1,1,1948,0,3.112906," ","integrate((f*x+e)^3*(C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x, algorithm=""giac"")","\frac{14 \, {\left({\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)}}{d^{4}} - \frac{21}{d^{4}}\right)} + \frac{133}{d^{4}}\right)} - \frac{295}{d^{4}}\right)} {\left(d x + 1\right)} + \frac{195}{d^{4}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{90 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}\right)} A d f^{3} + 7 \, {\left({\left({\left(2 \, {\left({\left(d x + 1\right)} {\left(4 \, {\left(d x + 1\right)} {\left(\frac{5 \, {\left(d x + 1\right)}}{d^{5}} - \frac{31}{d^{5}}\right)} + \frac{321}{d^{5}}\right)} - \frac{451}{d^{5}}\right)} {\left(d x + 1\right)} + \frac{745}{d^{5}}\right)} {\left(d x + 1\right)} - \frac{405}{d^{5}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{150 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{5}}\right)} B d f^{3} + {\left({\left({\left(2 \, {\left({\left(4 \, {\left(d x + 1\right)} {\left(5 \, {\left(d x + 1\right)} {\left(\frac{6 \, {\left(d x + 1\right)}}{d^{6}} - \frac{43}{d^{6}}\right)} + \frac{661}{d^{6}}\right)} - \frac{4551}{d^{6}}\right)} {\left(d x + 1\right)} + \frac{4781}{d^{6}}\right)} {\left(d x + 1\right)} - \frac{6335}{d^{6}}\right)} {\left(d x + 1\right)} + \frac{2835}{d^{6}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{1050 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{6}}\right)} C d f^{3} + 210 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} A d f^{2} e + 42 \, {\left({\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)}}{d^{4}} - \frac{21}{d^{4}}\right)} + \frac{133}{d^{4}}\right)} - \frac{295}{d^{4}}\right)} {\left(d x + 1\right)} + \frac{195}{d^{4}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{90 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}\right)} B d f^{2} e + 21 \, {\left({\left({\left(2 \, {\left({\left(d x + 1\right)} {\left(4 \, {\left(d x + 1\right)} {\left(\frac{5 \, {\left(d x + 1\right)}}{d^{5}} - \frac{31}{d^{5}}\right)} + \frac{321}{d^{5}}\right)} - \frac{451}{d^{5}}\right)} {\left(d x + 1\right)} + \frac{745}{d^{5}}\right)} {\left(d x + 1\right)} - \frac{405}{d^{5}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{150 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{5}}\right)} C d f^{2} e + 70 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} A f^{3} + 14 \, {\left({\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)}}{d^{4}} - \frac{21}{d^{4}}\right)} + \frac{133}{d^{4}}\right)} - \frac{295}{d^{4}}\right)} {\left(d x + 1\right)} + \frac{195}{d^{4}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{90 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}\right)} B f^{3} + 7 \, {\left({\left({\left(2 \, {\left({\left(d x + 1\right)} {\left(4 \, {\left(d x + 1\right)} {\left(\frac{5 \, {\left(d x + 1\right)}}{d^{5}} - \frac{31}{d^{5}}\right)} + \frac{321}{d^{5}}\right)} - \frac{451}{d^{5}}\right)} {\left(d x + 1\right)} + \frac{745}{d^{5}}\right)} {\left(d x + 1\right)} - \frac{405}{d^{5}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{150 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{5}}\right)} C f^{3} + 840 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} A d f e^{2} + 210 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} B d f e^{2} + 42 \, {\left({\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)}}{d^{4}} - \frac{21}{d^{4}}\right)} + \frac{133}{d^{4}}\right)} - \frac{295}{d^{4}}\right)} {\left(d x + 1\right)} + \frac{195}{d^{4}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{90 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}\right)} C d f e^{2} + 840 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} A f^{2} e + 210 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} B f^{2} e + 42 \, {\left({\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)}}{d^{4}} - \frac{21}{d^{4}}\right)} + \frac{133}{d^{4}}\right)} - \frac{295}{d^{4}}\right)} {\left(d x + 1\right)} + \frac{195}{d^{4}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{90 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}\right)} C f^{2} e + 280 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} B d e^{3} + 70 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} C d e^{3} + 840 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} B f e^{2} + 210 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} C f e^{2} + 840 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A e^{3} + 1680 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A e^{3} + 280 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} C e^{3} + \frac{2520 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A f e^{2}}{d} + \frac{840 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} B e^{3}}{d}}{1680 \, d}"," ",0,"1/1680*(14*(((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)/d^4 - 21/d^4) + 133/d^4) - 295/d^4)*(d*x + 1) + 195/d^4)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 90*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)*A*d*f^3 + 7*(((2*((d*x + 1)*(4*(d*x + 1)*(5*(d*x + 1)/d^5 - 31/d^5) + 321/d^5) - 451/d^5)*(d*x + 1) + 745/d^5)*(d*x + 1) - 405/d^5)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 150*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^5)*B*d*f^3 + (((2*((4*(d*x + 1)*(5*(d*x + 1)*(6*(d*x + 1)/d^6 - 43/d^6) + 661/d^6) - 4551/d^6)*(d*x + 1) + 4781/d^6)*(d*x + 1) - 6335/d^6)*(d*x + 1) + 2835/d^6)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 1050*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^6)*C*d*f^3 + 210*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*A*d*f^2*e + 42*(((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)/d^4 - 21/d^4) + 133/d^4) - 295/d^4)*(d*x + 1) + 195/d^4)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 90*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)*B*d*f^2*e + 21*(((2*((d*x + 1)*(4*(d*x + 1)*(5*(d*x + 1)/d^5 - 31/d^5) + 321/d^5) - 451/d^5)*(d*x + 1) + 745/d^5)*(d*x + 1) - 405/d^5)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 150*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^5)*C*d*f^2*e + 70*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*A*f^3 + 14*(((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)/d^4 - 21/d^4) + 133/d^4) - 295/d^4)*(d*x + 1) + 195/d^4)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 90*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)*B*f^3 + 7*(((2*((d*x + 1)*(4*(d*x + 1)*(5*(d*x + 1)/d^5 - 31/d^5) + 321/d^5) - 451/d^5)*(d*x + 1) + 745/d^5)*(d*x + 1) - 405/d^5)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 150*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^5)*C*f^3 + 840*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*A*d*f*e^2 + 210*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*B*d*f*e^2 + 42*(((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)/d^4 - 21/d^4) + 133/d^4) - 295/d^4)*(d*x + 1) + 195/d^4)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 90*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)*C*d*f*e^2 + 840*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*A*f^2*e + 210*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*B*f^2*e + 42*(((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)/d^4 - 21/d^4) + 133/d^4) - 295/d^4)*(d*x + 1) + 195/d^4)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 90*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)*C*f^2*e + 280*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*B*d*e^3 + 70*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*C*d*e^3 + 840*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*B*f*e^2 + 210*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*C*f*e^2 + 840*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A*e^3 + 1680*(sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A*e^3 + 280*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*C*e^3 + 2520*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A*f*e^2/d + 840*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*B*e^3/d)/d","B",0
2,1,1327,0,2.581060," ","integrate((f*x+e)^2*(C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x, algorithm=""giac"")","\frac{10 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} A d f^{2} + 2 \, {\left({\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)}}{d^{4}} - \frac{21}{d^{4}}\right)} + \frac{133}{d^{4}}\right)} - \frac{295}{d^{4}}\right)} {\left(d x + 1\right)} + \frac{195}{d^{4}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{90 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}\right)} B d f^{2} + {\left({\left({\left(2 \, {\left({\left(d x + 1\right)} {\left(4 \, {\left(d x + 1\right)} {\left(\frac{5 \, {\left(d x + 1\right)}}{d^{5}} - \frac{31}{d^{5}}\right)} + \frac{321}{d^{5}}\right)} - \frac{451}{d^{5}}\right)} {\left(d x + 1\right)} + \frac{745}{d^{5}}\right)} {\left(d x + 1\right)} - \frac{405}{d^{5}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{150 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{5}}\right)} C d f^{2} + 80 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} A d f e + 20 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} B d f e + 4 \, {\left({\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)}}{d^{4}} - \frac{21}{d^{4}}\right)} + \frac{133}{d^{4}}\right)} - \frac{295}{d^{4}}\right)} {\left(d x + 1\right)} + \frac{195}{d^{4}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{90 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}\right)} C d f e + 40 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} A f^{2} + 10 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} B f^{2} + 2 \, {\left({\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)}}{d^{4}} - \frac{21}{d^{4}}\right)} + \frac{133}{d^{4}}\right)} - \frac{295}{d^{4}}\right)} {\left(d x + 1\right)} + \frac{195}{d^{4}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{90 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}\right)} C f^{2} + 40 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} B d e^{2} + 10 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} C d e^{2} + 80 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} B f e + 20 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} C f e + 120 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A e^{2} + 240 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A e^{2} + 40 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} C e^{2} + \frac{240 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A f e}{d} + \frac{120 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} B e^{2}}{d}}{240 \, d}"," ",0,"1/240*(10*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*A*d*f^2 + 2*(((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)/d^4 - 21/d^4) + 133/d^4) - 295/d^4)*(d*x + 1) + 195/d^4)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 90*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)*B*d*f^2 + (((2*((d*x + 1)*(4*(d*x + 1)*(5*(d*x + 1)/d^5 - 31/d^5) + 321/d^5) - 451/d^5)*(d*x + 1) + 745/d^5)*(d*x + 1) - 405/d^5)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 150*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^5)*C*d*f^2 + 80*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*A*d*f*e + 20*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*B*d*f*e + 4*(((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)/d^4 - 21/d^4) + 133/d^4) - 295/d^4)*(d*x + 1) + 195/d^4)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 90*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)*C*d*f*e + 40*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*A*f^2 + 10*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*B*f^2 + 2*(((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)/d^4 - 21/d^4) + 133/d^4) - 295/d^4)*(d*x + 1) + 195/d^4)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 90*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)*C*f^2 + 40*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*B*d*e^2 + 10*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*C*d*e^2 + 80*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*B*f*e + 20*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*C*f*e + 120*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A*e^2 + 240*(sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A*e^2 + 40*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*C*e^2 + 240*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A*f*e/d + 120*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*B*e^2/d)/d","B",0
3,1,782,0,1.995917," ","integrate((f*x+e)*(C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x, algorithm=""giac"")","\frac{20 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} A d f + 5 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} B d f + {\left({\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)}}{d^{4}} - \frac{21}{d^{4}}\right)} + \frac{133}{d^{4}}\right)} - \frac{295}{d^{4}}\right)} {\left(d x + 1\right)} + \frac{195}{d^{4}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + \frac{90 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}\right)} C d f + 20 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} B d e + 5 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} C d e + 20 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} B f + 5 \, {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} C f + 60 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A e + 120 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A e + 20 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} C e + \frac{60 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A f}{d} + \frac{60 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} B e}{d}}{120 \, d}"," ",0,"1/120*(20*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*A*d*f + 5*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*B*d*f + (((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)/d^4 - 21/d^4) + 133/d^4) - 295/d^4)*(d*x + 1) + 195/d^4)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 90*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)*C*d*f + 20*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*B*d*e + 5*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*C*d*e + 20*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*B*f + 5*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*C*f + 60*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A*e + 120*(sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A*e + 20*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*C*e + 60*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A*f/d + 60*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*B*e/d)/d","B",0
4,1,336,0,1.535741," ","integrate((C*x^2+B*x+A)*(-d*x+1)^(1/2)*(d*x+1)^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} B d + {\left({\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)}}{d^{3}} - \frac{13}{d^{3}}\right)} + \frac{43}{d^{3}}\right)} - \frac{39}{d^{3}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{18 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{3}}\right)} C d + 12 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A + 24 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} A + 4 \, {\left(\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)}}{d^{2}} - \frac{7}{d^{2}}\right)} + \frac{9}{d^{2}}\right)} + \frac{6 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}\right)} C + \frac{12 \, {\left(\sqrt{d x + 1} {\left(d x - 2\right)} \sqrt{-d x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)\right)} B}{d}}{24 \, d}"," ",0,"1/24*(4*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*B*d + (((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)/d^3 - 13/d^3) + 43/d^3) - 39/d^3)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 18*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^3)*C*d + 12*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A + 24*(sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*A + 4*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)/d^2 - 7/d^2) + 9/d^2) + 6*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)*C + 12*(sqrt(d*x + 1)*(d*x - 2)*sqrt(-d*x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(d*x + 1)))*B/d)/d","B",0
5,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Undef/Unsigned Inf encountered in limit"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"","F(-2)",0
6,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Undef/Unsigned Inf encountered in limit"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"","F(-2)",0
7,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Undef/Unsigned Inf encountered in limit"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"","F(-2)",0
8,1,427,0,1.818725," ","integrate((f*x+e)^3*(C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-\frac{{\left({\left(2 \, {\left(d x + 1\right)} {\left(3 \, {\left(d x + 1\right)} {\left(\frac{4 \, {\left(d x + 1\right)} C f^{3}}{d^{5}} + \frac{5 \, B d^{26} f^{3} + 15 \, C d^{26} f^{2} e - 16 \, C d^{25} f^{3}}{d^{30}}\right)} + \frac{20 \, A d^{27} f^{3} + 60 \, B d^{27} f^{2} e - 45 \, B d^{26} f^{3} + 60 \, C d^{27} f e^{2} - 135 \, C d^{26} f^{2} e + 88 \, C d^{25} f^{3}}{d^{30}}\right)} + \frac{5 \, {\left(36 \, A d^{28} f^{2} e - 16 \, A d^{27} f^{3} + 36 \, B d^{28} f e^{2} - 48 \, B d^{27} f^{2} e + 27 \, B d^{26} f^{3} + 12 \, C d^{28} e^{3} - 48 \, C d^{27} f e^{2} + 81 \, C d^{26} f^{2} e - 32 \, C d^{25} f^{3}\right)}}{d^{30}}\right)} {\left(d x + 1\right)} + \frac{15 \, {\left(24 \, A d^{29} f e^{2} - 12 \, A d^{28} f^{2} e + 8 \, A d^{27} f^{3} + 8 \, B d^{29} e^{3} - 12 \, B d^{28} f e^{2} + 24 \, B d^{27} f^{2} e - 5 \, B d^{26} f^{3} - 4 \, C d^{28} e^{3} + 24 \, C d^{27} f e^{2} - 15 \, C d^{26} f^{2} e + 8 \, C d^{25} f^{3}\right)}}{d^{30}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{30 \, {\left(8 \, A d^{4} e^{3} + 12 \, A d^{2} f^{2} e + 12 \, B d^{2} f e^{2} + 3 \, B f^{3} + 4 \, C d^{2} e^{3} + 9 \, C f^{2} e\right)} \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}}{120 \, d}"," ",0,"-1/120*(((2*(d*x + 1)*(3*(d*x + 1)*(4*(d*x + 1)*C*f^3/d^5 + (5*B*d^26*f^3 + 15*C*d^26*f^2*e - 16*C*d^25*f^3)/d^30) + (20*A*d^27*f^3 + 60*B*d^27*f^2*e - 45*B*d^26*f^3 + 60*C*d^27*f*e^2 - 135*C*d^26*f^2*e + 88*C*d^25*f^3)/d^30) + 5*(36*A*d^28*f^2*e - 16*A*d^27*f^3 + 36*B*d^28*f*e^2 - 48*B*d^27*f^2*e + 27*B*d^26*f^3 + 12*C*d^28*e^3 - 48*C*d^27*f*e^2 + 81*C*d^26*f^2*e - 32*C*d^25*f^3)/d^30)*(d*x + 1) + 15*(24*A*d^29*f*e^2 - 12*A*d^28*f^2*e + 8*A*d^27*f^3 + 8*B*d^29*e^3 - 12*B*d^28*f*e^2 + 24*B*d^27*f^2*e - 5*B*d^26*f^3 - 4*C*d^28*e^3 + 24*C*d^27*f*e^2 - 15*C*d^26*f^2*e + 8*C*d^25*f^3)/d^30)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 30*(8*A*d^4*e^3 + 12*A*d^2*f^2*e + 12*B*d^2*f*e^2 + 3*B*f^3 + 4*C*d^2*e^3 + 9*C*f^2*e)*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)/d","A",0
