1,1,288,0,0.429471," ","integrate((e*x^3+d)/(c*x^6+a),x, algorithm=""giac"")","-\frac{{\left| c \right|} e \log\left(x^{2} + \left(\frac{a}{c}\right)^{\frac{1}{3}}\right)}{6 \, \left(a c^{5}\right)^{\frac{1}{3}}} + \frac{\left(a c^{5}\right)^{\frac{1}{6}} d \arctan\left(\frac{x}{\left(\frac{a}{c}\right)^{\frac{1}{6}}}\right)}{3 \, a c} + \frac{{\left(\left(a c^{5}\right)^{\frac{1}{6}} c^{3} d - \sqrt{3} \left(a c^{5}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{c}\right)^{\frac{1}{6}}}{\left(\frac{a}{c}\right)^{\frac{1}{6}}}\right)}{6 \, a c^{4}} + \frac{{\left(\left(a c^{5}\right)^{\frac{1}{6}} c^{3} d + \sqrt{3} \left(a c^{5}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{c}\right)^{\frac{1}{6}}}{\left(\frac{a}{c}\right)^{\frac{1}{6}}}\right)}{6 \, a c^{4}} + \frac{{\left(\sqrt{3} \left(a c^{5}\right)^{\frac{1}{6}} c^{3} d + \left(a c^{5}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{c}\right)^{\frac{1}{6}} + \left(\frac{a}{c}\right)^{\frac{1}{3}}\right)}{12 \, a c^{4}} - \frac{{\left(\sqrt{3} \left(a c^{5}\right)^{\frac{1}{6}} c^{3} d - \left(a c^{5}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{c}\right)^{\frac{1}{6}} + \left(\frac{a}{c}\right)^{\frac{1}{3}}\right)}{12 \, a c^{4}}"," ",0,"-1/6*abs(c)*e*log(x^2 + (a/c)^(1/3))/(a*c^5)^(1/3) + 1/3*(a*c^5)^(1/6)*d*arctan(x/(a/c)^(1/6))/(a*c) + 1/6*((a*c^5)^(1/6)*c^3*d - sqrt(3)*(a*c^5)^(2/3)*e)*arctan((2*x + sqrt(3)*(a/c)^(1/6))/(a/c)^(1/6))/(a*c^4) + 1/6*((a*c^5)^(1/6)*c^3*d + sqrt(3)*(a*c^5)^(2/3)*e)*arctan((2*x - sqrt(3)*(a/c)^(1/6))/(a/c)^(1/6))/(a*c^4) + 1/12*(sqrt(3)*(a*c^5)^(1/6)*c^3*d + (a*c^5)^(2/3)*e)*log(x^2 + sqrt(3)*x*(a/c)^(1/6) + (a/c)^(1/3))/(a*c^4) - 1/12*(sqrt(3)*(a*c^5)^(1/6)*c^3*d - (a*c^5)^(2/3)*e)*log(x^2 - sqrt(3)*x*(a/c)^(1/6) + (a/c)^(1/3))/(a*c^4)","A",0
2,1,308,0,0.378868," ","integrate((e*x^3+d)/(-c*x^6+a),x, algorithm=""giac"")","\frac{{\left| c \right|} e \log\left(x^{2} + \left(-\frac{a}{c}\right)^{\frac{1}{3}}\right)}{6 \, \left(-a c^{5}\right)^{\frac{1}{3}}} + \frac{\left(-a c^{5}\right)^{\frac{1}{6}} d \arctan\left(\frac{x}{\left(-\frac{a}{c}\right)^{\frac{1}{6}}}\right)}{3 \, a c} + \frac{{\left(\left(-a c^{5}\right)^{\frac{1}{6}} c^{3} d - \sqrt{3} \left(-a c^{5}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{2 \, x + \sqrt{3} \left(-\frac{a}{c}\right)^{\frac{1}{6}}}{\left(-\frac{a}{c}\right)^{\frac{1}{6}}}\right)}{6 \, a c^{4}} + \frac{{\left(\left(-a c^{5}\right)^{\frac{1}{6}} c^{3} d + \sqrt{3} \left(-a c^{5}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{2 \, x - \sqrt{3} \left(-\frac{a}{c}\right)^{\frac{1}{6}}}{\left(-\frac{a}{c}\right)^{\frac{1}{6}}}\right)}{6 \, a c^{4}} + \frac{{\left(\sqrt{3} \left(-a c^{5}\right)^{\frac{1}{6}} c^{3} d + \left(-a c^{5}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} + \sqrt{3} x \left(-\frac{a}{c}\right)^{\frac{1}{6}} + \left(-\frac{a}{c}\right)^{\frac{1}{3}}\right)}{12 \, a c^{4}} - \frac{{\left(\sqrt{3} \left(-a c^{5}\right)^{\frac{1}{6}} c^{3} d - \left(-a c^{5}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} - \sqrt{3} x \left(-\frac{a}{c}\right)^{\frac{1}{6}} + \left(-\frac{a}{c}\right)^{\frac{1}{3}}\right)}{12 \, a c^{4}}"," ",0,"1/6*abs(c)*e*log(x^2 + (-a/c)^(1/3))/(-a*c^5)^(1/3) + 1/3*(-a*c^5)^(1/6)*d*arctan(x/(-a/c)^(1/6))/(a*c) + 1/6*((-a*c^5)^(1/6)*c^3*d - sqrt(3)*(-a*c^5)^(2/3)*e)*arctan((2*x + sqrt(3)*(-a/c)^(1/6))/(-a/c)^(1/6))/(a*c^4) + 1/6*((-a*c^5)^(1/6)*c^3*d + sqrt(3)*(-a*c^5)^(2/3)*e)*arctan((2*x - sqrt(3)*(-a/c)^(1/6))/(-a/c)^(1/6))/(a*c^4) + 1/12*(sqrt(3)*(-a*c^5)^(1/6)*c^3*d + (-a*c^5)^(2/3)*e)*log(x^2 + sqrt(3)*x*(-a/c)^(1/6) + (-a/c)^(1/3))/(a*c^4) - 1/12*(sqrt(3)*(-a*c^5)^(1/6)*c^3*d - (-a*c^5)^(2/3)*e)*log(x^2 - sqrt(3)*x*(-a/c)^(1/6) + (-a/c)^(1/3))/(a*c^4)","A",0
3,1,601,0,0.737472," ","integrate((e*x^4+d)/(c*x^8+a),x, algorithm=""giac"")","-\frac{{\left(\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} - \frac{{\left(\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} + \frac{{\left(\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} + \frac{{\left(\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} - \frac{{\left(\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a} + \frac{{\left(\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a} + \frac{{\left(\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a} - \frac{{\left(\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a}"," ",0,"-1/8*(sqrt(-sqrt(2) + 2)*(a/c)^(5/8)*e - d*sqrt(sqrt(2) + 2)*(a/c)^(1/8))*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/c)^(1/8))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/a - 1/8*(sqrt(-sqrt(2) + 2)*(a/c)^(5/8)*e - d*sqrt(sqrt(2) + 2)*(a/c)^(1/8))*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/c)^(1/8))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/a + 1/8*(sqrt(sqrt(2) + 2)*(a/c)^(5/8)*e + d*sqrt(-sqrt(2) + 2)*(a/c)^(1/8))*arctan((2*x + sqrt(sqrt(2) + 2)*(a/c)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/a + 1/8*(sqrt(sqrt(2) + 2)*(a/c)^(5/8)*e + d*sqrt(-sqrt(2) + 2)*(a/c)^(1/8))*arctan((2*x - sqrt(sqrt(2) + 2)*(a/c)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/a - 1/16*(sqrt(-sqrt(2) + 2)*(a/c)^(5/8)*e - d*sqrt(sqrt(2) + 2)*(a/c)^(1/8))*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + (a/c)^(1/4))/a + 1/16*(sqrt(-sqrt(2) + 2)*(a/c)^(5/8)*e - d*sqrt(sqrt(2) + 2)*(a/c)^(1/8))*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + (a/c)^(1/4))/a + 1/16*(sqrt(sqrt(2) + 2)*(a/c)^(5/8)*e + d*sqrt(-sqrt(2) + 2)*(a/c)^(1/8))*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + (a/c)^(1/4))/a - 1/16*(sqrt(sqrt(2) + 2)*(a/c)^(5/8)*e + d*sqrt(-sqrt(2) + 2)*(a/c)^(1/8))*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + (a/c)^(1/4))/a","A",0
4,1,633,0,0.753152," ","integrate((e*x^4+d)/(-c*x^8+a),x, algorithm=""giac"")","-\frac{{\left(\sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{5}{8}} e - d \sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} - \frac{{\left(\sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{5}{8}} e - d \sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} + \frac{{\left(\sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{5}{8}} e + d \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} + \frac{{\left(\sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{5}{8}} e + d \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} - \frac{{\left(\sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{5}{8}} e - d \sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}} + \left(-\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a} + \frac{{\left(\sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{5}{8}} e - d \sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}} + \left(-\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a} + \frac{{\left(\sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{5}{8}} e + d \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}} + \left(-\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a} - \frac{{\left(\sqrt{\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{5}{8}} e + d \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{c}\right)^{\frac{1}{8}} + \left(-\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a}"," ",0,"-1/8*(sqrt(-sqrt(2) + 2)*(-a/c)^(5/8)*e - d*sqrt(sqrt(2) + 2)*(-a/c)^(1/8))*arctan((2*x + sqrt(-sqrt(2) + 2)*(-a/c)^(1/8))/(sqrt(sqrt(2) + 2)*(-a/c)^(1/8)))/a - 1/8*(sqrt(-sqrt(2) + 2)*(-a/c)^(5/8)*e - d*sqrt(sqrt(2) + 2)*(-a/c)^(1/8))*arctan((2*x - sqrt(-sqrt(2) + 2)*(-a/c)^(1/8))/(sqrt(sqrt(2) + 2)*(-a/c)^(1/8)))/a + 1/8*(sqrt(sqrt(2) + 2)*(-a/c)^(5/8)*e + d*sqrt(-sqrt(2) + 2)*(-a/c)^(1/8))*arctan((2*x + sqrt(sqrt(2) + 2)*(-a/c)^(1/8))/(sqrt(-sqrt(2) + 2)*(-a/c)^(1/8)))/a + 1/8*(sqrt(sqrt(2) + 2)*(-a/c)^(5/8)*e + d*sqrt(-sqrt(2) + 2)*(-a/c)^(1/8))*arctan((2*x - sqrt(sqrt(2) + 2)*(-a/c)^(1/8))/(sqrt(-sqrt(2) + 2)*(-a/c)^(1/8)))/a - 1/16*(sqrt(-sqrt(2) + 2)*(-a/c)^(5/8)*e - d*sqrt(sqrt(2) + 2)*(-a/c)^(1/8))*log(x^2 + x*sqrt(sqrt(2) + 2)*(-a/c)^(1/8) + (-a/c)^(1/4))/a + 1/16*(sqrt(-sqrt(2) + 2)*(-a/c)^(5/8)*e - d*sqrt(sqrt(2) + 2)*(-a/c)^(1/8))*log(x^2 - x*sqrt(sqrt(2) + 2)*(-a/c)^(1/8) + (-a/c)^(1/4))/a + 1/16*(sqrt(sqrt(2) + 2)*(-a/c)^(5/8)*e + d*sqrt(-sqrt(2) + 2)*(-a/c)^(1/8))*log(x^2 + x*sqrt(-sqrt(2) + 2)*(-a/c)^(1/8) + (-a/c)^(1/4))/a - 1/16*(sqrt(sqrt(2) + 2)*(-a/c)^(5/8)*e + d*sqrt(-sqrt(2) + 2)*(-a/c)^(1/8))*log(x^2 - x*sqrt(-sqrt(2) + 2)*(-a/c)^(1/8) + (-a/c)^(1/4))/a","B",0
