1,0,0,0,0.000000," ","integrate(1/(2**(2/3)+x)/(x**3+1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 2^{\frac{2}{3}}\right)}\, dx"," ",0,"Integral(1/(sqrt((x + 1)*(x**2 - x + 1))*(x + 2**(2/3))), x)","F",0
2,0,0,0,0.000000," ","integrate(1/(2**(2/3)-x)/(-x**3+1)**(1/2),x)","- \int \frac{1}{x \sqrt{1 - x^{3}} - 2^{\frac{2}{3}} \sqrt{1 - x^{3}}}\, dx"," ",0,"-Integral(1/(x*sqrt(1 - x**3) - 2**(2/3)*sqrt(1 - x**3)), x)","F",0
3,0,0,0,0.000000," ","integrate(1/(2**(2/3)-x)/(x**3-1)**(1/2),x)","- \int \frac{1}{x \sqrt{x^{3} - 1} - 2^{\frac{2}{3}} \sqrt{x^{3} - 1}}\, dx"," ",0,"-Integral(1/(x*sqrt(x**3 - 1) - 2**(2/3)*sqrt(x**3 - 1)), x)","F",0
4,0,0,0,0.000000," ","integrate(1/(2**(2/3)+x)/(-x**3-1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 2^{\frac{2}{3}}\right)}\, dx"," ",0,"Integral(1/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 2**(2/3))), x)","F",0
5,0,0,0,0.000000," ","integrate(1/(2**(2/3)*a**(1/3)+b**(1/3)*x)/(b*x**3+a)**(1/2),x)","\int \frac{1}{\sqrt{a + b x^{3}} \left(2^{\frac{2}{3}} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral(1/(sqrt(a + b*x**3)*(2**(2/3)*a**(1/3) + b**(1/3)*x)), x)","F",0
6,0,0,0,0.000000," ","integrate(1/(2**(2/3)*a**(1/3)-b**(1/3)*x)/(-b*x**3+a)**(1/2),x)","- \int \frac{1}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx"," ",0,"-Integral(1/(-2**(2/3)*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x)","F",0
7,0,0,0,0.000000," ","integrate(1/(2**(2/3)*a**(1/3)-b**(1/3)*x)/(b*x**3-a)**(1/2),x)","- \int \frac{1}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx"," ",0,"-Integral(1/(-2**(2/3)*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x)","F",0
8,0,0,0,0.000000," ","integrate(1/(2**(2/3)*a**(1/3)+b**(1/3)*x)/(-b*x**3-a)**(1/2),x)","\int \frac{1}{\sqrt{- a - b x^{3}} \left(2^{\frac{2}{3}} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral(1/(sqrt(-a - b*x**3)*(2**(2/3)*a**(1/3) + b**(1/3)*x)), x)","F",0
9,0,0,0,0.000000," ","integrate(1/(d*x+c)/(4*d**3*x**3+c**3)**(1/2),x)","\int \frac{1}{\left(c + d x\right) \sqrt{c^{3} + 4 d^{3} x^{3}}}\, dx"," ",0,"Integral(1/((c + d*x)*sqrt(c**3 + 4*d**3*x**3)), x)","F",0
10,0,0,0,0.000000," ","integrate(1/(1+x+3**(1/2))/(x**3+1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral(1/(sqrt((x + 1)*(x**2 - x + 1))*(x + 1 + sqrt(3))), x)","F",0
11,0,0,0,0.000000," ","integrate(1/(1-x+3**(1/2))/(-x**3+1)**(1/2),x)","- \int \frac{1}{x \sqrt{1 - x^{3}} - \sqrt{3} \sqrt{1 - x^{3}} - \sqrt{1 - x^{3}}}\, dx"," ",0,"-Integral(1/(x*sqrt(1 - x**3) - sqrt(3)*sqrt(1 - x**3) - sqrt(1 - x**3)), x)","F",0
12,0,0,0,0.000000," ","integrate(1/(1-x+3**(1/2))/(x**3-1)**(1/2),x)","- \int \frac{1}{x \sqrt{x^{3} - 1} - \sqrt{3} \sqrt{x^{3} - 1} - \sqrt{x^{3} - 1}}\, dx"," ",0,"-Integral(1/(x*sqrt(x**3 - 1) - sqrt(3)*sqrt(x**3 - 1) - sqrt(x**3 - 1)), x)","F",0
13,0,0,0,0.000000," ","integrate(1/(1+x+3**(1/2))/(-x**3-1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral(1/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 1 + sqrt(3))), x)","F",0
14,0,0,0,0.000000," ","integrate(1/(3+x)/(x**3+1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 3\right)}\, dx"," ",0,"Integral(1/(sqrt((x + 1)*(x**2 - x + 1))*(x + 3)), x)","F",0
15,0,0,0,0.000000," ","integrate(1/(3+x)/(-x**3+1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 3\right)}\, dx"," ",0,"Integral(1/(sqrt(-(x - 1)*(x**2 + x + 1))*(x + 3)), x)","F",0
16,0,0,0,0.000000," ","integrate(1/(3+x)/(x**3-1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 3\right)}\, dx"," ",0,"Integral(1/(sqrt((x - 1)*(x**2 + x + 1))*(x + 3)), x)","F",0
17,0,0,0,0.000000," ","integrate(1/(3+x)/(-x**3-1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 3\right)}\, dx"," ",0,"Integral(1/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 3)), x)","F",0
18,0,0,0,0.000000," ","integrate(1/(d*x+c)/(d**3*x**3-c**3)**(1/3),x)","\int \frac{1}{\sqrt[3]{\left(- c + d x\right) \left(c^{2} + c d x + d^{2} x^{2}\right)} \left(c + d x\right)}\, dx"," ",0,"Integral(1/(((-c + d*x)*(c**2 + c*d*x + d**2*x**2))**(1/3)*(c + d*x)), x)","F",0
19,0,0,0,0.000000," ","integrate(1/(d*x+c)/(d**3*x**3+2*c**3)**(1/3),x)","\int \frac{1}{\left(c + d x\right) \sqrt[3]{2 c^{3} + d^{3} x^{3}}}\, dx"," ",0,"Integral(1/((c + d*x)*(2*c**3 + d**3*x**3)**(1/3)), x)","F",0
20,0,0,0,0.000000," ","integrate(1/(d*x+c)/(d**3*x**3+2*c**3)**(2/3),x)","\int \frac{1}{\left(c + d x\right) \left(2 c^{3} + d^{3} x^{3}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((c + d*x)*(2*c**3 + d**3*x**3)**(2/3)), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(1+2**(1/3)*x)/(x**3+1)**(2/3),x)","\int \frac{1}{\left(\left(x + 1\right) \left(x^{2} - x + 1\right)\right)^{\frac{2}{3}} \left(\sqrt[3]{2} x + 1\right)}\, dx"," ",0,"Integral(1/(((x + 1)*(x**2 - x + 1))**(2/3)*(2**(1/3)*x + 1)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(1-2**(1/3)*x)/(-x**3+1)**(2/3),x)","- \int \frac{1}{\sqrt[3]{2} x \left(1 - x^{3}\right)^{\frac{2}{3}} - \left(1 - x^{3}\right)^{\frac{2}{3}}}\, dx"," ",0,"-Integral(1/(2**(1/3)*x*(1 - x**3)**(2/3) - (1 - x**3)**(2/3)), x)","F",0
23,1,212,0,4.952003," ","integrate((d*x+c)**4*(b*x**3+a)**(1/3),x)","\frac{\sqrt[3]{a} c^{4} 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{4 \sqrt[3]{a} c^{3} d 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + \frac{4 \sqrt[3]{a} c d^{3} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \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[3]{a} d^{4} x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \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)} + 6 c^{2} d^{2} \left(\begin{cases} \frac{\sqrt[3]{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{\left(a + b x^{3}\right)^{\frac{4}{3}}}{4 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**(1/3)*c**4*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + 4*a**(1/3)*c**3*d*x**2*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + 4*a**(1/3)*c*d**3*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + a**(1/3)*d**4*x**5*gamma(5/3)*hyper((-1/3, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(8/3)) + 6*c**2*d**2*Piecewise((a**(1/3)*x**3/3, Eq(b, 0)), ((a + b*x**3)**(4/3)/(4*b), True))","A",0
24,1,160,0,3.917166," ","integrate((d*x+c)**3*(b*x**3+a)**(1/3),x)","\frac{\sqrt[3]{a} c^{3} 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt[3]{a} c^{2} d 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{\Gamma\left(\frac{5}{3}\right)} + \frac{\sqrt[3]{a} d^{3} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \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)} + 3 c d^{2} \left(\begin{cases} \frac{\sqrt[3]{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{\left(a + b x^{3}\right)^{\frac{4}{3}}}{4 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**(1/3)*c**3*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(1/3)*c**2*d*x**2*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/gamma(5/3) + a**(1/3)*d**3*x**4*gamma(4/3)*hyper((-1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(7/3)) + 3*c*d**2*Piecewise((a**(1/3)*x**3/3, Eq(b, 0)), ((a + b*x**3)**(4/3)/(4*b), True))","A",0
25,1,114,0,3.237502," ","integrate((d*x+c)**2*(b*x**3+a)**(1/3),x)","\frac{\sqrt[3]{a} c^{2} 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{2 \sqrt[3]{a} c d 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)} + d^{2} \left(\begin{cases} \frac{\sqrt[3]{a} x^{3}}{3} & \text{for}\: b = 0 \\\frac{\left(a + b x^{3}\right)^{\frac{4}{3}}}{4 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**(1/3)*c**2*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + 2*a**(1/3)*c*d*x**2*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3)) + d**2*Piecewise((a**(1/3)*x**3/3, Eq(b, 0)), ((a + b*x**3)**(4/3)/(4*b), True))","A",0
26,1,82,0,2.658888," ","integrate((d*x+c)*(b*x**3+a)**(1/3),x)","\frac{\sqrt[3]{a} c 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{\sqrt[3]{a} d 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}"," ",0,"a**(1/3)*c*x*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(4/3)) + a**(1/3)*d*x**2*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*gamma(5/3))","C",0
27,0,0,0,0.000000," ","integrate((b*x**3+a)**(1/3)/(d*x+c),x)","\int \frac{\sqrt[3]{a + b x^{3}}}{c + d x}\, dx"," ",0,"Integral((a + b*x**3)**(1/3)/(c + d*x), x)","F",0
28,0,0,0,0.000000," ","integrate((b*x**3+a)**(1/3)/(d*x+c)**2,x)","\int \frac{\sqrt[3]{a + b x^{3}}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral((a + b*x**3)**(1/3)/(c + d*x)**2, x)","F",0
29,1,206,0,5.166357," ","integrate((d*x+c)**4/(b*x**3+a)**(1/3),x)","6 c^{2} d^{2} \left(\begin{cases} \frac{x^{3}}{3 \sqrt[3]{a}} & \text{for}\: b = 0 \\\frac{\left(a + b x^{3}\right)^{\frac{2}{3}}}{2 b} & \text{otherwise} \end{cases}\right) + \frac{c^{4} 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{4 c^{3} d 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)} + \frac{4 c d^{3} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{7}{3}\right)} + \frac{d^{4} x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{8}{3}\right)}"," ",0,"6*c**2*d**2*Piecewise((x**3/(3*a**(1/3)), Eq(b, 0)), ((a + b*x**3)**(2/3)/(2*b), True)) + c**4*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(4/3)) + 4*c**3*d*x**2*gamma(2/3)*hyper((1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(5/3)) + 4*c*d**3*x**4*gamma(4/3)*hyper((1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(7/3)) + d**4*x**5*gamma(5/3)*hyper((1/3, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(8/3))","A",0
30,1,155,0,4.313643," ","integrate((d*x+c)**3/(b*x**3+a)**(1/3),x)","3 c d^{2} \left(\begin{cases} \frac{x^{3}}{3 \sqrt[3]{a}} & \text{for}\: b = 0 \\\frac{\left(a + b x^{3}\right)^{\frac{2}{3}}}{2 b} & \text{otherwise} \end{cases}\right) + \frac{c^{3} 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{c^{2} d 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{\sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)} + \frac{d^{3} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{7}{3}\right)}"," ",0,"3*c*d**2*Piecewise((x**3/(3*a**(1/3)), Eq(b, 0)), ((a + b*x**3)**(2/3)/(2*b), True)) + c**3*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(4/3)) + c**2*d*x**2*gamma(2/3)*hyper((1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(a**(1/3)*gamma(5/3)) + d**3*x**4*gamma(4/3)*hyper((1/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(7/3))","A",0
31,1,110,0,3.329714," ","integrate((d*x+c)**2/(b*x**3+a)**(1/3),x)","d^{2} \left(\begin{cases} \frac{x^{3}}{3 \sqrt[3]{a}} & \text{for}\: b = 0 \\\frac{\left(a + b x^{3}\right)^{\frac{2}{3}}}{2 b} & \text{otherwise} \end{cases}\right) + \frac{c^{2} 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{4}{3}\right)} + \frac{2 c d 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"d**2*Piecewise((x**3/(3*a**(1/3)), Eq(b, 0)), ((a + b*x**3)**(2/3)/(2*b), True)) + c**2*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(4/3)) + 2*c*d*x**2*gamma(2/3)*hyper((1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(5/3))","A",0
32,1,78,0,2.269807," ","integrate((d*x+c)/(b*x**3+a)**(1/3),x)","\frac{c 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| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{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}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((1/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(1/3)*gamma(5/3))","C",0
33,0,0,0,0.000000," ","integrate(1/(d*x+c)/(b*x**3+a)**(1/3),x)","\int \frac{1}{\sqrt[3]{a + b x^{3}} \left(c + d x\right)}\, dx"," ",0,"Integral(1/((a + b*x**3)**(1/3)*(c + d*x)), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(d*x+c)**2/(b*x**3+a)**(1/3),x)","\int \frac{1}{\sqrt[3]{a + b x^{3}} \left(c + d x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(1/3)*(c + d*x)**2), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(d*x+c)**3/(b*x**3+a)**(1/3),x)","\int \frac{1}{\sqrt[3]{a + b x^{3}} \left(c + d x\right)^{3}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(1/3)*(c + d*x)**3), x)","F",0
36,1,204,0,5.155176," ","integrate((d*x+c)**4/(b*x**3+a)**(2/3),x)","6 c^{2} d^{2} \left(\begin{cases} \frac{x^{3}}{3 a^{\frac{2}{3}}} & \text{for}\: b = 0 \\\frac{\sqrt[3]{a + b x^{3}}}{b} & \text{otherwise} \end{cases}\right) + \frac{c^{4} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{4 c^{3} d x^{2} \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{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{4 c d^{3} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{d^{4} x^{5} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"6*c**2*d**2*Piecewise((x**3/(3*a**(2/3)), Eq(b, 0)), ((a + b*x**3)**(1/3)/b, True)) + c**4*x*gamma(1/3)*hyper((1/3, 2/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(4/3)) + 4*c**3*d*x**2*gamma(2/3)*hyper((2/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(5/3)) + 4*c*d**3*x**4*gamma(4/3)*hyper((2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(7/3)) + d**4*x**5*gamma(5/3)*hyper((2/3, 5/3), (8/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(8/3))","A",0
37,1,153,0,4.177763," ","integrate((d*x+c)**3/(b*x**3+a)**(2/3),x)","3 c d^{2} \left(\begin{cases} \frac{x^{3}}{3 a^{\frac{2}{3}}} & \text{for}\: b = 0 \\\frac{\sqrt[3]{a + b x^{3}}}{b} & \text{otherwise} \end{cases}\right) + \frac{c^{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{c^{2} d x^{2} \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{b x^{3} e^{i \pi}}{a}} \right)}}{a^{\frac{2}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{d^{3} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"3*c*d**2*Piecewise((x**3/(3*a**(2/3)), Eq(b, 0)), ((a + b*x**3)**(1/3)/b, True)) + c**3*x*gamma(1/3)*hyper((1/3, 2/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(4/3)) + c**2*d*x**2*gamma(2/3)*hyper((2/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(a**(2/3)*gamma(5/3)) + d**3*x**4*gamma(4/3)*hyper((2/3, 4/3), (7/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(7/3))","A",0
38,1,109,0,3.332947," ","integrate((d*x+c)**2/(b*x**3+a)**(2/3),x)","d^{2} \left(\begin{cases} \frac{x^{3}}{3 a^{\frac{2}{3}}} & \text{for}\: b = 0 \\\frac{\sqrt[3]{a + b x^{3}}}{b} & \text{otherwise} \end{cases}\right) + \frac{c^{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{2 c d x^{2} \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{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"d**2*Piecewise((x**3/(3*a**(2/3)), Eq(b, 0)), ((a + b*x**3)**(1/3)/b, True)) + c**2*x*gamma(1/3)*hyper((1/3, 2/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(4/3)) + 2*c*d*x**2*gamma(2/3)*hyper((2/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(5/3))","A",0
39,1,78,0,2.305410," ","integrate((d*x+c)/(b*x**3+a)**(2/3),x)","\frac{c x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \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{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{3} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"c*x*gamma(1/3)*hyper((1/3, 2/3), (4/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(4/3)) + d*x**2*gamma(2/3)*hyper((2/3, 2/3), (5/3,), b*x**3*exp_polar(I*pi)/a)/(3*a**(2/3)*gamma(5/3))","C",0
40,0,0,0,0.000000," ","integrate(1/(d*x+c)/(b*x**3+a)**(2/3),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{2}{3}} \left(c + d x\right)}\, dx"," ",0,"Integral(1/((a + b*x**3)**(2/3)*(c + d*x)), x)","F",0
41,0,0,0,0.000000," ","integrate(1/(d*x+c)**2/(b*x**3+a)**(2/3),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{2}{3}} \left(c + d x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(2/3)*(c + d*x)**2), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(d*x+c)**3/(b*x**3+a)**(2/3),x)","\int \frac{1}{\left(a + b x^{3}\right)^{\frac{2}{3}} \left(c + d x\right)^{3}}\, dx"," ",0,"Integral(1/((a + b*x**3)**(2/3)*(c + d*x)**3), x)","F",0
43,0,0,0,0.000000," ","integrate((2**(2/3)-2*x)/(2**(2/3)+x)/(x**3+1)**(1/2),x)","- \int \left(- \frac{2^{\frac{2}{3}}}{x \sqrt{x^{3} + 1} + 2^{\frac{2}{3}} \sqrt{x^{3} + 1}}\right)\, dx - \int \frac{2 x}{x \sqrt{x^{3} + 1} + 2^{\frac{2}{3}} \sqrt{x^{3} + 1}}\, dx"," ",0,"-Integral(-2**(2/3)/(x*sqrt(x**3 + 1) + 2**(2/3)*sqrt(x**3 + 1)), x) - Integral(2*x/(x*sqrt(x**3 + 1) + 2**(2/3)*sqrt(x**3 + 1)), x)","F",0
44,0,0,0,0.000000," ","integrate((2**(2/3)+2*x)/(2**(2/3)-x)/(-x**3+1)**(1/2),x)","- \int \frac{2^{\frac{2}{3}}}{x \sqrt{1 - x^{3}} - 2^{\frac{2}{3}} \sqrt{1 - x^{3}}}\, dx - \int \frac{2 x}{x \sqrt{1 - x^{3}} - 2^{\frac{2}{3}} \sqrt{1 - x^{3}}}\, dx"," ",0,"-Integral(2**(2/3)/(x*sqrt(1 - x**3) - 2**(2/3)*sqrt(1 - x**3)), x) - Integral(2*x/(x*sqrt(1 - x**3) - 2**(2/3)*sqrt(1 - x**3)), x)","F",0
45,0,0,0,0.000000," ","integrate((2**(2/3)+2*x)/(2**(2/3)-x)/(x**3-1)**(1/2),x)","- \int \frac{2^{\frac{2}{3}}}{x \sqrt{x^{3} - 1} - 2^{\frac{2}{3}} \sqrt{x^{3} - 1}}\, dx - \int \frac{2 x}{x \sqrt{x^{3} - 1} - 2^{\frac{2}{3}} \sqrt{x^{3} - 1}}\, dx"," ",0,"-Integral(2**(2/3)/(x*sqrt(x**3 - 1) - 2**(2/3)*sqrt(x**3 - 1)), x) - Integral(2*x/(x*sqrt(x**3 - 1) - 2**(2/3)*sqrt(x**3 - 1)), x)","F",0
46,0,0,0,0.000000," ","integrate((2**(2/3)-2*x)/(2**(2/3)+x)/(-x**3-1)**(1/2),x)","- \int \left(- \frac{2^{\frac{2}{3}}}{x \sqrt{- x^{3} - 1} + 2^{\frac{2}{3}} \sqrt{- x^{3} - 1}}\right)\, dx - \int \frac{2 x}{x \sqrt{- x^{3} - 1} + 2^{\frac{2}{3}} \sqrt{- x^{3} - 1}}\, dx"," ",0,"-Integral(-2**(2/3)/(x*sqrt(-x**3 - 1) + 2**(2/3)*sqrt(-x**3 - 1)), x) - Integral(2*x/(x*sqrt(-x**3 - 1) + 2**(2/3)*sqrt(-x**3 - 1)), x)","F",0
47,0,0,0,0.000000," ","integrate((2**(2/3)*a**(1/3)-2*b**(1/3)*x)/(2**(2/3)*a**(1/3)+b**(1/3)*x)/(b*x**3+a)**(1/2),x)","- \int \left(- \frac{2^{\frac{2}{3}} \sqrt[3]{a}}{2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{a + b x^{3}} + \sqrt[3]{b} x \sqrt{a + b x^{3}}}\right)\, dx - \int \frac{2 \sqrt[3]{b} x}{2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{a + b x^{3}} + \sqrt[3]{b} x \sqrt{a + b x^{3}}}\, dx"," ",0,"-Integral(-2**(2/3)*a**(1/3)/(2**(2/3)*a**(1/3)*sqrt(a + b*x**3) + b**(1/3)*x*sqrt(a + b*x**3)), x) - Integral(2*b**(1/3)*x/(2**(2/3)*a**(1/3)*sqrt(a + b*x**3) + b**(1/3)*x*sqrt(a + b*x**3)), x)","F",0
48,0,0,0,0.000000," ","integrate((2**(2/3)*a**(1/3)+2*b**(1/3)*x)/(2**(2/3)*a**(1/3)-b**(1/3)*x)/(-b*x**3+a)**(1/2),x)","- \int \frac{2^{\frac{2}{3}} \sqrt[3]{a}}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx - \int \frac{2 \sqrt[3]{b} x}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx"," ",0,"-Integral(2**(2/3)*a**(1/3)/(-2**(2/3)*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x) - Integral(2*b**(1/3)*x/(-2**(2/3)*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x)","F",0
49,0,0,0,0.000000," ","integrate((2**(2/3)*a**(1/3)+2*b**(1/3)*x)/(2**(2/3)*a**(1/3)-b**(1/3)*x)/(b*x**3-a)**(1/2),x)","- \int \frac{2^{\frac{2}{3}} \sqrt[3]{a}}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx - \int \frac{2 \sqrt[3]{b} x}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx"," ",0,"-Integral(2**(2/3)*a**(1/3)/(-2**(2/3)*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x) - Integral(2*b**(1/3)*x/(-2**(2/3)*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x)","F",0
50,0,0,0,0.000000," ","integrate((2**(2/3)*a**(1/3)-2*b**(1/3)*x)/(2**(2/3)*a**(1/3)+b**(1/3)*x)/(-b*x**3-a)**(1/2),x)","- \int \left(- \frac{2^{\frac{2}{3}} \sqrt[3]{a}}{2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{- a - b x^{3}} + \sqrt[3]{b} x \sqrt{- a - b x^{3}}}\right)\, dx - \int \frac{2 \sqrt[3]{b} x}{2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{- a - b x^{3}} + \sqrt[3]{b} x \sqrt{- a - b x^{3}}}\, dx"," ",0,"-Integral(-2**(2/3)*a**(1/3)/(2**(2/3)*a**(1/3)*sqrt(-a - b*x**3) + b**(1/3)*x*sqrt(-a - b*x**3)), x) - Integral(2*b**(1/3)*x/(2**(2/3)*a**(1/3)*sqrt(-a - b*x**3) + b**(1/3)*x*sqrt(-a - b*x**3)), x)","F",0
51,0,0,0,0.000000," ","integrate((-2*d*x+c)/(d*x+c)/(4*d**3*x**3+c**3)**(1/2),x)","- \int \left(- \frac{c}{c \sqrt{c^{3} + 4 d^{3} x^{3}} + d x \sqrt{c^{3} + 4 d^{3} x^{3}}}\right)\, dx - \int \frac{2 d x}{c \sqrt{c^{3} + 4 d^{3} x^{3}} + d x \sqrt{c^{3} + 4 d^{3} x^{3}}}\, dx"," ",0,"-Integral(-c/(c*sqrt(c**3 + 4*d**3*x**3) + d*x*sqrt(c**3 + 4*d**3*x**3)), x) - Integral(2*d*x/(c*sqrt(c**3 + 4*d**3*x**3) + d*x*sqrt(c**3 + 4*d**3*x**3)), x)","F",0
52,0,0,0,0.000000," ","integrate((2+3*x)/(2**(2/3)+x)/(x**3+1)**(1/2),x)","\int \frac{3 x + 2}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 2^{\frac{2}{3}}\right)}\, dx"," ",0,"Integral((3*x + 2)/(sqrt((x + 1)*(x**2 - x + 1))*(x + 2**(2/3))), x)","F",0
53,0,0,0,0.000000," ","integrate((2+3*x)/(2**(2/3)-x)/(-x**3+1)**(1/2),x)","- \int \frac{3 x}{x \sqrt{1 - x^{3}} - 2^{\frac{2}{3}} \sqrt{1 - x^{3}}}\, dx - \int \frac{2}{x \sqrt{1 - x^{3}} - 2^{\frac{2}{3}} \sqrt{1 - x^{3}}}\, dx"," ",0,"-Integral(3*x/(x*sqrt(1 - x**3) - 2**(2/3)*sqrt(1 - x**3)), x) - Integral(2/(x*sqrt(1 - x**3) - 2**(2/3)*sqrt(1 - x**3)), x)","F",0
54,0,0,0,0.000000," ","integrate((2+3*x)/(2**(2/3)-x)/(x**3-1)**(1/2),x)","- \int \frac{3 x}{x \sqrt{x^{3} - 1} - 2^{\frac{2}{3}} \sqrt{x^{3} - 1}}\, dx - \int \frac{2}{x \sqrt{x^{3} - 1} - 2^{\frac{2}{3}} \sqrt{x^{3} - 1}}\, dx"," ",0,"-Integral(3*x/(x*sqrt(x**3 - 1) - 2**(2/3)*sqrt(x**3 - 1)), x) - Integral(2/(x*sqrt(x**3 - 1) - 2**(2/3)*sqrt(x**3 - 1)), x)","F",0
55,0,0,0,0.000000," ","integrate((2+3*x)/(2**(2/3)+x)/(-x**3-1)**(1/2),x)","\int \frac{3 x + 2}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 2^{\frac{2}{3}}\right)}\, dx"," ",0,"Integral((3*x + 2)/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 2**(2/3))), x)","F",0
56,0,0,0,0.000000," ","integrate((f*x+e)/(2**(2/3)+x)/(x**3+1)**(1/2),x)","\int \frac{e + f x}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 2^{\frac{2}{3}}\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt((x + 1)*(x**2 - x + 1))*(x + 2**(2/3))), x)","F",0
57,0,0,0,0.000000," ","integrate((f*x+e)/(2**(2/3)-x)/(-x**3+1)**(1/2),x)","- \int \frac{e}{x \sqrt{1 - x^{3}} - 2^{\frac{2}{3}} \sqrt{1 - x^{3}}}\, dx - \int \frac{f x}{x \sqrt{1 - x^{3}} - 2^{\frac{2}{3}} \sqrt{1 - x^{3}}}\, dx"," ",0,"-Integral(e/(x*sqrt(1 - x**3) - 2**(2/3)*sqrt(1 - x**3)), x) - Integral(f*x/(x*sqrt(1 - x**3) - 2**(2/3)*sqrt(1 - x**3)), x)","F",0
58,0,0,0,0.000000," ","integrate((f*x+e)/(2**(2/3)-x)/(x**3-1)**(1/2),x)","- \int \frac{e}{x \sqrt{x^{3} - 1} - 2^{\frac{2}{3}} \sqrt{x^{3} - 1}}\, dx - \int \frac{f x}{x \sqrt{x^{3} - 1} - 2^{\frac{2}{3}} \sqrt{x^{3} - 1}}\, dx"," ",0,"-Integral(e/(x*sqrt(x**3 - 1) - 2**(2/3)*sqrt(x**3 - 1)), x) - Integral(f*x/(x*sqrt(x**3 - 1) - 2**(2/3)*sqrt(x**3 - 1)), x)","F",0
59,0,0,0,0.000000," ","integrate((f*x+e)/(2**(2/3)+x)/(-x**3-1)**(1/2),x)","\int \frac{e + f x}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 2^{\frac{2}{3}}\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 2**(2/3))), x)","F",0
60,0,0,0,0.000000," ","integrate((f*x+e)/(2**(2/3)*a**(1/3)+b**(1/3)*x)/(b*x**3+a)**(1/2),x)","\int \frac{e + f x}{\sqrt{a + b x^{3}} \left(2^{\frac{2}{3}} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(a + b*x**3)*(2**(2/3)*a**(1/3) + b**(1/3)*x)), x)","F",0
61,0,0,0,0.000000," ","integrate((f*x+e)/(2**(2/3)*a**(1/3)-b**(1/3)*x)/(-b*x**3+a)**(1/2),x)","- \int \frac{e}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx - \int \frac{f x}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx"," ",0,"-Integral(e/(-2**(2/3)*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x) - Integral(f*x/(-2**(2/3)*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x)","F",0
62,0,0,0,0.000000," ","integrate((f*x+e)/(2**(2/3)*a**(1/3)-b**(1/3)*x)/(b*x**3-a)**(1/2),x)","- \int \frac{e}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx - \int \frac{f x}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx"," ",0,"-Integral(e/(-2**(2/3)*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x) - Integral(f*x/(-2**(2/3)*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x)","F",0
63,0,0,0,0.000000," ","integrate((f*x+e)/(2**(2/3)*a**(1/3)+b**(1/3)*x)/(-b*x**3-a)**(1/2),x)","\int \frac{e + f x}{\sqrt{- a - b x^{3}} \left(2^{\frac{2}{3}} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(-a - b*x**3)*(2**(2/3)*a**(1/3) + b**(1/3)*x)), x)","F",0
64,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(4*d**3*x**3+c**3)**(1/2),x)","\int \frac{e + f x}{\left(c + d x\right) \sqrt{c^{3} + 4 d^{3} x^{3}}}\, dx"," ",0,"Integral((e + f*x)/((c + d*x)*sqrt(c**3 + 4*d**3*x**3)), x)","F",0
65,0,0,0,0.000000," ","integrate(x/(2**(2/3)+x)/(x**3+1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 2^{\frac{2}{3}}\right)}\, dx"," ",0,"Integral(x/(sqrt((x + 1)*(x**2 - x + 1))*(x + 2**(2/3))), x)","F",0
66,0,0,0,0.000000," ","integrate(x/(2**(2/3)-x)/(-x**3+1)**(1/2),x)","- \int \frac{x}{x \sqrt{1 - x^{3}} - 2^{\frac{2}{3}} \sqrt{1 - x^{3}}}\, dx"," ",0,"-Integral(x/(x*sqrt(1 - x**3) - 2**(2/3)*sqrt(1 - x**3)), x)","F",0
67,0,0,0,0.000000," ","integrate(x/(2**(2/3)-x)/(x**3-1)**(1/2),x)","- \int \frac{x}{x \sqrt{x^{3} - 1} - 2^{\frac{2}{3}} \sqrt{x^{3} - 1}}\, dx"," ",0,"-Integral(x/(x*sqrt(x**3 - 1) - 2**(2/3)*sqrt(x**3 - 1)), x)","F",0
68,0,0,0,0.000000," ","integrate(x/(2**(2/3)+x)/(-x**3-1)**(1/2),x)","\int \frac{x}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 2^{\frac{2}{3}}\right)}\, dx"," ",0,"Integral(x/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 2**(2/3))), x)","F",0
69,0,0,0,0.000000," ","integrate(x/(2**(2/3)*a**(1/3)+b**(1/3)*x)/(b*x**3+a)**(1/2),x)","\int \frac{x}{\sqrt{a + b x^{3}} \left(2^{\frac{2}{3}} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral(x/(sqrt(a + b*x**3)*(2**(2/3)*a**(1/3) + b**(1/3)*x)), x)","F",0
70,0,0,0,0.000000," ","integrate(x/(2**(2/3)*a**(1/3)-b**(1/3)*x)/(-b*x**3+a)**(1/2),x)","- \int \frac{x}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx"," ",0,"-Integral(x/(-2**(2/3)*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x)","F",0
71,0,0,0,0.000000," ","integrate(x/(2**(2/3)*a**(1/3)-b**(1/3)*x)/(b*x**3-a)**(1/2),x)","- \int \frac{x}{- 2^{\frac{2}{3}} \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx"," ",0,"-Integral(x/(-2**(2/3)*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x)","F",0
72,0,0,0,0.000000," ","integrate(x/(2**(2/3)*a**(1/3)+b**(1/3)*x)/(-b*x**3-a)**(1/2),x)","\int \frac{x}{\sqrt{- a - b x^{3}} \left(2^{\frac{2}{3}} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral(x/(sqrt(-a - b*x**3)*(2**(2/3)*a**(1/3) + b**(1/3)*x)), x)","F",0
73,0,0,0,0.000000," ","integrate(x/(d*x+c)/(4*d**3*x**3+c**3)**(1/2),x)","\int \frac{x}{\left(c + d x\right) \sqrt{c^{3} + 4 d^{3} x^{3}}}\, dx"," ",0,"Integral(x/((c + d*x)*sqrt(c**3 + 4*d**3*x**3)), x)","F",0
74,0,0,0,0.000000," ","integrate((1+x)/(2-x)/(x**3+1)**(1/2),x)","- \int \frac{x}{x \sqrt{x^{3} + 1} - 2 \sqrt{x^{3} + 1}}\, dx - \int \frac{1}{x \sqrt{x^{3} + 1} - 2 \sqrt{x^{3} + 1}}\, dx"," ",0,"-Integral(x/(x*sqrt(x**3 + 1) - 2*sqrt(x**3 + 1)), x) - Integral(1/(x*sqrt(x**3 + 1) - 2*sqrt(x**3 + 1)), x)","F",0
75,0,0,0,0.000000," ","integrate((1-x)/(2+x)/(-x**3+1)**(1/2),x)","- \int \frac{x}{x \sqrt{1 - x^{3}} + 2 \sqrt{1 - x^{3}}}\, dx - \int \left(- \frac{1}{x \sqrt{1 - x^{3}} + 2 \sqrt{1 - x^{3}}}\right)\, dx"," ",0,"-Integral(x/(x*sqrt(1 - x**3) + 2*sqrt(1 - x**3)), x) - Integral(-1/(x*sqrt(1 - x**3) + 2*sqrt(1 - x**3)), x)","F",0
76,0,0,0,0.000000," ","integrate((1-x)/(2+x)/(x**3-1)**(1/2),x)","- \int \frac{x}{x \sqrt{x^{3} - 1} + 2 \sqrt{x^{3} - 1}}\, dx - \int \left(- \frac{1}{x \sqrt{x^{3} - 1} + 2 \sqrt{x^{3} - 1}}\right)\, dx"," ",0,"-Integral(x/(x*sqrt(x**3 - 1) + 2*sqrt(x**3 - 1)), x) - Integral(-1/(x*sqrt(x**3 - 1) + 2*sqrt(x**3 - 1)), x)","F",0
77,0,0,0,0.000000," ","integrate((1+x)/(2-x)/(-x**3-1)**(1/2),x)","- \int \frac{x}{x \sqrt{- x^{3} - 1} - 2 \sqrt{- x^{3} - 1}}\, dx - \int \frac{1}{x \sqrt{- x^{3} - 1} - 2 \sqrt{- x^{3} - 1}}\, dx"," ",0,"-Integral(x/(x*sqrt(-x**3 - 1) - 2*sqrt(-x**3 - 1)), x) - Integral(1/(x*sqrt(-x**3 - 1) - 2*sqrt(-x**3 - 1)), x)","F",0
78,0,0,0,0.000000," ","integrate((a**(1/3)+b**(1/3)*x)/(2*a**(1/3)-b**(1/3)*x)/(b*x**3+a)**(1/2),x)","- \int \frac{\sqrt[3]{a}}{- 2 \sqrt[3]{a} \sqrt{a + b x^{3}} + \sqrt[3]{b} x \sqrt{a + b x^{3}}}\, dx - \int \frac{\sqrt[3]{b} x}{- 2 \sqrt[3]{a} \sqrt{a + b x^{3}} + \sqrt[3]{b} x \sqrt{a + b x^{3}}}\, dx"," ",0,"-Integral(a**(1/3)/(-2*a**(1/3)*sqrt(a + b*x**3) + b**(1/3)*x*sqrt(a + b*x**3)), x) - Integral(b**(1/3)*x/(-2*a**(1/3)*sqrt(a + b*x**3) + b**(1/3)*x*sqrt(a + b*x**3)), x)","F",0
79,0,0,0,0.000000," ","integrate((a**(1/3)-b**(1/3)*x)/(2*a**(1/3)+b**(1/3)*x)/(-b*x**3+a)**(1/2),x)","- \int \left(- \frac{\sqrt[3]{a}}{2 \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\right)\, dx - \int \frac{\sqrt[3]{b} x}{2 \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx"," ",0,"-Integral(-a**(1/3)/(2*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x) - Integral(b**(1/3)*x/(2*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x)","F",0
80,0,0,0,0.000000," ","integrate((a**(1/3)-b**(1/3)*x)/(2*a**(1/3)+b**(1/3)*x)/(b*x**3-a)**(1/2),x)","- \int \left(- \frac{\sqrt[3]{a}}{2 \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\right)\, dx - \int \frac{\sqrt[3]{b} x}{2 \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx"," ",0,"-Integral(-a**(1/3)/(2*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x) - Integral(b**(1/3)*x/(2*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x)","F",0
81,0,0,0,0.000000," ","integrate((a**(1/3)+b**(1/3)*x)/(2*a**(1/3)-b**(1/3)*x)/(-b*x**3-a)**(1/2),x)","- \int \frac{\sqrt[3]{a}}{- 2 \sqrt[3]{a} \sqrt{- a - b x^{3}} + \sqrt[3]{b} x \sqrt{- a - b x^{3}}}\, dx - \int \frac{\sqrt[3]{b} x}{- 2 \sqrt[3]{a} \sqrt{- a - b x^{3}} + \sqrt[3]{b} x \sqrt{- a - b x^{3}}}\, dx"," ",0,"-Integral(a**(1/3)/(-2*a**(1/3)*sqrt(-a - b*x**3) + b**(1/3)*x*sqrt(-a - b*x**3)), x) - Integral(b**(1/3)*x/(-2*a**(1/3)*sqrt(-a - b*x**3) + b**(1/3)*x*sqrt(-a - b*x**3)), x)","F",0
82,0,0,0,0.000000," ","integrate((-2*d*x+c)/(d*x+c)/(-8*d**3*x**3+c**3)**(1/2),x)","- \int \left(- \frac{c}{c \sqrt{c^{3} - 8 d^{3} x^{3}} + d x \sqrt{c^{3} - 8 d^{3} x^{3}}}\right)\, dx - \int \frac{2 d x}{c \sqrt{c^{3} - 8 d^{3} x^{3}} + d x \sqrt{c^{3} - 8 d^{3} x^{3}}}\, dx"," ",0,"-Integral(-c/(c*sqrt(c**3 - 8*d**3*x**3) + d*x*sqrt(c**3 - 8*d**3*x**3)), x) - Integral(2*d*x/(c*sqrt(c**3 - 8*d**3*x**3) + d*x*sqrt(c**3 - 8*d**3*x**3)), x)","F",0
83,0,0,0,0.000000," ","integrate((f*x+e)/(2-x)/(x**3+1)**(1/2),x)","- \int \frac{e}{x \sqrt{x^{3} + 1} - 2 \sqrt{x^{3} + 1}}\, dx - \int \frac{f x}{x \sqrt{x^{3} + 1} - 2 \sqrt{x^{3} + 1}}\, dx"," ",0,"-Integral(e/(x*sqrt(x**3 + 1) - 2*sqrt(x**3 + 1)), x) - Integral(f*x/(x*sqrt(x**3 + 1) - 2*sqrt(x**3 + 1)), x)","F",0
84,0,0,0,0.000000," ","integrate((f*x+e)/(2+x)/(-x**3+1)**(1/2),x)","\int \frac{e + f x}{\sqrt{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 2\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(-(x - 1)*(x**2 + x + 1))*(x + 2)), x)","F",0
85,0,0,0,0.000000," ","integrate((f*x+e)/(2+x)/(x**3-1)**(1/2),x)","\int \frac{e + f x}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 2\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt((x - 1)*(x**2 + x + 1))*(x + 2)), x)","F",0
86,0,0,0,0.000000," ","integrate((f*x+e)/(2-x)/(-x**3-1)**(1/2),x)","- \int \frac{e}{x \sqrt{- x^{3} - 1} - 2 \sqrt{- x^{3} - 1}}\, dx - \int \frac{f x}{x \sqrt{- x^{3} - 1} - 2 \sqrt{- x^{3} - 1}}\, dx"," ",0,"-Integral(e/(x*sqrt(-x**3 - 1) - 2*sqrt(-x**3 - 1)), x) - Integral(f*x/(x*sqrt(-x**3 - 1) - 2*sqrt(-x**3 - 1)), x)","F",0
87,0,0,0,0.000000," ","integrate((f*x+e)/(2*a**(1/3)-b**(1/3)*x)/(b*x**3+a)**(1/2),x)","- \int \frac{e}{- 2 \sqrt[3]{a} \sqrt{a + b x^{3}} + \sqrt[3]{b} x \sqrt{a + b x^{3}}}\, dx - \int \frac{f x}{- 2 \sqrt[3]{a} \sqrt{a + b x^{3}} + \sqrt[3]{b} x \sqrt{a + b x^{3}}}\, dx"," ",0,"-Integral(e/(-2*a**(1/3)*sqrt(a + b*x**3) + b**(1/3)*x*sqrt(a + b*x**3)), x) - Integral(f*x/(-2*a**(1/3)*sqrt(a + b*x**3) + b**(1/3)*x*sqrt(a + b*x**3)), x)","F",0
88,0,0,0,0.000000," ","integrate((f*x+e)/(2*a**(1/3)+b**(1/3)*x)/(-b*x**3+a)**(1/2),x)","\int \frac{e + f x}{\left(2 \sqrt[3]{a} + \sqrt[3]{b} x\right) \sqrt{a - b x^{3}}}\, dx"," ",0,"Integral((e + f*x)/((2*a**(1/3) + b**(1/3)*x)*sqrt(a - b*x**3)), x)","F",0
89,0,0,0,0.000000," ","integrate((f*x+e)/(2*a**(1/3)+b**(1/3)*x)/(b*x**3-a)**(1/2),x)","\int \frac{e + f x}{\left(2 \sqrt[3]{a} + \sqrt[3]{b} x\right) \sqrt{- a + b x^{3}}}\, dx"," ",0,"Integral((e + f*x)/((2*a**(1/3) + b**(1/3)*x)*sqrt(-a + b*x**3)), x)","F",0
90,0,0,0,0.000000," ","integrate((f*x+e)/(2*a**(1/3)-b**(1/3)*x)/(-b*x**3-a)**(1/2),x)","- \int \frac{e}{- 2 \sqrt[3]{a} \sqrt{- a - b x^{3}} + \sqrt[3]{b} x \sqrt{- a - b x^{3}}}\, dx - \int \frac{f x}{- 2 \sqrt[3]{a} \sqrt{- a - b x^{3}} + \sqrt[3]{b} x \sqrt{- a - b x^{3}}}\, dx"," ",0,"-Integral(e/(-2*a**(1/3)*sqrt(-a - b*x**3) + b**(1/3)*x*sqrt(-a - b*x**3)), x) - Integral(f*x/(-2*a**(1/3)*sqrt(-a - b*x**3) + b**(1/3)*x*sqrt(-a - b*x**3)), x)","F",0
91,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(-8*d**3*x**3+c**3)**(1/2),x)","\int \frac{e + f x}{\sqrt{- \left(- c + 2 d x\right) \left(c^{2} + 2 c d x + 4 d^{2} x^{2}\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(-(-c + 2*d*x)*(c**2 + 2*c*d*x + 4*d**2*x**2))*(c + d*x)), x)","F",0
92,0,0,0,0.000000," ","integrate(x/(2-x)/(x**3+1)**(1/2),x)","- \int \frac{x}{x \sqrt{x^{3} + 1} - 2 \sqrt{x^{3} + 1}}\, dx"," ",0,"-Integral(x/(x*sqrt(x**3 + 1) - 2*sqrt(x**3 + 1)), x)","F",0
93,0,0,0,0.000000," ","integrate(x/(2+x)/(-x**3+1)**(1/2),x)","\int \frac{x}{\sqrt{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 2\right)}\, dx"," ",0,"Integral(x/(sqrt(-(x - 1)*(x**2 + x + 1))*(x + 2)), x)","F",0
94,0,0,0,0.000000," ","integrate(x/(2+x)/(x**3-1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 2\right)}\, dx"," ",0,"Integral(x/(sqrt((x - 1)*(x**2 + x + 1))*(x + 2)), x)","F",0
95,0,0,0,0.000000," ","integrate(x/(2-x)/(-x**3-1)**(1/2),x)","- \int \frac{x}{x \sqrt{- x^{3} - 1} - 2 \sqrt{- x^{3} - 1}}\, dx"," ",0,"-Integral(x/(x*sqrt(-x**3 - 1) - 2*sqrt(-x**3 - 1)), x)","F",0
96,0,0,0,0.000000," ","integrate(x/(2*a**(1/3)-b**(1/3)*x)/(b*x**3+a)**(1/2),x)","- \int \frac{x}{- 2 \sqrt[3]{a} \sqrt{a + b x^{3}} + \sqrt[3]{b} x \sqrt{a + b x^{3}}}\, dx"," ",0,"-Integral(x/(-2*a**(1/3)*sqrt(a + b*x**3) + b**(1/3)*x*sqrt(a + b*x**3)), x)","F",0
97,0,0,0,0.000000," ","integrate(x/(2*a**(1/3)+b**(1/3)*x)/(-b*x**3+a)**(1/2),x)","\int \frac{x}{\left(2 \sqrt[3]{a} + \sqrt[3]{b} x\right) \sqrt{a - b x^{3}}}\, dx"," ",0,"Integral(x/((2*a**(1/3) + b**(1/3)*x)*sqrt(a - b*x**3)), x)","F",0
98,0,0,0,0.000000," ","integrate(x/(2*a**(1/3)+b**(1/3)*x)/(b*x**3-a)**(1/2),x)","\int \frac{x}{\left(2 \sqrt[3]{a} + \sqrt[3]{b} x\right) \sqrt{- a + b x^{3}}}\, dx"," ",0,"Integral(x/((2*a**(1/3) + b**(1/3)*x)*sqrt(-a + b*x**3)), x)","F",0
99,0,0,0,0.000000," ","integrate(x/(2*a**(1/3)-b**(1/3)*x)/(-b*x**3-a)**(1/2),x)","- \int \frac{x}{- 2 \sqrt[3]{a} \sqrt{- a - b x^{3}} + \sqrt[3]{b} x \sqrt{- a - b x^{3}}}\, dx"," ",0,"-Integral(x/(-2*a**(1/3)*sqrt(-a - b*x**3) + b**(1/3)*x*sqrt(-a - b*x**3)), x)","F",0
100,0,0,0,0.000000," ","integrate(x/(d*x+c)/(-8*d**3*x**3+c**3)**(1/2),x)","\int \frac{x}{\sqrt{- \left(- c + 2 d x\right) \left(c^{2} + 2 c d x + 4 d^{2} x^{2}\right)} \left(c + d x\right)}\, dx"," ",0,"Integral(x/(sqrt(-(-c + 2*d*x)*(c**2 + 2*c*d*x + 4*d**2*x**2))*(c + d*x)), x)","F",0
101,0,0,0,0.000000," ","integrate((1+x+3**(1/2))/(1+x-3**(1/2))/(x**3+1)**(1/2),x)","\int \frac{x + 1 + \sqrt{3}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x - \sqrt{3} + 1\right)}\, dx"," ",0,"Integral((x + 1 + sqrt(3))/(sqrt((x + 1)*(x**2 - x + 1))*(x - sqrt(3) + 1)), x)","F",0
102,0,0,0,0.000000," ","integrate((1-x+3**(1/2))/(1-x-3**(1/2))/(-x**3+1)**(1/2),x)","\int \frac{x - \sqrt{3} - 1}{\sqrt{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x - 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((x - sqrt(3) - 1)/(sqrt(-(x - 1)*(x**2 + x + 1))*(x - 1 + sqrt(3))), x)","F",0
103,0,0,0,0.000000," ","integrate((1-x+3**(1/2))/(1-x-3**(1/2))/(x**3-1)**(1/2),x)","\int \frac{x - \sqrt{3} - 1}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x - 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((x - sqrt(3) - 1)/(sqrt((x - 1)*(x**2 + x + 1))*(x - 1 + sqrt(3))), x)","F",0
104,0,0,0,0.000000," ","integrate((1+x+3**(1/2))/(1+x-3**(1/2))/(-x**3-1)**(1/2),x)","\int \frac{x + 1 + \sqrt{3}}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x - \sqrt{3} + 1\right)}\, dx"," ",0,"Integral((x + 1 + sqrt(3))/(sqrt(-(x + 1)*(x**2 - x + 1))*(x - sqrt(3) + 1)), x)","F",0
105,0,0,0,0.000000," ","integrate((b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b*x**3+a)**(1/2),x)","\int \frac{\sqrt[3]{a} + \sqrt{3} \sqrt[3]{a} + \sqrt[3]{b} x}{\sqrt{a + b x^{3}} \left(- \sqrt{3} \sqrt[3]{a} + \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((a**(1/3) + sqrt(3)*a**(1/3) + b**(1/3)*x)/(sqrt(a + b*x**3)*(-sqrt(3)*a**(1/3) + a**(1/3) + b**(1/3)*x)), x)","F",0
106,0,0,0,0.000000," ","integrate((-b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b*x**3+a)**(1/2),x)","\int \frac{- \sqrt{3} \sqrt[3]{a} - \sqrt[3]{a} + \sqrt[3]{b} x}{\sqrt{a - b x^{3}} \left(- \sqrt[3]{a} + \sqrt{3} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((-sqrt(3)*a**(1/3) - a**(1/3) + b**(1/3)*x)/(sqrt(a - b*x**3)*(-a**(1/3) + sqrt(3)*a**(1/3) + b**(1/3)*x)), x)","F",0
107,0,0,0,0.000000," ","integrate((-b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b*x**3-a)**(1/2),x)","\int \frac{- \sqrt{3} \sqrt[3]{a} - \sqrt[3]{a} + \sqrt[3]{b} x}{\sqrt{- a + b x^{3}} \left(- \sqrt[3]{a} + \sqrt{3} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((-sqrt(3)*a**(1/3) - a**(1/3) + b**(1/3)*x)/(sqrt(-a + b*x**3)*(-a**(1/3) + sqrt(3)*a**(1/3) + b**(1/3)*x)), x)","F",0
108,0,0,0,0.000000," ","integrate((b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b*x**3-a)**(1/2),x)","\int \frac{\sqrt[3]{a} + \sqrt{3} \sqrt[3]{a} + \sqrt[3]{b} x}{\sqrt{- a - b x^{3}} \left(- \sqrt{3} \sqrt[3]{a} + \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((a**(1/3) + sqrt(3)*a**(1/3) + b**(1/3)*x)/(sqrt(-a - b*x**3)*(-sqrt(3)*a**(1/3) + a**(1/3) + b**(1/3)*x)), x)","F",0
109,0,0,0,0.000000," ","integrate((1+(b/a)**(1/3)*x+3**(1/2))/(1+(b/a)**(1/3)*x-3**(1/2))/(b*x**3+a)**(1/2),x)","\int \frac{x \sqrt[3]{\frac{b}{a}} + 1 + \sqrt{3}}{\sqrt{a + b x^{3}} \left(x \sqrt[3]{\frac{b}{a}} - \sqrt{3} + 1\right)}\, dx"," ",0,"Integral((x*(b/a)**(1/3) + 1 + sqrt(3))/(sqrt(a + b*x**3)*(x*(b/a)**(1/3) - sqrt(3) + 1)), x)","F",0
110,0,0,0,0.000000," ","integrate((1-(b/a)**(1/3)*x+3**(1/2))/(1-(b/a)**(1/3)*x-3**(1/2))/(-b*x**3+a)**(1/2),x)","\int \frac{x \sqrt[3]{\frac{b}{a}} - \sqrt{3} - 1}{\sqrt{a - b x^{3}} \left(x \sqrt[3]{\frac{b}{a}} - 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((x*(b/a)**(1/3) - sqrt(3) - 1)/(sqrt(a - b*x**3)*(x*(b/a)**(1/3) - 1 + sqrt(3))), x)","F",0
111,0,0,0,0.000000," ","integrate((1-(b/a)**(1/3)*x+3**(1/2))/(1-(b/a)**(1/3)*x-3**(1/2))/(b*x**3-a)**(1/2),x)","\int \frac{x \sqrt[3]{\frac{b}{a}} - \sqrt{3} - 1}{\sqrt{- a + b x^{3}} \left(x \sqrt[3]{\frac{b}{a}} - 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((x*(b/a)**(1/3) - sqrt(3) - 1)/(sqrt(-a + b*x**3)*(x*(b/a)**(1/3) - 1 + sqrt(3))), x)","F",0
112,0,0,0,0.000000," ","integrate((1+(b/a)**(1/3)*x+3**(1/2))/(1+(b/a)**(1/3)*x-3**(1/2))/(-b*x**3-a)**(1/2),x)","\int \frac{x \sqrt[3]{\frac{b}{a}} + 1 + \sqrt{3}}{\sqrt{- a - b x^{3}} \left(x \sqrt[3]{\frac{b}{a}} - \sqrt{3} + 1\right)}\, dx"," ",0,"Integral((x*(b/a)**(1/3) + 1 + sqrt(3))/(sqrt(-a - b*x**3)*(x*(b/a)**(1/3) - sqrt(3) + 1)), x)","F",0
113,0,0,0,0.000000," ","integrate((1+x-3**(1/2))/(1+x+3**(1/2))/(x**3+1)**(1/2),x)","\int \frac{x - \sqrt{3} + 1}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((x - sqrt(3) + 1)/(sqrt((x + 1)*(x**2 - x + 1))*(x + 1 + sqrt(3))), x)","F",0
114,0,0,0,0.000000," ","integrate((1-x-3**(1/2))/(1-x+3**(1/2))/(-x**3+1)**(1/2),x)","\int \frac{x - 1 + \sqrt{3}}{\sqrt{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x - \sqrt{3} - 1\right)}\, dx"," ",0,"Integral((x - 1 + sqrt(3))/(sqrt(-(x - 1)*(x**2 + x + 1))*(x - sqrt(3) - 1)), x)","F",0
115,0,0,0,0.000000," ","integrate((1-x-3**(1/2))/(1-x+3**(1/2))/(x**3-1)**(1/2),x)","\int \frac{x - 1 + \sqrt{3}}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x - \sqrt{3} - 1\right)}\, dx"," ",0,"Integral((x - 1 + sqrt(3))/(sqrt((x - 1)*(x**2 + x + 1))*(x - sqrt(3) - 1)), x)","F",0
116,0,0,0,0.000000," ","integrate((1+x-3**(1/2))/(1+x+3**(1/2))/(-x**3-1)**(1/2),x)","\int \frac{x - \sqrt{3} + 1}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((x - sqrt(3) + 1)/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 1 + sqrt(3))), x)","F",0
117,0,0,0,0.000000," ","integrate((b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(b*x**3+a)**(1/2),x)","\int \frac{- \sqrt{3} \sqrt[3]{a} + \sqrt[3]{a} + \sqrt[3]{b} x}{\sqrt{a + b x^{3}} \left(\sqrt[3]{a} + \sqrt{3} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((-sqrt(3)*a**(1/3) + a**(1/3) + b**(1/3)*x)/(sqrt(a + b*x**3)*(a**(1/3) + sqrt(3)*a**(1/3) + b**(1/3)*x)), x)","F",0
118,0,0,0,0.000000," ","integrate((-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(-b*x**3+a)**(1/2),x)","\int \frac{- \sqrt[3]{a} + \sqrt{3} \sqrt[3]{a} + \sqrt[3]{b} x}{\sqrt{a - b x^{3}} \left(- \sqrt{3} \sqrt[3]{a} - \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((-a**(1/3) + sqrt(3)*a**(1/3) + b**(1/3)*x)/(sqrt(a - b*x**3)*(-sqrt(3)*a**(1/3) - a**(1/3) + b**(1/3)*x)), x)","F",0
119,0,0,0,0.000000," ","integrate((-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(b*x**3-a)**(1/2),x)","\int \frac{- \sqrt[3]{a} + \sqrt{3} \sqrt[3]{a} + \sqrt[3]{b} x}{\sqrt{- a + b x^{3}} \left(- \sqrt{3} \sqrt[3]{a} - \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((-a**(1/3) + sqrt(3)*a**(1/3) + b**(1/3)*x)/(sqrt(-a + b*x**3)*(-sqrt(3)*a**(1/3) - a**(1/3) + b**(1/3)*x)), x)","F",0
120,0,0,0,0.000000," ","integrate((b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b**(1/3)*x+a**(1/3)*(1+3**(1/2)))/(-b*x**3-a)**(1/2),x)","\int \frac{- \sqrt{3} \sqrt[3]{a} + \sqrt[3]{a} + \sqrt[3]{b} x}{\sqrt{- a - b x^{3}} \left(\sqrt[3]{a} + \sqrt{3} \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((-sqrt(3)*a**(1/3) + a**(1/3) + b**(1/3)*x)/(sqrt(-a - b*x**3)*(a**(1/3) + sqrt(3)*a**(1/3) + b**(1/3)*x)), x)","F",0
121,0,0,0,0.000000," ","integrate((1+(b/a)**(1/3)*x-3**(1/2))/(1+(b/a)**(1/3)*x+3**(1/2))/(b*x**3+a)**(1/2),x)","\int \frac{x \sqrt[3]{\frac{b}{a}} - \sqrt{3} + 1}{\sqrt{a + b x^{3}} \left(x \sqrt[3]{\frac{b}{a}} + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((x*(b/a)**(1/3) - sqrt(3) + 1)/(sqrt(a + b*x**3)*(x*(b/a)**(1/3) + 1 + sqrt(3))), x)","F",0
122,0,0,0,0.000000," ","integrate((1-(b/a)**(1/3)*x-3**(1/2))/(1-(b/a)**(1/3)*x+3**(1/2))/(-b*x**3+a)**(1/2),x)","\int \frac{x \sqrt[3]{\frac{b}{a}} - 1 + \sqrt{3}}{\sqrt{a - b x^{3}} \left(x \sqrt[3]{\frac{b}{a}} - \sqrt{3} - 1\right)}\, dx"," ",0,"Integral((x*(b/a)**(1/3) - 1 + sqrt(3))/(sqrt(a - b*x**3)*(x*(b/a)**(1/3) - sqrt(3) - 1)), x)","F",0
123,0,0,0,0.000000," ","integrate((1-(b/a)**(1/3)*x-3**(1/2))/(1-(b/a)**(1/3)*x+3**(1/2))/(b*x**3-a)**(1/2),x)","\int \frac{x \sqrt[3]{\frac{b}{a}} - 1 + \sqrt{3}}{\sqrt{- a + b x^{3}} \left(x \sqrt[3]{\frac{b}{a}} - \sqrt{3} - 1\right)}\, dx"," ",0,"Integral((x*(b/a)**(1/3) - 1 + sqrt(3))/(sqrt(-a + b*x**3)*(x*(b/a)**(1/3) - sqrt(3) - 1)), x)","F",0
124,0,0,0,0.000000," ","integrate((1+(b/a)**(1/3)*x-3**(1/2))/(1+(b/a)**(1/3)*x+3**(1/2))/(-b*x**3-a)**(1/2),x)","\int \frac{x \sqrt[3]{\frac{b}{a}} - \sqrt{3} + 1}{\sqrt{- a - b x^{3}} \left(x \sqrt[3]{\frac{b}{a}} + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((x*(b/a)**(1/3) - sqrt(3) + 1)/(sqrt(-a - b*x**3)*(x*(b/a)**(1/3) + 1 + sqrt(3))), x)","F",0
125,0,0,0,0.000000," ","integrate((1+x)/(1+x+3**(1/2))/(x**3+1)**(1/2),x)","\int \frac{x + 1}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((x + 1)/(sqrt((x + 1)*(x**2 - x + 1))*(x + 1 + sqrt(3))), x)","F",0
126,0,0,0,0.000000," ","integrate((1+x)/(1+x-3**(1/2))/(x**3+1)**(1/2),x)","\int \frac{x + 1}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x - \sqrt{3} + 1\right)}\, dx"," ",0,"Integral((x + 1)/(sqrt((x + 1)*(x**2 - x + 1))*(x - sqrt(3) + 1)), x)","F",0
127,0,0,0,0.000000," ","integrate((f*x+e)/(1+x+3**(1/2))/(x**3+1)**(1/2),x)","\int \frac{e + f x}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt((x + 1)*(x**2 - x + 1))*(x + 1 + sqrt(3))), x)","F",0
128,0,0,0,0.000000," ","integrate((f*x+e)/(1-x+3**(1/2))/(-x**3+1)**(1/2),x)","- \int \frac{e}{x \sqrt{1 - x^{3}} - \sqrt{3} \sqrt{1 - x^{3}} - \sqrt{1 - x^{3}}}\, dx - \int \frac{f x}{x \sqrt{1 - x^{3}} - \sqrt{3} \sqrt{1 - x^{3}} - \sqrt{1 - x^{3}}}\, dx"," ",0,"-Integral(e/(x*sqrt(1 - x**3) - sqrt(3)*sqrt(1 - x**3) - sqrt(1 - x**3)), x) - Integral(f*x/(x*sqrt(1 - x**3) - sqrt(3)*sqrt(1 - x**3) - sqrt(1 - x**3)), x)","F",0
129,0,0,0,0.000000," ","integrate((f*x+e)/(1-x+3**(1/2))/(x**3-1)**(1/2),x)","- \int \frac{e}{x \sqrt{x^{3} - 1} - \sqrt{3} \sqrt{x^{3} - 1} - \sqrt{x^{3} - 1}}\, dx - \int \frac{f x}{x \sqrt{x^{3} - 1} - \sqrt{3} \sqrt{x^{3} - 1} - \sqrt{x^{3} - 1}}\, dx"," ",0,"-Integral(e/(x*sqrt(x**3 - 1) - sqrt(3)*sqrt(x**3 - 1) - sqrt(x**3 - 1)), x) - Integral(f*x/(x*sqrt(x**3 - 1) - sqrt(3)*sqrt(x**3 - 1) - sqrt(x**3 - 1)), x)","F",0
130,0,0,0,0.000000," ","integrate((f*x+e)/(1+x+3**(1/2))/(-x**3-1)**(1/2),x)","\int \frac{e + f x}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 1 + sqrt(3))), x)","F",0
131,0,0,0,0.000000," ","integrate((f*x+e)/(b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b*x**3+a)**(1/2),x)","\int \frac{e + f x}{\sqrt{a + b x^{3}} \left(- \sqrt{3} \sqrt[3]{a} + \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(a + b*x**3)*(-sqrt(3)*a**(1/3) + a**(1/3) + b**(1/3)*x)), x)","F",0
132,0,0,0,0.000000," ","integrate((f*x+e)/(-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b*x**3+a)**(1/2),x)","- \int \frac{e}{- \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt{3} \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx - \int \frac{f x}{- \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt{3} \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx"," ",0,"-Integral(e/(-a**(1/3)*sqrt(a - b*x**3) + sqrt(3)*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x) - Integral(f*x/(-a**(1/3)*sqrt(a - b*x**3) + sqrt(3)*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x)","F",0
133,0,0,0,0.000000," ","integrate((f*x+e)/(-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b*x**3-a)**(1/2),x)","- \int \frac{e}{- \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt{3} \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx - \int \frac{f x}{- \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt{3} \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx"," ",0,"-Integral(e/(-a**(1/3)*sqrt(-a + b*x**3) + sqrt(3)*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x) - Integral(f*x/(-a**(1/3)*sqrt(-a + b*x**3) + sqrt(3)*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x)","F",0
