1,1,12,0,0.061801," ","integrate(1/(-a*x+1)**(1/2),x)","- \frac{2 \sqrt{- a x + 1}}{a}"," ",0,"-2*sqrt(-a*x + 1)/a","A",0
2,1,42,0,59.577315," ","integrate(1/2*(ln(a*x-1)-2*ln(-(a*x-1)**(1/2)))/pi/(a*x-1)**(1/2),x)","\frac{\begin{cases} \frac{- 2 \sqrt{a x - 1} \log{\left(- \sqrt{a x - 1} \right)} + \sqrt{a x - 1} \log{\left(a x - 1 \right)}}{a} & \text{for}\: a \neq 0 \\\pi x & \text{otherwise} \end{cases}}{\pi}"," ",0,"Piecewise(((-2*sqrt(a*x - 1)*log(-sqrt(a*x - 1)) + sqrt(a*x - 1)*log(a*x - 1))/a, Ne(a, 0)), (pi*x, True))/pi","A",0
3,0,0,0,0.000000," ","integrate(1/(2*x+(x**2+1)**(1/2))**2,x)","\int \frac{1}{\left(2 x + \sqrt{x^{2} + 1}\right)^{2}}\, dx"," ",0,"Integral((2*x + sqrt(x**2 + 1))**(-2), x)","F",0
4,0,0,0,0.000000," ","integrate(1/(3*x**2-4)**2/(x**2-1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \left(3 x^{2} - 4\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)*(x + 1))*(3*x**2 - 4)**2), x)","F",0
5,0,0,0,0.000000," ","integrate(1/(2*x**(1/2)+(1+x)**(1/2))**2,x)","\int \frac{1}{\left(2 \sqrt{x} + \sqrt{x + 1}\right)^{2}}\, dx"," ",0,"Integral((2*sqrt(x) + sqrt(x + 1))**(-2), x)","F",0
6,0,0,0,0.000000," ","integrate((x**2-1)**(1/2)/(-I+x)**2,x)","\int \frac{\sqrt{\left(x - 1\right) \left(x + 1\right)}}{\left(x - i\right)^{2}}\, dx"," ",0,"Integral(sqrt((x - 1)*(x + 1))/(x - I)**2, x)","F",0
7,0,0,0,0.000000," ","integrate(1/(x**2+1)**2/(x**2-1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)*(x + 1))*(x**2 + 1)**2), x)","F",0
8,1,53,0,0.753375," ","integrate(1/(-1+x)**(1/2)/((-1+x)**(1/2)+x**(1/2))**2,x)","- \frac{4 \sqrt{x}}{6 \sqrt{x} \sqrt{x - 1} + 6 x - 3} - \frac{2 \sqrt{x - 1}}{6 \sqrt{x} \sqrt{x - 1} + 6 x - 3}"," ",0,"-4*sqrt(x)/(6*sqrt(x)*sqrt(x - 1) + 6*x - 3) - 2*sqrt(x - 1)/(6*sqrt(x)*sqrt(x - 1) + 6*x - 3)","B",0
9,0,0,0,0.000000," ","integrate(1/(x**2-1)**(1/2)/(x**(1/2)+(x**2-1)**(1/2))**2,x)","\int \frac{1}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \left(\sqrt{x} + \sqrt{x^{2} - 1}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)*(x + 1))*(sqrt(x) + sqrt(x**2 - 1))**2), x)","F",0
10,-1,0,0,0.000000," ","integrate((x**(1/2)-(x**2-1)**(1/2))**2/(-x**2+x+1)**2/(x**2-1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
11,-2,0,0,0.000000," ","integrate(1/2/(1+x)**2*2**(1/2)/(-I+x**2)**(1/2)+1/2/(1+x)**2*2**(1/2)/(I+x**2)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
12,0,0,0,0.000000," ","integrate((x**2+(x**4+1)**(1/2))**(1/2)/(1+x)**2/(x**4+1)**(1/2),x)","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{\left(x + 1\right)^{2} \sqrt{x^{4} + 1}}\, dx"," ",0,"Integral(sqrt(x**2 + sqrt(x**4 + 1))/((x + 1)**2*sqrt(x**4 + 1)), x)","F",0
13,0,0,0,0.000000," ","integrate((x**2+(x**4+1)**(1/2))**(1/2)/(1+x)/(x**4+1)**(1/2),x)","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{\left(x + 1\right) \sqrt{x^{4} + 1}}\, dx"," ",0,"Integral(sqrt(x**2 + sqrt(x**4 + 1))/((x + 1)*sqrt(x**4 + 1)), x)","F",0
14,1,15,0,1.224713," ","integrate((x**2+(x**4+1)**(1/2))**(1/2)/(x**4+1)**(1/2),x)","\frac{{G_{3, 3}^{2, 2}\left(\begin{matrix} 1, 1 & \frac{1}{2} \\\frac{1}{4}, \frac{3}{4} & 0 \end{matrix} \middle| {x^{4}} \right)}}{4 \sqrt{\pi}}"," ",0,"meijerg(((1, 1), (1/2,)), ((1/4, 3/4), (0,)), x**4)/(4*sqrt(pi))","A",0
15,1,15,0,0.860117," ","integrate((-x**2+(x**4+1)**(1/2))**(1/2)/(x**4+1)**(1/2),x)","\frac{{G_{3, 3}^{2, 2}\left(\begin{matrix} \frac{1}{2}, 1 & 1 \\\frac{1}{4}, \frac{3}{4} & 0 \end{matrix} \middle| {x^{4}} \right)}}{4 \sqrt{\pi}}"," ",0,"meijerg(((1/2, 1), (1,)), ((1/4, 3/4), (0,)), x**4)/(4*sqrt(pi))","A",0
16,1,56,0,6.628913," ","integrate(((-1+x)**(3/2)+(1+x)**(3/2))/(-1+x)**(3/2)/(1+x)**(3/2),x)","- \frac{2 x \sqrt{x - 1}}{x^{2} - 1} - \frac{2 x \sqrt{x + 1}}{x^{2} - 1} - \frac{2 \sqrt{x - 1}}{x^{2} - 1} + \frac{2 \sqrt{x + 1}}{x^{2} - 1}"," ",0,"-2*x*sqrt(x - 1)/(x**2 - 1) - 2*x*sqrt(x + 1)/(x**2 - 1) - 2*sqrt(x - 1)/(x**2 - 1) + 2*sqrt(x + 1)/(x**2 - 1)","B",0
17,1,2147,0,3.533562," ","integrate((x+(x**2+a)**(1/2))**b,x)","\begin{cases} - \frac{a^{\frac{9}{2}} a^{\frac{b}{2}} b^{2} x \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{a^{\frac{9}{2}} a^{\frac{b}{2}} b x \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} - \frac{a^{\frac{7}{2}} a^{\frac{b}{2}} b^{2} x^{3} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{a^{\frac{7}{2}} a^{\frac{b}{2}} b x^{3} \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{2 a^{5} a^{\frac{b}{2}} b \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} - \frac{2 a^{5} a^{\frac{b}{2}} b \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} - \frac{2 a^{4} a^{\frac{b}{2}} b x^{2} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{4 a^{4} a^{\frac{b}{2}} b x^{2} \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} - \frac{2 a^{4} a^{\frac{b}{2}} b x^{2} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} - \frac{2 a^{4} a^{\frac{b}{2}} x^{2} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{2 a^{4} a^{\frac{b}{2}} x^{2} \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} - \frac{2 a^{3} a^{\frac{b}{2}} b x^{4} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{2 a^{3} a^{\frac{b}{2}} b x^{4} \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} - \frac{2 a^{3} a^{\frac{b}{2}} x^{4} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{2 a^{3} a^{\frac{b}{2}} x^{4} \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{9}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{b}{2}\right) + 2 a^{\frac{7}{2}} b^{2} x^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{b}{2}\right)} & \text{for}\: \left|{\frac{x^{2}}{a}}\right| > 1 \\- \frac{2 a^{\frac{5}{2}} a^{\frac{b}{2}} b x \sqrt{1 + \frac{x^{2}}{a}} \sinh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{5}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{a^{\frac{5}{2}} a^{\frac{b}{2}} b x \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{b}{2}\right)}{2 a^{\frac{5}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{b}{2}\right)} - \frac{2 a^{\frac{5}{2}} a^{\frac{b}{2}} x \sqrt{1 + \frac{x^{2}}{a}} \sinh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{5}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{b}{2}\right)} - \frac{a^{3} a^{\frac{b}{2}} b^{2} \sqrt{1 + \frac{x^{2}}{a}} \sinh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{b}{2}\right)}{2 a^{\frac{5}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{2 a^{3} a^{\frac{b}{2}} b \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{5}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{2 a^{2} a^{\frac{b}{2}} b x^{2} \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{5}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{b}{2}\right)} + \frac{2 a^{2} a^{\frac{b}{2}} x^{2} \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{2 a^{\frac{5}{2}} b^{2} \Gamma\left(1 - \frac{b}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{b}{2}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**(9/2)*a**(b/2)*b**2*x*sqrt(a/x**2 + 1)*sinh(b*asinh(x/sqrt(a)))*gamma(-b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) + a**(9/2)*a**(b/2)*b*x*cosh(b*asinh(x/sqrt(a)))*gamma(-b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) - a**(7/2)*a**(b/2)*b**2*x**3*sqrt(a/x**2 + 1)*sinh(b*asinh(x/sqrt(a)))*gamma(-b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) + a**(7/2)*a**(b/2)*b*x**3*cosh(b*asinh(x/sqrt(a)))*gamma(-b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) + 2*a**5*a**(b/2)*b*cosh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) - 2*a**5*a**(b/2)*b*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) - 2*a**4*a**(b/2)*b*x**2*sqrt(a/x**2 + 1)*sinh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) + 4*a**4*a**(b/2)*b*x**2*cosh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) - 2*a**4*a**(b/2)*b*x**2*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) - 2*a**4*a**(b/2)*x**2*sqrt(a/x**2 + 1)*sinh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) + 2*a**4*a**(b/2)*x**2*cosh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) - 2*a**3*a**(b/2)*b*x**4*sqrt(a/x**2 + 1)*sinh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) + 2*a**3*a**(b/2)*b*x**4*cosh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) - 2*a**3*a**(b/2)*x**4*sqrt(a/x**2 + 1)*sinh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)) + 2*a**3*a**(b/2)*x**4*cosh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(9/2)*b**2*gamma(1 - b/2) - 2*a**(9/2)*gamma(1 - b/2) + 2*a**(7/2)*b**2*x**2*gamma(1 - b/2) - 2*a**(7/2)*x**2*gamma(1 - b/2)), Abs(x**2/a) > 1), (-2*a**(5/2)*a**(b/2)*b*x*sqrt(1 + x**2/a)*sinh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(5/2)*b**2*gamma(1 - b/2) - 2*a**(5/2)*gamma(1 - b/2)) + a**(5/2)*a**(b/2)*b*x*cosh(b*asinh(x/sqrt(a)))*gamma(-b/2)/(2*a**(5/2)*b**2*gamma(1 - b/2) - 2*a**(5/2)*gamma(1 - b/2)) - 2*a**(5/2)*a**(b/2)*x*sqrt(1 + x**2/a)*sinh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(5/2)*b**2*gamma(1 - b/2) - 2*a**(5/2)*gamma(1 - b/2)) - a**3*a**(b/2)*b**2*sqrt(1 + x**2/a)*sinh(b*asinh(x/sqrt(a)))*gamma(-b/2)/(2*a**(5/2)*b**2*gamma(1 - b/2) - 2*a**(5/2)*gamma(1 - b/2)) + 2*a**3*a**(b/2)*b*cosh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(5/2)*b**2*gamma(1 - b/2) - 2*a**(5/2)*gamma(1 - b/2)) + 2*a**2*a**(b/2)*b*x**2*cosh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(5/2)*b**2*gamma(1 - b/2) - 2*a**(5/2)*gamma(1 - b/2)) + 2*a**2*a**(b/2)*x**2*cosh(b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - b/2)/(2*a**(5/2)*b**2*gamma(1 - b/2) - 2*a**(5/2)*gamma(1 - b/2)), True))","B",0
18,0,0,0,0.000000," ","integrate((x-(x**2+a)**(1/2))**b,x)","\int \left(x - \sqrt{a + x^{2}}\right)^{b}\, dx"," ",0,"Integral((x - sqrt(a + x**2))**b, x)","F",0
19,1,311,0,2.986373," ","integrate((x+(x**2+a)**(1/2))**b/(x**2+a)**(1/2),x)","\begin{cases} - \frac{\sqrt{a} a^{\frac{b}{2}} \sinh{\left(- b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{b x \sqrt{\frac{a}{x^{2}} + 1}} - \frac{2 a^{\frac{b}{2}} \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{b^{2} \Gamma\left(- \frac{b}{2}\right)} + \frac{a^{\frac{b}{2}} x \cosh{\left(- b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{\sqrt{a} b} - \frac{a^{\frac{b}{2}} x \sinh{\left(- b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{\sqrt{a} b \sqrt{\frac{a}{x^{2}} + 1}} & \text{for}\: \left|{\frac{x^{2}}{a}}\right| > 1 \\- \frac{a^{\frac{b}{2}} \sinh{\left(- b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{b \sqrt{1 + \frac{x^{2}}{a}}} - \frac{2 a^{\frac{b}{2}} \cosh{\left(b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{b}{2}\right)}{b^{2} \Gamma\left(- \frac{b}{2}\right)} - \frac{a^{\frac{b}{2}} x^{2} \sinh{\left(- b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{a b \sqrt{1 + \frac{x^{2}}{a}}} + \frac{a^{\frac{b}{2}} x \cosh{\left(- b \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{\sqrt{a} b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(a)*a**(b/2)*sinh(-b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(b*x*sqrt(a/x**2 + 1)) - 2*a**(b/2)*cosh(b*asinh(x/sqrt(a)))*gamma(1 - b/2)/(b**2*gamma(-b/2)) + a**(b/2)*x*cosh(-b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(sqrt(a)*b) - a**(b/2)*x*sinh(-b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(sqrt(a)*b*sqrt(a/x**2 + 1)), Abs(x**2/a) > 1), (-a**(b/2)*sinh(-b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(b*sqrt(1 + x**2/a)) - 2*a**(b/2)*cosh(b*asinh(x/sqrt(a)))*gamma(1 - b/2)/(b**2*gamma(-b/2)) - a**(b/2)*x**2*sinh(-b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(a*b*sqrt(1 + x**2/a)) + a**(b/2)*x*cosh(-b*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(sqrt(a)*b), True))","B",0