5,-1,0,0,0.000000," ","integrate((e*x^4+d)/(e^2*x^8+b*x^4+d^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
6,-1,0,0,0.000000," ","integrate((e*x^4+d)/(e^2*x^8+f*x^4+d^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,-1,0,0,0.000000," ","integrate((e*x^4+d)/(e^2*x^8-b*x^4+d^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate((e*x^4+d)/(e^2*x^8-f*x^4+d^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-2,0,0,0.000000," ","integrate((x^4+1)/(x^8+b*x^4+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.75Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
10,1,239,0,0.930757," ","integrate((x^4+1)/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{5 \, \sqrt{5} + 5} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{5 \, \sqrt{5} + 5} + \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{5 \, \sqrt{5} - 5} - \frac{1}{80} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{5 \, \sqrt{5} - 5} + \frac{1}{40} \, \sqrt{5 \, \sqrt{5} - 5} \log\left(16900 \, {\left(x + \sqrt{\sqrt{5} + 1}\right)}^{2} + 16900 \, x^{2}\right) - \frac{1}{40} \, \sqrt{5 \, \sqrt{5} - 5} \log\left(16900 \, {\left(x - \sqrt{\sqrt{5} + 1}\right)}^{2} + 16900 \, x^{2}\right) + \frac{1}{40} \, \sqrt{5 \, \sqrt{5} + 5} \log\left(2500 \, {\left(x + \sqrt{\sqrt{5} - 1}\right)}^{2} + 2500 \, x^{2}\right) - \frac{1}{40} \, \sqrt{5 \, \sqrt{5} + 5} \log\left(2500 \, {\left(x - \sqrt{\sqrt{5} - 1}\right)}^{2} + 2500 \, x^{2}\right)"," ",0,"1/80*(pi + 4*arctan(x*sqrt(sqrt(5) + 1) + 1))*sqrt(5*sqrt(5) + 5) - 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) + 1) + 1))*sqrt(5*sqrt(5) + 5) + 1/80*(pi + 4*arctan(x*sqrt(sqrt(5) - 1) - 1))*sqrt(5*sqrt(5) - 5) - 1/80*(pi + 4*arctan(-x*sqrt(sqrt(5) - 1) - 1))*sqrt(5*sqrt(5) - 5) + 1/40*sqrt(5*sqrt(5) - 5)*log(16900*(x + sqrt(sqrt(5) + 1))^2 + 16900*x^2) - 1/40*sqrt(5*sqrt(5) - 5)*log(16900*(x - sqrt(sqrt(5) + 1))^2 + 16900*x^2) + 1/40*sqrt(5*sqrt(5) + 5)*log(2500*(x + sqrt(sqrt(5) - 1))^2 + 2500*x^2) - 1/40*sqrt(5*sqrt(5) + 5)*log(2500*(x - sqrt(sqrt(5) - 1))^2 + 2500*x^2)","A",0
11,1,72,0,0.387897," ","integrate((x^4+1)/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{8} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right)"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/4*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/8*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/8*sqrt(2)*log(x^2 - sqrt(2)*x + 1)","A",0
12,1,108,0,0.419668," ","integrate((x^4+1)/(x^8+x^4+1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{24} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{24} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{4} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{4} \, \arctan\left(2 \, x - \sqrt{3}\right) + \frac{1}{8} \, \log\left(x^{2} + x + 1\right) - \frac{1}{8} \, \log\left(x^{2} - x + 1\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/24*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/24*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/4*arctan(2*x + sqrt(3)) + 1/4*arctan(2*x - sqrt(3)) + 1/8*log(x^2 + x + 1) - 1/8*log(x^2 - x + 1)","A",0
13,1,247,0,0.875154," ","integrate((x^4+1)/(x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, \sqrt{-2 \, \sqrt{2} + 4} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{-2 \, \sqrt{2} + 4} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{2 \, \sqrt{2} + 4} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{2 \, \sqrt{2} + 4} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"1/8*sqrt(-2*sqrt(2) + 4)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(-2*sqrt(2) + 4)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(2*sqrt(2) + 4)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/8*sqrt(2*sqrt(2) + 4)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/16*sqrt(-2*sqrt(2) + 4)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(-2*sqrt(2) + 4)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(2*sqrt(2) + 4)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/16*sqrt(2*sqrt(2) + 4)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","A",0
14,1,245,0,0.498065," ","integrate((x^4+1)/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{8} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{8} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{8} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{8} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{16} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{16} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{16} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{16} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right)"," ",0,"1/8*(sqrt(6) - sqrt(2))*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) + 1/8*(sqrt(6) - sqrt(2))*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) + 1/8*(sqrt(6) + sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/8*(sqrt(6) + sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/16*(sqrt(6) - sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/16*(sqrt(6) - sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/16*(sqrt(6) + sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/16*(sqrt(6) + sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1)","A",0
15,1,29,0,0.518090," ","integrate((x^4+1)/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x}{2 \, {\left(x^{4} - 1\right)}} + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/2*x/(x^4 - 1) + 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
16,1,147,0,0.959991," ","integrate((x^4+1)/(x^8-3*x^4+1),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 2} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{8} \, \sqrt{2 \, \sqrt{5} - 2} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{5} - 2} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{5} + 2} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{8} \, \sqrt{2 \, \sqrt{5} + 2} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right)"," ",0,"-1/4*sqrt(2*sqrt(5) - 2)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) + 1/4*sqrt(2*sqrt(5) + 2)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) - 1/8*sqrt(2*sqrt(5) - 2)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) + 1/8*sqrt(2*sqrt(5) - 2)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/8*sqrt(2*sqrt(5) + 2)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/8*sqrt(2*sqrt(5) + 2)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2)))","A",0
17,-2,0,0,0.000000," ","integrate((x^4+1)/(x^8-4*x^4+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
18,-2,0,0,0.000000," ","integrate((x^4+1)/(x^8-5*x^4+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