9,1,277,0,1.643153," ","integrate((f*x+e)^2*(C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-\frac{{\left({\left(d x + 1\right)} {\left(2 \, {\left(d x + 1\right)} {\left(\frac{3 \, {\left(d x + 1\right)} C f^{2}}{d^{4}} + \frac{4 \, B d^{17} f^{2} + 8 \, C d^{17} f e - 9 \, C d^{16} f^{2}}{d^{20}}\right)} + \frac{12 \, A d^{18} f^{2} + 24 \, B d^{18} f e - 16 \, B d^{17} f^{2} + 12 \, C d^{18} e^{2} - 32 \, C d^{17} f e + 27 \, C d^{16} f^{2}}{d^{20}}\right)} + \frac{3 \, {\left(16 \, A d^{19} f e - 4 \, A d^{18} f^{2} + 8 \, B d^{19} e^{2} - 8 \, B d^{18} f e + 8 \, B d^{17} f^{2} - 4 \, C d^{18} e^{2} + 16 \, C d^{17} f e - 5 \, C d^{16} f^{2}\right)}}{d^{20}}\right)} \sqrt{d x + 1} \sqrt{-d x + 1} - \frac{6 \, {\left(8 \, A d^{4} e^{2} + 4 \, A d^{2} f^{2} + 8 \, B d^{2} f e + 4 \, C d^{2} e^{2} + 3 \, C f^{2}\right)} \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{4}}}{24 \, d}"," ",0,"-1/24*(((d*x + 1)*(2*(d*x + 1)*(3*(d*x + 1)*C*f^2/d^4 + (4*B*d^17*f^2 + 8*C*d^17*f*e - 9*C*d^16*f^2)/d^20) + (12*A*d^18*f^2 + 24*B*d^18*f*e - 16*B*d^17*f^2 + 12*C*d^18*e^2 - 32*C*d^17*f*e + 27*C*d^16*f^2)/d^20) + 3*(16*A*d^19*f*e - 4*A*d^18*f^2 + 8*B*d^19*e^2 - 8*B*d^18*f*e + 8*B*d^17*f^2 - 4*C*d^18*e^2 + 16*C*d^17*f*e - 5*C*d^16*f^2)/d^20)*sqrt(d*x + 1)*sqrt(-d*x + 1) - 6*(8*A*d^4*e^2 + 4*A*d^2*f^2 + 8*B*d^2*f*e + 4*C*d^2*e^2 + 3*C*f^2)*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^4)/d","A",0
10,1,146,0,1.310401," ","integrate((f*x+e)*(C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)} C f}{d^{3}} + \frac{3 \, B d^{10} f + 3 \, C d^{10} e - 4 \, C d^{9} f}{d^{12}}\right)} + \frac{3 \, {\left(2 \, A d^{11} f + 2 \, B d^{11} e - B d^{10} f - C d^{10} e + 2 \, C d^{9} f\right)}}{d^{12}}\right)} - \frac{6 \, {\left(2 \, A d^{2} e + B f + C e\right)} \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}}{6 \, d}"," ",0,"-1/6*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)*C*f/d^3 + (3*B*d^10*f + 3*C*d^10*e - 4*C*d^9*f)/d^12) + 3*(2*A*d^11*f + 2*B*d^11*e - B*d^10*f - C*d^10*e + 2*C*d^9*f)/d^12) - 6*(2*A*d^2*e + B*f + C*e)*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)/d","A",0
11,1,76,0,1.285590," ","integrate((C*x^2+B*x+A)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{d x + 1} \sqrt{-d x + 1} {\left(\frac{{\left(d x + 1\right)} C}{d^{2}} + \frac{2 \, B d^{5} - C d^{4}}{d^{6}}\right)} - \frac{2 \, {\left(2 \, A d^{2} + C\right)} \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}}{2 \, d}"," ",0,"-1/2*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*C/d^2 + (2*B*d^5 - C*d^4)/d^6) - 2*(2*A*d^2 + C)*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)/d","A",0
12,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Undef/Unsigned Inf encountered in limit"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"","F(-2)",0
13,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Undef/Unsigned Inf encountered in limit"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"","F(-2)",0
14,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Undef/Unsigned Inf encountered in limit"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"","F(-2)",0
15,1,101,0,1.305243," ","integrate(x*(c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{d x + 1} \sqrt{-d x + 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)} c}{d^{3}} + \frac{3 \, b d^{10} - 4 \, c d^{9}}{d^{12}}\right)} + \frac{3 \, {\left(2 \, a d^{11} - b d^{10} + 2 \, c d^{9}\right)}}{d^{12}}\right)} - \frac{6 \, b \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}}{6 \, d}"," ",0,"-1/6*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*(2*(d*x + 1)*c/d^3 + (3*b*d^10 - 4*c*d^9)/d^12) + 3*(2*a*d^11 - b*d^10 + 2*c*d^9)/d^12) - 6*b*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)/d","A",0
16,1,76,0,1.324117," ","integrate((c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{d x + 1} \sqrt{-d x + 1} {\left(\frac{{\left(d x + 1\right)} c}{d^{2}} + \frac{2 \, b d^{5} - c d^{4}}{d^{6}}\right)} - \frac{2 \, {\left(2 \, a d^{2} + c\right)} \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{d x + 1}\right)}{d^{2}}}{2 \, d}"," ",0,"-1/2*(sqrt(d*x + 1)*sqrt(-d*x + 1)*((d*x + 1)*c/d^2 + (2*b*d^5 - c*d^4)/d^6) - 2*(2*a*d^2 + c)*arcsin(1/2*sqrt(2)*sqrt(d*x + 1))/d^2)/d","A",0
17,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)/x/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2,2]%%%}] at parameters values [70,22]Warning, choosing root of [1,0,-4,0,%%%{4,[2,2]%%%}] at parameters values [42,56]-a*ln(abs(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1)))+a*ln(abs(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1)))-2*b*(-1/2*pi-atan(sqrt(d*x+1)*((-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1))^2-1)/(-2*sqrt(-d*x+1)+2*sqrt(2))))/d-2*c*d^2/2/d^4*sqrt(d*x+1)*sqrt(-d*x+1)","F(-2)",0
18,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)/x^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2,2]%%%}] at parameters values [70,22]Warning, choosing root of [1,0,-4,0,%%%{4,[2,2]%%%}] at parameters values [42,56]1/d*(-2*c*(-1/2*pi-atan(sqrt(d*x+1)*((-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1))^2-1)/(-2*sqrt(-d*x+1)+2*sqrt(2))))-b*d*ln(abs(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1)))+b*d*ln(abs(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1)))-4*a*d^2*(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1))/(-(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1))^2+4))","F(-2)",0
19,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)/x^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2,2]%%%}] at parameters values [70,22]Warning, choosing root of [1,0,-4,0,%%%{4,[2,2]%%%}] at parameters values [42,56]1/d*(-1/2*(a*d^3+2*c*d)*ln(abs(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1)))+1/2*(a*d^3+2*c*d)*ln(abs(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1)))-(2*a*d^3*(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1))^3-4*b*d^2*(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1))^3+8*a*d^3*(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1))+16*b*d^2*(2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1)))/((2*sqrt(d*x+1)/(-2*sqrt(-d*x+1)+2*sqrt(2))-1/2*(-2*sqrt(-d*x+1)+2*sqrt(2))/sqrt(d*x+1))^2-4)^2)","F(-2)",0
20,-1,0,0,0.000000," ","integrate((f*x+e)^3*(C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,-1,0,0,0.000000," ","integrate((f*x+e)^2*(C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,-1,0,0,0.000000," ","integrate((f*x+e)*(C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
23,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(b*x+a)^(1/2)*(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)^2/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,1,1658,0,7.020659," ","integrate((C*x^2+B*x+A)/(f*x+e)^3/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","-\frac{{\left(2 \, C a^{4} \sqrt{-c} c^{2} f^{2} + A a^{2} b^{2} \sqrt{-c} c^{2} f^{2} - 3 \, B a^{2} b^{2} \sqrt{-c} c^{2} f e + C a^{2} b^{2} \sqrt{-c} c^{2} e^{2} + 2 \, A b^{4} \sqrt{-c} c^{2} e^{2}\right)} \arctan\left(\frac{2 \, b c^{2} e + {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} f}{2 \, \sqrt{a^{2} f^{2} - b^{2} e^{2}} c^{2}}\right)}{{\left(a^{4} f^{4} {\left| c \right|} - 2 \, a^{2} b^{2} f^{2} {\left| c \right|} e^{2} + b^{4} {\left| c \right|} e^{4}\right)} \sqrt{a^{2} f^{2} - b^{2} e^{2}} c^{2}} + \frac{2 \, {\left(16 \, B a^{6} b \sqrt{-c} c^{8} f^{5} - 32 \, C a^{6} b \sqrt{-c} c^{8} f^{4} e - 24 \, A a^{4} b^{3} \sqrt{-c} c^{8} f^{4} e + 4 \, A a^{4} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{5} + 8 \, B a^{4} b^{3} \sqrt{-c} c^{8} f^{3} e^{2} + 20 \, B a^{4} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{4} e + 4 \, B a^{4} b {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{5} + 8 \, C a^{4} b^{3} \sqrt{-c} c^{8} f^{2} e^{3} - 44 \, C a^{4} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{3} e^{2} - 40 \, A a^{2} b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{3} e^{2} - 8 \, C a^{4} b {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{4} e - 6 \, A a^{2} b^{3} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{4} e - A a^{2} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f^{5} + 16 \, B a^{2} b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{2} e^{3} + 10 \, B a^{2} b^{3} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{3} e^{2} + 3 \, B a^{2} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f^{4} e + 8 \, C a^{2} b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f e^{4} - 14 \, C a^{2} b^{3} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{2} e^{3} - 12 \, A b^{5} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{2} e^{3} - 5 \, C a^{2} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f^{3} e^{2} - 2 \, A b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f^{3} e^{2} + 4 \, B b^{5} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f e^{4} + 4 \, C b^{5} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} e^{5} + 2 \, C b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f e^{4}\right)}}{{\left(a^{4} f^{6} {\left| c \right|} - 2 \, a^{2} b^{2} f^{4} {\left| c \right|} e^{2} + b^{4} f^{2} {\left| c \right|} e^{4}\right)} {\left(4 \, a^{2} c^{4} f + 4 \, b {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} c^{2} e + {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} f\right)}^{2}}"," ",0,"-(2*C*a^4*sqrt(-c)*c^2*f^2 + A*a^2*b^2*sqrt(-c)*c^2*f^2 - 3*B*a^2*b^2*sqrt(-c)*c^2*f*e + C*a^2*b^2*sqrt(-c)*c^2*e^2 + 2*A*b^4*sqrt(-c)*c^2*e^2)*arctan(1/2*(2*b*c^2*e + (sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*f)/(sqrt(a^2*f^2 - b^2*e^2)*c^2))/((a^4*f^4*abs(c) - 2*a^2*b^2*f^2*abs(c)*e^2 + b^4*abs(c)*e^4)*sqrt(a^2*f^2 - b^2*e^2)*c^2) + 2*(16*B*a^6*b*sqrt(-c)*c^8*f^5 - 32*C*a^6*b*sqrt(-c)*c^8*f^4*e - 24*A*a^4*b^3*sqrt(-c)*c^8*f^4*e + 4*A*a^4*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^5 + 8*B*a^4*b^3*sqrt(-c)*c^8*f^3*e^2 + 20*B*a^4*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^4*e + 4*B*a^4*b*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^5 + 8*C*a^4*b^3*sqrt(-c)*c^8*f^2*e^3 - 44*C*a^4*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^3*e^2 - 40*A*a^2*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^3*e^2 - 8*C*a^4*b*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^4*e - 6*A*a^2*b^3*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^4*e - A*a^2*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f^5 + 16*B*a^2*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^2*e^3 + 10*B*a^2*b^3*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^3*e^2 + 3*B*a^2*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f^4*e + 8*C*a^2*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f*e^4 - 14*C*a^2*b^3*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^2*e^3 - 12*A*b^5*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^2*e^3 - 5*C*a^2*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f^3*e^2 - 2*A*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f^3*e^2 + 4*B*b^5*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f*e^4 + 4*C*b^5*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*e^5 + 2*C*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f*e^4)/((a^4*f^6*abs(c) - 2*a^2*b^2*f^4*abs(c)*e^2 + b^4*f^2*abs(c)*e^4)*(4*a^2*c^4*f + 4*b*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*c^2*e + (sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*f)^2)","B",0
27,-1,0,0,0.000000," ","integrate((f*x+e)^3*(C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,-1,0,0,0.000000," ","integrate((f*x+e)^2*(C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,-1,0,0,0.000000," ","integrate((f*x+e)*(C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(f*x+e)^2/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,1,1658,0,9.489822," ","integrate((C*x^2+B*x+A)/(f*x+e)^3/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""giac"")","-\frac{{\left(2 \, C a^{4} \sqrt{-c} c^{2} f^{2} + A a^{2} b^{2} \sqrt{-c} c^{2} f^{2} - 3 \, B a^{2} b^{2} \sqrt{-c} c^{2} f e + C a^{2} b^{2} \sqrt{-c} c^{2} e^{2} + 2 \, A b^{4} \sqrt{-c} c^{2} e^{2}\right)} \arctan\left(\frac{2 \, b c^{2} e + {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} f}{2 \, \sqrt{a^{2} f^{2} - b^{2} e^{2}} c^{2}}\right)}{{\left(a^{4} f^{4} {\left| c \right|} - 2 \, a^{2} b^{2} f^{2} {\left| c \right|} e^{2} + b^{4} {\left| c \right|} e^{4}\right)} \sqrt{a^{2} f^{2} - b^{2} e^{2}} c^{2}} + \frac{2 \, {\left(16 \, B a^{6} b \sqrt{-c} c^{8} f^{5} - 32 \, C a^{6} b \sqrt{-c} c^{8} f^{4} e - 24 \, A a^{4} b^{3} \sqrt{-c} c^{8} f^{4} e + 4 \, A a^{4} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{5} + 8 \, B a^{4} b^{3} \sqrt{-c} c^{8} f^{3} e^{2} + 20 \, B a^{4} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{4} e + 4 \, B a^{4} b {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{5} + 8 \, C a^{4} b^{3} \sqrt{-c} c^{8} f^{2} e^{3} - 44 \, C a^{4} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{3} e^{2} - 40 \, A a^{2} b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{3} e^{2} - 8 \, C a^{4} b {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{4} e - 6 \, A a^{2} b^{3} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{4} e - A a^{2} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f^{5} + 16 \, B a^{2} b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f^{2} e^{3} + 10 \, B a^{2} b^{3} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{3} e^{2} + 3 \, B a^{2} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f^{4} e + 8 \, C a^{2} b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} \sqrt{-c} c^{6} f e^{4} - 14 \, C a^{2} b^{3} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{2} e^{3} - 12 \, A b^{5} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f^{2} e^{3} - 5 \, C a^{2} b^{2} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f^{3} e^{2} - 2 \, A b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f^{3} e^{2} + 4 \, B b^{5} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} f e^{4} + 4 \, C b^{5} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} \sqrt{-c} c^{4} e^{5} + 2 \, C b^{4} {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{6} \sqrt{-c} c^{2} f e^{4}\right)}}{{\left(a^{4} f^{6} {\left| c \right|} - 2 \, a^{2} b^{2} f^{4} {\left| c \right|} e^{2} + b^{4} f^{2} {\left| c \right|} e^{4}\right)} {\left(4 \, a^{2} c^{4} f + 4 \, b {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{2} c^{2} e + {\left(\sqrt{-b c x + a c} \sqrt{-c} - \sqrt{2 \, a c^{2} + {\left(b c x - a c\right)} c}\right)}^{4} f\right)}^{2}}"," ",0,"-(2*C*a^4*sqrt(-c)*c^2*f^2 + A*a^2*b^2*sqrt(-c)*c^2*f^2 - 3*B*a^2*b^2*sqrt(-c)*c^2*f*e + C*a^2*b^2*sqrt(-c)*c^2*e^2 + 2*A*b^4*sqrt(-c)*c^2*e^2)*arctan(1/2*(2*b*c^2*e + (sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*f)/(sqrt(a^2*f^2 - b^2*e^2)*c^2))/((a^4*f^4*abs(c) - 2*a^2*b^2*f^2*abs(c)*e^2 + b^4*abs(c)*e^4)*sqrt(a^2*f^2 - b^2*e^2)*c^2) + 2*(16*B*a^6*b*sqrt(-c)*c^8*f^5 - 32*C*a^6*b*sqrt(-c)*c^8*f^4*e - 24*A*a^4*b^3*sqrt(-c)*c^8*f^4*e + 4*A*a^4*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^5 + 8*B*a^4*b^3*sqrt(-c)*c^8*f^3*e^2 + 20*B*a^4*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^4*e + 4*B*a^4*b*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^5 + 8*C*a^4*b^3*sqrt(-c)*c^8*f^2*e^3 - 44*C*a^4*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^3*e^2 - 40*A*a^2*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^3*e^2 - 8*C*a^4*b*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^4*e - 6*A*a^2*b^3*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^4*e - A*a^2*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f^5 + 16*B*a^2*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f^2*e^3 + 10*B*a^2*b^3*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^3*e^2 + 3*B*a^2*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f^4*e + 8*C*a^2*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*sqrt(-c)*c^6*f*e^4 - 14*C*a^2*b^3*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^2*e^3 - 12*A*b^5*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f^2*e^3 - 5*C*a^2*b^2*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f^3*e^2 - 2*A*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f^3*e^2 + 4*B*b^5*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*f*e^4 + 4*C*b^5*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*sqrt(-c)*c^4*e^5 + 2*C*b^4*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^6*sqrt(-c)*c^2*f*e^4)/((a^4*f^6*abs(c) - 2*a^2*b^2*f^4*abs(c)*e^2 + b^4*f^2*abs(c)*e^4)*(4*a^2*c^4*f + 4*b*(sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^2*c^2*e + (sqrt(-b*c*x + a*c)*sqrt(-c) - sqrt(2*a*c^2 + (b*c*x - a*c)*c))^4*f)^2)","B",0
34,1,105,0,1.456680," ","integrate(x*(c*x^2+b*x+a)/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{d x + 1} \sqrt{d x - 1} {\left({\left(d x + 1\right)} {\left(\frac{2 \, {\left(d x + 1\right)} c}{d^{3}} + \frac{3 \, b d^{10} - 4 \, c d^{9}}{d^{12}}\right)} + \frac{3 \, {\left(2 \, a d^{11} - b d^{10} + 2 \, c d^{9}\right)}}{d^{12}}\right)} - \frac{6 \, b \log\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}{d^{2}}}{6 \, d}"," ",0,"1/6*(sqrt(d*x + 1)*sqrt(d*x - 1)*((d*x + 1)*(2*(d*x + 1)*c/d^3 + (3*b*d^10 - 4*c*d^9)/d^12) + 3*(2*a*d^11 - b*d^10 + 2*c*d^9)/d^12) - 6*b*log(sqrt(d*x + 1) - sqrt(d*x - 1))/d^2)/d","A",0
35,1,80,0,1.385571," ","integrate((c*x^2+b*x+a)/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{d x + 1} \sqrt{d x - 1} {\left(\frac{{\left(d x + 1\right)} c}{d^{2}} + \frac{2 \, b d^{5} - c d^{4}}{d^{6}}\right)} - \frac{2 \, {\left(2 \, a d^{2} + c\right)} \log\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}{d^{2}}}{2 \, d}"," ",0,"1/2*(sqrt(d*x + 1)*sqrt(d*x - 1)*((d*x + 1)*c/d^2 + (2*b*d^5 - c*d^4)/d^6) - 2*(2*a*d^2 + c)*log(sqrt(d*x + 1) - sqrt(d*x - 1))/d^2)/d","A",0
36,1,71,0,1.366017," ","integrate((c*x^2+b*x+a)/x/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-2 \, a \arctan\left(\frac{1}{2} \, {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{2}\right) - \frac{b \log\left({\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{2}\right)}{d} + \frac{\sqrt{d x + 1} \sqrt{d x - 1} c}{d^{2}}"," ",0,"-2*a*arctan(1/2*(sqrt(d*x + 1) - sqrt(d*x - 1))^2) - b*log((sqrt(d*x + 1) - sqrt(d*x - 1))^2)/d + sqrt(d*x + 1)*sqrt(d*x - 1)*c/d^2","A",0
37,1,83,0,1.516559," ","integrate((c*x^2+b*x+a)/x^2/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-\frac{2 \, b d \arctan\left(\frac{1}{2} \, {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{2}\right) - \frac{8 \, a d^{2}}{{\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{4} + 4} + c \log\left({\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{2}\right)}{d}"," ",0,"-(2*b*d*arctan(1/2*(sqrt(d*x + 1) - sqrt(d*x - 1))^2) - 8*a*d^2/((sqrt(d*x + 1) - sqrt(d*x - 1))^4 + 4) + c*log((sqrt(d*x + 1) - sqrt(d*x - 1))^2))/d","A",0
38,1,145,0,1.442276," ","integrate((c*x^2+b*x+a)/x^3/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-\frac{{\left(a d^{3} + 2 \, c d\right)} \arctan\left(\frac{1}{2} \, {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{2}\right) + \frac{2 \, {\left(a d^{3} {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{6} - 4 \, b d^{2} {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{4} - 4 \, a d^{3} {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{2} - 16 \, b d^{2}\right)}}{{\left({\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{4} + 4\right)}^{2}}}{d}"," ",0,"-((a*d^3 + 2*c*d)*arctan(1/2*(sqrt(d*x + 1) - sqrt(d*x - 1))^2) + 2*(a*d^3*(sqrt(d*x + 1) - sqrt(d*x - 1))^6 - 4*b*d^2*(sqrt(d*x + 1) - sqrt(d*x - 1))^4 - 4*a*d^3*(sqrt(d*x + 1) - sqrt(d*x - 1))^2 - 16*b*d^2)/((sqrt(d*x + 1) - sqrt(d*x - 1))^4 + 4)^2)/d","B",0
