + \frac{b^{3} c x^{13}}{13} + \frac{b^{3} d x^{14}}{14} + \frac{b^{3} e x^{15}}{15} + \frac{b^{3} f x^{16}}{16}"," ",0,"a**3*c*x + a**3*d*x**2/2 + a**3*e*x**3/3 + a**3*f*x**4/4 + 3*a**2*b*c*x**5/5 + a**2*b*d*x**6/2 + 3*a**2*b*e*x**7/7 + 3*a**2*b*f*x**8/8 + a*b**2*c*x**9/3 + 3*a*b**2*d*x**10/10 + 3*a*b**2*e*x**11/11 + a*b**2*f*x**12/4 + b**3*c*x**13/13 + b**3*d*x**14/14 + b**3*e*x**15/15 + b**3*f*x**16/16","A",0
482,1,184,0,0.098724," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**3,x)","\frac{a^{3} c x^{4}}{4} + \frac{a^{3} d x^{5}}{5} + \frac{a^{3} e x^{6}}{6} + \frac{a^{3} f x^{7}}{7} + \frac{3 a^{2} b c x^{8}}{8} + \frac{a^{2} b d x^{9}}{3} + \frac{3 a^{2} b e x^{10}}{10} + \frac{3 a^{2} b f x^{11}}{11} + \frac{a b^{2} c x^{12}}{4} + \frac{3 a b^{2} d x^{13}}{13} + \frac{3 a b^{2} e x^{14}}{14} + \frac{a b^{2} f x^{15}}{5} + \frac{b^{3} c x^{16}}{16} + \frac{b^{3} d x^{17}}{17} + \frac{b^{3} e x^{18}}{18} + \frac{b^{3} f x^{19}}{19}"," ",0,"a**3*c*x**4/4 + a**3*d*x**5/5 + a**3*e*x**6/6 + a**3*f*x**7/7 + 3*a**2*b*c*x**8/8 + a**2*b*d*x**9/3 + 3*a**2*b*e*x**10/10 + 3*a**2*b*f*x**11/11 + a*b**2*c*x**12/4 + 3*a*b**2*d*x**13/13 + 3*a*b**2*e*x**14/14 + a*b**2*f*x**15/5 + b**3*c*x**16/16 + b**3*d*x**17/17 + b**3*e*x**18/18 + b**3*f*x**19/19","A",0
483,1,241,0,0.103079," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**4,x)","a^{4} c x + \frac{a^{4} d x^{2}}{2} + \frac{a^{4} e x^{3}}{3} + \frac{a^{4} f x^{4}}{4} + \frac{4 a^{3} b c x^{5}}{5} + \frac{2 a^{3} b d x^{6}}{3} + \frac{4 a^{3} b e x^{7}}{7} + \frac{a^{3} b f x^{8}}{2} + \frac{2 a^{2} b^{2} c x^{9}}{3} + \frac{3 a^{2} b^{2} d x^{10}}{5} + \frac{6 a^{2} b^{2} e x^{11}}{11} + \frac{a^{2} b^{2} f x^{12}}{2} + \frac{4 a b^{3} c x^{13}}{13} + \frac{2 a b^{3} d x^{14}}{7} + \frac{4 a b^{3} e x^{15}}{15} + \frac{a b^{3} f x^{16}}{4} + \frac{b^{4} c x^{17}}{17} + \frac{b^{4} d x^{18}}{18} + \frac{b^{4} e x^{19}}{19} + \frac{b^{4} f x^{20}}{20}"," ",0,"a**4*c*x + a**4*d*x**2/2 + a**4*e*x**3/3 + a**4*f*x**4/4 + 4*a**3*b*c*x**5/5 + 2*a**3*b*d*x**6/3 + 4*a**3*b*e*x**7/7 + a**3*b*f*x**8/2 + 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*b**3*c*x**13/13 + 2*a*b**3*d*x**14/7 + 4*a*b**3*e*x**15/15 + a*b**3*f*x**16/4 + b**4*c*x**17/17 + b**4*d*x**18/18 + b**4*e*x**19/19 + b**4*f*x**20/20","A",0
484,1,245,0,0.110237," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**4,x)","\frac{a^{4} c x^{4}}{4} + \frac{a^{4} d x^{5}}{5} + \frac{a^{4} e x^{6}}{6} + \frac{a^{4} f x^{7}}{7} + \frac{a^{3} b c x^{8}}{2} + \frac{4 a^{3} b d x^{9}}{9} + \frac{2 a^{3} b e x^{10}}{5} + \frac{4 a^{3} b f x^{11}}{11} + \frac{a^{2} b^{2} c x^{12}}{2} + \frac{6 a^{2} b^{2} d x^{13}}{13} + \frac{3 a^{2} b^{2} e x^{14}}{7} + \frac{2 a^{2} b^{2} f x^{15}}{5} + \frac{a b^{3} c x^{16}}{4} + \frac{4 a b^{3} d x^{17}}{17} + \frac{2 a b^{3} e x^{18}}{9} + \frac{4 a b^{3} f x^{19}}{19} + \frac{b^{4} c x^{20}}{20} + \frac{b^{4} d x^{21}}{21} + \frac{b^{4} e x^{22}}{22} + \frac{b^{4} f x^{23}}{23}"," ",0,"a**4*c*x**4/4 + a**4*d*x**5/5 + a**4*e*x**6/6 + a**4*f*x**7/7 + a**3*b*c*x**8/2 + 4*a**3*b*d*x**9/9 + 2*a**3*b*e*x**10/5 + 4*a**3*b*f*x**11/11 + 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*b**3*c*x**16/4 + 4*a*b**3*d*x**17/17 + 2*a*b**3*e*x**18/9 + 4*a*b**3*f*x**19/19 + b**4*c*x**20/20 + b**4*d*x**21/21 + b**4*e*x**22/22 + b**4*f*x**23/23","A",0
485,-1,0,0,0.000000," ","integrate((f*x**3+e*x**2+d*x+c)/(-b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)/(-b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate((f*x**3+e*x**2+d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,1,517,0,22.319379," ","integrate((f*x**3+e*x**2+d*x+c)/(b*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{7} b^{3} + t^{2} \left(3072 a^{4} b^{2} c e + 2048 a^{4} b^{2} d^{2}\right) + t \left(128 a^{3} b d e^{2} - 1152 a^{2} b^{2} c^{2} d\right) + a^{2} e^{4} + 18 a b c^{2} e^{2} - 48 a b c d^{2} e + 16 a b d^{4} + 81 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{4096 t^{3} a^{7} b^{2} e^{3} - 36864 t^{3} a^{6} b^{3} c^{2} e + 98304 t^{3} a^{6} b^{3} c d^{2} + 4608 t^{2} a^{5} b^{2} c d e^{2} - 4096 t^{2} a^{5} b^{2} d^{3} e + 13824 t^{2} a^{4} b^{3} c^{3} d + 144 t a^{4} b c e^{4} + 192 t a^{4} b d^{2} e^{3} - 1728 t a^{3} b^{2} c^{3} e^{2} + 5184 t a^{3} b^{2} c^{2} d^{2} e + 1536 t a^{3} b^{2} c d^{4} + 3888 t a^{2} b^{3} c^{5} + 6 a^{3} d e^{5} + 120 a^{2} b c d^{3} e^{2} - 64 a^{2} b d^{5} e + 810 a b^{2} c^{4} d e - 1080 a b^{2} c^{3} d^{3}}{a^{3} e^{6} - 9 a^{2} b c^{2} e^{4} + 96 a^{2} b c d^{2} e^{3} - 64 a^{2} b d^{4} e^{2} - 81 a b^{2} c^{4} e^{2} + 864 a b^{2} c^{3} d^{2} e - 576 a b^{2} c^{2} d^{4} + 729 b^{3} c^{6}} \right)} \right)\right)} + \frac{- a f + b c x + b d x^{2} + b e x^{3}}{4 a^{2} b + 4 a b^{2} x^{4}}"," ",0,"RootSum(65536*_t**4*a**7*b**3 + _t**2*(3072*a**4*b**2*c*e + 2048*a**4*b**2*d**2) + _t*(128*a**3*b*d*e**2 - 1152*a**2*b**2*c**2*d) + a**2*e**4 + 18*a*b*c**2*e**2 - 48*a*b*c*d**2*e + 16*a*b*d**4 + 81*b**2*c**4, Lambda(_t, _t*log(x + (4096*_t**3*a**7*b**2*e**3 - 36864*_t**3*a**6*b**3*c**2*e + 98304*_t**3*a**6*b**3*c*d**2 + 4608*_t**2*a**5*b**2*c*d*e**2 - 4096*_t**2*a**5*b**2*d**3*e + 13824*_t**2*a**4*b**3*c**3*d + 144*_t*a**4*b*c*e**4 + 192*_t*a**4*b*d**2*e**3 - 1728*_t*a**3*b**2*c**3*e**2 + 5184*_t*a**3*b**2*c**2*d**2*e + 1536*_t*a**3*b**2*c*d**4 + 3888*_t*a**2*b**3*c**5 + 6*a**3*d*e**5 + 120*a**2*b*c*d**3*e**2 - 64*a**2*b*d**5*e + 810*a*b**2*c**4*d*e - 1080*a*b**2*c**3*d**3)/(a**3*e**6 - 9*a**2*b*c**2*e**4 + 96*a**2*b*c*d**2*e**3 - 64*a**2*b*d**4*e**2 - 81*a*b**2*c**4*e**2 + 864*a*b**2*c**3*d**2*e - 576*a*b**2*c**2*d**4 + 729*b**3*c**6)))) + (-a*f + b*c*x + b*d*x**2 + b*e*x**3)/(4*a**2*b + 4*a*b**2*x**4)","A",0
490,1,510,0,44.228743," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{3} b^{7} + t^{2} \left(3072 a^{2} b^{4} d f + 2048 a^{2} b^{4} e^{2}\right) + t \left(1152 a^{2} b^{2} e f^{2} - 128 a b^{3} d^{2} e\right) + 81 a^{2} f^{4} + 18 a b d^{2} f^{2} - 48 a b d e^{2} f + 16 a b e^{4} + b^{2} d^{4}, \left( t \mapsto t \log{\left(x + \frac{110592 t^{3} a^{4} b^{5} f^{3} - 12288 t^{3} a^{3} b^{6} d^{2} f + 32768 t^{3} a^{3} b^{6} d e^{2} + 13824 t^{2} a^{3} b^{4} d e f^{2} - 12288 t^{2} a^{3} b^{4} e^{3} f + 512 t^{2} a^{2} b^{5} d^{3} e + 3888 t a^{3} b^{2} d f^{4} + 5184 t a^{3} b^{2} e^{2} f^{3} - 576 t a^{2} b^{3} d^{3} f^{2} + 1728 t a^{2} b^{3} d^{2} e^{2} f + 512 t a^{2} b^{3} d e^{4} + 16 t a b^{4} d^{5} + 1458 a^{3} e f^{5} + 360 a^{2} b d e^{3} f^{2} - 192 a^{2} b e^{5} f + 30 a b^{2} d^{4} e f - 40 a b^{2} d^{3} e^{3}}{729 a^{3} f^{6} - 81 a^{2} b d^{2} f^{4} + 864 a^{2} b d e^{2} f^{3} - 576 a^{2} b e^{4} f^{2} - 9 a b^{2} d^{4} f^{2} + 96 a b^{2} d^{3} e^{2} f - 64 a b^{2} d^{2} e^{4} + b^{3} d^{6}} \right)} \right)\right)} + \frac{- c - d x - e x^{2} - f x^{3}}{4 a b + 4 b^{2} x^{4}}"," ",0,"RootSum(65536*_t**4*a**3*b**7 + _t**2*(3072*a**2*b**4*d*f + 2048*a**2*b**4*e**2) + _t*(1152*a**2*b**2*e*f**2 - 128*a*b**3*d**2*e) + 81*a**2*f**4 + 18*a*b*d**2*f**2 - 48*a*b*d*e**2*f + 16*a*b*e**4 + b**2*d**4, Lambda(_t, _t*log(x + (110592*_t**3*a**4*b**5*f**3 - 12288*_t**3*a**3*b**6*d**2*f + 32768*_t**3*a**3*b**6*d*e**2 + 13824*_t**2*a**3*b**4*d*e*f**2 - 12288*_t**2*a**3*b**4*e**3*f + 512*_t**2*a**2*b**5*d**3*e + 3888*_t*a**3*b**2*d*f**4 + 5184*_t*a**3*b**2*e**2*f**3 - 576*_t*a**2*b**3*d**3*f**2 + 1728*_t*a**2*b**3*d**2*e**2*f + 512*_t*a**2*b**3*d*e**4 + 16*_t*a*b**4*d**5 + 1458*a**3*e*f**5 + 360*a**2*b*d*e**3*f**2 - 192*a**2*b*e**5*f + 30*a*b**2*d**4*e*f - 40*a*b**2*d**3*e**3)/(729*a**3*f**6 - 81*a**2*b*d**2*f**4 + 864*a**2*b*d*e**2*f**3 - 576*a**2*b*e**4*f**2 - 9*a*b**2*d**4*f**2 + 96*a*b**2*d**3*e**2*f - 64*a*b**2*d**2*e**4 + b**3*d**6)))) + (-c - d*x - e*x**2 - f*x**3)/(4*a*b + 4*b**2*x**4)","A",0
491,1,578,0,108.467360," ","integrate((f*x**3+e*x**2+d*x+c)/(b*x**4+a)**3,x)","\operatorname{RootSum} {\left(268435456 t^{4} a^{11} b^{3} + t^{2} \left(6881280 a^{6} b^{2} c e + 4718592 a^{6} b^{2} d^{2}\right) + t \left(153600 a^{4} b d e^{2} - 2709504 a^{3} b^{2} c^{2} d\right) + 625 a^{2} e^{4} + 22050 a b c^{2} e^{2} - 60480 a b c d^{2} e + 20736 a b d^{4} + 194481 b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{262144000 t^{3} a^{10} b^{2} e^{3} - 4624220160 t^{3} a^{9} b^{3} c^{2} e + 12683575296 t^{3} a^{9} b^{3} c d^{2} + 309657600 t^{2} a^{7} b^{2} c d e^{2} - 283115520 t^{2} a^{7} b^{2} d^{3} e + 1820786688 t^{2} a^{6} b^{3} c^{3} d + 5040000 t a^{5} b c e^{4} + 6912000 t a^{5} b d^{2} e^{3} - 118540800 t a^{4} b^{2} c^{3} e^{2} + 365783040 t a^{4} b^{2} c^{2} d^{2} e + 111476736 t a^{4} b^{2} c d^{4} + 522764928 t a^{3} b^{3} c^{5} + 112500 a^{3} d e^{5} + 4536000 a^{2} b c d^{3} e^{2} - 2488320 a^{2} b d^{5} e + 58344300 a b^{2} c^{4} d e - 80015040 a b^{2} c^{3} d^{3}}{15625 a^{3} e^{6} - 275625 a^{2} b c^{2} e^{4} + 3024000 a^{2} b c d^{2} e^{3} - 2073600 a^{2} b d^{4} e^{2} - 4862025 a b^{2} c^{4} e^{2} + 53343360 a b^{2} c^{3} d^{2} e - 36578304 a b^{2} c^{2} d^{4} + 85766121 b^{3} c^{6}} \right)} \right)\right)} + \frac{- 4 a^{2} f + 11 a b c x + 10 a b d x^{2} + 9 a b e x^{3} + 7 b^{2} c x^{5} + 6 b^{2} d x^{6} + 5 b^{2} e x^{7}}{32 a^{4} b + 64 a^{3} b^{2} x^{4} + 32 a^{2} b^{3} x^{8}}"," ",0,"RootSum(268435456*_t**4*a**11*b**3 + _t**2*(6881280*a**6*b**2*c*e + 4718592*a**6*b**2*d**2) + _t*(153600*a**4*b*d*e**2 - 2709504*a**3*b**2*c**2*d) + 625*a**2*e**4 + 22050*a*b*c**2*e**2 - 60480*a*b*c*d**2*e + 20736*a*b*d**4 + 194481*b**2*c**4, Lambda(_t, _t*log(x + (262144000*_t**3*a**10*b**2*e**3 - 4624220160*_t**3*a**9*b**3*c**2*e + 12683575296*_t**3*a**9*b**3*c*d**2 + 309657600*_t**2*a**7*b**2*c*d*e**2 - 283115520*_t**2*a**7*b**2*d**3*e + 1820786688*_t**2*a**6*b**3*c**3*d + 5040000*_t*a**5*b*c*e**4 + 6912000*_t*a**5*b*d**2*e**3 - 118540800*_t*a**4*b**2*c**3*e**2 + 365783040*_t*a**4*b**2*c**2*d**2*e + 111476736*_t*a**4*b**2*c*d**4 + 522764928*_t*a**3*b**3*c**5 + 112500*a**3*d*e**5 + 4536000*a**2*b*c*d**3*e**2 - 2488320*a**2*b*d**5*e + 58344300*a*b**2*c**4*d*e - 80015040*a*b**2*c**3*d**3)/(15625*a**3*e**6 - 275625*a**2*b*c**2*e**4 + 3024000*a**2*b*c*d**2*e**3 - 2073600*a**2*b*d**4*e**2 - 4862025*a*b**2*c**4*e**2 + 53343360*a*b**2*c**3*d**2*e - 36578304*a*b**2*c**2*d**4 + 85766121*b**3*c**6)))) + (-4*a**2*f + 11*a*b*c*x + 10*a*b*d*x**2 + 9*a*b*e*x**3 + 7*b**2*c*x**5 + 6*b**2*d*x**6 + 5*b**2*e*x**7)/(32*a**4*b + 64*a**3*b**2*x**4 + 32*a**2*b**3*x**8)","A",0
492,-1,0,0,0.000000," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate((f*x**3+e*x**2+d*x+c)/(b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,1,252,0,8.540836," ","integrate(x**4*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2),x)","\frac{a^{\frac{3}{2}} d x^{2}}{16 b \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} c x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{3 \sqrt{a} d x^{6}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} e x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} - \frac{a^{2} d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{16 b^{\frac{3}{2}}} + f \left(\begin{cases} - \frac{a^{2} \sqrt{a + b x^{4}}}{15 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{4}}}{30 b} + \frac{x^{8} \sqrt{a + b x^{4}}}{10} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + \frac{b d x^{10}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*d*x**2/(16*b*sqrt(1 + b*x**4/a)) + sqrt(a)*c*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 3*sqrt(a)*d*x**6/(16*sqrt(1 + b*x**4/a)) + sqrt(a)*e*x**7*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4)) - a**2*d*asinh(sqrt(b)*x**2/sqrt(a))/(16*b**(3/2)) + f*Piecewise((-a**2*sqrt(a + b*x**4)/(15*b**2) + a*x**4*sqrt(a + b*x**4)/(30*b) + x**8*sqrt(a + b*x**4)/10, Ne(b, 0)), (sqrt(a)*x**8/8, True)) + b*d*x**10/(8*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
496,1,212,0,7.505781," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2),x)","\frac{a^{\frac{3}{2}} e x^{2}}{16 b \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} d x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{3 \sqrt{a} e x^{6}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} f x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} - \frac{a^{2} e \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{16 b^{\frac{3}{2}}} + c \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right) + \frac{b e x^{10}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*e*x**2/(16*b*sqrt(1 + b*x**4/a)) + sqrt(a)*d*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 3*sqrt(a)*e*x**6/(16*sqrt(1 + b*x**4/a)) + sqrt(a)*f*x**7*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4)) - a**2*e*asinh(sqrt(b)*x**2/sqrt(a))/(16*b**(3/2)) + c*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True)) + b*e*x**10/(8*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
497,1,212,0,7.089109," ","integrate(x**2*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2),x)","\frac{a^{\frac{3}{2}} f x^{2}}{16 b \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} c x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{\sqrt{a} e x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{3 \sqrt{a} f x^{6}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} - \frac{a^{2} f \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{16 b^{\frac{3}{2}}} + d \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right) + \frac{b f x^{10}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*f*x**2/(16*b*sqrt(1 + b*x**4/a)) + sqrt(a)*c*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + sqrt(a)*e*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 3*sqrt(a)*f*x**6/(16*sqrt(1 + b*x**4/a)) - a**2*f*asinh(sqrt(b)*x**2/sqrt(a))/(16*b**(3/2)) + d*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True)) + b*f*x**10/(8*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