19,1,123,0,0.906695," ","integrate((x^4+1)/(x^8-6*x^4+1),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{\sqrt{2} - 1} \arctan\left(\frac{x}{\sqrt{\sqrt{2} + 1}}\right) + \frac{1}{4} \, \sqrt{\sqrt{2} + 1} \arctan\left(\frac{x}{\sqrt{\sqrt{2} - 1}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} - 1} \log\left({\left| x + \sqrt{\sqrt{2} + 1} \right|}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} - 1} \log\left({\left| x - \sqrt{\sqrt{2} + 1} \right|}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 1} \log\left({\left| x + \sqrt{\sqrt{2} - 1} \right|}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 1} \log\left({\left| x - \sqrt{\sqrt{2} - 1} \right|}\right)"," ",0,"-1/4*sqrt(sqrt(2) - 1)*arctan(x/sqrt(sqrt(2) + 1)) + 1/4*sqrt(sqrt(2) + 1)*arctan(x/sqrt(sqrt(2) - 1)) - 1/8*sqrt(sqrt(2) - 1)*log(abs(x + sqrt(sqrt(2) + 1))) + 1/8*sqrt(sqrt(2) - 1)*log(abs(x - sqrt(sqrt(2) + 1))) + 1/8*sqrt(sqrt(2) + 1)*log(abs(x + sqrt(sqrt(2) - 1))) - 1/8*sqrt(sqrt(2) + 1)*log(abs(x - sqrt(sqrt(2) - 1)))","A",0
20,-2,0,0,0.000000," ","integrate((-x^4+1)/(x^8+b*x^4+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.75Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
21,1,223,0,0.685420," ","integrate((-x^4+1)/(x^8+3*x^4+1),x, algorithm=""giac"")","\frac{1}{16} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{\sqrt{5} + 1} - \frac{1}{16} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} + 1} + 1\right)\right)} \sqrt{\sqrt{5} + 1} - \frac{1}{16} \, {\left(\pi + 4 \, \arctan\left(x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{\sqrt{5} - 1} + \frac{1}{16} \, {\left(\pi + 4 \, \arctan\left(-x \sqrt{\sqrt{5} - 1} - 1\right)\right)} \sqrt{\sqrt{5} - 1} - \frac{1}{8} \, \sqrt{\sqrt{5} - 1} \log\left(2500 \, {\left(x + \sqrt{\sqrt{5} + 1}\right)}^{2} + 2500 \, x^{2}\right) + \frac{1}{8} \, \sqrt{\sqrt{5} - 1} \log\left(2500 \, {\left(x - \sqrt{\sqrt{5} + 1}\right)}^{2} + 2500 \, x^{2}\right) + \frac{1}{8} \, \sqrt{\sqrt{5} + 1} \log\left(1156 \, {\left(x + \sqrt{\sqrt{5} - 1}\right)}^{2} + 1156 \, x^{2}\right) - \frac{1}{8} \, \sqrt{\sqrt{5} + 1} \log\left(1156 \, {\left(x - \sqrt{\sqrt{5} - 1}\right)}^{2} + 1156 \, x^{2}\right)"," ",0,"1/16*(pi + 4*arctan(x*sqrt(sqrt(5) + 1) + 1))*sqrt(sqrt(5) + 1) - 1/16*(pi + 4*arctan(-x*sqrt(sqrt(5) + 1) + 1))*sqrt(sqrt(5) + 1) - 1/16*(pi + 4*arctan(x*sqrt(sqrt(5) - 1) - 1))*sqrt(sqrt(5) - 1) + 1/16*(pi + 4*arctan(-x*sqrt(sqrt(5) - 1) - 1))*sqrt(sqrt(5) - 1) - 1/8*sqrt(sqrt(5) - 1)*log(2500*(x + sqrt(sqrt(5) + 1))^2 + 2500*x^2) + 1/8*sqrt(sqrt(5) - 1)*log(2500*(x - sqrt(sqrt(5) + 1))^2 + 2500*x^2) + 1/8*sqrt(sqrt(5) + 1)*log(1156*(x + sqrt(sqrt(5) - 1))^2 + 1156*x^2) - 1/8*sqrt(sqrt(5) + 1)*log(1156*(x - sqrt(sqrt(5) - 1))^2 + 1156*x^2)","A",0
22,1,82,0,0.300422," ","integrate((-x^4+1)/(x^8+2*x^4+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{x}{2 \, {\left(x^{4} + 1\right)}}"," ",0,"1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + 1/2*x/(x^4 + 1)","A",0
23,1,108,0,0.371486," ","integrate((-x^4+1)/(x^8+x^4+1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{8} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{8} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) - \frac{1}{4} \, \arctan\left(2 \, x + \sqrt{3}\right) - \frac{1}{4} \, \arctan\left(2 \, x - \sqrt{3}\right) - \frac{1}{8} \, \log\left(x^{2} + x + 1\right) + \frac{1}{8} \, \log\left(x^{2} - x + 1\right)"," ",0,"1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/8*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/8*sqrt(3)*log(x^2 - sqrt(3)*x + 1) - 1/4*arctan(2*x + sqrt(3)) - 1/4*arctan(2*x - sqrt(3)) - 1/8*log(x^2 + x + 1) + 1/8*log(x^2 - x + 1)","A",0
24,1,247,0,0.719128," ","integrate((-x^4+1)/(x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, \sqrt{2 \, \sqrt{2} + 4} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{2 \, \sqrt{2} + 4} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{-2 \, \sqrt{2} + 4} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{-2 \, \sqrt{2} + 4} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"1/8*sqrt(2*sqrt(2) + 4)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(2*sqrt(2) + 4)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(-2*sqrt(2) + 4)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(-2*sqrt(2) + 4)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/16*sqrt(2*sqrt(2) + 4)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(2*sqrt(2) + 4)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(-2*sqrt(2) + 4)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + 1/16*sqrt(-2*sqrt(2) + 4)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","A",0
25,1,253,0,0.462214," ","integrate((-x^4+1)/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} - \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{24} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} + \sqrt{2}\right)} + 1\right) + \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{48} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right)"," ",0,"1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x + sqrt(6) - sqrt(2))/(sqrt(6) + sqrt(2))) + 1/24*(sqrt(6) + 3*sqrt(2))*arctan((4*x - sqrt(6) + sqrt(2))/(sqrt(6) + sqrt(2))) + 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/24*(sqrt(6) - 3*sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) + sqrt(2)) + 1) - 1/48*(sqrt(6) + 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) + sqrt(2)) + 1) + 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/48*(sqrt(6) - 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1)","A",0
26,1,19,0,0.448601," ","integrate((-x^4+1)/(x^8-2*x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(x\right) + \frac{1}{4} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*arctan(x) + 1/4*log(abs(x + 1)) - 1/4*log(abs(x - 1))","B",0
27,1,147,0,0.745757," ","integrate((-x^4+1)/(x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{10 \, \sqrt{5} - 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{20} \, \sqrt{10 \, \sqrt{5} + 10} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} - 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{40} \, \sqrt{10 \, \sqrt{5} + 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right)"," ",0,"1/20*sqrt(10*sqrt(5) - 10)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) + 1/20*sqrt(10*sqrt(5) + 10)*arctan(x/sqrt(1/2*sqrt(5) - 1/2)) + 1/40*sqrt(10*sqrt(5) - 10)*log(abs(x + sqrt(1/2*sqrt(5) + 1/2))) - 1/40*sqrt(10*sqrt(5) - 10)*log(abs(x - sqrt(1/2*sqrt(5) + 1/2))) + 1/40*sqrt(10*sqrt(5) + 10)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) - 1/40*sqrt(10*sqrt(5) + 10)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2)))","A",0
28,-2,0,0,0.000000," ","integrate((-x^4+1)/(x^8-4*x^4+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
29,-2,0,0,0.000000," ","integrate((-x^4+1)/(x^8-5*x^4+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
30,1,135,0,0.633409," ","integrate((-x^4+1)/(x^8-6*x^4+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2 \, \sqrt{2} - 2} \arctan\left(\frac{x}{\sqrt{\sqrt{2} + 1}}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{2} + 2} \arctan\left(\frac{x}{\sqrt{\sqrt{2} - 1}}\right) + \frac{1}{16} \, \sqrt{2 \, \sqrt{2} - 2} \log\left({\left| x + \sqrt{\sqrt{2} + 1} \right|}\right) - \frac{1}{16} \, \sqrt{2 \, \sqrt{2} - 2} \log\left({\left| x - \sqrt{\sqrt{2} + 1} \right|}\right) + \frac{1}{16} \, \sqrt{2 \, \sqrt{2} + 2} \log\left({\left| x + \sqrt{\sqrt{2} - 1} \right|}\right) - \frac{1}{16} \, \sqrt{2 \, \sqrt{2} + 2} \log\left({\left| x - \sqrt{\sqrt{2} - 1} \right|}\right)"," ",0,"1/8*sqrt(2*sqrt(2) - 2)*arctan(x/sqrt(sqrt(2) + 1)) + 1/8*sqrt(2*sqrt(2) + 2)*arctan(x/sqrt(sqrt(2) - 1)) + 1/16*sqrt(2*sqrt(2) - 2)*log(abs(x + sqrt(sqrt(2) + 1))) - 1/16*sqrt(2*sqrt(2) - 2)*log(abs(x - sqrt(sqrt(2) + 1))) + 1/16*sqrt(2*sqrt(2) + 2)*log(abs(x + sqrt(sqrt(2) - 1))) - 1/16*sqrt(2*sqrt(2) + 2)*log(abs(x - sqrt(sqrt(2) - 1)))","A",0