39,1,197,0,1.402844," ","integrate((c*x^2+b*x+a)/x^4/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""giac"")","-\frac{3 \, b d^{3} \arctan\left(\frac{1}{2} \, {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{2}\right) + \frac{2 \, {\left(3 \, b d^{3} {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{10} - 12 \, c d^{2} {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{8} - 96 \, a d^{4} {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{4} - 96 \, c d^{2} {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{4} - 48 \, b d^{3} {\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{2} - 128 \, a d^{4} - 192 \, c d^{2}\right)}}{{\left({\left(\sqrt{d x + 1} - \sqrt{d x - 1}\right)}^{4} + 4\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*b*d^3*arctan(1/2*(sqrt(d*x + 1) - sqrt(d*x - 1))^2) + 2*(3*b*d^3*(sqrt(d*x + 1) - sqrt(d*x - 1))^10 - 12*c*d^2*(sqrt(d*x + 1) - sqrt(d*x - 1))^8 - 96*a*d^4*(sqrt(d*x + 1) - sqrt(d*x - 1))^4 - 96*c*d^2*(sqrt(d*x + 1) - sqrt(d*x - 1))^4 - 48*b*d^3*(sqrt(d*x + 1) - sqrt(d*x - 1))^2 - 128*a*d^4 - 192*c*d^2)/((sqrt(d*x + 1) - sqrt(d*x - 1))^4 + 4)^3)/d","B",0
40,1,605,0,3.244892," ","integrate((c*x^2+b*x+a)/(e*x+d)^3/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","-\frac{{\left(2 \, a d^{2} + c d^{2} - 3 \, b d e + a e^{2} + 2 \, c e^{2}\right)} \arctan\left(\frac{{\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{2} e + 2 \, d}{2 \, \sqrt{-d^{2} + e^{2}}}\right)}{{\left(d^{4} - 2 \, d^{2} e^{2} + e^{4}\right)} \sqrt{-d^{2} + e^{2}}} + \frac{2 \, {\left(2 \, c d^{4} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{6} e + 4 \, c d^{5} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} - 2 \, a d^{2} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{6} e^{3} - 5 \, c d^{2} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{6} e^{3} + 4 \, b d^{4} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} e + 3 \, b d {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{6} e^{4} - 12 \, a d^{3} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} e^{2} - 14 \, c d^{3} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} e^{2} - a {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{6} e^{5} + 10 \, b d^{2} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} e^{3} + 8 \, c d^{4} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{2} e - 6 \, a d {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} e^{4} - 8 \, c d {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} e^{4} + 16 \, b d^{3} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{2} e^{2} + 4 \, b {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} e^{5} - 40 \, a d^{2} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{2} e^{3} - 44 \, c d^{2} {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{2} e^{3} + 20 \, b d {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{2} e^{4} + 8 \, c d^{3} e^{2} + 4 \, a {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{2} e^{5} + 8 \, b d^{2} e^{3} - 24 \, a d e^{4} - 32 \, c d e^{4} + 16 \, b e^{5}\right)}}{{\left(d^{4} e^{2} - 2 \, d^{2} e^{4} + e^{6}\right)} {\left({\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} e + 4 \, d {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{2} + 4 \, e\right)}^{2}}"," ",0,"-(2*a*d^2 + c*d^2 - 3*b*d*e + a*e^2 + 2*c*e^2)*arctan(1/2*((sqrt(x + 1) - sqrt(x - 1))^2*e + 2*d)/sqrt(-d^2 + e^2))/((d^4 - 2*d^2*e^2 + e^4)*sqrt(-d^2 + e^2)) + 2*(2*c*d^4*(sqrt(x + 1) - sqrt(x - 1))^6*e + 4*c*d^5*(sqrt(x + 1) - sqrt(x - 1))^4 - 2*a*d^2*(sqrt(x + 1) - sqrt(x - 1))^6*e^3 - 5*c*d^2*(sqrt(x + 1) - sqrt(x - 1))^6*e^3 + 4*b*d^4*(sqrt(x + 1) - sqrt(x - 1))^4*e + 3*b*d*(sqrt(x + 1) - sqrt(x - 1))^6*e^4 - 12*a*d^3*(sqrt(x + 1) - sqrt(x - 1))^4*e^2 - 14*c*d^3*(sqrt(x + 1) - sqrt(x - 1))^4*e^2 - a*(sqrt(x + 1) - sqrt(x - 1))^6*e^5 + 10*b*d^2*(sqrt(x + 1) - sqrt(x - 1))^4*e^3 + 8*c*d^4*(sqrt(x + 1) - sqrt(x - 1))^2*e - 6*a*d*(sqrt(x + 1) - sqrt(x - 1))^4*e^4 - 8*c*d*(sqrt(x + 1) - sqrt(x - 1))^4*e^4 + 16*b*d^3*(sqrt(x + 1) - sqrt(x - 1))^2*e^2 + 4*b*(sqrt(x + 1) - sqrt(x - 1))^4*e^5 - 40*a*d^2*(sqrt(x + 1) - sqrt(x - 1))^2*e^3 - 44*c*d^2*(sqrt(x + 1) - sqrt(x - 1))^2*e^3 + 20*b*d*(sqrt(x + 1) - sqrt(x - 1))^2*e^4 + 8*c*d^3*e^2 + 4*a*(sqrt(x + 1) - sqrt(x - 1))^2*e^5 + 8*b*d^2*e^3 - 24*a*d*e^4 - 32*c*d*e^4 + 16*b*e^5)/((d^4*e^2 - 2*d^2*e^4 + e^6)*((sqrt(x + 1) - sqrt(x - 1))^4*e + 4*d*(sqrt(x + 1) - sqrt(x - 1))^2 + 4*e)^2)","B",0
41,1,4708,0,6.328042," ","integrate((b*x+a)^2*(C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{\frac{7680 \, {\left(\frac{{\left(c d f - d^{2} e\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f}} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c}\right)} A a^{2} c {\left| d \right|}}{d^{2}} + \frac{320 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} C a^{2} c {\left| d \right|}}{d^{2}} + \frac{640 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} B a b c {\left| d \right|}}{d^{2}} + \frac{80 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{3}} - \frac{25 \, c d^{11} f^{6} - d^{12} f^{5} e}{d^{14} f^{6}}\right)} + \frac{163 \, c^{2} d^{11} f^{6} - 14 \, c d^{12} f^{5} e - 5 \, d^{13} f^{4} e^{2}}{d^{14} f^{6}}\right)} - \frac{3 \, {\left(93 \, c^{3} d^{11} f^{6} - 15 \, c^{2} d^{12} f^{5} e - 9 \, c d^{13} f^{4} e^{2} - 5 \, d^{14} f^{3} e^{3}\right)}}{d^{14} f^{6}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, c^{4} f^{4} - 20 \, c^{3} d f^{3} e - 6 \, c^{2} d^{2} f^{2} e^{2} - 4 \, c d^{3} f e^{3} - 5 \, d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} C a b c {\left| d \right|}}{d^{2}} + \frac{320 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} A b^{2} c {\left| d \right|}}{d^{2}} + \frac{40 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{3}} - \frac{25 \, c d^{11} f^{6} - d^{12} f^{5} e}{d^{14} f^{6}}\right)} + \frac{163 \, c^{2} d^{11} f^{6} - 14 \, c d^{12} f^{5} e - 5 \, d^{13} f^{4} e^{2}}{d^{14} f^{6}}\right)} - \frac{3 \, {\left(93 \, c^{3} d^{11} f^{6} - 15 \, c^{2} d^{12} f^{5} e - 9 \, c d^{13} f^{4} e^{2} - 5 \, d^{14} f^{3} e^{3}\right)}}{d^{14} f^{6}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, c^{4} f^{4} - 20 \, c^{3} d f^{3} e - 6 \, c^{2} d^{2} f^{2} e^{2} - 4 \, c d^{3} f e^{3} - 5 \, d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} B b^{2} c {\left| d \right|}}{d^{2}} + \frac{4 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(4 \, {\left(d x + c\right)} {\left(6 \, {\left(d x + c\right)} {\left(\frac{8 \, {\left(d x + c\right)}}{d^{4}} - \frac{41 \, c d^{19} f^{8} - d^{20} f^{7} e}{d^{23} f^{8}}\right)} + \frac{513 \, c^{2} d^{19} f^{8} - 26 \, c d^{20} f^{7} e - 7 \, d^{21} f^{6} e^{2}}{d^{23} f^{8}}\right)} - \frac{5 \, {\left(447 \, c^{3} d^{19} f^{8} - 37 \, c^{2} d^{20} f^{7} e - 19 \, c d^{21} f^{6} e^{2} - 7 \, d^{22} f^{5} e^{3}\right)}}{d^{23} f^{8}}\right)} {\left(d x + c\right)} + \frac{15 \, {\left(193 \, c^{4} d^{19} f^{8} - 28 \, c^{3} d^{20} f^{7} e - 18 \, c^{2} d^{21} f^{6} e^{2} - 12 \, c d^{22} f^{5} e^{3} - 7 \, d^{23} f^{4} e^{4}\right)}}{d^{23} f^{8}}\right)} \sqrt{d x + c} + \frac{15 \, {\left(63 \, c^{5} f^{5} - 35 \, c^{4} d f^{4} e - 10 \, c^{3} d^{2} f^{3} e^{2} - 6 \, c^{2} d^{3} f^{2} e^{3} - 5 \, c d^{4} f e^{4} - 7 \, d^{5} e^{5}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{3} f^{4}}\right)} C b^{2} c {\left| d \right|}}{d^{2}} + \frac{320 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} B a^{2} {\left| d \right|}}{d} + \frac{40 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{3}} - \frac{25 \, c d^{11} f^{6} - d^{12} f^{5} e}{d^{14} f^{6}}\right)} + \frac{163 \, c^{2} d^{11} f^{6} - 14 \, c d^{12} f^{5} e - 5 \, d^{13} f^{4} e^{2}}{d^{14} f^{6}}\right)} - \frac{3 \, {\left(93 \, c^{3} d^{11} f^{6} - 15 \, c^{2} d^{12} f^{5} e - 9 \, c d^{13} f^{4} e^{2} - 5 \, d^{14} f^{3} e^{3}\right)}}{d^{14} f^{6}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, c^{4} f^{4} - 20 \, c^{3} d f^{3} e - 6 \, c^{2} d^{2} f^{2} e^{2} - 4 \, c d^{3} f e^{3} - 5 \, d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} C a^{2} {\left| d \right|}}{d} + \frac{640 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} A a b {\left| d \right|}}{d} + \frac{80 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{3}} - \frac{25 \, c d^{11} f^{6} - d^{12} f^{5} e}{d^{14} f^{6}}\right)} + \frac{163 \, c^{2} d^{11} f^{6} - 14 \, c d^{12} f^{5} e - 5 \, d^{13} f^{4} e^{2}}{d^{14} f^{6}}\right)} - \frac{3 \, {\left(93 \, c^{3} d^{11} f^{6} - 15 \, c^{2} d^{12} f^{5} e - 9 \, c d^{13} f^{4} e^{2} - 5 \, d^{14} f^{3} e^{3}\right)}}{d^{14} f^{6}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, c^{4} f^{4} - 20 \, c^{3} d f^{3} e - 6 \, c^{2} d^{2} f^{2} e^{2} - 4 \, c d^{3} f e^{3} - 5 \, d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} B a b {\left| d \right|}}{d} + \frac{8 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(4 \, {\left(d x + c\right)} {\left(6 \, {\left(d x + c\right)} {\left(\frac{8 \, {\left(d x + c\right)}}{d^{4}} - \frac{41 \, c d^{19} f^{8} - d^{20} f^{7} e}{d^{23} f^{8}}\right)} + \frac{513 \, c^{2} d^{19} f^{8} - 26 \, c d^{20} f^{7} e - 7 \, d^{21} f^{6} e^{2}}{d^{23} f^{8}}\right)} - \frac{5 \, {\left(447 \, c^{3} d^{19} f^{8} - 37 \, c^{2} d^{20} f^{7} e - 19 \, c d^{21} f^{6} e^{2} - 7 \, d^{22} f^{5} e^{3}\right)}}{d^{23} f^{8}}\right)} {\left(d x + c\right)} + \frac{15 \, {\left(193 \, c^{4} d^{19} f^{8} - 28 \, c^{3} d^{20} f^{7} e - 18 \, c^{2} d^{21} f^{6} e^{2} - 12 \, c d^{22} f^{5} e^{3} - 7 \, d^{23} f^{4} e^{4}\right)}}{d^{23} f^{8}}\right)} \sqrt{d x + c} + \frac{15 \, {\left(63 \, c^{5} f^{5} - 35 \, c^{4} d f^{4} e - 10 \, c^{3} d^{2} f^{3} e^{2} - 6 \, c^{2} d^{3} f^{2} e^{3} - 5 \, c d^{4} f e^{4} - 7 \, d^{5} e^{5}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{3} f^{4}}\right)} C a b {\left| d \right|}}{d} + \frac{40 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{3}} - \frac{25 \, c d^{11} f^{6} - d^{12} f^{5} e}{d^{14} f^{6}}\right)} + \frac{163 \, c^{2} d^{11} f^{6} - 14 \, c d^{12} f^{5} e - 5 \, d^{13} f^{4} e^{2}}{d^{14} f^{6}}\right)} - \frac{3 \, {\left(93 \, c^{3} d^{11} f^{6} - 15 \, c^{2} d^{12} f^{5} e - 9 \, c d^{13} f^{4} e^{2} - 5 \, d^{14} f^{3} e^{3}\right)}}{d^{14} f^{6}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, c^{4} f^{4} - 20 \, c^{3} d f^{3} e - 6 \, c^{2} d^{2} f^{2} e^{2} - 4 \, c d^{3} f e^{3} - 5 \, d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} A b^{2} {\left| d \right|}}{d} + \frac{4 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(4 \, {\left(d x + c\right)} {\left(6 \, {\left(d x + c\right)} {\left(\frac{8 \, {\left(d x + c\right)}}{d^{4}} - \frac{41 \, c d^{19} f^{8} - d^{20} f^{7} e}{d^{23} f^{8}}\right)} + \frac{513 \, c^{2} d^{19} f^{8} - 26 \, c d^{20} f^{7} e - 7 \, d^{21} f^{6} e^{2}}{d^{23} f^{8}}\right)} - \frac{5 \, {\left(447 \, c^{3} d^{19} f^{8} - 37 \, c^{2} d^{20} f^{7} e - 19 \, c d^{21} f^{6} e^{2} - 7 \, d^{22} f^{5} e^{3}\right)}}{d^{23} f^{8}}\right)} {\left(d x + c\right)} + \frac{15 \, {\left(193 \, c^{4} d^{19} f^{8} - 28 \, c^{3} d^{20} f^{7} e - 18 \, c^{2} d^{21} f^{6} e^{2} - 12 \, c d^{22} f^{5} e^{3} - 7 \, d^{23} f^{4} e^{4}\right)}}{d^{23} f^{8}}\right)} \sqrt{d x + c} + \frac{15 \, {\left(63 \, c^{5} f^{5} - 35 \, c^{4} d f^{4} e - 10 \, c^{3} d^{2} f^{3} e^{2} - 6 \, c^{2} d^{3} f^{2} e^{3} - 5 \, c d^{4} f e^{4} - 7 \, d^{5} e^{5}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{3} f^{4}}\right)} B b^{2} {\left| d \right|}}{d} + \frac{{\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(d x + c\right)} {\left(8 \, {\left(d x + c\right)} {\left(\frac{10 \, {\left(d x + c\right)}}{d^{5}} - \frac{61 \, c d^{29} f^{10} - d^{30} f^{9} e}{d^{34} f^{10}}\right)} + \frac{3 \, {\left(417 \, c^{2} d^{29} f^{10} - 14 \, c d^{30} f^{9} e - 3 \, d^{31} f^{8} e^{2}\right)}}{d^{34} f^{10}}\right)} - \frac{3481 \, c^{3} d^{29} f^{10} - 183 \, c^{2} d^{30} f^{9} e - 77 \, c d^{31} f^{8} e^{2} - 21 \, d^{32} f^{7} e^{3}}{d^{34} f^{10}}\right)} {\left(d x + c\right)} + \frac{5 \, {\left(2279 \, c^{4} d^{29} f^{10} - 176 \, c^{3} d^{30} f^{9} e - 106 \, c^{2} d^{31} f^{8} e^{2} - 56 \, c d^{32} f^{7} e^{3} - 21 \, d^{33} f^{6} e^{4}\right)}}{d^{34} f^{10}}\right)} {\left(d x + c\right)} - \frac{15 \, {\left(793 \, c^{5} d^{29} f^{10} - 105 \, c^{4} d^{30} f^{9} e - 70 \, c^{3} d^{31} f^{8} e^{2} - 50 \, c^{2} d^{32} f^{7} e^{3} - 35 \, c d^{33} f^{6} e^{4} - 21 \, d^{34} f^{5} e^{5}\right)}}{d^{34} f^{10}}\right)} \sqrt{d x + c} - \frac{15 \, {\left(231 \, c^{6} f^{6} - 126 \, c^{5} d f^{5} e - 35 \, c^{4} d^{2} f^{4} e^{2} - 20 \, c^{3} d^{3} f^{3} e^{3} - 15 \, c^{2} d^{4} f^{2} e^{4} - 14 \, c d^{5} f e^{5} - 21 \, d^{6} e^{6}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{4} f^{5}}\right)} C b^{2} {\left| d \right|}}{d} + \frac{1920 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, d x + 2 \, c - \frac{5 \, c f^{2} - d f e}{f^{2}}\right)} \sqrt{d x + c} - \frac{{\left(3 \, c^{2} d f^{2} - 2 \, c d^{2} f e - d^{3} e^{2}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} f}\right)} B a^{2} c {\left| d \right|}}{d^{3}} + \frac{3840 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, d x + 2 \, c - \frac{5 \, c f^{2} - d f e}{f^{2}}\right)} \sqrt{d x + c} - \frac{{\left(3 \, c^{2} d f^{2} - 2 \, c d^{2} f e - d^{3} e^{2}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} f}\right)} A a b c {\left| d \right|}}{d^{3}} + \frac{1920 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, d x + 2 \, c - \frac{5 \, c f^{2} - d f e}{f^{2}}\right)} \sqrt{d x + c} - \frac{{\left(3 \, c^{2} d f^{2} - 2 \, c d^{2} f e - d^{3} e^{2}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} f}\right)} A a^{2} {\left| d \right|}}{d^{2}}}{7680 \, d}"," ",0,"1/7680*(7680*((c*d*f - d^2*e)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/sqrt(d*f) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c))*A*a^2*c*abs(d)/d^2 + 320*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*C*a^2*c*abs(d)/d^2 + 640*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*B*a*b*c*abs(d)/d^2 + 80*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)/d^3 - (25*c*d^11*f^6 - d^12*f^5*e)/(d^14*f^6)) + (163*c^2*d^11*f^6 - 14*c*d^12*f^5*e - 5*d^13*f^4*e^2)/(d^14*f^6)) - 3*(93*c^3*d^11*f^6 - 15*c^2*d^12*f^5*e - 9*c*d^13*f^4*e^2 - 5*d^14*f^3*e^3)/(d^14*f^6))*sqrt(d*x + c) - 3*(35*c^4*f^4 - 20*c^3*d*f^3*e - 6*c^2*d^2*f^2*e^2 - 4*c*d^3*f*e^3 - 5*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*C*a*b*c*abs(d)/d^2 + 320*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*A*b^2*c*abs(d)/d^2 + 40*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)/d^3 - (25*c*d^11*f^6 - d^12*f^5*e)/(d^14*f^6)) + (163*c^2*d^11*f^6 - 14*c*d^12*f^5*e - 5*d^13*f^4*e^2)/(d^14*f^6)) - 3*(93*c^3*d^11*f^6 - 15*c^2*d^12*f^5*e - 9*c*d^13*f^4*e^2 - 5*d^14*f^3*e^3)/(d^14*f^6))*sqrt(d*x + c) - 3*(35*c^4*f^4 - 20*c^3*d*f^3*e - 6*c^2*d^2*f^2*e^2 - 4*c*d^3*f*e^3 - 5*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*B*b^2*c*abs(d)/d^2 + 4*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(4*(d*x + c)*(6*(d*x + c)*(8*(d*x + c)/d^4 - (41*c*d^19*f^8 - d^20*f^7*e)/(d^23*f^8)) + (513*c^2*d^19*f^8 - 26*c*d^20*f^7*e - 7*d^21*f^6*e^2)/(d^23*f^8)) - 5*(447*c^3*d^19*f^8 - 37*c^2*d^20*f^7*e - 19*c*d^21*f^6*e^2 - 7*d^22*f^5*e^3)/(d^23*f^8))*(d*x + c) + 15*(193*c^4*d^19*f^8 - 28*c^3*d^20*f^7*e - 18*c^2*d^21*f^6*e^2 - 12*c*d^22*f^5*e^3 - 7*d^23*f^4*e^4)/(d^23*f^8))*sqrt(d*x + c) + 15*(63*c^5*f^5 - 35*c^4*d*f^4*e - 10*c^3*d^2*f^3*e^2 - 6*c^2*d^3*f^2*e^3 - 5*c*d^4*f*e^4 - 7*d^5*e^5)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^3*f^4))*C*b^2*c*abs(d)/d^2 + 320*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*B*a^2*abs(d)/d + 40*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)/d^3 - (25*c*d^11*f^6 - d^12*f^5*e)/(d^14*f^6)) + (163*c^2*d^11*f^6 - 14*c*d^12*f^5*e - 5*d^13*f^4*e^2)/(d^14*f^6)) - 3*(93*c^3*d^11*f^6 - 15*c^2*d^12*f^5*e - 9*c*d^13*f^4*e^2 - 5*d^14*f^3*e^3)/(d^14*f^6))*sqrt(d*x + c) - 3*(35*c^4*f^4 - 20*c^3*d*f^3*e - 6*c^2*d^2*f^2*e^2 - 4*c*d^3*f*e^3 - 5*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*C*a^2*abs(d)/d + 640*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*A*a*b*abs(d)/d + 80*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)/d^3 - (25*c*d^11*f^6 - d^12*f^5*e)/(d^14*f^6)) + (163*c^2*d^11*f^6 - 14*c*d^12*f^5*e - 5*d^13*f^4*e^2)/(d^14*f^6)) - 3*(93*c^3*d^11*f^6 - 15*c^2*d^12*f^5*e - 9*c*d^13*f^4*e^2 - 5*d^14*f^3*e^3)/(d^14*f^6))*sqrt(d*x + c) - 3*(35*c^4*f^4 - 20*c^3*d*f^3*e - 6*c^2*d^2*f^2*e^2 - 4*c*d^3*f*e^3 - 5*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*B*a*b*abs(d)/d + 8*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(4*(d*x + c)*(6*(d*x + c)*(8*(d*x + c)/d^4 - (41*c*d^19*f^8 - d^20*f^7*e)/(d^23*f^8)) + (513*c^2*d^19*f^8 - 26*c*d^20*f^7*e - 7*d^21*f^6*e^2)/(d^23*f^8)) - 5*(447*c^3*d^19*f^8 - 37*c^2*d^20*f^7*e - 19*c*d^21*f^6*e^2 - 7*d^22*f^5*e^3)/(d^23*f^8))*(d*x + c) + 15*(193*c^4*d^19*f^8 - 28*c^3*d^20*f^7*e - 18*c^2*d^21*f^6*e^2 - 12*c*d^22*f^5*e^3 - 7*d^23*f^4*e^4)/(d^23*f^8))*sqrt(d*x + c) + 15*(63*c^5*f^5 - 35*c^4*d*f^4*e - 10*c^3*d^2*f^3*e^2 - 6*c^2*d^3*f^2*e^3 - 5*c*d^4*f*e^4 - 7*d^5*e^5)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^3*f^4))*C*a*b*abs(d)/d + 40*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)/d^3 - (25*c*d^11*f^6 - d^12*f^5*e)/(d^14*f^6)) + (163*c^2*d^11*f^6 - 14*c*d^12*f^5*e - 5*d^13*f^4*e^2)/(d^14*f^6)) - 3*(93*c^3*d^11*f^6 - 15*c^2*d^12*f^5*e - 9*c*d^13*f^4*e^2 - 5*d^14*f^3*e^3)/(d^14*f^6))*sqrt(d*x + c) - 3*(35*c^4*f^4 - 20*c^3*d*f^3*e - 6*c^2*d^2*f^2*e^2 - 4*c*d^3*f*e^3 - 5*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*A*b^2*abs(d)/d + 4*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(4*(d*x + c)*(6*(d*x + c)*(8*(d*x + c)/d^4 - (41*c*d^19*f^8 - d^20*f^7*e)/(d^23*f^8)) + (513*c^2*d^19*f^8 - 26*c*d^20*f^7*e - 7*d^21*f^6*e^2)/(d^23*f^8)) - 5*(447*c^3*d^19*f^8 - 37*c^2*d^20*f^7*e - 19*c*d^21*f^6*e^2 - 7*d^22*f^5*e^3)/(d^23*f^8))*(d*x + c) + 15*(193*c^4*d^19*f^8 - 28*c^3*d^20*f^7*e - 18*c^2*d^21*f^6*e^2 - 12*c*d^22*f^5*e^3 - 7*d^23*f^4*e^4)/(d^23*f^8))*sqrt(d*x + c) + 15*(63*c^5*f^5 - 35*c^4*d*f^4*e - 10*c^3*d^2*f^3*e^2 - 6*c^2*d^3*f^2*e^3 - 5*c*d^4*f*e^4 - 7*d^5*e^5)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^3*f^4))*B*b^2*abs(d)/d + (sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(4*(2*(d*x + c)*(8*(d*x + c)*(10*(d*x + c)/d^5 - (61*c*d^29*f^10 - d^30*f^9*e)/(d^34*f^10)) + 3*(417*c^2*d^29*f^10 - 14*c*d^30*f^9*e - 3*d^31*f^8*e^2)/(d^34*f^10)) - (3481*c^3*d^29*f^10 - 183*c^2*d^30*f^9*e - 77*c*d^31*f^8*e^2 - 21*d^32*f^7*e^3)/(d^34*f^10))*(d*x + c) + 5*(2279*c^4*d^29*f^10 - 176*c^3*d^30*f^9*e - 106*c^2*d^31*f^8*e^2 - 56*c*d^32*f^7*e^3 - 21*d^33*f^6*e^4)/(d^34*f^10))*(d*x + c) - 15*(793*c^5*d^29*f^10 - 105*c^4*d^30*f^9*e - 70*c^3*d^31*f^8*e^2 - 50*c^2*d^32*f^7*e^3 - 35*c*d^33*f^6*e^4 - 21*d^34*f^5*e^5)/(d^34*f^10))*sqrt(d*x + c) - 15*(231*c^6*f^6 - 126*c^5*d*f^5*e - 35*c^4*d^2*f^4*e^2 - 20*c^3*d^3*f^3*e^3 - 15*c^2*d^4*f^2*e^4 - 14*c*d^5*f*e^5 - 21*d^6*e^6)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^4*f^5))*C*b^2*abs(d)/d + 1920*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*d*x + 2*c - (5*c*f^2 - d*f*e)/f^2)*sqrt(d*x + c) - (3*c^2*d*f^2 - 2*c*d^2*f*e - d^3*e^2)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*f))*B*a^2*c*abs(d)/d^3 + 3840*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*d*x + 2*c - (5*c*f^2 - d*f*e)/f^2)*sqrt(d*x + c) - (3*c^2*d*f^2 - 2*c*d^2*f*e - d^3*e^2)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*f))*A*a*b*c*abs(d)/d^3 + 1920*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*d*x + 2*c - (5*c*f^2 - d*f*e)/f^2)*sqrt(d*x + c) - (3*c^2*d*f^2 - 2*c*d^2*f*e - d^3*e^2)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*f))*A*a^2*abs(d)/d^2)/d","B",0
