1,1,109,0,0.691398," ","integrate((d*x**2+c)/(b*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} b^{3} + 64 t^{2} a^{2} b^{2} c d + a^{2} d^{4} + 2 a b c^{2} d^{2} + b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a^{3} b^{2} d + 12 t a^{2} b c d^{2} - 4 t a b^{2} c^{3}}{a^{2} d^{4} - b^{2} c^{4}} \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*b**3 + 64*_t**2*a**2*b**2*c*d + a**2*d**4 + 2*a*b*c**2*d**2 + b**2*c**4, Lambda(_t, _t*log(x + (64*_t**3*a**3*b**2*d + 12*_t*a**2*b*c*d**2 - 4*_t*a*b**2*c**3)/(a**2*d**4 - b**2*c**4))))","A",0
2,1,110,0,0.679667," ","integrate((-d*x**2+c)/(b*x**4+a),x)","- \operatorname{RootSum} {\left(256 t^{4} a^{3} b^{3} - 64 t^{2} a^{2} b^{2} c d + a^{2} d^{4} + 2 a b c^{2} d^{2} + b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a^{3} b^{2} d - 12 t a^{2} b c d^{2} + 4 t a b^{2} c^{3}}{a^{2} d^{4} - b^{2} c^{4}} \right)} \right)\right)}"," ",0,"-RootSum(256*_t**4*a**3*b**3 - 64*_t**2*a**2*b**2*c*d + a**2*d**4 + 2*a*b*c**2*d**2 + b**2*c**4, Lambda(_t, _t*log(x + (64*_t**3*a**3*b**2*d - 12*_t*a**2*b*c*d**2 + 4*_t*a*b**2*c**3)/(a**2*d**4 - b**2*c**4))))","A",0
3,1,110,0,0.726390," ","integrate((d*x**2+c)/(-b*x**4+a),x)","- \operatorname{RootSum} {\left(256 t^{4} a^{3} b^{3} - 64 t^{2} a^{2} b^{2} c d - a^{2} d^{4} + 2 a b c^{2} d^{2} - b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{3} b^{2} d + 12 t a^{2} b c d^{2} + 4 t a b^{2} c^{3}}{a^{2} d^{4} - b^{2} c^{4}} \right)} \right)\right)}"," ",0,"-RootSum(256*_t**4*a**3*b**3 - 64*_t**2*a**2*b**2*c*d - a**2*d**4 + 2*a*b*c**2*d**2 - b**2*c**4, Lambda(_t, _t*log(x + (-64*_t**3*a**3*b**2*d + 12*_t*a**2*b*c*d**2 + 4*_t*a*b**2*c**3)/(a**2*d**4 - b**2*c**4))))","A",0
4,1,110,0,0.942972," ","integrate((-d*x**2+c)/(-b*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} b^{3} + 64 t^{2} a^{2} b^{2} c d - a^{2} d^{4} + 2 a b c^{2} d^{2} - b^{2} c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{3} b^{2} d - 12 t a^{2} b c d^{2} - 4 t a b^{2} c^{3}}{a^{2} d^{4} - b^{2} c^{4}} \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*b**3 + 64*_t**2*a**2*b**2*c*d - a**2*d**4 + 2*a*b*c**2*d**2 - b**2*c**4, Lambda(_t, _t*log(x + (-64*_t**3*a**3*b**2*d - 12*_t*a**2*b*c*d**2 - 4*_t*a*b**2*c**3)/(a**2*d**4 - b**2*c**4))))","A",0
5,1,41,0,0.124481," ","integrate((3*x**2+2)/(9*x**4+4),x)","\frac{\sqrt{3} \left(2 \operatorname{atan}{\left(\frac{\sqrt{3} x}{2} \right)} + 2 \operatorname{atan}{\left(\frac{3 \sqrt{3} x^{3}}{4} + \frac{\sqrt{3} x}{2} \right)}\right)}{12}"," ",0,"sqrt(3)*(2*atan(sqrt(3)*x/2) + 2*atan(3*sqrt(3)*x**3/4 + sqrt(3)*x/2))/12","A",0
6,1,49,0,0.124724," ","integrate((-3*x**2+2)/(9*x**4+4),x)","- \frac{\sqrt{3} \log{\left(x^{2} - \frac{2 \sqrt{3} x}{3} + \frac{2}{3} \right)}}{12} + \frac{\sqrt{3} \log{\left(x^{2} + \frac{2 \sqrt{3} x}{3} + \frac{2}{3} \right)}}{12}"," ",0,"-sqrt(3)*log(x**2 - 2*sqrt(3)*x/3 + 2/3)/12 + sqrt(3)*log(x**2 + 2*sqrt(3)*x/3 + 2/3)/12","A",0
7,1,32,0,0.114567," ","integrate((3*x**2+2)/(-9*x**4+4),x)","- \frac{\sqrt{6} \log{\left(x - \frac{\sqrt{6}}{3} \right)}}{12} + \frac{\sqrt{6} \log{\left(x + \frac{\sqrt{6}}{3} \right)}}{12}"," ",0,"-sqrt(6)*log(x - sqrt(6)/3)/12 + sqrt(6)*log(x + sqrt(6)/3)/12","B",0
8,1,15,0,0.112767," ","integrate((-3*x**2+2)/(-9*x**4+4),x)","\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{2} \right)}}{6}"," ",0,"sqrt(6)*atan(sqrt(6)*x/2)/6","A",0
9,1,138,0,0.393834," ","integrate((b*x**2+a**(1/2)*b**(1/2))/(b*x**4+a),x)","- \frac{\sqrt{2} \sqrt{- \frac{\sqrt{b}}{\sqrt{a}}} \log{\left(- \frac{\sqrt{2} \sqrt{a} x \sqrt{- \frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{b}} - \frac{\sqrt{a}}{\sqrt{b}} + x^{2} \right)}}{4} + \frac{\sqrt{2} \sqrt{- \frac{\sqrt{b}}{\sqrt{a}}} \log{\left(\frac{\sqrt{2} \sqrt{a} x \sqrt{- \frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{b}} - \frac{\sqrt{a}}{\sqrt{b}} + x^{2} \right)}}{4}"," ",0,"-sqrt(2)*sqrt(-sqrt(b)/sqrt(a))*log(-sqrt(2)*sqrt(a)*x*sqrt(-sqrt(b)/sqrt(a))/sqrt(b) - sqrt(a)/sqrt(b) + x**2)/4 + sqrt(2)*sqrt(-sqrt(b)/sqrt(a))*log(sqrt(2)*sqrt(a)*x*sqrt(-sqrt(b)/sqrt(a))/sqrt(b) - sqrt(a)/sqrt(b) + x**2)/4","A",0
10,1,131,0,0.457351," ","integrate((-b*x**2+a**(1/2)*b**(1/2))/(b*x**4+a),x)","- \frac{\sqrt{2} \sqrt{\frac{\sqrt{b}}{\sqrt{a}}} \log{\left(- \frac{\sqrt{2} \sqrt{a} x \sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{b}} + \frac{\sqrt{a}}{\sqrt{b}} + x^{2} \right)}}{4} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{b}}{\sqrt{a}}} \log{\left(\frac{\sqrt{2} \sqrt{a} x \sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{b}} + \frac{\sqrt{a}}{\sqrt{b}} + x^{2} \right)}}{4}"," ",0,"-sqrt(2)*sqrt(sqrt(b)/sqrt(a))*log(-sqrt(2)*sqrt(a)*x*sqrt(sqrt(b)/sqrt(a))/sqrt(b) + sqrt(a)/sqrt(b) + x**2)/4 + sqrt(2)*sqrt(sqrt(b)/sqrt(a))*log(sqrt(2)*sqrt(a)*x*sqrt(sqrt(b)/sqrt(a))/sqrt(b) + sqrt(a)/sqrt(b) + x**2)/4","A",0
11,1,87,0,0.223426," ","integrate((e*x**2+d)/(e**2*x**4+d**2),x)","- \frac{\sqrt{2} \sqrt{- \frac{1}{d e}} \log{\left(- \sqrt{2} d x \sqrt{- \frac{1}{d e}} - \frac{d}{e} + x^{2} \right)}}{4} + \frac{\sqrt{2} \sqrt{- \frac{1}{d e}} \log{\left(\sqrt{2} d x \sqrt{- \frac{1}{d e}} - \frac{d}{e} + x^{2} \right)}}{4}"," ",0,"-sqrt(2)*sqrt(-1/(d*e))*log(-sqrt(2)*d*x*sqrt(-1/(d*e)) - d/e + x**2)/4 + sqrt(2)*sqrt(-1/(d*e))*log(sqrt(2)*d*x*sqrt(-1/(d*e)) - d/e + x**2)/4","A",0
12,1,80,0,0.233946," ","integrate((-e*x**2+d)/(e**2*x**4+d**2),x)","- \frac{\sqrt{2} \sqrt{\frac{1}{d e}} \log{\left(- \sqrt{2} d x \sqrt{\frac{1}{d e}} + \frac{d}{e} + x^{2} \right)}}{4} + \frac{\sqrt{2} \sqrt{\frac{1}{d e}} \log{\left(\sqrt{2} d x \sqrt{\frac{1}{d e}} + \frac{d}{e} + x^{2} \right)}}{4}"," ",0,"-sqrt(2)*sqrt(1/(d*e))*log(-sqrt(2)*d*x*sqrt(1/(d*e)) + d/e + x**2)/4 + sqrt(2)*sqrt(1/(d*e))*log(sqrt(2)*d*x*sqrt(1/(d*e)) + d/e + x**2)/4","A",0
13,1,22,0,0.196518," ","integrate((2*x**2+5)/(x**4-1),x)","\frac{7 \log{\left(x - 1 \right)}}{4} - \frac{7 \log{\left(x + 1 \right)}}{4} - \frac{3 \operatorname{atan}{\left(x \right)}}{2}"," ",0,"7*log(x - 1)/4 - 7*log(x + 1)/4 - 3*atan(x)/2","A",0
14,1,70,0,2.551612," ","integrate((b*x**2+1)/(-b**2*x**4+1)**(1/2),x)","\frac{b 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| {b^{2} x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \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| {b^{2} x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"b*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b**2*x**4*exp_polar(2*I*pi))/(4*gamma(7/4)) + x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b**2*x**4*exp_polar(2*I*pi))/(4*gamma(5/4))","B",0
15,1,70,0,2.927097," ","integrate((-b*x**2+1)/(-b**2*x**4+1)**(1/2),x)","- \frac{b 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| {b^{2} x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \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| {b^{2} x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-b*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b**2*x**4*exp_polar(2*I*pi))/(4*gamma(7/4)) + x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b**2*x**4*exp_polar(2*I*pi))/(4*gamma(5/4))","B",0
16,1,61,0,2.316827," ","integrate((b*x**2+1)/(b**2*x**4-1)**(1/2),x)","- \frac{i b 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| {b^{2} x^{4}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} - \frac{i 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| {b^{2} x^{4}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-I*b*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b**2*x**4)/(4*gamma(7/4)) - I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b**2*x**4)/(4*gamma(5/4))","A",0
17,1,60,0,2.190377," ","integrate((-b*x**2+1)/(b**2*x**4-1)**(1/2),x)","\frac{i b 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| {b^{2} x^{4}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} - \frac{i 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| {b^{2} x^{4}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"I*b*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b**2*x**4)/(4*gamma(7/4)) - I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b**2*x**4)/(4*gamma(5/4))","A",0
18,1,66,0,2.200220," ","integrate((-b*x**2+1)/(b**2*x**4+1)**(1/2),x)","- \frac{b 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| {b^{2} x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \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| {b^{2} x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-b*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b**2*x**4*exp_polar(I*pi))/(4*gamma(7/4)) + x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b**2*x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
19,1,66,0,2.602723," ","integrate((b*x**2+1)/(b**2*x**4+1)**(1/2),x)","\frac{b 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| {b^{2} x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \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| {b^{2} x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"b*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b**2*x**4*exp_polar(I*pi))/(4*gamma(7/4)) + x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b**2*x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
20,1,70,0,2.098290," ","integrate((-b*x**2+1)/(-b**2*x**4-1)**(1/2),x)","\frac{i b 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| {b^{2} x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} - \frac{i 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| {b^{2} x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"I*b*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b**2*x**4*exp_polar(I*pi))/(4*gamma(7/4)) - I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b**2*x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
21,1,71,0,2.057253," ","integrate((b*x**2+1)/(-b**2*x**4-1)**(1/2),x)","- \frac{i b 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| {b^{2} x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} - \frac{i 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| {b^{2} x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-I*b*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b**2*x**4*exp_polar(I*pi))/(4*gamma(7/4)) - I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b**2*x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
22,0,0,0,0.000000," ","integrate((c**2*x**2+1)**(1/2)/(-c**2*x**2+1)**(1/2),x)","\int \frac{\sqrt{c^{2} x^{2} + 1}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral(sqrt(c**2*x**2 + 1)/sqrt(-(c*x - 1)*(c*x + 1)), x)","F",0
23,1,71,0,2.048401," ","integrate((c**2*x**2+1)/(-c**4*x**4+1)**(1/2),x)","\frac{c^{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| {c^{4} x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \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| {c^{4} x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"c**2*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c**4*x**4*exp_polar(2*I*pi))/(4*gamma(7/4)) + x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c**4*x**4*exp_polar(2*I*pi))/(4*gamma(5/4))","B",0
24,0,0,0,0.000000," ","integrate((-c**2*x**2+1)**(1/2)/(c**2*x**2+1)**(1/2),x)","\int \frac{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}{\sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(-(c*x - 1)*(c*x + 1))/sqrt(c**2*x**2 + 1), x)","F",0
25,1,71,0,2.030591," ","integrate((-c**2*x**2+1)/(-c**4*x**4+1)**(1/2),x)","- \frac{c^{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| {c^{4} x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \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| {c^{4} x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-c**2*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c**4*x**4*exp_polar(2*I*pi))/(4*gamma(7/4)) + x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c**4*x**4*exp_polar(2*I*pi))/(4*gamma(5/4))","B",0
26,1,122,0,0.537686," ","integrate((e*x**2+d)/(e**2*x**4+b*x**2+d**2),x)","- \frac{\sqrt{- \frac{1}{b + 2 d e}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(- b \sqrt{- \frac{1}{b + 2 d e}} - 2 d e \sqrt{- \frac{1}{b + 2 d e}}\right)}{e} \right)}}{2} + \frac{\sqrt{- \frac{1}{b + 2 d e}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(b \sqrt{- \frac{1}{b + 2 d e}} + 2 d e \sqrt{- \frac{1}{b + 2 d e}}\right)}{e} \right)}}{2}"," ",0,"-sqrt(-1/(b + 2*d*e))*log(-d/e + x**2 + x*(-b*sqrt(-1/(b + 2*d*e)) - 2*d*e*sqrt(-1/(b + 2*d*e)))/e)/2 + sqrt(-1/(b + 2*d*e))*log(-d/e + x**2 + x*(b*sqrt(-1/(b + 2*d*e)) + 2*d*e*sqrt(-1/(b + 2*d*e)))/e)/2","A",0
27,1,122,0,0.561463," ","integrate((e*x**2+d)/(e**2*x**4+f*x**2+d**2),x)","- \frac{\sqrt{- \frac{1}{2 d e + f}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(- 2 d e \sqrt{- \frac{1}{2 d e + f}} - f \sqrt{- \frac{1}{2 d e + f}}\right)}{e} \right)}}{2} + \frac{\sqrt{- \frac{1}{2 d e + f}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(2 d e \sqrt{- \frac{1}{2 d e + f}} + f \sqrt{- \frac{1}{2 d e + f}}\right)}{e} \right)}}{2}"," ",0,"-sqrt(-1/(2*d*e + f))*log(-d/e + x**2 + x*(-2*d*e*sqrt(-1/(2*d*e + f)) - f*sqrt(-1/(2*d*e + f)))/e)/2 + sqrt(-1/(2*d*e + f))*log(-d/e + x**2 + x*(2*d*e*sqrt(-1/(2*d*e + f)) + f*sqrt(-1/(2*d*e + f)))/e)/2","A",0
28,1,110,0,0.572371," ","integrate((e*x**2+d)/(e**2*x**4-b*x**2+d**2),x)","\frac{\sqrt{\frac{1}{b - 2 d e}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(- b \sqrt{\frac{1}{b - 2 d e}} + 2 d e \sqrt{\frac{1}{b - 2 d e}}\right)}{e} \right)}}{2} - \frac{\sqrt{\frac{1}{b - 2 d e}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(b \sqrt{\frac{1}{b - 2 d e}} - 2 d e \sqrt{\frac{1}{b - 2 d e}}\right)}{e} \right)}}{2}"," ",0,"sqrt(1/(b - 2*d*e))*log(-d/e + x**2 + x*(-b*sqrt(1/(b - 2*d*e)) + 2*d*e*sqrt(1/(b - 2*d*e)))/e)/2 - sqrt(1/(b - 2*d*e))*log(-d/e + x**2 + x*(b*sqrt(1/(b - 2*d*e)) - 2*d*e*sqrt(1/(b - 2*d*e)))/e)/2","A",0
29,1,121,0,0.549502," ","integrate((e*x**2+d)/(e**2*x**4-f*x**2+d**2),x)","- \frac{\sqrt{- \frac{1}{2 d e - f}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(- 2 d e \sqrt{- \frac{1}{2 d e - f}} + f \sqrt{- \frac{1}{2 d e - f}}\right)}{e} \right)}}{2} + \frac{\sqrt{- \frac{1}{2 d e - f}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(2 d e \sqrt{- \frac{1}{2 d e - f}} - f \sqrt{- \frac{1}{2 d e - f}}\right)}{e} \right)}}{2}"," ",0,"-sqrt(-1/(2*d*e - f))*log(-d/e + x**2 + x*(-2*d*e*sqrt(-1/(2*d*e - f)) + f*sqrt(-1/(2*d*e - f)))/e)/2 + sqrt(-1/(2*d*e - f))*log(-d/e + x**2 + x*(2*d*e*sqrt(-1/(2*d*e - f)) - f*sqrt(-1/(2*d*e - f)))/e)/2","A",0
30,1,121,0,0.583227," ","integrate((-e*x**2+d)/(e**2*x**4+b*x**2+d**2),x)","\frac{\sqrt{- \frac{1}{b - 2 d e}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(- b \sqrt{- \frac{1}{b - 2 d e}} + 2 d e \sqrt{- \frac{1}{b - 2 d e}}\right)}{e} \right)}}{2} - \frac{\sqrt{- \frac{1}{b - 2 d e}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(b \sqrt{- \frac{1}{b - 2 d e}} - 2 d e \sqrt{- \frac{1}{b - 2 d e}}\right)}{e} \right)}}{2}"," ",0,"sqrt(-1/(b - 2*d*e))*log(d/e + x**2 + x*(-b*sqrt(-1/(b - 2*d*e)) + 2*d*e*sqrt(-1/(b - 2*d*e)))/e)/2 - sqrt(-1/(b - 2*d*e))*log(d/e + x**2 + x*(b*sqrt(-1/(b - 2*d*e)) - 2*d*e*sqrt(-1/(b - 2*d*e)))/e)/2","A",0
31,1,110,0,0.568137," ","integrate((-e*x**2+d)/(e**2*x**4+f*x**2+d**2),x)","- \frac{\sqrt{\frac{1}{2 d e - f}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(- 2 d e \sqrt{\frac{1}{2 d e - f}} + f \sqrt{\frac{1}{2 d e - f}}\right)}{e} \right)}}{2} + \frac{\sqrt{\frac{1}{2 d e - f}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(2 d e \sqrt{\frac{1}{2 d e - f}} - f \sqrt{\frac{1}{2 d e - f}}\right)}{e} \right)}}{2}"," ",0,"-sqrt(1/(2*d*e - f))*log(d/e + x**2 + x*(-2*d*e*sqrt(1/(2*d*e - f)) + f*sqrt(1/(2*d*e - f)))/e)/2 + sqrt(1/(2*d*e - f))*log(d/e + x**2 + x*(2*d*e*sqrt(1/(2*d*e - f)) - f*sqrt(1/(2*d*e - f)))/e)/2","A",0
32,1,112,0,0.598430," ","integrate((-e*x**2+d)/(e**2*x**4-b*x**2+d**2),x)","- \frac{\sqrt{\frac{1}{b + 2 d e}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(- b \sqrt{\frac{1}{b + 2 d e}} - 2 d e \sqrt{\frac{1}{b + 2 d e}}\right)}{e} \right)}}{2} + \frac{\sqrt{\frac{1}{b + 2 d e}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(b \sqrt{\frac{1}{b + 2 d e}} + 2 d e \sqrt{\frac{1}{b + 2 d e}}\right)}{e} \right)}}{2}"," ",0,"-sqrt(1/(b + 2*d*e))*log(d/e + x**2 + x*(-b*sqrt(1/(b + 2*d*e)) - 2*d*e*sqrt(1/(b + 2*d*e)))/e)/2 + sqrt(1/(b + 2*d*e))*log(d/e + x**2 + x*(b*sqrt(1/(b + 2*d*e)) + 2*d*e*sqrt(1/(b + 2*d*e)))/e)/2","A",0
33,1,112,0,0.609262," ","integrate((-e*x**2+d)/(e**2*x**4-f*x**2+d**2),x)","- \frac{\sqrt{\frac{1}{2 d e + f}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(- 2 d e \sqrt{\frac{1}{2 d e + f}} - f \sqrt{\frac{1}{2 d e + f}}\right)}{e} \right)}}{2} + \frac{\sqrt{\frac{1}{2 d e + f}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(2 d e \sqrt{\frac{1}{2 d e + f}} + f \sqrt{\frac{1}{2 d e + f}}\right)}{e} \right)}}{2}"," ",0,"-sqrt(1/(2*d*e + f))*log(d/e + x**2 + x*(-2*d*e*sqrt(1/(2*d*e + f)) - f*sqrt(1/(2*d*e + f)))/e)/2 + sqrt(1/(2*d*e + f))*log(d/e + x**2 + x*(2*d*e*sqrt(1/(2*d*e + f)) + f*sqrt(1/(2*d*e + f)))/e)/2","A",0
34,1,158,0,0.862038," ","integrate((-e*x**2+d)/(c*d**2/e**2+b*x**2+c*x**4),x)","\frac{\sqrt{- \frac{e^{3}}{c \left(b e - 2 c d\right)}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(- b e \sqrt{- \frac{e^{3}}{c \left(b e - 2 c d\right)}} + 2 c d \sqrt{- \frac{e^{3}}{c \left(b e - 2 c d\right)}}\right)}{e^{2}} \right)}}{2} - \frac{\sqrt{- \frac{e^{3}}{c \left(b e - 2 c d\right)}} \log{\left(\frac{d}{e} + x^{2} + \frac{x \left(b e \sqrt{- \frac{e^{3}}{c \left(b e - 2 c d\right)}} - 2 c d \sqrt{- \frac{e^{3}}{c \left(b e - 2 c d\right)}}\right)}{e^{2}} \right)}}{2}"," ",0,"sqrt(-e**3/(c*(b*e - 2*c*d)))*log(d/e + x**2 + x*(-b*e*sqrt(-e**3/(c*(b*e - 2*c*d))) + 2*c*d*sqrt(-e**3/(c*(b*e - 2*c*d))))/e**2)/2 - sqrt(-e**3/(c*(b*e - 2*c*d)))*log(d/e + x**2 + x*(b*e*sqrt(-e**3/(c*(b*e - 2*c*d))) - 2*c*d*sqrt(-e**3/(c*(b*e - 2*c*d))))/e**2)/2","A",0
35,1,160,0,0.772380," ","integrate((e*x**2+d)/(c*d**2/e**2+b*x**2+c*x**4),x)","- \frac{\sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(- b e \sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}} - 2 c d \sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}}\right)}{e^{2}} \right)}}{2} + \frac{\sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(b e \sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}} + 2 c d \sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}}\right)}{e^{2}} \right)}}{2}"," ",0,"-sqrt(-e**3/(c*(b*e + 2*c*d)))*log(-d/e + x**2 + x*(-b*e*sqrt(-e**3/(c*(b*e + 2*c*d))) - 2*c*d*sqrt(-e**3/(c*(b*e + 2*c*d))))/e**2)/2 + sqrt(-e**3/(c*(b*e + 2*c*d)))*log(-d/e + x**2 + x*(b*e*sqrt(-e**3/(c*(b*e + 2*c*d))) + 2*c*d*sqrt(-e**3/(c*(b*e + 2*c*d))))/e**2)/2","A",0
36,1,160,0,0.794377," ","integrate((e*x**2+d)/(b*x**2+c*(d**2/e**2+x**4)),x)","- \frac{\sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(- b e \sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}} - 2 c d \sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}}\right)}{e^{2}} \right)}}{2} + \frac{\sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}} \log{\left(- \frac{d}{e} + x^{2} + \frac{x \left(b e \sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}} + 2 c d \sqrt{- \frac{e^{3}}{c \left(b e + 2 c d\right)}}\right)}{e^{2}} \right)}}{2}"," ",0,"-sqrt(-e**3/(c*(b*e + 2*c*d)))*log(-d/e + x**2 + x*(-b*e*sqrt(-e**3/(c*(b*e + 2*c*d))) - 2*c*d*sqrt(-e**3/(c*(b*e + 2*c*d))))/e**2)/2 + sqrt(-e**3/(c*(b*e + 2*c*d)))*log(-d/e + x**2 + x*(b*e*sqrt(-e**3/(c*(b*e + 2*c*d))) + 2*c*d*sqrt(-e**3/(c*(b*e + 2*c*d))))/e**2)/2","A",0
37,1,26,0,0.469541," ","integrate((-b*x**2+a)/(a**2+(2*a*b-1)*x**2+b**2*x**4),x)","- \frac{\log{\left(\frac{a}{b} + x^{2} - \frac{x}{b} \right)}}{2} + \frac{\log{\left(\frac{a}{b} + x^{2} + \frac{x}{b} \right)}}{2}"," ",0,"-log(a/b + x**2 - x/b)/2 + log(a/b + x**2 + x/b)/2","A",0
38,1,117,0,0.464392," ","integrate((b*x**2+a)/(a**2+(2*a*b-1)*x**2+b**2*x**4),x)","- \frac{\sqrt{- \frac{1}{4 a b - 1}} \log{\left(- \frac{a}{b} + x^{2} + \frac{x \left(- 4 a b \sqrt{- \frac{1}{4 a b - 1}} + \sqrt{- \frac{1}{4 a b - 1}}\right)}{b} \right)}}{2} + \frac{\sqrt{- \frac{1}{4 a b - 1}} \log{\left(- \frac{a}{b} + x^{2} + \frac{x \left(4 a b \sqrt{- \frac{1}{4 a b - 1}} - \sqrt{- \frac{1}{4 a b - 1}}\right)}{b} \right)}}{2}"," ",0,"-sqrt(-1/(4*a*b - 1))*log(-a/b + x**2 + x*(-4*a*b*sqrt(-1/(4*a*b - 1)) + sqrt(-1/(4*a*b - 1)))/b)/2 + sqrt(-1/(4*a*b - 1))*log(-a/b + x**2 + x*(4*a*b*sqrt(-1/(4*a*b - 1)) - sqrt(-1/(4*a*b - 1)))/b)/2","B",0
39,1,95,0,0.378412," ","integrate((2*x**2+1)/(4*x**4+b*x**2+1),x)","- \frac{\sqrt{- \frac{1}{b + 4}} \log{\left(x^{2} + x \left(- \frac{b \sqrt{- \frac{1}{b + 4}}}{2} - 2 \sqrt{- \frac{1}{b + 4}}\right) - \frac{1}{2} \right)}}{2} + \frac{\sqrt{- \frac{1}{b + 4}} \log{\left(x^{2} + x \left(\frac{b \sqrt{- \frac{1}{b + 4}}}{2} + 2 \sqrt{- \frac{1}{b + 4}}\right) - \frac{1}{2} \right)}}{2}"," ",0,"-sqrt(-1/(b + 4))*log(x**2 + x*(-b*sqrt(-1/(b + 4))/2 - 2*sqrt(-1/(b + 4))) - 1/2)/2 + sqrt(-1/(b + 4))*log(x**2 + x*(b*sqrt(-1/(b + 4))/2 + 2*sqrt(-1/(b + 4))) - 1/2)/2","A",0
40,1,83,0,0.385197," ","integrate((2*x**2+1)/(4*x**4-b*x**2+1),x)","\frac{\sqrt{\frac{1}{b - 4}} \log{\left(x^{2} + x \left(- \frac{b \sqrt{\frac{1}{b - 4}}}{2} + 2 \sqrt{\frac{1}{b - 4}}\right) - \frac{1}{2} \right)}}{2} - \frac{\sqrt{\frac{1}{b - 4}} \log{\left(x^{2} + x \left(\frac{b \sqrt{\frac{1}{b - 4}}}{2} - 2 \sqrt{\frac{1}{b - 4}}\right) - \frac{1}{2} \right)}}{2}"," ",0,"sqrt(1/(b - 4))*log(x**2 + x*(-b*sqrt(1/(b - 4))/2 + 2*sqrt(1/(b - 4))) - 1/2)/2 - sqrt(1/(b - 4))*log(x**2 + x*(b*sqrt(1/(b - 4))/2 - 2*sqrt(1/(b - 4))) - 1/2)/2","A",0
41,1,42,0,0.147455," ","integrate((2*x**2+1)/(4*x**4+6*x**2+1),x)","\frac{\sqrt{10} \left(2 \operatorname{atan}{\left(\frac{\sqrt{10} x}{5} \right)} + 2 \operatorname{atan}{\left(\frac{2 \sqrt{10} x^{3}}{5} + \frac{4 \sqrt{10} x}{5} \right)}\right)}{20}"," ",0,"sqrt(10)*(2*atan(sqrt(10)*x/5) + 2*atan(2*sqrt(10)*x**3/5 + 4*sqrt(10)*x/5))/20","A",0
42,1,22,0,0.121865," ","integrate((2*x**2+1)/(4*x**4+5*x**2+1),x)","\frac{\operatorname{atan}{\left(\frac{2 x}{3} \right)}}{3} + \frac{\operatorname{atan}{\left(\frac{4 x^{3}}{3} + \frac{7 x}{3} \right)}}{3}"," ",0,"atan(2*x/3)/3 + atan(4*x**3/3 + 7*x/3)/3","B",0
43,1,14,0,0.118128," ","integrate((2*x**2+1)/(4*x**4+4*x**2+1),x)","\frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x \right)}}{2}"," ",0,"sqrt(2)*atan(sqrt(2)*x)/2","A",0
44,1,44,0,0.135009," ","integrate((2*x**2+1)/(4*x**4+3*x**2+1),x)","\frac{\sqrt{7} \left(2 \operatorname{atan}{\left(\frac{2 \sqrt{7} x}{7} \right)} + 2 \operatorname{atan}{\left(\frac{4 \sqrt{7} x^{3}}{7} + \frac{5 \sqrt{7} x}{7} \right)}\right)}{14}"," ",0,"sqrt(7)*(2*atan(2*sqrt(7)*x/7) + 2*atan(4*sqrt(7)*x**3/7 + 5*sqrt(7)*x/7))/14","A",0
45,1,42,0,0.128830," ","integrate((2*x**2+1)/(4*x**4+2*x**2+1),x)","\frac{\sqrt{6} \left(2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} \right)} + 2 \operatorname{atan}{\left(\frac{2 \sqrt{6} x^{3}}{3} + \frac{2 \sqrt{6} x}{3} \right)}\right)}{12}"," ",0,"sqrt(6)*(2*atan(sqrt(6)*x/3) + 2*atan(2*sqrt(6)*x**3/3 + 2*sqrt(6)*x/3))/12","A",0
46,1,44,0,0.131449," ","integrate((2*x**2+1)/(4*x**4+x**2+1),x)","\frac{\sqrt{5} \left(2 \operatorname{atan}{\left(\frac{2 \sqrt{5} x}{5} \right)} + 2 \operatorname{atan}{\left(\frac{4 \sqrt{5} x^{3}}{5} + \frac{3 \sqrt{5} x}{5} \right)}\right)}{10}"," ",0,"sqrt(5)*(2*atan(2*sqrt(5)*x/5) + 2*atan(4*sqrt(5)*x**3/5 + 3*sqrt(5)*x/5))/10","A",0
47,1,14,0,0.113068," ","integrate((2*x**2+1)/(4*x**4+1),x)","\frac{\operatorname{atan}{\left(x \right)}}{2} + \frac{\operatorname{atan}{\left(2 x^{3} + x \right)}}{2}"," ",0,"atan(x)/2 + atan(2*x**3 + x)/2","A",0
48,1,42,0,0.143961," ","integrate((2*x**2+1)/(4*x**4-x**2+1),x)","\frac{\sqrt{3} \left(2 \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} \right)} + 2 \operatorname{atan}{\left(\frac{4 \sqrt{3} x^{3}}{3} + \frac{\sqrt{3} x}{3} \right)}\right)}{6}"," ",0,"sqrt(3)*(2*atan(2*sqrt(3)*x/3) + 2*atan(4*sqrt(3)*x**3/3 + sqrt(3)*x/3))/6","A",0
49,1,29,0,0.134763," ","integrate((2*x**2+1)/(4*x**4-2*x**2+1),x)","\frac{\sqrt{2} \left(2 \operatorname{atan}{\left(\sqrt{2} x \right)} + 2 \operatorname{atan}{\left(2 \sqrt{2} x^{3} \right)}\right)}{4}"," ",0,"sqrt(2)*(2*atan(sqrt(2)*x) + 2*atan(2*sqrt(2)*x**3))/4","A",0