31,1,107,0,0.493827," ","integrate((-1+2*x^4+3^(1/2))/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{4} \, \sqrt{2} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{4} \, \sqrt{2} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right)"," ",0,"1/2*sqrt(2)*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/2*sqrt(2)*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/4*sqrt(2)*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/4*sqrt(2)*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1)","A",0
32,1,123,0,0.431718," ","integrate((1+x^4*(1+3^(1/2)))/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{4} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{4} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{8} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{8} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right)"," ",0,"1/4*(sqrt(6) + sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/4*(sqrt(6) + sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/8*(sqrt(6) + sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/8*(sqrt(6) + sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1)","A",0
33,1,131,0,0.448250," ","integrate((3+x^4*(-3+3^(1/2))-2*3^(1/2))/(x^8-x^4+1),x, algorithm=""giac"")","\frac{1}{4} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x + \sqrt{6} + \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{4} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{4 \, x - \sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{8} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right) - \frac{1}{8} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{6} - \sqrt{2}\right)} + 1\right)"," ",0,"1/4*(sqrt(6) - 3*sqrt(2))*arctan((4*x + sqrt(6) + sqrt(2))/(sqrt(6) - sqrt(2))) + 1/4*(sqrt(6) - 3*sqrt(2))*arctan((4*x - sqrt(6) - sqrt(2))/(sqrt(6) - sqrt(2))) + 1/8*(sqrt(6) - 3*sqrt(2))*log(x^2 + 1/2*x*(sqrt(6) - sqrt(2)) + 1) - 1/8*(sqrt(6) - 3*sqrt(2))*log(x^2 - 1/2*x*(sqrt(6) - sqrt(2)) + 1)","A",0
34,1,43,0,0.268295," ","integrate((d+e/x)/(c+a/x^2),x, algorithm=""giac"")","-\frac{a d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c} + \frac{d x}{c} + \frac{e \log\left(c x^{2} + a\right)}{2 \, c}"," ",0,"-a*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c) + d*x/c + 1/2*e*log(c*x^2 + a)/c","A",0
35,1,85,0,0.324491," ","integrate((d+e/x)/(c+a/x^2+b/x),x, algorithm=""giac"")","\frac{d x}{c} - \frac{{\left(b d - c e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} + \frac{{\left(b^{2} d - 2 \, a c d - b c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"d*x/c - 1/2*(b*d - c*e)*log(c*x^2 + b*x + a)/c^2 + (b^2*d - 2*a*c*d - b*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
36,1,247,0,0.352022," ","integrate((d+e/x^2)/(c+a/x^4),x, algorithm=""giac"")","\frac{d x}{c} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} a c d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} a c d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} a c d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} a c d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}}"," ",0,"d*x/c - 1/4*sqrt(2)*((a*c^3)^(1/4)*a*c*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) - 1/4*sqrt(2)*((a*c^3)^(1/4)*a*c*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) - 1/8*sqrt(2)*((a*c^3)^(1/4)*a*c*d + (a*c^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3) + 1/8*sqrt(2)*((a*c^3)^(1/4)*a*c*d + (a*c^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3)","A",0
37,1,3183,0,3.756219," ","integrate((d+e/x^2)/(c+a/x^4+b/x^2),x, algorithm=""giac"")","\frac{d x}{c} + \frac{{\left({\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} d - {\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} c^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 32 \, a^{3} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} d {\left| c \right|} - {\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} d + {\left(2 \, b^{4} c^{5} - 8 \, a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}} + \frac{{\left({\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} d - {\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} c^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 32 \, a^{3} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} d {\left| c \right|} - {\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} d + {\left(2 \, b^{4} c^{5} - 8 \, a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}}"," ",0,"d*x/c + 1/8*((2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2*d - (2*b^4*c^3 - 16*a*b^2*c^4 + 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*c^2*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 32*a^3*c^5 - 2*(b^2 - 4*a*c)*a*b^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4)*d*abs(c) - (2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*d + (2*b^4*c^5 - 8*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^5)*e)*arctan(2*sqrt(1/2)*x/sqrt((b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) + 1/8*((2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2*d - (2*b^4*c^3 - 16*a*b^2*c^4 + 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*c^2*e - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 32*a^3*c^5 + 2*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*d*abs(c) - (2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*d + (2*b^4*c^5 - 8*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^5)*e)*arctan(2*sqrt(1/2)*x/sqrt((b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2)","B",0
38,1,295,0,0.533587," ","integrate((d+e/x^3)/(c+a/x^6),x, algorithm=""giac"")","-\frac{{\left| c \right|} e \log\left(x^{2} + \left(\frac{a}{c}\right)^{\frac{1}{3}}\right)}{6 \, \left(a c^{5}\right)^{\frac{1}{3}}} + \frac{d x}{c} - \frac{\left(a c^{5}\right)^{\frac{1}{6}} d \arctan\left(\frac{x}{\left(\frac{a}{c}\right)^{\frac{1}{6}}}\right)}{3 \, c^{2}} - \frac{{\left(\left(a c^{5}\right)^{\frac{1}{6}} a c^{2} d + \sqrt{3} \left(a c^{5}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{c}\right)^{\frac{1}{6}}}{\left(\frac{a}{c}\right)^{\frac{1}{6}}}\right)}{6 \, a c^{4}} - \frac{{\left(\left(a c^{5}\right)^{\frac{1}{6}} a c^{2} d - \sqrt{3} \left(a c^{5}\right)^{\frac{2}{3}} e\right)} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{c}\right)^{\frac{1}{6}}}{\left(\frac{a}{c}\right)^{\frac{1}{6}}}\right)}{6 \, a c^{4}} - \frac{{\left(\sqrt{3} \left(a c^{5}\right)^{\frac{1}{6}} a c^{2} d - \left(a c^{5}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{c}\right)^{\frac{1}{6}} + \left(\frac{a}{c}\right)^{\frac{1}{3}}\right)}{12 \, a c^{4}} + \frac{{\left(\sqrt{3} \left(a c^{5}\right)^{\frac{1}{6}} a c^{2} d + \left(a c^{5}\right)^{\frac{2}{3}} e\right)} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{c}\right)^{\frac{1}{6}} + \left(\frac{a}{c}\right)^{\frac{1}{3}}\right)}{12 \, a c^{4}}"," ",0,"-1/6*abs(c)*e*log(x^2 + (a/c)^(1/3))/(a*c^5)^(1/3) + d*x/c - 1/3*(a*c^5)^(1/6)*d*arctan(x/(a/c)^(1/6))/c^2 - 1/6*((a*c^5)^(1/6)*a*c^2*d + sqrt(3)*(a*c^5)^(2/3)*e)*arctan((2*x + sqrt(3)*(a/c)^(1/6))/(a/c)^(1/6))/(a*c^4) - 1/6*((a*c^5)^(1/6)*a*c^2*d - sqrt(3)*(a*c^5)^(2/3)*e)*arctan((2*x - sqrt(3)*(a/c)^(1/6))/(a/c)^(1/6))/(a*c^4) - 1/12*(sqrt(3)*(a*c^5)^(1/6)*a*c^2*d - (a*c^5)^(2/3)*e)*log(x^2 + sqrt(3)*x*(a/c)^(1/6) + (a/c)^(1/3))/(a*c^4) + 1/12*(sqrt(3)*(a*c^5)^(1/6)*a*c^2*d + (a*c^5)^(2/3)*e)*log(x^2 - sqrt(3)*x*(a/c)^(1/6) + (a/c)^(1/3))/(a*c^4)","A",0
39,0,0,0,0.000000," ","integrate((d+e/x^3)/(c+a/x^6+b/x^3),x, algorithm=""giac"")","\int \frac{d + \frac{e}{x^{3}}}{c + \frac{b}{x^{3}} + \frac{a}{x^{6}}}\,{d x}"," ",0,"integrate((d + e/x^3)/(c + b/x^3 + a/x^6), x)","F",0