42,1,2643,0,3.388745," ","integrate((b*x+a)*(C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{\frac{1920 \, {\left(\frac{{\left(c d f - d^{2} e\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f}} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c}\right)} A a c {\left| d \right|}}{d^{2}} + \frac{80 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} C a c {\left| d \right|}}{d^{2}} + \frac{80 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} B b c {\left| d \right|}}{d^{2}} + \frac{10 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{3}} - \frac{25 \, c d^{11} f^{6} - d^{12} f^{5} e}{d^{14} f^{6}}\right)} + \frac{163 \, c^{2} d^{11} f^{6} - 14 \, c d^{12} f^{5} e - 5 \, d^{13} f^{4} e^{2}}{d^{14} f^{6}}\right)} - \frac{3 \, {\left(93 \, c^{3} d^{11} f^{6} - 15 \, c^{2} d^{12} f^{5} e - 9 \, c d^{13} f^{4} e^{2} - 5 \, d^{14} f^{3} e^{3}\right)}}{d^{14} f^{6}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, c^{4} f^{4} - 20 \, c^{3} d f^{3} e - 6 \, c^{2} d^{2} f^{2} e^{2} - 4 \, c d^{3} f e^{3} - 5 \, d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} C b c {\left| d \right|}}{d^{2}} + \frac{80 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} B a {\left| d \right|}}{d} + \frac{10 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{3}} - \frac{25 \, c d^{11} f^{6} - d^{12} f^{5} e}{d^{14} f^{6}}\right)} + \frac{163 \, c^{2} d^{11} f^{6} - 14 \, c d^{12} f^{5} e - 5 \, d^{13} f^{4} e^{2}}{d^{14} f^{6}}\right)} - \frac{3 \, {\left(93 \, c^{3} d^{11} f^{6} - 15 \, c^{2} d^{12} f^{5} e - 9 \, c d^{13} f^{4} e^{2} - 5 \, d^{14} f^{3} e^{3}\right)}}{d^{14} f^{6}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, c^{4} f^{4} - 20 \, c^{3} d f^{3} e - 6 \, c^{2} d^{2} f^{2} e^{2} - 4 \, c d^{3} f e^{3} - 5 \, d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} C a {\left| d \right|}}{d} + \frac{80 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} A b {\left| d \right|}}{d} + \frac{10 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{3}} - \frac{25 \, c d^{11} f^{6} - d^{12} f^{5} e}{d^{14} f^{6}}\right)} + \frac{163 \, c^{2} d^{11} f^{6} - 14 \, c d^{12} f^{5} e - 5 \, d^{13} f^{4} e^{2}}{d^{14} f^{6}}\right)} - \frac{3 \, {\left(93 \, c^{3} d^{11} f^{6} - 15 \, c^{2} d^{12} f^{5} e - 9 \, c d^{13} f^{4} e^{2} - 5 \, d^{14} f^{3} e^{3}\right)}}{d^{14} f^{6}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, c^{4} f^{4} - 20 \, c^{3} d f^{3} e - 6 \, c^{2} d^{2} f^{2} e^{2} - 4 \, c d^{3} f e^{3} - 5 \, d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} B b {\left| d \right|}}{d} + \frac{{\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(4 \, {\left(d x + c\right)} {\left(6 \, {\left(d x + c\right)} {\left(\frac{8 \, {\left(d x + c\right)}}{d^{4}} - \frac{41 \, c d^{19} f^{8} - d^{20} f^{7} e}{d^{23} f^{8}}\right)} + \frac{513 \, c^{2} d^{19} f^{8} - 26 \, c d^{20} f^{7} e - 7 \, d^{21} f^{6} e^{2}}{d^{23} f^{8}}\right)} - \frac{5 \, {\left(447 \, c^{3} d^{19} f^{8} - 37 \, c^{2} d^{20} f^{7} e - 19 \, c d^{21} f^{6} e^{2} - 7 \, d^{22} f^{5} e^{3}\right)}}{d^{23} f^{8}}\right)} {\left(d x + c\right)} + \frac{15 \, {\left(193 \, c^{4} d^{19} f^{8} - 28 \, c^{3} d^{20} f^{7} e - 18 \, c^{2} d^{21} f^{6} e^{2} - 12 \, c d^{22} f^{5} e^{3} - 7 \, d^{23} f^{4} e^{4}\right)}}{d^{23} f^{8}}\right)} \sqrt{d x + c} + \frac{15 \, {\left(63 \, c^{5} f^{5} - 35 \, c^{4} d f^{4} e - 10 \, c^{3} d^{2} f^{3} e^{2} - 6 \, c^{2} d^{3} f^{2} e^{3} - 5 \, c d^{4} f e^{4} - 7 \, d^{5} e^{5}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{3} f^{4}}\right)} C b {\left| d \right|}}{d} + \frac{480 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, d x + 2 \, c - \frac{5 \, c f^{2} - d f e}{f^{2}}\right)} \sqrt{d x + c} - \frac{{\left(3 \, c^{2} d f^{2} - 2 \, c d^{2} f e - d^{3} e^{2}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} f}\right)} B a c {\left| d \right|}}{d^{3}} + \frac{480 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, d x + 2 \, c - \frac{5 \, c f^{2} - d f e}{f^{2}}\right)} \sqrt{d x + c} - \frac{{\left(3 \, c^{2} d f^{2} - 2 \, c d^{2} f e - d^{3} e^{2}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} f}\right)} A b c {\left| d \right|}}{d^{3}} + \frac{480 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, d x + 2 \, c - \frac{5 \, c f^{2} - d f e}{f^{2}}\right)} \sqrt{d x + c} - \frac{{\left(3 \, c^{2} d f^{2} - 2 \, c d^{2} f e - d^{3} e^{2}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} f}\right)} A a {\left| d \right|}}{d^{2}}}{1920 \, d}"," ",0,"1/1920*(1920*((c*d*f - d^2*e)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/sqrt(d*f) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c))*A*a*c*abs(d)/d^2 + 80*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*C*a*c*abs(d)/d^2 + 80*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*B*b*c*abs(d)/d^2 + 10*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)/d^3 - (25*c*d^11*f^6 - d^12*f^5*e)/(d^14*f^6)) + (163*c^2*d^11*f^6 - 14*c*d^12*f^5*e - 5*d^13*f^4*e^2)/(d^14*f^6)) - 3*(93*c^3*d^11*f^6 - 15*c^2*d^12*f^5*e - 9*c*d^13*f^4*e^2 - 5*d^14*f^3*e^3)/(d^14*f^6))*sqrt(d*x + c) - 3*(35*c^4*f^4 - 20*c^3*d*f^3*e - 6*c^2*d^2*f^2*e^2 - 4*c*d^3*f*e^3 - 5*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*C*b*c*abs(d)/d^2 + 80*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*B*a*abs(d)/d + 10*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)/d^3 - (25*c*d^11*f^6 - d^12*f^5*e)/(d^14*f^6)) + (163*c^2*d^11*f^6 - 14*c*d^12*f^5*e - 5*d^13*f^4*e^2)/(d^14*f^6)) - 3*(93*c^3*d^11*f^6 - 15*c^2*d^12*f^5*e - 9*c*d^13*f^4*e^2 - 5*d^14*f^3*e^3)/(d^14*f^6))*sqrt(d*x + c) - 3*(35*c^4*f^4 - 20*c^3*d*f^3*e - 6*c^2*d^2*f^2*e^2 - 4*c*d^3*f*e^3 - 5*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*C*a*abs(d)/d + 80*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*A*b*abs(d)/d + 10*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)/d^3 - (25*c*d^11*f^6 - d^12*f^5*e)/(d^14*f^6)) + (163*c^2*d^11*f^6 - 14*c*d^12*f^5*e - 5*d^13*f^4*e^2)/(d^14*f^6)) - 3*(93*c^3*d^11*f^6 - 15*c^2*d^12*f^5*e - 9*c*d^13*f^4*e^2 - 5*d^14*f^3*e^3)/(d^14*f^6))*sqrt(d*x + c) - 3*(35*c^4*f^4 - 20*c^3*d*f^3*e - 6*c^2*d^2*f^2*e^2 - 4*c*d^3*f*e^3 - 5*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*B*b*abs(d)/d + (sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(4*(d*x + c)*(6*(d*x + c)*(8*(d*x + c)/d^4 - (41*c*d^19*f^8 - d^20*f^7*e)/(d^23*f^8)) + (513*c^2*d^19*f^8 - 26*c*d^20*f^7*e - 7*d^21*f^6*e^2)/(d^23*f^8)) - 5*(447*c^3*d^19*f^8 - 37*c^2*d^20*f^7*e - 19*c*d^21*f^6*e^2 - 7*d^22*f^5*e^3)/(d^23*f^8))*(d*x + c) + 15*(193*c^4*d^19*f^8 - 28*c^3*d^20*f^7*e - 18*c^2*d^21*f^6*e^2 - 12*c*d^22*f^5*e^3 - 7*d^23*f^4*e^4)/(d^23*f^8))*sqrt(d*x + c) + 15*(63*c^5*f^5 - 35*c^4*d*f^4*e - 10*c^3*d^2*f^3*e^2 - 6*c^2*d^3*f^2*e^3 - 5*c*d^4*f*e^4 - 7*d^5*e^5)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^3*f^4))*C*b*abs(d)/d + 480*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*d*x + 2*c - (5*c*f^2 - d*f*e)/f^2)*sqrt(d*x + c) - (3*c^2*d*f^2 - 2*c*d^2*f*e - d^3*e^2)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*f))*B*a*c*abs(d)/d^3 + 480*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*d*x + 2*c - (5*c*f^2 - d*f*e)/f^2)*sqrt(d*x + c) - (3*c^2*d*f^2 - 2*c*d^2*f*e - d^3*e^2)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*f))*A*b*c*abs(d)/d^3 + 480*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*d*x + 2*c - (5*c*f^2 - d*f*e)/f^2)*sqrt(d*x + c) - (3*c^2*d*f^2 - 2*c*d^2*f*e - d^3*e^2)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*f))*A*a*abs(d)/d^2)/d","B",0
43,1,1103,0,2.334211," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{\frac{192 \, {\left(\frac{{\left(c d f - d^{2} e\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f}} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c}\right)} A c {\left| d \right|}}{d^{2}} + \frac{8 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} C c {\left| d \right|}}{d^{2}} + \frac{8 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{2}} - \frac{13 \, c d^{5} f^{4} - d^{6} f^{3} e}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(11 \, c^{2} d^{5} f^{4} - 2 \, c d^{6} f^{3} e - d^{7} f^{2} e^{2}\right)}}{d^{7} f^{4}}\right)} + \frac{3 \, {\left(5 \, c^{3} f^{3} - 3 \, c^{2} d f^{2} e - c d^{2} f e^{2} - d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d f^{2}}\right)} B {\left| d \right|}}{d} + \frac{{\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{3}} - \frac{25 \, c d^{11} f^{6} - d^{12} f^{5} e}{d^{14} f^{6}}\right)} + \frac{163 \, c^{2} d^{11} f^{6} - 14 \, c d^{12} f^{5} e - 5 \, d^{13} f^{4} e^{2}}{d^{14} f^{6}}\right)} - \frac{3 \, {\left(93 \, c^{3} d^{11} f^{6} - 15 \, c^{2} d^{12} f^{5} e - 9 \, c d^{13} f^{4} e^{2} - 5 \, d^{14} f^{3} e^{3}\right)}}{d^{14} f^{6}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, c^{4} f^{4} - 20 \, c^{3} d f^{3} e - 6 \, c^{2} d^{2} f^{2} e^{2} - 4 \, c d^{3} f e^{3} - 5 \, d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} C {\left| d \right|}}{d} + \frac{48 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, d x + 2 \, c - \frac{5 \, c f^{2} - d f e}{f^{2}}\right)} \sqrt{d x + c} - \frac{{\left(3 \, c^{2} d f^{2} - 2 \, c d^{2} f e - d^{3} e^{2}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} f}\right)} B c {\left| d \right|}}{d^{3}} + \frac{48 \, {\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, d x + 2 \, c - \frac{5 \, c f^{2} - d f e}{f^{2}}\right)} \sqrt{d x + c} - \frac{{\left(3 \, c^{2} d f^{2} - 2 \, c d^{2} f e - d^{3} e^{2}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} f}\right)} A {\left| d \right|}}{d^{2}}}{192 \, d}"," ",0,"1/192*(192*((c*d*f - d^2*e)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/sqrt(d*f) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c))*A*c*abs(d)/d^2 + 8*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*C*c*abs(d)/d^2 + 8*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)/d^2 - (13*c*d^5*f^4 - d^6*f^3*e)/(d^7*f^4)) + 3*(11*c^2*d^5*f^4 - 2*c*d^6*f^3*e - d^7*f^2*e^2)/(d^7*f^4)) + 3*(5*c^3*f^3 - 3*c^2*d*f^2*e - c*d^2*f*e^2 - d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d*f^2))*B*abs(d)/d + (sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)/d^3 - (25*c*d^11*f^6 - d^12*f^5*e)/(d^14*f^6)) + (163*c^2*d^11*f^6 - 14*c*d^12*f^5*e - 5*d^13*f^4*e^2)/(d^14*f^6)) - 3*(93*c^3*d^11*f^6 - 15*c^2*d^12*f^5*e - 9*c*d^13*f^4*e^2 - 5*d^14*f^3*e^3)/(d^14*f^6))*sqrt(d*x + c) - 3*(35*c^4*f^4 - 20*c^3*d*f^3*e - 6*c^2*d^2*f^2*e^2 - 4*c*d^3*f*e^3 - 5*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*C*abs(d)/d + 48*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*d*x + 2*c - (5*c*f^2 - d*f*e)/f^2)*sqrt(d*x + c) - (3*c^2*d*f^2 - 2*c*d^2*f*e - d^3*e^2)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*f))*B*c*abs(d)/d^3 + 48*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*d*x + 2*c - (5*c*f^2 - d*f*e)/f^2)*sqrt(d*x + c) - (3*c^2*d*f^2 - 2*c*d^2*f*e - d^3*e^2)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*f))*A*abs(d)/d^2)/d","B",0
44,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a),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: 1.1"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
45,1,1585,0,13.122429," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^2,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(\frac{2 \, {\left(d x + c\right)} C {\left| d \right|}}{b^{2} d^{3}} - \frac{C b^{7} c d^{3} f^{2} {\left| d \right|} + 8 \, C a b^{6} d^{4} f^{2} {\left| d \right|} - 4 \, B b^{7} d^{4} f^{2} {\left| d \right|} - C b^{7} d^{4} f {\left| d \right|} e}{b^{9} d^{6} f^{2}}\right)} - \frac{{\left(5 \, \sqrt{d f} C a^{2} b c f {\left| d \right|} - 3 \, \sqrt{d f} B a b^{2} c f {\left| d \right|} + \sqrt{d f} A b^{3} c f {\left| d \right|} - 6 \, \sqrt{d f} C a^{3} d f {\left| d \right|} + 4 \, \sqrt{d f} B a^{2} b d f {\left| d \right|} - 2 \, \sqrt{d f} A a b^{2} d f {\left| d \right|} - 4 \, \sqrt{d f} C a b^{2} c {\left| d \right|} e + 2 \, \sqrt{d f} B b^{3} c {\left| d \right|} e + 5 \, \sqrt{d f} C a^{2} b d {\left| d \right|} e - 3 \, \sqrt{d f} B a b^{2} d {\left| d \right|} e + \sqrt{d f} A b^{3} d {\left| d \right|} e\right)} \arctan\left(-\frac{b c d f - 2 \, a d^{2} f + b d^{2} e - {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b}{2 \, \sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} d}\right)}{\sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} b^{4} d} - \frac{2 \, {\left(\sqrt{d f} C a^{2} b c^{2} d f^{2} {\left| d \right|} - \sqrt{d f} B a b^{2} c^{2} d f^{2} {\left| d \right|} + \sqrt{d f} A b^{3} c^{2} d f^{2} {\left| d \right|} - 2 \, \sqrt{d f} C a^{2} b c d^{2} f {\left| d \right|} e + 2 \, \sqrt{d f} B a b^{2} c d^{2} f {\left| d \right|} e - 2 \, \sqrt{d f} A b^{3} c d^{2} f {\left| d \right|} e - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b c f {\left| d \right|} + \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{2} c f {\left| d \right|} - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{3} c f {\left| d \right|} + 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} d f {\left| d \right|} - 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b d f {\left| d \right|} + 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{2} d f {\left| d \right|} + \sqrt{d f} C a^{2} b d^{3} {\left| d \right|} e^{2} - \sqrt{d f} B a b^{2} d^{3} {\left| d \right|} e^{2} + \sqrt{d f} A b^{3} d^{3} {\left| d \right|} e^{2} - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b d {\left| d \right|} e + \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{2} d {\left| d \right|} e - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{3} d {\left| d \right|} e\right)}}{{\left(b c^{2} d^{2} f^{2} - 2 \, b c d^{3} f e - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b c d f + 4 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} a d^{2} f + b d^{4} e^{2} - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b d^{2} e + {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} b\right)} b^{4}} + \frac{{\left(\sqrt{d f} C b^{2} c^{2} f^{2} {\left| d \right|} + 8 \, \sqrt{d f} C a b c d f^{2} {\left| d \right|} - 4 \, \sqrt{d f} B b^{2} c d f^{2} {\left| d \right|} - 24 \, \sqrt{d f} C a^{2} d^{2} f^{2} {\left| d \right|} + 16 \, \sqrt{d f} B a b d^{2} f^{2} {\left| d \right|} - 8 \, \sqrt{d f} A b^{2} d^{2} f^{2} {\left| d \right|} - 2 \, \sqrt{d f} C b^{2} c d f {\left| d \right|} e + 8 \, \sqrt{d f} C a b d^{2} f {\left| d \right|} e - 4 \, \sqrt{d f} B b^{2} d^{2} f {\left| d \right|} e + \sqrt{d f} C b^{2} d^{2} {\left| d \right|} e^{2}\right)} \log\left({\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2}\right)}{8 \, b^{4} d^{3} f^{2}}"," ",0,"1/4*sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*C*abs(d)/(b^2*d^3) - (C*b^7*c*d^3*f^2*abs(d) + 8*C*a*b^6*d^4*f^2*abs(d) - 4*B*b^7*d^4*f^2*abs(d) - C*b^7*d^4*f*abs(d)*e)/(b^9*d^6*f^2)) - (5*sqrt(d*f)*C*a^2*b*c*f*abs(d) - 3*sqrt(d*f)*B*a*b^2*c*f*abs(d) + sqrt(d*f)*A*b^3*c*f*abs(d) - 6*sqrt(d*f)*C*a^3*d*f*abs(d) + 4*sqrt(d*f)*B*a^2*b*d*f*abs(d) - 2*sqrt(d*f)*A*a*b^2*d*f*abs(d) - 4*sqrt(d*f)*C*a*b^2*c*abs(d)*e + 2*sqrt(d*f)*B*b^3*c*abs(d)*e + 5*sqrt(d*f)*C*a^2*b*d*abs(d)*e - 3*sqrt(d*f)*B*a*b^2*d*abs(d)*e + sqrt(d*f)*A*b^3*d*abs(d)*e)*arctan(-1/2*(b*c*d*f - 2*a*d^2*f + b*d^2*e - (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b)/(sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*d))/(sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*b^4*d) - 2*(sqrt(d*f)*C*a^2*b*c^2*d*f^2*abs(d) - sqrt(d*f)*B*a*b^2*c^2*d*f^2*abs(d) + sqrt(d*f)*A*b^3*c^2*d*f^2*abs(d) - 2*sqrt(d*f)*C*a^2*b*c*d^2*f*abs(d)*e + 2*sqrt(d*f)*B*a*b^2*c*d^2*f*abs(d)*e - 2*sqrt(d*f)*A*b^3*c*d^2*f*abs(d)*e - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b*c*f*abs(d) + sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^2*c*f*abs(d) - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^3*c*f*abs(d) + 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*d*f*abs(d) - 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b*d*f*abs(d) + 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^2*d*f*abs(d) + sqrt(d*f)*C*a^2*b*d^3*abs(d)*e^2 - sqrt(d*f)*B*a*b^2*d^3*abs(d)*e^2 + sqrt(d*f)*A*b^3*d^3*abs(d)*e^2 - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b*d*abs(d)*e + sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^2*d*abs(d)*e - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^3*d*abs(d)*e)/((b*c^2*d^2*f^2 - 2*b*c*d^3*f*e - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*c*d*f + 4*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*a*d^2*f + b*d^4*e^2 - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*d^2*e + (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*b)*b^4) + 1/8*(sqrt(d*f)*C*b^2*c^2*f^2*abs(d) + 8*sqrt(d*f)*C*a*b*c*d*f^2*abs(d) - 4*sqrt(d*f)*B*b^2*c*d*f^2*abs(d) - 24*sqrt(d*f)*C*a^2*d^2*f^2*abs(d) + 16*sqrt(d*f)*B*a*b*d^2*f^2*abs(d) - 8*sqrt(d*f)*A*b^2*d^2*f^2*abs(d) - 2*sqrt(d*f)*C*b^2*c*d*f*abs(d)*e + 8*sqrt(d*f)*C*a*b*d^2*f*abs(d)*e - 4*sqrt(d*f)*B*b^2*d^2*f*abs(d)*e + sqrt(d*f)*C*b^2*d^2*abs(d)*e^2)*log((sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2)/(b^4*d^3*f^2)","B",0