50,1,12,0,0.114850," ","integrate((2*x**2+1)/(4*x**4-3*x**2+1),x)","\operatorname{atan}{\left(2 x \right)} + \operatorname{atan}{\left(4 x^{3} - x \right)}"," ",0,"atan(2*x) + atan(4*x**3 - x)","A",0
51,1,8,0,0.091357," ","integrate((2*x**2+1)/(4*x**4-4*x**2+1),x)","- \frac{x}{2 x^{2} - 1}"," ",0,"-x/(2*x**2 - 1)","A",0
52,1,26,0,0.125984," ","integrate((2*x**2+1)/(4*x**4-5*x**2+1),x)","\frac{\log{\left(x^{2} - \frac{x}{2} - \frac{1}{2} \right)}}{2} - \frac{\log{\left(x^{2} + \frac{x}{2} - \frac{1}{2} \right)}}{2}"," ",0,"log(x**2 - x/2 - 1/2)/2 - log(x**2 + x/2 - 1/2)/2","A",0
53,1,46,0,0.123470," ","integrate((2*x**2+1)/(4*x**4-6*x**2+1),x)","\frac{\sqrt{2} \log{\left(x^{2} - \frac{\sqrt{2} x}{2} - \frac{1}{2} \right)}}{4} - \frac{\sqrt{2} \log{\left(x^{2} + \frac{\sqrt{2} x}{2} - \frac{1}{2} \right)}}{4}"," ",0,"sqrt(2)*log(x**2 - sqrt(2)*x/2 - 1/2)/4 - sqrt(2)*log(x**2 + sqrt(2)*x/2 - 1/2)/4","A",0
54,1,94,0,0.377583," ","integrate((-2*x**2+1)/(4*x**4+b*x**2+1),x)","\frac{\sqrt{- \frac{1}{b - 4}} \log{\left(x^{2} + x \left(- \frac{b \sqrt{- \frac{1}{b - 4}}}{2} + 2 \sqrt{- \frac{1}{b - 4}}\right) + \frac{1}{2} \right)}}{2} - \frac{\sqrt{- \frac{1}{b - 4}} \log{\left(x^{2} + x \left(\frac{b \sqrt{- \frac{1}{b - 4}}}{2} - 2 \sqrt{- \frac{1}{b - 4}}\right) + \frac{1}{2} \right)}}{2}"," ",0,"sqrt(-1/(b - 4))*log(x**2 + x*(-b*sqrt(-1/(b - 4))/2 + 2*sqrt(-1/(b - 4))) + 1/2)/2 - sqrt(-1/(b - 4))*log(x**2 + x*(b*sqrt(-1/(b - 4))/2 - 2*sqrt(-1/(b - 4))) + 1/2)/2","A",0
55,1,39,0,0.131731," ","integrate((-2*x**2+1)/(4*x**4+6*x**2+1),x)","- \frac{\sqrt{2} \left(2 \operatorname{atan}{\left(\sqrt{2} x \right)} - 2 \operatorname{atan}{\left(2 \sqrt{2} x^{3} + 2 \sqrt{2} x \right)}\right)}{4}"," ",0,"-sqrt(2)*(2*atan(sqrt(2)*x) - 2*atan(2*sqrt(2)*x**3 + 2*sqrt(2)*x))/4","A",0
56,1,14,0,0.118433," ","integrate((-2*x**2+1)/(4*x**4+5*x**2+1),x)","- \operatorname{atan}{\left(2 x \right)} + \operatorname{atan}{\left(4 x^{3} + 3 x \right)}"," ",0,"-atan(2*x) + atan(4*x**3 + 3*x)","A",0
57,1,7,0,0.090358," ","integrate((-2*x**2+1)/(4*x**4+4*x**2+1),x)","\frac{x}{2 x^{2} + 1}"," ",0,"x/(2*x**2 + 1)","A",0
58,1,26,0,0.114239," ","integrate((-2*x**2+1)/(4*x**4+3*x**2+1),x)","- \frac{\log{\left(x^{2} - \frac{x}{2} + \frac{1}{2} \right)}}{2} + \frac{\log{\left(x^{2} + \frac{x}{2} + \frac{1}{2} \right)}}{2}"," ",0,"-log(x**2 - x/2 + 1/2)/2 + log(x**2 + x/2 + 1/2)/2","A",0
59,1,46,0,0.114398," ","integrate((-2*x**2+1)/(4*x**4+2*x**2+1),x)","- \frac{\sqrt{2} \log{\left(x^{2} - \frac{\sqrt{2} x}{2} + \frac{1}{2} \right)}}{4} + \frac{\sqrt{2} \log{\left(x^{2} + \frac{\sqrt{2} x}{2} + \frac{1}{2} \right)}}{4}"," ",0,"-sqrt(2)*log(x**2 - sqrt(2)*x/2 + 1/2)/4 + sqrt(2)*log(x**2 + sqrt(2)*x/2 + 1/2)/4","A",0
60,1,46,0,0.119697," ","integrate((-2*x**2+1)/(4*x**4+x**2+1),x)","- \frac{\sqrt{3} \log{\left(x^{2} - \frac{\sqrt{3} x}{2} + \frac{1}{2} \right)}}{6} + \frac{\sqrt{3} \log{\left(x^{2} + \frac{\sqrt{3} x}{2} + \frac{1}{2} \right)}}{6}"," ",0,"-sqrt(3)*log(x**2 - sqrt(3)*x/2 + 1/2)/6 + sqrt(3)*log(x**2 + sqrt(3)*x/2 + 1/2)/6","A",0
61,1,22,0,0.112398," ","integrate((-2*x**2+1)/(4*x**4+1),x)","- \frac{\log{\left(x^{2} - x + \frac{1}{2} \right)}}{4} + \frac{\log{\left(x^{2} + x + \frac{1}{2} \right)}}{4}"," ",0,"-log(x**2 - x + 1/2)/4 + log(x**2 + x + 1/2)/4","A",0
62,1,46,0,0.115600," ","integrate((-2*x**2+1)/(4*x**4-x**2+1),x)","- \frac{\sqrt{5} \log{\left(x^{2} - \frac{\sqrt{5} x}{2} + \frac{1}{2} \right)}}{10} + \frac{\sqrt{5} \log{\left(x^{2} + \frac{\sqrt{5} x}{2} + \frac{1}{2} \right)}}{10}"," ",0,"-sqrt(5)*log(x**2 - sqrt(5)*x/2 + 1/2)/10 + sqrt(5)*log(x**2 + sqrt(5)*x/2 + 1/2)/10","A",0
63,1,46,0,0.118890," ","integrate((-2*x**2+1)/(4*x**4-2*x**2+1),x)","- \frac{\sqrt{6} \log{\left(x^{2} - \frac{\sqrt{6} x}{2} + \frac{1}{2} \right)}}{12} + \frac{\sqrt{6} \log{\left(x^{2} + \frac{\sqrt{6} x}{2} + \frac{1}{2} \right)}}{12}"," ",0,"-sqrt(6)*log(x**2 - sqrt(6)*x/2 + 1/2)/12 + sqrt(6)*log(x**2 + sqrt(6)*x/2 + 1/2)/12","A",0
64,1,46,0,0.130415," ","integrate((-2*x**2+1)/(4*x**4-3*x**2+1),x)","- \frac{\sqrt{7} \log{\left(x^{2} - \frac{\sqrt{7} x}{2} + \frac{1}{2} \right)}}{14} + \frac{\sqrt{7} \log{\left(x^{2} + \frac{\sqrt{7} x}{2} + \frac{1}{2} \right)}}{14}"," ",0,"-sqrt(7)*log(x**2 - sqrt(7)*x/2 + 1/2)/14 + sqrt(7)*log(x**2 + sqrt(7)*x/2 + 1/2)/14","A",0
65,1,32,0,0.107264," ","integrate((-2*x**2+1)/(4*x**4-4*x**2+1),x)","- \frac{\sqrt{2} \log{\left(x - \frac{\sqrt{2}}{2} \right)}}{4} + \frac{\sqrt{2} \log{\left(x + \frac{\sqrt{2}}{2} \right)}}{4}"," ",0,"-sqrt(2)*log(x - sqrt(2)/2)/4 + sqrt(2)*log(x + sqrt(2)/2)/4","B",0
66,1,29,0,0.121536," ","integrate((-2*x**2+1)/(4*x**4-5*x**2+1),x)","- \frac{\log{\left(x^{2} - \frac{3 x}{2} + \frac{1}{2} \right)}}{6} + \frac{\log{\left(x^{2} + \frac{3 x}{2} + \frac{1}{2} \right)}}{6}"," ",0,"-log(x**2 - 3*x/2 + 1/2)/6 + log(x**2 + 3*x/2 + 1/2)/6","A",0
67,1,46,0,0.118436," ","integrate((-2*x**2+1)/(4*x**4-6*x**2+1),x)","- \frac{\sqrt{10} \log{\left(x^{2} - \frac{\sqrt{10} x}{2} + \frac{1}{2} \right)}}{20} + \frac{\sqrt{10} \log{\left(x^{2} + \frac{\sqrt{10} x}{2} + \frac{1}{2} \right)}}{20}"," ",0,"-sqrt(10)*log(x**2 - sqrt(10)*x/2 + 1/2)/20 + sqrt(10)*log(x**2 + sqrt(10)*x/2 + 1/2)/20","A",0
68,1,88,0,0.376282," ","integrate((x**2+1)/(x**4+b*x**2+1),x)","- \frac{\sqrt{- \frac{1}{b + 2}} \log{\left(x^{2} + x \left(- b \sqrt{- \frac{1}{b + 2}} - 2 \sqrt{- \frac{1}{b + 2}}\right) - 1 \right)}}{2} + \frac{\sqrt{- \frac{1}{b + 2}} \log{\left(x^{2} + x \left(b \sqrt{- \frac{1}{b + 2}} + 2 \sqrt{- \frac{1}{b + 2}}\right) - 1 \right)}}{2}"," ",0,"-sqrt(-1/(b + 2))*log(x**2 + x*(-b*sqrt(-1/(b + 2)) - 2*sqrt(-1/(b + 2))) - 1)/2 + sqrt(-1/(b + 2))*log(x**2 + x*(b*sqrt(-1/(b + 2)) + 2*sqrt(-1/(b + 2))) - 1)/2","A",0
69,1,41,0,0.124340," ","integrate((x**2+1)/(x**4+5*x**2+1),x)","\frac{\sqrt{7} \left(2 \operatorname{atan}{\left(\frac{\sqrt{7} x}{7} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{7} x^{3}}{7} + \frac{6 \sqrt{7} x}{7} \right)}\right)}{14}"," ",0,"sqrt(7)*(2*atan(sqrt(7)*x/7) + 2*atan(sqrt(7)*x**3/7 + 6*sqrt(7)*x/7))/14","A",0
70,1,41,0,0.141304," ","integrate((x**2+1)/(x**4+4*x**2+1),x)","\frac{\sqrt{6} \left(2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{6} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{6} x^{3}}{6} + \frac{5 \sqrt{6} x}{6} \right)}\right)}{12}"," ",0,"sqrt(6)*(2*atan(sqrt(6)*x/6) + 2*atan(sqrt(6)*x**3/6 + 5*sqrt(6)*x/6))/12","A",0
71,1,41,0,0.126580," ","integrate((x**2+1)/(x**4+3*x**2+1),x)","\frac{\sqrt{5} \left(2 \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{5} x^{3}}{5} + \frac{4 \sqrt{5} x}{5} \right)}\right)}{10}"," ",0,"sqrt(5)*(2*atan(sqrt(5)*x/5) + 2*atan(sqrt(5)*x**3/5 + 4*sqrt(5)*x/5))/10","A",0
72,1,2,0,0.099661," ","integrate((x**2+1)/(x**4+2*x**2+1),x)","\operatorname{atan}{\left(x \right)}"," ",0,"atan(x)","A",0
73,1,41,0,0.122751," ","integrate((x**2+1)/(x**4+x**2+1),x)","\frac{\sqrt{3} \left(2 \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{3} x^{3}}{3} + \frac{2 \sqrt{3} x}{3} \right)}\right)}{6}"," ",0,"sqrt(3)*(2*atan(sqrt(3)*x/3) + 2*atan(sqrt(3)*x**3/3 + 2*sqrt(3)*x/3))/6","A",0
74,1,39,0,0.122696," ","integrate((x**2+1)/(x**4+1),x)","\frac{\sqrt{2} \left(2 \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{2} x^{3}}{2} + \frac{\sqrt{2} x}{2} \right)}\right)}{4}"," ",0,"sqrt(2)*(2*atan(sqrt(2)*x/2) + 2*atan(sqrt(2)*x**3/2 + sqrt(2)*x/2))/4","A",0
75,1,7,0,0.109548," ","integrate((x**2+1)/(x**4-x**2+1),x)","\operatorname{atan}{\left(x \right)} + \operatorname{atan}{\left(x^{3} \right)}"," ",0,"atan(x) + atan(x**3)","A",0
76,1,7,0,0.086644," ","integrate((x**2+1)/(x**4-2*x**2+1),x)","- \frac{x}{x^{2} - 1}"," ",0,"-x/(x**2 - 1)","A",0
77,1,19,0,0.112929," ","integrate((x**2+1)/(x**4-3*x**2+1),x)","\frac{\log{\left(x^{2} - x - 1 \right)}}{2} - \frac{\log{\left(x^{2} + x - 1 \right)}}{2}"," ",0,"log(x**2 - x - 1)/2 - log(x**2 + x - 1)/2","A",0
78,1,39,0,0.114274," ","integrate((x**2+1)/(x**4-4*x**2+1),x)","\frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x - 1 \right)}}{4} - \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x - 1 \right)}}{4}"," ",0,"sqrt(2)*log(x**2 - sqrt(2)*x - 1)/4 - sqrt(2)*log(x**2 + sqrt(2)*x - 1)/4","A",0
79,1,39,0,0.118767," ","integrate((x**2+1)/(x**4-5*x**2+1),x)","\frac{\sqrt{3} \log{\left(x^{2} - \sqrt{3} x - 1 \right)}}{6} - \frac{\sqrt{3} \log{\left(x^{2} + \sqrt{3} x - 1 \right)}}{6}"," ",0,"sqrt(3)*log(x**2 - sqrt(3)*x - 1)/6 - sqrt(3)*log(x**2 + sqrt(3)*x - 1)/6","A",0
80,1,87,0,0.347514," ","integrate((-x**2+1)/(x**4+b*x**2+1),x)","\frac{\sqrt{- \frac{1}{b - 2}} \log{\left(x^{2} + x \left(- b \sqrt{- \frac{1}{b - 2}} + 2 \sqrt{- \frac{1}{b - 2}}\right) + 1 \right)}}{2} - \frac{\sqrt{- \frac{1}{b - 2}} \log{\left(x^{2} + x \left(b \sqrt{- \frac{1}{b - 2}} - 2 \sqrt{- \frac{1}{b - 2}}\right) + 1 \right)}}{2}"," ",0,"sqrt(-1/(b - 2))*log(x**2 + x*(-b*sqrt(-1/(b - 2)) + 2*sqrt(-1/(b - 2))) + 1)/2 - sqrt(-1/(b - 2))*log(x**2 + x*(b*sqrt(-1/(b - 2)) - 2*sqrt(-1/(b - 2))) + 1)/2","A",0
81,1,42,0,0.130005," ","integrate((-x**2+1)/(x**4+5*x**2+1),x)","- \frac{\sqrt{3} \left(2 \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)} - 2 \operatorname{atan}{\left(\frac{\sqrt{3} x^{3}}{3} + \frac{4 \sqrt{3} x}{3} \right)}\right)}{6}"," ",0,"-sqrt(3)*(2*atan(sqrt(3)*x/3) - 2*atan(sqrt(3)*x**3/3 + 4*sqrt(3)*x/3))/6","A",0
82,1,42,0,0.130856," ","integrate((-x**2+1)/(x**4+4*x**2+1),x)","- \frac{\sqrt{2} \left(2 \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} - 2 \operatorname{atan}{\left(\frac{\sqrt{2} x^{3}}{2} + \frac{3 \sqrt{2} x}{2} \right)}\right)}{4}"," ",0,"-sqrt(2)*(2*atan(sqrt(2)*x/2) - 2*atan(sqrt(2)*x**3/2 + 3*sqrt(2)*x/2))/4","A",0
83,1,10,0,0.119414," ","integrate((-x**2+1)/(x**4+3*x**2+1),x)","- \operatorname{atan}{\left(x \right)} + \operatorname{atan}{\left(x^{3} + 2 x \right)}"," ",0,"-atan(x) + atan(x**3 + 2*x)","A",0
84,1,5,0,0.094774," ","integrate((-x**2+1)/(x**4+2*x**2+1),x)","\frac{x}{x^{2} + 1}"," ",0,"x/(x**2 + 1)","A",0
85,1,19,0,0.116062," ","integrate((-x**2+1)/(x**4+x**2+1),x)","- \frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{\log{\left(x^{2} + x + 1 \right)}}{2}"," ",0,"-log(x**2 - x + 1)/2 + log(x**2 + x + 1)/2","A",0
86,1,39,0,0.112759," ","integrate((-x**2+1)/(x**4+1),x)","- \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{4} + \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{4}"," ",0,"-sqrt(2)*log(x**2 - sqrt(2)*x + 1)/4 + sqrt(2)*log(x**2 + sqrt(2)*x + 1)/4","A",0
87,1,39,0,0.120555," ","integrate((-x**2+1)/(x**4-x**2+1),x)","- \frac{\sqrt{3} \log{\left(x^{2} - \sqrt{3} x + 1 \right)}}{6} + \frac{\sqrt{3} \log{\left(x^{2} + \sqrt{3} x + 1 \right)}}{6}"," ",0,"-sqrt(3)*log(x**2 - sqrt(3)*x + 1)/6 + sqrt(3)*log(x**2 + sqrt(3)*x + 1)/6","A",0
88,1,12,0,0.108630," ","integrate((-x**2+1)/(x**4-2*x**2+1),x)","- \frac{\log{\left(x - 1 \right)}}{2} + \frac{\log{\left(x + 1 \right)}}{2}"," ",0,"-log(x - 1)/2 + log(x + 1)/2","B",0
89,1,39,0,0.116493," ","integrate((-x**2+1)/(x**4-3*x**2+1),x)","- \frac{\sqrt{5} \log{\left(x^{2} - \sqrt{5} x + 1 \right)}}{10} + \frac{\sqrt{5} \log{\left(x^{2} + \sqrt{5} x + 1 \right)}}{10}"," ",0,"-sqrt(5)*log(x**2 - sqrt(5)*x + 1)/10 + sqrt(5)*log(x**2 + sqrt(5)*x + 1)/10","A",0
90,1,39,0,0.118246," ","integrate((-x**2+1)/(x**4-4*x**2+1),x)","- \frac{\sqrt{6} \log{\left(x^{2} - \sqrt{6} x + 1 \right)}}{12} + \frac{\sqrt{6} \log{\left(x^{2} + \sqrt{6} x + 1 \right)}}{12}"," ",0,"-sqrt(6)*log(x**2 - sqrt(6)*x + 1)/12 + sqrt(6)*log(x**2 + sqrt(6)*x + 1)/12","A",0
91,1,39,0,0.142467," ","integrate((-x**2+1)/(x**4-5*x**2+1),x)","- \frac{\sqrt{7} \log{\left(x^{2} - \sqrt{7} x + 1 \right)}}{14} + \frac{\sqrt{7} \log{\left(x^{2} + \sqrt{7} x + 1 \right)}}{14}"," ",0,"-sqrt(7)*log(x**2 - sqrt(7)*x + 1)/14 + sqrt(7)*log(x**2 + sqrt(7)*x + 1)/14","A",0
92,1,46,0,0.142314," ","integrate((-3*x**2-1)/(9*x**4+2*x**2+1),x)","- \frac{\sqrt{2} \left(2 \operatorname{atan}{\left(\frac{3 \sqrt{2} x}{4} \right)} + 2 \operatorname{atan}{\left(\frac{9 \sqrt{2} x^{3}}{4} + \frac{5 \sqrt{2} x}{4} \right)}\right)}{8}"," ",0,"-sqrt(2)*(2*atan(3*sqrt(2)*x/4) + 2*atan(9*sqrt(2)*x**3/4 + 5*sqrt(2)*x/4))/8","A",0
93,1,46,0,0.150120," ","integrate((3*x**2+1)/(-9*x**4-2*x**2-1),x)","- \frac{\sqrt{2} \left(2 \operatorname{atan}{\left(\frac{3 \sqrt{2} x}{4} \right)} + 2 \operatorname{atan}{\left(\frac{9 \sqrt{2} x^{3}}{4} + \frac{5 \sqrt{2} x}{4} \right)}\right)}{8}"," ",0,"-sqrt(2)*(2*atan(3*sqrt(2)*x/4) + 2*atan(9*sqrt(2)*x**3/4 + 5*sqrt(2)*x/4))/8","A",0
94,1,22,0,0.128925," ","integrate((2*x**2+3)/(x**4-2*x**2+1),x)","- \frac{5 x}{2 x^{2} - 2} - \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}"," ",0,"-5*x/(2*x**2 - 2) - log(x - 1)/4 + log(x + 1)/4","A",0
95,1,53,0,0.605938," ","integrate((3*x**2+2)/(3*x**4-8*x**2+5),x)","- \frac{5 \log{\left(x - 1 \right)}}{4} + \frac{5 \log{\left(x + 1 \right)}}{4} + \frac{7 \sqrt{15} \log{\left(x - \frac{\sqrt{15}}{3} \right)}}{20} - \frac{7 \sqrt{15} \log{\left(x + \frac{\sqrt{15}}{3} \right)}}{20}"," ",0,"-5*log(x - 1)/4 + 5*log(x + 1)/4 + 7*sqrt(15)*log(x - sqrt(15)/3)/20 - 7*sqrt(15)*log(x + sqrt(15)/3)/20","B",0
96,1,474,0,1.502041," ","integrate((e*x**2+d)/(3*x**4-8*x**2+5),x)","\frac{\left(d + e\right) \log{\left(x + \frac{- 51 d^{3} \left(d + e\right) - 180 d^{2} e \left(d + e\right) - 225 d e^{2} \left(d + e\right) + 60 d \left(d + e\right)^{3} - 100 e^{3} \left(d + e\right) + 75 e \left(d + e\right)^{3}}{9 d^{4} + 24 d^{3} e - 40 d e^{3} - 25 e^{4}} \right)}}{4} - \frac{\left(d + e\right) \log{\left(x + \frac{51 d^{3} \left(d + e\right) + 180 d^{2} e \left(d + e\right) + 225 d e^{2} \left(d + e\right) - 60 d \left(d + e\right)^{3} + 100 e^{3} \left(d + e\right) - 75 e \left(d + e\right)^{3}}{9 d^{4} + 24 d^{3} e - 40 d e^{3} - 25 e^{4}} \right)}}{4} + \frac{\sqrt{15} \left(3 d + 5 e\right) \log{\left(x + \frac{- \frac{17 \sqrt{15} d^{3} \left(3 d + 5 e\right)}{5} - 12 \sqrt{15} d^{2} e \left(3 d + 5 e\right) - 15 \sqrt{15} d e^{2} \left(3 d + 5 e\right) + \frac{4 \sqrt{15} d \left(3 d + 5 e\right)^{3}}{15} - \frac{20 \sqrt{15} e^{3} \left(3 d + 5 e\right)}{3} + \frac{\sqrt{15} e \left(3 d + 5 e\right)^{3}}{3}}{9 d^{4} + 24 d^{3} e - 40 d e^{3} - 25 e^{4}} \right)}}{60} - \frac{\sqrt{15} \left(3 d + 5 e\right) \log{\left(x + \frac{\frac{17 \sqrt{15} d^{3} \left(3 d + 5 e\right)}{5} + 12 \sqrt{15} d^{2} e \left(3 d + 5 e\right) + 15 \sqrt{15} d e^{2} \left(3 d + 5 e\right) - \frac{4 \sqrt{15} d \left(3 d + 5 e\right)^{3}}{15} + \frac{20 \sqrt{15} e^{3} \left(3 d + 5 e\right)}{3} - \frac{\sqrt{15} e \left(3 d + 5 e\right)^{3}}{3}}{9 d^{4} + 24 d^{3} e - 40 d e^{3} - 25 e^{4}} \right)}}{60}"," ",0,"(d + e)*log(x + (-51*d**3*(d + e) - 180*d**2*e*(d + e) - 225*d*e**2*(d + e) + 60*d*(d + e)**3 - 100*e**3*(d + e) + 75*e*(d + e)**3)/(9*d**4 + 24*d**3*e - 40*d*e**3 - 25*e**4))/4 - (d + e)*log(x + (51*d**3*(d + e) + 180*d**2*e*(d + e) + 225*d*e**2*(d + e) - 60*d*(d + e)**3 + 100*e**3*(d + e) - 75*e*(d + e)**3)/(9*d**4 + 24*d**3*e - 40*d*e**3 - 25*e**4))/4 + sqrt(15)*(3*d + 5*e)*log(x + (-17*sqrt(15)*d**3*(3*d + 5*e)/5 - 12*sqrt(15)*d**2*e*(3*d + 5*e) - 15*sqrt(15)*d*e**2*(3*d + 5*e) + 4*sqrt(15)*d*(3*d + 5*e)**3/15 - 20*sqrt(15)*e**3*(3*d + 5*e)/3 + sqrt(15)*e*(3*d + 5*e)**3/3)/(9*d**4 + 24*d**3*e - 40*d*e**3 - 25*e**4))/60 - sqrt(15)*(3*d + 5*e)*log(x + (17*sqrt(15)*d**3*(3*d + 5*e)/5 + 12*sqrt(15)*d**2*e*(3*d + 5*e) + 15*sqrt(15)*d*e**2*(3*d + 5*e) - 4*sqrt(15)*d*(3*d + 5*e)**3/15 + 20*sqrt(15)*e**3*(3*d + 5*e)/3 - sqrt(15)*e*(3*d + 5*e)**3/3)/(9*d**4 + 24*d**3*e - 40*d*e**3 - 25*e**4))/60","B",0
97,1,46,0,0.209386," ","integrate((x**2+3)/(x**4+3*x**2+1),x)","2 \left(\frac{\sqrt{5}}{5} + \frac{1}{2}\right) \operatorname{atan}{\left(\frac{2 x}{-1 + \sqrt{5}} \right)} - 2 \left(\frac{1}{2} - \frac{\sqrt{5}}{5}\right) \operatorname{atan}{\left(\frac{2 x}{1 + \sqrt{5}} \right)}"," ",0,"2*(sqrt(5)/5 + 1/2)*atan(2*x/(-1 + sqrt(5))) - 2*(1/2 - sqrt(5)/5)*atan(2*x/(1 + sqrt(5)))","A",0
98,1,740,0,1.264082," ","integrate((b*x**2+a)/(x**4+x**2+1),x)","\left(- \frac{a}{4} + \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) \log{\left(x + \frac{2 a^{3} \left(- \frac{a}{4} + \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) + 6 a^{2} b \left(- \frac{a}{4} + \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) - 12 a b^{2} \left(- \frac{a}{4} + \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) + 24 a \left(- \frac{a}{4} + \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right)^{3} + 2 b^{3} \left(- \frac{a}{4} + \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) - 48 b \left(- \frac{a}{4} + \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right)^{3}}{a^{4} - a^{3} b + a b^{3} - b^{4}} \right)} + \left(- \frac{a}{4} + \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) \log{\left(x + \frac{2 a^{3} \left(- \frac{a}{4} + \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) + 6 a^{2} b \left(- \frac{a}{4} + \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) - 12 a b^{2} \left(- \frac{a}{4} + \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) + 24 a \left(- \frac{a}{4} + \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right)^{3} + 2 b^{3} \left(- \frac{a}{4} + \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) - 48 b \left(- \frac{a}{4} + \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right)^{3}}{a^{4} - a^{3} b + a b^{3} - b^{4}} \right)} + \left(\frac{a}{4} - \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) \log{\left(x + \frac{2 a^{3} \left(\frac{a}{4} - \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) + 6 a^{2} b \left(\frac{a}{4} - \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) - 12 a b^{2} \left(\frac{a}{4} - \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) + 24 a \left(\frac{a}{4} - \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right)^{3} + 2 b^{3} \left(\frac{a}{4} - \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right) - 48 b \left(\frac{a}{4} - \frac{b}{4} - \frac{\sqrt{3} i \left(a + b\right)}{12}\right)^{3}}{a^{4} - a^{3} b + a b^{3} - b^{4}} \right)} + \left(\frac{a}{4} - \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) \log{\left(x + \frac{2 a^{3} \left(\frac{a}{4} - \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) + 6 a^{2} b \left(\frac{a}{4} - \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) - 12 a b^{2} \left(\frac{a}{4} - \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) + 24 a \left(\frac{a}{4} - \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right)^{3} + 2 b^{3} \left(\frac{a}{4} - \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right) - 48 b \left(\frac{a}{4} - \frac{b}{4} + \frac{\sqrt{3} i \left(a + b\right)}{12}\right)^{3}}{a^{4} - a^{3} b + a b^{3} - b^{4}} \right)}"," ",0,"(-a/4 + b/4 - sqrt(3)*I*(a + b)/12)*log(x + (2*a**3*(-a/4 + b/4 - sqrt(3)*I*(a + b)/12) + 6*a**2*b*(-a/4 + b/4 - sqrt(3)*I*(a + b)/12) - 12*a*b**2*(-a/4 + b/4 - sqrt(3)*I*(a + b)/12) + 24*a*(-a/4 + b/4 - sqrt(3)*I*(a + b)/12)**3 + 2*b**3*(-a/4 + b/4 - sqrt(3)*I*(a + b)/12) - 48*b*(-a/4 + b/4 - sqrt(3)*I*(a + b)/12)**3)/(a**4 - a**3*b + a*b**3 - b**4)) + (-a/4 + b/4 + sqrt(3)*I*(a + b)/12)*log(x + (2*a**3*(-a/4 + b/4 + sqrt(3)*I*(a + b)/12) + 6*a**2*b*(-a/4 + b/4 + sqrt(3)*I*(a + b)/12) - 12*a*b**2*(-a/4 + b/4 + sqrt(3)*I*(a + b)/12) + 24*a*(-a/4 + b/4 + sqrt(3)*I*(a + b)/12)**3 + 2*b**3*(-a/4 + b/4 + sqrt(3)*I*(a + b)/12) - 48*b*(-a/4 + b/4 + sqrt(3)*I*(a + b)/12)**3)/(a**4 - a**3*b + a*b**3 - b**4)) + (a/4 - b/4 - sqrt(3)*I*(a + b)/12)*log(x + (2*a**3*(a/4 - b/4 - sqrt(3)*I*(a + b)/12) + 6*a**2*b*(a/4 - b/4 - sqrt(3)*I*(a + b)/12) - 12*a*b**2*(a/4 - b/4 - sqrt(3)*I*(a + b)/12) + 24*a*(a/4 - b/4 - sqrt(3)*I*(a + b)/12)**3 + 2*b**3*(a/4 - b/4 - sqrt(3)*I*(a + b)/12) - 48*b*(a/4 - b/4 - sqrt(3)*I*(a + b)/12)**3)/(a**4 - a**3*b + a*b**3 - b**4)) + (a/4 - b/4 + sqrt(3)*I*(a + b)/12)*log(x + (2*a**3*(a/4 - b/4 + sqrt(3)*I*(a + b)/12) + 6*a**2*b*(a/4 - b/4 + sqrt(3)*I*(a + b)/12) - 12*a*b**2*(a/4 - b/4 + sqrt(3)*I*(a + b)/12) + 24*a*(a/4 - b/4 + sqrt(3)*I*(a + b)/12)**3 + 2*b**3*(a/4 - b/4 + sqrt(3)*I*(a + b)/12) - 48*b*(a/4 - b/4 + sqrt(3)*I*(a + b)/12)**3)/(a**4 - a**3*b + a*b**3 - b**4))","C",0
99,1,874,0,1.894763," ","integrate((b*x**2+a)/(x**4+x**2+1)**2,x)","\frac{x^{3} \left(- a + 2 b\right) + x \left(a + b\right)}{6 x^{4} + 6 x^{2} + 6} + \left(- \frac{a}{4} + \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) \log{\left(x + \frac{76 a^{3} \left(- \frac{a}{4} + \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) + 948 a^{2} b \left(- \frac{a}{4} + \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) - 816 a b^{2} \left(- \frac{a}{4} + \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) + 12096 a \left(- \frac{a}{4} + \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right)^{3} + 148 b^{3} \left(- \frac{a}{4} + \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) - 8640 b \left(- \frac{a}{4} + \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right)^{3}}{248 a^{4} - 262 a^{3} b + 75 a^{2} b^{2} + 11 a b^{3} - 7 b^{4}} \right)} + \left(- \frac{a}{4} + \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) \log{\left(x + \frac{76 a^{3} \left(- \frac{a}{4} + \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) + 948 a^{2} b \left(- \frac{a}{4} + \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) - 816 a b^{2} \left(- \frac{a}{4} + \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) + 12096 a \left(- \frac{a}{4} + \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right)^{3} + 148 b^{3} \left(- \frac{a}{4} + \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) - 8640 b \left(- \frac{a}{4} + \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right)^{3}}{248 a^{4} - 262 a^{3} b + 75 a^{2} b^{2} + 11 a b^{3} - 7 b^{4}} \right)} + \left(\frac{a}{4} - \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) \log{\left(x + \frac{76 a^{3} \left(\frac{a}{4} - \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) + 948 a^{2} b \left(\frac{a}{4} - \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) - 816 a b^{2} \left(\frac{a}{4} - \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) + 12096 a \left(\frac{a}{4} - \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right)^{3} + 148 b^{3} \left(\frac{a}{4} - \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) - 8640 b \left(\frac{a}{4} - \frac{b}{8} - \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right)^{3}}{248 a^{4} - 262 a^{3} b + 75 a^{2} b^{2} + 11 a b^{3} - 7 b^{4}} \right)} + \left(\frac{a}{4} - \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) \log{\left(x + \frac{76 a^{3} \left(\frac{a}{4} - \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) + 948 a^{2} b \left(\frac{a}{4} - \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) - 816 a b^{2} \left(\frac{a}{4} - \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) + 12096 a \left(\frac{a}{4} - \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right)^{3} + 148 b^{3} \left(\frac{a}{4} - \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right) - 8640 b \left(\frac{a}{4} - \frac{b}{8} + \frac{\sqrt{3} i \left(4 a + b\right)}{72}\right)^{3}}{248 a^{4} - 262 a^{3} b + 75 a^{2} b^{2} + 11 a b^{3} - 7 b^{4}} \right)}"," ",0,"(x**3*(-a + 2*b) + x*(a + b))/(6*x**4 + 6*x**2 + 6) + (-a/4 + b/8 - sqrt(3)*I*(4*a + b)/72)*log(x + (76*a**3*(-a/4 + b/8 - sqrt(3)*I*(4*a + b)/72) + 948*a**2*b*(-a/4 + b/8 - sqrt(3)*I*(4*a + b)/72) - 816*a*b**2*(-a/4 + b/8 - sqrt(3)*I*(4*a + b)/72) + 12096*a*(-a/4 + b/8 - sqrt(3)*I*(4*a + b)/72)**3 + 148*b**3*(-a/4 + b/8 - sqrt(3)*I*(4*a + b)/72) - 8640*b*(-a/4 + b/8 - sqrt(3)*I*(4*a + b)/72)**3)/(248*a**4 - 262*a**3*b + 75*a**2*b**2 + 11*a*b**3 - 7*b**4)) + (-a/4 + b/8 + sqrt(3)*I*(4*a + b)/72)*log(x + (76*a**3*(-a/4 + b/8 + sqrt(3)*I*(4*a + b)/72) + 948*a**2*b*(-a/4 + b/8 + sqrt(3)*I*(4*a + b)/72) - 816*a*b**2*(-a/4 + b/8 + sqrt(3)*I*(4*a + b)/72) + 12096*a*(-a/4 + b/8 + sqrt(3)*I*(4*a + b)/72)**3 + 148*b**3*(-a/4 + b/8 + sqrt(3)*I*(4*a + b)/72) - 8640*b*(-a/4 + b/8 + sqrt(3)*I*(4*a + b)/72)**3)/(248*a**4 - 262*a**3*b + 75*a**2*b**2 + 11*a*b**3 - 7*b**4)) + (a/4 - b/8 - sqrt(3)*I*(4*a + b)/72)*log(x + (76*a**3*(a/4 - b/8 - sqrt(3)*I*(4*a + b)/72) + 948*a**2*b*(a/4 - b/8 - sqrt(3)*I*(4*a + b)/72) - 816*a*b**2*(a/4 - b/8 - sqrt(3)*I*(4*a + b)/72) + 12096*a*(a/4 - b/8 - sqrt(3)*I*(4*a + b)/72)**3 + 148*b**3*(a/4 - b/8 - sqrt(3)*I*(4*a + b)/72) - 8640*b*(a/4 - b/8 - sqrt(3)*I*(4*a + b)/72)**3)/(248*a**4 - 262*a**3*b + 75*a**2*b**2 + 11*a*b**3 - 7*b**4)) + (a/4 - b/8 + sqrt(3)*I*(4*a + b)/72)*log(x + (76*a**3*(a/4 - b/8 + sqrt(3)*I*(4*a + b)/72) + 948*a**2*b*(a/4 - b/8 + sqrt(3)*I*(4*a + b)/72) - 816*a*b**2*(a/4 - b/8 + sqrt(3)*I*(4*a + b)/72) + 12096*a*(a/4 - b/8 + sqrt(3)*I*(4*a + b)/72)**3 + 148*b**3*(a/4 - b/8 + sqrt(3)*I*(4*a + b)/72) - 8640*b*(a/4 - b/8 + sqrt(3)*I*(4*a + b)/72)**3)/(248*a**4 - 262*a**3*b + 75*a**2*b**2 + 11*a*b**3 - 7*b**4))","C",0