40,1,647,0,0.808048," ","integrate((d+e/x^4)/(c+a/x^8),x, algorithm=""giac"")","\frac{d x}{c} - \frac{{\left(c \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + a d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a c} - \frac{{\left(c \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + a d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a c} + \frac{{\left(c \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - a d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a c} + \frac{{\left(c \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - a d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a c} - \frac{{\left(c \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + a d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a c} + \frac{{\left(c \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + a d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a c} + \frac{{\left(c \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - a d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a c} - \frac{{\left(c \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - a d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a c}"," ",0,"d*x/c - 1/8*(c*sqrt(-sqrt(2) + 2)*(a/c)^(5/8)*e + a*d*sqrt(sqrt(2) + 2)*(a/c)^(1/8))*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/c)^(1/8))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c) - 1/8*(c*sqrt(-sqrt(2) + 2)*(a/c)^(5/8)*e + a*d*sqrt(sqrt(2) + 2)*(a/c)^(1/8))*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/c)^(1/8))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c) + 1/8*(c*sqrt(sqrt(2) + 2)*(a/c)^(5/8)*e - a*d*sqrt(-sqrt(2) + 2)*(a/c)^(1/8))*arctan((2*x + sqrt(sqrt(2) + 2)*(a/c)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c) + 1/8*(c*sqrt(sqrt(2) + 2)*(a/c)^(5/8)*e - a*d*sqrt(-sqrt(2) + 2)*(a/c)^(1/8))*arctan((2*x - sqrt(sqrt(2) + 2)*(a/c)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c) - 1/16*(c*sqrt(-sqrt(2) + 2)*(a/c)^(5/8)*e + a*d*sqrt(sqrt(2) + 2)*(a/c)^(1/8))*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + (a/c)^(1/4))/(a*c) + 1/16*(c*sqrt(-sqrt(2) + 2)*(a/c)^(5/8)*e + a*d*sqrt(sqrt(2) + 2)*(a/c)^(1/8))*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + (a/c)^(1/4))/(a*c) + 1/16*(c*sqrt(sqrt(2) + 2)*(a/c)^(5/8)*e - a*d*sqrt(-sqrt(2) + 2)*(a/c)^(1/8))*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + (a/c)^(1/4))/(a*c) - 1/16*(c*sqrt(sqrt(2) + 2)*(a/c)^(5/8)*e - a*d*sqrt(-sqrt(2) + 2)*(a/c)^(1/8))*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + (a/c)^(1/4))/(a*c)","A",0
41,-2,0,0,0.000000," ","integrate((d+e/x^4)/(c+a/x^8+b/x^4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 6.98Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
42,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{3}}{c x^{2 \, n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)^3/(c*x^(2*n) + a), x)","F",0
43,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{2}}{c x^{2 \, n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)^2/(c*x^(2*n) + a), x)","F",0
44,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{e x^{n} + d}{c x^{2 \, n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + a), x)","F",0
45,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + a\right)} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + a)*(e*x^n + d)), x)","F",0
46,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + a\right)} {\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + a)*(e*x^n + d)^2), x)","F",0
47,0,0,0,0.000000," ","integrate((d+e*x^n)/(a-c*x^(2*n)),x, algorithm=""giac"")","\int -\frac{e x^{n} + d}{c x^{2 \, n} - a}\,{d x}"," ",0,"integrate(-(e*x^n + d)/(c*x^(2*n) - a), x)","F",0
48,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{3}}{{\left(c x^{2 \, n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x^n + d)^3/(c*x^(2*n) + a)^2, x)","F",0
49,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{2}}{{\left(c x^{2 \, n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x^n + d)^2/(c*x^(2*n) + a)^2, x)","F",0
50,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{e x^{n} + d}{{\left(c x^{2 \, n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + a)^2, x)","F",0
51,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + a\right)}^{2} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + a)^2*(e*x^n + d)), x)","F",0
52,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + a\right)}^{2} {\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + a)^2*(e*x^n + d)^2), x)","F",0
53,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{3}}{{\left(c x^{2 \, n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*x^n + d)^3/(c*x^(2*n) + a)^3, x)","F",0
54,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{2}}{{\left(c x^{2 \, n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*x^n + d)^2/(c*x^(2*n) + a)^3, x)","F",0
55,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{e x^{n} + d}{{\left(c x^{2 \, n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + a)^3, x)","F",0
56,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + a\right)}^{3} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + a)^3*(e*x^n + d)), x)","F",0
57,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + a\right)}^{3} {\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + a)^3*(e*x^n + d)^2), x)","F",0
58,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2 \, n} + a} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^(2*n) + a)*(e*x^n + d)), x)","F",0
59,0,0,0,0.000000," ","integrate((d+e*x^n)^q*(a+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + a\right)}^{p} {\left(e x^{n} + d\right)}^{q}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p*(e*x^n + d)^q, x)","F",0
60,-2,0,0,0.000000," ","integrate((d+e*x^n)^3*(a+c*x^(2*n))^p,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{-16,[1,0,6,3,2,4,4,1]%%%}+%%%{-64,[1,0,6,3,2,3,4,1]%%%}+%%%{-96,[1,0,6,3,2,2,4,1]%%%}+%%%{-64,[1,0,6,3,2,1,4,1]%%%}+%%%{-16,[1,0,6,3,2,0,4,1]%%%} / %%%{16,[0,0,6,4,2,4,4,0]%%%}+%%%{64,[0,0,6,4,2,3,4,0]%%%}+%%%{96,[0,0,6,4,2,2,4,0]%%%}+%%%{64,[0,0,6,4,2,1,4,0]%%%}+%%%{16,[0,0,6,4,2,0,4,0]%%%} Error: Bad Argument Value","F(-2)",0
61,-2,0,0,0.000000," ","integrate((d+e*x^n)^2*(a+c*x^(2*n))^p,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{4,[0,0,3,2,0,2,3,1]%%%}+%%%{8,[0,0,3,2,0,1,3,1]%%%}+%%%{4,[0,0,3,2,0,0,3,1]%%%} / %%%{-8,[0,0,4,3,1,3,3,0]%%%}+%%%{-24,[0,0,4,3,1,2,3,0]%%%}+%%%{-24,[0,0,4,3,1,1,3,0]%%%}+%%%{-8,[0,0,4,3,1,0,3,0]%%%} Error: Bad Argument Value","F(-2)",0
62,0,0,0,0.000000," ","integrate((d+e*x^n)*(a+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(e x^{n} + d\right)} {\left(c x^{2 \, n} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^n + d)*(c*x^(2*n) + a)^p, x)","F",0
63,0,0,0,0.000000," ","integrate((a+c*x^(2*n))^p/(d+e*x^n),x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + a\right)}^{p}}{e x^{n} + d}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p/(e*x^n + d), x)","F",0
64,0,0,0,0.000000," ","integrate((a+c*x^(2*n))^p/(d+e*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + a\right)}^{p}}{{\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p/(e*x^n + d)^2, x)","F",0
65,0,0,0,0.000000," ","integrate((a+c*x^(2*n))^p/(d+e*x^n)^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + a\right)}^{p}}{{\left(e x^{n} + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p/(e*x^n + d)^3, x)","F",0