498,1,158,0,6.529183," ","integrate(x*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2),x)","\frac{\sqrt{a} c x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} + \frac{\sqrt{a} d x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{\sqrt{a} f x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{a c \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 \sqrt{b}} + e \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*c*x**2*sqrt(1 + b*x**4/a)/4 + sqrt(a)*d*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + sqrt(a)*f*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + a*c*asinh(sqrt(b)*x**2/sqrt(a))/(4*sqrt(b)) + e*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True))","A",0
499,1,156,0,5.970701," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2),x)","\frac{\sqrt{a} c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{a} d x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} + \frac{\sqrt{a} e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{a d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 \sqrt{b}} + f \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*c*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + sqrt(a)*d*x**2*sqrt(1 + b*x**4/a)/4 + sqrt(a)*e*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + a*d*asinh(sqrt(b)*x**2/sqrt(a))/(4*sqrt(b)) + f*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True))","A",0
500,1,204,0,10.125484," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x,x)","- \frac{\sqrt{a} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2} + \frac{\sqrt{a} d x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{a} e x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} + \frac{\sqrt{a} f x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{a c}{2 \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{a e \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 \sqrt{b}} + \frac{\sqrt{b} c x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}}"," ",0,"-sqrt(a)*c*asinh(sqrt(a)/(sqrt(b)*x**2))/2 + sqrt(a)*d*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + sqrt(a)*e*x**2*sqrt(1 + b*x**4/a)/4 + sqrt(a)*f*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + a*c/(2*sqrt(b)*x**2*sqrt(a/(b*x**4) + 1)) + a*e*asinh(sqrt(b)*x**2/sqrt(a))/(4*sqrt(b)) + sqrt(b)*c*x**2/(2*sqrt(a/(b*x**4) + 1))","C",0
501,1,206,0,6.997314," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x**2,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{\sqrt{a} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2} + \frac{\sqrt{a} e x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{a} f x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} + \frac{a d}{2 \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{a f \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 \sqrt{b}} + \frac{\sqrt{b} d x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}}"," ",0,"sqrt(a)*c*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - sqrt(a)*d*asinh(sqrt(a)/(sqrt(b)*x**2))/2 + sqrt(a)*e*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + sqrt(a)*f*x**2*sqrt(1 + b*x**4/a)/4 + a*d/(2*sqrt(b)*x**2*sqrt(a/(b*x**4) + 1)) + a*f*asinh(sqrt(b)*x**2/sqrt(a))/(4*sqrt(b)) + sqrt(b)*d*x**2/(2*sqrt(a/(b*x**4) + 1))","C",0
502,1,230,0,6.409795," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x**3,x)","- \frac{\sqrt{a} c}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} d \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{\sqrt{a} e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2} + \frac{\sqrt{a} f x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{a e}{2 \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{\sqrt{b} c \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2} + \frac{\sqrt{b} e x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b c x^{2}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"-sqrt(a)*c/(2*x**2*sqrt(1 + b*x**4/a)) + sqrt(a)*d*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - sqrt(a)*e*asinh(sqrt(a)/(sqrt(b)*x**2))/2 + sqrt(a)*f*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + a*e/(2*sqrt(b)*x**2*sqrt(a/(b*x**4) + 1)) + sqrt(b)*c*asinh(sqrt(b)*x**2/sqrt(a))/2 + sqrt(b)*e*x**2/(2*sqrt(a/(b*x**4) + 1)) - b*c*x**2/(2*sqrt(a)*sqrt(1 + b*x**4/a))","C",0
503,1,235,0,6.622373," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x**4,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{\sqrt{a} d}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} e \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{\sqrt{a} f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2} + \frac{a f}{2 \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{\sqrt{b} d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2} + \frac{\sqrt{b} f x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b d x^{2}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"sqrt(a)*c*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - sqrt(a)*d/(2*x**2*sqrt(1 + b*x**4/a)) + sqrt(a)*e*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - sqrt(a)*f*asinh(sqrt(a)/(sqrt(b)*x**2))/2 + a*f/(2*sqrt(b)*x**2*sqrt(a/(b*x**4) + 1)) + sqrt(b)*d*asinh(sqrt(b)*x**2/sqrt(a))/2 + sqrt(b)*f*x**2/(2*sqrt(a/(b*x**4) + 1)) - b*d*x**2/(2*sqrt(a)*sqrt(1 + b*x**4/a))","C",0
504,1,211,0,6.782773," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x**5,x)","\frac{\sqrt{a} d \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{\sqrt{a} e}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} f \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{\sqrt{b} c \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} + \frac{\sqrt{b} e \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2} - \frac{b c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 \sqrt{a}} - \frac{b e x^{2}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"sqrt(a)*d*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - sqrt(a)*e/(2*x**2*sqrt(1 + b*x**4/a)) + sqrt(a)*f*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - sqrt(b)*c*sqrt(a/(b*x**4) + 1)/(4*x**2) + sqrt(b)*e*asinh(sqrt(b)*x**2/sqrt(a))/2 - b*c*asinh(sqrt(a)/(sqrt(b)*x**2))/(4*sqrt(a)) - b*e*x**2/(2*sqrt(a)*sqrt(1 + b*x**4/a))","C",0
505,1,216,0,7.056741," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x**6,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} + \frac{\sqrt{a} e \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{\sqrt{a} f}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} - \frac{\sqrt{b} d \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} + \frac{\sqrt{b} f \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2} - \frac{b d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 \sqrt{a}} - \frac{b f x^{2}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"sqrt(a)*c*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) + sqrt(a)*e*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - sqrt(a)*f/(2*x**2*sqrt(1 + b*x**4/a)) - sqrt(b)*d*sqrt(a/(b*x**4) + 1)/(4*x**2) + sqrt(b)*f*asinh(sqrt(b)*x**2/sqrt(a))/2 - b*d*asinh(sqrt(a)/(sqrt(b)*x**2))/(4*sqrt(a)) - b*f*x**2/(2*sqrt(a)*sqrt(1 + b*x**4/a))","C",0
506,1,189,0,7.042490," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x**7,x)","\frac{\sqrt{a} d \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} + \frac{\sqrt{a} f \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{\sqrt{b} c \sqrt{\frac{a}{b x^{4}} + 1}}{6 x^{4}} - \frac{\sqrt{b} e \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} - \frac{b^{\frac{3}{2}} c \sqrt{\frac{a}{b x^{4}} + 1}}{6 a} - \frac{b e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 \sqrt{a}}"," ",0,"sqrt(a)*d*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) + sqrt(a)*f*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - sqrt(b)*c*sqrt(a/(b*x**4) + 1)/(6*x**4) - sqrt(b)*e*sqrt(a/(b*x**4) + 1)/(4*x**2) - b**(3/2)*c*sqrt(a/(b*x**4) + 1)/(6*a) - b*e*asinh(sqrt(a)/(sqrt(b)*x**2))/(4*sqrt(a))","C",0
507,1,192,0,6.927042," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x**8,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} + \frac{\sqrt{a} e \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} - \frac{\sqrt{b} d \sqrt{\frac{a}{b x^{4}} + 1}}{6 x^{4}} - \frac{\sqrt{b} f \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} - \frac{b^{\frac{3}{2}} d \sqrt{\frac{a}{b x^{4}} + 1}}{6 a} - \frac{b f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 \sqrt{a}}"," ",0,"sqrt(a)*c*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) + sqrt(a)*e*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) - sqrt(b)*d*sqrt(a/(b*x**4) + 1)/(6*x**4) - sqrt(b)*f*sqrt(a/(b*x**4) + 1)/(4*x**2) - b**(3/2)*d*sqrt(a/(b*x**4) + 1)/(6*a) - b*f*asinh(sqrt(a)/(sqrt(b)*x**2))/(4*sqrt(a))","C",0
508,1,246,0,9.615902," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x**9,x)","\frac{\sqrt{a} d \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} + \frac{\sqrt{a} f \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} - \frac{a c}{8 \sqrt{b} x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{3 \sqrt{b} c}{16 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{\sqrt{b} e \sqrt{\frac{a}{b x^{4}} + 1}}{6 x^{4}} - \frac{b^{\frac{3}{2}} c}{16 a x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} e \sqrt{\frac{a}{b x^{4}} + 1}}{6 a} + \frac{b^{2} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{16 a^{\frac{3}{2}}}"," ",0,"sqrt(a)*d*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) + sqrt(a)*f*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) - a*c/(8*sqrt(b)*x**10*sqrt(a/(b*x**4) + 1)) - 3*sqrt(b)*c/(16*x**6*sqrt(a/(b*x**4) + 1)) - sqrt(b)*e*sqrt(a/(b*x**4) + 1)/(6*x**4) - b**(3/2)*c/(16*a*x**2*sqrt(a/(b*x**4) + 1)) - b**(3/2)*e*sqrt(a/(b*x**4) + 1)/(6*a) + b**2*c*asinh(sqrt(a)/(sqrt(b)*x**2))/(16*a**(3/2))","C",0
509,1,246,0,10.707364," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(1/2)/x**10,x)","\frac{\sqrt{a} c \Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, - \frac{1}{2} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{9} \Gamma\left(- \frac{5}{4}\right)} + \frac{\sqrt{a} e \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} - \frac{a d}{8 \sqrt{b} x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{3 \sqrt{b} d}{16 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{\sqrt{b} f \sqrt{\frac{a}{b x^{4}} + 1}}{6 x^{4}} - \frac{b^{\frac{3}{2}} d}{16 a x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} f \sqrt{\frac{a}{b x^{4}} + 1}}{6 a} + \frac{b^{2} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{16 a^{\frac{3}{2}}}"," ",0,"sqrt(a)*c*gamma(-9/4)*hyper((-9/4, -1/2), (-5/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**9*gamma(-5/4)) + sqrt(a)*e*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) - a*d/(8*sqrt(b)*x**10*sqrt(a/(b*x**4) + 1)) - 3*sqrt(b)*d/(16*x**6*sqrt(a/(b*x**4) + 1)) - sqrt(b)*f*sqrt(a/(b*x**4) + 1)/(6*x**4) - b**(3/2)*d/(16*a*x**2*sqrt(a/(b*x**4) + 1)) - b**(3/2)*f*sqrt(a/(b*x**4) + 1)/(6*a) + b**2*d*asinh(sqrt(a)/(sqrt(b)*x**2))/(16*a**(3/2))","C",0
510,1,462,0,22.073772," ","integrate(x**4*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2),x)","\frac{a^{\frac{5}{2}} d x^{2}}{32 b \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} c x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{17 a^{\frac{3}{2}} d x^{6}}{96 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} e x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} + \frac{\sqrt{a} b c x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)} + \frac{11 \sqrt{a} b d x^{10}}{48 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b e x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{15}{4}\right)} - \frac{a^{3} d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{32 b^{\frac{3}{2}}} + a f \left(\begin{cases} - \frac{a^{2} \sqrt{a + b x^{4}}}{15 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{4}}}{30 b} + \frac{x^{8} \sqrt{a + b x^{4}}}{10} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + b f \left(\begin{cases} \frac{4 a^{3} \sqrt{a + b x^{4}}}{105 b^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + b x^{4}}}{105 b^{2}} + \frac{a x^{8} \sqrt{a + b x^{4}}}{70 b} + \frac{x^{12} \sqrt{a + b x^{4}}}{14} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{12}}{12} & \text{otherwise} \end{cases}\right) + \frac{b^{2} d x^{14}}{12 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(5/2)*d*x**2/(32*b*sqrt(1 + b*x**4/a)) + a**(3/2)*c*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 17*a**(3/2)*d*x**6/(96*sqrt(1 + b*x**4/a)) + a**(3/2)*e*x**7*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4)) + sqrt(a)*b*c*x**9*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(13/4)) + 11*sqrt(a)*b*d*x**10/(48*sqrt(1 + b*x**4/a)) + sqrt(a)*b*e*x**11*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(15/4)) - a**3*d*asinh(sqrt(b)*x**2/sqrt(a))/(32*b**(3/2)) + a*f*Piecewise((-a**2*sqrt(a + b*x**4)/(15*b**2) + a*x**4*sqrt(a + b*x**4)/(30*b) + x**8*sqrt(a + b*x**4)/10, Ne(b, 0)), (sqrt(a)*x**8/8, True)) + b*f*Piecewise((4*a**3*sqrt(a + b*x**4)/(105*b**3) - 2*a**2*x**4*sqrt(a + b*x**4)/(105*b**2) + a*x**8*sqrt(a + b*x**4)/(70*b) + x**12*sqrt(a + b*x**4)/14, Ne(b, 0)), (sqrt(a)*x**12/12, True)) + b**2*d*x**14/(12*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