100,1,122,0,1.322083," ","integrate((b*x**2+a)/(x**4+x**2+2),x)","\operatorname{RootSum} {\left(1568 t^{4} + t^{2} \left(- 28 a^{2} + 224 a b - 56 b^{2}\right) + a^{4} - 2 a^{3} b + 5 a^{2} b^{2} - 4 a b^{3} + 4 b^{4}, \left( t \mapsto t \log{\left(x + \frac{112 t^{3} a - 448 t^{3} b + 6 t a^{3} + 12 t a^{2} b - 48 t a b^{2} + 8 t b^{3}}{a^{4} - a^{3} b + 2 a b^{3} - 4 b^{4}} \right)} \right)\right)}"," ",0,"RootSum(1568*_t**4 + _t**2*(-28*a**2 + 224*a*b - 56*b**2) + a**4 - 2*a**3*b + 5*a**2*b**2 - 4*a*b**3 + 4*b**4, Lambda(_t, _t*log(x + (112*_t**3*a - 448*_t**3*b + 6*_t*a**3 + 12*_t*a**2*b - 48*_t*a*b**2 + 8*_t*b**3)/(a**4 - a**3*b + 2*a*b**3 - 4*b**4))))","A",0
101,1,165,0,1.801199," ","integrate((b*x**2+a)/(x**4+x**2+2)**2,x)","\frac{x^{3} \left(- a + 4 b\right) + x \left(3 a + 2 b\right)}{28 x^{4} + 28 x^{2} + 56} + \operatorname{RootSum} {\left(240945152 t^{4} + t^{2} \left(- 1157968 a^{2} + 2348864 a b - 548800 b^{2}\right) + 4489 a^{4} - 7102 a^{3} b + 5757 a^{2} b^{2} - 2332 a b^{3} + 484 b^{4}, \left( t \mapsto t \log{\left(x + \frac{2634240 t^{3} a - 3161088 t^{3} b + 11996 t a^{3} + 12792 t a^{2} b - 21936 t a b^{2} + 4384 t b^{3}}{1139 a^{4} - 1169 a^{3} b + 318 a^{2} b^{2} + 124 a b^{3} - 88 b^{4}} \right)} \right)\right)}"," ",0,"(x**3*(-a + 4*b) + x*(3*a + 2*b))/(28*x**4 + 28*x**2 + 56) + RootSum(240945152*_t**4 + _t**2*(-1157968*a**2 + 2348864*a*b - 548800*b**2) + 4489*a**4 - 7102*a**3*b + 5757*a**2*b**2 - 2332*a*b**3 + 484*b**4, Lambda(_t, _t*log(x + (2634240*_t**3*a - 3161088*_t**3*b + 11996*_t*a**3 + 12792*_t*a**2*b - 21936*_t*a*b**2 + 4384*_t*b**3)/(1139*a**4 - 1169*a**3*b + 318*a**2*b**2 + 124*a*b**3 - 88*b**4))))","A",0
102,-2,0,0,0.000000," ","integrate((-x**2+2**(1/2))/(1+x**4-x**2*2**(1/2)),x)","\text{Exception raised: PolynomialError}"," ",0,"Exception raised: PolynomialError","F(-2)",0
103,-2,0,0,0.000000," ","integrate((x**2+2**(1/2))/(1+x**4+x**2*2**(1/2)),x)","\text{Exception raised: PolynomialError}"," ",0,"Exception raised: PolynomialError","F(-2)",0
104,1,1469,0,2.862124," ","integrate((-x**2+2**(1/2))/(x**4+b*x**2+1),x)","- \operatorname{RootSum} {\left(t^{4} \left(16 b^{4} - 128 b^{2} + 256\right) + t^{2} \left(12 b^{3} + 16 \sqrt{2} b^{2} - 48 b - 64 \sqrt{2}\right) + 2 b^{2} + 6 \sqrt{2} b + 9, \left( t \mapsto t \log{\left(t^{3} \left(\frac{64 b^{12}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{672 \sqrt{2} b^{11}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{5760 b^{10}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{12064 \sqrt{2} b^{9}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{17744 b^{8}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{27480 \sqrt{2} b^{7}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{154608 b^{6}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{141376 \sqrt{2} b^{5}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{69072 b^{4}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{61704 \sqrt{2} b^{3}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{78192 b^{2}}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{2592 \sqrt{2} b}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{15552}{8 b^{10} + 88 \sqrt{2} b^{9} + 828 b^{8} + 2144 \sqrt{2} b^{7} + 6470 b^{6} + 5310 \sqrt{2} b^{5} + 2781 b^{4} - 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729}\right) + t \left(\frac{16 b^{7}}{4 b^{6} + 28 \sqrt{2} b^{5} + 152 b^{4} + 192 \sqrt{2} b^{3} + 189 b^{2} - 27 \sqrt{2} b - 81} + \frac{116 \sqrt{2} b^{6}}{4 b^{6} + 28 \sqrt{2} b^{5} + 152 b^{4} + 192 \sqrt{2} b^{3} + 189 b^{2} - 27 \sqrt{2} b - 81} + \frac{668 b^{5}}{4 b^{6} + 28 \sqrt{2} b^{5} + 152 b^{4} + 192 \sqrt{2} b^{3} + 189 b^{2} - 27 \sqrt{2} b - 81} + \frac{942 \sqrt{2} b^{4}}{4 b^{6} + 28 \sqrt{2} b^{5} + 152 b^{4} + 192 \sqrt{2} b^{3} + 189 b^{2} - 27 \sqrt{2} b - 81} + \frac{1226 b^{3}}{4 b^{6} + 28 \sqrt{2} b^{5} + 152 b^{4} + 192 \sqrt{2} b^{3} + 189 b^{2} - 27 \sqrt{2} b - 81} + \frac{144 \sqrt{2} b^{2}}{4 b^{6} + 28 \sqrt{2} b^{5} + 152 b^{4} + 192 \sqrt{2} b^{3} + 189 b^{2} - 27 \sqrt{2} b - 81} - \frac{378 b}{4 b^{6} + 28 \sqrt{2} b^{5} + 152 b^{4} + 192 \sqrt{2} b^{3} + 189 b^{2} - 27 \sqrt{2} b - 81} - \frac{108 \sqrt{2}}{4 b^{6} + 28 \sqrt{2} b^{5} + 152 b^{4} + 192 \sqrt{2} b^{3} + 189 b^{2} - 27 \sqrt{2} b - 81}\right) + x \right)} \right)\right)}"," ",0,"-RootSum(_t**4*(16*b**4 - 128*b**2 + 256) + _t**2*(12*b**3 + 16*sqrt(2)*b**2 - 48*b - 64*sqrt(2)) + 2*b**2 + 6*sqrt(2)*b + 9, Lambda(_t, _t*log(_t**3*(64*b**12/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 672*sqrt(2)*b**11/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 5760*b**10/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 12064*sqrt(2)*b**9/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 17744*b**8/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 27480*sqrt(2)*b**7/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 154608*b**6/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 141376*sqrt(2)*b**5/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 69072*b**4/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 61704*sqrt(2)*b**3/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 78192*b**2/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 2592*sqrt(2)*b/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 15552/(8*b**10 + 88*sqrt(2)*b**9 + 828*b**8 + 2144*sqrt(2)*b**7 + 6470*b**6 + 5310*sqrt(2)*b**5 + 2781*b**4 - 2322*sqrt(2)*b**3 - 3402*b**2 + 729)) + _t*(16*b**7/(4*b**6 + 28*sqrt(2)*b**5 + 152*b**4 + 192*sqrt(2)*b**3 + 189*b**2 - 27*sqrt(2)*b - 81) + 116*sqrt(2)*b**6/(4*b**6 + 28*sqrt(2)*b**5 + 152*b**4 + 192*sqrt(2)*b**3 + 189*b**2 - 27*sqrt(2)*b - 81) + 668*b**5/(4*b**6 + 28*sqrt(2)*b**5 + 152*b**4 + 192*sqrt(2)*b**3 + 189*b**2 - 27*sqrt(2)*b - 81) + 942*sqrt(2)*b**4/(4*b**6 + 28*sqrt(2)*b**5 + 152*b**4 + 192*sqrt(2)*b**3 + 189*b**2 - 27*sqrt(2)*b - 81) + 1226*b**3/(4*b**6 + 28*sqrt(2)*b**5 + 152*b**4 + 192*sqrt(2)*b**3 + 189*b**2 - 27*sqrt(2)*b - 81) + 144*sqrt(2)*b**2/(4*b**6 + 28*sqrt(2)*b**5 + 152*b**4 + 192*sqrt(2)*b**3 + 189*b**2 - 27*sqrt(2)*b - 81) - 378*b/(4*b**6 + 28*sqrt(2)*b**5 + 152*b**4 + 192*sqrt(2)*b**3 + 189*b**2 - 27*sqrt(2)*b - 81) - 108*sqrt(2)/(4*b**6 + 28*sqrt(2)*b**5 + 152*b**4 + 192*sqrt(2)*b**3 + 189*b**2 - 27*sqrt(2)*b - 81)) + x)))","B",0
105,1,1467,0,2.728712," ","integrate((x**2+2**(1/2))/(x**4+b*x**2+1),x)","\operatorname{RootSum} {\left(t^{4} \left(16 b^{4} - 128 b^{2} + 256\right) + t^{2} \left(12 b^{3} - 16 \sqrt{2} b^{2} - 48 b + 64 \sqrt{2}\right) + 2 b^{2} - 6 \sqrt{2} b + 9, \left( t \mapsto t \log{\left(t^{3} \left(\frac{64 b^{12}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{672 \sqrt{2} b^{11}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{5760 b^{10}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{12064 \sqrt{2} b^{9}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{17744 b^{8}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{27480 \sqrt{2} b^{7}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{154608 b^{6}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{141376 \sqrt{2} b^{5}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{69072 b^{4}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{61704 \sqrt{2} b^{3}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{78192 b^{2}}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} + \frac{2592 \sqrt{2} b}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729} - \frac{15552}{8 b^{10} - 88 \sqrt{2} b^{9} + 828 b^{8} - 2144 \sqrt{2} b^{7} + 6470 b^{6} - 5310 \sqrt{2} b^{5} + 2781 b^{4} + 2322 \sqrt{2} b^{3} - 3402 b^{2} + 729}\right) + t \left(\frac{16 b^{7}}{4 b^{6} - 28 \sqrt{2} b^{5} + 152 b^{4} - 192 \sqrt{2} b^{3} + 189 b^{2} + 27 \sqrt{2} b - 81} - \frac{116 \sqrt{2} b^{6}}{4 b^{6} - 28 \sqrt{2} b^{5} + 152 b^{4} - 192 \sqrt{2} b^{3} + 189 b^{2} + 27 \sqrt{2} b - 81} + \frac{668 b^{5}}{4 b^{6} - 28 \sqrt{2} b^{5} + 152 b^{4} - 192 \sqrt{2} b^{3} + 189 b^{2} + 27 \sqrt{2} b - 81} - \frac{942 \sqrt{2} b^{4}}{4 b^{6} - 28 \sqrt{2} b^{5} + 152 b^{4} - 192 \sqrt{2} b^{3} + 189 b^{2} + 27 \sqrt{2} b - 81} + \frac{1226 b^{3}}{4 b^{6} - 28 \sqrt{2} b^{5} + 152 b^{4} - 192 \sqrt{2} b^{3} + 189 b^{2} + 27 \sqrt{2} b - 81} - \frac{144 \sqrt{2} b^{2}}{4 b^{6} - 28 \sqrt{2} b^{5} + 152 b^{4} - 192 \sqrt{2} b^{3} + 189 b^{2} + 27 \sqrt{2} b - 81} - \frac{378 b}{4 b^{6} - 28 \sqrt{2} b^{5} + 152 b^{4} - 192 \sqrt{2} b^{3} + 189 b^{2} + 27 \sqrt{2} b - 81} + \frac{108 \sqrt{2}}{4 b^{6} - 28 \sqrt{2} b^{5} + 152 b^{4} - 192 \sqrt{2} b^{3} + 189 b^{2} + 27 \sqrt{2} b - 81}\right) + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(16*b**4 - 128*b**2 + 256) + _t**2*(12*b**3 - 16*sqrt(2)*b**2 - 48*b + 64*sqrt(2)) + 2*b**2 - 6*sqrt(2)*b + 9, Lambda(_t, _t*log(_t**3*(64*b**12/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 672*sqrt(2)*b**11/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 5760*b**10/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 12064*sqrt(2)*b**9/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 17744*b**8/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 27480*sqrt(2)*b**7/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 154608*b**6/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 141376*sqrt(2)*b**5/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 69072*b**4/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 61704*sqrt(2)*b**3/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 78192*b**2/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) + 2592*sqrt(2)*b/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729) - 15552/(8*b**10 - 88*sqrt(2)*b**9 + 828*b**8 - 2144*sqrt(2)*b**7 + 6470*b**6 - 5310*sqrt(2)*b**5 + 2781*b**4 + 2322*sqrt(2)*b**3 - 3402*b**2 + 729)) + _t*(16*b**7/(4*b**6 - 28*sqrt(2)*b**5 + 152*b**4 - 192*sqrt(2)*b**3 + 189*b**2 + 27*sqrt(2)*b - 81) - 116*sqrt(2)*b**6/(4*b**6 - 28*sqrt(2)*b**5 + 152*b**4 - 192*sqrt(2)*b**3 + 189*b**2 + 27*sqrt(2)*b - 81) + 668*b**5/(4*b**6 - 28*sqrt(2)*b**5 + 152*b**4 - 192*sqrt(2)*b**3 + 189*b**2 + 27*sqrt(2)*b - 81) - 942*sqrt(2)*b**4/(4*b**6 - 28*sqrt(2)*b**5 + 152*b**4 - 192*sqrt(2)*b**3 + 189*b**2 + 27*sqrt(2)*b - 81) + 1226*b**3/(4*b**6 - 28*sqrt(2)*b**5 + 152*b**4 - 192*sqrt(2)*b**3 + 189*b**2 + 27*sqrt(2)*b - 81) - 144*sqrt(2)*b**2/(4*b**6 - 28*sqrt(2)*b**5 + 152*b**4 - 192*sqrt(2)*b**3 + 189*b**2 + 27*sqrt(2)*b - 81) - 378*b/(4*b**6 - 28*sqrt(2)*b**5 + 152*b**4 - 192*sqrt(2)*b**3 + 189*b**2 + 27*sqrt(2)*b - 81) + 108*sqrt(2)/(4*b**6 - 28*sqrt(2)*b**5 + 152*b**4 - 192*sqrt(2)*b**3 + 189*b**2 + 27*sqrt(2)*b - 81)) + x)))","B",0
106,1,27,0,0.252850," ","integrate((-x**2+2*a)/(x**4-a*x**2+a**2),x)","- \operatorname{RootSum} {\left(16 t^{4} a^{2} - 4 t^{2} a + 1, \left( t \mapsto t \log{\left(- 2 t a + x \right)} \right)\right)}"," ",0,"-RootSum(16*_t**4*a**2 - 4*_t**2*a + 1, Lambda(_t, _t*log(-2*_t*a + x)))","A",0
107,-2,0,0,0.000000," ","integrate((-x**2+2*a**(1/2))/(a+x**4-x**2*a**(1/2)),x)","\text{Exception raised: PolynomialError}"," ",0,"Exception raised: PolynomialError","F(-2)",0
108,1,143,0,0.312883," ","integrate((2*b**(2/3)+x**2)/(b**(4/3)+b**(2/3)*x**2+x**4),x)","\frac{\left(- \frac{1}{4} - \frac{\sqrt{3} i}{4}\right) \log{\left(2 \sqrt[3]{b} \left(- \frac{1}{4} - \frac{\sqrt{3} i}{4}\right) + x \right)} + \left(- \frac{1}{4} + \frac{\sqrt{3} i}{4}\right) \log{\left(2 \sqrt[3]{b} \left(- \frac{1}{4} + \frac{\sqrt{3} i}{4}\right) + x \right)} + \left(\frac{1}{4} - \frac{\sqrt{3} i}{4}\right) \log{\left(2 \sqrt[3]{b} \left(\frac{1}{4} - \frac{\sqrt{3} i}{4}\right) + x \right)} + \left(\frac{1}{4} + \frac{\sqrt{3} i}{4}\right) \log{\left(2 \sqrt[3]{b} \left(\frac{1}{4} + \frac{\sqrt{3} i}{4}\right) + x \right)}}{\sqrt[3]{b}}"," ",0,"((-1/4 - sqrt(3)*I/4)*log(2*b**(1/3)*(-1/4 - sqrt(3)*I/4) + x) + (-1/4 + sqrt(3)*I/4)*log(2*b**(1/3)*(-1/4 + sqrt(3)*I/4) + x) + (1/4 - sqrt(3)*I/4)*log(2*b**(1/3)*(1/4 - sqrt(3)*I/4) + x) + (1/4 + sqrt(3)*I/4)*log(2*b**(1/3)*(1/4 + sqrt(3)*I/4) + x))/b**(1/3)","C",0
109,1,172,0,1.906915," ","integrate((B*x**2+A)/(x**4-a*x**2+a**2),x)","\operatorname{RootSum} {\left(144 t^{4} a^{6} + t^{2} \left(12 A^{2} a^{3} + 48 A B a^{4} + 12 B^{2} a^{5}\right) + A^{4} + 2 A^{3} B a + 3 A^{2} B^{2} a^{2} + 2 A B^{3} a^{3} + B^{4} a^{4}, \left( t \mapsto t \log{\left(x + \frac{24 t^{3} A a^{5} + 48 t^{3} B a^{6} - 2 t A^{3} a^{2} + 6 t A^{2} B a^{3} + 12 t A B^{2} a^{4} + 2 t B^{3} a^{5}}{- A^{4} - A^{3} B a + A B^{3} a^{3} + B^{4} a^{4}} \right)} \right)\right)}"," ",0,"RootSum(144*_t**4*a**6 + _t**2*(12*A**2*a**3 + 48*A*B*a**4 + 12*B**2*a**5) + A**4 + 2*A**3*B*a + 3*A**2*B**2*a**2 + 2*A*B**3*a**3 + B**4*a**4, Lambda(_t, _t*log(x + (24*_t**3*A*a**5 + 48*_t**3*B*a**6 - 2*_t*A**3*a**2 + 6*_t*A**2*B*a**3 + 12*_t*A*B**2*a**4 + 2*_t*B**3*a**5)/(-A**4 - A**3*B*a + A*B**3*a**3 + B**4*a**4))))","A",0
110,-2,0,0,0.000000," ","integrate((B*x**2+A)/(a+x**4-x**2*a**(1/2)),x)","\text{Exception raised: PolynomialError}"," ",0,"Exception raised: PolynomialError","F(-2)",0
111,-2,0,0,0.000000," ","integrate((B*x**2+A)/(a+c*x**4-x**2*(a*c)**(1/2)),x)","\text{Exception raised: PolynomialError}"," ",0,"Exception raised: PolynomialError","F(-2)",0
112,-2,0,0,0.000000," ","integrate((B*x**2+A)/(a+c*x**4-x**2*a**(1/2)*c**(1/2)),x)","\text{Exception raised: PolynomialError}"," ",0,"Exception raised: PolynomialError","F(-2)",0
113,0,0,0,0.000000," ","integrate((-x**2+3)/(-x**4+x**2+3)**(1/2),x)","- \int \frac{x^{2}}{\sqrt{- x^{4} + x^{2} + 3}}\, dx - \int \left(- \frac{3}{\sqrt{- x^{4} + x^{2} + 3}}\right)\, dx"," ",0,"-Integral(x**2/sqrt(-x**4 + x**2 + 3), x) - Integral(-3/sqrt(-x**4 + x**2 + 3), x)","F",0
114,0,0,0,0.000000," ","integrate((-x**2+3)/(-x**4+2*x**2+3)**(1/2),x)","- \int \frac{x^{2}}{\sqrt{- x^{4} + 2 x^{2} + 3}}\, dx - \int \left(- \frac{3}{\sqrt{- x^{4} + 2 x^{2} + 3}}\right)\, dx"," ",0,"-Integral(x**2/sqrt(-x**4 + 2*x**2 + 3), x) - Integral(-3/sqrt(-x**4 + 2*x**2 + 3), x)","F",0
115,0,0,0,0.000000," ","integrate((-x**2+3)/(-x**4+3*x**2+3)**(1/2),x)","- \int \frac{x^{2}}{\sqrt{- x^{4} + 3 x^{2} + 3}}\, dx - \int \left(- \frac{3}{\sqrt{- x^{4} + 3 x^{2} + 3}}\right)\, dx"," ",0,"-Integral(x**2/sqrt(-x**4 + 3*x**2 + 3), x) - Integral(-3/sqrt(-x**4 + 3*x**2 + 3), x)","F",0
116,0,0,0,0.000000," ","integrate((-x**2+3)/(-x**4-x**2+3)**(1/2),x)","- \int \frac{x^{2}}{\sqrt{- x^{4} - x^{2} + 3}}\, dx - \int \left(- \frac{3}{\sqrt{- x^{4} - x^{2} + 3}}\right)\, dx"," ",0,"-Integral(x**2/sqrt(-x**4 - x**2 + 3), x) - Integral(-3/sqrt(-x**4 - x**2 + 3), x)","F",0
117,0,0,0,0.000000," ","integrate((-x**2+3)/(-x**4-2*x**2+3)**(1/2),x)","- \int \frac{x^{2}}{\sqrt{- x^{4} - 2 x^{2} + 3}}\, dx - \int \left(- \frac{3}{\sqrt{- x^{4} - 2 x^{2} + 3}}\right)\, dx"," ",0,"-Integral(x**2/sqrt(-x**4 - 2*x**2 + 3), x) - Integral(-3/sqrt(-x**4 - 2*x**2 + 3), x)","F",0
118,0,0,0,0.000000," ","integrate((-x**2+3)/(-x**4-3*x**2+3)**(1/2),x)","- \int \frac{x^{2}}{\sqrt{- x^{4} - 3 x^{2} + 3}}\, dx - \int \left(- \frac{3}{\sqrt{- x^{4} - 3 x^{2} + 3}}\right)\, dx"," ",0,"-Integral(x**2/sqrt(-x**4 - 3*x**2 + 3), x) - Integral(-3/sqrt(-x**4 - 3*x**2 + 3), x)","F",0
119,0,0,0,0.000000," ","integrate((2*c*x**2-(-4*a*c+b**2)**(1/2)+b)/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{b + 2 c x^{2} - \sqrt{- 4 a c + b^{2}}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral((b + 2*c*x**2 - sqrt(-4*a*c + b**2))/sqrt(a + b*x**2 + c*x**4), x)","F",0
120,1,110,0,0.092638," ","integrate((e*x**2+d)**4*(c*x**4+a),x)","a d^{4} x + \frac{4 a d^{3} e x^{3}}{3} + \frac{4 c d e^{3} x^{11}}{11} + \frac{c e^{4} x^{13}}{13} + x^{9} \left(\frac{a e^{4}}{9} + \frac{2 c d^{2} e^{2}}{3}\right) + x^{7} \left(\frac{4 a d e^{3}}{7} + \frac{4 c d^{3} e}{7}\right) + x^{5} \left(\frac{6 a d^{2} e^{2}}{5} + \frac{c d^{4}}{5}\right)"," ",0,"a*d**4*x + 4*a*d**3*e*x**3/3 + 4*c*d*e**3*x**11/11 + c*e**4*x**13/13 + x**9*(a*e**4/9 + 2*c*d**2*e**2/3) + x**7*(4*a*d*e**3/7 + 4*c*d**3*e/7) + x**5*(6*a*d**2*e**2/5 + c*d**4/5)","A",0
121,1,78,0,0.087928," ","integrate((e*x**2+d)**3*(c*x**4+a),x)","a d^{3} x + a d^{2} e x^{3} + \frac{c d e^{2} x^{9}}{3} + \frac{c e^{3} x^{11}}{11} + x^{7} \left(\frac{a e^{3}}{7} + \frac{3 c d^{2} e}{7}\right) + x^{5} \left(\frac{3 a d e^{2}}{5} + \frac{c d^{3}}{5}\right)"," ",0,"a*d**3*x + a*d**2*e*x**3 + c*d*e**2*x**9/3 + c*e**3*x**11/11 + x**7*(a*e**3/7 + 3*c*d**2*e/7) + x**5*(3*a*d*e**2/5 + c*d**3/5)","A",0
122,1,56,0,0.076940," ","integrate((e*x**2+d)**2*(c*x**4+a),x)","a d^{2} x + \frac{2 a d e x^{3}}{3} + \frac{2 c d e x^{7}}{7} + \frac{c e^{2} x^{9}}{9} + x^{5} \left(\frac{a e^{2}}{5} + \frac{c d^{2}}{5}\right)"," ",0,"a*d**2*x + 2*a*d*e*x**3/3 + 2*c*d*e*x**7/7 + c*e**2*x**9/9 + x**5*(a*e**2/5 + c*d**2/5)","A",0
123,1,29,0,0.075623," ","integrate((e*x**2+d)*(c*x**4+a),x)","a d x + \frac{a e x^{3}}{3} + \frac{c d x^{5}}{5} + \frac{c e x^{7}}{7}"," ",0,"a*d*x + a*e*x**3/3 + c*d*x**5/5 + c*e*x**7/7","A",0
124,1,104,0,0.323506," ","integrate((c*x**4+a)/(e*x**2+d),x)","- \frac{c d x}{e^{2}} + \frac{c x^{3}}{3 e} - \frac{\sqrt{- \frac{1}{d e^{5}}} \left(a e^{2} + c d^{2}\right) \log{\left(- d e^{2} \sqrt{- \frac{1}{d e^{5}}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{d e^{5}}} \left(a e^{2} + c d^{2}\right) \log{\left(d e^{2} \sqrt{- \frac{1}{d e^{5}}} + x \right)}}{2}"," ",0,"-c*d*x/e**2 + c*x**3/(3*e) - sqrt(-1/(d*e**5))*(a*e**2 + c*d**2)*log(-d*e**2*sqrt(-1/(d*e**5)) + x)/2 + sqrt(-1/(d*e**5))*(a*e**2 + c*d**2)*log(d*e**2*sqrt(-1/(d*e**5)) + x)/2","B",0
125,1,138,0,0.509917," ","integrate((c*x**4+a)/(e*x**2+d)**2,x)","\frac{c x}{e^{2}} + \frac{x \left(a e^{2} + c d^{2}\right)}{2 d^{2} e^{2} + 2 d e^{3} x^{2}} - \frac{\sqrt{- \frac{1}{d^{3} e^{5}}} \left(a e^{2} - 3 c d^{2}\right) \log{\left(- d^{2} e^{2} \sqrt{- \frac{1}{d^{3} e^{5}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{d^{3} e^{5}}} \left(a e^{2} - 3 c d^{2}\right) \log{\left(d^{2} e^{2} \sqrt{- \frac{1}{d^{3} e^{5}}} + x \right)}}{4}"," ",0,"c*x/e**2 + x*(a*e**2 + c*d**2)/(2*d**2*e**2 + 2*d*e**3*x**2) - sqrt(-1/(d**3*e**5))*(a*e**2 - 3*c*d**2)*log(-d**2*e**2*sqrt(-1/(d**3*e**5)) + x)/4 + sqrt(-1/(d**3*e**5))*(a*e**2 - 3*c*d**2)*log(d**2*e**2*sqrt(-1/(d**3*e**5)) + x)/4","B",0
126,1,219,0,0.754824," ","integrate((c*x**4+a)/(e*x**2+d)**3,x)","- \frac{3 \sqrt{- \frac{1}{d^{5} e^{5}}} \left(a e^{2} + c d^{2}\right) \log{\left(- \frac{3 d^{3} e^{2} \sqrt{- \frac{1}{d^{5} e^{5}}} \left(a e^{2} + c d^{2}\right)}{3 a e^{2} + 3 c d^{2}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{d^{5} e^{5}}} \left(a e^{2} + c d^{2}\right) \log{\left(\frac{3 d^{3} e^{2} \sqrt{- \frac{1}{d^{5} e^{5}}} \left(a e^{2} + c d^{2}\right)}{3 a e^{2} + 3 c d^{2}} + x \right)}}{16} + \frac{x^{3} \left(3 a e^{3} - 5 c d^{2} e\right) + x \left(5 a d e^{2} - 3 c d^{3}\right)}{8 d^{4} e^{2} + 16 d^{3} e^{3} x^{2} + 8 d^{2} e^{4} x^{4}}"," ",0,"-3*sqrt(-1/(d**5*e**5))*(a*e**2 + c*d**2)*log(-3*d**3*e**2*sqrt(-1/(d**5*e**5))*(a*e**2 + c*d**2)/(3*a*e**2 + 3*c*d**2) + x)/16 + 3*sqrt(-1/(d**5*e**5))*(a*e**2 + c*d**2)*log(3*d**3*e**2*sqrt(-1/(d**5*e**5))*(a*e**2 + c*d**2)/(3*a*e**2 + 3*c*d**2) + x)/16 + (x**3*(3*a*e**3 - 5*c*d**2*e) + x*(5*a*d*e**2 - 3*c*d**3))/(8*d**4*e**2 + 16*d**3*e**3*x**2 + 8*d**2*e**4*x**4)","B",0
127,1,204,0,0.952099," ","integrate((c*x**4+a)/(e*x**2+d)**4,x)","- \frac{\sqrt{- \frac{1}{d^{7} e^{5}}} \left(5 a e^{2} + c d^{2}\right) \log{\left(- d^{4} e^{2} \sqrt{- \frac{1}{d^{7} e^{5}}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{d^{7} e^{5}}} \left(5 a e^{2} + c d^{2}\right) \log{\left(d^{4} e^{2} \sqrt{- \frac{1}{d^{7} e^{5}}} + x \right)}}{32} + \frac{x^{5} \left(15 a e^{4} + 3 c d^{2} e^{2}\right) + x^{3} \left(40 a d e^{3} - 8 c d^{3} e\right) + x \left(33 a d^{2} e^{2} - 3 c d^{4}\right)}{48 d^{6} e^{2} + 144 d^{5} e^{3} x^{2} + 144 d^{4} e^{4} x^{4} + 48 d^{3} e^{5} x^{6}}"," ",0,"-sqrt(-1/(d**7*e**5))*(5*a*e**2 + c*d**2)*log(-d**4*e**2*sqrt(-1/(d**7*e**5)) + x)/32 + sqrt(-1/(d**7*e**5))*(5*a*e**2 + c*d**2)*log(d**4*e**2*sqrt(-1/(d**7*e**5)) + x)/32 + (x**5*(15*a*e**4 + 3*c*d**2*e**2) + x**3*(40*a*d*e**3 - 8*c*d**3*e) + x*(33*a*d**2*e**2 - 3*c*d**4))/(48*d**6*e**2 + 144*d**5*e**3*x**2 + 144*d**4*e**4*x**4 + 48*d**3*e**5*x**6)","A",0
128,1,144,0,0.094707," ","integrate((e*x**2+d)**3*(c*x**4+a)**2,x)","a^{2} d^{3} x + a^{2} d^{2} e x^{3} + \frac{3 c^{2} d e^{2} x^{13}}{13} + \frac{c^{2} e^{3} x^{15}}{15} + x^{11} \left(\frac{2 a c e^{3}}{11} + \frac{3 c^{2} d^{2} e}{11}\right) + x^{9} \left(\frac{2 a c d e^{2}}{3} + \frac{c^{2} d^{3}}{9}\right) + x^{7} \left(\frac{a^{2} e^{3}}{7} + \frac{6 a c d^{2} e}{7}\right) + x^{5} \left(\frac{3 a^{2} d e^{2}}{5} + \frac{2 a c d^{3}}{5}\right)"," ",0,"a**2*d**3*x + a**2*d**2*e*x**3 + 3*c**2*d*e**2*x**13/13 + c**2*e**3*x**15/15 + x**11*(2*a*c*e**3/11 + 3*c**2*d**2*e/11) + x**9*(2*a*c*d*e**2/3 + c**2*d**3/9) + x**7*(a**2*e**3/7 + 6*a*c*d**2*e/7) + x**5*(3*a**2*d*e**2/5 + 2*a*c*d**3/5)","A",0
129,1,104,0,0.087791," ","integrate((e*x**2+d)**2*(c*x**4+a)**2,x)","a^{2} d^{2} x + \frac{2 a^{2} d e x^{3}}{3} + \frac{4 a c d e x^{7}}{7} + \frac{2 c^{2} d e x^{11}}{11} + \frac{c^{2} e^{2} x^{13}}{13} + x^{9} \left(\frac{2 a c e^{2}}{9} + \frac{c^{2} d^{2}}{9}\right) + x^{5} \left(\frac{a^{2} e^{2}}{5} + \frac{2 a c d^{2}}{5}\right)"," ",0,"a**2*d**2*x + 2*a**2*d*e*x**3/3 + 4*a*c*d*e*x**7/7 + 2*c**2*d*e*x**11/11 + c**2*e**2*x**13/13 + x**9*(2*a*c*e**2/9 + c**2*d**2/9) + x**5*(a**2*e**2/5 + 2*a*c*d**2/5)","A",0
130,1,60,0,0.075613," ","integrate((e*x**2+d)*(c*x**4+a)**2,x)","a^{2} d x + \frac{a^{2} e x^{3}}{3} + \frac{2 a c d x^{5}}{5} + \frac{2 a c e x^{7}}{7} + \frac{c^{2} d x^{9}}{9} + \frac{c^{2} e x^{11}}{11}"," ",0,"a**2*d*x + a**2*e*x**3/3 + 2*a*c*d*x**5/5 + 2*a*c*e*x**7/7 + c**2*d*x**9/9 + c**2*e*x**11/11","A",0
131,1,22,0,0.065352," ","integrate((c*x**4+a)**2,x)","a^{2} x + \frac{2 a c x^{5}}{5} + \frac{c^{2} x^{9}}{9}"," ",0,"a**2*x + 2*a*c*x**5/5 + c**2*x**9/9","A",0
132,1,236,0,0.497749," ","integrate((c*x**4+a)**2/(e*x**2+d),x)","- \frac{c^{2} d x^{5}}{5 e^{2}} + \frac{c^{2} x^{7}}{7 e} + x^{3} \left(\frac{2 a c}{3 e} + \frac{c^{2} d^{2}}{3 e^{3}}\right) + x \left(- \frac{2 a c d}{e^{2}} - \frac{c^{2} d^{3}}{e^{4}}\right) - \frac{\sqrt{- \frac{1}{d e^{9}}} \left(a e^{2} + c d^{2}\right)^{2} \log{\left(- \frac{d e^{4} \sqrt{- \frac{1}{d e^{9}}} \left(a e^{2} + c d^{2}\right)^{2}}{a^{2} e^{4} + 2 a c d^{2} e^{2} + c^{2} d^{4}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{d e^{9}}} \left(a e^{2} + c d^{2}\right)^{2} \log{\left(\frac{d e^{4} \sqrt{- \frac{1}{d e^{9}}} \left(a e^{2} + c d^{2}\right)^{2}}{a^{2} e^{4} + 2 a c d^{2} e^{2} + c^{2} d^{4}} + x \right)}}{2}"," ",0,"-c**2*d*x**5/(5*e**2) + c**2*x**7/(7*e) + x**3*(2*a*c/(3*e) + c**2*d**2/(3*e**3)) + x*(-2*a*c*d/e**2 - c**2*d**3/e**4) - sqrt(-1/(d*e**9))*(a*e**2 + c*d**2)**2*log(-d*e**4*sqrt(-1/(d*e**9))*(a*e**2 + c*d**2)**2/(a**2*e**4 + 2*a*c*d**2*e**2 + c**2*d**4) + x)/2 + sqrt(-1/(d*e**9))*(a*e**2 + c*d**2)**2*log(d*e**4*sqrt(-1/(d*e**9))*(a*e**2 + c*d**2)**2/(a**2*e**4 + 2*a*c*d**2*e**2 + c**2*d**4) + x)/2","B",0