134,0,0,0,0.000000," ","integrate((f*x+e)/(b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b*x**3-a)**(1/2),x)","\int \frac{e + f x}{\sqrt{- a - b x^{3}} \left(- \sqrt{3} \sqrt[3]{a} + \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(-a - b*x**3)*(-sqrt(3)*a**(1/3) + a**(1/3) + b**(1/3)*x)), x)","F",0
135,0,0,0,0.000000," ","integrate(x/(1+x+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 + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral(x/(sqrt((x + 1)*(x**2 - x + 1))*(x + 1 + sqrt(3))), x)","F",0
136,0,0,0,0.000000," ","integrate(x/(1-x+3**(1/2))/(-x**3+1)**(1/2),x)","- \int \frac{x}{x \sqrt{1 - x^{3}} - \sqrt{3} \sqrt{1 - x^{3}} - \sqrt{1 - x^{3}}}\, dx"," ",0,"-Integral(x/(x*sqrt(1 - x**3) - sqrt(3)*sqrt(1 - x**3) - sqrt(1 - x**3)), x)","F",0
137,0,0,0,0.000000," ","integrate(x/(1-x+3**(1/2))/(x**3-1)**(1/2),x)","- \int \frac{x}{x \sqrt{x^{3} - 1} - \sqrt{3} \sqrt{x^{3} - 1} - \sqrt{x^{3} - 1}}\, dx"," ",0,"-Integral(x/(x*sqrt(x**3 - 1) - sqrt(3)*sqrt(x**3 - 1) - sqrt(x**3 - 1)), x)","F",0
138,0,0,0,0.000000," ","integrate(x/(1+x+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 + 1 + \sqrt{3}\right)}\, dx"," ",0,"Integral(x/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 1 + sqrt(3))), x)","F",0
139,0,0,0,0.000000," ","integrate(x/(1+x-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 - \sqrt{3} + 1\right)}\, dx"," ",0,"Integral(x/(sqrt((x + 1)*(x**2 - x + 1))*(x - sqrt(3) + 1)), x)","F",0
140,0,0,0,0.000000," ","integrate(x/(b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b*x**3+a)**(1/2),x)","\int \frac{x}{\sqrt{a + b x^{3}} \left(- \sqrt{3} \sqrt[3]{a} + \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral(x/(sqrt(a + b*x**3)*(-sqrt(3)*a**(1/3) + a**(1/3) + b**(1/3)*x)), x)","F",0
141,0,0,0,0.000000," ","integrate(x/(-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b*x**3+a)**(1/2),x)","- \int \frac{x}{- \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt{3} \sqrt[3]{a} \sqrt{a - b x^{3}} + \sqrt[3]{b} x \sqrt{a - b x^{3}}}\, dx"," ",0,"-Integral(x/(-a**(1/3)*sqrt(a - b*x**3) + sqrt(3)*a**(1/3)*sqrt(a - b*x**3) + b**(1/3)*x*sqrt(a - b*x**3)), x)","F",0
142,0,0,0,0.000000," ","integrate(x/(-b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(b*x**3-a)**(1/2),x)","- \int \frac{x}{- \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt{3} \sqrt[3]{a} \sqrt{- a + b x^{3}} + \sqrt[3]{b} x \sqrt{- a + b x^{3}}}\, dx"," ",0,"-Integral(x/(-a**(1/3)*sqrt(-a + b*x**3) + sqrt(3)*a**(1/3)*sqrt(-a + b*x**3) + b**(1/3)*x*sqrt(-a + b*x**3)), x)","F",0
143,0,0,0,0.000000," ","integrate(x/(b**(1/3)*x+a**(1/3)*(1-3**(1/2)))/(-b*x**3-a)**(1/2),x)","\int \frac{x}{\sqrt{- a - b x^{3}} \left(- \sqrt{3} \sqrt[3]{a} + \sqrt[3]{a} + \sqrt[3]{b} x\right)}\, dx"," ",0,"Integral(x/(sqrt(-a - b*x**3)*(-sqrt(3)*a**(1/3) + a**(1/3) + b**(1/3)*x)), x)","F",0
144,0,0,0,0.000000," ","integrate((1+x+3**(1/2))/(d*x+c)/(x**3+1)**(1/2),x)","\int \frac{x + 1 + \sqrt{3}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((x + 1 + sqrt(3))/(sqrt((x + 1)*(x**2 - x + 1))*(c + d*x)), x)","F",0
145,0,0,0,0.000000," ","integrate((1-x+3**(1/2))/(d*x+c)/(-x**3+1)**(1/2),x)","- \int \left(- \frac{\sqrt{3}}{c \sqrt{1 - x^{3}} + d x \sqrt{1 - x^{3}}}\right)\, dx - \int \frac{x}{c \sqrt{1 - x^{3}} + d x \sqrt{1 - x^{3}}}\, dx - \int \left(- \frac{1}{c \sqrt{1 - x^{3}} + d x \sqrt{1 - x^{3}}}\right)\, dx"," ",0,"-Integral(-sqrt(3)/(c*sqrt(1 - x**3) + d*x*sqrt(1 - x**3)), x) - Integral(x/(c*sqrt(1 - x**3) + d*x*sqrt(1 - x**3)), x) - Integral(-1/(c*sqrt(1 - x**3) + d*x*sqrt(1 - x**3)), x)","F",0
146,0,0,0,0.000000," ","integrate((1-x+3**(1/2))/(d*x+c)/(x**3-1)**(1/2),x)","- \int \left(- \frac{\sqrt{3}}{c \sqrt{x^{3} - 1} + d x \sqrt{x^{3} - 1}}\right)\, dx - \int \frac{x}{c \sqrt{x^{3} - 1} + d x \sqrt{x^{3} - 1}}\, dx - \int \left(- \frac{1}{c \sqrt{x^{3} - 1} + d x \sqrt{x^{3} - 1}}\right)\, dx"," ",0,"-Integral(-sqrt(3)/(c*sqrt(x**3 - 1) + d*x*sqrt(x**3 - 1)), x) - Integral(x/(c*sqrt(x**3 - 1) + d*x*sqrt(x**3 - 1)), x) - Integral(-1/(c*sqrt(x**3 - 1) + d*x*sqrt(x**3 - 1)), x)","F",0
147,0,0,0,0.000000," ","integrate((1+x+3**(1/2))/(d*x+c)/(-x**3-1)**(1/2),x)","\int \frac{x + 1 + \sqrt{3}}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((x + 1 + sqrt(3))/(sqrt(-(x + 1)*(x**2 - x + 1))*(c + d*x)), x)","F",0
148,0,0,0,0.000000," ","integrate((1+x-3**(1/2))/(d*x+c)/(x**3+1)**(1/2),x)","\int \frac{x - \sqrt{3} + 1}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((x - sqrt(3) + 1)/(sqrt((x + 1)*(x**2 - x + 1))*(c + d*x)), x)","F",0
149,0,0,0,0.000000," ","integrate((1-x-3**(1/2))/(d*x+c)/(-x**3+1)**(1/2),x)","- \int \frac{\sqrt{3}}{c \sqrt{1 - x^{3}} + d x \sqrt{1 - x^{3}}}\, dx - \int \frac{x}{c \sqrt{1 - x^{3}} + d x \sqrt{1 - x^{3}}}\, dx - \int \left(- \frac{1}{c \sqrt{1 - x^{3}} + d x \sqrt{1 - x^{3}}}\right)\, dx"," ",0,"-Integral(sqrt(3)/(c*sqrt(1 - x**3) + d*x*sqrt(1 - x**3)), x) - Integral(x/(c*sqrt(1 - x**3) + d*x*sqrt(1 - x**3)), x) - Integral(-1/(c*sqrt(1 - x**3) + d*x*sqrt(1 - x**3)), x)","F",0
150,0,0,0,0.000000," ","integrate((1-x-3**(1/2))/(d*x+c)/(x**3-1)**(1/2),x)","- \int \frac{\sqrt{3}}{c \sqrt{x^{3} - 1} + d x \sqrt{x^{3} - 1}}\, dx - \int \frac{x}{c \sqrt{x^{3} - 1} + d x \sqrt{x^{3} - 1}}\, dx - \int \left(- \frac{1}{c \sqrt{x^{3} - 1} + d x \sqrt{x^{3} - 1}}\right)\, dx"," ",0,"-Integral(sqrt(3)/(c*sqrt(x**3 - 1) + d*x*sqrt(x**3 - 1)), x) - Integral(x/(c*sqrt(x**3 - 1) + d*x*sqrt(x**3 - 1)), x) - Integral(-1/(c*sqrt(x**3 - 1) + d*x*sqrt(x**3 - 1)), x)","F",0
151,0,0,0,0.000000," ","integrate((1+x-3**(1/2))/(d*x+c)/(-x**3-1)**(1/2),x)","\int \frac{x - \sqrt{3} + 1}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((x - sqrt(3) + 1)/(sqrt(-(x + 1)*(x**2 - x + 1))*(c + d*x)), x)","F",0
152,1,56,0,5.246065," ","integrate((1+x+3**(1/2))/x/(x**3+1)**(1/2),x)","\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{2 \sqrt{3} \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} - \frac{2 \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3}"," ",0,"x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) - 2*sqrt(3)*asinh(x**(-3/2))/3 - 2*asinh(x**(-3/2))/3","A",0
153,1,99,0,8.929806," ","integrate((1-x+3**(1/2))/x/(-x**3+1)**(1/2),x)","- \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)} + \begin{cases} - \frac{2 \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\\frac{2 i \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases} + \sqrt{3} \left(\begin{cases} - \frac{2 \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\\frac{2 i \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}\right)"," ",0,"-x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3)) + Piecewise((-2*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (2*I*asin(x**(-3/2))/3, True)) + sqrt(3)*Piecewise((-2*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (2*I*asin(x**(-3/2))/3, True))","A",0
154,1,94,0,8.927940," ","integrate((1-x+3**(1/2))/x/(x**3-1)**(1/2),x)","\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)} + \begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases} + \sqrt{3} \left(\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}\right)"," ",0,"I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3)) + Piecewise((2*I*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (-2*asin(x**(-3/2))/3, True)) + sqrt(3)*Piecewise((2*I*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (-2*asin(x**(-3/2))/3, True))","A",0
155,1,61,0,5.426314," ","integrate((1+x+3**(1/2))/x/(-x**3-1)**(1/2),x)","- \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{2 i \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} + \frac{2 \sqrt{3} i \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3}"," ",0,"-I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) + 2*I*asinh(x**(-3/2))/3 + 2*sqrt(3)*I*asinh(x**(-3/2))/3","A",0
156,1,56,0,5.196146," ","integrate((1+x-3**(1/2))/x/(x**3+1)**(1/2),x)","\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{2 \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} + \frac{2 \sqrt{3} \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3}"," ",0,"x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) - 2*asinh(x**(-3/2))/3 + 2*sqrt(3)*asinh(x**(-3/2))/3","A",0
157,1,99,0,9.002733," ","integrate((1-x-3**(1/2))/x/(-x**3+1)**(1/2),x)","- \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)} - \sqrt{3} \left(\begin{cases} - \frac{2 \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\\frac{2 i \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}\right) + \begin{cases} - \frac{2 \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\\frac{2 i \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"-x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3)) - sqrt(3)*Piecewise((-2*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (2*I*asin(x**(-3/2))/3, True)) + Piecewise((-2*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (2*I*asin(x**(-3/2))/3, True))","A",0
158,1,94,0,8.977919," ","integrate((1-x-3**(1/2))/x/(x**3-1)**(1/2),x)","\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)} - \sqrt{3} \left(\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}\right) + \begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3)) - sqrt(3)*Piecewise((2*I*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (-2*asin(x**(-3/2))/3, True)) + Piecewise((2*I*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (-2*asin(x**(-3/2))/3, True))","A",0
159,1,61,0,5.512858," ","integrate((1+x-3**(1/2))/x/(-x**3-1)**(1/2),x)","- \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{2 \sqrt{3} i \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} + \frac{2 i \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3}"," ",0,"-I*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3)) - 2*sqrt(3)*I*asinh(x**(-3/2))/3 + 2*I*asinh(x**(-3/2))/3","A",0
160,0,0,0,0.000000," ","integrate(x/(3+x)/(x**3+1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 3\right)}\, dx"," ",0,"Integral(x/(sqrt((x + 1)*(x**2 - x + 1))*(x + 3)), x)","F",0
161,0,0,0,0.000000," ","integrate(x/(3+x)/(-x**3+1)**(1/2),x)","\int \frac{x}{\sqrt{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 3\right)}\, dx"," ",0,"Integral(x/(sqrt(-(x - 1)*(x**2 + x + 1))*(x + 3)), x)","F",0
162,0,0,0,0.000000," ","integrate(x/(3+x)/(x**3-1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(x + 3\right)}\, dx"," ",0,"Integral(x/(sqrt((x - 1)*(x**2 + x + 1))*(x + 3)), x)","F",0
163,0,0,0,0.000000," ","integrate(x/(3+x)/(-x**3-1)**(1/2),x)","\int \frac{x}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(x + 3\right)}\, dx"," ",0,"Integral(x/(sqrt(-(x + 1)*(x**2 - x + 1))*(x + 3)), x)","F",0
164,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(x**3+1)**(1/2),x)","\int \frac{e + f x}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt((x + 1)*(x**2 - x + 1))*(c + d*x)), x)","F",0
165,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(-x**3+1)**(1/2),x)","\int \frac{e + f x}{\sqrt{- \left(x - 1\right) \left(x^{2} + x + 1\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(-(x - 1)*(x**2 + x + 1))*(c + d*x)), x)","F",0
166,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(x**3-1)**(1/2),x)","\int \frac{e + f x}{\sqrt{\left(x - 1\right) \left(x^{2} + x + 1\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt((x - 1)*(x**2 + x + 1))*(c + d*x)), x)","F",0
167,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(-x**3-1)**(1/2),x)","\int \frac{e + f x}{\sqrt{- \left(x + 1\right) \left(x^{2} - x + 1\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((e + f*x)/(sqrt(-(x + 1)*(x**2 - x + 1))*(c + d*x)), x)","F",0
168,1,42,0,2.960099," ","integrate((f*x+e)/x/(x**3+1)**(1/2),x)","- \frac{2 e \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} + \frac{f 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,"-2*e*asinh(x**(-3/2))/3 + f*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
169,1,65,0,3.333685," ","integrate((f*x+e)/x/(-x**3+1)**(1/2),x)","e \left(\begin{cases} - \frac{2 \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\\frac{2 i \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}\right) + \frac{f 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,"e*Piecewise((-2*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (2*I*asin(x**(-3/2))/3, True)) + f*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(2*I*pi))/(3*gamma(4/3))","A",0
170,1,60,0,3.086212," ","integrate((f*x+e)/x/(x**3-1)**(1/2),x)","e \left(\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x^{3}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} & \text{otherwise} \end{cases}\right) - \frac{i f 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,"e*Piecewise((2*I*acosh(x**(-3/2))/3, 1/Abs(x**3) > 1), (-2*asin(x**(-3/2))/3, True)) - I*f*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3)/(3*gamma(4/3))","A",0
171,1,46,0,3.287404," ","integrate((f*x+e)/x/(-x**3-1)**(1/2),x)","\frac{2 i e \operatorname{asinh}{\left(\frac{1}{x^{\frac{3}{2}}} \right)}}{3} - \frac{i f 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,"2*I*e*asinh(x**(-3/2))/3 - I*f*x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))","A",0
172,0,0,0,0.000000," ","integrate((-d*x+c)/(d*x+c)/(d**3*x**3+2*c**3)**(1/3),x)","- \int \left(- \frac{c}{c \sqrt[3]{2 c^{3} + d^{3} x^{3}} + d x \sqrt[3]{2 c^{3} + d^{3} x^{3}}}\right)\, dx - \int \frac{d x}{c \sqrt[3]{2 c^{3} + d^{3} x^{3}} + d x \sqrt[3]{2 c^{3} + d^{3} x^{3}}}\, dx"," ",0,"-Integral(-c/(c*(2*c**3 + d**3*x**3)**(1/3) + d*x*(2*c**3 + d**3*x**3)**(1/3)), x) - Integral(d*x/(c*(2*c**3 + d**3*x**3)**(1/3) + d*x*(2*c**3 + d**3*x**3)**(1/3)), x)","F",0
173,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(d**3*x**3-c**3)**(1/3),x)","\int \frac{e + f x}{\sqrt[3]{\left(- c + d x\right) \left(c^{2} + c d x + d^{2} x^{2}\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((e + f*x)/(((-c + d*x)*(c**2 + c*d*x + d**2*x**2))**(1/3)*(c + d*x)), x)","F",0
174,1,6397,0,7.627855," ","integrate(x**2*(b*x+a)**n*(d*x**3+c),x)","\begin{cases} a^{n} \left(\frac{c x^{3}}{3} + \frac{d x^{6}}{6}\right) & \text{for}\: b = 0 \\\frac{60 a^{5} d \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{137 a^{5} d}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a^{4} b d x \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{625 a^{4} b d x}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{600 a^{3} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{1100 a^{3} b^{2} d x^{2}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} - \frac{2 a^{2} b^{3} c}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{600 a^{2} b^{3} d x^{3} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{900 a^{2} b^{3} d x^{3}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} - \frac{10 a b^{4} c x}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a b^{4} d x^{4} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a b^{4} d x^{4}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} - \frac{20 b^{5} c x^{2}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{60 b^{5} d x^{5} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} & \text{for}\: n = -6 \\- \frac{60 a^{5} d \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{125 a^{5} d}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{4} b d x \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{440 a^{4} b d x}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{360 a^{3} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{540 a^{3} b^{2} d x^{2}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{a^{2} b^{3} c}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{2} b^{3} d x^{3} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{2} b^{3} d x^{3}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{4 a b^{4} c x}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{60 a b^{4} d x^{4} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{6 b^{5} c x^{2}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} + \frac{12 b^{5} d x^{5}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} & \text{for}\: n = -5 \\\frac{60 a^{5} d \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{110 a^{5} d}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{4} b d x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{270 a^{4} b d x}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{3} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{3} b^{2} d x^{2}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} - \frac{2 a^{2} b^{3} c}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{60 a^{2} b^{3} d x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} - \frac{6 a b^{4} c x}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} - \frac{15 a b^{4} d x^{4}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} - \frac{6 b^{5} c x^{2}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{3 b^{5} d x^{5}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} & \text{for}\: n = -4 \\- \frac{60 a^{5} d \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{90 a^{5} d}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{120 a^{4} b d x \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{120 a^{4} b d x}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{60 a^{3} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{6 a^{2} b^{3} c \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{9 a^{2} b^{3} c}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{20 a^{2} b^{3} d x^{3}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{12 a b^{4} c x \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{12 a b^{4} c x}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{5 a b^{4} d x^{4}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{6 b^{5} c x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{2 b^{5} d x^{5}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} & \text{for}\: n = -3 \\\frac{60 a^{5} d \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} + \frac{60 a^{5} d}{12 a b^{6} + 12 b^{7} x} + \frac{60 a^{4} b d x \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} - \frac{30 a^{3} b^{2} d x^{2}}{12 a b^{6} + 12 b^{7} x} - \frac{24 a^{2} b^{3} c \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} - \frac{24 a^{2} b^{3} c}{12 a b^{6} + 12 b^{7} x} + \frac{10 a^{2} b^{3} d x^{3}}{12 a b^{6} + 12 b^{7} x} - \frac{24 a b^{4} c x \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} - \frac{5 a b^{4} d x^{4}}{12 a b^{6} + 12 b^{7} x} + \frac{12 b^{5} c x^{2}}{12 a b^{6} + 12 b^{7} x} + \frac{3 b^{5} d x^{5}}{12 a b^{6} + 12 b^{7} x} & \text{for}\: n = -2 \\- \frac{a^{5} d \log{\left(\frac{a}{b} + x \right)}}{b^{6}} + \frac{a^{4} d x}{b^{5}} - \frac{a^{3} d x^{2}}{2 b^{4}} + \frac{a^{2} c \log{\left(\frac{a}{b} + x \right)}}{b^{3}} + \frac{a^{2} d x^{3}}{3 b^{3}} - \frac{a c x}{b^{2}} - \frac{a d x^{4}}{4 b^{2}} + \frac{c x^{2}}{2 b} + \frac{d x^{5}}{5 b} & \text{for}\: n = -1 \\- \frac{120 a^{6} d \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 a^{5} b d n x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{60 a^{4} b^{2} d n^{2} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{60 a^{4} b^{2} d n x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{2 a^{3} b^{3} c n^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{30 a^{3} b^{3} c n^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{148 a^{3} b^{3} c n \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{240 a^{3} b^{3} c \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{20 a^{3} b^{3} d n^{3} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{60 a^{3} b^{3} d n^{2} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{40 a^{3} b^{3} d n x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{2 a^{2} b^{4} c n^{4} x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{30 a^{2} b^{4} c n^{3} x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{148 a^{2} b^{4} c n^{2} x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{240 a^{2} b^{4} c n x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{5 a^{2} b^{4} d n^{4} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{30 a^{2} b^{4} d n^{3} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{55 a^{2} b^{4} d n^{2} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{30 a^{2} b^{4} d n x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{a b^{5} c n^{5} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{16 a b^{5} c n^{4} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{89 a b^{5} c n^{3} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{194 a b^{5} c n^{2} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 a b^{5} c n x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{a b^{5} d n^{5} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{10 a b^{5} d n^{4} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{35 a b^{5} d n^{3} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{50 a b^{5} d n^{2} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{24 a b^{5} d n x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{b^{6} c n^{5} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{18 b^{6} c n^{4} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{121 b^{6} c n^{3} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{372 b^{6} c n^{2} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{508 b^{6} c n x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{240 b^{6} c x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{b^{6} d n^{5} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{15 b^{6} d n^{4} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{85 b^{6} d n^{3} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{225 b^{6} d n^{2} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{274 b^{6} d n x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 b^{6} d x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c*x**3/3 + d*x**6/6), Eq(b, 0)), (60*a**5*d*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 137*a**5*d/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a**4*b*d*x*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 625*a**4*b*d*x/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 600*a**3*b**2*d*x**2*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 1100*a**3*b**2*d*x**2/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) - 2*a**2*b**3*c/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 600*a**2*b**3*d*x**3*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 900*a**2*b**3*d*x**3/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) - 10*a*b**4*c*x/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*d*x**4*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*d*x**4/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) - 20*b**5*c*x**2/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 60*b**5*d*x**5*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5), Eq(n, -6)), (-60*a**5*d*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 125*a**5*d/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**4*b*d*x*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 440*a**4*b*d*x/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 360*a**3*b**2*d*x**2*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 540*a**3*b**2*d*x**2/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - a**2*b**3*c/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*d*x**3*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*d*x**3/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 4*a*b**4*c*x/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 60*a*b**4*d*x**4*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 6*b**5*c*x**2/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) + 12*b**5*d*x**5/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4), Eq(n, -5)), (60*a**5*d*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 110*a**5*d/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**4*b*d*x*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 270*a**4*b*d*x/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**3*b**2*d*x**2*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**3*b**2*d*x**2/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - 2*a**2*b**3*c/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 60*a**2*b**3*d*x**3*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - 6*a*b**4*c*x/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - 15*a*b**4*d*x**4/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - 6*b**5*c*x**2/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 3*b**5*d*x**5/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3), Eq(n, -4)), (-60*a**5*d*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 90*a**5*d/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 120*a**4*b*d*x*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 120*a**4*b*d*x/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 60*a**3*b**2*d*x**2*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 6*a**2*b**3*c*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 9*a**2*b**3*c/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 20*a**2*b**3*d*x**3/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 12*a*b**4*c*x*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 12*a*b**4*c*x/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 5*a*b**4*d*x**4/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 6*b**5*c*x**2*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 2*b**5*d*x**5/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2), Eq(n, -3)), (60*a**5*d*log(a/b + x)/(12*a*b**6 + 12*b**7*x) + 60*a**5*d/(12*a*b**6 + 12*b**7*x) + 60*a**4*b*d*x*log(a/b + x)/(12*a*b**6 + 12*b**7*x) - 30*a**3*b**2*d*x**2/(12*a*b**6 + 12*b**7*x) - 24*a**2*b**3*c*log(a/b + x)/(12*a*b**6 + 12*b**7*x) - 24*a**2*b**3*c/(12*a*b**6 + 12*b**7*x) + 10*a**2*b**3*d*x**3/(12*a*b**6 + 12*b**7*x) - 24*a*b**4*c*x*log(a/b + x)/(12*a*b**6 + 12*b**7*x) - 5*a*b**4*d*x**4/(12*a*b**6 + 12*b**7*x) + 12*b**5*c*x**2/(12*a*b**6 + 12*b**7*x) + 3*b**5*d*x**5/(12*a*b**6 + 12*b**7*x), Eq(n, -2)), (-a**5*d*log(a/b + x)/b**6 + a**4*d*x/b**5 - a**3*d*x**2/(2*b**4) + a**2*c*log(a/b + x)/b**3 + a**2*d*x**3/(3*b**3) - a*c*x/b**2 - a*d*x**4/(4*b**2) + c*x**2/(2*b) + d*x**5/(5*b), Eq(n, -1)), (-120*a**6*d*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*a**5*b*d*n*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 60*a**4*b**2*d*n**2*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 60*a**4*b**2*d*n*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 2*a**3*b**3*c*n**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 30*a**3*b**3*c*n**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 148*a**3*b**3*c*n*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 240*a**3*b**3*c*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 20*a**3*b**3*d*n**3*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 60*a**3*b**3*d*n**2*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 40*a**3*b**3*d*n*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 2*a**2*b**4*c*n**4*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 30*a**2*b**4*c*n**3*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 148*a**2*b**4*c*n**2*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 240*a**2*b**4*c*n*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 5*a**2*b**4*d*n**4*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 30*a**2*b**4*d*n**3*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 55*a**2*b**4*d*n**2*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 30*a**2*b**4*d*n*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + a*b**5*c*n**5*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 16*a*b**5*c*n**4*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 89*a*b**5*c*n**3*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 194*a*b**5*c*n**2*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*a*b**5*c*n*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + a*b**5*d*n**5*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 10*a*b**5*d*n**4*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 35*a*b**5*d*n**3*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 50*a*b**5*d*n**2*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 24*a*b**5*d*n*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + b**6*c*n**5*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 18*b**6*c*n**4*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 121*b**6*c*n**3*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 372*b**6*c*n**2*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 508*b**6*c*n*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 240*b**6*c*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + b**6*d*n**5*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 15*b**6*d*n**4*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 85*b**6*d*n**3*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 225*b**6*d*n**2*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 274*b**6*d*n*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*b**6*d*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6), True))","A",0
175,1,3704,0,4.855592," ","integrate(x*(b*x+a)**n*(d*x**3+c),x)","\begin{cases} a^{n} \left(\frac{c x^{2}}{2} + \frac{d x^{5}}{5}\right) & \text{for}\: b = 0 \\\frac{12 a^{4} d \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{25 a^{4} d}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{48 a^{3} b d x \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{88 a^{3} b d x}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{72 a^{2} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{108 a^{2} b^{2} d x^{2}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} - \frac{a b^{3} c}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{48 a b^{3} d x^{3} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{48 a b^{3} d x^{3}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} - \frac{4 b^{4} c x}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{12 b^{4} d x^{4} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} & \text{for}\: n = -5 \\- \frac{24 a^{4} d \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{44 a^{4} d}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{72 a^{3} b d x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{108 a^{3} b d x}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{72 a^{2} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{72 a^{2} b^{2} d x^{2}}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{a b^{3} c}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{24 a b^{3} d x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} - \frac{3 b^{4} c x}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} + \frac{6 b^{4} d x^{4}}{6 a^{3} b^{5} + 18 a^{2} b^{6} x + 18 a b^{7} x^{2} + 6 b^{8} x^{3}} & \text{for}\: n = -4 \\\frac{12 a^{4} d \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{18 a^{4} d}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{24 a^{3} b d x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{24 a^{3} b d x}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{12 a^{2} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} - \frac{a b^{3} c}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} - \frac{4 a b^{3} d x^{3}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} - \frac{2 b^{4} c x}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{b^{4} d x^{4}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} & \text{for}\: n = -3 \\- \frac{12 a^{4} d \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} - \frac{12 a^{4} d}{3 a b^{5} + 3 b^{6} x} - \frac{12 a^{3} b d x \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} + \frac{6 a^{2} b^{2} d x^{2}}{3 a b^{5} + 3 b^{6} x} + \frac{3 a b^{3} c \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} + \frac{3 a b^{3} c}{3 a b^{5} + 3 b^{6} x} - \frac{2 a b^{3} d x^{3}}{3 a b^{5} + 3 b^{6} x} + \frac{3 b^{4} c x \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} + \frac{b^{4} d x^{4}}{3 a b^{5} + 3 b^{6} x} & \text{for}\: n = -2 \\\frac{a^{4} d \log{\left(\frac{a}{b} + x \right)}}{b^{5}} - \frac{a^{3} d x}{b^{4}} + \frac{a^{2} d x^{2}}{2 b^{3}} - \frac{a c \log{\left(\frac{a}{b} + x \right)}}{b^{2}} - \frac{a d x^{3}}{3 b^{2}} + \frac{c x}{b} + \frac{d x^{4}}{4 b} & \text{for}\: n = -1 \\\frac{24 a^{5} d \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{24 a^{4} b d n x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{12 a^{3} b^{2} d n^{2} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{12 a^{3} b^{2} d n x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{a^{2} b^{3} c n^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{12 a^{2} b^{3} c n^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{47 a^{2} b^{3} c n \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{60 a^{2} b^{3} c \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{4 a^{2} b^{3} d n^{3} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{12 a^{2} b^{3} d n^{2} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{8 a^{2} b^{3} d n x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{a b^{4} c n^{4} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{12 a b^{4} c n^{3} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{47 a b^{4} c n^{2} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{60 a b^{4} c n x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{a b^{4} d n^{4} x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{6 a b^{4} d n^{3} x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{11 a b^{4} d n^{2} x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{6 a b^{4} d n x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{b^{5} c n^{4} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{13 b^{5} c n^{3} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{59 b^{5} c n^{2} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{107 b^{5} c n x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{60 b^{5} c x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{b^{5} d n^{4} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{10 b^{5} d n^{3} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{35 b^{5} d n^{2} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{50 b^{5} d n x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{24 b^{5} d x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c*x**2/2 + d*x**5/5), Eq(b, 0)), (12*a**4*d*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 25*a**4*d/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 48*a**3*b*d*x*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 88*a**3*b*d*x/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 72*a**2*b**2*d*x**2*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 108*a**2*b**2*d*x**2/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) - a*b**3*c/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 48*a*b**3*d*x**3*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 48*a*b**3*d*x**3/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) - 4*b**4*c*x/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 12*b**4*d*x**4*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4), Eq(n, -5)), (-24*a**4*d*log(a/b + x)/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - 44*a**4*d/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - 72*a**3*b*d*x*log(a/b + x)/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - 108*a**3*b*d*x/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - 72*a**2*b**2*d*x**2*log(a/b + x)/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - 72*a**2*b**2*d*x**2/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - a*b**3*c/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - 24*a*b**3*d*x**3*log(a/b + x)/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) - 3*b**4*c*x/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3) + 6*b**4*d*x**4/(6*a**3*b**5 + 18*a**2*b**6*x + 18*a*b**7*x**2 + 6*b**8*x**3), Eq(n, -4)), (12*a**4*d*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 18*a**4*d/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 24*a**3*b*d*x*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 24*a**3*b*d*x/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 12*a**2*b**2*d*x**2*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) - a*b**3*c/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) - 4*a*b**3*d*x**3/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) - 2*b**4*c*x/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + b**4*d*x**4/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2), Eq(n, -3)), (-12*a**4*d*log(a/b + x)/(3*a*b**5 + 3*b**6*x) - 12*a**4*d/(3*a*b**5 + 3*b**6*x) - 12*a**3*b*d*x*log(a/b + x)/(3*a*b**5 + 3*b**6*x) + 6*a**2*b**2*d*x**2/(3*a*b**5 + 3*b**6*x) + 3*a*b**3*c*log(a/b + x)/(3*a*b**5 + 3*b**6*x) + 3*a*b**3*c/(3*a*b**5 + 3*b**6*x) - 2*a*b**3*d*x**3/(3*a*b**5 + 3*b**6*x) + 3*b**4*c*x*log(a/b + x)/(3*a*b**5 + 3*b**6*x) + b**4*d*x**4/(3*a*b**5 + 3*b**6*x), Eq(n, -2)), (a**4*d*log(a/b + x)/b**5 - a**3*d*x/b**4 + a**2*d*x**2/(2*b**3) - a*c*log(a/b + x)/b**2 - a*d*x**3/(3*b**2) + c*x/b + d*x**4/(4*b), Eq(n, -1)), (24*a**5*d*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 24*a**4*b*d*n*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 12*a**3*b**2*d*n**2*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 12*a**3*b**2*d*n*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - a**2*b**3*c*n**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 12*a**2*b**3*c*n**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 47*a**2*b**3*c*n*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 60*a**2*b**3*c*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 4*a**2*b**3*d*n**3*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 12*a**2*b**3*d*n**2*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 8*a**2*b**3*d*n*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + a*b**4*c*n**4*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 12*a*b**4*c*n**3*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 47*a*b**4*c*n**2*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 60*a*b**4*c*n*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + a*b**4*d*n**4*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 6*a*b**4*d*n**3*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 11*a*b**4*d*n**2*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 6*a*b**4*d*n*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + b**5*c*n**4*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 13*b**5*c*n**3*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 59*b**5*c*n**2*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 107*b**5*c*n*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 60*b**5*c*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + b**5*d*n**4*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 10*b**5*d*n**3*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 35*b**5*d*n**2*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 50*b**5*d*n*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 24*b**5*d*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5), True))","A",0
176,1,1906,0,2.785559," ","integrate((b*x+a)**n*(d*x**3+c),x)","\begin{cases} a^{n} \left(c x + \frac{d x^{4}}{4}\right) & \text{for}\: b = 0 \\\frac{6 a^{3} d \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{11 a^{3} d}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a^{2} b d x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{27 a^{2} b d x}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} d x^{2}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} - \frac{2 b^{3} c}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{6 b^{3} d x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} & \text{for}\: n = -4 \\- \frac{6 a^{3} d \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{9 a^{3} d}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b d x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b d x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{6 a b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{b^{3} c}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{2 b^{3} d x^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} & \text{for}\: n = -3 \\\frac{6 a^{3} d \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{3} d}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{2} b d x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} - \frac{3 a b^{2} d x^{2}}{2 a b^{4} + 2 b^{5} x} - \frac{2 b^{3} c}{2 a b^{4} + 2 b^{5} x} + \frac{b^{3} d x^{3}}{2 a b^{4} + 2 b^{5} x} & \text{for}\: n = -2 \\- \frac{a^{3} d \log{\left(\frac{a}{b} + x \right)}}{b^{4}} + \frac{a^{2} d x}{b^{3}} - \frac{a d x^{2}}{2 b^{2}} + \frac{c \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{d x^{3}}{3 b} & \text{for}\: n = -1 \\- \frac{6 a^{4} d \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 a^{3} b d n x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} d n^{2} x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} d n x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{a b^{3} c n^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{9 a b^{3} c n^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{26 a b^{3} c n \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{24 a b^{3} c \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{a b^{3} d n^{3} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{3 a b^{3} d n^{2} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{2 a b^{3} d n x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{b^{4} c n^{3} x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{9 b^{4} c n^{2} x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{26 b^{4} c n x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{24 b^{4} c x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{b^{4} d n^{3} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} d n^{2} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{11 b^{4} d n x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} d x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c*x + d*x**4/4), Eq(b, 0)), (6*a**3*d*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 11*a**3*d/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a**2*b*d*x*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 27*a**2*b*d*x/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*d*x**2*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*d*x**2/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) - 2*b**3*c/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 6*b**3*d*x**3*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3), Eq(n, -4)), (-6*a**3*d*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 9*a**3*d/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*d*x*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*d*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 6*a*b**2*d*x**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - b**3*c/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 2*b**3*d*x**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2), Eq(n, -3)), (6*a**3*d*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a**3*d/(2*a*b**4 + 2*b**5*x) + 6*a**2*b*d*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) - 3*a*b**2*d*x**2/(2*a*b**4 + 2*b**5*x) - 2*b**3*c/(2*a*b**4 + 2*b**5*x) + b**3*d*x**3/(2*a*b**4 + 2*b**5*x), Eq(n, -2)), (-a**3*d*log(a/b + x)/b**4 + a**2*d*x/b**3 - a*d*x**2/(2*b**2) + c*log(a/b + x)/b + d*x**3/(3*b), Eq(n, -1)), (-6*a**4*d*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*a**3*b*d*n*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*d*n**2*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*d*n*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + a*b**3*c*n**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 9*a*b**3*c*n**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 26*a*b**3*c*n*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 24*a*b**3*c*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + a*b**3*d*n**3*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 3*a*b**3*d*n**2*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 2*a*b**3*d*n*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + b**4*c*n**3*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 9*b**4*c*n**2*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 26*b**4*c*n*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 24*b**4*c*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + b**4*d*n**3*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*d*n**2*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 11*b**4*d*n*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*d*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4), True))","A",0
177,1,741,0,6.432563," ","integrate((b*x+a)**n*(d*x**3+c)/x,x)","- \frac{b^{n} c n \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} - \frac{b^{n} c \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + d \left(\begin{cases} \frac{a^{n} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{3 a^{2}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{2 b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} & \text{for}\: n = -3 \\- \frac{2 a^{2} \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{2 a^{2}}{a b^{3} + b^{4} x} - \frac{2 a b x \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} + \frac{b^{2} x^{2}}{a b^{3} + b^{4} x} & \text{for}\: n = -2 \\\frac{a^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{3}} - \frac{a x}{b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: n = -1 \\\frac{2 a^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} - \frac{2 a^{2} b n x \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{a b^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{a b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{b^{3} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{3 b^{3} n x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{2 b^{3} x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} & \text{otherwise} \end{cases}\right) - \frac{b b^{n} c n x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)} - \frac{b b^{n} c x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)}"," ",0,"-b**n*c*n*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) - b**n*c*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) + d*Piecewise((a**n*x**3/3, Eq(b, 0)), (2*a**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 3*a**2/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 2*b**2*x**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2), Eq(n, -3)), (-2*a**2*log(a/b + x)/(a*b**3 + b**4*x) - 2*a**2/(a*b**3 + b**4*x) - 2*a*b*x*log(a/b + x)/(a*b**3 + b**4*x) + b**2*x**2/(a*b**3 + b**4*x), Eq(n, -2)), (a**2*log(a/b + x)/b**3 - a*x/b**2 + x**2/(2*b), Eq(n, -1)), (2*a**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) - 2*a**2*b*n*x*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*n**2*x**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*n*x**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + b**3*n**2*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 3*b**3*n*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 2*b**3*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3), True)) - b*b**n*c*n*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2)) - b*b**n*c*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2))","B",0