511,1,398,0,17.952528," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2),x)","\frac{a^{\frac{5}{2}} e x^{2}}{32 b \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} d x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{17 a^{\frac{3}{2}} e x^{6}}{96 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} f x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} + \frac{\sqrt{a} b d x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)} + \frac{11 \sqrt{a} b e x^{10}}{48 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b f x^{11} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{15}{4}\right)} - \frac{a^{3} e \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{32 b^{\frac{3}{2}}} + a c \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right) + b c \left(\begin{cases} - \frac{a^{2} \sqrt{a + b x^{4}}}{15 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{4}}}{30 b} + \frac{x^{8} \sqrt{a + b x^{4}}}{10} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + \frac{b^{2} e x^{14}}{12 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(5/2)*e*x**2/(32*b*sqrt(1 + b*x**4/a)) + a**(3/2)*d*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 17*a**(3/2)*e*x**6/(96*sqrt(1 + b*x**4/a)) + a**(3/2)*f*x**7*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4)) + sqrt(a)*b*d*x**9*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(13/4)) + 11*sqrt(a)*b*e*x**10/(48*sqrt(1 + b*x**4/a)) + sqrt(a)*b*f*x**11*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(15/4)) - a**3*e*asinh(sqrt(b)*x**2/sqrt(a))/(32*b**(3/2)) + a*c*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True)) + b*c*Piecewise((-a**2*sqrt(a + b*x**4)/(15*b**2) + a*x**4*sqrt(a + b*x**4)/(30*b) + x**8*sqrt(a + b*x**4)/10, Ne(b, 0)), (sqrt(a)*x**8/8, True)) + b**2*e*x**14/(12*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
512,1,398,0,17.740763," ","integrate(x**2*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2),x)","\frac{a^{\frac{5}{2}} f x^{2}}{32 b \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} c x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{a^{\frac{3}{2}} e x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{17 a^{\frac{3}{2}} f x^{6}}{96 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b c x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} + \frac{\sqrt{a} b e x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)} + \frac{11 \sqrt{a} b f x^{10}}{48 \sqrt{1 + \frac{b x^{4}}{a}}} - \frac{a^{3} f \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{32 b^{\frac{3}{2}}} + a d \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right) + b d \left(\begin{cases} - \frac{a^{2} \sqrt{a + b x^{4}}}{15 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{4}}}{30 b} + \frac{x^{8} \sqrt{a + b x^{4}}}{10} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + \frac{b^{2} f x^{14}}{12 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(5/2)*f*x**2/(32*b*sqrt(1 + b*x**4/a)) + a**(3/2)*c*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + a**(3/2)*e*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 17*a**(3/2)*f*x**6/(96*sqrt(1 + b*x**4/a)) + sqrt(a)*b*c*x**7*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4)) + sqrt(a)*b*e*x**9*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(13/4)) + 11*sqrt(a)*b*f*x**10/(48*sqrt(1 + b*x**4/a)) - a**3*f*asinh(sqrt(b)*x**2/sqrt(a))/(32*b**(3/2)) + a*d*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True)) + b*d*Piecewise((-a**2*sqrt(a + b*x**4)/(15*b**2) + a*x**4*sqrt(a + b*x**4)/(30*b) + x**8*sqrt(a + b*x**4)/10, Ne(b, 0)), (sqrt(a)*x**8/8, True)) + b**2*f*x**14/(12*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
513,1,396,0,13.228077," ","integrate(x*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2),x)","\frac{a^{\frac{3}{2}} c x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} + \frac{a^{\frac{3}{2}} c x^{2}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} d x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{a^{\frac{3}{2}} f x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{3 \sqrt{a} b c x^{6}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b d x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} + \frac{\sqrt{a} b f x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{13}{4}\right)} + \frac{3 a^{2} c \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{16 \sqrt{b}} + a e \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right) + b e \left(\begin{cases} - \frac{a^{2} \sqrt{a + b x^{4}}}{15 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{4}}}{30 b} + \frac{x^{8} \sqrt{a + b x^{4}}}{10} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + \frac{b^{2} c x^{10}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*c*x**2*sqrt(1 + b*x**4/a)/4 + a**(3/2)*c*x**2/(16*sqrt(1 + b*x**4/a)) + a**(3/2)*d*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + a**(3/2)*f*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 3*sqrt(a)*b*c*x**6/(16*sqrt(1 + b*x**4/a)) + sqrt(a)*b*d*x**7*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4)) + sqrt(a)*b*f*x**9*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(13/4)) + 3*a**2*c*asinh(sqrt(b)*x**2/sqrt(a))/(16*sqrt(b)) + a*e*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True)) + b*e*Piecewise((-a**2*sqrt(a + b*x**4)/(15*b**2) + a*x**4*sqrt(a + b*x**4)/(30*b) + x**8*sqrt(a + b*x**4)/10, Ne(b, 0)), (sqrt(a)*x**8/8, True)) + b**2*c*x**10/(8*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
514,1,394,0,12.310001," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2),x)","\frac{a^{\frac{3}{2}} c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{a^{\frac{3}{2}} d x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} + \frac{a^{\frac{3}{2}} d x^{2}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{\sqrt{a} b c x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{3 \sqrt{a} b d x^{6}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b e x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} + \frac{3 a^{2} d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{16 \sqrt{b}} + a f \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right) + b f \left(\begin{cases} - \frac{a^{2} \sqrt{a + b x^{4}}}{15 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{4}}}{30 b} + \frac{x^{8} \sqrt{a + b x^{4}}}{10} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + \frac{b^{2} d x^{10}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*c*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + a**(3/2)*d*x**2*sqrt(1 + b*x**4/a)/4 + a**(3/2)*d*x**2/(16*sqrt(1 + b*x**4/a)) + a**(3/2)*e*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + sqrt(a)*b*c*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 3*sqrt(a)*b*d*x**6/(16*sqrt(1 + b*x**4/a)) + sqrt(a)*b*e*x**7*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4)) + 3*a**2*d*asinh(sqrt(b)*x**2/sqrt(a))/(16*sqrt(b)) + a*f*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True)) + b*f*Piecewise((-a**2*sqrt(a + b*x**4)/(15*b**2) + a*x**4*sqrt(a + b*x**4)/(30*b) + x**8*sqrt(a + b*x**4)/10, Ne(b, 0)), (sqrt(a)*x**8/8, True)) + b**2*d*x**10/(8*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
515,1,405,0,31.319385," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x,x)","- \frac{a^{\frac{3}{2}} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2} + \frac{a^{\frac{3}{2}} d x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{a^{\frac{3}{2}} e x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} + \frac{a^{\frac{3}{2}} e x^{2}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} f x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{\sqrt{a} b d x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{3 \sqrt{a} b e x^{6}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b f x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} + \frac{a^{2} c}{2 \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{3 a^{2} e \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{16 \sqrt{b}} + \frac{a \sqrt{b} c x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}} + b c \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right) + \frac{b^{2} e x^{10}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"-a**(3/2)*c*asinh(sqrt(a)/(sqrt(b)*x**2))/2 + a**(3/2)*d*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + a**(3/2)*e*x**2*sqrt(1 + b*x**4/a)/4 + a**(3/2)*e*x**2/(16*sqrt(1 + b*x**4/a)) + a**(3/2)*f*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + sqrt(a)*b*d*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 3*sqrt(a)*b*e*x**6/(16*sqrt(1 + b*x**4/a)) + sqrt(a)*b*f*x**7*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4)) + a**2*c/(2*sqrt(b)*x**2*sqrt(a/(b*x**4) + 1)) + 3*a**2*e*asinh(sqrt(b)*x**2/sqrt(a))/(16*sqrt(b)) + a*sqrt(b)*c*x**2/(2*sqrt(a/(b*x**4) + 1)) + b*c*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True)) + b**2*e*x**10/(8*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
516,1,406,0,14.145866," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**2,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{a^{\frac{3}{2}} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2} + \frac{a^{\frac{3}{2}} e x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{a^{\frac{3}{2}} f x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} + \frac{a^{\frac{3}{2}} f x^{2}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b c x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{\sqrt{a} b e x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{3 \sqrt{a} b f x^{6}}{16 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{2} d}{2 \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{3 a^{2} f \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{16 \sqrt{b}} + \frac{a \sqrt{b} d x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}} + b d \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right) + \frac{b^{2} f x^{10}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*c*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - a**(3/2)*d*asinh(sqrt(a)/(sqrt(b)*x**2))/2 + a**(3/2)*e*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + a**(3/2)*f*x**2*sqrt(1 + b*x**4/a)/4 + a**(3/2)*f*x**2/(16*sqrt(1 + b*x**4/a)) + sqrt(a)*b*c*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + sqrt(a)*b*e*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + 3*sqrt(a)*b*f*x**6/(16*sqrt(1 + b*x**4/a)) + a**2*d/(2*sqrt(b)*x**2*sqrt(a/(b*x**4) + 1)) + 3*a**2*f*asinh(sqrt(b)*x**2/sqrt(a))/(16*sqrt(b)) + a*sqrt(b)*d*x**2/(2*sqrt(a/(b*x**4) + 1)) + b*d*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True)) + b**2*f*x**10/(8*sqrt(a)*sqrt(1 + b*x**4/a))","A",0
517,1,377,0,11.480371," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**3,x)","- \frac{a^{\frac{3}{2}} c}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{a^{\frac{3}{2}} e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2} + \frac{a^{\frac{3}{2}} f x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{a} b c x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} - \frac{\sqrt{a} b c x^{2}}{2 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b d x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{\sqrt{a} b f x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{a^{2} e}{2 \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{3 a \sqrt{b} c \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4} + \frac{a \sqrt{b} e x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}} + b e \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right)"," ",0,"-a**(3/2)*c/(2*x**2*sqrt(1 + b*x**4/a)) + a**(3/2)*d*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - a**(3/2)*e*asinh(sqrt(a)/(sqrt(b)*x**2))/2 + a**(3/2)*f*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + sqrt(a)*b*c*x**2*sqrt(1 + b*x**4/a)/4 - sqrt(a)*b*c*x**2/(2*sqrt(1 + b*x**4/a)) + sqrt(a)*b*d*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + sqrt(a)*b*f*x**5*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + a**2*e/(2*sqrt(b)*x**2*sqrt(a/(b*x**4) + 1)) + 3*a*sqrt(b)*c*asinh(sqrt(b)*x**2/sqrt(a))/4 + a*sqrt(b)*e*x**2/(2*sqrt(a/(b*x**4) + 1)) + b*e*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True))","A",0
518,1,381,0,11.341238," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**4,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{a^{\frac{3}{2}} d}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{a^{\frac{3}{2}} f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2} + \frac{\sqrt{a} b c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{a} b d x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} - \frac{\sqrt{a} b d x^{2}}{2 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{a^{2} f}{2 \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{3 a \sqrt{b} d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4} + \frac{a \sqrt{b} f x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}} + b f \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\left(a + b x^{4}\right)^{\frac{3}{2}}}{6 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**(3/2)*c*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - a**(3/2)*d/(2*x**2*sqrt(1 + b*x**4/a)) + a**(3/2)*e*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - a**(3/2)*f*asinh(sqrt(a)/(sqrt(b)*x**2))/2 + sqrt(a)*b*c*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + sqrt(a)*b*d*x**2*sqrt(1 + b*x**4/a)/4 - sqrt(a)*b*d*x**2/(2*sqrt(1 + b*x**4/a)) + sqrt(a)*b*e*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + a**2*f/(2*sqrt(b)*x**2*sqrt(a/(b*x**4) + 1)) + 3*a*sqrt(b)*d*asinh(sqrt(b)*x**2/sqrt(a))/4 + a*sqrt(b)*f*x**2/(2*sqrt(a/(b*x**4) + 1)) + b*f*Piecewise((sqrt(a)*x**4/4, Eq(b, 0)), ((a + b*x**4)**(3/2)/(6*b), True))","A",0