133,1,314,0,0.931804," ","integrate((c*x**4+a)**2/(e*x**2+d)**2,x)","- \frac{2 c^{2} d x^{3}}{3 e^{3}} + \frac{c^{2} x^{5}}{5 e^{2}} + x \left(\frac{2 a c}{e^{2}} + \frac{3 c^{2} d^{2}}{e^{4}}\right) + \frac{x \left(a^{2} e^{4} + 2 a c d^{2} e^{2} + c^{2} d^{4}\right)}{2 d^{2} e^{4} + 2 d e^{5} x^{2}} - \frac{\sqrt{- \frac{1}{d^{3} e^{9}}} \left(a e^{2} - 7 c d^{2}\right) \left(a e^{2} + c d^{2}\right) \log{\left(- \frac{d^{2} e^{4} \sqrt{- \frac{1}{d^{3} e^{9}}} \left(a e^{2} - 7 c d^{2}\right) \left(a e^{2} + c d^{2}\right)}{a^{2} e^{4} - 6 a c d^{2} e^{2} - 7 c^{2} d^{4}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{d^{3} e^{9}}} \left(a e^{2} - 7 c d^{2}\right) \left(a e^{2} + c d^{2}\right) \log{\left(\frac{d^{2} e^{4} \sqrt{- \frac{1}{d^{3} e^{9}}} \left(a e^{2} - 7 c d^{2}\right) \left(a e^{2} + c d^{2}\right)}{a^{2} e^{4} - 6 a c d^{2} e^{2} - 7 c^{2} d^{4}} + x \right)}}{4}"," ",0,"-2*c**2*d*x**3/(3*e**3) + c**2*x**5/(5*e**2) + x*(2*a*c/e**2 + 3*c**2*d**2/e**4) + x*(a**2*e**4 + 2*a*c*d**2*e**2 + c**2*d**4)/(2*d**2*e**4 + 2*d*e**5*x**2) - sqrt(-1/(d**3*e**9))*(a*e**2 - 7*c*d**2)*(a*e**2 + c*d**2)*log(-d**2*e**4*sqrt(-1/(d**3*e**9))*(a*e**2 - 7*c*d**2)*(a*e**2 + c*d**2)/(a**2*e**4 - 6*a*c*d**2*e**2 - 7*c**2*d**4) + x)/4 + sqrt(-1/(d**3*e**9))*(a*e**2 - 7*c*d**2)*(a*e**2 + c*d**2)*log(d**2*e**4*sqrt(-1/(d**3*e**9))*(a*e**2 - 7*c*d**2)*(a*e**2 + c*d**2)/(a**2*e**4 - 6*a*c*d**2*e**2 - 7*c**2*d**4) + x)/4","B",0
134,1,257,0,1.713047," ","integrate((c*x**4+a)**2/(e*x**2+d)**3,x)","- \frac{3 c^{2} d x}{e^{4}} + \frac{c^{2} x^{3}}{3 e^{3}} - \frac{\sqrt{- \frac{1}{d^{5} e^{9}}} \left(3 a^{2} e^{4} + 6 a c d^{2} e^{2} + 35 c^{2} d^{4}\right) \log{\left(- d^{3} e^{4} \sqrt{- \frac{1}{d^{5} e^{9}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{d^{5} e^{9}}} \left(3 a^{2} e^{4} + 6 a c d^{2} e^{2} + 35 c^{2} d^{4}\right) \log{\left(d^{3} e^{4} \sqrt{- \frac{1}{d^{5} e^{9}}} + x \right)}}{16} + \frac{x^{3} \left(3 a^{2} e^{5} - 10 a c d^{2} e^{3} - 13 c^{2} d^{4} e\right) + x \left(5 a^{2} d e^{4} - 6 a c d^{3} e^{2} - 11 c^{2} d^{5}\right)}{8 d^{4} e^{4} + 16 d^{3} e^{5} x^{2} + 8 d^{2} e^{6} x^{4}}"," ",0,"-3*c**2*d*x/e**4 + c**2*x**3/(3*e**3) - sqrt(-1/(d**5*e**9))*(3*a**2*e**4 + 6*a*c*d**2*e**2 + 35*c**2*d**4)*log(-d**3*e**4*sqrt(-1/(d**5*e**9)) + x)/16 + sqrt(-1/(d**5*e**9))*(3*a**2*e**4 + 6*a*c*d**2*e**2 + 35*c**2*d**4)*log(d**3*e**4*sqrt(-1/(d**5*e**9)) + x)/16 + (x**3*(3*a**2*e**5 - 10*a*c*d**2*e**3 - 13*c**2*d**4*e) + x*(5*a**2*d*e**4 - 6*a*c*d**3*e**2 - 11*c**2*d**5))/(8*d**4*e**4 + 16*d**3*e**5*x**2 + 8*d**2*e**6*x**4)","A",0
135,1,292,0,2.612006," ","integrate((c*x**4+a)**2/(e*x**2+d)**4,x)","\frac{c^{2} x}{e^{4}} - \frac{\sqrt{- \frac{1}{d^{7} e^{9}}} \left(5 a^{2} e^{4} + 2 a c d^{2} e^{2} - 35 c^{2} d^{4}\right) \log{\left(- d^{4} e^{4} \sqrt{- \frac{1}{d^{7} e^{9}}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{d^{7} e^{9}}} \left(5 a^{2} e^{4} + 2 a c d^{2} e^{2} - 35 c^{2} d^{4}\right) \log{\left(d^{4} e^{4} \sqrt{- \frac{1}{d^{7} e^{9}}} + x \right)}}{32} + \frac{x^{5} \left(15 a^{2} e^{6} + 6 a c d^{2} e^{4} + 87 c^{2} d^{4} e^{2}\right) + x^{3} \left(40 a^{2} d e^{5} - 16 a c d^{3} e^{3} + 136 c^{2} d^{5} e\right) + x \left(33 a^{2} d^{2} e^{4} - 6 a c d^{4} e^{2} + 57 c^{2} d^{6}\right)}{48 d^{6} e^{4} + 144 d^{5} e^{5} x^{2} + 144 d^{4} e^{6} x^{4} + 48 d^{3} e^{7} x^{6}}"," ",0,"c**2*x/e**4 - sqrt(-1/(d**7*e**9))*(5*a**2*e**4 + 2*a*c*d**2*e**2 - 35*c**2*d**4)*log(-d**4*e**4*sqrt(-1/(d**7*e**9)) + x)/32 + sqrt(-1/(d**7*e**9))*(5*a**2*e**4 + 2*a*c*d**2*e**2 - 35*c**2*d**4)*log(d**4*e**4*sqrt(-1/(d**7*e**9)) + x)/32 + (x**5*(15*a**2*e**6 + 6*a*c*d**2*e**4 + 87*c**2*d**4*e**2) + x**3*(40*a**2*d*e**5 - 16*a*c*d**3*e**3 + 136*c**2*d**5*e) + x*(33*a**2*d**2*e**4 - 6*a*c*d**4*e**2 + 57*c**2*d**6))/(48*d**6*e**4 + 144*d**5*e**5*x**2 + 144*d**4*e**6*x**4 + 48*d**3*e**7*x**6)","A",0
136,1,335,0,4.114338," ","integrate((c*x**4+a)**2/(e*x**2+d)**5,x)","- \frac{\sqrt{- \frac{1}{d^{9} e^{9}}} \left(35 a^{2} e^{4} + 6 a c d^{2} e^{2} + 35 c^{2} d^{4}\right) \log{\left(- d^{5} e^{4} \sqrt{- \frac{1}{d^{9} e^{9}}} + x \right)}}{256} + \frac{\sqrt{- \frac{1}{d^{9} e^{9}}} \left(35 a^{2} e^{4} + 6 a c d^{2} e^{2} + 35 c^{2} d^{4}\right) \log{\left(d^{5} e^{4} \sqrt{- \frac{1}{d^{9} e^{9}}} + x \right)}}{256} + \frac{x^{7} \left(105 a^{2} e^{7} + 18 a c d^{2} e^{5} - 279 c^{2} d^{4} e^{3}\right) + x^{5} \left(385 a^{2} d e^{6} + 66 a c d^{3} e^{4} - 511 c^{2} d^{5} e^{2}\right) + x^{3} \left(511 a^{2} d^{2} e^{5} - 66 a c d^{4} e^{3} - 385 c^{2} d^{6} e\right) + x \left(279 a^{2} d^{3} e^{4} - 18 a c d^{5} e^{2} - 105 c^{2} d^{7}\right)}{384 d^{8} e^{4} + 1536 d^{7} e^{5} x^{2} + 2304 d^{6} e^{6} x^{4} + 1536 d^{5} e^{7} x^{6} + 384 d^{4} e^{8} x^{8}}"," ",0,"-sqrt(-1/(d**9*e**9))*(35*a**2*e**4 + 6*a*c*d**2*e**2 + 35*c**2*d**4)*log(-d**5*e**4*sqrt(-1/(d**9*e**9)) + x)/256 + sqrt(-1/(d**9*e**9))*(35*a**2*e**4 + 6*a*c*d**2*e**2 + 35*c**2*d**4)*log(d**5*e**4*sqrt(-1/(d**9*e**9)) + x)/256 + (x**7*(105*a**2*e**7 + 18*a*c*d**2*e**5 - 279*c**2*d**4*e**3) + x**5*(385*a**2*d*e**6 + 66*a*c*d**3*e**4 - 511*c**2*d**5*e**2) + x**3*(511*a**2*d**2*e**5 - 66*a*c*d**4*e**3 - 385*c**2*d**6*e) + x*(279*a**2*d**3*e**4 - 18*a*c*d**5*e**2 - 105*c**2*d**7))/(384*d**8*e**4 + 1536*d**7*e**5*x**2 + 2304*d**6*e**6*x**4 + 1536*d**5*e**7*x**6 + 384*d**4*e**8*x**8)","A",0
137,1,500,0,3.752485," ","integrate((e*x**2+d)**4/(c*x**4+a),x)","x \left(- \frac{a e^{4}}{c^{2}} + \frac{6 d^{2} e^{2}}{c}\right) + \operatorname{RootSum} {\left(256 t^{4} a^{3} c^{9} + t^{2} \left(- 256 a^{5} c^{5} d e^{7} + 1792 a^{4} c^{6} d^{3} e^{5} - 1792 a^{3} c^{7} d^{5} e^{3} + 256 a^{2} c^{8} d^{7} e\right) + a^{8} e^{16} + 8 a^{7} c d^{2} e^{14} + 28 a^{6} c^{2} d^{4} e^{12} + 56 a^{5} c^{3} d^{6} e^{10} + 70 a^{4} c^{4} d^{8} e^{8} + 56 a^{3} c^{5} d^{10} e^{6} + 28 a^{2} c^{6} d^{12} e^{4} + 8 a c^{7} d^{14} e^{2} + c^{8} d^{16}, \left( t \mapsto t \log{\left(x + \frac{256 t^{3} a^{4} c^{7} d e^{3} - 256 t^{3} a^{3} c^{8} d^{3} e + 4 t a^{7} c^{2} e^{12} - 264 t a^{6} c^{3} d^{2} e^{10} + 1980 t a^{5} c^{4} d^{4} e^{8} - 3696 t a^{4} c^{5} d^{6} e^{6} + 1980 t a^{3} c^{6} d^{8} e^{4} - 264 t a^{2} c^{7} d^{10} e^{2} + 4 t a c^{8} d^{12}}{a^{8} e^{16} - 24 a^{7} c d^{2} e^{14} - 36 a^{6} c^{2} d^{4} e^{12} + 88 a^{5} c^{3} d^{6} e^{10} + 198 a^{4} c^{4} d^{8} e^{8} + 88 a^{3} c^{5} d^{10} e^{6} - 36 a^{2} c^{6} d^{12} e^{4} - 24 a c^{7} d^{14} e^{2} + c^{8} d^{16}} \right)} \right)\right)} + \frac{4 d e^{3} x^{3}}{3 c} + \frac{e^{4} x^{5}}{5 c}"," ",0,"x*(-a*e**4/c**2 + 6*d**2*e**2/c) + RootSum(256*_t**4*a**3*c**9 + _t**2*(-256*a**5*c**5*d*e**7 + 1792*a**4*c**6*d**3*e**5 - 1792*a**3*c**7*d**5*e**3 + 256*a**2*c**8*d**7*e) + a**8*e**16 + 8*a**7*c*d**2*e**14 + 28*a**6*c**2*d**4*e**12 + 56*a**5*c**3*d**6*e**10 + 70*a**4*c**4*d**8*e**8 + 56*a**3*c**5*d**10*e**6 + 28*a**2*c**6*d**12*e**4 + 8*a*c**7*d**14*e**2 + c**8*d**16, Lambda(_t, _t*log(x + (256*_t**3*a**4*c**7*d*e**3 - 256*_t**3*a**3*c**8*d**3*e + 4*_t*a**7*c**2*e**12 - 264*_t*a**6*c**3*d**2*e**10 + 1980*_t*a**5*c**4*d**4*e**8 - 3696*_t*a**4*c**5*d**6*e**6 + 1980*_t*a**3*c**6*d**8*e**4 - 264*_t*a**2*c**7*d**10*e**2 + 4*_t*a*c**8*d**12)/(a**8*e**16 - 24*a**7*c*d**2*e**14 - 36*a**6*c**2*d**4*e**12 + 88*a**5*c**3*d**6*e**10 + 198*a**4*c**4*d**8*e**8 + 88*a**3*c**5*d**10*e**6 - 36*a**2*c**6*d**12*e**4 - 24*a*c**7*d**14*e**2 + c**8*d**16)))) + 4*d*e**3*x**3/(3*c) + e**4*x**5/(5*c)","A",0
138,1,350,0,2.273109," ","integrate((e*x**2+d)**3/(c*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} c^{7} + t^{2} \left(192 a^{4} c^{4} d e^{5} - 640 a^{3} c^{5} d^{3} e^{3} + 192 a^{2} c^{6} d^{5} e\right) + a^{6} e^{12} + 6 a^{5} c d^{2} e^{10} + 15 a^{4} c^{2} d^{4} e^{8} + 20 a^{3} c^{3} d^{6} e^{6} + 15 a^{2} c^{4} d^{8} e^{4} + 6 a c^{5} d^{10} e^{2} + c^{6} d^{12}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{4} c^{5} e^{3} + 192 t^{3} a^{3} c^{6} d^{2} e - 36 t a^{5} c^{2} d e^{8} + 336 t a^{4} c^{3} d^{3} e^{6} - 504 t a^{3} c^{4} d^{5} e^{4} + 144 t a^{2} c^{5} d^{7} e^{2} - 4 t a c^{6} d^{9}}{a^{6} e^{12} - 12 a^{5} c d^{2} e^{10} - 27 a^{4} c^{2} d^{4} e^{8} + 27 a^{2} c^{4} d^{8} e^{4} + 12 a c^{5} d^{10} e^{2} - c^{6} d^{12}} \right)} \right)\right)} + \frac{3 d e^{2} x}{c} + \frac{e^{3} x^{3}}{3 c}"," ",0,"RootSum(256*_t**4*a**3*c**7 + _t**2*(192*a**4*c**4*d*e**5 - 640*a**3*c**5*d**3*e**3 + 192*a**2*c**6*d**5*e) + a**6*e**12 + 6*a**5*c*d**2*e**10 + 15*a**4*c**2*d**4*e**8 + 20*a**3*c**3*d**6*e**6 + 15*a**2*c**4*d**8*e**4 + 6*a*c**5*d**10*e**2 + c**6*d**12, Lambda(_t, _t*log(x + (-64*_t**3*a**4*c**5*e**3 + 192*_t**3*a**3*c**6*d**2*e - 36*_t*a**5*c**2*d*e**8 + 336*_t*a**4*c**3*d**3*e**6 - 504*_t*a**3*c**4*d**5*e**4 + 144*_t*a**2*c**5*d**7*e**2 - 4*_t*a*c**6*d**9)/(a**6*e**12 - 12*a**5*c*d**2*e**10 - 27*a**4*c**2*d**4*e**8 + 27*a**2*c**4*d**8*e**4 + 12*a*c**5*d**10*e**2 - c**6*d**12)))) + 3*d*e**2*x/c + e**3*x**3/(3*c)","A",0
139,1,238,0,1.477616," ","integrate((e*x**2+d)**2/(c*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} c^{5} + t^{2} \left(- 128 a^{3} c^{3} d e^{3} + 128 a^{2} c^{4} d^{3} e\right) + a^{4} e^{8} + 4 a^{3} c d^{2} e^{6} + 6 a^{2} c^{2} d^{4} e^{4} + 4 a c^{3} d^{6} e^{2} + c^{4} d^{8}, \left( t \mapsto t \log{\left(x + \frac{- 128 t^{3} a^{3} c^{4} d e - 4 t a^{4} c e^{6} + 60 t a^{3} c^{2} d^{2} e^{4} - 60 t a^{2} c^{3} d^{4} e^{2} + 4 t a c^{4} d^{6}}{a^{4} e^{8} - 4 a^{3} c d^{2} e^{6} - 10 a^{2} c^{2} d^{4} e^{4} - 4 a c^{3} d^{6} e^{2} + c^{4} d^{8}} \right)} \right)\right)} + \frac{e^{2} x}{c}"," ",0,"RootSum(256*_t**4*a**3*c**5 + _t**2*(-128*a**3*c**3*d*e**3 + 128*a**2*c**4*d**3*e) + a**4*e**8 + 4*a**3*c*d**2*e**6 + 6*a**2*c**2*d**4*e**4 + 4*a*c**3*d**6*e**2 + c**4*d**8, Lambda(_t, _t*log(x + (-128*_t**3*a**3*c**4*d*e - 4*_t*a**4*c*e**6 + 60*_t*a**3*c**2*d**2*e**4 - 60*_t*a**2*c**3*d**4*e**2 + 4*_t*a*c**4*d**6)/(a**4*e**8 - 4*a**3*c*d**2*e**6 - 10*a**2*c**2*d**4*e**4 - 4*a*c**3*d**6*e**2 + c**4*d**8)))) + e**2*x/c","A",0
140,1,109,0,0.680235," ","integrate((e*x**2+d)/(c*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} c^{3} + 64 t^{2} a^{2} c^{2} d e + a^{2} e^{4} + 2 a c d^{2} e^{2} + c^{2} d^{4}, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a^{3} c^{2} e + 12 t a^{2} c d e^{2} - 4 t a c^{2} d^{3}}{a^{2} e^{4} - c^{2} d^{4}} \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*c**3 + 64*_t**2*a**2*c**2*d*e + a**2*e**4 + 2*a*c*d**2*e**2 + c**2*d**4, Lambda(_t, _t*log(x + (64*_t**3*a**3*c**2*e + 12*_t*a**2*c*d*e**2 - 4*_t*a*c**2*d**3)/(a**2*e**4 - c**2*d**4))))","A",0
141,1,20,0,0.174427," ","integrate(1/(c*x**4+a),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} c + 1, \left( t \mapsto t \log{\left(4 t a + x \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*c + 1, Lambda(_t, _t*log(4*_t*a + x)))","A",0
142,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)/(c*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(c*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,1,352,0,3.370943," ","integrate((e*x**2+d)**3/(c*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{7} c^{7} + t^{2} \left(9216 a^{6} c^{4} d e^{5} + 18432 a^{5} c^{5} d^{3} e^{3} + 9216 a^{4} c^{6} d^{5} e\right) + 81 a^{6} e^{12} + 486 a^{5} c d^{2} e^{10} + 1215 a^{4} c^{2} d^{4} e^{8} + 1620 a^{3} c^{3} d^{6} e^{6} + 1215 a^{2} c^{4} d^{8} e^{4} + 486 a c^{5} d^{10} e^{2} + 81 c^{6} d^{12}, \left( t \mapsto t \log{\left(x + \frac{4096 t^{3} a^{6} c^{5} e + 432 t a^{5} c^{2} d e^{6} + 720 t a^{4} c^{3} d^{3} e^{4} + 144 t a^{3} c^{4} d^{5} e^{2} - 144 t a^{2} c^{5} d^{7}}{27 a^{5} e^{10} + 81 a^{4} c d^{2} e^{8} + 54 a^{3} c^{2} d^{4} e^{6} - 54 a^{2} c^{3} d^{6} e^{4} - 81 a c^{4} d^{8} e^{2} - 27 c^{5} d^{10}} \right)} \right)\right)} + \frac{x^{3} \left(- a e^{3} + 3 c d^{2} e\right) + x \left(- 3 a d e^{2} + c d^{3}\right)}{4 a^{2} c + 4 a c^{2} x^{4}}"," ",0,"RootSum(65536*_t**4*a**7*c**7 + _t**2*(9216*a**6*c**4*d*e**5 + 18432*a**5*c**5*d**3*e**3 + 9216*a**4*c**6*d**5*e) + 81*a**6*e**12 + 486*a**5*c*d**2*e**10 + 1215*a**4*c**2*d**4*e**8 + 1620*a**3*c**3*d**6*e**6 + 1215*a**2*c**4*d**8*e**4 + 486*a*c**5*d**10*e**2 + 81*c**6*d**12, Lambda(_t, _t*log(x + (4096*_t**3*a**6*c**5*e + 432*_t*a**5*c**2*d*e**6 + 720*_t*a**4*c**3*d**3*e**4 + 144*_t*a**3*c**4*d**5*e**2 - 144*_t*a**2*c**5*d**7)/(27*a**5*e**10 + 81*a**4*c*d**2*e**8 + 54*a**3*c**2*d**4*e**6 - 54*a**2*c**3*d**6*e**4 - 81*a*c**4*d**8*e**2 - 27*c**5*d**10)))) + (x**3*(-a*e**3 + 3*c*d**2*e) + x*(-3*a*d*e**2 + c*d**3))/(4*a**2*c + 4*a*c**2*x**4)","A",0
145,1,275,0,2.068634," ","integrate((e*x**2+d)**2/(c*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{7} c^{5} + t^{2} \left(2048 a^{5} c^{3} d e^{3} + 6144 a^{4} c^{4} d^{3} e\right) + a^{4} e^{8} + 20 a^{3} c d^{2} e^{6} + 118 a^{2} c^{2} d^{4} e^{4} + 180 a c^{3} d^{6} e^{2} + 81 c^{4} d^{8}, \left( t \mapsto t \log{\left(x + \frac{- 8192 t^{3} a^{6} c^{4} d e + 16 t a^{5} c e^{6} - 48 t a^{4} c^{2} d^{2} e^{4} - 144 t a^{3} c^{3} d^{4} e^{2} + 432 t a^{2} c^{4} d^{6}}{a^{4} e^{8} + 12 a^{3} c d^{2} e^{6} + 38 a^{2} c^{2} d^{4} e^{4} + 108 a c^{3} d^{6} e^{2} + 81 c^{4} d^{8}} \right)} \right)\right)} + \frac{2 c d e x^{3} + x \left(- a e^{2} + c d^{2}\right)}{4 a^{2} c + 4 a c^{2} x^{4}}"," ",0,"RootSum(65536*_t**4*a**7*c**5 + _t**2*(2048*a**5*c**3*d*e**3 + 6144*a**4*c**4*d**3*e) + a**4*e**8 + 20*a**3*c*d**2*e**6 + 118*a**2*c**2*d**4*e**4 + 180*a*c**3*d**6*e**2 + 81*c**4*d**8, Lambda(_t, _t*log(x + (-8192*_t**3*a**6*c**4*d*e + 16*_t*a**5*c*e**6 - 48*_t*a**4*c**2*d**2*e**4 - 144*_t*a**3*c**3*d**4*e**2 + 432*_t*a**2*c**4*d**6)/(a**4*e**8 + 12*a**3*c*d**2*e**6 + 38*a**2*c**2*d**4*e**4 + 108*a*c**3*d**6*e**2 + 81*c**4*d**8)))) + (2*c*d*e*x**3 + x*(-a*e**2 + c*d**2))/(4*a**2*c + 4*a*c**2*x**4)","A",0
146,1,136,0,1.031911," ","integrate((e*x**2+d)/(c*x**4+a)**2,x)","\operatorname{RootSum} {\left(65536 t^{4} a^{7} c^{3} + 3072 t^{2} a^{4} c^{2} d e + a^{2} e^{4} + 18 a c d^{2} e^{2} + 81 c^{2} d^{4}, \left( t \mapsto t \log{\left(x + \frac{4096 t^{3} a^{6} c^{2} e + 144 t a^{3} c d e^{2} - 432 t a^{2} c^{2} d^{3}}{a^{2} e^{4} - 81 c^{2} d^{4}} \right)} \right)\right)} + \frac{d x + e x^{3}}{4 a^{2} + 4 a c x^{4}}"," ",0,"RootSum(65536*_t**4*a**7*c**3 + 3072*_t**2*a**4*c**2*d*e + a**2*e**4 + 18*a*c*d**2*e**2 + 81*c**2*d**4, Lambda(_t, _t*log(x + (4096*_t**3*a**6*c**2*e + 144*_t*a**3*c*d*e**2 - 432*_t*a**2*c**2*d**3)/(a**2*e**4 - 81*c**2*d**4)))) + (d*x + e*x**3)/(4*a**2 + 4*a*c*x**4)","A",0
147,1,39,0,0.348222," ","integrate(1/(c*x**4+a)**2,x)","\frac{x}{4 a^{2} + 4 a c x^{4}} + \operatorname{RootSum} {\left(65536 t^{4} a^{7} c + 81, \left( t \mapsto t \log{\left(\frac{16 t a^{2}}{3} + x \right)} \right)\right)}"," ",0,"x/(4*a**2 + 4*a*c*x**4) + RootSum(65536*_t**4*a**7*c + 81, Lambda(_t, _t*log(16*_t*a**2/3 + x)))","A",0
148,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(c*x**4+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,1,214,0,6.166671," ","integrate((e*x**2+d)**4/(c*x**4+a)**(1/2),x)","\frac{d^{4} 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{d^{3} e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(\frac{7}{4}\right)} + \frac{3 d^{2} e^{2} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{9}{4}\right)} + \frac{d e^{3} x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(\frac{11}{4}\right)} + \frac{e^{4} x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{13}{4}\right)}"," ",0,"d**4*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)) + d**3*e*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4*exp_polar(I*pi)/a)/(sqrt(a)*gamma(7/4)) + 3*d**2*e**2*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), c*x**4*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(9/4)) + d*e**3*x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), c*x**4*exp_polar(I*pi)/a)/(sqrt(a)*gamma(11/4)) + e**4*x**9*gamma(9/4)*hyper((1/2, 9/4), (13/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(13/4))","C",0
151,1,173,0,4.730164," ","integrate((e*x**2+d)**3/(c*x**4+a)**(1/2),x)","\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^{2} e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)} + \frac{3 d e^{2} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)} + \frac{e^{3} x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"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**2*e*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)) + 3*d*e**2*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(9/4)) + e**3*x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(11/4))","C",0
152,1,124,0,3.574136," ","integrate((e*x**2+d)**2/(c*x**4+a)**(1/2),x)","\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{d e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{7}{4}\right)} + \frac{e^{2} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"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)) + d*e*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(7/4)) + e**2*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(9/4))","C",0
153,1,78,0,2.060787," ","integrate((e*x**2+d)/(c*x**4+a)**(1/2),x)","\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)} + \frac{e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"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)) + e*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
154,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{4}} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**4)*(d + e*x**2)), x)","F",0
155,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{4}} \left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**4)*(d + e*x**2)**2), x)","F",0
156,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**3/(c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{4}} \left(d + e x^{2}\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**4)*(d + e*x**2)**3), x)","F",0
157,1,180,0,4.889868," ","integrate((e*x**2+d)**3/(-c*x**4+a)**(1/2),x)","\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^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} + \frac{3 d^{2} e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)} + \frac{3 d e^{2} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)} + \frac{e^{3} x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{c x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"d**3*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(5/4)) + 3*d**2*e*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(7/4)) + 3*d*e**2*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), c*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(9/4)) + e**3*x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), c*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(11/4))","A",0
158,1,129,0,3.773754," ","integrate((e*x**2+d)**2/(-c*x**4+a)**(1/2),x)","\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^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} + \frac{d e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{2 i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{7}{4}\right)} + \frac{e^{2} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"d**2*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(5/4)) + d*e*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4*exp_polar(2*I*pi)/a)/(2*sqrt(a)*gamma(7/4)) + e**2*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), c*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(9/4))","A",0
159,1,82,0,2.236113," ","integrate((e*x**2+d)/(-c*x**4+a)**(1/2),x)","\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^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} + \frac{e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{2 i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"d*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(5/4)) + e*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4*exp_polar(2*I*pi)/a)/(4*sqrt(a)*gamma(7/4))","A",0
160,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(-c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a - c x^{4}} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(a - c*x**4)*(d + e*x**2)), x)","F",0
161,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(-c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a - c x^{4}} \left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(a - c*x**4)*(d + e*x**2)**2), x)","F",0
162,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**3/(-c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a - c x^{4}} \left(d + e x^{2}\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(a - c*x**4)*(d + e*x**2)**3), x)","F",0
163,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**4/(-c*x**4+a)**(1/2),x)","\int \frac{1}{\sqrt{a - c x^{4}} \left(d + e x^{2}\right)^{4}}\, dx"," ",0,"Integral(1/(sqrt(a - c*x**4)*(d + e*x**2)**4), x)","F",0
164,1,73,0,2.182497," ","integrate((e*x**2+d)/(c*x**4-a)**(1/2),x)","- \frac{i 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}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)} - \frac{i e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-I*d*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4/a)/(4*sqrt(a)*gamma(5/4)) - I*e*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4/a)/(4*sqrt(a)*gamma(7/4))","A",0
165,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(c*x**4-a)**(1/2),x)","\int \frac{1}{\sqrt{- a + c x^{4}} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(-a + c*x**4)*(d + e*x**2)), x)","F",0
166,1,70,0,2.414243," ","integrate((a**(1/2)+x**2*c**(1/2))/(c*x**4-a)**(1/2),x)","- \frac{i 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}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} - \frac{i \sqrt{c} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4/a)/(4*gamma(5/4)) - I*sqrt(c)*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4/a)/(4*sqrt(a)*gamma(7/4))","A",0
167,1,76,0,2.295674," ","integrate((1+x**2*(c/a)**(1/2))/(c*x**4-a)**(1/2),x)","- \frac{i x^{3} \sqrt{\frac{c}{a}} \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}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)} - \frac{i 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}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"-I*x**3*sqrt(c/a)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4/a)/(4*sqrt(a)*gamma(7/4)) - I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4/a)/(4*sqrt(a)*gamma(5/4))","B",0
168,1,83,0,2.097919," ","integrate((e*x**2+d)/(-c*x**4-a)**(1/2),x)","- \frac{i 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)} - \frac{i e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-I*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)) - I*e*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
169,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(-c*x**4-a)**(1/2),x)","\int \frac{1}{\sqrt{- a - c x^{4}} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(-a - c*x**4)*(d + e*x**2)), x)","F",0
170,0,0,0,0.000000," ","integrate(1/(b*x**2+a)/(-5*x**4+4)**(1/2),x)","\int \frac{1}{\sqrt{4 - 5 x^{4}} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(4 - 5*x**4)*(a + b*x**2)), x)","F",0
171,0,0,0,0.000000," ","integrate(1/(b*x**2+a)/(5*x**4+4)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right) \sqrt{5 x^{4} + 4}}\, dx"," ",0,"Integral(1/((a + b*x**2)*sqrt(5*x**4 + 4)), x)","F",0
172,0,0,0,0.000000," ","integrate(1/(b*x**2+a)/(-d*x**4+4)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right) \sqrt{- d x^{4} + 4}}\, dx"," ",0,"Integral(1/((a + b*x**2)*sqrt(-d*x**4 + 4)), x)","F",0
173,0,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**4+4)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right) \sqrt{d x^{4} + 4}}\, dx"," ",0,"Integral(1/((a + b*x**2)*sqrt(d*x**4 + 4)), x)","F",0
174,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(-x**4+1)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{\sqrt{- \left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/sqrt(-(x - 1)*(x + 1)*(x**2 + 1)), x)","F",0
175,-1,0,0,0.000000," ","integrate((e*x**2+c)**q*(b*x**4+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,1,167,0,139.104191," ","integrate((e*x**2+c)**3*(b*x**4+a)**p,x)","\frac{a^{p} c^{3} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{3 a^{p} c^{2} e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, - p \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{3 a^{p} c e^{2} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, - p \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{a^{p} e^{3} x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, - p \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**p*c**3*x*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + 3*a**p*c**2*e*x**3*gamma(3/4)*hyper((3/4, -p), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4)) + 3*a**p*c*e**2*x**5*gamma(5/4)*hyper((5/4, -p), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4)) + a**p*e**3*x**7*gamma(7/4)*hyper((7/4, -p), (11/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(11/4))","C",0