178,-1,0,0,0.000000," ","integrate(x**2*(b*x+a)**n*(d*x**3+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate(x*(b*x+a)**n*(d*x**3+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,1,11851,0,14.439600," ","integrate((b*x+a)**n*(d*x**3+c)**2,x)","\begin{cases} a^{n} \left(c^{2} x + \frac{c d x^{4}}{2} + \frac{d^{2} x^{7}}{7}\right) & \text{for}\: b = 0 \\\frac{60 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{147 a^{6} d^{2}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{360 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{822 a^{5} b d^{2} x}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{900 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{1875 a^{4} b^{2} d^{2} x^{2}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{2 a^{3} b^{3} c d}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{1200 a^{3} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{2200 a^{3} b^{3} d^{2} x^{3}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{12 a^{2} b^{4} c d x}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{900 a^{2} b^{4} d^{2} x^{4} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{1350 a^{2} b^{4} d^{2} x^{4}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{30 a b^{5} c d x^{2}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{360 a b^{5} d^{2} x^{5} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{360 a b^{5} d^{2} x^{5}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{10 b^{6} c^{2}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{40 b^{6} c d x^{3}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{60 b^{6} d^{2} x^{6} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} & \text{for}\: n = -7 \\- \frac{60 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{137 a^{6} d^{2}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{300 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{625 a^{5} b d^{2} x}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{600 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{1100 a^{4} b^{2} d^{2} x^{2}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{a^{3} b^{3} c d}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{600 a^{3} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{900 a^{3} b^{3} d^{2} x^{3}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{5 a^{2} b^{4} c d x}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{300 a^{2} b^{4} d^{2} x^{4} \log{\left(\frac{a}{b} + x \right)}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{300 a^{2} b^{4} d^{2} x^{4}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{10 a b^{5} c d x^{2}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{60 a b^{5} d^{2} x^{5} \log{\left(\frac{a}{b} + x \right)}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{2 b^{6} c^{2}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} - \frac{10 b^{6} c d x^{3}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} + \frac{10 b^{6} d^{2} x^{6}}{10 a^{5} b^{7} + 50 a^{4} b^{8} x + 100 a^{3} b^{9} x^{2} + 100 a^{2} b^{10} x^{3} + 50 a b^{11} x^{4} + 10 b^{12} x^{5}} & \text{for}\: n = -6 \\\frac{60 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} + \frac{125 a^{6} d^{2}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} + \frac{240 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} + \frac{440 a^{5} b d^{2} x}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} + \frac{360 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} + \frac{540 a^{4} b^{2} d^{2} x^{2}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} - \frac{2 a^{3} b^{3} c d}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} + \frac{240 a^{3} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} + \frac{240 a^{3} b^{3} d^{2} x^{3}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} - \frac{8 a^{2} b^{4} c d x}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} + \frac{60 a^{2} b^{4} d^{2} x^{4} \log{\left(\frac{a}{b} + x \right)}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} - \frac{12 a b^{5} c d x^{2}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} - \frac{12 a b^{5} d^{2} x^{5}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} - \frac{b^{6} c^{2}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} - \frac{8 b^{6} c d x^{3}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} + \frac{2 b^{6} d^{2} x^{6}}{4 a^{4} b^{7} + 16 a^{3} b^{8} x + 24 a^{2} b^{9} x^{2} + 16 a b^{10} x^{3} + 4 b^{11} x^{4}} & \text{for}\: n = -5 \\- \frac{60 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{110 a^{6} d^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{180 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{270 a^{5} b d^{2} x}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{180 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{180 a^{4} b^{2} d^{2} x^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{6 a^{3} b^{3} c d \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{11 a^{3} b^{3} c d}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{60 a^{3} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{18 a^{2} b^{4} c d x \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{27 a^{2} b^{4} c d x}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{15 a^{2} b^{4} d^{2} x^{4}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{18 a b^{5} c d x^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{18 a b^{5} c d x^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{3 a b^{5} d^{2} x^{5}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{b^{6} c^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{6 b^{6} c d x^{3} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{b^{6} d^{2} x^{6}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} & \text{for}\: n = -4 \\\frac{60 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{90 a^{6} d^{2}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{120 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{120 a^{5} b d^{2} x}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{60 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{24 a^{3} b^{3} c d \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{36 a^{3} b^{3} c d}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{20 a^{3} b^{3} d^{2} x^{3}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{48 a^{2} b^{4} c d x \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{48 a^{2} b^{4} c d x}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{5 a^{2} b^{4} d^{2} x^{4}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{24 a b^{5} c d x^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{2 a b^{5} d^{2} x^{5}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{2 b^{6} c^{2}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{8 b^{6} c d x^{3}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{b^{6} d^{2} x^{6}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} & \text{for}\: n = -3 \\- \frac{60 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{10 a b^{7} + 10 b^{8} x} - \frac{60 a^{6} d^{2}}{10 a b^{7} + 10 b^{8} x} - \frac{60 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{10 a b^{7} + 10 b^{8} x} + \frac{30 a^{4} b^{2} d^{2} x^{2}}{10 a b^{7} + 10 b^{8} x} + \frac{60 a^{3} b^{3} c d \log{\left(\frac{a}{b} + x \right)}}{10 a b^{7} + 10 b^{8} x} + \frac{60 a^{3} b^{3} c d}{10 a b^{7} + 10 b^{8} x} - \frac{10 a^{3} b^{3} d^{2} x^{3}}{10 a b^{7} + 10 b^{8} x} + \frac{60 a^{2} b^{4} c d x \log{\left(\frac{a}{b} + x \right)}}{10 a b^{7} + 10 b^{8} x} + \frac{5 a^{2} b^{4} d^{2} x^{4}}{10 a b^{7} + 10 b^{8} x} - \frac{30 a b^{5} c d x^{2}}{10 a b^{7} + 10 b^{8} x} - \frac{3 a b^{5} d^{2} x^{5}}{10 a b^{7} + 10 b^{8} x} - \frac{10 b^{6} c^{2}}{10 a b^{7} + 10 b^{8} x} + \frac{10 b^{6} c d x^{3}}{10 a b^{7} + 10 b^{8} x} + \frac{2 b^{6} d^{2} x^{6}}{10 a b^{7} + 10 b^{8} x} & \text{for}\: n = -2 \\\frac{a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{7}} - \frac{a^{5} d^{2} x}{b^{6}} + \frac{a^{4} d^{2} x^{2}}{2 b^{5}} - \frac{2 a^{3} c d \log{\left(\frac{a}{b} + x \right)}}{b^{4}} - \frac{a^{3} d^{2} x^{3}}{3 b^{4}} + \frac{2 a^{2} c d x}{b^{3}} + \frac{a^{2} d^{2} x^{4}}{4 b^{3}} - \frac{a c d x^{2}}{b^{2}} - \frac{a d^{2} x^{5}}{5 b^{2}} + \frac{c^{2} \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{2 c d x^{3}}{3 b} + \frac{d^{2} x^{6}}{6 b} & \text{for}\: n = -1 \\\frac{720 a^{7} d^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{720 a^{6} b d^{2} n x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{360 a^{5} b^{2} d^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{360 a^{5} b^{2} d^{2} n x^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{12 a^{4} b^{3} c d n^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{216 a^{4} b^{3} c d n^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{1284 a^{4} b^{3} c d n \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{2520 a^{4} b^{3} c d \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{120 a^{4} b^{3} d^{2} n^{3} x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{360 a^{4} b^{3} d^{2} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{240 a^{4} b^{3} d^{2} n x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{12 a^{3} b^{4} c d n^{4} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{216 a^{3} b^{4} c d n^{3} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1284 a^{3} b^{4} c d n^{2} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{2520 a^{3} b^{4} c d n x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{30 a^{3} b^{4} d^{2} n^{4} x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{180 a^{3} b^{4} d^{2} n^{3} x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{330 a^{3} b^{4} d^{2} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{180 a^{3} b^{4} d^{2} n x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{6 a^{2} b^{5} c d n^{5} x^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{114 a^{2} b^{5} c d n^{4} x^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{750 a^{2} b^{5} c d n^{3} x^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{1902 a^{2} b^{5} c d n^{2} x^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{1260 a^{2} b^{5} c d n x^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{6 a^{2} b^{5} d^{2} n^{5} x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{60 a^{2} b^{5} d^{2} n^{4} x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{210 a^{2} b^{5} d^{2} n^{3} x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{300 a^{2} b^{5} d^{2} n^{2} x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{144 a^{2} b^{5} d^{2} n x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{a b^{6} c^{2} n^{6} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{27 a b^{6} c^{2} n^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{295 a b^{6} c^{2} n^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1665 a b^{6} c^{2} n^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{5104 a b^{6} c^{2} n^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{8028 a b^{6} c^{2} n \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{5040 a b^{6} c^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{2 a b^{6} c d n^{6} x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{42 a b^{6} c d n^{5} x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{326 a b^{6} c d n^{4} x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1134 a b^{6} c d n^{3} x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1688 a b^{6} c d n^{2} x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{840 a b^{6} c d n x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{a b^{6} d^{2} n^{6} x^{6} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{15 a b^{6} d^{2} n^{5} x^{6} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{85 a b^{6} d^{2} n^{4} x^{6} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{225 a b^{6} d^{2} n^{3} x^{6} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{274 a b^{6} d^{2} n^{2} x^{6} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{120 a b^{6} d^{2} n x^{6} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{b^{7} c^{2} n^{6} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{27 b^{7} c^{2} n^{5} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{295 b^{7} c^{2} n^{4} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1665 b^{7} c^{2} n^{3} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{5104 b^{7} c^{2} n^{2} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{8028 b^{7} c^{2} n x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{5040 b^{7} c^{2} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{2 b^{7} c d n^{6} x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{48 b^{7} c d n^{5} x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{452 b^{7} c d n^{4} x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{2112 b^{7} c d n^{3} x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{5090 b^{7} c d n^{2} x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{5904 b^{7} c d n x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{2520 b^{7} c d x^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{b^{7} d^{2} n^{6} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{21 b^{7} d^{2} n^{5} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{175 b^{7} d^{2} n^{4} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{735 b^{7} d^{2} n^{3} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1624 b^{7} d^{2} n^{2} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1764 b^{7} d^{2} n x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{720 b^{7} d^{2} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c**2*x + c*d*x**4/2 + d**2*x**7/7), Eq(b, 0)), (60*a**6*d**2*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 147*a**6*d**2/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 360*a**5*b*d**2*x*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 822*a**5*b*d**2*x/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 900*a**4*b**2*d**2*x**2*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 1875*a**4*b**2*d**2*x**2/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 2*a**3*b**3*c*d/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 1200*a**3*b**3*d**2*x**3*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 2200*a**3*b**3*d**2*x**3/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 12*a**2*b**4*c*d*x/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 900*a**2*b**4*d**2*x**4*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 1350*a**2*b**4*d**2*x**4/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 30*a*b**5*c*d*x**2/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 360*a*b**5*d**2*x**5*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 360*a*b**5*d**2*x**5/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 10*b**6*c**2/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 40*b**6*c*d*x**3/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 60*b**6*d**2*x**6*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6), Eq(n, -7)), (-60*a**6*d**2*log(a/b + x)/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 137*a**6*d**2/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 300*a**5*b*d**2*x*log(a/b + x)/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 625*a**5*b*d**2*x/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 600*a**4*b**2*d**2*x**2*log(a/b + x)/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 1100*a**4*b**2*d**2*x**2/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - a**3*b**3*c*d/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 600*a**3*b**3*d**2*x**3*log(a/b + x)/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 900*a**3*b**3*d**2*x**3/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 5*a**2*b**4*c*d*x/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 300*a**2*b**4*d**2*x**4*log(a/b + x)/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 300*a**2*b**4*d**2*x**4/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 10*a*b**5*c*d*x**2/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 60*a*b**5*d**2*x**5*log(a/b + x)/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 2*b**6*c**2/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) - 10*b**6*c*d*x**3/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5) + 10*b**6*d**2*x**6/(10*a**5*b**7 + 50*a**4*b**8*x + 100*a**3*b**9*x**2 + 100*a**2*b**10*x**3 + 50*a*b**11*x**4 + 10*b**12*x**5), Eq(n, -6)), (60*a**6*d**2*log(a/b + x)/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) + 125*a**6*d**2/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) + 240*a**5*b*d**2*x*log(a/b + x)/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) + 440*a**5*b*d**2*x/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) + 360*a**4*b**2*d**2*x**2*log(a/b + x)/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) + 540*a**4*b**2*d**2*x**2/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) - 2*a**3*b**3*c*d/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) + 240*a**3*b**3*d**2*x**3*log(a/b + x)/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) + 240*a**3*b**3*d**2*x**3/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) - 8*a**2*b**4*c*d*x/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) + 60*a**2*b**4*d**2*x**4*log(a/b + x)/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) - 12*a*b**5*c*d*x**2/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) - 12*a*b**5*d**2*x**5/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) - b**6*c**2/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) - 8*b**6*c*d*x**3/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4) + 2*b**6*d**2*x**6/(4*a**4*b**7 + 16*a**3*b**8*x + 24*a**2*b**9*x**2 + 16*a*b**10*x**3 + 4*b**11*x**4), Eq(n, -5)), (-60*a**6*d**2*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 110*a**6*d**2/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 180*a**5*b*d**2*x*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 270*a**5*b*d**2*x/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 180*a**4*b**2*d**2*x**2*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 180*a**4*b**2*d**2*x**2/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 6*a**3*b**3*c*d*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 11*a**3*b**3*c*d/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 60*a**3*b**3*d**2*x**3*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 18*a**2*b**4*c*d*x*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 27*a**2*b**4*c*d*x/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 15*a**2*b**4*d**2*x**4/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 18*a*b**5*c*d*x**2*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 18*a*b**5*c*d*x**2/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 3*a*b**5*d**2*x**5/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - b**6*c**2/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 6*b**6*c*d*x**3*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + b**6*d**2*x**6/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3), Eq(n, -4)), (60*a**6*d**2*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 90*a**6*d**2/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 120*a**5*b*d**2*x*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 120*a**5*b*d**2*x/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 60*a**4*b**2*d**2*x**2*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 24*a**3*b**3*c*d*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 36*a**3*b**3*c*d/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 20*a**3*b**3*d**2*x**3/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 48*a**2*b**4*c*d*x*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 48*a**2*b**4*c*d*x/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 5*a**2*b**4*d**2*x**4/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 24*a*b**5*c*d*x**2*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 2*a*b**5*d**2*x**5/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 2*b**6*c**2/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 8*b**6*c*d*x**3/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + b**6*d**2*x**6/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2), Eq(n, -3)), (-60*a**6*d**2*log(a/b + x)/(10*a*b**7 + 10*b**8*x) - 60*a**6*d**2/(10*a*b**7 + 10*b**8*x) - 60*a**5*b*d**2*x*log(a/b + x)/(10*a*b**7 + 10*b**8*x) + 30*a**4*b**2*d**2*x**2/(10*a*b**7 + 10*b**8*x) + 60*a**3*b**3*c*d*log(a/b + x)/(10*a*b**7 + 10*b**8*x) + 60*a**3*b**3*c*d/(10*a*b**7 + 10*b**8*x) - 10*a**3*b**3*d**2*x**3/(10*a*b**7 + 10*b**8*x) + 60*a**2*b**4*c*d*x*log(a/b + x)/(10*a*b**7 + 10*b**8*x) + 5*a**2*b**4*d**2*x**4/(10*a*b**7 + 10*b**8*x) - 30*a*b**5*c*d*x**2/(10*a*b**7 + 10*b**8*x) - 3*a*b**5*d**2*x**5/(10*a*b**7 + 10*b**8*x) - 10*b**6*c**2/(10*a*b**7 + 10*b**8*x) + 10*b**6*c*d*x**3/(10*a*b**7 + 10*b**8*x) + 2*b**6*d**2*x**6/(10*a*b**7 + 10*b**8*x), Eq(n, -2)), (a**6*d**2*log(a/b + x)/b**7 - a**5*d**2*x/b**6 + a**4*d**2*x**2/(2*b**5) - 2*a**3*c*d*log(a/b + x)/b**4 - a**3*d**2*x**3/(3*b**4) + 2*a**2*c*d*x/b**3 + a**2*d**2*x**4/(4*b**3) - a*c*d*x**2/b**2 - a*d**2*x**5/(5*b**2) + c**2*log(a/b + x)/b + 2*c*d*x**3/(3*b) + d**2*x**6/(6*b), Eq(n, -1)), (720*a**7*d**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 720*a**6*b*d**2*n*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 360*a**5*b**2*d**2*n**2*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 360*a**5*b**2*d**2*n*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 12*a**4*b**3*c*d*n**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 216*a**4*b**3*c*d*n**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 1284*a**4*b**3*c*d*n*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 2520*a**4*b**3*c*d*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 120*a**4*b**3*d**2*n**3*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 360*a**4*b**3*d**2*n**2*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 240*a**4*b**3*d**2*n*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 12*a**3*b**4*c*d*n**4*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 216*a**3*b**4*c*d*n**3*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1284*a**3*b**4*c*d*n**2*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2520*a**3*b**4*c*d*n*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 30*a**3*b**4*d**2*n**4*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 180*a**3*b**4*d**2*n**3*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 330*a**3*b**4*d**2*n**2*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 180*a**3*b**4*d**2*n*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 6*a**2*b**5*c*d*n**5*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 114*a**2*b**5*c*d*n**4*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 750*a**2*b**5*c*d*n**3*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 1902*a**2*b**5*c*d*n**2*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 1260*a**2*b**5*c*d*n*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 6*a**2*b**5*d**2*n**5*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 60*a**2*b**5*d**2*n**4*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 210*a**2*b**5*d**2*n**3*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 300*a**2*b**5*d**2*n**2*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 144*a**2*b**5*d**2*n*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + a*b**6*c**2*n**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 27*a*b**6*c**2*n**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 295*a*b**6*c**2*n**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1665*a*b**6*c**2*n**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 5104*a*b**6*c**2*n**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 8028*a*b**6*c**2*n*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 5040*a*b**6*c**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2*a*b**6*c*d*n**6*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 42*a*b**6*c*d*n**5*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 326*a*b**6*c*d*n**4*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1134*a*b**6*c*d*n**3*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1688*a*b**6*c*d*n**2*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 840*a*b**6*c*d*n*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + a*b**6*d**2*n**6*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 15*a*b**6*d**2*n**5*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 85*a*b**6*d**2*n**4*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 225*a*b**6*d**2*n**3*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 274*a*b**6*d**2*n**2*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 120*a*b**6*d**2*n*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + b**7*c**2*n**6*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 27*b**7*c**2*n**5*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 295*b**7*c**2*n**4*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1665*b**7*c**2*n**3*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 5104*b**7*c**2*n**2*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 8028*b**7*c**2*n*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 5040*b**7*c**2*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2*b**7*c*d*n**6*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 48*b**7*c*d*n**5*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 452*b**7*c*d*n**4*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2112*b**7*c*d*n**3*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 5090*b**7*c*d*n**2*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 5904*b**7*c*d*n*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2520*b**7*c*d*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + b**7*d**2*n**6*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 21*b**7*d**2*n**5*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 175*b**7*d**2*n**4*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 735*b**7*d**2*n**3*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1624*b**7*d**2*n**2*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1764*b**7*d**2*n*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 720*b**7*d**2*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7), True))","A",0
181,1,4760,0,12.991802," ","integrate((b*x+a)**n*(d*x**3+c)**2/x,x)","- \frac{b^{n} c^{2} n \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} - \frac{b^{n} c^{2} \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + 2 c d \left(\begin{cases} \frac{a^{n} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{3 a^{2}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{2 b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} & \text{for}\: n = -3 \\- \frac{2 a^{2} \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{2 a^{2}}{a b^{3} + b^{4} x} - \frac{2 a b x \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} + \frac{b^{2} x^{2}}{a b^{3} + b^{4} x} & \text{for}\: n = -2 \\\frac{a^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{3}} - \frac{a x}{b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: n = -1 \\\frac{2 a^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} - \frac{2 a^{2} b n x \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{a b^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{a b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{b^{3} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{3 b^{3} n x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{2 b^{3} x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} & \text{otherwise} \end{cases}\right) + d^{2} \left(\begin{cases} \frac{a^{n} x^{6}}{6} & \text{for}\: b = 0 \\\frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{137 a^{5}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{625 a^{4} b x}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{600 a^{3} b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{1100 a^{3} b^{2} x^{2}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{600 a^{2} b^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{900 a^{2} b^{3} x^{3}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a b^{4} x^{4} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a b^{4} x^{4}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{60 b^{5} x^{5} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} & \text{for}\: n = -6 \\- \frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{125 a^{5}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{440 a^{4} b x}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{360 a^{3} b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{540 a^{3} b^{2} x^{2}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{2} b^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{2} b^{3} x^{3}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{60 a b^{4} x^{4} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} + \frac{12 b^{5} x^{5}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} & \text{for}\: n = -5 \\\frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{110 a^{5}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{270 a^{4} b x}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{3} b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{3} b^{2} x^{2}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{60 a^{2} b^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} - \frac{15 a b^{4} x^{4}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{3 b^{5} x^{5}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} & \text{for}\: n = -4 \\- \frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{90 a^{5}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{120 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{120 a^{4} b x}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{60 a^{3} b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{20 a^{2} b^{3} x^{3}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{5 a b^{4} x^{4}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{2 b^{5} x^{5}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} & \text{for}\: n = -3 \\\frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} + \frac{60 a^{5}}{12 a b^{6} + 12 b^{7} x} + \frac{60 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} - \frac{30 a^{3} b^{2} x^{2}}{12 a b^{6} + 12 b^{7} x} + \frac{10 a^{2} b^{3} x^{3}}{12 a b^{6} + 12 b^{7} x} - \frac{5 a b^{4} x^{4}}{12 a b^{6} + 12 b^{7} x} + \frac{3 b^{5} x^{5}}{12 a b^{6} + 12 b^{7} x} & \text{for}\: n = -2 \\- \frac{a^{5} \log{\left(\frac{a}{b} + x \right)}}{b^{6}} + \frac{a^{4} x}{b^{5}} - \frac{a^{3} x^{2}}{2 b^{4}} + \frac{a^{2} x^{3}}{3 b^{3}} - \frac{a x^{4}}{4 b^{2}} + \frac{x^{5}}{5 b} & \text{for}\: n = -1 \\- \frac{120 a^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 a^{5} b n x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{60 a^{4} b^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{60 a^{4} b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{20 a^{3} b^{3} n^{3} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{60 a^{3} b^{3} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{40 a^{3} b^{3} n x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{5 a^{2} b^{4} n^{4} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{30 a^{2} b^{4} n^{3} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{55 a^{2} b^{4} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{30 a^{2} b^{4} n x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{a b^{5} n^{5} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{10 a b^{5} n^{4} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{35 a b^{5} n^{3} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{50 a b^{5} n^{2} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{24 a b^{5} n x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{b^{6} n^{5} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{15 b^{6} n^{4} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{85 b^{6} n^{3} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{225 b^{6} n^{2} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{274 b^{6} n x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 b^{6} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} & \text{otherwise} \end{cases}\right) - \frac{b b^{n} c^{2} n x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)} - \frac{b b^{n} c^{2} x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)}"," ",0,"-b**n*c**2*n*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) - b**n*c**2*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) + 2*c*d*Piecewise((a**n*x**3/3, Eq(b, 0)), (2*a**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 3*a**2/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 2*b**2*x**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2), Eq(n, -3)), (-2*a**2*log(a/b + x)/(a*b**3 + b**4*x) - 2*a**2/(a*b**3 + b**4*x) - 2*a*b*x*log(a/b + x)/(a*b**3 + b**4*x) + b**2*x**2/(a*b**3 + b**4*x), Eq(n, -2)), (a**2*log(a/b + x)/b**3 - a*x/b**2 + x**2/(2*b), Eq(n, -1)), (2*a**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) - 2*a**2*b*n*x*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*n**2*x**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*n*x**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + b**3*n**2*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 3*b**3*n*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 2*b**3*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3), True)) + d**2*Piecewise((a**n*x**6/6, Eq(b, 0)), (60*a**5*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 137*a**5/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a**4*b*x*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 625*a**4*b*x/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 600*a**3*b**2*x**2*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 1100*a**3*b**2*x**2/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 600*a**2*b**3*x**3*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 900*a**2*b**3*x**3/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*x**4*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*x**4/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 60*b**5*x**5*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5), Eq(n, -6)), (-60*a**5*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 125*a**5/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**4*b*x*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 440*a**4*b*x/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 360*a**3*b**2*x**2*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 540*a**3*b**2*x**2/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*x**3*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*x**3/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 60*a*b**4*x**4*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) + 12*b**5*x**5/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4), Eq(n, -5)), (60*a**5*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 110*a**5/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**4*b*x*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 270*a**4*b*x/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**3*b**2*x**2*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**3*b**2*x**2/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 60*a**2*b**3*x**3*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - 15*a*b**4*x**4/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 3*b**5*x**5/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3), Eq(n, -4)), (-60*a**5*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 90*a**5/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 120*a**4*b*x*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 120*a**4*b*x/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 60*a**3*b**2*x**2*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 20*a**2*b**3*x**3/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 5*a*b**4*x**4/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 2*b**5*x**5/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2), Eq(n, -3)), (60*a**5*log(a/b + x)/(12*a*b**6 + 12*b**7*x) + 60*a**5/(12*a*b**6 + 12*b**7*x) + 60*a**4*b*x*log(a/b + x)/(12*a*b**6 + 12*b**7*x) - 30*a**3*b**2*x**2/(12*a*b**6 + 12*b**7*x) + 10*a**2*b**3*x**3/(12*a*b**6 + 12*b**7*x) - 5*a*b**4*x**4/(12*a*b**6 + 12*b**7*x) + 3*b**5*x**5/(12*a*b**6 + 12*b**7*x), Eq(n, -2)), (-a**5*log(a/b + x)/b**6 + a**4*x/b**5 - a**3*x**2/(2*b**4) + a**2*x**3/(3*b**3) - a*x**4/(4*b**2) + x**5/(5*b), Eq(n, -1)), (-120*a**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*a**5*b*n*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 60*a**4*b**2*n**2*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 60*a**4*b**2*n*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 20*a**3*b**3*n**3*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 60*a**3*b**3*n**2*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 40*a**3*b**3*n*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 5*a**2*b**4*n**4*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 30*a**2*b**4*n**3*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 55*a**2*b**4*n**2*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 30*a**2*b**4*n*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + a*b**5*n**5*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 10*a*b**5*n**4*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 35*a*b**5*n**3*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 50*a*b**5*n**2*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 24*a*b**5*n*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + b**6*n**5*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 15*b**6*n**4*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 85*b**6*n**3*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 225*b**6*n**2*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 274*b**6*n*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*b**6*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6), True)) - b*b**n*c**2*n*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2)) - b*b**n*c**2*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2))","B",0
182,-1,0,0,0.000000," ","integrate(x**2*(b*x+a)**n*(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(x*(b*x+a)**n*(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate((b*x+a)**n*(d*x**3+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate((b*x+a)**n*(d*x**3+c)**3/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate(x**5*(f*x+e)**n/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate(x**4*(f*x+e)**n/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate(x**3*(f*x+e)**n/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate(x**2*(f*x+e)**n/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate(x*(f*x+e)**n/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate((f*x+e)**n/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,0,0,0,0.000000," ","integrate((f*x+e)**n/x/(b*x**3+a),x)","\int \frac{\left(e + f x\right)^{n}}{x \left(a + b x^{3}\right)}\, dx"," ",0,"Integral((e + f*x)**n/(x*(a + b*x**3)), x)","F",0
193,-1,0,0,0.000000," ","integrate((f*x+e)**n/x**2/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate(x**2*(d*x+c)**(1+n)/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate(x**m*(f*x+e)**n/(b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,0,0,0,0.000000," ","integrate((d*x**3+c)**(1/2)/(b*x+a),x)","\int \frac{\sqrt{c + d x^{3}}}{a + b x}\, dx"," ",0,"Integral(sqrt(c + d*x**3)/(a + b*x), x)","F",0
197,1,636,0,30.802725," ","integrate((e**3*x**3+d**3)**p/(e*x+d),x)","\frac{0^{p} \log{\left(1 + \frac{e^{3} x^{3}}{d^{3}} \right)} \Gamma\left(- \frac{2}{3}\right) \Gamma\left(- \frac{1}{3}\right) \Gamma\left(\frac{4}{3}\right) \Gamma\left(\frac{5}{3}\right)}{4 \pi^{2} e} + \frac{0^{p} e^{\frac{i \pi}{3}} \log{\left(1 - \frac{e x e^{\frac{i \pi}{3}}}{d} \right)} \Gamma\left(- \frac{1}{3}\right) \Gamma\left(\frac{1}{3}\right) \Gamma^{2}\left(\frac{2}{3}\right) \Gamma\left(\frac{4}{3}\right)}{6 \pi^{2} e \Gamma\left(\frac{5}{3}\right)} + \frac{0^{p} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{e x e^{\frac{i \pi}{3}}}{d} \right)} \Gamma^{3}\left(\frac{1}{3}\right) \Gamma^{2}\left(\frac{2}{3}\right)}{12 \pi^{2} e \Gamma\left(\frac{4}{3}\right)} - \frac{0^{p} \log{\left(1 - \frac{e x e^{i \pi}}{d} \right)} \Gamma\left(- \frac{1}{3}\right) \Gamma\left(\frac{1}{3}\right) \Gamma^{2}\left(\frac{2}{3}\right) \Gamma\left(\frac{4}{3}\right)}{6 \pi^{2} e \Gamma\left(\frac{5}{3}\right)} + \frac{0^{p} \log{\left(1 - \frac{e x e^{i \pi}}{d} \right)} \Gamma^{3}\left(\frac{1}{3}\right) \Gamma^{2}\left(\frac{2}{3}\right)}{12 \pi^{2} e \Gamma\left(\frac{4}{3}\right)} + \frac{0^{p} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{e x e^{\frac{5 i \pi}{3}}}{d} \right)} \Gamma^{3}\left(\frac{1}{3}\right) \Gamma^{2}\left(\frac{2}{3}\right)}{12 \pi^{2} e \Gamma\left(\frac{4}{3}\right)} + \frac{0^{p} e^{- \frac{i \pi}{3}} \log{\left(1 - \frac{e x e^{\frac{5 i \pi}{3}}}{d} \right)} \Gamma\left(- \frac{1}{3}\right) \Gamma\left(\frac{1}{3}\right) \Gamma^{2}\left(\frac{2}{3}\right) \Gamma\left(\frac{4}{3}\right)}{6 \pi^{2} e \Gamma\left(\frac{5}{3}\right)} - \frac{d^{2} e^{3 p} p x^{3 p} \Gamma\left(- \frac{2}{3}\right) \Gamma\left(- \frac{1}{3}\right) \Gamma\left(\frac{4}{3}\right) \Gamma\left(\frac{5}{3}\right) \Gamma\left(p\right) \Gamma\left(\frac{2}{3} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{2}{3} - p \\ \frac{5}{3} - p \end{matrix}\middle| {\frac{d^{3} e^{i \pi}}{e^{3} x^{3}}} \right)}}{4 \pi^{2} e^{3} x^{2} \Gamma\left(\frac{5}{3} - p\right) \Gamma\left(p + 1\right)} - \frac{d e^{3 p} p x^{3 p} \Gamma\left(- \frac{1}{3}\right) \Gamma\left(\frac{1}{3}\right) \Gamma\left(\frac{2}{3}\right) \Gamma\left(\frac{4}{3}\right) \Gamma\left(p\right) \Gamma\left(\frac{1}{3} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{1}{3} - p \\ \frac{4}{3} - p \end{matrix}\middle| {\frac{d^{3} e^{i \pi}}{e^{3} x^{3}}} \right)}}{4 \pi^{2} e^{2} x \Gamma\left(\frac{4}{3} - p\right) \Gamma\left(p + 1\right)} - \frac{d^{3 p} e^{2} x^{3} \Gamma^{2}\left(\frac{1}{3}\right) \Gamma^{2}\left(\frac{2}{3}\right) \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {\frac{e^{3} x^{3} e^{i \pi}}{d^{3}}} \right)}}{4 \pi^{2} d^{3} \Gamma\left(- p\right) \Gamma\left(p + 1\right)}"," ",0,"0**p*log(1 + e**3*x**3/d**3)*gamma(-2/3)*gamma(-1/3)*gamma(4/3)*gamma(5/3)/(4*pi**2*e) + 0**p*exp(I*pi/3)*log(1 - e*x*exp_polar(I*pi/3)/d)*gamma(-1/3)*gamma(1/3)*gamma(2/3)**2*gamma(4/3)/(6*pi**2*e*gamma(5/3)) + 0**p*exp(2*I*pi/3)*log(1 - e*x*exp_polar(I*pi/3)/d)*gamma(1/3)**3*gamma(2/3)**2/(12*pi**2*e*gamma(4/3)) - 0**p*log(1 - e*x*exp_polar(I*pi)/d)*gamma(-1/3)*gamma(1/3)*gamma(2/3)**2*gamma(4/3)/(6*pi**2*e*gamma(5/3)) + 0**p*log(1 - e*x*exp_polar(I*pi)/d)*gamma(1/3)**3*gamma(2/3)**2/(12*pi**2*e*gamma(4/3)) + 0**p*exp(-2*I*pi/3)*log(1 - e*x*exp_polar(5*I*pi/3)/d)*gamma(1/3)**3*gamma(2/3)**2/(12*pi**2*e*gamma(4/3)) + 0**p*exp(-I*pi/3)*log(1 - e*x*exp_polar(5*I*pi/3)/d)*gamma(-1/3)*gamma(1/3)*gamma(2/3)**2*gamma(4/3)/(6*pi**2*e*gamma(5/3)) - d**2*e**(3*p)*p*x**(3*p)*gamma(-2/3)*gamma(-1/3)*gamma(4/3)*gamma(5/3)*gamma(p)*gamma(2/3 - p)*hyper((1 - p, 2/3 - p), (5/3 - p,), d**3*exp_polar(I*pi)/(e**3*x**3))/(4*pi**2*e**3*x**2*gamma(5/3 - p)*gamma(p + 1)) - d*e**(3*p)*p*x**(3*p)*gamma(-1/3)*gamma(1/3)*gamma(2/3)*gamma(4/3)*gamma(p)*gamma(1/3 - p)*hyper((1 - p, 1/3 - p), (4/3 - p,), d**3*exp_polar(I*pi)/(e**3*x**3))/(4*pi**2*e**2*x*gamma(4/3 - p)*gamma(p + 1)) - d**(3*p)*e**2*x**3*gamma(1/3)**2*gamma(2/3)**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), e**3*x**3*exp_polar(I*pi)/d**3)/(4*pi**2*d**3*gamma(-p)*gamma(p + 1))","B",0
198,0,0,0,0.000000," ","integrate((-x**2-2*x+2)/(x**2+2)/(x**3+1)**(1/2),x)","- \int \frac{2 x}{x^{2} \sqrt{x^{3} + 1} + 2 \sqrt{x^{3} + 1}}\, dx - \int \frac{x^{2}}{x^{2} \sqrt{x^{3} + 1} + 2 \sqrt{x^{3} + 1}}\, dx - \int \left(- \frac{2}{x^{2} \sqrt{x^{3} + 1} + 2 \sqrt{x^{3} + 1}}\right)\, dx"," ",0,"-Integral(2*x/(x**2*sqrt(x**3 + 1) + 2*sqrt(x**3 + 1)), x) - Integral(x**2/(x**2*sqrt(x**3 + 1) + 2*sqrt(x**3 + 1)), x) - Integral(-2/(x**2*sqrt(x**3 + 1) + 2*sqrt(x**3 + 1)), x)","F",0
199,0,0,0,0.000000," ","integrate((-x**2+2*x+2)/(x**2+2)/(-x**3+1)**(1/2),x)","- \int \left(- \frac{2 x}{x^{2} \sqrt{1 - x^{3}} + 2 \sqrt{1 - x^{3}}}\right)\, dx - \int \frac{x^{2}}{x^{2} \sqrt{1 - x^{3}} + 2 \sqrt{1 - x^{3}}}\, dx - \int \left(- \frac{2}{x^{2} \sqrt{1 - x^{3}} + 2 \sqrt{1 - x^{3}}}\right)\, dx"," ",0,"-Integral(-2*x/(x**2*sqrt(1 - x**3) + 2*sqrt(1 - x**3)), x) - Integral(x**2/(x**2*sqrt(1 - x**3) + 2*sqrt(1 - x**3)), x) - Integral(-2/(x**2*sqrt(1 - x**3) + 2*sqrt(1 - x**3)), x)","F",0
200,0,0,0,0.000000," ","integrate((-x**2+2*x+2)/(x**2+2)/(x**3-1)**(1/2),x)","- \int \left(- \frac{2 x}{x^{2} \sqrt{x^{3} - 1} + 2 \sqrt{x^{3} - 1}}\right)\, dx - \int \frac{x^{2}}{x^{2} \sqrt{x^{3} - 1} + 2 \sqrt{x^{3} - 1}}\, dx - \int \left(- \frac{2}{x^{2} \sqrt{x^{3} - 1} + 2 \sqrt{x^{3} - 1}}\right)\, dx"," ",0,"-Integral(-2*x/(x**2*sqrt(x**3 - 1) + 2*sqrt(x**3 - 1)), x) - Integral(x**2/(x**2*sqrt(x**3 - 1) + 2*sqrt(x**3 - 1)), x) - Integral(-2/(x**2*sqrt(x**3 - 1) + 2*sqrt(x**3 - 1)), x)","F",0
201,0,0,0,0.000000," ","integrate((-x**2-2*x+2)/(x**2+2)/(-x**3-1)**(1/2),x)","- \int \frac{2 x}{x^{2} \sqrt{- x^{3} - 1} + 2 \sqrt{- x^{3} - 1}}\, dx - \int \frac{x^{2}}{x^{2} \sqrt{- x^{3} - 1} + 2 \sqrt{- x^{3} - 1}}\, dx - \int \left(- \frac{2}{x^{2} \sqrt{- x^{3} - 1} + 2 \sqrt{- x^{3} - 1}}\right)\, dx"," ",0,"-Integral(2*x/(x**2*sqrt(-x**3 - 1) + 2*sqrt(-x**3 - 1)), x) - Integral(x**2/(x**2*sqrt(-x**3 - 1) + 2*sqrt(-x**3 - 1)), x) - Integral(-2/(x**2*sqrt(-x**3 - 1) + 2*sqrt(-x**3 - 1)), x)","F",0
202,0,0,0,0.000000," ","integrate((-x**2-2*x+2)/(d*x+x**2+d+2)/(x**3+1)**(1/2),x)","- \int \frac{2 x}{d x \sqrt{x^{3} + 1} + d \sqrt{x^{3} + 1} + x^{2} \sqrt{x^{3} + 1} + 2 \sqrt{x^{3} + 1}}\, dx - \int \frac{x^{2}}{d x \sqrt{x^{3} + 1} + d \sqrt{x^{3} + 1} + x^{2} \sqrt{x^{3} + 1} + 2 \sqrt{x^{3} + 1}}\, dx - \int \left(- \frac{2}{d x \sqrt{x^{3} + 1} + d \sqrt{x^{3} + 1} + x^{2} \sqrt{x^{3} + 1} + 2 \sqrt{x^{3} + 1}}\right)\, dx"," ",0,"-Integral(2*x/(d*x*sqrt(x**3 + 1) + d*sqrt(x**3 + 1) + x**2*sqrt(x**3 + 1) + 2*sqrt(x**3 + 1)), x) - Integral(x**2/(d*x*sqrt(x**3 + 1) + d*sqrt(x**3 + 1) + x**2*sqrt(x**3 + 1) + 2*sqrt(x**3 + 1)), x) - Integral(-2/(d*x*sqrt(x**3 + 1) + d*sqrt(x**3 + 1) + x**2*sqrt(x**3 + 1) + 2*sqrt(x**3 + 1)), x)","F",0