20,1,36,0,1.597864," ","integrate((x-(x**2+a)**(1/2))**b/(x**2+a)**(1/2),x)","\begin{cases} - \frac{\left(x - \sqrt{a + x^{2}}\right)^{b}}{b} & \text{for}\: b \neq 0 \\\begin{cases} \operatorname{asinh}{\left(x \sqrt{\frac{1}{a}} \right)} & \text{for}\: a > 0 \\\operatorname{acosh}{\left(x \sqrt{- \frac{1}{a}} \right)} & \text{for}\: a < 0 \end{cases} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(x - sqrt(a + x**2))**b/b, Ne(b, 0)), (Piecewise((asinh(x*sqrt(1/a)), a > 0), (acosh(x*sqrt(-1/a)), a < 0)), True))","A",0
21,1,36,0,0.147139," ","integrate(1/(a+b*exp(p*x))**2,x)","\frac{1}{a^{2} p + a b p e^{p x}} + \frac{x}{a^{2}} - \frac{\log{\left(\frac{a}{b} + e^{p x} \right)}}{a^{2} p}"," ",0,"1/(a**2*p + a*b*p*exp(p*x)) + x/a**2 - log(a/b + exp(p*x))/(a**2*p)","A",0
22,1,20,0,0.119632," ","integrate(1/(b/exp(p*x)+a*exp(p*x))**2,x)","\frac{1}{2 a b p + 2 b^{2} p e^{- 2 p x}}"," ",0,"1/(2*a*b*p + 2*b**2*p*exp(-2*p*x))","A",0
23,1,51,0,0.184952," ","integrate(x/(b/exp(p*x)+a*exp(p*x))**2,x)","\frac{x}{2 a b p + 2 b^{2} p e^{- 2 p x}} - \frac{x}{2 a b p} - \frac{\log{\left(\frac{a}{b} + e^{- 2 p x} \right)}}{4 a b p^{2}}"," ",0,"x/(2*a*b*p + 2*b**2*p*exp(-2*p*x)) - x/(2*a*b*p) - log(a/b + exp(-2*p*x))/(4*a*b*p**2)","A",0
24,0,0,0,0.000000," ","integrate((3*x**2-x+1)/(x**2+x+1)**2/(x**2-x+1)**(1/2),x)","\int \frac{3 x^{2} - x + 1}{\sqrt{x^{2} - x + 1} \left(x^{2} + x + 1\right)^{2}}\, dx"," ",0,"Integral((3*x**2 - x + 1)/(sqrt(x**2 - x + 1)*(x**2 + x + 1)**2), x)","F",0
25,1,15,0,0.230116," ","integrate((x+(a**2+x**2)**(1/2))**(1/2)/(a**2+x**2)**(1/2),x)","2 \sqrt{x + \sqrt{a^{2} + x^{2}}}"," ",0,"2*sqrt(x + sqrt(a**2 + x**2))","A",0
26,1,27,0,1.071514," ","integrate((b*x+(b**2*x**2+a)**(1/2))**(1/2)/(b**2*x**2+a)**(1/2),x)","\begin{cases} \frac{2 \sqrt{b x + \sqrt{a + b^{2} x^{2}}}}{b} & \text{for}\: b \neq 0 \\\frac{x}{\sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b*x + sqrt(a + b**2*x**2))/b, Ne(b, 0)), (x/a**(1/4), True))","A",0
27,1,46,0,1.469163," ","integrate(1/x/(a**2+x**2)**(1/2)/(x+(a**2+x**2)**(1/2))**(1/2),x)","- \frac{\Gamma^{2}\left(\frac{3}{4}\right) \Gamma\left(\frac{5}{4}\right) {{}_{3}F_{2}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4}, \frac{5}{4} \\ \frac{3}{2}, \frac{7}{4} \end{matrix}\middle| {\frac{a^{2} e^{i \pi}}{x^{2}}} \right)}}{\pi x^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-gamma(3/4)**2*gamma(5/4)*hyper((3/4, 3/4, 5/4), (3/2, 7/4), a**2*exp_polar(I*pi)/x**2)/(pi*x**(3/2)*gamma(7/4))","C",0
28,1,51,0,1.315661," ","integrate((x+(a**2+x**2)**(1/2))**(1/2)/x,x)","\frac{\sqrt{x} \Gamma^{2}\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right) {{}_{3}F_{2}\left(\begin{matrix} - \frac{1}{4}, - \frac{1}{4}, \frac{1}{4} \\ \frac{1}{2}, \frac{3}{4} \end{matrix}\middle| {\frac{a^{2} e^{i \pi}}{x^{2}}} \right)}}{8 \pi \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(x)*gamma(-1/4)**2*gamma(1/4)*hyper((-1/4, -1/4, 1/4), (1/2, 3/4), a**2*exp_polar(I*pi)/x**2)/(8*pi*gamma(3/4))","C",0
29,-1,0,0,0.000000," ","integrate(x**3*ln(2+x)**3*ln(3+x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,1,311,0,2.577218," ","integrate((x+(x**2+b)**(1/2))**a/(x**2+b)**(1/2),x)","\begin{cases} - \frac{\sqrt{b} b^{\frac{a}{2}} \sinh{\left(- a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)}}{a x \sqrt{\frac{b}{x^{2}} + 1}} + \frac{b^{\frac{a}{2}} x \cosh{\left(- a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)}}{a \sqrt{b}} - \frac{b^{\frac{a}{2}} x \sinh{\left(- a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)}}{a \sqrt{b} \sqrt{\frac{b}{x^{2}} + 1}} - \frac{2 b^{\frac{a}{2}} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{a^{2} \Gamma\left(- \frac{a}{2}\right)} & \text{for}\: \left|{\frac{x^{2}}{b}}\right| > 1 \\- \frac{b^{\frac{a}{2}} \sinh{\left(- a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)}}{a \sqrt{1 + \frac{x^{2}}{b}}} - \frac{b^{\frac{a}{2}} x^{2} \sinh{\left(- a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)}}{a b \sqrt{1 + \frac{x^{2}}{b}}} + \frac{b^{\frac{a}{2}} x \cosh{\left(- a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)}}{a \sqrt{b}} - \frac{2 b^{\frac{a}{2}} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{a^{2} \Gamma\left(- \frac{a}{2}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(b)*b**(a/2)*sinh(-a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))/(a*x*sqrt(b/x**2 + 1)) + b**(a/2)*x*cosh(-a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))/(a*sqrt(b)) - b**(a/2)*x*sinh(-a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))/(a*sqrt(b)*sqrt(b/x**2 + 1)) - 2*b**(a/2)*cosh(a*asinh(x/sqrt(b)))*gamma(1 - a/2)/(a**2*gamma(-a/2)), Abs(x**2/b) > 1), (-b**(a/2)*sinh(-a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))/(a*sqrt(1 + x**2/b)) - b**(a/2)*x**2*sinh(-a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))/(a*b*sqrt(1 + x**2/b)) + b**(a/2)*x*cosh(-a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))/(a*sqrt(b)) - 2*b**(a/2)*cosh(a*asinh(x/sqrt(b)))*gamma(1 - a/2)/(a**2*gamma(-a/2)), True))","B",0