177,1,119,0,79.158566," ","integrate((e*x**2+c)**2*(b*x**4+a)**p,x)","\frac{a^{p} c^{2} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{a^{p} c e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, - p \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)} + \frac{a^{p} e^{2} x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, - p \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**p*c**2*x*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + a**p*c*e*x**3*gamma(3/4)*hyper((3/4, -p), (7/4,), b*x**4*exp_polar(I*pi)/a)/(2*gamma(7/4)) + a**p*e**2*x**5*gamma(5/4)*hyper((5/4, -p), (9/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(9/4))","C",0
178,1,75,0,42.838249," ","integrate((e*x**2+c)*(b*x**4+a)**p,x)","\frac{a^{p} c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{a^{p} e x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, - p \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**p*c*x*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4)) + a**p*e*x**3*gamma(3/4)*hyper((3/4, -p), (7/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(7/4))","C",0
179,1,34,0,9.182323," ","integrate((b*x**4+a)**p,x)","\frac{a^{p} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{4} e^{i \pi}}{a}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**p*x*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**4*exp_polar(I*pi)/a)/(4*gamma(5/4))","C",0
180,-1,0,0,0.000000," ","integrate((b*x**4+a)**p/(e*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate((b*x**4+a)**p/(e*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,1,129,0,120.365784," ","integrate((-x**2+1)**3*(b*x**4+1)**p,x)","- \frac{x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, - p \\ \frac{11}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)} + \frac{3 x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, - p \\ \frac{9}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} - \frac{3 x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, - p \\ \frac{7}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-x**7*gamma(7/4)*hyper((7/4, -p), (11/4,), b*x**4*exp_polar(I*pi))/(4*gamma(11/4)) + 3*x**5*gamma(5/4)*hyper((5/4, -p), (9/4,), b*x**4*exp_polar(I*pi))/(4*gamma(9/4)) - 3*x**3*gamma(3/4)*hyper((3/4, -p), (7/4,), b*x**4*exp_polar(I*pi))/(4*gamma(7/4)) + x*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
183,1,94,0,69.115814," ","integrate((-x**2+1)**2*(b*x**4+1)**p,x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, - p \\ \frac{9}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{9}{4}\right)} - \frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, - p \\ \frac{7}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)} + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((5/4, -p), (9/4,), b*x**4*exp_polar(I*pi))/(4*gamma(9/4)) - x**3*gamma(3/4)*hyper((3/4, -p), (7/4,), b*x**4*exp_polar(I*pi))/(2*gamma(7/4)) + x*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
184,1,61,0,35.981601," ","integrate((-x**2+1)*(b*x**4+1)**p,x)","- \frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, - p \\ \frac{7}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)} + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-x**3*gamma(3/4)*hyper((3/4, -p), (7/4,), b*x**4*exp_polar(I*pi))/(4*gamma(7/4)) + x*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
185,1,29,0,7.706713," ","integrate((b*x**4+1)**p,x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {b x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**4*exp_polar(I*pi))/(4*gamma(5/4))","C",0
186,-1,0,0,0.000000," ","integrate((b*x**4+1)**p/(-x**2+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((b*x**4+1)**p/(-x**2+1)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate((b*x**4+1)**p/(-x**2+1)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,1,75,0,0.241399," ","integrate((e*x**2+d)**4/(-e**2*x**4+d**2),x)","- 7 d^{2} x - \frac{4 d e x^{3}}{3} - \frac{e^{2} x^{5}}{5} - 4 \sqrt{\frac{d^{5}}{e}} \log{\left(x - \frac{\sqrt{\frac{d^{5}}{e}}}{d^{2}} \right)} + 4 \sqrt{\frac{d^{5}}{e}} \log{\left(x + \frac{\sqrt{\frac{d^{5}}{e}}}{d^{2}} \right)}"," ",0,"-7*d**2*x - 4*d*e*x**3/3 - e**2*x**5/5 - 4*sqrt(d**5/e)*log(x - sqrt(d**5/e)/d**2) + 4*sqrt(d**5/e)*log(x + sqrt(d**5/e)/d**2)","A",0
190,1,58,0,0.201144," ","integrate((e*x**2+d)**3/(-e**2*x**4+d**2),x)","- 3 d x - \frac{e x^{3}}{3} - 2 \sqrt{\frac{d^{3}}{e}} \log{\left(x - \frac{\sqrt{\frac{d^{3}}{e}}}{d} \right)} + 2 \sqrt{\frac{d^{3}}{e}} \log{\left(x + \frac{\sqrt{\frac{d^{3}}{e}}}{d} \right)}"," ",0,"-3*d*x - e*x**3/3 - 2*sqrt(d**3/e)*log(x - sqrt(d**3/e)/d) + 2*sqrt(d**3/e)*log(x + sqrt(d**3/e)/d)","A",0
191,1,34,0,0.183437," ","integrate((e*x**2+d)**2/(-e**2*x**4+d**2),x)","- x - \sqrt{\frac{d}{e}} \log{\left(x - \sqrt{\frac{d}{e}} \right)} + \sqrt{\frac{d}{e}} \log{\left(x + \sqrt{\frac{d}{e}} \right)}"," ",0,"-x - sqrt(d/e)*log(x - sqrt(d/e)) + sqrt(d/e)*log(x + sqrt(d/e))","A",0
192,1,46,0,0.154536," ","integrate((e*x**2+d)/(-e**2*x**4+d**2),x)","- \frac{\sqrt{\frac{1}{d e}} \log{\left(- d \sqrt{\frac{1}{d e}} + x \right)}}{2} + \frac{\sqrt{\frac{1}{d e}} \log{\left(d \sqrt{\frac{1}{d e}} + x \right)}}{2}"," ",0,"-sqrt(1/(d*e))*log(-d*sqrt(1/(d*e)) + x)/2 + sqrt(1/(d*e))*log(d*sqrt(1/(d*e)) + x)/2","B",0
193,1,226,0,0.452469," ","integrate(1/(e*x**2+d)/(-e**2*x**4+d**2),x)","\frac{x}{4 d^{3} + 4 d^{2} e x^{2}} - \frac{\sqrt{\frac{1}{d^{5} e}} \log{\left(- \frac{d^{8} e \left(\frac{1}{d^{5} e}\right)^{\frac{3}{2}}}{10} - \frac{9 d^{3} \sqrt{\frac{1}{d^{5} e}}}{10} + x \right)}}{8} + \frac{\sqrt{\frac{1}{d^{5} e}} \log{\left(\frac{d^{8} e \left(\frac{1}{d^{5} e}\right)^{\frac{3}{2}}}{10} + \frac{9 d^{3} \sqrt{\frac{1}{d^{5} e}}}{10} + x \right)}}{8} - \frac{\sqrt{- \frac{1}{d^{5} e}} \log{\left(- \frac{4 d^{8} e \left(- \frac{1}{d^{5} e}\right)^{\frac{3}{2}}}{5} - \frac{9 d^{3} \sqrt{- \frac{1}{d^{5} e}}}{5} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{d^{5} e}} \log{\left(\frac{4 d^{8} e \left(- \frac{1}{d^{5} e}\right)^{\frac{3}{2}}}{5} + \frac{9 d^{3} \sqrt{- \frac{1}{d^{5} e}}}{5} + x \right)}}{4}"," ",0,"x/(4*d**3 + 4*d**2*e*x**2) - sqrt(1/(d**5*e))*log(-d**8*e*(1/(d**5*e))**(3/2)/10 - 9*d**3*sqrt(1/(d**5*e))/10 + x)/8 + sqrt(1/(d**5*e))*log(d**8*e*(1/(d**5*e))**(3/2)/10 + 9*d**3*sqrt(1/(d**5*e))/10 + x)/8 - sqrt(-1/(d**5*e))*log(-4*d**8*e*(-1/(d**5*e))**(3/2)/5 - 9*d**3*sqrt(-1/(d**5*e))/5 + x)/4 + sqrt(-1/(d**5*e))*log(4*d**8*e*(-1/(d**5*e))**(3/2)/5 + 9*d**3*sqrt(-1/(d**5*e))/5 + x)/4","B",0
194,1,257,0,0.715221," ","integrate(1/(e*x**2+d)**2/(-e**2*x**4+d**2),x)","- \frac{\sqrt{\frac{1}{d^{7} e}} \log{\left(- \frac{20 d^{11} e \left(\frac{1}{d^{7} e}\right)^{\frac{3}{2}}}{371} - \frac{351 d^{4} \sqrt{\frac{1}{d^{7} e}}}{371} + x \right)}}{16} + \frac{\sqrt{\frac{1}{d^{7} e}} \log{\left(\frac{20 d^{11} e \left(\frac{1}{d^{7} e}\right)^{\frac{3}{2}}}{371} + \frac{351 d^{4} \sqrt{\frac{1}{d^{7} e}}}{371} + x \right)}}{16} - \frac{7 \sqrt{- \frac{1}{d^{7} e}} \log{\left(- \frac{245 d^{11} e \left(- \frac{1}{d^{7} e}\right)^{\frac{3}{2}}}{106} - \frac{351 d^{4} \sqrt{- \frac{1}{d^{7} e}}}{106} + x \right)}}{32} + \frac{7 \sqrt{- \frac{1}{d^{7} e}} \log{\left(\frac{245 d^{11} e \left(- \frac{1}{d^{7} e}\right)^{\frac{3}{2}}}{106} + \frac{351 d^{4} \sqrt{- \frac{1}{d^{7} e}}}{106} + x \right)}}{32} - \frac{- 7 d x - 5 e x^{3}}{16 d^{5} + 32 d^{4} e x^{2} + 16 d^{3} e^{2} x^{4}}"," ",0,"-sqrt(1/(d**7*e))*log(-20*d**11*e*(1/(d**7*e))**(3/2)/371 - 351*d**4*sqrt(1/(d**7*e))/371 + x)/16 + sqrt(1/(d**7*e))*log(20*d**11*e*(1/(d**7*e))**(3/2)/371 + 351*d**4*sqrt(1/(d**7*e))/371 + x)/16 - 7*sqrt(-1/(d**7*e))*log(-245*d**11*e*(-1/(d**7*e))**(3/2)/106 - 351*d**4*sqrt(-1/(d**7*e))/106 + x)/32 + 7*sqrt(-1/(d**7*e))*log(245*d**11*e*(-1/(d**7*e))**(3/2)/106 + 351*d**4*sqrt(-1/(d**7*e))/106 + x)/32 - (-7*d*x - 5*e*x**3)/(16*d**5 + 32*d**4*e*x**2 + 16*d**3*e**2*x**4)","B",0
195,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)/(-e**2*x**4+d**2),x)","- \int \frac{\sqrt{d + e x^{2}}}{- d + e x^{2}}\, dx"," ",0,"-Integral(sqrt(d + e*x**2)/(-d + e*x**2), x)","F",0
196,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)/(-e**2*x**4+d**2),x)","- \int \frac{1}{- d \sqrt{d + e x^{2}} + e x^{2} \sqrt{d + e x^{2}}}\, dx"," ",0,"-Integral(1/(-d*sqrt(d + e*x**2) + e*x**2*sqrt(d + e*x**2)), x)","F",0
197,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**(1/2)/(-e**2*x**4+d**2),x)","- \int \frac{1}{- d^{2} \sqrt{d + e x^{2}} + e^{2} x^{4} \sqrt{d + e x^{2}}}\, dx"," ",0,"-Integral(1/(-d**2*sqrt(d + e*x**2) + e**2*x**4*sqrt(d + e*x**2)), x)","F",0
198,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**(3/2)/(-e**2*x**4+d**2),x)","- \int \frac{1}{- d^{3} \sqrt{d + e x^{2}} - d^{2} e x^{2} \sqrt{d + e x^{2}} + d e^{2} x^{4} \sqrt{d + e x^{2}} + e^{3} x^{6} \sqrt{d + e x^{2}}}\, dx"," ",0,"-Integral(1/(-d**3*sqrt(d + e*x**2) - d**2*e*x**2*sqrt(d + e*x**2) + d*e**2*x**4*sqrt(d + e*x**2) + e**3*x**6*sqrt(d + e*x**2)), x)","F",0
199,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/sqrt(-(-a + b*x**2)*(a + b*x**2)), x)","F",0
200,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/sqrt(-(-a + b*x**2)*(a + b*x**2)), x)","F",0
201,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/sqrt(-(-a + b*x**2)*(a + b*x**2)), x)","F",0
202,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)} \sqrt{a + b x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(-(-a + b*x**2)*(a + b*x**2))*sqrt(a + b*x**2)), x)","F",0
203,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(3/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)} \left(a + b x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(-(-a + b*x**2)*(a + b*x**2))*(a + b*x**2)**(3/2)), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(5/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)} \left(a + b x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(-(-a + b*x**2)*(a + b*x**2))*(a + b*x**2)**(5/2)), x)","F",0
205,0,0,0,0.000000," ","integrate((-b*x**2+a)**(5/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{\left(a - b x^{2}\right)^{\frac{5}{2}}}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)}}\, dx"," ",0,"Integral((a - b*x**2)**(5/2)/sqrt(-(-a + b*x**2)*(a + b*x**2)), x)","F",0
206,0,0,0,0.000000," ","integrate((-b*x**2+a)**(3/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{\left(a - b x^{2}\right)^{\frac{3}{2}}}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)}}\, dx"," ",0,"Integral((a - b*x**2)**(3/2)/sqrt(-(-a + b*x**2)*(a + b*x**2)), x)","F",0
207,0,0,0,0.000000," ","integrate((-b*x**2+a)**(1/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{\sqrt{a - b x^{2}}}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)}}\, dx"," ",0,"Integral(sqrt(a - b*x**2)/sqrt(-(-a + b*x**2)*(a + b*x**2)), x)","F",0
208,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(1/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)} \sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(-(-a + b*x**2)*(a + b*x**2))*sqrt(a - b*x**2)), x)","F",0
209,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(3/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)} \left(a - b x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(-(-a + b*x**2)*(a + b*x**2))*(a - b*x**2)**(3/2)), x)","F",0
210,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(5/2)/(-b**2*x**4+a**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- a + b x^{2}\right) \left(a + b x^{2}\right)} \left(a - b x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(-(-a + b*x**2)*(a + b*x**2))*(a - b*x**2)**(5/2)), x)","F",0
211,0,0,0,0.000000," ","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
212,0,0,0,0.000000," ","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
213,0,0,0,0.000000," ","integrate((-(x**2-1)**(1/2)+(x**2+1)**(1/2))/(x**4-1)**(1/2),x)","\int \frac{- \sqrt{x^{2} - 1} + \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**2 + 1))/sqrt((x - 1)*(x + 1)*(x**2 + 1)), x)","F",0
214,1,345,0,0.996053," ","integrate((e*x**2+d)**4/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","x^{3} \left(- \frac{b e^{2}}{3 c^{2}} + \frac{4 d e}{3 c}\right) + x \left(\frac{b^{2} e^{2}}{c^{3}} - \frac{5 b d e}{c^{2}} + \frac{7 d^{2}}{c}\right) + \frac{\sqrt{- \frac{1}{c^{7} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{3} \log{\left(x + \frac{- b c^{3} e \sqrt{- \frac{1}{c^{7} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{3} + c^{4} d \sqrt{- \frac{1}{c^{7} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{3}}{b^{3} e^{3} - 6 b^{2} c d e^{2} + 12 b c^{2} d^{2} e - 8 c^{3} d^{3}} \right)}}{2} - \frac{\sqrt{- \frac{1}{c^{7} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{3} \log{\left(x + \frac{b c^{3} e \sqrt{- \frac{1}{c^{7} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{3} - c^{4} d \sqrt{- \frac{1}{c^{7} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{3}}{b^{3} e^{3} - 6 b^{2} c d e^{2} + 12 b c^{2} d^{2} e - 8 c^{3} d^{3}} \right)}}{2} + \frac{e^{2} x^{5}}{5 c}"," ",0,"x**3*(-b*e**2/(3*c**2) + 4*d*e/(3*c)) + x*(b**2*e**2/c**3 - 5*b*d*e/c**2 + 7*d**2/c) + sqrt(-1/(c**7*e*(b*e - c*d)))*(b*e - 2*c*d)**3*log(x + (-b*c**3*e*sqrt(-1/(c**7*e*(b*e - c*d)))*(b*e - 2*c*d)**3 + c**4*d*sqrt(-1/(c**7*e*(b*e - c*d)))*(b*e - 2*c*d)**3)/(b**3*e**3 - 6*b**2*c*d*e**2 + 12*b*c**2*d**2*e - 8*c**3*d**3))/2 - sqrt(-1/(c**7*e*(b*e - c*d)))*(b*e - 2*c*d)**3*log(x + (b*c**3*e*sqrt(-1/(c**7*e*(b*e - c*d)))*(b*e - 2*c*d)**3 - c**4*d*sqrt(-1/(c**7*e*(b*e - c*d)))*(b*e - 2*c*d)**3)/(b**3*e**3 - 6*b**2*c*d*e**2 + 12*b*c**2*d**2*e - 8*c**3*d**3))/2 + e**2*x**5/(5*c)","B",0
215,1,275,0,0.720051," ","integrate((e*x**2+d)**3/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","x \left(- \frac{b e}{c^{2}} + \frac{3 d}{c}\right) - \frac{\sqrt{- \frac{1}{c^{5} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{2} \log{\left(x + \frac{- b c^{2} e \sqrt{- \frac{1}{c^{5} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{2} + c^{3} d \sqrt{- \frac{1}{c^{5} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{2}}{b^{2} e^{2} - 4 b c d e + 4 c^{2} d^{2}} \right)}}{2} + \frac{\sqrt{- \frac{1}{c^{5} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{2} \log{\left(x + \frac{b c^{2} e \sqrt{- \frac{1}{c^{5} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{2} - c^{3} d \sqrt{- \frac{1}{c^{5} e \left(b e - c d\right)}} \left(b e - 2 c d\right)^{2}}{b^{2} e^{2} - 4 b c d e + 4 c^{2} d^{2}} \right)}}{2} + \frac{e x^{3}}{3 c}"," ",0,"x*(-b*e/c**2 + 3*d/c) - sqrt(-1/(c**5*e*(b*e - c*d)))*(b*e - 2*c*d)**2*log(x + (-b*c**2*e*sqrt(-1/(c**5*e*(b*e - c*d)))*(b*e - 2*c*d)**2 + c**3*d*sqrt(-1/(c**5*e*(b*e - c*d)))*(b*e - 2*c*d)**2)/(b**2*e**2 - 4*b*c*d*e + 4*c**2*d**2))/2 + sqrt(-1/(c**5*e*(b*e - c*d)))*(b*e - 2*c*d)**2*log(x + (b*c**2*e*sqrt(-1/(c**5*e*(b*e - c*d)))*(b*e - 2*c*d)**2 - c**3*d*sqrt(-1/(c**5*e*(b*e - c*d)))*(b*e - 2*c*d)**2)/(b**2*e**2 - 4*b*c*d*e + 4*c**2*d**2))/2 + e*x**3/(3*c)","B",0
216,1,212,0,0.485246," ","integrate((e*x**2+d)**2/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","\frac{\sqrt{- \frac{1}{c^{3} e \left(b e - c d\right)}} \left(b e - 2 c d\right) \log{\left(x + \frac{- b c e \sqrt{- \frac{1}{c^{3} e \left(b e - c d\right)}} \left(b e - 2 c d\right) + c^{2} d \sqrt{- \frac{1}{c^{3} e \left(b e - c d\right)}} \left(b e - 2 c d\right)}{b e - 2 c d} \right)}}{2} - \frac{\sqrt{- \frac{1}{c^{3} e \left(b e - c d\right)}} \left(b e - 2 c d\right) \log{\left(x + \frac{b c e \sqrt{- \frac{1}{c^{3} e \left(b e - c d\right)}} \left(b e - 2 c d\right) - c^{2} d \sqrt{- \frac{1}{c^{3} e \left(b e - c d\right)}} \left(b e - 2 c d\right)}{b e - 2 c d} \right)}}{2} + \frac{x}{c}"," ",0,"sqrt(-1/(c**3*e*(b*e - c*d)))*(b*e - 2*c*d)*log(x + (-b*c*e*sqrt(-1/(c**3*e*(b*e - c*d)))*(b*e - 2*c*d) + c**2*d*sqrt(-1/(c**3*e*(b*e - c*d)))*(b*e - 2*c*d))/(b*e - 2*c*d))/2 - sqrt(-1/(c**3*e*(b*e - c*d)))*(b*e - 2*c*d)*log(x + (b*c*e*sqrt(-1/(c**3*e*(b*e - c*d)))*(b*e - 2*c*d) - c**2*d*sqrt(-1/(c**3*e*(b*e - c*d)))*(b*e - 2*c*d))/(b*e - 2*c*d))/2 + x/c","B",0
217,1,124,0,0.324989," ","integrate((e*x**2+d)/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","- \frac{\sqrt{- \frac{1}{c e \left(b e - c d\right)}} \log{\left(- b e \sqrt{- \frac{1}{c e \left(b e - c d\right)}} + c d \sqrt{- \frac{1}{c e \left(b e - c d\right)}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{c e \left(b e - c d\right)}} \log{\left(b e \sqrt{- \frac{1}{c e \left(b e - c d\right)}} - c d \sqrt{- \frac{1}{c e \left(b e - c d\right)}} + x \right)}}{2}"," ",0,"-sqrt(-1/(c*e*(b*e - c*d)))*log(-b*e*sqrt(-1/(c*e*(b*e - c*d))) + c*d*sqrt(-1/(c*e*(b*e - c*d))) + x)/2 + sqrt(-1/(c*e*(b*e - c*d)))*log(b*e*sqrt(-1/(c*e*(b*e - c*d))) - c*d*sqrt(-1/(c*e*(b*e - c*d))) + x)/2","B",0
218,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,0,0,0,0.000000," ","integrate((e*x**2+d)**(5/2)/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","\int \frac{\left(d + e x^{2}\right)^{\frac{3}{2}}}{b e - c d + c e x^{2}}\, dx"," ",0,"Integral((d + e*x**2)**(3/2)/(b*e - c*d + c*e*x**2), x)","F",0
221,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","\int \frac{\sqrt{d + e x^{2}}}{b e - c d + c e x^{2}}\, dx"," ",0,"Integral(sqrt(d + e*x**2)/(b*e - c*d + c*e*x**2), x)","F",0
222,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","\int \frac{1}{\sqrt{d + e x^{2}} \left(b e - c d + c e x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(d + e*x**2)*(b*e - c*d + c*e*x**2)), x)","F",0
223,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**(1/2)/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","\int \frac{1}{\left(d + e x^{2}\right)^{\frac{3}{2}} \left(b e - c d + c e x^{2}\right)}\, dx"," ",0,"Integral(1/((d + e*x**2)**(3/2)*(b*e - c*d + c*e*x**2)), x)","F",0
224,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**(3/2)/(c*e**2*x**4+b*e**2*x**2+b*d*e-c*d**2),x)","\int \frac{1}{\left(d + e x^{2}\right)^{\frac{5}{2}} \left(b e - c d + c e x^{2}\right)}\, dx"," ",0,"Integral(1/((d + e*x**2)**(5/2)*(b*e - c*d + c*e*x**2)), x)","F",0
225,0,0,0,0.000000," ","integrate((x**2+1)**3*(x**4+x**2+1)**(1/2),x)","\int \sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)} \left(x^{2} + 1\right)^{3}\, dx"," ",0,"Integral(sqrt((x**2 - x + 1)*(x**2 + x + 1))*(x**2 + 1)**3, x)","F",0
226,0,0,0,0.000000," ","integrate((x**2+1)**2*(x**4+x**2+1)**(1/2),x)","\int \sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)} \left(x^{2} + 1\right)^{2}\, dx"," ",0,"Integral(sqrt((x**2 - x + 1)*(x**2 + x + 1))*(x**2 + 1)**2, x)","F",0
227,0,0,0,0.000000," ","integrate((x**2+1)*(x**4+x**2+1)**(1/2),x)","\int \sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)} \left(x^{2} + 1\right)\, dx"," ",0,"Integral(sqrt((x**2 - x + 1)*(x**2 + x + 1))*(x**2 + 1), x)","F",0
228,0,0,0,0.000000," ","integrate((x**4+x**2+1)**(1/2)/(x**2+1),x)","\int \frac{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}{x^{2} + 1}\, dx"," ",0,"Integral(sqrt((x**2 - x + 1)*(x**2 + x + 1))/(x**2 + 1), x)","F",0
229,0,0,0,0.000000," ","integrate((x**4+x**2+1)**(1/2)/(x**2+1)**2,x)","\int \frac{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}{\left(x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral(sqrt((x**2 - x + 1)*(x**2 + x + 1))/(x**2 + 1)**2, x)","F",0
230,0,0,0,0.000000," ","integrate((x**4+x**2+1)**(1/2)/(x**2+1)**3,x)","\int \frac{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}{\left(x^{2} + 1\right)^{3}}\, dx"," ",0,"Integral(sqrt((x**2 - x + 1)*(x**2 + x + 1))/(x**2 + 1)**3, x)","F",0
231,0,0,0,0.000000," ","integrate((x**4+x**2+1)**(1/2)/(x**2+1)**4,x)","\int \frac{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}{\left(x^{2} + 1\right)^{4}}\, dx"," ",0,"Integral(sqrt((x**2 - x + 1)*(x**2 + x + 1))/(x**2 + 1)**4, x)","F",0
232,0,0,0,0.000000," ","integrate((x**2+1)**3/(x**4+x**2+1)**(1/2),x)","\int \frac{\left(x^{2} + 1\right)^{3}}{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}\, dx"," ",0,"Integral((x**2 + 1)**3/sqrt((x**2 - x + 1)*(x**2 + x + 1)), x)","F",0
233,0,0,0,0.000000," ","integrate((x**2+1)**2/(x**4+x**2+1)**(1/2),x)","\int \frac{\left(x^{2} + 1\right)^{2}}{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}\, dx"," ",0,"Integral((x**2 + 1)**2/sqrt((x**2 - x + 1)*(x**2 + x + 1)), x)","F",0
234,0,0,0,0.000000," ","integrate((x**2+1)/(x**4+x**2+1)**(1/2),x)","\int \frac{x^{2} + 1}{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}\, dx"," ",0,"Integral((x**2 + 1)/sqrt((x**2 - x + 1)*(x**2 + x + 1)), x)","F",0
235,0,0,0,0.000000," ","integrate(1/(x**2+1)/(x**4+x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral(1/(sqrt((x**2 - x + 1)*(x**2 + x + 1))*(x**2 + 1)), x)","F",0
236,0,0,0,0.000000," ","integrate(1/(x**2+1)**2/(x**4+x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)} \left(x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt((x**2 - x + 1)*(x**2 + x + 1))*(x**2 + 1)**2), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(x**2+1)**3/(x**4+x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)} \left(x^{2} + 1\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt((x**2 - x + 1)*(x**2 + x + 1))*(x**2 + 1)**3), x)","F",0
238,0,0,0,0.000000," ","integrate((x**2+1)**3/(x**4+x**2+1)**(3/2),x)","\int \frac{\left(x^{2} + 1\right)^{3}}{\left(\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x**2 + 1)**3/((x**2 - x + 1)*(x**2 + x + 1))**(3/2), x)","F",0
239,0,0,0,0.000000," ","integrate((x**2+1)**2/(x**4+x**2+1)**(3/2),x)","\int \frac{\left(x^{2} + 1\right)^{2}}{\left(\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x**2 + 1)**2/((x**2 - x + 1)*(x**2 + x + 1))**(3/2), x)","F",0
240,0,0,0,0.000000," ","integrate((x**2+1)/(x**4+x**2+1)**(3/2),x)","\int \frac{x^{2} + 1}{\left(\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x**2 + 1)/((x**2 - x + 1)*(x**2 + x + 1))**(3/2), x)","F",0
241,0,0,0,0.000000," ","integrate(1/(x**2+1)/(x**4+x**2+1)**(3/2),x)","\int \frac{1}{\left(\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{3}{2}} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral(1/(((x**2 - x + 1)*(x**2 + x + 1))**(3/2)*(x**2 + 1)), x)","F",0
242,0,0,0,0.000000," ","integrate(1/(x**2+1)**2/(x**4+x**2+1)**(3/2),x)","\int \frac{1}{\left(\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{3}{2}} \left(x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral(1/(((x**2 - x + 1)*(x**2 + x + 1))**(3/2)*(x**2 + 1)**2), x)","F",0
243,0,0,0,0.000000," ","integrate(1/(x**2+1)**3/(x**4+x**2+1)**(3/2),x)","\int \frac{1}{\left(\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)\right)^{\frac{3}{2}} \left(x^{2} + 1\right)^{3}}\, dx"," ",0,"Integral(1/(((x**2 - x + 1)*(x**2 + x + 1))**(3/2)*(x**2 + 1)**3), x)","F",0
244,1,156,0,0.113383," ","integrate((e*x**2+d)**4*(c*x**4+b*x**2+a),x)","a d^{4} x + \frac{c e^{4} x^{13}}{13} + x^{11} \left(\frac{b e^{4}}{11} + \frac{4 c d e^{3}}{11}\right) + x^{9} \left(\frac{a e^{4}}{9} + \frac{4 b d e^{3}}{9} + \frac{2 c d^{2} e^{2}}{3}\right) + x^{7} \left(\frac{4 a d e^{3}}{7} + \frac{6 b d^{2} e^{2}}{7} + \frac{4 c d^{3} e}{7}\right) + x^{5} \left(\frac{6 a d^{2} e^{2}}{5} + \frac{4 b d^{3} e}{5} + \frac{c d^{4}}{5}\right) + x^{3} \left(\frac{4 a d^{3} e}{3} + \frac{b d^{4}}{3}\right)"," ",0,"a*d**4*x + c*e**4*x**13/13 + x**11*(b*e**4/11 + 4*c*d*e**3/11) + x**9*(a*e**4/9 + 4*b*d*e**3/9 + 2*c*d**2*e**2/3) + x**7*(4*a*d*e**3/7 + 6*b*d**2*e**2/7 + 4*c*d**3*e/7) + x**5*(6*a*d**2*e**2/5 + 4*b*d**3*e/5 + c*d**4/5) + x**3*(4*a*d**3*e/3 + b*d**4/3)","A",0
245,1,112,0,0.290994," ","integrate((e*x**2+d)**3*(c*x**4+b*x**2+a),x)","a d^{3} x + \frac{c e^{3} x^{11}}{11} + x^{9} \left(\frac{b e^{3}}{9} + \frac{c d e^{2}}{3}\right) + x^{7} \left(\frac{a e^{3}}{7} + \frac{3 b d e^{2}}{7} + \frac{3 c d^{2} e}{7}\right) + x^{5} \left(\frac{3 a d e^{2}}{5} + \frac{3 b d^{2} e}{5} + \frac{c d^{3}}{5}\right) + x^{3} \left(a d^{2} e + \frac{b d^{3}}{3}\right)"," ",0,"a*d**3*x + c*e**3*x**11/11 + x**9*(b*e**3/9 + c*d*e**2/3) + x**7*(a*e**3/7 + 3*b*d*e**2/7 + 3*c*d**2*e/7) + x**5*(3*a*d*e**2/5 + 3*b*d**2*e/5 + c*d**3/5) + x**3*(a*d**2*e + b*d**3/3)","A",0