203,0,0,0,0.000000," ","integrate((-x**2+2*x+2)/(d*x+x**2-d+2)/(-x**3+1)**(1/2),x)","- \int \left(- \frac{2 x}{d x \sqrt{1 - x^{3}} - d \sqrt{1 - x^{3}} + x^{2} \sqrt{1 - x^{3}} + 2 \sqrt{1 - x^{3}}}\right)\, dx - \int \frac{x^{2}}{d x \sqrt{1 - x^{3}} - d \sqrt{1 - x^{3}} + x^{2} \sqrt{1 - x^{3}} + 2 \sqrt{1 - x^{3}}}\, dx - \int \left(- \frac{2}{d x \sqrt{1 - x^{3}} - d \sqrt{1 - x^{3}} + x^{2} \sqrt{1 - x^{3}} + 2 \sqrt{1 - x^{3}}}\right)\, dx"," ",0,"-Integral(-2*x/(d*x*sqrt(1 - x**3) - d*sqrt(1 - x**3) + x**2*sqrt(1 - x**3) + 2*sqrt(1 - x**3)), x) - Integral(x**2/(d*x*sqrt(1 - x**3) - d*sqrt(1 - x**3) + x**2*sqrt(1 - x**3) + 2*sqrt(1 - x**3)), x) - Integral(-2/(d*x*sqrt(1 - x**3) - d*sqrt(1 - x**3) + x**2*sqrt(1 - x**3) + 2*sqrt(1 - x**3)), x)","F",0
204,0,0,0,0.000000," ","integrate((-x**2+2*x+2)/(d*x+x**2-d+2)/(x**3-1)**(1/2),x)","- \int \left(- \frac{2 x}{d x \sqrt{x^{3} - 1} - d \sqrt{x^{3} - 1} + x^{2} \sqrt{x^{3} - 1} + 2 \sqrt{x^{3} - 1}}\right)\, dx - \int \frac{x^{2}}{d x \sqrt{x^{3} - 1} - d \sqrt{x^{3} - 1} + x^{2} \sqrt{x^{3} - 1} + 2 \sqrt{x^{3} - 1}}\, dx - \int \left(- \frac{2}{d x \sqrt{x^{3} - 1} - d \sqrt{x^{3} - 1} + x^{2} \sqrt{x^{3} - 1} + 2 \sqrt{x^{3} - 1}}\right)\, dx"," ",0,"-Integral(-2*x/(d*x*sqrt(x**3 - 1) - d*sqrt(x**3 - 1) + x**2*sqrt(x**3 - 1) + 2*sqrt(x**3 - 1)), x) - Integral(x**2/(d*x*sqrt(x**3 - 1) - d*sqrt(x**3 - 1) + x**2*sqrt(x**3 - 1) + 2*sqrt(x**3 - 1)), x) - Integral(-2/(d*x*sqrt(x**3 - 1) - d*sqrt(x**3 - 1) + x**2*sqrt(x**3 - 1) + 2*sqrt(x**3 - 1)), x)","F",0
205,0,0,0,0.000000," ","integrate((-x**2-2*x+2)/(d*x+x**2+d+2)/(-x**3-1)**(1/2),x)","- \int \frac{2 x}{d x \sqrt{- x^{3} - 1} + d \sqrt{- x^{3} - 1} + x^{2} \sqrt{- x^{3} - 1} + 2 \sqrt{- x^{3} - 1}}\, dx - \int \frac{x^{2}}{d x \sqrt{- x^{3} - 1} + d \sqrt{- x^{3} - 1} + x^{2} \sqrt{- x^{3} - 1} + 2 \sqrt{- x^{3} - 1}}\, dx - \int \left(- \frac{2}{d x \sqrt{- x^{3} - 1} + d \sqrt{- x^{3} - 1} + x^{2} \sqrt{- x^{3} - 1} + 2 \sqrt{- x^{3} - 1}}\right)\, dx"," ",0,"-Integral(2*x/(d*x*sqrt(-x**3 - 1) + d*sqrt(-x**3 - 1) + x**2*sqrt(-x**3 - 1) + 2*sqrt(-x**3 - 1)), x) - Integral(x**2/(d*x*sqrt(-x**3 - 1) + d*sqrt(-x**3 - 1) + x**2*sqrt(-x**3 - 1) + 2*sqrt(-x**3 - 1)), x) - Integral(-2/(d*x*sqrt(-x**3 - 1) + d*sqrt(-x**3 - 1) + x**2*sqrt(-x**3 - 1) + 2*sqrt(-x**3 - 1)), x)","F",0
206,1,175,0,4.654002," ","integrate((e*x+d)**3*(c*x**4+a)**(1/2),x)","\frac{\sqrt{a} d^{3} 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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{3 \sqrt{a} d^{2} e x^{2} \sqrt{1 + \frac{c x^{4}}{a}}}{4} + \frac{3 \sqrt{a} d e^{2} 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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{3 a d^{2} e \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{4 \sqrt{c}} + e^{3} \left(\begin{cases} \frac{\sqrt{a} x^{4}}{4} & \text{for}\: c = 0 \\\frac{\left(a + c x^{4}\right)^{\frac{3}{2}}}{6 c} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*d**3*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + 3*sqrt(a)*d**2*e*x**2*sqrt(1 + c*x**4/a)/4 + 3*sqrt(a)*d*e**2*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + 3*a*d**2*e*asinh(sqrt(c)*x**2/sqrt(a))/(4*sqrt(c)) + e**3*Piecewise((sqrt(a)*x**4/4, Eq(c, 0)), ((a + c*x**4)**(3/2)/(6*c), True))","A",0
207,1,138,0,4.087789," ","integrate((e*x+d)**2*(c*x**4+a)**(1/2),x)","\frac{\sqrt{a} d^{2} 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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{a} d e x^{2} \sqrt{1 + \frac{c x^{4}}{a}}}{2} + \frac{\sqrt{a} e^{2} 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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{a d e \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{c}}"," ",0,"sqrt(a)*d**2*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + sqrt(a)*d*e*x**2*sqrt(1 + c*x**4/a)/2 + sqrt(a)*e**2*x**3*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + a*d*e*asinh(sqrt(c)*x**2/sqrt(a))/(2*sqrt(c))","C",0
208,1,88,0,3.453676," ","integrate((e*x+d)*(c*x**4+a)**(1/2),x)","\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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{a} e x^{2} \sqrt{1 + \frac{c x^{4}}{a}}}{4} + \frac{a e \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{4 \sqrt{c}}"," ",0,"sqrt(a)*d*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + sqrt(a)*e*x**2*sqrt(1 + c*x**4/a)/4 + a*e*asinh(sqrt(c)*x**2/sqrt(a))/(4*sqrt(c))","C",0
209,1,37,0,0.789116," ","integrate((c*x**4+a)**(1/2),x)","\frac{\sqrt{a} 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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(a)*x*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4))","C",0
210,0,0,0,0.000000," ","integrate((c*x**4+a)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{a + c x^{4}}}{d + e x}\, dx"," ",0,"Integral(sqrt(a + c*x**4)/(d + e*x), x)","F",0
211,0,0,0,0.000000," ","integrate((c*x**4+a)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{a + c x^{4}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + c*x**4)/(d + e*x)**2, x)","F",0
212,1,141,0,4.187812," ","integrate((e*x+d)**3/(c*x**4+a)**(1/2),x)","e^{3} \left(\begin{cases} \frac{x^{4}}{4 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{4}}}{2 c} & \text{otherwise} \end{cases}\right) + \frac{3 d^{2} e \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{c}} + \frac{d^{3} 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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} + \frac{3 d e^{2} 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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"e**3*Piecewise((x**4/(4*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**4)/(2*c), True)) + 3*d**2*e*asinh(sqrt(c)*x**2/sqrt(a))/(2*sqrt(c)) + d**3*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) + 3*d*e**2*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4))","A",0
213,1,105,0,3.438101," ","integrate((e*x+d)**2/(c*x**4+a)**(1/2),x)","\frac{d e \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{\sqrt{c}} + \frac{d^{2} 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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} + \frac{e^{2} 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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"d*e*asinh(sqrt(c)*x**2/sqrt(a))/sqrt(c) + d**2*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4)) + e**2*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4))","C",0
214,1,61,0,2.322184," ","integrate((e*x+d)/(c*x**4+a)**(1/2),x)","\frac{e \operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{c}} + \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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"e*asinh(sqrt(c)*x**2/sqrt(a))/(2*sqrt(c)) + d*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4))","C",0
215,1,36,0,0.734442," ","integrate(1/(c*x**4+a)**(1/2),x)","\frac{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{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4))","C",0
216,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{4}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**4)*(d + e*x)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{4}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**4)*(d + e*x)**2), x)","F",0
218,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{4}} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**4)*(d + e*x)**3), x)","F",0
219,0,0,0,0.000000," ","integrate((e*x+d)**3/(c*x**4+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(a + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(a + c*x**4)**(3/2), x)","F",0
220,0,0,0,0.000000," ","integrate((e*x+d)**2/(c*x**4+a)**(3/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(a + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(a + c*x**4)**(3/2), x)","F",0
221,1,61,0,8.094258," ","integrate((e*x+d)/(c*x**4+a)**(3/2),x)","\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{c 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{c x^{4}}{a}}}"," ",0,"d*x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(5/4)) + e*x**2/(2*a**(3/2)*sqrt(1 + c*x**4/a))","C",0
222,1,36,0,0.809031," ","integrate(1/(c*x**4+a)**(3/2),x)","\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| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 a^{\frac{3}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 3/2), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*a**(3/2)*gamma(5/4))","C",0
223,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**4+a)**(3/2),x)","\int \frac{1}{\left(a + c x^{4}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + c*x**4)**(3/2)*(d + e*x)), x)","F",0
224,-1,0,0,0.000000," ","integrate(x**3*(d*x+c)**n/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate(x**3*(d*x+c)**(1+n)/(b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,0,0,0,0.000000," ","integrate(1/(e*x**2+d*x+c)/(b*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a + b x^{4}} \left(c + d x + e x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(a + b*x**4)*(c + d*x + e*x**2)), x)","F",0
227,-1,0,0,0.000000," ","integrate(x**m*(c*(b*x**2+a)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate(x**5*(c*(b*x**2+a)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate(x**4*(c*(b*x**2+a)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate(x**3*(c*(b*x**2+a)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,0,0,0,0.000000," ","integrate(x**2*(c*(b*x**2+a)**2)**(3/2),x)","\int x^{2} \left(c \left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(c*(a + b*x**2)**2)**(3/2), x)","F",0
232,0,0,0,0.000000," ","integrate(x*(c*(b*x**2+a)**2)**(3/2),x)","\int x \left(c \left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(c*(a + b*x**2)**2)**(3/2), x)","F",0
233,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**2)**(3/2),x)","\int \left(c \left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*(a + b*x**2)**2)**(3/2), x)","F",0
234,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**2)**(3/2)/x,x)","\int \frac{\left(c \left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((c*(a + b*x**2)**2)**(3/2)/x, x)","F",0
235,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**2)**(3/2)/x**2,x)","\int \frac{\left(c \left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((c*(a + b*x**2)**2)**(3/2)/x**2, x)","F",0
236,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**2)**(3/2)/x**3,x)","\int \frac{\left(c \left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((c*(a + b*x**2)**2)**(3/2)/x**3, x)","F",0
237,-1,0,0,0.000000," ","integrate(x**2*(c*(b*x**2+a)**3)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,-1,0,0,0.000000," ","integrate(x*(c*(b*x**2+a)**3)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate((c*(b*x**2+a)**3)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**3)**(3/2)/x,x)","\int \frac{\left(c \left(a + b x^{2}\right)^{3}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((c*(a + b*x**2)**3)**(3/2)/x, x)","F",0
241,-1,0,0,0.000000," ","integrate((c*(b*x**2+a)**3)**(3/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate((c*(b*x**2+a)**3)**(3/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,0,0,0,0.000000," ","integrate(x**2*(c/(b*x**2+a))**(3/2),x)","\int x^{2} \left(\frac{c}{a + b x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(c/(a + b*x**2))**(3/2), x)","F",0
244,1,53,0,1.506753," ","integrate(x*(c/(b*x**2+a))**(3/2),x)","\begin{cases} - \frac{a c^{\frac{3}{2}} \left(\frac{1}{a + b x^{2}}\right)^{\frac{3}{2}}}{b} - c^{\frac{3}{2}} x^{2} \left(\frac{1}{a + b x^{2}}\right)^{\frac{3}{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \left(\frac{c}{a}\right)^{\frac{3}{2}}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**(3/2)*(1/(a + b*x**2))**(3/2)/b - c**(3/2)*x**2*(1/(a + b*x**2))**(3/2), Ne(b, 0)), (x**2*(c/a)**(3/2)/2, True))","A",0
245,1,66,0,1.463058," ","integrate((c/(b*x**2+a))**(3/2),x)","\begin{cases} c^{\frac{3}{2}} x \left(\frac{1}{a + b x^{2}}\right)^{\frac{3}{2}} + \frac{b c^{\frac{3}{2}} x^{3} \left(\frac{1}{a + b x^{2}}\right)^{\frac{3}{2}}}{a} & \text{for}\: a \neq 0 \\- \frac{c^{\frac{3}{2}} x \left(\frac{1}{b}\right)^{\frac{3}{2}} \left(\frac{1}{x^{2}}\right)^{\frac{3}{2}}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**(3/2)*x*(1/(a + b*x**2))**(3/2) + b*c**(3/2)*x**3*(1/(a + b*x**2))**(3/2)/a, Ne(a, 0)), (-c**(3/2)*x*(1/b)**(3/2)*(x**(-2))**(3/2)/2, True))","A",0
246,0,0,0,0.000000," ","integrate((c/(b*x**2+a))**(3/2)/x,x)","\int \frac{\left(\frac{c}{a + b x^{2}}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((c/(a + b*x**2))**(3/2)/x, x)","F",0
247,0,0,0,0.000000," ","integrate((c/(b*x**2+a))**(3/2)/x**2,x)","\int \frac{\left(\frac{c}{a + b x^{2}}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((c/(a + b*x**2))**(3/2)/x**2, x)","F",0
248,0,0,0,0.000000," ","integrate((c/(b*x**2+a))**(3/2)/x**3,x)","\int \frac{\left(\frac{c}{a + b x^{2}}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((c/(a + b*x**2))**(3/2)/x**3, x)","F",0
249,-1,0,0,0.000000," ","integrate(x**7*(c*(b*x**2+a)**(1/2))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,1,116,0,88.605057," ","integrate(x**5*(c*(b*x**2+a)**(1/2))**(3/2),x)","\begin{cases} \frac{64 a^{3} c^{\frac{3}{2}} \left(a + b x^{2}\right)^{\frac{3}{4}}}{1155 b^{3}} - \frac{16 a^{2} c^{\frac{3}{2}} x^{2} \left(a + b x^{2}\right)^{\frac{3}{4}}}{385 b^{2}} + \frac{2 a c^{\frac{3}{2}} x^{4} \left(a + b x^{2}\right)^{\frac{3}{4}}}{55 b} + \frac{2 c^{\frac{3}{2}} x^{6} \left(a + b x^{2}\right)^{\frac{3}{4}}}{15} & \text{for}\: b \neq 0 \\\frac{x^{6} \left(\sqrt{a} c\right)^{\frac{3}{2}}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((64*a**3*c**(3/2)*(a + b*x**2)**(3/4)/(1155*b**3) - 16*a**2*c**(3/2)*x**2*(a + b*x**2)**(3/4)/(385*b**2) + 2*a*c**(3/2)*x**4*(a + b*x**2)**(3/4)/(55*b) + 2*c**(3/2)*x**6*(a + b*x**2)**(3/4)/15, Ne(b, 0)), (x**6*(sqrt(a)*c)**(3/2)/6, True))","A",0
251,1,87,0,38.303936," ","integrate(x**3*(c*(b*x**2+a)**(1/2))**(3/2),x)","\begin{cases} - \frac{8 a^{2} c^{\frac{3}{2}} \left(a + b x^{2}\right)^{\frac{3}{4}}}{77 b^{2}} + \frac{6 a c^{\frac{3}{2}} x^{2} \left(a + b x^{2}\right)^{\frac{3}{4}}}{77 b} + \frac{2 c^{\frac{3}{2}} x^{4} \left(a + b x^{2}\right)^{\frac{3}{4}}}{11} & \text{for}\: b \neq 0 \\\frac{x^{4} \left(\sqrt{a} c\right)^{\frac{3}{2}}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*a**2*c**(3/2)*(a + b*x**2)**(3/4)/(77*b**2) + 6*a*c**(3/2)*x**2*(a + b*x**2)**(3/4)/(77*b) + 2*c**(3/2)*x**4*(a + b*x**2)**(3/4)/11, Ne(b, 0)), (x**4*(sqrt(a)*c)**(3/2)/4, True))","A",0
252,1,58,0,14.888529," ","integrate(x*(c*(b*x**2+a)**(1/2))**(3/2),x)","\begin{cases} \frac{2 a c^{\frac{3}{2}} \left(a + b x^{2}\right)^{\frac{3}{4}}}{7 b} + \frac{2 c^{\frac{3}{2}} x^{2} \left(a + b x^{2}\right)^{\frac{3}{4}}}{7} & \text{for}\: b \neq 0 \\\frac{x^{2} \left(\sqrt{a} c\right)^{\frac{3}{2}}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*c**(3/2)*(a + b*x**2)**(3/4)/(7*b) + 2*c**(3/2)*x**2*(a + b*x**2)**(3/4)/7, Ne(b, 0)), (x**2*(sqrt(a)*c)**(3/2)/2, True))","A",0
253,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**(1/2))**(3/2)/x,x)","\int \frac{\left(c \sqrt{a + b x^{2}}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((c*sqrt(a + b*x**2))**(3/2)/x, x)","F",0
254,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**(1/2))**(3/2)/x**3,x)","\int \frac{\left(c \sqrt{a + b x^{2}}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((c*sqrt(a + b*x**2))**(3/2)/x**3, x)","F",0
255,0,0,0,0.000000," ","integrate(x**2*(c*(b*x**2+a)**(1/2))**(3/2),x)","\int x^{2} \left(c \sqrt{a + b x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(c*sqrt(a + b*x**2))**(3/2), x)","F",0
256,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**(1/2))**(3/2),x)","\int \left(c \sqrt{a + b x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*sqrt(a + b*x**2))**(3/2), x)","F",0
257,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**(1/2))**(3/2)/x**2,x)","\int \frac{\left(c \sqrt{a + b x^{2}}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((c*sqrt(a + b*x**2))**(3/2)/x**2, x)","F",0
258,0,0,0,0.000000," ","integrate((c*(b*x**2+a)**(1/2))**(3/2)/x**4,x)","\int \frac{\left(c \sqrt{a + b x^{2}}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((c*sqrt(a + b*x**2))**(3/2)/x**4, x)","F",0
259,0,0,0,0.000000," ","integrate(((b-x)*(-a+x))**(1/2),x)","\int \sqrt{\left(- a + x\right) \left(b - x\right)}\, dx"," ",0,"Integral(sqrt((-a + x)*(b - x)), x)","F",0
260,0,0,0,0.000000," ","integrate(((-x**2+1)*(x**2+3))**(1/2),x)","\int \sqrt{\left(1 - x^{2}\right) \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(sqrt((1 - x**2)*(x**2 + 3)), x)","F",0
261,0,0,0,0.000000," ","integrate(1/((b-x)*(-a+x))**(1/2),x)","\int \frac{1}{\sqrt{\left(- a + x\right) \left(b - x\right)}}\, dx"," ",0,"Integral(1/sqrt((-a + x)*(b - x)), x)","F",0
262,0,0,0,0.000000," ","integrate(1/((-x**2+1)*(x**2+3))**(1/2),x)","\int \frac{1}{\sqrt{\left(1 - x^{2}\right) \left(x^{2} + 3\right)}}\, dx"," ",0,"Integral(1/sqrt((1 - x**2)*(x**2 + 3)), x)","F",0
263,-1,0,0,0.000000," ","integrate(x**5*(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate(x**3*(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate(x*(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(1/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(1/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
268,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(1/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(1/2)/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,-1,0,0,0.000000," ","integrate(x**4*(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate(x**2*(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(1/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(1/2)/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,-1,0,0,0.000000," ","integrate(x**5*(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,-1,0,0,0.000000," ","integrate(x**3*(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,-1,0,0,0.000000," ","integrate(x*(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(3/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(3/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(3/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(3/2)/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate(x**4*(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate(x**2*(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(3/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(3/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate((e*(b*x**2+a)/(d*x**2+c))**(3/2)/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,1,39,0,21.540770," ","integrate(x*((-x**2+1)/(x**2+1))**(1/2),x)","\begin{cases} \frac{\sqrt{1 - x^{2}} \sqrt{x^{2} + 1}}{2} - \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{1 - x^{2}}}{2} \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((sqrt(1 - x**2)*sqrt(x**2 + 1)/2 - asin(sqrt(2)*sqrt(1 - x**2)/2), (x > -1) & (x < 1)))","A",0
290,1,66,0,66.857446," ","integrate(x*((-7*x**2+5)/(5*x**2+7))**(1/2),x)","\begin{cases} \frac{5 \sqrt{35} \left(\frac{\sqrt{25 - 35 x^{2}} \sqrt{35 x^{2} + 49}}{125} - \frac{74 \operatorname{asin}{\left(\frac{\sqrt{74} \sqrt{25 - 35 x^{2}}}{74} \right)}}{125}\right)}{14} & \text{for}\: x > - \frac{\sqrt{35}}{7} \wedge x < \frac{\sqrt{35}}{7} \end{cases}"," ",0,"Piecewise((5*sqrt(35)*(sqrt(25 - 35*x**2)*sqrt(35*x**2 + 49)/125 - 74*asin(sqrt(74)*sqrt(25 - 35*x**2)/74)/125)/14, (x > -sqrt(35)/7) & (x < sqrt(35)/7)))","A",0
291,-1,0,0,0.000000," ","integrate(x**2*((-x**3+1)/(x**3+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate(x**8*((-x**3+1)/(x**3+1))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate(x**9*((-7*x**5+5)/(5*x**5+7))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,0,0,0,0.000000," ","integrate((x**2/(x**2-1))**(1/2)/(x**2+1),x)","\int \frac{\sqrt{\frac{x^{2}}{x^{2} - 1}}}{x^{2} + 1}\, dx"," ",0,"Integral(sqrt(x**2/(x**2 - 1))/(x**2 + 1), x)","F",0
295,0,0,0,0.000000," ","integrate((x**2/(-1+a+(1+a)*x**2))**(1/2)/(x**2+1),x)","\int \frac{\sqrt{\frac{x^{2}}{a x^{2} + a + x^{2} - 1}}}{x^{2} + 1}\, dx"," ",0,"Integral(sqrt(x**2/(a*x**2 + a + x**2 - 1))/(x**2 + 1), x)","F",0
296,-1,0,0,0.000000," ","integrate(x**5/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-1,0,0,0.000000," ","integrate(x**3/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate(x/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate(1/x/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate(1/x**3/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate(1/x**5/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate(x**4/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate(x**2/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,-1,0,0,0.000000," ","integrate(1/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate(1/x**2/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate(1/x**4/(e*(b*x**2+a)/(d*x**2+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,-1,0,0,0.000000," ","integrate(x**5/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,-1,0,0,0.000000," ","integrate(x**3/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,-1,0,0,0.000000," ","integrate(x/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate(1/x/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,-1,0,0,0.000000," ","integrate(1/x**3/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,-1,0,0,0.000000," ","integrate(1/x**5/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,-1,0,0,0.000000," ","integrate(x**4/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate(x**2/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate(1/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate(1/x**2/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate(1/x**4/(e*(b*x**2+a)/(d*x**2+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,0,0,0,0.000000," ","integrate(x**5*(a+b/(d*x**2+c))**(1/2),x)","\int x^{5} \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}\, dx"," ",0,"Integral(x**5*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
319,0,0,0,0.000000," ","integrate(x**3*(a+b/(d*x**2+c))**(1/2),x)","\int x^{3} \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}\, dx"," ",0,"Integral(x**3*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
320,0,0,0,0.000000," ","integrate(x*(a+b/(d*x**2+c))**(1/2),x)","\int x \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}\, dx"," ",0,"Integral(x*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
321,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(1/2)/x,x)","\int \frac{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}{x}\, dx"," ",0,"Integral(sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))/x, x)","F",0
322,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(1/2)/x**3,x)","\int \frac{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}{x^{3}}\, dx"," ",0,"Integral(sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))/x**3, x)","F",0
323,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(1/2)/x**5,x)","\int \frac{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}{x^{5}}\, dx"," ",0,"Integral(sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))/x**5, x)","F",0
324,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(1/2)/x**7,x)","\int \frac{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}{x^{7}}\, dx"," ",0,"Integral(sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))/x**7, x)","F",0
325,0,0,0,0.000000," ","integrate(x**4*(a+b/(d*x**2+c))**(1/2),x)","\int x^{4} \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}\, dx"," ",0,"Integral(x**4*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
326,0,0,0,0.000000," ","integrate(x**2*(a+b/(d*x**2+c))**(1/2),x)","\int x^{2} \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}\, dx"," ",0,"Integral(x**2*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
327,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(1/2),x)","\int \sqrt{a + \frac{b}{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b/(c + d*x**2)), x)","F",0
328,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(1/2)/x**2,x)","\int \frac{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}{x^{2}}\, dx"," ",0,"Integral(sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))/x**2, x)","F",0
329,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(1/2)/x**4,x)","\int \frac{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}{x^{4}}\, dx"," ",0,"Integral(sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))/x**4, x)","F",0
330,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(1/2)/x**6,x)","\int \frac{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}{x^{6}}\, dx"," ",0,"Integral(sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))/x**6, x)","F",0
331,0,0,0,0.000000," ","integrate(x**5*(a+b/(d*x**2+c))**(3/2),x)","\int x^{5} \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**5*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
332,0,0,0,0.000000," ","integrate(x**3*(a+b/(d*x**2+c))**(3/2),x)","\int x^{3} \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
333,0,0,0,0.000000," ","integrate(x*(a+b/(d*x**2+c))**(3/2),x)","\int x \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
334,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(3/2)/x,x)","\int \frac{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral(((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)/x, x)","F",0
335,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(3/2)/x**3,x)","\int \frac{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral(((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)/x**3, x)","F",0
336,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(3/2)/x**5,x)","\int \frac{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral(((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)/x**5, x)","F",0
337,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(3/2)/x**7,x)","\int \frac{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral(((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)/x**7, x)","F",0
338,0,0,0,0.000000," ","integrate(x**4*(a+b/(d*x**2+c))**(3/2),x)","\int x^{4} \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**4*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
339,0,0,0,0.000000," ","integrate(x**2*(a+b/(d*x**2+c))**(3/2),x)","\int x^{2} \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
340,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(3/2),x)","\int \left(a + \frac{b}{c + d x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b/(c + d*x**2))**(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(3/2)/x**2,x)","\int \frac{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral(((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)/x**2, x)","F",0
342,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(3/2)/x**4,x)","\int \frac{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral(((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)/x**4, x)","F",0
343,0,0,0,0.000000," ","integrate((a+b/(d*x**2+c))**(3/2)/x**6,x)","\int \frac{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral(((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)/x**6, x)","F",0
344,0,0,0,0.000000," ","integrate(x**5/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{x^{5}}{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(x**5/sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
345,0,0,0,0.000000," ","integrate(x**3/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{x^{3}}{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(x**3/sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
346,0,0,0,0.000000," ","integrate(x/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{x}{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(x/sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
347,0,0,0,0.000000," ","integrate(1/x/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{1}{x \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(1/(x*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))), x)","F",0
348,0,0,0,0.000000," ","integrate(1/x**3/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{1}{x^{3} \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(1/(x**3*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))), x)","F",0
349,0,0,0,0.000000," ","integrate(1/x**5/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{1}{x^{5} \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(1/(x**5*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))), x)","F",0
350,0,0,0,0.000000," ","integrate(x**4/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{x^{4}}{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(x**4/sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
351,0,0,0,0.000000," ","integrate(x**2/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{x^{2}}{\sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(x**2/sqrt((a*c + a*d*x**2 + b)/(c + d*x**2)), x)","F",0
352,0,0,0,0.000000," ","integrate(1/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{1}{\sqrt{a + \frac{b}{c + d x^{2}}}}\, dx"," ",0,"Integral(1/sqrt(a + b/(c + d*x**2)), x)","F",0
353,0,0,0,0.000000," ","integrate(1/x**2/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(1/(x**2*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))), x)","F",0
354,0,0,0,0.000000," ","integrate(1/x**4/(a+b/(d*x**2+c))**(1/2),x)","\int \frac{1}{x^{4} \sqrt{\frac{a c + a d x^{2} + b}{c + d x^{2}}}}\, dx"," ",0,"Integral(1/(x**4*sqrt((a*c + a*d*x**2 + b)/(c + d*x**2))), x)","F",0
355,0,0,0,0.000000," ","integrate(x**5/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{x^{5}}{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**5/((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
356,0,0,0,0.000000," ","integrate(x**3/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{x^{3}}{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
357,0,0,0,0.000000," ","integrate(x/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{x}{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
358,0,0,0,0.000000," ","integrate(1/x/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{1}{x \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)), x)","F",0
359,0,0,0,0.000000," ","integrate(1/x**3/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{1}{x^{3} \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)), x)","F",0
360,0,0,0,0.000000," ","integrate(1/x**5/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{1}{x^{5} \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**5*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)), x)","F",0
361,0,0,0,0.000000," ","integrate(x**4/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{x^{4}}{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4/((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
362,0,0,0,0.000000," ","integrate(x**2/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{x^{2}}{\left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2), x)","F",0
363,0,0,0,0.000000," ","integrate(1/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{1}{\left(a + \frac{b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b/(c + d*x**2))**(-3/2), x)","F",0
364,0,0,0,0.000000," ","integrate(1/x**2/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{1}{x^{2} \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)), x)","F",0
365,0,0,0,0.000000," ","integrate(1/x**4/(a+b/(d*x**2+c))**(3/2),x)","\int \frac{1}{x^{4} \left(\frac{a c + a d x^{2} + b}{c + d x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**4*((a*c + a*d*x**2 + b)/(c + d*x**2))**(3/2)), x)","F",0
366,0,0,0,0.000000," ","integrate((a*x**23)**(1/2)/(x**5+1)**(1/2),x)","\int \frac{\sqrt{a x^{23}}}{\sqrt{\left(x + 1\right) \left(x^{4} - x^{3} + x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a*x**23)/sqrt((x + 1)*(x**4 - x**3 + x**2 - x + 1)), x)","F",0
367,0,0,0,0.000000," ","integrate((a*x**13)**(1/2)/(x**5+1)**(1/2),x)","\int \frac{\sqrt{a x^{13}}}{\sqrt{\left(x + 1\right) \left(x^{4} - x^{3} + x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a*x**13)/sqrt((x + 1)*(x**4 - x**3 + x**2 - x + 1)), x)","F",0
368,0,0,0,0.000000," ","integrate((a*x**3)**(1/2)/(x**5+1)**(1/2),x)","\int \frac{\sqrt{a x^{3}}}{\sqrt{\left(x + 1\right) \left(x^{4} - x^{3} + x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a*x**3)/sqrt((x + 1)*(x**4 - x**3 + x**2 - x + 1)), x)","F",0
369,0,0,0,0.000000," ","integrate((a/x**7)**(1/2)/(x**5+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x^{7}}}}{\sqrt{\left(x + 1\right) \left(x^{4} - x^{3} + x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a/x**7)/sqrt((x + 1)*(x**4 - x**3 + x**2 - x + 1)), x)","F",0
370,0,0,0,0.000000," ","integrate((a/x**17)**(1/2)/(x**5+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x^{17}}}}{\sqrt{\left(x + 1\right) \left(x^{4} - x^{3} + x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a/x**17)/sqrt((x + 1)*(x**4 - x**3 + x**2 - x + 1)), x)","F",0
371,0,0,0,0.000000," ","integrate((a*x**6)**(1/2)/x/(-x**4+1),x)","- \int \frac{\sqrt{a x^{6}}}{x^{5} - x}\, dx"," ",0,"-Integral(sqrt(a*x**6)/(x**5 - x), x)","F",0
372,0,0,0,0.000000," ","integrate((a*x**6)**(1/2)/(-x**5+x),x)","- \int \frac{\sqrt{a x^{6}}}{x^{5} - x}\, dx"," ",0,"-Integral(sqrt(a*x**6)/(x**5 - x), x)","F",0
373,0,0,0,0.000000," ","integrate((a*x**6)**(3/2)/x/(-x**4+1),x)","- \int \frac{\left(a x^{6}\right)^{\frac{3}{2}}}{x^{5} - x}\, dx"," ",0,"-Integral((a*x**6)**(3/2)/(x**5 - x), x)","F",0
374,0,0,0,0.000000," ","integrate(1/(-x**4+1)-(a*x**6)**(1/2)/x/(-x**4+1),x)","- \int \frac{x}{x^{5} - x}\, dx - \int \left(- \frac{\sqrt{a x^{6}}}{x^{5} - x}\right)\, dx"," ",0,"-Integral(x/(x**5 - x), x) - Integral(-sqrt(a*x**6)/(x**5 - x), x)","F",0
375,0,0,0,0.000000," ","integrate(1/(-x**4+1)-(a*x**6)**(1/2)/(-x**5+x),x)","- \int \frac{x}{x^{5} - x}\, dx - \int \left(- \frac{\sqrt{a x^{6}}}{x^{5} - x}\right)\, dx"," ",0,"-Integral(x/(x**5 - x), x) - Integral(-sqrt(a*x**6)/(x**5 - x), x)","F",0
376,0,0,0,0.000000," ","integrate((a*x**3)**(1/2)/(-x**3+x),x)","- \int \frac{\sqrt{a x^{3}}}{x^{3} - x}\, dx"," ",0,"-Integral(sqrt(a*x**3)/(x**3 - x), x)","F",0
377,0,0,0,0.000000," ","integrate((a*x**4)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{\sqrt{a x^{4}}}{\sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(a*x**4)/sqrt(x**2 + 1), x)","F",0
378,0,0,0,0.000000," ","integrate((a*x**3)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{\sqrt{a x^{3}}}{\sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(a*x**3)/sqrt(x**2 + 1), x)","F",0
379,1,20,0,0.482002," ","integrate((a*x**2)**(1/2)/(x**2+1)**(1/2),x)","\frac{\sqrt{a} \sqrt{x^{2} + 1} \sqrt{x^{2}}}{x}"," ",0,"sqrt(a)*sqrt(x**2 + 1)*sqrt(x**2)/x","A",0
380,1,36,0,1.015578," ","integrate((a*x)**(1/2)/(x**2+1)**(1/2),x)","\frac{\sqrt{a} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {x^{2} e^{i \pi}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(a)*x**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), x**2*exp_polar(I*pi))/(2*gamma(7/4))","C",0
381,0,0,0,0.000000," ","integrate((a/x)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(a/x)/sqrt(x**2 + 1), x)","F",0
382,0,0,0,0.000000," ","integrate((a/x**2)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x^{2}}}}{\sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(a/x**2)/sqrt(x**2 + 1), x)","F",0
383,0,0,0,0.000000," ","integrate((a/x**3)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x^{3}}}}{\sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(a/x**3)/sqrt(x**2 + 1), x)","F",0
384,0,0,0,0.000000," ","integrate((a/x**4)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x^{4}}}}{\sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(a/x**4)/sqrt(x**2 + 1), x)","F",0
385,0,0,0,0.000000," ","integrate((a*x**4)**(1/2)/(x**3+1)**(1/2),x)","\int \frac{\sqrt{a x^{4}}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a*x**4)/sqrt((x + 1)*(x**2 - x + 1)), x)","F",0
386,0,0,0,0.000000," ","integrate((a*x**3)**(1/2)/(x**3+1)**(1/2),x)","\int \frac{\sqrt{a x^{3}}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a*x**3)/sqrt((x + 1)*(x**2 - x + 1)), x)","F",0
387,0,0,0,0.000000," ","integrate((a*x**2)**(1/2)/(x**3+1)**(1/2),x)","\int \frac{\sqrt{a x^{2}}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a*x**2)/sqrt((x + 1)*(x**2 - x + 1)), x)","F",0
388,1,14,0,1.152044," ","integrate((a*x)**(1/2)/(x**3+1)**(1/2),x)","\frac{2 \sqrt{a} \operatorname{asinh}{\left(x^{\frac{3}{2}} \right)}}{3}"," ",0,"2*sqrt(a)*asinh(x**(3/2))/3","A",0
389,0,0,0,0.000000," ","integrate((a/x)**(1/2)/(x**3+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a/x)/sqrt((x + 1)*(x**2 - x + 1)), x)","F",0
390,0,0,0,0.000000," ","integrate((a/x**2)**(1/2)/(x**3+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x^{2}}}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a/x**2)/sqrt((x + 1)*(x**2 - x + 1)), x)","F",0
391,0,0,0,0.000000," ","integrate((a/x**3)**(1/2)/(x**3+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x^{3}}}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a/x**3)/sqrt((x + 1)*(x**2 - x + 1)), x)","F",0
392,0,0,0,0.000000," ","integrate((a/x**4)**(1/2)/(x**3+1)**(1/2),x)","\int \frac{\sqrt{\frac{a}{x^{4}}}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)}}\, dx"," ",0,"Integral(sqrt(a/x**4)/sqrt((x + 1)*(x**2 - x + 1)), x)","F",0
393,0,0,0,0.000000," ","integrate((a*x**(2*n))**(1/2)/(1+x**n)**(1/2),x)","\int \frac{\sqrt{a x^{2 n}}}{\sqrt{x^{n} + 1}}\, dx"," ",0,"Integral(sqrt(a*x**(2*n))/sqrt(x**n + 1), x)","F",0
394,0,0,0,0.000000," ","integrate((a*x**n)**(1/2)/(1+x**n)**(1/2),x)","\int \frac{\sqrt{a x^{n}}}{\sqrt{x^{n} + 1}}\, dx"," ",0,"Integral(sqrt(a*x**n)/sqrt(x**n + 1), x)","F",0
395,0,0,0,0.000000," ","integrate((a*x**(1/2*n))**(1/2)/(1+x**n)**(1/2),x)","\int \frac{\sqrt{a x^{\frac{n}{2}}}}{\sqrt{x^{n} + 1}}\, dx"," ",0,"Integral(sqrt(a*x**(n/2))/sqrt(x**n + 1), x)","F",0
396,0,0,0,0.000000," ","integrate((a*x**(2*n))**(1/2)/(1+x**n)**(1/2)+2*(a*x**(2*n))**(1/2)/(2+n)/(x**n)/(1+x**n)**(1/2),x)","\frac{\int \frac{2 \sqrt{a x^{2 n}}}{\sqrt{x^{n} + 1}}\, dx + \int \frac{n \sqrt{a x^{2 n}}}{\sqrt{x^{n} + 1}}\, dx + \int \frac{2 x^{- n} \sqrt{a x^{2 n}}}{\sqrt{x^{n} + 1}}\, dx}{n + 2}"," ",0,"(Integral(2*sqrt(a*x**(2*n))/sqrt(x**n + 1), x) + Integral(n*sqrt(a*x**(2*n))/sqrt(x**n + 1), x) + Integral(2*x**(-n)*sqrt(a*x**(2*n))/sqrt(x**n + 1), x))/(n + 2)","F",0
397,0,0,0,0.000000," ","integrate((a*x)**(1/2)/(e*x+d)**(1/2)/(f*x+e)**(1/2),x)","\int \frac{\sqrt{a x}}{\sqrt{d + e x} \sqrt{e + f x}}\, dx"," ",0,"Integral(sqrt(a*x)/(sqrt(d + e*x)*sqrt(e + f*x)), x)","F",0
398,0,0,0,0.000000," ","integrate((a*x**m)**r,x)","\begin{cases} \frac{a^{r} x \left(x^{m}\right)^{r}}{m r + 1} & \text{for}\: m \neq - \frac{1}{r} \\\int \left(a x^{- \frac{1}{r}}\right)^{r}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**r*x*(x**m)**r/(m*r + 1), Ne(m, -1/r)), (Integral((a*x**(-1/r))**r, x), True))","F",0
399,0,0,0,0.000000," ","integrate((a*x**m)**r*(b*x**n)**s,x)","\begin{cases} \frac{a^{r} b^{s} x \left(x^{m}\right)^{r} \left(x^{n}\right)^{s}}{m r + n s + 1} & \text{for}\: m \neq - \frac{n s + 1}{r} \\\int \left(b x^{n}\right)^{s} \left(a x^{- \frac{1}{r}} x^{- \frac{n s}{r}}\right)^{r}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**r*b**s*x*(x**m)**r*(x**n)**s/(m*r + n*s + 1), Ne(m, -(n*s + 1)/r)), (Integral((b*x**n)**s*(a*x**(-1/r)*x**(-n*s/r))**r, x), True))","F",0
400,-1,0,0,0.000000," ","integrate((a*x**m)**r*(b*x**n)**s*(c*x**p)**t,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,0,0,0,0.000000," ","integrate(x**2/((b*x+a)**(1/2)+(b*x+c)**(1/2)),x)","\int \frac{x^{2}}{\sqrt{a + b x} + \sqrt{b x + c}}\, dx"," ",0,"Integral(x**2/(sqrt(a + b*x) + sqrt(b*x + c)), x)","F",0
402,0,0,0,0.000000," ","integrate(x/((b*x+a)**(1/2)+(b*x+c)**(1/2)),x)","\int \frac{x}{\sqrt{a + b x} + \sqrt{b x + c}}\, dx"," ",0,"Integral(x/(sqrt(a + b*x) + sqrt(b*x + c)), x)","F",0
403,1,136,0,0.712189," ","integrate(1/((b*x+a)**(1/2)+(b*x+c)**(1/2)),x)","\begin{cases} \frac{2 a}{3 b \sqrt{a + b x} + 3 b \sqrt{b x + c}} + \frac{4 b x}{3 b \sqrt{a + b x} + 3 b \sqrt{b x + c}} + \frac{2 c}{3 b \sqrt{a + b x} + 3 b \sqrt{b x + c}} + \frac{2 \sqrt{a + b x} \sqrt{b x + c}}{3 b \sqrt{a + b x} + 3 b \sqrt{b x + c}} & \text{for}\: b \neq 0 \\\frac{x}{\sqrt{a} + \sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a/(3*b*sqrt(a + b*x) + 3*b*sqrt(b*x + c)) + 4*b*x/(3*b*sqrt(a + b*x) + 3*b*sqrt(b*x + c)) + 2*c/(3*b*sqrt(a + b*x) + 3*b*sqrt(b*x + c)) + 2*sqrt(a + b*x)*sqrt(b*x + c)/(3*b*sqrt(a + b*x) + 3*b*sqrt(b*x + c)), Ne(b, 0)), (x/(sqrt(a) + sqrt(c)), True))","A",0
404,0,0,0,0.000000," ","integrate(1/x/((b*x+a)**(1/2)+(b*x+c)**(1/2)),x)","\int \frac{1}{x \left(\sqrt{a + b x} + \sqrt{b x + c}\right)}\, dx"," ",0,"Integral(1/(x*(sqrt(a + b*x) + sqrt(b*x + c))), x)","F",0
405,0,0,0,0.000000," ","integrate(1/x**2/((b*x+a)**(1/2)+(b*x+c)**(1/2)),x)","\int \frac{1}{x^{2} \left(\sqrt{a + b x} + \sqrt{b x + c}\right)}\, dx"," ",0,"Integral(1/(x**2*(sqrt(a + b*x) + sqrt(b*x + c))), x)","F",0
406,0,0,0,0.000000," ","integrate(x**2/((b*x+a)**(1/2)+(b*x+c)**(1/2))**2,x)","\int \frac{x^{2}}{\left(\sqrt{a + b x} + \sqrt{b x + c}\right)^{2}}\, dx"," ",0,"Integral(x**2/(sqrt(a + b*x) + sqrt(b*x + c))**2, x)","F",0
407,0,0,0,0.000000," ","integrate(x/((b*x+a)**(1/2)+(b*x+c)**(1/2))**2,x)","\int \frac{x}{\left(\sqrt{a + b x} + \sqrt{b x + c}\right)^{2}}\, dx"," ",0,"Integral(x/(sqrt(a + b*x) + sqrt(b*x + c))**2, x)","F",0
408,1,388,0,1.041668," ","integrate(1/((b*x+a)**(1/2)+(b*x+c)**(1/2))**2,x)","\begin{cases} \frac{2 a \log{\left(\sqrt{a + b x} + \sqrt{b x + c} \right)}}{4 a b + 8 b^{2} x + 4 b c + 8 b \sqrt{a + b x} \sqrt{b x + c}} + \frac{a}{4 a b + 8 b^{2} x + 4 b c + 8 b \sqrt{a + b x} \sqrt{b x + c}} + \frac{4 b x \log{\left(\sqrt{a + b x} + \sqrt{b x + c} \right)}}{4 a b + 8 b^{2} x + 4 b c + 8 b \sqrt{a + b x} \sqrt{b x + c}} + \frac{2 b x}{4 a b + 8 b^{2} x + 4 b c + 8 b \sqrt{a + b x} \sqrt{b x + c}} + \frac{2 c \log{\left(\sqrt{a + b x} + \sqrt{b x + c} \right)}}{4 a b + 8 b^{2} x + 4 b c + 8 b \sqrt{a + b x} \sqrt{b x + c}} + \frac{c}{4 a b + 8 b^{2} x + 4 b c + 8 b \sqrt{a + b x} \sqrt{b x + c}} + \frac{4 \sqrt{a + b x} \sqrt{b x + c} \log{\left(\sqrt{a + b x} + \sqrt{b x + c} \right)}}{4 a b + 8 b^{2} x + 4 b c + 8 b \sqrt{a + b x} \sqrt{b x + c}} & \text{for}\: b \neq 0 \\\frac{x}{\left(\sqrt{a} + \sqrt{c}\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*log(sqrt(a + b*x) + sqrt(b*x + c))/(4*a*b + 8*b**2*x + 4*b*c + 8*b*sqrt(a + b*x)*sqrt(b*x + c)) + a/(4*a*b + 8*b**2*x + 4*b*c + 8*b*sqrt(a + b*x)*sqrt(b*x + c)) + 4*b*x*log(sqrt(a + b*x) + sqrt(b*x + c))/(4*a*b + 8*b**2*x + 4*b*c + 8*b*sqrt(a + b*x)*sqrt(b*x + c)) + 2*b*x/(4*a*b + 8*b**2*x + 4*b*c + 8*b*sqrt(a + b*x)*sqrt(b*x + c)) + 2*c*log(sqrt(a + b*x) + sqrt(b*x + c))/(4*a*b + 8*b**2*x + 4*b*c + 8*b*sqrt(a + b*x)*sqrt(b*x + c)) + c/(4*a*b + 8*b**2*x + 4*b*c + 8*b*sqrt(a + b*x)*sqrt(b*x + c)) + 4*sqrt(a + b*x)*sqrt(b*x + c)*log(sqrt(a + b*x) + sqrt(b*x + c))/(4*a*b + 8*b**2*x + 4*b*c + 8*b*sqrt(a + b*x)*sqrt(b*x + c)), Ne(b, 0)), (x/(sqrt(a) + sqrt(c))**2, True))","A",0
409,0,0,0,0.000000," ","integrate(1/x/((b*x+a)**(1/2)+(b*x+c)**(1/2))**2,x)","\int \frac{1}{x \left(\sqrt{a + b x} + \sqrt{b x + c}\right)^{2}}\, dx"," ",0,"Integral(1/(x*(sqrt(a + b*x) + sqrt(b*x + c))**2), x)","F",0
410,0,0,0,0.000000," ","integrate(1/x**2/((b*x+a)**(1/2)+(b*x+c)**(1/2))**2,x)","\int \frac{1}{x^{2} \left(\sqrt{a + b x} + \sqrt{b x + c}\right)^{2}}\, dx"," ",0,"Integral(1/(x**2*(sqrt(a + b*x) + sqrt(b*x + c))**2), x)","F",0
411,0,0,0,0.000000," ","integrate(x**2/((b*x+a)**(1/2)+(b*x+c)**(1/2))**3,x)","\int \frac{x^{2}}{\left(\sqrt{a + b x} + \sqrt{b x + c}\right)^{3}}\, dx"," ",0,"Integral(x**2/(sqrt(a + b*x) + sqrt(b*x + c))**3, x)","F",0
412,1,942,0,2.700761," ","integrate(x/((b*x+a)**(1/2)+(b*x+c)**(1/2))**3,x)","\begin{cases} \frac{12 a^{2}}{35 a b^{2} \sqrt{a + b x} + 105 a b^{2} \sqrt{b x + c} + 140 b^{3} x \sqrt{a + b x} + 140 b^{3} x \sqrt{b x + c} + 105 b^{2} c \sqrt{a + b x} + 35 b^{2} c \sqrt{b x + c}} + \frac{54 a b x}{35 a b^{2} \sqrt{a + b x} + 105 a b^{2} \sqrt{b x + c} + 140 b^{3} x \sqrt{a + b x} + 140 b^{3} x \sqrt{b x + c} + 105 b^{2} c \sqrt{a + b x} + 35 b^{2} c \sqrt{b x + c}} + \frac{44 a c}{35 a b^{2} \sqrt{a + b x} + 105 a b^{2} \sqrt{b x + c} + 140 b^{3} x \sqrt{a + b x} + 140 b^{3} x \sqrt{b x + c} + 105 b^{2} c \sqrt{a + b x} + 35 b^{2} c \sqrt{b x + c}} + \frac{36 a \sqrt{a + b x} \sqrt{b x + c}}{35 a b^{2} \sqrt{a + b x} + 105 a b^{2} \sqrt{b x + c} + 140 b^{3} x \sqrt{a + b x} + 140 b^{3} x \sqrt{b x + c} + 105 b^{2} c \sqrt{a + b x} + 35 b^{2} c \sqrt{b x + c}} + \frac{40 b^{2} x^{2}}{35 a b^{2} \sqrt{a + b x} + 105 a b^{2} \sqrt{b x + c} + 140 b^{3} x \sqrt{a + b x} + 140 b^{3} x \sqrt{b x + c} + 105 b^{2} c \sqrt{a + b x} + 35 b^{2} c \sqrt{b x + c}} + \frac{54 b c x}{35 a b^{2} \sqrt{a + b x} + 105 a b^{2} \sqrt{b x + c} + 140 b^{3} x \sqrt{a + b x} + 140 b^{3} x \sqrt{b x + c} + 105 b^{2} c \sqrt{a + b x} + 35 b^{2} c \sqrt{b x + c}} + \frac{30 b x \sqrt{a + b x} \sqrt{b x + c}}{35 a b^{2} \sqrt{a + b x} + 105 a b^{2} \sqrt{b x + c} + 140 b^{3} x \sqrt{a + b x} + 140 b^{3} x \sqrt{b x + c} + 105 b^{2} c \sqrt{a + b x} + 35 b^{2} c \sqrt{b x + c}} + \frac{12 c^{2}}{35 a b^{2} \sqrt{a + b x} + 105 a b^{2} \sqrt{b x + c} + 140 b^{3} x \sqrt{a + b x} + 140 b^{3} x \sqrt{b x + c} + 105 b^{2} c \sqrt{a + b x} + 35 b^{2} c \sqrt{b x + c}} + \frac{36 c \sqrt{a + b x} \sqrt{b x + c}}{35 a b^{2} \sqrt{a + b x} + 105 a b^{2} \sqrt{b x + c} + 140 b^{3} x \sqrt{a + b x} + 140 b^{3} x \sqrt{b x + c} + 105 b^{2} c \sqrt{a + b x} + 35 b^{2} c \sqrt{b x + c}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 \left(\sqrt{a} + \sqrt{c}\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((12*a**2/(35*a*b**2*sqrt(a + b*x) + 105*a*b**2*sqrt(b*x + c) + 140*b**3*x*sqrt(a + b*x) + 140*b**3*x*sqrt(b*x + c) + 105*b**2*c*sqrt(a + b*x) + 35*b**2*c*sqrt(b*x + c)) + 54*a*b*x/(35*a*b**2*sqrt(a + b*x) + 105*a*b**2*sqrt(b*x + c) + 140*b**3*x*sqrt(a + b*x) + 140*b**3*x*sqrt(b*x + c) + 105*b**2*c*sqrt(a + b*x) + 35*b**2*c*sqrt(b*x + c)) + 44*a*c/(35*a*b**2*sqrt(a + b*x) + 105*a*b**2*sqrt(b*x + c) + 140*b**3*x*sqrt(a + b*x) + 140*b**3*x*sqrt(b*x + c) + 105*b**2*c*sqrt(a + b*x) + 35*b**2*c*sqrt(b*x + c)) + 36*a*sqrt(a + b*x)*sqrt(b*x + c)/(35*a*b**2*sqrt(a + b*x) + 105*a*b**2*sqrt(b*x + c) + 140*b**3*x*sqrt(a + b*x) + 140*b**3*x*sqrt(b*x + c) + 105*b**2*c*sqrt(a + b*x) + 35*b**2*c*sqrt(b*x + c)) + 40*b**2*x**2/(35*a*b**2*sqrt(a + b*x) + 105*a*b**2*sqrt(b*x + c) + 140*b**3*x*sqrt(a + b*x) + 140*b**3*x*sqrt(b*x + c) + 105*b**2*c*sqrt(a + b*x) + 35*b**2*c*sqrt(b*x + c)) + 54*b*c*x/(35*a*b**2*sqrt(a + b*x) + 105*a*b**2*sqrt(b*x + c) + 140*b**3*x*sqrt(a + b*x) + 140*b**3*x*sqrt(b*x + c) + 105*b**2*c*sqrt(a + b*x) + 35*b**2*c*sqrt(b*x + c)) + 30*b*x*sqrt(a + b*x)*sqrt(b*x + c)/(35*a*b**2*sqrt(a + b*x) + 105*a*b**2*sqrt(b*x + c) + 140*b**3*x*sqrt(a + b*x) + 140*b**3*x*sqrt(b*x + c) + 105*b**2*c*sqrt(a + b*x) + 35*b**2*c*sqrt(b*x + c)) + 12*c**2/(35*a*b**2*sqrt(a + b*x) + 105*a*b**2*sqrt(b*x + c) + 140*b**3*x*sqrt(a + b*x) + 140*b**3*x*sqrt(b*x + c) + 105*b**2*c*sqrt(a + b*x) + 35*b**2*c*sqrt(b*x + c)) + 36*c*sqrt(a + b*x)*sqrt(b*x + c)/(35*a*b**2*sqrt(a + b*x) + 105*a*b**2*sqrt(b*x + c) + 140*b**3*x*sqrt(a + b*x) + 140*b**3*x*sqrt(b*x + c) + 105*b**2*c*sqrt(a + b*x) + 35*b**2*c*sqrt(b*x + c)), Ne(b, 0)), (x**2/(2*(sqrt(a) + sqrt(c))**3), True))","A",0