519,1,379,0,13.190529," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**5,x)","\frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{a^{\frac{3}{2}} e}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{3 \sqrt{a} b c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4} + \frac{\sqrt{a} b d x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{a} b e x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} - \frac{\sqrt{a} b e x^{2}}{2 \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b f x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} - \frac{a \sqrt{b} c \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} + \frac{a \sqrt{b} c}{2 x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{3 a \sqrt{b} e \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4} + \frac{b^{\frac{3}{2}} c x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}}"," ",0,"a**(3/2)*d*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - a**(3/2)*e/(2*x**2*sqrt(1 + b*x**4/a)) + a**(3/2)*f*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - 3*sqrt(a)*b*c*asinh(sqrt(a)/(sqrt(b)*x**2))/4 + sqrt(a)*b*d*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + sqrt(a)*b*e*x**2*sqrt(1 + b*x**4/a)/4 - sqrt(a)*b*e*x**2/(2*sqrt(1 + b*x**4/a)) + sqrt(a)*b*f*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) - a*sqrt(b)*c*sqrt(a/(b*x**4) + 1)/(4*x**2) + a*sqrt(b)*c/(2*x**2*sqrt(a/(b*x**4) + 1)) + 3*a*sqrt(b)*e*asinh(sqrt(b)*x**2/sqrt(a))/4 + b**(3/2)*c*x**2/(2*sqrt(a/(b*x**4) + 1))","C",0
520,1,386,0,13.155259," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**6,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{a^{\frac{3}{2}} f}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{3 \sqrt{a} b d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4} + \frac{\sqrt{a} b e x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{a} b f x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4} - \frac{\sqrt{a} b f x^{2}}{2 \sqrt{1 + \frac{b x^{4}}{a}}} - \frac{a \sqrt{b} d \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} + \frac{a \sqrt{b} d}{2 x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} + \frac{3 a \sqrt{b} f \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4} + \frac{b^{\frac{3}{2}} d x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}}"," ",0,"a**(3/2)*c*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) + a**(3/2)*e*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - a**(3/2)*f/(2*x**2*sqrt(1 + b*x**4/a)) + sqrt(a)*b*c*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - 3*sqrt(a)*b*d*asinh(sqrt(a)/(sqrt(b)*x**2))/4 + sqrt(a)*b*e*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + sqrt(a)*b*f*x**2*sqrt(1 + b*x**4/a)/4 - sqrt(a)*b*f*x**2/(2*sqrt(1 + b*x**4/a)) - a*sqrt(b)*d*sqrt(a/(b*x**4) + 1)/(4*x**2) + a*sqrt(b)*d/(2*x**2*sqrt(a/(b*x**4) + 1)) + 3*a*sqrt(b)*f*asinh(sqrt(b)*x**2/sqrt(a))/4 + b**(3/2)*d*x**2/(2*sqrt(a/(b*x**4) + 1))","C",0
521,1,406,0,12.307760," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**7,x)","\frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{\sqrt{a} b c}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b d \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{3 \sqrt{a} b e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4} + \frac{\sqrt{a} b f x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} - \frac{a \sqrt{b} c \sqrt{\frac{a}{b x^{4}} + 1}}{6 x^{4}} - \frac{a \sqrt{b} e \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} + \frac{a \sqrt{b} e}{2 x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} c \sqrt{\frac{a}{b x^{4}} + 1}}{6} + \frac{b^{\frac{3}{2}} c \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2} + \frac{b^{\frac{3}{2}} e x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{2} c x^{2}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*d*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) + a**(3/2)*f*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - sqrt(a)*b*c/(2*x**2*sqrt(1 + b*x**4/a)) + sqrt(a)*b*d*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - 3*sqrt(a)*b*e*asinh(sqrt(a)/(sqrt(b)*x**2))/4 + sqrt(a)*b*f*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) - a*sqrt(b)*c*sqrt(a/(b*x**4) + 1)/(6*x**4) - a*sqrt(b)*e*sqrt(a/(b*x**4) + 1)/(4*x**2) + a*sqrt(b)*e/(2*x**2*sqrt(a/(b*x**4) + 1)) - b**(3/2)*c*sqrt(a/(b*x**4) + 1)/6 + b**(3/2)*c*asinh(sqrt(b)*x**2/sqrt(a))/2 + b**(3/2)*e*x**2/(2*sqrt(a/(b*x**4) + 1)) - b**2*c*x**2/(2*sqrt(a)*sqrt(1 + b*x**4/a))","C",0
522,1,415,0,13.002817," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**8,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} + \frac{\sqrt{a} b c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{\sqrt{a} b d}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b e \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{3 \sqrt{a} b f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4} - \frac{a \sqrt{b} d \sqrt{\frac{a}{b x^{4}} + 1}}{6 x^{4}} - \frac{a \sqrt{b} f \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} + \frac{a \sqrt{b} f}{2 x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} d \sqrt{\frac{a}{b x^{4}} + 1}}{6} + \frac{b^{\frac{3}{2}} d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2} + \frac{b^{\frac{3}{2}} f x^{2}}{2 \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{2} d x^{2}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*c*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) + a**(3/2)*e*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) + sqrt(a)*b*c*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - sqrt(a)*b*d/(2*x**2*sqrt(1 + b*x**4/a)) + sqrt(a)*b*e*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - 3*sqrt(a)*b*f*asinh(sqrt(a)/(sqrt(b)*x**2))/4 - a*sqrt(b)*d*sqrt(a/(b*x**4) + 1)/(6*x**4) - a*sqrt(b)*f*sqrt(a/(b*x**4) + 1)/(4*x**2) + a*sqrt(b)*f/(2*x**2*sqrt(a/(b*x**4) + 1)) - b**(3/2)*d*sqrt(a/(b*x**4) + 1)/6 + b**(3/2)*d*asinh(sqrt(b)*x**2/sqrt(a))/2 + b**(3/2)*f*x**2/(2*sqrt(a/(b*x**4) + 1)) - b**2*d*x**2/(2*sqrt(a)*sqrt(1 + b*x**4/a))","C",0
523,1,444,0,18.589565," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**9,x)","\frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} + \frac{\sqrt{a} b d \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{\sqrt{a} b e}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{\sqrt{a} b f \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)} - \frac{a^{2} c}{8 \sqrt{b} x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{3 a \sqrt{b} c}{16 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{a \sqrt{b} e \sqrt{\frac{a}{b x^{4}} + 1}}{6 x^{4}} - \frac{b^{\frac{3}{2}} c \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} - \frac{b^{\frac{3}{2}} c}{16 x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} e \sqrt{\frac{a}{b x^{4}} + 1}}{6} + \frac{b^{\frac{3}{2}} e \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2} - \frac{3 b^{2} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{16 \sqrt{a}} - \frac{b^{2} e x^{2}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*d*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) + a**(3/2)*f*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) + sqrt(a)*b*d*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - sqrt(a)*b*e/(2*x**2*sqrt(1 + b*x**4/a)) + sqrt(a)*b*f*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x*gamma(3/4)) - a**2*c/(8*sqrt(b)*x**10*sqrt(a/(b*x**4) + 1)) - 3*a*sqrt(b)*c/(16*x**6*sqrt(a/(b*x**4) + 1)) - a*sqrt(b)*e*sqrt(a/(b*x**4) + 1)/(6*x**4) - b**(3/2)*c*sqrt(a/(b*x**4) + 1)/(4*x**2) - b**(3/2)*c/(16*x**2*sqrt(a/(b*x**4) + 1)) - b**(3/2)*e*sqrt(a/(b*x**4) + 1)/6 + b**(3/2)*e*asinh(sqrt(b)*x**2/sqrt(a))/2 - 3*b**2*c*asinh(sqrt(a)/(sqrt(b)*x**2))/(16*sqrt(a)) - b**2*e*x**2/(2*sqrt(a)*sqrt(1 + b*x**4/a))","C",0
524,1,449,0,21.885020," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**10,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, - \frac{1}{2} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{9} \Gamma\left(- \frac{5}{4}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} + \frac{\sqrt{a} b c \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} + \frac{\sqrt{a} b e \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{\sqrt{a} b f}{2 x^{2} \sqrt{1 + \frac{b x^{4}}{a}}} - \frac{a^{2} d}{8 \sqrt{b} x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{3 a \sqrt{b} d}{16 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{a \sqrt{b} f \sqrt{\frac{a}{b x^{4}} + 1}}{6 x^{4}} - \frac{b^{\frac{3}{2}} d \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} - \frac{b^{\frac{3}{2}} d}{16 x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} f \sqrt{\frac{a}{b x^{4}} + 1}}{6} + \frac{b^{\frac{3}{2}} f \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2} - \frac{3 b^{2} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{16 \sqrt{a}} - \frac{b^{2} f x^{2}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"a**(3/2)*c*gamma(-9/4)*hyper((-9/4, -1/2), (-5/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**9*gamma(-5/4)) + a**(3/2)*e*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) + sqrt(a)*b*c*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) + sqrt(a)*b*e*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - sqrt(a)*b*f/(2*x**2*sqrt(1 + b*x**4/a)) - a**2*d/(8*sqrt(b)*x**10*sqrt(a/(b*x**4) + 1)) - 3*a*sqrt(b)*d/(16*x**6*sqrt(a/(b*x**4) + 1)) - a*sqrt(b)*f*sqrt(a/(b*x**4) + 1)/(6*x**4) - b**(3/2)*d*sqrt(a/(b*x**4) + 1)/(4*x**2) - b**(3/2)*d/(16*x**2*sqrt(a/(b*x**4) + 1)) - b**(3/2)*f*sqrt(a/(b*x**4) + 1)/6 + b**(3/2)*f*asinh(sqrt(b)*x**2/sqrt(a))/2 - 3*b**2*d*asinh(sqrt(a)/(sqrt(b)*x**2))/(16*sqrt(a)) - b**2*f*x**2/(2*sqrt(a)*sqrt(1 + b*x**4/a))","C",0
525,1,398,0,19.190181," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**11,x)","\frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, - \frac{1}{2} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{9} \Gamma\left(- \frac{5}{4}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} + \frac{\sqrt{a} b d \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} + \frac{\sqrt{a} b f \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{a^{2} e}{8 \sqrt{b} x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{a \sqrt{b} c \sqrt{\frac{a}{b x^{4}} + 1}}{10 x^{8}} - \frac{3 a \sqrt{b} e}{16 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} c \sqrt{\frac{a}{b x^{4}} + 1}}{5 x^{4}} - \frac{b^{\frac{3}{2}} e \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} - \frac{b^{\frac{3}{2}} e}{16 x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{5}{2}} c \sqrt{\frac{a}{b x^{4}} + 1}}{10 a} - \frac{3 b^{2} e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{16 \sqrt{a}}"," ",0,"a**(3/2)*d*gamma(-9/4)*hyper((-9/4, -1/2), (-5/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**9*gamma(-5/4)) + a**(3/2)*f*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) + sqrt(a)*b*d*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) + sqrt(a)*b*f*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**3*gamma(1/4)) - a**2*e/(8*sqrt(b)*x**10*sqrt(a/(b*x**4) + 1)) - a*sqrt(b)*c*sqrt(a/(b*x**4) + 1)/(10*x**8) - 3*a*sqrt(b)*e/(16*x**6*sqrt(a/(b*x**4) + 1)) - b**(3/2)*c*sqrt(a/(b*x**4) + 1)/(5*x**4) - b**(3/2)*e*sqrt(a/(b*x**4) + 1)/(4*x**2) - b**(3/2)*e/(16*x**2*sqrt(a/(b*x**4) + 1)) - b**(5/2)*c*sqrt(a/(b*x**4) + 1)/(10*a) - 3*b**2*e*asinh(sqrt(a)/(sqrt(b)*x**2))/(16*sqrt(a))","C",0
526,1,401,0,22.521331," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**12,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{11}{4}, - \frac{1}{2} \\ - \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{11} \Gamma\left(- \frac{7}{4}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, - \frac{1}{2} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{9} \Gamma\left(- \frac{5}{4}\right)} + \frac{\sqrt{a} b c \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} + \frac{\sqrt{a} b e \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} - \frac{a^{2} f}{8 \sqrt{b} x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{a \sqrt{b} d \sqrt{\frac{a}{b x^{4}} + 1}}{10 x^{8}} - \frac{3 a \sqrt{b} f}{16 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} d \sqrt{\frac{a}{b x^{4}} + 1}}{5 x^{4}} - \frac{b^{\frac{3}{2}} f \sqrt{\frac{a}{b x^{4}} + 1}}{4 x^{2}} - \frac{b^{\frac{3}{2}} f}{16 x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{5}{2}} d \sqrt{\frac{a}{b x^{4}} + 1}}{10 a} - \frac{3 b^{2} f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{16 \sqrt{a}}"," ",0,"a**(3/2)*c*gamma(-11/4)*hyper((-11/4, -1/2), (-7/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**11*gamma(-7/4)) + a**(3/2)*e*gamma(-9/4)*hyper((-9/4, -1/2), (-5/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**9*gamma(-5/4)) + sqrt(a)*b*c*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) + sqrt(a)*b*e*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) - a**2*f/(8*sqrt(b)*x**10*sqrt(a/(b*x**4) + 1)) - a*sqrt(b)*d*sqrt(a/(b*x**4) + 1)/(10*x**8) - 3*a*sqrt(b)*f/(16*x**6*sqrt(a/(b*x**4) + 1)) - b**(3/2)*d*sqrt(a/(b*x**4) + 1)/(5*x**4) - b**(3/2)*f*sqrt(a/(b*x**4) + 1)/(4*x**2) - b**(3/2)*f/(16*x**2*sqrt(a/(b*x**4) + 1)) - b**(5/2)*d*sqrt(a/(b*x**4) + 1)/(10*a) - 3*b**2*f*asinh(sqrt(a)/(sqrt(b)*x**2))/(16*sqrt(a))","C",0