31,1,2147,0,2.714685," ","integrate((x+(x**2+b)**(1/2))**a,x)","\begin{cases} - \frac{a^{2} b^{\frac{9}{2}} b^{\frac{a}{2}} x \sqrt{\frac{b}{x^{2}} + 1} \sinh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(- \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} - \frac{a^{2} b^{\frac{7}{2}} b^{\frac{a}{2}} x^{3} \sqrt{\frac{b}{x^{2}} + 1} \sinh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(- \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{a b^{\frac{9}{2}} b^{\frac{a}{2}} x \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(- \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{a b^{\frac{7}{2}} b^{\frac{a}{2}} x^{3} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(- \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{2 a b^{5} b^{\frac{a}{2}} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} - \frac{2 a b^{5} b^{\frac{a}{2}} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} - \frac{2 a b^{4} b^{\frac{a}{2}} x^{2} \sqrt{\frac{b}{x^{2}} + 1} \sinh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{4 a b^{4} b^{\frac{a}{2}} x^{2} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} - \frac{2 a b^{4} b^{\frac{a}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} - \frac{2 a b^{3} b^{\frac{a}{2}} x^{4} \sqrt{\frac{b}{x^{2}} + 1} \sinh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{2 a b^{3} b^{\frac{a}{2}} x^{4} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} - \frac{2 b^{4} b^{\frac{a}{2}} x^{2} \sqrt{\frac{b}{x^{2}} + 1} \sinh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{2 b^{4} b^{\frac{a}{2}} x^{2} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} - \frac{2 b^{3} b^{\frac{a}{2}} x^{4} \sqrt{\frac{b}{x^{2}} + 1} \sinh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{2 b^{3} b^{\frac{a}{2}} x^{4} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) + 2 a^{2} b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{9}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{a}{2}\right)} & \text{for}\: \left|{\frac{x^{2}}{b}}\right| > 1 \\- \frac{a^{2} b^{3} b^{\frac{a}{2}} \sqrt{1 + \frac{x^{2}}{b}} \sinh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(- \frac{a}{2}\right)}{2 a^{2} b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right)} - \frac{2 a b^{\frac{5}{2}} b^{\frac{a}{2}} x \sqrt{1 + \frac{x^{2}}{b}} \sinh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{a b^{\frac{5}{2}} b^{\frac{a}{2}} x \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(- \frac{a}{2}\right)}{2 a^{2} b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{2 a b^{3} b^{\frac{a}{2}} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{2 a b^{2} b^{\frac{a}{2}} x^{2} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right)} - \frac{2 b^{\frac{5}{2}} b^{\frac{a}{2}} x \sqrt{1 + \frac{x^{2}}{b}} \sinh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right)} + \frac{2 b^{2} b^{\frac{a}{2}} x^{2} \cosh{\left(a \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{b}} \right)} \right)} \Gamma\left(1 - \frac{a}{2}\right)}{2 a^{2} b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right) - 2 b^{\frac{5}{2}} \Gamma\left(1 - \frac{a}{2}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*b**(9/2)*b**(a/2)*x*sqrt(b/x**2 + 1)*sinh(a*asinh(x/sqrt(b)))*gamma(-a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) - a**2*b**(7/2)*b**(a/2)*x**3*sqrt(b/x**2 + 1)*sinh(a*asinh(x/sqrt(b)))*gamma(-a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) + a*b**(9/2)*b**(a/2)*x*cosh(a*asinh(x/sqrt(b)))*gamma(-a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) + a*b**(7/2)*b**(a/2)*x**3*cosh(a*asinh(x/sqrt(b)))*gamma(-a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) + 2*a*b**5*b**(a/2)*cosh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) - 2*a*b**5*b**(a/2)*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) - 2*a*b**4*b**(a/2)*x**2*sqrt(b/x**2 + 1)*sinh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) + 4*a*b**4*b**(a/2)*x**2*cosh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) - 2*a*b**4*b**(a/2)*x**2*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) - 2*a*b**3*b**(a/2)*x**4*sqrt(b/x**2 + 1)*sinh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) + 2*a*b**3*b**(a/2)*x**4*cosh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) - 2*b**4*b**(a/2)*x**2*sqrt(b/x**2 + 1)*sinh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) + 2*b**4*b**(a/2)*x**2*cosh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) - 2*b**3*b**(a/2)*x**4*sqrt(b/x**2 + 1)*sinh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)) + 2*b**3*b**(a/2)*x**4*cosh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(9/2)*gamma(1 - a/2) + 2*a**2*b**(7/2)*x**2*gamma(1 - a/2) - 2*b**(9/2)*gamma(1 - a/2) - 2*b**(7/2)*x**2*gamma(1 - a/2)), Abs(x**2/b) > 1), (-a**2*b**3*b**(a/2)*sqrt(1 + x**2/b)*sinh(a*asinh(x/sqrt(b)))*gamma(-a/2)/(2*a**2*b**(5/2)*gamma(1 - a/2) - 2*b**(5/2)*gamma(1 - a/2)) - 2*a*b**(5/2)*b**(a/2)*x*sqrt(1 + x**2/b)*sinh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(5/2)*gamma(1 - a/2) - 2*b**(5/2)*gamma(1 - a/2)) + a*b**(5/2)*b**(a/2)*x*cosh(a*asinh(x/sqrt(b)))*gamma(-a/2)/(2*a**2*b**(5/2)*gamma(1 - a/2) - 2*b**(5/2)*gamma(1 - a/2)) + 2*a*b**3*b**(a/2)*cosh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(5/2)*gamma(1 - a/2) - 2*b**(5/2)*gamma(1 - a/2)) + 2*a*b**2*b**(a/2)*x**2*cosh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(5/2)*gamma(1 - a/2) - 2*b**(5/2)*gamma(1 - a/2)) - 2*b**(5/2)*b**(a/2)*x*sqrt(1 + x**2/b)*sinh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(5/2)*gamma(1 - a/2) - 2*b**(5/2)*gamma(1 - a/2)) + 2*b**2*b**(a/2)*x**2*cosh(a*asinh(x/sqrt(b)) + asinh(x/sqrt(b)))*gamma(1 - a/2)/(2*a**2*b**(5/2)*gamma(1 - a/2) - 2*b**(5/2)*gamma(1 - a/2)), True))","B",0