413,1,384,0,1.820930," ","integrate(1/((b*x+a)**(1/2)+(b*x+c)**(1/2))**3,x)","\begin{cases} - \frac{2 a}{5 a b \sqrt{a + b x} + 15 a b \sqrt{b x + c} + 20 b^{2} x \sqrt{a + b x} + 20 b^{2} x \sqrt{b x + c} + 15 b c \sqrt{a + b x} + 5 b c \sqrt{b x + c}} - \frac{4 b x}{5 a b \sqrt{a + b x} + 15 a b \sqrt{b x + c} + 20 b^{2} x \sqrt{a + b x} + 20 b^{2} x \sqrt{b x + c} + 15 b c \sqrt{a + b x} + 5 b c \sqrt{b x + c}} - \frac{2 c}{5 a b \sqrt{a + b x} + 15 a b \sqrt{b x + c} + 20 b^{2} x \sqrt{a + b x} + 20 b^{2} x \sqrt{b x + c} + 15 b c \sqrt{a + b x} + 5 b c \sqrt{b x + c}} - \frac{6 \sqrt{a + b x} \sqrt{b x + c}}{5 a b \sqrt{a + b x} + 15 a b \sqrt{b x + c} + 20 b^{2} x \sqrt{a + b x} + 20 b^{2} x \sqrt{b x + c} + 15 b c \sqrt{a + b x} + 5 b c \sqrt{b x + c}} & \text{for}\: b \neq 0 \\\frac{x}{\left(\sqrt{a} + \sqrt{c}\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a/(5*a*b*sqrt(a + b*x) + 15*a*b*sqrt(b*x + c) + 20*b**2*x*sqrt(a + b*x) + 20*b**2*x*sqrt(b*x + c) + 15*b*c*sqrt(a + b*x) + 5*b*c*sqrt(b*x + c)) - 4*b*x/(5*a*b*sqrt(a + b*x) + 15*a*b*sqrt(b*x + c) + 20*b**2*x*sqrt(a + b*x) + 20*b**2*x*sqrt(b*x + c) + 15*b*c*sqrt(a + b*x) + 5*b*c*sqrt(b*x + c)) - 2*c/(5*a*b*sqrt(a + b*x) + 15*a*b*sqrt(b*x + c) + 20*b**2*x*sqrt(a + b*x) + 20*b**2*x*sqrt(b*x + c) + 15*b*c*sqrt(a + b*x) + 5*b*c*sqrt(b*x + c)) - 6*sqrt(a + b*x)*sqrt(b*x + c)/(5*a*b*sqrt(a + b*x) + 15*a*b*sqrt(b*x + c) + 20*b**2*x*sqrt(a + b*x) + 20*b**2*x*sqrt(b*x + c) + 15*b*c*sqrt(a + b*x) + 5*b*c*sqrt(b*x + c)), Ne(b, 0)), (x/(sqrt(a) + sqrt(c))**3, True))","A",0
414,0,0,0,0.000000," ","integrate(1/x/((b*x+a)**(1/2)+(b*x+c)**(1/2))**3,x)","\int \frac{1}{x \left(\sqrt{a + b x} + \sqrt{b x + c}\right)^{3}}\, dx"," ",0,"Integral(1/(x*(sqrt(a + b*x) + sqrt(b*x + c))**3), x)","F",0
415,0,0,0,0.000000," ","integrate(1/x**2/((b*x+a)**(1/2)+(b*x+c)**(1/2))**3,x)","\int \frac{1}{x^{2} \left(\sqrt{a + b x} + \sqrt{b x + c}\right)^{3}}\, dx"," ",0,"Integral(1/(x**2*(sqrt(a + b*x) + sqrt(b*x + c))**3), x)","F",0
416,1,63,0,0.940199," ","integrate(1/(x**(1/2)+(1+x)**(1/2)),x)","\frac{2 \sqrt{x} \sqrt{x + 1}}{3 \sqrt{x} + 3 \sqrt{x + 1}} + \frac{4 x}{3 \sqrt{x} + 3 \sqrt{x + 1}} + \frac{2}{3 \sqrt{x} + 3 \sqrt{x + 1}}"," ",0,"2*sqrt(x)*sqrt(x + 1)/(3*sqrt(x) + 3*sqrt(x + 1)) + 4*x/(3*sqrt(x) + 3*sqrt(x + 1)) + 2/(3*sqrt(x) + 3*sqrt(x + 1))","B",0
417,1,63,0,0.387689," ","integrate(1/((-1+x)**(1/2)+x**(1/2)),x)","\frac{2 \sqrt{x} \sqrt{x - 1}}{3 \sqrt{x} + 3 \sqrt{x - 1}} + \frac{4 x}{3 \sqrt{x} + 3 \sqrt{x - 1}} - \frac{2}{3 \sqrt{x} + 3 \sqrt{x - 1}}"," ",0,"2*sqrt(x)*sqrt(x - 1)/(3*sqrt(x) + 3*sqrt(x - 1)) + 4*x/(3*sqrt(x) + 3*sqrt(x - 1)) - 2/(3*sqrt(x) + 3*sqrt(x - 1))","B",0
418,1,51,0,0.406361," ","integrate(1/((-1+x)**(1/2)+(1+x)**(1/2)),x)","\frac{4 x}{3 \sqrt{x - 1} + 3 \sqrt{x + 1}} + \frac{2 \sqrt{x - 1} \sqrt{x + 1}}{3 \sqrt{x - 1} + 3 \sqrt{x + 1}}"," ",0,"4*x/(3*sqrt(x - 1) + 3*sqrt(x + 1)) + 2*sqrt(x - 1)*sqrt(x + 1)/(3*sqrt(x - 1) + 3*sqrt(x + 1))","B",0
419,-1,0,0,0.000000," ","integrate(x**3*((1-x)**(1/2)+(1+x)**(1/2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,-1,0,0,0.000000," ","integrate(x**2*((1-x)**(1/2)+(1+x)**(1/2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,1,110,0,106.391948," ","integrate(x*((1-x)**(1/2)+(1+x)**(1/2))**2,x)","- \frac{x^{3}}{3} - x + \frac{\left(x + 1\right)^{3}}{3} - 4 \left(\begin{cases} \frac{x \sqrt{1 - x} \sqrt{x + 1}}{4} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{2} & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right) + 4 \left(\begin{cases} \frac{x \sqrt{1 - x} \sqrt{x + 1}}{4} - \frac{\left(1 - x\right)^{\frac{3}{2}} \left(x + 1\right)^{\frac{3}{2}}}{6} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{2} & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right) - 1"," ",0,"-x**3/3 - x + (x + 1)**3/3 - 4*Piecewise((x*sqrt(1 - x)*sqrt(x + 1)/4 + asin(sqrt(2)*sqrt(x + 1)/2)/2, (x >= -1) & (x < 1))) + 4*Piecewise((x*sqrt(1 - x)*sqrt(x + 1)/4 - (1 - x)**(3/2)*(x + 1)**(3/2)/6 + asin(sqrt(2)*sqrt(x + 1)/2)/2, (x >= -1) & (x < 1))) - 1","A",0
422,1,44,0,31.433665," ","integrate(((1-x)**(1/2)+(1+x)**(1/2))**2,x)","2 x + 4 \left(\begin{cases} \frac{x \sqrt{1 - x} \sqrt{x + 1}}{4} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{2} & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right) + 2"," ",0,"2*x + 4*Piecewise((x*sqrt(1 - x)*sqrt(x + 1)/4 + asin(sqrt(2)*sqrt(x + 1)/2)/2, (x >= -1) & (x < 1))) + 2","A",0
423,0,0,0,0.000000," ","integrate(((1-x)**(1/2)+(1+x)**(1/2))**2/x,x)","\int \frac{\left(\sqrt{1 - x} + \sqrt{x + 1}\right)^{2}}{x}\, dx"," ",0,"Integral((sqrt(1 - x) + sqrt(x + 1))**2/x, x)","F",0
424,0,0,0,0.000000," ","integrate(((1-x)**(1/2)+(1+x)**(1/2))**2/x**2,x)","\int \frac{\left(\sqrt{1 - x} + \sqrt{x + 1}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((sqrt(1 - x) + sqrt(x + 1))**2/x**2, x)","F",0
425,0,0,0,0.000000," ","integrate(((1-x)**(1/2)+(1+x)**(1/2))**2/x**3,x)","\int \frac{\left(\sqrt{1 - x} + \sqrt{x + 1}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((sqrt(1 - x) + sqrt(x + 1))**2/x**3, x)","F",0
426,0,0,0,0.000000," ","integrate(x**3/((b*x+a)**(1/2)+(c*x+a)**(1/2)),x)","\int \frac{x^{3}}{\sqrt{a + b x} + \sqrt{a + c x}}\, dx"," ",0,"Integral(x**3/(sqrt(a + b*x) + sqrt(a + c*x)), x)","F",0
427,0,0,0,0.000000," ","integrate(x**2/((b*x+a)**(1/2)+(c*x+a)**(1/2)),x)","\int \frac{x^{2}}{\sqrt{a + b x} + \sqrt{a + c x}}\, dx"," ",0,"Integral(x**2/(sqrt(a + b*x) + sqrt(a + c*x)), x)","F",0
428,0,0,0,0.000000," ","integrate(x/((b*x+a)**(1/2)+(c*x+a)**(1/2)),x)","\int \frac{x}{\sqrt{a + b x} + \sqrt{a + c x}}\, dx"," ",0,"Integral(x/(sqrt(a + b*x) + sqrt(a + c*x)), x)","F",0
429,0,0,0,0.000000," ","integrate(1/((b*x+a)**(1/2)+(c*x+a)**(1/2)),x)","\int \frac{1}{\sqrt{a + b x} + \sqrt{a + c x}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x) + sqrt(a + c*x)), x)","F",0
430,0,0,0,0.000000," ","integrate(1/x/((b*x+a)**(1/2)+(c*x+a)**(1/2)),x)","\int \frac{1}{x \left(\sqrt{a + b x} + \sqrt{a + c x}\right)}\, dx"," ",0,"Integral(1/(x*(sqrt(a + b*x) + sqrt(a + c*x))), x)","F",0
431,0,0,0,0.000000," ","integrate(1/x**2/((b*x+a)**(1/2)+(c*x+a)**(1/2)),x)","\int \frac{1}{x^{2} \left(\sqrt{a + b x} + \sqrt{a + c x}\right)}\, dx"," ",0,"Integral(1/(x**2*(sqrt(a + b*x) + sqrt(a + c*x))), x)","F",0
432,0,0,0,0.000000," ","integrate(x**3/((b*x+a)**(1/2)+(c*x+a)**(1/2))**2,x)","\int \frac{x^{3}}{\left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{2}}\, dx"," ",0,"Integral(x**3/(sqrt(a + b*x) + sqrt(a + c*x))**2, x)","F",0
433,0,0,0,0.000000," ","integrate(x**2/((b*x+a)**(1/2)+(c*x+a)**(1/2))**2,x)","\int \frac{x^{2}}{\left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{2}}\, dx"," ",0,"Integral(x**2/(sqrt(a + b*x) + sqrt(a + c*x))**2, x)","F",0
434,0,0,0,0.000000," ","integrate(x/((b*x+a)**(1/2)+(c*x+a)**(1/2))**2,x)","\int \frac{x}{\left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{2}}\, dx"," ",0,"Integral(x/(sqrt(a + b*x) + sqrt(a + c*x))**2, x)","F",0
435,0,0,0,0.000000," ","integrate(1/((b*x+a)**(1/2)+(c*x+a)**(1/2))**2,x)","\int \frac{1}{\left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{2}}\, dx"," ",0,"Integral((sqrt(a + b*x) + sqrt(a + c*x))**(-2), x)","F",0
436,0,0,0,0.000000," ","integrate(1/x/((b*x+a)**(1/2)+(c*x+a)**(1/2))**2,x)","\int \frac{1}{x \left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{2}}\, dx"," ",0,"Integral(1/(x*(sqrt(a + b*x) + sqrt(a + c*x))**2), x)","F",0
437,0,0,0,0.000000," ","integrate(1/x**2/((b*x+a)**(1/2)+(c*x+a)**(1/2))**2,x)","\int \frac{1}{x^{2} \left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{2}}\, dx"," ",0,"Integral(1/(x**2*(sqrt(a + b*x) + sqrt(a + c*x))**2), x)","F",0
438,-1,0,0,0.000000," ","integrate(x**4/((b*x+a)**(1/2)+(c*x+a)**(1/2))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,0,0,0,0.000000," ","integrate(x**3/((b*x+a)**(1/2)+(c*x+a)**(1/2))**3,x)","\int \frac{x^{3}}{\left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{3}}\, dx"," ",0,"Integral(x**3/(sqrt(a + b*x) + sqrt(a + c*x))**3, x)","F",0
440,0,0,0,0.000000," ","integrate(x**2/((b*x+a)**(1/2)+(c*x+a)**(1/2))**3,x)","\int \frac{x^{2}}{\left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{3}}\, dx"," ",0,"Integral(x**2/(sqrt(a + b*x) + sqrt(a + c*x))**3, x)","F",0
441,0,0,0,0.000000," ","integrate(x/((b*x+a)**(1/2)+(c*x+a)**(1/2))**3,x)","\int \frac{x}{\left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{3}}\, dx"," ",0,"Integral(x/(sqrt(a + b*x) + sqrt(a + c*x))**3, x)","F",0
442,0,0,0,0.000000," ","integrate(1/((b*x+a)**(1/2)+(c*x+a)**(1/2))**3,x)","\int \frac{1}{\left(\sqrt{a + b x} + \sqrt{a + c x}\right)^{3}}\, dx"," ",0,"Integral((sqrt(a + b*x) + sqrt(a + c*x))**(-3), x)","F",0
443,1,48,0,3.072987," ","integrate((1-x)**(1/2)*((1-x)**(1/2)+(1+x)**(1/2)),x)","- \frac{\left(1 - x\right)^{2}}{2} - 2 \left(\begin{cases} - \frac{x \sqrt{1 - x} \sqrt{x + 1}}{4} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{1 - x}}{2} \right)}}{2} & \text{for}\: x \leq 1 \wedge x > -1 \end{cases}\right)"," ",0,"-(1 - x)**2/2 - 2*Piecewise((-x*sqrt(1 - x)*sqrt(x + 1)/4 + asin(sqrt(2)*sqrt(1 - x)/2)/2, (x <= 1) & (x > -1)))","A",0
444,-1,0,0,0.000000," ","integrate(x**3*(-(1-x)**(1/2)-(1+x)**(1/2))*((1-x)**(1/2)+(1+x)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,-1,0,0,0.000000," ","integrate(x**2*(-(1-x)**(1/2)-(1+x)**(1/2))*((1-x)**(1/2)+(1+x)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,1,110,0,101.264135," ","integrate(x*(-(1-x)**(1/2)-(1+x)**(1/2))*((1-x)**(1/2)+(1+x)**(1/2)),x)","\frac{x^{3}}{3} + x - \frac{\left(x + 1\right)^{3}}{3} + 4 \left(\begin{cases} \frac{x \sqrt{1 - x} \sqrt{x + 1}}{4} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{2} & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right) - 4 \left(\begin{cases} \frac{x \sqrt{1 - x} \sqrt{x + 1}}{4} - \frac{\left(1 - x\right)^{\frac{3}{2}} \left(x + 1\right)^{\frac{3}{2}}}{6} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{2} & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right) + 1"," ",0,"x**3/3 + x - (x + 1)**3/3 + 4*Piecewise((x*sqrt(1 - x)*sqrt(x + 1)/4 + asin(sqrt(2)*sqrt(x + 1)/2)/2, (x >= -1) & (x < 1))) - 4*Piecewise((x*sqrt(1 - x)*sqrt(x + 1)/4 - (1 - x)**(3/2)*(x + 1)**(3/2)/6 + asin(sqrt(2)*sqrt(x + 1)/2)/2, (x >= -1) & (x < 1))) + 1","A",0
447,1,46,0,37.873237," ","integrate((-(1-x)**(1/2)-(1+x)**(1/2))*((1-x)**(1/2)+(1+x)**(1/2)),x)","- 2 x - 4 \left(\begin{cases} \frac{x \sqrt{1 - x} \sqrt{x + 1}}{4} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{2} & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right) - 2"," ",0,"-2*x - 4*Piecewise((x*sqrt(1 - x)*sqrt(x + 1)/4 + asin(sqrt(2)*sqrt(x + 1)/2)/2, (x >= -1) & (x < 1))) - 2","A",0
448,0,0,0,0.000000," ","integrate((-(1-x)**(1/2)-(1+x)**(1/2))*((1-x)**(1/2)+(1+x)**(1/2))/x,x)","- \int \frac{2}{x}\, dx - \int \frac{2 \sqrt{1 - x} \sqrt{x + 1}}{x}\, dx"," ",0,"-Integral(2/x, x) - Integral(2*sqrt(1 - x)*sqrt(x + 1)/x, x)","F",0
449,0,0,0,0.000000," ","integrate((-(1-x)**(1/2)-(1+x)**(1/2))*((1-x)**(1/2)+(1+x)**(1/2))/x**2,x)","- \int \frac{2}{x^{2}}\, dx - \int \frac{2 \sqrt{1 - x} \sqrt{x + 1}}{x^{2}}\, dx"," ",0,"-Integral(2/x**2, x) - Integral(2*sqrt(1 - x)*sqrt(x + 1)/x**2, x)","F",0
450,0,0,0,0.000000," ","integrate((-(1-x)**(1/2)-(1+x)**(1/2))*((1-x)**(1/2)+(1+x)**(1/2))/x**3,x)","- \int \frac{2}{x^{3}}\, dx - \int \frac{2 \sqrt{1 - x} \sqrt{x + 1}}{x^{3}}\, dx"," ",0,"-Integral(2/x**3, x) - Integral(2*sqrt(1 - x)*sqrt(x + 1)/x**3, x)","F",0
451,0,0,0,0.000000," ","integrate(((1-x)**(1/2)+(1+x)**(1/2))/(-(1-x)**(1/2)+(1+x)**(1/2)),x)","- \int \frac{\sqrt{1 - x}}{\sqrt{1 - x} - \sqrt{x + 1}}\, dx - \int \frac{\sqrt{x + 1}}{\sqrt{1 - x} - \sqrt{x + 1}}\, dx"," ",0,"-Integral(sqrt(1 - x)/(sqrt(1 - x) - sqrt(x + 1)), x) - Integral(sqrt(x + 1)/(sqrt(1 - x) - sqrt(x + 1)), x)","F",0
452,1,226,0,31.387257," ","integrate((-(-1+x)**(1/2)+(1+x)**(1/2))/((-1+x)**(1/2)+(1+x)**(1/2)),x)","- \frac{\left(x - 1\right)^{\frac{5}{2}}}{4 \sqrt{x + 1}} - \frac{3 \left(x - 1\right)^{\frac{3}{2}}}{4 \sqrt{x + 1}} - \frac{\sqrt{x - 1}}{2 \sqrt{x + 1}} + \frac{\left(x - 1\right)^{2}}{4} + 2 \left(\begin{cases} \frac{\left(x + 1\right)^{2}}{8} + \frac{\operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} - \frac{\left(x + 1\right)^{\frac{5}{2}}}{8 \sqrt{x - 1}} + \frac{3 \left(x + 1\right)^{\frac{3}{2}}}{8 \sqrt{x - 1}} - \frac{\sqrt{x + 1}}{4 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{\left(x + 1\right)^{2}}{8} - \frac{i \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} + \frac{i \left(x + 1\right)^{\frac{5}{2}}}{8 \sqrt{1 - x}} - \frac{3 i \left(x + 1\right)^{\frac{3}{2}}}{8 \sqrt{1 - x}} + \frac{i \sqrt{x + 1}}{4 \sqrt{1 - x}} & \text{otherwise} \end{cases}\right) + \frac{\operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{x - 1}}{2} \right)}}{2}"," ",0,"-(x - 1)**(5/2)/(4*sqrt(x + 1)) - 3*(x - 1)**(3/2)/(4*sqrt(x + 1)) - sqrt(x - 1)/(2*sqrt(x + 1)) + (x - 1)**2/4 + 2*Piecewise(((x + 1)**2/8 + acosh(sqrt(2)*sqrt(x + 1)/2)/4 - (x + 1)**(5/2)/(8*sqrt(x - 1)) + 3*(x + 1)**(3/2)/(8*sqrt(x - 1)) - sqrt(x + 1)/(4*sqrt(x - 1)), Abs(x + 1)/2 > 1), ((x + 1)**2/8 - I*asin(sqrt(2)*sqrt(x + 1)/2)/4 + I*(x + 1)**(5/2)/(8*sqrt(1 - x)) - 3*I*(x + 1)**(3/2)/(8*sqrt(1 - x)) + I*sqrt(x + 1)/(4*sqrt(1 - x)), True)) + asinh(sqrt(2)*sqrt(x - 1)/2)/2","A",0
453,0,0,0,0.000000," ","integrate((d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**n,x)","\int \left(d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}\right)^{n}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + e**2*x**2/f**2))**n, x)","F",0
454,1,279,0,10.463799," ","integrate((d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**3,x)","\frac{a^{\frac{3}{2}} f^{3} x \sqrt{1 + \frac{e^{2} x^{2}}{a f^{2}}}}{2} + \frac{a^{\frac{3}{2}} f^{3} x}{2 \sqrt{1 + \frac{e^{2} x^{2}}{a f^{2}}}} + \frac{3 \sqrt{a} d^{2} f x \sqrt{1 + \frac{e^{2} x^{2}}{a f^{2}}}}{2} + \frac{3 \sqrt{a} e^{2} f x^{3}}{2 \sqrt{1 + \frac{e^{2} x^{2}}{a f^{2}}}} + \frac{3 a d^{2} f^{2} \operatorname{asinh}{\left(\frac{e x}{\sqrt{a} f} \right)}}{2 e} + 3 a d f^{2} x + \frac{3 a e f^{2} x^{2}}{2} + d^{3} x + \frac{3 d^{2} e x^{2}}{2} + 2 d e^{2} x^{3} + 6 d e f \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: e^{2} = 0 \\\frac{f^{2} \left(a + \frac{e^{2} x^{2}}{f^{2}}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + e^{3} x^{4} + \frac{e^{4} x^{5}}{\sqrt{a} f \sqrt{1 + \frac{e^{2} x^{2}}{a f^{2}}}}"," ",0,"a**(3/2)*f**3*x*sqrt(1 + e**2*x**2/(a*f**2))/2 + a**(3/2)*f**3*x/(2*sqrt(1 + e**2*x**2/(a*f**2))) + 3*sqrt(a)*d**2*f*x*sqrt(1 + e**2*x**2/(a*f**2))/2 + 3*sqrt(a)*e**2*f*x**3/(2*sqrt(1 + e**2*x**2/(a*f**2))) + 3*a*d**2*f**2*asinh(e*x/(sqrt(a)*f))/(2*e) + 3*a*d*f**2*x + 3*a*e*f**2*x**2/2 + d**3*x + 3*d**2*e*x**2/2 + 2*d*e**2*x**3 + 6*d*e*f*Piecewise((sqrt(a)*x**2/2, Eq(e**2, 0)), (f**2*(a + e**2*x**2/f**2)**(3/2)/(3*e**2), True)) + e**3*x**4 + e**4*x**5/(sqrt(a)*f*sqrt(1 + e**2*x**2/(a*f**2)))","A",0
455,1,116,0,4.480519," ","integrate((d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**2,x)","\sqrt{a} d f x \sqrt{1 + \frac{e^{2} x^{2}}{a f^{2}}} + \frac{a d f^{2} \operatorname{asinh}{\left(\frac{e x}{\sqrt{a} f} \right)}}{e} + a f^{2} x + d^{2} x + d e x^{2} + \frac{2 e^{2} x^{3}}{3} + 2 e f \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: e^{2} = 0 \\\frac{f^{2} \left(a + \frac{e^{2} x^{2}}{f^{2}}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*d*f*x*sqrt(1 + e**2*x**2/(a*f**2)) + a*d*f**2*asinh(e*x/(sqrt(a)*f))/e + a*f**2*x + d**2*x + d*e*x**2 + 2*e**2*x**3/3 + 2*e*f*Piecewise((sqrt(a)*x**2/2, Eq(e**2, 0)), (f**2*(a + e**2*x**2/f**2)**(3/2)/(3*e**2), True))","A",0
456,1,54,0,2.205473," ","integrate(d+e*x+f*(a+e**2*x**2/f**2)**(1/2),x)","d x + \frac{e x^{2}}{2} + f \left(\frac{\sqrt{a} x \sqrt{1 + \frac{e^{2} x^{2}}{a f^{2}}}}{2} + \frac{a f \operatorname{asinh}{\left(\frac{e x}{\sqrt{a} f} \right)}}{2 e}\right)"," ",0,"d*x + e*x**2/2 + f*(sqrt(a)*x*sqrt(1 + e**2*x**2/(a*f**2))/2 + a*f*asinh(e*x/(sqrt(a)*f))/(2*e))","A",0
457,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e**2*x**2/f**2)**(1/2)),x)","\int \frac{1}{d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}}\, dx"," ",0,"Integral(1/(d + e*x + f*sqrt(a + e**2*x**2/f**2)), x)","F",0
458,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**2,x)","\int \frac{1}{\left(d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}\right)^{2}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + e**2*x**2/f**2))**(-2), x)","F",0
459,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**3,x)","\int \frac{1}{\left(d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}\right)^{3}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + e**2*x**2/f**2))**(-3), x)","F",0
460,0,0,0,0.000000," ","integrate((d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**(5/2),x)","\int \left(d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + e**2*x**2/f**2))**(5/2), x)","F",0
461,0,0,0,0.000000," ","integrate((d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**(3/2),x)","\int \left(d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + e**2*x**2/f**2))**(3/2), x)","F",0
462,0,0,0,0.000000," ","integrate((d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**(1/2),x)","\int \sqrt{d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}}\, dx"," ",0,"Integral(sqrt(d + e*x + f*sqrt(a + e**2*x**2/f**2)), x)","F",0
463,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}}}\, dx"," ",0,"Integral(1/sqrt(d + e*x + f*sqrt(a + e**2*x**2/f**2)), x)","F",0
464,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**(3/2),x)","\int \frac{1}{\left(d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + e**2*x**2/f**2))**(-3/2), x)","F",0
465,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e**2*x**2/f**2)**(1/2))**(5/2),x)","\int \frac{1}{\left(d + e x + f \sqrt{a + \frac{e^{2} x^{2}}{f^{2}}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + e**2*x**2/f**2))**(-5/2), x)","F",0
466,0,0,0,0.000000," ","integrate((x-(x**2-4)**(1/2))**(1/2),x)","\int \sqrt{x - \sqrt{x^{2} - 4}}\, dx"," ",0,"Integral(sqrt(x - sqrt(x**2 - 4)), x)","F",0
467,0,0,0,0.000000," ","integrate((a*x+b*(c+a**2*x**2/b**2)**(1/2))**(1/2),x)","\int \sqrt{a x + b \sqrt{\frac{a^{2} x^{2}}{b^{2}} + c}}\, dx"," ",0,"Integral(sqrt(a*x + b*sqrt(a**2*x**2/b**2 + c)), x)","F",0
468,1,418,0,1.276506," ","integrate((1+(-x**2+1)**(1/2))**(1/2),x)","\begin{cases} - \frac{\sqrt{2} x^{3} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{- 12 i \pi \sqrt{x^{2} - 1} \sqrt{i \sqrt{x^{2} - 1} + 1} - 12 \pi \sqrt{i \sqrt{x^{2} - 1} + 1}} + \frac{3 \sqrt{2} i x \sqrt{x^{2} - 1} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{- 12 i \pi \sqrt{x^{2} - 1} \sqrt{i \sqrt{x^{2} - 1} + 1} - 12 \pi \sqrt{i \sqrt{x^{2} - 1} + 1}} + \frac{3 \sqrt{2} x \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{- 12 i \pi \sqrt{x^{2} - 1} \sqrt{i \sqrt{x^{2} - 1} + 1} - 12 \pi \sqrt{i \sqrt{x^{2} - 1} + 1}} & \text{for}\: \left|{x^{2}}\right| > 1 \\\frac{\sqrt{2} x^{3} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{12 \pi \sqrt{1 - x^{2}} \sqrt{\sqrt{1 - x^{2}} + 1} + 12 \pi \sqrt{\sqrt{1 - x^{2}} + 1}} - \frac{3 \sqrt{2} x \sqrt{1 - x^{2}} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{12 \pi \sqrt{1 - x^{2}} \sqrt{\sqrt{1 - x^{2}} + 1} + 12 \pi \sqrt{\sqrt{1 - x^{2}} + 1}} - \frac{3 \sqrt{2} x \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{12 \pi \sqrt{1 - x^{2}} \sqrt{\sqrt{1 - x^{2}} + 1} + 12 \pi \sqrt{\sqrt{1 - x^{2}} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(2)*x**3*gamma(-1/4)*gamma(1/4)/(-12*I*pi*sqrt(x**2 - 1)*sqrt(I*sqrt(x**2 - 1) + 1) - 12*pi*sqrt(I*sqrt(x**2 - 1) + 1)) + 3*sqrt(2)*I*x*sqrt(x**2 - 1)*gamma(-1/4)*gamma(1/4)/(-12*I*pi*sqrt(x**2 - 1)*sqrt(I*sqrt(x**2 - 1) + 1) - 12*pi*sqrt(I*sqrt(x**2 - 1) + 1)) + 3*sqrt(2)*x*gamma(-1/4)*gamma(1/4)/(-12*I*pi*sqrt(x**2 - 1)*sqrt(I*sqrt(x**2 - 1) + 1) - 12*pi*sqrt(I*sqrt(x**2 - 1) + 1)), Abs(x**2) > 1), (sqrt(2)*x**3*gamma(-1/4)*gamma(1/4)/(12*pi*sqrt(1 - x**2)*sqrt(sqrt(1 - x**2) + 1) + 12*pi*sqrt(sqrt(1 - x**2) + 1)) - 3*sqrt(2)*x*sqrt(1 - x**2)*gamma(-1/4)*gamma(1/4)/(12*pi*sqrt(1 - x**2)*sqrt(sqrt(1 - x**2) + 1) + 12*pi*sqrt(sqrt(1 - x**2) + 1)) - 3*sqrt(2)*x*gamma(-1/4)*gamma(1/4)/(12*pi*sqrt(1 - x**2)*sqrt(sqrt(1 - x**2) + 1) + 12*pi*sqrt(sqrt(1 - x**2) + 1)), True))","B",0
469,1,197,0,1.179886," ","integrate(((x**2+1)**(1/2)+1)**(1/2),x)","- \frac{\sqrt{2} x^{3} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{12 \pi \sqrt{x^{2} + 1} \sqrt{\sqrt{x^{2} + 1} + 1} + 12 \pi \sqrt{\sqrt{x^{2} + 1} + 1}} - \frac{3 \sqrt{2} x \sqrt{x^{2} + 1} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{12 \pi \sqrt{x^{2} + 1} \sqrt{\sqrt{x^{2} + 1} + 1} + 12 \pi \sqrt{\sqrt{x^{2} + 1} + 1}} - \frac{3 \sqrt{2} x \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{12 \pi \sqrt{x^{2} + 1} \sqrt{\sqrt{x^{2} + 1} + 1} + 12 \pi \sqrt{\sqrt{x^{2} + 1} + 1}}"," ",0,"-sqrt(2)*x**3*gamma(-1/4)*gamma(1/4)/(12*pi*sqrt(x**2 + 1)*sqrt(sqrt(x**2 + 1) + 1) + 12*pi*sqrt(sqrt(x**2 + 1) + 1)) - 3*sqrt(2)*x*sqrt(x**2 + 1)*gamma(-1/4)*gamma(1/4)/(12*pi*sqrt(x**2 + 1)*sqrt(sqrt(x**2 + 1) + 1) + 12*pi*sqrt(sqrt(x**2 + 1) + 1)) - 3*sqrt(2)*x*gamma(-1/4)*gamma(1/4)/(12*pi*sqrt(x**2 + 1)*sqrt(sqrt(x**2 + 1) + 1) + 12*pi*sqrt(sqrt(x**2 + 1) + 1))","B",0
470,1,197,0,1.222322," ","integrate((5+(x**2+25)**(1/2))**(1/2),x)","- \frac{\sqrt{2} x^{3} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{12 \pi \sqrt{x^{2} + 25} \sqrt{\sqrt{x^{2} + 25} + 5} + 60 \pi \sqrt{\sqrt{x^{2} + 25} + 5}} - \frac{15 \sqrt{2} x \sqrt{x^{2} + 25} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{12 \pi \sqrt{x^{2} + 25} \sqrt{\sqrt{x^{2} + 25} + 5} + 60 \pi \sqrt{\sqrt{x^{2} + 25} + 5}} - \frac{75 \sqrt{2} x \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{12 \pi \sqrt{x^{2} + 25} \sqrt{\sqrt{x^{2} + 25} + 5} + 60 \pi \sqrt{\sqrt{x^{2} + 25} + 5}}"," ",0,"-sqrt(2)*x**3*gamma(-1/4)*gamma(1/4)/(12*pi*sqrt(x**2 + 25)*sqrt(sqrt(x**2 + 25) + 5) + 60*pi*sqrt(sqrt(x**2 + 25) + 5)) - 15*sqrt(2)*x*sqrt(x**2 + 25)*gamma(-1/4)*gamma(1/4)/(12*pi*sqrt(x**2 + 25)*sqrt(sqrt(x**2 + 25) + 5) + 60*pi*sqrt(sqrt(x**2 + 25) + 5)) - 75*sqrt(2)*x*gamma(-1/4)*gamma(1/4)/(12*pi*sqrt(x**2 + 25)*sqrt(sqrt(x**2 + 25) + 5) + 60*pi*sqrt(sqrt(x**2 + 25) + 5))","B",0
471,0,0,0,0.000000," ","integrate((a+b*(a**2/b**2+c*x**2)**(1/2))**(1/2),x)","\int \sqrt{a + b \sqrt{\frac{a^{2}}{b^{2}} + c x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(a**2/b**2 + c*x**2)), x)","F",0
472,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**n,x)","\int \left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)^{n}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2))**n, x)","F",0
473,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**3,x)","\int \left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)^{3}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2))**3, x)","F",0
474,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**2,x)","\int \left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)^{2}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2))**2, x)","F",0
475,0,0,0,0.000000," ","integrate(d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2),x)","\int \left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)\, dx"," ",0,"Integral(d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2), x)","F",0
476,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2)),x)","\int \frac{1}{d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}}\, dx"," ",0,"Integral(1/(d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2)), x)","F",0
477,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**2,x)","\int \frac{1}{\left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)^{2}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2))**(-2), x)","F",0
478,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**3,x)","\int \frac{1}{\left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)^{3}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2))**(-3), x)","F",0
479,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**(5/2),x)","\int \left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2))**(5/2), x)","F",0
480,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**(3/2),x)","\int \left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2))**(3/2), x)","F",0
481,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**(1/2),x)","\int \sqrt{d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}}\, dx"," ",0,"Integral(sqrt(d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2)), x)","F",0
482,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}}}\, dx"," ",0,"Integral(1/sqrt(d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2)), x)","F",0
483,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**(3/2),x)","\int \frac{1}{\left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2))**(-3/2), x)","F",0
484,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e**2*x**2/f**2)**(1/2))**(5/2),x)","\int \frac{1}{\left(d + e x + f \sqrt{a + b x + \frac{e^{2} x^{2}}{f^{2}}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + b*x + e**2*x**2/f**2))**(-5/2), x)","F",0
485,-1,0,0,0.000000," ","integrate((x**2+a)**2*(x+(x**2+a)**(1/2))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate((x**2+a)*(x+(x**2+a)**(1/2))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,1,2147,0,2.749249," ","integrate((x+(x**2+a)**(1/2))**n,x)","\begin{cases} - \frac{a^{\frac{9}{2}} a^{\frac{n}{2}} n^{2} x \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{a^{\frac{9}{2}} a^{\frac{n}{2}} n x \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} - \frac{a^{\frac{7}{2}} a^{\frac{n}{2}} n^{2} x^{3} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{a^{\frac{7}{2}} a^{\frac{n}{2}} n x^{3} \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{2 a^{5} a^{\frac{n}{2}} n \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} - \frac{2 a^{5} a^{\frac{n}{2}} n \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} - \frac{2 a^{4} a^{\frac{n}{2}} n x^{2} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{4 a^{4} a^{\frac{n}{2}} n x^{2} \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} - \frac{2 a^{4} a^{\frac{n}{2}} n x^{2} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} - \frac{2 a^{4} a^{\frac{n}{2}} x^{2} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{2 a^{4} a^{\frac{n}{2}} x^{2} \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} - \frac{2 a^{3} a^{\frac{n}{2}} n x^{4} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{2 a^{3} a^{\frac{n}{2}} n x^{4} \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} - \frac{2 a^{3} a^{\frac{n}{2}} x^{4} \sqrt{\frac{a}{x^{2}} + 1} \sinh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{2 a^{3} a^{\frac{n}{2}} x^{4} \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{9}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{9}{2}} \Gamma\left(1 - \frac{n}{2}\right) + 2 a^{\frac{7}{2}} n^{2} x^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{7}{2}} x^{2} \Gamma\left(1 - \frac{n}{2}\right)} & \text{for}\: \left|{\frac{x^{2}}{a}}\right| > 1 \\- \frac{2 a^{\frac{5}{2}} a^{\frac{n}{2}} n x \sqrt{1 + \frac{x^{2}}{a}} \sinh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{5}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{a^{\frac{5}{2}} a^{\frac{n}{2}} n x \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{n}{2}\right)}{2 a^{\frac{5}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{n}{2}\right)} - \frac{2 a^{\frac{5}{2}} a^{\frac{n}{2}} x \sqrt{1 + \frac{x^{2}}{a}} \sinh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{5}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{n}{2}\right)} - \frac{a^{3} a^{\frac{n}{2}} n^{2} \sqrt{1 + \frac{x^{2}}{a}} \sinh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(- \frac{n}{2}\right)}{2 a^{\frac{5}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{2 a^{3} a^{\frac{n}{2}} n \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{5}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{2 a^{2} a^{\frac{n}{2}} n x^{2} \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{5}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{n}{2}\right)} + \frac{2 a^{2} a^{\frac{n}{2}} x^{2} \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{2 a^{\frac{5}{2}} n^{2} \Gamma\left(1 - \frac{n}{2}\right) - 2 a^{\frac{5}{2}} \Gamma\left(1 - \frac{n}{2}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**(9/2)*a**(n/2)*n**2*x*sqrt(a/x**2 + 1)*sinh(n*asinh(x/sqrt(a)))*gamma(-n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) + a**(9/2)*a**(n/2)*n*x*cosh(n*asinh(x/sqrt(a)))*gamma(-n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) - a**(7/2)*a**(n/2)*n**2*x**3*sqrt(a/x**2 + 1)*sinh(n*asinh(x/sqrt(a)))*gamma(-n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) + a**(7/2)*a**(n/2)*n*x**3*cosh(n*asinh(x/sqrt(a)))*gamma(-n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) + 2*a**5*a**(n/2)*n*cosh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) - 2*a**5*a**(n/2)*n*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) - 2*a**4*a**(n/2)*n*x**2*sqrt(a/x**2 + 1)*sinh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) + 4*a**4*a**(n/2)*n*x**2*cosh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) - 2*a**4*a**(n/2)*n*x**2*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) - 2*a**4*a**(n/2)*x**2*sqrt(a/x**2 + 1)*sinh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) + 2*a**4*a**(n/2)*x**2*cosh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) - 2*a**3*a**(n/2)*n*x**4*sqrt(a/x**2 + 1)*sinh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) + 2*a**3*a**(n/2)*n*x**4*cosh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) - 2*a**3*a**(n/2)*x**4*sqrt(a/x**2 + 1)*sinh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)) + 2*a**3*a**(n/2)*x**4*cosh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(9/2)*n**2*gamma(1 - n/2) - 2*a**(9/2)*gamma(1 - n/2) + 2*a**(7/2)*n**2*x**2*gamma(1 - n/2) - 2*a**(7/2)*x**2*gamma(1 - n/2)), Abs(x**2/a) > 1), (-2*a**(5/2)*a**(n/2)*n*x*sqrt(1 + x**2/a)*sinh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(5/2)*n**2*gamma(1 - n/2) - 2*a**(5/2)*gamma(1 - n/2)) + a**(5/2)*a**(n/2)*n*x*cosh(n*asinh(x/sqrt(a)))*gamma(-n/2)/(2*a**(5/2)*n**2*gamma(1 - n/2) - 2*a**(5/2)*gamma(1 - n/2)) - 2*a**(5/2)*a**(n/2)*x*sqrt(1 + x**2/a)*sinh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(5/2)*n**2*gamma(1 - n/2) - 2*a**(5/2)*gamma(1 - n/2)) - a**3*a**(n/2)*n**2*sqrt(1 + x**2/a)*sinh(n*asinh(x/sqrt(a)))*gamma(-n/2)/(2*a**(5/2)*n**2*gamma(1 - n/2) - 2*a**(5/2)*gamma(1 - n/2)) + 2*a**3*a**(n/2)*n*cosh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(5/2)*n**2*gamma(1 - n/2) - 2*a**(5/2)*gamma(1 - n/2)) + 2*a**2*a**(n/2)*n*x**2*cosh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(5/2)*n**2*gamma(1 - n/2) - 2*a**(5/2)*gamma(1 - n/2)) + 2*a**2*a**(n/2)*x**2*cosh(n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))*gamma(1 - n/2)/(2*a**(5/2)*n**2*gamma(1 - n/2) - 2*a**(5/2)*gamma(1 - n/2)), True))","B",0
488,0,0,0,0.000000," ","integrate((x+(x**2+a)**(1/2))**n/(x**2+a),x)","\int \frac{\left(x + \sqrt{a + x^{2}}\right)^{n}}{a + x^{2}}\, dx"," ",0,"Integral((x + sqrt(a + x**2))**n/(a + x**2), x)","F",0
489,0,0,0,0.000000," ","integrate((x+(x**2+a)**(1/2))**n/(x**2+a)**2,x)","\int \frac{\left(x + \sqrt{a + x^{2}}\right)^{n}}{\left(a + x^{2}\right)^{2}}\, dx"," ",0,"Integral((x + sqrt(a + x**2))**n/(a + x**2)**2, x)","F",0
490,0,0,0,0.000000," ","integrate((x**2+a)**2*(x-(x**2+a)**(1/2))**n,x)","\int \left(a + x^{2}\right)^{2} \left(x - \sqrt{a + x^{2}}\right)^{n}\, dx"," ",0,"Integral((a + x**2)**2*(x - sqrt(a + x**2))**n, x)","F",0
491,0,0,0,0.000000," ","integrate((x**2+a)*(x-(x**2+a)**(1/2))**n,x)","\int \left(a + x^{2}\right) \left(x - \sqrt{a + x^{2}}\right)^{n}\, dx"," ",0,"Integral((a + x**2)*(x - sqrt(a + x**2))**n, x)","F",0
492,0,0,0,0.000000," ","integrate((x-(x**2+a)**(1/2))**n,x)","\int \left(x - \sqrt{a + x^{2}}\right)^{n}\, dx"," ",0,"Integral((x - sqrt(a + x**2))**n, x)","F",0
493,0,0,0,0.000000," ","integrate((x-(x**2+a)**(1/2))**n/(x**2+a),x)","\int \frac{\left(x - \sqrt{a + x^{2}}\right)^{n}}{a + x^{2}}\, dx"," ",0,"Integral((x - sqrt(a + x**2))**n/(a + x**2), x)","F",0
494,0,0,0,0.000000," ","integrate((x-(x**2+a)**(1/2))**n/(x**2+a)**2,x)","\int \frac{\left(x - \sqrt{a + x^{2}}\right)^{n}}{\left(a + x^{2}\right)^{2}}\, dx"," ",0,"Integral((x - sqrt(a + x**2))**n/(a + x**2)**2, x)","F",0
495,0,0,0,0.000000," ","integrate((x**2+a)**(5/2)*(x+(x**2+a)**(1/2))**n,x)","\int \left(a + x^{2}\right)^{\frac{5}{2}} \left(x + \sqrt{a + x^{2}}\right)^{n}\, dx"," ",0,"Integral((a + x**2)**(5/2)*(x + sqrt(a + x**2))**n, x)","F",0
496,0,0,0,0.000000," ","integrate((x**2+a)**(3/2)*(x+(x**2+a)**(1/2))**n,x)","\int \left(a + x^{2}\right)^{\frac{3}{2}} \left(x + \sqrt{a + x^{2}}\right)^{n}\, dx"," ",0,"Integral((a + x**2)**(3/2)*(x + sqrt(a + x**2))**n, x)","F",0
497,0,0,0,0.000000," ","integrate((x**2+a)**(1/2)*(x+(x**2+a)**(1/2))**n,x)","\int \sqrt{a + x^{2}} \left(x + \sqrt{a + x^{2}}\right)^{n}\, dx"," ",0,"Integral(sqrt(a + x**2)*(x + sqrt(a + x**2))**n, x)","F",0
498,1,311,0,2.641016," ","integrate((x+(x**2+a)**(1/2))**n/(x**2+a)**(1/2),x)","\begin{cases} - \frac{\sqrt{a} a^{\frac{n}{2}} \sinh{\left(- n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{n x \sqrt{\frac{a}{x^{2}} + 1}} - \frac{2 a^{\frac{n}{2}} \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{n^{2} \Gamma\left(- \frac{n}{2}\right)} + \frac{a^{\frac{n}{2}} x \cosh{\left(- n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{\sqrt{a} n} - \frac{a^{\frac{n}{2}} x \sinh{\left(- n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{\sqrt{a} n \sqrt{\frac{a}{x^{2}} + 1}} & \text{for}\: \left|{\frac{x^{2}}{a}}\right| > 1 \\- \frac{a^{\frac{n}{2}} \sinh{\left(- n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{n \sqrt{1 + \frac{x^{2}}{a}}} - \frac{2 a^{\frac{n}{2}} \cosh{\left(n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)} \Gamma\left(1 - \frac{n}{2}\right)}{n^{2} \Gamma\left(- \frac{n}{2}\right)} - \frac{a^{\frac{n}{2}} x^{2} \sinh{\left(- n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{a n \sqrt{1 + \frac{x^{2}}{a}}} + \frac{a^{\frac{n}{2}} x \cosh{\left(- n \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} + \operatorname{asinh}{\left(\frac{x}{\sqrt{a}} \right)} \right)}}{\sqrt{a} n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(a)*a**(n/2)*sinh(-n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(n*x*sqrt(a/x**2 + 1)) - 2*a**(n/2)*cosh(n*asinh(x/sqrt(a)))*gamma(1 - n/2)/(n**2*gamma(-n/2)) + a**(n/2)*x*cosh(-n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(sqrt(a)*n) - a**(n/2)*x*sinh(-n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(sqrt(a)*n*sqrt(a/x**2 + 1)), Abs(x**2/a) > 1), (-a**(n/2)*sinh(-n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(n*sqrt(1 + x**2/a)) - 2*a**(n/2)*cosh(n*asinh(x/sqrt(a)))*gamma(1 - n/2)/(n**2*gamma(-n/2)) - a**(n/2)*x**2*sinh(-n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(a*n*sqrt(1 + x**2/a)) + a**(n/2)*x*cosh(-n*asinh(x/sqrt(a)) + asinh(x/sqrt(a)))/(sqrt(a)*n), True))","B",0
499,0,0,0,0.000000," ","integrate((x+(x**2+a)**(1/2))**n/(x**2+a)**(3/2),x)","\int \frac{\left(x + \sqrt{a + x^{2}}\right)^{n}}{\left(a + x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x + sqrt(a + x**2))**n/(a + x**2)**(3/2), x)","F",0
500,0,0,0,0.000000," ","integrate((x+(x**2+a)**(1/2))**n/(x**2+a)**(5/2),x)","\int \frac{\left(x + \sqrt{a + x^{2}}\right)^{n}}{\left(a + x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((x + sqrt(a + x**2))**n/(a + x**2)**(5/2), x)","F",0
501,0,0,0,0.000000," ","integrate((x**2+a)**(5/2)*(x-(x**2+a)**(1/2))**n,x)","\int \left(a + x^{2}\right)^{\frac{5}{2}} \left(x - \sqrt{a + x^{2}}\right)^{n}\, dx"," ",0,"Integral((a + x**2)**(5/2)*(x - sqrt(a + x**2))**n, x)","F",0
502,0,0,0,0.000000," ","integrate((x**2+a)**(3/2)*(x-(x**2+a)**(1/2))**n,x)","\int \left(a + x^{2}\right)^{\frac{3}{2}} \left(x - \sqrt{a + x^{2}}\right)^{n}\, dx"," ",0,"Integral((a + x**2)**(3/2)*(x - sqrt(a + x**2))**n, x)","F",0
503,0,0,0,0.000000," ","integrate((x**2+a)**(1/2)*(x-(x**2+a)**(1/2))**n,x)","\int \sqrt{a + x^{2}} \left(x - \sqrt{a + x^{2}}\right)^{n}\, dx"," ",0,"Integral(sqrt(a + x**2)*(x - sqrt(a + x**2))**n, x)","F",0
504,1,36,0,1.567608," ","integrate((x-(x**2+a)**(1/2))**n/(x**2+a)**(1/2),x)","\begin{cases} - \frac{\left(x - \sqrt{a + x^{2}}\right)^{n}}{n} & \text{for}\: n \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))**n/n, Ne(n, 0)), (Piecewise((asinh(x*sqrt(1/a)), a > 0), (acosh(x*sqrt(-1/a)), a < 0)), True))","A",0
505,0,0,0,0.000000," ","integrate((x-(x**2+a)**(1/2))**n/(x**2+a)**(3/2),x)","\int \frac{\left(x - \sqrt{a + x^{2}}\right)^{n}}{\left(a + x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x - sqrt(a + x**2))**n/(a + x**2)**(3/2), x)","F",0
506,0,0,0,0.000000," ","integrate((x-(x**2+a)**(1/2))**n/(x**2+a)**(5/2),x)","\int \frac{\left(x - \sqrt{a + x^{2}}\right)^{n}}{\left(a + x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((x - sqrt(a + x**2))**n/(a + x**2)**(5/2), x)","F",0
507,-1,0,0,0.000000," ","integrate((a+2*d*e*x/f**2+e**2*x**2/f**2)**2*(d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate((a+2*d*e*x/f**2+e**2*x**2/f**2)*(d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n,x)","\int \left(d + e x + f \sqrt{a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}}\right)^{n}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + 2*d*e*x/f**2 + e**2*x**2/f**2))**n, x)","F",0
510,-1,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n/(a+2*d*e*x/f**2+e**2*x**2/f**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,-1,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n/(a+2*d*e*x/f**2+e**2*x**2/f**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,-1,0,0,0.000000," ","integrate((d+e*x+f*((a*f**2+e*x*(e*x+2*d))/f**2)**(1/2))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
513,-1,0,0,0.000000," ","integrate((d+e*x+f*((a*f**2+e*x*(e*x+2*d))/f**2)**(1/2))**n/(a+2*d*e*x/f**2+e**2*x**2/f**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
514,-1,0,0,0.000000," ","integrate((a+2*d*e*x/f**2+e**2*x**2/f**2)**(3/2)*(d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,0,0,0,0.000000," ","integrate((a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2)*(d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n,x)","\int \sqrt{a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}} \left(d + e x + f \sqrt{a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}}\right)^{n}\, dx"," ",0,"Integral(sqrt(a + 2*d*e*x/f**2 + e**2*x**2/f**2)*(d + e*x + f*sqrt(a + 2*d*e*x/f**2 + e**2*x**2/f**2))**n, x)","F",0
516,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n/(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2),x)","\int \frac{\left(d + e x + f \sqrt{a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}}\right)^{n}}{\sqrt{a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + 2*d*e*x/f**2 + e**2*x**2/f**2))**n/sqrt(a + 2*d*e*x/f**2 + e**2*x**2/f**2), x)","F",0
517,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n/(a+2*d*e*x/f**2+e**2*x**2/f**2)**(3/2),x)","\int \frac{\left(d + e x + f \sqrt{a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}}\right)^{n}}{\left(a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + 2*d*e*x/f**2 + e**2*x**2/f**2))**n/(a + 2*d*e*x/f**2 + e**2*x**2/f**2)**(3/2), x)","F",0
518,-1,0,0,0.000000," ","integrate((d+e*x+f*((a*f**2+e*x*(e*x+2*d))/f**2)**(1/2))**n/((a*f**2+e*x*(e*x+2*d))/f**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,0,0,0,0.000000," ","integrate((a*g+2*d*e*g*x/f**2+e**2*g*x**2/f**2)**(1/2)*(d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n,x)","\int \sqrt{g \left(a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}\right)} \left(d + e x + f \sqrt{a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}}\right)^{n}\, dx"," ",0,"Integral(sqrt(g*(a + 2*d*e*x/f**2 + e**2*x**2/f**2))*(d + e*x + f*sqrt(a + 2*d*e*x/f**2 + e**2*x**2/f**2))**n, x)","F",0
520,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n/(a*g+2*d*e*g*x/f**2+e**2*g*x**2/f**2)**(1/2),x)","\int \frac{\left(d + e x + f \sqrt{a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}}\right)^{n}}{\sqrt{g \left(a + \frac{2 d e x}{f^{2}} + \frac{e^{2} x^{2}}{f^{2}}\right)}}\, dx"," ",0,"Integral((d + e*x + f*sqrt(a + 2*d*e*x/f**2 + e**2*x**2/f**2))**n/sqrt(g*(a + 2*d*e*x/f**2 + e**2*x**2/f**2)), x)","F",0
521,-1,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2))**n/(a*g+2*d*e*g*x/f**2+e**2*g*x**2/f**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,-1,0,0,0.000000," ","integrate((d+e*x+f*((a*f**2+e*x*(e*x+2*d))/f**2)**(1/2))**n/((a*f**2*g+e*g*x*(e*x+2*d))/f**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
523,0,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x**2+c)**(1/2)/(f*x**2+e)**(1/2),x)","\int \frac{1}{\left(a + b x\right) \sqrt{c + d x^{2}} \sqrt{e + f x^{2}}}\, dx"," ",0,"Integral(1/((a + b*x)*sqrt(c + d*x**2)*sqrt(e + f*x**2)), x)","F",0
524,1,70,0,0.560762," ","integrate((-2*f*x**2+e)/(4*f**2*x**4+4*d*f*x**2+4*e*f*x**2+e**2),x)","\frac{\sqrt{- \frac{1}{d f}} \log{\left(- d x \sqrt{- \frac{1}{d f}} + \frac{e}{2 f} + x^{2} \right)}}{4} - \frac{\sqrt{- \frac{1}{d f}} \log{\left(d x \sqrt{- \frac{1}{d f}} + \frac{e}{2 f} + x^{2} \right)}}{4}"," ",0,"sqrt(-1/(d*f))*log(-d*x*sqrt(-1/(d*f)) + e/(2*f) + x**2)/4 - sqrt(-1/(d*f))*log(d*x*sqrt(-1/(d*f)) + e/(2*f) + x**2)/4","A",0
525,1,63,0,0.578655," ","integrate((-2*f*x**2+e)/(4*f**2*x**4-4*d*f*x**2+4*e*f*x**2+e**2),x)","- \frac{\sqrt{\frac{1}{d f}} \log{\left(- d x \sqrt{\frac{1}{d f}} + \frac{e}{2 f} + x^{2} \right)}}{4} + \frac{\sqrt{\frac{1}{d f}} \log{\left(d x \sqrt{\frac{1}{d f}} + \frac{e}{2 f} + x^{2} \right)}}{4}"," ",0,"-sqrt(1/(d*f))*log(-d*x*sqrt(1/(d*f)) + e/(2*f) + x**2)/4 + sqrt(1/(d*f))*log(d*x*sqrt(1/(d*f)) + e/(2*f) + x**2)/4","A",0
526,1,70,0,0.747136," ","integrate((-4*f*x**3+e)/(4*f**2*x**6+4*e*f*x**3+4*d*f*x**2+e**2),x)","\frac{\sqrt{- \frac{1}{d f}} \log{\left(- d x \sqrt{- \frac{1}{d f}} + \frac{e}{2 f} + x^{3} \right)}}{4} - \frac{\sqrt{- \frac{1}{d f}} \log{\left(d x \sqrt{- \frac{1}{d f}} + \frac{e}{2 f} + x^{3} \right)}}{4}"," ",0,"sqrt(-1/(d*f))*log(-d*x*sqrt(-1/(d*f)) + e/(2*f) + x**3)/4 - sqrt(-1/(d*f))*log(d*x*sqrt(-1/(d*f)) + e/(2*f) + x**3)/4","B",0
527,1,63,0,0.739931," ","integrate((-4*f*x**3+e)/(4*f**2*x**6+4*e*f*x**3-4*d*f*x**2+e**2),x)","- \frac{\sqrt{\frac{1}{d f}} \log{\left(- d x \sqrt{\frac{1}{d f}} + \frac{e}{2 f} + x^{3} \right)}}{4} + \frac{\sqrt{\frac{1}{d f}} \log{\left(d x \sqrt{\frac{1}{d f}} + \frac{e}{2 f} + x^{3} \right)}}{4}"," ",0,"-sqrt(1/(d*f))*log(-d*x*sqrt(1/(d*f)) + e/(2*f) + x**3)/4 + sqrt(1/(d*f))*log(d*x*sqrt(1/(d*f)) + e/(2*f) + x**3)/4","A",0
528,0,0,0,0.000000," ","integrate((e-2*f*(-1+n)*x**n)/(e**2+4*d*f*x**2+4*e*f*x**n+4*f**2*x**(2*n)),x)","\int \frac{e - 2 f n x^{n} + 2 f x^{n}}{4 d f x^{2} + e^{2} + 4 e f x^{n} + 4 f^{2} x^{2 n}}\, dx"," ",0,"Integral((e - 2*f*n*x**n + 2*f*x**n)/(4*d*f*x**2 + e**2 + 4*e*f*x**n + 4*f**2*x**(2*n)), x)","F",0
529,0,0,0,0.000000," ","integrate((e-2*f*(-1+n)*x**n)/(e**2-4*d*f*x**2+4*e*f*x**n+4*f**2*x**(2*n)),x)","- \int \frac{e}{4 d f x^{2} - e^{2} - 4 e f x^{n} - 4 f^{2} x^{2 n}}\, dx - \int \frac{2 f x^{n}}{4 d f x^{2} - e^{2} - 4 e f x^{n} - 4 f^{2} x^{2 n}}\, dx - \int \left(- \frac{2 f n x^{n}}{4 d f x^{2} - e^{2} - 4 e f x^{n} - 4 f^{2} x^{2 n}}\right)\, dx"," ",0,"-Integral(e/(4*d*f*x**2 - e**2 - 4*e*f*x**n - 4*f**2*x**(2*n)), x) - Integral(2*f*x**n/(4*d*f*x**2 - e**2 - 4*e*f*x**n - 4*f**2*x**(2*n)), x) - Integral(-2*f*n*x**n/(4*d*f*x**2 - e**2 - 4*e*f*x**n - 4*f**2*x**(2*n)), x)","F",0
530,1,78,0,0.623219," ","integrate(x/(4*d*f*x**4+4*f**2*x**4+4*e*f*x**2+e**2),x)","\frac{- \frac{\sqrt{- \frac{1}{d f}} \log{\left(x^{2} + \frac{- d e \sqrt{- \frac{1}{d f}} + e}{2 d + 2 f} \right)}}{8} + \frac{\sqrt{- \frac{1}{d f}} \log{\left(x^{2} + \frac{d e \sqrt{- \frac{1}{d f}} + e}{2 d + 2 f} \right)}}{8}}{e}"," ",0,"(-sqrt(-1/(d*f))*log(x**2 + (-d*e*sqrt(-1/(d*f)) + e)/(2*d + 2*f))/8 + sqrt(-1/(d*f))*log(x**2 + (d*e*sqrt(-1/(d*f)) + e)/(2*d + 2*f))/8)/e","B",0
531,1,75,0,0.658743," ","integrate(x/(-4*d*f*x**4+4*f**2*x**4+4*e*f*x**2+e**2),x)","- \frac{\frac{\sqrt{\frac{1}{d f}} \log{\left(x^{2} + \frac{- d e \sqrt{\frac{1}{d f}} - e}{2 d - 2 f} \right)}}{8} - \frac{\sqrt{\frac{1}{d f}} \log{\left(x^{2} + \frac{d e \sqrt{\frac{1}{d f}} - e}{2 d - 2 f} \right)}}{8}}{e}"," ",0,"-(sqrt(1/(d*f))*log(x**2 + (-d*e*sqrt(1/(d*f)) - e)/(2*d - 2*f))/8 - sqrt(1/(d*f))*log(x**2 + (d*e*sqrt(1/(d*f)) - e)/(2*d - 2*f))/8)/e","A",0
532,1,90,0,1.133340," ","integrate(x**2*(2*f*x**2+3*e)/(4*d*f*x**6+4*f**2*x**4+4*e*f*x**2+e**2),x)","- \frac{\sqrt{- \frac{1}{d f}} \log{\left(- \frac{e \sqrt{- \frac{1}{d f}}}{2} - f x^{2} \sqrt{- \frac{1}{d f}} + x^{3} \right)}}{4} + \frac{\sqrt{- \frac{1}{d f}} \log{\left(\frac{e \sqrt{- \frac{1}{d f}}}{2} + f x^{2} \sqrt{- \frac{1}{d f}} + x^{3} \right)}}{4}"," ",0,"-sqrt(-1/(d*f))*log(-e*sqrt(-1/(d*f))/2 - f*x**2*sqrt(-1/(d*f)) + x**3)/4 + sqrt(-1/(d*f))*log(e*sqrt(-1/(d*f))/2 + f*x**2*sqrt(-1/(d*f)) + x**3)/4","B",0
533,1,80,0,1.123832," ","integrate(x**2*(2*f*x**2+3*e)/(-4*d*f*x**6+4*f**2*x**4+4*e*f*x**2+e**2),x)","- \frac{\sqrt{\frac{1}{d f}} \log{\left(- \frac{e \sqrt{\frac{1}{d f}}}{2} - f x^{2} \sqrt{\frac{1}{d f}} + x^{3} \right)}}{4} + \frac{\sqrt{\frac{1}{d f}} \log{\left(\frac{e \sqrt{\frac{1}{d f}}}{2} + f x^{2} \sqrt{\frac{1}{d f}} + x^{3} \right)}}{4}"," ",0,"-sqrt(1/(d*f))*log(-e*sqrt(1/(d*f))/2 - f*x**2*sqrt(1/(d*f)) + x**3)/4 + sqrt(1/(d*f))*log(e*sqrt(1/(d*f))/2 + f*x**2*sqrt(1/(d*f)) + x**3)/4","B",0