527,1,403,0,31.881309," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**13,x)","\frac{a^{\frac{3}{2}} d \Gamma\left(- \frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{11}{4}, - \frac{1}{2} \\ - \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{11} \Gamma\left(- \frac{7}{4}\right)} + \frac{a^{\frac{3}{2}} f \Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, - \frac{1}{2} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{9} \Gamma\left(- \frac{5}{4}\right)} + \frac{\sqrt{a} b d \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} + \frac{\sqrt{a} b f \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{5} \Gamma\left(- \frac{1}{4}\right)} - \frac{a^{2} c}{12 \sqrt{b} x^{14} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{11 a \sqrt{b} c}{48 x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{a \sqrt{b} e \sqrt{\frac{a}{b x^{4}} + 1}}{10 x^{8}} - \frac{17 b^{\frac{3}{2}} c}{96 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} e \sqrt{\frac{a}{b x^{4}} + 1}}{5 x^{4}} - \frac{b^{\frac{5}{2}} c}{32 a x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{5}{2}} e \sqrt{\frac{a}{b x^{4}} + 1}}{10 a} + \frac{b^{3} c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{32 a^{\frac{3}{2}}}"," ",0,"a**(3/2)*d*gamma(-11/4)*hyper((-11/4, -1/2), (-7/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**11*gamma(-7/4)) + a**(3/2)*f*gamma(-9/4)*hyper((-9/4, -1/2), (-5/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**9*gamma(-5/4)) + sqrt(a)*b*d*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) + sqrt(a)*b*f*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**5*gamma(-1/4)) - a**2*c/(12*sqrt(b)*x**14*sqrt(a/(b*x**4) + 1)) - 11*a*sqrt(b)*c/(48*x**10*sqrt(a/(b*x**4) + 1)) - a*sqrt(b)*e*sqrt(a/(b*x**4) + 1)/(10*x**8) - 17*b**(3/2)*c/(96*x**6*sqrt(a/(b*x**4) + 1)) - b**(3/2)*e*sqrt(a/(b*x**4) + 1)/(5*x**4) - b**(5/2)*c/(32*a*x**2*sqrt(a/(b*x**4) + 1)) - b**(5/2)*e*sqrt(a/(b*x**4) + 1)/(10*a) + b**3*c*asinh(sqrt(a)/(sqrt(b)*x**2))/(32*a**(3/2))","C",0
528,1,403,0,27.899781," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**(3/2)/x**14,x)","\frac{a^{\frac{3}{2}} c \Gamma\left(- \frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{13}{4}, - \frac{1}{2} \\ - \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{13} \Gamma\left(- \frac{9}{4}\right)} + \frac{a^{\frac{3}{2}} e \Gamma\left(- \frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{11}{4}, - \frac{1}{2} \\ - \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{11} \Gamma\left(- \frac{7}{4}\right)} + \frac{\sqrt{a} b c \Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, - \frac{1}{2} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{9} \Gamma\left(- \frac{5}{4}\right)} + \frac{\sqrt{a} b e \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 x^{7} \Gamma\left(- \frac{3}{4}\right)} - \frac{a^{2} d}{12 \sqrt{b} x^{14} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{11 a \sqrt{b} d}{48 x^{10} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{a \sqrt{b} f \sqrt{\frac{a}{b x^{4}} + 1}}{10 x^{8}} - \frac{17 b^{\frac{3}{2}} d}{96 x^{6} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{3}{2}} f \sqrt{\frac{a}{b x^{4}} + 1}}{5 x^{4}} - \frac{b^{\frac{5}{2}} d}{32 a x^{2} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{b^{\frac{5}{2}} f \sqrt{\frac{a}{b x^{4}} + 1}}{10 a} + \frac{b^{3} d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{32 a^{\frac{3}{2}}}"," ",0,"a**(3/2)*c*gamma(-13/4)*hyper((-13/4, -1/2), (-9/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**13*gamma(-9/4)) + a**(3/2)*e*gamma(-11/4)*hyper((-11/4, -1/2), (-7/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**11*gamma(-7/4)) + sqrt(a)*b*c*gamma(-9/4)*hyper((-9/4, -1/2), (-5/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**9*gamma(-5/4)) + sqrt(a)*b*e*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**4*exp_polar(I*pi)/a)/(4*x**7*gamma(-3/4)) - a**2*d/(12*sqrt(b)*x**14*sqrt(a/(b*x**4) + 1)) - 11*a*sqrt(b)*d/(48*x**10*sqrt(a/(b*x**4) + 1)) - a*sqrt(b)*f*sqrt(a/(b*x**4) + 1)/(10*x**8) - 17*b**(3/2)*d/(96*x**6*sqrt(a/(b*x**4) + 1)) - b**(3/2)*f*sqrt(a/(b*x**4) + 1)/(5*x**4) - b**(5/2)*d/(32*a*x**2*sqrt(a/(b*x**4) + 1)) - b**(5/2)*f*sqrt(a/(b*x**4) + 1)/(10*a) + b**3*d*asinh(sqrt(a)/(sqrt(b)*x**2))/(32*a**(3/2))","C",0
529,1,177,0,10.787412," ","integrate(x**4*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(1/2),x)","\frac{\sqrt{a} d x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4 b} - \frac{a d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} + f \left(\begin{cases} - \frac{a \sqrt{a + b x^{4}}}{3 b^{2}} + \frac{x^{4} \sqrt{a + b x^{4}}}{6 b} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 \sqrt{a}} & \text{otherwise} \end{cases}\right) + \frac{c x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)} + \frac{e x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"sqrt(a)*d*x**2*sqrt(1 + b*x**4/a)/(4*b) - a*d*asinh(sqrt(b)*x**2/sqrt(a))/(4*b**(3/2)) + f*Piecewise((-a*sqrt(a + b*x**4)/(3*b**2) + x**4*sqrt(a + b*x**4)/(6*b), Ne(b, 0)), (x**8/(8*sqrt(a)), True)) + c*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(9/4)) + e*x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(11/4))","A",0
530,1,156,0,10.298956," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(1/2),x)","\frac{\sqrt{a} e x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4 b} - \frac{a e \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} + c \left(\begin{cases} \frac{x^{4}}{4 \sqrt{a}} & \text{for}\: b = 0 \\\frac{\sqrt{a + b x^{4}}}{2 b} & \text{otherwise} \end{cases}\right) + \frac{d x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)} + \frac{f x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"sqrt(a)*e*x**2*sqrt(1 + b*x**4/a)/(4*b) - a*e*asinh(sqrt(b)*x**2/sqrt(a))/(4*b**(3/2)) + c*Piecewise((x**4/(4*sqrt(a)), Eq(b, 0)), (sqrt(a + b*x**4)/(2*b), True)) + d*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(9/4)) + f*x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(11/4))","A",0
531,1,156,0,10.862258," ","integrate(x**2*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(1/2),x)","\frac{\sqrt{a} f x^{2} \sqrt{1 + \frac{b x^{4}}{a}}}{4 b} - \frac{a f \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} + d \left(\begin{cases} \frac{x^{4}}{4 \sqrt{a}} & \text{for}\: b = 0 \\\frac{\sqrt{a + b x^{4}}}{2 b} & \text{otherwise} \end{cases}\right) + \frac{c x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)} + \frac{e x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"sqrt(a)*f*x**2*sqrt(1 + b*x**4/a)/(4*b) - a*f*asinh(sqrt(b)*x**2/sqrt(a))/(4*b**(3/2)) + d*Piecewise((x**4/(4*sqrt(a)), Eq(b, 0)), (sqrt(a + b*x**4)/(2*b), True)) + c*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4)) + e*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(9/4))","A",0
532,1,129,0,8.227742," ","integrate(x*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(1/2),x)","e \left(\begin{cases} \frac{x^{4}}{4 \sqrt{a}} & \text{for}\: b = 0 \\\frac{\sqrt{a + b x^{4}}}{2 b} & \text{otherwise} \end{cases}\right) + \frac{c \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{d x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)} + \frac{f x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"e*Piecewise((x**4/(4*sqrt(a)), Eq(b, 0)), (sqrt(a + b*x**4)/(2*b), True)) + c*asinh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)) + d*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4)) + f*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(9/4))","A",0
533,1,128,0,6.144623," ","integrate((f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(1/2),x)","f \left(\begin{cases} \frac{x^{4}}{4 \sqrt{a}} & \text{for}\: b = 0 \\\frac{\sqrt{a + b x^{4}}}{2 b} & \text{otherwise} \end{cases}\right) + \frac{d \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} + \frac{e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"f*Piecewise((x**4/(4*sqrt(a)), Eq(b, 0)), (sqrt(a + b*x**4)/(2*b), True)) + d*asinh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)) + c*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) + e*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4))","A",0
534,1,126,0,9.712188," ","integrate((f*x**3+e*x**2+d*x+c)/x/(b*x**4+a)**(1/2),x)","\frac{e \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} - \frac{c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2 \sqrt{a}} + \frac{d x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} + \frac{f x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"e*asinh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)) - c*asinh(sqrt(a)/(sqrt(b)*x**2))/(2*sqrt(a)) + d*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) + f*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4))","C",0
535,1,128,0,6.571657," ","integrate((f*x**3+e*x**2+d*x+c)/x**2/(b*x**4+a)**(1/2),x)","\frac{f \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x \Gamma\left(\frac{3}{4}\right)} - \frac{d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2 \sqrt{a}} + \frac{e x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"f*asinh(sqrt(b)*x**2/sqrt(a))/(2*sqrt(b)) + c*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x*gamma(3/4)) - d*asinh(sqrt(a)/(sqrt(b)*x**2))/(2*sqrt(a)) + e*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4))","C",0
536,1,126,0,6.332623," ","integrate((f*x**3+e*x**2+d*x+c)/x**3/(b*x**4+a)**(1/2),x)","- \frac{\sqrt{b} c \sqrt{\frac{a}{b x^{4}} + 1}}{2 a} + \frac{d \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x \Gamma\left(\frac{3}{4}\right)} - \frac{e \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2 \sqrt{a}} + \frac{f x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"-sqrt(b)*c*sqrt(a/(b*x**4) + 1)/(2*a) + d*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x*gamma(3/4)) - e*asinh(sqrt(a)/(sqrt(b)*x**2))/(2*sqrt(a)) + f*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4))","C",0
537,1,131,0,6.794672," ","integrate((f*x**3+e*x**2+d*x+c)/x**4/(b*x**4+a)**(1/2),x)","- \frac{\sqrt{b} d \sqrt{\frac{a}{b x^{4}} + 1}}{2 a} + \frac{c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x^{3} \Gamma\left(\frac{1}{4}\right)} + \frac{e \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x \Gamma\left(\frac{3}{4}\right)} - \frac{f \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{2 \sqrt{a}}"," ",0,"-sqrt(b)*d*sqrt(a/(b*x**4) + 1)/(2*a) + c*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x**3*gamma(1/4)) + e*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x*gamma(3/4)) - f*asinh(sqrt(a)/(sqrt(b)*x**2))/(2*sqrt(a))","C",0
538,1,158,0,8.547188," ","integrate((f*x**3+e*x**2+d*x+c)/x**5/(b*x**4+a)**(1/2),x)","- \frac{\sqrt{b} c \sqrt{\frac{a}{b x^{4}} + 1}}{4 a x^{2}} - \frac{\sqrt{b} e \sqrt{\frac{a}{b x^{4}} + 1}}{2 a} + \frac{d \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x^{3} \Gamma\left(\frac{1}{4}\right)} + \frac{f \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x \Gamma\left(\frac{3}{4}\right)} + \frac{b c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 a^{\frac{3}{2}}}"," ",0,"-sqrt(b)*c*sqrt(a/(b*x**4) + 1)/(4*a*x**2) - sqrt(b)*e*sqrt(a/(b*x**4) + 1)/(2*a) + d*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x**3*gamma(1/4)) + f*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x*gamma(3/4)) + b*c*asinh(sqrt(a)/(sqrt(b)*x**2))/(4*a**(3/2))","C",0
539,1,163,0,9.877170," ","integrate((f*x**3+e*x**2+d*x+c)/x**6/(b*x**4+a)**(1/2),x)","- \frac{\sqrt{b} d \sqrt{\frac{a}{b x^{4}} + 1}}{4 a x^{2}} - \frac{\sqrt{b} f \sqrt{\frac{a}{b x^{4}} + 1}}{2 a} + \frac{c \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x^{5} \Gamma\left(- \frac{1}{4}\right)} + \frac{e \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x^{3} \Gamma\left(\frac{1}{4}\right)} + \frac{b d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right)}}{4 a^{\frac{3}{2}}}"," ",0,"-sqrt(b)*d*sqrt(a/(b*x**4) + 1)/(4*a*x**2) - sqrt(b)*f*sqrt(a/(b*x**4) + 1)/(2*a) + c*gamma(-5/4)*hyper((-5/4, 1/2), (-1/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x**5*gamma(-1/4)) + e*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x**3*gamma(1/4)) + b*d*asinh(sqrt(a)/(sqrt(b)*x**2))/(4*a**(3/2))","C",0
540,1,202,0,51.872409," ","integrate(x**6*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(3/2),x)","d \left(\begin{cases} \frac{a}{b^{2} \sqrt{a + b x^{4}}} + \frac{x^{4}}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + f \left(\frac{3 \sqrt{a} x^{2}}{4 b^{2} \sqrt{1 + \frac{b x^{4}}{a}}} - \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{4 b^{\frac{5}{2}}} + \frac{x^{6}}{4 \sqrt{a} b \sqrt{1 + \frac{b x^{4}}{a}}}\right) + \frac{c x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)} + \frac{e x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"d*Piecewise((a/(b**2*sqrt(a + b*x**4)) + x**4/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**8/(8*a**(3/2)), True)) + f*(3*sqrt(a)*x**2/(4*b**2*sqrt(1 + b*x**4/a)) - 3*a*asinh(sqrt(b)*x**2/sqrt(a))/(4*b**(5/2)) + x**6/(4*sqrt(a)*b*sqrt(1 + b*x**4/a))) + c*x**7*gamma(7/4)*hyper((3/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(11/4)) + e*x**9*gamma(9/4)*hyper((3/2, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(13/4))","A",0
541,1,172,0,43.256580," ","integrate(x**5*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(3/2),x)","c \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} - \frac{x^{2}}{2 \sqrt{a} b \sqrt{1 + \frac{b x^{4}}{a}}}\right) + e \left(\begin{cases} \frac{a}{b^{2} \sqrt{a + b x^{4}}} + \frac{x^{4}}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{d x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)} + \frac{f x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"c*(asinh(sqrt(b)*x**2/sqrt(a))/(2*b**(3/2)) - x**2/(2*sqrt(a)*b*sqrt(1 + b*x**4/a))) + e*Piecewise((a/(b**2*sqrt(a + b*x**4)) + x**4/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**8/(8*a**(3/2)), True)) + d*x**7*gamma(7/4)*hyper((3/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(11/4)) + f*x**9*gamma(9/4)*hyper((3/2, 9/4), (13/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(13/4))","A",0