32,-1,0,0,0.000000," ","integrate((6+3*x**a+2*x**(2*a))**(1/a)*(x**a+x**(2*a)+x**(3*a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,1,36,0,0.944153," ","integrate(1/x/(-x**2+1)**(1/3),x)","- \frac{e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1}{x^{2}}} \right)}}{2 x^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-exp(-I*pi/3)*gamma(1/3)*hyper((1/3, 1/3), (4/3,), x**(-2))/(2*x**(2/3)*gamma(4/3))","C",0
34,1,37,0,0.977080," ","integrate(1/x/(-x**2+1)**(2/3),x)","- \frac{e^{- \frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{1}{x^{2}}} \right)}}{2 x^{\frac{4}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-exp(-2*I*pi/3)*gamma(2/3)*hyper((2/3, 2/3), (5/3,), x**(-2))/(2*x**(4/3)*gamma(5/3))","C",0
35,1,29,0,0.892619," ","integrate(1/(-x**3+1)**(1/3),x)","\frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3))","C",0
36,1,32,0,0.918914," ","integrate(1/x/(-x**3+1)**(1/3),x)","- \frac{e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1}{x^{3}}} \right)}}{3 x \Gamma\left(\frac{4}{3}\right)}"," ",0,"-exp(-I*pi/3)*gamma(1/3)*hyper((1/3, 1/3), (4/3,), x**(-3))/(3*x*gamma(4/3))","C",0
37,0,0,0,0.000000," ","integrate(1/(1+x)/(-x**3+1)**(1/3),x)","\int \frac{1}{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 1\right)}\, dx"," ",0,"Integral(1/((-(x - 1)*(x**2 + x + 1))**(1/3)*(x + 1)), x)","F",0
38,0,0,0,0.000000," ","integrate(x/(1+x)/(-x**3+1)**(1/3),x)","\int \frac{x}{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 1\right)}\, dx"," ",0,"Integral(x/((-(x - 1)*(x**2 + x + 1))**(1/3)*(x + 1)), x)","F",0
39,0,0,0,0.000000," ","integrate(1/x/(x**2-3*x+2)**(1/3),x)","\int \frac{1}{x \sqrt[3]{\left(x - 2\right) \left(x - 1\right)}}\, dx"," ",0,"Integral(1/(x*((x - 2)*(x - 1))**(1/3)), x)","F",0
40,0,0,0,0.000000," ","integrate(1/(x**3-3*x**2+7*x-5)**(1/3),x)","\int \frac{1}{\sqrt[3]{x^{3} - 3 x^{2} + 7 x - 5}}\, dx"," ",0,"Integral((x**3 - 3*x**2 + 7*x - 5)**(-1/3), x)","F",0
41,0,0,0,0.000000," ","integrate(1/(x*(x**2-q))**(1/3),x)","\int \frac{1}{\sqrt[3]{x \left(- q + x^{2}\right)}}\, dx"," ",0,"Integral((x*(-q + x**2))**(-1/3), x)","F",0
42,0,0,0,0.000000," ","integrate(1/((-1+x)*(x**2+q-2*x))**(1/3),x)","\int \frac{1}{\sqrt[3]{\left(x - 1\right) \left(q + x^{2} - 2 x\right)}}\, dx"," ",0,"Integral(((x - 1)*(q + x**2 - 2*x))**(-1/3), x)","F",0
43,-1,0,0,0.000000," ","integrate(1/x/((-1+x)*(-2*q*x+x**2+q))**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,0,0,0,0.000000," ","integrate((2-(1+k)*x)/((1-x)*x*(-k*x+1))**(1/3)/(1-(1+k)*x),x)","\int \frac{k x + x - 2}{\sqrt[3]{x \left(x - 1\right) \left(k x - 1\right)} \left(k x + x - 1\right)}\, dx"," ",0,"Integral((k*x + x - 2)/((x*(x - 1)*(k*x - 1))**(1/3)*(k*x + x - 1)), x)","F",0
45,0,0,0,0.000000," ","integrate((-k*x+1)/(1+(-2+k)*x)/((1-x)*x*(-k*x+1))**(2/3),x)","- \int \frac{k x}{k x \left(k x^{3} - k x^{2} - x^{2} + x\right)^{\frac{2}{3}} - 2 x \left(k x^{3} - k x^{2} - x^{2} + x\right)^{\frac{2}{3}} + \left(k x^{3} - k x^{2} - x^{2} + x\right)^{\frac{2}{3}}}\, dx - \int \left(- \frac{1}{k x \left(k x^{3} - k x^{2} - x^{2} + x\right)^{\frac{2}{3}} - 2 x \left(k x^{3} - k x^{2} - x^{2} + x\right)^{\frac{2}{3}} + \left(k x^{3} - k x^{2} - x^{2} + x\right)^{\frac{2}{3}}}\right)\, dx"," ",0,"-Integral(k*x/(k*x*(k*x**3 - k*x**2 - x**2 + x)**(2/3) - 2*x*(k*x**3 - k*x**2 - x**2 + x)**(2/3) + (k*x**3 - k*x**2 - x**2 + x)**(2/3)), x) - Integral(-1/(k*x*(k*x**3 - k*x**2 - x**2 + x)**(2/3) - 2*x*(k*x**3 - k*x**2 - x**2 + x)**(2/3) + (k*x**3 - k*x**2 - x**2 + x)**(2/3)), x)","F",0
46,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(x**2-x+1)/(-x**3+1)**(1/3),x)","\int \frac{a + b x + c x^{2}}{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x^{2} - x + 1\right)}\, dx"," ",0,"Integral((a + b*x + c*x**2)/((-(x - 1)*(x**2 + x + 1))**(1/3)*(x**2 - x + 1)), x)","F",0
47,-1,0,0,0.000000," ","integrate(1/(3-2*x)**(11/2)/(2*x**2+x+1)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate(1/(3-2*x)**(21/2)/(2*x**2+x+1)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate(1/(3-2*x)**(41/2)/(2*x**2+x+1)**20,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(1/(x**2-2*x+3)**(11/2)/(2*x**2+x+1)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(1/(x**2-2*x+3)**(21/2)/(2*x**2+x+1)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate((-a+x-(a**2+1)**(1/2))/(-a+x+(a**2+1)**(1/2))/((-a+x)*(x**2+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,0,0,0,0.000000," ","integrate((b*x+a)/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{a + b x}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral((a + b*x)/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
54,0,0,0,0.000000," ","integrate((b*x+a)/(-x**2+3)/(x**2+1)**(1/3),x)","- \int \frac{a}{x^{2} \sqrt[3]{x^{2} + 1} - 3 \sqrt[3]{x^{2} + 1}}\, dx - \int \frac{b x}{x^{2} \sqrt[3]{x^{2} + 1} - 3 \sqrt[3]{x^{2} + 1}}\, dx"," ",0,"-Integral(a/(x**2*(x**2 + 1)**(1/3) - 3*(x**2 + 1)**(1/3)), x) - Integral(b*x/(x**2*(x**2 + 1)**(1/3) - 3*(x**2 + 1)**(1/3)), x)","F",0
55,0,0,0,0.000000," ","integrate(1/x/(3*x**2-6*x+4)**(1/3),x)","\int \frac{1}{x \sqrt[3]{3 x^{2} - 6 x + 4}}\, dx"," ",0,"Integral(1/(x*(3*x**2 - 6*x + 4)**(1/3)), x)","F",0