534,-1,0,0,0.000000," ","integrate(x**m*(e*(1+m)+2*f*(-1+m)*x**2)/(e**2+4*e*f*x**2+4*f**2*x**4+4*d*f*x**(2+2*m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate(x**m*(e*(1+m)+2*f*(-1+m)*x**2)/(e**2+4*e*f*x**2+4*f**2*x**4-4*d*f*x**(2+2*m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,1,73,0,1.116734," ","integrate(x*(-2*f*x**3+2*e)/(4*f**2*x**6+4*d*f*x**4+4*e*f*x**3+e**2),x)","\frac{\sqrt{- \frac{1}{d f}} \log{\left(- d x^{2} \sqrt{- \frac{1}{d f}} + \frac{e}{2 f} + x^{3} \right)}}{4} - \frac{\sqrt{- \frac{1}{d f}} \log{\left(d x^{2} \sqrt{- \frac{1}{d f}} + \frac{e}{2 f} + x^{3} \right)}}{4}"," ",0,"sqrt(-1/(d*f))*log(-d*x**2*sqrt(-1/(d*f)) + e/(2*f) + x**3)/4 - sqrt(-1/(d*f))*log(d*x**2*sqrt(-1/(d*f)) + e/(2*f) + x**3)/4","B",0
537,1,66,0,1.123869," ","integrate(x*(-2*f*x**3+2*e)/(4*f**2*x**6-4*d*f*x**4+4*e*f*x**3+e**2),x)","- \frac{\sqrt{\frac{1}{d f}} \log{\left(- d x^{2} \sqrt{\frac{1}{d f}} + \frac{e}{2 f} + x^{3} \right)}}{4} + \frac{\sqrt{\frac{1}{d f}} \log{\left(d x^{2} \sqrt{\frac{1}{d f}} + \frac{e}{2 f} + x^{3} \right)}}{4}"," ",0,"-sqrt(1/(d*f))*log(-d*x**2*sqrt(1/(d*f)) + e/(2*f) + x**3)/4 + sqrt(1/(d*f))*log(d*x**2*sqrt(1/(d*f)) + e/(2*f) + x**3)/4","A",0
538,1,78,0,0.792909," ","integrate(x**2/(4*d*f*x**6+4*f**2*x**6+4*e*f*x**3+e**2),x)","\frac{- \frac{\sqrt{- \frac{1}{d f}} \log{\left(x^{3} + \frac{- d e \sqrt{- \frac{1}{d f}} + e}{2 d + 2 f} \right)}}{12} + \frac{\sqrt{- \frac{1}{d f}} \log{\left(x^{3} + \frac{d e \sqrt{- \frac{1}{d f}} + e}{2 d + 2 f} \right)}}{12}}{e}"," ",0,"(-sqrt(-1/(d*f))*log(x**3 + (-d*e*sqrt(-1/(d*f)) + e)/(2*d + 2*f))/12 + sqrt(-1/(d*f))*log(x**3 + (d*e*sqrt(-1/(d*f)) + e)/(2*d + 2*f))/12)/e","B",0
539,1,75,0,0.845946," ","integrate(x**2/(-4*d*f*x**6+4*f**2*x**6+4*e*f*x**3+e**2),x)","- \frac{\frac{\sqrt{\frac{1}{d f}} \log{\left(x^{3} + \frac{- d e \sqrt{\frac{1}{d f}} - e}{2 d - 2 f} \right)}}{12} - \frac{\sqrt{\frac{1}{d f}} \log{\left(x^{3} + \frac{d e \sqrt{\frac{1}{d f}} - e}{2 d - 2 f} \right)}}{12}}{e}"," ",0,"-(sqrt(1/(d*f))*log(x**3 + (-d*e*sqrt(1/(d*f)) - e)/(2*d - 2*f))/12 - sqrt(1/(d*f))*log(x**3 + (d*e*sqrt(1/(d*f)) - e)/(2*d - 2*f))/12)/e","A",0
540,-1,0,0,0.000000," ","integrate(x**m*(e*(1+m)+2*f*(-2+m)*x**3)/(e**2+4*e*f*x**3+4*f**2*x**6+4*d*f*x**(2+2*m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate(x**m*(e*(1+m)+2*f*(-2+m)*x**3)/(e**2+4*e*f*x**3+4*f**2*x**6-4*d*f*x**(2+2*m)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,0,0,0,0.000000," ","integrate(x**m*(e*(1+m)+2*f*(1+m-n)*x**n)/(e**2+4*d*f*x**(2+2*m)+4*e*f*x**n+4*f**2*x**(2*n)),x)","\int \frac{x^{m} \left(e m + e + 2 f m x^{n} - 2 f n x^{n} + 2 f x^{n}\right)}{4 d f x^{2} x^{2 m} + e^{2} + 4 e f x^{n} + 4 f^{2} x^{2 n}}\, dx"," ",0,"Integral(x**m*(e*m + e + 2*f*m*x**n - 2*f*n*x**n + 2*f*x**n)/(4*d*f*x**2*x**(2*m) + e**2 + 4*e*f*x**n + 4*f**2*x**(2*n)), x)","F",0
543,0,0,0,0.000000," ","integrate(x**m*(e*(1+m)+2*f*(1+m-n)*x**n)/(e**2-4*d*f*x**(2+2*m)+4*e*f*x**n+4*f**2*x**(2*n)),x)","- \int \frac{e x^{m}}{4 d f x^{2} x^{2 m} - e^{2} - 4 e f x^{n} - 4 f^{2} x^{2 n}}\, dx - \int \frac{e m x^{m}}{4 d f x^{2} x^{2 m} - e^{2} - 4 e f x^{n} - 4 f^{2} x^{2 n}}\, dx - \int \frac{2 f x^{m} x^{n}}{4 d f x^{2} x^{2 m} - e^{2} - 4 e f x^{n} - 4 f^{2} x^{2 n}}\, dx - \int \frac{2 f m x^{m} x^{n}}{4 d f x^{2} x^{2 m} - e^{2} - 4 e f x^{n} - 4 f^{2} x^{2 n}}\, dx - \int \left(- \frac{2 f n x^{m} x^{n}}{4 d f x^{2} x^{2 m} - e^{2} - 4 e f x^{n} - 4 f^{2} x^{2 n}}\right)\, dx"," ",0,"-Integral(e*x**m/(4*d*f*x**2*x**(2*m) - e**2 - 4*e*f*x**n - 4*f**2*x**(2*n)), x) - Integral(e*m*x**m/(4*d*f*x**2*x**(2*m) - e**2 - 4*e*f*x**n - 4*f**2*x**(2*n)), x) - Integral(2*f*x**m*x**n/(4*d*f*x**2*x**(2*m) - e**2 - 4*e*f*x**n - 4*f**2*x**(2*n)), x) - Integral(2*f*m*x**m*x**n/(4*d*f*x**2*x**(2*m) - e**2 - 4*e*f*x**n - 4*f**2*x**(2*n)), x) - Integral(-2*f*n*x**m*x**n/(4*d*f*x**2*x**(2*m) - e**2 - 4*e*f*x**n - 4*f**2*x**(2*n)), x)","F",0
544,0,0,0,0.000000," ","integrate(x**5/(a*c+b*c*x**2+d*(b*x**2+a)**(1/2)),x)","\int \frac{x^{5}}{a c + b c x^{2} + d \sqrt{a + b x^{2}}}\, dx"," ",0,"Integral(x**5/(a*c + b*c*x**2 + d*sqrt(a + b*x**2)), x)","F",0
545,1,88,0,6.510358," ","integrate(x**3/(a*c+b*c*x**2+d*(b*x**2+a)**(1/2)),x)","\begin{cases} \frac{\frac{a + b x^{2}}{2 b c} - \frac{d \sqrt{a + b x^{2}}}{b c^{2}} - \frac{\left(a c^{2} - d^{2}\right) \left(\begin{cases} \frac{\sqrt{a + b x^{2}}}{d} & \text{for}\: c = 0 \\\frac{\log{\left(c \sqrt{a + b x^{2}} + d \right)}}{c} & \text{otherwise} \end{cases}\right)}{b c^{2}}}{b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{2 \left(2 \sqrt{a} d + 2 a c\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((a + b*x**2)/(2*b*c) - d*sqrt(a + b*x**2)/(b*c**2) - (a*c**2 - d**2)*Piecewise((sqrt(a + b*x**2)/d, Eq(c, 0)), (log(c*sqrt(a + b*x**2) + d)/c, True))/(b*c**2))/b, Ne(b, 0)), (x**4/(2*(2*sqrt(a)*d + 2*a*c)), True))","A",0
546,1,29,0,4.479084," ","integrate(x/(a*c+b*c*x**2+d*(b*x**2+a)**(1/2)),x)","\frac{\begin{cases} \frac{\sqrt{a + b x^{2}}}{d} & \text{for}\: c = 0 \\\frac{\log{\left(c \sqrt{a + b x^{2}} + d \right)}}{c} & \text{otherwise} \end{cases}}{b}"," ",0,"Piecewise((sqrt(a + b*x**2)/d, Eq(c, 0)), (log(c*sqrt(a + b*x**2) + d)/c, True))/b","A",0
547,1,88,0,10.498336," ","integrate(1/x/(a*c+b*c*x**2+d*(b*x**2+a)**(1/2)),x)","- \frac{c^{2} \left(\begin{cases} \frac{\sqrt{a + b x^{2}}}{d} & \text{for}\: c = 0 \\\frac{\log{\left(c \sqrt{a + b x^{2}} + d \right)}}{c} & \text{otherwise} \end{cases}\right)}{a c^{2} - d^{2}} - \frac{- \frac{c \log{\left(- b x^{2} \right)}}{2} + \frac{d \operatorname{atan}{\left(\frac{\sqrt{a + b x^{2}}}{\sqrt{- a}} \right)}}{\sqrt{- a}}}{a c^{2} - d^{2}}"," ",0,"-c**2*Piecewise((sqrt(a + b*x**2)/d, Eq(c, 0)), (log(c*sqrt(a + b*x**2) + d)/c, True))/(a*c**2 - d**2) - (-c*log(-b*x**2)/2 + d*atan(sqrt(a + b*x**2)/sqrt(-a))/sqrt(-a))/(a*c**2 - d**2)","A",0
548,0,0,0,0.000000," ","integrate(1/x**3/(a*c+b*c*x**2+d*(b*x**2+a)**(1/2)),x)","\int \frac{1}{x^{3} \left(a c + b c x^{2} + d \sqrt{a + b x^{2}}\right)}\, dx"," ",0,"Integral(1/(x**3*(a*c + b*c*x**2 + d*sqrt(a + b*x**2))), x)","F",0
549,0,0,0,0.000000," ","integrate(x**2/(a*c+b*c*x**2+d*(b*x**2+a)**(1/2)),x)","\int \frac{x^{2}}{a c + b c x^{2} + d \sqrt{a + b x^{2}}}\, dx"," ",0,"Integral(x**2/(a*c + b*c*x**2 + d*sqrt(a + b*x**2)), x)","F",0
550,0,0,0,0.000000," ","integrate(1/(a*c+b*c*x**2+d*(b*x**2+a)**(1/2)),x)","\int \frac{1}{a c + b c x^{2} + d \sqrt{a + b x^{2}}}\, dx"," ",0,"Integral(1/(a*c + b*c*x**2 + d*sqrt(a + b*x**2)), x)","F",0
551,0,0,0,0.000000," ","integrate(1/x**2/(a*c+b*c*x**2+d*(b*x**2+a)**(1/2)),x)","\int \frac{1}{x^{2} \left(a c + b c x^{2} + d \sqrt{a + b x^{2}}\right)}\, dx"," ",0,"Integral(1/(x**2*(a*c + b*c*x**2 + d*sqrt(a + b*x**2))), x)","F",0
552,-1,0,0,0.000000," ","integrate(x**8/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,-1,0,0,0.000000," ","integrate(x**5/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate(x**2/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate(1/x/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate(1/x**4/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate(x**3/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,-1,0,0,0.000000," ","integrate(x/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,-1,0,0,0.000000," ","integrate(1/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
560,-1,0,0,0.000000," ","integrate(1/x**2/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
561,-1,0,0,0.000000," ","integrate(1/x**3/(a*c+b*c*x**3+d*(b*x**3+a)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,0,0,0,0.000000," ","integrate(1/(a*c+b*c*x**n+d*(a+b*x**n)**(1/2)),x)","\int \frac{1}{a c + b c x^{n} + d \sqrt{a + b x^{n}}}\, dx"," ",0,"Integral(1/(a*c + b*c*x**n + d*sqrt(a + b*x**n)), x)","F",0
563,0,0,0,0.000000," ","integrate(x**m/(a*c+b*c*x**n+d*(a+b*x**n)**(1/2)),x)","\int \frac{x^{m}}{a c + b c x^{n} + d \sqrt{a + b x^{n}}}\, dx"," ",0,"Integral(x**m/(a*c + b*c*x**n + d*sqrt(a + b*x**n)), x)","F",0
564,1,32,0,33.632256," ","integrate(x**(-1+n)/(a*c+b*c*x**n+d*(a+b*x**n)**(1/2)),x)","\frac{2 \left(\begin{cases} \frac{\sqrt{a + b x^{n}}}{d} & \text{for}\: c = 0 \\\frac{\log{\left(c \sqrt{a + b x^{n}} + d \right)}}{c} & \text{otherwise} \end{cases}\right)}{b n}"," ",0,"2*Piecewise((sqrt(a + b*x**n)/d, Eq(c, 0)), (log(c*sqrt(a + b*x**n) + d)/c, True))/(b*n)","A",0
565,1,7,0,0.221723," ","integrate(1/(4*x**(3/2)+x**(1/2)),x)","\operatorname{atan}{\left(2 \sqrt{x} \right)}"," ",0,"atan(2*sqrt(x))","A",0
566,1,26,0,0.397226," ","integrate(1/(-x**(5/2)+x**(1/2)),x)","- \frac{\log{\left(\sqrt{x} - 1 \right)}}{2} + \frac{\log{\left(\sqrt{x} + 1 \right)}}{2} + \operatorname{atan}{\left(\sqrt{x} \right)}"," ",0,"-log(sqrt(x) - 1)/2 + log(sqrt(x) + 1)/2 + atan(sqrt(x))","B",0
567,1,22,0,0.241457," ","integrate(1/(-x**(1/4)+x**(1/2)),x)","4 \sqrt[4]{x} + 2 \sqrt{x} + 4 \log{\left(\sqrt[4]{x} - 1 \right)}"," ",0,"4*x**(1/4) + 2*sqrt(x) + 4*log(x**(1/4) - 1)","A",0
568,0,0,0,0.000000," ","integrate(1/(x**(1/3)+x**(1/2)),x)","\int \frac{1}{\sqrt[3]{x} + \sqrt{x}}\, dx"," ",0,"Integral(1/(x**(1/3) + sqrt(x)), x)","F",0
569,1,22,0,0.237812," ","integrate(1/(x**(1/4)+x**(1/2)),x)","- 4 \sqrt[4]{x} + 2 \sqrt{x} + 4 \log{\left(\sqrt[4]{x} + 1 \right)}"," ",0,"-4*x**(1/4) + 2*sqrt(x) + 4*log(x**(1/4) + 1)","A",0
570,1,15,0,0.162003," ","integrate(1/(-x**(1/3)+x**(2/3)),x)","3 \sqrt[3]{x} + 3 \log{\left(\sqrt[3]{x} - 1 \right)}"," ",0,"3*x**(1/3) + 3*log(x**(1/3) - 1)","A",0
571,1,68,0,0.641068," ","integrate(1/(1/x**(1/4)+x**(1/2)),x)","2 \sqrt{x} + \frac{4 \log{\left(\sqrt[4]{x} + 1 \right)}}{3} - \frac{2 \log{\left(- 4 \sqrt[4]{x} + 4 \sqrt{x} + 4 \right)}}{3} - \frac{4 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \sqrt[4]{x}}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"2*sqrt(x) + 4*log(x**(1/4) + 1)/3 - 2*log(-4*x**(1/4) + 4*sqrt(x) + 4)/3 - 4*sqrt(3)*atan(2*sqrt(3)*x**(1/4)/3 - sqrt(3)/3)/3","A",0
572,0,0,0,0.000000," ","integrate(1/(x**(1/4)+x**(1/3)),x)","\int \frac{1}{\sqrt[4]{x} + \sqrt[3]{x}}\, dx"," ",0,"Integral(1/(x**(1/4) + x**(1/3)), x)","F",0
573,1,121,0,3.080706," ","integrate(1/(1/x**(1/3)+1/x**(1/4)),x)","\frac{12 x^{\frac{13}{12}}}{13} + \frac{12 x^{\frac{11}{12}}}{11} + \frac{12 x^{\frac{7}{12}}}{7} + \frac{12 x^{\frac{5}{12}}}{5} + 12 \sqrt[12]{x} - \frac{6 x^{\frac{7}{6}}}{7} - \frac{6 x^{\frac{5}{6}}}{5} - 6 \sqrt[6]{x} + \frac{4 x^{\frac{5}{4}}}{5} + \frac{4 x^{\frac{3}{4}}}{3} + 4 \sqrt[4]{x} - \frac{3 x^{\frac{2}{3}}}{2} - 3 \sqrt[3]{x} - 2 \sqrt{x} - x - 12 \log{\left(\sqrt[12]{x} + 1 \right)}"," ",0,"12*x**(13/12)/13 + 12*x**(11/12)/11 + 12*x**(7/12)/7 + 12*x**(5/12)/5 + 12*x**(1/12) - 6*x**(7/6)/7 - 6*x**(5/6)/5 - 6*x**(1/6) + 4*x**(5/4)/5 + 4*x**(3/4)/3 + 4*x**(1/4) - 3*x**(2/3)/2 - 3*x**(1/3) - 2*sqrt(x) - x - 12*log(x**(1/12) + 1)","A",0
574,0,0,0,0.000000," ","integrate(1/(-1/x**(1/3)+x**(1/2)),x)","\int \frac{\sqrt[3]{x}}{\left(\sqrt[6]{x} - 1\right) \left(\sqrt[6]{x} + x^{\frac{2}{3}} + \sqrt[3]{x} + \sqrt{x} + 1\right)}\, dx"," ",0,"Integral(x**(1/3)/((x**(1/6) - 1)*(x**(1/6) + x**(2/3) + x**(1/3) + sqrt(x) + 1)), x)","F",0
575,1,7,0,0.309618," ","integrate(x**(1/2)/(x**2+x),x)","2 \operatorname{atan}{\left(\sqrt{x} \right)}"," ",0,"2*atan(sqrt(x))","A",0
576,1,17,0,0.167934," ","integrate(x/(x+4*x**(1/2)),x)","- 8 \sqrt{x} + x + 32 \log{\left(\sqrt{x} + 4 \right)}"," ",0,"-8*sqrt(x) + x + 32*log(sqrt(x) + 4)","A",0
577,1,110,0,2.182176," ","integrate(x**(1/2)/(x**(1/3)+x),x)","2 \sqrt{x} - \frac{3 \sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt[6]{x} + 4 \sqrt[3]{x} + 4 \right)}}{4} + \frac{3 \sqrt{2} \log{\left(4 \sqrt{2} \sqrt[6]{x} + 4 \sqrt[3]{x} + 4 \right)}}{4} - \frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt[6]{x} - 1 \right)}}{2} - \frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt[6]{x} + 1 \right)}}{2}"," ",0,"2*sqrt(x) - 3*sqrt(2)*log(-4*sqrt(2)*x**(1/6) + 4*x**(1/3) + 4)/4 + 3*sqrt(2)*log(4*sqrt(2)*x**(1/6) + 4*x**(1/3) + 4)/4 - 3*sqrt(2)*atan(sqrt(2)*x**(1/6) - 1)/2 - 3*sqrt(2)*atan(sqrt(2)*x**(1/6) + 1)/2","A",0
578,0,0,0,0.000000," ","integrate(x**(1/3)/(x**(1/4)+x**(1/2)),x)","\int \frac{\sqrt[3]{x}}{\sqrt[4]{x} + \sqrt{x}}\, dx"," ",0,"Integral(x**(1/3)/(x**(1/4) + sqrt(x)), x)","F",0
579,0,0,0,0.000000," ","integrate(x**(1/2)/(x**(1/4)+x**(1/3)),x)","\int \frac{\sqrt{x}}{\sqrt[4]{x} + \sqrt[3]{x}}\, dx"," ",0,"Integral(sqrt(x)/(x**(1/4) + x**(1/3)), x)","F",0
580,1,311,0,24.147221," ","integrate(x**(1/2)/(-1/x**(1/3)+x**(1/2)),x)","6 \sqrt[6]{x} + x + \frac{6 \log{\left(\sqrt[6]{x} - 1 \right)}}{5} - \frac{3 \sqrt{5} \log{\left(8 \sqrt[6]{x} + 8 \sqrt{5} \sqrt[6]{x} + 16 \sqrt[3]{x} + 16 \right)}}{10} - \frac{3 \log{\left(8 \sqrt[6]{x} + 8 \sqrt{5} \sqrt[6]{x} + 16 \sqrt[3]{x} + 16 \right)}}{10} - \frac{3 \log{\left(- 8 \sqrt{5} \sqrt[6]{x} + 8 \sqrt[6]{x} + 16 \sqrt[3]{x} + 16 \right)}}{10} + \frac{3 \sqrt{5} \log{\left(- 8 \sqrt{5} \sqrt[6]{x} + 8 \sqrt[6]{x} + 16 \sqrt[3]{x} + 16 \right)}}{10} - \frac{3 \sqrt{2} \sqrt{5 - \sqrt{5}} \operatorname{atan}{\left(\frac{2 \sqrt{2} \sqrt[6]{x}}{\sqrt{5 - \sqrt{5}}} + \frac{\sqrt{2}}{2 \sqrt{5 - \sqrt{5}}} + \frac{\sqrt{10}}{2 \sqrt{5 - \sqrt{5}}} \right)}}{5} - \frac{3 \sqrt{2} \sqrt{\sqrt{5} + 5} \operatorname{atan}{\left(\frac{2 \sqrt{2} \sqrt[6]{x}}{\sqrt{\sqrt{5} + 5}} - \frac{\sqrt{10}}{2 \sqrt{\sqrt{5} + 5}} + \frac{\sqrt{2}}{2 \sqrt{\sqrt{5} + 5}} \right)}}{5}"," ",0,"6*x**(1/6) + x + 6*log(x**(1/6) - 1)/5 - 3*sqrt(5)*log(8*x**(1/6) + 8*sqrt(5)*x**(1/6) + 16*x**(1/3) + 16)/10 - 3*log(8*x**(1/6) + 8*sqrt(5)*x**(1/6) + 16*x**(1/3) + 16)/10 - 3*log(-8*sqrt(5)*x**(1/6) + 8*x**(1/6) + 16*x**(1/3) + 16)/10 + 3*sqrt(5)*log(-8*sqrt(5)*x**(1/6) + 8*x**(1/6) + 16*x**(1/3) + 16)/10 - 3*sqrt(2)*sqrt(5 - sqrt(5))*atan(2*sqrt(2)*x**(1/6)/sqrt(5 - sqrt(5)) + sqrt(2)/(2*sqrt(5 - sqrt(5))) + sqrt(10)/(2*sqrt(5 - sqrt(5))))/5 - 3*sqrt(2)*sqrt(sqrt(5) + 5)*atan(2*sqrt(2)*x**(1/6)/sqrt(sqrt(5) + 5) - sqrt(10)/(2*sqrt(sqrt(5) + 5)) + sqrt(2)/(2*sqrt(sqrt(5) + 5)))/5","A",0
581,0,0,0,0.000000," ","integrate(x**m*(b-a/x)**(1/2)/(-b*x+a)**(1/2),x)","\int \frac{x^{m} \sqrt{- \frac{a}{x} + b}}{\sqrt{a - b x}}\, dx"," ",0,"Integral(x**m*sqrt(-a/x + b)/sqrt(a - b*x), x)","F",0
582,0,0,0,0.000000," ","integrate(x**2*(b-a/x)**(1/2)/(-b*x+a)**(1/2),x)","\int \frac{x^{2} \sqrt{- \frac{a}{x} + b}}{\sqrt{a - b x}}\, dx"," ",0,"Integral(x**2*sqrt(-a/x + b)/sqrt(a - b*x), x)","F",0
583,0,0,0,0.000000," ","integrate(x*(b-a/x)**(1/2)/(-b*x+a)**(1/2),x)","\int \frac{x \sqrt{- \frac{a}{x} + b}}{\sqrt{a - b x}}\, dx"," ",0,"Integral(x*sqrt(-a/x + b)/sqrt(a - b*x), x)","F",0
584,0,0,0,0.000000," ","integrate((b-a/x)**(1/2)/(-b*x+a)**(1/2),x)","\int \frac{\sqrt{- \frac{a}{x} + b}}{\sqrt{a - b x}}\, dx"," ",0,"Integral(sqrt(-a/x + b)/sqrt(a - b*x), x)","F",0
585,0,0,0,0.000000," ","integrate((b-a/x)**(1/2)/x/(-b*x+a)**(1/2),x)","\int \frac{\sqrt{- \frac{a}{x} + b}}{x \sqrt{a - b x}}\, dx"," ",0,"Integral(sqrt(-a/x + b)/(x*sqrt(a - b*x)), x)","F",0
586,0,0,0,0.000000," ","integrate((b-a/x)**(1/2)/x**2/(-b*x+a)**(1/2),x)","\int \frac{\sqrt{- \frac{a}{x} + b}}{x^{2} \sqrt{a - b x}}\, dx"," ",0,"Integral(sqrt(-a/x + b)/(x**2*sqrt(a - b*x)), x)","F",0
587,0,0,0,0.000000," ","integrate((a+b/x)**m*(d*x+c)**n,x)","\int \left(a + \frac{b}{x}\right)^{m} \left(c + d x\right)^{n}\, dx"," ",0,"Integral((a + b/x)**m*(c + d*x)**n, x)","F",0
588,1,121,0,6.144377," ","integrate((a+b/x)**m*(d*x+c)**2,x)","\frac{b^{m} c^{2} x x^{- m} \Gamma\left(1 - m\right) {{}_{2}F_{1}\left(\begin{matrix} - m, 1 - m \\ 2 - m \end{matrix}\middle| {\frac{a x e^{i \pi}}{b}} \right)}}{\Gamma\left(2 - m\right)} + \frac{2 b^{m} c d x^{2} x^{- m} \Gamma\left(2 - m\right) {{}_{2}F_{1}\left(\begin{matrix} - m, 2 - m \\ 3 - m \end{matrix}\middle| {\frac{a x e^{i \pi}}{b}} \right)}}{\Gamma\left(3 - m\right)} + \frac{b^{m} d^{2} x^{3} x^{- m} \Gamma\left(3 - m\right) {{}_{2}F_{1}\left(\begin{matrix} - m, 3 - m \\ 4 - m \end{matrix}\middle| {\frac{a x e^{i \pi}}{b}} \right)}}{\Gamma\left(4 - m\right)}"," ",0,"b**m*c**2*x*x**(-m)*gamma(1 - m)*hyper((-m, 1 - m), (2 - m,), a*x*exp_polar(I*pi)/b)/gamma(2 - m) + 2*b**m*c*d*x**2*x**(-m)*gamma(2 - m)*hyper((-m, 2 - m), (3 - m,), a*x*exp_polar(I*pi)/b)/gamma(3 - m) + b**m*d**2*x**3*x**(-m)*gamma(3 - m)*hyper((-m, 3 - m), (4 - m,), a*x*exp_polar(I*pi)/b)/gamma(4 - m)","C",0
589,1,75,0,4.097779," ","integrate((a+b/x)**m*(d*x+c),x)","\frac{b^{m} c x x^{- m} \Gamma\left(1 - m\right) {{}_{2}F_{1}\left(\begin{matrix} - m, 1 - m \\ 2 - m \end{matrix}\middle| {\frac{a x e^{i \pi}}{b}} \right)}}{\Gamma\left(2 - m\right)} + \frac{b^{m} d x^{2} x^{- m} \Gamma\left(2 - m\right) {{}_{2}F_{1}\left(\begin{matrix} - m, 2 - m \\ 3 - m \end{matrix}\middle| {\frac{a x e^{i \pi}}{b}} \right)}}{\Gamma\left(3 - m\right)}"," ",0,"b**m*c*x*x**(-m)*gamma(1 - m)*hyper((-m, 1 - m), (2 - m,), a*x*exp_polar(I*pi)/b)/gamma(2 - m) + b**m*d*x**2*x**(-m)*gamma(2 - m)*hyper((-m, 2 - m), (3 - m,), a*x*exp_polar(I*pi)/b)/gamma(3 - m)","C",0
590,1,34,0,1.470155," ","integrate((a+b/x)**m,x)","\frac{b^{m} x x^{- m} \Gamma\left(1 - m\right) {{}_{2}F_{1}\left(\begin{matrix} - m, 1 - m \\ 2 - m \end{matrix}\middle| {\frac{a x e^{i \pi}}{b}} \right)}}{\Gamma\left(2 - m\right)}"," ",0,"b**m*x*x**(-m)*gamma(1 - m)*hyper((-m, 1 - m), (2 - m,), a*x*exp_polar(I*pi)/b)/gamma(2 - m)","C",0
591,0,0,0,0.000000," ","integrate((a+b/x)**m/(d*x+c),x)","\int \frac{\left(a + \frac{b}{x}\right)^{m}}{c + d x}\, dx"," ",0,"Integral((a + b/x)**m/(c + d*x), x)","F",0
592,0,0,0,0.000000," ","integrate((a+b/x)**m/(d*x+c)**2,x)","\int \frac{\left(a + \frac{b}{x}\right)^{m}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral((a + b/x)**m/(c + d*x)**2, x)","F",0
593,0,0,0,0.000000," ","integrate((a+b/x)**m/(d*x+c)**3,x)","\int \frac{\left(a + \frac{b}{x}\right)^{m}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral((a + b/x)**m/(c + d*x)**3, x)","F",0
594,0,0,0,0.000000," ","integrate((a+b/x)**m/(d*x+c)**4,x)","\int \frac{\left(a + \frac{b}{x}\right)^{m}}{\left(c + d x\right)^{4}}\, dx"," ",0,"Integral((a + b/x)**m/(c + d*x)**4, x)","F",0
595,0,0,0,0.000000," ","integrate(x**m*(b-a/x**2)**(1/2)/(-b*x**2+a)**(1/2),x)","\int \frac{x^{m} \sqrt{- \frac{a}{x^{2}} + b}}{\sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(x**m*sqrt(-a/x**2 + b)/sqrt(a - b*x**2), x)","F",0
596,0,0,0,0.000000," ","integrate(x**2*(b-a/x**2)**(1/2)/(-b*x**2+a)**(1/2),x)","\int \frac{x^{2} \sqrt{- \frac{a}{x^{2}} + b}}{\sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(x**2*sqrt(-a/x**2 + b)/sqrt(a - b*x**2), x)","F",0
597,0,0,0,0.000000," ","integrate(x*(b-a/x**2)**(1/2)/(-b*x**2+a)**(1/2),x)","\int \frac{x \sqrt{- \frac{a}{x^{2}} + b}}{\sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(x*sqrt(-a/x**2 + b)/sqrt(a - b*x**2), x)","F",0
598,0,0,0,0.000000," ","integrate((b-a/x**2)**(1/2)/(-b*x**2+a)**(1/2),x)","\int \frac{\sqrt{- \frac{a}{x^{2}} + b}}{\sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(-a/x**2 + b)/sqrt(a - b*x**2), x)","F",0
599,0,0,0,0.000000," ","integrate((b-a/x**2)**(1/2)/x/(-b*x**2+a)**(1/2),x)","\int \frac{\sqrt{- \frac{a}{x^{2}} + b}}{x \sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(-a/x**2 + b)/(x*sqrt(a - b*x**2)), x)","F",0
600,0,0,0,0.000000," ","integrate((b-a/x**2)**(1/2)/x**2/(-b*x**2+a)**(1/2),x)","\int \frac{\sqrt{- \frac{a}{x^{2}} + b}}{x^{2} \sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(-a/x**2 + b)/(x**2*sqrt(a - b*x**2)), x)","F",0
601,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(a+b/x**2)**(1/2),x)","\int \frac{\left(c + d x\right)^{\frac{3}{2}}}{\sqrt{a + \frac{b}{x^{2}}}}\, dx"," ",0,"Integral((c + d*x)**(3/2)/sqrt(a + b/x**2), x)","F",0
602,1,12,0,0.202935," ","integrate((x**3-1)/(x**4-4*x)**(2/3),x)","\frac{3 \sqrt[3]{x^{4} - 4 x}}{4}"," ",0,"3*(x**4 - 4*x)**(1/3)/4","A",0
603,1,31,0,0.266248," ","integrate((-x**2+2)*(-x**3+6*x)**(1/4),x)","- \frac{4 x^{3} \sqrt[4]{- x^{3} + 6 x}}{15} + \frac{8 x \sqrt[4]{- x^{3} + 6 x}}{5}"," ",0,"-4*x**3*(-x**3 + 6*x)**(1/4)/15 + 8*x*(-x**3 + 6*x)**(1/4)/5","B",0
604,1,31,0,0.262824," ","integrate((x**4+1)*(x**5+5*x)**(1/2),x)","\frac{2 x^{5} \sqrt{x^{5} + 5 x}}{15} + \frac{2 x \sqrt{x^{5} + 5 x}}{3}"," ",0,"2*x**5*sqrt(x**5 + 5*x)/15 + 2*x*sqrt(x**5 + 5*x)/3","B",0
605,1,31,0,0.263641," ","integrate((5*x**4+2)*(x**5+2*x)**(1/2),x)","\frac{2 x^{5} \sqrt{x^{5} + 2 x}}{3} + \frac{4 x \sqrt{x^{5} + 2 x}}{3}"," ",0,"2*x**5*sqrt(x**5 + 2*x)/3 + 4*x*sqrt(x**5 + 2*x)/3","B",0
606,1,10,0,0.160492," ","integrate((3*x**2+x)/(2*x**3+x**2)**(1/2),x)","\sqrt{2 x^{3} + x^{2}}"," ",0,"sqrt(2*x**3 + x**2)","A",0
607,1,39,0,0.197578," ","integrate((2+(1-5*x)**(1/3))/(3+(1-5*x)**(1/3)),x)","x + \frac{3 \left(1 - 5 x\right)^{\frac{2}{3}}}{10} - \frac{9 \sqrt[3]{1 - 5 x}}{5} + \frac{27 \log{\left(\sqrt[3]{1 - 5 x} + 3 \right)}}{5}"," ",0,"x + 3*(1 - 5*x)**(2/3)/10 - 9*(1 - 5*x)**(1/3)/5 + 27*log((1 - 5*x)**(1/3) + 3)/5","A",0
608,1,17,0,0.151725," ","integrate((1+x**(1/2))/(-1+x**(1/2)),x)","4 \sqrt{x} + x + 4 \log{\left(\sqrt{x} - 1 \right)}"," ",0,"4*sqrt(x) + x + 4*log(sqrt(x) - 1)","A",0
609,1,27,0,0.169545," ","integrate((1-(2+3*x)**(1/2))/(1+(2+3*x)**(1/2)),x)","- x + \frac{4 \sqrt{3 x + 2}}{3} - \frac{4 \log{\left(\sqrt{3 x + 2} + 1 \right)}}{3}"," ",0,"-x + 4*sqrt(3*x + 2)/3 - 4*log(sqrt(3*x + 2) + 1)/3","A",0
610,1,42,0,0.436076," ","integrate((-1+(b*x+a)**(1/2))/(1+(b*x+a)**(1/2)),x)","\begin{cases} x - \frac{4 \sqrt{a + b x}}{b} + \frac{4 \log{\left(\sqrt{a + b x} + 1 \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x \left(\sqrt{a} - 1\right)}{\sqrt{a} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x - 4*sqrt(a + b*x)/b + 4*log(sqrt(a + b*x) + 1)/b, Ne(b, 0)), (x*(sqrt(a) - 1)/(sqrt(a) + 1), True))","A",0
611,1,32,0,6.962827," ","integrate((a+b*n*x**(-1+n))/(a*x+b*x**n),x)","\begin{cases} \log{\left(x + \frac{b x^{n}}{a} \right)} & \text{for}\: a \neq 0 \\n \left(\frac{n^{2} \log{\left(x \right)}}{n^{2} - n} - \frac{n \log{\left(x \right)}}{n^{2} - n}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x + b*x**n/a), Ne(a, 0)), (n*(n**2*log(x)/(n**2 - n) - n*log(x)/(n**2 - n)), True))","A",0
612,1,8,0,53.072065," ","integrate((a+b*n*x**(-1+n))/(x**n)/(b+a*x**(1-n)),x)","\log{\left(a x + b x^{n} \right)}"," ",0,"log(a*x + b*x**n)","A",0
613,-1,0,0,0.000000," ","integrate(x*(c*x**2+b*x+a)**m*(g*x**3+f*x**2+e*x+d)**n*(2*a*d+(a*e*n+b*d*m+3*a*e+3*b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+4*a*f+4*b*e+4*c*d)*x**2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+5*a*g+5*b*f+5*c*e)*x**3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+6*b*g+6*c*f)*x**4+c*g*(7+2*m+3*n)*x**5),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**m*(g*x**3+f*x**2+e*x+d)**n*(a*d+(a*e*n+b*d*m+2*a*e+2*b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+3*a*f+3*b*e+3*c*d)*x**2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+4*a*g+4*b*f+4*c*e)*x**3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+5*b*g+5*c*f)*x**4+c*g*(6+2*m+3*n)*x**5),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**m*(g*x**3+f*x**2+e*x+d)**n*(b*d+a*e+b*d*m+a*e*n+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+2*a*f+2*b*e+2*c*d)*x+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+3*a*g+3*b*f+3*c*e)*x**2+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+4*b*g+4*c*f)*x**3+c*g*(5+2*m+3*n)*x**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**m*(g*x**3+f*x**2+e*x+d)**n*(-a*d+(a*e*n+b*d*m)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+a*f+b*e+c*d)*x**2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+2*a*g+2*b*f+2*c*e)*x**3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+3*b*g+3*c*f)*x**4+c*g*(4+2*m+3*n)*x**5)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**m*(g*x**3+f*x**2+e*x+d)**n*(-2*a*d+(a*e*n+b*d*m-a*e-b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m)*x**2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+a*g+b*f+c*e)*x**3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+2*b*g+2*c*f)*x**4+c*g*(3+2*m+3*n)*x**5)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,1,139,0,7.019676," ","integrate(x**3*(a+b*(d*x+c)**(1/2))**2,x)","\begin{cases} \frac{\frac{a^{2} d x^{4}}{4} + \frac{4 a b \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{3}} + \frac{2 b^{2} \left(- \frac{c^{3} \left(c + d x\right)^{2}}{4} + \frac{c^{2} \left(c + d x\right)^{3}}{2} - \frac{3 c \left(c + d x\right)^{4}}{8} + \frac{\left(c + d x\right)^{5}}{10}\right)}{d^{3}}}{d} & \text{for}\: d \neq 0 \\\frac{x^{4} \left(a + b \sqrt{c}\right)^{2}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a**2*d*x**4/4 + 4*a*b*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**3 + 2*b**2*(-c**3*(c + d*x)**2/4 + c**2*(c + d*x)**3/2 - 3*c*(c + d*x)**4/8 + (c + d*x)**5/10)/d**3)/d, Ne(d, 0)), (x**4*(a + b*sqrt(c))**2/4, True))","A",0
619,1,110,0,5.965720," ","integrate(x**2*(a+b*(d*x+c)**(1/2))**2,x)","\begin{cases} \frac{\frac{a^{2} d x^{3}}{3} + \frac{4 a b \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{2}} + \frac{2 b^{2} \left(\frac{c^{2} \left(c + d x\right)^{2}}{4} - \frac{c \left(c + d x\right)^{3}}{3} + \frac{\left(c + d x\right)^{4}}{8}\right)}{d^{2}}}{d} & \text{for}\: d \neq 0 \\\frac{x^{3} \left(a + b \sqrt{c}\right)^{2}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a**2*d*x**3/3 + 4*a*b*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**2 + 2*b**2*(c**2*(c + d*x)**2/4 - c*(c + d*x)**3/3 + (c + d*x)**4/8)/d**2)/d, Ne(d, 0)), (x**3*(a + b*sqrt(c))**2/3, True))","A",0
620,1,94,0,4.767341," ","integrate(x*(a+b*(d*x+c)**(1/2))**2,x)","\begin{cases} \frac{\frac{2 a^{2} \left(- \frac{c \left(c + d x\right)}{2} + \frac{\left(c + d x\right)^{2}}{4}\right)}{d} + \frac{4 a b \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d} + \frac{2 b^{2} \left(- \frac{c \left(c + d x\right)^{2}}{4} + \frac{\left(c + d x\right)^{3}}{6}\right)}{d}}{d} & \text{for}\: d \neq 0 \\\frac{x^{2} \left(a + b \sqrt{c}\right)^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((2*a**2*(-c*(c + d*x)/2 + (c + d*x)**2/4)/d + 4*a*b*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d + 2*b**2*(-c*(c + d*x)**2/4 + (c + d*x)**3/6)/d)/d, Ne(d, 0)), (x**2*(a + b*sqrt(c))**2/2, True))","A",0
621,1,68,0,0.209629," ","integrate((a+b*(d*x+c)**(1/2))**2,x)","\begin{cases} a^{2} x + \frac{4 a b c \sqrt{c + d x}}{3 d} + \frac{4 a b x \sqrt{c + d x}}{3} + b^{2} c x + \frac{b^{2} d x^{2}}{2} & \text{for}\: d \neq 0 \\x \left(a + b \sqrt{c}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 4*a*b*c*sqrt(c + d*x)/(3*d) + 4*a*b*x*sqrt(c + d*x)/3 + b**2*c*x + b**2*d*x**2/2, Ne(d, 0)), (x*(a + b*sqrt(c))**2, True))","A",0
622,1,65,0,27.294722," ","integrate((a+b*(d*x+c)**(1/2))**2/x,x)","a^{2} \log{\left(x \right)} - 2 a b \left(- \frac{2 c \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{- c}} \right)}}{\sqrt{- c}} - 2 \sqrt{c + d x}\right) + b^{2} c \log{\left(x \right)} + b^{2} d x"," ",0,"a**2*log(x) - 2*a*b*(-2*c*atan(sqrt(c + d*x)/sqrt(-c))/sqrt(-c) - 2*sqrt(c + d*x)) + b**2*c*log(x) + b**2*d*x","A",0
623,1,139,0,87.774567," ","integrate((a+b*(d*x+c)**(1/2))**2/x**2,x)","- \frac{a^{2}}{x} - a b c d \sqrt{\frac{1}{c^{3}}} \log{\left(- c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{c + d x} \right)} + a b c d \sqrt{\frac{1}{c^{3}}} \log{\left(c^{2} \sqrt{\frac{1}{c^{3}}} + \sqrt{c + d x} \right)} + \frac{4 a b d \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{- c}} \right)}}{\sqrt{- c}} - \frac{2 a b \sqrt{c + d x}}{x} - \frac{b^{2} c}{x} + b^{2} d \log{\left(x \right)}"," ",0,"-a**2/x - a*b*c*d*sqrt(c**(-3))*log(-c**2*sqrt(c**(-3)) + sqrt(c + d*x)) + a*b*c*d*sqrt(c**(-3))*log(c**2*sqrt(c**(-3)) + sqrt(c + d*x)) + 4*a*b*d*atan(sqrt(c + d*x)/sqrt(-c))/sqrt(-c) - 2*a*b*sqrt(c + d*x)/x - b**2*c/x + b**2*d*log(x)","B",0
624,-1,0,0,0.000000," ","integrate((a+b*(d*x+c)**(1/2))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,0,0,0,0.000000," ","integrate(x**3*(a+b*(d*x+c)**(1/2))**(1/2),x)","\int x^{3} \sqrt{a + b \sqrt{c + d x}}\, dx"," ",0,"Integral(x**3*sqrt(a + b*sqrt(c + d*x)), x)","F",0
626,0,0,0,0.000000," ","integrate(x**2*(a+b*(d*x+c)**(1/2))**(1/2),x)","\int x^{2} \sqrt{a + b \sqrt{c + d x}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*sqrt(c + d*x)), x)","F",0
627,0,0,0,0.000000," ","integrate(x*(a+b*(d*x+c)**(1/2))**(1/2),x)","\int x \sqrt{a + b \sqrt{c + d x}}\, dx"," ",0,"Integral(x*sqrt(a + b*sqrt(c + d*x)), x)","F",0
628,0,0,0,0.000000," ","integrate((a+b*(d*x+c)**(1/2))**(1/2),x)","\int \sqrt{a + b \sqrt{c + d x}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c + d*x)), x)","F",0
629,0,0,0,0.000000," ","integrate((a+b*(d*x+c)**(1/2))**(1/2)/x,x)","\int \frac{\sqrt{a + b \sqrt{c + d x}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c + d*x))/x, x)","F",0
630,0,0,0,0.000000," ","integrate((a+b*(d*x+c)**(1/2))**(1/2)/x**2,x)","\int \frac{\sqrt{a + b \sqrt{c + d x}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c + d*x))/x**2, x)","F",0
631,0,0,0,0.000000," ","integrate((a+b*(d*x+c)**(1/2))**(1/2)/x**3,x)","\int \frac{\sqrt{a + b \sqrt{c + d x}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(c + d*x))/x**3, x)","F",0
632,0,0,0,0.000000," ","integrate(x**3/(a+b*(d*x+c)**(1/2)),x)","\int \frac{x^{3}}{a + b \sqrt{c + d x}}\, dx"," ",0,"Integral(x**3/(a + b*sqrt(c + d*x)), x)","F",0
633,0,0,0,0.000000," ","integrate(x**2/(a+b*(d*x+c)**(1/2)),x)","\int \frac{x^{2}}{a + b \sqrt{c + d x}}\, dx"," ",0,"Integral(x**2/(a + b*sqrt(c + d*x)), x)","F",0
634,1,109,0,4.722416," ","integrate(x/(a+b*(d*x+c)**(1/2)),x)","\begin{cases} \frac{2 \left(- \frac{a \left(c + d x\right)}{2 b^{2} d} - \frac{a \left(a^{2} - b^{2} c\right) \left(\begin{cases} \frac{\sqrt{c + d x}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(a + b \sqrt{c + d x} \right)}}{b} & \text{otherwise} \end{cases}\right)}{b^{3} d} + \frac{\left(c + d x\right)^{\frac{3}{2}}}{3 b d} + \frac{\left(a^{2} - b^{2} c\right) \sqrt{c + d x}}{b^{3} d}\right)}{d} & \text{for}\: d \neq 0 \\\frac{x^{2}}{2 \left(a + b \sqrt{c}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*(-a*(c + d*x)/(2*b**2*d) - a*(a**2 - b**2*c)*Piecewise((sqrt(c + d*x)/a, Eq(b, 0)), (log(a + b*sqrt(c + d*x))/b, True))/(b**3*d) + (c + d*x)**(3/2)/(3*b*d) + (a**2 - b**2*c)*sqrt(c + d*x)/(b**3*d))/d, Ne(d, 0)), (x**2/(2*(a + b*sqrt(c))), True))","A",0
635,1,49,0,0.548687," ","integrate(1/(a+b*(d*x+c)**(1/2)),x)","\begin{cases} \frac{x}{a} & \text{for}\: b = 0 \wedge \left(b = 0 \vee d = 0\right) \\\frac{x}{a + b \sqrt{c}} & \text{for}\: d = 0 \\- \frac{2 a \log{\left(\frac{a}{b} + \sqrt{c + d x} \right)}}{b^{2} d} + \frac{2 \sqrt{c + d x}}{b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a, Eq(b, 0) & (Eq(b, 0) | Eq(d, 0))), (x/(a + b*sqrt(c)), Eq(d, 0)), (-2*a*log(a/b + sqrt(c + d*x))/(b**2*d) + 2*sqrt(c + d*x)/(b*d), True))","A",0
636,1,85,0,13.005775," ","integrate(1/x/(a+b*(d*x+c)**(1/2)),x)","- \frac{2 a b \left(\begin{cases} \frac{\sqrt{c + d x}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(a + b \sqrt{c + d x} \right)}}{b} & \text{otherwise} \end{cases}\right)}{a^{2} - b^{2} c} - \frac{2 \left(- \frac{a \log{\left(- d x \right)}}{2} + \frac{b c \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{- c}} \right)}}{\sqrt{- c}}\right)}{a^{2} - b^{2} c}"," ",0,"-2*a*b*Piecewise((sqrt(c + d*x)/a, Eq(b, 0)), (log(a + b*sqrt(c + d*x))/b, True))/(a**2 - b**2*c) - 2*(-a*log(-d*x)/2 + b*c*atan(sqrt(c + d*x)/sqrt(-c))/sqrt(-c))/(a**2 - b**2*c)","A",0
637,0,0,0,0.000000," ","integrate(1/x**2/(a+b*(d*x+c)**(1/2)),x)","\int \frac{1}{x^{2} \left(a + b \sqrt{c + d x}\right)}\, dx"," ",0,"Integral(1/(x**2*(a + b*sqrt(c + d*x))), x)","F",0
638,-1,0,0,0.000000," ","integrate(1/x**3/(a+b*(d*x+c)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,0,0,0,0.000000," ","integrate(x**3/(a+b*(d*x+c)**(1/2))**2,x)","\int \frac{x^{3}}{\left(a + b \sqrt{c + d x}\right)^{2}}\, dx"," ",0,"Integral(x**3/(a + b*sqrt(c + d*x))**2, x)","F",0
640,0,0,0,0.000000," ","integrate(x**2/(a+b*(d*x+c)**(1/2))**2,x)","\int \frac{x^{2}}{\left(a + b \sqrt{c + d x}\right)^{2}}\, dx"," ",0,"Integral(x**2/(a + b*sqrt(c + d*x))**2, x)","F",0
641,1,131,0,42.382092," ","integrate(x/(a+b*(d*x+c)**(1/2))**2,x)","\begin{cases} \frac{2 \left(- \frac{a \left(a^{2} - b^{2} c\right) \left(\begin{cases} \frac{\sqrt{c + d x}}{a^{2}} & \text{for}\: b = 0 \\- \frac{1}{b \left(a + b \sqrt{c + d x}\right)} & \text{otherwise} \end{cases}\right)}{b^{3} d} - \frac{2 a \sqrt{c + d x}}{b^{3} d} + \frac{c + d x}{2 b^{2} d} + \frac{\left(3 a^{2} - b^{2} c\right) \left(\begin{cases} \frac{\sqrt{c + d x}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(a + b \sqrt{c + d x} \right)}}{b} & \text{otherwise} \end{cases}\right)}{b^{3} d}\right)}{d} & \text{for}\: d \neq 0 \\\frac{x^{2}}{2 \left(a + b \sqrt{c}\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*(-a*(a**2 - b**2*c)*Piecewise((sqrt(c + d*x)/a**2, Eq(b, 0)), (-1/(b*(a + b*sqrt(c + d*x))), True))/(b**3*d) - 2*a*sqrt(c + d*x)/(b**3*d) + (c + d*x)/(2*b**2*d) + (3*a**2 - b**2*c)*Piecewise((sqrt(c + d*x)/a, Eq(b, 0)), (log(a + b*sqrt(c + d*x))/b, True))/(b**3*d))/d, Ne(d, 0)), (x**2/(2*(a + b*sqrt(c))**2), True))","A",0
642,1,124,0,1.090878," ","integrate(1/(a+b*(d*x+c)**(1/2))**2,x)","\begin{cases} \frac{x}{a^{2}} & \text{for}\: b = 0 \wedge \left(b = 0 \vee d = 0\right) \\\frac{x}{\left(a + b \sqrt{c}\right)^{2}} & \text{for}\: d = 0 \\\frac{2 a \log{\left(\frac{a}{b} + \sqrt{c + d x} \right)}}{a b^{2} d + b^{3} d \sqrt{c + d x}} + \frac{2 a}{a b^{2} d + b^{3} d \sqrt{c + d x}} + \frac{2 b \sqrt{c + d x} \log{\left(\frac{a}{b} + \sqrt{c + d x} \right)}}{a b^{2} d + b^{3} d \sqrt{c + d x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a**2, Eq(b, 0) & (Eq(b, 0) | Eq(d, 0))), (x/(a + b*sqrt(c))**2, Eq(d, 0)), (2*a*log(a/b + sqrt(c + d*x))/(a*b**2*d + b**3*d*sqrt(c + d*x)) + 2*a/(a*b**2*d + b**3*d*sqrt(c + d*x)) + 2*b*sqrt(c + d*x)*log(a/b + sqrt(c + d*x))/(a*b**2*d + b**3*d*sqrt(c + d*x)), True))","A",0
643,1,153,0,50.510002," ","integrate(1/x/(a+b*(d*x+c)**(1/2))**2,x)","- \frac{2 a b \left(\begin{cases} \frac{\sqrt{c + d x}}{a^{2}} & \text{for}\: b = 0 \\- \frac{1}{b \left(a + b \sqrt{c + d x}\right)} & \text{otherwise} \end{cases}\right)}{a^{2} - b^{2} c} - \frac{2 b \left(a^{2} + b^{2} c\right) \left(\begin{cases} \frac{\sqrt{c + d x}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(a + b \sqrt{c + d x} \right)}}{b} & \text{otherwise} \end{cases}\right)}{\left(a^{2} - b^{2} c\right)^{2}} - \frac{2 \left(\frac{2 a b c \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + \left(- \frac{a^{2}}{2} - \frac{b^{2} c}{2}\right) \log{\left(- d x \right)}\right)}{\left(a^{2} - b^{2} c\right)^{2}}"," ",0,"-2*a*b*Piecewise((sqrt(c + d*x)/a**2, Eq(b, 0)), (-1/(b*(a + b*sqrt(c + d*x))), True))/(a**2 - b**2*c) - 2*b*(a**2 + b**2*c)*Piecewise((sqrt(c + d*x)/a, Eq(b, 0)), (log(a + b*sqrt(c + d*x))/b, True))/(a**2 - b**2*c)**2 - 2*(2*a*b*c*atan(sqrt(c + d*x)/sqrt(-c))/sqrt(-c) + (-a**2/2 - b**2*c/2)*log(-d*x))/(a**2 - b**2*c)**2","A",0
644,-1,0,0,0.000000," ","integrate(1/x**2/(a+b*(d*x+c)**(1/2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,-1,0,0,0.000000," ","integrate(1/x**3/(a+b*(d*x+c)**(1/2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
646,0,0,0,0.000000," ","integrate(x**3/(a+b*(d*x+c)**(1/2))**(1/2),x)","\int \frac{x^{3}}{\sqrt{a + b \sqrt{c + d x}}}\, dx"," ",0,"Integral(x**3/sqrt(a + b*sqrt(c + d*x)), x)","F",0
647,0,0,0,0.000000," ","integrate(x**2/(a+b*(d*x+c)**(1/2))**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b \sqrt{c + d x}}}\, dx"," ",0,"Integral(x**2/sqrt(a + b*sqrt(c + d*x)), x)","F",0
648,0,0,0,0.000000," ","integrate(x/(a+b*(d*x+c)**(1/2))**(1/2),x)","\int \frac{x}{\sqrt{a + b \sqrt{c + d x}}}\, dx"," ",0,"Integral(x/sqrt(a + b*sqrt(c + d*x)), x)","F",0
649,0,0,0,0.000000," ","integrate(1/(a+b*(d*x+c)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sqrt{c + d x}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sqrt(c + d*x)), x)","F",0
650,0,0,0,0.000000," ","integrate(1/x/(a+b*(d*x+c)**(1/2))**(1/2),x)","\int \frac{1}{x \sqrt{a + b \sqrt{c + d x}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*sqrt(c + d*x))), x)","F",0
651,0,0,0,0.000000," ","integrate(1/x**2/(a+b*(d*x+c)**(1/2))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + b \sqrt{c + d x}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + b*sqrt(c + d*x))), x)","F",0
652,0,0,0,0.000000," ","integrate(1/x**3/(a+b*(d*x+c)**(1/2))**(1/2),x)","\int \frac{1}{x^{3} \sqrt{a + b \sqrt{c + d x}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(a + b*sqrt(c + d*x))), x)","F",0
653,0,0,0,0.000000," ","integrate(x**3*(a+b*(d*x+c)**(1/2))**p,x)","\int x^{3} \left(a + b \sqrt{c + d x}\right)^{p}\, dx"," ",0,"Integral(x**3*(a + b*sqrt(c + d*x))**p, x)","F",0
654,0,0,0,0.000000," ","integrate(x**2*(a+b*(d*x+c)**(1/2))**p,x)","\int x^{2} \left(a + b \sqrt{c + d x}\right)^{p}\, dx"," ",0,"Integral(x**2*(a + b*sqrt(c + d*x))**p, x)","F",0
655,0,0,0,0.000000," ","integrate(x*(a+b*(d*x+c)**(1/2))**p,x)","\int x \left(a + b \sqrt{c + d x}\right)^{p}\, dx"," ",0,"Integral(x*(a + b*sqrt(c + d*x))**p, x)","F",0
656,0,0,0,0.000000," ","integrate((a+b*(d*x+c)**(1/2))**p,x)","\int \left(a + b \sqrt{c + d x}\right)^{p}\, dx"," ",0,"Integral((a + b*sqrt(c + d*x))**p, x)","F",0
657,0,0,0,0.000000," ","integrate((a+b*(d*x+c)**(1/2))**p/x,x)","\int \frac{\left(a + b \sqrt{c + d x}\right)^{p}}{x}\, dx"," ",0,"Integral((a + b*sqrt(c + d*x))**p/x, x)","F",0
658,1,122,0,92.655509," ","integrate((a+b*(c*x)**n)**(5/2)/x,x)","\begin{cases} \frac{\frac{2 a^{3} \operatorname{atan}{\left(\frac{\sqrt{a + b \left(c x\right)^{n}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + 2 a^{2} \sqrt{a + b \left(c x\right)^{n}} + \frac{2 a \left(a + b \left(c x\right)^{n}\right)^{\frac{3}{2}}}{3} + \frac{2 \left(a + b \left(c x\right)^{n}\right)^{\frac{5}{2}}}{5}}{n} & \text{for}\: n \neq 0 \\- \left(- a^{2} \sqrt{a + b} - 2 a b \sqrt{a + b} - b^{2} \sqrt{a + b}\right) \log{\left(c x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((2*a**3*atan(sqrt(a + b*(c*x)**n)/sqrt(-a))/sqrt(-a) + 2*a**2*sqrt(a + b*(c*x)**n) + 2*a*(a + b*(c*x)**n)**(3/2)/3 + 2*(a + b*(c*x)**n)**(5/2)/5)/n, Ne(n, 0)), (-(-a**2*sqrt(a + b) - 2*a*b*sqrt(a + b) - b**2*sqrt(a + b))*log(c*x), True))","A",0
659,1,102,0,66.154322," ","integrate((a+b*(c*x)**n)**(3/2)/x,x)","\begin{cases} \frac{- a \left(- \frac{2 a \operatorname{atan}{\left(\frac{\sqrt{a + b \left(c x\right)^{n}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} - 2 \sqrt{a + b \left(c x\right)^{n}}\right) - b \left(\begin{cases} - \sqrt{a} \left(c x\right)^{n} & \text{for}\: b = 0 \\- \frac{2 \left(a + b \left(c x\right)^{n}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)}{n} & \text{for}\: n \neq 0 \\\left(a \sqrt{a + b} + b \sqrt{a + b}\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a*(-2*a*atan(sqrt(a + b*(c*x)**n)/sqrt(-a))/sqrt(-a) - 2*sqrt(a + b*(c*x)**n)) - b*Piecewise((-sqrt(a)*(c*x)**n, Eq(b, 0)), (-2*(a + b*(c*x)**n)**(3/2)/(3*b), True)))/n, Ne(n, 0)), ((a*sqrt(a + b) + b*sqrt(a + b))*log(x), True))","A",0
660,0,0,0,0.000000," ","integrate((a+b*(c*x)**n)**(1/2)/x,x)","\int \frac{\sqrt{a + b \left(c x\right)^{n}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*(c*x)**n)/x, x)","F",0
661,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*x)**n)**(1/2),x)","\int \frac{1}{x \sqrt{a + b \left(c x\right)^{n}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*(c*x)**n)), x)","F",0
662,1,48,0,11.425421," ","integrate(1/x/(a+b*(c*x)**n)**(3/2),x)","\frac{2}{a n \sqrt{a + b \left(c x\right)^{n}}} + \frac{2 \operatorname{atan}{\left(\frac{\sqrt{a + b \left(c x\right)^{n}}}{\sqrt{- a}} \right)}}{a n \sqrt{- a}}"," ",0,"2/(a*n*sqrt(a + b*(c*x)**n)) + 2*atan(sqrt(a + b*(c*x)**n)/sqrt(-a))/(a*n*sqrt(-a))","A",0
663,1,70,0,16.790201," ","integrate(1/x/(a+b*(c*x)**n)**(5/2),x)","\frac{2}{3 a n \left(a + b \left(c x\right)^{n}\right)^{\frac{3}{2}}} + \frac{2}{a^{2} n \sqrt{a + b \left(c x\right)^{n}}} + \frac{2 \operatorname{atan}{\left(\frac{\sqrt{a + b \left(c x\right)^{n}}}{\sqrt{- a}} \right)}}{a^{2} n \sqrt{- a}}"," ",0,"2/(3*a*n*(a + b*(c*x)**n)**(3/2)) + 2/(a**2*n*sqrt(a + b*(c*x)**n)) + 2*atan(sqrt(a + b*(c*x)**n)/sqrt(-a))/(a**2*n*sqrt(-a))","A",0
664,1,114,0,85.592017," ","integrate((-a+b*(c*x)**n)**(5/2)/x,x)","\begin{cases} \frac{- 2 a^{\frac{5}{2}} \operatorname{atan}{\left(\frac{\sqrt{- a + b \left(c x\right)^{n}}}{\sqrt{a}} \right)} + 2 a^{2} \sqrt{- a + b \left(c x\right)^{n}} - \frac{2 a \left(- a + b \left(c x\right)^{n}\right)^{\frac{3}{2}}}{3} + \frac{2 \left(- a + b \left(c x\right)^{n}\right)^{\frac{5}{2}}}{5}}{n} & \text{for}\: n \neq 0 \\- \left(- a^{2} \sqrt{- a + b} + 2 a b \sqrt{- a + b} - b^{2} \sqrt{- a + b}\right) \log{\left(c x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**(5/2)*atan(sqrt(-a + b*(c*x)**n)/sqrt(a)) + 2*a**2*sqrt(-a + b*(c*x)**n) - 2*a*(-a + b*(c*x)**n)**(3/2)/3 + 2*(-a + b*(c*x)**n)**(5/2)/5)/n, Ne(n, 0)), (-(-a**2*sqrt(-a + b) + 2*a*b*sqrt(-a + b) - b**2*sqrt(-a + b))*log(c*x), True))","A",0
665,1,95,0,70.063919," ","integrate((-a+b*(c*x)**n)**(3/2)/x,x)","\begin{cases} \frac{a \left(2 \sqrt{a} \operatorname{atan}{\left(\frac{\sqrt{- a + b \left(c x\right)^{n}}}{\sqrt{a}} \right)} - 2 \sqrt{- a + b \left(c x\right)^{n}}\right) - b \left(\begin{cases} - \sqrt{- a} \left(c x\right)^{n} & \text{for}\: b = 0 \\- \frac{2 \left(- a + b \left(c x\right)^{n}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)}{n} & \text{for}\: n \neq 0 \\\left(- a \sqrt{- a + b} + b \sqrt{- a + b}\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a*(2*sqrt(a)*atan(sqrt(-a + b*(c*x)**n)/sqrt(a)) - 2*sqrt(-a + b*(c*x)**n)) - b*Piecewise((-sqrt(-a)*(c*x)**n, Eq(b, 0)), (-2*(-a + b*(c*x)**n)**(3/2)/(3*b), True)))/n, Ne(n, 0)), ((-a*sqrt(-a + b) + b*sqrt(-a + b))*log(x), True))","A",0
666,0,0,0,0.000000," ","integrate((-a+b*(c*x)**n)**(1/2)/x,x)","\int \frac{\sqrt{- a + b \left(c x\right)^{n}}}{x}\, dx"," ",0,"Integral(sqrt(-a + b*(c*x)**n)/x, x)","F",0
667,0,0,0,0.000000," ","integrate(1/x/(-a+b*(c*x)**n)**(1/2),x)","\int \frac{1}{x \sqrt{- a + b \left(c x\right)^{n}}}\, dx"," ",0,"Integral(1/(x*sqrt(-a + b*(c*x)**n)), x)","F",0
668,1,44,0,15.942349," ","integrate(1/x/(-a+b*(c*x)**n)**(3/2),x)","- \frac{2}{a n \sqrt{- a + b \left(c x\right)^{n}}} - \frac{2 \operatorname{atan}{\left(\frac{\sqrt{- a + b \left(c x\right)^{n}}}{\sqrt{a}} \right)}}{a^{\frac{3}{2}} n}"," ",0,"-2/(a*n*sqrt(-a + b*(c*x)**n)) - 2*atan(sqrt(-a + b*(c*x)**n)/sqrt(a))/(a**(3/2)*n)","A",0
669,1,63,0,15.629099," ","integrate(1/x/(-a+b*(c*x)**n)**(5/2),x)","- \frac{2}{3 a n \left(- a + b \left(c x\right)^{n}\right)^{\frac{3}{2}}} + \frac{2}{a^{2} n \sqrt{- a + b \left(c x\right)^{n}}} + \frac{2 \operatorname{atan}{\left(\frac{\sqrt{- a + b \left(c x\right)^{n}}}{\sqrt{a}} \right)}}{a^{\frac{5}{2}} n}"," ",0,"-2/(3*a*n*(-a + b*(c*x)**n)**(3/2)) + 2/(a**2*n*sqrt(-a + b*(c*x)**n)) + 2*atan(sqrt(-a + b*(c*x)**n)/sqrt(a))/(a**(5/2)*n)","A",0
670,1,24,0,1.012387," ","integrate(1/x/(b*x+a)**(1/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}}"," ",0,"-2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a)","A",0
671,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*x)**m)**(1/2),x)","\int \frac{1}{x \sqrt{a + b \left(c x\right)^{m}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*(c*x)**m)), x)","F",0
672,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*(d*x)**m)**n)**(1/2),x)","\int \frac{1}{x \sqrt{a + b \left(c \left(d x\right)^{m}\right)^{n}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*(c*(d*x)**m)**n)), x)","F",0
673,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*(d*(e*x)**m)**n)**p)**(1/2),x)","\int \frac{1}{x \sqrt{a + b \left(c \left(d \left(e x\right)^{m}\right)^{n}\right)^{p}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*(c*(d*(e*x)**m)**n)**p)), x)","F",0
674,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*(d*(e*(f*x)**m)**n)**p)**q)**(1/2),x)","\int \frac{1}{x \sqrt{a + b \left(c \left(d \left(e \left(f x\right)^{m}\right)^{n}\right)^{p}\right)^{q}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*(c*(d*(e*(f*x)**m)**n)**p)**q)), x)","F",0
675,-1,0,0,0.000000," ","integrate((x**2-1)**3*(-1+1/x**2)**(1/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
676,1,60,0,118.561303," ","integrate((x**2-1)**2*(-1+1/x**2)**(1/2)/x,x)","\frac{x^{4} \sqrt{-1 + \frac{1}{x^{2}}} \left(2 - \frac{1}{x^{2}}\right)}{8} - x^{2} \sqrt{-1 + \frac{1}{x^{2}}} - \sqrt{-1 + \frac{1}{x^{2}}} + \frac{15 \operatorname{atan}{\left(\sqrt{-1 + \frac{1}{x^{2}}} \right)}}{8}"," ",0,"x**4*sqrt(-1 + x**(-2))*(2 - 1/x**2)/8 - x**2*sqrt(-1 + x**(-2)) - sqrt(-1 + x**(-2)) + 15*atan(sqrt(-1 + x**(-2)))/8","A",0
677,1,39,0,43.654170," ","integrate((x**2-1)*(-1+1/x**2)**(1/2)/x,x)","\frac{x^{2} \sqrt{-1 + \frac{1}{x^{2}}}}{2} + \sqrt{-1 + \frac{1}{x^{2}}} - \frac{3 \operatorname{atan}{\left(\sqrt{-1 + \frac{1}{x^{2}}} \right)}}{2}"," ",0,"x**2*sqrt(-1 + x**(-2))/2 + sqrt(-1 + x**(-2)) - 3*atan(sqrt(-1 + x**(-2)))/2","A",0
678,1,8,0,2.245948," ","integrate((-1+1/x**2)**(1/2)/x/(x**2-1),x)","\sqrt{-1 + \frac{1}{x^{2}}}"," ",0,"sqrt(-1 + x**(-2))","A",0
679,1,20,0,3.846621," ","integrate((-1+1/x**2)**(1/2)/x/(x**2-1)**2,x)","- \sqrt{-1 + \frac{1}{x^{2}}} + \frac{1}{\sqrt{-1 + \frac{1}{x^{2}}}}"," ",0,"-sqrt(-1 + x**(-2)) + 1/sqrt(-1 + x**(-2))","A",0
680,1,34,0,5.123705," ","integrate((-1+1/x**2)**(1/2)/x/(x**2-1)**3,x)","\sqrt{-1 + \frac{1}{x^{2}}} - \frac{2}{\sqrt{-1 + \frac{1}{x^{2}}}} - \frac{1}{3 \left(-1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}}}"," ",0,"sqrt(-1 + x**(-2)) - 2/sqrt(-1 + x**(-2)) - 1/(3*(-1 + x**(-2))**(3/2))","A",0
681,1,8,0,2.830553," ","integrate(x*(1+1/x**2)**(1/2)/(x**2+1)**2,x)","\frac{x}{\sqrt{x^{2} + 1}}"," ",0,"x/sqrt(x**2 + 1)","A",0
682,1,10,0,3.171434," ","integrate(1/x/(x**2+1)/(1+1/x**2)**(1/2),x)","\frac{1}{\sqrt{1 + \frac{1}{x^{2}}}}"," ",0,"1/sqrt(1 + x**(-2))","A",0
683,1,14,0,3.386782," ","integrate(x/(a+b*x**2+(b*x**2+a)**(1/2)),x)","\frac{\log{\left(\sqrt{a + b x^{2}} + 1 \right)}}{b}"," ",0,"log(sqrt(a + b*x**2) + 1)/b","A",0
684,1,19,0,0.215557," ","integrate(x/(x**2-(x**2)**(1/3)),x)","- \frac{\log{\left(x \right)}}{2} + \frac{3 \log{\left(x^{2} - \sqrt[3]{x^{2}} \right)}}{4}"," ",0,"-log(x)/2 + 3*log(x**2 - (x**2)**(1/3))/4","A",0
685,1,94,0,0.651902," ","integrate(x*(x**2+1)**3*(x**4+2*x**2+2)**(1/2),x)","\frac{x^{8} \sqrt{x^{4} + 2 x^{2} + 2}}{10} + \frac{2 x^{6} \sqrt{x^{4} + 2 x^{2} + 2}}{5} + \frac{19 x^{4} \sqrt{x^{4} + 2 x^{2} + 2}}{30} + \frac{7 x^{2} \sqrt{x^{4} + 2 x^{2} + 2}}{15} + \frac{\sqrt{x^{4} + 2 x^{2} + 2}}{15}"," ",0,"x**8*sqrt(x**4 + 2*x**2 + 2)/10 + 2*x**6*sqrt(x**4 + 2*x**2 + 2)/5 + 19*x**4*sqrt(x**4 + 2*x**2 + 2)/30 + 7*x**2*sqrt(x**4 + 2*x**2 + 2)/15 + sqrt(x**4 + 2*x**2 + 2)/15","B",0
686,1,133,0,12.714959," ","integrate(x**5*(x**9+1)**2*(-x**3+1)**(1/2),x)","\frac{2 x^{24} \sqrt{1 - x^{3}}}{51} - \frac{2 x^{21} \sqrt{1 - x^{3}}}{765} - \frac{28 x^{18} \sqrt{1 - x^{3}}}{9945} + \frac{1436 x^{15} \sqrt{1 - x^{3}}}{12155} - \frac{1108 x^{12} \sqrt{1 - x^{3}}}{65637} - \frac{8864 x^{9} \sqrt{1 - x^{3}}}{459459} + \frac{84374 x^{6} \sqrt{1 - x^{3}}}{765765} - \frac{173014 x^{3} \sqrt{1 - x^{3}}}{2297295} - \frac{346028 \sqrt{1 - x^{3}}}{2297295}"," ",0,"2*x**24*sqrt(1 - x**3)/51 - 2*x**21*sqrt(1 - x**3)/765 - 28*x**18*sqrt(1 - x**3)/9945 + 1436*x**15*sqrt(1 - x**3)/12155 - 1108*x**12*sqrt(1 - x**3)/65637 - 8864*x**9*sqrt(1 - x**3)/459459 + 84374*x**6*sqrt(1 - x**3)/765765 - 173014*x**3*sqrt(1 - x**3)/2297295 - 346028*sqrt(1 - x**3)/2297295","A",0