246,1,78,0,0.107968," ","integrate((e*x**2+d)**2*(c*x**4+b*x**2+a),x)","a d^{2} x + \frac{c e^{2} x^{9}}{9} + x^{7} \left(\frac{b e^{2}}{7} + \frac{2 c d e}{7}\right) + x^{5} \left(\frac{a e^{2}}{5} + \frac{2 b d e}{5} + \frac{c d^{2}}{5}\right) + x^{3} \left(\frac{2 a d e}{3} + \frac{b d^{2}}{3}\right)"," ",0,"a*d**2*x + c*e**2*x**9/9 + x**7*(b*e**2/7 + 2*c*d*e/7) + x**5*(a*e**2/5 + 2*b*d*e/5 + c*d**2/5) + x**3*(2*a*d*e/3 + b*d**2/3)","A",0
247,1,39,0,0.101348," ","integrate((e*x**2+d)*(c*x**4+b*x**2+a),x)","a d x + \frac{c e x^{7}}{7} + x^{5} \left(\frac{b e}{5} + \frac{c d}{5}\right) + x^{3} \left(\frac{a e}{3} + \frac{b d}{3}\right)"," ",0,"a*d*x + c*e*x**7/7 + x**5*(b*e/5 + c*d/5) + x**3*(a*e/3 + b*d/3)","A",0
248,1,117,0,0.728917," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d),x)","\frac{c x^{3}}{3 e} + x \left(\frac{b}{e} - \frac{c d}{e^{2}}\right) - \frac{\sqrt{- \frac{1}{d e^{5}}} \left(a e^{2} - b d e + c d^{2}\right) \log{\left(- d e^{2} \sqrt{- \frac{1}{d e^{5}}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{d e^{5}}} \left(a e^{2} - b d e + c d^{2}\right) \log{\left(d e^{2} \sqrt{- \frac{1}{d e^{5}}} + x \right)}}{2}"," ",0,"c*x**3/(3*e) + x*(b/e - c*d/e**2) - sqrt(-1/(d*e**5))*(a*e**2 - b*d*e + c*d**2)*log(-d*e**2*sqrt(-1/(d*e**5)) + x)/2 + sqrt(-1/(d*e**5))*(a*e**2 - b*d*e + c*d**2)*log(d*e**2*sqrt(-1/(d*e**5)) + x)/2","B",0
249,1,153,0,1.232871," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**2,x)","\frac{c x}{e^{2}} + \frac{x \left(a e^{2} - b d e + c d^{2}\right)}{2 d^{2} e^{2} + 2 d e^{3} x^{2}} - \frac{\sqrt{- \frac{1}{d^{3} e^{5}}} \left(a e^{2} + b d e - 3 c d^{2}\right) \log{\left(- d^{2} e^{2} \sqrt{- \frac{1}{d^{3} e^{5}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{d^{3} e^{5}}} \left(a e^{2} + b d e - 3 c d^{2}\right) \log{\left(d^{2} e^{2} \sqrt{- \frac{1}{d^{3} e^{5}}} + x \right)}}{4}"," ",0,"c*x/e**2 + x*(a*e**2 - b*d*e + c*d**2)/(2*d**2*e**2 + 2*d*e**3*x**2) - sqrt(-1/(d**3*e**5))*(a*e**2 + b*d*e - 3*c*d**2)*log(-d**2*e**2*sqrt(-1/(d**3*e**5)) + x)/4 + sqrt(-1/(d**3*e**5))*(a*e**2 + b*d*e - 3*c*d**2)*log(d**2*e**2*sqrt(-1/(d**3*e**5)) + x)/4","B",0
250,1,196,0,2.266234," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**3,x)","- \frac{\sqrt{- \frac{1}{d^{5} e^{5}}} \left(3 a e^{2} + b d e + 3 c d^{2}\right) \log{\left(- d^{3} e^{2} \sqrt{- \frac{1}{d^{5} e^{5}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{d^{5} e^{5}}} \left(3 a e^{2} + b d e + 3 c d^{2}\right) \log{\left(d^{3} e^{2} \sqrt{- \frac{1}{d^{5} e^{5}}} + x \right)}}{16} + \frac{x^{3} \left(3 a e^{3} + b d e^{2} - 5 c d^{2} e\right) + x \left(5 a d e^{2} - b d^{2} e - 3 c d^{3}\right)}{8 d^{4} e^{2} + 16 d^{3} e^{3} x^{2} + 8 d^{2} e^{4} x^{4}}"," ",0,"-sqrt(-1/(d**5*e**5))*(3*a*e**2 + b*d*e + 3*c*d**2)*log(-d**3*e**2*sqrt(-1/(d**5*e**5)) + x)/16 + sqrt(-1/(d**5*e**5))*(3*a*e**2 + b*d*e + 3*c*d**2)*log(d**3*e**2*sqrt(-1/(d**5*e**5)) + x)/16 + (x**3*(3*a*e**3 + b*d*e**2 - 5*c*d**2*e) + x*(5*a*d*e**2 - b*d**2*e - 3*c*d**3))/(8*d**4*e**2 + 16*d**3*e**3*x**2 + 8*d**2*e**4*x**4)","A",0
251,1,241,0,4.409209," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**4,x)","- \frac{\sqrt{- \frac{1}{d^{7} e^{5}}} \left(5 a e^{2} + b d e + c d^{2}\right) \log{\left(- d^{4} e^{2} \sqrt{- \frac{1}{d^{7} e^{5}}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{d^{7} e^{5}}} \left(5 a e^{2} + b d e + c d^{2}\right) \log{\left(d^{4} e^{2} \sqrt{- \frac{1}{d^{7} e^{5}}} + x \right)}}{32} + \frac{x^{5} \left(15 a e^{4} + 3 b d e^{3} + 3 c d^{2} e^{2}\right) + x^{3} \left(40 a d e^{3} + 8 b d^{2} e^{2} - 8 c d^{3} e\right) + x \left(33 a d^{2} e^{2} - 3 b d^{3} e - 3 c d^{4}\right)}{48 d^{6} e^{2} + 144 d^{5} e^{3} x^{2} + 144 d^{4} e^{4} x^{4} + 48 d^{3} e^{5} x^{6}}"," ",0,"-sqrt(-1/(d**7*e**5))*(5*a*e**2 + b*d*e + c*d**2)*log(-d**4*e**2*sqrt(-1/(d**7*e**5)) + x)/32 + sqrt(-1/(d**7*e**5))*(5*a*e**2 + b*d*e + c*d**2)*log(d**4*e**2*sqrt(-1/(d**7*e**5)) + x)/32 + (x**5*(15*a*e**4 + 3*b*d*e**3 + 3*c*d**2*e**2) + x**3*(40*a*d*e**3 + 8*b*d**2*e**2 - 8*c*d**3*e) + x*(33*a*d**2*e**2 - 3*b*d**3*e - 3*c*d**4))/(48*d**6*e**2 + 144*d**5*e**3*x**2 + 144*d**4*e**4*x**4 + 48*d**3*e**5*x**6)","A",0
252,1,272,0,0.220085," ","integrate((e*x**2+d)**3*(c*x**4+b*x**2+a)**2,x)","a^{2} d^{3} x + \frac{c^{2} e^{3} x^{15}}{15} + x^{13} \left(\frac{2 b c e^{3}}{13} + \frac{3 c^{2} d e^{2}}{13}\right) + x^{11} \left(\frac{2 a c e^{3}}{11} + \frac{b^{2} e^{3}}{11} + \frac{6 b c d e^{2}}{11} + \frac{3 c^{2} d^{2} e}{11}\right) + x^{9} \left(\frac{2 a b e^{3}}{9} + \frac{2 a c d e^{2}}{3} + \frac{b^{2} d e^{2}}{3} + \frac{2 b c d^{2} e}{3} + \frac{c^{2} d^{3}}{9}\right) + x^{7} \left(\frac{a^{2} e^{3}}{7} + \frac{6 a b d e^{2}}{7} + \frac{6 a c d^{2} e}{7} + \frac{3 b^{2} d^{2} e}{7} + \frac{2 b c d^{3}}{7}\right) + x^{5} \left(\frac{3 a^{2} d e^{2}}{5} + \frac{6 a b d^{2} e}{5} + \frac{2 a c d^{3}}{5} + \frac{b^{2} d^{3}}{5}\right) + x^{3} \left(a^{2} d^{2} e + \frac{2 a b d^{3}}{3}\right)"," ",0,"a**2*d**3*x + c**2*e**3*x**15/15 + x**13*(2*b*c*e**3/13 + 3*c**2*d*e**2/13) + x**11*(2*a*c*e**3/11 + b**2*e**3/11 + 6*b*c*d*e**2/11 + 3*c**2*d**2*e/11) + x**9*(2*a*b*e**3/9 + 2*a*c*d*e**2/3 + b**2*d*e**2/3 + 2*b*c*d**2*e/3 + c**2*d**3/9) + x**7*(a**2*e**3/7 + 6*a*b*d*e**2/7 + 6*a*c*d**2*e/7 + 3*b**2*d**2*e/7 + 2*b*c*d**3/7) + x**5*(3*a**2*d*e**2/5 + 6*a*b*d**2*e/5 + 2*a*c*d**3/5 + b**2*d**3/5) + x**3*(a**2*d**2*e + 2*a*b*d**3/3)","A",0
253,1,192,0,0.155082," ","integrate((e*x**2+d)**2*(c*x**4+b*x**2+a)**2,x)","a^{2} d^{2} x + \frac{c^{2} e^{2} x^{13}}{13} + x^{11} \left(\frac{2 b c e^{2}}{11} + \frac{2 c^{2} d e}{11}\right) + x^{9} \left(\frac{2 a c e^{2}}{9} + \frac{b^{2} e^{2}}{9} + \frac{4 b c d e}{9} + \frac{c^{2} d^{2}}{9}\right) + x^{7} \left(\frac{2 a b e^{2}}{7} + \frac{4 a c d e}{7} + \frac{2 b^{2} d e}{7} + \frac{2 b c d^{2}}{7}\right) + x^{5} \left(\frac{a^{2} e^{2}}{5} + \frac{4 a b d e}{5} + \frac{2 a c d^{2}}{5} + \frac{b^{2} d^{2}}{5}\right) + x^{3} \left(\frac{2 a^{2} d e}{3} + \frac{2 a b d^{2}}{3}\right)"," ",0,"a**2*d**2*x + c**2*e**2*x**13/13 + x**11*(2*b*c*e**2/11 + 2*c**2*d*e/11) + x**9*(2*a*c*e**2/9 + b**2*e**2/9 + 4*b*c*d*e/9 + c**2*d**2/9) + x**7*(2*a*b*e**2/7 + 4*a*c*d*e/7 + 2*b**2*d*e/7 + 2*b*c*d**2/7) + x**5*(a**2*e**2/5 + 4*a*b*d*e/5 + 2*a*c*d**2/5 + b**2*d**2/5) + x**3*(2*a**2*d*e/3 + 2*a*b*d**2/3)","A",0
254,1,107,0,0.246889," ","integrate((e*x**2+d)*(c*x**4+b*x**2+a)**2,x)","a^{2} d x + \frac{c^{2} e x^{11}}{11} + x^{9} \left(\frac{2 b c e}{9} + \frac{c^{2} d}{9}\right) + x^{7} \left(\frac{2 a c e}{7} + \frac{b^{2} e}{7} + \frac{2 b c d}{7}\right) + x^{5} \left(\frac{2 a b e}{5} + \frac{2 a c d}{5} + \frac{b^{2} d}{5}\right) + x^{3} \left(\frac{a^{2} e}{3} + \frac{2 a b d}{3}\right)"," ",0,"a**2*d*x + c**2*e*x**11/11 + x**9*(2*b*c*e/9 + c**2*d/9) + x**7*(2*a*c*e/7 + b**2*e/7 + 2*b*c*d/7) + x**5*(2*a*b*e/5 + 2*a*c*d/5 + b**2*d/5) + x**3*(a**2*e/3 + 2*a*b*d/3)","A",0
255,1,48,0,0.154073," ","integrate((c*x**4+b*x**2+a)**2,x)","a^{2} x + \frac{2 a b x^{3}}{3} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9} + x^{5} \left(\frac{2 a c}{5} + \frac{b^{2}}{5}\right)"," ",0,"a**2*x + 2*a*b*x**3/3 + 2*b*c*x**7/7 + c**2*x**9/9 + x**5*(2*a*c/5 + b**2/5)","A",0
256,1,371,0,1.529981," ","integrate((c*x**4+b*x**2+a)**2/(e*x**2+d),x)","\frac{c^{2} x^{7}}{7 e} + x^{5} \left(\frac{2 b c}{5 e} - \frac{c^{2} d}{5 e^{2}}\right) + x^{3} \left(\frac{2 a c}{3 e} + \frac{b^{2}}{3 e} - \frac{2 b c d}{3 e^{2}} + \frac{c^{2} d^{2}}{3 e^{3}}\right) + x \left(\frac{2 a b}{e} - \frac{2 a c d}{e^{2}} - \frac{b^{2} d}{e^{2}} + \frac{2 b c d^{2}}{e^{3}} - \frac{c^{2} d^{3}}{e^{4}}\right) - \frac{\sqrt{- \frac{1}{d e^{9}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} \log{\left(- \frac{d e^{4} \sqrt{- \frac{1}{d e^{9}}} \left(a e^{2} - b d e + c d^{2}\right)^{2}}{a^{2} e^{4} - 2 a b d e^{3} + 2 a c d^{2} e^{2} + b^{2} d^{2} e^{2} - 2 b c d^{3} e + c^{2} d^{4}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{d e^{9}}} \left(a e^{2} - b d e + c d^{2}\right)^{2} \log{\left(\frac{d e^{4} \sqrt{- \frac{1}{d e^{9}}} \left(a e^{2} - b d e + c d^{2}\right)^{2}}{a^{2} e^{4} - 2 a b d e^{3} + 2 a c d^{2} e^{2} + b^{2} d^{2} e^{2} - 2 b c d^{3} e + c^{2} d^{4}} + x \right)}}{2}"," ",0,"c**2*x**7/(7*e) + x**5*(2*b*c/(5*e) - c**2*d/(5*e**2)) + x**3*(2*a*c/(3*e) + b**2/(3*e) - 2*b*c*d/(3*e**2) + c**2*d**2/(3*e**3)) + x*(2*a*b/e - 2*a*c*d/e**2 - b**2*d/e**2 + 2*b*c*d**2/e**3 - c**2*d**3/e**4) - sqrt(-1/(d*e**9))*(a*e**2 - b*d*e + c*d**2)**2*log(-d*e**4*sqrt(-1/(d*e**9))*(a*e**2 - b*d*e + c*d**2)**2/(a**2*e**4 - 2*a*b*d*e**3 + 2*a*c*d**2*e**2 + b**2*d**2*e**2 - 2*b*c*d**3*e + c**2*d**4) + x)/2 + sqrt(-1/(d*e**9))*(a*e**2 - b*d*e + c*d**2)**2*log(d*e**4*sqrt(-1/(d*e**9))*(a*e**2 - b*d*e + c*d**2)**2/(a**2*e**4 - 2*a*b*d*e**3 + 2*a*c*d**2*e**2 + b**2*d**2*e**2 - 2*b*c*d**3*e + c**2*d**4) + x)/2","B",0
257,1,484,0,3.786112," ","integrate((c*x**4+b*x**2+a)**2/(e*x**2+d)**2,x)","\frac{c^{2} x^{5}}{5 e^{2}} + x^{3} \left(\frac{2 b c}{3 e^{2}} - \frac{2 c^{2} d}{3 e^{3}}\right) + x \left(\frac{2 a c}{e^{2}} + \frac{b^{2}}{e^{2}} - \frac{4 b c d}{e^{3}} + \frac{3 c^{2} d^{2}}{e^{4}}\right) + \frac{x \left(a^{2} e^{4} - 2 a b d e^{3} + 2 a c d^{2} e^{2} + b^{2} d^{2} e^{2} - 2 b c d^{3} e + c^{2} d^{4}\right)}{2 d^{2} e^{4} + 2 d e^{5} x^{2}} - \frac{\sqrt{- \frac{1}{d^{3} e^{9}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a e^{2} + 3 b d e - 7 c d^{2}\right) \log{\left(- \frac{d^{2} e^{4} \sqrt{- \frac{1}{d^{3} e^{9}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a e^{2} + 3 b d e - 7 c d^{2}\right)}{a^{2} e^{4} + 2 a b d e^{3} - 6 a c d^{2} e^{2} - 3 b^{2} d^{2} e^{2} + 10 b c d^{3} e - 7 c^{2} d^{4}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{d^{3} e^{9}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a e^{2} + 3 b d e - 7 c d^{2}\right) \log{\left(\frac{d^{2} e^{4} \sqrt{- \frac{1}{d^{3} e^{9}}} \left(a e^{2} - b d e + c d^{2}\right) \left(a e^{2} + 3 b d e - 7 c d^{2}\right)}{a^{2} e^{4} + 2 a b d e^{3} - 6 a c d^{2} e^{2} - 3 b^{2} d^{2} e^{2} + 10 b c d^{3} e - 7 c^{2} d^{4}} + x \right)}}{4}"," ",0,"c**2*x**5/(5*e**2) + x**3*(2*b*c/(3*e**2) - 2*c**2*d/(3*e**3)) + x*(2*a*c/e**2 + b**2/e**2 - 4*b*c*d/e**3 + 3*c**2*d**2/e**4) + x*(a**2*e**4 - 2*a*b*d*e**3 + 2*a*c*d**2*e**2 + b**2*d**2*e**2 - 2*b*c*d**3*e + c**2*d**4)/(2*d**2*e**4 + 2*d*e**5*x**2) - sqrt(-1/(d**3*e**9))*(a*e**2 - b*d*e + c*d**2)*(a*e**2 + 3*b*d*e - 7*c*d**2)*log(-d**2*e**4*sqrt(-1/(d**3*e**9))*(a*e**2 - b*d*e + c*d**2)*(a*e**2 + 3*b*d*e - 7*c*d**2)/(a**2*e**4 + 2*a*b*d*e**3 - 6*a*c*d**2*e**2 - 3*b**2*d**2*e**2 + 10*b*c*d**3*e - 7*c**2*d**4) + x)/4 + sqrt(-1/(d**3*e**9))*(a*e**2 - b*d*e + c*d**2)*(a*e**2 + 3*b*d*e - 7*c*d**2)*log(d**2*e**4*sqrt(-1/(d**3*e**9))*(a*e**2 - b*d*e + c*d**2)*(a*e**2 + 3*b*d*e - 7*c*d**2)/(a**2*e**4 + 2*a*b*d*e**3 - 6*a*c*d**2*e**2 - 3*b**2*d**2*e**2 + 10*b*c*d**3*e - 7*c**2*d**4) + x)/4","B",0
258,1,398,0,17.717308," ","integrate((c*x**4+b*x**2+a)**2/(e*x**2+d)**3,x)","\frac{c^{2} x^{3}}{3 e^{3}} + x \left(\frac{2 b c}{e^{3}} - \frac{3 c^{2} d}{e^{4}}\right) - \frac{\sqrt{- \frac{1}{d^{5} e^{9}}} \left(3 a^{2} e^{4} + 2 a b d e^{3} + 6 a c d^{2} e^{2} + 3 b^{2} d^{2} e^{2} - 30 b c d^{3} e + 35 c^{2} d^{4}\right) \log{\left(- d^{3} e^{4} \sqrt{- \frac{1}{d^{5} e^{9}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{d^{5} e^{9}}} \left(3 a^{2} e^{4} + 2 a b d e^{3} + 6 a c d^{2} e^{2} + 3 b^{2} d^{2} e^{2} - 30 b c d^{3} e + 35 c^{2} d^{4}\right) \log{\left(d^{3} e^{4} \sqrt{- \frac{1}{d^{5} e^{9}}} + x \right)}}{16} + \frac{x^{3} \left(3 a^{2} e^{5} + 2 a b d e^{4} - 10 a c d^{2} e^{3} - 5 b^{2} d^{2} e^{3} + 18 b c d^{3} e^{2} - 13 c^{2} d^{4} e\right) + x \left(5 a^{2} d e^{4} - 2 a b d^{2} e^{3} - 6 a c d^{3} e^{2} - 3 b^{2} d^{3} e^{2} + 14 b c d^{4} e - 11 c^{2} d^{5}\right)}{8 d^{4} e^{4} + 16 d^{3} e^{5} x^{2} + 8 d^{2} e^{6} x^{4}}"," ",0,"c**2*x**3/(3*e**3) + x*(2*b*c/e**3 - 3*c**2*d/e**4) - sqrt(-1/(d**5*e**9))*(3*a**2*e**4 + 2*a*b*d*e**3 + 6*a*c*d**2*e**2 + 3*b**2*d**2*e**2 - 30*b*c*d**3*e + 35*c**2*d**4)*log(-d**3*e**4*sqrt(-1/(d**5*e**9)) + x)/16 + sqrt(-1/(d**5*e**9))*(3*a**2*e**4 + 2*a*b*d*e**3 + 6*a*c*d**2*e**2 + 3*b**2*d**2*e**2 - 30*b*c*d**3*e + 35*c**2*d**4)*log(d**3*e**4*sqrt(-1/(d**5*e**9)) + x)/16 + (x**3*(3*a**2*e**5 + 2*a*b*d*e**4 - 10*a*c*d**2*e**3 - 5*b**2*d**2*e**3 + 18*b*c*d**3*e**2 - 13*c**2*d**4*e) + x*(5*a**2*d*e**4 - 2*a*b*d**2*e**3 - 6*a*c*d**3*e**2 - 3*b**2*d**3*e**2 + 14*b*c*d**4*e - 11*c**2*d**5))/(8*d**4*e**4 + 16*d**3*e**5*x**2 + 8*d**2*e**6*x**4)","A",0
259,1,457,0,93.999691," ","integrate((c*x**4+b*x**2+a)**2/(e*x**2+d)**4,x)","\frac{c^{2} x}{e^{4}} - \frac{\sqrt{- \frac{1}{d^{7} e^{9}}} \left(5 a^{2} e^{4} + 2 a b d e^{3} + 2 a c d^{2} e^{2} + b^{2} d^{2} e^{2} + 10 b c d^{3} e - 35 c^{2} d^{4}\right) \log{\left(- d^{4} e^{4} \sqrt{- \frac{1}{d^{7} e^{9}}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{d^{7} e^{9}}} \left(5 a^{2} e^{4} + 2 a b d e^{3} + 2 a c d^{2} e^{2} + b^{2} d^{2} e^{2} + 10 b c d^{3} e - 35 c^{2} d^{4}\right) \log{\left(d^{4} e^{4} \sqrt{- \frac{1}{d^{7} e^{9}}} + x \right)}}{32} + \frac{x^{5} \left(15 a^{2} e^{6} + 6 a b d e^{5} + 6 a c d^{2} e^{4} + 3 b^{2} d^{2} e^{4} - 66 b c d^{3} e^{3} + 87 c^{2} d^{4} e^{2}\right) + x^{3} \left(40 a^{2} d e^{5} + 16 a b d^{2} e^{4} - 16 a c d^{3} e^{3} - 8 b^{2} d^{3} e^{3} - 80 b c d^{4} e^{2} + 136 c^{2} d^{5} e\right) + x \left(33 a^{2} d^{2} e^{4} - 6 a b d^{3} e^{3} - 6 a c d^{4} e^{2} - 3 b^{2} d^{4} e^{2} - 30 b c d^{5} e + 57 c^{2} d^{6}\right)}{48 d^{6} e^{4} + 144 d^{5} e^{5} x^{2} + 144 d^{4} e^{6} x^{4} + 48 d^{3} e^{7} x^{6}}"," ",0,"c**2*x/e**4 - sqrt(-1/(d**7*e**9))*(5*a**2*e**4 + 2*a*b*d*e**3 + 2*a*c*d**2*e**2 + b**2*d**2*e**2 + 10*b*c*d**3*e - 35*c**2*d**4)*log(-d**4*e**4*sqrt(-1/(d**7*e**9)) + x)/32 + sqrt(-1/(d**7*e**9))*(5*a**2*e**4 + 2*a*b*d*e**3 + 2*a*c*d**2*e**2 + b**2*d**2*e**2 + 10*b*c*d**3*e - 35*c**2*d**4)*log(d**4*e**4*sqrt(-1/(d**7*e**9)) + x)/32 + (x**5*(15*a**2*e**6 + 6*a*b*d*e**5 + 6*a*c*d**2*e**4 + 3*b**2*d**2*e**4 - 66*b*c*d**3*e**3 + 87*c**2*d**4*e**2) + x**3*(40*a**2*d*e**5 + 16*a*b*d**2*e**4 - 16*a*c*d**3*e**3 - 8*b**2*d**3*e**3 - 80*b*c*d**4*e**2 + 136*c**2*d**5*e) + x*(33*a**2*d**2*e**4 - 6*a*b*d**3*e**3 - 6*a*c*d**4*e**2 - 3*b**2*d**4*e**2 - 30*b*c*d**5*e + 57*c**2*d**6))/(48*d**6*e**4 + 144*d**5*e**5*x**2 + 144*d**4*e**6*x**4 + 48*d**3*e**7*x**6)","A",0
260,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**2/(e*x**2+d)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,1,153,0,0.820092," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**2,x)","\frac{c x}{e^{2}} + \frac{x \left(a e^{2} - b d e + c d^{2}\right)}{2 d^{2} e^{2} + 2 d e^{3} x^{2}} - \frac{\sqrt{- \frac{1}{d^{3} e^{5}}} \left(a e^{2} + b d e - 3 c d^{2}\right) \log{\left(- d^{2} e^{2} \sqrt{- \frac{1}{d^{3} e^{5}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{d^{3} e^{5}}} \left(a e^{2} + b d e - 3 c d^{2}\right) \log{\left(d^{2} e^{2} \sqrt{- \frac{1}{d^{3} e^{5}}} + x \right)}}{4}"," ",0,"c*x/e**2 + x*(a*e**2 - b*d*e + c*d**2)/(2*d**2*e**2 + 2*d*e**3*x**2) - sqrt(-1/(d**3*e**5))*(a*e**2 + b*d*e - 3*c*d**2)*log(-d**2*e**2*sqrt(-1/(d**3*e**5)) + x)/4 + sqrt(-1/(d**3*e**5))*(a*e**2 + b*d*e - 3*c*d**2)*log(d**2*e**2*sqrt(-1/(d**3*e**5)) + x)/4","B",0
262,1,153,0,0.861576," ","integrate((a+x**2*(c*x**2+b))/(e*x**2+d)**2,x)","\frac{c x}{e^{2}} + \frac{x \left(a e^{2} - b d e + c d^{2}\right)}{2 d^{2} e^{2} + 2 d e^{3} x^{2}} - \frac{\sqrt{- \frac{1}{d^{3} e^{5}}} \left(a e^{2} + b d e - 3 c d^{2}\right) \log{\left(- d^{2} e^{2} \sqrt{- \frac{1}{d^{3} e^{5}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{d^{3} e^{5}}} \left(a e^{2} + b d e - 3 c d^{2}\right) \log{\left(d^{2} e^{2} \sqrt{- \frac{1}{d^{3} e^{5}}} + x \right)}}{4}"," ",0,"c*x/e**2 + x*(a*e**2 - b*d*e + c*d**2)/(2*d**2*e**2 + 2*d*e**3*x**2) - sqrt(-1/(d**3*e**5))*(a*e**2 + b*d*e - 3*c*d**2)*log(-d**2*e**2*sqrt(-1/(d**3*e**5)) + x)/4 + sqrt(-1/(d**3*e**5))*(a*e**2 + b*d*e - 3*c*d**2)*log(d**2*e**2*sqrt(-1/(d**3*e**5)) + x)/4","B",0
263,-1,0,0,0.000000," ","integrate((e*x**2+d)**4/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate((e*x**2+d)**3/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate((e*x**2+d)**2/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,1,314,0,20.946671," ","integrate((e*x**2+d)/(c*x**4+b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c^{3} - 128 a^{2} b^{2} c^{2} + 16 a b^{4} c\right) + t^{2} \left(- 16 a^{2} b c e^{2} + 64 a^{2} c^{2} d e + 4 a b^{3} e^{2} - 16 a b^{2} c d e - 16 a b c^{2} d^{2} + 4 b^{3} c d^{2}\right) + a^{2} e^{4} - 2 a b d e^{3} + 2 a c d^{2} e^{2} + b^{2} d^{2} e^{2} - 2 b c d^{3} e + c^{2} d^{4}, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a^{3} c^{2} e - 16 t^{3} a^{2} b^{2} c e - 32 t^{3} a^{2} b c^{2} d + 8 t^{3} a b^{3} c d - 2 t a^{2} b e^{3} + 12 t a^{2} c d e^{2} - 6 t a b c d^{2} e - 4 t a c^{2} d^{3} + 2 t b^{2} c d^{3}}{a^{2} e^{4} - a b d e^{3} + b c d^{3} e - c^{2} d^{4}} \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**3*c**3 - 128*a**2*b**2*c**2 + 16*a*b**4*c) + _t**2*(-16*a**2*b*c*e**2 + 64*a**2*c**2*d*e + 4*a*b**3*e**2 - 16*a*b**2*c*d*e - 16*a*b*c**2*d**2 + 4*b**3*c*d**2) + a**2*e**4 - 2*a*b*d*e**3 + 2*a*c*d**2*e**2 + b**2*d**2*e**2 - 2*b*c*d**3*e + c**2*d**4, Lambda(_t, _t*log(x + (64*_t**3*a**3*c**2*e - 16*_t**3*a**2*b**2*c*e - 32*_t**3*a**2*b*c**2*d + 8*_t**3*a*b**3*c*d - 2*_t*a**2*b*e**3 + 12*_t*a**2*c*d*e**2 - 6*_t*a*b*c*d**2*e - 4*_t*a*c**2*d**3 + 2*_t*b**2*c*d**3)/(a**2*e**4 - a*b*d*e**3 + b*c*d**3*e - c**2*d**4))))","A",0
267,1,87,0,1.272480," ","integrate(1/(c*x**4+b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c^{2} - 128 a^{2} b^{2} c + 16 a b^{4}\right) + t^{2} \left(- 16 a b c + 4 b^{3}\right) + c, \left( t \mapsto t \log{\left(x + \frac{32 t^{3} a^{2} b c - 8 t^{3} a b^{3} + 4 t a c - 2 t b^{2}}{c} \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**3*c**2 - 128*a**2*b**2*c + 16*a*b**4) + _t**2*(-16*a*b*c + 4*b**3) + c, Lambda(_t, _t*log(x + (32*_t**3*a**2*b*c - 8*_t**3*a*b**3 + 4*_t*a*c - 2*_t*b**2)/c)))","A",0
268,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,-1,0,0,0.000000," ","integrate((e*x**2+d)**3/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate((e*x**2+d)**2/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate((e*x**2+d)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,1,394,0,170.283553," ","integrate(1/(c*x**4+b*x**2+a)**2,x)","\frac{- b c x^{3} + x \left(2 a c - b^{2}\right)}{8 a^{3} c - 2 a^{2} b^{2} + x^{4} \left(8 a^{2} c^{2} - 2 a b^{2} c\right) + x^{2} \left(8 a^{2} b c - 2 a b^{3}\right)} + \operatorname{RootSum} {\left(t^{4} \left(1048576 a^{9} c^{6} - 1572864 a^{8} b^{2} c^{5} + 983040 a^{7} b^{4} c^{4} - 327680 a^{6} b^{6} c^{3} + 61440 a^{5} b^{8} c^{2} - 6144 a^{4} b^{10} c + 256 a^{3} b^{12}\right) + t^{2} \left(- 61440 a^{5} b c^{5} + 61440 a^{4} b^{3} c^{4} - 24064 a^{3} b^{5} c^{3} + 4608 a^{2} b^{7} c^{2} - 432 a b^{9} c + 16 b^{11}\right) + 1296 a^{2} c^{5} - 360 a b^{2} c^{4} + 25 b^{4} c^{3}, \left( t \mapsto t \log{\left(x + \frac{32768 t^{3} a^{7} b c^{4} - 28672 t^{3} a^{6} b^{3} c^{3} + 9216 t^{3} a^{5} b^{5} c^{2} - 1280 t^{3} a^{4} b^{7} c + 64 t^{3} a^{3} b^{9} + 1728 t a^{4} c^{4} - 2304 t a^{3} b^{2} c^{3} + 740 t a^{2} b^{4} c^{2} - 92 t a b^{6} c + 4 t b^{8}}{324 a^{2} c^{4} - 81 a b^{2} c^{3} + 5 b^{4} c^{2}} \right)} \right)\right)}"," ",0,"(-b*c*x**3 + x*(2*a*c - b**2))/(8*a**3*c - 2*a**2*b**2 + x**4*(8*a**2*c**2 - 2*a*b**2*c) + x**2*(8*a**2*b*c - 2*a*b**3)) + RootSum(_t**4*(1048576*a**9*c**6 - 1572864*a**8*b**2*c**5 + 983040*a**7*b**4*c**4 - 327680*a**6*b**6*c**3 + 61440*a**5*b**8*c**2 - 6144*a**4*b**10*c + 256*a**3*b**12) + _t**2*(-61440*a**5*b*c**5 + 61440*a**4*b**3*c**4 - 24064*a**3*b**5*c**3 + 4608*a**2*b**7*c**2 - 432*a*b**9*c + 16*b**11) + 1296*a**2*c**5 - 360*a*b**2*c**4 + 25*b**4*c**3, Lambda(_t, _t*log(x + (32768*_t**3*a**7*b*c**4 - 28672*_t**3*a**6*b**3*c**3 + 9216*_t**3*a**5*b**5*c**2 - 1280*_t**3*a**4*b**7*c + 64*_t**3*a**3*b**9 + 1728*_t*a**4*c**4 - 2304*_t*a**3*b**2*c**3 + 740*_t*a**2*b**4*c**2 - 92*_t*a*b**6*c + 4*_t*b**8)/(324*a**2*c**4 - 81*a*b**2*c**3 + 5*b**4*c**2))))","A",0
274,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,1,505,0,63.829813," ","integrate((e*x**2+d)**(5/2)*(c*x**4+b*x**2+a),x)","\frac{a d^{\frac{5}{2}} x \sqrt{1 + \frac{e x^{2}}{d}}}{2} + \frac{3 a d^{\frac{5}{2}} x}{16 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{35 a d^{\frac{3}{2}} e x^{3}}{48 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{17 a \sqrt{d} e^{2} x^{5}}{24 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{5 a d^{3} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{16 \sqrt{e}} + \frac{a e^{3} x^{7}}{6 \sqrt{d} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{5 b d^{\frac{7}{2}} x}{128 e \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{133 b d^{\frac{5}{2}} x^{3}}{384 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{127 b d^{\frac{3}{2}} e x^{5}}{192 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{23 b \sqrt{d} e^{2} x^{7}}{48 \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{5 b d^{4} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{128 e^{\frac{3}{2}}} + \frac{b e^{3} x^{9}}{8 \sqrt{d} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{3 c d^{\frac{9}{2}} x}{256 e^{2} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{c d^{\frac{7}{2}} x^{3}}{256 e \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{129 c d^{\frac{5}{2}} x^{5}}{640 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{73 c d^{\frac{3}{2}} e x^{7}}{160 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{29 c \sqrt{d} e^{2} x^{9}}{80 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{3 c d^{5} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{256 e^{\frac{5}{2}}} + \frac{c e^{3} x^{11}}{10 \sqrt{d} \sqrt{1 + \frac{e x^{2}}{d}}}"," ",0,"a*d**(5/2)*x*sqrt(1 + e*x**2/d)/2 + 3*a*d**(5/2)*x/(16*sqrt(1 + e*x**2/d)) + 35*a*d**(3/2)*e*x**3/(48*sqrt(1 + e*x**2/d)) + 17*a*sqrt(d)*e**2*x**5/(24*sqrt(1 + e*x**2/d)) + 5*a*d**3*asinh(sqrt(e)*x/sqrt(d))/(16*sqrt(e)) + a*e**3*x**7/(6*sqrt(d)*sqrt(1 + e*x**2/d)) + 5*b*d**(7/2)*x/(128*e*sqrt(1 + e*x**2/d)) + 133*b*d**(5/2)*x**3/(384*sqrt(1 + e*x**2/d)) + 127*b*d**(3/2)*e*x**5/(192*sqrt(1 + e*x**2/d)) + 23*b*sqrt(d)*e**2*x**7/(48*sqrt(1 + e*x**2/d)) - 5*b*d**4*asinh(sqrt(e)*x/sqrt(d))/(128*e**(3/2)) + b*e**3*x**9/(8*sqrt(d)*sqrt(1 + e*x**2/d)) - 3*c*d**(9/2)*x/(256*e**2*sqrt(1 + e*x**2/d)) - c*d**(7/2)*x**3/(256*e*sqrt(1 + e*x**2/d)) + 129*c*d**(5/2)*x**5/(640*sqrt(1 + e*x**2/d)) + 73*c*d**(3/2)*e*x**7/(160*sqrt(1 + e*x**2/d)) + 29*c*sqrt(d)*e**2*x**9/(80*sqrt(1 + e*x**2/d)) + 3*c*d**5*asinh(sqrt(e)*x/sqrt(d))/(256*e**(5/2)) + c*e**3*x**11/(10*sqrt(d)*sqrt(1 + e*x**2/d))","B",0
277,1,413,0,31.095467," ","integrate((e*x**2+d)**(3/2)*(c*x**4+b*x**2+a),x)","\frac{a d^{\frac{3}{2}} x \sqrt{1 + \frac{e x^{2}}{d}}}{2} + \frac{a d^{\frac{3}{2}} x}{8 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{3 a \sqrt{d} e x^{3}}{8 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{3 a d^{2} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{8 \sqrt{e}} + \frac{a e^{2} x^{5}}{4 \sqrt{d} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{b d^{\frac{5}{2}} x}{16 e \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{17 b d^{\frac{3}{2}} x^{3}}{48 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{11 b \sqrt{d} e x^{5}}{24 \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{b d^{3} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{16 e^{\frac{3}{2}}} + \frac{b e^{2} x^{7}}{6 \sqrt{d} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{3 c d^{\frac{7}{2}} x}{128 e^{2} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{c d^{\frac{5}{2}} x^{3}}{128 e \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{13 c d^{\frac{3}{2}} x^{5}}{64 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{5 c \sqrt{d} e x^{7}}{16 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{3 c d^{4} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{128 e^{\frac{5}{2}}} + \frac{c e^{2} x^{9}}{8 \sqrt{d} \sqrt{1 + \frac{e x^{2}}{d}}}"," ",0,"a*d**(3/2)*x*sqrt(1 + e*x**2/d)/2 + a*d**(3/2)*x/(8*sqrt(1 + e*x**2/d)) + 3*a*sqrt(d)*e*x**3/(8*sqrt(1 + e*x**2/d)) + 3*a*d**2*asinh(sqrt(e)*x/sqrt(d))/(8*sqrt(e)) + a*e**2*x**5/(4*sqrt(d)*sqrt(1 + e*x**2/d)) + b*d**(5/2)*x/(16*e*sqrt(1 + e*x**2/d)) + 17*b*d**(3/2)*x**3/(48*sqrt(1 + e*x**2/d)) + 11*b*sqrt(d)*e*x**5/(24*sqrt(1 + e*x**2/d)) - b*d**3*asinh(sqrt(e)*x/sqrt(d))/(16*e**(3/2)) + b*e**2*x**7/(6*sqrt(d)*sqrt(1 + e*x**2/d)) - 3*c*d**(7/2)*x/(128*e**2*sqrt(1 + e*x**2/d)) - c*d**(5/2)*x**3/(128*e*sqrt(1 + e*x**2/d)) + 13*c*d**(3/2)*x**5/(64*sqrt(1 + e*x**2/d)) + 5*c*sqrt(d)*e*x**7/(16*sqrt(1 + e*x**2/d)) + 3*c*d**4*asinh(sqrt(e)*x/sqrt(d))/(128*e**(5/2)) + c*e**2*x**9/(8*sqrt(d)*sqrt(1 + e*x**2/d))","B",0