56,1,32,0,1.022007," ","integrate(x*(-x**3+1)**(1/3),x)","\frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"x**2*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), x**3*exp_polar(2*I*pi))/(3*gamma(5/3))","C",0
57,1,37,0,0.985827," ","integrate((-x**3+1)**(1/3)/x,x)","- \frac{x e^{\frac{i \pi}{3}} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{1}{x^{3}}} \right)}}{3 \Gamma\left(\frac{2}{3}\right)}"," ",0,"-x*exp(I*pi/3)*gamma(-1/3)*hyper((-1/3, -1/3), (2/3,), x**(-3))/(3*gamma(2/3))","C",0
58,0,0,0,0.000000," ","integrate((-x**3+1)**(1/3)/(1+x),x)","\int \frac{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)}}{x + 1}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(1/3)/(x + 1), x)","F",0
59,0,0,0,0.000000," ","integrate((-x**3+1)**(1/3)/(x**2-x+1),x)","\int \frac{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)}}{x^{2} - x + 1}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(1/3)/(x**2 - x + 1), x)","F",0
60,0,0,0,0.000000," ","integrate((-x**3+1)**(1/3)/(2+x),x)","\int \frac{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)}}{x + 2}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(1/3)/(x + 2), x)","F",0
61,0,0,0,0.000000," ","integrate((2+x)/(x**2+x+1)/(x**3+2)**(1/3),x)","\int \frac{x + 2}{\sqrt[3]{x^{3} + 2} \left(x^{2} + x + 1\right)}\, dx"," ",0,"Integral((x + 2)/((x**3 + 2)**(1/3)*(x**2 + x + 1)), x)","F",0
62,1,22,0,0.106080," ","integrate((160*x**3+30*x**2-3*x+3)/(320*x**4+80*x**3-12*x**2+24*x+9),x)","\frac{\log{\left(320 x^{4} + 80 x^{3} - 12 x^{2} + 24 x + 9 \right)}}{8}"," ",0,"log(320*x**4 + 80*x**3 - 12*x**2 + 24*x + 9)/8","A",0
63,1,73,0,0.171824," ","integrate((20*x**2+12*x+3)/(320*x**4+80*x**3-12*x**2+24*x+9),x)","\frac{\sqrt{11} \left(2 \operatorname{atan}{\left(\frac{8 \sqrt{11} x}{11} - \frac{7 \sqrt{11}}{55} \right)} + 2 \operatorname{atan}{\left(\frac{400 \sqrt{11} x^{3}}{33} - \frac{20 \sqrt{11} x^{2}}{33} + \frac{5 \sqrt{11} x}{11} + \frac{19 \sqrt{11}}{22} \right)}\right)}{44}"," ",0,"sqrt(11)*(2*atan(8*sqrt(11)*x/11 - 7*sqrt(11)/55) + 2*atan(400*sqrt(11)*x**3/33 - 20*sqrt(11)*x**2/33 + 5*sqrt(11)*x/11 + 19*sqrt(11)/22))/44","A",0
64,1,100,0,0.183731," ","integrate((2560*x**3-400*x**2-576*x-84)/(320*x**4+80*x**3-12*x**2+24*x+9),x)","\sqrt{11} \left(- 2 \operatorname{atan}{\left(\frac{8 \sqrt{11} x}{11} - \frac{7 \sqrt{11}}{55} \right)} - 2 \operatorname{atan}{\left(\frac{400 \sqrt{11} x^{3}}{33} - \frac{20 \sqrt{11} x^{2}}{33} + \frac{5 \sqrt{11} x}{11} + \frac{19 \sqrt{11}}{22} \right)}\right) + 2 \log{\left(x^{4} + \frac{x^{3}}{4} - \frac{3 x^{2}}{80} + \frac{3 x}{40} + \frac{9}{320} \right)}"," ",0,"sqrt(11)*(-2*atan(8*sqrt(11)*x/11 - 7*sqrt(11)/55) - 2*atan(400*sqrt(11)*x**3/33 - 20*sqrt(11)*x**2/33 + 5*sqrt(11)*x/11 + 19*sqrt(11)/22)) + 2*log(x**4 + x**3/4 - 3*x**2/80 + 3*x/40 + 9/320)","A",0
65,0,0,0,0.000000," ","integrate((-x**4+1)**(1/2)/(x**4+1),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)}}{x^{4} + 1}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1)*(x**2 + 1))/(x**4 + 1), x)","F",0
66,0,0,0,0.000000," ","integrate((x**4+1)**(1/2)/(-x**4+1),x)","- \int \frac{\sqrt{x^{4} + 1}}{x^{4} - 1}\, dx"," ",0,"-Integral(sqrt(x**4 + 1)/(x**4 - 1), x)","F",0
67,0,0,0,0.000000," ","integrate((x**4+p*x**2+1)**(1/2)/(-x**4+1),x)","- \int \frac{\sqrt{p x^{2} + x^{4} + 1}}{x^{4} - 1}\, dx"," ",0,"-Integral(sqrt(p*x**2 + x**4 + 1)/(x**4 - 1), x)","F",0
68,0,0,0,0.000000," ","integrate((-x**4+p*x**2+1)**(1/2)/(x**4+1),x)","\int \frac{\sqrt{p x^{2} - x^{4} + 1}}{x^{4} + 1}\, dx"," ",0,"Integral(sqrt(p*x**2 - x**4 + 1)/(x**4 + 1), x)","F",0
69,0,0,0,0.000000," ","integrate((b*x+a)/(-x**2+2)/(x**2-1)**(1/4),x)","- \int \frac{a}{x^{2} \sqrt[4]{x^{2} - 1} - 2 \sqrt[4]{x^{2} - 1}}\, dx - \int \frac{b x}{x^{2} \sqrt[4]{x^{2} - 1} - 2 \sqrt[4]{x^{2} - 1}}\, dx"," ",0,"-Integral(a/(x**2*(x**2 - 1)**(1/4) - 2*(x**2 - 1)**(1/4)), x) - Integral(b*x/(x**2*(x**2 - 1)**(1/4) - 2*(x**2 - 1)**(1/4)), x)","F",0
70,0,0,0,0.000000," ","integrate((b*x+a)/(-x**2-1)**(1/4)/(x**2+2),x)","\int \frac{a + b x}{\sqrt[4]{- x^{2} - 1} \left(x^{2} + 2\right)}\, dx"," ",0,"Integral((a + b*x)/((-x**2 - 1)**(1/4)*(x**2 + 2)), x)","F",0
71,0,0,0,0.000000," ","integrate((b*x+a)/(-x**2+1)**(1/4)/(-x**2+2),x)","- \int \frac{a}{x^{2} \sqrt[4]{1 - x^{2}} - 2 \sqrt[4]{1 - x^{2}}}\, dx - \int \frac{b x}{x^{2} \sqrt[4]{1 - x^{2}} - 2 \sqrt[4]{1 - x^{2}}}\, dx"," ",0,"-Integral(a/(x**2*(1 - x**2)**(1/4) - 2*(1 - x**2)**(1/4)), x) - Integral(b*x/(x**2*(1 - x**2)**(1/4) - 2*(1 - x**2)**(1/4)), x)","F",0
72,0,0,0,0.000000," ","integrate((b*x+a)/(x**2+1)**(1/4)/(x**2+2),x)","\int \frac{a + b x}{\sqrt[4]{x^{2} + 1} \left(x^{2} + 2\right)}\, dx"," ",0,"Integral((a + b*x)/((x**2 + 1)**(1/4)*(x**2 + 2)), x)","F",0
73,0,0,0,0.000000," ","integrate(x/(-x**3+4)/(-x**3+1)**(1/2),x)","- \int \frac{x}{x^{3} \sqrt{1 - x^{3}} - 4 \sqrt{1 - x^{3}}}\, dx"," ",0,"-Integral(x/(x**3*sqrt(1 - x**3) - 4*sqrt(1 - x**3)), x)","F",0
74,0,0,0,0.000000," ","integrate(x/(-d*x**3+4)/(d*x**3-1)**(1/2),x)","- \int \frac{x}{d x^{3} \sqrt{d x^{3} - 1} - 4 \sqrt{d x^{3} - 1}}\, dx"," ",0,"-Integral(x/(d*x**3*sqrt(d*x**3 - 1) - 4*sqrt(d*x**3 - 1)), x)","F",0
75,0,0,0,0.000000," ","integrate(x/(x**3+8)/(x**3-1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 2\right) \left(x^{2} - 2 x + 4\right)}\, dx"," ",0,"Integral(x/(sqrt((x - 1)*(x**2 + x + 1))*(x + 2)*(x**2 - 2*x + 4)), x)","F",0