687,1,49,0,3.711495," ","integrate(x/(b*x**2+a)**(3/2)+x/(x**2+1)/(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{1}{b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases} + \frac{\operatorname{atan}{\left(\frac{\sqrt{a + b x^{2}}}{\sqrt{- a + b}} \right)}}{\sqrt{- a + b}}"," ",0,"Piecewise((-1/(b*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(3/2)), True)) + atan(sqrt(a + b*x**2)/sqrt(-a + b))/sqrt(-a + b)","A",0
688,1,37,0,79.827897," ","integrate(x*(b*x**2+x**2+a+1)/(x**2+1)/(b*x**2+a)**(3/2),x)","\frac{\operatorname{atan}{\left(\frac{\sqrt{a + b x^{2}}}{\sqrt{- a + b}} \right)}}{\sqrt{- a + b}} - \frac{1}{b \sqrt{a + b x^{2}}}"," ",0,"atan(sqrt(a + b*x**2)/sqrt(-a + b))/sqrt(-a + b) - 1/(b*sqrt(a + b*x**2))","A",0
689,1,97,0,4.393025," ","integrate(x/(b*x**2+a)**(5/2)+x/(b*x**2+a)**(3/2)+x/(x**2+1)/(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{1}{b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases} + \begin{cases} - \frac{1}{3 a b \sqrt{a + b x^{2}} + 3 b^{2} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{5}{2}}} & \text{otherwise} \end{cases} + \frac{\operatorname{atan}{\left(\frac{\sqrt{a + b x^{2}}}{\sqrt{- a + b}} \right)}}{\sqrt{- a + b}}"," ",0,"Piecewise((-1/(b*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(3/2)), True)) + Piecewise((-1/(3*a*b*sqrt(a + b*x**2) + 3*b**2*x**2*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(5/2)), True)) + atan(sqrt(a + b*x**2)/sqrt(-a + b))/sqrt(-a + b)","A",0
690,-1,0,0,0.000000," ","integrate(x*(b**2*x**4+b*x**4+2*a*b*x**2+a*x**2+b*x**2+a**2+x**2+a+1)/(x**2+1)/(b*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,0,0,0,0.000000," ","integrate(1/(x+x**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{\sqrt{x} + x}}\, dx"," ",0,"Integral(1/sqrt(sqrt(x) + x), x)","F",0
692,0,0,0,0.000000," ","integrate((x+x**(1/2))**(1/2),x)","\int \sqrt{\sqrt{x} + x}\, dx"," ",0,"Integral(sqrt(sqrt(x) + x), x)","F",0
693,1,14,0,0.192598," ","integrate((-x)**(1/2)*(x+(-x)**(1/2)),x)","\frac{2 i x^{\frac{5}{2}}}{5} - \frac{x^{2}}{2}"," ",0,"2*I*x**(5/2)/5 - x**2/2","C",0
694,1,100,0,1.453042," ","integrate((5+x**(1/4))/(-6+x),x)","4 \sqrt[4]{x} + \sqrt[4]{6} \log{\left(\sqrt[4]{x} - \sqrt[4]{6} \right)} + 5 \log{\left(\sqrt[4]{x} - \sqrt[4]{6} \right)} - \sqrt[4]{6} \log{\left(\sqrt[4]{x} + \sqrt[4]{6} \right)} + 5 \log{\left(\sqrt[4]{x} + \sqrt[4]{6} \right)} + 5 \log{\left(\sqrt{x} + \sqrt{6} \right)} - 2 \sqrt[4]{6} \operatorname{atan}{\left(\frac{6^{\frac{3}{4}} \sqrt[4]{x}}{6} \right)}"," ",0,"4*x**(1/4) + 6**(1/4)*log(x**(1/4) - 6**(1/4)) + 5*log(x**(1/4) - 6**(1/4)) - 6**(1/4)*log(x**(1/4) + 6**(1/4)) + 5*log(x**(1/4) + 6**(1/4)) + 5*log(sqrt(x) + sqrt(6)) - 2*6**(1/4)*atan(6**(3/4)*x**(1/4)/6)","A",0
695,1,32,0,4.230488," ","integrate(1/(4-x+(4-x)**(1/2)),x)","\log{\left(2 \sqrt{4 - x} \right)} - \log{\left(2 \sqrt{4 - x} + 2 \right)} - \log{\left(x - \sqrt{4 - x} - 4 \right)}"," ",0,"log(2*sqrt(4 - x)) - log(2*sqrt(4 - x) + 2) - log(x - sqrt(4 - x) - 4)","B",0
696,1,94,0,2.553546," ","integrate(1/(1+x-(2+x)**(1/2)),x)","4 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{2 \sqrt{5} \left(\sqrt{x + 2} - \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\sqrt{x + 2} - \frac{1}{2}\right)^{2} > \frac{5}{4} \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{2 \sqrt{5} \left(\sqrt{x + 2} - \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\sqrt{x + 2} - \frac{1}{2}\right)^{2} < \frac{5}{4} \end{cases}\right) + \log{\left(x - \sqrt{x + 2} + 1 \right)}"," ",0,"4*Piecewise((-sqrt(5)*acoth(2*sqrt(5)*(sqrt(x + 2) - 1/2)/5)/10, (sqrt(x + 2) - 1/2)**2 > 5/4), (-sqrt(5)*atanh(2*sqrt(5)*(sqrt(x + 2) - 1/2)/5)/10, (sqrt(x + 2) - 1/2)**2 < 5/4)) + log(x - sqrt(x + 2) + 1)","A",0
697,1,39,0,2.305428," ","integrate(1/(4+x+(1+x)**(1/2)),x)","\log{\left(x + \sqrt{x + 1} + 4 \right)} - \frac{2 \sqrt{11} \operatorname{atan}{\left(\frac{2 \sqrt{11} \left(\sqrt{x + 1} + \frac{1}{2}\right)}{11} \right)}}{11}"," ",0,"log(x + sqrt(x + 1) + 4) - 2*sqrt(11)*atan(2*sqrt(11)*(sqrt(x + 1) + 1/2)/11)/11","A",0
698,1,92,0,2.212869," ","integrate(1/(x-(1+x)**(1/2)),x)","4 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{2 \sqrt{5} \left(\sqrt{x + 1} - \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\sqrt{x + 1} - \frac{1}{2}\right)^{2} > \frac{5}{4} \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{2 \sqrt{5} \left(\sqrt{x + 1} - \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\sqrt{x + 1} - \frac{1}{2}\right)^{2} < \frac{5}{4} \end{cases}\right) + \log{\left(x - \sqrt{x + 1} \right)}"," ",0,"4*Piecewise((-sqrt(5)*acoth(2*sqrt(5)*(sqrt(x + 1) - 1/2)/5)/10, (sqrt(x + 1) - 1/2)**2 > 5/4), (-sqrt(5)*atanh(2*sqrt(5)*(sqrt(x + 1) - 1/2)/5)/10, (sqrt(x + 1) - 1/2)**2 < 5/4)) + log(x - sqrt(x + 1))","A",0
699,1,36,0,2.428215," ","integrate(1/(x-(2+x)**(1/2)),x)","\log{\left(x - \sqrt{x + 2} \right)} + \frac{\log{\left(2 \sqrt{x + 2} - 4 \right)}}{3} - \frac{\log{\left(2 \sqrt{x + 2} + 2 \right)}}{3}"," ",0,"log(x - sqrt(x + 2)) + log(2*sqrt(x + 2) - 4)/3 - log(2*sqrt(x + 2) + 2)/3","A",0
700,1,92,0,2.307308," ","integrate(1/(x-(1-x)**(1/2)),x)","- 4 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{2 \sqrt{5} \left(\sqrt{1 - x} + \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\sqrt{1 - x} + \frac{1}{2}\right)^{2} > \frac{5}{4} \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{2 \sqrt{5} \left(\sqrt{1 - x} + \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\sqrt{1 - x} + \frac{1}{2}\right)^{2} < \frac{5}{4} \end{cases}\right) + \log{\left(x - \sqrt{1 - x} \right)}"," ",0,"-4*Piecewise((-sqrt(5)*acoth(2*sqrt(5)*(sqrt(1 - x) + 1/2)/5)/10, (sqrt(1 - x) + 1/2)**2 > 5/4), (-sqrt(5)*atanh(2*sqrt(5)*(sqrt(1 - x) + 1/2)/5)/10, (sqrt(1 - x) + 1/2)**2 < 5/4)) + log(x - sqrt(1 - x))","A",0
701,0,0,0,0.000000," ","integrate((1+x+x**(1/2))**(1/2),x)","\int \sqrt{\sqrt{x} + x + 1}\, dx"," ",0,"Integral(sqrt(sqrt(x) + x + 1), x)","F",0
702,0,0,0,0.000000," ","integrate((1+x+(1+x)**(1/2))**(1/2),x)","\int \sqrt{x + \sqrt{x + 1} + 1}\, dx"," ",0,"Integral(sqrt(x + sqrt(x + 1) + 1), x)","F",0
703,0,0,0,0.000000," ","integrate((x+(-1+x)**(1/2))**(1/2),x)","\int \sqrt{x + \sqrt{x - 1}}\, dx"," ",0,"Integral(sqrt(x + sqrt(x - 1)), x)","F",0
704,0,0,0,0.000000," ","integrate((2*x+(-1+2*x)**(1/2))**(1/2),x)","\int \sqrt{2 x + \sqrt{2 x - 1}}\, dx"," ",0,"Integral(sqrt(2*x + sqrt(2*x - 1)), x)","F",0
705,0,0,0,0.000000," ","integrate((3*x+(-7+8*x)**(1/2))**(1/2),x)","\int \sqrt{3 x + \sqrt{8 x - 7}}\, dx"," ",0,"Integral(sqrt(3*x + sqrt(8*x - 7)), x)","F",0
706,0,0,0,0.000000," ","integrate(1/(x+(1+x)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{x + \sqrt{x + 1}}}\, dx"," ",0,"Integral(1/sqrt(x + sqrt(x + 1)), x)","F",0
707,1,58,0,38.422050," ","integrate((1+x)/(4+x+(-9+6*x)**(1/2)),x)","x - 2 \sqrt{6 x - 9} + 3 \log{\left(6 x + 6 \sqrt{6 x - 9} + 24 \right)} + 4 \sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \left(\sqrt{6 x - 9} + 3\right)}{12} \right)} - \frac{3}{2}"," ",0,"x - 2*sqrt(6*x - 9) + 3*log(6*x + 6*sqrt(6*x - 9) + 24) + 4*sqrt(6)*atan(sqrt(6)*(sqrt(6*x - 9) + 3)/12) - 3/2","A",0
708,1,60,0,73.416348," ","integrate((12-x)/(4+x+(-9+6*x)**(1/2)),x)","- x + 2 \sqrt{6 x - 9} + 10 \log{\left(6 x + 6 \sqrt{6 x - 9} + 24 \right)} - \frac{21 \sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \left(\sqrt{6 x - 9} + 3\right)}{12} \right)}}{2} + \frac{3}{2}"," ",0,"-x + 2*sqrt(6*x - 9) + 10*log(6*x + 6*sqrt(6*x - 9) + 24) - 21*sqrt(6)*atan(sqrt(6)*(sqrt(6*x - 9) + 3)/12)/2 + 3/2","A",0
709,1,44,0,0.769787," ","integrate((x**3-1)/(x**2+1)/x**(1/2),x)","\frac{2 x^{\frac{3}{2}}}{3} - \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)} - \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}"," ",0,"2*x**(3/2)/3 - sqrt(2)*atan(sqrt(2)*sqrt(x) - 1) - sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)","A",0
710,0,0,0,0.000000," ","integrate(1/2/(-1+x)**(1/2)/(x-(-1+x)**(1/2))**(1/2),x)","\frac{\int \frac{1}{\sqrt{x - 1} \sqrt{x - \sqrt{x - 1}}}\, dx}{2}"," ",0,"Integral(1/(sqrt(x - 1)*sqrt(x - sqrt(x - 1))), x)/2","F",0
711,1,36,0,2.430666," ","integrate((1+x**(7/2))/(-x**2+1),x)","- \frac{2 x^{\frac{5}{2}}}{5} - 2 \sqrt{x} - \log{\left(\sqrt{x} - 1 \right)} + \frac{\log{\left(x + 1 \right)}}{2} + \operatorname{atan}{\left(\sqrt{x} \right)}"," ",0,"-2*x**(5/2)/5 - 2*sqrt(x) - log(sqrt(x) - 1) + log(x + 1)/2 + atan(sqrt(x))","A",0
712,0,0,0,0.000000," ","integrate((4+2*x)/((-1+2*x)**(1/3)+(-1+2*x)**(1/2)),x)","2 \left(\int \frac{x}{\sqrt[3]{2 x - 1} + \sqrt{2 x - 1}}\, dx + \int \frac{2}{\sqrt[3]{2 x - 1} + \sqrt{2 x - 1}}\, dx\right)"," ",0,"2*(Integral(x/((2*x - 1)**(1/3) + sqrt(2*x - 1)), x) + Integral(2/((2*x - 1)**(1/3) + sqrt(2*x - 1)), x))","F",0
713,0,0,0,0.000000," ","integrate(1/(2+(1+x**(1/2))**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{\sqrt{\sqrt{x} + 1} + 2}}\, dx"," ",0,"Integral(1/sqrt(sqrt(sqrt(x) + 1) + 2), x)","F",0
714,1,216,0,2.509789," ","integrate((2+(4+x**(1/2))**(1/2))**(1/2),x)","- \frac{2 \sqrt{2} \sqrt{x} \sqrt{\sqrt{x} + 4} \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{63 \pi} - \frac{4 \sqrt{2} \sqrt{x} \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{315 \pi} - \frac{\sqrt{2} x \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{9 \pi} + \frac{64 \sqrt{2} \sqrt{\sqrt{x} + 4} \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{315 \pi} + \frac{128 \sqrt{2} \sqrt{\sqrt{\sqrt{x} + 4} + 2} \Gamma\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right)}{315 \pi}"," ",0,"-2*sqrt(2)*sqrt(x)*sqrt(sqrt(x) + 4)*sqrt(sqrt(sqrt(x) + 4) + 2)*gamma(-1/4)*gamma(1/4)/(63*pi) - 4*sqrt(2)*sqrt(x)*sqrt(sqrt(sqrt(x) + 4) + 2)*gamma(-1/4)*gamma(1/4)/(315*pi) - sqrt(2)*x*sqrt(sqrt(sqrt(x) + 4) + 2)*gamma(-1/4)*gamma(1/4)/(9*pi) + 64*sqrt(2)*sqrt(sqrt(x) + 4)*sqrt(sqrt(sqrt(x) + 4) + 2)*gamma(-1/4)*gamma(1/4)/(315*pi) + 128*sqrt(2)*sqrt(sqrt(sqrt(x) + 4) + 2)*gamma(-1/4)*gamma(1/4)/(315*pi)","B",0
715,0,0,0,0.000000," ","integrate((2-(4+(-9+5*x)**(1/2))**(1/2))**(1/2),x)","\int \sqrt{2 - \sqrt{\sqrt{5 x - 9} + 4}}\, dx"," ",0,"Integral(sqrt(2 - sqrt(sqrt(5*x - 9) + 4)), x)","F",0
716,0,0,0,0.000000," ","integrate(1/(2+(1+x**(1/2))**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{\sqrt{\sqrt{x} + 1} + 2}}\, dx"," ",0,"Integral(1/sqrt(sqrt(sqrt(x) + 1) + 2), x)","F",0
717,0,0,0,0.000000," ","integrate((1+(1+(1+x**(1/2))**(1/2))**(1/2))**(1/2),x)","\int \sqrt{\sqrt{\sqrt{\sqrt{x} + 1} + 1} + 1}\, dx"," ",0,"Integral(sqrt(sqrt(sqrt(sqrt(x) + 1) + 1) + 1), x)","F",0
718,0,0,0,0.000000," ","integrate((2+(3+(-1+2*x**(1/2))**(1/2))**(1/2))**(1/2),x)","\int \sqrt{\sqrt{\sqrt{2 \sqrt{x} - 1} + 3} + 2}\, dx"," ",0,"Integral(sqrt(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2), x)","F",0
719,0,0,0,0.000000," ","integrate(x*(1+(1+(-1+x)**(1/2))**(1/2))**(1/2),x)","\int x \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\, dx"," ",0,"Integral(x*sqrt(sqrt(sqrt(x - 1) + 1) + 1), x)","F",0
720,0,0,0,0.000000," ","integrate(1/(-1+x)**(1/2)/(x-(-1+x)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{x - 1} \sqrt{x - \sqrt{x - 1}}}\, dx"," ",0,"Integral(1/(sqrt(x - 1)*sqrt(x - sqrt(x - 1))), x)","F",0
721,0,0,0,0.000000," ","integrate(1/(1+x+(-1+2*x)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{x + \sqrt{2 x - 1} + 1}}\, dx"," ",0,"Integral(1/sqrt(x + sqrt(2*x - 1) + 1), x)","F",0
722,1,99,0,32.897803," ","integrate((p*x+q)/(a*x+b)**(1/2)/(f+(a*x+b)**(1/2)),x)","- \frac{2 f p \sqrt{a x + b}}{a^{2}} - \frac{2 f \left(- a q + b p - f^{2} p\right) \left(\begin{cases} \frac{1}{\sqrt{a x + b}} & \text{for}\: f = 0 \\\frac{\log{\left(\frac{f}{\sqrt{a x + b}} + 1 \right)}}{f} & \text{otherwise} \end{cases}\right)}{a^{2}} + \frac{p \left(a x + b\right)}{a^{2}} + \frac{2 \left(- a q + b p - f^{2} p\right) \log{\left(\frac{1}{\sqrt{a x + b}} \right)}}{a^{2}}"," ",0,"-2*f*p*sqrt(a*x + b)/a**2 - 2*f*(-a*q + b*p - f**2*p)*Piecewise((1/sqrt(a*x + b), Eq(f, 0)), (log(f/sqrt(a*x + b) + 1)/f, True))/a**2 + p*(a*x + b)/a**2 + 2*(-a*q + b*p - f**2*p)*log(1/sqrt(a*x + b))/a**2","A",0
723,0,0,0,0.000000," ","integrate((1-x-x**(1/2))**(1/2),x)","\int \sqrt{- \sqrt{x} - x + 1}\, dx"," ",0,"Integral(sqrt(-sqrt(x) - x + 1), x)","F",0
724,1,17,0,0.165516," ","integrate((9+x+6*x**(1/2))/(x+4*x**(1/2)),x)","4 \sqrt{x} + x + 2 \log{\left(\sqrt{x} + 4 \right)}"," ",0,"4*sqrt(x) + x + 2*log(sqrt(x) + 4)","A",0
725,1,71,0,2.322824," ","integrate((6-8*x**(7/2))/(5-9*x**(1/2)),x)","\frac{80 x^{\frac{7}{2}}}{567} + \frac{400 x^{\frac{5}{2}}}{6561} + \frac{50000 x^{\frac{3}{2}}}{1594323} - \frac{56145628 \sqrt{x}}{43046721} + \frac{2 x^{4}}{9} + \frac{200 x^{3}}{2187} + \frac{2500 x^{2}}{59049} + \frac{125000 x}{4782969} - \frac{280728140 \log{\left(\sqrt{x} - \frac{5}{9} \right)}}{387420489}"," ",0,"80*x**(7/2)/567 + 400*x**(5/2)/6561 + 50000*x**(3/2)/1594323 - 56145628*sqrt(x)/43046721 + 2*x**4/9 + 200*x**3/2187 + 2500*x**2/59049 + 125000*x/4782969 - 280728140*log(sqrt(x) - 5/9)/387420489","A",0
726,1,56,0,12.153124," ","integrate((x**3+1)*(1+x)**(1/2)/(x**2+1),x)","\frac{2 \left(x + 1\right)^{\frac{5}{2}}}{5} - \frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3} - 2 \sqrt{x + 1} + 4 \operatorname{RootSum} {\left(512 t^{4} + 32 t^{2} + 1, \left( t \mapsto t \log{\left(- 128 t^{3} + \sqrt{x + 1} \right)} \right)\right)}"," ",0,"2*(x + 1)**(5/2)/5 - 2*(x + 1)**(3/2)/3 - 2*sqrt(x + 1) + 4*RootSum(512*_t**4 + 32*_t**2 + 1, Lambda(_t, _t*log(-128*_t**3 + sqrt(x + 1))))","A",0
727,0,0,0,0.000000," ","integrate((-1+x-x**(1/2))**(1/2)/(-1+x)/x**(1/2),x)","\int \frac{\sqrt{- \sqrt{x} + x - 1}}{\sqrt{x} \left(x - 1\right)}\, dx"," ",0,"Integral(sqrt(-sqrt(x) + x - 1)/(sqrt(x)*(x - 1)), x)","F",0
728,0,0,0,0.000000," ","integrate((1+2*(1+x)**(1/2))/x/(1+x)**(1/2)/(x+(1+x)**(1/2))**(1/2),x)","\int \frac{2 \sqrt{x + 1} + 1}{x \sqrt{x + 1} \sqrt{x + \sqrt{x + 1}}}\, dx"," ",0,"Integral((2*sqrt(x + 1) + 1)/(x*sqrt(x + 1)*sqrt(x + sqrt(x + 1))), x)","F",0
729,1,26,0,0.953183," ","integrate(1/x**(1/2)/(1+x)**(1/2),x)","\begin{cases} 2 \operatorname{acosh}{\left(\sqrt{x + 1} \right)} & \text{for}\: \left|{x + 1}\right| > 1 \\- 2 i \operatorname{asin}{\left(\sqrt{x + 1} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*acosh(sqrt(x + 1)), Abs(x + 1) > 1), (-2*I*asin(sqrt(x + 1)), True))","A",0
730,0,0,0,0.000000," ","integrate((x/(1+x))**(1/2)/x,x)","\int \frac{\sqrt{\frac{x}{x + 1}}}{x}\, dx"," ",0,"Integral(sqrt(x/(x + 1))/x, x)","F",0
731,1,60,0,1.484279," ","integrate(x**(1/2)/(1+x)**(1/2),x)","\begin{cases} - \operatorname{acosh}{\left(\sqrt{x + 1} \right)} + \frac{\left(x + 1\right)^{\frac{3}{2}}}{\sqrt{x}} - \frac{\sqrt{x + 1}}{\sqrt{x}} & \text{for}\: \left|{x + 1}\right| > 1 \\i \sqrt{- x} \sqrt{x + 1} + i \operatorname{asin}{\left(\sqrt{x + 1} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(sqrt(x + 1)) + (x + 1)**(3/2)/sqrt(x) - sqrt(x + 1)/sqrt(x), Abs(x + 1) > 1), (I*sqrt(-x)*sqrt(x + 1) + I*asin(sqrt(x + 1)), True))","A",0
732,0,0,0,0.000000," ","integrate((x/(1+x))**(1/2),x)","\int \sqrt{\frac{x}{x + 1}}\, dx"," ",0,"Integral(sqrt(x/(x + 1)), x)","F",0
733,0,0,0,0.000000," ","integrate((-1+x)**(1/2)/x**2/(1+x)**(1/2),x)","\int \frac{\sqrt{x - 1}}{x^{2} \sqrt{x + 1}}\, dx"," ",0,"Integral(sqrt(x - 1)/(x**2*sqrt(x + 1)), x)","F",0
734,0,0,0,0.000000," ","integrate(((-1+x)/(1+x))**(1/2)/x**2,x)","\int \frac{\sqrt{\frac{x - 1}{x + 1}}}{x^{2}}\, dx"," ",0,"Integral(sqrt((x - 1)/(x + 1))/x**2, x)","F",0
735,1,83,0,13.845394," ","integrate(x**3*(-1+x)**(1/2)/(1+x)**(1/2),x)","\frac{\left(x - 1\right)^{\frac{7}{2}} \sqrt{x + 1}}{4} + \frac{5 \left(x - 1\right)^{\frac{5}{2}} \sqrt{x + 1}}{12} + \frac{11 \left(x - 1\right)^{\frac{3}{2}} \sqrt{x + 1}}{24} - \frac{3 \sqrt{x - 1} \sqrt{x + 1}}{8} + \frac{3 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{x - 1}}{2} \right)}}{4}"," ",0,"(x - 1)**(7/2)*sqrt(x + 1)/4 + 5*(x - 1)**(5/2)*sqrt(x + 1)/12 + 11*(x - 1)**(3/2)*sqrt(x + 1)/24 - 3*sqrt(x - 1)*sqrt(x + 1)/8 + 3*asinh(sqrt(2)*sqrt(x - 1)/2)/4","A",0
736,0,0,0,0.000000," ","integrate(x**3*((-1+x)/(1+x))**(1/2),x)","\int x^{3} \sqrt{\frac{x - 1}{x + 1}}\, dx"," ",0,"Integral(x**3*sqrt((x - 1)/(x + 1)), x)","F",0
737,0,0,0,0.000000," ","integrate((-x/(1+x))**(1/2)/x,x)","\int \frac{\sqrt{- \frac{x}{x + 1}}}{x}\, dx"," ",0,"Integral(sqrt(-x/(x + 1))/x, x)","F",0
738,0,0,0,0.000000," ","integrate(((1-x)/(1+x))**(1/2)/(-1+x),x)","\int \frac{\sqrt{- \frac{x - 1}{x + 1}}}{x - 1}\, dx"," ",0,"Integral(sqrt(-(x - 1)/(x + 1))/(x - 1), x)","F",0
739,0,0,0,0.000000," ","integrate(((b*x+a)/(-b*x+c))**(1/2)/(b*x+a),x)","\int \frac{\sqrt{\frac{a + b x}{- b x + c}}}{a + b x}\, dx"," ",0,"Integral(sqrt((a + b*x)/(-b*x + c))/(a + b*x), x)","F",0
740,0,0,0,0.000000," ","integrate(((b*x+a)/(d*x+c))**(1/2)/(b*x+a),x)","\int \frac{\sqrt{\frac{a + b x}{c + d x}}}{a + b x}\, dx"," ",0,"Integral(sqrt((a + b*x)/(c + d*x))/(a + b*x), x)","F",0
741,0,0,0,0.000000," ","integrate((-x/(1+x))**(1/2),x)","\int \sqrt{- \frac{x}{x + 1}}\, dx"," ",0,"Integral(sqrt(-x/(x + 1)), x)","F",0
742,0,0,0,0.000000," ","integrate(((1-x)/(1+x))**(1/2),x)","\int \sqrt{\frac{1 - x}{x + 1}}\, dx"," ",0,"Integral(sqrt((1 - x)/(x + 1)), x)","F",0
743,0,0,0,0.000000," ","integrate(((a+x)/(a-x))**(1/2),x)","\int \sqrt{\frac{a + x}{a - x}}\, dx"," ",0,"Integral(sqrt((a + x)/(a - x)), x)","F",0
744,0,0,0,0.000000," ","integrate(((-a+x)/(a+x))**(1/2),x)","\int \sqrt{\frac{- a + x}{a + x}}\, dx"," ",0,"Integral(sqrt((-a + x)/(a + x)), x)","F",0
745,0,0,0,0.000000," ","integrate(((b*x+a)/(d*x+c))**(1/2),x)","\int \sqrt{\frac{a + b x}{c + d x}}\, dx"," ",0,"Integral(sqrt((a + b*x)/(c + d*x)), x)","F",0
746,0,0,0,0.000000," ","integrate(((-1+x)/(5+3*x))**(1/2),x)","\int \sqrt{\frac{x - 1}{3 x + 5}}\, dx"," ",0,"Integral(sqrt((x - 1)/(3*x + 5)), x)","F",0
747,0,0,0,0.000000," ","integrate(((-1+5*x)/(1+7*x))**(1/2)/x**2,x)","\int \frac{\sqrt{\frac{5 x - 1}{7 x + 1}}}{x^{2}}\, dx"," ",0,"Integral(sqrt((5*x - 1)/(7*x + 1))/x**2, x)","F",0
748,0,0,0,0.000000," ","integrate(x/(1+x)/((1-x)/(1+x))**(1/2),x)","\int \frac{x}{\sqrt{- \frac{x - 1}{x + 1}} \left(x + 1\right)}\, dx"," ",0,"Integral(x/(sqrt(-(x - 1)/(x + 1))*(x + 1)), x)","F",0
749,0,0,0,0.000000," ","integrate(x/(1+x)/(-1+2/(1+x))**(1/2),x)","\int \frac{x}{\sqrt{- \frac{x - 1}{x + 1}} \left(x + 1\right)}\, dx"," ",0,"Integral(x/(sqrt(-(x - 1)/(x + 1))*(x + 1)), x)","F",0
750,0,0,0,0.000000," ","integrate(x/(1+x)/((2+x)/(3+x))**(1/2),x)","\int \frac{x}{\sqrt{\frac{x + 2}{x + 3}} \left(x + 1\right)}\, dx"," ",0,"Integral(x/(sqrt((x + 2)/(x + 3))*(x + 1)), x)","F",0
751,0,0,0,0.000000," ","integrate((1+1/x)**(1/2)/(1+x)**2,x)","\int \frac{\sqrt{1 + \frac{1}{x}}}{\left(x + 1\right)^{2}}\, dx"," ",0,"Integral(sqrt(1 + 1/x)/(x + 1)**2, x)","F",0
752,0,0,0,0.000000," ","integrate((1+1/x)**(1/2)/(-x**2+1)**(1/2),x)","\int \frac{\sqrt{1 + \frac{1}{x}}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral(sqrt(1 + 1/x)/sqrt(-(x - 1)*(x + 1)), x)","F",0
753,0,0,0,0.000000," ","integrate(1/(x+(-x**2-2*x+3)**(1/2)),x)","\int \frac{1}{x + \sqrt{- x^{2} - 2 x + 3}}\, dx"," ",0,"Integral(1/(x + sqrt(-x**2 - 2*x + 3)), x)","F",0
754,0,0,0,0.000000," ","integrate(1/(x+(-x**2-2*x+3)**(1/2))**2,x)","\int \frac{1}{\left(x + \sqrt{- x^{2} - 2 x + 3}\right)^{2}}\, dx"," ",0,"Integral((x + sqrt(-x**2 - 2*x + 3))**(-2), x)","F",0
755,0,0,0,0.000000," ","integrate(1/(x+(-x**2-2*x+3)**(1/2))**3,x)","\int \frac{1}{\left(x + \sqrt{- x^{2} - 2 x + 3}\right)^{3}}\, dx"," ",0,"Integral((x + sqrt(-x**2 - 2*x + 3))**(-3), x)","F",0
756,0,0,0,0.000000," ","integrate(1/(x+(x**2-2*x-3)**(1/2)),x)","\int \frac{1}{x + \sqrt{x^{2} - 2 x - 3}}\, dx"," ",0,"Integral(1/(x + sqrt(x**2 - 2*x - 3)), x)","F",0
757,0,0,0,0.000000," ","integrate(1/(x+(x**2-2*x-3)**(1/2))**2,x)","\int \frac{1}{\left(x + \sqrt{x^{2} - 2 x - 3}\right)^{2}}\, dx"," ",0,"Integral((x + sqrt(x**2 - 2*x - 3))**(-2), x)","F",0
758,0,0,0,0.000000," ","integrate(1/(x+(x**2-2*x-3)**(1/2))**3,x)","\int \frac{1}{\left(x + \sqrt{x^{2} - 2 x - 3}\right)^{3}}\, dx"," ",0,"Integral((x + sqrt(x**2 - 2*x - 3))**(-3), x)","F",0
759,0,0,0,0.000000," ","integrate(1/(x+(-x**2-4*x-3)**(1/2)),x)","\int \frac{1}{x + \sqrt{- x^{2} - 4 x - 3}}\, dx"," ",0,"Integral(1/(x + sqrt(-x**2 - 4*x - 3)), x)","F",0
760,0,0,0,0.000000," ","integrate(1/(x+(-x**2-4*x-3)**(1/2))**2,x)","\int \frac{1}{\left(x + \sqrt{- x^{2} - 4 x - 3}\right)^{2}}\, dx"," ",0,"Integral((x + sqrt(-x**2 - 4*x - 3))**(-2), x)","F",0
761,-1,0,0,0.000000," ","integrate(1/(x+(-x**2-4*x-3)**(1/2))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,1,182,0,0.701507," ","integrate(x**3*(1+x)**3*(1+2*x)*(-x**4-2*x**3-x**2+1)**(1/2),x)","\frac{x^{8} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{5} + \frac{4 x^{7} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{5} + \frac{6 x^{6} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{5} + \frac{4 x^{5} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{5} + \frac{2 x^{4} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{15} - \frac{2 x^{3} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{15} - \frac{x^{2} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{15} - \frac{2 \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{15}"," ",0,"x**8*sqrt(-x**4 - 2*x**3 - x**2 + 1)/5 + 4*x**7*sqrt(-x**4 - 2*x**3 - x**2 + 1)/5 + 6*x**6*sqrt(-x**4 - 2*x**3 - x**2 + 1)/5 + 4*x**5*sqrt(-x**4 - 2*x**3 - x**2 + 1)/5 + 2*x**4*sqrt(-x**4 - 2*x**3 - x**2 + 1)/15 - 2*x**3*sqrt(-x**4 - 2*x**3 - x**2 + 1)/15 - x**2*sqrt(-x**4 - 2*x**3 - x**2 + 1)/15 - 2*sqrt(-x**4 - 2*x**3 - x**2 + 1)/15","B",0
763,1,182,0,10.179184," ","integrate((1+2*x)*(x**2+x)**3*(1-(x**2+x)**2)**(1/2),x)","\frac{x^{8} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{5} + \frac{4 x^{7} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{5} + \frac{6 x^{6} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{5} + \frac{4 x^{5} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{5} + \frac{2 x^{4} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{15} - \frac{2 x^{3} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{15} - \frac{x^{2} \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{15} - \frac{2 \sqrt{- x^{4} - 2 x^{3} - x^{2} + 1}}{15}"," ",0,"x**8*sqrt(-x**4 - 2*x**3 - x**2 + 1)/5 + 4*x**7*sqrt(-x**4 - 2*x**3 - x**2 + 1)/5 + 6*x**6*sqrt(-x**4 - 2*x**3 - x**2 + 1)/5 + 4*x**5*sqrt(-x**4 - 2*x**3 - x**2 + 1)/5 + 2*x**4*sqrt(-x**4 - 2*x**3 - x**2 + 1)/15 - 2*x**3*sqrt(-x**4 - 2*x**3 - x**2 + 1)/15 - x**2*sqrt(-x**4 - 2*x**3 - x**2 + 1)/15 - 2*sqrt(-x**4 - 2*x**3 - x**2 + 1)/15","B",0
764,0,0,0,0.000000," ","integrate((-x**4+4*x**3-8*x**2+8*x)**(3/2),x)","\int \left(- x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-x**4 + 4*x**3 - 8*x**2 + 8*x)**(3/2), x)","F",0
765,0,0,0,0.000000," ","integrate((-x**4+4*x**3-8*x**2+8*x)**(1/2),x)","\int \sqrt{- x^{4} + 4 x^{3} - 8 x^{2} + 8 x}\, dx"," ",0,"Integral(sqrt(-x**4 + 4*x**3 - 8*x**2 + 8*x), x)","F",0
766,0,0,0,0.000000," ","integrate(1/(-x**4+4*x**3-8*x**2+8*x)**(1/2),x)","\int \frac{1}{\sqrt{- x^{4} + 4 x^{3} - 8 x^{2} + 8 x}}\, dx"," ",0,"Integral(1/sqrt(-x**4 + 4*x**3 - 8*x**2 + 8*x), x)","F",0
767,0,0,0,0.000000," ","integrate(1/(-x**4+4*x**3-8*x**2+8*x)**(3/2),x)","\int \frac{1}{\left(- x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-x**4 + 4*x**3 - 8*x**2 + 8*x)**(-3/2), x)","F",0
768,0,0,0,0.000000," ","integrate(1/(-x**4+4*x**3-8*x**2+8*x)**(5/2),x)","\int \frac{1}{\left(- x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-x**4 + 4*x**3 - 8*x**2 + 8*x)**(-5/2), x)","F",0
769,0,0,0,0.000000," ","integrate(((2-x)*x*(x**2-2*x+4))**(3/2),x)","\int \left(x \left(2 - x\right) \left(x^{2} - 2 x + 4\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((x*(2 - x)*(x**2 - 2*x + 4))**(3/2), x)","F",0
770,0,0,0,0.000000," ","integrate(((2-x)*x*(x**2-2*x+4))**(1/2),x)","\int \sqrt{x \left(2 - x\right) \left(x^{2} - 2 x + 4\right)}\, dx"," ",0,"Integral(sqrt(x*(2 - x)*(x**2 - 2*x + 4)), x)","F",0
771,0,0,0,0.000000," ","integrate(1/((2-x)*x*(x**2-2*x+4))**(1/2),x)","\int \frac{1}{\sqrt{x \left(2 - x\right) \left(x^{2} - 2 x + 4\right)}}\, dx"," ",0,"Integral(1/sqrt(x*(2 - x)*(x**2 - 2*x + 4)), x)","F",0
772,0,0,0,0.000000," ","integrate(1/((2-x)*x*(x**2-2*x+4))**(3/2),x)","\int \frac{1}{\left(x \left(2 - x\right) \left(x^{2} - 2 x + 4\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x*(2 - x)*(x**2 - 2*x + 4))**(-3/2), x)","F",0
773,0,0,0,0.000000," ","integrate(1/((2-x)*x*(x**2-2*x+4))**(5/2),x)","\int \frac{1}{\left(x \left(2 - x\right) \left(x^{2} - 2 x + 4\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((x*(2 - x)*(x**2 - 2*x + 4))**(-5/2), x)","F",0
774,0,0,0,0.000000," ","integrate((d**2*x**4+4*c*d*x**3+4*c**2*x**2+4*a*c)**(3/2),x)","\int \left(4 a c + 4 c^{2} x^{2} + 4 c d x^{3} + d^{2} x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((4*a*c + 4*c**2*x**2 + 4*c*d*x**3 + d**2*x**4)**(3/2), x)","F",0
775,0,0,0,0.000000," ","integrate((d**2*x**4+4*c*d*x**3+4*c**2*x**2+4*a*c)**(1/2),x)","\int \sqrt{4 a c + 4 c^{2} x^{2} + 4 c d x^{3} + d^{2} x^{4}}\, dx"," ",0,"Integral(sqrt(4*a*c + 4*c**2*x**2 + 4*c*d*x**3 + d**2*x**4), x)","F",0
776,0,0,0,0.000000," ","integrate(1/(d**2*x**4+4*c*d*x**3+4*c**2*x**2+4*a*c)**(1/2),x)","\int \frac{1}{\sqrt{4 a c + 4 c^{2} x^{2} + 4 c d x^{3} + d^{2} x^{4}}}\, dx"," ",0,"Integral(1/sqrt(4*a*c + 4*c**2*x**2 + 4*c*d*x**3 + d**2*x**4), x)","F",0
777,0,0,0,0.000000," ","integrate(1/(d**2*x**4+4*c*d*x**3+4*c**2*x**2+4*a*c)**(3/2),x)","\int \frac{1}{\left(4 a c + 4 c^{2} x^{2} + 4 c d x^{3} + d^{2} x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((4*a*c + 4*c**2*x**2 + 4*c*d*x**3 + d**2*x**4)**(-3/2), x)","F",0
778,0,0,0,0.000000," ","integrate((8*e**3*x**4+8*d*e**2*x**3-d**3*x+8*a*e**2)**(1/2),x)","\int \sqrt{8 a e^{2} - d^{3} x + 8 d e^{2} x^{3} + 8 e^{3} x^{4}}\, dx"," ",0,"Integral(sqrt(8*a*e**2 - d**3*x + 8*d*e**2*x**3 + 8*e**3*x**4), x)","F",0
779,0,0,0,0.000000," ","integrate(1/(8*e**3*x**4+8*d*e**2*x**3-d**3*x+8*a*e**2)**(1/2),x)","\int \frac{1}{\sqrt{8 a e^{2} - d^{3} x + 8 d e^{2} x^{3} + 8 e^{3} x^{4}}}\, dx"," ",0,"Integral(1/sqrt(8*a*e**2 - d**3*x + 8*d*e**2*x**3 + 8*e**3*x**4), x)","F",0
780,0,0,0,0.000000," ","integrate(1/(8*e**3*x**4+8*d*e**2*x**3-d**3*x+8*a*e**2)**(3/2),x)","\int \frac{1}{\left(8 a e^{2} - d^{3} x + 8 d e^{2} x^{3} + 8 e^{3} x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((8*a*e**2 - d**3*x + 8*d*e**2*x**3 + 8*e**3*x**4)**(-3/2), x)","F",0
781,0,0,0,0.000000," ","integrate((-x**4+4*x**3-8*x**2+a+8*x)**(3/2),x)","\int \left(a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a - x**4 + 4*x**3 - 8*x**2 + 8*x)**(3/2), x)","F",0
782,0,0,0,0.000000," ","integrate((-x**4+4*x**3-8*x**2+a+8*x)**(1/2),x)","\int \sqrt{a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x}\, dx"," ",0,"Integral(sqrt(a - x**4 + 4*x**3 - 8*x**2 + 8*x), x)","F",0
783,0,0,0,0.000000," ","integrate(1/(-x**4+4*x**3-8*x**2+a+8*x)**(1/2),x)","\int \frac{1}{\sqrt{a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x}}\, dx"," ",0,"Integral(1/sqrt(a - x**4 + 4*x**3 - 8*x**2 + 8*x), x)","F",0
784,0,0,0,0.000000," ","integrate(1/(-x**4+4*x**3-8*x**2+a+8*x)**(3/2),x)","\int \frac{1}{\left(a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a - x**4 + 4*x**3 - 8*x**2 + 8*x)**(-3/2), x)","F",0
785,0,0,0,0.000000," ","integrate(1/(-x**4+4*x**3-8*x**2+a+8*x)**(5/2),x)","\int \frac{1}{\left(a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a - x**4 + 4*x**3 - 8*x**2 + 8*x)**(-5/2), x)","F",0
786,0,0,0,0.000000," ","integrate(x*(-x**4+4*x**3-8*x**2+a+8*x)**(3/2),x)","\int x \left(a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a - x**4 + 4*x**3 - 8*x**2 + 8*x)**(3/2), x)","F",0
787,0,0,0,0.000000," ","integrate(x*(-x**4+4*x**3-8*x**2+a+8*x)**(1/2),x)","\int x \sqrt{a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x}\, dx"," ",0,"Integral(x*sqrt(a - x**4 + 4*x**3 - 8*x**2 + 8*x), x)","F",0
788,0,0,0,0.000000," ","integrate(x/(-x**4+4*x**3-8*x**2+a+8*x)**(1/2),x)","\int \frac{x}{\sqrt{a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x}}\, dx"," ",0,"Integral(x/sqrt(a - x**4 + 4*x**3 - 8*x**2 + 8*x), x)","F",0
789,0,0,0,0.000000," ","integrate(x/(-x**4+4*x**3-8*x**2+a+8*x)**(3/2),x)","\int \frac{x}{\left(a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(a - x**4 + 4*x**3 - 8*x**2 + 8*x)**(3/2), x)","F",0
790,0,0,0,0.000000," ","integrate(x/(-x**4+4*x**3-8*x**2+a+8*x)**(5/2),x)","\int \frac{x}{\left(a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/(a - x**4 + 4*x**3 - 8*x**2 + 8*x)**(5/2), x)","F",0
791,0,0,0,0.000000," ","integrate(x**2*(-x**4+4*x**3-8*x**2+a+8*x)**(3/2),x)","\int x^{2} \left(a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(a - x**4 + 4*x**3 - 8*x**2 + 8*x)**(3/2), x)","F",0
792,0,0,0,0.000000," ","integrate(x**2*(-x**4+4*x**3-8*x**2+a+8*x)**(1/2),x)","\int x^{2} \sqrt{a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x}\, dx"," ",0,"Integral(x**2*sqrt(a - x**4 + 4*x**3 - 8*x**2 + 8*x), x)","F",0
793,0,0,0,0.000000," ","integrate(x**2/(-x**4+4*x**3-8*x**2+a+8*x)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x}}\, dx"," ",0,"Integral(x**2/sqrt(a - x**4 + 4*x**3 - 8*x**2 + 8*x), x)","F",0
794,0,0,0,0.000000," ","integrate(x**2/(-x**4+4*x**3-8*x**2+a+8*x)**(3/2),x)","\int \frac{x^{2}}{\left(a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(a - x**4 + 4*x**3 - 8*x**2 + 8*x)**(3/2), x)","F",0
795,0,0,0,0.000000," ","integrate(x**2/(-x**4+4*x**3-8*x**2+a+8*x)**(5/2),x)","\int \frac{x^{2}}{\left(a - x^{4} + 4 x^{3} - 8 x^{2} + 8 x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/(a - x**4 + 4*x**3 - 8*x**2 + 8*x)**(5/2), x)","F",0
796,0,0,0,0.000000," ","integrate(1/(8*x**4-x**3+8*x+8)**(1/2),x)","\int \frac{1}{\sqrt{8 x^{4} - x^{3} + 8 x + 8}}\, dx"," ",0,"Integral(1/sqrt(8*x**4 - x**3 + 8*x + 8), x)","F",0
797,0,0,0,0.000000," ","integrate(1/(8*x**4-x**3+8*x+8)**(3/2),x)","\int \frac{1}{\left(8 x^{4} - x^{3} + 8 x + 8\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((8*x**4 - x**3 + 8*x + 8)**(-3/2), x)","F",0
798,0,0,0,0.000000," ","integrate(1/(4*x**4+4*x**2+4*x+1)**(1/2),x)","\int \frac{1}{\sqrt{4 x^{4} + 4 x^{2} + 4 x + 1}}\, dx"," ",0,"Integral(1/sqrt(4*x**4 + 4*x**2 + 4*x + 1), x)","F",0
799,0,0,0,0.000000," ","integrate(1/(4*x**4+4*x**2+4*x+1)**(3/2),x)","\int \frac{1}{\left(4 x^{4} + 4 x^{2} + 4 x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((4*x**4 + 4*x**2 + 4*x + 1)**(-3/2), x)","F",0
800,0,0,0,0.000000," ","integrate(1/(8*x**4-15*x**3+8*x**2+24*x+8)**(1/2),x)","\int \frac{1}{\sqrt{8 x^{4} - 15 x^{3} + 8 x^{2} + 24 x + 8}}\, dx"," ",0,"Integral(1/sqrt(8*x**4 - 15*x**3 + 8*x**2 + 24*x + 8), x)","F",0
801,0,0,0,0.000000," ","integrate(1/(8*x**4-15*x**3+8*x**2+24*x+8)**(3/2),x)","\int \frac{1}{\left(8 x^{4} - 15 x^{3} + 8 x^{2} + 24 x + 8\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((8*x**4 - 15*x**3 + 8*x**2 + 24*x + 8)**(-3/2), x)","F",0
802,0,0,0,0.000000," ","integrate(1/(8*x**4-15*x**3+8*x**2+24*x+8)**(5/2),x)","\int \frac{1}{\left(8 x^{4} - 15 x^{3} + 8 x^{2} + 24 x + 8\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((8*x**4 - 15*x**3 + 8*x**2 + 24*x + 8)**(-5/2), x)","F",0
803,0,0,0,0.000000," ","integrate(1/(3*x**4+15*x**3-44*x**2-6*x+9)**(1/2),x)","\int \frac{1}{\sqrt{3 x^{4} + 15 x^{3} - 44 x^{2} - 6 x + 9}}\, dx"," ",0,"Integral(1/sqrt(3*x**4 + 15*x**3 - 44*x**2 - 6*x + 9), x)","F",0
804,0,0,0,0.000000," ","integrate(1/(3*x**4+15*x**3-44*x**2-6*x+9)**(3/2),x)","\int \frac{1}{\left(3 x^{4} + 15 x^{3} - 44 x^{2} - 6 x + 9\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((3*x**4 + 15*x**3 - 44*x**2 - 6*x + 9)**(-3/2), x)","F",0
805,0,0,0,0.000000," ","integrate((2*(3-x)**(1/2)+3/(1+x)**(1/2))**2/x,x)","\int \frac{\left(2 \sqrt{3 - x} \sqrt{x + 1} + 3\right)^{2}}{x \left(x + 1\right)}\, dx"," ",0,"Integral((2*sqrt(3 - x)*sqrt(x + 1) + 3)**2/(x*(x + 1)), x)","F",0
806,1,63,0,4.509683," ","integrate((x**2+x-1)/((x**2+1)**(1/2)+1),x)","\frac{x \sqrt{x^{2} + 1}}{2} - x + \frac{x}{\sqrt{x^{2} + 1}} + \sqrt{x^{2} + 1} - \log{\left(\sqrt{x^{2} + 1} + 1 \right)} - \frac{\operatorname{asinh}{\left(x \right)}}{2} - \frac{1}{x} + \frac{1}{x \sqrt{x^{2} + 1}}"," ",0,"x*sqrt(x**2 + 1)/2 - x + x/sqrt(x**2 + 1) + sqrt(x**2 + 1) - log(sqrt(x**2 + 1) + 1) - asinh(x)/2 - 1/x + 1/(x*sqrt(x**2 + 1))","A",0
807,0,0,0,0.000000," ","integrate((x**2+x-1)/(1+x+(x**2+1)**(1/2)),x)","\int \frac{x^{2} + x - 1}{x + \sqrt{x^{2} + 1} + 1}\, dx"," ",0,"Integral((x**2 + x - 1)/(x + sqrt(x**2 + 1) + 1), x)","F",0
808,1,12,0,0.157415," ","integrate((x+2*(-1+x)**(1/2))/x/(-1+x)**(1/2),x)","2 \sqrt{x - 1} + 2 \log{\left(x \right)}"," ",0,"2*sqrt(x - 1) + 2*log(x)","A",0
809,1,60,0,2.419156," ","integrate((a+b*x**(2/3)+c*x**(1/2))**2,x)","a^{2} x + \frac{6 a b x^{\frac{5}{3}}}{5} + \frac{4 a c x^{\frac{3}{2}}}{3} + \frac{3 b^{2} x^{\frac{7}{3}}}{7} + \frac{12 b c x^{\frac{13}{6}}}{13} + \frac{c^{2} x^{2}}{2}"," ",0,"a**2*x + 6*a*b*x**(5/3)/5 + 4*a*c*x**(3/2)/3 + 3*b**2*x**(7/3)/7 + 12*b*c*x**(13/6)/13 + c**2*x**2/2","A",0
810,1,116,0,3.452600," ","integrate((a+b*x**(2/3)+c*x**(1/2))**3,x)","a^{3} x + \frac{9 a^{2} b x^{\frac{5}{3}}}{5} + 2 a^{2} c x^{\frac{3}{2}} + \frac{9 a b^{2} x^{\frac{7}{3}}}{7} + \frac{36 a b c x^{\frac{13}{6}}}{13} + \frac{3 a c^{2} x^{2}}{2} + \frac{b^{3} x^{3}}{3} + \frac{18 b^{2} c x^{\frac{17}{6}}}{17} + \frac{9 b c^{2} x^{\frac{8}{3}}}{8} + \frac{2 c^{3} x^{\frac{5}{2}}}{5}"," ",0,"a**3*x + 9*a**2*b*x**(5/3)/5 + 2*a**2*c*x**(3/2) + 9*a*b**2*x**(7/3)/7 + 36*a*b*c*x**(13/6)/13 + 3*a*c**2*x**2/2 + b**3*x**3/3 + 18*b**2*c*x**(17/6)/17 + 9*b*c**2*x**(8/3)/8 + 2*c**3*x**(5/2)/5","A",0
811,1,70,0,3.182950," ","integrate((x**2-1)/x**3/(a-b+b/x**2)**(1/2),x)","- \frac{\begin{cases} - \frac{1}{\sqrt{a} x^{2}} & \text{for}\: b = 0 \\- \frac{2 \sqrt{a - b + \frac{b}{x^{2}}}}{b} & \text{otherwise} \end{cases}}{2} - \frac{\operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{a - b}} \sqrt{a - b + \frac{b}{x^{2}}}} \right)}}{\sqrt{- \frac{1}{a - b}} \left(a - b\right)}"," ",0,"-Piecewise((-1/(sqrt(a)*x**2), Eq(b, 0)), (-2*sqrt(a - b + b/x**2)/b, True))/2 - atan(1/(sqrt(-1/(a - b))*sqrt(a - b + b/x**2)))/(sqrt(-1/(a - b))*(a - b))","A",0
812,1,70,0,7.025529," ","integrate((x**2-1)/x**3/(a+b*(-1+1/x**2))**(1/2),x)","- \frac{\begin{cases} - \frac{1}{\sqrt{a} x^{2}} & \text{for}\: b = 0 \\- \frac{2 \sqrt{a - b + \frac{b}{x^{2}}}}{b} & \text{otherwise} \end{cases}}{2} - \frac{\operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{a - b}} \sqrt{a - b + \frac{b}{x^{2}}}} \right)}}{\sqrt{- \frac{1}{a - b}} \left(a - b\right)}"," ",0,"-Piecewise((-1/(sqrt(a)*x**2), Eq(b, 0)), (-2*sqrt(a - b + b/x**2)/b, True))/2 - atan(1/(sqrt(-1/(a - b))*sqrt(a - b + b/x**2)))/(sqrt(-1/(a - b))*(a - b))","A",0
813,0,0,0,0.000000," ","integrate((1+x)/(x**2+4)/(x**2+9)**(1/2),x)","\int \frac{x + 1}{\left(x^{2} + 4\right) \sqrt{x^{2} + 9}}\, dx"," ",0,"Integral((x + 1)/((x**2 + 4)*sqrt(x**2 + 9)), x)","F",0
814,1,27,0,0.193604," ","integrate(x*(1+(-x**2+1)**(1/2)),x)","\frac{x^{2} \sqrt{1 - x^{2}}}{3} + \frac{x^{2}}{2} - \frac{\sqrt{1 - x^{2}}}{3}"," ",0,"x**2*sqrt(1 - x**2)/3 + x**2/2 - sqrt(1 - x**2)/3","A",0
815,1,105,0,92.595213," ","integrate(x*(1+(1-x)**(1/2)*(1+x)**(1/2)),x)","- x + \frac{\left(x + 1\right)^{2}}{2} - 2 \left(\begin{cases} \frac{x \sqrt{1 - x} \sqrt{x + 1}}{4} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{2} & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right) + 2 \left(\begin{cases} \frac{x \sqrt{1 - x} \sqrt{x + 1}}{4} - \frac{\left(1 - x\right)^{\frac{3}{2}} \left(x + 1\right)^{\frac{3}{2}}}{6} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{2} & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right) - 1"," ",0,"-x + (x + 1)**2/2 - 2*Piecewise((x*sqrt(1 - x)*sqrt(x + 1)/4 + asin(sqrt(2)*sqrt(x + 1)/2)/2, (x >= -1) & (x < 1))) + 2*Piecewise((x*sqrt(1 - x)*sqrt(x + 1)/4 - (1 - x)**(3/2)*(x + 1)**(3/2)/6 + asin(sqrt(2)*sqrt(x + 1)/2)/2, (x >= -1) & (x < 1))) - 1","A",0
816,0,0,0,0.000000," ","integrate(x*(1+1/(2+x)**(1/2)/(3+x)**(1/2)),x)","\int \frac{x \left(\sqrt{x + 2} \sqrt{x + 3} + 1\right)}{\sqrt{x + 2} \sqrt{x + 3}}\, dx"," ",0,"Integral(x*(sqrt(x + 2)*sqrt(x + 3) + 1)/(sqrt(x + 2)*sqrt(x + 3)), x)","F",0
817,1,2,0,0.105515," ","integrate((x-(x**6)**(1/2))/x/(-x**4+1),x)","\operatorname{atan}{\left(x \right)}"," ",0,"atan(x)","A",0
818,1,2,0,0.102016," ","integrate((1-(x**6)**(1/2)/x)/(-x**4+1),x)","\operatorname{atan}{\left(x \right)}"," ",0,"atan(x)","A",0
819,1,2,0,0.101993," ","integrate((x-(x**6)**(1/2))/(-x**5+x),x)","\operatorname{atan}{\left(x \right)}"," ",0,"atan(x)","A",0
820,1,2,0,0.098842," ","integrate(x/(x+(x**6)**(1/2)),x)","\operatorname{atan}{\left(x \right)}"," ",0,"atan(x)","A",0
821,0,0,0,0.000000," ","integrate((x**(1/2)-(x**3)**(1/2))/(-x**3+x),x)","- \int \frac{\sqrt{x}}{x^{3} - x}\, dx - \int \left(- \frac{\sqrt{x^{3}}}{x^{3} - x}\right)\, dx"," ",0,"-Integral(sqrt(x)/(x**3 - x), x) - Integral(-sqrt(x**3)/(x**3 - x), x)","F",0
822,0,0,0,0.000000," ","integrate(1/(x**(1/2)+(x**3)**(1/2)),x)","\int \frac{1}{\sqrt{x} + \sqrt{x^{3}}}\, dx"," ",0,"Integral(1/(sqrt(x) + sqrt(x**3)), x)","F",0
823,0,0,0,0.000000," ","integrate(1/((-1+x)**(1/2)+((-1+x)**3)**(1/2)),x)","\int \frac{1}{\sqrt{x - 1} + \sqrt{\left(x - 1\right)^{3}}}\, dx"," ",0,"Integral(1/(sqrt(x - 1) + sqrt((x - 1)**3)), x)","F",0
824,0,0,0,0.000000," ","integrate(-3/(4+5*x)**2+(-5-4*x)/(4+5*x)**2/(-x**2+1)**(1/2),x)","- \int \frac{4 x}{25 x^{2} \sqrt{1 - x^{2}} + 40 x \sqrt{1 - x^{2}} + 16 \sqrt{1 - x^{2}}}\, dx - \int \frac{3 \sqrt{1 - x^{2}}}{25 x^{2} \sqrt{1 - x^{2}} + 40 x \sqrt{1 - x^{2}} + 16 \sqrt{1 - x^{2}}}\, dx - \int \frac{5}{25 x^{2} \sqrt{1 - x^{2}} + 40 x \sqrt{1 - x^{2}} + 16 \sqrt{1 - x^{2}}}\, dx"," ",0,"-Integral(4*x/(25*x**2*sqrt(1 - x**2) + 40*x*sqrt(1 - x**2) + 16*sqrt(1 - x**2)), x) - Integral(3*sqrt(1 - x**2)/(25*x**2*sqrt(1 - x**2) + 40*x*sqrt(1 - x**2) + 16*sqrt(1 - x**2)), x) - Integral(5/(25*x**2*sqrt(1 - x**2) + 40*x*sqrt(1 - x**2) + 16*sqrt(1 - x**2)), x)","F",0
825,0,0,0,0.000000," ","integrate((-5-4*x-3*(-x**2+1)**(1/2))/(4+5*x)**2/(-x**2+1)**(1/2),x)","- \int \frac{4 x}{25 x^{2} \sqrt{1 - x^{2}} + 40 x \sqrt{1 - x^{2}} + 16 \sqrt{1 - x^{2}}}\, dx - \int \frac{3 \sqrt{1 - x^{2}}}{25 x^{2} \sqrt{1 - x^{2}} + 40 x \sqrt{1 - x^{2}} + 16 \sqrt{1 - x^{2}}}\, dx - \int \frac{5}{25 x^{2} \sqrt{1 - x^{2}} + 40 x \sqrt{1 - x^{2}} + 16 \sqrt{1 - x^{2}}}\, dx"," ",0,"-Integral(4*x/(25*x**2*sqrt(1 - x**2) + 40*x*sqrt(1 - x**2) + 16*sqrt(1 - x**2)), x) - Integral(3*sqrt(1 - x**2)/(25*x**2*sqrt(1 - x**2) + 40*x*sqrt(1 - x**2) + 16*sqrt(1 - x**2)), x) - Integral(5/(25*x**2*sqrt(1 - x**2) + 40*x*sqrt(1 - x**2) + 16*sqrt(1 - x**2)), x)","F",0
826,0,0,0,0.000000," ","integrate(1/(-3*x**2+3+(-5-4*x)*(-x**2+1)**(1/2)),x)","- \int \frac{1}{3 x^{2} + 4 x \sqrt{1 - x^{2}} + 5 \sqrt{1 - x^{2}} - 3}\, dx"," ",0,"-Integral(1/(3*x**2 + 4*x*sqrt(1 - x**2) + 5*sqrt(1 - x**2) - 3), x)","F",0
827,0,0,0,0.000000," ","integrate(1/(3-3*x**2-5*(-x**2+1)**(1/2)-4*x*(-x**2+1)**(1/2)),x)","- \int \frac{1}{3 x^{2} + 4 x \sqrt{1 - x^{2}} + 5 \sqrt{1 - x^{2}} - 3}\, dx"," ",0,"-Integral(1/(3*x**2 + 4*x*sqrt(1 - x**2) + 5*sqrt(1 - x**2) - 3), x)","F",0
828,0,0,0,0.000000," ","integrate((-1+(-x**2+1)**(1/2))/(2+x-2*(-x**2+1)**(1/2))**2/(-x**2+1)**(1/2),x)","\int \frac{\sqrt{1 - x^{2}} - 1}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x - 2 \sqrt{1 - x^{2}} + 2\right)^{2}}\, dx"," ",0,"Integral((sqrt(1 - x**2) - 1)/(sqrt(-(x - 1)*(x + 1))*(x - 2*sqrt(1 - x**2) + 2)**2), x)","F",0
829,1,212,0,10.183533," ","integrate((a+b*x**(-1+n))/(c*x+d*x**n),x)","\begin{cases} \tilde{\infty} \left(a + b\right) \log{\left(x \right)} & \text{for}\: c = 0 \wedge d = 0 \wedge n = 1 \\\frac{- \frac{a n x}{n^{2} x^{n} - n x^{n}} + \frac{b n^{2} x^{n} \log{\left(x \right)}}{n^{2} x^{n} - n x^{n}} - \frac{b n x^{n} \log{\left(x \right)}}{n^{2} x^{n} - n x^{n}} - \frac{b n x^{n}}{n^{2} x^{n} - n x^{n}}}{d} & \text{for}\: c = 0 \\\frac{\frac{a n x \log{\left(x \right)}}{n x - x} - \frac{a x \log{\left(x \right)}}{n x - x} + \frac{b x^{n}}{n x - x}}{c} & \text{for}\: d = 0 \\\frac{\left(a + b\right) \log{\left(x \right)}}{c + d} & \text{for}\: n = 1 \\\frac{a d n \log{\left(x \right)}}{c d n - c d} - \frac{a d \log{\left(x + \frac{d x^{n}}{c} \right)}}{c d n - c d} - \frac{b c \log{\left(x \right)}}{c d n - c d} + \frac{b c \log{\left(x + \frac{d x^{n}}{c} \right)}}{c d n - c d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(a + b)*log(x), Eq(c, 0) & Eq(d, 0) & Eq(n, 1)), ((-a*n*x/(n**2*x**n - n*x**n) + b*n**2*x**n*log(x)/(n**2*x**n - n*x**n) - b*n*x**n*log(x)/(n**2*x**n - n*x**n) - b*n*x**n/(n**2*x**n - n*x**n))/d, Eq(c, 0)), ((a*n*x*log(x)/(n*x - x) - a*x*log(x)/(n*x - x) + b*x**n/(n*x - x))/c, Eq(d, 0)), ((a + b)*log(x)/(c + d), Eq(n, 1)), (a*d*n*log(x)/(c*d*n - c*d) - a*d*log(x + d*x**n/c)/(c*d*n - c*d) - b*c*log(x)/(c*d*n - c*d) + b*c*log(x + d*x**n/c)/(c*d*n - c*d), True))","A",0
830,0,0,0,0.000000," ","integrate((2*x**2+1)**(1/2)/(1+(2*x**2+1)**(1/2)),x)","\int \frac{\sqrt{2 x^{2} + 1}}{\sqrt{2 x^{2} + 1} + 1}\, dx"," ",0,"Integral(sqrt(2*x**2 + 1)/(sqrt(2*x**2 + 1) + 1), x)","F",0
831,0,0,0,0.000000," ","integrate((4*x**2-1)**(1/2)/(x+(4*x**2-1)**(1/2)),x)","\int \frac{\sqrt{\left(2 x - 1\right) \left(2 x + 1\right)}}{x + \sqrt{4 x^{2} - 1}}\, dx"," ",0,"Integral(sqrt((2*x - 1)*(2*x + 1))/(x + sqrt(4*x**2 - 1)), x)","F",0
832,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**3/(x**2-1)**(1/2),x)","\int \frac{a + b x + c x^{2}}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*x + c*x**2)/(sqrt((x - 1)*(x + 1))*(d + e*x)**3), x)","F",0
833,1,37,0,22.796633," ","integrate((2*x**8+1)/x/(x**8+1)**(3/2),x)","\frac{\log{\left(\sqrt{x^{8} + 1} - 1 \right)}}{8} - \frac{\log{\left(\sqrt{x^{8} + 1} + 1 \right)}}{8} - \frac{1}{4 \sqrt{x^{8} + 1}}"," ",0,"log(sqrt(x**8 + 1) - 1)/8 - log(sqrt(x**8 + 1) + 1)/8 - 1/(4*sqrt(x**8 + 1))","A",0
834,0,0,0,0.000000," ","integrate((2*x**8+1)*(x**8+1)**(1/2)/(x**17+2*x**9+x),x)","\int \frac{2 x^{8} + 1}{x \left(x^{8} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((2*x**8 + 1)/(x*(x**8 + 1)**(3/2)), x)","F",0
835,1,17,0,0.148121," ","integrate(1-9*x**2+x/(-9*x**2+1)**(1/2),x)","- 3 x^{3} + x - \frac{\sqrt{1 - 9 x^{2}}}{9}"," ",0,"-3*x**3 + x - sqrt(1 - 9*x**2)/9","A",0
836,1,17,0,1.170177," ","integrate((x+(-9*x**2+1)**(3/2))/(-9*x**2+1)**(1/2),x)","- 3 x^{3} + x - \frac{\sqrt{1 - 9 x^{2}}}{9}"," ",0,"-3*x**3 + x - sqrt(1 - 9*x**2)/9","A",0
837,1,36,0,1.273045," ","integrate((x-3*x**(1/2))**(2/3)*(-3+2*x**(1/2))/x**(1/2),x)","- \frac{18 \sqrt{x} \left(- 3 \sqrt{x} + x\right)^{\frac{2}{3}}}{5} + \frac{6 x \left(- 3 \sqrt{x} + x\right)^{\frac{2}{3}}}{5}"," ",0,"-18*sqrt(x)*(-3*sqrt(x) + x)**(2/3)/5 + 6*x*(-3*sqrt(x) + x)**(2/3)/5","B",0
838,0,0,0,0.000000," ","integrate((9+2*x-9*x**(1/2))/(x-3*x**(1/2))**(1/3),x)","\int \frac{- 9 \sqrt{x} + 2 x + 9}{\sqrt[3]{- 3 \sqrt{x} + x}}\, dx"," ",0,"Integral((-9*sqrt(x) + 2*x + 9)/(-3*sqrt(x) + x)**(1/3), x)","F",0
839,1,7,0,0.150127," ","integrate(1/(-9*x**2+4)**(1/2),x)","\frac{\operatorname{asin}{\left(\frac{3 x}{2} \right)}}{3}"," ",0,"asin(3*x/2)/3","A",0
840,1,51,0,1.042209," ","integrate(1/(2-3*x)**(1/2)/(2+3*x)**(1/2),x)","\begin{cases} - \frac{2 i \operatorname{acosh}{\left(\frac{\sqrt{3} \sqrt{x + \frac{2}{3}}}{2} \right)}}{3} & \text{for}\: \frac{3 \left|{x + \frac{2}{3}}\right|}{4} > 1 \\\frac{2 \operatorname{asin}{\left(\frac{\sqrt{3} \sqrt{x + \frac{2}{3}}}{2} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(3)*sqrt(x + 2/3)/2)/3, 3*Abs(x + 2/3)/4 > 1), (2*asin(sqrt(3)*sqrt(x + 2/3)/2)/3, True))","B",0
841,1,7,0,1.392991," ","integrate(1/((2-3*x)*(2+3*x))**(1/2),x)","\frac{\operatorname{asin}{\left(\frac{3 x}{2} \right)}}{3}"," ",0,"asin(3*x/2)/3","A",0
842,0,0,0,0.000000," ","integrate(1/(-x**2-2*x+15)**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} - 2 x + 15}}\, dx"," ",0,"Integral(1/sqrt(-x**2 - 2*x + 15), x)","F",0
843,1,41,0,1.022756," ","integrate(1/(3-x)**(1/2)/(5+x)**(1/2),x)","\begin{cases} - 2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 5}}{4} \right)} & \text{for}\: \frac{\left|{x + 5}\right|}{8} > 1 \\2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 5}}{4} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(2)*sqrt(x + 5)/4), Abs(x + 5)/8 > 1), (2*asin(sqrt(2)*sqrt(x + 5)/4), True))","B",0
844,0,0,0,0.000000," ","integrate(1/((3-x)*(5+x))**(1/2),x)","\int \frac{1}{\sqrt{\left(3 - x\right) \left(x + 5\right)}}\, dx"," ",0,"Integral(1/sqrt((3 - x)*(x + 5)), x)","F",0
845,0,0,0,0.000000," ","integrate(1/(-x**2-8*x-15)**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} - 8 x - 15}}\, dx"," ",0,"Integral(1/sqrt(-x**2 - 8*x - 15), x)","F",0
846,1,41,0,1.022341," ","integrate(1/(-3-x)**(1/2)/(5+x)**(1/2),x)","\begin{cases} - 2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 5}}{2} \right)} & \text{for}\: \frac{\left|{x + 5}\right|}{2} > 1 \\2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 5}}{2} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(2)*sqrt(x + 5)/2), Abs(x + 5)/2 > 1), (2*asin(sqrt(2)*sqrt(x + 5)/2), True))","B",0
847,0,0,0,0.000000," ","integrate(1/((-3-x)*(5+x))**(1/2),x)","\int \frac{1}{\sqrt{\left(- x - 3\right) \left(x + 5\right)}}\, dx"," ",0,"Integral(1/sqrt((-x - 3)*(x + 5)), x)","F",0
848,1,8,0,0.058561," ","integrate(1-x**(1/2),x)","- \frac{2 x^{\frac{3}{2}}}{3} + x"," ",0,"-2*x**(3/2)/3 + x","A",0
849,1,8,0,0.151170," ","integrate((1-x)/(1+x**(1/2)),x)","- \frac{2 x^{\frac{3}{2}}}{3} + x"," ",0,"-2*x**(3/2)/3 + x","A",0
850,1,7,0,1.014306," ","integrate((1/(-x**2+1))**(1/2),x)","\begin{cases} \operatorname{asin}{\left(x \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((asin(x), (x > -1) & (x < 1)))","A",0
851,0,0,0,0.000000," ","integrate(((x**2+1)/(-x**4+1))**(1/2),x)","\int \sqrt{\frac{x^{2} + 1}{1 - x^{4}}}\, dx"," ",0,"Integral(sqrt((x**2 + 1)/(1 - x**4)), x)","F",0
852,1,15,0,1.518797," ","integrate((1/(x**2-1))**(1/2),x)","\begin{cases} \log{\left(x + \sqrt{x^{2} - 1} \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((log(x + sqrt(x**2 - 1)), (x > -1) & (x < 1)))","A",0
853,0,0,0,0.000000," ","integrate(((x**2+1)/(x**4-1))**(1/2),x)","\int \sqrt{\frac{x^{2} + 1}{x^{4} - 1}}\, dx"," ",0,"Integral(sqrt((x**2 + 1)/(x**4 - 1)), x)","F",0
854,1,8,0,0.060703," ","integrate(1/(1-x)**(1/2),x)","- 2 \sqrt{1 - x}"," ",0,"-2*sqrt(1 - x)","A",0