542,1,172,0,26.107602," ","integrate(x**4*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(3/2),x)","d \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} - \frac{x^{2}}{2 \sqrt{a} b \sqrt{1 + \frac{b x^{4}}{a}}}\right) + f \left(\begin{cases} \frac{a}{b^{2} \sqrt{a + b x^{4}}} + \frac{x^{4}}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{c x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{e x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"d*(asinh(sqrt(b)*x**2/sqrt(a))/(2*b**(3/2)) - x**2/(2*sqrt(a)*b*sqrt(1 + b*x**4/a))) + f*Piecewise((a/(b**2*sqrt(a + b*x**4)) + x**4/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**8/(8*a**(3/2)), True)) + c*x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(9/4)) + e*x**7*gamma(7/4)*hyper((3/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(11/4))","A",0
543,1,156,0,24.638024," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(3/2),x)","c \left(\begin{cases} - \frac{1}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + e \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} - \frac{x^{2}}{2 \sqrt{a} b \sqrt{1 + \frac{b x^{4}}{a}}}\right) + \frac{d x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{f x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c*Piecewise((-1/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**4/(4*a**(3/2)), True)) + e*(asinh(sqrt(b)*x**2/sqrt(a))/(2*b**(3/2)) - x**2/(2*sqrt(a)*b*sqrt(1 + b*x**4/a))) + d*x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(9/4)) + f*x**7*gamma(7/4)*hyper((3/2, 7/4), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(11/4))","A",0
544,1,156,0,21.067342," ","integrate(x**2*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(3/2),x)","d \left(\begin{cases} - \frac{1}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + f \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} - \frac{x^{2}}{2 \sqrt{a} b \sqrt{1 + \frac{b x^{4}}{a}}}\right) + \frac{c x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{e x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"d*Piecewise((-1/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**4/(4*a**(3/2)), True)) + f*(asinh(sqrt(b)*x**2/sqrt(a))/(2*b**(3/2)) - x**2/(2*sqrt(a)*b*sqrt(1 + b*x**4/a))) + c*x**3*gamma(3/4)*hyper((3/4, 3/2), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(7/4)) + e*x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(9/4))","A",0
545,1,133,0,19.338557," ","integrate(x*(f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(3/2),x)","e \left(\begin{cases} - \frac{1}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{c x^{2}}{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{d x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{f x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"e*Piecewise((-1/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**4/(4*a**(3/2)), True)) + c*x**2/(2*a**(3/2)*sqrt(1 + b*x**4/a)) + d*x**3*gamma(3/4)*hyper((3/4, 3/2), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(7/4)) + f*x**5*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(9/4))","A",0
546,1,131,0,18.323631," ","integrate((f*x**3+e*x**2+d*x+c)/(b*x**4+a)**(3/2),x)","f \left(\begin{cases} - \frac{1}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{d x^{2}}{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"f*Piecewise((-1/(2*b*sqrt(a + b*x**4)), Ne(b, 0)), (x**4/(4*a**(3/2)), True)) + c*x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(5/4)) + d*x**2/(2*a**(3/2)*sqrt(1 + b*x**4/a)) + e*x**3*gamma(3/4)*hyper((3/4, 3/2), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(7/4))","A",0
547,1,289,0,23.819277," ","integrate((f*x**3+e*x**2+d*x+c)/x/(b*x**4+a)**(3/2),x)","c \left(\frac{2 a^{3} \sqrt{1 + \frac{b x^{4}}{a}}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{3} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{2} b x^{4} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{2} b x^{4} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}}\right) + \frac{d x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{e x^{2}}{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{4}}{a}}} + \frac{f x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"c*(2*a**3*sqrt(1 + b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**3*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**3*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**2*b*x**4*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**2*b*x**4*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4)) + d*x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(5/4)) + e*x**2/(2*a**(3/2)*sqrt(1 + b*x**4/a)) + f*x**3*gamma(3/4)*hyper((3/4, 3/2), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(7/4))","C",0
548,1,291,0,28.558697," ","integrate((f*x**3+e*x**2+d*x+c)/x**2/(b*x**4+a)**(3/2),x)","d \left(\frac{2 a^{3} \sqrt{1 + \frac{b x^{4}}{a}}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{3} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{2} b x^{4} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{2} b x^{4} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}}\right) + \frac{c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} x \Gamma\left(\frac{3}{4}\right)} + \frac{e x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{f x^{2}}{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{4}}{a}}}"," ",0,"d*(2*a**3*sqrt(1 + b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**3*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**3*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**2*b*x**4*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**2*b*x**4*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4)) + c*gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*x*gamma(3/4)) + e*x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(5/4)) + f*x**2/(2*a**(3/2)*sqrt(1 + b*x**4/a))","C",0
549,1,316,0,25.302708," ","integrate((f*x**3+e*x**2+d*x+c)/x**3/(b*x**4+a)**(3/2),x)","c \left(- \frac{1}{2 a \sqrt{b} x^{4} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{\sqrt{b}}{a^{2} \sqrt{\frac{a}{b x^{4}} + 1}}\right) + e \left(\frac{2 a^{3} \sqrt{1 + \frac{b x^{4}}{a}}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{3} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{2} b x^{4} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{2} b x^{4} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}}\right) + \frac{d \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} x \Gamma\left(\frac{3}{4}\right)} + \frac{f x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"c*(-1/(2*a*sqrt(b)*x**4*sqrt(a/(b*x**4) + 1)) - sqrt(b)/(a**2*sqrt(a/(b*x**4) + 1))) + e*(2*a**3*sqrt(1 + b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**3*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**3*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**2*b*x**4*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**2*b*x**4*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4)) + d*gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*x*gamma(3/4)) + f*x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(5/4))","C",0
550,1,321,0,33.726475," ","integrate((f*x**3+e*x**2+d*x+c)/x**4/(b*x**4+a)**(3/2),x)","d \left(- \frac{1}{2 a \sqrt{b} x^{4} \sqrt{\frac{a}{b x^{4}} + 1}} - \frac{\sqrt{b}}{a^{2} \sqrt{\frac{a}{b x^{4}} + 1}}\right) + f \left(\frac{2 a^{3} \sqrt{1 + \frac{b x^{4}}{a}}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{3} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} + \frac{a^{2} b x^{4} \log{\left(\frac{b x^{4}}{a} \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}} - \frac{2 a^{2} b x^{4} \log{\left(\sqrt{1 + \frac{b x^{4}}{a}} + 1 \right)}}{4 a^{\frac{9}{2}} + 4 a^{\frac{7}{2}} b x^{4}}\right) + \frac{c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} x^{3} \Gamma\left(\frac{1}{4}\right)} + \frac{e \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} x \Gamma\left(\frac{3}{4}\right)}"," ",0,"d*(-1/(2*a*sqrt(b)*x**4*sqrt(a/(b*x**4) + 1)) - sqrt(b)/(a**2*sqrt(a/(b*x**4) + 1))) + f*(2*a**3*sqrt(1 + b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**3*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**3*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) + a**2*b*x**4*log(b*x**4/a)/(4*a**(9/2) + 4*a**(7/2)*b*x**4) - 2*a**2*b*x**4*log(sqrt(1 + b*x**4/a) + 1)/(4*a**(9/2) + 4*a**(7/2)*b*x**4)) + c*gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*x**3*gamma(1/4)) + e*gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), b*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*x*gamma(3/4))","C",0
551,-1,0,0,0.000000," ","integrate((g*x)**m*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,1,141,0,49.566307," ","integrate((f*x**3+e*x**2+d*x+c)*(b*x**4+a)**p,x)","\frac{a^{p} c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{a^{p} d x^{2} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2} + \frac{a^{p} e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, - p \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + f \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{4}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{4} \right)} & \text{otherwise} \end{cases}}{4 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*c*x*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + a**p*d*x**2*hyper((1/2, -p), (3/2,), b*x**4*exp_polar(I*pi)/a)/2 + a**p*e*x**3*gamma(3/4)*hyper((3/4, -p), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + f*Piecewise((a**p*x**4/4, Eq(b, 0)), (Piecewise(((a + b*x**4)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**4), True))/(4*b), True))","A",0
553,1,143,0,111.183338," ","integrate(x**3*(f*x**3+e*x**2+d*x+c)*(b*x**4+a)**p,x)","\frac{a^{p} d x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, - p \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{a^{p} e x^{6} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{6} + \frac{a^{p} f x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, - p \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} + c \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{4}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{4} \right)} & \text{otherwise} \end{cases}}{4 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d*x**5*gamma(5/4)*hyper((5/4, -p), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + a**p*e*x**6*hyper((3/2, -p), (5/2,), b*x**4*exp_polar(I*pi)/a)/6 + a**p*f*x**7*gamma(7/4)*hyper((7/4, -p), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4)) + c*Piecewise((a**p*x**4/4, Eq(b, 0)), (Piecewise(((a + b*x**4)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**4), True))/(4*b), True))","A",0
554,1,5,0,0.084633," ","integrate((x**4+x**3+x**2+x+1)/(-x**5+1),x)","- \log{\left(x - 1 \right)}"," ",0,"-log(x - 1)","A",0
555,1,7,0,0.080168," ","integrate((-32*x**5+48*x**4-72*x**3+108*x**2-162*x+243)/(-64*x**6+729),x)","\frac{\log{\left(2 x + 3 \right)}}{2}"," ",0,"log(2*x + 3)/2","A",0
556,1,8,0,0.092626," ","integrate((32*x**5+48*x**4+72*x**3+108*x**2+162*x+243)/(-64*x**6+729),x)","- \frac{\log{\left(2 x - 3 \right)}}{2}"," ",0,"-log(2*x - 3)/2","A",0
557,1,15,0,0.109534," ","integrate((16*x**4+36*x**2+81)/(-64*x**6+729),x)","- \frac{\log{\left(x - \frac{3}{2} \right)}}{12} + \frac{\log{\left(x + \frac{3}{2} \right)}}{12}"," ",0,"-log(x - 3/2)/12 + log(x + 3/2)/12","B",0
558,1,24,0,0.147406," ","integrate((-16*x**4-24*x**3+54*x+81)/(-64*x**6+729),x)","\frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/9","A",0
559,1,46,0,0.211597," ","integrate((3-2*x)/(-64*x**6+729),x)","\frac{\log{\left(x + \frac{3}{2} \right)}}{486} - \frac{\log{\left(4 x^{2} - 6 x + 9 \right)}}{972} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{486}"," ",0,"log(x + 3/2)/486 - log(4*x**2 - 6*x + 9)/972 + sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/486","A",0
560,1,46,0,0.242346," ","integrate((3+2*x)/(-64*x**6+729),x)","- \frac{\log{\left(x - \frac{3}{2} \right)}}{486} + \frac{\log{\left(4 x^{2} + 6 x + 9 \right)}}{972} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{486}"," ",0,"-log(x - 3/2)/486 + log(4*x**2 + 6*x + 9)/972 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/486","A",0
561,1,56,0,0.225747," ","integrate((4*x**2-6*x+9)/(-64*x**6+729),x)","- \frac{\log{\left(x - \frac{3}{2} \right)}}{324} + \frac{\log{\left(x + \frac{3}{2} \right)}}{108} - \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{324} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{162}"," ",0,"-log(x - 3/2)/324 + log(x + 3/2)/108 - log(x**2 + 3*x/2 + 9/4)/324 + sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/162","A",0
562,1,56,0,0.231939," ","integrate((4*x**2+6*x+9)/(-64*x**6+729),x)","- \frac{\log{\left(x - \frac{3}{2} \right)}}{108} + \frac{\log{\left(x + \frac{3}{2} \right)}}{324} + \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{324} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{162}"," ",0,"-log(x - 3/2)/108 + log(x + 3/2)/324 + log(x**2 - 3*x/2 + 9/4)/324 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/162","A",0
563,1,48,0,0.156177," ","integrate((-8*x**3+27)/(-64*x**6+729),x)","\frac{\log{\left(x + \frac{3}{2} \right)}}{54} - \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{108} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{54}"," ",0,"log(x + 3/2)/54 - log(x**2 - 3*x/2 + 9/4)/108 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/54","A",0
564,1,48,0,0.197980," ","integrate((8*x**3+24*x**2+36*x+27)/(-64*x**6+729),x)","- \frac{\log{\left(x - \frac{3}{2} \right)}}{18} + \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{36} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{54}"," ",0,"-log(x - 3/2)/18 + log(x**2 - 3*x/2 + 9/4)/36 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/54","A",0