76,0,0,0,0.000000," ","integrate(x/(-d*x**3+8)/(d*x**3+1)**(1/2),x)","- \int \frac{x}{d x^{3} \sqrt{d x^{3} + 1} - 8 \sqrt{d x^{3} + 1}}\, dx"," ",0,"-Integral(x/(d*x**3*sqrt(d*x**3 + 1) - 8*sqrt(d*x**3 + 1)), x)","F",0
77,0,0,0,0.000000," ","integrate(1/(-3*x**2+1)**(1/3)/(-x**2+3),x)","- \int \frac{1}{x^{2} \sqrt[3]{1 - 3 x^{2}} - 3 \sqrt[3]{1 - 3 x^{2}}}\, dx"," ",0,"-Integral(1/(x**2*(1 - 3*x**2)**(1/3) - 3*(1 - 3*x**2)**(1/3)), x)","F",0
78,0,0,0,0.000000," ","integrate(1/(x**2+3)/(3*x**2+1)**(1/3),x)","\int \frac{1}{\left(x^{2} + 3\right) \sqrt[3]{3 x^{2} + 1}}\, dx"," ",0,"Integral(1/((x**2 + 3)*(3*x**2 + 1)**(1/3)), x)","F",0
79,0,0,0,0.000000," ","integrate(1/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{1}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(1/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
80,0,0,0,0.000000," ","integrate(1/(-x**2+3)/(x**2+1)**(1/3),x)","- \int \frac{1}{x^{2} \sqrt[3]{x^{2} + 1} - 3 \sqrt[3]{x^{2} + 1}}\, dx"," ",0,"-Integral(1/(x**2*(x**2 + 1)**(1/3) - 3*(x**2 + 1)**(1/3)), x)","F",0
81,0,0,0,0.000000," ","integrate((a+x)/(-a+x)/(a**2*x-(a**2+1)*x**2+x**3)**(1/2),x)","\int \frac{a + x}{\sqrt{x \left(- a^{2} + x\right) \left(x - 1\right)} \left(- a + x\right)}\, dx"," ",0,"Integral((a + x)/(sqrt(x*(-a**2 + x)*(x - 1))*(-a + x)), x)","F",0
82,0,0,0,0.000000," ","integrate((-2+a+x)/(-a+x)/((2-a)*a*x+(a**2-2*a-1)*x**2+x**3)**(1/2),x)","\int \frac{a + x - 2}{\sqrt{x \left(x - 1\right) \left(a^{2} - 2 a + x\right)} \left(- a + x\right)}\, dx"," ",0,"Integral((a + x - 2)/(sqrt(x*(x - 1)*(a**2 - 2*a + x))*(-a + x)), x)","F",0
83,0,0,0,0.000000," ","integrate((-a+(-1+2*a)*x)/(-a+x)/(a**2*x-(a**2+2*a-1)*x**2+(-1+2*a)*x**3)**(1/2),x)","\int \frac{2 a x - a - x}{\sqrt{x \left(x - 1\right) \left(- a^{2} + 2 a x - x\right)} \left(- a + x\right)}\, dx"," ",0,"Integral((2*a*x - a - x)/(sqrt(x*(x - 1)*(-a**2 + 2*a*x - x))*(-a + x)), x)","F",0
84,0,0,0,0.000000," ","integrate((1-2**(1/3)*x)/(2**(2/3)+x)/(x**3+1)**(1/2),x)","- \int \frac{\sqrt[3]{2} x}{x \sqrt{x^{3} + 1} + 2^{\frac{2}{3}} \sqrt{x^{3} + 1}}\, dx - \int \left(- \frac{1}{x \sqrt{x^{3} + 1} + 2^{\frac{2}{3}} \sqrt{x^{3} + 1}}\right)\, dx"," ",0,"-Integral(2**(1/3)*x/(x*sqrt(x**3 + 1) + 2**(2/3)*sqrt(x**3 + 1)), x) - Integral(-1/(x*sqrt(x**3 + 1) + 2**(2/3)*sqrt(x**3 + 1)), x)","F",0
85,0,0,0,0.000000," ","integrate((1+x)/(-2+x)/(x**3+1)**(1/2),x)","\int \frac{x + 1}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x - 2\right)}\, dx"," ",0,"Integral((x + 1)/(sqrt((x + 1)*(x**2 - x + 1))*(x - 2)), x)","F",0
86,0,0,0,0.000000," ","integrate(x/(10+x**3+6*3**(1/2))/(x**3+1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x^{3} + 10 + 6 \sqrt{3}\right)}\, dx"," ",0,"Integral(x/(sqrt((x + 1)*(x**2 - x + 1))*(x**3 + 10 + 6*sqrt(3))), x)","F",0
87,0,0,0,0.000000," ","integrate(x/(10+x**3-6*3**(1/2))/(x**3+1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x^{3} - 6 \sqrt{3} + 10\right)}\, dx"," ",0,"Integral(x/(sqrt((x + 1)*(x**2 - x + 1))*(x**3 - 6*sqrt(3) + 10)), x)","F",0
88,0,0,0,0.000000," ","integrate(x/(-10+x**3-6*3**(1/2))/(x**3-1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x^{3} - 6 \sqrt{3} - 10\right)}\, dx"," ",0,"Integral(x/(sqrt((x - 1)*(x**2 + x + 1))*(x**3 - 6*sqrt(3) - 10)), x)","F",0
89,0,0,0,0.000000," ","integrate(x/(-10+x**3+6*3**(1/2))/(x**3-1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x^{3} - 10 + 6 \sqrt{3}\right)}\, dx"," ",0,"Integral(x/(sqrt((x - 1)*(x**2 + x + 1))*(x**3 - 10 + 6*sqrt(3))), x)","F",0
90,0,0,0,0.000000," ","integrate((1+x-3**(1/2))/(1+x+3**(1/2))/(-4+x**4+4*3**(1/2)*x**2)**(1/2),x)","\int \frac{x - \sqrt{3} + 1}{\left(x + 1 + \sqrt{3}\right) \sqrt{x^{4} + 4 \sqrt{3} x^{2} - 4}}\, dx"," ",0,"Integral((x - sqrt(3) + 1)/((x + 1 + sqrt(3))*sqrt(x**4 + 4*sqrt(3)*x**2 - 4)), x)","F",0
91,0,0,0,0.000000," ","integrate((1+x+3**(1/2))/(1+x-3**(1/2))/(-4+x**4-4*3**(1/2)*x**2)**(1/2),x)","\int \frac{x + 1 + \sqrt{3}}{\left(x - \sqrt{3} + 1\right) \sqrt{x^{4} - 4 \sqrt{3} x^{2} - 4}}\, dx"," ",0,"Integral((x + 1 + sqrt(3))/((x - sqrt(3) + 1)*sqrt(x**4 - 4*sqrt(3)*x**2 - 4)), x)","F",0
92,0,0,0,0.000000," ","integrate((-1+x)/(1+x)/(x**3+2)**(1/3),x)","\int \frac{x - 1}{\left(x + 1\right) \sqrt[3]{x^{3} + 2}}\, dx"," ",0,"Integral((x - 1)/((x + 1)*(x**3 + 2)**(1/3)), x)","F",0
93,0,0,0,0.000000," ","integrate(1/(1+x)/(x**3+2)**(1/3),x)","\int \frac{1}{\left(x + 1\right) \sqrt[3]{x^{3} + 2}}\, dx"," ",0,"Integral(1/((x + 1)*(x**3 + 2)**(1/3)), x)","F",0
94,0,0,0,0.000000," ","integrate(1/(-x**3+1)/(b*x**3+a)**(1/3),x)","- \int \frac{1}{x^{3} \sqrt[3]{a + b x^{3}} - \sqrt[3]{a + b x^{3}}}\, dx"," ",0,"-Integral(1/(x**3*(a + b*x**3)**(1/3) - (a + b*x**3)**(1/3)), x)","F",0
95,0,0,0,0.000000," ","integrate((1+x)/(x**2+x+1)/(b*x**3+a)**(1/3),x)","\int \frac{x + 1}{\sqrt[3]{a + b x^{3}} \left(x^{2} + x + 1\right)}\, dx"," ",0,"Integral((x + 1)/((a + b*x**3)**(1/3)*(x**2 + x + 1)), x)","F",0
96,0,0,0,0.000000," ","integrate(x**2/(-x**3+1)/(b*x**3+a)**(1/3),x)","- \int \frac{x^{2}}{x^{3} \sqrt[3]{a + b x^{3}} - \sqrt[3]{a + b x^{3}}}\, dx"," ",0,"-Integral(x**2/(x**3*(a + b*x**3)**(1/3) - (a + b*x**3)**(1/3)), x)","F",0
97,0,0,0,0.000000," ","integrate(1/(-x**3+1)**(1/3)/(x**3+1),x)","\int \frac{1}{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 1\right) \left(x^{2} - x + 1\right)}\, dx"," ",0,"Integral(1/((-(x - 1)*(x**2 + x + 1))**(1/3)*(x + 1)*(x**2 - x + 1)), x)","F",0