855,0,0,0,0.000000," ","integrate((1+x)**(1/2)/(-x**2+1)**(1/2),x)","\int \frac{\sqrt{x + 1}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral(sqrt(x + 1)/sqrt(-(x - 1)*(x + 1)), x)","F",0
856,1,7,0,0.056459," ","integrate(1/(1+x)**(1/2),x)","2 \sqrt{x + 1}"," ",0,"2*sqrt(x + 1)","A",0
857,0,0,0,0.000000," ","integrate((1-x)**(1/2)/(-x**2+1)**(1/2),x)","\int \frac{\sqrt{1 - x}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral(sqrt(1 - x)/sqrt(-(x - 1)*(x + 1)), x)","F",0
858,1,10,0,0.058248," ","integrate((1-x)**(1/2),x)","- \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3}"," ",0,"-2*(1 - x)**(3/2)/3","A",0
859,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(1+x)**(1/2),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}{\sqrt{x + 1}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))/sqrt(x + 1), x)","F",0
860,1,8,0,0.057207," ","integrate((1+x)**(1/2),x)","\frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3}"," ",0,"2*(x + 1)**(3/2)/3","A",0
861,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(1-x)**(1/2),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}{\sqrt{1 - x}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))/sqrt(1 - x), x)","F",0
862,1,97,0,1.618935," ","integrate((2+3*x)**(1/2)/(1+x)**(1/2),x)","\begin{cases} \frac{3 \left(x + 1\right)^{\frac{3}{2}}}{\sqrt{3 x + 2}} - \frac{\sqrt{x + 1}}{\sqrt{3 x + 2}} - \frac{\sqrt{3} \operatorname{acosh}{\left(\sqrt{3} \sqrt{x + 1} \right)}}{3} & \text{for}\: 3 \left|{x + 1}\right| > 1 \\i \sqrt{- 3 x - 2} \sqrt{x + 1} + \frac{\sqrt{3} i \operatorname{asin}{\left(\sqrt{3} \sqrt{x + 1} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*(x + 1)**(3/2)/sqrt(3*x + 2) - sqrt(x + 1)/sqrt(3*x + 2) - sqrt(3)*acosh(sqrt(3)*sqrt(x + 1))/3, 3*Abs(x + 1) > 1), (I*sqrt(-3*x - 2)*sqrt(x + 1) + sqrt(3)*I*asin(sqrt(3)*sqrt(x + 1))/3, True))","A",0
863,0,0,0,0.000000," ","integrate((1-x)**(1/2)*(2+3*x)**(1/2)/(-x**2+1)**(1/2),x)","\int \frac{\sqrt{1 - x} \sqrt{3 x + 2}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral(sqrt(1 - x)*sqrt(3*x + 2)/sqrt(-(x - 1)*(x + 1)), x)","F",0
864,0,0,0,0.000000," ","integrate((1+x)**(3/2)/(1-x)**(3/2)/x,x)","\int \frac{\left(x + 1\right)^{\frac{3}{2}}}{x \left(1 - x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x + 1)**(3/2)/(x*(1 - x)**(3/2)), x)","F",0
865,0,0,0,0.000000," ","integrate((1+x)**3/x/(-x**2+1)**(3/2),x)","\int \frac{\left(x + 1\right)^{3}}{x \left(- \left(x - 1\right) \left(x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x + 1)**3/(x*(-(x - 1)*(x + 1))**(3/2)), x)","F",0
866,0,0,0,0.000000," ","integrate((a*x+1)**(3/2)/x/(-a*x+1)**(3/2),x)","\int \frac{\left(a x + 1\right)^{\frac{3}{2}}}{x \left(- a x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*x + 1)**(3/2)/(x*(-a*x + 1)**(3/2)), x)","F",0
867,0,0,0,0.000000," ","integrate((a*x+1)**3/x/(-a**2*x**2+1)**(3/2),x)","\int \frac{\left(a x + 1\right)^{3}}{x \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*x + 1)**3/(x*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
868,1,2,0,0.141414," ","integrate(1/(-x**2+1)**(1/2),x)","\operatorname{asin}{\left(x \right)}"," ",0,"asin(x)","A",0
869,0,0,0,0.000000," ","integrate((x**2+1)**(1/2)/(-x**4+1)**(1/2),x)","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{- \left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)}}\, dx"," ",0,"Integral(sqrt(x**2 + 1)/sqrt(-(x - 1)*(x + 1)*(x**2 + 1)), x)","F",0
870,1,2,0,0.136754," ","integrate(1/(x**2+1)**(1/2),x)","\operatorname{asinh}{\left(x \right)}"," ",0,"asinh(x)","A",0
871,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(-x**4+1)**(1/2),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))/sqrt(-(x - 1)*(x + 1)*(x**2 + 1)), x)","F",0
872,1,15,0,0.195477," ","integrate((-x**2+1)**(1/2),x)","\frac{x \sqrt{1 - x^{2}}}{2} + \frac{\operatorname{asin}{\left(x \right)}}{2}"," ",0,"x*sqrt(1 - x**2)/2 + asin(x)/2","A",0
873,0,0,0,0.000000," ","integrate((-x**4+1)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)}}{\sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1)*(x**2 + 1))/sqrt(x**2 + 1), x)","F",0
874,1,15,0,0.193650," ","integrate((x**2+1)**(1/2),x)","\frac{x \sqrt{x^{2} + 1}}{2} + \frac{\operatorname{asinh}{\left(x \right)}}{2}"," ",0,"x*sqrt(x**2 + 1)/2 + asinh(x)/2","A",0
875,0,0,0,0.000000," ","integrate((-x**4+1)**(1/2)/(-x**2+1)**(1/2),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1)*(x**2 + 1))/sqrt(-(x - 1)*(x + 1)), x)","F",0
876,0,0,0,0.000000," ","integrate(((c*x**2+a+b)/d)**m,x)","\int \left(\frac{a + b + c x^{2}}{d}\right)^{m}\, dx"," ",0,"Integral(((a + b + c*x**2)/d)**m, x)","F",0
877,1,58,0,0.354019," ","integrate(1/(x-(x**2+1)**(1/2)),x)","- \frac{x \operatorname{asinh}{\left(x \right)}}{2 x - 2 \sqrt{x^{2} + 1}} + \frac{x}{2 x - 2 \sqrt{x^{2} + 1}} + \frac{\sqrt{x^{2} + 1} \operatorname{asinh}{\left(x \right)}}{2 x - 2 \sqrt{x^{2} + 1}}"," ",0,"-x*asinh(x)/(2*x - 2*sqrt(x**2 + 1)) + x/(2*x - 2*sqrt(x**2 + 1)) + sqrt(x**2 + 1)*asinh(x)/(2*x - 2*sqrt(x**2 + 1))","B",0
878,1,17,0,0.168746," ","integrate(1/(x-(-x**2+1)**(1/2)),x)","\frac{\log{\left(x - \sqrt{1 - x^{2}} \right)}}{2} - \frac{\operatorname{asin}{\left(x \right)}}{2}"," ",0,"log(x - sqrt(1 - x**2))/2 - asin(x)/2","A",0
879,1,27,0,0.208349," ","integrate(1/(x-(2*x**2+1)**(1/2)),x)","- \log{\left(x - \sqrt{2 x^{2} + 1} \right)} - \sqrt{2} \operatorname{asinh}{\left(\sqrt{2} x \right)}"," ",0,"-log(x - sqrt(2*x**2 + 1)) - sqrt(2)*asinh(sqrt(2)*x)","A",0
880,0,0,0,0.000000," ","integrate((2*x-x**3+x**2*(-x**2+2)**(1/2))/(2*x**2-2),x)","- \frac{\int \left(- \frac{2 x}{x^{2} - 1}\right)\, dx + \int \frac{x^{3}}{x^{2} - 1}\, dx + \int \left(- \frac{x^{2} \sqrt{2 - x^{2}}}{x^{2} - 1}\right)\, dx}{2}"," ",0,"-(Integral(-2*x/(x**2 - 1), x) + Integral(x**3/(x**2 - 1), x) + Integral(-x**2*sqrt(2 - x**2)/(x**2 - 1), x))/2","F",0
881,0,0,0,0.000000," ","integrate(x*(-x**2+2)**(1/2)/(x-(-x**2+2)**(1/2)),x)","\int \frac{x \sqrt{2 - x^{2}}}{x - \sqrt{2 - x^{2}}}\, dx"," ",0,"Integral(x*sqrt(2 - x**2)/(x - sqrt(2 - x**2)), x)","F",0
882,0,0,0,0.000000," ","integrate(x/(-x+(-x**2+2*x)**(1/2)),x)","- \int \frac{x}{x - \sqrt{- x^{2} + 2 x}}\, dx"," ",0,"-Integral(x/(x - sqrt(-x**2 + 2*x)), x)","F",0
883,0,0,0,0.000000," ","integrate((x+(-x**2+2*x)**(1/2))/(2-2*x),x)","- \frac{\int \frac{x}{x - 1}\, dx + \int \frac{\sqrt{- x^{2} + 2 x}}{x - 1}\, dx}{2}"," ",0,"-(Integral(x/(x - 1), x) + Integral(sqrt(-x**2 + 2*x)/(x - 1), x))/2","F",0
884,0,0,0,0.000000," ","integrate((x+(2-x)**(1/2)*x**(1/2))/(2-2*x),x)","- \frac{\int \frac{x}{x - 1}\, dx + \int \frac{\sqrt{x} \sqrt{2 - x}}{x - 1}\, dx}{2}"," ",0,"-(Integral(x/(x - 1), x) + Integral(sqrt(x)*sqrt(2 - x)/(x - 1), x))/2","F",0
885,0,0,0,0.000000," ","integrate(x**(1/2)/((2-x)**(1/2)-x**(1/2)),x)","\int \frac{\sqrt{x}}{- \sqrt{x} + \sqrt{2 - x}}\, dx"," ",0,"Integral(sqrt(x)/(-sqrt(x) + sqrt(2 - x)), x)","F",0
886,0,0,0,0.000000," ","integrate(1/((1+x)*(x**2-1))**(2/3),x)","\int \frac{1}{\left(\left(x + 1\right) \left(x^{2} - 1\right)\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(((x + 1)*(x**2 - 1))**(-2/3), x)","F",0
887,0,0,0,0.000000," ","integrate((x**2-1)/(x**2+1)/(x*(x**2+1))**(1/2),x)","\int \frac{\left(x - 1\right) \left(x + 1\right)}{\sqrt{x \left(x^{2} + 1\right)} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral((x - 1)*(x + 1)/(sqrt(x*(x**2 + 1))*(x**2 + 1)), x)","F",0
888,0,0,0,0.000000," ","integrate((x**2-1)/(x**2+1)/(x**3+x)**(1/2),x)","\int \frac{\left(x - 1\right) \left(x + 1\right)}{\sqrt{x \left(x^{2} + 1\right)} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral((x - 1)*(x + 1)/(sqrt(x*(x**2 + 1))*(x**2 + 1)), x)","F",0
889,0,0,0,0.000000," ","integrate(((x**2-1)**2/x/(x**2+1))**(1/2)/(x**2+1),x)","\int \frac{\sqrt{\frac{\left(x - 1\right)^{2} \left(x + 1\right)^{2}}{x^{3} + x}}}{x^{2} + 1}\, dx"," ",0,"Integral(sqrt((x - 1)**2*(x + 1)**2/(x**3 + x))/(x**2 + 1), x)","F",0
890,0,0,0,0.000000," ","integrate(((x**2-1)**2/(x**3+x))**(1/2)/(x**2+1),x)","\int \frac{\sqrt{\frac{\left(x - 1\right)^{2} \left(x + 1\right)^{2}}{x^{3} + x}}}{x^{2} + 1}\, dx"," ",0,"Integral(sqrt((x - 1)**2*(x + 1)**2/(x**3 + x))/(x**2 + 1), x)","F",0
891,0,0,0,0.000000," ","integrate(1/(a+b/x**2)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{a + \frac{b}{x^{2}}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b/x**2)*sqrt(c + d*x**2)), x)","F",0
892,0,0,0,0.000000," ","integrate((x**4-2*x**2)**(1/2)/(x**2-1)/(x**2+2),x)","\int \frac{\sqrt{x^{2} \left(x^{2} - 2\right)}}{\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 2\right)}\, dx"," ",0,"Integral(sqrt(x**2*(x**2 - 2))/((x - 1)*(x + 1)*(x**2 + 2)), x)","F",0
893,0,0,0,0.000000," ","integrate((1-1/(x**2-1)**2)**(1/2)/(-x**2+2),x)","- \int \frac{\sqrt{\frac{x^{4}}{x^{4} - 2 x^{2} + 1} - \frac{2 x^{2}}{x^{4} - 2 x^{2} + 1}}}{x^{2} - 2}\, dx"," ",0,"-Integral(sqrt(x**4/(x**4 - 2*x**2 + 1) - 2*x**2/(x**4 - 2*x**2 + 1))/(x**2 - 2), x)","F",0
894,-1,0,0,0.000000," ","integrate(((x**4-2*x**2)/(x**2-1)**2)**(1/2)/(x**2+2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,0,0,0,0.000000," ","integrate((1+2*x/(x**2+1))**(5/2),x)","\int \left(\frac{2 x}{x^{2} + 1} + 1\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((2*x/(x**2 + 1) + 1)**(5/2), x)","F",0
896,0,0,0,0.000000," ","integrate((1+2*x/(x**2+1))**(3/2),x)","\int \left(\frac{2 x}{x^{2} + 1} + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((2*x/(x**2 + 1) + 1)**(3/2), x)","F",0
897,0,0,0,0.000000," ","integrate((1+2*x/(x**2+1))**(1/2),x)","\int \sqrt{\frac{2 x}{x^{2} + 1} + 1}\, dx"," ",0,"Integral(sqrt(2*x/(x**2 + 1) + 1), x)","F",0
898,0,0,0,0.000000," ","integrate(1/(1+2*x/(x**2+1))**(1/2),x)","\int \frac{1}{\sqrt{\frac{2 x}{x^{2} + 1} + 1}}\, dx"," ",0,"Integral(1/sqrt(2*x/(x**2 + 1) + 1), x)","F",0
899,0,0,0,0.000000," ","integrate(1/(1+2*x/(x**2+1))**(3/2),x)","\int \frac{1}{\left(\frac{2 x}{x^{2} + 1} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((2*x/(x**2 + 1) + 1)**(-3/2), x)","F",0
900,0,0,0,0.000000," ","integrate((1+2*x/(x**2+1))**(1/2)/(x**2+1),x)","\int \frac{\sqrt{\frac{\left(x + 1\right)^{2}}{x^{2} + 1}}}{x^{2} + 1}\, dx"," ",0,"Integral(sqrt((x + 1)**2/(x**2 + 1))/(x**2 + 1), x)","F",0
901,0,0,0,0.000000," ","integrate(F(x)*(-x**2+x)**(1/2),x)","\int \sqrt{- x \left(x - 1\right)} F{\left(x \right)}\, dx"," ",0,"Integral(sqrt(-x*(x - 1))*F(x), x)","F",0
902,0,0,0,0.000000," ","integrate(F(x)/(-x**2+x)**(1/2),x)","\int \frac{F{\left(x \right)}}{\sqrt{- x \left(x - 1\right)}}\, dx"," ",0,"Integral(F(x)/sqrt(-x*(x - 1)), x)","F",0
903,0,0,0,0.000000," ","integrate(F(x)*(1-x)**(1/2)*x**(1/2),x)","\int \sqrt{x} \sqrt{1 - x} F{\left(x \right)}\, dx"," ",0,"Integral(sqrt(x)*sqrt(1 - x)*F(x), x)","F",0
904,0,0,0,0.000000," ","integrate(F(x)/(1-x)**(1/2)/x**(1/2),x)","\int \frac{F{\left(x \right)}}{\sqrt{x} \sqrt{1 - x}}\, dx"," ",0,"Integral(F(x)/(sqrt(x)*sqrt(1 - x)), x)","F",0
905,0,0,0,0.000000," ","integrate(F((b*x+a)/x),x)","\int F{\left(\frac{a + b x}{x} \right)}\, dx"," ",0,"Integral(F((a + b*x)/x), x)","F",0
906,0,0,0,0.000000," ","integrate(F((b*x**2+a)/x**2),x)","\int F{\left(\frac{a + b x^{2}}{x^{2}} \right)}\, dx"," ",0,"Integral(F((a + b*x**2)/x**2), x)","F",0
907,0,0,0,0.000000," ","integrate(F(x/(b*x+a)),x)","\int F{\left(\frac{x}{a + b x} \right)}\, dx"," ",0,"Integral(F(x/(a + b*x)), x)","F",0
908,0,0,0,0.000000," ","integrate(F(x**2/(b*x**2+a)),x)","\int F{\left(\frac{x^{2}}{a + b x^{2}} \right)}\, dx"," ",0,"Integral(F(x**2/(a + b*x**2)), x)","F",0
909,0,0,0,0.000000," ","integrate(F(x**2/(b*x+a)**2),x)","\int F{\left(\frac{x^{2}}{\left(a + b x\right)^{2}} \right)}\, dx"," ",0,"Integral(F(x**2/(a + b*x)**2), x)","F",0
910,0,0,0,0.000000," ","integrate(F(x**4/(b*x**2+a)**2),x)","\int F{\left(\frac{x^{4}}{\left(a + b x^{2}\right)^{2}} \right)}\, dx"," ",0,"Integral(F(x**4/(a + b*x**2)**2), x)","F",0
911,0,0,0,0.000000," ","integrate((b*x**2+(b**2*x**4+a)**(1/2))**(1/2)/(b**2*x**4+a)**(1/2),x)","\int \frac{\sqrt{b x^{2} + \sqrt{a + b^{2} x^{4}}}}{\sqrt{a + b^{2} x^{4}}}\, dx"," ",0,"Integral(sqrt(b*x**2 + sqrt(a + b**2*x**4))/sqrt(a + b**2*x**4), x)","F",0
912,0,0,0,0.000000," ","integrate((-b*x**2+(b**2*x**4+a)**(1/2))**(1/2)/(b**2*x**4+a)**(1/2),x)","\int \frac{\sqrt{- b x^{2} + \sqrt{a + b^{2} x^{4}}}}{\sqrt{a + b^{2} x^{4}}}\, dx"," ",0,"Integral(sqrt(-b*x**2 + sqrt(a + b**2*x**4))/sqrt(a + b**2*x**4), x)","F",0
913,0,0,0,0.000000," ","integrate((2*x**2+(4*x**4+3)**(1/2))**(1/2)/(d*x+c)/(4*x**4+3)**(1/2),x)","\int \frac{\sqrt{2 x^{2} + \sqrt{4 x^{4} + 3}}}{\left(c + d x\right) \sqrt{4 x^{4} + 3}}\, dx"," ",0,"Integral(sqrt(2*x**2 + sqrt(4*x**4 + 3))/((c + d*x)*sqrt(4*x**4 + 3)), x)","F",0
914,0,0,0,0.000000," ","integrate((2*x**2+(4*x**4+3)**(1/2))**(1/2)/(d*x+c)**2/(4*x**4+3)**(1/2),x)","\int \frac{\sqrt{2 x^{2} + \sqrt{4 x^{4} + 3}}}{\left(c + d x\right)^{2} \sqrt{4 x^{4} + 3}}\, dx"," ",0,"Integral(sqrt(2*x**2 + sqrt(4*x**4 + 3))/((c + d*x)**2*sqrt(4*x**4 + 3)), x)","F",0
915,1,37,0,11.870126," ","integrate((-4+x)/(1+x**(1/3))/x**(1/2),x)","\frac{6 x^{\frac{7}{6}}}{7} - \frac{6 x^{\frac{5}{6}}}{5} - 30 \sqrt[6]{x} + 2 \sqrt{x} + 30 \operatorname{atan}{\left(\sqrt[6]{x} \right)}"," ",0,"6*x**(7/6)/7 - 6*x**(5/6)/5 - 30*x**(1/6) + 2*sqrt(x) + 30*atan(x**(1/6))","A",0
916,1,24,0,3.662286," ","integrate((1+x**(1/2))/(x**(5/6)+x**(7/6)),x)","3 \sqrt[3]{x} - 3 \log{\left(\sqrt[3]{x} + 1 \right)} + 6 \operatorname{atan}{\left(\sqrt[6]{x} \right)}"," ",0,"3*x**(1/3) - 3*log(x**(1/3) + 1) + 6*atan(x**(1/6))","A",0
917,1,39,0,23.129502," ","integrate((1+x**(1/2))/(1+x**(1/3))/x**(1/2),x)","6 \sqrt[6]{x} + \frac{3 x^{\frac{2}{3}}}{2} - 3 \sqrt[3]{x} + 3 \log{\left(\sqrt[3]{x} + 1 \right)} - 6 \operatorname{atan}{\left(\sqrt[6]{x} \right)}"," ",0,"6*x**(1/6) + 3*x**(2/3)/2 - 3*x**(1/3) + 3*log(x**(1/3) + 1) - 6*atan(x**(1/6))","A",0
918,0,0,0,0.000000," ","integrate((2+b/x**2)**(1/2)/(2*x**2+b),x)","\int \frac{\sqrt{\frac{b}{x^{2}} + 2}}{b + 2 x^{2}}\, dx"," ",0,"Integral(sqrt(b/x**2 + 2)/(b + 2*x**2), x)","F",0
919,0,0,0,0.000000," ","integrate((2-b/x**2)**(1/2)/(2*x**2-b),x)","\int \frac{\sqrt{- \frac{b}{x^{2}} + 2}}{- b + 2 x^{2}}\, dx"," ",0,"Integral(sqrt(-b/x**2 + 2)/(-b + 2*x**2), x)","F",0
920,0,0,0,0.000000," ","integrate((a+c/x**2)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{a + \frac{c}{x^{2}}}}{d + e x}\, dx"," ",0,"Integral(sqrt(a + c/x**2)/(d + e*x), x)","F",0
921,0,0,0,0.000000," ","integrate((a+c/x**2+b/x)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}}}{d + e x}\, dx"," ",0,"Integral(sqrt(a + b/x + c/x**2)/(d + e*x), x)","F",0
922,-1,0,0,0.000000," ","integrate((x**(1/6)+(x**3)**(1/5))/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
923,0,0,0,0.000000," ","integrate((2+x)/(-x**2+4*x)**(1/2),x)","\int \frac{x + 2}{\sqrt{- x \left(x - 4\right)}}\, dx"," ",0,"Integral((x + 2)/sqrt(-x*(x - 4)), x)","F",0
924,1,12,0,0.157893," ","integrate((3+x)/(x**2+6*x)**(1/3),x)","\frac{3 \left(x^{2} + 6 x\right)^{\frac{2}{3}}}{4}"," ",0,"3*(x**2 + 6*x)**(2/3)/4","A",0
925,0,0,0,0.000000," ","integrate((4+x)/(-x**2+6*x)**(3/2),x)","\int \frac{x + 4}{\left(- x \left(x - 6\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x + 4)/(-x*(x - 6))**(3/2), x)","F",0
926,0,0,0,0.000000," ","integrate(1/(1+x)/(x**2+2*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(x + 2\right)} \left(x + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(x*(x + 2))*(x + 1)), x)","F",0
927,0,0,0,0.000000," ","integrate(1/(1+2*x)/(x**2+x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(x + 1\right)} \left(2 x + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(x*(x + 1))*(2*x + 1)), x)","F",0
928,1,10,0,0.139998," ","integrate((-1+x)/(-x**2+2*x)**(1/2),x)","- \sqrt{- x^{2} + 2 x}"," ",0,"-sqrt(-x**2 + 2*x)","A",0
929,0,0,0,0.000000," ","integrate((-x**2+x)**(1/2)/(1+x),x)","\int \frac{\sqrt{- x \left(x - 1\right)}}{x + 1}\, dx"," ",0,"Integral(sqrt(-x*(x - 1))/(x + 1), x)","F",0
930,0,0,0,0.000000," ","integrate((x**(1/4)+x)**(1/2),x)","\int \sqrt{\sqrt[4]{x} + x}\, dx"," ",0,"Integral(sqrt(x**(1/4) + x), x)","F",0
931,0,0,0,0.000000," ","integrate((x+x**(3/2))**(1/2),x)","\int \sqrt{x^{\frac{3}{2}} + x}\, dx"," ",0,"Integral(sqrt(x**(3/2) + x), x)","F",0
932,0,0,0,0.000000," ","integrate(x*(x+x**(3/2))**(1/2),x)","\int x \sqrt{x^{\frac{3}{2}} + x}\, dx"," ",0,"Integral(x*sqrt(x**(3/2) + x), x)","F",0
933,1,26,0,0.497047," ","integrate((-x**2+1)*(1/(-x**2+2))**(1/2),x)","- \frac{x^{3} \sqrt{\frac{1}{2 - x^{2}}}}{2} + x \sqrt{\frac{1}{2 - x^{2}}}"," ",0,"-x**3*sqrt(1/(2 - x**2))/2 + x*sqrt(1/(2 - x**2))","B",0
934,0,0,0,0.000000," ","integrate((-x**4+x**3+x**2)**(1/2),x)","\int \sqrt{- x^{4} + x^{3} + x^{2}}\, dx"," ",0,"Integral(sqrt(-x**4 + x**3 + x**2), x)","F",0
935,0,0,0,0.000000," ","integrate(1/((a**2+x**2)**3)**(1/2),x)","\int \frac{1}{\sqrt{\left(a^{2} + x^{2}\right)^{3}}}\, dx"," ",0,"Integral(1/sqrt((a**2 + x**2)**3), x)","F",0
936,1,49,0,0.247490," ","integrate(x**(1/2)/(1+x+x**(1/2)),x)","2 \sqrt{x} - \log{\left(4 \sqrt{x} + 4 x + 4 \right)} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \sqrt{x}}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"2*sqrt(x) - log(4*sqrt(x) + 4*x + 4) - 2*sqrt(3)*atan(2*sqrt(3)*sqrt(x)/3 + sqrt(3)/3)/3","A",0
937,1,37,0,0.230200," ","integrate(x/(1+x+x**(1/2)),x)","- 2 \sqrt{x} + x + \frac{4 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \sqrt{x}}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-2*sqrt(x) + x + 4*sqrt(3)*atan(2*sqrt(3)*sqrt(x)/3 + sqrt(3)/3)/3","A",0
938,0,0,0,0.000000," ","integrate(1/x**(1/2)/(1+x+x**(1/2))**(7/2),x)","\int \frac{1}{\sqrt{x} \left(\sqrt{x} + x + 1\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(1/(sqrt(x)*(sqrt(x) + x + 1)**(7/2)), x)","F",0
939,1,48,0,2.983840," ","integrate((-1+x)/((x**2+1)**(1/2)+1),x)","\frac{x}{\sqrt{x^{2} + 1}} + \sqrt{x^{2} + 1} - \log{\left(\sqrt{x^{2} + 1} + 1 \right)} - \operatorname{asinh}{\left(x \right)} - \frac{1}{x} + \frac{1}{x \sqrt{x^{2} + 1}}"," ",0,"x/sqrt(x**2 + 1) + sqrt(x**2 + 1) - log(sqrt(x**2 + 1) + 1) - asinh(x) - 1/x + 1/(x*sqrt(x**2 + 1))","A",0
940,0,0,0,0.000000," ","integrate(1/(1+x)**(2/3)/(x**2-1)**(2/3),x)","\int \frac{1}{\left(\left(x - 1\right) \left(x + 1\right)\right)^{\frac{2}{3}} \left(x + 1\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/(((x - 1)*(x + 1))**(2/3)*(x + 1)**(2/3)), x)","F",0
941,1,68,0,1.137224," ","integrate((-x**6+1)**(2/3)+(-x**6+1)**(2/3)/x**6,x)","\frac{x \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {x^{6} e^{2 i \pi}} \right)}}{6 \Gamma\left(\frac{7}{6}\right)} + \frac{\Gamma\left(- \frac{5}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{6}, - \frac{2}{3} \\ \frac{1}{6} \end{matrix}\middle| {x^{6} e^{2 i \pi}} \right)}}{6 x^{5} \Gamma\left(\frac{1}{6}\right)}"," ",0,"x*gamma(1/6)*hyper((-2/3, 1/6), (7/6,), x**6*exp_polar(2*I*pi))/(6*gamma(7/6)) + gamma(-5/6)*hyper((-5/6, -2/3), (1/6,), x**6*exp_polar(2*I*pi))/(6*x**5*gamma(1/6))","C",0
942,1,100,0,98.051635," ","integrate(1/2*x**(-1+m)*(2*a*m+b*(2*m-n)*x**n)/(a+b*x**n)**(3/2),x)","\frac{m x^{m} \Gamma\left(\frac{m}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{n} \\ \frac{m}{n} + 1 \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{\sqrt{a} n \Gamma\left(\frac{m}{n} + 1\right)} + \frac{b x^{m} x^{n} \left(2 m - n\right) \Gamma\left(\frac{m}{n} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{n} + 1 \\ \frac{m}{n} + 2 \end{matrix}\middle| {\frac{b x^{n} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} n \Gamma\left(\frac{m}{n} + 2\right)}"," ",0,"m*x**m*gamma(m/n)*hyper((3/2, m/n), (m/n + 1,), b*x**n*exp_polar(I*pi)/a)/(sqrt(a)*n*gamma(m/n + 1)) + b*x**m*x**n*(2*m - n)*gamma(m/n + 1)*hyper((3/2, m/n + 1), (m/n + 2,), b*x**n*exp_polar(I*pi)/a)/(2*a**(3/2)*n*gamma(m/n + 2))","C",0
943,1,46,0,11.727952," ","integrate((-2*x**3+x)/(2+3*x)**(1/2),x)","- \frac{4 \left(3 x + 2\right)^{\frac{7}{2}}}{567} + \frac{8 \left(3 x + 2\right)^{\frac{5}{2}}}{135} - \frac{10 \left(3 x + 2\right)^{\frac{3}{2}}}{81} - \frac{4 \sqrt{3 x + 2}}{81}"," ",0,"-4*(3*x + 2)**(7/2)/567 + 8*(3*x + 2)**(5/2)/135 - 10*(3*x + 2)**(3/2)/81 - 4*sqrt(3*x + 2)/81","A",0
944,1,27,0,0.239544," ","integrate(1/((1+x)**(1/4)+(1+x)**(1/2)),x)","- 4 \sqrt[4]{x + 1} + 2 \sqrt{x + 1} + 4 \log{\left(\sqrt[4]{x + 1} + 1 \right)}"," ",0,"-4*(x + 1)**(1/4) + 2*sqrt(x + 1) + 4*log((x + 1)**(1/4) + 1)","A",0
945,1,8,0,0.138884," ","integrate((1+2*x)/(x**2+x)**(1/2),x)","2 \sqrt{x^{2} + x}"," ",0,"2*sqrt(x**2 + x)","A",0
946,1,5,0,0.211248," ","integrate(1/2/(1+x)/x**(1/2),x)","\operatorname{atan}{\left(\sqrt{x} \right)}"," ",0,"atan(sqrt(x))","A",0
947,0,0,0,0.000000," ","integrate(1/x/(-x**2+6*x)**(1/2),x)","\int \frac{1}{x \sqrt{- x \left(x - 6\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(-x*(x - 6))), x)","F",0
948,1,12,0,0.138386," ","integrate(x**(1/2)*(1+x**(1/2)),x)","\frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}"," ",0,"2*x**(3/2)/3 + x**2/2","A",0
949,1,15,0,1.528972," ","integrate((1-x**(1/2))/x**(1/3),x)","- \frac{6 x^{\frac{7}{6}}}{7} + \frac{3 x^{\frac{2}{3}}}{2}"," ",0,"-6*x**(7/6)/7 + 3*x**(2/3)/2","A",0
950,1,37,0,3.362508," ","integrate(x**(1/2)/(1+x**(1/3)),x)","\frac{6 x^{\frac{7}{6}}}{7} - \frac{6 x^{\frac{5}{6}}}{5} - 6 \sqrt[6]{x} + 2 \sqrt{x} + 6 \operatorname{atan}{\left(\sqrt[6]{x} \right)}"," ",0,"6*x**(7/6)/7 - 6*x**(5/6)/5 - 6*x**(1/6) + 2*sqrt(x) + 6*atan(x**(1/6))","A",0
951,1,39,0,1.054734," ","integrate((1+x**(1/2))**(1/3)/x,x)","- \frac{2 \sqrt[6]{x} \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{e^{i \pi}}{\sqrt{x}}} \right)}}{\Gamma\left(\frac{2}{3}\right)}"," ",0,"-2*x**(1/6)*gamma(-1/3)*hyper((-1/3, -1/3), (2/3,), exp_polar(I*pi)/sqrt(x))/gamma(2/3)","C",0
952,1,8,0,0.058156," ","integrate(1-x**(1/2),x)","- \frac{2 x^{\frac{3}{2}}}{3} + x"," ",0,"-2*x**(3/2)/3 + x","A",0
953,1,8,0,0.058276," ","integrate(1-x**(1/4),x)","- \frac{4 x^{\frac{5}{4}}}{5} + x"," ",0,"-4*x**(5/4)/5 + x","A",0
954,1,8,0,4.355219," ","integrate((1-x**(1/2))/(1+x**(1/4)),x)","- \frac{4 x^{\frac{5}{4}}}{5} + x"," ",0,"-4*x**(5/4)/5 + x","A",0
955,0,0,0,0.000000," ","integrate(1/((b*x+a)*(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{\left(a + b x\right) \left(c + d x\right)}}\, dx"," ",0,"Integral(1/sqrt((a + b*x)*(c + d*x)), x)","F",0
956,0,0,0,0.000000," ","integrate(1/((b*x+a)*(-d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{\left(a + b x\right) \left(c - d x\right)}}\, dx"," ",0,"Integral(1/sqrt((a + b*x)*(c - d*x)), x)","F",0
957,1,26,0,0.386419," ","integrate(1/(-x**2+1)/x**(1/2),x)","- \frac{\log{\left(\sqrt{x} - 1 \right)}}{2} + \frac{\log{\left(\sqrt{x} + 1 \right)}}{2} + \operatorname{atan}{\left(\sqrt{x} \right)}"," ",0,"-log(sqrt(x) - 1)/2 + log(sqrt(x) + 1)/2 + atan(sqrt(x))","B",0
958,1,26,0,0.535224," ","integrate(x**(1/2)/(-x**3+x),x)","- \frac{\log{\left(\sqrt{x} - 1 \right)}}{2} + \frac{\log{\left(\sqrt{x} + 1 \right)}}{2} + \operatorname{atan}{\left(\sqrt{x} \right)}"," ",0,"-log(sqrt(x) - 1)/2 + log(sqrt(x) + 1)/2 + atan(sqrt(x))","B",0
959,1,202,0,1.547290," ","integrate(x/(2+x**2-3**(1/2)+x*(1+3**(1/2))),x)","\left(\frac{1}{2} - \frac{\sqrt{11 + 64 \sqrt{3}}}{2 \left(-31 + 12 \sqrt{3}\right)}\right) \log{\left(x - \frac{287 \sqrt{3}}{11 + 64 \sqrt{3}} + \left(\frac{1}{2} - \frac{\sqrt{11 + 64 \sqrt{3}}}{2 \left(-31 + 12 \sqrt{3}\right)}\right) \left(\frac{269}{214 + 139 \sqrt{3}} + \frac{459 \sqrt{3}}{214 + 139 \sqrt{3}}\right) + \frac{521}{11 + 64 \sqrt{3}} \right)} + \left(\frac{\sqrt{11 + 64 \sqrt{3}}}{2 \left(-31 + 12 \sqrt{3}\right)} + \frac{1}{2}\right) \log{\left(x - \frac{287 \sqrt{3}}{11 + 64 \sqrt{3}} + \left(\frac{\sqrt{11 + 64 \sqrt{3}}}{2 \left(-31 + 12 \sqrt{3}\right)} + \frac{1}{2}\right) \left(\frac{269}{214 + 139 \sqrt{3}} + \frac{459 \sqrt{3}}{214 + 139 \sqrt{3}}\right) + \frac{521}{11 + 64 \sqrt{3}} \right)}"," ",0,"(1/2 - sqrt(11 + 64*sqrt(3))/(2*(-31 + 12*sqrt(3))))*log(x - 287*sqrt(3)/(11 + 64*sqrt(3)) + (1/2 - sqrt(11 + 64*sqrt(3))/(2*(-31 + 12*sqrt(3))))*(269/(214 + 139*sqrt(3)) + 459*sqrt(3)/(214 + 139*sqrt(3))) + 521/(11 + 64*sqrt(3))) + (sqrt(11 + 64*sqrt(3))/(2*(-31 + 12*sqrt(3))) + 1/2)*log(x - 287*sqrt(3)/(11 + 64*sqrt(3)) + (sqrt(11 + 64*sqrt(3))/(2*(-31 + 12*sqrt(3))) + 1/2)*(269/(214 + 139*sqrt(3)) + 459*sqrt(3)/(214 + 139*sqrt(3))) + 521/(11 + 64*sqrt(3)))","B",0
960,0,0,0,0.000000," ","integrate((x**3+x**2)**(1/2),x)","\int \sqrt{x^{3} + x^{2}}\, dx"," ",0,"Integral(sqrt(x**3 + x**2), x)","F",0
961,0,0,0,0.000000," ","integrate(1/(1+x)/(x**2+2*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(x + 2\right)} \left(x + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(x*(x + 2))*(x + 1)), x)","F",0
962,0,0,0,0.000000," ","integrate(x**(1/2)*(1-x-x**(1/2))**(1/2),x)","\int \sqrt{x} \sqrt{- \sqrt{x} - x + 1}\, dx"," ",0,"Integral(sqrt(x)*sqrt(-sqrt(x) - x + 1), x)","F",0
963,1,184,0,1.165985," ","integrate((1+(-3+x)**(1/2))**(1/3),x)","\frac{12 \left(x - 3\right)^{\frac{7}{2}} \sqrt[3]{\sqrt{x - 3} + 1}}{14 \left(x - 3\right)^{\frac{5}{2}} + 14 \left(x - 3\right)^{2}} - \frac{6 \left(x - 3\right)^{\frac{5}{2}} \sqrt[3]{\sqrt{x - 3} + 1}}{14 \left(x - 3\right)^{\frac{5}{2}} + 14 \left(x - 3\right)^{2}} + \frac{9 \left(x - 3\right)^{\frac{5}{2}}}{14 \left(x - 3\right)^{\frac{5}{2}} + 14 \left(x - 3\right)^{2}} + \frac{15 \left(x - 3\right)^{3} \sqrt[3]{\sqrt{x - 3} + 1}}{14 \left(x - 3\right)^{\frac{5}{2}} + 14 \left(x - 3\right)^{2}} - \frac{9 \left(x - 3\right)^{2} \sqrt[3]{\sqrt{x - 3} + 1}}{14 \left(x - 3\right)^{\frac{5}{2}} + 14 \left(x - 3\right)^{2}} + \frac{9 \left(x - 3\right)^{2}}{14 \left(x - 3\right)^{\frac{5}{2}} + 14 \left(x - 3\right)^{2}}"," ",0,"12*(x - 3)**(7/2)*(sqrt(x - 3) + 1)**(1/3)/(14*(x - 3)**(5/2) + 14*(x - 3)**2) - 6*(x - 3)**(5/2)*(sqrt(x - 3) + 1)**(1/3)/(14*(x - 3)**(5/2) + 14*(x - 3)**2) + 9*(x - 3)**(5/2)/(14*(x - 3)**(5/2) + 14*(x - 3)**2) + 15*(x - 3)**3*(sqrt(x - 3) + 1)**(1/3)/(14*(x - 3)**(5/2) + 14*(x - 3)**2) - 9*(x - 3)**2*(sqrt(x - 3) + 1)**(1/3)/(14*(x - 3)**(5/2) + 14*(x - 3)**2) + 9*(x - 3)**2/(14*(x - 3)**(5/2) + 14*(x - 3)**2)","B",0
964,1,265,0,1.155230," ","integrate(1/(3+(-1+2*x)**(1/2))**(1/2),x)","- \frac{6 \sqrt{6} \left(x - \frac{1}{2}\right)^{\frac{5}{2}} \sqrt{\sqrt{2} \sqrt{x - \frac{1}{2}} + 3}}{3 \sqrt{6} \left(x - \frac{1}{2}\right)^{\frac{5}{2}} + 9 \sqrt{3} \left(x - \frac{1}{2}\right)^{2}} + \frac{36 \sqrt{2} \left(x - \frac{1}{2}\right)^{\frac{5}{2}}}{3 \sqrt{6} \left(x - \frac{1}{2}\right)^{\frac{5}{2}} + 9 \sqrt{3} \left(x - \frac{1}{2}\right)^{2}} + \frac{4 \sqrt{3} \left(x - \frac{1}{2}\right)^{3} \sqrt{\sqrt{2} \sqrt{x - \frac{1}{2}} + 3}}{3 \sqrt{6} \left(x - \frac{1}{2}\right)^{\frac{5}{2}} + 9 \sqrt{3} \left(x - \frac{1}{2}\right)^{2}} - \frac{36 \sqrt{3} \left(x - \frac{1}{2}\right)^{2} \sqrt{\sqrt{2} \sqrt{x - \frac{1}{2}} + 3}}{3 \sqrt{6} \left(x - \frac{1}{2}\right)^{\frac{5}{2}} + 9 \sqrt{3} \left(x - \frac{1}{2}\right)^{2}} + \frac{108 \left(x - \frac{1}{2}\right)^{2}}{3 \sqrt{6} \left(x - \frac{1}{2}\right)^{\frac{5}{2}} + 9 \sqrt{3} \left(x - \frac{1}{2}\right)^{2}}"," ",0,"-6*sqrt(6)*(x - 1/2)**(5/2)*sqrt(sqrt(2)*sqrt(x - 1/2) + 3)/(3*sqrt(6)*(x - 1/2)**(5/2) + 9*sqrt(3)*(x - 1/2)**2) + 36*sqrt(2)*(x - 1/2)**(5/2)/(3*sqrt(6)*(x - 1/2)**(5/2) + 9*sqrt(3)*(x - 1/2)**2) + 4*sqrt(3)*(x - 1/2)**3*sqrt(sqrt(2)*sqrt(x - 1/2) + 3)/(3*sqrt(6)*(x - 1/2)**(5/2) + 9*sqrt(3)*(x - 1/2)**2) - 36*sqrt(3)*(x - 1/2)**2*sqrt(sqrt(2)*sqrt(x - 1/2) + 3)/(3*sqrt(6)*(x - 1/2)**(5/2) + 9*sqrt(3)*(x - 1/2)**2) + 108*(x - 1/2)**2/(3*sqrt(6)*(x - 1/2)**(5/2) + 9*sqrt(3)*(x - 1/2)**2)","B",0
965,1,32,0,1.794800," ","integrate((1-x)**(1/2)/(1+x**(1/2)),x)","i \sqrt{x} \sqrt{x - 1} - 2 i \sqrt{x - 1} + i \operatorname{asinh}{\left(\sqrt{x - 1} \right)}"," ",0,"I*sqrt(x)*sqrt(x - 1) - 2*I*sqrt(x - 1) + I*asinh(sqrt(x - 1))","C",0
966,1,87,0,3.772879," ","integrate((1-x)**(1/2)/(1-x**(1/2)),x)","2 \left(\begin{cases} - \sqrt{1 - x} + \frac{i \operatorname{acosh}{\left(\sqrt{1 - x} \right)}}{2} - \frac{i \left(1 - x\right)^{\frac{3}{2}}}{2 \sqrt{- x}} + \frac{i \sqrt{1 - x}}{2 \sqrt{- x}} & \text{for}\: \left|{x - 1}\right| > 1 \\\frac{\sqrt{x} \sqrt{1 - x}}{2} - \sqrt{1 - x} + \frac{\operatorname{asin}{\left(\sqrt{1 - x} \right)}}{2} & \text{otherwise} \end{cases}\right)"," ",0,"2*Piecewise((-sqrt(1 - x) + I*acosh(sqrt(1 - x))/2 - I*(1 - x)**(3/2)/(2*sqrt(-x)) + I*sqrt(1 - x)/(2*sqrt(-x)), Abs(x - 1) > 1), (sqrt(x)*sqrt(1 - x)/2 - sqrt(1 - x) + asin(sqrt(1 - x))/2, True))","A",0
967,1,56,0,0.370026," ","integrate(x/(x-(x**2+1)**(1/2)),x)","\frac{2 x^{2}}{3 x - 3 \sqrt{x^{2} + 1}} - \frac{x \sqrt{x^{2} + 1}}{3 x - 3 \sqrt{x^{2} + 1}} + \frac{1}{3 x - 3 \sqrt{x^{2} + 1}}"," ",0,"2*x**2/(3*x - 3*sqrt(x**2 + 1)) - x*sqrt(x**2 + 1)/(3*x - 3*sqrt(x**2 + 1)) + 1/(3*x - 3*sqrt(x**2 + 1))","B",0
968,0,0,0,0.000000," ","integrate(x/(x-(-x**2+1)**(1/2)),x)","\int \frac{x}{x - \sqrt{1 - x^{2}}}\, dx"," ",0,"Integral(x/(x - sqrt(1 - x**2)), x)","F",0
969,0,0,0,0.000000," ","integrate(x/(x-(2*x**2+1)**(1/2)),x)","\int \frac{x}{x - \sqrt{2 x^{2} + 1}}\, dx"," ",0,"Integral(x/(x - sqrt(2*x**2 + 1)), x)","F",0
970,0,0,0,0.000000," ","integrate(x**(1/2)*(x+x**(1/2))**(1/2),x)","\int \sqrt{x} \sqrt{\sqrt{x} + x}\, dx"," ",0,"Integral(sqrt(x)*sqrt(sqrt(x) + x), x)","F",0
971,1,155,0,3.776637," ","integrate((1+x**(1/3))/(1+x**(1/2)),x)","\frac{16 x^{\frac{5}{6}} \Gamma\left(\frac{8}{3}\right)}{5 \Gamma\left(\frac{11}{3}\right)} - \frac{8 \sqrt[3]{x} \Gamma\left(\frac{8}{3}\right)}{\Gamma\left(\frac{11}{3}\right)} + 2 \sqrt{x} - 2 \log{\left(\sqrt{x} + 1 \right)} - \frac{16 e^{- \frac{2 i \pi}{3}} \log{\left(- \sqrt[6]{x} e^{\frac{i \pi}{3}} + 1 \right)} \Gamma\left(\frac{8}{3}\right)}{3 \Gamma\left(\frac{11}{3}\right)} - \frac{16 \log{\left(- \sqrt[6]{x} e^{i \pi} + 1 \right)} \Gamma\left(\frac{8}{3}\right)}{3 \Gamma\left(\frac{11}{3}\right)} - \frac{16 e^{\frac{2 i \pi}{3}} \log{\left(- \sqrt[6]{x} e^{\frac{5 i \pi}{3}} + 1 \right)} \Gamma\left(\frac{8}{3}\right)}{3 \Gamma\left(\frac{11}{3}\right)}"," ",0,"16*x**(5/6)*gamma(8/3)/(5*gamma(11/3)) - 8*x**(1/3)*gamma(8/3)/gamma(11/3) + 2*sqrt(x) - 2*log(sqrt(x) + 1) - 16*exp(-2*I*pi/3)*log(-x**(1/6)*exp_polar(I*pi/3) + 1)*gamma(8/3)/(3*gamma(11/3)) - 16*log(-x**(1/6)*exp_polar(I*pi) + 1)*gamma(8/3)/(3*gamma(11/3)) - 16*exp(2*I*pi/3)*log(-x**(1/6)*exp_polar(5*I*pi/3) + 1)*gamma(8/3)/(3*gamma(11/3))","C",0
972,1,221,0,5.432045," ","integrate((1+x**(1/3))/(1+x**(1/4)),x)","\frac{64 x^{\frac{13}{12}} \Gamma\left(\frac{16}{3}\right)}{13 \Gamma\left(\frac{19}{3}\right)} + \frac{64 x^{\frac{7}{12}} \Gamma\left(\frac{16}{3}\right)}{7 \Gamma\left(\frac{19}{3}\right)} + \frac{64 \sqrt[12]{x} \Gamma\left(\frac{16}{3}\right)}{\Gamma\left(\frac{19}{3}\right)} - \frac{32 x^{\frac{5}{6}} \Gamma\left(\frac{16}{3}\right)}{5 \Gamma\left(\frac{19}{3}\right)} + \frac{4 x^{\frac{3}{4}}}{3} + 4 \sqrt[4]{x} - \frac{16 \sqrt[3]{x} \Gamma\left(\frac{16}{3}\right)}{\Gamma\left(\frac{19}{3}\right)} - 2 \sqrt{x} - 4 \log{\left(\sqrt[4]{x} + 1 \right)} + \frac{64 e^{- \frac{i \pi}{3}} \log{\left(- \sqrt[12]{x} e^{\frac{i \pi}{3}} + 1 \right)} \Gamma\left(\frac{16}{3}\right)}{3 \Gamma\left(\frac{19}{3}\right)} - \frac{64 \log{\left(- \sqrt[12]{x} e^{i \pi} + 1 \right)} \Gamma\left(\frac{16}{3}\right)}{3 \Gamma\left(\frac{19}{3}\right)} + \frac{64 e^{\frac{i \pi}{3}} \log{\left(- \sqrt[12]{x} e^{\frac{5 i \pi}{3}} + 1 \right)} \Gamma\left(\frac{16}{3}\right)}{3 \Gamma\left(\frac{19}{3}\right)}"," ",0,"64*x**(13/12)*gamma(16/3)/(13*gamma(19/3)) + 64*x**(7/12)*gamma(16/3)/(7*gamma(19/3)) + 64*x**(1/12)*gamma(16/3)/gamma(19/3) - 32*x**(5/6)*gamma(16/3)/(5*gamma(19/3)) + 4*x**(3/4)/3 + 4*x**(1/4) - 16*x**(1/3)*gamma(16/3)/gamma(19/3) - 2*sqrt(x) - 4*log(x**(1/4) + 1) + 64*exp(-I*pi/3)*log(-x**(1/12)*exp_polar(I*pi/3) + 1)*gamma(16/3)/(3*gamma(19/3)) - 64*log(-x**(1/12)*exp_polar(I*pi) + 1)*gamma(16/3)/(3*gamma(19/3)) + 64*exp(I*pi/3)*log(-x**(1/12)*exp_polar(5*I*pi/3) + 1)*gamma(16/3)/(3*gamma(19/3))","C",0
973,0,0,0,0.000000," ","integrate(x**2/(-1+x**2+(-x**2+1)**(1/2)),x)","\int \frac{x^{2}}{x^{2} + \sqrt{1 - x^{2}} - 1}\, dx"," ",0,"Integral(x**2/(x**2 + sqrt(1 - x**2) - 1), x)","F",0
974,0,0,0,0.000000," ","integrate(((1+x)/x)**(1/2),x)","\int \sqrt{\frac{x + 1}{x}}\, dx"," ",0,"Integral(sqrt((x + 1)/x), x)","F",0
975,0,0,0,0.000000," ","integrate(((1-x)/x)**(1/2),x)","\int \sqrt{\frac{1 - x}{x}}\, dx"," ",0,"Integral(sqrt((1 - x)/x), x)","F",0
976,0,0,0,0.000000," ","integrate(((-1+x)/x)**(1/2),x)","\int \sqrt{\frac{x - 1}{x}}\, dx"," ",0,"Integral(sqrt((x - 1)/x), x)","F",0
977,1,32,0,3.227934," ","integrate(((1+x)/x)**(1/2)/x,x)","- 2 \sqrt{1 + \frac{1}{x}} - \log{\left(\sqrt{1 + \frac{1}{x}} - 1 \right)} + \log{\left(\sqrt{1 + \frac{1}{x}} + 1 \right)}"," ",0,"-2*sqrt(1 + 1/x) - log(sqrt(1 + 1/x) - 1) + log(sqrt(1 + 1/x) + 1)","A",0
978,0,0,0,0.000000," ","integrate((x/(1+x))**(1/2),x)","\int \sqrt{\frac{x}{x + 1}}\, dx"," ",0,"Integral(sqrt(x/(x + 1)), x)","F",0
979,0,0,0,0.000000," ","integrate(1/((-1-x)/x)**(1/2),x)","\int \frac{1}{\sqrt{\frac{- x - 1}{x}}}\, dx"," ",0,"Integral(1/sqrt((-x - 1)/x), x)","F",0
980,0,0,0,0.000000," ","integrate(((4-x)*x)**(1/2),x)","\int \sqrt{x \left(4 - x\right)}\, dx"," ",0,"Integral(sqrt(x*(4 - x)), x)","F",0
981,0,0,0,0.000000," ","integrate(1/((1-x)*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(1 - x\right)}}\, dx"," ",0,"Integral(1/sqrt(x*(1 - x)), x)","F",0
982,0,0,0,0.000000," ","integrate(x/(x*(2+x))**(3/2),x)","\int \frac{x}{\left(x \left(x + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(x*(x + 2))**(3/2), x)","F",0
983,0,0,0,0.000000," ","integrate((1+1/x)**(1/2)/(-x**2+1),x)","- \int \frac{\sqrt{1 + \frac{1}{x}}}{x^{2} - 1}\, dx"," ",0,"-Integral(sqrt(1 + 1/x)/(x**2 - 1), x)","F",0
984,1,15,0,0.579131," ","integrate(1/(1-x**2+5**(1/2)+x**2*5**(1/2)),x)","- \frac{\operatorname{atan}{\left(x \left(\frac{1}{2} - \frac{\sqrt{5}}{2}\right) \right)}}{2}"," ",0,"-atan(x*(1/2 - sqrt(5)/2))/2","A",0
985,0,0,0,0.000000," ","integrate(1/(b*x**2+a*x)**(1/2),x)","\int \frac{1}{\sqrt{a x + b x^{2}}}\, dx"," ",0,"Integral(1/sqrt(a*x + b*x**2), x)","F",0
986,0,0,0,0.000000," ","integrate(1/(x*(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{x \left(a + b x\right)}}\, dx"," ",0,"Integral(1/sqrt(x*(a + b*x)), x)","F",0
987,0,0,0,0.000000," ","integrate(1/((a/x+b)*x**2)**(1/2),x)","\int \frac{1}{\sqrt{x^{2} \left(\frac{a}{x} + b\right)}}\, dx"," ",0,"Integral(1/sqrt(x**2*(a/x + b)), x)","F",0
988,0,0,0,0.000000," ","integrate(1/((a/x**2+b/x)*x**3)**(1/2),x)","\int \frac{1}{\sqrt{x^{3} \left(\frac{a}{x^{2}} + \frac{b}{x}\right)}}\, dx"," ",0,"Integral(1/sqrt(x**3*(a/x**2 + b/x)), x)","F",0
989,0,0,0,0.000000," ","integrate(1/((b*x**3+a*x**2)/x)**(1/2),x)","\int \frac{1}{\sqrt{\frac{a x^{2} + b x^{3}}{x}}}\, dx"," ",0,"Integral(1/sqrt((a*x**2 + b*x**3)/x), x)","F",0
990,0,0,0,0.000000," ","integrate(1/((b*x**4+a*x**3)/x**2)**(1/2),x)","\int \frac{1}{\sqrt{\frac{a x^{3} + b x^{4}}{x^{2}}}}\, dx"," ",0,"Integral(1/sqrt((a*x**3 + b*x**4)/x**2), x)","F",0
991,0,0,0,0.000000," ","integrate(1/(b*c*x**2+a*c*x)**(1/2),x)","\int \frac{1}{\sqrt{a c x + b c x^{2}}}\, dx"," ",0,"Integral(1/sqrt(a*c*x + b*c*x**2), x)","F",0
992,0,0,0,0.000000," ","integrate(1/(c*(b*x**2+a*x))**(1/2),x)","\int \frac{1}{\sqrt{c \left(a x + b x^{2}\right)}}\, dx"," ",0,"Integral(1/sqrt(c*(a*x + b*x**2)), x)","F",0
993,0,0,0,0.000000," ","integrate(1/(c*x*(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{c x \left(a + b x\right)}}\, dx"," ",0,"Integral(1/sqrt(c*x*(a + b*x)), x)","F",0
994,0,0,0,0.000000," ","integrate(1/(c*(a/x+b)*x**2)**(1/2),x)","\int \frac{1}{\sqrt{c x^{2} \left(\frac{a}{x} + b\right)}}\, dx"," ",0,"Integral(1/sqrt(c*x**2*(a/x + b)), x)","F",0
995,0,0,0,0.000000," ","integrate((1-x**2+x*(x**2-1)**(1/2))**(1/2),x)","\int \sqrt{- x^{2} + x \sqrt{x^{2} - 1} + 1}\, dx"," ",0,"Integral(sqrt(-x**2 + x*sqrt(x**2 - 1) + 1), x)","F",0
996,0,0,0,0.000000," ","integrate((-x+x**(1/2)*(1+x)**(1/2))**(1/2)/(1+x)**(1/2),x)","\int \frac{\sqrt{\sqrt{x} \sqrt{x + 1} - x}}{\sqrt{x + 1}}\, dx"," ",0,"Integral(sqrt(sqrt(x)*sqrt(x + 1) - x)/sqrt(x + 1), x)","F",0
997,-1,0,0,0.000000," ","integrate((-x-2*(x**2+1)**(1/2))/(x+x**3+(x**2+1)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
998,0,0,0,0.000000," ","integrate((1+2*x)/(x**2+1)/(x**2+2*x+2)**(1/2),x)","\int \frac{2 x + 1}{\left(x^{2} + 1\right) \sqrt{x^{2} + 2 x + 2}}\, dx"," ",0,"Integral((2*x + 1)/((x**2 + 1)*sqrt(x**2 + 2*x + 2)), x)","F",0
999,0,0,0,0.000000," ","integrate(1/(x**4+1)/(-x**2+(x**4+1)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} + \sqrt{x^{4} + 1}} \left(x^{4} + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(-x**2 + sqrt(x**4 + 1))*(x**4 + 1)), x)","F",0
1000,0,0,0,0.000000," ","integrate(1/(b*x**4+a)/(c*x**2+d*(b*x**4+a)**(1/2))**(1/2),x)","\int \frac{1}{\left(a + b x^{4}\right) \sqrt{c x^{2} + d \sqrt{a + b x^{4}}}}\, dx"," ",0,"Integral(1/((a + b*x**4)*sqrt(c*x**2 + d*sqrt(a + b*x**4))), x)","F",0
1001,0,0,0,0.000000," ","integrate(1/(b*x**4+a)/(-c*x**2+d*(b*x**4+a)**(1/2))**(1/2),x)","\int \frac{1}{\left(a + b x^{4}\right) \sqrt{- c x^{2} + d \sqrt{a + b x^{4}}}}\, dx"," ",0,"Integral(1/((a + b*x**4)*sqrt(-c*x**2 + d*sqrt(a + b*x**4))), x)","F",0
1002,0,0,0,0.000000," ","integrate(x/(b*d**4*x**4+4*b*c*d**3*x**3+6*b*c**2*d**2*x**2+4*b*c**3*d*x+b*c**4+a)**(1/2),x)","\int \frac{x}{\sqrt{a + b c^{4} + 4 b c^{3} d x + 6 b c^{2} d^{2} x^{2} + 4 b c d^{3} x^{3} + b d^{4} x^{4}}}\, dx"," ",0,"Integral(x/sqrt(a + b*c**4 + 4*b*c**3*d*x + 6*b*c**2*d**2*x**2 + 4*b*c*d**3*x**3 + b*d**4*x**4), x)","F",0
1003,0,0,0,0.000000," ","integrate(1/(b*d**4*x**4+4*b*c*d**3*x**3+6*b*c**2*d**2*x**2+4*b*c**3*d*x+b*c**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a + b c^{4} + 4 b c^{3} d x + 6 b c^{2} d^{2} x^{2} + 4 b c d^{3} x^{3} + b d^{4} x^{4}}}\, dx"," ",0,"Integral(1/sqrt(a + b*c**4 + 4*b*c**3*d*x + 6*b*c**2*d**2*x**2 + 4*b*c*d**3*x**3 + b*d**4*x**4), x)","F",0
1004,0,0,0,0.000000," ","integrate((-c*x**4+a)/(c*d*x**4+a*e*x**2+a*d)/(c*x**4+b*x**2+a)**(1/2),x)","- \int \left(- \frac{a}{a d \sqrt{a + b x^{2} + c x^{4}} + a e x^{2} \sqrt{a + b x^{2} + c x^{4}} + c d x^{4} \sqrt{a + b x^{2} + c x^{4}}}\right)\, dx - \int \frac{c x^{4}}{a d \sqrt{a + b x^{2} + c x^{4}} + a e x^{2} \sqrt{a + b x^{2} + c x^{4}} + c d x^{4} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"-Integral(-a/(a*d*sqrt(a + b*x**2 + c*x**4) + a*e*x**2*sqrt(a + b*x**2 + c*x**4) + c*d*x**4*sqrt(a + b*x**2 + c*x**4)), x) - Integral(c*x**4/(a*d*sqrt(a + b*x**2 + c*x**4) + a*e*x**2*sqrt(a + b*x**2 + c*x**4) + c*d*x**4*sqrt(a + b*x**2 + c*x**4)), x)","F",0
1005,0,0,0,0.000000," ","integrate((-c*x**4+a)/(c*d*x**4+a*e*x**2+a*d)/(c*x**4-b*x**2+a)**(1/2),x)","- \int \left(- \frac{a}{a d \sqrt{a - b x^{2} + c x^{4}} + a e x^{2} \sqrt{a - b x^{2} + c x^{4}} + c d x^{4} \sqrt{a - b x^{2} + c x^{4}}}\right)\, dx - \int \frac{c x^{4}}{a d \sqrt{a - b x^{2} + c x^{4}} + a e x^{2} \sqrt{a - b x^{2} + c x^{4}} + c d x^{4} \sqrt{a - b x^{2} + c x^{4}}}\, dx"," ",0,"-Integral(-a/(a*d*sqrt(a - b*x**2 + c*x**4) + a*e*x**2*sqrt(a - b*x**2 + c*x**4) + c*d*x**4*sqrt(a - b*x**2 + c*x**4)), x) - Integral(c*x**4/(a*d*sqrt(a - b*x**2 + c*x**4) + a*e*x**2*sqrt(a - b*x**2 + c*x**4) + c*d*x**4*sqrt(a - b*x**2 + c*x**4)), x)","F",0
1006,0,0,0,0.000000," ","integrate(1/(x**3+8)/(x**2-2*x+5)**(1/2),x)","\int \frac{1}{\left(x + 2\right) \left(x^{2} - 2 x + 4\right) \sqrt{x^{2} - 2 x + 5}}\, dx"," ",0,"Integral(1/((x + 2)*(x**2 - 2*x + 4)*sqrt(x**2 - 2*x + 5)), x)","F",0
1007,1,36,0,0.442360," ","integrate((x**2/(x**2+1))**(1/2),x)","x \sqrt{x^{2}} \sqrt{\frac{1}{x^{2} + 1}} + \frac{\sqrt{x^{2}} \sqrt{\frac{1}{x^{2} + 1}}}{x}"," ",0,"x*sqrt(x**2)*sqrt(1/(x**2 + 1)) + sqrt(x**2)*sqrt(1/(x**2 + 1))/x","B",0
1008,0,0,0,0.000000," ","integrate((x**n/(1+x**n))**(1/2),x)","\int \sqrt{\frac{x^{n}}{x^{n} + 1}}\, dx"," ",0,"Integral(sqrt(x**n/(x**n + 1)), x)","F",0
1009,0,0,0,0.000000," ","integrate((-e*f*x**2+e*f)/(a*d*x**2+b*d*x+a*d)/(a*x**4+b*x**3+c*x**2+b*x+a)**(1/2),x)","- \frac{e f \left(\int \frac{x^{2}}{a x^{2} \sqrt{a x^{4} + a + b x^{3} + b x + c x^{2}} + a \sqrt{a x^{4} + a + b x^{3} + b x + c x^{2}} + b x \sqrt{a x^{4} + a + b x^{3} + b x + c x^{2}}}\, dx + \int \left(- \frac{1}{a x^{2} \sqrt{a x^{4} + a + b x^{3} + b x + c x^{2}} + a \sqrt{a x^{4} + a + b x^{3} + b x + c x^{2}} + b x \sqrt{a x^{4} + a + b x^{3} + b x + c x^{2}}}\right)\, dx\right)}{d}"," ",0,"-e*f*(Integral(x**2/(a*x**2*sqrt(a*x**4 + a + b*x**3 + b*x + c*x**2) + a*sqrt(a*x**4 + a + b*x**3 + b*x + c*x**2) + b*x*sqrt(a*x**4 + a + b*x**3 + b*x + c*x**2)), x) + Integral(-1/(a*x**2*sqrt(a*x**4 + a + b*x**3 + b*x + c*x**2) + a*sqrt(a*x**4 + a + b*x**3 + b*x + c*x**2) + b*x*sqrt(a*x**4 + a + b*x**3 + b*x + c*x**2)), x))/d","F",0
1010,0,0,0,0.000000," ","integrate((-e*f*x**2+e*f)/(-a*d*x**2+b*d*x-a*d)/(-a*x**4+b*x**3+c*x**2+b*x-a)**(1/2),x)","\frac{e f \left(\int \frac{x^{2}}{a x^{2} \sqrt{- a x^{4} - a + b x^{3} + b x + c x^{2}} + a \sqrt{- a x^{4} - a + b x^{3} + b x + c x^{2}} - b x \sqrt{- a x^{4} - a + b x^{3} + b x + c x^{2}}}\, dx + \int \left(- \frac{1}{a x^{2} \sqrt{- a x^{4} - a + b x^{3} + b x + c x^{2}} + a \sqrt{- a x^{4} - a + b x^{3} + b x + c x^{2}} - b x \sqrt{- a x^{4} - a + b x^{3} + b x + c x^{2}}}\right)\, dx\right)}{d}"," ",0,"e*f*(Integral(x**2/(a*x**2*sqrt(-a*x**4 - a + b*x**3 + b*x + c*x**2) + a*sqrt(-a*x**4 - a + b*x**3 + b*x + c*x**2) - b*x*sqrt(-a*x**4 - a + b*x**3 + b*x + c*x**2)), x) + Integral(-1/(a*x**2*sqrt(-a*x**4 - a + b*x**3 + b*x + c*x**2) + a*sqrt(-a*x**4 - a + b*x**3 + b*x + c*x**2) - b*x*sqrt(-a*x**4 - a + b*x**3 + b*x + c*x**2)), x))/d","F",0
1011,0,0,0,0.000000," ","integrate((a*x**2+b*x*(-a/b**2+a**2*x**2/b**2)**(1/2))**(1/2)/x/(-a/b**2+a**2*x**2/b**2)**(1/2),x)","\int \frac{\sqrt{x \left(a x + b \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}}\right)}}{x \sqrt{\frac{a \left(a x^{2} - 1\right)}{b^{2}}}}\, dx"," ",0,"Integral(sqrt(x*(a*x + b*sqrt(a**2*x**2/b**2 - a/b**2)))/(x*sqrt(a*(a*x**2 - 1)/b**2)), x)","F",0
1012,0,0,0,0.000000," ","integrate((-a*x**2+b*x*(a/b**2+a**2*x**2/b**2)**(1/2))**(1/2)/x/(a/b**2+a**2*x**2/b**2)**(1/2),x)","\int \frac{\sqrt{- x \left(a x - b \sqrt{\frac{a^{2} x^{2}}{b^{2}} + \frac{a}{b^{2}}}\right)}}{x \sqrt{\frac{a \left(a x^{2} + 1\right)}{b^{2}}}}\, dx"," ",0,"Integral(sqrt(-x*(a*x - b*sqrt(a**2*x**2/b**2 + a/b**2)))/(x*sqrt(a*(a*x**2 + 1)/b**2)), x)","F",0
1013,0,0,0,0.000000," ","integrate((x*(a*x+(-a/b**2+a**2*x**2/b**2)**(1/2)*b))**(1/2)/x/(-a/b**2+a**2*x**2/b**2)**(1/2),x)","\int \frac{\sqrt{x \left(a x + b \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}}\right)}}{x \sqrt{\frac{a \left(a x^{2} - 1\right)}{b^{2}}}}\, dx"," ",0,"Integral(sqrt(x*(a*x + b*sqrt(a**2*x**2/b**2 - a/b**2)))/(x*sqrt(a*(a*x**2 - 1)/b**2)), x)","F",0
1014,0,0,0,0.000000," ","integrate((x*((a/b**2+a**2*x**2/b**2)**(1/2)*b-a*x))**(1/2)/x/(a/b**2+a**2*x**2/b**2)**(1/2),x)","\int \frac{\sqrt{- x \left(a x - b \sqrt{\frac{a^{2} x^{2}}{b^{2}} + \frac{a}{b^{2}}}\right)}}{x \sqrt{\frac{a \left(a x^{2} + 1\right)}{b^{2}}}}\, dx"," ",0,"Integral(sqrt(-x*(a*x - b*sqrt(a**2*x**2/b**2 + a/b**2)))/(x*sqrt(a*(a*x**2 + 1)/b**2)), x)","F",0
1015,-1,0,0,0.000000," ","integrate((-(-4+x)**(1/2)+x*(-4+x)**(1/2)-4*(-1+x)**(1/2)+x*(-1+x)**(1/2))/(x**2-5*x+4)/(1+(-4+x)**(1/2)+(-1+x)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1016,0,0,0,0.000000," ","integrate(1/x/(x**2+3*x+3)/(x**3+3*x**2+3*x+3)**(1/3),x)","\int \frac{1}{x \left(x^{2} + 3 x + 3\right) \sqrt[3]{x^{3} + 3 x^{2} + 3 x + 3}}\, dx"," ",0,"Integral(1/(x*(x**2 + 3*x + 3)*(x**3 + 3*x**2 + 3*x + 3)**(1/3)), x)","F",0
1017,0,0,0,0.000000," ","integrate((-x**2+1)/(x**2-x+1)/(-x**3+1)**(2/3),x)","- \int \frac{x^{2}}{x^{2} \left(1 - x^{3}\right)^{\frac{2}{3}} - x \left(1 - x^{3}\right)^{\frac{2}{3}} + \left(1 - x^{3}\right)^{\frac{2}{3}}}\, dx - \int \left(- \frac{1}{x^{2} \left(1 - x^{3}\right)^{\frac{2}{3}} - x \left(1 - x^{3}\right)^{\frac{2}{3}} + \left(1 - x^{3}\right)^{\frac{2}{3}}}\right)\, dx"," ",0,"-Integral(x**2/(x**2*(1 - x**3)**(2/3) - x*(1 - x**3)**(2/3) + (1 - x**3)**(2/3)), x) - Integral(-1/(x**2*(1 - x**3)**(2/3) - x*(1 - x**3)**(2/3) + (1 - x**3)**(2/3)), x)","F",0
1018,0,0,0,0.000000," ","integrate(x**2/(x**4+1)/(x**4-1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)} \left(x^{4} + 1\right)}\, dx"," ",0,"Integral(x**2/(sqrt((x - 1)*(x + 1)*(x**2 + 1))*(x**4 + 1)), x)","F",0
1019,0,0,0,0.000000," ","integrate((-c*x**4+a)/(c*d*x**2+a*e)/(e*x**2+d)/(c*x**4+b*x**2+a)**(1/2),x)","- \int \left(- \frac{a}{a d e \sqrt{a + b x^{2} + c x^{4}} + a e^{2} x^{2} \sqrt{a + b x^{2} + c x^{4}} + c d^{2} x^{2} \sqrt{a + b x^{2} + c x^{4}} + c d e x^{4} \sqrt{a + b x^{2} + c x^{4}}}\right)\, dx - \int \frac{c x^{4}}{a d e \sqrt{a + b x^{2} + c x^{4}} + a e^{2} x^{2} \sqrt{a + b x^{2} + c x^{4}} + c d^{2} x^{2} \sqrt{a + b x^{2} + c x^{4}} + c d e x^{4} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"-Integral(-a/(a*d*e*sqrt(a + b*x**2 + c*x**4) + a*e**2*x**2*sqrt(a + b*x**2 + c*x**4) + c*d**2*x**2*sqrt(a + b*x**2 + c*x**4) + c*d*e*x**4*sqrt(a + b*x**2 + c*x**4)), x) - Integral(c*x**4/(a*d*e*sqrt(a + b*x**2 + c*x**4) + a*e**2*x**2*sqrt(a + b*x**2 + c*x**4) + c*d**2*x**2*sqrt(a + b*x**2 + c*x**4) + c*d*e*x**4*sqrt(a + b*x**2 + c*x**4)), x)","F",0
1020,1,0,0,0.058393," ","integrate(x+(-x**2+1)/(1+x),x)","x"," ",0,"x","A",0
1021,0,0,0,0.000000," ","integrate(1/(1/x+(-x**2+1)**(1/2)),x)","\int \frac{x}{x \sqrt{1 - x^{2}} + 1}\, dx"," ",0,"Integral(x/(x*sqrt(1 - x**2) + 1), x)","F",0
1022,0,0,0,0.000000," ","integrate(x*(-x**2+1)**(1/2)/(x-x**3+(-x**2+1)**(1/2)),x)","- \int \frac{x \sqrt{1 - x^{2}}}{x^{3} - x - \sqrt{1 - x^{2}}}\, dx"," ",0,"-Integral(x*sqrt(1 - x**2)/(x**3 - x - sqrt(1 - x**2)), x)","F",0
1023,1,73,0,72.392638," ","integrate((-x**4+1)**n/((x**3+x**2+x+1)**n),x)","\begin{cases} \frac{x \left(1 - x^{4}\right)^{n}}{n \left(x^{3} + x^{2} + x + 1\right)^{n} + \left(x^{3} + x^{2} + x + 1\right)^{n}} - \frac{\left(1 - x^{4}\right)^{n}}{n \left(x^{3} + x^{2} + x + 1\right)^{n} + \left(x^{3} + x^{2} + x + 1\right)^{n}} & \text{for}\: n \neq -1 \\- \log{\left(x - 1 \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(1 - x**4)**n/(n*(x**3 + x**2 + x + 1)**n + (x**3 + x**2 + x + 1)**n) - (1 - x**4)**n/(n*(x**3 + x**2 + x + 1)**n + (x**3 + x**2 + x + 1)**n), Ne(n, -1)), (-log(x - 1), True))","A",0
1024,0,0,0,0.000000," ","integrate(x/(5308416*c**4*x**4+576000*b**2*c**2*x**2+576000*b**3*c*x-44375*b**4)**(1/2),x)","\int \frac{x}{\sqrt{- 44375 b^{4} + 576000 b^{3} c x + 576000 b^{2} c^{2} x^{2} + 5308416 c^{4} x^{4}}}\, dx"," ",0,"Integral(x/sqrt(-44375*b**4 + 576000*b**3*c*x + 576000*b**2*c**2*x**2 + 5308416*c**4*x**4), x)","F",0
1025,0,0,0,0.000000," ","integrate((1+4*x)/(64*x**4+64*x**3+64*x**2+120*x+9)**(1/2),x)","\int \frac{4 x + 1}{\sqrt{64 x^{4} + 64 x^{3} + 64 x^{2} + 120 x + 9}}\, dx"," ",0,"Integral((4*x + 1)/sqrt(64*x**4 + 64*x**3 + 64*x**2 + 120*x + 9), x)","F",0