66,1,207,0,0.351143," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\frac{6 \, a d n^{3} x + 3 \, c d n^{2} x x^{2 \, n} + 6 \, b d n^{2} x x^{n} + 2 \, c n^{2} x x^{3 \, n} e + 3 \, b n^{2} x x^{2 \, n} e + 6 \, a n^{2} x x^{n} e + 11 \, a d n^{2} x + 4 \, c d n x x^{2 \, n} + 5 \, b d n x x^{n} + 3 \, c n x x^{3 \, n} e + 4 \, b n x x^{2 \, n} e + 5 \, a n x x^{n} e + 6 \, a d n x + c d x x^{2 \, n} + b d x x^{n} + c x x^{3 \, n} e + b x x^{2 \, n} e + a x x^{n} e + a d x}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"(6*a*d*n^3*x + 3*c*d*n^2*x*x^(2*n) + 6*b*d*n^2*x*x^n + 2*c*n^2*x*x^(3*n)*e + 3*b*n^2*x*x^(2*n)*e + 6*a*n^2*x*x^n*e + 11*a*d*n^2*x + 4*c*d*n*x*x^(2*n) + 5*b*d*n*x*x^n + 3*c*n*x*x^(3*n)*e + 4*b*n*x*x^(2*n)*e + 5*a*n*x*x^n*e + 6*a*d*n*x + c*d*x*x^(2*n) + b*d*x*x^n + c*x*x^(3*n)*e + b*x*x^(2*n)*e + a*x*x^n*e + a*d*x)/(6*n^3 + 11*n^2 + 6*n + 1)","B",0
67,1,828,0,0.453407," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^2,x, algorithm=""giac"")","\frac{120 \, a^{2} d n^{5} x + 30 \, c^{2} d n^{4} x x^{4 \, n} + 80 \, b c d n^{4} x x^{3 \, n} + 60 \, b^{2} d n^{4} x x^{2 \, n} + 120 \, a c d n^{4} x x^{2 \, n} + 240 \, a b d n^{4} x x^{n} + 24 \, c^{2} n^{4} x x^{5 \, n} e + 60 \, b c n^{4} x x^{4 \, n} e + 40 \, b^{2} n^{4} x x^{3 \, n} e + 80 \, a c n^{4} x x^{3 \, n} e + 120 \, a b n^{4} x x^{2 \, n} e + 120 \, a^{2} n^{4} x x^{n} e + 274 \, a^{2} d n^{4} x + 61 \, c^{2} d n^{3} x x^{4 \, n} + 156 \, b c d n^{3} x x^{3 \, n} + 107 \, b^{2} d n^{3} x x^{2 \, n} + 214 \, a c d n^{3} x x^{2 \, n} + 308 \, a b d n^{3} x x^{n} + 50 \, c^{2} n^{3} x x^{5 \, n} e + 122 \, b c n^{3} x x^{4 \, n} e + 78 \, b^{2} n^{3} x x^{3 \, n} e + 156 \, a c n^{3} x x^{3 \, n} e + 214 \, a b n^{3} x x^{2 \, n} e + 154 \, a^{2} n^{3} x x^{n} e + 225 \, a^{2} d n^{3} x + 41 \, c^{2} d n^{2} x x^{4 \, n} + 98 \, b c d n^{2} x x^{3 \, n} + 59 \, b^{2} d n^{2} x x^{2 \, n} + 118 \, a c d n^{2} x x^{2 \, n} + 142 \, a b d n^{2} x x^{n} + 35 \, c^{2} n^{2} x x^{5 \, n} e + 82 \, b c n^{2} x x^{4 \, n} e + 49 \, b^{2} n^{2} x x^{3 \, n} e + 98 \, a c n^{2} x x^{3 \, n} e + 118 \, a b n^{2} x x^{2 \, n} e + 71 \, a^{2} n^{2} x x^{n} e + 85 \, a^{2} d n^{2} x + 11 \, c^{2} d n x x^{4 \, n} + 24 \, b c d n x x^{3 \, n} + 13 \, b^{2} d n x x^{2 \, n} + 26 \, a c d n x x^{2 \, n} + 28 \, a b d n x x^{n} + 10 \, c^{2} n x x^{5 \, n} e + 22 \, b c n x x^{4 \, n} e + 12 \, b^{2} n x x^{3 \, n} e + 24 \, a c n x x^{3 \, n} e + 26 \, a b n x x^{2 \, n} e + 14 \, a^{2} n x x^{n} e + 15 \, a^{2} d n x + c^{2} d x x^{4 \, n} + 2 \, b c d x x^{3 \, n} + b^{2} d x x^{2 \, n} + 2 \, a c d x x^{2 \, n} + 2 \, a b d x x^{n} + c^{2} x x^{5 \, n} e + 2 \, b c x x^{4 \, n} e + b^{2} x x^{3 \, n} e + 2 \, a c x x^{3 \, n} e + 2 \, a b x x^{2 \, n} e + a^{2} x x^{n} e + a^{2} d x}{120 \, n^{5} + 274 \, n^{4} + 225 \, n^{3} + 85 \, n^{2} + 15 \, n + 1}"," ",0,"(120*a^2*d*n^5*x + 30*c^2*d*n^4*x*x^(4*n) + 80*b*c*d*n^4*x*x^(3*n) + 60*b^2*d*n^4*x*x^(2*n) + 120*a*c*d*n^4*x*x^(2*n) + 240*a*b*d*n^4*x*x^n + 24*c^2*n^4*x*x^(5*n)*e + 60*b*c*n^4*x*x^(4*n)*e + 40*b^2*n^4*x*x^(3*n)*e + 80*a*c*n^4*x*x^(3*n)*e + 120*a*b*n^4*x*x^(2*n)*e + 120*a^2*n^4*x*x^n*e + 274*a^2*d*n^4*x + 61*c^2*d*n^3*x*x^(4*n) + 156*b*c*d*n^3*x*x^(3*n) + 107*b^2*d*n^3*x*x^(2*n) + 214*a*c*d*n^3*x*x^(2*n) + 308*a*b*d*n^3*x*x^n + 50*c^2*n^3*x*x^(5*n)*e + 122*b*c*n^3*x*x^(4*n)*e + 78*b^2*n^3*x*x^(3*n)*e + 156*a*c*n^3*x*x^(3*n)*e + 214*a*b*n^3*x*x^(2*n)*e + 154*a^2*n^3*x*x^n*e + 225*a^2*d*n^3*x + 41*c^2*d*n^2*x*x^(4*n) + 98*b*c*d*n^2*x*x^(3*n) + 59*b^2*d*n^2*x*x^(2*n) + 118*a*c*d*n^2*x*x^(2*n) + 142*a*b*d*n^2*x*x^n + 35*c^2*n^2*x*x^(5*n)*e + 82*b*c*n^2*x*x^(4*n)*e + 49*b^2*n^2*x*x^(3*n)*e + 98*a*c*n^2*x*x^(3*n)*e + 118*a*b*n^2*x*x^(2*n)*e + 71*a^2*n^2*x*x^n*e + 85*a^2*d*n^2*x + 11*c^2*d*n*x*x^(4*n) + 24*b*c*d*n*x*x^(3*n) + 13*b^2*d*n*x*x^(2*n) + 26*a*c*d*n*x*x^(2*n) + 28*a*b*d*n*x*x^n + 10*c^2*n*x*x^(5*n)*e + 22*b*c*n*x*x^(4*n)*e + 12*b^2*n*x*x^(3*n)*e + 24*a*c*n*x*x^(3*n)*e + 26*a*b*n*x*x^(2*n)*e + 14*a^2*n*x*x^n*e + 15*a^2*d*n*x + c^2*d*x*x^(4*n) + 2*b*c*d*x*x^(3*n) + b^2*d*x*x^(2*n) + 2*a*c*d*x*x^(2*n) + 2*a*b*d*x*x^n + c^2*x*x^(5*n)*e + 2*b*c*x*x^(4*n)*e + b^2*x*x^(3*n)*e + 2*a*c*x*x^(3*n)*e + 2*a*b*x*x^(2*n)*e + a^2*x*x^n*e + a^2*d*x)/(120*n^5 + 274*n^4 + 225*n^3 + 85*n^2 + 15*n + 1)","B",0
68,1,2134,0,0.779000," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^3,x, algorithm=""giac"")","\frac{5040 \, a^{3} d n^{7} x + 840 \, c^{3} d n^{6} x x^{6 \, n} + 3024 \, b c^{2} d n^{6} x x^{5 \, n} + 3780 \, b^{2} c d n^{6} x x^{4 \, n} + 3780 \, a c^{2} d n^{6} x x^{4 \, n} + 1680 \, b^{3} d n^{6} x x^{3 \, n} + 10080 \, a b c d n^{6} x x^{3 \, n} + 7560 \, a b^{2} d n^{6} x x^{2 \, n} + 7560 \, a^{2} c d n^{6} x x^{2 \, n} + 15120 \, a^{2} b d n^{6} x x^{n} + 720 \, c^{3} n^{6} x x^{7 \, n} e + 2520 \, b c^{2} n^{6} x x^{6 \, n} e + 3024 \, b^{2} c n^{6} x x^{5 \, n} e + 3024 \, a c^{2} n^{6} x x^{5 \, n} e + 1260 \, b^{3} n^{6} x x^{4 \, n} e + 7560 \, a b c n^{6} x x^{4 \, n} e + 5040 \, a b^{2} n^{6} x x^{3 \, n} e + 5040 \, a^{2} c n^{6} x x^{3 \, n} e + 7560 \, a^{2} b n^{6} x x^{2 \, n} e + 5040 \, a^{3} n^{6} x x^{n} e + 13068 \, a^{3} d n^{6} x + 2038 \, c^{3} d n^{5} x x^{6 \, n} + 7236 \, b c^{2} d n^{5} x x^{5 \, n} + 8856 \, b^{2} c d n^{5} x x^{4 \, n} + 8856 \, a c^{2} d n^{5} x x^{4 \, n} + 3796 \, b^{3} d n^{5} x x^{3 \, n} + 22776 \, a b c d n^{5} x x^{3 \, n} + 15822 \, a b^{2} d n^{5} x x^{2 \, n} + 15822 \, a^{2} c d n^{5} x x^{2 \, n} + 24084 \, a^{2} b d n^{5} x x^{n} + 1764 \, c^{3} n^{5} x x^{7 \, n} e + 6114 \, b c^{2} n^{5} x x^{6 \, n} e + 7236 \, b^{2} c n^{5} x x^{5 \, n} e + 7236 \, a c^{2} n^{5} x x^{5 \, n} e + 2952 \, b^{3} n^{5} x x^{4 \, n} e + 17712 \, a b c n^{5} x x^{4 \, n} e + 11388 \, a b^{2} n^{5} x x^{3 \, n} e + 11388 \, a^{2} c n^{5} x x^{3 \, n} e + 15822 \, a^{2} b n^{5} x x^{2 \, n} e + 8028 \, a^{3} n^{5} x x^{n} e + 13132 \, a^{3} d n^{5} x + 1849 \, c^{3} d n^{4} x x^{6 \, n} + 6432 \, b c^{2} d n^{4} x x^{5 \, n} + 7635 \, b^{2} c d n^{4} x x^{4 \, n} + 7635 \, a c^{2} d n^{4} x x^{4 \, n} + 3112 \, b^{3} d n^{4} x x^{3 \, n} + 18672 \, a b c d n^{4} x x^{3 \, n} + 11787 \, a b^{2} d n^{4} x x^{2 \, n} + 11787 \, a^{2} c d n^{4} x x^{2 \, n} + 15312 \, a^{2} b d n^{4} x x^{n} + 1624 \, c^{3} n^{4} x x^{7 \, n} e + 5547 \, b c^{2} n^{4} x x^{6 \, n} e + 6432 \, b^{2} c n^{4} x x^{5 \, n} e + 6432 \, a c^{2} n^{4} x x^{5 \, n} e + 2545 \, b^{3} n^{4} x x^{4 \, n} e + 15270 \, a b c n^{4} x x^{4 \, n} e + 9336 \, a b^{2} n^{4} x x^{3 \, n} e + 9336 \, a^{2} c n^{4} x x^{3 \, n} e + 11787 \, a^{2} b n^{4} x x^{2 \, n} e + 5104 \, a^{3} n^{4} x x^{n} e + 6769 \, a^{3} d n^{4} x + 820 \, c^{3} d n^{3} x x^{6 \, n} + 2775 \, b c^{2} d n^{3} x x^{5 \, n} + 3168 \, b^{2} c d n^{3} x x^{4 \, n} + 3168 \, a c^{2} d n^{3} x x^{4 \, n} + 1219 \, b^{3} d n^{3} x x^{3 \, n} + 7314 \, a b c d n^{3} x x^{3 \, n} + 4260 \, a b^{2} d n^{3} x x^{2 \, n} + 4260 \, a^{2} c d n^{3} x x^{2 \, n} + 4995 \, a^{2} b d n^{3} x x^{n} + 735 \, c^{3} n^{3} x x^{7 \, n} e + 2460 \, b c^{2} n^{3} x x^{6 \, n} e + 2775 \, b^{2} c n^{3} x x^{5 \, n} e + 2775 \, a c^{2} n^{3} x x^{5 \, n} e + 1056 \, b^{3} n^{3} x x^{4 \, n} e + 6336 \, a b c n^{3} x x^{4 \, n} e + 3657 \, a b^{2} n^{3} x x^{3 \, n} e + 3657 \, a^{2} c n^{3} x x^{3 \, n} e + 4260 \, a^{2} b n^{3} x x^{2 \, n} e + 1665 \, a^{3} n^{3} x x^{n} e + 1960 \, a^{3} d n^{3} x + 190 \, c^{3} d n^{2} x x^{6 \, n} + 621 \, b c^{2} d n^{2} x x^{5 \, n} + 678 \, b^{2} c d n^{2} x x^{4 \, n} + 678 \, a c^{2} d n^{2} x x^{4 \, n} + 247 \, b^{3} d n^{2} x x^{3 \, n} + 1482 \, a b c d n^{2} x x^{3 \, n} + 810 \, a b^{2} d n^{2} x x^{2 \, n} + 810 \, a^{2} c d n^{2} x x^{2 \, n} + 885 \, a^{2} b d n^{2} x x^{n} + 175 \, c^{3} n^{2} x x^{7 \, n} e + 570 \, b c^{2} n^{2} x x^{6 \, n} e + 621 \, b^{2} c n^{2} x x^{5 \, n} e + 621 \, a c^{2} n^{2} x x^{5 \, n} e + 226 \, b^{3} n^{2} x x^{4 \, n} e + 1356 \, a b c n^{2} x x^{4 \, n} e + 741 \, a b^{2} n^{2} x x^{3 \, n} e + 741 \, a^{2} c