46,1,8347,0,39.569279," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(15 \, \sqrt{d f} C a^{2} b^{2} c^{2} f^{2} {\left| d \right|} - 3 \, \sqrt{d f} B a b^{3} c^{2} f^{2} {\left| d \right|} - \sqrt{d f} A b^{4} c^{2} f^{2} {\left| d \right|} - 40 \, \sqrt{d f} C a^{3} b c d f^{2} {\left| d \right|} + 12 \, \sqrt{d f} B a^{2} b^{2} c d f^{2} {\left| d \right|} + 24 \, \sqrt{d f} C a^{4} d^{2} f^{2} {\left| d \right|} - 8 \, \sqrt{d f} B a^{3} b d^{2} f^{2} {\left| d \right|} - 24 \, \sqrt{d f} C a b^{3} c^{2} f {\left| d \right|} e + 4 \, \sqrt{d f} B b^{4} c^{2} f {\left| d \right|} e + 66 \, \sqrt{d f} C a^{2} b^{2} c d f {\left| d \right|} e - 18 \, \sqrt{d f} B a b^{3} c d f {\left| d \right|} e + 2 \, \sqrt{d f} A b^{4} c d f {\left| d \right|} e - 40 \, \sqrt{d f} C a^{3} b d^{2} f {\left| d \right|} e + 12 \, \sqrt{d f} B a^{2} b^{2} d^{2} f {\left| d \right|} e + 8 \, \sqrt{d f} C b^{4} c^{2} {\left| d \right|} e^{2} - 24 \, \sqrt{d f} C a b^{3} c d {\left| d \right|} e^{2} + 4 \, \sqrt{d f} B b^{4} c d {\left| d \right|} e^{2} + 15 \, \sqrt{d f} C a^{2} b^{2} d^{2} {\left| d \right|} e^{2} - 3 \, \sqrt{d f} B a b^{3} d^{2} {\left| d \right|} e^{2} - \sqrt{d f} A b^{4} d^{2} {\left| d \right|} e^{2}\right)} \arctan\left(-\frac{b c d f - 2 \, a d^{2} f + b d^{2} e - {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b}{2 \, \sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} d}\right)}{4 \, {\left(a b^{5} c f - a^{2} b^{4} d f - b^{6} c e + a b^{5} d e\right)} \sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} d} + \frac{9 \, \sqrt{d f} C a^{2} b^{3} c^{5} d^{3} f^{5} {\left| d \right|} - 5 \, \sqrt{d f} B a b^{4} c^{5} d^{3} f^{5} {\left| d \right|} + \sqrt{d f} A b^{5} c^{5} d^{3} f^{5} {\left| d \right|} - 10 \, \sqrt{d f} C a^{3} b^{2} c^{4} d^{4} f^{5} {\left| d \right|} + 6 \, \sqrt{d f} B a^{2} b^{3} c^{4} d^{4} f^{5} {\left| d \right|} - 2 \, \sqrt{d f} A a b^{4} c^{4} d^{4} f^{5} {\left| d \right|} - 8 \, \sqrt{d f} C a b^{4} c^{5} d^{3} f^{4} {\left| d \right|} e + 4 \, \sqrt{d f} B b^{5} c^{5} d^{3} f^{4} {\left| d \right|} e - 27 \, \sqrt{d f} C a^{2} b^{3} c^{4} d^{4} f^{4} {\left| d \right|} e + 15 \, \sqrt{d f} B a b^{4} c^{4} d^{4} f^{4} {\left| d \right|} e - 3 \, \sqrt{d f} A b^{5} c^{4} d^{4} f^{4} {\left| d \right|} e + 40 \, \sqrt{d f} C a^{3} b^{2} c^{3} d^{5} f^{4} {\left| d \right|} e - 24 \, \sqrt{d f} B a^{2} b^{3} c^{3} d^{5} f^{4} {\left| d \right|} e + 8 \, \sqrt{d f} A a b^{4} c^{3} d^{5} f^{4} {\left| d \right|} e - 27 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} c^{4} d^{2} f^{4} {\left| d \right|} + 15 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} c^{4} d^{2} f^{4} {\left| d \right|} - 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} c^{4} d^{2} f^{4} {\left| d \right|} + 80 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} b^{2} c^{3} d^{3} f^{4} {\left| d \right|} - 44 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b^{3} c^{3} d^{3} f^{4} {\left| d \right|} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{4} c^{3} d^{3} f^{4} {\left| d \right|} - 56 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{4} b c^{2} d^{4} f^{4} {\left| d \right|} + 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{3} b^{2} c^{2} d^{4} f^{4} {\left| d \right|} - 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a^{2} b^{3} c^{2} d^{4} f^{4} {\left| d \right|} + 32 \, \sqrt{d f} C a b^{4} c^{4} d^{4} f^{3} {\left| d \right|} e^{2} - 16 \, \sqrt{d f} B b^{5} c^{4} d^{4} f^{3} {\left| d \right|} e^{2} + 18 \, \sqrt{d f} C a^{2} b^{3} c^{3} d^{5} f^{3} {\left| d \right|} e^{2} - 10 \, \sqrt{d f} B a b^{4} c^{3} d^{5} f^{3} {\left| d \right|} e^{2} + 2 \, \sqrt{d f} A b^{5} c^{3} d^{5} f^{3} {\left| d \right|} e^{2} - 60 \, \sqrt{d f} C a^{3} b^{2} c^{2} d^{6} f^{3} {\left| d \right|} e^{2} + 36 \, \sqrt{d f} B a^{2} b^{3} c^{2} d^{6} f^{3} {\left| d \right|} e^{2} - 12 \, \sqrt{d f} A a b^{4} c^{2} d^{6} f^{3} {\left| d \right|} e^{2} + 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a b^{4} c^{4} d^{2} f^{3} {\left| d \right|} e - 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B b^{5} c^{4} d^{2} f^{3} {\left| d \right|} e - 44 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} c^{3} d^{3} f^{3} {\left| d \right|} e + 20 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} c^{3} d^{3} f^{3} {\left| d \right|} e + 4 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} c^{3} d^{3} f^{3} {\left| d \right|} e - 80 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} b^{2} c^{2} d^{4} f^{3} {\left| d \right|} e + 44 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b^{3} c^{2} d^{4} f^{3} {\left| d \right|} e - 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{4} c^{2} d^{4} f^{3} {\left| d \right|} e + 112 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{4} b c d^{5} f^{3} {\left| d \right|} e - 64 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{3} b^{2} c d^{5} f^{3} {\left| d \right|} e + 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a^{2} b^{3} c d^{5} f^{3} {\left| d \right|} e + 27 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{2} b^{3} c^{3} d f^{3} {\left| d \right|} - 15 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a b^{4} c^{3} d f^{3} {\left| d \right|} + 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A b^{5} c^{3} d f^{3} {\left| d \right|} - 102 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{3} b^{2} c^{2} d^{2} f^{3} {\left| d \right|} + 58 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{2} b^{3} c^{2} d^{2} f^{3} {\left| d \right|} - 14 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a b^{4} c^{2} d^{2} f^{3} {\left| d \right|} + 152 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{4} b c d^{3} f^{3} {\left| d \right|} - 88 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{3} b^{2} c d^{3} f^{3} {\left| d \right|} + 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a^{2} b^{3} c d^{3} f^{3} {\left| d \right|} - 80 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{5} d^{4} f^{3} {\left| d \right|} + 48 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{4} b d^{4} f^{3} {\left| d \right|} - 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a^{3} b^{2} d^{4} f^{3} {\left| d \right|} - 48 \, \sqrt{d f} C a b^{4} c^{3} d^{5} f^{2} {\left| d \right|} e^{3} + 24 \, \sqrt{d f} B b^{5} c^{3} d^{5} f^{2} {\left| d \right|} e^{3} + 18 \, \sqrt{d f} C a^{2} b^{3} c^{2} d^{6} f^{2} {\left| d \right|} e^{3} - 10 \, \sqrt{d f} B a b^{4} c^{2} d^{6} f^{2} {\left| d \right|} e^{3} + 2 \, \sqrt{d f} A b^{5} c^{2} d^{6} f^{2} {\left| d \right|} e^{3} + 40 \, \sqrt{d f} C a^{3} b^{2} c d^{7} f^{2} {\left| d \right|} e^{3} - 24 \, \sqrt{d f} B a^{2} b^{3} c d^{7} f^{2} {\left| d \right|} e^{3} + 8 \, \sqrt{d f} A a b^{4} c d^{7} f^{2} {\left| d \right|} e^{3} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a b^{4} c^{3} d^{3} f^{2} {\left| d \right|} e^{2} + 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B b^{5} c^{3} d^{3} f^{2} {\left| d \right|} e^{2} + 142 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} c^{2} d^{4} f^{2} {\left| d \right|} e^{2} - 70 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} c^{2} d^{4} f^{2} {\left| d \right|} e^{2} - 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} c^{2} d^{4} f^{2} {\left| d \right|} e^{2} - 80 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} b^{2} c d^{5} f^{2} {\left| d \right|} e^{2} + 44 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b^{3} c d^{5} f^{2} {\left| d \right|} e^{2} - 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{4} c d^{5} f^{2} {\left| d \right|} e^{2} - 56 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{4} b d^{6} f^{2} {\left| d \right|} e^{2} + 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{3} b^{2} d^{6} f^{2} {\left| d \right|} e^{2} - 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a^{2} b^{3} d^{6} f^{2} {\left| d \right|} e^{2} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a b^{4} c^{3} d f^{2} {\left| d \right|} e + 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B b^{5} c^{3} d f^{2} {\left| d \right|} e + 109 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{2} b^{3} c^{2} d^{2} f^{2} {\left| d \right|} e - 57 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a b^{4} c^{2} d^{2} f^{2} {\left| d \right|} e + 5 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A b^{5} c^{2} d^{2} f^{2} {\left| d \right|} e - 228 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{3} b^{2} c d^{3} f^{2} {\left| d \right|} e + 124 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{2} b^{3} c d^{3} f^{2} {\left| d \right|} e - 20 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a b^{4} c d^{3} f^{2} {\left| d \right|} e + 152 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{4} b d^{4} f^{2} {\left| d \right|} e - 88 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{3} b^{2} d^{4} f^{2} {\left| d \right|} e + 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a^{2} b^{3} d^{4} f^{2} {\left| d \right|} e - 9 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{2} b^{3} c^{2} f^{2} {\left| d \right|} + 5 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a b^{4} c^{2} f^{2} {\left| d \right|} - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A b^{5} c^{2} f^{2} {\left| d \right|} + 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{3} b^{2} c d f^{2} {\left| d \right|} - 20 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a^{2} b^{3} c d f^{2} {\left| d \right|} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A a b^{4} c d f^{2} {\left| d \right|} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{4} b d^{2} f^{2} {\left| d \right|} + 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a^{3} b^{2} d^{2} f^{2} {\left| d \right|} - 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A a^{2} b^{3} d^{2} f^{2} {\left| d \right|} + 32 \, \sqrt{d f} C a b^{4} c^{2} d^{6} f {\left| d \right|} e^{4} - 16 \, \sqrt{d f} B b^{5} c^{2} d^{6} f {\left| d \right|} e^{4} - 27 \, \sqrt{d f} C a^{2} b^{3} c d^{7} f {\left| d \right|} e^{4} + 15 \, \sqrt{d f} B a b^{4} c d^{7} f {\left| d \right|} e^{4} - 3 \, \sqrt{d f} A b^{5} c d^{7} f {\left| d \right|} e^{4} - 10 \, \sqrt{d f} C a^{3} b^{2} d^{8} f {\left| d \right|} e^{4} + 6 \, \sqrt{d f} B a^{2} b^{3} d^{8} f {\left| d \right|} e^{4} - 2 \, \sqrt{d f} A a b^{4} d^{8} f {\left| d \right|} e^{4} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a b^{4} c^{2} d^{4} f {\left| d \right|} e^{3} + 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B b^{5} c^{2} d^{4} f {\left| d \right|} e^{3} - 44 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} c d^{5} f {\left| d \right|} e^{3} + 20 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} c d^{5} f {\left| d \right|} e^{3} + 4 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} c d^{5} f {\left| d \right|} e^{3} + 80 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} b^{2} d^{6} f {\left| d \right|} e^{3} - 44 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b^{3} d^{6} f {\left| d \right|} e^{3} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{4} d^{6} f {\left| d \right|} e^{3} - 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a b^{4} c^{2} d^{2} f {\left| d \right|} e^{2} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B b^{5} c^{2} d^{2} f {\left| d \right|} e^{2} + 109 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{2} b^{3} c d^{3} f {\left| d \right|} e^{2} - 57 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a b^{4} c d^{3} f {\left| d \right|} e^{2} + 5 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A b^{5} c d^{3} f {\left| d \right|} e^{2} - 102 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{3} b^{2} d^{4} f {\left| d \right|} e^{2} + 58 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{2} b^{3} d^{4} f {\left| d \right|} e^{2} - 14 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a b^{4} d^{4} f {\left| d \right|} e^{2} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a b^{4} c^{2} f {\left| d \right|} e - 4 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B b^{5} c^{2} f {\left| d \right|} e - 38 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{2} b^{3} c d f {\left| d \right|} e + 22 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a b^{4} c d f {\left| d \right|} e - 6 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A b^{5} c d f {\left| d \right|} e + 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{3} b^{2} d^{2} f {\left| d \right|} e - 20 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a^{2} b^{3} d^{2} f {\left| d \right|} e + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A a b^{4} d^{2} f {\left| d \right|} e - 8 \, \sqrt{d f} C a b^{4} c d^{7} {\left| d \right|} e^{5} + 4 \, \sqrt{d f} B b^{5} c d^{7} {\left| d \right|} e^{5} + 9 \, \sqrt{d f} C a^{2} b^{3} d^{8} {\left| d \right|} e^{5} - 5 \, \sqrt{d f} B a b^{4} d^{8} {\left| d \right|} e^{5} + \sqrt{d f} A b^{5} d^{8} {\left| d \right|} e^{5} + 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a b^{4} c d^{5} {\left| d \right|} e^{4} - 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B b^{5} c d^{5} {\left| d \right|} e^{4} - 27 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} d^{6} {\left| d \right|} e^{4} + 15 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} d^{6} {\left| d \right|} e^{4} - 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} d^{6} {\left| d \right|} e^{4} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a b^{4} c d^{3} {\left| d \right|} e^{3} + 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B b^{5} c d^{3} {\left| d \right|} e^{3} + 27 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{2} b^{3} d^{4} {\left| d \right|} e^{3} - 15 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a b^{4} d^{4} {\left| d \right|} e^{3} + 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A b^{5} d^{4} {\left| d \right|} e^{3} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a b^{4} c d {\left| d \right|} e^{2} - 4 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B b^{5} c d {\left| d \right|} e^{2} - 9 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{2} b^{3} d^{2} {\left| d \right|} e^{2} + 5 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a b^{4} d^{2} {\left| d \right|} e^{2} - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A b^{5} d^{2} {\left| d \right|} e^{2}}{2 \, {\left(a b^{5} c f - a^{2} b^{4} d f - b^{6} c e + a b^{5} d e\right)} {\left(b c^{2} d^{2} f^{2} - 2 \, b c d^{3} f e - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b c d f + 4 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} a d^{2} f + b d^{4} e^{2} - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b d^{2} e + {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} b\right)}^{2}} + \frac{\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} C {\left| d \right|}}{b^{3} d^{2}} - \frac{{\left(\sqrt{d f} C b c f {\left| d \right|} - 6 \, \sqrt{d f} C a d f {\left| d \right|} + 2 \, \sqrt{d f} B b d f {\left| d \right|} + \sqrt{d f} C b d {\left| d \right|} e\right)} \log\left({\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2}\right)}{2 \, b^{4} d^{2} f}"," ",0,"1/4*(15*sqrt(d*f)*C*a^2*b^2*c^2*f^2*abs(d) - 3*sqrt(d*f)*B*a*b^3*c^2*f^2*abs(d) - sqrt(d*f)*A*b^4*c^2*f^2*abs(d) - 40*sqrt(d*f)*C*a^3*b*c*d*f^2*abs(d) + 12*sqrt(d*f)*B*a^2*b^2*c*d*f^2*abs(d) + 24*sqrt(d*f)*C*a^4*d^2*f^2*abs(d) - 8*sqrt(d*f)*B*a^3*b*d^2*f^2*abs(d) - 24*sqrt(d*f)*C*a*b^3*c^2*f*abs(d)*e + 4*sqrt(d*f)*B*b^4*c^2*f*abs(d)*e + 66*sqrt(d*f)*C*a^2*b^2*c*d*f*abs(d)*e - 18*sqrt(d*f)*B*a*b^3*c*d*f*abs(d)*e + 2*sqrt(d*f)*A*b^4*c*d*f*abs(d)*e - 40*sqrt(d*f)*C*a^3*b*d^2*f*abs(d)*e + 12*sqrt(d*f)*B*a^2*b^2*d^2*f*abs(d)*e + 8*sqrt(d*f)*C*b^4*c^2*abs(d)*e^2 - 24*sqrt(d*f)*C*a*b^3*c*d*abs(d)*e^2 + 4*sqrt(d*f)*B*b^4*c*d*abs(d)*e^2 + 15*sqrt(d*f)*C*a^2*b^2*d^2*abs(d)*e^2 - 3*sqrt(d*f)*B*a*b^3*d^2*abs(d)*e^2 - sqrt(d*f)*A*b^4*d^2*abs(d)*e^2)*arctan(-1/2*(b*c*d*f - 2*a*d^2*f + b*d^2*e - (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b)/(sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*d))/((a*b^5*c*f - a^2*b^4*d*f - b^6*c*e + a*b^5*d*e)*sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*d) + 1/2*(9*sqrt(d*f)*C*a^2*b^3*c^5*d^3*f^5*abs(d) - 5*sqrt(d*f)*B*a*b^4*c^5*d^3*f^5*abs(d) + sqrt(d*f)*A*b^5*c^5*d^3*f^5*abs(d) - 10*sqrt(d*f)*C*a^3*b^2*c^4*d^4*f^5*abs(d) + 6*sqrt(d*f)*B*a^2*b^3*c^4*d^4*f^5*abs(d) - 2*sqrt(d*f)*A*a*b^4*c^4*d^4*f^5*abs(d) - 8*sqrt(d*f)*C*a*b^4*c^5*d^3*f^4*abs(d)*e + 4*sqrt(d*f)*B*b^5*c^5*d^3*f^4*abs(d)*e - 27*sqrt(d*f)*C*a^2*b^3*c^4*d^4*f^4*abs(d)*e + 15*sqrt(d*f)*B*a*b^4*c^4*d^4*f^4*abs(d)*e - 3*sqrt(d*f)*A*b^5*c^4*d^4*f^4*abs(d)*e + 40*sqrt(d*f)*C*a^3*b^2*c^3*d^5*f^4*abs(d)*e - 24*sqrt(d*f)*B*a^2*b^3*c^3*d^5*f^4*abs(d)*e + 8*sqrt(d*f)*A*a*b^4*c^3*d^5*f^4*abs(d)*e - 27*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*c^4*d^2*f^4*abs(d) + 15*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*c^4*d^2*f^4*abs(d) - 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*c^4*d^2*f^4*abs(d) + 80*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*b^2*c^3*d^3*f^4*abs(d) - 44*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b^3*c^3*d^3*f^4*abs(d) + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^4*c^3*d^3*f^4*abs(d) - 56*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^4*b*c^2*d^4*f^4*abs(d) + 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^3*b^2*c^2*d^4*f^4*abs(d) - 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a^2*b^3*c^2*d^4*f^4*abs(d) + 32*sqrt(d*f)*C*a*b^4*c^4*d^4*f^3*abs(d)*e^2 - 16*sqrt(d*f)*B*b^5*c^4*d^4*f^3*abs(d)*e^2 + 18*sqrt(d*f)*C*a^2*b^3*c^3*d^5*f^3*abs(d)*e^2 - 10*sqrt(d*f)*B*a*b^4*c^3*d^5*f^3*abs(d)*e^2 + 2*sqrt(d*f)*A*b^5*c^3*d^5*f^3*abs(d)*e^2 - 60*sqrt(d*f)*C*a^3*b^2*c^2*d^6*f^3*abs(d)*e^2 + 36*sqrt(d*f)*B*a^2*b^3*c^2*d^6*f^3*abs(d)*e^2 - 12*sqrt(d*f)*A*a*b^4*c^2*d^6*f^3*abs(d)*e^2 + 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a*b^4*c^4*d^2*f^3*abs(d)*e - 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*b^5*c^4*d^2*f^3*abs(d)*e - 44*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*c^3*d^3*f^3*abs(d)*e + 20*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*c^3*d^3*f^3*abs(d)*e + 4*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*c^3*d^3*f^3*abs(d)*e - 80*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*b^2*c^2*d^4*f^3*abs(d)*e + 44*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b^3*c^2*d^4*f^3*abs(d)*e - 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^4*c^2*d^4*f^3*abs(d)*e + 112*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^4*b*c*d^5*f^3*abs(d)*e - 64*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^3*b^2*c*d^5*f^3*abs(d)*e + 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a^2*b^3*c*d^5*f^3*abs(d)*e + 27*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^2*b^3*c^3*d*f^3*abs(d) - 15*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a*b^4*c^3*d*f^3*abs(d) + 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*b^5*c^3*d*f^3*abs(d) - 102*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^3*b^2*c^2*d^2*f^3*abs(d) + 58*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^2*b^3*c^2*d^2*f^3*abs(d) - 14*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a*b^4*c^2*d^2*f^3*abs(d) + 152*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^4*b*c*d^3*f^3*abs(d) - 88*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^3*b^2*c*d^3*f^3*abs(d) + 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a^2*b^3*c*d^3*f^3*abs(d) - 80*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^5*d^4*f^3*abs(d) + 48*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^4*b*d^4*f^3*abs(d) - 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a^3*b^2*d^4*f^3*abs(d) - 48*sqrt(d*f)*C*a*b^4*c^3*d^5*f^2*abs(d)*e^3 + 24*sqrt(d*f)*B*b^5*c^3*d^5*f^2*abs(d)*e^3 + 18*sqrt(d*f)*C*a^2*b^3*c^2*d^6*f^2*abs(d)*e^3 - 10*sqrt(d*f)*B*a*b^4*c^2*d^6*f^2*abs(d)*e^3 + 2*sqrt(d*f)*A*b^5*c^2*d^6*f^2*abs(d)*e^3 + 40*sqrt(d*f)*C*a^3*b^2*c*d^7*f^2*abs(d)*e^3 - 24*sqrt(d*f)*B*a^2*b^3*c*d^7*f^2*abs(d)*e^3 + 8*sqrt(d*f)*A*a*b^4*c*d^7*f^2*abs(d)*e^3 - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a*b^4*c^3*d^3*f^2*abs(d)*e^2 + 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*b^5*c^3*d^3*f^2*abs(d)*e^2 + 142*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*c^2*d^4*f^2*abs(d)*e^2 - 70*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*c^2*d^4*f^2*abs(d)*e^2 - 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*c^2*d^4*f^2*abs(d)*e^2 - 80*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*b^2*c*d^5*f^2*abs(d)*e^2 + 44*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b^3*c*d^5*f^2*abs(d)*e^2 - 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^4*c*d^5*f^2*abs(d)*e^2 - 56*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^4*b*d^6*f^2*abs(d)*e^2 + 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^3*b^2*d^6*f^2*abs(d)*e^2 - 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a^2*b^3*d^6*f^2*abs(d)*e^2 - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a*b^4*c^3*d*f^2*abs(d)*e + 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*b^5*c^3*d*f^2*abs(d)*e + 109*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^2*b^3*c^2*d^2*f^2*abs(d)*e - 57*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a*b^4*c^2*d^2*f^2*abs(d)*e + 5*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*b^5*c^2*d^2*f^2*abs(d)*e - 228*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^3*b^2*c*d^3*f^2*abs(d)*e + 124*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^2*b^3*c*d^3*f^2*abs(d)*e - 20*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a*b^4*c*d^3*f^2*abs(d)*e + 152*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^4*b*d^4*f^2*abs(d)*e - 88*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^3*b^2*d^4*f^2*abs(d)*e + 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a^2*b^3*d^4*f^2*abs(d)*e - 9*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^2*b^3*c^2*f^2*abs(d) + 5*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a*b^4*c^2*f^2*abs(d) - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*b^5*c^2*f^2*abs(d) + 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^3*b^2*c*d*f^2*abs(d) - 20*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a^2*b^3*c*d*f^2*abs(d) + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*a*b^4*c*d*f^2*abs(d) - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^4*b*d^2*f^2*abs(d) + 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a^3*b^2*d^2*f^2*abs(d) - 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*a^2*b^3*d^2*f^2*abs(d) + 32*sqrt(d*f)*C*a*b^4*c^2*d^6*f*abs(d)*e^4 - 16*sqrt(d*f)*B*b^5*c^2*d^6*f*abs(d)*e^4 - 27*sqrt(d*f)*C*a^2*b^3*c*d^7*f*abs(d)*e^4 + 15*sqrt(d*f)*B*a*b^4*c*d^7*f*abs(d)*e^4 - 3*sqrt(d*f)*A*b^5*c*d^7*f*abs(d)*e^4 - 10*sqrt(d*f)*C*a^3*b^2*d^8*f*abs(d)*e^4 + 6*sqrt(d*f)*B*a^2*b^3*d^8*f*abs(d)*e^4 - 2*sqrt(d*f)*A*a*b^4*d^8*f*abs(d)*e^4 - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a*b^4*c^2*d^4*f*abs(d)*e^3 + 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*b^5*c^2*d^4*f*abs(d)*e^3 - 44*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*c*d^5*f*abs(d)*e^3 + 20*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*c*d^5*f*abs(d)*e^3 + 4*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*c*d^5*f*abs(d)*e^3 + 80*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*b^2*d^6*f*abs(d)*e^3 - 44*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b^3*d^6*f*abs(d)*e^3 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^4*d^6*f*abs(d)*e^3 - 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a*b^4*c^2*d^2*f*abs(d)*e^2 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*b^5*c^2*d^2*f*abs(d)*e^2 + 109*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^2*b^3*c*d^3*f*abs(d)*e^2 - 57*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a*b^4*c*d^3*f*abs(d)*e^2 + 5*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*b^5*c*d^3*f*abs(d)*e^2 - 102*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^3*b^2*d^4*f*abs(d)*e^2 + 58*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^2*b^3*d^4*f*abs(d)*e^2 - 14*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a*b^4*d^4*f*abs(d)*e^2 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a*b^4*c^2*f*abs(d)*e - 4*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*b^5*c^2*f*abs(d)*e - 38*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^2*b^3*c*d*f*abs(d)*e + 22*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a*b^4*c*d*f*abs(d)*e - 6*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*b^5*c*d*f*abs(d)*e + 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^3*b^2*d^2*f*abs(d)*e - 20*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a^2*b^3*d^2*f*abs(d)*e + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*a*b^4*d^2*f*abs(d)*e - 8*sqrt(d*f)*C*a*b^4*c*d^7*abs(d)*e^5 + 4*sqrt(d*f)*B*b^5*c*d^7*abs(d)*e^5 + 9*sqrt(d*f)*C*a^2*b^3*d^8*abs(d)*e^5 - 5*sqrt(d*f)*B*a*b^4*d^8*abs(d)*e^5 + sqrt(d*f)*A*b^5*d^8*abs(d)*e^5 + 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a*b^4*c*d^5*abs(d)*e^4 - 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*b^5*c*d^5*abs(d)*e^4 - 27*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*d^6*abs(d)*e^4 + 15*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*d^6*abs(d)*e^4 - 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*d^6*abs(d)*e^4 - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a*b^4*c*d^3*abs(d)*e^3 + 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*b^5*c*d^3*abs(d)*e^3 + 27*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^2*b^3*d^4*abs(d)*e^3 - 15*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a*b^4*d^4*abs(d)*e^3 + 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*b^5*d^4*abs(d)*e^3 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a*b^4*c*d*abs(d)*e^2 - 4*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*b^5*c*d*abs(d)*e^2 - 9*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^2*b^3*d^2*abs(d)*e^2 + 5*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a*b^4*d^2*abs(d)*e^2 - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*b^5*d^2*abs(d)*e^2)/((a*b^5*c*f - a^2*b^4*d*f - b^6*c*e + a*b^5*d*e)*(b*c^2*d^2*f^2 - 2*b*c*d^3*f*e - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*c*d*f + 4*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*a*d^2*f + b*d^4*e^2 - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*d^2*e + (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*b)^2) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*C*abs(d)/(b^3*d^2) - 1/2*(sqrt(d*f)*C*b*c*f*abs(d) - 6*sqrt(d*f)*C*a*d*f*abs(d) + 2*sqrt(d*f)*B*b*d*f*abs(d) + sqrt(d*f)*C*b*d*abs(d)*e)*log((sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2)/(b^4*d^2*f)","B",0
47,1,1505,0,2.759480," ","integrate((b*x+a)^2*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(4 \, {\left(d x + c\right)} {\left(6 \, {\left(d x + c\right)} {\left(\frac{8 \, {\left(d x + c\right)} C b^{2}}{d^{5} f} - \frac{31 \, C b^{2} c d^{20} f^{8} - 20 \, C a b d^{21} f^{8} - 10 \, B b^{2} d^{21} f^{8} + 9 \, C b^{2} d^{21} f^{7} e}{d^{25} f^{9}}\right)} + \frac{263 \, C b^{2} c^{2} d^{20} f^{8} - 340 \, C a b c d^{21} f^{8} - 170 \, B b^{2} c d^{21} f^{8} + 80 \, C a^{2} d^{22} f^{8} + 160 \, B a b d^{22} f^{8} + 80 \, A b^{2} d^{22} f^{8} + 154 \, C b^{2} c d^{21} f^{7} e - 140 \, C a b d^{22} f^{7} e - 70 \, B b^{2} d^{22} f^{7} e + 63 \, C b^{2} d^{22} f^{6} e^{2}}{d^{25} f^{9}}\right)} - \frac{5 \, {\left(121 \, C b^{2} c^{3} d^{20} f^{8} - 236 \, C a b c^{2} d^{21} f^{8} - 118 \, B b^{2} c^{2} d^{21} f^{8} + 112 \, C a^{2} c d^{22} f^{8} + 224 \, B a b c d^{22} f^{8} + 112 \, A b^{2} c d^{22} f^{8} - 96 \, B a^{2} d^{23} f^{8} - 192 \, A a b d^{23} f^{8} + 109 \, C b^{2} c^{2} d^{21} f^{7} e - 200 \, C a b c d^{22} f^{7} e - 100 \, B b^{2} c d^{22} f^{7} e + 80 \, C a^{2} d^{23} f^{7} e + 160 \, B a b d^{23} f^{7} e + 80 \, A b^{2} d^{23} f^{7} e + 91 \, C b^{2} c d^{22} f^{6} e^{2} - 140 \, C a b d^{23} f^{6} e^{2} - 70 \, B b^{2} d^{23} f^{6} e^{2} + 63 \, C b^{2} d^{23} f^{5} e^{3}\right)}}{d^{25} f^{9}}\right)} {\left(d x + c\right)} + \frac{15 \, {\left(7 \, C b^{2} c^{4} d^{20} f^{8} - 20 \, C a b c^{3} d^{21} f^{8} - 10 \, B b^{2} c^{3} d^{21} f^{8} + 16 \, C a^{2} c^{2} d^{22} f^{8} + 32 \, B a b c^{2} d^{22} f^{8} + 16 \, A b^{2} c^{2} d^{22} f^{8} - 32 \, B a^{2} c d^{23} f^{8} - 64 \, A a b c d^{23} f^{8} + 128 \, A a^{2} d^{24} f^{8} + 12 \, C b^{2} c^{3} d^{21} f^{7} e - 36 \, C a b c^{2} d^{22} f^{7} e - 18 \, B b^{2} c^{2} d^{22} f^{7} e + 32 \, C a^{2} c d^{23} f^{7} e + 64 \, B a b c d^{23} f^{7} e + 32 \, A b^{2} c d^{23} f^{7} e - 96 \, B a^{2} d^{24} f^{7} e - 192 \, A a b d^{24} f^{7} e + 18 \, C b^{2} c^{2} d^{22} f^{6} e^{2} - 60 \, C a b c d^{23} f^{6} e^{2} - 30 \, B b^{2} c d^{23} f^{6} e^{2} + 80 \, C a^{2} d^{24} f^{6} e^{2} + 160 \, B a b d^{24} f^{6} e^{2} + 80 \, A b^{2} d^{24} f^{6} e^{2} + 28 \, C b^{2} c d^{23} f^{5} e^{3} - 140 \, C a b d^{24} f^{5} e^{3} - 70 \, B b^{2} d^{24} f^{5} e^{3} + 63 \, C b^{2} d^{24} f^{4} e^{4}\right)}}{d^{25} f^{9}}\right)} \sqrt{d x + c} - \frac{15 \, {\left(7 \, C b^{2} c^{5} f^{5} - 20 \, C a b c^{4} d f^{5} - 10 \, B b^{2} c^{4} d f^{5} + 16 \, C a^{2} c^{3} d^{2} f^{5} + 32 \, B a b c^{3} d^{2} f^{5} + 16 \, A b^{2} c^{3} d^{2} f^{5} - 32 \, B a^{2} c^{2} d^{3} f^{5} - 64 \, A a b c^{2} d^{3} f^{5} + 128 \, A a^{2} c d^{4} f^{5} + 5 \, C b^{2} c^{4} d f^{4} e - 16 \, C a b c^{3} d^{2} f^{4} e - 8 \, B b^{2} c^{3} d^{2} f^{4} e + 16 \, C a^{2} c^{2} d^{3} f^{4} e + 32 \, B a b c^{2} d^{3} f^{4} e + 16 \, A b^{2} c^{2} d^{3} f^{4} e - 64 \, B a^{2} c d^{4} f^{4} e - 128 \, A a b c d^{4} f^{4} e - 128 \, A a^{2} d^{5} f^{4} e + 6 \, C b^{2} c^{3} d^{2} f^{3} e^{2} - 24 \, C a b c^{2} d^{3} f^{3} e^{2} - 12 \, B b^{2} c^{2} d^{3} f^{3} e^{2} + 48 \, C a^{2} c d^{4} f^{3} e^{2} + 96 \, B a b c d^{4} f^{3} e^{2} + 48 \, A b^{2} c d^{4} f^{3} e^{2} + 96 \, B a^{2} d^{5} f^{3} e^{2} + 192 \, A a b d^{5} f^{3} e^{2} + 10 \, C b^{2} c^{2} d^{3} f^{2} e^{3} - 80 \, C a b c d^{4} f^{2} e^{3} - 40 \, B b^{2} c d^{4} f^{2} e^{3} - 80 \, C a^{2} d^{5} f^{2} e^{3} - 160 \, B a b d^{5} f^{2} e^{3} - 80 \, A b^{2} d^{5} f^{2} e^{3} + 35 \, C b^{2} c d^{4} f e^{4} + 140 \, C a b d^{5} f e^{4} + 70 \, B b^{2} d^{5} f e^{4} - 63 \, C b^{2} d^{5} e^{5}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{4} f^{5}}\right)} d}{1920 \, {\left| d \right|}}"," ",0,"1/1920*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(4*(d*x + c)*(6*(d*x + c)*(8*(d*x + c)*C*b^2/(d^5*f) - (31*C*b^2*c*d^20*f^8 - 20*C*a*b*d^21*f^8 - 10*B*b^2*d^21*f^8 + 9*C*b^2*d^21*f^7*e)/(d^25*f^9)) + (263*C*b^2*c^2*d^20*f^8 - 340*C*a*b*c*d^21*f^8 - 170*B*b^2*c*d^21*f^8 + 80*C*a^2*d^22*f^8 + 160*B*a*b*d^22*f^8 + 80*A*b^2*d^22*f^8 + 154*C*b^2*c*d^21*f^7*e - 140*C*a*b*d^22*f^7*e - 70*B*b^2*d^22*f^7*e + 63*C*b^2*d^22*f^6*e^2)/(d^25*f^9)) - 5*(121*C*b^2*c^3*d^20*f^8 - 236*C*a*b*c^2*d^21*f^8 - 118*B*b^2*c^2*d^21*f^8 + 112*C*a^2*c*d^22*f^8 + 224*B*a*b*c*d^22*f^8 + 112*A*b^2*c*d^22*f^8 - 96*B*a^2*d^23*f^8 - 192*A*a*b*d^23*f^8 + 109*C*b^2*c^2*d^21*f^7*e - 200*C*a*b*c*d^22*f^7*e - 100*B*b^2*c*d^22*f^7*e + 80*C*a^2*d^23*f^7*e + 160*B*a*b*d^23*f^7*e + 80*A*b^2*d^23*f^7*e + 91*C*b^2*c*d^22*f^6*e^2 - 140*C*a*b*d^23*f^6*e^2 - 70*B*b^2*d^23*f^6*e^2 + 63*C*b^2*d^23*f^5*e^3)/(d^25*f^9))*(d*x + c) + 15*(7*C*b^2*c^4*d^20*f^8 - 20*C*a*b*c^3*d^21*f^8 - 10*B*b^2*c^3*d^21*f^8 + 16*C*a^2*c^2*d^22*f^8 + 32*B*a*b*c^2*d^22*f^8 + 16*A*b^2*c^2*d^22*f^8 - 32*B*a^2*c*d^23*f^8 - 64*A*a*b*c*d^23*f^8 + 128*A*a^2*d^24*f^8 + 12*C*b^2*c^3*d^21*f^7*e - 36*C*a*b*c^2*d^22*f^7*e - 18*B*b^2*c^2*d^22*f^7*e + 32*C*a^2*c*d^23*f^7*e + 64*B*a*b*c*d^23*f^7*e + 32*A*b^2*c*d^23*f^7*e - 96*B*a^2*d^24*f^7*e - 192*A*a*b*d^24*f^7*e + 18*C*b^2*c^2*d^22*f^6*e^2 - 60*C*a*b*c*d^23*f^6*e^2 - 30*B*b^2*c*d^23*f^6*e^2 + 80*C*a^2*d^24*f^6*e^2 + 160*B*a*b*d^24*f^6*e^2 + 80*A*b^2*d^24*f^6*e^2 + 28*C*b^2*c*d^23*f^5*e^3 - 140*C*a*b*d^24*f^5*e^3 - 70*B*b^2*d^24*f^5*e^3 + 63*C*b^2*d^24*f^4*e^4)/(d^25*f^9))*sqrt(d*x + c) - 15*(7*C*b^2*c^5*f^5 - 20*C*a*b*c^4*d*f^5 - 10*B*b^2*c^4*d*f^5 + 16*C*a^2*c^3*d^2*f^5 + 32*B*a*b*c^3*d^2*f^5 + 16*A*b^2*c^3*d^2*f^5 - 32*B*a^2*c^2*d^3*f^5 - 64*A*a*b*c^2*d^3*f^5 + 128*A*a^2*c*d^4*f^5 + 5*C*b^2*c^4*d*f^4*e - 16*C*a*b*c^3*d^2*f^4*e - 8*B*b^2*c^3*d^2*f^4*e + 16*C*a^2*c^2*d^3*f^4*e + 32*B*a*b*c^2*d^3*f^4*e + 16*A*b^2*c^2*d^3*f^4*e - 64*B*a^2*c*d^4*f^4*e - 128*A*a*b*c*d^4*f^4*e - 128*A*a^2*d^5*f^4*e + 6*C*b^2*c^3*d^2*f^3*e^2 - 24*C*a*b*c^2*d^3*f^3*e^2 - 12*B*b^2*c^2*d^3*f^3*e^2 + 48*C*a^2*c*d^4*f^3*e^2 + 96*B*a*b*c*d^4*f^3*e^2 + 48*A*b^2*c*d^4*f^3*e^2 + 96*B*a^2*d^5*f^3*e^2 + 192*A*a*b*d^5*f^3*e^2 + 10*C*b^2*c^2*d^3*f^2*e^3 - 80*C*a*b*c*d^4*f^2*e^3 - 40*B*b^2*c*d^4*f^2*e^3 - 80*C*a^2*d^5*f^2*e^3 - 160*B*a*b*d^5*f^2*e^3 - 80*A*b^2*d^5*f^2*e^3 + 35*C*b^2*c*d^4*f*e^4 + 140*C*a*b*d^5*f*e^4 + 70*B*b^2*d^5*f*e^4 - 63*C*b^2*d^5*e^5)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^4*f^5))*d/abs(d)","A",0
48,1,736,0,1.818779," ","integrate((b*x+a)*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)} C b}{d^{4} f} - \frac{17 \, C b c d^{12} f^{6} - 8 \, C a d^{13} f^{6} - 8 \, B b d^{13} f^{6} + 7 \, C b d^{13} f^{5} e}{d^{16} f^{7}}\right)} + \frac{59 \, C b c^{2} d^{12} f^{6} - 56 \, C a c d^{13} f^{6} - 56 \, B b c d^{13} f^{6} + 48 \, B a d^{14} f^{6} + 48 \, A b d^{14} f^{6} + 50 \, C b c d^{13} f^{5} e - 40 \, C a d^{14} f^{5} e - 40 \, B b d^{14} f^{5} e + 35 \, C b d^{14} f^{4} e^{2}}{d^{16} f^{7}}\right)} - \frac{3 \, {\left(5 \, C b c^{3} d^{12} f^{6} - 8 \, C a c^{2} d^{13} f^{6} - 8 \, B b c^{2} d^{13} f^{6} + 16 \, B a c d^{14} f^{6} + 16 \, A b c d^{14} f^{6} - 64 \, A a d^{15} f^{6} + 9 \, C b c^{2} d^{13} f^{5} e - 16 \, C a c d^{14} f^{5} e - 16 \, B b c d^{14} f^{5} e + 48 \, B a d^{15} f^{5} e + 48 \, A b d^{15} f^{5} e + 15 \, C b c d^{14} f^{4} e^{2} - 40 \, C a d^{15} f^{4} e^{2} - 40 \, B b d^{15} f^{4} e^{2} + 35 \, C b d^{15} f^{3} e^{3}\right)}}{d^{16} f^{7}}\right)} \sqrt{d x + c} + \frac{3 \, {\left(5 \, C b c^{4} f^{4} - 8 \, C a c^{3} d f^{4} - 8 \, B b c^{3} d f^{4} + 16 \, B a c^{2} d^{2} f^{4} + 16 \, A b c^{2} d^{2} f^{4} - 64 \, A a c d^{3} f^{4} + 4 \, C b c^{3} d f^{3} e - 8 \, C a c^{2} d^{2} f^{3} e - 8 \, B b c^{2} d^{2} f^{3} e + 32 \, B a c d^{3} f^{3} e + 32 \, A b c d^{3} f^{3} e + 64 \, A a d^{4} f^{3} e + 6 \, C b c^{2} d^{2} f^{2} e^{2} - 24 \, C a c d^{3} f^{2} e^{2} - 24 \, B b c d^{3} f^{2} e^{2} - 48 \, B a d^{4} f^{2} e^{2} - 48 \, A b d^{4} f^{2} e^{2} + 20 \, C b c d^{3} f e^{3} + 40 \, C a d^{4} f e^{3} + 40 \, B b d^{4} f e^{3} - 35 \, C b d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{3} f^{4}}\right)} d}{192 \, {\left| d \right|}}"," ",0,"1/192*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)*C*b/(d^4*f) - (17*C*b*c*d^12*f^6 - 8*C*a*d^13*f^6 - 8*B*b*d^13*f^6 + 7*C*b*d^13*f^5*e)/(d^16*f^7)) + (59*C*b*c^2*d^12*f^6 - 56*C*a*c*d^13*f^6 - 56*B*b*c*d^13*f^6 + 48*B*a*d^14*f^6 + 48*A*b*d^14*f^6 + 50*C*b*c*d^13*f^5*e - 40*C*a*d^14*f^5*e - 40*B*b*d^14*f^5*e + 35*C*b*d^14*f^4*e^2)/(d^16*f^7)) - 3*(5*C*b*c^3*d^12*f^6 - 8*C*a*c^2*d^13*f^6 - 8*B*b*c^2*d^13*f^6 + 16*B*a*c*d^14*f^6 + 16*A*b*c*d^14*f^6 - 64*A*a*d^15*f^6 + 9*C*b*c^2*d^13*f^5*e - 16*C*a*c*d^14*f^5*e - 16*B*b*c*d^14*f^5*e + 48*B*a*d^15*f^5*e + 48*A*b*d^15*f^5*e + 15*C*b*c*d^14*f^4*e^2 - 40*C*a*d^15*f^4*e^2 - 40*B*b*d^15*f^4*e^2 + 35*C*b*d^15*f^3*e^3)/(d^16*f^7))*sqrt(d*x + c) + 3*(5*C*b*c^4*f^4 - 8*C*a*c^3*d*f^4 - 8*B*b*c^3*d*f^4 + 16*B*a*c^2*d^2*f^4 + 16*A*b*c^2*d^2*f^4 - 64*A*a*c*d^3*f^4 + 4*C*b*c^3*d*f^3*e - 8*C*a*c^2*d^2*f^3*e - 8*B*b*c^2*d^2*f^3*e + 32*B*a*c*d^3*f^3*e + 32*A*b*c*d^3*f^3*e + 64*A*a*d^4*f^3*e + 6*C*b*c^2*d^2*f^2*e^2 - 24*C*a*c*d^3*f^2*e^2 - 24*B*b*c*d^3*f^2*e^2 - 48*B*a*d^4*f^2*e^2 - 48*A*b*d^4*f^2*e^2 + 20*C*b*c*d^3*f*e^3 + 40*C*a*d^4*f*e^3 + 40*B*b*d^4*f*e^3 - 35*C*b*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^3*f^4))*d/abs(d)","A",0
49,1,315,0,1.347674," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)} C}{d^{3} f} - \frac{7 \, C c d^{6} f^{4} - 6 \, B d^{7} f^{4} + 5 \, C d^{7} f^{3} e}{d^{9} f^{5}}\right)} + \frac{3 \, {\left(C c^{2} d^{6} f^{4} - 2 \, B c d^{7} f^{4} + 8 \, A d^{8} f^{4} + 2 \, C c d^{7} f^{3} e - 6 \, B d^{8} f^{3} e + 5 \, C d^{8} f^{2} e^{2}\right)}}{d^{9} f^{5}}\right)} - \frac{3 \, {\left(C c^{3} f^{3} - 2 \, B c^{2} d f^{3} + 8 \, A c d^{2} f^{3} + C c^{2} d f^{2} e - 4 \, B c d^{2} f^{2} e - 8 \, A d^{3} f^{2} e + 3 \, C c d^{2} f e^{2} + 6 \, B d^{3} f e^{2} - 5 \, C d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{3}}\right)} d}{24 \, {\left| d \right|}}"," ",0,"1/24*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)*C/(d^3*f) - (7*C*c*d^6*f^4 - 6*B*d^7*f^4 + 5*C*d^7*f^3*e)/(d^9*f^5)) + 3*(C*c^2*d^6*f^4 - 2*B*c*d^7*f^4 + 8*A*d^8*f^4 + 2*C*c*d^7*f^3*e - 6*B*d^8*f^3*e + 5*C*d^8*f^2*e^2)/(d^9*f^5)) - 3*(C*c^3*f^3 - 2*B*c^2*d*f^3 + 8*A*c*d^2*f^3 + C*c^2*d*f^2*e - 4*B*c*d^2*f^2*e - 8*A*d^3*f^2*e + 3*C*c*d^2*f*e^2 + 6*B*d^3*f*e^2 - 5*C*d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^3))*d/abs(d)","A",0
50,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)/(f*x+e)^(1/2),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: 0.47"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
51,1,1388,0,10.820240," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^2/(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{d f} C a^{2} b c d^{2} f - \sqrt{d f} B a b^{2} c d^{2} f - \sqrt{d f} A b^{3} c d^{2} f - 4 \, \sqrt{d f} C a^{3} d^{3} f + 2 \, \sqrt{d f} B a^{2} b d^{3} f - 4 \, \sqrt{d f} C a b^{2} c d^{2} e + 2 \, \sqrt{d f} B b^{3} c d^{2} e + 5 \, \sqrt{d f} C a^{2} b d^{3} e - 3 \, \sqrt{d f} B a b^{2} d^{3} e + \sqrt{d f} A b^{3} d^{3} e\right)} \arctan\left(-\frac{b c d f - 2 \, a d^{2} f + b d^{2} e - {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b}{2 \, \sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} d}\right)}{\sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} {\left(a b^{3} f {\left| d \right|} - b^{4} {\left| d \right|} e\right)} d} + \frac{2 \, {\left(\sqrt{d f} C a^{2} b c^{2} d^{3} f^{2} - \sqrt{d f} B a b^{2} c^{2} d^{3} f^{2} + \sqrt{d f} A b^{3} c^{2} d^{3} f^{2} - 2 \, \sqrt{d f} C a^{2} b c d^{4} f e + 2 \, \sqrt{d f} B a b^{2} c d^{4} f e - 2 \, \sqrt{d f} A b^{3} c d^{4} f e - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b c d^{2} f + \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{2} c d^{2} f - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{3} c d^{2} f + 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} d^{3} f - 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b d^{3} f + 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{2} d^{3} f + \sqrt{d f} C a^{2} b d^{5} e^{2} - \sqrt{d f} B a b^{2} d^{5} e^{2} + \sqrt{d f} A b^{3} d^{5} e^{2} - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b d^{3} e + \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{2} d^{3} e - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{3} d^{3} e\right)}}{{\left(b c^{2} d^{2} f^{2} - 2 \, b c d^{3} f e - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b c d f + 4 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} a d^{2} f + b d^{4} e^{2} - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b d^{2} e + {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} b\right)} {\left(a b^{3} f {\left| d \right|} - b^{4} {\left| d \right|} e\right)}} + \frac{\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} C {\left| d \right|}}{b^{2} d^{2} f} - \frac{{\left(\sqrt{d f} C b c f - 4 \, \sqrt{d f} C a d f + 2 \, \sqrt{d f} B b d f - \sqrt{d f} C b d e\right)} \log\left({\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2}\right)}{2 \, b^{3} f^{2} {\left| d \right|}}"," ",0,"(3*sqrt(d*f)*C*a^2*b*c*d^2*f - sqrt(d*f)*B*a*b^2*c*d^2*f - sqrt(d*f)*A*b^3*c*d^2*f - 4*sqrt(d*f)*C*a^3*d^3*f + 2*sqrt(d*f)*B*a^2*b*d^3*f - 4*sqrt(d*f)*C*a*b^2*c*d^2*e + 2*sqrt(d*f)*B*b^3*c*d^2*e + 5*sqrt(d*f)*C*a^2*b*d^3*e - 3*sqrt(d*f)*B*a*b^2*d^3*e + sqrt(d*f)*A*b^3*d^3*e)*arctan(-1/2*(b*c*d*f - 2*a*d^2*f + b*d^2*e - (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b)/(sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*d))/(sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*(a*b^3*f*abs(d) - b^4*abs(d)*e)*d) + 2*(sqrt(d*f)*C*a^2*b*c^2*d^3*f^2 - sqrt(d*f)*B*a*b^2*c^2*d^3*f^2 + sqrt(d*f)*A*b^3*c^2*d^3*f^2 - 2*sqrt(d*f)*C*a^2*b*c*d^4*f*e + 2*sqrt(d*f)*B*a*b^2*c*d^4*f*e - 2*sqrt(d*f)*A*b^3*c*d^4*f*e - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b*c*d^2*f + sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^2*c*d^2*f - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^3*c*d^2*f + 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*d^3*f - 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b*d^3*f + 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^2*d^3*f + sqrt(d*f)*C*a^2*b*d^5*e^2 - sqrt(d*f)*B*a*b^2*d^5*e^2 + sqrt(d*f)*A*b^3*d^5*e^2 - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b*d^3*e + sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^2*d^3*e - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^3*d^3*e)/((b*c^2*d^2*f^2 - 2*b*c*d^3*f*e - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*c*d*f + 4*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*a*d^2*f + b*d^4*e^2 - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*d^2*e + (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*b)*(a*b^3*f*abs(d) - b^4*abs(d)*e)) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*C*abs(d)/(b^2*d^2*f) - 1/2*(sqrt(d*f)*C*b*c*f - 4*sqrt(d*f)*C*a*d*f + 2*sqrt(d*f)*B*b*d*f - sqrt(d*f)*C*b*d*e)*log((sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2)/(b^3*f^2*abs(d))","B",0