565,1,105,0,0.432111," ","integrate((-32*x**5+48*x**4-72*x**3+108*x**2-162*x+243)/(-64*x**6+729)**2,x)","- \frac{\log{\left(x - \frac{3}{2} \right)}}{17496} + \frac{5 \log{\left(x + \frac{3}{2} \right)}}{17496} - \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{17496} - \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{17496} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{26244} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{8748} - \frac{1}{5832 x + 8748}"," ",0,"-log(x - 3/2)/17496 + 5*log(x + 3/2)/17496 - log(x**2 - 3*x/2 + 9/4)/17496 - log(x**2 + 3*x/2 + 9/4)/17496 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/26244 + sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/8748 - 1/(5832*x + 8748)","A",0
566,1,105,0,0.468246," ","integrate((32*x**5+48*x**4+72*x**3+108*x**2+162*x+243)/(-64*x**6+729)**2,x)","- \frac{5 \log{\left(x - \frac{3}{2} \right)}}{17496} + \frac{\log{\left(x + \frac{3}{2} \right)}}{17496} + \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{17496} + \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{17496} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{8748} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{26244} - \frac{1}{5832 x - 8748}"," ",0,"-5*log(x - 3/2)/17496 + log(x + 3/2)/17496 + log(x**2 - 3*x/2 + 9/4)/17496 + log(x**2 + 3*x/2 + 9/4)/17496 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/8748 + sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/26244 - 1/(5832*x - 8748)","A",0
567,1,70,0,0.229203," ","integrate((16*x**4+36*x**2+81)/(-64*x**6+729)**2,x)","- \frac{x}{17496 x^{2} - 39366} + \frac{\sqrt{3} \left(2 \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{9} \right)} + 2 \operatorname{atan}{\left(\frac{8 \sqrt{3} x^{3}}{81} + \frac{4 \sqrt{3} x}{9} \right)}\right)}{78732} - \frac{\log{\left(x - \frac{3}{2} \right)}}{17496} + \frac{\log{\left(x + \frac{3}{2} \right)}}{17496}"," ",0,"-x/(17496*x**2 - 39366) + sqrt(3)*(2*atan(2*sqrt(3)*x/9) + 2*atan(8*sqrt(3)*x**3/81 + 4*sqrt(3)*x/9))/78732 - log(x - 3/2)/17496 + log(x + 3/2)/17496","A",0
568,1,82,0,0.421821," ","integrate((-16*x**4-24*x**3+54*x+81)/(-64*x**6+729)**2,x)","\frac{x}{17496 x^{2} - 26244 x + 39366} - \frac{\log{\left(x - \frac{3}{2} \right)}}{26244} + \frac{\log{\left(x + \frac{3}{2} \right)}}{78732} - \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{157464} + \frac{\log{\left(4 x^{2} + 6 x + 9 \right)}}{52488} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{13122}"," ",0,"x/(17496*x**2 - 26244*x + 39366) - log(x - 3/2)/26244 + log(x + 3/2)/78732 - log(x**2 - 3*x/2 + 9/4)/157464 + log(4*x**2 + 6*x + 9)/52488 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/13122","A",0
569,1,124,0,0.651448," ","integrate((3-2*x)/(-64*x**6+729)**2,x)","\frac{x}{139968 x^{5} + 209952 x^{4} + 314928 x^{3} + 472392 x^{2} + 708588 x + 1062882} - \frac{\log{\left(x - \frac{3}{2} \right)}}{4251528} + \frac{\log{\left(x + \frac{3}{2} \right)}}{472392} - \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{944784} + \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{8503056} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{4251528} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{472392}"," ",0,"x/(139968*x**5 + 209952*x**4 + 314928*x**3 + 472392*x**2 + 708588*x + 1062882) - log(x - 3/2)/4251528 + log(x + 3/2)/472392 - log(x**2 - 3*x/2 + 9/4)/944784 + log(x**2 + 3*x/2 + 9/4)/8503056 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/4251528 + sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/472392","A",0
570,1,124,0,0.646575," ","integrate((3+2*x)/(-64*x**6+729)**2,x)","- \frac{x}{139968 x^{5} - 209952 x^{4} + 314928 x^{3} - 472392 x^{2} + 708588 x - 1062882} - \frac{\log{\left(x - \frac{3}{2} \right)}}{472392} + \frac{\log{\left(x + \frac{3}{2} \right)}}{4251528} - \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{8503056} + \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{944784} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{472392} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{4251528}"," ",0,"-x/(139968*x**5 - 209952*x**4 + 314928*x**3 - 472392*x**2 + 708588*x - 1062882) - log(x - 3/2)/472392 + log(x + 3/2)/4251528 - log(x**2 - 3*x/2 + 9/4)/8503056 + log(x**2 + 3*x/2 + 9/4)/944784 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/472392 + sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/4251528","A",0
571,1,116,0,0.638929," ","integrate((4*x**2-6*x+9)/(-64*x**6+729)**2,x)","- \frac{x}{69984 x^{4} + 104976 x^{3} - 236196 x - 354294} - \frac{\log{\left(x - \frac{3}{2} \right)}}{354294} + \frac{\log{\left(x + \frac{3}{2} \right)}}{118098} - \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{944784} - \frac{5 \log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{2834352} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{1417176} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{157464}"," ",0,"-x/(69984*x**4 + 104976*x**3 - 236196*x - 354294) - log(x - 3/2)/354294 + log(x + 3/2)/118098 - log(x**2 - 3*x/2 + 9/4)/944784 - 5*log(x**2 + 3*x/2 + 9/4)/2834352 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/1417176 + sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/157464","A",0
572,1,116,0,0.571698," ","integrate((4*x**2+6*x+9)/(-64*x**6+729)**2,x)","- \frac{x}{69984 x^{4} - 104976 x^{3} + 236196 x - 354294} - \frac{\log{\left(x - \frac{3}{2} \right)}}{118098} + \frac{\log{\left(x + \frac{3}{2} \right)}}{354294} + \frac{5 \log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{2834352} + \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{944784} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{157464} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{1417176}"," ",0,"-x/(69984*x**4 - 104976*x**3 + 236196*x - 354294) - log(x - 3/2)/118098 + log(x + 3/2)/354294 + 5*log(x**2 - 3*x/2 + 9/4)/2834352 + log(x**2 + 3*x/2 + 9/4)/944784 + sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/157464 + sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/1417176","A",0
573,1,110,0,0.528908," ","integrate((-8*x**3+27)/(-64*x**6+729)**2,x)","\frac{x}{34992 x^{3} + 118098} - \frac{\log{\left(x - \frac{3}{2} \right)}}{157464} + \frac{7 \log{\left(x + \frac{3}{2} \right)}}{472392} - \frac{7 \log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{944784} + \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{314928} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{472392} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{157464}"," ",0,"x/(34992*x**3 + 118098) - log(x - 3/2)/157464 + 7*log(x + 3/2)/472392 - 7*log(x**2 - 3*x/2 + 9/4)/944784 + log(x**2 + 3*x/2 + 9/4)/314928 + 7*sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/472392 + sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/157464","A",0
574,1,119,0,0.695176," ","integrate((8*x**3+24*x**2+36*x+27)/(-64*x**6+729)**2,x)","- \frac{x}{34992 x^{3} - 104976 x^{2} + 157464 x - 118098} - \frac{7 \log{\left(x - \frac{3}{2} \right)}}{157464} + \frac{\log{\left(x + \frac{3}{2} \right)}}{472392} + \frac{17 \log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{944784} + \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{314928} + \frac{11 \sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{472392} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{472392}"," ",0,"-x/(34992*x**3 - 104976*x**2 + 157464*x - 118098) - 7*log(x - 3/2)/157464 + log(x + 3/2)/472392 + 17*log(x**2 - 3*x/2 + 9/4)/944784 + log(x**2 + 3*x/2 + 9/4)/314928 + 11*sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/472392 - sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/472392","A",0
575,1,102,0,0.395205," ","integrate(x*(-2*x**3+27)/(-64*x**6+729),x)","- \frac{\log{\left(x - \frac{3}{2} \right)}}{96} - \frac{5 \log{\left(x + \frac{3}{2} \right)}}{288} + \frac{5 \log{\left(x^{2} - \frac{3 x}{2} + \frac{9}{4} \right)}}{576} + \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{9}{4} \right)}}{192} + \frac{5 \sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} - \frac{\sqrt{3}}{3} \right)}}{288} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3} x}{9} + \frac{\sqrt{3}}{3} \right)}}{96}"," ",0,"-log(x - 3/2)/96 - 5*log(x + 3/2)/288 + 5*log(x**2 - 3*x/2 + 9/4)/576 + log(x**2 + 3*x/2 + 9/4)/192 + 5*sqrt(3)*atan(4*sqrt(3)*x/9 - sqrt(3)/3)/288 - sqrt(3)*atan(4*sqrt(3)*x/9 + sqrt(3)/3)/96","A",0
576,1,654,0,57.805463," ","integrate((c*x)**m*(d+e*x**n+f*x**(2*n)+g*x**(3*n))/(a+b*x**n),x)","\frac{c^{m} d m x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{c^{m} d x x^{m} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{c^{m} e m x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + 1 + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right)} + \frac{c^{m} e x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + 1 + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}{a n \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right)} + \frac{c^{m} e x x^{m} x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + 1 + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right)} + \frac{c^{m} f m x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + 2 + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 3 + \frac{1}{n}\right)} + \frac{2 c^{m} f x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + 2 + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right)}{a n \Gamma\left(\frac{m}{n} + 3 + \frac{1}{n}\right)} + \frac{c^{m} f x x^{m} x^{2 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + 2 + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 3 + \frac{1}{n}\right)} + \frac{c^{m} g m x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + 3 + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + 3 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 4 + \frac{1}{n}\right)} + \frac{3 c^{m} g x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + 3 + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + 3 + \frac{1}{n}\right)}{a n \Gamma\left(\frac{m}{n} + 4 + \frac{1}{n}\right)} + \frac{c^{m} g x x^{m} x^{3 n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{m}{n} + 3 + \frac{1}{n}\right) \Gamma\left(\frac{m}{n} + 3 + \frac{1}{n}\right)}{a n^{2} \Gamma\left(\frac{m}{n} + 4 + \frac{1}{n}\right)}"," ",0,"c**m*d*m*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*n**2*gamma(m/n + 1 + 1/n)) + c**m*d*x*x**m*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1/n)*gamma(m/n + 1/n)/(a*n**2*gamma(m/n + 1 + 1/n)) + c**m*e*m*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1 + 1/n)*gamma(m/n + 1 + 1/n)/(a*n**2*gamma(m/n + 2 + 1/n)) + c**m*e*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1 + 1/n)*gamma(m/n + 1 + 1/n)/(a*n*gamma(m/n + 2 + 1/n)) + c**m*e*x*x**m*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 1 + 1/n)*gamma(m/n + 1 + 1/n)/(a*n**2*gamma(m/n + 2 + 1/n)) + c**m*f*m*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 2 + 1/n)*gamma(m/n + 2 + 1/n)/(a*n**2*gamma(m/n + 3 + 1/n)) + 2*c**m*f*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 2 + 1/n)*gamma(m/n + 2 + 1/n)/(a*n*gamma(m/n + 3 + 1/n)) + c**m*f*x*x**m*x**(2*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 2 + 1/n)*gamma(m/n + 2 + 1/n)/(a*n**2*gamma(m/n + 3 + 1/n)) + c**m*g*m*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 3 + 1/n)*gamma(m/n + 3 + 1/n)/(a*n**2*gamma(m/n + 4 + 1/n)) + 3*c**m*g*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 3 + 1/n)*gamma(m/n + 3 + 1/n)/(a*n*gamma(m/n + 4 + 1/n)) + c**m*g*x*x**m*x**(3*n)*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, m/n + 3 + 1/n)*gamma(m/n + 3 + 1/n)/(a*n**2*gamma(m/n + 4 + 1/n))","C",0