n^{2} x x^{3 \, n} e + 810 \, a^{2} b n^{2} x x^{2 \, n} e + 295 \, a^{3} n^{2} x x^{n} e + 322 \, a^{3} d n^{2} x + 22 \, c^{3} d n x x^{6 \, n} + 69 \, b c^{2} d n x x^{5 \, n} + 72 \, b^{2} c d n x x^{4 \, n} + 72 \, a c^{2} d n x x^{4 \, n} + 25 \, b^{3} d n x x^{3 \, n} + 150 \, a b c d n x x^{3 \, n} + 78 \, a b^{2} d n x x^{2 \, n} + 78 \, a^{2} c d n x x^{2 \, n} + 81 \, a^{2} b d n x x^{n} + 21 \, c^{3} n x x^{7 \, n} e + 66 \, b c^{2} n x x^{6 \, n} e + 69 \, b^{2} c n x x^{5 \, n} e + 69 \, a c^{2} n x x^{5 \, n} e + 24 \, b^{3} n x x^{4 \, n} e + 144 \, a b c n x x^{4 \, n} e + 75 \, a b^{2} n x x^{3 \, n} e + 75 \, a^{2} c n x x^{3 \, n} e + 78 \, a^{2} b n x x^{2 \, n} e + 27 \, a^{3} n x x^{n} e + 28 \, a^{3} d n x + c^{3} d x x^{6 \, n} + 3 \, b c^{2} d x x^{5 \, n} + 3 \, b^{2} c d x x^{4 \, n} + 3 \, a c^{2} d x x^{4 \, n} + b^{3} d x x^{3 \, n} + 6 \, a b c d x x^{3 \, n} + 3 \, a b^{2} d x x^{2 \, n} + 3 \, a^{2} c d x x^{2 \, n} + 3 \, a^{2} b d x x^{n} + c^{3} x x^{7 \, n} e + 3 \, b c^{2} x x^{6 \, n} e + 3 \, b^{2} c x x^{5 \, n} e + 3 \, a c^{2} x x^{5 \, n} e + b^{3} x x^{4 \, n} e + 6 \, a b c x x^{4 \, n} e + 3 \, a b^{2} x x^{3 \, n} e + 3 \, a^{2} c x x^{3 \, n} e + 3 \, a^{2} b x x^{2 \, n} e + a^{3} x x^{n} e + a^{3} d x}{5040 \, n^{7} + 13068 \, n^{6} + 13132 \, n^{5} + 6769 \, n^{4} + 1960 \, n^{3} + 322 \, n^{2} + 28 \, n + 1}"," ",0,"(5040*a^3*d*n^7*x + 840*c^3*d*n^6*x*x^(6*n) + 3024*b*c^2*d*n^6*x*x^(5*n) + 3780*b^2*c*d*n^6*x*x^(4*n) + 3780*a*c^2*d*n^6*x*x^(4*n) + 1680*b^3*d*n^6*x*x^(3*n) + 10080*a*b*c*d*n^6*x*x^(3*n) + 7560*a*b^2*d*n^6*x*x^(2*n) + 7560*a^2*c*d*n^6*x*x^(2*n) + 15120*a^2*b*d*n^6*x*x^n + 720*c^3*n^6*x*x^(7*n)*e + 2520*b*c^2*n^6*x*x^(6*n)*e + 3024*b^2*c*n^6*x*x^(5*n)*e + 3024*a*c^2*n^6*x*x^(5*n)*e + 1260*b^3*n^6*x*x^(4*n)*e + 7560*a*b*c*n^6*x*x^(4*n)*e + 5040*a*b^2*n^6*x*x^(3*n)*e + 5040*a^2*c*n^6*x*x^(3*n)*e + 7560*a^2*b*n^6*x*x^(2*n)*e + 5040*a^3*n^6*x*x^n*e + 13068*a^3*d*n^6*x + 2038*c^3*d*n^5*x*x^(6*n) + 7236*b*c^2*d*n^5*x*x^(5*n) + 8856*b^2*c*d*n^5*x*x^(4*n) + 8856*a*c^2*d*n^5*x*x^(4*n) + 3796*b^3*d*n^5*x*x^(3*n) + 22776*a*b*c*d*n^5*x*x^(3*n) + 15822*a*b^2*d*n^5*x*x^(2*n) + 15822*a^2*c*d*n^5*x*x^(2*n) + 24084*a^2*b*d*n^5*x*x^n + 1764*c^3*n^5*x*x^(7*n)*e + 6114*b*c^2*n^5*x*x^(6*n)*e + 7236*b^2*c*n^5*x*x^(5*n)*e + 7236*a*c^2*n^5*x*x^(5*n)*e + 2952*b^3*n^5*x*x^(4*n)*e + 17712*a*b*c*n^5*x*x^(4*n)*e + 11388*a*b^2*n^5*x*x^(3*n)*e + 11388*a^2*c*n^5*x*x^(3*n)*e + 15822*a^2*b*n^5*x*x^(2*n)*e + 8028*a^3*n^5*x*x^n*e + 13132*a^3*d*n^5*x + 1849*c^3*d*n^4*x*x^(6*n) + 6432*b*c^2*d*n^4*x*x^(5*n) + 7635*b^2*c*d*n^4*x*x^(4*n) + 7635*a*c^2*d*n^4*x*x^(4*n) + 3112*b^3*d*n^4*x*x^(3*n) + 18672*a*b*c*d*n^4*x*x^(3*n) + 11787*a*b^2*d*n^4*x*x^(2*n) + 11787*a^2*c*d*n^4*x*x^(2*n) + 15312*a^2*b*d*n^4*x*x^n + 1624*c^3*n^4*x*x^(7*n)*e + 5547*b*c^2*n^4*x*x^(6*n)*e + 6432*b^2*c*n^4*x*x^(5*n)*e + 6432*a*c^2*n^4*x*x^(5*n)*e + 2545*b^3*n^4*x*x^(4*n)*e + 15270*a*b*c*n^4*x*x^(4*n)*e + 9336*a*b^2*n^4*x*x^(3*n)*e + 9336*a^2*c*n^4*x*x^(3*n)*e + 11787*a^2*b*n^4*x*x^(2*n)*e + 5104*a^3*n^4*x*x^n*e + 6769*a^3*d*n^4*x + 820*c^3*d*n^3*x*x^(6*n) + 2775*b*c^2*d*n^3*x*x^(5*n) + 3168*b^2*c*d*n^3*x*x^(4*n) + 3168*a*c^2*d*n^3*x*x^(4*n) + 1219*b^3*d*n^3*x*x^(3*n) + 7314*a*b*c*d*n^3*x*x^(3*n) + 4260*a*b^2*d*n^3*x*x^(2*n) + 4260*a^2*c*d*n^3*x*x^(2*n) + 4995*a^2*b*d*n^3*x*x^n + 735*c^3*n^3*x*x^(7*n)*e + 2460*b*c^2*n^3*x*x^(6*n)*e + 2775*b^2*c*n^3*x*x^(5*n)*e + 2775*a*c^2*n^3*x*x^(5*n)*e + 1056*b^3*n^3*x*x^(4*n)*e + 6336*a*b*c*n^3*x*x^(4*n)*e + 3657*a*b^2*n^3*x*x^(3*n)*e + 3657*a^2*c*n^3*x*x^(3*n)*e + 4260*a^2*b*n^3*x*x^(2*n)*e + 1665*a^3*n^3*x*x^n*e + 1960*a^3*d*n^3*x + 190*c^3*d*n^2*x*x^(6*n) + 621*b*c^2*d*n^2*x*x^(5*n) + 678*b^2*c*d*n^2*x*x^(4*n) + 678*a*c^2*d*n^2*x*x^(4*n) + 247*b^3*d*n^2*x*x^(3*n) + 1482*a*b*c*d*n^2*x*x^(3*n) + 810*a*b^2*d*n^2*x*x^(2*n) + 810*a^2*c*d*n^2*x*x^(2*n) + 885*a^2*b*d*n^2*x*x^n + 175*c^3*n^2*x*x^(7*n)*e + 570*b*c^2*n^2*x*x^(6*n)*e + 621*b^2*c*n^2*x*x^(5*n)*e + 621*a*c^2*n^2*x*x^(5*n)*e + 226*b^3*n^2*x*x^(4*n)*e + 1356*a*b*c*n^2*x*x^(4*n)*e + 741*a*b^2*n^2*x*x^(3*n)*e + 741*a^2*c*n^2*x*x^(3*n)*e + 810*a^2*b*n^2*x*x^(2*n)*e + 295*a^3*n^2*x*x^n*e + 322*a^3*d*n^2*x + 22*c^3*d*n*x*x^(6*n) + 69*b*c^2*d*n*x*x^(5*n) + 72*b^2*c*d*n*x*x^(4*n) + 72*a*c^2*d*n*x*x^(4*n) + 25*b^3*d*n*x*x^(3*n) + 150*a*b*c*d*n*x*x^(3*n) + 78*a*b^2*d*n*x*x^(2*n) + 78*a^2*c*d*n*x*x^(2*n) + 81*a^2*b*d*n*x*x^n + 21*c^3*n*x*x^(7*n)*e + 66*b*c^2*n*x*x^(6*n)*e + 69*b^2*c*n*x*x^(5*n)*e + 69*a*c^2*n*x*x^(5*n)*e + 24*b^3*n*x*x^(4*n)*e + 144*a*b*c*n*x*x^(4*n)*e + 75*a*b^2*n*x*x^(3*n)*e + 75*a^2*c*n*x*x^(3*n)*e + 78*a^2*b*n*x*x^(2*n)*e + 27*a^3*n*x*x^n*e + 28*a^3*d*n*x + c^3*d*x*x^(6*n) + 3*b*c^2*d*x*x^(5*n) + 3*b^2*c*d*x*x^(4*n) + 3*a*c^2*d*x*x^(4*n) + b^3*d*x*x^(3*n) + 6*a*b*c*d*x*x^(3*n) + 3*a*b^2*d*x*x^(2*n) + 3*a^2*c*d*x*x^(2*n) + 3*a^2*b*d*x*x^n + c^3*x*x^(7*n)*e + 3*b*c^2*x*x^(6*n)*e + 3*b^2*c*x*x^(5*n)*e + 3*a*c^2*x*x^(5*n)*e + b^3*x*x^(4*n)*e + 6*a*b*c*x*x^(4*n)*e + 3*a*b^2*x*x^(3*n)*e + 3*a^2*c*x*x^(3*n)*e + 3*a^2*b*x*x^(2*n)*e + a^3*x*x^n*e + a^3*d*x)/(5040*n^7 + 13068*n^6 + 13132*n^5 + 6769*n^4 + 1960*n^3 + 322*n^2 + 28*n + 1)","B",0
69,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{3}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)^3/(c*x^(2*n) + b*x^n + a), x)","F",0
70,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{2}}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)^2/(c*x^(2*n) + b*x^n + a), x)","F",0
71,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{e x^{n} + d}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + b*x^n + a), x)","F",0
72,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)*(e*x^n + d)), x)","F",0
73,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)} {\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)*(e*x^n + d)^2), x)","F",0
74,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)} {\left(e x^{n} + d\right)}^{3}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)*(e*x^n + d)^3), x)","F",0
75,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{3}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x^n + d)^3/(c*x^(2*n) + b*x^n + a)^2, x)","F",0
76,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{2}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x^n + d)^2/(c*x^(2*n) + b*x^n + a)^2, x)","F",0
77,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{e x^{n} + d}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + b*x^n + a)^2, x)","F",0
78,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{2} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)^2*(e*x^n + d)), x)","F",0
79,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{2} {\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)^2*(e*x^n + d)^2), x)","F",0
80,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{3}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*x^n + d)^3/(c*x^(2*n) + b*x^n + a)^3, x)","F",0
81,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{n} + d\right)}^{2}}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*x^n + d)^2/(c*x^(2*n) + b*x^n + a)^3, x)","F",0
82,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{e x^{n} + d}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + b*x^n + a)^3, x)","F",0
83,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{3} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)^3*(e*x^n + d)), x)","F",0
84,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{3} {\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)^3*(e*x^n + d)^2), x)","F",0
85,0,0,0,0.000000," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2 \, n} + b x^{n} + a} {\left(e x^{n} + d\right)}\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a)*(e*x^n + d), x)","F",0