52,1,8004,0,134.872066," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^3/(f*x+e)^(1/2),x, algorithm=""giac"")","-\frac{{\left(3 \, \sqrt{d f} C a^{2} b^{2} c^{2} d^{2} f^{2} + \sqrt{d f} B a b^{3} c^{2} d^{2} f^{2} + 3 \, \sqrt{d f} A b^{4} c^{2} d^{2} f^{2} - 12 \, \sqrt{d f} C a^{3} b c d^{3} f^{2} - 4 \, \sqrt{d f} A a b^{3} c d^{3} f^{2} + 8 \, \sqrt{d f} C a^{4} d^{4} f^{2} - 8 \, \sqrt{d f} C a b^{3} c^{2} d^{2} f e - 4 \, \sqrt{d f} B b^{4} c^{2} d^{2} f e + 30 \, \sqrt{d f} C a^{2} b^{2} c d^{3} f e + 2 \, \sqrt{d f} B a b^{3} c d^{3} f e - 2 \, \sqrt{d f} A b^{4} c d^{3} f e - 20 \, \sqrt{d f} C a^{3} b d^{4} f e + 4 \, \sqrt{d f} A a b^{3} d^{4} f e + 8 \, \sqrt{d f} C b^{4} c^{2} d^{2} e^{2} - 24 \, \sqrt{d f} C a b^{3} c d^{3} e^{2} + 4 \, \sqrt{d f} B b^{4} c d^{3} e^{2} + 15 \, \sqrt{d f} C a^{2} b^{2} d^{4} e^{2} - 3 \, \sqrt{d f} B a b^{3} d^{4} e^{2} - \sqrt{d f} A b^{4} d^{4} e^{2}\right)} \arctan\left(-\frac{b c d f - 2 \, a d^{2} f + b d^{2} e - {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b}{2 \, \sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} d}\right)}{4 \, {\left(a^{2} b^{4} c f^{2} {\left| d \right|} - a^{3} b^{3} d f^{2} {\left| d \right|} - 2 \, a b^{5} c f {\left| d \right|} e + 2 \, a^{2} b^{4} d f {\left| d \right|} e + b^{6} c {\left| d \right|} e^{2} - a b^{5} d {\left| d \right|} e^{2}\right)} \sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} d} - \frac{\sqrt{d f} C d \log\left({\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2}\right)}{b^{3} f {\left| d \right|}} - \frac{5 \, \sqrt{d f} C a^{2} b^{3} c^{5} d^{5} f^{5} - \sqrt{d f} B a b^{4} c^{5} d^{5} f^{5} - 3 \, \sqrt{d f} A b^{5} c^{5} d^{5} f^{5} - 6 \, \sqrt{d f} C a^{3} b^{2} c^{4} d^{6} f^{5} + 2 \, \sqrt{d f} B a^{2} b^{3} c^{4} d^{6} f^{5} + 2 \, \sqrt{d f} A a b^{4} c^{4} d^{6} f^{5} - 8 \, \sqrt{d f} C a b^{4} c^{5} d^{5} f^{4} e + 4 \, \sqrt{d f} B b^{5} c^{5} d^{5} f^{4} e - 11 \, \sqrt{d f} C a^{2} b^{3} c^{4} d^{6} f^{4} e - \sqrt{d f} B a b^{4} c^{4} d^{6} f^{4} e + 13 \, \sqrt{d f} A b^{5} c^{4} d^{6} f^{4} e + 24 \, \sqrt{d f} C a^{3} b^{2} c^{3} d^{7} f^{4} e - 8 \, \sqrt{d f} B a^{2} b^{3} c^{3} d^{7} f^{4} e - 8 \, \sqrt{d f} A a b^{4} c^{3} d^{7} f^{4} e - 15 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} c^{4} d^{4} f^{4} + 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} c^{4} d^{4} f^{4} + 9 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} c^{4} d^{4} f^{4} + 44 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} b^{2} c^{3} d^{5} f^{4} - 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b^{3} c^{3} d^{5} f^{4} - 28 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{4} c^{3} d^{5} f^{4} - 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{4} b c^{2} d^{6} f^{4} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{3} b^{2} c^{2} d^{6} f^{4} + 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a^{2} b^{3} c^{2} d^{6} f^{4} + 32 \, \sqrt{d f} C a b^{4} c^{4} d^{6} f^{3} e^{2} - 16 \, \sqrt{d f} B b^{5} c^{4} d^{6} f^{3} e^{2} - 6 \, \sqrt{d f} C a^{2} b^{3} c^{3} d^{7} f^{3} e^{2} + 14 \, \sqrt{d f} B a b^{4} c^{3} d^{7} f^{3} e^{2} - 22 \, \sqrt{d f} A b^{5} c^{3} d^{7} f^{3} e^{2} - 36 \, \sqrt{d f} C a^{3} b^{2} c^{2} d^{8} f^{3} e^{2} + 12 \, \sqrt{d f} B a^{2} b^{3} c^{2} d^{8} f^{3} e^{2} + 12 \, \sqrt{d f} A a b^{4} c^{2} d^{8} f^{3} e^{2} + 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a b^{4} c^{4} d^{4} f^{3} e - 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B b^{5} c^{4} d^{4} f^{3} e - 56 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} c^{3} d^{5} f^{3} e + 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} c^{3} d^{5} f^{3} e - 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} c^{3} d^{5} f^{3} e - 20 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} b^{2} c^{2} d^{6} f^{3} e - 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b^{3} c^{2} d^{6} f^{3} e + 52 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{4} c^{2} d^{6} f^{3} e + 64 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{4} b c d^{7} f^{3} e - 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{3} b^{2} c d^{7} f^{3} e - 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a^{2} b^{3} c d^{7} f^{3} e + 15 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{2} b^{3} c^{3} d^{3} f^{3} - 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a b^{4} c^{3} d^{3} f^{3} - 9 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A b^{5} c^{3} d^{3} f^{3} - 58 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{3} b^{2} c^{2} d^{4} f^{3} + 14 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{2} b^{3} c^{2} d^{4} f^{3} + 30 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a b^{4} c^{2} d^{4} f^{3} + 88 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{4} b c d^{5} f^{3} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{3} b^{2} c d^{5} f^{3} - 40 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a^{2} b^{3} c d^{5} f^{3} - 48 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{5} d^{6} f^{3} + 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{4} b d^{6} f^{3} + 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a^{3} b^{2} d^{6} f^{3} - 48 \, \sqrt{d f} C a b^{4} c^{3} d^{7} f^{2} e^{3} + 24 \, \sqrt{d f} B b^{5} c^{3} d^{7} f^{2} e^{3} + 34 \, \sqrt{d f} C a^{2} b^{3} c^{2} d^{8} f^{2} e^{3} - 26 \, \sqrt{d f} B a b^{4} c^{2} d^{8} f^{2} e^{3} + 18 \, \sqrt{d f} A b^{5} c^{2} d^{8} f^{2} e^{3} + 24 \, \sqrt{d f} C a^{3} b^{2} c d^{9} f^{2} e^{3} - 8 \, \sqrt{d f} B a^{2} b^{3} c d^{9} f^{2} e^{3} - 8 \, \sqrt{d f} A a b^{4} c d^{9} f^{2} e^{3} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a b^{4} c^{3} d^{5} f^{2} e^{2} + 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B b^{5} c^{3} d^{5} f^{2} e^{2} + 130 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} c^{2} d^{6} f^{2} e^{2} - 58 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} c^{2} d^{6} f^{2} e^{2} - 14 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} c^{2} d^{6} f^{2} e^{2} - 92 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} b^{2} c d^{7} f^{2} e^{2} + 56 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b^{3} c d^{7} f^{2} e^{2} - 20 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{4} c d^{7} f^{2} e^{2} - 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{4} b d^{8} f^{2} e^{2} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{3} b^{2} d^{8} f^{2} e^{2} + 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a^{2} b^{3} d^{8} f^{2} e^{2} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a b^{4} c^{3} d^{3} f^{2} e + 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B b^{5} c^{3} d^{3} f^{2} e + 101 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{2} b^{3} c^{2} d^{4} f^{2} e - 49 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a b^{4} c^{2} d^{4} f^{2} e - 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A b^{5} c^{2} d^{4} f^{2} e - 188 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{3} b^{2} c d^{5} f^{2} e + 84 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{2} b^{3} c d^{5} f^{2} e + 20 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a b^{4} c d^{5} f^{2} e + 120 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{4} b d^{6} f^{2} e - 56 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{3} b^{2} d^{6} f^{2} e - 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a^{2} b^{3} d^{6} f^{2} e - 5 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{2} b^{3} c^{2} d^{2} f^{2} + \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a b^{4} c^{2} d^{2} f^{2} + 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A b^{5} c^{2} d^{2} f^{2} + 20 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{3} b^{2} c d^{3} f^{2} - 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a^{2} b^{3} c d^{3} f^{2} - 4 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A a b^{4} c d^{3} f^{2} - 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{4} b d^{4} f^{2} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a^{3} b^{2} d^{4} f^{2} + 32 \, \sqrt{d f} C a b^{4} c^{2} d^{8} f e^{4} - 16 \, \sqrt{d f} B b^{5} c^{2} d^{8} f e^{4} - 31 \, \sqrt{d f} C a^{2} b^{3} c d^{9} f e^{4} + 19 \, \sqrt{d f} B a b^{4} c d^{9} f e^{4} - 7 \, \sqrt{d f} A b^{5} c d^{9} f e^{4} - 6 \, \sqrt{d f} C a^{3} b^{2} d^{10} f e^{4} + 2 \, \sqrt{d f} B a^{2} b^{3} d^{10} f e^{4} + 2 \, \sqrt{d f} A a b^{4} d^{10} f e^{4} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a b^{4} c^{2} d^{6} f e^{3} + 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B b^{5} c^{2} d^{6} f e^{3} - 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} c d^{7} f e^{3} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} c d^{7} f e^{3} + 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} c d^{7} f e^{3} + 68 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} b^{2} d^{8} f e^{3} - 32 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b^{3} d^{8} f e^{3} - 4 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{4} d^{8} f e^{3} - 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a b^{4} c^{2} d^{4} f e^{2} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B b^{5} c^{2} d^{4} f e^{2} + 97 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{2} b^{3} c d^{5} f e^{2} - 45 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a b^{4} c d^{5} f e^{2} - 7 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A b^{5} c d^{5} f e^{2} - 90 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{3} b^{2} d^{6} f e^{2} + 46 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a^{2} b^{3} d^{6} f e^{2} - 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A a b^{4} d^{6} f e^{2} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a b^{4} c^{2} d^{2} f e - 4 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B b^{5} c^{2} d^{2} f e - 34 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{2} b^{3} c d^{3} f e + 18 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a b^{4} c d^{3} f e - 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A b^{5} c d^{3} f e + 28 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{3} b^{2} d^{4} f e - 16 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a^{2} b^{3} d^{4} f e + 4 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A a b^{4} d^{4} f e - 8 \, \sqrt{d f} C a b^{4} c d^{9} e^{5} + 4 \, \sqrt{d f} B b^{5} c d^{9} e^{5} + 9 \, \sqrt{d f} C a^{2} b^{3} d^{10} e^{5} - 5 \, \sqrt{d f} B a b^{4} d^{10} e^{5} + \sqrt{d f} A b^{5} d^{10} e^{5} + 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a b^{4} c d^{7} e^{4} - 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B b^{5} c d^{7} e^{4} - 27 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b^{3} d^{8} e^{4} + 15 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{4} d^{8} e^{4} - 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{5} d^{8} e^{4} - 24 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a b^{4} c d^{5} e^{3} + 12 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B b^{5} c d^{5} e^{3} + 27 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} C a^{2} b^{3} d^{6} e^{3} - 15 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} B a b^{4} d^{6} e^{3} + 3 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} A b^{5} d^{6} e^{3} + 8 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a b^{4} c d^{3} e^{2} - 4 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B b^{5} c d^{3} e^{2} - 9 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} C a^{2} b^{3} d^{4} e^{2} + 5 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} B a b^{4} d^{4} e^{2} - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{6} A b^{5} d^{4} e^{2}}{2 \, {\left(a^{2} b^{4} c f^{2} {\left| d \right|} - a^{3} b^{3} d f^{2} {\left| d \right|} - 2 \, a b^{5} c f {\left| d \right|} e + 2 \, a^{2} b^{4} d f {\left| d \right|} e + b^{6} c {\left| d \right|} e^{2} - a b^{5} d {\left| d \right|} e^{2}\right)} {\left(b c^{2} d^{2} f^{2} - 2 \, b c d^{3} f e - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b c d f + 4 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} a d^{2} f + b d^{4} e^{2} - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b d^{2} e + {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} b\right)}^{2}}"," ",0,"-1/4*(3*sqrt(d*f)*C*a^2*b^2*c^2*d^2*f^2 + sqrt(d*f)*B*a*b^3*c^2*d^2*f^2 + 3*sqrt(d*f)*A*b^4*c^2*d^2*f^2 - 12*sqrt(d*f)*C*a^3*b*c*d^3*f^2 - 4*sqrt(d*f)*A*a*b^3*c*d^3*f^2 + 8*sqrt(d*f)*C*a^4*d^4*f^2 - 8*sqrt(d*f)*C*a*b^3*c^2*d^2*f*e - 4*sqrt(d*f)*B*b^4*c^2*d^2*f*e + 30*sqrt(d*f)*C*a^2*b^2*c*d^3*f*e + 2*sqrt(d*f)*B*a*b^3*c*d^3*f*e - 2*sqrt(d*f)*A*b^4*c*d^3*f*e - 20*sqrt(d*f)*C*a^3*b*d^4*f*e + 4*sqrt(d*f)*A*a*b^3*d^4*f*e + 8*sqrt(d*f)*C*b^4*c^2*d^2*e^2 - 24*sqrt(d*f)*C*a*b^3*c*d^3*e^2 + 4*sqrt(d*f)*B*b^4*c*d^3*e^2 + 15*sqrt(d*f)*C*a^2*b^2*d^4*e^2 - 3*sqrt(d*f)*B*a*b^3*d^4*e^2 - sqrt(d*f)*A*b^4*d^4*e^2)*arctan(-1/2*(b*c*d*f - 2*a*d^2*f + b*d^2*e - (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b)/(sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*d))/((a^2*b^4*c*f^2*abs(d) - a^3*b^3*d*f^2*abs(d) - 2*a*b^5*c*f*abs(d)*e + 2*a^2*b^4*d*f*abs(d)*e + b^6*c*abs(d)*e^2 - a*b^5*d*abs(d)*e^2)*sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*d) - sqrt(d*f)*C*d*log((sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2)/(b^3*f*abs(d)) - 1/2*(5*sqrt(d*f)*C*a^2*b^3*c^5*d^5*f^5 - sqrt(d*f)*B*a*b^4*c^5*d^5*f^5 - 3*sqrt(d*f)*A*b^5*c^5*d^5*f^5 - 6*sqrt(d*f)*C*a^3*b^2*c^4*d^6*f^5 + 2*sqrt(d*f)*B*a^2*b^3*c^4*d^6*f^5 + 2*sqrt(d*f)*A*a*b^4*c^4*d^6*f^5 - 8*sqrt(d*f)*C*a*b^4*c^5*d^5*f^4*e + 4*sqrt(d*f)*B*b^5*c^5*d^5*f^4*e - 11*sqrt(d*f)*C*a^2*b^3*c^4*d^6*f^4*e - sqrt(d*f)*B*a*b^4*c^4*d^6*f^4*e + 13*sqrt(d*f)*A*b^5*c^4*d^6*f^4*e + 24*sqrt(d*f)*C*a^3*b^2*c^3*d^7*f^4*e - 8*sqrt(d*f)*B*a^2*b^3*c^3*d^7*f^4*e - 8*sqrt(d*f)*A*a*b^4*c^3*d^7*f^4*e - 15*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*c^4*d^4*f^4 + 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*c^4*d^4*f^4 + 9*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*c^4*d^4*f^4 + 44*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*b^2*c^3*d^5*f^4 - 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b^3*c^3*d^5*f^4 - 28*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^4*c^3*d^5*f^4 - 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^4*b*c^2*d^6*f^4 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^3*b^2*c^2*d^6*f^4 + 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a^2*b^3*c^2*d^6*f^4 + 32*sqrt(d*f)*C*a*b^4*c^4*d^6*f^3*e^2 - 16*sqrt(d*f)*B*b^5*c^4*d^6*f^3*e^2 - 6*sqrt(d*f)*C*a^2*b^3*c^3*d^7*f^3*e^2 + 14*sqrt(d*f)*B*a*b^4*c^3*d^7*f^3*e^2 - 22*sqrt(d*f)*A*b^5*c^3*d^7*f^3*e^2 - 36*sqrt(d*f)*C*a^3*b^2*c^2*d^8*f^3*e^2 + 12*sqrt(d*f)*B*a^2*b^3*c^2*d^8*f^3*e^2 + 12*sqrt(d*f)*A*a*b^4*c^2*d^8*f^3*e^2 + 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a*b^4*c^4*d^4*f^3*e - 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*b^5*c^4*d^4*f^3*e - 56*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*c^3*d^5*f^3*e + 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*c^3*d^5*f^3*e - 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*c^3*d^5*f^3*e - 20*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*b^2*c^2*d^6*f^3*e - 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b^3*c^2*d^6*f^3*e + 52*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^4*c^2*d^6*f^3*e + 64*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^4*b*c*d^7*f^3*e - 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^3*b^2*c*d^7*f^3*e - 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a^2*b^3*c*d^7*f^3*e + 15*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^2*b^3*c^3*d^3*f^3 - 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a*b^4*c^3*d^3*f^3 - 9*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*b^5*c^3*d^3*f^3 - 58*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^3*b^2*c^2*d^4*f^3 + 14*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^2*b^3*c^2*d^4*f^3 + 30*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a*b^4*c^2*d^4*f^3 + 88*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^4*b*c*d^5*f^3 - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^3*b^2*c*d^5*f^3 - 40*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a^2*b^3*c*d^5*f^3 - 48*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^5*d^6*f^3 + 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^4*b*d^6*f^3 + 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a^3*b^2*d^6*f^3 - 48*sqrt(d*f)*C*a*b^4*c^3*d^7*f^2*e^3 + 24*sqrt(d*f)*B*b^5*c^3*d^7*f^2*e^3 + 34*sqrt(d*f)*C*a^2*b^3*c^2*d^8*f^2*e^3 - 26*sqrt(d*f)*B*a*b^4*c^2*d^8*f^2*e^3 + 18*sqrt(d*f)*A*b^5*c^2*d^8*f^2*e^3 + 24*sqrt(d*f)*C*a^3*b^2*c*d^9*f^2*e^3 - 8*sqrt(d*f)*B*a^2*b^3*c*d^9*f^2*e^3 - 8*sqrt(d*f)*A*a*b^4*c*d^9*f^2*e^3 - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a*b^4*c^3*d^5*f^2*e^2 + 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*b^5*c^3*d^5*f^2*e^2 + 130*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*c^2*d^6*f^2*e^2 - 58*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*c^2*d^6*f^2*e^2 - 14*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*c^2*d^6*f^2*e^2 - 92*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*b^2*c*d^7*f^2*e^2 + 56*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b^3*c*d^7*f^2*e^2 - 20*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^4*c*d^7*f^2*e^2 - 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^4*b*d^8*f^2*e^2 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^3*b^2*d^8*f^2*e^2 + 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a^2*b^3*d^8*f^2*e^2 - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a*b^4*c^3*d^3*f^2*e + 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*b^5*c^3*d^3*f^2*e + 101*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^2*b^3*c^2*d^4*f^2*e - 49*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a*b^4*c^2*d^4*f^2*e - 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*b^5*c^2*d^4*f^2*e - 188*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^3*b^2*c*d^5*f^2*e + 84*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^2*b^3*c*d^5*f^2*e + 20*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a*b^4*c*d^5*f^2*e + 120*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^4*b*d^6*f^2*e - 56*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^3*b^2*d^6*f^2*e - 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a^2*b^3*d^6*f^2*e - 