278,1,272,0,12.265440," ","integrate((e*x**2+d)**(1/2)*(c*x**4+b*x**2+a),x)","\frac{a \sqrt{d} x \sqrt{1 + \frac{e x^{2}}{d}}}{2} + \frac{a d \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{2 \sqrt{e}} + \frac{b d^{\frac{3}{2}} x}{8 e \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{3 b \sqrt{d} x^{3}}{8 \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{b d^{2} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{8 e^{\frac{3}{2}}} + \frac{b e x^{5}}{4 \sqrt{d} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{c d^{\frac{5}{2}} x}{16 e^{2} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{c d^{\frac{3}{2}} x^{3}}{48 e \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{5 c \sqrt{d} x^{5}}{24 \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{c d^{3} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{16 e^{\frac{5}{2}}} + \frac{c e x^{7}}{6 \sqrt{d} \sqrt{1 + \frac{e x^{2}}{d}}}"," ",0,"a*sqrt(d)*x*sqrt(1 + e*x**2/d)/2 + a*d*asinh(sqrt(e)*x/sqrt(d))/(2*sqrt(e)) + b*d**(3/2)*x/(8*e*sqrt(1 + e*x**2/d)) + 3*b*sqrt(d)*x**3/(8*sqrt(1 + e*x**2/d)) - b*d**2*asinh(sqrt(e)*x/sqrt(d))/(8*e**(3/2)) + b*e*x**5/(4*sqrt(d)*sqrt(1 + e*x**2/d)) - c*d**(5/2)*x/(16*e**2*sqrt(1 + e*x**2/d)) - c*d**(3/2)*x**3/(48*e*sqrt(1 + e*x**2/d)) + 5*c*sqrt(d)*x**5/(24*sqrt(1 + e*x**2/d)) + c*d**3*asinh(sqrt(e)*x/sqrt(d))/(16*e**(5/2)) + c*e*x**7/(6*sqrt(d)*sqrt(1 + e*x**2/d))","B",0
279,1,230,0,7.045295," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**(1/2),x)","a \left(\begin{cases} \frac{\sqrt{- \frac{d}{e}} \operatorname{asin}{\left(x \sqrt{- \frac{e}{d}} \right)}}{\sqrt{d}} & \text{for}\: d > 0 \wedge e < 0 \\\frac{\sqrt{\frac{d}{e}} \operatorname{asinh}{\left(x \sqrt{\frac{e}{d}} \right)}}{\sqrt{d}} & \text{for}\: d > 0 \wedge e > 0 \\\frac{\sqrt{- \frac{d}{e}} \operatorname{acosh}{\left(x \sqrt{- \frac{e}{d}} \right)}}{\sqrt{- d}} & \text{for}\: e > 0 \wedge d < 0 \end{cases}\right) + \frac{b \sqrt{d} x \sqrt{1 + \frac{e x^{2}}{d}}}{2 e} - \frac{b d \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{2 e^{\frac{3}{2}}} - \frac{3 c d^{\frac{3}{2}} x}{8 e^{2} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{c \sqrt{d} x^{3}}{8 e \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{3 c d^{2} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{8 e^{\frac{5}{2}}} + \frac{c x^{5}}{4 \sqrt{d} \sqrt{1 + \frac{e x^{2}}{d}}}"," ",0,"a*Piecewise((sqrt(-d/e)*asin(x*sqrt(-e/d))/sqrt(d), (d > 0) & (e < 0)), (sqrt(d/e)*asinh(x*sqrt(e/d))/sqrt(d), (d > 0) & (e > 0)), (sqrt(-d/e)*acosh(x*sqrt(-e/d))/sqrt(-d), (e > 0) & (d < 0))) + b*sqrt(d)*x*sqrt(1 + e*x**2/d)/(2*e) - b*d*asinh(sqrt(e)*x/sqrt(d))/(2*e**(3/2)) - 3*c*d**(3/2)*x/(8*e**2*sqrt(1 + e*x**2/d)) - c*sqrt(d)*x**3/(8*e*sqrt(1 + e*x**2/d)) + 3*c*d**2*asinh(sqrt(e)*x/sqrt(d))/(8*e**(5/2)) + c*x**5/(4*sqrt(d)*sqrt(1 + e*x**2/d))","A",0
280,1,134,0,9.984416," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**(3/2),x)","\frac{a x}{d^{\frac{3}{2}} \sqrt{1 + \frac{e x^{2}}{d}}} + b \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{e^{\frac{3}{2}}} - \frac{x}{\sqrt{d} e \sqrt{1 + \frac{e x^{2}}{d}}}\right) + c \left(\frac{3 \sqrt{d} x}{2 e^{2} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{3 d \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{2 e^{\frac{5}{2}}} + \frac{x^{3}}{2 \sqrt{d} e \sqrt{1 + \frac{e x^{2}}{d}}}\right)"," ",0,"a*x/(d**(3/2)*sqrt(1 + e*x**2/d)) + b*(asinh(sqrt(e)*x/sqrt(d))/e**(3/2) - x/(sqrt(d)*e*sqrt(1 + e*x**2/d))) + c*(3*sqrt(d)*x/(2*e**2*sqrt(1 + e*x**2/d)) - 3*d*asinh(sqrt(e)*x/sqrt(d))/(2*e**(5/2)) + x**3/(2*sqrt(d)*e*sqrt(1 + e*x**2/d)))","A",0
281,1,450,0,18.951259," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**(5/2),x)","a \left(\frac{3 d x}{3 d^{\frac{7}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 3 d^{\frac{5}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{2 e x^{3}}{3 d^{\frac{7}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 3 d^{\frac{5}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}}}\right) + \frac{b x^{3}}{3 d^{\frac{5}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 3 d^{\frac{3}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}}} + c \left(\frac{3 d^{\frac{39}{2}} e^{11} \sqrt{1 + \frac{e x^{2}}{d}} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{3 d^{\frac{39}{2}} e^{\frac{27}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 3 d^{\frac{37}{2}} e^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{3 d^{\frac{37}{2}} e^{12} x^{2} \sqrt{1 + \frac{e x^{2}}{d}} \operatorname{asinh}{\left(\frac{\sqrt{e} x}{\sqrt{d}} \right)}}{3 d^{\frac{39}{2}} e^{\frac{27}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 3 d^{\frac{37}{2}} e^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{3 d^{19} e^{\frac{23}{2}} x}{3 d^{\frac{39}{2}} e^{\frac{27}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 3 d^{\frac{37}{2}} e^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{e x^{2}}{d}}} - \frac{4 d^{18} e^{\frac{25}{2}} x^{3}}{3 d^{\frac{39}{2}} e^{\frac{27}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 3 d^{\frac{37}{2}} e^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{e x^{2}}{d}}}\right)"," ",0,"a*(3*d*x/(3*d**(7/2)*sqrt(1 + e*x**2/d) + 3*d**(5/2)*e*x**2*sqrt(1 + e*x**2/d)) + 2*e*x**3/(3*d**(7/2)*sqrt(1 + e*x**2/d) + 3*d**(5/2)*e*x**2*sqrt(1 + e*x**2/d))) + b*x**3/(3*d**(5/2)*sqrt(1 + e*x**2/d) + 3*d**(3/2)*e*x**2*sqrt(1 + e*x**2/d)) + c*(3*d**(39/2)*e**11*sqrt(1 + e*x**2/d)*asinh(sqrt(e)*x/sqrt(d))/(3*d**(39/2)*e**(27/2)*sqrt(1 + e*x**2/d) + 3*d**(37/2)*e**(29/2)*x**2*sqrt(1 + e*x**2/d)) + 3*d**(37/2)*e**12*x**2*sqrt(1 + e*x**2/d)*asinh(sqrt(e)*x/sqrt(d))/(3*d**(39/2)*e**(27/2)*sqrt(1 + e*x**2/d) + 3*d**(37/2)*e**(29/2)*x**2*sqrt(1 + e*x**2/d)) - 3*d**19*e**(23/2)*x/(3*d**(39/2)*e**(27/2)*sqrt(1 + e*x**2/d) + 3*d**(37/2)*e**(29/2)*x**2*sqrt(1 + e*x**2/d)) - 4*d**18*e**(25/2)*x**3/(3*d**(39/2)*e**(27/2)*sqrt(1 + e*x**2/d) + 3*d**(37/2)*e**(29/2)*x**2*sqrt(1 + e*x**2/d)))","B",0
282,1,639,0,45.984983," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**(7/2),x)","a \left(\frac{15 d^{5} x}{15 d^{\frac{17}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 45 d^{\frac{15}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 45 d^{\frac{13}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 15 d^{\frac{11}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{35 d^{4} e x^{3}}{15 d^{\frac{17}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 45 d^{\frac{15}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 45 d^{\frac{13}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 15 d^{\frac{11}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{28 d^{3} e^{2} x^{5}}{15 d^{\frac{17}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 45 d^{\frac{15}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 45 d^{\frac{13}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 15 d^{\frac{11}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{8 d^{2} e^{3} x^{7}}{15 d^{\frac{17}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 45 d^{\frac{15}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 45 d^{\frac{13}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 15 d^{\frac{11}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}}}\right) + b \left(\frac{5 d x^{3}}{15 d^{\frac{9}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 30 d^{\frac{7}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 15 d^{\frac{5}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{2 e x^{5}}{15 d^{\frac{9}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 30 d^{\frac{7}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 15 d^{\frac{5}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}}}\right) + \frac{c x^{5}}{5 d^{\frac{7}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 10 d^{\frac{5}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 5 d^{\frac{3}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}}}"," ",0,"a*(15*d**5*x/(15*d**(17/2)*sqrt(1 + e*x**2/d) + 45*d**(15/2)*e*x**2*sqrt(1 + e*x**2/d) + 45*d**(13/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 15*d**(11/2)*e**3*x**6*sqrt(1 + e*x**2/d)) + 35*d**4*e*x**3/(15*d**(17/2)*sqrt(1 + e*x**2/d) + 45*d**(15/2)*e*x**2*sqrt(1 + e*x**2/d) + 45*d**(13/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 15*d**(11/2)*e**3*x**6*sqrt(1 + e*x**2/d)) + 28*d**3*e**2*x**5/(15*d**(17/2)*sqrt(1 + e*x**2/d) + 45*d**(15/2)*e*x**2*sqrt(1 + e*x**2/d) + 45*d**(13/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 15*d**(11/2)*e**3*x**6*sqrt(1 + e*x**2/d)) + 8*d**2*e**3*x**7/(15*d**(17/2)*sqrt(1 + e*x**2/d) + 45*d**(15/2)*e*x**2*sqrt(1 + e*x**2/d) + 45*d**(13/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 15*d**(11/2)*e**3*x**6*sqrt(1 + e*x**2/d))) + b*(5*d*x**3/(15*d**(9/2)*sqrt(1 + e*x**2/d) + 30*d**(7/2)*e*x**2*sqrt(1 + e*x**2/d) + 15*d**(5/2)*e**2*x**4*sqrt(1 + e*x**2/d)) + 2*e*x**5/(15*d**(9/2)*sqrt(1 + e*x**2/d) + 30*d**(7/2)*e*x**2*sqrt(1 + e*x**2/d) + 15*d**(5/2)*e**2*x**4*sqrt(1 + e*x**2/d))) + c*x**5/(5*d**(7/2)*sqrt(1 + e*x**2/d) + 10*d**(5/2)*e*x**2*sqrt(1 + e*x**2/d) + 5*d**(3/2)*e**2*x**4*sqrt(1 + e*x**2/d))","B",0
283,1,1989,0,119.187221," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**(9/2),x)","a \left(\frac{35 d^{14} x}{35 d^{\frac{37}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{35}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{33}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 700 d^{\frac{31}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{29}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{27}{2}} e^{5} x^{10} \sqrt{1 + \frac{e x^{2}}{d}} + 35 d^{\frac{25}{2}} e^{6} x^{12} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{175 d^{13} e x^{3}}{35 d^{\frac{37}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{35}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{33}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 700 d^{\frac{31}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{29}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{27}{2}} e^{5} x^{10} \sqrt{1 + \frac{e x^{2}}{d}} + 35 d^{\frac{25}{2}} e^{6} x^{12} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{371 d^{12} e^{2} x^{5}}{35 d^{\frac{37}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{35}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{33}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 700 d^{\frac{31}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{29}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{27}{2}} e^{5} x^{10} \sqrt{1 + \frac{e x^{2}}{d}} + 35 d^{\frac{25}{2}} e^{6} x^{12} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{429 d^{11} e^{3} x^{7}}{35 d^{\frac{37}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{35}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{33}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 700 d^{\frac{31}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{29}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{27}{2}} e^{5} x^{10} \sqrt{1 + \frac{e x^{2}}{d}} + 35 d^{\frac{25}{2}} e^{6} x^{12} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{286 d^{10} e^{4} x^{9}}{35 d^{\frac{37}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{35}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{33}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 700 d^{\frac{31}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{29}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{27}{2}} e^{5} x^{10} \sqrt{1 + \frac{e x^{2}}{d}} + 35 d^{\frac{25}{2}} e^{6} x^{12} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{104 d^{9} e^{5} x^{11}}{35 d^{\frac{37}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{35}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{33}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 700 d^{\frac{31}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{29}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{27}{2}} e^{5} x^{10} \sqrt{1 + \frac{e x^{2}}{d}} + 35 d^{\frac{25}{2}} e^{6} x^{12} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{16 d^{8} e^{6} x^{13}}{35 d^{\frac{37}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{35}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{33}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 700 d^{\frac{31}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 525 d^{\frac{29}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}} + 210 d^{\frac{27}{2}} e^{5} x^{10} \sqrt{1 + \frac{e x^{2}}{d}} + 35 d^{\frac{25}{2}} e^{6} x^{12} \sqrt{1 + \frac{e x^{2}}{d}}}\right) + b \left(\frac{35 d^{5} x^{3}}{105 d^{\frac{19}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 420 d^{\frac{17}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 630 d^{\frac{15}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 420 d^{\frac{13}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 105 d^{\frac{11}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{63 d^{4} e x^{5}}{105 d^{\frac{19}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 420 d^{\frac{17}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 630 d^{\frac{15}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 420 d^{\frac{13}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 105 d^{\frac{11}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{36 d^{3} e^{2} x^{7}}{105 d^{\frac{19}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 420 d^{\frac{17}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 630 d^{\frac{15}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 420 d^{\frac{13}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 105 d^{\frac{11}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{8 d^{2} e^{3} x^{9}}{105 d^{\frac{19}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 420 d^{\frac{17}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 630 d^{\frac{15}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 420 d^{\frac{13}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}} + 105 d^{\frac{11}{2}} e^{4} x^{8} \sqrt{1 + \frac{e x^{2}}{d}}}\right) + c \left(\frac{7 d x^{5}}{35 d^{\frac{11}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 105 d^{\frac{9}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 105 d^{\frac{7}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 35 d^{\frac{5}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}}} + \frac{2 e x^{7}}{35 d^{\frac{11}{2}} \sqrt{1 + \frac{e x^{2}}{d}} + 105 d^{\frac{9}{2}} e x^{2} \sqrt{1 + \frac{e x^{2}}{d}} + 105 d^{\frac{7}{2}} e^{2} x^{4} \sqrt{1 + \frac{e x^{2}}{d}} + 35 d^{\frac{5}{2}} e^{3} x^{6} \sqrt{1 + \frac{e x^{2}}{d}}}\right)"," ",0,"a*(35*d**14*x/(35*d**(37/2)*sqrt(1 + e*x**2/d) + 210*d**(35/2)*e*x**2*sqrt(1 + e*x**2/d) + 525*d**(33/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 700*d**(31/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 525*d**(29/2)*e**4*x**8*sqrt(1 + e*x**2/d) + 210*d**(27/2)*e**5*x**10*sqrt(1 + e*x**2/d) + 35*d**(25/2)*e**6*x**12*sqrt(1 + e*x**2/d)) + 175*d**13*e*x**3/(35*d**(37/2)*sqrt(1 + e*x**2/d) + 210*d**(35/2)*e*x**2*sqrt(1 + e*x**2/d) + 525*d**(33/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 700*d**(31/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 525*d**(29/2)*e**4*x**8*sqrt(1 + e*x**2/d) + 210*d**(27/2)*e**5*x**10*sqrt(1 + e*x**2/d) + 35*d**(25/2)*e**6*x**12*sqrt(1 + e*x**2/d)) + 371*d**12*e**2*x**5/(35*d**(37/2)*sqrt(1 + e*x**2/d) + 210*d**(35/2)*e*x**2*sqrt(1 + e*x**2/d) + 525*d**(33/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 700*d**(31/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 525*d**(29/2)*e**4*x**8*sqrt(1 + e*x**2/d) + 210*d**(27/2)*e**5*x**10*sqrt(1 + e*x**2/d) + 35*d**(25/2)*e**6*x**12*sqrt(1 + e*x**2/d)) + 429*d**11*e**3*x**7/(35*d**(37/2)*sqrt(1 + e*x**2/d) + 210*d**(35/2)*e*x**2*sqrt(1 + e*x**2/d) + 525*d**(33/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 700*d**(31/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 525*d**(29/2)*e**4*x**8*sqrt(1 + e*x**2/d) + 210*d**(27/2)*e**5*x**10*sqrt(1 + e*x**2/d) + 35*d**(25/2)*e**6*x**12*sqrt(1 + e*x**2/d)) + 286*d**10*e**4*x**9/(35*d**(37/2)*sqrt(1 + e*x**2/d) + 210*d**(35/2)*e*x**2*sqrt(1 + e*x**2/d) + 525*d**(33/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 700*d**(31/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 525*d**(29/2)*e**4*x**8*sqrt(1 + e*x**2/d) + 210*d**(27/2)*e**5*x**10*sqrt(1 + e*x**2/d) + 35*d**(25/2)*e**6*x**12*sqrt(1 + e*x**2/d)) + 104*d**9*e**5*x**11/(35*d**(37/2)*sqrt(1 + e*x**2/d) + 210*d**(35/2)*e*x**2*sqrt(1 + e*x**2/d) + 525*d**(33/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 700*d**(31/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 525*d**(29/2)*e**4*x**8*sqrt(1 + e*x**2/d) + 210*d**(27/2)*e**5*x**10*sqrt(1 + e*x**2/d) + 35*d**(25/2)*e**6*x**12*sqrt(1 + e*x**2/d)) + 16*d**8*e**6*x**13/(35*d**(37/2)*sqrt(1 + e*x**2/d) + 210*d**(35/2)*e*x**2*sqrt(1 + e*x**2/d) + 525*d**(33/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 700*d**(31/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 525*d**(29/2)*e**4*x**8*sqrt(1 + e*x**2/d) + 210*d**(27/2)*e**5*x**10*sqrt(1 + e*x**2/d) + 35*d**(25/2)*e**6*x**12*sqrt(1 + e*x**2/d))) + b*(35*d**5*x**3/(105*d**(19/2)*sqrt(1 + e*x**2/d) + 420*d**(17/2)*e*x**2*sqrt(1 + e*x**2/d) + 630*d**(15/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 420*d**(13/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 105*d**(11/2)*e**4*x**8*sqrt(1 + e*x**2/d)) + 63*d**4*e*x**5/(105*d**(19/2)*sqrt(1 + e*x**2/d) + 420*d**(17/2)*e*x**2*sqrt(1 + e*x**2/d) + 630*d**(15/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 420*d**(13/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 105*d**(11/2)*e**4*x**8*sqrt(1 + e*x**2/d)) + 36*d**3*e**2*x**7/(105*d**(19/2)*sqrt(1 + e*x**2/d) + 420*d**(17/2)*e*x**2*sqrt(1 + e*x**2/d) + 630*d**(15/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 420*d**(13/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 105*d**(11/2)*e**4*x**8*sqrt(1 + e*x**2/d)) + 8*d**2*e**3*x**9/(105*d**(19/2)*sqrt(1 + e*x**2/d) + 420*d**(17/2)*e*x**2*sqrt(1 + e*x**2/d) + 630*d**(15/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 420*d**(13/2)*e**3*x**6*sqrt(1 + e*x**2/d) + 105*d**(11/2)*e**4*x**8*sqrt(1 + e*x**2/d))) + c*(7*d*x**5/(35*d**(11/2)*sqrt(1 + e*x**2/d) + 105*d**(9/2)*e*x**2*sqrt(1 + e*x**2/d) + 105*d**(7/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 35*d**(5/2)*e**3*x**6*sqrt(1 + e*x**2/d)) + 2*e*x**7/(35*d**(11/2)*sqrt(1 + e*x**2/d) + 105*d**(9/2)*e*x**2*sqrt(1 + e*x**2/d) + 105*d**(7/2)*e**2*x**4*sqrt(1 + e*x**2/d) + 35*d**(5/2)*e**3*x**6*sqrt(1 + e*x**2/d)))","B",0
284,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)/(e*x**2+d)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,0,0,0,0.000000," ","integrate((5*x**2+7)**3*(x**4+3*x**2+2)**(1/2),x)","\int \sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)} \left(5 x^{2} + 7\right)^{3}\, dx"," ",0,"Integral(sqrt((x**2 + 1)*(x**2 + 2))*(5*x**2 + 7)**3, x)","F",0
287,0,0,0,0.000000," ","integrate((5*x**2+7)**2*(x**4+3*x**2+2)**(1/2),x)","\int \sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)} \left(5 x^{2} + 7\right)^{2}\, dx"," ",0,"Integral(sqrt((x**2 + 1)*(x**2 + 2))*(5*x**2 + 7)**2, x)","F",0
288,0,0,0,0.000000," ","integrate((5*x**2+7)*(x**4+3*x**2+2)**(1/2),x)","\int \sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)} \left(5 x^{2} + 7\right)\, dx"," ",0,"Integral(sqrt((x**2 + 1)*(x**2 + 2))*(5*x**2 + 7), x)","F",0
289,0,0,0,0.000000," ","integrate((x**4+3*x**2+2)**(1/2),x)","\int \sqrt{x^{4} + 3 x^{2} + 2}\, dx"," ",0,"Integral(sqrt(x**4 + 3*x**2 + 2), x)","F",0
290,0,0,0,0.000000," ","integrate((x**4+3*x**2+2)**(1/2)/(5*x**2+7),x)","\int \frac{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}}{5 x^{2} + 7}\, dx"," ",0,"Integral(sqrt((x**2 + 1)*(x**2 + 2))/(5*x**2 + 7), x)","F",0
291,0,0,0,0.000000," ","integrate((x**4+3*x**2+2)**(1/2)/(5*x**2+7)**2,x)","\int \frac{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}}{\left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(sqrt((x**2 + 1)*(x**2 + 2))/(5*x**2 + 7)**2, x)","F",0
292,0,0,0,0.000000," ","integrate((x**4+3*x**2+2)**(1/2)/(5*x**2+7)**3,x)","\int \frac{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}}{\left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(sqrt((x**2 + 1)*(x**2 + 2))/(5*x**2 + 7)**3, x)","F",0
293,0,0,0,0.000000," ","integrate((5*x**2+7)**3*(x**4+3*x**2+2)**(3/2),x)","\int \left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{3}\, dx"," ",0,"Integral(((x**2 + 1)*(x**2 + 2))**(3/2)*(5*x**2 + 7)**3, x)","F",0
294,0,0,0,0.000000," ","integrate((5*x**2+7)**2*(x**4+3*x**2+2)**(3/2),x)","\int \left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{2}\, dx"," ",0,"Integral(((x**2 + 1)*(x**2 + 2))**(3/2)*(5*x**2 + 7)**2, x)","F",0
295,0,0,0,0.000000," ","integrate((5*x**2+7)*(x**4+3*x**2+2)**(3/2),x)","\int \left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)\, dx"," ",0,"Integral(((x**2 + 1)*(x**2 + 2))**(3/2)*(5*x**2 + 7), x)","F",0
296,0,0,0,0.000000," ","integrate((x**4+3*x**2+2)**(3/2),x)","\int \left(x^{4} + 3 x^{2} + 2\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((x**4 + 3*x**2 + 2)**(3/2), x)","F",0
297,0,0,0,0.000000," ","integrate((x**4+3*x**2+2)**(3/2)/(5*x**2+7),x)","\int \frac{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}}}{5 x^{2} + 7}\, dx"," ",0,"Integral(((x**2 + 1)*(x**2 + 2))**(3/2)/(5*x**2 + 7), x)","F",0
298,0,0,0,0.000000," ","integrate((x**4+3*x**2+2)**(3/2)/(5*x**2+7)**2,x)","\int \frac{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}}}{\left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(((x**2 + 1)*(x**2 + 2))**(3/2)/(5*x**2 + 7)**2, x)","F",0
299,0,0,0,0.000000," ","integrate((x**4+3*x**2+2)**(3/2)/(5*x**2+7)**3,x)","\int \frac{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}}}{\left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(((x**2 + 1)*(x**2 + 2))**(3/2)/(5*x**2 + 7)**3, x)","F",0
300,0,0,0,0.000000," ","integrate((5*x**2+7)**3/(x**4+3*x**2+2)**(1/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{3}}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}}\, dx"," ",0,"Integral((5*x**2 + 7)**3/sqrt((x**2 + 1)*(x**2 + 2)), x)","F",0
301,0,0,0,0.000000," ","integrate((5*x**2+7)**2/(x**4+3*x**2+2)**(1/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{2}}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}}\, dx"," ",0,"Integral((5*x**2 + 7)**2/sqrt((x**2 + 1)*(x**2 + 2)), x)","F",0
302,0,0,0,0.000000," ","integrate((5*x**2+7)/(x**4+3*x**2+2)**(1/2),x)","\int \frac{5 x^{2} + 7}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}}\, dx"," ",0,"Integral((5*x**2 + 7)/sqrt((x**2 + 1)*(x**2 + 2)), x)","F",0
303,0,0,0,0.000000," ","integrate(1/(x**4+3*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{x^{4} + 3 x^{2} + 2}}\, dx"," ",0,"Integral(1/sqrt(x**4 + 3*x**2 + 2), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(5*x**2+7)/(x**4+3*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)} \left(5 x^{2} + 7\right)}\, dx"," ",0,"Integral(1/(sqrt((x**2 + 1)*(x**2 + 2))*(5*x**2 + 7)), x)","F",0
305,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**2/(x**4+3*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)} \left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt((x**2 + 1)*(x**2 + 2))*(5*x**2 + 7)**2), x)","F",0