86,0,0,0,0.000000," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}} {\left(e x^{n} + d\right)}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2)*(e*x^n + d), x)","F",0
87,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""giac"")","\int \frac{e x^{n} + d}{\sqrt{c x^{2 \, n} + b x^{n} + a}}\,{d x}"," ",0,"integrate((e*x^n + d)/sqrt(c*x^(2*n) + b*x^n + a), x)","F",0
88,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""giac"")","\int \frac{e x^{n} + d}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + b*x^n + a)^(3/2), x)","F",0
89,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^(5/2),x, algorithm=""giac"")","\int \frac{e x^{n} + d}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + b*x^n + a)^(5/2), x)","F",0
90,0,0,0,0.000000," ","integrate((d+e*x^n)^q*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} {\left(e x^{n} + d\right)}^{q}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p*(e*x^n + d)^q, x)","F",0
91,-2,0,0,0.000000," ","integrate((d+e*x^n)^3*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{-256,[1,0,7,4,7,5,2,8,1]%%%}+%%%{-1280,[1,0,7,4,7,4,2,8,1]%%%}+%%%{-2560,[1,0,7,4,7,3,2,8,1]%%%}+%%%{-2560,[1,0,7,4,7,2,2,8,1]%%%}+%%%{-1280,[1,0,7,4,7,1,2,8,1]%%%}+%%%{-256,[1,0,7,4,7,0,2,8,1]%%%}+%%%{256,[1,0,7,4,6,5,4,7,1]%%%}+%%%{1280,[1,0,7,4,6,4,4,7,1]%%%}+%%%{2560,[1,0,7,4,6,3,4,7,1]%%%}+%%%{2560,[1,0,7,4,6,2,4,7,1]%%%}+%%%{1280,[1,0,7,4,6,1,4,7,1]%%%}+%%%{256,[1,0,7,4,6,0,4,7,1]%%%}+%%%{-96,[1,0,7,4,5,5,6,6,1]%%%}+%%%{-480,[1,0,7,4,5,4,6,6,1]%%%}+%%%{-960,[1,0,7,4,5,3,6,6,1]%%%}+%%%{-960,[1,0,7,4,5,2,6,6,1]%%%}+%%%{-480,[1,0,7,4,5,1,6,6,1]%%%}+%%%{-96,[1,0,7,4,5,0,6,6,1]%%%}+%%%{16,[1,0,7,4,4,5,8,5,1]%%%}+%%%{80,[1,0,7,4,4,4,8,5,1]%%%}+%%%{160,[1,0,7,4,4,3,8,5,1]%%%}+%%%{160,[1,0,7,4,4,2,8,5,1]%%%}+%%%{80,[1,0,7,4,4,1,8,5,1]%%%}+%%%{16,[1,0,7,4,4,0,8,5,1]%%%}+%%%{-1,[1,0,7,4,3,5,10,4,1]%%%}+%%%{-5,[1,0,7,4,3,4,10,4,1]%%%}+%%%{-10,[1,0,7,4,3,3,10,4,1]%%%}+%%%{-10,[1,0,7,4,3,2,10,4,1]%%%}+%%%{-5,[1,0,7,4,3,1,10,4,1]%%%}+%%%{-1,[1,0,7,4,3,0,10,4,1]%%%}+%%%{512,[1,0,7,3,8,4,0,9,1]%%%}+%%%{2048,[1,0,7,3,8,3,0,9,1]%%%}+%%%{3072,[1,0,7,3,8,2,0,9,1]%%%}+%%%{2048,[1,0,7,3,8,1,0,9,1]%%%}+%%%{512,[1,0,7,3,8,0,0,9,1]%%%}+%%%{-768,[1,0,7,3,7,4,2,8,1]%%%}+%%%{-3072,[1,0,7,3,7,3,2,8,1]%%%}+%%%{-4608,[1,0,7,3,7,2,2,8,1]%%%}+%%%{-3072,[1,0,7,3,7,1,2,8,1]%%%}+%%%{-768,[1,0,7,3,7,0,2,8,1]%%%}+%%%{448,[1,0,7,3,6,4,4,7,1]%%%}+%%%{1792,[1,0,7,3,6,3,4,7,1]%%%}+%%%{2688,[1,0,7,3,6,2,4,7,1]%%%}+%%%{1792,[1,0,7,3,6,1,4,7,1]%%%}+%%%{448,[1,0,7,3,6,0,4,7,1]%%%}+%%%{-128,[1,0,7,3,5,4,6,6,1]%%%}+%%%{-512,[1,0,7,3,5,3,6,6,1]%%%}+%%%{-768,[1,0,7,3,5,2,6,6,1]%%%}+%%%{-512,[1,0,7,3,5,1,6,6,1]%%%}+%%%{-128,[1,0,7,3,5,0,6,6,1]%%%}+%%%{18,[1,0,7,3,4,4,8,5,1]%%%}+%%%{72,[1,0,7,3,4,3,8,5,1]%%%}+%%%{108,[1,0,7,3,4,2,8,5,1]%%%}+%%%{72,[1,0,7,3,4,1,8,5,1]%%%}+%%%{18,[1,0,7,3,4,0,8,5,1]%%%}+%%%{-1,[1,0,7,3,3,4,10,4,1]%%%}+%%%{-4,[1,0,7,3,3,3,10,4,1]%%%}+%%%{-6,[1,0,7,3,3,2,10,4,1]%%%}+%%%{-4,[1,0,7,3,3,1,10,4,1]%%%}+%%%{-1,[1,0,7,3,3,0,10,4,1]%%%}+%%%{-256,[0,0,7,3,7,4,1,9,1]%%%}+%%%{-1024,[0,0,7,3,7,3,1,9,1]%%%}+%%%{-1536,[0,0,7,3,7,2,1,9,1]%%%}+%%%{-1024,[0,0,7,3,7,1,1,9,1]%%%}+%%%{-256,[0,0,7,3,7,0,1,9,1]%%%}+%%%{256,[0,0,7,3,6,4,3,8,1]%%%}+%%%{1024,[0,0,7,3,6,3,3,8,1]%%%}+%%%{1536,[0,0,7,3,6,2,3,8,1]%%%}+%%%{1024,[0,0,7,3,6,1,3,8,1]%%%}+%%%{256,[0,0,7,3,6,0,3,8,1]%%%}+%%%{-96,[0,0,7,3,5,4,5,7,1]%%%}+%%%{-384,[0,0,7,3,5,3,5,7,1]%%%}+%%%{-576,[0,0,7,3,5,2,5,7,1]%%%}+%%%{-384,[0,0,7,3,5,1,5,7,1]%%%}+%%%{-96,[0,0,7,3,5,0,5,7,1]%%%}+%%%{16,[0,0,7,3,4,4,7,6,1]%%%}+%%%{64,[0,0,7,3,4,3,7,6,1]%%%}+%%%{96,[0,0,7,3,4,2,7,6,1]%%%}+%%%{64,[0,0,7,3,4,1,7,6,1]%%%}+%%%{16,[0,0,7,3,4,0,7,6,1]%%%}+%%%{-1,[0,0,7,3,3,4,9,5,1]%%%}+%%%{-4,[0,0,7,3,3,3,9,5,1]%%%}+%%%{-6,[0,0,7,3,3,2,9,5,1]%%%}+%%%{-4,[0,0,7,3,3,1,9,5,1]%%%}+%%%{-1,[0,0,7,3,3,0,9,5,1]%%%} / %%%{256,[0,0,7,4,7,4,0,8,0]%%%}+%%%{1024,[0,0,7,4,7,3,0,8,0]%%%}+%%%{1536,[0,0,7,4,7,2,0,8,0]%%%}+%%%{1024,[0,0,7,4,7,1,0,8,0]%%%}+%%%{256,[0,0,7,4,7,0,0,8,0]%%%}+%%%{-256,[0,0,7,4,6,4,2,7,0]%%%}+%%%{-1024,[0,0,7,4,6,3,2,7,0]%%%}+%%%{-1536,[0,0,7,4,6,2,2,7,0]%%%}+%%%{-1024,[0,0,7,4,6,1,2,7,0]%%%}+%%%{-256,[0,0,7,4,6,0,2,7,0]%%%}+%%%{96,[0,0,7,4,5,4,4,6,0]%%%}+%%%{384,[0,0,7,4,5,3,4,6,0]%%%}+%%%{576,[0,0,7,4,5,2,4,6,0]%%%}+%%%{384,[0,0,7,4,5,1,4,6,0]%%%}+%%%{96,[0,0,7,4,5,0,4,6,0]%%%}+%%%{-16,[0,0,7,4,4,4,6,5,0]%%%}+%%%{-64,[0,0,7,4,4,3,6,5,0]%%%}+%%%{-96,[0,0,7,4,4,2,6,5,0]%%%}+%%%{-64,[0,0,7,4,4,1,6,5,0]%%%}+%%%{-16,[0,0,7,4,4,0,6,5,0]%%%}+%%%{1,[0,0,7,4,3,4,8,4,0]%%%}+%%%{4,[0,0,7,4,3,3,8,4,0]%%%}+%%%{6,[0,0,7,4,3,2,8,4,0]%%%}+%%%{4,[0,0,7,4,3,1,8,4,0]%%%}+%%%{1,[0,0,7,4,3,0,8,4,0]%%%} Error: Bad Argument Value","F(-2)",0
92,-2,0,0,0.000000," ","integrate((d+e*x^n)^2*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{128,[1,0,5,3,5,4,1,6,1]%%%}+%%%{512,[1,0,5,3,5,3,1,6,1]%%%}+%%%{768,[1,0,5,3,5,2,1,6,1]%%%}+%%%{512,[1,0,5,3,5,1,1,6,1]%%%}+%%%{128,[1,0,5,3,5,0,1,6,1]%%%}+%%%{-96,[1,0,5,3,4,4,3,5,1]%%%}+%%%{-384,[1,0,5,3,4,3,3,5,1]%%%}+%%%{-576,[1,0,5,3,4,2,3,5,1]%%%}+%%%{-384,[1,0,5,3,4,1,3,5,1]%%%}+%%%{-96,[1,0,5,3,4,0,3,5,1]%%%}+%%%{24,[1,0,5,3,3,4,5,4,1]%%%}+%%%{96,[1,0,5,3,3,3,5,4,1]%%%}+%%%{144,[1,0,5,3,3,2,5,4,1]%%%}+%%%{96,[1,0,5,3,3,1,5,4,1]%%%}+%%%{24,[1,0,5,3,3,0,5,4,1]%%%}+%%%{-2,[1,0,5,3,2,4,7,3,1]%%%}+%%%{-8,[1,0,5,3,2,3,7,3,1]%%%}+%%%{-12,[1,0,5,3,2,2,7,3,1]%%%}+%%%{-8,[1,0,5,3,2,1,7,3,1]%%%}+%%%{-2,[1,0,5,3,2,0,7,3,1]%%%}+%%%{64,[1,0,5,2,5,3,1,6,1]%%%}+%%%{192,[1,0,5,2,5,2,1,6,1]%%%}+%%%{192,[1,0,5,2,5,1,1,6,1]%%%}+%%%{64,[1,0,5,2,5,0,1,6,1]%%%}+%%%{-48,[1,0,5,2,4,3,3,5,1]%%%}+%%%{-144,[1,0,5,2,4,2,3,5,1]%%%}+%%%{-144,[1,0,5,2,4,1,3,5,1]%%%}+%%%{-48,[1,0,5,2,4,0,3,5,1]%%%}+%%%{12,[1,0,5,2,3,3,5,4,1]%%%}+%%%{36,[1,0,5,2,3,2,5,4,1]%%%}+%%%{36,[1,0,5,2,3,1,5,4,1]%%%}+%%%{12,[1,0,5,2,3,0,5,4,1]%%%}+%%%{-1,[1,0,5,2,2,3,7,3,1]%%%}+%%%{-3,[1,0,5,2,2,2,7,3,1]%%%}+%%%{-3,[1,0,5,2,2,1,7,3,1]%%%}+%%%{-1,[1,0,5,2,2,0,7,3,1]%%%}+%%%{128,[0,0,5,2,5,3,0,7,1]%%%}+%%%{384,[0,0,5,2,5,2,0,7,1]%%%}+%%%{384,[0,0,5,2,5,1,0,7,1]%%%}+%%%{128,[0,0,5,2,5,0,0,7,1]%%%}+%%%{-96,[0,0,5,2,4,3,2,6,1]%%%}+%%%{-288,[0,0,5,2,4,2,2,6,1]%%%}+%%%{-288,[0,0,5,2,4,1,2,6,1]%%%}+%%%{-96,[0,0,5,2,4,0,2,6,1]%%%}+%%%{24,[0,0,5,2,3,3,4,5,1]%%%}+%%%{72,[0,0,5,2,3,2,4,5,1]%%%}+%%%{72,[0,0,5,2,3,1,4,5,1]%%%}+%%%{24,[0,0,5,2,3,0,4,5,1]%%%}+%%%{-2,[0,0,5,2,2,3,6,4,1]%%%}+%%%{-6,[0,0,5,2,2,2,6,4,1]%%%}+%%%{-6,[0,0,5,2,2,1,6,4,1]%%%}+%%%{-2,[0,0,5,2,2,0,6,4,1]%%%} / %%%{64,[0,0,5,3,5,3,0,6,0]%%%}+%%%{192,[0,0,5,3,5,2,0,6,0]%%%}+%%%{192,[0,0,5,3,5,1,0,6,0]%%%}+%%%{64,[0,0,5,3,5,0,0,6,0]%%%}+%%%{-48,[0,0,5,3,4,3,2,5,0]%%%}+%%%{-144,[0,0,5,3,4,2,2,5,0]%%%}+%%%{-144,[0,0,5,3,4,1,2,5,0]%%%}+%%%{-48,[0,0,5,3,4,0,2,5,0]%%%}+%%%{12,[0,0,5,3,3,3,4,4,0]%%%}+%%%{36,[0,0,5,3,3,2,4,4,0]%%%}+%%%{36,[0,0,5,3,3,1,4,4,0]%%%}+%%%{12,[0,0,5,3,3,0,4,4,0]%%%}+%%%{-1,[0,0,5,3,2,3,6,3,0]%%%}+%%%{-3,[0,0,5,3,2,2,6,3,0]%%%}+%%%{-3,[0,0,5,3,2,1,6,3,0]%%%}+%%%{-1,[0,0,5,3,2,0,6,3,0]%%%} Error: Bad Argument Value","F(-2)",0
93,0,0,0,0.000000," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(e x^{n} + d\right)} {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^n + d)*(c*x^(2*n) + b*x^n + a)^p, x)","F",0
94,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^p/(d+e*x^n),x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}}{e x^{n} + d}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p/(e*x^n + d), x)","F",0
95,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}}{{\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p/(e*x^n + d)^2, x)","F",0
96,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}}{{\left(e x^{n} + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p/(e*x^n + d)^3, x)","F",0