5*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^2*b^3*c^2*d^2*f^2 + sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a*b^4*c^2*d^2*f^2 + 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*b^5*c^2*d^2*f^2 + 20*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^3*b^2*c*d^3*f^2 - 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a^2*b^3*c*d^3*f^2 - 4*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*a*b^4*c*d^3*f^2 - 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^4*b*d^4*f^2 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a^3*b^2*d^4*f^2 + 32*sqrt(d*f)*C*a*b^4*c^2*d^8*f*e^4 - 16*sqrt(d*f)*B*b^5*c^2*d^8*f*e^4 - 31*sqrt(d*f)*C*a^2*b^3*c*d^9*f*e^4 + 19*sqrt(d*f)*B*a*b^4*c*d^9*f*e^4 - 7*sqrt(d*f)*A*b^5*c*d^9*f*e^4 - 6*sqrt(d*f)*C*a^3*b^2*d^10*f*e^4 + 2*sqrt(d*f)*B*a^2*b^3*d^10*f*e^4 + 2*sqrt(d*f)*A*a*b^4*d^10*f*e^4 - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a*b^4*c^2*d^6*f*e^3 + 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*b^5*c^2*d^6*f*e^3 - 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*c*d^7*f*e^3 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*c*d^7*f*e^3 + 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*c*d^7*f*e^3 + 68*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*b^2*d^8*f*e^3 - 32*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b^3*d^8*f*e^3 - 4*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^4*d^8*f*e^3 - 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a*b^4*c^2*d^4*f*e^2 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*b^5*c^2*d^4*f*e^2 + 97*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^2*b^3*c*d^5*f*e^2 - 45*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a*b^4*c*d^5*f*e^2 - 7*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*b^5*c*d^5*f*e^2 - 90*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^3*b^2*d^6*f*e^2 + 46*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a^2*b^3*d^6*f*e^2 - 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*a*b^4*d^6*f*e^2 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a*b^4*c^2*d^2*f*e - 4*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*b^5*c^2*d^2*f*e - 34*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^2*b^3*c*d^3*f*e + 18*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a*b^4*c*d^3*f*e - 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*b^5*c*d^3*f*e + 28*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^3*b^2*d^4*f*e - 16*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a^2*b^3*d^4*f*e + 4*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*a*b^4*d^4*f*e - 8*sqrt(d*f)*C*a*b^4*c*d^9*e^5 + 4*sqrt(d*f)*B*b^5*c*d^9*e^5 + 9*sqrt(d*f)*C*a^2*b^3*d^10*e^5 - 5*sqrt(d*f)*B*a*b^4*d^10*e^5 + sqrt(d*f)*A*b^5*d^10*e^5 + 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a*b^4*c*d^7*e^4 - 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*b^5*c*d^7*e^4 - 27*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b^3*d^8*e^4 + 15*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^4*d^8*e^4 - 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^5*d^8*e^4 - 24*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a*b^4*c*d^5*e^3 + 12*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*b^5*c*d^5*e^3 + 27*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*C*a^2*b^3*d^6*e^3 - 15*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*B*a*b^4*d^6*e^3 + 3*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*A*b^5*d^6*e^3 + 8*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a*b^4*c*d^3*e^2 - 4*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*b^5*c*d^3*e^2 - 9*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*C*a^2*b^3*d^4*e^2 + 5*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*B*a*b^4*d^4*e^2 - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^6*A*b^5*d^4*e^2)/((a^2*b^4*c*f^2*abs(d) - a^3*b^3*d*f^2*abs(d) - 2*a*b^5*c*f*abs(d)*e + 2*a^2*b^4*d*f*abs(d)*e + b^6*c*abs(d)*e^2 - a*b^5*d*abs(d)*e^2)*(b*c^2*d^2*f^2 - 2*b*c*d^3*f*e - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*c*d*f + 4*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*a*d^2*f + b*d^4*e^2 - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*d^2*e + (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*b)^2)","B",0
53,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^4/(f*x+e)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,1,951,0,2.511966," ","integrate((b*x+a)^2*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} {\left(2 \, {\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)} C b^{2}}{d^{5} f} - \frac{25 \, C b^{2} c d^{19} f^{6} - 16 \, C a b d^{20} f^{6} - 8 \, B b^{2} d^{20} f^{6} + 7 \, C b^{2} d^{20} f^{5} e}{d^{24} f^{7}}\right)} + \frac{163 \, C b^{2} c^{2} d^{19} f^{6} - 208 \, C a b c d^{20} f^{6} - 104 \, B b^{2} c d^{20} f^{6} + 48 \, C a^{2} d^{21} f^{6} + 96 \, B a b d^{21} f^{6} + 48 \, A b^{2} d^{21} f^{6} + 90 \, C b^{2} c d^{20} f^{5} e - 80 \, C a b d^{21} f^{5} e - 40 \, B b^{2} d^{21} f^{5} e + 35 \, C b^{2} d^{21} f^{4} e^{2}}{d^{24} f^{7}}\right)} - \frac{3 \, {\left(93 \, C b^{2} c^{3} d^{19} f^{6} - 176 \, C a b c^{2} d^{20} f^{6} - 88 \, B b^{2} c^{2} d^{20} f^{6} + 80 \, C a^{2} c d^{21} f^{6} + 160 \, B a b c d^{21} f^{6} + 80 \, A b^{2} c d^{21} f^{6} - 64 \, B a^{2} d^{22} f^{6} - 128 \, A a b d^{22} f^{6} + 73 \, C b^{2} c^{2} d^{20} f^{5} e - 128 \, C a b c d^{21} f^{5} e - 64 \, B b^{2} c d^{21} f^{5} e + 48 \, C a^{2} d^{22} f^{5} e + 96 \, B a b d^{22} f^{5} e + 48 \, A b^{2} d^{22} f^{5} e + 55 \, C b^{2} c d^{21} f^{4} e^{2} - 80 \, C a b d^{22} f^{4} e^{2} - 40 \, B b^{2} d^{22} f^{4} e^{2} + 35 \, C b^{2} d^{22} f^{3} e^{3}\right)}}{d^{24} f^{7}}\right)} \sqrt{d x + c} - \frac{3 \, {\left(35 \, C b^{2} c^{4} f^{4} - 80 \, C a b c^{3} d f^{4} - 40 \, B b^{2} c^{3} d f^{4} + 48 \, C a^{2} c^{2} d^{2} f^{4} + 96 \, B a b c^{2} d^{2} f^{4} + 48 \, A b^{2} c^{2} d^{2} f^{4} - 64 \, B a^{2} c d^{3} f^{4} - 128 \, A a b c d^{3} f^{4} + 128 \, A a^{2} d^{4} f^{4} + 20 \, C b^{2} c^{3} d f^{3} e - 48 \, C a b c^{2} d^{2} f^{3} e - 24 \, B b^{2} c^{2} d^{2} f^{3} e + 32 \, C a^{2} c d^{3} f^{3} e + 64 \, B a b c d^{3} f^{3} e + 32 \, A b^{2} c d^{3} f^{3} e - 64 \, B a^{2} d^{4} f^{3} e - 128 \, A a b d^{4} f^{3} e + 18 \, C b^{2} c^{2} d^{2} f^{2} e^{2} - 48 \, C a b c d^{3} f^{2} e^{2} - 24 \, B b^{2} c d^{3} f^{2} e^{2} + 48 \, C a^{2} d^{4} f^{2} e^{2} + 96 \, B a b d^{4} f^{2} e^{2} + 48 \, A b^{2} d^{4} f^{2} e^{2} + 20 \, C b^{2} c d^{3} f e^{3} - 80 \, C a b d^{4} f e^{3} - 40 \, B b^{2} d^{4} f e^{3} + 35 \, C b^{2} d^{4} e^{4}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{4} f^{4}}\right)} d}{192 \, {\left| d \right|}}"," ",0,"1/192*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*(2*(d*x + c)*(4*(d*x + c)*(6*(d*x + c)*C*b^2/(d^5*f) - (25*C*b^2*c*d^19*f^6 - 16*C*a*b*d^20*f^6 - 8*B*b^2*d^20*f^6 + 7*C*b^2*d^20*f^5*e)/(d^24*f^7)) + (163*C*b^2*c^2*d^19*f^6 - 208*C*a*b*c*d^20*f^6 - 104*B*b^2*c*d^20*f^6 + 48*C*a^2*d^21*f^6 + 96*B*a*b*d^21*f^6 + 48*A*b^2*d^21*f^6 + 90*C*b^2*c*d^20*f^5*e - 80*C*a*b*d^21*f^5*e - 40*B*b^2*d^21*f^5*e + 35*C*b^2*d^21*f^4*e^2)/(d^24*f^7)) - 3*(93*C*b^2*c^3*d^19*f^6 - 176*C*a*b*c^2*d^20*f^6 - 88*B*b^2*c^2*d^20*f^6 + 80*C*a^2*c*d^21*f^6 + 160*B*a*b*c*d^21*f^6 + 80*A*b^2*c*d^21*f^6 - 64*B*a^2*d^22*f^6 - 128*A*a*b*d^22*f^6 + 73*C*b^2*c^2*d^20*f^5*e - 128*C*a*b*c*d^21*f^5*e - 64*B*b^2*c*d^21*f^5*e + 48*C*a^2*d^22*f^5*e + 96*B*a*b*d^22*f^5*e + 48*A*b^2*d^22*f^5*e + 55*C*b^2*c*d^21*f^4*e^2 - 80*C*a*b*d^22*f^4*e^2 - 40*B*b^2*d^22*f^4*e^2 + 35*C*b^2*d^22*f^3*e^3)/(d^24*f^7))*sqrt(d*x + c) - 3*(35*C*b^2*c^4*f^4 - 80*C*a*b*c^3*d*f^4 - 40*B*b^2*c^3*d*f^4 + 48*C*a^2*c^2*d^2*f^4 + 96*B*a*b*c^2*d^2*f^4 + 48*A*b^2*c^2*d^2*f^4 - 64*B*a^2*c*d^3*f^4 - 128*A*a*b*c*d^3*f^4 + 128*A*a^2*d^4*f^4 + 20*C*b^2*c^3*d*f^3*e - 48*C*a*b*c^2*d^2*f^3*e - 24*B*b^2*c^2*d^2*f^3*e + 32*C*a^2*c*d^3*f^3*e + 64*B*a*b*c*d^3*f^3*e + 32*A*b^2*c*d^3*f^3*e - 64*B*a^2*d^4*f^3*e - 128*A*a*b*d^4*f^3*e + 18*C*b^2*c^2*d^2*f^2*e^2 - 48*C*a*b*c*d^3*f^2*e^2 - 24*B*b^2*c*d^3*f^2*e^2 + 48*C*a^2*d^4*f^2*e^2 + 96*B*a*b*d^4*f^2*e^2 + 48*A*b^2*d^4*f^2*e^2 + 20*C*b^2*c*d^3*f*e^3 - 80*C*a*b*d^4*f*e^3 - 40*B*b^2*d^4*f*e^3 + 35*C*b^2*d^4*e^4)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^4*f^4))*d/abs(d)","A",0
55,1,447,0,1.968436," ","integrate((b*x+a)*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(2 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)} C b}{d^{4} f} - \frac{13 \, C b c d^{11} f^{4} - 6 \, C a d^{12} f^{4} - 6 \, B b d^{12} f^{4} + 5 \, C b d^{12} f^{3} e}{d^{15} f^{5}}\right)} + \frac{3 \, {\left(11 \, C b c^{2} d^{11} f^{4} - 10 \, C a c d^{12} f^{4} - 10 \, B b c d^{12} f^{4} + 8 \, B a d^{13} f^{4} + 8 \, A b d^{13} f^{4} + 8 \, C b c d^{12} f^{3} e - 6 \, C a d^{13} f^{3} e - 6 \, B b d^{13} f^{3} e + 5 \, C b d^{13} f^{2} e^{2}\right)}}{d^{15} f^{5}}\right)} + \frac{3 \, {\left(5 \, C b c^{3} f^{3} - 6 \, C a c^{2} d f^{3} - 6 \, B b c^{2} d f^{3} + 8 \, B a c d^{2} f^{3} + 8 \, A b c d^{2} f^{3} - 16 \, A a d^{3} f^{3} + 3 \, C b c^{2} d f^{2} e - 4 \, C a c d^{2} f^{2} e - 4 \, B b c d^{2} f^{2} e + 8 \, B a d^{3} f^{2} e + 8 \, A b d^{3} f^{2} e + 3 \, C b c d^{2} f e^{2} - 6 \, C a d^{3} f e^{2} - 6 \, B b d^{3} f e^{2} + 5 \, C b d^{3} e^{3}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{3} f^{3}}\right)} d}{24 \, {\left| d \right|}}"," ",0,"1/24*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*(4*(d*x + c)*C*b/(d^4*f) - (13*C*b*c*d^11*f^4 - 6*C*a*d^12*f^4 - 6*B*b*d^12*f^4 + 5*C*b*d^12*f^3*e)/(d^15*f^5)) + 3*(11*C*b*c^2*d^11*f^4 - 10*C*a*c*d^12*f^4 - 10*B*b*c*d^12*f^4 + 8*B*a*d^13*f^4 + 8*A*b*d^13*f^4 + 8*C*b*c*d^12*f^3*e - 6*C*a*d^13*f^3*e - 6*B*b*d^13*f^3*e + 5*C*b*d^13*f^2*e^2)/(d^15*f^5)) + 3*(5*C*b*c^3*f^3 - 6*C*a*c^2*d*f^3 - 6*B*b*c^2*d*f^3 + 8*B*a*c*d^2*f^3 + 8*A*b*c*d^2*f^3 - 16*A*a*d^3*f^3 + 3*C*b*c^2*d*f^2*e - 4*C*a*c*d^2*f^2*e - 4*B*b*c*d^2*f^2*e + 8*B*a*d^3*f^2*e + 8*A*b*d^3*f^2*e + 3*C*b*c*d^2*f*e^2 - 6*C*a*d^3*f*e^2 - 6*B*b*d^3*f*e^2 + 5*C*b*d^3*e^3)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^3*f^3))*d/abs(d)","A",0
56,1,194,0,1.215550," ","integrate((C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \sqrt{d x + c} {\left(\frac{2 \, {\left(d x + c\right)} C}{d^{3} f} - \frac{5 \, C c d^{5} f^{2} - 4 \, B d^{6} f^{2} + 3 \, C d^{6} f e}{d^{8} f^{3}}\right)} - \frac{{\left(3 \, C c^{2} f^{2} - 4 \, B c d f^{2} + 8 \, A d^{2} f^{2} + 2 \, C c d f e - 4 \, B d^{2} f e + 3 \, C d^{2} e^{2}\right)} \log\left({\left| -\sqrt{d f} \sqrt{d x + c} + \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e} \right|}\right)}{\sqrt{d f} d^{2} f^{2}}\right)} d}{4 \, {\left| d \right|}}"," ",0,"1/4*(sqrt((d*x + c)*d*f - c*d*f + d^2*e)*sqrt(d*x + c)*(2*(d*x + c)*C/(d^3*f) - (5*C*c*d^5*f^2 - 4*B*d^6*f^2 + 3*C*d^6*f*e)/(d^8*f^3)) - (3*C*c^2*f^2 - 4*B*c*d*f^2 + 8*A*d^2*f^2 + 2*C*c*d*f*e - 4*B*d^2*f*e + 3*C*d^2*e^2)*log(abs(-sqrt(d*f)*sqrt(d*x + c) + sqrt((d*x + c)*d*f - c*d*f + d^2*e)))/(sqrt(d*f)*d^2*f^2))*d/abs(d)","A",0
57,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
58,1,1356,0,9.374407," ","integrate((C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{d f} C a^{2} b c d^{2} f - \sqrt{d f} B a b^{2} c d^{2} f - \sqrt{d f} A b^{3} c d^{2} f - 2 \, \sqrt{d f} C a^{3} d^{3} f + 2 \, \sqrt{d f} A a b^{2} d^{3} f - 4 \, \sqrt{d f} C a b^{2} c d^{2} e + 2 \, \sqrt{d f} B b^{3} c d^{2} e + 3 \, \sqrt{d f} C a^{2} b d^{3} e - \sqrt{d f} B a b^{2} d^{3} e - \sqrt{d f} A b^{3} d^{3} e\right)} \arctan\left(-\frac{b c d f - 2 \, a d^{2} f + b d^{2} e - {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b}{2 \, \sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} d}\right)}{{\left(a b^{3} c f {\left| d \right|} - a^{2} b^{2} d f {\left| d \right|} - b^{4} c {\left| d \right|} e + a b^{3} d {\left| d \right|} e\right)} \sqrt{a b c d f^{2} - a^{2} d^{2} f^{2} - b^{2} c d f e + a b d^{2} f e} d} + \frac{2 \, {\left(\sqrt{d f} C a^{2} b c^{2} d^{3} f^{2} - \sqrt{d f} B a b^{2} c^{2} d^{3} f^{2} + \sqrt{d f} A b^{3} c^{2} d^{3} f^{2} - 2 \, \sqrt{d f} C a^{2} b c d^{4} f e + 2 \, \sqrt{d f} B a b^{2} c d^{4} f e - 2 \, \sqrt{d f} A b^{3} c d^{4} f e - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b c d^{2} f + \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{2} c d^{2} f - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{3} c d^{2} f + 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{3} d^{3} f - 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a^{2} b d^{3} f + 2 \, \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A a b^{2} d^{3} f + \sqrt{d f} C a^{2} b d^{5} e^{2} - \sqrt{d f} B a b^{2} d^{5} e^{2} + \sqrt{d f} A b^{3} d^{5} e^{2} - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} C a^{2} b d^{3} e + \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} B a b^{2} d^{3} e - \sqrt{d f} {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} A b^{3} d^{3} e\right)}}{{\left(b c^{2} d^{2} f^{2} - 2 \, b c d^{3} f e - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b c d f + 4 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} a d^{2} f + b d^{4} e^{2} - 2 \, {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2} b d^{2} e + {\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{4} b\right)} {\left(a b^{3} c f {\left| d \right|} - a^{2} b^{2} d f {\left| d \right|} - b^{4} c {\left| d \right|} e + a b^{3} d {\left| d \right|} e\right)}} - \frac{\sqrt{d f} C \log\left({\left(\sqrt{d f} \sqrt{d x + c} - \sqrt{{\left(d x + c\right)} d f - c d f + d^{2} e}\right)}^{2}\right)}{b^{2} f {\left| d \right|}}"," ",0,"(3*sqrt(d*f)*C*a^2*b*c*d^2*f - sqrt(d*f)*B*a*b^2*c*d^2*f - sqrt(d*f)*A*b^3*c*d^2*f - 2*sqrt(d*f)*C*a^3*d^3*f + 2*sqrt(d*f)*A*a*b^2*d^3*f - 4*sqrt(d*f)*C*a*b^2*c*d^2*e + 2*sqrt(d*f)*B*b^3*c*d^2*e + 3*sqrt(d*f)*C*a^2*b*d^3*e - sqrt(d*f)*B*a*b^2*d^3*e - sqrt(d*f)*A*b^3*d^3*e)*arctan(-1/2*(b*c*d*f - 2*a*d^2*f + b*d^2*e - (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b)/(sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*d))/((a*b^3*c*f*abs(d) - a^2*b^2*d*f*abs(d) - b^4*c*abs(d)*e + a*b^3*d*abs(d)*e)*sqrt(a*b*c*d*f^2 - a^2*d^2*f^2 - b^2*c*d*f*e + a*b*d^2*f*e)*d) + 2*(sqrt(d*f)*C*a^2*b*c^2*d^3*f^2 - sqrt(d*f)*B*a*b^2*c^2*d^3*f^2 + sqrt(d*f)*A*b^3*c^2*d^3*f^2 - 2*sqrt(d*f)*C*a^2*b*c*d^4*f*e + 2*sqrt(d*f)*B*a*b^2*c*d^4*f*e - 2*sqrt(d*f)*A*b^3*c*d^4*f*e - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b*c*d^2*f + sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^2*c*d^2*f - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^3*c*d^2*f + 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^3*d^3*f - 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a^2*b*d^3*f + 2*sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*a*b^2*d^3*f + sqrt(d*f)*C*a^2*b*d^5*e^2 - sqrt(d*f)*B*a*b^2*d^5*e^2 + sqrt(d*f)*A*b^3*d^5*e^2 - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*C*a^2*b*d^3*e + sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*B*a*b^2*d^3*e - sqrt(d*f)*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*A*b^3*d^3*e)/((b*c^2*d^2*f^2 - 2*b*c*d^3*f*e - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*c*d*f + 4*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*a*d^2*f + b*d^4*e^2 - 2*(sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2*b*d^2*e + (sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^4*b)*(a*b^3*c*f*abs(d) - a^2*b^2*d*f*abs(d) - b^4*c*abs(d)*e + a*b^3*d*abs(d)*e)) - sqrt(d*f)*C*log((sqrt(d*f)*sqrt(d*x + c) - sqrt((d*x + c)*d*f - c*d*f + d^2*e))^2)/(b^2*f*abs(d))","B",0
59,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^4/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,0,0,0,0.000000," ","integrate((b*x+a)^(1/2)*(C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2),x, algorithm=""giac"")","\int {\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e), x)","F",0
62,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c} \sqrt{f x + e}}{\sqrt{b x + a}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(d*x + c)*sqrt(f*x + e)/sqrt(b*x + a), x)","F",0
63,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c} \sqrt{f x + e}}{{\left(b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(d*x + c)*sqrt(f*x + e)/(b*x + a)^(3/2), x)","F",0
64,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c} \sqrt{f x + e}}{{\left(b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(d*x + c)*sqrt(f*x + e)/(b*x + a)^(5/2), x)","F",0
65,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c} \sqrt{f x + e}}{{\left(b x + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(d*x + c)*sqrt(f*x + e)/(b*x + a)^(7/2), x)","F",0
66,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)*(f*x+e)^(1/2)/(b*x+a)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c} \sqrt{f x + e}}{{\left(b x + a\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(d*x + c)*sqrt(f*x + e)/(b*x + a)^(9/2), x)","F",0
67,0,0,0,0.000000," ","integrate((b*x+a)^(3/2)*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} {\left(b x + a\right)}^{\frac{3}{2}} \sqrt{d x + c}}{\sqrt{f x + e}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(b*x + a)^(3/2)*sqrt(d*x + c)/sqrt(f*x + e), x)","F",0
68,0,0,0,0.000000," ","integrate((b*x+a)^(1/2)*(C*x^2+B*x+A)*(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a} \sqrt{d x + c}}{\sqrt{f x + e}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(b*x + a)*sqrt(d*x + c)/sqrt(f*x + e), x)","F",0
69,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c}}{\sqrt{b x + a} \sqrt{f x + e}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(d*x + c)/(sqrt(b*x + a)*sqrt(f*x + e)), x)","F",0
70,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(3/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c}}{{\left(b x + a\right)}^{\frac{3}{2}} \sqrt{f x + e}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(d*x + c)/((b*x + a)^(3/2)*sqrt(f*x + e)), x)","F",0
71,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(5/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c}}{{\left(b x + a\right)}^{\frac{5}{2}} \sqrt{f x + e}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(d*x + c)/((b*x + a)^(5/2)*sqrt(f*x + e)), x)","F",0
72,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)*(d*x+c)^(1/2)/(b*x+a)^(7/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{d x + c}}{{\left(b x + a\right)}^{\frac{7}{2}} \sqrt{f x + e}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(d*x + c)/((b*x + a)^(7/2)*sqrt(f*x + e)), x)","F",0
73,0,0,0,0.000000," ","integrate((b*x+a)^(3/2)*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} {\left(b x + a\right)}^{\frac{3}{2}}}{\sqrt{d x + c} \sqrt{f x + e}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(b*x + a)^(3/2)/(sqrt(d*x + c)*sqrt(f*x + e)), x)","F",0
74,0,0,0,0.000000," ","integrate((b*x+a)^(1/2)*(C*x^2+B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(C x^{2} + B x + A\right)} \sqrt{b x + a}}{\sqrt{d x + c} \sqrt{f x + e}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*sqrt(b*x + a)/(sqrt(d*x + c)*sqrt(f*x + e)), x)","F",0
75,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{C x^{2} + B x + A}{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)), x)","F",0
76,-2,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError >> type","F(-2)",0
77,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^(5/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(b*x+a)^(7/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