577,1,1251,0,8.171079," ","integrate((c+d*x**(-1+n))*(a+b*x**n)**3,x)","\begin{cases} a^{3} c x - \frac{a^{3} d}{x} + 3 a^{2} b c \log{\left(x \right)} - \frac{3 a^{2} b d}{2 x^{2}} - \frac{3 a b^{2} c}{x} - \frac{a b^{2} d}{x^{3}} - \frac{b^{3} c}{2 x^{2}} - \frac{b^{3} d}{4 x^{4}} & \text{for}\: n = -1 \\a^{3} c x - \frac{2 a^{3} d}{\sqrt{x}} + 6 a^{2} b c \sqrt{x} - \frac{3 a^{2} b d}{x} + 3 a b^{2} c \log{\left(x \right)} - \frac{2 a b^{2} d}{x^{\frac{3}{2}}} - \frac{2 b^{3} c}{\sqrt{x}} - \frac{b^{3} d}{2 x^{2}} & \text{for}\: n = - \frac{1}{2} \\a^{3} c x - \frac{3 a^{3} d}{\sqrt[3]{x}} + \frac{9 a^{2} b c x^{\frac{2}{3}}}{2} - \frac{9 a^{2} b d}{2 x^{\frac{2}{3}}} + 9 a b^{2} c \sqrt[3]{x} - \frac{3 a b^{2} d}{x} + b^{3} c \log{\left(x \right)} - \frac{3 b^{3} d}{4 x^{\frac{4}{3}}} & \text{for}\: n = - \frac{1}{3} \\\left(a + b\right)^{3} \left(c x + d \log{\left(x \right)}\right) & \text{for}\: n = 0 \\\frac{24 a^{3} c n^{4} x}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{44 a^{3} c n^{3} x}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{24 a^{3} c n^{2} x}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{4 a^{3} c n x}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{24 a^{3} d n^{3} x^{n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{44 a^{3} d n^{2} x^{n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{24 a^{3} d n x^{n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{4 a^{3} d x^{n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{72 a^{2} b c n^{3} x x^{n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{60 a^{2} b c n^{2} x x^{n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{12 a^{2} b c n x x^{n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{36 a^{2} b d n^{3} x^{2 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{66 a^{2} b d n^{2} x^{2 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{36 a^{2} b d n x^{2 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{6 a^{2} b d x^{2 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{36 a b^{2} c n^{3} x x^{2 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{48 a b^{2} c n^{2} x x^{2 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{12 a b^{2} c n x x^{2 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{24 a b^{2} d n^{3} x^{3 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{44 a b^{2} d n^{2} x^{3 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{24 a b^{2} d n x^{3 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{4 a b^{2} d x^{3 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{8 b^{3} c n^{3} x x^{3 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{12 b^{3} c n^{2} x x^{3 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{4 b^{3} c n x x^{3 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{6 b^{3} d n^{3} x^{4 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{11 b^{3} d n^{2} x^{4 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{6 b^{3} d n x^{4 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} + \frac{b^{3} d x^{4 n}}{24 n^{4} + 44 n^{3} + 24 n^{2} + 4 n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c*x - a**3*d/x + 3*a**2*b*c*log(x) - 3*a**2*b*d/(2*x**2) - 3*a*b**2*c/x - a*b**2*d/x**3 - b**3*c/(2*x**2) - b**3*d/(4*x**4), Eq(n, -1)), (a**3*c*x - 2*a**3*d/sqrt(x) + 6*a**2*b*c*sqrt(x) - 3*a**2*b*d/x + 3*a*b**2*c*log(x) - 2*a*b**2*d/x**(3/2) - 2*b**3*c/sqrt(x) - b**3*d/(2*x**2), Eq(n, -1/2)), (a**3*c*x - 3*a**3*d/x**(1/3) + 9*a**2*b*c*x**(2/3)/2 - 9*a**2*b*d/(2*x**(2/3)) + 9*a*b**2*c*x**(1/3) - 3*a*b**2*d/x + b**3*c*log(x) - 3*b**3*d/(4*x**(4/3)), Eq(n, -1/3)), ((a + b)**3*(c*x + d*log(x)), Eq(n, 0)), (24*a**3*c*n**4*x/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 44*a**3*c*n**3*x/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 24*a**3*c*n**2*x/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 4*a**3*c*n*x/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 24*a**3*d*n**3*x**n/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 44*a**3*d*n**2*x**n/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 24*a**3*d*n*x**n/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 4*a**3*d*x**n/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 72*a**2*b*c*n**3*x*x**n/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 60*a**2*b*c*n**2*x*x**n/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 12*a**2*b*c*n*x*x**n/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 36*a**2*b*d*n**3*x**(2*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 66*a**2*b*d*n**2*x**(2*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 36*a**2*b*d*n*x**(2*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 6*a**2*b*d*x**(2*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 36*a*b**2*c*n**3*x*x**(2*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 48*a*b**2*c*n**2*x*x**(2*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 12*a*b**2*c*n*x*x**(2*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 24*a*b**2*d*n**3*x**(3*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 44*a*b**2*d*n**2*x**(3*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 24*a*b**2*d*n*x**(3*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 4*a*b**2*d*x**(3*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 8*b**3*c*n**3*x*x**(3*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 12*b**3*c*n**2*x*x**(3*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 4*b**3*c*n*x*x**(3*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 6*b**3*d*n**3*x**(4*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 11*b**3*d*n**2*x**(4*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + 6*b**3*d*n*x**(4*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n) + b**3*d*x**(4*n)/(24*n**4 + 44*n**3 + 24*n**2 + 4*n), True))","A",0
578,1,552,0,4.268712," ","integrate((c+d*x**(-1+n))*(a+b*x**n)**2,x)","\begin{cases} a^{2} c x - \frac{a^{2} d}{x} + 2 a b c \log{\left(x \right)} - \frac{a b d}{x^{2}} - \frac{b^{2} c}{x} - \frac{b^{2} d}{3 x^{3}} & \text{for}\: n = -1 \\a^{2} c x - \frac{2 a^{2} d}{\sqrt{x}} + 4 a b c \sqrt{x} - \frac{2 a b d}{x} + b^{2} c \log{\left(x \right)} - \frac{2 b^{2} d}{3 x^{\frac{3}{2}}} & \text{for}\: n = - \frac{1}{2} \\\left(a + b\right)^{2} \left(c x + d \log{\left(x \right)}\right) & \text{for}\: n = 0 \\\frac{6 a^{2} c n^{3} x}{6 n^{3} + 9 n^{2} + 3 n} + \frac{9 a^{2} c n^{2} x}{6 n^{3} + 9 n^{2} + 3 n} + \frac{3 a^{2} c n x}{6 n^{3} + 9 n^{2} + 3 n} + \frac{6 a^{2} d n^{2} x^{n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{9 a^{2} d n x^{n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{3 a^{2} d x^{n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{12 a b c n^{2} x x^{n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{6 a b c n x x^{n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{6 a b d n^{2} x^{2 n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{9 a b d n x^{2 n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{3 a b d x^{2 n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{3 b^{2} c n^{2} x x^{2 n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{3 b^{2} c n x x^{2 n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{2 b^{2} d n^{2} x^{3 n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{3 b^{2} d n x^{3 n}}{6 n^{3} + 9 n^{2} + 3 n} + \frac{b^{2} d x^{3 n}}{6 n^{3} + 9 n^{2} + 3 n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x - a**2*d/x + 2*a*b*c*log(x) - a*b*d/x**2 - b**2*c/x - b**2*d/(3*x**3), Eq(n, -1)), (a**2*c*x - 2*a**2*d/sqrt(x) + 4*a*b*c*sqrt(x) - 2*a*b*d/x + b**2*c*log(x) - 2*b**2*d/(3*x**(3/2)), Eq(n, -1/2)), ((a + b)**2*(c*x + d*log(x)), Eq(n, 0)), (6*a**2*c*n**3*x/(6*n**3 + 9*n**2 + 3*n) + 9*a**2*c*n**2*x/(6*n**3 + 9*n**2 + 3*n) + 3*a**2*c*n*x/(6*n**3 + 9*n**2 + 3*n) + 6*a**2*d*n**2*x**n/(6*n**3 + 9*n**2 + 3*n) + 9*a**2*d*n*x**n/(6*n**3 + 9*n**2 + 3*n) + 3*a**2*d*x**n/(6*n**3 + 9*n**2 + 3*n) + 12*a*b*c*n**2*x*x**n/(6*n**3 + 9*n**2 + 3*n) + 6*a*b*c*n*x*x**n/(6*n**3 + 9*n**2 + 3*n) + 6*a*b*d*n**2*x**(2*n)/(6*n**3 + 9*n**2 + 3*n) + 9*a*b*d*n*x**(2*n)/(6*n**3 + 9*n**2 + 3*n) + 3*a*b*d*x**(2*n)/(6*n**3 + 9*n**2 + 3*n) + 3*b**2*c*n**2*x*x**(2*n)/(6*n**3 + 9*n**2 + 3*n) + 3*b**2*c*n*x*x**(2*n)/(6*n**3 + 9*n**2 + 3*n) + 2*b**2*d*n**2*x**(3*n)/(6*n**3 + 9*n**2 + 3*n) + 3*b**2*d*n*x**(3*n)/(6*n**3 + 9*n**2 + 3*n) + b**2*d*x**(3*n)/(6*n**3 + 9*n**2 + 3*n), True))","A",0
579,1,163,0,2.026803," ","integrate((c+d*x**(-1+n))*(a+b*x**n),x)","\begin{cases} a c x - \frac{a d}{x} + b c \log{\left(x \right)} - \frac{b d}{2 x^{2}} & \text{for}\: n = -1 \\\left(a + b\right) \left(c x + d \log{\left(x \right)}\right) & \text{for}\: n = 0 \\\frac{2 a c n^{2} x}{2 n^{2} + 2 n} + \frac{2 a c n x}{2 n^{2} + 2 n} + \frac{2 a d n x^{n}}{2 n^{2} + 2 n} + \frac{2 a d x^{n}}{2 n^{2} + 2 n} + \frac{2 b c n x x^{n}}{2 n^{2} + 2 n} + \frac{b d n x^{2 n}}{2 n^{2} + 2 n} + \frac{b d x^{2 n}}{2 n^{2} + 2 n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*x - a*d/x + b*c*log(x) - b*d/(2*x**2), Eq(n, -1)), ((a + b)*(c*x + d*log(x)), Eq(n, 0)), (2*a*c*n**2*x/(2*n**2 + 2*n) + 2*a*c*n*x/(2*n**2 + 2*n) + 2*a*d*n*x**n/(2*n**2 + 2*n) + 2*a*d*x**n/(2*n**2 + 2*n) + 2*b*c*n*x*x**n/(2*n**2 + 2*n) + b*d*n*x**(2*n)/(2*n**2 + 2*n) + b*d*x**(2*n)/(2*n**2 + 2*n), True))","A",0
580,1,15,0,0.067200," ","integrate(c+d*x**(-1+n),x)","c x + d \left(\begin{cases} \frac{x^{n}}{n} & \text{for}\: n - 1 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right)"," ",0,"c*x + d*Piecewise((x**n/n, Ne(n - 1, -1)), (log(x), True))","A",0
581,1,65,0,17.153463," ","integrate((c+d*x**(-1+n))/(a+b*x**n),x)","d \left(\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b} & \text{for}\: n = 0 \\\frac{x^{n}}{a n} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + x^{n} \right)}}{b n} & \text{otherwise} \end{cases}\right) + \frac{c x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a n^{2} \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"d*Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b), Eq(n, 0)), (x**n/(a*n), Eq(b, 0)), (log(a/b + x**n)/(b*n), True)) + c*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*n**2*gamma(1 + 1/n))","A",0
582,1,299,0,51.151496," ","integrate((c+d*x**(-1+n))/(a+b*x**n)**2,x)","c \left(\frac{n x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{n x \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{x \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} + \frac{b n x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)} - \frac{b x x^{n} \Phi\left(\frac{b x^{n} e^{i \pi}}{a}, 1, \frac{1}{n}\right) \Gamma\left(\frac{1}{n}\right)}{a^{2} \left(a n^{3} \Gamma\left(1 + \frac{1}{n}\right) + b n^{3} x^{n} \Gamma\left(1 + \frac{1}{n}\right)\right)}\right) + d \left(\begin{cases} \frac{\log{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \wedge n = 0 \\\frac{x^{n}}{a^{2} n} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{\left(a + b\right)^{2}} & \text{for}\: n = 0 \\- \frac{1}{a b n + b^{2} n x^{n}} & \text{otherwise} \end{cases}\right)"," ",0,"c*(n*x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) + n*x*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) - x*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) + b*n*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n))) - b*x*x**n*lerchphi(b*x**n*exp_polar(I*pi)/a, 1, 1/n)*gamma(1/n)/(a**2*(a*n**3*gamma(1 + 1/n) + b*n**3*x**n*gamma(1 + 1/n)))) + d*Piecewise((log(x)/a**2, Eq(b, 0) & Eq(n, 0)), (x**n/(a**2*n), Eq(b, 0)), (log(x)/(a + b)**2, Eq(n, 0)), (-1/(a*b*n + b**2*n*x**n), True))","C",0
583,-1,0,0,0.000000," ","integrate((c+d*x**(-1+n))/(a+b*x**n)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,1,274,0,55.355913," ","integrate((c*x)**m*(d+e*x**n+f*x**(2*n)+g*x**(3*n))/(a+b*x**n)**(1/2),x)","\frac{c^{m} d x x^{m} \Gamma\left(\frac{m}{n} + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} + \frac{1}{n} \\ \frac{m}{n} + 1 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right)} + \frac{c^{m} e x x^{m} x^{n} \Gamma\left(\frac{m}{n} + 1 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} + 1 + \frac{1}{n} \\ \frac{m}{n} + 2 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right)} + \frac{c^{m} f x x^{m} x^{2 n} \Gamma\left(\frac{m}{n} + 2 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} + 2 + \frac{1}{n} \\ \frac{m}{n} + 3 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 3 + \frac{1}{n}\right)} + \frac{c^{m} g x x^{m} x^{3 n} \Gamma\left(\frac{m}{n} + 3 + \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{n} + 3 + \frac{1}{n} \\ \frac{m}{n} + 4 + \frac{1}{n} \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 4 + \frac{1}{n}\right)}"," ",0,"c**m*d*x*x**m*gamma(m/n + 1/n)*hyper((1/2, m/n + 1/n), (m/n + 1 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 1 + 1/n)) + c**m*e*x*x**m*x**n*gamma(m/n + 1 + 1/n)*hyper((1/2, m/n + 1 + 1/n), (m/n + 2 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 2 + 1/n)) + c**m*f*x*x**m*x**(2*n)*gamma(m/n + 2 + 1/n)*hyper((1/2, m/n + 2 + 1/n), (m/n + 3 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 3 + 1/n)) + c**m*g*x*x**m*x**(3*n)*gamma(m/n + 3 + 1/n)*hyper((1/2, m/n + 3 + 1/n), (m/n + 4 + 1/n,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 4 + 1/n))","C",0
585,-1,0,0,0.000000," ","integrate((-a*h*x**(-1+1/4*n)+b*f*x**(-1+1/2*n)+b*g*x**(-1+n)+b*h*x**(-1+5/4*n))/(a+b*x**n)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((c*x)**m*(g*x**3+f*x**2+e*x+d)*(a+b*x**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate((c*x)**m*(a+b*x**n)**p*(d+e*x**n+f*x**(2*n)+g*x**(3*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((c+d*x**(1/2*n)+e*x**n+f*x**(3/2*n))/(a+b*x**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,0,0,0,0.000000," ","integrate((a*c+2*(a*d+b*c)*x**2+3*b*d*x**4)/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{a c + 2 a d x^{2} + 2 b c x^{2} + 3 b d x^{4}}{\sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a*c + 2*a*d*x**2 + 2*b*c*x**2 + 3*b*d*x**4)/(sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
590,0,0,0,0.000000," ","integrate((x**3+1)/(-x**4+1)/(x**4+1)**(1/4),x)","- \int \left(- \frac{x}{x^{3} \sqrt[4]{x^{4} + 1} - x^{2} \sqrt[4]{x^{4} + 1} + x \sqrt[4]{x^{4} + 1} - \sqrt[4]{x^{4} + 1}}\right)\, dx - \int \frac{x^{2}}{x^{3} \sqrt[4]{x^{4} + 1} - x^{2} \sqrt[4]{x^{4} + 1} + x \sqrt[4]{x^{4} + 1} - \sqrt[4]{x^{4} + 1}}\, dx - \int \frac{1}{x^{3} \sqrt[4]{x^{4} + 1} - x^{2} \sqrt[4]{x^{4} + 1} + x \sqrt[4]{x^{4} + 1} - \sqrt[4]{x^{4} + 1}}\, dx"," ",0,"-Integral(-x/(x**3*(x**4 + 1)**(1/4) - x**2*(x**4 + 1)**(1/4) + x*(x**4 + 1)**(1/4) - (x**4 + 1)**(1/4)), x) - Integral(x**2/(x**3*(x**4 + 1)**(1/4) - x**2*(x**4 + 1)**(1/4) + x*(x**4 + 1)**(1/4) - (x**4 + 1)**(1/4)), x) - Integral(1/(x**3*(x**4 + 1)**(1/4) - x**2*(x**4 + 1)**(1/4) + x*(x**4 + 1)**(1/4) - (x**4 + 1)**(1/4)), x)","F",0
591,-1,0,0,0.000000," ","integrate((a+b*x**n)**((-1-n)/n)*(c+d*x**n)**((-1-n)/n)*(a*c-b*d*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate((h*x)**(-n*p-n-1)*(a+b*x**n)**p*(c+d*x**n)**p*(a*c-b*d*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-2,0,0,0.000000," ","integrate((a+b*x**n)**p*(c+d*x**n)**p*(e+(a*d+b*c)*e*(n*p+n+1)*x**n/a/c+b*d*e*(2*n*p+2*n+1)*x**(2*n)/a/c),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
594,-1,0,0,0.000000," ","integrate((h*x)**m*(a+b*x**n)**p*(c+d*x**n)**p*(e+(a*d+b*c)*e*(n*p+m+n+1)*x**n/a/c/(1+m)+b*d*e*(2*n*p+m+2*n+1)*x**(2*n)/a/c/(1+m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