306,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**3/(x**4+3*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)} \left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt((x**2 + 1)*(x**2 + 2))*(5*x**2 + 7)**3), x)","F",0
307,0,0,0,0.000000," ","integrate((5*x**2+7)**5/(x**4+3*x**2+2)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{5}}{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**5/((x**2 + 1)*(x**2 + 2))**(3/2), x)","F",0
308,0,0,0,0.000000," ","integrate((5*x**2+7)**4/(x**4+3*x**2+2)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{4}}{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**4/((x**2 + 1)*(x**2 + 2))**(3/2), x)","F",0
309,0,0,0,0.000000," ","integrate((5*x**2+7)**3/(x**4+3*x**2+2)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{3}}{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**3/((x**2 + 1)*(x**2 + 2))**(3/2), x)","F",0
310,0,0,0,0.000000," ","integrate((5*x**2+7)**2/(x**4+3*x**2+2)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{2}}{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**2/((x**2 + 1)*(x**2 + 2))**(3/2), x)","F",0
311,0,0,0,0.000000," ","integrate((5*x**2+7)/(x**4+3*x**2+2)**(3/2),x)","\int \frac{5 x^{2} + 7}{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)/((x**2 + 1)*(x**2 + 2))**(3/2), x)","F",0
312,0,0,0,0.000000," ","integrate(1/(x**4+3*x**2+2)**(3/2),x)","\int \frac{1}{\left(x^{4} + 3 x^{2} + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x**4 + 3*x**2 + 2)**(-3/2), x)","F",0
313,0,0,0,0.000000," ","integrate(1/(5*x**2+7)/(x**4+3*x**2+2)**(3/2),x)","\int \frac{1}{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)}\, dx"," ",0,"Integral(1/(((x**2 + 1)*(x**2 + 2))**(3/2)*(5*x**2 + 7)), x)","F",0
314,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**2/(x**4+3*x**2+2)**(3/2),x)","\int \frac{1}{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(1/(((x**2 + 1)*(x**2 + 2))**(3/2)*(5*x**2 + 7)**2), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**3/(x**4+3*x**2+2)**(3/2),x)","\int \frac{1}{\left(\left(x^{2} + 1\right) \left(x^{2} + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(1/(((x**2 + 1)*(x**2 + 2))**(3/2)*(5*x**2 + 7)**3), x)","F",0
316,0,0,0,0.000000," ","integrate((5*x**2+7)**4*(-x**4+x**2+2)**(1/2),x)","\int \sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)} \left(5 x^{2} + 7\right)^{4}\, dx"," ",0,"Integral(sqrt(-(x**2 - 2)*(x**2 + 1))*(5*x**2 + 7)**4, x)","F",0
317,0,0,0,0.000000," ","integrate((5*x**2+7)**3*(-x**4+x**2+2)**(1/2),x)","\int \sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)} \left(5 x^{2} + 7\right)^{3}\, dx"," ",0,"Integral(sqrt(-(x**2 - 2)*(x**2 + 1))*(5*x**2 + 7)**3, x)","F",0
318,0,0,0,0.000000," ","integrate((5*x**2+7)**2*(-x**4+x**2+2)**(1/2),x)","\int \sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)} \left(5 x^{2} + 7\right)^{2}\, dx"," ",0,"Integral(sqrt(-(x**2 - 2)*(x**2 + 1))*(5*x**2 + 7)**2, x)","F",0
319,0,0,0,0.000000," ","integrate((5*x**2+7)*(-x**4+x**2+2)**(1/2),x)","\int \sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)} \left(5 x^{2} + 7\right)\, dx"," ",0,"Integral(sqrt(-(x**2 - 2)*(x**2 + 1))*(5*x**2 + 7), x)","F",0
320,0,0,0,0.000000," ","integrate((-x**4+x**2+2)**(1/2),x)","\int \sqrt{- x^{4} + x^{2} + 2}\, dx"," ",0,"Integral(sqrt(-x**4 + x**2 + 2), x)","F",0
321,0,0,0,0.000000," ","integrate((-x**4+x**2+2)**(1/2)/(5*x**2+7),x)","\int \frac{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)}}{5 x^{2} + 7}\, dx"," ",0,"Integral(sqrt(-(x**2 - 2)*(x**2 + 1))/(5*x**2 + 7), x)","F",0
322,0,0,0,0.000000," ","integrate((-x**4+x**2+2)**(1/2)/(5*x**2+7)**2,x)","\int \frac{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)}}{\left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(sqrt(-(x**2 - 2)*(x**2 + 1))/(5*x**2 + 7)**2, x)","F",0
323,0,0,0,0.000000," ","integrate((-x**4+x**2+2)**(1/2)/(5*x**2+7)**3,x)","\int \frac{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)}}{\left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(sqrt(-(x**2 - 2)*(x**2 + 1))/(5*x**2 + 7)**3, x)","F",0
324,0,0,0,0.000000," ","integrate((5*x**2+7)**4*(-x**4+x**2+2)**(3/2),x)","\int \left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{4}\, dx"," ",0,"Integral((-(x**2 - 2)*(x**2 + 1))**(3/2)*(5*x**2 + 7)**4, x)","F",0
325,0,0,0,0.000000," ","integrate((5*x**2+7)**3*(-x**4+x**2+2)**(3/2),x)","\int \left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{3}\, dx"," ",0,"Integral((-(x**2 - 2)*(x**2 + 1))**(3/2)*(5*x**2 + 7)**3, x)","F",0
326,0,0,0,0.000000," ","integrate((5*x**2+7)**2*(-x**4+x**2+2)**(3/2),x)","\int \left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{2}\, dx"," ",0,"Integral((-(x**2 - 2)*(x**2 + 1))**(3/2)*(5*x**2 + 7)**2, x)","F",0
327,0,0,0,0.000000," ","integrate((5*x**2+7)*(-x**4+x**2+2)**(3/2),x)","\int \left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)\, dx"," ",0,"Integral((-(x**2 - 2)*(x**2 + 1))**(3/2)*(5*x**2 + 7), x)","F",0
328,0,0,0,0.000000," ","integrate((-x**4+x**2+2)**(3/2),x)","\int \left(- x^{4} + x^{2} + 2\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-x**4 + x**2 + 2)**(3/2), x)","F",0
329,0,0,0,0.000000," ","integrate((-x**4+x**2+2)**(3/2)/(5*x**2+7),x)","\int \frac{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}}}{5 x^{2} + 7}\, dx"," ",0,"Integral((-(x**2 - 2)*(x**2 + 1))**(3/2)/(5*x**2 + 7), x)","F",0
330,0,0,0,0.000000," ","integrate((-x**4+x**2+2)**(3/2)/(5*x**2+7)**2,x)","\int \frac{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}}}{\left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral((-(x**2 - 2)*(x**2 + 1))**(3/2)/(5*x**2 + 7)**2, x)","F",0
331,0,0,0,0.000000," ","integrate((-x**4+x**2+2)**(3/2)/(5*x**2+7)**3,x)","\int \frac{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}}}{\left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral((-(x**2 - 2)*(x**2 + 1))**(3/2)/(5*x**2 + 7)**3, x)","F",0
332,0,0,0,0.000000," ","integrate((5*x**2+7)**3/(-x**4+x**2+2)**(1/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{3}}{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)}}\, dx"," ",0,"Integral((5*x**2 + 7)**3/sqrt(-(x**2 - 2)*(x**2 + 1)), x)","F",0
333,0,0,0,0.000000," ","integrate((5*x**2+7)**2/(-x**4+x**2+2)**(1/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{2}}{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)}}\, dx"," ",0,"Integral((5*x**2 + 7)**2/sqrt(-(x**2 - 2)*(x**2 + 1)), x)","F",0
334,0,0,0,0.000000," ","integrate((5*x**2+7)/(-x**4+x**2+2)**(1/2),x)","\int \frac{5 x^{2} + 7}{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)}}\, dx"," ",0,"Integral((5*x**2 + 7)/sqrt(-(x**2 - 2)*(x**2 + 1)), x)","F",0
335,0,0,0,0.000000," ","integrate(1/(-x**4+x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- x^{4} + x^{2} + 2}}\, dx"," ",0,"Integral(1/sqrt(-x**4 + x**2 + 2), x)","F",0
336,0,0,0,0.000000," ","integrate(1/(5*x**2+7)/(-x**4+x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)} \left(5 x^{2} + 7\right)}\, dx"," ",0,"Integral(1/(sqrt(-(x**2 - 2)*(x**2 + 1))*(5*x**2 + 7)), x)","F",0
337,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**2/(-x**4+x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)} \left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(-(x**2 - 2)*(x**2 + 1))*(5*x**2 + 7)**2), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**3/(-x**4+x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 1\right)} \left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(-(x**2 - 2)*(x**2 + 1))*(5*x**2 + 7)**3), x)","F",0
339,0,0,0,0.000000," ","integrate((5*x**2+7)**5/(-x**4+x**2+2)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{5}}{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**5/(-(x**2 - 2)*(x**2 + 1))**(3/2), x)","F",0
340,0,0,0,0.000000," ","integrate((5*x**2+7)**4/(-x**4+x**2+2)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{4}}{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**4/(-(x**2 - 2)*(x**2 + 1))**(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate((5*x**2+7)**3/(-x**4+x**2+2)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{3}}{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**3/(-(x**2 - 2)*(x**2 + 1))**(3/2), x)","F",0
342,0,0,0,0.000000," ","integrate((5*x**2+7)**2/(-x**4+x**2+2)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{2}}{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**2/(-(x**2 - 2)*(x**2 + 1))**(3/2), x)","F",0
343,0,0,0,0.000000," ","integrate((5*x**2+7)/(-x**4+x**2+2)**(3/2),x)","\int \frac{5 x^{2} + 7}{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)/(-(x**2 - 2)*(x**2 + 1))**(3/2), x)","F",0
344,0,0,0,0.000000," ","integrate(1/(-x**4+x**2+2)**(3/2),x)","\int \frac{1}{\left(- x^{4} + x^{2} + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-x**4 + x**2 + 2)**(-3/2), x)","F",0
345,0,0,0,0.000000," ","integrate(1/(5*x**2+7)/(-x**4+x**2+2)**(3/2),x)","\int \frac{1}{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)}\, dx"," ",0,"Integral(1/((-(x**2 - 2)*(x**2 + 1))**(3/2)*(5*x**2 + 7)), x)","F",0
346,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**2/(-x**4+x**2+2)**(3/2),x)","\int \frac{1}{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(1/((-(x**2 - 2)*(x**2 + 1))**(3/2)*(5*x**2 + 7)**2), x)","F",0
347,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**3/(-x**4+x**2+2)**(3/2),x)","\int \frac{1}{\left(- \left(x^{2} - 2\right) \left(x^{2} + 1\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(1/((-(x**2 - 2)*(x**2 + 1))**(3/2)*(5*x**2 + 7)**3), x)","F",0
348,0,0,0,0.000000," ","integrate((5*x**2+7)**4*(x**4+3*x**2+4)**(1/2),x)","\int \sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)} \left(5 x^{2} + 7\right)^{4}\, dx"," ",0,"Integral(sqrt((x**2 - x + 2)*(x**2 + x + 2))*(5*x**2 + 7)**4, x)","F",0
349,0,0,0,0.000000," ","integrate((5*x**2+7)**3*(x**4+3*x**2+4)**(1/2),x)","\int \sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)} \left(5 x^{2} + 7\right)^{3}\, dx"," ",0,"Integral(sqrt((x**2 - x + 2)*(x**2 + x + 2))*(5*x**2 + 7)**3, x)","F",0
350,0,0,0,0.000000," ","integrate((5*x**2+7)**2*(x**4+3*x**2+4)**(1/2),x)","\int \sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)} \left(5 x^{2} + 7\right)^{2}\, dx"," ",0,"Integral(sqrt((x**2 - x + 2)*(x**2 + x + 2))*(5*x**2 + 7)**2, x)","F",0
351,0,0,0,0.000000," ","integrate((5*x**2+7)*(x**4+3*x**2+4)**(1/2),x)","\int \sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)} \left(5 x^{2} + 7\right)\, dx"," ",0,"Integral(sqrt((x**2 - x + 2)*(x**2 + x + 2))*(5*x**2 + 7), x)","F",0
352,0,0,0,0.000000," ","integrate((x**4+3*x**2+4)**(1/2),x)","\int \sqrt{x^{4} + 3 x^{2} + 4}\, dx"," ",0,"Integral(sqrt(x**4 + 3*x**2 + 4), x)","F",0
353,0,0,0,0.000000," ","integrate((x**4+3*x**2+4)**(1/2)/(5*x**2+7),x)","\int \frac{\sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)}}{5 x^{2} + 7}\, dx"," ",0,"Integral(sqrt((x**2 - x + 2)*(x**2 + x + 2))/(5*x**2 + 7), x)","F",0
354,0,0,0,0.000000," ","integrate((x**4+3*x**2+4)**(1/2)/(5*x**2+7)**2,x)","\int \frac{\sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)}}{\left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(sqrt((x**2 - x + 2)*(x**2 + x + 2))/(5*x**2 + 7)**2, x)","F",0
355,0,0,0,0.000000," ","integrate((x**4+3*x**2+4)**(1/2)/(5*x**2+7)**3,x)","\int \frac{\sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)}}{\left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(sqrt((x**2 - x + 2)*(x**2 + x + 2))/(5*x**2 + 7)**3, x)","F",0
356,0,0,0,0.000000," ","integrate((5*x**2+7)**4*(x**4+3*x**2+4)**(3/2),x)","\int \left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{4}\, dx"," ",0,"Integral(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)*(5*x**2 + 7)**4, x)","F",0
357,0,0,0,0.000000," ","integrate((5*x**2+7)**3*(x**4+3*x**2+4)**(3/2),x)","\int \left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{3}\, dx"," ",0,"Integral(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)*(5*x**2 + 7)**3, x)","F",0
358,0,0,0,0.000000," ","integrate((5*x**2+7)**2*(x**4+3*x**2+4)**(3/2),x)","\int \left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{2}\, dx"," ",0,"Integral(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)*(5*x**2 + 7)**2, x)","F",0
359,0,0,0,0.000000," ","integrate((5*x**2+7)*(x**4+3*x**2+4)**(3/2),x)","\int \left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)\, dx"," ",0,"Integral(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)*(5*x**2 + 7), x)","F",0
360,0,0,0,0.000000," ","integrate((x**4+3*x**2+4)**(3/2),x)","\int \left(x^{4} + 3 x^{2} + 4\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((x**4 + 3*x**2 + 4)**(3/2), x)","F",0
361,0,0,0,0.000000," ","integrate((x**4+3*x**2+4)**(3/2)/(5*x**2+7),x)","\int \frac{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}}}{5 x^{2} + 7}\, dx"," ",0,"Integral(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)/(5*x**2 + 7), x)","F",0
362,0,0,0,0.000000," ","integrate((x**4+3*x**2+4)**(3/2)/(5*x**2+7)**2,x)","\int \frac{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}}}{\left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)/(5*x**2 + 7)**2, x)","F",0
363,0,0,0,0.000000," ","integrate((x**4+3*x**2+4)**(3/2)/(5*x**2+7)**3,x)","\int \frac{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}}}{\left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)/(5*x**2 + 7)**3, x)","F",0
364,0,0,0,0.000000," ","integrate((5*x**2+7)**3/(x**4+3*x**2+4)**(1/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{3}}{\sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)}}\, dx"," ",0,"Integral((5*x**2 + 7)**3/sqrt((x**2 - x + 2)*(x**2 + x + 2)), x)","F",0
365,0,0,0,0.000000," ","integrate((5*x**2+7)**2/(x**4+3*x**2+4)**(1/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{2}}{\sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)}}\, dx"," ",0,"Integral((5*x**2 + 7)**2/sqrt((x**2 - x + 2)*(x**2 + x + 2)), x)","F",0
366,0,0,0,0.000000," ","integrate((5*x**2+7)/(x**4+3*x**2+4)**(1/2),x)","\int \frac{5 x^{2} + 7}{\sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)}}\, dx"," ",0,"Integral((5*x**2 + 7)/sqrt((x**2 - x + 2)*(x**2 + x + 2)), x)","F",0
367,0,0,0,0.000000," ","integrate(1/(x**4+3*x**2+4)**(1/2),x)","\int \frac{1}{\sqrt{x^{4} + 3 x^{2} + 4}}\, dx"," ",0,"Integral(1/sqrt(x**4 + 3*x**2 + 4), x)","F",0
368,0,0,0,0.000000," ","integrate(1/(5*x**2+7)/(x**4+3*x**2+4)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)} \left(5 x^{2} + 7\right)}\, dx"," ",0,"Integral(1/(sqrt((x**2 - x + 2)*(x**2 + x + 2))*(5*x**2 + 7)), x)","F",0
369,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**2/(x**4+3*x**2+4)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)} \left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt((x**2 - x + 2)*(x**2 + x + 2))*(5*x**2 + 7)**2), x)","F",0
370,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**3/(x**4+3*x**2+4)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)} \left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt((x**2 - x + 2)*(x**2 + x + 2))*(5*x**2 + 7)**3), x)","F",0
371,0,0,0,0.000000," ","integrate((5*x**2+7)**5/(x**4+3*x**2+4)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{5}}{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**5/((x**2 - x + 2)*(x**2 + x + 2))**(3/2), x)","F",0
372,0,0,0,0.000000," ","integrate((5*x**2+7)**4/(x**4+3*x**2+4)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{4}}{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**4/((x**2 - x + 2)*(x**2 + x + 2))**(3/2), x)","F",0
373,0,0,0,0.000000," ","integrate((5*x**2+7)**3/(x**4+3*x**2+4)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{3}}{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**3/((x**2 - x + 2)*(x**2 + x + 2))**(3/2), x)","F",0
374,0,0,0,0.000000," ","integrate((5*x**2+7)**2/(x**4+3*x**2+4)**(3/2),x)","\int \frac{\left(5 x^{2} + 7\right)^{2}}{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)**2/((x**2 - x + 2)*(x**2 + x + 2))**(3/2), x)","F",0
375,0,0,0,0.000000," ","integrate((5*x**2+7)/(x**4+3*x**2+4)**(3/2),x)","\int \frac{5 x^{2} + 7}{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**2 + 7)/((x**2 - x + 2)*(x**2 + x + 2))**(3/2), x)","F",0
376,0,0,0,0.000000," ","integrate(1/(x**4+3*x**2+4)**(3/2),x)","\int \frac{1}{\left(x^{4} + 3 x^{2} + 4\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x**4 + 3*x**2 + 4)**(-3/2), x)","F",0
377,0,0,0,0.000000," ","integrate(1/(5*x**2+7)/(x**4+3*x**2+4)**(3/2),x)","\int \frac{1}{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)}\, dx"," ",0,"Integral(1/(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)*(5*x**2 + 7)), x)","F",0
378,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**2/(x**4+3*x**2+4)**(3/2),x)","\int \frac{1}{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{2}}\, dx"," ",0,"Integral(1/(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)*(5*x**2 + 7)**2), x)","F",0
379,0,0,0,0.000000," ","integrate(1/(5*x**2+7)**3/(x**4+3*x**2+4)**(3/2),x)","\int \frac{1}{\left(\left(x^{2} - x + 2\right) \left(x^{2} + x + 2\right)\right)^{\frac{3}{2}} \left(5 x^{2} + 7\right)^{3}}\, dx"," ",0,"Integral(1/(((x**2 - x + 2)*(x**2 + x + 2))**(3/2)*(5*x**2 + 7)**3), x)","F",0
380,0,0,0,0.000000," ","integrate((e*x**2+d)**3/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{\left(d + e x^{2}\right)^{3}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral((d + e*x**2)**3/sqrt(a + b*x**2 + c*x**4), x)","F",0
381,0,0,0,0.000000," ","integrate((e*x**2+d)**2/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{\left(d + e x^{2}\right)^{2}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral((d + e*x**2)**2/sqrt(a + b*x**2 + c*x**4), x)","F",0
382,0,0,0,0.000000," ","integrate((e*x**2+d)/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{d + e x^{2}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral((d + e*x**2)/sqrt(a + b*x**2 + c*x**4), x)","F",0
383,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{\left(d + e x^{2}\right) \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/((d + e*x**2)*sqrt(a + b*x**2 + c*x**4)), x)","F",0
384,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{\left(d + e x^{2}\right)^{2} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/((d + e*x**2)**2*sqrt(a + b*x**2 + c*x**4)), x)","F",0
385,0,0,0,0.000000," ","integrate((e*x**2+d)**3/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{\left(d + e x^{2}\right)^{3}}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral((d + e*x**2)**3/sqrt(a + b*x**2 - c*x**4), x)","F",0
386,0,0,0,0.000000," ","integrate((e*x**2+d)**2/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{\left(d + e x^{2}\right)^{2}}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral((d + e*x**2)**2/sqrt(a + b*x**2 - c*x**4), x)","F",0
387,0,0,0,0.000000," ","integrate((e*x**2+d)/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{d + e x^{2}}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral((d + e*x**2)/sqrt(a + b*x**2 - c*x**4), x)","F",0
388,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{\left(d + e x^{2}\right) \sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(1/((d + e*x**2)*sqrt(a + b*x**2 - c*x**4)), x)","F",0
389,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{\left(d + e x^{2}\right)^{2} \sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(1/((d + e*x**2)**2*sqrt(a + b*x**2 - c*x**4)), x)","F",0
390,0,0,0,0.000000," ","integrate((e*x**2+d)/(c*x**4+b*x**2-a)**(1/2),x)","\int \frac{d + e x^{2}}{\sqrt{- a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral((d + e*x**2)/sqrt(-a + b*x**2 + c*x**4), x)","F",0
391,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(c*x**4+b*x**2-a)**(1/2),x)","\int \frac{1}{\left(d + e x^{2}\right) \sqrt{- a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/((d + e*x**2)*sqrt(-a + b*x**2 + c*x**4)), x)","F",0
392,0,0,0,0.000000," ","integrate((e*x**2+d)/(-c*x**4+b*x**2-a)**(1/2),x)","\int \frac{d + e x^{2}}{\sqrt{- a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral((d + e*x**2)/sqrt(-a + b*x**2 - c*x**4), x)","F",0
393,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(-c*x**4+b*x**2-a)**(1/2),x)","\int \frac{1}{\left(d + e x^{2}\right) \sqrt{- a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(1/((d + e*x**2)*sqrt(-a + b*x**2 - c*x**4)), x)","F",0
394,0,0,0,0.000000," ","integrate((e*x**2+d)**3/(x**4+3*x**2+2)**(1/2),x)","\int \frac{\left(d + e x^{2}\right)^{3}}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}}\, dx"," ",0,"Integral((d + e*x**2)**3/sqrt((x**2 + 1)*(x**2 + 2)), x)","F",0
395,0,0,0,0.000000," ","integrate((e*x**2+d)**2/(x**4+3*x**2+2)**(1/2),x)","\int \frac{\left(d + e x^{2}\right)^{2}}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}}\, dx"," ",0,"Integral((d + e*x**2)**2/sqrt((x**2 + 1)*(x**2 + 2)), x)","F",0
396,0,0,0,0.000000," ","integrate((e*x**2+d)/(x**4+3*x**2+2)**(1/2),x)","\int \frac{d + e x^{2}}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)}}\, dx"," ",0,"Integral((d + e*x**2)/sqrt((x**2 + 1)*(x**2 + 2)), x)","F",0
397,0,0,0,0.000000," ","integrate(1/(e*x**2+d)/(x**4+3*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt((x**2 + 1)*(x**2 + 2))*(d + e*x**2)), x)","F",0
398,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(x**4+3*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{\left(x^{2} + 1\right) \left(x^{2} + 2\right)} \left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt((x**2 + 1)*(x**2 + 2))*(d + e*x**2)**2), x)","F",0
399,-1,0,0,0.000000," ","integrate((e*x**2+c)**q*(b*x**4+c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate((e*x**2+c)**3*(b*x**4+c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate((e*x**2+c)**2*(b*x**4+c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate((e*x**2+c)*(b*x**4+c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,0,0,0,0.000000," ","integrate((b*x**4+c*x**2+a)**p,x)","\int \left(a + b x^{4} + c x^{2}\right)^{p}\, dx"," ",0,"Integral((a + b*x**4 + c*x**2)**p, x)","F",0
404,-1,0,0,0.000000," ","integrate((b*x**4+c*x**2+a)**p/(e*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,-1,0,0,0.000000," ","integrate((b*x**4+c*x**2+a)**p/(e*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x**4+a)**(1/2),x)","\int \frac{f + g x}{\sqrt{a + c x^{4}} \left(d + e x\right)}\, dx"," ",0,"Integral((f + g*x)/(sqrt(a + c*x**4)*(d + e*x)), x)","F",0
407,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x**4-a)**(1/2),x)","\int \frac{f + g x}{\sqrt{- a + c x^{4}} \left(d + e x\right)}\, dx"," ",0,"Integral((f + g*x)/(sqrt(-a + c*x**4)*(d + e*x)), x)","F",0
408,0,0,0,0.000000," ","integrate((1+x-3**(1/2))/(1+x+3**(1/2))/(-4+x**4+4*3**(1/2)*x**2)**(1/2),x)","\int \frac{x - \sqrt{3} + 1}{\left(x + 1 + \sqrt{3}\right) \sqrt{x^{4} + 4 \sqrt{3} x^{2} - 4}}\, dx"," ",0,"Integral((x - sqrt(3) + 1)/((x + 1 + sqrt(3))*sqrt(x**4 + 4*sqrt(3)*x**2 - 4)), x)","F",0
409,0,0,0,0.000000," ","integrate((1+x+3**(1/2))/(1+x-3**(1/2))/(-4+x**4-4*3**(1/2)*x**2)**(1/2),x)","\int \frac{x + 1 + \sqrt{3}}{\left(x - \sqrt{3} + 1\right) \sqrt{x^{4} - 4 \sqrt{3} x^{2} - 4}}\, dx"," ",0,"Integral((x + 1 + sqrt(3))/((x - sqrt(3) + 1)*sqrt(x**4 - 4*sqrt(3)*x**2 - 4)), x)","F",0
410,0,0,0,0.000000," ","integrate((1+2*x-3**(1/2))/(1+2*x+3**(1/2))/(-1+4*x**4+4*3**(1/2)*x**2)**(1/2),x)","\int \frac{2 x - \sqrt{3} + 1}{\left(2 x + 1 + \sqrt{3}\right) \sqrt{4 x^{4} + 4 \sqrt{3} x^{2} - 1}}\, dx"," ",0,"Integral((2*x - sqrt(3) + 1)/((2*x + 1 + sqrt(3))*sqrt(4*x**4 + 4*sqrt(3)*x**2 - 1)), x)","F",0
411,0,0,0,0.000000," ","integrate((1+2*x+3**(1/2))/(1+2*x-3**(1/2))/(-1+4*x**4-4*3**(1/2)*x**2)**(1/2),x)","\int \frac{2 x + 1 + \sqrt{3}}{\left(2 x - \sqrt{3} + 1\right) \sqrt{4 x^{4} - 4 \sqrt{3} x^{2} - 1}}\, dx"," ",0,"Integral((2*x + 1 + sqrt(3))/((2*x - sqrt(3) + 1)*sqrt(4*x**4 - 4*sqrt(3)*x**2 - 1)), x)","F",0
412,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{f + g x}{\left(d + e x\right) \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral((f + g*x)/((d + e*x)*sqrt(a + b*x**2 + c*x**4)), x)","F",0
413,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x**4+b*x**2-a)**(1/2),x)","\int \frac{f + g x}{\left(d + e x\right) \sqrt{- a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral((f + g*x)/((d + e*x)*sqrt(-a + b*x**2 + c*x**4)), x)","F",0