98,0,0,0,0.000000," ","integrate(x/(-x**3+1)**(1/3)/(x**3+1),x)","\int \frac{x}{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 1\right) \left(x^{2} - x + 1\right)}\, dx"," ",0,"Integral(x/((-(x - 1)*(x**2 + x + 1))**(1/3)*(x + 1)*(x**2 - x + 1)), x)","F",0
99,0,0,0,0.000000," ","integrate(x**2/(-x**3+1)**(1/3)/(x**3+1),x)","\int \frac{x^{2}}{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 1\right) \left(x^{2} - x + 1\right)}\, dx"," ",0,"Integral(x**2/((-(x - 1)*(x**2 + x + 1))**(1/3)*(x + 1)*(x**2 - x + 1)), x)","F",0
100,0,0,0,0.000000," ","integrate((1+x)/(x**2-x+1)/(-x**3+1)**(1/3),x)","\int \frac{x + 1}{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x^{2} - x + 1\right)}\, dx"," ",0,"Integral((x + 1)/((-(x - 1)*(x**2 + x + 1))**(1/3)*(x**2 - x + 1)), x)","F",0
101,0,0,0,0.000000," ","integrate((1+x)**2/(-x**3+1)**(1/3)/(x**3+1),x)","\int \frac{x + 1}{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x^{2} - x + 1\right)}\, dx"," ",0,"Integral((x + 1)/((-(x - 1)*(x**2 + x + 1))**(1/3)*(x**2 - x + 1)), x)","F",0
102,0,0,0,0.000000," ","integrate((1-x)/(x**2+x+1)/(x**3+1)**(1/3),x)","- \int \frac{x}{x^{2} \sqrt[3]{x^{3} + 1} + x \sqrt[3]{x^{3} + 1} + \sqrt[3]{x^{3} + 1}}\, dx - \int \left(- \frac{1}{x^{2} \sqrt[3]{x^{3} + 1} + x \sqrt[3]{x^{3} + 1} + \sqrt[3]{x^{3} + 1}}\right)\, dx"," ",0,"-Integral(x/(x**2*(x**3 + 1)**(1/3) + x*(x**3 + 1)**(1/3) + (x**3 + 1)**(1/3)), x) - Integral(-1/(x**2*(x**3 + 1)**(1/3) + x*(x**3 + 1)**(1/3) + (x**3 + 1)**(1/3)), x)","F",0
103,0,0,0,0.000000," ","integrate((-x**3+1)**(2/3)/(x**2+x+1)**2,x)","\int \frac{\left(- \left(x - 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{2}{3}}}{\left(x^{2} + x + 1\right)^{2}}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(2/3)/(x**2 + x + 1)**2, x)","F",0
104,0,0,0,0.000000," ","integrate((1-x)/(x**2+x+1)/(-x**3+1)**(1/3),x)","- \int \frac{x}{x^{2} \sqrt[3]{1 - x^{3}} + x \sqrt[3]{1 - x^{3}} + \sqrt[3]{1 - x^{3}}}\, dx - \int \left(- \frac{1}{x^{2} \sqrt[3]{1 - x^{3}} + x \sqrt[3]{1 - x^{3}} + \sqrt[3]{1 - x^{3}}}\right)\, dx"," ",0,"-Integral(x/(x**2*(1 - x**3)**(1/3) + x*(1 - x**3)**(1/3) + (1 - x**3)**(1/3)), x) - Integral(-1/(x**2*(1 - x**3)**(1/3) + x*(1 - x**3)**(1/3) + (1 - x**3)**(1/3)), x)","F",0
105,0,0,0,0.000000," ","integrate((1-x)**2/(-x**3+1)**(4/3),x)","\int \frac{\left(x - 1\right)^{2}}{\left(- \left(x - 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((x - 1)**2/(-(x - 1)*(x**2 + x + 1))**(4/3), x)","F",0
106,1,31,0,1.021344," ","integrate((-x**3+1)**(2/3),x)","\frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}"," ",0,"x*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3))","C",0
107,1,41,0,1.016526," ","integrate((-x**3+1)**(2/3)/x,x)","- \frac{x^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{1}{x^{3}}} \right)}}{3 \Gamma\left(\frac{1}{3}\right)}"," ",0,"-x**2*exp(2*I*pi/3)*gamma(-2/3)*hyper((-2/3, -2/3), (1/3,), x**(-3))/(3*gamma(1/3))","C",0
108,0,0,0,0.000000," ","integrate((-x**3+1)**(2/3)/(b*x+a),x)","\int \frac{\left(- \left(x - 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{2}{3}}}{a + b x}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(2/3)/(a + b*x), x)","F",0
109,0,0,0,0.000000," ","integrate((-x**3+1)**(2/3)/(x**2-x+1)**2,x)","\int \frac{\left(- \left(x - 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{2}{3}}}{\left(x^{2} - x + 1\right)^{2}}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(2/3)/(x**2 - x + 1)**2, x)","F",0
110,0,0,0,0.000000," ","integrate((1-2*x)*(-x**3+1)**(2/3)/(x**2-x+1)**2,x)","- \int \left(- \frac{\left(1 - x^{3}\right)^{\frac{2}{3}}}{x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1}\right)\, dx - \int \frac{2 x \left(1 - x^{3}\right)^{\frac{2}{3}}}{x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1}\, dx"," ",0,"-Integral(-(1 - x**3)**(2/3)/(x**4 - 2*x**3 + 3*x**2 - 2*x + 1), x) - Integral(2*x*(1 - x**3)**(2/3)/(x**4 - 2*x**3 + 3*x**2 - 2*x + 1), x)","F",0
111,0,0,0,0.000000," ","integrate((-x**3+1)**(2/3)/(1+x),x)","\int \frac{\left(- \left(x - 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{2}{3}}}{x + 1}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(2/3)/(x + 1), x)","F",0
112,0,0,0,0.000000," ","integrate((x**2-x+1)*(-x**3+1)**(2/3)/(x**3+1),x)","\int \frac{\left(- \left(x - 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{2}{3}}}{x + 1}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(2/3)/(x + 1), x)","F",0
113,0,0,0,0.000000," ","integrate((-x**3+1)**(2/3)/(x**3+1),x)","\int \frac{\left(- \left(x - 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{2}{3}}}{\left(x + 1\right) \left(x^{2} - x + 1\right)}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(2/3)/((x + 1)*(x**2 - x + 1)), x)","F",0
114,0,0,0,0.000000," ","integrate(x*(-x**3+1)**(2/3)/(x**3+1),x)","\int \frac{x \left(- \left(x - 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{2}{3}}}{\left(x + 1\right) \left(x^{2} - x + 1\right)}\, dx"," ",0,"Integral(x*(-(x - 1)*(x**2 + x + 1))**(2/3)/((x + 1)*(x**2 - x + 1)), x)","F",0
115,0,0,0,0.000000," ","integrate((1-x)*(-x**3+1)**(2/3)/(x**3+1),x)","- \int \left(- \frac{\left(1 - x^{3}\right)^{\frac{2}{3}}}{x^{3} + 1}\right)\, dx - \int \frac{x \left(1 - x^{3}\right)^{\frac{2}{3}}}{x^{3} + 1}\, dx"," ",0,"-Integral(-(1 - x**3)**(2/3)/(x**3 + 1), x) - Integral(x*(1 - x**3)**(2/3)/(x**3 + 1), x)","F",0
116,0,0,0,0.000000," ","integrate((-x**3+1)**(1/3)/(x**3+1),x)","\int \frac{\sqrt[3]{- \left(x - 1\right) \left(x^{2} + x + 1\right)}}{\left(x + 1\right) \left(x^{2} - x + 1\right)}\, dx"," ",0,"Integral((-(x - 1)*(x**2 + x + 1))**(1/3)/((x + 1)*(x**2 - x + 1)), x)","F",0
